Subgroups — C₃₁×#62539 #21519298

Order 7936.

2042 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3498	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3368	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3324	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3310	C₂	1	8	yes	maximal, complemented
6	C₃₁×#3228	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3226	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3208	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3182	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3138	C₂	1	2	yes	maximal, complemented
13	C₂×C₃₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2965	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×H(5,𝔽₂)	—	2	1	no	—
16	C₃₁×#557	—	2	1	no	—
17	C₃₁×#557	C₂²	1	2	yes	complemented
18	C₃₁×#556	—	2	1	no	—
19	C₃₁×#556	C₂²	1	2	yes	complemented
20	C₃₁×#552	—	2	2	no	—
21	C₃₁×#552	C₂²	1	4	yes	complemented
22	C₃₁×#550	—	2	1	no	—
23	C₃₁×#550	C₂²	1	2	yes	—
24	D₄²×C₃₁	—	2	2	no	—
25	D₄²×C₃₁	—	2	1	no	—
26	D₄²×C₃₁	C₂²	1	4	yes	—
27	D₄²×C₃₁	C₂²	1	2	yes	—
28	C₃₁×#541	—	2	2	no	—
29	C₃₁×#536	—	2	1	no	—
30	C₃₁×#535	—	2	1	no	—
31	C₃₁×#535	—	2	2	no	—
32	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#533	C₂²	1	2	yes	complemented
34	C₃₁×#533	C₂²	1	2	yes	complemented
35	C₃₁×#532	C₂²	1	1	yes	characteristic
36	C₃₁×#532	C₂²	1	2	yes	—
37	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
39	C₂×C₃₁×#127	C₂²	1	2	yes	—
40	C₃₁×#519	—	2	1	no	—
41	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#500	C₂²	1	2	yes	complemented
43	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#492	C₂²	1	2	yes	complemented
46	C₃₁×#490	C₂²	1	8	yes	complemented
47	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#486	C₂²	1	4	yes	complemented
49	C₃₁×#486	C₂²	1	2	yes	complemented
50	C₃₁×#486	C₂²	1	2	yes	complemented
51	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#486	C₂²	1	2	yes	complemented
53	C₃₁×#486	C₂²	1	2	yes	complemented
54	C₃₁×#482	C₂²	1	8	yes	complemented
55	C₃₁×#480	C₂²	1	4	yes	complemented
56	C₃₁×#478	C₂²	1	8	yes	complemented
57	C₃₁×#474	C₂²	1	4	yes	complemented
58	C₃₁×#468	C₂²	1	8	yes	complemented
59	C₃₁×#465	C₂²	1	4	yes	complemented
60	C₃₁×#460	C₂²	1	8	yes	complemented
61	C₃₁×#460	C₂²	1	4	yes	complemented
62	C₃₁×#450	C₂²	1	4	yes	complemented
63	C₃₁×#450	C₂²	1	8	yes	complemented
64	C₃₁×#446	C₂²	1	2	yes	complemented
65	C₃₁×#440	C₂²	1	8	yes	complemented
66	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
67	C₃₁×#436	C₂²	1	2	yes	complemented
68	C₃₁×#435	C₂²	1	4	yes	complemented
69	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#431	C₂²	1	2	yes	complemented
71	C₃₁×#418	C₂²	1	8	yes	complemented
72	C₂×C₃₁×#102	C₂²	1	4	yes	complemented
73	C₄×M₁₆×C₃₁	C₂²	1	2	yes	complemented
74	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
75	C₃₁×H(5,𝔽₂)	—	4	8	no	—
76	C₂×#41×C₃₁	—	2	2	no	—
77	C₂×#41×C₃₁	—	2	2	no	—
78	C₂×#41×C₃₁	—	2	1	no	—
79	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
80	C₂²×Q₈×C₃₁	—	2	1	no	—
81	C₂²×D₄×C₃₁	—	2	4	no	—
82	C₂²×D₄×C₃₁	—	2	2	no	—
83	C₂²×D₄×C₃₁	—	2	2	no	—
84	C₂²×D₄×C₃₁	—	2	1	no	—
85	C₂²×D₄×C₃₁	—	2	1	no	—
86	C₂²×D₄×C₃₁	—	2	2	no	—
87	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
88	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
