Subgroups — C₃₁×#62578 #21519337

Order 7936.

1792 conjugacy classes of subgroups.

The subgroup lattice has 1272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3371	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3317	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3314	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3309	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3306	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3297	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3296	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3236	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3234	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3219	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3219	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3217	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3181	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3180	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3171	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3142	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3135	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#490	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2970	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#559	—	2	1	no	—
25	C₃₁×#559	C₂²	1	2	yes	—
26	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#554	C₂²	1	1	yes	characteristic
28	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#553	C₂²	1	1	yes	characteristic
30	C₃₁×#553	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#552	—	2	1	no	—
32	C₃₁×#552	—	2	1	no	—
33	C₃₁×#552	—	2	1	no	—
34	C₃₁×#552	C₂²	1	1	yes	characteristic
35	C₃₁×#552	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#550	—	2	1	no	—
37	C₃₁×#550	C₂²	1	2	yes	—
38	C₃₁×#547	—	2	1	no	—
39	C₃₁×#547	C₂²	1	1	yes	characteristic
40	C₃₁×#546	—	2	1	no	—
41	C₃₁×#546	—	2	1	no	—
42	C₃₁×#546	C₂²	1	2	yes	—
43	C₃₁×#546	C₂²	1	2	yes	—
44	C₃₁×#541	—	2	1	no	—
45	C₃₁×#540	—	2	1	no	—
46	C₃₁×#540	—	2	1	no	—
47	C₃₁×#539	—	2	1	no	—
48	C₃₁×#539	—	2	1	no	—
49	C₃₁×#535	—	2	1	no	—
50	C₃₁×#533	C₂²	1	1	yes	characteristic
51	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#532	C₂²	1	1	yes	characteristic
53	C₃₁×#532	C₂²	1	1	yes	characteristic
54	C₃₁×#532	C₂²	1	1	yes	characteristic
55	C₃₁×#532	C₂²	1	1	yes	characteristic
56	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
57	C₃₁×#529	C₂²	1	1	yes	characteristic
58	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
61	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#520	—	2	1	no	—
63	C₃₁×#518	—	2	1	no	—
64	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
65	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#496	C₂²	1	1	yes	characteristic
70	C₃₁×#496	C₂²	1	1	yes	characteristic
71	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#490	C₂²	1	2	yes	—
75	C₃₁×#490	C₂²	1	2	yes	—
76	C₃₁×#490	C₂²	1	1	yes	characteristic
77	C₃₁×#490	C₂²	1	1	yes	characteristic
78	C₃₁×#490	C₂²	1	1	yes	characteristic
79	C₃₁×#490	C₂²	1	1	yes	characteristic
80	C₃₁×#490	C₂²	1	1	yes	characteristic
81	C₃₁×#490	C₂²	1	1	yes	characteristic
82	C₃₁×#489	C₂²	1	2	yes	complemented
83	C₃₁×#489	C₂²	1	2	yes	complemented
84	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#488	C₂²	1	2	yes	complemented
86	C₃₁×#488	C₂²	1	2	yes	complemented
87	C₃₁×#484	C₂²	1	2	yes	—
88	C₃₁×#483	C₂²	1	2	yes	—
89	C₃₁×#482	C₂²	1	2	yes	complemented
90	C₃₁×#482	C₂²	1	2	yes	complemented
91	C₃₁×#481	C₂²	1	2	yes	complemented
92	C₃₁×#480	C₂²	1	2	yes	complemented
93	C₃₁×#479	C₂²	1	2	yes	complemented
94	C₃₁×#479	C₂²	1	2	yes	complemented
95	C₃₁×#478	C₂²	1	2	yes	complemented
96	C₃₁×#478	C₂²	1	2	yes	complemented
97	C₃₁×#476	C₂²	1	2	yes	complemented
98	C₃₁×#474	C₂²	1	2	yes	complemented
99	C₃₁×#469	C₂²	1	2	yes	complemented
100	C₃₁×#468	C₂²	1	2	yes	complemented
101	C₃₁×#467	C₂²	1	2	yes	—
102	C₃₁×#466	C₂²	1	2	yes	complemented
103	C₃₁×#465	C₂²	1	2	yes	—
104	C₃₁×#465	C₂²	1	2	yes	complemented
105	C₃₁×#464	C₂²	1	2	yes	complemented
106	C₃₁×#464	C₂²	1	2	yes	complemented
107	C₃₁×#463	C₂²	1	2	yes	complemented
108	C₃₁×#463	C₂²	1	2	yes	complemented
109	C₃₁×#460	C₂²	1	2	yes	—
110	C₃₁×#459	C₂²	1	2	yes	—
111	C₃₁×#452	C₂²	1	2	yes	complemented
112	C₃₁×#452	C₂²	1	2	yes	complemented
113	C₃₁×#450	C₂²	1	2	yes	—
114	C₃₁×#449	C₂²	1	2	yes	complemented
115	C₃₁×#449	C₂²	1	2	yes	complemented
116	C₃₁×#447	C₂²	1	2	yes	—
117	C₃₁×#446	C₂²	1	2	yes	complemented
118	C₃₁×#442	C₂²	1	2	yes	complemented
119	C₃₁×#441	C₂²	1	2	yes	complemented
120	C₃₁×#440	C₂²	1	2	yes	complemented
121	C₃₁×#440	C₂²	1	2	yes	complemented
122	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
123	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
124	C₃₁×#435	C₂²	1	2	yes	—
125	C₃₁×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₃₁	C₂²	1	2	yes	—
127	C₃₁×#432	C₂²	1	1	yes	characteristic
128	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#417	C₂²	1	2	yes	complemented
131	C₃₁×#417	C₂²	1	2	yes	complemented
132	C₃₁×#416	C₂²	1	2	yes	complemented
133	C₃₁×#416	C₂²	1	2	yes	complemented
134	C₂×C₃₁×#102	C₂²	1	2	yes	—
135	C₂×C₃₁×#102	C₂²	1	2	yes	—
136	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
137	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
138	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic, complemented
139	C₂×#41×C₃₁	—	2	1	no	—
140	C₂×#41×C₃₁	—	2	1	no	—
141	C₂×#41×C₃₁	—	2	1	no	—
142	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
143	C₂×#41×C₃₁	C₂³	1	2	yes	—
144	C₂×#41×C₃₁	C₂³	1	2	yes	—
145	C₂²×D₄×C₃₁	—	2	1	no	—
146	C₂²×D₄×C₃₁	—	2	1	no	—
