Subgroups — C₃₁×#62016 #21518775

Order 7936.

1902 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3397	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3321	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3320	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3297	C₂	1	2	yes	maximal, complemented
8	D₄×SD₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3265	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3264	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3257	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3221	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3042	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
23	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₃₁×#563	—	2	1	no	—
25	C₃₁×#562	—	2	1	no	—
26	C₃₁×#556	C₂²	1	2	yes	complemented
27	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#553	—	2	1	no	—
30	C₃₁×#553	C₂²	1	2	yes	—
31	C₃₁×#551	—	2	2	no	—
32	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
33	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
34	C₃₁×#548	C₂²	1	2	yes	complemented
35	C₃₁×#546	—	2	1	no	—
36	C₃₁×#546	—	2	2	no	—
37	C₃₁×#546	C₂²	1	2	yes	complemented
38	D₄²×C₃₁	C₂²	1	2	yes	—
39	D₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#543	—	2	1	no	—
41	C₃₁×#542	—	2	2	no	—
42	C₃₁×#542	C₂²	1	2	yes	complemented
43	C₃₁×#540	C₂²	1	2	yes	complemented
44	C₃₁×#538	—	2	2	no	—
45	C₃₁×#538	—	2	1	no	—
46	C₃₁×#536	C₂²	1	2	yes	complemented
47	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#532	C₂²	1	1	yes	characteristic
49	C₃₁×#529	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#525	—	2	1	no	—
52	C₂×C₃₁×#121	—	2	1	no	—
53	C₃₁×#518	C₂²	1	2	yes	complemented
54	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
55	C₃₁×#496	C₂²	1	2	yes	complemented
56	C₃₁×#496	C₂²	1	2	yes	complemented
57	C₃₁×#492	C₂²	1	2	yes	complemented
58	C₃₁×#491	C₂²	1	2	yes	complemented
59	C₃₁×#489	C₂²	1	2	yes	complemented
60	C₃₁×#488	C₂²	1	2	yes	complemented
61	C₃₁×#485	C₂²	1	2	yes	complemented
62	C₃₁×#484	C₂²	1	2	yes	complemented
63	C₃₁×#482	C₂²	1	2	yes	complemented
64	C₃₁×#479	C₂²	1	2	yes	complemented
65	C₃₁×#478	C₂²	1	2	yes	complemented
66	C₃₁×#476	C₂²	1	2	yes	complemented
67	C₃₁×#475	C₂²	1	2	yes	complemented
68	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#469	C₂²	1	2	yes	complemented
71	C₃₁×#468	C₂²	1	2	yes	complemented
72	C₃₁×#466	C₂²	1	2	yes	complemented
73	C₃₁×#465	C₂²	1	2	yes	complemented
74	C₃₁×#465	C₂²	1	2	yes	complemented
75	C₃₁×#465	C₂²	1	2	yes	complemented
76	C₃₁×#463	C₂²	1	2	yes	—
77	C₃₁×#463	C₂²	1	2	yes	—
78	C₃₁×#463	C₂²	1	2	yes	—
79	C₃₁×#463	C₂²	1	2	yes	complemented
80	C₃₁×#463	C₂²	1	2	yes	complemented
81	C₃₁×#463	C₂²	1	2	yes	complemented
82	C₃₁×#463	C₂²	1	2	yes	complemented
83	C₃₁×#463	C₂²	1	2	yes	complemented
84	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#461	C₂²	1	2	yes	complemented
87	C₃₁×#461	C₂²	1	2	yes	complemented
88	C₃₁×#461	C₂²	1	2	yes	complemented
89	C₃₁×#460	C₂²	1	2	yes	complemented
90	C₃₁×#460	C₂²	1	2	yes	complemented
91	C₃₁×#459	C₂²	1	2	yes	complemented
92	C₃₁×#450	C₂²	1	2	yes	—
93	C₃₁×#450	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×#448	C₂²	1	2	yes	complemented
98	C₃₁×#448	C₂²	1	2	yes	complemented
99	C₃₁×#447	C₂²	1	2	yes	—
100	C₃₁×#447	C₂²	1	2	yes	complemented
101	C₃₁×#446	C₂²	1	2	yes	complemented
102	C₃₁×#442	C₂²	1	2	yes	—
103	C₃₁×#440	C₂²	1	2	yes	complemented
104	C₃₁×#440	C₂²	1	2	yes	complemented
105	C₃₁×#440	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
107	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
108	C₃₁×#435	C₂²	1	2	yes	complemented
109	C₃₁×#435	C₂²	1	2	yes	complemented
110	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
111	C₃₁×#433	C₂²	1	2	yes	complemented
112	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#424	C₂²	1	2	yes	complemented
114	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
115	C₃₁×#419	C₂²	1	2	yes	complemented
116	C₃₁×#416	C₂²	1	2	yes	complemented
117	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₃₁	—	2	1	no	—
120	C₂×#41×C₃₁	—	2	1	no	—
121	C₂×#41×C₃₁	C₂³	1	2	yes	—
122	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
124	C₂²×D₄×C₃₁	—	2	2	no	—
125	C₂²×D₄×C₃₁	—	2	1	no	—
126	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
127	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₃₁	—	2	1	no	—
130	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
131	C₂×SD₁₆×C₃₁	—	4	2	no	—
132	C₂×SD₁₆×C₃₁	—	4	4	no	—
133	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
134	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
135	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
136	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
137	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
