Subgroups — C₅₃×#36858 #27244370

Order 13568.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2849	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2797	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2781	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2780	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2763	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2757	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2738	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2735	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2729	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2715	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2706	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2700	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2696	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×#2674	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2670	C₂	1	1	yes	maximal, characteristic
19	C₅₃×#2638	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2636	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2575	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2574	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2560	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#2553	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#2461	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#2457	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#2452	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2447	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#2337	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#2334	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×#120×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
51	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#399	C₂²	1	1	yes	characteristic
56	C₅₃×#399	C₂²	1	1	yes	characteristic
57	C₅₃×#399	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#397	C₂²	1	1	yes	characteristic
63	C₅₃×#397	C₂²	1	1	yes	characteristic
64	C₅₃×#397	C₂²	1	1	yes	characteristic
65	C₅₃×#397	C₂²	1	1	yes	characteristic
66	C₅₃×#397	C₂²	1	1	yes	characteristic
67	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#396	C₂²	1	1	yes	characteristic
73	C₅₃×#396	C₂²	1	1	yes	characteristic
74	C₅₃×#396	C₂²	1	1	yes	characteristic
75	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#394	C₂²	1	1	yes	characteristic
83	C₅₃×#394	C₂²	1	1	yes	characteristic
84	C₅₃×#394	C₂²	1	1	yes	characteristic
85	C₅₃×#394	C₂²	1	1	yes	characteristic
86	C₅₃×#394	C₂²	1	1	yes	characteristic
87	C₅₃×#394	C₂²	1	1	yes	characteristic
88	C₅₃×#394	C₂²	1	1	yes	characteristic
89	C₅₃×#394	C₂²	1	1	yes	characteristic
90	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#393	C₂²	1	1	yes	characteristic
92	C₅₃×#393	C₂²	1	1	yes	characteristic
93	C₅₃×#393	C₂²	1	1	yes	characteristic
94	C₅₃×#393	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#393	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#392	C₂²	1	1	yes	characteristic
97	C₅₃×#392	C₂²	1	1	yes	characteristic
98	C₅₃×#392	C₂²	1	1	yes	characteristic
99	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#390	C₂²	1	1	yes	characteristic
104	C₅₃×#390	C₂²	1	1	yes	characteristic
105	C₅₃×#390	C₂²	1	1	yes	characteristic
106	C₅₃×#390	C₂²	1	1	yes	characteristic
107	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#388	C₂²	1	1	yes	characteristic
113	C₅₃×#388	C₂²	1	1	yes	characteristic
114	C₅₃×#388	C₂²	1	1	yes	characteristic
115	C₅₃×#388	C₂²	1	1	yes	characteristic
116	C₅₃×#388	C₂²	1	1	yes	characteristic
117	C₅₃×#388	C₂²	1	1	yes	characteristic
118	C₅₃×#388	C₂²	1	1	yes	characteristic
119	C₅₃×#388	C₂²	1	1	yes	characteristic
120	C₅₃×#388	C₂²	1	1	yes	characteristic
121	C₅₃×#388	C₂²	1	1	yes	characteristic
122	C₅₃×#388	C₂²	1	1	yes	characteristic
123	C₅₃×#388	C₂²	1	1	yes	characteristic
124	C₅₃×#388	C₂²	1	1	yes	characteristic
125	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
139	C₅₃×#386	C₂²	1	1	yes	characteristic
140	C₅₃×#386	C₂²	1	1	yes	characteristic
141	C₅₃×#386	C₂²	1	1	yes	characteristic
142	C₅₃×#386	C₂²	1	1	yes	characteristic
143	C₅₃×#386	C₂²	1	1	yes	characteristic
144	C₅₃×#386	C₂²	1	1	yes	characteristic
145	C₅₃×#386	C₂²	1	1	yes	characteristic
146	C₅₃×#386	C₂²	1	1	yes	characteristic
147	C₅₃×#386	C₂²	1	1	yes	characteristic
148	C₅₃×#386	C₂²	1	1	yes	characteristic
149	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#385	C₂²	1	1	yes	characteristic
151	C₅₃×#385	C₂²	1	1	yes	characteristic
152	C₅₃×#385	C₂²	1	1	yes	characteristic
153	C₅₃×#385	C₂²	1	1	yes	characteristic
154	C₅₃×#385	C₂²	1	1	yes	characteristic
155	C₅₃×#385	C₂²	1	1	yes	characteristic
156	C₅₃×#385	C₂²	1	1	yes	characteristic
157	C₅₃×#385	C₂²	1	1	yes	characteristic
158	C₅₃×#385	C₂²	1	1	yes	characteristic
159	C₅₃×#385	C₂²	1	1	yes	characteristic
160	C₅₃×#385	C₂²	1	1	yes	characteristic
161	C₅₃×#385	C₂²	1	1	yes	characteristic
162	C₅₃×#385	C₂²	1	1	yes	characteristic
163	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
164	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
165	C₅₃×#383	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
168	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
169	C₅₃×#381	C₂²	1	1	yes	characteristic
170	C₅₃×#381	C₂²	1	1	yes	characteristic
171	C₅₃×#381	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#380	C₂²	1	1	yes	characteristic
173	C₅₃×#380	C₂²	1	1	yes	characteristic
174	C₅₃×#380	C₂²	1	1	yes	characteristic
175	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#379	C₂²	1	1	yes	characteristic
177	C₅₃×#379	C₂²	1	1	yes	characteristic
178	C₅₃×#379	C₂²	1	1	yes	characteristic
179	C₅₃×#379	C₂²	1	1	yes	characteristic
180	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
181	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
184	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
185	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
188	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
189	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
190	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
191	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
192	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
193	C₂²×D₄×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	C₂³×C₄×C₅₃	—	4	2	no	—
199	C₂³×C₄×C₅₃	—	4	2	no	—
200	C₂³×C₄×C₅₃	—	4	2	no	—
201	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
205	C₂³×C₄×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	C₄⋊Q₈×C₅₃	—	4	2	no	—
210	#126×C₅₃	—	2	4	no	—
211	#126×C₅₃	—	4	2	no	—
212	#124×C₅₃	—	2	4	no	—
213	#124×C₅₃	—	4	2	no	—
214	#124×C₅₃	—	4	2	no	—
215	#123×C₅₃	—	4	2	no	—
216	#123×C₅₃	—	4	2	no	—
217	#123×C₅₃	—	4	2	no	—
218	C₂²⋊Q₈×C₅₃	—	4	2	no	—
219	C₂²⋊Q₈×C₅₃	—	4	2	no	—
220	C₂²⋊Q₈×C₅₃	—	4	2	no	—
221	C₂²⋊Q₈×C₅₃	—	4	2	no	—
222	#120×C₅₃	—	2	4	no	—
223	#120×C₅₃	—	4	2	no	—
