Subgroups — #28328307

Order 13568.

710 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811682	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₅₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#20291098	C₂	1	1	yes	maximal, characteristic, complemented
4	#20291097	C₂	1	1	yes	maximal, characteristic, complemented
5	#20291096	C₂	1	1	yes	maximal, characteristic, complemented
6	#20291095	C₂	1	1	yes	maximal, characteristic, complemented
7	#20291094	C₂	1	1	yes	maximal, characteristic, complemented
8	#20291093	C₂	1	1	yes	maximal, characteristic, complemented
9	#20291093	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×#11719910	C₂	1	1	yes	maximal, characteristic, complemented
11	#20291051	C₂	1	1	yes	maximal, characteristic, complemented
12	#20290946	C₂	1	1	yes	maximal, characteristic, complemented
13	#20290943	C₂	1	1	yes	maximal, characteristic, complemented
14	#20290925	C₂	1	1	yes	maximal, characteristic, complemented
15	#20283406	C₂	1	1	yes	maximal, characteristic
16	#16811682	—	2	4	no	—
17	C₂×#13133292	C₂²	1	1	yes	characteristic
18	C₂×#13133292	C₂²	1	1	yes	characteristic
19	C₂×#13133292	C₂²	1	1	yes	characteristic, complemented
20	C₂×#13133291	C₂²	1	1	yes	characteristic, complemented
21	C₂×D₅₃⋊C₁₆	—	2	4	no	—
22	C₂×D₅₃⋊C₁₆	C₂²	1	1	yes	characteristic
23	C₂×D₅₃⋊C₁₆	C₂²	1	1	yes	characteristic
24	C₂×D₅₃⋊C₁₆	C₂²	1	1	yes	characteristic
25	C₂×D₅₃⋊C₁₆	C₂²	1	1	yes	characteristic
26	C₂×D₅₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#11719910	C₂²	1	1	yes	characteristic
28	C₂²×#11719910	C₂²	1	1	yes	characteristic
29	C₂²×#11719910	C₂²	1	1	yes	characteristic, complemented
30	#16811544	C₂²	1	1	yes	characteristic, complemented
31	#16811544	C₂²	1	1	yes	characteristic, complemented
32	C₄⋊#11719910	C₂²	1	1	yes	characteristic, complemented
33	C₄⋊#11719910	C₂²	1	1	yes	characteristic, complemented
34	#16811518	C₂²	1	1	yes	characteristic
35	#16811518	C₂²	1	1	yes	characteristic
36	#16811518	C₂²	1	1	yes	characteristic, complemented
37	#16811518	C₂²	1	1	yes	characteristic, complemented
38	C₂²⋊#11719910	C₂²	1	1	yes	characteristic
39	C₂²⋊#11719910	C₂²	1	1	yes	characteristic
40	C₂²⋊#11719910	C₂²	1	1	yes	characteristic, complemented
41	C₂²⋊#11719910	C₂²	1	1	yes	characteristic, complemented
42	#16811512	C₂²	1	1	yes	characteristic, complemented
43	#16811511	C₂²	1	1	yes	characteristic, complemented
44	#16811509	C₂²	1	1	yes	characteristic, complemented
45	C₄×#11719910	C₂²	1	1	yes	characteristic, complemented
46	C₂×#13133225	C₂²	1	1	yes	characteristic
47	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
48	#16811132	C₄	1	1	yes	characteristic
49	#16810696	C₄	1	1	yes	characteristic
50	#16810694	C₄	1	1	yes	characteristic
51	#16810692	C₄	1	1	yes	characteristic
52	D₄×#88322	C₂²	1	1	yes	characteristic
53	#16810688	C₂²	1	1	yes	characteristic
