Subgroups — C₃₁×#62130 #21518889

Order 7936.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3482	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3390	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3349	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3343	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3336	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3313	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3312	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3300	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3252	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3249	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3248	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×#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3104	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#557	—	2	1	no	—
25	C₃₁×#557	C₂²	1	2	yes	—
26	C₃₁×#557	C₂²	1	1	yes	characteristic
27	C₃₁×#556	—	2	1	no	—
28	C₃₁×#556	—	2	1	no	—
29	C₃₁×#556	C₂²	1	1	yes	characteristic
30	C₃₁×#556	C₂²	1	2	yes	—
31	C₃₁×#552	—	2	1	no	—
32	C₃₁×#552	—	2	1	no	—
33	C₃₁×#552	—	2	1	no	—
34	C₃₁×#552	—	2	1	no	—
35	C₃₁×#552	C₂²	1	1	yes	characteristic
36	C₃₁×#552	C₂²	1	2	yes	—
37	C₃₁×#552	C₂²	1	2	yes	—
38	C₃₁×#552	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
40	C₃₁×#548	C₂²	1	1	yes	characteristic
41	C₃₁×#548	C₂²	1	1	yes	characteristic
42	C₃₁×#547	—	2	1	no	—
43	C₃₁×#547	C₂²	1	1	yes	characteristic
44	C₃₁×#541	—	2	1	no	—
45	C₃₁×#541	—	2	1	no	—
46	C₃₁×#536	—	2	1	no	—
47	C₃₁×#533	—	2	1	no	—
48	C₃₁×#533	C₂²	1	1	yes	characteristic
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#533	C₂²	1	1	yes	characteristic
51	C₃₁×#533	C₂²	1	1	yes	characteristic
52	C₃₁×#533	C₂²	1	1	yes	characteristic
53	C₃₁×#533	C₂²	1	1	yes	characteristic
54	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
55	C₃₁×#529	—	2	1	no	—
56	C₃₁×#529	—	2	1	no	—
57	C₃₁×#529	C₂²	1	1	yes	characteristic
58	C₃₁×#529	C₂²	1	1	yes	characteristic
59	C₃₁×#519	—	2	1	no	—
60	C₄×#41×C₃₁	—	2	1	no	—
61	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
62	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
63	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
64	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
65	C₃₁×#501	C₂²	1	2	yes	—
66	C₃₁×#501	C₂²	1	2	yes	—
67	C₃₁×#499	C₂²	1	2	yes	—
68	C₃₁×#491	C₂²	1	2	yes	—
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	—
74	C₃₁×#485	C₂²	1	2	yes	—
75	C₃₁×#484	C₂²	1	2	yes	—
76	C₃₁×#483	C₂²	1	2	yes	—
77	C₃₁×#483	C₂²	1	2	yes	—
78	C₃₁×#482	C₂²	1	2	yes	—
79	C₃₁×#480	C₂²	1	2	yes	—
80	C₃₁×#479	C₂²	1	2	yes	—
81	C₃₁×#479	C₂²	1	2	yes	—
82	C₃₁×#479	C₂²	1	2	yes	—
83	C₃₁×#479	C₂²	1	2	yes	—
84	C₃₁×#479	C₂²	1	2	yes	—
85	C₃₁×#478	C₂²	1	2	yes	—
86	C₃₁×#477	C₂²	1	1	yes	characteristic
87	C₃₁×#477	C₂²	1	1	yes	characteristic
88	C₃₁×#477	C₂²	1	1	yes	characteristic
89	C₃₁×#477	C₂²	1	2	yes	—
90	C₃₁×#477	C₂²	1	2	yes	—
91	C₃₁×#477	C₂²	1	1	yes	characteristic
92	C₃₁×#477	C₂²	1	2	yes	—
93	C₃₁×#477	C₂²	1	1	yes	characteristic
94	C₃₁×#477	C₂²	1	1	yes	characteristic
95	C₃₁×#476	C₂²	1	1	yes	characteristic
96	C₃₁×#476	C₂²	1	1	yes	characteristic
97	C₃₁×#475	C₂²	1	1	yes	characteristic
98	C₃₁×#475	C₂²	1	1	yes	characteristic
99	C₃₁×#475	C₂²	1	1	yes	characteristic
100	C₃₁×#474	C₂²	1	1	yes	characteristic
101	C₃₁×#470	C₂²	1	2	yes	—
102	C₃₁×#468	C₂²	1	2	yes	—
103	C₃₁×#467	C₂²	1	2	yes	—
104	C₃₁×#467	C₂²	1	2	yes	—
105	C₃₁×#467	C₂²	1	2	yes	—
106	C₃₁×#465	C₂²	1	2	yes	—
107	C₃₁×#464	C₂²	1	2	yes	—
108	C₃₁×#464	C₂²	1	2	yes	—
109	C₃₁×#462	C₂²	1	1	yes	characteristic
110	C₃₁×#462	C₂²	1	1	yes	characteristic
111	C₃₁×#462	C₂²	1	1	yes	characteristic
112	C₃₁×#462	C₂²	1	2	yes	—
113	C₃₁×#461	C₂²	1	1	yes	characteristic
114	C₃₁×#452	C₂²	1	2	yes	—
115	C₃₁×#451	C₂²	1	2	yes	—
116	C₃₁×#451	C₂²	1	2	yes	—
117	C₃₁×#446	C₂²	1	2	yes	—
118	C₃₁×#441	C₂²	1	2	yes	—
119	C₃₁×#441	C₂²	1	2	yes	—
120	C₃₁×#441	C₂²	1	2	yes	—
121	C₃₁×#440	C₂²	1	2	yes	—
122	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
123	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
124	C₃₁×#435	C₂²	1	2	yes	—
125	C₃₁×#435	C₂²	1	2	yes	—
126	C₈×D₄×C₃₁	C₂²	1	2	yes	—
127	C₃₁×#432	C₂²	1	1	yes	characteristic
128	C₃₁×#432	C₂²	1	1	yes	characteristic
129	C₃₁×#431	C₂²	1	1	yes	characteristic
130	C₃₁×#428	C₂²	1	2	yes	—
131	C₃₁×#427	C₂²	1	2	yes	—
132	C₂×C₃₁×#107	C₂²	1	2	yes	—
133	C₃₁×#423	C₂²	1	1	yes	characteristic
134	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
135	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
136	C₃₁×#419	C₂²	1	2	yes	—
137	C₃₁×#416	C₂²	1	2	yes	—
138	C₂×C₃₁×#103	C₂²	1	2	yes	—
139	C₂×#41×C₃₁	—	2	1	no	—
140	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
