Subgroups — C₃₁×#61926 #21518685

Order 7936.

1774 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3403	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3396	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3391	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3361	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3358	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3220	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3212	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3124	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3119	C₂	1	2	yes	maximal, complemented
21	C₃₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#562	—	2	2	no	—
25	C₃₁×#559	C₂²	1	2	yes	—
26	C₃₁×#559	C₂²	1	2	yes	—
27	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#559	C₂²	1	2	yes	complemented
29	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#556	C₂²	1	1	yes	characteristic
31	C₃₁×#556	C₂²	1	1	yes	characteristic
32	C₃₁×#555	—	2	1	no	—
33	C₃₁×#554	C₂²	1	2	yes	complemented
34	C₃₁×#553	—	2	2	no	—
35	C₃₁×#550	C₂²	1	1	yes	characteristic
36	C₃₁×#550	C₂²	1	1	yes	characteristic
37	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
38	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#548	—	2	1	no	—
40	C₃₁×#547	—	2	1	no	—
41	C₃₁×#547	—	2	1	no	—
42	C₃₁×#542	—	2	1	no	—
43	C₃₁×#542	C₂²	1	2	yes	—
44	C₃₁×#540	C₂²	1	2	yes	—
45	C₃₁×#539	—	2	2	no	—
46	C₃₁×#538	—	2	2	no	—
47	C₃₁×#536	—	2	1	no	—
48	C₃₁×#535	C₂²	1	2	yes	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#532	C₂²	1	1	yes	characteristic
51	C₃₁×#532	C₂²	1	1	yes	characteristic
52	C₃₁×#529	C₂²	1	1	yes	characteristic
53	C₃₁×#525	—	2	1	no	—
54	C₃₁×#525	—	2	1	no	—
55	C₃₁×#520	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#496	C₂²	1	2	yes	—
58	C₃₁×#496	C₂²	1	2	yes	—
59	C₃₁×#495	C₂²	1	2	yes	—
60	C₃₁×#495	C₂²	1	2	yes	complemented
61	C₃₁×#493	C₂²	1	2	yes	—
62	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#490	C₂²	1	2	yes	—
65	C₃₁×#489	C₂²	1	2	yes	—
66	C₃₁×#488	C₂²	1	2	yes	—
67	C₃₁×#488	C₂²	1	2	yes	complemented
68	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#486	C₂²	1	2	yes	—
70	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#484	C₂²	1	1	yes	characteristic
72	C₃₁×#481	C₂²	1	1	yes	characteristic
73	C₃₁×#480	C₂²	1	2	yes	—
74	C₃₁×#479	C₂²	1	2	yes	complemented
75	C₃₁×#478	C₂²	1	1	yes	characteristic
76	C₃₁×#478	C₂²	1	1	yes	characteristic
77	C₃₁×#478	C₂²	1	2	yes	complemented
78	C₃₁×#477	C₂²	1	2	yes	complemented
79	C₃₁×#474	C₂²	1	1	yes	characteristic
80	C₃₁×#474	C₂²	1	1	yes	characteristic
81	C₃₁×#474	C₂²	1	2	yes	complemented
82	C₃₁×#464	C₂²	1	2	yes	—
83	C₃₁×#464	C₂²	1	2	yes	complemented
84	C₃₁×#463	C₂²	1	1	yes	characteristic
85	C₃₁×#463	C₂²	1	1	yes	characteristic
86	C₃₁×#463	C₂²	1	2	yes	—
87	C₃₁×#463	C₂²	1	2	yes	—
88	C₃₁×#463	C₂²	1	2	yes	—
89	C₃₁×#463	C₂²	1	2	yes	complemented
90	C₃₁×#463	C₂²	1	2	yes	complemented
91	C₃₁×#463	C₂²	1	2	yes	complemented
92	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#460	C₂²	1	2	yes	—
95	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#460	C₂²	1	2	yes	complemented
97	C₃₁×#459	C₂²	1	1	yes	characteristic
98	C₃₁×#459	C₂²	1	1	yes	characteristic
99	C₃₁×#459	C₂²	1	2	yes	—
100	C₃₁×#459	C₂²	1	2	yes	—
101	C₃₁×#459	C₂²	1	2	yes	—
102	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#459	C₂²	1	2	yes	complemented
104	C₃₁×#452	C₂²	1	2	yes	—
105	C₃₁×#450	C₂²	1	1	yes	characteristic
106	C₃₁×#449	C₂²	1	2	yes	—
107	C₃₁×#449	C₂²	1	2	yes	—
108	C₃₁×#449	C₂²	1	2	yes	—
109	C₃₁×#447	C₂²	1	2	yes	—
110	C₃₁×#447	C₂²	1	1	yes	characteristic
111	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#446	C₂²	1	2	yes	complemented
114	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
116	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
117	C₃₁×#442	C₂²	1	2	yes	complemented
118	C₃₁×#440	C₂²	1	2	yes	complemented
119	C₃₁×#440	C₂²	1	2	yes	complemented
120	C₃₁×#440	C₂²	1	2	yes	complemented
121	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
122	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
124	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
125	C₄×D₈×C₃₁	C₂²	1	2	yes	—
126	C₄×D₈×C₃₁	C₂²	1	2	yes	—
