Subgroups — C₃₁×#61377 #21518136

Order 7936.

1742 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3502	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3501	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3388	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3388	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3386	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3385	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3164	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3162	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3082	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3081	C₂	1	2	yes	maximal
11	C₃₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2949	C₂	1	2	yes	maximal
15	C₂×C₃₁×#440	C₂	1	1	yes	maximal, characteristic
16	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
17	Q₈²×C₃₁	—	2	1	no	—
18	Q₈²×C₃₁	C₂²	1	2	yes	complemented
19	C₃₁×#557	—	2	1	no	—
20	C₃₁×#557	—	2	2	no	—
21	C₃₁×#557	C₂²	1	4	yes	complemented
22	C₃₁×#557	C₂²	1	2	yes	complemented
23	C₃₁×#554	—	2	1	no	—
24	C₃₁×#554	—	2	2	no	—
25	C₃₁×#554	C₂²	1	4	yes	—
26	C₃₁×#554	C₂²	1	2	yes	—
27	D₄×Q₈×C₃₁	—	2	1	no	—
28	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
29	C₃₁×#544	—	2	2	no	—
30	C₃₁×#544	C₂²	1	2	yes	—
31	C₃₁×#544	C₂²	1	2	yes	—
32	C₃₁×#543	—	2	2	no	—
33	C₃₁×#533	—	2	2	no	—
34	C₃₁×#533	C₂²	1	1	yes	characteristic
35	C₃₁×#533	C₂²	1	1	yes	characteristic
36	C₃₁×#533	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
38	C₃₁×#519	C₂²	1	2	yes	—
39	C₃₁×#518	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#501	C₂²	1	2	yes	complemented
43	C₃₁×#501	C₂²	1	4	yes	complemented
44	C₃₁×#501	C₂²	1	2	yes	complemented
45	C₃₁×#501	C₂²	1	4	yes	complemented
46	C₃₁×#501	C₂²	1	2	yes	complemented
47	C₃₁×#501	C₂²	1	2	yes	complemented
48	C₃₁×#500	C₂²	1	4	yes	complemented
49	C₃₁×#499	C₂²	1	4	yes	complemented
50	C₃₁×#479	C₂²	1	4	yes	complemented
51	C₃₁×#479	C₂²	1	4	yes	complemented
52	C₃₁×#479	C₂²	1	4	yes	complemented
53	C₃₁×#478	C₂²	1	4	yes	—
54	C₃₁×#478	C₂²	1	4	yes	—
55	C₃₁×#478	C₂²	1	4	yes	—
56	C₃₁×#477	C₂²	1	2	yes	complemented
57	C₃₁×#477	C₂²	1	4	yes	complemented
58	C₃₁×#476	C₂²	1	2	yes	—
59	C₃₁×#476	C₂²	1	4	yes	—
60	C₃₁×#475	C₂²	1	2	yes	complemented
61	C₃₁×#475	C₂²	1	4	yes	complemented
62	C₃₁×#474	C₂²	1	2	yes	—
63	C₃₁×#474	C₂²	1	4	yes	—
64	C₃₁×#446	C₂²	1	4	yes	complemented
65	C₃₁×#446	C₂²	1	4	yes	complemented
66	C₃₁×#440	C₂²	1	4	yes	—
67	C₃₁×#440	C₂²	1	4	yes	—
68	C₃₁×#440	C₂²	1	4	yes	—
69	C₃₁×#440	C₂²	1	4	yes	—
70	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
71	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
72	C₃₁×#428	C₂²	1	2	yes	—
73	C₃₁×#428	C₂²	1	2	yes	—
74	C₃₁×#427	C₂²	1	2	yes	—
75	C₃₁×#427	C₂²	1	2	yes	—
76	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
77	C₃₁×#424	C₂²	1	2	yes	—
78	C₃₁×#423	C₂²	1	1	yes	characteristic
79	C₃₁×#419	C₂²	1	2	yes	—
80	C₃₁×#418	C₂²	1	2	yes	—
81	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
82	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
