Subgroups — C₃₁×#61329 #21518088

Order 7936.

1896 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3375	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3373	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3368	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3366	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3365	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3362	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3361	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3358	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3136	C₂	1	2	yes	maximal, complemented
12	C₂×C₃₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3081	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3045	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2960	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2946	C₂	1	2	yes	maximal, complemented
19	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
22	C₃₁×#559	C₂²	1	2	yes	—
23	C₃₁×#559	C₂²	1	2	yes	—
24	Q₈²×C₃₁	C₂²	1	2	yes	complemented
25	C₃₁×#557	C₂²	1	2	yes	complemented
26	C₃₁×#554	—	2	2	no	—
27	C₃₁×#554	C₂²	1	2	yes	complemented
28	C₃₁×#550	C₂²	1	2	yes	—
29	C₃₁×#550	C₂²	1	2	yes	—
30	D₄×Q₈×C₃₁	—	2	2	no	—
31	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
32	C₃₁×#546	—	2	2	no	—
33	C₃₁×#546	—	2	2	no	—
34	C₃₁×#544	—	2	2	no	—
35	C₃₁×#544	C₂²	1	2	yes	—
36	C₃₁×#540	—	2	2	no	—
37	C₃₁×#535	C₂²	1	2	yes	—
38	C₃₁×#533	—	2	1	no	—
39	C₃₁×#533	C₂²	1	1	yes	characteristic
40	C₃₁×#532	—	2	1	no	—
41	C₃₁×#532	—	2	1	no	—
42	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
43	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
45	C₃₁×#520	C₂²	1	2	yes	—
46	C₃₁×#518	C₂²	1	2	yes	—
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
48	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
49	C₃₁×#490	C₂²	1	4	yes	complemented
50	C₃₁×#489	C₂²	1	4	yes	complemented
51	C₃₁×#488	C₂²	1	4	yes	complemented
52	C₃₁×#486	C₂²	1	2	yes	—
53	C₃₁×#486	C₂²	1	2	yes	—
54	C₃₁×#486	C₂²	1	2	yes	—
55	C₃₁×#486	C₂²	1	2	yes	—
56	C₃₁×#486	C₂²	1	4	yes	complemented
57	C₃₁×#478	C₂²	1	4	yes	complemented
58	C₃₁×#478	C₂²	1	4	yes	complemented
59	C₃₁×#477	C₂²	1	2	yes	complemented
60	C₃₁×#476	C₂²	1	2	yes	complemented
61	C₃₁×#476	C₂²	1	4	yes	complemented
62	C₃₁×#475	C₂²	1	2	yes	complemented
63	C₃₁×#474	C₂²	1	2	yes	complemented
64	C₃₁×#474	C₂²	1	4	yes	complemented
65	C₃₁×#464	C₂²	1	4	yes	complemented
66	C₃₁×#463	C₂²	1	4	yes	complemented
67	C₃₁×#460	C₂²	1	2	yes	—
68	C₃₁×#460	C₂²	1	2	yes	—
69	C₃₁×#460	C₂²	1	4	yes	complemented
70	C₃₁×#459	C₂²	1	2	yes	—
71	C₃₁×#459	C₂²	1	2	yes	—
72	C₃₁×#459	C₂²	1	4	yes	complemented
73	C₃₁×#446	C₂²	1	2	yes	complemented
74	C₃₁×#446	C₂²	1	2	yes	complemented
75	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
76	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
77	C₃₁×#442	C₂²	1	4	yes	complemented
78	C₃₁×#440	C₂²	1	4	yes	complemented
79	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
80	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
81	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
82	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
83	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
84	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
85	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
86	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
87	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
88	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#428	C₂²	1	2	yes	—
90	C₃₁×#427	C₂²	1	1	yes	characteristic
91	C₃₁×#424	C₂²	1	2	yes	—
92	C₃₁×#423	C₂²	1	1	yes	characteristic
93	C₃₁×#418	C₂²	1	2	yes	—
94	C₃₁×#417	C₂²	1	2	yes	—
95	C₃₁×#416	C₂²	1	1	yes	characteristic
96	C₃₁×#416	C₂²	1	1	yes	characteristic
97	C₂×C₃₁×#102	C₂²	1	2	yes	—
98	C₂×C₃₁×#102	C₂²	1	2	yes	—
99	C₃₁×#405	C₂²	1	2	yes	—
100	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
