Subgroups — C₂×#20289761 #28310243

Order 13568.

630 conjugacy classes of subgroups.

The subgroup lattice has 442 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	C₂²×#13133271	C₂	1	1	yes	maximal, characteristic
3	#20289761	C₂	1	4	yes	maximal, direct product factor
4	C₂×M₃₂×D₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×D₅₃⋊C₈	C₄	1	1	yes	characteristic
6	C₂²×C₄×#6157	C₄	1	1	yes	characteristic
7	C₂×#13133292	—	2	1	no	—
8	D₅₃⋊M₃₂	—	2	1	no	—
9	D₅₃⋊M₃₂	—	2	1	no	—
10	D₅₃⋊M₃₂	C₄	1	2	yes	complemented
11	D₅₃⋊M₃₂	C₂²	1	2	yes	—
12	C₂×#13133291	C₄	1	2	yes	complemented
13	C₂×D₅₃⋊C₁₆	—	2	1	no	—
14	C₂×#13133271	—	2	1	no	—
15	C₂×#13133271	—	2	1	no	—
16	C₂×#13133271	—	2	1	no	—
17	C₂×#13133271	—	2	1	no	—
18	C₂×#13133271	C₄	1	2	yes	—
19	C₂×#13133271	C₂²	1	2	yes	—
20	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
21	C₂×#13133157	C₄	1	1	yes	characteristic, complemented
22	C₂×#13133156	—	2	1	no	—
23	M₃₂×D₅₃	—	2	1	no	—
24	M₃₂×D₅₃	—	2	1	no	—
25	M₃₂×D₅₃	C₄	1	2	yes	complemented
26	M₃₂×D₅₃	C₂²	1	2	yes	—
27	C₂×C₁₆×D₅₃	—	2	1	no	—
28	C₂×M₃₂×C₅₃	C₄	1	1	yes	characteristic, complemented
29	C₂³×#6157	C₈	1	2	yes	—
30	C₂×D₅₃⋊C₈	—	2	1	no	—
31	C₂×D₅₃⋊C₈	—	2	1	no	—
32	C₂×D₅₃⋊C₈	—	2	1	no	—
33	C₂×D₅₃⋊C₈	—	2	1	no	—
34	C₂×D₅₃⋊C₈	C₈	1	2	yes	—
35	C₂×D₅₃⋊C₈	C₂×C₄	1	2	yes	—
36	C₂²×#88324	C₈	1	2	yes	—
37	C₂×C₄×#6157	—	2	1	no	—
38	C₂×C₄×#6157	—	2	1	no	—
39	C₂×C₄×#6157	—	2	1	no	—
40	C₂×C₄×#6157	—	2	1	no	—
41	C₂×C₄×#6157	C₈	1	2	yes	—
42	C₂×C₄×#6157	C₂×C₄	1	2	yes	—
43	#13133292	—	2	2	no	—
44	#13133292	—	2	2	no	—
45	#13133291	—	2	2	no	—
46	#13133291	C₂×C₄	1	4	yes	complemented
47	D₅₃⋊C₁₆	—	2	2	no	—
48	D₅₃⋊C₁₆	—	2	2	no	—
49	C₂×#11719910	—	2	2	no	—
50	#13133271	—	2	2	no	—
51	#13133271	—	2	2	no	—
52	#13133271	—	2	2	no	—
53	#13133271	—	2	2	no	—
54	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
60	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
61	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
62	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
63	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
64	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
65	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
66	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
67	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
68	#13133157	—	2	1	no	—
69	#13133157	C₂×C₄	1	2	yes	complemented
70	#13133156	—	2	2	no	—
71	#13133156	—	2	2	no	—
72	C₂×#11719908	—	2	1	no	—
73	C₁₆×D₅₃	—	2	2	no	—
74	C₁₆×D₅₃	—	2	2	no	—
75	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
76	M₃₂×C₅₃	—	2	1	no	—
77	M₃₂×C₅₃	C₂×C₄	1	2	yes	complemented
78	C₂×C₁₆×C₅₃	—	2	1	no	—
79	C₂³×D₅₃	C₂×C₈	1	1	yes	characteristic
