Subgroups — #27366838

Order 13568.

642 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20285294	C₂	1	1	yes	maximal, characteristic, complemented
2	#20284775	C₂	1	2	yes	maximal, complemented
3	#20274255	C₂	1	2	yes	maximal, complemented
4	#20274248	C₂	1	2	yes	maximal, complemented
5	#20274243	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274238	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274199	C₂	1	1	yes	maximal, characteristic, complemented
8	#20274194	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273463	C₂	1	1	yes	maximal, characteristic, complemented
10	#20273375	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811173	C₂²	1	2	yes	—
13	#16811028	C₂²	1	1	yes	characteristic
14	#16811000	C₂²	1	1	yes	characteristic
15	#16810970	C₂²	1	2	yes	—
16	#16810947	—	2	2	no	—
17	#16810918	C₂²	1	2	yes	—
18	#16810913	C₂²	1	2	yes	—
19	#16810859	—	2	1	no	—
20	#16810859	—	2	1	no	—
21	#16810823	C₂²	1	2	yes	—
22	#16810818	C₂²	1	2	yes	—
23	#16810768	—	2	2	no	—
24	C₄×#11719924	—	2	2	no	—
25	C₄×D₄₂₄	—	2	1	no	—
26	C₄×D₄₂₄	—	2	1	no	—
27	C₄×#11719922	—	2	2	no	—
28	#16810676	C₂²	1	2	yes	—
29	#16810376	C₂²	1	2	yes	—
30	#16810374	C₂²	1	1	yes	characteristic
31	#16810374	C₂²	1	1	yes	characteristic
32	#16810371	C₂²	1	2	yes	—
33	#16810371	C₂²	1	2	yes	—
34	#16810366	C₂²	1	2	yes	—
35	#16810366	C₂²	1	2	yes	—
36	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
37	C₅₃×#446	C₂²	1	1	yes	characteristic
38	C₅₃×#446	C₂²	1	1	yes	characteristic
39	C₅₃×#436	C₂²	1	1	yes	characteristic
40	C₅₃×#436	C₂²	1	1	yes	characteristic
41	C₅₃×#435	—	2	1	no	—
42	C₅₃×#435	—	2	1	no	—
43	C₅₃×#431	—	2	1	no	—
44	C₅₃×#431	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₅₃	—	2	1	no	—
46	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×#11719945	—	2	2	no	—
48	C₂×#11719924	—	2	2	no	—
49	C₂×D₄₂₄	—	2	1	no	—
50	C₂×D₄₂₄	—	2	1	no	—
51	C₂×#11719922	—	2	2	no	—
52	#13133217	C₂³	1	2	yes	—
53	#13133214	C₂³	1	2	yes	—
54	#13133205	—	2	2	no	—
55	#13133191	—	2	2	no	—
56	#13133191	—	2	2	no	—
57	C₄×D₂₁₂	—	2	2	no	—
58	C₄×D₂₁₂	—	2	2	no	—
59	#13133151	—	2	1	no	—
60	#13133151	—	2	1	no	—
61	#13133150	—	2	2	no	—
62	#13133148	—	2	2	no	—
63	C₄⋊#88322	C₂³	1	2	yes	—
64	C₄⋊#88322	C₂³	1	2	yes	—
65	#13133141	—	2	2	no	—
66	#13133139	—	2	2	no	—
67	#13133139	—	2	2	no	—
68	#13133138	—	2	2	no	—
69	#13133137	—	2	2	no	—
70	#13133137	—	2	2	no	—
71	C₂²⋊#88322	—	2	2	no	—
72	C₄×#88322	—	2	2	no	—
73	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
74	C₂×M₁₆×C₅₃	—	2	1	no	—
75	C₂×M₁₆×C₅₃	—	2	1	no	—
76	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
79	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
80	C₄×D₄×C₅₃	—	2	1	no	—
81	C₄×D₄×C₅₃	—	2	1	no	—
82	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
83	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
84	#117×C₅₃	—	2	1	no	—
85	#117×C₅₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₅₃	—	2	1	no	—
87	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₅₃	—	2	1	no	—
89	C₄⋊C₈×C₅₃	—	2	1	no	—
90	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
92	C₂²⋊C₈×C₅₃	—	2	1	no	—
93	C₂²⋊C₈×C₅₃	—	2	1	no	—
94	C₂²⋊C₈×C₅₃	—	2	1	no	—
95	#97×C₅₃	—	2	1	no	—
96	#97×C₅₃	—	2	1	no	—
97	C₄×C₈×C₅₃	—	2	1	no	—
98	C₄×C₈×C₅₃	D₄	1	1	yes	characteristic
