Subgroups — C₃₁×#61981 #21518740

Order 7936.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1324 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×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3401	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3371	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3317	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3306	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3296	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3282	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3271	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3266	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3251	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3248	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3217	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3216	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3212	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3103	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
25	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
27	C₃₁×#559	—	2	1	no	—
28	C₃₁×#559	C₂²	1	2	yes	—
29	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#556	—	2	1	no	—
31	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#552	—	2	1	no	—
33	C₃₁×#552	—	2	1	no	—
34	C₃₁×#552	C₂²	1	1	yes	characteristic
35	C₃₁×#552	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#550	—	2	1	no	—
37	C₃₁×#550	C₂²	1	2	yes	—
38	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
39	C₃₁×#548	C₂²	1	1	yes	characteristic
40	C₃₁×#548	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#547	—	2	1	no	—
42	C₃₁×#547	C₂²	1	1	yes	characteristic
43	C₃₁×#546	—	2	1	no	—
44	C₃₁×#546	—	2	1	no	—
45	C₃₁×#546	C₂²	1	2	yes	—
46	C₃₁×#546	C₂²	1	2	yes	—
47	C₃₁×#540	—	2	1	no	—
48	C₃₁×#540	—	2	1	no	—
49	C₃₁×#535	—	2	1	no	—
50	C₃₁×#533	—	2	1	no	—
51	C₃₁×#533	C₂²	1	1	yes	characteristic
52	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#532	C₂²	1	1	yes	characteristic
54	C₃₁×#532	C₂²	1	1	yes	characteristic
55	C₃₁×#532	C₂²	1	1	yes	characteristic
56	C₃₁×#532	C₂²	1	1	yes	characteristic
57	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
58	C₃₁×#529	—	2	1	no	—
59	C₃₁×#529	—	2	1	no	—
60	C₃₁×#529	C₂²	1	1	yes	characteristic
61	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#518	—	2	1	no	—
63	C₄×#41×C₃₁	—	2	1	no	—
64	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
65	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
67	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#497	C₂²	1	2	yes	complemented
69	C₃₁×#496	C₂²	1	2	yes	—
70	C₃₁×#495	C₂²	1	2	yes	complemented
71	C₃₁×#490	C₂²	1	2	yes	—
72	C₃₁×#489	C₂²	1	2	yes	complemented
73	C₃₁×#488	C₂²	1	2	yes	complemented
74	C₃₁×#483	C₂²	1	2	yes	—
75	C₃₁×#482	C₂²	1	2	yes	complemented
76	C₃₁×#481	C₂²	1	2	yes	complemented
77	C₃₁×#479	C₂²	1	2	yes	complemented
78	C₃₁×#478	C₂²	1	2	yes	complemented
79	C₃₁×#476	C₂²	1	2	yes	complemented
80	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#469	C₂²	1	2	yes	complemented
85	C₃₁×#468	C₂²	1	2	yes	complemented
86	C₃₁×#467	C₂²	1	2	yes	—
87	C₃₁×#465	C₂²	1	2	yes	—
88	C₃₁×#465	C₂²	1	2	yes	complemented
89	C₃₁×#465	C₂²	1	2	yes	complemented
90	C₃₁×#464	C₂²	1	2	yes	complemented
91	C₃₁×#464	C₂²	1	2	yes	complemented
92	C₃₁×#464	C₂²	1	2	yes	complemented
93	C₃₁×#464	C₂²	1	2	yes	complemented
94	C₃₁×#463	C₂²	1	2	yes	complemented
95	C₃₁×#463	C₂²	1	2	yes	complemented
96	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#461	C₂²	1	2	yes	complemented
100	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×#460	C₂²	1	1	yes	characteristic
102	C₃₁×#460	C₂²	1	1	yes	characteristic
103	C₃₁×#460	C₂²	1	1	yes	characteristic
104	C₃₁×#460	C₂²	1	2	yes	—
105	C₃₁×#460	C₂²	1	2	yes	—
106	C₃₁×#460	C₂²	1	1	yes	characteristic
107	C₃₁×#460	C₂²	1	1	yes	characteristic
108	C₃₁×#460	C₂²	1	1	yes	characteristic
109	C₃₁×#459	C₂²	1	1	yes	characteristic
110	C₃₁×#459	C₂²	1	1	yes	characteristic
111	C₃₁×#452	C₂²	1	2	yes	complemented
112	C₃₁×#452	C₂²	1	2	yes	complemented
113	C₃₁×#452	C₂²	1	2	yes	complemented
114	C₃₁×#451	C₂²	1	2	yes	—
115	C₃₁×#450	C₂²	1	2	yes	—
116	C₃₁×#449	C₂²	1	2	yes	complemented
117	C₃₁×#449	C₂²	1	2	yes	complemented
118	C₃₁×#448	C₂²	1	2	yes	complemented
119	C₃₁×#447	C₂²	1	2	yes	—
120	C₃₁×#446	C₂²	1	2	yes	complemented
121	C₃₁×#442	C₂²	1	2	yes	complemented
122	C₃₁×#441	C₂²	1	2	yes	complemented
123	C₃₁×#441	C₂²	1	2	yes	complemented
124	C₃₁×#440	C₂²	1	2	yes	complemented
125	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
126	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
127	C₃₁×#435	C₂²	1	2	yes	—
128	C₃₁×#435	C₂²	1	2	yes	complemented
129	C₈×D₄×C₃₁	C₂²	1	2	yes	—
130	C₃₁×#432	C₂²	1	1	yes	characteristic
131	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
133	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
135	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
136	C₃₁×#417	C₂²	1	2	yes	complemented
137	C₃₁×#416	C₂²	1	2	yes	complemented
138	C₂×C₃₁×#102	C₂²	1	2	yes	—
139	C₂×#41×C₃₁	—	2	1	no	—
140	C₂×#41×C₃₁	—	2	1	no	—
141	C₂×#41×C₃₁	—	2	1	no	—
142	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
143	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×#41×C₃₁	C₂³	1	2	yes	—
145	C₂×#41×C₃₁	C₂³	1	2	yes	—
146	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
147	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
148	C₂²×D₄×C₃₁	—	2	1	no	—
149	C₂²×D₄×C₃₁	—	2	1	no	—
150	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
151	C₃₁×#137	—	4	4	no	—
