Subgroups — C₅₃×#36745 #27244257

Order 13568.

2184 conjugacy classes of subgroups.

The subgroup lattice has 1636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2723	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2716	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2715	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2712	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2700	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2698	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2696	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2691	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2688	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2686	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2685	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2684	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2676	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2674	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2670	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2668	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2663	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2661	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2610	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#2604	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#2602	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#2601	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#2592	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2561	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#2415	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#2411	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
32	C₅₃×#542	—	2	8	no	—
33	C₅₃×#538	—	2	8	no	—
34	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
55	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
56	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
57	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
58	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
59	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
60	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
61	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
62	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
64	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
65	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
66	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
67	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
68	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#399	C₂²	1	1	yes	characteristic
72	C₅₃×#399	C₂²	1	1	yes	characteristic
73	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
74	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#397	C₂²	1	1	yes	characteristic
76	C₅₃×#397	C₂²	1	1	yes	characteristic
77	C₅₃×#397	C₂²	1	1	yes	characteristic
78	C₅₃×#397	C₂²	1	1	yes	characteristic
79	C₅₃×#397	C₂²	1	1	yes	characteristic
80	C₅₃×#397	C₂²	1	1	yes	characteristic
81	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#396	C₂²	1	1	yes	characteristic
86	C₅₃×#396	C₂²	1	1	yes	characteristic
87	C₅₃×#396	C₂²	1	1	yes	characteristic
88	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#394	C₂²	1	1	yes	characteristic
93	C₅₃×#394	C₂²	1	1	yes	characteristic
94	C₅₃×#394	C₂²	1	1	yes	characteristic
95	C₅₃×#394	C₂²	1	1	yes	characteristic
96	C₅₃×#394	C₂²	1	1	yes	characteristic
97	C₅₃×#394	C₂²	1	1	yes	characteristic
98	C₅₃×#394	C₂²	1	1	yes	characteristic
99	C₅₃×#394	C₂²	1	1	yes	characteristic
100	C₅₃×#394	C₂²	1	1	yes	characteristic
101	C₅₃×#394	C₂²	1	1	yes	characteristic
102	C₅₃×#394	C₂²	1	1	yes	characteristic
103	C₅₃×#394	C₂²	1	1	yes	characteristic
104	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#393	C₂²	1	1	yes	characteristic
106	C₅₃×#393	C₂²	1	1	yes	characteristic
107	C₅₃×#393	C₂²	1	1	yes	characteristic
108	C₅₃×#393	C₂²	1	1	yes	characteristic
109	C₅₃×#393	C₂²	1	1	yes	characteristic
110	C₅₃×#393	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#393	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#392	C₂²	1	1	yes	characteristic
113	C₅₃×#392	C₂²	1	1	yes	characteristic
114	C₅₃×#392	C₂²	1	1	yes	characteristic
115	C₅₃×#392	C₂²	1	1	yes	characteristic
116	C₅₃×#392	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#390	C₂²	1	1	yes	characteristic
122	C₅₃×#390	C₂²	1	1	yes	characteristic
123	C₅₃×#390	C₂²	1	1	yes	characteristic
124	C₅₃×#390	C₂²	1	1	yes	characteristic
125	C₅₃×#390	C₂²	1	1	yes	characteristic
126	C₅₃×#390	C₂²	1	1	yes	characteristic
127	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#388	C₂²	1	1	yes	characteristic
134	C₅₃×#388	C₂²	1	1	yes	characteristic
135	C₅₃×#388	C₂²	1	1	yes	characteristic
136	C₅₃×#388	C₂²	1	1	yes	characteristic
137	C₅₃×#388	C₂²	1	1	yes	characteristic
138	C₅₃×#388	C₂²	1	1	yes	characteristic
139	C₅₃×#388	C₂²	1	1	yes	characteristic
140	C₅₃×#388	C₂²	1	1	yes	characteristic
141	C₅₃×#388	C₂²	1	1	yes	characteristic
142	C₅₃×#388	C₂²	1	1	yes	characteristic
143	C₅₃×#388	C₂²	1	1	yes	characteristic
144	C₅₃×#388	C₂²	1	1	yes	characteristic
145	C₅₃×#388	C₂²	1	1	yes	characteristic
146	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
152	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
158	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
159	C₅₃×#386	C₂²	1	1	yes	characteristic
160	C₅₃×#386	C₂²	1	1	yes	characteristic
161	C₅₃×#386	C₂²	1	1	yes	characteristic
162	C₅₃×#386	C₂²	1	1	yes	characteristic
163	C₅₃×#386	C₂²	1	1	yes	characteristic
164	C₅₃×#386	C₂²	1	1	yes	characteristic
165	C₅₃×#386	C₂²	1	1	yes	characteristic
166	C₅₃×#386	C₂²	1	1	yes	characteristic
167	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
168	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
169	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
170	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
171	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#385	C₂²	1	1	yes	characteristic
173	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
177	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
178	C₅₃×#381	C₂²	1	1	yes	characteristic
179	C₅₃×#381	C₂²	1	1	yes	characteristic
180	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
181	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#379	C₂²	1	1	yes	characteristic
183	C₅₃×#379	C₂²	1	1	yes	characteristic
184	C₅₃×#379	C₂²	1	1	yes	characteristic
185	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
186	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
188	C₅₃×#376	C₂²	1	1	yes	characteristic, complemented
189	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
190	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
191	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
192	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
193	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
194	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
195	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
197	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
199	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
200	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
201	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
205	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
206	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
209	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
210	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
211	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
212	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₄⋊Q₈×C₅₃	—	2	4	no	—
214	#126×C₅₃	—	2	4	no	—
215	#126×C₅₃	—	2	4	no	—
216	#126×C₅₃	—	2	4	no	—
217	#126×C₅₃	—	2	4	no	—
218	#124×C₅₃	—	2	4	no	—