83	C₃₁×#405	C₂²	1	2	yes	—
84	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
85	C₂²×Q₈×C₃₁	—	2	2	no	—
86	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₃₁	—	2	1	no	—
89	C₂×SD₁₆×C₃₁	Q₈	1	8	yes	complemented
90	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
91	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
92	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
94	C₃₁×C₄⋊Q₈	—	2	2	no	—
95	C₃₁×C₄⋊Q₈	—	2	4	no	—
96	C₃₁×C₄⋊Q₈	—	2	2	no	—
97	C₃₁×C₄⋊Q₈	—	2	4	no	—
98	C₃₁×C₄⋊Q₈	—	2	2	no	—
99	C₃₁×C₄⋊Q₈	—	2	2	no	—
100	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
101	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
102	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
104	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
106	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
107	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
108	C₃₁×#125	—	2	4	no	—
109	C₃₁×#125	—	2	4	no	—
110	C₃₁×#125	—	2	4	no	—
111	C₃₁×#125	—	2	2	no	—
112	C₃₁×#125	—	2	2	no	—
113	C₃₁×#125	D₄	1	2	yes	—
114	C₃₁×#125	C₂³	1	4	yes	—
115	C₃₁×#125	C₂³	1	2	yes	—
116	C₃₁×#125	C₂³	1	4	yes	—
117	C₃₁×#125	C₂³	1	2	yes	—
118	C₃₁×C₂²⋊Q₈	—	2	2	no	—
119	C₃₁×C₂²⋊Q₈	—	2	4	no	—
120	C₃₁×C₂²⋊Q₈	—	2	1	no	—
121	C₃₁×C₂²⋊Q₈	—	2	1	no	—
122	C₃₁×C₂²⋊Q₈	—	2	1	no	—
123	C₃₁×C₂²⋊Q₈	—	2	1	no	—
124	C₃₁×C₂²⋊Q₈	—	2	2	no	—
125	C₃₁×C₂²⋊Q₈	—	2	4	no	—
126	C₃₁×C₂²⋊Q₈	—	2	4	no	—
127	C₃₁×C₂²⋊Q₈	—	2	4	no	—
128	C₃₁×C₂²⋊Q₈	—	2	4	no	—
129	C₃₁×C₂²⋊Q₈	—	2	4	no	—
130	C₃₁×C₂²⋊Q₈	—	2	4	no	—
131	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
132	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
133	C₄×Q₈×C₃₁	—	2	2	no	—
134	C₄×Q₈×C₃₁	—	2	2	no	—
135	C₄×Q₈×C₃₁	—	2	2	no	—
136	C₄×Q₈×C₃₁	—	2	4	no	—
137	C₄×Q₈×C₃₁	—	2	2	no	—
138	C₄×Q₈×C₃₁	—	2	1	no	—
139	C₄×Q₈×C₃₁	—	2	1	no	—
140	C₄×Q₈×C₃₁	—	2	1	no	—
141	C₄×Q₈×C₃₁	—	2	1	no	—
142	C₄×Q₈×C₃₁	—	2	1	no	—
143	C₄×Q₈×C₃₁	—	2	1	no	—
144	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
145	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
146	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
147	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
148	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
149	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
150	C₄×D₄×C₃₁	—	2	2	no	—
151	C₄×D₄×C₃₁	—	2	2	no	—
152	C₄×D₄×C₃₁	—	2	1	no	—
153	C₄×D₄×C₃₁	—	2	1	no	—
154	C₄×D₄×C₃₁	C₂³	1	4	yes	—
155	C₄×D₄×C₃₁	C₂³	1	4	yes	—
156	C₄×D₄×C₃₁	C₂³	1	2	yes	—
157	C₄×D₄×C₃₁	C₂³	1	2	yes	—
158	C₃₁×#117	—	2	4	no	—
159	C₃₁×#117	C₂³	1	2	yes	—
160	C₃₁×#117	C₂³	1	2	yes	—
161	C₃₁×#117	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
163	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
164	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
168	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
169	C₂×C₄²×C₃₁	—	2	1	no	—
170	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
171	C₃₁×#107	C₂³	1	4	yes	—
172	C₃₁×#107	C₂³	1	2	yes	—
173	C₃₁×#107	C₂³	1	2	yes	—