99	C₄×C₈×C₅₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
102	#41×C₅₃	—	4	2	no	—
103	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
104	C₂×D₄×C₅₃	—	2	1	no	—
105	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₅₃	—	2	1	no	—
107	C₂²×C₄×C₅₃	—	2	1	no	—
108	C₂²×C₄×C₅₃	—	2	1	no	—
109	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
112	C₂×C₂²⋊D₅₃	—	4	2	no	—
113	#11719945	—	8	4	no	—
114	C₂×D₂₁₂	—	2	2	no	—
115	C₂×D₂₁₂	—	2	2	no	—
116	C₂×D₂₁₂	—	2	2	no	—
117	C₂×C₄×D₅₃	—	4	2	no	—
118	C₂×Dic₁₀₆	—	2	2	no	—
119	M₁₆×C₅₃	—	4	2	no	—
120	M₁₆×C₅₃	—	4	2	no	—
121	C₂×C₈×C₅₃	—	2	2	no	—
122	C₂×C₈×C₅₃	—	2	1	no	—
123	C₂×C₈×C₅₃	—	2	1	no	—
124	C₂×C₈×C₅₃	—	4	1	no	—
125	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
129	C₄⋊C₄×C₅₃	—	2	1	no	—
130	C₄⋊C₄×C₅₃	—	2	1	no	—
131	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
132	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
133	C₂²⋊C₄×C₅₃	—	2	1	no	—
134	C₂²⋊C₄×C₅₃	—	2	1	no	—
135	C₂²⋊C₄×C₅₃	—	2	1	no	—
136	C₄²×C₅₃	—	2	1	no	—
137	C₄²×C₅₃	—	2	1	no	—
138	C₄²×C₅₃	—	2	1	no	—
139	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₅₃	#41	1	1	yes	characteristic
142	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
143	#11719924	—	4	4	no	—
144	#11719922	—	4	4	no	—
145	#11719921	—	4	2	no	—
146	#11719921	—	4	2	no	—
147	C₄⋊Dic₅₃	—	2	2	no	—
148	C₄⋊Dic₅₃	—	2	2	no	—
149	C₂×#88322	—	2	2	no	—
150	C₂×#88322	—	2	2	no	—
151	D₄₂₄	—	4	2	no	—
152	D₄₂₄	—	4	2	no	—
153	C₂³×C₅₃	—	2	1	no	—
154	C₂³×C₅₃	#121	1	1	yes	characteristic
155	C₂²×D₅₃	—	4	2	no	—
156	Q₈×C₅₃	—	2	2	no	—
157	D₄×C₅₃	—	2	2	no	—
158	D₄×C₅₃	—	4	2	no	—
159	C₂×C₄×C₅₃	—	2	1	no	—
160	C₂×C₄×C₅₃	—	2	2	no	—
161	C₂×C₄×C₅₃	—	2	1	no	—
162	C₂×C₄×C₅₃	—	2	2	no	—
163	C₂×C₄×C₅₃	—	2	1	no	—
164	C₂×C₄×C₅₃	—	2	1	no	—
165	C₂×C₄×C₅₃	—	2	1	no	—
166	C₂×C₄×C₅₃	—	4	2	no	—
167	C₂×C₄×C₅₃	—	4	1	no	—
168	C₂×C₄×C₅₃	—	4	1	no	—
169	C₂×C₄×C₅₃	—	4	2	no	—
170	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
171	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
172	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
173	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
176	C₂²⋊D₅₃	—	8	4	no	—
177	C₂×Dic₅₃	—	4	2	no	—
178	D₂₁₂	—	4	2	no	—
179	D₂₁₂	—	4	2	no	—
180	D₂₁₂	—	4	2	no	—
181	D₂₁₂	—	4	2	no	—
182	D₂₁₂	—	8	2	no	—
183	C₄×D₅₃	—	8	4	no	—
184	Dic₁₀₆	—	8	2	no	—
185	C₈×C₅₃	—	2	1	no	—
186	C₈×C₅₃	—	2	1	no	—
187	C₈×C₅₃	—	2	1	no	—
188	C₈×C₅₃	—	4	1	no	—
189	C₈×C₅₃	—	4	1	no	—
190	C₈×C₅₃	#135	1	2	yes	—
191	#88322	—	4	2	no	—
192	#88322	—	4	2	no	—
193	#19160	—	53	1	no	maximal, Sylow
194	C₂²×C₅₃	—	2	1	no	—
195	C₂²×C₅₃	—	2	1	no	—
196	C₂²×C₅₃	—	2	1	no	—
197	C₂²×C₅₃	—	4	1	no	—
198	C₂²×C₅₃	—	4	1	no	—
199	C₂²×C₅₃	—	4	1	no	—
200	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
201	C₂×D₅₃	—	8	2	no	—
202	C₂×D₅₃	—	8	2	no	—
203	C₂×D₅₃	—	8	2	no	—
204	C₄×C₅₃	—	2	1	no	—
205	C₄×C₅₃	—	2	1	no	—
206	C₄×C₅₃	—	2	1	no	—
207	C₄×C₅₃	—	4	1	no	—
208	C₄×C₅₃	—	4	1	no	—
209	C₄×C₅₃	—	4	1	no	—
210	C₄×C₅₃	#472	1	2	yes	—
211	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
212	C₄×C₅₃	#575	1	1	yes	characteristic
213	C₄×C₅₃	#575	1	2	yes	—
214	Dic₅₃	—	8	2	no	—
215	#3169	—	53	1	no	—
216	#3106	—	53	2	no	—
217	#2965	D₅₃	1	1	yes	characteristic, complemented
218	#1698	—	53	2	no	—
