Subgroups — #28293331

Order 13568.

7498 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289072	C₂	1	4	yes	maximal, complemented
2	#20289048	C₂	1	4	yes	maximal, complemented
3	#20289018	C₂	1	16	yes	maximal, complemented
4	#20288905	C₂	1	8	yes	maximal, complemented
5	#20288888	C₂	1	8	yes	maximal, complemented
6	#20288869	C₂	1	8	yes	maximal, complemented
7	#20288413	C₂	1	2	yes	maximal, complemented
8	#20288402	C₂	1	4	yes	maximal, complemented
9	#20288359	C₂	1	2	yes	maximal, complemented
10	#20288344	C₂	1	4	yes	maximal, complemented
11	C₂×#16811182	C₂	1	2	yes	maximal, complemented
12	C₂×C₅₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#13133262	C₂²	1	2	yes	complemented
14	C₂³×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
15	#16811373	C₂²	1	4	yes	complemented
16	#16811368	C₂²	1	16	yes	complemented
17	#16811367	C₂²	1	8	yes	complemented
18	#16811365	C₂²	1	4	yes	complemented
19	#16811361	C₂²	1	16	yes	complemented
20	#16811360	C₂²	1	8	yes	complemented
21	#16811360	C₂²	1	8	yes	complemented
22	#16811359	C₂²	1	4	yes	complemented
23	#16811335	C₂²	1	8	yes	complemented
24	#16811316	C₂²	1	16	yes	complemented
25	#16811306	C₂²	1	16	yes	complemented
26	#16811304	C₂²	1	16	yes	complemented
27	#16811303	C₂²	1	8	yes	complemented
28	#16811299	C₂²	1	16	yes	complemented
29	#16811297	C₂²	1	16	yes	complemented
30	#16811293	C₂²	1	8	yes	complemented
31	#16811272	C₂²	1	16	yes	complemented
32	#16811267	C₂²	1	16	yes	complemented
33	#16811263	C₂²	1	16	yes	complemented
34	#16811262	C₂²	1	16	yes	complemented
35	#16811261	C₂²	1	16	yes	complemented
36	#16811260	C₂²	1	16	yes	complemented
37	#16811260	C₂²	1	16	yes	complemented
38	#16811258	C₂²	1	4	yes	complemented
39	D₄×C₂²⋊D₅₃	C₂²	1	16	yes	complemented
40	#16811255	C₂²	1	16	yes	complemented
41	#16811249	C₂²	1	2	yes	complemented
42	#16811237	C₂²	1	16	yes	complemented
43	#16811227	C₂²	1	16	yes	complemented
44	#16811223	C₂²	1	16	yes	complemented
45	#16811220	C₂²	1	8	yes	complemented
46	#16811218	C₂²	1	8	yes	complemented
47	#16811210	C₂²	1	8	yes	complemented
48	#16811208	C₂²	1	16	yes	complemented
49	#16811207	C₂²	1	16	yes	complemented
50	#16811205	C₂²	1	16	yes	complemented
51	#16811200	C₂²	1	8	yes	complemented
52	#16811197	C₂²	1	4	yes	complemented
53	#16811188	C₂²	1	8	yes	complemented
54	#16811186	C₂²	1	16	yes	complemented
55	#16811185	C₂²	1	2	yes	—
56	#16811183	C₂²	1	8	yes	complemented
57	#16811182	C₂²	1	8	yes	complemented
58	#16811182	C₂²	1	8	yes	complemented
59	#16811182	C₂²	1	4	yes	complemented
60	#16811182	C₂²	1	8	yes	complemented
61	#16811182	C₂²	1	8	yes	complemented
62	#16811182	C₂²	1	4	yes	complemented
63	#16811181	C₂²	1	8	yes	complemented
64	#16811157	C₂²	1	8	yes	complemented
65	#16811134	C₂²	1	4	yes	complemented
66	#16811129	C₂²	1	16	yes	complemented
67	#16811129	C₂²	1	8	yes	complemented
68	C₂×#13133200	C₂²	1	4	yes	complemented
69	C₂×#13133200	C₂²	1	4	yes	complemented
70	C₂×#13133198	C₂²	1	4	yes	complemented
71	C₂×#13133189	C₂²	1	8	yes	complemented
72	C₂×#13133186	C₂²	1	4	yes	complemented
73	C₂×#13133185	C₂²	1	4	yes	complemented
74	#120×D₅₃	C₂²	1	8	yes	complemented
75	#16811098	C₂²	1	2	yes	complemented
76	#16811096	C₂²	1	4	yes	complemented
77	C₂²×C₂²⋊Dic₅₃	C₂²	1	2	yes	complemented
78	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
79	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#535	C₂²	1	8	yes	complemented
81	C₅₃×#535	C₂²	1	8	yes	complemented
82	C₂×#127×C₅₃	C₂²	1	2	yes	complemented
83	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
84	C₂×#121×C₅₃	C₂²	1	4	yes	complemented
85	C₂×#120×C₅₃	C₂²	1	4	yes	complemented
86	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
87	C₂⁴×D₅₃	C₂³	1	2	yes	complemented
88	#13133262	—	4	8	no	—
89	C₂×#11719945	C₂³	1	4	yes	—
90	C₂×#11719947	C₂³	1	8	yes	—
91	C₂×#11719947	C₂³	1	16	yes	complemented
92	C₂²×C₂²⋊D₅₃	—	4	8	no	—
93	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
94	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
95	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
96	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
97	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
98	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
99	C₂×D₄×D₅₃	C₂³	1	8	yes	—
100	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
101	C₂³×Dic₅₃	C₂³	1	2	yes	complemented
102	C₂³×Dic₅₃	C₂³	1	4	yes	complemented
103	#13133215	C₂³	1	8	yes	complemented
