Subgroups — #27366801

Order 13568.

704 conjugacy classes of subgroups.

The subgroup lattice has 454 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	#20284170	C₂	1	2	yes	maximal, complemented
3	#20274283	C₂	1	2	yes	maximal, complemented
4	#20274276	C₂	1	2	yes	maximal, complemented
5	#20274233	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274228	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	C₂×#16810374	C₂	1	1	yes	maximal, characteristic, complemented
10	#20273362	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133237	—	2	2	no	—
13	#16811173	C₂²	1	2	yes	—
14	#16811028	C₂²	1	1	yes	characteristic
15	#16811000	C₂²	1	1	yes	characteristic
16	#16810970	C₂²	1	2	yes	—
17	#16810859	—	2	1	no	—
18	#16810859	—	2	1	no	—
19	#16810845	—	2	2	no	—
20	#16810838	—	2	2	no	—
21	#16810833	C₂²	1	2	yes	—
22	#16810828	C₂²	1	2	yes	—
23	#16810823	C₂²	1	2	yes	—
24	#16810818	C₂²	1	2	yes	—
25	C₄×D₄₂₄	—	2	1	no	—
26	C₄×D₄₂₄	—	2	1	no	—
27	C₂×C₄⋊#88322	C₂²	1	2	yes	—
28	#16810617	—	2	2	no	—
29	#16810374	C₂²	1	1	yes	characteristic
30	#16810374	C₂²	1	1	yes	characteristic
31	#16810374	C₂²	1	2	yes	—
32	#16810368	C₂²	1	2	yes	—
33	#16810368	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	#13133237	—	4	8	no	—
49	C₂×#11719925	—	2	2	no	—
50	C₂×#11719923	—	2	2	no	—
51	C₂×#11719924	—	2	2	no	—
52	C₂×D₄₂₄	—	2	1	no	—
53	C₂×D₄₂₄	—	2	1	no	—
54	C₂×#11719922	—	2	2	no	—
55	C₂²×#88322	—	2	2	no	—
56	#13133217	C₂³	1	2	yes	—
57	#13133214	C₂³	1	2	yes	—
58	#13133205	—	2	2	no	—
59	#13133191	—	2	2	no	—
60	#13133191	—	2	2	no	—
61	C₄×D₂₁₂	—	2	2	no	—
62	C₄×D₂₁₂	—	2	2	no	—
63	#13133151	—	2	1	no	—
64	#13133151	—	2	1	no	—
65	C₄⋊#88322	—	2	2	no	—
66	C₄⋊#88322	C₂³	1	2	yes	—
67	C₄⋊#88322	C₂³	1	2	yes	—
68	#13133140	—	2	2	no	—
69	#13133140	—	2	2	no	—
70	#13133139	—	2	2	no	—
71	#13133139	—	2	2	no	—
72	#13133137	—	2	2	no	—
73	#13133137	—	2	2	no	—
74	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
75	C₂×M₁₆×C₅₃	—	2	1	no	—
76	C₂×M₁₆×C₅₃	—	2	1	no	—
77	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
79	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
80	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
81	C₄×D₄×C₅₃	—	2	1	no	—
82	C₄×D₄×C₅₃	—	2	1	no	—
83	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
84	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
85	#117×C₅₃	—	2	1	no	—
86	#117×C₅₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₅₃	—	2	1	no	—
88	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₅₃	—	2	1	no	—
90	C₄⋊C₈×C₅₃	—	2	1	no	—
91	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₂²⋊C₈×C₅₃	—	2	1	no	—
94	C₂²⋊C₈×C₅₃	—	2	1	no	—
95	C₂²⋊C₈×C₅₃	—	2	1	no	—
96	#97×C₅₃	—	2	1	no	—
97	#97×C₅₃	—	2	1	no	—
98	C₄×C₈×C₅₃	—	2	1	no	—
99	C₄×C₈×C₅₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₅₃	D₄	1	1	yes	characteristic
101	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
103	#41×C₅₃	—	2	4	no	—
104	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₅₃	—	2	1	no	—
106	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₅₃	—	2	1	no	—
108	C₂²×C₄×C₅₃	—	2	1	no	—
109	C₂²×C₄×C₅₃	—	2	1	no	—
110	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
113	C₂×C₂²⋊D₅₃	—	4	2	no	—
114	#11719945	—	4	4	no	—