152	C₃₁×#135	—	4	4	no	—
153	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₃₁	—	4	4	no	—
157	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
164	C₂×D₈×C₃₁	C₂³	1	2	yes	—
165	C₂×D₈×C₃₁	C₂³	1	2	yes	—
166	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
167	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
168	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
169	C₃₁×C₄⋊Q₈	—	2	1	no	—
170	C₃₁×C₄⋊Q₈	—	2	1	no	—
171	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
173	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
174	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
175	C₃₁×#127	—	2	2	no	—
176	C₃₁×#127	—	2	1	no	—
177	C₃₁×#127	—	2	1	no	—
178	C₃₁×#127	C₂³	1	1	yes	characteristic
179	C₃₁×#127	C₂³	1	1	yes	characteristic
180	C₃₁×#127	C₂³	1	2	yes	—
181	C₃₁×#126	—	2	1	no	—
182	C₃₁×#126	—	2	1	no	—
183	C₃₁×#126	—	2	1	no	—
184	C₃₁×#126	—	2	1	no	—
185	C₃₁×#126	—	2	1	no	—
186	C₃₁×#126	—	2	1	no	—
187	C₃₁×#125	—	2	1	no	—
188	C₃₁×#125	—	2	1	no	—
189	C₃₁×#125	—	2	1	no	—
190	C₃₁×#125	—	2	1	no	—
191	C₃₁×#125	—	2	1	no	—
192	C₃₁×#125	—	2	1	no	—
193	C₃₁×#125	C₂³	1	1	yes	characteristic
194	C₃₁×#125	C₂³	1	1	yes	characteristic
195	C₃₁×#124	—	2	2	no	—
196	C₃₁×#124	—	2	1	no	—
197	C₃₁×#124	—	2	1	no	—
198	C₃₁×#124	—	2	1	no	—
199	C₃₁×#124	—	2	1	no	—
200	C₃₁×#124	C₂³	1	1	yes	characteristic
201	C₃₁×#124	C₂³	1	2	yes	—
202	C₃₁×#124	C₂³	1	2	yes	—
203	C₃₁×#124	C₂³	1	1	yes	characteristic
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×#123	—	2	2	no	—
211	C₃₁×#123	—	2	2	no	—
212	C₃₁×#123	—	2	1	no	—
213	C₃₁×#123	—	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	1	no	—
221	C₃₁×C₂²⋊Q₈	—	2	1	no	—
222	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
226	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
227	C₃₁×#121	—	2	1	no	—
228	C₃₁×#121	—	2	1	no	—
229	C₃₁×#121	—	2	1	no	—
230	C₃₁×#121	—	2	1	no	—
231	C₃₁×#121	—	2	1	no	—
232	C₃₁×#121	—	2	1	no	—
233	C₃₁×#121	—	2	1	no	—
234	C₃₁×#121	—	2	1	no	—
235	C₃₁×#121	—	2	2	no	—
236	C₃₁×#121	—	2	2	no	—
237	C₃₁×#121	—	2	2	no	—
238	C₃₁×#121	—	2	2	no	—
239	C₃₁×#121	C₂³	1	1	yes	characteristic
240	C₃₁×#121	C₂³	1	2	yes	—
241	C₃₁×#121	C₂³	1	1	yes	characteristic
242	C₃₁×#121	C₂³	1	2	yes	—
243	C₃₁×#120	—	2	2	no	—
244	C₃₁×#120	—	2	2	no	—
245	C₄×Q₈×C₃₁	—	2	1	no	—
246	C₄×Q₈×C₃₁	—	2	1	no	—
247	C₄×Q₈×C₃₁	—	2	1	no	—
248	C₄×Q₈×C₃₁	—	2	1	no	—
249	C₄×Q₈×C₃₁	—	2	1	no	—
250	C₄×Q₈×C₃₁	—	2	1	no	—
251	C₄×Q₈×C₃₁	—	2	1	no	—
252	C₄×Q₈×C₃₁	D₄	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×Q₈×C₃₁	C₂³	1	1	yes	characteristic
257	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
258	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
259	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
260	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
261	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
262	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
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	1	no	—
267	C₄×D₄×C₃₁	—	2	1	no	—
268	C₄×D₄×C₃₁	—	2	2	no	—
269	C₄×D₄×C₃₁	—	2	2	no	—
270	C₄×D₄×C₃₁	—	2	1	no	—
271	C₄×D₄×C₃₁	—	2	1	no	—
272	C₄×D₄×C₃₁	—	2	1	no	—
273	C₄×D₄×C₃₁	—	2	1	no	—
274	C₄×D₄×C₃₁	—	2	1	no	—
275	C₄×D₄×C₃₁	—	2	1	no	—
276	C₄×D₄×C₃₁	—	2	1	no	—
277	C₄×D₄×C₃₁	—	2	1	no	—
278	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
279	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
280	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
281	C₄×D₄×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
287	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
288	C₃₁×#117	—	2	1	no	—
289	C₃₁×#117	—	2	1	no	—
290	C₃₁×#117	—	2	1	no	—
291	C₃₁×#117	—	2	1	no	—
292	C₃₁×#117	—	2	1	no	—
293	C₃₁×#117	—	2	1	no	—
294	C₃₁×#117	—	2	1	no	—
295	C₃₁×#117	—	2	1	no	—
296	C₃₁×#117	D₄	1	1	yes	characteristic
297	C₃₁×#117	D₄	1	1	yes	characteristic
298	C₃₁×#117	D₄	1	1	yes	characteristic
299	C₃₁×#117	C₂³	1	1	yes	characteristic
300	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
301	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
302	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
303	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
305	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
306	C₂×C₄²×C₃₁	—	2	1	no	—
307	C₂×C₄²×C₃₁	—	2	1	no	—
308	C₂×C₄²×C₃₁	—	2	1	no	—
309	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
310	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
312	C₃₁×#107	C₂³	1	2	yes	—
313	C₃₁×#106	C₂³	1	2	yes	—
314	C₃₁×#106	C₂³	1	2	yes	—
315	C₃₁×#106	C₂³	1	2	yes	—
316	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
317	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
318	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
319	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
320	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
321	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
322	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#102	C₂³	1	2	yes	—
331	C₃₁×#102	C₂³	1	2	yes	—
332	C₃₁×#102	C₂³	1	2	yes	—
333	C₃₁×#102	C₂³	1	2	yes	—
334	C₃₁×#102	C₂³	1	2	yes	—
335	C₃₁×#102	C₂³	1	2	yes	—
336	C₃₁×#102	C₂³	1	2	yes	—
337	C₃₁×#102	C₂³	1	2	yes	—
338	C₃₁×#102	C₂³	1	2	yes	—
339	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
340	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
341	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
342	C₃₁×#97	C₂³	1	2	yes	—
343	C₃₁×#97	C₂³	1	2	yes	—
344	C₄×C₈×C₃₁	C₂³	1	2	yes	—
345	C₂⁴×C₃₁	—	2	2	no	—
346	#41×C₃₁	—	2	2	no	—
347	#41×C₃₁	—	4	2	no	—