147	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×D₈×C₃₁	C₂³	1	2	yes	—
153	C₂×D₈×C₃₁	C₂³	1	2	yes	—
154	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
156	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
157	C₃₁×C₄⋊Q₈	—	2	1	no	—
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	1	yes	characteristic
162	C₃₁×#127	—	2	2	no	—
163	C₃₁×#127	—	2	1	no	—
164	C₃₁×#127	—	2	1	no	—
165	C₃₁×#127	C₂³	1	2	yes	—
166	C₃₁×#127	C₂³	1	1	yes	characteristic
167	C₃₁×#127	C₂³	1	1	yes	characteristic
168	C₃₁×#126	—	2	1	no	—
169	C₃₁×#126	—	2	1	no	—
170	C₃₁×#126	—	2	1	no	—
171	C₃₁×#126	—	2	1	no	—
172	C₃₁×#126	—	2	1	no	—
173	C₃₁×#126	—	2	1	no	—
174	C₃₁×#126	—	2	1	no	—
175	C₃₁×#125	—	2	1	no	—
176	C₃₁×#125	—	2	1	no	—
177	C₃₁×#125	—	2	1	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	—	2	1	no	—
183	C₃₁×#125	—	2	1	no	—
184	C₃₁×#125	—	2	1	no	—
185	C₃₁×#125	C₂³	1	1	yes	characteristic
186	C₃₁×#125	C₂³	1	1	yes	characteristic
187	C₃₁×#125	C₂³	1	1	yes	characteristic
188	C₃₁×#125	C₂³	1	1	yes	characteristic
189	C₃₁×#125	C₂³	1	1	yes	characteristic
190	C₃₁×#125	C₂³	1	1	yes	characteristic
191	C₃₁×#125	C₂³	1	1	yes	characteristic
192	C₃₁×#124	—	2	2	no	—
193	C₃₁×#124	—	2	1	no	—
194	C₃₁×#124	—	2	1	no	—
195	C₃₁×#124	C₂³	1	2	yes	—
196	C₃₁×#124	C₂³	1	2	yes	—
197	C₃₁×#124	C₂³	1	1	yes	characteristic
198	C₃₁×#123	—	2	1	no	—
199	C₃₁×#123	—	2	1	no	—
200	C₃₁×#123	—	2	1	no	—
201	C₃₁×#123	—	2	1	no	—
202	C₃₁×#123	—	2	1	no	—
203	C₃₁×#123	—	2	2	no	—
204	C₃₁×#123	—	2	2	no	—
205	C₃₁×#123	—	2	2	no	—
206	C₃₁×#123	—	2	2	no	—
207	C₃₁×#123	—	2	1	no	—
208	C₃₁×#123	—	2	1	no	—
209	C₃₁×#123	—	2	1	no	—
210	C₃₁×#123	—	2	1	no	—
211	C₃₁×C₂²⋊Q₈	—	2	1	no	—
212	C₃₁×C₂²⋊Q₈	—	2	1	no	—
213	C₃₁×C₂²⋊Q₈	—	2	1	no	—
214	C₃₁×C₂²⋊Q₈	—	2	1	no	—
215	C₃₁×C₂²⋊Q₈	—	2	1	no	—
216	C₃₁×C₂²⋊Q₈	—	2	1	no	—
217	C₃₁×C₂²⋊Q₈	—	2	1	no	—
218	C₃₁×C₂²⋊Q₈	—	2	1	no	—
219	C₃₁×C₂²⋊Q₈	—	2	1	no	—
220	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₃₁×#121	—	2	1	no	—
225	C₃₁×#121	—	2	1	no	—
226	C₃₁×#121	—	2	1	no	—
227	C₃₁×#121	—	2	1	no	—
228	C₃₁×#121	—	2	1	no	—
229	C₃₁×#121	—	2	1	no	—
230	C₃₁×#121	—	2	1	no	—
231	C₃₁×#121	—	2	1	no	—
232	C₃₁×#121	—	2	2	no	—
233	C₃₁×#121	—	2	2	no	—
234	C₃₁×#121	—	2	2	no	—
235	C₃₁×#121	—	2	2	no	—
236	C₃₁×#121	C₂³	1	1	yes	characteristic
237	C₃₁×#121	C₂³	1	1	yes	characteristic
238	C₃₁×#121	C₂³	1	1	yes	characteristic
239	C₃₁×#121	C₂³	1	2	yes	—
240	C₃₁×#121	C₂³	1	2	yes	—
241	C₃₁×#120	—	2	2	no	—
242	C₃₁×#120	—	2	2	no	—
243	C₄×Q₈×C₃₁	—	2	1	no	—
244	C₄×Q₈×C₃₁	—	2	1	no	—
245	C₄×Q₈×C₃₁	—	2	1	no	—
246	C₄×Q₈×C₃₁	—	2	1	no	—
247	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
248	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
251	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
252	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₃₁	—	2	1	no	—
254	C₄×D₄×C₃₁	—	2	1	no	—
255	C₄×D₄×C₃₁	—	2	1	no	—
256	C₄×D₄×C₃₁	—	2	1	no	—
257	C₄×D₄×C₃₁	—	2	2	no	—
258	C₄×D₄×C₃₁	—	2	2	no	—
259	C₄×D₄×C₃₁	—	2	1	no	—
260	C₄×D₄×C₃₁	—	2	1	no	—
261	C₄×D₄×C₃₁	—	2	1	no	—
262	C₄×D₄×C₃₁	—	2	1	no	—
263	C₄×D₄×C₃₁	—	2	1	no	—
264	C₄×D₄×C₃₁	—	2	1	no	—
265	C₄×D₄×C₃₁	—	2	1	no	—
266	C₄×D₄×C₃₁	—	2	1	no	—
267	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
268	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
269	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
270	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
271	C₄×D₄×C₃₁	C₂³	1	2	yes	—
272	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
273	C₄×D₄×C₃₁	C₂³	1	2	yes	—
274	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
275	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
276	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
277	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
278	C₃₁×#117	—	2	1	no	—
279	C₃₁×#117	—	2	1	no	—
280	C₃₁×#117	—	2	1	no	—
281	C₃₁×#117	—	2	1	no	—
282	C₃₁×#117	—	2	1	no	—
283	C₃₁×#117	—	2	1	no	—
284	C₃₁×#117	D₄	1	1	yes	characteristic
285	C₃₁×#117	D₄	1	1	yes	characteristic
286	C₃₁×#117	D₄	1	1	yes	characteristic
287	C₃₁×#117	C₂³	1	1	yes	characteristic
288	C₃₁×#117	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
290	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
291	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
292	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
293	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
294	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
296	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
297	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
298	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
299	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
300	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
303	C₃₁×#107	C₂³	1	2	yes	—
304	C₃₁×#107	C₂³	1	2	yes	—
305	C₃₁×#107	C₂³	1	2	yes	—
306	C₃₁×#106	C₂³	1	2	yes	—
307	C₃₁×#106	C₂³	1	2	yes	—
308	C₃₁×#106	C₂³	1	2	yes	—
309	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
310	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
311	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
312	C₃₁×#103	C₂³	1	2	yes	—
313	C₃₁×#103	C₂³	1	2	yes	—
314	C₃₁×#103	C₂³	1	2	yes	—
315	C₃₁×#103	C₂³	1	2	yes	—
316	C₃₁×#103	C₂³	1	2	yes	—
317	C₃₁×#103	C₂³	1	2	yes	—
318	C₃₁×#103	C₂³	1	2	yes	—
319	C₃₁×#102	C₂³	1	2	yes	—
320	C₃₁×#102	C₂³	1	2	yes	—
321	C₃₁×#102	C₂³	1	2	yes	—
322	C₃₁×#102	C₂³	1	2	yes	—
323	C₃₁×#102	C₂³	1	2	yes	—
324	C₃₁×#102	C₂³	1	2	yes	—
325	C₃₁×#102	C₂³	1	2	yes	—
326	C₃₁×#102	C₂³	1	2	yes	—
327	C₃₁×#102	C₂³	1	2	yes	—
328	C₃₁×#102	C₂³	1	2	yes	—
329	C₃₁×#102	C₂³	1	2	yes	—
330	C₃₁×#102	C₂³	1	2	yes	—
331	C₃₁×#102	C₂³	1	2	yes	—
332	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
