Subgroups — C₃₁×#62584 #21519343

Order 7936.

1792 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3321	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3320	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3319	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3318	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3301	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3297	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3240	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3240	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3239	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3214	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3213	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3213	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3180	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×#3140	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3135	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#489	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2970	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#559	C₂²	1	1	yes	characteristic
25	C₃₁×#556	—	2	1	no	—
26	C₃₁×#556	C₂²	1	1	yes	characteristic
27	C₃₁×#555	—	2	1	no	—
28	C₃₁×#555	C₂²	1	2	yes	complemented
29	C₃₁×#554	C₂²	1	2	yes	complemented
30	C₃₁×#553	C₂²	1	2	yes	—
31	C₃₁×#553	C₂²	1	2	yes	complemented
32	C₃₁×#551	—	2	1	no	—
33	C₃₁×#551	—	2	1	no	—
34	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#548	—	2	1	no	—
36	C₃₁×#548	—	2	1	no	—
37	C₃₁×#548	C₂²	1	1	yes	characteristic
38	C₃₁×#548	C₂²	1	1	yes	characteristic
39	C₃₁×#547	—	2	1	no	—
40	C₃₁×#546	—	2	1	no	—
41	C₃₁×#546	C₂²	1	1	yes	characteristic
42	C₃₁×#546	C₂²	1	1	yes	characteristic
43	D₄²×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#542	—	2	1	no	—
45	C₃₁×#542	—	2	1	no	—
46	C₃₁×#542	—	2	1	no	—
47	C₃₁×#538	—	2	1	no	—
48	C₃₁×#538	—	2	1	no	—
49	C₃₁×#537	—	2	1	no	—
50	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
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, complemented
54	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#529	C₂²	1	1	yes	characteristic
58	C₃₁×#529	C₂²	1	1	yes	characteristic
59	C₃₁×#529	C₂²	1	1	yes	characteristic
60	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
61	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
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×#496	C₂²	1	1	yes	characteristic
69	C₃₁×#496	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#496	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#491	C₂²	1	2	yes	complemented
72	C₃₁×#490	C₂²	1	2	yes	—
73	C₃₁×#490	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#489	C₂²	1	2	yes	—
75	C₃₁×#489	C₂²	1	1	yes	characteristic
76	C₃₁×#489	C₂²	1	1	yes	characteristic
77	C₃₁×#489	C₂²	1	1	yes	characteristic
78	C₃₁×#489	C₂²	1	2	yes	complemented
79	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#488	C₂²	1	2	yes	—
86	C₃₁×#488	C₂²	1	2	yes	complemented
87	C₃₁×#485	C₂²	1	2	yes	complemented
88	C₃₁×#485	C₂²	1	2	yes	complemented
89	C₃₁×#484	C₂²	1	2	yes	complemented
90	C₃₁×#482	C₂²	1	2	yes	—
91	C₃₁×#482	C₂²	1	2	yes	—
92	C₃₁×#481	C₂²	1	2	yes	—
93	C₃₁×#479	C₂²	1	2	yes	complemented
94	C₃₁×#479	C₂²	1	2	yes	complemented
95	C₃₁×#478	C₂²	1	2	yes	—
96	C₃₁×#478	C₂²	1	2	yes	complemented
97	C₃₁×#475	C₂²	1	2	yes	complemented
98	C₃₁×#474	C₂²	1	2	yes	complemented
99	C₃₁×#469	C₂²	1	2	yes	—
100	C₃₁×#468	C₂²	1	2	yes	complemented
101	C₃₁×#466	C₂²	1	2	yes	—
102	C₃₁×#466	C₂²	1	2	yes	—
103	C₃₁×#465	C₂²	1	2	yes	complemented
104	C₃₁×#465	C₂²	1	2	yes	complemented
105	C₃₁×#463	C₂²	1	2	yes	—
106	C₃₁×#463	C₂²	1	2	yes	—
107	C₃₁×#463	C₂²	1	2	yes	complemented
108	C₃₁×#463	C₂²	1	2	yes	complemented
109	C₃₁×#461	C₂²	1	2	yes	complemented
110	C₃₁×#459	C₂²	1	2	yes	—
111	C₃₁×#449	C₂²	1	2	yes	complemented
112	C₃₁×#449	C₂²	1	2	yes	complemented
113	C₃₁×#448	C₂²	1	2	yes	complemented
114	C₃₁×#448	C₂²	1	2	yes	complemented
115	C₃₁×#447	C₂²	1	2	yes	—
116	C₃₁×#447	C₂²	1	2	yes	—
117	C₃₁×#446	C₂²	1	2	yes	complemented
118	C₃₁×#442	C₂²	1	2	yes	—
119	C₃₁×#442	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	complemented
127	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
128	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#419	C₂²	1	2	yes	complemented
131	C₃₁×#418	C₂²	1	2	yes	—
132	C₃₁×#416	C₂²	1	2	yes	complemented
133	C₃₁×#416	C₂²	1	2	yes	complemented
134	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
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, complemented
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	1	yes	characteristic
144	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
145	C₂²×Q₈×C₃₁	—	2	1	no	—
146	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
147	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
148	C₂²×D₄×C₃₁	—	2	1	no	—
149	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
150	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×D₈×C₃₁	C₂³	1	2	yes	—
155	C₂×D₈×C₃₁	C₂³	1	2	yes	—
156	C₂×D₈×C₃₁	C₂³	1	2	yes	—
157	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
159	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
160	C₃₁×C₄⋊Q₈	—	2	1	no	—
161	C₃₁×C₄⋊Q₈	—	2	1	no	—
162	C₃₁×C₄⋊Q₈	—	2	1	no	—
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₃₁×#127	C₂³	1	1	yes	characteristic