89	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
90	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
91	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
92	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
93	C₃₁×C₄⋊Q₈	—	2	2	no	—
94	C₃₁×C₄⋊Q₈	—	2	1	no	—
95	C₃₁×C₄⋊Q₈	—	2	1	no	—
96	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
97	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
100	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
101	C₃₁×#127	—	2	2	no	—
102	C₃₁×#127	—	2	1	no	—
103	C₃₁×#127	—	2	2	no	—
104	C₃₁×#127	—	2	1	no	—
105	C₃₁×#127	C₂³	1	2	yes	—
106	C₃₁×#127	C₂³	1	4	yes	—
107	C₃₁×#127	C₂³	1	2	yes	—
108	C₃₁×#127	C₂³	1	1	yes	characteristic
109	C₃₁×#126	—	2	4	no	—
110	C₃₁×#126	—	2	4	no	—
111	C₃₁×#125	—	2	4	no	—
112	C₃₁×#125	—	2	4	no	—
113	C₃₁×#125	—	2	1	no	—
114	C₃₁×#125	—	2	2	no	—
115	C₃₁×#125	C₂³	1	4	yes	—
116	C₃₁×#124	—	2	2	no	—
117	C₃₁×#124	—	2	2	no	—
118	C₃₁×#124	—	2	1	no	—
119	C₃₁×#123	—	2	4	no	—
120	C₃₁×C₂²⋊Q₈	—	2	2	no	—
121	C₃₁×C₂²⋊Q₈	—	2	2	no	—
122	C₃₁×C₂²⋊Q₈	—	2	1	no	—
123	C₃₁×C₂²⋊Q₈	—	2	2	no	—
124	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
125	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
126	C₃₁×#121	—	2	1	no	—
127	C₃₁×#121	—	2	2	no	—
128	C₃₁×#121	—	2	2	no	—
129	C₃₁×#121	—	2	4	no	—
130	C₃₁×#121	—	2	2	no	—
131	C₃₁×#121	—	2	4	no	—
132	C₃₁×#121	C₂³	1	2	yes	—
133	C₃₁×#121	C₂³	1	4	yes	—
134	C₃₁×#120	—	2	4	no	—
135	C₃₁×#120	—	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	2	no	—
141	C₄×Q₈×C₃₁	—	2	2	no	—
142	C₄×Q₈×C₃₁	—	2	1	no	—
143	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
144	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
145	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
146	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
147	C₄×D₄×C₃₁	—	2	2	no	—
148	C₄×D₄×C₃₁	—	2	1	no	—
149	C₄×D₄×C₃₁	D₄	1	2	yes	—
150	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
151	C₄×D₄×C₃₁	C₂³	1	2	yes	—
152	C₄×D₄×C₃₁	C₂³	1	4	yes	—
153	C₄×D₄×C₃₁	C₂³	1	2	yes	—
154	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
155	C₃₁×#117	—	2	1	no	—
156	C₃₁×#117	—	2	2	no	—
157	C₃₁×#117	—	2	4	no	—
158	C₃₁×#117	D₄	1	1	yes	characteristic
159	C₃₁×#117	D₄	1	2	yes	—
160	C₃₁×#117	C₂³	1	4	yes	—
161	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
165	C₃₁×#107	C₂³	1	8	yes	—
166	C₃₁×#106	C₂³	1	4	yes	—
167	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
168	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
169	C₃₁×#103	C₂³	1	4	yes	—
170	C₃₁×#102	C₂³	1	8	yes	—
171	C₃₁×#102	C₂³	1	8	yes	—
172	C₃₁×#102	C₂³	1	4	yes	—
173	C₃₁×#102	C₂³	1	8	yes	—
174	C₃₁×#102	C₂³	1	8	yes	—
175	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
176	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₃₁×#97	C₂³	1	4	yes	—
178	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
179	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
180	C₄×C₈×C₃₁	C₂³	1	2	yes	—
181	C₄×C₈×C₃₁	C₂³	1	2	yes	—
182	C₂⁴×C₃₁	—	2	4	no	—
183	C₂⁴×C₃₁	—	2	2	no	—
184	#41×C₃₁	—	2	4	no	—
185	#41×C₃₁	—	4	8	no	—
186	#41×C₃₁	—	4	8	no	—
187	#41×C₃₁	—	4	4	no	—
188	C₂×Q₈×C₃₁	—	2	1	no	—
189	C₂×Q₈×C₃₁	—	2	2	no	—
190	C₂×Q₈×C₃₁	—	2	2	no	—
191	C₂×Q₈×C₃₁	—	2	1	no	—
192	C₂×Q₈×C₃₁	—	4	4	no	—
