Subgroups — #28327923

Order 13568.

738 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₃⋊M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#16811586	C₂	1	1	yes	maximal, characteristic
3	#20290935	C₂	1	4	yes	maximal, complemented
4	#20290934	C₂	1	4	yes	maximal, complemented
5	#20290930	C₂	1	4	yes	maximal, complemented
6	C₂×M₃₂×D₅₃	C₂	1	1	yes	maximal, characteristic
7	C₂×D₅₃⋊M₁₆	C₄	1	1	yes	characteristic
8	C₂×#13133296	C₄	1	1	yes	characteristic
9	C₂×#13133292	C₂²	1	2	yes	—
10	D₅₃⋊M₃₂	C₄	1	2	yes	complemented
11	D₅₃⋊M₃₂	C₄	1	2	yes	complemented
12	D₅₃⋊M₃₂	C₂²	1	2	yes	—
13	D₅₃⋊M₃₂	C₂²	1	2	yes	—
14	C₂×#13133291	C₄	1	2	yes	complemented
15	C₂×D₅₃⋊C₁₆	C₄	1	2	yes	complemented
16	#16811586	C₄	1	2	yes	—
17	#16811586	C₄	1	2	yes	—
18	#16811586	C₂²	1	2	yes	—
19	#16811586	C₂²	1	2	yes	—
20	C₂×#13133271	C₂²	1	2	yes	—
21	C₂×C₈×#6157	C₄	1	2	yes	—
22	#16811514	C₂²	1	8	yes	complemented
23	#16811513	C₂²	1	8	yes	complemented
24	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
25	C₂×#13133157	C₄	1	1	yes	characteristic, complemented
26	C₂×#13133156	C₂²	1	2	yes	—
27	M₃₂×D₅₃	C₄	1	2	yes	complemented
28	M₃₂×D₅₃	C₄	1	2	yes	complemented
29	M₃₂×D₅₃	C₂²	1	2	yes	—
30	M₃₂×D₅₃	C₂²	1	2	yes	—
31	C₂×C₁₆×D₅₃	C₄	1	2	yes	complemented
32	C₂×M₃₂×C₅₃	C₄	1	1	yes	characteristic, complemented
33	C₂×#11719936	—	2	1	no	—
34	D₅₃⋊M₁₆	—	2	1	no	—
35	D₅₃⋊M₁₆	—	2	1	no	—
36	D₅₃⋊M₁₆	C₂×C₄	1	2	yes	—
37	D₅₃⋊M₁₆	C₂×C₄	1	2	yes	—
38	C₂×#11719940	—	2	1	no	—
39	C₂×D₅₃⋊C₈	C₂×C₄	1	2	yes	—
40	#13133296	—	2	1	no	—
41	#13133296	—	2	1	no	—
42	#13133296	C₂×C₄	1	2	yes	—
43	#13133296	C₂×C₄	1	2	yes	—
44	C₂×C₄⋊#6157	—	2	1	no	—
45	C₂×C₂²⋊#6157	—	2	1	no	—
46	C₂×C₄×#6157	C₂×C₄	1	2	yes	—
47	#13133292	C₂×C₄	1	4	yes	complemented
48	#13133292	C₂³	1	4	yes	—
49	#13133291	C₂×C₄	1	4	yes	—
50	#13133291	C₂×C₄	1	4	yes	complemented
51	D₅₃⋊C₁₆	C₂×C₄	1	4	yes	—
52	D₅₃⋊C₁₆	C₂×C₄	1	4	yes	complemented
53	C₂×#11719910	C₂×C₄	1	4	yes	complemented
54	#13133271	C₂×C₄	1	4	yes	—
55	#13133271	C₂³	1	4	yes	—
56	C₈×#6157	C₂×C₄	1	4	yes	—
57	C₈×#6157	C₂×C₄	1	4	yes	—
58	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
59	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
70	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
71	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
72	#13133157	C₂×C₄	1	2	yes	—
73	#13133157	C₂×C₄	1	2	yes	complemented
74	#13133156	C₂×C₄	1	4	yes	complemented
75	#13133156	C₂³	1	4	yes	—
