Subgroups — #28292970

Order 13568.

8650 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289047	C₂	1	8	yes	maximal, complemented
2	#20289042	C₂	1	8	yes	maximal, complemented
3	#20289040	C₂	1	8	yes	maximal, complemented
4	#20288590	C₂	1	2	yes	maximal, complemented
5	#20288586	C₂	1	2	yes	maximal, complemented
6	#20288583	C₂	1	8	yes	maximal, complemented
7	#20288490	C₂	1	2	yes	maximal, complemented
8	#20288489	C₂	1	2	yes	maximal, complemented
9	#20288487	C₂	1	8	yes	maximal, complemented
10	#20288350	C₂	1	1	yes	maximal, characteristic, complemented
11	#20288348	C₂	1	2	yes	maximal, complemented
12	#20288344	C₂	1	8	yes	maximal, complemented
13	#20288007	C₂	1	2	yes	maximal, complemented
14	C₂²×#13133213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3484	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13133263	C₂²	1	2	yes	complemented
17	C₂×#13133262	C₂²	1	8	yes	complemented
18	C₂×#13133262	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
21	#16811363	C₂²	1	8	yes	complemented
22	#16811362	C₂²	1	8	yes	complemented
23	#16811361	C₂²	1	16	yes	complemented
24	#16811357	C₂²	1	8	yes	complemented
25	#16811356	C₂²	1	8	yes	complemented
26	#16811355	C₂²	1	8	yes	complemented
27	#16811294	C₂²	1	8	yes	complemented
28	#16811293	C₂²	1	8	yes	complemented
29	#16811292	C₂²	1	8	yes	complemented
30	#16811291	C₂²	1	8	yes	complemented
31	#16811291	C₂²	1	16	yes	complemented
32	#16811269	C₂²	1	8	yes	complemented
33	#16811267	C₂²	1	8	yes	complemented
34	#16811264	C₂²	1	8	yes	complemented
35	#16811263	C₂²	1	16	yes	complemented
36	#16811263	C₂²	1	16	yes	complemented
37	#16811260	C₂²	1	16	yes	complemented
38	#16811260	C₂²	1	16	yes	complemented
39	D₄×D₂₁₂	C₂²	1	8	yes	complemented
40	#16811257	C₂²	1	8	yes	complemented
41	#16811257	C₂²	1	8	yes	complemented
42	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
43	D₄×C₂²⋊D₅₃	C₂²	1	16	yes	complemented
44	D₄×C₂²⋊D₅₃	C₂²	1	16	yes	complemented
45	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
46	#16811255	C₂²	1	16	yes	complemented
47	#16811255	C₂²	1	16	yes	complemented
48	#16811255	C₂²	1	8	yes	complemented
49	#16811226	C₂²	1	8	yes	complemented
50	#16811225	C₂²	1	16	yes	complemented
51	#16811224	C₂²	1	8	yes	complemented
52	#16811223	C₂²	1	16	yes	complemented
53	#16811192	C₂²	1	2	yes	complemented
54	#16811191	C₂²	1	4	yes	complemented
55	#16811190	C₂²	1	2	yes	complemented
56	#16811190	C₂²	1	4	yes	complemented
57	#16811189	C₂²	1	16	yes	complemented
58	#16811188	C₂²	1	16	yes	complemented
59	#16811188	C₂²	1	16	yes	complemented
60	#16811187	C₂²	1	2	yes	complemented
61	#16811187	C₂²	1	4	yes	complemented
62	#16811186	C₂²	1	4	yes	complemented
63	#16811185	C₂²	1	8	yes	complemented
64	#16811184	C₂²	1	8	yes	complemented
65	#16811183	C₂²	1	16	yes	complemented
66	#16811182	C₂²	1	8	yes	complemented
67	#16811182	C₂²	1	4	yes	complemented
68	#16811176	C₂²	1	2	yes	complemented
69	#16811175	C₂²	1	4	yes	complemented
70	#16811172	C₂²	1	4	yes	complemented
71	#16811170	C₂²	1	8	yes	complemented
72	#16811169	C₂²	1	2	yes	complemented
73	#16811169	C₂²	1	4	yes	complemented
74	#16811168	C₂²	1	4	yes	complemented
75	#16811168	C₂²	1	8	yes	complemented
76	C₂×#13133213	C₂²	1	8	yes	complemented
77	C₂×#13133213	C₂²	1	4	yes	complemented
78	C₂×#13133213	C₂²	1	8	yes	complemented
79	C₂×#13133213	C₂²	1	2	yes	complemented
80	C₂×#13133213	C₂²	1	2	yes	complemented
81	C₂×#13133213	C₂²	1	4	yes	complemented
82	#127×D₅₃	C₂²	1	4	yes	complemented
83	#16811159	C₂²	1	4	yes	complemented
84	#16811154	C₂²	1	4	yes	complemented
85	#16811153	C₂²	1	8	yes	complemented
86	#16811150	C₂²	1	8	yes	complemented
87	#16811134	C₂²	1	2	yes	complemented
88	#16811129	C₂²	1	8	yes	complemented
89	C₂×#13133186	C₂²	1	4	yes	complemented
90	#120×D₅₃	C₂²	1	8	yes	complemented
91	#16811098	C₂²	1	1	yes	characteristic, complemented
92	#16811097	C₂²	1	2	yes	complemented
93	#16811096	C₂²	1	8	yes	complemented
94	#41×Dic₅₃	C₂²	1	2	yes	complemented
95	#16811091	C₂²	1	2	yes	complemented
96	C₄×#11719947	C₂²	1	8	yes	complemented
97	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
98	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic, complemented
99	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#546	C₂²	1	8	yes	complemented
101	D₄²×C₅₃	C₂²	1	8	yes	complemented
102	C₅₃×#535	C₂²	1	2	yes	complemented
103	C₅₃×#534	C₂²	1	4	yes	complemented
104	C₅₃×#525	C₂²	1	2	yes	complemented
105	C₂×#120×C₅₃	C₂²	1	4	yes	complemented
106	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
107	C₂⁴×D₅₃	C₂³	1	2	yes	—
108	#13133263	—	4	8	no	—
109	#13133262	—	4	4	no	—
110	#13133262	—	4	32	no	—
111	C₂×#11719949	C₂³	1	4	yes	complemented
112	C₂×#11719945	C₂³	1	2	yes	—
113	C₂×#11719945	C₂³	1	4	yes	complemented
114	C₂×#11719945	C₂³	1	16	yes	complemented
115	C₂×#11719947	C₂³	1	8	yes	—
116	C₂×#11719947	C₂³	1	4	yes	complemented
117	C₂×#11719947	C₂³	1	16	yes	complemented
118	C₂²×D₂₁₂	—	4	4	no	—
119	C₂²×D₂₁₂	C₂³	1	2	yes	—
120	C₂²×D₂₁₂	C₂³	1	8	yes	—
121	C₂²×D₂₁₂	C₂³	1	2	yes	—
122	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
123	C₂²×C₂²⋊D₅₃	—	4	16	no	—
124	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