104	#13133213	C₂³	1	16	yes	complemented
105	#13133212	C₂³	1	16	yes	complemented
106	#13133211	C₂³	1	16	yes	complemented
107	#13133210	C₂³	1	16	yes	complemented
108	#13133210	C₂³	1	16	yes	complemented
109	#13133209	C₂³	1	8	yes	complemented
110	#13133207	C₂³	1	16	yes	complemented
111	#13133206	C₂³	1	8	yes	complemented
112	#13133205	C₂³	1	8	yes	complemented
113	#13133204	C₂³	1	16	yes	complemented
114	#13133203	C₂³	1	16	yes	complemented
115	#13133203	C₂³	1	16	yes	complemented
116	#13133202	C₂³	1	16	yes	complemented
117	#13133201	C₂³	1	8	yes	—
118	#13133201	C₂³	1	16	yes	complemented
119	#13133200	C₂³	1	16	yes	—
120	#13133200	C₂³	1	16	yes	complemented
121	#13133200	C₂³	1	8	yes	complemented
122	#13133200	C₂³	1	8	yes	complemented
123	#13133200	C₂³	1	8	yes	complemented
124	#13133199	C₂³	1	16	yes	complemented
125	#13133199	C₂³	1	16	yes	complemented
126	#13133198	C₂³	1	8	yes	—
127	#13133198	C₂³	1	8	yes	—
128	#13133198	C₂³	1	16	yes	complemented
129	#13133198	C₂³	1	16	yes	complemented
130	#13133198	C₂³	1	8	yes	complemented
131	#13133198	C₂³	1	8	yes	complemented
132	#13133198	C₂³	1	8	yes	complemented
133	#13133198	C₂³	1	8	yes	complemented
134	#13133196	C₂³	1	8	yes	complemented
135	#13133196	C₂³	1	8	yes	complemented
136	#13133195	C₂³	1	16	yes	complemented
137	#13133194	C₂³	1	16	yes	complemented
138	#13133194	C₂³	1	16	yes	complemented
139	#13133194	C₂³	1	16	yes	complemented
140	#13133193	C₂³	1	16	yes	complemented
141	#13133191	C₂³	1	8	yes	—
142	#13133191	C₂³	1	8	yes	complemented
143	#13133190	C₂³	1	16	yes	complemented
144	#13133190	C₂³	1	16	yes	complemented
145	#13133189	C₂³	1	16	yes	—
146	#13133189	C₂³	1	16	yes	—
147	#13133189	C₂³	1	16	yes	—
148	#13133189	C₂³	1	16	yes	complemented
149	#13133189	C₂³	1	16	yes	complemented
150	#13133189	C₂³	1	16	yes	complemented
151	#13133189	C₂³	1	16	yes	complemented
152	#13133189	C₂³	1	16	yes	complemented
153	#13133189	C₂³	1	16	yes	complemented
154	#13133189	C₂³	1	16	yes	complemented
155	#13133188	C₂³	1	16	yes	complemented
156	#13133188	C₂³	1	16	yes	complemented
157	#13133187	C₂³	1	8	yes	—
158	#13133187	C₂³	1	16	yes	complemented
159	#13133186	C₂³	1	16	yes	—
160	#13133186	C₂³	1	8	yes	—
161	#13133186	C₂³	1	8	yes	—
162	#13133186	C₂³	1	8	yes	complemented
163	#13133185	C₂³	1	8	yes	—
164	#13133185	C₂³	1	8	yes	—
165	#13133185	C₂³	1	16	yes	complemented
166	#13133185	C₂³	1	8	yes	complemented
167	#13133185	C₂³	1	16	yes	complemented
168	#13133185	C₂³	1	8	yes	complemented
169	#13133185	C₂³	1	8	yes	complemented
170	#13133185	C₂³	1	8	yes	complemented
171	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
172	C₄×D₂₁₂	C₂³	1	8	yes	complemented
173	D₄×Dic₅₃	C₂³	1	16	yes	complemented
174	D₄×Dic₅₃	C₂³	1	16	yes	complemented
175	D₄×Dic₅₃	C₂³	1	16	yes	complemented
176	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
177	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
178	#13133177	C₂³	1	16	yes	—
179	#13133177	C₂³	1	16	yes	complemented
180	#13133177	C₂³	1	16	yes	complemented
181	#13133176	C₂³	1	4	yes	complemented
182	#13133174	C₂³	1	16	yes	complemented
183	#13133173	C₂³	1	16	yes	complemented
184	#13133173	C₂³	1	8	yes	complemented
185	C₂×#11719919	C₂³	1	8	yes	complemented
186	C₂×#11719919	C₂³	1	8	yes	complemented
187	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	—
188	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	—
189	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
190	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
191	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
192	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
193	C₂×#11719921	C₂³	1	8	yes	complemented
194	C₂×#11719921	C₂³	1	8	yes	complemented
195	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
196	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
197	C₂⁵×C₅₃	C₂³	1	2	yes	—
198	C₂×#41×C₅₃	—	4	4	no	—
199	C₂×#41×C₅₃	C₂³	1	8	yes	complemented
200	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
201	C₂²×D₄×C₅₃	—	4	4	no	—
202	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
203	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
204	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
205	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
206	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
207	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
208	C₂²×D₄×C₅₃	C₂³	1	8	yes	complemented
