Subgroups — #27367991

Order 13568.

702 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	#494×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#20284525	C₂	1	2	yes	maximal
3	C₈×#11719949	C₂	1	1	yes	maximal, characteristic
4	#20274085	C₂	1	1	yes	maximal, characteristic, complemented
5	#20274083	C₂	1	2	yes	maximal, complemented
6	#20274081	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274079	C₂	1	2	yes	maximal, complemented
8	#20274077	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273472	C₂	1	1	yes	maximal, characteristic, complemented
10	#20273398	C₂	1	2	yes	maximal, complemented
11	C₅₃×#1670	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₅₃	—	2	1	no	—
13	C₂×Q₁₆×D₅₃	—	2	1	no	—
14	C₄⋊Q₈×D₅₃	C₂²	1	2	yes	—
15	C₄×#11719949	C₂²	1	1	yes	characteristic
16	#16811003	C₂²	1	1	yes	characteristic
17	#16811002	C₂²	1	2	yes	—
18	#16811001	—	2	1	no	—
19	#16811001	—	2	1	no	—
20	#16810916	—	2	2	no	—
21	#16810912	—	2	2	no	—
22	#16810908	C₂²	1	2	yes	—
23	#16810904	C₂²	1	2	yes	—
24	#16810900	C₂²	1	2	yes	—
25	Q₈×#88322	C₂²	1	1	yes	characteristic
26	C₈×D₂₁₂	—	2	1	no	—
27	C₈×D₂₁₂	C₂²	1	1	yes	characteristic
28	#16810688	—	2	1	no	—
29	#16810688	C₂²	1	1	yes	characteristic
30	#16810675	—	2	1	no	—
31	#16810675	C₂²	1	1	yes	characteristic
32	#16810662	—	2	2	no	—
33	#16810645	C₂²	1	2	yes	—
34	#16810623	—	2	2	no	—
35	C₄×C₈×D₅₃	—	2	1	no	—
36	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
37	#16810376	C₂²	1	1	yes	characteristic
38	#16810375	C₂²	1	2	yes	—
39	#16810370	C₂²	1	2	yes	—
40	#16810369	C₂²	1	2	yes	—
41	#16810368	C₂²	1	2	yes	—
42	C₅₃×#494	C₂²	1	1	yes	characteristic
43	C₅₃×#475	C₂²	1	2	yes	—
44	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#335	C₂²	1	1	yes	characteristic
46	C₅₃×#332	C₂²	1	2	yes	—
47	C₂×#11719949	D₄	1	1	yes	characteristic
48	C₂×Q₈×D₅₃	—	2	2	no	—
49	C₂×Dic₂₁₂	—	2	1	no	—
50	C₂×Dic₂₁₂	—	2	1	no	—
51	C₂×#11719925	—	2	2	no	—
52	C₂×#11719925	—	2	2	no	—
53	Q₁₆×D₅₃	—	4	4	no	—
54	Q₁₆×D₅₃	—	4	4	no	—
55	C₂×#11719912	—	2	2	no	—
56	C₂×C₈×D₅₃	—	2	1	no	—
57	C₂×C₈×D₅₃	—	2	1	no	—
58	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
59	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
60	#13133217	C₂³	1	2	yes	—
61	#13133216	—	2	2	no	—
62	#13133216	—	2	2	no	—
63	#13133215	—	2	2	no	—
64	Q₈×Dic₅₃	D₄	1	1	yes	characteristic
65	C₄×D₂₁₂	—	2	1	no	—
66	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
67	#13133179	—	2	1	no	—
68	#13133179	D₄	1	1	yes	characteristic
69	#13133175	—	2	1	no	—
70	#13133175	D₄	1	1	yes	characteristic
71	C₄⋊C₄×D₅₃	—	2	2	no	—
72	C₄⋊C₄×D₅₃	—	2	2	no	—
73	C₄²×D₅₃	—	2	1	no	—
74	C₄²×D₅₃	C₂³	1	1	yes	characteristic
75	#13133151	—	2	2	no	—
76	#13133150	—	2	2	no	—
77	#13133148	—	2	2	no	—
78	C₄⋊#88322	—	2	1	no	—