333	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
334	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
335	C₃₁×#97	C₂³	1	1	yes	characteristic
336	C₃₁×#97	C₂³	1	1	yes	characteristic
337	C₃₁×#97	C₂³	1	2	yes	—
338	C₃₁×#97	C₂³	1	1	yes	characteristic
339	C₃₁×#97	C₂³	1	2	yes	—
340	C₃₁×#97	C₂³	1	1	yes	characteristic
341	C₄×C₈×C₃₁	C₂³	1	2	yes	—
342	C₂⁴×C₃₁	—	2	2	no	—
343	#41×C₃₁	—	4	2	no	—
344	#41×C₃₁	—	4	2	no	—
345	#41×C₃₁	—	4	2	no	—
346	#41×C₃₁	—	4	2	no	—
347	#41×C₃₁	—	4	2	no	—
348	#41×C₃₁	—	4	4	no	—
349	#41×C₃₁	—	8	2	no	—
350	#41×C₃₁	—	8	2	no	—
351	C₂×Q₈×C₃₁	—	2	1	no	—
352	C₂×Q₈×C₃₁	—	2	1	no	—
353	C₂×Q₈×C₃₁	—	2	1	no	—
354	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
355	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
356	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₃₁	—	2	1	no	—
358	C₂×D₄×C₃₁	—	2	1	no	—
359	C₂×D₄×C₃₁	—	2	1	no	—
360	C₂×D₄×C₃₁	—	2	2	no	—
361	C₂×D₄×C₃₁	—	2	2	no	—
362	C₂×D₄×C₃₁	—	2	2	no	—
363	C₂×D₄×C₃₁	—	2	2	no	—
364	C₂×D₄×C₃₁	—	2	1	no	—
365	C₂×D₄×C₃₁	—	2	1	no	—
366	C₂×D₄×C₃₁	—	2	2	no	—
367	C₂×D₄×C₃₁	—	2	1	no	—
368	C₂×D₄×C₃₁	—	2	1	no	—
369	C₂×D₄×C₃₁	—	2	2	no	—
370	C₂×D₄×C₃₁	—	2	2	no	—
371	C₂×D₄×C₃₁	—	4	2	no	—
372	C₂×D₄×C₃₁	—	4	2	no	—
373	C₂×D₄×C₃₁	—	4	4	no	—
374	C₂×D₄×C₃₁	—	8	2	no	—
375	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
376	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
377	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
378	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
379	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
380	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₃₁	—	2	1	no	—
382	C₂²×C₄×C₃₁	—	2	1	no	—
383	C₂²×C₄×C₃₁	—	2	1	no	—
384	C₂²×C₄×C₃₁	—	2	1	no	—
385	C₂²×C₄×C₃₁	—	2	1	no	—
386	C₂²×C₄×C₃₁	—	2	2	no	—
387	C₂²×C₄×C₃₁	—	2	2	no	—
388	C₂²×C₄×C₃₁	—	2	2	no	—
389	C₂²×C₄×C₃₁	—	2	2	no	—
390	C₂²×C₄×C₃₁	—	2	1	no	—
391	C₂²×C₄×C₃₁	—	2	1	no	—
392	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
401	Q₁₆×C₃₁	—	4	2	no	—
402	SD₁₆×C₃₁	—	4	2	no	—
403	SD₁₆×C₃₁	—	4	2	no	—
404	SD₁₆×C₃₁	—	4	2	no	—
405	D₈×C₃₁	—	4	2	no	—
406	D₈×C₃₁	—	4	2	no	—
407	M₁₆×C₃₁	—	4	2	no	—
408	C₂×C₈×C₃₁	—	4	2	no	—
409	C₂×C₈×C₃₁	—	4	2	no	—
410	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
411	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
412	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
413	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	1	no	—
420	C₄⋊C₄×C₃₁	—	2	1	no	—
421	C₄⋊C₄×C₃₁	—	2	1	no	—
422	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
429	C₄⋊C₄×C₃₁	—	2	1	no	—
430	C₄⋊C₄×C₃₁	—	2	1	no	—
431	C₄⋊C₄×C₃₁	—	2	1	no	—
432	C₄⋊C₄×C₃₁	—	2	1	no	—
433	C₄⋊C₄×C₃₁	—	2	1	no	—
434	C₄⋊C₄×C₃₁	—	2	1	no	—
435	C₄⋊C₄×C₃₁	—	2	1	no	—
436	C₄⋊C₄×C₃₁	—	2	1	no	—
437	C₄⋊C₄×C₃₁	—	2	1	no	—
438	C₄⋊C₄×C₃₁	—	2	1	no	—
439	C₄⋊C₄×C₃₁	—	2	2	no	—
440	C₄⋊C₄×C₃₁	—	2	1	no	—
441	C₄⋊C₄×C₃₁	—	2	2	no	—
442	C₄⋊C₄×C₃₁	—	2	1	no	—
443	C₄⋊C₄×C₃₁	—	2	1	no	—
444	C₄⋊C₄×C₃₁	—	2	1	no	—
445	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
453	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
455	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
456	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
457	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
458	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
465	C₂²⋊C₄×C₃₁	—	2	2	no	—
466	C₂²⋊C₄×C₃₁	—	2	2	no	—
467	C₂²⋊C₄×C₃₁	—	2	2	no	—
468	C₂²⋊C₄×C₃₁	—	2	1	no	—
469	C₂²⋊C₄×C₃₁	—	2	1	no	—
470	C₂²⋊C₄×C₃₁	—	2	1	no	—
471	C₂²⋊C₄×C₃₁	—	2	1	no	—
472	C₂²⋊C₄×C₃₁	—	2	1	no	—
473	C₂²⋊C₄×C₃₁	—	2	2	no	—
474	C₂²⋊C₄×C₃₁	—	2	2	no	—
475	C₂²⋊C₄×C₃₁	—	2	2	no	—
476	C₂²⋊C₄×C₃₁	—	2	2	no	—
477	C₂²⋊C₄×C₃₁	—	2	1	no	—
478	C₂²⋊C₄×C₃₁	—	2	1	no	—
479	C₂²⋊C₄×C₃₁	—	2	1	no	—
480	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
481	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
482	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
483	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
484	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
485	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
486	C₄²×C₃₁	—	2	1	no	—
487	C₄²×C₃₁	—	2	1	no	—
488	C₄²×C₃₁	—	2	1	no	—
489	C₄²×C₃₁	—	2	1	no	—
490	C₄²×C₃₁	—	2	2	no	—
491	C₄²×C₃₁	—	2	1	no	—
492	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
495	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
496	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
497	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
498	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
499	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
500	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
501	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
502	#62578	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
503	C₂³×C₃₁	—	2	1	no	—
504	C₂³×C₃₁	—	2	2	no	—
505	C₂³×C₃₁	—	2	2	no	—
506	C₂³×C₃₁	—	4	4	no	—
507	C₂³×C₃₁	—	8	2	no	—
508	C₂³×C₃₁	—	8	2	no	—
509	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
510	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
512	Q₈×C₃₁	—	2	2	no	—
513	Q₈×C₃₁	—	2	2	no	—
514	Q₈×C₃₁	—	2	2	no	—
515	Q₈×C₃₁	—	4	1	no	—
516	Q₈×C₃₁	—	4	2	no	—
517	Q₈×C₃₁	—	4	2	no	—
518	Q₈×C₃₁	—	8	1	no	—
519	D₄×C₃₁	—	2	2	no	—
520	D₄×C₃₁	—	2	2	no	—
521	D₄×C₃₁	—	2	2	no	—
522	D₄×C₃₁	—	2	2	no	—
523	D₄×C₃₁	—	2	2	no	—
524	D₄×C₃₁	—	2	2	no	—
525	D₄×C₃₁	—	2	2	no	—
526	D₄×C₃₁	—	4	1	no	—
527	D₄×C₃₁	—	4	2	no	—
528	D₄×C₃₁	—	4	2	no	—
529	D₄×C₃₁	—	4	4	no	—
530	D₄×C₃₁	—	4	2	no	—
531	D₄×C₃₁	—	4	2	no	—
532	D₄×C₃₁	—	4	2	no	—
533	D₄×C₃₁	—	4	2	no	—
534	D₄×C₃₁	—	8	2	no	—
535	D₄×C₃₁	—	8	2	no	—
536	D₄×C₃₁	—	8	1	no	—
537	D₄×C₃₁	—	8	2	no	—
