Subgroups — C₃₁×#61811 #21518570

Order 7936.

1788 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3353	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3353	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3347	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3346	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3342	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3334	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3332	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3324	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3319	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3314	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3304	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3239	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3226	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3203	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3198	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3098	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3096	C₂	1	2	yes	maximal, complemented
23	C₃₁×#2981	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#560	—	2	2	no	—
25	C₃₁×#556	C₂²	1	1	yes	characteristic
26	C₃₁×#556	C₂²	1	1	yes	characteristic
27	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#555	C₂²	1	2	yes	complemented
29	C₃₁×#554	C₂²	1	2	yes	complemented
30	C₃₁×#553	—	2	2	no	—
31	C₃₁×#553	C₂²	1	2	yes	—
32	C₃₁×#550	—	2	1	no	—
33	C₃₁×#550	C₂²	1	1	yes	characteristic
34	C₃₁×#548	—	2	1	no	—
35	C₃₁×#548	—	2	1	no	—
36	C₃₁×#547	C₂²	1	1	yes	characteristic
37	C₃₁×#547	C₂²	1	1	yes	characteristic
38	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#546	—	2	1	no	—
40	C₃₁×#546	C₂²	1	2	yes	—
41	D₄²×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#542	—	2	1	no	—
43	C₃₁×#542	—	2	2	no	—
44	C₃₁×#538	—	2	2	no	—
45	C₃₁×#537	C₂²	1	2	yes	—
46	C₃₁×#537	C₂²	1	2	yes	complemented
47	C₃₁×#535	—	2	1	no	—
48	C₃₁×#535	C₂²	1	2	yes	—
49	C₃₁×#533	—	2	1	no	—
50	C₃₁×#532	—	2	1	no	—
51	C₃₁×#532	C₂²	1	1	yes	characteristic
52	C₃₁×#532	C₂²	1	1	yes	characteristic
53	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#529	C₂²	1	1	yes	characteristic
55	C₃₁×#520	C₂²	1	2	yes	complemented
56	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#501	C₂²	1	2	yes	complemented
58	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#489	C₂²	1	2	yes	—
61	C₃₁×#486	C₂²	1	1	yes	characteristic
62	C₃₁×#486	C₂²	1	1	yes	characteristic
63	C₃₁×#485	C₂²	1	2	yes	complemented
64	C₃₁×#485	C₂²	1	2	yes	complemented
65	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#484	C₂²	1	2	yes	complemented
67	C₃₁×#484	C₂²	1	2	yes	complemented
68	C₃₁×#484	C₂²	1	2	yes	complemented
69	C₃₁×#482	C₂²	1	2	yes	—
70	C₃₁×#482	C₂²	1	1	yes	characteristic
71	C₃₁×#482	C₂²	1	2	yes	—
72	C₃₁×#482	C₂²	1	2	yes	complemented
73	C₃₁×#482	C₂²	1	2	yes	complemented
74	C₃₁×#482	C₂²	1	2	yes	complemented
75	C₃₁×#481	C₂²	1	2	yes	—
76	C₃₁×#481	C₂²	1	2	yes	complemented
77	C₃₁×#480	C₂²	1	2	yes	—
78	C₃₁×#480	C₂²	1	2	yes	—
79	C₃₁×#480	C₂²	1	2	yes	complemented
80	C₃₁×#480	C₂²	1	2	yes	complemented
81	C₃₁×#480	C₂²	1	2	yes	complemented
82	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#474	C₂²	1	1	yes	characteristic
88	C₃₁×#474	C₂²	1	1	yes	characteristic
89	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#474	C₂²	1	2	yes	complemented
91	C₃₁×#474	C₂²	1	2	yes	complemented
92	C₃₁×#469	C₂²	1	2	yes	complemented
93	C₃₁×#468	C₂²	1	2	yes	—
94	C₃₁×#468	C₂²	1	2	yes	—
95	C₃₁×#468	C₂²	1	2	yes	complemented
96	C₃₁×#467	C₂²	1	2	yes	complemented
97	C₃₁×#466	C₂²	1	2	yes	—
98	C₃₁×#466	C₂²	1	2	yes	—
99	C₃₁×#465	C₂²	1	2	yes	complemented
100	C₃₁×#464	C₂²	1	1	yes	characteristic
101	C₃₁×#463	C₂²	1	1	yes	characteristic
102	C₃₁×#460	C₂²	1	1	yes	characteristic
103	C₃₁×#459	C₂²	1	1	yes	characteristic
104	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
105	C₃₁×#452	C₂²	1	2	yes	complemented
106	C₃₁×#450	C₂²	1	2	yes	—
107	C₃₁×#449	C₂²	1	1	yes	characteristic
108	C₃₁×#449	C₂²	1	2	yes	complemented
109	C₃₁×#449	C₂²	1	2	yes	complemented
110	C₃₁×#447	C₂²	1	2	yes	—
111	C₃₁×#442	C₂²	1	2	yes	complemented
112	C₃₁×#440	C₂²	1	2	yes	complemented
113	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
