Subgroups — C₅₃×#34727 #27242239

Order 13568.

2736 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2479	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2471	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2467	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2456	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2454	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2448	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2441	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2431	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2428	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2423	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2414	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2407	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2397	C₂	1	2	yes	maximal, complemented
16	C₅₃×#2392	C₂	1	2	yes	maximal, complemented
17	C₄×#127×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#121×C₅₃	C₂	1	2	yes	maximal, complemented
21	C₅₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2290	C₂	1	2	yes	maximal, complemented
23	C₄²×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
26	C₅₃×#529	—	2	8	no	—
27	C₂×#126×C₅₃	C₂²	1	2	yes	—
28	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×#123×C₅₃	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×#121×C₅₃	C₂²	1	2	yes	—
33	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
36	C₄×#41×C₅₃	—	2	8	no	—
37	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
45	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
48	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
49	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
51	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
52	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
53	C₂×#117×C₅₃	C₂²	1	2	yes	—
54	C₂×#117×C₅₃	C₂²	1	2	yes	—
55	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
56	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
57	C₂²×C₄²×C₅₃	C₂²	1	2	yes	—
58	C₅₃×#399	C₂²	1	2	yes	—
59	C₅₃×#399	C₂²	1	2	yes	—
60	C₅₃×#399	C₂²	1	2	yes	—
61	C₅₃×#399	C₂²	1	2	yes	—
62	C₅₃×#398	C₂²	1	2	yes	—
63	C₅₃×#397	C₂²	1	2	yes	—
64	C₅₃×#396	C₂²	1	2	yes	—
65	C₅₃×#396	C₂²	1	2	yes	—
66	C₅₃×#394	C₂²	1	2	yes	—
67	C₅₃×#394	C₂²	1	2	yes	—
68	C₅₃×#394	C₂²	1	2	yes	—
69	C₅₃×#392	C₂²	1	2	yes	—
70	C₅₃×#392	C₂²	1	2	yes	—
71	C₅₃×#392	C₂²	1	2	yes	—
72	C₅₃×#392	C₂²	1	2	yes	—
73	C₅₃×#392	C₂²	1	2	yes	—
74	C₅₃×#391	C₂²	1	1	yes	characteristic
75	C₅₃×#391	C₂²	1	1	yes	characteristic
76	C₅₃×#390	C₂²	1	1	yes	characteristic
77	C₅₃×#390	C₂²	1	1	yes	characteristic
78	C₅₃×#390	C₂²	1	1	yes	characteristic
79	C₅₃×#390	C₂²	1	1	yes	characteristic
80	C₅₃×#390	C₂²	1	2	yes	—
81	C₅₃×#390	C₂²	1	2	yes	—
82	C₅₃×#390	C₂²	1	2	yes	—
83	C₅₃×#389	C₂²	1	1	yes	characteristic
84	C₅₃×#389	C₂²	1	1	yes	characteristic
85	C₅₃×#389	C₂²	1	1	yes	characteristic
86	C₅₃×#389	C₂²	1	2	yes	—
87	C₅₃×#389	C₂²	1	1	yes	characteristic
88	C₅₃×#388	C₂²	1	2	yes	—
89	C₅₃×#388	C₂²	1	2	yes	—
90	C₅₃×#388	C₂²	1	2	yes	—
91	C₅₃×#388	C₂²	1	2	yes	—
92	C₅₃×#388	C₂²	1	2	yes	—
93	C₅₃×#388	C₂²	1	2	yes	—
94	C₅₃×#387	C₂²	1	2	yes	—
95	C₅₃×#387	C₂²	1	2	yes	—
96	C₅₃×#387	C₂²	1	2	yes	—
97	C₅₃×#387	C₂²	1	2	yes	—
98	C₅₃×#386	C₂²	1	2	yes	—
99	C₅₃×#386	C₂²	1	2	yes	—
100	C₅₃×#386	C₂²	1	2	yes	—
101	C₅₃×#386	C₂²	1	2	yes	—
102	C₅₃×#386	C₂²	1	2	yes	—
103	C₅₃×#386	C₂²	1	2	yes	—
104	C₅₃×#385	C₂²	1	2	yes	—
105	C₅₃×#385	C₂²	1	2	yes	—
106	C₅₃×#384	C₂²	1	1	yes	characteristic
107	C₅₃×#380	C₂²	1	1	yes	characteristic
108	C₅₃×#380	C₂²	1	1	yes	characteristic
109	C₅₃×#380	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
123	C₅₃×#376	C₂²	1	2	yes	—
124	C₄³×C₅₃	C₂²	1	1	yes	characteristic
125	C₂×#41×C₅₃	—	2	4	no	—
126	C₂×#41×C₅₃	—	2	4	no	—
127	C₂×#41×C₅₃	—	2	4	no	—
128	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
131	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
133	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
134	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
135	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
136	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
138	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
139	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
144	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
146	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
148	#127×C₅₃	—	2	4	no	—