125	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
126	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
127	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
128	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
129	C₂²×C₂²⋊D₅₃	C₂³	1	16	yes	—
130	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
131	C₂²×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
132	C₂×D₄×D₅₃	C₂³	1	16	yes	—
133	C₂×D₄×D₅₃	C₂³	1	8	yes	—
134	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
135	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
136	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
137	C₂³×Dic₅₃	C₂³	1	2	yes	—
138	#13133216	C₂³	1	4	yes	complemented
139	#13133215	C₂³	1	2	yes	complemented
140	#13133214	C₂³	1	4	yes	complemented
141	#13133213	C₂³	1	8	yes	—
142	#13133213	C₂³	1	8	yes	—
143	#13133213	C₂³	1	8	yes	—
144	#13133213	C₂³	1	8	yes	—
145	#13133213	C₂³	1	4	yes	—
146	#13133213	C₂³	1	4	yes	—
147	#13133213	C₂³	1	4	yes	—
148	#13133213	C₂³	1	4	yes	—
149	#13133213	C₂³	1	16	yes	—
150	#13133213	C₂³	1	16	yes	complemented
151	#13133213	C₂³	1	16	yes	complemented
152	#13133213	C₂³	1	4	yes	complemented
153	#13133213	C₂³	1	4	yes	complemented
154	#13133213	C₂³	1	2	yes	complemented
155	#13133212	C₂³	1	8	yes	complemented
156	#13133210	C₂³	1	8	yes	complemented
157	#13133208	C₂³	1	4	yes	complemented
158	#13133207	C₂³	1	8	yes	complemented
159	#13133206	C₂³	1	4	yes	complemented
160	#13133206	C₂³	1	2	yes	complemented
161	#13133205	C₂³	1	4	yes	complemented
162	#13133204	C₂³	1	4	yes	complemented
163	#13133204	C₂³	1	2	yes	complemented
164	#13133203	C₂³	1	16	yes	complemented
165	#13133203	C₂³	1	16	yes	complemented
166	#13133203	C₂³	1	8	yes	complemented
167	#13133202	C₂³	1	16	yes	complemented
168	#13133201	C₂³	1	8	yes	—
169	#13133201	C₂³	1	16	yes	complemented
170	#13133200	C₂³	1	4	yes	—
171	#13133200	C₂³	1	16	yes	complemented
172	#13133199	C₂³	1	16	yes	complemented
173	#13133199	C₂³	1	16	yes	complemented
174	#13133198	C₂³	1	8	yes	—
175	#13133198	C₂³	1	8	yes	complemented
176	#13133196	C₂³	1	4	yes	—
177	#13133194	C₂³	1	8	yes	—
178	#13133194	C₂³	1	8	yes	—
179	#13133192	C₂³	1	16	yes	complemented
180	#13133192	C₂³	1	8	yes	complemented
181	#13133191	C₂³	1	4	yes	—
182	#13133191	C₂³	1	8	yes	complemented
183	#13133191	C₂³	1	16	yes	complemented
184	#13133191	C₂³	1	16	yes	complemented
185	#13133190	C₂³	1	16	yes	complemented
186	#13133190	C₂³	1	16	yes	complemented
187	#13133190	C₂³	1	16	yes	complemented
188	#13133190	C₂³	1	16	yes	complemented
189	#13133190	C₂³	1	16	yes	complemented
190	#13133189	C₂³	1	8	yes	—
191	#13133189	C₂³	1	8	yes	—
192	#13133189	C₂³	1	16	yes	complemented
193	#13133189	C₂³	1	16	yes	complemented
194	#13133189	C₂³	1	16	yes	complemented
195	#13133189	C₂³	1	16	yes	complemented
196	#13133189	C₂³	1	16	yes	complemented
197	#13133188	C₂³	1	8	yes	complemented
198	#13133188	C₂³	1	16	yes	complemented
199	#13133188	C₂³	1	16	yes	complemented
200	#13133187	C₂³	1	16	yes	—
201	#13133187	C₂³	1	8	yes	—
202	#13133187	C₂³	1	16	yes	complemented
203	#13133187	C₂³	1	16	yes	complemented
204	#13133186	C₂³	1	16	yes	—
205	#13133186	C₂³	1	4	yes	—
206	#13133186	C₂³	1	8	yes	—
207	#13133186	C₂³	1	16	yes	complemented
208	#13133185	C₂³	1	16	yes	—
209	#13133185	C₂³	1	8	yes	—
210	#13133185	C₂³	1	16	yes	complemented
211	#13133185	C₂³	1	16	yes	complemented
212	#13133185	C₂³	1	8	yes	complemented
213	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
214	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
215	#13133182	C₂³	1	8	yes	complemented
216	#13133182	C₂³	1	4	yes	complemented
217	C₄×D₂₁₂	C₂³	1	8	yes	complemented
218	D₄×Dic₅₃	C₂³	1	8	yes	—
219	D₄×Dic₅₃	C₂³	1	8	yes	—
220	D₄×Dic₅₃	C₂³	1	8	yes	complemented
221	D₄×Dic₅₃	C₂³	1	4	yes	complemented
222	#13133179	C₂³	1	8	yes	complemented
223	#13133179	C₂³	1	4	yes	complemented
224	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
225	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
226	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
227	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
228	#13133177	C₂³	1	8	yes	—
229	#13133177	C₂³	1	8	yes	—
230	#13133177	C₂³	1	8	yes	complemented
231	#13133177	C₂³	1	16	yes	complemented
232	#13133177	C₂³	1	16	yes	complemented
233	#13133176	C₂³	1	2	yes	—
234	#13133176	C₂³	1	4	yes	complemented
235	#13133175	C₂³	1	8	yes	complemented
236	#13133174	C₂³	1	4	yes	complemented
237	#13133173	C₂³	1	8	yes	—
238	#13133173	C₂³	1	8	yes	complemented
239	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	—
240	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
241	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
242	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
243	C₂×C₄×Dic₅₃	C₂³	1	4	yes	—
244	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
245	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
246	C₂×C₄×Dic₅₃	C₂³	1	4	yes	—
247	C₂×C₄×Dic₅₃	C₂³	1	4	yes	complemented
248	C₄²×D₅₃	C₂³	1	4	yes	complemented
249	C₂⁵×C₅₃	C₂³	1	2	yes	—
250	H(5,𝔽₂)×C₅₃	—	4	4	no	—
251	C₂×#41×C₅₃	C₂³	1	2	yes	—
252	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
