Subgroups — #27537616

Order 13568.

558 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#11719945	C₂	1	1	yes	maximal, characteristic
2	#20276622	C₂	1	2	yes	maximal, complemented
3	#20276544	C₂	1	2	yes	maximal, complemented
4	#20276543	C₂	1	2	yes	maximal, complemented
5	#20276539	C₂	1	2	yes	maximal, complemented
6	#20276512	C₂	1	1	yes	maximal, characteristic, complemented
7	#20276512	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#13133157	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#13133156	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2162	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#11719945	C₄	1	1	yes	characteristic
13	C₂×#13133157	C₂²	1	2	yes	—
14	C₂×#13133156	C₂²	1	2	yes	—
15	C₂×C₁₆×D₅₃	C₂²	1	2	yes	—
16	C₈×Dic₁₀₆	C₄	1	1	yes	characteristic
17	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
18	C₈×D₂₁₂	C₄	1	1	yes	characteristic
19	C₈×D₂₁₂	C₂²	1	1	yes	characteristic
20	C₈×C₂²⋊D₅₃	C₄	1	1	yes	characteristic
21	C₈×C₂²⋊D₅₃	C₄	1	1	yes	characteristic
22	C₈×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
23	C₈×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
24	#16810676	C₄	1	1	yes	characteristic
25	#16810674	C₄	1	1	yes	characteristic
26	#16810674	C₄	1	1	yes	characteristic
27	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
28	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
29	#16810441	C₂²	1	2	yes	—
30	#16810441	C₂²	1	2	yes	—
31	#16810402	C₂²	1	2	yes	—
32	#16810402	C₂²	1	2	yes	—
33	#16810399	C₂²	1	2	yes	—
34	#16810398	C₂²	1	2	yes	—
35	C₄×#11719908	C₂²	1	1	yes	characteristic
36	C₄×#11719908	C₂²	1	1	yes	characteristic
37	C₁₆×Dic₅₃	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
39	C₅₃×C₄⋊C₁₆	C₂²	1	2	yes	—
40	C₅₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₄×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
42	C₄×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×#11719945	C₈	1	1	yes	characteristic
44	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
47	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
48	C₄×Dic₁₀₆	C₈	1	1	yes	characteristic
49	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
50	C₄×D₂₁₂	C₈	1	1	yes	characteristic
51	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
52	C₄×C₂²⋊D₅₃	C₈	1	1	yes	characteristic
53	C₄×C₂²⋊D₅₃	C₈	1	1	yes	characteristic
54	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
55	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
56	#13133176	C₈	1	1	yes	characteristic
57	#13133174	C₈	1	1	yes	characteristic
58	#13133174	C₈	1	1	yes	characteristic
59	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
61	#13133157	—	2	4	no	—
62	#13133156	—	2	4	no	—
63	C₂×#11719908	C₂³	1	2	yes	—
64	C₂×#11719908	C₂³	1	2	yes	—
65	C₁₆×D₅₃	—	2	4	no	—
66	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
