Subgroups — C₃₁×#62216 #21518975

Order 7936.

1706 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×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3514	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3386	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3348	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3342	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3340	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3324	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3311	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3296	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3258	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3123	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3081	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	C₃₁×#559	C₂²	1	1	yes	characteristic
26	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#557	—	2	1	no	—
28	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#556	—	2	1	no	—
30	C₃₁×#556	C₂²	1	1	yes	characteristic
31	C₃₁×#556	C₂²	1	1	yes	characteristic
32	C₃₁×#556	C₂²	1	2	yes	complemented
33	C₃₁×#555	C₂²	1	2	yes	—
34	C₃₁×#554	C₂²	1	1	yes	characteristic
35	C₃₁×#552	C₂²	1	2	yes	complemented
36	C₃₁×#551	—	2	2	no	—
37	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#548	—	2	1	no	—
39	C₃₁×#546	—	2	1	no	—
40	C₃₁×#546	C₂²	1	2	yes	—
41	D₄²×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#544	C₂²	1	2	yes	complemented
43	C₃₁×#542	—	2	1	no	—
44	C₃₁×#542	C₂²	1	2	yes	—
45	C₃₁×#541	—	2	2	no	—
46	C₃₁×#541	—	2	1	no	—
47	C₃₁×#541	C₂²	1	2	yes	complemented
48	C₃₁×#538	—	2	2	no	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#532	C₂²	1	1	yes	characteristic
52	C₃₁×#529	—	2	1	no	—
53	C₃₁×#529	C₂²	1	1	yes	characteristic
54	C₂×C₃₁×#124	—	2	1	no	—
55	C₃₁×#518	C₂²	1	2	yes	—
56	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	complemented
58	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#498	C₂²	1	2	yes	complemented
60	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#489	C₂²	1	2	yes	complemented
62	C₃₁×#488	C₂²	1	2	yes	complemented
63	C₃₁×#486	C₂²	1	1	yes	characteristic
64	C₃₁×#486	C₂²	1	1	yes	characteristic
65	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#485	C₂²	1	2	yes	complemented
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#485	C₂²	1	2	yes	complemented
69	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#483	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	2	yes	—
72	C₃₁×#482	C₂²	1	2	yes	complemented
73	C₃₁×#482	C₂²	1	2	yes	complemented
74	C₃₁×#481	C₂²	1	2	yes	—
75	C₃₁×#479	C₂²	1	2	yes	complemented
76	C₃₁×#478	C₂²	1	2	yes	—
77	C₃₁×#478	C₂²	1	2	yes	—
78	C₃₁×#478	C₂²	1	2	yes	complemented
79	C₃₁×#478	C₂²	1	2	yes	complemented
80	C₃₁×#478	C₂²	1	2	yes	complemented
81	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#477	C₂²	1	2	yes	complemented
83	C₃₁×#476	C₂²	1	1	yes	characteristic
84	C₃₁×#476	C₂²	1	2	yes	—
85	C₃₁×#476	C₂²	1	2	yes	complemented
86	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#475	C₂²	1	2	yes	complemented
89	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#474	C₂²	1	1	yes	characteristic
92	C₃₁×#474	C₂²	1	1	yes	characteristic
93	C₃₁×#474	C₂²	1	2	yes	complemented
94	C₃₁×#470	C₂²	1	2	yes	complemented
95	C₃₁×#468	C₂²	1	2	yes	—
96	C₃₁×#467	C₂²	1	2	yes	complemented
97	C₃₁×#465	C₂²	1	2	yes	—
98	C₃₁×#465	C₂²	1	2	yes	complemented
99	C₃₁×#465	C₂²	1	2	yes	complemented
100	C₃₁×#464	C₂²	1	2	yes	complemented
101	C₃₁×#464	C₂²	1	2	yes	complemented
102	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#461	C₂²	1	1	yes	characteristic
104	C₃₁×#461	C₂²	1	2	yes	complemented
105	C₃₁×#460	C₂²	1	1	yes	characteristic
106	C₃₁×#460	C₂²	1	1	yes	characteristic
107	C₃₁×#452	C₂²	1	1	yes	characteristic
108	C₃₁×#452	C₂²	1	1	yes	characteristic
109	C₃₁×#450	C₂²	1	2	yes	—
110	C₃₁×#450	C₂²	1	2	yes	—
111	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#440	C₂²	1	2	yes	—
114	C₃₁×#440	C₂²	1	2	yes	complemented
115	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
120	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
125	C₃₁×#433	C₂²	1	2	yes	complemented
126	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#428	C₂²	1	2	yes	complemented
128	C₃₁×#427	C₂²	1	2	yes	complemented
129	C₃₁×#427	C₂²	1	2	yes	complemented
130	C₃₁×#424	C₂²	1	2	yes	complemented