127	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
128	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
129	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
130	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
131	C₃₁×#433	C₂²	1	2	yes	—
132	C₃₁×#433	C₂²	1	2	yes	—
133	C₃₁×#431	C₂²	1	1	yes	characteristic
134	C₃₁×#431	C₂²	1	1	yes	characteristic
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	—	2	1	no	—
139	C₂×#41×C₃₁	C₂³	1	2	yes	—
140	C₂²×Q₈×C₃₁	—	2	1	no	—
141	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₃₁	—	2	1	no	—
143	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×D₈×C₃₁	C₂³	1	2	yes	—
151	C₂×D₈×C₃₁	C₂³	1	2	yes	—
152	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₃₁	C₂³	1	2	yes	—
155	C₂×D₈×C₃₁	C₂³	1	2	yes	—
156	C₂×D₈×C₃₁	C₂³	1	2	yes	—
157	C₃₁×C₄⋊Q₈	—	2	1	no	—
158	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
159	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₃₁×#127	C₂³	1	2	yes	—
164	C₃₁×#127	C₂³	1	1	yes	characteristic
165	C₃₁×#127	C₂³	1	2	yes	—
166	C₃₁×#127	C₂³	1	1	yes	characteristic
167	C₃₁×#127	C₂³	1	2	yes	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	1	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	D₄	1	2	yes	—
174	C₃₁×#125	C₂³	1	1	yes	characteristic
175	C₃₁×#125	C₂³	1	2	yes	—
176	C₃₁×#124	—	2	1	no	—
177	C₃₁×#124	—	2	2	no	—
178	C₃₁×#124	—	2	2	no	—
179	C₃₁×#124	—	2	2	no	—
180	C₃₁×#124	—	2	2	no	—
181	C₃₁×#124	—	2	1	no	—
182	C₃₁×#124	C₂³	1	2	yes	—
183	C₃₁×#124	C₂³	1	1	yes	characteristic
184	C₃₁×#124	C₂³	1	2	yes	—
185	C₃₁×#124	C₂³	1	2	yes	—
186	C₃₁×#124	C₂³	1	2	yes	—
187	C₃₁×#123	—	2	1	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
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	—	2	2	no	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×#123	—	2	2	no	—
197	C₃₁×#123	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	1	no	—
199	C₃₁×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	1	no	—
206	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
207	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
209	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₃₁×#121	—	2	1	no	—
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	1	no	—
213	C₃₁×#121	—	2	1	no	—
214	C₃₁×#121	—	2	1	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	—	2	2	no	—
217	C₃₁×#121	—	2	2	no	—
218	C₃₁×#121	—	2	2	no	—
219	C₃₁×#121	—	2	2	no	—
220	C₃₁×#121	—	2	1	no	—
221	C₃₁×#121	—	2	2	no	—
222	C₃₁×#121	—	2	2	no	—
223	C₃₁×#121	C₂³	1	2	yes	—
224	C₃₁×#121	C₂³	1	1	yes	characteristic
225	C₃₁×#120	—	2	2	no	—
226	C₃₁×#120	—	2	2	no	—
227	C₄×Q₈×C₃₁	—	2	1	no	—
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	2	yes	—
232	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	—	2	2	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	2	no	—
241	C₄×D₄×C₃₁	—	2	2	no	—
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	—	2	1	no	—
245	C₄×D₄×C₃₁	—	2	1	no	—
246	C₄×D₄×C₃₁	—	2	1	no	—
247	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₃₁	C₂³	1	2	yes	—
251	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₃₁	C₂³	1	2	yes	—
254	C₄×D₄×C₃₁	C₂³	1	2	yes	—
255	C₄×D₄×C₃₁	C₂³	1	2	yes	—
256	C₄×D₄×C₃₁	C₂³	1	2	yes	—
257	C₄×D₄×C₃₁	C₂³	1	2	yes	—
258	C₃₁×#117	—	2	2	no	—
259	C₃₁×#117	—	2	1	no	—
260	C₃₁×#117	—	2	1	no	—
261	C₃₁×#117	—	2	1	no	—
262	C₃₁×#117	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
264	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
267	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
268	C₃₁×#107	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#107	C₂³	1	2	yes	—
271	C₃₁×#107	C₂³	1	1	yes	characteristic
272	C₃₁×#106	C₂³	1	1	yes	characteristic
273	C₃₁×#106	C₂³	1	1	yes	characteristic
274	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
279	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×#103	C₂³	1	1	yes	characteristic
283	C₃₁×#103	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	2	yes	—
288	C₃₁×#102	C₂³	1	1	yes	characteristic
289	C₃₁×#102	C₂³	1	2	yes	—
290	C₃₁×#102	C₂³	1	1	yes	characteristic
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	1	yes	characteristic
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
