Subgroups — C₃₁×#61847 #21518606

Order 7936.

1772 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3389	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3384	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3380	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3366	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3366	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3358	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3241	C₂	1	4	yes	maximal, complemented
10	C₃₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3122	C₂	1	4	yes	maximal, complemented
13	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#562	—	2	2	no	—
17	C₃₁×#554	—	2	1	no	—
18	C₃₁×#554	—	2	2	no	—
19	C₃₁×#554	C₂²	1	2	yes	—
20	C₃₁×#554	C₂²	1	4	yes	—
21	C₃₁×#554	C₂²	1	2	yes	complemented
22	C₃₁×#554	C₂²	1	2	yes	complemented
23	C₃₁×#550	C₂²	1	2	yes	complemented
24	C₃₁×#550	C₂²	1	2	yes	complemented
25	D₄×Q₈×C₃₁	—	2	1	no	—
26	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
27	C₃₁×#547	—	2	1	no	—
28	C₃₁×#547	—	2	1	no	—
29	C₃₁×#544	C₂²	1	2	yes	—
30	C₃₁×#543	—	2	2	no	—
31	C₃₁×#540	C₂²	1	4	yes	—
32	C₃₁×#537	—	2	2	no	—
33	C₃₁×#537	—	2	2	no	—
34	C₃₁×#533	C₂²	1	1	yes	characteristic
35	C₃₁×#533	C₂²	1	1	yes	characteristic
36	C₃₁×#532	C₂²	1	1	yes	characteristic
37	C₃₁×#532	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
39	C₃₁×#518	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₃₁×#501	C₂²	1	4	yes	complemented
42	C₃₁×#501	C₂²	1	2	yes	complemented
43	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#499	C₂²	1	4	yes	complemented
45	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#490	C₂²	1	2	yes	complemented
47	C₃₁×#490	C₂²	1	4	yes	complemented
48	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#486	C₂²	1	4	yes	complemented
50	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#482	C₂²	1	4	yes	—
52	C₃₁×#482	C₂²	1	4	yes	—
53	C₃₁×#481	C₂²	1	2	yes	—
54	C₃₁×#480	C₂²	1	2	yes	—
55	C₃₁×#478	C₂²	1	4	yes	—
56	C₃₁×#478	C₂²	1	4	yes	—
57	C₃₁×#478	C₂²	1	4	yes	complemented
58	C₃₁×#478	C₂²	1	4	yes	complemented
59	C₃₁×#478	C₂²	1	4	yes	complemented
60	C₃₁×#476	C₂²	1	2	yes	—
61	C₃₁×#476	C₂²	1	2	yes	complemented
62	C₃₁×#476	C₂²	1	4	yes	complemented
63	C₃₁×#474	C₂²	1	2	yes	—
64	C₃₁×#474	C₂²	1	2	yes	complemented
65	C₃₁×#474	C₂²	1	4	yes	complemented
66	C₃₁×#459	C₂²	1	2	yes	—
67	C₃₁×#459	C₂²	1	2	yes	—
68	C₃₁×#459	C₂²	1	4	yes	—
69	C₃₁×#459	C₂²	1	4	yes	—
70	C₃₁×#447	C₂²	1	2	yes	—
71	C₃₁×#447	C₂²	1	2	yes	—
72	C₃₁×#446	C₂²	1	2	yes	complemented
73	C₃₁×#446	C₂²	1	4	yes	complemented
74	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
75	C₃₁×#442	C₂²	1	4	yes	—
76	C₃₁×#442	C₂²	1	4	yes	—
77	C₃₁×#442	C₂²	1	4	yes	—
78	C₄×D₈×C₃₁	C₂²	1	2	yes	—
79	C₄×D₈×C₃₁	C₂²	1	2	yes	—
80	C₄×D₈×C₃₁	C₂²	1	4	yes	—
81	C₄×D₈×C₃₁	C₂²	1	4	yes	—
82	C₃₁×#433	C₂²	1	4	yes	—