224	C₄×D₄×C₅₃	—	4	2	no	—
225	C₄×D₄×C₅₃	—	4	2	no	—
226	C₄×D₄×C₅₃	—	4	2	no	—
227	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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×C₄²×C₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
312	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
313	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
314	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
315	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
316	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
317	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
318	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
319	#95×C₅₃	C₂³	1	1	yes	characteristic
320	#95×C₅₃	C₂³	1	1	yes	characteristic
321	#95×C₅₃	C₂³	1	1	yes	characteristic
322	#95×C₅₃	C₂³	1	1	yes	characteristic
323	#95×C₅₃	C₂³	1	1	yes	characteristic
324	#95×C₅₃	C₂³	1	1	yes	characteristic
325	#95×C₅₃	C₂³	1	1	yes	characteristic
326	#95×C₅₃	C₂³	1	1	yes	characteristic
327	#95×C₅₃	C₂³	1	1	yes	characteristic
328	#95×C₅₃	C₂³	1	1	yes	characteristic
329	#95×C₅₃	C₂³	1	1	yes	characteristic
330	#95×C₅₃	C₂³	1	1	yes	characteristic
331	#95×C₅₃	C₂³	1	1	yes	characteristic
332	#95×C₅₃	C₂³	1	1	yes	characteristic
333	#95×C₅₃	C₂³	1	1	yes	characteristic
334	#95×C₅₃	C₂³	1	1	yes	characteristic
335	#95×C₅₃	C₂³	1	1	yes	characteristic
336	#95×C₅₃	C₂³	1	1	yes	characteristic
337	#95×C₅₃	C₂³	1	1	yes	characteristic
338	#95×C₅₃	C₂³	1	1	yes	characteristic
339	#95×C₅₃	C₂³	1	1	yes	characteristic
340	#95×C₅₃	C₂³	1	1	yes	characteristic
341	#95×C₅₃	C₂³	1	1	yes	characteristic
342	#95×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	C₂⁴×C₅₃	—	2	2	no	—
364	C₂⁴×C₅₃	—	2	2	no	—
365	C₂⁴×C₅₃	—	2	2	no	—
366	C₂⁴×C₅₃	—	4	1	no	—
367	C₂⁴×C₅₃	—	4	1	no	—
368	C₂⁴×C₅₃	—	4	1	no	—
369	C₂⁴×C₅₃	—	4	1	no	—
370	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂×Q₈×C₅₃	—	2	2	no	—
376	C₂×Q₈×C₅₃	—	2	2	no	—
377	C₂×Q₈×C₅₃	—	4	1	no	—
378	C₂×Q₈×C₅₃	—	4	1	no	—
379	C₂×Q₈×C₅₃	—	4	1	no	—
380	C₂×Q₈×C₅₃	—	4	1	no	—
381	C₂×Q₈×C₅₃	—	4	1	no	—
382	C₂×Q₈×C₅₃	—	4	1	no	—
383	C₂×Q₈×C₅₃	—	4	1	no	—
384	C₂×D₄×C₅₃	—	2	2	no	—
385	C₂×D₄×C₅₃	—	2	2	no	—
386	C₂×D₄×C₅₃	—	2	2	no	—
387	C₂×D₄×C₅₃	—	2	2	no	—
388	C₂×D₄×C₅₃	—	2	2	no	—
389	C₂×D₄×C₅₃	—	2	2	no	—
390	C₂×D₄×C₅₃	—	2	2	no	—
391	C₂×D₄×C₅₃	—	2	2	no	—
392	C₂×D₄×C₅₃	—	4	1	no	—
393	C₂×D₄×C₅₃	—	4	1	no	—
394	C₂×D₄×C₅₃	—	4	1	no	—
395	C₂×D₄×C₅₃	—	4	1	no	—
396	C₂×D₄×C₅₃	—	4	1	no	—
397	C₂×D₄×C₅₃	—	4	1	no	—
398	C₂×D₄×C₅₃	—	4	1	no	—
399	C₂×D₄×C₅₃	—	4	1	no	—
400	C₂×D₄×C₅₃	—	4	1	no	—
401	C₂×D₄×C₅₃	—	4	1	no	—
402	C₂×D₄×C₅₃	—	4	1	no	—
403	C₂×D₄×C₅₃	—	4	1	no	—
404	C₂×D₄×C₅₃	—	4	1	no	—
405	C₂²×C₄×C₅₃	—	2	2	no	—
406	C₂²×C₄×C₅₃	—	2	2	no	—
407	C₂²×C₄×C₅₃	—	2	2	no	—
408	C₂²×C₄×C₅₃	—	2	2	no	—
409	C₂²×C₄×C₅₃	—	2	2	no	—
410	C₂²×C₄×C₅₃	—	2	2	no	—
411	C₂²×C₄×C₅₃	—	2	2	no	—
412	C₂²×C₄×C₅₃	—	2	2	no	—
413	C₂²×C₄×C₅₃	—	2	2	no	—
414	C₂²×C₄×C₅₃	—	4	1	no	—
415	C₂²×C₄×C₅₃	—	4	1	no	—
416	C₂²×C₄×C₅₃	—	4	1	no	—
417	C₂²×C₄×C₅₃	—	4	1	no	—
418	C₂²×C₄×C₅₃	—	4	1	no	—
419	C₂²×C₄×C₅₃	—	4	1	no	—
420	C₂²×C₄×C₅₃	—	4	1	no	—
421	C₂²×C₄×C₅₃	—	4	1	no	—
422	C₂²×C₄×C₅₃	—	4	1	no	—
423	C₂²×C₄×C₅₃	—	4	1	no	—
424	C₂²×C₄×C₅₃	—	4	1	no	—
425	C₂²×C₄×C₅₃	—	4	1	no	—
426	C₂²×C₄×C₅₃	—	4	1	no	—
427	C₂²×C₄×C₅₃	—	4	1	no	—
428	C₂²×C₄×C₅₃	—	4	1	no	—
429	C₂²×C₄×C₅₃	—	4	16	no	—
430	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
432	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
433	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
434	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
436	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
437	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
438	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
439	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
440	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
441	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
442	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
443	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
444	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
445	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
446	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
447	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
448	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
449	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
451	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
452	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
453	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
454	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
455	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
456	C₄⋊C₄×C₅₃	—	2	2	no	—
457	C₄⋊C₄×C₅₃	—	2	2	no	—
458	C₄⋊C₄×C₅₃	—	2	2	no	—
459	C₄⋊C₄×C₅₃	—	2	2	no	—
460	C₄⋊C₄×C₅₃	—	2	2	no	—
461	C₄⋊C₄×C₅₃	—	2	2	no	—
462	C₄⋊C₄×C₅₃	—	2	2	no	—
463	C₄⋊C₄×C₅₃	—	2	2	no	—
464	C₄⋊C₄×C₅₃	—	2	2	no	—
465	C₄⋊C₄×C₅₃	—	4	1	no	—
466	C₄⋊C₄×C₅₃	—	4	1	no	—
467	C₄⋊C₄×C₅₃	—	4	1	no	—
468	C₄⋊C₄×C₅₃	—	4	1	no	—
469	C₄⋊C₄×C₅₃	—	4	1	no	—
470	C₄⋊C₄×C₅₃	—	4	1	no	—
471	C₄⋊C₄×C₅₃	—	4	1	no	—
472	C₄⋊C₄×C₅₃	—	4	1	no	—
473	C₄⋊C₄×C₅₃	—	4	1	no	—
474	C₄⋊C₄×C₅₃	—	4	1	no	—
475	C₄⋊C₄×C₅₃	—	4	1	no	—
476	C₄⋊C₄×C₅₃	—	4	1	no	—
477	C₄⋊C₄×C₅₃	—	4	1	no	—
478	C₄⋊C₄×C₅₃	—	4	1	no	—
479	C₄⋊C₄×C₅₃	—	4	1	no	—
480	C₄⋊C₄×C₅₃	—	4	1	no	—
481	C₄⋊C₄×C₅₃	—	4	1	no	—
482	C₄⋊C₄×C₅₃	—	4	1	no	—
483	C₄⋊C₄×C₅₃	—	4	1	no	—
484	C₄⋊C₄×C₅₃	—	4	1	no	—
485	C₄⋊C₄×C₅₃	—	4	1	no	—
486	C₄⋊C₄×C₅₃	—	4	1	no	—
487	C₄⋊C₄×C₅₃	—	4	1	no	—
488	C₂²⋊C₄×C₅₃	—	2	2	no	—
489	C₂²⋊C₄×C₅₃	—	2	2	no	—
490	C₂²⋊C₄×C₅₃	—	2	2	no	—
491	C₂²⋊C₄×C₅₃	—	2	2	no	—
492	C₂²⋊C₄×C₅₃	—	2	2	no	—
493	C₂²⋊C₄×C₅₃	—	2	2	no	—
494	C₂²⋊C₄×C₅₃	—	2	2	no	—
495	C₂²⋊C₄×C₅₃	—	2	2	no	—
496	C₂²⋊C₄×C₅₃	—	2	2	no	—
497	C₂²⋊C₄×C₅₃	—	2	2	no	—
498	C₂²⋊C₄×C₅₃	—	2	2	no	—
499	C₂²⋊C₄×C₅₃	—	2	2	no	—
500	C₂²⋊C₄×C₅₃	—	2	2	no	—
501	C₂²⋊C₄×C₅₃	—	2	2	no	—
502	C₂²⋊C₄×C₅₃	—	2	2	no	—
503	C₂²⋊C₄×C₅₃	—	2	2	no	—
504	C₂²⋊C₄×C₅₃	—	4	1	no	—
505	C₂²⋊C₄×C₅₃	—	4	1	no	—
506	C₂²⋊C₄×C₅₃	—	4	1	no	—
507	C₂²⋊C₄×C₅₃	—	4	1	no	—
508	C₂²⋊C₄×C₅₃	—	4	1	no	—
509	C₂²⋊C₄×C₅₃	—	4	1	no	—
510	C₂²⋊C₄×C₅₃	—	4	1	no	—
511	C₂²⋊C₄×C₅₃	—	4	1	no	—
512	C₂²⋊C₄×C₅₃	—	4	1	no	—
513	C₂²⋊C₄×C₅₃	—	4	1	no	—
514	C₂²⋊C₄×C₅₃	—	4	1	no	—
515	C₂²⋊C₄×C₅₃	—	4	1	no	—
516	C₂²⋊C₄×C₅₃	—	4	1	no	—
517	C₂²⋊C₄×C₅₃	—	4	1	no	—
518	C₂²⋊C₄×C₅₃	—	4	1	no	—
519	C₂²⋊C₄×C₅₃	—	4	1	no	—
520	C₂²⋊C₄×C₅₃	—	4	1	no	—
521	C₂²⋊C₄×C₅₃	—	4	1	no	—
522	C₂²⋊C₄×C₅₃	—	4	1	no	—
523	C₂²⋊C₄×C₅₃	—	4	1	no	—
524	C₂²⋊C₄×C₅₃	—	4	1	no	—
525	C₂²⋊C₄×C₅₃	—	4	1	no	—
526	C₂²⋊C₄×C₅₃	—	4	1	no	—
527	C₂²⋊C₄×C₅₃	—	4	1	no	—
528	C₂²⋊C₄×C₅₃	—	4	1	no	—
529	C₂²⋊C₄×C₅₃	—	4	1	no	—
530	C₂²⋊C₄×C₅₃	—	4	1	no	—
531	C₂²⋊C₄×C₅₃	—	4	1	no	—
532	C₂²⋊C₄×C₅₃	—	4	1	no	—
533	C₂²⋊C₄×C₅₃	—	4	1	no	—
534	C₂²⋊C₄×C₅₃	—	4	1	no	—
535	C₂²⋊C₄×C₅₃	—	4	1	no	—
536	C₂²⋊C₄×C₅₃	—	4	1	no	—
537	C₂²⋊C₄×C₅₃	#41	1	4	yes	—
538	C₄²×C₅₃	—	2	2	no	—
