Subgroups — C₃₁×#62200 #21518959

Order 7936.

1808 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3385	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3345	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3341	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3337	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3310	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3294	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3257	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3241	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3226	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3081	C₂	1	2	yes	maximal, complemented
22	C₂×C₃₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
26	C₃₁×#555	C₂²	1	1	yes	characteristic
27	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#554	C₂²	1	1	yes	characteristic
29	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#553	—	2	1	no	—
32	C₃₁×#553	C₂²	1	2	yes	—
33	C₃₁×#552	—	2	1	no	—
34	C₃₁×#552	C₂²	1	2	yes	complemented
35	C₃₁×#550	C₂²	1	1	yes	characteristic
36	C₃₁×#547	—	2	1	no	—
37	C₃₁×#547	C₂²	1	2	yes	complemented
38	C₃₁×#546	—	2	1	no	—
39	C₃₁×#546	—	2	2	no	—
40	D₄²×C₃₁	C₂²	1	2	yes	—
41	D₄²×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#544	—	2	1	no	—
43	C₃₁×#544	C₂²	1	2	yes	complemented
44	C₃₁×#542	—	2	1	no	—
45	C₃₁×#542	C₂²	1	2	yes	complemented
46	C₃₁×#540	C₂²	1	2	yes	—
47	C₃₁×#538	—	2	2	no	—
48	C₃₁×#536	—	2	2	no	—
49	C₃₁×#532	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#529	C₂²	1	1	yes	characteristic
52	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#525	—	2	1	no	—
54	C₂×C₃₁×#121	—	2	1	no	—
55	C₃₁×#518	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	complemented
58	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#499	C₂²	1	2	yes	complemented
61	C₃₁×#490	C₂²	1	2	yes	complemented
62	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#486	C₂²	1	2	yes	complemented
64	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#485	C₂²	1	2	yes	complemented
66	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#482	C₂²	1	2	yes	complemented
68	C₃₁×#482	C₂²	1	2	yes	complemented
69	C₃₁×#482	C₂²	1	2	yes	complemented
70	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#481	C₂²	1	2	yes	complemented
72	C₃₁×#480	C₂²	1	2	yes	complemented
73	C₃₁×#480	C₂²	1	2	yes	complemented
74	C₃₁×#480	C₂²	1	2	yes	complemented
75	C₃₁×#479	C₂²	1	2	yes	complemented
76	C₃₁×#478	C₂²	1	1	yes	characteristic
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×#478	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#476	C₂²	1	2	yes	—
84	C₃₁×#476	C₂²	1	1	yes	characteristic
85	C₃₁×#476	C₂²	1	1	yes	characteristic
86	C₃₁×#476	C₂²	1	2	yes	complemented
87	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#476	C₂²	1	2	yes	complemented
91	C₃₁×#474	C₂²	1	2	yes	—
92	C₃₁×#474	C₂²	1	2	yes	complemented
93	C₃₁×#474	C₂²	1	2	yes	complemented
94	C₃₁×#469	C₂²	1	2	yes	complemented
95	C₃₁×#468	C₂²	1	2	yes	complemented
96	C₃₁×#466	C₂²	1	2	yes	complemented
97	C₃₁×#466	C₂²	1	2	yes	complemented
98	C₃₁×#465	C₂²	1	2	yes	complemented
99	C₃₁×#465	C₂²	1	2	yes	complemented
100	C₃₁×#463	C₂²	1	1	yes	characteristic
101	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#463	C₂²	1	2	yes	complemented
103	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#460	C₂²	1	2	yes	complemented
105	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#459	C₂²	1	2	yes	complemented
107	C₃₁×#450	C₂²	1	1	yes	characteristic
108	C₃₁×#450	C₂²	1	2	yes	—
109	C₃₁×#447	C₂²	1	1	yes	characteristic
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	complemented
114	C₃₁×#440	C₂²	1	2	yes	—
115	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₃₁	C₂²	1	2	yes	—
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, 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	C₂×C₃₁×#106	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	C₂×C₃₁×#102	C₂²	1	2	yes	—
134	C₂×C₃₁×#102	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	2	no	—
137	C₂×#41×C₃₁	—	2	1	no	—
138	C₂²×Q₈×C₃₁	—	2	1	no	—
139	C₂²×D₄×C₃₁	—	2	1	no	—
140	C₂²×D₄×C₃₁	—	2	2	no	—
141	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
143	C₂³×C₄×C₃₁	—	2	1	no	—
