Subgroups — C₃₁×#60990 #21517749

Order 7936.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3253	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3251	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3247	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3245	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3241	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3233	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3220	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3217	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3199	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3198	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3179	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3176	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3122	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#559	—	2	1	no	—
25	C₃₁×#559	—	2	1	no	—
26	C₃₁×#550	—	2	1	no	—
27	C₃₁×#550	—	2	1	no	—
28	C₃₁×#546	—	2	1	no	—
29	C₃₁×#546	—	2	1	no	—
30	C₃₁×#546	—	2	1	no	—
31	C₃₁×#546	—	2	1	no	—
32	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#542	—	2	1	no	—
34	C₃₁×#542	C₂²	1	1	yes	characteristic
35	C₃₁×#542	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#540	—	2	1	no	—
37	C₃₁×#540	C₂²	1	1	yes	characteristic
38	C₃₁×#540	C₂²	1	2	yes	—
39	C₃₁×#540	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#540	C₂²	1	2	yes	complemented
41	C₃₁×#538	—	2	1	no	—
42	C₃₁×#538	—	2	1	no	—
43	C₃₁×#537	C₂²	1	1	yes	characteristic
44	C₃₁×#535	C₂²	1	2	yes	—
45	C₃₁×#535	C₂²	1	1	yes	characteristic
46	C₃₁×#535	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#532	—	2	1	no	—
49	C₃₁×#532	C₂²	1	1	yes	characteristic
50	C₃₁×#532	C₂²	1	1	yes	characteristic
51	C₃₁×#532	C₂²	1	1	yes	characteristic
52	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#529	—	2	1	no	—
57	C₃₁×#529	C₂²	1	1	yes	characteristic
58	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#525	—	2	1	no	—
60	C₃₁×#525	—	2	1	no	—
61	C₃₁×#518	C₂²	1	2	yes	complemented
62	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
63	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#501	C₂²	1	2	yes	complemented
66	C₃₁×#499	C₂²	1	2	yes	complemented
67	C₃₁×#496	C₂²	1	2	yes	—
68	C₃₁×#493	C₂²	1	2	yes	—
69	C₃₁×#490	C₂²	1	2	yes	complemented
70	C₃₁×#490	C₂²	1	2	yes	complemented
71	C₃₁×#488	C₂²	1	2	yes	complemented
72	C₃₁×#486	C₂²	1	2	yes	complemented
73	C₃₁×#485	C₂²	1	2	yes	complemented
74	C₃₁×#482	C₂²	1	2	yes	—
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×#482	C₂²	1	2	yes	complemented
79	C₃₁×#481	C₂²	1	2	yes	complemented
80	C₃₁×#480	C₂²	1	2	yes	complemented
81	C₃₁×#478	C₂²	1	2	yes	complemented
82	C₃₁×#478	C₂²	1	2	yes	complemented
83	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#476	C₂²	1	2	yes	complemented
88	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#474	C₂²	1	2	yes	complemented
93	C₃₁×#469	C₂²	1	2	yes	complemented
94	C₃₁×#469	C₂²	1	2	yes	complemented
95	C₃₁×#469	C₂²	1	2	yes	complemented
96	C₃₁×#468	C₂²	1	2	yes	complemented
97	C₃₁×#466	C₂²	1	2	yes	complemented
98	C₃₁×#466	C₂²	1	2	yes	complemented
99	C₃₁×#466	C₂²	1	2	yes	complemented
100	C₃₁×#465	C₂²	1	2	yes	complemented
101	C₃₁×#463	C₂²	1	2	yes	complemented
102	C₃₁×#463	C₂²	1	2	yes	complemented
103	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
105	C₃₁×#459	C₂²	1	1	yes	characteristic
106	C₃₁×#459	C₂²	1	1	yes	characteristic
107	C₃₁×#459	C₂²	1	1	yes	characteristic
108	C₃₁×#459	C₂²	1	1	yes	characteristic
109	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
110	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#459	C₂²	1	2	yes	complemented
112	C₃₁×#459	C₂²	1	2	yes	complemented
113	C₃₁×#450	C₂²	1	2	yes	complemented
114	C₃₁×#449	C₂²	1	2	yes	complemented
115	C₃₁×#449	C₂²	1	2	yes	complemented
116	C₃₁×#447	C₂²	1	2	yes	—
117	C₃₁×#447	C₂²	1	2	yes	—
118	C₃₁×#447	C₂²	1	2	yes	complemented
119	C₃₁×#447	C₂²	1	2	yes	complemented
120	C₃₁×#447	C₂²	1	2	yes	complemented
121	C₃₁×#442	C₂²	1	2	yes	complemented
122	C₃₁×#442	C₂²	1	2	yes	complemented
123	C₃₁×#442	C₂²	1	2	yes	complemented
124	C₃₁×#440	C₂²	1	2	yes	complemented
125	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
126	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
127	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
128	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
129	C₃₁×#433	C₂²	1	2	yes	complemented
130	C₃₁×#433	C₂²	1	2	yes	complemented
131	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
133	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
134	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
135	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
136	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
137	C₃₁×#408	C₂²	1	2	yes	—
138	C₃₁×#405	C₂²	1	2	yes	complemented
139	C₂×#41×C₃₁	—	2	1	no	—
140	C₂×#41×C₃₁	—	2	1	no	—
141	C₂×#41×C₃₁	—	2	1	no	—
142	C₂×#41×C₃₁	—	2	1	no	—
143	C₂×#41×C₃₁	—	2	1	no	—
144	C₂×#41×C₃₁	—	2	1	no	—
145	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
147	C₂²×D₄×C₃₁	—	2	1	no	—
148	C₂²×D₄×C₃₁	—	2	1	no	—
149	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
150	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₃₁	—	2	1	no	—
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×D₈×C₃₁	C₂³	1	2	yes	—
155	C₂×D₈×C₃₁	C₂³	1	2	yes	—
156	C₂×D₈×C₃₁	C₂³	1	2	yes	—
157	C₂×D₈×C₃₁	C₂³	1	2	yes	—
158	C₂×D₈×C₃₁	C₂³	1	2	yes	—
159	C₂×D₈×C₃₁	C₂³	1	2	yes	—
160	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
162	C₃₁×C₄⋊Q₈	—	2	1	no	—
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	1	yes	characteristic
167	C₃₁×#127	—	2	1	no	—
168	C₃₁×#127	—	2	2	no	—
169	C₃₁×#127	—	2	1	no	—
170	C₃₁×#127	—	2	1	no	—
171	C₃₁×#127	C₂³	1	1	yes	characteristic
172	C₃₁×#127	C₂³	1	1	yes	characteristic
173	C₃₁×#127	C₂³	1	1	yes	characteristic
174	C₃₁×#127	C₂³	1	2	yes	—
175	C₃₁×#127	C₂³	1	1	yes	characteristic
176	C₃₁×#126	—	2	1	no	—
177	C₃₁×#126	—	2	1	no	—
178	C₃₁×#126	—	2	1	no	—
179	C₃₁×#126	—	2	1	no	—
180	C₃₁×#125	—	2	1	no	—
181	C₃₁×#125	C₂³	1	1	yes	characteristic