169	C₃₁×#127	C₂³	1	1	yes	characteristic
170	C₃₁×#126	—	2	1	no	—
171	C₃₁×#126	—	2	1	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	1	no	—
175	C₃₁×#126	—	2	1	no	—
176	C₃₁×#126	—	2	1	no	—
177	C₃₁×#125	C₂³	1	2	yes	—
178	C₃₁×#125	C₂³	1	2	yes	—
179	C₃₁×#125	C₂³	1	1	yes	characteristic
180	C₃₁×#124	—	2	1	no	—
181	C₃₁×#124	—	2	1	no	—
182	C₃₁×#124	—	2	1	no	—
183	C₃₁×#124	—	2	2	no	—
184	C₃₁×#124	—	2	2	no	—
185	C₃₁×#124	—	2	1	no	—
186	C₃₁×#124	—	2	1	no	—
187	C₃₁×#124	—	2	1	no	—
188	C₃₁×#124	—	2	1	no	—
189	C₃₁×#124	—	2	1	no	—
190	C₃₁×#124	—	2	1	no	—
191	C₃₁×#124	—	2	1	no	—
192	C₃₁×#124	C₂³	1	1	yes	characteristic
193	C₃₁×#124	C₂³	1	1	yes	characteristic
194	C₃₁×#124	C₂³	1	1	yes	characteristic
195	C₃₁×#124	C₂³	1	1	yes	characteristic
196	C₃₁×#124	C₂³	1	1	yes	characteristic
197	C₃₁×#124	C₂³	1	1	yes	characteristic
198	C₃₁×#124	C₂³	1	1	yes	characteristic
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	1	no	—
204	C₃₁×#123	—	2	1	no	—
205	C₃₁×#123	—	2	1	no	—
206	C₃₁×#123	—	2	2	no	—
207	C₃₁×#123	—	2	2	no	—
208	C₃₁×C₂²⋊Q₈	—	2	2	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	—	2	1	no	—
214	C₃₁×C₂²⋊Q₈	—	2	2	no	—
215	C₃₁×C₂²⋊Q₈	—	2	2	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×#121	—	2	2	no	—
224	C₃₁×#121	—	2	2	no	—
225	C₃₁×#121	—	2	2	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	1	no	—
233	C₃₁×#121	—	2	1	no	—
234	C₃₁×#121	—	2	1	no	—
235	C₃₁×#121	—	2	1	no	—
236	C₃₁×#121	C₂³	1	2	yes	—
237	C₃₁×#121	C₂³	1	2	yes	—
238	C₃₁×#121	C₂³	1	2	yes	—
239	C₃₁×#121	C₂³	1	1	yes	characteristic
240	C₃₁×#121	C₂³	1	1	yes	characteristic
241	C₃₁×#121	C₂³	1	1	yes	characteristic
242	C₃₁×#120	—	2	1	no	—
243	C₃₁×#120	—	2	1	no	—
244	C₃₁×#120	—	2	1	no	—
245	C₃₁×#120	—	2	1	no	—
246	C₄×Q₈×C₃₁	—	2	1	no	—
247	C₄×Q₈×C₃₁	—	2	1	no	—
248	C₄×Q₈×C₃₁	—	2	1	no	—
249	C₄×Q₈×C₃₁	—	2	1	no	—
250	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
251	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
252	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
253	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
254	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₃₁	—	2	1	no	—
256	C₄×D₄×C₃₁	—	2	1	no	—
257	C₄×D₄×C₃₁	—	2	1	no	—
258	C₄×D₄×C₃₁	—	2	1	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	2	no	—
263	C₄×D₄×C₃₁	—	2	2	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	—	2	1	no	—
268	C₄×D₄×C₃₁	—	2	1	no	—
269	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
270	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
271	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
272	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
273	C₄×D₄×C₃₁	C₂³	1	2	yes	—
274	C₄×D₄×C₃₁	C₂³	1	2	yes	—
275	C₄×D₄×C₃₁	C₂³	1	2	yes	—
276	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
277	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
278	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
279	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
280	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
281	C₃₁×#117	—	2	1	no	—
282	C₃₁×#117	—	2	2	no	—
283	C₃₁×#117	—	2	1	no	—
284	C₃₁×#117	—	2	1	no	—
285	C₃₁×#117	—	2	1	no	—
286	C₃₁×#117	D₄	1	1	yes	characteristic
287	C₃₁×#117	D₄	1	1	yes	characteristic
288	C₃₁×#117	D₄	1	1	yes	characteristic
289	C₃₁×#117	C₂³	1	2	yes	—
290	C₃₁×#117	C₂³	1	2	yes	—
291	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
292	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
294	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
295	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
297	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
298	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
299	C₂×C₂²⋊C₄×C₃₁	—	2	1	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×#103	C₂³	1	2	yes	—
320	C₃₁×#103	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	1	yes	characteristic
338	C₃₁×#97	C₂³	1	2	yes	—
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	1	no	—
343	C₂⁴×C₃₁	—	2	1	no	—
344	#41×C₃₁	—	4	2	no	—
345	#41×C₃₁	—	4	4	no	—
346	#41×C₃₁	—	4	2	no	—
347	#41×C₃₁	—	4	2	no	—
348	#41×C₃₁	—	8	2	no	—
349	#41×C₃₁	—	8	2	no	—
350	C₂×Q₈×C₃₁	—	2	1	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	—	2	1	no	—
355	C₂×Q₈×C₃₁	—	2	2	no	—
356	C₂×Q₈×C₃₁	—	4	2	no	—
357	C₂×Q₈×C₃₁	—	4	2	no	—
358	C₂×Q₈×C₃₁	—	8	2	no	—
359	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
360	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
361	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
362	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
363	C₂×D₄×C₃₁	—	2	1	no	—
364	C₂×D₄×C₃₁	—	2	1	no	—
365	C₂×D₄×C₃₁	—	2	2	no	—
366	C₂×D₄×C₃₁	—	2	1	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	—	2	1	no	—
372	C₂×D₄×C₃₁	—	2	1	no	—
373	C₂×D₄×C₃₁	—	2	1	no	—
374	C₂×D₄×C₃₁	—	2	1	no	—
375	C₂×D₄×C₃₁	—	2	1	no	—
376	C₂×D₄×C₃₁	—	2	1	no	—
377	C₂×D₄×C₃₁	—	4	2	no	—
378	C₂×D₄×C₃₁	—	4	2	no	—
379	C₂×D₄×C₃₁	—	4	4	no	—
380	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
381	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
382	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
383	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
386	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
387	C₂²×C₄×C₃₁	—	2	1	no	—
388	C₂²×C₄×C₃₁	—	2	1	no	—
389	C₂²×C₄×C₃₁	—	2	2	no	—
390	C₂²×C₄×C₃₁	—	2	2	no	—
391	C₂²×C₄×C₃₁	—	2	1	no	—
