Subgroups — C₃₁×#61631 #21518390

Order 7936.

2222 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3484	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3310	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3296	C₂	1	4	yes	maximal, complemented
5	D₄×SD₁₆×C₃₁	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3266	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3222	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3200	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3190	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3123	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3009	C₂	1	2	yes	maximal, complemented
12	C₂×C₃₁×#450	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2977	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
17	C₂²×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
18	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
19	C₃₁×#563	—	2	2	no	—
20	C₃₁×#552	C₂²	1	4	yes	complemented
21	C₃₁×#551	—	2	2	no	—
22	D₄×Q₈×C₃₁	C₂²	1	4	yes	complemented
23	C₃₁×#546	—	2	2	no	—
24	C₃₁×#546	C₂²	1	4	yes	—
25	D₄²×C₃₁	—	2	2	no	—
26	D₄²×C₃₁	C₂²	1	4	yes	—
27	C₃₁×#544	—	2	2	no	—
28	C₃₁×#541	C₂²	1	2	yes	complemented
29	C₃₁×#539	—	2	2	no	—
30	C₃₁×#536	C₂²	1	2	yes	complemented
31	C₃₁×#535	C₂²	1	1	yes	characteristic
32	C₃₁×#535	C₂²	1	1	yes	characteristic
33	C₃₁×#534	—	2	2	no	—
34	C₃₁×#525	C₂²	1	1	yes	characteristic
35	C₃₁×#525	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₂×C₃₁×#120	—	2	2	no	—
38	C₃₁×#518	C₂²	1	1	yes	characteristic
39	C₃₁×#497	C₂²	1	2	yes	complemented
40	C₃₁×#492	C₂²	1	2	yes	complemented
41	C₃₁×#490	C₂²	1	2	yes	complemented
42	C₃₁×#488	C₂²	1	2	yes	complemented
43	C₃₁×#485	C₂²	1	4	yes	complemented
44	C₃₁×#483	C₂²	1	2	yes	complemented
45	C₃₁×#482	C₂²	1	4	yes	complemented
46	C₃₁×#480	C₂²	1	2	yes	complemented
47	C₃₁×#478	C₂²	1	4	yes	complemented
48	C₃₁×#468	C₂²	1	4	yes	complemented
49	C₃₁×#467	C₂²	1	4	yes	complemented
50	C₃₁×#465	C₂²	1	4	yes	complemented
51	C₃₁×#465	C₂²	1	4	yes	complemented
52	C₃₁×#464	C₂²	1	4	yes	complemented
53	C₃₁×#461	C₂²	1	4	yes	complemented
54	C₃₁×#460	C₂²	1	4	yes	complemented
55	C₃₁×#452	C₂²	1	4	yes	complemented
56	C₃₁×#452	C₂²	1	4	yes	complemented
57	C₃₁×#451	C₂²	1	2	yes	complemented
58	C₃₁×#450	C₂²	1	4	yes	—
59	C₃₁×#450	C₂²	1	4	yes	complemented
60	C₃₁×#450	C₂²	1	4	yes	complemented
61	C₃₁×#450	C₂²	1	4	yes	complemented
62	C₃₁×#450	C₂²	1	4	yes	complemented
63	C₃₁×#448	C₂²	1	2	yes	complemented
64	C₃₁×#448	C₂²	1	4	yes	complemented
65	C₃₁×#440	C₂²	1	4	yes	complemented
66	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
67	C₃₁×#435	C₂²	1	4	yes	complemented
68	C₈×D₄×C₃₁	C₂²	1	4	yes	complemented
69	C₃₁×#433	C₂²	1	2	yes	complemented
70	C₃₁×#418	C₂²	1	2	yes	complemented
71	C₃₁×#416	C₂²	1	2	yes	complemented
72	C₂×C₃₁×#102	C₂²	1	4	yes	complemented
73	C₃₁×#408	C₂²	1	2	yes	complemented
74	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
75	C₂⁵×C₃₁	—	2	1	no	—
76	C₃₁×H(5,𝔽₂)	—	4	4	no	—
77	C₂×#41×C₃₁	—	2	1	no	—
78	C₂×#41×C₃₁	C₂³	1	2	yes	—
79	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
80	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
82	C₂²×Q₈×C₃₁	C₂³	1	2	yes	complemented
83	C₂²×D₄×C₃₁	—	2	2	no	—
84	C₂²×D₄×C₃₁	—	2	1	no	—
85	C₂²×D₄×C₃₁	—	2	4	no	—
86	C₂²×D₄×C₃₁	—	2	1	no	—
87	C₂²×D₄×C₃₁	—	2	2	no	—
88	C₂²×D₄×C₃₁	—	4	4	no	—
89	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
91	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
