Subgroups — C₃₁×#62015 #21518774

Order 7936.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3558	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3399	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3319	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3318	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3301	C₂	1	2	yes	maximal, complemented
8	D₄×D₈×C₃₁	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3265	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3264	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3257	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3245	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3220	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3041	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
21	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
22	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
23	C₂²×D₈×C₃₁	C₂²	1	2	yes	complemented
24	C₃₁×#562	—	2	1	no	—
25	C₃₁×H(3,𝔽₄)	—	2	1	no	—
26	C₃₁×#559	C₂²	1	2	yes	complemented
27	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#553	—	2	1	no	—
30	C₃₁×#553	C₂²	1	2	yes	complemented
31	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#548	C₂²	1	2	yes	complemented
33	C₃₁×#546	—	2	1	no	—
34	C₃₁×#546	—	2	2	no	—
35	C₃₁×#546	—	2	2	no	—
36	C₃₁×#546	C₂²	1	2	yes	complemented
37	D₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
38	D₄²×C₃₁	C₂²	1	2	yes	complemented
39	D₄²×C₃₁	C₂²	1	2	yes	complemented
40	C₃₁×#542	C₂²	1	2	yes	complemented
41	C₃₁×#540	C₂²	1	2	yes	complemented
42	C₃₁×#538	—	2	2	no	—
43	C₃₁×#538	—	2	2	no	—
44	C₃₁×#538	—	2	1	no	—
45	C₃₁×#535	C₂²	1	2	yes	complemented
46	C₃₁×#534	—	2	1	no	—
47	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#529	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#525	—	2	1	no	—
52	C₂×C₃₁×#121	—	2	1	no	—
53	C₃₁×#518	C₂²	1	2	yes	complemented
54	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#496	C₂²	1	2	yes	complemented
56	C₃₁×#496	C₂²	1	2	yes	complemented
57	C₃₁×#493	C₂²	1	2	yes	complemented
58	C₃₁×#490	C₂²	1	2	yes	complemented
59	C₃₁×#489	C₂²	1	2	yes	complemented
60	C₃₁×#488	C₂²	1	2	yes	complemented
61	C₃₁×#485	C₂²	1	2	yes	complemented
62	C₃₁×#482	C₂²	1	2	yes	complemented
63	C₃₁×#481	C₂²	1	2	yes	complemented
64	C₃₁×#479	C₂²	1	2	yes	complemented
65	C₃₁×#478	C₂²	1	2	yes	complemented
66	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#474	C₂²	1	2	yes	complemented
69	C₃₁×#474	C₂²	1	2	yes	complemented
70	C₃₁×#469	C₂²	1	2	yes	complemented
71	C₃₁×#468	C₂²	1	2	yes	complemented
72	C₃₁×#466	C₂²	1	2	yes	complemented
73	C₃₁×#466	C₂²	1	2	yes	complemented
74	C₃₁×#466	C₂²	1	2	yes	complemented
75	C₃₁×#465	C₂²	1	2	yes	complemented
76	C₃₁×#463	C₂²	1	2	yes	complemented
77	C₃₁×#463	C₂²	1	2	yes	complemented
78	C₃₁×#463	C₂²	1	2	yes	complemented
79	C₃₁×#463	C₂²	1	2	yes	complemented
80	C₃₁×#463	C₂²	1	2	yes	complemented
81	C₃₁×#463	C₂²	1	2	yes	complemented
82	C₃₁×#463	C₂²	1	2	yes	complemented
83	C₃₁×#463	C₂²	1	2	yes	complemented
84	C₃₁×#460	C₂²	1	2	yes	complemented
85	C₃₁×#459	C₂²	1	2	yes	—
86	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#459	C₂²	1	2	yes	complemented
89	C₃₁×#459	C₂²	1	2	yes	complemented
90	C₃₁×#459	C₂²	1	2	yes	complemented
91	C₃₁×#459	C₂²	1	2	yes	complemented
92	C₃₁×#450	C₂²	1	2	yes	complemented
93	C₃₁×#449	C₂²	1	2	yes	complemented
94	C₃₁×#449	C₂²	1	2	yes	complemented
95	C₃₁×#448	C₂²	1	2	yes	complemented
96	C₃₁×#447	C₂²	1	2	yes	—
97	C₃₁×#447	C₂²	1	2	yes	complemented
98	C₃₁×#447	C₂²	1	2	yes	complemented
99	C₃₁×#447	C₂²	1	2	yes	complemented
100	C₃₁×#447	C₂²	1	2	yes	complemented
101	C₃₁×#446	C₂²	1	2	yes	complemented
102	C₃₁×#442	C₂²	1	2	yes	complemented
103	C₃₁×#442	C₂²	1	2	yes	complemented
104	C₃₁×#442	C₂²	1	2	yes	complemented
105	C₃₁×#440	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
107	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
108	C₃₁×#435	C₂²	1	2	yes	complemented
109	C₃₁×#435	C₂²	1	2	yes	complemented
110	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
111	C₃₁×#433	C₂²	1	2	yes	complemented
112	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#424	C₂²	1	2	yes	complemented
114	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
115	C₃₁×#418	C₂²	1	2	yes	complemented
116	C₃₁×#416	C₂²	1	2	yes	complemented
117	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₃₁	—	2	1	no	—
120	C₂×#41×C₃₁	—	2	1	no	—
121	C₂×#41×C₃₁	—	2	1	no	—
122	C₂×#41×C₃₁	C₂³	1	2	yes	—
123	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₃₁	—	2	1	no	—
125	C₂²×D₄×C₃₁	—	2	2	no	—
126	C₂²×D₄×C₃₁	—	2	2	no	—
127	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
128	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
131	C₂³×C₄×C₃₁	—	2	1	no	—
132	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
133	C₂×SD₁₆×C₃₁	—	4	2	no	—
134	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
135	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