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	2	yes	—
302	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₃₁×#97	C₂³	1	2	yes	—
306	C₃₁×#97	C₂³	1	2	yes	—
307	C₄×C₈×C₃₁	C₂³	1	2	yes	—
308	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	2	yes	—
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	C₂⁴×C₃₁	—	2	1	no	—
313	#41×C₃₁	—	4	2	no	—
314	#41×C₃₁	—	4	2	no	—
315	#41×C₃₁	—	8	2	no	—
316	#41×C₃₁	—	8	2	no	—
317	#41×C₃₁	—	8	2	no	—
318	#41×C₃₁	—	8	2	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	8	2	no	—
322	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
325	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₃₁	—	2	2	no	—
328	C₂×D₄×C₃₁	—	2	1	no	—
329	C₂×D₄×C₃₁	—	2	2	no	—
330	C₂×D₄×C₃₁	—	2	1	no	—
331	C₂×D₄×C₃₁	—	2	1	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	—	2	2	no	—
341	C₂×D₄×C₃₁	—	4	1	no	—
342	C₂×D₄×C₃₁	—	4	1	no	—
343	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
345	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
346	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
347	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₃₁	—	2	1	no	—
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	2	no	—
354	C₂²×C₄×C₃₁	—	2	2	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	1	no	—
359	C₂²×C₄×C₃₁	—	2	1	no	—
360	C₂²×C₄×C₃₁	—	2	2	no	—
361	C₂²×C₄×C₃₁	—	8	2	no	—
362	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
365	Q₁₆×C₃₁	—	4	2	no	—
366	SD₁₆×C₃₁	—	4	1	no	—
367	SD₁₆×C₃₁	—	4	2	no	—
368	SD₁₆×C₃₁	—	4	2	no	—
369	SD₁₆×C₃₁	—	4	2	no	—
370	SD₁₆×C₃₁	—	4	2	no	—
371	SD₁₆×C₃₁	—	4	1	no	—
372	D₈×C₃₁	—	4	2	no	—
373	D₈×C₃₁	—	4	1	no	—
374	D₈×C₃₁	—	4	2	no	—
375	D₈×C₃₁	—	4	2	no	—
376	D₈×C₃₁	—	4	2	no	—
377	D₈×C₃₁	—	4	1	no	—
378	D₈×C₃₁	—	4	2	no	—
379	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
381	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
383	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₂²⋊C₄×C₃₁	—	2	1	no	—
414	C₂²⋊C₄×C₃₁	—	2	1	no	—
415	C₂²⋊C₄×C₃₁	—	2	1	no	—
416	C₂²⋊C₄×C₃₁	—	2	1	no	—
417	C₂²⋊C₄×C₃₁	—	2	1	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	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	1	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	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	1	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	no	—
435	C₂²⋊C₄×C₃₁	—	2	2	no	—
436	C₂²⋊C₄×C₃₁	—	2	2	no	—
437	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
439	C₄²×C₃₁	—	2	2	no	—
440	C₄²×C₃₁	—	2	2	no	—
441	C₄²×C₃₁	—	2	1	no	—
442	C₄²×C₃₁	—	2	2	no	—
443	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
446	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
447	C₄²×C₃₁	C₂⁴	1	2	yes	—
448	C₄²×C₃₁	C₂⁴	1	2	yes	—
449	#61926	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
450	C₂³×C₃₁	—	2	2	no	—
451	C₂³×C₃₁	—	2	1	no	—
452	C₂³×C₃₁	—	2	1	no	—
453	C₂³×C₃₁	—	2	1	no	—
454	C₂³×C₃₁	—	2	2	no	—
455	C₂³×C₃₁	—	4	2	no	—
456	C₂³×C₃₁	—	8	1	no	—
457	C₂³×C₃₁	—	8	1	no	—
458	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
459	Q₈×C₃₁	—	2	2	no	—
460	Q₈×C₃₁	—	2	2	no	—
461	Q₈×C₃₁	—	2	1	no	—
462	Q₈×C₃₁	—	2	2	no	—
463	Q₈×C₃₁	—	2	1	no	—
464	Q₈×C₃₁	—	2	2	no	—
465	Q₈×C₃₁	—	4	2	no	—
466	Q₈×C₃₁	—	4	2	no	—
467	Q₈×C₃₁	—	8	2	no	—
468	D₄×C₃₁	—	2	1	no	—
469	D₄×C₃₁	—	2	2	no	—
470	D₄×C₃₁	—	2	2	no	—
471	D₄×C₃₁	—	2	1	no	—
472	D₄×C₃₁	—	2	1	no	—
473	D₄×C₃₁	—	2	2	no	—
474	D₄×C₃₁	—	2	1	no	—
475	D₄×C₃₁	—	2	1	no	—
476	D₄×C₃₁	—	2	1	no	—
477	D₄×C₃₁	—	2	2	no	—
478	D₄×C₃₁	—	4	2	no	—
479	D₄×C₃₁	—	4	4	no	—
480	D₄×C₃₁	—	4	2	no	—
481	D₄×C₃₁	—	4	2	no	—
482	D₄×C₃₁	—	8	1	no	—
483	D₄×C₃₁	—	8	1	no	—
484	D₄×C₃₁	—	8	2	no	—
485	D₄×C₃₁	—	8	2	no	—
486	D₄×C₃₁	—	8	2	no	—
487	D₄×C₃₁	—	8	2	no	—
488	D₄×C₃₁	—	8	2	no	—
489	D₄×C₃₁	—	8	2	no	—
490	D₄×C₃₁	—	8	1	no	—
491	D₄×C₃₁	—	8	2	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	1	no	—
496	C₂×C₄×C₃₁	—	2	2	no	—
497	C₂×C₄×C₃₁	—	2	1	no	—
498	C₂×C₄×C₃₁	—	2	1	no	—
499	C₂×C₄×C₃₁	—	2	1	no	—
500	C₂×C₄×C₃₁	—	2	2	no	—
501	C₂×C₄×C₃₁	—	2	1	no	—
502	C₂×C₄×C₃₁	—	4	1	no	—
503	C₂×C₄×C₃₁	—	4	4	no	—
504	C₂×C₄×C₃₁	—	4	2	no	—
505	C₂×C₄×C₃₁	—	4	2	no	—
506	C₂×C₄×C₃₁	—	4	2	no	—
507	C₂×C₄×C₃₁	—	8	2	no	—
508	C₂×C₄×C₃₁	—	8	1	no	—
509	C₂×C₄×C₃₁	—	8	1	no	—
510	C₂×C₄×C₃₁	—	8	2	no	—
