Subgroups — C₃₁×#61650 #21518409

Order 7936.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3333	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3332	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3316	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3308	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3277	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3275	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3271	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3268	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3198	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3196	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3194	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3121	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3013	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3007	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3006	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2978	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
21	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
23	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
24	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
26	C₃₁×#562	—	2	2	no	—
27	C₃₁×#554	C₂²	1	2	yes	complemented
28	C₃₁×#550	—	2	1	no	—
29	C₃₁×#550	—	2	1	no	—
30	C₃₁×#550	C₂²	1	2	yes	—
31	C₃₁×#550	C₂²	1	2	yes	complemented
32	C₃₁×#548	—	2	1	no	—
33	C₃₁×#548	—	2	1	no	—
34	C₃₁×#548	C₂²	1	2	yes	—
35	C₃₁×#548	C₂²	1	2	yes	complemented
36	C₃₁×#548	C₂²	1	2	yes	complemented
37	C₃₁×#547	C₂²	1	2	yes	complemented
38	C₃₁×#546	—	2	2	no	—
39	C₃₁×#546	C₂²	1	2	yes	complemented
40	C₃₁×#543	—	2	1	no	—
41	C₃₁×#542	C₂²	1	2	yes	—
42	C₃₁×#539	—	2	1	no	—
43	C₃₁×#538	—	2	1	no	—
44	C₃₁×#537	—	2	1	no	—
45	C₃₁×#537	C₂²	1	2	yes	—
46	C₃₁×#535	—	2	2	no	—
47	C₃₁×#535	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#535	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#525	—	2	2	no	—
50	C₃₁×#525	C₂²	1	1	yes	characteristic
51	C₃₁×#525	C₂²	1	1	yes	characteristic
52	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
53	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
54	C₃₁×#519	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#496	C₂²	1	2	yes	complemented
56	C₃₁×#495	C₂²	1	2	yes	complemented
57	C₃₁×#489	C₂²	1	2	yes	complemented
58	C₃₁×#486	C₂²	1	2	yes	complemented
59	C₃₁×#485	C₂²	1	2	yes	complemented
60	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#482	C₂²	1	2	yes	—
63	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#481	C₂²	1	2	yes	complemented
65	C₃₁×#480	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#480	C₂²	1	2	yes	complemented
67	C₃₁×#477	C₂²	1	2	yes	complemented
68	C₃₁×#475	C₂²	1	2	yes	complemented
69	C₃₁×#470	C₂²	1	2	yes	complemented
70	C₃₁×#469	C₂²	1	2	yes	complemented
71	C₃₁×#469	C₂²	1	2	yes	complemented
72	C₃₁×#468	C₂²	1	2	yes	complemented
73	C₃₁×#468	C₂²	1	2	yes	complemented
74	C₃₁×#468	C₂²	1	2	yes	complemented
75	C₃₁×#466	C₂²	1	2	yes	complemented
76	C₃₁×#465	C₂²	1	2	yes	complemented
77	C₃₁×#464	C₂²	1	2	yes	complemented
78	C₃₁×#464	C₂²	1	2	yes	complemented
79	C₃₁×#464	C₂²	1	2	yes	complemented
80	C₃₁×#463	C₂²	1	2	yes	complemented
81	C₃₁×#460	C₂²	1	2	yes	complemented
82	C₃₁×#459	C₂²	1	2	yes	complemented
83	C₃₁×#452	C₂²	1	2	yes	—
84	C₃₁×#452	C₂²	1	2	yes	—
85	C₃₁×#452	C₂²	1	2	yes	complemented
86	C₃₁×#452	C₂²	1	2	yes	complemented
87	C₃₁×#451	C₂²	1	2	yes	complemented
88	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#451	C₂²	1	2	yes	complemented
90	C₃₁×#450	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#450	C₂²	1	2	yes	complemented
92	C₃₁×#449	C₂²	1	2	yes	—
93	C₃₁×#449	C₂²	1	2	yes	—
94	C₃₁×#449	C₂²	1	2	yes	—
95	C₃₁×#449	C₂²	1	2	yes	complemented
96	C₃₁×#449	C₂²	1	2	yes	complemented
97	C₃₁×#449	C₂²	1	2	yes	complemented
98	C₃₁×#448	C₂²	1	2	yes	—
99	C₃₁×#448	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#448	C₂²	1	2	yes	complemented
101	C₃₁×#447	C₂²	1	2	yes	—
102	C₃₁×#447	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#441	C₂²	1	2	yes	complemented
104	C₃₁×#440	C₂²	1	2	yes	complemented
105	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
107	C₃₁×#436	C₂²	1	2	yes	complemented
108	C₃₁×#436	C₂²	1	2	yes	complemented
109	C₃₁×#435	C₂²	1	2	yes	complemented
110	C₃₁×#435	C₂²	1	2	yes	complemented
111	C₃₁×#433	C₂²	1	2	yes	complemented
112	C₃₁×#417	C₂²	1	2	yes	—
113	C₃₁×#417	C₂²	1	2	yes	complemented
114	C₃₁×#417	C₂²	1	2	yes	complemented
115	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