136	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
137	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
138	C₂×D₈×C₃₁	—	4	2	no	—
139	C₂×D₈×C₃₁	—	4	4	no	—
140	C₂×D₈×C₃₁	C₂³	1	2	yes	—
141	C₂×D₈×C₃₁	C₂³	1	2	yes	—
142	C₂×D₈×C₃₁	C₂³	1	2	yes	—
143	C₂×D₈×C₃₁	C₂³	1	2	yes	—
144	C₂×D₈×C₃₁	C₂³	1	2	yes	—
145	C₂×D₈×C₃₁	C₂³	1	2	yes	—
146	C₂×D₈×C₃₁	C₂³	1	2	yes	—
147	C₂×D₈×C₃₁	C₂³	1	2	yes	—
148	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
152	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₃₁×#127	C₂³	1	2	yes	—
155	C₃₁×#127	C₂³	1	1	yes	characteristic
156	C₃₁×#127	C₂³	1	1	yes	characteristic
157	C₃₁×#127	C₂³	1	2	yes	—
158	C₃₁×#126	—	2	2	no	—
159	C₃₁×#126	—	2	2	no	—
160	C₃₁×#126	D₄	1	2	yes	—
161	C₃₁×#125	D₄	1	1	yes	characteristic
162	C₃₁×#125	C₂³	1	2	yes	—
163	C₃₁×#124	—	2	2	no	—
164	C₃₁×#124	—	2	2	no	—
165	C₃₁×#124	—	2	2	no	—
166	C₃₁×#124	—	2	2	no	—
167	C₃₁×#124	—	2	1	no	—
168	C₃₁×#124	—	2	1	no	—
169	C₃₁×#124	—	2	1	no	—
170	C₃₁×#124	—	2	1	no	—
171	C₃₁×#124	D₄	1	1	yes	characteristic
172	C₃₁×#124	C₂³	1	2	yes	—
173	C₃₁×#124	C₂³	1	2	yes	—
174	C₃₁×#124	C₂³	1	2	yes	—
175	C₃₁×#123	—	2	2	no	—
176	C₃₁×#123	—	2	2	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	—	2	2	no	—
182	C₃₁×#123	D₄	1	2	yes	—
183	C₃₁×C₂²⋊Q₈	—	2	1	no	—
184	C₃₁×C₂²⋊Q₈	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
188	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₃₁×#121	—	2	2	no	—
190	C₃₁×#121	—	2	1	no	—
191	C₃₁×#121	—	2	2	no	—
192	C₃₁×#121	—	2	1	no	—
193	C₃₁×#121	—	2	1	no	—
194	C₃₁×#121	—	2	1	no	—
195	C₃₁×#121	—	2	1	no	—
196	C₃₁×#121	—	2	2	no	—
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	—	2	2	no	—
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	D₄	1	1	yes	characteristic
205	C₃₁×#121	C₂³	1	2	yes	—
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₃₁×#121	C₂³	1	2	yes	—
208	C₃₁×#121	C₂³	1	2	yes	—
209	C₃₁×#121	C₂³	1	2	yes	—
210	C₃₁×#120	—	2	2	no	—
211	C₃₁×#120	—	2	2	no	—
212	C₃₁×#120	—	2	2	no	—
213	C₃₁×#120	—	2	2	no	—
214	C₃₁×#120	—	2	2	no	—
215	C₃₁×#120	—	2	2	no	—
216	C₃₁×#120	—	2	2	no	—
217	C₃₁×#120	—	2	2	no	—
218	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₃₁	—	2	2	no	—
221	C₄×D₄×C₃₁	—	2	2	no	—
222	C₄×D₄×C₃₁	—	2	2	no	—
223	C₄×D₄×C₃₁	—	2	2	no	—
224	C₄×D₄×C₃₁	—	2	2	no	—
225	C₄×D₄×C₃₁	—	2	1	no	—
226	C₄×D₄×C₃₁	—	2	1	no	—
227	C₄×D₄×C₃₁	—	2	1	no	—
228	C₄×D₄×C₃₁	—	2	1	no	—
229	C₄×D₄×C₃₁	C₂³	1	2	yes	—
230	C₄×D₄×C₃₁	C₂³	1	2	yes	—
231	C₄×D₄×C₃₁	C₂³	1	2	yes	—
232	C₄×D₄×C₃₁	C₂³	1	2	yes	—
233	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₃₁	C₂³	1	2	yes	—
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₃₁	C₂³	1	2	yes	—
239	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₃₁×#117	—	2	1	no	—
241	C₃₁×#117	C₂³	1	2	yes	—
242	C₃₁×#117	C₂³	1	2	yes	—
243	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
244	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
246	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
247	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
248	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
249	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
250	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
251	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
252	C₃₁×#107	C₂³	1	2	yes	—
253	C₃₁×#107	C₂³	1	2	yes	—
254	C₃₁×#106	C₂³	1	2	yes	—
255	C₃₁×#106	C₂³	1	2	yes	—
256	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
258	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
260	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
261	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#102	C₂³	1	2	yes	—
267	C₃₁×#102	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×#102	C₂³	1	2	yes	—
277	C₃₁×#102	C₂³	1	2	yes	—
278	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
279	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₃₁×#97	C₂³	1	2	yes	—
282	C₃₁×#97	C₂³	1	2	yes	—
283	C₄×C₈×C₃₁	C₂³	1	2	yes	—
284	C₂⁴×C₃₁	—	2	1	no	—
285	C₂⁴×C₃₁	—	2	2	no	—
286	C₂⁴×C₃₁	—	2	1	no	—
287	C₂⁴×C₃₁	—	2	2	no	—
288	#41×C₃₁	—	4	2	no	—
289	#41×C₃₁	—	4	2	no	—
290	#41×C₃₁	—	8	2	no	—
291	#41×C₃₁	—	8	2	no	—
292	#41×C₃₁	—	8	2	no	—
293	C₂×Q₈×C₃₁	—	2	1	no	—
294	C₂×Q₈×C₃₁	—	2	1	no	—
295	C₂×Q₈×C₃₁	—	2	1	no	—
296	C₂×Q₈×C₃₁	—	4	1	no	—
297	C₂×Q₈×C₃₁	—	4	1	no	—
298	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
299	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
300	C₂×D₄×C₃₁	—	2	2	no	—
301	C₂×D₄×C₃₁	—	2	4	no	—
302	C₂×D₄×C₃₁	—	2	2	no	—
303	C₂×D₄×C₃₁	—	2	2	no	—
304	C₂×D₄×C₃₁	—	2	2	no	—
305	C₂×D₄×C₃₁	—	2	2	no	—
306	C₂×D₄×C₃₁	—	2	2	no	—
307	C₂×D₄×C₃₁	—	2	2	no	—
308	C₂×D₄×C₃₁	—	2	2	no	—
309	C₂×D₄×C₃₁	—	2	1	no	—
310	C₂×D₄×C₃₁	—	2	1	no	—
311	C₂×D₄×C₃₁	—	2	2	no	—
312	C₂×D₄×C₃₁	—	2	1	no	—
313	C₂×D₄×C₃₁	—	2	2	no	—
314	C₂×D₄×C₃₁	—	2	1	no	—
315	C₂×D₄×C₃₁	—	2	1	no	—
316	C₂×D₄×C₃₁	—	2	1	no	—
317	C₂×D₄×C₃₁	—	2	2	no	—
318	C₂×D₄×C₃₁	—	2	2	no	—