144	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×D₈×C₃₁	C₂³	1	2	yes	—
150	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
152	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
153	C₃₁×C₄⋊Q₈	—	2	2	no	—
154	C₃₁×C₄⋊Q₈	—	2	2	no	—
155	C₃₁×C₄⋊Q₈	—	2	1	no	—
156	C₃₁×C₄⋊Q₈	—	2	1	no	—
157	C₃₁×C₄⋊Q₈	—	2	1	no	—
158	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×#127	C₂³	1	1	yes	characteristic
164	C₃₁×#127	C₂³	1	2	yes	—
165	C₃₁×#126	—	2	2	no	—
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	1	no	—
169	C₃₁×#126	D₄	1	2	yes	—
170	C₃₁×#125	—	2	1	no	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	D₄	1	1	yes	characteristic
174	C₃₁×#125	C₂³	1	1	yes	characteristic
175	C₃₁×#125	C₂³	1	2	yes	—
176	C₃₁×#125	C₂³	1	2	yes	—
177	C₃₁×#124	—	2	2	no	—
178	C₃₁×#124	—	2	2	no	—
179	C₃₁×#124	—	2	2	no	—
180	C₃₁×#124	—	2	1	no	—
181	C₃₁×#124	D₄	1	1	yes	characteristic
182	C₃₁×#124	C₂³	1	1	yes	characteristic
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	1	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	D₄	1	2	yes	—
192	C₃₁×C₂²⋊Q₈	—	2	1	no	—
193	C₃₁×C₂²⋊Q₈	—	2	1	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	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	1	yes	characteristic
203	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	—	2	1	no	—
206	C₃₁×#121	—	2	1	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	—	2	2	no	—
214	C₃₁×#121	D₄	1	1	yes	characteristic
215	C₃₁×#121	C₂³	1	1	yes	characteristic
216	C₃₁×#121	C₂³	1	2	yes	—
217	C₃₁×#121	C₂³	1	2	yes	—
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	C₃₁×#120	—	2	2	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₃₁	—	2	1	no	—
228	C₄×D₄×C₃₁	—	2	1	no	—
229	C₄×D₄×C₃₁	—	2	2	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	1	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	C₂³	1	2	yes	—
238	C₄×D₄×C₃₁	C₂³	1	2	yes	—
239	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₃₁	C₂³	1	2	yes	—
241	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	C₃₁×#117	—	2	1	no	—
247	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	C₂³	1	2	yes	—
251	C₃₁×#117	C₂³	1	2	yes	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
254	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
255	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
256	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
260	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
261	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
262	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
263	C₃₁×#107	C₂³	1	1	yes	characteristic
264	C₃₁×#107	C₂³	1	2	yes	—
265	C₃₁×#107	C₂³	1	2	yes	—
266	C₃₁×#107	C₂³	1	2	yes	—
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#106	C₂³	1	2	yes	—
271	C₃₁×#106	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#102	C₂³	1	2	yes	—
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	2	yes	—
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	1	yes	characteristic
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	1	no	—
313	C₂⁴×C₃₁	—	2	2	no	—
314	#41×C₃₁	—	8	2	no	—
315	#41×C₃₁	—	8	4	no	—
316	#41×C₃₁	—	8	2	no	—
317	C₂×Q₈×C₃₁	—	2	1	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	2	1	no	—
322	C₂×Q₈×C₃₁	—	8	2	no	—
323	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₃₁	—	2	2	no	—
326	C₂×D₄×C₃₁	—	2	4	no	—
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	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	1	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	4	1	no	—
339	C₂×D₄×C₃₁	—	4	2	no	—
340	C₂×D₄×C₃₁	—	8	2	no	—
341	C₂×D₄×C₃₁	—	8	4	no	—
342	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
343	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
345	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
347	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₃₁	—	2	2	no	—
349	C₂²×C₄×C₃₁	—	2	1	no	—
350	C₂²×C₄×C₃₁	—	2	2	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	1	no	—
360	C₂²×C₄×C₃₁	—	8	2	no	—
361	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
365	SD₁₆×C₃₁	—	2	2	no	—
366	SD₁₆×C₃₁	—	4	2	no	—
367	SD₁₆×C₃₁	—	4	1	no	—
368	D₈×C₃₁	—	2	2	no	—
369	D₈×C₃₁	—	4	1	no	—
370	D₈×C₃₁	—	4	2	no	—
371	M₁₆×C₃₁	—	4	2	no	—
372	C₂×C₈×C₃₁	—	4	2	no	—
373	C₂×C₈×C₃₁	—	4	2	no	—