101	C₂×#41×C₃₁	—	2	2	no	—
102	C₂×#41×C₃₁	—	2	2	no	—
103	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
104	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
105	C₂²×Q₈×C₃₁	—	2	2	no	—
106	C₂²×Q₈×C₃₁	—	2	1	no	—
107	C₂²×D₄×C₃₁	—	2	1	no	—
108	C₂²×D₄×C₃₁	—	2	1	no	—
109	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
110	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
111	C₃₁×#135	—	2	4	no	—
112	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
113	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
114	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
115	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
116	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
117	C₂×D₈×C₃₁	C₂³	1	4	yes	—
118	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
119	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
121	C₃₁×C₄⋊Q₈	—	2	2	no	—
122	C₃₁×C₄⋊Q₈	—	2	2	no	—
123	C₃₁×C₄⋊Q₈	—	2	2	no	—
124	C₃₁×C₄⋊Q₈	—	2	4	no	—
125	C₃₁×C₄⋊Q₈	—	2	1	no	—
126	C₃₁×C₄⋊Q₈	—	2	1	no	—
127	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
128	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
129	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
130	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
131	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
132	C₃₁×#127	—	2	1	no	—
133	C₃₁×#127	—	2	1	no	—
134	C₃₁×#127	C₂³	1	2	yes	—
135	C₃₁×#127	C₂³	1	2	yes	—
136	C₃₁×#127	C₂³	1	4	yes	—
137	C₃₁×#125	—	2	2	no	—
138	C₃₁×#125	—	2	4	no	—
139	C₃₁×#125	D₄	1	2	yes	—
140	C₃₁×#125	C₂³	1	4	yes	—
141	C₃₁×#124	—	2	2	no	—
142	C₃₁×#124	—	2	2	no	—
143	C₃₁×#124	C₂³	1	4	yes	—
144	C₃₁×#123	—	2	4	no	—
145	C₃₁×#123	—	2	4	no	—
146	C₃₁×C₂²⋊Q₈	—	2	2	no	—
147	C₃₁×C₂²⋊Q₈	—	2	2	no	—
148	C₃₁×C₂²⋊Q₈	—	2	4	no	—
149	C₃₁×C₂²⋊Q₈	—	2	4	no	—
150	C₃₁×C₂²⋊Q₈	—	2	4	no	—
151	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
152	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
153	C₃₁×#121	—	2	2	no	—
154	C₃₁×#121	—	2	2	no	—
155	C₃₁×#121	—	2	2	no	—
156	C₃₁×#121	—	2	2	no	—
157	C₃₁×#121	—	2	4	no	—
158	C₃₁×#121	—	2	4	no	—
159	C₃₁×#120	—	2	4	no	—
160	C₄×Q₈×C₃₁	—	2	2	no	—
161	C₄×Q₈×C₃₁	—	2	2	no	—
162	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
167	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
168	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
169	C₄×D₄×C₃₁	—	2	1	no	—
170	C₄×D₄×C₃₁	—	2	1	no	—
171	C₄×D₄×C₃₁	—	2	1	no	—
172	C₄×D₄×C₃₁	—	2	1	no	—
173	C₄×D₄×C₃₁	—	2	2	no	—
174	C₄×D₄×C₃₁	—	2	2	no	—
175	C₄×D₄×C₃₁	—	2	2	no	—
176	C₄×D₄×C₃₁	—	2	2	no	—
177	C₄×D₄×C₃₁	—	2	4	no	—
178	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₃₁	C₂³	1	4	yes	—
183	C₄×D₄×C₃₁	C₂³	1	4	yes	—
184	C₄×D₄×C₃₁	C₂³	1	4	yes	—
185	C₃₁×#117	—	2	2	no	—
186	C₃₁×#117	—	2	1	no	—
187	C₃₁×#117	—	2	1	no	—
188	C₃₁×#117	C₂³	1	1	yes	characteristic
189	C₃₁×#117	C₂³	1	1	yes	characteristic
190	C₃₁×#117	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
192	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
193	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
194	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
196	C₂×C₄²×C₃₁	—	2	1	no	—
197	C₂×C₄²×C₃₁	—	2	1	no	—
198	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
199	C₃₁×#107	C₂³	1	1	yes	characteristic
200	C₃₁×#107	C₂³	1	1	yes	characteristic
201	C₃₁×#107	C₂³	1	4	yes	—
202	C₃₁×#106	C₂³	1	1	yes	characteristic
203	C₃₁×#106	C₂³	1	1	yes	characteristic
204	C₃₁×#106	C₂³	1	4	yes	—
205	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
206	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
207	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
208	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
209	C₃₁×#103	C₂³	1	1	yes	characteristic
210	C₃₁×#103	C₂³	1	1	yes	characteristic
211	C₃₁×#103	C₂³	1	1	yes	characteristic
212	C₃₁×#103	C₂³	1	1	yes	characteristic
213	C₃₁×#103	C₂³	1	4	yes	—
