Subgroups — C₃₁×#60993 #21517752

Order 7936.

1718 conjugacy classes of subgroups.

The subgroup lattice has 1264 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×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3252	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3249	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3247	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3243	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3238	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3230	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3225	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3216	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3212	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3203	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3201	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3178	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3175	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3124	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3120	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3104	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#556	—	2	1	no	—
25	C₃₁×#555	—	2	1	no	—
26	C₃₁×#554	—	2	1	no	—
27	C₃₁×#553	—	2	1	no	—
28	C₃₁×#553	—	2	1	no	—
29	C₃₁×#548	—	2	1	no	—
30	C₃₁×#548	—	2	1	no	—
31	C₃₁×#547	—	2	1	no	—
32	C₃₁×#544	C₂²	1	1	yes	characteristic
33	C₃₁×#542	—	2	1	no	—
34	C₃₁×#542	C₂²	1	1	yes	characteristic
35	C₃₁×#542	C₂²	1	1	yes	characteristic
36	C₃₁×#542	C₂²	1	2	yes	—
37	C₃₁×#542	C₂²	1	2	yes	—
38	C₃₁×#541	—	2	1	no	—
39	C₃₁×#541	C₂²	1	1	yes	characteristic
40	C₃₁×#541	C₂²	1	1	yes	characteristic
41	C₃₁×#539	—	2	1	no	—
42	C₃₁×#539	—	2	1	no	—
43	C₃₁×#537	C₂²	1	2	yes	—
44	C₃₁×#537	C₂²	1	1	yes	characteristic
45	C₃₁×#536	C₂²	1	1	yes	characteristic
46	C₃₁×#536	C₂²	1	1	yes	characteristic
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×#532	C₂²	1	1	yes	characteristic
53	C₃₁×#532	C₂²	1	1	yes	characteristic
54	C₃₁×#532	C₂²	1	1	yes	characteristic
55	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
56	C₃₁×#529	—	2	1	no	—
57	C₃₁×#529	—	2	1	no	—
58	C₃₁×#529	—	2	1	no	—
59	C₃₁×#529	C₂²	1	1	yes	characteristic
60	C₃₁×#529	C₂²	1	1	yes	characteristic
61	C₃₁×#520	C₂²	1	2	yes	—
62	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
63	C₄×#41×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×#500	C₂²	1	2	yes	—
67	C₃₁×#497	C₂²	1	2	yes	—
68	C₃₁×#495	C₂²	1	2	yes	—
69	C₃₁×#489	C₂²	1	2	yes	—
70	C₃₁×#489	C₂²	1	2	yes	—
71	C₃₁×#488	C₂²	1	2	yes	—
72	C₃₁×#487	C₂²	1	2	yes	—
73	C₃₁×#485	C₂²	1	2	yes	—
74	C₃₁×#484	C₂²	1	2	yes	—
75	C₃₁×#484	C₂²	1	2	yes	—
76	C₃₁×#484	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×#480	C₂²	1	2	yes	—
81	C₃₁×#479	C₂²	1	2	yes	—
82	C₃₁×#478	C₂²	1	2	yes	—
83	C₃₁×#477	C₂²	1	1	yes	characteristic
84	C₃₁×#477	C₂²	1	1	yes	characteristic
85	C₃₁×#477	C₂²	1	1	yes	characteristic
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×#476	C₂²	1	1	yes	characteristic
91	C₃₁×#476	C₂²	1	1	yes	characteristic
92	C₃₁×#474	C₂²	1	2	yes	—
93	C₃₁×#470	C₂²	1	2	yes	—
94	C₃₁×#468	C₂²	1	2	yes	—
95	C₃₁×#468	C₂²	1	2	yes	—
96	C₃₁×#468	C₂²	1	2	yes	—
97	C₃₁×#467	C₂²	1	2	yes	—
98	C₃₁×#467	C₂²	1	2	yes	—
99	C₃₁×#466	C₂²	1	2	yes	—
100	C₃₁×#465	C₂²	1	2	yes	—
101	C₃₁×#464	C₂²	1	2	yes	—
102	C₃₁×#463	C₂²	1	2	yes	—
103	C₃₁×#462	C₂²	1	1	yes	characteristic
104	C₃₁×#462	C₂²	1	1	yes	characteristic
105	C₃₁×#462	C₂²	1	1	yes	characteristic
106	C₃₁×#462	C₂²	1	2	yes	—
107	C₃₁×#461	C₂²	1	1	yes	characteristic
108	C₃₁×#461	C₂²	1	2	yes	—
109	C₃₁×#460	C₂²	1	1	yes	characteristic
110	C₃₁×#460	C₂²	1	1	yes	characteristic
111	C₃₁×#460	C₂²	1	1	yes	characteristic
112	C₃₁×#459	C₂²	1	1	yes	characteristic
113	C₃₁×#452	C₂²	1	2	yes	—
114	C₃₁×#452	C₂²	1	2	yes	—
115	C₃₁×#452	C₂²	1	2	yes	—
116	C₃₁×#452	C₂²	1	2	yes	—
117	C₃₁×#451	C₂²	1	2	yes	—
118	C₃₁×#449	C₂²	1	2	yes	—
119	C₃₁×#449	C₂²	1	2	yes	—
120	C₃₁×#448	C₂²	1	2	yes	—
121	C₃₁×#441	C₂²	1	2	yes	—
122	C₃₁×#440	C₂²	1	2	yes	—
123	C₃₁×#440	C₂²	1	2	yes	—
124	C₃₁×#440	C₂²	1	2	yes	—
125	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
126	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
127	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
128	C₄×D₈×C₃₁	C₂²	1	2	yes	—
129	C₃₁×#433	C₂²	1	2	yes	—
130	C₃₁×#433	C₂²	1	2	yes	—
131	C₃₁×#432	C₂²	1	1	yes	characteristic
132	C₃₁×#432	C₂²	1	1	yes	characteristic
133	C₃₁×#431	C₂²	1	1	yes	characteristic
134	C₃₁×#431	C₂²	1	1	yes	characteristic
135	C₃₁×#423	C₂²	1	1	yes	characteristic
136	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
137	C₃₁×#408	C₂²	1	2	yes	—
138	C₃₁×#405	C₂²	1	2	yes	—