539	C₄²×C₅₃	—	2	2	no	—
540	C₄²×C₅₃	—	2	2	no	—
541	C₄²×C₅₃	—	4	1	no	—
542	C₄²×C₅₃	—	4	1	no	—
543	C₄²×C₅₃	—	4	1	no	—
544	C₄²×C₅₃	—	4	1	no	—
545	C₄²×C₅₃	—	4	1	no	—
546	C₄²×C₅₃	—	4	1	no	—
547	C₄²×C₅₃	—	4	1	no	—
548	C₂³×C₅₃	—	2	1	no	—
549	C₂³×C₅₃	—	2	1	no	—
550	C₂³×C₅₃	—	2	1	no	—
551	C₂³×C₅₃	—	2	1	no	—
552	C₂³×C₅₃	—	2	1	no	—
553	C₂³×C₅₃	—	2	1	no	—
554	C₂³×C₅₃	—	2	1	no	—
555	C₂³×C₅₃	—	2	1	no	—
556	C₂³×C₅₃	—	2	1	no	—
557	C₂³×C₅₃	—	2	1	no	—
558	C₂³×C₅₃	—	2	1	no	—
559	C₂³×C₅₃	—	2	1	no	—
560	C₂³×C₅₃	—	2	1	no	—
561	C₂³×C₅₃	—	2	1	no	—
562	C₂³×C₅₃	—	2	1	no	—
563	C₂³×C₅₃	—	2	1	no	—
564	C₂³×C₅₃	—	2	1	no	—
565	C₂³×C₅₃	—	2	1	no	—
566	C₂³×C₅₃	—	2	1	no	—
567	C₂³×C₅₃	—	2	1	no	—
568	C₂³×C₅₃	—	2	1	no	—
569	C₂³×C₅₃	—	2	1	no	—
570	C₂³×C₅₃	—	2	1	no	—
571	C₂³×C₅₃	—	2	1	no	—
572	C₂³×C₅₃	—	2	1	no	—
573	C₂³×C₅₃	—	2	1	no	—
574	C₂³×C₅₃	—	2	1	no	—
575	C₂³×C₅₃	—	2	1	no	—
576	C₂³×C₅₃	—	2	1	no	—
577	C₂³×C₅₃	—	2	1	no	—
578	C₂³×C₅₃	—	2	1	no	—
579	C₂³×C₅₃	—	2	1	no	—
580	C₂³×C₅₃	—	4	4	no	—
581	C₂³×C₅₃	—	4	4	no	—
582	C₂³×C₅₃	—	4	4	no	—
583	C₂³×C₅₃	—	4	4	no	—
584	C₂³×C₅₃	—	4	4	no	—
585	C₂³×C₅₃	—	4	4	no	—
586	C₂³×C₅₃	—	4	4	no	—
587	C₂³×C₅₃	C₂×#41	1	2	yes	—
588	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
589	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
590	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
591	Q₈×C₅₃	—	8	2	no	—
592	Q₈×C₅₃	—	8	2	no	—
593	Q₈×C₅₃	—	8	2	no	—
594	D₄×C₅₃	—	4	4	no	—
595	D₄×C₅₃	—	4	4	no	—
596	D₄×C₅₃	—	4	4	no	—
597	D₄×C₅₃	—	8	2	no	—
598	D₄×C₅₃	—	8	2	no	—
599	D₄×C₅₃	—	8	2	no	—
600	D₄×C₅₃	—	8	2	no	—
601	C₂×C₄×C₅₃	—	2	1	no	—
602	C₂×C₄×C₅₃	—	2	1	no	—
603	C₂×C₄×C₅₃	—	2	1	no	—
604	C₂×C₄×C₅₃	—	2	1	no	—
605	C₂×C₄×C₅₃	—	2	1	no	—
606	C₂×C₄×C₅₃	—	2	1	no	—
607	C₂×C₄×C₅₃	—	2	1	no	—
608	C₂×C₄×C₅₃	—	2	1	no	—
609	C₂×C₄×C₅₃	—	2	1	no	—
610	C₂×C₄×C₅₃	—	2	1	no	—
611	C₂×C₄×C₅₃	—	2	1	no	—
612	C₂×C₄×C₅₃	—	2	1	no	—
613	C₂×C₄×C₅₃	—	2	1	no	—
614	C₂×C₄×C₅₃	—	2	1	no	—
615	C₂×C₄×C₅₃	—	2	1	no	—
616	C₂×C₄×C₅₃	—	2	1	no	—
617	C₂×C₄×C₅₃	—	2	1	no	—
618	C₂×C₄×C₅₃	—	2	1	no	—
619	C₂×C₄×C₅₃	—	2	1	no	—
620	C₂×C₄×C₅₃	—	2	1	no	—
621	C₂×C₄×C₅₃	—	2	1	no	—
622	C₂×C₄×C₅₃	—	2	1	no	—
623	C₂×C₄×C₅₃	—	2	1	no	—
624	C₂×C₄×C₅₃	—	2	1	no	—
625	C₂×C₄×C₅₃	—	2	1	no	—
626	C₂×C₄×C₅₃	—	2	1	no	—
627	C₂×C₄×C₅₃	—	2	1	no	—
628	C₂×C₄×C₅₃	—	2	1	no	—
629	C₂×C₄×C₅₃	—	2	1	no	—
630	C₂×C₄×C₅₃	—	2	1	no	—
631	C₂×C₄×C₅₃	—	2	1	no	—
632	C₂×C₄×C₅₃	—	2	1	no	—
633	C₂×C₄×C₅₃	—	2	1	no	—
634	C₂×C₄×C₅₃	—	2	1	no	—
635	C₂×C₄×C₅₃	—	2	1	no	—
636	C₂×C₄×C₅₃	—	2	1	no	—
637	C₂×C₄×C₅₃	—	2	1	no	—
638	C₂×C₄×C₅₃	—	2	1	no	—
639	C₂×C₄×C₅₃	—	2	1	no	—
640	C₂×C₄×C₅₃	—	2	1	no	—
641	C₂×C₄×C₅₃	—	2	1	no	—
642	C₂×C₄×C₅₃	—	2	1	no	—
643	C₂×C₄×C₅₃	—	2	1	no	—
644	C₂×C₄×C₅₃	—	2	1	no	—
645	C₂×C₄×C₅₃	—	2	1	no	—
646	C₂×C₄×C₅₃	—	2	1	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	—	4	4	no	—
676	C₂×C₄×C₅₃	—	4	4	no	—
677	C₂×C₄×C₅₃	—	4	4	no	—
678	C₂×C₄×C₅₃	—	4	4	no	—
679	C₂×C₄×C₅₃	—	4	4	no	—
680	C₂×C₄×C₅₃	—	4	4	no	—
681	C₂×C₄×C₅₃	—	8	2	no	—
682	C₂×C₄×C₅₃	—	8	2	no	—
683	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
684	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
685	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
686	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
687	#36858	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
688	C₂²×C₅₃	—	2	2	no	—
689	C₂²×C₅₃	—	2	2	no	—
690	C₂²×C₅₃	—	2	2	no	—
691	C₂²×C₅₃	—	2	2	no	—
692	C₂²×C₅₃	—	2	2	no	—
693	C₂²×C₅₃	—	2	2	no	—
694	C₂²×C₅₃	—	2	2	no	—
695	C₂²×C₅₃	—	2	2	no	—
696	C₂²×C₅₃	—	2	2	no	—
697	C₂²×C₅₃	—	4	16	no	—
698	C₂²×C₅₃	—	4	1	no	—
699	C₂²×C₅₃	—	4	1	no	—
700	C₂²×C₅₃	—	4	1	no	—
701	C₂²×C₅₃	—	4	1	no	—
702	C₂²×C₅₃	—	4	1	no	—
703	C₂²×C₅₃	—	4	1	no	—
704	C₂²×C₅₃	—	4	1	no	—
705	C₂²×C₅₃	—	4	1	no	—
706	C₂²×C₅₃	—	4	1	no	—
707	C₂²×C₅₃	—	4	1	no	—
708	C₂²×C₅₃	—	4	1	no	—
709	C₂²×C₅₃	—	4	1	no	—
710	C₂²×C₅₃	—	4	1	no	—
711	C₂²×C₅₃	—	4	1	no	—
712	C₂²×C₅₃	—	4	1	no	—
713	C₂²×C₅₃	—	4	1	no	—
714	C₂²×C₅₃	—	4	1	no	—
715	C₂²×C₅₃	—	4	1	no	—
716	C₂²×C₅₃	—	4	1	no	—
717	C₂²×C₅₃	—	4	1	no	—
718	C₂²×C₅₃	—	4	1	no	—
719	C₂²×C₅₃	—	4	1	no	—
720	C₂²×C₅₃	—	4	1	no	—
721	C₂²×C₅₃	—	4	1	no	—
722	C₂²×C₅₃	—	4	1	no	—
723	C₂²×C₅₃	—	4	1	no	—
724	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
725	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
726	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
727	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
728	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
729	C₂²×C₅₃	#585	1	1	yes	characteristic
730	C₂²×C₅₃	#585	1	1	yes	characteristic
731	C₄×C₅₃	—	2	2	no	—
732	C₄×C₅₃	—	2	2	no	—
733	C₄×C₅₃	—	2	2	no	—
734	C₄×C₅₃	—	2	2	no	—
735	C₄×C₅₃	—	4	1	no	—
736	C₄×C₅₃	—	4	1	no	—
737	C₄×C₅₃	—	4	1	no	—
738	C₄×C₅₃	—	4	1	no	—
739	C₄×C₅₃	—	4	1	no	—
740	C₄×C₅₃	—	4	1	no	—
741	C₄×C₅₃	—	4	1	no	—
742	C₄×C₅₃	—	4	1	no	—
743	C₄×C₅₃	—	4	1	no	—
744	C₄×C₅₃	—	4	1	no	—
745	C₄×C₅₃	—	4	1	no	—
746	C₄×C₅₃	—	4	1	no	—
747	C₄×C₅₃	—	4	1	no	—
748	C₄×C₅₃	—	4	1	no	—
749	C₄×C₅₃	—	4	1	no	—
750	C₄×C₅₃	—	4	1	no	—
751	C₄×C₅₃	—	4	1	no	—
752	C₄×C₅₃	—	4	1	no	—
753	C₄×C₅₃	—	4	1	no	—
754	C₄×C₅₃	—	4	1	no	—
755	C₄×C₅₃	—	4	1	no	—
756	C₄×C₅₃	—	4	1	no	—
757	#2849	C₂×C₅₃	1	1	yes	characteristic, complemented
758	#2848	C₂×C₅₃	1	1	yes	characteristic, complemented
759	#2797	C₂×C₅₃	1	1	yes	characteristic, complemented
760	#2781	C₂×C₅₃	1	1	yes	characteristic, complemented
761	#2780	C₂×C₅₃	1	1	yes	characteristic, complemented
762	#2763	C₂×C₅₃	1	1	yes	characteristic, complemented
763	#2757	C₂×C₅₃	1	1	yes	characteristic, complemented
764	#2738	C₂×C₅₃	1	1	yes	characteristic, complemented
765	#2735	C₂×C₅₃	1	1	yes	characteristic, complemented
766	#2729	C₂×C₅₃	1	1	yes	characteristic, complemented
767	#2715	C₂×C₅₃	1	1	yes	characteristic, complemented
768	#2706	C₂×C₅₃	1	1	yes	characteristic, complemented
769	#2700	C₂×C₅₃	1	1	yes	characteristic, complemented
770	#2696	C₂×C₅₃	1	1	yes	characteristic, complemented
771	#2685	C₂×C₅₃	1	1	yes	characteristic, complemented
772	#2684	C₂×C₅₃	1	1	yes	characteristic, complemented
773	#2674	C₂×C₅₃	1	1	yes	characteristic, complemented
774	#2670	C₂×C₅₃	1	1	yes	characteristic
775	#2638	C₂×C₅₃	1	1	yes	characteristic, complemented
776	#2636	C₂×C₅₃	1	1	yes	characteristic, complemented
777	#2575	C₂×C₅₃	1	1	yes	characteristic, complemented
778	#2574	C₂×C₅₃	1	1	yes	characteristic, complemented
779	#2560	C₂×C₅₃	1	1	yes	characteristic, complemented
780	#2553	C₂×C₅₃	1	1	yes	characteristic, complemented
781	#2461	C₂×C₅₃	1	1	yes	characteristic, complemented
782	#2457	C₂×C₅₃	1	1	yes	characteristic, complemented
783	#2452	C₂×C₅₃	1	1	yes	characteristic, complemented
784	#2447	C₂×C₅₃	1	1	yes	characteristic, complemented
785	#2337	C₂×C₅₃	1	1	yes	characteristic, complemented
786	#2334	C₂×C₅₃	1	1	yes	characteristic, complemented
787	C₄×#120	C₂×C₅₃	1	1	yes	characteristic, complemented
788	C₂×C₅₃	—	4	2	no	—
789	C₂×C₅₃	—	4	2	no	—
