Subgroups — C₃₁×#61967 #21518726

Order 7936.

1856 conjugacy classes of subgroups.

The subgroup lattice has 1312 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×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3402	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3327	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3321	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3315	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3275	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3269	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3267	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3255	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×#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×#3110	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×#3036	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×AGL(1,ℤ/8)	C₂²	1	2	yes	—
26	C₂×C₃₁×#135	C₂²	1	2	yes	—
27	C₃₁×#556	C₂²	1	1	yes	characteristic
28	C₃₁×#556	C₂²	1	2	yes	complemented
29	C₃₁×#555	—	2	1	no	—
30	C₃₁×#555	C₂²	1	1	yes	characteristic
31	C₃₁×#554	—	2	1	no	—
32	C₃₁×#554	C₂²	1	1	yes	characteristic
33	C₃₁×#553	—	2	1	no	—
34	C₃₁×#553	—	2	1	no	—
35	C₃₁×#553	—	2	1	no	—
36	C₃₁×#552	—	2	1	no	—
37	C₃₁×#552	C₂²	1	1	yes	characteristic
38	C₃₁×#552	C₂²	1	1	yes	characteristic
39	C₃₁×#551	—	2	1	no	—
40	C₃₁×#551	—	2	1	no	—
41	C₃₁×#548	C₂²	1	2	yes	—
42	C₃₁×#548	C₂²	1	2	yes	complemented
43	C₃₁×#547	C₂²	1	1	yes	characteristic
44	C₃₁×#547	C₂²	1	2	yes	—
45	C₃₁×#546	C₂²	1	1	yes	characteristic
46	C₃₁×#546	C₂²	1	1	yes	characteristic
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×#533	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#532	C₂²	1	1	yes	characteristic
54	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#529	—	2	1	no	—
58	C₃₁×#529	—	2	1	no	—
59	C₃₁×#529	C₂²	1	1	yes	characteristic
60	C₃₁×#529	C₂²	1	1	yes	characteristic
61	C₃₁×#525	—	2	1	no	—
62	C₃₁×#520	—	2	1	no	—
63	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
64	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
65	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
66	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
67	C₂×C₃₁×#117	—	2	1	no	—
68	C₃₁×#497	C₂²	1	2	yes	—
69	C₃₁×#497	C₂²	1	2	yes	complemented
70	C₃₁×#495	C₂²	1	2	yes	—
71	C₃₁×#491	C₂²	1	2	yes	complemented
72	C₃₁×#489	C₂²	1	2	yes	complemented
73	C₃₁×#488	C₂²	1	2	yes	complemented
74	C₃₁×#485	C₂²	1	2	yes	complemented
75	C₃₁×#484	C₂²	1	2	yes	—
76	C₃₁×#482	C₂²	1	2	yes	complemented
77	C₃₁×#479	C₂²	1	2	yes	complemented
78	C₃₁×#478	C₂²	1	2	yes	complemented
79	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#475	C₂²	1	2	yes	complemented
82	C₃₁×#474	C₂²	1	1	yes	characteristic
83	C₃₁×#474	C₂²	1	1	yes	characteristic
84	C₃₁×#470	C₂²	1	2	yes	—
85	C₃₁×#470	C₂²	1	2	yes	—
86	C₃₁×#469	C₂²	1	2	yes	—
87	C₃₁×#468	C₂²	1	2	yes	complemented
88	C₃₁×#467	C₂²	1	2	yes	complemented
89	C₃₁×#465	C₂²	1	2	yes	—
90	C₃₁×#464	C₂²	1	2	yes	—
91	C₃₁×#464	C₂²	1	2	yes	complemented
92	C₃₁×#463	C₂²	1	2	yes	—
93	C₃₁×#463	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, complemented
97	C₃₁×#462	C₂²	1	2	yes	complemented
98	C₃₁×#462	C₂²	1	2	yes	complemented
99	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#461	C₂²	1	1	yes	characteristic
103	C₃₁×#461	C₂²	1	1	yes	characteristic
104	C₃₁×#461	C₂²	1	1	yes	characteristic
105	C₃₁×#461	C₂²	1	2	yes	—
106	C₃₁×#461	C₂²	1	1	yes	characteristic
107	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
108	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
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×#452	C₂²	1	2	yes	—
114	C₃₁×#452	C₂²	1	2	yes	complemented
115	C₃₁×#451	C₂²	1	2	yes	complemented
116	C₃₁×#450	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	complemented
121	C₃₁×#442	C₂²	1	2	yes	—
122	C₃₁×#440	C₂²	1	2	yes	—
123	C₃₁×#440	C₂²	1	2	yes	—
124	C₃₁×#440	C₂²	1	2	yes	complemented
125	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
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	complemented
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
134	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
136	C₃₁×#419	C₂²	1	2	yes	complemented
137	C₃₁×#417	C₂²	1	2	yes	—
138	C₃₁×#416	C₂²	1	2	yes	complemented
139	C₂×#41×C₃₁	—	2	1	no	—