54	#16810686	C₂²	1	1	yes	characteristic
55	#16810686	C₂²	1	1	yes	characteristic
56	#16810648	C₄	1	1	yes	characteristic
57	#16810588	C₄	1	1	yes	characteristic
58	#16810585	C₄	1	1	yes	characteristic
59	#16810580	C₂²	1	1	yes	characteristic
60	C₅₃×#435	C₄	1	1	yes	characteristic
61	#13133292	—	2	2	no	—
62	#13133292	—	2	2	no	—
63	#13133292	—	2	2	no	—
64	#13133291	—	2	2	no	—
65	D₅₃⋊C₁₆	—	2	2	no	—
66	D₅₃⋊C₁₆	—	2	2	no	—
67	D₅₃⋊C₁₆	—	2	2	no	—
68	D₅₃⋊C₁₆	—	2	2	no	—
69	D₅₃⋊C₁₆	D₄	1	4	yes	complemented
70	C₂×#11719910	—	2	2	no	—
71	C₂×#11719910	—	2	2	no	—
72	C₂×#11719910	—	2	2	no	—
73	C₂×#11719910	C₂³	1	1	yes	characteristic
74	C₂×#11719910	C₂³	1	1	yes	characteristic
75	C₂×#11719910	C₂³	1	1	yes	characteristic
76	C₂×#11719910	C₂³	1	1	yes	characteristic
77	C₂×#11719910	C₂³	1	1	yes	characteristic
78	C₂×#11719910	C₂³	1	1	yes	characteristic
79	C₂×#11719910	C₂³	1	1	yes	characteristic
80	C₂×#11719910	C₂³	1	1	yes	characteristic
81	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
83	#13133225	—	2	2	no	—
84	#13133225	—	2	2	no	—
85	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
86	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
87	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
88	C₂²×#88322	C₂³	1	1	yes	characteristic
89	C₂²×#88322	C₂³	1	1	yes	characteristic
90	C₂×C₈×D₅₃	—	2	2	no	—
91	C₂×C₈×D₅₃	—	2	2	no	—
92	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
95	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
96	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
97	#13133202	C₈	1	1	yes	characteristic
98	#13133199	C₈	1	1	yes	characteristic
99	#13133195	C₈	1	1	yes	characteristic
100	#13133194	C₈	1	1	yes	characteristic
101	#13133190	C₈	1	1	yes	characteristic
102	#13133189	C₈	1	1	yes	characteristic
103	#13133187	C₈	1	1	yes	characteristic
104	#13133185	C₈	1	1	yes	characteristic
105	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
106	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
107	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
108	#13133174	C₂×C₄	1	1	yes	characteristic
109	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
110	#13133146	C₂×C₄	1	1	yes	characteristic
111	#13133146	C₂×C₄	1	1	yes	characteristic
112	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic
114	#13133129	C₂×C₄	1	1	yes	characteristic
115	#13133129	C₂×C₄	1	1	yes	characteristic
116	#13133129	C₂×C₄	1	1	yes	characteristic
117	#13133129	C₂×C₄	1	1	yes	characteristic
118	#13133127	C₂×C₄	1	1	yes	characteristic
119	C₄×#88322	C₂³	1	1	yes	characteristic
120	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
121	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
122	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
123	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
124	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
