Subgroups — C₃₁×#62215 #21518974

Order 7936.

1762 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3384	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3353	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3347	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3341	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3340	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3319	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3297	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3257	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3245	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3243	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3122	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3106	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×#562	—	2	2	no	—
25	C₃₁×#559	C₂²	1	1	yes	characteristic
26	C₃₁×#556	C₂²	1	1	yes	characteristic
27	C₃₁×#555	C₂²	1	1	yes	characteristic
28	C₃₁×#555	C₂²	1	2	yes	—
29	C₃₁×#555	C₂²	1	2	yes	complemented
30	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#553	C₂²	1	2	yes	complemented
32	C₃₁×#552	—	2	1	no	—
33	C₃₁×#551	—	2	2	no	—
34	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#548	—	2	1	no	—
37	C₃₁×#548	—	2	1	no	—
38	C₃₁×#547	C₂²	1	1	yes	characteristic
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	2	no	—
44	C₃₁×#542	C₂²	1	2	yes	—
45	C₃₁×#540	C₂²	1	2	yes	complemented
46	C₃₁×#538	—	2	2	no	—
47	C₃₁×#537	—	2	1	no	—
48	C₃₁×#536	—	2	1	no	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#532	C₂²	1	1	yes	characteristic
51	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
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	2	yes	complemented
59	C₃₁×#500	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
66	C₃₁×#484	C₂²	1	2	yes	complemented
67	C₃₁×#482	C₂²	1	2	yes	—
68	C₃₁×#482	C₂²	1	2	yes	complemented
69	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#482	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	2	yes	complemented
72	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#482	C₂²	1	2	yes	complemented
74	C₃₁×#480	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	1	yes	characteristic, complemented
83	C₃₁×#476	C₂²	1	1	yes	characteristic
84	C₃₁×#476	C₂²	1	1	yes	characteristic
85	C₃₁×#476	C₂²	1	2	yes	complemented
86	C₃₁×#476	C₂²	1	2	yes	complemented
87	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#474	C₂²	1	1	yes	characteristic
89	C₃₁×#474	C₂²	1	2	yes	—
90	C₃₁×#474	C₂²	1	2	yes	complemented
91	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#474	C₂²	1	2	yes	complemented
93	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#469	C₂²	1	2	yes	—
95	C₃₁×#468	C₂²	1	2	yes	complemented
96	C₃₁×#466	C₂²	1	2	yes	—
97	C₃₁×#466	C₂²	1	2	yes	complemented
98	C₃₁×#466	C₂²	1	2	yes	complemented
99	C₃₁×#465	C₂²	1	2	yes	complemented
100	C₃₁×#463	C₂²	1	2	yes	complemented
101	C₃₁×#463	C₂²	1	2	yes	complemented
102	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#459	C₂²	1	1	yes	characteristic
104	C₃₁×#459	C₂²	1	1	yes	characteristic
105	C₃₁×#459	C₂²	1	1	yes	characteristic
106	C₃₁×#459	C₂²	1	2	yes	complemented
107	C₃₁×#449	C₂²	1	1	yes	characteristic
108	C₃₁×#449	C₂²	1	1	yes	characteristic
109	C₃₁×#447	C₂²	1	2	yes	—
110	C₃₁×#447	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×#442	C₂²	1	2	yes	—
114	C₃₁×#442	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₃₁	C₂²	1	2	yes	—
120	C₄×D₈×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	—	2	1	no	—
137	C₂×#41×C₃₁	—	2	1	no	—
138	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₃₁	—	2	1	no	—
140	C₂²×Q₈×C₃₁	—	2	1	no	—
141	C₂²×D₄×C₃₁	—	2	1	no	—
142	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₃₁	C₂³	1	2	yes	—
148	C₂×D₈×C₃₁	C₂³	1	2	yes	—
149	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
151	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
152	C₃₁×C₄⋊Q₈	—	2	2	no	—
153	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