141	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₃₁	—	2	1	no	—
143	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
151	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
152	C₃₁×C₄⋊Q₈	—	2	1	no	—
153	C₃₁×C₄⋊Q₈	—	2	2	no	—
154	C₃₁×C₄⋊Q₈	—	2	1	no	—
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	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×#126	—	2	1	no	—
165	C₃₁×#126	—	2	1	no	—
166	C₃₁×#126	—	2	1	no	—
167	C₃₁×#126	—	2	1	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	1	no	—
173	C₃₁×#126	—	2	1	no	—
174	C₃₁×#125	—	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	2	no	—
179	C₃₁×#125	—	2	2	no	—
180	C₃₁×#125	—	2	2	no	—
181	C₃₁×#125	—	2	2	no	—
182	C₃₁×#125	—	2	1	no	—
183	C₃₁×#125	—	2	1	no	—
184	C₃₁×#125	—	2	1	no	—
185	C₃₁×#125	—	2	1	no	—
186	C₃₁×#125	C₂³	1	2	yes	—
187	C₃₁×#125	C₂³	1	2	yes	—
188	C₃₁×#125	C₂³	1	1	yes	characteristic
189	C₃₁×#125	C₂³	1	1	yes	characteristic
190	C₃₁×#124	—	2	2	no	—
191	C₃₁×#124	—	2	1	no	—
192	C₃₁×#124	—	2	1	no	—
193	C₃₁×#124	C₂³	1	1	yes	characteristic
194	C₃₁×#124	C₂³	1	1	yes	characteristic
195	C₃₁×#123	—	2	1	no	—
196	C₃₁×#123	—	2	1	no	—
197	C₃₁×#123	—	2	2	no	—
198	C₃₁×#123	—	2	2	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×C₂²⋊Q₈	—	2	1	no	—
204	C₃₁×C₂²⋊Q₈	—	2	1	no	—
205	C₃₁×C₂²⋊Q₈	—	2	1	no	—
206	C₃₁×C₂²⋊Q₈	—	2	1	no	—
207	C₃₁×C₂²⋊Q₈	—	2	1	no	—
208	C₃₁×C₂²⋊Q₈	—	2	1	no	—
209	C₃₁×C₂²⋊Q₈	—	2	1	no	—
210	C₃₁×C₂²⋊Q₈	—	2	1	no	—
211	C₃₁×C₂²⋊Q₈	—	2	1	no	—
212	C₃₁×C₂²⋊Q₈	—	2	1	no	—
213	C₃₁×C₂²⋊Q₈	—	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	C₂³	1	2	yes	—
218	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
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	1	yes	characteristic
224	C₃₁×#121	—	2	1	no	—
225	C₃₁×#121	—	2	1	no	—
226	C₃₁×#121	C₂³	1	1	yes	characteristic
227	C₃₁×#121	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₃₁	—	2	1	no	—
229	C₄×Q₈×C₃₁	—	2	2	no	—
230	C₄×Q₈×C₃₁	—	2	2	no	—
231	C₄×Q₈×C₃₁	—	2	1	no	—
232	C₄×Q₈×C₃₁	—	2	1	no	—
233	C₄×Q₈×C₃₁	—	2	1	no	—
234	C₄×Q₈×C₃₁	—	2	1	no	—
235	C₄×Q₈×C₃₁	—	2	1	no	—
236	C₄×Q₈×C₃₁	—	2	1	no	—
237	C₄×Q₈×C₃₁	—	2	1	no	—
238	C₄×Q₈×C₃₁	—	2	1	no	—
239	C₄×Q₈×C₃₁	—	2	1	no	—
240	C₄×Q₈×C₃₁	—	2	1	no	—
241	C₄×Q₈×C₃₁	—	2	1	no	—
242	C₄×Q₈×C₃₁	—	2	1	no	—
243	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
244	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
245	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
247	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
248	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
249	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₃₁	C₂³	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×Q₈×C₃₁	C₂³	1	1	yes	characteristic
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	1	no	—
263	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
264	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
265	C₄×D₄×C₃₁	D₄	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	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
271	C₃₁×#117	—	2	1	no	—
272	C₃₁×#117	—	2	1	no	—
273	C₃₁×#117	—	2	1	no	—
274	C₃₁×#117	—	2	1	no	—
275	C₃₁×#117	—	2	1	no	—
276	C₃₁×#117	—	2	1	no	—
277	C₃₁×#117	—	2	1	no	—
278	C₃₁×#117	—	2	2	no	—
279	C₃₁×#117	—	2	2	no	—
280	C₃₁×#117	—	2	1	no	—
281	C₃₁×#117	—	2	1	no	—
282	C₃₁×#117	—	2	1	no	—
283	C₃₁×#117	D₄	1	1	yes	characteristic
284	C₃₁×#117	D₄	1	1	yes	characteristic
285	C₃₁×#117	D₄	1	1	yes	characteristic
286	C₃₁×#117	C₂³	1	2	yes	—
287	C₃₁×#117	C₂³	1	2	yes	—
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	C₂³	1	2	yes	—
293	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
295	C₂×C₄²×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×#107	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	1	yes	characteristic
316	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
317	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
318	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
319	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
320	C₃₁×#103	C₂³	1	2	yes	—
321	C₃₁×#103	C₂³	1	2	yes	—
322	C₃₁×#103	C₂³	1	2	yes	—
323	C₃₁×#103	C₂³	1	2	yes	—
324	C₃₁×#103	C₂³	1	2	yes	—
325	C₃₁×#103	C₂³	1	2	yes	—
326	C₃₁×#103	C₂³	1	2	yes	—
327	C₃₁×#103	C₂³	1	2	yes	—
328	C₃₁×#103	C₂³	1	2	yes	—
329	C₃₁×#103	C₂³	1	2	yes	—
330	C₃₁×#103	C₂³	1	2	yes	—
331	C₃₁×#103	C₂³	1	2	yes	—
332	C₃₁×#103	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	#41×C₃₁	—	2	2	no	—
343	#41×C₃₁	—	4	2	no	—
344	#41×C₃₁	—	4	1	no	—
345	#41×C₃₁	—	4	4	no	—
346	C₂×Q₈×C₃₁	—	2	1	no	—
347	C₂×Q₈×C₃₁	—	2	1	no	—
348	C₂×Q₈×C₃₁	—	2	1	no	—
349	C₂×Q₈×C₃₁	—	2	1	no	—
350	C₂×Q₈×C₃₁	—	2	1	no	—
351	C₂×Q₈×C₃₁	—	2	1	no	—
352	C₂×Q₈×C₃₁	—	2	2	no	—
