Subgroups — C₃₁×#61635 #21518394

Order 7936.

2070 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3315	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3307	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3297	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3296	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3284	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3283	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3268	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3267	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3223	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3221	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3201	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3191	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3123	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3122	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3012	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3002	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2977	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
21	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
23	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
24	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
25	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
26	C₃₁×#560	—	2	2	no	—
27	C₃₁×#553	—	2	2	no	—
28	C₃₁×#553	C₂²	1	2	yes	complemented
29	C₃₁×#552	C₂²	1	2	yes	complemented
30	C₃₁×#550	C₂²	1	2	yes	complemented
31	C₃₁×#547	—	2	2	no	—
32	C₃₁×#547	C₂²	1	2	yes	—
33	C₃₁×#547	C₂²	1	2	yes	—
34	C₃₁×#547	C₂²	1	2	yes	complemented
35	C₃₁×#546	—	2	2	no	—
36	C₃₁×#546	C₂²	1	2	yes	—
37	C₃₁×#546	C₂²	1	2	yes	—
38	C₃₁×#541	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#540	—	2	2	no	—
40	C₃₁×#540	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#539	—	2	2	no	—
42	C₃₁×#537	C₂²	1	2	yes	—
43	C₃₁×#536	C₂²	1	1	yes	characteristic
44	C₃₁×#536	C₂²	1	1	yes	characteristic
45	C₃₁×#534	—	2	2	no	—
46	C₃₁×#525	C₂²	1	1	yes	characteristic
47	C₃₁×#525	C₂²	1	1	yes	characteristic
48	C₃₁×#525	C₂²	1	2	yes	complemented
49	C₂×C₃₁×#123	—	2	2	no	—
50	C₃₁×#518	C₂²	1	1	yes	characteristic
51	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#496	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#485	C₂²	1	2	yes	complemented
60	C₃₁×#485	C₂²	1	2	yes	complemented
61	C₃₁×#484	C₂²	1	2	yes	complemented
62	C₃₁×#483	C₂²	1	2	yes	complemented
63	C₃₁×#482	C₂²	1	2	yes	complemented
64	C₃₁×#482	C₂²	1	2	yes	complemented
65	C₃₁×#478	C₂²	1	2	yes	complemented
66	C₃₁×#478	C₂²	1	2	yes	complemented
67	C₃₁×#470	C₂²	1	2	yes	complemented
68	C₃₁×#468	C₂²	1	2	yes	complemented
69	C₃₁×#467	C₂²	1	2	yes	complemented
70	C₃₁×#467	C₂²	1	2	yes	complemented
71	C₃₁×#466	C₂²	1	2	yes	complemented
72	C₃₁×#465	C₂²	1	2	yes	complemented
73	C₃₁×#465	C₂²	1	2	yes	complemented
74	C₃₁×#465	C₂²	1	2	yes	complemented
75	C₃₁×#464	C₂²	1	2	yes	complemented
76	C₃₁×#463	C₂²	1	2	yes	complemented
77	C₃₁×#462	C₂²	1	2	yes	complemented
78	C₃₁×#461	C₂²	1	2	yes	complemented
79	C₃₁×#461	C₂²	1	2	yes	complemented
80	C₃₁×#459	C₂²	1	2	yes	complemented
81	C₃₁×#452	C₂²	1	2	yes	—
82	C₃₁×#452	C₂²	1	2	yes	complemented
83	C₃₁×#452	C₂²	1	2	yes	complemented
84	C₃₁×#452	C₂²	1	2	yes	complemented
85	C₃₁×#452	C₂²	1	2	yes	complemented
86	C₃₁×#452	C₂²	1	2	yes	complemented
87	C₃₁×#452	C₂²	1	2	yes	complemented
88	C₃₁×#451	C₂²	1	2	yes	complemented
89	C₃₁×#450	C₂²	1	2	yes	—
90	C₃₁×#450	C₂²	1	2	yes	complemented
91	C₃₁×#449	C₂²	1	2	yes	—
92	C₃₁×#449	C₂²	1	2	yes	complemented
93	C₃₁×#449	C₂²	1	2	yes	complemented
94	C₃₁×#449	C₂²	1	2	yes	complemented
95	C₃₁×#449	C₂²	1	2	yes	complemented
96	C₃₁×#448	C₂²	1	2	yes	complemented
97	C₃₁×#447	C₂²	1	2	yes	—
98	C₃₁×#447	C₂²	1	2	yes	complemented
99	C₃₁×#442	C₂²	1	2	yes	complemented
100	C₃₁×#440	C₂²	1	2	yes	complemented
101	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
102	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
103	C₃₁×#435	C₂²	1	2	yes	complemented
104	C₃₁×#435	C₂²	1	2	yes	complemented
105	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
106	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
107	C₃₁×#433	C₂²	1	1	yes	characteristic, complemented
108	C₃₁×#433	C₂²	1	1	yes	characteristic, complemented
109	C₃₁×#417	C₂²	1	2	yes	complemented
110	C₃₁×#416	C₂²	1	2	yes	complemented
111	C₃₁×#416	C₂²	1	2	yes	complemented
112	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
113	C₃₁×#408	C₂²	1	2	yes	—
114	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
115	C₃₁×H(5,𝔽₂)	—	4	4	no	—
116	C₂×#41×C₃₁	—	2	1	no	—
117	C₂×#41×C₃₁	—	2	2	no	—
118	C₂×#41×C₃₁	—	4	4	no	—
119	C₂×#41×C₃₁	C₂³	1	2	yes	—
120	C₂×#41×C₃₁	C₂³	1	2	yes	—
121	C₂×#41×C₃₁	C₂³	1	2	yes	—
122	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