790	C₂×C₅₃	—	4	2	no	—
791	C₂×C₅₃	—	8	1	no	—
792	C₂×C₅₃	—	8	1	no	—
793	C₂×C₅₃	#3460	1	1	yes	characteristic
794	C₂×C₅₃	#3513	1	1	yes	characteristic
795	C₂×C₅₃	#3520	1	1	yes	characteristic
796	C₂×C₅₃	#3532	1	1	yes	characteristic
797	C₂×C₅₃	#3535	1	1	yes	characteristic
798	C₂×C₅₃	#3540	1	1	yes	characteristic
799	C₂×C₅₃	#3541	1	1	yes	characteristic
800	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
801	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
802	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
803	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic, complemented
804	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
805	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
806	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
807	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
808	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
809	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
810	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
811	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
812	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
813	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
814	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
815	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
816	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
817	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
818	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
819	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
820	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
821	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
822	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
823	#399	C₂²×C₅₃	1	1	yes	characteristic
824	#399	C₂²×C₅₃	1	1	yes	characteristic
825	#399	C₂²×C₅₃	1	1	yes	characteristic, complemented
826	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
827	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
828	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
829	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
830	#397	C₂²×C₅₃	1	1	yes	characteristic
831	#397	C₂²×C₅₃	1	1	yes	characteristic
832	#397	C₂²×C₅₃	1	1	yes	characteristic
833	#397	C₂²×C₅₃	1	1	yes	characteristic
834	#397	C₂²×C₅₃	1	1	yes	characteristic
835	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
836	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
837	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
838	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
839	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
840	#396	C₂²×C₅₃	1	1	yes	characteristic
841	#396	C₂²×C₅₃	1	1	yes	characteristic
842	#396	C₂²×C₅₃	1	1	yes	characteristic
843	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
844	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
845	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
846	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
847	#395	C₂²×C₅₃	1	1	yes	characteristic, complemented
848	#395	C₂²×C₅₃	1	1	yes	characteristic, complemented
849	#395	C₂²×C₅₃	1	1	yes	characteristic, complemented
850	#394	C₂²×C₅₃	1	1	yes	characteristic
851	#394	C₂²×C₅₃	1	1	yes	characteristic
852	#394	C₂²×C₅₃	1	1	yes	characteristic
853	#394	C₂²×C₅₃	1	1	yes	characteristic
854	#394	C₂²×C₅₃	1	1	yes	characteristic
855	#394	C₂²×C₅₃	1	1	yes	characteristic
856	#394	C₂²×C₅₃	1	1	yes	characteristic
857	#394	C₂²×C₅₃	1	1	yes	characteristic
858	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
859	#393	C₂²×C₅₃	1	1	yes	characteristic
860	#393	C₂²×C₅₃	1	1	yes	characteristic
861	#393	C₂²×C₅₃	1	1	yes	characteristic
862	#393	C₂²×C₅₃	1	1	yes	characteristic, complemented
863	#393	C₂²×C₅₃	1	1	yes	characteristic, complemented
864	#392	C₂²×C₅₃	1	1	yes	characteristic
865	#392	C₂²×C₅₃	1	1	yes	characteristic
866	#392	C₂²×C₅₃	1	1	yes	characteristic
867	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
868	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
869	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
870	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
871	#390	C₂²×C₅₃	1	1	yes	characteristic
872	#390	C₂²×C₅₃	1	1	yes	characteristic
873	#390	C₂²×C₅₃	1	1	yes	characteristic
874	#390	C₂²×C₅₃	1	1	yes	characteristic
875	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
876	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
877	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
878	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
879	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
880	#388	C₂²×C₅₃	1	1	yes	characteristic
881	#388	C₂²×C₅₃	1	1	yes	characteristic
882	#388	C₂²×C₅₃	1	1	yes	characteristic
883	#388	C₂²×C₅₃	1	1	yes	characteristic
884	#388	C₂²×C₅₃	1	1	yes	characteristic
885	#388	C₂²×C₅₃	1	1	yes	characteristic
886	#388	C₂²×C₅₃	1	1	yes	characteristic
887	#388	C₂²×C₅₃	1	1	yes	characteristic
888	#388	C₂²×C₅₃	1	1	yes	characteristic
889	#388	C₂²×C₅₃	1	1	yes	characteristic
890	#388	C₂²×C₅₃	1	1	yes	characteristic
891	#388	C₂²×C₅₃	1	1	yes	characteristic
892	#388	C₂²×C₅₃	1	1	yes	characteristic
893	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
894	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
895	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
896	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
897	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
898	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
899	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
900	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
901	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
902	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
903	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
904	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
905	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
906	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
907	#386	C₂²×C₅₃	1	1	yes	characteristic
908	#386	C₂²×C₅₃	1	1	yes	characteristic
909	#386	C₂²×C₅₃	1	1	yes	characteristic
910	#386	C₂²×C₅₃	1	1	yes	characteristic
911	#386	C₂²×C₅₃	1	1	yes	characteristic
912	#386	C₂²×C₅₃	1	1	yes	characteristic
913	#386	C₂²×C₅₃	1	1	yes	characteristic
914	#386	C₂²×C₅₃	1	1	yes	characteristic
915	#386	C₂²×C₅₃	1	1	yes	characteristic
916	#386	C₂²×C₅₃	1	1	yes	characteristic
917	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
918	#385	C₂²×C₅₃	1	1	yes	characteristic
919	#385	C₂²×C₅₃	1	1	yes	characteristic
920	#385	C₂²×C₅₃	1	1	yes	characteristic
921	#385	C₂²×C₅₃	1	1	yes	characteristic
922	#385	C₂²×C₅₃	1	1	yes	characteristic
923	#385	C₂²×C₅₃	1	1	yes	characteristic
924	#385	C₂²×C₅₃	1	1	yes	characteristic
925	#385	C₂²×C₅₃	1	1	yes	characteristic
926	#385	C₂²×C₅₃	1	1	yes	characteristic
927	#385	C₂²×C₅₃	1	1	yes	characteristic
928	#385	C₂²×C₅₃	1	1	yes	characteristic