353	C₂×Q₈×C₃₁	—	2	2	no	—
354	C₂×Q₈×C₃₁	—	2	2	no	—
355	C₂×Q₈×C₃₁	—	4	1	no	—
356	C₂×Q₈×C₃₁	—	4	1	no	—
357	C₂×Q₈×C₃₁	—	4	4	no	—
358	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
359	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
360	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
361	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
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	1	no	—
366	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
368	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
369	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₃₁	—	2	1	no	—
371	C₂²×C₄×C₃₁	—	2	1	no	—
372	C₂²×C₄×C₃₁	—	2	1	no	—
373	C₂²×C₄×C₃₁	—	2	1	no	—
374	C₂²×C₄×C₃₁	—	2	2	no	—
375	C₂²×C₄×C₃₁	—	2	1	no	—
376	C₂²×C₄×C₃₁	—	2	1	no	—
377	C₂²×C₄×C₃₁	—	2	1	no	—
378	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
379	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
380	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
381	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
387	Q₁₆×C₃₁	—	2	4	no	—
388	Q₁₆×C₃₁	—	4	2	no	—
389	Q₁₆×C₃₁	—	4	2	no	—
390	SD₁₆×C₃₁	—	4	2	no	—
391	M₁₆×C₃₁	—	4	2	no	—
392	C₂×C₈×C₃₁	—	4	2	no	—
393	C₂×C₈×C₃₁	—	4	2	no	—
394	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
395	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
396	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
397	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	—	2	1	no	—
400	C₄⋊C₄×C₃₁	—	2	1	no	—
401	C₄⋊C₄×C₃₁	—	2	1	no	—
402	C₄⋊C₄×C₃₁	—	2	1	no	—
403	C₄⋊C₄×C₃₁	—	2	1	no	—
404	C₄⋊C₄×C₃₁	—	2	1	no	—
405	C₄⋊C₄×C₃₁	—	2	1	no	—
406	C₄⋊C₄×C₃₁	—	2	1	no	—
407	C₄⋊C₄×C₃₁	—	2	2	no	—
408	C₄⋊C₄×C₃₁	—	2	1	no	—
409	C₄⋊C₄×C₃₁	—	2	1	no	—
410	C₄⋊C₄×C₃₁	—	2	2	no	—
411	C₄⋊C₄×C₃₁	—	2	1	no	—
412	C₄⋊C₄×C₃₁	—	2	1	no	—
413	C₄⋊C₄×C₃₁	—	2	1	no	—
414	C₄⋊C₄×C₃₁	—	2	1	no	—
415	C₄⋊C₄×C₃₁	—	2	1	no	—
416	C₄⋊C₄×C₃₁	—	2	1	no	—
417	C₄⋊C₄×C₃₁	—	2	1	no	—
418	C₄⋊C₄×C₃₁	—	2	1	no	—
419	C₄⋊C₄×C₃₁	—	2	1	no	—
420	C₄⋊C₄×C₃₁	—	2	2	no	—
421	C₄⋊C₄×C₃₁	—	2	2	no	—
422	C₄⋊C₄×C₃₁	—	2	2	no	—
423	C₄⋊C₄×C₃₁	—	2	2	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	2	no	—
431	C₄⋊C₄×C₃₁	—	2	2	no	—
432	C₄⋊C₄×C₃₁	—	2	2	no	—
433	C₄⋊C₄×C₃₁	—	2	2	no	—
434	C₄⋊C₄×C₃₁	—	2	2	no	—
435	C₄⋊C₄×C₃₁	—	2	2	no	—
436	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
437	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
438	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
439	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
443	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
444	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
445	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	2	no	—
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	1	no	—
465	C₂²⋊C₄×C₃₁	—	2	1	no	—
466	C₂²⋊C₄×C₃₁	—	2	1	no	—
467	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
468	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
469	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
470	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
471	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
472	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
473	C₄²×C₃₁	—	2	1	no	—
474	C₄²×C₃₁	—	2	1	no	—
475	C₄²×C₃₁	—	2	1	no	—
476	C₄²×C₃₁	—	2	1	no	—
477	C₄²×C₃₁	—	2	1	no	—
478	C₄²×C₃₁	—	2	1	no	—
479	C₄²×C₃₁	—	2	1	no	—
480	C₄²×C₃₁	—	2	1	no	—
481	C₄²×C₃₁	—	2	1	no	—
482	C₄²×C₃₁	—	2	2	no	—
483	C₄²×C₃₁	—	2	2	no	—
484	C₄²×C₃₁	—	2	2	no	—
485	C₄²×C₃₁	—	2	2	no	—
486	C₄²×C₃₁	—	2	2	no	—
487	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
488	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
489	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
490	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
491	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
492	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
494	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
495	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
496	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
497	#62130	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
498	C₂³×C₃₁	—	2	1	no	—
499	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
500	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
501	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
502	Q₈×C₃₁	—	2	1	no	—
503	Q₈×C₃₁	—	2	2	no	—
504	Q₈×C₃₁	—	2	1	no	—
505	Q₈×C₃₁	—	2	1	no	—
506	Q₈×C₃₁	—	2	2	no	—
507	Q₈×C₃₁	—	2	1	no	—
508	Q₈×C₃₁	—	2	1	no	—
509	Q₈×C₃₁	—	4	1	no	—
510	Q₈×C₃₁	—	4	2	no	—
511	Q₈×C₃₁	—	4	2	no	—
512	Q₈×C₃₁	—	4	2	no	—
513	Q₈×C₃₁	—	4	2	no	—
514	Q₈×C₃₁	—	4	4	no	—
515	Q₈×C₃₁	—	4	2	no	—
516	Q₈×C₃₁	—	4	2	no	—
517	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
