Subgroups — C₃₁×#62115 #21518874

Order 7936.

1772 conjugacy classes of subgroups.

The subgroup lattice has 1280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3389	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3351	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3348	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3347	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3322	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3319	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3307	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3251	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3247	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3238	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×#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3106	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×#556	—	2	1	no	—
25	C₃₁×#556	C₂²	1	1	yes	characteristic
26	C₃₁×#555	C₂²	1	1	yes	characteristic
27	C₃₁×#555	C₂²	1	2	yes	—
28	C₃₁×#554	C₂²	1	1	yes	characteristic
29	C₃₁×#554	C₂²	1	2	yes	complemented
30	C₃₁×#553	—	2	1	no	—
31	C₃₁×#553	C₂²	1	2	yes	—
32	C₃₁×#553	C₂²	1	2	yes	complemented
33	C₃₁×#552	—	2	1	no	—
34	C₃₁×#552	C₂²	1	1	yes	characteristic
35	C₃₁×#552	C₂²	1	1	yes	characteristic
36	C₃₁×#551	—	2	1	no	—
37	C₃₁×#551	—	2	1	no	—
38	C₃₁×#548	—	2	1	no	—
39	C₃₁×#548	—	2	1	no	—
40	C₃₁×#547	—	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×#542	—	2	1	no	—
45	C₃₁×#542	—	2	1	no	—
46	C₃₁×#537	—	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, complemented
50	C₃₁×#532	C₂²	1	1	yes	characteristic
51	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#532	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×#520	—	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×#483	C₂²	1	2	yes	complemented
75	C₃₁×#482	C₂²	1	2	yes	—
76	C₃₁×#482	C₂²	1	2	yes	complemented
77	C₃₁×#482	C₂²	1	2	yes	complemented
78	C₃₁×#481	C₂²	1	2	yes	—
79	C₃₁×#480	C₂²	1	2	yes	—
80	C₃₁×#479	C₂²	1	2	yes	complemented
81	C₃₁×#478	C₂²	1	2	yes	—
82	C₃₁×#478	C₂²	1	2	yes	—
83	C₃₁×#478	C₂²	1	2	yes	—
84	C₃₁×#478	C₂²	1	2	yes	complemented
85	C₃₁×#478	C₂²	1	2	yes	complemented
86	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#476	C₂²	1	1	yes	characteristic
91	C₃₁×#476	C₂²	1	1	yes	characteristic
92	C₃₁×#476	C₂²	1	1	yes	characteristic
93	C₃₁×#476	C₂²	1	1	yes	characteristic
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	2	yes	—
100	C₃₁×#474	C₂²	1	2	yes	complemented
101	C₃₁×#469	C₂²	1	2	yes	—
102	C₃₁×#468	C₂²	1	2	yes	—
103	C₃₁×#468	C₂²	1	2	yes	—
104	C₃₁×#468	C₂²	1	2	yes	complemented
105	C₃₁×#466	C₂²	1	2	yes	—
106	C₃₁×#465	C₂²	1	2	yes	complemented
107	C₃₁×#463	C₂²	1	2	yes	—
108	C₃₁×#463	C₂²	1	2	yes	—
109	C₃₁×#461	C₂²	1	2	yes	complemented
110	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#459	C₂²	1	1	yes	characteristic
113	C₃₁×#459	C₂²	1	1	yes	characteristic
114	C₃₁×#449	C₂²	1	2	yes	—
115	C₃₁×#449	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	—
120	C₃₁×#442	C₂²	1	2	yes	—
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	—
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	—	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×D₄×C₃₁	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₃₁	—	2	1	no	—
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×D₈×C₃₁	C₂³	1	2	yes	—
151	C₂×D₈×C₃₁	C₂³	1	2	yes	—
152	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
155	C₃₁×C₄⋊Q₈	—	2	1	no	—
156	C₃₁×C₄⋊Q₈	—	2	1	no	—
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×#127	C₂³	1	1	yes	characteristic
164	C₃₁×#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	1	no	—
169	C₃₁×#126	—	2	1	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	1	no	—
175	C₃₁×#125	C₂³	1	2	yes	—
176	C₃₁×#125	C₂³	1	2	yes	—
177	C₃₁×#125	C₂³	1	1	yes	characteristic
178	C₃₁×#125	C₂³	1	1	yes	characteristic
179	C₃₁×#124	—	2	1	no	—
180	C₃₁×#124	—	2	1	no	—
181	C₃₁×#124	—	2	2	no	—
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	—	2	1	no	—
184	C₃₁×#124	—	2	1	no	—
185	C₃₁×#124	—	2	1	no	—
186	C₃₁×#124	C₂³	1	1	yes	characteristic
187	C₃₁×#124	C₂³	1	1	yes	characteristic
188	C₃₁×#123	—	2	1	no	—
189	C₃₁×#123	—	2	1	no	—
190	C₃₁×#123	—	2	1	no	—
191	C₃₁×#123	—	2	1	no	—
192	C₃₁×#123	—	2	1	no	—
193	C₃₁×#123	—	2	1	no	—
194	C₃₁×#123	—	2	1	no	—
195	C₃₁×#123	—	2	1	no	—
196	C₃₁×#123	—	2	2	no	—
197	C₃₁×#123	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	1	no	—
