Subgroups — C₃₁×#33165 #21489924

Order 7936.

1126 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#464	C₂	1	4	yes	maximal, complemented
2	C₂×C₃₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#460	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2858	C₂	1	1	yes	maximal, characteristic
5	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1983	C₂	1	4	yes	maximal, complemented
7	C₃₁×#1982	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#1981	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1842	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
11	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
12	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#124	C₂²	1	4	yes	—
15	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
17	C₃₁×#464	—	2	16	no	—
18	C₃₁×#462	—	2	4	no	—
19	C₃₁×#460	—	2	4	no	—
20	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×C₄⋊C₈	C₂²	1	4	yes	—
23	C₂×C₃₁×#103	C₂²	1	4	yes	—
24	C₂×C₃₁×#103	C₂²	1	2	yes	—
25	C₂×C₃₁×#102	C₂²	1	4	yes	—
26	C₂×C₃₁×#102	C₂²	1	2	yes	—
27	C₃₁×#390	—	2	1	no	—
28	C₃₁×#390	—	2	1	no	—
29	C₃₁×#390	—	2	2	no	—
30	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
31	C₄×C₄⋊C₄×C₃₁	—	2	2	no	—
32	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
34	C₄³×C₃₁	—	2	1	no	—
35	C₄³×C₃₁	C₂²	1	1	yes	characteristic
36	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
37	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
38	C₂²×D₄×C₃₁	—	2	1	no	—
39	C₂²×D₄×C₃₁	—	2	1	no	—
40	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
41	C₂×Q₁₆×C₃₁	—	2	4	no	—
42	C₂×Q₁₆×C₃₁	—	2	8	no	—
43	C₂×SD₁₆×C₃₁	—	2	4	no	—
44	C₂×SD₁₆×C₃₁	—	2	8	no	—
45	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
47	C₃₁×C₄⋊Q₈	—	2	2	no	—
48	C₃₁×C₄⋊Q₈	—	2	2	no	—
49	C₃₁×#127	—	2	2	no	—
50	C₃₁×#127	—	2	2	no	—
51	C₃₁×#124	—	2	8	no	—
52	C₃₁×#124	—	2	8	no	—
53	C₄×Q₈×C₃₁	—	2	2	no	—
54	C₄×Q₈×C₃₁	—	2	4	no	—
55	C₄×Q₈×C₃₁	D₄	1	4	yes	—
56	C₄×Q₈×C₃₁	D₄	1	8	yes	complemented
57	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
65	C₂×C₄²×C₃₁	—	2	1	no	—
66	C₂×C₄²×C₃₁	—	2	2	no	—
67	C₂×C₄²×C₃₁	—	2	2	no	—
68	C₂×C₄²×C₃₁	—	2	1	no	—
69	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₃₁	D₄	1	2	yes	—
72	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
73	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
74	C₃₁×C₄⋊C₈	—	2	2	no	—
75	C₃₁×C₄⋊C₈	—	2	2	no	—
76	C₃₁×C₄⋊C₈	—	2	8	no	—
77	C₃₁×#103	—	2	4	no	—
78	C₃₁×#103	—	2	8	no	—
79	C₃₁×#102	—	2	4	no	—
80	C₃₁×#102	—	2	8	no	—
81	C₃₁×#95	—	2	2	no	—
82	C₃₁×#95	—	2	1	no	—
83	C₂⁴×C₃₁	—	2	2	no	—
84	C₂×Q₈×C₃₁	—	2	1	no	—
85	C₂×Q₈×C₃₁	—	2	2	no	—
86	C₂×Q₈×C₃₁	—	2	4	no	—
87	C₂×Q₈×C₃₁	—	2	2	no	—
88	C₂×Q₈×C₃₁	—	2	4	no	—
89	C₂×Q₈×C₃₁	—	2	2	no	—
90	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
91	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
92	C₂×D₄×C₃₁	—	2	4	no	—
93	C₂×D₄×C₃₁	—	2	2	no	—
94	C₂×D₄×C₃₁	—	2	4	no	—
95	C₂×D₄×C₃₁	—	2	2	no	—
96	C₂×D₄×C₃₁	—	4	4	no	—
97	C₂×D₄×C₃₁	—	4	2	no	—