193	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
194	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
195	C₂×D₄×C₃₁	—	2	4	no	—
196	C₂×D₄×C₃₁	—	2	2	no	—
197	C₂×D₄×C₃₁	—	2	2	no	—
198	C₂×D₄×C₃₁	—	2	1	no	—
199	C₂×D₄×C₃₁	—	2	4	no	—
200	C₂×D₄×C₃₁	—	2	2	no	—
201	C₂×D₄×C₃₁	—	2	1	no	—
202	C₂×D₄×C₃₁	—	2	2	no	—
203	C₂×D₄×C₃₁	—	2	4	no	—
204	C₂×D₄×C₃₁	—	2	2	no	—
205	C₂×D₄×C₃₁	—	2	4	no	—
206	C₂×D₄×C₃₁	—	2	2	no	—
207	C₂×D₄×C₃₁	—	4	4	no	—
208	C₂×D₄×C₃₁	—	4	8	no	—
209	C₂×D₄×C₃₁	—	4	8	no	—
210	C₂×D₄×C₃₁	—	4	16	no	—
211	C₂×D₄×C₃₁	—	4	8	no	—
212	C₂×D₄×C₃₁	—	4	4	no	—
213	C₂×D₄×C₃₁	—	8	2	no	—
214	C₂×D₄×C₃₁	—	8	4	no	—
215	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
216	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
217	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
218	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₃₁	—	2	2	no	—
220	C₂²×C₄×C₃₁	—	2	4	no	—
221	C₂²×C₄×C₃₁	—	2	2	no	—
222	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
224	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
228	SD₁₆×C₃₁	—	4	4	no	—
229	SD₁₆×C₃₁	—	4	8	no	—
230	M₁₆×C₃₁	—	4	4	no	—
231	C₂×C₈×C₃₁	—	4	2	no	—
232	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
233	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
234	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
235	C₄⋊C₄×C₃₁	—	2	2	no	—
236	C₄⋊C₄×C₃₁	—	2	2	no	—
237	C₄⋊C₄×C₃₁	—	2	2	no	—
238	C₄⋊C₄×C₃₁	—	2	1	no	—
239	C₄⋊C₄×C₃₁	—	2	1	no	—
240	C₄⋊C₄×C₃₁	—	2	1	no	—
241	C₄⋊C₄×C₃₁	—	2	4	no	—
242	C₄⋊C₄×C₃₁	—	2	4	no	—
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	4	no	—
247	C₄⋊C₄×C₃₁	—	2	2	no	—
248	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
249	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
250	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
251	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
252	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
254	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
255	C₂²⋊C₄×C₃₁	—	2	2	no	—
256	C₂²⋊C₄×C₃₁	—	2	4	no	—
257	C₂²⋊C₄×C₃₁	—	2	4	no	—
258	C₂²⋊C₄×C₃₁	—	2	4	no	—
259	C₂²⋊C₄×C₃₁	—	2	2	no	—
260	C₂²⋊C₄×C₃₁	—	2	4	no	—
261	C₂²⋊C₄×C₃₁	—	2	2	no	—
262	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
263	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
264	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
265	C₄²×C₃₁	—	2	4	no	—
266	C₄²×C₃₁	—	2	4	no	—
267	C₄²×C₃₁	—	2	2	no	—
268	C₄²×C₃₁	C₂×D₄	1	2	yes	—
269	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
270	C₄²×C₃₁	C₂×D₄	1	2	yes	—
271	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
273	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
274	C₄²×C₃₁	C₂⁴	1	2	yes	—
275	#62539	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂³×C₃₁	—	2	4	no	—
277	C₂³×C₃₁	—	2	2	no	—
278	C₂³×C₃₁	—	4	8	no	—
279	C₂³×C₃₁	—	4	4	no	—
280	C₂³×C₃₁	—	8	2	no	—
281	C₂³×C₃₁	—	8	4	no	—
282	C₂³×C₃₁	—	8	2	no	—
283	C₂³×C₃₁	—	8	4	no	—
284	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
285	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
286	Q₈×C₃₁	—	2	2	no	—
287	Q₈×C₃₁	—	2	4	no	—
288	Q₈×C₃₁	—	4	4	no	—
289	Q₈×C₃₁	—	4	4	no	—
290	Q₈×C₃₁	—	4	2	no	—
291	Q₈×C₃₁	—	4	2	no	—
292	D₄×C₃₁	—	2	4	no	—
293	D₄×C₃₁	—	2	2	no	—
294	D₄×C₃₁	—	2	4	no	—
295	D₄×C₃₁	—	2	8	no	—
296	D₄×C₃₁	—	4	8	no	—
297	D₄×C₃₁	—	4	8	no	—