319	C₂×D₄×C₃₁	—	2	2	no	—
320	C₂×D₄×C₃₁	—	4	1	no	—
321	C₂×D₄×C₃₁	—	4	2	no	—
322	C₂×D₄×C₃₁	—	4	1	no	—
323	C₂×D₄×C₃₁	—	4	2	no	—
324	C₂×D₄×C₃₁	—	4	1	no	—
325	C₂×D₄×C₃₁	—	4	2	no	—
326	C₂×D₄×C₃₁	—	8	2	no	—
327	C₂×D₄×C₃₁	—	8	4	no	—
328	C₂×D₄×C₃₁	—	8	4	no	—
329	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
330	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
331	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
332	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
333	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
334	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₃₁	—	2	1	no	—
337	C₂²×C₄×C₃₁	—	2	1	no	—
338	C₂²×C₄×C₃₁	—	2	1	no	—
339	C₂²×C₄×C₃₁	—	2	1	no	—
340	C₂²×C₄×C₃₁	—	2	1	no	—
341	C₂²×C₄×C₃₁	—	2	2	no	—
342	C₂²×C₄×C₃₁	—	2	2	no	—
343	C₂²×C₄×C₃₁	—	2	2	no	—
344	C₂²×C₄×C₃₁	—	2	2	no	—
345	C₂²×C₄×C₃₁	—	2	2	no	—
346	C₂²×C₄×C₃₁	—	2	1	no	—
347	C₂²×C₄×C₃₁	—	2	2	no	—
348	C₂²×C₄×C₃₁	—	8	2	no	—
349	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
353	SD₁₆×C₃₁	—	2	4	no	—
354	SD₁₆×C₃₁	—	4	2	no	—
355	SD₁₆×C₃₁	—	4	2	no	—
356	SD₁₆×C₃₁	—	4	2	no	—
357	D₈×C₃₁	—	2	4	no	—
358	D₈×C₃₁	—	2	4	no	—
359	D₈×C₃₁	—	4	2	no	—
360	D₈×C₃₁	—	4	2	no	—
361	D₈×C₃₁	—	4	2	no	—
362	D₈×C₃₁	—	4	2	no	—
363	D₈×C₃₁	—	4	2	no	—
364	D₈×C₃₁	—	4	2	no	—
365	M₁₆×C₃₁	—	4	2	no	—
366	C₂×C₈×C₃₁	—	4	1	no	—
367	C₂×C₈×C₃₁	—	4	2	no	—
368	C₂×C₈×C₃₁	—	4	1	no	—
369	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
370	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
371	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
372	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
373	C₄⋊C₄×C₃₁	—	2	1	no	—
374	C₄⋊C₄×C₃₁	—	2	2	no	—
375	C₄⋊C₄×C₃₁	—	2	1	no	—
376	C₄⋊C₄×C₃₁	—	2	2	no	—
377	C₄⋊C₄×C₃₁	—	2	2	no	—
378	C₄⋊C₄×C₃₁	—	2	1	no	—
379	C₄⋊C₄×C₃₁	—	2	2	no	—
380	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
382	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
383	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
384	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
385	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
386	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
387	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
389	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
390	C₂²⋊C₄×C₃₁	—	2	2	no	—
391	C₂²⋊C₄×C₃₁	—	2	2	no	—
392	C₂²⋊C₄×C₃₁	—	2	1	no	—
393	C₂²⋊C₄×C₃₁	—	2	2	no	—
394	C₂²⋊C₄×C₃₁	—	2	2	no	—
395	C₂²⋊C₄×C₃₁	—	2	1	no	—
396	C₂²⋊C₄×C₃₁	—	2	2	no	—
397	C₂²⋊C₄×C₃₁	—	2	1	no	—
398	C₂²⋊C₄×C₃₁	—	2	2	no	—
399	C₂²⋊C₄×C₃₁	—	2	1	no	—
400	C₂²⋊C₄×C₃₁	—	2	2	no	—
401	C₂²⋊C₄×C₃₁	—	2	2	no	—
402	C₂²⋊C₄×C₃₁	—	2	2	no	—
403	C₂²⋊C₄×C₃₁	—	2	2	no	—
404	C₂²⋊C₄×C₃₁	—	2	2	no	—
405	C₂²⋊C₄×C₃₁	—	2	2	no	—
406	C₂²⋊C₄×C₃₁	—	2	2	no	—
407	C₂²⋊C₄×C₃₁	—	2	2	no	—
408	C₂²⋊C₄×C₃₁	—	2	2	no	—
409	C₂²⋊C₄×C₃₁	—	2	2	no	—
410	C₂²⋊C₄×C₃₁	—	2	2	no	—
411	C₂²⋊C₄×C₃₁	—	2	2	no	—
412	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
413	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
414	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
415	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
416	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
417	C₄²×C₃₁	—	2	2	no	—
418	C₄²×C₃₁	—	2	2	no	—
419	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
420	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
421	C₄²×C₃₁	C₂⁴	1	2	yes	—
422	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
423	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
424	#62015	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
425	C₂³×C₃₁	—	2	1	no	—
426	C₂³×C₃₁	—	2	2	no	—
427	C₂³×C₃₁	—	2	1	no	—
428	C₂³×C₃₁	—	2	2	no	—
429	C₂³×C₃₁	—	2	2	no	—
430	C₂³×C₃₁	—	4	2	no	—
431	C₂³×C₃₁	—	4	4	no	—
432	C₂³×C₃₁	—	4	2	no	—
433	C₂³×C₃₁	—	4	2	no	—
434	C₂³×C₃₁	—	8	1	no	—
435	C₂³×C₃₁	—	8	1	no	—
436	C₂³×C₃₁	—	8	2	no	—
437	C₂³×C₃₁	—	8	2	no	—
438	C₂³×C₃₁	—	8	2	no	—
439	C₂³×C₃₁	—	8	2	no	—
440	C₂³×C₃₁	—	8	1	no	—
441	C₂³×C₃₁	—	8	2	no	—
442	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
443	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
444	Q₈×C₃₁	—	2	2	no	—
445	Q₈×C₃₁	—	2	2	no	—
446	Q₈×C₃₁	—	4	1	no	—
447	Q₈×C₃₁	—	8	1	no	—
448	Q₈×C₃₁	—	8	1	no	—
449	Q₈×C₃₁	—	8	1	no	—
450	D₄×C₃₁	—	2	4	no	—
451	D₄×C₃₁	—	2	2	no	—
452	D₄×C₃₁	—	2	2	no	—
453	D₄×C₃₁	—	2	2	no	—
454	D₄×C₃₁	—	2	1	no	—
455	D₄×C₃₁	—	2	1	no	—
456	D₄×C₃₁	—	2	1	no	—
457	D₄×C₃₁	—	2	2	no	—
458	D₄×C₃₁	—	2	2	no	—
459	D₄×C₃₁	—	2	2	no	—
460	D₄×C₃₁	—	4	1	no	—
461	D₄×C₃₁	—	4	4	no	—
462	D₄×C₃₁	—	4	2	no	—
463	D₄×C₃₁	—	4	2	no	—
464	D₄×C₃₁	—	4	4	no	—
465	D₄×C₃₁	—	4	4	no	—
466	D₄×C₃₁	—	8	1	no	—
467	D₄×C₃₁	—	8	2	no	—
468	D₄×C₃₁	—	8	2	no	—
469	D₄×C₃₁	—	8	1	no	—
470	D₄×C₃₁	—	8	2	no	—
471	D₄×C₃₁	—	8	2	no	—
472	D₄×C₃₁	—	8	2	no	—
473	D₄×C₃₁	—	8	1	no	—
474	D₄×C₃₁	—	8	1	no	—
475	D₄×C₃₁	—	8	2	no	—
476	D₄×C₃₁	—	8	2	no	—
477	D₄×C₃₁	—	8	2	no	—
478	D₄×C₃₁	—	8	2	no	—
479	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