131	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#418	C₂²	1	2	yes	—
133	C₃₁×#416	C₂²	1	2	yes	—
134	C₂×C₃₁×#102	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₃₁	—	2	1	no	—
138	C₂²×D₄×C₃₁	—	2	1	no	—
139	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
148	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
149	C₃₁×C₄⋊Q₈	—	2	1	no	—
150	C₃₁×C₄⋊Q₈	—	2	2	no	—
151	C₃₁×C₄⋊Q₈	—	2	1	no	—
152	C₃₁×C₄⋊Q₈	—	2	2	no	—
153	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃₁×#127	C₂³	1	1	yes	characteristic
161	C₃₁×#126	—	2	2	no	—
162	C₃₁×#126	—	2	2	no	—
163	C₃₁×#126	—	2	2	no	—
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#126	—	2	2	no	—
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	D₄	1	2	yes	—
170	C₃₁×#125	—	2	2	no	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	—	2	1	no	—
174	C₃₁×#125	—	2	2	no	—
175	C₃₁×#125	—	2	2	no	—
176	C₃₁×#125	—	2	1	no	—
177	C₃₁×#125	D₄	1	1	yes	characteristic
178	C₃₁×#125	C₂³	1	2	yes	—
179	C₃₁×#125	C₂³	1	2	yes	—
180	C₃₁×#124	—	2	1	no	—
181	C₃₁×#124	—	2	1	no	—
182	C₃₁×#124	—	2	1	no	—
183	C₃₁×#124	—	2	2	no	—
184	C₃₁×#124	—	2	2	no	—
185	C₃₁×#124	—	2	2	no	—
186	C₃₁×#124	—	2	2	no	—
187	C₃₁×#124	—	2	1	no	—
188	C₃₁×#124	D₄	1	1	yes	characteristic
189	C₃₁×#124	C₂³	1	2	yes	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	D₄	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	1	no	—
197	C₃₁×C₂²⋊Q₈	—	2	1	no	—
198	C₃₁×C₂²⋊Q₈	—	2	1	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
205	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
208	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
209	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	1	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	D₄	1	1	yes	characteristic
215	C₃₁×#121	C₂³	1	2	yes	—
216	C₃₁×#121	C₂³	1	2	yes	—
217	C₃₁×#120	—	2	2	no	—
218	C₃₁×#120	—	2	2	no	—
219	C₄×Q₈×C₃₁	—	2	1	no	—
220	C₄×Q₈×C₃₁	—	2	1	no	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	—	2	2	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	—	2	1	no	—
226	C₄×Q₈×C₃₁	—	2	1	no	—
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
231	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	—	2	1	no	—
237	C₄×D₄×C₃₁	—	2	2	no	—
238	C₄×D₄×C₃₁	—	2	2	no	—
239	C₄×D₄×C₃₁	—	2	1	no	—
240	C₄×D₄×C₃₁	—	2	1	no	—
241	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₃₁	C₂³	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	2	yes	—
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	2	yes	—
246	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₃₁	C₂³	1	2	yes	—
248	C₃₁×#117	—	2	1	no	—
249	C₃₁×#117	—	2	2	no	—
250	C₃₁×#117	—	2	2	no	—
251	C₃₁×#117	—	2	1	no	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₃₁×#117	C₂³	1	1	yes	characteristic
255	C₃₁×#117	C₂³	1	2	yes	—
256	C₃₁×#117	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
261	C₂×C₄²×C₃₁	—	2	1	no	—
262	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
263	C₃₁×#107	C₂³	1	1	yes	characteristic
264	C₃₁×#107	C₂³	1	2	yes	—
265	C₃₁×#107	C₂³	1	2	yes	—
266	C₃₁×#107	C₂³	1	2	yes	—
267	C₃₁×#107	C₂³	1	1	yes	characteristic
268	C₃₁×#107	C₂³	1	2	yes	—
269	C₃₁×#106	C₂³	1	2	yes	—
270	C₃₁×#106	C₂³	1	2	yes	—
271	C₃₁×#106	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	1	yes	characteristic
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×#103	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	1	yes	characteristic
291	C₃₁×#103	C₂³	1	1	yes	characteristic
292	C₃₁×#103	C₂³	1	1	yes	characteristic
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	C₂⁴×C₃₁	—	2	2	no	—
313	#41×C₃₁	—	2	2	no	—
314	#41×C₃₁	—	4	1	no	—
315	#41×C₃₁	—	8	2	no	—
316	C₂×Q₈×C₃₁	—	2	1	no	—
317	C₂×Q₈×C₃₁	—	2	1	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	8	2	no	—
323	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₃₁	—	2	4	no	—
328	C₂×D₄×C₃₁	—	2	1	no	—
329	C₂×D₄×C₃₁	—	2	2	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	2	1	no	—
334	C₂×D₄×C₃₁	—	4	2	no	—
335	C₂×D₄×C₃₁	—	8	2	no	—
336	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
338	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
339	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₃₁	—	2	2	no	—
341	C₂²×C₄×C₃₁	—	2	1	no	—
342	C₂²×C₄×C₃₁	—	2	1	no	—
343	C₂²×C₄×C₃₁	—	2	1	no	—
344	C₂²×C₄×C₃₁	—	2	2	no	—
345	C₂²×C₄×C₃₁	—	2	2	no	—
346	C₂²×C₄×C₃₁	—	2	2	no	—
