Subgroups — C₃₁×#61805 #21518564

Order 7936.

1796 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3549	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3357	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3348	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3340	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3324	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3310	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3295	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3200	C₂	1	4	yes	maximal, complemented
12	C₃₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3103	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3096	C₂	1	4	yes	maximal, complemented
15	C₃₁×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×H(3,𝔽₄)	—	2	2	no	—
17	C₃₁×#559	—	2	1	no	—
18	C₃₁×#557	—	2	1	no	—
19	C₃₁×#556	—	2	2	no	—
20	C₃₁×#556	C₂²	1	2	yes	complemented
21	C₃₁×#555	—	2	1	no	—
22	C₃₁×#555	C₂²	1	2	yes	—
23	C₃₁×#555	C₂²	1	2	yes	—
24	C₃₁×#554	C₂²	1	2	yes	complemented
25	C₃₁×#552	C₂²	1	4	yes	complemented
26	D₄²×C₃₁	—	2	1	no	—
27	D₄²×C₃₁	C₂²	1	2	yes	—
28	D₄²×C₃₁	C₂²	1	2	yes	—
29	C₃₁×#539	—	2	2	no	—
30	C₃₁×#536	C₂²	1	2	yes	complemented
31	C₃₁×#535	—	2	2	no	—
32	C₃₁×#535	—	2	2	no	—
33	C₃₁×#535	C₂²	1	4	yes	—
34	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
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×#529	—	2	2	no	—
39	C₃₁×#520	C₂²	1	2	yes	complemented
40	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#501	C₂²	1	2	yes	complemented
42	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
43	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#490	C₂²	1	2	yes	—
45	C₃₁×#486	C₂²	1	1	yes	characteristic
46	C₃₁×#486	C₂²	1	1	yes	characteristic
47	C₃₁×#485	C₂²	1	4	yes	complemented
48	C₃₁×#485	C₂²	1	4	yes	complemented
49	C₃₁×#482	C₂²	1	4	yes	complemented
50	C₃₁×#482	C₂²	1	4	yes	complemented
51	C₃₁×#482	C₂²	1	4	yes	complemented
52	C₃₁×#482	C₂²	1	4	yes	complemented
53	C₃₁×#481	C₂²	1	4	yes	complemented
54	C₃₁×#481	C₂²	1	2	yes	complemented
55	C₃₁×#480	C₂²	1	2	yes	complemented
56	C₃₁×#480	C₂²	1	4	yes	complemented
57	C₃₁×#478	C₂²	1	4	yes	complemented
58	C₃₁×#477	C₂²	1	2	yes	complemented
59	C₃₁×#476	C₂²	1	2	yes	complemented
60	C₃₁×#475	C₂²	1	2	yes	complemented
61	C₃₁×#474	C₂²	1	2	yes	complemented
62	C₃₁×#468	C₂²	1	4	yes	complemented
63	C₃₁×#468	C₂²	1	4	yes	complemented
64	C₃₁×#465	C₂²	1	4	yes	complemented
65	C₃₁×#465	C₂²	1	4	yes	complemented
66	C₃₁×#460	C₂²	1	2	yes	—
67	C₃₁×#460	C₂²	1	2	yes	—
68	C₃₁×#450	C₂²	1	4	yes	complemented
69	C₃₁×#450	C₂²	1	4	yes	complemented
70	C₃₁×#448	C₂²	1	2	yes	complemented
71	C₃₁×#448	C₂²	1	2	yes	complemented
72	C₃₁×#440	C₂²	1	4	yes	complemented
73	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
74	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
75	C₃₁×#436	C₂²	1	2	yes	complemented
76	C₃₁×#435	C₂²	1	4	yes	complemented
77	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
78	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#428	C₂²	1	4	yes	complemented
81	C₃₁×#427	C₂²	1	4	yes	complemented