511	C₂×C₄×C₃₁	—	8	2	no	—
512	C₂×C₄×C₃₁	—	8	2	no	—
513	C₂×C₄×C₃₁	—	8	2	no	—
514	C₂×C₄×C₃₁	—	8	2	no	—
515	C₂×C₄×C₃₁	—	8	1	no	—
516	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
524	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
526	C₈×C₃₁	—	2	1	no	—
527	C₈×C₃₁	—	2	1	no	—
528	C₈×C₃₁	—	2	2	no	—
529	C₈×C₃₁	—	2	2	no	—
530	C₈×C₃₁	—	2	1	no	—
531	C₈×C₃₁	—	2	1	no	—
532	#3554	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3506	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3403	C₂×C₃₁	1	2	yes	complemented
535	#3399	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3397	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3396	C₂×C₃₁	1	2	yes	complemented
538	#3394	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3391	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3370	C₂×C₃₁	1	2	yes	complemented
541	#3368	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3367	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3364	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3361	C₂×C₃₁	1	2	yes	complemented
545	#3358	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3224	C₂×C₃₁	1	2	yes	complemented
547	#3220	C₂×C₃₁	1	2	yes	complemented
548	#3212	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3207	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3124	C₂×C₃₁	1	2	yes	complemented
551	#3119	C₂×C₃₁	1	2	yes	complemented
552	#3105	C₂×C₃₁	1	1	yes	characteristic, complemented
553	#3100	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#2986	C₂×C₃₁	1	1	yes	characteristic, complemented
555	C₂²×C₃₁	—	2	1	no	—
556	C₂²×C₃₁	—	2	1	no	—
557	C₂²×C₃₁	—	2	1	no	—
558	C₂²×C₃₁	—	4	2	no	—
559	C₂²×C₃₁	—	4	2	no	—
560	C₂²×C₃₁	—	4	1	no	—
561	C₂²×C₃₁	—	4	1	no	—
562	C₂²×C₃₁	—	4	1	no	—
563	C₂²×C₃₁	—	4	2	no	—
564	C₂²×C₃₁	—	4	1	no	—
565	C₂²×C₃₁	—	4	1	no	—
566	C₂²×C₃₁	—	4	1	no	—
567	C₂²×C₃₁	—	4	2	no	—
568	C₂²×C₃₁	—	4	1	no	—
569	C₂²×C₃₁	—	4	1	no	—
570	C₂²×C₃₁	—	4	1	no	—
571	C₂²×C₃₁	—	4	2	no	—
572	C₂²×C₃₁	—	4	2	no	—
573	C₂²×C₃₁	—	8	4	no	—
574	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
575	C₄×C₃₁	—	2	1	no	—
576	C₄×C₃₁	—	2	1	no	—
577	C₄×C₃₁	—	2	2	no	—
578	C₄×C₃₁	—	2	2	no	—
579	C₄×C₃₁	—	2	1	no	—
580	C₄×C₃₁	—	2	1	no	—
581	C₄×C₃₁	—	2	2	no	—
582	C₄×C₃₁	—	2	2	no	—
583	C₄×C₃₁	—	4	1	no	—
584	C₄×C₃₁	—	4	2	no	—
585	C₄×C₃₁	—	4	1	no	—
586	C₄×C₃₁	—	4	1	no	—
587	C₄×C₃₁	—	4	1	no	—
588	C₄×C₃₁	—	4	1	no	—
589	C₄×C₃₁	—	4	2	no	—
590	C₄×C₃₁	#576	1	2	yes	—
591	C₄×C₃₁	#585	1	1	yes	characteristic
592	C₄×C₃₁	#585	1	1	yes	characteristic
593	#562	—	2	2	no	—
594	#559	C₂²×C₃₁	1	2	yes	—
595	#559	C₂²×C₃₁	1	2	yes	—
596	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
597	#559	C₂²×C₃₁	1	2	yes	complemented
598	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
599	#556	C₂²×C₃₁	1	1	yes	characteristic
600	#556	C₂²×C₃₁	1	1	yes	characteristic
601	#555	—	2	1	no	—
602	#554	C₂²×C₃₁	1	2	yes	complemented
603	#553	—	2	2	no	—
604	#550	C₂²×C₃₁	1	1	yes	characteristic
605	#550	C₂²×C₃₁	1	1	yes	characteristic
606	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
607	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
608	#548	—	2	1	no	—
609	#547	—	2	1	no	—
610	#547	—	2	1	no	—
611	#542	—	2	1	no	—
612	#542	C₂²×C₃₁	1	2	yes	—
613	#540	C₂²×C₃₁	1	2	yes	—
614	#539	—	2	2	no	—
615	#538	—	2	2	no	—
616	#536	—	2	1	no	—
617	#535	C₂²×C₃₁	1	2	yes	—
618	#533	C₂²×C₃₁	1	1	yes	characteristic
619	#532	C₂²×C₃₁	1	1	yes	characteristic
620	#532	C₂²×C₃₁	1	1	yes	characteristic
621	#529	C₂²×C₃₁	1	1	yes	characteristic
622	#525	—	2	1	no	—
623	#525	—	2	1	no	—
624	#520	C₂²×C₃₁	1	2	yes	—
625	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
626	#496	C₂²×C₃₁	1	2	yes	—
627	#496	C₂²×C₃₁	1	2	yes	—
628	#495	C₂²×C₃₁	1	2	yes	—
629	#495	C₂²×C₃₁	1	2	yes	complemented
630	#493	C₂²×C₃₁	1	2	yes	—
631	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
632	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
633	#490	C₂²×C₃₁	1	2	yes	—
634	#489	C₂²×C₃₁	1	2	yes	—
635	#488	C₂²×C₃₁	1	2	yes	—
636	#488	C₂²×C₃₁	1	2	yes	complemented
637	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	#486	C₂²×C₃₁	1	2	yes	—
639	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	#484	C₂²×C₃₁	1	1	yes	characteristic