518	D₄×C₃₁	—	2	2	no	—
519	D₄×C₃₁	—	2	2	no	—
520	D₄×C₃₁	—	2	1	no	—
521	D₄×C₃₁	—	2	1	no	—
522	D₄×C₃₁	—	4	1	no	—
523	D₄×C₃₁	—	4	2	no	—
524	D₄×C₃₁	—	4	2	no	—
525	D₄×C₃₁	—	4	2	no	—
526	C₂×C₄×C₃₁	—	2	2	no	—
527	C₂×C₄×C₃₁	—	2	1	no	—
528	C₂×C₄×C₃₁	—	2	2	no	—
529	C₂×C₄×C₃₁	—	2	2	no	—
530	C₂×C₄×C₃₁	—	2	2	no	—
531	C₂×C₄×C₃₁	—	2	1	no	—
532	C₂×C₄×C₃₁	—	2	1	no	—
533	C₂×C₄×C₃₁	—	2	1	no	—
534	C₂×C₄×C₃₁	—	2	1	no	—
535	C₂×C₄×C₃₁	—	2	1	no	—
536	C₂×C₄×C₃₁	—	2	1	no	—
537	C₂×C₄×C₃₁	—	2	1	no	—
538	C₂×C₄×C₃₁	—	2	2	no	—
539	C₂×C₄×C₃₁	—	2	2	no	—
540	C₂×C₄×C₃₁	—	2	1	no	—
541	C₂×C₄×C₃₁	—	2	1	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	2	no	—
546	C₂×C₄×C₃₁	—	2	2	no	—
547	C₂×C₄×C₃₁	—	4	1	no	—
548	C₂×C₄×C₃₁	—	4	1	no	—
549	C₂×C₄×C₃₁	—	4	2	no	—
550	C₂×C₄×C₃₁	—	4	2	no	—
551	C₂×C₄×C₃₁	—	4	2	no	—
552	C₂×C₄×C₃₁	—	4	2	no	—
553	C₂×C₄×C₃₁	—	4	2	no	—
554	C₂×C₄×C₃₁	—	4	4	no	—
555	C₂×C₄×C₃₁	—	4	2	no	—
556	C₂×C₄×C₃₁	—	4	2	no	—
557	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
560	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
569	C₈×C₃₁	—	2	2	no	—
570	C₈×C₃₁	—	2	2	no	—
571	C₈×C₃₁	—	2	2	no	—
572	C₈×C₃₁	—	2	2	no	—
573	#3509	C₂×C₃₁	1	1	yes	characteristic, complemented
574	#3482	C₂×C₃₁	1	1	yes	characteristic
575	#3390	C₂×C₃₁	1	2	yes	complemented
576	#3377	C₂×C₃₁	1	2	yes	complemented
577	#3349	C₂×C₃₁	1	2	yes	complemented
578	#3343	C₂×C₃₁	1	2	yes	complemented
579	#3336	C₂×C₃₁	1	2	yes	complemented
580	#3313	C₂×C₃₁	1	2	yes	complemented
581	#3312	C₂×C₃₁	1	2	yes	complemented
582	#3300	C₂×C₃₁	1	2	yes	complemented
583	#3252	C₂×C₃₁	1	1	yes	characteristic, complemented
584	#3249	C₂×C₃₁	1	1	yes	characteristic, complemented
585	#3248	C₂×C₃₁	1	1	yes	characteristic, complemented
586	#3238	C₂×C₃₁	1	1	yes	characteristic, complemented
587	#3237	C₂×C₃₁	1	1	yes	characteristic, complemented
588	#3233	C₂×C₃₁	1	1	yes	characteristic, complemented
589	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
590	#3113	C₂×C₃₁	1	1	yes	characteristic, complemented
591	#3104	C₂×C₃₁	1	1	yes	characteristic, complemented
592	#3078	C₂×C₃₁	1	1	yes	characteristic, complemented
593	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
594	C₂×#477	C₂×C₃₁	1	1	yes	characteristic, complemented
595	#2990	C₂×C₃₁	1	1	yes	characteristic, complemented
596	C₂²×C₃₁	—	2	1	no	—
597	C₂²×C₃₁	—	2	1	no	—
598	C₂²×C₃₁	—	2	1	no	—
599	C₂²×C₃₁	—	2	1	no	—
600	C₂²×C₃₁	—	2	1	no	—
601	C₂²×C₃₁	—	2	1	no	—
602	C₂²×C₃₁	—	2	1	no	—
603	C₂²×C₃₁	—	2	1	no	—
604	C₂²×C₃₁	—	4	1	no	—
605	C₂²×C₃₁	—	4	1	no	—
606	C₂²×C₃₁	—	4	1	no	—
607	C₂²×C₃₁	#575	1	2	yes	—
608	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
609	C₄×C₃₁	—	2	1	no	—
610	C₄×C₃₁	—	2	1	no	—
611	C₄×C₃₁	—	2	1	no	—
612	C₄×C₃₁	—	2	2	no	—
613	C₄×C₃₁	—	2	1	no	—
614	C₄×C₃₁	—	2	1	no	—
615	C₄×C₃₁	—	2	1	no	—
616	C₄×C₃₁	—	2	1	no	—
617	C₄×C₃₁	—	2	1	no	—
618	C₄×C₃₁	—	2	1	no	—
619	C₄×C₃₁	—	2	1	no	—
620	C₄×C₃₁	—	4	1	no	—
621	C₄×C₃₁	—	4	1	no	—
622	C₄×C₃₁	—	4	2	no	—
623	C₄×C₃₁	—	4	1	no	—
624	C₄×C₃₁	—	4	1	no	—
625	C₄×C₃₁	—	4	1	no	—
626	C₄×C₃₁	—	4	2	no	—
627	C₄×C₃₁	—	4	2	no	—
628	C₄×C₃₁	—	4	1	no	—
629	C₄×C₃₁	—	4	2	no	—
630	C₄×C₃₁	#578	1	2	yes	—
631	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
632	C₄×C₃₁	#585	1	1	yes	characteristic
633	#557	—	2	1	no	—
634	#557	C₂²×C₃₁	1	2	yes	—
635	#557	C₂²×C₃₁	1	1	yes	characteristic
636	#556	—	2	1	no	—
637	#556	—	2	1	no	—
638	#556	C₂²×C₃₁	1	1	yes	characteristic
639	#556	C₂²×C₃₁	1	2	yes	—
640	#552	—	2	1	no	—
641	#552	—	2	1	no	—
642	#552	—	2	1	no	—
643	#552	—	2	1	no	—
644	#552	C₂²×C₃₁	1	1	yes	characteristic
645	#552	C₂²×C₃₁	1	2	yes	—
646	#552	C₂²×C₃₁	1	2	yes	—
647	#552	C₂²×C₃₁	1	1	yes	characteristic
648	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
649	#548	C₂²×C₃₁	1	1	yes	characteristic
650	#548	C₂²×C₃₁	1	1	yes	characteristic
651	#547	—	2	1	no	—
652	#547	C₂²×C₃₁	1	1	yes	characteristic
653	#541	—	2	1	no	—
654	#541	—	2	1	no	—
655	#536	—	2	1	no	—
656	#533	—	2	1	no	—
657	#533	C₂²×C₃₁	1	1	yes	characteristic
658	#533	C₂²×C₃₁	1	1	yes	characteristic
659	#533	C₂²×C₃₁	1	1	yes	characteristic
660	#533	C₂²×C₃₁	1	1	yes	characteristic
661	#533	C₂²×C₃₁	1	1	yes	characteristic
662	#533	C₂²×C₃₁	1	1	yes	characteristic
663	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
664	#529	—	2	1	no	—
665	#529	—	2	1	no	—
666	#529	C₂²×C₃₁	1	1	yes	characteristic
667	#529	C₂²×C₃₁	1	1	yes	characteristic
668	#519	—	2	1	no	—
669	C₄×#41	—	2	1	no	—
670	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
671	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
672	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
673	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
674	#501	C₂²×C₃₁	1	2	yes	—
