Subgroups — #27353439

Order 13568.

592 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283847	C₂	1	1	yes	maximal, characteristic
2	#20283840	C₂	1	1	yes	maximal, characteristic
3	#20273504	C₂	1	1	yes	maximal, characteristic, complemented
4	#20273504	C₂	1	1	yes	maximal, characteristic, complemented
5	#20273495	C₂	1	2	yes	maximal, complemented
6	#20273486	C₂	1	2	yes	maximal, complemented
7	#20273482	C₂	1	2	yes	maximal, complemented
8	#20273471	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273467	C₂	1	2	yes	maximal, complemented
10	#20273463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2965	C₂	1	1	yes	maximal, characteristic
12	#16810754	—	2	1	no	—
13	Q₈×#88322	—	2	1	no	—
14	#16810701	—	2	1	no	—
15	#16810701	—	2	2	no	—
16	#16810695	—	2	2	no	—
17	D₄×#88322	—	2	1	no	—
18	#16810680	C₂²	1	2	yes	—
19	#16810676	C₂²	1	1	yes	characteristic
20	#16810676	C₂²	1	1	yes	characteristic
21	#16810676	C₂²	1	2	yes	—
22	#16810647	C₂²	1	1	yes	characteristic
23	#16810647	C₂²	1	1	yes	characteristic
24	#16810647	C₂²	1	2	yes	—
25	C₂×C₄⋊#88322	C₂²	1	2	yes	—
26	#16810376	C₂²	1	1	yes	characteristic
27	#16810376	C₂²	1	1	yes	characteristic
28	#16810376	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	#16810374	C₂²	1	2	yes	—
33	#16810374	C₂²	1	2	yes	—
34	#16810374	C₂²	1	2	yes	—
35	#16810374	C₂²	1	2	yes	—
36	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
37	C₅₃×#446	C₄	1	1	yes	characteristic
38	C₅₃×#446	C₄	1	1	yes	characteristic
39	C₅₃×#436	C₄	1	1	yes	characteristic
40	C₅₃×#436	C₄	1	1	yes	characteristic
41	C₅₃×#435	C₄	1	2	yes	—
42	C₅₃×#435	C₄	1	2	yes	—
43	C₅₃×#431	C₂²	1	2	yes	—
44	C₅₃×#431	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₅₃	C₂²	1	2	yes	—
46	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×#11719917	—	2	1	no	—
48	C₂×#11719917	—	2	2	no	—
49	C₂×#11719917	—	2	1	no	—
50	C₂²×#88322	—	2	2	no	—
51	C₄⋊#88322	—	2	2	no	—
52	C₄⋊#88322	—	2	1	no	—
53	C₄⋊#88322	—	2	1	no	—
54	C₄⋊#88322	—	2	2	no	—
55	C₄⋊#88322	C₂³	1	1	yes	characteristic
56	C₄⋊#88322	C₂³	1	2	yes	—
57	C₄⋊#88322	C₂³	1	1	yes	characteristic
58	C₄⋊#88322	C₂³	1	2	yes	—
59	C₄⋊#88322	C₂³	1	1	yes	characteristic
60	C₄⋊#88322	C₂³	1	1	yes	characteristic
61	C₂²⋊#88322	—	2	1	no	—
62	C₂²⋊#88322	—	2	2	no	—
63	C₂²⋊#88322	—	2	1	no	—
64	C₂²⋊#88322	—	2	2	no	—
65	#13133128	—	2	2	no	—
66	C₄×#88322	—	2	1	no	—
67	C₄×#88322	—	2	1	no	—
68	C₄×#88322	—	2	2	no	—
69	C₂×#41×C₅₃	Q₈	1	1	yes	characteristic
70	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
71	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