538	D₄×C₃₁	—	8	2	no	—
539	D₄×C₃₁	—	8	2	no	—
540	D₄×C₃₁	—	8	2	no	—
541	C₂×C₄×C₃₁	—	2	2	no	—
542	C₂×C₄×C₃₁	—	2	2	no	—
543	C₂×C₄×C₃₁	—	2	2	no	—
544	C₂×C₄×C₃₁	—	2	2	no	—
545	C₂×C₄×C₃₁	—	2	1	no	—
546	C₂×C₄×C₃₁	—	2	1	no	—
547	C₂×C₄×C₃₁	—	2	1	no	—
548	C₂×C₄×C₃₁	—	2	2	no	—
549	C₂×C₄×C₃₁	—	2	2	no	—
550	C₂×C₄×C₃₁	—	2	1	no	—
551	C₂×C₄×C₃₁	—	2	1	no	—
552	C₂×C₄×C₃₁	—	2	1	no	—
553	C₂×C₄×C₃₁	—	2	1	no	—
554	C₂×C₄×C₃₁	—	4	1	no	—
555	C₂×C₄×C₃₁	—	4	1	no	—
556	C₂×C₄×C₃₁	—	4	1	no	—
557	C₂×C₄×C₃₁	—	4	1	no	—
558	C₂×C₄×C₃₁	—	4	1	no	—
559	C₂×C₄×C₃₁	—	4	2	no	—
560	C₂×C₄×C₃₁	—	4	2	no	—
561	C₂×C₄×C₃₁	—	4	2	no	—
562	C₂×C₄×C₃₁	—	8	1	no	—
563	C₂×C₄×C₃₁	—	8	1	no	—
564	C₂×C₄×C₃₁	—	8	2	no	—
565	C₂×C₄×C₃₁	—	8	2	no	—
566	C₂×C₄×C₃₁	—	8	2	no	—
567	C₂×C₄×C₃₁	—	8	2	no	—
568	C₂×C₄×C₃₁	—	8	1	no	—
569	C₂×C₄×C₃₁	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
582	C₈×C₃₁	—	2	2	no	—
583	C₈×C₃₁	—	2	2	no	—
584	C₈×C₃₁	—	2	2	no	—
585	C₈×C₃₁	—	2	2	no	—
586	#3515	C₂×C₃₁	1	1	yes	characteristic, complemented
587	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
588	#3371	C₂×C₃₁	1	2	yes	complemented
589	#3370	C₂×C₃₁	1	2	yes	complemented
590	#3317	C₂×C₃₁	1	2	yes	complemented
591	#3314	C₂×C₃₁	1	2	yes	complemented
592	#3309	C₂×C₃₁	1	2	yes	complemented
593	#3306	C₂×C₃₁	1	2	yes	complemented
594	#3297	C₂×C₃₁	1	2	yes	complemented
595	#3296	C₂×C₃₁	1	2	yes	complemented
596	#3236	C₂×C₃₁	1	1	yes	characteristic, complemented
597	#3235	C₂×C₃₁	1	1	yes	characteristic, complemented
598	#3234	C₂×C₃₁	1	1	yes	characteristic, complemented
599	#3219	C₂×C₃₁	1	1	yes	characteristic, complemented
600	#3219	C₂×C₃₁	1	1	yes	characteristic, complemented
601	#3217	C₂×C₃₁	1	1	yes	characteristic, complemented
602	#3181	C₂×C₃₁	1	1	yes	characteristic, complemented
603	#3180	C₂×C₃₁	1	1	yes	characteristic, complemented
604	#3171	C₂×C₃₁	1	1	yes	characteristic, complemented
605	#3142	C₂×C₃₁	1	1	yes	characteristic, complemented
606	#3135	C₂×C₃₁	1	1	yes	characteristic, complemented
607	C₂×#490	C₂×C₃₁	1	1	yes	characteristic, complemented
608	#2970	C₂×C₃₁	1	1	yes	characteristic, complemented
609	C₂²×C₃₁	—	2	1	no	—
610	C₂²×C₃₁	—	2	1	no	—
611	C₂²×C₃₁	—	2	1	no	—
612	C₂²×C₃₁	—	2	1	no	—
613	C₂²×C₃₁	—	2	1	no	—
614	C₂²×C₃₁	—	2	1	no	—
615	C₂²×C₃₁	—	2	1	no	—
616	C₂²×C₃₁	—	2	1	no	—
617	C₂²×C₃₁	—	4	1	no	—
618	C₂²×C₃₁	—	4	2	no	—
619	C₂²×C₃₁	—	4	2	no	—
620	C₂²×C₃₁	—	4	2	no	—
621	C₂²×C₃₁	—	4	2	no	—
622	C₂²×C₃₁	—	4	1	no	—
623	C₂²×C₃₁	—	4	1	no	—
624	C₂²×C₃₁	—	4	2	no	—
625	C₂²×C₃₁	—	4	2	no	—
626	C₂²×C₃₁	—	16	4	no	—
627	C₂²×C₃₁	#575	1	2	yes	—
628	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
629	C₄×C₃₁	—	2	1	no	—
630	C₄×C₃₁	—	2	1	no	—
631	C₄×C₃₁	—	2	1	no	—
632	C₄×C₃₁	—	2	1	no	—
633	C₄×C₃₁	—	2	1	no	—
634	C₄×C₃₁	—	2	1	no	—
635	C₄×C₃₁	—	2	1	no	—
636	C₄×C₃₁	—	2	1	no	—
637	C₄×C₃₁	—	2	1	no	—
638	C₄×C₃₁	—	2	1	no	—
639	C₄×C₃₁	—	2	1	no	—
640	C₄×C₃₁	—	4	1	no	—
641	C₄×C₃₁	—	4	2	no	—
642	C₄×C₃₁	—	4	1	no	—
643	C₄×C₃₁	—	4	1	no	—
644	C₄×C₃₁	—	4	2	no	—
645	C₄×C₃₁	—	4	1	no	—
646	C₄×C₃₁	—	4	1	no	—
647	C₄×C₃₁	—	4	1	no	—
648	C₄×C₃₁	—	4	1	no	—
649	C₄×C₃₁	#585	1	2	yes	—
650	#559	—	2	1	no	—
651	#559	C₂²×C₃₁	1	2	yes	—
652	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
653	#554	C₂²×C₃₁	1	1	yes	characteristic
654	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	#553	C₂²×C₃₁	1	1	yes	characteristic
656	#553	C₂²×C₃₁	1	1	yes	characteristic, complemented
657	#552	—	2	1	no	—
658	#552	—	2	1	no	—
659	#552	—	2	1	no	—
660	#552	C₂²×C₃₁	1	1	yes	characteristic
661	#552	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	#550	—	2	1	no	—
663	#550	C₂²×C₃₁	1	2	yes	—
664	#547	—	2	1	no	—
665	#547	C₂²×C₃₁	1	1	yes	characteristic
666	#546	—	2	1	no	—
667	#546	—	2	1	no	—
668	#546	C₂²×C₃₁	1	2	yes	—
669	#546	C₂²×C₃₁	1	2	yes	—
670	#541	—	2	1	no	—
671	#540	—	2	1	no	—
672	#540	—	2	1	no	—
673	#539	—	2	1	no	—
674	#539	—	2	1	no	—
675	#535	—	2	1	no	—
676	#533	C₂²×C₃₁	1	1	yes	characteristic
677	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
678	#532	C₂²×C₃₁	1	1	yes	characteristic
679	#532	C₂²×C₃₁	1	1	yes	characteristic
680	#532	C₂²×C₃₁	1	1	yes	characteristic
681	#532	C₂²×C₃₁	1	1	yes	characteristic
682	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
683	#529	C₂²×C₃₁	1	1	yes	characteristic
684	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
685	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
686	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
687	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
688	#520	—	2	1	no	—
689	#518	—	2	1	no	—
690	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
691	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
692	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
693	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
694	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
695	#496	C₂²×C₃₁	1	1	yes	characteristic
696	#496	C₂²×C₃₁	1	1	yes	characteristic
697	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
700	#490	C₂²×C₃₁	1	2	yes	—
701	#490	C₂²×C₃₁	1	2	yes	—
702	#490	C₂²×C₃₁	1	1	yes	characteristic
703	#490	C₂²×C₃₁	1	1	yes	characteristic
704	#490	C₂²×C₃₁	1	1	yes	characteristic
705	#490	C₂²×C₃₁	1	1	yes	characteristic
706	#490	C₂²×C₃₁	1	1	yes	characteristic
707	#490	C₂²×C₃₁	1	1	yes	characteristic
708	#489	C₂²×C₃₁	1	2	yes	complemented
709	#489	C₂²×C₃₁	1	2	yes	complemented
710	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
711	#488	C₂²×C₃₁	1	2	yes	complemented
712	#488	C₂²×C₃₁	1	2	yes	complemented
713	#484	C₂²×C₃₁	1	2	yes	—
714	#483	C₂²×C₃₁	1	2	yes	—
715	#482	C₂²×C₃₁	1	2	yes	complemented
716	#482	C₂²×C₃₁	1	2	yes	complemented