139	C₂×#41×C₃₁	—	2	1	no	—
140	C₂×#41×C₃₁	—	2	1	no	—
141	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×#41×C₃₁	C₂³	1	2	yes	—
143	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₃₁	—	2	1	no	—
145	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×D₈×C₃₁	C₂³	1	2	yes	—
154	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
156	C₃₁×C₄⋊Q₈	—	2	1	no	—
157	C₃₁×C₄⋊Q₈	—	2	1	no	—
158	C₃₁×C₄⋊Q₈	—	2	1	no	—
159	C₃₁×C₄⋊Q₈	—	2	1	no	—
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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₃₁×#127	C₂³	1	1	yes	characteristic
169	C₃₁×#126	—	2	1	no	—
170	C₃₁×#126	—	2	1	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	—	2	1	no	—
174	C₃₁×#126	—	2	1	no	—
175	C₃₁×#126	—	2	1	no	—
176	C₃₁×#126	—	2	1	no	—
177	C₃₁×#126	—	2	1	no	—
178	C₃₁×#126	—	2	1	no	—
179	C₃₁×#125	—	2	1	no	—
180	C₃₁×#125	—	2	1	no	—
181	C₃₁×#125	—	2	1	no	—
182	C₃₁×#125	—	2	1	no	—
183	C₃₁×#125	—	2	1	no	—
184	C₃₁×#125	—	2	1	no	—
185	C₃₁×#125	—	2	1	no	—
186	C₃₁×#125	—	2	1	no	—
187	C₃₁×#125	—	2	1	no	—
188	C₃₁×#125	C₂³	1	1	yes	characteristic
189	C₃₁×#125	C₂³	1	1	yes	characteristic
190	C₃₁×#124	—	2	1	no	—
191	C₃₁×#124	—	2	1	no	—
192	C₃₁×#124	—	2	1	no	—
193	C₃₁×#124	—	2	2	no	—
194	C₃₁×#124	—	2	2	no	—
195	C₃₁×#124	—	2	1	no	—
196	C₃₁×#124	—	2	1	no	—
197	C₃₁×#124	C₂³	1	1	yes	characteristic
198	C₃₁×#124	C₂³	1	2	yes	—
199	C₃₁×#124	C₂³	1	1	yes	characteristic
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	1	no	—
207	C₃₁×#123	—	2	1	no	—
208	C₃₁×#123	—	2	2	no	—
209	C₃₁×#123	—	2	2	no	—
210	C₃₁×C₂²⋊Q₈	—	2	1	no	—
211	C₃₁×C₂²⋊Q₈	—	2	2	no	—
212	C₃₁×C₂²⋊Q₈	—	2	1	no	—
213	C₃₁×C₂²⋊Q₈	—	2	1	no	—
214	C₃₁×C₂²⋊Q₈	—	2	1	no	—
215	C₃₁×C₂²⋊Q₈	—	2	1	no	—
216	C₃₁×C₂²⋊Q₈	—	2	1	no	—
217	C₃₁×C₂²⋊Q₈	—	2	1	no	—
218	C₃₁×C₂²⋊Q₈	—	2	1	no	—
219	C₃₁×C₂²⋊Q₈	—	2	1	no	—
220	C₃₁×C₂²⋊Q₈	—	2	2	no	—
221	C₃₁×C₂²⋊Q₈	—	2	2	no	—
222	C₃₁×C₂²⋊Q₈	—	2	1	no	—
223	C₃₁×C₂²⋊Q₈	—	2	1	no	—
224	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
226	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
227	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
228	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
229	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
230	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
231	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
232	C₃₁×#121	—	2	1	no	—
233	C₃₁×#121	—	2	1	no	—
234	C₃₁×#121	—	2	1	no	—
235	C₃₁×#121	—	2	2	no	—
236	C₃₁×#121	—	2	2	no	—
237	C₃₁×#121	—	2	2	no	—
238	C₃₁×#121	—	2	1	no	—
239	C₃₁×#121	—	2	1	no	—
240	C₃₁×#121	—	2	1	no	—
241	C₃₁×#121	—	2	1	no	—
242	C₃₁×#121	C₂³	1	2	yes	—
243	C₃₁×#121	C₂³	1	1	yes	characteristic
244	C₃₁×#121	C₂³	1	2	yes	—
245	C₃₁×#121	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
251	C₄×Q₈×C₃₁	—	2	1	no	—
252	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
253	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
254	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
255	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
256	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
257	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
258	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
259	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
260	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
261	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
262	C₄×D₄×C₃₁	—	2	1	no	—
263	C₄×D₄×C₃₁	—	2	1	no	—
264	C₄×D₄×C₃₁	—	2	1	no	—
265	C₄×D₄×C₃₁	—	2	1	no	—
266	C₄×D₄×C₃₁	—	2	2	no	—
267	C₄×D₄×C₃₁	—	2	2	no	—
268	C₄×D₄×C₃₁	—	2	1	no	—
269	C₄×D₄×C₃₁	—	2	1	no	—
270	C₄×D₄×C₃₁	—	2	1	no	—
271	C₄×D₄×C₃₁	—	2	1	no	—
272	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
273	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
274	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
275	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
276	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
277	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
278	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
279	C₄×D₄×C₃₁	C₂³	1	2	yes	—
280	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
281	C₄×D₄×C₃₁	C₂³	1	2	yes	—
282	C₃₁×#117	—	2	1	no	—
283	C₃₁×#117	—	2	1	no	—
284	C₃₁×#117	—	2	1	no	—
285	C₃₁×#117	—	2	1	no	—
286	C₃₁×#117	—	2	2	no	—
287	C₃₁×#117	—	2	1	no	—
288	C₃₁×#117	—	2	1	no	—
289	C₃₁×#117	—	2	1	no	—
290	C₃₁×#117	C₂³	1	1	yes	characteristic
291	C₃₁×#117	C₂³	1	1	yes	characteristic
292	C₃₁×#117	C₂³	1	1	yes	characteristic
293	C₃₁×#117	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
295	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
