Subgroups — C₃₁×#23699 #21480458

Order 7936.

894 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#431	C₂	1	1	yes	maximal, characteristic
3	C₄×C₃₁×C₂²⋊Q₈	C₂	1	2	yes	maximal
4	C₃₁×#2086	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2075	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#2066	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2035	C₂	1	2	yes	maximal
9	C₃₁×#2001	C₂	1	1	yes	maximal, characteristic
10	C₄×C₃₁×#106	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₃₁×#103	C₂	1	2	yes	maximal, complemented
12	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
15	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
16	C₄×Q₁₆×C₃₁	—	2	4	no	—
17	C₃₁×#431	—	2	4	no	—
18	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#106	C₂²	1	2	yes	—
20	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#103	C₂²	1	2	yes	—
23	C₂×C₃₁×#103	C₂²	1	2	yes	—
24	C₂×C₃₁×#103	C₂²	1	2	yes	—
25	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#391	C₂²	1	2	yes	—
30	C₃₁×#389	C₂²	1	2	yes	—
31	C₃₁×#387	—	2	2	no	—
32	C₃₁×#385	—	2	2	no	—
33	C₃₁×#380	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₃₁	—	2	2	no	—
35	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
36	C₄×C₂²⋊C₄×C₃₁	—	2	2	no	—
37	C₃₁×#340	C₂²	1	1	yes	characteristic
38	C₃₁×#340	C₂²	1	2	yes	—
39	C₃₁×#340	C₂²	1	1	yes	characteristic
40	C₃₁×#340	C₂²	1	2	yes	—
41	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
45	C₂×Q₁₆×C₃₁	—	2	4	no	—
46	C₂×Q₁₆×C₃₁	—	2	2	no	—
47	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
51	C₃₁×C₂²⋊Q₈	—	2	4	no	—
52	C₃₁×C₂²⋊Q₈	—	2	4	no	—
53	C₄×Q₈×C₃₁	—	2	4	no	—
54	C₄×Q₈×C₃₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
63	C₂×C₄²×C₃₁	—	2	2	no	—
64	C₂×C₄²×C₃₁	—	2	2	no	—
65	C₂×C₄²×C₃₁	—	2	2	no	—
66	C₂×C₄²×C₃₁	—	2	2	no	—
67	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
71	C₃₁×#107	—	2	2	no	—
72	C₃₁×#106	—	2	4	no	—
73	C₃₁×C₄⋊C₈	—	2	2	no	—
74	C₃₁×C₄⋊C₈	—	2	2	no	—
75	C₃₁×#103	—	2	4	no	—
76	C₃₁×#103	—	2	4	no	—
77	C₃₁×#103	—	2	4	no	—
78	C₃₁×C₂²⋊C₈	—	2	2	no	—
79	C₃₁×C₂²⋊C₈	—	2	2	no	—
80	C₄×C₈×C₃₁	—	2	2	no	—
81	C₄×C₈×C₃₁	D₄	1	4	yes	—
82	C₃₁×#95	—	2	2	no	—
83	C₃₁×#95	—	2	2	no	—
84	C₃₁×#95	—	2	2	no	—
85	C₃₁×#95	—	2	2	no	—
86	C₃₁×#95	—	2	2	no	—
87	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
88	C₂×Q₈×C₃₁	—	2	2	no	—
89	C₂×Q₈×C₃₁	—	2	2	no	—
90	C₂×Q₈×C₃₁	—	2	2	no	—
91	C₂×Q₈×C₃₁	—	2	2	no	—
92	C₂×Q₈×C₃₁	—	2	2	no	—
93	C₂×Q₈×C₃₁	#41	1	4	yes	—
94	C₂²×C₄×C₃₁	—	2	2	no	—
95	C₂²×C₄×C₃₁	—	2	2	no	—
96	C₂²×C₄×C₃₁	—	2	2	no	—
97	C₂²×C₄×C₃₁	—	2	2	no	—
98	C₂²×C₄×C₃₁	—	2	2	no	—
99	C₂²×C₄×C₃₁	—	2	2	no	—
100	C₂²×C₄×C₃₁	—	2	4	no	—
101	C₂²×C₄×C₃₁	—	2	1	no	—
102	C₂²×C₄×C₃₁	—	2	1	no	—
103	C₂²×C₄×C₃₁	—	2	2	no	—
104	C₂²×C₄×C₃₁	—	2	2	no	—
105	C₂²×C₄×C₃₁	—	2	2	no	—
106	C₂²×C₄×C₃₁	—	2	2	no	—
