Subgroups — C₃₁×#62116 #21518875

Order 7936.

1716 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3475	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3388	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3352	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3349	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3348	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3323	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3315	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3311	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3255	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3252	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3248	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3239	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3237	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3233	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#557	—	2	1	no	—
25	C₃₁×#557	C₂²	1	2	yes	complemented
26	C₃₁×#556	—	2	1	no	—
27	C₃₁×#556	C₂²	1	1	yes	characteristic
28	C₃₁×#556	C₂²	1	2	yes	—
29	C₃₁×#555	C₂²	1	1	yes	characteristic
30	C₃₁×#554	C₂²	1	1	yes	characteristic
31	C₃₁×#553	—	2	1	no	—
32	C₃₁×#552	—	2	1	no	—
33	C₃₁×#552	—	2	1	no	—
34	C₃₁×#552	—	2	1	no	—
35	C₃₁×#552	C₂²	1	1	yes	characteristic
36	C₃₁×#552	C₂²	1	1	yes	characteristic
37	C₃₁×#552	C₂²	1	2	yes	—
38	C₃₁×#552	C₂²	1	2	yes	complemented
39	C₃₁×#551	—	2	1	no	—
40	C₃₁×#551	—	2	1	no	—
41	C₃₁×#547	C₂²	1	1	yes	characteristic
42	C₃₁×#546	C₂²	1	1	yes	characteristic
43	C₃₁×#546	C₂²	1	1	yes	characteristic
44	C₃₁×#541	—	2	1	no	—
45	C₃₁×#541	—	2	1	no	—
46	C₃₁×#536	—	2	1	no	—
47	C₃₁×#533	C₂²	1	1	yes	characteristic
48	C₃₁×#533	C₂²	1	1	yes	characteristic
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#529	—	2	1	no	—
55	C₃₁×#529	—	2	1	no	—
56	C₃₁×#529	C₂²	1	1	yes	characteristic
57	C₃₁×#529	C₂²	1	1	yes	characteristic
58	C₃₁×#525	—	2	1	no	—
59	C₃₁×#519	—	2	1	no	—
60	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
61	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
62	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
63	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
64	C₂×C₃₁×#117	—	2	1	no	—
65	C₃₁×#501	C₂²	1	2	yes	complemented
66	C₃₁×#501	C₂²	1	2	yes	complemented
67	C₃₁×#499	C₂²	1	2	yes	complemented
68	C₃₁×#491	C₂²	1	2	yes	complemented
69	C₃₁×#489	C₂²	1	2	yes	—
70	C₃₁×#488	C₂²	1	2	yes	—
71	C₃₁×#485	C₂²	1	2	yes	—
72	C₃₁×#485	C₂²	1	2	yes	—
73	C₃₁×#485	C₂²	1	2	yes	complemented
74	C₃₁×#485	C₂²	1	2	yes	complemented
75	C₃₁×#485	C₂²	1	2	yes	complemented
76	C₃₁×#484	C₂²	1	2	yes	—
77	C₃₁×#484	C₂²	1	2	yes	complemented
78	C₃₁×#482	C₂²	1	2	yes	—
79	C₃₁×#481	C₂²	1	2	yes	—
80	C₃₁×#479	C₂²	1	2	yes	complemented
81	C₃₁×#479	C₂²	1	2	yes	complemented
82	C₃₁×#479	C₂²	1	2	yes	complemented
83	C₃₁×#478	C₂²	1	2	yes	—
84	C₃₁×#478	C₂²	1	2	yes	—
85	C₃₁×#478	C₂²	1	2	yes	—
86	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#477	C₂²	1	2	yes	complemented
88	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#476	C₂²	1	1	yes	characteristic
90	C₃₁×#476	C₂²	1	1	yes	characteristic
91	C₃₁×#476	C₂²	1	2	yes	—
92	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#475	C₂²	1	2	yes	complemented
96	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#474	C₂²	1	1	yes	characteristic
98	C₃₁×#474	C₂²	1	1	yes	characteristic
99	C₃₁×#474	C₂²	1	1	yes	characteristic
100	C₃₁×#474	C₂²	1	1	yes	characteristic
101	C₃₁×#470	C₂²	1	2	yes	—
102	C₃₁×#470	C₂²	1	2	yes	—
103	C₃₁×#470	C₂²	1	2	yes	complemented
104	C₃₁×#468	C₂²	1	2	yes	—
105	C₃₁×#467	C₂²	1	2	yes	complemented
106	C₃₁×#465	C₂²	1	2	yes	—
107	C₃₁×#464	C₂²	1	2	yes	—
108	C₃₁×#464	C₂²	1	2	yes	—
109	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
110	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#462	C₂²	1	2	yes	complemented
112	C₃₁×#461	C₂²	1	1	yes	characteristic
113	C₃₁×#461	C₂²	1	1	yes	characteristic
114	C₃₁×#452	C₂²	1	2	yes	—
115	C₃₁×#452	C₂²	1	2	yes	—
116	C₃₁×#450	C₂²	1	2	yes	—
117	C₃₁×#446	C₂²	1	2	yes	complemented
118	C₃₁×#441	C₂²	1	2	yes	complemented
119	C₃₁×#440	C₂²	1	2	yes	—
120	C₃₁×#440	C₂²	1	2	yes	—
121	C₃₁×#440	C₂²	1	2	yes	—
122	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
123	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
124	C₃₁×#436	C₂²	1	2	yes	—
125	C₃₁×#435	C₂²	1	2	yes	—
126	C₃₁×#435	C₂²	1	2	yes	complemented
127	C₃₁×#432	C₂²	1	1	yes	characteristic
128	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#428	C₂²	1	2	yes	—
131	C₃₁×#428	C₂²	1	2	yes	complemented
132	C₃₁×#427	C₂²	1	2	yes	complemented
133	C₃₁×#423	C₂²	1	1	yes	characteristic
134	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
136	C₃₁×#418	C₂²	1	2	yes	—
137	C₃₁×#417	C₂²	1	2	yes	—
138	C₃₁×#416	C₂²	1	2	yes	—
139	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
140	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₃₁	—	2	1	no	—
143	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₃₁	—	2	1	no	—
145	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
152	C₃₁×C₄⋊Q₈	—	2	2	no	—
153	C₃₁×C₄⋊Q₈	—	2	1	no	—
154	C₃₁×C₄⋊Q₈	—	2	1	no	—
155	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×C₄⋊Q₈	C₂³	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×#126	—	2	1	no	—