125	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
126	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
127	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
128	C₂³×D₅₃	C₂×C₈	1	1	yes	characteristic
129	C₂×D₄×C₅₃	C₂×C₈	1	1	yes	characteristic
130	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
133	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
134	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
135	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
136	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
137	#11719945	—	2	2	no	—
138	#11719945	—	2	2	no	—
139	C₂×D₂₁₂	C₂×C₈	1	1	yes	characteristic
140	C₂×D₂₁₂	C₂×C₈	1	1	yes	characteristic
141	C₂×C₄×D₅₃	—	2	2	no	—
142	C₂×C₄×D₅₃	—	2	2	no	—
143	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
144	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
145	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₁₀₆	C₂×C₈	1	1	yes	characteristic
149	M₁₆×C₅₃	—	2	2	no	—
150	C₂×C₈×C₅₃	—	2	2	no	—
151	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
155	C₄⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
156	C₂²⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
157	C₂²⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
158	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
159	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
160	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
161	#11719921	C₂×C₈	1	1	yes	characteristic
162	#11719921	C₂×C₈	1	1	yes	characteristic
163	#11719921	C₂×C₈	1	1	yes	characteristic
164	#11719921	C₂×C₈	1	1	yes	characteristic
165	#11719921	C₂×C₈	1	1	yes	characteristic
166	#11719921	C₂×C₈	1	1	yes	characteristic
167	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
168	#11719919	C₂×C₈	1	1	yes	characteristic
169	#11719919	C₂×C₈	1	1	yes	characteristic
170	#11719919	C₂×C₈	1	1	yes	characteristic
171	#11719919	C₂×C₈	1	1	yes	characteristic
172	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
173	C₂×#88322	—	2	1	no	—
174	C₂×#88322	—	2	1	no	—
175	C₂×#88322	—	2	1	no	—
176	C₂×#88322	—	2	1	no	—
177	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
178	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
179	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
180	C₂×#88322	C₂⁴	1	1	yes	characteristic
181	#11719912	—	2	2	no	—
182	#11719912	—	2	2	no	—
183	#11719912	—	2	2	no	—
184	C₈×D₅₃	—	2	2	no	—
185	C₈×D₅₃	—	2	2	no	—
186	C₈×D₅₃	—	2	1	no	—
187	C₈×D₅₃	—	2	1	no	—
188	C₈×D₅₃	—	2	1	no	—
189	C₈×D₅₃	—	2	1	no	—
190	C₈×D₅₃	C₂×D₄	1	2	yes	—
191	C₈×D₅₃	#41	1	2	yes	—
192	#11719910	—	2	1	no	—
193	#11719910	—	2	1	no	—
194	#11719910	—	2	1	no	—
195	#11719910	—	2	1	no	—
196	#11719910	—	2	1	no	—
197	#11719910	—	2	1	no	—
198	#11719910	C₂×D₄	1	2	yes	—
199	#11719910	C₂×D₄	1	2	yes	—
200	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