140	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
141	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×#41×C₃₁	C₂³	1	2	yes	—
144	C₂×#41×C₃₁	C₂³	1	2	yes	—
145	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
146	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₃₁	—	2	1	no	—
148	C₃₁×#137	—	4	4	no	—
149	C₃₁×AGL(1,ℤ/8)	—	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	C₂³	1	1	yes	characteristic
169	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
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×#127	C₂³	1	1	yes	characteristic
175	C₃₁×#126	—	2	1	no	—
176	C₃₁×#126	—	2	1	no	—
177	C₃₁×#126	—	2	2	no	—
178	C₃₁×#126	—	2	2	no	—
179	C₃₁×#126	—	2	1	no	—
180	C₃₁×#126	—	2	1	no	—
181	C₃₁×#126	—	2	1	no	—
182	C₃₁×#126	—	2	1	no	—
183	C₃₁×#125	—	2	1	no	—
184	C₃₁×#125	—	2	1	no	—
185	C₃₁×#125	—	2	1	no	—
186	C₃₁×#125	—	2	1	no	—
187	C₃₁×#125	—	2	1	no	—
188	C₃₁×#125	C₂³	1	1	yes	characteristic
189	C₃₁×#125	C₂³	1	1	yes	characteristic
190	C₃₁×#124	—	2	1	no	—
191	C₃₁×#124	—	2	1	no	—
192	C₃₁×#124	—	2	2	no	—
193	C₃₁×#124	—	2	2	no	—
194	C₃₁×#124	—	2	1	no	—
195	C₃₁×#124	C₂³	1	2	yes	—
196	C₃₁×#124	C₂³	1	1	yes	characteristic
197	C₃₁×#124	C₂³	1	2	yes	—
198	C₃₁×#124	C₂³	1	1	yes	characteristic
199	C₃₁×#123	—	2	1	no	—
200	C₃₁×#123	—	2	1	no	—
201	C₃₁×#123	—	2	1	no	—
202	C₃₁×#123	—	2	1	no	—
203	C₃₁×#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	2	no	—
208	C₃₁×#123	—	2	2	no	—
209	C₃₁×C₂²⋊Q₈	—	2	1	no	—
210	C₃₁×C₂²⋊Q₈	—	2	1	no	—
211	C₃₁×C₂²⋊Q₈	—	2	2	no	—
212	C₃₁×C₂²⋊Q₈	—	2	1	no	—
213	C₃₁×C₂²⋊Q₈	—	2	1	no	—
214	C₃₁×C₂²⋊Q₈	—	2	1	no	—
215	C₃₁×C₂²⋊Q₈	—	2	1	no	—
216	C₃₁×C₂²⋊Q₈	—	2	1	no	—
217	C₃₁×C₂²⋊Q₈	—	2	2	no	—
218	C₃₁×C₂²⋊Q₈	—	2	2	no	—
219	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₃₁×#121	—	2	1	no	—
226	C₃₁×#121	—	2	1	no	—
227	C₃₁×#121	—	2	2	no	—
228	C₃₁×#121	—	2	2	no	—
229	C₃₁×#121	—	2	2	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	2	yes	—
240	C₃₁×#120	—	2	1	no	—
241	C₃₁×#120	—	2	1	no	—
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	D₄	1	1	yes	characteristic
246	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
247	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
249	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
251	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
252	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₃₁	—	2	1	no	—
254	C₄×D₄×C₃₁	—	2	1	no	—
255	C₄×D₄×C₃₁	—	2	1	no	—
256	C₄×D₄×C₃₁	—	2	1	no	—
257	C₄×D₄×C₃₁	—	2	1	no	—
258	C₄×D₄×C₃₁	—	2	1	no	—
259	C₄×D₄×C₃₁	—	2	2	no	—
260	C₄×D₄×C₃₁	—	2	2	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	D₄	1	1	yes	characteristic
269	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
270	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
271	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
272	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
273	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
274	C₄×D₄×C₃₁	C₂³	1	2	yes	—
275	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
276	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
277	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
278	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
279	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
280	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
281	C₃₁×#117	—	2	1	no	—
282	C₃₁×#117	—	2	1	no	—
283	C₃₁×#117	—	2	1	no	—
284	C₃₁×#117	—	2	1	no	—
285	C₃₁×#117	—	2	1	no	—
286	C₃₁×#117	—	2	2	no	—
287	C₃₁×#117	—	2	1	no	—
288	C₃₁×#117	—	2	1	no	—
289	C₃₁×#117	—	2	1	no	—
290	C₃₁×#117	—	2	1	no	—
291	C₃₁×#117	—	2	1	no	—
292	C₃₁×#117	—	2	1	no	—
293	C₃₁×#117	D₄	1	1	yes	characteristic
294	C₃₁×#117	D₄	1	1	yes	characteristic
295	C₃₁×#117	D₄	1	1	yes	characteristic
296	C₃₁×#117	C₂³	1	1	yes	characteristic
297	C₃₁×#117	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
299	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
300	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
301	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
302	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
303	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
305	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
306	C₂×C₂²⋊C₄×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	C₂⁴×C₃₁	—	2	1	no	—
346	#41×C₃₁	—	2	2	no	—