199	C₃₁×C₂²⋊Q₈	—	2	1	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	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	2	no	—
209	C₃₁×C₂²⋊Q₈	—	2	2	no	—
210	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₃₁×#121	—	2	1	no	—
215	C₃₁×#121	—	2	1	no	—
216	C₃₁×#121	—	2	2	no	—
217	C₃₁×#121	—	2	2	no	—
218	C₃₁×#121	—	2	2	no	—
219	C₃₁×#121	—	2	1	no	—
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	2	yes	—
225	C₃₁×#121	C₂³	1	2	yes	—
226	C₃₁×#121	C₂³	1	2	yes	—
227	C₃₁×#121	C₂³	1	1	yes	characteristic
228	C₃₁×#121	C₂³	1	1	yes	characteristic
229	C₃₁×#120	—	2	1	no	—
230	C₃₁×#120	—	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	D₄	1	1	yes	characteristic
237	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	—	2	1	no	—
245	C₄×D₄×C₃₁	—	2	1	no	—
246	C₄×D₄×C₃₁	—	2	1	no	—
247	C₄×D₄×C₃₁	—	2	1	no	—
248	C₄×D₄×C₃₁	—	2	2	no	—
249	C₄×D₄×C₃₁	—	2	2	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	2	yes	—
260	C₄×D₄×C₃₁	C₂³	1	2	yes	—
261	C₄×D₄×C₃₁	C₂³	1	2	yes	—
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	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
268	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
269	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
270	C₃₁×#117	—	2	1	no	—
271	C₃₁×#117	—	2	1	no	—
272	C₃₁×#117	—	2	1	no	—
273	C₃₁×#117	—	2	2	no	—
274	C₃₁×#117	—	2	1	no	—
275	C₃₁×#117	—	2	1	no	—
276	C₃₁×#117	—	2	1	no	—
277	C₃₁×#117	—	2	1	no	—
278	C₃₁×#117	—	2	1	no	—
279	C₃₁×#117	—	2	1	no	—
280	C₃₁×#117	D₄	1	1	yes	characteristic
281	C₃₁×#117	D₄	1	1	yes	characteristic
282	C₃₁×#117	D₄	1	1	yes	characteristic
283	C₃₁×#117	C₂³	1	2	yes	—
284	C₃₁×#117	C₂³	1	2	yes	—
285	C₃₁×#117	C₂³	1	1	yes	characteristic
286	C₃₁×#117	C₂³	1	1	yes	characteristic
287	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
288	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
289	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
290	C₂×C₄⋊C₄×C₃₁	—	2	2	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×#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×#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	#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	—	2	1	no	—
355	C₂×Q₈×C₃₁	—	2	2	no	—
356	C₂×Q₈×C₃₁	—	8	2	no	—
357	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
358	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
359	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
360	C₂×D₄×C₃₁	—	2	2	no	—
361	C₂×D₄×C₃₁	—	2	1	no	—
362	C₂×D₄×C₃₁	—	2	1	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	2	no	—
368	C₂×D₄×C₃₁	—	2	1	no	—
369	C₂×D₄×C₃₁	—	2	1	no	—
370	C₂×D₄×C₃₁	—	2	1	no	—
371	C₂×D₄×C₃₁	—	4	1	no	—
372	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
373	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
374	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
375	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
377	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₃₁	—	2	1	no	—
379	C₂²×C₄×C₃₁	—	2	2	no	—
380	C₂²×C₄×C₃₁	—	2	1	no	—
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	2	no	—
385	C₂²×C₄×C₃₁	—	2	1	no	—
386	C₂²×C₄×C₃₁	—	2	1	no	—
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	—	4	4	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	SD₁₆×C₃₁	—	4	2	no	—
402	SD₁₆×C₃₁	—	4	2	no	—
403	D₈×C₃₁	—	2	4	no	—
404	D₈×C₃₁	—	4	2	no	—
405	M₁₆×C₃₁	—	4	2	no	—
406	M₁₆×C₃₁	—	4	2	no	—
407	C₂×C₈×C₃₁	—	4	2	no	—
408	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
409	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
410	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
411	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
412	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
420	C₄⋊C₄×C₃₁	—	2	1	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	2	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	2	no	—
433	C₄⋊C₄×C₃₁	—	2	2	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	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	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	C₂⁴	1	2	yes	—
444	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
445	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
446	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
447	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	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	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	2	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	C₂×D₄	1	1	yes	characteristic
477	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