374	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
377	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
380	C₄⋊C₄×C₃₁	—	2	1	no	—
381	C₄⋊C₄×C₃₁	—	2	1	no	—
382	C₄⋊C₄×C₃₁	—	2	1	no	—
383	C₄⋊C₄×C₃₁	—	2	2	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	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	2	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
411	C₂²⋊C₄×C₃₁	—	2	2	no	—
412	C₂²⋊C₄×C₃₁	—	2	1	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	1	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	1	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	1	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	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	1	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	1	no	—
431	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
436	C₄²×C₃₁	—	2	2	no	—
437	C₄²×C₃₁	—	2	2	no	—
438	C₄²×C₃₁	—	2	1	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	2	yes	—
444	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
445	#62200	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
446	C₂³×C₃₁	—	2	1	no	—
447	C₂³×C₃₁	—	2	1	no	—
448	C₂³×C₃₁	—	2	2	no	—
449	C₂³×C₃₁	—	2	1	no	—
450	C₂³×C₃₁	—	4	2	no	—
451	C₂³×C₃₁	—	4	4	no	—
452	C₂³×C₃₁	—	4	2	no	—
453	C₂³×C₃₁	—	8	1	no	—
454	C₂³×C₃₁	—	8	2	no	—
455	C₂³×C₃₁	—	8	2	no	—
456	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
457	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
458	Q₈×C₃₁	—	2	2	no	—
459	Q₈×C₃₁	—	2	1	no	—
460	Q₈×C₃₁	—	2	1	no	—
461	Q₈×C₃₁	—	8	2	no	—
462	Q₈×C₃₁	—	8	1	no	—
463	Q₈×C₃₁	—	8	1	no	—
464	Q₈×C₃₁	—	8	1	no	—
465	Q₈×C₃₁	—	8	2	no	—
466	D₄×C₃₁	—	2	4	no	—
467	D₄×C₃₁	—	2	2	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	1	no	—
474	D₄×C₃₁	—	2	2	no	—
475	D₄×C₃₁	—	4	2	no	—
476	D₄×C₃₁	—	4	4	no	—
477	D₄×C₃₁	—	4	4	no	—
478	D₄×C₃₁	—	4	2	no	—
479	D₄×C₃₁	—	4	2	no	—
480	D₄×C₃₁	—	8	2	no	—
481	D₄×C₃₁	—	8	1	no	—
482	D₄×C₃₁	—	8	2	no	—
483	D₄×C₃₁	—	8	2	no	—
484	D₄×C₃₁	—	8	2	no	—
485	D₄×C₃₁	—	8	2	no	—
486	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
487	C₂×C₄×C₃₁	—	2	2	no	—
488	C₂×C₄×C₃₁	—	2	2	no	—
489	C₂×C₄×C₃₁	—	2	1	no	—
490	C₂×C₄×C₃₁	—	2	2	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	1	no	—
496	C₂×C₄×C₃₁	—	2	2	no	—
497	C₂×C₄×C₃₁	—	2	2	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	—	4	4	no	—
502	C₂×C₄×C₃₁	—	4	2	no	—
503	C₂×C₄×C₃₁	—	4	2	no	—
504	C₂×C₄×C₃₁	—	4	2	no	—
505	C₂×C₄×C₃₁	—	8	1	no	—
506	C₂×C₄×C₃₁	—	8	1	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	—	8	2	no	—
511	C₂×C₄×C₃₁	—	8	1	no	—
512	C₂×C₄×C₃₁	—	8	2	no	—
513	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
520	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
522	C₈×C₃₁	—	2	1	no	—
523	C₈×C₃₁	—	2	1	no	—
524	C₈×C₃₁	—	2	1	no	—
525	C₈×C₃₁	—	2	2	no	—
526	C₈×C₃₁	—	2	2	no	—
527	C₈×C₃₁	—	2	1	no	—
528	#3544	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3519	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3385	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3380	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3362	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3357	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3345	C₂×C₃₁	1	2	yes	complemented
536	#3341	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3337	C₂×C₃₁	1	2	yes	complemented
538	#3325	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3310	C₂×C₃₁	1	2	yes	complemented
540	#3295	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3294	C₂×C₃₁	1	2	yes	complemented
542	#3257	C₂×C₃₁	1	2	yes	complemented
543	#3247	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3241	C₂×C₃₁	1	2	yes	complemented
545	#3226	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3118	C₂×C₃₁	1	2	yes	complemented
547	#3105	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3081	C₂×C₃₁	1	2	yes	complemented
549	C₂×#476	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#2994	C₂×C₃₁	1	1	yes	characteristic, complemented
551	C₂²×C₃₁	—	2	1	no	—
552	C₂²×C₃₁	—	2	1	no	—
553	C₂²×C₃₁	—	2	2	no	—
554	C₂²×C₃₁	—	2	2	no	—
555	C₂²×C₃₁	—	2	2	no	—
556	C₂²×C₃₁	—	2	2	no	—
557	C₂²×C₃₁	—	4	1	no	—
558	C₂²×C₃₁	—	4	1	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	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	—	8	4	no	—