348	#41×C₃₁	—	4	1	no	—
349	#41×C₃₁	—	4	2	no	—
350	#41×C₃₁	—	4	2	no	—
351	#41×C₃₁	—	4	2	no	—
352	#41×C₃₁	—	4	2	no	—
353	#41×C₃₁	—	4	4	no	—
354	#41×C₃₁	—	8	2	no	—
355	#41×C₃₁	—	8	2	no	—
356	C₂×Q₈×C₃₁	—	2	1	no	—
357	C₂×Q₈×C₃₁	—	2	1	no	—
358	C₂×Q₈×C₃₁	—	2	1	no	—
359	C₂×Q₈×C₃₁	—	2	1	no	—
360	C₂×Q₈×C₃₁	—	2	2	no	—
361	C₂×Q₈×C₃₁	—	2	2	no	—
362	C₂×Q₈×C₃₁	—	4	1	no	—
363	C₂×Q₈×C₃₁	—	4	1	no	—
364	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
365	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
366	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	no	—
374	C₂×D₄×C₃₁	—	2	2	no	—
375	C₂×D₄×C₃₁	—	2	2	no	—
376	C₂×D₄×C₃₁	—	2	1	no	—
377	C₂×D₄×C₃₁	—	2	1	no	—
378	C₂×D₄×C₃₁	—	2	2	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	4	no	—
386	C₂×D₄×C₃₁	—	8	2	no	—
387	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
388	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
389	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
390	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
391	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
392	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₃₁	—	2	1	no	—
394	C₂²×C₄×C₃₁	—	2	1	no	—
395	C₂²×C₄×C₃₁	—	2	1	no	—
396	C₂²×C₄×C₃₁	—	2	1	no	—
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	2	no	—
401	C₂²×C₄×C₃₁	—	2	2	no	—
402	C₂²×C₄×C₃₁	—	2	2	no	—
403	C₂²×C₄×C₃₁	—	2	2	no	—
404	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
405	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
406	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
407	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
408	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
409	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
410	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
413	Q₁₆×C₃₁	—	2	4	no	—
414	Q₁₆×C₃₁	—	4	2	no	—
415	Q₁₆×C₃₁	—	4	2	no	—
416	SD₁₆×C₃₁	—	2	4	no	—
417	SD₁₆×C₃₁	—	2	4	no	—
418	SD₁₆×C₃₁	—	4	2	no	—
419	SD₁₆×C₃₁	—	4	2	no	—
420	SD₁₆×C₃₁	—	4	2	no	—
421	SD₁₆×C₃₁	—	4	2	no	—
422	SD₁₆×C₃₁	—	4	2	no	—
423	D₈×C₃₁	—	4	2	no	—
424	D₈×C₃₁	—	4	2	no	—
425	M₁₆×C₃₁	—	4	2	no	—
426	C₂×C₈×C₃₁	—	4	2	no	—
427	C₂×C₈×C₃₁	—	4	2	no	—
428	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₃₁	—	2	1	no	—
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	1	no	—
447	C₄⋊C₄×C₃₁	—	2	1	no	—
448	C₄⋊C₄×C₃₁	—	2	1	no	—
449	C₄⋊C₄×C₃₁	—	2	1	no	—
450	C₄⋊C₄×C₃₁	—	2	1	no	—
451	C₄⋊C₄×C₃₁	—	2	1	no	—
452	C₄⋊C₄×C₃₁	—	2	1	no	—
453	C₄⋊C₄×C₃₁	—	2	1	no	—
454	C₄⋊C₄×C₃₁	—	2	1	no	—
455	C₄⋊C₄×C₃₁	—	2	1	no	—
456	C₄⋊C₄×C₃₁	—	2	2	no	—
457	C₄⋊C₄×C₃₁	—	2	2	no	—
458	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
459	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
460	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
461	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
462	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
463	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
464	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
465	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
466	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
467	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
468	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
469	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
476	C₂²⋊C₄×C₃₁	—	2	2	no	—
477	C₂²⋊C₄×C₃₁	—	2	2	no	—
478	C₂²⋊C₄×C₃₁	—	2	2	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	1	no	—
483	C₂²⋊C₄×C₃₁	—	2	1	no	—
484	C₂²⋊C₄×C₃₁	—	2	1	no	—
485	C₂²⋊C₄×C₃₁	—	2	1	no	—
486	C₂²⋊C₄×C₃₁	—	2	1	no	—
487	C₂²⋊C₄×C₃₁	—	2	2	no	—
488	C₂²⋊C₄×C₃₁	—	2	2	no	—
489	C₂²⋊C₄×C₃₁	—	2	2	no	—
490	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
495	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
496	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
497	C₄²×C₃₁	—	2	1	no	—
498	C₄²×C₃₁	—	2	1	no	—
499	C₄²×C₃₁	—	2	1	no	—
500	C₄²×C₃₁	—	2	1	no	—
501	C₄²×C₃₁	—	2	1	no	—
502	C₄²×C₃₁	—	2	1	no	—
503	C₄²×C₃₁	—	2	1	no	—
504	C₄²×C₃₁	—	2	1	no	—
505	C₄²×C₃₁	—	2	1	no	—
506	C₄²×C₃₁	—	2	2	no	—
507	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
508	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
509	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
510	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
511	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
512	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
513	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
514	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
515	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
516	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
517	#61981	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
518	C₂³×C₃₁	—	2	1	no	—
519	C₂³×C₃₁	—	2	2	no	—
520	C₂³×C₃₁	—	2	2	no	—
521	C₂³×C₃₁	—	4	4	no	—
522	C₂³×C₃₁	—	8	2	no	—
523	C₂³×C₃₁	—	8	2	no	—
524	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
525	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
526	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
527	Q₈×C₃₁	—	2	1	no	—
528	Q₈×C₃₁	—	2	1	no	—
529	Q₈×C₃₁	—	2	1	no	—
530	Q₈×C₃₁	—	2	2	no	—
531	Q₈×C₃₁	—	2	1	no	—
532	Q₈×C₃₁	—	2	1	no	—
533	Q₈×C₃₁	—	2	2	no	—
534	Q₈×C₃₁	—	4	1	no	—
535	Q₈×C₃₁	—	4	2	no	—
536	Q₈×C₃₁	—	4	2	no	—
537	Q₈×C₃₁	—	4	2	no	—
538	Q₈×C₃₁	—	4	2	no	—
539	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
540	D₄×C₃₁	—	2	2	no	—
541	D₄×C₃₁	—	2	2	no	—
542	D₄×C₃₁	—	2	1	no	—
543	D₄×C₃₁	—	2	2	no	—
544	D₄×C₃₁	—	2	2	no	—
545	D₄×C₃₁	—	2	1	no	—
546	D₄×C₃₁	—	2	2	no	—
547	D₄×C₃₁	—	2	2	no	—
548	D₄×C₃₁	—	4	1	no	—
