Subgroups — C₃₁×#61910 #21518669

Order 7936.

1816 conjugacy classes of subgroups.

The subgroup lattice has 772 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×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3399	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3397	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3391	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3370	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3366	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3360	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3220	C₂	1	4	yes	maximal, complemented
10	C₃₁×#3214	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3119	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×#559	C₂²	1	4	yes	—
18	C₃₁×#556	C₂²	1	2	yes	—
19	C₃₁×#555	—	2	1	no	—
20	C₃₁×#554	C₂²	1	2	yes	complemented
21	C₃₁×#554	C₂²	1	2	yes	complemented
22	C₃₁×#553	—	2	2	no	—
23	C₃₁×#550	C₂²	1	2	yes	—
24	C₃₁×#550	C₂²	1	2	yes	complemented
25	C₃₁×#550	C₂²	1	2	yes	complemented
26	C₃₁×#547	—	2	1	no	—
27	C₃₁×#547	—	2	1	no	—
28	C₃₁×#547	—	2	1	no	—
29	C₃₁×#540	C₂²	1	4	yes	—
30	C₃₁×#538	—	2	2	no	—
31	C₃₁×#537	—	2	2	no	—
32	C₃₁×#537	—	2	2	no	—
33	C₃₁×#535	C₂²	1	2	yes	—
34	C₃₁×#533	C₂²	1	1	yes	characteristic
35	C₃₁×#532	C₂²	1	1	yes	characteristic
36	C₃₁×#532	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	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₃₁×#496	C₂²	1	4	yes	—
42	C₃₁×#496	C₂²	1	2	yes	complemented
43	C₃₁×#493	C₂²	1	4	yes	—
44	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#490	C₂²	1	4	yes	—
47	C₃₁×#489	C₂²	1	2	yes	complemented
48	C₃₁×#488	C₂²	1	4	yes	—
49	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#481	C₂²	1	2	yes	—
52	C₃₁×#480	C₂²	1	2	yes	—
53	C₃₁×#479	C₂²	1	4	yes	complemented
54	C₃₁×#478	C₂²	1	4	yes	complemented
55	C₃₁×#476	C₂²	1	2	yes	—
56	C₃₁×#474	C₂²	1	2	yes	—
57	C₃₁×#463	C₂²	1	4	yes	—
58	C₃₁×#463	C₂²	1	4	yes	—
59	C₃₁×#463	C₂²	1	4	yes	complemented
60	C₃₁×#461	C₂²	1	2	yes	complemented
61	C₃₁×#460	C₂²	1	4	yes	complemented
62	C₃₁×#459	C₂²	1	2	yes	—
63	C₃₁×#459	C₂²	1	2	yes	—
64	C₃₁×#459	C₂²	1	4	yes	—
65	C₃₁×#459	C₂²	1	4	yes	—
66	C₃₁×#459	C₂²	1	2	yes	complemented
67	C₃₁×#459	C₂²	1	4	yes	complemented
68	C₃₁×#449	C₂²	1	4	yes	—
69	C₃₁×#449	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	complemented
77	C₃₁×#440	C₂²	1	4	yes	complemented
78	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
79	C₄×D₈×C₃₁	C₂²	1	2	yes	—
80	C₄×D₈×C₃₁	C₂²	1	2	yes	—
81	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
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	2	no	—
88	C₂×#41×C₃₁	—	2	1	no	—
89	C₂×#41×C₃₁	—	2	1	no	—
90	C₂×#41×C₃₁	C₂³	1	2	yes	—
91	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₃₁	—	2	1	no	—
93	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
94	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
95	C₂×D₈×C₃₁	C₂³	1	2	yes	—
