Subgroups — C₃₁×#61969 #21518728

Order 7936.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3401	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3326	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3313	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3307	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3277	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3271	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3269	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3251	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3248	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3218	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3214	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×#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3039	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#137	C₂²	1	2	yes	—
25	C₂×C₃₁×#137	C₂²	1	2	yes	—
26	C₂×C₃₁×#135	C₂²	1	2	yes	—
27	C₃₁×#559	—	2	1	no	—
28	C₃₁×#559	C₂²	1	1	yes	characteristic
29	C₃₁×#557	C₂²	1	1	yes	characteristic
30	C₃₁×#556	—	2	1	no	—
31	C₃₁×#556	C₂²	1	2	yes	—
32	C₃₁×#556	C₂²	1	1	yes	characteristic
33	C₃₁×#555	—	2	1	no	—
34	C₃₁×#554	—	2	1	no	—
35	C₃₁×#553	—	2	1	no	—
36	C₃₁×#553	—	2	1	no	—
37	C₃₁×#553	—	2	1	no	—
38	C₃₁×#553	—	2	1	no	—
39	C₃₁×#553	C₂²	1	1	yes	characteristic
40	C₃₁×#553	C₂²	1	1	yes	characteristic
41	C₃₁×#550	C₂²	1	1	yes	characteristic
42	C₃₁×#548	C₂²	1	1	yes	characteristic
43	C₃₁×#548	C₂²	1	1	yes	characteristic
44	C₃₁×#548	C₂²	1	2	yes	—
45	C₃₁×#548	C₂²	1	2	yes	—
46	C₃₁×#547	C₂²	1	2	yes	—
47	C₃₁×#542	—	2	1	no	—
48	C₃₁×#542	—	2	1	no	—
49	C₃₁×#537	—	2	1	no	—
50	C₃₁×#533	C₂²	1	1	yes	characteristic
51	C₃₁×#533	C₂²	1	1	yes	characteristic
52	C₃₁×#532	—	2	1	no	—
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×C₄⋊Q₈	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
62	C₃₁×#520	—	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
66	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
67	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
68	C₃₁×#497	C₂²	1	2	yes	—
69	C₃₁×#496	C₂²	1	2	yes	—
70	C₃₁×#495	C₂²	1	2	yes	—
71	C₃₁×#491	C₂²	1	2	yes	—
72	C₃₁×#489	C₂²	1	2	yes	—
73	C₃₁×#488	C₂²	1	2	yes	—
74	C₃₁×#485	C₂²	1	2	yes	—
75	C₃₁×#483	C₂²	1	2	yes	—
76	C₃₁×#482	C₂²	1	2	yes	—
77	C₃₁×#479	C₂²	1	2	yes	—
78	C₃₁×#478	C₂²	1	2	yes	—
79	C₃₁×#477	C₂²	1	2	yes	—
80	C₃₁×#475	C₂²	1	1	yes	characteristic
81	C₃₁×#475	C₂²	1	1	yes	characteristic
82	C₃₁×#474	C₂²	1	1	yes	characteristic
83	C₃₁×#474	C₂²	1	1	yes	characteristic
84	C₃₁×#469	C₂²	1	2	yes	—
85	C₃₁×#468	C₂²	1	2	yes	—
86	C₃₁×#468	C₂²	1	2	yes	—
87	C₃₁×#468	C₂²	1	2	yes	—
88	C₃₁×#467	C₂²	1	2	yes	—
89	C₃₁×#465	C₂²	1	2	yes	—
90	C₃₁×#464	C₂²	1	2	yes	—
91	C₃₁×#464	C₂²	1	2	yes	—
92	C₃₁×#464	C₂²	1	2	yes	—
93	C₃₁×#464	C₂²	1	2	yes	—
94	C₃₁×#463	C₂²	1	2	yes	—
95	C₃₁×#463	C₂²	1	2	yes	—
96	C₃₁×#462	C₂²	1	1	yes	characteristic
97	C₃₁×#462	C₂²	1	1	yes	characteristic
98	C₃₁×#462	C₂²	1	1	yes	characteristic
99	C₃₁×#462	C₂²	1	2	yes	—
100	C₃₁×#462	C₂²	1	1	yes	characteristic
101	C₃₁×#461	C₂²	1	1	yes	characteristic
102	C₃₁×#461	C₂²	1	2	yes	—
103	C₃₁×#461	C₂²	1	1	yes	characteristic
104	C₃₁×#461	C₂²	1	1	yes	characteristic
105	C₃₁×#461	C₂²	1	1	yes	characteristic
106	C₃₁×#460	C₂²	1	1	yes	characteristic
107	C₃₁×#460	C₂²	1	2	yes	—
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	—
112	C₃₁×#452	C₂²	1	2	yes	—
113	C₃₁×#451	C₂²	1	2	yes	—
114	C₃₁×#451	C₂²	1	2	yes	—
115	C₃₁×#449	C₂²	1	2	yes	—
116	C₃₁×#449	C₂²	1	2	yes	—
117	C₃₁×#449	C₂²	1	2	yes	—
118	C₃₁×#449	C₂²	1	2	yes	—
119	C₃₁×#448	C₂²	1	2	yes	—
120	C₃₁×#446	C₂²	1	2	yes	—
121	C₃₁×#442	C₂²	1	2	yes	—
122	C₃₁×#441	C₂²	1	2	yes	—
123	C₃₁×#441	C₂²	1	2	yes	—
124	C₃₁×#440	C₂²	1	2	yes	—
125	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
126	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
127	C₃₁×#436	C₂²	1	2	yes	—
128	C₃₁×#435	C₂²	1	2	yes	—
129	C₃₁×#435	C₂²	1	2	yes	—
130	C₃₁×#432	C₂²	1	1	yes	characteristic
131	C₃₁×#432	C₂²	1	1	yes	characteristic
132	C₃₁×#431	C₂²	1	1	yes	characteristic
133	C₃₁×#423	C₂²	1	1	yes	characteristic
134	C₃₁×#423	C₂²	1	1	yes	characteristic
135	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
136	C₃₁×#419	C₂²	1	2	yes	—
137	C₃₁×#417	C₂²	1	2	yes	—
138	C₃₁×#416	C₂²	1	2	yes	—
139	C₂×#41×C₃₁	—	2	1	no	—
140	C₂×#41×C₃₁	—	2	1	no	—
141	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
142	C₂×#41×C₃₁	C₂³	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	2	yes	—
148	C₃₁×#137	—	4	4	no	—
149	C₃₁×#137	—	4	4	no	—
150	C₃₁×#135	—	4	4	no	—
151	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
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×D₈×C₃₁	C₂³	1	2	yes	—
162	C₂×D₈×C₃₁	C₂³	1	2	yes	—
163	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
164	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
165	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
166	C₃₁×C₄⋊Q₈	—	2	1	no	—
