Subgroups — C₃₁×#61334 #21518093

Order 7936.

1794 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3506	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3377	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3375	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3371	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3368	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3136	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3135	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3083	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3043	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2947	C₂	1	2	yes	maximal, complemented
15	C₂×C₃₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#137	C₂²	1	2	yes	—
17	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
18	C₃₁×#559	C₂²	1	4	yes	—
19	Q₈²×C₃₁	—	2	1	no	—
20	Q₈²×C₃₁	C₂²	1	2	yes	complemented
21	C₃₁×#557	—	2	1	no	—
22	C₃₁×#557	—	2	2	no	—
23	C₃₁×#557	C₂²	1	4	yes	complemented
24	C₃₁×#557	C₂²	1	2	yes	complemented
25	C₃₁×#556	C₂²	1	2	yes	—
26	C₃₁×#555	—	2	1	no	—
27	C₃₁×#553	—	2	2	no	—
28	C₃₁×#550	C₂²	1	2	yes	—
29	C₃₁×#547	—	2	1	no	—
30	C₃₁×#544	—	2	2	no	—
31	C₃₁×#544	C₂²	1	2	yes	—
32	C₃₁×#538	—	2	2	no	—
33	C₃₁×#535	C₂²	1	2	yes	—
34	C₃₁×#533	—	2	2	no	—
35	C₃₁×#533	C₂²	1	1	yes	characteristic
36	C₃₁×#533	C₂²	1	1	yes	characteristic
37	C₃₁×#532	C₂²	1	1	yes	characteristic
38	C₃₁×#525	—	2	2	no	—
39	C₃₁×#520	C₂²	1	2	yes	—
40	C₃₁×#519	C₂²	1	2	yes	—
41	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₃₁×#491	C₂²	1	2	yes	complemented
44	C₃₁×#490	C₂²	1	4	yes	—
45	C₃₁×#490	C₂²	1	2	yes	complemented
46	C₃₁×#489	C₂²	1	4	yes	—
47	C₃₁×#489	C₂²	1	2	yes	complemented
48	C₃₁×#489	C₂²	1	2	yes	complemented
49	C₃₁×#488	C₂²	1	4	yes	—
50	C₃₁×#486	C₂²	1	4	yes	—
51	C₃₁×#479	C₂²	1	4	yes	complemented
52	C₃₁×#478	C₂²	1	4	yes	—
53	C₃₁×#478	C₂²	1	4	yes	complemented
54	C₃₁×#477	C₂²	1	4	yes	complemented
55	C₃₁×#476	C₂²	1	2	yes	—
56	C₃₁×#474	C₂²	1	2	yes	—
57	C₃₁×#474	C₂²	1	4	yes	complemented
58	C₃₁×#464	C₂²	1	4	yes	—
59	C₃₁×#464	C₂²	1	4	yes	—
60	C₃₁×#464	C₂²	1	4	yes	complemented
61	C₃₁×#462	C₂²	1	2	yes	complemented
62	C₃₁×#460	C₂²	1	4	yes	—
63	C₃₁×#460	C₂²	1	4	yes	—
64	C₃₁×#460	C₂²	1	2	yes	complemented
65	C₃₁×#446	C₂²	1	4	yes	complemented
66	C₃₁×#446	C₂²	1	4	yes	complemented
67	C₃₁×#441	C₂²	1	4	yes	complemented
68	C₃₁×#440	C₂²	1	4	yes	—
69	C₃₁×#440	C₂²	1	4	yes	—
70	C₃₁×#440	C₂²	1	4	yes	complemented
71	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	complemented
72	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
73	C₃₁×#428	C₂²	1	2	yes	—
74	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
75	C₃₁×#424	C₂²	1	2	yes	—
76	C₃₁×#423	C₂²	1	1	yes	characteristic
77	C₃₁×#418	C₂²	1	2	yes	—
78	C₃₁×#417	C₂²	1	2	yes	—
79	C₃₁×#416	C₂²	1	2	yes	—
80	C₃₁×#416	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	C₂×#41×C₃₁	—	2	2	no	—
86	C₂×#41×C₃₁	C₂³	1	2	yes	—
87	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₃₁	—	2	1	no	—
90	C₃₁×#137	—	2	8	no	—
91	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