138	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂×D₈×C₃₁	—	4	2	no	—
142	C₂×D₈×C₃₁	C₂³	1	2	yes	—
143	C₂×D₈×C₃₁	C₂³	1	2	yes	—
144	C₂×D₈×C₃₁	C₂³	1	2	yes	—
145	C₂×D₈×C₃₁	C₂³	1	2	yes	—
146	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
150	C₃₁×C₄⋊Q₈	—	2	2	no	—
151	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
152	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
153	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃₁×#127	C₂³	1	2	yes	—
156	C₃₁×#127	C₂³	1	1	yes	characteristic
157	C₃₁×#126	—	2	2	no	—
158	C₃₁×#126	—	2	2	no	—
159	C₃₁×#126	—	2	2	no	—
160	C₃₁×#126	—	2	2	no	—
161	C₃₁×#126	D₄	1	2	yes	—
162	C₃₁×#125	—	2	1	no	—
163	C₃₁×#125	D₄	1	1	yes	characteristic
164	C₃₁×#125	C₂³	1	2	yes	—
165	C₃₁×#124	—	2	2	no	—
166	C₃₁×#124	—	2	2	no	—
167	C₃₁×#124	—	2	2	no	—
168	C₃₁×#124	—	2	1	no	—
169	C₃₁×#124	—	2	1	no	—
170	C₃₁×#124	—	2	1	no	—
171	C₃₁×#124	D₄	1	1	yes	characteristic
172	C₃₁×#124	C₂³	1	2	yes	—
173	C₃₁×#124	C₂³	1	2	yes	—
174	C₃₁×#124	C₂³	1	2	yes	—
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	D₄	1	2	yes	—
183	C₃₁×C₂²⋊Q₈	—	2	1	no	—
184	C₃₁×C₂²⋊Q₈	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	—	2	1	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
194	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×#121	—	2	2	no	—
197	C₃₁×#121	—	2	1	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	1	no	—
200	C₃₁×#121	—	2	1	no	—
201	C₃₁×#121	—	2	1	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	1	yes	characteristic
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	2	no	—
213	C₃₁×#120	—	2	2	no	—
214	C₃₁×#120	—	2	2	no	—
215	C₃₁×#120	—	2	2	no	—
216	C₄×Q₈×C₃₁	—	2	1	no	—
217	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
218	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
225	C₄×D₄×C₃₁	—	2	1	no	—
226	C₄×D₄×C₃₁	—	2	1	no	—
227	C₄×D₄×C₃₁	—	2	1	no	—
228	C₄×D₄×C₃₁	C₂³	1	2	yes	—
229	C₄×D₄×C₃₁	C₂³	1	2	yes	—
230	C₄×D₄×C₃₁	C₂³	1	2	yes	—
231	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₃₁	C₂³	1	2	yes	—
236	C₄×D₄×C₃₁	C₂³	1	2	yes	—
237	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₃₁×#117	—	2	1	no	—
239	C₃₁×#117	—	2	1	no	—
240	C₃₁×#117	—	2	2	no	—
241	C₃₁×#117	C₂³	1	2	yes	—
242	C₃₁×#117	C₂³	1	2	yes	—
243	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
244	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
246	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
247	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
248	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
249	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
250	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
251	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
252	C₃₁×#107	C₂³	1	2	yes	—
253	C₃₁×#107	C₂³	1	2	yes	—
254	C₃₁×#106	C₂³	1	2	yes	—
255	C₃₁×#106	C₂³	1	2	yes	—
256	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
258	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
260	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
261	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#103	C₂³	1	2	yes	—
264	C₃₁×#103	C₂³	1	2	yes	—
265	C₃₁×#103	C₂³	1	2	yes	—
266	C₃₁×#103	C₂³	1	2	yes	—
267	C₃₁×#103	C₂³	1	2	yes	—
268	C₃₁×#103	C₂³	1	2	yes	—
269	C₃₁×#103	C₂³	1	2	yes	—
270	C₃₁×#102	C₂³	1	2	yes	—
271	C₃₁×#102	C₂³	1	2	yes	—
272	C₃₁×#102	C₂³	1	2	yes	—
273	C₃₁×#102	C₂³	1	2	yes	—
274	C₃₁×#102	C₂³	1	2	yes	—
275	C₃₁×#102	C₂³	1	2	yes	—
276	C₃₁×#102	C₂³	1	2	yes	—
277	C₃₁×#102	C₂³	1	2	yes	—
278	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
279	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₃₁×#97	C₂³	1	2	yes	—
282	C₃₁×#97	C₂³	1	2	yes	—
283	C₄×C₈×C₃₁	C₂³	1	2	yes	—
284	C₂⁴×C₃₁	—	2	1	no	—
285	C₂⁴×C₃₁	—	2	1	no	—
286	C₂⁴×C₃₁	—	2	2	no	—
287	#41×C₃₁	—	4	2	no	—
288	#41×C₃₁	—	4	2	no	—
289	#41×C₃₁	—	8	2	no	—
290	#41×C₃₁	—	8	2	no	—
291	C₂×Q₈×C₃₁	—	2	1	no	—
292	C₂×Q₈×C₃₁	—	2	2	no	—
293	C₂×Q₈×C₃₁	—	2	1	no	—
294	C₂×Q₈×C₃₁	—	2	1	no	—
295	C₂×Q₈×C₃₁	—	4	1	no	—
296	C₂×Q₈×C₃₁	—	4	2	no	—
297	C₂×Q₈×C₃₁	—	4	1	no	—
298	C₂×Q₈×C₃₁	—	4	2	no	—
299	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
300	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
301	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
302	C₂×D₄×C₃₁	—	2	2	no	—
303	C₂×D₄×C₃₁	—	2	4	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	2	no	—
309	C₂×D₄×C₃₁	—	2	2	no	—
310	C₂×D₄×C₃₁	—	2	1	no	—
311	C₂×D₄×C₃₁	—	2	1	no	—
312	C₂×D₄×C₃₁	—	2	2	no	—
313	C₂×D₄×C₃₁	—	2	1	no	—
314	C₂×D₄×C₃₁	—	2	2	no	—
315	C₂×D₄×C₃₁	—	2	1	no	—
316	C₂×D₄×C₃₁	—	4	1	no	—
317	C₂×D₄×C₃₁	—	4	2	no	—
318	C₂×D₄×C₃₁	—	4	1	no	—
319	C₂×D₄×C₃₁	—	4	1	no	—
320	C₂×D₄×C₃₁	—	8	2	no	—
321	C₂×D₄×C₃₁	—	8	4	no	—
322	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
