Subgroups — C₃₁×#60924 #21517683

Order 7936.

1868 conjugacy classes of subgroups.

The subgroup lattice has 896 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×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3260	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3257	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3254	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3251	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3247	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3246	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3081	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3062	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3057	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3042	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2906	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
20	C₂×C₃₁×#131	C₂²	1	2	yes	—
21	C₃₁×#559	—	2	1	no	—
22	C₃₁×#559	—	2	1	no	—
23	C₃₁×#550	—	2	1	no	—
24	C₃₁×#550	—	2	1	no	—
25	C₃₁×#546	—	2	2	no	—
26	C₃₁×#546	—	2	2	no	—
27	C₃₁×#544	C₂²	1	1	yes	characteristic
28	C₃₁×#542	—	2	1	no	—
29	C₃₁×#542	C₂²	1	2	yes	complemented
30	C₃₁×#541	—	2	1	no	—
31	C₃₁×#541	C₂²	1	2	yes	complemented
32	C₃₁×#540	C₂²	1	4	yes	—
33	C₃₁×#539	—	2	2	no	—
34	C₃₁×#537	C₂²	1	1	yes	characteristic
35	C₃₁×#536	C₂²	1	1	yes	characteristic
36	C₃₁×#536	C₂²	1	1	yes	characteristic
37	C₃₁×#535	C₂²	1	2	yes	—
38	C₃₁×#533	—	2	1	no	—
39	C₃₁×#533	C₂²	1	1	yes	characteristic
40	C₃₁×#533	C₂²	1	2	yes	complemented
41	C₃₁×#532	C₂²	1	2	yes	—
42	C₃₁×#532	C₂²	1	2	yes	—
43	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
44	C₃₁×#529	—	2	2	no	—
45	C₃₁×#529	—	2	1	no	—
46	C₃₁×#529	C₂²	1	2	yes	complemented
47	C₃₁×#518	C₂²	1	2	yes	—
48	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
49	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
50	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#479	C₂²	1	2	yes	complemented
52	C₃₁×#479	C₂²	1	4	yes	complemented
53	C₃₁×#478	C₂²	1	2	yes	complemented
54	C₃₁×#478	C₂²	1	4	yes	complemented
55	C₃₁×#478	C₂²	1	4	yes	complemented
56	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#477	C₂²	1	2	yes	complemented
58	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#476	C₂²	1	4	yes	complemented
60	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#475	C₂²	1	2	yes	complemented
62	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#474	C₂²	1	4	yes	complemented
64	C₃₁×#469	C₂²	1	4	yes	complemented
65	C₃₁×#468	C₂²	1	4	yes	complemented
66	C₃₁×#468	C₂²	1	4	yes	complemented
67	C₃₁×#468	C₂²	1	4	yes	complemented
68	C₃₁×#466	C₂²	1	4	yes	complemented
69	C₃₁×#465	C₂²	1	4	yes	complemented
70	C₃₁×#465	C₂²	1	4	yes	complemented
71	C₃₁×#465	C₂²	1	4	yes	complemented
72	C₃₁×#463	C₂²	1	4	yes	complemented
73	C₃₁×#463	C₂²	1	4	yes	complemented
74	C₃₁×#461	C₂²	1	4	yes	complemented
75	C₃₁×#461	C₂²	1	4	yes	complemented
76	C₃₁×#460	C₂²	1	2	yes	—
77	C₃₁×#460	C₂²	1	2	yes	—
78	C₃₁×#460	C₂²	1	2	yes	—
79	C₃₁×#460	C₂²	1	4	yes	—
80	C₃₁×#460	C₂²	1	2	yes	—
81	C₃₁×#459	C₂²	1	2	yes	—
82	C₃₁×#459	C₂²	1	2	yes	—
83	C₃₁×#428	C₂²	1	2	yes	—
84	C₃₁×#427	C₂²	1	2	yes	—
85	C₃₁×#424	C₂²	1	2	yes	—
86	C₃₁×#424	C₂²	1	4	yes	complemented
87	C₃₁×#423	C₂²	1	1	yes	characteristic
88	C₃₁×#423	C₂²	1	2	yes	complemented