96	C₂×D₈×C₃₁	C₂³	1	2	yes	—
97	C₂×D₈×C₃₁	C₂³	1	4	yes	—
98	C₂×D₈×C₃₁	C₂³	1	4	yes	—
99	C₂×D₈×C₃₁	C₂³	1	4	yes	—
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	1	yes	characteristic
104	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₃₁×#127	C₂³	1	4	yes	—
106	C₃₁×#127	C₂³	1	1	yes	characteristic
107	C₃₁×#127	C₂³	1	1	yes	characteristic
108	C₃₁×#127	C₂³	1	1	yes	characteristic
109	C₃₁×#127	C₂³	1	4	yes	—
110	C₃₁×#126	—	2	4	no	—
111	C₃₁×#125	D₄	1	2	yes	—
112	C₃₁×#125	C₂³	1	4	yes	—
113	C₃₁×#124	—	2	4	no	—
114	C₃₁×#124	—	2	1	no	—
115	C₃₁×#124	—	2	1	no	—
116	C₃₁×#124	C₂³	1	4	yes	—
117	C₃₁×#124	C₂³	1	2	yes	—
118	C₃₁×#123	—	2	4	no	—
119	C₃₁×#123	—	2	4	no	—
120	C₃₁×#123	—	2	4	no	—
121	C₃₁×#123	—	2	4	no	—
122	C₃₁×C₂²⋊Q₈	—	2	2	no	—
123	C₃₁×C₂²⋊Q₈	—	2	2	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	D₄	1	2	yes	—
128	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
129	C₃₁×#121	—	2	1	no	—
130	C₃₁×#121	—	2	1	no	—
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	2	no	—
136	C₃₁×#121	—	2	2	no	—
137	C₃₁×#121	—	2	2	no	—
138	C₃₁×#121	—	2	4	no	—
139	C₃₁×#121	—	2	4	no	—
140	C₃₁×#121	—	2	4	no	—
141	C₃₁×#121	—	2	4	no	—
142	C₃₁×#121	—	2	4	no	—
143	C₃₁×#121	C₂³	1	2	yes	—
144	C₃₁×#121	C₂³	1	2	yes	—
145	C₃₁×#120	—	2	4	no	—
146	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
147	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
148	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
149	C₄×D₄×C₃₁	—	2	4	no	—
150	C₄×D₄×C₃₁	—	2	4	no	—
151	C₄×D₄×C₃₁	—	2	1	no	—
152	C₄×D₄×C₃₁	—	2	1	no	—
153	C₄×D₄×C₃₁	—	2	1	no	—
154	C₄×D₄×C₃₁	—	2	1	no	—
155	C₄×D₄×C₃₁	—	2	1	no	—
156	C₄×D₄×C₃₁	—	2	1	no	—
157	C₄×D₄×C₃₁	C₂³	1	2	yes	—
158	C₄×D₄×C₃₁	C₂³	1	2	yes	—
159	C₄×D₄×C₃₁	C₂³	1	4	yes	—
160	C₄×D₄×C₃₁	C₂³	1	4	yes	—
161	C₄×D₄×C₃₁	C₂³	1	4	yes	—
162	C₄×D₄×C₃₁	C₂³	1	2	yes	—
163	C₄×D₄×C₃₁	C₂³	1	2	yes	—
164	C₃₁×#117	—	2	2	no	—
165	C₃₁×#117	—	2	2	no	—
166	C₃₁×#117	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
168	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
169	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
172	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
173	C₃₁×#107	C₂³	1	2	yes	—
174	C₃₁×#107	C₂³	1	2	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×#103	C₂³	1	4	yes	—
181	C₃₁×#103	C₂³	1	4	yes	—
182	C₃₁×#102	C₂³	1	2	yes	—
183	C₃₁×#102	C₂³	1	2	yes	—
184	C₃₁×#102	C₂³	1	2	yes	—
185	C₃₁×#102	C₂³	1	2	yes	—
186	C₃₁×#102	C₂³	1	4	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	—	4	4	no	—
199	#41×C₃₁	—	8	2	no	—
200	#41×C₃₁	—	8	2	no	—
201	#41×C₃₁	—	8	4	no	—
202	#41×C₃₁	—	8	4	no	—
203	#41×C₃₁	—	8	4	no	—
204	C₂×Q₈×C₃₁	—	2	1	no	—
205	C₂×Q₈×C₃₁	—	2	1	no	—
206	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
207	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
209	C₂×D₄×C₃₁	—	2	2	no	—
210	C₂×D₄×C₃₁	—	2	2	no	—
211	C₂×D₄×C₃₁	—	2	2	no	—