163	C₃₁×#126	—	2	1	no	—
164	C₃₁×#126	—	2	1	no	—
165	C₃₁×#126	—	2	1	no	—
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	1	no	—
171	C₃₁×#126	—	2	1	no	—
172	C₃₁×#125	—	2	1	no	—
173	C₃₁×#125	—	2	1	no	—
174	C₃₁×#125	—	2	2	no	—
175	C₃₁×#125	—	2	2	no	—
176	C₃₁×#125	—	2	2	no	—
177	C₃₁×#125	—	2	2	no	—
178	C₃₁×#125	—	2	1	no	—
179	C₃₁×#125	—	2	1	no	—
180	C₃₁×#125	—	2	1	no	—
181	C₃₁×#125	—	2	1	no	—
182	C₃₁×#125	C₂³	1	2	yes	—
183	C₃₁×#125	C₂³	1	2	yes	—
184	C₃₁×#125	C₂³	1	1	yes	characteristic
185	C₃₁×#125	C₂³	1	1	yes	characteristic
186	C₃₁×#124	—	2	2	no	—
187	C₃₁×#124	—	2	1	no	—
188	C₃₁×#124	—	2	1	no	—
189	C₃₁×#124	C₂³	1	1	yes	characteristic
190	C₃₁×#124	C₂³	1	1	yes	characteristic
191	C₃₁×#123	—	2	1	no	—
192	C₃₁×#123	—	2	1	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×#123	—	2	1	no	—
196	C₃₁×#123	—	2	1	no	—
197	C₃₁×#123	—	2	1	no	—
198	C₃₁×#123	—	2	1	no	—
199	C₃₁×#123	—	2	1	no	—
200	C₃₁×#123	—	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	1	no	—
205	C₃₁×C₂²⋊Q₈	—	2	1	no	—
206	C₃₁×C₂²⋊Q₈	—	2	1	no	—
207	C₃₁×C₂²⋊Q₈	—	2	1	no	—
208	C₃₁×C₂²⋊Q₈	—	2	1	no	—
209	C₃₁×C₂²⋊Q₈	—	2	1	no	—
210	C₃₁×C₂²⋊Q₈	—	2	1	no	—
211	C₃₁×C₂²⋊Q₈	—	2	1	no	—
212	C₃₁×C₂²⋊Q₈	—	2	1	no	—
213	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
220	C₃₁×#121	—	2	1	no	—
221	C₃₁×#121	—	2	1	no	—
222	C₃₁×#121	—	2	1	no	—
223	C₃₁×#121	—	2	1	no	—
224	C₃₁×#121	C₂³	1	1	yes	characteristic
225	C₃₁×#121	C₂³	1	1	yes	characteristic
226	C₃₁×#120	—	2	1	no	—
227	C₃₁×#120	—	2	1	no	—
228	C₄×Q₈×C₃₁	—	2	2	no	—
229	C₄×Q₈×C₃₁	—	2	2	no	—
230	C₄×Q₈×C₃₁	—	2	1	no	—
231	C₄×Q₈×C₃₁	—	2	1	no	—
232	C₄×Q₈×C₃₁	—	2	1	no	—
233	C₄×Q₈×C₃₁	—	2	1	no	—
234	C₄×Q₈×C₃₁	—	2	1	no	—
235	C₄×Q₈×C₃₁	—	2	1	no	—
236	C₄×Q₈×C₃₁	—	2	1	no	—
237	C₄×Q₈×C₃₁	—	2	1	no	—
238	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
239	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
240	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
242	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
243	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₃₁	—	2	1	no	—
248	C₄×D₄×C₃₁	—	2	1	no	—
249	C₄×D₄×C₃₁	—	2	1	no	—
250	C₄×D₄×C₃₁	—	2	1	no	—
251	C₄×D₄×C₃₁	—	2	1	no	—
252	C₄×D₄×C₃₁	—	2	1	no	—
253	C₄×D₄×C₃₁	—	2	1	no	—
254	C₄×D₄×C₃₁	—	2	1	no	—
255	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
256	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
257	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
258	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
266	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
267	C₃₁×#117	—	2	1	no	—
268	C₃₁×#117	—	2	1	no	—
269	C₃₁×#117	—	2	1	no	—
270	C₃₁×#117	—	2	1	no	—
271	C₃₁×#117	—	2	1	no	—
272	C₃₁×#117	—	2	1	no	—
273	C₃₁×#117	—	2	1	no	—
274	C₃₁×#117	—	2	1	no	—
275	C₃₁×#117	—	2	2	no	—
276	C₃₁×#117	—	2	2	no	—
277	C₃₁×#117	—	2	1	no	—
278	C₃₁×#117	—	2	1	no	—
279	C₃₁×#117	—	2	1	no	—
280	C₃₁×#117	—	2	1	no	—
281	C₃₁×#117	D₄	1	1	yes	characteristic
282	C₃₁×#117	D₄	1	1	yes	characteristic
283	C₃₁×#117	D₄	1	1	yes	characteristic
284	C₃₁×#117	C₂³	1	2	yes	—
285	C₃₁×#117	C₂³	1	2	yes	—
286	C₃₁×#117	C₂³	1	1	yes	characteristic
287	C₃₁×#117	C₂³	1	1	yes	characteristic
288	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
289	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
290	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
291	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
292	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
294	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
295	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
296	C₂×C₄²×C₃₁	—	2	1	no	—
297	C₂×C₄²×C₃₁	—	2	1	no	—
298	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
300	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
301	C₃₁×#107	C₂³	1	2	yes	—
302	C₃₁×#107	C₂³	1	2	yes	—
303	C₃₁×#107	C₂³	1	2	yes	—
304	C₃₁×#107	C₂³	1	2	yes	—
305	C₃₁×#107	C₂³	1	2	yes	—
306	C₃₁×#107	C₂³	1	2	yes	—
307	C₃₁×#106	C₂³	1	2	yes	—
308	C₃₁×#106	C₂³	1	2	yes	—
309	C₃₁×#106	C₂³	1	2	yes	—
310	C₃₁×#106	C₂³	1	2	yes	—
311	C₃₁×#106	C₂³	1	2	yes	—
312	C₃₁×#106	C₂³	1	2	yes	—
313	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
314	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
315	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
316	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
317	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
318	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
319	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
320	C₃₁×#103	C₂³	1	2	yes	—
321	C₃₁×#103	C₂³	1	2	yes	—
322	C₃₁×#103	C₂³	1	2	yes	—
323	C₃₁×#103	C₂³	1	2	yes	—
324	C₃₁×#103	C₂³	1	2	yes	—
325	C₃₁×#103	C₂³	1	2	yes	—
326	C₃₁×#103	C₂³	1	2	yes	—
327	C₃₁×#103	C₂³	1	2	yes	—
328	C₃₁×#103	C₂³	1	2	yes	—
329	C₃₁×#103	C₂³	1	2	yes	—
330	C₃₁×#102	C₂³	1	2	yes	—
331	C₃₁×#102	C₂³	1	2	yes	—
332	C₃₁×#102	C₂³	1	2	yes	—
333	C₃₁×#102	C₂³	1	2	yes	—
334	C₃₁×#102	C₂³	1	2	yes	—
335	C₃₁×#102	C₂³	1	2	yes	—
336	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
337	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
339	C₃₁×#97	C₂³	1	2	yes	—
340	C₃₁×#97	C₂³	1	2	yes	—
341	C₄×C₈×C₃₁	C₂³	1	2	yes	—
342	C₂⁴×C₃₁	—	2	1	no	—
343	#41×C₃₁	—	2	2	no	—
344	#41×C₃₁	—	2	2	no	—