209	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
210	C₂³×C₄×C₅₃	C₂³	1	2	yes	complemented
211	#127×C₅₃	C₂³	1	4	yes	—
212	#127×C₅₃	C₂³	1	4	yes	complemented
213	#127×C₅₃	C₂³	1	8	yes	complemented
214	#124×C₅₃	C₂³	1	4	yes	—
215	#124×C₅₃	C₂³	1	4	yes	complemented
216	#124×C₅₃	C₂³	1	8	yes	complemented
217	#121×C₅₃	C₂³	1	8	yes	—
218	#121×C₅₃	C₂³	1	16	yes	complemented
219	#121×C₅₃	C₂³	1	8	yes	complemented
220	#120×C₅₃	C₂³	1	16	yes	—
221	#120×C₅₃	C₂³	1	8	yes	complemented
222	#120×C₅₃	C₂³	1	8	yes	complemented
223	#117×C₅₃	C₂³	1	8	yes	complemented
224	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
225	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
227	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
228	C₂⁴×C₅₃	—	2	8	no	—
229	C₂⁴×C₅₃	—	8	4	no	—
230	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
231	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
232	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
233	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
234	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
235	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
236	C₂³×D₅₃	—	4	4	no	—
237	C₂³×D₅₃	—	8	4	no	—
238	C₂³×D₅₃	C₂⁴	1	4	yes	—
239	C₂³×D₅₃	C₂⁴	1	8	yes	—
240	C₂³×D₅₃	C₂⁴	1	4	yes	—
241	#41×C₅₃	—	4	16	no	—
242	C₂×Q₈×C₅₃	—	4	2	no	—
243	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
244	C₂×D₄×C₅₃	—	2	8	no	—
245	C₂×D₄×C₅₃	—	4	4	no	—
246	C₂×D₄×C₅₃	—	4	4	no	—
247	C₂×D₄×C₅₃	—	4	8	no	—
248	C₂×D₄×C₅₃	—	4	8	no	—
249	C₂×D₄×C₅₃	—	4	2	no	—
250	C₂×D₄×C₅₃	—	8	8	no	—
251	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
252	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
253	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
254	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
255	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
256	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
257	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
258	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
259	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
260	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
261	C₂²×C₄×C₅₃	—	2	4	no	—
262	C₂²×C₄×C₅₃	—	4	4	no	—
263	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
267	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
268	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
269	C₂×C₂²⋊D₅₃	—	2	16	no	—
270	C₂×C₂²⋊D₅₃	—	4	8	no	—
271	C₂×C₂²⋊D₅₃	—	4	16	no	—
272	C₂×C₂²⋊D₅₃	—	4	16	no	—
273	C₂×C₂²⋊D₅₃	—	4	8	no	—
274	C₂×C₂²⋊D₅₃	—	8	8	no	—
275	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
276	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
277	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
278	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
279	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
280	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
281	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
282	C₂²×Dic₅₃	—	4	4	no	—
283	C₂²×Dic₅₃	—	8	4	no	—
284	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
285	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
286	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
287	C₂²×Dic₅₃	C₂⁴	1	16	yes	—
288	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
289	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
290	#11719947	—	4	16	no	—
291	#11719947	—	8	16	no	—
292	D₄×D₅₃	—	4	16	no	—
293	D₄×D₅₃	—	8	16	no	—
294	#11719945	—	4	8	no	—
295	C₂×D₂₁₂	C₂⁴	1	8	yes	—
296	C₂×D₂₁₂	C₂⁴	1	4	yes	—
297	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
298	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
299	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
300	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
301	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
302	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
303	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
304	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
305	C₄²×C₅₃	C₂⁴	1	4	yes	—
306	C₄²×C₅₃	C₂⁴	1	4	yes	—
307	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
308	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
309	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
310	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
311	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
312	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
313	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