549	D₄×C₃₁	—	4	2	no	—
550	D₄×C₃₁	—	4	2	no	—
551	D₄×C₃₁	—	4	2	no	—
552	D₄×C₃₁	—	4	4	no	—
553	D₄×C₃₁	—	4	2	no	—
554	D₄×C₃₁	—	4	2	no	—
555	D₄×C₃₁	—	4	2	no	—
556	D₄×C₃₁	—	4	2	no	—
557	D₄×C₃₁	—	8	2	no	—
558	D₄×C₃₁	—	8	2	no	—
559	D₄×C₃₁	—	8	2	no	—
560	D₄×C₃₁	—	8	2	no	—
561	D₄×C₃₁	—	8	2	no	—
562	D₄×C₃₁	—	8	2	no	—
563	C₂×C₄×C₃₁	—	2	2	no	—
564	C₂×C₄×C₃₁	—	2	1	no	—
565	C₂×C₄×C₃₁	—	2	2	no	—
566	C₂×C₄×C₃₁	—	2	2	no	—
567	C₂×C₄×C₃₁	—	2	2	no	—
568	C₂×C₄×C₃₁	—	2	1	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	1	no	—
579	C₂×C₄×C₃₁	—	2	1	no	—
580	C₂×C₄×C₃₁	—	2	2	no	—
581	C₂×C₄×C₃₁	—	2	2	no	—
582	C₂×C₄×C₃₁	—	4	1	no	—
583	C₂×C₄×C₃₁	—	4	1	no	—
584	C₂×C₄×C₃₁	—	4	2	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	—	4	2	no	—
590	C₂×C₄×C₃₁	—	4	2	no	—
591	C₂×C₄×C₃₁	—	8	2	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	C₂²×D₄	1	1	yes	characteristic
596	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
607	C₈×C₃₁	—	2	2	no	—
608	C₈×C₃₁	—	2	2	no	—
609	C₈×C₃₁	—	2	2	no	—
610	C₈×C₃₁	—	2	2	no	—
611	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
612	#3482	C₂×C₃₁	1	1	yes	characteristic, complemented
613	#3401	C₂×C₃₁	1	2	yes	complemented
614	#3371	C₂×C₃₁	1	2	yes	complemented
615	#3317	C₂×C₃₁	1	2	yes	complemented
616	#3306	C₂×C₃₁	1	2	yes	complemented
617	#3296	C₂×C₃₁	1	2	yes	complemented
618	#3282	C₂×C₃₁	1	2	yes	complemented
619	#3271	C₂×C₃₁	1	2	yes	complemented
620	#3266	C₂×C₃₁	1	2	yes	complemented
621	#3251	C₂×C₃₁	1	1	yes	characteristic, complemented
622	#3248	C₂×C₃₁	1	1	yes	characteristic, complemented
623	#3246	C₂×C₃₁	1	1	yes	characteristic, complemented
624	#3217	C₂×C₃₁	1	1	yes	characteristic, complemented
625	#3216	C₂×C₃₁	1	1	yes	characteristic, complemented
626	#3212	C₂×C₃₁	1	1	yes	characteristic, complemented
627	#3115	C₂×C₃₁	1	1	yes	characteristic, complemented
628	#3113	C₂×C₃₁	1	1	yes	characteristic, complemented
629	#3103	C₂×C₃₁	1	1	yes	characteristic, complemented
630	#3037	C₂×C₃₁	1	1	yes	characteristic, complemented
631	#3035	C₂×C₃₁	1	1	yes	characteristic, complemented
632	C₂×#460	C₂×C₃₁	1	1	yes	characteristic, complemented
633	#2990	C₂×C₃₁	1	1	yes	characteristic, complemented
634	C₂²×C₃₁	—	2	1	no	—
635	C₂²×C₃₁	—	2	1	no	—
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	—	4	1	no	—
643	C₂²×C₃₁	—	4	2	no	—
644	C₂²×C₃₁	—	4	2	no	—
645	C₂²×C₃₁	—	4	1	no	—
646	C₂²×C₃₁	—	4	2	no	—
647	C₂²×C₃₁	—	4	2	no	—
648	C₂²×C₃₁	—	4	1	no	—
649	C₂²×C₃₁	—	4	2	no	—
650	C₂²×C₃₁	—	4	2	no	—
651	C₂²×C₃₁	—	16	4	no	—
652	C₂²×C₃₁	#575	1	2	yes	—
653	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
654	C₄×C₃₁	—	2	1	no	—
655	C₄×C₃₁	—	2	1	no	—
656	C₄×C₃₁	—	2	1	no	—
657	C₄×C₃₁	—	2	2	no	—
658	C₄×C₃₁	—	2	1	no	—
659	C₄×C₃₁	—	2	1	no	—
660	C₄×C₃₁	—	2	1	no	—
661	C₄×C₃₁	—	2	1	no	—
662	C₄×C₃₁	—	2	1	no	—
663	C₄×C₃₁	—	2	1	no	—
664	C₄×C₃₁	—	2	1	no	—
665	C₄×C₃₁	—	4	1	no	—
666	C₄×C₃₁	—	4	1	no	—
667	C₄×C₃₁	—	4	2	no	—
668	C₄×C₃₁	—	4	1	no	—
669	C₄×C₃₁	—	4	1	no	—
670	C₄×C₃₁	—	4	1	no	—
671	C₄×C₃₁	—	4	1	no	—
672	C₄×C₃₁	—	4	2	no	—
673	C₄×C₃₁	#577	1	2	yes	—
674	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
675	C₄×C₃₁	#585	1	1	yes	characteristic
676	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
677	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
678	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
679	#559	—	2	1	no	—
680	#559	C₂²×C₃₁	1	2	yes	—
681	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
682	#556	—	2	1	no	—
683	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	#552	—	2	1	no	—
685	#552	—	2	1	no	—
686	#552	C₂²×C₃₁	1	1	yes	characteristic
687	#552	C₂²×C₃₁	1	1	yes	characteristic, complemented
688	#550	—	2	1	no	—
689	#550	C₂²×C₃₁	1	2	yes	—
690	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
691	#548	C₂²×C₃₁	1	1	yes	characteristic
692	#548	C₂²×C₃₁	1	1	yes	characteristic, complemented
693	#547	—	2	1	no	—
694	#547	C₂²×C₃₁	1	1	yes	characteristic
695	#546	—	2	1	no	—
696	#546	—	2	1	no	—
697	#546	C₂²×C₃₁	1	2	yes	—
698	#546	C₂²×C₃₁	1	2	yes	—
699	#540	—	2	1	no	—
700	#540	—	2	1	no	—
701	#535	—	2	1	no	—
702	#533	—	2	1	no	—
703	#533	C₂²×C₃₁	1	1	yes	characteristic
704	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
705	#532	C₂²×C₃₁	1	1	yes	characteristic
706	#532	C₂²×C₃₁	1	1	yes	characteristic
707	#532	C₂²×C₃₁	1	1	yes	characteristic
708	#532	C₂²×C₃₁	1	1	yes	characteristic
709	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
710	#529	—	2	1	no	—
711	#529	—	2	1	no	—
712	#529	C₂²×C₃₁	1	1	yes	characteristic
713	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
714	#518	—	2	1	no	—
715	C₄×#41	—	2	1	no	—
716	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
717	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
718	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
719	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
720	#497	C₂²×C₃₁	1	2	yes	complemented
721	#496	C₂²×C₃₁	1	2	yes	—
722	#495	C₂²×C₃₁	1	2	yes	complemented
723	#490	C₂²×C₃₁	1	2	yes	—
724	#489	C₂²×C₃₁	1	2	yes	complemented
725	#488	C₂²×C₃₁	1	2	yes	complemented
726	#483	C₂²×C₃₁	1	2	yes	—
727	#482	C₂²×C₃₁	1	2	yes	complemented
728	#481	C₂²×C₃₁	1	2	yes	complemented
729	#479	C₂²×C₃₁	1	2	yes	complemented
730	#478	C₂²×C₃₁	1	2	yes	complemented
731	#476	C₂²×C₃₁	1	2	yes	complemented
732	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
733	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
734	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
735	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
736	#469	C₂²×C₃₁	1	2	yes	complemented
