Subgroups — C₃₁×#9133 #21465892

Order 7936.

784 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2856	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#1797	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#331	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1296	C₂	1	2	yes	maximal, complemented
6	C₂³×C₈×C₃₁	—	2	1	no	—
7	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
8	C₂×C₃₁×#121	—	2	1	no	—
9	C₂×C₃₁×#121	—	2	1	no	—
10	C₂×C₃₁×#121	C₄	1	2	yes	—
11	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
13	C₂×C₃₁×C₄⋊C₈	—	2	4	no	—
14	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
17	C₃₁×#390	—	2	1	no	—
18	C₃₁×#390	—	2	1	no	—
19	C₃₁×#390	C₄	1	2	yes	—
20	C₃₁×#384	C₂²	1	1	yes	characteristic
21	C₃₁×#336	—	2	1	no	—
22	C₃₁×#331	—	2	4	no	—
23	C₂²×D₄×C₃₁	—	2	2	no	—
24	C₂²×D₄×C₃₁	—	2	1	no	—
25	C₂²×D₄×C₃₁	—	2	1	no	—
26	C₂²×D₄×C₃₁	C₂×C₄	1	2	yes	—
27	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₃₁	—	2	4	no	—
31	C₂²×C₈×C₃₁	—	2	2	no	—
32	C₂²×C₈×C₃₁	—	2	2	no	—
33	C₂²×C₈×C₃₁	—	4	2	no	—
34	C₂²×C₈×C₃₁	—	4	2	no	—
35	C₃₁×#127	—	2	2	no	—
36	C₃₁×#127	—	2	2	no	—
37	C₃₁×#121	—	4	4	no	—
38	C₃₁×#121	—	4	2	no	—
39	C₃₁×#121	—	4	2	no	—
40	C₃₁×#121	—	4	2	no	—
41	C₃₁×#121	—	4	2	no	—
42	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
43	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
44	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
45	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
46	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
47	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
48	C₂×C₄²×C₃₁	—	2	2	no	—
49	C₂×C₄²×C₃₁	—	2	2	no	—
50	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
54	C₃₁×C₄⋊C₈	—	2	4	no	—
55	C₃₁×C₄⋊C₈	—	2	2	no	—
56	C₃₁×C₄⋊C₈	—	2	2	no	—
57	C₃₁×C₄⋊C₈	—	2	2	no	—
58	C₃₁×C₄⋊C₈	D₄	1	4	yes	complemented
59	C₃₁×C₂²⋊C₈	—	4	2	no	—
60	C₂⁴×C₃₁	—	2	2	no	—
61	C₂⁴×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×D₄×C₃₁	—	2	4	no	—
63	C₂×D₄×C₃₁	—	4	2	no	—
64	C₂×D₄×C₃₁	—	4	2	no	—
65	C₂×D₄×C₃₁	—	4	4	no	—
66	C₂×D₄×C₃₁	—	4	4	no	—
67	C₂×D₄×C₃₁	—	4	4	no	—
68	C₂×D₄×C₃₁	—	4	1	no	—
69	C₂×D₄×C₃₁	—	4	2	no	—
70	C₂×D₄×C₃₁	—	4	1	no	—
71	C₂×D₄×C₃₁	—	4	1	no	—
72	C₂×D₄×C₃₁	—	4	1	no	—
73	C₂×D₄×C₃₁	—	4	1	no	—
74	C₂×D₄×C₃₁	—	4	1	no	—
75	C₂×D₄×C₃₁	—	4	2	no	—
76	C₂×D₄×C₃₁	—	4	1	no	—
77	C₂×D₄×C₃₁	—	4	1	no	—
78	C₂²×C₄×C₃₁	—	2	1	no	—
79	C₂²×C₄×C₃₁	—	2	2	no	—
80	C₂²×C₄×C₃₁	—	2	1	no	—
81	C₂²×C₄×C₃₁	—	2	2	no	—
82	C₂²×C₄×C₃₁	—	2	1	no	—
83	C₂²×C₄×C₃₁	—	2	1	no	—
84	C₂²×C₄×C₃₁	—	2	2	no	—
85	C₂²×C₄×C₃₁	—	2	2	no	—
86	C₂²×C₄×C₃₁	—	2	2	no	—
87	C₂²×C₄×C₃₁	—	4	1	no	—
88	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₃₁	D₈	1	2	yes	—
92	C₂²×C₄×C₃₁	D₈	1	2	yes	—
93	C₂²×C₄×C₃₁	SD₁₆	1	2	yes	—
94	C₂²×C₄×C₃₁	SD₁₆	1	2	yes	—
95	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
98	C₂×C₈×C₃₁	—	2	4	no	—
99	C₂×C₈×C₃₁	—	4	8	no	—
100	C₂×C₈×C₃₁	—	4	2	no	—
101	C₂×C₈×C₃₁	—	4	2	no	—
102	C₂×C₈×C₃₁	—	4	2	no	—
103	C₂×C₈×C₃₁	—	4	2	no	—