116	C₃₁×#408	C₂²	1	2	yes	complemented
117	C₃₁×#407	C₂²	1	1	yes	characteristic
118	C₃₁×#407	C₂²	1	1	yes	characteristic
119	C₃₁×2₋¹⁺⁴	—	4	4	no	—
120	C₂×#41×C₃₁	—	2	2	no	—
121	C₂×#41×C₃₁	—	2	1	no	—
122	C₂×#41×C₃₁	—	2	2	no	—
123	C₂×#41×C₃₁	—	2	1	no	—
124	C₂×#41×C₃₁	—	2	1	no	—
125	C₂×#41×C₃₁	—	4	4	no	—
126	C₂×#41×C₃₁	C₂³	1	2	yes	—
127	C₂×#41×C₃₁	C₂³	1	2	yes	—
128	C₂×#41×C₃₁	C₂³	1	2	yes	—
129	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
130	C₂×#41×C₃₁	C₂³	1	2	yes	—
131	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₃₁	—	2	1	no	—
133	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
134	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
135	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₃₁	—	2	1	no	—
137	C₂²×D₄×C₃₁	—	2	1	no	—
138	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₃₁	—	2	1	no	—
141	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₃₁×#137	—	4	4	no	—
143	C₃₁×#137	—	4	4	no	—
144	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
145	C₃₁×#135	—	4	4	no	—
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂×D₈×C₃₁	C₂³	1	2	yes	—
156	C₂×D₈×C₃₁	C₂³	1	2	yes	—
157	C₂×D₈×C₃₁	C₂³	1	2	yes	—
158	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
160	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
162	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₃₁×#127	—	2	2	no	—
164	C₃₁×#127	—	2	2	no	—
165	C₃₁×#127	—	2	1	no	—
166	C₃₁×#127	C₂³	1	2	yes	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#125	—	2	2	no	—
169	C₃₁×#124	—	2	1	no	—
170	C₃₁×#124	—	2	2	no	—
171	C₃₁×#124	—	2	2	no	—
172	C₃₁×#124	—	2	2	no	—
173	C₃₁×#124	—	2	2	no	—
174	C₃₁×#124	C₂³	1	2	yes	—
175	C₃₁×#124	C₂³	1	2	yes	—
176	C₃₁×#123	—	2	1	no	—
177	C₃₁×#123	—	2	2	no	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	D₄	1	2	yes	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	1	no	—
184	C₃₁×C₂²⋊Q₈	—	2	1	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
193	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
194	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
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	1	no	—
206	C₃₁×#121	—	2	1	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	—	2	2	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	D₄	1	1	yes	characteristic
215	C₃₁×#121	D₄	1	1	yes	characteristic
216	C₃₁×#121	C₂³	1	2	yes	—
217	C₃₁×#121	C₂³	1	1	yes	characteristic
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#121	C₂³	1	1	yes	characteristic
220	C₃₁×#121	C₂³	1	2	yes	—
221	C₃₁×#121	C₂³	1	2	yes	—
222	C₃₁×#121	C₂³	1	2	yes	—
223	C₃₁×#120	—	2	1	no	—
224	C₃₁×#120	—	2	2	no	—
225	C₃₁×#120	—	2	2	no	—
226	C₃₁×#120	—	2	2	no	—
227	C₃₁×#120	D₄	1	2	yes	—
228	C₄×Q₈×C₃₁	—	2	1	no	—
229	C₄×Q₈×C₃₁	—	2	1	no	—
230	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
231	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
232	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	—	2	2	no	—
237	C₄×D₄×C₃₁	—	2	2	no	—
238	C₄×D₄×C₃₁	—	2	2	no	—
239	C₄×D₄×C₃₁	—	2	2	no	—
240	C₄×D₄×C₃₁	—	2	2	no	—
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	2	yes	—
244	C₃₁×#117	—	2	2	no	—
245	C₃₁×#117	C₂³	1	1	yes	characteristic
246	C₃₁×#117	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
248	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
249	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
252	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
253	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
254	C₃₁×#107	C₂³	1	2	yes	—
255	C₃₁×#107	C₂³	1	2	yes	—
256	C₃₁×#106	C₂³	1	2	yes	—
257	C₃₁×#106	C₂³	1	2	yes	—
258	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
259	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
260	C₃₁×#103	C₂³	1	2	yes	—
261	C₃₁×#103	C₂³	1	2	yes	—
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#103	C₂³	1	2	yes	—
264	C₃₁×#103	C₂³	1	2	yes	—
265	C₃₁×#103	C₂³	1	2	yes	—
266	C₃₁×#103	C₂³	1	2	yes	—
267	C₃₁×#103	C₂³	1	2	yes	—
268	C₃₁×#102	C₂³	1	2	yes	—
269	C₃₁×#102	C₂³	1	2	yes	—
270	C₃₁×#102	C₂³	1	2	yes	—
271	C₃₁×#102	C₂³	1	2	yes	—
272	C₃₁×#102	C₂³	1	2	yes	—
273	C₃₁×#102	C₂³	1	2	yes	—
274	C₃₁×#102	C₂³	1	2	yes	—
275	C₃₁×#102	C₂³	1	2	yes	—
276	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
280	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₃₁×#97	C₂³	1	2	yes	—
285	C₄×C₈×C₃₁	C₂³	1	2	yes	—
286	C₂⁴×C₃₁	—	2	1	no	—
287	C₂⁴×C₃₁	—	2	1	no	—
288	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
289	#41×C₃₁	—	2	4	no	—
290	#41×C₃₁	—	2	4	no	—
291	#41×C₃₁	—	2	4	no	—
292	#41×C₃₁	—	4	2	no	—