717	#481	C₂²×C₃₁	1	2	yes	complemented
718	#480	C₂²×C₃₁	1	2	yes	complemented
719	#479	C₂²×C₃₁	1	2	yes	complemented
720	#479	C₂²×C₃₁	1	2	yes	complemented
721	#478	C₂²×C₃₁	1	2	yes	complemented
722	#478	C₂²×C₃₁	1	2	yes	complemented
723	#476	C₂²×C₃₁	1	2	yes	complemented
724	#474	C₂²×C₃₁	1	2	yes	complemented
725	#469	C₂²×C₃₁	1	2	yes	complemented
726	#468	C₂²×C₃₁	1	2	yes	complemented
727	#467	C₂²×C₃₁	1	2	yes	—
728	#466	C₂²×C₃₁	1	2	yes	complemented
729	#465	C₂²×C₃₁	1	2	yes	—
730	#465	C₂²×C₃₁	1	2	yes	complemented
731	#464	C₂²×C₃₁	1	2	yes	complemented
732	#464	C₂²×C₃₁	1	2	yes	complemented
733	#463	C₂²×C₃₁	1	2	yes	complemented
734	#463	C₂²×C₃₁	1	2	yes	complemented
735	#460	C₂²×C₃₁	1	2	yes	—
736	#459	C₂²×C₃₁	1	2	yes	—
737	#452	C₂²×C₃₁	1	2	yes	complemented
738	#452	C₂²×C₃₁	1	2	yes	complemented
739	#450	C₂²×C₃₁	1	2	yes	—
740	#449	C₂²×C₃₁	1	2	yes	complemented
741	#449	C₂²×C₃₁	1	2	yes	complemented
742	#447	C₂²×C₃₁	1	2	yes	—
743	#446	C₂²×C₃₁	1	2	yes	complemented
744	#442	C₂²×C₃₁	1	2	yes	complemented
745	#441	C₂²×C₃₁	1	2	yes	complemented
746	#440	C₂²×C₃₁	1	2	yes	complemented
747	#440	C₂²×C₃₁	1	2	yes	complemented
748	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
749	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
750	#435	C₂²×C₃₁	1	2	yes	—
751	#435	C₂²×C₃₁	1	2	yes	complemented
752	C₈×D₄	C₂²×C₃₁	1	2	yes	—
753	#432	C₂²×C₃₁	1	1	yes	characteristic
754	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
755	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
756	#417	C₂²×C₃₁	1	2	yes	complemented
757	#417	C₂²×C₃₁	1	2	yes	complemented
758	#416	C₂²×C₃₁	1	2	yes	complemented
759	#416	C₂²×C₃₁	1	2	yes	complemented
760	C₂×#102	C₂²×C₃₁	1	2	yes	—
761	C₂×#102	C₂²×C₃₁	1	2	yes	—
762	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
763	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
764	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic, complemented
765	C₂×C₃₁	—	2	2	no	—
766	C₂×C₃₁	—	4	1	no	—
767	C₂×C₃₁	—	4	1	no	—
768	C₂×C₃₁	—	8	1	no	—
769	C₂×C₃₁	—	8	2	no	—
770	C₂×C₃₁	—	8	2	no	—
771	C₂×C₃₁	#3500	1	1	yes	characteristic
772	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
773	C₂×C₃₁	#3585	1	1	yes	characteristic
774	C₂×#41	—	2	1	no	—
775	C₂×#41	—	2	1	no	—
776	C₂×#41	—	2	1	no	—
777	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
778	C₂×#41	C₂³×C₃₁	1	2	yes	—
779	C₂×#41	C₂³×C₃₁	1	2	yes	—
780	C₂²×D₄	—	2	1	no	—
781	C₂²×D₄	—	2	1	no	—
782	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
783	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
784	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
785	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
786	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
787	C₂×D₈	C₂³×C₃₁	1	2	yes	—
788	C₂×D₈	C₂³×C₃₁	1	2	yes	—
789	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
790	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
791	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
792	C₄⋊Q₈	—	2	1	no	—
793	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
794	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
795	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
796	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
797	#127	—	2	2	no	—
798	#127	—	2	1	no	—
799	#127	—	2	1	no	—
800	#127	C₂³×C₃₁	1	1	yes	characteristic
801	#127	C₂³×C₃₁	1	1	yes	characteristic
802	#127	C₂³×C₃₁	1	2	yes	—
803	#126	—	2	1	no	—
804	#126	—	2	1	no	—
805	#126	—	2	1	no	—
806	#126	—	2	1	no	—
807	#126	—	2	1	no	—
808	#126	—	2	1	no	—
809	#126	—	2	1	no	—
810	#125	—	2	1	no	—
811	#125	—	2	1	no	—
812	#125	—	2	1	no	—
813	#125	—	2	1	no	—
814	#125	—	2	1	no	—
815	#125	—	2	1	no	—
816	#125	—	2	1	no	—
817	#125	—	2	1	no	—
818	#125	—	2	1	no	—
819	#125	—	2	1	no	—
820	#125	C₂³×C₃₁	1	1	yes	characteristic
821	#125	C₂³×C₃₁	1	1	yes	characteristic
822	#125	C₂³×C₃₁	1	1	yes	characteristic
823	#125	C₂³×C₃₁	1	1	yes	characteristic
824	#125	C₂³×C₃₁	1	1	yes	characteristic
825	#125	C₂³×C₃₁	1	1	yes	characteristic
826	#125	C₂³×C₃₁	1	1	yes	characteristic
827	#124	—	2	2	no	—
828	#124	—	2	1	no	—
829	#124	—	2	1	no	—
830	#124	C₂³×C₃₁	1	1	yes	characteristic
831	#124	C₂³×C₃₁	1	2	yes	—
832	#124	C₂³×C₃₁	1	2	yes	—
833	#123	—	2	1	no	—
834	#123	—	2	1	no	—
835	#123	—	2	1	no	—
836	#123	—	2	1	no	—
837	#123	—	2	1	no	—
838	#123	—	2	2	no	—
839	#123	—	2	2	no	—
840	#123	—	2	2	no	—
841	#123	—	2	2	no	—
842	#123	—	2	1	no	—
843	#123	—	2	1	no	—
844	#123	—	2	1	no	—
845	#123	—	2	1	no	—
846	C₂²⋊Q₈	—	2	1	no	—
847	C₂²⋊Q₈	—	2	1	no	—
848	C₂²⋊Q₈	—	2	1	no	—
849	C₂²⋊Q₈	—	2	1	no	—
850	C₂²⋊Q₈	—	2	1	no	—
851	C₂²⋊Q₈	—	2	1	no	—
852	C₂²⋊Q₈	—	2	1	no	—
853	C₂²⋊Q₈	—	2	1	no	—
854	C₂²⋊Q₈	—	2	1	no	—
855	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
856	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
857	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
858	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
859	#121	—	2	1	no	—
860	#121	—	2	1	no	—
861	#121	—	2	1	no	—
862	#121	—	2	1	no	—
863	#121	—	2	1	no	—
864	#121	—	2	1	no	—
865	#121	—	2	1	no	—
866	#121	—	2	1	no	—
867	#121	—	2	2	no	—
868	#121	—	2	2	no	—
869	#121	—	2	2	no	—
870	#121	—	2	2	no	—
871	#121	C₂³×C₃₁	1	1	yes	characteristic
872	#121	C₂³×C₃₁	1	1	yes	characteristic
873	#121	C₂³×C₃₁	1	1	yes	characteristic
874	#121	C₂³×C₃₁	1	2	yes	—
875	#121	C₂³×C₃₁	1	2	yes	—
876	#120	—	2	2	no	—
877	#120	—	2	2	no	—
878	C₄×Q₈	—	2	1	no	—
879	C₄×Q₈	—	2	1	no	—
880	C₄×Q₈	—	2	1	no	—
881	C₄×Q₈	—	2	1	no	—
882	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
883	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
884	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