83	C₃₁×#432	C₂²	1	1	yes	characteristic
84	C₃₁×#431	C₂²	1	1	yes	characteristic
85	C₂×#41×C₃₁	—	2	2	no	—
86	C₂×#41×C₃₁	—	2	2	no	—
87	C₂×#41×C₃₁	—	2	1	no	—
88	C₂×#41×C₃₁	—	2	1	no	—
89	C₂²×Q₈×C₃₁	—	2	2	no	—
90	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₃₁	—	2	1	no	—
92	C₂×D₈×C₃₁	C₂³	1	2	yes	—
93	C₂×D₈×C₃₁	C₂³	1	2	yes	—
94	C₂×D₈×C₃₁	C₂³	1	4	yes	—
95	C₃₁×C₄⋊Q₈	—	2	2	no	—
96	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
97	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
98	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
101	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
102	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₃₁×#127	C₂³	1	1	yes	characteristic
104	C₃₁×#127	C₂³	1	4	yes	—
105	C₃₁×#127	C₂³	1	1	yes	characteristic
106	C₃₁×#125	—	2	2	no	—
107	C₃₁×#125	D₄	1	2	yes	—
108	C₃₁×#125	C₂³	1	4	yes	—
109	C₃₁×#125	C₂³	1	4	yes	—
110	C₃₁×#125	C₂³	1	2	yes	—
111	C₃₁×#124	—	2	1	no	—
112	C₃₁×#124	—	2	1	no	—
113	C₃₁×#123	—	2	4	no	—
114	C₃₁×#123	—	2	4	no	—
115	C₃₁×C₂²⋊Q₈	—	2	2	no	—
116	C₃₁×C₂²⋊Q₈	—	2	2	no	—
117	C₃₁×C₂²⋊Q₈	—	2	2	no	—
118	C₃₁×C₂²⋊Q₈	—	2	4	no	—
119	C₃₁×C₂²⋊Q₈	—	2	1	no	—
120	C₃₁×C₂²⋊Q₈	—	2	1	no	—
121	C₃₁×C₂²⋊Q₈	—	2	2	no	—
122	C₃₁×C₂²⋊Q₈	—	2	4	no	—
123	C₃₁×C₂²⋊Q₈	—	2	4	no	—
124	C₃₁×C₂²⋊Q₈	—	2	4	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	D₄	1	2	yes	—
130	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
131	C₃₁×#121	—	2	1	no	—
132	C₃₁×#121	—	2	1	no	—
133	C₃₁×#121	—	2	2	no	—
134	C₃₁×#121	—	2	2	no	—
135	C₃₁×#121	—	2	4	no	—
136	C₃₁×#121	—	2	4	no	—
137	C₃₁×#121	—	2	4	no	—
138	C₃₁×#121	—	2	4	no	—
139	C₃₁×#121	C₂³	1	2	yes	—
140	C₃₁×#121	C₂³	1	2	yes	—
141	C₄×Q₈×C₃₁	—	2	1	no	—
142	C₄×Q₈×C₃₁	—	2	1	no	—
143	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
144	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
145	C₄×D₄×C₃₁	—	2	2	no	—
146	C₄×D₄×C₃₁	—	2	2	no	—
147	C₄×D₄×C₃₁	—	2	1	no	—
148	C₄×D₄×C₃₁	—	2	1	no	—
149	C₄×D₄×C₃₁	—	2	1	no	—
150	C₄×D₄×C₃₁	—	2	1	no	—
151	C₄×D₄×C₃₁	C₂³	1	2	yes	—
152	C₄×D₄×C₃₁	C₂³	1	2	yes	—
153	C₄×D₄×C₃₁	C₂³	1	4	yes	—
154	C₄×D₄×C₃₁	C₂³	1	4	yes	—
155	C₄×D₄×C₃₁	C₂³	1	4	yes	—
156	C₄×D₄×C₃₁	C₂³	1	4	yes	—
157	C₄×D₄×C₃₁	C₂³	1	2	yes	—
158	C₄×D₄×C₃₁	C₂³	1	2	yes	—
159	C₃₁×#117	C₂³	1	2	yes	—
160	C₃₁×#117	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
162	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
163	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
164	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
167	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
168	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
169	C₃₁×#107	C₂³	1	2	yes	—
170	C₃₁×#107	C₂³	1	2	yes	—
171	C₃₁×#107	C₂³	1	4	yes	—
172	C₃₁×#107	C₂³	1	4	yes	—
173	C₃₁×#106	C₂³	1	4	yes	—
174	C₃₁×#106	C₂³	1	4	yes	—
175	C₃₁×#106	C₂³	1	4	yes	—
176	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
