Subgroups — C₃₁×#61927 #21518686

Order 7936.

1718 conjugacy classes of subgroups.

The subgroup lattice has 1130 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×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3401	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3394	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3393	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3392	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3371	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3365	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3362	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3360	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3222	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3212	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3125	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3120	C₂	1	2	yes	maximal, complemented
21	C₃₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	C₃₁×#559	C₂²	1	2	yes	—
26	C₃₁×#559	C₂²	1	2	yes	—
27	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#557	C₂²	1	2	yes	complemented
30	C₃₁×#556	—	2	1	no	—
31	C₃₁×#556	C₂²	1	1	yes	characteristic
32	C₃₁×#556	C₂²	1	1	yes	characteristic
33	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#556	C₂²	1	2	yes	complemented
35	C₃₁×#555	—	2	1	no	—
36	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#553	—	2	2	no	—
38	C₃₁×#552	—	2	1	no	—
39	C₃₁×#550	C₂²	1	1	yes	characteristic
40	C₃₁×#550	C₂²	1	1	yes	characteristic
41	C₃₁×#547	—	2	1	no	—
42	C₃₁×#544	—	2	1	no	—
43	C₃₁×#542	C₂²	1	2	yes	—
44	C₃₁×#541	—	2	1	no	—
45	C₃₁×#541	—	2	2	no	—
46	C₃₁×#541	C₂²	1	2	yes	—
47	C₃₁×#538	—	2	2	no	—
48	C₃₁×#535	C₂²	1	2	yes	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#533	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×#497	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×#494	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#492	C₂²	1	2	yes	—
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×#483	C₂²	1	2	yes	—
73	C₃₁×#481	C₂²	1	1	yes	characteristic
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×#476	C₂²	1	1	yes	characteristic
79	C₃₁×#476	C₂²	1	1	yes	characteristic
80	C₃₁×#476	C₂²	1	2	yes	complemented
81	C₃₁×#475	C₂²	1	2	yes	complemented
82	C₃₁×#464	C₂²	1	2	yes	—
83	C₃₁×#464	C₂²	1	2	yes	—
84	C₃₁×#464	C₂²	1	2	yes	—
85	C₃₁×#464	C₂²	1	2	yes	complemented
86	C₃₁×#464	C₂²	1	2	yes	complemented
87	C₃₁×#464	C₂²	1	2	yes	complemented
88	C₃₁×#463	C₂²	1	2	yes	—
89	C₃₁×#463	C₂²	1	1	yes	characteristic
90	C₃₁×#463	C₂²	1	1	yes	characteristic
91	C₃₁×#463	C₂²	1	2	yes	complemented
92	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#462	C₂²	1	2	yes	complemented
94	C₃₁×#461	C₂²	1	1	yes	characteristic
95	C₃₁×#461	C₂²	1	1	yes	characteristic
96	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#461	C₂²	1	2	yes	complemented
98	C₃₁×#460	C₂²	1	2	yes	—
99	C₃₁×#460	C₂²	1	2	yes	—
100	C₃₁×#460	C₂²	1	2	yes	—
101	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#459	C₂²	1	2	yes	—
103	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#452	C₂²	1	2	yes	—
105	C₃₁×#452	C₂²	1	2	yes	—
106	C₃₁×#452	C₂²	1	2	yes	—
107	C₃₁×#450	C₂²	1	2	yes	—
108	C₃₁×#450	C₂²	1	1	yes	characteristic
109	C₃₁×#449	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	1	yes	characteristic, complemented
116	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
117	C₃₁×#442	C₂²	1	2	yes	complemented
118	C₃₁×#441	C₂²	1	2	yes	complemented
119	C₃₁×#441	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	2	yes	—
123	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
124	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
125	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
127	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
128	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
129	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
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	C₂³	1	2	yes	—