347	#41×C₃₁	—	2	2	no	—
348	#41×C₃₁	—	4	2	no	—
349	#41×C₃₁	—	4	1	no	—
350	#41×C₃₁	—	4	1	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	2	no	—
359	C₂×Q₈×C₃₁	—	4	2	no	—
360	C₂×Q₈×C₃₁	—	4	2	no	—
361	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
362	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
363	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
364	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	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	1	no	—
375	C₂×D₄×C₃₁	—	2	1	no	—
376	C₂×D₄×C₃₁	—	2	1	no	—
377	C₂×D₄×C₃₁	—	4	1	no	—
378	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
379	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
380	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
381	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
382	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₃₁	—	2	1	no	—
385	C₂²×C₄×C₃₁	—	2	2	no	—
386	C₂²×C₄×C₃₁	—	2	1	no	—
387	C₂²×C₄×C₃₁	—	2	1	no	—
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	2	no	—
397	C₂²×C₄×C₃₁	—	4	4	no	—
398	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	Q₁₆×C₃₁	—	4	2	no	—
408	Q₁₆×C₃₁	—	4	2	no	—
409	Q₁₆×C₃₁	—	4	2	no	—
410	Q₁₆×C₃₁	—	4	2	no	—
411	SD₁₆×C₃₁	—	2	4	no	—
412	SD₁₆×C₃₁	—	2	4	no	—
413	SD₁₆×C₃₁	—	4	2	no	—
414	SD₁₆×C₃₁	—	4	2	no	—
415	SD₁₆×C₃₁	—	4	2	no	—
416	SD₁₆×C₃₁	—	4	2	no	—
417	D₈×C₃₁	—	2	4	no	—
418	D₈×C₃₁	—	4	2	no	—
419	M₁₆×C₃₁	—	4	2	no	—
420	M₁₆×C₃₁	—	4	2	no	—
421	C₂×C₈×C₃₁	—	4	2	no	—
422	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
423	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
424	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
425	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
426	C₄⋊C₄×C₃₁	—	2	2	no	—
427	C₄⋊C₄×C₃₁	—	2	1	no	—
428	C₄⋊C₄×C₃₁	—	2	1	no	—
429	C₄⋊C₄×C₃₁	—	2	1	no	—
430	C₄⋊C₄×C₃₁	—	2	1	no	—
431	C₄⋊C₄×C₃₁	—	2	1	no	—
432	C₄⋊C₄×C₃₁	—	2	1	no	—
433	C₄⋊C₄×C₃₁	—	2	1	no	—
434	C₄⋊C₄×C₃₁	—	2	1	no	—
435	C₄⋊C₄×C₃₁	—	2	1	no	—
436	C₄⋊C₄×C₃₁	—	2	1	no	—
437	C₄⋊C₄×C₃₁	—	2	2	no	—
438	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
465	C₂²⋊C₄×C₃₁	—	2	1	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	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	1	no	—
485	C₂²⋊C₄×C₃₁	—	2	1	no	—
486	C₂²⋊C₄×C₃₁	—	2	2	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	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	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
495	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	#61967	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	—	4	2	no	—
519	C₂³×C₃₁	—	4	2	no	—
520	C₂³×C₃₁	—	8	1	no	—
521	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
522	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
523	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
524	Q₈×C₃₁	—	2	2	no	—
525	Q₈×C₃₁	—	2	2	no	—
526	Q₈×C₃₁	—	2	1	no	—
527	Q₈×C₃₁	—	2	1	no	—
528	Q₈×C₃₁	—	2	1	no	—
529	Q₈×C₃₁	—	2	2	no	—
530	Q₈×C₃₁	—	2	1	no	—
531	Q₈×C₃₁	—	2	2	no	—
532	Q₈×C₃₁	—	4	1	no	—
533	Q₈×C₃₁	—	4	2	no	—
534	Q₈×C₃₁	—	8	1	no	—
535	Q₈×C₃₁	—	8	2	no	—
536	D₄×C₃₁	—	2	2	no	—
537	D₄×C₃₁	—	2	1	no	—
538	D₄×C₃₁	—	2	1	no	—
539	D₄×C₃₁	—	2	1	no	—
540	D₄×C₃₁	—	2	2	no	—
541	D₄×C₃₁	—	4	1	no	—
542	D₄×C₃₁	—	4	1	no	—
543	D₄×C₃₁	—	4	1	no	—
544	D₄×C₃₁	—	4	2	no	—
545	D₄×C₃₁	—	4	2	no	—
546	D₄×C₃₁	—	4	2	no	—
547	D₄×C₃₁	—	4	2	no	—
548	D₄×C₃₁	—	4	4	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	H(5,𝔽₂)	1	2	yes	—
555	C₂×C₄×C₃₁	—	2	2	no	—
556	C₂×C₄×C₃₁	—	2	2	no	—
557	C₂×C₄×C₃₁	—	2	2	no	—
558	C₂×C₄×C₃₁	—	2	1	no	—
559	C₂×C₄×C₃₁	—	2	1	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	2	no	—
570	C₂×C₄×C₃₁	—	2	2	no	—
571	C₂×C₄×C₃₁	—	2	2	no	—
572	C₂×C₄×C₃₁	—	2	1	no	—
573	C₂×C₄×C₃₁	—	4	1	no	—
574	C₂×C₄×C₃₁	—	4	1	no	—
575	C₂×C₄×C₃₁	—	4	1	no	—
576	C₂×C₄×C₃₁	—	4	2	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	—	4	2	no	—
584	C₂×C₄×C₃₁	—	8	1	no	—
585	C₂×C₄×C₃₁	—	8	1	no	—
586	C₂×C₄×C₃₁	—	8	2	no	—
587	C₂×C₄×C₃₁	—	8	2	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	#3475	C₂×C₃₁	1	1	yes	characteristic, complemented
607	#3402	C₂×C₃₁	1	2	yes	complemented
608	#3376	C₂×C₃₁	1	2	yes	complemented
609	#3327	C₂×C₃₁	1	2	yes	complemented
610	#3321	C₂×C₃₁	1	2	yes	complemented
611	#3315	C₂×C₃₁	1	2	yes	complemented
612	#3275	C₂×C₃₁	1	2	yes	complemented