80	C₂²×#6157	—	2	2	no	—
81	C₂²×#6157	—	2	2	no	—
82	C₂²×#6157	—	4	4	no	—
83	C₂²×#6157	C₂×C₈	1	4	yes	—
84	C₂²×C₄×C₅₃	C₄²	1	1	yes	characteristic
85	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
86	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
87	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
90	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
92	C₂×C₄×D₅₃	C₂×C₈	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	M₁₆	1	1	yes	characteristic
97	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×#88324	—	2	2	no	—
99	C₂×#88324	—	2	2	no	—
100	C₂×#88324	C₂×C₈	1	4	yes	—
101	C₄×#6157	—	2	2	no	—
102	C₄×#6157	—	2	2	no	—
103	C₄×#6157	—	2	2	no	—
104	C₄×#6157	—	2	2	no	—
105	D₅₃⋊C₈	—	2	2	no	—
106	D₅₃⋊C₈	—	2	2	no	—
107	D₅₃⋊C₈	—	2	2	no	—
108	D₅₃⋊C₈	—	2	2	no	—
109	C₂×C₈×C₅₃	C₄²	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	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×#88322	C₄²	1	1	yes	characteristic
116	C₂×#88322	C₂²⋊C₄	1	1	yes	characteristic
117	C₂×#88322	C₂²⋊C₄	1	1	yes	characteristic
118	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
119	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
120	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
121	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
128	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
129	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
130	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
131	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
132	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
133	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
134	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
135	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
136	C₈×D₅₃	C₂×Q₈	1	1	yes	characteristic
137	#11719910	—	2	4	no	—
138	C₁₆×C₅₃	—	2	2	no	—
139	#11719908	—	2	2	no	—
140	C₂³×C₅₃	C₄×C₈	1	1	yes	characteristic
141	C₂²×D₅₃	—	2	4	no	—
142	C₂²×D₅₃	C₄×C₈	1	1	yes	characteristic
143	C₂²×D₅₃	C₂²⋊C₈	1	1	yes	characteristic
144	C₂²×D₅₃	C₂²⋊C₈	1	1	yes	characteristic
145	C₂²×D₅₃	C₄⋊C₈	1	1	yes	characteristic
146	C₂²×D₅₃	C₄⋊C₈	1	1	yes	characteristic
147	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
148	C₂×#6157	—	2	4	no	—
149	C₂×#6157	—	4	4	no	—
150	C₂×#6157	—	4	4	no	—
151	C₂×#6157	—	4	4	no	—
152	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
153	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
154	C₂×C₄×C₅₃	C₄×C₈	1	1	yes	characteristic
155	C₂×C₄×C₅₃	#97	1	1	yes	characteristic
156	C₂×C₄×C₅₃	#97	1	1	yes	characteristic
157	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
158	C₂×Dic₅₃	C₄×C₈	1	1	yes	characteristic