347	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
351	Q₁₆×C₃₁	—	4	1	no	—
352	Q₁₆×C₃₁	—	4	1	no	—
353	SD₁₆×C₃₁	—	2	2	no	—
354	SD₁₆×C₃₁	—	2	2	no	—
355	SD₁₆×C₃₁	—	4	2	no	—
356	SD₁₆×C₃₁	—	4	2	no	—
357	M₁₆×C₃₁	—	4	2	no	—
358	C₂×C₈×C₃₁	—	4	2	no	—
359	C₂×C₈×C₃₁	—	4	2	no	—
360	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
365	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₃₁	—	2	2	no	—
367	C₄⋊C₄×C₃₁	—	2	1	no	—
368	C₄⋊C₄×C₃₁	—	2	1	no	—
369	C₄⋊C₄×C₃₁	—	2	1	no	—
370	C₄⋊C₄×C₃₁	—	2	2	no	—
371	C₄⋊C₄×C₃₁	—	2	1	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	—	2	1	no	—
374	C₄⋊C₄×C₃₁	—	2	1	no	—
375	C₄⋊C₄×C₃₁	—	2	1	no	—
376	C₄⋊C₄×C₃₁	—	2	1	no	—
377	C₄⋊C₄×C₃₁	—	2	2	no	—
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	2	no	—
380	C₄⋊C₄×C₃₁	—	2	2	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	1	no	—
383	C₄⋊C₄×C₃₁	—	2	1	no	—
384	C₄⋊C₄×C₃₁	—	2	2	no	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
391	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
393	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₂²⋊C₄×C₃₁	—	2	2	no	—
404	C₂²⋊C₄×C₃₁	—	2	2	no	—
405	C₂²⋊C₄×C₃₁	—	2	1	no	—
406	C₂²⋊C₄×C₃₁	—	2	1	no	—
407	C₂²⋊C₄×C₃₁	—	2	2	no	—
408	C₂²⋊C₄×C₃₁	—	2	1	no	—
409	C₂²⋊C₄×C₃₁	—	2	2	no	—
410	C₂²⋊C₄×C₃₁	—	2	2	no	—
411	C₂²⋊C₄×C₃₁	—	2	2	no	—
412	C₂²⋊C₄×C₃₁	—	2	1	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	1	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
422	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
423	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
426	C₄²×C₃₁	—	2	1	no	—
427	C₄²×C₃₁	—	2	1	no	—
428	C₄²×C₃₁	—	2	1	no	—
429	C₄²×C₃₁	—	2	2	no	—
430	C₄²×C₃₁	—	2	2	no	—
431	C₄²×C₃₁	—	2	1	no	—
432	C₄²×C₃₁	—	2	1	no	—
433	C₄²×C₃₁	—	2	2	no	—
434	C₄²×C₃₁	—	2	2	no	—
435	C₄²×C₃₁	—	2	2	no	—
436	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
439	C₄²×C₃₁	C₂⁴	1	2	yes	—
440	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
441	#62216	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
442	C₂³×C₃₁	—	2	1	no	—
443	C₂³×C₃₁	—	2	2	no	—
444	C₂³×C₃₁	—	4	4	no	—
445	C₂³×C₃₁	—	8	2	no	—
446	C₂³×C₃₁	—	8	2	no	—
447	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
448	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
449	Q₈×C₃₁	—	2	2	no	—
450	Q₈×C₃₁	—	2	1	no	—
451	Q₈×C₃₁	—	2	1	no	—
452	Q₈×C₃₁	—	2	1	no	—
453	Q₈×C₃₁	—	2	1	no	—
454	Q₈×C₃₁	—	2	1	no	—
455	Q₈×C₃₁	—	2	1	no	—
456	Q₈×C₃₁	—	4	2	no	—
457	Q₈×C₃₁	—	4	2	no	—
458	Q₈×C₃₁	—	8	1	no	—
459	Q₈×C₃₁	—	8	1	no	—
460	Q₈×C₃₁	—	8	2	no	—
461	Q₈×C₃₁	—	8	2	no	—
462	D₄×C₃₁	—	2	2	no	—
463	D₄×C₃₁	—	2	2	no	—
464	D₄×C₃₁	—	2	1	no	—
465	D₄×C₃₁	—	2	2	no	—
466	D₄×C₃₁	—	4	2	no	—
467	D₄×C₃₁	—	4	4	no	—
468	D₄×C₃₁	—	4	2	no	—
469	D₄×C₃₁	—	4	2	no	—
470	D₄×C₃₁	—	8	1	no	—
471	D₄×C₃₁	—	8	2	no	—
472	D₄×C₃₁	—	8	2	no	—
473	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
474	C₂×C₄×C₃₁	—	2	2	no	—
475	C₂×C₄×C₃₁	—	2	2	no	—
476	C₂×C₄×C₃₁	—	2	1	no	—
477	C₂×C₄×C₃₁	—	2	1	no	—
478	C₂×C₄×C₃₁	—	2	2	no	—
479	C₂×C₄×C₃₁	—	2	1	no	—
480	C₂×C₄×C₃₁	—	2	1	no	—
481	C₂×C₄×C₃₁	—	2	1	no	—
482	C₂×C₄×C₃₁	—	2	2	no	—
483	C₂×C₄×C₃₁	—	2	1	no	—
484	C₂×C₄×C₃₁	—	2	1	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	2	no	—
487	C₂×C₄×C₃₁	—	2	2	no	—
488	C₂×C₄×C₃₁	—	2	1	no	—
489	C₂×C₄×C₃₁	—	4	1	no	—
490	C₂×C₄×C₃₁	—	4	2	no	—
491	C₂×C₄×C₃₁	—	4	2	no	—
492	C₂×C₄×C₃₁	—	8	1	no	—
493	C₂×C₄×C₃₁	—	8	2	no	—
494	C₂×C₄×C₃₁	—	8	2	no	—
495	C₂×C₄×C₃₁	—	8	2	no	—
496	C₂×C₄×C₃₁	—	8	2	no	—
497	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
506	C₈×C₃₁	—	2	1	no	—
507	C₈×C₃₁	—	2	1	no	—
508	C₈×C₃₁	—	2	2	no	—
509	C₈×C₃₁	—	2	1	no	—
510	C₈×C₃₁	—	2	2	no	—
511	C₈×C₃₁	—	2	1	no	—
512	#3555	C₂×C₃₁	1	1	yes	characteristic, complemented
513	#3514	C₂×C₃₁	1	1	yes	characteristic
514	#3386	C₂×C₃₁	1	1	yes	characteristic, complemented
515	Q₈×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
516	#3375	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#3365	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#3356	C₂×C₃₁	1	1	yes	characteristic, complemented
519	#3348	C₂×C₃₁	1	2	yes	complemented
520	#3342	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3340	C₂×C₃₁	1	2	yes	complemented
522	#3324	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3311	C₂×C₃₁	1	2	yes	complemented
524	#3296	C₂×C₃₁	1	2	yes	complemented
525	#3295	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3258	C₂×C₃₁	1	2	yes	complemented