480	C₂×C₄×C₃₁	—	2	2	no	—
481	C₂×C₄×C₃₁	—	2	1	no	—
482	C₂×C₄×C₃₁	—	2	2	no	—
483	C₂×C₄×C₃₁	—	2	1	no	—
484	C₂×C₄×C₃₁	—	2	2	no	—
485	C₂×C₄×C₃₁	—	2	1	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	1	no	—
490	C₂×C₄×C₃₁	—	4	1	no	—
491	C₂×C₄×C₃₁	—	4	2	no	—
492	C₂×C₄×C₃₁	—	4	2	no	—
493	C₂×C₄×C₃₁	—	8	1	no	—
494	C₂×C₄×C₃₁	—	8	1	no	—
495	C₂×C₄×C₃₁	—	8	2	no	—
496	C₂×C₄×C₃₁	—	8	2	no	—
497	C₂×C₄×C₃₁	—	8	2	no	—
498	C₂×C₄×C₃₁	—	8	2	no	—
499	C₂×C₄×C₃₁	—	8	2	no	—
500	C₂×C₄×C₃₁	—	8	2	no	—
501	C₂×C₄×C₃₁	—	8	1	no	—
502	C₂×C₄×C₃₁	—	8	1	no	—
503	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
512	C₈×C₃₁	—	2	2	no	—
513	C₈×C₃₁	—	2	2	no	—
514	C₈×C₃₁	—	2	2	no	—
515	C₈×C₃₁	—	2	2	no	—
516	#3558	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#3519	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#3399	C₂×C₃₁	1	2	yes	complemented
519	#3370	C₂×C₃₁	1	2	yes	complemented
520	#3319	C₂×C₃₁	1	2	yes	complemented
521	#3318	C₂×C₃₁	1	2	yes	complemented
522	#3301	C₂×C₃₁	1	2	yes	complemented
523	D₄×D₈	C₂×C₃₁	1	2	yes	complemented
524	#3265	C₂×C₃₁	1	2	yes	complemented
525	#3264	C₂×C₃₁	1	2	yes	complemented
526	#3257	C₂×C₃₁	1	2	yes	complemented
527	#3245	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3220	C₂×C₃₁	1	2	yes	complemented
529	#3213	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3118	C₂×C₃₁	1	2	yes	complemented
531	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3041	C₂×C₃₁	1	2	yes	complemented
533	C₂×#463	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#2992	C₂×C₃₁	1	1	yes	characteristic, complemented
535	C₂²×C₃₁	—	2	1	no	—
536	C₂²×C₃₁	—	2	1	no	—
537	C₂²×C₃₁	—	2	2	no	—
538	C₂²×C₃₁	—	2	2	no	—
539	C₂²×C₃₁	—	2	2	no	—
540	C₂²×C₃₁	—	2	2	no	—
541	C₂²×C₃₁	—	4	1	no	—
542	C₂²×C₃₁	—	4	1	no	—
543	C₂²×C₃₁	—	4	1	no	—
544	C₂²×C₃₁	—	4	2	no	—
545	C₂²×C₃₁	—	4	2	no	—
546	C₂²×C₃₁	—	4	2	no	—
547	C₂²×C₃₁	—	4	2	no	—
548	C₂²×C₃₁	—	4	1	no	—
549	C₂²×C₃₁	—	4	2	no	—
550	C₂²×C₃₁	—	4	2	no	—
551	C₂²×C₃₁	—	4	2	no	—
552	C₂²×C₃₁	—	4	2	no	—
553	C₂²×C₃₁	—	4	2	no	—
554	C₂²×C₃₁	—	4	1	no	—
555	C₂²×C₃₁	—	8	4	no	—
556	C₂²×C₃₁	—	16	2	no	—
557	C₂²×C₃₁	—	16	4	no	—
558	C₂²×C₃₁	—	16	4	no	—
559	C₂²×C₃₁	#576	1	2	yes	—
560	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
561	C₄×C₃₁	—	2	1	no	—
562	C₄×C₃₁	—	2	1	no	—
563	C₄×C₃₁	—	2	2	no	—
564	C₄×C₃₁	—	2	2	no	—
565	C₄×C₃₁	—	2	1	no	—
566	C₄×C₃₁	—	2	1	no	—
567	C₄×C₃₁	—	2	1	no	—
568	C₄×C₃₁	—	2	2	no	—
569	C₄×C₃₁	—	4	1	no	—
570	C₄×C₃₁	—	4	1	no	—
571	C₄×C₃₁	—	4	2	no	—
572	C₄×C₃₁	—	4	2	no	—
573	C₄×C₃₁	—	4	2	no	—
574	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
575	C₄×C₃₁	#585	1	1	yes	characteristic
576	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
577	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
578	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
579	C₂²×D₈	C₂²×C₃₁	1	2	yes	complemented
580	#562	—	2	1	no	—
581	H(3,𝔽₄)	—	2	1	no	—
582	#559	C₂²×C₃₁	1	2	yes	complemented
583	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
584	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
585	#553	—	2	1	no	—
586	#553	C₂²×C₃₁	1	2	yes	complemented
587	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
588	#548	C₂²×C₃₁	1	2	yes	complemented
589	#546	—	2	1	no	—
590	#546	—	2	2	no	—
591	#546	—	2	2	no	—
592	#546	C₂²×C₃₁	1	2	yes	complemented
593	D₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
594	D₄²	C₂²×C₃₁	1	2	yes	complemented
595	D₄²	C₂²×C₃₁	1	2	yes	complemented
596	#542	C₂²×C₃₁	1	2	yes	complemented
597	#540	C₂²×C₃₁	1	2	yes	complemented
598	#538	—	2	2	no	—
599	#538	—	2	2	no	—
600	#538	—	2	1	no	—
601	#535	C₂²×C₃₁	1	2	yes	complemented
602	#534	—	2	1	no	—
603	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
604	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
605	#529	C₂²×C₃₁	1	1	yes	characteristic
606	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
607	#525	—	2	1	no	—
608	C₂×#121	—	2	1	no	—
609	#518	C₂²×C₃₁	1	2	yes	complemented
610	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
611	#496	C₂²×C₃₁	1	2	yes	complemented
612	#496	C₂²×C₃₁	1	2	yes	complemented
613	#493	C₂²×C₃₁	1	2	yes	complemented
614	#490	C₂²×C₃₁	1	2	yes	complemented
615	#489	C₂²×C₃₁	1	2	yes	complemented
616	#488	C₂²×C₃₁	1	2	yes	complemented
617	#485	C₂²×C₃₁	1	2	yes	complemented
618	#482	C₂²×C₃₁	1	2	yes	complemented
619	#481	C₂²×C₃₁	1	2	yes	complemented
620	#479	C₂²×C₃₁	1	2	yes	complemented
621	#478	C₂²×C₃₁	1	2	yes	complemented
622	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
623	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
624	#474	C₂²×C₃₁	1	2	yes	complemented
625	#474	C₂²×C₃₁	1	2	yes	complemented
626	#469	C₂²×C₃₁	1	2	yes	complemented
627	#468	C₂²×C₃₁	1	2	yes	complemented
628	#466	C₂²×C₃₁	1	2	yes	complemented
629	#466	C₂²×C₃₁	1	2	yes	complemented
630	#466	C₂²×C₃₁	1	2	yes	complemented
631	#465	C₂²×C₃₁	1	2	yes	complemented
632	#463	C₂²×C₃₁	1	2	yes	complemented
633	#463	C₂²×C₃₁	1	2	yes	complemented
