Subgroups — #28319496

Order 13568.

810 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20291193	C₂	1	2	yes	maximal
2	#20290652	C₂	1	1	yes	maximal, characteristic, complemented
3	#20290650	C₂	1	1	yes	maximal, characteristic, complemented
4	#20290638	C₂	1	2	yes	maximal, complemented
5	#20290593	C₂	1	2	yes	maximal
6	#20290591	C₂	1	2	yes	maximal
7	#20290529	C₂	1	2	yes	maximal, complemented
8	C₄×#13133285	C₂	1	2	yes	maximal, complemented
9	#405×D₅₃	C₂	1	1	yes	maximal, characteristic
10	C₂×#13133286	C₂²	1	2	yes	—
11	C₂×#13133285	C₂²	1	2	yes	—
12	C₂×#13133285	C₂²	1	2	yes	—
13	C₂×#13133285	C₂²	1	2	yes	—
14	#16811573	—	2	4	no	—
15	#16811572	—	2	4	no	—
16	#16811569	C₂²	1	2	yes	—
17	#16811567	C₂²	1	2	yes	—
18	#16811565	C₂²	1	4	yes	—
19	C₄×C₄⋊#6157	C₂²	1	4	yes	—
20	#16811497	C₂²	1	4	yes	—
21	#16811497	C₂²	1	4	yes	—
22	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
23	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
24	#117×D₅₃	C₂²	1	1	yes	characteristic
25	#16810581	C₄	1	1	yes	characteristic, complemented
26	#16810580	C₄	1	1	yes	characteristic, complemented
27	#16810580	C₄	1	1	yes	characteristic, complemented
28	#16810579	C₄	1	1	yes	characteristic, complemented
29	#16810578	C₄	1	1	yes	characteristic, complemented
30	#16810577	C₄	1	1	yes	characteristic, complemented
31	#16810577	C₄	1	1	yes	characteristic, complemented
32	#97×D₅₃	C₂²	1	1	yes	characteristic
33	#97×D₅₃	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
36	C₅₃×#405	C₄	1	1	yes	characteristic, complemented
37	C₂×C₄⋊#6157	—	2	4	no	—
38	C₂×C₄⋊#6157	C₂³	1	4	yes	—
39	C₂×C₄⋊#6157	C₂³	1	4	yes	—
40	C₂×C₂²⋊#6157	—	2	4	no	—
41	C₂×C₄×#6157	—	2	4	no	—
42	#13133286	—	2	4	no	—
43	#13133285	—	2	4	no	—
44	#13133285	—	2	4	no	—
45	#13133285	—	2	4	no	—
46	(C₂×#6157)⋊C₄	—	2	4	no	—
47	(C₂×#6157)⋊C₄	—	2	4	no	—
48	(C₂×#6157)⋊C₄	—	2	4	no	—
49	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
50	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
51	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
52	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
53	M₁₆×D₅₃	—	2	2	no	—
54	M₁₆×D₅₃	—	2	2	no	—
55	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₅₃	—	2	2	no	—
57	C₂×C₈×D₅₃	—	2	2	no	—
58	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
61	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
63	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
64	#13133176	C₂×C₄	1	1	yes	characteristic
65	#13133175	Q₈	1	2	yes	—
66	#13133174	C₂×C₄	1	1	yes	characteristic
67	#13133174	C₂×C₄	1	1	yes	characteristic
68	#13133173	Q₈	1	2	yes	—
69	C₄⋊C₄×D₅₃	D₄	1	2	yes	—
70	C₂²⋊C₄×D₅₃	D₄	1	2	yes	—
71	C₄²×D₅₃	C₂³	1	1	yes	characteristic
72	C₄²×D₅₃	C₂³	1	1	yes	characteristic
73	#13133128	C₂×C₄	1	1	yes	characteristic
74	#13133128	C₂×C₄	1	1	yes	characteristic