298	D₄×C₃₁	—	4	4	no	—
299	D₄×C₃₁	—	4	2	no	—
300	D₄×C₃₁	—	4	4	no	—
301	D₄×C₃₁	—	4	4	no	—
302	D₄×C₃₁	—	4	4	no	—
303	D₄×C₃₁	—	4	2	no	—
304	D₄×C₃₁	—	8	2	no	—
305	D₄×C₃₁	—	8	4	no	—
306	D₄×C₃₁	—	8	4	no	—
307	D₄×C₃₁	—	8	2	no	—
308	C₂×C₄×C₃₁	—	2	4	no	—
309	C₂×C₄×C₃₁	—	2	2	no	—
310	C₂×C₄×C₃₁	—	2	4	no	—
311	C₂×C₄×C₃₁	—	2	2	no	—
312	C₂×C₄×C₃₁	—	2	4	no	—
313	C₂×C₄×C₃₁	—	2	2	no	—
314	C₂×C₄×C₃₁	—	2	2	no	—
315	C₂×C₄×C₃₁	—	2	4	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	4	8	no	—
318	C₂×C₄×C₃₁	—	4	4	no	—
319	C₂×C₄×C₃₁	—	4	4	no	—
320	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
321	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
330	C₈×C₃₁	—	2	2	no	—
331	C₈×C₃₁	—	2	2	no	—
332	C₈×C₃₁	—	2	4	no	—
333	#3509	C₂×C₃₁	1	1	yes	characteristic, complemented
334	#3498	C₂×C₃₁	1	1	yes	characteristic
335	#3368	C₂×C₃₁	1	4	yes	complemented
336	#3324	C₂×C₃₁	1	4	yes	complemented
337	#3310	C₂×C₃₁	1	8	yes	complemented
338	#3228	C₂×C₃₁	1	2	yes	complemented
339	#3226	C₂×C₃₁	1	1	yes	characteristic, complemented
340	#3208	C₂×C₃₁	1	1	yes	characteristic, complemented
341	#3208	C₂×C₃₁	1	2	yes	complemented
342	#3182	C₂×C₃₁	1	2	yes	complemented
343	#3167	C₂×C₃₁	1	1	yes	characteristic, complemented
344	#3138	C₂×C₃₁	1	2	yes	complemented
345	C₂×#486	C₂×C₃₁	1	1	yes	characteristic, complemented
346	#2965	C₂×C₃₁	1	1	yes	characteristic, complemented
347	C₂²×C₃₁	—	2	1	no	—
348	C₂²×C₃₁	—	2	1	no	—
349	C₂²×C₃₁	—	2	2	no	—
350	C₂²×C₃₁	—	2	2	no	—
351	C₂²×C₃₁	—	2	2	no	—
352	C₂²×C₃₁	—	4	4	no	—
353	C₂²×C₃₁	—	4	2	no	—
354	C₂²×C₃₁	—	4	4	no	—
355	C₂²×C₃₁	—	4	2	no	—
356	C₂²×C₃₁	—	4	4	no	—
357	C₂²×C₃₁	—	4	2	no	—
358	C₂²×C₃₁	—	16	4	no	—
359	C₂²×C₃₁	—	16	8	no	—
360	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
361	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
362	C₄×C₃₁	—	2	1	no	—
363	C₄×C₃₁	—	2	2	no	—
364	C₄×C₃₁	—	2	2	no	—
365	C₄×C₃₁	—	2	2	no	—
366	C₄×C₃₁	—	2	1	no	—
367	C₄×C₃₁	—	4	2	no	—
368	C₄×C₃₁	—	4	2	no	—
369	C₄×C₃₁	—	4	4	no	—
370	C₄×C₃₁	—	4	2	no	—
371	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
372	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
373	C₄×C₃₁	#577	1	2	yes	—
374	C₄×C₃₁	#585	1	2	yes	—
375	C₂×H(5,𝔽₂)	—	2	1	no	—
376	#557	—	2	1	no	—
377	#557	C₂²×C₃₁	1	2	yes	complemented
378	#556	—	2	1	no	—
379	#556	C₂²×C₃₁	1	2	yes	complemented
380	#552	—	2	2	no	—
381	#552	C₂²×C₃₁	1	4	yes	complemented
382	#550	—	2	1	no	—
383	#550	C₂²×C₃₁	1	2	yes	—
384	D₄²	—	2	2	no	—
385	D₄²	—	2	1	no	—
386	D₄²	C₂²×C₃₁	1	4	yes	—
387	D₄²	C₂²×C₃₁	1	2	yes	—
388	#541	—	2	2	no	—
389	#536	—	2	1	no	—
390	#535	—	2	1	no	—
391	#535	—	2	2	no	—
392	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
393	#533	C₂²×C₃₁	1	2	yes	complemented
394	#533	C₂²×C₃₁	1	2	yes	complemented
395	#532	C₂²×C₃₁	1	1	yes	characteristic
396	#532	C₂²×C₃₁	1	2	yes	—
397	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
398	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
399	C₂×#127	C₂²×C₃₁	1	2	yes	—
400	#519	—	2	1	no	—
401	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
402	#500	C₂²×C₃₁	1	2	yes	complemented
403	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
404	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
405	#492	C₂²×C₃₁	1	2	yes	complemented
406	#490	C₂²×C₃₁	1	8	yes	complemented