569	C₂²×C₃₁	—	16	4	no	—
570	C₂²×C₃₁	#576	1	2	yes	—
571	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
572	C₄×C₃₁	—	2	1	no	—
573	C₄×C₃₁	—	2	2	no	—
574	C₄×C₃₁	—	2	1	no	—
575	C₄×C₃₁	—	2	1	no	—
576	C₄×C₃₁	—	2	2	no	—
577	C₄×C₃₁	—	2	1	no	—
578	C₄×C₃₁	—	2	2	no	—
579	C₄×C₃₁	—	4	1	no	—
580	C₄×C₃₁	—	4	2	no	—
581	C₄×C₃₁	—	4	2	no	—
582	C₄×C₃₁	—	4	2	no	—
583	C₄×C₃₁	—	4	1	no	—
584	C₄×C₃₁	—	4	1	no	—
585	C₄×C₃₁	—	4	1	no	—
586	C₄×C₃₁	—	4	1	no	—
587	C₄×C₃₁	#577	1	2	yes	—
588	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
589	C₄×C₃₁	#585	1	1	yes	characteristic
590	#563	—	2	2	no	—
591	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
592	#555	C₂²×C₃₁	1	1	yes	characteristic
593	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
594	#554	C₂²×C₃₁	1	1	yes	characteristic
595	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
596	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
597	#553	—	2	1	no	—
598	#553	C₂²×C₃₁	1	2	yes	—
599	#552	—	2	1	no	—
600	#552	C₂²×C₃₁	1	2	yes	complemented
601	#550	C₂²×C₃₁	1	1	yes	characteristic
602	#547	—	2	1	no	—
603	#547	C₂²×C₃₁	1	2	yes	complemented
604	#546	—	2	1	no	—
605	#546	—	2	2	no	—
606	D₄²	C₂²×C₃₁	1	2	yes	—
607	D₄²	C₂²×C₃₁	1	1	yes	characteristic
608	#544	—	2	1	no	—
609	#544	C₂²×C₃₁	1	2	yes	complemented
610	#542	—	2	1	no	—
611	#542	C₂²×C₃₁	1	2	yes	complemented
612	#540	C₂²×C₃₁	1	2	yes	—
613	#538	—	2	2	no	—
614	#536	—	2	2	no	—
615	#532	C₂²×C₃₁	1	1	yes	characteristic
616	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
617	#529	C₂²×C₃₁	1	1	yes	characteristic
618	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
619	#525	—	2	1	no	—
620	C₂×#121	—	2	1	no	—
621	#518	C₂²×C₃₁	1	2	yes	—
622	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
623	#501	C₂²×C₃₁	1	2	yes	complemented
624	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
625	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
626	#499	C₂²×C₃₁	1	2	yes	complemented
627	#490	C₂²×C₃₁	1	2	yes	complemented
628	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
629	#486	C₂²×C₃₁	1	2	yes	complemented
630	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
631	#485	C₂²×C₃₁	1	2	yes	complemented
632	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
633	#482	C₂²×C₃₁	1	2	yes	complemented
634	#482	C₂²×C₃₁	1	2	yes	complemented
635	#482	C₂²×C₃₁	1	2	yes	complemented
636	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
637	#481	C₂²×C₃₁	1	2	yes	complemented
638	#480	C₂²×C₃₁	1	2	yes	complemented
639	#480	C₂²×C₃₁	1	2	yes	complemented
640	#480	C₂²×C₃₁	1	2	yes	complemented
641	#479	C₂²×C₃₁	1	2	yes	complemented
642	#478	C₂²×C₃₁	1	1	yes	characteristic
643	#478	C₂²×C₃₁	1	2	yes	—
644	#478	C₂²×C₃₁	1	2	yes	complemented
645	#478	C₂²×C₃₁	1	2	yes	complemented
646	#478	C₂²×C₃₁	1	2	yes	complemented
647	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#476	C₂²×C₃₁	1	2	yes	—
650	#476	C₂²×C₃₁	1	1	yes	characteristic
651	#476	C₂²×C₃₁	1	1	yes	characteristic
652	#476	C₂²×C₃₁	1	2	yes	complemented
653	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	#476	C₂²×C₃₁	1	2	yes	complemented
657	#474	C₂²×C₃₁	1	2	yes	—
658	#474	C₂²×C₃₁	1	2	yes	complemented
659	#474	C₂²×C₃₁	1	2	yes	complemented
660	#469	C₂²×C₃₁	1	2	yes	complemented
661	#468	C₂²×C₃₁	1	2	yes	complemented
662	#466	C₂²×C₃₁	1	2	yes	complemented
663	#466	C₂²×C₃₁	1	2	yes	complemented
664	#465	C₂²×C₃₁	1	2	yes	complemented
665	#465	C₂²×C₃₁	1	2	yes	complemented
666	#463	C₂²×C₃₁	1	1	yes	characteristic
667	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#463	C₂²×C₃₁	1	2	yes	complemented
669	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	#460	C₂²×C₃₁	1	2	yes	complemented
671	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
672	#459	C₂²×C₃₁	1	2	yes	complemented
673	#450	C₂²×C₃₁	1	1	yes	characteristic
674	#450	C₂²×C₃₁	1	2	yes	—
675	#447	C₂²×C₃₁	1	1	yes	characteristic
676	#447	C₂²×C₃₁	1	2	yes	—
677	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
678	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	#442	C₂²×C₃₁	1	2	yes	complemented
680	#440	C₂²×C₃₁	1	2	yes	—
681	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
682	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