115	#11719945	—	4	4	no	—
116	C₂×D₂₁₂	—	2	2	no	—
117	C₂×D₂₁₂	—	2	2	no	—
118	C₂×D₂₁₂	—	2	2	no	—
119	C₂×C₄×D₅₃	—	4	2	no	—
120	C₂×Dic₁₀₆	—	2	2	no	—
121	M₁₆×C₅₃	—	4	2	no	—
122	M₁₆×C₅₃	—	4	2	no	—
123	C₂×C₈×C₅₃	—	2	2	no	—
124	C₂×C₈×C₅₃	—	2	1	no	—
125	C₂×C₈×C₅₃	—	2	1	no	—
126	C₂×C₈×C₅₃	—	4	1	no	—
127	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
131	C₄⋊C₄×C₅₃	—	2	1	no	—
132	C₄⋊C₄×C₅₃	—	2	1	no	—
133	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
134	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
135	C₂²⋊C₄×C₅₃	—	2	1	no	—
136	C₂²⋊C₄×C₅₃	—	2	1	no	—
137	C₂²⋊C₄×C₅₃	—	2	1	no	—
138	C₄²×C₅₃	—	2	1	no	—
139	C₄²×C₅₃	—	2	1	no	—
140	C₄²×C₅₃	—	2	1	no	—
141	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₅₃	#41	1	1	yes	characteristic
144	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
145	#11719925	—	4	4	no	—
146	#11719924	—	4	4	no	—
147	#11719923	—	4	4	no	—
148	#11719922	—	4	4	no	—
149	#11719921	—	4	2	no	—
150	#11719921	—	4	2	no	—
151	C₄⋊Dic₅₃	—	2	2	no	—
152	C₄⋊Dic₅₃	—	2	2	no	—
153	C₂×#88322	—	2	2	no	—
154	C₂×#88322	—	2	2	no	—
155	C₂×#88322	—	4	4	no	—
156	D₄₂₄	—	4	2	no	—
157	D₄₂₄	—	4	2	no	—
158	C₂³×C₅₃	—	2	1	no	—
159	C₂³×C₅₃	#121	1	1	yes	characteristic
160	C₂²×D₅₃	—	4	2	no	—
161	Q₈×C₅₃	—	2	2	no	—
162	D₄×C₅₃	—	2	2	no	—
163	D₄×C₅₃	—	4	2	no	—
164	C₂×C₄×C₅₃	—	2	1	no	—
165	C₂×C₄×C₅₃	—	2	1	no	—
166	C₂×C₄×C₅₃	—	2	1	no	—
167	C₂×C₄×C₅₃	—	2	1	no	—
168	C₂×C₄×C₅₃	—	2	1	no	—
169	C₂×C₄×C₅₃	—	4	1	no	—
170	C₂×C₄×C₅₃	—	4	2	no	—
171	C₂×C₄×C₅₃	—	4	1	no	—
172	C₂×C₄×C₅₃	—	4	1	no	—
173	C₂×C₄×C₅₃	—	4	2	no	—
174	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
175	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
176	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
177	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	4	yes	—
178	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
181	C₂²⋊D₅₃	—	8	4	no	—
182	C₂×Dic₅₃	—	4	2	no	—
183	D₂₁₂	—	4	2	no	—
184	D₂₁₂	—	4	2	no	—
185	D₂₁₂	—	4	2	no	—
186	D₂₁₂	—	4	2	no	—
187	D₂₁₂	—	8	2	no	—
188	C₄×D₅₃	—	8	4	no	—
189	Dic₁₀₆	—	4	2	no	—
190	Dic₁₀₆	—	4	2	no	—
191	C₈×C₅₃	—	2	1	no	—
192	C₈×C₅₃	—	2	1	no	—
193	C₈×C₅₃	—	2	1	no	—
194	C₈×C₅₃	—	4	1	no	—
195	C₈×C₅₃	—	4	1	no	—
196	C₈×C₅₃	#135	1	2	yes	complemented
197	#88322	—	4	2	no	—
198	#88322	—	4	2	no	—
199	#19157	—	53	1	no	maximal, Sylow
200	C₂²×C₅₃	—	2	1	no	—
201	C₂²×C₅₃	—	2	1	no	—
202	C₂²×C₅₃	—	4	1	no	—
203	C₂²×C₅₃	—	4	1	no	—
204	C₂²×C₅₃	—	4	1	no	—
205	C₂²×C₅₃	#469	1	2	yes	—
206	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
207	C₂×D₅₃	—	8	2	no	—
208	C₂×D₅₃	—	8	2	no	—
209	C₂×D₅₃	—	8	2	no	—
210	C₄×C₅₃	—	2	1	no	—
211	C₄×C₅₃	—	2	1	no	—
212	C₄×C₅₃	—	2	1	no	—
213	C₄×C₅₃	—	4	1	no	—
214	C₄×C₅₃	—	4	1	no	—
215	C₄×C₅₃	—	4	1	no	—
216	C₄×C₅₃	#469	1	2	yes	—
217	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
218	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
219	C₄×C₅₃	#575	1	1	yes	characteristic
220	Dic₅₃	—	8	2	no	—
221	#3169	—	53	1	no	—
222	#3035	—	53	2	no	—
223	#2965	D₅₃	1	1	yes	characteristic, complemented
224	#1702	—	53	2	no	—
225	#1701	—	53	2	no	—
226	#1694	—	53	1	no	—
227	#1693	—	53	1	no	—
228	#1688	—	53	1	no	—
229	#1687	—	53	1	no	—
230	C₂×#334	—	53	1	no	—
231	#1540	—	53	2	no	—