634	#463	C₂²×C₃₁	1	2	yes	complemented
635	#463	C₂²×C₃₁	1	2	yes	complemented
636	#463	C₂²×C₃₁	1	2	yes	complemented
637	#463	C₂²×C₃₁	1	2	yes	complemented
638	#463	C₂²×C₃₁	1	2	yes	complemented
639	#463	C₂²×C₃₁	1	2	yes	complemented
640	#460	C₂²×C₃₁	1	2	yes	complemented
641	#459	C₂²×C₃₁	1	2	yes	—
642	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
643	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#459	C₂²×C₃₁	1	2	yes	complemented
645	#459	C₂²×C₃₁	1	2	yes	complemented
646	#459	C₂²×C₃₁	1	2	yes	complemented
647	#459	C₂²×C₃₁	1	2	yes	complemented
648	#450	C₂²×C₃₁	1	2	yes	complemented
649	#449	C₂²×C₃₁	1	2	yes	complemented
650	#449	C₂²×C₃₁	1	2	yes	complemented
651	#448	C₂²×C₃₁	1	2	yes	complemented
652	#447	C₂²×C₃₁	1	2	yes	—
653	#447	C₂²×C₃₁	1	2	yes	complemented
654	#447	C₂²×C₃₁	1	2	yes	complemented
655	#447	C₂²×C₃₁	1	2	yes	complemented
656	#447	C₂²×C₃₁	1	2	yes	complemented
657	#446	C₂²×C₃₁	1	2	yes	complemented
658	#442	C₂²×C₃₁	1	2	yes	complemented
659	#442	C₂²×C₃₁	1	2	yes	complemented
660	#442	C₂²×C₃₁	1	2	yes	complemented
661	#440	C₂²×C₃₁	1	2	yes	complemented
662	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
663	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
664	#435	C₂²×C₃₁	1	2	yes	complemented
665	#435	C₂²×C₃₁	1	2	yes	complemented
666	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
667	#433	C₂²×C₃₁	1	2	yes	complemented
668	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	#424	C₂²×C₃₁	1	2	yes	complemented
670	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
671	#418	C₂²×C₃₁	1	2	yes	complemented
672	#416	C₂²×C₃₁	1	2	yes	complemented
673	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
674	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic, complemented
675	C₂×C₃₁	—	2	2	no	—
676	C₂×C₃₁	—	4	2	no	—
677	C₂×C₃₁	—	4	2	no	—
678	C₂×C₃₁	—	8	1	no	—
679	C₂×C₃₁	—	8	2	no	—
680	C₂×C₃₁	—	8	2	no	—
681	C₂×C₃₁	—	8	2	no	—
682	C₂×C₃₁	#3488	1	1	yes	characteristic
683	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
684	C₂×C₃₁	#3585	1	1	yes	characteristic
685	C₂×#41	—	2	1	no	—
686	C₂×#41	—	2	1	no	—
687	C₂×#41	—	2	1	no	—
688	C₂×#41	C₂³×C₃₁	1	2	yes	—
689	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
690	C₂²×D₄	—	2	1	no	—
691	C₂²×D₄	—	2	2	no	—
692	C₂²×D₄	—	2	2	no	—
693	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
694	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
695	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
696	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
697	C₂³×C₄	—	2	1	no	—
698	AGL(1,ℤ/8)	—	4	4	no	—
699	C₂×SD₁₆	—	4	2	no	—
700	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
701	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
702	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
703	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
704	C₂×D₈	—	4	2	no	—
705	C₂×D₈	—	4	4	no	—
706	C₂×D₈	C₂³×C₃₁	1	2	yes	—
707	C₂×D₈	C₂³×C₃₁	1	2	yes	—
708	C₂×D₈	C₂³×C₃₁	1	2	yes	—
709	C₂×D₈	C₂³×C₃₁	1	2	yes	—
710	C₂×D₈	C₂³×C₃₁	1	2	yes	—
711	C₂×D₈	C₂³×C₃₁	1	2	yes	—
712	C₂×D₈	C₂³×C₃₁	1	2	yes	—
713	C₂×D₈	C₂³×C₃₁	1	2	yes	—
714	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
715	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
716	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
717	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
718	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
719	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
720	#127	C₂³×C₃₁	1	1	yes	characteristic
721	#127	C₂³×C₃₁	1	1	yes	characteristic
722	#127	C₂³×C₃₁	1	2	yes	—
723	#127	C₂³×C₃₁	1	2	yes	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	D₄×C₃₁	1	2	yes	—
727	#125	D₄×C₃₁	1	1	yes	characteristic
728	#125	C₂³×C₃₁	1	2	yes	—
729	#124	—	2	2	no	—
730	#124	—	2	2	no	—
731	#124	—	2	2	no	—
732	#124	—	2	2	no	—
733	#124	—	2	1	no	—
734	#124	—	2	1	no	—
735	#124	—	2	1	no	—
736	#124	—	2	1	no	—
737	#124	D₄×C₃₁	1	1	yes	characteristic
738	#124	C₂³×C₃₁	1	2	yes	—
739	#124	C₂³×C₃₁	1	2	yes	—
740	#124	C₂³×C₃₁	1	2	yes	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	D₄×C₃₁	1	2	yes	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
754	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
755	#121	—	2	2	no	—
756	#121	—	2	1	no	—
757	#121	—	2	2	no	—
758	#121	—	2	1	no	—
759	#121	—	2	1	no	—
760	#121	—	2	1	no	—
761	#121	—	2	1	no	—
762	#121	—	2	2	no	—
763	#121	—	2	2	no	—
764	#121	—	2	2	no	—
765	#121	—	2	2	no	—
766	#121	—	2	2	no	—
767	#121	—	2	2	no	—
768	#121	—	2	2	no	—
769	#121	—	2	2	no	—
770	#121	D₄×C₃₁	1	1	yes	characteristic
771	#121	C₂³×C₃₁	1	2	yes	—
772	#121	C₂³×C₃₁	1	2	yes	—
773	#121	C₂³×C₃₁	1	2	yes	—
774	#121	C₂³×C₃₁	1	2	yes	—
775	#121	C₂³×C₃₁	1	2	yes	—
776	#120	—	2	2	no	—
777	#120	—	2	2	no	—
778	#120	—	2	2	no	—
779	#120	—	2	2	no	—
780	#120	—	2	2	no	—
781	#120	—	2	2	no	—
782	#120	—	2	2	no	—
783	#120	—	2	2	no	—
784	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