675	#501	C₂²×C₃₁	1	2	yes	—
676	#499	C₂²×C₃₁	1	2	yes	—
677	#491	C₂²×C₃₁	1	2	yes	—
678	#489	C₂²×C₃₁	1	2	yes	—
679	#488	C₂²×C₃₁	1	2	yes	—
680	#485	C₂²×C₃₁	1	2	yes	—
681	#485	C₂²×C₃₁	1	2	yes	—
682	#485	C₂²×C₃₁	1	2	yes	—
683	#485	C₂²×C₃₁	1	2	yes	—
684	#484	C₂²×C₃₁	1	2	yes	—
685	#483	C₂²×C₃₁	1	2	yes	—
686	#483	C₂²×C₃₁	1	2	yes	—
687	#482	C₂²×C₃₁	1	2	yes	—
688	#480	C₂²×C₃₁	1	2	yes	—
689	#479	C₂²×C₃₁	1	2	yes	—
690	#479	C₂²×C₃₁	1	2	yes	—
691	#479	C₂²×C₃₁	1	2	yes	—
692	#479	C₂²×C₃₁	1	2	yes	—
693	#479	C₂²×C₃₁	1	2	yes	—
694	#478	C₂²×C₃₁	1	2	yes	—
695	#477	C₂²×C₃₁	1	1	yes	characteristic
696	#477	C₂²×C₃₁	1	1	yes	characteristic
697	#477	C₂²×C₃₁	1	2	yes	—
698	#477	C₂²×C₃₁	1	2	yes	—
699	#477	C₂²×C₃₁	1	1	yes	characteristic
700	#477	C₂²×C₃₁	1	1	yes	characteristic
701	#477	C₂²×C₃₁	1	1	yes	characteristic
702	#477	C₂²×C₃₁	1	2	yes	—
703	#477	C₂²×C₃₁	1	1	yes	characteristic
704	#476	C₂²×C₃₁	1	1	yes	characteristic
705	#476	C₂²×C₃₁	1	1	yes	characteristic
706	#475	C₂²×C₃₁	1	1	yes	characteristic
707	#475	C₂²×C₃₁	1	1	yes	characteristic
708	#475	C₂²×C₃₁	1	1	yes	characteristic
709	#474	C₂²×C₃₁	1	1	yes	characteristic
710	#470	C₂²×C₃₁	1	2	yes	—
711	#468	C₂²×C₃₁	1	2	yes	—
712	#467	C₂²×C₃₁	1	2	yes	—
713	#467	C₂²×C₃₁	1	2	yes	—
714	#467	C₂²×C₃₁	1	2	yes	—
715	#465	C₂²×C₃₁	1	2	yes	—
716	#464	C₂²×C₃₁	1	2	yes	—
717	#464	C₂²×C₃₁	1	2	yes	—
718	#462	C₂²×C₃₁	1	1	yes	characteristic
719	#462	C₂²×C₃₁	1	1	yes	characteristic
720	#462	C₂²×C₃₁	1	1	yes	characteristic
721	#462	C₂²×C₃₁	1	2	yes	—
722	#461	C₂²×C₃₁	1	1	yes	characteristic
723	#452	C₂²×C₃₁	1	2	yes	—
724	#451	C₂²×C₃₁	1	2	yes	—
725	#451	C₂²×C₃₁	1	2	yes	—
726	#446	C₂²×C₃₁	1	2	yes	—
727	#441	C₂²×C₃₁	1	2	yes	—
728	#441	C₂²×C₃₁	1	2	yes	—
729	#441	C₂²×C₃₁	1	2	yes	—
730	#440	C₂²×C₃₁	1	2	yes	—
731	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
732	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
733	#435	C₂²×C₃₁	1	2	yes	—
734	#435	C₂²×C₃₁	1	2	yes	—
735	C₈×D₄	C₂²×C₃₁	1	2	yes	—
736	#432	C₂²×C₃₁	1	1	yes	characteristic
737	#432	C₂²×C₃₁	1	1	yes	characteristic
738	#431	C₂²×C₃₁	1	1	yes	characteristic
739	#428	C₂²×C₃₁	1	2	yes	—
740	#427	C₂²×C₃₁	1	2	yes	—
741	C₂×#107	C₂²×C₃₁	1	2	yes	—
742	#423	C₂²×C₃₁	1	1	yes	characteristic
743	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
744	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
745	#419	C₂²×C₃₁	1	2	yes	—
746	#416	C₂²×C₃₁	1	2	yes	—
747	C₂×#103	C₂²×C₃₁	1	2	yes	—
748	C₂×C₃₁	—	2	2	no	—
749	C₂×C₃₁	—	4	1	no	—
750	C₂×C₃₁	—	4	1	no	—
751	C₂×C₃₁	—	8	1	no	—
752	C₂×C₃₁	#3489	1	1	yes	characteristic
753	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
754	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
755	C₂×#41	—	2	1	no	—
756	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
757	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
758	C₂²×Q₈	—	2	1	no	—
759	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
760	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
761	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
762	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
763	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
764	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
765	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
766	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
767	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
768	C₄⋊Q₈	—	2	1	no	—
769	C₄⋊Q₈	—	2	2	no	—
770	C₄⋊Q₈	—	2	1	no	—
771	C₄⋊Q₈	—	2	1	no	—
772	C₄⋊Q₈	—	2	1	no	—
773	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
774	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
775	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
776	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
777	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
778	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
779	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
780	#126	—	2	1	no	—
781	#126	—	2	1	no	—
782	#126	—	2	1	no	—
783	#126	—	2	1	no	—
784	#126	—	2	2	no	—
785	#126	—	2	2	no	—
786	#126	—	2	2	no	—
787	#126	—	2	2	no	—
788	#126	—	2	1	no	—
789	#126	—	2	1	no	—
790	#125	—	2	1	no	—
791	#125	—	2	1	no	—
792	#125	—	2	1	no	—
793	#125	—	2	1	no	—
794	#125	—	2	2	no	—
795	#125	—	2	2	no	—
796	#125	—	2	2	no	—
797	#125	—	2	2	no	—
798	#125	—	2	1	no	—
799	#125	—	2	1	no	—
800	#125	—	2	1	no	—
801	#125	—	2	1	no	—
802	#125	C₂³×C₃₁	1	1	yes	characteristic
803	#125	C₂³×C₃₁	1	1	yes	characteristic
804	#125	C₂³×C₃₁	1	2	yes	—
805	#125	C₂³×C₃₁	1	2	yes	—
806	#124	—	2	2	no	—
807	#124	—	2	1	no	—
808	#124	—	2	1	no	—
809	#124	C₂³×C₃₁	1	1	yes	characteristic
810	#124	C₂³×C₃₁	1	1	yes	characteristic
811	#123	—	2	1	no	—