314	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
315	#11719921	C₂⁴	1	16	yes	—
316	#11719921	C₂⁴	1	16	yes	—
317	#11719921	C₂⁴	1	16	yes	—
318	#11719921	C₂⁴	1	16	yes	—
319	#11719921	C₂⁴	1	16	yes	—
320	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
321	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
322	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
323	#11719919	C₂⁴	1	16	yes	—
324	#11719919	C₂⁴	1	16	yes	—
325	#11719919	C₂⁴	1	16	yes	—
326	#11719919	C₂⁴	1	16	yes	—
327	#11719919	C₂⁴	1	16	yes	—
328	C₄×Dic₅₃	C₂⁴	1	16	yes	—
329	C₄×Dic₅₃	C₂⁴	1	8	yes	—
330	C₂³×C₅₃	—	2	4	no	—
331	C₂³×C₅₃	—	2	4	no	—
332	C₂³×C₅₃	—	2	4	no	—
333	C₂³×C₅₃	—	2	8	no	—
334	C₂³×C₅₃	—	2	8	no	—
335	C₂³×C₅₃	—	4	4	no	—
336	C₂³×C₅₃	—	4	4	no	—
337	C₂³×C₅₃	—	4	2	no	—
338	C₂³×C₅₃	—	4	8	no	—
339	C₂³×C₅₃	—	4	4	no	—
340	C₂³×C₅₃	—	4	8	no	—
341	C₂³×C₅₃	—	8	16	no	—
342	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
343	C₂³×C₅₃	C₂⁵	1	4	yes	—
344	C₂³×C₅₃	C₂⁵	1	4	yes	—
345	C₂³×C₅₃	C₂⁵	1	4	yes	—
346	C₂³×C₅₃	C₂⁵	1	2	yes	—
347	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
348	C₂²×D₅₃	—	2	8	no	—
349	C₂²×D₅₃	—	4	16	no	—
350	C₂²×D₅₃	—	4	8	no	—
351	C₂²×D₅₃	—	4	8	no	—
352	C₂²×D₅₃	—	4	4	no	—
353	C₂²×D₅₃	—	4	8	no	—
354	C₂²×D₅₃	—	8	16	no	—
355	C₂²×D₅₃	C₂⁵	1	8	yes	—
356	Q₈×C₅₃	—	4	4	no	—
357	D₄×C₅₃	—	2	16	no	—
358	D₄×C₅₃	—	4	16	no	—
359	D₄×C₅₃	—	4	16	no	—
360	D₄×C₅₃	—	4	2	no	—
361	D₄×C₅₃	—	4	4	no	—
362	D₄×C₅₃	—	4	2	no	—
363	D₄×C₅₃	—	4	2	no	—
364	D₄×C₅₃	—	4	4	no	—
365	D₄×C₅₃	—	4	2	no	—
366	D₄×C₅₃	—	4	4	no	—
367	C₂×C₄×C₅₃	—	2	4	no	—
368	C₂×C₄×C₅₃	—	2	2	no	—
369	C₂×C₄×C₅₃	—	2	2	no	—
370	C₂×C₄×C₅₃	—	2	8	no	—
371	C₂×C₄×C₅₃	—	4	8	no	—
372	C₂×C₄×C₅₃	—	4	4	no	—
373	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
374	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
375	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
376	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
377	C₂²⋊D₅₃	—	2	16	no	—
378	C₂²⋊D₅₃	—	2	16	no	—
379	C₂²⋊D₅₃	—	4	8	no	—
380	C₂²⋊D₅₃	—	4	16	no	—
381	C₂²⋊D₅₃	—	4	16	no	—
382	C₂²⋊D₅₃	—	4	16	no	—
383	C₂²⋊D₅₃	—	4	16	no	—
384	C₂×Dic₅₃	—	2	8	no	—
385	C₂×Dic₅₃	—	4	4	no	—
386	C₂×Dic₅₃	—	4	8	no	—
387	C₂×Dic₅₃	—	4	16	no	—
388	C₂×Dic₅₃	—	4	8	no	—
389	C₂×Dic₅₃	—	4	8	no	—
390	C₂×Dic₅₃	C₂⁵	1	8	yes	—
391	C₂×Dic₅₃	C₂⁵	1	16	yes	—
392	D₂₁₂	—	4	4	no	—
393	D₂₁₂	—	4	8	no	—
394	C₄×D₅₃	—	4	8	no	—
395	C₄×D₅₃	—	4	16	no	—
396	Dic₁₀₆	—	4	4	no	—
397	Dic₁₀₆	—	4	8	no	—
398	#62862	—	53	1	no	maximal, Sylow
399	C₂²×C₅₃	—	2	4	no	—
400	C₂²×C₅₃	—	2	2	no	—
401	C₂²×C₅₃	—	2	4	no	—
402	C₂²×C₅₃	—	2	4	no	—
403	C₂²×C₅₃	—	2	4	no	—
404	C₂²×C₅₃	—	2	8	no	—
405	C₂²×C₅₃	—	2	8	no	—
406	C₂²×C₅₃	—	2	8	no	—
407	C₂²×C₅₃	—	4	4	no	—
408	C₂²×C₅₃	—	4	8	no	—
409	C₂²×C₅₃	—	4	8	no	—
410	C₂²×C₅₃	—	8	4	no	—
411	C₂²×C₅₃	—	8	8	no	—
412	C₂²×C₅₃	—	8	8	no	—
413	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
414	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
415	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
416	C₂×D₅₃	—	2	8	no	—
417	C₂×D₅₃	—	2	16	no	—
418	C₂×D₅₃	—	8	8	no	—
419	C₂×D₅₃	—	8	16	no	—
420	C₂×D₅₃	—	16	4	no	—
421	C₄×C₅₃	—	2	4	no	—
422	C₄×C₅₃	—	2	2	no	—
423	C₄×C₅₃	—	2	2	no	—
424	C₄×C₅₃	—	2	8	no	—
425	Dic₅₃	—	2	8	no	—
426	Dic₅₃	—	2	16	no	—
427	#3545	—	53	4	no	—
428	#3543	—	53	4	no	—
429	#3542	—	53	16	no	—
430	#3534	—	53	8	no	—
431	#3533	—	53	8	no	—
432	#3532	—	53	8	no	—
433	#3491	—	53	2	no	—
434	#3490	—	53	4	no	—
435	#3485	—	53	2	no	—
436	#3484	—	53	4	no	—
437	C₂×#535	D₅₃	1	1	yes	characteristic, complemented
438	C₂×#534	—	53	2	no	—
439	C₂×C₅₃	—	2	4	no	—
440	C₂×C₅₃	—	2	2	no	—
441	C₂×C₅₃	—	4	4	no	—
442	C₂×C₅₃	—	4	4	no	—
443	C₂×C₅₃	—	4	4	no	—
444	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
445	C₂×C₅₃	H(7,𝔽₂)	1	2	yes	—
446	D₅₃	—	4	8	no	—
447	C₂×H(5,𝔽₂)	—	53	2	no	—
448	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
449	C₂³×D₄	—	53	2	no	—
450	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
451	#563	—	53	4	no	—
452	#562	—	53	8	no	—
453	#562	—	53	16	no	—
454	H(3,𝔽₄)	—	53	4	no	—
455	#560	—	53	8	no	—
456	#560	—	53	8	no	—
457	#560	—	53	16	no	—
458	#559	—	53	4	no	—
459	#555	—	53	8	no	—
460	#553	—	53	16	no	—
461	#552	—	53	16	no	—
462	#551	—	53	8	no	—
463	#551	—	53	16	no	—
464	#551	—	53	16	no	—
465	#551	—	53	16	no	—
466	#550	—	53	8	no	—
467	#547	—	53	16	no	—
468	#546	—	53	16	no	—
469	#546	—	53	16	no	—
470	#546	—	53	16	no	—
471	#546	—	53	16	no	—