345	#41×C₃₁	—	4	2	no	—
346	#41×C₃₁	—	4	1	no	—
347	#41×C₃₁	—	4	1	no	—
348	C₂×Q₈×C₃₁	—	2	1	no	—
349	C₂×Q₈×C₃₁	—	2	1	no	—
350	C₂×Q₈×C₃₁	—	2	1	no	—
351	C₂×Q₈×C₃₁	—	2	2	no	—
352	C₂×Q₈×C₃₁	—	2	1	no	—
353	C₂×Q₈×C₃₁	—	4	4	no	—
354	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
355	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
358	C₂×D₄×C₃₁	—	2	2	no	—
359	C₂×D₄×C₃₁	—	2	1	no	—
360	C₂×D₄×C₃₁	—	2	1	no	—
361	C₂×D₄×C₃₁	—	2	1	no	—
362	C₂×D₄×C₃₁	—	2	1	no	—
363	C₂×D₄×C₃₁	—	2	1	no	—
364	C₂×D₄×C₃₁	—	4	1	no	—
365	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
368	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₃₁	—	2	1	no	—
371	C₂²×C₄×C₃₁	—	2	2	no	—
372	C₂²×C₄×C₃₁	—	2	1	no	—
373	C₂²×C₄×C₃₁	—	2	1	no	—
374	C₂²×C₄×C₃₁	—	2	1	no	—
375	C₂²×C₄×C₃₁	—	2	1	no	—
376	C₂²×C₄×C₃₁	—	2	1	no	—
377	C₂²×C₄×C₃₁	—	2	1	no	—
378	C₂²×C₄×C₃₁	—	2	1	no	—
379	C₂²×C₄×C₃₁	—	2	1	no	—
380	C₂²×C₄×C₃₁	—	4	4	no	—
381	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
390	Q₁₆×C₃₁	—	4	2	no	—
391	Q₁₆×C₃₁	—	4	2	no	—
392	SD₁₆×C₃₁	—	2	4	no	—
393	SD₁₆×C₃₁	—	4	2	no	—
394	M₁₆×C₃₁	—	4	2	no	—
395	M₁₆×C₃₁	—	4	2	no	—
396	C₂×C₈×C₃₁	—	4	2	no	—
397	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
398	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
399	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
400	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₃₁	—	2	1	no	—
402	C₄⋊C₄×C₃₁	—	2	1	no	—
403	C₄⋊C₄×C₃₁	—	2	1	no	—
404	C₄⋊C₄×C₃₁	—	2	1	no	—
405	C₄⋊C₄×C₃₁	—	2	1	no	—
406	C₄⋊C₄×C₃₁	—	2	1	no	—
407	C₄⋊C₄×C₃₁	—	2	1	no	—
408	C₄⋊C₄×C₃₁	—	2	1	no	—
409	C₄⋊C₄×C₃₁	—	2	2	no	—
410	C₄⋊C₄×C₃₁	—	2	1	no	—
411	C₄⋊C₄×C₃₁	—	2	2	no	—
412	C₄⋊C₄×C₃₁	—	2	1	no	—
413	C₄⋊C₄×C₃₁	—	2	1	no	—
414	C₄⋊C₄×C₃₁	—	2	1	no	—
415	C₄⋊C₄×C₃₁	—	2	1	no	—
416	C₄⋊C₄×C₃₁	—	2	1	no	—
417	C₄⋊C₄×C₃₁	—	2	1	no	—
418	C₄⋊C₄×C₃₁	—	2	1	no	—
419	C₄⋊C₄×C₃₁	—	2	2	no	—
420	C₄⋊C₄×C₃₁	—	2	2	no	—
421	C₄⋊C₄×C₃₁	—	2	2	no	—
422	C₄⋊C₄×C₃₁	—	2	2	no	—
423	C₄⋊C₄×C₃₁	—	2	1	no	—
424	C₄⋊C₄×C₃₁	—	2	1	no	—
425	C₄⋊C₄×C₃₁	—	2	1	no	—
426	C₄⋊C₄×C₃₁	—	2	1	no	—
427	C₄⋊C₄×C₃₁	—	2	1	no	—
428	C₄⋊C₄×C₃₁	—	2	2	no	—
429	C₄⋊C₄×C₃₁	—	2	2	no	—
430	C₄⋊C₄×C₃₁	—	2	2	no	—
431	C₄⋊C₄×C₃₁	—	2	2	no	—
432	C₄⋊C₄×C₃₁	—	2	2	no	—
433	C₄⋊C₄×C₃₁	—	2	2	no	—
434	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
437	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
438	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
439	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
441	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
442	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
443	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
444	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
445	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
447	C₂²⋊C₄×C₃₁	—	2	1	no	—
448	C₂²⋊C₄×C₃₁	—	2	1	no	—
449	C₂²⋊C₄×C₃₁	—	2	2	no	—
450	C₂²⋊C₄×C₃₁	—	2	2	no	—
451	C₂²⋊C₄×C₃₁	—	2	2	no	—
452	C₂²⋊C₄×C₃₁	—	2	1	no	—
453	C₂²⋊C₄×C₃₁	—	2	1	no	—
454	C₂²⋊C₄×C₃₁	—	2	2	no	—
455	C₂²⋊C₄×C₃₁	—	2	2	no	—
456	C₂²⋊C₄×C₃₁	—	2	1	no	—
457	C₂²⋊C₄×C₃₁	—	2	1	no	—
458	C₂²⋊C₄×C₃₁	—	2	1	no	—
459	C₂²⋊C₄×C₃₁	—	2	1	no	—
460	C₂²⋊C₄×C₃₁	—	2	1	no	—
461	C₂²⋊C₄×C₃₁	—	2	1	no	—
462	C₂²⋊C₄×C₃₁	—	2	1	no	—
463	C₂²⋊C₄×C₃₁	—	2	1	no	—
464	C₂²⋊C₄×C₃₁	—	2	1	no	—
465	C₂²⋊C₄×C₃₁	—	2	1	no	—
466	C₂²⋊C₄×C₃₁	—	2	1	no	—
467	C₂²⋊C₄×C₃₁	—	2	1	no	—
468	C₂²⋊C₄×C₃₁	—	2	1	no	—
469	C₂²⋊C₄×C₃₁	—	2	1	no	—
470	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
471	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
472	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
473	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
474	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
475	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
476	C₄²×C₃₁	—	2	1	no	—
477	C₄²×C₃₁	—	2	1	no	—
478	C₄²×C₃₁	—	2	1	no	—
479	C₄²×C₃₁	—	2	1	no	—
480	C₄²×C₃₁	—	2	1	no	—
481	C₄²×C₃₁	—	2	1	no	—
482	C₄²×C₃₁	—	2	2	no	—
483	C₄²×C₃₁	—	2	2	no	—
484	C₄²×C₃₁	—	2	2	no	—
485	C₄²×C₃₁	—	2	2	no	—
486	C₄²×C₃₁	—	2	2	no	—
487	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
488	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
489	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
490	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
491	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
492	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
494	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
495	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
496	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
497	#62116	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
498	C₂³×C₃₁	—	2	1	no	—
499	C₂³×C₃₁	—	2	1	no	—
500	C₂³×C₃₁	—	4	2	no	—
501	C₂³×C₃₁	—	4	2	no	—
502	C₂³×C₃₁	—	8	1	no	—
503	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
504	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
505	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
506	Q₈×C₃₁	—	2	2	no	—
507	Q₈×C₃₁	—	2	1	no	—
508	Q₈×C₃₁	—	2	1	no	—
509	Q₈×C₃₁	—	2	2	no	—
510	Q₈×C₃₁	—	2	1	no	—
511	Q₈×C₃₁	—	2	1	no	—
512	Q₈×C₃₁	—	4	1	no	—
513	Q₈×C₃₁	—	4	2	no	—
514	Q₈×C₃₁	—	4	4	no	—
515	Q₈×C₃₁	—	4	2	no	—
516	Q₈×C₃₁	—	4	2	no	—
517	Q₈×C₃₁	—	8	1	no	—
518	D₄×C₃₁	—	2	1	no	—
519	D₄×C₃₁	—	2	1	no	—
520	D₄×C₃₁	—	2	1	no	—