138	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₃₁	—	2	1	no	—
140	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
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×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
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×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₃₁	C₂³	1	2	yes	—
154	C₃₁×C₄⋊Q₈	—	2	2	no	—
155	C₃₁×C₄⋊Q₈	—	2	2	no	—
156	C₃₁×C₄⋊Q₈	—	2	1	no	—
157	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
158	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
159	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×#127	C₂³	1	2	yes	—
165	C₃₁×#127	C₂³	1	1	yes	characteristic
166	C₃₁×#127	C₂³	1	2	yes	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	2	no	—
175	C₃₁×#126	—	2	1	no	—
176	C₃₁×#125	—	2	2	no	—
177	C₃₁×#125	—	2	2	no	—
178	C₃₁×#125	—	2	2	no	—
179	C₃₁×#125	—	2	2	no	—
180	C₃₁×#125	—	2	2	no	—
181	C₃₁×#125	—	2	1	no	—
182	C₃₁×#125	—	2	1	no	—
183	C₃₁×#125	D₄	1	2	yes	—
184	C₃₁×#125	C₂³	1	1	yes	characteristic
185	C₃₁×#125	C₂³	1	2	yes	—
186	C₃₁×#124	—	2	2	no	—
187	C₃₁×#124	—	2	2	no	—
188	C₃₁×#124	—	2	2	no	—
189	C₃₁×#124	C₂³	1	1	yes	characteristic
190	C₃₁×#124	C₂³	1	2	yes	—
191	C₃₁×#124	C₂³	1	2	yes	—
192	C₃₁×#124	C₂³	1	2	yes	—
193	C₃₁×#124	C₂³	1	2	yes	—
194	C₃₁×#123	—	2	1	no	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×#123	—	2	2	no	—
197	C₃₁×#123	—	2	2	no	—
198	C₃₁×#123	—	2	2	no	—
199	C₃₁×#123	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	1	no	—
201	C₃₁×C₂²⋊Q₈	—	2	1	no	—
202	C₃₁×C₂²⋊Q₈	—	2	1	no	—
203	C₃₁×C₂²⋊Q₈	—	2	1	no	—
204	C₃₁×C₂²⋊Q₈	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	1	no	—
206	C₃₁×C₂²⋊Q₈	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	—	2	2	no	—
208	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
211	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₃₁×#121	—	2	1	no	—
214	C₃₁×#121	—	2	1	no	—
215	C₃₁×#121	—	2	1	no	—
216	C₃₁×#121	—	2	1	no	—
217	C₃₁×#121	—	2	2	no	—
218	C₃₁×#121	—	2	2	no	—
219	C₃₁×#121	—	2	2	no	—
220	C₃₁×#121	—	2	2	no	—
221	C₃₁×#121	C₂³	1	1	yes	characteristic
222	C₃₁×#120	—	2	2	no	—
223	C₃₁×#120	—	2	2	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	—	2	1	no	—
226	C₄×Q₈×C₃₁	—	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	2	yes	—
233	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
234	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
235	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
238	C₄×D₄×C₃₁	—	2	1	no	—
239	C₄×D₄×C₃₁	—	2	2	no	—
240	C₄×D₄×C₃₁	—	2	2	no	—
241	C₄×D₄×C₃₁	—	2	2	no	—
242	C₄×D₄×C₃₁	—	2	2	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	1	yes	characteristic
251	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₃₁	C₂³	1	2	yes	—
253	C₄×D₄×C₃₁	C₂³	1	2	yes	—
254	C₄×D₄×C₃₁	C₂³	1	2	yes	—
255	C₃₁×#117	—	2	1	no	—
256	C₃₁×#117	—	2	2	no	—
257	C₃₁×#117	—	2	1	no	—
258	C₃₁×#117	—	2	1	no	—
259	C₃₁×#117	—	2	2	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	1	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	1	yes	characteristic
270	C₃₁×#106	C₂³	1	1	yes	characteristic
271	C₃₁×#106	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	1	yes	characteristic
273	C₃₁×#106	C₂³	1	2	yes	—
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	2	yes	—
284	C₃₁×#103	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#102	C₂³	1	1	yes	characteristic
291	C₃₁×#102	C₂³	1	1	yes	characteristic
292	C₃₁×#102	C₂³	1	1	yes	characteristic
293	C₃₁×#102	C₂³	1	1	yes	characteristic
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	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
308	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₃₁	C₂³	1	2	yes	—
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	C₂×Q₈×C₃₁	—	2	1	no	—
318	C₂×Q₈×C₃₁	—	2	2	no	—
319	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
320	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