76	C₂×#11719908	C₂×C₄	1	2	yes	complemented
77	C₁₆×D₅₃	C₂×C₄	1	4	yes	—
78	C₁₆×D₅₃	C₂×C₄	1	4	yes	complemented
79	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
80	M₃₂×C₅₃	C₂×C₄	1	2	yes	—
81	M₃₂×C₅₃	C₂×C₄	1	2	yes	complemented
82	C₂×C₁₆×C₅₃	C₂×C₄	1	2	yes	complemented
83	C₂³×D₅₃	M₁₆	1	1	yes	characteristic
84	C₂²×#6157	—	2	2	no	—
85	C₂²×C₄×C₅₃	C₄²	1	1	yes	characteristic
86	C₂²×Dic₅₃	M₁₆	1	1	yes	characteristic
87	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
88	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
89	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
90	C₂×C₄×D₅₃	M₁₆	1	1	yes	characteristic
91	C₂×C₄×D₅₃	M₁₆	1	1	yes	characteristic
92	C₂×C₄×D₅₃	M₁₆	1	1	yes	characteristic
93	C₂×C₄×D₅₃	M₁₆	1	1	yes	characteristic
94	C₂×C₄×D₅₃	M₁₆	1	1	yes	characteristic
95	C₂×C₄×D₅₃	M₁₆	1	1	yes	characteristic
96	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²⋊#6157	—	2	2	no	—
100	C₂²⋊#6157	—	2	2	no	—
101	#11719940	—	2	2	no	—
102	#11719940	—	2	2	no	—
103	C₂×#88324	—	2	2	no	—
104	C₄⋊#6157	—	2	2	no	—
105	C₄⋊#6157	—	2	2	no	—
106	C₄×#6157	—	2	2	no	—
107	C₄×#6157	C₂²×C₄	1	4	yes	—
108	#11719936	—	2	2	no	—
109	#11719936	—	2	2	no	—
110	D₅₃⋊C₈	—	2	2	no	—
111	D₅₃⋊C₈	C₂²×C₄	1	4	yes	—
112	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
113	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
114	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
115	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×#88322	C₄²	1	1	yes	characteristic
119	C₂×#88322	C₄²	1	1	yes	characteristic
120	C₂×#88322	C₄²	1	1	yes	characteristic
121	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
122	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
123	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
124	C₈×D₅₃	C₄²	1	1	yes	characteristic
125	C₈×D₅₃	C₄²	1	1	yes	characteristic
126	C₈×D₅₃	C₄²	1	1	yes	characteristic
127	C₈×D₅₃	C₄²	1	1	yes	characteristic
128	C₈×D₅₃	C₄²	1	1	yes	characteristic
129	C₈×D₅₃	C₄²	1	1	yes	characteristic
130	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
131	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
132	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
133	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
134	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
135	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
136	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