253	C₂²×D₄×C₅₃	—	4	4	no	—
254	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂²×D₄×C₅₃	C₂³	1	8	yes	—
257	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
258	C₂²×D₄×C₅₃	C₂³	1	8	yes	—
259	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
260	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
261	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
262	#127×C₅₃	C₂³	1	4	yes	complemented
263	#124×C₅₃	C₂³	1	4	yes	complemented
264	#123×C₅₃	C₂³	1	4	yes	—
265	#123×C₅₃	C₂³	1	8	yes	complemented
266	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
267	#121×C₅₃	C₂³	1	4	yes	—
268	#121×C₅₃	C₂³	1	16	yes	complemented
269	#121×C₅₃	C₂³	1	8	yes	complemented
270	#120×C₅₃	C₂³	1	4	yes	—
271	#120×C₅₃	C₂³	1	8	yes	—
272	#120×C₅₃	C₂³	1	16	yes	—
273	#120×C₅₃	C₂³	1	8	yes	complemented
274	C₄×D₄×C₅₃	C₂³	1	8	yes	—
275	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
276	#117×C₅₃	C₂³	1	2	yes	—
277	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
278	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
279	C₂⁴×C₅₃	—	4	4	no	—
280	C₂⁴×C₅₃	—	4	8	no	—
281	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
282	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
283	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
284	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
285	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
286	C₂³×D₅₃	—	4	8	no	—
287	C₂³×D₅₃	—	4	4	no	—
288	C₂³×D₅₃	C₂⁴	1	4	yes	—
289	C₂³×D₅₃	C₂⁴	1	8	yes	—
290	C₂³×D₅₃	C₂⁴	1	8	yes	—
291	C₂³×D₅₃	C₂⁴	1	4	yes	—
292	#41×C₅₃	—	2	8	no	—
293	#41×C₅₃	—	4	8	no	—
294	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
295	C₂×D₄×C₅₃	—	2	4	no	—
296	C₂×D₄×C₅₃	—	2	4	no	—
297	C₂×D₄×C₅₃	—	4	16	no	—
298	C₂×D₄×C₅₃	—	4	8	no	—
299	C₂×D₄×C₅₃	—	4	4	no	—
300	C₂×D₄×C₅₃	—	4	8	no	—
301	C₂×D₄×C₅₃	—	4	16	no	—
302	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
303	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
304	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
305	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
306	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
307	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
308	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
309	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
310	C₂²×C₄×C₅₃	—	2	4	no	—
311	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
312	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
313	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
315	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
316	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
317	C₂×C₂²⋊D₅₃	—	2	32	no	—
318	C₂×C₂²⋊D₅₃	—	4	16	no	—
319	C₂×C₂²⋊D₅₃	—	4	32	no	—
320	C₂×C₂²⋊D₅₃	—	4	16	no	—
321	C₂×C₂²⋊D₅₃	—	4	32	no	—
322	C₂×C₂²⋊D₅₃	—	4	16	no	—
323	C₂×C₂²⋊D₅₃	—	4	8	no	—
324	C₂×C₂²⋊D₅₃	—	4	16	no	—
325	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
326	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
327	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
328	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
329	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
330	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
331	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
332	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
333	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
334	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
335	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
336	C₂²×Dic₅₃	—	2	8	no	—
337	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
338	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
339	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
340	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
341	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
342	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
343	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
344	#11719949	—	4	8	no	—
345	#11719947	—	2	32	no	—
346	#11719947	—	4	8	no	—
347	#11719947	—	4	32	no	—
348	D₄×D₅₃	—	4	8	no	—
349	D₄×D₅₃	—	4	8	no	—
350	D₄×D₅₃	—	4	32	no	—
351	D₄×D₅₃	—	4	32	no	—
352	D₄×D₅₃	—	4	16	no	—
353	#11719945	—	2	8	no	—
354	#11719945	—	4	32	no	—
355	#11719945	—	4	8	no	—
356	C₂×D₂₁₂	—	2	8	no	—
357	C₂×D₂₁₂	—	4	16	no	—
358	C₂×D₂₁₂	—	4	8	no	—
359	C₂×D₂₁₂	—	4	4	no	—
360	C₂×D₂₁₂	C₂⁴	1	2	yes	—
361	C₂×D₂₁₂	C₂⁴	1	4	yes	—
362	C₂×D₂₁₂	C₂⁴	1	4	yes	—
363	C₂×D₂₁₂	C₂⁴	1	16	yes	—
364	C₂×D₂₁₂	C₂⁴	1	8	yes	—
365	C₂×D₂₁₂	C₂⁴	1	8	yes	—
366	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
367	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
368	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
369	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
370	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
371	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
372	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
373	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
374	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
375	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