123	C₂×#41×C₃₁	C₂³	1	2	yes	—
124	C₂×#41×C₃₁	C₂³	1	2	yes	—
125	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₃₁	—	2	1	no	—
128	C₂²×D₄×C₃₁	—	2	2	no	—
129	C₂²×D₄×C₃₁	—	2	1	no	—
130	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
132	C₂³×C₄×C₃₁	—	2	1	no	—
133	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
135	C₃₁×#135	—	4	4	no	—
136	C₃₁×#135	—	4	4	no	—
137	C₃₁×#135	—	4	4	no	—
138	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
139	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×D₈×C₃₁	C₂³	1	2	yes	—
148	C₂×D₈×C₃₁	C₂³	1	2	yes	—
149	C₂×D₈×C₃₁	C₂³	1	2	yes	—
150	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
152	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
153	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
154	C₃₁×C₄⋊Q₈	—	2	1	no	—
155	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×#127	—	2	2	no	—
159	C₃₁×#127	C₂³	1	1	yes	characteristic
160	C₃₁×#126	—	2	2	no	—
161	C₃₁×#126	—	2	2	no	—
162	C₃₁×#126	—	2	2	no	—
163	C₃₁×#125	—	2	2	no	—
164	C₃₁×#125	—	2	2	no	—
165	C₃₁×#125	C₂³	1	1	yes	characteristic
166	C₃₁×#125	C₂³	1	1	yes	characteristic
167	C₃₁×#124	—	2	1	no	—
168	C₃₁×#124	C₂³	1	1	yes	characteristic
169	C₃₁×#124	C₂³	1	1	yes	characteristic
170	C₃₁×#123	—	2	2	no	—
171	C₃₁×#123	—	2	2	no	—
172	C₃₁×#123	—	2	1	no	—
173	C₃₁×#123	—	2	2	no	—
174	C₃₁×#123	—	2	2	no	—
175	C₃₁×#123	—	2	2	no	—
176	C₃₁×#123	—	2	2	no	—
177	C₃₁×#123	—	2	2	no	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	D₄	1	2	yes	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
189	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₃₁×#121	—	2	2	no	—
196	C₃₁×#121	—	2	2	no	—
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	—	2	2	no	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	D₄	1	2	yes	—
208	C₃₁×#121	C₂³	1	2	yes	—
209	C₃₁×#121	C₂³	1	2	yes	—
210	C₃₁×#121	C₂³	1	2	yes	—
211	C₃₁×#121	C₂³	1	2	yes	—
212	C₃₁×#120	—	2	1	no	—
213	C₃₁×#120	—	2	2	no	—
214	C₃₁×#120	—	2	2	no	—
215	C₃₁×#120	—	2	2	no	—
216	C₃₁×#120	D₄	1	2	yes	—
217	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
218	C₄×D₄×C₃₁	—	2	2	no	—
219	C₄×D₄×C₃₁	—	2	2	no	—
220	C₄×D₄×C₃₁	—	2	2	no	—
221	C₄×D₄×C₃₁	—	2	2	no	—
222	C₄×D₄×C₃₁	—	2	2	no	—
223	C₄×D₄×C₃₁	—	2	2	no	—
224	C₄×D₄×C₃₁	C₂³	1	2	yes	—
225	C₄×D₄×C₃₁	C₂³	1	2	yes	—
226	C₄×D₄×C₃₁	C₂³	1	2	yes	—
227	C₄×D₄×C₃₁	C₂³	1	2	yes	—
228	C₄×D₄×C₃₁	C₂³	1	2	yes	—
229	C₃₁×#117	—	2	2	no	—
230	C₃₁×#117	C₂³	1	2	yes	—
231	C₃₁×#117	C₂³	1	1	yes	characteristic
232	C₃₁×#117	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
234	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
235	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
238	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
239	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
240	C₃₁×#107	C₂³	1	2	yes	—
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#106	C₂³	1	2	yes	—
243	C₃₁×#106	C₂³	1	2	yes	—
244	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
245	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
246	C₃₁×#103	C₂³	1	2	yes	—
247	C₃₁×#103	C₂³	1	2	yes	—
248	C₃₁×#103	C₂³	1	2	yes	—
249	C₃₁×#103	C₂³	1	2	yes	—
250	C₃₁×#103	C₂³	1	2	yes	—
251	C₃₁×#103	C₂³	1	2	yes	—
252	C₃₁×#103	C₂³	1	2	yes	—
253	C₃₁×#103	C₂³	1	2	yes	—
254	C₃₁×#102	C₂³	1	2	yes	—
255	C₃₁×#102	C₂³	1	2	yes	—
256	C₃₁×#102	C₂³	1	2	yes	—
257	C₃₁×#102	C₂³	1	2	yes	—
258	C₃₁×#102	C₂³	1	2	yes	—
259	C₃₁×#102	C₂³	1	2	yes	—
260	C₃₁×#102	C₂³	1	2	yes	—
261	C₃₁×#102	C₂³	1	2	yes	—
262	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
263	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
264	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
265	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
266	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
267	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
268	C₃₁×#97	C₂³	1	1	yes	characteristic
269	C₃₁×#97	C₂³	1	1	yes	characteristic
270	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
271	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
272	C₂⁴×C₃₁	—	2	1	no	—
273	C₂⁴×C₃₁	—	2	2	no	—
274	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
275	#41×C₃₁	—	2	4	no	—
276	#41×C₃₁	—	2	4	no	—
277	#41×C₃₁	—	2	4	no	—
278	#41×C₃₁	—	4	2	no	—
279	#41×C₃₁	—	4	2	no	—
280	#41×C₃₁	—	4	2	no	—
281	#41×C₃₁	—	4	2	no	—
282	#41×C₃₁	—	4	2	no	—
283	#41×C₃₁	—	4	2	no	—
284	#41×C₃₁	—	4	2	no	—
285	#41×C₃₁	—	4	2	no	—
286	#41×C₃₁	—	4	2	no	—
287	#41×C₃₁	—	4	8	no	—
288	#41×C₃₁	—	4	4	no	—
289	C₂×Q₈×C₃₁	—	2	1	no	—
290	C₂×Q₈×C₃₁	—	4	2	no	—
291	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
292	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
293	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
294	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