177	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
178	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
179	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
180	C₃₁×#102	C₂³	1	2	yes	—
181	C₃₁×#102	C₂³	1	2	yes	—
182	C₃₁×#102	C₂³	1	4	yes	—
183	C₃₁×#102	C₂³	1	4	yes	—
184	C₃₁×#102	C₂³	1	2	yes	—
185	C₃₁×#102	C₂³	1	4	yes	—
186	C₃₁×#102	C₂³	1	2	yes	—
187	C₃₁×#102	C₂³	1	4	yes	—
188	C₃₁×#102	C₂³	1	4	yes	—
189	C₃₁×#102	C₂³	1	4	yes	—
190	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₃₁×#97	C₂³	1	2	yes	—
193	C₃₁×#97	C₂³	1	4	yes	—
194	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₃₁	C₂³	1	4	yes	—
197	C₂⁴×C₃₁	—	2	1	no	—
198	#41×C₃₁	—	8	2	no	—
199	#41×C₃₁	—	8	2	no	—
200	#41×C₃₁	—	8	4	no	—
201	#41×C₃₁	—	8	4	no	—
202	C₂×Q₈×C₃₁	—	2	1	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	—	8	4	no	—
208	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	2	2	no	—
212	C₂×D₄×C₃₁	—	2	2	no	—
213	C₂×D₄×C₃₁	—	2	1	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	4	no	—
218	C₂×D₄×C₃₁	—	2	1	no	—
219	C₂×D₄×C₃₁	—	2	1	no	—
220	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
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	2	no	—
225	C₂²×C₄×C₃₁	—	2	2	no	—
226	C₂²×C₄×C₃₁	—	2	2	no	—
227	C₂²×C₄×C₃₁	—	2	4	no	—
228	C₂²×C₄×C₃₁	—	2	4	no	—
229	C₂²×C₄×C₃₁	—	2	2	no	—
230	C₂²×C₄×C₃₁	—	2	4	no	—
231	C₂²×C₄×C₃₁	—	2	4	no	—
232	C₂²×C₄×C₃₁	—	8	2	no	—
233	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
236	D₈×C₃₁	—	2	4	no	—
237	D₈×C₃₁	—	2	4	no	—
238	D₈×C₃₁	—	2	8	no	—
239	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
240	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
241	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
242	C₄⋊C₄×C₃₁	—	2	1	no	—
243	C₄⋊C₄×C₃₁	—	2	1	no	—
244	C₄⋊C₄×C₃₁	—	2	2	no	—
245	C₄⋊C₄×C₃₁	—	2	1	no	—
246	C₄⋊C₄×C₃₁	—	2	4	no	—
247	C₄⋊C₄×C₃₁	—	2	4	no	—
248	C₄⋊C₄×C₃₁	—	2	4	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	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	2	yes	—
259	C₄⋊C₄×C₃₁	C₂×D₄	1	4	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	C₂²⋊C₄×C₃₁	—	2	2	no	—
266	C₂²⋊C₄×C₃₁	—	2	4	no	—
267	C₂²⋊C₄×C₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	2	no	—
276	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
277	C₄²×C₃₁	—	2	2	no	—
278	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
281	C₄²×C₃₁	C₂⁴	1	4	yes	—
282	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
283	#61847	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂³×C₃₁	—	2	4	no	—
285	C₂³×C₃₁	—	2	2	no	—
286	C₂³×C₃₁	—	2	2	no	—
287	C₂³×C₃₁	—	2	2	no	—
288	C₂³×C₃₁	—	8	1	no	—
289	C₂³×C₃₁	—	8	1	no	—
290	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
291	Q₈×C₃₁	—	2	4	no	—
292	Q₈×C₃₁	—	4	2	no	—
293	Q₈×C₃₁	—	4	2	no	—
294	Q₈×C₃₁	—	8	1	no	—
295	Q₈×C₃₁	—	8	4	no	—
296	Q₈×C₃₁	—	8	1	no	—
297	Q₈×C₃₁	—	8	1	no	—