82	C₃₁×#418	C₂²	1	4	yes	complemented
83	C₂×C₃₁×#102	C₂²	1	4	yes	complemented
84	C₃₁×#408	C₂²	1	4	yes	complemented
85	C₂×#41×C₃₁	—	2	1	no	—
86	C₂×#41×C₃₁	—	2	1	no	—
87	C₂×#41×C₃₁	C₂³	1	2	yes	—
88	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₃₁	—	2	2	no	—
90	C₂²×D₄×C₃₁	—	2	2	no	—
91	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
92	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
93	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
94	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
95	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
96	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
97	C₃₁×C₄⋊Q₈	—	2	2	no	—
98	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
99	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
101	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
102	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₃₁×#127	—	2	4	no	—
104	C₃₁×#127	D₄	1	1	yes	characteristic
105	C₃₁×#127	C₂³	1	1	yes	characteristic
106	C₃₁×#127	C₂³	1	1	yes	characteristic
107	C₃₁×#126	—	2	4	no	—
108	C₃₁×#126	—	2	4	no	—
109	C₃₁×#125	—	2	2	no	—
110	C₃₁×#125	—	2	4	no	—
111	C₃₁×#125	C₂³	1	2	yes	—
112	C₃₁×#124	—	2	4	no	—
113	C₃₁×#124	—	2	2	no	—
114	C₃₁×#124	—	2	2	no	—
115	C₃₁×#124	—	2	4	no	—
116	C₃₁×#124	—	2	4	no	—
117	C₃₁×#124	—	2	1	no	—
118	C₃₁×#124	—	2	1	no	—
119	C₃₁×#124	D₄	1	2	yes	—
120	C₃₁×#123	—	2	4	no	—
121	C₃₁×#123	—	2	4	no	—
122	C₃₁×C₂²⋊Q₈	—	2	1	no	—
123	C₃₁×C₂²⋊Q₈	—	2	1	no	—
124	C₃₁×C₂²⋊Q₈	—	2	4	no	—
125	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
126	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
127	C₃₁×#121	—	2	2	no	—
128	C₃₁×#121	—	2	2	no	—
129	C₃₁×#121	—	2	1	no	—
130	C₃₁×#121	—	2	1	no	—
131	C₃₁×#121	—	2	2	no	—
132	C₃₁×#121	—	2	2	no	—
133	C₃₁×#121	D₄	1	2	yes	—
134	C₃₁×#121	D₄	1	2	yes	—
135	C₃₁×#121	C₂³	1	2	yes	—
136	C₃₁×#121	C₂³	1	2	yes	—
137	C₃₁×#121	C₂³	1	4	yes	—
138	C₃₁×#121	C₂³	1	4	yes	—
139	C₃₁×#120	—	2	4	no	—
140	C₃₁×#120	—	2	4	no	—
141	C₃₁×#120	—	2	4	no	—
142	C₃₁×#120	—	2	4	no	—
143	C₄×Q₈×C₃₁	—	2	2	no	—
144	C₄×Q₈×C₃₁	—	2	2	no	—
145	C₄×Q₈×C₃₁	—	2	1	no	—
146	C₄×Q₈×C₃₁	—	2	1	no	—
147	C₄×Q₈×C₃₁	—	2	1	no	—
148	C₄×Q₈×C₃₁	—	2	1	no	—
149	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
150	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
151	C₄×D₄×C₃₁	—	2	4	no	—
152	C₄×D₄×C₃₁	—	2	2	no	—
153	C₄×D₄×C₃₁	—	2	2	no	—
154	C₄×D₄×C₃₁	—	2	1	no	—
155	C₄×D₄×C₃₁	—	2	1	no	—
156	C₄×D₄×C₃₁	C₂³	1	2	yes	—
157	C₄×D₄×C₃₁	C₂³	1	2	yes	—
158	C₄×D₄×C₃₁	C₂³	1	2	yes	—
159	C₄×D₄×C₃₁	C₂³	1	2	yes	—
160	C₃₁×#117	—	2	2	no	—
161	C₃₁×#117	—	2	2	no	—
162	C₃₁×#117	—	2	4	no	—
163	C₃₁×#117	C₂³	1	4	yes	—
164	C₃₁×#117	C₂³	1	4	yes	—
165	C₃₁×#117	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	4	yes	—
173	C₃₁×#107	C₂³	1	4	yes	—
174	C₃₁×#106	C₂³	1	2	yes	—
175	C₃₁×#106	C₂³	1	4	yes	—
176	C₃₁×#106	C₂³	1	2	yes	—
177	C₃₁×#106	C₂³	1	4	yes	—
178	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
179	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
180	C₃₁×#103	C₂³	1	2	yes	—
181	C₃₁×#103	C₂³	1	2	yes	—
182	C₃₁×#103	C₂³	1	4	yes	—
183	C₃₁×#102	C₂³	1	2	yes	—