323	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
325	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
327	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₃₁	—	2	1	no	—
329	C₂²×C₄×C₃₁	—	2	1	no	—
330	C₂²×C₄×C₃₁	—	2	2	no	—
331	C₂²×C₄×C₃₁	—	2	1	no	—
332	C₂²×C₄×C₃₁	—	2	1	no	—
333	C₂²×C₄×C₃₁	—	2	1	no	—
334	C₂²×C₄×C₃₁	—	2	2	no	—
335	C₂²×C₄×C₃₁	—	2	2	no	—
336	C₂²×C₄×C₃₁	—	2	2	no	—
337	C₂²×C₄×C₃₁	—	2	2	no	—
338	C₂²×C₄×C₃₁	—	2	2	no	—
339	C₂²×C₄×C₃₁	—	2	1	no	—
340	C₂²×C₄×C₃₁	—	8	2	no	—
341	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
345	SD₁₆×C₃₁	—	2	4	no	—
346	SD₁₆×C₃₁	—	2	4	no	—
347	SD₁₆×C₃₁	—	4	2	no	—
348	SD₁₆×C₃₁	—	4	2	no	—
349	SD₁₆×C₃₁	—	4	2	no	—
350	SD₁₆×C₃₁	—	4	2	no	—
351	SD₁₆×C₃₁	—	4	2	no	—
352	SD₁₆×C₃₁	—	4	2	no	—
353	D₈×C₃₁	—	2	4	no	—
354	D₈×C₃₁	—	4	2	no	—
355	D₈×C₃₁	—	4	2	no	—
356	D₈×C₃₁	—	4	2	no	—
357	M₁₆×C₃₁	—	4	2	no	—
358	C₂×C₈×C₃₁	—	4	1	no	—
359	C₂×C₈×C₃₁	—	4	1	no	—
360	C₂×C₈×C₃₁	—	4	2	no	—
361	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
362	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
363	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
364	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₃₁	—	2	1	no	—
366	C₄⋊C₄×C₃₁	—	2	2	no	—
367	C₄⋊C₄×C₃₁	—	2	1	no	—
368	C₄⋊C₄×C₃₁	—	2	2	no	—
369	C₄⋊C₄×C₃₁	—	2	1	no	—
370	C₄⋊C₄×C₃₁	—	2	1	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	—	2	2	no	—
374	C₄⋊C₄×C₃₁	—	2	2	no	—
375	C₄⋊C₄×C₃₁	—	2	1	no	—
376	C₄⋊C₄×C₃₁	—	2	2	no	—
377	C₄⋊C₄×C₃₁	—	2	2	no	—
378	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
381	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
382	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
383	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
384	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
385	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
386	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
387	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	1	no	—
392	C₂²⋊C₄×C₃₁	—	2	2	no	—
393	C₂²⋊C₄×C₃₁	—	2	2	no	—
394	C₂²⋊C₄×C₃₁	—	2	1	no	—
395	C₂²⋊C₄×C₃₁	—	2	2	no	—
396	C₂²⋊C₄×C₃₁	—	2	1	no	—
397	C₂²⋊C₄×C₃₁	—	2	2	no	—
398	C₂²⋊C₄×C₃₁	—	2	1	no	—
399	C₂²⋊C₄×C₃₁	—	2	2	no	—
400	C₂²⋊C₄×C₃₁	—	2	2	no	—
401	C₂²⋊C₄×C₃₁	—	2	2	no	—
402	C₂²⋊C₄×C₃₁	—	2	2	no	—
403	C₂²⋊C₄×C₃₁	—	2	2	no	—
404	C₂²⋊C₄×C₃₁	—	2	2	no	—
405	C₂²⋊C₄×C₃₁	—	2	2	no	—
406	C₂²⋊C₄×C₃₁	—	2	2	no	—
407	C₂²⋊C₄×C₃₁	—	2	2	no	—
408	C₂²⋊C₄×C₃₁	—	2	2	no	—
409	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
410	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
411	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
412	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
413	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
414	C₄²×C₃₁	—	2	2	no	—
415	C₄²×C₃₁	—	2	2	no	—
416	C₄²×C₃₁	—	2	2	no	—
417	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
418	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
419	C₄²×C₃₁	C₂⁴	1	2	yes	—
420	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
421	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
422	#62016	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
423	C₂³×C₃₁	—	2	1	no	—
424	C₂³×C₃₁	—	2	2	no	—
425	C₂³×C₃₁	—	2	1	no	—
426	C₂³×C₃₁	—	2	2	no	—
427	C₂³×C₃₁	—	4	2	no	—
428	C₂³×C₃₁	—	4	4	no	—
429	C₂³×C₃₁	—	4	2	no	—
430	C₂³×C₃₁	—	4	2	no	—
431	C₂³×C₃₁	—	8	1	no	—
432	C₂³×C₃₁	—	8	1	no	—
433	C₂³×C₃₁	—	8	2	no	—
434	C₂³×C₃₁	—	8	2	no	—
435	C₂³×C₃₁	—	8	1	no	—
436	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
437	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
438	Q₈×C₃₁	—	2	2	no	—
439	Q₈×C₃₁	—	2	2	no	—
440	Q₈×C₃₁	—	2	2	no	—
441	Q₈×C₃₁	—	2	2	no	—
442	Q₈×C₃₁	—	4	1	no	—
443	Q₈×C₃₁	—	8	1	no	—
444	Q₈×C₃₁	—	8	2	no	—
445	Q₈×C₃₁	—	8	1	no	—
446	Q₈×C₃₁	—	8	1	no	—
447	D₄×C₃₁	—	2	4	no	—
448	D₄×C₃₁	—	2	2	no	—
449	D₄×C₃₁	—	2	1	no	—
450	D₄×C₃₁	—	2	2	no	—
451	D₄×C₃₁	—	2	1	no	—
452	D₄×C₃₁	—	2	2	no	—
453	D₄×C₃₁	—	2	2	no	—
454	D₄×C₃₁	—	2	1	no	—
455	D₄×C₃₁	—	4	1	no	—
456	D₄×C₃₁	—	4	4	no	—
457	D₄×C₃₁	—	4	2	no	—
458	D₄×C₃₁	—	4	2	no	—
459	D₄×C₃₁	—	4	4	no	—
460	D₄×C₃₁	—	8	1	no	—
461	D₄×C₃₁	—	8	2	no	—
462	D₄×C₃₁	—	8	2	no	—
463	D₄×C₃₁	—	8	1	no	—
464	D₄×C₃₁	—	8	2	no	—
465	D₄×C₃₁	—	8	2	no	—
466	D₄×C₃₁	—	8	2	no	—
467	D₄×C₃₁	—	8	2	no	—
468	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
469	C₂×C₄×C₃₁	—	2	2	no	—
470	C₂×C₄×C₃₁	—	2	1	no	—
471	C₂×C₄×C₃₁	—	2	2	no	—
472	C₂×C₄×C₃₁	—	2	1	no	—
473	C₂×C₄×C₃₁	—	2	2	no	—
474	C₂×C₄×C₃₁	—	2	1	no	—
475	C₂×C₄×C₃₁	—	2	2	no	—
476	C₂×C₄×C₃₁	—	2	2	no	—
477	C₂×C₄×C₃₁	—	2	2	no	—
478	C₂×C₄×C₃₁	—	2	2	no	—
479	C₂×C₄×C₃₁	—	2	1	no	—
480	C₂×C₄×C₃₁	—	4	1	no	—
481	C₂×C₄×C₃₁	—	4	2	no	—
482	C₂×C₄×C₃₁	—	4	2	no	—
483	C₂×C₄×C₃₁	—	8	2	no	—
484	C₂×C₄×C₃₁	—	8	1	no	—
485	C₂×C₄×C₃₁	—	8	1	no	—
486	C₂×C₄×C₃₁	—	8	2	no	—
487	C₂×C₄×C₃₁	—	8	2	no	—