785	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
799	C₄×D₄	C₂³×C₃₁	1	2	yes	—
800	C₄×D₄	C₂³×C₃₁	1	2	yes	—
801	C₄×D₄	C₂³×C₃₁	1	2	yes	—
802	C₄×D₄	C₂³×C₃₁	1	2	yes	—
803	C₄×D₄	C₂³×C₃₁	1	2	yes	—
804	C₄×D₄	C₂³×C₃₁	1	2	yes	—
805	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
806	#117	—	2	1	no	—
807	#117	C₂³×C₃₁	1	2	yes	—
808	#117	C₂³×C₃₁	1	2	yes	—
809	C₂×C₄⋊C₄	—	2	1	no	—
810	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
811	C₂×C₂²⋊C₄	—	2	1	no	—
812	C₂×C₂²⋊C₄	—	2	1	no	—
813	C₂×C₂²⋊C₄	—	2	1	no	—
814	C₂×C₂²⋊C₄	—	2	2	no	—
815	C₂×C₂²⋊C₄	—	2	2	no	—
816	C₂×C₂²⋊C₄	—	2	2	no	—
817	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
818	#107	C₂³×C₃₁	1	2	yes	—
819	#107	C₂³×C₃₁	1	2	yes	—
820	#106	C₂³×C₃₁	1	2	yes	—
821	#106	C₂³×C₃₁	1	2	yes	—
822	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
823	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
824	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
825	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
826	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
827	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
828	#103	C₂³×C₃₁	1	2	yes	—
829	#103	C₂³×C₃₁	1	2	yes	—
830	#103	C₂³×C₃₁	1	2	yes	—
831	#103	C₂³×C₃₁	1	2	yes	—
832	#102	C₂³×C₃₁	1	2	yes	—
833	#102	C₂³×C₃₁	1	2	yes	—
834	#102	C₂³×C₃₁	1	2	yes	—
835	#102	C₂³×C₃₁	1	2	yes	—
836	#102	C₂³×C₃₁	1	2	yes	—
837	#102	C₂³×C₃₁	1	2	yes	—
838	#102	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	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
845	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
846	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
847	#97	C₂³×C₃₁	1	2	yes	—
848	#97	C₂³×C₃₁	1	2	yes	—
849	C₄×C₈	C₂³×C₃₁	1	2	yes	—
850	C₃₁	#62015	1	1	yes	characteristic, direct product factor, Sylow
851	C₂⁴	—	2	1	no	—
852	C₂⁴	—	2	2	no	—
853	C₂⁴	—	2	1	no	—
854	C₂⁴	—	2	2	no	—
855	#41	—	4	2	no	—
856	#41	—	4	2	no	—
857	#41	—	8	2	no	—
858	#41	—	8	2	no	—
859	#41	—	8	2	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	1	no	—
862	C₂×Q₈	—	2	1	no	—
863	C₂×Q₈	—	4	1	no	—
864	C₂×Q₈	—	4	1	no	—
865	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
866	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
867	C₂×D₄	—	2	2	no	—
868	C₂×D₄	—	2	4	no	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	2	2	no	—
871	C₂×D₄	—	2	2	no	—
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	2	no	—
874	C₂×D₄	—	2	2	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	2	1	no	—
877	C₂×D₄	—	2	1	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	1	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	1	no	—
882	C₂×D₄	—	2	1	no	—
883	C₂×D₄	—	2	1	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	4	1	no	—
888	C₂×D₄	—	4	2	no	—
889	C₂×D₄	—	4	1	no	—
890	C₂×D₄	—	4	2	no	—
891	C₂×D₄	—	4	1	no	—
892	C₂×D₄	—	4	2	no	—
893	C₂×D₄	—	8	2	no	—
894	C₂×D₄	—	8	4	no	—
895	C₂×D₄	—	8	4	no	—
896	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
897	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
898	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
899	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
900	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
901	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
902	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	8	2	no	—
916	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
917	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
920	SD₁₆	—	2	4	no	—
921	SD₁₆	—	4	2	no	—
922	SD₁₆	—	4	2	no	—
923	SD₁₆	—	4	2	no	—
924	D₈	—	2	4	no	—
925	D₈	—	2	4	no	—
926	D₈	—	4	2	no	—
927	D₈	—	4	2	no	—
928	D₈	—	4	2	no	—
929	D₈	—	4	2	no	—
930	D₈	—	4	2	no	—
931	D₈	—	4	2	no	—
932	M₁₆	—	4	2	no	—
933	C₂×C₈	—	4	1	no	—
934	C₂×C₈	—	4	2	no	—
935	C₂×C₈	—	4	1	no	—
936	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
937	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
938	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
939	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
948	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
949	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
950	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
951	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
952	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
953	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
954	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
955	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
956	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
980	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
981	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
982	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
983	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
984	C₄²	—	2	2	no	—
985	C₄²	—	2	2	no	—
986	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
