Subgroups — C₃₁×#10871 #21467630

Order 7936.

746 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#427	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#427	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#405	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1740	C₂	1	2	yes	maximal
5	C₃₁×#1733	C₂	1	2	yes	maximal
6	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
8	C₂×C₃₁×#117	C₂²	1	2	yes	—
9	C₂×C₃₁×#117	C₂²	1	2	yes	—
10	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
11	C₃₁×#427	—	2	2	no	—
12	C₃₁×#427	—	2	1	no	—
13	C₃₁×#427	—	2	1	no	—
14	C₃₁×#427	—	2	1	no	—
15	C₃₁×#427	—	2	1	no	—
16	C₃₁×#427	C₄	1	4	yes	complemented
17	C₂×C₃₁×#107	—	2	1	no	—
18	C₂×C₃₁×#107	C₄	1	2	yes	complemented
19	C₂×C₃₁×#106	—	2	1	no	—
20	C₂×C₃₁×#106	C₄	1	2	yes	complemented
21	C₃₁×#405	—	2	2	no	—
22	C₃₁×#405	C₄	1	4	yes	complemented
23	C₂×C₃₁×#97	—	2	1	no	—
24	C₂×C₄×C₈×C₃₁	—	2	1	no	—
25	C₃₁×#342	—	2	4	no	—
26	C₃₁×#339	—	2	4	no	—
27	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
28	C₂×M₁₆×C₃₁	—	2	1	no	—
29	C₂×M₁₆×C₃₁	—	2	1	no	—
30	C₂×M₁₆×C₃₁	—	2	1	no	—
31	C₂×M₁₆×C₃₁	C₂×C₄	1	2	yes	—
32	C₂×M₁₆×C₃₁	D₄	1	2	yes	—
33	C₂×M₁₆×C₃₁	Q₈	1	2	yes	—
34	C₂²×C₈×C₃₁	—	2	1	no	—
35	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
39	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₃₁	D₄	1	2	yes	—
42	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₃₁	Q₈	1	2	yes	—
45	C₃₁×#117	—	2	1	no	—
46	C₃₁×#117	—	2	1	no	—
47	C₃₁×#117	—	2	2	no	—
48	C₃₁×#117	—	2	2	no	—
49	C₃₁×#117	—	2	2	no	—
50	C₃₁×#117	—	2	2	no	—
51	C₃₁×#117	—	2	2	no	—
52	C₃₁×#117	—	2	2	no	—
53	C₃₁×#117	—	2	2	no	—
54	C₃₁×#117	C₂×C₄	1	4	yes	—
55	C₃₁×#117	C₂×C₄	1	2	yes	—
56	C₃₁×#117	Q₈	1	2	yes	—
57	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
60	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
63	C₂×C₄²×C₃₁	—	2	1	no	—
64	C₂×C₄²×C₃₁	—	2	2	no	—
65	C₂×C₄²×C₃₁	—	2	2	no	—
66	C₃₁×#107	—	2	4	no	—
67	C₃₁×#107	—	2	2	no	—
68	C₃₁×#107	—	2	2	no	—
69	C₃₁×#106	—	2	4	no	—
70	C₃₁×#106	—	2	2	no	—
71	C₃₁×#106	—	2	2	no	—
72	C₃₁×#97	—	2	4	no	—
73	C₄×C₈×C₃₁	—	2	4	no	—
74	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₃₁	—	2	2	no	—
76	C₂²×C₄×C₃₁	—	2	4	no	—
77	C₂²×C₄×C₃₁	—	4	2	no	—
78	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
89	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
91	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
92	M₁₆×C₃₁	—	2	2	no	—
93	M₁₆×C₃₁	—	2	2	no	—
94	M₁₆×C₃₁	—	2	2	no	—
95	M₁₆×C₃₁	C₄⋊C₄	1	4	yes	—
96	C₂×C₈×C₃₁	—	2	2	no	—
97	C₂×C₈×C₃₁	—	2	2	no	—
98	C₂×C₈×C₃₁	—	2	2	no	—
99	C₂×C₈×C₃₁	C₄²	1	2	yes	—
100	C₂×C₈×C₃₁	C₄²	1	2	yes	—
101	C₂×C₈×C₃₁	C₂²⋊C₄	1	2	yes	—
102	C₂×C₈×C₃₁	C₂²⋊C₄	1	2	yes	—
103	C₂×C₈×C₃₁	C₂²⋊C₄	1	2	yes	—
104	C₂×C₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₈×C₃₁	C₂²⋊C₄	1	2	yes	—
107	C₂×C₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₈×C₃₁	C₄⋊C₄	1	2	yes	—
110	C₂×C₈×C₃₁	C₄⋊C₄	1	2	yes	—
111	C₂×C₈×C₃₁	C₄⋊C₄	1	2	yes	—
112	C₂×C₈×C₃₁	C₄⋊C₄	1	2	yes	—
113	C₂×C₈×C₃₁	C₄⋊C₄	1	2	yes	—
114	C₂×C₈×C₃₁	C₄⋊C₄	1	2	yes	—
115	C₄⋊C₄×C₃₁	—	2	2	no	—
116	C₄⋊C₄×C₃₁	—	2	2	no	—
117	C₄⋊C₄×C₃₁	—	2	4	no	—
118	C₄⋊C₄×C₃₁	—	2	4	no	—
119	C₄⋊C₄×C₃₁	—	2	4	no	—
120	C₄⋊C₄×C₃₁	—	4	2	no	—
121	C₂²⋊C₄×C₃₁	—	2	2	no	—
122	C₂²⋊C₄×C₃₁	—	2	4	no	—
123	C₂²⋊C₄×C₃₁	—	4	2	no	—
124	C₂²⋊C₄×C₃₁	—	4	2	no	—
125	C₂²⋊C₄×C₃₁	—	4	2	no	—
126	C₂²⋊C₄×C₃₁	C₄⋊C₄	1	4	yes	—
127	C₄²×C₃₁	—	2	2	no	—
128	C₄²×C₃₁	—	2	2	no	—