92	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₃₁×#137	—	4	4	no	—
95	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	complemented
96	C₂×SD₁₆×C₃₁	—	4	8	no	—
97	C₂×SD₁₆×C₃₁	—	4	4	no	—
98	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	complemented
103	C₂×M₁₆×C₃₁	C₂³	1	2	yes	complemented
104	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
105	C₂²×C₈×C₃₁	C₂³	1	2	yes	complemented
106	C₃₁×C₄⋊Q₈	—	2	2	no	—
107	C₃₁×C₄⋊Q₈	—	2	4	no	—
108	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	complemented
109	C₃₁×#127	—	2	1	no	—
110	C₃₁×#127	C₂³	1	2	yes	—
111	C₃₁×#126	—	2	4	no	—
112	C₃₁×#126	—	2	4	no	—
113	C₃₁×#125	—	2	4	no	—
114	C₃₁×#125	—	2	4	no	—
115	C₃₁×#125	C₂³	1	2	yes	complemented
116	C₃₁×#124	—	2	1	no	—
117	C₃₁×#124	—	2	2	no	—
118	C₃₁×#124	C₂³	1	2	yes	—
119	C₃₁×#123	—	2	2	no	—
120	C₃₁×#123	—	2	2	no	—
121	C₃₁×#123	—	2	4	no	—
122	C₃₁×#123	—	2	1	no	—
123	C₃₁×#123	—	2	4	no	—
124	C₃₁×#123	D₄	1	2	yes	—
125	C₃₁×C₂²⋊Q₈	—	2	2	no	—
126	C₃₁×C₂²⋊Q₈	—	2	2	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	C₂³	1	4	yes	—
131	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
132	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
133	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	complemented
134	C₃₁×#121	—	2	4	no	—
135	C₃₁×#121	—	2	2	no	—
136	C₃₁×#121	—	2	4	no	—
137	C₃₁×#121	D₄	1	2	yes	—
138	C₃₁×#121	C₂³	1	2	yes	—
139	C₃₁×#121	C₂³	1	4	yes	—
140	C₃₁×#120	—	2	1	no	—
141	C₃₁×#120	—	2	2	no	—
142	C₃₁×#120	—	2	4	no	—
143	C₃₁×#120	—	2	2	no	—
144	C₃₁×#120	—	2	4	no	—
145	C₃₁×#120	—	2	4	no	—
146	C₃₁×#120	D₄	1	2	yes	—
147	C₄×Q₈×C₃₁	C₂³	1	4	yes	complemented
148	C₄×D₄×C₃₁	—	2	4	no	—
149	C₄×D₄×C₃₁	—	2	2	no	—
150	C₄×D₄×C₃₁	—	2	2	no	—
151	C₄×D₄×C₃₁	C₂³	1	4	yes	—
152	C₄×D₄×C₃₁	C₂³	1	4	yes	—
153	C₃₁×#117	—	2	4	no	—
154	C₃₁×#117	C₂³	1	1	yes	characteristic
155	C₃₁×#117	C₂³	1	1	yes	characteristic
156	C₃₁×#117	C₂³	1	2	yes	complemented
157	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
160	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
161	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
162	C₃₁×#107	C₂³	1	4	yes	complemented
163	C₃₁×#106	C₂³	1	4	yes	complemented
164	C₃₁×C₄⋊C₈	C₂³	1	4	yes	complemented
165	C₃₁×#103	C₂³	1	4	yes	complemented
166	C₃₁×#103	C₂³	1	4	yes	complemented
167	C₃₁×#103	C₂³	1	4	yes	complemented
168	C₃₁×#102	C₂³	1	4	yes	—
169	C₃₁×#102	C₂³	1	4	yes	—
170	C₃₁×#102	C₂³	1	4	yes	—
171	C₃₁×#102	C₂³	1	4	yes	—
172	C₃₁×#102	C₂³	1	4	yes	complemented
173	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
174	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
175	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
176	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	complemented
177	C₃₁×#97	C₂³	1	2	yes	complemented
178	C₄×C₈×C₃₁	C₂³	1	2	yes	complemented
179	C₂⁴×C₃₁	—	2	1	no	—
180	C₂⁴×C₃₁	—	2	4	no	—
181	C₂⁴×C₃₁	—	2	1	no	—
182	C₂⁴×C₃₁	—	2	2	no	—
183	C₂⁴×C₃₁	—	4	4	no	—
184	C₂⁴×C₃₁	—	8	4	no	—
185	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
186	#41×C₃₁	—	2	4	no	—
187	#41×C₃₁	—	4	2	no	—
188	#41×C₃₁	—	4	2	no	—
189	#41×C₃₁	—	4	2	no	—
190	#41×C₃₁	—	4	4	no	—
191	C₂×Q₈×C₃₁	—	2	2	no	—
192	C₂×Q₈×C₃₁	—	2	2	no	—
193	C₂×Q₈×C₃₁	—	4	4	no	—
194	C₂×Q₈×C₃₁	—	4	2	no	—
195	C₂×Q₈×C₃₁	—	4	2	no	—
196	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
197	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
198	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
199	C₂×D₄×C₃₁	—	2	4	no	—
200	C₂×D₄×C₃₁	—	2	8	no	—