293	#41×C₃₁	—	4	2	no	—
294	#41×C₃₁	—	4	2	no	—
295	#41×C₃₁	—	4	2	no	—
296	#41×C₃₁	—	4	2	no	—
297	#41×C₃₁	—	4	8	no	—
298	#41×C₃₁	—	4	2	no	—
299	#41×C₃₁	—	4	2	no	—
300	#41×C₃₁	—	4	4	no	—
301	#41×C₃₁	—	4	4	no	—
302	#41×C₃₁	—	4	4	no	—
303	#41×C₃₁	—	8	4	no	—
304	C₂×Q₈×C₃₁	—	2	4	no	—
305	C₂×Q₈×C₃₁	—	2	1	no	—
306	C₂×Q₈×C₃₁	—	2	2	no	—
307	C₂×Q₈×C₃₁	—	2	1	no	—
308	C₂×Q₈×C₃₁	—	2	2	no	—
309	C₂×Q₈×C₃₁	—	2	4	no	—
310	C₂×Q₈×C₃₁	—	4	2	no	—
311	C₂×Q₈×C₃₁	—	4	2	no	—
312	C₂×Q₈×C₃₁	—	4	4	no	—
313	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
314	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
315	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
316	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
317	C₂×D₄×C₃₁	—	2	2	no	—
318	C₂×D₄×C₃₁	—	2	1	no	—
319	C₂×D₄×C₃₁	—	2	2	no	—
320	C₂×D₄×C₃₁	—	2	2	no	—
321	C₂×D₄×C₃₁	—	2	2	no	—
322	C₂×D₄×C₃₁	—	2	2	no	—
323	C₂×D₄×C₃₁	—	2	2	no	—
324	C₂×D₄×C₃₁	—	2	1	no	—
325	C₂×D₄×C₃₁	—	2	1	no	—
326	C₂×D₄×C₃₁	—	2	2	no	—
327	C₂×D₄×C₃₁	—	2	2	no	—
328	C₂×D₄×C₃₁	—	2	2	no	—
329	C₂×D₄×C₃₁	—	2	1	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	4	2	no	—
334	C₂×D₄×C₃₁	—	4	2	no	—
335	C₂×D₄×C₃₁	—	4	4	no	—
336	C₂×D₄×C₃₁	—	8	2	no	—
337	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
338	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
340	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
341	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
342	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₃₁	—	2	1	no	—
345	C₂²×C₄×C₃₁	—	2	1	no	—
346	C₂²×C₄×C₃₁	—	2	2	no	—
347	C₂²×C₄×C₃₁	—	2	1	no	—
348	C₂²×C₄×C₃₁	—	2	1	no	—
349	C₂²×C₄×C₃₁	—	2	2	no	—
350	C₂²×C₄×C₃₁	—	2	2	no	—
351	C₂²×C₄×C₃₁	—	2	1	no	—
352	C₂²×C₄×C₃₁	—	2	2	no	—
353	C₂²×C₄×C₃₁	—	2	2	no	—
354	C₂²×C₄×C₃₁	—	2	2	no	—
355	C₂²×C₄×C₃₁	—	2	2	no	—
356	C₂²×C₄×C₃₁	—	4	2	no	—
357	C₂²×C₄×C₃₁	—	4	4	no	—
358	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
365	Q₁₆×C₃₁	—	2	4	no	—
366	Q₁₆×C₃₁	—	2	4	no	—
367	Q₁₆×C₃₁	—	4	2	no	—
368	SD₁₆×C₃₁	—	2	4	no	—
369	SD₁₆×C₃₁	—	2	4	no	—
370	SD₁₆×C₃₁	—	4	2	no	—
371	SD₁₆×C₃₁	—	4	2	no	—
372	SD₁₆×C₃₁	—	4	2	no	—
373	SD₁₆×C₃₁	—	4	2	no	—
374	D₈×C₃₁	—	4	2	no	—
375	D₈×C₃₁	—	4	2	no	—
376	D₈×C₃₁	—	4	2	no	—
377	M₁₆×C₃₁	—	4	2	no	—
378	M₁₆×C₃₁	—	4	2	no	—
379	M₁₆×C₃₁	—	4	2	no	—
380	C₂×C₈×C₃₁	—	4	2	no	—
381	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
382	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
383	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
384	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	2	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₂²⋊C₄×C₃₁	—	2	2	no	—
406	C₂²⋊C₄×C₃₁	—	2	2	no	—
407	C₂²⋊C₄×C₃₁	—	2	1	no	—
408	C₂²⋊C₄×C₃₁	—	2	1	no	—
409	C₂²⋊C₄×C₃₁	—	2	1	no	—
410	C₂²⋊C₄×C₃₁	—	2	2	no	—
411	C₂²⋊C₄×C₃₁	—	2	2	no	—
412	C₂²⋊C₄×C₃₁	—	2	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	1	no	—
416	C₂²⋊C₄×C₃₁	—	2	1	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
428	C₄²×C₃₁	—	2	2	no	—
429	C₄²×C₃₁	—	2	2	no	—
430	C₄²×C₃₁	—	2	1	no	—
431	C₄²×C₃₁	—	2	2	no	—
432	C₄²×C₃₁	C₂⁴	1	2	yes	—
433	#61650	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
434	C₂³×C₃₁	—	2	2	no	—
435	C₂³×C₃₁	—	2	2	no	—
436	C₂³×C₃₁	—	2	1	no	—
437	C₂³×C₃₁	—	4	1	no	—
438	C₂³×C₃₁	—	4	1	no	—
439	C₂³×C₃₁	—	4	1	no	—
440	C₂³×C₃₁	—	4	2	no	—
441	C₂³×C₃₁	—	4	2	no	—
442	C₂³×C₃₁	—	8	1	no	—
443	C₂³×C₃₁	—	8	1	no	—
444	C₂³×C₃₁	—	8	1	no	—
445	C₂³×C₃₁	—	8	1	no	—
446	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
447	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
448	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
449	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
450	Q₈×C₃₁	—	2	4	no	—
451	Q₈×C₃₁	—	2	2	no	—
452	Q₈×C₃₁	—	2	2	no	—
453	Q₈×C₃₁	—	2	2	no	—
454	Q₈×C₃₁	—	2	2	no	—
455	Q₈×C₃₁	—	4	1	no	—
456	Q₈×C₃₁	—	4	4	no	—
457	Q₈×C₃₁	—	8	1	no	—
458	Q₈×C₃₁	—	8	2	no	—
459	Q₈×C₃₁	H(5,𝔽₂)	1	4	yes	—
460	D₄×C₃₁	—	2	2	no	—
461	D₄×C₃₁	—	2	2	no	—
462	D₄×C₃₁	—	2	2	no	—
463	D₄×C₃₁	—	2	2	no	—
464	D₄×C₃₁	—	2	2	no	—
465	D₄×C₃₁	—	4	2	no	—
466	D₄×C₃₁	—	4	1	no	—
467	D₄×C₃₁	—	4	2	no	—
468	D₄×C₃₁	—	4	2	no	—
469	D₄×C₃₁	—	4	4	no	—
470	D₄×C₃₁	—	4	4	no	—
471	D₄×C₃₁	—	4	4	no	—
472	D₄×C₃₁	—	4	2	no	—
473	D₄×C₃₁	—	4	4	no	—
474	D₄×C₃₁	—	4	2	no	—
475	D₄×C₃₁	—	8	2	no	—
476	D₄×C₃₁	—	8	2	no	—
477	D₄×C₃₁	—	8	1	no	—
478	D₄×C₃₁	—	8	2	no	—
479	D₄×C₃₁	—	8	1	no	—
480	D₄×C₃₁	—	8	2	no	—
481	D₄×C₃₁	—	8	1	no	—
482	D₄×C₃₁	—	8	2	no	—
483	D₄×C₃₁	—	8	2	no	—
484	D₄×C₃₁	—	8	2	no	—
485	C₂×C₄×C₃₁	—	2	4	no	—
486	C₂×C₄×C₃₁	—	2	2	no	—
487	C₂×C₄×C₃₁	—	2	2	no	—