92	C₂×SD₁₆×C₃₁	—	2	4	no	—
93	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
94	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
95	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
96	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
98	C₃₁×C₄⋊Q₈	—	2	2	no	—
99	C₃₁×C₄⋊Q₈	—	2	4	no	—
100	C₃₁×C₄⋊Q₈	—	2	2	no	—
101	C₃₁×C₄⋊Q₈	—	2	4	no	—
102	C₃₁×C₄⋊Q₈	—	2	2	no	—
103	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
104	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
105	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
106	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
107	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
108	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
109	C₃₁×#127	C₂³	1	4	yes	—
110	C₃₁×#127	C₂³	1	1	yes	characteristic
111	C₃₁×#126	—	2	4	no	—
112	C₃₁×#125	—	2	4	no	—
113	C₃₁×#125	—	2	4	no	—
114	C₃₁×#125	—	2	4	no	—
115	C₃₁×#125	—	2	2	no	—
116	C₃₁×#125	D₄	1	2	yes	—
117	C₃₁×#125	C₂³	1	2	yes	—
118	C₃₁×#125	C₂³	1	4	yes	—
119	C₃₁×#124	—	2	4	no	—
120	C₃₁×#124	C₂³	1	4	yes	—
121	C₃₁×#124	C₂³	1	2	yes	—
122	C₃₁×#123	—	2	4	no	—
123	C₃₁×#123	—	2	4	no	—
124	C₃₁×C₂²⋊Q₈	—	2	2	no	—
125	C₃₁×C₂²⋊Q₈	—	2	1	no	—
126	C₃₁×C₂²⋊Q₈	—	2	1	no	—
127	C₃₁×C₂²⋊Q₈	—	2	4	no	—
128	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
129	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
130	C₃₁×#121	—	2	1	no	—
131	C₃₁×#121	—	2	1	no	—
132	C₃₁×#121	—	2	2	no	—
133	C₃₁×#121	—	2	2	no	—
134	C₃₁×#121	—	2	2	no	—
135	C₃₁×#121	—	2	4	no	—
136	C₃₁×#120	—	2	4	no	—
137	C₄×Q₈×C₃₁	—	2	2	no	—
138	C₄×Q₈×C₃₁	—	2	2	no	—
139	C₄×Q₈×C₃₁	—	2	2	no	—
140	C₄×Q₈×C₃₁	—	2	4	no	—
141	C₄×Q₈×C₃₁	—	2	2	no	—
142	C₄×Q₈×C₃₁	—	2	1	no	—
143	C₄×Q₈×C₃₁	—	2	1	no	—
144	C₄×Q₈×C₃₁	—	2	1	no	—
145	C₄×Q₈×C₃₁	—	2	1	no	—
146	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
147	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
148	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
149	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
150	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
151	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
152	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
153	C₄×D₄×C₃₁	—	2	4	no	—
154	C₄×D₄×C₃₁	—	2	4	no	—
155	C₄×D₄×C₃₁	—	2	1	no	—
156	C₄×D₄×C₃₁	—	2	1	no	—
157	C₄×D₄×C₃₁	—	2	1	no	—
158	C₄×D₄×C₃₁	—	2	1	no	—
159	C₄×D₄×C₃₁	C₂³	1	4	yes	—
160	C₄×D₄×C₃₁	C₂³	1	2	yes	—
161	C₄×D₄×C₃₁	C₂³	1	2	yes	—
162	C₃₁×#117	—	2	2	no	—
163	C₃₁×#117	—	2	2	no	—
164	C₃₁×#117	—	2	4	no	—
165	C₃₁×#117	C₂³	1	2	yes	—
166	C₃₁×#117	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
168	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
172	C₂×C₄²×C₃₁	—	2	1	no	—
173	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
174	C₃₁×#107	C₂³	1	4	yes	—
175	C₃₁×#107	C₂³	1	4	yes	—
176	C₃₁×#106	C₂³	1	4	yes	—
177	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
178	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
179	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
180	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