201	C₂×D₄×C₃₁	—	2	4	no	—
202	C₂×D₄×C₃₁	—	2	2	no	—
203	C₂×D₄×C₃₁	—	2	1	no	—
204	C₂×D₄×C₃₁	—	2	2	no	—
205	C₂×D₄×C₃₁	—	2	4	no	—
206	C₂×D₄×C₃₁	—	2	1	no	—
207	C₂×D₄×C₃₁	—	2	2	no	—
208	C₂×D₄×C₃₁	—	2	4	no	—
209	C₂×D₄×C₃₁	—	2	1	no	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	4	4	no	—
212	C₂×D₄×C₃₁	—	4	2	no	—
213	C₂×D₄×C₃₁	—	4	2	no	—
214	C₂×D₄×C₃₁	—	4	8	no	—
215	C₂×D₄×C₃₁	—	4	4	no	—
216	C₂×D₄×C₃₁	—	4	4	no	—
217	C₂×D₄×C₃₁	—	4	8	no	—
218	C₂×D₄×C₃₁	—	8	8	no	—
219	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
220	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
221	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
222	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
223	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
224	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₃₁	—	2	2	no	—
226	C₂²×C₄×C₃₁	—	2	2	no	—
227	C₂²×C₄×C₃₁	—	2	2	no	—
228	C₂²×C₄×C₃₁	—	2	2	no	—
229	C₂²×C₄×C₃₁	—	2	1	no	—
230	C₂²×C₄×C₃₁	—	2	4	no	—
231	C₂²×C₄×C₃₁	—	4	2	no	—
232	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
233	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
237	Q₁₆×C₃₁	—	4	4	no	—
238	SD₁₆×C₃₁	—	2	8	no	—
239	SD₁₆×C₃₁	—	2	8	no	—
240	SD₁₆×C₃₁	—	4	4	no	—
241	SD₁₆×C₃₁	—	4	4	no	—
242	SD₁₆×C₃₁	—	4	4	no	—
243	M₁₆×C₃₁	—	4	2	no	—
244	C₂×C₈×C₃₁	—	4	4	no	—
245	C₂×C₈×C₃₁	—	4	2	no	—
246	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
247	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
248	C₄⋊C₄×C₃₁	—	2	4	no	—
249	C₄⋊C₄×C₃₁	—	2	4	no	—
250	C₄⋊C₄×C₃₁	—	2	2	no	—
251	C₄⋊C₄×C₃₁	—	2	4	no	—
252	C₄⋊C₄×C₃₁	—	2	4	no	—
253	C₄⋊C₄×C₃₁	—	2	2	no	—
254	C₄⋊C₄×C₃₁	—	2	4	no	—
255	C₄⋊C₄×C₃₁	—	2	4	no	—
256	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
258	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
259	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
260	C₂²⋊C₄×C₃₁	—	2	1	no	—
261	C₂²⋊C₄×C₃₁	—	2	2	no	—
262	C₂²⋊C₄×C₃₁	—	2	4	no	—
263	C₂²⋊C₄×C₃₁	—	2	4	no	—
264	C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂²⋊C₄×C₃₁	—	2	4	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	2	no	—
270	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
271	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
272	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
273	C₄²×C₃₁	—	2	2	no	—
274	C₄²×C₃₁	—	2	4	no	—
275	C₄²×C₃₁	—	2	1	no	—
276	C₄²×C₃₁	C₂⁴	1	2	yes	—
277	#61631	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂³×C₃₁	—	2	4	no	—
279	C₂³×C₃₁	—	2	4	no	—
280	C₂³×C₃₁	—	2	2	no	—
281	C₂³×C₃₁	—	2	2	no	—
282	C₂³×C₃₁	—	2	1	no	—
283	C₂³×C₃₁	—	4	1	no	—
284	C₂³×C₃₁	—	4	8	no	—
285	C₂³×C₃₁	—	4	4	no	—
286	C₂³×C₃₁	—	4	2	no	—
287	C₂³×C₃₁	—	4	8	no	—
288	C₂³×C₃₁	—	8	4	no	—
289	C₂³×C₃₁	—	8	2	no	—
290	C₂³×C₃₁	—	8	2	no	—
291	C₂³×C₃₁	—	8	4	no	—
292	C₂³×C₃₁	—	8	16	no	—
293	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
294	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
295	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
296	Q₈×C₃₁	—	2	4	no	—
297	Q₈×C₃₁	—	2	4	no	—
298	Q₈×C₃₁	—	2	2	no	—
299	Q₈×C₃₁	—	4	1	no	—
300	Q₈×C₃₁	—	8	2	no	—
301	Q₈×C₃₁	—	8	2	no	—
302	D₄×C₃₁	—	2	4	no	—
303	D₄×C₃₁	—	2	8	no	—
304	D₄×C₃₁	—	2	2	no	—
305	D₄×C₃₁	—	2	4	no	—
306	D₄×C₃₁	—	2	2	no	—
307	D₄×C₃₁	—	4	1	no	—
308	D₄×C₃₁	—	4	2	no	—
309	D₄×C₃₁	—	4	8	no	—
310	D₄×C₃₁	—	4	4	no	—
311	D₄×C₃₁	—	4	2	no	—
312	D₄×C₃₁	—	4	4	no	—
313	D₄×C₃₁	—	4	2	no	—
314	D₄×C₃₁	—	4	4	no	—
315	D₄×C₃₁	—	8	4	no	—
316	D₄×C₃₁	—	8	4	no	—
317	D₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