174	C₃₁×#107	C₂³	1	2	yes	—
175	C₃₁×#107	C₂³	1	2	yes	—
176	C₃₁×#107	C₂³	1	4	yes	—
177	C₃₁×#107	C₂³	1	4	yes	—
178	C₃₁×#106	C₂³	1	2	yes	—
179	C₃₁×#106	C₂³	1	2	yes	—
180	C₃₁×#106	C₂³	1	2	yes	—
181	C₃₁×#106	C₂³	1	2	yes	—
182	C₃₁×#106	C₂³	1	4	yes	—
183	C₃₁×#106	C₂³	1	4	yes	—
184	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
185	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
186	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
187	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
188	C₃₁×#103	C₂³	1	4	yes	—
189	C₃₁×#103	C₂³	1	4	yes	—
190	C₃₁×#103	C₂³	1	4	yes	—
191	C₃₁×#102	C₂³	1	4	yes	—
192	C₃₁×#102	C₂³	1	4	yes	—
193	C₃₁×#102	C₂³	1	4	yes	—
194	C₃₁×#97	C₂³	1	2	yes	—
195	C₃₁×#97	C₂³	1	2	yes	—
196	C₃₁×#97	C₂³	1	4	yes	—
197	C₄×C₈×C₃₁	C₂³	1	4	yes	—
198	C₂⁴×C₃₁	—	2	1	no	—
199	C₂×Q₈×C₃₁	—	2	1	no	—
200	C₂×Q₈×C₃₁	—	2	1	no	—
201	C₂×Q₈×C₃₁	—	2	1	no	—
202	C₂×Q₈×C₃₁	—	2	1	no	—
203	C₂×Q₈×C₃₁	—	2	1	no	—
204	C₂×Q₈×C₃₁	—	2	4	no	—
205	C₂×Q₈×C₃₁	—	2	4	no	—
206	C₂×Q₈×C₃₁	—	2	2	no	—
207	C₂×Q₈×C₃₁	—	8	4	no	—
208	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
210	C₂×Q₈×C₃₁	C₂×Q₈	1	4	yes	complemented
211	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
212	C₂×D₄×C₃₁	—	2	1	no	—
213	C₂×D₄×C₃₁	—	2	2	no	—
214	C₂×D₄×C₃₁	C₂×Q₈	1	4	yes	—
215	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₃₁	—	2	1	no	—
217	C₂²×C₄×C₃₁	—	2	1	no	—
218	C₂²×C₄×C₃₁	—	2	1	no	—
219	C₂²×C₄×C₃₁	—	2	2	no	—
220	C₂²×C₄×C₃₁	—	2	4	no	—
221	C₂²×C₄×C₃₁	—	2	4	no	—
222	C₂²×C₄×C₃₁	—	2	2	no	—
223	C₂²×C₄×C₃₁	—	8	2	no	—
224	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
227	SD₁₆×C₃₁	C₂×Q₈	1	16	yes	complemented
228	M₁₆×C₃₁	—	2	4	no	—
229	C₂×C₈×C₃₁	—	2	2	no	—
230	C₂×C₈×C₃₁	C₂×Q₈	1	4	yes	complemented
231	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
232	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
233	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
234	C₄⋊C₄×C₃₁	—	2	2	no	—
235	C₄⋊C₄×C₃₁	—	2	1	no	—
236	C₄⋊C₄×C₃₁	—	2	2	no	—
237	C₄⋊C₄×C₃₁	—	2	2	no	—
238	C₄⋊C₄×C₃₁	—	2	4	no	—
239	C₄⋊C₄×C₃₁	—	2	4	no	—
240	C₄⋊C₄×C₃₁	—	2	4	no	—
241	C₄⋊C₄×C₃₁	—	2	1	no	—
242	C₄⋊C₄×C₃₁	—	2	1	no	—
243	C₄⋊C₄×C₃₁	—	2	4	no	—
244	C₄⋊C₄×C₃₁	—	2	4	no	—
245	C₄⋊C₄×C₃₁	—	2	2	no	—
246	C₄⋊C₄×C₃₁	—	2	1	no	—
247	C₄⋊C₄×C₃₁	—	2	2	no	—
248	C₄⋊C₄×C₃₁	—	2	1	no	—
249	C₄⋊C₄×C₃₁	—	2	1	no	—
250	C₄⋊C₄×C₃₁	—	2	4	no	—
251	C₄⋊C₄×C₃₁	—	2	4	no	—
252	C₄⋊C₄×C₃₁	—	2	2	no	—
253	C₄⋊C₄×C₃₁	—	2	4	no	—
254	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
256	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
259	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
266	C₂²⋊C₄×C₃₁	—	2	2	no	—
267	C₂²⋊C₄×C₃₁	—	2	2	no	—
268	C₂²⋊C₄×C₃₁	—	2	4	no	—
269	C₂²⋊C₄×C₃₁	—	2	4	no	—
270	C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂²⋊C₄×C₃₁	—	2	2	no	—
272	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
273	C₄²×C₃₁	—	2	2	no	—
274	C₄²×C₃₁	—	2	2	no	—
275	C₄²×C₃₁	—	2	4	no	—
276	C₄²×C₃₁	—	2	4	no	—
277	C₄²×C₃₁	—	2	2	no	—
278	C₄²×C₃₁	—	2	2	no	—