137	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
138	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
139	C₈×D₅₃	C₂⁴	1	1	yes	characteristic
140	#11719910	C₂²×C₄	1	8	yes	—
141	C₁₆×C₅₃	C₂²×C₄	1	4	yes	—
142	#11719908	C₂²×C₄	1	4	yes	—
143	C₂³×C₅₃	#97	1	1	yes	characteristic
144	C₂²×D₅₃	—	4	2	no	—
145	C₂²×D₅₃	#97	1	1	yes	characteristic
146	C₂²×D₅₃	#97	1	1	yes	characteristic
147	C₂²×D₅₃	#97	1	1	yes	characteristic
148	C₂²×D₅₃	C₂×M₁₆	1	1	yes	characteristic
149	C₂²×D₅₃	C₂×M₁₆	1	1	yes	characteristic
150	C₂²×D₅₃	C₂×M₁₆	1	1	yes	characteristic
151	C₂×#6157	—	2	4	no	—
152	C₂×#6157	—	4	4	no	—
153	C₂×C₄×C₅₃	#97	1	1	yes	characteristic
154	C₂×C₄×C₅₃	#97	1	1	yes	characteristic
155	C₂×C₄×C₅₃	#97	1	1	yes	characteristic
156	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
159	C₂×Dic₅₃	#97	1	1	yes	characteristic
160	C₂×Dic₅₃	#97	1	1	yes	characteristic
161	C₂×Dic₅₃	#97	1	1	yes	characteristic
162	C₂×Dic₅₃	C₂×M₁₆	1	1	yes	characteristic
163	C₂×Dic₅₃	C₂×M₁₆	1	1	yes	characteristic
164	C₂×Dic₅₃	C₂×M₁₆	1	1	yes	characteristic
165	C₄×D₅₃	#97	1	1	yes	characteristic
166	C₄×D₅₃	#97	1	1	yes	characteristic
167	C₄×D₅₃	#97	1	1	yes	characteristic
168	C₄×D₅₃	#97	1	1	yes	characteristic
169	C₄×D₅₃	#97	1	1	yes	characteristic
170	C₄×D₅₃	#97	1	1	yes	characteristic
171	C₄×D₅₃	C₂×C₄²	1	1	yes	characteristic
172	C₄×D₅₃	C₂×C₄²	1	1	yes	characteristic
173	C₄×D₅₃	C₂×C₄²	1	1	yes	characteristic
174	C₄×D₅₃	C₂×M₁₆	1	1	yes	characteristic
175	C₄×D₅₃	C₂×M₁₆	1	1	yes	characteristic
176	C₄×D₅₃	C₂×M₁₆	1	1	yes	characteristic
177	C₄×D₅₃	C₂×M₁₆	1	1	yes	characteristic
178	C₄×D₅₃	C₂×M₁₆	1	1	yes	characteristic
179	C₄×D₅₃	C₂×M₁₆	1	1	yes	characteristic
180	C₄×D₅₃	C₂³×C₄	1	1	yes	characteristic
181	#88324	—	2	4	no	—
182	C₈×C₅₃	C₂×C₄²	1	1	yes	characteristic
183	C₈×C₅₃	C₂×C₄²	1	1	yes	characteristic
184	C₈×C₅₃	C₂×C₄²	1	1	yes	characteristic
185	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
186	#88322	C₂×C₄²	1	1	yes	characteristic
187	#88322	C₂×C₄²	1	1	yes	characteristic
188	#88322	C₂×C₄²	1	1	yes	characteristic
189	#88322	C₂³×C₄	1	1	yes	characteristic
190	C₂×#2110	—	53	1	no	maximal, Sylow
191	C₂²×C₅₃	—	4	1	no	—
192	C₂²×C₅₃	C₂×#97	1	1	yes	characteristic
193	C₂²×C₅₃	C₂×#97	1	1	yes	characteristic
194	C₂²×C₅₃	C₂×#97	1	1	yes	characteristic
195	C₂×D₅₃	—	2	2	no	—
196	C₂×D₅₃	—	2	2	no	—
197	C₂×D₅₃	—	2	2	no	—
198	C₂×D₅₃	—	4	1	no	—
199	C₂×D₅₃	—	4	1	no	—
200	C₂×D₅₃	—	4	1	no	—