641	#481	C₂²×C₃₁	1	1	yes	characteristic
642	#480	C₂²×C₃₁	1	2	yes	—
643	#479	C₂²×C₃₁	1	2	yes	complemented
644	#478	C₂²×C₃₁	1	1	yes	characteristic
645	#478	C₂²×C₃₁	1	1	yes	characteristic
646	#478	C₂²×C₃₁	1	2	yes	complemented
647	#477	C₂²×C₃₁	1	2	yes	complemented
648	#474	C₂²×C₃₁	1	1	yes	characteristic
649	#474	C₂²×C₃₁	1	1	yes	characteristic
650	#474	C₂²×C₃₁	1	2	yes	complemented
651	#464	C₂²×C₃₁	1	2	yes	—
652	#464	C₂²×C₃₁	1	2	yes	complemented
653	#463	C₂²×C₃₁	1	1	yes	characteristic
654	#463	C₂²×C₃₁	1	1	yes	characteristic
655	#463	C₂²×C₃₁	1	2	yes	—
656	#463	C₂²×C₃₁	1	2	yes	—
657	#463	C₂²×C₃₁	1	2	yes	—
658	#463	C₂²×C₃₁	1	2	yes	complemented
659	#463	C₂²×C₃₁	1	2	yes	complemented
660	#463	C₂²×C₃₁	1	2	yes	complemented
661	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
663	#460	C₂²×C₃₁	1	2	yes	—
664	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	#460	C₂²×C₃₁	1	2	yes	complemented
666	#459	C₂²×C₃₁	1	1	yes	characteristic
667	#459	C₂²×C₃₁	1	1	yes	characteristic
668	#459	C₂²×C₃₁	1	2	yes	—
669	#459	C₂²×C₃₁	1	2	yes	—
670	#459	C₂²×C₃₁	1	2	yes	—
671	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
672	#459	C₂²×C₃₁	1	2	yes	complemented
673	#452	C₂²×C₃₁	1	2	yes	—
674	#450	C₂²×C₃₁	1	1	yes	characteristic
675	#449	C₂²×C₃₁	1	2	yes	—
676	#449	C₂²×C₃₁	1	2	yes	—
677	#449	C₂²×C₃₁	1	2	yes	—
678	#447	C₂²×C₃₁	1	2	yes	—
679	#447	C₂²×C₃₁	1	1	yes	characteristic
680	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
681	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
682	#446	C₂²×C₃₁	1	2	yes	complemented
683	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
685	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
686	#442	C₂²×C₃₁	1	2	yes	complemented
687	#440	C₂²×C₃₁	1	2	yes	complemented
688	#440	C₂²×C₃₁	1	2	yes	complemented
689	#440	C₂²×C₃₁	1	2	yes	complemented
690	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
691	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
692	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
693	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
694	C₄×D₈	C₂²×C₃₁	1	2	yes	—
695	C₄×D₈	C₂²×C₃₁	1	2	yes	—
696	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
697	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
698	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
699	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
700	#433	C₂²×C₃₁	1	2	yes	—
701	#433	C₂²×C₃₁	1	2	yes	—
702	#431	C₂²×C₃₁	1	1	yes	characteristic
703	#431	C₂²×C₃₁	1	1	yes	characteristic
704	C₂×C₃₁	—	4	1	no	—
705	C₂×C₃₁	—	8	2	no	—
706	C₂×C₃₁	—	8	2	no	—
707	C₂×C₃₁	—	8	1	no	—
708	C₂×C₃₁	—	8	1	no	—
709	C₂×C₃₁	—	8	1	no	—
710	C₂×C₃₁	#3487	1	1	yes	characteristic
711	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
712	C₂×C₃₁	#3584	1	1	yes	characteristic
713	C₂×#41	—	2	1	no	—
714	C₂×#41	—	2	1	no	—
715	C₂×#41	—	2	1	no	—
716	C₂×#41	—	2	1	no	—
717	C₂×#41	C₂³×C₃₁	1	2	yes	—
718	C₂²×Q₈	—	2	1	no	—
719	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
720	C₂³×C₄	—	2	1	no	—
721	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
723	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
724	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
725	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
726	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
727	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
728	C₂×D₈	C₂³×C₃₁	1	2	yes	—
729	C₂×D₈	C₂³×C₃₁	1	2	yes	—
730	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
731	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
732	C₂×D₈	C₂³×C₃₁	1	2	yes	—
733	C₂×D₈	C₂³×C₃₁	1	2	yes	—
734	C₂×D₈	C₂³×C₃₁	1	2	yes	—
735	C₄⋊Q₈	—	2	1	no	—
736	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
737	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
738	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
739	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
740	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
741	#127	C₂³×C₃₁	1	1	yes	characteristic
742	#127	C₂³×C₃₁	1	1	yes	characteristic
743	#127	C₂³×C₃₁	1	2	yes	—
744	#127	C₂³×C₃₁	1	2	yes	—
745	#127	C₂³×C₃₁	1	2	yes	—
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#126	—	2	2	no	—
749	#126	—	2	1	no	—