117	C₃₁×#436	C₂²	1	1	yes	characteristic
118	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
119	C₃₁×#435	C₂²	1	2	yes	complemented
120	C₃₁×#435	C₂²	1	2	yes	complemented
121	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#428	C₂²	1	2	yes	complemented
126	C₃₁×#428	C₂²	1	2	yes	complemented
127	C₃₁×#427	C₂²	1	2	yes	complemented
128	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
129	C₃₁×#418	C₂²	1	2	yes	—
130	C₃₁×#417	C₂²	1	2	yes	complemented
131	C₃₁×#416	C₂²	1	2	yes	complemented
132	C₂×C₃₁×#102	C₂²	1	2	yes	—
133	C₃₁×#408	C₂²	1	2	yes	complemented
134	C₃₁×#408	C₂²	1	2	yes	complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	—	2	1	no	—
138	C₂×#41×C₃₁	—	2	1	no	—
139	C₂×#41×C₃₁	C₂³	1	2	yes	—
140	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×#41×C₃₁	C₂³	1	2	yes	—
142	C₂²×Q₈×C₃₁	—	2	1	no	—
143	C₂²×D₄×C₃₁	—	2	1	no	—
144	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×D₈×C₃₁	C₂³	1	2	yes	—
151	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
154	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
155	C₃₁×C₄⋊Q₈	—	2	1	no	—
156	C₃₁×C₄⋊Q₈	—	2	1	no	—
157	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
158	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×#127	—	2	1	no	—
163	C₃₁×#127	—	2	2	no	—
164	C₃₁×#127	D₄	1	1	yes	characteristic
165	C₃₁×#127	C₂³	1	1	yes	characteristic
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	1	no	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	C₂³	1	1	yes	characteristic
173	C₃₁×#124	—	2	2	no	—
174	C₃₁×#124	—	2	1	no	—
175	C₃₁×#124	—	2	1	no	—
176	C₃₁×#124	—	2	1	no	—
177	C₃₁×#124	—	2	2	no	—
178	C₃₁×#124	—	2	2	no	—
179	C₃₁×#124	—	2	1	no	—
180	C₃₁×#124	D₄	1	2	yes	—
181	C₃₁×#124	C₂³	1	1	yes	characteristic
182	C₃₁×#123	—	2	1	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	1	no	—
192	C₃₁×C₂²⋊Q₈	—	2	1	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
198	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	—	2	2	no	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	—	2	1	no	—
208	C₃₁×#121	—	2	1	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	D₄	1	1	yes	characteristic
212	C₃₁×#121	D₄	1	1	yes	characteristic
213	C₃₁×#121	D₄	1	2	yes	—
214	C₃₁×#121	C₂³	1	2	yes	—
215	C₃₁×#121	C₂³	1	1	yes	characteristic
216	C₃₁×#121	C₂³	1	2	yes	—
217	C₃₁×#121	C₂³	1	2	yes	—
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#121	C₂³	1	2	yes	—
220	C₃₁×#121	C₂³	1	2	yes	—
221	C₃₁×#120	—	2	2	no	—
222	C₃₁×#120	—	2	2	no	—
223	C₃₁×#120	—	2	2	no	—
224	C₃₁×#120	—	2	2	no	—
225	C₄×Q₈×C₃₁	—	2	2	no	—
226	C₄×Q₈×C₃₁	—	2	1	no	—
227	C₄×Q₈×C₃₁	—	2	1	no	—
228	C₄×Q₈×C₃₁	—	2	1	no	—
229	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₃₁	—	2	2	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	2	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	1	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	—	2	1	no	—
239	C₄×D₄×C₃₁	—	2	1	no	—
240	C₄×D₄×C₃₁	—	2	2	no	—
241	C₄×D₄×C₃₁	—	2	1	no	—
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	2	yes	—
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₃₁	C₂³	1	2	yes	—
249	C₃₁×#117	—	2	2	no	—
250	C₃₁×#117	—	2	1	no	—
251	C₃₁×#117	—	2	1	no	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₃₁×#117	C₂³	1	2	yes	—
255	C₃₁×#117	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
261	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
262	C₂×C₄²×C₃₁	—	2	1	no	—
263	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
264	C₃₁×#107	C₂³	1	1	yes	characteristic
265	C₃₁×#107	C₂³	1	2	yes	—
266	C₃₁×#107	C₂³	1	2	yes	—
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#107	C₂³	1	2	yes	—
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#107	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	1	yes	characteristic
277	C₃₁×#106	C₂³	1	2	yes	—
278	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×#103	C₂³	1	1	yes	characteristic
283	C₃₁×#103	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#102	C₂³	1	1	yes	characteristic
290	C₃₁×#102	C₂³	1	2	yes	—
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	C₂⁴×C₃₁	—	2	2	no	—
313	#41×C₃₁	—	4	2	no	—
314	#41×C₃₁	—	4	2	no	—
315	#41×C₃₁	—	4	1	no	—
316	#41×C₃₁	—	4	1	no	—
317	#41×C₃₁	—	4	2	no	—