155	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃₁×#127	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	D₄	1	2	yes	—
165	C₃₁×#125	—	2	2	no	—
166	C₃₁×#125	D₄	1	1	yes	characteristic
167	C₃₁×#125	C₂³	1	2	yes	—
168	C₃₁×#125	C₂³	1	2	yes	—
169	C₃₁×#124	—	2	1	no	—
170	C₃₁×#124	—	2	1	no	—
171	C₃₁×#124	—	2	2	no	—
172	C₃₁×#124	—	2	2	no	—
173	C₃₁×#124	—	2	2	no	—
174	C₃₁×#124	—	2	2	no	—
175	C₃₁×#124	—	2	2	no	—
176	C₃₁×#124	—	2	2	no	—
177	C₃₁×#124	—	2	1	no	—
178	C₃₁×#124	—	2	1	no	—
179	C₃₁×#124	D₄	1	1	yes	characteristic
180	C₃₁×#124	C₂³	1	2	yes	—
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	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	D₄	1	2	yes	—
189	C₃₁×C₂²⋊Q₈	—	2	1	no	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	1	no	—
192	C₃₁×C₂²⋊Q₈	—	2	1	no	—
193	C₃₁×C₂²⋊Q₈	—	2	1	no	—
194	C₃₁×C₂²⋊Q₈	—	2	1	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
202	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₃₁×#121	—	2	1	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	—	2	2	no	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	—	2	1	no	—
208	C₃₁×#121	—	2	1	no	—
209	C₃₁×#121	—	2	1	no	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	2	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	D₄	1	1	yes	characteristic
214	C₃₁×#121	C₂³	1	2	yes	—
215	C₃₁×#121	C₂³	1	2	yes	—
216	C₃₁×#121	C₂³	1	1	yes	characteristic
217	C₃₁×#121	C₂³	1	1	yes	characteristic
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#121	C₂³	1	2	yes	—
220	C₃₁×#120	—	2	2	no	—
221	C₃₁×#120	—	2	2	no	—
222	C₄×Q₈×C₃₁	—	2	1	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₃₁	—	2	1	no	—
229	C₄×D₄×C₃₁	—	2	1	no	—
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	—	2	2	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₃₁	C₂³	1	2	yes	—
240	C₄×D₄×C₃₁	C₂³	1	2	yes	—
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	2	yes	—
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₃₁×#117	—	2	2	no	—
248	C₃₁×#117	—	2	1	no	—
249	C₃₁×#117	—	2	2	no	—
250	C₃₁×#117	—	2	1	no	—
251	C₃₁×#117	C₂³	1	2	yes	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₃₁×#117	C₂³	1	1	yes	characteristic
254	C₃₁×#117	C₂³	1	2	yes	—
255	C₃₁×#117	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
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	2	yes	—
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	2	yes	—
268	C₃₁×#107	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	2	yes	—
271	C₃₁×#106	C₂³	1	1	yes	characteristic
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
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	1	yes	characteristic
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#102	C₂³	1	1	yes	characteristic
289	C₃₁×#102	C₂³	1	2	yes	—
290	C₃₁×#102	C₂³	1	2	yes	—
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	1	yes	characteristic
294	C₃₁×#102	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	1	yes	characteristic
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	#41×C₃₁	—	8	2	no	—
317	#41×C₃₁	—	8	2	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	8	2	no	—
325	C₂×Q₈×C₃₁	—	8	2	no	—
326	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₃₁	—	2	4	no	—
329	C₂×D₄×C₃₁	—	2	1	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	1	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	1	no	—
338	C₂×D₄×C₃₁	—	2	1	no	—
339	C₂×D₄×C₃₁	—	2	1	no	—
340	C₂×D₄×C₃₁	—	2	1	no	—
341	C₂×D₄×C₃₁	—	4	2	no	—
342	C₂×D₄×C₃₁	—	8	2	no	—
343	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
344	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
345	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
346	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
347	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₃₁	—	2	2	no	—
350	C₂²×C₄×C₃₁	—	2	1	no	—
351	C₂²×C₄×C₃₁	—	2	1	no	—
352	C₂²×C₄×C₃₁	—	2	1	no	—
353	C₂²×C₄×C₃₁	—	2	1	no	—
354	C₂²×C₄×C₃₁	—	2	1	no	—
355	C₂²×C₄×C₃₁	—	2	2	no	—
356	C₂²×C₄×C₃₁	—	2	2	no	—
357	C₂²×C₄×C₃₁	—	2	2	no	—
358	C₂²×C₄×C₃₁	—	2	2	no	—
359	C₂²×C₄×C₃₁	—	2	2	no	—
360	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