488	C₂×C₄×C₃₁	—	2	2	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	2	no	—
491	C₂×C₄×C₃₁	—	2	2	no	—
492	C₂×C₄×C₃₁	—	2	1	no	—
493	C₂×C₄×C₃₁	—	2	1	no	—
494	C₂×C₄×C₃₁	—	2	2	no	—
495	C₂×C₄×C₃₁	—	2	2	no	—
496	C₂×C₄×C₃₁	—	2	1	no	—
497	C₂×C₄×C₃₁	—	2	2	no	—
498	C₂×C₄×C₃₁	—	4	1	no	—
499	C₂×C₄×C₃₁	—	4	1	no	—
500	C₂×C₄×C₃₁	—	4	1	no	—
501	C₂×C₄×C₃₁	—	4	4	no	—
502	C₂×C₄×C₃₁	—	4	4	no	—
503	C₂×C₄×C₃₁	—	4	4	no	—
504	C₂×C₄×C₃₁	—	4	4	no	—
505	C₂×C₄×C₃₁	—	4	2	no	—
506	C₂×C₄×C₃₁	—	4	2	no	—
507	C₂×C₄×C₃₁	—	8	2	no	—
508	C₂×C₄×C₃₁	—	8	2	no	—
509	C₂×C₄×C₃₁	—	8	1	no	—
510	C₂×C₄×C₃₁	—	8	1	no	—
511	C₂×C₄×C₃₁	—	8	2	no	—
512	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
519	C₈×C₃₁	—	2	2	no	—
520	C₈×C₃₁	—	2	2	no	—
521	C₈×C₃₁	—	2	2	no	—
522	C₈×C₃₁	—	2	2	no	—
523	#3536	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3487	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3333	C₂×C₃₁	1	2	yes	complemented
526	#3332	C₂×C₃₁	1	2	yes	complemented
527	#3316	C₂×C₃₁	1	2	yes	complemented
528	#3308	C₂×C₃₁	1	2	yes	complemented
529	#3277	C₂×C₃₁	1	2	yes	complemented
530	#3275	C₂×C₃₁	1	2	yes	complemented
531	#3271	C₂×C₃₁	1	2	yes	complemented
532	#3268	C₂×C₃₁	1	2	yes	complemented
533	#3224	C₂×C₃₁	1	2	yes	complemented
534	#3198	C₂×C₃₁	1	2	yes	complemented
535	#3196	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3194	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3121	C₂×C₃₁	1	2	yes	complemented
538	#3013	C₂×C₃₁	1	2	yes	complemented
539	#3007	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3006	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#2978	C₂×C₃₁	1	1	yes	characteristic, complemented
542	C₂²×C₃₁	—	2	1	no	—
543	C₂²×C₃₁	—	2	2	no	—
544	C₂²×C₃₁	—	2	1	no	—
545	C₂²×C₃₁	—	2	1	no	—
546	C₂²×C₃₁	—	2	1	no	—
547	C₂²×C₃₁	—	2	2	no	—
548	C₂²×C₃₁	—	2	1	no	—
549	C₂²×C₃₁	—	2	1	no	—
550	C₂²×C₃₁	—	2	1	no	—
551	C₂²×C₃₁	—	2	2	no	—
552	C₂²×C₃₁	—	2	1	no	—
553	C₂²×C₃₁	—	2	1	no	—
554	C₂²×C₃₁	—	4	2	no	—
555	C₂²×C₃₁	—	4	1	no	—
556	C₂²×C₃₁	—	4	2	no	—
557	C₂²×C₃₁	—	4	1	no	—
558	C₂²×C₃₁	—	4	2	no	—
559	C₂²×C₃₁	—	4	2	no	—
560	C₂²×C₃₁	—	4	1	no	—
561	C₂²×C₃₁	—	4	2	no	—
562	C₂²×C₃₁	—	4	2	no	—
563	C₂²×C₃₁	—	8	2	no	—
564	C₂²×C₃₁	—	8	4	no	—
565	C₂²×C₃₁	—	16	2	no	—
566	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
567	C₄×C₃₁	—	2	2	no	—
568	C₄×C₃₁	—	2	2	no	—
569	C₄×C₃₁	—	2	4	no	—
570	C₄×C₃₁	—	2	1	no	—
571	C₄×C₃₁	—	2	1	no	—
572	C₄×C₃₁	—	2	1	no	—
573	C₄×C₃₁	—	2	2	no	—
574	C₄×C₃₁	—	4	2	no	—
575	C₄×C₃₁	—	4	2	no	—
576	C₄×C₃₁	—	4	1	no	—
577	C₄×C₃₁	—	4	1	no	—
578	C₄×C₃₁	—	4	1	no	—
579	C₄×C₃₁	—	4	2	no	—
580	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
581	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic, complemented
582	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
583	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
584	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
585	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
586	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
587	#562	—	2	2	no	—
588	#554	C₂²×C₃₁	1	2	yes	complemented
589	#550	—	2	1	no	—
590	#550	—	2	1	no	—
591	#550	C₂²×C₃₁	1	2	yes	—
592	#550	C₂²×C₃₁	1	2	yes	complemented
593	#548	—	2	1	no	—
594	#548	—	2	1	no	—
595	#548	C₂²×C₃₁	1	2	yes	—
596	#548	C₂²×C₃₁	1	2	yes	complemented
597	#548	C₂²×C₃₁	1	2	yes	complemented
598	#547	C₂²×C₃₁	1	2	yes	complemented
599	#546	—	2	2	no	—
600	#546	C₂²×C₃₁	1	2	yes	complemented
601	#543	—	2	1	no	—
602	#542	C₂²×C₃₁	1	2	yes	—
603	#539	—	2	1	no	—
604	#538	—	2	1	no	—
605	#537	—	2	1	no	—
606	#537	C₂²×C₃₁	1	2	yes	—
607	#535	—	2	2	no	—
608	#535	C₂²×C₃₁	1	1	yes	characteristic, complemented
609	#535	C₂²×C₃₁	1	1	yes	characteristic, complemented
610	#525	—	2	2	no	—
611	#525	C₂²×C₃₁	1	1	yes	characteristic
612	#525	C₂²×C₃₁	1	1	yes	characteristic
613	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
614	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
615	#519	C₂²×C₃₁	1	1	yes	characteristic, complemented
616	#496	C₂²×C₃₁	1	2	yes	complemented
617	#495	C₂²×C₃₁	1	2	yes	complemented
618	#489	C₂²×C₃₁	1	2	yes	complemented
619	#486	C₂²×C₃₁	1	2	yes	complemented
620	#485	C₂²×C₃₁	1	2	yes	complemented
621	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
622	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
623	#482	C₂²×C₃₁	1	2	yes	—
624	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
625	#481	C₂²×C₃₁	1	2	yes	complemented
626	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
627	#480	C₂²×C₃₁	1	2	yes	complemented
628	#477	C₂²×C₃₁	1	2	yes	complemented
629	#475	C₂²×C₃₁	1	2	yes	complemented