392	C₂²×C₄×C₃₁	—	2	1	no	—
393	C₂²×C₄×C₃₁	—	2	1	no	—
394	C₂²×C₄×C₃₁	—	2	1	no	—
395	C₂²×C₄×C₃₁	—	2	1	no	—
396	C₂²×C₄×C₃₁	—	2	2	no	—
397	C₂²×C₄×C₃₁	—	2	2	no	—
398	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
404	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	SD₁₆×C₃₁	—	4	2	no	—
408	SD₁₆×C₃₁	—	4	2	no	—
409	SD₁₆×C₃₁	—	4	2	no	—
410	D₈×C₃₁	—	4	2	no	—
411	D₈×C₃₁	—	4	2	no	—
412	D₈×C₃₁	—	4	2	no	—
413	M₁₆×C₃₁	—	4	2	no	—
414	C₂×C₈×C₃₁	—	4	2	no	—
415	C₂×C₈×C₃₁	—	4	2	no	—
416	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
417	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
418	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
419	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
420	C₄⋊C₄×C₃₁	—	2	2	no	—
421	C₄⋊C₄×C₃₁	—	2	1	no	—
422	C₄⋊C₄×C₃₁	—	2	1	no	—
423	C₄⋊C₄×C₃₁	—	2	2	no	—
424	C₄⋊C₄×C₃₁	—	2	2	no	—
425	C₄⋊C₄×C₃₁	—	2	2	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	2	no	—
435	C₄⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
446	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
447	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
448	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
450	C₂²⋊C₄×C₃₁	—	2	1	no	—
451	C₂²⋊C₄×C₃₁	—	2	1	no	—
452	C₂²⋊C₄×C₃₁	—	2	2	no	—
453	C₂²⋊C₄×C₃₁	—	2	2	no	—
454	C₂²⋊C₄×C₃₁	—	2	1	no	—
455	C₂²⋊C₄×C₃₁	—	2	1	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	—	2	2	no	—
471	C₂²⋊C₄×C₃₁	—	2	2	no	—
472	C₂²⋊C₄×C₃₁	—	2	1	no	—
473	C₂²⋊C₄×C₃₁	—	2	1	no	—
474	C₂²⋊C₄×C₃₁	—	2	2	no	—
475	C₂²⋊C₄×C₃₁	—	2	1	no	—
476	C₂²⋊C₄×C₃₁	—	2	1	no	—
477	C₂²⋊C₄×C₃₁	—	2	1	no	—
478	C₂²⋊C₄×C₃₁	—	2	2	no	—
479	C₂²⋊C₄×C₃₁	—	2	2	no	—
480	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
487	C₄²×C₃₁	—	2	1	no	—
488	C₄²×C₃₁	—	2	1	no	—
489	C₄²×C₃₁	—	2	2	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	#62584	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	1	no	—
506	C₂³×C₃₁	—	2	1	no	—
507	C₂³×C₃₁	—	4	2	no	—
508	C₂³×C₃₁	—	4	2	no	—
509	C₂³×C₃₁	—	8	1	no	—
510	C₂³×C₃₁	—	8	1	no	—
511	C₂³×C₃₁	—	8	1	no	—
512	C₂³×C₃₁	—	8	1	no	—
513	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
514	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
515	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
516	Q₈×C₃₁	—	2	2	no	—
517	Q₈×C₃₁	—	2	2	no	—
518	Q₈×C₃₁	—	2	2	no	—
519	Q₈×C₃₁	—	4	1	no	—
520	Q₈×C₃₁	—	4	2	no	—
521	Q₈×C₃₁	—	4	2	no	—
522	Q₈×C₃₁	—	4	2	no	—
523	Q₈×C₃₁	—	8	1	no	—
524	Q₈×C₃₁	—	8	1	no	—
525	Q₈×C₃₁	—	8	2	no	—
526	D₄×C₃₁	—	2	2	no	—
527	D₄×C₃₁	—	2	2	no	—
528	D₄×C₃₁	—	2	2	no	—
529	D₄×C₃₁	—	2	2	no	—
530	D₄×C₃₁	—	2	2	no	—
531	D₄×C₃₁	—	2	2	no	—
532	D₄×C₃₁	—	2	2	no	—
533	D₄×C₃₁	—	4	1	no	—
534	D₄×C₃₁	—	4	2	no	—
535	D₄×C₃₁	—	4	2	no	—
536	D₄×C₃₁	—	4	2	no	—
537	D₄×C₃₁	—	4	2	no	—
538	D₄×C₃₁	—	4	2	no	—
539	D₄×C₃₁	—	4	4	no	—
540	D₄×C₃₁	—	8	1	no	—
541	D₄×C₃₁	—	8	1	no	—
542	D₄×C₃₁	—	8	1	no	—
543	D₄×C₃₁	—	8	1	no	—
544	D₄×C₃₁	—	8	1	no	—
545	D₄×C₃₁	—	8	1	no	—
546	D₄×C₃₁	—	8	2	no	—
547	D₄×C₃₁	—	8	2	no	—
548	C₂×C₄×C₃₁	—	2	2	no	—
549	C₂×C₄×C₃₁	—	2	2	no	—
550	C₂×C₄×C₃₁	—	2	2	no	—
551	C₂×C₄×C₃₁	—	2	2	no	—
552	C₂×C₄×C₃₁	—	2	1	no	—
553	C₂×C₄×C₃₁	—	2	2	no	—
554	C₂×C₄×C₃₁	—	2	1	no	—
555	C₂×C₄×C₃₁	—	2	1	no	—
556	C₂×C₄×C₃₁	—	2	1	no	—
557	C₂×C₄×C₃₁	—	2	1	no	—
558	C₂×C₄×C₃₁	—	2	2	no	—
559	C₂×C₄×C₃₁	—	2	2	no	—
560	C₂×C₄×C₃₁	—	4	1	no	—
561	C₂×C₄×C₃₁	—	4	1	no	—
562	C₂×C₄×C₃₁	—	4	1	no	—
563	C₂×C₄×C₃₁	—	4	1	no	—
564	C₂×C₄×C₃₁	—	4	1	no	—
565	C₂×C₄×C₃₁	—	4	2	no	—
566	C₂×C₄×C₃₁	—	4	4	no	—
567	C₂×C₄×C₃₁	—	8	1	no	—
568	C₂×C₄×C₃₁	—	8	1	no	—
569	C₂×C₄×C₃₁	—	8	1	no	—
570	C₂×C₄×C₃₁	—	8	1	no	—
571	C₂×C₄×C₃₁	—	8	2	no	—
572	C₂×C₄×C₃₁	—	8	2	no	—
573	C₂×C₄×C₃₁	—	8	1	no	—
574	C₂×C₄×C₃₁	—	8	1	no	—
575	C₂×C₄×C₃₁	—	8	2	no	—
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	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
586	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
587	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
588	C₈×C₃₁	—	2	2	no	—
589	C₈×C₃₁	—	2	2	no	—
590	C₈×C₃₁	—	2	2	no	—
591	C₈×C₃₁	—	2	2	no	—
592	#3514	C₂×C₃₁	1	1	yes	characteristic, complemented
593	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
594	#3376	C₂×C₃₁	1	2	yes	complemented
595	#3370	C₂×C₃₁	1	2	yes	complemented
596	#3321	C₂×C₃₁	1	2	yes	complemented
597	#3320	C₂×C₃₁	1	2	yes	complemented
598	#3319	C₂×C₃₁	1	2	yes	complemented
599	#3318	C₂×C₃₁	1	2	yes	complemented
600	#3301	C₂×C₃₁	1	2	yes	complemented
601	#3297	C₂×C₃₁	1	2	yes	complemented
602	#3240	C₂×C₃₁	1	1	yes	characteristic, complemented
603	#3240	C₂×C₃₁	1	1	yes	characteristic, complemented
604	#3239	C₂×C₃₁	1	1	yes	characteristic, complemented
605	#3214	C₂×C₃₁	1	1	yes	characteristic, complemented
606	#3213	C₂×C₃₁	1	1	yes	characteristic, complemented
607	#3213	C₂×C₃₁	1	1	yes	characteristic, complemented
608	#3180	C₂×C₃₁	1	1	yes	characteristic, complemented
609	#3180	C₂×C₃₁	1	1	yes	characteristic, complemented
610	#3171	C₂×C₃₁	1	1	yes	characteristic, complemented
611	#3140	C₂×C₃₁	1	1	yes	characteristic, complemented
612	#3135	C₂×C₃₁	1	1	yes	characteristic, complemented
613	C₂×#489	C₂×C₃₁	1	1	yes	characteristic, complemented
614	#2970	C₂×C₃₁	1	1	yes	characteristic, complemented
615	C₂²×C₃₁	—	2	1	no	—
616	C₂²×C₃₁	—	2	1	no	—
617	C₂²×C₃₁	—	2	1	no	—
618	C₂²×C₃₁	—	2	1	no	—
619	C₂²×C₃₁	—	2	1	no	—
620	C₂²×C₃₁	—	2	1	no	—
621	C₂²×C₃₁	—	2	1	no	—