279	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₃₁	C₂⁴	1	4	yes	—
282	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
283	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
284	#61377	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
285	C₂³×C₃₁	—	2	2	no	—
286	C₂³×C₃₁	—	2	4	no	—
287	C₂³×C₃₁	—	8	1	no	—
288	C₂³×C₃₁	—	8	1	no	—
289	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
290	Q₈×C₃₁	—	2	4	no	—
291	Q₈×C₃₁	—	2	2	no	—
292	Q₈×C₃₁	—	4	2	no	—
293	Q₈×C₃₁	—	4	2	no	—
294	Q₈×C₃₁	—	4	2	no	—
295	Q₈×C₃₁	—	4	2	no	—
296	Q₈×C₃₁	—	8	1	no	—
297	Q₈×C₃₁	—	8	4	no	—
298	Q₈×C₃₁	—	8	1	no	—
299	Q₈×C₃₁	—	8	4	no	—
300	Q₈×C₃₁	C₂²×Q₈	1	4	yes	—
301	D₄×C₃₁	—	2	4	no	—
302	D₄×C₃₁	—	2	2	no	—
303	D₄×C₃₁	C₂²×Q₈	1	4	yes	—
304	C₂×C₄×C₃₁	—	2	4	no	—
305	C₂×C₄×C₃₁	—	2	2	no	—
306	C₂×C₄×C₃₁	—	2	2	no	—
307	C₂×C₄×C₃₁	—	2	2	no	—
308	C₂×C₄×C₃₁	—	2	2	no	—
309	C₂×C₄×C₃₁	—	2	2	no	—
310	C₂×C₄×C₃₁	—	2	2	no	—
311	C₂×C₄×C₃₁	—	2	2	no	—
312	C₂×C₄×C₃₁	—	4	1	no	—
313	C₂×C₄×C₃₁	—	4	1	no	—
314	C₂×C₄×C₃₁	—	4	4	no	—
315	C₂×C₄×C₃₁	—	8	4	no	—
316	C₂×C₄×C₃₁	—	8	2	no	—
317	C₂×C₄×C₃₁	—	8	4	no	—
318	C₂×C₄×C₃₁	—	8	1	no	—
319	C₂×C₄×C₃₁	—	8	1	no	—
320	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
323	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
324	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
328	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
329	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
330	C₈×C₃₁	—	2	2	no	—
331	C₈×C₃₁	—	2	4	no	—
332	C₈×C₃₁	C₂²×Q₈	1	4	yes	—
333	#3502	C₂×C₃₁	1	1	yes	characteristic, complemented
334	#3501	C₂×C₃₁	1	1	yes	characteristic
335	#3388	C₂×C₃₁	1	4	yes	complemented
336	#3388	C₂×C₃₁	1	4	yes	complemented
337	#3386	C₂×C₃₁	1	4	yes	complemented
338	#3385	C₂×C₃₁	1	4	yes	complemented
339	#3164	C₂×C₃₁	1	2	yes	complemented
340	#3162	C₂×C₃₁	1	1	yes	characteristic, complemented
341	#3082	C₂×C₃₁	1	2	yes	complemented
342	#3081	C₂×C₃₁	1	2	yes	—
343	#3078	C₂×C₃₁	1	1	yes	characteristic, complemented
344	#3077	C₂×C₃₁	1	1	yes	characteristic
345	#2961	C₂×C₃₁	1	1	yes	characteristic, complemented
346	#2949	C₂×C₃₁	1	2	yes	—
347	C₂×#440	C₂×C₃₁	1	1	yes	characteristic
348	C₂²×C₃₁	—	2	1	no	—
349	C₂²×C₃₁	—	2	1	no	—
350	C₂²×C₃₁	—	2	4	no	—
351	C₂²×C₃₁	—	4	2	no	—
352	C₂²×C₃₁	—	4	2	no	—
353	C₂²×C₃₁	—	8	4	no	—
354	C₂²×C₃₁	D₄×Q₈	1	2	yes	—
355	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
356	C₄×C₃₁	—	2	1	no	—
357	C₄×C₃₁	—	2	1	no	—
358	C₄×C₃₁	—	2	4	no	—
359	C₄×C₃₁	—	2	1	no	—
360	C₄×C₃₁	—	2	1	no	—
361	C₄×C₃₁	—	2	4	no	—
362	C₄×C₃₁	—	2	4	no	—
363	C₄×C₃₁	—	4	2	no	—
364	C₄×C₃₁	—	4	2	no	—
365	C₄×C₃₁	—	4	2	no	—
366	C₄×C₃₁	—	4	2	no	—
367	C₄×C₃₁	—	4	2	no	—
368	C₄×C₃₁	—	4	2	no	—
369	C₄×C₃₁	D₄×Q₈	1	2	yes	—
370	C₄×C₃₁	C₂³×Q₈	1	1	yes	characteristic
371	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
372	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
373	Q₈²	—	2	1	no	—
374	Q₈²	C₂²×C₃₁	1	2	yes	complemented
375	#557	—	2	1	no	—
376	#557	—	2	2	no	—
377	#557	C₂²×C₃₁	1	4	yes	complemented
378	#557	C₂²×C₃₁	1	2	yes	complemented
