Subgroups — C₃₁×#35151 #21491910

Order 7936.

2358 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#117	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2855	C₂	1	4	yes	maximal, complemented
4	C₃₁×#2626	C₂	1	4	yes	maximal
5	C₃₁×#2441	C₂	1	8	yes	maximal, complemented
6	C₃₁×#2439	C₂	1	8	yes	maximal, complemented
7	C₃₁×#2317	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2316	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2280	C₂	1	2	yes	maximal
10	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
11	C₃₁×#544	—	2	8	no	—
12	C₂×C₃₁×C₄⋊Q₈	C₂²	1	4	yes	complemented
13	C₂×C₃₁×#125	C₂²	1	4	yes	complemented
14	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
15	C₂×C₃₁×#117	—	2	8	no	—
16	C₂×C₃₁×#117	C₂²	1	2	yes	—
17	C₂×C₃₁×#117	C₂²	1	2	yes	—
18	C₂×C₃₁×#117	C₂²	1	8	yes	—
19	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
22	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
23	C₃₁×#399	C₂²	1	8	yes	—
24	C₃₁×#396	C₂²	1	16	yes	—
25	C₃₁×#393	C₂²	1	8	yes	—
26	C₃₁×#391	C₂²	1	8	yes	complemented
27	C₃₁×#389	C₂²	1	8	yes	complemented
28	C₃₁×#389	C₂²	1	8	yes	complemented
29	C₃₁×#389	C₂²	1	8	yes	complemented
30	C₃₁×#387	C₂²	1	16	yes	complemented
31	C₃₁×#385	C₂²	1	8	yes	—
32	C₃₁×#384	C₂²	1	4	yes	complemented
33	C₃₁×#382	C₂²	1	4	yes	complemented
34	C₃₁×#381	C₂²	1	4	yes	—
35	C₃₁×#380	C₂²	1	4	yes	—
36	C₃₁×#380	C₂²	1	4	yes	—
37	C₃₁×#380	C₂²	1	4	yes	—
38	C₃₁×#379	C₂²	1	4	yes	—
39	C₄×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	—
40	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
41	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
42	C₂³×C₄×C₃₁	—	2	4	no	—
43	C₂³×C₄×C₃₁	—	2	4	no	—
44	C₂³×C₄×C₃₁	Q₈	1	8	yes	complemented
45	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
47	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
48	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
50	C₃₁×C₄⋊Q₈	—	2	16	no	—
51	C₃₁×#125	—	2	16	no	—
52	C₃₁×C₂²⋊Q₈	—	2	16	no	—
53	C₃₁×#117	—	2	8	no	—
54	C₃₁×#117	—	2	8	no	—
55	C₃₁×#117	—	2	32	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
57	C₂×C₄⋊C₄×C₃₁	D₄	1	8	yes	—
58	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
59	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
64	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
65	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	—
66	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
67	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
68	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
69	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
70	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
71	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
72	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
73	C₂×C₄²×C₃₁	—	2	8	no	—
74	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
75	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