182	C₃₁×#125	C₂³	1	2	yes	—
183	C₃₁×#125	C₂³	1	1	yes	characteristic
184	C₃₁×#124	—	2	1	no	—
185	C₃₁×#124	—	2	2	no	—
186	C₃₁×#124	—	2	1	no	—
187	C₃₁×#124	—	2	1	no	—
188	C₃₁×#124	—	2	1	no	—
189	C₃₁×#124	—	2	1	no	—
190	C₃₁×#124	—	2	1	no	—
191	C₃₁×#124	—	2	1	no	—
192	C₃₁×#124	—	2	1	no	—
193	C₃₁×#124	—	2	1	no	—
194	C₃₁×#124	C₂³	1	1	yes	characteristic
195	C₃₁×#124	C₂³	1	1	yes	characteristic
196	C₃₁×#123	—	2	1	no	—
197	C₃₁×#123	—	2	1	no	—
198	C₃₁×#123	—	2	1	no	—
199	C₃₁×#123	—	2	1	no	—
200	C₃₁×#123	—	2	1	no	—
201	C₃₁×#123	—	2	1	no	—
202	C₃₁×#123	—	2	2	no	—
203	C₃₁×#123	—	2	2	no	—
204	C₃₁×#123	—	2	2	no	—
205	C₃₁×#123	—	2	2	no	—
206	C₃₁×#123	—	2	1	no	—
207	C₃₁×#123	—	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	C₂³	1	1	yes	characteristic
216	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₃₁×#121	—	2	1	no	—
218	C₃₁×#121	—	2	1	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	—	2	1	no	—
225	C₃₁×#121	—	2	1	no	—
226	C₃₁×#121	—	2	1	no	—
227	C₃₁×#121	—	2	1	no	—
228	C₃₁×#121	—	2	1	no	—
229	C₃₁×#121	—	2	1	no	—
230	C₃₁×#121	—	2	1	no	—
231	C₃₁×#121	—	2	1	no	—
232	C₃₁×#121	—	2	2	no	—
233	C₃₁×#121	—	2	2	no	—
234	C₃₁×#121	—	2	2	no	—
235	C₃₁×#121	—	2	2	no	—
236	C₃₁×#121	C₂³	1	1	yes	characteristic
237	C₃₁×#121	C₂³	1	1	yes	characteristic
238	C₃₁×#121	C₂³	1	1	yes	characteristic
239	C₃₁×#121	C₂³	1	2	yes	—
240	C₃₁×#121	C₂³	1	2	yes	—
241	C₃₁×#121	C₂³	1	2	yes	—
242	C₃₁×#121	C₂³	1	2	yes	—
243	C₃₁×#121	C₂³	1	1	yes	characteristic
244	C₃₁×#121	C₂³	1	1	yes	characteristic
245	C₃₁×#121	C₂³	1	1	yes	characteristic
246	C₃₁×#120	—	2	1	no	—
247	C₃₁×#120	—	2	1	no	—
248	C₃₁×#120	—	2	2	no	—
249	C₃₁×#120	—	2	2	no	—
250	C₃₁×#120	—	2	1	no	—
251	C₃₁×#120	—	2	1	no	—
252	C₄×Q₈×C₃₁	—	2	1	no	—
253	C₄×Q₈×C₃₁	—	2	1	no	—
254	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
255	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
256	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
257	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₃₁	—	2	1	no	—
259	C₄×D₄×C₃₁	—	2	1	no	—
260	C₄×D₄×C₃₁	—	2	1	no	—
261	C₄×D₄×C₃₁	—	2	1	no	—
262	C₄×D₄×C₃₁	—	2	2	no	—
263	C₄×D₄×C₃₁	—	2	2	no	—
264	C₄×D₄×C₃₁	—	2	1	no	—
265	C₄×D₄×C₃₁	—	2	1	no	—
266	C₄×D₄×C₃₁	—	2	1	no	—
267	C₄×D₄×C₃₁	—	2	1	no	—
268	C₄×D₄×C₃₁	—	2	1	no	—
269	C₄×D₄×C₃₁	—	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	2	yes	—
279	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
280	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
281	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
282	C₄×D₄×C₃₁	C₂³	1	2	yes	—
283	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
284	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
285	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₃₁	C₂³	1	2	yes	—
287	C₄×D₄×C₃₁	C₂³	1	2	yes	—
288	C₃₁×#117	—	2	1	no	—
289	C₃₁×#117	—	2	1	no	—
290	C₃₁×#117	—	2	1	no	—
291	C₃₁×#117	C₂³	1	2	yes	—
292	C₃₁×#117	C₂³	1	1	yes	characteristic
293	C₃₁×#117	C₂³	1	1	yes	characteristic
294	C₃₁×#117	C₂³	1	1	yes	characteristic
295	C₃₁×#117	C₂³	1	1	yes	characteristic
296	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
298	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
299	C₂×C₂²⋊C₄×C₃₁	—	2	2	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×#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×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×#102	C₂³	1	2	yes	—
321	C₃₁×#102	C₂³	1	2	yes	—
322	C₃₁×#102	C₂³	1	2	yes	—
323	C₃₁×#102	C₂³	1	2	yes	—
324	C₃₁×#102	C₂³	1	2	yes	—
325	C₃₁×#102	C₂³	1	2	yes	—
326	C₃₁×#102	C₂³	1	2	yes	—
327	C₃₁×#102	C₂³	1	2	yes	—
328	C₃₁×#102	C₂³	1	2	yes	—
329	C₃₁×#102	C₂³	1	2	yes	—
330	C₃₁×#102	C₂³	1	2	yes	—
331	C₃₁×#102	C₂³	1	2	yes	—
332	C₃₁×#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	C₂⁴×C₃₁	—	2	2	no	—
343	C₂⁴×C₃₁	—	2	1	no	—
344	#41×C₃₁	—	4	1	no	—
345	#41×C₃₁	—	4	1	no	—
346	#41×C₃₁	—	4	1	no	—
347	#41×C₃₁	—	4	1	no	—
348	#41×C₃₁	—	8	2	no	—
349	#41×C₃₁	—	8	2	no	—
350	#41×C₃₁	—	8	2	no	—
351	#41×C₃₁	—	8	2	no	—
352	#41×C₃₁	—	8	2	no	—
353	#41×C₃₁	—	8	2	no	—
354	C₂×Q₈×C₃₁	—	2	1	no	—
355	C₂×Q₈×C₃₁	—	2	1	no	—
356	C₂×Q₈×C₃₁	—	2	1	no	—
357	C₂×Q₈×C₃₁	—	2	1	no	—
358	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
359	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
360	C₂×D₄×C₃₁	—	2	1	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	2	no	—
365	C₂×D₄×C₃₁	—	2	2	no	—
366	C₂×D₄×C₃₁	—	2	2	no	—
367	C₂×D₄×C₃₁	—	2	1	no	—
368	C₂×D₄×C₃₁	—	2	1	no	—
369	C₂×D₄×C₃₁	—	2	1	no	—
370	C₂×D₄×C₃₁	—	2	1	no	—
371	C₂×D₄×C₃₁	—	2	1	no	—
372	C₂×D₄×C₃₁	—	2	2	no	—
373	C₂×D₄×C₃₁	—	2	1	no	—
374	C₂×D₄×C₃₁	—	2	1	no	—
375	C₂×D₄×C₃₁	—	2	1	no	—
376	C₂×D₄×C₃₁	—	2	1	no	—
377	C₂×D₄×C₃₁	—	2	1	no	—
378	C₂×D₄×C₃₁	—	2	1	no	—
379	C₂×D₄×C₃₁	—	2	1	no	—
380	C₂×D₄×C₃₁	—	2	1	no	—
381	C₂×D₄×C₃₁	—	2	2	no	—
382	C₂×D₄×C₃₁	—	2	2	no	—
383	C₂×D₄×C₃₁	—	4	2	no	—
384	C₂×D₄×C₃₁	—	4	2	no	—
385	C₂×D₄×C₃₁	—	4	1	no	—
386	C₂×D₄×C₃₁	—	4	1	no	—
387	C₂×D₄×C₃₁	—	8	2	no	—
388	C₂×D₄×C₃₁	—	8	2	no	—
389	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
390	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
391	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
392	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
393	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
394	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
395	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
396	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
397	C₂²×C₄×C₃₁	—	2	1	no	—
398	C₂²×C₄×C₃₁	—	2	1	no	—
399	C₂²×C₄×C₃₁	—	2	1	no	—
400	C₂²×C₄×C₃₁	—	2	1	no	—
401	C₂²×C₄×C₃₁	—	2	1	no	—
402	C₂²×C₄×C₃₁	—	2	1	no	—
403	C₂²×C₄×C₃₁	—	2	2	no	—
404	C₂²×C₄×C₃₁	—	2	2	no	—
405	C₂²×C₄×C₃₁	—	2	2	no	—
406	C₂²×C₄×C₃₁	—	2	2	no	—
407	C₂²×C₄×C₃₁	—	2	1	no	—
408	C₂²×C₄×C₃₁	—	2	1	no	—
409	C₂²×C₄×C₃₁	—	8	2	no	—
410	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
411	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
412	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
413	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
414	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