630	#470	C₂²×C₃₁	1	2	yes	complemented
631	#469	C₂²×C₃₁	1	2	yes	complemented
632	#469	C₂²×C₃₁	1	2	yes	complemented
633	#468	C₂²×C₃₁	1	2	yes	complemented
634	#468	C₂²×C₃₁	1	2	yes	complemented
635	#468	C₂²×C₃₁	1	2	yes	complemented
636	#466	C₂²×C₃₁	1	2	yes	complemented
637	#465	C₂²×C₃₁	1	2	yes	complemented
638	#464	C₂²×C₃₁	1	2	yes	complemented
639	#464	C₂²×C₃₁	1	2	yes	complemented
640	#464	C₂²×C₃₁	1	2	yes	complemented
641	#463	C₂²×C₃₁	1	2	yes	complemented
642	#460	C₂²×C₃₁	1	2	yes	complemented
643	#459	C₂²×C₃₁	1	2	yes	complemented
644	#452	C₂²×C₃₁	1	2	yes	—
645	#452	C₂²×C₃₁	1	2	yes	—
646	#452	C₂²×C₃₁	1	2	yes	complemented
647	#452	C₂²×C₃₁	1	2	yes	complemented
648	#451	C₂²×C₃₁	1	2	yes	complemented
649	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#451	C₂²×C₃₁	1	2	yes	complemented
651	#450	C₂²×C₃₁	1	1	yes	characteristic, complemented
652	#450	C₂²×C₃₁	1	2	yes	complemented
653	#449	C₂²×C₃₁	1	2	yes	—
654	#449	C₂²×C₃₁	1	2	yes	—
655	#449	C₂²×C₃₁	1	2	yes	—
656	#449	C₂²×C₃₁	1	2	yes	complemented
657	#449	C₂²×C₃₁	1	2	yes	complemented
658	#449	C₂²×C₃₁	1	2	yes	complemented
659	#448	C₂²×C₃₁	1	2	yes	—
660	#448	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	#448	C₂²×C₃₁	1	2	yes	complemented
662	#447	C₂²×C₃₁	1	2	yes	—
663	#447	C₂²×C₃₁	1	1	yes	characteristic, complemented
664	#441	C₂²×C₃₁	1	2	yes	complemented
665	#440	C₂²×C₃₁	1	2	yes	complemented
666	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
667	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
668	#436	C₂²×C₃₁	1	2	yes	complemented
669	#436	C₂²×C₃₁	1	2	yes	complemented
670	#435	C₂²×C₃₁	1	2	yes	complemented
671	#435	C₂²×C₃₁	1	2	yes	complemented
672	#433	C₂²×C₃₁	1	2	yes	complemented
673	#417	C₂²×C₃₁	1	2	yes	—
674	#417	C₂²×C₃₁	1	2	yes	complemented
675	#417	C₂²×C₃₁	1	2	yes	complemented
676	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
677	#408	C₂²×C₃₁	1	2	yes	complemented
678	#407	C₂²×C₃₁	1	1	yes	characteristic
679	#407	C₂²×C₃₁	1	1	yes	characteristic
680	C₂×C₃₁	—	4	2	no	—
681	C₂×C₃₁	—	4	1	no	—
682	C₂×C₃₁	—	4	1	no	—
683	C₂×C₃₁	—	4	1	no	—
684	C₂×C₃₁	—	8	1	no	—
685	C₂×C₃₁	—	8	2	no	—
686	C₂×C₃₁	—	8	2	no	—
687	C₂×C₃₁	#3484	1	1	yes	characteristic
688	C₂×C₃₁	#3585	1	1	yes	characteristic
689	C₂×C₃₁	#3586	1	1	yes	characteristic
690	2₋¹⁺⁴	—	4	4	no	—
691	C₂×#41	—	2	2	no	—
692	C₂×#41	—	2	1	no	—
693	C₂×#41	—	2	2	no	—
694	C₂×#41	—	2	1	no	—
695	C₂×#41	—	2	1	no	—
696	C₂×#41	—	4	4	no	—
697	C₂×#41	C₂³×C₃₁	1	2	yes	—
698	C₂×#41	C₂³×C₃₁	1	2	yes	—
699	C₂×#41	C₂³×C₃₁	1	2	yes	—
700	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
701	C₂×#41	C₂³×C₃₁	1	2	yes	—
702	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
703	C₂²×Q₈	—	2	1	no	—
704	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
705	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
706	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
707	C₂²×D₄	—	2	1	no	—
708	C₂²×D₄	—	2	1	no	—
709	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
710	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
711	C₂³×C₄	—	2	1	no	—
712	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
713	#137	—	4	4	no	—
714	#137	—	4	4	no	—
715	AGL(1,ℤ/8)	—	4	4	no	—
716	#135	—	4	4	no	—
717	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
718	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
719	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
720	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
724	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
725	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
726	C₂×D₈	C₂³×C₃₁	1	2	yes	—
727	C₂×D₈	C₂³×C₃₁	1	2	yes	—
728	C₂×D₈	C₂³×C₃₁	1	2	yes	—
729	C₂×M₁₆	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	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
734	#127	—	2	2	no	—
735	#127	—	2	2	no	—
736	#127	—	2	1	no	—
737	#127	C₂³×C₃₁	1	2	yes	—
738	#126	—	2	2	no	—
739	#125	—	2	2	no	—
740	#124	—	2	1	no	—
741	#124	—	2	2	no	—
742	#124	—	2	2	no	—
743	#124	—	2	2	no	—
744	#124	—	2	2	no	—
745	#124	C₂³×C₃₁	1	2	yes	—
746	#124	C₂³×C₃₁	1	2	yes	—
747	#123	—	2	1	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	D₄×C₃₁	1	2	yes	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	1	no	—
755	C₂²⋊Q₈	—	2	1	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
764	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
765	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
766	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
767	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