75	#13133127	C₂×C₄	1	1	yes	characteristic
76	#13133127	C₂×C₄	1	1	yes	characteristic
77	#13133127	C₂×C₄	1	1	yes	characteristic
78	#13133127	C₂×C₄	1	1	yes	characteristic
79	C₄×#88322	C₂×C₄	1	1	yes	characteristic
80	C₄×#88322	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
85	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
87	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
88	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
89	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
92	C₂³×D₅₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×#6157	—	2	4	no	—
94	C₂²×#6157	—	2	4	no	—
95	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
97	C₂×C₄×D₅₃	—	2	1	no	—
98	C₂×C₄×D₅₃	—	2	1	no	—
99	C₂×C₄×D₅₃	—	2	1	no	—
100	C₂×C₄×D₅₃	—	2	1	no	—
101	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
103	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
104	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
105	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
106	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
107	C₂²⋊#6157	—	8	4	no	—
108	C₄⋊#6157	—	2	4	no	—
109	C₄⋊#6157	—	2	4	no	—
110	C₄⋊#6157	—	2	4	no	—
111	C₄⋊#6157	—	2	4	no	—
112	C₄⋊#6157	—	8	4	no	—
113	C₄×#6157	—	8	4	no	—
114	M₁₆×C₅₃	—	2	2	no	—
115	C₂×C₈×C₅₃	—	2	2	no	—
116	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
120	C₄⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
121	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
122	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²⋊Dic₅₃	C₄⋊C₄	1	2	yes	—
125	#11719921	C₄⋊C₄	1	2	yes	—
126	#11719921	C₄⋊C₄	1	2	yes	—
127	C₄⋊Dic₅₃	C₄⋊C₄	1	2	yes	—
128	#11719919	C₄⋊C₄	1	2	yes	—
129	#11719919	C₄⋊C₄	1	2	yes	—
130	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₅₃	C₂×Q₈	1	2	yes	—
133	C₄×Dic₅₃	C₂×Q₈	1	2	yes	—
134	#11719917	—	2	2	no	—
135	C₂×#88322	—	2	2	no	—
136	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
137	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
138	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
139	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
140	#11719912	—	2	2	no	—
141	#11719912	—	2	2	no	—
142	C₈×D₅₃	—	2	1	no	—
143	C₈×D₅₃	—	2	1	no	—
144	C₈×D₅₃	—	2	1	no	—
145	C₈×D₅₃	—	2	1	no	—
146	C₈×D₅₃	—	2	2	no	—
147	C₈×D₅₃	—	2	2	no	—
148	C₈×D₅₃	#41	1	2	yes	—
149	C₈×D₅₃	#41	1	2	yes	—
150	C₈×D₅₃	#41	1	2	yes	—
151	C₈×D₅₃	#41	1	2	yes	—
152	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂²×D₅₃	—	2	1	no	—
154	C₂²×D₅₃	—	2	1	no	—
155	C₂²×D₅₃	—	2	4	no	—
156	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
158	C₂×#6157	—	4	4	no	—
159	C₂×#6157	—	4	4	no	—
160	C₂×#6157	—	4	4	no	—
161	C₂×#6157	—	4	4	no	—
162	C₂×#6157	—	4	4	no	—
163	C₂×#6157	—	4	4	no	—
164	C₂×C₄×C₅₃	—	2	1	no	—
165	C₂×C₄×C₅₃	—	2	1	no	—
166	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