212	C₂×D₄×C₃₁	—	2	1	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	1	no	—
218	C₂×D₄×C₃₁	—	2	4	no	—
219	C₂×D₄×C₃₁	—	2	4	no	—
220	C₂×D₄×C₃₁	—	2	4	no	—
221	C₂×D₄×C₃₁	—	2	1	no	—
222	C₂×D₄×C₃₁	—	2	1	no	—
223	C₂×D₄×C₃₁	—	4	2	no	—
224	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
225	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
226	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
227	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₃₁	—	2	1	no	—
229	C₂²×C₄×C₃₁	—	2	2	no	—
230	C₂²×C₄×C₃₁	—	2	2	no	—
231	C₂²×C₄×C₃₁	—	2	2	no	—
232	C₂²×C₄×C₃₁	—	2	2	no	—
233	C₂²×C₄×C₃₁	—	2	4	no	—
234	C₂²×C₄×C₃₁	—	2	4	no	—
235	C₂²×C₄×C₃₁	—	2	4	no	—
236	C₂²×C₄×C₃₁	—	2	2	no	—
237	C₂²×C₄×C₃₁	—	8	2	no	—
238	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
241	SD₁₆×C₃₁	—	4	4	no	—
242	SD₁₆×C₃₁	—	4	4	no	—
243	D₈×C₃₁	—	4	4	no	—
244	D₈×C₃₁	—	4	2	no	—
245	D₈×C₃₁	—	4	4	no	—
246	D₈×C₃₁	—	4	4	no	—
247	D₈×C₃₁	—	4	2	no	—
248	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
249	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
250	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
251	C₄⋊C₄×C₃₁	—	2	1	no	—
252	C₄⋊C₄×C₃₁	—	2	1	no	—
253	C₄⋊C₄×C₃₁	—	2	1	no	—
254	C₄⋊C₄×C₃₁	—	2	4	no	—
255	C₄⋊C₄×C₃₁	—	2	4	no	—
256	C₄⋊C₄×C₃₁	—	2	4	no	—
257	C₄⋊C₄×C₃₁	—	2	1	no	—
258	C₄⋊C₄×C₃₁	—	2	1	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	2	yes	—
263	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
264	C₄⋊C₄×C₃₁	C₂×D₄	1	4	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	C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂²⋊C₄×C₃₁	—	2	4	no	—
271	C₂²⋊C₄×C₃₁	—	2	4	no	—
272	C₂²⋊C₄×C₃₁	—	2	2	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	—	2	2	no	—
277	C₂²⋊C₄×C₃₁	—	2	4	no	—
278	C₂²⋊C₄×C₃₁	—	2	4	no	—
279	C₂²⋊C₄×C₃₁	—	2	2	no	—
280	C₂²⋊C₄×C₃₁	—	2	2	no	—
281	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
282	C₄²×C₃₁	—	2	4	no	—
283	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
286	C₄²×C₃₁	C₂⁴	1	4	yes	—
287	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
288	#61910	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
289	C₂³×C₃₁	—	2	2	no	—
290	C₂³×C₃₁	—	2	2	no	—
291	C₂³×C₃₁	—	2	2	no	—
292	C₂³×C₃₁	—	2	2	no	—
293	C₂³×C₃₁	—	4	2	no	—
294	C₂³×C₃₁	—	8	1	no	—
295	C₂³×C₃₁	—	8	1	no	—
296	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
297	Q₈×C₃₁	—	2	4	no	—
298	Q₈×C₃₁	—	2	4	no	—
299	Q₈×C₃₁	—	4	2	no	—
300	Q₈×C₃₁	—	8	1	no	—
301	Q₈×C₃₁	—	8	1	no	—
302	D₄×C₃₁	—	2	2	no	—
303	D₄×C₃₁	—	2	4	no	—
304	D₄×C₃₁	—	2	2	no	—
305	D₄×C₃₁	—	2	2	no	—
306	D₄×C₃₁	—	2	4	no	—
307	D₄×C₃₁	—	2	2	no	—
308	D₄×C₃₁	—	4	2	no	—
309	D₄×C₃₁	—	4	2	no	—
310	D₄×C₃₁	—	4	4	no	—
311	D₄×C₃₁	—	4	2	no	—
312	D₄×C₃₁	—	4	2	no	—
313	D₄×C₃₁	—	8	1	no	—
314	D₄×C₃₁	—	8	4	no	—
315	D₄×C₃₁	—	8	1	no	—
316	D₄×C₃₁	—	8	4	no	—
317	D₄×C₃₁	—	8	1	no	—
318	D₄×C₃₁	—	8	4	no	—
319	D₄×C₃₁	—	8	4	no	—
320	D₄×C₃₁	—	8	2	no	—
321	D₄×C₃₁	—	8	2	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	2	no	—