107	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
113	Q₁₆×C₃₁	—	2	8	no	—
114	C₂×C₈×C₃₁	—	2	2	no	—
115	C₂×C₈×C₃₁	—	2	2	no	—
116	C₂×C₈×C₃₁	—	2	1	no	—
117	C₂×C₈×C₃₁	—	2	1	no	—
118	C₂×C₈×C₃₁	—	2	2	no	—
119	C₂×C₈×C₃₁	—	2	2	no	—
120	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
122	C₄⋊C₄×C₃₁	—	2	8	no	—
123	C₄⋊C₄×C₃₁	—	2	2	no	—
124	C₄⋊C₄×C₃₁	—	2	2	no	—
125	C₄⋊C₄×C₃₁	—	2	2	no	—
126	C₄⋊C₄×C₃₁	—	2	2	no	—
127	C₄⋊C₄×C₃₁	—	2	2	no	—
128	C₄⋊C₄×C₃₁	—	4	4	no	—
129	C₄⋊C₄×C₃₁	—	4	4	no	—
130	C₄⋊C₄×C₃₁	#41	1	4	yes	—
131	C₂²⋊C₄×C₃₁	—	2	8	no	—
132	C₂²⋊C₄×C₃₁	—	4	4	no	—
133	C₄²×C₃₁	—	2	2	no	—
134	C₄²×C₃₁	—	2	2	no	—
135	C₄²×C₃₁	—	2	1	no	—
136	C₄²×C₃₁	—	2	1	no	—
137	C₄²×C₃₁	—	4	4	no	—
138	C₄²×C₃₁	—	4	4	no	—
139	C₄²×C₃₁	C₂×D₄	1	2	yes	—
140	C₄²×C₃₁	#41	1	2	yes	—
141	#23699	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₃₁	—	2	1	no	—
143	C₂³×C₃₁	—	2	2	no	—
144	C₂³×C₃₁	—	2	1	no	—
145	C₂³×C₃₁	—	2	2	no	—
146	C₂³×C₃₁	#135	1	2	yes	—
147	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₃₁	—	2	4	no	—
149	Q₈×C₃₁	—	2	4	no	—
150	Q₈×C₃₁	—	4	2	no	—
151	Q₈×C₃₁	—	4	2	no	—
152	C₂×C₄×C₃₁	—	2	8	no	—
153	C₂×C₄×C₃₁	—	2	1	no	—
154	C₂×C₄×C₃₁	—	2	1	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	—	2	1	no	—
159	C₂×C₄×C₃₁	—	2	4	no	—
160	C₂×C₄×C₃₁	—	2	4	no	—
161	C₂×C₄×C₃₁	—	2	2	no	—
162	C₂×C₄×C₃₁	—	2	2	no	—
163	C₂×C₄×C₃₁	—	4	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	1	no	—
168	C₂×C₄×C₃₁	—	4	2	no	—
169	C₂×C₄×C₃₁	—	4	1	no	—
170	C₂×C₄×C₃₁	—	4	4	no	—
171	C₂×C₄×C₃₁	—	4	2	no	—
172	C₂×C₄×C₃₁	—	4	2	no	—
173	C₂×C₄×C₃₁	—	4	2	no	—
174	C₂×C₄×C₃₁	—	4	2	no	—
175	C₂×C₄×C₃₁	—	4	2	no	—
176	C₂×C₄×C₃₁	—	4	2	no	—
177	C₂×C₄×C₃₁	#121	1	2	yes	—
178	C₂×C₄×C₃₁	#121	1	2	yes	—
179	C₂×C₄×C₃₁	#135	1	2	yes	—
180	C₂×C₄×C₃₁	#137	1	4	yes	—
181	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
183	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
185	C₈×C₃₁	—	2	2	no	—
186	C₈×C₃₁	—	2	2	no	—
187	C₈×C₃₁	—	4	1	no	—
188	C₈×C₃₁	—	4	1	no	—
189	C₂×C₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
190	C₂×#431	C₂×C₃₁	1	1	yes	characteristic
191	C₄×C₂²⋊Q₈	C₂×C₃₁	1	2	yes	—
192	#2086	C₂×C₃₁	1	1	yes	characteristic, complemented
193	#2075	C₂×C₃₁	1	1	yes	characteristic
194	#2066	C₂×C₃₁	1	2	yes	complemented
195	#2056	C₂×C₃₁	1	1	yes	characteristic, complemented
196	#2035	C₂×C₃₁	1	2	yes	—
197	#2001	C₂×C₃₁	1	1	yes	characteristic
198	C₄×#106	C₂×C₃₁	1	1	yes	characteristic, complemented
199	C₄×#103	C₂×C₃₁	1	2	yes	complemented
200	C₂²×C₃₁	—	2	4	no	—
201	C₂²×C₃₁	—	2	2	no	—
202	C₂²×C₃₁	—	4	2	no	—
203	C₂²×C₃₁	—	4	1	no	—
204	C₂²×C₃₁	—	4	1	no	—
205	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
206	C₂²×C₃₁	#525	1	2	yes	—
207	C₂²×C₃₁	C₂×#135	1	1	yes	characteristic
208	C₂²×C₃₁	C₂×#135	1	1	yes	characteristic