298	D₄×C₃₁	—	2	4	no	—
299	D₄×C₃₁	—	2	2	no	—
300	D₄×C₃₁	—	2	2	no	—
301	D₄×C₃₁	—	2	4	no	—
302	D₄×C₃₁	—	2	2	no	—
303	D₄×C₃₁	—	4	2	no	—
304	D₄×C₃₁	—	4	2	no	—
305	D₄×C₃₁	—	8	1	no	—
306	D₄×C₃₁	—	8	4	no	—
307	D₄×C₃₁	—	8	1	no	—
308	D₄×C₃₁	—	8	4	no	—
309	D₄×C₃₁	—	8	2	no	—
310	D₄×C₃₁	—	8	2	no	—
311	D₄×C₃₁	2₋¹⁺⁴	1	4	yes	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	2	2	no	—
314	C₂×C₄×C₃₁	—	2	2	no	—
315	C₂×C₄×C₃₁	—	2	2	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	2	no	—
318	C₂×C₄×C₃₁	—	2	2	no	—
319	C₂×C₄×C₃₁	—	4	1	no	—
320	C₂×C₄×C₃₁	—	4	4	no	—
321	C₂×C₄×C₃₁	—	4	4	no	—
322	C₂×C₄×C₃₁	—	4	4	no	—
323	C₂×C₄×C₃₁	—	8	4	no	—
324	C₂×C₄×C₃₁	—	8	2	no	—
325	C₂×C₄×C₃₁	—	8	4	no	—
326	C₂×C₄×C₃₁	—	8	4	no	—
327	C₂×C₄×C₃₁	—	8	4	no	—
328	C₂×C₄×C₃₁	—	8	1	no	—
329	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
337	C₈×C₃₁	—	2	2	no	—
338	C₈×C₃₁	—	2	2	no	—
339	C₈×C₃₁	—	2	4	no	—
340	#3548	C₂×C₃₁	1	1	yes	characteristic, complemented
341	#3501	C₂×C₃₁	1	1	yes	characteristic, complemented
342	#3389	C₂×C₃₁	1	4	yes	complemented
343	#3384	C₂×C₃₁	1	2	yes	complemented
344	#3380	C₂×C₃₁	1	2	yes	complemented
345	#3366	C₂×C₃₁	1	2	yes	complemented
346	#3366	C₂×C₃₁	1	4	yes	complemented
347	#3358	C₂×C₃₁	1	2	yes	complemented
348	#3241	C₂×C₃₁	1	4	yes	complemented
349	#3235	C₂×C₃₁	1	1	yes	characteristic, complemented
350	#3228	C₂×C₃₁	1	1	yes	characteristic, complemented
351	#3122	C₂×C₃₁	1	4	yes	complemented
352	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
353	#3100	C₂×C₃₁	1	1	yes	characteristic, complemented
354	#2985	C₂×C₃₁	1	1	yes	characteristic, complemented
355	C₂²×C₃₁	—	2	1	no	—
356	C₂²×C₃₁	—	2	1	no	—
357	C₂²×C₃₁	—	2	4	no	—
358	C₂²×C₃₁	—	2	1	no	—
359	C₂²×C₃₁	—	4	2	no	—
360	C₂²×C₃₁	—	4	2	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	C₂³×D₄	1	1	yes	characteristic
369	C₄×C₃₁	—	2	1	no	—
370	C₄×C₃₁	—	2	1	no	—
371	C₄×C₃₁	—	2	4	no	—
372	C₄×C₃₁	—	2	1	no	—
373	C₄×C₃₁	—	2	1	no	—
374	C₄×C₃₁	—	2	4	no	—
375	C₄×C₃₁	—	4	2	no	—
376	C₄×C₃₁	—	4	2	no	—
377	C₄×C₃₁	—	4	2	no	—
378	C₄×C₃₁	—	4	2	no	—
379	C₄×C₃₁	—	4	2	no	—
380	C₄×C₃₁	#576	1	2	yes	—
381	C₄×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
382	#562	—	2	2	no	—
383	#554	—	2	1	no	—
384	#554	—	2	2	no	—
385	#554	C₂²×C₃₁	1	2	yes	—
386	#554	C₂²×C₃₁	1	4	yes	—
387	#554	C₂²×C₃₁	1	2	yes	complemented
388	#554	C₂²×C₃₁	1	2	yes	complemented
389	#550	C₂²×C₃₁	1	2	yes	complemented
390	#550	C₂²×C₃₁	1	2	yes	complemented
391	D₄×Q₈	—	2	1	no	—
392	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
393	#547	—	2	1	no	—
394	#547	—	2	1	no	—
395	#544	C₂²×C₃₁	1	2	yes	—
396	#543	—	2	2	no	—
397	#540	C₂²×C₃₁	1	4	yes	—
398	#537	—	2	2	no	—
399	#537	—	2	2	no	—
400	#533	C₂²×C₃₁	1	1	yes	characteristic
401	#533	C₂²×C₃₁	1	1	yes	characteristic
402	#532	C₂²×C₃₁	1	1	yes	characteristic
403	#532	C₂²×C₃₁	1	1	yes	characteristic