324	C₂×C₄×C₃₁	—	2	2	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	4	1	no	—
329	C₂×C₄×C₃₁	—	4	4	no	—
330	C₂×C₄×C₃₁	—	4	4	no	—
331	C₂×C₄×C₃₁	—	4	4	no	—
332	C₂×C₄×C₃₁	—	4	4	no	—
333	C₂×C₄×C₃₁	—	8	2	no	—
334	C₂×C₄×C₃₁	—	8	4	no	—
335	C₂×C₄×C₃₁	—	8	4	no	—
336	C₂×C₄×C₃₁	—	8	4	no	—
337	C₂×C₄×C₃₁	—	8	1	no	—
338	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
339	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
344	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
346	C₈×C₃₁	—	2	2	no	—
347	C₈×C₃₁	—	2	4	no	—
348	C₈×C₃₁	—	2	2	no	—
349	#3548	C₂×C₃₁	1	1	yes	characteristic, complemented
350	#3506	C₂×C₃₁	1	1	yes	characteristic, complemented
351	#3399	C₂×C₃₁	1	4	yes	complemented
352	#3397	C₂×C₃₁	1	2	yes	complemented
353	#3391	C₂×C₃₁	1	2	yes	complemented
354	#3370	C₂×C₃₁	1	4	yes	complemented
355	#3366	C₂×C₃₁	1	2	yes	complemented
356	#3360	C₂×C₃₁	1	2	yes	complemented
357	#3220	C₂×C₃₁	1	4	yes	complemented
358	#3214	C₂×C₃₁	1	1	yes	characteristic, complemented
359	#3207	C₂×C₃₁	1	1	yes	characteristic, complemented
360	#3119	C₂×C₃₁	1	4	yes	complemented
361	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
362	#3100	C₂×C₃₁	1	1	yes	characteristic, complemented
363	#2985	C₂×C₃₁	1	1	yes	characteristic, complemented
364	C₂²×C₃₁	—	2	1	no	—
365	C₂²×C₃₁	—	2	1	no	—
366	C₂²×C₃₁	—	2	1	no	—
367	C₂²×C₃₁	—	4	2	no	—
368	C₂²×C₃₁	—	4	2	no	—
369	C₂²×C₃₁	—	4	2	no	—
370	C₂²×C₃₁	—	4	2	no	—
371	C₂²×C₃₁	—	4	2	no	—
372	C₂²×C₃₁	—	4	2	no	—
373	C₂²×C₃₁	—	4	2	no	—
374	C₂²×C₃₁	—	4	2	no	—
375	C₂²×C₃₁	—	4	2	no	—
376	C₂²×C₃₁	—	4	2	no	—
377	C₂²×C₃₁	—	4	2	no	—
378	C₂²×C₃₁	—	4	2	no	—
379	C₂²×C₃₁	—	8	4	no	—
380	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
381	C₄×C₃₁	—	2	1	no	—
382	C₄×C₃₁	—	2	1	no	—
383	C₄×C₃₁	—	2	4	no	—
384	C₄×C₃₁	—	2	1	no	—
385	C₄×C₃₁	—	2	1	no	—
386	C₄×C₃₁	—	2	4	no	—
387	C₄×C₃₁	—	4	2	no	—
388	C₄×C₃₁	—	4	2	no	—
389	C₄×C₃₁	—	4	2	no	—
390	C₄×C₃₁	—	4	2	no	—
391	C₄×C₃₁	#576	1	2	yes	—
392	C₄×C₃₁	#585	1	2	yes	—
393	#562	—	2	2	no	—
394	#559	C₂²×C₃₁	1	4	yes	—
395	#556	C₂²×C₃₁	1	2	yes	—
396	#555	—	2	1	no	—
397	#554	C₂²×C₃₁	1	2	yes	complemented
398	#554	C₂²×C₃₁	1	2	yes	complemented
399	#553	—	2	2	no	—
400	#550	C₂²×C₃₁	1	2	yes	—
401	#550	C₂²×C₃₁	1	2	yes	complemented
402	#550	C₂²×C₃₁	1	2	yes	complemented
403	#547	—	2	1	no	—
404	#547	—	2	1	no	—
405	#547	—	2	1	no	—
406	#540	C₂²×C₃₁	1	4	yes	—
407	#538	—	2	2	no	—
408	#537	—	2	2	no	—
409	#537	—	2	2	no	—
410	#535	C₂²×C₃₁	1	2	yes	—
411	#533	C₂²×C₃₁	1	1	yes	characteristic
412	#532	C₂²×C₃₁	1	1	yes	characteristic
413	#532	C₂²×C₃₁	1	1	yes	characteristic
414	#532	C₂²×C₃₁	1	1	yes	characteristic
415	#525	—	2	2	no	—
416	#520	C₂²×C₃₁	1	2	yes	—
417	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
418	#496	C₂²×C₃₁	1	4	yes	—
419	#496	C₂²×C₃₁	1	2	yes	complemented
420	#493	C₂²×C₃₁	1	4	yes	—
421	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