104	C₂×C₈×C₃₁	—	4	2	no	—
105	C₄⋊C₄×C₃₁	—	4	2	no	—
106	C₄⋊C₄×C₃₁	—	4	1	no	—
107	C₄⋊C₄×C₃₁	—	4	1	no	—
108	C₄⋊C₄×C₃₁	—	4	1	no	—
109	C₄⋊C₄×C₃₁	—	4	1	no	—
110	C₂²⋊C₄×C₃₁	—	4	4	no	—
111	C₂²⋊C₄×C₃₁	—	4	4	no	—
112	C₂²⋊C₄×C₃₁	—	4	4	no	—
113	C₄²×C₃₁	—	2	2	no	—
114	C₄²×C₃₁	—	2	1	no	—
115	C₄²×C₃₁	—	2	2	no	—
116	C₄²×C₃₁	—	2	1	no	—
117	C₄²×C₃₁	C₂×D₄	1	2	yes	—
118	C₄²×C₃₁	#41	1	2	yes	—
119	#9133	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₃₁	—	2	1	no	—
121	C₂³×C₃₁	—	2	1	no	—
122	C₂³×C₃₁	—	2	1	no	—
123	C₂³×C₃₁	—	2	1	no	—
124	C₂³×C₃₁	—	4	2	no	—
125	C₂³×C₃₁	—	4	2	no	—
126	C₂³×C₃₁	—	4	2	no	—
127	C₂³×C₃₁	—	4	2	no	—
128	C₂³×C₃₁	—	4	2	no	—
129	C₂³×C₃₁	—	4	2	no	—
130	C₂³×C₃₁	—	4	2	no	—
131	C₂³×C₃₁	#100	1	2	yes	—
132	C₂³×C₃₁	#102	1	2	yes	—
133	C₂³×C₃₁	#102	1	2	yes	—
134	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	D₄×C₃₁	—	8	4	no	—
136	D₄×C₃₁	—	8	8	no	—
137	D₄×C₃₁	—	8	1	no	—
138	D₄×C₃₁	—	8	1	no	—
139	D₄×C₃₁	—	8	2	no	—
140	D₄×C₃₁	—	8	2	no	—
141	D₄×C₃₁	—	8	1	no	—
142	D₄×C₃₁	—	8	1	no	—
143	C₂×C₄×C₃₁	—	2	1	no	—
144	C₂×C₄×C₃₁	—	2	1	no	—
145	C₂×C₄×C₃₁	—	2	1	no	—
146	C₂×C₄×C₃₁	—	2	1	no	—
147	C₂×C₄×C₃₁	—	2	1	no	—
148	C₂×C₄×C₃₁	—	2	1	no	—
149	C₂×C₄×C₃₁	—	2	2	no	—
150	C₂×C₄×C₃₁	—	2	2	no	—
151	C₂×C₄×C₃₁	—	2	4	no	—
152	C₂×C₄×C₃₁	—	2	4	no	—
153	C₂×C₄×C₃₁	—	2	2	no	—
154	C₂×C₄×C₃₁	—	2	2	no	—
155	C₂×C₄×C₃₁	—	2	1	no	—
156	C₂×C₄×C₃₁	—	2	1	no	—
157	C₂×C₄×C₃₁	—	2	1	no	—
158	C₂×C₄×C₃₁	—	4	4	no	—
159	C₂×C₄×C₃₁	—	4	2	no	—
160	C₂×C₄×C₃₁	—	4	2	no	—
161	C₂×C₄×C₃₁	—	4	2	no	—
162	C₂×C₄×C₃₁	#102	1	2	yes	—
163	C₂×C₄×C₃₁	#102	1	2	yes	—
164	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
166	C₂×C₄×C₃₁	#121	1	2	yes	—
167	C₂×C₄×C₃₁	#123	1	1	yes	characteristic
168	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₃₁	C₂×SD₁₆	1	1	yes	characteristic
171	C₂×C₄×C₃₁	C₂×SD₁₆	1	1	yes	characteristic
172	C₂×C₄×C₃₁	#135	1	2	yes	—
173	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₂×C₄×C₃₁	#137	1	1	yes	characteristic
175	C₈×C₃₁	—	4	4	no	—
176	C₈×C₃₁	—	8	2	no	—
177	C₂²×C₄⋊C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
178	#2856	C₂×C₃₁	1	1	yes	characteristic
179	#1797	C₂×C₃₁	1	1	yes	characteristic, complemented
180	C₂×#331	C₂×C₃₁	1	2	yes	complemented
181	#1296	C₂×C₃₁	1	2	yes	complemented
182	C₂²×C₃₁	—	2	2	no	—
183	C₂²×C₃₁	—	2	2	no	—
184	C₂²×C₃₁	—	2	2	no	—
185	C₂²×C₃₁	—	2	2	no	—
186	C₂²×C₃₁	—	2	2	no	—
187	C₂²×C₃₁	—	2	2	no	—
188	C₂²×C₃₁	—	8	2	no	—
189	C₂²×C₃₁	—	8	2	no	—
190	C₂²×C₃₁	—	8	2	no	—
191	C₂²×C₃₁	—	8	2	no	—
192	C₂²×C₃₁	—	8	2	no	—
193	C₂²×C₃₁	—	8	2	no	—
194	C₂²×C₃₁	—	8	2	no	—
195	C₂²×C₃₁	#331	1	4	yes	complemented
196	C₂²×C₃₁	#386	1	1	yes	characteristic
197	C₂²×C₃₁	C₂×#100	1	1	yes	characteristic
198	C₂²×C₃₁	#413	1	1	yes	characteristic
199	C₂²×C₃₁	C₂×#102	1	1	yes	characteristic
200	C₂²×C₃₁	C₂×#102	1	1	yes	characteristic
201	C₂²×C₃₁	#416	1	1	yes	characteristic
202	C₂²×C₃₁	#417	1	1	yes	characteristic
203	C₄×C₃₁	—	2	2	no	—
204	C₄×C₃₁	—	2	2	no	—
205	C₄×C₃₁	—	2	2	no	—