89	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
90	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
91	C₃₁×#419	C₂²	1	2	yes	—
92	C₃₁×#418	C₂²	1	2	yes	—
93	C₃₁×#416	C₂²	1	2	yes	—
94	C₂×C₃₁×#102	C₂²	1	2	yes	—
95	C₂×#41×C₃₁	—	2	2	no	—
96	C₂×#41×C₃₁	—	2	2	no	—
97	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
98	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₃₁	—	2	1	no	—
101	C₂²×D₄×C₃₁	—	2	1	no	—
102	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
103	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
104	C₂×SD₁₆×C₃₁	—	4	4	no	—
105	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
108	C₂×D₈×C₃₁	C₂³	1	4	yes	—
109	C₃₁×#131	—	4	4	no	—
110	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
111	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
112	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
113	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
114	C₃₁×C₄⋊Q₈	—	2	1	no	—
115	C₃₁×C₄⋊Q₈	—	2	1	no	—
116	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₃₁×#127	—	2	2	no	—
121	C₃₁×#127	—	2	1	no	—
122	C₃₁×#127	—	2	1	no	—
123	C₃₁×#127	C₂³	1	2	yes	—
124	C₃₁×#127	C₂³	1	2	yes	—
125	C₃₁×#126	—	2	2	no	—
126	C₃₁×#126	—	2	2	no	—
127	C₃₁×#126	—	2	2	no	—
128	C₃₁×#126	—	2	2	no	—
129	C₃₁×#125	—	2	2	no	—
130	C₃₁×#125	—	2	1	no	—
131	C₃₁×#125	—	2	2	no	—
132	C₃₁×#125	—	2	2	no	—
133	C₃₁×#125	C₂³	1	2	yes	—
134	C₃₁×#125	C₂³	1	2	yes	—
135	C₃₁×#124	—	2	2	no	—
136	C₃₁×#124	—	2	1	no	—
137	C₃₁×#124	—	2	2	no	—
138	C₃₁×#124	—	2	2	no	—
139	C₃₁×#124	—	2	2	no	—
140	C₃₁×#124	C₂³	1	2	yes	—
141	C₃₁×#123	—	2	2	no	—
142	C₃₁×#123	—	2	2	no	—
143	C₃₁×#123	—	2	4	no	—
144	C₃₁×#123	—	2	4	no	—
145	C₃₁×#123	—	2	2	no	—
146	C₃₁×#123	—	2	2	no	—
147	C₃₁×C₂²⋊Q₈	—	2	1	no	—
148	C₃₁×C₂²⋊Q₈	—	2	1	no	—
149	C₃₁×C₂²⋊Q₈	—	2	1	no	—
150	C₃₁×C₂²⋊Q₈	—	2	2	no	—
151	C₃₁×C₂²⋊Q₈	—	2	1	no	—
152	C₃₁×C₂²⋊Q₈	—	2	1	no	—
153	C₃₁×C₂²⋊Q₈	—	2	2	no	—
154	C₃₁×C₂²⋊Q₈	—	2	2	no	—
155	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
156	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
157	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
158	C₃₁×#121	—	2	2	no	—
159	C₃₁×#121	—	2	1	no	—
160	C₃₁×#121	—	2	2	no	—
161	C₃₁×#121	—	2	2	no	—
162	C₃₁×#121	—	2	4	no	—
163	C₃₁×#121	—	2	4	no	—
164	C₃₁×#121	C₂³	1	4	yes	—
165	C₃₁×#121	C₂³	1	4	yes	—
166	C₃₁×#121	C₂³	1	2	yes	—
167	C₃₁×#120	—	2	4	no	—
168	C₄×Q₈×C₃₁	—	2	1	no	—
169	C₄×Q₈×C₃₁	—	2	1	no	—
170	C₄×Q₈×C₃₁	—	2	2	no	—
171	C₄×Q₈×C₃₁	—	2	1	no	—
172	C₄×Q₈×C₃₁	—	2	1	no	—
173	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
174	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
175	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
176	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
177	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
178	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₃₁	—	2	1	no	—
180	C₄×D₄×C₃₁	—	2	1	no	—
181	C₄×D₄×C₃₁	—	2	2	no	—
182	C₄×D₄×C₃₁	—	2	2	no	—
183	C₄×D₄×C₃₁	—	2	2	no	—
184	C₄×D₄×C₃₁	—	2	2	no	—
185	C₄×D₄×C₃₁	—	2	2	no	—
186	C₄×D₄×C₃₁	D₄	1	2	yes	—
187	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
188	C₄×D₄×C₃₁	D₄	1	2	yes	—
189	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
190	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
192	C₄×D₄×C₃₁	C₂³	1	4	yes	—