79	C₄⋊#88322	C₂³	1	1	yes	characteristic
80	C₄⋊#88322	C₂³	1	2	yes	—
81	#13133146	—	2	2	no	—
82	#13133141	—	2	2	no	—
83	#13133139	—	2	2	no	—
84	#13133137	—	2	2	no	—
85	#13133129	—	2	1	no	—
86	#13133129	—	2	1	no	—
87	#13133129	—	2	1	no	—
88	C₄×#88322	—	2	1	no	—
89	C₄×#88322	C₂³	1	1	yes	characteristic
90	C₈×Dic₅₃	—	2	1	no	—
91	C₈×Dic₅₃	D₄	1	1	yes	characteristic
92	C₈×Dic₅₃	D₄	1	1	yes	characteristic
93	C₂×Q₁₆×C₅₃	—	2	1	no	—
94	C₂×Q₁₆×C₅₃	—	2	1	no	—
95	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
96	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
97	#106×C₅₃	—	2	2	no	—
98	C₄⋊C₈×C₅₃	—	2	1	no	—
99	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
101	#103×C₅₃	—	2	2	no	—
102	C₄×C₈×C₅₃	—	2	1	no	—
103	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
104	C₂×Q₈×C₅₃	—	2	2	no	—
105	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
106	#11719949	—	2	2	no	—
107	#11719949	Q₁₆	1	4	yes	complemented
108	Q₈×D₅₃	—	4	4	no	—
109	Q₈×D₅₃	—	4	4	no	—
110	C₂×D₂₁₂	—	2	1	no	—
111	C₂×D₂₁₂	C₂×D₄	1	1	yes	characteristic
112	C₂×C₄×D₅₃	—	2	1	no	—
113	C₂×C₄×D₅₃	—	2	1	no	—
114	C₂×C₄×D₅₃	—	2	1	no	—
115	C₂×C₄×D₅₃	—	4	2	no	—
116	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
119	C₂×Dic₁₀₆	—	2	2	no	—
120	C₂×Dic₁₀₆	—	4	2	no	—
121	Q₁₆×C₅₃	—	4	2	no	—
122	Q₁₆×C₅₃	—	4	2	no	—
123	C₂×C₈×C₅₃	—	2	1	no	—
124	C₂×C₈×C₅₃	—	2	2	no	—
125	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₅₃	—	2	1	no	—
128	C₄⋊C₄×C₅₃	—	2	2	no	—
129	C₄⋊C₄×C₅₃	—	2	2	no	—
130	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₅₃	—	2	1	no	—
132	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
133	#11719925	—	4	4	no	—
134	#11719925	—	4	4	no	—
135	#11719921	—	2	1	no	—
136	#11719921	—	2	1	no	—
137	#11719921	—	2	1	no	—
138	C₄⋊Dic₅₃	—	2	1	no	—
139	C₄⋊Dic₅₃	—	2	2	no	—
140	C₄⋊Dic₅₃	—	2	2	no	—
141	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
142	#11719919	—	4	2	no	—
143	#11719919	—	4	2	no	—
144	C₄×Dic₅₃	—	2	1	no	—
145	C₄×Dic₅₃	—	2	1	no	—
146	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
147	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
148	C₄×Dic₅₃	#41	1	1	yes	characteristic
149	C₂×#88322	—	2	1	no	—
150	C₂×#88322	—	2	2	no	—
151	C₂×#88322	C₂×D₄	1	1	yes	characteristic
152	C₂×#88322	C₂×D₄	1	1	yes	characteristic
153	Dic₂₁₂	—	4	2	no	—
154	Dic₂₁₂	—	4	2	no	—
155	#11719912	—	4	4	no	—
156	C₈×D₅₃	—	2	2	no	—
157	C₈×D₅₃	—	2	2	no	—
158	C₈×D₅₃	—	4	2	no	—
159	C₈×D₅₃	—	4	2	no	—
160	C₂²×D₅₃	—	2	1	no	—
161	C₂²×D₅₃	#121	1	1	yes	characteristic
162	Q₈×C₅₃	—	2	1	no	—
163	Q₈×C₅₃	—	4	2	no	—
164	Q₈×C₅₃	—	4	2	no	—
165	Q₈×C₅₃	C₂×Q₁₆	1	2	yes	complemented
166	C₂×C₄×C₅₃	—	2	1	no	—
167	C₂×C₄×C₅₃	—	2	1	no	—
168	C₂×C₄×C₅₃	—	4	2	no	—
169	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
172	C₂×Dic₅₃	—	2	1	no	—