622	C₂²×C₃₁	—	2	1	no	—
623	C₂²×C₃₁	—	4	2	no	—
624	C₂²×C₃₁	—	4	1	no	—
625	C₂²×C₃₁	—	4	1	no	—
626	C₂²×C₃₁	—	4	1	no	—
627	C₂²×C₃₁	—	4	1	no	—
628	C₂²×C₃₁	—	4	1	no	—
629	C₂²×C₃₁	—	4	1	no	—
630	C₂²×C₃₁	—	4	2	no	—
631	C₂²×C₃₁	—	4	2	no	—
632	C₂²×C₃₁	—	4	1	no	—
633	C₂²×C₃₁	—	4	1	no	—
634	C₂²×C₃₁	—	4	1	no	—
635	C₂²×C₃₁	—	16	2	no	—
636	C₂²×C₃₁	—	16	2	no	—
637	C₂²×C₃₁	#575	1	2	yes	—
638	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
639	C₄×C₃₁	—	2	1	no	—
640	C₄×C₃₁	—	2	1	no	—
641	C₄×C₃₁	—	2	1	no	—
642	C₄×C₃₁	—	2	1	no	—
643	C₄×C₃₁	—	2	1	no	—
644	C₄×C₃₁	—	2	1	no	—
645	C₄×C₃₁	—	2	1	no	—
646	C₄×C₃₁	—	2	1	no	—
647	C₄×C₃₁	—	2	1	no	—
648	C₄×C₃₁	—	2	1	no	—
649	C₄×C₃₁	—	2	1	no	—
650	C₄×C₃₁	—	4	1	no	—
651	C₄×C₃₁	—	4	2	no	—
652	C₄×C₃₁	—	4	2	no	—
653	C₄×C₃₁	—	4	1	no	—
654	C₄×C₃₁	—	4	1	no	—
655	C₄×C₃₁	—	4	1	no	—
656	C₄×C₃₁	—	4	1	no	—
657	C₄×C₃₁	—	4	2	no	—
658	C₄×C₃₁	#585	1	2	yes	—
659	#559	C₂²×C₃₁	1	1	yes	characteristic
660	#556	—	2	1	no	—
661	#556	C₂²×C₃₁	1	1	yes	characteristic
662	#555	—	2	1	no	—
663	#555	C₂²×C₃₁	1	2	yes	complemented
664	#554	C₂²×C₃₁	1	2	yes	complemented
665	#553	C₂²×C₃₁	1	2	yes	—
666	#553	C₂²×C₃₁	1	2	yes	complemented
667	#551	—	2	1	no	—
668	#551	—	2	1	no	—
669	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
670	#548	—	2	1	no	—
671	#548	—	2	1	no	—
672	#548	C₂²×C₃₁	1	1	yes	characteristic
673	#548	C₂²×C₃₁	1	1	yes	characteristic
674	#547	—	2	1	no	—
675	#546	—	2	1	no	—
676	#546	C₂²×C₃₁	1	1	yes	characteristic
677	#546	C₂²×C₃₁	1	1	yes	characteristic
678	D₄²	C₂²×C₃₁	1	1	yes	characteristic
679	#542	—	2	1	no	—
680	#542	—	2	1	no	—
681	#542	—	2	1	no	—
682	#538	—	2	1	no	—
683	#538	—	2	1	no	—
684	#537	—	2	1	no	—
685	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
686	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	#532	C₂²×C₃₁	1	1	yes	characteristic
688	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
689	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
690	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
691	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
692	#529	C₂²×C₃₁	1	1	yes	characteristic
693	#529	C₂²×C₃₁	1	1	yes	characteristic
694	#529	C₂²×C₃₁	1	1	yes	characteristic
695	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
696	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
697	#520	—	2	1	no	—
698	#518	—	2	1	no	—
699	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
700	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
702	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
703	#496	C₂²×C₃₁	1	1	yes	characteristic
704	#496	C₂²×C₃₁	1	1	yes	characteristic, complemented
705	#496	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	#491	C₂²×C₃₁	1	2	yes	complemented
707	#490	C₂²×C₃₁	1	2	yes	—
708	#490	C₂²×C₃₁	1	1	yes	characteristic, complemented
709	#489	C₂²×C₃₁	1	2	yes	—
710	#489	C₂²×C₃₁	1	1	yes	characteristic
711	#489	C₂²×C₃₁	1	1	yes	characteristic
712	#489	C₂²×C₃₁	1	1	yes	characteristic
713	#489	C₂²×C₃₁	1	2	yes	complemented
714	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
715	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
716	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
717	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
718	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
719	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
720	#488	C₂²×C₃₁	1	2	yes	—
721	#488	C₂²×C₃₁	1	2	yes	complemented
722	#485	C₂²×C₃₁	1	2	yes	complemented
723	#485	C₂²×C₃₁	1	2	yes	complemented
724	#484	C₂²×C₃₁	1	2	yes	complemented
725	#482	C₂²×C₃₁	1	2	yes	—
726	#482	C₂²×C₃₁	1	2	yes	—
727	#481	C₂²×C₃₁	1	2	yes	—
728	#479	C₂²×C₃₁	1	2	yes	complemented
729	#479	C₂²×C₃₁	1	2	yes	complemented
730	#478	C₂²×C₃₁	1	2	yes	—
731	#478	C₂²×C₃₁	1	2	yes	complemented
732	#475	C₂²×C₃₁	1	2	yes	complemented
733	#474	C₂²×C₃₁	1	2	yes	complemented
734	#469	C₂²×C₃₁	1	2	yes	—
735	#468	C₂²×C₃₁	1	2	yes	complemented
736	#466	C₂²×C₃₁	1	2	yes	—
737	#466	C₂²×C₃₁	1	2	yes	—
738	#465	C₂²×C₃₁	1	2	yes	complemented
739	#465	C₂²×C₃₁	1	2	yes	complemented
740	#463	C₂²×C₃₁	1	2	yes	—
741	#463	C₂²×C₃₁	1	2	yes	—
742	#463	C₂²×C₃₁	1	2	yes	complemented
743	#463	C₂²×C₃₁	1	2	yes	complemented
744	#461	C₂²×C₃₁	1	2	yes	complemented
745	#459	C₂²×C₃₁	1	2	yes	—
746	#449	C₂²×C₃₁	1	2	yes	complemented
747	#449	C₂²×C₃₁	1	2	yes	complemented
748	#448	C₂²×C₃₁	1	2	yes	complemented
749	#448	C₂²×C₃₁	1	2	yes	complemented
750	#447	C₂²×C₃₁	1	2	yes	—
751	#447	C₂²×C₃₁	1	2	yes	—
752	#446	C₂²×C₃₁	1	2	yes	complemented
753	#442	C₂²×C₃₁	1	2	yes	—
754	#442	C₂²×C₃₁	1	2	yes	complemented
755	#440	C₂²×C₃₁	1	2	yes	complemented
756	#440	C₂²×C₃₁	1	2	yes	complemented
757	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
758	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
759	#435	C₂²×C₃₁	1	2	yes	—
760	#435	C₂²×C₃₁	1	2	yes	complemented
761	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
762	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
763	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
764	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
765	#419	C₂²×C₃₁	1	2	yes	complemented
766	#418	C₂²×C₃₁	1	2	yes	—
767	#416	C₂²×C₃₁	1	2	yes	complemented
768	#416	C₂²×C₃₁	1	2	yes	complemented
769	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
770	C₂×#102	C₂²×C₃₁	1	2	yes	—