181	C₃₁×#103	C₂³	1	4	yes	—
182	C₃₁×#103	C₂³	1	2	yes	—
183	C₃₁×#103	C₂³	1	2	yes	—
184	C₃₁×#103	C₂³	1	2	yes	—
185	C₃₁×#103	C₂³	1	2	yes	—
186	C₃₁×#103	C₂³	1	4	yes	—
187	C₃₁×#102	C₂³	1	4	yes	—
188	C₃₁×#102	C₂³	1	2	yes	—
189	C₃₁×#102	C₂³	1	2	yes	—
190	C₃₁×#102	C₂³	1	2	yes	—
191	C₃₁×#102	C₂³	1	2	yes	—
192	C₃₁×#102	C₂³	1	4	yes	—
193	C₃₁×#102	C₂³	1	4	yes	—
194	C₃₁×#102	C₂³	1	4	yes	—
195	C₃₁×#97	C₂³	1	2	yes	—
196	C₃₁×#97	C₂³	1	2	yes	—
197	C₃₁×#97	C₂³	1	4	yes	—
198	C₄×C₈×C₃₁	C₂³	1	4	yes	—
199	C₂⁴×C₃₁	—	2	1	no	—
200	#41×C₃₁	—	2	4	no	—
201	#41×C₃₁	—	2	4	no	—
202	#41×C₃₁	—	8	4	no	—
203	C₂×Q₈×C₃₁	—	2	1	no	—
204	C₂×Q₈×C₃₁	—	2	1	no	—
205	C₂×Q₈×C₃₁	—	2	1	no	—
206	C₂×Q₈×C₃₁	—	2	4	no	—
207	C₂×Q₈×C₃₁	—	2	2	no	—
208	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
210	C₂×Q₈×C₃₁	#41	1	4	yes	complemented
211	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
212	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
213	C₂×D₄×C₃₁	—	2	2	no	—
214	C₂×D₄×C₃₁	—	2	1	no	—
215	C₂×D₄×C₃₁	—	2	1	no	—
216	C₂×D₄×C₃₁	—	2	4	no	—
217	C₂×D₄×C₃₁	—	2	1	no	—
218	C₂×D₄×C₃₁	—	2	4	no	—
219	C₂×D₄×C₃₁	—	2	2	no	—
220	C₂×D₄×C₃₁	—	2	2	no	—
221	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
222	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₃₁	—	2	1	no	—
224	C₂²×C₄×C₃₁	—	2	1	no	—
225	C₂²×C₄×C₃₁	—	2	1	no	—
226	C₂²×C₄×C₃₁	—	2	2	no	—
227	C₂²×C₄×C₃₁	—	2	2	no	—
228	C₂²×C₄×C₃₁	—	2	4	no	—
229	C₂²×C₄×C₃₁	—	2	2	no	—
230	C₂²×C₄×C₃₁	—	8	2	no	—
231	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
234	Q₁₆×C₃₁	—	2	8	no	—
235	SD₁₆×C₃₁	—	2	8	no	—
236	SD₁₆×C₃₁	—	2	8	no	—
237	M₁₆×C₃₁	—	2	4	no	—
238	C₂×C₈×C₃₁	—	2	2	no	—
239	C₂×C₈×C₃₁	—	2	2	no	—
240	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
241	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
242	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
243	C₄⋊C₄×C₃₁	—	2	1	no	—
244	C₄⋊C₄×C₃₁	—	2	4	no	—
245	C₄⋊C₄×C₃₁	—	2	2	no	—
246	C₄⋊C₄×C₃₁	—	2	2	no	—
247	C₄⋊C₄×C₃₁	—	2	1	no	—
248	C₄⋊C₄×C₃₁	—	2	1	no	—
249	C₄⋊C₄×C₃₁	—	2	4	no	—
250	C₄⋊C₄×C₃₁	—	2	4	no	—
251	C₄⋊C₄×C₃₁	—	2	1	no	—
252	C₄⋊C₄×C₃₁	—	2	2	no	—
253	C₄⋊C₄×C₃₁	—	2	1	no	—
254	C₄⋊C₄×C₃₁	—	2	1	no	—
255	C₄⋊C₄×C₃₁	—	2	4	no	—
256	C₄⋊C₄×C₃₁	—	2	4	no	—
257	C₄⋊C₄×C₃₁	—	2	2	no	—
258	C₄⋊C₄×C₃₁	—	2	4	no	—
259	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
263	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
264	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
265	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
267	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
268	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
269	C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂²⋊C₄×C₃₁	—	2	2	no	—
272	C₂²⋊C₄×C₃₁	—	2	4	no	—
273	C₂²⋊C₄×C₃₁	—	2	4	no	—
274	C₂²⋊C₄×C₃₁	—	2	2	no	—
275	C₂²⋊C₄×C₃₁	—	2	4	no	—
276	C₂²⋊C₄×C₃₁	—	2	2	no	—
277	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
278	C₄²×C₃₁	—	2	2	no	—
279	C₄²×C₃₁	—	2	2	no	—
280	C₄²×C₃₁	—	2	4	no	—
281	C₄²×C₃₁	—	2	4	no	—
282	C₄²×C₃₁	—	2	4	no	—
283	C₄²×C₃₁	—	2	2	no	—