929	#385	C₂²×C₅₃	1	1	yes	characteristic
930	#385	C₂²×C₅₃	1	1	yes	characteristic
931	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
932	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
933	#383	C₂²×C₅₃	1	1	yes	characteristic, complemented
934	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
935	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
936	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
937	#381	C₂²×C₅₃	1	1	yes	characteristic
938	#381	C₂²×C₅₃	1	1	yes	characteristic
939	#381	C₂²×C₅₃	1	1	yes	characteristic, complemented
940	#380	C₂²×C₅₃	1	1	yes	characteristic
941	#380	C₂²×C₅₃	1	1	yes	characteristic
942	#380	C₂²×C₅₃	1	1	yes	characteristic
943	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
944	#379	C₂²×C₅₃	1	1	yes	characteristic
945	#379	C₂²×C₅₃	1	1	yes	characteristic
946	#379	C₂²×C₅₃	1	1	yes	characteristic
947	#379	C₂²×C₅₃	1	1	yes	characteristic
948	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
949	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
950	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
951	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
952	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
953	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
954	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
955	C₅₃	#36858	1	1	yes	characteristic, direct product factor, Sylow
956	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
957	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
958	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
959	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
960	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
961	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
962	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
963	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
964	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
965	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
966	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
967	C₂³×C₄	—	4	2	no	—
968	C₂³×C₄	—	4	2	no	—
969	C₂³×C₄	—	4	2	no	—
970	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
971	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
972	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
973	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
974	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
975	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
976	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
977	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
978	C₄⋊Q₈	—	4	2	no	—
979	#126	—	2	4	no	—
980	#126	—	4	2	no	—
981	#124	—	2	4	no	—
982	#124	—	4	2	no	—
983	#124	—	4	2	no	—
984	#123	—	4	2	no	—
985	#123	—	4	2	no	—
986	#123	—	4	2	no	—
987	C₂²⋊Q₈	—	4	2	no	—
988	C₂²⋊Q₈	—	4	2	no	—
989	C₂²⋊Q₈	—	4	2	no	—
990	C₂²⋊Q₈	—	4	2	no	—
991	#120	—	2	4	no	—
992	#120	—	4	2	no	—
993	C₄×D₄	—	4	2	no	—
994	C₄×D₄	—	4	2	no	—
995	C₄×D₄	—	4	2	no	—
996	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
997	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
998	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
999	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1000	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1001	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1002	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1003	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1004	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1005	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1006	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1007	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1008	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1009	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1010	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1011	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1012	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1013	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1014	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1015	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1016	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1017	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1018	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1019	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1020	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1021	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1022	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1023	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1024	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1025	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1026	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1027	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1028	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1029	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1030	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1031	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1032	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1033	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1034	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1035	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1036	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1037	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1038	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1039	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1040	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1041	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1042	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1043	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1044	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1045	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1046	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1047	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1048	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1049	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1050	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1051	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1052	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1053	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1054	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1055	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1056	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1057	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1058	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1059	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1060	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1061	