812	#123	—	2	1	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	1	no	—
816	#123	—	2	1	no	—
817	#123	—	2	1	no	—
818	#123	—	2	1	no	—
819	C₂²⋊Q₈	—	2	1	no	—
820	C₂²⋊Q₈	—	2	1	no	—
821	C₂²⋊Q₈	—	2	1	no	—
822	C₂²⋊Q₈	—	2	1	no	—
823	C₂²⋊Q₈	—	2	1	no	—
824	C₂²⋊Q₈	—	2	1	no	—
825	C₂²⋊Q₈	—	2	1	no	—
826	C₂²⋊Q₈	—	2	1	no	—
827	C₂²⋊Q₈	—	2	1	no	—
828	C₂²⋊Q₈	—	2	1	no	—
829	C₂²⋊Q₈	—	2	1	no	—
830	C₂²⋊Q₈	—	2	1	no	—
831	C₂²⋊Q₈	—	2	1	no	—
832	C₂²⋊Q₈	—	2	1	no	—
833	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
834	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
835	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
836	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
837	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
838	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
839	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
840	#121	—	2	1	no	—
841	#121	—	2	1	no	—
842	#121	C₂³×C₃₁	1	1	yes	characteristic
843	#121	C₂³×C₃₁	1	1	yes	characteristic
844	C₄×Q₈	—	2	1	no	—
845	C₄×Q₈	—	2	2	no	—
846	C₄×Q₈	—	2	2	no	—
847	C₄×Q₈	—	2	1	no	—
848	C₄×Q₈	—	2	1	no	—
849	C₄×Q₈	—	2	1	no	—
850	C₄×Q₈	—	2	1	no	—
851	C₄×Q₈	—	2	1	no	—
852	C₄×Q₈	—	2	1	no	—
853	C₄×Q₈	—	2	1	no	—
854	C₄×Q₈	—	2	1	no	—
855	C₄×Q₈	—	2	1	no	—
856	C₄×Q₈	—	2	1	no	—
857	C₄×Q₈	—	2	1	no	—
858	C₄×Q₈	—	2	1	no	—
859	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
860	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
861	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
862	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
863	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
864	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
865	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
866	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
867	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
868	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
869	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
870	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
871	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
872	C₄×D₄	—	2	1	no	—
873	C₄×D₄	—	2	1	no	—
874	C₄×D₄	—	2	1	no	—
875	C₄×D₄	—	2	1	no	—
876	C₄×D₄	—	2	1	no	—
877	C₄×D₄	—	2	1	no	—
878	C₄×D₄	—	2	1	no	—
879	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
880	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
881	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
882	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
883	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
884	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
885	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
886	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
887	#117	—	2	1	no	—
888	#117	—	2	1	no	—
889	#117	—	2	1	no	—
890	#117	—	2	1	no	—
891	#117	—	2	1	no	—
892	#117	—	2	1	no	—
893	#117	—	2	1	no	—
894	#117	—	2	2	no	—
895	#117	—	2	2	no	—
896	#117	—	2	1	no	—
897	#117	—	2	1	no	—
898	#117	—	2	1	no	—
899	#117	D₄×C₃₁	1	1	yes	characteristic
900	#117	D₄×C₃₁	1	1	yes	characteristic
901	#117	D₄×C₃₁	1	1	yes	characteristic
902	#117	C₂³×C₃₁	1	1	yes	characteristic
903	#117	C₂³×C₃₁	1	2	yes	—
904	#117	C₂³×C₃₁	1	2	yes	—
905	C₂×C₄⋊C₄	—	2	1	no	—
906	C₂×C₄⋊C₄	—	2	1	no	—
907	C₂×C₄⋊C₄	—	2	1	no	—
908	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
909	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
910	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
911	C₂×C₄²	—	2	1	no	—
912	C₂×C₄²	—	2	1	no	—
913	C₂×C₄²	—	2	1	no	—
914	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
915	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
916	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
917	#107	C₂³×C₃₁	1	2	yes	—
918	#107	C₂³×C₃₁	1	2	yes	—
919	#107	C₂³×C₃₁	1	2	yes	—
920	#107	C₂³×C₃₁	1	2	yes	—
921	#107	C₂³×C₃₁	1	2	yes	—
922	#107	C₂³×C₃₁	1	2	yes	—
923	#107	C₂³×C₃₁	1	2	yes	—
924	#106	C₂³×C₃₁	1	2	yes	—
925	#106	C₂³×C₃₁	1	2	yes	—
926	#106	C₂³×C₃₁	1	2	yes	—
927	#106	C₂³×C₃₁	1	2	yes	—
928	#106	C₂³×C₃₁	1	2	yes	—
929	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
930	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
931	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
932	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
933	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
934	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
935	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
936	#103	C₂³×C₃₁	1	2	yes	—
937	#103	C₂³×C₃₁	1	2	yes	—
938	#103	C₂³×C₃₁	1	2	yes	—
939	#103	C₂³×C₃₁	1	2	yes	—
940	#103	C₂³×C₃₁	1	2	yes	—
941	#103	C₂³×C₃₁	1	2	yes	—
942	#103	C₂³×C₃₁	1	2	yes	—
943	#103	C₂³×C₃₁	1	2	yes	—
944	#103	C₂³×C₃₁	1	2	yes	—
945	#103	C₂³×C₃₁	1	2	yes	—
946	#103	C₂³×C₃₁	1	2	yes	—