159	C₂×Dic₅₃	C₂²⋊C₈	1	1	yes	characteristic
160	C₂×Dic₅₃	C₂²⋊C₈	1	1	yes	characteristic
161	C₂×Dic₅₃	C₄⋊C₈	1	1	yes	characteristic
162	C₂×Dic₅₃	C₄⋊C₈	1	1	yes	characteristic
163	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
164	C₄×D₅₃	#95	1	1	yes	characteristic
165	C₄×D₅₃	#95	1	1	yes	characteristic
166	C₄×D₅₃	#97	1	1	yes	characteristic
167	C₄×D₅₃	#97	1	1	yes	characteristic
168	C₄×D₅₃	C₂²⋊C₈	1	1	yes	characteristic
169	C₄×D₅₃	C₂²⋊C₈	1	1	yes	characteristic
170	C₄×D₅₃	C₂²⋊C₈	1	1	yes	characteristic
171	C₄×D₅₃	C₂²⋊C₈	1	1	yes	characteristic
172	C₄×D₅₃	C₄⋊C₈	1	1	yes	characteristic
173	C₄×D₅₃	C₄⋊C₈	1	1	yes	characteristic
174	C₄×D₅₃	C₄⋊C₈	1	1	yes	characteristic
175	C₄×D₅₃	C₄⋊C₈	1	1	yes	characteristic
176	C₄×D₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₄×D₅₃	C₂×M₁₆	1	1	yes	characteristic
179	C₄×D₅₃	C₂×M₁₆	1	1	yes	characteristic
180	#88324	—	2	4	no	—
181	C₈×C₅₃	#95	1	1	yes	characteristic
182	C₈×C₅₃	#95	1	1	yes	characteristic
183	C₈×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
185	#88322	#95	1	1	yes	characteristic
186	#88322	#95	1	1	yes	characteristic
187	#88322	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	#88322	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×#1377	—	53	1	no	maximal, Sylow
190	C₂²×C₅₃	—	2	2	no	—
191	C₂²×C₅₃	#336	1	1	yes	characteristic
192	C₂²×C₅₃	#336	1	1	yes	characteristic
193	C₂²×C₅₃	C₂×C₄×C₈	1	1	yes	characteristic
194	C₂×D₅₃	—	2	2	no	—
195	C₂×D₅₃	—	2	2	no	—
196	C₂×D₅₃	—	2	2	no	—
197	C₂×D₅₃	—	2	2	no	—
198	C₂×D₅₃	—	2	2	no	—
199	C₂×D₅₃	#336	1	1	yes	characteristic
200	C₂×D₅₃	#336	1	1	yes	characteristic
201	C₂×D₅₃	#349	1	4	yes	—
202	C₂×D₅₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
203	C₂×D₅₃	C₂×C₄⋊C₈	1	1	yes	characteristic
204	#6157	—	4	4	no	—
205	C₄×C₅₃	#336	1	1	yes	characteristic
206	C₄×C₅₃	#336	1	1	yes	characteristic
207	C₄×C₅₃	C₂×#95	1	1	yes	characteristic
208	C₄×C₅₃	C₂×#97	1	1	yes	characteristic
209	Dic₅₃	#336	1	1	yes	characteristic
210	Dic₅₃	#336	1	1	yes	characteristic
211	Dic₅₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
212	Dic₅₃	C₂×C₄⋊C₈	1	1	yes	characteristic
213	C₂²×M₃₂	—	53	1	no	—
214	C₂²×M₃₂	—	53	1	no	—
215	C₂²×#97	—	53	1	no	—
216	#1377	—	53	4	no	—
217	C₂×C₅₃	—	2	1	no	—
218	C₂×C₅₃	—	2	1	no	—
219	C₂×C₅₃	#1377	1	2	yes	complemented
220	C₂×C₅₃	C₂×#336	1	1	yes	characteristic
221	D₅₃	—	2	1	no	—
222	D₅₃	—	2	1	no	—
223	D₅₃	#1377	1	2	yes	complemented
224	D₅₃	C₂×#349	1	2	yes	—
225	C₂³×C₈	—	53	1	no	—
226	C₂³×C₈	—	53	1	no	—
227	C₂²×C₄²	—	53	1	no	—
228	C₂×M₃₂	—	53	2	no	—
229	C₂×M₃₂	—	53	2	no	—
230	C₂×M₃₂	—	53	2	no	—
231	C₂×M₃₂	—	53	1	no	—
232	C₂×M₃₂	—	53	2	no	—
233	C₂×M₃₂	—	53	2	no	—
234	C₂×M₃₂	—	106	1	no	—
235	C₂×M₃₂	—	106	1	no	—