214	C₃₁×#102	C₂³	1	4	yes	—
215	C₃₁×#102	C₂³	1	4	yes	—
216	C₃₁×#102	C₂³	1	4	yes	—
217	C₃₁×#102	C₂³	1	4	yes	—
218	C₃₁×#102	C₂³	1	1	yes	characteristic
219	C₃₁×#102	C₂³	1	1	yes	characteristic
220	C₃₁×#102	C₂³	1	1	yes	characteristic
221	C₃₁×#102	C₂³	1	1	yes	characteristic
222	C₃₁×#102	C₂³	1	4	yes	—
223	C₃₁×#102	C₂³	1	4	yes	—
224	C₃₁×#102	C₂³	1	4	yes	—
225	C₃₁×#97	C₂³	1	4	yes	—
226	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
230	C₄×C₈×C₃₁	C₂³	1	4	yes	—
231	C₂⁴×C₃₁	—	2	2	no	—
232	#41×C₃₁	—	2	2	no	—
233	#41×C₃₁	—	2	2	no	—
234	#41×C₃₁	—	2	2	no	—
235	#41×C₃₁	—	8	4	no	—
236	#41×C₃₁	—	8	4	no	—
237	#41×C₃₁	#41	1	4	yes	complemented
238	C₂×Q₈×C₃₁	—	2	2	no	—
239	C₂×Q₈×C₃₁	—	2	4	no	—
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	—	8	2	no	—
242	C₂×Q₈×C₃₁	—	8	4	no	—
243	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
244	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
245	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
246	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
247	C₂×D₄×C₃₁	—	2	1	no	—
248	C₂×D₄×C₃₁	—	2	1	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	2	no	—
251	C₂×D₄×C₃₁	—	2	2	no	—
252	C₂×D₄×C₃₁	—	2	4	no	—
253	C₂×D₄×C₃₁	—	2	4	no	—
254	C₂×D₄×C₃₁	—	2	2	no	—
255	C₂×D₄×C₃₁	—	2	2	no	—
256	C₂×D₄×C₃₁	—	2	4	no	—
257	C₂×D₄×C₃₁	—	2	4	no	—
258	C₂×D₄×C₃₁	—	8	2	no	—
259	C₂×D₄×C₃₁	—	8	2	no	—
260	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
261	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
262	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₃₁	—	2	1	no	—
264	C₂²×C₄×C₃₁	—	2	2	no	—
265	C₂²×C₄×C₃₁	—	2	1	no	—
266	C₂²×C₄×C₃₁	—	2	1	no	—
267	C₂²×C₄×C₃₁	—	2	1	no	—
268	C₂²×C₄×C₃₁	—	2	1	no	—
269	C₂²×C₄×C₃₁	—	2	1	no	—
270	C₂²×C₄×C₃₁	—	2	4	no	—
271	C₂²×C₄×C₃₁	—	2	4	no	—
272	C₂²×C₄×C₃₁	—	2	4	no	—
273	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
276	Q₁₆×C₃₁	—	2	2	no	—
277	SD₁₆×C₃₁	—	2	2	no	—
278	SD₁₆×C₃₁	—	2	8	no	—
279	SD₁₆×C₃₁	—	2	2	no	—
280	D₈×C₃₁	—	2	2	no	—
281	D₈×C₃₁	—	2	8	no	—
282	M₁₆×C₃₁	—	2	4	no	—
283	C₂×C₈×C₃₁	—	2	2	no	—
284	C₂×C₈×C₃₁	—	2	2	no	—
285	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
286	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
287	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
288	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
289	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	4	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	4	no	—
295	C₄⋊C₄×C₃₁	—	2	1	no	—
296	C₄⋊C₄×C₃₁	—	2	1	no	—
297	C₄⋊C₄×C₃₁	—	2	1	no	—
298	C₄⋊C₄×C₃₁	—	2	1	no	—
299	C₄⋊C₄×C₃₁	—	2	4	no	—
300	C₄⋊C₄×C₃₁	—	2	4	no	—
301	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
303	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
306	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
307	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
308	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
309	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
312	C₂²⋊C₄×C₃₁	—	2	1	no	—
313	C₂²⋊C₄×C₃₁	—	2	1	no	—
314	C₂²⋊C₄×C₃₁	—	2	4	no	—
315	C₂²⋊C₄×C₃₁	—	2	4	no	—
316	C₂²⋊C₄×C₃₁	—	2	1	no	—
317	C₂²⋊C₄×C₃₁	—	2	1	no	—
318	C₂²⋊C₄×C₃₁	—	2	1	no	—
319	C₂²⋊C₄×C₃₁	—	2	1	no	—
320	C₂²⋊C₄×C₃₁	—	2	4	no	—
321	C₂²⋊C₄×C₃₁	—	2	4	no	—
322	C₂²⋊C₄×C₃₁	—	2	4	no	—
323	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
324	C₄²×C₃₁	—	2	1	no	—
325	C₄²×C₃₁	—	2	1	no	—
326	C₄²×C₃₁	—	2	1	no	—
327	C₄²×C₃₁	—	2	1	no	—
328	C₄²×C₃₁	—	2	1	no	—
329	C₄²×C₃₁	—	2	1	no	—
330	C₄²×C₃₁	—	2	4	no	—
331	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
335	C₄²×C₃₁	C₂⁴	1	4	yes	—
336	#61329	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
337	C₂³×C₃₁	—	2	1	no	—
338	C₂³×C₃₁	—	2	4	no	—
339	C₂³×C₃₁	—	2	1	no	—
340	C₂³×C₃₁	—	4	4	no	—
341	C₂³×C₃₁	—	8	2	no	—
342	C₂³×C₃₁	—	8	2	no	—
343	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
344	Q₈×C₃₁	—	2	4	no	—
345	Q₈×C₃₁	—	2	4	no	—