167	C₃₁×C₄⋊Q₈	—	2	1	no	—
168	C₃₁×C₄⋊Q₈	—	2	1	no	—
169	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
172	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
173	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
174	C₃₁×#127	—	2	1	no	—
175	C₃₁×#127	C₂³	1	1	yes	characteristic
176	C₃₁×#127	C₂³	1	1	yes	characteristic
177	C₃₁×#126	—	2	1	no	—
178	C₃₁×#126	—	2	1	no	—
179	C₃₁×#126	—	2	2	no	—
180	C₃₁×#126	—	2	2	no	—
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×#125	—	2	1	no	—
186	C₃₁×#125	—	2	1	no	—
187	C₃₁×#125	—	2	1	no	—
188	C₃₁×#125	—	2	1	no	—
189	C₃₁×#125	C₂³	1	1	yes	characteristic
190	C₃₁×#125	C₂³	1	1	yes	characteristic
191	C₃₁×#124	—	2	1	no	—
192	C₃₁×#124	—	2	1	no	—
193	C₃₁×#124	—	2	1	no	—
194	C₃₁×#124	—	2	1	no	—
195	C₃₁×#124	—	2	2	no	—
196	C₃₁×#124	—	2	2	no	—
197	C₃₁×#124	—	2	1	no	—
198	C₃₁×#124	—	2	1	no	—
199	C₃₁×#124	C₂³	1	1	yes	characteristic
200	C₃₁×#124	C₂³	1	2	yes	—
201	C₃₁×#124	C₂³	1	2	yes	—
202	C₃₁×#124	C₂³	1	1	yes	characteristic
203	C₃₁×#123	—	2	1	no	—
204	C₃₁×#123	—	2	1	no	—
205	C₃₁×#123	—	2	1	no	—
206	C₃₁×#123	—	2	1	no	—
207	C₃₁×#123	—	2	1	no	—
208	C₃₁×#123	—	2	1	no	—
209	C₃₁×#123	—	2	2	no	—
210	C₃₁×#123	—	2	2	no	—
211	C₃₁×C₂²⋊Q₈	—	2	2	no	—
212	C₃₁×C₂²⋊Q₈	—	2	1	no	—
213	C₃₁×C₂²⋊Q₈	—	2	1	no	—
214	C₃₁×C₂²⋊Q₈	—	2	1	no	—
215	C₃₁×C₂²⋊Q₈	—	2	1	no	—
216	C₃₁×C₂²⋊Q₈	—	2	2	no	—
217	C₃₁×C₂²⋊Q₈	—	2	2	no	—
218	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
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	2	no	—
227	C₃₁×#121	—	2	2	no	—
228	C₃₁×#121	—	2	2	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	1	no	—
236	C₃₁×#121	—	2	1	no	—
237	C₃₁×#121	C₂³	1	1	yes	characteristic
238	C₃₁×#121	C₂³	1	1	yes	characteristic
239	C₃₁×#121	C₂³	1	1	yes	characteristic
240	C₃₁×#121	C₂³	1	1	yes	characteristic
241	C₃₁×#121	C₂³	1	2	yes	—
242	C₄×Q₈×C₃₁	—	2	1	no	—
243	C₄×Q₈×C₃₁	—	2	1	no	—
244	C₄×Q₈×C₃₁	—	2	1	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	D₄	1	1	yes	characteristic
249	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
250	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
251	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
252	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
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×D₄×C₃₁	—	2	1	no	—
259	C₄×D₄×C₃₁	—	2	1	no	—
260	C₄×D₄×C₃₁	—	2	1	no	—
261	C₄×D₄×C₃₁	—	2	1	no	—
262	C₄×D₄×C₃₁	—	2	1	no	—
263	C₄×D₄×C₃₁	—	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	1	no	—
269	C₄×D₄×C₃₁	—	2	1	no	—
270	C₄×D₄×C₃₁	—	2	2	no	—
271	C₄×D₄×C₃₁	—	2	2	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	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	1	yes	characteristic
287	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
289	C₃₁×#117	—	2	1	no	—
290	C₃₁×#117	—	2	1	no	—
291	C₃₁×#117	—	2	2	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	C₃₁×#117	C₂³	1	1	yes	characteristic
301	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
302	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
303	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
304	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
305	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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×#107	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×#103	C₂³	1	2	yes	—
331	C₃₁×#103	C₂³	1	2	yes	—
332	C₃₁×#103	C₂³	1	2	yes	—
333	C₃₁×#102	C₂³	1	2	yes	—
334	C₃₁×#102	C₂³	1	2	yes	—
335	C₃₁×#102	C₂³	1	2	yes	—
336	C₃₁×#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	#41×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	1	no	—
350	#41×C₃₁	—	4	4	no	—
351	#41×C₃₁	—	4	4	no	—
352	#41×C₃₁	—	4	2	no	—
353	#41×C₃₁	—	4	2	no	—
354	#41×C₃₁	—	4	2	no	—
355	#41×C₃₁	—	4	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	2	no	—
360	C₂×Q₈×C₃₁	—	2	2	no	—
361	C₂×Q₈×C₃₁	—	4	1	no	—
362	C₂×Q₈×C₃₁	—	4	2	no	—
363	C₂×Q₈×C₃₁	—	4	2	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	2	yes	—
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	2	no	—
372	C₂×D₄×C₃₁	—	2	1	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	2	no	—
377	C₂×D₄×C₃₁	—	2	2	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	1	no	—
382	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
383	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
384	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
385	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
386	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
387	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₃₁	—	2	1	no	—
389	C₂²×C₄×C₃₁	—	2	1	no	—
390	C₂²×C₄×C₃₁	—	2	2	no	—
391	C₂²×C₄×C₃₁	—	2	1	no	—
392	C₂²×C₄×C₃₁	—	2	1	no	—
393	C₂²×C₄×C₃₁	—	2	1	no	—
394	C₂²×C₄×C₃₁	—	2	1	no	—
395	C₂²×C₄×C₃₁	—	2	2	no	—
396	C₂²×C₄×C₃₁	—	2	1	no	—
397	C₂²×C₄×C₃₁	—	2	1	no	—
398	C₂²×C₄×C₃₁	—	2	2	no	—
399	C₂²×C₄×C₃₁	—	2	2	no	—
400	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