404	C₂×C₂²⋊Q₈	—	2	2	no	—
405	#518	C₂²×C₃₁	1	2	yes	—
406	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
407	#501	C₂²×C₃₁	1	4	yes	complemented
408	#501	C₂²×C₃₁	1	2	yes	complemented
409	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
410	#499	C₂²×C₃₁	1	4	yes	complemented
411	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
412	#490	C₂²×C₃₁	1	2	yes	complemented
413	#490	C₂²×C₃₁	1	4	yes	complemented
414	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
415	#486	C₂²×C₃₁	1	4	yes	complemented
416	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
417	#482	C₂²×C₃₁	1	4	yes	—
418	#482	C₂²×C₃₁	1	4	yes	—
419	#481	C₂²×C₃₁	1	2	yes	—
420	#480	C₂²×C₃₁	1	2	yes	—
421	#478	C₂²×C₃₁	1	4	yes	—
422	#478	C₂²×C₃₁	1	4	yes	—
423	#478	C₂²×C₃₁	1	4	yes	complemented
424	#478	C₂²×C₃₁	1	4	yes	complemented
425	#478	C₂²×C₃₁	1	4	yes	complemented
426	#476	C₂²×C₃₁	1	2	yes	—
427	#476	C₂²×C₃₁	1	2	yes	complemented
428	#476	C₂²×C₃₁	1	4	yes	complemented
429	#474	C₂²×C₃₁	1	2	yes	—
430	#474	C₂²×C₃₁	1	2	yes	complemented
431	#474	C₂²×C₃₁	1	4	yes	complemented
432	#459	C₂²×C₃₁	1	2	yes	—
433	#459	C₂²×C₃₁	1	2	yes	—
434	#459	C₂²×C₃₁	1	4	yes	—
435	#459	C₂²×C₃₁	1	4	yes	—
436	#447	C₂²×C₃₁	1	2	yes	—
437	#447	C₂²×C₃₁	1	2	yes	—
438	#446	C₂²×C₃₁	1	2	yes	complemented
439	#446	C₂²×C₃₁	1	4	yes	complemented
440	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
441	#442	C₂²×C₃₁	1	4	yes	—
442	#442	C₂²×C₃₁	1	4	yes	—
443	#442	C₂²×C₃₁	1	4	yes	—
444	C₄×D₈	C₂²×C₃₁	1	2	yes	—
445	C₄×D₈	C₂²×C₃₁	1	2	yes	—
446	C₄×D₈	C₂²×C₃₁	1	4	yes	—
447	C₄×D₈	C₂²×C₃₁	1	4	yes	—
448	#433	C₂²×C₃₁	1	4	yes	—
449	#432	C₂²×C₃₁	1	1	yes	characteristic
450	#431	C₂²×C₃₁	1	1	yes	characteristic
451	C₂×C₃₁	—	4	1	no	—
452	C₂×C₃₁	—	4	4	no	—
453	C₂×C₃₁	—	8	2	no	—
454	C₂×C₃₁	—	8	2	no	—
455	C₂×C₃₁	#3486	1	1	yes	characteristic
456	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
457	C₂×C₃₁	#3585	1	1	yes	characteristic
458	C₂×#41	—	2	2	no	—
459	C₂×#41	—	2	2	no	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	—	2	1	no	—
462	C₂²×Q₈	—	2	2	no	—
463	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
464	C₂³×C₄	—	2	1	no	—
465	C₂×D₈	C₂³×C₃₁	1	2	yes	—
466	C₂×D₈	C₂³×C₃₁	1	2	yes	—
467	C₂×D₈	C₂³×C₃₁	1	4	yes	—
468	C₄⋊Q₈	—	2	2	no	—
469	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
470	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
471	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
472	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
473	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
474	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
475	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
476	#127	C₂³×C₃₁	1	1	yes	characteristic
477	#127	C₂³×C₃₁	1	1	yes	characteristic
478	#127	C₂³×C₃₁	1	4	yes	—
479	#125	—	2	2	no	—
480	#125	D₄×C₃₁	1	2	yes	—
481	#125	C₂³×C₃₁	1	2	yes	—
482	#125	C₂³×C₃₁	1	4	yes	—