149	#126×C₅₃	—	2	8	no	—
150	#125×C₅₃	—	2	4	no	—
151	#124×C₅₃	—	2	4	no	—
152	#123×C₅₃	—	2	8	no	—
153	C₂²⋊Q₈×C₅₃	—	2	4	no	—
154	#121×C₅₃	—	2	4	no	—
155	#121×C₅₃	—	2	8	no	—
156	#121×C₅₃	—	2	4	no	—
157	#121×C₅₃	—	2	4	no	—
158	C₄×Q₈×C₅₃	—	2	4	no	—
159	C₄×Q₈×C₅₃	D₄	1	8	yes	complemented
160	C₄×D₄×C₅₃	—	2	4	no	—
161	C₄×D₄×C₅₃	—	2	8	no	—
162	C₄×D₄×C₅₃	—	2	4	no	—
163	C₄×D₄×C₅₃	—	2	4	no	—
164	C₄×D₄×C₅₃	—	2	8	no	—
165	C₄×D₄×C₅₃	—	2	8	no	—
166	C₄×D₄×C₅₃	—	2	4	no	—
167	C₄×D₄×C₅₃	—	2	4	no	—
168	C₄×D₄×C₅₃	—	2	8	no	—
169	C₄×D₄×C₅₃	—	2	4	no	—
170	C₄×D₄×C₅₃	—	4	4	no	—
171	C₄×D₄×C₅₃	—	4	4	no	—
172	C₄×D₄×C₅₃	—	4	4	no	—
173	#117×C₅₃	—	2	4	no	—
174	#117×C₅₃	—	2	8	no	—
175	#117×C₅₃	—	2	8	no	—
176	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₅₃	—	2	4	no	—
222	C₂×C₄²×C₅₃	—	2	8	no	—
223	C₂×C₄²×C₅₃	—	2	4	no	—
224	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
226	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
228	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
238	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
240	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
241	#95×C₅₃	C₂³	1	2	yes	—
242	#95×C₅₃	C₂³	1	2	yes	—
243	#95×C₅₃	C₂³	1	2	yes	—
244	#95×C₅₃	C₂³	1	2	yes	—
245	#95×C₅₃	C₂³	1	1	yes	characteristic
246	#95×C₅₃	C₂³	1	1	yes	characteristic
247	#95×C₅₃	C₂³	1	1	yes	characteristic
248	#95×C₅₃	C₂³	1	1	yes	characteristic
249	#95×C₅₃	C₂³	1	1	yes	characteristic
250	#95×C₅₃	C₂³	1	1	yes	characteristic
251	#95×C₅₃	C₂³	1	2	yes	—
252	#95×C₅₃	C₂³	1	2	yes	—
253	#95×C₅₃	C₂³	1	2	yes	—
254	#95×C₅₃	C₂³	1	2	yes	—
255	#95×C₅₃	C₂³	1	2	yes	—
256	#95×C₅₃	C₂³	1	2	yes	—
257	#95×C₅₃	C₂³	1	2	yes	—
258	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
259	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
260	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
261	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
262	#41×C₅₃	—	2	32	no	—
263	C₂×Q₈×C₅₃	—	2	2	no	—
264	C₂×Q₈×C₅₃	—	2	2	no	—
265	C₂×Q₈×C₅₃	C₂×D₄	1	4	yes	—
266	C₂×D₄×C₅₃	—	2	2	no	—
267	C₂×D₄×C₅₃	—	2	2	no	—
268	C₂×D₄×C₅₃	—	2	4	no	—
269	C₂×D₄×C₅₃	—	2	4	no	—
270	C₂×D₄×C₅₃	—	2	4	no	—
271	C₂×D₄×C₅₃	—	2	4	no	—
272	C₂×D₄×C₅₃	—	2	4	no	—
273	C₂×D₄×C₅₃	—	2	4	no	—
274	C₂×D₄×C₅₃	—	2	4	no	—
275	C₂×D₄×C₅₃	—	2	4	no	—
276	C₂×D₄×C₅₃	—	2	4	no	—
277	C₂×D₄×C₅₃	—	2	2	no	—
278	C₂×D₄×C₅₃	—	2	4	no	—
279	C₂×D₄×C₅₃	—	2	2	no	—
280	C₂×D₄×C₅₃	—	2	2	no	—
281	C₂×D₄×C₅₃	—	2	2	no	—
282	C₂×D₄×C₅₃	—	2	4	no	—
283	C₂×D₄×C₅₃	—	2	4	no	—
284	C₂×D₄×C₅₃	—	2	2	no	—
285	C₂×D₄×C₅₃	—	2	2	no	—
286	C₂×D₄×C₅₃	—	4	2	no	—
287	C₂×D₄×C₅₃	—	4	2	no	—
288	C₂×D₄×C₅₃	—	4	2	no	—
289	C₂×D₄×C₅₃	—	4	2	no	—
290	C₂×D₄×C₅₃	—	4	2	no	—
291	C₂×D₄×C₅₃	—	4	2	no	—
292	C₂×D₄×C₅₃	#41	1	4	yes	—
293	C₂²×C₄×C₅₃	—	2	4	no	—
294	C₂²×C₄×C₅₃	—	2	4	no	—
295	C₂²×C₄×C₅₃	—	2	2	no	—
296	C₂²×C₄×C₅₃	—	2	4	no	—
297	C₂²×C₄×C₅₃	—	2	2	no	—
298	C₂²×C₄×C₅₃	—	2	2	no	—
299	C₂²×C₄×C₅₃	—	2	2	no	—
300	C₂²×C₄×C₅₃	—	2	4	no	—
301	C₂²×C₄×C₅₃	—	2	2	no	—
302	C₂²×C₄×C₅₃	—	2	4	no	—
303	C₂²×C₄×C₅₃	—	2	2	no	—
304	C₂²×C₄×C₅₃	—	2	2	no	—
305	C₂²×C₄×C₅₃	—	2	2	no	—
306	C₂²×C₄×C₅₃	—	2	4	no	—
307	C₂²×C₄×C₅₃	—	2	2	no	—
308	C₂²×C₄×C₅₃	—	2	2	no	—
309	C₂²×C₄×C₅₃	—	2	2	no	—
310	C₂²×C₄×C₅₃	—	2	2	no	—
311	C₂²×C₄×C₅₃	—	2	4	no	—
312	C₂²×C₄×C₅₃	—	2	4	no	—
313	C₂²×C₄×C₅₃	—	2	4	no	—
314	C₂²×C₄×C₅₃	—	2	2	no	—
315	C₂²×C₄×C₅₃	—	2	2	no	—
316	C₂²×C₄×C₅₃	—	2	2	no	—
317	C₂²×C₄×C₅₃	—	2	4	no	—
318	C₂²×C₄×C₅₃	—	2	4	no	—
319	C₂²×C₄×C₅₃	—	4	1	no	—
320	C₂²×C₄×C₅₃	—	4	2	no	—
321	C₂²×C₄×C₅₃	—	4	1	no	—
322	C₂²×C₄×C₅₃	#41	1	4	yes	—
323	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
342	C₄⋊C₄×C₅₃	—	2	4	no	—
343	C₄⋊C₄×C₅₃	—	2	2	no	—
344	C₄⋊C₄×C₅₃	—	2	4	no	—
345	C₄⋊C₄×C₅₃	—	2	4	no	—
346	C₄⋊C₄×C₅₃	—	2	2	no	—
347	C₄⋊C₄×C₅₃	—	2	4	no	—
348	C₄⋊C₄×C₅₃	—	2	2	no	—
349	C₄⋊C₄×C₅₃	—	2	2	no	—
350	C₄⋊C₄×C₅₃	—	2	4	no	—
351	C₄⋊C₄×C₅₃	—	2	2	no	—
352	C₄⋊C₄×C₅₃	—	2	4	no	—
353	C₄⋊C₄×C₅₃	—	2	2	no	—
354	C₄⋊C₄×C₅₃	—	2	2	no	—
355	C₄⋊C₄×C₅₃	—	4	2	no	—
356	C₄⋊C₄×C₅₃	—	4	2	no	—
357	C₄⋊C₄×C₅₃	—	4	2	no	—
358	C₄⋊C₄×C₅₃	—	4	2	no	—
359	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
360	C₄⋊C₄×C₅₃	C₂×D₄	1	8	yes	—
361	C₂²⋊C₄×C₅₃	—	2	2	no	—
362	C₂²⋊C₄×C₅₃	—	2	4	no	—
363	C₂²⋊C₄×C₅₃	—	2	4	no	—
364	C₂²⋊C₄×C₅₃	—	2	4	no	—
365	C₂²⋊C₄×C₅₃	—	2	4	no	—
366	C₂²⋊C₄×C₅₃	—	2	4	no	—
367	C₂²⋊C₄×C₅₃	—	2	4	no	—
368	C₂²⋊C₄×C₅₃	—	2	4	no	—
369	C₂²⋊C₄×C₅₃	—	2	4	no	—
370	C₂²⋊C₄×C₅₃	—	2	4	no	—
371	C₂²⋊C₄×C₅₃	—	2	2	no	—