296	C₂×D₄×C₃₁	—	2	4	no	—
297	C₂×D₄×C₃₁	—	2	4	no	—
298	C₂×D₄×C₃₁	—	2	2	no	—
299	C₂×D₄×C₃₁	—	2	2	no	—
300	C₂×D₄×C₃₁	—	2	1	no	—
301	C₂×D₄×C₃₁	—	2	2	no	—
302	C₂×D₄×C₃₁	—	2	2	no	—
303	C₂×D₄×C₃₁	—	2	2	no	—
304	C₂×D₄×C₃₁	—	2	2	no	—
305	C₂×D₄×C₃₁	—	2	2	no	—
306	C₂×D₄×C₃₁	—	2	2	no	—
307	C₂×D₄×C₃₁	—	2	2	no	—
308	C₂×D₄×C₃₁	—	2	1	no	—
309	C₂×D₄×C₃₁	—	2	2	no	—
310	C₂×D₄×C₃₁	—	2	2	no	—
311	C₂×D₄×C₃₁	—	4	2	no	—
312	C₂×D₄×C₃₁	—	4	4	no	—
313	C₂×D₄×C₃₁	—	4	4	no	—
314	C₂×D₄×C₃₁	—	4	8	no	—
315	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
316	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
317	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
318	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
319	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
320	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
321	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₃₁	—	2	1	no	—
323	C₂²×C₄×C₃₁	—	2	2	no	—
324	C₂²×C₄×C₃₁	—	2	2	no	—
325	C₂²×C₄×C₃₁	—	2	2	no	—
326	C₂²×C₄×C₃₁	—	2	2	no	—
327	C₂²×C₄×C₃₁	—	2	1	no	—
328	C₂²×C₄×C₃₁	—	2	2	no	—
329	C₂²×C₄×C₃₁	—	2	2	no	—
330	C₂²×C₄×C₃₁	—	2	2	no	—
331	C₂²×C₄×C₃₁	—	2	2	no	—
332	C₂²×C₄×C₃₁	—	2	2	no	—
333	C₂²×C₄×C₃₁	—	4	2	no	—
334	C₂²×C₄×C₃₁	—	4	4	no	—
335	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
336	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
339	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
340	Q₁₆×C₃₁	—	4	2	no	—
341	Q₁₆×C₃₁	—	4	2	no	—
342	Q₁₆×C₃₁	—	4	2	no	—
343	SD₁₆×C₃₁	—	2	4	no	—
344	SD₁₆×C₃₁	—	2	4	no	—
345	SD₁₆×C₃₁	—	4	2	no	—
346	SD₁₆×C₃₁	—	4	2	no	—
347	SD₁₆×C₃₁	—	4	2	no	—
348	SD₁₆×C₃₁	—	4	2	no	—
349	D₈×C₃₁	—	2	4	no	—
350	D₈×C₃₁	—	2	4	no	—
351	D₈×C₃₁	—	4	2	no	—
352	M₁₆×C₃₁	—	4	2	no	—
353	C₂×C₈×C₃₁	—	4	2	no	—
354	C₂×C₈×C₃₁	—	4	2	no	—
355	C₂×C₈×C₃₁	—	4	2	no	—
356	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
357	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
358	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
359	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₃₁	—	2	2	no	—
361	C₄⋊C₄×C₃₁	—	2	2	no	—
362	C₄⋊C₄×C₃₁	—	2	2	no	—
363	C₄⋊C₄×C₃₁	—	2	2	no	—
364	C₄⋊C₄×C₃₁	—	2	2	no	—
365	C₄⋊C₄×C₃₁	—	2	2	no	—
366	C₄⋊C₄×C₃₁	—	2	2	no	—
367	C₄⋊C₄×C₃₁	—	2	2	no	—
368	C₄⋊C₄×C₃₁	—	2	2	no	—
369	C₄⋊C₄×C₃₁	—	2	2	no	—
370	C₄⋊C₄×C₃₁	—	2	2	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
375	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
377	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
378	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
379	C₂²⋊C₄×C₃₁	—	2	1	no	—
380	C₂²⋊C₄×C₃₁	—	2	2	no	—
381	C₂²⋊C₄×C₃₁	—	2	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	2	no	—
383	C₂²⋊C₄×C₃₁	—	2	2	no	—
384	C₂²⋊C₄×C₃₁	—	2	2	no	—
385	C₂²⋊C₄×C₃₁	—	2	2	no	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	—	2	2	no	—
388	C₂²⋊C₄×C₃₁	—	2	2	no	—
389	C₂²⋊C₄×C₃₁	—	2	2	no	—
390	C₂²⋊C₄×C₃₁	—	2	2	no	—
391	C₂²⋊C₄×C₃₁	—	2	2	no	—
392	C₂²⋊C₄×C₃₁	—	2	2	no	—
393	C₂²⋊C₄×C₃₁	—	2	2	no	—
394	C₂²⋊C₄×C₃₁	—	2	2	no	—
395	C₂²⋊C₄×C₃₁	—	2	2	no	—
396	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
397	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
398	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
399	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
400	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
401	C₄²×C₃₁	—	2	2	no	—
402	C₄²×C₃₁	—	2	2	no	—
403	C₄²×C₃₁	—	2	1	no	—
404	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
406	#61635	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
407	C₂³×C₃₁	—	2	4	no	—
408	C₂³×C₃₁	—	2	2	no	—
409	C₂³×C₃₁	—	2	1	no	—
410	C₂³×C₃₁	—	2	2	no	—
411	C₂³×C₃₁	—	4	1	no	—
412	C₂³×C₃₁	—	4	2	no	—
413	C₂³×C₃₁	—	4	4	no	—
414	C₂³×C₃₁	—	8	2	no	—
415	C₂³×C₃₁	—	8	2	no	—
416	C₂³×C₃₁	—	8	2	no	—
417	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
418	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
419	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
420	Q₈×C₃₁	—	2	2	no	—
421	Q₈×C₃₁	—	2	2	no	—
422	Q₈×C₃₁	—	2	2	no	—
423	Q₈×C₃₁	—	2	2	no	—
424	Q₈×C₃₁	—	2	2	no	—
425	Q₈×C₃₁	—	4	1	no	—
426	Q₈×C₃₁	—	4	2	no	—
427	D₄×C₃₁	—	2	4	no	—
428	D₄×C₃₁	—	2	2	no	—
429	D₄×C₃₁	—	2	2	no	—
430	D₄×C₃₁	—	2	2	no	—
431	D₄×C₃₁	—	2	2	no	—
432	D₄×C₃₁	—	4	1	no	—
433	D₄×C₃₁	—	4	2	no	—
434	D₄×C₃₁	—	4	2	no	—
435	D₄×C₃₁	—	4	2	no	—
436	D₄×C₃₁	—	4	4	no	—
437	D₄×C₃₁	—	4	4	no	—
438	D₄×C₃₁	—	4	4	no	—
439	D₄×C₃₁	—	4	4	no	—
440	D₄×C₃₁	—	4	2	no	—
441	D₄×C₃₁	—	8	2	no	—
442	D₄×C₃₁	—	8	2	no	—
443	D₄×C₃₁	—	8	2	no	—
444	D₄×C₃₁	—	8	2	no	—
445	D₄×C₃₁	—	8	2	no	—
446	D₄×C₃₁	—	8	2	no	—
447	D₄×C₃₁	—	8	2	no	—
448	D₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
449	C₂×C₄×C₃₁	—	2	2	no	—
450	C₂×C₄×C₃₁	—	2	2	no	—
451	C₂×C₄×C₃₁	—	2	2	no	—
452	C₂×C₄×C₃₁	—	2	2	no	—