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1062	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1063	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1064	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1065	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1066	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1067	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1068	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1069	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1070	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1071	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1072	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1073	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1074	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1075	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1076	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1077	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1078	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1079	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1080	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1081	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1082	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1083	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1084	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1085	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1086	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1087	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1088	#95	C₂³×C₅₃	1	1	yes	characteristic
1089	#95	C₂³×C₅₃	1	1	yes	characteristic
1090	#95	C₂³×C₅₃	1	1	yes	characteristic
1091	#95	C₂³×C₅₃	1	1	yes	characteristic
1092	#95	C₂³×C₅₃	1	1	yes	characteristic
1093	#95	C₂³×C₅₃	1	1	yes	characteristic
1094	#95	C₂³×C₅₃	1	1	yes	characteristic
1095	#95	C₂³×C₅₃	1	1	yes	characteristic
1096	#95	C₂³×C₅₃	1	1	yes	characteristic
1097	#95	C₂³×C₅₃	1	1	yes	characteristic
1098	#95	C₂³×C₅₃	1	1	yes	characteristic
1099	#95	C₂³×C₅₃	1	1	yes	characteristic
1100	#95	C₂³×C₅₃	1	1	yes	characteristic
1101	#95	C₂³×C₅₃	1	1	yes	characteristic
1102	#95	C₂³×C₅₃	1	1	yes	characteristic
1103	#95	C₂³×C₅₃	1	1	yes	characteristic
1104	#95	C₂³×C₅₃	1	1	yes	characteristic
1105	#95	C₂³×C₅₃	1	1	yes	characteristic
1106	#95	C₂³×C₅₃	1	1	yes	characteristic
1107	#95	C₂³×C₅₃	1	1	yes	characteristic
1108	#95	C₂³×C₅₃	1	1	yes	characteristic
1109	#95	C₂³×C₅₃	1	1	yes	characteristic
1110	#95	C₂³×C₅₃	1	1	yes	characteristic
1111	#95	C₂³×C₅₃	1	1	yes	characteristic
1112	#95	C₂³×C₅₃	1	1	yes	characteristic
1113	#95	C₂³×C₅₃	1	1	yes	characteristic
1114	#95	C₂³×C₅₃	1	1	yes	characteristic
1115	#95	C₂³×C₅₃	1	1	yes	characteristic
1116	#95	C₂³×C₅₃	1	1	yes	characteristic
1117	#95	C₂³×C₅₃	1	1	yes	characteristic
1118	#95	C₂³×C₅₃	1	1	yes	characteristic
1119	#95	C₂³×C₅₃	1	1	yes	characteristic
1120	#95	C₂³×C₅₃	1	1	yes	characteristic
1121	#95	C₂³×C₅₃	1	1	yes	characteristic
1122	#95	C₂³×C₅₃	1	1	yes	characteristic
1123	#95	C₂³×C₅₃	1	1	yes	characteristic
1124	#95	C₂³×C₅₃	1	1	yes	characteristic
1125	#95	C₂³×C₅₃	1	1	yes	characteristic
1126	#95	C₂³×C₅₃	1	1	yes	characteristic
1127	#95	C₂³×C₅₃	1	1	yes	characteristic
1128	#95	C₂³×C₅₃	1	1	yes	characteristic
1129	#95	C₂³×C₅₃	1	1	yes	characteristic
1130	#95	C₂³×C₅₃	1	1	yes	characteristic
1131	#95	C₂³×C₅₃	1	1	yes	characteristic
1132	C₂⁴	—	2	2	no	—
1133	C₂⁴	—	2	2	no	—
1134	C₂⁴	—	2	2	no	—
1135	C₂⁴	—	4	1	no	—
1136	C₂⁴	—	4	1	no	—
1137	C₂⁴	—	4	1	no	—
1138	C₂⁴	—	4	1	no	—
1139	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1140	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1141	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1142	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1143	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1144	C₂×Q₈	—	2	2	no	—
1145	C₂×Q₈	—	2	2	no	—
1146	C₂×Q₈	—	4	1	no	—
1147	C₂×Q₈	—	4	1	no	—
1148	C₂×Q₈	—	4	1	no	—
1149	C₂×Q₈	—	4	1	no	—
1150	C₂×Q₈	—	4	1	no	—
1151	C₂×Q₈	—	4	1	no	—
1152	C₂×Q₈	—	4	1	no	—
1153	C₂×D₄	—	2	2	no	—
1154	C₂×D₄	—	2	2	no	—
1155	C₂×D₄	—	2	2	no	—
1156	C₂×D₄	—	2	2	no	—
1157	C₂×D₄	—	2	2	no	—
1158	C₂×D₄	—	2	2	no	—
1159	C₂×D₄	—	2	2	no	—
1160	C₂×D₄	—	2	2	no	—
1161	C₂×D₄	—	4	1	no	—
1162	C₂×D₄	—	4	1	no	—
1163	C₂×D₄	—	4	1	no	—
1164	C₂×D₄	—	4	1	no	—
1165	C₂×D₄	—	4	1	no	—
1166	C₂×D₄	—	4	1	no	—
1167	C₂×D₄	—	4	1	no	—
1168	C₂×D₄	—	4	1	no	—
1169	C₂×D₄	—	4	1	no	—
1170	C₂×D₄	—	4	1	no	—
1171	C₂×D₄	—	4	1	no	—
1172	C₂×D₄	—	4	1	no	—
1173	C₂×D₄	—	4	1	no	—
1174	C₂²×C₄	—	2	2	no	—
1175	C₂²×C₄	—	2	2	no	—
1176	C₂²×C₄	—	2	2	no	—
1177	C₂²×C₄	—	2	2	no	—
1178	C₂²×C₄	—	2	2	no	—
1179	C₂²×C₄	—	2	2	no	—
1180	C₂²×C₄	—	2	2	no	—
1181	C₂²×C₄	—	2	2	no	—
1182	C₂²×C₄	—	2	2	no	—
1183	C₂²×C₄	—	4	1	no	—
1184	C₂²×C₄	—	4	1	no	—
1185	C₂²×C₄	—	4	1	no	—
1186	C₂²×C₄	—	4	1	no	—
1187	C₂²×C₄	—	4	1	no	—
1188	C₂²×C₄	—	4	1	no	—
1189	C₂²×C₄	—	4	1	no	—
1190	C₂²×C₄	—	4	1	no	—
1191	C₂²×C₄	—	4	1	no	—
1192	C₂²×C₄	—	4	1	no	—
1193	C₂²×C₄	—	4	1	no	—
1194	C₂²×C₄	—	4	1	no	—
1195	C₂²×C₄	—	4	1	no	—
1196	C₂²×C₄	—	4	1	no	—
1197	C₂²×C₄	—	4	1	no	—
1198	C₂²×C₄	—	4	16	no	—
1199	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1200	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1201	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1202	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1203	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1204	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1205	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1206	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1207	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1208	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1209	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1210	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1211	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1212	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1213	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1214	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1215	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1216	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1217	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1218	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1219	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1220	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1221	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1222	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1223	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1224	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1225	C₄⋊C₄	—	2	2	no	—
1226	C₄⋊C₄	—	2	2	no	—
1227	C₄⋊C₄	—	2	2	no	—
1228	C₄⋊C₄	—	2	2	no	—
1229	C₄⋊C₄	—	2	2	no	—
1230	C₄⋊C₄	—	2	2	no	—
1231	C₄⋊C₄	—	2	2	no	—
1232	C₄⋊C₄	—	2	2	no	—