322	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
323	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
325	C₂×D₄×C₃₁	—	2	2	no	—
326	C₂×D₄×C₃₁	—	2	1	no	—
327	C₂×D₄×C₃₁	—	2	1	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	1	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	4	1	no	—
335	C₂×D₄×C₃₁	—	4	1	no	—
336	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
337	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
338	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
339	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₃₁	—	2	1	no	—
341	C₂²×C₄×C₃₁	—	2	1	no	—
342	C₂²×C₄×C₃₁	—	2	2	no	—
343	C₂²×C₄×C₃₁	—	2	1	no	—
344	C₂²×C₄×C₃₁	—	2	1	no	—
345	C₂²×C₄×C₃₁	—	2	2	no	—
346	C₂²×C₄×C₃₁	—	2	2	no	—
347	C₂²×C₄×C₃₁	—	2	2	no	—
348	C₂²×C₄×C₃₁	—	2	1	no	—
349	C₂²×C₄×C₃₁	—	2	1	no	—
350	C₂²×C₄×C₃₁	—	8	2	no	—
351	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
353	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
354	Q₁₆×C₃₁	—	4	2	no	—
355	Q₁₆×C₃₁	—	4	2	no	—
356	Q₁₆×C₃₁	—	4	2	no	—
357	SD₁₆×C₃₁	—	4	2	no	—
358	SD₁₆×C₃₁	—	4	2	no	—
359	SD₁₆×C₃₁	—	4	2	no	—
360	SD₁₆×C₃₁	—	4	1	no	—
361	SD₁₆×C₃₁	—	4	2	no	—
362	SD₁₆×C₃₁	—	4	2	no	—
363	SD₁₆×C₃₁	—	4	2	no	—
364	SD₁₆×C₃₁	—	4	1	no	—
365	D₈×C₃₁	—	4	1	no	—
366	D₈×C₃₁	—	4	2	no	—
367	D₈×C₃₁	—	4	1	no	—
368	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
371	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
373	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₄⋊C₄×C₃₁	—	2	1	no	—
375	C₄⋊C₄×C₃₁	—	2	1	no	—
376	C₄⋊C₄×C₃₁	—	2	2	no	—
377	C₄⋊C₄×C₃₁	—	2	2	no	—
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	1	no	—
380	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	2	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
403	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
410	C₂²⋊C₄×C₃₁	—	2	2	no	—
411	C₂²⋊C₄×C₃₁	—	2	1	no	—
412	C₂²⋊C₄×C₃₁	—	2	1	no	—
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	2	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	1	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	2	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	1	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
433	C₄²×C₃₁	—	2	2	no	—
434	C₄²×C₃₁	—	2	2	no	—
435	C₄²×C₃₁	—	2	2	no	—
436	C₄²×C₃₁	—	2	1	no	—
437	C₄²×C₃₁	—	2	2	no	—
438	C₄²×C₃₁	—	2	2	no	—
439	C₄²×C₃₁	—	2	2	no	—
440	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
443	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
444	C₄²×C₃₁	C₂⁴	1	2	yes	—
445	C₄²×C₃₁	C₂⁴	1	2	yes	—
446	#61927	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂³×C₃₁	—	2	1	no	—
448	C₂³×C₃₁	—	2	1	no	—
449	C₂³×C₃₁	—	2	1	no	—
450	C₂³×C₃₁	—	2	2	no	—
451	C₂³×C₃₁	—	4	2	no	—
452	C₂³×C₃₁	—	8	1	no	—
453	C₂³×C₃₁	—	8	1	no	—
454	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
455	Q₈×C₃₁	—	2	2	no	—
456	Q₈×C₃₁	—	2	2	no	—
457	Q₈×C₃₁	—	2	1	no	—
458	Q₈×C₃₁	—	2	2	no	—
459	Q₈×C₃₁	—	2	2	no	—
460	Q₈×C₃₁	—	2	1	no	—
461	Q₈×C₃₁	—	2	2	no	—
462	Q₈×C₃₁	—	2	2	no	—
463	Q₈×C₃₁	—	4	2	no	—
464	Q₈×C₃₁	—	8	1	no	—
465	Q₈×C₃₁	—	8	2	no	—
466	D₄×C₃₁	—	2	1	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	—	2	1	no	—
472	D₄×C₃₁	—	2	1	no	—
473	D₄×C₃₁	—	2	2	no	—
474	D₄×C₃₁	—	4	2	no	—
475	D₄×C₃₁	—	4	4	no	—
476	D₄×C₃₁	—	4	2	no	—
477	D₄×C₃₁	—	8	1	no	—
478	D₄×C₃₁	—	8	2	no	—
479	D₄×C₃₁	—	8	2	no	—
480	D₄×C₃₁	—	8	2	no	—
481	D₄×C₃₁	—	8	2	no	—
482	D₄×C₃₁	—	8	1	no	—
483	C₂×C₄×C₃₁	—	2	2	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	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	1	no	—
493	C₂×C₄×C₃₁	—	2	2	no	—
494	C₂×C₄×C₃₁	—	4	1	no	—
495	C₂×C₄×C₃₁	—	4	4	no	—
496	C₂×C₄×C₃₁	—	4	2	no	—
497	C₂×C₄×C₃₁	—	4	2	no	—
498	C₂×C₄×C₃₁	—	4	2	no	—
499	C₂×C₄×C₃₁	—	8	2	no	—
500	C₂×C₄×C₃₁	—	8	1	no	—
501	C₂×C₄×C₃₁	—	8	1	no	—
502	C₂×C₄×C₃₁	—	8	2	no	—
503	C₂×C₄×C₃₁	—	8	2	no	—
504	C₂×C₄×C₃₁	—	8	1	no	—
505	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
515	C₈×C₃₁	—	2	1	no	—
516	C₈×C₃₁	—	2	2	no	—
517	C₈×C₃₁	—	2	1	no	—
518	C₈×C₃₁	—	2	2	no	—