372	C₂²⋊C₄×C₅₃	—	2	2	no	—
373	C₂²⋊C₄×C₅₃	—	2	2	no	—
374	C₂²⋊C₄×C₅₃	—	2	4	no	—
375	C₂²⋊C₄×C₅₃	—	2	4	no	—
376	C₂²⋊C₄×C₅₃	—	2	2	no	—
377	C₂²⋊C₄×C₅₃	—	2	4	no	—
378	C₂²⋊C₄×C₅₃	—	2	4	no	—
379	C₂²⋊C₄×C₅₃	—	4	2	no	—
380	C₂²⋊C₄×C₅₃	—	4	2	no	—
381	C₂²⋊C₄×C₅₃	—	4	2	no	—
382	C₂²⋊C₄×C₅₃	—	4	2	no	—
383	C₂²⋊C₄×C₅₃	—	4	2	no	—
384	C₂²⋊C₄×C₅₃	—	4	2	no	—
385	C₂²⋊C₄×C₅₃	—	4	2	no	—
386	C₂²⋊C₄×C₅₃	#41	1	4	yes	complemented
387	C₄²×C₅₃	—	2	2	no	—
388	C₄²×C₅₃	—	2	2	no	—
389	C₄²×C₅₃	—	2	4	no	—
390	C₄²×C₅₃	—	2	2	no	—
391	C₄²×C₅₃	—	2	4	no	—
392	C₄²×C₅₃	—	2	2	no	—
393	C₄²×C₅₃	—	2	2	no	—
394	C₄²×C₅₃	—	2	2	no	—
395	C₄²×C₅₃	—	2	2	no	—
396	C₄²×C₅₃	—	2	2	no	—
397	C₄²×C₅₃	—	2	2	no	—
398	C₄²×C₅₃	—	2	2	no	—
399	C₄²×C₅₃	—	2	4	no	—
400	C₄²×C₅₃	—	4	1	no	—
401	C₄²×C₅₃	C₂×D₄	1	4	yes	—
402	C₄²×C₅₃	C₂×D₄	1	8	yes	—
403	C₄²×C₅₃	#41	1	4	yes	complemented
404	C₂³×C₅₃	—	2	2	no	—
405	C₂³×C₅₃	—	2	1	no	—
406	C₂³×C₅₃	—	2	1	no	—
407	C₂³×C₅₃	—	2	2	no	—
408	C₂³×C₅₃	—	2	1	no	—
409	C₂³×C₅₃	—	2	1	no	—
410	C₂³×C₅₃	—	2	2	no	—
411	C₂³×C₅₃	—	2	1	no	—
412	C₂³×C₅₃	—	2	1	no	—
413	C₂³×C₅₃	—	2	1	no	—
414	C₂³×C₅₃	—	2	1	no	—
415	C₂³×C₅₃	—	2	2	no	—
416	C₂³×C₅₃	—	2	1	no	—
417	C₂³×C₅₃	—	2	2	no	—
418	C₂³×C₅₃	—	2	1	no	—
419	C₂³×C₅₃	—	2	1	no	—
420	C₂³×C₅₃	—	2	1	no	—
421	C₂³×C₅₃	—	2	2	no	—
422	C₂³×C₅₃	—	2	2	no	—
423	C₂³×C₅₃	—	2	2	no	—
424	C₂³×C₅₃	—	2	2	no	—
425	C₂³×C₅₃	—	2	2	no	—
426	C₂³×C₅₃	—	2	2	no	—
427	C₂³×C₅₃	—	2	2	no	—
428	C₂³×C₅₃	—	2	2	no	—
429	C₂³×C₅₃	C₂×#41	1	2	yes	—
430	C₂³×C₅₃	C₂×#41	1	4	yes	—
431	C₂³×C₅₃	C₂×#41	1	2	yes	—
432	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
433	Q₈×C₅₃	—	2	8	no	—
434	D₄×C₅₃	—	2	8	no	—
435	D₄×C₅₃	—	2	16	no	—
436	D₄×C₅₃	—	2	8	no	—
437	D₄×C₅₃	—	4	8	no	—
438	D₄×C₅₃	—	4	8	no	—
439	D₄×C₅₃	—	4	8	no	—
440	D₄×C₅₃	—	4	8	no	—
441	D₄×C₅₃	—	4	8	no	—
442	D₄×C₅₃	—	4	4	no	—
443	C₂×C₄×C₅₃	—	2	16	no	—
444	C₂×C₄×C₅₃	—	2	1	no	—
445	C₂×C₄×C₅₃	—	2	1	no	—
446	C₂×C₄×C₅₃	—	2	1	no	—
447	C₂×C₄×C₅₃	—	2	1	no	—
448	C₂×C₄×C₅₃	—	2	2	no	—
449	C₂×C₄×C₅₃	—	2	2	no	—
450	C₂×C₄×C₅₃	—	2	2	no	—
451	C₂×C₄×C₅₃	—	2	1	no	—
452	C₂×C₄×C₅₃	—	2	1	no	—
453	C₂×C₄×C₅₃	—	2	1	no	—
454	C₂×C₄×C₅₃	—	2	1	no	—
455	C₂×C₄×C₅₃	—	2	1	no	—
456	C₂×C₄×C₅₃	—	2	1	no	—
457	C₂×C₄×C₅₃	—	2	1	no	—
458	C₂×C₄×C₅₃	—	2	2	no	—
459	C₂×C₄×C₅₃	—	2	1	no	—
460	C₂×C₄×C₅₃	—	2	8	no	—
461	C₂×C₄×C₅₃	—	2	1	no	—
462	C₂×C₄×C₅₃	—	2	1	no	—
463	C₂×C₄×C₅₃	—	2	2	no	—
464	C₂×C₄×C₅₃	—	2	1	no	—
465	C₂×C₄×C₅₃	—	2	1	no	—
466	C₂×C₄×C₅₃	—	2	2	no	—
467	C₂×C₄×C₅₃	—	2	1	no	—
468	C₂×C₄×C₅₃	—	2	1	no	—
469	C₂×C₄×C₅₃	—	2	1	no	—
470	C₂×C₄×C₅₃	—	2	1	no	—
471	C₂×C₄×C₅₃	—	2	2	no	—
472	C₂×C₄×C₅₃	—	2	2	no	—
473	C₂×C₄×C₅₃	—	2	1	no	—
474	C₂×C₄×C₅₃	—	2	2	no	—
475	C₂×C₄×C₅₃	—	2	2	no	—
476	C₂×C₄×C₅₃	—	2	2	no	—
477	C₂×C₄×C₅₃	—	2	1	no	—
478	C₂×C₄×C₅₃	—	2	1	no	—
479	C₂×C₄×C₅₃	—	2	1	no	—
480	C₂×C₄×C₅₃	—	2	2	no	—
481	C₂×C₄×C₅₃	—	2	2	no	—
482	C₂×C₄×C₅₃	—	2	2	no	—
483	C₂×C₄×C₅₃	—	2	2	no	—
484	C₂×C₄×C₅₃	—	2	1	no	—
485	C₂×C₄×C₅₃	—	2	1	no	—
486	C₂×C₄×C₅₃	—	2	2	no	—
487	C₂×C₄×C₅₃	—	2	1	no	—
488	C₂×C₄×C₅₃	—	4	4	no	—
489	C₂×C₄×C₅₃	—	4	8	no	—
490	C₂×C₄×C₅₃	—	4	4	no	—
491	C₂×C₄×C₅₃	—	4	4	no	—
492	C₂×C₄×C₅₃	—	4	4	no	—
493	C₂×C₄×C₅₃	—	4	8	no	—
494	C₂×C₄×C₅₃	—	4	4	no	—
495	C₂×C₄×C₅₃	—	4	8	no	—
496	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
498	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
499	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
502	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
503	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
504	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
505	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
506	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
507	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
508	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
509	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
510	#34727	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
511	C₂²×C₅₃	—	2	4	no	—
512	C₂²×C₅₃	—	2	2	no	—
513	C₂²×C₅₃	—	2	2	no	—
514	C₂²×C₅₃	—	2	2	no	—
515	C₂²×C₅₃	—	2	2	no	—
516	C₂²×C₅₃	—	2	2	no	—
517	C₂²×C₅₃	—	2	4	no	—
518	C₂²×C₅₃	—	2	4	no	—
519	C₂²×C₅₃	—	2	2	no	—
520	C₂²×C₅₃	—	4	1	no	—
521	C₂²×C₅₃	—	4	2	no	—
522	C₂²×C₅₃	—	4	2	no	—
523	C₂²×C₅₃	—	4	1	no	—
524	C₂²×C₅₃	—	4	1	no	—
525	C₂²×C₅₃	—	4	2	no	—
526	C₂²×C₅₃	—	4	1	no	—
527	C₂²×C₅₃	—	4	2	no	—
528	C₂²×C₅₃	—	4	1	no	—
529	C₂²×C₅₃	—	4	1	no	—
530	C₂²×C₅₃	—	4	1	no	—
531	C₂²×C₅₃	—	4	1	no	—