219	#124×C₅₃	—	2	4	no	—
220	#124×C₅₃	—	2	4	no	—
221	#124×C₅₃	—	2	4	no	—
222	#124×C₅₃	—	2	4	no	—
223	#124×C₅₃	—	4	2	no	—
224	#123×C₅₃	—	2	4	no	—
225	#123×C₅₃	—	2	4	no	—
226	#123×C₅₃	—	2	4	no	—
227	#123×C₅₃	—	2	4	no	—
228	C₂²⋊Q₈×C₅₃	—	2	4	no	—
229	C₂²⋊Q₈×C₅₃	—	2	4	no	—
230	C₂²⋊Q₈×C₅₃	—	2	4	no	—
231	C₂²⋊Q₈×C₅₃	—	2	4	no	—
232	C₂²⋊Q₈×C₅₃	—	4	2	no	—
233	#121×C₅₃	—	2	4	no	—
234	#121×C₅₃	—	2	4	no	—
235	#121×C₅₃	—	2	4	no	—
236	#121×C₅₃	—	2	4	no	—
237	#121×C₅₃	—	4	2	no	—
238	#120×C₅₃	—	2	4	no	—
239	#120×C₅₃	—	2	4	no	—
240	#120×C₅₃	—	4	2	no	—
241	C₄×Q₈×C₅₃	—	2	4	no	—
242	C₄×D₄×C₅₃	—	2	4	no	—
243	C₄×D₄×C₅₃	D₄	1	8	yes	complemented
244	#117×C₅₃	—	2	4	no	—
245	#117×C₅₃	—	4	2	no	—
246	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
275	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
291	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
292	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
298	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
299	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
300	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
301	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
302	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
305	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
307	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
308	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
309	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
311	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
312	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
313	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
314	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
315	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
316	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
317	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
318	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
319	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
320	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
321	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
322	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
323	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
324	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
325	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
326	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
327	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
328	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
329	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
330	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
331	C₂×C₄²×C₅₃	—	4	2	no	—
332	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
333	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
334	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
335	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
336	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
343	#95×C₅₃	C₂³	1	1	yes	characteristic
344	#95×C₅₃	C₂³	1	1	yes	characteristic
345	#95×C₅₃	C₂³	1	1	yes	characteristic
346	#95×C₅₃	C₂³	1	1	yes	characteristic
347	#95×C₅₃	C₂³	1	1	yes	characteristic
348	#95×C₅₃	C₂³	1	1	yes	characteristic
349	#95×C₅₃	C₂³	1	1	yes	characteristic
350	#95×C₅₃	C₂³	1	1	yes	characteristic
351	#95×C₅₃	C₂³	1	1	yes	characteristic
352	#95×C₅₃	C₂³	1	1	yes	characteristic
353	#95×C₅₃	C₂³	1	1	yes	characteristic
354	#95×C₅₃	C₂³	1	1	yes	characteristic
355	#95×C₅₃	C₂³	1	1	yes	characteristic
356	#95×C₅₃	C₂³	1	1	yes	characteristic
357	#95×C₅₃	C₂³	1	1	yes	characteristic
358	#95×C₅₃	C₂³	1	1	yes	characteristic
359	#95×C₅₃	C₂³	1	1	yes	characteristic
360	#95×C₅₃	C₂³	1	1	yes	characteristic
361	#95×C₅₃	C₂³	1	1	yes	characteristic
362	#95×C₅₃	C₂³	1	1	yes	characteristic
363	#95×C₅₃	C₂³	1	1	yes	characteristic
364	#95×C₅₃	C₂³	1	1	yes	characteristic
365	#95×C₅₃	C₂³	1	1	yes	characteristic
366	#95×C₅₃	C₂³	1	1	yes	characteristic
367	#95×C₅₃	C₂³	1	1	yes	characteristic
368	#95×C₅₃	C₂³	1	1	yes	characteristic
369	#95×C₅₃	C₂³	1	1	yes	characteristic
370	#95×C₅₃	C₂³	1	1	yes	characteristic
371	#95×C₅₃	C₂³	1	1	yes	characteristic
372	#95×C₅₃	C₂³	1	1	yes	characteristic
373	#95×C₅₃	C₂³	1	1	yes	characteristic
374	#95×C₅₃	C₂³	1	1	yes	characteristic
375	#95×C₅₃	C₂³	1	1	yes	characteristic
376	#95×C₅₃	C₂³	1	1	yes	characteristic
377	#95×C₅₃	C₂³	1	1	yes	characteristic
378	#95×C₅₃	C₂³	1	1	yes	characteristic
379	C₂⁴×C₅₃	—	2	2	no	—
380	C₂⁴×C₅₃	—	4	1	no	—
381	C₂⁴×C₅₃	—	4	1	no	—
382	C₂⁴×C₅₃	—	4	1	no	—
383	C₂⁴×C₅₃	—	4	1	no	—
384	C₂⁴×C₅₃	—	4	1	no	—
385	C₂⁴×C₅₃	—	4	1	no	—
386	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂×Q₈×C₅₃	—	2	2	no	—
393	C₂×Q₈×C₅₃	—	2	2	no	—
394	C₂×Q₈×C₅₃	—	2	2	no	—
395	C₂×Q₈×C₅₃	—	2	2	no	—
396	C₂×Q₈×C₅₃	—	4	1	no	—
397	C₂×Q₈×C₅₃	—	4	1	no	—
398	C₂×Q₈×C₅₃	—	4	1	no	—
399	C₂×Q₈×C₅₃	—	4	1	no	—
400	C₂×Q₈×C₅₃	—	4	1	no	—
401	C₂×Q₈×C₅₃	—	4	1	no	—
402	C₂×Q₈×C₅₃	—	4	1	no	—
403	C₂×Q₈×C₅₃	—	4	1	no	—
404	C₂×D₄×C₅₃	—	2	2	no	—
405	C₂×D₄×C₅₃	—	2	2	no	—
406	C₂×D₄×C₅₃	—	2	2	no	—
407	C₂×D₄×C₅₃	—	2	2	no	—
408	C₂×D₄×C₅₃	—	2	2	no	—
409	C₂×D₄×C₅₃	—	2	2	no	—
410	C₂×D₄×C₅₃	—	2	2	no	—
411	C₂×D₄×C₅₃	—	2	2	no	—
412	C₂×D₄×C₅₃	—	2	2	no	—
413	C₂×D₄×C₅₃	—	4	1	no	—
414	C₂×D₄×C₅₃	—	4	1	no	—
415	C₂×D₄×C₅₃	—	4	1	no	—
416	C₂×D₄×C₅₃	—	4	1	no	—
417	C₂×D₄×C₅₃	—	4	1	no	—
418	C₂×D₄×C₅₃	—	4	1	no	—
419	C₂×D₄×C₅₃	—	4	1	no	—
420	C₂×D₄×C₅₃	—	4	1	no	—
421	C₂×D₄×C₅₃	—	4	1	no	—
422	C₂×D₄×C₅₃	—	4	1	no	—
423	C₂×D₄×C₅₃	—	4	1	no	—
424	C₂×D₄×C₅₃	—	4	1	no	—
425	C₂×D₄×C₅₃	—	4	1	no	—
426	C₂×D₄×C₅₃	—	4	1	no	—
427	C₂×D₄×C₅₃	—	4	1	no	—
428	C₂×D₄×C₅₃	—	4	1	no	—
429	C₂×D₄×C₅₃	—	4	1	no	—
430	C₂×D₄×C₅₃	—	4	1	no	—
431	C₂×D₄×C₅₃	—	4	1	no	—
432	C₂×D₄×C₅₃	—	4	1	no	—
433	C₂×D₄×C₅₃	—	4	1	no	—
434	C₂×D₄×C₅₃	—	4	1	no	—
435	C₂×D₄×C₅₃	—	4	1	no	—
436	C₂×D₄×C₅₃	—	4	1	no	—
437	C₂×D₄×C₅₃	—	4	1	no	—
438	C₂×D₄×C₅₃	—	4	1	no	—
439	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
440	C₂²×C₄×C₅₃	—	2	2	no	—
441	C₂²×C₄×C₅₃	—	2	2	no	—
442	C₂²×C₄×C₅₃	—	2	2	no	—
443	C₂²×C₄×C₅₃	—	2	2	no	—
444	C₂²×C₄×C₅₃	—	4	1	no	—
445	C₂²×C₄×C₅₃	—	4	1	no	—
446	C₂²×C₄×C₅₃	—	4	1	no	—
447	C₂²×C₄×C₅₃	—	4	1	no	—
448	C₂²×C₄×C₅₃	—	4	1	no	—
449	C₂²×C₄×C₅₃	—	4	1	no	—
450	C₂²×C₄×C₅₃	—	4	1	no	—
451	C₂²×C₄×C₅₃	—	4	1	no	—
452	C₂²×C₄×C₅₃	—	4	1	no	—
453	C₂²×C₄×C₅₃	—	4	1	no	—
454	C₂²×C₄×C₅₃	—	4	1	no	—
455	C₂²×C₄×C₅₃	—	4	1	no	—
456	C₂²×C₄×C₅₃	—	4	1	no	—
457	C₂²×C₄×C₅₃	—	4	1	no	—
458	C₂²×C₄×C₅₃	—	4	1	no	—
459	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
460	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
461	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
462	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
463	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
464	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
465	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
466	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
467	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
468	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
469	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
470	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
471	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
472	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
473	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
474	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
475	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
476	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
477	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
478	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
479	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
480	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
481	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