683	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
685	C₄×D₈	C₂²×C₃₁	1	2	yes	—
686	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
688	#435	C₂²×C₃₁	1	2	yes	complemented
689	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
690	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
691	#433	C₂²×C₃₁	1	2	yes	complemented
692	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
693	#428	C₂²×C₃₁	1	2	yes	complemented
694	#427	C₂²×C₃₁	1	2	yes	complemented
695	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
696	#424	C₂²×C₃₁	1	2	yes	complemented
697	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	#418	C₂²×C₃₁	1	2	yes	—
699	C₂×#102	C₂²×C₃₁	1	2	yes	—
700	C₂×#102	C₂²×C₃₁	1	2	yes	—
701	C₂×C₃₁	—	2	2	no	—
702	C₂×C₃₁	—	4	2	no	—
703	C₂×C₃₁	—	4	2	no	—
704	C₂×C₃₁	—	8	1	no	—
705	C₂×C₃₁	—	8	1	no	—
706	C₂×C₃₁	—	8	2	no	—
707	C₂×C₃₁	#3489	1	1	yes	characteristic
708	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
709	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
710	C₂×#41	—	2	1	no	—
711	C₂×#41	—	2	2	no	—
712	C₂×#41	—	2	1	no	—
713	C₂²×Q₈	—	2	1	no	—
714	C₂²×D₄	—	2	1	no	—
715	C₂²×D₄	—	2	2	no	—
716	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
717	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
718	C₂³×C₄	—	2	1	no	—
719	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
720	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
722	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
723	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
724	C₂×D₈	C₂³×C₃₁	1	2	yes	—
725	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
726	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
727	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
728	C₄⋊Q₈	—	2	2	no	—
729	C₄⋊Q₈	—	2	2	no	—
730	C₄⋊Q₈	—	2	1	no	—
731	C₄⋊Q₈	—	2	1	no	—
732	C₄⋊Q₈	—	2	1	no	—
733	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
734	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
735	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
736	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
738	#127	C₂³×C₃₁	1	1	yes	characteristic
739	#127	C₂³×C₃₁	1	2	yes	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	1	no	—
744	#126	D₄×C₃₁	1	2	yes	—
745	#125	—	2	1	no	—
746	#125	—	2	2	no	—
747	#125	—	2	2	no	—
748	#125	D₄×C₃₁	1	1	yes	characteristic
749	#125	C₂³×C₃₁	1	1	yes	characteristic
750	#125	C₂³×C₃₁	1	2	yes	—
751	#125	C₂³×C₃₁	1	2	yes	—
752	#124	—	2	2	no	—
753	#124	—	2	2	no	—
754	#124	—	2	2	no	—
755	#124	—	2	1	no	—
756	#124	D₄×C₃₁	1	1	yes	characteristic
757	#124	C₂³×C₃₁	1	1	yes	characteristic
758	#123	—	2	2	no	—
759	#123	—	2	1	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	D₄×C₃₁	1	2	yes	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
777	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
778	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
779	#121	—	2	2	no	—
780	#121	—	2	1	no	—
781	#121	—	2	1	no	—
782	#121	—	2	1	no	—
783	#121	—	2	1	no	—
784	#121	—	2	1	no	—
785	#121	—	2	2	no	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	D₄×C₃₁	1	1	yes	characteristic
790	#121	C₂³×C₃₁	1	1	yes	characteristic
791	#121	C₂³×C₃₁	1	2	yes	—
792	#121	C₂³×C₃₁	1	2	yes	—
793	#121	C₂³×C₃₁	1	2	yes	—
794	#121	C₂³×C₃₁	1	2	yes	—
795	#120	—	2	2	no	—
796	#120	—	2	2	no	—
797	#120	—	2	2	no	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
801	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	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	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
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	C₄×D₄	C₂³×C₃₁	1	2	yes	—
820	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
821	#117	—	2	1	no	—
822	#117	—	2	1	no	—
823	#117	—	2	2	no	—
824	#117	—	2	1	no	—
825	#117	C₂³×C₃₁	1	2	yes	—
826	#117	C₂³×C₃₁	1	2	yes	—
827	#117	C₂³×C₃₁	1	2	yes	—
828	C₂×C₄⋊C₄	—	2	1	no	—
829	C₂×C₄⋊C₄	—	2	1	no	—
830	C₂×C₄⋊C₄	—	2	1	no	—
831	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
832	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
833	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
834	C₂×C₂²⋊C₄	—	2	1	no	—
835	C₂×C₂²⋊C₄	—	2	2	no	—
836	C₂×C₂²⋊C₄	—	2	2	no	—
837	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