885	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
886	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
887	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
888	C₄×D₄	—	2	1	no	—
889	C₄×D₄	—	2	1	no	—
890	C₄×D₄	—	2	1	no	—
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	2	2	no	—
893	C₄×D₄	—	2	2	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	1	no	—
896	C₄×D₄	—	2	1	no	—
897	C₄×D₄	—	2	1	no	—
898	C₄×D₄	—	2	1	no	—
899	C₄×D₄	—	2	1	no	—
900	C₄×D₄	—	2	1	no	—
901	C₄×D₄	—	2	1	no	—
902	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
903	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
904	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
905	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
906	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
907	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
908	C₄×D₄	C₂³×C₃₁	1	2	yes	—
909	C₄×D₄	C₂³×C₃₁	1	2	yes	—
910	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
911	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
912	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
913	#117	—	2	1	no	—
914	#117	—	2	1	no	—
915	#117	—	2	1	no	—
916	#117	—	2	1	no	—
917	#117	—	2	1	no	—
918	#117	—	2	1	no	—
919	#117	D₄×C₃₁	1	1	yes	characteristic
920	#117	D₄×C₃₁	1	1	yes	characteristic
921	#117	D₄×C₃₁	1	1	yes	characteristic
922	#117	C₂³×C₃₁	1	1	yes	characteristic
923	#117	C₂³×C₃₁	1	1	yes	characteristic
924	C₂×C₄⋊C₄	—	2	1	no	—
925	C₂×C₄⋊C₄	—	2	1	no	—
926	C₂×C₄⋊C₄	—	2	1	no	—
927	C₂×C₄⋊C₄	—	2	1	no	—
928	C₂×C₄⋊C₄	—	2	1	no	—
929	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
930	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
931	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
932	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
933	C₂×C₂²⋊C₄	—	2	2	no	—
934	C₂×C₂²⋊C₄	—	2	2	no	—
935	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
936	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
937	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
938	#107	C₂³×C₃₁	1	2	yes	—
939	#107	C₂³×C₃₁	1	2	yes	—
940	#107	C₂³×C₃₁	1	2	yes	—
941	#106	C₂³×C₃₁	1	2	yes	—
942	#106	C₂³×C₃₁	1	2	yes	—
943	#106	C₂³×C₃₁	1	2	yes	—
944	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
945	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
946	C₄⋊C₈	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	#102	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	#102	C₂³×C₃₁	1	2	yes	—
962	#102	C₂³×C₃₁	1	2	yes	—
963	#102	C₂³×C₃₁	1	2	yes	—
964	#102	C₂³×C₃₁	1	2	yes	—
965	#102	C₂³×C₃₁	1	2	yes	—
966	#102	C₂³×C₃₁	1	2	yes	—
967	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
968	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
969	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
970	#97	C₂³×C₃₁	1	1	yes	characteristic
971	#97	C₂³×C₃₁	1	1	yes	characteristic
972	#97	C₂³×C₃₁	1	2	yes	—
973	#97	C₂³×C₃₁	1	1	yes	characteristic
974	#97	C₂³×C₃₁	1	2	yes	—
975	#97	C₂³×C₃₁	1	1	yes	characteristic
976	C₄×C₈	C₂³×C₃₁	1	2	yes	—
977	C₃₁	#62578	1	1	yes	characteristic, direct product factor, Sylow
978	C₂⁴	—	2	2	no	—
979	#41	—	4	2	no	—
980	#41	—	4	2	no	—
981	#41	—	4	2	no	—
982	#41	—	4	2	no	—
983	#41	—	4	2	no	—
984	#41	—	4	4	no	—
985	#41	—	8	2	no	—
986	#41	—	8	2	no	—
987	C₂×Q₈	—	2	1	no	—
988	C₂×Q₈	—	2	1	no	—
989	C₂×Q₈	—	2	1	no	—
990	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
991	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
992	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
993	C₂×D₄	—	2	1	no	—
994	C₂×D₄	—	2	1	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	2	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	2	2	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	1	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	2	2	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	2	no	—
1006	C₂×D₄	—	2	2	no	—
1007	C₂×D₄	—	4	2	no	—
1008	C₂×D₄	—	4	2	no	—
1009	C₂×D₄	—	4	4	no	—
1010	C₂×D₄	—	8	2	no	—
1011	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1012	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1013	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1014	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1015	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1016	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1017	C₂²×C₄	—	2	1	no	—
1018	C₂²×C₄	—	2	1	no	—
1019	C₂²×C₄	—	2	1	no	—
1020	C₂²×C₄	—	2	1	no	—
1021	C₂²×C₄	—	2	1	no	—
1022	C₂²×C₄	—	2	2	no	—
1023	C₂²×C₄	—	2	2	no	—
1024	C₂²×C₄	—	2	2	no	—
1025	C₂²×C₄	—	2	2	no	—
1026	C₂²×C₄	—	2	1	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1029	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1030	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1031	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1032	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1033	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1034	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1035	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1036	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1037	Q₁₆	—	4	2	no	—
1038	SD₁₆	—	4	2	no	—
1039	SD₁₆	—	4	2	no	—
1040	SD₁₆	—	4	2	no	—
1041	D₈	—	4	2	no	—
1042	D₈	—	4	2	no	—
1043	M₁₆	—	4	2	no	—
1044	C₂×C₈	—	4	2	no	—
1045	C₂×C₈	—	4	2	no	—
1046	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1047	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1048	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1049	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
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	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	—	2	1	no	—