318	C₂×C₄×C₃₁	—	2	4	no	—
319	C₂×C₄×C₃₁	—	2	2	no	—
320	C₂×C₄×C₃₁	—	2	2	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	2	4	no	—
323	C₂×C₄×C₃₁	—	2	2	no	—
324	C₂×C₄×C₃₁	—	2	4	no	—
325	C₂×C₄×C₃₁	—	2	1	no	—
326	C₂×C₄×C₃₁	—	4	2	no	—
327	C₂×C₄×C₃₁	—	4	1	no	—
328	C₂×C₄×C₃₁	—	4	4	no	—
329	C₂×C₄×C₃₁	—	4	2	no	—
330	C₂×C₄×C₃₁	—	4	4	no	—
331	C₂×C₄×C₃₁	—	8	4	no	—
332	C₂×C₄×C₃₁	—	8	2	no	—
333	C₂×C₄×C₃₁	—	8	2	no	—
334	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
335	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
339	C₈×C₃₁	—	2	4	no	—
340	C₈×C₃₁	—	2	4	no	—
341	#3538	C₂×C₃₁	1	1	yes	characteristic, complemented
342	#3484	C₂×C₃₁	1	1	yes	characteristic
343	#3310	C₂×C₃₁	1	4	yes	complemented
344	#3296	C₂×C₃₁	1	4	yes	complemented
345	D₄×SD₁₆	C₂×C₃₁	1	4	yes	complemented
346	#3266	C₂×C₃₁	1	4	yes	complemented
347	#3222	C₂×C₃₁	1	2	yes	complemented
348	#3200	C₂×C₃₁	1	2	yes	complemented
349	#3190	C₂×C₃₁	1	2	yes	complemented
350	#3123	C₂×C₃₁	1	2	yes	complemented
351	#3009	C₂×C₃₁	1	2	yes	complemented
352	C₂×#450	C₂×C₃₁	1	2	yes	complemented
353	#2977	C₂×C₃₁	1	1	yes	characteristic, complemented
354	C₂²×C₃₁	—	2	2	no	—
355	C₂²×C₃₁	—	2	2	no	—
356	C₂²×C₃₁	—	2	1	no	—
357	C₂²×C₃₁	—	2	2	no	—
358	C₂²×C₃₁	—	2	4	no	—
359	C₂²×C₃₁	—	2	4	no	—
360	C₂²×C₃₁	—	2	2	no	—
361	C₂²×C₃₁	—	4	4	no	—
362	C₂²×C₃₁	—	4	4	no	—
363	C₂²×C₃₁	—	4	1	no	—
364	C₂²×C₃₁	—	4	2	no	—
365	C₂²×C₃₁	—	4	2	no	—
366	C₂²×C₃₁	—	4	4	no	—
367	C₂²×C₃₁	—	8	16	no	—
368	C₂²×C₃₁	—	8	4	no	—
369	C₂²×C₃₁	—	8	4	no	—
370	C₂²×C₃₁	—	16	4	no	—
371	C₂²×C₃₁	#577	1	4	yes	—
372	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
373	C₄×C₃₁	—	2	1	no	—
374	C₄×C₃₁	—	2	2	no	—
375	C₄×C₃₁	—	2	2	no	—
376	C₄×C₃₁	—	2	4	no	—
377	C₄×C₃₁	—	4	1	no	—
378	C₄×C₃₁	—	4	4	no	—
379	C₄×C₃₁	—	4	4	no	—
380	C₄×C₃₁	—	4	2	no	—
381	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
382	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
383	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
384	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
385	C₂²×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
386	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
387	#563	—	2	2	no	—
388	#552	C₂²×C₃₁	1	4	yes	complemented
389	#551	—	2	2	no	—
390	D₄×Q₈	C₂²×C₃₁	1	4	yes	complemented
391	#546	—	2	2	no	—
392	#546	C₂²×C₃₁	1	4	yes	—
393	D₄²	—	2	2	no	—
394	D₄²	C₂²×C₃₁	1	4	yes	—
395	#544	—	2	2	no	—
396	#541	C₂²×C₃₁	1	2	yes	complemented
397	#539	—	2	2	no	—
398	#536	C₂²×C₃₁	1	2	yes	complemented
399	#535	C₂²×C₃₁	1	1	yes	characteristic
400	#535	C₂²×C₃₁	1	1	yes	characteristic
401	#534	—	2	2	no	—
402	#525	C₂²×C₃₁	1	1	yes	characteristic
403	#525	C₂²×C₃₁	1	1	yes	characteristic
404	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
405	C₂×#120	—	2	2	no	—
406	#518	C₂²×C₃₁	1	1	yes	characteristic
407	#497	C₂²×C₃₁	1	2	yes	complemented
408	#492	C₂²×C₃₁	1	2	yes	complemented
409	#490	C₂²×C₃₁	1	2	yes	complemented
410	#488	C₂²×C₃₁	1	2	yes	complemented
411	#485	C₂²×C₃₁	1	4	yes	complemented
412	#483	C₂²×C₃₁	1	2	yes	complemented
413	#482	C₂²×C₃₁	1	4	yes	complemented
414	#480	C₂²×C₃₁	1	2	yes	complemented
415	#478	C₂²×C₃₁	1	4	yes	complemented
416	#468	C₂²×C₃₁	1	4	yes	complemented
417	#467	C₂²×C₃₁	1	4	yes	complemented
418	#465	C₂²×C₃₁	1	4	yes	complemented
419	#465	C₂²×C₃₁	1	4	yes	complemented
420	#464	C₂²×C₃₁	1	4	yes	complemented
421	#461	C₂²×C₃₁	1	4	yes	complemented
422	#460	C₂²×C₃₁	1	4	yes	complemented
423	#452	C₂²×C₃₁	1	4	yes	complemented