488	C₂×C₄×C₃₁	—	8	2	no	—
489	C₂×C₄×C₃₁	—	8	2	no	—
490	C₂×C₄×C₃₁	—	8	1	no	—
491	C₂×C₄×C₃₁	—	8	2	no	—
492	C₂×C₄×C₃₁	—	8	1	no	—
493	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
502	C₈×C₃₁	—	2	2	no	—
503	C₈×C₃₁	—	2	2	no	—
504	C₈×C₃₁	—	2	2	no	—
505	C₈×C₃₁	—	2	2	no	—
506	#3561	C₂×C₃₁	1	1	yes	characteristic, complemented
507	#3519	C₂×C₃₁	1	1	yes	characteristic, complemented
508	#3397	C₂×C₃₁	1	2	yes	complemented
509	#3376	C₂×C₃₁	1	2	yes	complemented
510	#3321	C₂×C₃₁	1	2	yes	complemented
511	#3320	C₂×C₃₁	1	2	yes	complemented
512	#3297	C₂×C₃₁	1	2	yes	complemented
513	D₄×SD₁₆	C₂×C₃₁	1	2	yes	complemented
514	#3265	C₂×C₃₁	1	2	yes	complemented
515	#3264	C₂×C₃₁	1	2	yes	complemented
516	#3257	C₂×C₃₁	1	2	yes	complemented
517	#3246	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#3221	C₂×C₃₁	1	2	yes	complemented
519	#3213	C₂×C₃₁	1	1	yes	characteristic, complemented
520	#3118	C₂×C₃₁	1	2	yes	complemented
521	#3110	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3042	C₂×C₃₁	1	2	yes	complemented
523	C₂×#463	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#2992	C₂×C₃₁	1	1	yes	characteristic, complemented
525	C₂²×C₃₁	—	2	1	no	—
526	C₂²×C₃₁	—	2	1	no	—
527	C₂²×C₃₁	—	2	2	no	—
528	C₂²×C₃₁	—	2	2	no	—
529	C₂²×C₃₁	—	2	2	no	—
530	C₂²×C₃₁	—	2	2	no	—
531	C₂²×C₃₁	—	4	1	no	—
532	C₂²×C₃₁	—	4	1	no	—
533	C₂²×C₃₁	—	4	1	no	—
534	C₂²×C₃₁	—	4	2	no	—
535	C₂²×C₃₁	—	4	2	no	—
536	C₂²×C₃₁	—	4	2	no	—
537	C₂²×C₃₁	—	4	1	no	—
538	C₂²×C₃₁	—	4	2	no	—
539	C₂²×C₃₁	—	4	2	no	—
540	C₂²×C₃₁	—	4	1	no	—
541	C₂²×C₃₁	—	4	2	no	—
542	C₂²×C₃₁	—	8	4	no	—
543	C₂²×C₃₁	—	16	2	no	—
544	C₂²×C₃₁	—	16	4	no	—
545	C₂²×C₃₁	#577	1	2	yes	—
546	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
547	C₄×C₃₁	—	2	1	no	—
548	C₄×C₃₁	—	2	1	no	—
549	C₄×C₃₁	—	2	2	no	—
550	C₄×C₃₁	—	2	2	no	—
551	C₄×C₃₁	—	2	1	no	—
552	C₄×C₃₁	—	2	1	no	—
553	C₄×C₃₁	—	2	1	no	—
554	C₄×C₃₁	—	2	2	no	—
555	C₄×C₃₁	—	4	1	no	—
556	C₄×C₃₁	—	4	1	no	—
557	C₄×C₃₁	—	4	2	no	—
558	C₄×C₃₁	—	4	2	no	—
559	C₄×C₃₁	—	4	2	no	—
560	C₄×C₃₁	—	4	2	no	—
561	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
562	C₄×C₃₁	#585	1	1	yes	characteristic
563	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
564	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
565	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
566	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
567	#563	—	2	1	no	—
568	#562	—	2	1	no	—
569	#556	C₂²×C₃₁	1	2	yes	complemented
570	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
571	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
572	#553	—	2	1	no	—
573	#553	C₂²×C₃₁	1	2	yes	—
574	#551	—	2	2	no	—
575	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
576	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
577	#548	C₂²×C₃₁	1	2	yes	complemented
578	#546	—	2	1	no	—
579	#546	—	2	2	no	—
580	#546	C₂²×C₃₁	1	2	yes	complemented
581	D₄²	C₂²×C₃₁	1	2	yes	—
582	D₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
583	#543	—	2	1	no	—
584	#542	—	2	2	no	—
585	#542	C₂²×C₃₁	1	2	yes	complemented
586	#540	C₂²×C₃₁	1	2	yes	complemented
587	#538	—	2	2	no	—
588	#538	—	2	1	no	—
589	#536	C₂²×C₃₁	1	2	yes	complemented
590	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
591	#532	C₂²×C₃₁	1	1	yes	characteristic
592	#529	C₂²×C₃₁	1	1	yes	characteristic
593	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
594	#525	—	2	1	no	—
595	C₂×#121	—	2	1	no	—
596	#518	C₂²×C₃₁	1	2	yes	complemented
597	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
598	#496	C₂²×C₃₁	1	2	yes	complemented
599	#496	C₂²×C₃₁	1	2	yes	complemented
600	#492	C₂²×C₃₁	1	2	yes	complemented
601	#491	C₂²×C₃₁	1	2	yes	complemented
602	#489	C₂²×C₃₁	1	2	yes	complemented
603	#488	C₂²×C₃₁	1	2	yes	complemented
604	#485	C₂²×C₃₁	1	2	yes	complemented
605	#484	C₂²×C₃₁	1	2	yes	complemented
606	#482	C₂²×C₃₁	1	2	yes	complemented
607	#479	C₂²×C₃₁	1	2	yes	complemented
608	#478	C₂²×C₃₁	1	2	yes	complemented
609	#476	C₂²×C₃₁	1	2	yes	complemented
610	#475	C₂²×C₃₁	1	2	yes	complemented
611	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
612	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
613	#469	C₂²×C₃₁	1	2	yes	complemented
614	#468	C₂²×C₃₁	1	2	yes	complemented
615	#466	C₂²×C₃₁	1	2	yes	complemented
616	#465	C₂²×C₃₁	1	2	yes	complemented
617	#465	C₂²×C₃₁	1	2	yes	complemented
618	#465	C₂²×C₃₁	1	2	yes	complemented
619	#463	C₂²×C₃₁	1	2	yes	—
620	#463	C₂²×C₃₁	1	2	yes	—
621	#463	C₂²×C₃₁	1	2	yes	—
622	#463	C₂²×C₃₁	1	2	yes	complemented
623	#463	C₂²×C₃₁	1	2	yes	complemented
624	#463	C₂²×C₃₁	1	2	yes	complemented
625	#463	C₂²×C₃₁	1	2	yes	complemented
626	#463	C₂²×C₃₁	1	2	yes	complemented
627	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
628	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