478	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
479	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
480	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
481	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
482	C₄²×C₃₁	—	2	1	no	—
483	C₄²×C₃₁	—	2	1	no	—
484	C₄²×C₃₁	—	2	1	no	—
485	C₄²×C₃₁	—	2	1	no	—
486	C₄²×C₃₁	—	2	1	no	—
487	C₄²×C₃₁	—	2	1	no	—
488	C₄²×C₃₁	—	2	2	no	—
489	C₄²×C₃₁	—	2	2	no	—
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	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	C₂⁴	1	1	yes	characteristic
497	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
498	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
499	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
500	#62115	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
501	C₂³×C₃₁	—	2	1	no	—
502	C₂³×C₃₁	—	2	1	no	—
503	C₂³×C₃₁	—	2	2	no	—
504	C₂³×C₃₁	—	4	2	no	—
505	C₂³×C₃₁	—	4	2	no	—
506	C₂³×C₃₁	—	8	1	no	—
507	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
508	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
509	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
510	Q₈×C₃₁	—	2	1	no	—
511	Q₈×C₃₁	—	2	1	no	—
512	Q₈×C₃₁	—	2	1	no	—
513	Q₈×C₃₁	—	2	1	no	—
514	Q₈×C₃₁	—	4	1	no	—
515	Q₈×C₃₁	—	4	2	no	—
516	Q₈×C₃₁	—	4	2	no	—
517	Q₈×C₃₁	—	4	2	no	—
518	Q₈×C₃₁	—	8	1	no	—
519	Q₈×C₃₁	—	8	2	no	—
520	D₄×C₃₁	—	2	2	no	—
521	D₄×C₃₁	—	2	1	no	—
522	D₄×C₃₁	—	2	1	no	—
523	D₄×C₃₁	—	2	1	no	—
524	D₄×C₃₁	—	2	2	no	—
525	D₄×C₃₁	—	4	1	no	—
526	D₄×C₃₁	—	4	1	no	—
527	D₄×C₃₁	—	4	1	no	—
528	D₄×C₃₁	—	4	2	no	—
529	D₄×C₃₁	—	4	2	no	—
530	D₄×C₃₁	—	4	2	no	—
531	D₄×C₃₁	—	4	2	no	—
532	D₄×C₃₁	—	4	4	no	—
533	D₄×C₃₁	—	4	2	no	—
534	D₄×C₃₁	—	8	1	no	—
535	D₄×C₃₁	—	8	1	no	—
536	D₄×C₃₁	—	8	2	no	—
537	D₄×C₃₁	—	8	2	no	—
538	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
539	C₂×C₄×C₃₁	—	2	2	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	1	no	—
547	C₂×C₄×C₃₁	—	2	1	no	—
548	C₂×C₄×C₃₁	—	2	1	no	—
549	C₂×C₄×C₃₁	—	2	1	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	2	no	—
554	C₂×C₄×C₃₁	—	2	2	no	—
555	C₂×C₄×C₃₁	—	2	2	no	—
556	C₂×C₄×C₃₁	—	2	1	no	—
557	C₂×C₄×C₃₁	—	4	1	no	—
558	C₂×C₄×C₃₁	—	4	1	no	—
559	C₂×C₄×C₃₁	—	4	1	no	—
560	C₂×C₄×C₃₁	—	4	2	no	—
561	C₂×C₄×C₃₁	—	4	2	no	—
562	C₂×C₄×C₃₁	—	4	2	no	—
563	C₂×C₄×C₃₁	—	4	2	no	—
564	C₂×C₄×C₃₁	—	4	4	no	—
565	C₂×C₄×C₃₁	—	4	2	no	—
566	C₂×C₄×C₃₁	—	4	2	no	—
567	C₂×C₄×C₃₁	—	4	2	no	—
568	C₂×C₄×C₃₁	—	8	1	no	—
569	C₂×C₄×C₃₁	—	8	1	no	—
570	C₂×C₄×C₃₁	—	8	2	no	—
571	C₂×C₄×C₃₁	—	8	2	no	—
572	C₂×C₄×C₃₁	—	8	2	no	—
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	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	C₂⁵	1	1	yes	characteristic
585	C₈×C₃₁	—	2	2	no	—
586	C₈×C₃₁	—	2	2	no	—
587	C₈×C₃₁	—	2	2	no	—
588	C₈×C₃₁	—	2	2	no	—
589	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
590	#3475	C₂×C₃₁	1	1	yes	characteristic, complemented
591	#3389	C₂×C₃₁	1	2	yes	complemented
592	#3376	C₂×C₃₁	1	2	yes	complemented
593	#3351	C₂×C₃₁	1	2	yes	complemented
594	#3348	C₂×C₃₁	1	2	yes	complemented
595	#3347	C₂×C₃₁	1	2	yes	complemented
596	#3322	C₂×C₃₁	1	2	yes	complemented
597	#3319	C₂×C₃₁	1	2	yes	complemented
598	#3307	C₂×C₃₁	1	2	yes	complemented
599	#3254	C₂×C₃₁	1	1	yes	characteristic, complemented
600	#3251	C₂×C₃₁	1	1	yes	characteristic, complemented
601	#3247	C₂×C₃₁	1	1	yes	characteristic, complemented
602	#3238	C₂×C₃₁	1	1	yes	characteristic, complemented
603	#3237	C₂×C₃₁	1	1	yes	characteristic, complemented
604	#3233	C₂×C₃₁	1	1	yes	characteristic, complemented
605	#3115	C₂×C₃₁	1	1	yes	characteristic, complemented
606	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
607	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
608	#3079	C₂×C₃₁	1	1	yes	characteristic, complemented
609	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
610	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
611	#2989	C₂×C₃₁	1	1	yes	characteristic, complemented
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	—	2	1	no	—
618	C₂²×C₃₁	—	2	2	no	—
619	C₂²×C₃₁	—	2	1	no	—
620	C₂²×C₃₁	—	2	1	no	—
621	C₂²×C₃₁	—	2	1	no	—
622	C₂²×C₃₁	—	4	1	no	—
623	C₂²×C₃₁	—	4	1	no	—
624	C₂²×C₃₁	—	4	2	no	—
625	C₂²×C₃₁	—	4	1	no	—
626	C₂²×C₃₁	—	4	1	no	—
627	C₂²×C₃₁	—	4	2	no	—
628	C₂²×C₃₁	—	4	1	no	—
629	C₂²×C₃₁	—	4	2	no	—
630	C₂²×C₃₁	—	8	4	no	—
631	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
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	—	2	1	no	—
641	C₄×C₃₁	—	2	1	no	—
642	C₄×C₃₁	—	4	2	no	—
643	C₄×C₃₁	—	4	2	no	—