193	C₄×D₄×C₃₁	C₂³	1	4	yes	—
194	C₃₁×#117	—	2	2	no	—
195	C₃₁×#117	—	2	1	no	—
196	C₃₁×#117	—	2	2	no	—
197	C₃₁×#117	C₂³	1	2	yes	—
198	C₃₁×#117	C₂³	1	1	yes	characteristic
199	C₃₁×#117	C₂³	1	1	yes	characteristic
200	C₃₁×#117	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
202	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
204	C₂×C₄²×C₃₁	—	2	1	no	—
205	C₂×C₄²×C₃₁	—	2	1	no	—
206	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
208	C₃₁×#107	C₂³	1	2	yes	—
209	C₃₁×#107	C₂³	1	2	yes	—
210	C₃₁×#107	C₂³	1	4	yes	—
211	C₃₁×#106	C₂³	1	2	yes	—
212	C₃₁×#106	C₂³	1	2	yes	—
213	C₃₁×#106	C₂³	1	4	yes	—
214	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
217	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
218	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
219	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
220	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
221	C₃₁×#103	C₂³	1	2	yes	—
222	C₃₁×#103	C₂³	1	2	yes	—
223	C₃₁×#103	C₂³	1	4	yes	—
224	C₃₁×#103	C₂³	1	4	yes	—
225	C₃₁×#102	C₂³	1	4	yes	—
226	C₃₁×#102	C₂³	1	4	yes	—
227	C₃₁×#102	C₂³	1	2	yes	—
228	C₃₁×#102	C₂³	1	2	yes	—
229	C₃₁×#102	C₂³	1	4	yes	—
230	C₃₁×#102	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	—	2	2	no	—
236	#41×C₃₁	—	8	4	no	—
237	#41×C₃₁	—	8	4	no	—
238	C₂×Q₈×C₃₁	—	2	1	no	—
239	C₂×Q₈×C₃₁	—	2	1	no	—
240	C₂×Q₈×C₃₁	—	2	1	no	—
241	C₂×Q₈×C₃₁	—	2	2	no	—
242	C₂×Q₈×C₃₁	—	2	2	no	—
243	C₂×Q₈×C₃₁	—	2	2	no	—
244	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
247	C₂×D₄×C₃₁	—	2	1	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	4	no	—
250	C₂×D₄×C₃₁	—	2	4	no	—
251	C₂×D₄×C₃₁	—	2	2	no	—
252	C₂×D₄×C₃₁	—	2	2	no	—
253	C₂×D₄×C₃₁	—	2	2	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	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
262	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
263	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
264	C₂²×C₄×C₃₁	—	2	1	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	4	no	—
270	C₂²×C₄×C₃₁	—	2	4	no	—
271	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
277	SD₁₆×C₃₁	—	4	4	no	—
278	SD₁₆×C₃₁	—	4	4	no	—
279	SD₁₆×C₃₁	—	4	4	no	—
280	D₈×C₃₁	—	4	4	no	—
281	M₁₆×C₃₁	—	2	4	no	—
282	M₁₆×C₃₁	—	4	4	no	—
283	C₂×C₈×C₃₁	—	2	4	no	—
284	C₂×C₈×C₃₁	—	4	4	no	—
285	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
286	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
287	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	2	no	—
290	C₄⋊C₄×C₃₁	—	2	1	no	—
291	C₄⋊C₄×C₃₁	—	2	1	no	—
292	C₄⋊C₄×C₃₁	—	2	1	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	2	no	—
295	C₄⋊C₄×C₃₁	—	2	2	no	—
296	C₄⋊C₄×C₃₁	—	2	2	no	—
297	C₄⋊C₄×C₃₁	—	2	1	no	—
298	C₄⋊C₄×C₃₁	—	2	1	no	—
299	C₄⋊C₄×C₃₁	—	2	2	no	—
300	C₄⋊C₄×C₃₁	—	2	2	no	—
301	C₄⋊C₄×C₃₁	—	2	2	no	—
302	C₄⋊C₄×C₃₁	—	2	2	no	—
303	C₄⋊C₄×C₃₁	—	2	2	no	—
304	C₄⋊C₄×C₃₁	—	2	2	no	—
305	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
306	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
307	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
308	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
309	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
310	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
312	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
314	C₂²⋊C₄×C₃₁	—	2	2	no	—