947	#103	C₂³×C₃₁	1	2	yes	—
948	#103	C₂³×C₃₁	1	2	yes	—
949	#102	C₂³×C₃₁	1	2	yes	—
950	#102	C₂³×C₃₁	1	2	yes	—
951	#102	C₂³×C₃₁	1	2	yes	—
952	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
953	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
954	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
955	#97	C₂³×C₃₁	1	2	yes	—
956	#97	C₂³×C₃₁	1	2	yes	—
957	C₄×C₈	C₂³×C₃₁	1	2	yes	—
958	C₃₁	#62130	1	1	yes	characteristic, direct product factor, Sylow
959	#41	—	2	2	no	—
960	#41	—	4	2	no	—
961	#41	—	4	1	no	—
962	#41	—	4	4	no	—
963	C₂×Q₈	—	2	1	no	—
964	C₂×Q₈	—	2	1	no	—
965	C₂×Q₈	—	2	1	no	—
966	C₂×Q₈	—	2	1	no	—
967	C₂×Q₈	—	2	1	no	—
968	C₂×Q₈	—	2	1	no	—
969	C₂×Q₈	—	2	2	no	—
970	C₂×Q₈	—	2	2	no	—
971	C₂×Q₈	—	2	2	no	—
972	C₂×Q₈	—	4	1	no	—
973	C₂×Q₈	—	4	1	no	—
974	C₂×Q₈	—	4	4	no	—
975	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
976	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
977	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
978	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
979	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	1	no	—
983	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
984	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
985	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
986	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	2	1	no	—
989	C₂²×C₄	—	2	1	no	—
990	C₂²×C₄	—	2	1	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
996	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
997	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
998	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
999	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1000	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1001	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1002	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1003	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1004	Q₁₆	—	2	4	no	—
1005	Q₁₆	—	4	2	no	—
1006	Q₁₆	—	4	2	no	—
1007	SD₁₆	—	4	2	no	—
1008	M₁₆	—	4	2	no	—
1009	C₂×C₈	—	4	2	no	—
1010	C₂×C₈	—	4	2	no	—
1011	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1012	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1013	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1014	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	—	2	1	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	—	2	1	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	1	no	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1054	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1055	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1056	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1057	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1058	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1059	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1060	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1061	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1062	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1063	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1064	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1065	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	1	no	—
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	1	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1085	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1086	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1087	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1088	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1089	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1090	C₄²	—	2	1	no	—
1091	C₄²	—	2	1	no	—
1092	C₄²	—	2	1	no	—
1093	C₄²	—	2	1	no	—
1094	C₄²	—	2	1	no	—
1095	C₄²	—	2	1	no	—
1096	C₄²	—	2	1	no	—
1097	C₄²	—	2	1	no	—
1098	C₄²	—	2	1	no	—
1099	C₄²	—	2	2	no	—
1100	C₄²	—	2	2	no	—
1101	C₄²	—	2	2	no	—
1102	C₄²	—	2	2	no	—
1103	C₄²	—	2	2	no	—
1104	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1105	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1106	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1107	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1108	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1109	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1110	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1111	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1112	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1113	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1114	C₂³	—	2	1	no	—
1115	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1116	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1117	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1118	Q₈	—	2	1	no	—