364	SD₁₆×C₃₁	—	4	1	no	—
365	SD₁₆×C₃₁	—	4	1	no	—
366	D₈×C₃₁	—	2	2	no	—
367	D₈×C₃₁	—	2	2	no	—
368	D₈×C₃₁	—	4	2	no	—
369	D₈×C₃₁	—	4	2	no	—
370	M₁₆×C₃₁	—	4	2	no	—
371	C₂×C₈×C₃₁	—	4	2	no	—
372	C₂×C₈×C₃₁	—	4	2	no	—
373	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
378	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
379	C₄⋊C₄×C₃₁	—	2	1	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	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₂²⋊C₄×C₃₁	—	2	2	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	1	no	—
412	C₂²⋊C₄×C₃₁	—	2	2	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	1	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	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	1	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	1	no	—
428	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
433	C₄²×C₃₁	—	2	1	no	—
434	C₄²×C₃₁	—	2	1	no	—
435	C₄²×C₃₁	—	2	1	no	—
436	C₄²×C₃₁	—	2	2	no	—
437	C₄²×C₃₁	—	2	2	no	—
438	C₄²×C₃₁	—	2	2	no	—
439	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
442	C₄²×C₃₁	C₂⁴	1	2	yes	—
443	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
444	#62215	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
445	C₂³×C₃₁	—	2	1	no	—
446	C₂³×C₃₁	—	2	1	no	—
447	C₂³×C₃₁	—	2	1	no	—
448	C₂³×C₃₁	—	2	2	no	—
449	C₂³×C₃₁	—	4	4	no	—
450	C₂³×C₃₁	—	8	2	no	—
451	C₂³×C₃₁	—	8	2	no	—
452	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
453	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
454	Q₈×C₃₁	—	2	2	no	—
455	Q₈×C₃₁	—	2	1	no	—
456	Q₈×C₃₁	—	2	1	no	—
457	Q₈×C₃₁	—	4	2	no	—
458	Q₈×C₃₁	—	4	2	no	—
459	Q₈×C₃₁	—	8	1	no	—
460	Q₈×C₃₁	—	8	2	no	—
461	Q₈×C₃₁	—	8	2	no	—
462	Q₈×C₃₁	—	8	1	no	—
463	D₄×C₃₁	—	2	2	no	—
464	D₄×C₃₁	—	2	1	no	—
465	D₄×C₃₁	—	2	1	no	—
466	D₄×C₃₁	—	2	2	no	—
467	D₄×C₃₁	—	2	1	no	—
468	D₄×C₃₁	—	2	1	no	—
469	D₄×C₃₁	—	2	1	no	—
470	D₄×C₃₁	—	2	2	no	—
471	D₄×C₃₁	—	4	2	no	—
472	D₄×C₃₁	—	4	4	no	—
473	D₄×C₃₁	—	4	2	no	—
474	D₄×C₃₁	—	4	2	no	—
475	D₄×C₃₁	—	8	1	no	—
476	D₄×C₃₁	—	8	1	no	—
477	D₄×C₃₁	—	8	1	no	—
478	D₄×C₃₁	—	8	2	no	—
479	D₄×C₃₁	—	8	2	no	—
480	D₄×C₃₁	—	8	1	no	—
481	D₄×C₃₁	—	8	1	no	—
482	D₄×C₃₁	—	8	2	no	—
483	D₄×C₃₁	—	8	2	no	—
484	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
485	C₂×C₄×C₃₁	—	2	2	no	—
486	C₂×C₄×C₃₁	—	2	2	no	—
487	C₂×C₄×C₃₁	—	2	1	no	—
488	C₂×C₄×C₃₁	—	2	1	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	2	1	no	—
492	C₂×C₄×C₃₁	—	2	2	no	—
493	C₂×C₄×C₃₁	—	2	1	no	—
494	C₂×C₄×C₃₁	—	2	1	no	—
495	C₂×C₄×C₃₁	—	2	2	no	—
496	C₂×C₄×C₃₁	—	2	2	no	—
497	C₂×C₄×C₃₁	—	2	1	no	—
498	C₂×C₄×C₃₁	—	4	1	no	—
499	C₂×C₄×C₃₁	—	4	2	no	—
500	C₂×C₄×C₃₁	—	4	2	no	—
501	C₂×C₄×C₃₁	—	4	2	no	—
502	C₂×C₄×C₃₁	—	4	2	no	—
503	C₂×C₄×C₃₁	—	8	1	no	—
504	C₂×C₄×C₃₁	—	8	2	no	—
505	C₂×C₄×C₃₁	—	8	2	no	—
506	C₂×C₄×C₃₁	—	8	2	no	—
507	C₂×C₄×C₃₁	—	8	2	no	—
508	C₂×C₄×C₃₁	—	8	2	no	—
509	C₂×C₄×C₃₁	—	8	2	no	—
510	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
519	C₈×C₃₁	—	2	1	no	—
520	C₈×C₃₁	—	2	1	no	—
521	C₈×C₃₁	—	2	2	no	—
522	C₈×C₃₁	—	2	1	no	—
523	C₈×C₃₁	—	2	2	no	—
524	C₈×C₃₁	—	2	1	no	—
525	#3547	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3514	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3384	C₂×C₃₁	1	1	yes	characteristic, complemented
528	Q₈×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3373	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3361	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3353	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3347	C₂×C₃₁	1	2	yes	complemented
533	#3341	C₂×C₃₁	1	2	yes	complemented
534	#3340	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3325	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3319	C₂×C₃₁	1	2	yes	complemented
537	#3297	C₂×C₃₁	1	2	yes	complemented
538	#3294	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3257	C₂×C₃₁	1	2	yes	complemented
540	#3245	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3243	C₂×C₃₁	1	2	yes	complemented
542	#3228	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3122	C₂×C₃₁	1	2	yes	complemented