482	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
483	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
484	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
485	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
486	C₄⋊C₄×C₅₃	—	2	2	no	—
487	C₄⋊C₄×C₅₃	—	2	2	no	—
488	C₄⋊C₄×C₅₃	—	2	2	no	—
489	C₄⋊C₄×C₅₃	—	2	2	no	—
490	C₄⋊C₄×C₅₃	—	2	2	no	—
491	C₄⋊C₄×C₅₃	—	2	2	no	—
492	C₄⋊C₄×C₅₃	—	2	2	no	—
493	C₄⋊C₄×C₅₃	—	2	2	no	—
494	C₄⋊C₄×C₅₃	—	2	2	no	—
495	C₄⋊C₄×C₅₃	—	2	2	no	—
496	C₄⋊C₄×C₅₃	—	2	2	no	—
497	C₄⋊C₄×C₅₃	—	2	2	no	—
498	C₄⋊C₄×C₅₃	—	2	2	no	—
499	C₄⋊C₄×C₅₃	—	2	2	no	—
500	C₄⋊C₄×C₅₃	—	2	2	no	—
501	C₄⋊C₄×C₅₃	—	2	2	no	—
502	C₄⋊C₄×C₅₃	—	4	1	no	—
503	C₄⋊C₄×C₅₃	—	4	1	no	—
504	C₄⋊C₄×C₅₃	—	4	1	no	—
505	C₄⋊C₄×C₅₃	—	4	1	no	—
506	C₄⋊C₄×C₅₃	—	4	1	no	—
507	C₄⋊C₄×C₅₃	—	4	1	no	—
508	C₄⋊C₄×C₅₃	—	4	1	no	—
509	C₄⋊C₄×C₅₃	—	4	1	no	—
510	C₄⋊C₄×C₅₃	—	4	1	no	—
511	C₄⋊C₄×C₅₃	—	4	1	no	—
512	C₄⋊C₄×C₅₃	—	4	1	no	—
513	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
514	C₂²⋊C₄×C₅₃	—	2	2	no	—
515	C₂²⋊C₄×C₅₃	—	2	2	no	—
516	C₂²⋊C₄×C₅₃	—	2	2	no	—
517	C₂²⋊C₄×C₅₃	—	2	2	no	—
518	C₂²⋊C₄×C₅₃	—	2	2	no	—
519	C₂²⋊C₄×C₅₃	—	2	2	no	—
520	C₂²⋊C₄×C₅₃	—	2	2	no	—
521	C₂²⋊C₄×C₅₃	—	2	2	no	—
522	C₂²⋊C₄×C₅₃	—	2	2	no	—
523	C₂²⋊C₄×C₅₃	—	2	2	no	—
524	C₂²⋊C₄×C₅₃	—	2	2	no	—
525	C₂²⋊C₄×C₅₃	—	2	2	no	—
526	C₂²⋊C₄×C₅₃	—	2	2	no	—
527	C₂²⋊C₄×C₅₃	—	2	2	no	—
528	C₂²⋊C₄×C₅₃	—	2	2	no	—
529	C₂²⋊C₄×C₅₃	—	2	2	no	—
530	C₂²⋊C₄×C₅₃	—	2	2	no	—
531	C₂²⋊C₄×C₅₃	—	2	2	no	—
532	C₂²⋊C₄×C₅₃	—	2	2	no	—
533	C₂²⋊C₄×C₅₃	—	2	2	no	—
534	C₂²⋊C₄×C₅₃	—	2	2	no	—
535	C₂²⋊C₄×C₅₃	—	2	2	no	—
536	C₂²⋊C₄×C₅₃	—	2	2	no	—
537	C₂²⋊C₄×C₅₃	—	2	2	no	—
538	C₂²⋊C₄×C₅₃	—	2	2	no	—
539	C₂²⋊C₄×C₅₃	—	4	1	no	—
540	C₂²⋊C₄×C₅₃	—	4	1	no	—
541	C₂²⋊C₄×C₅₃	—	4	1	no	—
542	C₂²⋊C₄×C₅₃	—	4	1	no	—
543	C₂²⋊C₄×C₅₃	—	4	1	no	—
544	C₂²⋊C₄×C₅₃	—	4	1	no	—
545	C₂²⋊C₄×C₅₃	—	4	1	no	—
546	C₂²⋊C₄×C₅₃	—	4	1	no	—
547	C₂²⋊C₄×C₅₃	—	4	1	no	—
548	C₂²⋊C₄×C₅₃	—	4	1	no	—
549	C₂²⋊C₄×C₅₃	—	4	1	no	—
550	C₂²⋊C₄×C₅₃	—	4	1	no	—
551	C₂²⋊C₄×C₅₃	—	4	1	no	—
552	C₂²⋊C₄×C₅₃	—	4	1	no	—
553	C₂²⋊C₄×C₅₃	—	4	1	no	—
554	C₂²⋊C₄×C₅₃	—	4	1	no	—
555	C₂²⋊C₄×C₅₃	—	4	1	no	—
556	C₂²⋊C₄×C₅₃	—	4	1	no	—
557	C₂²⋊C₄×C₅₃	—	4	1	no	—
558	C₂²⋊C₄×C₅₃	—	4	1	no	—
559	C₂²⋊C₄×C₅₃	—	4	1	no	—
560	C₂²⋊C₄×C₅₃	—	4	1	no	—
561	C₂²⋊C₄×C₅₃	—	4	1	no	—
562	C₂²⋊C₄×C₅₃	—	4	1	no	—
563	C₂²⋊C₄×C₅₃	—	4	1	no	—
564	C₂²⋊C₄×C₅₃	—	4	1	no	—
565	C₂²⋊C₄×C₅₃	—	4	1	no	—
566	C₂²⋊C₄×C₅₃	—	4	1	no	—
567	C₂²⋊C₄×C₅₃	—	4	1	no	—
568	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
569	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
570	C₄²×C₅₃	—	2	2	no	—
571	C₄²×C₅₃	—	2	2	no	—
572	C₄²×C₅₃	—	2	2	no	—
573	C₄²×C₅₃	—	2	2	no	—
574	C₄²×C₅₃	—	2	2	no	—
575	C₄²×C₅₃	—	2	2	no	—
576	C₄²×C₅₃	—	4	1	no	—
577	C₄²×C₅₃	—	4	1	no	—
578	C₄²×C₅₃	—	4	1	no	—
579	C₄²×C₅₃	—	4	1	no	—
580	C₄²×C₅₃	C₂×D₄	1	4	yes	—
581	C₂³×C₅₃	—	2	1	no	—
582	C₂³×C₅₃	—	2	1	no	—
583	C₂³×C₅₃	—	2	1	no	—
584	C₂³×C₅₃	—	2	1	no	—
585	C₂³×C₅₃	—	2	1	no	—
586	C₂³×C₅₃	—	2	1	no	—
587	C₂³×C₅₃	—	2	1	no	—
588	C₂³×C₅₃	—	2	1	no	—
589	C₂³×C₅₃	—	2	1	no	—
590	C₂³×C₅₃	—	2	1	no	—
591	C₂³×C₅₃	—	2	1	no	—
592	C₂³×C₅₃	—	2	1	no	—
593	C₂³×C₅₃	—	2	1	no	—
594	C₂³×C₅₃	—	2	1	no	—
595	C₂³×C₅₃	—	2	1	no	—
596	C₂³×C₅₃	—	2	1	no	—
597	C₂³×C₅₃	—	2	1	no	—
598	C₂³×C₅₃	—	2	1	no	—
599	C₂³×C₅₃	—	2	1	no	—
600	C₂³×C₅₃	—	2	1	no	—
601	C₂³×C₅₃	—	2	1	no	—
602	C₂³×C₅₃	—	2	1	no	—
603	C₂³×C₅₃	—	2	1	no	—
604	C₂³×C₅₃	—	2	1	no	—
605	C₂³×C₅₃	—	2	1	no	—
606	C₂³×C₅₃	—	2	1	no	—
607	C₂³×C₅₃	—	2	1	no	—
608	C₂³×C₅₃	—	2	1	no	—
609	C₂³×C₅₃	—	2	1	no	—
610	C₂³×C₅₃	—	2	1	no	—
611	C₂³×C₅₃	—	2	1	no	—
612	C₂³×C₅₃	—	2	1	no	—
613	C₂³×C₅₃	—	2	1	no	—
614	C₂³×C₅₃	—	2	1	no	—
615	C₂³×C₅₃	—	2	1	no	—
616	C₂³×C₅₃	—	2	1	no	—
617	C₂³×C₅₃	—	2	1	no	—
618	C₂³×C₅₃	—	2	1	no	—
619	C₂³×C₅₃	—	2	1	no	—
620	C₂³×C₅₃	—	2	1	no	—
621	C₂³×C₅₃	—	4	4	no	—
622	C₂³×C₅₃	—	8	2	no	—
623	C₂³×C₅₃	—	8	2	no	—
624	C₂³×C₅₃	—	8	2	no	—
625	C₂³×C₅₃	—	8	2	no	—
626	C₂³×C₅₃	—	8	2	no	—
627	C₂³×C₅₃	—	8	2	no	—
628	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
629	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
630	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
631	Q₈×C₅₃	—	4	4	no	—
632	Q₈×C₅₃	—	8	2	no	—
633	Q₈×C₅₃	—	8	2	no	—
634	Q₈×C₅₃	—	8	2	no	—
635	D₄×C₅₃	—	4	4	no	—
636	D₄×C₅₃	—	4	4	no	—
637	D₄×C₅₃	—	8	2	no	—
638	D₄×C₅₃	—	8	2	no	—
639	D₄×C₅₃	—	8	2	no	—
640	D₄×C₅₃	—	8	2	no	—
641	D₄×C₅₃	—	8	2	no	—
642	D₄×C₅₃	—	8	2	no	—
643	D₄×C₅₃	—	8	2	no	—
644	D₄×C₅₃	—	8	2	no	—
645	D₄×C₅₃	—	8	2	no	—
646	D₄×C₅₃	—	8	2	no	—
647	C₂×C₄×C₅₃	—	2	1	no	—
648	C₂×C₄×C₅₃	—	2	1	no	—
649	C₂×C₄×C₅₃	—	2	1	no	—
650	C₂×C₄×C₅₃	—	2	1	no	—
651	C₂×C₄×C₅₃	—	2	1	no	—
652	C₂×C₄×C₅₃	—	2	1	no	—
653	C₂×C₄×C₅₃	—	2	1	no	—
654	C₂×C₄×C₅₃	—	2	1	no	—
655	C₂×C₄×C₅₃	—	2	1	no	—
656	C₂×C₄×C₅₃	—	2	1	no	—
657	C₂×C₄×C₅₃	—	2	1	no	—
658	C₂×C₄×C₅₃	—	2	1	no	—
659	C₂×C₄×C₅₃	—	2	1	no	—
660	C₂×C₄×C₅₃	—	2	1	no	—
661	C₂×C₄×C₅₃	—	2	1	no	—
662	C₂×C₄×C₅₃	—	2	1	no	—
663	C₂×C₄×C₅₃	—	2	1	no	—
664	C₂×C₄×C₅₃	—	2	1	no	—
665	C₂×C₄×C₅₃	—	2	1	no	—
666	C₂×C₄×C₅₃	—	2	1	no	—
667	C₂×C₄×C₅₃	—	2	1	no	—
668	C₂×C₄×C₅₃	—	2	1	no	—
669	C₂×C₄×C₅₃	—	2	1	no	—
670	C₂×C₄×C₅₃	—	2	1	no	—
671	C₂×C₄×C₅₃	—	2	1	no	—
672	C₂×C₄×C₅₃	—	2	1	no	—
673	C₂×C₄×C₅₃	—	2	1	no	—
674	C₂×C₄×C₅₃	—	2	1	no	—
675	C₂×C₄×C₅₃	—	2	1	no	—
676	C₂×C₄×C₅₃	—	2	1	no	—
677	C₂×C₄×C₅₃	—	2	1	no	—
678	C₂×C₄×C₅₃	—	2	1	no	—
679	C₂×C₄×C₅₃	—	2	1	no	—
680	C₂×C₄×C₅₃	—	2	1	no	—
681	C₂×C₄×C₅₃	—	2	1	no	—
682	C₂×C₄×C₅₃	—	2	1	no	—
683	C₂×C₄×C₅₃	—	2	1	no	—
684	C₂×C₄×C₅₃	—	2	1	no	—
685	C₂×C₄×C₅₃	—	2	1	no	—
686	C₂×C₄×C₅₃	—	2	1	no	—
687	C₂×C₄×C₅₃	—	2	1	no	—
688	C₂×C₄×C₅₃	—	2	1	no	—
689	C₂×C₄×C₅₃	—	2	1	no	—
690	C₂×C₄×C₅₃	—	2	1	no	—
691	C₂×C₄×C₅₃	—	2	1	no	—
692	C₂×C₄×C₅₃	—	2	1	no	—
693	C₂×C₄×C₅₃	—	2	1	no	—
694	C₂×C₄×C₅₃	—	2	1	no	—
695	C₂×C₄×C₅₃	—	2	1	no	—
696	C₂×C₄×C₅₃	—	2	1	no	—
697	C₂×C₄×C₅₃	—	2	1	no	—
698	C₂×C₄×C₅₃	—	2	1	no	—
699	C₂×C₄×C₅₃	—	2	1	no	—
700	C₂×C₄×C₅₃	—	2	1	no	—
701	C₂×C₄×C₅₃	—	2	1	no	—
702	C₂×C₄×C₅₃	—	2	1	no	—
703	C₂×C₄×C₅₃	—	2	1	no	—
704	C₂×C₄×C₅₃	—	2	1	no	—
705	C₂×C₄×C₅₃	—	2	1	no	—
706	C₂×C₄×C₅₃	—	2	1	no	—
707	C₂×C₄×C₅₃	—	2	1	no	—
708	C₂×C₄×C₅₃	—	2	1	no	—
709	C₂×C₄×C₅₃	—	2	1	no	—
710	C₂×C₄×C₅₃	—	2	1	no	—
711	C₂×C₄×C₅₃	—	2	1	no	—
712	C₂×C₄×C₅₃	—	2	1	no	—
713	C₂×C₄×C₅₃	—	2	1	no	—
714	C₂×C₄×C₅₃	—	2	1	no	—
715	C₂×C₄×C₅₃	—	2	1	no	—
716	C₂×C₄×C₅₃	—	4	4	no	—
717	C₂×C₄×C₅₃	—	4	4	no	—
718	C₂×C₄×C₅₃	—	4	4	no	—
719	C₂×C₄×C₅₃	—	4	4	no	—
720	C₂×C₄×C₅₃	—	4	4	no	—
721	C₂×C₄×C₅₃	—	8	2	no	—
722	C₂×C₄×C₅₃	—	8	2	no	—
723	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
724	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
725	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
726	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
727	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
728	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
729	#36745	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
730	C₂²×C₅₃	—	2	2	no	—
731	C₂²×C₅₃	—	2	2	no	—
732	C₂²×C₅₃	—	2	2	no	—
733	C₂²×C₅₃	—	2	2	no	—
734	C₂²×C₅₃	—	2	2	no	—
735	C₂²×C₅₃	—	2	2	no	—
736	C₂²×C₅₃	—	4	1	no	—
737	C₂²×C₅₃	—	4	1	no	—
738	C₂²×C₅₃	—	4	1	no	—
739	C₂²×C₅₃	—	4	1	no	—
740	C₂²×C₅₃	—	4	1	no	—
741	C₂²×C₅₃	—	4	1	no	—
742	C₂²×C₅₃	—	4	1	no	—
743	C₂²×C₅₃	—	4	1	no	—
744	C₂²×C₅₃	—	4	1	no	—
745	C₂²×C₅₃	—	4	1	no	—
746	C₂²×C₅₃	—	4	1	no	—
747	C₂²×C₅₃	—	4	1	no	—
748	C₂²×C₅₃	—	4	1	no	—
749	C₂²×C₅₃	—	4	1	no	—
750	C₂²×C₅₃	—	4	1	no	—
751	C₂²×C₅₃	—	4	1	no	—
752	C₂²×C₅₃	—	4	1	no	—
753	C₂²×C₅₃	—	4	1	no	—
754	C₂²×C₅₃	—	4	1	no	—
755	C₂²×C₅₃	—	4	1	no	—
756	C₂²×C₅₃	—	4	1	no	—
757	C₂²×C₅₃	—	4	1	no	—
758	C₂²×C₅₃	—	4	1	no	—
759	C₂²×C₅₃	—	4	1	no	—
760	C₂²×C₅₃	—	4	1	no	—
761	C₂²×C₅₃	—	4	1	no	—
762	C₂²×C₅₃	—	4	1	no	—
763	C₂²×C₅₃	—	4	1	no	—
764	C₂²×C₅₃	—	4	1	no	—
765	C₂²×C₅₃	—	4	1	no	—
766	C₂²×C₅₃	—	4	1	no	—
767	C₂²×C₅₃	—	4	1	no	—