67	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
68	#13133146	C₂×C₄	1	1	yes	characteristic
69	#13133146	C₂×C₄	1	1	yes	characteristic
70	#13133146	C₂×C₄	1	1	yes	characteristic
71	#13133146	C₂×C₄	1	1	yes	characteristic
72	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic
73	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic
74	#13133129	C₂×C₄	1	1	yes	characteristic
75	#13133129	C₂×C₄	1	1	yes	characteristic
76	#13133129	C₂×C₄	1	1	yes	characteristic
77	#13133129	C₂×C₄	1	1	yes	characteristic
78	C₄×#88322	C₂×C₄	1	1	yes	characteristic
79	C₄×#88322	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
83	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₁₆×C₅₃	C₂³	1	2	yes	—
88	C₂×C₁₆×C₅₃	C₂³	1	2	yes	—
89	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
94	C₂²×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
97	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
98	#11719945	—	2	4	no	—
99	C₂×D₂₁₂	C₂×C₈	1	1	yes	characteristic
100	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
101	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
102	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
103	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×Dic₁₀₆	C₂×C₈	1	1	yes	characteristic
107	C₂×C₈×C₅₃	—	2	2	no	—
108	C₂×C₈×C₅₃	—	2	2	no	—
109	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
113	C₄²×C₅₃	C₂×C₈	1	1	yes	characteristic
114	C₄²×C₅₃	C₂×C₈	1	1	yes	characteristic
115	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
118	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
119	#11719921	C₂×C₈	1	1	yes	characteristic
120	#11719921	C₂×C₈	1	1	yes	characteristic
121	#11719921	C₂×C₈	1	1	yes	characteristic
122	#11719921	C₂×C₈	1	1	yes	characteristic
123	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
124	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
125	#11719919	C₂×C₈	1	1	yes	characteristic
126	#11719919	C₂×C₈	1	1	yes	characteristic
127	#11719919	C₂×C₈	1	1	yes	characteristic
128	#11719919	C₂×C₈	1	1	yes	characteristic
129	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
130	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
131	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
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	C₈×D₅₃	—	2	2	no	—
140	C₈×D₅₃	—	2	2	no	—
141	C₈×D₅₃	—	2	2	no	—
142	C₈×D₅₃	—	2	2	no	—
143	C₁₆×C₅₃	—	2	2	no	—
144	C₁₆×C₅₃	—	2	2	no	—
145	#11719908	—	2	2	no	—
146	#11719908	#41	1	4	yes	complemented
147	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
148	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
149	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
150	C₂×C₄×C₅₃	—	2	1	no	—
151	C₂×C₄×C₅₃	—	2	1	no	—
152	C₂×C₄×C₅₃	—	2	2	no	—
153	C₂×C₄×C₅₃	—	2	2	no	—
154	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