521	D₄×C₃₁	—	4	1	no	—
522	D₄×C₃₁	—	4	1	no	—
523	D₄×C₃₁	—	4	1	no	—
524	D₄×C₃₁	—	4	2	no	—
525	D₄×C₃₁	—	4	2	no	—
526	D₄×C₃₁	—	4	2	no	—
527	D₄×C₃₁	—	8	1	no	—
528	D₄×C₃₁	—	8	1	no	—
529	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
530	C₂×C₄×C₃₁	—	2	2	no	—
531	C₂×C₄×C₃₁	—	2	2	no	—
532	C₂×C₄×C₃₁	—	2	2	no	—
533	C₂×C₄×C₃₁	—	2	1	no	—
534	C₂×C₄×C₃₁	—	2	1	no	—
535	C₂×C₄×C₃₁	—	2	1	no	—
536	C₂×C₄×C₃₁	—	2	1	no	—
537	C₂×C₄×C₃₁	—	2	1	no	—
538	C₂×C₄×C₃₁	—	2	1	no	—
539	C₂×C₄×C₃₁	—	2	1	no	—
540	C₂×C₄×C₃₁	—	2	2	no	—
541	C₂×C₄×C₃₁	—	2	2	no	—
542	C₂×C₄×C₃₁	—	2	1	no	—
543	C₂×C₄×C₃₁	—	2	1	no	—
544	C₂×C₄×C₃₁	—	2	1	no	—
545	C₂×C₄×C₃₁	—	2	1	no	—
546	C₂×C₄×C₃₁	—	2	2	no	—
547	C₂×C₄×C₃₁	—	2	2	no	—
548	C₂×C₄×C₃₁	—	2	1	no	—
549	C₂×C₄×C₃₁	—	4	1	no	—
550	C₂×C₄×C₃₁	—	4	1	no	—
551	C₂×C₄×C₃₁	—	4	1	no	—
552	C₂×C₄×C₃₁	—	4	2	no	—
553	C₂×C₄×C₃₁	—	4	2	no	—
554	C₂×C₄×C₃₁	—	4	2	no	—
555	C₂×C₄×C₃₁	—	4	2	no	—
556	C₂×C₄×C₃₁	—	4	2	no	—
557	C₂×C₄×C₃₁	—	4	4	no	—
558	C₂×C₄×C₃₁	—	4	2	no	—
559	C₂×C₄×C₃₁	—	4	2	no	—
560	C₂×C₄×C₃₁	—	8	1	no	—
561	C₂×C₄×C₃₁	—	8	1	no	—
562	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
574	C₈×C₃₁	—	2	2	no	—
575	C₈×C₃₁	—	2	2	no	—
576	C₈×C₃₁	—	2	2	no	—
577	C₈×C₃₁	—	2	2	no	—
578	#3509	C₂×C₃₁	1	1	yes	characteristic, complemented
579	#3475	C₂×C₃₁	1	1	yes	characteristic
580	#3388	C₂×C₃₁	1	2	yes	complemented
581	#3377	C₂×C₃₁	1	2	yes	complemented
582	#3352	C₂×C₃₁	1	2	yes	complemented
583	#3349	C₂×C₃₁	1	2	yes	complemented
584	#3348	C₂×C₃₁	1	2	yes	complemented
585	#3323	C₂×C₃₁	1	2	yes	complemented
586	#3315	C₂×C₃₁	1	2	yes	complemented
587	#3311	C₂×C₃₁	1	2	yes	complemented
588	#3255	C₂×C₃₁	1	1	yes	characteristic, complemented
589	#3252	C₂×C₃₁	1	1	yes	characteristic, complemented
590	#3248	C₂×C₃₁	1	1	yes	characteristic, complemented
591	#3239	C₂×C₃₁	1	1	yes	characteristic, complemented
592	#3237	C₂×C₃₁	1	1	yes	characteristic, complemented
593	#3233	C₂×C₃₁	1	1	yes	characteristic, complemented
594	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
595	#3110	C₂×C₃₁	1	1	yes	characteristic, complemented
596	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
597	#3079	C₂×C₃₁	1	1	yes	characteristic, complemented
598	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
599	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
600	#2989	C₂×C₃₁	1	1	yes	characteristic, complemented
601	C₂²×C₃₁	—	2	1	no	—
602	C₂²×C₃₁	—	2	1	no	—
603	C₂²×C₃₁	—	2	1	no	—
604	C₂²×C₃₁	—	2	1	no	—
605	C₂²×C₃₁	—	2	1	no	—
606	C₂²×C₃₁	—	2	1	no	—
607	C₂²×C₃₁	—	2	2	no	—
608	C₂²×C₃₁	—	2	1	no	—
609	C₂²×C₃₁	—	2	1	no	—
610	C₂²×C₃₁	—	2	1	no	—
611	C₂²×C₃₁	—	4	1	no	—
612	C₂²×C₃₁	—	4	1	no	—
613	C₂²×C₃₁	—	4	1	no	—
614	C₂²×C₃₁	—	4	1	no	—
615	C₂²×C₃₁	—	4	1	no	—
616	C₂²×C₃₁	—	8	4	no	—
617	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
618	C₄×C₃₁	—	2	1	no	—
619	C₄×C₃₁	—	2	1	no	—
620	C₄×C₃₁	—	2	1	no	—
621	C₄×C₃₁	—	2	1	no	—
622	C₄×C₃₁	—	2	1	no	—
623	C₄×C₃₁	—	2	1	no	—
624	C₄×C₃₁	—	2	1	no	—
625	C₄×C₃₁	—	2	1	no	—
626	C₄×C₃₁	—	2	1	no	—
627	C₄×C₃₁	—	2	1	no	—
628	C₄×C₃₁	—	4	1	no	—
629	C₄×C₃₁	—	4	1	no	—
630	C₄×C₃₁	—	4	2	no	—
631	C₄×C₃₁	—	4	1	no	—
632	C₄×C₃₁	—	4	1	no	—
633	C₄×C₃₁	—	4	2	no	—
634	C₄×C₃₁	—	4	1	no	—
635	C₄×C₃₁	—	4	1	no	—
636	C₄×C₃₁	—	4	2	no	—
637	C₄×C₃₁	—	4	2	no	—
638	C₄×C₃₁	#575	1	2	yes	—
639	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
640	C₄×C₃₁	#585	1	1	yes	characteristic
641	#557	—	2	1	no	—
642	#557	C₂²×C₃₁	1	2	yes	complemented
643	#556	—	2	1	no	—
644	#556	C₂²×C₃₁	1	1	yes	characteristic
645	#556	C₂²×C₃₁	1	2	yes	—
646	#555	C₂²×C₃₁	1	1	yes	characteristic
647	#554	C₂²×C₃₁	1	1	yes	characteristic
648	#553	—	2	1	no	—
649	#552	—	2	1	no	—
650	#552	—	2	1	no	—
651	#552	—	2	1	no	—
652	#552	C₂²×C₃₁	1	1	yes	characteristic
653	#552	C₂²×C₃₁	1	1	yes	characteristic
654	#552	C₂²×C₃₁	1	2	yes	—
655	#552	C₂²×C₃₁	1	2	yes	complemented
656	#551	—	2	1	no	—
657	#551	—	2	1	no	—
658	#547	C₂²×C₃₁	1	1	yes	characteristic
659	#546	C₂²×C₃₁	1	1	yes	characteristic
660	#546	C₂²×C₃₁	1	1	yes	characteristic
661	#541	—	2	1	no	—
662	#541	—	2	1	no	—
663	#536	—	2	1	no	—
664	#533	C₂²×C₃₁	1	1	yes	characteristic
665	#533	C₂²×C₃₁	1	1	yes	characteristic
666	#533	C₂²×C₃₁	1	1	yes	characteristic
667	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
671	#529	—	2	1	no	—
672	#529	—	2	1	no	—
673	#529	C₂²×C₃₁	1	1	yes	characteristic
674	#529	C₂²×C₃₁	1	1	yes	characteristic
675	#525	—	2	1	no	—
676	#519	—	2	1	no	—
677	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
678	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
679	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
680	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
681	C₂×#117	—	2	1	no	—
682	#501	C₂²×C₃₁	1	2	yes	complemented
683	#501	C₂²×C₃₁	1	2	yes	complemented
684	#499	C₂²×C₃₁	1	2	yes	complemented
685	#491	C₂²×C₃₁	1	2	yes	complemented
686	#489	C₂²×C₃₁	1	2	yes	—
687	#488	C₂²×C₃₁	1	2	yes	—
688	#485	C₂²×C₃₁	1	2	yes	—
689	#485	C₂²×C₃₁	1	2	yes	—
690	#485	C₂²×C₃₁	1	2	yes	complemented
691	#485	C₂²×C₃₁	1	2	yes	complemented
692	#485	C₂²×C₃₁	1	2	yes	complemented
693	#484	C₂²×C₃₁	1	2	yes	—
694	#484	C₂²×C₃₁	1	2	yes	complemented
695	#482	C₂²×C₃₁	1	2	yes	—
696	#481	C₂²×C₃₁	1	2	yes	—
697	#479	C₂²×C₃₁	1	2	yes	complemented