232	C₂×C₅₃	—	2	2	no	—
233	C₂×C₅₃	—	8	1	no	—
234	C₂×C₅₃	#3035	1	1	yes	characteristic
235	C₂×C₅₃	C₂×#469	1	1	yes	characteristic
236	C₂×C₅₃	#3067	1	1	yes	characteristic
237	D₅₃	—	16	2	no	—
238	C₂×#135	—	106	2	no	—
239	#532	—	53	2	no	—
240	C₄×#41	C₂×D₅₃	1	1	yes	characteristic
241	#500	—	53	1	no	—
242	#493	—	53	1	no	—
243	#486	—	53	2	no	—
244	#466	—	106	1	no	—
245	#466	—	106	1	no	—
246	#464	—	106	2	no	—
247	#463	—	106	2	no	—
248	#462	—	53	2	no	—
249	#461	—	53	2	no	—
250	#460	—	53	2	no	—
251	#459	—	53	2	no	—
252	#446	C₂×D₅₃	1	1	yes	characteristic
253	#446	C₂×D₅₃	1	1	yes	characteristic
254	C₄×D₈	—	106	1	no	—
255	C₄×D₈	—	106	1	no	—
256	#436	C₂×D₅₃	1	1	yes	characteristic
257	#436	C₂×D₅₃	1	1	yes	characteristic
258	#435	—	2	1	no	—
259	#435	—	2	1	no	—
260	#431	—	2	1	no	—
261	#431	C₂×D₅₃	1	1	yes	characteristic
262	C₂×C₄⋊C₈	—	53	2	no	—
263	#416	—	106	2	no	—
264	C₄×M₁₆	—	2	1	no	—
265	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
266	#334	—	53	1	no	—
267	#334	—	53	1	no	—
268	#334	—	53	2	no	—
269	#332	—	53	2	no	—
270	#332	—	53	2	no	—
271	#331	—	53	2	no	—
272	#331	—	53	2	no	—
273	C₅₃	#19157	1	1	yes	characteristic, complemented, Sylow
274	C₂×#41	—	106	2	no	—
275	C₂×#41	D₂₁₂	1	1	yes	characteristic
276	#135	—	212	8	no	—
277	C₂×Q₁₆	—	106	2	no	—
278	C₂×SD₁₆	—	106	2	no	—
279	C₂×SD₁₆	—	106	2	no	—
280	C₂×D₈	—	106	2	no	—
281	C₂×D₈	—	106	1	no	—
282	C₂×D₈	—	106	1	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	—	2	1	no	—
285	C₂²×C₈	—	106	2	no	—
286	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
287	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
288	C₄⋊Q₈	—	53	2	no	—
289	#127	—	53	2	no	—
290	#124	—	106	2	no	—
291	#121	—	106	2	no	—
292	#121	—	106	2	no	—
293	C₄×Q₈	D₂₁₂	1	1	yes	characteristic
294	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	—	106	2	no	—
298	C₄×D₄	—	106	2	no	—
299	C₄×D₄	D₂₁₂	1	1	yes	characteristic
300	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
301	#117	—	2	1	no	—
302	#117	D₂₁₂	1	1	yes	characteristic
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
305	#107	—	106	1	no	—
306	#107	—	106	1	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	—	2	1	no	—
309	C₄⋊C₈	—	53	2	no	—
310	C₄⋊C₈	—	53	2	no	—
311	C₄⋊C₈	—	106	2	no	—
312	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
313	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
314	#103	—	106	2	no	—
315	#103	—	106	2	no	—
316	#102	—	106	2	no	—
317	#102	—	106	2	no	—
318	#102	—	106	2	no	—
319	#102	—	106	2	no	—
320	C₂²⋊C₈	—	2	1	no	—
321	C₂²⋊C₈	—	2	1	no	—
322	C₂²⋊C₈	—	2	1	no	—
323	#97	—	2	1	no	—
324	#97	—	2	1	no	—
325	C₄×C₈	—	2	1	no	—
326	C₄×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
327	C₄×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
328	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
330	#41	—	2	4	no	—
331	#41	—	212	4	no	—
332	#41	—	212	4	no	—
333	C₂×Q₈	—	106	2	no	—
334	C₂×Q₈	C₂×D₂₁₂	1	1	yes	characteristic
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	106	2	no	—
337	C₂×D₄	—	106	2	no	—
338	C₂×D₄	—	106	2	no	—
339	C₂×D₄	—	212	2	no	—
340	C₂×D₄	C₂×D₂₁₂	1	1	yes	characteristic
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	212	2	no	—