74	C₄×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
75	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
76	C₄×D₄×C₅₃	C₂×C₄	1	2	yes	—
77	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
78	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
79	C₄×D₄×C₅₃	D₄	1	2	yes	—
80	#117×C₅₃	Q₈	1	1	yes	characteristic
81	#117×C₅₃	Q₈	1	2	yes	—
82	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
83	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
85	C₄⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
86	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
87	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
88	C₂²⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
89	C₂²⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
90	C₂²⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
91	#97×C₅₃	C₂×C₄	1	2	yes	—
92	#97×C₅₃	C₂×C₄	1	2	yes	—
93	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
94	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₅₃	C₂³	1	2	yes	—
98	#41×C₅₃	—	4	2	no	—
99	C₂×Q₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂×D₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂×D₄×C₅₃	C₄⋊C₄	1	2	yes	—
102	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₅₃	C₂×Q₈	1	2	yes	—
108	M₁₆×C₅₃	—	2	4	no	—
109	M₁₆×C₅₃	—	4	2	no	—
110	C₂×C₈×C₅₃	—	2	2	no	—
111	C₂×C₈×C₅₃	—	4	1	no	—
112	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
118	C₄⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
119	C₄⋊C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
120	C₄⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
121	C₄⋊C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
122	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
123	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
124	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
125	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
127	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₅₃	C₂×D₄	1	2	yes	—
129	C₄²×C₅₃	C₂×Q₈	1	2	yes	—
130	C₄²×C₅₃	C₂×Q₈	1	1	yes	characteristic
131	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
132	#11719917	—	8	1	no	—
133	#11719917	—	8	2	no	—
134	#11719917	—	8	1	no	—
135	C₂×#88322	—	2	1	no	—
136	C₂×#88322	—	2	1	no	—
137	C₂×#88322	—	2	1	no	—
138	C₂×#88322	—	2	1	no	—
139	C₂×#88322	—	2	2	no	—
140	C₂×#88322	—	2	2	no	—
141	C₂×#88322	—	8	2	no	—
142	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂³×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
144	Q₈×C₅₃	—	2	2	no	—
145	D₄×C₅₃	—	2	2	no	—
146	D₄×C₅₃	—	4	2	no	—
147	C₂×C₄×C₅₃	—	2	1	no	—
148	C₂×C₄×C₅₃	—	2	2	no	—