613	#3269	C₂×C₃₁	1	2	yes	complemented
614	#3267	C₂×C₃₁	1	2	yes	complemented
615	#3255	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	#3216	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	#3110	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	#3036	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	2	no	—
635	C₂²×C₃₁	—	2	1	no	—
636	C₂²×C₃₁	—	2	1	no	—
637	C₂²×C₃₁	—	2	1	no	—
638	C₂²×C₃₁	—	4	1	no	—
639	C₂²×C₃₁	—	4	1	no	—
640	C₂²×C₃₁	—	4	2	no	—
641	C₂²×C₃₁	—	4	1	no	—
642	C₂²×C₃₁	—	4	2	no	—
643	C₂²×C₃₁	—	4	1	no	—
644	C₂²×C₃₁	—	4	1	no	—
645	C₂²×C₃₁	—	4	2	no	—
646	C₂²×C₃₁	—	8	4	no	—
647	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
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	1	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	1	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	—	4	2	no	—
667	C₄×C₃₁	#575	1	2	yes	—
668	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
669	C₄×C₃₁	#585	1	1	yes	characteristic
670	C₂×#137	C₂²×C₃₁	1	2	yes	—
671	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
672	C₂×#135	C₂²×C₃₁	1	2	yes	—
673	#556	C₂²×C₃₁	1	1	yes	characteristic
674	#556	C₂²×C₃₁	1	2	yes	complemented
675	#555	—	2	1	no	—
676	#555	C₂²×C₃₁	1	1	yes	characteristic
677	#554	—	2	1	no	—
678	#554	C₂²×C₃₁	1	1	yes	characteristic
679	#553	—	2	1	no	—
680	#553	—	2	1	no	—
681	#553	—	2	1	no	—
682	#552	—	2	1	no	—
683	#552	C₂²×C₃₁	1	1	yes	characteristic
684	#552	C₂²×C₃₁	1	1	yes	characteristic
685	#551	—	2	1	no	—
686	#551	—	2	1	no	—
687	#548	C₂²×C₃₁	1	2	yes	—
688	#548	C₂²×C₃₁	1	2	yes	complemented
689	#547	C₂²×C₃₁	1	1	yes	characteristic
690	#547	C₂²×C₃₁	1	2	yes	—
691	#546	C₂²×C₃₁	1	1	yes	characteristic
692	#546	C₂²×C₃₁	1	1	yes	characteristic
693	#542	—	2	1	no	—
694	#542	—	2	1	no	—
695	#537	—	2	1	no	—
696	#533	C₂²×C₃₁	1	1	yes	characteristic
697	#533	C₂²×C₃₁	1	1	yes	characteristic
698	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	#532	C₂²×C₃₁	1	1	yes	characteristic
700	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
702	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
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	#525	—	2	1	no	—
708	#520	—	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×D₄	C₂²×C₃₁	1	1	yes	characteristic
713	C₂×#117	—	2	1	no	—
714	#497	C₂²×C₃₁	1	2	yes	—
715	#497	C₂²×C₃₁	1	2	yes	complemented
716	#495	C₂²×C₃₁	1	2	yes	—
717	#491	C₂²×C₃₁	1	2	yes	complemented
718	#489	C₂²×C₃₁	1	2	yes	complemented
719	#488	C₂²×C₃₁	1	2	yes	complemented
720	#485	C₂²×C₃₁	1	2	yes	complemented
721	#484	C₂²×C₃₁	1	2	yes	—
722	#482	C₂²×C₃₁	1	2	yes	complemented
723	#479	C₂²×C₃₁	1	2	yes	complemented
724	#478	C₂²×C₃₁	1	2	yes	complemented
725	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
726	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
727	#475	C₂²×C₃₁	1	2	yes	complemented
728	#474	C₂²×C₃₁	1	1	yes	characteristic
729	#474	C₂²×C₃₁	1	1	yes	characteristic
730	#470	C₂²×C₃₁	1	2	yes	—
731	#470	C₂²×C₃₁	1	2	yes	—
732	#469	C₂²×C₃₁	1	2	yes	—
733	#468	C₂²×C₃₁	1	2	yes	complemented
734	#467	C₂²×C₃₁	1	2	yes	complemented
735	#465	C₂²×C₃₁	1	2	yes	—
736	#464	C₂²×C₃₁	1	2	yes	—
737	#464	C₂²×C₃₁	1	2	yes	complemented
738	#463	C₂²×C₃₁	1	2	yes	—
739	#463	C₂²×C₃₁	1	2	yes	—
740	#463	C₂²×C₃₁	1	2	yes	—
741	#463	C₂²×C₃₁	1	2	yes	—
742	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
743	#462	C₂²×C₃₁	1	2	yes	complemented
744	#462	C₂²×C₃₁	1	2	yes	complemented
745	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
746	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
747	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
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	#461	C₂²×C₃₁	1	2	yes	—
752	#461	C₂²×C₃₁	1	1	yes	characteristic
753	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
754	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
755	#459	C₂²×C₃₁	1	1	yes	characteristic
756	#459	C₂²×C₃₁	1	1	yes	characteristic
757	#452	C₂²×C₃₁	1	2	yes	—
758	#452	C₂²×C₃₁	1	2	yes	—
759	#452	C₂²×C₃₁	1	2	yes	—
760	#452	C₂²×C₃₁	1	2	yes	complemented
761	#451	C₂²×C₃₁	1	2	yes	complemented
762	#450	C₂²×C₃₁	1	2	yes	—
763	#449	C₂²×C₃₁	1	2	yes	—
764	#449	C₂²×C₃₁	1	2	yes	—
765	#448	C₂²×C₃₁	1	2	yes	—
766	#446	C₂²×C₃₁	1	2	yes	complemented
767	#442	C₂²×C₃₁	1	2	yes	—
768	#440	C₂²×C₃₁	1	2	yes	—