544	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3081	C₂×C₃₁	1	2	yes	complemented
546	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#2994	C₂×C₃₁	1	1	yes	characteristic, complemented
548	C₂²×C₃₁	—	2	1	no	—
549	C₂²×C₃₁	—	2	2	no	—
550	C₂²×C₃₁	—	2	1	no	—
551	C₂²×C₃₁	—	2	2	no	—
552	C₂²×C₃₁	—	2	2	no	—
553	C₂²×C₃₁	—	2	1	no	—
554	C₂²×C₃₁	—	2	2	no	—
555	C₂²×C₃₁	—	4	1	no	—
556	C₂²×C₃₁	—	4	1	no	—
557	C₂²×C₃₁	—	4	1	no	—
558	C₂²×C₃₁	—	4	2	no	—
559	C₂²×C₃₁	—	4	1	no	—
560	C₂²×C₃₁	—	4	2	no	—
561	C₂²×C₃₁	—	4	1	no	—
562	C₂²×C₃₁	—	4	1	no	—
563	C₂²×C₃₁	—	4	1	no	—
564	C₂²×C₃₁	—	4	1	no	—
565	C₂²×C₃₁	—	4	2	no	—
566	C₂²×C₃₁	—	16	4	no	—
567	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
568	C₄×C₃₁	—	2	1	no	—
569	C₄×C₃₁	—	2	1	no	—
570	C₄×C₃₁	—	2	2	no	—
571	C₄×C₃₁	—	2	1	no	—
572	C₄×C₃₁	—	2	2	no	—
573	C₄×C₃₁	—	2	1	no	—
574	C₄×C₃₁	—	2	2	no	—
575	C₄×C₃₁	—	4	1	no	—
576	C₄×C₃₁	—	4	2	no	—
577	C₄×C₃₁	—	4	1	no	—
578	C₄×C₃₁	—	4	1	no	—
579	C₄×C₃₁	—	4	1	no	—
580	C₄×C₃₁	—	4	1	no	—
581	C₄×C₃₁	—	4	2	no	—
582	C₄×C₃₁	—	4	2	no	—
583	C₄×C₃₁	#576	1	2	yes	—
584	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
585	C₄×C₃₁	#585	1	1	yes	characteristic
586	#562	—	2	2	no	—
587	#559	C₂²×C₃₁	1	1	yes	characteristic
588	#556	C₂²×C₃₁	1	1	yes	characteristic
589	#555	C₂²×C₃₁	1	1	yes	characteristic
590	#555	C₂²×C₃₁	1	2	yes	—
591	#555	C₂²×C₃₁	1	2	yes	complemented
592	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
593	#553	C₂²×C₃₁	1	2	yes	complemented
594	#552	—	2	1	no	—
595	#551	—	2	2	no	—
596	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
597	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
598	#548	—	2	1	no	—
599	#548	—	2	1	no	—
600	#547	C₂²×C₃₁	1	1	yes	characteristic
601	#546	—	2	1	no	—
602	#546	C₂²×C₃₁	1	2	yes	—
603	D₄²	C₂²×C₃₁	1	1	yes	characteristic
604	#544	C₂²×C₃₁	1	2	yes	complemented
605	#542	—	2	2	no	—
606	#542	C₂²×C₃₁	1	2	yes	—
607	#540	C₂²×C₃₁	1	2	yes	complemented
608	#538	—	2	2	no	—
609	#537	—	2	1	no	—
610	#536	—	2	1	no	—
611	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
612	#532	C₂²×C₃₁	1	1	yes	characteristic
613	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
614	#529	—	2	1	no	—
615	#529	C₂²×C₃₁	1	1	yes	characteristic
616	C₂×#124	—	2	1	no	—
617	#518	C₂²×C₃₁	1	2	yes	—
618	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
619	#501	C₂²×C₃₁	1	2	yes	complemented
620	#500	C₂²×C₃₁	1	2	yes	complemented
621	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
622	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
623	#489	C₂²×C₃₁	1	2	yes	complemented
624	#488	C₂²×C₃₁	1	2	yes	complemented
625	#486	C₂²×C₃₁	1	1	yes	characteristic
626	#486	C₂²×C₃₁	1	1	yes	characteristic
627	#485	C₂²×C₃₁	1	2	yes	complemented
628	#484	C₂²×C₃₁	1	2	yes	complemented
629	#482	C₂²×C₃₁	1	2	yes	—
630	#482	C₂²×C₃₁	1	2	yes	complemented
631	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
632	#482	C₂²×C₃₁	1	2	yes	complemented
633	#482	C₂²×C₃₁	1	2	yes	complemented
634	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	#482	C₂²×C₃₁	1	2	yes	complemented
636	#480	C₂²×C₃₁	1	2	yes	—
637	#479	C₂²×C₃₁	1	2	yes	complemented
638	#478	C₂²×C₃₁	1	2	yes	—
639	#478	C₂²×C₃₁	1	2	yes	—
640	#478	C₂²×C₃₁	1	2	yes	complemented
641	#478	C₂²×C₃₁	1	2	yes	complemented
642	#478	C₂²×C₃₁	1	2	yes	complemented
643	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
645	#476	C₂²×C₃₁	1	1	yes	characteristic
646	#476	C₂²×C₃₁	1	1	yes	characteristic
647	#476	C₂²×C₃₁	1	2	yes	complemented
648	#476	C₂²×C₃₁	1	2	yes	complemented
649	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#474	C₂²×C₃₁	1	1	yes	characteristic
651	#474	C₂²×C₃₁	1	2	yes	—
652	#474	C₂²×C₃₁	1	2	yes	complemented
653	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	#474	C₂²×C₃₁	1	2	yes	complemented
655	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	#469	C₂²×C₃₁	1	2	yes	—
657	#468	C₂²×C₃₁	1	2	yes	complemented
658	#466	C₂²×C₃₁	1	2	yes	—
659	#466	C₂²×C₃₁	1	2	yes	complemented
660	#466	C₂²×C₃₁	1	2	yes	complemented