768	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
769	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
770	#121	—	2	2	no	—
771	#121	—	2	2	no	—
772	#121	—	2	2	no	—
773	#121	—	2	2	no	—
774	#121	—	2	2	no	—
775	#121	—	2	2	no	—
776	#121	—	2	1	no	—
777	#121	—	2	1	no	—
778	#121	—	2	1	no	—
779	#121	—	2	1	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	D₄×C₃₁	1	1	yes	characteristic
786	#121	D₄×C₃₁	1	1	yes	characteristic
787	#121	C₂³×C₃₁	1	2	yes	—
788	#121	C₂³×C₃₁	1	2	yes	—
789	#121	C₂³×C₃₁	1	1	yes	characteristic
790	#121	C₂³×C₃₁	1	1	yes	characteristic
791	#121	C₂³×C₃₁	1	2	yes	—
792	#121	C₂³×C₃₁	1	2	yes	—
793	#121	C₂³×C₃₁	1	2	yes	—
794	#120	—	2	1	no	—
795	#120	—	2	2	no	—
796	#120	—	2	2	no	—
797	#120	—	2	2	no	—
798	#120	D₄×C₃₁	1	2	yes	—
799	C₄×Q₈	—	2	1	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
802	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
803	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	C₂³×C₃₁	1	2	yes	—
813	C₄×D₄	C₂³×C₃₁	1	2	yes	—
814	C₄×D₄	C₂³×C₃₁	1	2	yes	—
815	#117	—	2	2	no	—
816	#117	C₂³×C₃₁	1	1	yes	characteristic
817	#117	C₂³×C₃₁	1	1	yes	characteristic
818	C₂×C₄⋊C₄	—	2	1	no	—
819	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
820	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
821	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
822	C₂×C₂²⋊C₄	—	2	1	no	—
823	C₂×C₂²⋊C₄	—	2	1	no	—
824	C₂×C₂²⋊C₄	—	2	2	no	—
825	#107	C₂³×C₃₁	1	2	yes	—
826	#107	C₂³×C₃₁	1	2	yes	—
827	#106	C₂³×C₃₁	1	2	yes	—
828	#106	C₂³×C₃₁	1	2	yes	—
829	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
830	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
831	#103	C₂³×C₃₁	1	2	yes	—
832	#103	C₂³×C₃₁	1	2	yes	—
833	#103	C₂³×C₃₁	1	2	yes	—
834	#103	C₂³×C₃₁	1	2	yes	—
835	#103	C₂³×C₃₁	1	2	yes	—
836	#103	C₂³×C₃₁	1	2	yes	—
837	#103	C₂³×C₃₁	1	2	yes	—
838	#103	C₂³×C₃₁	1	2	yes	—
839	#102	C₂³×C₃₁	1	2	yes	—
840	#102	C₂³×C₃₁	1	2	yes	—
841	#102	C₂³×C₃₁	1	2	yes	—
842	#102	C₂³×C₃₁	1	2	yes	—
843	#102	C₂³×C₃₁	1	2	yes	—
844	#102	C₂³×C₃₁	1	2	yes	—
845	#102	C₂³×C₃₁	1	2	yes	—
846	#102	C₂³×C₃₁	1	2	yes	—
847	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
848	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
849	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
850	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
851	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
852	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
853	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
854	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
855	#97	C₂³×C₃₁	1	2	yes	—
856	C₄×C₈	C₂³×C₃₁	1	2	yes	—
857	C₃₁	#61650	1	1	yes	characteristic, direct product factor, Sylow
858	C₂⁴	—	2	1	no	—
859	C₂⁴	—	2	1	no	—
860	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
861	#41	—	2	4	no	—
862	#41	—	2	4	no	—
863	#41	—	2	4	no	—
864	#41	—	4	2	no	—
865	#41	—	4	2	no	—
866	#41	—	4	2	no	—
867	#41	—	4	2	no	—
868	#41	—	4	2	no	—
869	#41	—	4	8	no	—
870	#41	—	4	2	no	—
871	#41	—	4	2	no	—
872	#41	—	4	4	no	—
873	#41	—	4	4	no	—
874	#41	—	4	4	no	—
875	#41	—	8	4	no	—
876	C₂×Q₈	—	2	4	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	—	2	1	no	—
880	C₂×Q₈	—	2	2	no	—
881	C₂×Q₈	—	2	4	no	—
882	C₂×Q₈	—	4	2	no	—
883	C₂×Q₈	—	4	2	no	—
884	C₂×Q₈	—	4	4	no	—
885	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
886	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
887	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
888	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	4	2	no	—
906	C₂×D₄	—	4	2	no	—
907	C₂×D₄	—	4	4	no	—
908	C₂×D₄	—	8	2	no	—
909	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
910	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
911	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
912	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
913	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
914	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
915	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	4	2	no	—
929	C₂²×C₄	—	4	4	no	—
930	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
931	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
932	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
933	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
935	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
937	Q₁₆	—	2	4	no	—
938	Q₁₆	—	2	4	no	—
939	Q₁₆	—	4	2	no	—
940	SD₁₆	—	2	4	no	—
941	SD₁₆	—	2	4	no	—
942	SD₁₆	—	4	2	no	—
943	SD₁₆	—	4	2	no	—
944	SD₁₆	—	4	2	no	—
945	SD₁₆	—	4	2	no	—
946	D₈	—	4	2	no	—
947	D₈	—	4	2	no	—