168	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
169	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
170	C₂×Dic₅₃	—	2	1	no	—
171	C₂×Dic₅₃	—	2	1	no	—
172	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×Dic₅₃	C₂×C₄⋊C₄	1	2	yes	—
174	C₂×Dic₅₃	C₂×C₄⋊C₄	1	2	yes	—
175	C₂×Dic₅₃	C₂²×Q₈	1	1	yes	characteristic
176	C₄×D₅₃	—	2	1	no	—
177	C₄×D₅₃	—	2	1	no	—
178	C₄×D₅₃	—	2	4	no	—
179	C₄×D₅₃	—	2	4	no	—
180	C₄×D₅₃	—	2	1	no	—
181	C₄×D₅₃	—	2	1	no	—
182	C₄×D₅₃	—	2	1	no	—
183	C₄×D₅₃	—	2	1	no	—
184	C₄×D₅₃	C₂×#41	1	1	yes	characteristic
185	C₄×D₅₃	C₂×#41	1	1	yes	characteristic
186	C₄×D₅₃	C₂×#41	1	1	yes	characteristic
187	C₄×D₅₃	C₂×#41	1	1	yes	characteristic
188	C₈×C₅₃	—	2	1	no	—
189	C₈×C₅₃	—	2	1	no	—
190	C₈×C₅₃	#117	1	2	yes	—
191	C₈×C₅₃	#117	1	2	yes	—
192	#88322	—	2	1	no	—
193	#88322	—	2	1	no	—
194	#88322	#117	1	2	yes	—
195	#88322	#117	1	2	yes	—
196	#20820	—	53	1	no	maximal, Sylow
197	C₂²×C₅₃	—	2	2	no	—
198	C₂²×C₅₃	—	2	1	no	—
199	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
200	C₂×D₅₃	—	2	2	no	—
201	C₂×D₅₃	—	2	1	no	—
202	C₂×D₅₃	—	4	2	no	—
203	C₂×D₅₃	—	4	2	no	—
204	C₂×D₅₃	#532	1	1	yes	characteristic
205	C₂×D₅₃	#532	1	1	yes	characteristic
206	C₂×D₅₃	#577	1	4	yes	—
207	#6157	—	8	4	no	—
208	#6157	—	8	4	no	—
209	C₄×C₅₃	—	2	2	no	—
210	C₄×C₅₃	—	2	2	no	—
211	C₄×C₅₃	—	2	1	no	—
212	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
213	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
214	Dic₅₃	—	2	2	no	—
215	Dic₅₃	—	2	2	no	—
216	Dic₅₃	—	2	1	no	—
217	Dic₅₃	#533	1	1	yes	characteristic
218	Dic₅₃	#533	1	1	yes	characteristic
219	C₂×#405	—	53	1	no	—
220	#2314	—	53	2	no	—
221	#1846	—	53	1	no	—
222	#1844	—	53	1	no	—
223	#1836	—	53	2	no	—
224	#1809	—	53	2	no	—
225	#1807	—	53	2	no	—
226	#1776	—	53	2	no	—
227	C₄×#106	—	53	2	no	—
228	C₂×C₅₃	—	4	1	no	—
229	C₂×C₅₃	#2285	1	1	yes	characteristic
230	C₂×C₅₃	#2912	1	2	yes	—
231	D₅₃	—	4	1	no	—
232	D₅₃	#3173	1	2	yes	—
233	D₅₃	#3174	1	2	yes	—
234	C₂²×M₁₆	—	53	1	no	—
235	C₂³×C₈	—	53	1	no	—
236	C₂×#117	—	53	1	no	—
237	C₂×#107	—	53	2	no	—
238	C₂×#106	—	53	2	no	—
239	C₂×#106	—	53	2	no	—
240	C₂×#106	—	53	2	no	—
241	#405	—	53	1	no	—
242	#405	—	53	1	no	—
243	#405	—	53	1	no	—
244	#405	—	53	1	no	—
245	#405	—	53	1	no	—
246	#405	—	53	1	no	—
247	#405	—	53	1	no	—
248	#405	#6157	1	1	yes	characteristic, complemented
249	C₂×#97	—	53	1	no	—
250	C₂×#97	—	53	1	no	—
251	C₂×C₄×C₈	—	53	1	no	—
252	C₂×C₄×C₈	—	53	1	no	—
253	#388	—	106	4	no	—
254	#387	—	106	4	no	—
255	#384	—	53	2	no	—
256	#382	—	53	2	no	—
257	#380	—	53	4	no	—
258	C₄×C₄⋊C₄	—	53	4	no	—
259	#340	—	53	4	no	—
260	#340	—	53	4	no	—
261	C₅₃	#20820	1	1	yes	characteristic, complemented, Sylow
262	C₂³×C₄	—	53	1	no	—
263	C₂×M₁₆	—	53	1	no	—
264	C₂×M₁₆	—	53	1	no	—
265	C₂×M₁₆	—	53	1	no	—
266	C₂×M₁₆	—	106	2	no	—
267	C₂×M₁₆	—	106	2	no	—