453	C₂×C₄×C₃₁	—	2	2	no	—
454	C₂×C₄×C₃₁	—	2	2	no	—
455	C₂×C₄×C₃₁	—	2	2	no	—
456	C₂×C₄×C₃₁	—	2	2	no	—
457	C₂×C₄×C₃₁	—	2	2	no	—
458	C₂×C₄×C₃₁	—	2	1	no	—
459	C₂×C₄×C₃₁	—	2	1	no	—
460	C₂×C₄×C₃₁	—	2	1	no	—
461	C₂×C₄×C₃₁	—	4	1	no	—
462	C₂×C₄×C₃₁	—	4	2	no	—
463	C₂×C₄×C₃₁	—	4	4	no	—
464	C₂×C₄×C₃₁	—	4	4	no	—
465	C₂×C₄×C₃₁	—	4	4	no	—
466	C₂×C₄×C₃₁	—	4	2	no	—
467	C₂×C₄×C₃₁	—	4	2	no	—
468	C₂×C₄×C₃₁	—	8	2	no	—
469	C₂×C₄×C₃₁	—	8	2	no	—
470	C₂×C₄×C₃₁	—	8	2	no	—
471	C₂×C₄×C₃₁	—	8	2	no	—
472	C₂×C₄×C₃₁	—	8	2	no	—
473	C₂×C₄×C₃₁	—	8	2	no	—
474	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
476	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
478	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
479	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
480	C₈×C₃₁	—	2	2	no	—
481	C₈×C₃₁	—	2	2	no	—
482	C₈×C₃₁	—	2	2	no	—
483	C₈×C₃₁	—	2	2	no	—
484	#3539	C₂×C₃₁	1	1	yes	characteristic, complemented
485	#3485	C₂×C₃₁	1	1	yes	characteristic, complemented
486	#3315	C₂×C₃₁	1	2	yes	complemented
487	#3307	C₂×C₃₁	1	2	yes	complemented
488	#3297	C₂×C₃₁	1	2	yes	complemented
489	#3296	C₂×C₃₁	1	2	yes	complemented
490	#3284	C₂×C₃₁	1	2	yes	complemented
491	#3283	C₂×C₃₁	1	2	yes	complemented
492	#3268	C₂×C₃₁	1	2	yes	complemented
493	#3267	C₂×C₃₁	1	2	yes	complemented
494	#3223	C₂×C₃₁	1	1	yes	characteristic, complemented
495	#3221	C₂×C₃₁	1	1	yes	characteristic, complemented
496	#3201	C₂×C₃₁	1	2	yes	complemented
497	#3191	C₂×C₃₁	1	2	yes	complemented
498	#3123	C₂×C₃₁	1	1	yes	characteristic, complemented
499	#3122	C₂×C₃₁	1	1	yes	characteristic, complemented
500	#3012	C₂×C₃₁	1	2	yes	complemented
501	#3002	C₂×C₃₁	1	2	yes	complemented
502	#2977	C₂×C₃₁	1	1	yes	characteristic, complemented
503	C₂²×C₃₁	—	2	2	no	—
504	C₂²×C₃₁	—	2	2	no	—
505	C₂²×C₃₁	—	2	2	no	—
506	C₂²×C₃₁	—	2	2	no	—
507	C₂²×C₃₁	—	2	2	no	—
508	C₂²×C₃₁	—	2	1	no	—
509	C₂²×C₃₁	—	2	2	no	—
510	C₂²×C₃₁	—	2	2	no	—
511	C₂²×C₃₁	—	2	4	no	—
512	C₂²×C₃₁	—	4	2	no	—
513	C₂²×C₃₁	—	4	2	no	—
514	C₂²×C₃₁	—	4	2	no	—
515	C₂²×C₃₁	—	4	2	no	—
516	C₂²×C₃₁	—	4	2	no	—
517	C₂²×C₃₁	—	4	1	no	—
518	C₂²×C₃₁	—	4	2	no	—
519	C₂²×C₃₁	—	8	4	no	—
520	C₂²×C₃₁	—	8	2	no	—
521	C₂²×C₃₁	—	16	4	no	—
522	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
523	C₄×C₃₁	—	2	2	no	—
524	C₄×C₃₁	—	2	2	no	—
525	C₄×C₃₁	—	2	2	no	—
526	C₄×C₃₁	—	2	1	no	—
527	C₄×C₃₁	—	2	2	no	—
528	C₄×C₃₁	—	4	2	no	—
529	C₄×C₃₁	—	4	2	no	—
530	C₄×C₃₁	—	4	2	no	—
531	C₄×C₃₁	—	4	1	no	—
532	C₄×C₃₁	—	4	1	no	—
533	C₄×C₃₁	—	4	1	no	—
534	C₄×C₃₁	—	4	2	no	—
535	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
536	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
537	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
538	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
539	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
540	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
541	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
542	#560	—	2	2	no	—
543	#553	—	2	2	no	—
544	#553	C₂²×C₃₁	1	2	yes	complemented
545	#552	C₂²×C₃₁	1	2	yes	complemented
546	#550	C₂²×C₃₁	1	2	yes	complemented
547	#547	—	2	2	no	—
548	#547	C₂²×C₃₁	1	2	yes	—
549	#547	C₂²×C₃₁	1	2	yes	—
550	#547	C₂²×C₃₁	1	2	yes	complemented
551	#546	—	2	2	no	—
552	#546	C₂²×C₃₁	1	2	yes	—
553	#546	C₂²×C₃₁	1	2	yes	—
554	#541	C₂²×C₃₁	1	1	yes	characteristic, complemented
555	#540	—	2	2	no	—
556	#540	C₂²×C₃₁	1	1	yes	characteristic, complemented
557	#539	—	2	2	no	—
558	#537	C₂²×C₃₁	1	2	yes	—
559	#536	C₂²×C₃₁	1	1	yes	characteristic
560	#536	C₂²×C₃₁	1	1	yes	characteristic
561	#534	—	2	2	no	—
562	#525	C₂²×C₃₁	1	1	yes	characteristic
563	#525	C₂²×C₃₁	1	1	yes	characteristic
564	#525	C₂²×C₃₁	1	2	yes	complemented
565	C₂×#123	—	2	2	no	—
566	#518	C₂²×C₃₁	1	1	yes	characteristic
567	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
568	#496	C₂²×C₃₁	1	1	yes	characteristic, complemented
569	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
570	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
571	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
572	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
573	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
574	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
575	#485	C₂²×C₃₁	1	2	yes	complemented
576	#485	C₂²×C₃₁	1	2	yes	complemented
577	#484	C₂²×C₃₁	1	2	yes	complemented
578	#483	C₂²×C₃₁	1	2	yes	complemented
579	#482	C₂²×C₃₁	1	2	yes	complemented
580	#482	C₂²×C₃₁	1	2	yes	complemented
581	#478	C₂²×C₃₁	1	2	yes	complemented
582	#478	C₂²×C₃₁	1	2	yes	complemented
583	#470	C₂²×C₃₁	1	2	yes	complemented
584	#468	C₂²×C₃₁	1	2	yes	complemented
585	#467	C₂²×C₃₁	1	2	yes	complemented
586	#467	C₂²×C₃₁	1	2	yes	complemented
587	#466	C₂²×C₃₁	1	2	yes	complemented
588	#465	C₂²×C₃₁	1	2	yes	complemented
589	#465	C₂²×C₃₁	1	2	yes	complemented