415	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
416	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
419	SD₁₆×C₃₁	—	4	2	no	—
420	SD₁₆×C₃₁	—	4	2	no	—
421	D₈×C₃₁	—	4	2	no	—
422	D₈×C₃₁	—	4	2	no	—
423	D₈×C₃₁	—	4	2	no	—
424	D₈×C₃₁	—	4	2	no	—
425	D₈×C₃₁	—	4	2	no	—
426	D₈×C₃₁	—	4	2	no	—
427	M₁₆×C₃₁	—	4	2	no	—
428	C₂×C₈×C₃₁	—	4	2	no	—
429	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
430	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
431	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
432	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
433	C₄⋊C₄×C₃₁	—	2	1	no	—
434	C₄⋊C₄×C₃₁	—	2	1	no	—
435	C₄⋊C₄×C₃₁	—	2	1	no	—
436	C₄⋊C₄×C₃₁	—	2	1	no	—
437	C₄⋊C₄×C₃₁	—	2	1	no	—
438	C₄⋊C₄×C₃₁	—	2	1	no	—
439	C₄⋊C₄×C₃₁	—	2	1	no	—
440	C₄⋊C₄×C₃₁	—	2	1	no	—
441	C₄⋊C₄×C₃₁	—	2	1	no	—
442	C₄⋊C₄×C₃₁	—	2	1	no	—
443	C₄⋊C₄×C₃₁	—	2	1	no	—
444	C₄⋊C₄×C₃₁	—	2	1	no	—
445	C₄⋊C₄×C₃₁	—	2	1	no	—
446	C₄⋊C₄×C₃₁	—	2	2	no	—
447	C₄⋊C₄×C₃₁	—	2	2	no	—
448	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
452	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
453	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
454	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
455	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
456	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
457	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
458	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
459	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
460	C₂²⋊C₄×C₃₁	—	2	2	no	—
461	C₂²⋊C₄×C₃₁	—	2	1	no	—
462	C₂²⋊C₄×C₃₁	—	2	1	no	—
463	C₂²⋊C₄×C₃₁	—	2	1	no	—
464	C₂²⋊C₄×C₃₁	—	2	2	no	—
465	C₂²⋊C₄×C₃₁	—	2	2	no	—
466	C₂²⋊C₄×C₃₁	—	2	2	no	—
467	C₂²⋊C₄×C₃₁	—	2	2	no	—
468	C₂²⋊C₄×C₃₁	—	2	1	no	—
469	C₂²⋊C₄×C₃₁	—	2	1	no	—
470	C₂²⋊C₄×C₃₁	—	2	1	no	—
471	C₂²⋊C₄×C₃₁	—	2	1	no	—
472	C₂²⋊C₄×C₃₁	—	2	1	no	—
473	C₂²⋊C₄×C₃₁	—	2	1	no	—
474	C₂²⋊C₄×C₃₁	—	2	1	no	—
475	C₂²⋊C₄×C₃₁	—	2	1	no	—
476	C₂²⋊C₄×C₃₁	—	2	1	no	—
477	C₂²⋊C₄×C₃₁	—	2	1	no	—
478	C₂²⋊C₄×C₃₁	—	2	1	no	—
479	C₂²⋊C₄×C₃₁	—	2	1	no	—
480	C₂²⋊C₄×C₃₁	—	2	1	no	—
481	C₂²⋊C₄×C₃₁	—	2	1	no	—
482	C₂²⋊C₄×C₃₁	—	2	2	no	—
483	C₂²⋊C₄×C₃₁	—	2	2	no	—
484	C₂²⋊C₄×C₃₁	—	2	2	no	—
485	C₂²⋊C₄×C₃₁	—	2	2	no	—
486	C₂²⋊C₄×C₃₁	—	2	1	no	—
487	C₂²⋊C₄×C₃₁	—	2	1	no	—
488	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
489	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
490	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
491	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
492	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
493	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₃₁	—	2	1	no	—
495	C₄²×C₃₁	—	2	1	no	—
496	C₄²×C₃₁	—	2	1	no	—
497	C₄²×C₃₁	—	2	2	no	—
498	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
499	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
500	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
501	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
502	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
503	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
504	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
505	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
506	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
507	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
508	#60990	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
509	C₂³×C₃₁	—	2	1	no	—
510	C₂³×C₃₁	—	2	1	no	—
511	C₂³×C₃₁	—	2	1	no	—
512	C₂³×C₃₁	—	2	2	no	—
513	C₂³×C₃₁	—	2	2	no	—
514	C₂³×C₃₁	—	4	2	no	—
515	C₂³×C₃₁	—	4	4	no	—
516	C₂³×C₃₁	—	8	1	no	—
517	C₂³×C₃₁	—	8	1	no	—
518	C₂³×C₃₁	—	8	2	no	—
519	C₂³×C₃₁	—	8	2	no	—
520	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
521	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
522	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
523	Q₈×C₃₁	—	2	1	no	—
524	Q₈×C₃₁	—	2	1	no	—
525	Q₈×C₃₁	—	4	1	no	—
526	Q₈×C₃₁	—	4	2	no	—
527	Q₈×C₃₁	—	4	2	no	—
528	Q₈×C₃₁	—	8	1	no	—
529	Q₈×C₃₁	—	8	1	no	—
530	D₄×C₃₁	—	2	1	no	—
531	D₄×C₃₁	—	2	1	no	—
532	D₄×C₃₁	—	2	1	no	—
533	D₄×C₃₁	—	2	1	no	—
534	D₄×C₃₁	—	2	2	no	—
535	D₄×C₃₁	—	2	2	no	—
536	D₄×C₃₁	—	2	1	no	—
537	D₄×C₃₁	—	2	1	no	—
538	D₄×C₃₁	—	2	2	no	—
539	D₄×C₃₁	—	2	2	no	—
540	D₄×C₃₁	—	4	1	no	—
541	D₄×C₃₁	—	4	1	no	—
542	D₄×C₃₁	—	4	1	no	—
543	D₄×C₃₁	—	4	2	no	—
544	D₄×C₃₁	—	4	4	no	—
545	D₄×C₃₁	—	4	2	no	—
546	D₄×C₃₁	—	4	2	no	—
547	D₄×C₃₁	—	4	2	no	—
548	D₄×C₃₁	—	4	2	no	—
549	D₄×C₃₁	—	4	2	no	—
550	D₄×C₃₁	—	8	1	no	—
551	D₄×C₃₁	—	8	1	no	—
552	D₄×C₃₁	—	8	2	no	—
553	D₄×C₃₁	—	8	2	no	—
554	D₄×C₃₁	—	8	1	no	—
555	D₄×C₃₁	—	8	1	no	—
556	D₄×C₃₁	—	8	1	no	—
557	D₄×C₃₁	—	8	1	no	—
558	D₄×C₃₁	—	8	2	no	—
559	D₄×C₃₁	—	8	2	no	—
560	D₄×C₃₁	—	8	1	no	—
561	D₄×C₃₁	—	8	1	no	—
562	D₄×C₃₁	—	8	1	no	—
563	D₄×C₃₁	—	8	1	no	—
564	D₄×C₃₁	—	8	2	no	—
565	D₄×C₃₁	—	8	2	no	—
566	C₂×C₄×C₃₁	—	2	2	no	—
567	C₂×C₄×C₃₁	—	2	2	no	—
568	C₂×C₄×C₃₁	—	2	2	no	—
569	C₂×C₄×C₃₁	—	2	1	no	—
570	C₂×C₄×C₃₁	—	2	1	no	—
571	C₂×C₄×C₃₁	—	2	1	no	—
572	C₂×C₄×C₃₁	—	2	1	no	—
573	C₂×C₄×C₃₁	—	2	1	no	—
574	C₂×C₄×C₃₁	—	2	1	no	—
575	C₂×C₄×C₃₁	—	2	1	no	—
576	C₂×C₄×C₃₁	—	2	1	no	—
577	C₂×C₄×C₃₁	—	2	1	no	—
578	C₂×C₄×C₃₁	—	2	2	no	—
579	C₂×C₄×C₃₁	—	2	2	no	—
580	C₂×C₄×C₃₁	—	2	1	no	—
581	C₂×C₄×C₃₁	—	2	1	no	—
582	C₂×C₄×C₃₁	—	4	1	no	—
583	C₂×C₄×C₃₁	—	4	1	no	—
584	C₂×C₄×C₃₁	—	4	1	no	—
585	C₂×C₄×C₃₁	—	4	2	no	—
586	C₂×C₄×C₃₁	—	4	2	no	—
587	C₂×C₄×C₃₁	—	4	2	no	—
588	C₂×C₄×C₃₁	—	4	2	no	—
589	C₂×C₄×C₃₁	—	8	1	no	—
590	C₂×C₄×C₃₁	—	8	1	no	—
591	C₂×C₄×C₃₁	—	8	1	no	—
592	C₂×C₄×C₃₁	—	8	2	no	—
593	C₂×C₄×C₃₁	—	8	2	no	—
594	C₂×C₄×C₃₁	—	8	2	no	—
595	C₂×C₄×C₃₁	—	8	2	no	—
596	C₂×C₄×C₃₁	—	8	1	no	—
597	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
598	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
599	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
600	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
601	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
602	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
603	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
604	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
605	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