768	C₂²×C₅₃	—	4	1	no	—
769	C₂²×C₅₃	—	4	1	no	—
770	C₂²×C₅₃	—	4	1	no	—
771	C₂²×C₅₃	—	4	1	no	—
772	C₂²×C₅₃	—	8	8	no	—
773	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
774	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
775	C₂²×C₅₃	#585	1	1	yes	characteristic
776	C₂²×C₅₃	#585	1	1	yes	characteristic
777	C₂²×C₅₃	#585	1	1	yes	characteristic
778	C₂²×C₅₃	#585	1	1	yes	characteristic
779	C₂²×C₅₃	#585	1	1	yes	characteristic
780	C₄×C₅₃	—	2	2	no	—
781	C₄×C₅₃	—	2	2	no	—
782	C₄×C₅₃	—	2	2	no	—
783	C₄×C₅₃	—	2	2	no	—
784	C₄×C₅₃	—	2	2	no	—
785	C₄×C₅₃	—	2	2	no	—
786	C₄×C₅₃	—	4	1	no	—
787	C₄×C₅₃	—	4	1	no	—
788	C₄×C₅₃	—	4	1	no	—
789	C₄×C₅₃	—	4	1	no	—
790	C₄×C₅₃	—	4	1	no	—
791	C₄×C₅₃	—	4	1	no	—
792	C₄×C₅₃	—	4	1	no	—
793	C₄×C₅₃	—	4	1	no	—
794	C₄×C₅₃	—	4	1	no	—
795	C₄×C₅₃	—	4	1	no	—
796	C₄×C₅₃	—	4	1	no	—
797	C₄×C₅₃	—	4	1	no	—
798	C₄×C₅₃	—	4	1	no	—
799	C₄×C₅₃	—	4	1	no	—
800	C₄×C₅₃	—	4	1	no	—
801	C₄×C₅₃	—	4	1	no	—
802	C₄×C₅₃	—	4	1	no	—
803	C₄×C₅₃	—	4	1	no	—
804	C₄×C₅₃	—	4	1	no	—
805	C₂×#542	C₂×C₅₃	1	1	yes	characteristic, complemented
806	C₂×#538	C₂×C₅₃	1	1	yes	characteristic, complemented
807	#2854	C₂×C₅₃	1	1	yes	characteristic, complemented
808	#2850	C₂×C₅₃	1	1	yes	characteristic, complemented
809	#2723	C₂×C₅₃	1	1	yes	characteristic, complemented
810	#2716	C₂×C₅₃	1	1	yes	characteristic, complemented
811	#2715	C₂×C₅₃	1	1	yes	characteristic, complemented
812	#2712	C₂×C₅₃	1	1	yes	characteristic, complemented
813	#2700	C₂×C₅₃	1	1	yes	characteristic, complemented
814	#2698	C₂×C₅₃	1	1	yes	characteristic, complemented
815	#2696	C₂×C₅₃	1	1	yes	characteristic, complemented
816	#2691	C₂×C₅₃	1	1	yes	characteristic, complemented
817	#2688	C₂×C₅₃	1	1	yes	characteristic, complemented
818	#2686	C₂×C₅₃	1	1	yes	characteristic, complemented
819	#2685	C₂×C₅₃	1	1	yes	characteristic, complemented
820	#2684	C₂×C₅₃	1	1	yes	characteristic, complemented
821	#2676	C₂×C₅₃	1	1	yes	characteristic, complemented
822	#2674	C₂×C₅₃	1	1	yes	characteristic, complemented
823	#2670	C₂×C₅₃	1	1	yes	characteristic, complemented
824	#2668	C₂×C₅₃	1	1	yes	characteristic, complemented
825	#2663	C₂×C₅₃	1	1	yes	characteristic, complemented
826	#2661	C₂×C₅₃	1	1	yes	characteristic, complemented
827	#2610	C₂×C₅₃	1	1	yes	characteristic, complemented
828	#2604	C₂×C₅₃	1	1	yes	characteristic, complemented
829	#2602	C₂×C₅₃	1	1	yes	characteristic, complemented
830	#2601	C₂×C₅₃	1	1	yes	characteristic, complemented
831	#2592	C₂×C₅₃	1	1	yes	characteristic, complemented
832	#2561	C₂×C₅₃	1	1	yes	characteristic, complemented
833	#2415	C₂×C₅₃	1	1	yes	characteristic, complemented
834	#2411	C₂×C₅₃	1	1	yes	characteristic, complemented
835	#2290	C₂×C₅₃	1	1	yes	characteristic, complemented
836	C₂×C₅₃	—	4	2	no	—
837	C₂×C₅₃	—	4	2	no	—
838	C₂×C₅₃	—	8	1	no	—
839	C₂×C₅₃	—	8	1	no	—
840	C₂×C₅₃	—	8	1	no	—
841	C₂×C₅₃	—	8	1	no	—
842	C₂×C₅₃	#3449	1	1	yes	characteristic
843	C₂×C₅₃	#3496	1	1	yes	characteristic
844	C₂×C₅₃	#3500	1	1	yes	characteristic
845	C₂×C₅₃	#3533	1	1	yes	characteristic
846	C₂×C₅₃	#3540	1	1	yes	characteristic
847	C₂×C₅₃	#3566	1	1	yes	characteristic
848	C₂×C₅₃	#3568	1	1	yes	characteristic
849	#542	—	2	8	no	—
850	#538	—	2	8	no	—
851	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
852	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
853	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
854	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
855	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic, complemented
856	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
857	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
858	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
859	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
860	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
861	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
862	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
863	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
864	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
865	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
866	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
867	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
868	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
869	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
870	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
871	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
872	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
873	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
874	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
875	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
876	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
877	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
878	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
879	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
880	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
881	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
882	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
883	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
884	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
885	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
886	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
887	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
888	#399	C₂²×C₅₃	1	1	yes	characteristic
889	#399	C₂²×C₅₃	1	1	yes	characteristic
890	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
891	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
892	#397	C₂²×C₅₃	1	1	yes	characteristic
893	#397	C₂²×C₅₃	1	1	yes	characteristic
894	#397	C₂²×C₅₃	1	1	yes	characteristic
895	#397	C₂²×C₅₃	1	1	yes	characteristic
896	#397	C₂²×C₅₃	1	1	yes	characteristic
897	#397	C₂²×C₅₃	1	1	yes	characteristic
898	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
899	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
900	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
901	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
902	#396	C₂²×C₅₃	1	1	yes	characteristic
903	#396	C₂²×C₅₃	1	1	yes	characteristic
904	#396	C₂²×C₅₃	1	1	yes	characteristic
905	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
906	#395	C₂²×C₅₃	1	1	yes	characteristic, complemented
907	#395	C₂²×C₅₃	1	1	yes	characteristic, complemented
908	#395	C₂²×C₅₃	1	1	yes	characteristic, complemented
909	#394	C₂²×C₅₃	1	1	yes	characteristic
910	#394	C₂²×C₅₃	1	1	yes	characteristic
911	#394	C₂²×C₅₃	1	1	yes	characteristic
912	#394	C₂²×C₅₃	1	1	yes	characteristic
913	#394	C₂²×C₅₃	1	1	yes	characteristic
914	#394	C₂²×C₅₃	1	1	yes	characteristic
915	#394	C₂²×C₅₃	1	1	yes	characteristic
916	#394	C₂²×C₅₃	1	1	yes	characteristic
917	#394	C₂²×C₅₃	1	1	yes	characteristic
918	#394	C₂²×C₅₃	1	1	yes	characteristic
919	#394	C₂²×C₅₃	1	1	yes	characteristic
920	#394	C₂²×C₅₃	1	1	yes	characteristic
921	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
922	#393	C₂²×C₅₃	1	1	yes	characteristic
923	#393	C₂²×C₅₃	1	1	yes	characteristic
924	#393	C₂²×C₅₃	1	1	yes	characteristic
925	#393	C₂²×C₅₃	1	1	yes	characteristic
926	#393	C₂²×C₅₃	1	1	yes	characteristic
927	#393	C₂²×C₅₃	1	1	yes	characteristic, complemented
928	#393	C₂²×C₅₃	1	1	yes	characteristic, complemented
929	#392	C₂²×C₅₃	1	1	yes	characteristic
930	#392	C₂²×C₅₃	1	1	yes	characteristic
931	#392	C₂²×C₅₃	1	1	yes	characteristic
932	#392	C₂²×C₅₃	1	1	yes	characteristic
933	#392	C₂²×C₅₃	1	1	yes	characteristic, complemented
934	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
935	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
936	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
937	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