236	C₂×M₃₂	—	106	1	no	—
237	C₂×M₃₂	—	106	1	no	—
238	C₂×M₃₂	—	106	1	no	—
239	C₂×M₃₂	—	106	1	no	—
240	C₂×M₃₂	#6157	1	1	yes	characteristic, complemented
241	C₂²×C₁₆	—	106	1	no	—
242	C₂²×C₁₆	—	106	1	no	—
243	C₂×#97	—	53	2	no	—
244	C₂×#97	—	53	2	no	—
245	C₂×#97	—	106	1	no	—
246	C₂×#97	—	106	1	no	—
247	C₂×#97	—	106	1	no	—
248	C₂×#97	—	106	1	no	—
249	C₅₃	C₂×#1377	1	1	yes	characteristic, complemented, Sylow
250	C₂³×C₄	—	53	1	no	—
251	C₂³×C₄	—	53	2	no	—
252	C₂²×C₈	—	53	1	no	—
253	C₂²×C₈	—	53	1	no	—
254	C₂²×C₈	—	53	1	no	—
255	C₂²×C₈	—	53	1	no	—
256	C₂²×C₈	—	53	1	no	—
257	C₂²×C₈	—	53	1	no	—
258	C₂²×C₈	—	53	1	no	—
259	C₂²×C₈	—	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	—	53	1	no	—
265	C₂²×C₈	—	53	2	no	—
266	C₂²×C₈	—	53	2	no	—
267	C₂²×C₈	—	53	2	no	—
268	C₂²×C₈	—	106	1	no	—
269	C₂²×C₈	—	106	1	no	—
270	C₂²×C₈	—	106	1	no	—
271	C₂²×C₈	—	106	1	no	—
272	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
273	C₂×C₄²	—	53	2	no	—
274	C₂×C₄²	—	53	2	no	—
275	C₂×C₄²	—	106	1	no	—
276	C₂×C₄²	—	106	1	no	—
277	C₂×C₄²	—	106	1	no	—
278	C₂×C₄²	—	106	1	no	—
279	M₃₂	—	2	1	no	—
280	M₃₂	—	53	4	no	—
281	M₃₂	—	53	2	no	—
282	M₃₂	—	106	2	no	—
283	M₃₂	—	106	2	no	—
284	M₃₂	—	106	2	no	—
285	M₃₂	—	106	2	no	—
286	M₃₂	—	106	2	no	—
287	M₃₂	—	106	1	no	—
288	M₃₂	C₂×#6157	1	2	yes	complemented
289	C₂×C₁₆	—	2	1	no	—
290	C₂×C₁₆	—	106	2	no	—
291	C₂×C₁₆	—	106	2	no	—
292	C₂×C₁₆	—	106	2	no	—
293	C₂×C₁₆	—	106	2	no	—
294	C₂×C₁₆	—	106	2	no	—
295	C₂×C₁₆	—	106	1	no	—
296	#97	—	106	2	no	—
297	#97	—	106	2	no	—
298	#97	—	106	2	no	—
299	#97	—	106	2	no	—
300	C₂⁴	—	53	1	no	—
301	C₂²×C₄	—	53	1	no	—
302	C₂²×C₄	—	53	1	no	—
303	C₂²×C₄	—	53	1	no	—
304	C₂²×C₄	—	53	1	no	—
305	C₂²×C₄	—	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	4	no	—
315	C₂²×C₄	—	106	2	no	—
316	C₂²×C₄	—	106	2	no	—
317	C₂²×C₄	—	212	4	no	—
318	C₂²×C₄	C₄×#6157	1	1	yes	characteristic
319	C₂×C₈	—	53	1	no	—
320	C₂×C₈	—	53	1	no	—
321	C₂×C₈	—	53	1	no	—
322	C₂×C₈	—	53	1	no	—
323	C₂×C₈	—	53	1	no	—
324	C₂×C₈	—	53	1	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	4	no	—
342	C₂×C₈	—	106	2	no	—
343	C₂×C₈	—	106	2	no	—
344	C₂×C₈	—	106	2	no	—
345	C₂×C₈	—	106	2	no	—
346	C₂×C₈	—	106	2	no	—
347	C₂×C₈	—	106	2	no	—
348	C₂×C₈	C₄×#6157	1	1	yes	characteristic
349	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
350	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
351	C₂×C₈	C₂²⋊#6157	1	1	yes	characteristic
352	C₂×C₈	C₂²⋊#6157	1	1	yes	characteristic
353	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
354	C₄²	—	106	2	no	—
355	C₄²	—	106	2	no	—
356	C₄²	—	106	2	no	—
357	C₄²	—	106	2	no	—
358	C₁₆	—	2	2	no	—
359	C₁₆	—	106	4	no	—
360	C₁₆	—	106	2	no	—
361	C₂³	—	53	1	no	—