407	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
408	#486	C₂²×C₃₁	1	4	yes	complemented
409	#486	C₂²×C₃₁	1	2	yes	complemented
410	#486	C₂²×C₃₁	1	2	yes	complemented
411	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
412	#486	C₂²×C₃₁	1	2	yes	complemented
413	#486	C₂²×C₃₁	1	2	yes	complemented
414	#482	C₂²×C₃₁	1	8	yes	complemented
415	#480	C₂²×C₃₁	1	4	yes	complemented
416	#478	C₂²×C₃₁	1	8	yes	complemented
417	#474	C₂²×C₃₁	1	4	yes	complemented
418	#468	C₂²×C₃₁	1	8	yes	complemented
419	#465	C₂²×C₃₁	1	4	yes	complemented
420	#460	C₂²×C₃₁	1	8	yes	complemented
421	#460	C₂²×C₃₁	1	4	yes	complemented
422	#450	C₂²×C₃₁	1	4	yes	complemented
423	#450	C₂²×C₃₁	1	8	yes	complemented
424	#446	C₂²×C₃₁	1	2	yes	complemented
425	#440	C₂²×C₃₁	1	8	yes	complemented
426	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
427	#436	C₂²×C₃₁	1	2	yes	complemented
428	#435	C₂²×C₃₁	1	4	yes	complemented
429	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
430	#431	C₂²×C₃₁	1	2	yes	complemented
431	#418	C₂²×C₃₁	1	8	yes	complemented
432	C₂×#102	C₂²×C₃₁	1	4	yes	complemented
433	C₄×M₁₆	C₂²×C₃₁	1	2	yes	complemented
434	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
435	C₂×C₃₁	—	2	2	no	—
436	C₂×C₃₁	—	4	2	no	—
437	C₂×C₃₁	—	8	4	no	—
438	C₂×C₃₁	—	8	2	no	—
439	C₂×C₃₁	#3500	1	1	yes	characteristic
440	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
441	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
442	H(5,𝔽₂)	—	4	8	no	—
443	C₂×#41	—	2	2	no	—
444	C₂×#41	—	2	2	no	—
445	C₂×#41	—	2	1	no	—
446	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
447	C₂²×Q₈	—	2	1	no	—
448	C₂²×D₄	—	2	4	no	—
449	C₂²×D₄	—	2	2	no	—
450	C₂²×D₄	—	2	2	no	—
451	C₂²×D₄	—	2	1	no	—
452	C₂²×D₄	—	2	1	no	—
453	C₂²×D₄	—	2	2	no	—
454	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
455	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
456	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
457	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
458	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
459	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
460	C₄⋊Q₈	—	2	2	no	—
461	C₄⋊Q₈	—	2	1	no	—
462	C₄⋊Q₈	—	2	1	no	—
463	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
464	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
465	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
466	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
467	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
468	#127	—	2	2	no	—
469	#127	—	2	1	no	—
470	#127	—	2	2	no	—
471	#127	—	2	1	no	—
472	#127	C₂³×C₃₁	1	2	yes	—
473	#127	C₂³×C₃₁	1	1	yes	characteristic
474	#127	C₂³×C₃₁	1	2	yes	—
475	#127	C₂³×C₃₁	1	4	yes	—
476	#126	—	2	4	no	—
477	#126	—	2	4	no	—
478	#125	—	2	4	no	—
479	#125	—	2	4	no	—
480	#125	—	2	1	no	—
481	#125	—	2	2	no	—
482	#125	C₂³×C₃₁	1	4	yes	—
483	#124	—	2	2	no	—
484	#124	—	2	2	no	—
485	#124	—	2	1	no	—
486	#123	—	2	4	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	—	2	1	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
492	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
493	#121	—	2	1	no	—
494	#121	—	2	2	no	—
495	#121	—	2	2	no	—
496	#121	—	2	4	no	—
497	#121	—	2	2	no	—
498	#121	—	2	4	no	—
499	#121	C₂³×C₃₁	1	2	yes	—
500	#121	C₂³×C₃₁	1	4	yes	—
501	#120	—	2	4	no	—