532	C₂²×C₅₃	—	4	2	no	—
533	C₂²×C₅₃	—	4	2	no	—
534	C₂²×C₅₃	—	4	2	no	—
535	C₂²×C₅₃	—	4	2	no	—
536	C₂²×C₅₃	—	4	2	no	—
537	C₂²×C₅₃	—	4	2	no	—
538	C₂²×C₅₃	—	4	2	no	—
539	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
540	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
541	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
542	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
543	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
544	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
545	C₂²×C₅₃	#585	1	1	yes	characteristic
546	C₄×C₅₃	—	2	2	no	—
547	C₄×C₅₃	—	2	4	no	—
548	C₄×C₅₃	—	2	2	no	—
549	C₄×C₅₃	—	2	2	no	—
550	C₄×C₅₃	—	2	2	no	—
551	C₄×C₅₃	—	2	4	no	—
552	C₄×C₅₃	—	2	2	no	—
553	C₄×C₅₃	—	2	2	no	—
554	C₄×C₅₃	—	4	1	no	—
555	C₄×C₅₃	—	4	1	no	—
556	C₄×C₅₃	—	4	2	no	—
557	C₄×C₅₃	—	4	1	no	—
558	C₄×C₅₃	—	4	2	no	—
559	C₄×C₅₃	—	4	1	no	—
560	C₄×C₅₃	—	4	2	no	—
561	C₄×C₅₃	—	4	1	no	—
562	C₄×C₅₃	—	4	2	no	—
563	C₄×C₅₃	#525	1	4	yes	—
564	C₄×C₅₃	#550	1	4	yes	—
565	C₂×#529	C₂×C₅₃	1	1	yes	characteristic, complemented
566	C₂×C₄×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
567	#2479	C₂×C₅₃	1	2	yes	complemented
568	#2471	C₂×C₅₃	1	2	yes	complemented
569	#2467	C₂×C₅₃	1	2	yes	complemented
570	#2456	C₂×C₅₃	1	2	yes	complemented
571	#2454	C₂×C₅₃	1	1	yes	characteristic, complemented
572	#2448	C₂×C₅₃	1	1	yes	characteristic, complemented
573	#2441	C₂×C₅₃	1	1	yes	characteristic, complemented
574	#2431	C₂×C₅₃	1	1	yes	characteristic, complemented
575	#2428	C₂×C₅₃	1	1	yes	characteristic, complemented
576	#2423	C₂×C₅₃	1	1	yes	characteristic, complemented
577	#2414	C₂×C₅₃	1	1	yes	characteristic, complemented
578	#2407	C₂×C₅₃	1	1	yes	characteristic, complemented
579	#2397	C₂×C₅₃	1	2	yes	complemented
580	#2392	C₂×C₅₃	1	2	yes	complemented
581	C₄×#127	C₂×C₅₃	1	1	yes	characteristic, complemented
582	C₄×#121	C₂×C₅₃	1	1	yes	characteristic, complemented
583	C₄×#121	C₂×C₅₃	1	1	yes	characteristic, complemented
584	C₄×#121	C₂×C₅₃	1	2	yes	complemented
585	#2295	C₂×C₅₃	1	1	yes	characteristic, complemented
586	#2290	C₂×C₅₃	1	2	yes	complemented
587	C₄²×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
588	C₂×C₅₃	—	4	2	no	—
589	C₂×C₅₃	—	4	4	no	—
590	C₂×C₅₃	—	4	2	no	—
591	C₂×C₅₃	—	8	2	no	—
592	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
593	C₂×C₅₃	#3444	1	1	yes	characteristic
594	C₂×C₅₃	#3460	1	1	yes	characteristic
595	C₂×C₅₃	C₂×#550	1	1	yes	characteristic
596	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
597	C₂×C₅₃	#3475	1	1	yes	characteristic
598	C₂×C₅₃	#3481	1	1	yes	characteristic
599	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
600	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
601	#529	—	2	8	no	—
602	C₂×#126	C₂²×C₅₃	1	2	yes	—
603	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
604	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
605	C₂×#123	C₂²×C₅₃	1	2	yes	—
606	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
607	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
608	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
609	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
610	C₂×#121	C₂²×C₅₃	1	2	yes	—
611	C₄×#41	—	2	8	no	—
612	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
613	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
614	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
615	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
616	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
617	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
618	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
619	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
620	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
621	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
622	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
623	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
624	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
625	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
626	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
627	C₂×#117	C₂²×C₅₃	1	2	yes	—
628	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
629	C₂×#117	C₂²×C₅₃	1	2	yes	—
630	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
631	C₂²×C₄²	C₂²×C₅₃	1	2	yes	—
632	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
633	#399	C₂²×C₅₃	1	2	yes	—