629	#461	C₂²×C₃₁	1	2	yes	complemented
630	#461	C₂²×C₃₁	1	2	yes	complemented
631	#461	C₂²×C₃₁	1	2	yes	complemented
632	#460	C₂²×C₃₁	1	2	yes	complemented
633	#460	C₂²×C₃₁	1	2	yes	complemented
634	#459	C₂²×C₃₁	1	2	yes	complemented
635	#450	C₂²×C₃₁	1	2	yes	—
636	#450	C₂²×C₃₁	1	2	yes	complemented
637	#449	C₂²×C₃₁	1	2	yes	complemented
638	#449	C₂²×C₃₁	1	2	yes	complemented
639	#448	C₂²×C₃₁	1	2	yes	complemented
640	#448	C₂²×C₃₁	1	2	yes	complemented
641	#448	C₂²×C₃₁	1	2	yes	complemented
642	#447	C₂²×C₃₁	1	2	yes	—
643	#447	C₂²×C₃₁	1	2	yes	complemented
644	#446	C₂²×C₃₁	1	2	yes	complemented
645	#442	C₂²×C₃₁	1	2	yes	—
646	#440	C₂²×C₃₁	1	2	yes	complemented
647	#440	C₂²×C₃₁	1	2	yes	complemented
648	#440	C₂²×C₃₁	1	2	yes	complemented
649	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
650	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
651	#435	C₂²×C₃₁	1	2	yes	complemented
652	#435	C₂²×C₃₁	1	2	yes	complemented
653	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
654	#433	C₂²×C₃₁	1	2	yes	complemented
655	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	#424	C₂²×C₃₁	1	2	yes	complemented
657	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
658	#419	C₂²×C₃₁	1	2	yes	complemented
659	#416	C₂²×C₃₁	1	2	yes	complemented
660	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	C₂×C₃₁	—	2	2	no	—
663	C₂×C₃₁	—	4	2	no	—
664	C₂×C₃₁	—	4	2	no	—
665	C₂×C₃₁	—	8	1	no	—
666	C₂×C₃₁	—	8	2	no	—
667	C₂×C₃₁	—	8	2	no	—
668	C₂×C₃₁	#3488	1	1	yes	characteristic
669	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
670	C₂×C₃₁	#3585	1	1	yes	characteristic
671	C₂×#41	—	2	1	no	—
672	C₂×#41	—	2	1	no	—
673	C₂×#41	C₂³×C₃₁	1	2	yes	—
674	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
675	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
676	C₂²×D₄	—	2	2	no	—
677	C₂²×D₄	—	2	1	no	—
678	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
679	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
680	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
681	C₂³×C₄	—	2	1	no	—
682	AGL(1,ℤ/8)	—	4	4	no	—
683	C₂×SD₁₆	—	4	2	no	—
684	C₂×SD₁₆	—	4	4	no	—
685	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
686	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
687	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
688	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
689	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
690	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
691	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
692	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
693	C₂×D₈	—	4	2	no	—
694	C₂×D₈	C₂³×C₃₁	1	2	yes	—
695	C₂×D₈	C₂³×C₃₁	1	2	yes	—
696	C₂×D₈	C₂³×C₃₁	1	2	yes	—
697	C₂×D₈	C₂³×C₃₁	1	2	yes	—
698	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
699	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
700	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
701	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
702	C₄⋊Q₈	—	2	2	no	—
703	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
705	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
706	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
707	#127	C₂³×C₃₁	1	1	yes	characteristic
708	#127	C₂³×C₃₁	1	2	yes	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#126	D₄×C₃₁	1	2	yes	—
714	#125	—	2	1	no	—
715	#125	D₄×C₃₁	1	1	yes	characteristic
716	#125	C₂³×C₃₁	1	2	yes	—
717	#124	—	2	2	no	—
718	#124	—	2	2	no	—
719	#124	—	2	2	no	—
720	#124	—	2	1	no	—
721	#124	—	2	1	no	—
722	#124	—	2	1	no	—
723	#124	D₄×C₃₁	1	1	yes	characteristic
724	#124	C₂³×C₃₁	1	2	yes	—
725	#124	C₂³×C₃₁	1	2	yes	—
726	#124	C₂³×C₃₁	1	2	yes	—
727	#123	—	2	2	no	—
728	#123	—	2	2	no	—
729	#123	—	2	2	no	—
730	#123	—	2	2	no	—
731	#123	—	2	2	no	—
732	#123	—	2	2	no	—
733	#123	—	2	2	no	—
734	#123	D₄×C₃₁	1	2	yes	—
735	C₂²⋊Q₈	—	2	1	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	1	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
746	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
747	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
748	#121	—	2	2	no	—
749	#121	—	2	1	no	—
750	#121	—	2	2	no	—
751	#121	—	2	1	no	—
752	#121	—	2	1	no	—
753	#121	—	2	1	no	—
754	#121	—	2	2	no	—
755	#121	—	2	2	no	—
756	#121	—	2	2	no	—
757	#121	—	2	2	no	—
758	#121	—	2	2	no	—
759	#121	D₄×C₃₁	1	1	yes	characteristic
760	#121	C₂³×C₃₁	1	2	yes	—
761	#121	C₂³×C₃₁	1	2	yes	—
762	#121	C₂³×C₃₁	1	2	yes	—
763	#121	C₂³×C₃₁	1	2	yes	—
764	#120	—	2	2	no	—
765	#120	—	2	2	no	—
766	#120	—	2	2	no	—
767	#120	—	2	2	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
770	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
771	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
772	C₄×D₄	—	2	2	no	—
773	C₄×D₄	—	2	2	no	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	—	2	1	no	—