838	#107	C₂³×C₃₁	1	1	yes	characteristic
839	#107	C₂³×C₃₁	1	2	yes	—
840	#107	C₂³×C₃₁	1	2	yes	—
841	#107	C₂³×C₃₁	1	2	yes	—
842	#107	C₂³×C₃₁	1	2	yes	—
843	#107	C₂³×C₃₁	1	1	yes	characteristic
844	#107	C₂³×C₃₁	1	2	yes	—
845	#106	C₂³×C₃₁	1	2	yes	—
846	#106	C₂³×C₃₁	1	2	yes	—
847	#106	C₂³×C₃₁	1	2	yes	—
848	#106	C₂³×C₃₁	1	2	yes	—
849	#106	C₂³×C₃₁	1	2	yes	—
850	#106	C₂³×C₃₁	1	1	yes	characteristic
851	#106	C₂³×C₃₁	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
859	#103	C₂³×C₃₁	1	1	yes	characteristic
860	#103	C₂³×C₃₁	1	1	yes	characteristic
861	#103	C₂³×C₃₁	1	2	yes	—
862	#102	C₂³×C₃₁	1	2	yes	—
863	#102	C₂³×C₃₁	1	1	yes	characteristic
864	#102	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
869	#102	C₂³×C₃₁	1	1	yes	characteristic
870	#102	C₂³×C₃₁	1	2	yes	—
871	#102	C₂³×C₃₁	1	2	yes	—
872	#102	C₂³×C₃₁	1	2	yes	—
873	#102	C₂³×C₃₁	1	1	yes	characteristic
874	#102	C₂³×C₃₁	1	1	yes	characteristic
875	#102	C₂³×C₃₁	1	1	yes	characteristic
876	#102	C₂³×C₃₁	1	2	yes	—
877	#102	C₂³×C₃₁	1	1	yes	characteristic
878	#102	C₂³×C₃₁	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
880	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
881	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
883	#97	C₂³×C₃₁	1	2	yes	—
884	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
885	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
886	C₄×C₈	C₂³×C₃₁	1	2	yes	—
887	C₃₁	#62200	1	1	yes	characteristic, direct product factor, Sylow
888	C₂⁴	—	2	1	no	—
889	C₂⁴	—	2	2	no	—
890	#41	—	8	2	no	—
891	#41	—	8	4	no	—
892	#41	—	8	2	no	—
893	C₂×Q₈	—	2	1	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	2	no	—
896	C₂×Q₈	—	2	2	no	—
897	C₂×Q₈	—	2	1	no	—
898	C₂×Q₈	—	8	2	no	—
899	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
900	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	4	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	4	1	no	—
915	C₂×D₄	—	4	2	no	—
916	C₂×D₄	—	8	2	no	—
917	C₂×D₄	—	8	4	no	—
918	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
919	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
920	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
921	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
922	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
923	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	8	2	no	—
937	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
938	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
939	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
940	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
941	SD₁₆	—	2	2	no	—
942	SD₁₆	—	4	2	no	—
943	SD₁₆	—	4	1	no	—
944	D₈	—	2	2	no	—
945	D₈	—	4	1	no	—
946	D₈	—	4	2	no	—
947	M₁₆	—	4	2	no	—
948	C₂×C₈	—	4	2	no	—
949	C₂×C₈	—	4	2	no	—
950	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
953	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
954	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
955	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
975	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
976	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
977	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
978	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
981	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
983	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
986	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	1	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	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1008	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1010	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1011	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1012	C₄²	—	2	2	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1017	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1018	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1019	C₄²	C₂⁴×C₃₁	1	2	yes	—
1020	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1021	C₂³	—	2	1	no	—
1022	C₂³	—	2	1	no	—
1023	C₂³	—	2	2	no	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	4	2	no	—
1026	C₂³	—	4	4	no	—
1027	C₂³	—	4	2	no	—
1028	C₂³	—	8	1	no	—
1029	C₂³	—	8	2	no	—
1030	C₂³	—	8	2	no	—