634	#399	C₂²×C₅₃	1	2	yes	—
635	#399	C₂²×C₅₃	1	2	yes	—
636	#399	C₂²×C₅₃	1	2	yes	—
637	#398	C₂²×C₅₃	1	2	yes	—
638	#397	C₂²×C₅₃	1	2	yes	—
639	#396	C₂²×C₅₃	1	2	yes	—
640	#396	C₂²×C₅₃	1	2	yes	—
641	#394	C₂²×C₅₃	1	2	yes	—
642	#394	C₂²×C₅₃	1	2	yes	—
643	#394	C₂²×C₅₃	1	2	yes	—
644	#392	C₂²×C₅₃	1	2	yes	—
645	#392	C₂²×C₅₃	1	2	yes	—
646	#392	C₂²×C₅₃	1	2	yes	—
647	#392	C₂²×C₅₃	1	2	yes	—
648	#392	C₂²×C₅₃	1	2	yes	—
649	#391	C₂²×C₅₃	1	1	yes	characteristic
650	#391	C₂²×C₅₃	1	1	yes	characteristic
651	#390	C₂²×C₅₃	1	1	yes	characteristic
652	#390	C₂²×C₅₃	1	1	yes	characteristic
653	#390	C₂²×C₅₃	1	2	yes	—
654	#390	C₂²×C₅₃	1	2	yes	—
655	#390	C₂²×C₅₃	1	2	yes	—
656	#390	C₂²×C₅₃	1	1	yes	characteristic
657	#390	C₂²×C₅₃	1	1	yes	characteristic
658	#389	C₂²×C₅₃	1	1	yes	characteristic
659	#389	C₂²×C₅₃	1	1	yes	characteristic
660	#389	C₂²×C₅₃	1	1	yes	characteristic
661	#389	C₂²×C₅₃	1	1	yes	characteristic
662	#389	C₂²×C₅₃	1	2	yes	—
663	#388	C₂²×C₅₃	1	2	yes	—
664	#388	C₂²×C₅₃	1	2	yes	—
665	#388	C₂²×C₅₃	1	2	yes	—
666	#388	C₂²×C₅₃	1	2	yes	—
667	#388	C₂²×C₅₃	1	2	yes	—
668	#388	C₂²×C₅₃	1	2	yes	—
669	#387	C₂²×C₅₃	1	2	yes	—
670	#387	C₂²×C₅₃	1	2	yes	—
671	#387	C₂²×C₅₃	1	2	yes	—
672	#387	C₂²×C₅₃	1	2	yes	—
673	#386	C₂²×C₅₃	1	2	yes	—
674	#386	C₂²×C₅₃	1	2	yes	—
675	#386	C₂²×C₅₃	1	2	yes	—
676	#386	C₂²×C₅₃	1	2	yes	—
677	#386	C₂²×C₅₃	1	2	yes	—
678	#386	C₂²×C₅₃	1	2	yes	—
679	#385	C₂²×C₅₃	1	2	yes	—
680	#385	C₂²×C₅₃	1	2	yes	—
681	#384	C₂²×C₅₃	1	1	yes	characteristic
682	#380	C₂²×C₅₃	1	1	yes	characteristic
683	#380	C₂²×C₅₃	1	1	yes	characteristic
684	#380	C₂²×C₅₃	1	2	yes	—
685	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
686	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
687	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
688	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
689	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
690	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
691	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
692	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
693	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
694	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
695	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
696	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
697	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
698	#376	C₂²×C₅₃	1	2	yes	—
699	C₄³	C₂²×C₅₃	1	1	yes	characteristic
700	C₅₃	#34727	1	1	yes	characteristic, direct product factor, Sylow
701	C₂×#41	—	2	4	no	—
702	C₂×#41	—	2	4	no	—
703	C₂×#41	—	2	4	no	—
704	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
705	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
706	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
707	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
708	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
709	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
710	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
711	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
712	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
713	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
714	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
715	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
716	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
717	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
718	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
719	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
720	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
721	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
722	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
723	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
724	#127	—	2	4	no	—
725	#126	—	2	8	no	—
726	#125	—	2	4	no	—
727	#124	—	2	4	no	—
728	#123	—	2	8	no	—
729	C₂²⋊Q₈	—	2	4	no	—
730	#121	—	2	4	no	—
731	#121	—	2	4	no	—
732	#121	—	2	4	no	—
733	#121	—	2	8	no	—
734	C₄×Q₈	—	2	4	no	—
735	C₄×Q₈	D₄×C₅₃	1	8	yes	complemented
736	C₄×D₄	—	2	4	no	—
737	C₄×D₄	—	2	4	no	—
738	C₄×D₄	—	2	8	no	—
739	C₄×D₄	—	2	4	no	—
740	C₄×D₄	—	2	4	no	—
741	C₄×D₄	—	2	8	no	—
742	C₄×D₄	—	2	4	no	—
743	C₄×D₄	—	2	8	no	—
744	C₄×D₄	—	2	4	no	—
745	C₄×D₄	—	2	8	no	—
746	C₄×D₄	—	4	4	no	—
747	C₄×D₄	—	4	4	no	—
748	C₄×D₄	—	4	4	no	—
749	#117	—	2	4	no	—
750	#117	—	2	8	no	—
751	#117	—	2	8	no	—
752	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