948	D₈	—	4	2	no	—
949	M₁₆	—	4	2	no	—
950	M₁₆	—	4	2	no	—
951	M₁₆	—	4	2	no	—
952	C₂×C₈	—	4	2	no	—
953	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
954	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
955	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
956	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
970	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
971	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
972	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
973	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
996	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
997	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
998	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	C₂⁴×C₃₁	1	2	yes	—
1005	C₂³	—	2	2	no	—
1006	C₂³	—	2	2	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	4	1	no	—
1009	C₂³	—	4	1	no	—
1010	C₂³	—	4	1	no	—
1011	C₂³	—	4	2	no	—
1012	C₂³	—	4	2	no	—
1013	C₂³	—	8	1	no	—
1014	C₂³	—	8	1	no	—
1015	C₂³	—	8	1	no	—
1016	C₂³	—	8	1	no	—
1017	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1018	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1019	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1020	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1021	Q₈	—	2	4	no	—
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	2	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	4	1	no	—
1027	Q₈	—	4	4	no	—
1028	Q₈	—	8	1	no	—
1029	Q₈	—	8	2	no	—
1030	Q₈	C₃₁×H(5,𝔽₂)	1	4	yes	—
1031	D₄	—	2	2	no	—
1032	D₄	—	2	2	no	—
1033	D₄	—	2	2	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	4	2	no	—
1037	D₄	—	4	1	no	—
1038	D₄	—	4	2	no	—
1039	D₄	—	4	2	no	—
1040	D₄	—	4	4	no	—
1041	D₄	—	4	4	no	—
1042	D₄	—	4	4	no	—
1043	D₄	—	4	2	no	—
1044	D₄	—	4	4	no	—
1045	D₄	—	4	2	no	—
1046	D₄	—	8	2	no	—
1047	D₄	—	8	2	no	—
1048	D₄	—	8	1	no	—
1049	D₄	—	8	2	no	—
1050	D₄	—	8	1	no	—
1051	D₄	—	8	2	no	—
1052	D₄	—	8	1	no	—
1053	D₄	—	8	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	2	no	—
1056	C₂×C₄	—	2	4	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	4	1	no	—
1072	C₂×C₄	—	4	4	no	—
1073	C₂×C₄	—	4	4	no	—
1074	C₂×C₄	—	4	4	no	—
1075	C₂×C₄	—	4	4	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	—	8	2	no	—
1080	C₂×C₄	—	8	1	no	—
1081	C₂×C₄	—	8	1	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1084	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1085	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1087	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1088	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1089	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1090	C₈	—	2	2	no	—
1091	C₈	—	2	2	no	—
1092	C₈	—	2	2	no	—
1093	C₈	—	2	2	no	—
1094	C₂²	—	2	1	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	2	1	no	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	2	1	no	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	2	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	2	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	—	8	2	no	—
1116	C₂²	—	8	4	no	—
1117	C₂²	—	16	2	no	—
1118	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1119	C₄	—	2	4	no	—
1120	C₄	—	2	1	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	2	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	1	no	—
1132	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
1133	C₂	—	4	1	no	—
1134	C₂	—	4	1	no	—
1135	C₂	—	4	1	no	—
1136	C₂	—	4	2	no	—
1137	C₂	—	8	2	no	—
1138	C₂	—	8	2	no	—
1139	C₂	—	8	1	no	—
1140	C₂	C₃₁×#3484	1	1	yes	characteristic
1141	C₂	C₃₁×#3585	1	1	yes	characteristic
1142	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3536	C₂	semidirect
2. C₃₁×#3487	C₂	semidirect
3. C₃₁×#3333	C₂	semidirect
4. C₃₁×#3332	C₂	semidirect
5. C₃₁×#3316	C₂	semidirect
6. C₃₁×#3308	C₂	semidirect
7. C₃₁×#3277	C₂	semidirect
8. C₃₁×#3275	C₂	semidirect
9. C₃₁×#3271	C₂	semidirect
10. C₃₁×#3268	C₂	semidirect
11. C₃₁×#3224	C₂	semidirect
12. C₃₁×#3198	C₂	semidirect
13. C₃₁×#3196	C₂	semidirect
14. C₃₁×#3194	C₂	semidirect
15. C₃₁×#3121	C₂	semidirect
16. C₃₁×#3013	C₂	semidirect
17. C₃₁×#3007	C₂	semidirect
18. C₃₁×#3006	C₂	semidirect
19. C₃₁×#2978	C₂	semidirect
20. C₂×C₃₁×2₋¹⁺⁴	C₂²	semidirect
22. C₂×C₃₁×#137	C₂²	semidirect
23. C₂×C₃₁×#137	C₂²	semidirect
25. C₂×C₃₁×#135	C₂²	semidirect
27. C₃₁×#554	C₂²	semidirect
31. C₃₁×#550	C₂²	semidirect
35. C₃₁×#548	C₂²	semidirect
36. C₃₁×#548	C₂²	semidirect
37. C₃₁×#547	C₂²	semidirect
39. C₃₁×#546	C₂²	semidirect
47. C₃₁×#535	C₂²	semidirect
48. C₃₁×#535	C₂²	semidirect
54. C₃₁×#519	C₂²	semidirect