737	#468	C₂²×C₃₁	1	2	yes	complemented
738	#467	C₂²×C₃₁	1	2	yes	—
739	#465	C₂²×C₃₁	1	2	yes	—
740	#465	C₂²×C₃₁	1	2	yes	complemented
741	#465	C₂²×C₃₁	1	2	yes	complemented
742	#464	C₂²×C₃₁	1	2	yes	complemented
743	#464	C₂²×C₃₁	1	2	yes	complemented
744	#464	C₂²×C₃₁	1	2	yes	complemented
745	#464	C₂²×C₃₁	1	2	yes	complemented
746	#463	C₂²×C₃₁	1	2	yes	complemented
747	#463	C₂²×C₃₁	1	2	yes	complemented
748	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
749	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
750	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
751	#461	C₂²×C₃₁	1	2	yes	complemented
752	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
753	#460	C₂²×C₃₁	1	1	yes	characteristic
754	#460	C₂²×C₃₁	1	1	yes	characteristic
755	#460	C₂²×C₃₁	1	1	yes	characteristic
756	#460	C₂²×C₃₁	1	2	yes	—
757	#460	C₂²×C₃₁	1	2	yes	—
758	#460	C₂²×C₃₁	1	1	yes	characteristic
759	#460	C₂²×C₃₁	1	1	yes	characteristic
760	#460	C₂²×C₃₁	1	1	yes	characteristic
761	#459	C₂²×C₃₁	1	1	yes	characteristic
762	#459	C₂²×C₃₁	1	1	yes	characteristic
763	#452	C₂²×C₃₁	1	2	yes	complemented
764	#452	C₂²×C₃₁	1	2	yes	complemented
765	#452	C₂²×C₃₁	1	2	yes	complemented
766	#451	C₂²×C₃₁	1	2	yes	—
767	#450	C₂²×C₃₁	1	2	yes	—
768	#449	C₂²×C₃₁	1	2	yes	complemented
769	#449	C₂²×C₃₁	1	2	yes	complemented
770	#448	C₂²×C₃₁	1	2	yes	complemented
771	#447	C₂²×C₃₁	1	2	yes	—
772	#446	C₂²×C₃₁	1	2	yes	complemented
773	#442	C₂²×C₃₁	1	2	yes	complemented
774	#441	C₂²×C₃₁	1	2	yes	complemented
775	#441	C₂²×C₃₁	1	2	yes	complemented
776	#440	C₂²×C₃₁	1	2	yes	complemented
777	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
778	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
779	#435	C₂²×C₃₁	1	2	yes	—
780	#435	C₂²×C₃₁	1	2	yes	complemented
781	C₈×D₄	C₂²×C₃₁	1	2	yes	—
782	#432	C₂²×C₃₁	1	1	yes	characteristic
783	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
784	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
785	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
786	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
787	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
788	#417	C₂²×C₃₁	1	2	yes	complemented
789	#416	C₂²×C₃₁	1	2	yes	complemented
790	C₂×#102	C₂²×C₃₁	1	2	yes	—
791	C₂×C₃₁	—	2	2	no	—
792	C₂×C₃₁	—	4	1	no	—
793	C₂×C₃₁	—	4	1	no	—
794	C₂×C₃₁	—	8	1	no	—
795	C₂×C₃₁	—	8	2	no	—
796	C₂×C₃₁	—	8	2	no	—
797	C₂×C₃₁	#3488	1	1	yes	characteristic
798	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
799	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
800	C₂×#41	—	2	1	no	—
801	C₂×#41	—	2	1	no	—
802	C₂×#41	—	2	1	no	—
803	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
804	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
805	C₂×#41	C₂³×C₃₁	1	2	yes	—
806	C₂×#41	C₂³×C₃₁	1	2	yes	—
807	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
808	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
809	C₂²×D₄	—	2	1	no	—
810	C₂²×D₄	—	2	1	no	—
811	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
812	#137	—	4	4	no	—
813	#135	—	4	4	no	—
814	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
815	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
816	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
817	C₂×SD₁₆	—	4	4	no	—
818	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
819	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
820	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
821	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
822	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
823	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
824	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
825	C₂×D₈	C₂³×C₃₁	1	2	yes	—
826	C₂×D₈	C₂³×C₃₁	1	2	yes	—
827	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
828	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
829	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
830	C₄⋊Q₈	—	2	1	no	—
831	C₄⋊Q₈	—	2	1	no	—
832	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
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	#127	—	2	2	no	—
837	#127	—	2	1	no	—
838	#127	—	2	1	no	—
839	#127	C₂³×C₃₁	1	1	yes	characteristic
840	#127	C₂³×C₃₁	1	1	yes	characteristic
841	#127	C₂³×C₃₁	1	2	yes	—
842	#126	—	2	1	no	—
843	#126	—	2	1	no	—
844	#126	—	2	1	no	—
845	#126	—	2	1	no	—
846	#126	—	2	1	no	—
847	#126	—	2	1	no	—
848	#125	—	2	1	no	—
849	#125	—	2	1	no	—
850	#125	—	2	1	no	—
851	#125	—	2	1	no	—
852	#125	—	2	1	no	—
853	#125	—	2	1	no	—
854	#125	C₂³×C₃₁	1	1	yes	characteristic
855	#125	C₂³×C₃₁	1	1	yes	characteristic
856	#124	—	2	2	no	—
857	#124	—	2	1	no	—
858	#124	—	2	1	no	—
859	#124	—	2	1	no	—
860	#124	—	2	1	no	—
861	#124	C₂³×C₃₁	1	1	yes	characteristic
862	#124	C₂³×C₃₁	1	1	yes	characteristic
863	#124	C₂³×C₃₁	1	2	yes	—
864	#124	C₂³×C₃₁	1	2	yes	—
865	#123	—	2	1	no	—
866	#123	—	2	1	no	—
867	#123	—	2	1	no	—
868	#123	—	2	1	no	—
869	#123	—	2	2	no	—
870	#123	—	2	2	no	—
871	#123	—	2	2	no	—
872	#123	—	2	2	no	—
873	#123	—	2	1	no	—
874	#123	—	2	1	no	—
875	C₂²⋊Q₈	—	2	1	no	—
876	C₂²⋊Q₈	—	2	1	no	—
877	C₂²⋊Q₈	—	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	C₂³×C₃₁	1	1	yes	characteristic
884	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
885	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
886	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
887	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
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	2	no	—
897	#121	—	2	2	no	—
898	#121	—	2	2	no	—
899	#121	—	2	2	no	—
900	#121	C₂³×C₃₁	1	1	yes	characteristic