404	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
405	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
406	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	Q₁₆×C₃₁	—	2	4	no	—
410	Q₁₆×C₃₁	—	2	4	no	—
411	Q₁₆×C₃₁	—	4	2	no	—
412	Q₁₆×C₃₁	—	4	2	no	—
413	SD₁₆×C₃₁	—	2	4	no	—
414	SD₁₆×C₃₁	—	4	2	no	—
415	SD₁₆×C₃₁	—	4	2	no	—
416	SD₁₆×C₃₁	—	4	2	no	—
417	SD₁₆×C₃₁	—	4	2	no	—
418	SD₁₆×C₃₁	—	4	2	no	—
419	D₈×C₃₁	—	4	2	no	—
420	D₈×C₃₁	—	4	2	no	—
421	M₁₆×C₃₁	—	4	2	no	—
422	M₁₆×C₃₁	—	4	2	no	—
423	C₂×C₈×C₃₁	—	4	2	no	—
424	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
425	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
426	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
427	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
428	C₄⋊C₄×C₃₁	—	2	2	no	—
429	C₄⋊C₄×C₃₁	—	2	1	no	—
430	C₄⋊C₄×C₃₁	—	2	1	no	—
431	C₄⋊C₄×C₃₁	—	2	1	no	—
432	C₄⋊C₄×C₃₁	—	2	1	no	—
433	C₄⋊C₄×C₃₁	—	2	1	no	—
434	C₄⋊C₄×C₃₁	—	2	2	no	—
435	C₄⋊C₄×C₃₁	—	2	2	no	—
436	C₄⋊C₄×C₃₁	—	2	1	no	—
437	C₄⋊C₄×C₃₁	—	2	1	no	—
438	C₄⋊C₄×C₃₁	—	2	1	no	—
439	C₄⋊C₄×C₃₁	—	2	2	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	2	no	—
452	C₄⋊C₄×C₃₁	—	2	2	no	—
453	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
454	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
455	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
456	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
457	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
458	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
459	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
460	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
461	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
462	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
463	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
464	C₂²⋊C₄×C₃₁	—	2	2	no	—
465	C₂²⋊C₄×C₃₁	—	2	2	no	—
466	C₂²⋊C₄×C₃₁	—	2	1	no	—
467	C₂²⋊C₄×C₃₁	—	2	1	no	—
468	C₂²⋊C₄×C₃₁	—	2	1	no	—
469	C₂²⋊C₄×C₃₁	—	2	1	no	—
470	C₂²⋊C₄×C₃₁	—	2	1	no	—
471	C₂²⋊C₄×C₃₁	—	2	1	no	—
472	C₂²⋊C₄×C₃₁	—	2	2	no	—
473	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
481	C₂²⋊C₄×C₃₁	—	2	2	no	—
482	C₂²⋊C₄×C₃₁	—	2	1	no	—
483	C₂²⋊C₄×C₃₁	—	2	1	no	—
484	C₂²⋊C₄×C₃₁	—	2	2	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	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	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	2	no	—
503	C₄²×C₃₁	—	2	2	no	—
504	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
505	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
506	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
511	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
512	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
513	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
514	#61969	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
515	C₂³×C₃₁	—	2	1	no	—
516	C₂³×C₃₁	—	2	1	no	—
517	C₂³×C₃₁	—	2	2	no	—
518	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
519	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
520	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
521	Q₈×C₃₁	—	2	1	no	—
522	Q₈×C₃₁	—	2	2	no	—
523	Q₈×C₃₁	—	2	1	no	—
524	Q₈×C₃₁	—	2	2	no	—
525	Q₈×C₃₁	—	2	2	no	—
526	Q₈×C₃₁	—	2	1	no	—
527	Q₈×C₃₁	—	2	2	no	—
528	Q₈×C₃₁	—	4	1	no	—
529	Q₈×C₃₁	—	4	2	no	—
530	Q₈×C₃₁	—	4	2	no	—
531	Q₈×C₃₁	—	4	2	no	—
532	Q₈×C₃₁	—	8	2	no	—
533	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
534	D₄×C₃₁	—	2	1	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	1	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	2	no	—
545	D₄×C₃₁	—	4	2	no	—
546	D₄×C₃₁	—	4	2	no	—
547	D₄×C₃₁	—	4	4	no	—
548	D₄×C₃₁	—	4	2	no	—
549	D₄×C₃₁	—	4	2	no	—
550	D₄×C₃₁	—	4	2	no	—
551	D₄×C₃₁	—	8	1	no	—
552	D₄×C₃₁	—	8	1	no	—
553	D₄×C₃₁	—	8	1	no	—
554	D₄×C₃₁	—	8	2	no	—
555	D₄×C₃₁	—	8	2	no	—
556	C₂×C₄×C₃₁	—	2	1	no	—
557	C₂×C₄×C₃₁	—	2	2	no	—
558	C₂×C₄×C₃₁	—	2	2	no	—
559	C₂×C₄×C₃₁	—	2	2	no	—
560	C₂×C₄×C₃₁	—	2	1	no	—
561	C₂×C₄×C₃₁	—	2	1	no	—
562	C₂×C₄×C₃₁	—	2	1	no	—
563	C₂×C₄×C₃₁	—	2	1	no	—
564	C₂×C₄×C₃₁	—	2	1	no	—
565	C₂×C₄×C₃₁	—	2	1	no	—
566	C₂×C₄×C₃₁	—	2	1	no	—
567	C₂×C₄×C₃₁	—	2	1	no	—
568	C₂×C₄×C₃₁	—	2	1	no	—
569	C₂×C₄×C₃₁	—	2	1	no	—
570	C₂×C₄×C₃₁	—	2	2	no	—
571	C₂×C₄×C₃₁	—	2	1	no	—
572	C₂×C₄×C₃₁	—	2	2	no	—
573	C₂×C₄×C₃₁	—	2	2	no	—
574	C₂×C₄×C₃₁	—	4	1	no	—
575	C₂×C₄×C₃₁	—	4	1	no	—
576	C₂×C₄×C₃₁	—	4	1	no	—
577	C₂×C₄×C₃₁	—	4	2	no	—
578	C₂×C₄×C₃₁	—	4	2	no	—
579	C₂×C₄×C₃₁	—	4	2	no	—
580	C₂×C₄×C₃₁	—	4	4	no	—
581	C₂×C₄×C₃₁	—	4	2	no	—
582	C₂×C₄×C₃₁	—	4	2	no	—
583	C₂×C₄×C₃₁	—	8	1	no	—
584	C₂×C₄×C₃₁	—	8	1	no	—
585	C₂×C₄×C₃₁	—	8	2	no	—
586	C₂×C₄×C₃₁	—	8	2	no	—
587	C₂×C₄×C₃₁	—	8	1	no	—
588	C₂×C₄×C₃₁	—	8	2	no	—
589	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
590	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
591	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
592	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