206	C₄×C₃₁	—	4	1	no	—
207	C₄×C₃₁	—	8	2	no	—
208	C₄×C₃₁	#447	1	1	yes	characteristic
209	C₄×C₃₁	#448	1	1	yes	characteristic
210	C₄×C₃₁	#465	1	2	yes	—
211	C₄×C₃₁	#466	1	2	yes	—
212	C₄×C₃₁	#480	1	1	yes	characteristic
213	C₄×C₃₁	#481	1	1	yes	characteristic
214	C₂³×C₈	—	2	1	no	—
215	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
216	C₂×#121	—	2	1	no	—
217	C₂×#121	—	2	1	no	—
218	C₂×#121	C₄×C₃₁	1	2	yes	—
219	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
220	C₂×C₄⋊C₈	—	2	1	no	—
221	C₂×C₄⋊C₈	—	2	4	no	—
222	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
223	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
224	C₂×C₂²⋊C₈	—	2	1	no	—
225	#390	—	2	1	no	—
226	#390	—	2	1	no	—
227	#390	C₄×C₃₁	1	2	yes	—
228	#384	C₂²×C₃₁	1	1	yes	characteristic
229	#336	—	2	1	no	—
230	#331	—	2	4	no	—
231	C₂×C₃₁	—	2	4	no	—
232	C₂×C₃₁	—	16	2	no	—
233	C₂×C₃₁	C₂×#331	1	1	yes	characteristic
234	C₂×C₃₁	#1540	1	1	yes	characteristic
235	C₂×C₃₁	#1547	1	1	yes	characteristic
236	C₂×C₃₁	#1551	1	1	yes	characteristic
237	C₂×C₃₁	#1874	1	1	yes	characteristic
238	C₂×C₃₁	#1893	1	1	yes	characteristic
239	C₂×C₃₁	#1900	1	1	yes	characteristic
240	C₂²×D₄	—	2	2	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	—	2	1	no	—
243	C₂²×D₄	C₂×C₄×C₃₁	1	2	yes	—
244	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
245	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
246	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
247	C₂²×C₈	—	2	4	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	4	2	no	—
251	C₂²×C₈	—	4	2	no	—
252	#127	—	2	2	no	—
253	#127	—	2	2	no	—
254	#121	—	4	4	no	—
255	#121	—	4	2	no	—
256	#121	—	4	2	no	—
257	#121	—	4	2	no	—
258	#121	—	4	2	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
268	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
269	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
271	C₄⋊C₈	—	2	4	no	—
272	C₄⋊C₈	—	2	2	no	—
273	C₄⋊C₈	—	2	2	no	—
274	C₄⋊C₈	—	2	2	no	—
275	C₄⋊C₈	D₄×C₃₁	1	4	yes	complemented
276	C₂²⋊C₈	—	4	2	no	—
277	C₃₁	#9133	1	1	yes	characteristic, direct product factor, Sylow
278	C₂⁴	—	2	2	no	—
279	C₂⁴	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	4	2	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂×D₄	—	4	4	no	—
284	C₂×D₄	—	4	4	no	—
285	C₂×D₄	—	4	4	no	—
286	C₂×D₄	—	4	1	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	1	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
307	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
308	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
309	C₂²×C₄	D₈×C₃₁	1	2	yes	—
310	C₂²×C₄	D₈×C₃₁	1	2	yes	—
311	C₂²×C₄	SD₁₆×C₃₁	1	2	yes	—
312	C₂²×C₄	SD₁₆×C₃₁	1	2	yes	—
313	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	4	8	no	—
318	C₂×C₈	—	4	2	no	—
319	C₂×C₈	—	4	2	no	—
320	C₂×C₈	—	4	2	no	—
321	C₂×C₈	—	4	2	no	—
322	C₂×C₈	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₂²⋊C₄	—	4	4	no	—
329	C₂²⋊C₄	—	4	4	no	—