379	#554	—	2	1	no	—
380	#554	—	2	2	no	—
381	#554	C₂²×C₃₁	1	4	yes	—
382	#554	C₂²×C₃₁	1	2	yes	—
383	D₄×Q₈	—	2	1	no	—
384	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
385	#544	—	2	2	no	—
386	#544	C₂²×C₃₁	1	2	yes	—
387	#544	C₂²×C₃₁	1	2	yes	—
388	#543	—	2	2	no	—
389	#533	—	2	2	no	—
390	#533	C₂²×C₃₁	1	1	yes	characteristic
391	#533	C₂²×C₃₁	1	1	yes	characteristic
392	#533	C₂²×C₃₁	1	1	yes	characteristic
393	C₂×C₂²⋊Q₈	—	2	2	no	—
394	#519	C₂²×C₃₁	1	2	yes	—
395	#518	C₂²×C₃₁	1	2	yes	—
396	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
397	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
398	#501	C₂²×C₃₁	1	2	yes	complemented
399	#501	C₂²×C₃₁	1	4	yes	complemented
400	#501	C₂²×C₃₁	1	2	yes	complemented
401	#501	C₂²×C₃₁	1	4	yes	complemented
402	#501	C₂²×C₃₁	1	2	yes	complemented
403	#501	C₂²×C₃₁	1	2	yes	complemented
404	#500	C₂²×C₃₁	1	4	yes	complemented
405	#499	C₂²×C₃₁	1	4	yes	complemented
406	#479	C₂²×C₃₁	1	4	yes	complemented
407	#479	C₂²×C₃₁	1	4	yes	complemented
408	#479	C₂²×C₃₁	1	4	yes	complemented
409	#478	C₂²×C₃₁	1	4	yes	—
410	#478	C₂²×C₃₁	1	4	yes	—
411	#478	C₂²×C₃₁	1	4	yes	—
412	#477	C₂²×C₃₁	1	2	yes	complemented
413	#477	C₂²×C₃₁	1	4	yes	complemented
414	#476	C₂²×C₃₁	1	2	yes	—
415	#476	C₂²×C₃₁	1	4	yes	—
416	#475	C₂²×C₃₁	1	2	yes	complemented
417	#475	C₂²×C₃₁	1	4	yes	complemented
418	#474	C₂²×C₃₁	1	2	yes	—
419	#474	C₂²×C₃₁	1	4	yes	—
420	#446	C₂²×C₃₁	1	4	yes	complemented
421	#446	C₂²×C₃₁	1	4	yes	complemented
422	#440	C₂²×C₃₁	1	4	yes	—
423	#440	C₂²×C₃₁	1	4	yes	—
424	#440	C₂²×C₃₁	1	4	yes	—
425	#440	C₂²×C₃₁	1	4	yes	—
426	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
427	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
428	#428	C₂²×C₃₁	1	2	yes	—
429	#428	C₂²×C₃₁	1	2	yes	—
430	#427	C₂²×C₃₁	1	2	yes	—
431	#427	C₂²×C₃₁	1	2	yes	—
432	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
433	#424	C₂²×C₃₁	1	2	yes	—
434	#423	C₂²×C₃₁	1	1	yes	characteristic
435	#419	C₂²×C₃₁	1	2	yes	—
436	#418	C₂²×C₃₁	1	2	yes	—
437	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
438	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
439	#405	C₂²×C₃₁	1	2	yes	—
440	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
441	C₂×C₃₁	—	2	2	no	—
442	C₂×C₃₁	—	4	4	no	—
443	C₂×C₃₁	C₂×D₄×Q₈	1	1	yes	characteristic
444	C₂×C₃₁	#3585	1	1	yes	characteristic
445	C₂×C₃₁	#3586	1	1	yes	characteristic
446	C₂²×Q₈	—	2	2	no	—
447	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
448	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
449	C₂³×C₄	—	2	1	no	—
450	C₂×SD₁₆	Q₈×C₃₁	1	8	yes	complemented
451	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
452	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
453	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
454	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
455	C₄⋊Q₈	—	2	2	no	—
456	C₄⋊Q₈	—	2	4	no	—
457	C₄⋊Q₈	—	2	2	no	—
458	C₄⋊Q₈	—	2	4	no	—
459	C₄⋊Q₈	—	2	2	no	—
460	C₄⋊Q₈	—	2	2	no	—
461	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