424	#452	C₂²×C₃₁	1	4	yes	complemented
425	#451	C₂²×C₃₁	1	2	yes	complemented
426	#450	C₂²×C₃₁	1	4	yes	—
427	#450	C₂²×C₃₁	1	4	yes	complemented
428	#450	C₂²×C₃₁	1	4	yes	complemented
429	#450	C₂²×C₃₁	1	4	yes	complemented
430	#450	C₂²×C₃₁	1	4	yes	complemented
431	#448	C₂²×C₃₁	1	2	yes	complemented
432	#448	C₂²×C₃₁	1	4	yes	complemented
433	#440	C₂²×C₃₁	1	4	yes	complemented
434	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
435	#435	C₂²×C₃₁	1	4	yes	complemented
436	C₈×D₄	C₂²×C₃₁	1	4	yes	complemented
437	#433	C₂²×C₃₁	1	2	yes	complemented
438	#418	C₂²×C₃₁	1	2	yes	complemented
439	#416	C₂²×C₃₁	1	2	yes	complemented
440	C₂×#102	C₂²×C₃₁	1	4	yes	complemented
441	#408	C₂²×C₃₁	1	2	yes	complemented
442	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	complemented
443	C₂×C₃₁	—	2	4	no	—
444	C₂×C₃₁	—	4	1	no	—
445	C₂×C₃₁	—	4	2	no	—
446	C₂×C₃₁	—	4	4	no	—
447	C₂×C₃₁	—	8	2	no	—
448	C₂×C₃₁	—	8	1	no	—
449	C₂×C₃₁	#3484	1	1	yes	characteristic
450	C₂×C₃₁	C₂×#577	1	2	yes	—
451	C₂⁵	—	2	1	no	—
452	H(5,𝔽₂)	—	4	4	no	—
453	C₂×#41	—	2	1	no	—
454	C₂×#41	C₂³×C₃₁	1	2	yes	—
455	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
456	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
457	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
458	C₂²×Q₈	C₂³×C₃₁	1	2	yes	complemented
459	C₂²×D₄	—	2	2	no	—
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	—	2	4	no	—
462	C₂²×D₄	—	2	1	no	—
463	C₂²×D₄	—	2	2	no	—
464	C₂²×D₄	—	4	4	no	—
465	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
466	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
467	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
468	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
470	#137	—	4	4	no	—
471	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	complemented
472	C₂×SD₁₆	—	4	8	no	—
473	C₂×SD₁₆	—	4	4	no	—
474	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
475	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
476	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
477	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
478	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	complemented
479	C₂×M₁₆	C₂³×C₃₁	1	2	yes	complemented
480	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
481	C₂²×C₈	C₂³×C₃₁	1	2	yes	complemented
482	C₄⋊Q₈	—	2	2	no	—
483	C₄⋊Q₈	—	2	4	no	—
484	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	complemented
485	#127	—	2	1	no	—
486	#127	C₂³×C₃₁	1	2	yes	—
487	#126	—	2	4	no	—
488	#126	—	2	4	no	—
489	#125	—	2	4	no	—
490	#125	—	2	4	no	—
491	#125	C₂³×C₃₁	1	2	yes	complemented
492	#124	—	2	1	no	—
493	#124	—	2	2	no	—
494	#124	C₂³×C₃₁	1	2	yes	—
495	#123	—	2	2	no	—
496	#123	—	2	2	no	—
497	#123	—	2	4	no	—
498	#123	—	2	1	no	—
499	#123	—	2	4	no	—
500	#123	D₄×C₃₁	1	2	yes	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	2	no	—
503	C₂²⋊Q₈	—	2	4	no	—
504	C₂²⋊Q₈	—	2	4	no	—
505	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
506	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
507	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
508	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
509	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	complemented
510	#121	—	2	4	no	—
511	#121	—	2	2	no	—
512	#121	—	2	4	no	—
513	#121	D₄×C₃₁	1	2	yes	—
514	#121	C₂³×C₃₁	1	2	yes	—
515	#121	C₂³×C₃₁	1	4	yes	—
516	#120	—	2	1	no	—
517	#120	—	2	2	no	—
518	#120	—	2	4	no	—
519	#120	—	2	2	no	—
520	#120	—	2	4	no	—
521	#120	—	2	4	no	—