330	C₂²⋊C₄	—	4	4	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	1	no	—
335	C₄²	C₂×D₄×C₃₁	1	2	yes	—
336	C₄²	#41×C₃₁	1	2	yes	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	C₃₁×#100	1	2	yes	—
349	C₂³	C₃₁×#102	1	2	yes	—
350	C₂³	C₃₁×#102	1	2	yes	—
351	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
352	D₄	—	8	4	no	—
353	D₄	—	8	8	no	—
354	D₄	—	8	1	no	—
355	D₄	—	8	1	no	—
356	D₄	—	8	2	no	—
357	D₄	—	8	2	no	—
358	D₄	—	8	1	no	—
359	D₄	—	8	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	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	—	2	1	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	C₃₁×#102	1	2	yes	—
380	C₂×C₄	C₃₁×#102	1	2	yes	—
381	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
382	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
383	C₂×C₄	C₃₁×#121	1	2	yes	—
384	C₂×C₄	C₃₁×#123	1	1	yes	characteristic
385	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
386	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
387	C₂×C₄	C₂×SD₁₆×C₃₁	1	1	yes	characteristic
388	C₂×C₄	C₂×SD₁₆×C₃₁	1	1	yes	characteristic
389	C₂×C₄	C₃₁×#135	1	2	yes	—
390	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
391	C₂×C₄	C₃₁×#137	1	1	yes	characteristic
392	C₈	—	4	4	no	—
393	C₈	—	8	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	C₃₁×#331	1	4	yes	complemented
408	C₂²	C₃₁×#386	1	1	yes	characteristic
409	C₂²	C₂×C₃₁×#100	1	1	yes	characteristic
410	C₂²	C₃₁×#413	1	1	yes	characteristic
411	C₂²	C₂×C₃₁×#102	1	1	yes	characteristic
412	C₂²	C₂×C₃₁×#102	1	1	yes	characteristic
413	C₂²	C₃₁×#416	1	1	yes	characteristic
414	C₂²	C₃₁×#417	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	8	2	no	—
420	C₄	C₃₁×#447	1	1	yes	characteristic
421	C₄	C₃₁×#448	1	1	yes	characteristic
422	C₄	C₃₁×#465	1	2	yes	—
423	C₄	C₃₁×#466	1	2	yes	—
424	C₄	C₃₁×#480	1	1	yes	characteristic
425	C₄	C₃₁×#481	1	1	yes	characteristic
426	C₂	—	2	4	no	—
427	C₂	—	16	2	no	—
428	C₂	C₂×C₃₁×#331	1	1	yes	characteristic
429	C₂	C₃₁×#1540	1	1	yes	characteristic
430	C₂	C₃₁×#1547	1	1	yes	characteristic
431	C₂	C₃₁×#1551	1	1	yes	characteristic
432	C₂	C₃₁×#1874	1	1	yes	characteristic
433	C₂	C₃₁×#1893	1	1	yes	characteristic
434	C₂	C₃₁×#1900	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₃₁
Frattini, cosocle	C₂×C₄²	C₂³×C₃₁
prime radical	C₃₁×#2856	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₁×C₄⋊C₈	C₂	semidirect
3. C₃₁×#1797	C₂	semidirect
4. C₂×C₃₁×#331	C₂	semidirect
5. C₃₁×#1296	C₂	semidirect
58. C₃₁×C₄⋊C₈	D₄	semidirect
119. #9133	C₃₁	direct (N × H)
177. C₂²×C₄⋊C₈	C₂×C₃₁	semidirect
179. #1797	C₂×C₃₁	semidirect
180. C₂×#331	C₂×C₃₁	semidirect
181. #1296	C₂×C₃₁	semidirect
195. C₂²×C₃₁	#331	semidirect
275. C₄⋊C₈	D₄×C₃₁	semidirect
277. C₃₁	#9133	direct (N × H)
407. C₂²	C₃₁×#331	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×C₄⋊C₈	2
C₃₁×#2856	2
C₃₁×#1797	2
C₂×C₃₁×#331	2
C₃₁×#1296	2
#9133	31

Subgroups — C31×#9133 #21465892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#9133 #21465892