593	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
594	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
601	C₈×C₃₁	—	2	2	no	—
602	C₈×C₃₁	—	2	2	no	—
603	C₈×C₃₁	—	2	2	no	—
604	C₈×C₃₁	—	2	2	no	—
605	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
606	#3480	C₂×C₃₁	1	1	yes	characteristic, complemented
607	#3401	C₂×C₃₁	1	2	yes	complemented
608	#3377	C₂×C₃₁	1	2	yes	complemented
609	#3326	C₂×C₃₁	1	2	yes	complemented
610	#3313	C₂×C₃₁	1	2	yes	complemented
611	#3307	C₂×C₃₁	1	2	yes	complemented
612	#3277	C₂×C₃₁	1	2	yes	complemented
613	#3271	C₂×C₃₁	1	2	yes	complemented
614	#3269	C₂×C₃₁	1	2	yes	complemented
615	#3254	C₂×C₃₁	1	1	yes	characteristic, complemented
616	#3251	C₂×C₃₁	1	1	yes	characteristic, complemented
617	#3248	C₂×C₃₁	1	1	yes	characteristic, complemented
618	#3218	C₂×C₃₁	1	1	yes	characteristic, complemented
619	#3214	C₂×C₃₁	1	1	yes	characteristic, complemented
620	#3212	C₂×C₃₁	1	1	yes	characteristic, complemented
621	#3115	C₂×C₃₁	1	1	yes	characteristic, complemented
622	#3113	C₂×C₃₁	1	1	yes	characteristic, complemented
623	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
624	#3039	C₂×C₃₁	1	1	yes	characteristic, complemented
625	#3037	C₂×C₃₁	1	1	yes	characteristic, complemented
626	#3035	C₂×C₃₁	1	1	yes	characteristic, complemented
627	#2989	C₂×C₃₁	1	1	yes	characteristic, complemented
628	C₂²×C₃₁	—	2	1	no	—
629	C₂²×C₃₁	—	2	1	no	—
630	C₂²×C₃₁	—	2	1	no	—
631	C₂²×C₃₁	—	2	1	no	—
632	C₂²×C₃₁	—	2	1	no	—
633	C₂²×C₃₁	—	2	1	no	—
634	C₂²×C₃₁	—	2	1	no	—
635	C₂²×C₃₁	—	2	1	no	—
636	C₂²×C₃₁	—	2	1	no	—
637	C₂²×C₃₁	—	4	1	no	—
638	C₂²×C₃₁	—	4	1	no	—
639	C₂²×C₃₁	—	4	2	no	—
640	C₂²×C₃₁	—	4	1	no	—
641	C₂²×C₃₁	—	4	1	no	—
642	C₂²×C₃₁	—	4	2	no	—
643	C₂²×C₃₁	—	4	2	no	—
644	C₂²×C₃₁	—	4	1	no	—
645	C₂²×C₃₁	—	4	1	no	—
646	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
647	C₄×C₃₁	—	2	1	no	—
648	C₄×C₃₁	—	2	1	no	—
649	C₄×C₃₁	—	2	1	no	—
650	C₄×C₃₁	—	2	1	no	—
651	C₄×C₃₁	—	2	1	no	—
652	C₄×C₃₁	—	2	1	no	—
653	C₄×C₃₁	—	2	1	no	—
654	C₄×C₃₁	—	2	2	no	—
655	C₄×C₃₁	—	2	1	no	—
656	C₄×C₃₁	—	2	1	no	—
657	C₄×C₃₁	—	2	1	no	—
658	C₄×C₃₁	—	4	1	no	—
659	C₄×C₃₁	—	4	1	no	—
660	C₄×C₃₁	—	4	1	no	—
661	C₄×C₃₁	—	4	2	no	—
662	C₄×C₃₁	—	4	2	no	—
663	C₄×C₃₁	—	4	2	no	—
664	C₄×C₃₁	—	4	1	no	—
665	C₄×C₃₁	—	4	1	no	—
666	C₄×C₃₁	#575	1	2	yes	—
667	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
668	C₄×C₃₁	#585	1	1	yes	characteristic
669	C₂×#137	C₂²×C₃₁	1	2	yes	—
670	C₂×#137	C₂²×C₃₁	1	2	yes	—
671	C₂×#135	C₂²×C₃₁	1	2	yes	—
672	#559	—	2	1	no	—
673	#559	C₂²×C₃₁	1	1	yes	characteristic
674	#557	C₂²×C₃₁	1	1	yes	characteristic
675	#556	—	2	1	no	—
676	#556	C₂²×C₃₁	1	2	yes	—
677	#556	C₂²×C₃₁	1	1	yes	characteristic
678	#555	—	2	1	no	—
679	#554	—	2	1	no	—
680	#553	—	2	1	no	—
681	#553	—	2	1	no	—
682	#553	—	2	1	no	—
683	#553	—	2	1	no	—
684	#553	C₂²×C₃₁	1	1	yes	characteristic
685	#553	C₂²×C₃₁	1	1	yes	characteristic
686	#550	C₂²×C₃₁	1	1	yes	characteristic
687	#548	C₂²×C₃₁	1	1	yes	characteristic
688	#548	C₂²×C₃₁	1	1	yes	characteristic
689	#548	C₂²×C₃₁	1	2	yes	—
690	#548	C₂²×C₃₁	1	2	yes	—
691	#547	C₂²×C₃₁	1	2	yes	—
692	#542	—	2	1	no	—
693	#542	—	2	1	no	—
694	#537	—	2	1	no	—
695	#533	C₂²×C₃₁	1	1	yes	characteristic
696	#533	C₂²×C₃₁	1	1	yes	characteristic
697	#532	—	2	1	no	—
698	#532	C₂²×C₃₁	1	1	yes	characteristic
699	#532	C₂²×C₃₁	1	1	yes	characteristic
700	#532	C₂²×C₃₁	1	1	yes	characteristic
701	#532	C₂²×C₃₁	1	1	yes	characteristic
702	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
703	#529	—	2	1	no	—
704	#529	—	2	1	no	—
705	#529	C₂²×C₃₁	1	1	yes	characteristic
706	#529	C₂²×C₃₁	1	1	yes	characteristic
707	#520	—	2	1	no	—
708	C₄×#41	—	2	1	no	—
709	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
710	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
711	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
712	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
713	#497	C₂²×C₃₁	1	2	yes	—
714	#496	C₂²×C₃₁	1	2	yes	—
715	#495	C₂²×C₃₁	1	2	yes	—
716	#491	C₂²×C₃₁	1	2	yes	—
717	#489	C₂²×C₃₁	1	2	yes	—
718	#488	C₂²×C₃₁	1	2	yes	—
719	#485	C₂²×C₃₁	1	2	yes	—
720	#483	C₂²×C₃₁	1	2	yes	—
721	#482	C₂²×C₃₁	1	2	yes	—
722	#479	C₂²×C₃₁	1	2	yes	—
723	#478	C₂²×C₃₁	1	2	yes	—
724	#477	C₂²×C₃₁	1	2	yes	—
725	#475	C₂²×C₃₁	1	1	yes	characteristic
726	#475	C₂²×C₃₁	1	1	yes	characteristic
727	#474	C₂²×C₃₁	1	1	yes	characteristic
728	#474	C₂²×C₃₁	1	1	yes	characteristic
729	#469	C₂²×C₃₁	1	2	yes	—
730	#468	C₂²×C₃₁	1	2	yes	—
731	#468	C₂²×C₃₁	1	2	yes	—
732	#468	C₂²×C₃₁	1	2	yes	—
733	#467	C₂²×C₃₁	1	2	yes	—
734	#465	C₂²×C₃₁	1	2	yes	—
735	#464	C₂²×C₃₁	1	2	yes	—
736	#464	C₂²×C₃₁	1	2	yes	—
737	#464	C₂²×C₃₁	1	2	yes	—
738	#464	C₂²×C₃₁	1	2	yes	—
739	#463	C₂²×C₃₁	1	2	yes	—
740	#463	C₂²×C₃₁	1	2	yes	—
741	#462	C₂²×C₃₁	1	1	yes	characteristic
742	#462	C₂²×C₃₁	1	1	yes	characteristic
743	#462	C₂²×C₃₁	1	1	yes	characteristic
744	#462	C₂²×C₃₁	1	2	yes	—
745	#462	C₂²×C₃₁	1	1	yes	characteristic
746	#461	C₂²×C₃₁	1	1	yes	characteristic