346	Q₈×C₃₁	—	2	1	no	—
347	Q₈×C₃₁	—	2	1	no	—
348	Q₈×C₃₁	—	2	1	no	—
349	Q₈×C₃₁	—	4	4	no	—
350	Q₈×C₃₁	—	8	2	no	—
351	Q₈×C₃₁	—	8	4	no	—
352	Q₈×C₃₁	C₂×#41	1	2	yes	—
353	D₄×C₃₁	—	2	4	no	—
354	D₄×C₃₁	—	2	4	no	—
355	D₄×C₃₁	—	2	1	no	—
356	D₄×C₃₁	—	2	1	no	—
357	D₄×C₃₁	—	2	4	no	—
358	D₄×C₃₁	—	2	1	no	—
359	D₄×C₃₁	—	4	2	no	—
360	D₄×C₃₁	—	4	4	no	—
361	D₄×C₃₁	—	4	4	no	—
362	D₄×C₃₁	—	4	4	no	—
363	D₄×C₃₁	—	8	2	no	—
364	D₄×C₃₁	—	8	2	no	—
365	D₄×C₃₁	—	8	4	no	—
366	D₄×C₃₁	—	8	4	no	—
367	D₄×C₃₁	C₂×#41	1	2	yes	—
368	C₂×C₄×C₃₁	—	2	1	no	—
369	C₂×C₄×C₃₁	—	2	4	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	2	no	—
372	C₂×C₄×C₃₁	—	2	1	no	—
373	C₂×C₄×C₃₁	—	2	1	no	—
374	C₂×C₄×C₃₁	—	2	1	no	—
375	C₂×C₄×C₃₁	—	2	1	no	—
376	C₂×C₄×C₃₁	—	2	1	no	—
377	C₂×C₄×C₃₁	—	2	4	no	—
378	C₂×C₄×C₃₁	—	4	2	no	—
379	C₂×C₄×C₃₁	—	4	2	no	—
380	C₂×C₄×C₃₁	—	4	2	no	—
381	C₂×C₄×C₃₁	—	4	2	no	—
382	C₂×C₄×C₃₁	—	4	2	no	—
383	C₂×C₄×C₃₁	—	8	4	no	—
384	C₂×C₄×C₃₁	—	8	4	no	—
385	C₂×C₄×C₃₁	—	8	4	no	—
386	C₂×C₄×C₃₁	—	8	2	no	—
387	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
388	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
391	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
395	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
396	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
397	C₈×C₃₁	—	2	1	no	—
398	C₈×C₃₁	—	2	1	no	—
399	C₈×C₃₁	—	2	4	no	—
400	C₈×C₃₁	—	2	1	no	—
401	C₈×C₃₁	—	2	1	no	—
402	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
403	#3503	C₂×C₃₁	1	1	yes	characteristic, complemented
404	#3375	C₂×C₃₁	1	2	yes	complemented
405	#3373	C₂×C₃₁	1	2	yes	complemented
406	#3368	C₂×C₃₁	1	2	yes	complemented
407	#3366	C₂×C₃₁	1	2	yes	complemented
408	#3365	C₂×C₃₁	1	2	yes	complemented
409	#3362	C₂×C₃₁	1	2	yes	complemented
410	#3361	C₂×C₃₁	1	2	yes	complemented
411	#3358	C₂×C₃₁	1	2	yes	complemented
412	#3136	C₂×C₃₁	1	2	yes	complemented
413	C₂×#486	C₂×C₃₁	1	1	yes	characteristic, complemented
414	#3081	C₂×C₃₁	1	2	yes	complemented
415	#3079	C₂×C₃₁	1	1	yes	characteristic, complemented
416	#3045	C₂×C₃₁	1	2	yes	complemented
417	#3038	C₂×C₃₁	1	1	yes	characteristic, complemented
418	#2960	C₂×C₃₁	1	1	yes	characteristic, complemented
419	#2946	C₂×C₃₁	1	2	yes	complemented
420	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
421	C₂²×C₃₁	—	2	1	no	—
422	C₂²×C₃₁	—	2	1	no	—
423	C₂²×C₃₁	—	2	2	no	—
424	C₂²×C₃₁	—	4	1	no	—
425	C₂²×C₃₁	—	4	1	no	—
426	C₂²×C₃₁	—	4	1	no	—
427	C₂²×C₃₁	—	4	4	no	—
428	C₂²×C₃₁	—	4	1	no	—
429	C₂²×C₃₁	—	4	4	no	—
430	C₂²×C₃₁	—	4	1	no	—
431	C₂²×C₃₁	—	4	4	no	—
432	C₂²×C₃₁	—	16	4	no	—
433	C₂²×C₃₁	#548	1	2	yes	—
434	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
435	C₄×C₃₁	—	2	2	no	—
436	C₄×C₃₁	—	2	1	no	—
437	C₄×C₃₁	—	2	4	no	—
438	C₄×C₃₁	—	2	1	no	—
439	C₄×C₃₁	—	2	4	no	—
440	C₄×C₃₁	—	4	1	no	—
441	C₄×C₃₁	—	4	1	no	—
442	C₄×C₃₁	—	4	1	no	—
443	C₄×C₃₁	—	4	4	no	—
444	C₄×C₃₁	—	4	1	no	—
445	C₄×C₃₁	—	4	1	no	—
446	C₄×C₃₁	#548	1	2	yes	—
447	C₄×C₃₁	#576	1	2	yes	—
448	C₄×C₃₁	#577	1	2	yes	—
449	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
450	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
451	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
452	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
453	#559	C₂²×C₃₁	1	2	yes	—
454	#559	C₂²×C₃₁	1	2	yes	—
455	Q₈²	C₂²×C₃₁	1	2	yes	complemented
456	#557	C₂²×C₃₁	1	2	yes	complemented
457	#554	—	2	2	no	—
458	#554	C₂²×C₃₁	1	2	yes	complemented
459	#550	C₂²×C₃₁	1	2	yes	—
460	#550	C₂²×C₃₁	1	2	yes	—
461	D₄×Q₈	—	2	2	no	—
462	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
463	#546	—	2	2	no	—
464	#546	—	2	2	no	—
465	#544	—	2	2	no	—
466	#544	C₂²×C₃₁	1	2	yes	—
467	#540	—	2	2	no	—
468	#535	C₂²×C₃₁	1	2	yes	—
469	#533	—	2	1	no	—
470	#533	C₂²×C₃₁	1	1	yes	characteristic
471	#532	—	2	1	no	—
472	#532	—	2	1	no	—
473	C₂×C₄⋊Q₈	—	2	1	no	—
474	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