318	#41×C₃₁	—	4	2	no	—
319	#41×C₃₁	—	8	2	no	—
320	#41×C₃₁	—	8	2	no	—
321	#41×C₃₁	—	8	2	no	—
322	#41×C₃₁	—	8	2	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	2	1	no	—
325	C₂×Q₈×C₃₁	—	2	1	no	—
326	C₂×Q₈×C₃₁	—	2	2	no	—
327	C₂×Q₈×C₃₁	—	8	2	no	—
328	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
329	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₃₁	—	2	1	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	—	2	1	no	—
341	C₂×D₄×C₃₁	—	2	1	no	—
342	C₂×D₄×C₃₁	—	2	2	no	—
343	C₂×D₄×C₃₁	—	4	2	no	—
344	C₂×D₄×C₃₁	—	4	2	no	—
345	C₂×D₄×C₃₁	—	8	2	no	—
346	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
348	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
350	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
354	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₃₁	—	2	2	no	—
356	C₂²×C₄×C₃₁	—	2	2	no	—
357	C₂²×C₄×C₃₁	—	2	2	no	—
358	C₂²×C₄×C₃₁	—	2	2	no	—
359	C₂²×C₄×C₃₁	—	2	1	no	—
360	C₂²×C₄×C₃₁	—	2	1	no	—
361	C₂²×C₄×C₃₁	—	2	1	no	—
362	C₂²×C₄×C₃₁	—	2	1	no	—
363	C₂²×C₄×C₃₁	—	2	2	no	—
364	C₂²×C₄×C₃₁	—	2	2	no	—
365	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
369	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
370	Q₁₆×C₃₁	—	4	1	no	—
371	SD₁₆×C₃₁	—	4	2	no	—
372	SD₁₆×C₃₁	—	4	1	no	—
373	SD₁₆×C₃₁	—	4	1	no	—
374	D₈×C₃₁	—	4	1	no	—
375	D₈×C₃₁	—	4	2	no	—
376	M₁₆×C₃₁	—	4	2	no	—
377	M₁₆×C₃₁	—	4	2	no	—
378	C₂×C₈×C₃₁	—	4	2	no	—
379	C₂×C₈×C₃₁	—	4	2	no	—
380	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
385	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
386	C₄⋊C₄×C₃₁	—	2	2	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
401	C₄⋊C₄×C₃₁	—	2	2	no	—
402	C₄⋊C₄×C₃₁	—	2	1	no	—
403	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	1	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	1	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	1	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	no	—
426	C₂²⋊C₄×C₃₁	—	2	1	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	1	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
438	C₄²×C₃₁	—	2	1	no	—
439	C₄²×C₃₁	—	2	1	no	—
440	C₄²×C₃₁	—	2	1	no	—
441	C₄²×C₃₁	—	2	2	no	—
442	C₄²×C₃₁	—	2	2	no	—
443	C₄²×C₃₁	—	2	1	no	—
444	C₄²×C₃₁	—	2	2	no	—
445	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
448	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
449	#61811	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
450	C₂³×C₃₁	—	2	1	no	—
451	C₂³×C₃₁	—	2	1	no	—
452	C₂³×C₃₁	—	2	2	no	—
453	C₂³×C₃₁	—	8	2	no	—
454	C₂³×C₃₁	—	8	2	no	—
455	C₂³×C₃₁	—	8	2	no	—
456	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
457	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
458	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
459	Q₈×C₃₁	—	2	1	no	—
460	Q₈×C₃₁	—	2	1	no	—
461	Q₈×C₃₁	—	2	1	no	—
462	Q₈×C₃₁	—	2	1	no	—
463	Q₈×C₃₁	—	4	2	no	—
464	Q₈×C₃₁	—	4	2	no	—
465	Q₈×C₃₁	—	4	2	no	—
466	Q₈×C₃₁	—	4	2	no	—
467	Q₈×C₃₁	—	8	2	no	—
468	D₄×C₃₁	—	2	2	no	—
469	D₄×C₃₁	—	2	2	no	—
470	D₄×C₃₁	—	2	1	no	—
471	D₄×C₃₁	—	2	1	no	—
472	D₄×C₃₁	—	2	1	no	—
473	D₄×C₃₁	—	2	2	no	—
474	D₄×C₃₁	—	2	1	no	—
475	D₄×C₃₁	—	2	2	no	—
476	D₄×C₃₁	—	4	2	no	—
477	D₄×C₃₁	—	4	2	no	—
478	D₄×C₃₁	—	4	2	no	—
479	D₄×C₃₁	—	4	2	no	—
480	D₄×C₃₁	—	4	2	no	—
481	D₄×C₃₁	—	4	2	no	—
482	D₄×C₃₁	—	8	1	no	—
483	D₄×C₃₁	—	8	2	no	—
484	D₄×C₃₁	—	8	1	no	—
485	D₄×C₃₁	—	8	2	no	—
486	D₄×C₃₁	—	8	2	no	—
487	D₄×C₃₁	—	8	2	no	—
488	D₄×C₃₁	—	8	2	no	—
489	D₄×C₃₁	—	8	2	no	—
490	D₄×C₃₁	—	8	2	no	—
491	D₄×C₃₁	—	8	2	no	—
492	C₂×C₄×C₃₁	—	2	2	no	—
493	C₂×C₄×C₃₁	—	2	2	no	—
494	C₂×C₄×C₃₁	—	2	2	no	—
495	C₂×C₄×C₃₁	—	2	2	no	—
496	C₂×C₄×C₃₁	—	2	2	no	—
497	C₂×C₄×C₃₁	—	2	1	no	—
498	C₂×C₄×C₃₁	—	2	1	no	—
499	C₂×C₄×C₃₁	—	2	1	no	—
500	C₂×C₄×C₃₁	—	2	1	no	—
501	C₂×C₄×C₃₁	—	2	1	no	—
502	C₂×C₄×C₃₁	—	2	1	no	—
503	C₂×C₄×C₃₁	—	2	1	no	—
504	C₂×C₄×C₃₁	—	2	2	no	—
505	C₂×C₄×C₃₁	—	2	2	no	—
506	C₂×C₄×C₃₁	—	2	2	no	—
507	C₂×C₄×C₃₁	—	2	1	no	—
508	C₂×C₄×C₃₁	—	4	1	no	—
509	C₂×C₄×C₃₁	—	4	2	no	—
510	C₂×C₄×C₃₁	—	4	2	no	—
511	C₂×C₄×C₃₁	—	4	2	no	—
512	C₂×C₄×C₃₁	—	4	2	no	—
513	C₂×C₄×C₃₁	—	8	2	no	—
514	C₂×C₄×C₃₁	—	8	2	no	—
515	C₂×C₄×C₃₁	—	8	2	no	—
516	C₂×C₄×C₃₁	—	8	2	no	—
517	C₂×C₄×C₃₁	—	8	2	no	—
518	C₂×C₄×C₃₁	—	8	2	no	—
519	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