219	#1697	—	53	2	no	—
220	#1696	—	53	1	no	—
221	#1695	—	53	1	no	—
222	#1688	—	53	1	no	—
223	#1687	—	53	1	no	—
224	#1564	—	53	1	no	—
225	#1543	—	53	2	no	—
226	C₂×C₅₃	—	4	1	no	—
227	C₂×C₅₃	—	8	1	no	—
228	C₂×C₅₃	#3035	1	1	yes	characteristic
229	C₂×C₅₃	#3054	1	1	yes	characteristic
230	C₂×C₅₃	C₂×#472	1	1	yes	characteristic
231	D₅₃	—	16	2	no	—
232	#532	—	53	2	no	—
233	C₄×#41	C₂×D₅₃	1	1	yes	characteristic
234	#500	—	53	1	no	—
235	#493	—	53	1	no	—
236	#486	—	53	2	no	—
237	#482	—	106	2	no	—
238	#477	—	53	2	no	—
239	#476	—	53	2	no	—
240	#466	—	106	1	no	—
241	#466	—	106	1	no	—
242	#460	—	53	2	no	—
243	#459	—	53	2	no	—
244	#449	—	106	2	no	—
245	#446	C₂×D₅₃	1	1	yes	characteristic
246	#446	C₂×D₅₃	1	1	yes	characteristic
247	C₄×SD₁₆	—	106	2	no	—
248	C₄×D₈	—	106	2	no	—
249	C₄×D₈	—	106	1	no	—
250	C₄×D₈	—	106	1	no	—
251	#436	C₂×D₅₃	1	1	yes	characteristic
252	#436	C₂×D₅₃	1	1	yes	characteristic
253	#435	—	2	1	no	—
254	#435	—	2	1	no	—
255	#431	—	2	1	no	—
256	#431	—	53	2	no	—
257	#431	C₂×D₅₃	1	1	yes	characteristic
258	C₄×M₁₆	—	2	1	no	—
259	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
260	#335	—	53	2	no	—
261	#334	—	53	1	no	—
262	#334	—	53	1	no	—
263	#333	—	53	2	no	—
264	#333	—	53	2	no	—
265	#331	—	53	2	no	—
266	#331	—	53	2	no	—
267	C₅₃	#19160	1	1	yes	characteristic, complemented, Sylow
268	C₂×#41	—	106	2	no	—
269	C₂×#41	D₂₁₂	1	1	yes	characteristic
270	C₂×SD₁₆	—	106	2	no	—
271	C₂×D₈	—	106	2	no	—
272	C₂×D₈	—	106	1	no	—
273	C₂×D₈	—	106	1	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
277	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
278	C₄⋊Q₈	—	53	2	no	—
279	#127	—	53	2	no	—
280	#124	—	106	2	no	—
281	#121	—	106	2	no	—
282	#121	—	106	2	no	—
283	C₄×Q₈	D₂₁₂	1	1	yes	characteristic
284	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	—	106	2	no	—
288	C₄×D₄	—	106	2	no	—
289	C₄×D₄	D₂₁₂	1	1	yes	characteristic
290	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
291	#117	—	2	1	no	—
292	#117	D₂₁₂	1	1	yes	characteristic
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
295	#107	—	106	1	no	—
296	#107	—	106	1	no	—
297	#107	—	106	2	no	—
298	#106	—	106	2	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	—	53	2	no	—
302	C₄⋊C₈	—	53	2	no	—
303	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
304	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
305	#103	—	106	2	no	—
306	#102	—	106	2	no	—
307	#102	—	106	2	no	—
308	#102	—	106	2	no	—
309	#102	—	106	2	no	—
310	#102	—	106	2	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	106	2	no	—
315	#97	—	2	1	no	—
316	#97	—	2	1	no	—
317	C₄×C₈	—	2	1	no	—
318	C₄×C₈	—	106	2	no	—
319	C₄×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
320	C₄×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
321	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
322	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
323	#41	—	4	2	no	—
324	#41	—	424	4	no	—
325	C₂×Q₈	—	106	2	no	—
326	C₂×Q₈	C₂×D₂₁₂	1	1	yes	characteristic
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	106	2	no	—
329	C₂×D₄	—	106	2	no	—
330	C₂×D₄	—	106	2	no	—
331	C₂×D₄	—	212	2	no	—
332	C₂×D₄	C₂×D₂₁₂	1	1	yes	characteristic
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	212	2	no	—