422	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
423	#490	C₂²×C₃₁	1	4	yes	—
424	#489	C₂²×C₃₁	1	2	yes	complemented
425	#488	C₂²×C₃₁	1	4	yes	—
426	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
427	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
428	#481	C₂²×C₃₁	1	2	yes	—
429	#480	C₂²×C₃₁	1	2	yes	—
430	#479	C₂²×C₃₁	1	4	yes	complemented
431	#478	C₂²×C₃₁	1	4	yes	complemented
432	#476	C₂²×C₃₁	1	2	yes	—
433	#474	C₂²×C₃₁	1	2	yes	—
434	#463	C₂²×C₃₁	1	4	yes	—
435	#463	C₂²×C₃₁	1	4	yes	—
436	#463	C₂²×C₃₁	1	4	yes	complemented
437	#461	C₂²×C₃₁	1	2	yes	complemented
438	#460	C₂²×C₃₁	1	4	yes	complemented
439	#459	C₂²×C₃₁	1	2	yes	—
440	#459	C₂²×C₃₁	1	2	yes	—
441	#459	C₂²×C₃₁	1	4	yes	—
442	#459	C₂²×C₃₁	1	4	yes	—
443	#459	C₂²×C₃₁	1	2	yes	complemented
444	#459	C₂²×C₃₁	1	4	yes	complemented
445	#449	C₂²×C₃₁	1	4	yes	—
446	#449	C₂²×C₃₁	1	4	yes	—
447	#447	C₂²×C₃₁	1	2	yes	—
448	#447	C₂²×C₃₁	1	2	yes	—
449	#446	C₂²×C₃₁	1	2	yes	complemented
450	#446	C₂²×C₃₁	1	4	yes	complemented
451	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
452	#442	C₂²×C₃₁	1	4	yes	—
453	#442	C₂²×C₃₁	1	4	yes	complemented
454	#440	C₂²×C₃₁	1	4	yes	complemented
455	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
456	C₄×D₈	C₂²×C₃₁	1	2	yes	—
457	C₄×D₈	C₂²×C₃₁	1	2	yes	—
458	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
459	#433	C₂²×C₃₁	1	4	yes	—
460	#432	C₂²×C₃₁	1	1	yes	characteristic
461	#431	C₂²×C₃₁	1	1	yes	characteristic
462	C₂×C₃₁	—	4	1	no	—
463	C₂×C₃₁	—	8	2	no	—
464	C₂×C₃₁	—	8	2	no	—
465	C₂×C₃₁	—	8	2	no	—
466	C₂×C₃₁	—	8	2	no	—
467	C₂×C₃₁	#3487	1	1	yes	characteristic
468	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
469	C₂×C₃₁	#3585	1	1	yes	characteristic
470	C₂×#41	—	2	2	no	—
471	C₂×#41	—	2	2	no	—
472	C₂×#41	—	2	2	no	—
473	C₂×#41	—	2	1	no	—
474	C₂×#41	—	2	1	no	—
475	C₂×#41	C₂³×C₃₁	1	2	yes	—
476	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
477	C₂³×C₄	—	2	1	no	—
478	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
479	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
480	C₂×D₈	C₂³×C₃₁	1	2	yes	—
481	C₂×D₈	C₂³×C₃₁	1	2	yes	—
482	C₂×D₈	C₂³×C₃₁	1	4	yes	—
483	C₂×D₈	C₂³×C₃₁	1	4	yes	—
484	C₂×D₈	C₂³×C₃₁	1	4	yes	—
485	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
486	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
487	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
488	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
489	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
490	#127	C₂³×C₃₁	1	1	yes	characteristic
491	#127	C₂³×C₃₁	1	1	yes	characteristic
492	#127	C₂³×C₃₁	1	1	yes	characteristic
493	#127	C₂³×C₃₁	1	4	yes	—
494	#127	C₂³×C₃₁	1	4	yes	—
495	#126	—	2	4	no	—
496	#125	D₄×C₃₁	1	2	yes	—
497	#125	C₂³×C₃₁	1	4	yes	—
498	#124	—	2	4	no	—
499	#124	—	2	1	no	—
500	#124	—	2	1	no	—
501	#124	C₂³×C₃₁	1	2	yes	—
502	#124	C₂³×C₃₁	1	4	yes	—
503	#123	—	2	4	no	—