606	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
607	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
608	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
609	C₈×C₃₁	—	2	2	no	—
610	C₈×C₃₁	—	2	2	no	—
611	C₈×C₃₁	—	2	2	no	—
612	C₈×C₃₁	—	2	2	no	—
613	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
614	#3460	C₂×C₃₁	1	1	yes	characteristic, complemented
615	#3253	C₂×C₃₁	1	1	yes	characteristic, complemented
616	#3251	C₂×C₃₁	1	1	yes	characteristic, complemented
617	#3247	C₂×C₃₁	1	1	yes	characteristic, complemented
618	#3245	C₂×C₃₁	1	1	yes	characteristic, complemented
619	#3241	C₂×C₃₁	1	2	yes	complemented
620	#3235	C₂×C₃₁	1	1	yes	characteristic, complemented
621	#3233	C₂×C₃₁	1	1	yes	characteristic, complemented
622	#3220	C₂×C₃₁	1	2	yes	complemented
623	#3217	C₂×C₃₁	1	1	yes	characteristic, complemented
624	#3205	C₂×C₃₁	1	1	yes	characteristic, complemented
625	#3199	C₂×C₃₁	1	2	yes	complemented
626	#3198	C₂×C₃₁	1	2	yes	complemented
627	#3179	C₂×C₃₁	1	2	yes	complemented
628	#3176	C₂×C₃₁	1	2	yes	complemented
629	#3122	C₂×C₃₁	1	2	yes	complemented
630	#3118	C₂×C₃₁	1	2	yes	complemented
631	#3115	C₂×C₃₁	1	1	yes	characteristic, complemented
632	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
633	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
634	#3100	C₂×C₃₁	1	1	yes	characteristic, complemented
635	#2925	C₂×C₃₁	1	1	yes	characteristic, complemented
636	C₂²×C₃₁	—	2	1	no	—
637	C₂²×C₃₁	—	2	1	no	—
638	C₂²×C₃₁	—	2	1	no	—
639	C₂²×C₃₁	—	2	1	no	—
640	C₂²×C₃₁	—	2	1	no	—
641	C₂²×C₃₁	—	2	1	no	—
642	C₂²×C₃₁	—	2	1	no	—
643	C₂²×C₃₁	—	2	1	no	—
644	C₂²×C₃₁	—	2	1	no	—
645	C₂²×C₃₁	—	4	2	no	—
646	C₂²×C₃₁	—	4	2	no	—
647	C₂²×C₃₁	—	4	1	no	—
648	C₂²×C₃₁	—	4	1	no	—
649	C₂²×C₃₁	—	4	1	no	—
650	C₂²×C₃₁	—	4	1	no	—
651	C₂²×C₃₁	—	4	1	no	—
652	C₂²×C₃₁	—	4	1	no	—
653	C₂²×C₃₁	—	4	2	no	—
654	C₂²×C₃₁	—	4	2	no	—
655	C₂²×C₃₁	—	4	1	no	—
656	C₂²×C₃₁	—	4	1	no	—
657	C₂²×C₃₁	—	4	1	no	—
658	C₂²×C₃₁	—	4	2	no	—
659	C₂²×C₃₁	—	4	2	no	—
660	C₂²×C₃₁	—	8	4	no	—
661	C₂²×C₃₁	—	16	4	no	—
662	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
663	C₄×C₃₁	—	2	1	no	—
664	C₄×C₃₁	—	2	1	no	—
665	C₄×C₃₁	—	2	1	no	—
666	C₄×C₃₁	—	2	1	no	—
667	C₄×C₃₁	—	2	1	no	—
668	C₄×C₃₁	—	2	1	no	—
669	C₄×C₃₁	—	2	1	no	—
670	C₄×C₃₁	—	2	1	no	—
671	C₄×C₃₁	—	2	1	no	—
672	C₄×C₃₁	—	2	1	no	—
673	C₄×C₃₁	—	4	2	no	—
674	C₄×C₃₁	—	4	1	no	—
675	C₄×C₃₁	—	4	1	no	—
676	C₄×C₃₁	—	4	1	no	—
677	C₄×C₃₁	—	4	1	no	—
678	C₄×C₃₁	—	4	1	no	—
679	C₄×C₃₁	—	4	2	no	—
680	C₄×C₃₁	#576	1	2	yes	—
681	C₄×C₃₁	#585	1	1	yes	characteristic
682	C₄×C₃₁	#585	1	1	yes	characteristic
683	#559	—	2	1	no	—
684	#559	—	2	1	no	—
685	#550	—	2	1	no	—
686	#550	—	2	1	no	—
687	#546	—	2	1	no	—
688	#546	—	2	1	no	—
689	#546	—	2	1	no	—
690	#546	—	2	1	no	—
691	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
692	#542	—	2	1	no	—
693	#542	C₂²×C₃₁	1	1	yes	characteristic
694	#542	C₂²×C₃₁	1	1	yes	characteristic, complemented
695	#540	—	2	1	no	—
696	#540	C₂²×C₃₁	1	1	yes	characteristic
697	#540	C₂²×C₃₁	1	2	yes	—
698	#540	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	#540	C₂²×C₃₁	1	2	yes	complemented
700	#538	—	2	1	no	—
701	#538	—	2	1	no	—
702	#537	C₂²×C₃₁	1	1	yes	characteristic
703	#535	C₂²×C₃₁	1	2	yes	—
704	#535	C₂²×C₃₁	1	1	yes	characteristic
705	#535	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
707	#532	—	2	1	no	—
708	#532	C₂²×C₃₁	1	1	yes	characteristic
709	#532	C₂²×C₃₁	1	1	yes	characteristic
710	#532	C₂²×C₃₁	1	1	yes	characteristic
711	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
712	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
713	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
714	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
715	#529	—	2	1	no	—
716	#529	C₂²×C₃₁	1	1	yes	characteristic
717	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
718	#525	—	2	1	no	—
719	#525	—	2	1	no	—
720	#518	C₂²×C₃₁	1	2	yes	complemented
721	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
722	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
723	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
724	#501	C₂²×C₃₁	1	2	yes	complemented
725	#499	C₂²×C₃₁	1	2	yes	complemented
726	#496	C₂²×C₃₁	1	2	yes	—
727	#493	C₂²×C₃₁	1	2	yes	—
728	#490	C₂²×C₃₁	1	2	yes	complemented
729	#490	C₂²×C₃₁	1	2	yes	complemented
730	#488	C₂²×C₃₁	1	2	yes	complemented
731	#486	C₂²×C₃₁	1	2	yes	complemented
732	#485	C₂²×C₃₁	1	2	yes	complemented
733	#482	C₂²×C₃₁	1	2	yes	—
734	#482	C₂²×C₃₁	1	2	yes	—
735	#482	C₂²×C₃₁	1	2	yes	complemented
736	#482	C₂²×C₃₁	1	2	yes	complemented
737	#482	C₂²×C₃₁	1	2	yes	complemented
738	#481	C₂²×C₃₁	1	2	yes	complemented
739	#480	C₂²×C₃₁	1	2	yes	complemented
740	#478	C₂²×C₃₁	1	2	yes	complemented
741	#478	C₂²×C₃₁	1	2	yes	complemented
742	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
743	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
744	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
745	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
746	#476	C₂²×C₃₁	1	2	yes	complemented
747	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
748	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
749	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
750	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
751	#474	C₂²×C₃₁	1	2	yes	complemented
752	#469	C₂²×C₃₁	1	2	yes	complemented
753	#469	C₂²×C₃₁	1	2	yes	complemented
754	#469	C₂²×C₃₁	1	2	yes	complemented
755	#468	C₂²×C₃₁	1	2	yes	complemented
756	#466	C₂²×C₃₁	1	2	yes	complemented
757	#466	C₂²×C₃₁	1	2	yes	complemented
758	#466	C₂²×C₃₁	1	2	yes	complemented
759	#465	C₂²×C₃₁	1	2	yes	complemented
760	#463	C₂²×C₃₁	1	2	yes	complemented
761	#463	C₂²×C₃₁	1	2	yes	complemented
762	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
763	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
764	#459	C₂²×C₃₁	1	1	yes	characteristic
765	#459	C₂²×C₃₁	1	1	yes	characteristic
766	#459	C₂²×C₃₁	1	1	yes	characteristic
767	#459	C₂²×C₃₁	1	1	yes	characteristic
768	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