149	C₂×C₄×C₅₃	—	2	1	no	—
150	C₂×C₄×C₅₃	—	2	2	no	—
151	C₂×C₄×C₅₃	—	2	2	no	—
152	C₂×C₄×C₅₃	—	2	2	no	—
153	C₂×C₄×C₅₃	—	2	1	no	—
154	C₂×C₄×C₅₃	—	2	1	no	—
155	C₂×C₄×C₅₃	—	2	2	no	—
156	C₂×C₄×C₅₃	—	4	2	no	—
157	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
160	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
166	C₈×C₅₃	—	2	1	no	—
167	C₈×C₅₃	—	2	2	no	—
168	C₈×C₅₃	—	2	1	no	—
169	C₈×C₅₃	—	2	1	no	—
170	C₈×C₅₃	—	2	2	no	—
171	C₈×C₅₃	#131	1	2	yes	—
172	#88322	—	4	1	no	—
173	#88322	—	4	1	no	—
174	#88322	—	4	1	no	—
175	#88322	—	4	2	no	—
176	#88322	—	4	1	no	—
177	#88322	—	4	2	no	—
178	#17841	—	53	1	no	maximal, Sylow
179	C₂²×C₅₃	—	2	1	no	—
180	C₂²×C₅₃	—	2	2	no	—
181	C₂²×C₅₃	—	2	2	no	—
182	C₂²×C₅₃	—	2	1	no	—
183	C₂²×C₅₃	—	2	1	no	—
184	C₂²×C₅₃	—	2	2	no	—
185	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
186	C₄×C₅₃	—	2	1	no	—
187	C₄×C₅₃	—	2	2	no	—
188	C₄×C₅₃	—	2	2	no	—
189	C₄×C₅₃	—	2	1	no	—
190	C₄×C₅₃	—	2	1	no	—
191	C₄×C₅₃	—	2	2	no	—
192	C₄×C₅₃	#430	1	2	yes	—
193	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
194	C₄×C₅₃	#568	1	1	yes	characteristic
195	C₄×C₅₃	#577	1	1	yes	characteristic
196	C₄×C₅₃	#577	1	1	yes	characteristic
197	#2991	—	53	1	no	—
198	#2990	—	53	1	no	—
199	#2965	D₅₃	1	1	yes	characteristic
200	#1574	—	53	1	no	—
201	#1574	—	53	1	no	—
202	#1572	—	53	2	no	—
203	#1570	—	53	2	no	—
204	#1569	—	53	2	no	—
205	#1566	—	53	1	no	—
206	#1565	—	53	2	no	—
207	#1564	—	53	1	no	—
208	C₂×C₅₃	—	4	1	no	—
209	C₂×C₅₃	—	4	2	no	—
210	C₂×C₅₃	#2906	1	1	yes	characteristic
211	C₂×C₅₃	#2912	1	1	yes	characteristic
212	C₂×C₅₃	C₂×#430	1	1	yes	characteristic
213	C₄×#41	C₂×D₅₃	1	1	yes	characteristic
214	#446	—	106	1	no	—
215	#446	Dic₅₃	1	1	yes	characteristic
216	#446	Dic₅₃	1	1	yes	characteristic
217	C₈×Q₈	—	106	1	no	—
218	#436	—	106	1	no	—
219	#436	—	106	2	no	—
220	#436	Dic₅₃	1	1	yes	characteristic
221	#436	Dic₅₃	1	1	yes	characteristic
222	#435	—	106	2	no	—
223	#435	Dic₅₃	1	2	yes	—
224	#435	Dic₅₃	1	2	yes	—
225	C₈×D₄	—	106	1	no	—
226	#432	—	53	2	no	—
227	#431	—	53	1	no	—
228	#431	—	53	1	no	—
229	#431	—	53	2	no	—
230	#431	C₂×D₅₃	1	2	yes	—
231	#431	C₂×D₅₃	1	1	yes	characteristic
232	#423	—	53	1	no	—
233	#423	—	53	1	no	—
234	#423	—	53	2	no	—
235	C₂×C₄⋊C₈	—	53	2	no	—
236	C₄×M₁₆	C₂×D₅₃	1	2	yes	—
237	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
238	#335	—	53	1	no	—
239	#335	—	53	1	no	—
240	#335	—	53	2	no	—
241	#335	—	53	2	no	—
242	#334	—	53	1	no	—
243	#334	—	53	1	no	—
244	#334	—	53	2	no	—
245	#334	—	53	2	no	—
246	#334	—	53	2	no	—
247	#334	—	53	2	no	—
248	C₅₃	#17841	1	1	yes	characteristic, complemented, Sylow