1031	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1032	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1033	Q₈	—	2	2	no	—
1034	Q₈	—	2	1	no	—
1035	Q₈	—	2	1	no	—
1036	Q₈	—	8	2	no	—
1037	Q₈	—	8	1	no	—
1038	Q₈	—	8	1	no	—
1039	Q₈	—	8	1	no	—
1040	Q₈	—	8	2	no	—
1041	D₄	—	2	4	no	—
1042	D₄	—	2	2	no	—
1043	D₄	—	2	1	no	—
1044	D₄	—	2	1	no	—
1045	D₄	—	2	2	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	2	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	4	4	no	—
1052	D₄	—	4	4	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	4	2	no	—
1055	D₄	—	8	2	no	—
1056	D₄	—	8	1	no	—
1057	D₄	—	8	2	no	—
1058	D₄	—	8	2	no	—
1059	D₄	—	8	2	no	—
1060	D₄	—	8	2	no	—
1061	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	4	4	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	4	2	no	—
1080	C₂×C₄	—	8	1	no	—
1081	C₂×C₄	—	8	1	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	—	8	1	no	—
1087	C₂×C₄	—	8	2	no	—
1088	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1089	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1090	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1091	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1092	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1093	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1094	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1095	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1096	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1097	C₈	—	2	1	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	2	1	no	—
1100	C₈	—	2	2	no	—
1101	C₈	—	2	2	no	—
1102	C₈	—	2	1	no	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	4	2	no	—
1120	C₂²	—	8	4	no	—
1121	C₂²	—	16	4	no	—
1122	C₂²	C₃₁×#576	1	2	yes	—
1123	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1124	C₄	—	2	1	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	2	1	no	—
1127	C₄	—	2	1	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	2	2	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	2	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	2	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	C₃₁×#577	1	2	yes	—
1140	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1141	C₄	C₃₁×#585	1	1	yes	characteristic
1142	C₂	—	2	2	no	—
1143	C₂	—	4	2	no	—
1144	C₂	—	4	2	no	—
1145	C₂	—	8	1	no	—
1146	C₂	—	8	2	no	—
1147	C₂	—	8	1	no	—
1148	C₂	C₃₁×#3489	1	1	yes	characteristic
1149	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1150	C₂	C₂×C₃₁×#577	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×#3544	C₂	semidirect
2. C₃₁×#3519	C₂	semidirect
3. C₃₁×#3385	C₂	semidirect
4. C₃₁×#3380	C₂	semidirect
5. C₃₁×#3366	C₂	semidirect
6. C₃₁×#3362	C₂	semidirect
7. C₃₁×#3357	C₂	semidirect
8. C₃₁×#3345	C₂	semidirect
9. C₃₁×#3341	C₂	semidirect
10. C₃₁×#3337	C₂	semidirect
11. C₃₁×#3325	C₂	semidirect
12. C₃₁×#3310	C₂	semidirect
13. C₃₁×#3295	C₂	semidirect
14. C₃₁×#3294	C₂	semidirect
15. C₃₁×#3257	C₂	semidirect
16. C₃₁×#3247	C₂	semidirect
17. C₃₁×#3241	C₂	semidirect
18. C₃₁×#3226	C₂	semidirect
19. C₃₁×#3118	C₂	semidirect
20. C₃₁×#3105	C₂	semidirect
21. C₃₁×#3081	C₂	semidirect
22. C₂×C₃₁×#476	C₂	semidirect
23. C₃₁×#2994	C₂	semidirect
25. Q₈²×C₃₁	C₂²	semidirect
27. C₃₁×#555	C₂²	semidirect
29. C₃₁×#554	C₂²	semidirect
30. C₃₁×#554	C₂²	semidirect
34. C₃₁×#552	C₂²	semidirect
37. C₃₁×#547	C₂²	semidirect
43. C₃₁×#544	C₂²	semidirect
45. C₃₁×#542	C₂²	semidirect
50. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
52. C₃₁×#529	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#500	C₂²	semidirect
59. C₃₁×#500	C₂²	semidirect
60. C₃₁×#499	C₂²	semidirect
61. C₃₁×#490	C₂²	semidirect
62. C₃₁×#486	C₂²	semidirect
63. C₃₁×#486	C₂²	semidirect
64. C₃₁×#486	C₂²	semidirect
65. C₃₁×#485	C₂²	semidirect
66. C₃₁×#484	C₂²	semidirect
67. C₃₁×#482	C₂²	semidirect
68. C₃₁×#482	C₂²	semidirect
69. C₃₁×#482	C₂²	semidirect
70. C₃₁×#481	C₂²	semidirect
71. C₃₁×#481	C₂²	semidirect
72. C₃₁×#480	C₂²	semidirect
73. C₃₁×#480	C₂²	semidirect
74. C₃₁×#480	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
78. C₃₁×#478	C₂²	semidirect
79. C₃₁×#478	C₂²	semidirect
80. C₃₁×#478	C₂²	semidirect
81. C₃₁×#478	C₂²	semidirect
82. C₃₁×#477	C₂²	semidirect
86. C₃₁×#476	C₂²	semidirect
87. C₃₁×#476	C₂²	semidirect
88. C₃₁×#476	C₂²	semidirect