76	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
77	C₃₁×#95	C₂³	1	16	yes	—
78	C₃₁×#95	C₂³	1	8	yes	—
79	C₃₁×#95	C₂³	1	8	yes	—
80	C₃₁×#95	C₂³	1	8	yes	—
81	C₂⁴×C₃₁	—	2	2	no	—
82	C₂⁴×C₃₁	—	2	2	no	—
83	C₂⁴×C₃₁	—	4	2	no	—
84	C₂⁴×C₃₁	—	4	2	no	—
85	C₂⁴×C₃₁	C₂×Q₈	1	4	yes	—
86	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
87	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
88	C₂×Q₈×C₃₁	—	2	8	no	—
89	C₂×Q₈×C₃₁	—	4	8	no	—
90	C₂²×C₄×C₃₁	—	2	2	no	—
91	C₂²×C₄×C₃₁	—	2	2	no	—
92	C₂²×C₄×C₃₁	—	2	32	no	—
93	C₂²×C₄×C₃₁	—	2	8	no	—
94	C₂²×C₄×C₃₁	—	2	8	no	—
95	C₂²×C₄×C₃₁	—	2	4	no	—
96	C₂²×C₄×C₃₁	—	4	4	no	—
97	C₂²×C₄×C₃₁	—	4	4	no	—
98	C₂²×C₄×C₃₁	C₂×D₄	1	8	yes	—
99	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₃₁	C₂×Q₈	1	4	yes	—
101	C₂²×C₄×C₃₁	C₂×Q₈	1	16	yes	—
102	C₂²×C₄×C₃₁	C₂×Q₈	1	4	yes	—
103	C₂²×C₄×C₃₁	#41	1	4	yes	—
104	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
105	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
106	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
107	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
108	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
109	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
110	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
111	C₄⋊C₄×C₃₁	—	2	8	no	—
112	C₄⋊C₄×C₃₁	—	2	4	no	—
113	C₄⋊C₄×C₃₁	—	2	4	no	—
114	C₄⋊C₄×C₃₁	—	2	8	no	—
115	C₄⋊C₄×C₃₁	—	2	16	no	—
116	C₄⋊C₄×C₃₁	—	2	8	no	—
117	C₄⋊C₄×C₃₁	—	4	8	no	—
118	C₄⋊C₄×C₃₁	—	4	16	no	—
119	C₄⋊C₄×C₃₁	C₂×D₄	1	16	yes	—
120	C₂²⋊C₄×C₃₁	—	2	8	no	—
121	C₂²⋊C₄×C₃₁	—	2	8	no	—
122	C₂²⋊C₄×C₃₁	—	2	16	no	—
123	C₂²⋊C₄×C₃₁	—	4	8	no	—
124	C₂²⋊C₄×C₃₁	—	4	8	no	—
125	C₄²×C₃₁	—	2	16	no	—
126	C₄²×C₃₁	—	2	8	no	—
127	C₄²×C₃₁	—	2	8	no	—
128	#35151	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₃₁	—	2	2	no	—
130	C₂³×C₃₁	—	2	2	no	—
131	C₂³×C₃₁	—	2	8	no	—
132	C₂³×C₃₁	—	2	2	no	—
133	C₂³×C₃₁	—	2	2	no	—
134	C₂³×C₃₁	—	2	4	no	—
135	C₂³×C₃₁	—	2	4	no	—
136	C₂³×C₃₁	—	4	8	no	—
137	C₂³×C₃₁	—	4	4	no	—
138	C₂³×C₃₁	—	4	4	no	—
139	C₂³×C₃₁	—	4	8	no	—
140	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
141	C₂³×C₃₁	C₂²×Q₈	1	4	yes	—
142	C₂³×C₃₁	C₂²×Q₈	1	2	yes	—
143	C₂³×C₃₁	C₂×#41	1	2	yes	—
144	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
145	Q₈×C₃₁	—	8	8	no	—
146	C₂×C₄×C₃₁	—	2	8	no	—
147	C₂×C₄×C₃₁	—	2	2	no	—
148	C₂×C₄×C₃₁	—	2	2	no	—
149	C₂×C₄×C₃₁	—	2	8	no	—
150	C₂×C₄×C₃₁	—	2	32	no	—
151	C₂×C₄×C₃₁	—	2	4	no	—
152	C₂×C₄×C₃₁	—	2	4	no	—
153	C₂×C₄×C₃₁	—	2	4	no	—
154	C₂×C₄×C₃₁	—	2	8	no	—
155	C₂×C₄×C₃₁	—	2	8	no	—
156	C₂×C₄×C₃₁	—	2	8	no	—
157	C₂×C₄×C₃₁	—	2	8	no	—
158	C₂×C₄×C₃₁	—	2	8	no	—
159	C₂×C₄×C₃₁	—	2	8	no	—
160	C₂×C₄×C₃₁	—	4	8	no	—
161	C₂×C₄×C₃₁	—	4	8	no	—
162	C₂×C₄×C₃₁	C₂²⋊Q₈	1	16	yes	—
163	C₂×C₄×C₃₁	C₂²×D₄	1	8	yes	—
164	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
165	C₂×C₄×C₃₁	C₂²×Q₈	1	4	yes	—
166	C₂×C₄×C₃₁	C₂²×Q₈	1	4	yes	—
167	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