527	#3246	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3244	C₂×C₃₁	1	2	yes	complemented
529	#3228	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3123	C₂×C₃₁	1	2	yes	complemented
531	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3081	C₂×C₃₁	1	2	yes	complemented
533	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#2994	C₂×C₃₁	1	1	yes	characteristic, complemented
535	C₂²×C₃₁	—	2	1	no	—
536	C₂²×C₃₁	—	2	2	no	—
537	C₂²×C₃₁	—	2	1	no	—
538	C₂²×C₃₁	—	2	2	no	—
539	C₂²×C₃₁	—	2	2	no	—
540	C₂²×C₃₁	—	2	1	no	—
541	C₂²×C₃₁	—	2	2	no	—
542	C₂²×C₃₁	—	4	1	no	—
543	C₂²×C₃₁	—	4	1	no	—
544	C₂²×C₃₁	—	4	2	no	—
545	C₂²×C₃₁	—	4	2	no	—
546	C₂²×C₃₁	—	4	2	no	—
547	C₂²×C₃₁	—	16	4	no	—
548	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
549	C₄×C₃₁	—	2	1	no	—
550	C₄×C₃₁	—	2	1	no	—
551	C₄×C₃₁	—	2	2	no	—
552	C₄×C₃₁	—	2	1	no	—
553	C₄×C₃₁	—	2	2	no	—
554	C₄×C₃₁	—	2	1	no	—
555	C₄×C₃₁	—	2	2	no	—
556	C₄×C₃₁	—	4	1	no	—
557	C₄×C₃₁	—	4	1	no	—
558	C₄×C₃₁	—	4	2	no	—
559	C₄×C₃₁	—	4	1	no	—
560	C₄×C₃₁	—	4	1	no	—
561	C₄×C₃₁	—	4	1	no	—
562	C₄×C₃₁	—	4	1	no	—
563	C₄×C₃₁	—	4	1	no	—
564	C₄×C₃₁	—	4	2	no	—
565	C₄×C₃₁	—	4	2	no	—
566	C₄×C₃₁	#577	1	2	yes	—
567	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
568	C₄×C₃₁	#585	1	1	yes	characteristic
569	#563	—	2	2	no	—
570	#559	C₂²×C₃₁	1	1	yes	characteristic
571	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
572	#557	—	2	1	no	—
573	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
574	#556	—	2	1	no	—
575	#556	C₂²×C₃₁	1	1	yes	characteristic
576	#556	C₂²×C₃₁	1	1	yes	characteristic
577	#556	C₂²×C₃₁	1	2	yes	complemented
578	#555	C₂²×C₃₁	1	2	yes	—
579	#554	C₂²×C₃₁	1	1	yes	characteristic
580	#552	C₂²×C₃₁	1	2	yes	complemented
581	#551	—	2	2	no	—
582	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
583	#548	—	2	1	no	—
584	#546	—	2	1	no	—
585	#546	C₂²×C₃₁	1	2	yes	—
586	D₄²	C₂²×C₃₁	1	1	yes	characteristic
587	#544	C₂²×C₃₁	1	2	yes	complemented
588	#542	—	2	1	no	—
589	#542	C₂²×C₃₁	1	2	yes	—
590	#541	—	2	2	no	—
591	#541	—	2	1	no	—
592	#541	C₂²×C₃₁	1	2	yes	complemented
593	#538	—	2	2	no	—
594	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
595	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
596	#532	C₂²×C₃₁	1	1	yes	characteristic
597	#529	—	2	1	no	—
598	#529	C₂²×C₃₁	1	1	yes	characteristic
599	C₂×#124	—	2	1	no	—
600	#518	C₂²×C₃₁	1	2	yes	—
601	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
602	#501	C₂²×C₃₁	1	2	yes	complemented
603	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
604	#498	C₂²×C₃₁	1	2	yes	complemented
605	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
606	#489	C₂²×C₃₁	1	2	yes	complemented
607	#488	C₂²×C₃₁	1	2	yes	complemented
608	#486	C₂²×C₃₁	1	1	yes	characteristic
609	#486	C₂²×C₃₁	1	1	yes	characteristic
610	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
611	#485	C₂²×C₃₁	1	2	yes	complemented
612	#485	C₂²×C₃₁	1	2	yes	complemented
613	#485	C₂²×C₃₁	1	2	yes	complemented
614	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
615	#483	C₂²×C₃₁	1	2	yes	complemented
616	#482	C₂²×C₃₁	1	2	yes	—
617	#482	C₂²×C₃₁	1	2	yes	complemented
618	#482	C₂²×C₃₁	1	2	yes	complemented
619	#481	C₂²×C₃₁	1	2	yes	—
620	#479	C₂²×C₃₁	1	2	yes	complemented
621	#478	C₂²×C₃₁	1	2	yes	—
622	#478	C₂²×C₃₁	1	2	yes	—
623	#478	C₂²×C₃₁	1	2	yes	complemented
624	#478	C₂²×C₃₁	1	2	yes	complemented
625	#478	C₂²×C₃₁	1	2	yes	complemented
626	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
627	#477	C₂²×C₃₁	1	2	yes	complemented
628	#476	C₂²×C₃₁	1	1	yes	characteristic
629	#476	C₂²×C₃₁	1	2	yes	—
630	#476	C₂²×C₃₁	1	2	yes	complemented
631	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
632	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
633	#475	C₂²×C₃₁	1	2	yes	complemented
634	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
636	#474	C₂²×C₃₁	1	1	yes	characteristic
637	#474	C₂²×C₃₁	1	1	yes	characteristic
638	#474	C₂²×C₃₁	1	2	yes	complemented
639	#470	C₂²×C₃₁	1	2	yes	complemented
640	#468	C₂²×C₃₁	1	2	yes	—
641	#467	C₂²×C₃₁	1	2	yes	complemented
642	#465	C₂²×C₃₁	1	2	yes	—
643	#465	C₂²×C₃₁	1	2	yes	complemented
644	#465	C₂²×C₃₁	1	2	yes	complemented
645	#464	C₂²×C₃₁	1	2	yes	complemented
646	#464	C₂²×C₃₁	1	2	yes	complemented
647	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#461	C₂²×C₃₁	1	1	yes	characteristic