1061	C₄⋊C₄	—	2	1	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	1	no	—
1064	C₄⋊C₄	—	2	1	no	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	1	no	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	2	no	—
1076	C₄⋊C₄	—	2	1	no	—
1077	C₄⋊C₄	—	2	2	no	—
1078	C₄⋊C₄	—	2	1	no	—
1079	C₄⋊C₄	—	2	1	no	—
1080	C₄⋊C₄	—	2	1	no	—
1081	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1082	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1083	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1084	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1085	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1086	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1087	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1088	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1089	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1090	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1091	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1092	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1093	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1094	C₂²⋊C₄	—	2	2	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	1	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	—	2	2	no	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	2	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	1	no	—
1115	C₂²⋊C₄	—	2	1	no	—
1116	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1117	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1118	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1119	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1120	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1121	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1122	C₄²	—	2	1	no	—
1123	C₄²	—	2	1	no	—
1124	C₄²	—	2	1	no	—
1125	C₄²	—	2	1	no	—
1126	C₄²	—	2	2	no	—
1127	C₄²	—	2	1	no	—
1128	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1129	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1130	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1131	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1132	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1133	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1134	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1135	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1136	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1137	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1138	C₂³	—	2	1	no	—
1139	C₂³	—	2	2	no	—
1140	C₂³	—	2	2	no	—
1141	C₂³	—	4	4	no	—
1142	C₂³	—	8	2	no	—
1143	C₂³	—	8	2	no	—
1144	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1145	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1146	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1147	Q₈	—	2	2	no	—
1148	Q₈	—	2	2	no	—
1149	Q₈	—	2	2	no	—
1150	Q₈	—	4	1	no	—
1151	Q₈	—	4	2	no	—
1152	Q₈	—	4	2	no	—
1153	Q₈	—	8	1	no	—
1154	D₄	—	2	2	no	—
1155	D₄	—	2	2	no	—
1156	D₄	—	2	2	no	—
1157	D₄	—	2	2	no	—
1158	D₄	—	2	2	no	—
1159	D₄	—	2	2	no	—
1160	D₄	—	2	2	no	—
1161	D₄	—	4	1	no	—
1162	D₄	—	4	2	no	—
1163	D₄	—	4	2	no	—
1164	D₄	—	4	4	no	—
1165	D₄	—	4	2	no	—
1166	D₄	—	4	2	no	—
1167	D₄	—	4	2	no	—
1168	D₄	—	4	2	no	—
1169	D₄	—	8	2	no	—
1170	D₄	—	8	2	no	—
1171	D₄	—	8	1	no	—
1172	D₄	—	8	2	no	—
1173	D₄	—	8	2	no	—
1174	D₄	—	8	2	no	—
1175	D₄	—	8	2	no	—
1176	C₂×C₄	—	2	2	no	—
1177	C₂×C₄	—	2	2	no	—
1178	C₂×C₄	—	2	2	no	—
1179	C₂×C₄	—	2	2	no	—
1180	C₂×C₄	—	2	1	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	2	no	—
1184	C₂×C₄	—	2	2	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	2	1	no	—
1187	C₂×C₄	—	2	1	no	—
1188	C₂×C₄	—	2	1	no	—
1189	C₂×C₄	—	4	1	no	—
1190	C₂×C₄	—	4	1	no	—
1191	C₂×C₄	—	4	1	no	—
1192	C₂×C₄	—	4	1	no	—
1193	C₂×C₄	—	4	1	no	—
1194	C₂×C₄	—	4	2	no	—
1195	C₂×C₄	—	4	2	no	—
1196	C₂×C₄	—	4	2	no	—
1197	C₂×C₄	—	8	1	no	—
1198	C₂×C₄	—	8	1	no	—
1199	C₂×C₄	—	8	2	no	—
1200	C₂×C₄	—	8	2	no	—
1201	C₂×C₄	—	8	2	no	—
1202	C₂×C₄	—	8	2	no	—
1203	C₂×C₄	—	8	1	no	—
1204	C₂×C₄	—	8	1	no	—
1205	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1206	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1207	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1208	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1209	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1210	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1211	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1212	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1213	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1214	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1215	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1216	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1217	C₈	—	2	2	no	—
1218	C₈	—	2	2	no	—
1219	C₈	—	2	2	no	—
1220	C₈	—	2	2	no	—
1221	C₂²	—	2	1	no	—
1222	C₂²	—	2	1	no	—
1223	C₂²	—	2	1	no	—
1224	C₂²	—	2	1	no	—
1225	C₂²	—	2	1	no	—
1226	C₂²	—	2	1	no	—
1227	C₂²	—	2	1	no	—
1228	C₂²	—	2	1	no	—
1229	C₂²	—	4	2	no	—
1230	C₂²	—	4	2	no	—
1231	C₂²	—	4	1	no	—
1232	C₂²	—	4	1	no	—
1233	C₂²	—	4	2	no	—
1234	C₂²	—	4	2	no	—
1235	C₂²	—	4	1	no	—
1236	C₂²	—	4	2	no	—
1237	C₂²	—	4	2	no	—
1238	C₂²	—	16	4	no	—
1239	C₂²	C₃₁×#575	1	2	yes	—
1240	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1241	C₄	—	2	1	no	—
1242	C₄	—	2	1	no	—
1243	C₄	—	2	1	no	—
1244	C₄	—	2	1	no	—
1245	C₄	—	2	1	no	—
1246	C₄	—	2	1	no	—
1247	C₄	—	2	1	no	—
1248	C₄	—	2	1	no	—
1249	C₄	—	2	1	no	—
1250	C₄	—	2	1	no	—
1251	C₄	—	2	1	no	—
1252	C₄	—	4	2	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	1	no	—
1255	C₄	—	4	1	no	—
1256	C₄	—	4	1	no	—
1257	C₄	—	4	2	no	—
1258	C₄	—	4	1	no	—