337	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
338	C₂²×C₄	#11719945	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
340	SD₁₆	—	212	4	no	—
341	D₈	—	212	2	no	—
342	D₈	—	212	4	no	—
343	D₈	—	212	2	no	—
344	M₁₆	—	4	2	no	—
345	M₁₆	—	4	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	106	2	no	—
351	C₂×C₈	—	106	2	no	—
352	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
353	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
354	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
355	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	106	2	no	—
359	C₄⋊C₄	—	106	2	no	—
360	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
361	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	212	2	no	—
366	C₂²⋊C₄	—	212	2	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	C₂×D₂₁₂	1	1	yes	characteristic
371	C₄²	#11719945	1	1	yes	characteristic
372	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
373	C₄²	C₂³×D₅₃	1	1	yes	characteristic
374	C₂³	—	2	1	no	—
375	C₂³	—	212	2	no	—
376	C₂³	#13133191	1	1	yes	characteristic
377	Q₈	—	2	2	no	—
378	Q₈	—	424	2	no	—
379	D₄	—	2	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	424	2	no	—
382	D₄	—	424	4	no	—
383	D₄	—	212	2	no	—
384	D₄	—	212	2	no	—
385	D₄	—	212	2	no	—
386	D₄	—	212	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	424	4	no	—
399	C₂×C₄	—	212	2	no	—
400	C₂×C₄	#13133191	1	1	yes	characteristic
401	C₂×C₄	#13133191	1	1	yes	characteristic
402	C₂×C₄	#13133191	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
404	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
405	C₂×C₄	C₂×#11719945	1	1	yes	characteristic
406	C₈	—	2	1	no	—
407	C₈	—	2	1	no	—
408	C₈	—	2	1	no	—
409	C₈	—	4	1	no	—
410	C₈	—	4	1	no	—
411	C₈	—	212	2	no	—
412	C₈	—	212	2	no	—
413	C₈	#13133237	1	2	yes	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	424	2	no	—
421	C₂²	—	424	2	no	—
422	C₂²	—	424	2	no	—
423	C₂²	C₂×#13133191	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	1	no	—
429	C₄	—	4	1	no	—
430	C₄	—	424	2	no	—
431	C₄	#16810893	1	2	yes	—
432	C₄	C₂×#13133237	1	1	yes	characteristic
433	C₄	#16811421	1	1	yes	characteristic
434	C₄	#16811423	1	2	yes	—
435	C₂	—	4	1	no	—
436	C₂	—	8	1	no	—
437	C₂	—	848	2	no	—
438	C₂	#20284170	1	1	yes	characteristic
439	C₂	#20284324	1	1	yes	characteristic
440	C₂	C₂×#16810893	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13133191
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#2965	C₂
socle	C₂²×C₅₃	C₂×#121
hypercenter	#2965	D₅₃
hypocenter	C₅₃	#19160
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2965

Complements

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

N	H ≅ G/N	type
1. #20285294	C₂	semidirect
2. #20284775	C₂	semidirect
3. #20274255	C₂	semidirect
4. #20274248	C₂	semidirect
5. #20274243	C₂	semidirect
6. #20274238	C₂	semidirect
7. #20274199	C₂	semidirect
8. #20274194	C₂	semidirect
9. #20273463	C₂	semidirect
10. #20273375	C₂	semidirect
11. C₅₃×#2965	C₂	semidirect
217. #2965	D₅₃	semidirect
267. C₅₃	#19160	semidirect

Maximal subgroups

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

subgroup	index
#20285294	2
#20284775	2
#20274255	2
#20274248	2
#20274243	2
#20274238	2
#20274199	2
#20274194	2
#20273463	2
#20273375	2
C₅₃×#2965	2
#19160	53