129	C₄²×C₃₁	—	2	4	no	—
130	C₄²×C₃₁	—	4	2	no	—
131	C₄²×C₃₁	—	4	2	no	—
132	C₄²×C₃₁	—	4	2	no	—
133	#10871	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₃₁	—	4	2	no	—
135	C₂³×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
137	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
138	C₂³×C₃₁	#121	1	1	yes	characteristic
139	C₂³×C₃₁	#121	1	1	yes	characteristic
140	C₂³×C₃₁	#127	1	1	yes	characteristic
141	C₂³×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
142	C₂×C₄×C₃₁	—	2	4	no	—
143	C₂×C₄×C₃₁	—	4	4	no	—
144	C₂×C₄×C₃₁	—	4	4	no	—
145	C₂×C₄×C₃₁	—	4	4	no	—
146	C₂×C₄×C₃₁	—	8	4	no	—
147	C₂×C₄×C₃₁	—	8	4	no	—
148	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₃₁	#117	1	1	yes	characteristic
157	C₂×C₄×C₃₁	#117	1	1	yes	characteristic
158	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₃₁	C₄×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₃₁	C₄×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₃₁	C₄×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₃₁	C₄×Q₈	1	1	yes	characteristic
164	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
165	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
166	C₂×C₄×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
167	C₂×C₄×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
168	C₂×C₄×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
169	C₂×C₄×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
170	C₂×C₄×C₃₁	#124	1	1	yes	characteristic
171	C₂×C₄×C₃₁	#124	1	1	yes	characteristic
172	C₂×C₄×C₃₁	#125	1	1	yes	characteristic
173	C₂×C₄×C₃₁	#125	1	1	yes	characteristic
174	C₂×C₄×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
175	C₂×C₄×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
176	C₈×C₃₁	—	2	4	no	—
177	C₈×C₃₁	#95	1	2	yes	—
178	C₈×C₃₁	#95	1	2	yes	—
179	C₈×C₃₁	#95	1	2	yes	—
180	C₈×C₃₁	#95	1	2	yes	—
181	C₂×#427	C₂×C₃₁	1	1	yes	characteristic
182	C₂×#427	C₂×C₃₁	1	1	yes	characteristic
183	C₂×#405	C₂×C₃₁	1	1	yes	characteristic
184	#1740	C₂×C₃₁	1	2	yes	—
185	#1733	C₂×C₃₁	1	2	yes	—
186	C₂²×C₃₁	—	2	2	no	—
187	C₂²×C₃₁	—	2	2	no	—
188	C₂²×C₃₁	—	2	2	no	—
189	C₂²×C₃₁	—	4	1	no	—
190	C₂²×C₃₁	—	4	1	no	—
191	C₂²×C₃₁	—	4	1	no	—
192	C₂²×C₃₁	—	4	1	no	—
193	C₂²×C₃₁	C₄×C₄⋊C₄	1	1	yes	characteristic
194	C₂²×C₃₁	#380	1	1	yes	characteristic
195	C₂²×C₃₁	#384	1	1	yes	characteristic
196	C₂²×C₃₁	#389	1	1	yes	characteristic
197	C₂²×C₃₁	#389	1	1	yes	characteristic
198	C₂²×C₃₁	#390	1	1	yes	characteristic
199	C₂²×C₃₁	#390	1	1	yes	characteristic
200	C₄×C₃₁	—	4	4	no	—
201	C₄×C₃₁	—	8	4	no	—
202	C₄×C₃₁	—	8	4	no	—
203	C₄×C₃₁	C₂×#95	1	1	yes	characteristic
204	C₄×C₃₁	C₄×C₄⋊C₄	1	1	yes	characteristic
205	C₄×C₃₁	#380	1	1	yes	characteristic
206	C₄×C₃₁	#382	1	1	yes	characteristic
207	C₄×C₃₁	#389	1	1	yes	characteristic
208	C₄×C₃₁	#389	1	1	yes	characteristic
209	C₄×C₃₁	#391	1	1	yes	characteristic
210	C₄×C₃₁	#391	1	1	yes	characteristic
211	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
212	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
213	C₂×#117	C₂²×C₃₁	1	2	yes	—
214	C₂×#117	C₂²×C₃₁	1	2	yes	—
215	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
216	#427	—	2	2	no	—
217	#427	—	2	1	no	—
218	#427	—	2	1	no	—
219	#427	—	2	1	no	—
220	#427	—	2	1	no	—
221	#427	C₄×C₃₁	1	4	yes	complemented
222	C₂×#107	—	2	1	no	—
223	C₂×#107	C₄×C₃₁	1	2	yes	complemented
224	C₂×#106	—	2	1	no	—
225	C₂×#106	C₄×C₃₁	1	2	yes	complemented