644	C₄×C₃₁	—	4	1	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	—	4	1	no	—
650	C₄×C₃₁	—	4	2	no	—
651	C₄×C₃₁	#575	1	2	yes	—
652	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
653	C₄×C₃₁	#585	1	1	yes	characteristic
654	#556	—	2	1	no	—
655	#556	C₂²×C₃₁	1	1	yes	characteristic
656	#555	C₂²×C₃₁	1	1	yes	characteristic
657	#555	C₂²×C₃₁	1	2	yes	—
658	#554	C₂²×C₃₁	1	1	yes	characteristic
659	#554	C₂²×C₃₁	1	2	yes	complemented
660	#553	—	2	1	no	—
661	#553	C₂²×C₃₁	1	2	yes	—
662	#553	C₂²×C₃₁	1	2	yes	complemented
663	#552	—	2	1	no	—
664	#552	C₂²×C₃₁	1	1	yes	characteristic
665	#552	C₂²×C₃₁	1	1	yes	characteristic
666	#551	—	2	1	no	—
667	#551	—	2	1	no	—
668	#548	—	2	1	no	—
669	#548	—	2	1	no	—
670	#547	—	2	1	no	—
671	#547	C₂²×C₃₁	1	1	yes	characteristic
672	#546	C₂²×C₃₁	1	1	yes	characteristic
673	#546	C₂²×C₃₁	1	1	yes	characteristic
674	#542	—	2	1	no	—
675	#542	—	2	1	no	—
676	#537	—	2	1	no	—
677	#533	C₂²×C₃₁	1	1	yes	characteristic
678	#533	C₂²×C₃₁	1	1	yes	characteristic
679	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
680	#532	C₂²×C₃₁	1	1	yes	characteristic
681	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
682	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
683	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	#529	—	2	1	no	—
685	#529	—	2	1	no	—
686	#529	C₂²×C₃₁	1	1	yes	characteristic
687	#529	C₂²×C₃₁	1	1	yes	characteristic
688	#525	—	2	1	no	—
689	#520	—	2	1	no	—
690	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
691	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
692	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
693	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
694	C₂×#117	—	2	1	no	—
695	#501	C₂²×C₃₁	1	2	yes	complemented
696	#501	C₂²×C₃₁	1	2	yes	complemented
697	#499	C₂²×C₃₁	1	2	yes	complemented
698	#491	C₂²×C₃₁	1	2	yes	complemented
699	#489	C₂²×C₃₁	1	2	yes	—
700	#488	C₂²×C₃₁	1	2	yes	—
701	#485	C₂²×C₃₁	1	2	yes	—
702	#485	C₂²×C₃₁	1	2	yes	—
703	#485	C₂²×C₃₁	1	2	yes	complemented
704	#483	C₂²×C₃₁	1	2	yes	complemented
705	#482	C₂²×C₃₁	1	2	yes	—
706	#482	C₂²×C₃₁	1	2	yes	complemented
707	#482	C₂²×C₃₁	1	2	yes	complemented
708	#481	C₂²×C₃₁	1	2	yes	—
709	#480	C₂²×C₃₁	1	2	yes	—
710	#479	C₂²×C₃₁	1	2	yes	complemented
711	#478	C₂²×C₃₁	1	2	yes	—
712	#478	C₂²×C₃₁	1	2	yes	—
713	#478	C₂²×C₃₁	1	2	yes	—
714	#478	C₂²×C₃₁	1	2	yes	complemented
715	#478	C₂²×C₃₁	1	2	yes	complemented
716	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
717	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
718	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
719	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
720	#476	C₂²×C₃₁	1	1	yes	characteristic
721	#476	C₂²×C₃₁	1	1	yes	characteristic
722	#476	C₂²×C₃₁	1	1	yes	characteristic
723	#476	C₂²×C₃₁	1	1	yes	characteristic
724	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
725	#475	C₂²×C₃₁	1	2	yes	complemented
726	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
727	#474	C₂²×C₃₁	1	1	yes	characteristic
728	#474	C₂²×C₃₁	1	1	yes	characteristic
729	#474	C₂²×C₃₁	1	2	yes	—
730	#474	C₂²×C₃₁	1	2	yes	complemented
731	#469	C₂²×C₃₁	1	2	yes	—
732	#468	C₂²×C₃₁	1	2	yes	—
733	#468	C₂²×C₃₁	1	2	yes	—
734	#468	C₂²×C₃₁	1	2	yes	complemented
735	#466	C₂²×C₃₁	1	2	yes	—
736	#465	C₂²×C₃₁	1	2	yes	complemented
737	#463	C₂²×C₃₁	1	2	yes	—
738	#463	C₂²×C₃₁	1	2	yes	—
739	#461	C₂²×C₃₁	1	2	yes	complemented
740	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
741	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
742	#459	C₂²×C₃₁	1	1	yes	characteristic
743	#459	C₂²×C₃₁	1	1	yes	characteristic
744	#449	C₂²×C₃₁	1	2	yes	—
745	#449	C₂²×C₃₁	1	2	yes	—
746	#447	C₂²×C₃₁	1	2	yes	—
747	#446	C₂²×C₃₁	1	2	yes	complemented
748	#442	C₂²×C₃₁	1	2	yes	—
749	#442	C₂²×C₃₁	1	2	yes	—
750	#442	C₂²×C₃₁	1	2	yes	—
751	#440	C₂²×C₃₁	1	2	yes	complemented
752	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
753	C₄×D₈	C₂²×C₃₁	1	2	yes	—
754	#436	C₂²×C₃₁	1	2	yes	—
755	#435	C₂²×C₃₁	1	2	yes	—
756	#435	C₂²×C₃₁	1	2	yes	complemented
757	#432	C₂²×C₃₁	1	1	yes	characteristic
758	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
759	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
760	#428	C₂²×C₃₁	1	2	yes	—
761	#428	C₂²×C₃₁	1	2	yes	complemented
762	#427	C₂²×C₃₁	1	2	yes	complemented
763	#423	C₂²×C₃₁	1	1	yes	characteristic
764	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
765	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
766	#418	C₂²×C₃₁	1	2	yes	—
767	#417	C₂²×C₃₁	1	2	yes	—