698	#479	C₂²×C₃₁	1	2	yes	complemented
699	#479	C₂²×C₃₁	1	2	yes	complemented
700	#478	C₂²×C₃₁	1	2	yes	—
701	#478	C₂²×C₃₁	1	2	yes	—
702	#478	C₂²×C₃₁	1	2	yes	—
703	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
704	#477	C₂²×C₃₁	1	2	yes	complemented
705	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	#476	C₂²×C₃₁	1	1	yes	characteristic
707	#476	C₂²×C₃₁	1	1	yes	characteristic
708	#476	C₂²×C₃₁	1	2	yes	—
709	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
710	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
711	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
712	#475	C₂²×C₃₁	1	2	yes	complemented
713	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
714	#474	C₂²×C₃₁	1	1	yes	characteristic
715	#474	C₂²×C₃₁	1	1	yes	characteristic
716	#474	C₂²×C₃₁	1	1	yes	characteristic
717	#474	C₂²×C₃₁	1	1	yes	characteristic
718	#470	C₂²×C₃₁	1	2	yes	—
719	#470	C₂²×C₃₁	1	2	yes	—
720	#470	C₂²×C₃₁	1	2	yes	complemented
721	#468	C₂²×C₃₁	1	2	yes	—
722	#467	C₂²×C₃₁	1	2	yes	complemented
723	#465	C₂²×C₃₁	1	2	yes	—
724	#464	C₂²×C₃₁	1	2	yes	—
725	#464	C₂²×C₃₁	1	2	yes	—
726	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
727	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
728	#462	C₂²×C₃₁	1	2	yes	complemented
729	#461	C₂²×C₃₁	1	1	yes	characteristic
730	#461	C₂²×C₃₁	1	1	yes	characteristic
731	#452	C₂²×C₃₁	1	2	yes	—
732	#452	C₂²×C₃₁	1	2	yes	—
733	#450	C₂²×C₃₁	1	2	yes	—
734	#446	C₂²×C₃₁	1	2	yes	complemented
735	#441	C₂²×C₃₁	1	2	yes	complemented
736	#440	C₂²×C₃₁	1	2	yes	—
737	#440	C₂²×C₃₁	1	2	yes	—
738	#440	C₂²×C₃₁	1	2	yes	—
739	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
740	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
741	#436	C₂²×C₃₁	1	2	yes	—
742	#435	C₂²×C₃₁	1	2	yes	—
743	#435	C₂²×C₃₁	1	2	yes	complemented
744	#432	C₂²×C₃₁	1	1	yes	characteristic
745	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
746	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
747	#428	C₂²×C₃₁	1	2	yes	—
748	#428	C₂²×C₃₁	1	2	yes	complemented
749	#427	C₂²×C₃₁	1	2	yes	complemented
750	#423	C₂²×C₃₁	1	1	yes	characteristic
751	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
752	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
753	#418	C₂²×C₃₁	1	2	yes	—
754	#417	C₂²×C₃₁	1	2	yes	—
755	#416	C₂²×C₃₁	1	2	yes	—
756	C₂×C₃₁	—	4	1	no	—
757	C₂×C₃₁	—	4	1	no	—
758	C₂×C₃₁	—	4	1	no	—
759	C₂×C₃₁	—	4	2	no	—
760	C₂×C₃₁	—	8	1	no	—
761	C₂×C₃₁	#3489	1	1	yes	characteristic
762	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
763	C₂×C₃₁	#3586	1	1	yes	characteristic
764	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
765	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
766	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
767	C₂²×Q₈	—	2	1	no	—
768	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
769	C₂³×C₄	—	2	1	no	—
770	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
771	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
772	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
773	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
774	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
775	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
776	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
777	C₄⋊Q₈	—	2	2	no	—
778	C₄⋊Q₈	—	2	1	no	—
779	C₄⋊Q₈	—	2	1	no	—
780	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
781	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
782	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
783	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
784	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
785	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
786	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
787	#126	—	2	1	no	—
788	#126	—	2	1	no	—
789	#126	—	2	1	no	—
790	#126	—	2	1	no	—
791	#126	—	2	2	no	—
792	#126	—	2	2	no	—
793	#126	—	2	2	no	—
794	#126	—	2	2	no	—
795	#126	—	2	1	no	—
796	#126	—	2	1	no	—
797	#125	—	2	1	no	—
798	#125	—	2	1	no	—
799	#125	—	2	2	no	—
800	#125	—	2	2	no	—
801	#125	—	2	2	no	—
802	#125	—	2	2	no	—
803	#125	—	2	1	no	—
804	#125	—	2	1	no	—
805	#125	—	2	1	no	—
806	#125	—	2	1	no	—
807	#125	C₂³×C₃₁	1	1	yes	characteristic
808	#125	C₂³×C₃₁	1	1	yes	characteristic
809	#125	C₂³×C₃₁	1	2	yes	—
810	#125	C₂³×C₃₁	1	2	yes	—
811	#124	—	2	2	no	—
812	#124	—	2	1	no	—
813	#124	—	2	1	no	—
814	#124	C₂³×C₃₁	1	1	yes	characteristic
815	#124	C₂³×C₃₁	1	1	yes	characteristic
816	#123	—	2	1	no	—
817	#123	—	2	1	no	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	#123	—	2	1	no	—
821	#123	—	2	1	no	—
822	#123	—	2	1	no	—
823	#123	—	2	1	no	—
824	#123	—	2	1	no	—
825	#123	—	2	1	no	—
826	C₂²⋊Q₈	—	2	1	no	—
827	C₂²⋊Q₈	—	2	1	no	—
828	C₂²⋊Q₈	—	2	1	no	—
829	C₂²⋊Q₈	—	2	1	no	—
830	C₂²⋊Q₈	—	2	1	no	—
831	C₂²⋊Q₈	—	2	1	no	—
832	C₂²⋊Q₈	—	2	1	no	—
833	C₂²⋊Q₈	—	2	1	no	—
834	C₂²⋊Q₈	—	2	1	no	—
835	C₂²⋊Q₈	—	2	1	no	—
836	C₂²⋊Q₈	—	2	1	no	—
837	C₂²⋊Q₈	—	2	1	no	—
838	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
839	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
840	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
841	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
842	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