771	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
772	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic, complemented
773	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic, complemented
774	C₂×C₃₁	—	2	2	no	—
775	C₂×C₃₁	—	4	1	no	—
776	C₂×C₃₁	—	4	1	no	—
777	C₂×C₃₁	—	8	2	no	—
778	C₂×C₃₁	—	8	1	no	—
779	C₂×C₃₁	—	8	1	no	—
780	C₂×C₃₁	—	8	1	no	—
781	C₂×C₃₁	#3500	1	1	yes	characteristic
782	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
783	C₂×C₃₁	#3585	1	1	yes	characteristic
784	C₂×#41	—	2	1	no	—
785	C₂×#41	—	2	1	no	—
786	C₂×#41	—	2	1	no	—
787	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
788	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
789	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
790	C₂²×Q₈	—	2	1	no	—
791	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
792	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
793	C₂²×D₄	—	2	1	no	—
794	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
795	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
796	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
797	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
798	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
799	C₂×D₈	C₂³×C₃₁	1	2	yes	—
800	C₂×D₈	C₂³×C₃₁	1	2	yes	—
801	C₂×D₈	C₂³×C₃₁	1	2	yes	—
802	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
803	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
804	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
805	C₄⋊Q₈	—	2	1	no	—
806	C₄⋊Q₈	—	2	1	no	—
807	C₄⋊Q₈	—	2	1	no	—
808	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
809	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
810	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
811	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
812	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
813	#127	C₂³×C₃₁	1	1	yes	characteristic
814	#127	C₂³×C₃₁	1	1	yes	characteristic
815	#126	—	2	1	no	—
816	#126	—	2	1	no	—
817	#126	—	2	2	no	—
818	#126	—	2	2	no	—
819	#126	—	2	1	no	—
820	#126	—	2	1	no	—
821	#126	—	2	1	no	—
822	#125	C₂³×C₃₁	1	1	yes	characteristic
823	#125	C₂³×C₃₁	1	2	yes	—
824	#125	C₂³×C₃₁	1	2	yes	—
825	#124	—	2	1	no	—
826	#124	—	2	1	no	—
827	#124	—	2	1	no	—
828	#124	—	2	2	no	—
829	#124	—	2	2	no	—
830	#124	—	2	1	no	—
831	#124	—	2	1	no	—
832	#124	—	2	1	no	—
833	#124	—	2	1	no	—
834	#124	—	2	1	no	—
835	#124	—	2	1	no	—
836	#124	—	2	1	no	—
837	#124	C₂³×C₃₁	1	1	yes	characteristic
838	#124	C₂³×C₃₁	1	1	yes	characteristic
839	#124	C₂³×C₃₁	1	1	yes	characteristic
840	#124	C₂³×C₃₁	1	1	yes	characteristic
841	#124	C₂³×C₃₁	1	1	yes	characteristic
842	#124	C₂³×C₃₁	1	1	yes	characteristic
843	#124	C₂³×C₃₁	1	1	yes	characteristic
844	#123	—	2	1	no	—
845	#123	—	2	1	no	—
846	#123	—	2	1	no	—
847	#123	—	2	1	no	—
848	#123	—	2	1	no	—
849	#123	—	2	1	no	—
850	#123	—	2	1	no	—
851	#123	—	2	2	no	—
852	#123	—	2	2	no	—
853	C₂²⋊Q₈	—	2	2	no	—
854	C₂²⋊Q₈	—	2	1	no	—
855	C₂²⋊Q₈	—	2	1	no	—
856	C₂²⋊Q₈	—	2	1	no	—
857	C₂²⋊Q₈	—	2	1	no	—
858	C₂²⋊Q₈	—	2	1	no	—
859	C₂²⋊Q₈	—	2	2	no	—
860	C₂²⋊Q₈	—	2	2	no	—
861	C₂²⋊Q₈	—	2	1	no	—
862	C₂²⋊Q₈	—	2	1	no	—
863	C₂²⋊Q₈	—	2	1	no	—
864	C₂²⋊Q₈	—	2	1	no	—
865	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
866	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
867	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
868	#121	—	2	2	no	—
869	#121	—	2	2	no	—
870	#121	—	2	2	no	—
871	#121	—	2	1	no	—
872	#121	—	2	1	no	—
873	#121	—	2	1	no	—
874	#121	—	2	1	no	—
875	#121	—	2	1	no	—
876	#121	—	2	1	no	—
877	#121	—	2	1	no	—
878	#121	—	2	1	no	—
879	#121	—	2	1	no	—
880	#121	—	2	1	no	—
881	#121	C₂³×C₃₁	1	1	yes	characteristic
882	#121	C₂³×C₃₁	1	1	yes	characteristic
883	#121	C₂³×C₃₁	1	1	yes	characteristic
884	#121	C₂³×C₃₁	1	2	yes	—
885	#121	C₂³×C₃₁	1	2	yes	—
886	#121	C₂³×C₃₁	1	2	yes	—
887	#120	—	2	1	no	—
888	#120	—	2	1	no	—
889	#120	—	2	1	no	—
890	#120	—	2	1	no	—
891	C₄×Q₈	—	2	1	no	—
892	C₄×Q₈	—	2	1	no	—
893	C₄×Q₈	—	2	1	no	—
894	C₄×Q₈	—	2	1	no	—
895	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
896	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
897	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
898	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
899	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
900	C₄×D₄	—	2	1	no	—
901	C₄×D₄	—	2	1	no	—
902	C₄×D₄	—	2	1	no	—
903	C₄×D₄	—	2	1	no	—
904	C₄×D₄	—	2	1	no	—
905	C₄×D₄	—	2	1	no	—
906	C₄×D₄	—	2	1	no	—
907	C₄×D₄	—	2	2	no	—
908	C₄×D₄	—	2	2	no	—
909	C₄×D₄	—	2	1	no	—
910	C₄×D₄	—	2	1	no	—
911	C₄×D₄	—	2	1	no	—
912	C₄×D₄	—	2	1	no	—
913	C₄×D₄	—	2	1	no	—
914	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
915	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
916	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
917	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
918	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
919	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
920	C₄×D₄	C₂³×C₃₁	1	2	yes	—
921	C₄×D₄	C₂³×C₃₁	1	2	yes	—
922	C₄×D₄	C₂³×C₃₁	1	2	yes	—
923	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
924	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
925	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
926	#117	—	2	1	no	—
927	#117	—	2	2	no	—
928	#117	—	2	1	no	—
929	#117	—	2	1	no	—
930	#117	—	2	1	no	—
931	#117	D₄×C₃₁	1	1	yes	characteristic