522	#120	D₄×C₃₁	1	2	yes	—
523	C₄×Q₈	C₂³×C₃₁	1	4	yes	complemented
524	C₄×D₄	—	2	4	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	C₂³×C₃₁	1	4	yes	—
528	C₄×D₄	C₂³×C₃₁	1	4	yes	—
529	#117	—	2	4	no	—
530	#117	C₂³×C₃₁	1	1	yes	characteristic
531	#117	C₂³×C₃₁	1	1	yes	characteristic
532	#117	C₂³×C₃₁	1	2	yes	complemented
533	C₂×C₄⋊C₄	—	2	2	no	—
534	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
535	C₂×C₂²⋊C₄	—	2	2	no	—
536	C₂×C₂²⋊C₄	—	2	2	no	—
537	C₂×C₂²⋊C₄	—	2	4	no	—
538	#107	C₂³×C₃₁	1	4	yes	complemented
539	#106	C₂³×C₃₁	1	4	yes	complemented
540	C₄⋊C₈	C₂³×C₃₁	1	4	yes	complemented
541	#103	C₂³×C₃₁	1	4	yes	complemented
542	#103	C₂³×C₃₁	1	4	yes	complemented
543	#103	C₂³×C₃₁	1	4	yes	complemented
544	#102	C₂³×C₃₁	1	4	yes	—
545	#102	C₂³×C₃₁	1	4	yes	—
546	#102	C₂³×C₃₁	1	4	yes	—
547	#102	C₂³×C₃₁	1	4	yes	—
548	#102	C₂³×C₃₁	1	4	yes	complemented
549	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
550	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
551	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
552	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	complemented
553	#97	C₂³×C₃₁	1	2	yes	complemented
554	C₄×C₈	C₂³×C₃₁	1	2	yes	complemented
555	C₃₁	#61631	1	1	yes	characteristic, direct product factor, Sylow
556	C₂⁴	—	2	1	no	—
557	C₂⁴	—	2	4	no	—
558	C₂⁴	—	2	1	no	—
559	C₂⁴	—	2	2	no	—
560	C₂⁴	—	4	4	no	—
561	C₂⁴	—	8	4	no	—
562	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
563	#41	—	2	4	no	—
564	#41	—	4	2	no	—
565	#41	—	4	2	no	—
566	#41	—	4	2	no	—
567	#41	—	4	4	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	—	2	2	no	—
570	C₂×Q₈	—	4	4	no	—
571	C₂×Q₈	—	4	2	no	—
572	C₂×Q₈	—	4	2	no	—
573	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
574	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
575	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	8	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	4	4	no	—
589	C₂×D₄	—	4	2	no	—
590	C₂×D₄	—	4	2	no	—
591	C₂×D₄	—	4	8	no	—
592	C₂×D₄	—	4	4	no	—
593	C₂×D₄	—	4	4	no	—
594	C₂×D₄	—	4	8	no	—
595	C₂×D₄	—	8	8	no	—
596	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
597	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
598	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
599	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
600	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
601	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	4	2	no	—
609	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
610	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
614	Q₁₆	—	4	4	no	—
615	SD₁₆	—	2	8	no	—
616	SD₁₆	—	2	8	no	—
617	SD₁₆	—	4	4	no	—
618	SD₁₆	—	4	4	no	—
619	SD₁₆	—	4	4	no	—
620	M₁₆	—	4	2	no	—
621	C₂×C₈	—	4	4	no	—
622	C₂×C₈	—	4	2	no	—
623	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
624	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
634	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
635	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
636	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
637	C₂²⋊C₄	—	2	1	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
648	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
649	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
650	C₄²	—	2	2	no	—
651	C₄²	—	2	4	no	—
652	C₄²	—	2	1	no	—
653	C₄²	C₂⁴×C₃₁	1	2	yes	—
654	C₂³	—	2	4	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	8	no	—
661	C₂³	—	4	4	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	4	8	no	—