296	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
297	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
299	C₂×C₄²×C₃₁	—	2	1	no	—
300	C₂×C₄²×C₃₁	—	2	1	no	—
301	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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×#107	C₂³	1	2	yes	—
309	C₃₁×#107	C₂³	1	2	yes	—
310	C₃₁×#106	C₂³	1	2	yes	—
311	C₃₁×#106	C₂³	1	2	yes	—
312	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
313	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
314	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
315	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
316	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
317	C₃₁×C₄⋊C₈	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×#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×#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×C₂²⋊C₈	C₂³	1	2	yes	—
335	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
336	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
337	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₃₁×#97	C₂³	1	2	yes	—
339	C₃₁×#97	C₂³	1	2	yes	—
340	C₄×C₈×C₃₁	C₂³	1	2	yes	—
341	C₄×C₈×C₃₁	C₂³	1	2	yes	—
342	#41×C₃₁	—	4	1	no	—
343	#41×C₃₁	—	4	1	no	—
344	#41×C₃₁	—	4	1	no	—
345	#41×C₃₁	—	4	1	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	1	no	—
357	C₂×Q₈×C₃₁	—	4	1	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	2	yes	—
363	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂×D₄×C₃₁	—	2	2	no	—
365	C₂×D₄×C₃₁	—	2	1	no	—
366	C₂×D₄×C₃₁	—	2	1	no	—
367	C₂×D₄×C₃₁	—	2	1	no	—
368	C₂×D₄×C₃₁	—	2	2	no	—
369	C₂×D₄×C₃₁	—	2	2	no	—
370	C₂×D₄×C₃₁	—	2	1	no	—
371	C₂×D₄×C₃₁	—	2	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	C₂²×C₄×C₃₁	—	2	1	no	—
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	2	no	—
383	C₂²×C₄×C₃₁	—	2	1	no	—
384	C₂²×C₄×C₃₁	—	2	2	no	—
385	C₂²×C₄×C₃₁	—	2	2	no	—
386	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
395	Q₁₆×C₃₁	—	4	2	no	—
396	Q₁₆×C₃₁	—	4	2	no	—
397	Q₁₆×C₃₁	—	4	2	no	—
398	SD₁₆×C₃₁	—	4	2	no	—
399	SD₁₆×C₃₁	—	4	2	no	—
400	SD₁₆×C₃₁	—	4	2	no	—
401	SD₁₆×C₃₁	—	4	2	no	—
402	D₈×C₃₁	—	4	2	no	—
403	M₁₆×C₃₁	—	4	2	no	—
404	C₂×C₈×C₃₁	—	4	2	no	—
405	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
406	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
407	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
408	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₃₁	—	2	2	no	—
410	C₄⋊C₄×C₃₁	—	2	1	no	—
411	C₄⋊C₄×C₃₁	—	2	1	no	—
412	C₄⋊C₄×C₃₁	—	2	2	no	—
413	C₄⋊C₄×C₃₁	—	2	2	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	2	no	—
419	C₄⋊C₄×C₃₁	—	2	1	no	—
420	C₄⋊C₄×C₃₁	—	2	1	no	—
421	C₄⋊C₄×C₃₁	—	2	1	no	—
422	C₄⋊C₄×C₃₁	—	2	1	no	—
423	C₄⋊C₄×C₃₁	—	2	1	no	—
424	C₄⋊C₄×C₃₁	—	2	1	no	—
425	C₄⋊C₄×C₃₁	—	2	1	no	—
426	C₄⋊C₄×C₃₁	—	2	1	no	—
427	C₄⋊C₄×C₃₁	—	2	1	no	—
428	C₄⋊C₄×C₃₁	—	2	1	no	—
429	C₄⋊C₄×C₃₁	—	2	1	no	—
430	C₄⋊C₄×C₃₁	—	2	1	no	—
431	C₄⋊C₄×C₃₁	—	2	1	no	—
432	C₄⋊C₄×C₃₁	—	2	1	no	—
433	C₄⋊C₄×C₃₁	—	2	1	no	—
434	C₄⋊C₄×C₃₁	—	2	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	—	2	1	no	—
440	C₄⋊C₄×C₃₁	—	2	1	no	—
441	C₄⋊C₄×C₃₁	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
451	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
453	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	2	no	—
464	C₂²⋊C₄×C₃₁	—	2	2	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	1	no	—
471	C₂²⋊C₄×C₃₁	—	2	2	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	1	no	—
476	C₂²⋊C₄×C₃₁	—	2	1	no	—
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	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	1	no	—
489	C₄²×C₃₁	—	2	1	no	—
490	C₄²×C₃₁	—	2	2	no	—
491	C₄²×C₃₁	—	2	2	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	#60993	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	C₂²×D₄	1	1	yes	characteristic
506	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
507	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
508	Q₈×C₃₁	—	2	1	no	—
509	Q₈×C₃₁	—	2	1	no	—
510	Q₈×C₃₁	—	2	1	no	—
511	Q₈×C₃₁	—	2	2	no	—
512	Q₈×C₃₁	—	2	1	no	—
513	Q₈×C₃₁	—	2	1	no	—
514	Q₈×C₃₁	—	2	2	no	—
515	Q₈×C₃₁	—	2	1	no	—
516	Q₈×C₃₁	—	4	1	no	—
517	Q₈×C₃₁	—	4	2	no	—
518	Q₈×C₃₁	—	4	2	no	—
519	Q₈×C₃₁	—	4	2	no	—
520	Q₈×C₃₁	—	8	1	no	—
521	Q₈×C₃₁	—	8	1	no	—
522	Q₈×C₃₁	—	8	2	no	—
523	D₄×C₃₁	—	2	1	no	—
524	D₄×C₃₁	—	2	2	no	—
525	D₄×C₃₁	—	2	1	no	—
526	D₄×C₃₁	—	2	2	no	—
527	D₄×C₃₁	—	4	1	no	—
528	D₄×C₃₁	—	4	1	no	—
529	D₄×C₃₁	—	4	1	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	C₂×C₄×C₃₁	—	2	2	no	—
539	C₂×C₄×C₃₁	—	2	2	no	—
540	C₂×C₄×C₃₁	—	2	2	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	1	no	—
546	C₂×C₄×C₃₁	—	2	1	no	—