768	#416	C₂²×C₃₁	1	2	yes	—
769	C₂×C₃₁	—	4	1	no	—
770	C₂×C₃₁	—	4	1	no	—
771	C₂×C₃₁	—	4	1	no	—
772	C₂×C₃₁	—	4	2	no	—
773	C₂×C₃₁	—	8	2	no	—
774	C₂×C₃₁	—	8	1	no	—
775	C₂×C₃₁	#3489	1	1	yes	characteristic
776	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
777	C₂×C₃₁	#3585	1	1	yes	characteristic
778	C₂×#41	—	2	1	no	—
779	C₂×#41	—	2	1	no	—
780	C₂×#41	—	2	1	no	—
781	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
782	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
783	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
784	C₂²×Q₈	—	2	1	no	—
785	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
786	C₂³×C₄	—	2	1	no	—
787	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
788	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
789	C₂×D₈	C₂³×C₃₁	1	2	yes	—
790	C₂×D₈	C₂³×C₃₁	1	2	yes	—
791	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
792	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
793	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
794	C₄⋊Q₈	—	2	1	no	—
795	C₄⋊Q₈	—	2	1	no	—
796	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
797	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
798	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
799	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
800	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
801	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
802	#127	C₂³×C₃₁	1	1	yes	characteristic
803	#126	—	2	1	no	—
804	#126	—	2	1	no	—
805	#126	—	2	2	no	—
806	#126	—	2	2	no	—
807	#126	—	2	1	no	—
808	#126	—	2	1	no	—
809	#126	—	2	1	no	—
810	#126	—	2	1	no	—
811	#125	—	2	1	no	—
812	#125	—	2	1	no	—
813	#125	—	2	1	no	—
814	#125	C₂³×C₃₁	1	1	yes	characteristic
815	#125	C₂³×C₃₁	1	1	yes	characteristic
816	#125	C₂³×C₃₁	1	2	yes	—
817	#125	C₂³×C₃₁	1	2	yes	—
818	#124	—	2	1	no	—
819	#124	—	2	1	no	—
820	#124	—	2	2	no	—
821	#124	—	2	2	no	—
822	#124	—	2	1	no	—
823	#124	—	2	1	no	—
824	#124	—	2	1	no	—
825	#124	C₂³×C₃₁	1	1	yes	characteristic
826	#124	C₂³×C₃₁	1	1	yes	characteristic
827	#123	—	2	1	no	—
828	#123	—	2	1	no	—
829	#123	—	2	1	no	—
830	#123	—	2	1	no	—
831	#123	—	2	1	no	—
832	#123	—	2	1	no	—
833	#123	—	2	1	no	—
834	#123	—	2	1	no	—
835	#123	—	2	2	no	—
836	#123	—	2	2	no	—
837	C₂²⋊Q₈	—	2	1	no	—
838	C₂²⋊Q₈	—	2	1	no	—
839	C₂²⋊Q₈	—	2	2	no	—
840	C₂²⋊Q₈	—	2	1	no	—
841	C₂²⋊Q₈	—	2	1	no	—
842	C₂²⋊Q₈	—	2	1	no	—
843	C₂²⋊Q₈	—	2	1	no	—
844	C₂²⋊Q₈	—	2	1	no	—
845	C₂²⋊Q₈	—	2	1	no	—
846	C₂²⋊Q₈	—	2	1	no	—
847	C₂²⋊Q₈	—	2	2	no	—
848	C₂²⋊Q₈	—	2	2	no	—
849	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
850	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
851	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
852	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
853	#121	—	2	1	no	—
854	#121	—	2	1	no	—
855	#121	—	2	2	no	—
856	#121	—	2	2	no	—
857	#121	—	2	2	no	—
858	#121	—	2	1	no	—
859	#121	—	2	1	no	—
860	#121	—	2	1	no	—
861	#121	—	2	1	no	—
862	#121	—	2	1	no	—
863	#121	C₂³×C₃₁	1	1	yes	characteristic
864	#121	C₂³×C₃₁	1	1	yes	characteristic
865	#121	C₂³×C₃₁	1	2	yes	—
866	#121	C₂³×C₃₁	1	2	yes	—
867	#121	C₂³×C₃₁	1	2	yes	—
868	#120	—	2	1	no	—
869	#120	—	2	1	no	—
870	C₄×Q₈	—	2	1	no	—
871	C₄×Q₈	—	2	1	no	—
872	C₄×Q₈	—	2	1	no	—
873	C₄×Q₈	—	2	1	no	—
874	C₄×Q₈	—	2	1	no	—
875	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
876	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
877	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
878	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
879	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
880	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	—	2	1	no	—
883	C₄×D₄	—	2	1	no	—
884	C₄×D₄	—	2	1	no	—
885	C₄×D₄	—	2	1	no	—
886	C₄×D₄	—	2	1	no	—
887	C₄×D₄	—	2	2	no	—
888	C₄×D₄	—	2	2	no	—
889	C₄×D₄	—	2	1	no	—
890	C₄×D₄	—	2	1	no	—
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	2	1	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
895	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
896	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
897	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
898	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
899	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
900	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
901	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
902	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
903	C₄×D₄	C₂³×C₃₁	1	2	yes	—
904	C₄×D₄	C₂³×C₃₁	1	2	yes	—
905	C₄×D₄	C₂³×C₃₁	1	2	yes	—