769	#440	C₂²×C₃₁	1	2	yes	—
770	#440	C₂²×C₃₁	1	2	yes	complemented
771	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
772	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
773	#436	C₂²×C₃₁	1	2	yes	—
774	#435	C₂²×C₃₁	1	2	yes	—
775	#435	C₂²×C₃₁	1	2	yes	complemented
776	#432	C₂²×C₃₁	1	1	yes	characteristic
777	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
778	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
779	#423	C₂²×C₃₁	1	1	yes	characteristic
780	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
781	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
782	#419	C₂²×C₃₁	1	2	yes	complemented
783	#417	C₂²×C₃₁	1	2	yes	—
784	#416	C₂²×C₃₁	1	2	yes	complemented
785	C₂×C₃₁	—	4	1	no	—
786	C₂×C₃₁	—	4	1	no	—
787	C₂×C₃₁	—	4	1	no	—
788	C₂×C₃₁	—	4	2	no	—
789	C₂×C₃₁	—	8	2	no	—
790	C₂×C₃₁	—	8	1	no	—
791	C₂×C₃₁	#3488	1	1	yes	characteristic
792	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
793	C₂×C₃₁	#3586	1	1	yes	characteristic
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	2	yes	—
801	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
802	C₂³×C₄	—	2	1	no	—
803	#137	—	4	4	no	—
804	AGL(1,ℤ/8)	—	4	4	no	—
805	#135	—	4	4	no	—
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×Q₁₆	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×SD₁₆	C₂³×C₃₁	1	2	yes	—
816	C₂×D₈	C₂³×C₃₁	1	2	yes	—
817	C₂×D₈	C₂³×C₃₁	1	2	yes	—
818	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
819	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
820	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
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	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
829	#127	C₂³×C₃₁	1	1	yes	characteristic
830	#126	—	2	1	no	—
831	#126	—	2	1	no	—
832	#126	—	2	2	no	—
833	#126	—	2	2	no	—
834	#126	—	2	1	no	—
835	#126	—	2	1	no	—
836	#126	—	2	1	no	—
837	#126	—	2	1	no	—
838	#125	—	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	2	no	—
848	#124	—	2	2	no	—
849	#124	—	2	1	no	—
850	#124	C₂³×C₃₁	1	1	yes	characteristic
851	#124	C₂³×C₃₁	1	1	yes	characteristic
852	#124	C₂³×C₃₁	1	2	yes	—
853	#124	C₂³×C₃₁	1	2	yes	—
854	#123	—	2	1	no	—
855	#123	—	2	1	no	—
856	#123	—	2	1	no	—
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	2	no	—
863	#123	—	2	2	no	—
864	C₂²⋊Q₈	—	2	1	no	—
865	C₂²⋊Q₈	—	2	1	no	—
866	C₂²⋊Q₈	—	2	2	no	—
867	C₂²⋊Q₈	—	2	1	no	—
868	C₂²⋊Q₈	—	2	1	no	—
869	C₂²⋊Q₈	—	2	1	no	—
870	C₂²⋊Q₈	—	2	1	no	—
871	C₂²⋊Q₈	—	2	1	no	—
872	C₂²⋊Q₈	—	2	2	no	—
873	C₂²⋊Q₈	—	2	2	no	—
874	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
875	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
876	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
877	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
878	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
879	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
880	#121	—	2	1	no	—
881	#121	—	2	1	no	—
882	#121	—	2	2	no	—
883	#121	—	2	2	no	—
884	#121	—	2	2	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	—	2	1	no	—
892	#121	C₂³×C₃₁	1	1	yes	characteristic
893	#121	C₂³×C₃₁	1	1	yes	characteristic
894	#121	C₂³×C₃₁	1	2	yes	—
895	#120	—	2	1	no	—
896	#120	—	2	1	no	—
897	C₄×Q₈	—	2	1	no	—
898	C₄×Q₈	—	2	1	no	—
899	C₄×Q₈	—	2	1	no	—
900	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
901	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
902	C₄×Q₈	C₂³×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	2	yes	—
906	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
907	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
908	C₄×D₄	—	2	1	no	—
909	C₄×D₄	—	2	1	no	—
910	C₄×D₄	—	2	1	no	—
911	C₄×D₄	—	2	1	no	—
912	C₄×D₄	—	2	1	no	—
913	C₄×D₄	—	2	1	no	—
914	C₄×D₄	—	2	2	no	—
915	C₄×D₄	—	2	2	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	D₄×C₃₁	1	1	yes	characteristic
924	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
925	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
926	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
927	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
928	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
929	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
930	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
931	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