184	C₃₁×#102	C₂³	1	4	yes	—
185	C₃₁×#102	C₂³	1	4	yes	—
186	C₃₁×#102	C₂³	1	4	yes	—
187	C₃₁×#102	C₂³	1	2	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×C₂²⋊C₈	C₂³	1	4	yes	—
193	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
194	C₃₁×#97	C₂³	1	2	yes	—
195	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
197	C₂⁴×C₃₁	—	2	4	no	—
198	#41×C₃₁	—	4	4	no	—
199	#41×C₃₁	—	8	2	no	—
200	#41×C₃₁	—	8	2	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	1	no	—
205	C₂×Q₈×C₃₁	—	2	1	no	—
206	C₂×Q₈×C₃₁	—	4	2	no	—
207	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
209	C₂×D₄×C₃₁	—	2	4	no	—
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	1	no	—
217	C₂×D₄×C₃₁	—	2	4	no	—
218	C₂×D₄×C₃₁	—	4	4	no	—
219	C₂×D₄×C₃₁	—	4	4	no	—
220	C₂×D₄×C₃₁	—	8	4	no	—
221	C₂×D₄×C₃₁	—	8	4	no	—
222	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
223	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
224	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
225	C₂×D₄×C₃₁	C₂×D₄	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	1	no	—
230	C₂²×C₄×C₃₁	—	2	4	no	—
231	C₂²×C₄×C₃₁	—	2	2	no	—
232	C₂²×C₄×C₃₁	—	2	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	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
237	SD₁₆×C₃₁	—	4	2	no	—
238	SD₁₆×C₃₁	—	4	4	no	—
239	SD₁₆×C₃₁	—	4	2	no	—
240	M₁₆×C₃₁	—	4	4	no	—
241	C₂×C₈×C₃₁	—	4	4	no	—
242	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
243	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
244	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
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	4	no	—
249	C₄⋊C₄×C₃₁	—	2	1	no	—
250	C₄⋊C₄×C₃₁	—	2	1	no	—
251	C₄⋊C₄×C₃₁	—	2	2	no	—
252	C₄⋊C₄×C₃₁	—	2	4	no	—
253	C₄⋊C₄×C₃₁	—	2	1	no	—
254	C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₄⋊C₄×C₃₁	—	2	1	no	—
256	C₄⋊C₄×C₃₁	—	2	4	no	—
257	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₃₁	C₂⁴	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	C₂²⋊C₄×C₃₁	—	2	4	no	—
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	4	no	—
269	C₂²⋊C₄×C₃₁	—	2	4	no	—
270	C₂²⋊C₄×C₃₁	—	2	4	no	—
271	C₂²⋊C₄×C₃₁	—	2	2	no	—
272	C₂²⋊C₄×C₃₁	—	2	2	no	—
273	C₂²⋊C₄×C₃₁	—	2	2	no	—
274	C₂²⋊C₄×C₃₁	—	2	2	no	—
275	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
276	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
277	C₄²×C₃₁	—	2	2	no	—
278	C₄²×C₃₁	—	2	2	no	—
279	C₄²×C₃₁	—	2	4	no	—
280	C₄²×C₃₁	—	2	4	no	—
281	C₄²×C₃₁	—	2	2	no	—
282	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
285	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
286	#61805	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂³×C₃₁	—	2	2	no	—
288	C₂³×C₃₁	—	2	2	no	—
289	C₂³×C₃₁	—	8	4	no	—
290	C₂³×C₃₁	—	8	4	no	—
291	C₂³×C₃₁	—	8	4	no	—
292	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
293	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
294	Q₈×C₃₁	—	2	2	no	—
295	Q₈×C₃₁	—	2	2	no	—
296	Q₈×C₃₁	—	4	2	no	—
297	Q₈×C₃₁	—	4	2	no	—
298	Q₈×C₃₁	—	4	2	no	—
299	Q₈×C₃₁	—	8	1	no	—
300	Q₈×C₃₁	—	8	1	no	—
301	Q₈×C₃₁	—	8	1	no	—
302	D₄×C₃₁	—	2	4	no	—
303	D₄×C₃₁	—	2	2	no	—