747	#461	C₂²×C₃₁	1	2	yes	—
748	#461	C₂²×C₃₁	1	1	yes	characteristic
749	#461	C₂²×C₃₁	1	1	yes	characteristic
750	#461	C₂²×C₃₁	1	1	yes	characteristic
751	#460	C₂²×C₃₁	1	1	yes	characteristic
752	#460	C₂²×C₃₁	1	2	yes	—
753	#460	C₂²×C₃₁	1	1	yes	characteristic
754	#459	C₂²×C₃₁	1	1	yes	characteristic
755	#459	C₂²×C₃₁	1	1	yes	characteristic
756	#452	C₂²×C₃₁	1	2	yes	—
757	#452	C₂²×C₃₁	1	2	yes	—
758	#451	C₂²×C₃₁	1	2	yes	—
759	#451	C₂²×C₃₁	1	2	yes	—
760	#449	C₂²×C₃₁	1	2	yes	—
761	#449	C₂²×C₃₁	1	2	yes	—
762	#449	C₂²×C₃₁	1	2	yes	—
763	#449	C₂²×C₃₁	1	2	yes	—
764	#448	C₂²×C₃₁	1	2	yes	—
765	#446	C₂²×C₃₁	1	2	yes	—
766	#442	C₂²×C₃₁	1	2	yes	—
767	#441	C₂²×C₃₁	1	2	yes	—
768	#441	C₂²×C₃₁	1	2	yes	—
769	#440	C₂²×C₃₁	1	2	yes	—
770	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
771	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
772	#436	C₂²×C₃₁	1	2	yes	—
773	#435	C₂²×C₃₁	1	2	yes	—
774	#435	C₂²×C₃₁	1	2	yes	—
775	#432	C₂²×C₃₁	1	1	yes	characteristic
776	#432	C₂²×C₃₁	1	1	yes	characteristic
777	#431	C₂²×C₃₁	1	1	yes	characteristic
778	#423	C₂²×C₃₁	1	1	yes	characteristic
779	#423	C₂²×C₃₁	1	1	yes	characteristic
780	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
781	#419	C₂²×C₃₁	1	2	yes	—
782	#417	C₂²×C₃₁	1	2	yes	—
783	#416	C₂²×C₃₁	1	2	yes	—
784	C₂×C₃₁	—	4	1	no	—
785	C₂×C₃₁	—	4	1	no	—
786	C₂×C₃₁	—	4	1	no	—
787	C₂×C₃₁	—	8	1	no	—
788	C₂×C₃₁	—	8	1	no	—
789	C₂×C₃₁	—	8	2	no	—
790	C₂×C₃₁	#3488	1	1	yes	characteristic
791	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
792	C₂×C₃₁	#3586	1	1	yes	characteristic
793	C₂×#41	—	2	1	no	—
794	C₂×#41	—	2	1	no	—
795	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
796	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
797	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
798	C₂×#41	C₂³×C₃₁	1	2	yes	—
799	C₂×#41	C₂³×C₃₁	1	2	yes	—
800	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
801	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
802	#137	—	4	4	no	—
803	#137	—	4	4	no	—
804	#135	—	4	4	no	—
805	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
806	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
807	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
808	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
809	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
810	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
811	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
812	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
813	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
814	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
815	C₂×D₈	C₂³×C₃₁	1	2	yes	—
816	C₂×D₈	C₂³×C₃₁	1	2	yes	—
817	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
818	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
819	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
820	C₄⋊Q₈	—	2	1	no	—
821	C₄⋊Q₈	—	2	1	no	—
822	C₄⋊Q₈	—	2	1	no	—
823	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
824	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
825	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
826	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
827	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
828	#127	—	2	1	no	—
829	#127	C₂³×C₃₁	1	1	yes	characteristic
830	#127	C₂³×C₃₁	1	1	yes	characteristic
831	#126	—	2	1	no	—
832	#126	—	2	1	no	—
833	#126	—	2	2	no	—
834	#126	—	2	2	no	—
835	#126	—	2	1	no	—
836	#126	—	2	1	no	—
837	#126	—	2	1	no	—
838	#126	—	2	1	no	—
839	#125	—	2	1	no	—
840	#125	—	2	1	no	—
841	#125	—	2	1	no	—
842	#125	—	2	1	no	—
843	#125	C₂³×C₃₁	1	1	yes	characteristic
844	#125	C₂³×C₃₁	1	1	yes	characteristic
845	#124	—	2	1	no	—
846	#124	—	2	1	no	—
847	#124	—	2	1	no	—
848	#124	—	2	1	no	—
849	#124	—	2	2	no	—
850	#124	—	2	2	no	—
851	#124	—	2	1	no	—
852	#124	—	2	1	no	—
853	#124	C₂³×C₃₁	1	1	yes	characteristic
854	#124	C₂³×C₃₁	1	1	yes	characteristic
855	#124	C₂³×C₃₁	1	2	yes	—
856	#124	C₂³×C₃₁	1	2	yes	—
857	#123	—	2	1	no	—
858	#123	—	2	1	no	—
859	#123	—	2	1	no	—
860	#123	—	2	1	no	—
861	#123	—	2	1	no	—
862	#123	—	2	1	no	—
863	#123	—	2	2	no	—
864	#123	—	2	2	no	—
865	C₂²⋊Q₈	—	2	2	no	—
866	C₂²⋊Q₈	—	2	1	no	—
867	C₂²⋊Q₈	—	2	1	no	—
868	C₂²⋊Q₈	—	2	1	no	—
869	C₂²⋊Q₈	—	2	1	no	—
870	C₂²⋊Q₈	—	2	2	no	—
871	C₂²⋊Q₈	—	2	2	no	—
872	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
873	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
874	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
875	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
876	#121	—	2	1	no	—
877	#121	—	2	1	no	—
878	#121	—	2	1	no	—
879	#121	—	2	1	no	—
880	#121	—	2	2	no	—
881	#121	—	2	2	no	—
882	#121	—	2	2	no	—
883	#121	—	2	1	no	—
884	#121	—	2	1	no	—
885	#121	—	2	1	no	—
886	#121	—	2	1	no	—
887	#121	—	2	1	no	—
888	#121	—	2	1	no	—
889	#121	—	2	1	no	—
890	#121	—	2	1	no	—
891	#121	C₂³×C₃₁	1	1	yes	characteristic
892	#121	C₂³×C₃₁	1	1	yes	characteristic