843	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
844	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
845	#121	—	2	1	no	—
846	#121	—	2	1	no	—
847	#121	—	2	1	no	—
848	#121	—	2	1	no	—
849	#121	C₂³×C₃₁	1	1	yes	characteristic
850	#121	C₂³×C₃₁	1	1	yes	characteristic
851	#120	—	2	1	no	—
852	#120	—	2	1	no	—
853	C₄×Q₈	—	2	2	no	—
854	C₄×Q₈	—	2	2	no	—
855	C₄×Q₈	—	2	1	no	—
856	C₄×Q₈	—	2	1	no	—
857	C₄×Q₈	—	2	1	no	—
858	C₄×Q₈	—	2	1	no	—
859	C₄×Q₈	—	2	1	no	—
860	C₄×Q₈	—	2	1	no	—
861	C₄×Q₈	—	2	1	no	—
862	C₄×Q₈	—	2	1	no	—
863	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
864	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
865	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
866	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
867	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
868	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
869	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
870	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
871	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
872	C₄×D₄	—	2	1	no	—
873	C₄×D₄	—	2	1	no	—
874	C₄×D₄	—	2	1	no	—
875	C₄×D₄	—	2	1	no	—
876	C₄×D₄	—	2	1	no	—
877	C₄×D₄	—	2	1	no	—
878	C₄×D₄	—	2	1	no	—
879	C₄×D₄	—	2	1	no	—
880	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
881	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
882	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
883	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
884	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
885	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
886	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
887	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
888	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
889	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
890	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
891	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
892	#117	—	2	1	no	—
893	#117	—	2	1	no	—
894	#117	—	2	1	no	—
895	#117	—	2	1	no	—
896	#117	—	2	1	no	—
897	#117	—	2	1	no	—
898	#117	—	2	1	no	—
899	#117	—	2	1	no	—
900	#117	—	2	2	no	—
901	#117	—	2	2	no	—
902	#117	—	2	1	no	—
903	#117	—	2	1	no	—
904	#117	—	2	1	no	—
905	#117	—	2	1	no	—
906	#117	D₄×C₃₁	1	1	yes	characteristic
907	#117	D₄×C₃₁	1	1	yes	characteristic
908	#117	D₄×C₃₁	1	1	yes	characteristic
909	#117	C₂³×C₃₁	1	1	yes	characteristic
910	#117	C₂³×C₃₁	1	1	yes	characteristic
911	#117	C₂³×C₃₁	1	2	yes	—
912	#117	C₂³×C₃₁	1	2	yes	—
913	C₂×C₄⋊C₄	—	2	1	no	—
914	C₂×C₄⋊C₄	—	2	1	no	—
915	C₂×C₄⋊C₄	—	2	1	no	—
916	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
917	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
918	C₂×C₂²⋊C₄	—	2	1	no	—
919	C₂×C₂²⋊C₄	—	2	1	no	—
920	C₂×C₂²⋊C₄	—	2	1	no	—
921	C₂×C₄²	—	2	1	no	—
922	C₂×C₄²	—	2	1	no	—
923	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
924	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
925	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
926	#107	C₂³×C₃₁	1	2	yes	—
927	#107	C₂³×C₃₁	1	2	yes	—
928	#107	C₂³×C₃₁	1	2	yes	—
929	#107	C₂³×C₃₁	1	2	yes	—
930	#107	C₂³×C₃₁	1	2	yes	—
931	#107	C₂³×C₃₁	1	2	yes	—
932	#106	C₂³×C₃₁	1	2	yes	—
933	#106	C₂³×C₃₁	1	2	yes	—
934	#106	C₂³×C₃₁	1	2	yes	—
935	#106	C₂³×C₃₁	1	2	yes	—
936	#106	C₂³×C₃₁	1	2	yes	—
937	#106	C₂³×C₃₁	1	2	yes	—
938	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
939	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
940	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
941	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
942	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
943	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
944	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
945	#103	C₂³×C₃₁	1	2	yes	—
946	#103	C₂³×C₃₁	1	2	yes	—
947	#103	C₂³×C₃₁	1	2	yes	—
948	#103	C₂³×C₃₁	1	2	yes	—
949	#103	C₂³×C₃₁	1	2	yes	—
950	#103	C₂³×C₃₁	1	2	yes	—
951	#103	C₂³×C₃₁	1	2	yes	—
952	#103	C₂³×C₃₁	1	2	yes	—
953	#103	C₂³×C₃₁	1	2	yes	—
954	#103	C₂³×C₃₁	1	2	yes	—
955	#102	C₂³×C₃₁	1	2	yes	—
956	#102	C₂³×C₃₁	1	2	yes	—
957	#102	C₂³×C₃₁	1	2	yes	—
958	#102	C₂³×C₃₁	1	2	yes	—
959	#102	C₂³×C₃₁	1	2	yes	—
960	#102	C₂³×C₃₁	1	2	yes	—
961	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
962	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
963	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
964	#97	C₂³×C₃₁	1	2	yes	—
965	#97	C₂³×C₃₁	1	2	yes	—
966	C₄×C₈	C₂³×C₃₁	1	2	yes	—
967	C₃₁	#62116	1	1	yes	characteristic, direct product factor, Sylow
968	C₂⁴	—	2	1	no	—
969	#41	—	2	2	no	—
970	#41	—	2	2	no	—
971	#41	—	4	2	no	—
972	#41	—	4	1	no	—
973	#41	—	4	1	no	—
974	C₂×Q₈	—	2	1	no	—
975	C₂×Q₈	—	2	1	no	—
976	C₂×Q₈	—	2	1	no	—
977	C₂×Q₈	—	2	2	no	—
978	C₂×Q₈	—	2	1	no	—
979	C₂×Q₈	—	4	4	no	—
980	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
981	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
982	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
983	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
984	C₂×D₄	—	2	2	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	2	1	no	—
987	C₂×D₄	—	2	1	no	—
988	C₂×D₄	—	2	1	no	—
989	C₂×D₄	—	2	1	no	—
990	C₂×D₄	—	4	1	no	—
991	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