938	#390	C₂²×C₅₃	1	1	yes	characteristic
939	#390	C₂²×C₅₃	1	1	yes	characteristic
940	#390	C₂²×C₅₃	1	1	yes	characteristic
941	#390	C₂²×C₅₃	1	1	yes	characteristic
942	#390	C₂²×C₅₃	1	1	yes	characteristic
943	#390	C₂²×C₅₃	1	1	yes	characteristic
944	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
945	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
946	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
947	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
948	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
949	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
950	#388	C₂²×C₅₃	1	1	yes	characteristic
951	#388	C₂²×C₅₃	1	1	yes	characteristic
952	#388	C₂²×C₅₃	1	1	yes	characteristic
953	#388	C₂²×C₅₃	1	1	yes	characteristic
954	#388	C₂²×C₅₃	1	1	yes	characteristic
955	#388	C₂²×C₅₃	1	1	yes	characteristic
956	#388	C₂²×C₅₃	1	1	yes	characteristic
957	#388	C₂²×C₅₃	1	1	yes	characteristic
958	#388	C₂²×C₅₃	1	1	yes	characteristic
959	#388	C₂²×C₅₃	1	1	yes	characteristic
960	#388	C₂²×C₅₃	1	1	yes	characteristic
961	#388	C₂²×C₅₃	1	1	yes	characteristic
962	#388	C₂²×C₅₃	1	1	yes	characteristic
963	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
964	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
965	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
966	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
967	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
968	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
969	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
970	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
971	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
972	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
973	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
974	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
975	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
976	#386	C₂²×C₅₃	1	1	yes	characteristic
977	#386	C₂²×C₅₃	1	1	yes	characteristic
978	#386	C₂²×C₅₃	1	1	yes	characteristic
979	#386	C₂²×C₅₃	1	1	yes	characteristic
980	#386	C₂²×C₅₃	1	1	yes	characteristic
981	#386	C₂²×C₅₃	1	1	yes	characteristic
982	#386	C₂²×C₅₃	1	1	yes	characteristic
983	#386	C₂²×C₅₃	1	1	yes	characteristic
984	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
985	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
987	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
989	#385	C₂²×C₅₃	1	1	yes	characteristic
990	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
991	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
992	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
993	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
995	#381	C₂²×C₅₃	1	1	yes	characteristic
996	#381	C₂²×C₅₃	1	1	yes	characteristic
997	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
998	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	#379	C₂²×C₅₃	1	1	yes	characteristic
1000	#379	C₂²×C₅₃	1	1	yes	characteristic
1001	#379	C₂²×C₅₃	1	1	yes	characteristic
1002	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
1004	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	#376	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	C₅₃	#36745	1	1	yes	characteristic, direct product factor, Sylow
1007	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
1008	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1009	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1010	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1011	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1012	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1013	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1014	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1015	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1016	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1017	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1018	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1019	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1020	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1021	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1022	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1023	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1024	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1025	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1026	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1027	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1028	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1029	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1030	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1031	C₄⋊Q₈	—	2	4	no	—
1032	#126	—	2	4	no	—
1033	#126	—	2	4	no	—
1034	#126	—	2	4	no	—
1035	#126	—	2	4	no	—
1036	#124	—	2	4	no	—
1037	#124	—	2	4	no	—
1038	#124	—	2	4	no	—
1039	#124	—	2	4	no	—
1040	#124	—	2	4	no	—
1041	#124	—	4	2	no	—
1042	#123	—	2	4	no	—
1043	#123	—	2	4	no	—
1044	#123	—	2	4	no	—
1045	#123	—	2	4	no	—
1046	C₂²⋊Q₈	—	2	4	no	—
1047	C₂²⋊Q₈	—	2	4	no	—
1048	C₂²⋊Q₈	—	2	4	no	—
1049	C₂²⋊Q₈	—	2	4	no	—
1050	C₂²⋊Q₈	—	4	2	no	—
1051	#121	—	2	4	no	—
1052	#121	—	2	4	no	—
1053	#121	—	2	4	no	—
1054	#121	—	2	4	no	—
1055	#121	—	4	2	no	—
1056	#120	—	2	4	no	—
1057	#120	—	2	4	no	—
1058	#120	—	4	2	no	—
1059	C₄×Q₈	—	2	4	no	—
1060	C₄×D₄	—	2	4	no	—
1061	C₄×D₄	D₄×C₅₃	1	8	yes	complemented
1062	#117	—	2	4	no	—
1063	#117	—	4	2	no	—
1064	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1065	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1066	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1067	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1068	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1069	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1070	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1071	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1072	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1073	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1074	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1075	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1076	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1077	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1078	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1079	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1080	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1081	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1082	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1083	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1084	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1085	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1086	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1087	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1088	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1089	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1090	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1091	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1092	C₂×C₂²⋊C₄	—	2	4	no	—