168	C₂×#544	C₂×C₃₁	1	1	yes	characteristic, complemented
169	C₂²×#117	C₂×C₃₁	1	1	yes	characteristic
170	#2855	C₂×C₃₁	1	4	yes	complemented
171	#2626	C₂×C₃₁	1	4	yes	—
172	#2441	C₂×C₃₁	1	8	yes	complemented
173	#2439	C₂×C₃₁	1	8	yes	complemented
174	#2317	C₂×C₃₁	1	2	yes	complemented
175	#2316	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#2280	C₂×C₃₁	1	2	yes	—
177	C₂²×C₃₁	—	2	4	no	—
178	C₂²×C₃₁	—	2	2	no	—
179	C₂²×C₃₁	—	2	2	no	—
180	C₂²×C₃₁	—	2	4	no	—
181	C₂²×C₃₁	—	2	4	no	—
182	C₂²×C₃₁	—	2	8	no	—
183	C₂²×C₃₁	—	4	16	no	—
184	C₂²×C₃₁	—	4	2	no	—
185	C₂²×C₃₁	—	4	2	no	—
186	C₂²×C₃₁	—	4	4	no	—
187	C₂²×C₃₁	C₂×C₂²⋊Q₈	1	4	yes	—
188	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
189	C₂²×C₃₁	C₂³×Q₈	1	1	yes	characteristic
190	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
191	C₂²×C₃₁	#585	1	2	yes	—
192	C₂²×C₃₁	#585	1	2	yes	—
193	C₄×C₃₁	—	2	4	no	—
194	C₄×C₃₁	—	2	8	no	—
195	C₄×C₃₁	—	4	4	no	—
196	C₄×C₃₁	—	4	4	no	—
197	C₄×C₃₁	—	4	4	no	—
198	C₄×C₃₁	—	4	8	no	—
199	C₄×C₃₁	C₂×C₂²⋊Q₈	1	8	yes	—
200	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
201	#544	—	2	8	no	—
202	C₂×C₄⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
203	C₂×#125	C₂²×C₃₁	1	4	yes	complemented
204	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
205	C₂×#117	—	2	8	no	—
206	C₂×#117	C₂²×C₃₁	1	2	yes	—
207	C₂×#117	C₂²×C₃₁	1	2	yes	—
208	C₂×#117	C₂²×C₃₁	1	8	yes	—
209	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
210	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
211	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
212	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
213	#399	C₂²×C₃₁	1	8	yes	—
214	#396	C₂²×C₃₁	1	16	yes	—
215	#393	C₂²×C₃₁	1	8	yes	—
216	#391	C₂²×C₃₁	1	8	yes	complemented
217	#389	C₂²×C₃₁	1	8	yes	complemented
218	#389	C₂²×C₃₁	1	8	yes	complemented
219	#389	C₂²×C₃₁	1	8	yes	complemented
220	#387	C₂²×C₃₁	1	16	yes	complemented
221	#385	C₂²×C₃₁	1	8	yes	—
222	#384	C₂²×C₃₁	1	4	yes	complemented
223	#382	C₂²×C₃₁	1	4	yes	complemented
224	#381	C₂²×C₃₁	1	4	yes	—
225	#380	C₂²×C₃₁	1	4	yes	—
226	#380	C₂²×C₃₁	1	4	yes	—
227	#380	C₂²×C₃₁	1	4	yes	—
228	#379	C₂²×C₃₁	1	4	yes	—
229	C₄×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	—
230	C₂×C₃₁	—	2	4	no	—
231	C₂×C₃₁	—	4	4	no	—
232	C₂×C₃₁	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
233	C₂×C₃₁	#3458	1	2	yes	—
234	C₂×C₃₁	#3485	1	1	yes	characteristic
235	C₂×C₃₁	#3487	1	1	yes	characteristic
236	C₂×C₃₁	#3493	1	2	yes	—
237	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
238	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
239	C₂³×C₄	—	2	4	no	—
240	C₂³×C₄	—	2	4	no	—
241	C₂³×C₄	Q₈×C₃₁	1	8	yes	complemented
242	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
243	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
244	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
245	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