483	#125	C₂³×C₃₁	1	4	yes	—
484	#124	—	2	1	no	—
485	#124	—	2	1	no	—
486	#123	—	2	4	no	—
487	#123	—	2	4	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	—	2	1	no	—
493	C₂²⋊Q₈	—	2	1	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	4	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	—	2	4	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	—	2	4	no	—
501	C₂²⋊Q₈	—	2	4	no	—
502	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
503	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
504	#121	—	2	1	no	—
505	#121	—	2	1	no	—
506	#121	—	2	2	no	—
507	#121	—	2	2	no	—
508	#121	—	2	4	no	—
509	#121	—	2	4	no	—
510	#121	—	2	4	no	—
511	#121	—	2	4	no	—
512	#121	C₂³×C₃₁	1	2	yes	—
513	#121	C₂³×C₃₁	1	2	yes	—
514	C₄×Q₈	—	2	1	no	—
515	C₄×Q₈	—	2	1	no	—
516	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
517	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	1	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	—	2	1	no	—
524	C₄×D₄	C₂³×C₃₁	1	2	yes	—
525	C₄×D₄	C₂³×C₃₁	1	2	yes	—
526	C₄×D₄	C₂³×C₃₁	1	4	yes	—
527	C₄×D₄	C₂³×C₃₁	1	4	yes	—
528	C₄×D₄	C₂³×C₃₁	1	2	yes	—
529	C₄×D₄	C₂³×C₃₁	1	2	yes	—
530	C₄×D₄	C₂³×C₃₁	1	4	yes	—
531	C₄×D₄	C₂³×C₃₁	1	4	yes	—
532	#117	C₂³×C₃₁	1	2	yes	—
533	#117	C₂³×C₃₁	1	2	yes	—
534	C₂×C₄⋊C₄	—	2	4	no	—
535	C₂×C₄⋊C₄	—	2	2	no	—
536	C₂×C₄⋊C₄	—	2	2	no	—
537	C₂×C₄⋊C₄	—	2	2	no	—
538	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	—	2	1	no	—
540	C₂×C₂²⋊C₄	—	2	4	no	—
541	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
542	#107	C₂³×C₃₁	1	2	yes	—
543	#107	C₂³×C₃₁	1	2	yes	—
544	#107	C₂³×C₃₁	1	4	yes	—
545	#107	C₂³×C₃₁	1	4	yes	—
546	#106	C₂³×C₃₁	1	4	yes	—
547	#106	C₂³×C₃₁	1	4	yes	—
548	#106	C₂³×C₃₁	1	4	yes	—
549	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
550	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
551	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
552	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
553	#102	C₂³×C₃₁	1	2	yes	—
554	#102	C₂³×C₃₁	1	2	yes	—
555	#102	C₂³×C₃₁	1	4	yes	—
556	#102	C₂³×C₃₁	1	4	yes	—
557	#102	C₂³×C₃₁	1	2	yes	—
558	#102	C₂³×C₃₁	1	4	yes	—
559	#102	C₂³×C₃₁	1	2	yes	—
560	#102	C₂³×C₃₁	1	4	yes	—
561	#102	C₂³×C₃₁	1	4	yes	—
562	#102	C₂³×C₃₁	1	4	yes	—
563	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
564	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
565	#97	C₂³×C₃₁	1	2	yes	—
566	#97	C₂³×C₃₁	1	4	yes	—
567	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
568	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
569	C₄×C₈	C₂³×C₃₁	1	4	yes	—
570	C₃₁	#61847	1	1	yes	characteristic, direct product factor, Sylow
571	C₂⁴	—	2	1	no	—
572	#41	—	8	2	no	—
573	#41	—	8	2	no	—
574	#41	—	8	4	no	—
575	#41	—	8	4	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	4	no	—
581	C₂×Q₈	—	8	4	no	—
582	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