376	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
377	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
378	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
379	C₄²×C₅₃	C₂⁴	1	4	yes	—
380	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
381	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
382	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
383	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
384	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
385	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
386	#11719921	C₂⁴	1	16	yes	—
387	#11719921	C₂⁴	1	16	yes	—
388	#11719921	C₂⁴	1	16	yes	—
389	#11719921	C₂⁴	1	8	yes	—
390	#11719921	C₂⁴	1	8	yes	—
391	#11719921	C₂⁴	1	8	yes	—
392	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
393	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
394	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
395	#11719919	C₂⁴	1	8	yes	—
396	#11719919	C₂⁴	1	8	yes	—
397	#11719919	C₂⁴	1	8	yes	—
398	#11719919	C₂⁴	1	8	yes	—
399	#11719919	C₂⁴	1	8	yes	—
400	C₄×Dic₅₃	C₂⁴	1	2	yes	—
401	C₄×Dic₅₃	C₂⁴	1	8	yes	—
402	C₄×Dic₅₃	C₂⁴	1	4	yes	—
403	C₄×Dic₅₃	C₂⁴	1	2	yes	—
404	C₄×Dic₅₃	C₂⁴	1	2	yes	—
405	C₄×Dic₅₃	C₂⁴	1	4	yes	—
406	C₄×Dic₅₃	C₂⁴	1	2	yes	—
407	C₄×Dic₅₃	C₂⁴	1	8	yes	—
408	C₄×Dic₅₃	C₂⁴	1	4	yes	—
409	C₂³×C₅₃	—	2	4	no	—
410	C₂³×C₅₃	—	2	2	no	—
411	C₂³×C₅₃	—	2	16	no	—
412	C₂³×C₅₃	—	2	4	no	—
413	C₂³×C₅₃	—	2	4	no	—
414	C₂³×C₅₃	—	4	4	no	—
415	C₂³×C₅₃	—	4	8	no	—
416	C₂³×C₅₃	—	4	4	no	—
417	C₂³×C₅₃	—	4	8	no	—
418	C₂³×C₅₃	—	4	8	no	—
419	C₂³×C₅₃	—	4	4	no	—
420	C₂³×C₅₃	—	8	16	no	—
421	C₂³×C₅₃	C₂⁵	1	4	yes	—
422	C₂³×C₅₃	C₂⁵	1	4	yes	—
423	C₂³×C₅₃	C₂⁵	1	4	yes	—
424	C₂³×C₅₃	C₂⁵	1	2	yes	—
425	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
426	C₂²×D₅₃	—	2	8	no	—
427	C₂²×D₅₃	—	2	16	no	—
428	C₂²×D₅₃	—	4	8	no	—
429	C₂²×D₅₃	—	4	8	no	—
430	C₂²×D₅₃	—	4	8	no	—
431	C₂²×D₅₃	—	4	8	no	—
432	C₂²×D₅₃	—	4	4	no	—
433	C₂²×D₅₃	—	4	8	no	—
434	C₂²×D₅₃	—	4	16	no	—
435	C₂²×D₅₃	—	8	16	no	—
436	C₂²×D₅₃	C₂⁵	1	4	yes	—
437	C₂²×D₅₃	C₂⁵	1	8	yes	—
438	Q₈×C₅₃	—	2	4	no	—
439	D₄×C₅₃	—	2	16	no	—
440	D₄×C₅₃	—	2	8	no	—
441	D₄×C₅₃	—	2	4	no	—
442	D₄×C₅₃	—	2	8	no	—
443	D₄×C₅₃	—	2	8	no	—
444	D₄×C₅₃	—	4	16	no	—
445	D₄×C₅₃	—	4	8	no	—
446	D₄×C₅₃	—	4	8	no	—
447	C₂×C₄×C₅₃	—	2	2	no	—
448	C₂×C₄×C₅₃	—	2	8	no	—
449	C₂×C₄×C₅₃	—	2	8	no	—
450	C₂×C₄×C₅₃	—	4	8	no	—
451	C₂×C₄×C₅₃	—	4	4	no	—
452	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	complemented
453	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
454	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
455	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
456	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
457	C₂²⋊D₅₃	—	2	8	no	—
458	C₂²⋊D₅₃	—	2	16	no	—
459	C₂²⋊D₅₃	—	2	32	no	—
460	C₂²⋊D₅₃	—	2	16	no	—
461	C₂²⋊D₅₃	—	2	32	no	—
462	C₂²⋊D₅₃	—	4	8	no	—
463	C₂²⋊D₅₃	—	4	16	no	—
464	C₂²⋊D₅₃	—	4	8	no	—
465	C₂²⋊D₅₃	—	4	16	no	—
466	C₂²⋊D₅₃	—	4	16	no	—
467	C₂²⋊D₅₃	—	4	16	no	—
468	C₂×Dic₅₃	—	2	4	no	—
469	C₂×Dic₅₃	—	2	16	no	—
470	C₂×Dic₅₃	—	2	8	no	—
471	C₂×Dic₅₃	—	2	8	no	—
472	C₂×Dic₅₃	—	4	4	no	—
473	C₂×Dic₅₃	—	4	8	no	—
474	C₂×Dic₅₃	H(5,𝔽₂)	1	8	yes	complemented
475	C₂×Dic₅₃	C₂⁵	1	4	yes	—
476	C₂×Dic₅₃	C₂⁵	1	8	yes	—
477	C₂×Dic₅₃	C₂⁵	1	4	yes	—
478	C₂×Dic₅₃	C₂⁵	1	4	yes	—
479	D₂₁₂	—	2	8	no	—
480	D₂₁₂	—	2	8	no	—
481	D₂₁₂	—	2	4	no	—
482	D₂₁₂	—	4	8	no	—
483	D₂₁₂	—	4	8	no	—
484	D₂₁₂	—	4	16	no	—
485	C₄×D₅₃	—	2	8	no	—
486	C₄×D₅₃	—	2	16	no	—
487	C₄×D₅₃	—	4	16	no	—
488	C₄×D₅₃	—	4	8	no	—
489	Dic₁₀₆	—	2	4	no	—
490	Dic₁₀₆	—	2	16	no	—
491	#62832	—	53	1	no	maximal, Sylow
492	C₂²×C₅₃	—	2	8	no	—
493	C₂²×C₅₃	—	2	2	no	—
494	C₂²×C₅₃	—	2	2	no	—
495	C₂²×C₅₃	—	2	2	no	—
496	C₂²×C₅₃	—	2	8	no	—
497	C₂²×C₅₃	—	2	8	no	—
498	C₂²×C₅₃	—	2	4	no	—
499	C₂²×C₅₃	—	2	8	no	—
500	C₂²×C₅₃	—	2	4	no	—
501	C₂²×C₅₃	—	2	4	no	—
502	C₂²×C₅₃	—	8	4	no	—
503	C₂²×C₅₃	—	8	16	no	—
504	C₂²×C₅₃	—	8	4	no	—
505	C₂²×C₅₃	—	16	4	no	—
506	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
507	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
508	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
509	C₂×D₅₃	—	2	4	no	—
510	C₂×D₅₃	—	2	8	no	—
511	C₂×D₅₃	—	2	8	no	—
512	C₂×D₅₃	—	2	16	no	—
513	C₂×D₅₃	—	8	8	no	—
514	C₂×D₅₃	—	8	16	no	—
515	C₂×D₅₃	—	16	8	no	—
516	C₂×D₅₃	—	16	4	no	—
517	C₄×C₅₃	—	2	8	no	—
518	C₄×C₅₃	—	2	4	no	—
519	C₄×C₅₃	—	2	2	no	—
520	C₄×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
521	Dic₅₃	—	2	4	no	—
522	Dic₅₃	—	2	8	no	—
523	Dic₅₃	—	2	4	no	—
524	Dic₅₃	C₂×H(5,𝔽₂)	1	8	yes	—
525	#3543	—	53	8	no	—
526	#3543	—	53	8	no	—
527	#3543	—	53	8	no	—
528	#3508	—	53	8	no	—
529	#3508	—	53	2	no	—
530	#3508	—	53	2	no	—
531	#3498	—	53	2	no	—
532	#3498	—	53	8	no	—
533	#3498	—	53	2	no	—
534	#3484	—	53	1	no	—
535	#3484	—	53	2	no	—
536	#3484	—	53	8	no	—
537	#3484	D₅₃	1	1	yes	characteristic, complemented
538	#3444	—	53	2	no	—
539	C₂²×#127	—	53	1	no	—
540	C₂×C₅₃	—	2	4	no	—
541	C₂×C₅₃	—	2	2	no	—
542	C₂×C₅₃	—	4	4	no	—
543	C₂×C₅₃	—	4	4	no	—
544	C₂×C₅₃	—	4	4	no	—
545	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	2	yes	—
546	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
547	D₅₃	—	4	8	no	—
548	D₅₃	—	4	4	no	—