472	#546	—	53	16	no	—
473	#546	—	53	16	no	—
474	D₄²	—	53	16	no	—
475	D₄²	—	53	4	no	—
476	D₄²	—	53	16	no	—
477	#543	—	53	2	no	—
478	#542	—	53	16	no	—
479	#540	—	53	16	no	—
480	#540	—	53	16	no	—
481	#539	—	53	8	no	—
482	#539	—	53	8	no	—
483	#538	—	53	16	no	—
484	#538	—	53	16	no	—
485	#538	—	53	8	no	—
486	#538	—	53	16	no	—
487	#537	—	53	8	no	—
488	#536	—	53	4	no	—
489	#535	—	53	16	no	—
490	#535	—	53	8	no	—
491	#535	C₂×D₅₃	1	8	yes	complemented
492	#535	C₂×D₅₃	1	8	yes	complemented
493	#534	—	53	8	no	—
494	#534	—	53	8	no	—
495	#534	—	53	8	no	—
496	#534	—	53	8	no	—
497	#534	—	53	4	no	—
498	#534	—	53	4	no	—
499	#534	—	53	8	no	—
500	#534	—	53	8	no	—
501	#534	—	53	2	no	—
502	C₂×#127	C₂×D₅₃	1	2	yes	complemented
503	#529	—	53	8	no	—
504	C₂×#124	C₂×D₅₃	1	2	yes	complemented
505	#525	—	53	4	no	—
506	#525	—	53	8	no	—
507	#525	—	53	16	no	—
508	C₂×#123	—	53	4	no	—
509	C₂×#123	—	53	4	no	—
510	C₂×#123	—	53	4	no	—
511	C₂×#121	—	53	8	no	—
512	C₂×#121	C₂×D₅₃	1	4	yes	complemented
513	C₂×#120	—	53	4	no	—
514	C₂×#120	—	53	4	no	—
515	C₂×#120	—	53	8	no	—
516	C₂×#120	C₂×D₅₃	1	4	yes	complemented
517	#518	—	53	2	no	—
518	#518	—	53	4	no	—
519	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
520	C₂²×C₂²⋊C₄	—	53	2	no	—
521	C₅₃	#62862	1	1	yes	characteristic, complemented, Sylow
522	C₂⁵	—	53	2	no	—
523	C₂⁵	C₂²×D₅₃	1	2	yes	—
524	H(5,𝔽₂)	—	212	8	no	—
525	C₂×#41	—	4	4	no	—
526	C₂×#41	—	53	16	no	—
527	C₂×#41	—	53	8	no	—
528	C₂×#41	—	53	4	no	—
529	C₂×#41	C₂²×D₅₃	1	8	yes	complemented
530	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
531	C₂²×D₄	—	4	4	no	—
532	C₂²×D₄	—	53	4	no	—
533	C₂²×D₄	—	53	8	no	—
534	C₂²×D₄	—	53	4	no	—
535	C₂²×D₄	—	53	4	no	—
536	C₂²×D₄	—	53	8	no	—
537	C₂²×D₄	—	53	8	no	—
538	C₂²×D₄	—	53	16	no	—
539	C₂²×D₄	—	53	8	no	—
540	C₂²×D₄	—	212	8	no	—
541	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
542	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
543	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
544	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
545	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
546	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
547	C₂²×D₄	C₂²×D₅₃	1	8	yes	complemented
548	C₂³×C₄	—	53	4	no	—
549	C₂³×C₄	—	53	2	no	—
550	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
551	C₂³×C₄	C₂²×D₅₃	1	2	yes	complemented
552	C₄⋊Q₈	—	53	8	no	—
553	#127	—	53	16	no	—
554	#127	C₂²×D₅₃	1	4	yes	—
555	#127	C₂²×D₅₃	1	8	yes	complemented
556	#127	C₂²×D₅₃	1	4	yes	complemented
557	#126	—	53	16	no	—
558	#126	—	53	16	no	—
559	#126	—	53	16	no	—
560	#126	—	53	16	no	—
561	#125	—	53	16	no	—
562	#125	—	53	8	no	—
563	#124	—	53	8	no	—
564	#124	—	53	16	no	—
565	#124	—	53	16	no	—
566	#124	—	53	16	no	—
567	#124	—	53	8	no	—
568	#124	C₂²×D₅₃	1	4	yes	—
569	#124	C₂²×D₅₃	1	8	yes	complemented
570	#124	C₂²×D₅₃	1	4	yes	complemented
571	#123	—	53	8	no	—
572	#123	—	53	8	no	—
573	#123	—	53	8	no	—
574	#123	—	53	8	no	—
575	#123	—	53	8	no	—
576	#123	—	53	16	no	—
577	#123	—	53	8	no	—
578	#123	—	53	16	no	—
579	#123	—	53	8	no	—
580	#123	—	53	8	no	—
581	#123	—	53	16	no	—
582	#123	—	53	8	no	—
583	#123	—	53	16	no	—
584	#123	—	53	16	no	—
585	#123	—	53	8	no	—
586	#123	—	53	16	no	—
587	#123	—	53	16	no	—
588	#123	—	53	16	no	—
589	C₂²⋊Q₈	—	53	16	no	—
590	C₂²⋊Q₈	—	53	8	no	—
591	C₂²⋊Q₈	—	53	8	no	—
592	C₂²⋊Q₈	—	53	16	no	—
593	C₂²⋊Q₈	—	53	16	no	—
594	C₂²⋊Q₈	—	53	16	no	—
595	C₂²⋊Q₈	—	53	16	no	—
596	#121	—	53	16	no	—
597	#121	—	53	16	no	—
598	#121	—	53	16	no	—
599	#121	—	53	16	no	—
600	#121	—	53	16	no	—
601	#121	—	53	16	no	—
602	#121	—	53	16	no	—
603	#121	—	53	16	no	—
604	#121	—	53	16	no	—
605	#121	—	53	16	no	—
606	#121	—	53	16	no	—
607	#121	—	53	16	no	—
608	#121	—	53	8	no	—
609	#121	—	53	8	no	—
610	#121	—	53	16	no	—
611	#121	—	53	16	no	—
612	#121	C₂²×D₅₃	1	8	yes	—
613	#121	C₂²×D₅₃	1	8	yes	complemented
614	#121	C₂²×D₅₃	1	16	yes	complemented
615	#120	—	53	8	no	—
616	#120	—	53	8	no	—
617	#120	—	53	16	no	—
618	#120	—	53	8	no	—
619	#120	—	53	8	no	—
620	#120	—	53	8	no	—
621	#120	—	53	8	no	—
622	#120	—	53	8	no	—
623	#120	—	53	8	no	—
624	#120	—	53	16	no	—
625	#120	—	53	8	no	—
626	#120	—	53	16	no	—
627	#120	—	53	8	no	—
628	#120	—	53	16	no	—
629	#120	C₂²×D₅₃	1	16	yes	—
630	#120	C₂²×D₅₃	1	8	yes	complemented
631	#120	C₂²×D₅₃	1	8	yes	complemented
632	C₄×Q₈	—	53	8	no	—
633	C₄×D₄	—	53	16	no	—
634	C₄×D₄	—	53	16	no	—
635	C₄×D₄	—	53	16	no	—
636	C₄×D₄	—	53	16	no	—
637	C₄×D₄	—	53	16	no	—