992	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
993	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
994	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
995	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	2	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	4	4	no	—
1007	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1008	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1009	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1010	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1011	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1012	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1013	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1014	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1015	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1016	Q₁₆	—	4	2	no	—
1017	Q₁₆	—	4	2	no	—
1018	SD₁₆	—	2	4	no	—
1019	SD₁₆	—	4	2	no	—
1020	M₁₆	—	4	2	no	—
1021	M₁₆	—	4	2	no	—
1022	C₂×C₈	—	4	2	no	—
1023	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1024	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1025	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1026	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1061	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1062	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1063	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1064	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1065	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1067	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1068	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1069	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1070	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1071	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1072	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	1	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1097	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1098	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1099	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1100	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1101	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1102	C₄²	—	2	1	no	—
1103	C₄²	—	2	1	no	—
1104	C₄²	—	2	1	no	—
1105	C₄²	—	2	1	no	—
1106	C₄²	—	2	1	no	—
1107	C₄²	—	2	1	no	—
1108	C₄²	—	2	2	no	—
1109	C₄²	—	2	2	no	—
1110	C₄²	—	2	2	no	—
1111	C₄²	—	2	2	no	—
1112	C₄²	—	2	2	no	—
1113	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1114	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1115	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1116	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1117	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1118	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1119	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1120	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1121	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1122	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1123	C₂³	—	2	1	no	—
1124	C₂³	—	2	1	no	—
1125	C₂³	—	4	2	no	—
1126	C₂³	—	4	2	no	—
1127	C₂³	—	8	1	no	—
1128	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1129	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1130	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1131	Q₈	—	2	2	no	—
1132	Q₈	—	2	1	no	—
1133	Q₈	—	2	1	no	—
1134	Q₈	—	2	2	no	—
1135	Q₈	—	2	1	no	—
1136	Q₈	—	2	1	no	—
1137	Q₈	—	4	1	no	—
1138	Q₈	—	4	2	no	—
1139	Q₈	—	4	4	no	—
1140	Q₈	—	4	2	no	—
1141	Q₈	—	4	2	no	—
1142	Q₈	—	8	1	no	—
1143	D₄	—	2	1	no	—
1144	D₄	—	2	1	no	—
1145	D₄	—	2	1	no	—
1146	D₄	—	4	1	no	—
1147	D₄	—	4	1	no	—
1148	D₄	—	4	1	no	—
1149	D₄	—	4	2	no	—
1150	D₄	—	4	2	no	—
1151	D₄	—	4	2	no	—
1152	D₄	—	8	1	no	—
1153	D₄	—	8	1	no	—
1154	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	2	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	1	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	2	no	—
1178	C₂×C₄	—	4	2	no	—
1179	C₂×C₄	—	4	2	no	—
1180	C₂×C₄	—	4	2	no	—
1181	C₂×C₄	—	4	2	no	—
1182	C₂×C₄	—	4	4	no	—
1183	C₂×C₄	—	4	2	no	—
1184	C₂×C₄	—	4	2	no	—
1185	C₂×C₄	—	8	1	no	—
1186	C₂×C₄	—	8	1	no	—
1187	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1188	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1189	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1190	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1191	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1192	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1193	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1194	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1195	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1196	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1197	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1198	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1199	C₈	—	2	2	no	—
1200	C₈	—	2	2	no	—
1201	C₈	—	2	2	no	—
1202	C₈	—	2	2	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	1	no	—
1205	C₂²	—	2	1	no	—
1206	C₂²	—	2	2	no	—
1207	C₂²	—	2	1	no	—
1208	C₂²	—	2	1	no	—
1209	C₂²	—	2	1	no	—
1210	C₂²	—	2	1	no	—
1211	C₂²	—	2	1	no	—