987	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
988	C₄²	C₂⁴×C₃₁	1	2	yes	—
989	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
990	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
991	C₂³	—	2	1	no	—
992	C₂³	—	2	2	no	—
993	C₂³	—	2	2	no	—
994	C₂³	—	2	2	no	—
995	C₂³	—	2	1	no	—
996	C₂³	—	4	2	no	—
997	C₂³	—	4	4	no	—
998	C₂³	—	4	2	no	—
999	C₂³	—	4	2	no	—
1000	C₂³	—	8	1	no	—
1001	C₂³	—	8	1	no	—
1002	C₂³	—	8	2	no	—
1003	C₂³	—	8	2	no	—
1004	C₂³	—	8	2	no	—
1005	C₂³	—	8	2	no	—
1006	C₂³	—	8	1	no	—
1007	C₂³	—	8	2	no	—
1008	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1009	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1010	Q₈	—	2	2	no	—
1011	Q₈	—	2	2	no	—
1012	Q₈	—	4	1	no	—
1013	Q₈	—	8	1	no	—
1014	Q₈	—	8	1	no	—
1015	Q₈	—	8	1	no	—
1016	D₄	—	2	4	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	2	2	no	—
1019	D₄	—	2	2	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	2	1	no	—
1022	D₄	—	2	1	no	—
1023	D₄	—	2	2	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	2	2	no	—
1026	D₄	—	4	1	no	—
1027	D₄	—	4	4	no	—
1028	D₄	—	4	2	no	—
1029	D₄	—	4	2	no	—
1030	D₄	—	4	4	no	—
1031	D₄	—	4	4	no	—
1032	D₄	—	8	1	no	—
1033	D₄	—	8	2	no	—
1034	D₄	—	8	2	no	—
1035	D₄	—	8	1	no	—
1036	D₄	—	8	2	no	—
1037	D₄	—	8	2	no	—
1038	D₄	—	8	1	no	—
1039	D₄	—	8	1	no	—
1040	D₄	—	8	2	no	—
1041	D₄	—	8	2	no	—
1042	D₄	—	8	2	no	—
1043	D₄	—	8	2	no	—
1044	D₄	—	8	2	no	—
1045	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	4	1	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	8	1	no	—
1060	C₂×C₄	—	8	1	no	—
1061	C₂×C₄	—	8	2	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	—	8	2	no	—
1067	C₂×C₄	—	8	1	no	—
1068	C₂×C₄	—	8	1	no	—
1069	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1070	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1071	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1072	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1073	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1074	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1076	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1077	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1078	C₈	—	2	2	no	—
1079	C₈	—	2	2	no	—
1080	C₈	—	2	2	no	—
1081	C₈	—	2	2	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	2	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	2	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	8	4	no	—
1103	C₂²	—	16	2	no	—
1104	C₂²	—	16	4	no	—
1105	C₂²	—	16	4	no	—
1106	C₂²	C₃₁×#576	1	2	yes	—
1107	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1108	C₄	—	2	2	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	2	1	no	—
1111	C₄	—	2	1	no	—
1112	C₄	—	2	2	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	1	no	—
1115	C₄	—	2	2	no	—
1116	C₄	—	4	2	no	—
1117	C₄	—	4	2	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	1	no	—
1121	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1122	C₄	C₃₁×#585	1	1	yes	characteristic
1123	C₂	—	2	2	no	—
1124	C₂	—	4	2	no	—
1125	C₂	—	4	2	no	—
1126	C₂	—	8	1	no	—
1127	C₂	—	8	2	no	—
1128	C₂	—	8	2	no	—
1129	C₂	—	8	2	no	—
1130	C₂	C₃₁×#3488	1	1	yes	characteristic
1131	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1132	C₂	C₃₁×#3585	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3558	C₂	semidirect
2. C₃₁×#3519	C₂	semidirect
3. C₃₁×#3399	C₂	semidirect
4. C₃₁×#3370	C₂	semidirect
5. C₃₁×#3319	C₂	semidirect
6. C₃₁×#3318	C₂	semidirect
7. C₃₁×#3301	C₂	semidirect
8. D₄×D₈×C₃₁	C₂	semidirect
9. C₃₁×#3265	C₂	semidirect
10. C₃₁×#3264	C₂	semidirect
11. C₃₁×#3257	C₂	semidirect
12. C₃₁×#3245	C₂	semidirect
13. C₃₁×#3220	C₂	semidirect
14. C₃₁×#3213	C₂	semidirect
15. C₃₁×#3118	C₂	semidirect
16. C₃₁×#3109	C₂	semidirect
17. C₃₁×#3041	C₂	semidirect
18. C₂×C₃₁×#463	C₂	semidirect
19. C₃₁×#2992	C₂	semidirect
20. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂²×SD₁₆×C₃₁	C₂²	semidirect
23. C₂²×D₈×C₃₁	C₂²	semidirect
26. C₃₁×#559	C₂²	semidirect
27. C₃₁×#555	C₂²	semidirect
28. C₃₁×#554	C₂²	semidirect
30. C₃₁×#553	C₂²	semidirect
31. C₃₁×#550	C₂²	semidirect
32. C₃₁×#548	C₂²	semidirect
36. C₃₁×#546	C₂²	semidirect
37. D₄²×C₃₁	C₂²	semidirect
38. D₄²×C₃₁	C₂²	semidirect
39. D₄²×C₃₁	C₂²	semidirect
40. C₃₁×#542	C₂²	semidirect
41. C₃₁×#540	C₂²	semidirect
45. C₃₁×#535	C₂²	semidirect
47. C₃₁×#532	C₂²	semidirect
48. C₃₁×#532	C₂²	semidirect
50. C₂×C₃₁×#124	C₂²	semidirect
53. C₃₁×#518	C₂²	semidirect
54. C₂×C₄×D₄×C₃₁	C₂²	semidirect
55. C₃₁×#496	C₂²	semidirect
56. C₃₁×#496	C₂²	semidirect
57. C₃₁×#493	C₂²	semidirect
58. C₃₁×#490	C₂²	semidirect
59. C₃₁×#489	C₂²	semidirect
60. C₃₁×#488	C₂²	semidirect
61. C₃₁×#485	C₂²	semidirect
62. C₃₁×#482	C₂²	semidirect
63. C₃₁×#481	C₂²	semidirect
64. C₃₁×#479	C₂²	semidirect
65. C₃₁×#478	C₂²	semidirect
66. C₃₁×#476	C₂²	semidirect
67. C₃₁×#476	C₂²	semidirect
68. C₃₁×#474	C₂²	semidirect
69. C₃₁×#474	C₂²	semidirect
70. C₃₁×#469	C₂²	semidirect
71. C₃₁×#468	C₂²	semidirect