590	#465	C₂²×C₃₁	1	2	yes	complemented
591	#464	C₂²×C₃₁	1	2	yes	complemented
592	#463	C₂²×C₃₁	1	2	yes	complemented
593	#462	C₂²×C₃₁	1	2	yes	complemented
594	#461	C₂²×C₃₁	1	2	yes	complemented
595	#461	C₂²×C₃₁	1	2	yes	complemented
596	#459	C₂²×C₃₁	1	2	yes	complemented
597	#452	C₂²×C₃₁	1	2	yes	—
598	#452	C₂²×C₃₁	1	2	yes	complemented
599	#452	C₂²×C₃₁	1	2	yes	complemented
600	#452	C₂²×C₃₁	1	2	yes	complemented
601	#452	C₂²×C₃₁	1	2	yes	complemented
602	#452	C₂²×C₃₁	1	2	yes	complemented
603	#452	C₂²×C₃₁	1	2	yes	complemented
604	#451	C₂²×C₃₁	1	2	yes	complemented
605	#450	C₂²×C₃₁	1	2	yes	—
606	#450	C₂²×C₃₁	1	2	yes	complemented
607	#449	C₂²×C₃₁	1	2	yes	—
608	#449	C₂²×C₃₁	1	2	yes	complemented
609	#449	C₂²×C₃₁	1	2	yes	complemented
610	#449	C₂²×C₃₁	1	2	yes	complemented
611	#449	C₂²×C₃₁	1	2	yes	complemented
612	#448	C₂²×C₃₁	1	2	yes	complemented
613	#447	C₂²×C₃₁	1	2	yes	—
614	#447	C₂²×C₃₁	1	2	yes	complemented
615	#442	C₂²×C₃₁	1	2	yes	complemented
616	#440	C₂²×C₃₁	1	2	yes	complemented
617	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
618	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
619	#435	C₂²×C₃₁	1	2	yes	complemented
620	#435	C₂²×C₃₁	1	2	yes	complemented
621	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
622	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
623	#433	C₂²×C₃₁	1	1	yes	characteristic, complemented
624	#433	C₂²×C₃₁	1	1	yes	characteristic, complemented
625	#417	C₂²×C₃₁	1	2	yes	complemented
626	#416	C₂²×C₃₁	1	2	yes	complemented
627	#416	C₂²×C₃₁	1	2	yes	complemented
628	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
629	#408	C₂²×C₃₁	1	2	yes	—
630	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	complemented
631	C₂×C₃₁	—	4	2	no	—
632	C₂×C₃₁	—	4	1	no	—
633	C₂×C₃₁	—	4	2	no	—
634	C₂×C₃₁	—	4	4	no	—
635	C₂×C₃₁	—	8	2	no	—
636	C₂×C₃₁	—	8	1	no	—
637	C₂×C₃₁	#3484	1	1	yes	characteristic
638	C₂×C₃₁	#3584	1	2	yes	—
639	H(5,𝔽₂)	—	4	4	no	—
640	C₂×#41	—	2	1	no	—
641	C₂×#41	—	2	2	no	—
642	C₂×#41	—	4	4	no	—
643	C₂×#41	C₂³×C₃₁	1	2	yes	—
644	C₂×#41	C₂³×C₃₁	1	2	yes	—
645	C₂×#41	C₂³×C₃₁	1	2	yes	—
646	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
647	C₂×#41	C₂³×C₃₁	1	2	yes	—
648	C₂×#41	C₂³×C₃₁	1	2	yes	—
649	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
650	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
651	C₂²×D₄	—	2	1	no	—
652	C₂²×D₄	—	2	2	no	—
653	C₂²×D₄	—	2	1	no	—
654	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
655	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
656	C₂³×C₄	—	2	1	no	—
657	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
658	AGL(1,ℤ/8)	—	4	4	no	—
659	#135	—	4	4	no	—
660	#135	—	4	4	no	—
661	#135	—	4	4	no	—
662	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
663	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
664	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
665	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
666	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
667	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
668	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
669	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
670	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
671	C₂×D₈	C₂³×C₃₁	1	2	yes	—
672	C₂×D₈	C₂³×C₃₁	1	2	yes	—
673	C₂×D₈	C₂³×C₃₁	1	2	yes	—
674	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
675	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
676	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
677	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
678	C₄⋊Q₈	—	2	1	no	—
679	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
680	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
681	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
682	#127	—	2	2	no	—
683	#127	C₂³×C₃₁	1	1	yes	characteristic
684	#126	—	2	2	no	—
685	#126	—	2	2	no	—
686	#126	—	2	2	no	—
687	#125	—	2	2	no	—
688	#125	—	2	2	no	—
689	#125	C₂³×C₃₁	1	1	yes	characteristic
690	#125	C₂³×C₃₁	1	1	yes	characteristic
691	#124	—	2	1	no	—
692	#124	C₂³×C₃₁	1	1	yes	characteristic
693	#124	C₂³×C₃₁	1	1	yes	characteristic
694	#123	—	2	2	no	—
695	#123	—	2	2	no	—
696	#123	—	2	1	no	—
697	#123	—	2	2	no	—
698	#123	—	2	2	no	—
699	#123	—	2	2	no	—
700	#123	—	2	2	no	—
701	#123	—	2	2	no	—
702	#123	—	2	2	no	—
703	#123	—	2	2	no	—
704	#123	—	2	2	no	—
705	#123	—	2	2	no	—
706	#123	—	2	2	no	—
707	#123	—	2	2	no	—
708	#123	—	2	2	no	—
709	#123	D₄×C₃₁	1	2	yes	—
710	C₂²⋊Q₈	—	2	2	no	—
711	C₂²⋊Q₈	—	2	2	no	—
712	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
713	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
714	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
715	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
716	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