284	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₃₁	C₂⁴	1	4	yes	—
287	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
288	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
289	#61334	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
290	C₂³×C₃₁	—	2	2	no	—
291	C₂³×C₃₁	—	2	2	no	—
292	C₂³×C₃₁	—	4	2	no	—
293	C₂³×C₃₁	—	8	1	no	—
294	C₂³×C₃₁	—	8	1	no	—
295	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
296	Q₈×C₃₁	—	2	4	no	—
297	Q₈×C₃₁	—	2	2	no	—
298	Q₈×C₃₁	—	2	2	no	—
299	Q₈×C₃₁	—	2	2	no	—
300	Q₈×C₃₁	—	4	2	no	—
301	Q₈×C₃₁	—	4	2	no	—
302	Q₈×C₃₁	—	4	2	no	—
303	Q₈×C₃₁	—	8	1	no	—
304	Q₈×C₃₁	—	8	4	no	—
305	Q₈×C₃₁	C₂×#41	1	4	yes	—
306	D₄×C₃₁	—	2	2	no	—
307	D₄×C₃₁	—	2	2	no	—
308	D₄×C₃₁	—	2	2	no	—
309	D₄×C₃₁	—	2	2	no	—
310	D₄×C₃₁	—	4	2	no	—
311	D₄×C₃₁	—	4	4	no	—
312	D₄×C₃₁	—	4	2	no	—
313	D₄×C₃₁	—	8	1	no	—
314	D₄×C₃₁	—	8	4	no	—
315	D₄×C₃₁	—	8	4	no	—
316	C₂×C₄×C₃₁	—	2	4	no	—
317	C₂×C₄×C₃₁	—	2	2	no	—
318	C₂×C₄×C₃₁	—	2	2	no	—
319	C₂×C₄×C₃₁	—	2	2	no	—
320	C₂×C₄×C₃₁	—	2	2	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	4	1	no	—
324	C₂×C₄×C₃₁	—	4	1	no	—
325	C₂×C₄×C₃₁	—	4	4	no	—
326	C₂×C₄×C₃₁	—	4	4	no	—
327	C₂×C₄×C₃₁	—	8	2	no	—
328	C₂×C₄×C₃₁	—	8	4	no	—
329	C₂×C₄×C₃₁	—	8	1	no	—
330	C₂×C₄×C₃₁	—	8	1	no	—
331	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
334	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
335	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
339	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
340	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
341	C₈×C₃₁	—	2	2	no	—
342	C₈×C₃₁	—	2	4	no	—
343	C₈×C₃₁	—	2	2	no	—
344	#3506	C₂×C₃₁	1	1	yes	characteristic
345	#3502	C₂×C₃₁	1	1	yes	characteristic, complemented
346	#3377	C₂×C₃₁	1	4	yes	complemented
347	#3375	C₂×C₃₁	1	4	yes	complemented
348	#3371	C₂×C₃₁	1	4	yes	complemented
349	#3368	C₂×C₃₁	1	4	yes	complemented
350	#3136	C₂×C₃₁	1	2	yes	complemented
351	#3135	C₂×C₃₁	1	1	yes	characteristic, complemented
352	#3083	C₂×C₃₁	1	2	yes	complemented
353	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
354	#3043	C₂×C₃₁	1	2	yes	complemented
355	#3037	C₂×C₃₁	1	1	yes	characteristic, complemented
356	#2961	C₂×C₃₁	1	1	yes	characteristic, complemented
357	#2947	C₂×C₃₁	1	2	yes	complemented
358	C₂×#440	C₂×C₃₁	1	1	yes	characteristic, complemented
359	C₂²×C₃₁	—	2	1	no	—
360	C₂²×C₃₁	—	2	1	no	—
361	C₂²×C₃₁	—	4	2	no	—
362	C₂²×C₃₁	—	4	2	no	—
363	C₂²×C₃₁	—	4	2	no	—
364	C₂²×C₃₁	—	4	2	no	—
365	C₂²×C₃₁	—	4	2	no	—
366	C₂²×C₃₁	—	4	2	no	—
367	C₂²×C₃₁	—	8	4	no	—
368	C₂²×C₃₁	#548	1	2	yes	—
369	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
370	C₄×C₃₁	—	2	1	no	—
371	C₄×C₃₁	—	2	1	no	—
372	C₄×C₃₁	—	2	4	no	—
373	C₄×C₃₁	—	2	1	no	—
374	C₄×C₃₁	—	2	1	no	—
375	C₄×C₃₁	—	2	4	no	—
376	C₄×C₃₁	—	2	4	no	—
377	C₄×C₃₁	—	4	2	no	—
378	C₄×C₃₁	—	4	2	no	—
379	C₄×C₃₁	—	4	2	no	—
380	C₄×C₃₁	—	4	2	no	—
381	C₄×C₃₁	—	4	2	no	—
382	C₄×C₃₁	#548	1	2	yes	—
383	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
384	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
385	C₂×#137	C₂²×C₃₁	1	2	yes	—