55. C₃₁×#496	C₂²	semidirect
56. C₃₁×#495	C₂²	semidirect
57. C₃₁×#489	C₂²	semidirect
58. C₃₁×#486	C₂²	semidirect
59. C₃₁×#485	C₂²	semidirect
60. C₃₁×#484	C₂²	semidirect
61. C₃₁×#483	C₂²	semidirect
63. C₃₁×#481	C₂²	semidirect
64. C₃₁×#481	C₂²	semidirect
65. C₃₁×#480	C₂²	semidirect
66. C₃₁×#480	C₂²	semidirect
67. C₃₁×#477	C₂²	semidirect
68. C₃₁×#475	C₂²	semidirect
69. C₃₁×#470	C₂²	semidirect
70. C₃₁×#469	C₂²	semidirect
71. C₃₁×#469	C₂²	semidirect
72. C₃₁×#468	C₂²	semidirect
73. C₃₁×#468	C₂²	semidirect
74. C₃₁×#468	C₂²	semidirect
75. C₃₁×#466	C₂²	semidirect
76. C₃₁×#465	C₂²	semidirect
77. C₃₁×#464	C₂²	semidirect
78. C₃₁×#464	C₂²	semidirect
79. C₃₁×#464	C₂²	semidirect
80. C₃₁×#463	C₂²	semidirect
81. C₃₁×#460	C₂²	semidirect
82. C₃₁×#459	C₂²	semidirect
85. C₃₁×#452	C₂²	semidirect
86. C₃₁×#452	C₂²	semidirect
87. C₃₁×#451	C₂²	semidirect
88. C₃₁×#451	C₂²	semidirect
89. C₃₁×#451	C₂²	semidirect
90. C₃₁×#450	C₂²	semidirect
91. C₃₁×#450	C₂²	semidirect
95. C₃₁×#449	C₂²	semidirect
96. C₃₁×#449	C₂²	semidirect
97. C₃₁×#449	C₂²	semidirect
99. C₃₁×#448	C₂²	semidirect
100. C₃₁×#448	C₂²	semidirect
102. C₃₁×#447	C₂²	semidirect
103. C₃₁×#441	C₂²	semidirect
104. C₃₁×#440	C₂²	semidirect
105. C₄×Q₁₆×C₃₁	C₂²	semidirect
106. C₄×SD₁₆×C₃₁	C₂²	semidirect
107. C₃₁×#436	C₂²	semidirect
108. C₃₁×#436	C₂²	semidirect
109. C₃₁×#435	C₂²	semidirect
110. C₃₁×#435	C₂²	semidirect
111. C₃₁×#433	C₂²	semidirect
113. C₃₁×#417	C₂²	semidirect
114. C₃₁×#417	C₂²	semidirect
115. C₂×C₃₁×#103	C₂²	semidirect
116. C₃₁×#408	C₂²	semidirect
433. #61650	C₃₁	direct (N × H)
523. #3536	C₂×C₃₁	semidirect
524. #3487	C₂×C₃₁	semidirect
525. #3333	C₂×C₃₁	semidirect
526. #3332	C₂×C₃₁	semidirect
527. #3316	C₂×C₃₁	semidirect
528. #3308	C₂×C₃₁	semidirect
529. #3277	C₂×C₃₁	semidirect
530. #3275	C₂×C₃₁	semidirect
531. #3271	C₂×C₃₁	semidirect
532. #3268	C₂×C₃₁	semidirect
533. #3224	C₂×C₃₁	semidirect
534. #3198	C₂×C₃₁	semidirect
535. #3196	C₂×C₃₁	semidirect
536. #3194	C₂×C₃₁	semidirect
537. #3121	C₂×C₃₁	semidirect
538. #3013	C₂×C₃₁	semidirect
539. #3007	C₂×C₃₁	semidirect
540. #3006	C₂×C₃₁	semidirect
541. #2978	C₂×C₃₁	semidirect
581. C₂×2₋¹⁺⁴	C₂²×C₃₁	semidirect
583. C₂×#137	C₂²×C₃₁	semidirect
584. C₂×#137	C₂²×C₃₁	semidirect
586. C₂×#135	C₂²×C₃₁	semidirect
588. #554	C₂²×C₃₁	semidirect
592. #550	C₂²×C₃₁	semidirect
596. #548	C₂²×C₃₁	semidirect
597. #548	C₂²×C₃₁	semidirect
598. #547	C₂²×C₃₁	semidirect
600. #546	C₂²×C₃₁	semidirect
608. #535	C₂²×C₃₁	semidirect
609. #535	C₂²×C₃₁	semidirect
615. #519	C₂²×C₃₁	semidirect
616. #496	C₂²×C₃₁	semidirect
617. #495	C₂²×C₃₁	semidirect
618. #489	C₂²×C₃₁	semidirect
619. #486	C₂²×C₃₁	semidirect
620. #485	C₂²×C₃₁	semidirect
621. #484	C₂²×C₃₁	semidirect
622. #483	C₂²×C₃₁	semidirect
624. #481	C₂²×C₃₁	semidirect
625. #481	C₂²×C₃₁	semidirect
626. #480	C₂²×C₃₁	semidirect
627. #480	C₂²×C₃₁	semidirect
628. #477	C₂²×C₃₁	semidirect
629. #475	C₂²×C₃₁	semidirect
630. #470	C₂²×C₃₁	semidirect
631. #469	C₂²×C₃₁	semidirect
632. #469	C₂²×C₃₁	semidirect
633. #468	C₂²×C₃₁	semidirect
634. #468	C₂²×C₃₁	semidirect
635. #468	C₂²×C₃₁	semidirect
636. #466	C₂²×C₃₁	semidirect
637. #465	C₂²×C₃₁	semidirect
638. #464	C₂²×C₃₁	semidirect
639. #464	C₂²×C₃₁	semidirect
640. #464	C₂²×C₃₁	semidirect
641. #463	C₂²×C₃₁	semidirect
642. #460	C₂²×C₃₁	semidirect
643. #459	C₂²×C₃₁	semidirect
646. #452	C₂²×C₃₁	semidirect
647. #452	C₂²×C₃₁	semidirect
648. #451	C₂²×C₃₁	semidirect
649. #451	C₂²×C₃₁	semidirect
650. #451	C₂²×C₃₁	semidirect
651. #450	C₂²×C₃₁	semidirect
652. #450	C₂²×C₃₁	semidirect
656. #449	C₂²×C₃₁	semidirect
657. #449	C₂²×C₃₁	semidirect
658. #449	C₂²×C₃₁	semidirect
660. #448	C₂²×C₃₁	semidirect
661. #448	C₂²×C₃₁	semidirect
663. #447	C₂²×C₃₁	semidirect
664. #441	C₂²×C₃₁	semidirect
665. #440	C₂²×C₃₁	semidirect
666. C₄×Q₁₆	C₂²×C₃₁	semidirect
667. C₄×SD₁₆	C₂²×C₃₁	semidirect
668. #436	C₂²×C₃₁	semidirect
669. #436	C₂²×C₃₁	semidirect
670. #435	C₂²×C₃₁	semidirect
671. #435	C₂²×C₃₁	semidirect
672. #433	C₂²×C₃₁	semidirect
674. #417	C₂²×C₃₁	semidirect
675. #417	C₂²×C₃₁	semidirect
676. C₂×#103	C₂²×C₃₁	semidirect
677. #408	C₂²×C₃₁	semidirect
857. C₃₁	#61650	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×#3536	2
C₃₁×#3487	2
C₃₁×#3333	2
C₃₁×#3332	2
C₃₁×#3316	2
C₃₁×#3308	2
C₃₁×#3277	2
C₃₁×#3275	2
C₃₁×#3271	2
C₃₁×#3268	2
C₃₁×#3224	2
C₃₁×#3198	2
C₃₁×#3196	2
C₃₁×#3194	2
C₃₁×#3121	2
C₃₁×#3013	2
C₃₁×#3007	2
C₃₁×#3006	2
C₃₁×#2978	2
#61650	31

Subgroups — C31×#61650 #21518409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61650 #21518409