750	#125	—	2	2	no	—
751	#125	D₄×C₃₁	1	2	yes	—
752	#125	C₂³×C₃₁	1	1	yes	characteristic
753	#125	C₂³×C₃₁	1	2	yes	—
754	#124	—	2	1	no	—
755	#124	—	2	2	no	—
756	#124	—	2	2	no	—
757	#124	—	2	2	no	—
758	#124	—	2	2	no	—
759	#124	—	2	1	no	—
760	#124	C₂³×C₃₁	1	1	yes	characteristic
761	#124	C₂³×C₃₁	1	2	yes	—
762	#124	C₂³×C₃₁	1	2	yes	—
763	#124	C₂³×C₃₁	1	2	yes	—
764	#124	C₂³×C₃₁	1	2	yes	—
765	#123	—	2	1	no	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
785	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
786	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
788	#121	—	2	1	no	—
789	#121	—	2	1	no	—
790	#121	—	2	1	no	—
791	#121	—	2	1	no	—
792	#121	—	2	1	no	—
793	#121	—	2	2	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	1	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	C₂³×C₃₁	1	1	yes	characteristic
802	#121	C₂³×C₃₁	1	2	yes	—
803	#120	—	2	2	no	—
804	#120	—	2	2	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
807	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
808	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
810	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₃₁	1	2	yes	—
830	C₄×D₄	C₂³×C₃₁	1	2	yes	—
831	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₃₁	1	2	yes	—
833	C₄×D₄	C₂³×C₃₁	1	2	yes	—
834	C₄×D₄	C₂³×C₃₁	1	2	yes	—
835	C₄×D₄	C₂³×C₃₁	1	2	yes	—
836	#117	—	2	2	no	—
837	#117	—	2	1	no	—
838	#117	—	2	1	no	—
839	#117	—	2	1	no	—
840	#117	C₂³×C₃₁	1	2	yes	—
841	C₂×C₄⋊C₄	—	2	2	no	—
842	C₂×C₄⋊C₄	—	2	2	no	—
843	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
844	C₂×C₂²⋊C₄	—	2	1	no	—
845	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
846	#107	C₂³×C₃₁	1	1	yes	characteristic
847	#107	C₂³×C₃₁	1	2	yes	—
848	#107	C₂³×C₃₁	1	2	yes	—
849	#107	C₂³×C₃₁	1	1	yes	characteristic
850	#106	C₂³×C₃₁	1	1	yes	characteristic
851	#106	C₂³×C₃₁	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
855	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
856	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
857	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
858	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
859	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
860	#103	C₂³×C₃₁	1	1	yes	characteristic
861	#103	C₂³×C₃₁	1	1	yes	characteristic
862	#103	C₂³×C₃₁	1	2	yes	—
863	#103	C₂³×C₃₁	1	2	yes	—
864	#103	C₂³×C₃₁	1	2	yes	—
865	#103	C₂³×C₃₁	1	2	yes	—
866	#102	C₂³×C₃₁	1	1	yes	characteristic
867	#102	C₂³×C₃₁	1	2	yes	—
868	#102	C₂³×C₃₁	1	1	yes	characteristic
869	#102	C₂³×C₃₁	1	2	yes	—
870	#102	C₂³×C₃₁	1	2	yes	—
871	#102	C₂³×C₃₁	1	2	yes	—
872	#102	C₂³×C₃₁	1	1	yes	characteristic
873	#102	C₂³×C₃₁	1	1	yes	characteristic
874	#102	C₂³×C₃₁	1	2	yes	—
875	#102	C₂³×C₃₁	1	2	yes	—
876	#102	C₂³×C₃₁	1	1	yes	characteristic
877	#102	C₂³×C₃₁	1	1	yes	characteristic
878	#102	C₂³×C₃₁	1	2	yes	—
879	#102	C₂³×C₃₁	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
881	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
883	#97	C₂³×C₃₁	1	2	yes	—
884	#97	C₂³×C₃₁	1	2	yes	—
885	C₄×C₈	C₂³×C₃₁	1	2	yes	—
886	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
887	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
888	C₄×C₈	C₂³×C₃₁	1	2	yes	—
889	C₄×C₈	C₂³×C₃₁	1	2	yes	—
890	C₃₁	#61926	1	1	yes	characteristic, direct product factor, Sylow
891	C₂⁴	—	2	1	no	—
892	#41	—	4	2	no	—
893	#41	—	4	2	no	—
894	#41	—	8	2	no	—
895	#41	—	8	2	no	—
896	#41	—	8	2	no	—
897	#41	—	8	2	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	8	2	no	—
901	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
902	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
903	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
904	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
905	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
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	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	4	1	no	—
921	C₂×D₄	—	4	1	no	—
922	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
923	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
924	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
925	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
926	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	8	2	no	—