664	C₂³	—	8	4	no	—
665	C₂³	—	8	2	no	—
666	C₂³	—	8	2	no	—
667	C₂³	—	8	4	no	—
668	C₂³	—	8	16	no	—
669	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
670	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
671	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
672	Q₈	—	2	4	no	—
673	Q₈	—	2	4	no	—
674	Q₈	—	2	2	no	—
675	Q₈	—	4	1	no	—
676	Q₈	—	8	2	no	—
677	Q₈	—	8	2	no	—
678	D₄	—	2	4	no	—
679	D₄	—	2	8	no	—
680	D₄	—	2	2	no	—
681	D₄	—	2	4	no	—
682	D₄	—	2	2	no	—
683	D₄	—	4	1	no	—
684	D₄	—	4	2	no	—
685	D₄	—	4	8	no	—
686	D₄	—	4	4	no	—
687	D₄	—	4	2	no	—
688	D₄	—	4	4	no	—
689	D₄	—	4	2	no	—
690	D₄	—	4	4	no	—
691	D₄	—	8	4	no	—
692	D₄	—	8	4	no	—
693	D₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	4	2	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	2	no	—
706	C₂×C₄	—	4	4	no	—
707	C₂×C₄	—	8	4	no	—
708	C₂×C₄	—	8	2	no	—
709	C₂×C₄	—	8	2	no	—
710	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
711	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
712	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
713	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
714	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
715	C₈	—	2	4	no	—
716	C₈	—	2	4	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	4	no	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	4	no	—
730	C₂²	—	8	16	no	—
731	C₂²	—	8	4	no	—
732	C₂²	—	8	4	no	—
733	C₂²	—	16	4	no	—
734	C₂²	C₃₁×#577	1	4	yes	—
735	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
736	C₄	—	2	1	no	—
737	C₄	—	2	2	no	—
738	C₄	—	2	2	no	—
739	C₄	—	2	4	no	—
740	C₄	—	4	1	no	—
741	C₄	—	4	4	no	—
742	C₄	—	4	4	no	—
743	C₄	—	4	2	no	—
744	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
745	C₂	—	2	4	no	—
746	C₂	—	4	1	no	—
747	C₂	—	4	2	no	—
748	C₂	—	4	4	no	—
749	C₂	—	8	2	no	—
750	C₂	—	8	1	no	—
751	C₂	C₃₁×#3484	1	1	yes	characteristic
752	C₂	C₂×C₃₁×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3484	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3538	C₂	semidirect
3. C₃₁×#3310	C₂	semidirect
4. C₃₁×#3296	C₂	semidirect
5. D₄×SD₁₆×C₃₁	C₂	semidirect
6. C₃₁×#3266	C₂	semidirect
7. C₃₁×#3222	C₂	semidirect
8. C₃₁×#3200	C₂	semidirect
9. C₃₁×#3190	C₂	semidirect
10. C₃₁×#3123	C₂	semidirect
11. C₃₁×#3009	C₂	semidirect
12. C₂×C₃₁×#450	C₂	semidirect
13. C₃₁×#2977	C₂	semidirect
16. C₂×C₃₁×#137	C₂²	semidirect
17. C₂²×SD₁₆×C₃₁	C₂²	semidirect
18. C₂²×SD₁₆×C₃₁	C₂²	semidirect
20. C₃₁×#552	C₂²	semidirect
22. D₄×Q₈×C₃₁	C₂²	semidirect
28. C₃₁×#541	C₂²	semidirect
30. C₃₁×#536	C₂²	semidirect
36. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
39. C₃₁×#497	C₂²	semidirect
40. C₃₁×#492	C₂²	semidirect
41. C₃₁×#490	C₂²	semidirect
42. C₃₁×#488	C₂²	semidirect
43. C₃₁×#485	C₂²	semidirect
44. C₃₁×#483	C₂²	semidirect
45. C₃₁×#482	C₂²	semidirect
46. C₃₁×#480	C₂²	semidirect
47. C₃₁×#478	C₂²	semidirect
48. C₃₁×#468	C₂²	semidirect
49. C₃₁×#467	C₂²	semidirect
50. C₃₁×#465	C₂²	semidirect
51. C₃₁×#465	C₂²	semidirect
52. C₃₁×#464	C₂²	semidirect
53. C₃₁×#461	C₂²	semidirect
54. C₃₁×#460	C₂²	semidirect
55. C₃₁×#452	C₂²	semidirect
56. C₃₁×#452	C₂²	semidirect
57. C₃₁×#451	C₂²	semidirect
59. C₃₁×#450	C₂²	semidirect
60. C₃₁×#450	C₂²	semidirect
61. C₃₁×#450	C₂²	semidirect
62. C₃₁×#450	C₂²	semidirect
63. C₃₁×#448	C₂²	semidirect
64. C₃₁×#448	C₂²	semidirect
65. C₃₁×#440	C₂²	semidirect
66. C₄×SD₁₆×C₃₁	C₂²	semidirect
67. C₃₁×#435	C₂²	semidirect
68. C₈×D₄×C₃₁	C₂²	semidirect
69. C₃₁×#433	C₂²	semidirect
70. C₃₁×#418	C₂²	semidirect