246	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
247	C₄⋊Q₈	—	2	16	no	—
248	#125	—	2	16	no	—
249	C₂²⋊Q₈	—	2	16	no	—
250	#117	—	2	8	no	—
251	#117	—	2	8	no	—
252	#117	—	2	32	no	—
253	C₂×C₄⋊C₄	—	2	4	no	—
254	C₂×C₄⋊C₄	D₄×C₃₁	1	8	yes	—
255	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
256	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
259	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
260	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
261	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
262	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	—
263	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
264	C₂×C₂²⋊C₄	—	2	8	no	—
265	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
266	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
267	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
268	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
269	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
270	C₂×C₄²	—	2	8	no	—
271	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
272	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
273	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
274	#95	C₂³×C₃₁	1	8	yes	—
275	#95	C₂³×C₃₁	1	8	yes	—
276	#95	C₂³×C₃₁	1	8	yes	—
277	#95	C₂³×C₃₁	1	16	yes	—
278	C₃₁	#35151	1	1	yes	characteristic, direct product factor, Sylow
279	C₂⁴	—	2	2	no	—
280	C₂⁴	—	2	2	no	—
281	C₂⁴	—	4	2	no	—
282	C₂⁴	—	4	2	no	—
283	C₂⁴	C₂×Q₈×C₃₁	1	4	yes	—
284	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
285	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
286	C₂×Q₈	—	2	8	no	—
287	C₂×Q₈	—	4	8	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	32	no	—
291	C₂²×C₄	—	2	8	no	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	4	4	no	—
295	C₂²×C₄	—	4	4	no	—
296	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	—
297	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
298	C₂²×C₄	C₂×Q₈×C₃₁	1	4	yes	—
299	C₂²×C₄	C₂×Q₈×C₃₁	1	16	yes	—
300	C₂²×C₄	C₂×Q₈×C₃₁	1	4	yes	—
301	C₂²×C₄	#41×C₃₁	1	4	yes	—
302	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
303	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
304	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
305	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
306	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
307	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
308	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
309	C₄⋊C₄	—	2	8	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	8	no	—
313	C₄⋊C₄	—	2	16	no	—
314	C₄⋊C₄	—	2	8	no	—
315	C₄⋊C₄	—	4	8	no	—
316	C₄⋊C₄	—	4	16	no	—
317	C₄⋊C₄	C₂×D₄×C₃₁	1	16	yes	—
318	C₂²⋊C₄	—	2	8	no	—
319	C₂²⋊C₄	—	2	8	no	—
320	C₂²⋊C₄	—	2	16	no	—
321	C₂²⋊C₄	—	4	8	no	—
322	C₂²⋊C₄	—	4	8	no	—
323	C₄²	—	2	16	no	—
324	C₄²	—	2	8	no	—
325	C₄²	—	2	8	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	8	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	4	no	—