304	D₄×C₃₁	—	2	4	no	—
305	D₄×C₃₁	—	2	2	no	—
306	D₄×C₃₁	—	4	2	no	—
307	D₄×C₃₁	—	4	2	no	—
308	D₄×C₃₁	—	4	4	no	—
309	D₄×C₃₁	—	4	2	no	—
310	D₄×C₃₁	—	4	2	no	—
311	D₄×C₃₁	—	8	4	no	—
312	D₄×C₃₁	—	8	1	no	—
313	D₄×C₃₁	—	8	1	no	—
314	D₄×C₃₁	—	8	4	no	—
315	D₄×C₃₁	—	8	4	no	—
316	D₄×C₃₁	—	8	2	no	—
317	D₄×C₃₁	—	8	2	no	—
318	C₂×C₄×C₃₁	—	2	2	no	—
319	C₂×C₄×C₃₁	—	2	4	no	—
320	C₂×C₄×C₃₁	—	2	4	no	—
321	C₂×C₄×C₃₁	—	2	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	2	no	—
331	C₂×C₄×C₃₁	—	4	4	no	—
332	C₂×C₄×C₃₁	—	8	1	no	—
333	C₂×C₄×C₃₁	—	8	4	no	—
334	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
337	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	#3549	C₂×C₃₁	1	1	yes	characteristic
345	#3507	C₂×C₃₁	1	1	yes	characteristic, complemented
346	#3357	C₂×C₃₁	1	2	yes	complemented
347	#3348	C₂×C₃₁	1	4	yes	complemented
348	#3340	C₂×C₃₁	1	2	yes	complemented
349	#3324	C₂×C₃₁	1	2	yes	complemented
350	#3310	C₂×C₃₁	1	4	yes	complemented
351	#3295	C₂×C₃₁	1	2	yes	complemented
352	#3235	C₂×C₃₁	1	1	yes	characteristic, complemented
353	#3228	C₂×C₃₁	1	1	yes	characteristic, complemented
354	#3200	C₂×C₃₁	1	4	yes	complemented
355	#3112	C₂×C₃₁	1	1	yes	characteristic, complemented
356	#3103	C₂×C₃₁	1	1	yes	characteristic, complemented
357	#3096	C₂×C₃₁	1	4	yes	complemented
358	#2981	C₂×C₃₁	1	1	yes	characteristic, complemented
359	C₂²×C₃₁	—	2	1	no	—
360	C₂²×C₃₁	—	2	4	no	—
361	C₂²×C₃₁	—	2	1	no	—
362	C₂²×C₃₁	—	2	4	no	—
363	C₂²×C₃₁	—	2	1	no	—
364	C₂²×C₃₁	—	2	4	no	—
365	C₂²×C₃₁	—	4	2	no	—
366	C₂²×C₃₁	—	4	2	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	—	16	8	no	—
372	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
373	C₄×C₃₁	—	2	1	no	—
374	C₄×C₃₁	—	2	1	no	—
375	C₄×C₃₁	—	2	1	no	—
376	C₄×C₃₁	—	2	4	no	—
377	C₄×C₃₁	—	2	1	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	—	4	2	no	—
383	C₄×C₃₁	—	4	2	no	—
384	C₄×C₃₁	#577	1	2	yes	—
385	C₄×C₃₁	#585	1	2	yes	—
386	H(3,𝔽₄)	—	2	2	no	—
387	#559	—	2	1	no	—
388	#557	—	2	1	no	—
389	#556	—	2	2	no	—
390	#556	C₂²×C₃₁	1	2	yes	complemented
391	#555	—	2	1	no	—
392	#555	C₂²×C₃₁	1	2	yes	—
393	#555	C₂²×C₃₁	1	2	yes	—
394	#554	C₂²×C₃₁	1	2	yes	complemented
395	#552	C₂²×C₃₁	1	4	yes	complemented
396	D₄²	—	2	1	no	—
397	D₄²	C₂²×C₃₁	1	2	yes	—
398	D₄²	C₂²×C₃₁	1	2	yes	—
399	#539	—	2	2	no	—
400	#536	C₂²×C₃₁	1	2	yes	complemented
401	#535	—	2	2	no	—
402	#535	—	2	2	no	—
403	#535	C₂²×C₃₁	1	4	yes	—
404	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
405	#532	C₂²×C₃₁	1	1	yes	characteristic
406	#532	C₂²×C₃₁	1	1	yes	characteristic
407	#532	C₂²×C₃₁	1	1	yes	characteristic
408	#529	—	2	2	no	—
409	#520	C₂²×C₃₁	1	2	yes	complemented
410	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
411	#501	C₂²×C₃₁	1	2	yes	complemented
412	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
413	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
414	#490	C₂²×C₃₁	1	2	yes	—
415	#486	C₂²×C₃₁	1	1	yes	characteristic
416	#486	C₂²×C₃₁	1	1	yes	characteristic
417	#485	C₂²×C₃₁	1	4	yes	complemented
418	#485	C₂²×C₃₁	1	4	yes	complemented
419	#482	C₂²×C₃₁	1	4	yes	complemented
420	#482	C₂²×C₃₁	1	4	yes	complemented