475	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
476	#520	C₂²×C₃₁	1	2	yes	—
477	#518	C₂²×C₃₁	1	2	yes	—
478	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
479	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
480	#490	C₂²×C₃₁	1	4	yes	complemented
481	#489	C₂²×C₃₁	1	4	yes	complemented
482	#488	C₂²×C₃₁	1	4	yes	complemented
483	#486	C₂²×C₃₁	1	2	yes	—
484	#486	C₂²×C₃₁	1	2	yes	—
485	#486	C₂²×C₃₁	1	2	yes	—
486	#486	C₂²×C₃₁	1	2	yes	—
487	#486	C₂²×C₃₁	1	4	yes	complemented
488	#478	C₂²×C₃₁	1	4	yes	complemented
489	#478	C₂²×C₃₁	1	4	yes	complemented
490	#477	C₂²×C₃₁	1	2	yes	complemented
491	#476	C₂²×C₃₁	1	2	yes	complemented
492	#476	C₂²×C₃₁	1	4	yes	complemented
493	#475	C₂²×C₃₁	1	2	yes	complemented
494	#474	C₂²×C₃₁	1	2	yes	complemented
495	#474	C₂²×C₃₁	1	4	yes	complemented
496	#464	C₂²×C₃₁	1	4	yes	complemented
497	#463	C₂²×C₃₁	1	4	yes	complemented
498	#460	C₂²×C₃₁	1	2	yes	—
499	#460	C₂²×C₃₁	1	2	yes	—
500	#460	C₂²×C₃₁	1	4	yes	complemented
501	#459	C₂²×C₃₁	1	2	yes	—
502	#459	C₂²×C₃₁	1	2	yes	—
503	#459	C₂²×C₃₁	1	4	yes	complemented
504	#446	C₂²×C₃₁	1	2	yes	complemented
505	#446	C₂²×C₃₁	1	2	yes	complemented
506	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
507	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
508	#442	C₂²×C₃₁	1	4	yes	complemented
509	#440	C₂²×C₃₁	1	4	yes	complemented
510	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
511	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
512	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
513	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
514	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
515	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
516	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
517	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
518	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
519	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
520	#428	C₂²×C₃₁	1	2	yes	—
521	#427	C₂²×C₃₁	1	1	yes	characteristic
522	#424	C₂²×C₃₁	1	2	yes	—
523	#423	C₂²×C₃₁	1	1	yes	characteristic
524	#418	C₂²×C₃₁	1	2	yes	—
525	#417	C₂²×C₃₁	1	2	yes	—
526	#416	C₂²×C₃₁	1	1	yes	characteristic
527	#416	C₂²×C₃₁	1	1	yes	characteristic
528	C₂×#102	C₂²×C₃₁	1	2	yes	—
529	C₂×#102	C₂²×C₃₁	1	2	yes	—
530	#405	C₂²×C₃₁	1	2	yes	—
531	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
532	C₂×C₃₁	—	2	2	no	—
533	C₂×C₃₁	—	4	2	no	—
534	C₂×C₃₁	—	8	1	no	—
535	C₂×C₃₁	—	8	4	no	—
536	C₂×C₃₁	C₂×#548	1	1	yes	characteristic
537	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
538	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
539	C₂×#41	—	2	2	no	—
540	C₂×#41	—	2	2	no	—
541	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
542	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
543	C₂²×Q₈	—	2	2	no	—
544	C₂²×Q₈	—	2	1	no	—
545	C₂²×D₄	—	2	1	no	—
546	C₂²×D₄	—	2	1	no	—
547	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
548	AGL(1,ℤ/8)	—	2	8	no	—
549	#135	—	2	4	no	—
550	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
551	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
552	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
553	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
554	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
555	C₂×D₈	C₂³×C₃₁	1	4	yes	—
556	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
557	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
558	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
559	C₄⋊Q₈	—	2	2	no	—
560	C₄⋊Q₈	—	2	2	no	—
561	C₄⋊Q₈	—	2	2	no	—
562	C₄⋊Q₈	—	2	4	no	—
563	C₄⋊Q₈	—	2	1	no	—
564	C₄⋊Q₈	—	2	1	no	—
565	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
566	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
567	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
568	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
569	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