661	#465	C₂²×C₃₁	1	2	yes	complemented
662	#463	C₂²×C₃₁	1	2	yes	complemented
663	#463	C₂²×C₃₁	1	2	yes	complemented
664	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	#459	C₂²×C₃₁	1	1	yes	characteristic
666	#459	C₂²×C₃₁	1	1	yes	characteristic
667	#459	C₂²×C₃₁	1	1	yes	characteristic
668	#459	C₂²×C₃₁	1	2	yes	complemented
669	#449	C₂²×C₃₁	1	1	yes	characteristic
670	#449	C₂²×C₃₁	1	1	yes	characteristic
671	#447	C₂²×C₃₁	1	2	yes	—
672	#447	C₂²×C₃₁	1	2	yes	—
673	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
674	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
675	#442	C₂²×C₃₁	1	2	yes	—
676	#442	C₂²×C₃₁	1	2	yes	complemented
677	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
678	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
680	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
681	C₄×D₈	C₂²×C₃₁	1	2	yes	—
682	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
683	#436	C₂²×C₃₁	1	1	yes	characteristic
684	#435	C₂²×C₃₁	1	2	yes	complemented
685	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
686	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
687	#433	C₂²×C₃₁	1	2	yes	complemented
688	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
689	#428	C₂²×C₃₁	1	2	yes	complemented
690	#427	C₂²×C₃₁	1	2	yes	complemented
691	#427	C₂²×C₃₁	1	2	yes	complemented
692	#424	C₂²×C₃₁	1	2	yes	complemented
693	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
694	#418	C₂²×C₃₁	1	2	yes	—
695	#416	C₂²×C₃₁	1	2	yes	—
696	C₂×#102	C₂²×C₃₁	1	2	yes	—
697	C₂×C₃₁	—	4	1	no	—
698	C₂×C₃₁	—	4	2	no	—
699	C₂×C₃₁	—	4	2	no	—
700	C₂×C₃₁	—	8	1	no	—
701	C₂×C₃₁	—	8	1	no	—
702	C₂×C₃₁	—	8	2	no	—
703	C₂×C₃₁	#3489	1	1	yes	characteristic
704	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
705	C₂×C₃₁	#3584	1	1	yes	characteristic
706	C₂×#41	—	2	1	no	—
707	C₂×#41	—	2	1	no	—
708	C₂×#41	—	2	1	no	—
709	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
710	C₂²×Q₈	—	2	1	no	—
711	C₂²×Q₈	—	2	1	no	—
712	C₂²×D₄	—	2	1	no	—
713	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
714	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
715	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
716	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
717	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
718	C₂×D₈	C₂³×C₃₁	1	2	yes	—
719	C₂×D₈	C₂³×C₃₁	1	2	yes	—
720	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
721	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
722	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
723	C₄⋊Q₈	—	2	2	no	—
724	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
727	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
729	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
730	#127	C₂³×C₃₁	1	1	yes	characteristic
731	#127	C₂³×C₃₁	1	1	yes	characteristic
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	D₄×C₃₁	1	2	yes	—
736	#125	—	2	2	no	—
737	#125	D₄×C₃₁	1	1	yes	characteristic
738	#125	C₂³×C₃₁	1	2	yes	—
739	#125	C₂³×C₃₁	1	2	yes	—
740	#124	—	2	1	no	—
741	#124	—	2	1	no	—
742	#124	—	2	2	no	—
743	#124	—	2	2	no	—
744	#124	—	2	2	no	—
745	#124	—	2	2	no	—
746	#124	—	2	2	no	—
747	#124	—	2	2	no	—
748	#124	—	2	1	no	—
749	#124	—	2	1	no	—
750	#124	D₄×C₃₁	1	1	yes	characteristic
751	#124	C₂³×C₃₁	1	2	yes	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	D₄×C₃₁	1	2	yes	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
773	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
774	#121	—	2	1	no	—
775	#121	—	2	2	no	—
776	#121	—	2	2	no	—
777	#121	—	2	2	no	—
778	#121	—	2	1	no	—
779	#121	—	2	1	no	—
780	#121	—	2	1	no	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	D₄×C₃₁	1	1	yes	characteristic
785	#121	C₂³×C₃₁	1	2	yes	—
786	#121	C₂³×C₃₁	1	1	yes	characteristic
787	#121	C₂³×C₃₁	1	1	yes	characteristic
788	#121	C₂³×C₃₁	1	2	yes	—
789	#121	C₂³×C₃₁	1	2	yes	—
790	#121	C₂³×C₃₁	1	2	yes	—
791	#120	—	2	2	no	—
792	#120	—	2	2	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	—	2	1	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