547	C₂×C₄×C₃₁	—	2	1	no	—
548	C₂×C₄×C₃₁	—	2	2	no	—
549	C₂×C₄×C₃₁	—	2	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	1	no	—
554	C₂×C₄×C₃₁	—	2	1	no	—
555	C₂×C₄×C₃₁	—	2	2	no	—
556	C₂×C₄×C₃₁	—	2	2	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	4	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	—	8	1	no	—
565	C₂×C₄×C₃₁	—	8	2	no	—
566	C₂×C₄×C₃₁	—	8	2	no	—
567	C₂×C₄×C₃₁	—	8	1	no	—
568	C₂×C₄×C₃₁	—	8	2	no	—
569	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄×C₃₁	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	C₂⁵	1	1	yes	characteristic
581	C₈×C₃₁	—	2	2	no	—
582	C₈×C₃₁	—	2	2	no	—
583	C₈×C₃₁	—	2	2	no	—
584	C₈×C₃₁	—	2	2	no	—
585	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
586	#3461	C₂×C₃₁	1	1	yes	characteristic, complemented
587	#3254	C₂×C₃₁	1	1	yes	characteristic, complemented
588	#3252	C₂×C₃₁	1	1	yes	characteristic, complemented
589	#3249	C₂×C₃₁	1	1	yes	characteristic, complemented
590	#3247	C₂×C₃₁	1	1	yes	characteristic, complemented
591	#3243	C₂×C₃₁	1	2	yes	complemented
592	#3238	C₂×C₃₁	1	1	yes	characteristic, complemented
593	#3230	C₂×C₃₁	1	1	yes	characteristic, complemented
594	#3225	C₂×C₃₁	1	2	yes	complemented
595	#3216	C₂×C₃₁	1	1	yes	characteristic, complemented
596	#3212	C₂×C₃₁	1	1	yes	characteristic, complemented
597	#3203	C₂×C₃₁	1	2	yes	complemented
598	#3201	C₂×C₃₁	1	2	yes	complemented
599	#3178	C₂×C₃₁	1	2	yes	complemented
600	#3175	C₂×C₃₁	1	2	yes	complemented
601	#3124	C₂×C₃₁	1	2	yes	complemented
602	#3120	C₂×C₃₁	1	2	yes	complemented
603	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
604	#3112	C₂×C₃₁	1	1	yes	characteristic, complemented
605	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
606	#3104	C₂×C₃₁	1	1	yes	characteristic, complemented
607	#2925	C₂×C₃₁	1	1	yes	characteristic, complemented
608	C₂²×C₃₁	—	2	1	no	—
609	C₂²×C₃₁	—	2	1	no	—
610	C₂²×C₃₁	—	2	1	no	—
611	C₂²×C₃₁	—	2	1	no	—
612	C₂²×C₃₁	—	2	1	no	—
613	C₂²×C₃₁	—	2	1	no	—
614	C₂²×C₃₁	—	2	1	no	—
615	C₂²×C₃₁	—	2	1	no	—
616	C₂²×C₃₁	—	2	1	no	—
617	C₂²×C₃₁	—	4	2	no	—
618	C₂²×C₃₁	—	4	1	no	—
619	C₂²×C₃₁	—	4	1	no	—
620	C₂²×C₃₁	—	4	2	no	—
621	C₂²×C₃₁	—	4	1	no	—
622	C₂²×C₃₁	—	4	2	no	—
623	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
624	C₄×C₃₁	—	2	1	no	—
625	C₄×C₃₁	—	2	1	no	—
626	C₄×C₃₁	—	2	1	no	—
627	C₄×C₃₁	—	2	1	no	—
628	C₄×C₃₁	—	2	1	no	—
629	C₄×C₃₁	—	2	1	no	—
630	C₄×C₃₁	—	2	1	no	—
631	C₄×C₃₁	—	2	1	no	—
632	C₄×C₃₁	—	2	1	no	—
633	C₄×C₃₁	—	2	1	no	—
634	C₄×C₃₁	—	4	2	no	—
635	C₄×C₃₁	—	4	2	no	—
636	C₄×C₃₁	—	4	1	no	—
637	C₄×C₃₁	—	4	1	no	—
638	C₄×C₃₁	—	4	1	no	—
639	C₄×C₃₁	—	4	2	no	—
640	C₄×C₃₁	—	4	1	no	—
641	C₄×C₃₁	—	4	1	no	—
642	C₄×C₃₁	—	4	1	no	—
643	C₄×C₃₁	—	4	1	no	—
644	C₄×C₃₁	#578	1	2	yes	—
645	C₄×C₃₁	#585	1	1	yes	characteristic
646	C₄×C₃₁	#585	1	1	yes	characteristic
647	#556	—	2	1	no	—
648	#555	—	2	1	no	—
649	#554	—	2	1	no	—
650	#553	—	2	1	no	—
651	#553	—	2	1	no	—
652	#548	—	2	1	no	—
653	#548	—	2	1	no	—
654	#547	—	2	1	no	—
655	#544	C₂²×C₃₁	1	1	yes	characteristic
656	#542	—	2	1	no	—
657	#542	C₂²×C₃₁	1	1	yes	characteristic
658	#542	C₂²×C₃₁	1	1	yes	characteristic
659	#542	C₂²×C₃₁	1	2	yes	—
660	#542	C₂²×C₃₁	1	2	yes	—
661	#541	—	2	1	no	—
662	#541	C₂²×C₃₁	1	1	yes	characteristic
663	#541	C₂²×C₃₁	1	1	yes	characteristic
664	#539	—	2	1	no	—
665	#539	—	2	1	no	—
666	#537	C₂²×C₃₁	1	2	yes	—
667	#537	C₂²×C₃₁	1	1	yes	characteristic
668	#536	C₂²×C₃₁	1	1	yes	characteristic
669	#536	C₂²×C₃₁	1	1	yes	characteristic
670	#533	—	2	1	no	—
671	#533	C₂²×C₃₁	1	1	yes	characteristic
672	#533	C₂²×C₃₁	1	1	yes	characteristic
673	#533	C₂²×C₃₁	1	1	yes	characteristic
674	#533	C₂²×C₃₁	1	1	yes	characteristic
675	#532	C₂²×C₃₁	1	1	yes	characteristic
676	#532	C₂²×C₃₁	1	1	yes	characteristic
677	#532	C₂²×C₃₁	1	1	yes	characteristic
678	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
679	#529	—	2	1	no	—
680	#529	—	2	1	no	—
681	#529	—	2	1	no	—
682	#529	C₂²×C₃₁	1	1	yes	characteristic
683	#529	C₂²×C₃₁	1	1	yes	characteristic
684	#520	C₂²×C₃₁	1	2	yes	—
685	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
686	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
687	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
688	#501	C₂²×C₃₁	1	2	yes	—
689	#500	C₂²×C₃₁	1	2	yes	—
690	#497	C₂²×C₃₁	1	2	yes	—
691	#495	C₂²×C₃₁	1	2	yes	—
692	#489	C₂²×C₃₁	1	2	yes	—
693	#489	C₂²×C₃₁	1	2	yes	—
694	#488	C₂²×C₃₁	1	2	yes	—
695	#487	C₂²×C₃₁	1	2	yes	—
696	#485	C₂²×C₃₁	1	2	yes	—
697	#484	C₂²×C₃₁	1	2	yes	—
698	#484	C₂²×C₃₁	1	2	yes	—
699	#484	C₂²×C₃₁	1	2	yes	—
700	#483	C₂²×C₃₁	1	2	yes	—
701	#482	C₂²×C₃₁	1	2	yes	—
702	#480	C₂²×C₃₁	1	2	yes	—
703	#480	C₂²×C₃₁	1	2	yes	—