502	#120	—	2	4	no	—
503	#120	—	2	4	no	—
504	C₄×Q₈	—	2	2	no	—
505	C₄×Q₈	—	2	2	no	—
506	C₄×Q₈	—	2	2	no	—
507	C₄×Q₈	—	2	2	no	—
508	C₄×Q₈	—	2	2	no	—
509	C₄×Q₈	—	2	1	no	—
510	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
511	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
512	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
513	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
514	C₄×D₄	—	2	2	no	—
515	C₄×D₄	—	2	1	no	—
516	C₄×D₄	D₄×C₃₁	1	2	yes	—
517	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
518	C₄×D₄	C₂³×C₃₁	1	2	yes	—
519	C₄×D₄	C₂³×C₃₁	1	4	yes	—
520	C₄×D₄	C₂³×C₃₁	1	2	yes	—
521	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
522	#117	—	2	1	no	—
523	#117	—	2	2	no	—
524	#117	—	2	4	no	—
525	#117	D₄×C₃₁	1	1	yes	characteristic
526	#117	D₄×C₃₁	1	2	yes	—
527	#117	C₂³×C₃₁	1	4	yes	—
528	C₂×C₄⋊C₄	—	2	1	no	—
529	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
530	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
532	#107	C₂³×C₃₁	1	8	yes	—
533	#106	C₂³×C₃₁	1	4	yes	—
534	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
535	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
536	#103	C₂³×C₃₁	1	4	yes	—
537	#102	C₂³×C₃₁	1	8	yes	—
538	#102	C₂³×C₃₁	1	8	yes	—
539	#102	C₂³×C₃₁	1	4	yes	—
540	#102	C₂³×C₃₁	1	8	yes	—
541	#102	C₂³×C₃₁	1	8	yes	—
542	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
543	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
544	#97	C₂³×C₃₁	1	4	yes	—
545	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
546	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
547	C₄×C₈	C₂³×C₃₁	1	2	yes	—
548	C₄×C₈	C₂³×C₃₁	1	2	yes	—
549	C₃₁	#62539	1	1	yes	characteristic, direct product factor, Sylow
550	C₂⁴	—	2	4	no	—
551	C₂⁴	—	2	2	no	—
552	#41	—	2	4	no	—
553	#41	—	4	8	no	—
554	#41	—	4	8	no	—
555	#41	—	4	4	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	2	no	—
558	C₂×Q₈	—	2	2	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	4	4	no	—
561	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
562	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	4	4	no	—
576	C₂×D₄	—	4	8	no	—
577	C₂×D₄	—	4	8	no	—
578	C₂×D₄	—	4	16	no	—
579	C₂×D₄	—	4	8	no	—
580	C₂×D₄	—	4	4	no	—
581	C₂×D₄	—	8	2	no	—
582	C₂×D₄	—	8	4	no	—
583	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
584	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
585	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
586	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
591	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
592	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
593	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
596	SD₁₆	—	4	4	no	—
597	SD₁₆	—	4	8	no	—
598	M₁₆	—	4	4	no	—
599	C₂×C₈	—	4	2	no	—
600	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
601	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
602	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
617	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
618	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
619	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
620	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
621	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
622	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