520	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
527	C₈×C₃₁	—	2	1	no	—
528	C₈×C₃₁	—	2	1	no	—
529	C₈×C₃₁	—	2	2	no	—
530	C₈×C₃₁	—	2	2	no	—
531	C₈×C₃₁	—	2	1	no	—
532	C₈×C₃₁	—	2	1	no	—
533	#3546	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3353	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3353	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3347	C₂×C₃₁	1	2	yes	complemented
538	#3346	C₂×C₃₁	1	2	yes	complemented
539	#3342	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3334	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3332	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3324	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3319	C₂×C₃₁	1	2	yes	complemented
544	#3314	C₂×C₃₁	1	2	yes	complemented
545	#3304	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3294	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3239	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3226	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3203	C₂×C₃₁	1	2	yes	complemented
550	#3198	C₂×C₃₁	1	2	yes	complemented
551	#3115	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
553	#3098	C₂×C₃₁	1	2	yes	complemented
554	#3096	C₂×C₃₁	1	2	yes	complemented
555	#2981	C₂×C₃₁	1	1	yes	characteristic, complemented
556	C₂²×C₃₁	—	2	1	no	—
557	C₂²×C₃₁	—	2	2	no	—
558	C₂²×C₃₁	—	2	2	no	—
559	C₂²×C₃₁	—	2	1	no	—
560	C₂²×C₃₁	—	2	2	no	—
561	C₂²×C₃₁	—	2	2	no	—
562	C₂²×C₃₁	—	2	1	no	—
563	C₂²×C₃₁	—	2	2	no	—
564	C₂²×C₃₁	—	2	2	no	—
565	C₂²×C₃₁	—	4	1	no	—
566	C₂²×C₃₁	—	4	2	no	—
567	C₂²×C₃₁	—	4	1	no	—
568	C₂²×C₃₁	—	4	1	no	—
569	C₂²×C₃₁	—	4	2	no	—
570	C₂²×C₃₁	—	4	1	no	—
571	C₂²×C₃₁	—	4	1	no	—
572	C₂²×C₃₁	—	4	1	no	—
573	C₂²×C₃₁	—	4	2	no	—
574	C₂²×C₃₁	—	16	4	no	—
575	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
576	C₄×C₃₁	—	2	1	no	—
577	C₄×C₃₁	—	2	1	no	—
578	C₄×C₃₁	—	2	1	no	—
579	C₄×C₃₁	—	2	2	no	—
580	C₄×C₃₁	—	2	2	no	—
581	C₄×C₃₁	—	2	1	no	—
582	C₄×C₃₁	—	4	1	no	—
583	C₄×C₃₁	—	4	1	no	—
584	C₄×C₃₁	—	4	1	no	—
585	C₄×C₃₁	—	4	1	no	—
586	C₄×C₃₁	—	4	1	no	—
587	C₄×C₃₁	—	4	1	no	—
588	C₄×C₃₁	—	4	2	no	—
589	C₄×C₃₁	—	4	2	no	—
590	C₄×C₃₁	—	4	2	no	—
591	C₄×C₃₁	#576	1	2	yes	—
592	C₄×C₃₁	#585	1	1	yes	characteristic
593	C₄×C₃₁	#585	1	1	yes	characteristic
594	#560	—	2	2	no	—
595	#556	C₂²×C₃₁	1	1	yes	characteristic
596	#556	C₂²×C₃₁	1	1	yes	characteristic
597	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
598	#555	C₂²×C₃₁	1	2	yes	complemented
599	#554	C₂²×C₃₁	1	2	yes	complemented
600	#553	—	2	2	no	—
601	#553	C₂²×C₃₁	1	2	yes	—
602	#550	—	2	1	no	—
603	#550	C₂²×C₃₁	1	1	yes	characteristic
604	#548	—	2	1	no	—
605	#548	—	2	1	no	—
606	#547	C₂²×C₃₁	1	1	yes	characteristic
607	#547	C₂²×C₃₁	1	1	yes	characteristic
608	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
609	#546	—	2	1	no	—
610	#546	C₂²×C₃₁	1	2	yes	—
611	D₄²	C₂²×C₃₁	1	1	yes	characteristic
612	#542	—	2	1	no	—
613	#542	—	2	2	no	—
614	#538	—	2	2	no	—
615	#537	C₂²×C₃₁	1	2	yes	—
616	#537	C₂²×C₃₁	1	2	yes	complemented
617	#535	—	2	1	no	—
618	#535	C₂²×C₃₁	1	2	yes	—
619	#533	—	2	1	no	—
620	#532	—	2	1	no	—
621	#532	C₂²×C₃₁	1	1	yes	characteristic
622	#532	C₂²×C₃₁	1	1	yes	characteristic
623	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
624	#529	C₂²×C₃₁	1	1	yes	characteristic
625	#520	C₂²×C₃₁	1	2	yes	complemented
626	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
627	#501	C₂²×C₃₁	1	2	yes	complemented
628	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
629	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
630	#489	C₂²×C₃₁	1	2	yes	—
631	#486	C₂²×C₃₁	1	1	yes	characteristic
632	#486	C₂²×C₃₁	1	1	yes	characteristic
633	#485	C₂²×C₃₁	1	2	yes	complemented
634	#485	C₂²×C₃₁	1	2	yes	complemented
635	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
636	#484	C₂²×C₃₁	1	2	yes	complemented
637	#484	C₂²×C₃₁	1	2	yes	complemented
638	#484	C₂²×C₃₁	1	2	yes	complemented
639	#482	C₂²×C₃₁	1	2	yes	—
640	#482	C₂²×C₃₁	1	1	yes	characteristic
641	#482	C₂²×C₃₁	1	2	yes	—
642	#482	C₂²×C₃₁	1	2	yes	complemented
643	#482	C₂²×C₃₁	1	2	yes	complemented
644	#482	C₂²×C₃₁	1	2	yes	complemented
645	#481	C₂²×C₃₁	1	2	yes	—
646	#481	C₂²×C₃₁	1	2	yes	complemented
647	#480	C₂²×C₃₁	1	2	yes	—
648	#480	C₂²×C₃₁	1	2	yes	—
649	#480	C₂²×C₃₁	1	2	yes	complemented