1259	C₄	—	4	1	no	—
1260	C₄	—	4	1	no	—
1261	C₄	C₃₁×#585	1	2	yes	—
1262	C₂	—	2	2	no	—
1263	C₂	—	4	1	no	—
1264	C₂	—	4	1	no	—
1265	C₂	—	8	2	no	—
1266	C₂	—	8	2	no	—
1267	C₂	—	8	1	no	—
1268	C₂	C₃₁×#3500	1	1	yes	characteristic
1269	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1270	C₂	C₃₁×#3585	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3515	C₂	semidirect
2. C₃₁×#3508	C₂	semidirect
3. C₃₁×#3371	C₂	semidirect
4. C₃₁×#3370	C₂	semidirect
5. C₃₁×#3317	C₂	semidirect
6. C₃₁×#3314	C₂	semidirect
7. C₃₁×#3309	C₂	semidirect
8. C₃₁×#3306	C₂	semidirect
9. C₃₁×#3297	C₂	semidirect
10. C₃₁×#3296	C₂	semidirect
11. C₃₁×#3236	C₂	semidirect
12. C₃₁×#3235	C₂	semidirect
13. C₃₁×#3234	C₂	semidirect
14. C₃₁×#3219	C₂	semidirect
15. C₃₁×#3219	C₂	semidirect
16. C₃₁×#3217	C₂	semidirect
17. C₃₁×#3181	C₂	semidirect
18. C₃₁×#3180	C₂	semidirect
19. C₃₁×#3171	C₂	semidirect
20. C₃₁×#3142	C₂	semidirect
21. C₃₁×#3135	C₂	semidirect
22. C₂×C₃₁×#490	C₂	semidirect
23. C₃₁×#2970	C₂	semidirect
26. C₃₁×#557	C₂²	semidirect
28. C₃₁×#554	C₂²	semidirect
30. C₃₁×#553	C₂²	semidirect
35. C₃₁×#552	C₂²	semidirect
51. C₃₁×#533	C₂²	semidirect
58. C₃₁×#529	C₂²	semidirect
59. C₃₁×#529	C₂²	semidirect
61. C₂×C₃₁×#125	C₂²	semidirect
65. C₃₁×#501	C₂²	semidirect
66. C₃₁×#501	C₂²	semidirect
67. C₃₁×#501	C₂²	semidirect
68. C₃₁×#497	C₂²	semidirect
71. C₃₁×#491	C₂²	semidirect
72. C₃₁×#491	C₂²	semidirect
73. C₃₁×#491	C₂²	semidirect
82. C₃₁×#489	C₂²	semidirect
83. C₃₁×#489	C₂²	semidirect
84. C₃₁×#489	C₂²	semidirect
85. C₃₁×#488	C₂²	semidirect
86. C₃₁×#488	C₂²	semidirect
89. C₃₁×#482	C₂²	semidirect
90. C₃₁×#482	C₂²	semidirect
91. C₃₁×#481	C₂²	semidirect
92. C₃₁×#480	C₂²	semidirect
93. C₃₁×#479	C₂²	semidirect
94. C₃₁×#479	C₂²	semidirect
95. C₃₁×#478	C₂²	semidirect
96. C₃₁×#478	C₂²	semidirect
97. C₃₁×#476	C₂²	semidirect
98. C₃₁×#474	C₂²	semidirect
99. C₃₁×#469	C₂²	semidirect
100. C₃₁×#468	C₂²	semidirect
102. C₃₁×#466	C₂²	semidirect
104. C₃₁×#465	C₂²	semidirect
105. C₃₁×#464	C₂²	semidirect
106. C₃₁×#464	C₂²	semidirect
107. C₃₁×#463	C₂²	semidirect
108. C₃₁×#463	C₂²	semidirect
111. C₃₁×#452	C₂²	semidirect
112. C₃₁×#452	C₂²	semidirect
114. C₃₁×#449	C₂²	semidirect
115. C₃₁×#449	C₂²	semidirect
117. C₃₁×#446	C₂²	semidirect
118. C₃₁×#442	C₂²	semidirect
119. C₃₁×#441	C₂²	semidirect
120. C₃₁×#440	C₂²	semidirect
121. C₃₁×#440	C₂²	semidirect
122. C₄×SD₁₆×C₃₁	C₂²	semidirect
123. C₄×D₈×C₃₁	C₂²	semidirect
125. C₃₁×#435	C₂²	semidirect
128. C₃₁×#432	C₂²	semidirect
129. C₃₁×#432	C₂²	semidirect
130. C₃₁×#417	C₂²	semidirect
131. C₃₁×#417	C₂²	semidirect
132. C₃₁×#416	C₂²	semidirect
133. C₃₁×#416	C₂²	semidirect
136. C₄×M₁₆×C₃₁	C₂²	semidirect
138. C₂×C₃₁×#97	C₂²	semidirect
502. #62578	C₃₁	direct (N × H)
586. #3515	C₂×C₃₁	semidirect
587. #3508	C₂×C₃₁	semidirect
588. #3371	C₂×C₃₁	semidirect
589. #3370	C₂×C₃₁	semidirect
590. #3317	C₂×C₃₁	semidirect
591. #3314	C₂×C₃₁	semidirect
592. #3309	C₂×C₃₁	semidirect
593. #3306	C₂×C₃₁	semidirect
594. #3297	C₂×C₃₁	semidirect
595. #3296	C₂×C₃₁	semidirect
596. #3236	C₂×C₃₁	semidirect
597. #3235	C₂×C₃₁	semidirect
598. #3234	C₂×C₃₁	semidirect
599. #3219	C₂×C₃₁	semidirect
600. #3219	C₂×C₃₁	semidirect
601. #3217	C₂×C₃₁	semidirect
602. #3181	C₂×C₃₁	semidirect
603. #3180	C₂×C₃₁	semidirect
604. #3171	C₂×C₃₁	semidirect
605. #3142	C₂×C₃₁	semidirect
606. #3135	C₂×C₃₁	semidirect
607. C₂×#490	C₂×C₃₁	semidirect
608. #2970	C₂×C₃₁	semidirect
652. #557	C₂²×C₃₁	semidirect
654. #554	C₂²×C₃₁	semidirect
656. #553	C₂²×C₃₁	semidirect
661. #552	C₂²×C₃₁	semidirect
677. #533	C₂²×C₃₁	semidirect
684. #529	C₂²×C₃₁	semidirect
685. #529	C₂²×C₃₁	semidirect
687. C₂×#125	C₂²×C₃₁	semidirect
691. #501	C₂²×C₃₁	semidirect
692. #501	C₂²×C₃₁	semidirect
693. #501	C₂²×C₃₁	semidirect
694. #497	C₂²×C₃₁	semidirect
697. #491	C₂²×C₃₁	semidirect
698. #491	C₂²×C₃₁	semidirect
699. #491	C₂²×C₃₁	semidirect
708. #489	C₂²×C₃₁	semidirect
709. #489	C₂²×C₃₁	semidirect
710. #489	C₂²×C₃₁	semidirect
711. #488	C₂²×C₃₁	semidirect
712. #488	C₂²×C₃₁	semidirect
715. #482	C₂²×C₃₁	semidirect
716. #482	C₂²×C₃₁	semidirect
717. #481	C₂²×C₃₁	semidirect
718. #480	C₂²×C₃₁	semidirect
719. #479	C₂²×C₃₁	semidirect
720. #479	C₂²×C₃₁	semidirect
721. #478	C₂²×C₃₁	semidirect
722. #478	C₂²×C₃₁	semidirect
723. #476	C₂²×C₃₁	semidirect
724. #474	C₂²×C₃₁	semidirect
725. #469	C₂²×C₃₁	semidirect
726. #468	C₂²×C₃₁	semidirect
728. #466	C₂²×C₃₁	semidirect
730. #465	C₂²×C₃₁	semidirect
731. #464	C₂²×C₃₁	semidirect
732. #464	C₂²×C₃₁	semidirect
733. #463	C₂²×C₃₁	semidirect
734. #463	C₂²×C₃₁	semidirect
737. #452	C₂²×C₃₁	semidirect
738. #452	C₂²×C₃₁	semidirect
740. #449	C₂²×C₃₁	semidirect
741. #449	C₂²×C₃₁	semidirect
743. #446	C₂²×C₃₁	semidirect
744. #442	C₂²×C₃₁	semidirect
745. #441	C₂²×C₃₁	semidirect
746. #440	C₂²×C₃₁	semidirect
747. #440	C₂²×C₃₁	semidirect
748. C₄×SD₁₆	C₂²×C₃₁	semidirect
749. C₄×D₈	C₂²×C₃₁	semidirect
751. #435	C₂²×C₃₁	semidirect
754. #432	C₂²×C₃₁	semidirect
755. #432	C₂²×C₃₁	semidirect
756. #417	C₂²×C₃₁	semidirect
757. #417	C₂²×C₃₁	semidirect
758. #416	C₂²×C₃₁	semidirect
759. #416	C₂²×C₃₁	semidirect
762. C₄×M₁₆	C₂²×C₃₁	semidirect
764. C₂×#97	C₂²×C₃₁	semidirect
977. C₃₁	#62578	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×#3515	2
C₃₁×#3508	2
C₃₁×#3371	2
C₃₁×#3370	2
C₃₁×#3317	2
C₃₁×#3314	2
C₃₁×#3309	2
C₃₁×#3306	2
C₃₁×#3297	2
C₃₁×#3296	2
C₃₁×#3236	2
C₃₁×#3235	2
C₃₁×#3234	2
C₃₁×#3219	2
C₃₁×#3217	2
C₃₁×#3181	2
C₃₁×#3180	2
C₃₁×#3171	2
C₃₁×#3142	2
C₃₁×#3135	2
C₂×C₃₁×#490	2
C₃₁×#2970	2
#62578	31

Subgroups — C31×#62578 #21519337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62578 #21519337