704	#479	C₂²×C₃₁	1	2	yes	—
705	#478	C₂²×C₃₁	1	2	yes	—
706	#477	C₂²×C₃₁	1	1	yes	characteristic
707	#477	C₂²×C₃₁	1	1	yes	characteristic
708	#477	C₂²×C₃₁	1	1	yes	characteristic
709	#477	C₂²×C₃₁	1	1	yes	characteristic
710	#477	C₂²×C₃₁	1	1	yes	characteristic
711	#477	C₂²×C₃₁	1	1	yes	characteristic
712	#477	C₂²×C₃₁	1	2	yes	—
713	#476	C₂²×C₃₁	1	1	yes	characteristic
714	#476	C₂²×C₃₁	1	1	yes	characteristic
715	#474	C₂²×C₃₁	1	2	yes	—
716	#470	C₂²×C₃₁	1	2	yes	—
717	#468	C₂²×C₃₁	1	2	yes	—
718	#468	C₂²×C₃₁	1	2	yes	—
719	#468	C₂²×C₃₁	1	2	yes	—
720	#467	C₂²×C₃₁	1	2	yes	—
721	#467	C₂²×C₃₁	1	2	yes	—
722	#466	C₂²×C₃₁	1	2	yes	—
723	#465	C₂²×C₃₁	1	2	yes	—
724	#464	C₂²×C₃₁	1	2	yes	—
725	#463	C₂²×C₃₁	1	2	yes	—
726	#462	C₂²×C₃₁	1	1	yes	characteristic
727	#462	C₂²×C₃₁	1	1	yes	characteristic
728	#462	C₂²×C₃₁	1	1	yes	characteristic
729	#462	C₂²×C₃₁	1	2	yes	—
730	#461	C₂²×C₃₁	1	1	yes	characteristic
731	#461	C₂²×C₃₁	1	2	yes	—
732	#460	C₂²×C₃₁	1	1	yes	characteristic
733	#460	C₂²×C₃₁	1	1	yes	characteristic
734	#460	C₂²×C₃₁	1	1	yes	characteristic
735	#459	C₂²×C₃₁	1	1	yes	characteristic
736	#452	C₂²×C₃₁	1	2	yes	—
737	#452	C₂²×C₃₁	1	2	yes	—
738	#452	C₂²×C₃₁	1	2	yes	—
739	#452	C₂²×C₃₁	1	2	yes	—
740	#451	C₂²×C₃₁	1	2	yes	—
741	#449	C₂²×C₃₁	1	2	yes	—
742	#449	C₂²×C₃₁	1	2	yes	—
743	#448	C₂²×C₃₁	1	2	yes	—
744	#441	C₂²×C₃₁	1	2	yes	—
745	#440	C₂²×C₃₁	1	2	yes	—
746	#440	C₂²×C₃₁	1	2	yes	—
747	#440	C₂²×C₃₁	1	2	yes	—
748	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
749	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
750	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
751	C₄×D₈	C₂²×C₃₁	1	2	yes	—
752	#433	C₂²×C₃₁	1	2	yes	—
753	#433	C₂²×C₃₁	1	2	yes	—
754	#432	C₂²×C₃₁	1	1	yes	characteristic
755	#432	C₂²×C₃₁	1	1	yes	characteristic
756	#431	C₂²×C₃₁	1	1	yes	characteristic
757	#431	C₂²×C₃₁	1	1	yes	characteristic
758	#423	C₂²×C₃₁	1	1	yes	characteristic
759	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
760	#408	C₂²×C₃₁	1	2	yes	—
761	#405	C₂²×C₃₁	1	2	yes	—
762	C₂×C₃₁	—	4	1	no	—
763	C₂×C₃₁	—	4	1	no	—
764	C₂×C₃₁	—	4	1	no	—
765	C₂×C₃₁	—	8	2	no	—
766	C₂×C₃₁	—	8	1	no	—
767	C₂×C₃₁	#3449	1	1	yes	characteristic
768	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
769	C₂×C₃₁	#3585	1	1	yes	characteristic
770	C₂×#41	—	2	1	no	—
771	C₂×#41	—	2	1	no	—
772	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
773	C₂×#41	C₂³×C₃₁	1	2	yes	—
774	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
775	C₂²×Q₈	—	2	1	no	—
776	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
777	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
778	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
779	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
780	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
781	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
782	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
783	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
784	C₂×D₈	C₂³×C₃₁	1	2	yes	—
785	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
786	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
787	C₄⋊Q₈	—	2	1	no	—
788	C₄⋊Q₈	—	2	1	no	—
789	C₄⋊Q₈	—	2	1	no	—
790	C₄⋊Q₈	—	2	1	no	—
791	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
792	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
793	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
794	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
795	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
796	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
797	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
798	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
799	#127	C₂³×C₃₁	1	1	yes	characteristic
800	#126	—	2	1	no	—
801	#126	—	2	1	no	—
802	#126	—	2	2	no	—
803	#126	—	2	2	no	—
804	#126	—	2	1	no	—
805	#126	—	2	1	no	—
806	#126	—	2	1	no	—
807	#126	—	2	1	no	—
808	#126	—	2	1	no	—
809	#126	—	2	1	no	—
810	#125	—	2	1	no	—
811	#125	—	2	1	no	—
812	#125	—	2	1	no	—
813	#125	—	2	1	no	—
814	#125	—	2	1	no	—
815	#125	—	2	1	no	—
816	#125	—	2	1	no	—
817	#125	—	2	1	no	—
818	#125	—	2	1	no	—
819	#125	C₂³×C₃₁	1	1	yes	characteristic
820	#125	C₂³×C₃₁	1	1	yes	characteristic
821	#124	—	2	1	no	—
822	#124	—	2	1	no	—
823	#124	—	2	1	no	—
824	#124	—	2	2	no	—
825	#124	—	2	2	no	—
826	#124	—	2	1	no	—
827	#124	—	2	1	no	—
828	#124	C₂³×C₃₁	1	1	yes	characteristic
829	#124	C₂³×C₃₁	1	1	yes	characteristic
830	#124	C₂³×C₃₁	1	2	yes	—
831	#123	—	2	1	no	—
832	#123	—	2	1	no	—
833	#123	—	2	1	no	—
834	#123	—	2	1	no	—
835	#123	—	2	1	no	—
836	#123	—	2	1	no	—
837	#123	—	2	1	no	—
838	#123	—	2	1	no	—
839	#123	—	2	2	no	—
840	#123	—	2	2	no	—