173	C₂×Dic₅₃	—	4	2	no	—
174	C₂×Dic₅₃	#121	1	1	yes	characteristic
175	C₂×Dic₅₃	#121	1	1	yes	characteristic
176	C₂×Dic₅₃	#121	1	1	yes	characteristic
177	D₂₁₂	—	2	4	no	—
178	D₂₁₂	—	2	1	no	—
179	D₂₁₂	C₂×Q₁₆	1	2	yes	complemented
180	C₄×D₅₃	—	2	1	no	—
181	C₄×D₅₃	—	2	1	no	—
182	C₄×D₅₃	—	2	4	no	—
183	C₄×D₅₃	—	2	2	no	—
184	C₄×D₅₃	—	4	1	no	—
185	C₄×D₅₃	—	4	1	no	—
186	C₄×D₅₃	—	4	2	no	—
187	C₄×D₅₃	—	8	4	no	—
188	C₄×D₅₃	C₂×Q₁₆	1	2	yes	—
189	C₄×D₅₃	#135	1	2	yes	—
190	Dic₁₀₆	—	4	2	no	—
191	Dic₁₀₆	—	4	2	no	—
192	Dic₁₀₆	—	8	4	no	—
193	C₈×C₅₃	—	2	1	no	—
194	C₈×C₅₃	—	4	2	no	—
195	C₈×C₅₃	—	4	1	no	—
196	C₈×C₅₃	AGL(1,ℤ/8)	1	2	yes	—
197	#88322	—	2	1	no	—
198	#88322	—	4	2	no	—
199	#88322	—	4	1	no	—
200	#88322	AGL(1,ℤ/8)	1	2	yes	—
201	#19268	—	53	1	no	maximal, Sylow
202	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
203	C₂×D₅₃	—	2	1	no	—
204	C₂×D₅₃	—	2	1	no	—
205	C₂×D₅₃	—	2	2	no	—
206	C₂×D₅₃	—	4	1	no	—
207	C₂×D₅₃	—	4	1	no	—
208	C₂×D₅₃	#467	1	2	yes	—
209	C₄×C₅₃	—	2	2	no	—
210	C₄×C₅₃	—	2	1	no	—
211	C₄×C₅₃	—	4	1	no	—
212	C₄×C₅₃	—	8	2	no	—
213	C₄×C₅₃	C₂²×Q₁₆	1	1	yes	characteristic
214	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
215	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
216	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
217	Dic₅₃	—	2	1	no	—
218	Dic₅₃	—	4	1	no	—
219	Dic₅₃	—	8	2	no	—
220	Dic₅₃	#467	1	2	yes	—
221	Dic₅₃	#473	1	2	yes	—
222	C₂×#494	—	53	1	no	—
223	#3079	—	53	2	no	—
224	C₈×#41	—	53	1	no	—
225	#1670	—	53	2	no	—
226	#1670	—	53	1	no	—
227	#1670	D₅₃	1	1	yes	characteristic, complemented
228	#1669	—	53	1	no	—
229	#1669	—	53	1	no	—
230	#1669	—	53	2	no	—
231	#1567	—	53	1	no	—
232	#1549	—	53	2	no	—
233	C₂×C₅₃	#3038	1	1	yes	characteristic
234	C₂×C₅₃	C₂×#467	1	1	yes	characteristic
235	C₂×C₅₃	C₂×#473	1	1	yes	characteristic
236	D₅₃	—	2	2	no	—
237	D₅₃	—	4	2	no	—
238	C₂²×Q₁₆	—	106	1	no	—
239	C₂²×Q₁₆	—	106	1	no	—
240	C₂×C₄⋊Q₈	—	53	2	no	—
241	C₄×#41	—	53	1	no	—
242	#494	—	53	2	no	—
243	#494	—	53	1	no	—
244	#494	—	106	1	no	—
245	#494	—	106	1	no	—
246	#494	C₂×D₅₃	1	1	yes	characteristic
247	#477	—	106	2	no	—
248	#476	—	106	2	no	—
249	#475	—	53	2	no	—
250	#475	C₂×D₅₃	1	2	yes	—
251	#474	—	53	2	no	—
252	#474	—	53	2	no	—
253	C₈×Q₈	—	53	1	no	—
254	C₈×Q₈	C₂×D₅₃	1	1	yes	characteristic
255	C₈×D₄	—	53	1	no	—
256	C₈×D₄	—	53	1	no	—
257	C₈×D₄	—	106	1	no	—
258	C₈×D₄	—	106	1	no	—
259	#431	—	53	1	no	—
260	#431	—	106	1	no	—
261	#428	—	106	2	no	—
262	#423	—	53	2	no	—
263	#417	—	106	2	no	—
264	C₂×C₄×C₈	—	53	1	no	—
265	C₂×C₄×C₈	—	106	1	no	—
266	#335	—	53	2	no	—
267	#335	—	53	1	no	—
268	#335	C₂×D₅₃	1	1	yes	characteristic
269	#332	—	53	2	no	—
270	#332	—	53	2	no	—
271	#332	—	53	2	no	—
272	#332	C₂×D₅₃	1	2	yes	—
273	C₅₃	#19268	1	1	yes	characteristic, complemented, Sylow