901	#121	C₂³×C₃₁	1	1	yes	characteristic
902	#121	C₂³×C₃₁	1	2	yes	—
903	#121	C₂³×C₃₁	1	2	yes	—
904	#120	—	2	2	no	—
905	#120	—	2	2	no	—
906	C₄×Q₈	—	2	1	no	—
907	C₄×Q₈	—	2	1	no	—
908	C₄×Q₈	—	2	1	no	—
909	C₄×Q₈	—	2	1	no	—
910	C₄×Q₈	—	2	1	no	—
911	C₄×Q₈	—	2	1	no	—
912	C₄×Q₈	—	2	1	no	—
913	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
914	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
915	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
916	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
917	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
918	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
919	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
920	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
921	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
922	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
923	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
924	C₄×D₄	—	2	1	no	—
925	C₄×D₄	—	2	1	no	—
926	C₄×D₄	—	2	1	no	—
927	C₄×D₄	—	2	1	no	—
928	C₄×D₄	—	2	1	no	—
929	C₄×D₄	—	2	2	no	—
930	C₄×D₄	—	2	2	no	—
931	C₄×D₄	—	2	1	no	—
932	C₄×D₄	—	2	1	no	—
933	C₄×D₄	—	2	1	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	D₄×C₃₁	1	1	yes	characteristic
940	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
941	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
942	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
943	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
944	C₄×D₄	C₂³×C₃₁	1	2	yes	—
945	C₄×D₄	C₂³×C₃₁	1	2	yes	—
946	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
947	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
948	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
949	#117	—	2	1	no	—
950	#117	—	2	1	no	—
951	#117	—	2	1	no	—
952	#117	—	2	1	no	—
953	#117	—	2	1	no	—
954	#117	—	2	1	no	—
955	#117	—	2	1	no	—
956	#117	—	2	1	no	—
957	#117	D₄×C₃₁	1	1	yes	characteristic
958	#117	D₄×C₃₁	1	1	yes	characteristic
959	#117	D₄×C₃₁	1	1	yes	characteristic
960	#117	C₂³×C₃₁	1	1	yes	characteristic
961	C₂×C₄⋊C₄	—	2	1	no	—
962	C₂×C₄⋊C₄	—	2	1	no	—
963	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
964	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
965	C₂×C₂²⋊C₄	—	2	2	no	—
966	C₂×C₂²⋊C₄	—	2	2	no	—
967	C₂×C₄²	—	2	1	no	—
968	C₂×C₄²	—	2	1	no	—
969	C₂×C₄²	—	2	1	no	—
970	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
971	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
972	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
973	#107	C₂³×C₃₁	1	2	yes	—
974	#106	C₂³×C₃₁	1	2	yes	—
975	#106	C₂³×C₃₁	1	2	yes	—
976	#106	C₂³×C₃₁	1	2	yes	—
977	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
978	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
979	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
980	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
981	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
982	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
983	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
984	#103	C₂³×C₃₁	1	2	yes	—
985	#103	C₂³×C₃₁	1	2	yes	—
986	#103	C₂³×C₃₁	1	2	yes	—
987	#103	C₂³×C₃₁	1	2	yes	—
988	#103	C₂³×C₃₁	1	2	yes	—
989	#103	C₂³×C₃₁	1	2	yes	—
990	#103	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	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
1001	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
1002	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
1003	#97	C₂³×C₃₁	1	2	yes	—
1004	#97	C₂³×C₃₁	1	2	yes	—
1005	C₄×C₈	C₂³×C₃₁	1	2	yes	—
1006	C₃₁	#61981	1	1	yes	characteristic, direct product factor, Sylow
1007	C₂⁴	—	2	2	no	—
1008	#41	—	2	2	no	—
1009	#41	—	4	2	no	—
1010	#41	—	4	1	no	—
1011	#41	—	4	2	no	—
1012	#41	—	4	2	no	—
1013	#41	—	4	2	no	—
1014	#41	—	4	2	no	—
1015	#41	—	4	4	no	—
1016	#41	—	8	2	no	—
1017	#41	—	8	2	no	—
1018	C₂×Q₈	—	2	1	no	—
1019	C₂×Q₈	—	2	1	no	—
1020	C₂×Q₈	—	2	1	no	—
1021	C₂×Q₈	—	2	1	no	—
1022	C₂×Q₈	—	2	2	no	—
1023	C₂×Q₈	—	2	2	no	—
1024	C₂×Q₈	—	4	1	no	—
1025	C₂×Q₈	—	4	1	no	—
1026	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1027	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1028	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1029	C₂×Q₈	C₂⁴×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	2	no	—
1041	C₂×D₄	—	2	1	no	—
1042	C₂×D₄	—	2	1	no	—
1043	C₂×D₄	—	2	2	no	—
1044	C₂×D₄	—	2	2	no	—
1045	C₂×D₄	—	4	2	no	—
1046	C₂×D₄	—	4	2	no	—
1047	C₂×D₄	—	4	4	no	—
1048	C₂×D₄	—	8	2	no	—
1049	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1050	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1051	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1052	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1053	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1054	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1055	C₂²×C₄	—	2	1	no	—
1056	C₂²×C₄	—	2	1	no	—
1057	C₂²×C₄	—	2	1	no	—
1058	C₂²×C₄	—	2	1	no	—
1059	C₂²×C₄	—	2	1	no	—
1060	C₂²×C₄	—	2	1	no	—
1061	C₂²×C₄	—	2	1	no	—
1062	C₂²×C₄	—	2	2	no	—
1063	C₂²×C₄	—	2	2	no	—
1064	C₂²×C₄	—	2	2	no	—
1065	C₂²×C₄	—	2	2	no	—
1066	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1067	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1068	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1069	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1070	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1071	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1072	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1073	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1074	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1075	Q₁₆	—	2	4	no	—