98	C₂×D₄×C₃₁	—	4	2	no	—
99	C₂×D₄×C₃₁	—	4	2	no	—
100	C₂×D₄×C₃₁	—	4	2	no	—
101	C₂²×C₄×C₃₁	—	2	1	no	—
102	C₂²×C₄×C₃₁	—	2	2	no	—
103	C₂²×C₄×C₃₁	—	2	1	no	—
104	C₂²×C₄×C₃₁	—	2	2	no	—
105	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
110	Q₁₆×C₃₁	—	4	8	no	—
111	SD₁₆×C₃₁	—	4	8	no	—
112	C₂×C₈×C₃₁	—	2	2	no	—
113	C₂×C₈×C₃₁	—	2	4	no	—
114	C₂×C₈×C₃₁	—	2	4	no	—
115	C₂×C₈×C₃₁	—	2	2	no	—
116	C₄⋊C₄×C₃₁	—	2	4	no	—
117	C₄⋊C₄×C₃₁	—	2	8	no	—
118	C₄⋊C₄×C₃₁	—	2	2	no	—
119	C₄⋊C₄×C₃₁	—	2	1	no	—
120	C₄⋊C₄×C₃₁	—	4	2	no	—
121	C₄⋊C₄×C₃₁	—	4	2	no	—
122	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
123	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
124	C₂²⋊C₄×C₃₁	—	4	8	no	—
125	C₂²⋊C₄×C₃₁	—	4	8	no	—
126	C₄²×C₃₁	—	2	4	no	—
127	C₄²×C₃₁	—	2	8	no	—
128	C₄²×C₃₁	—	2	2	no	—
129	C₄²×C₃₁	—	2	2	no	—
130	C₄²×C₃₁	—	4	2	no	—
131	C₄²×C₃₁	—	4	4	no	—
132	C₄²×C₃₁	—	4	2	no	—
133	C₄²×C₃₁	C₂×D₄	1	2	yes	—
134	C₄²×C₃₁	C₂×D₄	1	4	yes	—
135	C₄²×C₃₁	#41	1	4	yes	—
136	C₄²×C₃₁	#41	1	2	yes	—
137	#33165	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂³×C₃₁	—	4	4	no	—
139	C₂³×C₃₁	—	4	2	no	—
140	C₂³×C₃₁	—	4	2	no	—
141	C₂³×C₃₁	—	4	2	no	—
142	C₂³×C₃₁	—	4	4	no	—
143	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₃₁	—	2	2	no	—
145	Q₈×C₃₁	—	2	4	no	—
146	Q₈×C₃₁	—	4	2	no	—
147	Q₈×C₃₁	—	4	4	no	—
148	Q₈×C₃₁	—	4	2	no	—
149	Q₈×C₃₁	#127	1	4	yes	—
150	D₄×C₃₁	—	4	2	no	—
151	D₄×C₃₁	—	4	4	no	—
152	D₄×C₃₁	—	4	2	no	—
153	D₄×C₃₁	—	8	4	no	—
154	D₄×C₃₁	—	8	4	no	—
155	C₂×C₄×C₃₁	—	2	2	no	—
156	C₂×C₄×C₃₁	—	2	4	no	—
157	C₂×C₄×C₃₁	—	2	2	no	—
158	C₂×C₄×C₃₁	—	2	2	no	—
159	C₂×C₄×C₃₁	—	2	2	no	—
160	C₂×C₄×C₃₁	—	2	2	no	—
161	C₂×C₄×C₃₁	—	2	2	no	—
162	C₂×C₄×C₃₁	—	2	4	no	—
163	C₂×C₄×C₃₁	—	2	2	no	—
164	C₂×C₄×C₃₁	—	4	2	no	—
165	C₂×C₄×C₃₁	—	4	2	no	—
166	C₂×C₄×C₃₁	—	4	2	no	—
167	C₂×C₄×C₃₁	—	4	4	no	—
168	C₂×C₄×C₃₁	—	4	2	no	—
169	C₂×C₄×C₃₁	#121	1	4	yes	—
170	C₂×C₄×C₃₁	#121	1	4	yes	—
171	C₂×C₄×C₃₁	#121	1	2	yes	—
172	C₂×C₄×C₃₁	#121	1	2	yes	—
173	C₂×C₄×C₃₁	#135	1	2	yes	—
174	C₂×C₄×C₃₁	#137	1	2	yes	—
175	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
177	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
179	C₈×C₃₁	—	4	2	no	—
180	C₈×C₃₁	—	4	2	no	—
181	C₂×#464	C₂×C₃₁	1	4	yes	complemented
182	C₂×#462	C₂×C₃₁	1	1	yes	characteristic, complemented
183	C₂×#460	C₂×C₃₁	1	1	yes	characteristic
184	#2858	C₂×C₃₁	1	1	yes	characteristic
185	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
186	#1983	C₂×C₃₁	1	4	yes	complemented
187	#1982	C₂×C₃₁	1	1	yes	characteristic
188	#1981	C₂×C₃₁	1	1	yes	characteristic, complemented
189	#1842	C₂×C₃₁	1	1	yes	characteristic, complemented
190	C₂²×C₃₁	—	8	2	no	—
191	C₂²×C₃₁	—	8	2	no	—
192	C₂²×C₃₁	—	8	4	no	—
193	C₂²×C₃₁	—	8	4	no	—
194	C₂²×C₃₁	—	8	2	no	—
195	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
196	C₂²×C₃₁	C₂×#121	1	2	yes	—
197	C₂²×C₃₁	C₂×#135	1	1	yes	characteristic
198	C₂²×C₃₁	C₂×#137	1	1	yes	characteristic
199	C₂²×C₃₁	#575	1	2	yes	—
200	C₄×C₃₁	—	2	4	no	—
201	C₄×C₃₁	—	2	4	no	—