1093	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1094	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1095	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1096	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1097	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1098	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1099	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1100	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1101	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1102	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1103	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1104	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1105	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1106	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1107	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1108	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1109	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1110	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1111	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1112	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1113	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1114	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1115	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1116	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1117	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1118	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1119	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1120	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1121	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1122	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1123	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1124	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1125	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1126	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1127	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1128	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1129	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1130	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1131	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1132	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1133	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1134	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1135	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1136	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1137	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1138	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1139	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1140	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1141	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1142	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1143	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1144	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1145	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1146	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1147	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1148	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1149	C₂×C₄²	—	4	2	no	—
1150	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1151	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1152	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1153	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1154	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1155	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1156	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1157	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1158	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1159	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1160	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1161	#95	C₂³×C₅₃	1	1	yes	characteristic
1162	#95	C₂³×C₅₃	1	1	yes	characteristic
1163	#95	C₂³×C₅₃	1	1	yes	characteristic
1164	#95	C₂³×C₅₃	1	1	yes	characteristic
1165	#95	C₂³×C₅₃	1	1	yes	characteristic
1166	#95	C₂³×C₅₃	1	1	yes	characteristic
1167	#95	C₂³×C₅₃	1	1	yes	characteristic
1168	#95	C₂³×C₅₃	1	1	yes	characteristic
1169	#95	C₂³×C₅₃	1	1	yes	characteristic
1170	#95	C₂³×C₅₃	1	1	yes	characteristic
1171	#95	C₂³×C₅₃	1	1	yes	characteristic
1172	#95	C₂³×C₅₃	1	1	yes	characteristic
1173	#95	C₂³×C₅₃	1	1	yes	characteristic
1174	#95	C₂³×C₅₃	1	1	yes	characteristic
1175	#95	C₂³×C₅₃	1	1	yes	characteristic
1176	#95	C₂³×C₅₃	1	1	yes	characteristic
1177	#95	C₂³×C₅₃	1	1	yes	characteristic
1178	#95	C₂³×C₅₃	1	1	yes	characteristic
1179	#95	C₂³×C₅₃	1	1	yes	characteristic
1180	#95	C₂³×C₅₃	1	1	yes	characteristic
1181	#95	C₂³×C₅₃	1	1	yes	characteristic
1182	#95	C₂³×C₅₃	1	1	yes	characteristic
1183	#95	C₂³×C₅₃	1	1	yes	characteristic
1184	#95	C₂³×C₅₃	1	1	yes	characteristic
1185	#95	C₂³×C₅₃	1	1	yes	characteristic
1186	#95	C₂³×C₅₃	1	1	yes	characteristic
1187	#95	C₂³×C₅₃	1	1	yes	characteristic
1188	#95	C₂³×C₅₃	1	1	yes	characteristic
1189	#95	C₂³×C₅₃	1	1	yes	characteristic
1190	#95	C₂³×C₅₃	1	1	yes	characteristic
1191	#95	C₂³×C₅₃	1	1	yes	characteristic
1192	#95	C₂³×C₅₃	1	1	yes	characteristic
1193	#95	C₂³×C₅₃	1	1	yes	characteristic
1194	#95	C₂³×C₅₃	1	1	yes	characteristic
1195	#95	C₂³×C₅₃	1	1	yes	characteristic
1196	#95	C₂³×C₅₃	1	1	yes	characteristic
1197	C₂⁴	—	2	2	no	—
1198	C₂⁴	—	4	1	no	—
1199	C₂⁴	—	4	1	no	—
1200	C₂⁴	—	4	1	no	—
1201	C₂⁴	—	4	1	no	—
1202	C₂⁴	—	4	1	no	—
1203	C₂⁴	—	4	1	no	—
1204	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1205	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1206	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1207	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1208	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1209	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1210	C₂×Q₈	—	2	2	no	—
1211	C₂×Q₈	—	2	2	no	—
1212	C₂×Q₈	—	2	2	no	—
1213	C₂×Q₈	—	2	2	no	—
1214	C₂×Q₈	—	4	1	no	—
1215	C₂×Q₈	—	4	1	no	—
1216	C₂×Q₈	—	4	1	no	—
1217	C₂×Q₈	—	4	1	no	—
1218	C₂×Q₈	—	4	1	no	—
1219	C₂×Q₈	—	4	1	no	—
1220	C₂×Q₈	—	4	1	no	—
1221	C₂×Q₈	—	4	1	no	—
1222	C₂×D₄	—	2	2	no	—
1223	C₂×D₄	—	2	2	no	—
1224	C₂×D₄	—	2	2	no	—
1225	C₂×D₄	—	2	2	no	—
1226	C₂×D₄	—	2	2	no	—
1227	C₂×D₄	—	2	2	no	—
1228	C₂×D₄	—	2	2	no	—
1229	C₂×D₄	—	2	2	no	—
1230	C₂×D₄	—	2	2	no	—
1231	C₂×D₄	—	4	1	no	—
1232	C₂×D₄	—	4	1	no	—
1233	C₂×D₄	—	4	1	no	—
1234	C₂×D₄	—	4	1	no	—
1235	C₂×D₄	—	4	1	no	—
1236	C₂×D₄	—	4	1	no	—
1237	C₂×D₄	—	4	1	no	—
1238	C₂×D₄	—	4	1	no	—
1239	C₂×D₄	—	4	1	no	—
1240	C₂×D₄	—	4	1	no	—
1241	C₂×D₄	—	4	1	no	—
1242	C₂×D₄	—	4	1	no	—
1243	C₂×D₄	—	4	1	no	—
1244	C₂×D₄	—	4	1	no	—
1245	C₂×D₄	—	4	1	no	—
1246	C₂×D₄	—	4	1	no	—
1247	C₂×D₄	—	4	1	no	—
1248	C₂×D₄	—	4	1	no	—
1249	C₂×D₄	—	4	1	no	—
1250	C₂×D₄	—	4	1	no	—
1251	C₂×D₄	—	4	1	no	—
1252	C₂×D₄	—	4	1	no	—
1253	C₂×D₄	—	4	1	no	—
1254	C₂×D₄	—	4	1	no	—
1255	C₂×D₄	—	4	1	no	—
1256	C₂×D₄	—	4	1	no	—
1257	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
1258	C₂²×C₄	—	2	2	no	—
1259	C₂²×C₄	—	2	2	no	—
1260	C₂²×C₄	—	2	2	no	—
1261	C₂²×C₄	—	2	2	no	—
1262	C₂²×C₄	—	4	1	no	—
1263	C₂²×C₄	—	4	1	no	—
1264	C₂²×C₄	—	4	1	no	—
1265	C₂²×C₄	—	4	1	no	—
1266	C₂²×C₄	—	4	1	no	—
1267	C₂²×C₄	—	4	1	no	—
1268	C₂²×C₄	—	4	1	no	—
1269	C₂²×C₄	—	4	1	no	—
1270	C₂²×C₄	—	4	1	no	—
1271	C₂²×C₄	—	4	1	no	—
1272	C₂²×C₄	—	4	1	no	—
1273	C₂²×C₄	—	4	1	no	—
1274	C₂²×C₄	—	4	1	no	—
1275	C₂²×C₄	—	4	1	no	—
1276	C₂²×C₄	—	4	1	no	—
1277	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
1278	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