386	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
387	#559	C₂²×C₃₁	1	4	yes	—
388	Q₈²	—	2	1	no	—
389	Q₈²	C₂²×C₃₁	1	2	yes	complemented
390	#557	—	2	1	no	—
391	#557	—	2	2	no	—
392	#557	C₂²×C₃₁	1	4	yes	complemented
393	#557	C₂²×C₃₁	1	2	yes	complemented
394	#556	C₂²×C₃₁	1	2	yes	—
395	#555	—	2	1	no	—
396	#553	—	2	2	no	—
397	#550	C₂²×C₃₁	1	2	yes	—
398	#547	—	2	1	no	—
399	#544	—	2	2	no	—
400	#544	C₂²×C₃₁	1	2	yes	—
401	#538	—	2	2	no	—
402	#535	C₂²×C₃₁	1	2	yes	—
403	#533	—	2	2	no	—
404	#533	C₂²×C₃₁	1	1	yes	characteristic
405	#533	C₂²×C₃₁	1	1	yes	characteristic
406	#532	C₂²×C₃₁	1	1	yes	characteristic
407	#525	—	2	2	no	—
408	#520	C₂²×C₃₁	1	2	yes	—
409	#519	C₂²×C₃₁	1	2	yes	—
410	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
411	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
412	#491	C₂²×C₃₁	1	2	yes	complemented
413	#490	C₂²×C₃₁	1	4	yes	—
414	#490	C₂²×C₃₁	1	2	yes	complemented
415	#489	C₂²×C₃₁	1	4	yes	—
416	#489	C₂²×C₃₁	1	2	yes	complemented
417	#489	C₂²×C₃₁	1	2	yes	complemented
418	#488	C₂²×C₃₁	1	4	yes	—
419	#486	C₂²×C₃₁	1	4	yes	—
420	#479	C₂²×C₃₁	1	4	yes	complemented
421	#478	C₂²×C₃₁	1	4	yes	—
422	#478	C₂²×C₃₁	1	4	yes	complemented
423	#477	C₂²×C₃₁	1	4	yes	complemented
424	#476	C₂²×C₃₁	1	2	yes	—
425	#474	C₂²×C₃₁	1	2	yes	—
426	#474	C₂²×C₃₁	1	4	yes	complemented
427	#464	C₂²×C₃₁	1	4	yes	—
428	#464	C₂²×C₃₁	1	4	yes	—
429	#464	C₂²×C₃₁	1	4	yes	complemented
430	#462	C₂²×C₃₁	1	2	yes	complemented
431	#460	C₂²×C₃₁	1	4	yes	—
432	#460	C₂²×C₃₁	1	4	yes	—
433	#460	C₂²×C₃₁	1	2	yes	complemented
434	#446	C₂²×C₃₁	1	4	yes	complemented
435	#446	C₂²×C₃₁	1	4	yes	complemented
436	#441	C₂²×C₃₁	1	4	yes	complemented
437	#440	C₂²×C₃₁	1	4	yes	—
438	#440	C₂²×C₃₁	1	4	yes	—
439	#440	C₂²×C₃₁	1	4	yes	complemented
440	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	complemented
441	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
442	#428	C₂²×C₃₁	1	2	yes	—
443	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
444	#424	C₂²×C₃₁	1	2	yes	—
445	#423	C₂²×C₃₁	1	1	yes	characteristic
446	#418	C₂²×C₃₁	1	2	yes	—
447	#417	C₂²×C₃₁	1	2	yes	—
448	#416	C₂²×C₃₁	1	2	yes	—
449	#416	C₂²×C₃₁	1	2	yes	—
450	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
451	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
452	#405	C₂²×C₃₁	1	2	yes	—
453	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
454	C₂×C₃₁	—	2	2	no	—
455	C₂×C₃₁	—	8	2	no	—
456	C₂×C₃₁	—	8	2	no	—
457	C₂×C₃₁	C₂×#548	1	1	yes	characteristic
458	C₂×C₃₁	#3585	1	1	yes	characteristic
459	C₂×C₃₁	#3586	1	1	yes	characteristic
460	C₂×#41	—	2	2	no	—
461	C₂×#41	C₂³×C₃₁	1	2	yes	—
462	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
463	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
464	C₂³×C₄	—	2	1	no	—
465	#137	—	2	8	no	—
466	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
467	C₂×SD₁₆	—	2	4	no	—
468	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
469	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
470	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
471	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