570	#127	—	2	1	no	—
571	#127	—	2	1	no	—
572	#127	C₂³×C₃₁	1	2	yes	—
573	#127	C₂³×C₃₁	1	2	yes	—
574	#127	C₂³×C₃₁	1	4	yes	—
575	#125	—	2	2	no	—
576	#125	—	2	4	no	—
577	#125	D₄×C₃₁	1	2	yes	—
578	#125	C₂³×C₃₁	1	4	yes	—
579	#124	—	2	2	no	—
580	#124	—	2	2	no	—
581	#124	C₂³×C₃₁	1	4	yes	—
582	#123	—	2	4	no	—
583	#123	—	2	4	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	4	no	—
587	C₂²⋊Q₈	—	2	4	no	—
588	C₂²⋊Q₈	—	2	4	no	—
589	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
590	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
591	#121	—	2	2	no	—
592	#121	—	2	2	no	—
593	#121	—	2	2	no	—
594	#121	—	2	2	no	—
595	#121	—	2	4	no	—
596	#121	—	2	4	no	—
597	#120	—	2	4	no	—
598	C₄×Q₈	—	2	2	no	—
599	C₄×Q₈	—	2	2	no	—
600	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
602	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
603	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
604	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
605	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
606	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	4	no	—
616	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
617	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
618	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
619	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
620	C₄×D₄	C₂³×C₃₁	1	4	yes	—
621	C₄×D₄	C₂³×C₃₁	1	4	yes	—
622	C₄×D₄	C₂³×C₃₁	1	4	yes	—
623	#117	—	2	2	no	—
624	#117	—	2	1	no	—
625	#117	—	2	1	no	—
626	#117	C₂³×C₃₁	1	1	yes	characteristic
627	#117	C₂³×C₃₁	1	1	yes	characteristic
628	#117	C₂³×C₃₁	1	2	yes	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	—	2	2	no	—
631	C₂×C₄⋊C₄	—	2	2	no	—
632	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
633	C₂×C₂²⋊C₄	—	2	4	no	—
634	C₂×C₄²	—	2	1	no	—
635	C₂×C₄²	—	2	1	no	—
636	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
637	#107	C₂³×C₃₁	1	1	yes	characteristic
638	#107	C₂³×C₃₁	1	1	yes	characteristic
639	#107	C₂³×C₃₁	1	4	yes	—
640	#106	C₂³×C₃₁	1	1	yes	characteristic
641	#106	C₂³×C₃₁	1	1	yes	characteristic
642	#106	C₂³×C₃₁	1	4	yes	—
643	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
644	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
645	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
646	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
647	#103	C₂³×C₃₁	1	1	yes	characteristic
648	#103	C₂³×C₃₁	1	1	yes	characteristic
649	#103	C₂³×C₃₁	1	1	yes	characteristic
650	#103	C₂³×C₃₁	1	1	yes	characteristic
651	#103	C₂³×C₃₁	1	4	yes	—
652	#102	C₂³×C₃₁	1	4	yes	—
653	#102	C₂³×C₃₁	1	4	yes	—
654	#102	C₂³×C₃₁	1	4	yes	—
655	#102	C₂³×C₃₁	1	4	yes	—
656	#102	C₂³×C₃₁	1	1	yes	characteristic
657	#102	C₂³×C₃₁	1	1	yes	characteristic
658	#102	C₂³×C₃₁	1	1	yes	characteristic
659	#102	C₂³×C₃₁	1	1	yes	characteristic
660	#102	C₂³×C₃₁	1	4	yes	—
661	#102	C₂³×C₃₁	1	4	yes	—
662	#102	C₂³×C₃₁	1	4	yes	—
663	#97	C₂³×C₃₁	1	4	yes	—
664	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
665	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
666	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
667	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
668	C₄×C₈	C₂³×C₃₁	1	4	yes	—
669	C₃₁	#61329	1	1	yes	characteristic, direct product factor, Sylow
670	C₂⁴	—	2	2	no	—
671	#41	—	2	2	no	—
672	#41	—	2	2	no	—
673	#41	—	2	2	no	—
674	#41	—	8	4	no	—
675	#41	—	8	4	no	—
676	#41	#41×C₃₁	1	4	yes	complemented
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	2	4	no	—
679	C₂×Q₈	—	2	2	no	—
680	C₂×Q₈	—	8	2	no	—
681	C₂×Q₈	—	8	4	no	—
682	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
683	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
684	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
685	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	4	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	8	2	no	—
698	C₂×D₄	—	8	2	no	—