753	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
754	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
755	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
756	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
757	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
758	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
759	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
760	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
761	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
762	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
763	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
764	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
765	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
766	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
767	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
768	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
769	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
770	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
780	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
781	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
782	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
783	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
784	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
785	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
789	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
791	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
792	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
794	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
795	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
796	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
797	C₂×C₄²	—	2	4	no	—
798	C₂×C₄²	—	2	8	no	—
799	C₂×C₄²	—	2	4	no	—
800	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
801	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
802	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
803	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
804	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
805	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
806	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
807	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
808	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
809	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
810	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
811	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
812	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
813	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
814	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
815	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
816	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
817	#95	C₂³×C₅₃	1	2	yes	—
818	#95	C₂³×C₅₃	1	2	yes	—
819	#95	C₂³×C₅₃	1	2	yes	—
820	#95	C₂³×C₅₃	1	2	yes	—
821	#95	C₂³×C₅₃	1	1	yes	characteristic
822	#95	C₂³×C₅₃	1	1	yes	characteristic
823	#95	C₂³×C₅₃	1	1	yes	characteristic
824	#95	C₂³×C₅₃	1	1	yes	characteristic
825	#95	C₂³×C₅₃	1	1	yes	characteristic
826	#95	C₂³×C₅₃	1	1	yes	characteristic
827	#95	C₂³×C₅₃	1	2	yes	—
828	#95	C₂³×C₅₃	1	2	yes	—
829	#95	C₂³×C₅₃	1	2	yes	—
830	#95	C₂³×C₅₃	1	2	yes	—
831	#95	C₂³×C₅₃	1	2	yes	—
832	#95	C₂³×C₅₃	1	2	yes	—
833	#95	C₂³×C₅₃	1	2	yes	—
834	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
835	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
836	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
837	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
838	#41	—	2	32	no	—
839	C₂×Q₈	—	2	2	no	—
840	C₂×Q₈	—	2	2	no	—
841	C₂×Q₈	C₂×D₄×C₅₃	1	4	yes	—
842	C₂×D₄	—	2	2	no	—
843	C₂×D₄	—	2	2	no	—
844	C₂×D₄	—	2	4	no	—
845	C₂×D₄	—	2	4	no	—
846	C₂×D₄	—	2	4	no	—
847	C₂×D₄	—	2	4	no	—
848	C₂×D₄	—	2	4	no	—
849	C₂×D₄	—	2	4	no	—
850	C₂×D₄	—	2	4	no	—
851	C₂×D₄	—	2	4	no	—
852	C₂×D₄	—	2	4	no	—
853	C₂×D₄	—	2	2	no	—
854	C₂×D₄	—	2	4	no	—
855	C₂×D₄	—	2	2	no	—
856	C₂×D₄	—	2	2	no	—
857	C₂×D₄	—	2	2	no	—
858	C₂×D₄	—	2	4	no	—
859	C₂×D₄	—	2	4	no	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	2	2	no	—
862	C₂×D₄	—	4	2	no	—
863	C₂×D₄	—	4	2	no	—
864	C₂×D₄	—	4	2	no	—
865	C₂×D₄	—	4	2	no	—
866	C₂×D₄	—	4	2	no	—
867	C₂×D₄	—	4	2	no	—
868	C₂×D₄	#41×C₅₃	1	4	yes	—
869	C₂²×C₄	—	2	4	no	—