201	C₂×D₅₃	C₂×#97	1	1	yes	characteristic
202	C₂×D₅₃	C₂×#97	1	1	yes	characteristic
203	C₂×D₅₃	C₂×#97	1	1	yes	characteristic
204	C₂×D₅₃	C₂²×M₁₆	1	1	yes	characteristic
205	#6157	—	4	4	no	—
206	C₄×C₅₃	C₂×#97	1	1	yes	characteristic
207	C₄×C₅₃	C₂×#97	1	1	yes	characteristic
208	C₄×C₅₃	C₂×#97	1	1	yes	characteristic
209	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
210	Dic₅₃	C₂×#97	1	1	yes	characteristic
211	Dic₅₃	C₂×#97	1	1	yes	characteristic
212	Dic₅₃	C₂×#97	1	1	yes	characteristic
213	Dic₅₃	C₂²×M₁₆	1	1	yes	characteristic
214	C₂²×M₃₂	—	53	1	no	—
215	C₂²×M₃₂	—	53	1	no	—
216	C₂×#405	—	53	1	no	—
217	#2110	—	53	4	no	—
218	#2110	—	53	4	no	—
219	C₂×#347	—	53	4	no	—
220	C₂×C₅₃	—	2	1	no	—
221	C₂×C₅₃	—	2	1	no	—
222	C₂×C₅₃	—	2	1	no	—
223	C₂×C₅₃	C₂²×#97	1	1	yes	characteristic
224	D₅₃	—	2	1	no	—
225	D₅₃	—	2	1	no	—
226	D₅₃	—	2	1	no	—
227	D₅₃	#2110	1	2	yes	complemented
228	C₂²×M₁₆	—	53	1	no	—
229	C₂³×C₈	—	53	1	no	—
230	C₂×#117	—	53	1	no	—
231	C₂×M₃₂	—	53	2	no	—
232	C₂×M₃₂	—	53	2	no	—
233	C₂×M₃₂	—	53	2	no	—
234	C₂×M₃₂	—	53	2	no	—
235	C₂×M₃₂	—	53	2	no	—
236	C₂×M₃₂	—	53	2	no	—
237	C₂×M₃₂	—	53	1	no	—
238	C₂×M₃₂	—	53	2	no	—
239	C₂×M₃₂	—	53	2	no	—
240	C₂×M₃₂	—	53	2	no	—
241	C₂×M₃₂	—	53	2	no	—
242	C₂×M₃₂	—	53	2	no	—
243	C₂×M₃₂	#6157	1	1	yes	characteristic, complemented
244	C₂²×C₁₆	—	53	2	no	—
245	C₂²×C₁₆	—	53	2	no	—
246	#405	—	53	2	no	—
247	#405	—	53	2	no	—
248	#405	—	53	2	no	—
249	#405	—	53	2	no	—
250	C₂×#97	—	53	2	no	—
251	C₂×C₄×C₈	—	53	2	no	—
252	#347	—	53	8	no	—
253	#347	—	53	8	no	—
254	C₅₃	C₂×#2110	1	1	yes	characteristic, complemented, Sylow
255	C₂³×C₄	—	53	1	no	—
256	C₂×M₁₆	—	53	2	no	—
257	C₂×M₁₆	—	53	2	no	—
258	C₂×M₁₆	—	106	1	no	—
259	C₂×M₁₆	—	106	1	no	—
260	C₂×M₁₆	—	106	1	no	—
261	C₂×M₁₆	—	106	1	no	—
262	C₂²×C₈	—	53	1	no	—
263	C₂²×C₈	—	53	1	no	—
264	C₂²×C₈	—	53	1	no	—
265	C₂²×C₈	—	53	1	no	—
266	C₂²×C₈	—	53	1	no	—
267	C₂²×C₈	—	53	1	no	—
268	C₂²×C₈	—	53	1	no	—
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	2	no	—
276	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
277	#117	—	53	2	no	—
278	#117	—	53	2	no	—
279	#117	—	106	1	no	—
280	#117	—	106	1	no	—
281	C₂×C₄⋊C₄	—	106	1	no	—
282	C₂×C₂²⋊C₄	—	106	1	no	—
283	C₂×C₄²	—	53	2	no	—
284	M₃₂	—	53	4	no	—
285	M₃₂	—	53	4	no	—
286	M₃₂	—	53	4	no	—
287	M₃₂	—	53	4	no	—
288	M₃₂	—	53	2	no	—
289	M₃₂	—	53	2	no	—
290	M₃₂	—	53	4	no	—
291	M₃₂	—	53	4	no	—
292	M₃₂	C₂×#6157	1	2	yes	—