650	#480	C₂²×C₃₁	1	2	yes	complemented
651	#480	C₂²×C₃₁	1	2	yes	complemented
652	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
653	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
657	#474	C₂²×C₃₁	1	1	yes	characteristic
658	#474	C₂²×C₃₁	1	1	yes	characteristic
659	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
660	#474	C₂²×C₃₁	1	2	yes	complemented
661	#474	C₂²×C₃₁	1	2	yes	complemented
662	#469	C₂²×C₃₁	1	2	yes	complemented
663	#468	C₂²×C₃₁	1	2	yes	—
664	#468	C₂²×C₃₁	1	2	yes	—
665	#468	C₂²×C₃₁	1	2	yes	complemented
666	#467	C₂²×C₃₁	1	2	yes	complemented
667	#466	C₂²×C₃₁	1	2	yes	—
668	#466	C₂²×C₃₁	1	2	yes	—
669	#465	C₂²×C₃₁	1	2	yes	complemented
670	#464	C₂²×C₃₁	1	1	yes	characteristic
671	#463	C₂²×C₃₁	1	1	yes	characteristic
672	#460	C₂²×C₃₁	1	1	yes	characteristic
673	#459	C₂²×C₃₁	1	1	yes	characteristic
674	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
675	#452	C₂²×C₃₁	1	2	yes	complemented
676	#450	C₂²×C₃₁	1	2	yes	—
677	#449	C₂²×C₃₁	1	1	yes	characteristic
678	#449	C₂²×C₃₁	1	2	yes	complemented
679	#449	C₂²×C₃₁	1	2	yes	complemented
680	#447	C₂²×C₃₁	1	2	yes	—
681	#442	C₂²×C₃₁	1	2	yes	complemented
682	#440	C₂²×C₃₁	1	2	yes	complemented
683	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
685	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
686	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
687	#436	C₂²×C₃₁	1	1	yes	characteristic
688	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
689	#435	C₂²×C₃₁	1	2	yes	complemented
690	#435	C₂²×C₃₁	1	2	yes	complemented
691	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
692	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
693	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
694	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
695	#428	C₂²×C₃₁	1	2	yes	complemented
696	#428	C₂²×C₃₁	1	2	yes	complemented
697	#427	C₂²×C₃₁	1	2	yes	complemented
698	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
699	#418	C₂²×C₃₁	1	2	yes	—
700	#417	C₂²×C₃₁	1	2	yes	complemented
701	#416	C₂²×C₃₁	1	2	yes	complemented
702	C₂×#102	C₂²×C₃₁	1	2	yes	—
703	#408	C₂²×C₃₁	1	2	yes	complemented
704	#408	C₂²×C₃₁	1	2	yes	complemented
705	C₂×C₃₁	—	4	1	no	—
706	C₂×C₃₁	—	4	2	no	—
707	C₂×C₃₁	—	4	2	no	—
708	C₂×C₃₁	—	8	1	no	—
709	C₂×C₃₁	—	8	2	no	—
710	C₂×C₃₁	—	8	1	no	—
711	C₂×C₃₁	#3485	1	1	yes	characteristic
712	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
713	C₂×C₃₁	#3586	1	1	yes	characteristic
714	C₂×#41	—	2	1	no	—
715	C₂×#41	—	2	1	no	—
716	C₂×#41	—	2	1	no	—
717	C₂×#41	—	2	1	no	—
718	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
719	C₂×#41	C₂³×C₃₁	1	2	yes	—
720	C₂×#41	C₂³×C₃₁	1	2	yes	—
721	C₂²×Q₈	—	2	1	no	—
722	C₂²×D₄	—	2	1	no	—
723	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
724	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
725	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
727	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
728	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
729	C₂×D₈	C₂³×C₃₁	1	2	yes	—
730	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
731	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
732	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
733	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
734	C₄⋊Q₈	—	2	1	no	—
735	C₄⋊Q₈	—	2	1	no	—
736	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
738	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
739	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
740	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
741	#127	—	2	1	no	—
742	#127	—	2	2	no	—
743	#127	D₄×C₃₁	1	1	yes	characteristic
744	#127	C₂³×C₃₁	1	1	yes	characteristic
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#126	—	2	2	no	—
749	#126	—	2	1	no	—
750	#125	—	2	2	no	—
751	#125	C₂³×C₃₁	1	1	yes	characteristic
752	#124	—	2	2	no	—
753	#124	—	2	1	no	—
754	#124	—	2	1	no	—
755	#124	—	2	1	no	—
756	#124	—	2	2	no	—
757	#124	—	2	2	no	—
758	#124	—	2	1	no	—
759	#124	D₄×C₃₁	1	2	yes	—
760	#124	C₂³×C₃₁	1	1	yes	characteristic
761	#123	—	2	1	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	1	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
775	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