249	C₂×#41	Dic₁₀₆	1	1	yes	characteristic
250	C₂×M₁₆	—	106	1	no	—
251	C₂×M₁₆	—	106	2	no	—
252	C₂×M₁₆	—	106	1	no	—
253	C₂×M₁₆	C₂×Dic₅₃	1	2	yes	—
254	C₂×M₁₆	C₂×Dic₅₃	1	2	yes	—
255	C₂²×C₈	—	106	2	no	—
256	C₂²×C₈	C₂×Dic₅₃	1	1	yes	characteristic
257	C₂²×C₈	C₂×Dic₅₃	1	1	yes	characteristic
258	C₄×Q₈	D₂₁₂	1	1	yes	characteristic
259	C₄×Q₈	C₂×Dic₅₃	1	1	yes	characteristic
260	C₄×D₄	D₂₁₂	1	1	yes	characteristic
261	C₄×D₄	D₂₁₂	1	2	yes	—
262	C₄×D₄	C₂×Dic₅₃	1	2	yes	—
263	C₄×D₄	C₂×Dic₅₃	1	1	yes	characteristic
264	#117	Dic₁₀₆	1	1	yes	characteristic
265	#117	Dic₁₀₆	1	2	yes	—
266	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
267	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
268	C₄⋊C₈	—	53	1	no	—
269	C₄⋊C₈	—	53	2	no	—
270	C₄⋊C₈	—	53	1	no	—
271	C₄⋊C₈	—	53	2	no	—
272	C₄⋊C₈	—	53	1	no	—
273	C₄⋊C₈	—	53	1	no	—
274	C₄⋊C₈	—	106	2	no	—
275	C₄⋊C₈	—	106	1	no	—
276	C₄⋊C₈	—	106	1	no	—
277	C₄⋊C₈	—	106	2	no	—
278	C₄⋊C₈	C₂×Dic₅₃	1	2	yes	—
279	C₄⋊C₈	C₂×Dic₅₃	1	2	yes	—
280	C₄⋊C₈	C₂×Dic₅₃	1	1	yes	characteristic
281	C₄⋊C₈	C₂×Dic₅₃	1	1	yes	characteristic
282	C₂²⋊C₈	—	106	1	no	—
283	C₂²⋊C₈	—	106	2	no	—
284	C₂²⋊C₈	—	106	1	no	—
285	C₂²⋊C₈	—	106	2	no	—
286	C₂²⋊C₈	C₂×Dic₅₃	1	2	yes	—
287	C₂²⋊C₈	C₂×Dic₅₃	1	2	yes	—
288	C₂²⋊C₈	C₂×Dic₅₃	1	2	yes	—
289	#97	—	106	2	no	—
290	#97	C₂×Dic₅₃	1	2	yes	—
291	#97	C₂×Dic₅₃	1	2	yes	—
292	C₄×C₈	—	106	1	no	—
293	C₄×C₈	—	106	1	no	—
294	C₄×C₈	—	106	2	no	—
295	C₄×C₈	C₂×Dic₅₃	1	1	yes	characteristic
296	C₄×C₈	C₂×Dic₅₃	1	1	yes	characteristic
297	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
299	C₄×C₈	C₂²×D₅₃	1	2	yes	—
300	#41	—	4	2	no	—
301	C₂×Q₈	C₄⋊Dic₅₃	1	1	yes	characteristic
302	C₂×D₄	C₄⋊Dic₅₃	1	1	yes	characteristic
303	C₂×D₄	C₄⋊Dic₅₃	1	2	yes	—
304	C₂²×C₄	C₂×Dic₁₀₆	1	1	yes	characteristic
305	C₂²×C₄	C₂×Dic₁₀₆	1	2	yes	—
306	C₂²×C₄	C₂×D₂₁₂	1	2	yes	—
307	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
308	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
309	C₂²×C₄	C₂²×Dic₅₃	1	2	yes	—
310	M₁₆	—	2	4	no	—
311	M₁₆	—	4	2	no	—
312	M₁₆	—	424	1	no	—
313	M₁₆	—	424	2	no	—
314	M₁₆	—	424	1	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	106	1	no	—
318	C₂×C₈	—	106	1	no	—
319	C₂×C₈	—	106	1	no	—
320	C₂×C₈	—	106	1	no	—
321	C₂×C₈	—	106	2	no	—
322	C₂×C₈	—	106	2	no	—
323	C₂×C₈	—	424	2	no	—
324	C₂×C₈	C₂²×Dic₅₃	1	1	yes	characteristic
325	C₂×C₈	C₂²×Dic₅₃	1	1	yes	characteristic
326	C₂×C₈	C₂²×Dic₅₃	1	1	yes	characteristic
327	C₂×C₈	C₂²×Dic₅₃	1	2	yes	—
328	C₂×C₈	C₂²×Dic₅₃	1	2	yes	—
329	C₂×C₈	C₂²×Dic₅₃	1	1	yes	characteristic
330	C₄⋊C₄	C₄⋊Dic₅₃	1	2	yes	—
331	C₄⋊C₄	C₄⋊Dic₅₃	1	1	yes	characteristic