504	#123	—	2	4	no	—
505	#123	—	2	4	no	—
506	#123	—	2	4	no	—
507	C₂²⋊Q₈	—	2	2	no	—
508	C₂²⋊Q₈	—	2	2	no	—
509	C₂²⋊Q₈	—	2	2	no	—
510	C₂²⋊Q₈	—	2	4	no	—
511	C₂²⋊Q₈	—	2	4	no	—
512	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
513	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
514	#121	—	2	1	no	—
515	#121	—	2	1	no	—
516	#121	—	2	1	no	—
517	#121	—	2	1	no	—
518	#121	—	2	2	no	—
519	#121	—	2	2	no	—
520	#121	—	2	2	no	—
521	#121	—	2	2	no	—
522	#121	—	2	2	no	—
523	#121	—	2	4	no	—
524	#121	—	2	4	no	—
525	#121	—	2	4	no	—
526	#121	—	2	4	no	—
527	#121	—	2	4	no	—
528	#121	C₂³×C₃₁	1	2	yes	—
529	#121	C₂³×C₃₁	1	2	yes	—
530	#120	—	2	4	no	—
531	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
532	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
533	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
534	C₄×D₄	—	2	4	no	—
535	C₄×D₄	—	2	4	no	—
536	C₄×D₄	—	2	1	no	—
537	C₄×D₄	—	2	1	no	—
538	C₄×D₄	—	2	1	no	—
539	C₄×D₄	—	2	1	no	—
540	C₄×D₄	—	2	1	no	—
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	C₂³×C₃₁	1	2	yes	—
543	C₄×D₄	C₂³×C₃₁	1	2	yes	—
544	C₄×D₄	C₂³×C₃₁	1	4	yes	—
545	C₄×D₄	C₂³×C₃₁	1	2	yes	—
546	C₄×D₄	C₂³×C₃₁	1	2	yes	—
547	C₄×D₄	C₂³×C₃₁	1	4	yes	—
548	C₄×D₄	C₂³×C₃₁	1	4	yes	—
549	#117	—	2	2	no	—
550	#117	—	2	2	no	—
551	#117	C₂³×C₃₁	1	2	yes	—
552	C₂×C₄⋊C₄	—	2	2	no	—
553	C₂×C₄⋊C₄	—	2	2	no	—
554	C₂×C₄⋊C₄	—	2	2	no	—
555	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	—	2	1	no	—
557	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
558	#107	C₂³×C₃₁	1	2	yes	—
559	#107	C₂³×C₃₁	1	2	yes	—
560	#106	C₂³×C₃₁	1	4	yes	—
561	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
562	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
563	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
564	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
565	#103	C₂³×C₃₁	1	4	yes	—
566	#103	C₂³×C₃₁	1	4	yes	—
567	#102	C₂³×C₃₁	1	2	yes	—
568	#102	C₂³×C₃₁	1	2	yes	—
569	#102	C₂³×C₃₁	1	2	yes	—
570	#102	C₂³×C₃₁	1	2	yes	—
571	#102	C₂³×C₃₁	1	4	yes	—
572	#102	C₂³×C₃₁	1	4	yes	—
573	#102	C₂³×C₃₁	1	4	yes	—
574	#102	C₂³×C₃₁	1	4	yes	—
575	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
576	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
577	#97	C₂³×C₃₁	1	2	yes	—
578	#97	C₂³×C₃₁	1	4	yes	—
579	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
580	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
581	C₄×C₈	C₂³×C₃₁	1	4	yes	—
582	C₃₁	#61910	1	1	yes	characteristic, direct product factor, Sylow
583	C₂⁴	—	2	1	no	—
584	#41	—	4	4	no	—
585	#41	—	8	2	no	—
586	#41	—	8	2	no	—
587	#41	—	8	4	no	—
588	#41	—	8	4	no	—
589	#41	—	8	4	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
593	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
594	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	4	2	no	—
610	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
611	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