778	C₄×D₄	—	2	1	no	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
781	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
782	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
783	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
784	C₄×D₄	C₂³×C₃₁	1	2	yes	—
785	C₄×D₄	C₂³×C₃₁	1	2	yes	—
786	C₄×D₄	C₂³×C₃₁	1	2	yes	—
787	C₄×D₄	C₂³×C₃₁	1	2	yes	—
788	C₄×D₄	C₂³×C₃₁	1	2	yes	—
789	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
790	#117	—	2	1	no	—
791	#117	—	2	1	no	—
792	#117	—	2	2	no	—
793	#117	C₂³×C₃₁	1	2	yes	—
794	#117	C₂³×C₃₁	1	2	yes	—
795	C₂×C₄⋊C₄	—	2	1	no	—
796	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
797	C₂×C₂²⋊C₄	—	2	1	no	—
798	C₂×C₂²⋊C₄	—	2	1	no	—
799	C₂×C₂²⋊C₄	—	2	1	no	—
800	C₂×C₂²⋊C₄	—	2	2	no	—
801	C₂×C₂²⋊C₄	—	2	2	no	—
802	C₂×C₂²⋊C₄	—	2	2	no	—
803	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
804	#107	C₂³×C₃₁	1	2	yes	—
805	#107	C₂³×C₃₁	1	2	yes	—
806	#106	C₂³×C₃₁	1	2	yes	—
807	#106	C₂³×C₃₁	1	2	yes	—
808	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
809	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
810	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
811	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
812	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
813	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
814	#103	C₂³×C₃₁	1	2	yes	—
815	#103	C₂³×C₃₁	1	2	yes	—
816	#103	C₂³×C₃₁	1	2	yes	—
817	#103	C₂³×C₃₁	1	2	yes	—
818	#103	C₂³×C₃₁	1	2	yes	—
819	#103	C₂³×C₃₁	1	2	yes	—
820	#103	C₂³×C₃₁	1	2	yes	—
821	#103	C₂³×C₃₁	1	2	yes	—
822	#102	C₂³×C₃₁	1	2	yes	—
823	#102	C₂³×C₃₁	1	2	yes	—
824	#102	C₂³×C₃₁	1	2	yes	—
825	#102	C₂³×C₃₁	1	2	yes	—
826	#102	C₂³×C₃₁	1	2	yes	—
827	#102	C₂³×C₃₁	1	2	yes	—
828	#102	C₂³×C₃₁	1	2	yes	—
829	#102	C₂³×C₃₁	1	2	yes	—
830	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
831	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
832	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
833	#97	C₂³×C₃₁	1	2	yes	—
834	#97	C₂³×C₃₁	1	2	yes	—
835	C₄×C₈	C₂³×C₃₁	1	2	yes	—
836	C₃₁	#62016	1	1	yes	characteristic, direct product factor, Sylow
837	C₂⁴	—	2	1	no	—
838	C₂⁴	—	2	1	no	—
839	C₂⁴	—	2	2	no	—
840	#41	—	4	2	no	—
841	#41	—	4	2	no	—
842	#41	—	8	2	no	—
843	#41	—	8	2	no	—
844	C₂×Q₈	—	2	1	no	—
845	C₂×Q₈	—	2	2	no	—
846	C₂×Q₈	—	2	1	no	—
847	C₂×Q₈	—	2	1	no	—
848	C₂×Q₈	—	4	1	no	—
849	C₂×Q₈	—	4	2	no	—
850	C₂×Q₈	—	4	1	no	—
851	C₂×Q₈	—	4	2	no	—
852	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
853	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
854	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
855	C₂×D₄	—	2	2	no	—
856	C₂×D₄	—	2	4	no	—
857	C₂×D₄	—	2	2	no	—
858	C₂×D₄	—	2	2	no	—
859	C₂×D₄	—	2	2	no	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	2	2	no	—
862	C₂×D₄	—	2	2	no	—
863	C₂×D₄	—	2	1	no	—
864	C₂×D₄	—	2	1	no	—
865	C₂×D₄	—	2	2	no	—
866	C₂×D₄	—	2	1	no	—
867	C₂×D₄	—	2	2	no	—
868	C₂×D₄	—	2	1	no	—
869	C₂×D₄	—	4	1	no	—
870	C₂×D₄	—	4	2	no	—
871	C₂×D₄	—	4	1	no	—
872	C₂×D₄	—	4	1	no	—
873	C₂×D₄	—	8	2	no	—
874	C₂×D₄	—	8	4	no	—
875	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
876	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
877	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
878	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
879	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
880	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	1	no	—
886	C₂²×C₄	—	2	1	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	8	2	no	—
894	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
895	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
896	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
898	SD₁₆	—	2	4	no	—
899	SD₁₆	—	2	4	no	—
900	SD₁₆	—	4	2	no	—
901	SD₁₆	—	4	2	no	—
902	SD₁₆	—	4	2	no	—
903	SD₁₆	—	4	2	no	—
904	SD₁₆	—	4	2	no	—
905	SD₁₆	—	4	2	no	—
906	D₈	—	2	4	no	—
907	D₈	—	4	2	no	—
908	D₈	—	4	2	no	—
909	D₈	—	4	2	no	—
910	M₁₆	—	4	2	no	—
911	C₂×C₈	—	4	1	no	—
912	C₂×C₈	—	4	1	no	—
913	C₂×C₈	—	4	2	no	—
914	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
915	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
916	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
917	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
932	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
933	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
934	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
935	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
936	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
937	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
938	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
939	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