769	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
770	#459	C₂²×C₃₁	1	2	yes	complemented
771	#459	C₂²×C₃₁	1	2	yes	complemented
772	#450	C₂²×C₃₁	1	2	yes	complemented
773	#449	C₂²×C₃₁	1	2	yes	complemented
774	#449	C₂²×C₃₁	1	2	yes	complemented
775	#447	C₂²×C₃₁	1	2	yes	—
776	#447	C₂²×C₃₁	1	2	yes	—
777	#447	C₂²×C₃₁	1	2	yes	complemented
778	#447	C₂²×C₃₁	1	2	yes	complemented
779	#447	C₂²×C₃₁	1	2	yes	complemented
780	#442	C₂²×C₃₁	1	2	yes	complemented
781	#442	C₂²×C₃₁	1	2	yes	complemented
782	#442	C₂²×C₃₁	1	2	yes	complemented
783	#440	C₂²×C₃₁	1	2	yes	complemented
784	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
785	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
786	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
787	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
788	#433	C₂²×C₃₁	1	2	yes	complemented
789	#433	C₂²×C₃₁	1	2	yes	complemented
790	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
791	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
792	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
793	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
794	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
795	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
796	#408	C₂²×C₃₁	1	2	yes	—
797	#405	C₂²×C₃₁	1	2	yes	complemented
798	C₂×C₃₁	—	4	1	no	—
799	C₂×C₃₁	—	4	1	no	—
800	C₂×C₃₁	—	4	1	no	—
801	C₂×C₃₁	—	8	1	no	—
802	C₂×C₃₁	—	8	1	no	—
803	C₂×C₃₁	—	8	1	no	—
804	C₂×C₃₁	—	8	2	no	—
805	C₂×C₃₁	—	8	2	no	—
806	C₂×C₃₁	#3449	1	1	yes	characteristic
807	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
808	C₂×C₃₁	#3585	1	1	yes	characteristic
809	C₂×#41	—	2	1	no	—
810	C₂×#41	—	2	1	no	—
811	C₂×#41	—	2	1	no	—
812	C₂×#41	—	2	1	no	—
813	C₂×#41	—	2	1	no	—
814	C₂×#41	—	2	1	no	—
815	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
816	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
817	C₂²×D₄	—	2	1	no	—
818	C₂²×D₄	—	2	1	no	—
819	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
820	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
821	C₂³×C₄	—	2	1	no	—
822	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
823	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
824	C₂×D₈	C₂³×C₃₁	1	2	yes	—
825	C₂×D₈	C₂³×C₃₁	1	2	yes	—
826	C₂×D₈	C₂³×C₃₁	1	2	yes	—
827	C₂×D₈	C₂³×C₃₁	1	2	yes	—
828	C₂×D₈	C₂³×C₃₁	1	2	yes	—
829	C₂×D₈	C₂³×C₃₁	1	2	yes	—
830	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
831	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
832	C₄⋊Q₈	—	2	1	no	—
833	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
834	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
835	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
836	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
837	#127	—	2	1	no	—
838	#127	—	2	2	no	—
839	#127	—	2	1	no	—
840	#127	—	2	1	no	—
841	#127	C₂³×C₃₁	1	1	yes	characteristic
842	#127	C₂³×C₃₁	1	1	yes	characteristic
843	#127	C₂³×C₃₁	1	2	yes	—
844	#127	C₂³×C₃₁	1	1	yes	characteristic
845	#127	C₂³×C₃₁	1	1	yes	characteristic
846	#126	—	2	1	no	—
847	#126	—	2	1	no	—
848	#126	—	2	1	no	—
849	#126	—	2	1	no	—
850	#125	—	2	1	no	—
851	#125	C₂³×C₃₁	1	1	yes	characteristic
852	#125	C₂³×C₃₁	1	1	yes	characteristic
853	#125	C₂³×C₃₁	1	2	yes	—
854	#124	—	2	1	no	—
855	#124	—	2	2	no	—
856	#124	—	2	1	no	—
857	#124	—	2	1	no	—
858	#124	—	2	1	no	—
859	#124	—	2	1	no	—
860	#124	—	2	1	no	—
861	#124	—	2	1	no	—
862	#124	—	2	1	no	—
863	#124	—	2	1	no	—
864	#124	C₂³×C₃₁	1	1	yes	characteristic
865	#124	C₂³×C₃₁	1	1	yes	characteristic
866	#123	—	2	1	no	—
867	#123	—	2	1	no	—
868	#123	—	2	1	no	—
869	#123	—	2	1	no	—
870	#123	—	2	1	no	—
871	#123	—	2	1	no	—
872	#123	—	2	2	no	—
873	#123	—	2	2	no	—
874	#123	—	2	2	no	—
875	#123	—	2	2	no	—
876	#123	—	2	1	no	—
877	#123	—	2	1	no	—
878	C₂²⋊Q₈	—	2	1	no	—
879	C₂²⋊Q₈	—	2	1	no	—
880	C₂²⋊Q₈	—	2	1	no	—
881	C₂²⋊Q₈	—	2	1	no	—
882	C₂²⋊Q₈	—	2	1	no	—
883	C₂²⋊Q₈	—	2	1	no	—
884	C₂²⋊Q₈	—	2	1	no	—
885	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
886	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
887	#121	—	2	1	no	—
888	#121	—	2	1	no	—
889	#121	—	2	1	no	—
890	#121	—	2	1	no	—
891	#121	—	2	1	no	—
892	#121	—	2	1	no	—
893	#121	—	2	1	no	—
894	#121	—	2	1	no	—
895	#121	—	2	1	no	—
896	#121	—	2	1	no	—
897	#121	—	2	1	no	—
898	#121	—	2	1	no	—
899	#121	—	2	1	no	—
900	#121	—	2	1	no	—
901	#121	—	2	1	no	—
902	#121	—	2	2	no	—
903	#121	—	2	2	no	—
904	#121	—	2	2	no	—
905	#121	—	2	2	no	—
906	#121	C₂³×C₃₁	1	1	yes	characteristic
907	#121	C₂³×C₃₁	1	1	yes	characteristic
908	#121	C₂³×C₃₁	1	2	yes	—
909	#121	C₂³×C₃₁	1	2	yes	—
910	#121	C₂³×C₃₁	1	1	yes	characteristic
911	#121	C₂³×C₃₁	1	1	yes	characteristic
912	#121	C₂³×C₃₁	1	2	yes	—
913	#121	C₂³×C₃₁	1	2	yes	—
914	#121	C₂³×C₃₁	1	1	yes	characteristic
915	#121	C₂³×C₃₁	1	1	yes	characteristic
916	#120	—	2	1	no	—
917	#120	—	2	1	no	—
918	#120	—	2	2	no	—
919	#120	—	2	2	no	—
920	#120	—	2	1	no	—
921	#120	—	2	1	no	—
922	C₄×Q₈	—	2	1	no	—
923	C₄×Q₈	—	2	1	no	—
924	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
925	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
926	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
927	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
928	C₄×D₄	—	2	1	no	—
929	C₄×D₄	—	2	1	no	—
930	C₄×D₄	—	2	1	no	—
931	C₄×D₄	—	2	1	no	—
932	C₄×D₄	—	2	2	no	—
933	C₄×D₄	—	2	2	no	—
934	C₄×D₄	—	2	1	no	—
935	C₄×D₄	—	2	1	no	—
936	C₄×D₄	—	2	1	no	—
937	C₄×D₄	—	2	1	no	—
938	C₄×D₄	—	2	1	no	—
939	C₄×D₄	—	2	1	no	—
940	C₄×D₄	—	2	1	no	—
941	C₄×D₄	—	2	1	no	—
942	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
943	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
944	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
945	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
946	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
947	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
948	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
949	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
950	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