71. C₃₁×#416	C₂²	semidirect
72. C₂×C₃₁×#102	C₂²	semidirect
73. C₃₁×#408	C₂²	semidirect
74. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
82. C₂²×Q₈×C₃₁	C₂³	semidirect
95. C₂×Q₁₆×C₃₁	C₂³	semidirect
102. C₂×SD₁₆×C₃₁	C₂³	semidirect
103. C₂×M₁₆×C₃₁	C₂³	semidirect
105. C₂²×C₈×C₃₁	C₂³	semidirect
108. C₃₁×C₄⋊Q₈	C₂³	semidirect
115. C₃₁×#125	C₂³	semidirect
133. C₃₁×C₂²⋊Q₈	C₂³	semidirect
147. C₄×Q₈×C₃₁	C₂³	semidirect
156. C₃₁×#117	C₂³	semidirect
162. C₃₁×#107	C₂³	semidirect
163. C₃₁×#106	C₂³	semidirect
164. C₃₁×C₄⋊C₈	C₂³	semidirect
165. C₃₁×#103	C₂³	semidirect
166. C₃₁×#103	C₂³	semidirect
167. C₃₁×#103	C₂³	semidirect
172. C₃₁×#102	C₂³	semidirect
176. C₃₁×C₂²⋊C₈	C₂³	semidirect
177. C₃₁×#97	C₂³	semidirect
178. C₄×C₈×C₃₁	C₂³	semidirect
277. #61631	C₃₁	direct (N × H)
341. #3538	C₂×C₃₁	semidirect
343. #3310	C₂×C₃₁	semidirect
344. #3296	C₂×C₃₁	semidirect
345. D₄×SD₁₆	C₂×C₃₁	semidirect
346. #3266	C₂×C₃₁	semidirect
347. #3222	C₂×C₃₁	semidirect
348. #3200	C₂×C₃₁	semidirect
349. #3190	C₂×C₃₁	semidirect
350. #3123	C₂×C₃₁	semidirect
351. #3009	C₂×C₃₁	semidirect
352. C₂×#450	C₂×C₃₁	semidirect
353. #2977	C₂×C₃₁	semidirect
384. C₂×#137	C₂²×C₃₁	semidirect
385. C₂²×SD₁₆	C₂²×C₃₁	semidirect
386. C₂²×SD₁₆	C₂²×C₃₁	semidirect
388. #552	C₂²×C₃₁	semidirect
390. D₄×Q₈	C₂²×C₃₁	semidirect
396. #541	C₂²×C₃₁	semidirect
398. #536	C₂²×C₃₁	semidirect
404. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
407. #497	C₂²×C₃₁	semidirect
408. #492	C₂²×C₃₁	semidirect
409. #490	C₂²×C₃₁	semidirect
410. #488	C₂²×C₃₁	semidirect
411. #485	C₂²×C₃₁	semidirect
412. #483	C₂²×C₃₁	semidirect
413. #482	C₂²×C₃₁	semidirect
414. #480	C₂²×C₃₁	semidirect
415. #478	C₂²×C₃₁	semidirect
416. #468	C₂²×C₃₁	semidirect
417. #467	C₂²×C₃₁	semidirect
418. #465	C₂²×C₃₁	semidirect
419. #465	C₂²×C₃₁	semidirect
420. #464	C₂²×C₃₁	semidirect
421. #461	C₂²×C₃₁	semidirect
422. #460	C₂²×C₃₁	semidirect
423. #452	C₂²×C₃₁	semidirect
424. #452	C₂²×C₃₁	semidirect
425. #451	C₂²×C₃₁	semidirect
427. #450	C₂²×C₃₁	semidirect
428. #450	C₂²×C₃₁	semidirect
429. #450	C₂²×C₃₁	semidirect
430. #450	C₂²×C₃₁	semidirect
431. #448	C₂²×C₃₁	semidirect
432. #448	C₂²×C₃₁	semidirect
433. #440	C₂²×C₃₁	semidirect
434. C₄×SD₁₆	C₂²×C₃₁	semidirect
435. #435	C₂²×C₃₁	semidirect
436. C₈×D₄	C₂²×C₃₁	semidirect
437. #433	C₂²×C₃₁	semidirect
438. #418	C₂²×C₃₁	semidirect
439. #416	C₂²×C₃₁	semidirect
440. C₂×#102	C₂²×C₃₁	semidirect
441. #408	C₂²×C₃₁	semidirect
442. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
458. C₂²×Q₈	C₂³×C₃₁	semidirect
471. C₂×Q₁₆	C₂³×C₃₁	semidirect
478. C₂×SD₁₆	C₂³×C₃₁	semidirect
479. C₂×M₁₆	C₂³×C₃₁	semidirect
481. C₂²×C₈	C₂³×C₃₁	semidirect
484. C₄⋊Q₈	C₂³×C₃₁	semidirect
491. #125	C₂³×C₃₁	semidirect
509. C₂²⋊Q₈	C₂³×C₃₁	semidirect
523. C₄×Q₈	C₂³×C₃₁	semidirect
532. #117	C₂³×C₃₁	semidirect
538. #107	C₂³×C₃₁	semidirect
539. #106	C₂³×C₃₁	semidirect
540. C₄⋊C₈	C₂³×C₃₁	semidirect
541. #103	C₂³×C₃₁	semidirect
542. #103	C₂³×C₃₁	semidirect
543. #103	C₂³×C₃₁	semidirect
548. #102	C₂³×C₃₁	semidirect
552. C₂²⋊C₈	C₂³×C₃₁	semidirect
553. #97	C₂³×C₃₁	semidirect
554. C₄×C₈	C₂³×C₃₁	semidirect
555. C₃₁	#61631	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×#3538	2
C₃₁×#3484	2
C₃₁×#3310	2
C₃₁×#3296	2
D₄×SD₁₆×C₃₁	2
C₃₁×#3266	2
C₃₁×#3222	2
C₃₁×#3200	2
C₃₁×#3190	2
C₃₁×#3123	2
C₃₁×#3009	2
C₂×C₃₁×#450	2
C₃₁×#2977	2
#61631	31

Subgroups — C31×#61631 #21518390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61631 #21518390