699	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
700	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
701	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
715	Q₁₆	—	2	2	no	—
716	SD₁₆	—	2	2	no	—
717	SD₁₆	—	2	8	no	—
718	SD₁₆	—	2	2	no	—
719	D₈	—	2	2	no	—
720	D₈	—	2	8	no	—
721	M₁₆	—	2	4	no	—
722	C₂×C₈	—	2	2	no	—
723	C₂×C₈	—	2	2	no	—
724	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
725	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
726	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
727	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
728	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
741	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
742	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
743	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
744	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
745	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
746	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
747	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
748	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
749	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
750	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	1	no	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	1	no	—
767	C₄²	—	2	1	no	—
768	C₄²	—	2	1	no	—
769	C₄²	—	2	4	no	—
770	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
771	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
772	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
773	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
774	C₄²	C₂⁴×C₃₁	1	4	yes	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	4	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	4	4	no	—
779	C₂³	—	8	2	no	—
780	C₂³	—	8	2	no	—
781	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
782	Q₈	—	2	4	no	—
783	Q₈	—	2	4	no	—
784	Q₈	—	2	1	no	—
785	Q₈	—	2	1	no	—
786	Q₈	—	2	1	no	—
787	Q₈	—	4	4	no	—
788	Q₈	—	8	2	no	—
789	Q₈	—	8	4	no	—
790	Q₈	C₂×#41×C₃₁	1	2	yes	—
791	D₄	—	2	4	no	—
792	D₄	—	2	4	no	—
793	D₄	—	2	1	no	—
794	D₄	—	2	1	no	—
795	D₄	—	2	4	no	—
796	D₄	—	2	1	no	—
797	D₄	—	4	2	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	4	no	—
800	D₄	—	4	4	no	—
801	D₄	—	8	2	no	—
802	D₄	—	8	2	no	—
803	D₄	—	8	4	no	—
804	D₄	—	8	4	no	—
805	D₄	C₂×#41×C₃₁	1	2	yes	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	4	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	8	4	no	—
822	C₂×C₄	—	8	4	no	—
823	C₂×C₄	—	8	4	no	—
824	C₂×C₄	—	8	2	no	—
825	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
826	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
829	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
831	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
832	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
833	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
834	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
835	C₈	—	2	1	no	—
836	C₈	—	2	1	no	—
837	C₈	—	2	4	no	—
838	C₈	—	2	1	no	—
839	C₈	—	2	1	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	4	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	4	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	4	4	no	—
851	C₂²	—	16	4	no	—
852	C₂²	C₃₁×#548	1	2	yes	—
853	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
854	C₄	—	2	2	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	4	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	4	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	4	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	1	no	—
865	C₄	C₃₁×#548	1	2	yes	—
866	C₄	C₃₁×#576	1	2	yes	—
867	C₄	C₃₁×#577	1	2	yes	—
868	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
869	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
870	C₂	—	2	2	no	—
871	C₂	—	4	2	no	—
872	C₂	—	8	4	no	—
873	C₂	—	8	1	no	—
874	C₂	C₂×C₃₁×#548	1	1	yes	characteristic