932	C₄×D₄	C₂³×C₃₁	1	2	yes	—
933	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
934	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
935	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
936	#117	—	2	1	no	—
937	#117	—	2	1	no	—
938	#117	—	2	1	no	—
939	#117	—	2	1	no	—
940	#117	—	2	1	no	—
941	#117	—	2	2	no	—
942	#117	—	2	1	no	—
943	#117	—	2	1	no	—
944	#117	—	2	1	no	—
945	#117	—	2	1	no	—
946	#117	—	2	1	no	—
947	#117	—	2	1	no	—
948	#117	D₄×C₃₁	1	1	yes	characteristic
949	#117	D₄×C₃₁	1	1	yes	characteristic
950	#117	D₄×C₃₁	1	1	yes	characteristic
951	#117	C₂³×C₃₁	1	1	yes	characteristic
952	#117	C₂³×C₃₁	1	1	yes	characteristic
953	C₂×C₄⋊C₄	—	2	1	no	—
954	C₂×C₄⋊C₄	—	2	1	no	—
955	C₂×C₄⋊C₄	—	2	1	no	—
956	C₂×C₄⋊C₄	—	2	1	no	—
957	C₂×C₄⋊C₄	—	2	2	no	—
958	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
959	C₂×C₂²⋊C₄	—	2	1	no	—
960	C₂×C₂²⋊C₄	—	2	1	no	—
961	C₂×C₂²⋊C₄	—	2	1	no	—
962	C₂×C₄²	—	2	1	no	—
963	C₂×C₄²	—	2	1	no	—
964	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
965	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
966	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
967	#107	C₂³×C₃₁	1	2	yes	—
968	#107	C₂³×C₃₁	1	2	yes	—
969	#106	C₂³×C₃₁	1	2	yes	—
970	#106	C₂³×C₃₁	1	2	yes	—
971	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
972	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
973	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
974	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
975	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
976	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
977	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
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	#103	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	#102	C₂³×C₃₁	1	2	yes	—
994	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
995	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
996	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
997	#97	C₂³×C₃₁	1	2	yes	—
998	#97	C₂³×C₃₁	1	2	yes	—
999	C₄×C₈	C₂³×C₃₁	1	2	yes	—
1000	C₃₁	#61967	1	1	yes	characteristic, direct product factor, Sylow
1001	C₂⁴	—	2	1	no	—
1002	#41	—	2	2	no	—
1003	#41	—	2	2	no	—
1004	#41	—	4	2	no	—
1005	#41	—	4	1	no	—
1006	#41	—	4	1	no	—
1007	#41	—	4	4	no	—
1008	#41	—	4	2	no	—
1009	#41	—	4	2	no	—
1010	#41	—	4	2	no	—
1011	#41	—	4	2	no	—
1012	C₂×Q₈	—	2	1	no	—
1013	C₂×Q₈	—	2	1	no	—
1014	C₂×Q₈	—	2	2	no	—
1015	C₂×Q₈	—	4	2	no	—
1016	C₂×Q₈	—	4	2	no	—
1017	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1018	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1019	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1020	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1021	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1022	C₂×D₄	—	2	2	no	—
1023	C₂×D₄	—	2	1	no	—
1024	C₂×D₄	—	2	1	no	—
1025	C₂×D₄	—	2	2	no	—
1026	C₂×D₄	—	2	1	no	—
1027	C₂×D₄	—	2	1	no	—
1028	C₂×D₄	—	2	2	no	—
1029	C₂×D₄	—	2	2	no	—
1030	C₂×D₄	—	2	1	no	—
1031	C₂×D₄	—	2	1	no	—
1032	C₂×D₄	—	2	1	no	—
1033	C₂×D₄	—	4	1	no	—
1034	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1035	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1036	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1037	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1038	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1039	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1040	C₂²×C₄	—	2	1	no	—
1041	C₂²×C₄	—	2	2	no	—
1042	C₂²×C₄	—	2	1	no	—
1043	C₂²×C₄	—	2	1	no	—
1044	C₂²×C₄	—	2	1	no	—
1045	C₂²×C₄	—	2	1	no	—
1046	C₂²×C₄	—	2	2	no	—
1047	C₂²×C₄	—	2	1	no	—
1048	C₂²×C₄	—	2	1	no	—
1049	C₂²×C₄	—	2	1	no	—
1050	C₂²×C₄	—	2	1	no	—
1051	C₂²×C₄	—	2	2	no	—
1052	C₂²×C₄	—	2	2	no	—
1053	C₂²×C₄	—	4	4	no	—
1054	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	C₂⁴×C₃₁	1	1	yes	characteristic
1061	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1062	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1063	Q₁₆	—	4	2	no	—
1064	Q₁₆	—	4	2	no	—
1065	Q₁₆	—	4	2	no	—
1066	Q₁₆	—	4	2	no	—
1067	SD₁₆	—	2	4	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	D₈	—	2	4	no	—
1074	D₈	—	4	2	no	—
1075	M₁₆	—	4	2	no	—
1076	M₁₆	—	4	2	no	—
1077	C₂×C₈	—	4	2	no	—
1078	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
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	C₄⋊C₄	—	2	2	no	—