274	C₂×#41	—	53	1	no	—
275	C₂²×Q₈	—	106	2	no	—
276	C₂×Q₁₆	—	2	1	no	—
277	C₂×Q₁₆	—	2	1	no	—
278	C₂×Q₁₆	—	106	2	no	—
279	C₂×Q₁₆	—	106	2	no	—
280	C₂×Q₁₆	—	106	1	no	—
281	C₂×Q₁₆	—	106	1	no	—
282	C₂×Q₁₆	—	212	4	no	—
283	C₂×Q₁₆	—	212	4	no	—
284	C₂×M₁₆	—	106	2	no	—
285	C₂²×C₈	—	53	1	no	—
286	C₂²×C₈	—	53	1	no	—
287	C₂²×C₈	—	106	1	no	—
288	C₂²×C₈	—	106	1	no	—
289	C₄⋊Q₈	—	53	2	no	—
290	C₄⋊Q₈	—	106	2	no	—
291	C₄⋊Q₈	—	106	2	no	—
292	C₄⋊Q₈	—	106	2	no	—
293	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	—
294	C₄×Q₈	—	53	1	no	—
295	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
296	C₄×D₄	—	53	1	no	—
297	C₄×D₄	—	53	1	no	—
298	C₄×D₄	—	106	1	no	—
299	C₄×D₄	—	106	1	no	—
300	#117	—	53	1	no	—
301	#117	—	106	1	no	—
302	C₂×C₄⋊C₄	—	106	2	no	—
303	C₂×C₄⋊C₄	—	106	2	no	—
304	C₂×C₄²	—	53	1	no	—
305	C₂×C₄²	—	106	1	no	—
306	#107	—	106	2	no	—
307	#107	—	106	2	no	—
308	#106	—	2	2	no	—
309	#106	—	106	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	53	1	no	—
312	C₄⋊C₈	—	53	2	no	—
313	C₄⋊C₈	—	106	1	no	—
314	C₄⋊C₈	—	106	2	no	—
315	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
316	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
317	#103	—	2	2	no	—
318	#103	—	106	2	no	—
319	#102	—	106	2	no	—
320	#102	—	106	2	no	—
321	C₂²⋊C₈	—	106	1	no	—
322	C₂²⋊C₈	—	106	1	no	—
323	C₂²⋊C₈	—	106	1	no	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	—	53	1	no	—
326	C₄×C₈	—	53	1	no	—
327	C₄×C₈	—	53	1	no	—
328	C₄×C₈	—	106	1	no	—
329	C₄×C₈	—	106	1	no	—
330	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
331	#41	—	53	4	no	—
332	#41	—	106	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	106	2	no	—
335	C₂×Q₈	—	212	2	no	—
336	C₂×Q₈	—	212	4	no	—
337	C₂×Q₈	—	212	4	no	—
338	C₂×Q₈	D₄×D₅₃	1	1	yes	characteristic
339	C₂×D₄	—	53	1	no	—
340	C₂×D₄	—	106	1	no	—
341	C₂²×C₄	—	53	1	no	—
342	C₂²×C₄	—	53	1	no	—
343	C₂²×C₄	—	53	1	no	—
344	C₂²×C₄	—	106	1	no	—
345	C₂²×C₄	—	106	1	no	—
346	C₂²×C₄	—	106	1	no	—
347	C₂²×C₄	—	212	2	no	—
348	Q₁₆	—	4	2	no	—
349	Q₁₆	—	4	2	no	—
350	Q₁₆	—	212	2	no	—
351	Q₁₆	—	212	4	no	—
352	Q₁₆	—	212	4	no	—
353	Q₁₆	—	212	2	no	—
354	M₁₆	—	212	4	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	53	1	no	—
358	C₂×C₈	—	53	1	no	—
359	C₂×C₈	—	106	2	no	—
360	C₂×C₈	—	106	2	no	—
361	C₂×C₈	—	106	1	no	—
362	C₂×C₈	—	106	2	no	—
363	C₂×C₈	—	212	2	no	—
364	C₂×C₈	—	212	2	no	—
365	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
366	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	53	1	no	—
371	C₄⋊C₄	—	106	1	no	—
372	C₄⋊C₄	—	106	2	no	—
373	C₄⋊C₄	—	106	2	no	—
374	C₄⋊C₄	—	212	2	no	—
375	C₄⋊C₄	—	212	2	no	—
376	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
377	C₂²⋊C₄	—	106	1	no	—
378	C₂²⋊C₄	—	106	1	no	—
379	C₂²⋊C₄	—	106	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	53	1	no	—