201	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
202	C₂²×D₅₃	—	2	2	no	—
203	C₂²×D₅₃	—	2	2	no	—
204	C₂²×D₅₃	—	2	2	no	—
205	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
206	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
207	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
208	D₄×C₅₃	—	2	2	no	—
209	C₂×C₄×C₅₃	—	2	1	no	—
210	C₂×C₄×C₅₃	—	2	1	no	—
211	C₂×C₄×C₅₃	—	2	1	no	—
212	C₂×C₄×C₅₃	—	2	1	no	—
213	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
214	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
215	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
216	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
217	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
218	C₂²⋊D₅₃	—	2	2	no	—
219	C₂²⋊D₅₃	—	2	2	no	—
220	C₂²⋊D₅₃	—	2	2	no	—
221	C₂²⋊D₅₃	—	2	2	no	—
222	C₂×Dic₅₃	—	2	2	no	—
223	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
224	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
225	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
226	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
227	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
228	D₂₁₂	—	2	2	no	—
229	D₂₁₂	—	2	2	no	—
230	C₄×D₅₃	—	2	2	no	—
231	C₄×D₅₃	—	2	1	no	—
232	C₄×D₅₃	—	2	1	no	—
233	C₄×D₅₃	—	2	1	no	—
234	C₄×D₅₃	—	2	1	no	—
235	C₄×D₅₃	—	2	2	no	—
236	C₄×D₅₃	C₄×D₄	1	2	yes	—
237	C₄×D₅₃	#131	1	2	yes	—
238	Dic₁₀₆	—	2	2	no	—
239	C₈×C₅₃	—	2	1	no	—
240	C₈×C₅₃	—	2	1	no	—
241	C₈×C₅₃	—	2	1	no	—
242	C₈×C₅₃	C₄×D₄	1	2	yes	—
243	#88322	—	2	1	no	—
244	#88322	—	2	1	no	—
245	#88322	—	2	1	no	—
246	#88322	C₂²×D₄	1	1	yes	characteristic
247	#88322	C₂×#41	1	1	yes	characteristic
248	#33432	—	53	1	no	maximal, Sylow
249	C₂²×C₅₃	—	2	1	no	—
250	C₂²×C₅₃	—	2	1	no	—
251	C₂²×C₅₃	—	2	1	no	—
252	C₂²×C₅₃	—	2	1	no	—
253	C₂²×C₅₃	—	2	1	no	—
254	C₂²×C₅₃	#504	1	2	yes	complemented
255	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
256	C₂×D₅₃	—	2	8	no	—
257	C₂×D₅₃	—	2	1	no	—
258	C₂×D₅₃	—	2	1	no	—
259	C₂×D₅₃	—	2	1	no	—
260	C₂×D₅₃	—	2	1	no	—
261	C₂×D₅₃	—	2	1	no	—
262	C₂×D₅₃	—	2	1	no	—
263	C₂×D₅₃	—	2	1	no	—
264	C₂×D₅₃	C₈×D₄	1	2	yes	—
265	C₂×D₅₃	#504	1	2	yes	complemented
266	C₄×C₅₃	—	2	1	no	—
267	C₄×C₅₃	—	2	1	no	—
268	C₄×C₅₃	—	2	1	no	—
269	C₄×C₅₃	—	2	1	no	—
270	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
271	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
272	Dic₅₃	—	2	1	no	—
273	Dic₅₃	—	2	1	no	—
274	Dic₅₃	—	2	1	no	—
275	Dic₅₃	—	2	1	no	—
276	Dic₅₃	C₈×D₄	1	2	yes	—
277	C₂×#504	—	53	1	no	—
278	C₂³×C₁₆	—	53	1	no	—
279	#2929	—	53	1	no	—
280	#2168	—	53	1	no	—
281	#2168	—	53	1	no	—
282	#2168	—	53	1	no	—
283	#2168	—	53	1	no	—
284	D₄×C₁₆	—	53	1	no	—
285	D₄×C₁₆	—	53	1	no	—
286	D₄×C₁₆	—	53	1	no	—
287	D₄×C₁₆	—	53	1	no	—
288	#2151	—	53	1	no	—
289	#2113	—	53	1	no	—
290	#2112	—	53	1	no	—
291	#2108	—	53	1	no	—