462	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
463	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
464	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
465	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
466	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
467	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
468	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
469	#125	—	2	4	no	—
470	#125	—	2	4	no	—
471	#125	—	2	4	no	—
472	#125	—	2	2	no	—
473	#125	—	2	2	no	—
474	#125	D₄×C₃₁	1	2	yes	—
475	#125	C₂³×C₃₁	1	2	yes	—
476	#125	C₂³×C₃₁	1	2	yes	—
477	#125	C₂³×C₃₁	1	4	yes	—
478	#125	C₂³×C₃₁	1	4	yes	—
479	C₂²⋊Q₈	—	2	2	no	—
480	C₂²⋊Q₈	—	2	4	no	—
481	C₂²⋊Q₈	—	2	1	no	—
482	C₂²⋊Q₈	—	2	1	no	—
483	C₂²⋊Q₈	—	2	1	no	—
484	C₂²⋊Q₈	—	2	1	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	4	no	—
487	C₂²⋊Q₈	—	2	4	no	—
488	C₂²⋊Q₈	—	2	4	no	—
489	C₂²⋊Q₈	—	2	4	no	—
490	C₂²⋊Q₈	—	2	4	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
493	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
494	C₄×Q₈	—	2	2	no	—
495	C₄×Q₈	—	2	2	no	—
496	C₄×Q₈	—	2	2	no	—
497	C₄×Q₈	—	2	4	no	—
498	C₄×Q₈	—	2	2	no	—
499	C₄×Q₈	—	2	1	no	—
500	C₄×Q₈	—	2	1	no	—
501	C₄×Q₈	—	2	1	no	—
502	C₄×Q₈	—	2	1	no	—
503	C₄×Q₈	—	2	1	no	—
504	C₄×Q₈	—	2	1	no	—
505	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
506	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
507	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
508	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
509	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
510	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	1	no	—
514	C₄×D₄	—	2	1	no	—
515	C₄×D₄	C₂³×C₃₁	1	2	yes	—
516	C₄×D₄	C₂³×C₃₁	1	2	yes	—
517	C₄×D₄	C₂³×C₃₁	1	4	yes	—
518	C₄×D₄	C₂³×C₃₁	1	4	yes	—
519	#117	—	2	4	no	—
520	#117	C₂³×C₃₁	1	2	yes	—
521	#117	C₂³×C₃₁	1	2	yes	—
522	#117	C₂³×C₃₁	1	2	yes	—
523	C₂×C₄⋊C₄	—	2	1	no	—
524	C₂×C₄⋊C₄	—	2	4	no	—
525	C₂×C₄⋊C₄	—	2	2	no	—
526	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₂²⋊C₄	—	2	4	no	—
530	C₂×C₄²	—	2	1	no	—
531	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
532	#107	C₂³×C₃₁	1	4	yes	—
533	#107	C₂³×C₃₁	1	2	yes	—
534	#107	C₂³×C₃₁	1	2	yes	—
535	#107	C₂³×C₃₁	1	2	yes	—
536	#107	C₂³×C₃₁	1	2	yes	—
537	#107	C₂³×C₃₁	1	4	yes	—
538	#107	C₂³×C₃₁	1	4	yes	—
539	#106	C₂³×C₃₁	1	2	yes	—
540	#106	C₂³×C₃₁	1	2	yes	—
541	#106	C₂³×C₃₁	1	2	yes	—
542	#106	C₂³×C₃₁	1	2	yes	—
543	#106	C₂³×C₃₁	1	4	yes	—
544	#106	C₂³×C₃₁	1	4	yes	—
545	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
546	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
547	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
548	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
549	#103	C₂³×C₃₁	1	4	yes	—
550	#103	C₂³×C₃₁	1	4	yes	—
551	#103	C₂³×C₃₁	1	4	yes	—
552	#102	C₂³×C₃₁	1	4	yes	—
553	#102	C₂³×C₃₁	1	4	yes	—
554	#102	C₂³×C₃₁	1	4	yes	—
555	#97	C₂³×C₃₁	1	2	yes	—
556	#97	C₂³×C₃₁	1	2	yes	—
557	#97	C₂³×C₃₁	1	4	yes	—
558	C₄×C₈	C₂³×C₃₁	1	4	yes	—