268	C₂×M₁₆	C₂×#6157	1	1	yes	characteristic
269	C₂²×C₈	—	53	1	no	—
270	C₂²×C₈	—	53	1	no	—
271	C₂²×C₈	—	53	1	no	—
272	C₂²×C₈	—	53	1	no	—
273	C₂²×C₈	—	53	1	no	—
274	C₂²×C₈	—	53	1	no	—
275	C₂²×C₈	—	53	1	no	—
276	C₂²×C₈	—	106	2	no	—
277	C₂²×C₈	—	106	2	no	—
278	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
279	#117	—	53	1	no	—
280	#117	—	53	2	no	—
281	#117	—	53	2	no	—
282	#117	—	53	1	no	—
283	#117	—	53	1	no	—
284	#117	C₂×#6157	1	1	yes	characteristic
285	C₂×C₄⋊C₄	—	53	2	no	—
286	C₂×C₄⋊C₄	—	53	4	no	—
287	C₂×C₄⋊C₄	—	53	4	no	—
288	C₂×C₄⋊C₄	—	106	4	no	—
289	C₂×C₂²⋊C₄	—	53	2	no	—
290	C₂×C₂²⋊C₄	—	106	4	no	—
291	C₂×C₄²	—	53	1	no	—
292	C₂×C₄²	—	53	1	no	—
293	C₂×C₄²	—	106	4	no	—
294	#107	—	106	4	no	—
295	#106	—	106	4	no	—
296	#106	—	106	4	no	—
297	#106	—	106	4	no	—
298	#97	—	53	1	no	—
299	#97	—	53	1	no	—
300	#97	—	53	1	no	—
301	#97	—	53	1	no	—
302	#97	—	53	1	no	—
303	#97	—	53	1	no	—
304	#97	C₂×#6157	1	1	yes	characteristic
305	#97	C₂×#6157	1	1	yes	characteristic
306	C₄×C₈	—	53	1	no	—
307	C₄×C₈	—	53	1	no	—
308	C₄×C₈	—	53	1	no	—
309	C₄×C₈	—	53	1	no	—
310	C₄×C₈	—	53	1	no	—
311	C₄×C₈	—	53	1	no	—
312	C₄×C₈	C₂×#6157	1	1	yes	characteristic
313	C₄×C₈	C₂×#6157	1	1	yes	characteristic
314	#95	—	106	4	no	—
315	#95	—	106	4	no	—
316	#95	—	106	4	no	—
317	C₂⁴	—	53	1	no	—
318	C₂²×C₄	—	53	1	no	—
319	C₂²×C₄	—	53	1	no	—
320	C₂²×C₄	—	53	1	no	—
321	C₂²×C₄	—	53	2	no	—
322	C₂²×C₄	—	53	2	no	—
323	C₂²×C₄	—	53	1	no	—
324	C₂²×C₄	—	53	1	no	—
325	C₂²×C₄	—	106	1	no	—
326	C₂²×C₄	—	106	1	no	—
327	C₂²×C₄	—	106	1	no	—
328	C₂²×C₄	—	106	1	no	—
329	C₂²×C₄	—	106	4	no	—
330	C₂²×C₄	—	106	4	no	—
331	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
332	M₁₆	—	2	2	no	—
333	M₁₆	—	106	2	no	—
334	M₁₆	—	106	2	no	—
335	M₁₆	—	106	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	53	1	no	—
338	C₂×C₈	—	53	1	no	—
339	C₂×C₈	—	53	2	no	—
340	C₂×C₈	—	53	2	no	—
341	C₂×C₈	—	53	2	no	—
342	C₂×C₈	—	53	2	no	—
343	C₂×C₈	—	53	1	no	—
344	C₂×C₈	—	53	1	no	—
345	C₂×C₈	—	106	2	no	—
346	C₂×C₈	—	106	1	no	—
347	C₂×C₈	—	106	1	no	—
348	C₂×C₈	—	106	1	no	—
349	C₂×C₈	—	106	1	no	—
350	C₂×C₈	—	106	2	no	—
351	C₂×C₈	—	106	2	no	—
352	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
353	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
354	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
355	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
356	C₄⋊C₄	—	53	2	no	—
357	C₄⋊C₄	—	53	2	no	—
358	C₄⋊C₄	—	53	2	no	—
359	C₄⋊C₄	—	106	4	no	—
360	C₄⋊C₄	—	106	4	no	—
361	C₄⋊C₄	—	106	4	no	—
362	C₄⋊C₄	—	106	4	no	—
363	C₄⋊C₄	—	424	4	no	—
364	C₄⋊C₄	C₄⋊#6157	1	2	yes	—
365	C₂²⋊C₄	—	53	2	no	—
366	C₂²⋊C₄	—	53	2	no	—
367	C₂²⋊C₄	—	53	2	no	—
368	C₂²⋊C₄	—	424	4	no	—
369	C₂²⋊C₄	C₄⋊#6157	1	2	yes	—
370	C₄²	—	53	2	no	—
371	C₄²	—	53	2	no	—
372	C₄²	—	53	1	no	—
373	C₄²	—	53	1	no	—
374	C₄²	—	424	4	no	—