875	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
876	C₂	C₂×C₃₁×#577	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3508	C₂	semidirect
2. C₃₁×#3503	C₂	semidirect
3. C₃₁×#3375	C₂	semidirect
4. C₃₁×#3373	C₂	semidirect
5. C₃₁×#3368	C₂	semidirect
6. C₃₁×#3366	C₂	semidirect
7. C₃₁×#3365	C₂	semidirect
8. C₃₁×#3362	C₂	semidirect
9. C₃₁×#3361	C₂	semidirect
10. C₃₁×#3358	C₂	semidirect
11. C₃₁×#3136	C₂	semidirect
12. C₂×C₃₁×#486	C₂	semidirect
13. C₃₁×#3081	C₂	semidirect
14. C₃₁×#3079	C₂	semidirect
15. C₃₁×#3045	C₂	semidirect
16. C₃₁×#3038	C₂	semidirect
17. C₃₁×#2960	C₂	semidirect
18. C₃₁×#2946	C₂	semidirect
19. C₄×C₃₁×#135	C₂	semidirect
24. Q₈²×C₃₁	C₂²	semidirect
25. C₃₁×#557	C₂²	semidirect
27. C₃₁×#554	C₂²	semidirect
31. D₄×Q₈×C₃₁	C₂²	semidirect
49. C₃₁×#490	C₂²	semidirect
50. C₃₁×#489	C₂²	semidirect
51. C₃₁×#488	C₂²	semidirect
56. C₃₁×#486	C₂²	semidirect
57. C₃₁×#478	C₂²	semidirect
58. C₃₁×#478	C₂²	semidirect
59. C₃₁×#477	C₂²	semidirect
60. C₃₁×#476	C₂²	semidirect
61. C₃₁×#476	C₂²	semidirect
62. C₃₁×#475	C₂²	semidirect
63. C₃₁×#474	C₂²	semidirect
64. C₃₁×#474	C₂²	semidirect
65. C₃₁×#464	C₂²	semidirect
66. C₃₁×#463	C₂²	semidirect
69. C₃₁×#460	C₂²	semidirect
72. C₃₁×#459	C₂²	semidirect
73. C₃₁×#446	C₂²	semidirect
74. C₃₁×#446	C₂²	semidirect
75. C₈×Q₈×C₃₁	C₂²	semidirect
76. C₈×Q₈×C₃₁	C₂²	semidirect
77. C₃₁×#442	C₂²	semidirect
78. C₃₁×#440	C₂²	semidirect
79. C₄×Q₁₆×C₃₁	C₂²	semidirect
80. C₄×Q₁₆×C₃₁	C₂²	semidirect
81. C₄×SD₁₆×C₃₁	C₂²	semidirect
82. C₄×SD₁₆×C₃₁	C₂²	semidirect
83. C₄×SD₁₆×C₃₁	C₂²	semidirect
84. C₄×SD₁₆×C₃₁	C₂²	semidirect
85. C₄×SD₁₆×C₃₁	C₂²	semidirect
86. C₄×D₈×C₃₁	C₂²	semidirect
87. C₄×D₈×C₃₁	C₂²	semidirect
88. C₄×D₈×C₃₁	C₂²	semidirect
237. #41×C₃₁	#41	semidirect
336. #61329	C₃₁	direct (N × H)
402. #3508	C₂×C₃₁	semidirect
403. #3503	C₂×C₃₁	semidirect
404. #3375	C₂×C₃₁	semidirect
405. #3373	C₂×C₃₁	semidirect
406. #3368	C₂×C₃₁	semidirect
407. #3366	C₂×C₃₁	semidirect
408. #3365	C₂×C₃₁	semidirect
409. #3362	C₂×C₃₁	semidirect
410. #3361	C₂×C₃₁	semidirect
411. #3358	C₂×C₃₁	semidirect
412. #3136	C₂×C₃₁	semidirect
413. C₂×#486	C₂×C₃₁	semidirect
414. #3081	C₂×C₃₁	semidirect
415. #3079	C₂×C₃₁	semidirect
416. #3045	C₂×C₃₁	semidirect
417. #3038	C₂×C₃₁	semidirect
418. #2960	C₂×C₃₁	semidirect
419. #2946	C₂×C₃₁	semidirect
420. C₄×#135	C₂×C₃₁	semidirect
455. Q₈²	C₂²×C₃₁	semidirect
456. #557	C₂²×C₃₁	semidirect
458. #554	C₂²×C₃₁	semidirect
462. D₄×Q₈	C₂²×C₃₁	semidirect
480. #490	C₂²×C₃₁	semidirect
481. #489	C₂²×C₃₁	semidirect
482. #488	C₂²×C₃₁	semidirect
487. #486	C₂²×C₃₁	semidirect
488. #478	C₂²×C₃₁	semidirect
489. #478	C₂²×C₃₁	semidirect
490. #477	C₂²×C₃₁	semidirect
491. #476	C₂²×C₃₁	semidirect
492. #476	C₂²×C₃₁	semidirect
493. #475	C₂²×C₃₁	semidirect
494. #474	C₂²×C₃₁	semidirect
495. #474	C₂²×C₃₁	semidirect
496. #464	C₂²×C₃₁	semidirect
497. #463	C₂²×C₃₁	semidirect
500. #460	C₂²×C₃₁	semidirect
503. #459	C₂²×C₃₁	semidirect
504. #446	C₂²×C₃₁	semidirect
505. #446	C₂²×C₃₁	semidirect
506. C₈×Q₈	C₂²×C₃₁	semidirect
507. C₈×Q₈	C₂²×C₃₁	semidirect
508. #442	C₂²×C₃₁	semidirect
509. #440	C₂²×C₃₁	semidirect
510. C₄×Q₁₆	C₂²×C₃₁	semidirect
511. C₄×Q₁₆	C₂²×C₃₁	semidirect
512. C₄×SD₁₆	C₂²×C₃₁	semidirect
513. C₄×SD₁₆	C₂²×C₃₁	semidirect
514. C₄×SD₁₆	C₂²×C₃₁	semidirect
515. C₄×SD₁₆	C₂²×C₃₁	semidirect
516. C₄×SD₁₆	C₂²×C₃₁	semidirect
517. C₄×D₈	C₂²×C₃₁	semidirect
518. C₄×D₈	C₂²×C₃₁	semidirect
519. C₄×D₈	C₂²×C₃₁	semidirect
669. C₃₁	#61329	direct (N × H)
676. #41	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3508	2
C₃₁×#3503	2
C₃₁×#3375	2
C₃₁×#3373	2
C₃₁×#3368	2
C₃₁×#3366	2
C₃₁×#3365	2
C₃₁×#3362	2
C₃₁×#3361	2
C₃₁×#3358	2
C₃₁×#3136	2
C₂×C₃₁×#486	2
C₃₁×#3081	2
C₃₁×#3079	2
C₃₁×#3045	2
C₃₁×#3038	2
C₃₁×#2960	2
C₃₁×#2946	2
C₄×C₃₁×#135	2
#61329	31

Subgroups — C31×#61329 #21518088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61329 #21518088