473	C₄⋊Q₈	—	2	2	no	—
474	C₄⋊Q₈	—	2	4	no	—
475	C₄⋊Q₈	—	2	2	no	—
476	C₄⋊Q₈	—	2	4	no	—
477	C₄⋊Q₈	—	2	2	no	—
478	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
479	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
480	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
481	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
482	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
483	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
484	#127	C₂³×C₃₁	1	1	yes	characteristic
485	#127	C₂³×C₃₁	1	4	yes	—
486	#126	—	2	4	no	—
487	#125	—	2	4	no	—
488	#125	—	2	4	no	—
489	#125	—	2	4	no	—
490	#125	—	2	2	no	—
491	#125	D₄×C₃₁	1	2	yes	—
492	#125	C₂³×C₃₁	1	2	yes	—
493	#125	C₂³×C₃₁	1	4	yes	—
494	#124	—	2	4	no	—
495	#124	C₂³×C₃₁	1	2	yes	—
496	#124	C₂³×C₃₁	1	4	yes	—
497	#123	—	2	4	no	—
498	#123	—	2	4	no	—
499	C₂²⋊Q₈	—	2	2	no	—
500	C₂²⋊Q₈	—	2	1	no	—
501	C₂²⋊Q₈	—	2	1	no	—
502	C₂²⋊Q₈	—	2	4	no	—
503	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
504	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
505	#121	—	2	1	no	—
506	#121	—	2	1	no	—
507	#121	—	2	2	no	—
508	#121	—	2	2	no	—
509	#121	—	2	2	no	—
510	#121	—	2	4	no	—
511	#120	—	2	4	no	—
512	C₄×Q₈	—	2	2	no	—
513	C₄×Q₈	—	2	2	no	—
514	C₄×Q₈	—	2	2	no	—
515	C₄×Q₈	—	2	4	no	—
516	C₄×Q₈	—	2	2	no	—
517	C₄×Q₈	—	2	1	no	—
518	C₄×Q₈	—	2	1	no	—
519	C₄×Q₈	—	2	1	no	—
520	C₄×Q₈	—	2	1	no	—
521	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
522	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
523	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
524	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
525	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
526	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
527	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
528	C₄×D₄	—	2	4	no	—
529	C₄×D₄	—	2	4	no	—
530	C₄×D₄	—	2	1	no	—
531	C₄×D₄	—	2	1	no	—
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	—	2	1	no	—
534	C₄×D₄	C₂³×C₃₁	1	2	yes	—
535	C₄×D₄	C₂³×C₃₁	1	2	yes	—
536	C₄×D₄	C₂³×C₃₁	1	4	yes	—
537	#117	—	2	2	no	—
538	#117	—	2	2	no	—
539	#117	—	2	4	no	—
540	#117	C₂³×C₃₁	1	2	yes	—
541	#117	C₂³×C₃₁	1	2	yes	—
542	C₂×C₄⋊C₄	—	2	1	no	—
543	C₂×C₄⋊C₄	—	2	2	no	—
544	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₄²	—	2	1	no	—
548	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
549	#107	C₂³×C₃₁	1	4	yes	—
550	#107	C₂³×C₃₁	1	4	yes	—
551	#106	C₂³×C₃₁	1	4	yes	—
552	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
553	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
554	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
555	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
556	#103	C₂³×C₃₁	1	4	yes	—
557	#103	C₂³×C₃₁	1	2	yes	—
558	#103	C₂³×C₃₁	1	2	yes	—
559	#103	C₂³×C₃₁	1	2	yes	—
560	#103	C₂³×C₃₁	1	2	yes	—
561	#103	C₂³×C₃₁	1	4	yes	—
562	#102	C₂³×C₃₁	1	4	yes	—
563	#102	C₂³×C₃₁	1	2	yes	—
564	#102	C₂³×C₃₁	1	2	yes	—
565	#102	C₂³×C₃₁	1	2	yes	—
566	#102	C₂³×C₃₁	1	2	yes	—
567	#102	C₂³×C₃₁	1	4	yes	—
568	#102	C₂³×C₃₁	1	4	yes	—
569	#102	C₂³×C₃₁	1	4	yes	—