209	C₂²×C₃₁	C₂×#137	1	2	yes	—
210	C₄×C₃₁	—	2	2	no	—
211	C₄×C₃₁	—	2	2	no	—
212	C₄×C₃₁	—	4	4	no	—
213	C₄×C₃₁	—	4	1	no	—
214	C₄×C₃₁	—	4	4	no	—
215	C₄×C₃₁	—	4	1	no	—
216	C₄×C₃₁	—	8	2	no	—
217	C₄×C₃₁	—	8	2	no	—
218	C₄×C₃₁	#470	1	4	yes	—
219	C₄×C₃₁	#525	1	1	yes	characteristic
220	C₄×C₃₁	#529	1	2	yes	—
221	C₄×C₃₁	#532	1	1	yes	characteristic
222	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
223	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
224	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
225	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
226	C₄×Q₁₆	—	2	4	no	—
227	#431	—	2	4	no	—
228	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
229	C₂×#106	C₂²×C₃₁	1	2	yes	—
230	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
232	C₂×#103	C₂²×C₃₁	1	2	yes	—
233	C₂×#103	C₂²×C₃₁	1	2	yes	—
234	C₂×#103	C₂²×C₃₁	1	2	yes	—
235	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
236	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
237	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
238	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
239	#391	C₂²×C₃₁	1	2	yes	—
240	#389	C₂²×C₃₁	1	2	yes	—
241	#387	—	2	2	no	—
242	#385	—	2	2	no	—
243	#380	C₂²×C₃₁	1	2	yes	—
244	C₄×C₄⋊C₄	—	2	2	no	—
245	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
246	C₄×C₂²⋊C₄	—	2	2	no	—
247	#340	C₂²×C₃₁	1	1	yes	characteristic
248	#340	C₂²×C₃₁	1	2	yes	—
249	#340	C₂²×C₃₁	1	1	yes	characteristic
250	#340	C₂²×C₃₁	1	2	yes	—
251	C₂×C₃₁	—	4	2	no	—
252	C₂×C₃₁	#2392	1	1	yes	characteristic
253	C₂×C₃₁	#3050	1	1	yes	characteristic
254	C₂×C₃₁	C₂×#470	1	1	yes	characteristic
255	C₂×C₃₁	#3107	1	2	yes	—
256	C₂×C₃₁	#3108	1	2	yes	—
257	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
258	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
259	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
260	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
261	C₂×Q₁₆	—	2	4	no	—
262	C₂×Q₁₆	—	2	2	no	—
263	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
267	C₂²⋊Q₈	—	2	4	no	—
268	C₂²⋊Q₈	—	2	4	no	—
269	C₄×Q₈	—	2	4	no	—
270	C₄×Q₈	—	2	4	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	—	2	2	no	—
281	C₂×C₄²	—	2	2	no	—
282	C₂×C₄²	—	2	2	no	—
283	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
284	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
287	#107	—	2	2	no	—
288	#106	—	2	4	no	—
289	C₄⋊C₈	—	2	2	no	—
290	C₄⋊C₈	—	2	2	no	—
291	#103	—	2	4	no	—
292	#103	—	2	4	no	—
293	#103	—	2	4	no	—
294	C₂²⋊C₈	—	2	2	no	—
295	C₂²⋊C₈	—	2	2	no	—
296	C₄×C₈	—	2	2	no	—
297	C₄×C₈	D₄×C₃₁	1	4	yes	—
298	#95	—	2	2	no	—
299	#95	—	2	2	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	C₃₁	#23699	1	1	yes	characteristic, direct product factor, Sylow