549	C₂×H(5,𝔽₂)	—	53	2	no	—
550	C₂×H(5,𝔽₂)	—	53	8	no	—
551	C₂×H(5,𝔽₂)	—	53	1	no	—
552	C₂×H(5,𝔽₂)	C₂×D₅₃	1	1	yes	characteristic, complemented
553	C₂³×D₄	—	53	4	no	—
554	C₂³×D₄	—	53	1	no	—
555	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
556	#560	—	53	8	no	—
557	#560	—	53	16	no	—
558	#560	—	53	8	no	—
559	#559	—	53	8	no	—
560	#559	—	53	8	no	—
561	#559	—	53	8	no	—
562	#550	—	53	8	no	—
563	#550	—	53	8	no	—
564	#550	—	53	8	no	—
565	#550	—	53	16	no	—
566	#550	—	53	8	no	—
567	#546	—	53	8	no	—
568	#546	—	53	8	no	—
569	#546	—	53	16	no	—
570	#546	—	53	16	no	—
571	#546	—	53	8	no	—
572	#546	—	53	16	no	—
573	#546	—	53	16	no	—
574	#546	C₂×D₅₃	1	8	yes	complemented
575	D₄²	—	53	16	no	—
576	D₄²	—	53	16	no	—
577	D₄²	—	53	8	no	—
578	D₄²	—	53	8	no	—
579	D₄²	—	53	8	no	—
580	D₄²	—	53	8	no	—
581	D₄²	—	53	16	no	—
582	D₄²	—	53	16	no	—
583	D₄²	—	53	8	no	—
584	D₄²	—	53	8	no	—
585	D₄²	C₂×D₅₃	1	8	yes	complemented
586	#540	—	53	16	no	—
587	#540	—	53	16	no	—
588	#540	—	53	8	no	—
589	#540	—	53	8	no	—
590	#535	—	53	2	no	—
591	#535	—	53	4	no	—
592	#535	—	53	2	no	—
593	#535	—	53	4	no	—
594	#535	—	53	4	no	—
595	#535	—	53	4	no	—
596	#535	—	53	16	no	—
597	#535	—	53	16	no	—
598	#535	—	53	16	no	—
599	#535	—	53	2	no	—
600	#535	C₂×D₅₃	1	2	yes	complemented
601	#534	—	53	4	no	—
602	#534	—	53	8	no	—
603	#534	—	53	8	no	—
604	#534	—	53	16	no	—
605	#534	—	53	8	no	—
606	#534	C₂×D₅₃	1	4	yes	complemented
607	#533	—	53	4	no	—
608	#533	—	53	2	no	—
609	#532	—	53	2	no	—
610	#532	—	53	4	no	—
611	#532	—	53	4	no	—
612	#532	—	53	4	no	—
613	#532	—	53	8	no	—
614	#532	—	53	8	no	—
615	C₂×#127	—	53	8	no	—
616	C₂×#127	—	53	2	no	—
617	C₂×#127	—	53	2	no	—
618	C₂×#127	—	53	8	no	—
619	C₂×#127	—	53	4	no	—
620	C₂×#127	—	53	4	no	—
621	C₂×#127	—	53	4	no	—
622	#529	—	53	8	no	—
623	#529	—	53	4	no	—
624	#529	—	53	4	no	—
625	#529	—	53	8	no	—
626	#525	—	53	2	no	—
627	#525	—	53	8	no	—
628	#525	C₂×D₅₃	1	2	yes	complemented
629	C₂×#120	—	53	4	no	—
630	C₂×#120	—	53	8	no	—
631	C₂×#120	C₂×D₅₃	1	4	yes	complemented
632	#518	—	53	1	no	—
633	#518	—	53	2	no	—
634	#518	—	53	8	no	—
635	#518	C₂×D₅₃	1	1	yes	characteristic, complemented
636	C₄×#41	—	53	2	no	—
637	C₄×#41	—	53	8	no	—
638	C₄×#41	—	53	2	no	—
639	C₂²×C₄²	—	53	1	no	—
640	C₅₃	#62832	1	1	yes	characteristic, complemented, Sylow
641	C₂⁵	—	53	2	no	—
642	C₂⁵	C₂²×D₅₃	1	2	yes	—
643	H(5,𝔽₂)	—	4	4	no	—
644	H(5,𝔽₂)	—	212	4	no	—
645	H(5,𝔽₂)	—	212	32	no	—
646	H(5,𝔽₂)	—	212	8	no	—
647	C₂×#41	—	53	4	no	—
648	C₂×#41	—	53	8	no	—
649	C₂×#41	—	53	16	no	—
650	C₂×#41	—	53	4	no	—
651	C₂×#41	—	53	2	no	—
652	C₂×#41	—	53	16	no	—
653	C₂×#41	—	53	4	no	—
654	C₂×#41	C₂²×D₅₃	1	2	yes	—
655	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
656	C₂²×D₄	—	4	4	no	—
657	C₂²×D₄	—	53	8	no	—
658	C₂²×D₄	—	53	4	no	—
659	C₂²×D₄	—	53	8	no	—
660	C₂²×D₄	—	53	8	no	—
661	C₂²×D₄	—	53	8	no	—
662	C₂²×D₄	—	53	16	no	—
663	C₂²×D₄	—	53	8	no	—
664	C₂²×D₄	—	53	16	no	—
665	C₂²×D₄	—	53	8	no	—
666	C₂²×D₄	—	53	16	no	—
667	C₂²×D₄	—	53	16	no	—
668	C₂²×D₄	—	53	4	no	—
669	C₂²×D₄	—	53	4	no	—
670	C₂²×D₄	—	53	2	no	—
671	C₂²×D₄	—	53	2	no	—
672	C₂²×D₄	—	53	8	no	—
673	C₂²×D₄	—	53	4	no	—
674	C₂²×D₄	—	212	4	no	—
675	C₂²×D₄	—	212	16	no	—
676	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
677	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
678	C₂²×D₄	C₂²×D₅₃	1	8	yes	—
679	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
680	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
681	C₂²×D₄	C₂²×D₅₃	1	8	yes	—
682	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
683	C₂³×C₄	—	53	2	no	—
684	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
685	C₄⋊Q₈	—	53	2	no	—
686	C₄⋊Q₈	—	53	4	no	—
687	#127	—	53	4	no	—
688	#127	—	53	4	no	—
689	#127	—	53	2	no	—
690	#127	—	53	16	no	—
691	#127	—	53	4	no	—
692	#127	—	53	4	no	—
693	#127	—	53	8	no	—
694	#127	—	53	8	no	—
695	#127	—	53	8	no	—
696	#127	—	53	8	no	—
697	#127	—	53	16	no	—
698	#127	—	53	16	no	—
699	#127	—	53	4	no	—
700	#127	—	53	4	no	—
701	#127	—	53	4	no	—
702	#127	C₂²×D₅₃	1	4	yes	complemented
703	#126	—	53	8	no	—
704	#126	—	53	8	no	—
705	#125	—	53	8	no	—
706	#125	—	53	4	no	—
707	#124	—	53	2	no	—
708	#124	—	53	4	no	—
709	#124	—	53	2	no	—
710	#124	—	53	4	no	—
711	#124	—	53	8	no	—
712	#124	—	53	16	no	—
713	#124	—	53	16	no	—
714	#124	—	53	4	no	—
715	#124	C₂²×D₅₃	1	4	yes	complemented
716	#123	—	53	8	no	—
717	#123	—	53	8	no	—
718	#123	—	53	4	no	—
719	#123	—	53	16	no	—
720	#123	—	53	16	no	—
721	#123	—	53	8	no	—
722	#123	—	53	16	no	—
723	#123	—	53	16	no	—
724	#123	—	53	16	no	—
725	#123	C₂²×D₅₃	1	4	yes	—
726	#123	C₂²×D₅₃	1	8	yes	complemented
727	C₂²⋊Q₈	—	53	4	no	—
728	C₂²⋊Q₈	—	53	8	no	—
729	C₂²⋊Q₈	—	53	8	no	—
730	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
731	#121	—	53	8	no	—
732	#121	—	53	8	no	—
733	#121	—	53	8	no	—
734	#121	—	53	16	no	—
735	#121	—	53	16	no	—
736	#121	—	53	16	no	—
737	#121	—	53	16	no	—
738	#121	—	53	16	no	—
739	#121	—	53	16	no	—
740	#121	—	53	16	no	—
741	#121	—	53	4	no	—
742	#121	—	53	8	no	—
743	#121	—	53	16	no	—
744	#121	—	53	16	no	—
745	#121	—	53	8	no	—
746	#121	—	53	16	no	—
747	#121	—	53	16	no	—
748	#121	—	53	16	no	—
749	#121	—	53	16	no	—