870	C₂²×C₄	—	2	4	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	4	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	2	2	no	—
875	C₂²×C₄	—	2	2	no	—
876	C₂²×C₄	—	2	4	no	—
877	C₂²×C₄	—	2	2	no	—
878	C₂²×C₄	—	2	4	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	4	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	4	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	4	no	—
889	C₂²×C₄	—	2	4	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	4	no	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	4	no	—
895	C₂²×C₄	—	4	1	no	—
896	C₂²×C₄	—	4	1	no	—
897	C₂²×C₄	—	4	2	no	—
898	C₂²×C₄	#41×C₅₃	1	4	yes	—
899	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
900	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
901	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
902	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
903	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
904	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
905	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
906	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
907	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
908	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
911	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
913	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
914	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
915	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
916	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
917	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
918	C₄⋊C₄	—	2	4	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	4	no	—
921	C₄⋊C₄	—	2	4	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	4	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	4	no	—
928	C₄⋊C₄	—	2	4	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	4	2	no	—
932	C₄⋊C₄	—	4	2	no	—
933	C₄⋊C₄	—	4	2	no	—
934	C₄⋊C₄	—	4	2	no	—
935	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
936	C₄⋊C₄	C₂×D₄×C₅₃	1	8	yes	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	4	no	—
939	C₂²⋊C₄	—	2	4	no	—
940	C₂²⋊C₄	—	2	4	no	—
941	C₂²⋊C₄	—	2	4	no	—
942	C₂²⋊C₄	—	2	4	no	—
943	C₂²⋊C₄	—	2	4	no	—
944	C₂²⋊C₄	—	2	4	no	—
945	C₂²⋊C₄	—	2	4	no	—
946	C₂²⋊C₄	—	2	4	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	4	no	—
950	C₂²⋊C₄	—	2	4	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	4	no	—
954	C₂²⋊C₄	—	2	4	no	—
955	C₂²⋊C₄	—	4	2	no	—
956	C₂²⋊C₄	—	4	2	no	—
957	C₂²⋊C₄	—	4	2	no	—
958	C₂²⋊C₄	—	4	2	no	—
959	C₂²⋊C₄	—	4	2	no	—
960	C₂²⋊C₄	—	4	2	no	—
961	C₂²⋊C₄	—	4	2	no	—
962	C₂²⋊C₄	#41×C₅₃	1	4	yes	complemented
963	C₄²	—	2	2	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	4	no	—
966	C₄²	—	2	2	no	—
967	C₄²	—	2	4	no	—
968	C₄²	—	2	2	no	—
969	C₄²	—	2	2	no	—
970	C₄²	—	2	2	no	—
971	C₄²	—	2	2	no	—
972	C₄²	—	2	2	no	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	4	no	—
976	C₄²	—	4	1	no	—
977	C₄²	C₂×D₄×C₅₃	1	4	yes	—
978	C₄²	C₂×D₄×C₅₃	1	8	yes	—
979	C₄²	#41×C₅₃	1	4	yes	complemented
980	C₂³	—	2	1	no	—
981	C₂³	—	2	2	no	—
982	C₂³	—	2	1	no	—
983	C₂³	—	2	2	no	—
984	C₂³	—	2	1	no	—
985	C₂³	—	2	1	no	—
986	C₂³	—	2	1	no	—
987	C₂³	—	2	1	no	—
988	C₂³	—	2	2	no	—
989	C₂³	—	2	1	no	—
990	C₂³	—	2	2	no	—
991	C₂³	—	2	1	no	—
992	C₂³	—	2	1	no	—
993	C₂³	—	2	2	no	—
994	C₂³	—	2	1	no	—
995	C₂³	—	2	2	no	—
996	C₂³	—	2	1	no	—
997	C₂³	—	2	1	no	—
998	C₂³	—	2	2	no	—
999	C₂³	—	2	2	no	—
1000	C₂³	—	2	2	no	—
1001	C₂³	—	2	2	no	—
1002	C₂³	—	2	2	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	2	2	no	—
1005	C₂³	C₂×#41×C₅₃	1	4	yes	—
1006	C₂³	C₂×#41×C₅₃	1	2	yes	—
1007	C₂³	C₂×#41×C₅₃	1	2	yes	—
1008	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1009	Q₈	—	2	8	no	—
1010	D₄	—	2	8	no	—
1011	D₄	—	2	16	no	—
1012	D₄	—	2	8	no	—
1013	D₄	—	4	8	no	—
1014	D₄	—	4	8	no	—
1015	D₄	—	4	8	no	—
1016	D₄	—	4	8	no	—
1017	D₄	—	4	8	no	—
1018	D₄	—	4	4	no	—
1019	C₂×C₄	—	2	16	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	8	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	4	4	no	—
1065	C₂×C₄	—	4	8	no	—
1066	C₂×C₄	—	4	4	no	—
1067	C₂×C₄	—	4	4	no	—
1068	C₂×C₄	—	4	4	no	—
1069	C₂×C₄	—	4	8	no	—
1070	C₂×C₄	—	4	4	no	—
1071	C₂×C₄	—	4	8	no	—
1072	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1073	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
1074	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