421	#482	C₂²×C₃₁	1	4	yes	complemented
422	#482	C₂²×C₃₁	1	4	yes	complemented
423	#481	C₂²×C₃₁	1	4	yes	complemented
424	#481	C₂²×C₃₁	1	2	yes	complemented
425	#480	C₂²×C₃₁	1	2	yes	complemented
426	#480	C₂²×C₃₁	1	4	yes	complemented
427	#478	C₂²×C₃₁	1	4	yes	complemented
428	#477	C₂²×C₃₁	1	2	yes	complemented
429	#476	C₂²×C₃₁	1	2	yes	complemented
430	#475	C₂²×C₃₁	1	2	yes	complemented
431	#474	C₂²×C₃₁	1	2	yes	complemented
432	#468	C₂²×C₃₁	1	4	yes	complemented
433	#468	C₂²×C₃₁	1	4	yes	complemented
434	#465	C₂²×C₃₁	1	4	yes	complemented
435	#465	C₂²×C₃₁	1	4	yes	complemented
436	#460	C₂²×C₃₁	1	2	yes	—
437	#460	C₂²×C₃₁	1	2	yes	—
438	#450	C₂²×C₃₁	1	4	yes	complemented
439	#450	C₂²×C₃₁	1	4	yes	complemented
440	#448	C₂²×C₃₁	1	2	yes	complemented
441	#448	C₂²×C₃₁	1	2	yes	complemented
442	#440	C₂²×C₃₁	1	4	yes	complemented
443	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
444	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
445	#436	C₂²×C₃₁	1	2	yes	complemented
446	#435	C₂²×C₃₁	1	4	yes	complemented
447	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
448	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
449	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
450	#428	C₂²×C₃₁	1	4	yes	complemented
451	#427	C₂²×C₃₁	1	4	yes	complemented
452	#418	C₂²×C₃₁	1	4	yes	complemented
453	C₂×#102	C₂²×C₃₁	1	4	yes	complemented
454	#408	C₂²×C₃₁	1	4	yes	complemented
455	C₂×C₃₁	—	4	1	no	—
456	C₂×C₃₁	—	4	4	no	—
457	C₂×C₃₁	—	8	2	no	—
458	C₂×C₃₁	—	8	2	no	—
459	C₂×C₃₁	#3485	1	1	yes	characteristic
460	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
461	C₂×C₃₁	#3585	1	1	yes	characteristic
462	C₂×#41	—	2	1	no	—
463	C₂×#41	—	2	1	no	—
464	C₂×#41	C₂³×C₃₁	1	2	yes	—
465	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
466	C₂²×D₄	—	2	2	no	—
467	C₂²×D₄	—	2	2	no	—
468	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
469	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
470	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
471	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
472	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
473	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
474	C₄⋊Q₈	—	2	2	no	—
475	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
476	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
477	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
478	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
479	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
480	#127	—	2	4	no	—
481	#127	D₄×C₃₁	1	1	yes	characteristic
482	#127	C₂³×C₃₁	1	1	yes	characteristic
483	#127	C₂³×C₃₁	1	1	yes	characteristic
484	#126	—	2	4	no	—
485	#126	—	2	4	no	—
486	#125	—	2	2	no	—
487	#125	—	2	4	no	—
488	#125	C₂³×C₃₁	1	2	yes	—
489	#124	—	2	4	no	—
490	#124	—	2	2	no	—
491	#124	—	2	2	no	—
492	#124	—	2	4	no	—
493	#124	—	2	4	no	—
494	#124	—	2	1	no	—
495	#124	—	2	1	no	—
496	#124	D₄×C₃₁	1	2	yes	—
497	#123	—	2	4	no	—
498	#123	—	2	4	no	—
499	C₂²⋊Q₈	—	2	1	no	—
500	C₂²⋊Q₈	—	2	1	no	—
501	C₂²⋊Q₈	—	2	4	no	—
502	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