951	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
952	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
953	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
954	C₄×D₄	C₂³×C₃₁	1	2	yes	—
955	C₄×D₄	C₂³×C₃₁	1	2	yes	—
956	C₄×D₄	C₂³×C₃₁	1	2	yes	—
957	C₄×D₄	C₂³×C₃₁	1	2	yes	—
958	#117	—	2	1	no	—
959	#117	—	2	1	no	—
960	#117	—	2	1	no	—
961	#117	C₂³×C₃₁	1	1	yes	characteristic
962	#117	C₂³×C₃₁	1	2	yes	—
963	#117	C₂³×C₃₁	1	1	yes	characteristic
964	#117	C₂³×C₃₁	1	1	yes	characteristic
965	#117	C₂³×C₃₁	1	1	yes	characteristic
966	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
967	C₂×C₂²⋊C₄	—	2	1	no	—
968	C₂×C₂²⋊C₄	—	2	2	no	—
969	C₂×C₂²⋊C₄	—	2	2	no	—
970	C₂×C₄²	—	2	1	no	—
971	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
972	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
973	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
974	#107	C₂³×C₃₁	1	2	yes	—
975	#107	C₂³×C₃₁	1	2	yes	—
976	#107	C₂³×C₃₁	1	2	yes	—
977	#107	C₂³×C₃₁	1	2	yes	—
978	#106	C₂³×C₃₁	1	2	yes	—
979	#106	C₂³×C₃₁	1	2	yes	—
980	#106	C₂³×C₃₁	1	2	yes	—
981	#106	C₂³×C₃₁	1	2	yes	—
982	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
983	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
984	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
985	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
986	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
987	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
988	#103	C₂³×C₃₁	1	2	yes	—
989	#103	C₂³×C₃₁	1	2	yes	—
990	#102	C₂³×C₃₁	1	2	yes	—
991	#102	C₂³×C₃₁	1	2	yes	—
992	#102	C₂³×C₃₁	1	2	yes	—
993	#102	C₂³×C₃₁	1	2	yes	—
994	#102	C₂³×C₃₁	1	2	yes	—
995	#102	C₂³×C₃₁	1	2	yes	—
996	#102	C₂³×C₃₁	1	2	yes	—
997	#102	C₂³×C₃₁	1	2	yes	—
998	#102	C₂³×C₃₁	1	2	yes	—
999	#102	C₂³×C₃₁	1	2	yes	—
1000	#102	C₂³×C₃₁	1	2	yes	—
1001	#102	C₂³×C₃₁	1	2	yes	—
1002	#102	C₂³×C₃₁	1	2	yes	—
1003	#102	C₂³×C₃₁	1	2	yes	—
1004	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
1005	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
1006	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
1007	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
1008	#97	C₂³×C₃₁	1	2	yes	—
1009	#97	C₂³×C₃₁	1	2	yes	—
1010	C₄×C₈	C₂³×C₃₁	1	2	yes	—
1011	C₄×C₈	C₂³×C₃₁	1	2	yes	—
1012	C₃₁	#60990	1	1	yes	characteristic, direct product factor, Sylow
1013	C₂⁴	—	2	2	no	—
1014	C₂⁴	—	2	1	no	—
1015	#41	—	4	1	no	—
1016	#41	—	4	1	no	—
1017	#41	—	4	1	no	—
1018	#41	—	4	1	no	—
1019	#41	—	8	2	no	—
1020	#41	—	8	2	no	—
1021	#41	—	8	2	no	—
1022	#41	—	8	2	no	—
1023	#41	—	8	2	no	—
1024	#41	—	8	2	no	—
1025	C₂×Q₈	—	2	1	no	—
1026	C₂×Q₈	—	2	1	no	—
1027	C₂×Q₈	—	2	1	no	—
1028	C₂×Q₈	—	2	1	no	—
1029	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1030	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1031	C₂×D₄	—	2	1	no	—
1032	C₂×D₄	—	2	1	no	—
1033	C₂×D₄	—	2	1	no	—
1034	C₂×D₄	—	2	2	no	—
1035	C₂×D₄	—	2	2	no	—
1036	C₂×D₄	—	2	2	no	—
1037	C₂×D₄	—	2	2	no	—
1038	C₂×D₄	—	2	1	no	—
1039	C₂×D₄	—	2	1	no	—
1040	C₂×D₄	—	2	1	no	—
1041	C₂×D₄	—	2	1	no	—
1042	C₂×D₄	—	2	1	no	—
1043	C₂×D₄	—	2	2	no	—
1044	C₂×D₄	—	2	1	no	—
1045	C₂×D₄	—	2	1	no	—
1046	C₂×D₄	—	2	1	no	—
1047	C₂×D₄	—	2	1	no	—
1048	C₂×D₄	—	2	1	no	—
1049	C₂×D₄	—	2	1	no	—
1050	C₂×D₄	—	2	1	no	—
1051	C₂×D₄	—	2	1	no	—
1052	C₂×D₄	—	2	2	no	—
1053	C₂×D₄	—	2	2	no	—
1054	C₂×D₄	—	4	2	no	—
1055	C₂×D₄	—	4	2	no	—
1056	C₂×D₄	—	4	1	no	—
1057	C₂×D₄	—	4	1	no	—
1058	C₂×D₄	—	8	2	no	—
1059	C₂×D₄	—	8	2	no	—
1060	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1061	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1062	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1063	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1064	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1065	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1066	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1067	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1068	C₂²×C₄	—	2	1	no	—
1069	C₂²×C₄	—	2	1	no	—
1070	C₂²×C₄	—	2	1	no	—
1071	C₂²×C₄	—	2	1	no	—
1072	C₂²×C₄	—	2	1	no	—
1073	C₂²×C₄	—	2	1	no	—
1074	C₂²×C₄	—	2	2	no	—
1075	C₂²×C₄	—	2	2	no	—
1076	C₂²×C₄	—	2	2	no	—
1077	C₂²×C₄	—	2	2	no	—
1078	C₂²×C₄	—	2	1	no	—
1079	C₂²×C₄	—	2	1	no	—
1080	C₂²×C₄	—	8	2	no	—
1081	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1082	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1083	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	C₂⁴×C₃₁	1	1	yes	characteristic
1088	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1089	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1090	SD₁₆	—	4	2	no	—
1091	SD₁₆	—	4	2	no	—
1092	D₈	—	4	2	no	—
1093	D₈	—	4	2	no	—
1094	D₈	—	4	2	no	—
1095	D₈	—	4	2	no	—
1096	D₈	—	4	2	no	—
1097	D₈	—	4	2	no	—
1098	M₁₆	—	4	2	no	—
1099	C₂×C₈	—	4	2	no	—
1100	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1101	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1102	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1103	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1104	C₄⋊C₄	—	2	1	no	—
1105	C₄⋊C₄	—	2	1	no	—
1106	C₄⋊C₄	—	2	1	no	—
1107	C₄⋊C₄	—	2	1	no	—
1108	C₄⋊C₄	—	2	1	no	—
1109	C₄⋊C₄	—	2	1	no	—
1110	C₄⋊C₄	—	2	1	no	—
1111	C₄⋊C₄	—	2	1	no	—
1112	C₄⋊C₄	—	2	1	no	—
1113	C₄⋊C₄	—	2	1	no	—
1114	C₄⋊C₄	—	2	1	no	—
1115	C₄⋊C₄	—	2	1	no	—
1116	C₄⋊C₄	—	2	1	no	—
1117	C₄⋊C₄	—	2	2	no	—
1118	C₄⋊C₄	—	2	2	no	—
1119	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1120	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1121	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1122	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1123	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1124	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1125	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1126	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1127	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1128	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1129	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1130	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1131	C₂²⋊C₄	—	2	2	no	—