932	#117	D₄×C₃₁	1	1	yes	characteristic
933	#117	D₄×C₃₁	1	1	yes	characteristic
934	#117	C₂³×C₃₁	1	2	yes	—
935	#117	C₂³×C₃₁	1	2	yes	—
936	C₂×C₄⋊C₄	—	2	1	no	—
937	C₂×C₄⋊C₄	—	2	2	no	—
938	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
939	C₂×C₂²⋊C₄	—	2	1	no	—
940	C₂×C₂²⋊C₄	—	2	1	no	—
941	C₂×C₂²⋊C₄	—	2	1	no	—
942	C₂×C₂²⋊C₄	—	2	1	no	—
943	C₂×C₂²⋊C₄	—	2	1	no	—
944	C₂×C₂²⋊C₄	—	2	1	no	—
945	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
946	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
947	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
948	#107	C₂³×C₃₁	1	2	yes	—
949	#107	C₂³×C₃₁	1	2	yes	—
950	#107	C₂³×C₃₁	1	2	yes	—
951	#106	C₂³×C₃₁	1	2	yes	—
952	#106	C₂³×C₃₁	1	2	yes	—
953	#106	C₂³×C₃₁	1	2	yes	—
954	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
955	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
956	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
957	#103	C₂³×C₃₁	1	2	yes	—
958	#103	C₂³×C₃₁	1	2	yes	—
959	#103	C₂³×C₃₁	1	2	yes	—
960	#103	C₂³×C₃₁	1	2	yes	—
961	#103	C₂³×C₃₁	1	2	yes	—
962	#103	C₂³×C₃₁	1	2	yes	—
963	#103	C₂³×C₃₁	1	2	yes	—
964	#103	C₂³×C₃₁	1	2	yes	—
965	#103	C₂³×C₃₁	1	2	yes	—
966	#102	C₂³×C₃₁	1	2	yes	—
967	#102	C₂³×C₃₁	1	2	yes	—
968	#102	C₂³×C₃₁	1	2	yes	—
969	#102	C₂³×C₃₁	1	2	yes	—
970	#102	C₂³×C₃₁	1	2	yes	—
971	#102	C₂³×C₃₁	1	2	yes	—
972	#102	C₂³×C₃₁	1	2	yes	—
973	#102	C₂³×C₃₁	1	2	yes	—
974	#102	C₂³×C₃₁	1	2	yes	—
975	#102	C₂³×C₃₁	1	2	yes	—
976	#102	C₂³×C₃₁	1	2	yes	—
977	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
978	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
979	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
980	#97	C₂³×C₃₁	1	1	yes	characteristic
981	#97	C₂³×C₃₁	1	1	yes	characteristic
982	#97	C₂³×C₃₁	1	1	yes	characteristic
983	#97	C₂³×C₃₁	1	2	yes	—
984	#97	C₂³×C₃₁	1	2	yes	—
985	#97	C₂³×C₃₁	1	1	yes	characteristic
986	C₄×C₈	C₂³×C₃₁	1	2	yes	—
987	C₃₁	#62584	1	1	yes	characteristic, direct product factor, Sylow
988	C₂⁴	—	2	1	no	—
989	C₂⁴	—	2	1	no	—
990	#41	—	4	2	no	—
991	#41	—	4	4	no	—
992	#41	—	4	2	no	—
993	#41	—	4	2	no	—
994	#41	—	8	2	no	—
995	#41	—	8	2	no	—
996	C₂×Q₈	—	2	1	no	—
997	C₂×Q₈	—	2	1	no	—
998	C₂×Q₈	—	2	1	no	—
999	C₂×Q₈	—	2	1	no	—
1000	C₂×Q₈	—	2	1	no	—
1001	C₂×Q₈	—	2	2	no	—
1002	C₂×Q₈	—	4	2	no	—
1003	C₂×Q₈	—	4	2	no	—
1004	C₂×Q₈	—	8	2	no	—
1005	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1006	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1007	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	2	no	—
1012	C₂×D₄	—	2	1	no	—
1013	C₂×D₄	—	2	1	no	—
1014	C₂×D₄	—	2	1	no	—
1015	C₂×D₄	—	2	2	no	—
1016	C₂×D₄	—	2	2	no	—
1017	C₂×D₄	—	2	1	no	—
1018	C₂×D₄	—	2	1	no	—
1019	C₂×D₄	—	2	1	no	—
1020	C₂×D₄	—	2	1	no	—
1021	C₂×D₄	—	2	1	no	—
1022	C₂×D₄	—	2	1	no	—
1023	C₂×D₄	—	4	2	no	—
1024	C₂×D₄	—	4	2	no	—
1025	C₂×D₄	—	4	4	no	—
1026	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1027	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1028	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1029	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1030	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1031	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1032	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1033	C₂²×C₄	—	2	1	no	—
1034	C₂²×C₄	—	2	1	no	—
1035	C₂²×C₄	—	2	2	no	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	2	1	no	—
1038	C₂²×C₄	—	2	1	no	—
1039	C₂²×C₄	—	2	1	no	—
1040	C₂²×C₄	—	2	1	no	—
1041	C₂²×C₄	—	2	1	no	—
1042	C₂²×C₄	—	2	2	no	—
1043	C₂²×C₄	—	2	2	no	—
1044	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1045	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1046	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1047	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1048	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1049	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1050	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1051	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1052	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1053	SD₁₆	—	4	2	no	—
1054	SD₁₆	—	4	2	no	—
1055	SD₁₆	—	4	2	no	—
1056	D₈	—	4	2	no	—
1057	D₈	—	4	2	no	—
1058	D₈	—	4	2	no	—
1059	M₁₆	—	4	2	no	—
1060	C₂×C₈	—	4	2	no	—
1061	C₂×C₈	—	4	2	no	—
1062	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1063	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1064	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1065	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1066	C₄⋊C₄	—	2	2	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	—	2	2	no	—
1071	C₄⋊C₄	—	2	2	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	1	no	—
1076	C₄⋊C₄	—	2	1	no	—
1077	C₄⋊C₄	—	2	1	no	—
1078	C₄⋊C₄	—	2	1	no	—
1079	C₄⋊C₄	—	2	1	no	—
1080	C₄⋊C₄	—	2	2	no	—
1081	C₄⋊C₄	—	2	2	no	—
1082	C₄⋊C₄	—	2	1	no	—
1083	C₄⋊C₄	—	2	1	no	—
1084	C₄⋊C₄	—	2	1	no	—
1085	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1086	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1087	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1088	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1089	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1090	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1091	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1092	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1093	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1094	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1095	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	1	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	1	no	—