1233	C₄⋊C₄	—	2	2	no	—
1234	C₄⋊C₄	—	4	1	no	—
1235	C₄⋊C₄	—	4	1	no	—
1236	C₄⋊C₄	—	4	1	no	—
1237	C₄⋊C₄	—	4	1	no	—
1238	C₄⋊C₄	—	4	1	no	—
1239	C₄⋊C₄	—	4	1	no	—
1240	C₄⋊C₄	—	4	1	no	—
1241	C₄⋊C₄	—	4	1	no	—
1242	C₄⋊C₄	—	4	1	no	—
1243	C₄⋊C₄	—	4	1	no	—
1244	C₄⋊C₄	—	4	1	no	—
1245	C₄⋊C₄	—	4	1	no	—
1246	C₄⋊C₄	—	4	1	no	—
1247	C₄⋊C₄	—	4	1	no	—
1248	C₄⋊C₄	—	4	1	no	—
1249	C₄⋊C₄	—	4	1	no	—
1250	C₄⋊C₄	—	4	1	no	—
1251	C₄⋊C₄	—	4	1	no	—
1252	C₄⋊C₄	—	4	1	no	—
1253	C₄⋊C₄	—	4	1	no	—
1254	C₄⋊C₄	—	4	1	no	—
1255	C₄⋊C₄	—	4	1	no	—
1256	C₄⋊C₄	—	4	1	no	—
1257	C₂²⋊C₄	—	2	2	no	—
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	—	2	2	no	—
1263	C₂²⋊C₄	—	2	2	no	—
1264	C₂²⋊C₄	—	2	2	no	—
1265	C₂²⋊C₄	—	2	2	no	—
1266	C₂²⋊C₄	—	2	2	no	—
1267	C₂²⋊C₄	—	2	2	no	—
1268	C₂²⋊C₄	—	2	2	no	—
1269	C₂²⋊C₄	—	2	2	no	—
1270	C₂²⋊C₄	—	2	2	no	—
1271	C₂²⋊C₄	—	2	2	no	—
1272	C₂²⋊C₄	—	2	2	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	—	4	1	no	—
1278	C₂²⋊C₄	—	4	1	no	—
1279	C₂²⋊C₄	—	4	1	no	—
1280	C₂²⋊C₄	—	4	1	no	—
1281	C₂²⋊C₄	—	4	1	no	—
1282	C₂²⋊C₄	—	4	1	no	—
1283	C₂²⋊C₄	—	4	1	no	—
1284	C₂²⋊C₄	—	4	1	no	—
1285	C₂²⋊C₄	—	4	1	no	—
1286	C₂²⋊C₄	—	4	1	no	—
1287	C₂²⋊C₄	—	4	1	no	—
1288	C₂²⋊C₄	—	4	1	no	—
1289	C₂²⋊C₄	—	4	1	no	—
1290	C₂²⋊C₄	—	4	1	no	—
1291	C₂²⋊C₄	—	4	1	no	—
1292	C₂²⋊C₄	—	4	1	no	—
1293	C₂²⋊C₄	—	4	1	no	—
1294	C₂²⋊C₄	—	4	1	no	—
1295	C₂²⋊C₄	—	4	1	no	—
1296	C₂²⋊C₄	—	4	1	no	—
1297	C₂²⋊C₄	—	4	1	no	—
1298	C₂²⋊C₄	—	4	1	no	—
1299	C₂²⋊C₄	—	4	1	no	—
1300	C₂²⋊C₄	—	4	1	no	—
1301	C₂²⋊C₄	—	4	1	no	—
1302	C₂²⋊C₄	—	4	1	no	—
1303	C₂²⋊C₄	—	4	1	no	—
1304	C₂²⋊C₄	—	4	1	no	—
1305	C₂²⋊C₄	—	4	1	no	—
1306	C₂²⋊C₄	#41×C₅₃	1	4	yes	—
1307	C₄²	—	2	2	no	—
1308	C₄²	—	2	2	no	—
1309	C₄²	—	2	2	no	—
1310	C₄²	—	4	1	no	—
1311	C₄²	—	4	1	no	—
1312	C₄²	—	4	1	no	—
1313	C₄²	—	4	1	no	—
1314	C₄²	—	4	1	no	—
1315	C₄²	—	4	1	no	—
1316	C₄²	—	4	1	no	—
1317	C₂³	—	2	1	no	—
1318	C₂³	—	2	1	no	—
1319	C₂³	—	2	1	no	—
1320	C₂³	—	2	1	no	—
1321	C₂³	—	2	1	no	—
1322	C₂³	—	2	1	no	—
1323	C₂³	—	2	1	no	—
1324	C₂³	—	2	1	no	—
1325	C₂³	—	2	1	no	—
1326	C₂³	—	2	1	no	—
1327	C₂³	—	2	1	no	—
1328	C₂³	—	2	1	no	—
1329	C₂³	—	2	1	no	—
1330	C₂³	—	2	1	no	—
1331	C₂³	—	2	1	no	—
1332	C₂³	—	2	1	no	—
1333	C₂³	—	2	1	no	—
1334	C₂³	—	2	1	no	—
1335	C₂³	—	2	1	no	—
1336	C₂³	—	2	1	no	—
1337	C₂³	—	2	1	no	—
1338	C₂³	—	2	1	no	—
1339	C₂³	—	2	1	no	—
1340	C₂³	—	2	1	no	—
1341	C₂³	—	2	1	no	—
1342	C₂³	—	2	1	no	—
1343	C₂³	—	2	1	no	—
1344	C₂³	—	2	1	no	—
1345	C₂³	—	2	1	no	—
1346	C₂³	—	2	1	no	—
1347	C₂³	—	2	1	no	—
1348	C₂³	—	2	1	no	—
1349	C₂³	—	4	4	no	—
1350	C₂³	—	4	4	no	—
1351	C₂³	—	4	4	no	—
1352	C₂³	—	4	4	no	—
1353	C₂³	—	4	4	no	—
1354	C₂³	—	4	4	no	—
1355	C₂³	—	4	4	no	—
1356	C₂³	C₂×#41×C₅₃	1	2	yes	—
1357	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
1358	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
1359	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1360	Q₈	—	8	2	no	—
1361	Q₈	—	8	2	no	—
1362	Q₈	—	8	2	no	—
1363	D₄	—	4	4	no	—
1364	D₄	—	4	4	no	—
1365	D₄	—	4	4	no	—
1366	D₄	—	8	2	no	—
1367	D₄	—	8	2	no	—
1368	D₄	—	8	2	no	—
1369	D₄	—	8	2	no	—
1370	C₂×C₄	—	2	1	no	—
1371	C₂×C₄	—	2	1	no	—
1372	C₂×C₄	—	2	1	no	—
1373	C₂×C₄	—	2	1	no	—
1374	C₂×C₄	—	2	1	no	—
1375	C₂×C₄	—	2	1	no	—
1376	C₂×C₄	—	2	1	no	—
1377	C₂×C₄	—	2	1	no	—
1378	C₂×C₄	—	2	1	no	—
1379	C₂×C₄	—	2	1	no	—
1380	C₂×C₄	—	2	1	no	—
1381	C₂×C₄	—	2	1	no	—
1382	C₂×C₄	—	2	1	no	—
1383	C₂×C₄	—	2	1	no	—
1384	C₂×C₄	—	2	1	no	—
1385	C₂×C₄	—	2	1	no	—
1386	C₂×C₄	—	2	1	no	—
1387	C₂×C₄	—	2	1	no	—
1388	C₂×C₄	—	2	1	no	—
1389	C₂×C₄	—	2	1	no	—
1390	C₂×C₄	—	2	1	no	—
1391	C₂×C₄	—	2	1	no	—
1392	C₂×C₄	—	2	1	no	—
1393	C₂×C₄	—	2	1	no	—
1394	C₂×C₄	—	2	1	no	—
1395	C₂×C₄	—	2	1	no	—
1396	C₂×C₄	—	2	1	no	—
1397	C₂×C₄	—	2	1	no	—
1398	C₂×C₄	—	2	1	no	—
1399	C₂×C₄	—	2	1	no	—
1400	C₂×C₄	—	2	1	no	—
1401	C₂×C₄	—	2	1	no	—
1402	C₂×C₄	—	2	1	no	—
1403	C₂×C₄	—	2	1	no	—
1404	C₂×C₄	—	2	1	no	—
1405	C₂×C₄	—	2	1	no	—
1406	C₂×C₄	—	2	1	no	—
1407	C₂×C₄	—	2	1	no	—
1408	C₂×C₄	—	2	1	no	—
1409	C₂×C₄	—	2	1	no	—
1410	C₂×C₄	—	2	1	no	—
1411	C₂×C₄	—	2	1	no	—
1412	C₂×C₄	—	2	1	no	—
1413	C₂×C₄	—	2	1	no	—
1414	C₂×C₄	—	2	1	no	—
1415	C₂×C₄	—	2	1	no	—
1416	C₂×C₄	—	2	1	no	—
1417	C₂×C₄	—	2	1	no	—
1418	C₂×C₄	—	2	1	no	—
1419	C₂×C₄	—	2	1	no	—
1420	C₂×C₄	—	2	1	no	—
1421	C₂×C₄	—	2	1	no	—
1422	C₂×C₄	—	2	1	no	—
1423	C₂×C₄	—	2	1	no	—
1424	C₂×C₄	—	2	1	no	—
1425	C₂×C₄	—	2	1	no	—
1426	C₂×C₄	—	2	1	no	—
1427	C₂×C₄	—	2	1	no	—
1428	C₂×C₄	—	2	1	no	—
1429	C₂×C₄	—	2	1	no	—
1430	C₂×C₄	—	2	1	no	—
1431	C₂×C₄	—	2	1	no	—
1432	C₂×C₄	—	2	1	no	—
1433	C₂×C₄	—	2	1	no	—
1434	C₂×C₄	—	2	1	no	—
1435	C₂×C₄	—	2	1	no	—
1436	C₂×C₄	—	2	1	no	—
1437	C₂×C₄	—	2	1	no	—
1438	C₂×C₄	—	2	1	no	—
1439	C₂×C₄	—	2	1	no	—
1440	C₂×C₄	—	2	1	no	—
1441	C₂×C₄	—	2	1	no	—
1442	C₂×C₄	—	2	1	no	—
1443	C₂×C₄	—	2	1	no	—
1444	C₂×C₄	—	4	4	no	—
1445	C₂×C₄	—	4	4	no	—
1446	C₂×C₄	—	4	4	no	—
1447	C₂×C₄	—	4	4	no	—
1448	C₂×C₄	—	4	4	no	—
1449	C₂×C₄	—	4	4	no	—
1450	C₂×C₄	—	8	2	no	—
1451	C₂×C₄	—	8	2	no	—
1452	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1453	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1454	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1455	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1456	C₂²	—	2	2	no	—
1457	C₂²	—	2	2	no	—
1458	C₂²	—	2	2	no	—
1459	C₂²	—	2	2	no	—
1460	C₂²	—	2	2	no	—
1461	C₂²	—	2	2	no	—
1462	C₂²	—	2	2	no	—
1463	C₂²	—	2	2	no	—
1464	C₂²	—	2	2	no	—
1465	C₂²	—	4	16	no	—
1466	C₂²	—	4	1	no	—
1467	C₂²	—	4	1	no	—
1468	C₂²	—	4	1	no	—
1469	C₂²	—	4	1	no	—
1470	C₂²	—	4	1	no	—
1471	C₂²	—	4	1	no	—
1472	C₂²	—	4	1	no	—
1473	C₂²	—	4	1	no	—
1474	C₂²	—	4	1	no	—
1475	C₂²	—	4	1	no	—
1476	C₂²	—	4	1	no	—
1477	C₂²	—	4	1	no	—
1478	C₂²	—	4	1	no	—
1479	C₂²	—	4	1	no	—
1480	C₂²	—	4	1	no	—
1481	C₂²	—	4	1	no	—
1482	C₂²	—	4	1	no	—
1483	C₂²	—	4	1	no	—
1484	C₂²	—	4	1	no	—
1485	C₂²	—	4	1	no	—
1486	C₂²	—	4	1	no	—
1487	C₂²	—	4	1	no	—
1488	C₂²	—	4	1	no	—
1489	C₂²	—	4	1	no	—
1490	C₂²	—	4	1	no	—
1491	C₂²	—	4	1	no	—
1492	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1493	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1494	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1495	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1496	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1497	C₂²	C₅₃×#585	1	1	yes	characteristic
1498	C₂²	C₅₃×#585	1	1	yes	characteristic
1499	C₄	—	2	2	no	—
1500	C₄	—	2	2	no	—
1501	C₄	—	2	2	no	—
1502	C₄	—	2	2	no	—
1503	C₄	—	4	1	no	—
1504	C₄	—	4	1	no	—
1505	C₄	—	4	1	no	—
1506	C₄	—	4	1	no	—
1507	C₄	—	4	1	no	—
1508	C₄	—	4	1	no	—
1509	C₄	—	4	1	no	—
1510	C₄	—	4	1	no	—
1511	C₄	—	4	1	no	—
1512	C₄	—	4	1	no	—
1513	C₄	—	4	1	no	—
1514	C₄	—	4	1	no	—
1515	C₄	—	4	1	no	—
1516	C₄	—	4	1	no	—
1517	C₄	—	4	1	no	—
1518	C₄	—	4	1	no	—
1519	C₄	—	4	1	no	—
1520	C₄	—	4	1	no	—
1521	C₄	—	4	1	no	—
1522	C₄	—	4	1	no	—
1523	C₄	—	4	1	no	—
1524	C₄	—	4	1	no	—
1525	C₂	—	4	2	no	—
1526	C₂	—	4	2	no	—
1527	C₂	—	4	2	no	—
1528	C₂	—	8	1	no	—
1529	C₂	—	8	1	no	—
1530	C₂	C₅₃×#3460	1	1	yes	characteristic