623	C₂²⋊C₄	—	2	2	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
631	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
632	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	2	no	—
636	C₄²	C₂×D₄×C₃₁	1	2	yes	—
637	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
638	C₄²	C₂×D₄×C₃₁	1	2	yes	—
639	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
640	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
641	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
642	C₄²	C₂⁴×C₃₁	1	2	yes	—
643	C₂³	—	2	4	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	4	8	no	—
646	C₂³	—	4	4	no	—
647	C₂³	—	8	2	no	—
648	C₂³	—	8	4	no	—
649	C₂³	—	8	2	no	—
650	C₂³	—	8	4	no	—
651	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
652	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
653	Q₈	—	2	2	no	—
654	Q₈	—	2	4	no	—
655	Q₈	—	4	4	no	—
656	Q₈	—	4	4	no	—
657	Q₈	—	4	2	no	—
658	Q₈	—	4	2	no	—
659	D₄	—	2	4	no	—
660	D₄	—	2	2	no	—
661	D₄	—	2	4	no	—
662	D₄	—	2	8	no	—
663	D₄	—	4	8	no	—
664	D₄	—	4	8	no	—
665	D₄	—	4	4	no	—
666	D₄	—	4	2	no	—
667	D₄	—	4	4	no	—
668	D₄	—	4	4	no	—
669	D₄	—	4	4	no	—
670	D₄	—	4	2	no	—
671	D₄	—	8	2	no	—
672	D₄	—	8	4	no	—
673	D₄	—	8	4	no	—
674	D₄	—	8	2	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	4	8	no	—
685	C₂×C₄	—	4	4	no	—
686	C₂×C₄	—	4	4	no	—
687	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
688	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
689	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
690	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
691	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
692	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
693	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
694	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
695	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
696	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
697	C₈	—	2	2	no	—
698	C₈	—	2	2	no	—
699	C₈	—	2	4	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	2	2	no	—
705	C₂²	—	4	4	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	4	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	4	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	16	4	no	—
712	C₂²	—	16	8	no	—
713	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
714	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
715	C₄	—	2	1	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	2	no	—
719	C₄	—	2	1	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	4	no	—
723	C₄	—	4	2	no	—
724	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
725	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
726	C₄	C₃₁×#577	1	2	yes	—
727	C₄	C₃₁×#585	1	2	yes	—
728	C₂	—	2	2	no	—
729	C₂	—	4	2	no	—
730	C₂	—	8	4	no	—
731	C₂	—	8	2	no	—
732	C₂	C₃₁×#3500	1	1	yes	characteristic
733	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
734	C₂	C₂×C₃₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3498	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3509	C₂	semidirect
3. C₃₁×#3368	C₂	semidirect
4. C₃₁×#3324	C₂	semidirect
5. C₃₁×#3310	C₂	semidirect
6. C₃₁×#3228	C₂	semidirect
7. C₃₁×#3226	C₂	semidirect
8. C₃₁×#3208	C₂	semidirect
9. C₃₁×#3208	C₂	semidirect
10. C₃₁×#3182	C₂	semidirect
11. C₃₁×#3167	C₂	semidirect