638	C₄×D₄	—	53	16	no	—
639	C₄×D₄	—	53	16	no	—
640	C₄×D₄	—	53	16	no	—
641	C₄×D₄	—	53	8	no	—
642	#117	—	53	4	no	—
643	#117	—	53	8	no	—
644	#117	—	53	16	no	—
645	#117	—	53	16	no	—
646	#117	C₂²×D₅₃	1	8	yes	complemented
647	C₂×C₄⋊C₄	—	53	8	no	—
648	C₂×C₄⋊C₄	—	53	8	no	—
649	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
650	C₂×C₂²⋊C₄	—	53	4	no	—
651	C₂×C₂²⋊C₄	—	53	4	no	—
652	C₂×C₂²⋊C₄	—	53	8	no	—
653	C₂×C₂²⋊C₄	—	53	8	no	—
654	C₂×C₂²⋊C₄	—	53	4	no	—
655	C₂×C₂²⋊C₄	—	53	8	no	—
656	C₂×C₂²⋊C₄	—	53	8	no	—
657	C₂×C₂²⋊C₄	—	53	8	no	—
658	C₂×C₂²⋊C₄	—	53	8	no	—
659	C₂×C₂²⋊C₄	—	53	16	no	—
660	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	complemented
662	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
663	C₂⁴	—	2	8	no	—
664	C₂⁴	—	8	4	no	—
665	C₂⁴	—	53	4	no	—
666	C₂⁴	—	53	8	no	—
667	C₂⁴	—	53	4	no	—
668	C₂⁴	—	424	4	no	—
669	C₂⁴	—	212	4	no	—
670	C₂⁴	C₂³×D₅₃	1	4	yes	—
671	C₂⁴	C₂³×D₅₃	1	4	yes	—
672	C₂⁴	C₂³×D₅₃	1	2	yes	—
673	C₂⁴	C₂³×D₅₃	1	2	yes	—
674	C₂⁴	C₂³×D₅₃	1	2	yes	—
675	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
676	#41	—	4	16	no	—
677	#41	—	424	16	no	—
678	#41	—	212	8	no	—
679	#41	—	212	16	no	—
680	C₂×Q₈	—	4	2	no	—
681	C₂×Q₈	—	53	8	no	—
682	C₂×Q₈	—	53	4	no	—
683	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
684	C₂×D₄	—	2	8	no	—
685	C₂×D₄	—	4	4	no	—
686	C₂×D₄	—	4	4	no	—
687	C₂×D₄	—	4	8	no	—
688	C₂×D₄	—	4	8	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	8	8	no	—
691	C₂×D₄	—	53	8	no	—
692	C₂×D₄	—	53	8	no	—
693	C₂×D₄	—	53	16	no	—
694	C₂×D₄	—	53	16	no	—
695	C₂×D₄	—	53	16	no	—
696	C₂×D₄	—	53	8	no	—
697	C₂×D₄	—	53	16	no	—
698	C₂×D₄	—	53	8	no	—
699	C₂×D₄	—	53	4	no	—
700	C₂×D₄	—	106	16	no	—
701	C₂×D₄	—	424	16	no	—
702	C₂×D₄	—	424	8	no	—
703	C₂×D₄	—	212	8	no	—
704	C₂×D₄	—	212	16	no	—
705	C₂×D₄	—	212	16	no	—
706	C₂×D₄	—	212	16	no	—
707	C₂×D₄	—	212	8	no	—
708	C₂×D₄	C₂³×D₅₃	1	8	yes	—
709	C₂×D₄	C₂³×D₅₃	1	16	yes	—
710	C₂×D₄	C₂³×D₅₃	1	16	yes	—
711	C₂×D₄	C₂³×D₅₃	1	2	yes	—
712	C₂×D₄	C₂³×D₅₃	1	2	yes	—
713	C₂×D₄	C₂³×D₅₃	1	4	yes	—
714	C₂×D₄	C₂³×D₅₃	1	4	yes	—
715	C₂×D₄	C₂³×D₅₃	1	4	yes	—
716	C₂×D₄	C₂³×D₅₃	1	2	yes	—
717	C₂×D₄	C₂³×D₅₃	1	2	yes	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	4	4	no	—
720	C₂²×C₄	—	53	4	no	—
721	C₂²×C₄	—	53	8	no	—
722	C₂²×C₄	—	53	8	no	—
723	C₂²×C₄	—	53	16	no	—
724	C₂²×C₄	—	53	4	no	—
725	C₂²×C₄	—	53	8	no	—
726	C₂²×C₄	—	53	16	no	—
727	C₂²×C₄	—	53	8	no	—
728	C₂²×C₄	—	424	4	no	—
729	C₂²×C₄	—	212	4	no	—
730	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
731	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
732	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
733	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
734	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
735	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
736	C₄⋊C₄	—	53	16	no	—
737	C₄⋊C₄	—	53	16	no	—
738	C₄⋊C₄	—	53	16	no	—
739	C₄⋊C₄	—	53	16	no	—
740	C₄⋊C₄	—	53	16	no	—
741	C₄⋊C₄	—	53	8	no	—
742	C₄⋊C₄	—	53	8	no	—
743	C₄⋊C₄	—	53	8	no	—
744	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
745	C₂²⋊C₄	—	53	8	no	—
746	C₂²⋊C₄	—	53	8	no	—
747	C₂²⋊C₄	—	53	8	no	—
748	C₂²⋊C₄	—	53	8	no	—
749	C₂²⋊C₄	—	53	16	no	—
750	C₂²⋊C₄	—	53	16	no	—
751	C₂²⋊C₄	—	53	8	no	—
752	C₂²⋊C₄	—	53	16	no	—
753	C₂²⋊C₄	—	53	16	no	—
754	C₂²⋊C₄	—	53	16	no	—
755	C₂²⋊C₄	—	53	16	no	—
756	C₂²⋊C₄	—	53	16	no	—
757	C₂²⋊C₄	—	53	16	no	—
758	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
759	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
760	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
761	C₄²	—	53	8	no	—
762	C₄²	—	53	16	no	—
763	C₄²	C₂³×D₅₃	1	4	yes	—
764	C₄²	C₂³×D₅₃	1	4	yes	—
765	C₂³	—	2	4	no	—
766	C₂³	—	2	4	no	—
767	C₂³	—	2	4	no	—
768	C₂³	—	2	8	no	—
769	C₂³	—	2	8	no	—
770	C₂³	—	4	4	no	—
771	C₂³	—	4	2	no	—
772	C₂³	—	4	4	no	—
773	C₂³	—	4	4	no	—
774	C₂³	—	4	8	no	—
775	C₂³	—	4	8	no	—
776	C₂³	—	8	16	no	—
777	C₂³	—	53	8	no	—
778	C₂³	—	106	8	no	—
779	C₂³	—	424	16	no	—
780	C₂³	—	212	8	no	—
781	C₂³	—	212	4	no	—
782	C₂³	—	212	8	no	—
783	C₂³	—	212	16	no	—
784	C₂³	—	212	8	no	—
785	C₂³	#13133262	1	4	yes	—
786	C₂³	C₂⁴×D₅₃	1	4	yes	—
787	C₂³	C₂⁴×D₅₃	1	4	yes	—
788	C₂³	C₂⁴×D₅₃	1	4	yes	—
789	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
790	C₂³	C₂⁴×D₅₃	1	2	yes	—
791	Q₈	—	4	4	no	—
792	Q₈	—	212	8	no	—
793	Q₈	—	212	4	no	—
794	D₄	—	2	16	no	—
795	D₄	—	4	2	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	2	no	—
798	D₄	—	4	2	no	—
799	D₄	—	4	4	no	—