292	C₂×C₅₃	—	2	2	no	—
293	C₂×C₅₃	—	4	1	no	—
294	C₂×C₅₃	C₂×C₈×D₄	1	1	yes	characteristic
295	C₂×C₅₃	C₂×#504	1	1	yes	characteristic
296	C₂×C₅₃	C₂×#504	1	1	yes	characteristic
297	D₅₃	—	2	2	no	—
298	D₅₃	—	2	2	no	—
299	D₅₃	—	4	1	no	—
300	C₂×#131	—	53	1	no	—
301	C₂³×C₈	—	53	1	no	—
302	#525	—	53	1	no	—
303	#504	—	106	4	no	—
304	C₂×M₃₂	—	53	1	no	—
305	C₂×M₃₂	—	53	1	no	—
306	C₂×M₃₂	—	53	1	no	—
307	C₂×M₃₂	—	53	1	no	—
308	C₂²×C₁₆	—	53	1	no	—
309	C₂²×C₁₆	—	53	1	no	—
310	C₂²×C₁₆	—	53	1	no	—
311	C₂²×C₁₆	—	53	1	no	—
312	C₂²×C₁₆	—	53	1	no	—
313	C₂²×C₁₆	—	53	1	no	—
314	C₂²×C₁₆	—	53	1	no	—
315	C₂²×C₁₆	—	53	1	no	—
316	C₂²×C₁₆	—	106	4	no	—
317	#435	—	53	1	no	—
318	#435	—	53	1	no	—
319	#435	—	53	1	no	—
320	#435	#6157	1	1	yes	characteristic
321	C₈×D₄	—	53	1	no	—
322	C₈×D₄	—	53	1	no	—
323	C₈×D₄	—	53	1	no	—
324	C₈×D₄	—	53	1	no	—
325	#424	—	53	1	no	—
326	#408	—	53	1	no	—
327	#407	—	53	1	no	—
328	#405	—	53	1	no	—
329	C₄⋊C₁₆	—	53	1	no	—
330	C₄⋊C₁₆	—	53	1	no	—
331	C₄⋊C₁₆	—	53	1	no	—
332	C₄⋊C₁₆	—	53	1	no	—
333	C₂²⋊C₁₆	—	53	1	no	—
334	C₂²⋊C₁₆	—	53	1	no	—
335	C₂²⋊C₁₆	—	53	1	no	—
336	C₂²⋊C₁₆	—	53	1	no	—
337	C₂²⋊C₁₆	—	53	1	no	—
338	C₂²⋊C₁₆	—	53	1	no	—
339	C₂²⋊C₁₆	—	53	1	no	—
340	C₂²⋊C₁₆	—	53	1	no	—
341	#346	—	53	1	no	—
342	#346	—	53	1	no	—
343	C₄×C₁₆	—	53	1	no	—
344	C₄×C₁₆	—	53	1	no	—
345	C₅₃	#33432	1	1	yes	characteristic, complemented, Sylow
346	C₂×#41	—	53	1	no	—
347	C₂³×C₄	—	53	1	no	—
348	#131	—	106	2	no	—
349	#131	—	106	2	no	—
350	C₂×M₁₆	—	53	1	no	—
351	C₂×M₁₆	—	53	1	no	—
352	C₂×M₁₆	—	53	1	no	—
353	C₂×M₁₆	C₂×#6157	1	1	yes	characteristic
354	C₂²×C₈	—	53	1	no	—
355	C₂²×C₈	—	53	1	no	—
356	C₂²×C₈	—	53	1	no	—
357	C₂²×C₈	—	53	1	no	—
358	C₂²×C₈	—	53	1	no	—
359	C₂²×C₈	—	53	1	no	—
360	C₂²×C₈	—	53	1	no	—
361	C₂²×C₈	—	106	2	no	—
362	C₂²×C₈	—	106	2	no	—
363	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
364	#123	—	53	1	no	—
365	#123	—	53	1	no	—
366	C₂²⋊Q₈	—	53	1	no	—
367	C₂²⋊Q₈	—	53	1	no	—
368	#121	—	53	1	no	—
369	#121	—	53	1	no	—
370	#120	—	53	1	no	—
371	#120	—	53	1	no	—
372	C₄×D₄	—	53	1	no	—
373	C₄×D₄	—	53	1	no	—
374	C₄×D₄	—	53	1	no	—
375	C₄×D₄	C₂×#6157	1	1	yes	characteristic
376	#117	—	53	1	no	—
377	M₃₂	—	106	2	no	—
378	M₃₂	—	106	2	no	—
379	M₃₂	—	106	2	no	—
380	M₃₂	—	106	2	no	—
381	C₂×C₁₆	—	53	1	no	—
382	C₂×C₁₆	—	53	1	no	—
383	C₂×C₁₆	—	53	4	no	—
384	C₂×C₁₆	—	53	1	no	—
385	C₂×C₁₆	—	53	1	no	—
386	C₂×C₁₆	—	53	1	no	—
387	C₂×C₁₆	—	53	1	no	—
388	C₂×C₁₆	—	53	1	no	—
389	C₂×C₁₆	—	53	1	no	—
390	C₂×C₁₆	—	106	2	no	—
391	C₂×C₁₆	—	106	2	no	—
392	C₂×C₁₆	—	106	2	no	—
393	C₂×C₁₆	—	106	2	no	—
394	C₂×C₁₆	—	106	2	no	—
395	C₂×C₁₆	—	106	2	no	—
396	C₂×C₁₆	—	106	2	no	—
397	C₄⋊C₈	—	53	1	no	—
398	C₄⋊C₈	—	53	1	no	—
399	C₄⋊C₈	—	53	1	no	—
400	C₄⋊C₈	C₂×#6157	1	1	yes	characteristic
401	C₂²⋊C₈	—	53	1	no	—
402	C₂²⋊C₈	—	53	1	no	—
403	C₂²⋊C₈	—	53	1	no	—
404	C₂²⋊C₈	—	53	1	no	—