12. C₃₁×#3138	C₂	semidirect
13. C₂×C₃₁×#486	C₂	semidirect
14. C₃₁×#2965	C₂	semidirect
17. C₃₁×#557	C₂²	semidirect
19. C₃₁×#556	C₂²	semidirect
21. C₃₁×#552	C₂²	semidirect
32. C₃₁×#533	C₂²	semidirect
33. C₃₁×#533	C₂²	semidirect
34. C₃₁×#533	C₂²	semidirect
37. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
42. C₃₁×#500	C₂²	semidirect
43. C₃₁×#498	C₂²	semidirect
44. C₃₁×#492	C₂²	semidirect
45. C₃₁×#492	C₂²	semidirect
46. C₃₁×#490	C₂²	semidirect
47. C₃₁×#487	C₂²	semidirect
48. C₃₁×#486	C₂²	semidirect
49. C₃₁×#486	C₂²	semidirect
50. C₃₁×#486	C₂²	semidirect
51. C₃₁×#486	C₂²	semidirect
52. C₃₁×#486	C₂²	semidirect
53. C₃₁×#486	C₂²	semidirect
54. C₃₁×#482	C₂²	semidirect
55. C₃₁×#480	C₂²	semidirect
56. C₃₁×#478	C₂²	semidirect
57. C₃₁×#474	C₂²	semidirect
58. C₃₁×#468	C₂²	semidirect
59. C₃₁×#465	C₂²	semidirect
60. C₃₁×#460	C₂²	semidirect
61. C₃₁×#460	C₂²	semidirect
62. C₃₁×#450	C₂²	semidirect
63. C₃₁×#450	C₂²	semidirect
64. C₃₁×#446	C₂²	semidirect
65. C₃₁×#440	C₂²	semidirect
66. C₄×SD₁₆×C₃₁	C₂²	semidirect
67. C₃₁×#436	C₂²	semidirect
68. C₃₁×#435	C₂²	semidirect
69. C₃₁×#431	C₂²	semidirect
70. C₃₁×#431	C₂²	semidirect
71. C₃₁×#418	C₂²	semidirect
72. C₂×C₃₁×#102	C₂²	semidirect
73. C₄×M₁₆×C₃₁	C₂²	semidirect
74. C₂×C₄×C₈×C₃₁	C₂²	semidirect
275. #62539	C₃₁	direct (N × H)
333. #3509	C₂×C₃₁	semidirect
335. #3368	C₂×C₃₁	semidirect
336. #3324	C₂×C₃₁	semidirect
337. #3310	C₂×C₃₁	semidirect
338. #3228	C₂×C₃₁	semidirect
339. #3226	C₂×C₃₁	semidirect
340. #3208	C₂×C₃₁	semidirect
341. #3208	C₂×C₃₁	semidirect
342. #3182	C₂×C₃₁	semidirect
343. #3167	C₂×C₃₁	semidirect
344. #3138	C₂×C₃₁	semidirect
345. C₂×#486	C₂×C₃₁	semidirect
346. #2965	C₂×C₃₁	semidirect
377. #557	C₂²×C₃₁	semidirect
379. #556	C₂²×C₃₁	semidirect
381. #552	C₂²×C₃₁	semidirect
392. #533	C₂²×C₃₁	semidirect
393. #533	C₂²×C₃₁	semidirect
394. #533	C₂²×C₃₁	semidirect
397. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
402. #500	C₂²×C₃₁	semidirect
403. #498	C₂²×C₃₁	semidirect
404. #492	C₂²×C₃₁	semidirect
405. #492	C₂²×C₃₁	semidirect
406. #490	C₂²×C₃₁	semidirect
407. #487	C₂²×C₃₁	semidirect
408. #486	C₂²×C₃₁	semidirect
409. #486	C₂²×C₃₁	semidirect
410. #486	C₂²×C₃₁	semidirect
411. #486	C₂²×C₃₁	semidirect
412. #486	C₂²×C₃₁	semidirect
413. #486	C₂²×C₃₁	semidirect
414. #482	C₂²×C₃₁	semidirect
415. #480	C₂²×C₃₁	semidirect
416. #478	C₂²×C₃₁	semidirect
417. #474	C₂²×C₃₁	semidirect
418. #468	C₂²×C₃₁	semidirect
419. #465	C₂²×C₃₁	semidirect
420. #460	C₂²×C₃₁	semidirect
421. #460	C₂²×C₃₁	semidirect
422. #450	C₂²×C₃₁	semidirect
423. #450	C₂²×C₃₁	semidirect
424. #446	C₂²×C₃₁	semidirect
425. #440	C₂²×C₃₁	semidirect
426. C₄×SD₁₆	C₂²×C₃₁	semidirect
427. #436	C₂²×C₃₁	semidirect
428. #435	C₂²×C₃₁	semidirect
429. #431	C₂²×C₃₁	semidirect
430. #431	C₂²×C₃₁	semidirect
431. #418	C₂²×C₃₁	semidirect
432. C₂×#102	C₂²×C₃₁	semidirect
433. C₄×M₁₆	C₂²×C₃₁	semidirect
434. C₂×C₄×C₈	C₂²×C₃₁	semidirect
549. C₃₁	#62539	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×#3509	2
C₃₁×#3498	2
C₃₁×#3368	2
C₃₁×#3324	2
C₃₁×#3310	2
C₃₁×#3228	2
C₃₁×#3226	2
C₃₁×#3208	2
C₃₁×#3182	2
C₃₁×#3167	2
C₃₁×#3138	2
C₂×C₃₁×#486	2
C₃₁×#2965	2
#62539	31

Subgroups — C31×#62539 #21519298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62539 #21519298