940	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	1	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	1	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	1	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
963	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
964	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
965	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
966	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
967	C₄²	—	2	2	no	—
968	C₄²	—	2	2	no	—
969	C₄²	—	2	2	no	—
970	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
971	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
972	C₄²	C₂⁴×C₃₁	1	2	yes	—
973	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
974	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
975	C₂³	—	2	1	no	—
976	C₂³	—	2	2	no	—
977	C₂³	—	2	2	no	—
978	C₂³	—	2	1	no	—
979	C₂³	—	4	2	no	—
980	C₂³	—	4	4	no	—
981	C₂³	—	4	2	no	—
982	C₂³	—	4	2	no	—
983	C₂³	—	8	1	no	—
984	C₂³	—	8	1	no	—
985	C₂³	—	8	2	no	—
986	C₂³	—	8	2	no	—
987	C₂³	—	8	1	no	—
988	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
989	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
990	Q₈	—	2	2	no	—
991	Q₈	—	2	2	no	—
992	Q₈	—	2	2	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	4	1	no	—
995	Q₈	—	8	1	no	—
996	Q₈	—	8	2	no	—
997	Q₈	—	8	1	no	—
998	Q₈	—	8	1	no	—
999	D₄	—	2	4	no	—
1000	D₄	—	2	2	no	—
1001	D₄	—	2	1	no	—
1002	D₄	—	2	2	no	—
1003	D₄	—	2	1	no	—
1004	D₄	—	2	2	no	—
1005	D₄	—	2	2	no	—
1006	D₄	—	2	1	no	—
1007	D₄	—	4	1	no	—
1008	D₄	—	4	4	no	—
1009	D₄	—	4	2	no	—
1010	D₄	—	4	2	no	—
1011	D₄	—	4	4	no	—
1012	D₄	—	8	1	no	—
1013	D₄	—	8	2	no	—
1014	D₄	—	8	1	no	—
1015	D₄	—	8	2	no	—
1016	D₄	—	8	2	no	—
1017	D₄	—	8	2	no	—
1018	D₄	—	8	2	no	—
1019	D₄	—	8	2	no	—
1020	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	4	1	no	—
1033	C₂×C₄	—	4	2	no	—
1034	C₂×C₄	—	4	2	no	—
1035	C₂×C₄	—	8	2	no	—
1036	C₂×C₄	—	8	1	no	—
1037	C₂×C₄	—	8	1	no	—
1038	C₂×C₄	—	8	2	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	—	8	2	no	—
1042	C₂×C₄	—	8	1	no	—
1043	C₂×C₄	—	8	2	no	—
1044	C₂×C₄	—	8	1	no	—
1045	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1046	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1047	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1048	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1050	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1051	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1052	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1053	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1054	C₈	—	2	2	no	—
1055	C₈	—	2	2	no	—
1056	C₈	—	2	2	no	—
1057	C₈	—	2	2	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	2	2	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	8	4	no	—
1076	C₂²	—	16	2	no	—
1077	C₂²	—	16	4	no	—
1078	C₂²	C₃₁×#577	1	2	yes	—
1079	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1080	C₄	—	2	2	no	—
1081	C₄	—	2	1	no	—
1082	C₄	—	2	1	no	—
1083	C₄	—	2	1	no	—
1084	C₄	—	2	2	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	1	no	—
1087	C₄	—	2	2	no	—
1088	C₄	—	4	2	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	2	no	—
1091	C₄	—	4	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	2	no	—
1094	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1095	C₄	C₃₁×#585	1	1	yes	characteristic
1096	C₂	—	2	2	no	—
1097	C₂	—	4	2	no	—
1098	C₂	—	4	2	no	—
1099	C₂	—	8	1	no	—
1100	C₂	—	8	2	no	—
1101	C₂	—	8	2	no	—
1102	C₂	C₃₁×#3488	1	1	yes	characteristic
1103	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1104	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3561	C₂	semidirect
2. C₃₁×#3519	C₂	semidirect
3. C₃₁×#3397	C₂	semidirect
4. C₃₁×#3376	C₂	semidirect
5. C₃₁×#3321	C₂	semidirect
6. C₃₁×#3320	C₂	semidirect
7. C₃₁×#3297	C₂	semidirect
8. D₄×SD₁₆×C₃₁	C₂	semidirect
9. C₃₁×#3265	C₂	semidirect
10. C₃₁×#3264	C₂	semidirect
11. C₃₁×#3257	C₂	semidirect
12. C₃₁×#3246	C₂	semidirect
13. C₃₁×#3221	C₂	semidirect
14. C₃₁×#3213	C₂	semidirect
15. C₃₁×#3118	C₂	semidirect
16. C₃₁×#3110	C₂	semidirect
17. C₃₁×#3042	C₂	semidirect
18. C₂×C₃₁×#463	C₂	semidirect
19. C₃₁×#2992	C₂	semidirect
22. C₂²×SD₁₆×C₃₁	C₂²	semidirect
26. C₃₁×#556	C₂²	semidirect
27. C₃₁×#555	C₂²	semidirect
28. C₃₁×#554	C₂²	semidirect
32. C₃₁×#550	C₂²	semidirect
33. D₄×Q₈×C₃₁	C₂²	semidirect
34. C₃₁×#548	C₂²	semidirect
37. C₃₁×#546	C₂²	semidirect
39. D₄²×C₃₁	C₂²	semidirect
42. C₃₁×#542	C₂²	semidirect
43. C₃₁×#540	C₂²	semidirect
46. C₃₁×#536	C₂²	semidirect
47. C₃₁×#533	C₂²	semidirect
50. C₂×C₃₁×#124	C₂²	semidirect
53. C₃₁×#518	C₂²	semidirect
55. C₃₁×#496	C₂²	semidirect
56. C₃₁×#496	C₂²	semidirect
57. C₃₁×#492	C₂²	semidirect
58. C₃₁×#491	C₂²	semidirect
59. C₃₁×#489	C₂²	semidirect
60. C₃₁×#488	C₂²	semidirect
61. C₃₁×#485	C₂²	semidirect