570	#97	C₂³×C₃₁	1	2	yes	—
571	#97	C₂³×C₃₁	1	2	yes	—
572	#97	C₂³×C₃₁	1	4	yes	—
573	C₄×C₈	C₂³×C₃₁	1	4	yes	—
574	C₃₁	#61334	1	1	yes	characteristic, direct product factor, Sylow
575	C₂⁴	—	2	1	no	—
576	#41	—	2	4	no	—
577	#41	—	2	4	no	—
578	#41	—	8	4	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	4	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
585	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
586	C₂×Q₈	#41×C₃₁	1	4	yes	complemented
587	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
588	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
598	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	8	2	no	—
607	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
610	Q₁₆	—	2	8	no	—
611	SD₁₆	—	2	8	no	—
612	SD₁₆	—	2	8	no	—
613	M₁₆	—	2	4	no	—
614	C₂×C₈	—	2	2	no	—
615	C₂×C₈	—	2	2	no	—
616	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
617	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
618	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
636	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
637	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
638	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
639	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
640	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
642	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
643	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
644	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	2	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	2	no	—
660	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
661	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
662	C₄²	C₂⁴×C₃₁	1	4	yes	—
663	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
664	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	4	2	no	—
668	C₂³	—	8	1	no	—
669	C₂³	—	8	1	no	—
670	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
671	Q₈	—	2	4	no	—
672	Q₈	—	2	2	no	—
673	Q₈	—	2	2	no	—
674	Q₈	—	2	2	no	—
675	Q₈	—	4	2	no	—
676	Q₈	—	4	2	no	—
677	Q₈	—	4	2	no	—
678	Q₈	—	8	1	no	—
679	Q₈	—	8	4	no	—
680	Q₈	C₂×#41×C₃₁	1	4	yes	—
681	D₄	—	2	2	no	—
682	D₄	—	2	2	no	—
683	D₄	—	2	2	no	—
684	D₄	—	2	2	no	—
685	D₄	—	4	2	no	—
686	D₄	—	4	4	no	—
687	D₄	—	4	2	no	—
688	D₄	—	8	1	no	—
689	D₄	—	8	4	no	—
690	D₄	—	8	4	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	4	no	—
702	C₂×C₄	—	8	2	no	—
703	C₂×C₄	—	8	4	no	—
704	C₂×C₄	—	8	1	no	—
705	C₂×C₄	—	8	1	no	—
706	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
709	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
710	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
711	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
713	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
714	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
715	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
716	C₈	—	2	2	no	—
717	C₈	—	2	4	no	—
718	C₈	—	2	2	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	8	4	no	—
728	C₂²	C₃₁×#548	1	2	yes	—
729	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