649	#461	C₂²×C₃₁	1	2	yes	complemented
650	#460	C₂²×C₃₁	1	1	yes	characteristic
651	#460	C₂²×C₃₁	1	1	yes	characteristic
652	#452	C₂²×C₃₁	1	1	yes	characteristic
653	#452	C₂²×C₃₁	1	1	yes	characteristic
654	#450	C₂²×C₃₁	1	2	yes	—
655	#450	C₂²×C₃₁	1	2	yes	—
656	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
657	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
658	#440	C₂²×C₃₁	1	2	yes	—
659	#440	C₂²×C₃₁	1	2	yes	complemented
660	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
663	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
664	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
665	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
666	#436	C₂²×C₃₁	1	1	yes	characteristic
667	#435	C₂²×C₃₁	1	2	yes	complemented
668	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
669	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
670	#433	C₂²×C₃₁	1	2	yes	complemented
671	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
672	#428	C₂²×C₃₁	1	2	yes	complemented
673	#427	C₂²×C₃₁	1	2	yes	complemented
674	#427	C₂²×C₃₁	1	2	yes	complemented
675	#424	C₂²×C₃₁	1	2	yes	complemented
676	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
677	#418	C₂²×C₃₁	1	2	yes	—
678	#416	C₂²×C₃₁	1	2	yes	—
679	C₂×#102	C₂²×C₃₁	1	2	yes	—
680	C₂×C₃₁	—	4	1	no	—
681	C₂×C₃₁	—	4	2	no	—
682	C₂×C₃₁	—	4	2	no	—
683	C₂×C₃₁	—	8	2	no	—
684	C₂×C₃₁	#3489	1	1	yes	characteristic
685	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
686	C₂×C₃₁	#3584	1	1	yes	characteristic
687	C₂×#41	—	2	1	no	—
688	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
689	C₂²×Q₈	—	2	1	no	—
690	C₂²×D₄	—	2	1	no	—
691	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
692	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
693	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
694	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
695	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
696	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
697	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
698	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
699	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
700	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
701	C₄⋊Q₈	—	2	1	no	—
702	C₄⋊Q₈	—	2	2	no	—
703	C₄⋊Q₈	—	2	1	no	—
704	C₄⋊Q₈	—	2	2	no	—
705	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
706	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
708	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
711	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
712	#127	C₂³×C₃₁	1	1	yes	characteristic
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#126	D₄×C₃₁	1	2	yes	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	1	no	—
726	#125	—	2	2	no	—
727	#125	—	2	2	no	—
728	#125	—	2	1	no	—
729	#125	D₄×C₃₁	1	1	yes	characteristic
730	#125	C₂³×C₃₁	1	2	yes	—
731	#125	C₂³×C₃₁	1	2	yes	—
732	#124	—	2	1	no	—
733	#124	—	2	1	no	—
734	#124	—	2	1	no	—
735	#124	—	2	2	no	—
736	#124	—	2	2	no	—
737	#124	—	2	2	no	—
738	#124	—	2	2	no	—
739	#124	—	2	1	no	—
740	#124	D₄×C₃₁	1	1	yes	characteristic
741	#124	C₂³×C₃₁	1	2	yes	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	D₄×C₃₁	1	2	yes	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
757	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
758	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
759	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
762	#121	—	2	2	no	—
763	#121	—	2	1	no	—
764	#121	—	2	1	no	—
765	#121	—	2	2	no	—
766	#121	D₄×C₃₁	1	1	yes	characteristic
767	#121	C₂³×C₃₁	1	2	yes	—
768	#121	C₂³×C₃₁	1	2	yes	—
769	#120	—	2	2	no	—
770	#120	—	2	2	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	2	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
784	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
785	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
794	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
795	C₄×D₄	C₂³×C₃₁	1	2	yes	—
796	C₄×D₄	C₂³×C₃₁	1	2	yes	—
797	C₄×D₄	C₂³×C₃₁	1	2	yes	—
798	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
799	C₄×D₄	C₂³×C₃₁	1	2	yes	—
800	#117	—	2	1	no	—
801	#117	—	2	2	no	—
802	#117	—	2	2	no	—
803	#117	—	2	1	no	—
804	#117	C₂³×C₃₁	1	1	yes	characteristic
805	#117	C₂³×C₃₁	1	2	yes	—
806	#117	C₂³×C₃₁	1	2	yes	—
807	#117	C₂³×C₃₁	1	2	yes	—