612	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
613	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	8	2	no	—
624	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
627	SD₁₆	—	4	4	no	—
628	SD₁₆	—	4	4	no	—
629	D₈	—	4	4	no	—
630	D₈	—	4	2	no	—
631	D₈	—	4	4	no	—
632	D₈	—	4	4	no	—
633	D₈	—	4	2	no	—
634	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
635	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
636	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
646	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
647	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
648	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
649	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
650	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
651	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
652	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	2	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	2	2	no	—
667	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
668	C₄²	—	2	4	no	—
669	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
670	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
671	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
672	C₄²	C₂⁴×C₃₁	1	4	yes	—
673	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	—	8	1	no	—
680	C₂³	—	8	1	no	—
681	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
682	Q₈	—	2	4	no	—
683	Q₈	—	2	4	no	—
684	Q₈	—	4	2	no	—
685	Q₈	—	8	1	no	—
686	Q₈	—	8	1	no	—
687	D₄	—	2	2	no	—
688	D₄	—	2	4	no	—
689	D₄	—	2	2	no	—
690	D₄	—	2	2	no	—
691	D₄	—	2	4	no	—
692	D₄	—	2	2	no	—
693	D₄	—	4	2	no	—
694	D₄	—	4	2	no	—
695	D₄	—	4	4	no	—
696	D₄	—	4	2	no	—
697	D₄	—	4	2	no	—
698	D₄	—	8	1	no	—
699	D₄	—	8	4	no	—
700	D₄	—	8	1	no	—
701	D₄	—	8	4	no	—
702	D₄	—	8	4	no	—
703	D₄	—	8	1	no	—
704	D₄	—	8	4	no	—
705	D₄	—	8	2	no	—
706	D₄	—	8	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	4	no	—
715	C₂×C₄	—	4	4	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	8	2	no	—
719	C₂×C₄	—	8	4	no	—
720	C₂×C₄	—	8	4	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	—	8	1	no	—
723	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
724	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
726	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
727	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
729	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
730	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
731	C₈	—	2	2	no	—
732	C₈	—	2	4	no	—
733	C₈	—	2	2	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	8	4	no	—
750	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
751	C₄	—	2	1	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	4	no	—
754	C₄	—	2	1	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	4	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	2	no	—
761	C₄	C₃₁×#576	1	2	yes	—