1083	C₄⋊C₄	—	2	1	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	1	no	—
1090	C₄⋊C₄	—	2	1	no	—
1091	C₄⋊C₄	—	2	1	no	—
1092	C₄⋊C₄	—	2	1	no	—
1093	C₄⋊C₄	—	2	2	no	—
1094	C₄⋊C₄	—	2	2	no	—
1095	C₄⋊C₄	—	2	2	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	2	no	—
1108	C₄⋊C₄	—	2	2	no	—
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	C₂×D₄×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	1	yes	characteristic
1119	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1120	C₂²⋊C₄	—	2	1	no	—
1121	C₂²⋊C₄	—	2	1	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	2	no	—
1124	C₂²⋊C₄	—	2	1	no	—
1125	C₂²⋊C₄	—	2	1	no	—
1126	C₂²⋊C₄	—	2	1	no	—
1127	C₂²⋊C₄	—	2	1	no	—
1128	C₂²⋊C₄	—	2	1	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	1	no	—
1136	C₂²⋊C₄	—	2	2	no	—
1137	C₂²⋊C₄	—	2	2	no	—
1138	C₂²⋊C₄	—	2	1	no	—
1139	C₂²⋊C₄	—	2	1	no	—
1140	C₂²⋊C₄	—	2	1	no	—
1141	C₂²⋊C₄	—	2	1	no	—
1142	C₂²⋊C₄	—	2	2	no	—
1143	C₂²⋊C₄	—	2	2	no	—
1144	C₂²⋊C₄	—	2	2	no	—
1145	C₂²⋊C₄	—	2	2	no	—
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	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1150	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1151	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	1	no	—
1158	C₄²	—	2	2	no	—
1159	C₄²	—	2	2	no	—
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	C₂×D₄×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	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1170	C₂³	—	2	1	no	—
1171	C₂³	—	2	1	no	—
1172	C₂³	—	2	2	no	—
1173	C₂³	—	4	2	no	—
1174	C₂³	—	4	2	no	—
1175	C₂³	—	8	1	no	—
1176	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1177	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1178	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1179	Q₈	—	2	2	no	—
1180	Q₈	—	2	2	no	—
1181	Q₈	—	2	1	no	—
1182	Q₈	—	2	1	no	—
1183	Q₈	—	2	1	no	—
1184	Q₈	—	2	2	no	—
1185	Q₈	—	2	1	no	—
1186	Q₈	—	2	2	no	—
1187	Q₈	—	4	1	no	—
1188	Q₈	—	4	2	no	—
1189	Q₈	—	8	1	no	—
1190	Q₈	—	8	2	no	—
1191	D₄	—	2	2	no	—
1192	D₄	—	2	1	no	—
1193	D₄	—	2	1	no	—
1194	D₄	—	2	1	no	—
1195	D₄	—	2	2	no	—
1196	D₄	—	4	1	no	—
1197	D₄	—	4	1	no	—
1198	D₄	—	4	1	no	—
1199	D₄	—	4	2	no	—
1200	D₄	—	4	2	no	—
1201	D₄	—	4	2	no	—
1202	D₄	—	4	2	no	—
1203	D₄	—	4	4	no	—
1204	D₄	—	4	2	no	—
1205	D₄	—	8	1	no	—
1206	D₄	—	8	1	no	—
1207	D₄	—	8	2	no	—
1208	D₄	—	8	2	no	—
1209	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1210	C₂×C₄	—	2	2	no	—
1211	C₂×C₄	—	2	2	no	—
1212	C₂×C₄	—	2	2	no	—
1213	C₂×C₄	—	2	1	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	2	no	—
1223	C₂×C₄	—	2	1	no	—
1224	C₂×C₄	—	2	1	no	—
1225	C₂×C₄	—	2	2	no	—
1226	C₂×C₄	—	2	2	no	—
1227	C₂×C₄	—	2	1	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	2	no	—
1235	C₂×C₄	—	4	4	no	—
1236	C₂×C₄	—	4	2	no	—
1237	C₂×C₄	—	4	2	no	—
1238	C₂×C₄	—	4	2	no	—
1239	C₂×C₄	—	8	1	no	—
1240	C₂×C₄	—	8	1	no	—
1241	C₂×C₄	—	8	2	no	—
1242	C₂×C₄	—	8	2	no	—
1243	C₂×C₄	—	8	2	no	—
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	C₂²×D₄×C₃₁	1	1	yes	characteristic
1255	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1256	C₈	—	2	2	no	—
1257	C₈	—	2	2	no	—
1258	C₈	—	2	2	no	—
1259	C₈	—	2	2	no	—
1260	C₂²	—	2	1	no	—
1261	C₂²	—	2	1	no	—
1262	C₂²	—	2	1	no	—
1263	C₂²	—	2	2	no	—
1264	C₂²	—	2	1	no	—
1265	C₂²	—	2	1	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	1	no	—
1268	C₂²	—	2	1	no	—
1269	C₂²	—	2	1	no	—
1270	C₂²	—	4	1	no	—
1271	C₂²	—	4	1	no	—
1272	C₂²	—	4	2	no	—
1273	C₂²	—	4	1	no	—
1274	C₂²	—	4	1	no	—
1275	C₂²	—	4	2	no	—
1276	C₂²	—	4	2	no	—
1277	C₂²	—	4	1	no	—
1278	C₂²	—	8	4	no	—
1279	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1280	C₄	—	2	1	no	—
1281	C₄	—	2	1	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	—	2	1	no	—
1290	C₄	—	4	1	no	—
1291	C₄	—	4	1	no	—
1292	C₄	—	4	2	no	—
1293	C₄	—	4	2	no	—
1294	C₄	—	4	1	no	—
1295	C₄	—	4	1	no	—
1296	C₄	—	4	2	no	—
1297	C₄	—	4	1	no	—
1298	C₄	—	4	1	no	—
1299	C₄	C₃₁×#575	1	2	yes	—
1300	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1301	C₄	C₃₁×#585	1	1	yes	characteristic
1302	C₂	—	4	1	no	—
1303	C₂	—	4	1	no	—
1304	C₂	—	4	1	no	—
1305	C₂	—	4	2	no	—
1306	C₂	—	8	1	no	—
1307	C₂	—	8	2	no	—
1308	C₂	C₃₁×#3488	1	1	yes	characteristic
1309	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1310	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×#3475	C₂	semidirect