808	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₃₁	1	2	yes	—
810	C₄×D₄	C₂³×C₃₁	1	2	yes	—
811	C₄×D₄	C₂³×C₃₁	1	2	yes	—
812	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₃₁	1	2	yes	—
815	C₄×D₄	C₂³×C₃₁	1	2	yes	—
816	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₃₁	1	2	yes	—
818	#117	—	2	2	no	—
819	#117	—	2	1	no	—
820	#117	—	2	2	no	—
821	#117	—	2	1	no	—
822	#117	C₂³×C₃₁	1	1	yes	characteristic
823	#117	C₂³×C₃₁	1	2	yes	—
824	#117	C₂³×C₃₁	1	2	yes	—
825	#117	C₂³×C₃₁	1	2	yes	—
826	#117	C₂³×C₃₁	1	2	yes	—
827	C₂×C₄⋊C₄	—	2	1	no	—
828	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
829	C₂×C₂²⋊C₄	—	2	2	no	—
830	C₂×C₂²⋊C₄	—	2	2	no	—
831	C₂×C₂²⋊C₄	—	2	2	no	—
832	C₂×C₄²	—	2	1	no	—
833	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
834	#107	C₂³×C₃₁	1	2	yes	—
835	#107	C₂³×C₃₁	1	2	yes	—
836	#107	C₂³×C₃₁	1	2	yes	—
837	#107	C₂³×C₃₁	1	2	yes	—
838	#107	C₂³×C₃₁	1	2	yes	—
839	#107	C₂³×C₃₁	1	1	yes	characteristic
840	#107	C₂³×C₃₁	1	1	yes	characteristic
841	#107	C₂³×C₃₁	1	2	yes	—
842	#106	C₂³×C₃₁	1	1	yes	characteristic
843	#106	C₂³×C₃₁	1	2	yes	—
844	#106	C₂³×C₃₁	1	2	yes	—
845	#106	C₂³×C₃₁	1	2	yes	—
846	#106	C₂³×C₃₁	1	1	yes	characteristic
847	#106	C₂³×C₃₁	1	2	yes	—
848	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
849	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
850	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
851	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
853	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
854	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
855	#103	C₂³×C₃₁	1	2	yes	—
856	#103	C₂³×C₃₁	1	2	yes	—
857	#103	C₂³×C₃₁	1	1	yes	characteristic
858	#103	C₂³×C₃₁	1	1	yes	characteristic
859	#102	C₂³×C₃₁	1	1	yes	characteristic
860	#102	C₂³×C₃₁	1	2	yes	—
861	#102	C₂³×C₃₁	1	2	yes	—
862	#102	C₂³×C₃₁	1	2	yes	—
863	#102	C₂³×C₃₁	1	2	yes	—
864	#102	C₂³×C₃₁	1	1	yes	characteristic
865	#102	C₂³×C₃₁	1	2	yes	—
866	#102	C₂³×C₃₁	1	2	yes	—
867	#102	C₂³×C₃₁	1	2	yes	—
868	#102	C₂³×C₃₁	1	1	yes	characteristic
869	#102	C₂³×C₃₁	1	1	yes	characteristic
870	#102	C₂³×C₃₁	1	1	yes	characteristic
871	#102	C₂³×C₃₁	1	2	yes	—
872	#102	C₂³×C₃₁	1	1	yes	characteristic
873	#102	C₂³×C₃₁	1	2	yes	—
874	#102	C₂³×C₃₁	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
876	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
877	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
879	#97	C₂³×C₃₁	1	2	yes	—
880	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
881	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
882	C₄×C₈	C₂³×C₃₁	1	2	yes	—
883	C₃₁	#62215	1	1	yes	characteristic, direct product factor, Sylow
884	C₂⁴	—	2	2	no	—
885	#41	—	2	2	no	—
886	#41	—	4	1	no	—
887	#41	—	8	2	no	—
888	#41	—	8	2	no	—
889	#41	—	8	2	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	1	no	—
892	C₂×Q₈	—	2	1	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	2	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	8	2	no	—
897	C₂×Q₈	—	8	2	no	—
898	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
899	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
900	C₂×D₄	—	2	4	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	4	2	no	—
914	C₂×D₄	—	8	2	no	—
915	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
916	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
917	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
918	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
919	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
920	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
933	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
935	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
936	SD₁₆	—	4	1	no	—
937	SD₁₆	—	4	1	no	—
938	D₈	—	2	2	no	—
939	D₈	—	2	2	no	—
940	D₈	—	4	2	no	—
941	D₈	—	4	2	no	—
942	M₁₆	—	4	2	no	—
943	C₂×C₈	—	4	2	no	—
944	C₂×C₈	—	4	2	no	—
945	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
946	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
947	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