155	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
156	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
157	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
159	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
160	C₂²⋊D₅₃	—	2	2	no	—
161	C₂²⋊D₅₃	—	2	2	no	—
162	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
163	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
164	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
165	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
166	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
167	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
168	D₂₁₂	—	2	2	no	—
169	C₄×D₅₃	—	2	1	no	—
170	C₄×D₅₃	—	2	1	no	—
171	C₄×D₅₃	—	2	1	no	—
172	C₄×D₅₃	—	2	1	no	—
173	C₄×D₅₃	—	2	2	no	—
174	C₄×D₅₃	—	2	2	no	—
175	C₄×D₅₃	—	2	2	no	—
176	C₄×D₅₃	M₃₂	1	4	yes	complemented
177	Dic₁₀₆	—	2	2	no	—
178	C₈×C₅₃	—	2	1	no	—
179	C₈×C₅₃	—	2	1	no	—
180	C₈×C₅₃	#131	1	2	yes	—
181	C₈×C₅₃	C₂×#41	1	2	yes	—
182	#88322	—	2	1	no	—
183	#88322	—	2	1	no	—
184	#88322	—	2	1	no	—
185	#88322	—	2	1	no	—
186	#33479	—	53	1	no	maximal, Sylow
187	C₂²×C₅₃	—	2	1	no	—
188	C₂²×C₅₃	—	2	1	no	—
189	C₂²×C₅₃	—	2	1	no	—
190	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
191	C₂×D₅₃	—	2	1	no	—
192	C₂×D₅₃	—	2	1	no	—
193	C₂×D₅₃	—	2	1	no	—
194	C₂×D₅₃	—	2	1	no	—
195	C₂×D₅₃	—	2	1	no	—
196	C₂×D₅₃	C₂×M₃₂	1	2	yes	—
197	C₄×C₅₃	—	2	1	no	—
198	C₄×C₅₃	—	2	1	no	—
199	C₄×C₅₃	—	2	1	no	—
200	C₄×C₅₃	C₂×M₃₂	1	2	yes	—
201	C₄×C₅₃	#504	1	2	yes	—
202	C₄×C₅₃	C₄×#41	1	1	yes	characteristic
203	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
204	Dic₅₃	—	2	1	no	—
205	Dic₅₃	—	2	1	no	—
206	Dic₅₃	—	2	1	no	—
207	Dic₅₃	—	2	1	no	—
208	Dic₅₃	—	2	1	no	—
209	Dic₅₃	C₂×M₃₂	1	2	yes	—
210	C₈×#41	—	53	1	no	—
211	#2183	—	53	2	no	—
212	#2169	—	53	2	no	—
213	#2168	—	53	2	no	—
214	#2168	—	53	2	no	—
215	#2162	—	53	1	no	—
216	#2162	—	53	1	no	—
217	#2162	D₅₃	1	1	yes	characteristic, complemented
218	C₄×M₃₂	—	53	1	no	—
219	C₄×M₃₂	—	53	1	no	—
220	C₂×C₄×C₁₆	—	53	1	no	—
221	C₂×C₅₃	—	4	1	no	—
222	C₂×C₅₃	C₈×#41	1	1	yes	characteristic
223	C₂×C₅₃	C₂²×M₃₂	1	1	yes	characteristic
224	C₂×C₅₃	C₂×#504	1	1	yes	characteristic
225	D₅₃	—	2	2	no	—
226	D₅₃	—	4	1	no	—
227	C₄×#41	—	53	1	no	—
228	C₂×M₃₂	—	53	2	no	—
229	C₂×M₃₂	—	53	2	no	—
230	C₂²×C₁₆	—	53	2	no	—
231	C₈×Q₈	—	53	1	no	—
232	C₈×Q₈	—	53	1	no	—
233	C₈×D₄	—	53	1	no	—
234	C₈×D₄	—	53	1	no	—
235	C₈×D₄	—	53	1	no	—
236	C₈×D₄	—	53	1	no	—
237	C₈×D₄	—	53	1	no	—
238	C₈×D₄	—	53	1	no	—
239	#431	—	53	1	no	—
240	#431	—	53	1	no	—
241	#431	—	53	1	no	—
242	C₂×C₄×C₈	—	53	1	no	—
243	C₂×C₄×C₈	—	53	1	no	—
244	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
245	C₄⋊C₁₆	—	53	2	no	—
246	C₄⋊C₁₆	—	53	2	no	—
247	C₄⋊C₁₆	C₂×D₅₃	1	2	yes	—
248	C₂²⋊C₁₆	—	53	2	no	—
249	C₂²⋊C₁₆	—	53	2	no	—
250	C₂²⋊C₁₆	C₂×D₅₃	1	2	yes	—
251	#346	—	53	2	no	—