1212	C₂²	—	2	1	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	1	no	—
1217	C₂²	—	4	1	no	—
1218	C₂²	—	8	4	no	—
1219	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1220	C₄	—	2	1	no	—
1221	C₄	—	2	1	no	—
1222	C₄	—	2	1	no	—
1223	C₄	—	2	1	no	—
1224	C₄	—	2	1	no	—
1225	C₄	—	2	1	no	—
1226	C₄	—	2	1	no	—
1227	C₄	—	2	1	no	—
1228	C₄	—	2	1	no	—
1229	C₄	—	2	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	2	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	2	no	—
1236	C₄	—	4	2	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	2	no	—
1240	C₄	C₃₁×#575	1	2	yes	—
1241	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1242	C₄	C₃₁×#585	1	1	yes	characteristic
1243	C₂	—	4	1	no	—
1244	C₂	—	4	1	no	—
1245	C₂	—	4	1	no	—
1246	C₂	—	4	2	no	—
1247	C₂	—	8	1	no	—
1248	C₂	C₃₁×#3489	1	1	yes	characteristic
1249	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1250	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3475	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3509	C₂	semidirect
3. C₃₁×#3388	C₂	semidirect
4. C₃₁×#3377	C₂	semidirect
5. C₃₁×#3352	C₂	semidirect
6. C₃₁×#3349	C₂	semidirect
7. C₃₁×#3348	C₂	semidirect
8. C₃₁×#3323	C₂	semidirect
9. C₃₁×#3315	C₂	semidirect
10. C₃₁×#3311	C₂	semidirect
11. C₃₁×#3255	C₂	semidirect
12. C₃₁×#3252	C₂	semidirect
13. C₃₁×#3248	C₂	semidirect
14. C₃₁×#3239	C₂	semidirect
15. C₃₁×#3237	C₂	semidirect
16. C₃₁×#3233	C₂	semidirect
17. C₃₁×#3116	C₂	semidirect
18. C₃₁×#3110	C₂	semidirect
19. C₃₁×#3107	C₂	semidirect
20. C₃₁×#3079	C₂	semidirect
21. C₃₁×#3077	C₂	semidirect
22. C₃₁×#3076	C₂	semidirect
23. C₃₁×#2989	C₂	semidirect
25. C₃₁×#557	C₂²	semidirect
38. C₃₁×#552	C₂²	semidirect
50. C₃₁×#533	C₂²	semidirect
51. C₃₁×#533	C₂²	semidirect
52. C₃₁×#533	C₂²	semidirect
53. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
65. C₃₁×#501	C₂²	semidirect
66. C₃₁×#501	C₂²	semidirect
67. C₃₁×#499	C₂²	semidirect
68. C₃₁×#491	C₂²	semidirect
73. C₃₁×#485	C₂²	semidirect
74. C₃₁×#485	C₂²	semidirect
75. C₃₁×#485	C₂²	semidirect
77. C₃₁×#484	C₂²	semidirect
80. C₃₁×#479	C₂²	semidirect
81. C₃₁×#479	C₂²	semidirect
82. C₃₁×#479	C₂²	semidirect
86. C₃₁×#477	C₂²	semidirect
87. C₃₁×#477	C₂²	semidirect
88. C₃₁×#477	C₂²	semidirect
92. C₃₁×#475	C₂²	semidirect
93. C₃₁×#475	C₂²	semidirect
94. C₃₁×#475	C₂²	semidirect
95. C₃₁×#475	C₂²	semidirect
96. C₃₁×#475	C₂²	semidirect
103. C₃₁×#470	C₂²	semidirect
105. C₃₁×#467	C₂²	semidirect
109. C₃₁×#462	C₂²	semidirect
110. C₃₁×#462	C₂²	semidirect
111. C₃₁×#462	C₂²	semidirect
117. C₃₁×#446	C₂²	semidirect
118. C₃₁×#441	C₂²	semidirect
122. C₄×Q₁₆×C₃₁	C₂²	semidirect
126. C₃₁×#435	C₂²	semidirect
128. C₃₁×#432	C₂²	semidirect
129. C₃₁×#431	C₂²	semidirect
131. C₃₁×#428	C₂²	semidirect
132. C₃₁×#427	C₂²	semidirect
134. C₃₁×#423	C₂²	semidirect
135. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
497. #62116	C₃₁	direct (N × H)
578. #3509	C₂×C₃₁	semidirect
580. #3388	C₂×C₃₁	semidirect
581. #3377	C₂×C₃₁	semidirect
582. #3352	C₂×C₃₁	semidirect
583. #3349	C₂×C₃₁	semidirect
584. #3348	C₂×C₃₁	semidirect
585. #3323	C₂×C₃₁	semidirect
586. #3315	C₂×C₃₁	semidirect
587. #3311	C₂×C₃₁	semidirect
588. #3255	C₂×C₃₁	semidirect
589. #3252	C₂×C₃₁	semidirect
590. #3248	C₂×C₃₁	semidirect
591. #3239	C₂×C₃₁	semidirect
592. #3237	C₂×C₃₁	semidirect
593. #3233	C₂×C₃₁	semidirect
594. #3116	C₂×C₃₁	semidirect
595. #3110	C₂×C₃₁	semidirect
596. #3107	C₂×C₃₁	semidirect
597. #3079	C₂×C₃₁	semidirect
598. #3077	C₂×C₃₁	semidirect
599. #3076	C₂×C₃₁	semidirect
600. #2989	C₂×C₃₁	semidirect
642. #557	C₂²×C₃₁	semidirect
655. #552	C₂²×C₃₁	semidirect
667. #533	C₂²×C₃₁	semidirect
668. #533	C₂²×C₃₁	semidirect
669. #533	C₂²×C₃₁	semidirect
670. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
682. #501	C₂²×C₃₁	semidirect
683. #501	C₂²×C₃₁	semidirect
684. #499	C₂²×C₃₁	semidirect
685. #491	C₂²×C₃₁	semidirect
690. #485	C₂²×C₃₁	semidirect
691. #485	C₂²×C₃₁	semidirect
692. #485	C₂²×C₃₁	semidirect
694. #484	C₂²×C₃₁	semidirect
697. #479	C₂²×C₃₁	semidirect
698. #479	C₂²×C₃₁	semidirect
699. #479	C₂²×C₃₁	semidirect
703. #477	C₂²×C₃₁	semidirect
704. #477	C₂²×C₃₁	semidirect
705. #477	C₂²×C₃₁	semidirect
709. #475	C₂²×C₃₁	semidirect
710. #475	C₂²×C₃₁	semidirect
711. #475	C₂²×C₃₁	semidirect
712. #475	C₂²×C₃₁	semidirect
713. #475	C₂²×C₃₁	semidirect
720. #470	C₂²×C₃₁	semidirect
722. #467	C₂²×C₃₁	semidirect
726. #462	C₂²×C₃₁	semidirect
727. #462	C₂²×C₃₁	semidirect
728. #462	C₂²×C₃₁	semidirect
734. #446	C₂²×C₃₁	semidirect
735. #441	C₂²×C₃₁	semidirect
739. C₄×Q₁₆	C₂²×C₃₁	semidirect
743. #435	C₂²×C₃₁	semidirect
745. #432	C₂²×C₃₁	semidirect
746. #431	C₂²×C₃₁	semidirect
748. #428	C₂²×C₃₁	semidirect
749. #427	C₂²×C₃₁	semidirect
751. #423	C₂²×C₃₁	semidirect
752. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
967. C₃₁	#62116	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×#3509	2
C₃₁×#3475	2
C₃₁×#3388	2
C₃₁×#3377	2
C₃₁×#3352	2
C₃₁×#3349	2
C₃₁×#3348	2
C₃₁×#3323	2
C₃₁×#3315	2
C₃₁×#3311	2
C₃₁×#3255	2
C₃₁×#3252	2
C₃₁×#3248	2
C₃₁×#3239	2
C₃₁×#3237	2
C₃₁×#3233	2
C₃₁×#3116	2
C₃₁×#3110	2
C₃₁×#3107	2
C₃₁×#3079	2
C₃₁×#3077	2
C₃₁×#3076	2
C₃₁×#2989	2
#62116	31

Subgroups — C31×#62116 #21518875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62116 #21518875