893	#121	C₂³×C₃₁	1	2	yes	—
894	#121	C₂³×C₃₁	1	1	yes	characteristic
895	#121	C₂³×C₃₁	1	1	yes	characteristic
896	C₄×Q₈	—	2	1	no	—
897	C₄×Q₈	—	2	1	no	—
898	C₄×Q₈	—	2	1	no	—
899	C₄×Q₈	—	2	1	no	—
900	C₄×Q₈	—	2	1	no	—
901	C₄×Q₈	—	2	1	no	—
902	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
903	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
904	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
905	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
906	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
907	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
908	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
909	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
910	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
911	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
912	C₄×D₄	—	2	1	no	—
913	C₄×D₄	—	2	1	no	—
914	C₄×D₄	—	2	1	no	—
915	C₄×D₄	—	2	1	no	—
916	C₄×D₄	—	2	1	no	—
917	C₄×D₄	—	2	1	no	—
918	C₄×D₄	—	2	1	no	—
919	C₄×D₄	—	2	1	no	—
920	C₄×D₄	—	2	1	no	—
921	C₄×D₄	—	2	1	no	—
922	C₄×D₄	—	2	1	no	—
923	C₄×D₄	—	2	1	no	—
924	C₄×D₄	—	2	2	no	—
925	C₄×D₄	—	2	2	no	—
926	C₄×D₄	—	2	1	no	—
927	C₄×D₄	—	2	1	no	—
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	D₄×C₃₁	1	1	yes	characteristic
933	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
934	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
935	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
936	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
937	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
938	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
939	C₄×D₄	C₂³×C₃₁	1	2	yes	—
940	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
941	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
942	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
943	#117	—	2	1	no	—
944	#117	—	2	1	no	—
945	#117	—	2	2	no	—
946	#117	—	2	1	no	—
947	#117	—	2	1	no	—
948	#117	—	2	1	no	—
949	#117	—	2	1	no	—
950	#117	D₄×C₃₁	1	1	yes	characteristic
951	#117	D₄×C₃₁	1	1	yes	characteristic
952	#117	D₄×C₃₁	1	1	yes	characteristic
953	#117	C₂³×C₃₁	1	1	yes	characteristic
954	#117	C₂³×C₃₁	1	1	yes	characteristic
955	C₂×C₄⋊C₄	—	2	1	no	—
956	C₂×C₄⋊C₄	—	2	1	no	—
957	C₂×C₄⋊C₄	—	2	1	no	—
958	C₂×C₄⋊C₄	—	2	2	no	—
959	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
960	C₂×C₄²	—	2	1	no	—
961	C₂×C₄²	—	2	1	no	—
962	C₂×C₄²	—	2	1	no	—
963	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
964	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
965	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
966	#107	C₂³×C₃₁	1	2	yes	—
967	#107	C₂³×C₃₁	1	2	yes	—
968	#106	C₂³×C₃₁	1	2	yes	—
969	#106	C₂³×C₃₁	1	2	yes	—
970	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
971	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
972	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
973	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
974	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
975	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
976	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
977	#103	C₂³×C₃₁	1	2	yes	—
978	#103	C₂³×C₃₁	1	2	yes	—
979	#103	C₂³×C₃₁	1	2	yes	—
980	#103	C₂³×C₃₁	1	2	yes	—
981	#103	C₂³×C₃₁	1	2	yes	—
982	#103	C₂³×C₃₁	1	2	yes	—
983	#103	C₂³×C₃₁	1	2	yes	—
984	#103	C₂³×C₃₁	1	2	yes	—
985	#103	C₂³×C₃₁	1	2	yes	—
986	#103	C₂³×C₃₁	1	2	yes	—
987	#102	C₂³×C₃₁	1	2	yes	—
988	#102	C₂³×C₃₁	1	2	yes	—
989	#102	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	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
994	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
995	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
996	#97	C₂³×C₃₁	1	2	yes	—
997	#97	C₂³×C₃₁	1	2	yes	—
998	C₄×C₈	C₂³×C₃₁	1	2	yes	—
999	C₃₁	#61969	1	1	yes	characteristic, direct product factor, Sylow
1000	#41	—	2	2	no	—
1001	#41	—	2	2	no	—
1002	#41	—	4	2	no	—
1003	#41	—	4	1	no	—
1004	#41	—	4	1	no	—
1005	#41	—	4	4	no	—
1006	#41	—	4	4	no	—
1007	#41	—	4	2	no	—
1008	#41	—	4	2	no	—
1009	#41	—	4	2	no	—
1010	#41	—	4	2	no	—
1011	C₂×Q₈	—	2	1	no	—
1012	C₂×Q₈	—	2	1	no	—
1013	C₂×Q₈	—	2	1	no	—
1014	C₂×Q₈	—	2	2	no	—
1015	C₂×Q₈	—	2	2	no	—
1016	C₂×Q₈	—	4	1	no	—
1017	C₂×Q₈	—	4	2	no	—
1018	C₂×Q₈	—	4	2	no	—
1019	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1020	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1021	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1022	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1023	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1024	C₂×D₄	—	2	1	no	—
1025	C₂×D₄	—	2	1	no	—
1026	C₂×D₄	—	2	2	no	—
1027	C₂×D₄	—	2	1	no	—
1028	C₂×D₄	—	2	1	no	—
1029	C₂×D₄	—	2	1	no	—
1030	C₂×D₄	—	2	1	no	—
1031	C₂×D₄	—	2	2	no	—
1032	C₂×D₄	—	2	2	no	—
1033	C₂×D₄	—	2	1	no	—
1034	C₂×D₄	—	2	1	no	—
1035	C₂×D₄	—	2	1	no	—
1036	C₂×D₄	—	2	1	no	—