519	C₈×C₃₁	—	2	1	no	—
520	C₈×C₃₁	—	2	1	no	—
521	#3555	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3506	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3401	C₂×C₃₁	1	2	yes	complemented
524	#3398	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3397	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3394	C₂×C₃₁	1	2	yes	complemented
527	#3393	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3392	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3371	C₂×C₃₁	1	2	yes	complemented
530	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3365	C₂×C₃₁	1	2	yes	complemented
533	#3362	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3360	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3224	C₂×C₃₁	1	2	yes	complemented
536	#3222	C₂×C₃₁	1	2	yes	complemented
537	#3212	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3210	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3125	C₂×C₃₁	1	2	yes	complemented
540	#3120	C₂×C₃₁	1	2	yes	complemented
541	#3105	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3101	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#2986	C₂×C₃₁	1	1	yes	characteristic, complemented
544	C₂²×C₃₁	—	2	1	no	—
545	C₂²×C₃₁	—	2	1	no	—
546	C₂²×C₃₁	—	2	1	no	—
547	C₂²×C₃₁	—	4	1	no	—
548	C₂²×C₃₁	—	4	2	no	—
549	C₂²×C₃₁	—	4	1	no	—
550	C₂²×C₃₁	—	4	1	no	—
551	C₂²×C₃₁	—	4	2	no	—
552	C₂²×C₃₁	—	4	1	no	—
553	C₂²×C₃₁	—	4	1	no	—
554	C₂²×C₃₁	—	4	1	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	—	8	4	no	—
560	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
561	C₄×C₃₁	—	2	1	no	—
562	C₄×C₃₁	—	2	1	no	—
563	C₄×C₃₁	—	2	2	no	—
564	C₄×C₃₁	—	2	2	no	—
565	C₄×C₃₁	—	2	1	no	—
566	C₄×C₃₁	—	2	1	no	—
567	C₄×C₃₁	—	2	2	no	—
568	C₄×C₃₁	—	2	2	no	—
569	C₄×C₃₁	—	4	2	no	—
570	C₄×C₃₁	—	4	1	no	—
571	C₄×C₃₁	—	4	2	no	—
572	C₄×C₃₁	—	4	1	no	—
573	C₄×C₃₁	—	4	2	no	—
574	C₄×C₃₁	—	4	1	no	—
575	C₄×C₃₁	—	4	1	no	—
576	C₄×C₃₁	—	4	1	no	—
577	C₄×C₃₁	#577	1	2	yes	—
578	C₄×C₃₁	#585	1	1	yes	characteristic
579	C₄×C₃₁	#585	1	1	yes	characteristic
580	#563	—	2	2	no	—
581	#559	C₂²×C₃₁	1	2	yes	—
582	#559	C₂²×C₃₁	1	2	yes	—
583	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
584	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
585	#557	C₂²×C₃₁	1	2	yes	complemented
586	#556	—	2	1	no	—
587	#556	C₂²×C₃₁	1	1	yes	characteristic
588	#556	C₂²×C₃₁	1	1	yes	characteristic
589	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
590	#556	C₂²×C₃₁	1	2	yes	complemented
591	#555	—	2	1	no	—
592	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
593	#553	—	2	2	no	—
594	#552	—	2	1	no	—
595	#550	C₂²×C₃₁	1	1	yes	characteristic
596	#550	C₂²×C₃₁	1	1	yes	characteristic
597	#547	—	2	1	no	—
598	#544	—	2	1	no	—
599	#542	C₂²×C₃₁	1	2	yes	—
600	#541	—	2	1	no	—
601	#541	—	2	2	no	—
602	#541	C₂²×C₃₁	1	2	yes	—
603	#538	—	2	2	no	—
604	#535	C₂²×C₃₁	1	2	yes	—
605	#533	C₂²×C₃₁	1	1	yes	characteristic
606	#533	C₂²×C₃₁	1	1	yes	characteristic
607	#532	C₂²×C₃₁	1	1	yes	characteristic
608	#529	C₂²×C₃₁	1	1	yes	characteristic
609	#525	—	2	1	no	—
610	#525	—	2	1	no	—
611	#520	C₂²×C₃₁	1	2	yes	—
612	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
613	#497	C₂²×C₃₁	1	2	yes	—
614	#496	C₂²×C₃₁	1	2	yes	—
615	#495	C₂²×C₃₁	1	2	yes	—
616	#495	C₂²×C₃₁	1	2	yes	complemented
617	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
618	#492	C₂²×C₃₁	1	2	yes	—
619	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
620	#490	C₂²×C₃₁	1	2	yes	—
621	#489	C₂²×C₃₁	1	2	yes	—
622	#488	C₂²×C₃₁	1	2	yes	—
623	#488	C₂²×C₃₁	1	2	yes	complemented
624	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
625	#486	C₂²×C₃₁	1	2	yes	—
626	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
627	#484	C₂²×C₃₁	1	1	yes	characteristic
628	#483	C₂²×C₃₁	1	2	yes	—
629	#481	C₂²×C₃₁	1	1	yes	characteristic
630	#479	C₂²×C₃₁	1	2	yes	complemented
631	#478	C₂²×C₃₁	1	1	yes	characteristic
632	#478	C₂²×C₃₁	1	1	yes	characteristic
633	#478	C₂²×C₃₁	1	2	yes	complemented