226	#405	—	2	2	no	—
227	#405	C₄×C₃₁	1	4	yes	complemented
228	C₂×#97	—	2	1	no	—
229	C₂×C₄×C₈	—	2	1	no	—
230	#342	—	2	4	no	—
231	#339	—	2	4	no	—
232	C₂×C₃₁	—	2	1	no	—
233	C₂×C₃₁	—	2	1	no	—
234	C₂×C₃₁	—	2	1	no	—
235	C₂×C₃₁	—	2	1	no	—
236	C₂×C₃₁	—	2	1	no	—
237	C₂×C₃₁	—	2	1	no	—
238	C₂×C₃₁	C₄⋊#95	1	1	yes	characteristic
239	C₂×C₃₁	#1976	1	2	yes	—
240	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
241	C₂×M₁₆	—	2	1	no	—
242	C₂×M₁₆	—	2	1	no	—
243	C₂×M₁₆	—	2	1	no	—
244	C₂×M₁₆	C₂×C₄×C₃₁	1	2	yes	—
245	C₂×M₁₆	D₄×C₃₁	1	2	yes	—
246	C₂×M₁₆	Q₈×C₃₁	1	2	yes	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
249	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
250	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
251	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
252	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
253	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
254	C₂²×C₈	D₄×C₃₁	1	2	yes	—
255	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
256	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
257	C₂²×C₈	Q₈×C₃₁	1	2	yes	—
258	#117	—	2	1	no	—
259	#117	—	2	1	no	—
260	#117	—	2	2	no	—
261	#117	—	2	2	no	—
262	#117	—	2	2	no	—
263	#117	—	2	2	no	—
264	#117	—	2	2	no	—
265	#117	—	2	2	no	—
266	#117	—	2	2	no	—
267	#117	C₂×C₄×C₃₁	1	4	yes	—
268	#117	C₂×C₄×C₃₁	1	2	yes	—
269	#117	Q₈×C₃₁	1	2	yes	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	—	2	2	no	—
279	#107	—	2	4	no	—
280	#107	—	2	2	no	—
281	#107	—	2	2	no	—
282	#106	—	2	4	no	—
283	#106	—	2	2	no	—
284	#106	—	2	2	no	—
285	#97	—	2	4	no	—
286	C₄×C₈	—	2	4	no	—
287	C₃₁	#10871	1	1	yes	characteristic, direct product factor, Sylow
288	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
299	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
300	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
301	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
302	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
303	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
304	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
305	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
306	M₁₆	—	2	2	no	—
307	M₁₆	—	2	2	no	—
308	M₁₆	—	2	2	no	—
309	M₁₆	C₄⋊C₄×C₃₁	1	4	yes	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	C₄²×C₃₁	1	2	yes	—
314	C₂×C₈	C₄²×C₃₁	1	2	yes	—
315	C₂×C₈	C₂²⋊C₄×C₃₁	1	2	yes	—
316	C₂×C₈	C₂²⋊C₄×C₃₁	1	2	yes	—
317	C₂×C₈	C₂²⋊C₄×C₃₁	1	2	yes	—
318	C₂×C₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
319	C₂×C₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
320	C₂×C₈	C₂²⋊C₄×C₃₁	1	2	yes	—
321	C₂×C₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
322	C₂×C₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
323	C₂×C₈	C₄⋊C₄×C₃₁	1	2	yes	—
324	C₂×C₈	C₄⋊C₄×C₃₁	1	2	yes	—
325	C₂×C₈	C₄⋊C₄×C₃₁	1	2	yes	—
326	C₂×C₈	C₄⋊C₄×C₃₁	1	2	yes	—
327	C₂×C₈	C₄⋊C₄×C₃₁	1	2	yes	—
328	C₂×C₈	C₄⋊C₄×C₃₁	1	2	yes	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	4	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	C₄⋊C₄×C₃₁	1	4	yes	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	4	no	—
344	C₄²	—	4	2	no	—
345	C₄²	—	4	2	no	—
346	C₄²	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
349	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
350	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
351	C₂³	C₃₁×#121	1	1	yes	characteristic
352	C₂³	C₃₁×#121	1	1	yes	characteristic