750	#121	—	53	16	no	—
751	#121	—	53	16	no	—
752	#121	C₂²×D₅₃	1	4	yes	—
753	#121	C₂²×D₅₃	1	8	yes	complemented
754	#121	C₂²×D₅₃	1	16	yes	complemented
755	#120	—	53	4	no	—
756	#120	—	53	16	no	—
757	#120	—	53	8	no	—
758	#120	—	53	16	no	—
759	#120	—	53	8	no	—
760	#120	—	53	16	no	—
761	#120	—	53	8	no	—
762	#120	—	53	16	no	—
763	#120	—	53	16	no	—
764	#120	—	53	16	no	—
765	#120	—	53	8	no	—
766	#120	—	53	16	no	—
767	#120	—	53	16	no	—
768	#120	C₂²×D₅₃	1	4	yes	—
769	#120	C₂²×D₅₃	1	16	yes	—
770	#120	C₂²×D₅₃	1	8	yes	—
771	#120	C₂²×D₅₃	1	8	yes	complemented
772	C₄×Q₈	—	53	4	no	—
773	C₄×Q₈	—	53	8	no	—
774	C₄×Q₈	—	53	4	no	—
775	C₄×Q₈	—	53	8	no	—
776	C₄×D₄	—	53	8	no	—
777	C₄×D₄	—	53	8	no	—
778	C₄×D₄	—	53	4	no	—
779	C₄×D₄	—	53	8	no	—
780	C₄×D₄	—	53	8	no	—
781	C₄×D₄	—	53	8	no	—
782	C₄×D₄	—	53	16	no	—
783	C₄×D₄	—	53	16	no	—
784	C₄×D₄	—	53	4	no	—
785	C₄×D₄	—	53	8	no	—
786	C₄×D₄	—	53	8	no	—
787	C₄×D₄	—	53	8	no	—
788	C₄×D₄	—	53	8	no	—
789	C₄×D₄	—	53	16	no	—
790	C₄×D₄	—	53	16	no	—
791	C₄×D₄	—	53	8	no	—
792	C₄×D₄	C₂²×D₅₃	1	8	yes	—
793	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
794	#117	—	53	2	no	—
795	#117	—	53	4	no	—
796	#117	—	53	8	no	—
797	#117	—	53	8	no	—
798	#117	—	53	8	no	—
799	#117	—	53	4	no	—
800	#117	C₂²×D₅₃	1	2	yes	—
801	C₂×C₂²⋊C₄	—	53	4	no	—
802	C₂×C₂²⋊C₄	—	53	8	no	—
803	C₂×C₂²⋊C₄	—	53	16	no	—
804	C₂×C₂²⋊C₄	—	53	8	no	—
805	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	—
806	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
807	C₂×C₄²	—	53	4	no	—
808	C₂×C₄²	—	53	4	no	—
809	C₂×C₄²	—	53	2	no	—
810	C₂×C₄²	—	53	2	no	—
811	C₂×C₄²	—	53	4	no	—
812	C₂×C₄²	—	53	4	no	—
813	C₂⁴	—	4	4	no	—
814	C₂⁴	—	4	8	no	—
815	C₂⁴	—	53	8	no	—
816	C₂⁴	—	53	4	no	—
817	C₂⁴	—	53	8	no	—
818	C₂⁴	—	53	4	no	—
819	C₂⁴	—	212	8	no	—
820	C₂⁴	—	212	4	no	—
821	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
822	C₂⁴	C₂³×D₅₃	1	2	yes	—
823	C₂⁴	C₂³×D₅₃	1	8	yes	—
824	C₂⁴	C₂³×D₅₃	1	2	yes	—
825	C₂⁴	C₂³×D₅₃	1	4	yes	—
826	#41	—	2	8	no	—
827	#41	—	4	8	no	—
828	#41	—	106	32	no	—
829	#41	—	106	8	no	—
830	#41	—	212	8	no	—
831	#41	—	212	32	no	—
832	#41	—	212	8	no	—
833	#41	—	212	32	no	—
834	#41	—	212	8	no	—
835	C₂×Q₈	—	53	8	no	—
836	C₂×Q₈	—	53	2	no	—
837	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
838	C₂×D₄	—	2	4	no	—
839	C₂×D₄	—	2	4	no	—
840	C₂×D₄	—	4	16	no	—
841	C₂×D₄	—	4	8	no	—
842	C₂×D₄	—	4	4	no	—
843	C₂×D₄	—	4	8	no	—
844	C₂×D₄	—	4	16	no	—
845	C₂×D₄	—	53	8	no	—
846	C₂×D₄	—	53	4	no	—
847	C₂×D₄	—	53	16	no	—
848	C₂×D₄	—	53	16	no	—
849	C₂×D₄	—	53	8	no	—
850	C₂×D₄	—	53	8	no	—
851	C₂×D₄	—	53	16	no	—
852	C₂×D₄	—	53	16	no	—
853	C₂×D₄	—	53	8	no	—
854	C₂×D₄	—	53	16	no	—
855	C₂×D₄	—	53	16	no	—
856	C₂×D₄	—	53	4	no	—
857	C₂×D₄	—	53	4	no	—
858	C₂×D₄	—	53	2	no	—
859	C₂×D₄	—	53	8	no	—
860	C₂×D₄	—	53	16	no	—
861	C₂×D₄	—	53	8	no	—
862	C₂×D₄	—	106	32	no	—
863	C₂×D₄	—	106	8	no	—
864	C₂×D₄	—	212	16	no	—
865	C₂×D₄	—	212	8	no	—
866	C₂×D₄	—	212	4	no	—
867	C₂×D₄	—	212	8	no	—
868	C₂×D₄	—	212	8	no	—
869	C₂×D₄	—	212	32	no	—
870	C₂×D₄	—	212	16	no	—
871	C₂×D₄	—	212	32	no	—
872	C₂×D₄	—	212	16	no	—
873	C₂×D₄	—	212	32	no	—
874	C₂×D₄	—	212	16	no	—
875	C₂×D₄	—	212	32	no	—
876	C₂×D₄	—	212	16	no	—
877	C₂×D₄	—	212	16	no	—
878	C₂×D₄	—	212	8	no	—
879	C₂×D₄	C₂³×D₅₃	1	4	yes	—
880	C₂×D₄	C₂³×D₅₃	1	2	yes	—
881	C₂×D₄	C₂³×D₅₃	1	4	yes	—
882	C₂×D₄	C₂³×D₅₃	1	8	yes	—
883	C₂×D₄	C₂³×D₅₃	1	4	yes	—
884	C₂×D₄	C₂³×D₅₃	1	8	yes	—
885	C₂×D₄	C₂³×D₅₃	1	16	yes	—
886	C₂×D₄	C₂³×D₅₃	1	8	yes	—
887	C₂²×C₄	—	2	4	no	—
888	C₂²×C₄	—	53	2	no	—
889	C₂²×C₄	—	53	4	no	—
890	C₂²×C₄	—	53	4	no	—
891	C₂²×C₄	—	53	2	no	—
892	C₂²×C₄	—	53	8	no	—
893	C₂²×C₄	—	53	4	no	—
894	C₂²×C₄	—	53	8	no	—
895	C₂²×C₄	—	53	8	no	—
896	C₂²×C₄	—	53	4	no	—
897	C₂²×C₄	—	53	8	no	—
898	C₂²×C₄	—	53	16	no	—
899	C₂²×C₄	—	106	8	no	—
900	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
901	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
902	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
903	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
904	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
905	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
906	C₄⋊C₄	—	53	8	no	—
907	C₄⋊C₄	—	53	8	no	—
908	C₄⋊C₄	—	53	4	no	—
909	C₄⋊C₄	—	53	8	no	—
910	C₄⋊C₄	—	53	8	no	—
911	C₄⋊C₄	—	53	8	no	—
912	C₄⋊C₄	—	53	8	no	—
913	C₄⋊C₄	—	53	8	no	—
914	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
915	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
916	C₂²⋊C₄	—	53	8	no	—
917	C₂²⋊C₄	—	53	4	no	—
918	C₂²⋊C₄	—	53	16	no	—
919	C₂²⋊C₄	—	53	8	no	—
920	C₂²⋊C₄	—	53	8	no	—
921	C₂²⋊C₄	—	53	8	no	—
922	C₂²⋊C₄	—	53	16	no	—
923	C₂²⋊C₄	—	53	16	no	—
924	C₂²⋊C₄	—	53	16	no	—
925	C₂²⋊C₄	—	53	8	no	—
926	C₂²⋊C₄	—	53	8	no	—
927	C₂²⋊C₄	—	53	8	no	—
928	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
929	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
930	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
931	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
932	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
933	C₄²	—	53	2	no	—
934	C₄²	—	53	4	no	—
935	C₄²	—	53	2	no	—
936	C₄²	—	53	2	no	—
937	C₄²	—	53	4	no	—
938	C₄²	—	53	2	no	—
939	C₄²	—	53	8	no	—