1037	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1038	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1039	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1040	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1041	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1042	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1043	C₂²×C₄	—	2	1	no	—
1044	C₂²×C₄	—	2	1	no	—
1045	C₂²×C₄	—	2	2	no	—
1046	C₂²×C₄	—	2	1	no	—
1047	C₂²×C₄	—	2	1	no	—
1048	C₂²×C₄	—	2	1	no	—
1049	C₂²×C₄	—	2	1	no	—
1050	C₂²×C₄	—	2	2	no	—
1051	C₂²×C₄	—	2	1	no	—
1052	C₂²×C₄	—	2	1	no	—
1053	C₂²×C₄	—	2	2	no	—
1054	C₂²×C₄	—	2	2	no	—
1055	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1056	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1057	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1058	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1059	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1060	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1061	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1062	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1063	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1064	Q₁₆	—	2	4	no	—
1065	Q₁₆	—	2	4	no	—
1066	Q₁₆	—	4	2	no	—
1067	Q₁₆	—	4	2	no	—
1068	SD₁₆	—	2	4	no	—
1069	SD₁₆	—	4	2	no	—
1070	SD₁₆	—	4	2	no	—
1071	SD₁₆	—	4	2	no	—
1072	SD₁₆	—	4	2	no	—
1073	SD₁₆	—	4	2	no	—
1074	D₈	—	4	2	no	—
1075	D₈	—	4	2	no	—
1076	M₁₆	—	4	2	no	—
1077	M₁₆	—	4	2	no	—
1078	C₂×C₈	—	4	2	no	—
1079	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1080	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1081	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1082	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1083	C₄⋊C₄	—	2	2	no	—
1084	C₄⋊C₄	—	2	1	no	—
1085	C₄⋊C₄	—	2	1	no	—
1086	C₄⋊C₄	—	2	1	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	—	2	1	no	—
1089	C₄⋊C₄	—	2	2	no	—
1090	C₄⋊C₄	—	2	2	no	—
1091	C₄⋊C₄	—	2	1	no	—
1092	C₄⋊C₄	—	2	1	no	—
1093	C₄⋊C₄	—	2	1	no	—
1094	C₄⋊C₄	—	2	2	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	2	no	—
1107	C₄⋊C₄	—	2	2	no	—
1108	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1109	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1110	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1111	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1112	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1113	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1114	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1115	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1116	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1117	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1118	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1119	C₂²⋊C₄	—	2	2	no	—
1120	C₂²⋊C₄	—	2	2	no	—
1121	C₂²⋊C₄	—	2	1	no	—
1122	C₂²⋊C₄	—	2	1	no	—
1123	C₂²⋊C₄	—	2	1	no	—
1124	C₂²⋊C₄	—	2	1	no	—
1125	C₂²⋊C₄	—	2	1	no	—
1126	C₂²⋊C₄	—	2	1	no	—
1127	C₂²⋊C₄	—	2	2	no	—
1128	C₂²⋊C₄	—	2	2	no	—
1129	C₂²⋊C₄	—	2	1	no	—
1130	C₂²⋊C₄	—	2	1	no	—
1131	C₂²⋊C₄	—	2	1	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	1	no	—
1138	C₂²⋊C₄	—	2	1	no	—
1139	C₂²⋊C₄	—	2	2	no	—
1140	C₂²⋊C₄	—	2	1	no	—
1141	C₂²⋊C₄	—	2	1	no	—
1142	C₂²⋊C₄	—	2	2	no	—
1143	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1144	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1145	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1146	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1147	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1148	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1149	C₄²	—	2	1	no	—
1150	C₄²	—	2	1	no	—
1151	C₄²	—	2	1	no	—
1152	C₄²	—	2	1	no	—
1153	C₄²	—	2	1	no	—
1154	C₄²	—	2	1	no	—
1155	C₄²	—	2	1	no	—
1156	C₄²	—	2	1	no	—
1157	C₄²	—	2	2	no	—
1158	C₄²	—	2	2	no	—
1159	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1160	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1161	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1162	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1163	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1164	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1165	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1166	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1167	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1168	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1169	C₂³	—	2	1	no	—
1170	C₂³	—	2	1	no	—
1171	C₂³	—	2	2	no	—
1172	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1173	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1174	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1175	Q₈	—	2	1	no	—
1176	Q₈	—	2	2	no	—
1177	Q₈	—	2	1	no	—
1178	Q₈	—	2	2	no	—
1179	Q₈	—	2	2	no	—
1180	Q₈	—	2	1	no	—
1181	Q₈	—	2	2	no	—
1182	Q₈	—	4	1	no	—
1183	Q₈	—	4	2	no	—
1184	Q₈	—	4	2	no	—
1185	Q₈	—	4	2	no	—
1186	Q₈	—	8	2	no	—
1187	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
1188	D₄	—	2	1	no	—
1189	D₄	—	2	2	no	—
1190	D₄	—	2	1	no	—
1191	D₄	—	2	1	no	—