634	#476	C₂²×C₃₁	1	1	yes	characteristic
635	#476	C₂²×C₃₁	1	1	yes	characteristic
636	#476	C₂²×C₃₁	1	2	yes	complemented
637	#475	C₂²×C₃₁	1	2	yes	complemented
638	#464	C₂²×C₃₁	1	2	yes	—
639	#464	C₂²×C₃₁	1	2	yes	—
640	#464	C₂²×C₃₁	1	2	yes	—
641	#464	C₂²×C₃₁	1	2	yes	complemented
642	#464	C₂²×C₃₁	1	2	yes	complemented
643	#464	C₂²×C₃₁	1	2	yes	complemented
644	#463	C₂²×C₃₁	1	2	yes	—
645	#463	C₂²×C₃₁	1	1	yes	characteristic
646	#463	C₂²×C₃₁	1	1	yes	characteristic
647	#463	C₂²×C₃₁	1	2	yes	complemented
648	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#462	C₂²×C₃₁	1	2	yes	complemented
650	#461	C₂²×C₃₁	1	1	yes	characteristic
651	#461	C₂²×C₃₁	1	1	yes	characteristic
652	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
653	#461	C₂²×C₃₁	1	2	yes	complemented
654	#460	C₂²×C₃₁	1	2	yes	—
655	#460	C₂²×C₃₁	1	2	yes	—
656	#460	C₂²×C₃₁	1	2	yes	—
657	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
658	#459	C₂²×C₃₁	1	2	yes	—
659	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
660	#452	C₂²×C₃₁	1	2	yes	—
661	#452	C₂²×C₃₁	1	2	yes	—
662	#452	C₂²×C₃₁	1	2	yes	—
663	#450	C₂²×C₃₁	1	2	yes	—
664	#450	C₂²×C₃₁	1	1	yes	characteristic
665	#449	C₂²×C₃₁	1	2	yes	—
666	#447	C₂²×C₃₁	1	1	yes	characteristic
667	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	#446	C₂²×C₃₁	1	2	yes	complemented
670	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
671	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
672	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
673	#442	C₂²×C₃₁	1	2	yes	complemented
674	#441	C₂²×C₃₁	1	2	yes	complemented
675	#441	C₂²×C₃₁	1	2	yes	complemented
676	#440	C₂²×C₃₁	1	2	yes	complemented
677	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
678	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
679	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
680	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
681	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
682	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
683	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
684	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
685	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
686	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
687	#433	C₂²×C₃₁	1	2	yes	—
688	#433	C₂²×C₃₁	1	2	yes	—
689	#431	C₂²×C₃₁	1	1	yes	characteristic
690	#431	C₂²×C₃₁	1	1	yes	characteristic
691	C₂×C₃₁	—	4	1	no	—
692	C₂×C₃₁	—	8	1	no	—
693	C₂×C₃₁	—	8	2	no	—
694	C₂×C₃₁	—	8	1	no	—
695	C₂×C₃₁	—	8	1	no	—
696	C₂×C₃₁	#3487	1	1	yes	characteristic
697	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
698	C₂×C₃₁	#3584	1	1	yes	characteristic
699	C₂×#41	—	2	1	no	—
700	C₂×#41	—	2	1	no	—
701	C₂×#41	C₂³×C₃₁	1	2	yes	—
702	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
703	C₂³×C₄	—	2	1	no	—
704	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
705	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
706	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
707	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
708	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
709	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
710	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
711	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
712	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
714	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
715	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
716	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
717	C₂×D₈	C₂³×C₃₁	1	2	yes	—
718	C₄⋊Q₈	—	2	2	no	—
719	C₄⋊Q₈	—	2	2	no	—
720	C₄⋊Q₈	—	2	1	no	—
721	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
722	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
726	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
727	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
728	#127	C₂³×C₃₁	1	1	yes	characteristic
729	#127	C₂³×C₃₁	1	2	yes	—
730	#127	C₂³×C₃₁	1	2	yes	—