808	#117	C₂³×C₃₁	1	2	yes	—
809	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
810	C₂×C₂²⋊C₄	—	2	2	no	—
811	C₂×C₂²⋊C₄	—	2	2	no	—
812	C₂×C₂²⋊C₄	—	2	2	no	—
813	C₂×C₄²	—	2	1	no	—
814	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
815	#107	C₂³×C₃₁	1	1	yes	characteristic
816	#107	C₂³×C₃₁	1	2	yes	—
817	#107	C₂³×C₃₁	1	2	yes	—
818	#107	C₂³×C₃₁	1	2	yes	—
819	#107	C₂³×C₃₁	1	1	yes	characteristic
820	#107	C₂³×C₃₁	1	2	yes	—
821	#106	C₂³×C₃₁	1	2	yes	—
822	#106	C₂³×C₃₁	1	2	yes	—
823	#106	C₂³×C₃₁	1	2	yes	—
824	#106	C₂³×C₃₁	1	2	yes	—
825	#106	C₂³×C₃₁	1	2	yes	—
826	#106	C₂³×C₃₁	1	1	yes	characteristic
827	#106	C₂³×C₃₁	1	1	yes	characteristic
828	#106	C₂³×C₃₁	1	2	yes	—
829	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
830	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
831	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
832	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
833	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
834	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
835	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
836	#103	C₂³×C₃₁	1	2	yes	—
837	#103	C₂³×C₃₁	1	2	yes	—
838	#103	C₂³×C₃₁	1	2	yes	—
839	#103	C₂³×C₃₁	1	1	yes	characteristic
840	#103	C₂³×C₃₁	1	1	yes	characteristic
841	#103	C₂³×C₃₁	1	1	yes	characteristic
842	#103	C₂³×C₃₁	1	1	yes	characteristic
843	#103	C₂³×C₃₁	1	1	yes	characteristic
844	#103	C₂³×C₃₁	1	1	yes	characteristic
845	#103	C₂³×C₃₁	1	2	yes	—
846	#102	C₂³×C₃₁	1	1	yes	characteristic
847	#102	C₂³×C₃₁	1	2	yes	—
848	#102	C₂³×C₃₁	1	2	yes	—
849	#102	C₂³×C₃₁	1	2	yes	—
850	#102	C₂³×C₃₁	1	2	yes	—
851	#102	C₂³×C₃₁	1	1	yes	characteristic
852	#102	C₂³×C₃₁	1	2	yes	—
853	#102	C₂³×C₃₁	1	2	yes	—
854	#102	C₂³×C₃₁	1	2	yes	—
855	#102	C₂³×C₃₁	1	2	yes	—
856	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
857	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
858	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
859	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
860	#97	C₂³×C₃₁	1	2	yes	—
861	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
862	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
863	C₄×C₈	C₂³×C₃₁	1	2	yes	—
864	C₃₁	#62216	1	1	yes	characteristic, direct product factor, Sylow
865	C₂⁴	—	2	2	no	—
866	#41	—	2	2	no	—
867	#41	—	4	1	no	—
868	#41	—	8	2	no	—
869	C₂×Q₈	—	2	1	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	1	no	—
872	C₂×Q₈	—	2	1	no	—
873	C₂×Q₈	—	2	2	no	—
874	C₂×Q₈	—	2	2	no	—
875	C₂×Q₈	—	8	2	no	—
876	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
877	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
878	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
879	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
880	C₂×D₄	—	2	4	no	—
881	C₂×D₄	—	2	1	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	1	no	—
887	C₂×D₄	—	4	2	no	—
888	C₂×D₄	—	8	2	no	—
889	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
890	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
891	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
892	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
901	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
902	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
903	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
904	Q₁₆	—	4	1	no	—
905	Q₁₆	—	4	1	no	—
906	SD₁₆	—	2	2	no	—
907	SD₁₆	—	2	2	no	—
908	SD₁₆	—	4	2	no	—
909	SD₁₆	—	4	2	no	—
910	M₁₆	—	4	2	no	—
911	C₂×C₈	—	4	2	no	—
912	C₂×C₈	—	4	2	no	—
913	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
914	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
915	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
916	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
917	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
918	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
944	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
946	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
947	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
948	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
950	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
951	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
952	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
953	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
954	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