1119	Q₈	—	2	2	no	—
1120	Q₈	—	2	1	no	—
1121	Q₈	—	2	1	no	—
1122	Q₈	—	2	2	no	—
1123	Q₈	—	2	1	no	—
1124	Q₈	—	2	1	no	—
1125	Q₈	—	4	1	no	—
1126	Q₈	—	4	2	no	—
1127	Q₈	—	4	2	no	—
1128	Q₈	—	4	2	no	—
1129	Q₈	—	4	2	no	—
1130	Q₈	—	4	4	no	—
1131	Q₈	—	4	2	no	—
1132	Q₈	—	4	2	no	—
1133	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
1134	D₄	—	2	2	no	—
1135	D₄	—	2	2	no	—
1136	D₄	—	2	1	no	—
1137	D₄	—	2	1	no	—
1138	D₄	—	4	1	no	—
1139	D₄	—	4	2	no	—
1140	D₄	—	4	2	no	—
1141	D₄	—	4	2	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	2	no	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	2	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	4	1	no	—
1164	C₂×C₄	—	4	1	no	—
1165	C₂×C₄	—	4	2	no	—
1166	C₂×C₄	—	4	2	no	—
1167	C₂×C₄	—	4	2	no	—
1168	C₂×C₄	—	4	2	no	—
1169	C₂×C₄	—	4	2	no	—
1170	C₂×C₄	—	4	4	no	—
1171	C₂×C₄	—	4	2	no	—
1172	C₂×C₄	—	4	2	no	—
1173	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1174	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1175	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1176	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1177	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1178	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1179	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1180	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1181	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1182	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1183	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1184	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1185	C₈	—	2	2	no	—
1186	C₈	—	2	2	no	—
1187	C₈	—	2	2	no	—
1188	C₈	—	2	2	no	—
1189	C₂²	—	2	1	no	—
1190	C₂²	—	2	1	no	—
1191	C₂²	—	2	1	no	—
1192	C₂²	—	2	1	no	—
1193	C₂²	—	2	1	no	—
1194	C₂²	—	2	1	no	—
1195	C₂²	—	2	1	no	—
1196	C₂²	—	2	1	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	—	4	1	no	—
1199	C₂²	—	4	1	no	—
1200	C₂²	C₃₁×#575	1	2	yes	—
1201	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1202	C₄	—	2	1	no	—
1203	C₄	—	2	1	no	—
1204	C₄	—	2	1	no	—
1205	C₄	—	2	2	no	—
1206	C₄	—	2	1	no	—
1207	C₄	—	2	1	no	—
1208	C₄	—	2	1	no	—
1209	C₄	—	2	1	no	—
1210	C₄	—	2	1	no	—
1211	C₄	—	2	1	no	—
1212	C₄	—	2	1	no	—
1213	C₄	—	4	1	no	—
1214	C₄	—	4	1	no	—
1215	C₄	—	4	2	no	—
1216	C₄	—	4	1	no	—
1217	C₄	—	4	1	no	—
1218	C₄	—	4	1	no	—
1219	C₄	—	4	2	no	—
1220	C₄	—	4	2	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	4	2	no	—
1223	C₄	C₃₁×#578	1	2	yes	—
1224	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1225	C₄	C₃₁×#585	1	1	yes	characteristic
1226	C₂	—	2	2	no	—
1227	C₂	—	4	1	no	—
1228	C₂	—	4	1	no	—
1229	C₂	—	8	1	no	—
1230	C₂	C₃₁×#3489	1	1	yes	characteristic
1231	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1232	C₂	C₂×C₃₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3482	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3509	C₂	semidirect
3. C₃₁×#3390	C₂	semidirect
4. C₃₁×#3377	C₂	semidirect
5. C₃₁×#3349	C₂	semidirect
6. C₃₁×#3343	C₂	semidirect
7. C₃₁×#3336	C₂	semidirect
8. C₃₁×#3313	C₂	semidirect
9. C₃₁×#3312	C₂	semidirect
10. C₃₁×#3300	C₂	semidirect
11. C₃₁×#3252	C₂	semidirect
12. C₃₁×#3249	C₂	semidirect
13. C₃₁×#3248	C₂	semidirect
14. C₃₁×#3238	C₂	semidirect
15. C₃₁×#3237	C₂	semidirect
16. C₃₁×#3233	C₂	semidirect
17. C₃₁×#3116	C₂	semidirect
18. C₃₁×#3113	C₂	semidirect
19. C₃₁×#3104	C₂	semidirect
20. C₃₁×#3078	C₂	semidirect
21. C₃₁×#3076	C₂	semidirect
22. C₂×C₃₁×#477	C₂	semidirect
23. C₃₁×#2990	C₂	semidirect
497. #62130	C₃₁	direct (N × H)
573. #3509	C₂×C₃₁	semidirect
575. #3390	C₂×C₃₁	semidirect
576. #3377	C₂×C₃₁	semidirect
577. #3349	C₂×C₃₁	semidirect
578. #3343	C₂×C₃₁	semidirect
579. #3336	C₂×C₃₁	semidirect
580. #3313	C₂×C₃₁	semidirect
581. #3312	C₂×C₃₁	semidirect
582. #3300	C₂×C₃₁	semidirect
583. #3252	C₂×C₃₁	semidirect
584. #3249	C₂×C₃₁	semidirect
585. #3248	C₂×C₃₁	semidirect
586. #3238	C₂×C₃₁	semidirect
587. #3237	C₂×C₃₁	semidirect
588. #3233	C₂×C₃₁	semidirect
589. #3116	C₂×C₃₁	semidirect
590. #3113	C₂×C₃₁	semidirect
591. #3104	C₂×C₃₁	semidirect
592. #3078	C₂×C₃₁	semidirect
593. #3076	C₂×C₃₁	semidirect
594. C₂×#477	C₂×C₃₁	semidirect
595. #2990	C₂×C₃₁	semidirect
958. C₃₁	#62130	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3509	2
C₃₁×#3482	2
C₃₁×#3390	2
C₃₁×#3377	2
C₃₁×#3349	2
C₃₁×#3343	2
C₃₁×#3336	2
C₃₁×#3313	2
C₃₁×#3312	2
C₃₁×#3300	2
C₃₁×#3252	2
C₃₁×#3249	2
C₃₁×#3248	2
C₃₁×#3238	2
C₃₁×#3237	2
C₃₁×#3233	2
C₃₁×#3116	2
C₃₁×#3113	2
C₃₁×#3104	2
C₃₁×#3078	2
C₃₁×#3076	2
C₂×C₃₁×#477	2
C₃₁×#2990	2
#62130	31

Subgroups — C31×#62130 #21518889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62130 #21518889