1279	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1280	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1281	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1282	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1283	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1284	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1285	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1286	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1287	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1288	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1289	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1290	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1291	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1292	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1293	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1294	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1295	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1296	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1297	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1298	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1299	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1300	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1301	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1302	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1303	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1304	C₄⋊C₄	—	2	2	no	—
1305	C₄⋊C₄	—	2	2	no	—
1306	C₄⋊C₄	—	2	2	no	—
1307	C₄⋊C₄	—	2	2	no	—
1308	C₄⋊C₄	—	2	2	no	—
1309	C₄⋊C₄	—	2	2	no	—
1310	C₄⋊C₄	—	2	2	no	—
1311	C₄⋊C₄	—	2	2	no	—
1312	C₄⋊C₄	—	2	2	no	—
1313	C₄⋊C₄	—	2	2	no	—
1314	C₄⋊C₄	—	2	2	no	—
1315	C₄⋊C₄	—	2	2	no	—
1316	C₄⋊C₄	—	2	2	no	—
1317	C₄⋊C₄	—	2	2	no	—
1318	C₄⋊C₄	—	2	2	no	—
1319	C₄⋊C₄	—	2	2	no	—
1320	C₄⋊C₄	—	4	1	no	—
1321	C₄⋊C₄	—	4	1	no	—
1322	C₄⋊C₄	—	4	1	no	—
1323	C₄⋊C₄	—	4	1	no	—
1324	C₄⋊C₄	—	4	1	no	—
1325	C₄⋊C₄	—	4	1	no	—
1326	C₄⋊C₄	—	4	1	no	—
1327	C₄⋊C₄	—	4	1	no	—
1328	C₄⋊C₄	—	4	1	no	—
1329	C₄⋊C₄	—	4	1	no	—
1330	C₄⋊C₄	—	4	1	no	—
1331	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
1332	C₂²⋊C₄	—	2	2	no	—
1333	C₂²⋊C₄	—	2	2	no	—
1334	C₂²⋊C₄	—	2	2	no	—
1335	C₂²⋊C₄	—	2	2	no	—
1336	C₂²⋊C₄	—	2	2	no	—
1337	C₂²⋊C₄	—	2	2	no	—
1338	C₂²⋊C₄	—	2	2	no	—
1339	C₂²⋊C₄	—	2	2	no	—
1340	C₂²⋊C₄	—	2	2	no	—
1341	C₂²⋊C₄	—	2	2	no	—
1342	C₂²⋊C₄	—	2	2	no	—
1343	C₂²⋊C₄	—	2	2	no	—
1344	C₂²⋊C₄	—	2	2	no	—
1345	C₂²⋊C₄	—	2	2	no	—
1346	C₂²⋊C₄	—	2	2	no	—
1347	C₂²⋊C₄	—	2	2	no	—
1348	C₂²⋊C₄	—	2	2	no	—
1349	C₂²⋊C₄	—	2	2	no	—
1350	C₂²⋊C₄	—	2	2	no	—
1351	C₂²⋊C₄	—	2	2	no	—
1352	C₂²⋊C₄	—	2	2	no	—
1353	C₂²⋊C₄	—	2	2	no	—
1354	C₂²⋊C₄	—	2	2	no	—
1355	C₂²⋊C₄	—	2	2	no	—
1356	C₂²⋊C₄	—	2	2	no	—
1357	C₂²⋊C₄	—	4	1	no	—
1358	C₂²⋊C₄	—	4	1	no	—
1359	C₂²⋊C₄	—	4	1	no	—
1360	C₂²⋊C₄	—	4	1	no	—
1361	C₂²⋊C₄	—	4	1	no	—
1362	C₂²⋊C₄	—	4	1	no	—
1363	C₂²⋊C₄	—	4	1	no	—
1364	C₂²⋊C₄	—	4	1	no	—
1365	C₂²⋊C₄	—	4	1	no	—
1366	C₂²⋊C₄	—	4	1	no	—
1367	C₂²⋊C₄	—	4	1	no	—
1368	C₂²⋊C₄	—	4	1	no	—
1369	C₂²⋊C₄	—	4	1	no	—
1370	C₂²⋊C₄	—	4	1	no	—
1371	C₂²⋊C₄	—	4	1	no	—
1372	C₂²⋊C₄	—	4	1	no	—
1373	C₂²⋊C₄	—	4	1	no	—
1374	C₂²⋊C₄	—	4	1	no	—
1375	C₂²⋊C₄	—	4	1	no	—
1376	C₂²⋊C₄	—	4	1	no	—
1377	C₂²⋊C₄	—	4	1	no	—
1378	C₂²⋊C₄	—	4	1	no	—
1379	C₂²⋊C₄	—	4	1	no	—
1380	C₂²⋊C₄	—	4	1	no	—
1381	C₂²⋊C₄	—	4	1	no	—
1382	C₂²⋊C₄	—	4	1	no	—
1383	C₂²⋊C₄	—	4	1	no	—
1384	C₂²⋊C₄	—	4	1	no	—
1385	C₂²⋊C₄	—	4	1	no	—
1386	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
1387	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
1388	C₄²	—	2	2	no	—
1389	C₄²	—	2	2	no	—
1390	C₄²	—	2	2	no	—
1391	C₄²	—	2	2	no	—
1392	C₄²	—	2	2	no	—
1393	C₄²	—	2	2	no	—
1394	C₄²	—	4	1	no	—
1395	C₄²	—	4	1	no	—
1396	C₄²	—	4	1	no	—
1397	C₄²	—	4	1	no	—
1398	C₄²	C₂×D₄×C₅₃	1	4	yes	—
1399	C₂³	—	2	1	no	—
1400	C₂³	—	2	1	no	—
1401	C₂³	—	2	1	no	—
1402	C₂³	—	2	1	no	—
1403	C₂³	—	2	1	no	—
1404	C₂³	—	2	1	no	—
1405	C₂³	—	2	1	no	—
1406	C₂³	—	2	1	no	—
1407	C₂³	—	2	1	no	—
1408	C₂³	—	2	1	no	—
1409	C₂³	—	2	1	no	—
1410	C₂³	—	2	1	no	—
1411	C₂³	—	2	1	no	—
1412	C₂³	—	2	1	no	—
1413	C₂³	—	2	1	no	—
1414	C₂³	—	2	1	no	—
1415	C₂³	—	2	1	no	—
1416	C₂³	—	2	1	no	—
1417	C₂³	—	2	1	no	—
1418	C₂³	—	2	1	no	—
1419	C₂³	—	2	1	no	—
1420	C₂³	—	2	1	no	—
1421	C₂³	—	2	1	no	—
1422	C₂³	—	2	1	no	—
1423	C₂³	—	2	1	no	—
1424	C₂³	—	2	1	no	—
1425	C₂³	—	2	1	no	—
1426	C₂³	—	2	1	no	—
1427	C₂³	—	2	1	no	—
1428	C₂³	—	2	1	no	—
1429	C₂³	—	2	1	no	—
1430	C₂³	—	2	1	no	—
1431	C₂³	—	2	1	no	—
1432	C₂³	—	2	1	no	—
1433	C₂³	—	2	1	no	—
1434	C₂³	—	2	1	no	—
1435	C₂³	—	2	1	no	—
1436	C₂³	—	2	1	no	—
1437	C₂³	—	2	1	no	—
1438	C₂³	—	2	1	no	—
1439	C₂³	—	4	4	no	—
1440	C₂³	—	8	2	no	—
1441	C₂³	—	8	2	no	—
1442	C₂³	—	8	2	no	—
1443	C₂³	—	8	2	no	—
1444	C₂³	—	8	2	no	—
1445	C₂³	—	8	2	no	—
1446	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1447	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1448	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1449	Q₈	—	4	4	no	—
1450	Q₈	—	8	2	no	—
1451	Q₈	—	8	2	no	—
1452	Q₈	—	8	2	no	—
1453	D₄	—	4	4	no	—
1454	D₄	—	4	4	no	—
1455	D₄	—	8	2	no	—
1456	D₄	—	8	2	no	—
1457	D₄	—	8	2	no	—
1458	D₄	—	8	2	no	—
1459	D₄	—	8	2	no	—
1460	D₄	—	8	2	no	—
1461	D₄	—	8	2	no	—
1462	D₄	—	8	2	no	—
1463	D₄	—	8	2	no	—
1464	D₄	—	8	2	no	—
1465	C₂×C₄	—	2	1	no	—
1466	C₂×C₄	—	2	1	no	—
1467	C₂×C₄	—	2	1	no	—
1468	C₂×C₄	—	2	1	no	—
1469	C₂×C₄	—	2	1	no	—
1470	C₂×C₄	—	2	1	no	—
1471	C₂×C₄	—	2	1	no	—
1472	C₂×C₄	—	2	1	no	—
1473	C₂×C₄	—	2	1	no	—
1474	C₂×C₄	—	2	1	no	—
1475	C₂×C₄	—	2	1	no	—
1476	C₂×C₄	—	2	1	no	—
1477	C₂×C₄	—	2	1	no	—
1478	C₂×C₄	—	2	1	no	—
1479	C₂×C₄	—	2	1	no	—
1480	C₂×C₄	—	2	1	no	—
1481	C₂×C₄	—	2	1	no	—
1482	C₂×C₄	—	2	1	no	—
1483	C₂×C₄	—	2	1	no	—
1484	C₂×C₄	—	2	1	no	—
1485	C₂×C₄	—	2	1	no	—
1486	C₂×C₄	—	2	1	no	—
1487	C₂×C₄	—	2	1	no	—
1488	C₂×C₄	—	2	1	no	—
1489	C₂×C₄	—	2	1	no	—
1490	C₂×C₄	—	2	1	no	—
1491	C₂×C₄	—	2	1	no	—
1492	C₂×C₄	—	2	1	no	—
1493	C₂×C₄	—	2	1	no	—
1494	C₂×C₄	—	2	1	no	—
1495	C₂×C₄	—	2	1	no	—
1496	C₂×C₄	—	2	1	no	—
1497	C₂×C₄	—	2	1	no	—
1498	C₂×C₄	—	2	1	no	—
1499	C₂×C₄	—	2	1	no	—
1500	C₂×C₄	—	2	1	no	—
1501	C₂×C₄	—	2	1	no	—
1502	C₂×C₄	—	2	1	no	—
1503	C₂×C₄	—	2	1	no	—
1504	C₂×C₄	—	2	1	no	—
1505	C₂×C₄	—	2	1	no	—
1506	C₂×C₄	—	2	1	no	—
1507	C₂×C₄	—	2	1	no	—
1508	C₂×C₄	—	2	1	no	—
1509	C₂×C₄	—	2	1	no	—
1510	C₂×C₄	—	2	1	no	—
1511	C₂×C₄	—	2	1	no	—
1512	C₂×C₄	—	2	1	no	—
1513	C₂×C₄	—	2	1	no	—
1514	C₂×C₄	—	2	1	no	—
1515	C₂×C₄	—	2	1	no	—
1516	C₂×C₄	—	2	1	no	—
1517	C₂×C₄	—	2	1	no	—
1518	C₂×C₄	—	2	1	no	—
1519	C₂×C₄	—	2	1	no	—
1520	C₂×C₄	—	2	1	no	—
1521	C₂×C₄	—	2	1	no	—
1522	C₂×C₄	—	2	1	no	—
1523	C₂×C₄	—	2	1	no	—
1524	C₂×C₄	—	2	1	no	—
1525	C₂×C₄	—	2	1	no	—
1526	C₂×C₄	—	2	1	no	—
1527	C₂×C₄	—	2	1	no	—
1528	C₂×C₄	—	2	1	no	—
1529	C₂×C₄	—	2	1	no	—
1530	C₂×C₄	—	2	1	no	—
1531	C₂×C₄	—	2	1	no	—
1532	C₂×C₄	—	2	1	no	—
1533	C₂×C₄	—	2	1	no	—
1534	C₂×C₄	—	4	4	no	—
1535	C₂×C₄	—	4	4	no	—
1536	C₂×C₄	—	4	4	no	—
1537	C₂×C₄	—	4	4	no	—
1538	C₂×C₄	—	4	4	no	—
1539	C₂×C₄	—	8	2	no	—
1540	C₂×C₄	—	8	2	no	—
1541	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1542	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1543	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1544	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1545	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1546	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1547	C₂²	—	2	2	no	—
1548	C₂²	—	2	2	no	—
1549	C₂²	—	2	2	no	—
1550	C₂²	—	2	2	no	—
1551	C₂²	—	2	2	no	—
1552	C₂²	—	2	2	no	—
1553	C₂²	—	4	1	no	—
1554	C₂²	—	4	1	no	—
1555	C₂²	—	4	1	no	—
1556	C₂²	—	4	1	no	—
1557	C₂²	—	4	1	no	—
1558	C₂²	—	4	1	no	—
1559	C₂²	—	4	1	no	—
1560	C₂²	—	4	1	no	—
1561	C₂²	—	4	1	no	—
1562	C₂²	—	4	1	no	—
1563	C₂²	—	4	1	no	—
1564	C₂²	—	4	1	no	—
1565	C₂²	—	4	1	no	—
1566	C₂²	—	4	1	no	—
1567	C₂²	—	4	1	no	—
1568	C₂²	—	4	1	no	—
1569	C₂²	—	4	1	no	—
1570	C₂²	—	4	1	no	—
1571	C₂²	—	4	1	no	—
1572	C₂²	—	4	1	no	—
1573	C₂²	—	4	1	no	—
1574	C₂²	—	4	1	no	—
1575	C₂²	—	4	1	no	—
1576	C₂²	—	4	1	no	—
1577	C₂²	—	4	1	no	—
1578	C₂²	—	4	1	no	—
1579	C₂²	—	4	1	no	—
1580	C₂²	—	4	1	no	—
1581	C₂²	—	4	1	no	—
1582	C₂²	—	4	1	no	—
1583	C₂²	—	4	1	no	—
1584	C₂²	—	4	1	no	—
1585	C₂²	—	4	1	no	—
1586	C₂²	—	4	1	no	—
1587	C₂²	—	4	1	no	—
1588	C₂²	—	4	1	no	—
1589	C₂²	—	8	8	no	—
1590	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1591	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1592	C₂²	C₅₃×#585	1	1	yes	characteristic
1593	C₂²	C₅₃×#585	1	1	yes	characteristic