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	1	no	—
740	#125	—	2	2	no	—
741	#125	—	2	2	no	—
742	#125	—	2	2	no	—
743	#125	—	2	2	no	—
744	#125	—	2	2	no	—
745	#125	—	2	1	no	—
746	#125	—	2	1	no	—
747	#125	D₄×C₃₁	1	2	yes	—
748	#125	C₂³×C₃₁	1	1	yes	characteristic
749	#125	C₂³×C₃₁	1	2	yes	—
750	#124	—	2	2	no	—
751	#124	—	2	2	no	—
752	#124	—	2	2	no	—
753	#124	C₂³×C₃₁	1	1	yes	characteristic
754	#124	C₂³×C₃₁	1	2	yes	—
755	#124	C₂³×C₃₁	1	2	yes	—
756	#124	C₂³×C₃₁	1	2	yes	—
757	#124	C₂³×C₃₁	1	2	yes	—
758	#123	—	2	1	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	1	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	D₄×C₃₁	1	1	yes	characteristic
774	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
775	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
776	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
777	#121	—	2	1	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	—	2	2	no	—
785	#121	C₂³×C₃₁	1	1	yes	characteristic
786	#120	—	2	2	no	—
787	#120	—	2	2	no	—
788	C₄×Q₈	—	2	1	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	2	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
793	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
794	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
795	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
796	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
797	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
798	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
799	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
812	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₃₁	1	2	yes	—
816	C₄×D₄	C₂³×C₃₁	1	2	yes	—
817	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₃₁	1	2	yes	—
819	#117	—	2	1	no	—
820	#117	—	2	2	no	—
821	#117	—	2	1	no	—
822	#117	—	2	1	no	—
823	#117	—	2	2	no	—
824	#117	—	2	1	no	—
825	#117	—	2	1	no	—
826	#117	C₂³×C₃₁	1	2	yes	—
827	C₂×C₄⋊C₄	—	2	2	no	—
828	C₂×C₄⋊C₄	—	2	1	no	—
829	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
830	C₂×C₂²⋊C₄	—	2	1	no	—
831	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
832	#107	C₂³×C₃₁	1	1	yes	characteristic
833	#107	C₂³×C₃₁	1	1	yes	characteristic
834	#106	C₂³×C₃₁	1	1	yes	characteristic
835	#106	C₂³×C₃₁	1	2	yes	—
836	#106	C₂³×C₃₁	1	1	yes	characteristic
837	#106	C₂³×C₃₁	1	2	yes	—
838	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
839	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
840	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
841	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
843	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
844	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
845	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
846	#103	C₂³×C₃₁	1	1	yes	characteristic
847	#103	C₂³×C₃₁	1	2	yes	—
848	#103	C₂³×C₃₁	1	2	yes	—
849	#103	C₂³×C₃₁	1	1	yes	characteristic
850	#103	C₂³×C₃₁	1	2	yes	—
851	#103	C₂³×C₃₁	1	2	yes	—
852	#103	C₂³×C₃₁	1	2	yes	—
853	#103	C₂³×C₃₁	1	2	yes	—
854	#102	C₂³×C₃₁	1	1	yes	characteristic
855	#102	C₂³×C₃₁	1	1	yes	characteristic
856	#102	C₂³×C₃₁	1	1	yes	characteristic
857	#102	C₂³×C₃₁	1	1	yes	characteristic
858	#102	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	2	yes	—
865	#102	C₂³×C₃₁	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
867	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
869	#97	C₂³×C₃₁	1	2	yes	—
870	#97	C₂³×C₃₁	1	2	yes	—
871	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₃₁	1	2	yes	—
874	C₄×C₈	C₂³×C₃₁	1	2	yes	—
875	C₄×C₈	C₂³×C₃₁	1	2	yes	—
876	C₃₁	#61927	1	1	yes	characteristic, direct product factor, Sylow
877	C₂⁴	—	2	1	no	—
878	#41	—	4	2	no	—
879	#41	—	4	2	no	—
880	#41	—	8	2	no	—
881	#41	—	8	2	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
885	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
886	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
887	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
888	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