941	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
942	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
944	Q₁₆	—	4	2	no	—
945	SD₁₆	—	4	1	no	—
946	SD₁₆	—	4	2	no	—
947	SD₁₆	—	4	2	no	—
948	SD₁₆	—	4	2	no	—
949	SD₁₆	—	4	2	no	—
950	SD₁₆	—	4	1	no	—
951	D₈	—	4	2	no	—
952	D₈	—	4	1	no	—
953	D₈	—	4	2	no	—
954	D₈	—	4	2	no	—
955	D₈	—	4	2	no	—
956	D₈	—	4	1	no	—
957	D₈	—	4	2	no	—
958	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
960	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
962	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
980	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
981	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
982	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
983	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
984	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
985	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
986	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
987	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
988	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
989	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
990	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
991	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1023	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1024	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1025	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1026	C₄²	C₂⁴×C₃₁	1	2	yes	—
1027	C₄²	C₂⁴×C₃₁	1	2	yes	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	2	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	2	no	—
1033	C₂³	—	4	2	no	—
1034	C₂³	—	8	1	no	—
1035	C₂³	—	8	1	no	—
1036	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1037	Q₈	—	2	2	no	—
1038	Q₈	—	2	2	no	—
1039	Q₈	—	2	1	no	—
1040	Q₈	—	2	2	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	2	2	no	—
1043	Q₈	—	4	2	no	—
1044	Q₈	—	4	2	no	—
1045	Q₈	—	8	2	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	2	2	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	2	no	—
1052	D₄	—	2	1	no	—
1053	D₄	—	2	1	no	—
1054	D₄	—	2	1	no	—
1055	D₄	—	2	2	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	4	no	—
1058	D₄	—	4	2	no	—
1059	D₄	—	4	2	no	—
1060	D₄	—	8	1	no	—
1061	D₄	—	8	1	no	—
1062	D₄	—	8	2	no	—
1063	D₄	—	8	2	no	—
1064	D₄	—	8	2	no	—
1065	D₄	—	8	2	no	—
1066	D₄	—	8	2	no	—
1067	D₄	—	8	2	no	—
1068	D₄	—	8	1	no	—
1069	D₄	—	8	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	4	1	no	—
1081	C₂×C₄	—	4	4	no	—
1082	C₂×C₄	—	4	2	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	—	8	1	no	—
1087	C₂×C₄	—	8	1	no	—
1088	C₂×C₄	—	8	2	no	—
1089	C₂×C₄	—	8	2	no	—
1090	C₂×C₄	—	8	2	no	—
1091	C₂×C₄	—	8	2	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	1	no	—
1094	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1095	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1096	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1097	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1098	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1099	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1101	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1102	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1103	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1104	C₈	—	2	1	no	—
1105	C₈	—	2	1	no	—
1106	C₈	—	2	2	no	—
1107	C₈	—	2	2	no	—
1108	C₈	—	2	1	no	—
1109	C₈	—	2	1	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	1	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	4	2	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	8	4	no	—
1129	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1130	C₄	—	2	1	no	—
1131	C₄	—	2	1	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	4	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	1	no	—
1145	C₄	C₃₁×#576	1	2	yes	—
1146	C₄	C₃₁×#585	1	1	yes	characteristic
1147	C₄	C₃₁×#585	1	1	yes	characteristic
1148	C₂	—	4	1	no	—
1149	C₂	—	8	1	no	—
1150	C₂	—	8	1	no	—
1151	C₂	—	8	2	no	—
1152	C₂	—	8	1	no	—
1153	C₂	—	8	2	no	—
1154	C₂	C₃₁×#3487	1	1	yes	characteristic
1155	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1156	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3554	C₂	semidirect