1103	C₂²⋊C₄	—	2	1	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	1	no	—
1110	C₂²⋊C₄	—	2	1	no	—
1111	C₂²⋊C₄	—	2	1	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	1	no	—
1115	C₂²⋊C₄	—	2	1	no	—
1116	C₂²⋊C₄	—	2	2	no	—
1117	C₂²⋊C₄	—	2	2	no	—
1118	C₂²⋊C₄	—	2	1	no	—
1119	C₂²⋊C₄	—	2	1	no	—
1120	C₂²⋊C₄	—	2	2	no	—
1121	C₂²⋊C₄	—	2	1	no	—
1122	C₂²⋊C₄	—	2	1	no	—
1123	C₂²⋊C₄	—	2	1	no	—
1124	C₂²⋊C₄	—	2	2	no	—
1125	C₂²⋊C₄	—	2	2	no	—
1126	C₂²⋊C₄	—	2	2	no	—
1127	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1128	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1129	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1130	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1131	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1132	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1133	C₄²	—	2	1	no	—
1134	C₄²	—	2	1	no	—
1135	C₄²	—	2	2	no	—
1136	C₄²	—	2	2	no	—
1137	C₄²	—	2	1	no	—
1138	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1139	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1140	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1141	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1142	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1143	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1144	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1145	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1146	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1147	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1148	C₂³	—	2	1	no	—
1149	C₂³	—	2	2	no	—
1150	C₂³	—	2	1	no	—
1151	C₂³	—	2	1	no	—
1152	C₂³	—	4	2	no	—
1153	C₂³	—	4	2	no	—
1154	C₂³	—	8	1	no	—
1155	C₂³	—	8	1	no	—
1156	C₂³	—	8	1	no	—
1157	C₂³	—	8	1	no	—
1158	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1159	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1160	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1161	Q₈	—	2	2	no	—
1162	Q₈	—	2	2	no	—
1163	Q₈	—	2	2	no	—
1164	Q₈	—	4	1	no	—
1165	Q₈	—	4	2	no	—
1166	Q₈	—	4	2	no	—
1167	Q₈	—	4	2	no	—
1168	Q₈	—	8	1	no	—
1169	Q₈	—	8	1	no	—
1170	Q₈	—	8	2	no	—
1171	D₄	—	2	2	no	—
1172	D₄	—	2	2	no	—
1173	D₄	—	2	2	no	—
1174	D₄	—	2	2	no	—
1175	D₄	—	2	2	no	—
1176	D₄	—	2	2	no	—
1177	D₄	—	2	2	no	—
1178	D₄	—	4	1	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	4	2	no	—
1181	D₄	—	4	2	no	—
1182	D₄	—	4	2	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	4	no	—
1185	D₄	—	8	1	no	—
1186	D₄	—	8	1	no	—
1187	D₄	—	8	1	no	—
1188	D₄	—	8	1	no	—
1189	D₄	—	8	1	no	—
1190	D₄	—	8	1	no	—
1191	D₄	—	8	2	no	—
1192	D₄	—	8	2	no	—
1193	C₂×C₄	—	2	2	no	—
1194	C₂×C₄	—	2	2	no	—
1195	C₂×C₄	—	2	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	2	no	—
1204	C₂×C₄	—	2	2	no	—
1205	C₂×C₄	—	4	1	no	—
1206	C₂×C₄	—	4	1	no	—
1207	C₂×C₄	—	4	1	no	—
1208	C₂×C₄	—	4	1	no	—
1209	C₂×C₄	—	4	1	no	—
1210	C₂×C₄	—	4	2	no	—
1211	C₂×C₄	—	4	4	no	—
1212	C₂×C₄	—	8	1	no	—
1213	C₂×C₄	—	8	1	no	—
1214	C₂×C₄	—	8	1	no	—
1215	C₂×C₄	—	8	1	no	—
1216	C₂×C₄	—	8	2	no	—
1217	C₂×C₄	—	8	2	no	—
1218	C₂×C₄	—	8	1	no	—
1219	C₂×C₄	—	8	1	no	—
1220	C₂×C₄	—	8	2	no	—
1221	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1222	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1223	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1224	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1225	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1226	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1227	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1228	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1229	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1230	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1231	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1232	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1233	C₈	—	2	2	no	—
1234	C₈	—	2	2	no	—
1235	C₈	—	2	2	no	—
1236	C₈	—	2	2	no	—
1237	C₂²	—	2	1	no	—
1238	C₂²	—	2	1	no	—
1239	C₂²	—	2	1	no	—
1240	C₂²	—	2	1	no	—
1241	C₂²	—	2	1	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	1	no	—
1245	C₂²	—	4	1	no	—
1246	C₂²	—	4	1	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	4	2	no	—
1249	C₂²	—	4	2	no	—
1250	C₂²	—	4	1	no	—
1251	C₂²	—	4	1	no	—
1252	C₂²	—	4	1	no	—
1253	C₂²	—	4	2	no	—
1254	C₂²	—	4	1	no	—
1255	C₂²	—	4	1	no	—
1256	C₂²	—	4	1	no	—
1257	C₂²	—	16	2	no	—
1258	C₂²	—	16	2	no	—
1259	C₂²	C₃₁×#575	1	2	yes	—
1260	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1261	C₄	—	2	1	no	—
1262	C₄	—	2	1	no	—
1263	C₄	—	2	1	no	—
1264	C₄	—	2	1	no	—
1265	C₄	—	2	1	no	—
1266	C₄	—	2	1	no	—
1267	C₄	—	2	1	no	—
1268	C₄	—	2	1	no	—
1269	C₄	—	2	1	no	—
1270	C₄	—	2	1	no	—
1271	C₄	—	2	1	no	—
1272	C₄	—	4	1	no	—
1273	C₄	—	4	1	no	—
1274	C₄	—	4	1	no	—
1275	C₄	—	4	1	no	—
1276	C₄	—	4	2	no	—
1277	C₄	—	4	2	no	—
1278	C₄	—	4	2	no	—
1279	C₄	—	4	1	no	—
1280	C₄	C₃₁×#585	1	2	yes	—
1281	C₂	—	2	2	no	—
1282	C₂	—	4	1	no	—
1283	C₂	—	4	1	no	—
1284	C₂	—	8	1	no	—
1285	C₂	—	8	1	no	—
1286	C₂	—	8	1	no	—
1287	C₂	—	8	2	no	—
1288	C₂	C₃₁×#3500	1	1	yes	characteristic
1289	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1290	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×#3514	C₂	semidirect