1594	C₂²	C₅₃×#585	1	1	yes	characteristic
1595	C₂²	C₅₃×#585	1	1	yes	characteristic
1596	C₂²	C₅₃×#585	1	1	yes	characteristic
1597	C₄	—	2	2	no	—
1598	C₄	—	2	2	no	—
1599	C₄	—	2	2	no	—
1600	C₄	—	2	2	no	—
1601	C₄	—	2	2	no	—
1602	C₄	—	2	2	no	—
1603	C₄	—	4	1	no	—
1604	C₄	—	4	1	no	—
1605	C₄	—	4	1	no	—
1606	C₄	—	4	1	no	—
1607	C₄	—	4	1	no	—
1608	C₄	—	4	1	no	—
1609	C₄	—	4	1	no	—
1610	C₄	—	4	1	no	—
1611	C₄	—	4	1	no	—
1612	C₄	—	4	1	no	—
1613	C₄	—	4	1	no	—
1614	C₄	—	4	1	no	—
1615	C₄	—	4	1	no	—
1616	C₄	—	4	1	no	—
1617	C₄	—	4	1	no	—
1618	C₄	—	4	1	no	—
1619	C₄	—	4	1	no	—
1620	C₄	—	4	1	no	—
1621	C₄	—	4	1	no	—
1622	C₂	—	4	2	no	—
1623	C₂	—	4	2	no	—
1624	C₂	—	8	1	no	—
1625	C₂	—	8	1	no	—
1626	C₂	—	8	1	no	—
1627	C₂	—	8	1	no	—
1628	C₂	C₅₃×#3449	1	1	yes	characteristic
1629	C₂	C₅₃×#3496	1	1	yes	characteristic
1630	C₂	C₅₃×#3500	1	1	yes	characteristic
1631	C₂	C₅₃×#3533	1	1	yes	characteristic
1632	C₂	C₅₃×#3540	1	1	yes	characteristic
1633	C₂	C₅₃×#3566	1	1	yes	characteristic
1634	C₂	C₅₃×#3568	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₅₃×#542	C₂	semidirect
2. C₂×C₅₃×#538	C₂	semidirect
3. C₅₃×#2854	C₂	semidirect
4. C₅₃×#2850	C₂	semidirect
5. C₅₃×#2723	C₂	semidirect
6. C₅₃×#2716	C₂	semidirect
7. C₅₃×#2715	C₂	semidirect
8. C₅₃×#2712	C₂	semidirect
9. C₅₃×#2700	C₂	semidirect
10. C₅₃×#2698	C₂	semidirect
11. C₅₃×#2696	C₂	semidirect
12. C₅₃×#2691	C₂	semidirect
13. C₅₃×#2688	C₂	semidirect
14. C₅₃×#2686	C₂	semidirect
15. C₅₃×#2685	C₂	semidirect
16. C₅₃×#2684	C₂	semidirect
17. C₅₃×#2676	C₂	semidirect
18. C₅₃×#2674	C₂	semidirect
19. C₅₃×#2670	C₂	semidirect
20. C₅₃×#2668	C₂	semidirect
21. C₅₃×#2663	C₂	semidirect
22. C₅₃×#2661	C₂	semidirect
23. C₅₃×#2610	C₂	semidirect
24. C₅₃×#2604	C₂	semidirect
25. C₅₃×#2602	C₂	semidirect
26. C₅₃×#2601	C₂	semidirect
27. C₅₃×#2592	C₂	semidirect
28. C₅₃×#2561	C₂	semidirect
29. C₅₃×#2415	C₂	semidirect
30. C₅₃×#2411	C₂	semidirect
31. C₅₃×#2290	C₂	semidirect
34. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
38. C₂×#126×C₅₃	C₂²	semidirect
44. C₂×#124×C₅₃	C₂²	semidirect
48. C₂×#123×C₅₃	C₂²	semidirect
51. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
52. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
53. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
62. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
66. C₂×#117×C₅₃	C₂²	semidirect
68. C₂²×C₄²×C₅₃	C₂²	semidirect
69. C₅₃×#400	C₂²	semidirect
70. C₅₃×#400	C₂²	semidirect
73. C₅₃×#398	C₂²	semidirect
74. C₅₃×#398	C₂²	semidirect
81. C₅₃×#397	C₂²	semidirect
82. C₅₃×#397	C₂²	semidirect
83. C₅₃×#397	C₂²	semidirect
84. C₅₃×#397	C₂²	semidirect
88. C₅₃×#396	C₂²	semidirect
89. C₅₃×#395	C₂²	semidirect
90. C₅₃×#395	C₂²	semidirect
91. C₅₃×#395	C₂²	semidirect
104. C₅₃×#394	C₂²	semidirect
110. C₅₃×#393	C₂²	semidirect
111. C₅₃×#393	C₂²	semidirect
116. C₅₃×#392	C₂²	semidirect
117. C₅₃×#391	C₂²	semidirect
118. C₅₃×#391	C₂²	semidirect
119. C₅₃×#391	C₂²	semidirect
120. C₅₃×#391	C₂²	semidirect
127. C₅₃×#390	C₂²	semidirect
128. C₅₃×#389	C₂²	semidirect
129. C₅₃×#389	C₂²	semidirect
130. C₅₃×#389	C₂²	semidirect
131. C₅₃×#389	C₂²	semidirect
132. C₅₃×#389	C₂²	semidirect
146. C₅₃×#388	C₂²	semidirect
147. C₅₃×#388	C₂²	semidirect
148. C₅₃×#388	C₂²	semidirect
149. C₅₃×#388	C₂²	semidirect
150. C₅₃×#388	C₂²	semidirect
151. C₅₃×#388	C₂²	semidirect
152. C₅₃×#388	C₂²	semidirect
153. C₅₃×#387	C₂²	semidirect
154. C₅₃×#387	C₂²	semidirect
155. C₅₃×#387	C₂²	semidirect
156. C₅₃×#387	C₂²	semidirect
157. C₅₃×#387	C₂²	semidirect
158. C₅₃×#387	C₂²	semidirect
167. C₅₃×#386	C₂²	semidirect
168. C₅₃×#386	C₂²	semidirect
169. C₅₃×#386	C₂²	semidirect
170. C₅₃×#386	C₂²	semidirect
171. C₅₃×#386	C₂²	semidirect
173. C₅₃×#385	C₂²	semidirect
174. C₅₃×#385	C₂²	semidirect
175. C₅₃×#385	C₂²	semidirect
176. C₅₃×#385	C₂²	semidirect
177. C₅₃×#382	C₂²	semidirect
180. C₅₃×#380	C₂²	semidirect
181. C₅₃×#380	C₂²	semidirect
185. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
187. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
188. C₅₃×#376	C₂²	semidirect
243. C₄×D₄×C₅₃	D₄	semidirect
729. #36745	C₅₃	direct (N × H)
805. C₂×#542	C₂×C₅₃	semidirect
806. C₂×#538	C₂×C₅₃	semidirect
807. #2854	C₂×C₅₃	semidirect
808. #2850	C₂×C₅₃	semidirect
809. #2723	C₂×C₅₃	semidirect
810. #2716	C₂×C₅₃	semidirect
811. #2715	C₂×C₅₃	semidirect
812. #2712	C₂×C₅₃	semidirect
813. #2700	C₂×C₅₃	semidirect
814. #2698	C₂×C₅₃	semidirect
815. #2696	C₂×C₅₃	semidirect
816. #2691	C₂×C₅₃	semidirect
817. #2688	C₂×C₅₃	semidirect
818. #2686	C₂×C₅₃	semidirect
819. #2685	C₂×C₅₃	semidirect
820. #2684	C₂×C₅₃	semidirect
821. #2676	C₂×C₅₃	semidirect
822. #2674	C₂×C₅₃	semidirect
823. #2670	C₂×C₅₃	semidirect
824. #2668	C₂×C₅₃	semidirect
825. #2663	C₂×C₅₃	semidirect
826. #2661	C₂×C₅₃	semidirect
827. #2610	C₂×C₅₃	semidirect
828. #2604	C₂×C₅₃	semidirect
829. #2602	C₂×C₅₃	semidirect
830. #2601	C₂×C₅₃	semidirect
831. #2592	C₂×C₅₃	semidirect
832. #2561	C₂×C₅₃	semidirect
833. #2415	C₂×C₅₃	semidirect
834. #2411	C₂×C₅₃	semidirect
835. #2290	C₂×C₅₃	semidirect
851. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
855. C₂×#126	C₂²×C₅₃	semidirect
861. C₂×#124	C₂²×C₅₃	semidirect
865. C₂×#123	C₂²×C₅₃	semidirect
868. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
869. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
870. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
879. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
883. C₂×#117	C₂²×C₅₃	semidirect
885. C₂²×C₄²	C₂²×C₅₃	semidirect
886. #400	C₂²×C₅₃	semidirect
887. #400	C₂²×C₅₃	semidirect
890. #398	C₂²×C₅₃	semidirect
891. #398	C₂²×C₅₃	semidirect
898. #397	C₂²×C₅₃	semidirect
899. #397	C₂²×C₅₃	semidirect
900. #397	C₂²×C₅₃	semidirect
901. #397	C₂²×C₅₃	semidirect
905. #396	C₂²×C₅₃	semidirect
906. #395	C₂²×C₅₃	semidirect
907. #395	C₂²×C₅₃	semidirect
908. #395	C₂²×C₅₃	semidirect
921. #394	C₂²×C₅₃	semidirect
927. #393	C₂²×C₅₃	semidirect
928. #393	C₂²×C₅₃	semidirect
933. #392	C₂²×C₅₃	semidirect
934. #391	C₂²×C₅₃	semidirect
935. #391	C₂²×C₅₃	semidirect
936. #391	C₂²×C₅₃	semidirect
937. #391	C₂²×C₅₃	semidirect
944. #390	C₂²×C₅₃	semidirect
945. #389	C₂²×C₅₃	semidirect
946. #389	C₂²×C₅₃	semidirect
947. #389	C₂²×C₅₃	semidirect
948. #389	C₂²×C₅₃	semidirect
949. #389	C₂²×C₅₃	semidirect
963. #388	C₂²×C₅₃	semidirect
964. #388	C₂²×C₅₃	semidirect
965. #388	C₂²×C₅₃	semidirect
966. #388	C₂²×C₅₃	semidirect
967. #388	C₂²×C₅₃	semidirect
968. #388	C₂²×C₅₃	semidirect
969. #388	C₂²×C₅₃	semidirect
970. #387	C₂²×C₅₃	semidirect
971. #387	C₂²×C₅₃	semidirect
972. #387	C₂²×C₅₃	semidirect
973. #387	C₂²×C₅₃	semidirect
974. #387	C₂²×C₅₃	semidirect
975. #387	C₂²×C₅₃	semidirect
984. #386	C₂²×C₅₃	semidirect
985. #386	C₂²×C₅₃	semidirect
986. #386	C₂²×C₅₃	semidirect
987. #386	C₂²×C₅₃	semidirect
988. #386	C₂²×C₅₃	semidirect
990. #385	C₂²×C₅₃	semidirect
991. #385	C₂²×C₅₃	semidirect
992. #385	C₂²×C₅₃	semidirect
993. #385	C₂²×C₅₃	semidirect
994. #382	C₂²×C₅₃	semidirect
997. #380	C₂²×C₅₃	semidirect
998. #380	C₂²×C₅₃	semidirect
1002. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
1004. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
1005. #376	C₂²×C₅₃	semidirect
1006. C₅₃	#36745	direct (N × H)
1061. C₄×D₄	D₄×C₅₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅₃×#542	2
C₂×C₅₃×#538	2
C₅₃×#2854	2
C₅₃×#2850	2
C₅₃×#2723	2
C₅₃×#2716	2
C₅₃×#2715	2
C₅₃×#2712	2
C₅₃×#2700	2
C₅₃×#2698	2
C₅₃×#2696	2
C₅₃×#2691	2
C₅₃×#2688	2
C₅₃×#2686	2
C₅₃×#2685	2
C₅₃×#2684	2
C₅₃×#2676	2
C₅₃×#2674	2
C₅₃×#2670	2
C₅₃×#2668	2
C₅₃×#2663	2
C₅₃×#2661	2
C₅₃×#2610	2
C₅₃×#2604	2
C₅₃×#2602	2
C₅₃×#2601	2
C₅₃×#2592	2
C₅₃×#2561	2
C₅₃×#2415	2
C₅₃×#2411	2
C₅₃×#2290	2
#36745	53

Subgroups — C53×#36745 #27244257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36745 #27244257