583	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
595	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
596	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	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	D₈	—	2	4	no	—
611	D₈	—	2	4	no	—
612	D₈	—	2	8	no	—
613	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
614	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
615	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
629	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
630	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
631	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
632	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
633	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
634	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
635	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
636	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
651	C₄²	—	2	2	no	—
652	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
653	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
654	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
655	C₄²	C₂⁴×C₃₁	1	4	yes	—
656	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
657	C₂³	—	2	4	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	8	1	no	—
662	C₂³	—	8	1	no	—
663	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
664	Q₈	—	2	4	no	—
665	Q₈	—	4	2	no	—
666	Q₈	—	4	2	no	—
667	Q₈	—	8	1	no	—
668	Q₈	—	8	4	no	—
669	Q₈	—	8	1	no	—
670	Q₈	—	8	1	no	—
671	D₄	—	2	4	no	—
672	D₄	—	2	2	no	—
673	D₄	—	2	2	no	—
674	D₄	—	2	4	no	—
675	D₄	—	2	2	no	—
676	D₄	—	4	2	no	—
677	D₄	—	4	2	no	—
678	D₄	—	8	1	no	—
679	D₄	—	8	4	no	—
680	D₄	—	8	1	no	—
681	D₄	—	8	4	no	—
682	D₄	—	8	2	no	—
683	D₄	—	8	2	no	—
684	D₄	C₃₁×2₋¹⁺⁴	1	4	yes	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	8	4	no	—
697	C₂×C₄	—	8	2	no	—
698	C₂×C₄	—	8	4	no	—
699	C₂×C₄	—	8	4	no	—
700	C₂×C₄	—	8	4	no	—
701	C₂×C₄	—	8	1	no	—
702	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
703	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
705	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
707	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
708	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
709	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
710	C₈	—	2	2	no	—
711	C₈	—	2	2	no	—
712	C₈	—	2	4	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	2	4	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	8	4	no	—
726	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
727	C₄	—	2	1	no	—
728	C₄	—	2	1	no	—
729	C₄	—	2	4	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	4	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	C₃₁×#576	1	2	yes	—
739	C₄	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
740	C₂	—	4	1	no	—
741	C₂	—	4	4	no	—
742	C₂	—	8	2	no	—
743	C₂	—	8	2	no	—