72. C₃₁×#466	C₂²	semidirect
73. C₃₁×#466	C₂²	semidirect
74. C₃₁×#466	C₂²	semidirect
75. C₃₁×#465	C₂²	semidirect
76. C₃₁×#463	C₂²	semidirect
77. C₃₁×#463	C₂²	semidirect
78. C₃₁×#463	C₂²	semidirect
79. C₃₁×#463	C₂²	semidirect
80. C₃₁×#463	C₂²	semidirect
81. C₃₁×#463	C₂²	semidirect
82. C₃₁×#463	C₂²	semidirect
83. C₃₁×#463	C₂²	semidirect
84. C₃₁×#460	C₂²	semidirect
86. C₃₁×#459	C₂²	semidirect
87. C₃₁×#459	C₂²	semidirect
88. C₃₁×#459	C₂²	semidirect
89. C₃₁×#459	C₂²	semidirect
90. C₃₁×#459	C₂²	semidirect
91. C₃₁×#459	C₂²	semidirect
92. C₃₁×#450	C₂²	semidirect
93. C₃₁×#449	C₂²	semidirect
94. C₃₁×#449	C₂²	semidirect
95. C₃₁×#448	C₂²	semidirect
97. C₃₁×#447	C₂²	semidirect
98. C₃₁×#447	C₂²	semidirect
99. C₃₁×#447	C₂²	semidirect
100. C₃₁×#447	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₃₁×#442	C₂²	semidirect
103. C₃₁×#442	C₂²	semidirect
104. C₃₁×#442	C₂²	semidirect
105. C₃₁×#440	C₂²	semidirect
106. C₄×SD₁₆×C₃₁	C₂²	semidirect
107. C₄×D₈×C₃₁	C₂²	semidirect
108. C₃₁×#435	C₂²	semidirect
109. C₃₁×#435	C₂²	semidirect
110. C₈×D₄×C₃₁	C₂²	semidirect
111. C₃₁×#433	C₂²	semidirect
112. C₃₁×#432	C₂²	semidirect
113. C₃₁×#424	C₂²	semidirect
114. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
115. C₃₁×#418	C₂²	semidirect
116. C₃₁×#416	C₂²	semidirect
117. C₂×C₃₁×#103	C₂²	semidirect
118. C₂×C₃₁×#102	C₂²	semidirect
424. #62015	C₃₁	direct (N × H)
516. #3558	C₂×C₃₁	semidirect
517. #3519	C₂×C₃₁	semidirect
518. #3399	C₂×C₃₁	semidirect
519. #3370	C₂×C₃₁	semidirect
520. #3319	C₂×C₃₁	semidirect
521. #3318	C₂×C₃₁	semidirect
522. #3301	C₂×C₃₁	semidirect
523. D₄×D₈	C₂×C₃₁	semidirect
524. #3265	C₂×C₃₁	semidirect
525. #3264	C₂×C₃₁	semidirect
526. #3257	C₂×C₃₁	semidirect
527. #3245	C₂×C₃₁	semidirect
528. #3220	C₂×C₃₁	semidirect
529. #3213	C₂×C₃₁	semidirect
530. #3118	C₂×C₃₁	semidirect
531. #3109	C₂×C₃₁	semidirect
532. #3041	C₂×C₃₁	semidirect
533. C₂×#463	C₂×C₃₁	semidirect
534. #2992	C₂×C₃₁	semidirect
576. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
577. C₂²×SD₁₆	C₂²×C₃₁	semidirect
579. C₂²×D₈	C₂²×C₃₁	semidirect
582. #559	C₂²×C₃₁	semidirect
583. #555	C₂²×C₃₁	semidirect
584. #554	C₂²×C₃₁	semidirect
586. #553	C₂²×C₃₁	semidirect
587. #550	C₂²×C₃₁	semidirect
588. #548	C₂²×C₃₁	semidirect
592. #546	C₂²×C₃₁	semidirect
593. D₄²	C₂²×C₃₁	semidirect
594. D₄²	C₂²×C₃₁	semidirect
595. D₄²	C₂²×C₃₁	semidirect
596. #542	C₂²×C₃₁	semidirect
597. #540	C₂²×C₃₁	semidirect
601. #535	C₂²×C₃₁	semidirect
603. #532	C₂²×C₃₁	semidirect
604. #532	C₂²×C₃₁	semidirect
606. C₂×#124	C₂²×C₃₁	semidirect
609. #518	C₂²×C₃₁	semidirect
610. C₂×C₄×D₄	C₂²×C₃₁	semidirect
611. #496	C₂²×C₃₁	semidirect
612. #496	C₂²×C₃₁	semidirect
613. #493	C₂²×C₃₁	semidirect
614. #490	C₂²×C₃₁	semidirect
615. #489	C₂²×C₃₁	semidirect
616. #488	C₂²×C₃₁	semidirect
617. #485	C₂²×C₃₁	semidirect
618. #482	C₂²×C₃₁	semidirect
619. #481	C₂²×C₃₁	semidirect
620. #479	C₂²×C₃₁	semidirect
621. #478	C₂²×C₃₁	semidirect
622. #476	C₂²×C₃₁	semidirect
623. #476	C₂²×C₃₁	semidirect
624. #474	C₂²×C₃₁	semidirect
625. #474	C₂²×C₃₁	semidirect
626. #469	C₂²×C₃₁	semidirect
627. #468	C₂²×C₃₁	semidirect
628. #466	C₂²×C₃₁	semidirect
629. #466	C₂²×C₃₁	semidirect
630. #466	C₂²×C₃₁	semidirect
631. #465	C₂²×C₃₁	semidirect
632. #463	C₂²×C₃₁	semidirect
633. #463	C₂²×C₃₁	semidirect
634. #463	C₂²×C₃₁	semidirect
635. #463	C₂²×C₃₁	semidirect
636. #463	C₂²×C₃₁	semidirect
637. #463	C₂²×C₃₁	semidirect
638. #463	C₂²×C₃₁	semidirect
639. #463	C₂²×C₃₁	semidirect
640. #460	C₂²×C₃₁	semidirect
642. #459	C₂²×C₃₁	semidirect
643. #459	C₂²×C₃₁	semidirect
644. #459	C₂²×C₃₁	semidirect
645. #459	C₂²×C₃₁	semidirect
646. #459	C₂²×C₃₁	semidirect
647. #459	C₂²×C₃₁	semidirect
648. #450	C₂²×C₃₁	semidirect
649. #449	C₂²×C₃₁	semidirect
650. #449	C₂²×C₃₁	semidirect
651. #448	C₂²×C₃₁	semidirect
653. #447	C₂²×C₃₁	semidirect
654. #447	C₂²×C₃₁	semidirect
655. #447	C₂²×C₃₁	semidirect
656. #447	C₂²×C₃₁	semidirect
657. #446	C₂²×C₃₁	semidirect
658. #442	C₂²×C₃₁	semidirect
659. #442	C₂²×C₃₁	semidirect
660. #442	C₂²×C₃₁	semidirect
661. #440	C₂²×C₃₁	semidirect
662. C₄×SD₁₆	C₂²×C₃₁	semidirect
663. C₄×D₈	C₂²×C₃₁	semidirect
664. #435	C₂²×C₃₁	semidirect
665. #435	C₂²×C₃₁	semidirect
666. C₈×D₄	C₂²×C₃₁	semidirect
667. #433	C₂²×C₃₁	semidirect
668. #432	C₂²×C₃₁	semidirect
669. #424	C₂²×C₃₁	semidirect
670. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
671. #418	C₂²×C₃₁	semidirect
672. #416	C₂²×C₃₁	semidirect
673. C₂×#103	C₂²×C₃₁	semidirect
674. C₂×#102	C₂²×C₃₁	semidirect
850. C₃₁	#62015	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×#3558	2
C₃₁×#3519	2
C₃₁×#3399	2
C₃₁×#3370	2
C₃₁×#3319	2
C₃₁×#3318	2
C₃₁×#3301	2
D₄×D₈×C₃₁	2
C₃₁×#3265	2
C₃₁×#3264	2
C₃₁×#3257	2
C₃₁×#3245	2
C₃₁×#3220	2
C₃₁×#3213	2
C₃₁×#3118	2
C₃₁×#3109	2
C₃₁×#3041	2
C₂×C₃₁×#463	2
C₃₁×#2992	2
#62015	31

Subgroups — C31×#62015 #21518774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62015 #21518774