362	C₂³	—	53	1	no	—
363	C₂³	—	53	1	no	—
364	C₂³	—	53	1	no	—
365	C₂³	—	53	1	no	—
366	C₂³	—	53	1	no	—
367	C₂³	—	106	4	no	—
368	C₂³	C₈×#6157	1	1	yes	characteristic
369	C₂×C₄	—	53	1	no	—
370	C₂×C₄	—	53	1	no	—
371	C₂×C₄	—	53	1	no	—
372	C₂×C₄	—	53	1	no	—
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	—	106	4	no	—
392	C₂×C₄	—	212	4	no	—
393	C₂×C₄	—	212	4	no	—
394	C₂×C₄	—	212	4	no	—
395	C₂×C₄	(C₂×#6157)⋊C₄	1	1	yes	characteristic
396	C₂×C₄	(C₂×#6157)⋊C₄	1	1	yes	characteristic
397	C₂×C₄	C₈×#6157	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	C₈	—	53	1	no	—
402	C₈	—	53	1	no	—
403	C₈	—	53	1	no	—
404	C₈	—	53	1	no	—
405	C₈	—	106	4	no	—
406	C₈	(C₂×#6157)⋊C₄	1	1	yes	characteristic
407	C₈	(C₂×#6157)⋊C₄	1	1	yes	characteristic
408	C₈	C₂×C₂²⋊#6157	1	1	yes	characteristic
409	C₈	C₂×C₄⋊#6157	1	1	yes	characteristic
410	C₂²	—	2	2	no	—
411	C₂²	—	53	1	no	—
412	C₂²	—	53	1	no	—
413	C₂²	—	53	4	no	—
414	C₂²	—	53	1	no	—
415	C₂²	—	53	1	no	—
416	C₂²	—	106	2	no	—
417	C₂²	—	106	2	no	—
418	C₂²	—	106	2	no	—
419	C₂²	—	106	2	no	—
420	C₂²	—	106	2	no	—
421	C₂²	(C₂×#6157)⋊C₈	1	1	yes	characteristic
422	C₂²	(C₂×#6157)⋊C₈	1	1	yes	characteristic
423	C₂²	C₂×C₈×#6157	1	1	yes	characteristic
424	C₄	—	53	1	no	—
425	C₄	—	53	1	no	—
426	C₄	—	53	1	no	—
427	C₄	—	53	1	no	—
428	C₄	—	212	4	no	—
429	C₄	(C₂×#6157)⋊C₈	1	1	yes	characteristic
430	C₄	(C₂×#6157)⋊C₈	1	1	yes	characteristic
431	C₄	C₂×(C₂×#6157)⋊C₄	1	1	yes	characteristic
432	C₄	C₂×#13133271	1	1	yes	characteristic
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	53	2	no	—
436	C₂	—	53	2	no	—
437	C₂	—	106	1	no	—
438	C₂	—	106	1	no	—
439	C₂	#20289761	1	2	yes	direct product factor
440	C₂	C₂×(C₂×#6157)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×#6157)⋊C₄
commutator	C₂²×C₅₃	C₂×C₄×C₈
Frattini	C₂×C₈	C₂²×#6157
Fitting	C₂×M₃₂×C₅₃	C₄
socle	C₂²×C₅₃	#336
prime radical	C₂³×D₅₃	C₂×C₈
cosocle	C₂×C₈×D₅₃	C₂³
hypercenter	C₂×M₃₂	#6157
hypocenter	C₅₃	C₂×#1377
LCS	G ▷ C₂²×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. #20289761	C₂	direct (N × H)
10. D₅₃⋊M₃₂	C₄	semidirect
12. C₂×#13133291	C₄	semidirect
21. C₂×#13133157	C₄	semidirect
25. M₃₂×D₅₃	C₄	semidirect
28. C₂×M₃₂×C₅₃	C₄	semidirect
46. #13133291	C₂×C₄	semidirect
69. #13133157	C₂×C₄	semidirect
77. M₃₂×C₅₃	C₂×C₄	semidirect
219. C₂×C₅₃	#1377	semidirect
223. D₅₃	#1377	semidirect
240. C₂×M₃₂	#6157	semidirect
249. C₅₃	C₂×#1377	semidirect
288. M₃₂	C₂×#6157	semidirect
439. C₂	#20289761	direct (N × H)

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
C₂²×#13133271	2
#20289761	2
C₂×M₃₂×D₅₃	2
C₂×#1377	53

Subgroups — C2×#20289761 #28310243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20289761 #28310243