940	C₄²	—	53	8	no	—
941	C₄²	—	53	4	no	—
942	C₄²	C₂³×D₅₃	1	4	yes	—
943	C₂³	—	2	4	no	—
944	C₂³	—	2	2	no	—
945	C₂³	—	2	16	no	—
946	C₂³	—	2	4	no	—
947	C₂³	—	2	4	no	—
948	C₂³	—	4	8	no	—
949	C₂³	—	4	4	no	—
950	C₂³	—	4	8	no	—
951	C₂³	—	4	4	no	—
952	C₂³	—	4	4	no	—
953	C₂³	—	4	8	no	—
954	C₂³	—	8	16	no	—
955	C₂³	—	53	4	no	—
956	C₂³	—	53	8	no	—
957	C₂³	—	106	16	no	—
958	C₂³	—	106	8	no	—
959	C₂³	—	424	16	no	—
960	C₂³	—	212	16	no	—
961	C₂³	—	212	8	no	—
962	C₂³	—	212	8	no	—
963	C₂³	—	212	4	no	—
964	C₂³	—	212	8	no	—
965	C₂³	—	212	8	no	—
966	C₂³	—	212	8	no	—
967	C₂³	C₂⁴×D₅₃	1	4	yes	—
968	C₂³	C₂⁴×D₅₃	1	4	yes	—
969	C₂³	C₂⁴×D₅₃	1	4	yes	—
970	C₂³	C₂⁴×D₅₃	1	2	yes	—
971	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
972	Q₈	—	2	4	no	—
973	Q₈	—	106	16	no	—
974	Q₈	—	106	4	no	—
975	D₄	—	2	16	no	—
976	D₄	—	2	8	no	—
977	D₄	—	2	8	no	—
978	D₄	—	2	8	no	—
979	D₄	—	2	4	no	—
980	D₄	—	4	8	no	—
981	D₄	—	4	8	no	—
982	D₄	—	4	16	no	—
983	D₄	—	106	32	no	—
984	D₄	—	106	32	no	—
985	D₄	—	106	16	no	—
986	D₄	—	106	16	no	—
987	D₄	—	106	8	no	—
988	D₄	—	106	8	no	—
989	D₄	—	106	8	no	—
990	D₄	—	106	4	no	—
991	D₄	—	212	8	no	—
992	D₄	—	212	16	no	—
993	D₄	—	212	8	no	—
994	D₄	—	212	16	no	—
995	D₄	—	212	16	no	—
996	D₄	—	212	16	no	—
997	D₄	—	212	16	no	—
998	D₄	—	212	8	no	—
999	D₄	—	212	8	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	8	no	—
1002	C₂×C₄	—	2	8	no	—
1003	C₂×C₄	—	4	4	no	—
1004	C₂×C₄	—	4	8	no	—
1005	C₂×C₄	—	53	8	no	—
1006	C₂×C₄	—	53	4	no	—
1007	C₂×C₄	—	53	4	no	—
1008	C₂×C₄	—	53	8	no	—
1009	C₂×C₄	—	53	4	no	—
1010	C₂×C₄	—	106	16	no	—
1011	C₂×C₄	—	106	8	no	—
1012	C₂×C₄	—	106	8	no	—
1013	C₂×C₄	—	106	16	no	—
1014	C₂×C₄	—	106	4	no	—
1015	C₂×C₄	—	106	8	no	—
1016	C₂×C₄	—	212	16	no	—
1017	C₂×C₄	—	212	8	no	—
1018	C₂×C₄	—	212	8	no	—
1019	C₂×C₄	—	212	4	no	—
1020	C₂×C₄	#13133262	1	4	yes	complemented
1021	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1022	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1023	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1024	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1025	C₂²	—	2	8	no	—
1026	C₂²	—	2	2	no	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	2	no	—
1029	C₂²	—	2	8	no	—
1030	C₂²	—	2	8	no	—
1031	C₂²	—	2	8	no	—
1032	C₂²	—	2	4	no	—
1033	C₂²	—	2	4	no	—
1034	C₂²	—	2	4	no	—
1035	C₂²	—	8	16	no	—
1036	C₂²	—	8	4	no	—
1037	C₂²	—	8	4	no	—
1038	C₂²	—	16	4	no	—
1039	C₂²	—	848	4	no	—
1040	C₂²	—	848	8	no	—
1041	C₂²	—	106	8	no	—
1042	C₂²	—	106	16	no	—
1043	C₂²	—	106	4	no	—
1044	C₂²	—	106	8	no	—
1045	C₂²	—	424	16	no	—
1046	C₂²	—	424	8	no	—
1047	C₂²	H(5,𝔽₂)×D₅₃	1	4	yes	—
1048	C₂²	C₂×#13133262	1	2	yes	—
1049	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1050	C₄	—	2	8	no	—
1051	C₄	—	2	2	no	—
1052	C₄	—	2	4	no	—
1053	C₄	—	53	8	no	—
1054	C₄	—	106	4	no	—
1055	C₄	—	106	8	no	—
1056	C₄	—	106	4	no	—
1057	C₄	C₂×#13133262	1	4	yes	—
1058	C₂	—	2	4	no	—
1059	C₂	—	2	2	no	—
1060	C₂	—	4	4	no	—
1061	C₂	—	4	4	no	—
1062	C₂	—	4	4	no	—
1063	C₂	—	212	4	no	—
1064	C₂	—	212	8	no	—
1065	C₂	C₂×H(5,𝔽₂)×D₅₃	1	2	yes	—
1066	C₂	C₂²×#13133262	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3484	C₂
hypercenter	#3484	D₅₃
hypocenter	C₅₃	#62832
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3484

Complements

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

N	H ≅ G/N	type
1. #20289047	C₂	semidirect
2. #20289042	C₂	semidirect
3. #20289040	C₂	semidirect
4. #20288590	C₂	semidirect
5. #20288586	C₂	semidirect
6. #20288583	C₂	semidirect
7. #20288490	C₂	semidirect
8. #20288489	C₂	semidirect
9. #20288487	C₂	semidirect
10. #20288350	C₂	semidirect
11. #20288348	C₂	semidirect
12. #20288344	C₂	semidirect
13. #20288007	C₂	semidirect
14. C₂²×#13133213	C₂	semidirect
15. C₅₃×#3484	C₂	semidirect
16. C₂×#13133263	C₂²	semidirect
17. C₂×#13133262	C₂²	semidirect
18. C₂×#13133262	C₂²	semidirect
19. C₂³×D₂₁₂	C₂²	semidirect
20. C₂³×C₂²⋊D₅₃	C₂²	semidirect
21. #16811363	C₂²	semidirect
22. #16811362	C₂²	semidirect
23. #16811361	C₂²	semidirect
24. #16811357	C₂²	semidirect
25. #16811356	C₂²	semidirect
26. #16811355	C₂²	semidirect
27. #16811294	C₂²	semidirect
28. #16811293	C₂²	semidirect
29. #16811292	C₂²	semidirect
30. #16811291	C₂²	semidirect
31. #16811291	C₂²	semidirect
32. #16811269	C₂²	semidirect
33. #16811267	C₂²	semidirect
34. #16811264	C₂²	semidirect
35. #16811263	C₂²	semidirect
36. #16811263	C₂²	semidirect
37. #16811260	C₂²	semidirect
38. #16811260	C₂²	semidirect
39. D₄×D₂₁₂	C₂²	semidirect
40. #16811257	C₂²	semidirect
41. #16811257	C₂²	semidirect
42. D₄×C₂²⋊D₅₃	C₂²	semidirect
43. D₄×C₂²⋊D₅₃	C₂²	semidirect
44. D₄×C₂²⋊D₅₃	C₂²	semidirect
45. D₄×C₂²⋊D₅₃	C₂²	semidirect
46. #16811255	C₂²	semidirect
47. #16811255	C₂²	semidirect
48. #16811255	C₂²	semidirect
49. #16811226	C₂²	semidirect
50. #16811225	C₂²	semidirect
51. #16811224	C₂²	semidirect
52. #16811223	C₂²	semidirect
53. #16811192	C₂²	semidirect
54. #16811191	C₂²	semidirect
55. #16811190	C₂²	semidirect
56. #16811190	C₂²	semidirect
57. #16811189	C₂²	semidirect
58. #16811188	C₂²	semidirect
59. #16811188	C₂²	semidirect
60. #16811187	C₂²	semidirect
61. #16811187	C₂²	semidirect
62. #16811186	C₂²	semidirect