948	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
950	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
966	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
967	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
968	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
969	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
970	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
972	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1001	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1002	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1003	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1004	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1012	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1013	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1014	C₄²	C₂⁴×C₃₁	1	2	yes	—
1015	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1016	C₂³	—	2	1	no	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	2	no	—
1020	C₂³	—	4	4	no	—
1021	C₂³	—	8	2	no	—
1022	C₂³	—	8	2	no	—
1023	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1024	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	4	2	no	—
1029	Q₈	—	4	2	no	—
1030	Q₈	—	8	1	no	—
1031	Q₈	—	8	2	no	—
1032	Q₈	—	8	2	no	—
1033	Q₈	—	8	1	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	1	no	—
1039	D₄	—	2	1	no	—
1040	D₄	—	2	1	no	—
1041	D₄	—	2	2	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	4	4	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	4	2	no	—
1046	D₄	—	8	1	no	—
1047	D₄	—	8	1	no	—
1048	D₄	—	8	1	no	—
1049	D₄	—	8	2	no	—
1050	D₄	—	8	2	no	—
1051	D₄	—	8	1	no	—
1052	D₄	—	8	1	no	—
1053	D₄	—	8	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	4	2	no	—
1074	C₂×C₄	—	8	1	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	8	2	no	—
1077	C₂×C₄	—	8	2	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	—	8	2	no	—
1080	C₂×C₄	—	8	2	no	—
1081	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1082	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1083	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1084	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1085	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1087	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1088	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1089	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1090	C₈	—	2	1	no	—
1091	C₈	—	2	1	no	—
1092	C₈	—	2	2	no	—
1093	C₈	—	2	1	no	—
1094	C₈	—	2	2	no	—
1095	C₈	—	2	1	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	2	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	16	4	no	—
1115	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	2	2	no	—
1120	C₄	—	2	1	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	2	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	2	no	—
1131	C₄	C₃₁×#576	1	2	yes	—
1132	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1133	C₄	C₃₁×#585	1	1	yes	characteristic
1134	C₂	—	4	2	no	—
1135	C₂	—	4	1	no	—
1136	C₂	—	4	2	no	—
1137	C₂	—	8	2	no	—
1138	C₂	—	8	1	no	—
1139	C₂	—	8	1	no	—
1140	C₂	C₃₁×#3489	1	1	yes	characteristic
1141	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1142	C₂	C₃₁×#3584	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×#3547	C₂	semidirect
2. C₃₁×#3514	C₂	semidirect
3. C₃₁×#3384	C₂	semidirect
4. Q₈×D₈×C₃₁	C₂	semidirect
5. C₃₁×#3373	C₂	semidirect
6. C₃₁×#3361	C₂	semidirect
7. C₃₁×#3353	C₂	semidirect
8. C₃₁×#3347	C₂	semidirect
9. C₃₁×#3341	C₂	semidirect
10. C₃₁×#3340	C₂	semidirect
11. C₃₁×#3325	C₂	semidirect
12. C₃₁×#3319	C₂	semidirect
13. C₃₁×#3297	C₂	semidirect
14. C₃₁×#3294	C₂	semidirect
15. C₃₁×#3257	C₂	semidirect
16. C₃₁×#3245	C₂	semidirect
17. C₃₁×#3243	C₂	semidirect
18. C₃₁×#3228	C₂	semidirect
19. C₃₁×#3122	C₂	semidirect
20. C₃₁×#3106	C₂	semidirect
21. C₃₁×#3081	C₂	semidirect
22. C₃₁×#3076	C₂	semidirect
23. C₃₁×#2994	C₂	semidirect
29. C₃₁×#555	C₂²	semidirect
30. C₃₁×#554	C₂²	semidirect
31. C₃₁×#553	C₂²	semidirect
35. D₄×Q₈×C₃₁	C₂²	semidirect
42. C₃₁×#544	C₂²	semidirect