777	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
778	#121	—	2	2	no	—
779	#121	—	2	2	no	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	—	2	1	no	—
787	#121	—	2	1	no	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#121	D₄×C₃₁	1	1	yes	characteristic
791	#121	D₄×C₃₁	1	1	yes	characteristic
792	#121	D₄×C₃₁	1	2	yes	—
793	#121	C₂³×C₃₁	1	1	yes	characteristic
794	#121	C₂³×C₃₁	1	2	yes	—
795	#121	C₂³×C₃₁	1	2	yes	—
796	#121	C₂³×C₃₁	1	2	yes	—
797	#121	C₂³×C₃₁	1	2	yes	—
798	#121	C₂³×C₃₁	1	2	yes	—
799	#121	C₂³×C₃₁	1	2	yes	—
800	#120	—	2	2	no	—
801	#120	—	2	2	no	—
802	#120	—	2	2	no	—
803	#120	—	2	2	no	—
804	C₄×Q₈	—	2	2	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	—	2	1	no	—
808	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₃₁	1	2	yes	—
825	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₃₁	1	2	yes	—
827	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
828	#117	—	2	2	no	—
829	#117	—	2	1	no	—
830	#117	—	2	1	no	—
831	#117	C₂³×C₃₁	1	1	yes	characteristic
832	#117	C₂³×C₃₁	1	2	yes	—
833	#117	C₂³×C₃₁	1	2	yes	—
834	#117	C₂³×C₃₁	1	2	yes	—
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
837	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
838	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
839	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
840	C₂×C₂²⋊C₄	—	2	2	no	—
841	C₂×C₄²	—	2	1	no	—
842	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
843	#107	C₂³×C₃₁	1	1	yes	characteristic
844	#107	C₂³×C₃₁	1	2	yes	—
845	#107	C₂³×C₃₁	1	2	yes	—
846	#107	C₂³×C₃₁	1	2	yes	—
847	#107	C₂³×C₃₁	1	1	yes	characteristic
848	#107	C₂³×C₃₁	1	2	yes	—
849	#107	C₂³×C₃₁	1	2	yes	—
850	#107	C₂³×C₃₁	1	2	yes	—
851	#107	C₂³×C₃₁	1	2	yes	—
852	#106	C₂³×C₃₁	1	2	yes	—
853	#106	C₂³×C₃₁	1	2	yes	—
854	#106	C₂³×C₃₁	1	1	yes	characteristic
855	#106	C₂³×C₃₁	1	1	yes	characteristic
856	#106	C₂³×C₃₁	1	2	yes	—
857	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
861	#103	C₂³×C₃₁	1	1	yes	characteristic
862	#103	C₂³×C₃₁	1	2	yes	—
863	#103	C₂³×C₃₁	1	1	yes	characteristic
864	#103	C₂³×C₃₁	1	2	yes	—
865	#103	C₂³×C₃₁	1	1	yes	characteristic
866	#103	C₂³×C₃₁	1	1	yes	characteristic
867	#103	C₂³×C₃₁	1	2	yes	—
868	#102	C₂³×C₃₁	1	1	yes	characteristic
869	#102	C₂³×C₃₁	1	2	yes	—
870	#102	C₂³×C₃₁	1	2	yes	—
871	#102	C₂³×C₃₁	1	2	yes	—
872	#102	C₂³×C₃₁	1	2	yes	—
873	#102	C₂³×C₃₁	1	2	yes	—
874	#102	C₂³×C₃₁	1	2	yes	—
875	#102	C₂³×C₃₁	1	1	yes	characteristic
876	#102	C₂³×C₃₁	1	2	yes	—
877	#102	C₂³×C₃₁	1	2	yes	—
878	#102	C₂³×C₃₁	1	1	yes	characteristic
879	#102	C₂³×C₃₁	1	1	yes	characteristic
880	#102	C₂³×C₃₁	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
882	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
883	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
888	#97	C₂³×C₃₁	1	2	yes	—
889	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
890	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
891	C₃₁	#61811	1	1	yes	characteristic, direct product factor, Sylow
892	C₂⁴	—	2	2	no	—
893	#41	—	4	2	no	—
894	#41	—	4	2	no	—
895	#41	—	4	1	no	—
896	#41	—	4	1	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	#41	—	8	2	no	—
900	#41	—	8	2	no	—
901	#41	—	8	2	no	—
902	#41	—	8	2	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	1	no	—
906	C₂×Q₈	—	2	2	no	—
907	C₂×Q₈	—	8	2	no	—
908	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
909	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
910	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	4	2	no	—
924	C₂×D₄	—	4	2	no	—
925	C₂×D₄	—	8	2	no	—
926	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
927	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
928	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
929	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
930	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
931	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
932	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
933	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
934	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
946	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
947	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
949	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