293	M₃₂	C₂×#6157	1	2	yes	complemented
294	C₂×C₁₆	—	53	4	no	—
295	C₂×C₁₆	—	53	4	no	—
296	C₂×C₁₆	—	53	4	no	—
297	C₂×C₁₆	—	53	2	no	—
298	C₂×C₁₆	—	53	4	no	—
299	C₂×C₁₆	—	53	4	no	—
300	C₂×C₁₆	C₂×#6157	1	2	yes	complemented
301	#97	—	53	4	no	—
302	#97	—	53	4	no	—
303	C₄×C₈	—	53	4	no	—
304	C₄×C₈	—	53	4	no	—
305	C₂⁴	—	53	1	no	—
306	C₂²×C₄	—	53	1	no	—
307	C₂²×C₄	—	53	1	no	—
308	C₂²×C₄	—	53	1	no	—
309	C₂²×C₄	—	53	1	no	—
310	C₂²×C₄	—	53	1	no	—
311	C₂²×C₄	—	53	1	no	—
312	C₂²×C₄	—	53	1	no	—
313	C₂²×C₄	—	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	—	106	2	no	—
320	C₂²×C₄	C₄×#6157	1	1	yes	characteristic
321	M₁₆	—	106	2	no	—
322	M₁₆	—	106	2	no	—
323	M₁₆	—	106	2	no	—
324	M₁₆	—	106	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	—	53	1	no	—
330	C₂×C₈	—	53	1	no	—
331	C₂×C₈	—	53	1	no	—
332	C₂×C₈	—	53	1	no	—
333	C₂×C₈	—	53	1	no	—
334	C₂×C₈	—	53	1	no	—
335	C₂×C₈	—	53	1	no	—
336	C₂×C₈	—	53	1	no	—
337	C₂×C₈	—	53	1	no	—
338	C₂×C₈	—	53	1	no	—
339	C₂×C₈	—	53	1	no	—
340	C₂×C₈	—	53	1	no	—
341	C₂×C₈	—	53	1	no	—
342	C₂×C₈	—	53	1	no	—
343	C₂×C₈	—	53	1	no	—
344	C₂×C₈	—	53	1	no	—
345	C₂×C₈	—	53	1	no	—
346	C₂×C₈	—	53	1	no	—
347	C₂×C₈	—	53	4	no	—
348	C₂×C₈	—	106	2	no	—
349	C₂×C₈	—	106	2	no	—
350	C₂×C₈	C₄×#6157	1	1	yes	characteristic
351	C₂×C₈	C₄×#6157	1	1	yes	characteristic
352	C₂×C₈	C₄×#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	—	106	2	no	—
357	C₄⋊C₄	—	106	2	no	—
358	C₂²⋊C₄	—	106	2	no	—
359	C₂²⋊C₄	—	106	2	no	—
360	C₄²	—	53	4	no	—
361	C₄²	—	106	2	no	—
362	C₁₆	—	53	8	no	—
363	C₁₆	—	53	4	no	—
364	C₁₆	C₂²×#6157	1	4	yes	—
365	C₂³	—	53	1	no	—
366	C₂³	—	53	1	no	—
367	C₂³	—	53	1	no	—
368	C₂³	—	53	1	no	—
369	C₂³	—	53	1	no	—
370	C₂³	—	53	1	no	—
371	C₂³	—	212	2	no	—
372	C₂³	#13133271	1	1	yes	characteristic
373	C₂×C₄	—	53	1	no	—
374	C₂×C₄	—	53	1	no	—
375	C₂×C₄	—	53	1	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	—	53	1	no	—
382	C₂×C₄	—	53	1	no	—
383	C₂×C₄	—	53	1	no	—
384	C₂×C₄	—	53	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	1	no	—
391	C₂×C₄	—	53	1	no	—
392	C₂×C₄	—	53	1	no	—
393	C₂×C₄	—	53	1	no	—
394	C₂×C₄	—	53	1	no	—
395	C₂×C₄	—	106	4	no	—
396	C₂×C₄	—	212	4	no	—
397	C₂×C₄	#13133271	1	1	yes	characteristic
398	C₂×C₄	#13133271	1	1	yes	characteristic
399	C₂×C₄	#13133271	1	1	yes	characteristic
400	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
401	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
402	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