353	C₂³	C₃₁×#127	1	1	yes	characteristic
354	C₂³	C₃₁×C₄⋊Q₈	1	1	yes	characteristic
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	8	4	no	—
360	C₂×C₄	—	8	4	no	—
361	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
362	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
363	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
364	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
365	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
366	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
367	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
368	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
369	C₂×C₄	C₃₁×#117	1	1	yes	characteristic
370	C₂×C₄	C₃₁×#117	1	1	yes	characteristic
371	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
372	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
373	C₂×C₄	C₄×Q₈×C₃₁	1	1	yes	characteristic
374	C₂×C₄	C₄×Q₈×C₃₁	1	1	yes	characteristic
375	C₂×C₄	C₄×Q₈×C₃₁	1	1	yes	characteristic
376	C₂×C₄	C₄×Q₈×C₃₁	1	1	yes	characteristic
377	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
378	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
379	C₂×C₄	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
380	C₂×C₄	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
381	C₂×C₄	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
382	C₂×C₄	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
383	C₂×C₄	C₃₁×#124	1	1	yes	characteristic
384	C₂×C₄	C₃₁×#124	1	1	yes	characteristic
385	C₂×C₄	C₃₁×#125	1	1	yes	characteristic
386	C₂×C₄	C₃₁×#125	1	1	yes	characteristic
387	C₂×C₄	C₃₁×C₄⋊Q₈	1	1	yes	characteristic
388	C₂×C₄	C₃₁×C₄⋊Q₈	1	1	yes	characteristic
389	C₈	—	2	4	no	—
390	C₈	C₃₁×#95	1	2	yes	—
391	C₈	C₃₁×#95	1	2	yes	—
392	C₈	C₃₁×#95	1	2	yes	—
393	C₈	C₃₁×#95	1	2	yes	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	C₄×C₄⋊C₄×C₃₁	1	1	yes	characteristic
402	C₂²	C₃₁×#380	1	1	yes	characteristic
403	C₂²	C₃₁×#384	1	1	yes	characteristic
404	C₂²	C₃₁×#389	1	1	yes	characteristic
405	C₂²	C₃₁×#389	1	1	yes	characteristic
406	C₂²	C₃₁×#390	1	1	yes	characteristic
407	C₂²	C₃₁×#390	1	1	yes	characteristic
408	C₄	—	4	4	no	—
409	C₄	—	8	4	no	—
410	C₄	—	8	4	no	—
411	C₄	C₂×C₃₁×#95	1	1	yes	characteristic
412	C₄	C₄×C₄⋊C₄×C₃₁	1	1	yes	characteristic
413	C₄	C₃₁×#380	1	1	yes	characteristic
414	C₄	C₃₁×#382	1	1	yes	characteristic
415	C₄	C₃₁×#389	1	1	yes	characteristic
416	C₄	C₃₁×#389	1	1	yes	characteristic
417	C₄	C₃₁×#391	1	1	yes	characteristic
418	C₄	C₃₁×#391	1	1	yes	characteristic
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	C₃₁×C₄⋊#95	1	1	yes	characteristic
426	C₂	C₃₁×#1976	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₃₁	#121
commutator	C₂×C₄	C₂×C₄²×C₃₁
Frattini, cosocle	C₂³×C₄	C₂³×C₃₁
socle	C₂²×C₃₁	#390
prime radical	C₂⁴×C₃₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂³×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
16. C₃₁×#427	C₄	semidirect
18. C₂×C₃₁×#107	C₄	semidirect
20. C₂×C₃₁×#106	C₄	semidirect
22. C₃₁×#405	C₄	semidirect
133. #10871	C₃₁	direct (N × H)
221. #427	C₄×C₃₁	semidirect
223. C₂×#107	C₄×C₃₁	semidirect
225. C₂×#106	C₄×C₃₁	semidirect
227. #405	C₄×C₃₁	semidirect
287. C₃₁	#10871	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×#427	2
C₂×C₃₁×#405	2
C₃₁×#1740	2
C₃₁×#1733	2
#10871	31

Subgroups — C31×#10871 #21467630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#10871 #21467630