889	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	4	1	no	—
900	C₂×D₄	—	4	1	no	—
901	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
902	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
903	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
904	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	8	2	no	—
916	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
917	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
919	Q₁₆	—	4	2	no	—
920	Q₁₆	—	4	2	no	—
921	Q₁₆	—	4	2	no	—
922	SD₁₆	—	4	2	no	—
923	SD₁₆	—	4	2	no	—
924	SD₁₆	—	4	2	no	—
925	SD₁₆	—	4	1	no	—
926	SD₁₆	—	4	2	no	—
927	SD₁₆	—	4	2	no	—
928	SD₁₆	—	4	2	no	—
929	SD₁₆	—	4	1	no	—
930	D₈	—	4	1	no	—
931	D₈	—	4	2	no	—
932	D₈	—	4	1	no	—
933	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
936	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
938	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
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	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
962	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
963	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
964	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
965	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
966	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
967	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
968	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
969	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
970	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	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	C₂×D₄×C₃₁	1	2	yes	—
997	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1006	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1007	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1009	C₄²	C₂⁴×C₃₁	1	2	yes	—
1010	C₄²	C₂⁴×C₃₁	1	2	yes	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	2	2	no	—
1015	C₂³	—	4	2	no	—
1016	C₂³	—	8	1	no	—
1017	C₂³	—	8	1	no	—
1018	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1019	Q₈	—	2	2	no	—
1020	Q₈	—	2	2	no	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	2	no	—
1027	Q₈	—	4	2	no	—
1028	Q₈	—	8	1	no	—
1029	Q₈	—	8	2	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	2	1	no	—
1032	D₄	—	2	1	no	—
1033	D₄	—	2	1	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	4	2	no	—
1039	D₄	—	4	4	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	8	1	no	—
1042	D₄	—	8	2	no	—
1043	D₄	—	8	2	no	—
1044	D₄	—	8	2	no	—
1045	D₄	—	8	2	no	—
1046	D₄	—	8	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	4	1	no	—
1059	C₂×C₄	—	4	4	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	1	no	—
1065	C₂×C₄	—	8	1	no	—
1066	C₂×C₄	—	8	2	no	—
1067	C₂×C₄	—	8	2	no	—
1068	C₂×C₄	—	8	1	no	—
1069	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1070	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1071	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1072	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1073	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1074	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1076	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1077	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1078	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1079	C₈	—	2	1	no	—
1080	C₈	—	2	2	no	—
1081	C₈	—	2	1	no	—
1082	C₈	—	2	2	no	—
1083	C₈	—	2	1	no	—
1084	C₈	—	2	1	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	4	2	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	8	4	no	—
1101	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1102	C₄	—	2	1	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	2	no	—
1117	C₄	—	4	1	no	—
1118	C₄	C₃₁×#577	1	2	yes	—
1119	C₄	C₃₁×#585	1	1	yes	characteristic
1120	C₄	C₃₁×#585	1	1	yes	characteristic
1121	C₂	—	4	1	no	—
1122	C₂	—	8	1	no	—
1123	C₂	—	8	1	no	—
1124	C₂	—	8	2	no	—
1125	C₂	—	8	1	no	—
1126	C₂	C₃₁×#3487	1	1	yes	characteristic