89. C₃₁×#476	C₂²	semidirect
90. C₃₁×#476	C₂²	semidirect
92. C₃₁×#474	C₂²	semidirect
93. C₃₁×#474	C₂²	semidirect
94. C₃₁×#469	C₂²	semidirect
95. C₃₁×#468	C₂²	semidirect
96. C₃₁×#466	C₂²	semidirect
97. C₃₁×#466	C₂²	semidirect
98. C₃₁×#465	C₂²	semidirect
99. C₃₁×#465	C₂²	semidirect
101. C₃₁×#463	C₂²	semidirect
102. C₃₁×#463	C₂²	semidirect
103. C₃₁×#460	C₂²	semidirect
104. C₃₁×#460	C₂²	semidirect
105. C₃₁×#459	C₂²	semidirect
106. C₃₁×#459	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₈×Q₈×C₃₁	C₂²	semidirect
113. C₃₁×#442	C₂²	semidirect
116. C₄×SD₁₆×C₃₁	C₂²	semidirect
117. C₄×SD₁₆×C₃₁	C₂²	semidirect
120. C₄×D₈×C₃₁	C₂²	semidirect
121. C₃₁×#436	C₂²	semidirect
122. C₃₁×#435	C₂²	semidirect
123. C₈×D₄×C₃₁	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. C₂×C₃₁×#106	C₂²	semidirect
130. C₃₁×#424	C₂²	semidirect
131. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
445. #62200	C₃₁	direct (N × H)
528. #3544	C₂×C₃₁	semidirect
529. #3519	C₂×C₃₁	semidirect
530. #3385	C₂×C₃₁	semidirect
531. #3380	C₂×C₃₁	semidirect
532. #3366	C₂×C₃₁	semidirect
533. #3362	C₂×C₃₁	semidirect
534. #3357	C₂×C₃₁	semidirect
535. #3345	C₂×C₃₁	semidirect
536. #3341	C₂×C₃₁	semidirect
537. #3337	C₂×C₃₁	semidirect
538. #3325	C₂×C₃₁	semidirect
539. #3310	C₂×C₃₁	semidirect
540. #3295	C₂×C₃₁	semidirect
541. #3294	C₂×C₃₁	semidirect
542. #3257	C₂×C₃₁	semidirect
543. #3247	C₂×C₃₁	semidirect
544. #3241	C₂×C₃₁	semidirect
545. #3226	C₂×C₃₁	semidirect
546. #3118	C₂×C₃₁	semidirect
547. #3105	C₂×C₃₁	semidirect
548. #3081	C₂×C₃₁	semidirect
549. C₂×#476	C₂×C₃₁	semidirect
550. #2994	C₂×C₃₁	semidirect
591. Q₈²	C₂²×C₃₁	semidirect
593. #555	C₂²×C₃₁	semidirect
595. #554	C₂²×C₃₁	semidirect
596. #554	C₂²×C₃₁	semidirect
600. #552	C₂²×C₃₁	semidirect
603. #547	C₂²×C₃₁	semidirect
609. #544	C₂²×C₃₁	semidirect
611. #542	C₂²×C₃₁	semidirect
616. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
618. #529	C₂²×C₃₁	semidirect
623. #501	C₂²×C₃₁	semidirect
624. #500	C₂²×C₃₁	semidirect
625. #500	C₂²×C₃₁	semidirect
626. #499	C₂²×C₃₁	semidirect
627. #490	C₂²×C₃₁	semidirect
628. #486	C₂²×C₃₁	semidirect
629. #486	C₂²×C₃₁	semidirect
630. #486	C₂²×C₃₁	semidirect
631. #485	C₂²×C₃₁	semidirect
632. #484	C₂²×C₃₁	semidirect
633. #482	C₂²×C₃₁	semidirect
634. #482	C₂²×C₃₁	semidirect
635. #482	C₂²×C₃₁	semidirect
636. #481	C₂²×C₃₁	semidirect
637. #481	C₂²×C₃₁	semidirect
638. #480	C₂²×C₃₁	semidirect
639. #480	C₂²×C₃₁	semidirect
640. #480	C₂²×C₃₁	semidirect
641. #479	C₂²×C₃₁	semidirect
644. #478	C₂²×C₃₁	semidirect
645. #478	C₂²×C₃₁	semidirect
646. #478	C₂²×C₃₁	semidirect
647. #478	C₂²×C₃₁	semidirect
648. #477	C₂²×C₃₁	semidirect
652. #476	C₂²×C₃₁	semidirect
653. #476	C₂²×C₃₁	semidirect
654. #476	C₂²×C₃₁	semidirect
655. #476	C₂²×C₃₁	semidirect
656. #476	C₂²×C₃₁	semidirect
658. #474	C₂²×C₃₁	semidirect
659. #474	C₂²×C₃₁	semidirect
660. #469	C₂²×C₃₁	semidirect
661. #468	C₂²×C₃₁	semidirect
662. #466	C₂²×C₃₁	semidirect
663. #466	C₂²×C₃₁	semidirect
664. #465	C₂²×C₃₁	semidirect
665. #465	C₂²×C₃₁	semidirect
667. #463	C₂²×C₃₁	semidirect
668. #463	C₂²×C₃₁	semidirect
669. #460	C₂²×C₃₁	semidirect
670. #460	C₂²×C₃₁	semidirect
671. #459	C₂²×C₃₁	semidirect
672. #459	C₂²×C₃₁	semidirect
677. #446	C₂²×C₃₁	semidirect
678. C₈×Q₈	C₂²×C₃₁	semidirect
679. #442	C₂²×C₃₁	semidirect
682. C₄×SD₁₆	C₂²×C₃₁	semidirect
683. C₄×SD₁₆	C₂²×C₃₁	semidirect
686. C₄×D₈	C₂²×C₃₁	semidirect
687. #436	C₂²×C₃₁	semidirect
688. #435	C₂²×C₃₁	semidirect
689. C₈×D₄	C₂²×C₃₁	semidirect
690. C₈×D₄	C₂²×C₃₁	semidirect
691. #433	C₂²×C₃₁	semidirect
692. #431	C₂²×C₃₁	semidirect
693. #428	C₂²×C₃₁	semidirect
694. #427	C₂²×C₃₁	semidirect
695. C₂×#106	C₂²×C₃₁	semidirect
696. #424	C₂²×C₃₁	semidirect
697. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
887. C₃₁	#62200	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×#3544	2
C₃₁×#3519	2
C₃₁×#3385	2
C₃₁×#3380	2
C₃₁×#3366	2
C₃₁×#3362	2
C₃₁×#3357	2
C₃₁×#3345	2
C₃₁×#3341	2
C₃₁×#3337	2
C₃₁×#3325	2
C₃₁×#3310	2
C₃₁×#3295	2
C₃₁×#3294	2
C₃₁×#3257	2
C₃₁×#3247	2
C₃₁×#3241	2
C₃₁×#3226	2
C₃₁×#3118	2
C₃₁×#3105	2
C₃₁×#3081	2
C₂×C₃₁×#476	2
C₃₁×#2994	2
#62200	31

Subgroups — C31×#62200 #21518959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62200 #21518959