762	C₄	C₃₁×#585	1	2	yes	—
763	C₂	—	4	1	no	—
764	C₂	—	8	2	no	—
765	C₂	—	8	2	no	—
766	C₂	—	8	2	no	—
767	C₂	—	8	2	no	—
768	C₂	C₃₁×#3487	1	1	yes	characteristic
769	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
770	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×#3506	C₂	semidirect
3. C₃₁×#3399	C₂	semidirect
4. C₃₁×#3397	C₂	semidirect
5. C₃₁×#3391	C₂	semidirect
6. C₃₁×#3370	C₂	semidirect
7. C₃₁×#3366	C₂	semidirect
8. C₃₁×#3360	C₂	semidirect
9. C₃₁×#3220	C₂	semidirect
10. C₃₁×#3214	C₂	semidirect
11. C₃₁×#3207	C₂	semidirect
12. C₃₁×#3119	C₂	semidirect
13. C₃₁×#3109	C₂	semidirect
14. C₃₁×#3100	C₂	semidirect
15. C₃₁×#2985	C₂	semidirect
20. C₃₁×#554	C₂²	semidirect
21. C₃₁×#554	C₂²	semidirect
24. C₃₁×#550	C₂²	semidirect
25. C₃₁×#550	C₂²	semidirect
42. C₃₁×#496	C₂²	semidirect
44. C₃₁×#493	C₂²	semidirect
45. C₃₁×#492	C₂²	semidirect
47. C₃₁×#489	C₂²	semidirect
49. C₃₁×#487	C₂²	semidirect
50. C₃₁×#486	C₂²	semidirect
53. C₃₁×#479	C₂²	semidirect
54. C₃₁×#478	C₂²	semidirect
59. C₃₁×#463	C₂²	semidirect
60. C₃₁×#461	C₂²	semidirect
61. C₃₁×#460	C₂²	semidirect
66. C₃₁×#459	C₂²	semidirect
67. C₃₁×#459	C₂²	semidirect
72. C₃₁×#446	C₂²	semidirect
73. C₃₁×#446	C₂²	semidirect
74. C₈×Q₈×C₃₁	C₂²	semidirect
76. C₃₁×#442	C₂²	semidirect
77. C₃₁×#440	C₂²	semidirect
78. C₄×SD₁₆×C₃₁	C₂²	semidirect
81. C₄×D₈×C₃₁	C₂²	semidirect
288. #61910	C₃₁	direct (N × H)
349. #3548	C₂×C₃₁	semidirect
350. #3506	C₂×C₃₁	semidirect
351. #3399	C₂×C₃₁	semidirect
352. #3397	C₂×C₃₁	semidirect
353. #3391	C₂×C₃₁	semidirect
354. #3370	C₂×C₃₁	semidirect
355. #3366	C₂×C₃₁	semidirect
356. #3360	C₂×C₃₁	semidirect
357. #3220	C₂×C₃₁	semidirect
358. #3214	C₂×C₃₁	semidirect
359. #3207	C₂×C₃₁	semidirect
360. #3119	C₂×C₃₁	semidirect
361. #3109	C₂×C₃₁	semidirect
362. #3100	C₂×C₃₁	semidirect
363. #2985	C₂×C₃₁	semidirect
397. #554	C₂²×C₃₁	semidirect
398. #554	C₂²×C₃₁	semidirect
401. #550	C₂²×C₃₁	semidirect
402. #550	C₂²×C₃₁	semidirect
419. #496	C₂²×C₃₁	semidirect
421. #493	C₂²×C₃₁	semidirect
422. #492	C₂²×C₃₁	semidirect
424. #489	C₂²×C₃₁	semidirect
426. #487	C₂²×C₃₁	semidirect
427. #486	C₂²×C₃₁	semidirect
430. #479	C₂²×C₃₁	semidirect
431. #478	C₂²×C₃₁	semidirect
436. #463	C₂²×C₃₁	semidirect
437. #461	C₂²×C₃₁	semidirect
438. #460	C₂²×C₃₁	semidirect
443. #459	C₂²×C₃₁	semidirect
444. #459	C₂²×C₃₁	semidirect
449. #446	C₂²×C₃₁	semidirect
450. #446	C₂²×C₃₁	semidirect
451. C₈×Q₈	C₂²×C₃₁	semidirect
453. #442	C₂²×C₃₁	semidirect
454. #440	C₂²×C₃₁	semidirect
455. C₄×SD₁₆	C₂²×C₃₁	semidirect
458. C₄×D₈	C₂²×C₃₁	semidirect
582. C₃₁	#61910	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×#3506	2
C₃₁×#3399	2
C₃₁×#3397	2
C₃₁×#3391	2
C₃₁×#3370	2
C₃₁×#3366	2
C₃₁×#3360	2
C₃₁×#3220	2
C₃₁×#3214	2
C₃₁×#3207	2
C₃₁×#3119	2
C₃₁×#3109	2
C₃₁×#3100	2
C₃₁×#2985	2
#61910	31

Subgroups — C31×#61910 #21518669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61910 #21518669