1192	D₄	—	2	2	no	—
1193	D₄	—	2	1	no	—
1194	D₄	—	4	1	no	—
1195	D₄	—	4	1	no	—
1196	D₄	—	4	1	no	—
1197	D₄	—	4	2	no	—
1198	D₄	—	4	2	no	—
1199	D₄	—	4	2	no	—
1200	D₄	—	4	2	no	—
1201	D₄	—	4	4	no	—
1202	D₄	—	4	2	no	—
1203	D₄	—	4	2	no	—
1204	D₄	—	4	2	no	—
1205	D₄	—	8	1	no	—
1206	D₄	—	8	1	no	—
1207	D₄	—	8	1	no	—
1208	D₄	—	8	2	no	—
1209	D₄	—	8	2	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	2	no	—
1212	C₂×C₄	—	2	2	no	—
1213	C₂×C₄	—	2	2	no	—
1214	C₂×C₄	—	2	1	no	—
1215	C₂×C₄	—	2	1	no	—
1216	C₂×C₄	—	2	1	no	—
1217	C₂×C₄	—	2	1	no	—
1218	C₂×C₄	—	2	1	no	—
1219	C₂×C₄	—	2	1	no	—
1220	C₂×C₄	—	2	1	no	—
1221	C₂×C₄	—	2	1	no	—
1222	C₂×C₄	—	2	1	no	—
1223	C₂×C₄	—	2	1	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	—	4	1	no	—
1229	C₂×C₄	—	4	1	no	—
1230	C₂×C₄	—	4	1	no	—
1231	C₂×C₄	—	4	2	no	—
1232	C₂×C₄	—	4	2	no	—
1233	C₂×C₄	—	4	2	no	—
1234	C₂×C₄	—	4	4	no	—
1235	C₂×C₄	—	4	2	no	—
1236	C₂×C₄	—	4	2	no	—
1237	C₂×C₄	—	8	1	no	—
1238	C₂×C₄	—	8	1	no	—
1239	C₂×C₄	—	8	2	no	—
1240	C₂×C₄	—	8	2	no	—
1241	C₂×C₄	—	8	1	no	—
1242	C₂×C₄	—	8	2	no	—
1243	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1244	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1245	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1246	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1247	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1248	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1249	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1250	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1251	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1252	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1253	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1254	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1255	C₈	—	2	2	no	—
1256	C₈	—	2	2	no	—
1257	C₈	—	2	2	no	—
1258	C₈	—	2	2	no	—
1259	C₂²	—	2	1	no	—
1260	C₂²	—	2	1	no	—
1261	C₂²	—	2	1	no	—
1262	C₂²	—	2	1	no	—
1263	C₂²	—	2	1	no	—
1264	C₂²	—	2	1	no	—
1265	C₂²	—	2	1	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	1	no	—
1268	C₂²	—	4	1	no	—
1269	C₂²	—	4	1	no	—
1270	C₂²	—	4	2	no	—
1271	C₂²	—	4	2	no	—
1272	C₂²	—	4	1	no	—
1273	C₂²	—	4	1	no	—
1274	C₂²	—	4	1	no	—
1275	C₂²	—	4	1	no	—
1276	C₂²	—	4	2	no	—
1277	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1278	C₄	—	2	1	no	—
1279	C₄	—	2	1	no	—
1280	C₄	—	2	1	no	—
1281	C₄	—	2	2	no	—
1282	C₄	—	2	1	no	—
1283	C₄	—	2	1	no	—
1284	C₄	—	2	1	no	—
1285	C₄	—	2	1	no	—
1286	C₄	—	2	1	no	—
1287	C₄	—	2	1	no	—
1288	C₄	—	2	1	no	—
1289	C₄	—	4	1	no	—
1290	C₄	—	4	2	no	—
1291	C₄	—	4	2	no	—
1292	C₄	—	4	2	no	—
1293	C₄	—	4	1	no	—
1294	C₄	—	4	1	no	—
1295	C₄	—	4	1	no	—
1296	C₄	—	4	1	no	—
1297	C₄	C₃₁×#575	1	2	yes	—
1298	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1299	C₄	C₃₁×#585	1	1	yes	characteristic
1300	C₂	—	4	1	no	—
1301	C₂	—	4	1	no	—
1302	C₂	—	4	1	no	—
1303	C₂	—	8	1	no	—
1304	C₂	—	8	1	no	—
1305	C₂	—	8	2	no	—
1306	C₂	C₃₁×#3488	1	1	yes	characteristic
1307	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1308	C₂	C₃₁×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3511	C₂	semidirect
2. C₃₁×#3480	C₂	semidirect
3. C₃₁×#3401	C₂	semidirect
4. C₃₁×#3377	C₂	semidirect
5. C₃₁×#3326	C₂	semidirect
6. C₃₁×#3313	C₂	semidirect
7. C₃₁×#3307	C₂	semidirect
8. C₃₁×#3277	C₂	semidirect
9. C₃₁×#3271	C₂	semidirect
10. C₃₁×#3269	C₂	semidirect
11. C₃₁×#3254	C₂	semidirect
12. C₃₁×#3251	C₂	semidirect
13. C₃₁×#3248	C₂	semidirect
14. C₃₁×#3218	C₂	semidirect
15. C₃₁×#3214	C₂	semidirect
16. C₃₁×#3212	C₂	semidirect
17. C₃₁×#3115	C₂	semidirect
18. C₃₁×#3113	C₂	semidirect
19. C₃₁×#3107	C₂	semidirect
20. C₃₁×#3039	C₂	semidirect
21. C₃₁×#3037	C₂	semidirect
22. C₃₁×#3035	C₂	semidirect
23. C₃₁×#2989	C₂	semidirect
514. #61969	C₃₁	direct (N × H)
605. #3511	C₂×C₃₁	semidirect
606. #3480	C₂×C₃₁	semidirect
607. #3401	C₂×C₃₁	semidirect
608. #3377	C₂×C₃₁	semidirect
609. #3326	C₂×C₃₁	semidirect
610. #3313	C₂×C₃₁	semidirect
611. #3307	C₂×C₃₁	semidirect
612. #3277	C₂×C₃₁	semidirect
613. #3271	C₂×C₃₁	semidirect
614. #3269	C₂×C₃₁	semidirect
615. #3254	C₂×C₃₁	semidirect
616. #3251	C₂×C₃₁	semidirect
617. #3248	C₂×C₃₁	semidirect
618. #3218	C₂×C₃₁	semidirect
619. #3214	C₂×C₃₁	semidirect
620. #3212	C₂×C₃₁	semidirect
621. #3115	C₂×C₃₁	semidirect
622. #3113	C₂×C₃₁	semidirect
623. #3107	C₂×C₃₁	semidirect
624. #3039	C₂×C₃₁	semidirect
625. #3037	C₂×C₃₁	semidirect
626. #3035	C₂×C₃₁	semidirect
627. #2989	C₂×C₃₁	semidirect
999. C₃₁	#61969	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3511	2
C₃₁×#3480	2
C₃₁×#3401	2
C₃₁×#3377	2
C₃₁×#3326	2
C₃₁×#3313	2
C₃₁×#3307	2
C₃₁×#3277	2
C₃₁×#3271	2
C₃₁×#3269	2
C₃₁×#3254	2
C₃₁×#3251	2
C₃₁×#3248	2
C₃₁×#3218	2
C₃₁×#3214	2
C₃₁×#3212	2
C₃₁×#3115	2
C₃₁×#3113	2
C₃₁×#3107	2
C₃₁×#3039	2
C₃₁×#3037	2
C₃₁×#3035	2
C₃₁×#2989	2
#61969	31

Subgroups — C31×#61969 #21518728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61969 #21518728