906	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
907	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
908	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
909	#117	—	2	1	no	—
910	#117	—	2	1	no	—
911	#117	—	2	1	no	—
912	#117	—	2	2	no	—
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	#117	C₂³×C₃₁	1	2	yes	—
925	#117	C₂³×C₃₁	1	2	yes	—
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	—	2	2	no	—
930	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
931	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
932	C₂×C₂²⋊C₄	—	2	1	no	—
933	C₂×C₂²⋊C₄	—	2	1	no	—
934	C₂×C₂²⋊C₄	—	2	1	no	—
935	C₂×C₄²	—	2	1	no	—
936	C₂×C₄²	—	2	1	no	—
937	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
938	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
939	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
940	#107	C₂³×C₃₁	1	2	yes	—
941	#107	C₂³×C₃₁	1	2	yes	—
942	#107	C₂³×C₃₁	1	2	yes	—
943	#107	C₂³×C₃₁	1	2	yes	—
944	#107	C₂³×C₃₁	1	2	yes	—
945	#107	C₂³×C₃₁	1	2	yes	—
946	#106	C₂³×C₃₁	1	2	yes	—
947	#106	C₂³×C₃₁	1	2	yes	—
948	#106	C₂³×C₃₁	1	2	yes	—
949	#106	C₂³×C₃₁	1	2	yes	—
950	#106	C₂³×C₃₁	1	2	yes	—
951	#106	C₂³×C₃₁	1	2	yes	—
952	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
953	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
954	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
955	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
956	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
957	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
958	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
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	#102	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	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
976	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
977	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
978	#97	C₂³×C₃₁	1	2	yes	—
979	#97	C₂³×C₃₁	1	2	yes	—
980	C₄×C₈	C₂³×C₃₁	1	2	yes	—
981	C₃₁	#62115	1	1	yes	characteristic, direct product factor, Sylow
982	C₂⁴	—	2	1	no	—
983	#41	—	2	2	no	—
984	#41	—	2	2	no	—
985	#41	—	4	2	no	—
986	#41	—	4	1	no	—
987	#41	—	4	1	no	—
988	#41	—	4	4	no	—
989	#41	—	8	2	no	—
990	#41	—	8	2	no	—
991	C₂×Q₈	—	2	1	no	—
992	C₂×Q₈	—	2	1	no	—
993	C₂×Q₈	—	2	1	no	—
994	C₂×Q₈	—	2	1	no	—
995	C₂×Q₈	—	2	2	no	—
996	C₂×Q₈	—	8	2	no	—
997	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
998	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
999	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	2	no	—
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	1	no	—
1006	C₂×D₄	—	2	2	no	—
1007	C₂×D₄	—	2	2	no	—
1008	C₂×D₄	—	2	1	no	—
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	4	1	no	—
1012	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1013	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1014	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1015	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1016	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1017	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1018	C₂²×C₄	—	2	1	no	—
1019	C₂²×C₄	—	2	2	no	—
1020	C₂²×C₄	—	2	1	no	—
1021	C₂²×C₄	—	2	1	no	—
1022	C₂²×C₄	—	2	1	no	—
1023	C₂²×C₄	—	2	1	no	—
1024	C₂²×C₄	—	2	2	no	—
1025	C₂²×C₄	—	2	1	no	—
1026	C₂²×C₄	—	2	1	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	—	2	1	no	—
1029	C₂²×C₄	—	2	2	no	—
1030	C₂²×C₄	—	2	2	no	—
1031	C₂²×C₄	—	4	4	no	—
1032	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1033	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1034	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1035	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1036	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1037	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1038	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1039	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1040	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1041	SD₁₆	—	4	2	no	—
1042	SD₁₆	—	4	2	no	—
1043	D₈	—	2	4	no	—
1044	D₈	—	4	2	no	—
1045	M₁₆	—	4	2	no	—
1046	M₁₆	—	4	2	no	—
1047	C₂×C₈	—	4	2	no	—
1048	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1049	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1050	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1051	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1052	C₄⋊C₄	—	2	2	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	2	no	—
1062	C₄⋊C₄	—	2	2	no	—
1063	C₄⋊C₄	—	2	1	no	—