375	C₄²	C₂²×#6157	1	1	yes	characteristic
376	C₄²	C₂²×#6157	1	1	yes	characteristic
377	C₂³	—	53	1	no	—
378	C₂³	—	53	1	no	—
379	C₂³	—	106	4	no	—
380	C₂³	—	106	1	no	—
381	C₂³	—	106	1	no	—
382	C₂³	C₂×C₄⋊#6157	1	1	yes	characteristic
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	53	1	no	—
386	C₂×C₄	—	53	1	no	—
387	C₂×C₄	—	53	1	no	—
388	C₂×C₄	—	53	1	no	—
389	C₂×C₄	—	53	1	no	—
390	C₂×C₄	—	53	2	no	—
391	C₂×C₄	—	53	2	no	—
392	C₂×C₄	—	53	1	no	—
393	C₂×C₄	—	106	1	no	—
394	C₂×C₄	—	106	1	no	—
395	C₂×C₄	—	106	4	no	—
396	C₂×C₄	—	106	4	no	—
397	C₂×C₄	—	106	1	no	—
398	C₂×C₄	—	106	1	no	—
399	C₂×C₄	—	106	1	no	—
400	C₂×C₄	—	106	1	no	—
401	C₂×C₄	—	106	1	no	—
402	C₂×C₄	—	106	1	no	—
403	C₂×C₄	—	212	4	no	—
404	C₂×C₄	—	212	4	no	—
405	C₂×C₄	—	212	4	no	—
406	C₂×C₄	—	212	4	no	—
407	C₂×C₄	—	212	4	no	—
408	C₂×C₄	—	212	4	no	—
409	C₂×C₄	C₂×C₄⋊#6157	1	2	yes	—
410	C₂×C₄	C₂×C₄⋊#6157	1	2	yes	—
411	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
412	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
413	C₈	—	2	1	no	—
414	C₈	—	2	1	no	—
415	C₈	—	53	2	no	—
416	C₈	—	53	2	no	—
417	C₈	—	106	1	no	—
418	C₈	—	106	1	no	—
419	C₈	#13133296	1	2	yes	—
420	C₈	#13133296	1	2	yes	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	53	4	no	—
424	C₂²	—	53	1	no	—
425	C₂²	—	53	1	no	—
426	C₂²	—	106	2	no	—
427	C₂²	—	106	1	no	—
428	C₂²	—	212	2	no	—
429	C₂²	—	212	2	no	—
430	C₂²	C₂²×C₄⋊#6157	1	1	yes	characteristic
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	1	no	—
434	C₄	—	53	1	no	—
435	C₄	—	53	1	no	—
436	C₄	—	106	2	no	—
437	C₄	—	106	2	no	—
438	C₄	—	106	1	no	—
439	C₄	—	424	4	no	—
440	C₄	—	424	4	no	—
441	C₄	C₂×#13133296	1	1	yes	characteristic
442	C₄	C₂×#13133296	1	1	yes	characteristic
443	C₂	—	4	1	no	—
444	C₂	—	53	2	no	—
445	C₂	—	53	2	no	—
446	C₂	—	212	1	no	—
447	C₂	#20291164	1	1	yes	characteristic
448	C₂	#20291369	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#6157
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₅₃×#405	C₄
socle	C₂²×C₅₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₅₃	C₂×D₄
cosocle	C₂×C₄×D₅₃	C₂⁴
hypercenter	#405	#6157
hypocenter	C₅₃	#20820
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
2. #20290652	C₂	semidirect
3. #20290650	C₂	semidirect
4. #20290638	C₂	semidirect
7. #20290529	C₂	semidirect
8. C₄×#13133285	C₂	semidirect
25. #16810581	C₄	semidirect
26. #16810580	C₄	semidirect
27. #16810580	C₄	semidirect
28. #16810579	C₄	semidirect
29. #16810578	C₄	semidirect
30. #16810577	C₄	semidirect
31. #16810577	C₄	semidirect
36. C₅₃×#405	C₄	semidirect
248. #405	#6157	semidirect
261. C₅₃	#20820	semidirect

Maximal subgroups

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

subgroup	index
#20291193	2
#20290652	2
#20290650	2
#20290638	2
#20290593	2
#20290591	2
#20290529	2
C₄×#13133285	2
#405×D₅₃	2
#20820	53