841	C₂²⋊Q₈	—	2	1	no	—
842	C₂²⋊Q₈	—	2	2	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	1	no	—
848	C₂²⋊Q₈	—	2	1	no	—
849	C₂²⋊Q₈	—	2	1	no	—
850	C₂²⋊Q₈	—	2	1	no	—
851	C₂²⋊Q₈	—	2	2	no	—
852	C₂²⋊Q₈	—	2	2	no	—
853	C₂²⋊Q₈	—	2	1	no	—
854	C₂²⋊Q₈	—	2	1	no	—
855	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
856	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
857	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
858	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
859	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
860	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
861	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
862	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
863	#121	—	2	1	no	—
864	#121	—	2	1	no	—
865	#121	—	2	1	no	—
866	#121	—	2	2	no	—
867	#121	—	2	2	no	—
868	#121	—	2	2	no	—
869	#121	—	2	1	no	—
870	#121	—	2	1	no	—
871	#121	—	2	1	no	—
872	#121	—	2	1	no	—
873	#121	C₂³×C₃₁	1	1	yes	characteristic
874	#121	C₂³×C₃₁	1	1	yes	characteristic
875	#121	C₂³×C₃₁	1	2	yes	—
876	#121	C₂³×C₃₁	1	2	yes	—
877	C₄×Q₈	—	2	1	no	—
878	C₄×Q₈	—	2	1	no	—
879	C₄×Q₈	—	2	1	no	—
880	C₄×Q₈	—	2	1	no	—
881	C₄×Q₈	—	2	1	no	—
882	C₄×Q₈	—	2	1	no	—
883	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
884	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
885	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
886	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
887	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
888	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
889	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
890	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
891	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
892	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	1	no	—
896	C₄×D₄	—	2	1	no	—
897	C₄×D₄	—	2	2	no	—
898	C₄×D₄	—	2	2	no	—
899	C₄×D₄	—	2	1	no	—
900	C₄×D₄	—	2	1	no	—
901	C₄×D₄	—	2	1	no	—
902	C₄×D₄	—	2	1	no	—
903	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
904	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
905	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
906	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
907	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
908	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
909	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
910	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
911	C₄×D₄	C₂³×C₃₁	1	2	yes	—
912	C₄×D₄	C₂³×C₃₁	1	2	yes	—
913	#117	—	2	1	no	—
914	#117	—	2	1	no	—
915	#117	—	2	1	no	—
916	#117	—	2	1	no	—
917	#117	—	2	2	no	—
918	#117	—	2	1	no	—
919	#117	—	2	1	no	—
920	#117	—	2	1	no	—
921	#117	C₂³×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	1	yes	characteristic
925	C₂×C₄⋊C₄	—	2	1	no	—
926	C₂×C₄⋊C₄	—	2	1	no	—
927	C₂×C₄⋊C₄	—	2	2	no	—
928	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
929	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
930	C₂×C₄²	—	2	1	no	—
931	C₂×C₄²	—	2	1	no	—
932	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
933	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
934	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
935	#107	C₂³×C₃₁	1	2	yes	—
936	#107	C₂³×C₃₁	1	2	yes	—
937	#107	C₂³×C₃₁	1	2	yes	—
938	#107	C₂³×C₃₁	1	2	yes	—
939	#107	C₂³×C₃₁	1	2	yes	—
940	#107	C₂³×C₃₁	1	2	yes	—
941	#106	C₂³×C₃₁	1	2	yes	—
942	#106	C₂³×C₃₁	1	2	yes	—
943	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
944	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
945	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
946	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
947	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
948	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
949	#103	C₂³×C₃₁	1	2	yes	—
950	#103	C₂³×C₃₁	1	2	yes	—
951	#103	C₂³×C₃₁	1	2	yes	—
952	#103	C₂³×C₃₁	1	2	yes	—
953	#103	C₂³×C₃₁	1	2	yes	—
954	#103	C₂³×C₃₁	1	2	yes	—
955	#103	C₂³×C₃₁	1	2	yes	—
956	#103	C₂³×C₃₁	1	2	yes	—
957	#103	C₂³×C₃₁	1	2	yes	—
958	#103	C₂³×C₃₁	1	2	yes	—
959	#102	C₂³×C₃₁	1	2	yes	—
960	#102	C₂³×C₃₁	1	2	yes	—
961	#102	C₂³×C₃₁	1	2	yes	—
962	#102	C₂³×C₃₁	1	2	yes	—
963	#102	C₂³×C₃₁	1	2	yes	—
964	#102	C₂³×C₃₁	1	2	yes	—
965	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
966	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
967	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
968	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
969	#97	C₂³×C₃₁	1	2	yes	—
970	#97	C₂³×C₃₁	1	2	yes	—
971	C₄×C₈	C₂³×C₃₁	1	2	yes	—
972	C₄×C₈	C₂³×C₃₁	1	2	yes	—
973	C₃₁	#60993	1	1	yes	characteristic, direct product factor, Sylow
974	#41	—	4	1	no	—