503	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
504	#121	—	2	2	no	—
505	#121	—	2	2	no	—
506	#121	—	2	1	no	—
507	#121	—	2	1	no	—
508	#121	—	2	2	no	—
509	#121	—	2	2	no	—
510	#121	D₄×C₃₁	1	2	yes	—
511	#121	D₄×C₃₁	1	2	yes	—
512	#121	C₂³×C₃₁	1	2	yes	—
513	#121	C₂³×C₃₁	1	2	yes	—
514	#121	C₂³×C₃₁	1	4	yes	—
515	#121	C₂³×C₃₁	1	4	yes	—
516	#120	—	2	4	no	—
517	#120	—	2	4	no	—
518	#120	—	2	4	no	—
519	#120	—	2	4	no	—
520	C₄×Q₈	—	2	2	no	—
521	C₄×Q₈	—	2	2	no	—
522	C₄×Q₈	—	2	1	no	—
523	C₄×Q₈	—	2	1	no	—
524	C₄×Q₈	—	2	1	no	—
525	C₄×Q₈	—	2	1	no	—
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	2	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	2	1	no	—
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	C₂³×C₃₁	1	2	yes	—
534	C₄×D₄	C₂³×C₃₁	1	2	yes	—
535	C₄×D₄	C₂³×C₃₁	1	2	yes	—
536	C₄×D₄	C₂³×C₃₁	1	2	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	4	yes	—
542	#117	C₂³×C₃₁	1	4	yes	—
543	C₂×C₄⋊C₄	—	2	1	no	—
544	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
546	C₂×C₄²	—	2	1	no	—
547	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
548	#107	C₂³×C₃₁	1	4	yes	—
549	#107	C₂³×C₃₁	1	4	yes	—
550	#107	C₂³×C₃₁	1	4	yes	—
551	#106	C₂³×C₃₁	1	2	yes	—
552	#106	C₂³×C₃₁	1	4	yes	—
553	#106	C₂³×C₃₁	1	2	yes	—
554	#106	C₂³×C₃₁	1	4	yes	—
555	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
556	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
557	#103	C₂³×C₃₁	1	2	yes	—
558	#103	C₂³×C₃₁	1	2	yes	—
559	#103	C₂³×C₃₁	1	4	yes	—
560	#102	C₂³×C₃₁	1	2	yes	—
561	#102	C₂³×C₃₁	1	4	yes	—
562	#102	C₂³×C₃₁	1	4	yes	—
563	#102	C₂³×C₃₁	1	4	yes	—
564	#102	C₂³×C₃₁	1	2	yes	—
565	#102	C₂³×C₃₁	1	4	yes	—
566	#102	C₂³×C₃₁	1	4	yes	—
567	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
568	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
569	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
570	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
571	#97	C₂³×C₃₁	1	2	yes	—
572	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
573	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
574	C₃₁	#61805	1	1	yes	characteristic, direct product factor, Sylow
575	C₂⁴	—	2	4	no	—
576	#41	—	4	4	no	—
577	#41	—	8	2	no	—
578	#41	—	8	2	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	4	2	no	—
585	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
586	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	—	4	4	no	—
598	C₂×D₄	—	8	4	no	—
599	C₂×D₄	—	8	4	no	—
600	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
601	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
602	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
603	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
604	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
605	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
615	SD₁₆	—	4	2	no	—
616	SD₁₆	—	4	4	no	—
617	SD₁₆	—	4	2	no	—
618	M₁₆	—	4	4	no	—
619	C₂×C₈	—	4	4	no	—
620	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
621	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