1064	C₄⋊C₄	—	2	2	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	2	no	—
1073	C₄⋊C₄	—	2	2	no	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	1	no	—
1076	C₄⋊C₄	—	2	1	no	—
1077	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1078	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1079	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1080	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1081	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1082	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1083	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1084	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1085	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1086	C₄⋊C₄	C₂⁴×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	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	2	no	—
1095	C₂²⋊C₄	—	2	2	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	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	2	no	—
1107	C₂²⋊C₄	—	2	2	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	2	no	—
1113	C₂²⋊C₄	—	2	2	no	—
1114	C₂²⋊C₄	—	2	2	no	—
1115	C₂²⋊C₄	—	2	2	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	1	no	—
1127	C₄²	—	2	1	no	—
1128	C₄²	—	2	2	no	—
1129	C₄²	—	2	2	no	—
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	C₂×D₄×C₃₁	1	1	yes	characteristic
1135	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1136	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1137	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1138	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1139	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1140	C₂³	—	2	1	no	—
1141	C₂³	—	2	1	no	—
1142	C₂³	—	2	2	no	—
1143	C₂³	—	4	2	no	—
1144	C₂³	—	4	2	no	—
1145	C₂³	—	8	1	no	—
1146	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1147	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1148	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1149	Q₈	—	2	1	no	—
1150	Q₈	—	2	1	no	—
1151	Q₈	—	2	1	no	—
1152	Q₈	—	2	1	no	—
1153	Q₈	—	4	1	no	—
1154	Q₈	—	4	2	no	—
1155	Q₈	—	4	2	no	—
1156	Q₈	—	4	2	no	—
1157	Q₈	—	8	1	no	—
1158	Q₈	—	8	2	no	—
1159	D₄	—	2	2	no	—
1160	D₄	—	2	1	no	—
1161	D₄	—	2	1	no	—
1162	D₄	—	2	1	no	—
1163	D₄	—	2	2	no	—
1164	D₄	—	4	1	no	—
1165	D₄	—	4	1	no	—
1166	D₄	—	4	1	no	—
1167	D₄	—	4	2	no	—
1168	D₄	—	4	2	no	—
1169	D₄	—	4	2	no	—
1170	D₄	—	4	2	no	—
1171	D₄	—	4	4	no	—
1172	D₄	—	4	2	no	—
1173	D₄	—	8	1	no	—
1174	D₄	—	8	1	no	—
1175	D₄	—	8	2	no	—
1176	D₄	—	8	2	no	—
1177	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1178	C₂×C₄	—	2	2	no	—
1179	C₂×C₄	—	2	2	no	—
1180	C₂×C₄	—	2	2	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	1	no	—
1184	C₂×C₄	—	2	1	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	—	2	1	no	—
1190	C₂×C₄	—	2	2	no	—
1191	C₂×C₄	—	2	1	no	—
1192	C₂×C₄	—	2	1	no	—
1193	C₂×C₄	—	2	2	no	—
1194	C₂×C₄	—	2	2	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	4	1	no	—
1197	C₂×C₄	—	4	1	no	—
1198	C₂×C₄	—	4	1	no	—
1199	C₂×C₄	—	4	2	no	—
1200	C₂×C₄	—	4	2	no	—
1201	C₂×C₄	—	4	2	no	—
1202	C₂×C₄	—	4	2	no	—
1203	C₂×C₄	—	4	4	no	—
1204	C₂×C₄	—	4	2	no	—
1205	C₂×C₄	—	4	2	no	—
1206	C₂×C₄	—	4	2	no	—
1207	C₂×C₄	—	8	1	no	—
1208	C₂×C₄	—	8	1	no	—
1209	C₂×C₄	—	8	2	no	—
1210	C₂×C₄	—	8	2	no	—
1211	C₂×C₄	—	8	2	no	—
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	C₂²×D₄×C₃₁	1	1	yes	characteristic
1217	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1218	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1219	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1220	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1221	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1222	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1223	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1224	C₈	—	2	2	no	—
1225	C₈	—	2	2	no	—
1226	C₈	—	2	2	no	—
1227	C₈	—	2	2	no	—
1228	C₂²	—	2	1	no	—
1229	C₂²	—	2	1	no	—
1230	C₂²	—	2	1	no	—
1231	C₂²	—	2	2	no	—
1232	C₂²	—	2	1	no	—
1233	C₂²	—	2	1	no	—
1234	C₂²	—	2	1	no	—
1235	C₂²	—	2	1	no	—
1236	C₂²	—	2	1	no	—
1237	C₂²	—	2	1	no	—
1238	C₂²	—	4	1	no	—
1239	C₂²	—	4	1	no	—
1240	C₂²	—	4	1	no	—
1241	C₂²	—	4	2	no	—
1242	C₂²	—	4	1	no	—
1243	C₂²	—	4	2	no	—
1244	C₂²	—	4	2	no	—
1245	C₂²	—	4	1	no	—
1246	C₂²	—	8	4	no	—
1247	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1248	C₄	—	2	1	no	—
1249	C₄	—	2	1	no	—
1250	C₄	—	2	1	no	—
1251	C₄	—	2	1	no	—
1252	C₄	—	2	1	no	—
1253	C₄	—	2	1	no	—
1254	C₄	—	2	1	no	—
1255	C₄	—	2	1	no	—
1256	C₄	—	2	1	no	—
1257	C₄	—	2	1	no	—
1258	C₄	—	4	1	no	—