975	#41	—	4	1	no	—
976	#41	—	4	1	no	—
977	#41	—	4	1	no	—
978	#41	—	4	2	no	—
979	#41	—	4	2	no	—
980	#41	—	8	2	no	—
981	#41	—	8	2	no	—
982	C₂×Q₈	—	2	1	no	—
983	C₂×Q₈	—	2	1	no	—
984	C₂×Q₈	—	2	1	no	—
985	C₂×Q₈	—	2	1	no	—
986	C₂×Q₈	—	2	1	no	—
987	C₂×Q₈	—	2	2	no	—
988	C₂×Q₈	—	4	1	no	—
989	C₂×Q₈	—	4	1	no	—
990	C₂×Q₈	—	8	2	no	—
991	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
992	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
993	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
994	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
995	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
996	C₂×D₄	—	2	2	no	—
997	C₂×D₄	—	2	1	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	1	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1005	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1006	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1007	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	1	no	—
1011	C₂²×C₄	—	2	2	no	—
1012	C₂²×C₄	—	2	1	no	—
1013	C₂²×C₄	—	2	1	no	—
1014	C₂²×C₄	—	2	2	no	—
1015	C₂²×C₄	—	2	1	no	—
1016	C₂²×C₄	—	2	2	no	—
1017	C₂²×C₄	—	2	2	no	—
1018	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1019	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1020	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1021	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1022	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1023	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1024	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1025	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1026	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1027	Q₁₆	—	4	2	no	—
1028	Q₁₆	—	4	2	no	—
1029	Q₁₆	—	4	2	no	—
1030	SD₁₆	—	4	2	no	—
1031	SD₁₆	—	4	2	no	—
1032	SD₁₆	—	4	2	no	—
1033	SD₁₆	—	4	2	no	—
1034	D₈	—	4	2	no	—
1035	M₁₆	—	4	2	no	—
1036	C₂×C₈	—	4	2	no	—
1037	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1038	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1039	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1040	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	—	2	1	no	—
1061	C₄⋊C₄	—	2	1	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	1	no	—
1064	C₄⋊C₄	—	2	1	no	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	2	no	—
1067	C₄⋊C₄	—	2	2	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	1	no	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1075	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1076	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	C₂⁴×C₃₁	1	1	yes	characteristic
1081	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1082	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1083	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1084	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1085	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	2	no	—
1096	C₂²⋊C₄	—	2	2	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	2	no	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	—	2	2	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1110	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1111	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1112	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1113	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1114	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1115	C₄²	—	2	1	no	—
1116	C₄²	—	2	1	no	—
1117	C₄²	—	2	1	no	—
1118	C₄²	—	2	1	no	—
1119	C₄²	—	2	1	no	—
1120	C₄²	—	2	1	no	—
1121	C₄²	—	2	1	no	—
1122	C₄²	—	2	2	no	—
1123	C₄²	—	2	2	no	—
1124	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1125	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1126	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1127	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1128	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1129	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1130	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1131	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1132	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1133	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1134	C₂³	—	2	1	no	—
1135	C₂³	—	2	2	no	—
1136	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1137	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1138	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1139	Q₈	—	2	1	no	—
1140	Q₈	—	2	1	no	—
1141	Q₈	—	2	1	no	—
1142	Q₈	—	2	2	no	—
1143	Q₈	—	2	1	no	—
1144	Q₈	—	2	1	no	—
1145	Q₈	—	2	2	no	—
1146	Q₈	—	2	1	no	—
1147	Q₈	—	4	1	no	—
1148	Q₈	—	4	2	no	—
1149	Q₈	—	4	2	no	—
1150	Q₈	—	4	2	no	—
1151	Q₈	—	8	1	no	—