382	C₄²	—	53	1	no	—
383	C₄²	—	53	1	no	—
384	C₄²	—	106	1	no	—
385	C₄²	—	106	1	no	—
386	C₄²	C₂³×D₅₃	1	1	yes	characteristic
387	C₂³	—	53	1	no	—
388	C₂³	—	106	1	no	—
389	Q₈	—	2	1	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	424	4	no	—
393	Q₈	—	212	2	no	—
394	Q₈	—	212	2	no	—
395	Q₈	Q₁₆×D₅₃	1	2	yes	complemented
396	D₄	—	53	2	no	—
397	D₄	—	106	4	no	—
398	D₄	—	106	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	53	1	no	—
403	C₂×C₄	—	53	1	no	—
404	C₂×C₄	—	53	2	no	—
405	C₂×C₄	—	53	2	no	—
406	C₂×C₄	—	53	1	no	—
407	C₂×C₄	—	106	2	no	—
408	C₂×C₄	—	106	4	no	—
409	C₂×C₄	—	106	1	no	—
410	C₂×C₄	—	106	1	no	—
411	C₂×C₄	—	106	1	no	—
412	C₂×C₄	—	424	4	no	—
413	C₂×C₄	—	212	2	no	—
414	C₂×C₄	—	212	2	no	—
415	C₂×C₄	—	212	1	no	—
416	C₂×C₄	—	212	1	no	—
417	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
418	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
419	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
420	C₈	—	2	1	no	—
421	C₈	—	4	2	no	—
422	C₈	—	4	1	no	—
423	C₈	—	53	2	no	—
424	C₈	—	106	1	no	—
425	C₈	—	212	2	no	—
426	C₈	—	212	1	no	—
427	C₈	#13133244	1	2	yes	—
428	C₂²	—	53	2	no	—
429	C₂²	—	106	1	no	—
430	C₂²	—	106	1	no	—
431	C₂²	—	106	2	no	—
432	C₂²	—	212	1	no	—
433	C₂²	—	212	1	no	—
434	C₂²	#121×D₅₃	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	2	no	—
437	C₄	—	4	1	no	—
438	C₄	—	8	2	no	—
439	C₄	—	53	2	no	—
440	C₄	—	53	2	no	—
441	C₄	—	106	1	no	—
442	C₄	—	424	2	no	—
443	C₄	—	212	1	no	—
444	C₄	C₂×Q₁₆×D₅₃	1	1	yes	characteristic
445	C₄	#135×D₅₃	1	1	yes	characteristic
446	C₄	AGL(1,ℤ/8)×D₅₃	1	1	yes	characteristic
447	C₄	C₂×#13133244	1	1	yes	characteristic
448	C₂	—	106	2	no	—
449	C₂	—	212	2	no	—
450	C₂	#20284192	1	1	yes	characteristic
451	C₂	#467×D₅₃	1	1	yes	characteristic
452	C₂	#473×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₅₃
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1670	C₂
socle	C₂²×C₅₃	C₂×#121
prime radical	C₂×#11719949	D₄
hypercenter	#1670	D₅₃
hypocenter	C₅₃	#19268
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1670

Complements

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

N	H ≅ G/N	type
1. #494×D₅₃	C₂	semidirect
4. #20274085	C₂	semidirect
5. #20274083	C₂	semidirect
6. #20274081	C₂	semidirect
7. #20274079	C₂	semidirect
8. #20274077	C₂	semidirect
9. #20273472	C₂	semidirect
10. #20273398	C₂	semidirect
11. C₅₃×#1670	C₂	semidirect
107. #11719949	Q₁₆	semidirect
165. Q₈×C₅₃	C₂×Q₁₆	semidirect
179. D₂₁₂	C₂×Q₁₆	semidirect
227. #1670	D₅₃	semidirect
273. C₅₃	#19268	semidirect
395. Q₈	Q₁₆×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#494×D₅₃	2
#20284525	2
C₈×#11719949	2
#20274085	2
#20274083	2
#20274081	2
#20274079	2
#20274077	2
#20273472	2
#20273398	2
C₅₃×#1670	2
#19268	53