744	C₂	C₃₁×#3486	1	1	yes	characteristic
745	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
746	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
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×#3548	C₂	semidirect
2. C₃₁×#3501	C₂	semidirect
3. C₃₁×#3389	C₂	semidirect
4. C₃₁×#3384	C₂	semidirect
5. C₃₁×#3380	C₂	semidirect
6. C₃₁×#3366	C₂	semidirect
7. C₃₁×#3366	C₂	semidirect
8. C₃₁×#3358	C₂	semidirect
9. C₃₁×#3241	C₂	semidirect
10. C₃₁×#3235	C₂	semidirect
11. C₃₁×#3228	C₂	semidirect
12. C₃₁×#3122	C₂	semidirect
13. C₃₁×#3109	C₂	semidirect
14. C₃₁×#3100	C₂	semidirect
15. C₃₁×#2985	C₂	semidirect
21. C₃₁×#554	C₂²	semidirect
22. C₃₁×#554	C₂²	semidirect
23. C₃₁×#550	C₂²	semidirect
24. C₃₁×#550	C₂²	semidirect
41. C₃₁×#501	C₂²	semidirect
42. C₃₁×#501	C₂²	semidirect
43. C₃₁×#500	C₂²	semidirect
44. C₃₁×#499	C₂²	semidirect
45. C₃₁×#498	C₂²	semidirect
46. C₃₁×#490	C₂²	semidirect
47. C₃₁×#490	C₂²	semidirect
48. C₃₁×#486	C₂²	semidirect
49. C₃₁×#486	C₂²	semidirect
50. C₃₁×#486	C₂²	semidirect
57. C₃₁×#478	C₂²	semidirect
58. C₃₁×#478	C₂²	semidirect
59. C₃₁×#478	C₂²	semidirect
61. C₃₁×#476	C₂²	semidirect
62. C₃₁×#476	C₂²	semidirect
64. C₃₁×#474	C₂²	semidirect
65. C₃₁×#474	C₂²	semidirect
72. C₃₁×#446	C₂²	semidirect
73. C₃₁×#446	C₂²	semidirect
74. C₈×Q₈×C₃₁	C₂²	semidirect
283. #61847	C₃₁	direct (N × H)
340. #3548	C₂×C₃₁	semidirect
341. #3501	C₂×C₃₁	semidirect
342. #3389	C₂×C₃₁	semidirect
343. #3384	C₂×C₃₁	semidirect
344. #3380	C₂×C₃₁	semidirect
345. #3366	C₂×C₃₁	semidirect
346. #3366	C₂×C₃₁	semidirect
347. #3358	C₂×C₃₁	semidirect
348. #3241	C₂×C₃₁	semidirect
349. #3235	C₂×C₃₁	semidirect
350. #3228	C₂×C₃₁	semidirect
351. #3122	C₂×C₃₁	semidirect
352. #3109	C₂×C₃₁	semidirect
353. #3100	C₂×C₃₁	semidirect
354. #2985	C₂×C₃₁	semidirect
387. #554	C₂²×C₃₁	semidirect
388. #554	C₂²×C₃₁	semidirect
389. #550	C₂²×C₃₁	semidirect
390. #550	C₂²×C₃₁	semidirect
407. #501	C₂²×C₃₁	semidirect
408. #501	C₂²×C₃₁	semidirect
409. #500	C₂²×C₃₁	semidirect
410. #499	C₂²×C₃₁	semidirect
411. #498	C₂²×C₃₁	semidirect
412. #490	C₂²×C₃₁	semidirect
413. #490	C₂²×C₃₁	semidirect
414. #486	C₂²×C₃₁	semidirect
415. #486	C₂²×C₃₁	semidirect
416. #486	C₂²×C₃₁	semidirect
423. #478	C₂²×C₃₁	semidirect
424. #478	C₂²×C₃₁	semidirect
425. #478	C₂²×C₃₁	semidirect
427. #476	C₂²×C₃₁	semidirect
428. #476	C₂²×C₃₁	semidirect
430. #474	C₂²×C₃₁	semidirect
431. #474	C₂²×C₃₁	semidirect
438. #446	C₂²×C₃₁	semidirect
439. #446	C₂²×C₃₁	semidirect
440. C₈×Q₈	C₂²×C₃₁	semidirect
570. C₃₁	#61847	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3548	2
C₃₁×#3501	2
C₃₁×#3389	2
C₃₁×#3384	2
C₃₁×#3380	2
C₃₁×#3366	2
C₃₁×#3358	2
C₃₁×#3241	2
C₃₁×#3235	2
C₃₁×#3228	2
C₃₁×#3122	2
C₃₁×#3109	2
C₃₁×#3100	2
C₃₁×#2985	2
#61847	31

Subgroups — C31×#61847 #21518606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61847 #21518606