1152	Q₈	—	8	1	no	—
1153	Q₈	—	8	2	no	—
1154	D₄	—	2	1	no	—
1155	D₄	—	2	2	no	—
1156	D₄	—	2	1	no	—
1157	D₄	—	2	2	no	—
1158	D₄	—	4	1	no	—
1159	D₄	—	4	1	no	—
1160	D₄	—	4	1	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	4	2	no	—
1163	D₄	—	4	4	no	—
1164	D₄	—	4	2	no	—
1165	D₄	—	8	1	no	—
1166	D₄	—	8	1	no	—
1167	D₄	—	8	2	no	—
1168	D₄	—	8	2	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	2	no	—
1180	C₂×C₄	—	2	1	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	1	no	—
1184	C₂×C₄	—	2	1	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	2	2	no	—
1187	C₂×C₄	—	2	2	no	—
1188	C₂×C₄	—	4	1	no	—
1189	C₂×C₄	—	4	1	no	—
1190	C₂×C₄	—	4	1	no	—
1191	C₂×C₄	—	4	4	no	—
1192	C₂×C₄	—	4	2	no	—
1193	C₂×C₄	—	4	2	no	—
1194	C₂×C₄	—	4	2	no	—
1195	C₂×C₄	—	8	1	no	—
1196	C₂×C₄	—	8	2	no	—
1197	C₂×C₄	—	8	2	no	—
1198	C₂×C₄	—	8	1	no	—
1199	C₂×C₄	—	8	2	no	—
1200	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1201	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1202	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1203	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1204	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1205	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1206	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1207	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1208	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1209	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1210	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1211	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1212	C₈	—	2	2	no	—
1213	C₈	—	2	2	no	—
1214	C₈	—	2	2	no	—
1215	C₈	—	2	2	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	2	1	no	—
1218	C₂²	—	2	1	no	—
1219	C₂²	—	2	1	no	—
1220	C₂²	—	2	1	no	—
1221	C₂²	—	2	1	no	—
1222	C₂²	—	2	1	no	—
1223	C₂²	—	2	1	no	—
1224	C₂²	—	2	1	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	4	2	no	—
1227	C₂²	—	4	1	no	—
1228	C₂²	—	4	2	no	—
1229	C₂²	—	4	2	no	—
1230	C₂²	—	4	1	no	—
1231	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1232	C₄	—	2	1	no	—
1233	C₄	—	2	1	no	—
1234	C₄	—	2	1	no	—
1235	C₄	—	2	1	no	—
1236	C₄	—	2	1	no	—
1237	C₄	—	2	1	no	—
1238	C₄	—	2	1	no	—
1239	C₄	—	2	1	no	—
1240	C₄	—	2	1	no	—
1241	C₄	—	2	1	no	—
1242	C₄	—	4	2	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	1	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	2	no	—
1248	C₄	—	4	2	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	1	no	—
1252	C₄	C₃₁×#578	1	2	yes	—
1253	C₄	C₃₁×#585	1	1	yes	characteristic
1254	C₄	C₃₁×#585	1	1	yes	characteristic
1255	C₂	—	4	1	no	—
1256	C₂	—	4	1	no	—
1257	C₂	—	4	1	no	—
1258	C₂	—	8	1	no	—
1259	C₂	—	8	2	no	—
1260	C₂	C₃₁×#3449	1	1	yes	characteristic
1261	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
1262	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×#3461	C₂	semidirect
3. C₃₁×#3254	C₂	semidirect
4. C₃₁×#3252	C₂	semidirect
5. C₃₁×#3249	C₂	semidirect
6. C₃₁×#3247	C₂	semidirect
7. C₃₁×#3243	C₂	semidirect
8. C₃₁×#3238	C₂	semidirect
9. C₃₁×#3230	C₂	semidirect
10. C₃₁×#3225	C₂	semidirect
11. C₃₁×#3216	C₂	semidirect
12. C₃₁×#3212	C₂	semidirect
13. C₃₁×#3203	C₂	semidirect
14. C₃₁×#3201	C₂	semidirect
15. C₃₁×#3178	C₂	semidirect
16. C₃₁×#3175	C₂	semidirect
17. C₃₁×#3124	C₂	semidirect
18. C₃₁×#3120	C₂	semidirect
19. C₃₁×#3116	C₂	semidirect
20. C₃₁×#3112	C₂	semidirect
21. C₃₁×#3106	C₂	semidirect
22. C₃₁×#3104	C₂	semidirect
23. C₃₁×#2925	C₂	semidirect
502. #60993	C₃₁	direct (N × H)
585. #3511	C₂×C₃₁	semidirect
586. #3461	C₂×C₃₁	semidirect
587. #3254	C₂×C₃₁	semidirect
588. #3252	C₂×C₃₁	semidirect
589. #3249	C₂×C₃₁	semidirect
590. #3247	C₂×C₃₁	semidirect
591. #3243	C₂×C₃₁	semidirect
592. #3238	C₂×C₃₁	semidirect
593. #3230	C₂×C₃₁	semidirect
594. #3225	C₂×C₃₁	semidirect
595. #3216	C₂×C₃₁	semidirect
596. #3212	C₂×C₃₁	semidirect
597. #3203	C₂×C₃₁	semidirect
598. #3201	C₂×C₃₁	semidirect
599. #3178	C₂×C₃₁	semidirect
600. #3175	C₂×C₃₁	semidirect
601. #3124	C₂×C₃₁	semidirect
602. #3120	C₂×C₃₁	semidirect
603. #3116	C₂×C₃₁	semidirect
604. #3112	C₂×C₃₁	semidirect
605. #3106	C₂×C₃₁	semidirect
606. #3104	C₂×C₃₁	semidirect
607. #2925	C₂×C₃₁	semidirect
973. C₃₁	#60993	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×#3461	2
C₃₁×#3254	2
C₃₁×#3252	2
C₃₁×#3249	2
C₃₁×#3247	2
C₃₁×#3243	2
C₃₁×#3238	2
C₃₁×#3230	2
C₃₁×#3225	2
C₃₁×#3216	2
C₃₁×#3212	2
C₃₁×#3203	2
C₃₁×#3201	2
C₃₁×#3178	2
C₃₁×#3175	2
C₃₁×#3124	2
C₃₁×#3120	2
C₃₁×#3116	2
C₃₁×#3112	2
C₃₁×#3106	2
C₃₁×#3104	2
C₃₁×#2925	2
#60993	31

Subgroups — C31×#60993 #21517752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60993 #21517752