622	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	1	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	C₂⁴×C₃₁	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
639	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
640	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
654	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
655	C₄²	—	2	2	no	—
656	C₄²	—	2	2	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	1	yes	characteristic
663	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	8	4	no	—
667	C₂³	—	8	4	no	—
668	C₂³	—	8	4	no	—
669	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
670	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
671	Q₈	—	2	2	no	—
672	Q₈	—	2	2	no	—
673	Q₈	—	4	2	no	—
674	Q₈	—	4	2	no	—
675	Q₈	—	4	2	no	—
676	Q₈	—	8	1	no	—
677	Q₈	—	8	1	no	—
678	Q₈	—	8	1	no	—
679	D₄	—	2	4	no	—
680	D₄	—	2	2	no	—
681	D₄	—	2	4	no	—
682	D₄	—	2	2	no	—
683	D₄	—	4	2	no	—
684	D₄	—	4	2	no	—
685	D₄	—	4	4	no	—
686	D₄	—	4	2	no	—
687	D₄	—	4	2	no	—
688	D₄	—	8	4	no	—
689	D₄	—	8	1	no	—
690	D₄	—	8	1	no	—
691	D₄	—	8	4	no	—
692	D₄	—	8	4	no	—
693	D₄	—	8	2	no	—
694	D₄	—	8	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	4	no	—
707	C₂×C₄	—	4	2	no	—
708	C₂×C₄	—	4	4	no	—
709	C₂×C₄	—	8	1	no	—
710	C₂×C₄	—	8	4	no	—
711	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
713	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
714	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
715	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
716	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
717	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
718	C₈	—	2	2	no	—
719	C₈	—	2	4	no	—
720	C₈	—	2	2	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	16	8	no	—
734	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
735	C₄	—	2	1	no	—
736	C₄	—	2	4	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	1	no	—
739	C₄	—	2	1	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	C₃₁×#577	1	2	yes	—
747	C₄	C₃₁×#585	1	2	yes	—
748	C₂	—	4	4	no	—
749	C₂	—	4	1	no	—
750	C₂	—	8	2	no	—
751	C₂	—	8	2	no	—
752	C₂	C₃₁×#3485	1	1	yes	characteristic
753	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
754	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3549	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3507	C₂	semidirect
3. C₃₁×#3357	C₂	semidirect
4. C₃₁×#3348	C₂	semidirect
5. C₃₁×#3340	C₂	semidirect
6. C₃₁×#3324	C₂	semidirect
7. C₃₁×#3310	C₂	semidirect
8. C₃₁×#3295	C₂	semidirect
9. C₃₁×#3235	C₂	semidirect
10. C₃₁×#3228	C₂	semidirect
11. C₃₁×#3200	C₂	semidirect
12. C₃₁×#3112	C₂	semidirect
13. C₃₁×#3103	C₂	semidirect
14. C₃₁×#3096	C₂	semidirect
15. C₃₁×#2981	C₂	semidirect
20. C₃₁×#556	C₂²	semidirect
24. C₃₁×#554	C₂²	semidirect
25. C₃₁×#552	C₂²	semidirect
30. C₃₁×#536	C₂²	semidirect
34. C₃₁×#533	C₂²	semidirect
39. C₃₁×#520	C₂²	semidirect
40. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
41. C₃₁×#501	C₂²	semidirect
42. C₃₁×#500	C₂²	semidirect
43. C₃₁×#498	C₂²	semidirect
47. C₃₁×#485	C₂²	semidirect
48. C₃₁×#485	C₂²	semidirect
49. C₃₁×#482	C₂²	semidirect
50. C₃₁×#482	C₂²	semidirect
51. C₃₁×#482	C₂²	semidirect
52. C₃₁×#482	C₂²	semidirect