202	C₄×C₃₁	—	2	4	no	—
203	C₄×C₃₁	—	2	2	no	—
204	C₄×C₃₁	—	4	4	no	—
205	C₄×C₃₁	—	4	2	no	—
206	C₄×C₃₁	—	8	2	no	—
207	C₄×C₃₁	#464	1	4	yes	complemented
208	C₄×C₃₁	C₂×#127	1	1	yes	characteristic
209	C₄×C₃₁	#532	1	1	yes	characteristic
210	C₄×C₃₁	#532	1	2	yes	—
211	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
212	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
213	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
214	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
215	C₂×#124	C₂²×C₃₁	1	4	yes	—
216	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
217	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
218	#464	—	2	16	no	—
219	#462	—	2	4	no	—
220	#460	—	2	4	no	—
221	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
222	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
223	C₂×C₄⋊C₈	C₂²×C₃₁	1	4	yes	—
224	C₂×#103	C₂²×C₃₁	1	4	yes	—
225	C₂×#103	C₂²×C₃₁	1	2	yes	—
226	C₂×#102	C₂²×C₃₁	1	4	yes	—
227	C₂×#102	C₂²×C₃₁	1	2	yes	—
228	#390	—	2	1	no	—
229	#390	—	2	1	no	—
230	#390	—	2	2	no	—
231	C₄×C₄⋊C₄	—	2	1	no	—
232	C₄×C₄⋊C₄	—	2	2	no	—
233	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
234	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
235	C₄³	—	2	1	no	—
236	C₄³	C₂²×C₃₁	1	1	yes	characteristic
237	C₂×C₃₁	—	16	2	no	—
238	C₂×C₃₁	#2856	1	1	yes	characteristic
239	C₂×C₃₁	C₂×#464	1	1	yes	characteristic
240	C₂×C₃₁	#3035	1	2	yes	—
241	C₂×C₃₁	#3037	1	2	yes	—
242	C₂×C₃₁	#3040	1	1	yes	characteristic
243	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
244	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
248	C₂×Q₁₆	—	2	4	no	—
249	C₂×Q₁₆	—	2	8	no	—
250	C₂×SD₁₆	—	2	4	no	—
251	C₂×SD₁₆	—	2	8	no	—
252	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
253	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
254	C₄⋊Q₈	—	2	2	no	—
255	C₄⋊Q₈	—	2	2	no	—
256	#127	—	2	2	no	—
257	#127	—	2	2	no	—
258	#124	—	2	8	no	—
259	#124	—	2	8	no	—
260	C₄×Q₈	—	2	2	no	—
261	C₄×Q₈	—	2	4	no	—
262	C₄×Q₈	D₄×C₃₁	1	4	yes	—
263	C₄×Q₈	D₄×C₃₁	1	8	yes	complemented
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
270	C₂×C₂²⋊C₄	—	2	4	no	—
271	C₂×C₂²⋊C₄	—	2	4	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
277	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
278	C₂×C₄²	D₄×C₃₁	1	2	yes	—
279	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
280	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
281	C₄⋊C₈	—	2	2	no	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	—	2	8	no	—
284	#103	—	2	4	no	—
285	#103	—	2	8	no	—
286	#102	—	2	4	no	—
287	#102	—	2	8	no	—
288	#95	—	2	2	no	—
289	#95	—	2	1	no	—
290	C₃₁	#33165	1	1	yes	characteristic, direct product factor, Sylow
291	C₂⁴	—	2	2	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	4	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
299	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	4	4	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
317	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