403	C₈	—	53	1	no	—
404	C₈	—	53	1	no	—
405	C₈	—	53	1	no	—
406	C₈	—	53	1	no	—
407	C₈	—	106	4	no	—
408	C₈	C₂×C₄×#6157	1	1	yes	characteristic
409	C₈	C₂×C₄×#6157	1	1	yes	characteristic
410	C₈	C₂×C₄×#6157	1	1	yes	characteristic
411	C₈	C₂³×#6157	1	1	yes	characteristic
412	C₂²	—	4	1	no	—
413	C₂²	—	53	1	no	—
414	C₂²	—	53	1	no	—
415	C₂²	—	53	1	no	—
416	C₂²	—	53	1	no	—
417	C₂²	—	106	2	no	—
418	C₂²	—	106	2	no	—
419	C₂²	—	106	2	no	—
420	C₂²	—	212	1	no	—
421	C₂²	—	212	1	no	—
422	C₂²	—	212	1	no	—
423	C₂²	C₂×#13133271	1	1	yes	characteristic
424	C₂²	C₂×#13133271	1	1	yes	characteristic
425	C₂²	C₂×#13133271	1	1	yes	characteristic
426	C₄	—	53	1	no	—
427	C₄	—	53	1	no	—
428	C₄	—	53	1	no	—
429	C₄	—	53	1	no	—
430	C₄	—	212	4	no	—
431	C₄	C₂×#13133271	1	1	yes	characteristic
432	C₄	C₂×#13133271	1	1	yes	characteristic
433	C₄	C₂×#13133271	1	1	yes	characteristic
434	C₄	C₂²×C₄×#6157	1	1	yes	characteristic
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	—	2	1	no	—
438	C₂	—	53	2	no	—
439	C₂	—	106	1	no	—
440	C₂	—	106	1	no	—
441	C₂	—	106	1	no	—
442	C₂	C₂²×#13133271	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×C₄×#6157
commutator	C₄×C₅₃	C₂²×C₄²
Frattini	C₈	C₂³×#6157
Fitting	C₂×M₃₂×C₅₃	C₄
socle	C₂×C₅₃	C₂²×#97
prime radical	C₂³×D₅₃	M₁₆
cosocle	C₈×D₅₃	C₂⁴
hypercenter	C₂×M₃₂	#6157
hypocenter	C₅₃	C₂×#2110
LCS	G ▷ C₄×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. #20290935	C₂	semidirect
4. #20290934	C₂	semidirect
5. #20290930	C₂	semidirect
10. D₅₃⋊M₃₂	C₄	semidirect
11. D₅₃⋊M₃₂	C₄	semidirect
14. C₂×#13133291	C₄	semidirect
15. C₂×D₅₃⋊C₁₆	C₄	semidirect
22. #16811514	C₂²	semidirect
23. #16811513	C₂²	semidirect
25. C₂×#13133157	C₄	semidirect
27. M₃₂×D₅₃	C₄	semidirect
28. M₃₂×D₅₃	C₄	semidirect
31. C₂×C₁₆×D₅₃	C₄	semidirect
32. C₂×M₃₂×C₅₃	C₄	semidirect
47. #13133292	C₂×C₄	semidirect
50. #13133291	C₂×C₄	semidirect
52. D₅₃⋊C₁₆	C₂×C₄	semidirect
53. C₂×#11719910	C₂×C₄	semidirect
73. #13133157	C₂×C₄	semidirect
74. #13133156	C₂×C₄	semidirect
76. C₂×#11719908	C₂×C₄	semidirect
78. C₁₆×D₅₃	C₂×C₄	semidirect
81. M₃₂×C₅₃	C₂×C₄	semidirect
82. C₂×C₁₆×C₅₃	C₂×C₄	semidirect
227. D₅₃	#2110	semidirect
243. C₂×M₃₂	#6157	semidirect
254. C₅₃	C₂×#2110	semidirect
293. M₃₂	C₂×#6157	semidirect
300. C₂×C₁₆	C₂×#6157	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅₃⋊M₃₂	2
C₂×#16811586	2
#20290935	2
#20290934	2
#20290930	2
C₂×M₃₂×D₅₃	2
C₂×#2110	53