53. C₃₁×#481	C₂²	semidirect
54. C₃₁×#481	C₂²	semidirect
55. C₃₁×#480	C₂²	semidirect
56. C₃₁×#480	C₂²	semidirect
57. C₃₁×#478	C₂²	semidirect
58. C₃₁×#477	C₂²	semidirect
59. C₃₁×#476	C₂²	semidirect
60. C₃₁×#475	C₂²	semidirect
61. C₃₁×#474	C₂²	semidirect
62. C₃₁×#468	C₂²	semidirect
63. C₃₁×#468	C₂²	semidirect
64. C₃₁×#465	C₂²	semidirect
65. C₃₁×#465	C₂²	semidirect
68. C₃₁×#450	C₂²	semidirect
69. C₃₁×#450	C₂²	semidirect
70. C₃₁×#448	C₂²	semidirect
71. C₃₁×#448	C₂²	semidirect
72. C₃₁×#440	C₂²	semidirect
73. C₄×SD₁₆×C₃₁	C₂²	semidirect
74. C₄×SD₁₆×C₃₁	C₂²	semidirect
75. C₃₁×#436	C₂²	semidirect
76. C₃₁×#435	C₂²	semidirect
77. C₈×D₄×C₃₁	C₂²	semidirect
78. C₃₁×#432	C₂²	semidirect
79. C₃₁×#431	C₂²	semidirect
80. C₃₁×#428	C₂²	semidirect
81. C₃₁×#427	C₂²	semidirect
82. C₃₁×#418	C₂²	semidirect
83. C₂×C₃₁×#102	C₂²	semidirect
84. C₃₁×#408	C₂²	semidirect
286. #61805	C₃₁	direct (N × H)
345. #3507	C₂×C₃₁	semidirect
346. #3357	C₂×C₃₁	semidirect
347. #3348	C₂×C₃₁	semidirect
348. #3340	C₂×C₃₁	semidirect
349. #3324	C₂×C₃₁	semidirect
350. #3310	C₂×C₃₁	semidirect
351. #3295	C₂×C₃₁	semidirect
352. #3235	C₂×C₃₁	semidirect
353. #3228	C₂×C₃₁	semidirect
354. #3200	C₂×C₃₁	semidirect
355. #3112	C₂×C₃₁	semidirect
356. #3103	C₂×C₃₁	semidirect
357. #3096	C₂×C₃₁	semidirect
358. #2981	C₂×C₃₁	semidirect
390. #556	C₂²×C₃₁	semidirect
394. #554	C₂²×C₃₁	semidirect
395. #552	C₂²×C₃₁	semidirect
400. #536	C₂²×C₃₁	semidirect
404. #533	C₂²×C₃₁	semidirect
409. #520	C₂²×C₃₁	semidirect
410. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
411. #501	C₂²×C₃₁	semidirect
412. #500	C₂²×C₃₁	semidirect
413. #498	C₂²×C₃₁	semidirect
417. #485	C₂²×C₃₁	semidirect
418. #485	C₂²×C₃₁	semidirect
419. #482	C₂²×C₃₁	semidirect
420. #482	C₂²×C₃₁	semidirect
421. #482	C₂²×C₃₁	semidirect
422. #482	C₂²×C₃₁	semidirect
423. #481	C₂²×C₃₁	semidirect
424. #481	C₂²×C₃₁	semidirect
425. #480	C₂²×C₃₁	semidirect
426. #480	C₂²×C₃₁	semidirect
427. #478	C₂²×C₃₁	semidirect
428. #477	C₂²×C₃₁	semidirect
429. #476	C₂²×C₃₁	semidirect
430. #475	C₂²×C₃₁	semidirect
431. #474	C₂²×C₃₁	semidirect
432. #468	C₂²×C₃₁	semidirect
433. #468	C₂²×C₃₁	semidirect
434. #465	C₂²×C₃₁	semidirect
435. #465	C₂²×C₃₁	semidirect
438. #450	C₂²×C₃₁	semidirect
439. #450	C₂²×C₃₁	semidirect
440. #448	C₂²×C₃₁	semidirect
441. #448	C₂²×C₃₁	semidirect
442. #440	C₂²×C₃₁	semidirect
443. C₄×SD₁₆	C₂²×C₃₁	semidirect
444. C₄×SD₁₆	C₂²×C₃₁	semidirect
445. #436	C₂²×C₃₁	semidirect
446. #435	C₂²×C₃₁	semidirect
447. C₈×D₄	C₂²×C₃₁	semidirect
448. #432	C₂²×C₃₁	semidirect
449. #431	C₂²×C₃₁	semidirect
450. #428	C₂²×C₃₁	semidirect
451. #427	C₂²×C₃₁	semidirect
452. #418	C₂²×C₃₁	semidirect
453. C₂×#102	C₂²×C₃₁	semidirect
454. #408	C₂²×C₃₁	semidirect
574. C₃₁	#61805	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×#3549	2
C₃₁×#3507	2
C₃₁×#3357	2
C₃₁×#3348	2
C₃₁×#3340	2
C₃₁×#3324	2
C₃₁×#3310	2
C₃₁×#3295	2
C₃₁×#3235	2
C₃₁×#3228	2
C₃₁×#3200	2
C₃₁×#3112	2
C₃₁×#3103	2
C₃₁×#3096	2
C₃₁×#2981	2
#61805	31

Subgroups — C31×#61805 #21518564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61805 #21518564