559	C₃₁	#61377	1	1	yes	characteristic, direct product factor, Sylow
560	C₂⁴	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	4	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	—	8	4	no	—
570	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
571	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
572	C₂×Q₈	C₂×Q₈×C₃₁	1	4	yes	complemented
573	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	C₂×Q₈×C₃₁	1	4	yes	—
577	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	8	2	no	—
586	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
589	SD₁₆	C₂×Q₈×C₃₁	1	16	yes	complemented
590	M₁₆	—	2	4	no	—
591	C₂×C₈	—	2	2	no	—
592	C₂×C₈	C₂×Q₈×C₃₁	1	4	yes	complemented
593	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
594	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
595	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
617	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
618	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
619	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
620	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
621	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
622	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
623	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
624	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
625	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
635	C₄²	—	2	2	no	—
636	C₄²	—	2	2	no	—
637	C₄²	—	2	4	no	—
638	C₄²	—	2	4	no	—
639	C₄²	—	2	2	no	—
640	C₄²	—	2	2	no	—
641	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
642	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
643	C₄²	C₂⁴×C₃₁	1	4	yes	—
644	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
645	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
646	C₂³	—	2	2	no	—
647	C₂³	—	2	4	no	—
648	C₂³	—	8	1	no	—
649	C₂³	—	8	1	no	—
650	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
651	Q₈	—	2	4	no	—
652	Q₈	—	2	2	no	—
653	Q₈	—	4	2	no	—
654	Q₈	—	4	2	no	—
655	Q₈	—	4	2	no	—
656	Q₈	—	4	2	no	—
657	Q₈	—	8	1	no	—
658	Q₈	—	8	4	no	—
659	Q₈	—	8	1	no	—
660	Q₈	—	8	4	no	—
661	Q₈	C₂²×Q₈×C₃₁	1	4	yes	—
662	D₄	—	2	4	no	—
663	D₄	—	2	2	no	—
664	D₄	C₂²×Q₈×C₃₁	1	4	yes	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	4	no	—
676	C₂×C₄	—	8	4	no	—
677	C₂×C₄	—	8	2	no	—
678	C₂×C₄	—	8	4	no	—
679	C₂×C₄	—	8	1	no	—
680	C₂×C₄	—	8	1	no	—
681	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
682	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
683	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
684	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
685	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
686	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
687	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
688	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
689	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
690	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
691	C₈	—	2	2	no	—
692	C₈	—	2	4	no	—