950	Q₁₆	—	4	1	no	—
951	SD₁₆	—	4	2	no	—
952	SD₁₆	—	4	1	no	—
953	SD₁₆	—	4	1	no	—
954	D₈	—	4	1	no	—
955	D₈	—	4	2	no	—
956	M₁₆	—	4	2	no	—
957	M₁₆	—	4	2	no	—
958	C₂×C₈	—	4	2	no	—
959	C₂×C₈	—	4	2	no	—
960	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
965	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
984	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
985	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
986	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
987	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
988	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
989	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
990	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
991	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
992	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1015	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1016	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1026	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1027	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1028	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	2	no	—
1032	C₂³	—	8	2	no	—
1033	C₂³	—	8	2	no	—
1034	C₂³	—	8	2	no	—
1035	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1036	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1037	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1038	Q₈	—	2	1	no	—
1039	Q₈	—	2	1	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	4	2	no	—
1043	Q₈	—	4	2	no	—
1044	Q₈	—	4	2	no	—
1045	Q₈	—	4	2	no	—
1046	Q₈	—	8	2	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	2	2	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	2	2	no	—
1053	D₄	—	2	1	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	4	2	no	—
1059	D₄	—	4	2	no	—
1060	D₄	—	4	2	no	—
1061	D₄	—	8	1	no	—
1062	D₄	—	8	2	no	—
1063	D₄	—	8	1	no	—
1064	D₄	—	8	2	no	—
1065	D₄	—	8	2	no	—
1066	D₄	—	8	2	no	—
1067	D₄	—	8	2	no	—
1068	D₄	—	8	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1099	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1102	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1103	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1104	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1105	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1106	C₈	—	2	1	no	—
1107	C₈	—	2	1	no	—
1108	C₈	—	2	2	no	—
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	2	2	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	16	4	no	—
1131	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	2	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	2	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	1	no	—
1147	C₄	C₃₁×#576	1	2	yes	—
1148	C₄	C₃₁×#585	1	1	yes	characteristic
1149	C₄	C₃₁×#585	1	1	yes	characteristic
1150	C₂	—	4	2	no	—
1151	C₂	—	4	1	no	—
1152	C₂	—	4	2	no	—
1153	C₂	—	8	1	no	—
1154	C₂	—	8	2	no	—
1155	C₂	—	8	1	no	—
1156	C₂	C₃₁×#3485	1	1	yes	characteristic
1157	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1158	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 ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3546	C₂	semidirect
2. C₃₁×#3511	C₂	semidirect
3. C₃₁×#3353	C₂	semidirect
4. C₃₁×#3353	C₂	semidirect
5. C₃₁×#3347	C₂	semidirect
6. C₃₁×#3346	C₂	semidirect
7. C₃₁×#3342	C₂	semidirect
8. C₃₁×#3334	C₂	semidirect
9. C₃₁×#3332	C₂	semidirect
10. C₃₁×#3324	C₂	semidirect
11. C₃₁×#3319	C₂	semidirect
12. C₃₁×#3314	C₂	semidirect
13. C₃₁×#3304	C₂	semidirect
14. C₃₁×#3294	C₂	semidirect
15. C₃₁×#3239	C₂	semidirect
16. C₃₁×#3226	C₂	semidirect
17. C₃₁×#3203	C₂	semidirect
18. C₃₁×#3198	C₂	semidirect
19. C₃₁×#3115	C₂	semidirect
20. C₃₁×#3102	C₂	semidirect
21. C₃₁×#3098	C₂	semidirect
22. C₃₁×#3096	C₂	semidirect
23. C₃₁×#2981	C₂	semidirect
27. C₃₁×#556	C₂²	semidirect
28. C₃₁×#555	C₂²	semidirect
29. C₃₁×#554	C₂²	semidirect
38. C₃₁×#547	C₂²	semidirect
46. C₃₁×#537	C₂²	semidirect
53. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
55. C₃₁×#520	C₂²	semidirect
56. C₄×#41×C₃₁	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#500	C₂²	semidirect
59. C₃₁×#500	C₂²	semidirect
63. C₃₁×#485	C₂²	semidirect
64. C₃₁×#485	C₂²	semidirect
65. C₃₁×#485	C₂²	semidirect