318	Q₁₆	—	4	8	no	—
319	SD₁₆	—	4	8	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	2	2	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
331	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
332	C₂²⋊C₄	—	4	8	no	—
333	C₂²⋊C₄	—	4	8	no	—
334	C₄²	—	2	4	no	—
335	C₄²	—	2	8	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	4	2	no	—
339	C₄²	—	4	4	no	—
340	C₄²	—	4	2	no	—
341	C₄²	C₂×D₄×C₃₁	1	2	yes	—
342	C₄²	C₂×D₄×C₃₁	1	4	yes	—
343	C₄²	#41×C₃₁	1	4	yes	—
344	C₄²	#41×C₃₁	1	2	yes	—
345	C₂³	—	4	4	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	4	no	—
350	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
351	Q₈	—	2	2	no	—
352	Q₈	—	2	4	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	4	4	no	—
355	Q₈	—	4	2	no	—
356	Q₈	C₃₁×#127	1	4	yes	—
357	D₄	—	4	2	no	—
358	D₄	—	4	4	no	—
359	D₄	—	4	2	no	—
360	D₄	—	8	4	no	—
361	D₄	—	8	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	C₃₁×#121	1	4	yes	—
377	C₂×C₄	C₃₁×#121	1	4	yes	—
378	C₂×C₄	C₃₁×#121	1	2	yes	—
379	C₂×C₄	C₃₁×#121	1	2	yes	—
380	C₂×C₄	C₃₁×#135	1	2	yes	—
381	C₂×C₄	C₃₁×#137	1	2	yes	—
382	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
383	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
384	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
385	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	2	no	—
390	C₂²	—	8	4	no	—
391	C₂²	—	8	4	no	—
392	C₂²	—	8	2	no	—
393	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
394	C₂²	C₂×C₃₁×#121	1	2	yes	—
395	C₂²	C₂×C₃₁×#135	1	1	yes	characteristic
396	C₂²	C₂×C₃₁×#137	1	1	yes	characteristic
397	C₂²	C₃₁×#575	1	2	yes	—
398	C₄	—	2	4	no	—
399	C₄	—	2	4	no	—
400	C₄	—	2	4	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	4	no	—
403	C₄	—	4	2	no	—
404	C₄	—	8	2	no	—
405	C₄	C₃₁×#464	1	4	yes	complemented
406	C₄	C₂×C₃₁×#127	1	1	yes	characteristic
407	C₄	C₃₁×#532	1	1	yes	characteristic
408	C₄	C₃₁×#532	1	2	yes	—
409	C₂	—	16	2	no	—
410	C₂	C₃₁×#2856	1	1	yes	characteristic
411	C₂	C₂×C₃₁×#464	1	1	yes	characteristic
412	C₂	C₃₁×#3035	1	2	yes	—
413	C₂	C₃₁×#3037	1	2	yes	—
414	C₂	C₃₁×#3040	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₄³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#464	C₂	semidirect
2. C₂×C₃₁×#462	C₂	semidirect
5. C₄²×Q₈×C₃₁	C₂	semidirect
6. C₃₁×#1983	C₂	semidirect
8. C₃₁×#1981	C₂	semidirect
9. C₃₁×#1842	C₂	semidirect
56. C₄×Q₈×C₃₁	D₄	semidirect
137. #33165	C₃₁	direct (N × H)
181. C₂×#464	C₂×C₃₁	semidirect
182. C₂×#462	C₂×C₃₁	semidirect
185. C₄²×Q₈	C₂×C₃₁	semidirect
186. #1983	C₂×C₃₁	semidirect
188. #1981	C₂×C₃₁	semidirect
189. #1842	C₂×C₃₁	semidirect
207. C₄×C₃₁	#464	semidirect
263. C₄×Q₈	D₄×C₃₁	semidirect
290. C₃₁	#33165	direct (N × H)
405. C₄	C₃₁×#464	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#464	2
C₂×C₃₁×#462	2
C₂×C₃₁×#460	2
C₃₁×#2858	2
C₄²×Q₈×C₃₁	2
C₃₁×#1983	2
C₃₁×#1982	2
C₃₁×#1981	2
C₃₁×#1842	2
#33165	31

Subgroups — C31×#33165 #21489924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33165 #21489924