332	C₂³	—	2	4	no	—
333	C₂³	—	4	8	no	—
334	C₂³	—	4	4	no	—
335	C₂³	—	4	4	no	—
336	C₂³	—	4	8	no	—
337	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
338	C₂³	C₂²×Q₈×C₃₁	1	4	yes	—
339	C₂³	C₂²×Q₈×C₃₁	1	2	yes	—
340	C₂³	C₂×#41×C₃₁	1	2	yes	—
341	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
342	Q₈	—	8	8	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	32	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	4	8	no	—
358	C₂×C₄	—	4	8	no	—
359	C₂×C₄	C₃₁×C₂²⋊Q₈	1	16	yes	—
360	C₂×C₄	C₂²×D₄×C₃₁	1	8	yes	—
361	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
362	C₂×C₄	C₂²×Q₈×C₃₁	1	4	yes	—
363	C₂×C₄	C₂²×Q₈×C₃₁	1	4	yes	—
364	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	2	8	no	—
371	C₂²	—	4	16	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	4	no	—
375	C₂²	C₂×C₃₁×C₂²⋊Q₈	1	4	yes	—
376	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
377	C₂²	C₂³×Q₈×C₃₁	1	1	yes	characteristic
378	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
379	C₂²	C₃₁×#585	1	2	yes	—
380	C₂²	C₃₁×#585	1	2	yes	—
381	C₄	—	2	4	no	—
382	C₄	—	2	8	no	—
383	C₄	—	4	4	no	—
384	C₄	—	4	4	no	—
385	C₄	—	4	4	no	—
386	C₄	—	4	8	no	—
387	C₄	C₂×C₃₁×C₂²⋊Q₈	1	8	yes	—
388	C₂	—	2	4	no	—
389	C₂	—	4	4	no	—
390	C₂	C₂²×C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
391	C₂	C₃₁×#3458	1	2	yes	—
392	C₂	C₃₁×#3485	1	1	yes	characteristic
393	C₂	C₃₁×#3487	1	1	yes	characteristic
394	C₂	C₃₁×#3493	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂⁵×C₃₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#544	C₂	semidirect
3. C₃₁×#2855	C₂	semidirect
5. C₃₁×#2441	C₂	semidirect
6. C₃₁×#2439	C₂	semidirect
7. C₃₁×#2317	C₂	semidirect
8. C₃₁×#2316	C₂	semidirect
12. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
13. C₂×C₃₁×#125	C₂²	semidirect
26. C₃₁×#391	C₂²	semidirect
27. C₃₁×#389	C₂²	semidirect
28. C₃₁×#389	C₂²	semidirect
29. C₃₁×#389	C₂²	semidirect
30. C₃₁×#387	C₂²	semidirect
32. C₃₁×#384	C₂²	semidirect
33. C₃₁×#382	C₂²	semidirect
44. C₂³×C₄×C₃₁	Q₈	semidirect
128. #35151	C₃₁	direct (N × H)
168. C₂×#544	C₂×C₃₁	semidirect
170. #2855	C₂×C₃₁	semidirect
172. #2441	C₂×C₃₁	semidirect
173. #2439	C₂×C₃₁	semidirect
174. #2317	C₂×C₃₁	semidirect
175. #2316	C₂×C₃₁	semidirect
202. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
203. C₂×#125	C₂²×C₃₁	semidirect
216. #391	C₂²×C₃₁	semidirect
217. #389	C₂²×C₃₁	semidirect
218. #389	C₂²×C₃₁	semidirect
219. #389	C₂²×C₃₁	semidirect
220. #387	C₂²×C₃₁	semidirect
222. #384	C₂²×C₃₁	semidirect
223. #382	C₂²×C₃₁	semidirect
241. C₂³×C₄	Q₈×C₃₁	semidirect
278. C₃₁	#35151	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×C₃₁×#544	2
C₂²×C₃₁×#117	2
C₃₁×#2855	2
C₃₁×#2626	2
C₃₁×#2441	2
C₃₁×#2439	2
C₃₁×#2317	2
C₃₁×#2316	2
C₃₁×#2280	2
#35151	31

Subgroups — C31×#35151 #21491910

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35151 #21491910