1127	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1128	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×#3555	C₂	semidirect
2. C₃₁×#3506	C₂	semidirect
3. C₃₁×#3401	C₂	semidirect
4. C₃₁×#3398	C₂	semidirect
5. C₃₁×#3397	C₂	semidirect
6. C₃₁×#3394	C₂	semidirect
7. C₃₁×#3393	C₂	semidirect
8. C₃₁×#3392	C₂	semidirect
9. C₃₁×#3371	C₂	semidirect
10. C₃₁×#3369	C₂	semidirect
11. C₃₁×#3366	C₂	semidirect
12. C₃₁×#3365	C₂	semidirect
13. C₃₁×#3362	C₂	semidirect
14. C₃₁×#3360	C₂	semidirect
15. C₃₁×#3224	C₂	semidirect
16. C₃₁×#3222	C₂	semidirect
17. C₃₁×#3212	C₂	semidirect
18. C₃₁×#3210	C₂	semidirect
19. C₃₁×#3125	C₂	semidirect
20. C₃₁×#3120	C₂	semidirect
21. C₃₁×#3105	C₂	semidirect
22. C₃₁×#3101	C₂	semidirect
23. C₃₁×#2986	C₂	semidirect
27. Q₈²×C₃₁	C₂²	semidirect
28. C₃₁×#557	C₂²	semidirect
29. C₃₁×#557	C₂²	semidirect
33. C₃₁×#556	C₂²	semidirect
34. C₃₁×#556	C₂²	semidirect
36. C₃₁×#554	C₂²	semidirect
60. C₃₁×#495	C₂²	semidirect
61. C₃₁×#494	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
80. C₃₁×#476	C₂²	semidirect
81. C₃₁×#475	C₂²	semidirect
85. C₃₁×#464	C₂²	semidirect
86. C₃₁×#464	C₂²	semidirect
87. C₃₁×#464	C₂²	semidirect
91. C₃₁×#463	C₂²	semidirect
92. C₃₁×#462	C₂²	semidirect
93. C₃₁×#462	C₂²	semidirect
96. C₃₁×#461	C₂²	semidirect
97. C₃₁×#461	C₂²	semidirect
101. C₃₁×#460	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×#441	C₂²	semidirect
119. C₃₁×#441	C₂²	semidirect
120. C₃₁×#440	C₂²	semidirect
121. C₄×Q₁₆×C₃₁	C₂²	semidirect
126. C₄×SD₁₆×C₃₁	C₂²	semidirect
127. C₄×SD₁₆×C₃₁	C₂²	semidirect
128. C₄×SD₁₆×C₃₁	C₂²	semidirect
446. #61927	C₃₁	direct (N × H)
521. #3555	C₂×C₃₁	semidirect
522. #3506	C₂×C₃₁	semidirect
523. #3401	C₂×C₃₁	semidirect
524. #3398	C₂×C₃₁	semidirect
525. #3397	C₂×C₃₁	semidirect
526. #3394	C₂×C₃₁	semidirect
527. #3393	C₂×C₃₁	semidirect
528. #3392	C₂×C₃₁	semidirect
529. #3371	C₂×C₃₁	semidirect
530. #3369	C₂×C₃₁	semidirect
531. #3366	C₂×C₃₁	semidirect
532. #3365	C₂×C₃₁	semidirect
533. #3362	C₂×C₃₁	semidirect
534. #3360	C₂×C₃₁	semidirect
535. #3224	C₂×C₃₁	semidirect
536. #3222	C₂×C₃₁	semidirect
537. #3212	C₂×C₃₁	semidirect
538. #3210	C₂×C₃₁	semidirect
539. #3125	C₂×C₃₁	semidirect
540. #3120	C₂×C₃₁	semidirect
541. #3105	C₂×C₃₁	semidirect
542. #3101	C₂×C₃₁	semidirect
543. #2986	C₂×C₃₁	semidirect
583. Q₈²	C₂²×C₃₁	semidirect
584. #557	C₂²×C₃₁	semidirect
585. #557	C₂²×C₃₁	semidirect
589. #556	C₂²×C₃₁	semidirect
590. #556	C₂²×C₃₁	semidirect
592. #554	C₂²×C₃₁	semidirect
616. #495	C₂²×C₃₁	semidirect
617. #494	C₂²×C₃₁	semidirect
619. #492	C₂²×C₃₁	semidirect
623. #488	C₂²×C₃₁	semidirect
624. #487	C₂²×C₃₁	semidirect
626. #486	C₂²×C₃₁	semidirect
630. #479	C₂²×C₃₁	semidirect
633. #478	C₂²×C₃₁	semidirect
636. #476	C₂²×C₃₁	semidirect
637. #475	C₂²×C₃₁	semidirect
641. #464	C₂²×C₃₁	semidirect
642. #464	C₂²×C₃₁	semidirect
643. #464	C₂²×C₃₁	semidirect
647. #463	C₂²×C₃₁	semidirect
648. #462	C₂²×C₃₁	semidirect
649. #462	C₂²×C₃₁	semidirect
652. #461	C₂²×C₃₁	semidirect
653. #461	C₂²×C₃₁	semidirect
657. #460	C₂²×C₃₁	semidirect
659. #459	C₂²×C₃₁	semidirect
667. #446	C₂²×C₃₁	semidirect
668. #446	C₂²×C₃₁	semidirect
669. #446	C₂²×C₃₁	semidirect
670. C₈×Q₈	C₂²×C₃₁	semidirect
671. C₈×Q₈	C₂²×C₃₁	semidirect
672. C₈×Q₈	C₂²×C₃₁	semidirect
673. #442	C₂²×C₃₁	semidirect
674. #441	C₂²×C₃₁	semidirect
675. #441	C₂²×C₃₁	semidirect
676. #440	C₂²×C₃₁	semidirect
677. C₄×Q₁₆	C₂²×C₃₁	semidirect
682. C₄×SD₁₆	C₂²×C₃₁	semidirect
683. C₄×SD₁₆	C₂²×C₃₁	semidirect
684. C₄×SD₁₆	C₂²×C₃₁	semidirect
876. C₃₁	#61927	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×#3506	2
C₃₁×#3401	2
C₃₁×#3398	2
C₃₁×#3397	2
C₃₁×#3394	2
C₃₁×#3393	2
C₃₁×#3392	2
C₃₁×#3371	2
C₃₁×#3369	2
C₃₁×#3366	2
C₃₁×#3365	2
C₃₁×#3362	2
C₃₁×#3360	2
C₃₁×#3224	2
C₃₁×#3222	2
C₃₁×#3212	2
C₃₁×#3210	2
C₃₁×#3125	2
C₃₁×#3120	2
C₃₁×#3105	2
C₃₁×#3101	2
C₃₁×#2986	2
#61927	31

Subgroups — C31×#61927 #21518686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61927 #21518686