717	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
718	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
719	#121	—	2	2	no	—
720	#121	—	2	2	no	—
721	#121	—	2	2	no	—
722	#121	—	2	2	no	—
723	#121	—	2	2	no	—
724	#121	—	2	2	no	—
725	#121	—	2	2	no	—
726	#121	—	2	2	no	—
727	#121	—	2	2	no	—
728	#121	—	2	2	no	—
729	#121	—	2	2	no	—
730	#121	—	2	2	no	—
731	#121	D₄×C₃₁	1	2	yes	—
732	#121	C₂³×C₃₁	1	2	yes	—
733	#121	C₂³×C₃₁	1	2	yes	—
734	#121	C₂³×C₃₁	1	2	yes	—
735	#121	C₂³×C₃₁	1	2	yes	—
736	#120	—	2	1	no	—
737	#120	—	2	2	no	—
738	#120	—	2	2	no	—
739	#120	—	2	2	no	—
740	#120	D₄×C₃₁	1	2	yes	—
741	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
742	C₄×D₄	—	2	2	no	—
743	C₄×D₄	—	2	2	no	—
744	C₄×D₄	—	2	2	no	—
745	C₄×D₄	—	2	2	no	—
746	C₄×D₄	—	2	2	no	—
747	C₄×D₄	—	2	2	no	—
748	C₄×D₄	C₂³×C₃₁	1	2	yes	—
749	C₄×D₄	C₂³×C₃₁	1	2	yes	—
750	C₄×D₄	C₂³×C₃₁	1	2	yes	—
751	C₄×D₄	C₂³×C₃₁	1	2	yes	—
752	C₄×D₄	C₂³×C₃₁	1	2	yes	—
753	#117	—	2	2	no	—
754	#117	C₂³×C₃₁	1	1	yes	characteristic
755	#117	C₂³×C₃₁	1	2	yes	—
756	#117	C₂³×C₃₁	1	1	yes	characteristic
757	C₂×C₄⋊C₄	—	2	2	no	—
758	C₂×C₄⋊C₄	—	2	2	no	—
759	C₂×C₄⋊C₄	—	2	2	no	—
760	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
761	C₂×C₂²⋊C₄	—	2	2	no	—
762	C₂×C₂²⋊C₄	—	2	2	no	—
763	C₂×C₂²⋊C₄	—	2	2	no	—
764	#107	C₂³×C₃₁	1	2	yes	—
765	#107	C₂³×C₃₁	1	2	yes	—
766	#106	C₂³×C₃₁	1	2	yes	—
767	#106	C₂³×C₃₁	1	2	yes	—
768	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
769	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
770	#103	C₂³×C₃₁	1	2	yes	—
771	#103	C₂³×C₃₁	1	2	yes	—
772	#103	C₂³×C₃₁	1	2	yes	—
773	#103	C₂³×C₃₁	1	2	yes	—
774	#103	C₂³×C₃₁	1	2	yes	—
775	#103	C₂³×C₃₁	1	2	yes	—
776	#103	C₂³×C₃₁	1	2	yes	—
777	#103	C₂³×C₃₁	1	2	yes	—
778	#102	C₂³×C₃₁	1	2	yes	—
779	#102	C₂³×C₃₁	1	2	yes	—
780	#102	C₂³×C₃₁	1	2	yes	—
781	#102	C₂³×C₃₁	1	2	yes	—
782	#102	C₂³×C₃₁	1	2	yes	—
783	#102	C₂³×C₃₁	1	2	yes	—
784	#102	C₂³×C₃₁	1	2	yes	—
785	#102	C₂³×C₃₁	1	2	yes	—
786	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
787	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
788	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
789	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
790	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
791	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
792	#97	C₂³×C₃₁	1	1	yes	characteristic
793	#97	C₂³×C₃₁	1	1	yes	characteristic
794	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
795	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
796	C₃₁	#61635	1	1	yes	characteristic, direct product factor, Sylow
797	C₂⁴	—	2	1	no	—
798	C₂⁴	—	2	2	no	—
799	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
800	#41	—	2	4	no	—
801	#41	—	2	4	no	—
802	#41	—	2	4	no	—
803	#41	—	4	2	no	—
804	#41	—	4	2	no	—
805	#41	—	4	2	no	—
806	#41	—	4	2	no	—
807	#41	—	4	2	no	—
808	#41	—	4	2	no	—
809	#41	—	4	2	no	—
810	#41	—	4	2	no	—
811	#41	—	4	2	no	—
812	#41	—	4	8	no	—
813	#41	—	4	4	no	—
814	C₂×Q₈	—	2	1	no	—
815	C₂×Q₈	—	4	2	no	—
816	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
817	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
818	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
819	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
820	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
821	C₂×D₄	—	2	4	no	—
822	C₂×D₄	—	2	4	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	2	1	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	1	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	4	2	no	—
837	C₂×D₄	—	4	4	no	—
838	C₂×D₄	—	4	4	no	—
839	C₂×D₄	—	4	8	no	—
840	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
841	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
842	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
843	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
844	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
845	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
846	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
847	C₂²×C₄	—	2	1	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	1	no	—
853	C₂²×C₄	—	2	2	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	4	2	no	—
859	C₂²×C₄	—	4	4	no	—
860	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
861	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
862	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
864	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
865	Q₁₆	—	4	2	no	—
866	Q₁₆	—	4	2	no	—
867	Q₁₆	—	4	2	no	—
868	SD₁₆	—	2	4	no	—
869	SD₁₆	—	2	4	no	—
870	SD₁₆	—	4	2	no	—
871	SD₁₆	—	4	2	no	—
872	SD₁₆	—	4	2	no	—
873	SD₁₆	—	4	2	no	—
874	D₈	—	2	4	no	—
875	D₈	—	2	4	no	—
876	D₈	—	4	2	no	—
877	M₁₆	—	4	2	no	—
878	C₂×C₈	—	4	2	no	—
879	C₂×C₈	—	4	2	no	—
880	C₂×C₈	—	4	2	no	—