1531	C₂	C₅₃×#3513	1	1	yes	characteristic
1532	C₂	C₅₃×#3520	1	1	yes	characteristic
1533	C₂	C₅₃×#3532	1	1	yes	characteristic
1534	C₂	C₅₃×#3535	1	1	yes	characteristic
1535	C₂	C₅₃×#3540	1	1	yes	characteristic
1536	C₂	C₅₃×#3541	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₅₃×#2670	C₂
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. C₅₃×#2849	C₂	semidirect
2. C₅₃×#2848	C₂	semidirect
3. C₅₃×#2797	C₂	semidirect
4. C₅₃×#2781	C₂	semidirect
5. C₅₃×#2780	C₂	semidirect
6. C₅₃×#2763	C₂	semidirect
7. C₅₃×#2757	C₂	semidirect
8. C₅₃×#2738	C₂	semidirect
9. C₅₃×#2735	C₂	semidirect
10. C₅₃×#2729	C₂	semidirect
11. C₅₃×#2715	C₂	semidirect
12. C₅₃×#2706	C₂	semidirect
13. C₅₃×#2700	C₂	semidirect
14. C₅₃×#2696	C₂	semidirect
15. C₅₃×#2685	C₂	semidirect
16. C₅₃×#2684	C₂	semidirect
17. C₅₃×#2674	C₂	semidirect
19. C₅₃×#2638	C₂	semidirect
20. C₅₃×#2636	C₂	semidirect
21. C₅₃×#2575	C₂	semidirect
22. C₅₃×#2574	C₂	semidirect
23. C₅₃×#2560	C₂	semidirect
24. C₅₃×#2553	C₂	semidirect
25. C₅₃×#2461	C₂	semidirect
26. C₅₃×#2457	C₂	semidirect
27. C₅₃×#2452	C₂	semidirect
28. C₅₃×#2447	C₂	semidirect
29. C₅₃×#2337	C₂	semidirect
30. C₅₃×#2334	C₂	semidirect
31. C₄×#120×C₅₃	C₂	semidirect
33. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
35. C₂×#126×C₅₃	C₂²	semidirect
41. C₂×#123×C₅₃	C₂²	semidirect
45. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
51. C₅₃×#400	C₂²	semidirect
52. C₅₃×#400	C₂²	semidirect
53. C₅₃×#400	C₂²	semidirect
54. C₅₃×#400	C₂²	semidirect
57. C₅₃×#399	C₂²	semidirect
58. C₅₃×#398	C₂²	semidirect
59. C₅₃×#398	C₂²	semidirect
60. C₅₃×#398	C₂²	semidirect
61. C₅₃×#398	C₂²	semidirect
67. C₅₃×#397	C₂²	semidirect
68. C₅₃×#397	C₂²	semidirect
69. C₅₃×#397	C₂²	semidirect
70. C₅₃×#397	C₂²	semidirect
71. C₅₃×#397	C₂²	semidirect
75. C₅₃×#396	C₂²	semidirect
76. C₅₃×#396	C₂²	semidirect
77. C₅₃×#396	C₂²	semidirect
78. C₅₃×#396	C₂²	semidirect
79. C₅₃×#395	C₂²	semidirect
80. C₅₃×#395	C₂²	semidirect
81. C₅₃×#395	C₂²	semidirect
90. C₅₃×#394	C₂²	semidirect
94. C₅₃×#393	C₂²	semidirect
95. C₅₃×#393	C₂²	semidirect
99. C₅₃×#391	C₂²	semidirect
100. C₅₃×#391	C₂²	semidirect
101. C₅₃×#391	C₂²	semidirect
102. C₅₃×#391	C₂²	semidirect
107. C₅₃×#390	C₂²	semidirect
108. C₅₃×#389	C₂²	semidirect
109. C₅₃×#389	C₂²	semidirect
110. C₅₃×#389	C₂²	semidirect
111. C₅₃×#389	C₂²	semidirect
125. C₅₃×#388	C₂²	semidirect
126. C₅₃×#388	C₂²	semidirect
127. C₅₃×#388	C₂²	semidirect
128. C₅₃×#388	C₂²	semidirect
129. C₅₃×#388	C₂²	semidirect
130. C₅₃×#387	C₂²	semidirect
131. C₅₃×#387	C₂²	semidirect
132. C₅₃×#387	C₂²	semidirect
133. C₅₃×#387	C₂²	semidirect
134. C₅₃×#387	C₂²	semidirect
135. C₅₃×#387	C₂²	semidirect
136. C₅₃×#387	C₂²	semidirect
137. C₅₃×#387	C₂²	semidirect
138. C₅₃×#387	C₂²	semidirect
149. C₅₃×#386	C₂²	semidirect
163. C₅₃×#385	C₂²	semidirect
164. C₅₃×#385	C₂²	semidirect
165. C₅₃×#383	C₂²	semidirect
166. C₅₃×#382	C₂²	semidirect
167. C₅₃×#382	C₂²	semidirect
168. C₅₃×#382	C₂²	semidirect
171. C₅₃×#381	C₂²	semidirect
175. C₅₃×#380	C₂²	semidirect
180. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
181. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
182. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
186. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
687. #36858	C₅₃	direct (N × H)
757. #2849	C₂×C₅₃	semidirect
758. #2848	C₂×C₅₃	semidirect
759. #2797	C₂×C₅₃	semidirect
760. #2781	C₂×C₅₃	semidirect
761. #2780	C₂×C₅₃	semidirect
762. #2763	C₂×C₅₃	semidirect
763. #2757	C₂×C₅₃	semidirect
764. #2738	C₂×C₅₃	semidirect
765. #2735	C₂×C₅₃	semidirect
766. #2729	C₂×C₅₃	semidirect
767. #2715	C₂×C₅₃	semidirect
768. #2706	C₂×C₅₃	semidirect
769. #2700	C₂×C₅₃	semidirect
770. #2696	C₂×C₅₃	semidirect
771. #2685	C₂×C₅₃	semidirect
772. #2684	C₂×C₅₃	semidirect
773. #2674	C₂×C₅₃	semidirect
775. #2638	C₂×C₅₃	semidirect
776. #2636	C₂×C₅₃	semidirect
777. #2575	C₂×C₅₃	semidirect
778. #2574	C₂×C₅₃	semidirect
779. #2560	C₂×C₅₃	semidirect
780. #2553	C₂×C₅₃	semidirect
781. #2461	C₂×C₅₃	semidirect
782. #2457	C₂×C₅₃	semidirect
783. #2452	C₂×C₅₃	semidirect
784. #2447	C₂×C₅₃	semidirect
785. #2337	C₂×C₅₃	semidirect
786. #2334	C₂×C₅₃	semidirect
787. C₄×#120	C₂×C₅₃	semidirect
801. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
803. C₂×#126	C₂²×C₅₃	semidirect
809. C₂×#123	C₂²×C₅₃	semidirect
813. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
819. #400	C₂²×C₅₃	semidirect
820. #400	C₂²×C₅₃	semidirect
821. #400	C₂²×C₅₃	semidirect
822. #400	C₂²×C₅₃	semidirect
825. #399	C₂²×C₅₃	semidirect
826. #398	C₂²×C₅₃	semidirect
827. #398	C₂²×C₅₃	semidirect
828. #398	C₂²×C₅₃	semidirect
829. #398	C₂²×C₅₃	semidirect
835. #397	C₂²×C₅₃	semidirect
836. #397	C₂²×C₅₃	semidirect
837. #397	C₂²×C₅₃	semidirect
838. #397	C₂²×C₅₃	semidirect
839. #397	C₂²×C₅₃	semidirect
843. #396	C₂²×C₅₃	semidirect
844. #396	C₂²×C₅₃	semidirect
845. #396	C₂²×C₅₃	semidirect
846. #396	C₂²×C₅₃	semidirect
847. #395	C₂²×C₅₃	semidirect
848. #395	C₂²×C₅₃	semidirect
849. #395	C₂²×C₅₃	semidirect
858. #394	C₂²×C₅₃	semidirect
862. #393	C₂²×C₅₃	semidirect
863. #393	C₂²×C₅₃	semidirect
867. #391	C₂²×C₅₃	semidirect
868. #391	C₂²×C₅₃	semidirect
869. #391	C₂²×C₅₃	semidirect
870. #391	C₂²×C₅₃	semidirect
875. #390	C₂²×C₅₃	semidirect
876. #389	C₂²×C₅₃	semidirect
877. #389	C₂²×C₅₃	semidirect
878. #389	C₂²×C₅₃	semidirect
879. #389	C₂²×C₅₃	semidirect
893. #388	C₂²×C₅₃	semidirect
894. #388	C₂²×C₅₃	semidirect
895. #388	C₂²×C₅₃	semidirect
896. #388	C₂²×C₅₃	semidirect
897. #388	C₂²×C₅₃	semidirect
898. #387	C₂²×C₅₃	semidirect
899. #387	C₂²×C₅₃	semidirect
900. #387	C₂²×C₅₃	semidirect
901. #387	C₂²×C₅₃	semidirect
902. #387	C₂²×C₅₃	semidirect
903. #387	C₂²×C₅₃	semidirect
904. #387	C₂²×C₅₃	semidirect
905. #387	C₂²×C₅₃	semidirect
906. #387	C₂²×C₅₃	semidirect
917. #386	C₂²×C₅₃	semidirect
931. #385	C₂²×C₅₃	semidirect
932. #385	C₂²×C₅₃	semidirect
933. #383	C₂²×C₅₃	semidirect
934. #382	C₂²×C₅₃	semidirect
935. #382	C₂²×C₅₃	semidirect
936. #382	C₂²×C₅₃	semidirect
939. #381	C₂²×C₅₃	semidirect
943. #380	C₂²×C₅₃	semidirect
948. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
949. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
950. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
954. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
955. C₅₃	#36858	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#2849	2
C₅₃×#2848	2
C₅₃×#2797	2
C₅₃×#2781	2
C₅₃×#2780	2
C₅₃×#2763	2
C₅₃×#2757	2
C₅₃×#2738	2
C₅₃×#2735	2
C₅₃×#2729	2
C₅₃×#2715	2
C₅₃×#2706	2
C₅₃×#2700	2
C₅₃×#2696	2
C₅₃×#2685	2
C₅₃×#2684	2
C₅₃×#2674	2
C₅₃×#2670	2
C₅₃×#2638	2
C₅₃×#2636	2
C₅₃×#2575	2
C₅₃×#2574	2
C₅₃×#2560	2
C₅₃×#2553	2
C₅₃×#2461	2
C₅₃×#2457	2
C₅₃×#2452	2
C₅₃×#2447	2
C₅₃×#2337	2
C₅₃×#2334	2
C₄×#120×C₅₃	2
#36858	53

Subgroups — C53×#36858 #27244370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36858 #27244370