2. C₃₁×#3506	C₂	semidirect
3. C₃₁×#3403	C₂	semidirect
4. C₃₁×#3399	C₂	semidirect
5. C₃₁×#3397	C₂	semidirect
6. C₃₁×#3396	C₂	semidirect
7. C₃₁×#3394	C₂	semidirect
8. C₃₁×#3391	C₂	semidirect
9. C₃₁×#3370	C₂	semidirect
10. C₃₁×#3368	C₂	semidirect
11. C₃₁×#3367	C₂	semidirect
12. C₃₁×#3364	C₂	semidirect
13. C₃₁×#3361	C₂	semidirect
14. C₃₁×#3358	C₂	semidirect
15. C₃₁×#3224	C₂	semidirect
16. C₃₁×#3220	C₂	semidirect
17. C₃₁×#3212	C₂	semidirect
18. C₃₁×#3207	C₂	semidirect
19. C₃₁×#3124	C₂	semidirect
20. C₃₁×#3119	C₂	semidirect
21. C₃₁×#3105	C₂	semidirect
22. C₃₁×#3100	C₂	semidirect
23. C₃₁×#2986	C₂	semidirect
27. C₃₁×#559	C₂²	semidirect
28. C₃₁×#559	C₂²	semidirect
29. C₃₁×#557	C₂²	semidirect
33. C₃₁×#554	C₂²	semidirect
37. C₃₁×#550	C₂²	semidirect
38. D₄×Q₈×C₃₁	C₂²	semidirect
60. C₃₁×#495	C₂²	semidirect
62. C₃₁×#493	C₂²	semidirect
63. C₃₁×#492	C₂²	semidirect
67. C₃₁×#488	C₂²	semidirect
68. C₃₁×#487	C₂²	semidirect
70. C₃₁×#486	C₂²	semidirect
74. C₃₁×#479	C₂²	semidirect
77. C₃₁×#478	C₂²	semidirect
78. C₃₁×#477	C₂²	semidirect
81. C₃₁×#474	C₂²	semidirect
83. C₃₁×#464	C₂²	semidirect
89. C₃₁×#463	C₂²	semidirect
90. C₃₁×#463	C₂²	semidirect
91. C₃₁×#463	C₂²	semidirect
92. C₃₁×#462	C₂²	semidirect
93. C₃₁×#461	C₂²	semidirect
95. C₃₁×#460	C₂²	semidirect
96. C₃₁×#460	C₂²	semidirect
102. C₃₁×#459	C₂²	semidirect
103. C₃₁×#459	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₃₁×#446	C₂²	semidirect
113. C₃₁×#446	C₂²	semidirect
114. C₈×Q₈×C₃₁	C₂²	semidirect
115. C₈×Q₈×C₃₁	C₂²	semidirect
116. C₈×Q₈×C₃₁	C₂²	semidirect
117. C₃₁×#442	C₂²	semidirect
118. C₃₁×#440	C₂²	semidirect
119. C₃₁×#440	C₂²	semidirect
120. C₃₁×#440	C₂²	semidirect
121. C₄×Q₁₆×C₃₁	C₂²	semidirect
124. C₄×SD₁₆×C₃₁	C₂²	semidirect
129. C₄×D₈×C₃₁	C₂²	semidirect
130. C₄×D₈×C₃₁	C₂²	semidirect
449. #61926	C₃₁	direct (N × H)
532. #3554	C₂×C₃₁	semidirect
533. #3506	C₂×C₃₁	semidirect
534. #3403	C₂×C₃₁	semidirect
535. #3399	C₂×C₃₁	semidirect
536. #3397	C₂×C₃₁	semidirect
537. #3396	C₂×C₃₁	semidirect
538. #3394	C₂×C₃₁	semidirect
539. #3391	C₂×C₃₁	semidirect
540. #3370	C₂×C₃₁	semidirect
541. #3368	C₂×C₃₁	semidirect
542. #3367	C₂×C₃₁	semidirect
543. #3364	C₂×C₃₁	semidirect
544. #3361	C₂×C₃₁	semidirect
545. #3358	C₂×C₃₁	semidirect
546. #3224	C₂×C₃₁	semidirect
547. #3220	C₂×C₃₁	semidirect
548. #3212	C₂×C₃₁	semidirect
549. #3207	C₂×C₃₁	semidirect
550. #3124	C₂×C₃₁	semidirect
551. #3119	C₂×C₃₁	semidirect
552. #3105	C₂×C₃₁	semidirect
553. #3100	C₂×C₃₁	semidirect
554. #2986	C₂×C₃₁	semidirect
596. #559	C₂²×C₃₁	semidirect
597. #559	C₂²×C₃₁	semidirect
598. #557	C₂²×C₃₁	semidirect
602. #554	C₂²×C₃₁	semidirect
606. #550	C₂²×C₃₁	semidirect
607. D₄×Q₈	C₂²×C₃₁	semidirect
629. #495	C₂²×C₃₁	semidirect
631. #493	C₂²×C₃₁	semidirect
632. #492	C₂²×C₃₁	semidirect
636. #488	C₂²×C₃₁	semidirect
637. #487	C₂²×C₃₁	semidirect
639. #486	C₂²×C₃₁	semidirect
643. #479	C₂²×C₃₁	semidirect
646. #478	C₂²×C₃₁	semidirect
647. #477	C₂²×C₃₁	semidirect
650. #474	C₂²×C₃₁	semidirect
652. #464	C₂²×C₃₁	semidirect
658. #463	C₂²×C₃₁	semidirect
659. #463	C₂²×C₃₁	semidirect
660. #463	C₂²×C₃₁	semidirect
661. #462	C₂²×C₃₁	semidirect
662. #461	C₂²×C₃₁	semidirect
664. #460	C₂²×C₃₁	semidirect
665. #460	C₂²×C₃₁	semidirect
671. #459	C₂²×C₃₁	semidirect
672. #459	C₂²×C₃₁	semidirect
680. #446	C₂²×C₃₁	semidirect
681. #446	C₂²×C₃₁	semidirect
682. #446	C₂²×C₃₁	semidirect
683. C₈×Q₈	C₂²×C₃₁	semidirect
684. C₈×Q₈	C₂²×C₃₁	semidirect
685. C₈×Q₈	C₂²×C₃₁	semidirect
686. #442	C₂²×C₃₁	semidirect
687. #440	C₂²×C₃₁	semidirect
688. #440	C₂²×C₃₁	semidirect
689. #440	C₂²×C₃₁	semidirect
690. C₄×Q₁₆	C₂²×C₃₁	semidirect
693. C₄×SD₁₆	C₂²×C₃₁	semidirect
698. C₄×D₈	C₂²×C₃₁	semidirect
699. C₄×D₈	C₂²×C₃₁	semidirect
890. C₃₁	#61926	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×#3554	2
C₃₁×#3506	2
C₃₁×#3403	2
C₃₁×#3399	2
C₃₁×#3397	2
C₃₁×#3396	2
C₃₁×#3394	2
C₃₁×#3391	2
C₃₁×#3370	2
C₃₁×#3368	2
C₃₁×#3367	2
C₃₁×#3364	2
C₃₁×#3361	2
C₃₁×#3358	2
C₃₁×#3224	2
C₃₁×#3220	2
C₃₁×#3212	2
C₃₁×#3207	2
C₃₁×#3124	2
C₃₁×#3119	2
C₃₁×#3105	2
C₃₁×#3100	2
C₃₁×#2986	2
#61926	31

Subgroups — C31×#61926 #21518685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61926 #21518685