3. C₃₁×#3402	C₂	semidirect
4. C₃₁×#3376	C₂	semidirect
5. C₃₁×#3327	C₂	semidirect
6. C₃₁×#3321	C₂	semidirect
7. C₃₁×#3315	C₂	semidirect
8. C₃₁×#3275	C₂	semidirect
9. C₃₁×#3269	C₂	semidirect
10. C₃₁×#3267	C₂	semidirect
11. C₃₁×#3255	C₂	semidirect
12. C₃₁×#3251	C₂	semidirect
13. C₃₁×#3248	C₂	semidirect
14. C₃₁×#3218	C₂	semidirect
15. C₃₁×#3216	C₂	semidirect
16. C₃₁×#3212	C₂	semidirect
17. C₃₁×#3115	C₂	semidirect
18. C₃₁×#3110	C₂	semidirect
19. C₃₁×#3107	C₂	semidirect
20. C₃₁×#3039	C₂	semidirect
21. C₃₁×#3036	C₂	semidirect
22. C₃₁×#3035	C₂	semidirect
23. C₃₁×#2989	C₂	semidirect
28. C₃₁×#556	C₂²	semidirect
42. C₃₁×#548	C₂²	semidirect
52. C₃₁×#533	C₂²	semidirect
54. C₃₁×#532	C₂²	semidirect
55. C₃₁×#532	C₂²	semidirect
56. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
69. C₃₁×#497	C₂²	semidirect
71. C₃₁×#491	C₂²	semidirect
72. C₃₁×#489	C₂²	semidirect
73. C₃₁×#488	C₂²	semidirect
74. C₃₁×#485	C₂²	semidirect
76. C₃₁×#482	C₂²	semidirect
77. C₃₁×#479	C₂²	semidirect
78. C₃₁×#478	C₂²	semidirect
79. C₃₁×#475	C₂²	semidirect
80. C₃₁×#475	C₂²	semidirect
81. C₃₁×#475	C₂²	semidirect
87. C₃₁×#468	C₂²	semidirect
88. C₃₁×#467	C₂²	semidirect
91. C₃₁×#464	C₂²	semidirect
96. C₃₁×#462	C₂²	semidirect
97. C₃₁×#462	C₂²	semidirect
98. C₃₁×#462	C₂²	semidirect
99. C₃₁×#462	C₂²	semidirect
100. C₃₁×#462	C₂²	semidirect
101. C₃₁×#462	C₂²	semidirect
107. C₃₁×#460	C₂²	semidirect
108. C₃₁×#460	C₂²	semidirect
114. C₃₁×#452	C₂²	semidirect
115. C₃₁×#451	C₂²	semidirect
120. C₃₁×#446	C₂²	semidirect
124. C₃₁×#440	C₂²	semidirect
125. C₄×Q₁₆×C₃₁	C₂²	semidirect
129. C₃₁×#435	C₂²	semidirect
131. C₃₁×#432	C₂²	semidirect
132. C₃₁×#431	C₂²	semidirect
134. C₃₁×#423	C₂²	semidirect
135. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
136. C₃₁×#419	C₂²	semidirect
138. C₃₁×#416	C₂²	semidirect
514. #61967	C₃₁	direct (N × H)
605. #3511	C₂×C₃₁	semidirect
606. #3475	C₂×C₃₁	semidirect
607. #3402	C₂×C₃₁	semidirect
608. #3376	C₂×C₃₁	semidirect
609. #3327	C₂×C₃₁	semidirect
610. #3321	C₂×C₃₁	semidirect
611. #3315	C₂×C₃₁	semidirect
612. #3275	C₂×C₃₁	semidirect
613. #3269	C₂×C₃₁	semidirect
614. #3267	C₂×C₃₁	semidirect
615. #3255	C₂×C₃₁	semidirect
616. #3251	C₂×C₃₁	semidirect
617. #3248	C₂×C₃₁	semidirect
618. #3218	C₂×C₃₁	semidirect
619. #3216	C₂×C₃₁	semidirect
620. #3212	C₂×C₃₁	semidirect
621. #3115	C₂×C₃₁	semidirect
622. #3110	C₂×C₃₁	semidirect
623. #3107	C₂×C₃₁	semidirect
624. #3039	C₂×C₃₁	semidirect
625. #3036	C₂×C₃₁	semidirect
626. #3035	C₂×C₃₁	semidirect
627. #2989	C₂×C₃₁	semidirect
674. #556	C₂²×C₃₁	semidirect
688. #548	C₂²×C₃₁	semidirect
698. #533	C₂²×C₃₁	semidirect
700. #532	C₂²×C₃₁	semidirect
701. #532	C₂²×C₃₁	semidirect
702. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
715. #497	C₂²×C₃₁	semidirect
717. #491	C₂²×C₃₁	semidirect
718. #489	C₂²×C₃₁	semidirect
719. #488	C₂²×C₃₁	semidirect
720. #485	C₂²×C₃₁	semidirect
722. #482	C₂²×C₃₁	semidirect
723. #479	C₂²×C₃₁	semidirect
724. #478	C₂²×C₃₁	semidirect
725. #475	C₂²×C₃₁	semidirect
726. #475	C₂²×C₃₁	semidirect
727. #475	C₂²×C₃₁	semidirect
733. #468	C₂²×C₃₁	semidirect
734. #467	C₂²×C₃₁	semidirect
737. #464	C₂²×C₃₁	semidirect
742. #462	C₂²×C₃₁	semidirect
743. #462	C₂²×C₃₁	semidirect
744. #462	C₂²×C₃₁	semidirect
745. #462	C₂²×C₃₁	semidirect
746. #462	C₂²×C₃₁	semidirect
747. #462	C₂²×C₃₁	semidirect
753. #460	C₂²×C₃₁	semidirect
754. #460	C₂²×C₃₁	semidirect
760. #452	C₂²×C₃₁	semidirect
761. #451	C₂²×C₃₁	semidirect
766. #446	C₂²×C₃₁	semidirect
770. #440	C₂²×C₃₁	semidirect
771. C₄×Q₁₆	C₂²×C₃₁	semidirect
775. #435	C₂²×C₃₁	semidirect
777. #432	C₂²×C₃₁	semidirect
778. #431	C₂²×C₃₁	semidirect
780. #423	C₂²×C₃₁	semidirect
781. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
782. #419	C₂²×C₃₁	semidirect
784. #416	C₂²×C₃₁	semidirect
1000. C₃₁	#61967	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×#3475	2
C₃₁×#3402	2
C₃₁×#3376	2
C₃₁×#3327	2
C₃₁×#3321	2
C₃₁×#3315	2
C₃₁×#3275	2
C₃₁×#3269	2
C₃₁×#3267	2
C₃₁×#3255	2
C₃₁×#3251	2
C₃₁×#3248	2
C₃₁×#3218	2
C₃₁×#3216	2
C₃₁×#3212	2
C₃₁×#3115	2
C₃₁×#3110	2
C₃₁×#3107	2
C₃₁×#3039	2
C₃₁×#3036	2
C₃₁×#3035	2
C₃₁×#2989	2
#61967	31

Subgroups — C31×#61967 #21518726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61967 #21518726