881	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
882	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
883	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
884	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
899	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
900	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
901	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
902	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
903	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
904	C₂²⋊C₄	—	2	1	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	2	no	—
921	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
922	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
923	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
924	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
925	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
926	C₄²	—	2	2	no	—
927	C₄²	—	2	2	no	—
928	C₄²	—	2	1	no	—
929	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
930	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
931	C₂³	—	2	4	no	—
932	C₂³	—	2	2	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	2	no	—
935	C₂³	—	4	1	no	—
936	C₂³	—	4	2	no	—
937	C₂³	—	4	4	no	—
938	C₂³	—	8	2	no	—
939	C₂³	—	8	2	no	—
940	C₂³	—	8	2	no	—
941	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
942	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
943	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
944	Q₈	—	2	2	no	—
945	Q₈	—	2	2	no	—
946	Q₈	—	2	2	no	—
947	Q₈	—	2	2	no	—
948	Q₈	—	2	2	no	—
949	Q₈	—	4	1	no	—
950	Q₈	—	4	2	no	—
951	D₄	—	2	4	no	—
952	D₄	—	2	2	no	—
953	D₄	—	2	2	no	—
954	D₄	—	2	2	no	—
955	D₄	—	2	2	no	—
956	D₄	—	4	1	no	—
957	D₄	—	4	2	no	—
958	D₄	—	4	2	no	—
959	D₄	—	4	2	no	—
960	D₄	—	4	4	no	—
961	D₄	—	4	4	no	—
962	D₄	—	4	4	no	—
963	D₄	—	4	4	no	—
964	D₄	—	4	2	no	—
965	D₄	—	8	2	no	—
966	D₄	—	8	2	no	—
967	D₄	—	8	2	no	—
968	D₄	—	8	2	no	—
969	D₄	—	8	2	no	—
970	D₄	—	8	2	no	—
971	D₄	—	8	2	no	—
972	D₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	4	1	no	—
986	C₂×C₄	—	4	2	no	—
987	C₂×C₄	—	4	4	no	—
988	C₂×C₄	—	4	4	no	—
989	C₂×C₄	—	4	4	no	—
990	C₂×C₄	—	4	2	no	—
991	C₂×C₄	—	4	2	no	—
992	C₂×C₄	—	8	2	no	—
993	C₂×C₄	—	8	2	no	—
994	C₂×C₄	—	8	2	no	—
995	C₂×C₄	—	8	2	no	—
996	C₂×C₄	—	8	2	no	—
997	C₂×C₄	—	8	2	no	—
998	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
999	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1000	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1001	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1002	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1003	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1004	C₈	—	2	2	no	—
1005	C₈	—	2	2	no	—
1006	C₈	—	2	2	no	—
1007	C₈	—	2	2	no	—
1008	C₂²	—	2	1	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	4	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	4	2	no	—
1018	C₂²	—	4	2	no	—
1019	C₂²	—	4	1	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	2	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	8	4	no	—
1025	C₂²	—	8	2	no	—
1026	C₂²	—	16	4	no	—
1027	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1028	C₄	—	2	2	no	—
1029	C₄	—	2	1	no	—
1030	C₄	—	2	2	no	—
1031	C₄	—	2	2	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	4	1	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	2	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	2	no	—
1039	C₄	—	4	2	no	—
1040	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
1041	C₂	—	4	1	no	—
1042	C₂	—	4	2	no	—
1043	C₂	—	4	2	no	—
1044	C₂	—	4	4	no	—
1045	C₂	—	8	1	no	—
1046	C₂	—	8	2	no	—
1047	C₂	C₃₁×#3484	1	1	yes	characteristic
1048	C₂	C₃₁×#3584	1	2	yes	—

	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3539	C₂	semidirect
2. C₃₁×#3485	C₂	semidirect
3. C₃₁×#3315	C₂	semidirect
4. C₃₁×#3307	C₂	semidirect
5. C₃₁×#3297	C₂	semidirect
6. C₃₁×#3296	C₂	semidirect
7. C₃₁×#3284	C₂	semidirect
8. C₃₁×#3283	C₂	semidirect
9. C₃₁×#3268	C₂	semidirect
10. C₃₁×#3267	C₂	semidirect
11. C₃₁×#3223	C₂	semidirect
12. C₃₁×#3221	C₂	semidirect
13. C₃₁×#3201	C₂	semidirect
14. C₃₁×#3191	C₂	semidirect
15. C₃₁×#3123	C₂	semidirect
16. C₃₁×#3122	C₂	semidirect
17. C₃₁×#3012	C₂	semidirect
18. C₃₁×#3002	C₂	semidirect
19. C₃₁×#2977	C₂	semidirect
22. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₃₁×#135	C₂²	semidirect
24. C₂×C₃₁×#135	C₂²	semidirect
25. C₂×C₃₁×#135	C₂²	semidirect
28. C₃₁×#553	C₂²	semidirect
29. C₃₁×#552	C₂²	semidirect
30. C₃₁×#550	C₂²	semidirect
34. C₃₁×#547	C₂²	semidirect
38. C₃₁×#541	C₂²	semidirect
40. C₃₁×#540	C₂²	semidirect
48. C₃₁×#525	C₂²	semidirect
51. C₃₁×#497	C₂²	semidirect
52. C₃₁×#496	C₂²	semidirect
53. C₃₁×#494	C₂²	semidirect
54. C₃₁×#492	C₂²	semidirect
55. C₃₁×#491	C₂²	semidirect