332	C₄⋊C₄	C₄⋊Dic₅₃	1	2	yes	—
333	C₄⋊C₄	C₄⋊Dic₅₃	1	1	yes	characteristic
334	C₂²⋊C₄	C₄⋊Dic₅₃	1	2	yes	—
335	C₂²⋊C₄	C₄⋊Dic₅₃	1	2	yes	—
336	C₂²⋊C₄	C₄⋊Dic₅₃	1	2	yes	—
337	C₄²	C₂×Dic₁₀₆	1	1	yes	characteristic
338	C₄²	C₂×Dic₁₀₆	1	2	yes	—
339	C₄²	C₂×D₂₁₂	1	1	yes	characteristic
340	C₄²	C₂×D₂₁₂	1	2	yes	—
341	C₄²	C₂²×Dic₅₃	1	1	yes	characteristic
342	C₄²	C₂²×Dic₅₃	1	2	yes	—
343	C₄²	C₂³×D₅₃	1	1	yes	characteristic
344	C₂³	C₂×C₄⋊Dic₅₃	1	1	yes	characteristic
345	C₂³	C₂×C₄⋊Dic₅₃	1	2	yes	—
346	Q₈	—	2	2	no	—
347	D₄	—	2	2	no	—
348	D₄	—	4	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₂×C₄⋊Dic₅₃	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄⋊Dic₅₃	1	2	yes	—
361	C₂×C₄	C₂×C₄⋊Dic₅₃	1	1	yes	characteristic
362	C₂×C₄	C₂×C₄⋊Dic₅₃	1	2	yes	—
363	C₂×C₄	C₂×C₄⋊Dic₅₃	1	2	yes	—
364	C₂×C₄	C₂×C₄⋊Dic₅₃	1	1	yes	characteristic
365	C₂×C₄	C₂³×Dic₅₃	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
367	C₂×C₄	C₂²×Dic₁₀₆	1	1	yes	characteristic
368	C₈	—	2	1	no	—
369	C₈	—	2	2	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	2	no	—
373	C₈	—	212	1	no	—
374	C₈	—	212	1	no	—
375	C₈	—	212	1	no	—
376	C₈	—	212	2	no	—
377	C₈	—	212	1	no	—
378	C₈	—	212	2	no	—
379	C₈	#13133224	1	2	yes	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	2	no	—
386	C₂²	C₂²×C₄⋊Dic₅₃	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	2	no	—
393	C₄	#16810672	1	2	yes	—
394	C₄	C₂×#13133224	1	1	yes	characteristic
395	C₄	#16811390	1	1	yes	characteristic
396	C₄	#16811435	1	1	yes	characteristic
397	C₄	#16811435	1	1	yes	characteristic
398	C₂	—	4	1	no	—
399	C₂	—	4	2	no	—
400	C₂	#20283283	1	1	yes	characteristic
401	C₂	#20283310	1	1	yes	characteristic
402	C₂	C₂×#16810672	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₁₂
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#2965	C₂
socle	C₂²×C₅₃	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₅₃	Q₈
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	#2965	D₅₃
hypocenter	C₅₃	#17841
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2965

Complements

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

N	H ≅ G/N	type
3. #20273504	C₂	semidirect
4. #20273504	C₂	semidirect
5. #20273495	C₂	semidirect
6. #20273486	C₂	semidirect
7. #20273482	C₂	semidirect
8. #20273471	C₂	semidirect
9. #20273467	C₂	semidirect
10. #20273463	C₂	semidirect
248. C₅₃	#17841	semidirect

Maximal subgroups

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

subgroup	index
#20283847	2
#20283840	2
#20273504	2
#20273495	2
#20273486	2
#20273482	2
#20273471	2
#20273467	2
#20273463	2
C₅₃×#2965	2
#17841	53