800	D₄	—	4	2	no	—
801	D₄	—	4	4	no	—
802	D₄	—	4	16	no	—
803	D₄	—	4	16	no	—
804	D₄	—	106	16	no	—
805	D₄	—	106	16	no	—
806	D₄	—	212	8	no	—
807	D₄	—	212	4	no	—
808	D₄	—	212	16	no	—
809	D₄	—	212	16	no	—
810	D₄	—	212	16	no	—
811	D₄	—	212	16	no	—
812	D₄	—	212	8	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	8	no	—
816	C₂×C₄	—	2	4	no	—
817	C₂×C₄	—	4	8	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	53	16	no	—
820	C₂×C₄	—	53	8	no	—
821	C₂×C₄	—	106	8	no	—
822	C₂×C₄	—	212	16	no	—
823	C₂×C₄	—	212	8	no	—
824	C₂×C₄	—	212	8	no	—
825	C₂×C₄	—	212	16	no	—
826	C₂×C₄	—	212	8	no	—
827	C₂×C₄	—	212	4	no	—
828	C₂×C₄	—	212	8	no	—
829	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
830	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
831	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
832	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	4	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	4	no	—
837	C₂²	—	2	4	no	—
838	C₂²	—	2	8	no	—
839	C₂²	—	2	8	no	—
840	C₂²	—	2	8	no	—
841	C₂²	—	4	4	no	—
842	C₂²	—	4	8	no	—
843	C₂²	—	4	8	no	—
844	C₂²	—	8	8	no	—
845	C₂²	—	8	8	no	—
846	C₂²	—	8	4	no	—
847	C₂²	—	848	4	no	—
848	C₂²	—	106	8	no	—
849	C₂²	—	106	16	no	—
850	C₂²	—	424	8	no	—
851	C₂²	—	424	16	no	—
852	C₂²	C₂×#13133262	1	2	yes	—
853	C₂²	C₂×#13133262	1	4	yes	—
854	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
855	C₄	—	2	2	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	4	no	—
858	C₄	—	2	8	no	—
859	C₄	—	106	8	no	—
860	C₄	—	106	16	no	—
861	C₂	—	2	4	no	—
862	C₂	—	2	2	no	—
863	C₂	—	4	4	no	—
864	C₂	—	4	4	no	—
865	C₂	—	4	4	no	—
866	C₂	—	212	8	no	—
867	C₂	C₂²×#13133262	1	1	yes	characteristic
868	C₂	#20289525	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₂×C₅₃×#535	C₂
hypercenter	C₂×#535	D₅₃
hypocenter	C₅₃	#62862
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×#535

Complements

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

N	H ≅ G/N	type
1. #20289072	C₂	semidirect
2. #20289048	C₂	semidirect
3. #20289018	C₂	semidirect
4. #20288905	C₂	semidirect
5. #20288888	C₂	semidirect
6. #20288869	C₂	semidirect
7. #20288413	C₂	semidirect
8. #20288402	C₂	semidirect
9. #20288359	C₂	semidirect
10. #20288344	C₂	semidirect
11. C₂×#16811182	C₂	semidirect
12. C₂×C₅₃×#535	C₂	semidirect
13. C₂×#13133262	C₂²	semidirect
14. C₂³×C₂²⋊D₅₃	C₂²	semidirect
15. #16811373	C₂²	semidirect
16. #16811368	C₂²	semidirect
17. #16811367	C₂²	semidirect
18. #16811365	C₂²	semidirect
19. #16811361	C₂²	semidirect
20. #16811360	C₂²	semidirect
21. #16811360	C₂²	semidirect
22. #16811359	C₂²	semidirect
23. #16811335	C₂²	semidirect
24. #16811316	C₂²	semidirect
25. #16811306	C₂²	semidirect
26. #16811304	C₂²	semidirect
27. #16811303	C₂²	semidirect
28. #16811299	C₂²	semidirect
29. #16811297	C₂²	semidirect
30. #16811293	C₂²	semidirect
31. #16811272	C₂²	semidirect
32. #16811267	C₂²	semidirect
33. #16811263	C₂²	semidirect
34. #16811262	C₂²	semidirect
35. #16811261	C₂²	semidirect
36. #16811260	C₂²	semidirect
37. #16811260	C₂²	semidirect
38. #16811258	C₂²	semidirect
39. D₄×C₂²⋊D₅₃	C₂²	semidirect
40. #16811255	C₂²	semidirect
41. #16811249	C₂²	semidirect
42. #16811237	C₂²	semidirect
43. #16811227	C₂²	semidirect
44. #16811223	C₂²	semidirect
45. #16811220	C₂²	semidirect
46. #16811218	C₂²	semidirect
47. #16811210	C₂²	semidirect
48. #16811208	C₂²	semidirect
49. #16811207	C₂²	semidirect
50. #16811205	C₂²	semidirect
51. #16811200	C₂²	semidirect
52. #16811197	C₂²	semidirect
53. #16811188	C₂²	semidirect
54. #16811186	C₂²	semidirect
56. #16811183	C₂²	semidirect
57. #16811182	C₂²	semidirect
58. #16811182	C₂²	semidirect
59. #16811182	C₂²	semidirect
60. #16811182	C₂²	semidirect
61. #16811182	C₂²	semidirect
62. #16811182	C₂²	semidirect
63. #16811181	C₂²	semidirect
64. #16811157	C₂²	semidirect
65. #16811134	C₂²	semidirect
66. #16811129	C₂²	semidirect
67. #16811129	C₂²	semidirect
68. C₂×#13133200	C₂²	semidirect
69. C₂×#13133200	C₂²	semidirect
70. C₂×#13133198	C₂²	semidirect
71. C₂×#13133189	C₂²	semidirect
72. C₂×#13133186	C₂²	semidirect
73. C₂×#13133185	C₂²	semidirect
74. #120×D₅₃	C₂²	semidirect
75. #16811098	C₂²	semidirect
76. #16811096	C₂²	semidirect
77. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
78. C₂²×#41×C₅₃	C₂²	semidirect
79. C₂³×D₄×C₅₃	C₂²	semidirect
80. C₅₃×#535	C₂²	semidirect
81. C₅₃×#535	C₂²	semidirect
82. C₂×#127×C₅₃	C₂²	semidirect
83. C₂×#124×C₅₃	C₂²	semidirect