405	C₂²⋊C₈	—	53	1	no	—
406	C₂²⋊C₈	—	53	1	no	—
407	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic
408	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic
409	#97	—	53	1	no	—
410	#97	C₂×#6157	1	1	yes	characteristic
411	C₄×C₈	—	53	1	no	—
412	C₄×C₈	—	53	1	no	—
413	C₂⁴	—	53	1	no	—
414	#41	—	106	2	no	—
415	#41	—	106	2	no	—
416	C₂×Q₈	—	53	1	no	—
417	C₂×D₄	—	53	1	no	—
418	C₂×D₄	—	53	1	no	—
419	C₂×D₄	—	53	1	no	—
420	C₂×D₄	—	53	1	no	—
421	C₂×D₄	—	53	1	no	—
422	C₂×D₄	—	53	1	no	—
423	C₂×D₄	D₅₃⋊C₈	1	1	yes	characteristic
424	C₂²×C₄	—	53	1	no	—
425	C₂²×C₄	—	53	1	no	—
426	C₂²×C₄	—	53	1	no	—
427	C₂²×C₄	—	53	1	no	—
428	C₂²×C₄	—	53	1	no	—
429	C₂²×C₄	—	53	1	no	—
430	C₂²×C₄	—	106	2	no	—
431	C₂²×C₄	—	106	2	no	—
432	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
433	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
434	M₁₆	—	2	2	no	—
435	M₁₆	—	106	2	no	—
436	M₁₆	—	106	2	no	—
437	M₁₆	—	106	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	53	1	no	—
440	C₂×C₈	—	53	2	no	—
441	C₂×C₈	—	53	2	no	—
442	C₂×C₈	—	53	1	no	—
443	C₂×C₈	—	53	1	no	—
444	C₂×C₈	—	53	1	no	—
445	C₂×C₈	—	106	1	no	—
446	C₂×C₈	—	106	1	no	—
447	C₂×C₈	—	106	1	no	—
448	C₂×C₈	—	106	1	no	—
449	C₂×C₈	—	106	2	no	—
450	C₂×C₈	—	106	1	no	—
451	C₂×C₈	—	106	1	no	—
452	C₂×C₈	—	106	1	no	—
453	C₂×C₈	—	106	1	no	—
454	C₂×C₈	—	106	2	no	—
455	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
456	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
457	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
458	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
459	C₄⋊C₄	—	53	1	no	—
460	C₄⋊C₄	—	53	1	no	—
461	C₄⋊C₄	—	53	1	no	—
462	C₄⋊C₄	—	53	1	no	—
463	C₄⋊C₄	—	53	1	no	—
464	C₄⋊C₄	D₅₃⋊C₈	1	1	yes	characteristic
465	C₂²⋊C₄	—	53	1	no	—
466	C₂²⋊C₄	—	53	1	no	—
467	C₂²⋊C₄	—	53	1	no	—
468	C₂²⋊C₄	—	53	1	no	—
469	C₂²⋊C₄	—	53	1	no	—
470	C₂²⋊C₄	—	53	1	no	—
471	C₂²⋊C₄	—	53	1	no	—
472	C₂²⋊C₄	—	53	1	no	—
473	C₂²⋊C₄	D₅₃⋊C₈	1	1	yes	characteristic
474	C₂²⋊C₄	D₅₃⋊C₈	1	1	yes	characteristic
475	C₄²	—	53	1	no	—
476	C₄²	C₂²×#6157	1	1	yes	characteristic
477	C₁₆	—	53	2	no	—
478	C₁₆	—	53	2	no	—
479	C₁₆	—	106	1	no	—
480	C₁₆	—	106	1	no	—
481	C₁₆	—	106	1	no	—
482	C₁₆	—	106	1	no	—
483	C₁₆	—	106	1	no	—
484	C₁₆	—	106	1	no	—
485	C₂³	—	53	1	no	—
486	C₂³	—	53	1	no	—
487	C₂³	—	53	1	no	—
488	C₂³	—	106	2	no	—
489	C₂³	—	106	2	no	—
490	C₂³	—	106	2	no	—
491	C₂³	C₂×D₅₃⋊C₈	1	1	yes	characteristic
492	C₂³	C₂×D₅₃⋊C₈	1	1	yes	characteristic
493	Q₈	—	106	2	no	—
494	D₄	—	2	2	no	—
495	D₄	—	106	2	no	—
496	D₄	—	106	2	no	—
497	D₄	—	106	2	no	—
498	D₄	—	106	2	no	—
499	D₄	—	106	2	no	—
500	D₄	—	106	2	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	53	1	no	—
506	C₂×C₄	—	53	2	no	—
507	C₂×C₄	—	53	2	no	—
508	C₂×C₄	—	53	1	no	—
509	C₂×C₄	—	53	1	no	—
510	C₂×C₄	—	53	1	no	—
511	C₂×C₄	—	53	1	no	—
512	C₂×C₄	—	106	2	no	—
513	C₂×C₄	—	106	2	no	—