56. C₃₁×#491	C₂²	semidirect
57. C₃₁×#488	C₂²	semidirect
58. C₃₁×#488	C₂²	semidirect
59. C₃₁×#485	C₂²	semidirect
60. C₃₁×#485	C₂²	semidirect
61. C₃₁×#484	C₂²	semidirect
62. C₃₁×#483	C₂²	semidirect
63. C₃₁×#482	C₂²	semidirect
64. C₃₁×#482	C₂²	semidirect
65. C₃₁×#478	C₂²	semidirect
66. C₃₁×#478	C₂²	semidirect
67. C₃₁×#470	C₂²	semidirect
68. C₃₁×#468	C₂²	semidirect
69. C₃₁×#467	C₂²	semidirect
70. C₃₁×#467	C₂²	semidirect
71. C₃₁×#466	C₂²	semidirect
72. C₃₁×#465	C₂²	semidirect
73. C₃₁×#465	C₂²	semidirect
74. C₃₁×#465	C₂²	semidirect
75. C₃₁×#464	C₂²	semidirect
76. C₃₁×#463	C₂²	semidirect
77. C₃₁×#462	C₂²	semidirect
78. C₃₁×#461	C₂²	semidirect
79. C₃₁×#461	C₂²	semidirect
80. C₃₁×#459	C₂²	semidirect
82. C₃₁×#452	C₂²	semidirect
83. C₃₁×#452	C₂²	semidirect
84. C₃₁×#452	C₂²	semidirect
85. C₃₁×#452	C₂²	semidirect
86. C₃₁×#452	C₂²	semidirect
87. C₃₁×#452	C₂²	semidirect
88. C₃₁×#451	C₂²	semidirect
90. C₃₁×#450	C₂²	semidirect
92. C₃₁×#449	C₂²	semidirect
93. C₃₁×#449	C₂²	semidirect
94. C₃₁×#449	C₂²	semidirect
95. C₃₁×#449	C₂²	semidirect
96. C₃₁×#448	C₂²	semidirect
98. C₃₁×#447	C₂²	semidirect
99. C₃₁×#442	C₂²	semidirect
100. C₃₁×#440	C₂²	semidirect
101. C₄×SD₁₆×C₃₁	C₂²	semidirect
102. C₄×D₈×C₃₁	C₂²	semidirect
103. C₃₁×#435	C₂²	semidirect
104. C₃₁×#435	C₂²	semidirect
105. C₈×D₄×C₃₁	C₂²	semidirect
106. C₈×D₄×C₃₁	C₂²	semidirect
107. C₃₁×#433	C₂²	semidirect
108. C₃₁×#433	C₂²	semidirect
109. C₃₁×#417	C₂²	semidirect
110. C₃₁×#416	C₂²	semidirect
111. C₃₁×#416	C₂²	semidirect
112. C₂×C₃₁×#102	C₂²	semidirect
114. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
406. #61635	C₃₁	direct (N × H)
484. #3539	C₂×C₃₁	semidirect
485. #3485	C₂×C₃₁	semidirect
486. #3315	C₂×C₃₁	semidirect
487. #3307	C₂×C₃₁	semidirect
488. #3297	C₂×C₃₁	semidirect
489. #3296	C₂×C₃₁	semidirect
490. #3284	C₂×C₃₁	semidirect
491. #3283	C₂×C₃₁	semidirect
492. #3268	C₂×C₃₁	semidirect
493. #3267	C₂×C₃₁	semidirect
494. #3223	C₂×C₃₁	semidirect
495. #3221	C₂×C₃₁	semidirect
496. #3201	C₂×C₃₁	semidirect
497. #3191	C₂×C₃₁	semidirect
498. #3123	C₂×C₃₁	semidirect
499. #3122	C₂×C₃₁	semidirect
500. #3012	C₂×C₃₁	semidirect
501. #3002	C₂×C₃₁	semidirect
502. #2977	C₂×C₃₁	semidirect
538. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
539. C₂×#135	C₂²×C₃₁	semidirect
540. C₂×#135	C₂²×C₃₁	semidirect
541. C₂×#135	C₂²×C₃₁	semidirect
544. #553	C₂²×C₃₁	semidirect
545. #552	C₂²×C₃₁	semidirect
546. #550	C₂²×C₃₁	semidirect
550. #547	C₂²×C₃₁	semidirect
554. #541	C₂²×C₃₁	semidirect
556. #540	C₂²×C₃₁	semidirect
564. #525	C₂²×C₃₁	semidirect
567. #497	C₂²×C₃₁	semidirect
568. #496	C₂²×C₃₁	semidirect
569. #494	C₂²×C₃₁	semidirect
570. #492	C₂²×C₃₁	semidirect
571. #491	C₂²×C₃₁	semidirect
572. #491	C₂²×C₃₁	semidirect
573. #488	C₂²×C₃₁	semidirect
574. #488	C₂²×C₃₁	semidirect
575. #485	C₂²×C₃₁	semidirect
576. #485	C₂²×C₃₁	semidirect
577. #484	C₂²×C₃₁	semidirect
578. #483	C₂²×C₃₁	semidirect
579. #482	C₂²×C₃₁	semidirect
580. #482	C₂²×C₃₁	semidirect
581. #478	C₂²×C₃₁	semidirect
582. #478	C₂²×C₃₁	semidirect
583. #470	C₂²×C₃₁	semidirect
584. #468	C₂²×C₃₁	semidirect
585. #467	C₂²×C₃₁	semidirect
586. #467	C₂²×C₃₁	semidirect
587. #466	C₂²×C₃₁	semidirect
588. #465	C₂²×C₃₁	semidirect
589. #465	C₂²×C₃₁	semidirect
590. #465	C₂²×C₃₁	semidirect
591. #464	C₂²×C₃₁	semidirect
592. #463	C₂²×C₃₁	semidirect
593. #462	C₂²×C₃₁	semidirect
594. #461	C₂²×C₃₁	semidirect
595. #461	C₂²×C₃₁	semidirect
596. #459	C₂²×C₃₁	semidirect
598. #452	C₂²×C₃₁	semidirect
599. #452	C₂²×C₃₁	semidirect
600. #452	C₂²×C₃₁	semidirect
601. #452	C₂²×C₃₁	semidirect
602. #452	C₂²×C₃₁	semidirect
603. #452	C₂²×C₃₁	semidirect
604. #451	C₂²×C₃₁	semidirect
606. #450	C₂²×C₃₁	semidirect
608. #449	C₂²×C₃₁	semidirect
609. #449	C₂²×C₃₁	semidirect
610. #449	C₂²×C₃₁	semidirect
611. #449	C₂²×C₃₁	semidirect
612. #448	C₂²×C₃₁	semidirect
614. #447	C₂²×C₃₁	semidirect
615. #442	C₂²×C₃₁	semidirect
616. #440	C₂²×C₃₁	semidirect
617. C₄×SD₁₆	C₂²×C₃₁	semidirect
618. C₄×D₈	C₂²×C₃₁	semidirect
619. #435	C₂²×C₃₁	semidirect
620. #435	C₂²×C₃₁	semidirect
621. C₈×D₄	C₂²×C₃₁	semidirect
622. C₈×D₄	C₂²×C₃₁	semidirect
623. #433	C₂²×C₃₁	semidirect
624. #433	C₂²×C₃₁	semidirect
625. #417	C₂²×C₃₁	semidirect
626. #416	C₂²×C₃₁	semidirect
627. #416	C₂²×C₃₁	semidirect
628. C₂×#102	C₂²×C₃₁	semidirect
630. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
796. C₃₁	#61635	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×#3539	2
C₃₁×#3485	2
C₃₁×#3315	2
C₃₁×#3307	2
C₃₁×#3297	2
C₃₁×#3296	2
C₃₁×#3284	2
C₃₁×#3283	2
C₃₁×#3268	2
C₃₁×#3267	2
C₃₁×#3223	2
C₃₁×#3221	2
C₃₁×#3201	2
C₃₁×#3191	2
C₃₁×#3123	2
C₃₁×#3122	2
C₃₁×#3012	2
C₃₁×#3002	2
C₃₁×#2977	2
#61635	31

Subgroups — C31×#61635 #21518394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61635 #21518394