1132	C₂²⋊C₄	—	2	1	no	—
1133	C₂²⋊C₄	—	2	1	no	—
1134	C₂²⋊C₄	—	2	1	no	—
1135	C₂²⋊C₄	—	2	2	no	—
1136	C₂²⋊C₄	—	2	2	no	—
1137	C₂²⋊C₄	—	2	2	no	—
1138	C₂²⋊C₄	—	2	2	no	—
1139	C₂²⋊C₄	—	2	1	no	—
1140	C₂²⋊C₄	—	2	1	no	—
1141	C₂²⋊C₄	—	2	1	no	—
1142	C₂²⋊C₄	—	2	1	no	—
1143	C₂²⋊C₄	—	2	1	no	—
1144	C₂²⋊C₄	—	2	1	no	—
1145	C₂²⋊C₄	—	2	1	no	—
1146	C₂²⋊C₄	—	2	1	no	—
1147	C₂²⋊C₄	—	2	1	no	—
1148	C₂²⋊C₄	—	2	1	no	—
1149	C₂²⋊C₄	—	2	1	no	—
1150	C₂²⋊C₄	—	2	1	no	—
1151	C₂²⋊C₄	—	2	1	no	—
1152	C₂²⋊C₄	—	2	1	no	—
1153	C₂²⋊C₄	—	2	2	no	—
1154	C₂²⋊C₄	—	2	2	no	—
1155	C₂²⋊C₄	—	2	2	no	—
1156	C₂²⋊C₄	—	2	2	no	—
1157	C₂²⋊C₄	—	2	1	no	—
1158	C₂²⋊C₄	—	2	1	no	—
1159	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1160	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1161	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1162	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1163	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1164	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1165	C₄²	—	2	1	no	—
1166	C₄²	—	2	1	no	—
1167	C₄²	—	2	1	no	—
1168	C₄²	—	2	2	no	—
1169	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1170	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1171	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1172	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1173	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1174	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1175	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1176	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1177	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1178	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1179	C₂³	—	2	1	no	—
1180	C₂³	—	2	1	no	—
1181	C₂³	—	2	1	no	—
1182	C₂³	—	2	2	no	—
1183	C₂³	—	2	2	no	—
1184	C₂³	—	4	2	no	—
1185	C₂³	—	4	4	no	—
1186	C₂³	—	8	1	no	—
1187	C₂³	—	8	1	no	—
1188	C₂³	—	8	2	no	—
1189	C₂³	—	8	2	no	—
1190	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1191	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1192	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1193	Q₈	—	2	1	no	—
1194	Q₈	—	2	1	no	—
1195	Q₈	—	4	1	no	—
1196	Q₈	—	4	2	no	—
1197	Q₈	—	4	2	no	—
1198	Q₈	—	8	1	no	—
1199	Q₈	—	8	1	no	—
1200	D₄	—	2	1	no	—
1201	D₄	—	2	1	no	—
1202	D₄	—	2	1	no	—
1203	D₄	—	2	1	no	—
1204	D₄	—	2	2	no	—
1205	D₄	—	2	2	no	—
1206	D₄	—	2	1	no	—
1207	D₄	—	2	1	no	—
1208	D₄	—	2	2	no	—
1209	D₄	—	2	2	no	—
1210	D₄	—	4	1	no	—
1211	D₄	—	4	1	no	—
1212	D₄	—	4	1	no	—
1213	D₄	—	4	2	no	—
1214	D₄	—	4	4	no	—
1215	D₄	—	4	2	no	—
1216	D₄	—	4	2	no	—
1217	D₄	—	4	2	no	—
1218	D₄	—	4	2	no	—
1219	D₄	—	4	2	no	—
1220	D₄	—	8	1	no	—
1221	D₄	—	8	1	no	—
1222	D₄	—	8	2	no	—
1223	D₄	—	8	2	no	—
1224	D₄	—	8	1	no	—
1225	D₄	—	8	1	no	—
1226	D₄	—	8	1	no	—
1227	D₄	—	8	1	no	—
1228	D₄	—	8	1	no	—
1229	D₄	—	8	1	no	—
1230	D₄	—	8	1	no	—
1231	D₄	—	8	1	no	—
1232	D₄	—	8	2	no	—
1233	D₄	—	8	2	no	—
1234	D₄	—	8	2	no	—
1235	D₄	—	8	2	no	—
1236	C₂×C₄	—	2	2	no	—
1237	C₂×C₄	—	2	2	no	—
1238	C₂×C₄	—	2	2	no	—
1239	C₂×C₄	—	2	1	no	—
1240	C₂×C₄	—	2	1	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	1	no	—
1247	C₂×C₄	—	2	1	no	—
1248	C₂×C₄	—	2	2	no	—
1249	C₂×C₄	—	2	2	no	—
1250	C₂×C₄	—	2	1	no	—
1251	C₂×C₄	—	2	1	no	—
1252	C₂×C₄	—	4	1	no	—
1253	C₂×C₄	—	4	1	no	—
1254	C₂×C₄	—	4	1	no	—
1255	C₂×C₄	—	4	2	no	—
1256	C₂×C₄	—	4	2	no	—
1257	C₂×C₄	—	4	2	no	—
1258	C₂×C₄	—	4	2	no	—
1259	C₂×C₄	—	8	1	no	—
1260	C₂×C₄	—	8	1	no	—
1261	C₂×C₄	—	8	1	no	—
1262	C₂×C₄	—	8	2	no	—
1263	C₂×C₄	—	8	2	no	—
1264	C₂×C₄	—	8	2	no	—
1265	C₂×C₄	—	8	2	no	—
1266	C₂×C₄	—	8	1	no	—
1267	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1268	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1269	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1270	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1271	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1272	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1273	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1274	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1275	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1276	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1277	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1278	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1279	C₈	—	2	2	no	—
1280	C₈	—	2	2	no	—
1281	C₈	—	2	2	no	—
1282	C₈	—	2	2	no	—
1283	C₂²	—	2	1	no	—
1284	C₂²	—	2	1	no	—
1285	C₂²	—	2	1	no	—
1286	C₂²	—	2	1	no	—
1287	C₂²	—	2	1	no	—
1288	C₂²	—	2	1	no	—
1289	C₂²	—	2	1	no	—
1290	C₂²	—	2	1	no	—
1291	C₂²	—	2	1	no	—
1292	C₂²	—	4	1	no	—
1293	C₂²	—	4	1	no	—
1294	C₂²	—	4	1	no	—
1295	C₂²	—	4	2	no	—
1296	C₂²	—	4	2	no	—
1297	C₂²	—	4	1	no	—
1298	C₂²	—	4	1	no	—
1299	C₂²	—	4	1	no	—
1300	C₂²	—	4	2	no	—
1301	C₂²	—	4	2	no	—
1302	C₂²	—	4	2	no	—
1303	C₂²	—	4	2	no	—
1304	C₂²	—	4	1	no	—
1305	C₂²	—	4	1	no	—
1306	C₂²	—	4	1	no	—
1307	C₂²	—	8	4	no	—
1308	C₂²	—	16	4	no	—
1309	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1310	C₄	—	2	1	no	—
1311	C₄	—	2	1	no	—
1312	C₄	—	2	1	no	—
1313	C₄	—	2	1	no	—
1314	C₄	—	2	1	no	—
1315	C₄	—	2	1	no	—
1316	C₄	—	2	1	no	—
1317	C₄	—	2	1	no	—
1318	C₄	—	2	1	no	—
1319	C₄	—	2	1	no	—
1320	C₄	—	4	1	no	—
1321	C₄	—	4	1	no	—
1322	C₄	—	4	1	no	—
1323	C₄	—	4	1	no	—
1324	C₄	—	4	2	no	—
1325	C₄	—	4	2	no	—
1326	C₄	—	4	1	no	—
1327	C₄	C₃₁×#576	1	2	yes	—
1328	C₄	C₃₁×#585	1	1	yes	characteristic
1329	C₄	C₃₁×#585	1	1	yes	characteristic
1330	C₂	—	4	1	no	—
1331	C₂	—	4	1	no	—
1332	C₂	—	4	1	no	—
1333	C₂	—	8	1	no	—
1334	C₂	—	8	1	no	—
1335	C₂	—	8	2	no	—
1336	C₂	—	8	2	no	—
1337	C₂	—	8	1	no	—
1338	C₂	C₃₁×#3449	1	1	yes	characteristic
1339	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1340	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×#3508	C₂	semidirect
2. C₃₁×#3460	C₂	semidirect
3. C₃₁×#3253	C₂	semidirect
4. C₃₁×#3251	C₂	semidirect
5. C₃₁×#3247	C₂	semidirect
6. C₃₁×#3245	C₂	semidirect
7. C₃₁×#3241	C₂	semidirect
8. C₃₁×#3235	C₂	semidirect
9. C₃₁×#3233	C₂	semidirect
10. C₃₁×#3220	C₂	semidirect
11. C₃₁×#3217	C₂	semidirect
12. C₃₁×#3205	C₂	semidirect
13. C₃₁×#3199	C₂	semidirect
14. C₃₁×#3198	C₂	semidirect