514	C₂×C₄	—	106	2	no	—
515	C₂×C₄	—	106	1	no	—
516	C₂×C₄	—	106	1	no	—
517	C₂×C₄	—	106	1	no	—
518	C₂×C₄	—	106	1	no	—
519	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
520	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
521	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
522	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
523	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	53	1	no	—
528	C₈	—	53	1	no	—
529	C₈	—	106	1	no	—
530	C₈	—	106	1	no	—
531	C₈	—	106	1	no	—
532	C₈	D₄×#6157	1	2	yes	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	53	2	no	—
539	C₂²	—	53	2	no	—
540	C₂²	—	106	8	no	—
541	C₂²	—	106	1	no	—
542	C₂²	—	106	1	no	—
543	C₂²	—	106	1	no	—
544	C₂²	—	106	1	no	—
545	C₂²	—	106	1	no	—
546	C₂²	—	106	1	no	—
547	C₂²	—	106	1	no	—
548	C₂²	#16811682	1	2	yes	complemented
549	C₂²	C₂²×D₅₃⋊C₈	1	1	yes	characteristic
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	53	2	no	—
555	C₄	—	106	1	no	—
556	C₄	—	106	1	no	—
557	C₄	—	106	1	no	—
558	C₄	—	106	1	no	—
559	C₄	C₂×D₄×#6157	1	1	yes	characteristic
560	C₄	D₅₃⋊#131	1	1	yes	characteristic
561	C₂	—	2	2	no	—
562	C₂	—	4	1	no	—
563	C₂	—	106	2	no	—
564	C₂	—	106	2	no	—
565	C₂	—	212	1	no	—
566	C₂	D₄×D₅₃⋊C₈	1	1	yes	characteristic
567	C₂	D₅₃⋊#504	1	1	yes	characteristic
568	C₂	C₂×#16811682	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#6157
commutator, socle	C₂²×C₅₃	C₂³×C₈
Fitting	C₅₃×#435	C₄
prime radical	#16811132	C₄
cosocle	C₂×#88322	C₂⁴
hypercenter	#435	#6157
hypocenter	C₅₃	#33432
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. C₂×#16811682	C₂	semidirect
2. C₂²×D₅₃⋊C₁₆	C₂	semidirect
3. #20291098	C₂	semidirect
4. #20291097	C₂	semidirect
5. #20291096	C₂	semidirect
6. #20291095	C₂	semidirect
7. #20291094	C₂	semidirect
8. #20291093	C₂	semidirect
9. #20291093	C₂	semidirect
10. D₄×#11719910	C₂	semidirect
11. #20291051	C₂	semidirect
12. #20290946	C₂	semidirect
13. #20290943	C₂	semidirect
14. #20290925	C₂	semidirect
19. C₂×#13133292	C₂²	semidirect
20. C₂×#13133291	C₂²	semidirect
26. C₂×D₅₃⋊C₁₆	C₂²	semidirect
29. C₂²×#11719910	C₂²	semidirect
30. #16811544	C₂²	semidirect
31. #16811544	C₂²	semidirect
32. C₄⋊#11719910	C₂²	semidirect
33. C₄⋊#11719910	C₂²	semidirect
36. #16811518	C₂²	semidirect
37. #16811518	C₂²	semidirect
40. C₂²⋊#11719910	C₂²	semidirect
41. C₂²⋊#11719910	C₂²	semidirect
42. #16811512	C₂²	semidirect
43. #16811511	C₂²	semidirect
44. #16811509	C₂²	semidirect
45. C₄×#11719910	C₂²	semidirect
69. D₅₃⋊C₁₆	D₄	semidirect
254. C₂²×C₅₃	#504	semidirect
265. C₂×D₅₃	#504	semidirect
345. C₅₃	#33432	semidirect
548. C₂²	#16811682	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811682	2
C₂²×D₅₃⋊C₁₆	2
#20291098	2
#20291097	2
#20291096	2
#20291095	2
#20291094	2
#20291093	2
D₄×#11719910	2
#20291051	2
#20290946	2
#20290943	2
#20290925	2
#20283406	2
#33432	53