693	C₈	C₂²×Q₈×C₃₁	1	4	yes	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	8	4	no	—
700	C₂²	D₄×Q₈×C₃₁	1	2	yes	—
701	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
702	C₄	—	2	4	no	—
703	C₄	—	2	1	no	—
704	C₄	—	2	1	no	—
705	C₄	—	2	4	no	—
706	C₄	—	2	1	no	—
707	C₄	—	2	1	no	—
708	C₄	—	2	4	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	D₄×Q₈×C₃₁	1	2	yes	—
716	C₄	C₂³×Q₈×C₃₁	1	1	yes	characteristic
717	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
718	C₂	—	2	2	no	—
719	C₂	—	4	4	no	—
720	C₂	C₂×D₄×Q₈×C₃₁	1	1	yes	characteristic
721	C₂	C₃₁×#3585	1	1	yes	characteristic
722	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3502	C₂	semidirect
3. C₃₁×#3388	C₂	semidirect
4. C₃₁×#3388	C₂	semidirect
5. C₃₁×#3386	C₂	semidirect
6. C₃₁×#3385	C₂	semidirect
7. C₃₁×#3164	C₂	semidirect
8. C₃₁×#3162	C₂	semidirect
9. C₃₁×#3082	C₂	semidirect
11. C₃₁×#3078	C₂	semidirect
13. C₃₁×#2961	C₂	semidirect
18. Q₈²×C₃₁	C₂²	semidirect
21. C₃₁×#557	C₂²	semidirect
22. C₃₁×#557	C₂²	semidirect
42. C₃₁×#501	C₂²	semidirect
43. C₃₁×#501	C₂²	semidirect
44. C₃₁×#501	C₂²	semidirect
45. C₃₁×#501	C₂²	semidirect
46. C₃₁×#501	C₂²	semidirect
47. C₃₁×#501	C₂²	semidirect
48. C₃₁×#500	C₂²	semidirect
49. C₃₁×#499	C₂²	semidirect
50. C₃₁×#479	C₂²	semidirect
51. C₃₁×#479	C₂²	semidirect
52. C₃₁×#479	C₂²	semidirect
56. C₃₁×#477	C₂²	semidirect
57. C₃₁×#477	C₂²	semidirect
60. C₃₁×#475	C₂²	semidirect
61. C₃₁×#475	C₂²	semidirect
64. C₃₁×#446	C₂²	semidirect
65. C₃₁×#446	C₂²	semidirect
89. C₂×SD₁₆×C₃₁	Q₈	semidirect
210. C₂×Q₈×C₃₁	C₂×Q₈	semidirect
227. SD₁₆×C₃₁	C₂×Q₈	semidirect
230. C₂×C₈×C₃₁	C₂×Q₈	semidirect
284. #61377	C₃₁	direct (N × H)
333. #3502	C₂×C₃₁	semidirect
335. #3388	C₂×C₃₁	semidirect
336. #3388	C₂×C₃₁	semidirect
337. #3386	C₂×C₃₁	semidirect
338. #3385	C₂×C₃₁	semidirect
339. #3164	C₂×C₃₁	semidirect
340. #3162	C₂×C₃₁	semidirect
341. #3082	C₂×C₃₁	semidirect
343. #3078	C₂×C₃₁	semidirect
345. #2961	C₂×C₃₁	semidirect
374. Q₈²	C₂²×C₃₁	semidirect
377. #557	C₂²×C₃₁	semidirect
378. #557	C₂²×C₃₁	semidirect
398. #501	C₂²×C₃₁	semidirect
399. #501	C₂²×C₃₁	semidirect
400. #501	C₂²×C₃₁	semidirect
401. #501	C₂²×C₃₁	semidirect
402. #501	C₂²×C₃₁	semidirect
403. #501	C₂²×C₃₁	semidirect
404. #500	C₂²×C₃₁	semidirect
405. #499	C₂²×C₃₁	semidirect
406. #479	C₂²×C₃₁	semidirect
407. #479	C₂²×C₃₁	semidirect
408. #479	C₂²×C₃₁	semidirect
412. #477	C₂²×C₃₁	semidirect
413. #477	C₂²×C₃₁	semidirect
416. #475	C₂²×C₃₁	semidirect
417. #475	C₂²×C₃₁	semidirect
420. #446	C₂²×C₃₁	semidirect
421. #446	C₂²×C₃₁	semidirect
450. C₂×SD₁₆	Q₈×C₃₁	semidirect
559. C₃₁	#61377	direct (N × H)
572. C₂×Q₈	C₂×Q₈×C₃₁	semidirect
589. SD₁₆	C₂×Q₈×C₃₁	semidirect
592. C₂×C₈	C₂×Q₈×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3502	2
C₃₁×#3501	2
C₃₁×#3388	2
C₃₁×#3386	2
C₃₁×#3385	2
C₃₁×#3164	2
C₃₁×#3162	2
C₃₁×#3082	2
C₃₁×#3081	2
C₃₁×#3078	2
C₃₁×#3077	2
C₃₁×#2961	2
C₃₁×#2949	2
C₂×C₃₁×#440	2
#61377	31

Subgroups — C31×#61377 #21518136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61377 #21518136