15. C₃₁×#3179	C₂	semidirect
16. C₃₁×#3176	C₂	semidirect
17. C₃₁×#3122	C₂	semidirect
18. C₃₁×#3118	C₂	semidirect
19. C₃₁×#3115	C₂	semidirect
20. C₃₁×#3109	C₂	semidirect
21. C₃₁×#3106	C₂	semidirect
22. C₃₁×#3100	C₂	semidirect
23. C₃₁×#2925	C₂	semidirect
32. C₃₁×#544	C₂²	semidirect
35. C₃₁×#542	C₂²	semidirect
39. C₃₁×#540	C₂²	semidirect
40. C₃₁×#540	C₂²	semidirect
46. C₃₁×#535	C₂²	semidirect
47. C₃₁×#533	C₂²	semidirect
52. C₃₁×#532	C₂²	semidirect
53. C₃₁×#532	C₂²	semidirect
54. C₃₁×#532	C₂²	semidirect
55. C₂×C₃₁×#127	C₂²	semidirect
58. C₃₁×#529	C₂²	semidirect
61. C₃₁×#518	C₂²	semidirect
63. C₄×#41×C₃₁	C₂²	semidirect
64. C₂×C₄×D₄×C₃₁	C₂²	semidirect
65. C₃₁×#501	C₂²	semidirect
66. C₃₁×#499	C₂²	semidirect
69. C₃₁×#490	C₂²	semidirect
70. C₃₁×#490	C₂²	semidirect
71. C₃₁×#488	C₂²	semidirect
72. C₃₁×#486	C₂²	semidirect
73. C₃₁×#485	C₂²	semidirect
76. C₃₁×#482	C₂²	semidirect
77. C₃₁×#482	C₂²	semidirect
78. C₃₁×#482	C₂²	semidirect
79. C₃₁×#481	C₂²	semidirect
80. C₃₁×#480	C₂²	semidirect
81. C₃₁×#478	C₂²	semidirect
82. C₃₁×#478	C₂²	semidirect
83. C₃₁×#477	C₂²	semidirect
84. C₃₁×#476	C₂²	semidirect
85. C₃₁×#476	C₂²	semidirect
86. C₃₁×#476	C₂²	semidirect
87. C₃₁×#476	C₂²	semidirect
88. C₃₁×#475	C₂²	semidirect
89. C₃₁×#474	C₂²	semidirect
90. C₃₁×#474	C₂²	semidirect
91. C₃₁×#474	C₂²	semidirect
92. C₃₁×#474	C₂²	semidirect
93. C₃₁×#469	C₂²	semidirect
94. C₃₁×#469	C₂²	semidirect
95. C₃₁×#469	C₂²	semidirect
96. C₃₁×#468	C₂²	semidirect
97. C₃₁×#466	C₂²	semidirect
98. C₃₁×#466	C₂²	semidirect
99. C₃₁×#466	C₂²	semidirect
100. C₃₁×#465	C₂²	semidirect
101. C₃₁×#463	C₂²	semidirect
102. C₃₁×#463	C₂²	semidirect
103. C₃₁×#460	C₂²	semidirect
104. C₃₁×#460	C₂²	semidirect
109. C₃₁×#459	C₂²	semidirect
110. C₃₁×#459	C₂²	semidirect
111. C₃₁×#459	C₂²	semidirect
112. C₃₁×#459	C₂²	semidirect
113. C₃₁×#450	C₂²	semidirect
114. C₃₁×#449	C₂²	semidirect
115. C₃₁×#449	C₂²	semidirect
118. C₃₁×#447	C₂²	semidirect
119. C₃₁×#447	C₂²	semidirect
120. C₃₁×#447	C₂²	semidirect
121. C₃₁×#442	C₂²	semidirect
122. C₃₁×#442	C₂²	semidirect
123. C₃₁×#442	C₂²	semidirect
124. C₃₁×#440	C₂²	semidirect
125. C₄×SD₁₆×C₃₁	C₂²	semidirect
126. C₄×D₈×C₃₁	C₂²	semidirect
127. C₄×D₈×C₃₁	C₂²	semidirect
128. C₄×D₈×C₃₁	C₂²	semidirect
129. C₃₁×#433	C₂²	semidirect
130. C₃₁×#433	C₂²	semidirect
131. C₃₁×#432	C₂²	semidirect
132. C₃₁×#432	C₂²	semidirect
133. C₃₁×#431	C₂²	semidirect
134. C₃₁×#431	C₂²	semidirect
135. C₃₁×#423	C₂²	semidirect
136. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
138. C₃₁×#405	C₂²	semidirect
508. #60990	C₃₁	direct (N × H)
613. #3508	C₂×C₃₁	semidirect
614. #3460	C₂×C₃₁	semidirect
615. #3253	C₂×C₃₁	semidirect
616. #3251	C₂×C₃₁	semidirect
617. #3247	C₂×C₃₁	semidirect
618. #3245	C₂×C₃₁	semidirect
619. #3241	C₂×C₃₁	semidirect
620. #3235	C₂×C₃₁	semidirect
621. #3233	C₂×C₃₁	semidirect
622. #3220	C₂×C₃₁	semidirect
623. #3217	C₂×C₃₁	semidirect
624. #3205	C₂×C₃₁	semidirect
625. #3199	C₂×C₃₁	semidirect
626. #3198	C₂×C₃₁	semidirect
627. #3179	C₂×C₃₁	semidirect
628. #3176	C₂×C₃₁	semidirect
629. #3122	C₂×C₃₁	semidirect
630. #3118	C₂×C₃₁	semidirect
631. #3115	C₂×C₃₁	semidirect
632. #3109	C₂×C₃₁	semidirect
633. #3106	C₂×C₃₁	semidirect
634. #3100	C₂×C₃₁	semidirect
635. #2925	C₂×C₃₁	semidirect
691. #544	C₂²×C₃₁	semidirect
694. #542	C₂²×C₃₁	semidirect
698. #540	C₂²×C₃₁	semidirect
699. #540	C₂²×C₃₁	semidirect
705. #535	C₂²×C₃₁	semidirect
706. #533	C₂²×C₃₁	semidirect
711. #532	C₂²×C₃₁	semidirect
712. #532	C₂²×C₃₁	semidirect
713. #532	C₂²×C₃₁	semidirect
714. C₂×#127	C₂²×C₃₁	semidirect
717. #529	C₂²×C₃₁	semidirect
720. #518	C₂²×C₃₁	semidirect
722. C₄×#41	C₂²×C₃₁	semidirect
723. C₂×C₄×D₄	C₂²×C₃₁	semidirect
724. #501	C₂²×C₃₁	semidirect
725. #499	C₂²×C₃₁	semidirect
728. #490	C₂²×C₃₁	semidirect
729. #490	C₂²×C₃₁	semidirect
730. #488	C₂²×C₃₁	semidirect
731. #486	C₂²×C₃₁	semidirect
732. #485	C₂²×C₃₁	semidirect
735. #482	C₂²×C₃₁	semidirect
736. #482	C₂²×C₃₁	semidirect
737. #482	C₂²×C₃₁	semidirect
738. #481	C₂²×C₃₁	semidirect
739. #480	C₂²×C₃₁	semidirect
740. #478	C₂²×C₃₁	semidirect
741. #478	C₂²×C₃₁	semidirect
742. #477	C₂²×C₃₁	semidirect
743. #476	C₂²×C₃₁	semidirect
744. #476	C₂²×C₃₁	semidirect
745. #476	C₂²×C₃₁	semidirect
746. #476	C₂²×C₃₁	semidirect
747. #475	C₂²×C₃₁	semidirect
748. #474	C₂²×C₃₁	semidirect
749. #474	C₂²×C₃₁	semidirect
750. #474	C₂²×C₃₁	semidirect
751. #474	C₂²×C₃₁	semidirect
752. #469	C₂²×C₃₁	semidirect
753. #469	C₂²×C₃₁	semidirect
754. #469	C₂²×C₃₁	semidirect
755. #468	C₂²×C₃₁	semidirect
756. #466	C₂²×C₃₁	semidirect
757. #466	C₂²×C₃₁	semidirect
758. #466	C₂²×C₃₁	semidirect
759. #465	C₂²×C₃₁	semidirect
760. #463	C₂²×C₃₁	semidirect
761. #463	C₂²×C₃₁	semidirect
762. #460	C₂²×C₃₁	semidirect
763. #460	C₂²×C₃₁	semidirect
768. #459	C₂²×C₃₁	semidirect
769. #459	C₂²×C₃₁	semidirect
770. #459	C₂²×C₃₁	semidirect
771. #459	C₂²×C₃₁	semidirect
772. #450	C₂²×C₃₁	semidirect
773. #449	C₂²×C₃₁	semidirect
774. #449	C₂²×C₃₁	semidirect
777. #447	C₂²×C₃₁	semidirect
778. #447	C₂²×C₃₁	semidirect
779. #447	C₂²×C₃₁	semidirect
780. #442	C₂²×C₃₁	semidirect
781. #442	C₂²×C₃₁	semidirect
782. #442	C₂²×C₃₁	semidirect
783. #440	C₂²×C₃₁	semidirect
784. C₄×SD₁₆	C₂²×C₃₁	semidirect
785. C₄×D₈	C₂²×C₃₁	semidirect
786. C₄×D₈	C₂²×C₃₁	semidirect
787. C₄×D₈	C₂²×C₃₁	semidirect
788. #433	C₂²×C₃₁	semidirect
789. #433	C₂²×C₃₁	semidirect
790. #432	C₂²×C₃₁	semidirect
791. #432	C₂²×C₃₁	semidirect
792. #431	C₂²×C₃₁	semidirect
793. #431	C₂²×C₃₁	semidirect
794. #423	C₂²×C₃₁	semidirect
795. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
797. #405	C₂²×C₃₁	semidirect
1012. C₃₁	#60990	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×#3508	2
C₃₁×#3460	2
C₃₁×#3253	2
C₃₁×#3251	2
C₃₁×#3247	2
C₃₁×#3245	2
C₃₁×#3241	2
C₃₁×#3235	2
C₃₁×#3233	2
C₃₁×#3220	2
C₃₁×#3217	2
C₃₁×#3205	2
C₃₁×#3199	2
C₃₁×#3198	2
C₃₁×#3179	2
C₃₁×#3176	2
C₃₁×#3122	2
C₃₁×#3118	2
C₃₁×#3115	2
C₃₁×#3109	2
C₃₁×#3106	2
C₃₁×#3100	2
C₃₁×#2925	2
#60990	31

Subgroups — C31×#60990 #21517749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60990 #21517749