955	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	1	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	1	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
975	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
976	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
977	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
978	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
979	C₄²	—	2	1	no	—
980	C₄²	—	2	1	no	—
981	C₄²	—	2	1	no	—
982	C₄²	—	2	2	no	—
983	C₄²	—	2	2	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	1	no	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	2	no	—
989	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
990	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
991	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
992	C₄²	C₂⁴×C₃₁	1	2	yes	—
993	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
994	C₂³	—	2	1	no	—
995	C₂³	—	2	2	no	—
996	C₂³	—	4	4	no	—
997	C₂³	—	8	2	no	—
998	C₂³	—	8	2	no	—
999	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1000	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1001	Q₈	—	2	2	no	—
1002	Q₈	—	2	1	no	—
1003	Q₈	—	2	1	no	—
1004	Q₈	—	2	1	no	—
1005	Q₈	—	2	1	no	—
1006	Q₈	—	2	1	no	—
1007	Q₈	—	2	1	no	—
1008	Q₈	—	4	2	no	—
1009	Q₈	—	4	2	no	—
1010	Q₈	—	8	1	no	—
1011	Q₈	—	8	1	no	—
1012	Q₈	—	8	2	no	—
1013	Q₈	—	8	2	no	—
1014	D₄	—	2	2	no	—
1015	D₄	—	2	2	no	—
1016	D₄	—	2	1	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	4	2	no	—
1019	D₄	—	4	4	no	—
1020	D₄	—	4	2	no	—
1021	D₄	—	4	2	no	—
1022	D₄	—	8	1	no	—
1023	D₄	—	8	2	no	—
1024	D₄	—	8	2	no	—
1025	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	4	1	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	2	no	—
1044	C₂×C₄	—	8	1	no	—
1045	C₂×C₄	—	8	2	no	—
1046	C₂×C₄	—	8	2	no	—
1047	C₂×C₄	—	8	2	no	—
1048	C₂×C₄	—	8	2	no	—
1049	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1050	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1051	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1052	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1053	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1054	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1055	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1056	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1057	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1058	C₈	—	2	1	no	—
1059	C₈	—	2	1	no	—
1060	C₈	—	2	2	no	—
1061	C₈	—	2	1	no	—
1062	C₈	—	2	2	no	—
1063	C₈	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	2	2	no	—
1066	C₂²	—	2	2	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	2	1	no	—
1070	C₂²	—	2	2	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	16	4	no	—
1077	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1078	C₄	—	2	1	no	—
1079	C₄	—	2	2	no	—
1080	C₄	—	2	1	no	—
1081	C₄	—	2	2	no	—
1082	C₄	—	2	1	no	—
1083	C₄	—	2	1	no	—
1084	C₄	—	2	2	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	1	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	—	4	1	no	—
1095	C₄	C₃₁×#577	1	2	yes	—
1096	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1097	C₄	C₃₁×#585	1	1	yes	characteristic
1098	C₂	—	4	2	no	—
1099	C₂	—	4	1	no	—
1100	C₂	—	4	2	no	—
1101	C₂	—	8	2	no	—
1102	C₂	C₃₁×#3489	1	1	yes	characteristic
1103	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1104	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3514	C₂
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×#3555	C₂	semidirect
3. C₃₁×#3386	C₂	semidirect
4. Q₈×SD₁₆×C₃₁	C₂	semidirect
5. C₃₁×#3375	C₂	semidirect
6. C₃₁×#3365	C₂	semidirect
7. C₃₁×#3356	C₂	semidirect
8. C₃₁×#3348	C₂	semidirect
9. C₃₁×#3342	C₂	semidirect
10. C₃₁×#3340	C₂	semidirect
11. C₃₁×#3324	C₂	semidirect
12. C₃₁×#3311	C₂	semidirect
13. C₃₁×#3296	C₂	semidirect
14. C₃₁×#3295	C₂	semidirect
15. C₃₁×#3258	C₂	semidirect
16. C₃₁×#3246	C₂	semidirect
17. C₃₁×#3244	C₂	semidirect
18. C₃₁×#3228	C₂	semidirect
19. C₃₁×#3123	C₂	semidirect
20. C₃₁×#3107	C₂	semidirect
21. C₃₁×#3081	C₂	semidirect
22. C₃₁×#3076	C₂	semidirect
23. C₃₁×#2994	C₂	semidirect
26. Q₈²×C₃₁	C₂²	semidirect
28. C₃₁×#557	C₂²	semidirect
32. C₃₁×#556	C₂²	semidirect
35. C₃₁×#552	C₂²	semidirect
42. C₃₁×#544	C₂²	semidirect
47. C₃₁×#541	C₂²	semidirect
49. C₃₁×#533	C₂²	semidirect
50. C₃₁×#533	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#500	C₂²	semidirect