252	#346	—	53	2	no	—
253	C₄×C₁₆	—	53	2	no	—
254	C₄×C₁₆	—	53	1	no	—
255	C₄×C₁₆	—	53	1	no	—
256	C₄×C₁₆	C₂×D₅₃	1	1	yes	characteristic
257	C₄×C₁₆	C₂×D₅₃	1	1	yes	characteristic
258	C₅₃	#33479	1	1	yes	characteristic, complemented, Sylow
259	C₂×#41	—	53	1	no	—
260	C₂²×C₈	—	53	1	no	—
261	C₂²×C₈	—	53	1	no	—
262	C₂²×C₈	—	53	1	no	—
263	C₂²×C₈	—	53	1	no	—
264	C₂²×C₈	C₄×D₅₃	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
266	C₄×Q₈	—	53	1	no	—
267	C₄×Q₈	—	53	1	no	—
268	C₄×D₄	—	53	1	no	—
269	C₄×D₄	—	53	1	no	—
270	C₄×D₄	—	53	1	no	—
271	C₄×D₄	—	53	1	no	—
272	C₄×D₄	—	53	1	no	—
273	C₄×D₄	—	53	1	no	—
274	#117	—	53	1	no	—
275	#117	—	53	1	no	—
276	#117	—	53	1	no	—
277	C₂×C₄²	—	53	1	no	—
278	C₂×C₄²	—	53	1	no	—
279	C₂×C₄²	C₄×D₅₃	1	1	yes	characteristic
280	M₃₂	—	106	4	no	—
281	M₃₂	—	106	4	no	—
282	C₂×C₁₆	—	53	2	no	—
283	C₂×C₁₆	—	53	2	no	—
284	C₂×C₁₆	—	106	4	no	—
285	C₂×C₁₆	C₂²×D₅₃	1	2	yes	—
286	C₂×C₁₆	C₂²×D₅₃	1	2	yes	—
287	C₄⋊C₈	—	53	1	no	—
288	C₄⋊C₈	—	53	1	no	—
289	C₄⋊C₈	—	53	1	no	—
290	C₄⋊C₈	—	53	1	no	—
291	C₄⋊C₈	—	53	1	no	—
292	C₄⋊C₈	—	53	1	no	—
293	C₂²⋊C₈	—	53	1	no	—
294	C₂²⋊C₈	—	53	1	no	—
295	C₂²⋊C₈	—	53	1	no	—
296	C₂²⋊C₈	—	53	1	no	—
297	C₂²⋊C₈	—	53	1	no	—
298	C₂²⋊C₈	—	53	1	no	—
299	C₄×C₈	—	53	1	no	—
300	C₄×C₈	—	53	1	no	—
301	C₄×C₈	—	53	1	no	—
302	C₄×C₈	—	53	1	no	—
303	C₄×C₈	—	53	1	no	—
304	C₄×C₈	—	53	1	no	—
305	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
306	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
307	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
308	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
309	#41	—	106	4	no	—
310	C₂×Q₈	—	53	1	no	—
311	C₂×D₄	—	53	1	no	—
312	C₂×D₄	—	53	1	no	—
313	C₂×D₄	—	53	1	no	—
314	C₂²×C₄	—	53	1	no	—
315	C₂²×C₄	—	53	1	no	—
316	C₂²×C₄	—	53	1	no	—
317	C₂²×C₄	—	53	1	no	—
318	C₂²×C₄	—	53	1	no	—
319	C₂²×C₄	—	53	1	no	—
320	C₂²×C₄	C₈×D₅₃	1	1	yes	characteristic
321	C₂²×C₄	C₈×D₅₃	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	53	1	no	—
326	C₂×C₈	—	53	1	no	—
327	C₂×C₈	—	53	1	no	—
328	C₂×C₈	—	53	1	no	—
329	C₂×C₈	—	106	2	no	—
330	C₂×C₈	—	106	2	no	—
331	C₂×C₈	—	106	2	no	—
332	C₂×C₈	—	106	2	no	—
333	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
335	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
336	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
337	C₄⋊C₄	—	53	1	no	—
338	C₄⋊C₄	—	53	1	no	—
339	C₄⋊C₄	—	53	1	no	—
340	C₄⋊C₄	—	53	1	no	—
341	C₄⋊C₄	—	53	1	no	—
342	C₄⋊C₄	—	53	1	no	—
343	C₂²⋊C₄	—	53	1	no	—
344	C₂²⋊C₄	—	53	1	no	—
345	C₂²⋊C₄	—	53	1	no	—
346	C₂²⋊C₄	—	53	1	no	—
347	C₂²⋊C₄	—	53	1	no	—
348	C₂²⋊C₄	—	53	1	no	—
349	C₄²	—	53	1	no	—
350	C₄²	—	53	1	no	—
351	C₄²	—	53	1	no	—
352	C₄²	—	53	1	no	—
353	C₄²	—	53	1	no	—
354	C₄²	—	53	1	no	—
355	C₄²	C₈×D₅₃	1	1	yes	characteristic
356	C₄²	C₈×D₅₃	1	1	yes	characteristic
357	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