1259	C₄	—	4	1	no	—
1260	C₄	—	4	1	no	—
1261	C₄	—	4	1	no	—
1262	C₄	—	4	2	no	—
1263	C₄	—	4	2	no	—
1264	C₄	—	4	2	no	—
1265	C₄	—	4	1	no	—
1266	C₄	—	4	1	no	—
1267	C₄	C₃₁×#575	1	2	yes	—
1268	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1269	C₄	C₃₁×#585	1	1	yes	characteristic
1270	C₂	—	4	1	no	—
1271	C₂	—	4	1	no	—
1272	C₂	—	4	1	no	—
1273	C₂	—	4	2	no	—
1274	C₂	—	8	1	no	—
1275	C₂	—	8	2	no	—
1276	C₂	C₃₁×#3489	1	1	yes	characteristic
1277	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1278	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×#3511	C₂	semidirect
2. C₃₁×#3475	C₂	semidirect
3. C₃₁×#3389	C₂	semidirect
4. C₃₁×#3376	C₂	semidirect
5. C₃₁×#3351	C₂	semidirect
6. C₃₁×#3348	C₂	semidirect
7. C₃₁×#3347	C₂	semidirect
8. C₃₁×#3322	C₂	semidirect
9. C₃₁×#3319	C₂	semidirect
10. C₃₁×#3307	C₂	semidirect
11. C₃₁×#3254	C₂	semidirect
12. C₃₁×#3251	C₂	semidirect
13. C₃₁×#3247	C₂	semidirect
14. C₃₁×#3238	C₂	semidirect
15. C₃₁×#3237	C₂	semidirect
16. C₃₁×#3233	C₂	semidirect
17. C₃₁×#3115	C₂	semidirect
18. C₃₁×#3109	C₂	semidirect
19. C₃₁×#3106	C₂	semidirect
20. C₃₁×#3079	C₂	semidirect
21. C₃₁×#3077	C₂	semidirect
22. C₃₁×#3076	C₂	semidirect
23. C₃₁×#2989	C₂	semidirect
29. C₃₁×#554	C₂²	semidirect
32. C₃₁×#553	C₂²	semidirect
49. C₃₁×#533	C₂²	semidirect
51. C₃₁×#532	C₂²	semidirect
52. C₃₁×#532	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×#483	C₂²	semidirect
76. C₃₁×#482	C₂²	semidirect
77. C₃₁×#482	C₂²	semidirect
80. C₃₁×#479	C₂²	semidirect
84. C₃₁×#478	C₂²	semidirect
85. C₃₁×#478	C₂²	semidirect
86. C₃₁×#477	C₂²	semidirect
87. C₃₁×#477	C₂²	semidirect
88. C₃₁×#477	C₂²	semidirect
89. C₃₁×#477	C₂²	semidirect
94. C₃₁×#475	C₂²	semidirect
95. C₃₁×#475	C₂²	semidirect
96. C₃₁×#475	C₂²	semidirect
100. C₃₁×#474	C₂²	semidirect
104. C₃₁×#468	C₂²	semidirect
106. C₃₁×#465	C₂²	semidirect
109. C₃₁×#461	C₂²	semidirect
110. C₃₁×#460	C₂²	semidirect
111. C₃₁×#460	C₂²	semidirect
117. C₃₁×#446	C₂²	semidirect
121. C₃₁×#440	C₂²	semidirect
122. C₄×SD₁₆×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
500. #62115	C₃₁	direct (N × H)
589. #3511	C₂×C₃₁	semidirect
590. #3475	C₂×C₃₁	semidirect
591. #3389	C₂×C₃₁	semidirect
592. #3376	C₂×C₃₁	semidirect
593. #3351	C₂×C₃₁	semidirect
594. #3348	C₂×C₃₁	semidirect
595. #3347	C₂×C₃₁	semidirect
596. #3322	C₂×C₃₁	semidirect
597. #3319	C₂×C₃₁	semidirect
598. #3307	C₂×C₃₁	semidirect
599. #3254	C₂×C₃₁	semidirect
600. #3251	C₂×C₃₁	semidirect
601. #3247	C₂×C₃₁	semidirect
602. #3238	C₂×C₃₁	semidirect
603. #3237	C₂×C₃₁	semidirect
604. #3233	C₂×C₃₁	semidirect
605. #3115	C₂×C₃₁	semidirect
606. #3109	C₂×C₃₁	semidirect
607. #3106	C₂×C₃₁	semidirect
608. #3079	C₂×C₃₁	semidirect
609. #3077	C₂×C₃₁	semidirect
610. #3076	C₂×C₃₁	semidirect
611. #2989	C₂×C₃₁	semidirect
659. #554	C₂²×C₃₁	semidirect
662. #553	C₂²×C₃₁	semidirect
679. #533	C₂²×C₃₁	semidirect
681. #532	C₂²×C₃₁	semidirect
682. #532	C₂²×C₃₁	semidirect
683. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
695. #501	C₂²×C₃₁	semidirect
696. #501	C₂²×C₃₁	semidirect
697. #499	C₂²×C₃₁	semidirect
698. #491	C₂²×C₃₁	semidirect
703. #485	C₂²×C₃₁	semidirect
704. #483	C₂²×C₃₁	semidirect
706. #482	C₂²×C₃₁	semidirect
707. #482	C₂²×C₃₁	semidirect
710. #479	C₂²×C₃₁	semidirect
714. #478	C₂²×C₃₁	semidirect
715. #478	C₂²×C₃₁	semidirect
716. #477	C₂²×C₃₁	semidirect
717. #477	C₂²×C₃₁	semidirect
718. #477	C₂²×C₃₁	semidirect
719. #477	C₂²×C₃₁	semidirect
724. #475	C₂²×C₃₁	semidirect
725. #475	C₂²×C₃₁	semidirect
726. #475	C₂²×C₃₁	semidirect
730. #474	C₂²×C₃₁	semidirect
734. #468	C₂²×C₃₁	semidirect
736. #465	C₂²×C₃₁	semidirect
739. #461	C₂²×C₃₁	semidirect
740. #460	C₂²×C₃₁	semidirect
741. #460	C₂²×C₃₁	semidirect
747. #446	C₂²×C₃₁	semidirect
751. #440	C₂²×C₃₁	semidirect
752. C₄×SD₁₆	C₂²×C₃₁	semidirect
756. #435	C₂²×C₃₁	semidirect
758. #432	C₂²×C₃₁	semidirect
759. #431	C₂²×C₃₁	semidirect
761. #428	C₂²×C₃₁	semidirect
762. #427	C₂²×C₃₁	semidirect
764. #423	C₂²×C₃₁	semidirect
765. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
981. C₃₁	#62115	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×#3511	2
C₃₁×#3475	2
C₃₁×#3389	2
C₃₁×#3376	2
C₃₁×#3351	2
C₃₁×#3348	2
C₃₁×#3347	2
C₃₁×#3322	2
C₃₁×#3319	2
C₃₁×#3307	2
C₃₁×#3254	2
C₃₁×#3251	2
C₃₁×#3247	2
C₃₁×#3238	2
C₃₁×#3237	2
C₃₁×#3233	2
C₃₁×#3115	2
C₃₁×#3109	2
C₃₁×#3106	2
C₃₁×#3079	2
C₃₁×#3077	2
C₃₁×#3076	2
C₃₁×#2989	2
#62115	31

Subgroups — C31×#62115 #21518874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62115 #21518874