2. C₃₁×#3511	C₂	semidirect
3. C₃₁×#3376	C₂	semidirect
4. C₃₁×#3370	C₂	semidirect
5. C₃₁×#3321	C₂	semidirect
6. C₃₁×#3320	C₂	semidirect
7. C₃₁×#3319	C₂	semidirect
8. C₃₁×#3318	C₂	semidirect
9. C₃₁×#3301	C₂	semidirect
10. C₃₁×#3297	C₂	semidirect
11. C₃₁×#3240	C₂	semidirect
12. C₃₁×#3240	C₂	semidirect
13. C₃₁×#3239	C₂	semidirect
14. C₃₁×#3214	C₂	semidirect
15. C₃₁×#3213	C₂	semidirect
16. C₃₁×#3213	C₂	semidirect
17. C₃₁×#3180	C₂	semidirect
18. C₃₁×#3180	C₂	semidirect
19. C₃₁×#3171	C₂	semidirect
20. C₃₁×#3140	C₂	semidirect
21. C₃₁×#3135	C₂	semidirect
22. C₂×C₃₁×#489	C₂	semidirect
23. C₃₁×#2970	C₂	semidirect
28. C₃₁×#555	C₂²	semidirect
29. C₃₁×#554	C₂²	semidirect
31. C₃₁×#553	C₂²	semidirect
50. C₃₁×#533	C₂²	semidirect
51. C₃₁×#533	C₂²	semidirect
53. C₃₁×#532	C₂²	semidirect
54. C₃₁×#532	C₂²	semidirect
55. C₃₁×#532	C₂²	semidirect
56. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
65. C₃₁×#501	C₂²	semidirect
66. C₃₁×#501	C₂²	semidirect
67. C₃₁×#501	C₂²	semidirect
69. C₃₁×#496	C₂²	semidirect
70. C₃₁×#496	C₂²	semidirect
71. C₃₁×#491	C₂²	semidirect
73. C₃₁×#490	C₂²	semidirect
78. C₃₁×#489	C₂²	semidirect
79. C₃₁×#489	C₂²	semidirect
80. C₃₁×#489	C₂²	semidirect
81. C₃₁×#489	C₂²	semidirect
82. C₃₁×#489	C₂²	semidirect
83. C₃₁×#489	C₂²	semidirect
84. C₃₁×#489	C₂²	semidirect
86. C₃₁×#488	C₂²	semidirect
87. C₃₁×#485	C₂²	semidirect
88. C₃₁×#485	C₂²	semidirect
89. C₃₁×#484	C₂²	semidirect
93. C₃₁×#479	C₂²	semidirect
94. C₃₁×#479	C₂²	semidirect
96. C₃₁×#478	C₂²	semidirect
97. C₃₁×#475	C₂²	semidirect
98. C₃₁×#474	C₂²	semidirect
100. C₃₁×#468	C₂²	semidirect
103. C₃₁×#465	C₂²	semidirect
104. C₃₁×#465	C₂²	semidirect
107. C₃₁×#463	C₂²	semidirect
108. C₃₁×#463	C₂²	semidirect
109. C₃₁×#461	C₂²	semidirect
111. C₃₁×#449	C₂²	semidirect
112. C₃₁×#449	C₂²	semidirect
113. C₃₁×#448	C₂²	semidirect
114. C₃₁×#448	C₂²	semidirect
117. C₃₁×#446	C₂²	semidirect
119. C₃₁×#442	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
126. C₈×D₄×C₃₁	C₂²	semidirect
127. C₃₁×#432	C₂²	semidirect
128. C₃₁×#432	C₂²	semidirect
129. C₃₁×#432	C₂²	semidirect
130. C₃₁×#419	C₂²	semidirect
132. C₃₁×#416	C₂²	semidirect
133. C₃₁×#416	C₂²	semidirect
134. C₂×C₃₁×#103	C₂²	semidirect
136. C₄×M₁₆×C₃₁	C₂²	semidirect
137. C₂×C₃₁×#97	C₂²	semidirect
138. C₂×C₃₁×#97	C₂²	semidirect
502. #62584	C₃₁	direct (N × H)
592. #3514	C₂×C₃₁	semidirect
593. #3511	C₂×C₃₁	semidirect
594. #3376	C₂×C₃₁	semidirect
595. #3370	C₂×C₃₁	semidirect
596. #3321	C₂×C₃₁	semidirect
597. #3320	C₂×C₃₁	semidirect
598. #3319	C₂×C₃₁	semidirect
599. #3318	C₂×C₃₁	semidirect
600. #3301	C₂×C₃₁	semidirect
601. #3297	C₂×C₃₁	semidirect
602. #3240	C₂×C₃₁	semidirect
603. #3240	C₂×C₃₁	semidirect
604. #3239	C₂×C₃₁	semidirect
605. #3214	C₂×C₃₁	semidirect
606. #3213	C₂×C₃₁	semidirect
607. #3213	C₂×C₃₁	semidirect
608. #3180	C₂×C₃₁	semidirect
609. #3180	C₂×C₃₁	semidirect
610. #3171	C₂×C₃₁	semidirect
611. #3140	C₂×C₃₁	semidirect
612. #3135	C₂×C₃₁	semidirect
613. C₂×#489	C₂×C₃₁	semidirect
614. #2970	C₂×C₃₁	semidirect
663. #555	C₂²×C₃₁	semidirect
664. #554	C₂²×C₃₁	semidirect
666. #553	C₂²×C₃₁	semidirect
685. #533	C₂²×C₃₁	semidirect
686. #533	C₂²×C₃₁	semidirect
688. #532	C₂²×C₃₁	semidirect
689. #532	C₂²×C₃₁	semidirect
690. #532	C₂²×C₃₁	semidirect
691. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
700. #501	C₂²×C₃₁	semidirect
701. #501	C₂²×C₃₁	semidirect
702. #501	C₂²×C₃₁	semidirect
704. #496	C₂²×C₃₁	semidirect
705. #496	C₂²×C₃₁	semidirect
706. #491	C₂²×C₃₁	semidirect
708. #490	C₂²×C₃₁	semidirect
713. #489	C₂²×C₃₁	semidirect
714. #489	C₂²×C₃₁	semidirect
715. #489	C₂²×C₃₁	semidirect
716. #489	C₂²×C₃₁	semidirect
717. #489	C₂²×C₃₁	semidirect
718. #489	C₂²×C₃₁	semidirect
719. #489	C₂²×C₃₁	semidirect
721. #488	C₂²×C₃₁	semidirect
722. #485	C₂²×C₃₁	semidirect
723. #485	C₂²×C₃₁	semidirect
724. #484	C₂²×C₃₁	semidirect
728. #479	C₂²×C₃₁	semidirect
729. #479	C₂²×C₃₁	semidirect
731. #478	C₂²×C₃₁	semidirect
732. #475	C₂²×C₃₁	semidirect
733. #474	C₂²×C₃₁	semidirect
735. #468	C₂²×C₃₁	semidirect
738. #465	C₂²×C₃₁	semidirect
739. #465	C₂²×C₃₁	semidirect
742. #463	C₂²×C₃₁	semidirect
743. #463	C₂²×C₃₁	semidirect
744. #461	C₂²×C₃₁	semidirect
746. #449	C₂²×C₃₁	semidirect
747. #449	C₂²×C₃₁	semidirect
748. #448	C₂²×C₃₁	semidirect
749. #448	C₂²×C₃₁	semidirect
752. #446	C₂²×C₃₁	semidirect
754. #442	C₂²×C₃₁	semidirect
755. #440	C₂²×C₃₁	semidirect
756. #440	C₂²×C₃₁	semidirect
757. C₄×SD₁₆	C₂²×C₃₁	semidirect
758. C₄×D₈	C₂²×C₃₁	semidirect
760. #435	C₂²×C₃₁	semidirect
761. C₈×D₄	C₂²×C₃₁	semidirect
762. #432	C₂²×C₃₁	semidirect
763. #432	C₂²×C₃₁	semidirect
764. #432	C₂²×C₃₁	semidirect
765. #419	C₂²×C₃₁	semidirect
767. #416	C₂²×C₃₁	semidirect
768. #416	C₂²×C₃₁	semidirect
769. C₂×#103	C₂²×C₃₁	semidirect
771. C₄×M₁₆	C₂²×C₃₁	semidirect
772. C₂×#97	C₂²×C₃₁	semidirect
773. C₂×#97	C₂²×C₃₁	semidirect
987. C₃₁	#62584	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×#3514	2
C₃₁×#3511	2
C₃₁×#3376	2
C₃₁×#3370	2
C₃₁×#3321	2
C₃₁×#3320	2
C₃₁×#3319	2
C₃₁×#3318	2
C₃₁×#3301	2
C₃₁×#3297	2
C₃₁×#3240	2
C₃₁×#3239	2
C₃₁×#3214	2
C₃₁×#3213	2
C₃₁×#3180	2
C₃₁×#3171	2
C₃₁×#3140	2
C₃₁×#3135	2
C₂×C₃₁×#489	2
C₃₁×#2970	2
#62584	31

Subgroups — C31×#62584 #21519343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62584 #21519343