1076	Q₁₆	—	4	2	no	—
1077	Q₁₆	—	4	2	no	—
1078	SD₁₆	—	2	4	no	—
1079	SD₁₆	—	2	4	no	—
1080	SD₁₆	—	4	2	no	—
1081	SD₁₆	—	4	2	no	—
1082	SD₁₆	—	4	2	no	—
1083	SD₁₆	—	4	2	no	—
1084	SD₁₆	—	4	2	no	—
1085	D₈	—	4	2	no	—
1086	D₈	—	4	2	no	—
1087	M₁₆	—	4	2	no	—
1088	C₂×C₈	—	4	2	no	—
1089	C₂×C₈	—	4	2	no	—
1090	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1091	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1092	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1093	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1094	C₄⋊C₄	—	2	1	no	—
1095	C₄⋊C₄	—	2	1	no	—
1096	C₄⋊C₄	—	2	1	no	—
1097	C₄⋊C₄	—	2	1	no	—
1098	C₄⋊C₄	—	2	1	no	—
1099	C₄⋊C₄	—	2	1	no	—
1100	C₄⋊C₄	—	2	1	no	—
1101	C₄⋊C₄	—	2	1	no	—
1102	C₄⋊C₄	—	2	1	no	—
1103	C₄⋊C₄	—	2	1	no	—
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	1	no	—
1118	C₄⋊C₄	—	2	2	no	—
1119	C₄⋊C₄	—	2	2	no	—
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	C₂×D₄×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	1	yes	characteristic
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	1	no	—
1136	C₂²⋊C₄	—	2	1	no	—
1137	C₂²⋊C₄	—	2	2	no	—
1138	C₂²⋊C₄	—	2	2	no	—
1139	C₂²⋊C₄	—	2	2	no	—
1140	C₂²⋊C₄	—	2	2	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	2	no	—
1150	C₂²⋊C₄	—	2	2	no	—
1151	C₂²⋊C₄	—	2	2	no	—
1152	C₂²⋊C₄	—	2	2	no	—
1153	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1154	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1155	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1156	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1157	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1158	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1159	C₄²	—	2	1	no	—
1160	C₄²	—	2	1	no	—
1161	C₄²	—	2	1	no	—
1162	C₄²	—	2	1	no	—
1163	C₄²	—	2	1	no	—
1164	C₄²	—	2	1	no	—
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	2	no	—
1181	C₂³	—	2	2	no	—
1182	C₂³	—	4	4	no	—
1183	C₂³	—	8	2	no	—
1184	C₂³	—	8	2	no	—
1185	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1186	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1187	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1188	Q₈	—	2	1	no	—
1189	Q₈	—	2	1	no	—
1190	Q₈	—	2	1	no	—
1191	Q₈	—	2	2	no	—
1192	Q₈	—	2	1	no	—
1193	Q₈	—	2	1	no	—
1194	Q₈	—	2	2	no	—
1195	Q₈	—	4	1	no	—
1196	Q₈	—	4	2	no	—
1197	Q₈	—	4	2	no	—
1198	Q₈	—	4	2	no	—
1199	Q₈	—	4	2	no	—
1200	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
1201	D₄	—	2	2	no	—
1202	D₄	—	2	2	no	—
1203	D₄	—	2	1	no	—
1204	D₄	—	2	2	no	—
1205	D₄	—	2	2	no	—
1206	D₄	—	2	1	no	—
1207	D₄	—	2	2	no	—
1208	D₄	—	2	2	no	—
1209	D₄	—	4	1	no	—
1210	D₄	—	4	2	no	—
1211	D₄	—	4	2	no	—
1212	D₄	—	4	2	no	—
1213	D₄	—	4	4	no	—
1214	D₄	—	4	2	no	—
1215	D₄	—	4	2	no	—
1216	D₄	—	4	2	no	—
1217	D₄	—	4	2	no	—
1218	D₄	—	8	2	no	—
1219	D₄	—	8	2	no	—
1220	D₄	—	8	2	no	—
1221	D₄	—	8	2	no	—
1222	D₄	—	8	2	no	—
1223	D₄	—	8	2	no	—
1224	C₂×C₄	—	2	2	no	—
1225	C₂×C₄	—	2	1	no	—
1226	C₂×C₄	—	2	2	no	—
1227	C₂×C₄	—	2	2	no	—
1228	C₂×C₄	—	2	2	no	—
1229	C₂×C₄	—	2	1	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	1	no	—
1232	C₂×C₄	—	2	1	no	—
1233	C₂×C₄	—	2	1	no	—
1234	C₂×C₄	—	2	1	no	—
1235	C₂×C₄	—	2	1	no	—
1236	C₂×C₄	—	2	1	no	—
1237	C₂×C₄	—	2	1	no	—
1238	C₂×C₄	—	2	1	no	—
1239	C₂×C₄	—	2	1	no	—
1240	C₂×C₄	—	2	1	no	—
1241	C₂×C₄	—	2	2	no	—
1242	C₂×C₄	—	2	2	no	—
1243	C₂×C₄	—	4	1	no	—
1244	C₂×C₄	—	4	1	no	—
1245	C₂×C₄	—	4	2	no	—
1246	C₂×C₄	—	4	2	no	—
1247	C₂×C₄	—	4	2	no	—
1248	C₂×C₄	—	4	2	no	—
1249	C₂×C₄	—	4	2	no	—
1250	C₂×C₄	—	4	2	no	—
1251	C₂×C₄	—	4	2	no	—
1252	C₂×C₄	—	8	2	no	—
1253	C₂×C₄	—	8	2	no	—
1254	C₂×C₄	—	8	2	no	—
1255	C₂×C₄	—	8	2	no	—
1256	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1257	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1258	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1259	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1260	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1261	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1262	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1263	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1264	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1265	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1266	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1267	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1268	C₈	—	2	2	no	—
1269	C₈	—	2	2	no	—
1270	C₈	—	2	2	no	—
1271	C₈	—	2	2	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	1	no	—
1275	C₂²	—	2	1	no	—
1276	C₂²	—	2	1	no	—
1277	C₂²	—	2	1	no	—
1278	C₂²	—	2	1	no	—
1279	C₂²	—	2	1	no	—
1280	C₂²	—	4	1	no	—
1281	C₂²	—	4	2	no	—
1282	C₂²	—	4	2	no	—
1283	C₂²	—	4	1	no	—
1284	C₂²	—	4	2	no	—
1285	C₂²	—	4	2	no	—
1286	C₂²	—	4	1	no	—
1287	C₂²	—	4	2	no	—
1288	C₂²	—	4	2	no	—
1289	C₂²	—	16	4	no	—
1290	C₂²	C₃₁×#575	1	2	yes	—
1291	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1292	C₄	—	2	1	no	—
1293	C₄	—	2	1	no	—
1294	C₄	—	2	1	no	—
1295	C₄	—	2	2	no	—
1296	C₄	—	2	1	no	—
1297	C₄	—	2	1	no	—
1298	C₄	—	2	1	no	—
1299	C₄	—	2	1	no	—
1300	C₄	—	2	1	no	—
1301	C₄	—	2	1	no	—
1302	C₄	—	2	1	no	—
1303	C₄	—	4	1	no	—
1304	C₄	—	4	1	no	—
1305	C₄	—	4	2	no	—
1306	C₄	—	4	1	no	—
1307	C₄	—	4	1	no	—
1308	C₄	—	4	1	no	—
1309	C₄	—	4	1	no	—
1310	C₄	—	4	2	no	—
1311	C₄	C₃₁×#577	1	2	yes	—
1312	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1313	C₄	C₃₁×#585	1	1	yes	characteristic
1314	C₂	—	2	2	no	—
1315	C₂	—	4	1	no	—
1316	C₂	—	4	1	no	—
1317	C₂	—	8	2	no	—
1318	C₂	—	8	2	no	—
1319	C₂	—	8	1	no	—