345	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
346	C₂²×C₄	#11719945	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
348	Q₁₆	—	212	4	no	—
349	SD₁₆	—	212	4	no	—
350	SD₁₆	—	212	4	no	—
351	D₈	—	212	2	no	—
352	D₈	—	212	4	no	—
353	D₈	—	212	2	no	—
354	M₁₆	—	4	2	no	—
355	M₁₆	—	4	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	106	2	no	—
361	C₂×C₈	—	106	2	no	—
362	C₂×C₈	—	212	4	no	—
363	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
364	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
365	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
366	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	106	2	no	—
370	C₄⋊C₄	—	106	2	no	—
371	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
372	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
373	C₂²⋊C₄	—	2	1	no	—
374	C₂²⋊C₄	—	2	1	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	212	2	no	—
377	C₂²⋊C₄	—	212	2	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	C₂×D₂₁₂	1	1	yes	characteristic
382	C₄²	#11719945	1	1	yes	characteristic
383	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
384	C₄²	C₂³×D₅₃	1	1	yes	characteristic
385	C₂³	—	2	1	no	—
386	C₂³	—	212	2	no	—
387	C₂³	#13133191	1	1	yes	characteristic
388	Q₈	—	2	2	no	—
389	Q₈	—	212	2	no	—
390	Q₈	—	212	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	424	2	no	—
394	D₄	—	424	4	no	—
395	D₄	—	212	2	no	—
396	D₄	—	212	2	no	—
397	D₄	—	212	2	no	—
398	D₄	—	212	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	424	4	no	—
410	C₂×C₄	—	212	2	no	—
411	C₂×C₄	#13133191	1	1	yes	characteristic
412	C₂×C₄	#13133191	1	1	yes	characteristic
413	C₂×C₄	#13133191	1	1	yes	characteristic
414	C₂×C₄	#13133245	1	4	yes	—
415	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
417	C₂×C₄	C₂×#11719945	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	4	1	no	—
422	C₈	—	4	1	no	—
423	C₈	—	212	2	no	—
424	C₈	—	212	2	no	—
425	C₈	#13133237	1	2	yes	complemented
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	424	2	no	—
432	C₂²	—	424	2	no	—
433	C₂²	—	424	2	no	—
434	C₂²	#16810876	1	2	yes	—
435	C₂²	C₂×#13133191	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	—	424	2	no	—
443	C₄	#16810876	1	2	yes	—
444	C₄	C₂×#13133237	1	1	yes	characteristic
445	C₄	C₂×#13133245	1	2	yes	—
446	C₄	#16811421	1	1	yes	characteristic
447	C₂	—	2	2	no	—
448	C₂	—	8	1	no	—
449	C₂	—	848	2	no	—
450	C₂	#20284170	1	1	yes	characteristic
451	C₂	C₂×#16810876	1	1	yes	characteristic
452	C₂	#20284435	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	#19157
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. #20284170	C₂	semidirect
3. #20274283	C₂	semidirect
4. #20274276	C₂	semidirect
5. #20274233	C₂	semidirect
6. #20274228	C₂	semidirect
7. #20274199	C₂	semidirect
8. #20274194	C₂	semidirect
9. C₂×#16810374	C₂	semidirect
10. #20273362	C₂	semidirect
11. C₅₃×#2965	C₂	semidirect
196. C₈×C₅₃	#135	semidirect
223. #2965	D₅₃	semidirect
273. C₅₃	#19157	semidirect
425. C₈	#13133237	semidirect

Maximal subgroups

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

subgroup	index
#20285294	2
#20284170	2
#20274283	2
#20274276	2
#20274233	2
#20274228	2
#20274199	2
#20274194	2
C₂×#16810374	2
#20273362	2
C₅₃×#2965	2
#19157	53