1075	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1076	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1077	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1078	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1079	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1080	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1081	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1082	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1083	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1084	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1085	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	4	no	—
1089	C₂²	—	2	4	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	4	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	2	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	2	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	4	1	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	1	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	—	4	2	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	2	no	—
1110	C₂²	—	4	2	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1115	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1116	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1117	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1118	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1119	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1120	C₂²	C₅₃×#585	1	1	yes	characteristic
1121	C₄	—	2	2	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	4	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	2	4	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	2	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	2	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	2	no	—
1137	C₄	—	4	1	no	—
1138	C₄	C₅₃×#525	1	4	yes	—
1139	C₄	C₅₃×#550	1	4	yes	—
1140	C₂	—	4	2	no	—
1141	C₂	—	4	2	no	—
1142	C₂	—	4	4	no	—
1143	C₂	—	8	2	no	—
1144	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
1145	C₂	C₅₃×#3444	1	1	yes	characteristic
1146	C₂	C₅₃×#3460	1	1	yes	characteristic
1147	C₂	C₂×C₅₃×#550	1	1	yes	characteristic
1148	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
1149	C₂	C₅₃×#3475	1	1	yes	characteristic
1150	C₂	C₅₃×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
socle	C₂³×C₅₃	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#529	C₂	semidirect
2. C₂×C₄×#41×C₅₃	C₂	semidirect
3. C₅₃×#2479	C₂	semidirect
4. C₅₃×#2471	C₂	semidirect
5. C₅₃×#2467	C₂	semidirect
6. C₅₃×#2456	C₂	semidirect
7. C₅₃×#2454	C₂	semidirect
8. C₅₃×#2448	C₂	semidirect
9. C₅₃×#2441	C₂	semidirect
10. C₅₃×#2431	C₂	semidirect
11. C₅₃×#2428	C₂	semidirect
12. C₅₃×#2423	C₂	semidirect
13. C₅₃×#2414	C₂	semidirect
14. C₅₃×#2407	C₂	semidirect
15. C₅₃×#2397	C₂	semidirect
16. C₅₃×#2392	C₂	semidirect
17. C₄×#127×C₅₃	C₂	semidirect
18. C₄×#121×C₅₃	C₂	semidirect
19. C₄×#121×C₅₃	C₂	semidirect
20. C₄×#121×C₅₃	C₂	semidirect
21. C₅₃×#2295	C₂	semidirect
22. C₅₃×#2290	C₂	semidirect
23. C₄²×D₄×C₅₃	C₂	semidirect
159. C₄×Q₈×C₅₃	D₄	semidirect
386. C₂²⋊C₄×C₅₃	#41	semidirect
403. C₄²×C₅₃	#41	semidirect
510. #34727	C₅₃	direct (N × H)
565. C₂×#529	C₂×C₅₃	semidirect
566. C₂×C₄×#41	C₂×C₅₃	semidirect
567. #2479	C₂×C₅₃	semidirect
568. #2471	C₂×C₅₃	semidirect
569. #2467	C₂×C₅₃	semidirect
570. #2456	C₂×C₅₃	semidirect
571. #2454	C₂×C₅₃	semidirect
572. #2448	C₂×C₅₃	semidirect
573. #2441	C₂×C₅₃	semidirect
574. #2431	C₂×C₅₃	semidirect
575. #2428	C₂×C₅₃	semidirect
576. #2423	C₂×C₅₃	semidirect
577. #2414	C₂×C₅₃	semidirect
578. #2407	C₂×C₅₃	semidirect
579. #2397	C₂×C₅₃	semidirect
580. #2392	C₂×C₅₃	semidirect
581. C₄×#127	C₂×C₅₃	semidirect
582. C₄×#121	C₂×C₅₃	semidirect
583. C₄×#121	C₂×C₅₃	semidirect
584. C₄×#121	C₂×C₅₃	semidirect
585. #2295	C₂×C₅₃	semidirect
586. #2290	C₂×C₅₃	semidirect
587. C₄²×D₄	C₂×C₅₃	semidirect
700. C₅₃	#34727	direct (N × H)
735. C₄×Q₈	D₄×C₅₃	semidirect
962. C₂²⋊C₄	#41×C₅₃	semidirect
979. C₄²	#41×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×#529	2
C₂×C₄×#41×C₅₃	2
C₅₃×#2479	2
C₅₃×#2471	2
C₅₃×#2467	2
C₅₃×#2456	2
C₅₃×#2454	2
C₅₃×#2448	2
C₅₃×#2441	2
C₅₃×#2431	2
C₅₃×#2428	2
C₅₃×#2423	2
C₅₃×#2414	2
C₅₃×#2407	2
C₅₃×#2397	2
C₅₃×#2392	2
C₄×#127×C₅₃	2
C₄×#121×C₅₃	2
C₅₃×#2295	2
C₅₃×#2290	2
C₄²×D₄×C₅₃	2
#34727	53

Subgroups — C53×#34727 #27242239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34727 #27242239