66. C₃₁×#484	C₂²	semidirect
67. C₃₁×#484	C₂²	semidirect
68. C₃₁×#484	C₂²	semidirect
72. C₃₁×#482	C₂²	semidirect
73. C₃₁×#482	C₂²	semidirect
74. C₃₁×#482	C₂²	semidirect
76. C₃₁×#481	C₂²	semidirect
79. C₃₁×#480	C₂²	semidirect
80. C₃₁×#480	C₂²	semidirect
81. C₃₁×#480	C₂²	semidirect
82. C₃₁×#479	C₂²	semidirect
83. C₃₁×#478	C₂²	semidirect
84. C₃₁×#475	C₂²	semidirect
85. C₃₁×#475	C₂²	semidirect
86. C₃₁×#475	C₂²	semidirect
89. C₃₁×#474	C₂²	semidirect
90. C₃₁×#474	C₂²	semidirect
91. C₃₁×#474	C₂²	semidirect
92. C₃₁×#469	C₂²	semidirect
95. C₃₁×#468	C₂²	semidirect
96. C₃₁×#467	C₂²	semidirect
99. C₃₁×#465	C₂²	semidirect
104. C₃₁×#452	C₂²	semidirect
105. C₃₁×#452	C₂²	semidirect
108. C₃₁×#449	C₂²	semidirect
109. C₃₁×#449	C₂²	semidirect
111. C₃₁×#442	C₂²	semidirect
112. C₃₁×#440	C₂²	semidirect
113. C₄×Q₁₆×C₃₁	C₂²	semidirect
115. C₄×SD₁₆×C₃₁	C₂²	semidirect
118. C₃₁×#436	C₂²	semidirect
119. C₃₁×#435	C₂²	semidirect
120. C₃₁×#435	C₂²	semidirect
122. C₈×D₄×C₃₁	C₂²	semidirect
123. C₃₁×#432	C₂²	semidirect
124. C₃₁×#431	C₂²	semidirect
125. C₃₁×#428	C₂²	semidirect
126. C₃₁×#428	C₂²	semidirect
127. C₃₁×#427	C₂²	semidirect
128. C₂×C₃₁×#107	C₂²	semidirect
130. C₃₁×#417	C₂²	semidirect
131. C₃₁×#416	C₂²	semidirect
133. C₃₁×#408	C₂²	semidirect
134. C₃₁×#408	C₂²	semidirect
449. #61811	C₃₁	direct (N × H)
533. #3546	C₂×C₃₁	semidirect
534. #3511	C₂×C₃₁	semidirect
535. #3353	C₂×C₃₁	semidirect
536. #3353	C₂×C₃₁	semidirect
537. #3347	C₂×C₃₁	semidirect
538. #3346	C₂×C₃₁	semidirect
539. #3342	C₂×C₃₁	semidirect
540. #3334	C₂×C₃₁	semidirect
541. #3332	C₂×C₃₁	semidirect
542. #3324	C₂×C₃₁	semidirect
543. #3319	C₂×C₃₁	semidirect
544. #3314	C₂×C₃₁	semidirect
545. #3304	C₂×C₃₁	semidirect
546. #3294	C₂×C₃₁	semidirect
547. #3239	C₂×C₃₁	semidirect
548. #3226	C₂×C₃₁	semidirect
549. #3203	C₂×C₃₁	semidirect
550. #3198	C₂×C₃₁	semidirect
551. #3115	C₂×C₃₁	semidirect
552. #3102	C₂×C₃₁	semidirect
553. #3098	C₂×C₃₁	semidirect
554. #3096	C₂×C₃₁	semidirect
555. #2981	C₂×C₃₁	semidirect
597. #556	C₂²×C₃₁	semidirect
598. #555	C₂²×C₃₁	semidirect
599. #554	C₂²×C₃₁	semidirect
608. #547	C₂²×C₃₁	semidirect
616. #537	C₂²×C₃₁	semidirect
623. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
625. #520	C₂²×C₃₁	semidirect
626. C₄×#41	C₂²×C₃₁	semidirect
627. #501	C₂²×C₃₁	semidirect
628. #500	C₂²×C₃₁	semidirect
629. #500	C₂²×C₃₁	semidirect
633. #485	C₂²×C₃₁	semidirect
634. #485	C₂²×C₃₁	semidirect
635. #485	C₂²×C₃₁	semidirect
636. #484	C₂²×C₃₁	semidirect
637. #484	C₂²×C₃₁	semidirect
638. #484	C₂²×C₃₁	semidirect
642. #482	C₂²×C₃₁	semidirect
643. #482	C₂²×C₃₁	semidirect
644. #482	C₂²×C₃₁	semidirect
646. #481	C₂²×C₃₁	semidirect
649. #480	C₂²×C₃₁	semidirect
650. #480	C₂²×C₃₁	semidirect
651. #480	C₂²×C₃₁	semidirect
652. #479	C₂²×C₃₁	semidirect
653. #478	C₂²×C₃₁	semidirect
654. #475	C₂²×C₃₁	semidirect
655. #475	C₂²×C₃₁	semidirect
656. #475	C₂²×C₃₁	semidirect
659. #474	C₂²×C₃₁	semidirect
660. #474	C₂²×C₃₁	semidirect
661. #474	C₂²×C₃₁	semidirect
662. #469	C₂²×C₃₁	semidirect
665. #468	C₂²×C₃₁	semidirect
666. #467	C₂²×C₃₁	semidirect
669. #465	C₂²×C₃₁	semidirect
674. #452	C₂²×C₃₁	semidirect
675. #452	C₂²×C₃₁	semidirect
678. #449	C₂²×C₃₁	semidirect
679. #449	C₂²×C₃₁	semidirect
681. #442	C₂²×C₃₁	semidirect
682. #440	C₂²×C₃₁	semidirect
683. C₄×Q₁₆	C₂²×C₃₁	semidirect
685. C₄×SD₁₆	C₂²×C₃₁	semidirect
688. #436	C₂²×C₃₁	semidirect
689. #435	C₂²×C₃₁	semidirect
690. #435	C₂²×C₃₁	semidirect
692. C₈×D₄	C₂²×C₃₁	semidirect
693. #432	C₂²×C₃₁	semidirect
694. #431	C₂²×C₃₁	semidirect
695. #428	C₂²×C₃₁	semidirect
696. #428	C₂²×C₃₁	semidirect
697. #427	C₂²×C₃₁	semidirect
698. C₂×#107	C₂²×C₃₁	semidirect
700. #417	C₂²×C₃₁	semidirect
701. #416	C₂²×C₃₁	semidirect
703. #408	C₂²×C₃₁	semidirect
704. #408	C₂²×C₃₁	semidirect
891. C₃₁	#61811	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×#3546	2
C₃₁×#3511	2
C₃₁×#3353	2
C₃₁×#3347	2
C₃₁×#3346	2
C₃₁×#3342	2
C₃₁×#3334	2
C₃₁×#3332	2
C₃₁×#3324	2
C₃₁×#3319	2
C₃₁×#3314	2
C₃₁×#3304	2
C₃₁×#3294	2
C₃₁×#3239	2
C₃₁×#3226	2
C₃₁×#3203	2
C₃₁×#3198	2
C₃₁×#3115	2
C₃₁×#3102	2
C₃₁×#3098	2
C₃₁×#3096	2
C₃₁×#2981	2
#61811	31

Subgroups — C31×#61811 #21518570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61811 #21518570