1320	C₂	C₃₁×#3488	1	1	yes	characteristic
1321	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1322	C₂	C₂×C₃₁×#577	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×#3482	C₂	semidirect
3. C₃₁×#3401	C₂	semidirect
4. C₃₁×#3371	C₂	semidirect
5. C₃₁×#3317	C₂	semidirect
6. C₃₁×#3306	C₂	semidirect
7. C₃₁×#3296	C₂	semidirect
8. C₃₁×#3282	C₂	semidirect
9. C₃₁×#3271	C₂	semidirect
10. C₃₁×#3266	C₂	semidirect
11. C₃₁×#3251	C₂	semidirect
12. C₃₁×#3248	C₂	semidirect
13. C₃₁×#3246	C₂	semidirect
14. C₃₁×#3217	C₂	semidirect
15. C₃₁×#3216	C₂	semidirect
16. C₃₁×#3212	C₂	semidirect
17. C₃₁×#3115	C₂	semidirect
18. C₃₁×#3113	C₂	semidirect
19. C₃₁×#3103	C₂	semidirect
20. C₃₁×#3037	C₂	semidirect
21. C₃₁×#3035	C₂	semidirect
22. C₂×C₃₁×#460	C₂	semidirect
23. C₃₁×#2990	C₂	semidirect
24. C₂×C₃₁×#137	C₂²	semidirect
25. C₂×C₃₁×#135	C₂²	semidirect
29. C₃₁×#557	C₂²	semidirect
31. C₃₁×#556	C₂²	semidirect
35. C₃₁×#552	C₂²	semidirect
40. C₃₁×#548	C₂²	semidirect
52. C₃₁×#533	C₂²	semidirect
61. C₃₁×#529	C₂²	semidirect
65. C₄×#41×C₃₁	C₂²	semidirect
67. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
68. C₃₁×#497	C₂²	semidirect
70. C₃₁×#495	C₂²	semidirect
72. C₃₁×#489	C₂²	semidirect
73. C₃₁×#488	C₂²	semidirect
75. C₃₁×#482	C₂²	semidirect
76. C₃₁×#481	C₂²	semidirect
77. C₃₁×#479	C₂²	semidirect
78. C₃₁×#478	C₂²	semidirect
79. C₃₁×#476	C₂²	semidirect
80. C₃₁×#475	C₂²	semidirect
81. C₃₁×#475	C₂²	semidirect
82. C₃₁×#475	C₂²	semidirect
83. C₃₁×#474	C₂²	semidirect
84. C₃₁×#469	C₂²	semidirect
85. C₃₁×#468	C₂²	semidirect
88. C₃₁×#465	C₂²	semidirect
89. C₃₁×#465	C₂²	semidirect
90. C₃₁×#464	C₂²	semidirect
91. C₃₁×#464	C₂²	semidirect
92. C₃₁×#464	C₂²	semidirect
93. C₃₁×#464	C₂²	semidirect
94. C₃₁×#463	C₂²	semidirect
95. C₃₁×#463	C₂²	semidirect
96. C₃₁×#462	C₂²	semidirect
97. C₃₁×#462	C₂²	semidirect
98. C₃₁×#462	C₂²	semidirect
99. C₃₁×#461	C₂²	semidirect
100. C₃₁×#461	C₂²	semidirect
111. C₃₁×#452	C₂²	semidirect
112. C₃₁×#452	C₂²	semidirect
113. C₃₁×#452	C₂²	semidirect
116. C₃₁×#449	C₂²	semidirect
117. C₃₁×#449	C₂²	semidirect
118. C₃₁×#448	C₂²	semidirect
120. C₃₁×#446	C₂²	semidirect
121. C₃₁×#442	C₂²	semidirect
122. C₃₁×#441	C₂²	semidirect
123. C₃₁×#441	C₂²	semidirect
124. C₃₁×#440	C₂²	semidirect
125. C₄×SD₁₆×C₃₁	C₂²	semidirect
126. C₄×SD₁₆×C₃₁	C₂²	semidirect
128. C₃₁×#435	C₂²	semidirect
131. C₃₁×#432	C₂²	semidirect
132. C₃₁×#431	C₂²	semidirect
133. C₃₁×#423	C₂²	semidirect
135. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
136. C₃₁×#417	C₂²	semidirect
137. C₃₁×#416	C₂²	semidirect
517. #61981	C₃₁	direct (N × H)
611. #3508	C₂×C₃₁	semidirect
612. #3482	C₂×C₃₁	semidirect
613. #3401	C₂×C₃₁	semidirect
614. #3371	C₂×C₃₁	semidirect
615. #3317	C₂×C₃₁	semidirect
616. #3306	C₂×C₃₁	semidirect
617. #3296	C₂×C₃₁	semidirect
618. #3282	C₂×C₃₁	semidirect
619. #3271	C₂×C₃₁	semidirect
620. #3266	C₂×C₃₁	semidirect
621. #3251	C₂×C₃₁	semidirect
622. #3248	C₂×C₃₁	semidirect
623. #3246	C₂×C₃₁	semidirect
624. #3217	C₂×C₃₁	semidirect
625. #3216	C₂×C₃₁	semidirect
626. #3212	C₂×C₃₁	semidirect
627. #3115	C₂×C₃₁	semidirect
628. #3113	C₂×C₃₁	semidirect
629. #3103	C₂×C₃₁	semidirect
630. #3037	C₂×C₃₁	semidirect
631. #3035	C₂×C₃₁	semidirect
632. C₂×#460	C₂×C₃₁	semidirect
633. #2990	C₂×C₃₁	semidirect
676. C₂×#137	C₂²×C₃₁	semidirect
677. C₂×#135	C₂²×C₃₁	semidirect
681. #557	C₂²×C₃₁	semidirect
683. #556	C₂²×C₃₁	semidirect
687. #552	C₂²×C₃₁	semidirect
692. #548	C₂²×C₃₁	semidirect
704. #533	C₂²×C₃₁	semidirect
713. #529	C₂²×C₃₁	semidirect
717. C₄×#41	C₂²×C₃₁	semidirect
719. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
720. #497	C₂²×C₃₁	semidirect
722. #495	C₂²×C₃₁	semidirect
724. #489	C₂²×C₃₁	semidirect
725. #488	C₂²×C₃₁	semidirect
727. #482	C₂²×C₃₁	semidirect
728. #481	C₂²×C₃₁	semidirect
729. #479	C₂²×C₃₁	semidirect
730. #478	C₂²×C₃₁	semidirect
731. #476	C₂²×C₃₁	semidirect
732. #475	C₂²×C₃₁	semidirect
733. #475	C₂²×C₃₁	semidirect
734. #475	C₂²×C₃₁	semidirect
735. #474	C₂²×C₃₁	semidirect
736. #469	C₂²×C₃₁	semidirect
737. #468	C₂²×C₃₁	semidirect
740. #465	C₂²×C₃₁	semidirect
741. #465	C₂²×C₃₁	semidirect
742. #464	C₂²×C₃₁	semidirect
743. #464	C₂²×C₃₁	semidirect
744. #464	C₂²×C₃₁	semidirect
745. #464	C₂²×C₃₁	semidirect
746. #463	C₂²×C₃₁	semidirect
747. #463	C₂²×C₃₁	semidirect
748. #462	C₂²×C₃₁	semidirect
749. #462	C₂²×C₃₁	semidirect
750. #462	C₂²×C₃₁	semidirect
751. #461	C₂²×C₃₁	semidirect
752. #461	C₂²×C₃₁	semidirect
763. #452	C₂²×C₃₁	semidirect
764. #452	C₂²×C₃₁	semidirect
765. #452	C₂²×C₃₁	semidirect
768. #449	C₂²×C₃₁	semidirect
769. #449	C₂²×C₃₁	semidirect
770. #448	C₂²×C₃₁	semidirect
772. #446	C₂²×C₃₁	semidirect
773. #442	C₂²×C₃₁	semidirect
774. #441	C₂²×C₃₁	semidirect
775. #441	C₂²×C₃₁	semidirect
776. #440	C₂²×C₃₁	semidirect
777. C₄×SD₁₆	C₂²×C₃₁	semidirect
778. C₄×SD₁₆	C₂²×C₃₁	semidirect
780. #435	C₂²×C₃₁	semidirect
783. #432	C₂²×C₃₁	semidirect
784. #431	C₂²×C₃₁	semidirect
785. #423	C₂²×C₃₁	semidirect
787. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
788. #417	C₂²×C₃₁	semidirect
789. #416	C₂²×C₃₁	semidirect
1006. C₃₁	#61981	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×#3482	2
C₃₁×#3401	2
C₃₁×#3371	2
C₃₁×#3317	2
C₃₁×#3306	2
C₃₁×#3296	2
C₃₁×#3282	2
C₃₁×#3271	2
C₃₁×#3266	2
C₃₁×#3251	2
C₃₁×#3248	2
C₃₁×#3246	2
C₃₁×#3217	2
C₃₁×#3216	2
C₃₁×#3212	2
C₃₁×#3115	2
C₃₁×#3113	2
C₃₁×#3103	2
C₃₁×#3037	2
C₃₁×#3035	2
C₂×C₃₁×#460	2
C₃₁×#2990	2
#61981	31

Subgroups — C31×#61981 #21518740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61981 #21518740