59. C₃₁×#498	C₂²	semidirect
60. C₃₁×#498	C₂²	semidirect
61. C₃₁×#489	C₂²	semidirect
62. C₃₁×#488	C₂²	semidirect
65. C₃₁×#485	C₂²	semidirect
66. C₃₁×#485	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#485	C₂²	semidirect
69. C₃₁×#485	C₂²	semidirect
70. C₃₁×#483	C₂²	semidirect
72. C₃₁×#482	C₂²	semidirect
73. C₃₁×#482	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
78. C₃₁×#478	C₂²	semidirect
79. C₃₁×#478	C₂²	semidirect
80. C₃₁×#478	C₂²	semidirect
81. C₃₁×#477	C₂²	semidirect
82. C₃₁×#477	C₂²	semidirect
85. C₃₁×#476	C₂²	semidirect
86. C₃₁×#475	C₂²	semidirect
87. C₃₁×#475	C₂²	semidirect
88. C₃₁×#475	C₂²	semidirect
89. C₃₁×#475	C₂²	semidirect
90. C₃₁×#475	C₂²	semidirect
93. C₃₁×#474	C₂²	semidirect
94. C₃₁×#470	C₂²	semidirect
96. C₃₁×#467	C₂²	semidirect
98. C₃₁×#465	C₂²	semidirect
99. C₃₁×#465	C₂²	semidirect
100. C₃₁×#464	C₂²	semidirect
101. C₃₁×#464	C₂²	semidirect
102. C₃₁×#462	C₂²	semidirect
104. C₃₁×#461	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₈×Q₈×C₃₁	C₂²	semidirect
114. C₃₁×#440	C₂²	semidirect
115. C₄×Q₁₆×C₃₁	C₂²	semidirect
116. C₄×Q₁₆×C₃₁	C₂²	semidirect
120. C₄×SD₁₆×C₃₁	C₂²	semidirect
122. C₃₁×#435	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
126. C₃₁×#431	C₂²	semidirect
127. C₃₁×#428	C₂²	semidirect
128. C₃₁×#427	C₂²	semidirect
129. C₃₁×#427	C₂²	semidirect
130. C₃₁×#424	C₂²	semidirect
131. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
441. #62216	C₃₁	direct (N × H)
512. #3555	C₂×C₃₁	semidirect
514. #3386	C₂×C₃₁	semidirect
515. Q₈×SD₁₆	C₂×C₃₁	semidirect
516. #3375	C₂×C₃₁	semidirect
517. #3365	C₂×C₃₁	semidirect
518. #3356	C₂×C₃₁	semidirect
519. #3348	C₂×C₃₁	semidirect
520. #3342	C₂×C₃₁	semidirect
521. #3340	C₂×C₃₁	semidirect
522. #3324	C₂×C₃₁	semidirect
523. #3311	C₂×C₃₁	semidirect
524. #3296	C₂×C₃₁	semidirect
525. #3295	C₂×C₃₁	semidirect
526. #3258	C₂×C₃₁	semidirect
527. #3246	C₂×C₃₁	semidirect
528. #3244	C₂×C₃₁	semidirect
529. #3228	C₂×C₃₁	semidirect
530. #3123	C₂×C₃₁	semidirect
531. #3107	C₂×C₃₁	semidirect
532. #3081	C₂×C₃₁	semidirect
533. #3076	C₂×C₃₁	semidirect
534. #2994	C₂×C₃₁	semidirect
571. Q₈²	C₂²×C₃₁	semidirect
573. #557	C₂²×C₃₁	semidirect
577. #556	C₂²×C₃₁	semidirect
580. #552	C₂²×C₃₁	semidirect
587. #544	C₂²×C₃₁	semidirect
592. #541	C₂²×C₃₁	semidirect
594. #533	C₂²×C₃₁	semidirect
595. #533	C₂²×C₃₁	semidirect
602. #501	C₂²×C₃₁	semidirect
603. #500	C₂²×C₃₁	semidirect
604. #498	C₂²×C₃₁	semidirect
605. #498	C₂²×C₃₁	semidirect
606. #489	C₂²×C₃₁	semidirect
607. #488	C₂²×C₃₁	semidirect
610. #485	C₂²×C₃₁	semidirect
611. #485	C₂²×C₃₁	semidirect
612. #485	C₂²×C₃₁	semidirect
613. #485	C₂²×C₃₁	semidirect
614. #485	C₂²×C₃₁	semidirect
615. #483	C₂²×C₃₁	semidirect
617. #482	C₂²×C₃₁	semidirect
618. #482	C₂²×C₃₁	semidirect
620. #479	C₂²×C₃₁	semidirect
623. #478	C₂²×C₃₁	semidirect
624. #478	C₂²×C₃₁	semidirect
625. #478	C₂²×C₃₁	semidirect
626. #477	C₂²×C₃₁	semidirect
627. #477	C₂²×C₃₁	semidirect
630. #476	C₂²×C₃₁	semidirect
631. #475	C₂²×C₃₁	semidirect
632. #475	C₂²×C₃₁	semidirect
633. #475	C₂²×C₃₁	semidirect
634. #475	C₂²×C₃₁	semidirect
635. #475	C₂²×C₃₁	semidirect
638. #474	C₂²×C₃₁	semidirect
639. #470	C₂²×C₃₁	semidirect
641. #467	C₂²×C₃₁	semidirect
643. #465	C₂²×C₃₁	semidirect
644. #465	C₂²×C₃₁	semidirect
645. #464	C₂²×C₃₁	semidirect
646. #464	C₂²×C₃₁	semidirect
647. #462	C₂²×C₃₁	semidirect
649. #461	C₂²×C₃₁	semidirect
656. #446	C₂²×C₃₁	semidirect
657. C₈×Q₈	C₂²×C₃₁	semidirect
659. #440	C₂²×C₃₁	semidirect
660. C₄×Q₁₆	C₂²×C₃₁	semidirect
661. C₄×Q₁₆	C₂²×C₃₁	semidirect
665. C₄×SD₁₆	C₂²×C₃₁	semidirect
667. #435	C₂²×C₃₁	semidirect
669. C₈×D₄	C₂²×C₃₁	semidirect
670. #433	C₂²×C₃₁	semidirect
671. #431	C₂²×C₃₁	semidirect
672. #428	C₂²×C₃₁	semidirect
673. #427	C₂²×C₃₁	semidirect
674. #427	C₂²×C₃₁	semidirect
675. #424	C₂²×C₃₁	semidirect
676. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
864. C₃₁	#62216	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×#3555	2
C₃₁×#3514	2
C₃₁×#3386	2
Q₈×SD₁₆×C₃₁	2
C₃₁×#3375	2
C₃₁×#3365	2
C₃₁×#3356	2
C₃₁×#3348	2
C₃₁×#3342	2
C₃₁×#3340	2
C₃₁×#3324	2
C₃₁×#3311	2
C₃₁×#3296	2
C₃₁×#3295	2
C₃₁×#3258	2
C₃₁×#3246	2
C₃₁×#3244	2
C₃₁×#3228	2
C₃₁×#3123	2
C₃₁×#3107	2
C₃₁×#3081	2
C₃₁×#3076	2
C₃₁×#2994	2
#62216	31

Subgroups — C31×#62216 #21518975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62216 #21518975