730	C₄	—	2	4	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	4	no	—
734	C₄	—	2	1	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	4	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	C₃₁×#548	1	2	yes	—
743	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
744	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
745	C₂	—	2	2	no	—
746	C₂	—	8	2	no	—
747	C₂	—	8	2	no	—
748	C₂	C₂×C₃₁×#548	1	1	yes	characteristic
749	C₂	C₃₁×#3585	1	1	yes	characteristic
750	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	C₃₁×#3506	C₂
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
2. C₃₁×#3502	C₂	semidirect
3. C₃₁×#3377	C₂	semidirect
4. C₃₁×#3375	C₂	semidirect
5. C₃₁×#3371	C₂	semidirect
6. C₃₁×#3368	C₂	semidirect
7. C₃₁×#3136	C₂	semidirect
8. C₃₁×#3135	C₂	semidirect
9. C₃₁×#3083	C₂	semidirect
10. C₃₁×#3077	C₂	semidirect
11. C₃₁×#3043	C₂	semidirect
12. C₃₁×#3037	C₂	semidirect
13. C₃₁×#2961	C₂	semidirect
14. C₃₁×#2947	C₂	semidirect
15. C₂×C₃₁×#440	C₂	semidirect
20. Q₈²×C₃₁	C₂²	semidirect
23. C₃₁×#557	C₂²	semidirect
24. C₃₁×#557	C₂²	semidirect
43. C₃₁×#491	C₂²	semidirect
45. C₃₁×#490	C₂²	semidirect
47. C₃₁×#489	C₂²	semidirect
48. C₃₁×#489	C₂²	semidirect
51. C₃₁×#479	C₂²	semidirect
53. C₃₁×#478	C₂²	semidirect
54. C₃₁×#477	C₂²	semidirect
57. C₃₁×#474	C₂²	semidirect
60. C₃₁×#464	C₂²	semidirect
61. C₃₁×#462	C₂²	semidirect
64. C₃₁×#460	C₂²	semidirect
65. C₃₁×#446	C₂²	semidirect
66. C₃₁×#446	C₂²	semidirect
67. C₃₁×#441	C₂²	semidirect
70. C₃₁×#440	C₂²	semidirect
71. C₄×Q₁₆×C₃₁	C₂²	semidirect
72. C₄×SD₁₆×C₃₁	C₂²	semidirect
210. C₂×Q₈×C₃₁	#41	semidirect
289. #61334	C₃₁	direct (N × H)
345. #3502	C₂×C₃₁	semidirect
346. #3377	C₂×C₃₁	semidirect
347. #3375	C₂×C₃₁	semidirect
348. #3371	C₂×C₃₁	semidirect
349. #3368	C₂×C₃₁	semidirect
350. #3136	C₂×C₃₁	semidirect
351. #3135	C₂×C₃₁	semidirect
352. #3083	C₂×C₃₁	semidirect
353. #3077	C₂×C₃₁	semidirect
354. #3043	C₂×C₃₁	semidirect
355. #3037	C₂×C₃₁	semidirect
356. #2961	C₂×C₃₁	semidirect
357. #2947	C₂×C₃₁	semidirect
358. C₂×#440	C₂×C₃₁	semidirect
389. Q₈²	C₂²×C₃₁	semidirect
392. #557	C₂²×C₃₁	semidirect
393. #557	C₂²×C₃₁	semidirect
412. #491	C₂²×C₃₁	semidirect
414. #490	C₂²×C₃₁	semidirect
416. #489	C₂²×C₃₁	semidirect
417. #489	C₂²×C₃₁	semidirect
420. #479	C₂²×C₃₁	semidirect
422. #478	C₂²×C₃₁	semidirect
423. #477	C₂²×C₃₁	semidirect
426. #474	C₂²×C₃₁	semidirect
429. #464	C₂²×C₃₁	semidirect
430. #462	C₂²×C₃₁	semidirect
433. #460	C₂²×C₃₁	semidirect
434. #446	C₂²×C₃₁	semidirect
435. #446	C₂²×C₃₁	semidirect
436. #441	C₂²×C₃₁	semidirect
439. #440	C₂²×C₃₁	semidirect
440. C₄×Q₁₆	C₂²×C₃₁	semidirect
441. C₄×SD₁₆	C₂²×C₃₁	semidirect
574. C₃₁	#61334	direct (N × H)
586. C₂×Q₈	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3506	2
C₃₁×#3502	2
C₃₁×#3377	2
C₃₁×#3375	2
C₃₁×#3371	2
C₃₁×#3368	2
C₃₁×#3136	2
C₃₁×#3135	2
C₃₁×#3083	2
C₃₁×#3077	2
C₃₁×#3043	2
C₃₁×#3037	2
C₃₁×#2961	2
C₃₁×#2947	2
C₂×C₃₁×#440	2
#61334	31

Subgroups — C31×#61334 #21518093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61334 #21518093