45. C₃₁×#540	C₂²	semidirect
49. C₃₁×#533	C₂²	semidirect
51. C₃₁×#532	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#500	C₂²	semidirect
59. C₃₁×#500	C₂²	semidirect
60. C₃₁×#498	C₂²	semidirect
61. C₃₁×#489	C₂²	semidirect
62. C₃₁×#488	C₂²	semidirect
65. C₃₁×#485	C₂²	semidirect
66. C₃₁×#484	C₂²	semidirect
68. C₃₁×#482	C₂²	semidirect
69. C₃₁×#482	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#482	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×#476	C₂²	semidirect
87. C₃₁×#475	C₂²	semidirect
90. C₃₁×#474	C₂²	semidirect
91. C₃₁×#474	C₂²	semidirect
92. C₃₁×#474	C₂²	semidirect
93. C₃₁×#474	C₂²	semidirect
95. C₃₁×#468	C₂²	semidirect
97. C₃₁×#466	C₂²	semidirect
98. C₃₁×#466	C₂²	semidirect
99. C₃₁×#465	C₂²	semidirect
100. C₃₁×#463	C₂²	semidirect
101. C₃₁×#463	C₂²	semidirect
102. C₃₁×#460	C₂²	semidirect
106. C₃₁×#459	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₈×Q₈×C₃₁	C₂²	semidirect
114. C₃₁×#442	C₂²	semidirect
115. C₄×SD₁₆×C₃₁	C₂²	semidirect
116. C₄×SD₁₆×C₃₁	C₂²	semidirect
120. C₄×D₈×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
444. #62215	C₃₁	direct (N × H)
525. #3547	C₂×C₃₁	semidirect
526. #3514	C₂×C₃₁	semidirect
527. #3384	C₂×C₃₁	semidirect
528. Q₈×D₈	C₂×C₃₁	semidirect
529. #3373	C₂×C₃₁	semidirect
530. #3361	C₂×C₃₁	semidirect
531. #3353	C₂×C₃₁	semidirect
532. #3347	C₂×C₃₁	semidirect
533. #3341	C₂×C₃₁	semidirect
534. #3340	C₂×C₃₁	semidirect
535. #3325	C₂×C₃₁	semidirect
536. #3319	C₂×C₃₁	semidirect
537. #3297	C₂×C₃₁	semidirect
538. #3294	C₂×C₃₁	semidirect
539. #3257	C₂×C₃₁	semidirect
540. #3245	C₂×C₃₁	semidirect
541. #3243	C₂×C₃₁	semidirect
542. #3228	C₂×C₃₁	semidirect
543. #3122	C₂×C₃₁	semidirect
544. #3106	C₂×C₃₁	semidirect
545. #3081	C₂×C₃₁	semidirect
546. #3076	C₂×C₃₁	semidirect
547. #2994	C₂×C₃₁	semidirect
591. #555	C₂²×C₃₁	semidirect
592. #554	C₂²×C₃₁	semidirect
593. #553	C₂²×C₃₁	semidirect
597. D₄×Q₈	C₂²×C₃₁	semidirect
604. #544	C₂²×C₃₁	semidirect
607. #540	C₂²×C₃₁	semidirect
611. #533	C₂²×C₃₁	semidirect
613. #532	C₂²×C₃₁	semidirect
619. #501	C₂²×C₃₁	semidirect
620. #500	C₂²×C₃₁	semidirect
621. #500	C₂²×C₃₁	semidirect
622. #498	C₂²×C₃₁	semidirect
623. #489	C₂²×C₃₁	semidirect
624. #488	C₂²×C₃₁	semidirect
627. #485	C₂²×C₃₁	semidirect
628. #484	C₂²×C₃₁	semidirect
630. #482	C₂²×C₃₁	semidirect
631. #482	C₂²×C₃₁	semidirect
632. #482	C₂²×C₃₁	semidirect
633. #482	C₂²×C₃₁	semidirect
634. #482	C₂²×C₃₁	semidirect
635. #482	C₂²×C₃₁	semidirect
637. #479	C₂²×C₃₁	semidirect
640. #478	C₂²×C₃₁	semidirect
641. #478	C₂²×C₃₁	semidirect
642. #478	C₂²×C₃₁	semidirect
643. #477	C₂²×C₃₁	semidirect
644. #477	C₂²×C₃₁	semidirect
647. #476	C₂²×C₃₁	semidirect
648. #476	C₂²×C₃₁	semidirect
649. #475	C₂²×C₃₁	semidirect
652. #474	C₂²×C₃₁	semidirect
653. #474	C₂²×C₃₁	semidirect
654. #474	C₂²×C₃₁	semidirect
655. #474	C₂²×C₃₁	semidirect
657. #468	C₂²×C₃₁	semidirect
659. #466	C₂²×C₃₁	semidirect
660. #466	C₂²×C₃₁	semidirect
661. #465	C₂²×C₃₁	semidirect
662. #463	C₂²×C₃₁	semidirect
663. #463	C₂²×C₃₁	semidirect
664. #460	C₂²×C₃₁	semidirect
668. #459	C₂²×C₃₁	semidirect
673. #446	C₂²×C₃₁	semidirect
674. C₈×Q₈	C₂²×C₃₁	semidirect
676. #442	C₂²×C₃₁	semidirect
677. C₄×SD₁₆	C₂²×C₃₁	semidirect
678. C₄×SD₁₆	C₂²×C₃₁	semidirect
682. C₄×D₈	C₂²×C₃₁	semidirect
684. #435	C₂²×C₃₁	semidirect
686. C₈×D₄	C₂²×C₃₁	semidirect
687. #433	C₂²×C₃₁	semidirect
688. #431	C₂²×C₃₁	semidirect
689. #428	C₂²×C₃₁	semidirect
690. #427	C₂²×C₃₁	semidirect
691. #427	C₂²×C₃₁	semidirect
692. #424	C₂²×C₃₁	semidirect
693. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
883. C₃₁	#62215	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×#3547	2
C₃₁×#3514	2
C₃₁×#3384	2
Q₈×D₈×C₃₁	2
C₃₁×#3373	2
C₃₁×#3361	2
C₃₁×#3353	2
C₃₁×#3347	2
C₃₁×#3341	2
C₃₁×#3340	2
C₃₁×#3325	2
C₃₁×#3319	2
C₃₁×#3297	2
C₃₁×#3294	2
C₃₁×#3257	2
C₃₁×#3245	2
C₃₁×#3243	2
C₃₁×#3228	2
C₃₁×#3122	2
C₃₁×#3106	2
C₃₁×#3081	2
C₃₁×#3076	2
C₃₁×#2994	2
#62215	31

Subgroups — C31×#62215 #21518974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62215 #21518974