84. C₂×#121×C₅₃	C₂²	semidirect
85. C₂×#120×C₅₃	C₂²	semidirect
86. C₂×#117×C₅₃	C₂²	semidirect
87. C₂⁴×D₅₃	C₂³	semidirect
91. C₂×#11719947	C₂³	semidirect
97. C₂²×C₂²⋊D₅₃	C₂³	semidirect
98. C₂²×C₂²⋊D₅₃	C₂³	semidirect
100. C₂×D₄×D₅₃	C₂³	semidirect
101. C₂³×Dic₅₃	C₂³	semidirect
102. C₂³×Dic₅₃	C₂³	semidirect
103. #13133215	C₂³	semidirect
104. #13133213	C₂³	semidirect
105. #13133212	C₂³	semidirect
106. #13133211	C₂³	semidirect
107. #13133210	C₂³	semidirect
108. #13133210	C₂³	semidirect
109. #13133209	C₂³	semidirect
110. #13133207	C₂³	semidirect
111. #13133206	C₂³	semidirect
112. #13133205	C₂³	semidirect
113. #13133204	C₂³	semidirect
114. #13133203	C₂³	semidirect
115. #13133203	C₂³	semidirect
116. #13133202	C₂³	semidirect
118. #13133201	C₂³	semidirect
120. #13133200	C₂³	semidirect
121. #13133200	C₂³	semidirect
122. #13133200	C₂³	semidirect
123. #13133200	C₂³	semidirect
124. #13133199	C₂³	semidirect
125. #13133199	C₂³	semidirect
128. #13133198	C₂³	semidirect
129. #13133198	C₂³	semidirect
130. #13133198	C₂³	semidirect
131. #13133198	C₂³	semidirect
132. #13133198	C₂³	semidirect
133. #13133198	C₂³	semidirect
134. #13133196	C₂³	semidirect
135. #13133196	C₂³	semidirect
136. #13133195	C₂³	semidirect
137. #13133194	C₂³	semidirect
138. #13133194	C₂³	semidirect
139. #13133194	C₂³	semidirect
140. #13133193	C₂³	semidirect
142. #13133191	C₂³	semidirect
143. #13133190	C₂³	semidirect
144. #13133190	C₂³	semidirect
148. #13133189	C₂³	semidirect
149. #13133189	C₂³	semidirect
150. #13133189	C₂³	semidirect
151. #13133189	C₂³	semidirect
152. #13133189	C₂³	semidirect
153. #13133189	C₂³	semidirect
154. #13133189	C₂³	semidirect
155. #13133188	C₂³	semidirect
156. #13133188	C₂³	semidirect
158. #13133187	C₂³	semidirect
162. #13133186	C₂³	semidirect
165. #13133185	C₂³	semidirect
166. #13133185	C₂³	semidirect
167. #13133185	C₂³	semidirect
168. #13133185	C₂³	semidirect
169. #13133185	C₂³	semidirect
170. #13133185	C₂³	semidirect
171. C₄×Dic₁₀₆	C₂³	semidirect
172. C₄×D₂₁₂	C₂³	semidirect
173. D₄×Dic₅₃	C₂³	semidirect
174. D₄×Dic₅₃	C₂³	semidirect
175. D₄×Dic₅₃	C₂³	semidirect
176. C₄×C₂²⋊D₅₃	C₂³	semidirect
177. C₄×C₂²⋊D₅₃	C₂³	semidirect
179. #13133177	C₂³	semidirect
180. #13133177	C₂³	semidirect
181. #13133176	C₂³	semidirect
182. #13133174	C₂³	semidirect
183. #13133173	C₂³	semidirect
184. #13133173	C₂³	semidirect
185. C₂×#11719919	C₂³	semidirect
186. C₂×#11719919	C₂³	semidirect
190. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
191. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
192. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
193. C₂×#11719921	C₂³	semidirect
194. C₂×#11719921	C₂³	semidirect
195. C₂²⋊C₄×D₅₃	C₂³	semidirect
196. C₂²⋊C₄×D₅₃	C₂³	semidirect
199. C₂×#41×C₅₃	C₂³	semidirect
200. C₂²×Q₈×C₅₃	C₂³	semidirect
207. C₂²×D₄×C₅₃	C₂³	semidirect
208. C₂²×D₄×C₅₃	C₂³	semidirect
210. C₂³×C₄×C₅₃	C₂³	semidirect
212. #127×C₅₃	C₂³	semidirect
213. #127×C₅₃	C₂³	semidirect
215. #124×C₅₃	C₂³	semidirect
216. #124×C₅₃	C₂³	semidirect
218. #121×C₅₃	C₂³	semidirect
219. #121×C₅₃	C₂³	semidirect
221. #120×C₅₃	C₂³	semidirect
222. #120×C₅₃	C₂³	semidirect
223. #117×C₅₃	C₂³	semidirect
224. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
226. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
227. C₂×C₄²×C₅₃	C₂³	semidirect
437. C₂×#535	D₅₃	semidirect
448. C₂²×#41	C₂×D₅₃	semidirect
450. C₂³×D₄	C₂×D₅₃	semidirect
491. #535	C₂×D₅₃	semidirect
492. #535	C₂×D₅₃	semidirect
502. C₂×#127	C₂×D₅₃	semidirect
504. C₂×#124	C₂×D₅₃	semidirect
512. C₂×#121	C₂×D₅₃	semidirect
516. C₂×#120	C₂×D₅₃	semidirect
519. C₂×#117	C₂×D₅₃	semidirect
521. C₅₃	#62862	semidirect
529. C₂×#41	C₂²×D₅₃	semidirect
530. C₂²×Q₈	C₂²×D₅₃	semidirect
546. C₂²×D₄	C₂²×D₅₃	semidirect
547. C₂²×D₄	C₂²×D₅₃	semidirect
551. C₂³×C₄	C₂²×D₅₃	semidirect
555. #127	C₂²×D₅₃	semidirect
556. #127	C₂²×D₅₃	semidirect
569. #124	C₂²×D₅₃	semidirect
570. #124	C₂²×D₅₃	semidirect
613. #121	C₂²×D₅₃	semidirect
614. #121	C₂²×D₅₃	semidirect
630. #120	C₂²×D₅₃	semidirect
631. #120	C₂²×D₅₃	semidirect
646. #117	C₂²×D₅₃	semidirect
649. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
661. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
662. C₂×C₄²	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20289072	2
#20289048	2
#20289018	2
#20288905	2
#20288888	2
#20288869	2
#20288413	2
#20288402	2
#20288359	2
#20288344	2
C₂×#16811182	2
C₂×C₅₃×#535	2
#62862	53