358	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
359	C₁₆	—	2	2	no	—
360	C₁₆	—	2	2	no	—
361	C₁₆	—	53	4	no	—
362	C₁₆	—	106	2	no	—
363	C₂³	—	53	1	no	—
364	C₂³	—	53	1	no	—
365	C₂³	C₂×C₈×D₅₃	1	1	yes	characteristic
366	Q₈	—	106	2	no	—
367	D₄	—	106	2	no	—
368	D₄	—	106	2	no	—
369	D₄	—	106	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	53	1	no	—
375	C₂×C₄	—	53	4	no	—
376	C₂×C₄	—	53	1	no	—
377	C₂×C₄	—	53	1	no	—
378	C₂×C₄	—	53	1	no	—
379	C₂×C₄	—	53	1	no	—
380	C₂×C₄	—	53	1	no	—
381	C₂×C₄	—	106	2	no	—
382	C₂×C₄	—	106	2	no	—
383	C₂×C₄	—	106	2	no	—
384	C₂×C₄	—	106	1	no	—
385	C₂×C₄	—	106	1	no	—
386	C₂×C₄	—	106	1	no	—
387	C₂×C₄	—	106	1	no	—
388	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
389	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
390	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
391	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
392	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	106	1	no	—
397	C₈	—	106	1	no	—
398	C₈	—	106	1	no	—
399	C₈	—	106	1	no	—
400	C₈	#13133225	1	2	yes	—
401	C₈	#41×D₅₃	1	2	yes	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	53	2	no	—
406	C₂²	—	106	1	no	—
407	C₂²	—	106	1	no	—
408	C₂²	—	106	1	no	—
409	C₂²	—	106	1	no	—
410	C₂²	—	106	1	no	—
411	C₂²	C₂²×C₈×D₅₃	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	53	2	no	—
416	C₄	—	106	1	no	—
417	C₄	—	106	1	no	—
418	C₄	—	106	1	no	—
419	C₄	—	106	1	no	—
420	C₄	—	106	1	no	—
421	C₄	M₃₂×D₅₃	1	2	yes	—
422	C₄	#16811039	1	2	yes	—
423	C₄	#16811091	1	1	yes	characteristic
424	C₄	C₂×#13133225	1	1	yes	characteristic
425	C₂	—	4	1	no	—
426	C₂	—	106	2	no	—
427	C₂	—	212	1	no	—
428	C₂	#20283671	1	1	yes	characteristic
429	C₂	C₂×M₃₂×D₅₃	1	1	yes	characteristic
430	C₂	C₂×#16811039	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂²×D₅₃
commutator, socle	C₂²×C₅₃	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₅₃×#2162	C₂
prime radical	C₂×#11719945	C₈
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	#2162	D₅₃
hypocenter	C₅₃	#33479
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄×C₈ ◁ #2162

Complements

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

N	H ≅ G/N	type
2. #20276622	C₂	semidirect
3. #20276544	C₂	semidirect
4. #20276543	C₂	semidirect
5. #20276539	C₂	semidirect
6. #20276512	C₂	semidirect
7. #20276512	C₂	semidirect
8. C₄×#13133157	C₂	semidirect
9. C₄×#13133156	C₂	semidirect
10. C₄×C₁₆×D₅₃	C₂	semidirect
11. C₅₃×#2162	C₂	semidirect
146. #11719908	#41	semidirect
176. C₄×D₅₃	M₃₂	semidirect
217. #2162	D₅₃	semidirect
258. C₅₃	#33479	semidirect

Maximal subgroups

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

subgroup	index
C₈×#11719945	2
#20276622	2
#20276544	2
#20276543	2
#20276539	2
#20276512	2
C₄×#13133157	2
C₄×#13133156	2
C₄×C₁₆×D₅₃	2
C₅₃×#2162	2
#33479	53