62. C₃₁×#484	C₂²	semidirect
63. C₃₁×#482	C₂²	semidirect
64. C₃₁×#479	C₂²	semidirect
65. C₃₁×#478	C₂²	semidirect
66. C₃₁×#476	C₂²	semidirect
67. C₃₁×#475	C₂²	semidirect
68. C₃₁×#474	C₂²	semidirect
69. C₃₁×#474	C₂²	semidirect
70. C₃₁×#469	C₂²	semidirect
71. C₃₁×#468	C₂²	semidirect
72. C₃₁×#466	C₂²	semidirect
73. C₃₁×#465	C₂²	semidirect
74. C₃₁×#465	C₂²	semidirect
75. C₃₁×#465	C₂²	semidirect
79. C₃₁×#463	C₂²	semidirect
80. C₃₁×#463	C₂²	semidirect
81. C₃₁×#463	C₂²	semidirect
82. C₃₁×#463	C₂²	semidirect
83. C₃₁×#463	C₂²	semidirect
84. C₃₁×#461	C₂²	semidirect
85. C₃₁×#461	C₂²	semidirect
86. C₃₁×#461	C₂²	semidirect
87. C₃₁×#461	C₂²	semidirect
88. C₃₁×#461	C₂²	semidirect
89. C₃₁×#460	C₂²	semidirect
90. C₃₁×#460	C₂²	semidirect
91. C₃₁×#459	C₂²	semidirect
93. C₃₁×#450	C₂²	semidirect
94. C₃₁×#449	C₂²	semidirect
95. C₃₁×#449	C₂²	semidirect
96. C₃₁×#448	C₂²	semidirect
97. C₃₁×#448	C₂²	semidirect
98. C₃₁×#448	C₂²	semidirect
100. C₃₁×#447	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
103. C₃₁×#440	C₂²	semidirect
104. C₃₁×#440	C₂²	semidirect
105. C₃₁×#440	C₂²	semidirect
106. C₄×SD₁₆×C₃₁	C₂²	semidirect
107. C₄×D₈×C₃₁	C₂²	semidirect
108. C₃₁×#435	C₂²	semidirect
109. C₃₁×#435	C₂²	semidirect
110. C₈×D₄×C₃₁	C₂²	semidirect
111. C₃₁×#433	C₂²	semidirect
112. C₃₁×#432	C₂²	semidirect
113. C₃₁×#424	C₂²	semidirect
114. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
115. C₃₁×#419	C₂²	semidirect
116. C₃₁×#416	C₂²	semidirect
117. C₂×C₃₁×#103	C₂²	semidirect
118. C₂×C₃₁×#102	C₂²	semidirect
422. #62016	C₃₁	direct (N × H)
506. #3561	C₂×C₃₁	semidirect
507. #3519	C₂×C₃₁	semidirect
508. #3397	C₂×C₃₁	semidirect
509. #3376	C₂×C₃₁	semidirect
510. #3321	C₂×C₃₁	semidirect
511. #3320	C₂×C₃₁	semidirect
512. #3297	C₂×C₃₁	semidirect
513. D₄×SD₁₆	C₂×C₃₁	semidirect
514. #3265	C₂×C₃₁	semidirect
515. #3264	C₂×C₃₁	semidirect
516. #3257	C₂×C₃₁	semidirect
517. #3246	C₂×C₃₁	semidirect
518. #3221	C₂×C₃₁	semidirect
519. #3213	C₂×C₃₁	semidirect
520. #3118	C₂×C₃₁	semidirect
521. #3110	C₂×C₃₁	semidirect
522. #3042	C₂×C₃₁	semidirect
523. C₂×#463	C₂×C₃₁	semidirect
524. #2992	C₂×C₃₁	semidirect
565. C₂²×SD₁₆	C₂²×C₃₁	semidirect
569. #556	C₂²×C₃₁	semidirect
570. #555	C₂²×C₃₁	semidirect
571. #554	C₂²×C₃₁	semidirect
575. #550	C₂²×C₃₁	semidirect
576. D₄×Q₈	C₂²×C₃₁	semidirect
577. #548	C₂²×C₃₁	semidirect
580. #546	C₂²×C₃₁	semidirect
582. D₄²	C₂²×C₃₁	semidirect
585. #542	C₂²×C₃₁	semidirect
586. #540	C₂²×C₃₁	semidirect
589. #536	C₂²×C₃₁	semidirect
590. #533	C₂²×C₃₁	semidirect
593. C₂×#124	C₂²×C₃₁	semidirect
596. #518	C₂²×C₃₁	semidirect
598. #496	C₂²×C₃₁	semidirect
599. #496	C₂²×C₃₁	semidirect
600. #492	C₂²×C₃₁	semidirect
601. #491	C₂²×C₃₁	semidirect
602. #489	C₂²×C₃₁	semidirect
603. #488	C₂²×C₃₁	semidirect
604. #485	C₂²×C₃₁	semidirect
605. #484	C₂²×C₃₁	semidirect
606. #482	C₂²×C₃₁	semidirect
607. #479	C₂²×C₃₁	semidirect
608. #478	C₂²×C₃₁	semidirect
609. #476	C₂²×C₃₁	semidirect
610. #475	C₂²×C₃₁	semidirect
611. #474	C₂²×C₃₁	semidirect
612. #474	C₂²×C₃₁	semidirect
613. #469	C₂²×C₃₁	semidirect
614. #468	C₂²×C₃₁	semidirect
615. #466	C₂²×C₃₁	semidirect
616. #465	C₂²×C₃₁	semidirect
617. #465	C₂²×C₃₁	semidirect
618. #465	C₂²×C₃₁	semidirect
622. #463	C₂²×C₃₁	semidirect
623. #463	C₂²×C₃₁	semidirect
624. #463	C₂²×C₃₁	semidirect
625. #463	C₂²×C₃₁	semidirect
626. #463	C₂²×C₃₁	semidirect
627. #461	C₂²×C₃₁	semidirect
628. #461	C₂²×C₃₁	semidirect
629. #461	C₂²×C₃₁	semidirect
630. #461	C₂²×C₃₁	semidirect
631. #461	C₂²×C₃₁	semidirect
632. #460	C₂²×C₃₁	semidirect
633. #460	C₂²×C₃₁	semidirect
634. #459	C₂²×C₃₁	semidirect
636. #450	C₂²×C₃₁	semidirect
637. #449	C₂²×C₃₁	semidirect
638. #449	C₂²×C₃₁	semidirect
639. #448	C₂²×C₃₁	semidirect
640. #448	C₂²×C₃₁	semidirect
641. #448	C₂²×C₃₁	semidirect
643. #447	C₂²×C₃₁	semidirect
644. #446	C₂²×C₃₁	semidirect
646. #440	C₂²×C₃₁	semidirect
647. #440	C₂²×C₃₁	semidirect
648. #440	C₂²×C₃₁	semidirect
649. C₄×SD₁₆	C₂²×C₃₁	semidirect
650. C₄×D₈	C₂²×C₃₁	semidirect
651. #435	C₂²×C₃₁	semidirect
652. #435	C₂²×C₃₁	semidirect
653. C₈×D₄	C₂²×C₃₁	semidirect
654. #433	C₂²×C₃₁	semidirect
655. #432	C₂²×C₃₁	semidirect
656. #424	C₂²×C₃₁	semidirect
657. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
658. #419	C₂²×C₃₁	semidirect
659. #416	C₂²×C₃₁	semidirect
660. C₂×#103	C₂²×C₃₁	semidirect
661. C₂×#102	C₂²×C₃₁	semidirect
836. C₃₁	#62016	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×#3561	2
C₃₁×#3519	2
C₃₁×#3397	2
C₃₁×#3376	2
C₃₁×#3321	2
C₃₁×#3320	2
C₃₁×#3297	2
D₄×SD₁₆×C₃₁	2
C₃₁×#3265	2
C₃₁×#3264	2
C₃₁×#3257	2
C₃₁×#3246	2
C₃₁×#3221	2
C₃₁×#3213	2
C₃₁×#3118	2
C₃₁×#3110	2
C₃₁×#3042	2
C₂×C₃₁×#463	2
C₃₁×#2992	2
#62016	31

Subgroups — C31×#62016 #21518775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62016 #21518775