304	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	#41×C₃₁	1	4	yes	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
329	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
330	Q₁₆	—	2	8	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
338	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
339	C₄⋊C₄	—	2	8	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	4	no	—
346	C₄⋊C₄	—	4	4	no	—
347	C₄⋊C₄	#41×C₃₁	1	4	yes	—
348	C₂²⋊C₄	—	2	8	no	—
349	C₂²⋊C₄	—	4	4	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	2	1	no	—
354	C₄²	—	4	4	no	—
355	C₄²	—	4	4	no	—
356	C₄²	C₂×D₄×C₃₁	1	2	yes	—
357	C₄²	#41×C₃₁	1	2	yes	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	2	no	—
362	C₂³	C₃₁×#135	1	2	yes	—
363	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
364	Q₈	—	2	4	no	—
365	Q₈	—	2	4	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	4	2	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	C₃₁×#121	1	2	yes	—
394	C₂×C₄	C₃₁×#121	1	2	yes	—
395	C₂×C₄	C₃₁×#135	1	2	yes	—
396	C₂×C₄	C₃₁×#137	1	4	yes	—
397	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
398	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
399	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
400	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
401	C₈	—	2	2	no	—
402	C₈	—	2	2	no	—
403	C₈	—	4	1	no	—
404	C₈	—	4	1	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
411	C₂²	C₃₁×#525	1	2	yes	—
412	C₂²	C₂×C₃₁×#135	1	1	yes	characteristic
413	C₂²	C₂×C₃₁×#135	1	1	yes	characteristic
414	C₂²	C₂×C₃₁×#137	1	2	yes	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	4	4	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	4	no	—
420	C₄	—	4	1	no	—
421	C₄	—	8	2	no	—
422	C₄	—	8	2	no	—
423	C₄	C₃₁×#470	1	4	yes	—
424	C₄	C₃₁×#525	1	1	yes	characteristic
425	C₄	C₃₁×#529	1	2	yes	—
426	C₄	C₃₁×#532	1	1	yes	characteristic
427	C₂	—	4	2	no	—
428	C₂	C₃₁×#2392	1	1	yes	characteristic
429	C₂	C₃₁×#3050	1	1	yes	characteristic
430	C₂	C₂×C₃₁×#470	1	1	yes	characteristic
431	C₂	C₃₁×#3107	1	2	yes	—
432	C₂	C₃₁×#3108	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×Q₁₆×C₃₁	C₂	semidirect
4. C₃₁×#2086	C₂	semidirect
6. C₃₁×#2066	C₂	semidirect
7. C₃₁×#2056	C₂	semidirect
10. C₄×C₃₁×#106	C₂	semidirect
11. C₄×C₃₁×#103	C₂	semidirect
141. #23699	C₃₁	direct (N × H)
189. C₂×C₄×Q₁₆	C₂×C₃₁	semidirect
192. #2086	C₂×C₃₁	semidirect
194. #2066	C₂×C₃₁	semidirect
195. #2056	C₂×C₃₁	semidirect
198. C₄×#106	C₂×C₃₁	semidirect
199. C₄×#103	C₂×C₃₁	semidirect
303. C₃₁	#23699	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×C₄×Q₁₆×C₃₁	2
C₂×C₃₁×#431	2
C₄×C₃₁×C₂²⋊Q₈	2
C₃₁×#2086	2
C₃₁×#2075	2
C₃₁×#2066	2
C₃₁×#2056	2
C₃₁×#2035	2
C₃₁×#2001	2
C₄×C₃₁×#106	2
C₄×C₃₁×#103	2
#23699	31

Subgroups — C31×#23699 #21480458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#23699 #21480458