63. #16811185	C₂²	semidirect
64. #16811184	C₂²	semidirect
65. #16811183	C₂²	semidirect
66. #16811182	C₂²	semidirect
67. #16811182	C₂²	semidirect
68. #16811176	C₂²	semidirect
69. #16811175	C₂²	semidirect
70. #16811172	C₂²	semidirect
71. #16811170	C₂²	semidirect
72. #16811169	C₂²	semidirect
73. #16811169	C₂²	semidirect
74. #16811168	C₂²	semidirect
75. #16811168	C₂²	semidirect
76. C₂×#13133213	C₂²	semidirect
77. C₂×#13133213	C₂²	semidirect
78. C₂×#13133213	C₂²	semidirect
79. C₂×#13133213	C₂²	semidirect
80. C₂×#13133213	C₂²	semidirect
81. C₂×#13133213	C₂²	semidirect
82. #127×D₅₃	C₂²	semidirect
83. #16811159	C₂²	semidirect
84. #16811154	C₂²	semidirect
85. #16811153	C₂²	semidirect
86. #16811150	C₂²	semidirect
87. #16811134	C₂²	semidirect
88. #16811129	C₂²	semidirect
89. C₂×#13133186	C₂²	semidirect
90. #120×D₅₃	C₂²	semidirect
91. #16811098	C₂²	semidirect
92. #16811097	C₂²	semidirect
93. #16811096	C₂²	semidirect
94. #41×Dic₅₃	C₂²	semidirect
95. #16811091	C₂²	semidirect
96. C₄×#11719947	C₂²	semidirect
97. C₂²×C₄×Dic₅₃	C₂²	semidirect
98. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
99. C₂³×D₄×C₅₃	C₂²	semidirect
100. C₅₃×#546	C₂²	semidirect
101. D₄²×C₅₃	C₂²	semidirect
102. C₅₃×#535	C₂²	semidirect
103. C₅₃×#534	C₂²	semidirect
104. C₅₃×#525	C₂²	semidirect
105. C₂×#120×C₅₃	C₂²	semidirect
106. C₅₃×#518	C₂²	semidirect
111. C₂×#11719949	C₂³	semidirect
113. C₂×#11719945	C₂³	semidirect
114. C₂×#11719945	C₂³	semidirect
116. C₂×#11719947	C₂³	semidirect
117. C₂×#11719947	C₂³	semidirect
122. C₂²×D₂₁₂	C₂³	semidirect
131. C₂²×C₂²⋊D₅₃	C₂³	semidirect
134. C₂×D₄×D₅₃	C₂³	semidirect
135. C₂×D₄×D₅₃	C₂³	semidirect
136. C₂×D₄×D₅₃	C₂³	semidirect
138. #13133216	C₂³	semidirect
139. #13133215	C₂³	semidirect
140. #13133214	C₂³	semidirect
150. #13133213	C₂³	semidirect
151. #13133213	C₂³	semidirect
152. #13133213	C₂³	semidirect
153. #13133213	C₂³	semidirect
154. #13133213	C₂³	semidirect
155. #13133212	C₂³	semidirect
156. #13133210	C₂³	semidirect
157. #13133208	C₂³	semidirect
158. #13133207	C₂³	semidirect
159. #13133206	C₂³	semidirect
160. #13133206	C₂³	semidirect
161. #13133205	C₂³	semidirect
162. #13133204	C₂³	semidirect
163. #13133204	C₂³	semidirect
164. #13133203	C₂³	semidirect
165. #13133203	C₂³	semidirect
166. #13133203	C₂³	semidirect
167. #13133202	C₂³	semidirect
169. #13133201	C₂³	semidirect
171. #13133200	C₂³	semidirect
172. #13133199	C₂³	semidirect
173. #13133199	C₂³	semidirect
175. #13133198	C₂³	semidirect
179. #13133192	C₂³	semidirect
180. #13133192	C₂³	semidirect
182. #13133191	C₂³	semidirect
183. #13133191	C₂³	semidirect
184. #13133191	C₂³	semidirect
185. #13133190	C₂³	semidirect
186. #13133190	C₂³	semidirect
187. #13133190	C₂³	semidirect
188. #13133190	C₂³	semidirect
189. #13133190	C₂³	semidirect
192. #13133189	C₂³	semidirect
193. #13133189	C₂³	semidirect
194. #13133189	C₂³	semidirect
195. #13133189	C₂³	semidirect
196. #13133189	C₂³	semidirect
197. #13133188	C₂³	semidirect
198. #13133188	C₂³	semidirect
199. #13133188	C₂³	semidirect
202. #13133187	C₂³	semidirect
203. #13133187	C₂³	semidirect
207. #13133186	C₂³	semidirect
210. #13133185	C₂³	semidirect
211. #13133185	C₂³	semidirect
212. #13133185	C₂³	semidirect
213. Q₈×Dic₅₃	C₂³	semidirect
214. C₄×Dic₁₀₆	C₂³	semidirect
215. #13133182	C₂³	semidirect
216. #13133182	C₂³	semidirect
217. C₄×D₂₁₂	C₂³	semidirect
220. D₄×Dic₅₃	C₂³	semidirect
221. D₄×Dic₅₃	C₂³	semidirect
222. #13133179	C₂³	semidirect
223. #13133179	C₂³	semidirect
225. C₄×C₂²⋊D₅₃	C₂³	semidirect
226. C₄×C₂²⋊D₅₃	C₂³	semidirect
227. C₄×C₂²⋊D₅₃	C₂³	semidirect
230. #13133177	C₂³	semidirect
231. #13133177	C₂³	semidirect
232. #13133177	C₂³	semidirect
234. #13133176	C₂³	semidirect
235. #13133175	C₂³	semidirect
236. #13133174	C₂³	semidirect
238. #13133173	C₂³	semidirect
247. C₂×C₄×Dic₅₃	C₂³	semidirect
248. C₄²×D₅₃	C₂³	semidirect
252. C₂×#41×C₅₃	C₂³	semidirect
260. C₂²×D₄×C₅₃	C₂³	semidirect
262. #127×C₅₃	C₂³	semidirect
263. #124×C₅₃	C₂³	semidirect
265. #123×C₅₃	C₂³	semidirect
268. #121×C₅₃	C₂³	semidirect
269. #121×C₅₃	C₂³	semidirect
273. #120×C₅₃	C₂³	semidirect
275. C₄×D₄×C₅₃	C₂³	semidirect
452. C₂×C₄×C₅₃	H(5,𝔽₂)	semidirect
474. C₂×Dic₅₃	H(5,𝔽₂)	semidirect
537. #3484	D₅₃	semidirect
552. C₂×H(5,𝔽₂)	C₂×D₅₃	semidirect
555. C₂³×D₄	C₂×D₅₃	semidirect
574. #546	C₂×D₅₃	semidirect
585. D₄²	C₂×D₅₃	semidirect
600. #535	C₂×D₅₃	semidirect
606. #534	C₂×D₅₃	semidirect
628. #525	C₂×D₅₃	semidirect
631. C₂×#120	C₂×D₅₃	semidirect
635. #518	C₂×D₅₃	semidirect
640. C₅₃	#62832	semidirect
655. C₂×#41	C₂²×D₅₃	semidirect
682. C₂²×D₄	C₂²×D₅₃	semidirect
702. #127	C₂²×D₅₃	semidirect
715. #124	C₂²×D₅₃	semidirect
726. #123	C₂²×D₅₃	semidirect
753. #121	C₂²×D₅₃	semidirect
754. #121	C₂²×D₅₃	semidirect
771. #120	C₂²×D₅₃	semidirect
793. C₄×D₄	C₂²×D₅₃	semidirect
1020. C₂×C₄	#13133262	semidirect

Maximal subgroups

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

subgroup	index
#20289047	2
#20289042	2
#20289040	2
#20288590	2
#20288586	2
#20288583	2
#20288490	2
#20288489	2
#20288487	2
#20288350	2
#20288348	2
#20288344	2
#20288007	2
C₂²×#13133213	2
C₅₃×#3484	2
#62832	53