315	C₂²⋊C₄×C₃₁	—	2	2	no	—
316	C₂²⋊C₄×C₃₁	—	2	2	no	—
317	C₂²⋊C₄×C₃₁	—	2	1	no	—
318	C₂²⋊C₄×C₃₁	—	2	2	no	—
319	C₂²⋊C₄×C₃₁	—	2	4	no	—
320	C₂²⋊C₄×C₃₁	—	2	4	no	—
321	C₂²⋊C₄×C₃₁	—	2	1	no	—
322	C₂²⋊C₄×C₃₁	—	2	1	no	—
323	C₂²⋊C₄×C₃₁	—	2	2	no	—
324	C₂²⋊C₄×C₃₁	—	2	2	no	—
325	C₂²⋊C₄×C₃₁	—	2	4	no	—
326	C₂²⋊C₄×C₃₁	—	2	4	no	—
327	C₂²⋊C₄×C₃₁	—	2	2	no	—
328	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
329	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
331	C₄²×C₃₁	—	2	2	no	—
332	C₄²×C₃₁	—	2	1	no	—
333	C₄²×C₃₁	—	2	1	no	—
334	C₄²×C₃₁	—	2	1	no	—
335	C₄²×C₃₁	—	2	2	no	—
336	C₄²×C₃₁	—	2	2	no	—
337	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₃₁	C₂×D₄	1	2	yes	—
339	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₃₁	C₂×D₄	1	2	yes	—
341	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
342	C₄²×C₃₁	C₂⁴	1	2	yes	—
343	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
344	#60924	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
345	C₂³×C₃₁	—	2	1	no	—
346	C₂³×C₃₁	—	2	4	no	—
347	C₂³×C₃₁	—	4	4	no	—
348	C₂³×C₃₁	—	8	2	no	—
349	C₂³×C₃₁	—	8	2	no	—
350	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
351	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
352	Q₈×C₃₁	—	2	2	no	—
353	Q₈×C₃₁	—	2	2	no	—
354	Q₈×C₃₁	—	2	1	no	—
355	Q₈×C₃₁	—	2	2	no	—
356	Q₈×C₃₁	—	2	1	no	—
357	Q₈×C₃₁	—	4	2	no	—
358	Q₈×C₃₁	—	4	2	no	—
359	Q₈×C₃₁	—	4	2	no	—
360	Q₈×C₃₁	—	8	2	no	—
361	D₄×C₃₁	—	2	4	no	—
362	D₄×C₃₁	—	2	2	no	—
363	D₄×C₃₁	—	2	1	no	—
364	D₄×C₃₁	—	2	4	no	—
365	D₄×C₃₁	—	2	4	no	—
366	D₄×C₃₁	—	2	1	no	—
367	D₄×C₃₁	—	4	4	no	—
368	D₄×C₃₁	—	4	2	no	—
369	D₄×C₃₁	—	4	4	no	—
370	D₄×C₃₁	—	4	4	no	—
371	D₄×C₃₁	—	8	2	no	—
372	D₄×C₃₁	—	8	2	no	—
373	D₄×C₃₁	—	8	2	no	—
374	D₄×C₃₁	—	8	4	no	—
375	D₄×C₃₁	—	8	4	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	—	2	4	no	—
378	C₂×C₄×C₃₁	—	2	2	no	—
379	C₂×C₄×C₃₁	—	2	2	no	—
380	C₂×C₄×C₃₁	—	2	1	no	—
381	C₂×C₄×C₃₁	—	2	2	no	—
382	C₂×C₄×C₃₁	—	2	1	no	—
383	C₂×C₄×C₃₁	—	2	1	no	—
384	C₂×C₄×C₃₁	—	2	2	no	—
385	C₂×C₄×C₃₁	—	2	2	no	—
386	C₂×C₄×C₃₁	—	2	2	no	—
387	C₂×C₄×C₃₁	—	4	1	no	—
388	C₂×C₄×C₃₁	—	4	2	no	—
389	C₂×C₄×C₃₁	—	4	2	no	—
390	C₂×C₄×C₃₁	—	4	2	no	—
391	C₂×C₄×C₃₁	—	4	2	no	—
392	C₂×C₄×C₃₁	—	8	1	no	—
393	C₂×C₄×C₃₁	—	8	4	no	—
394	C₂×C₄×C₃₁	—	8	4	no	—
395	C₂×C₄×C₃₁	—	8	1	no	—
396	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
405	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
406	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
407	C₈×C₃₁	—	2	2	no	—
408	C₈×C₃₁	—	2	2	no	—
409	C₈×C₃₁	—	2	4	no	—
410	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
411	#3461	C₂×C₃₁	1	1	yes	characteristic, complemented
412	#3260	C₂×C₃₁	1	4	yes	complemented
413	#3257	C₂×C₃₁	1	4	yes	complemented
414	#3254	C₂×C₃₁	1	2	yes	complemented
415	#3251	C₂×C₃₁	1	2	yes	complemented
416	#3247	C₂×C₃₁	1	2	yes	complemented
417	#3246	C₂×C₃₁	1	2	yes	complemented
418	#3081	C₂×C₃₁	1	2	yes	complemented
419	#3078	C₂×C₃₁	1	1	yes	characteristic, complemented
420	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
421	#3062	C₂×C₃₁	1	2	yes	complemented
422	#3057	C₂×C₃₁	1	2	yes	complemented
423	#3042	C₂×C₃₁	1	2	yes	complemented
424	#3038	C₂×C₃₁	1	1	yes	characteristic, complemented
425	C₂×#460	C₂×C₃₁	1	1	yes	characteristic, complemented
426	#2906	C₂×C₃₁	1	1	yes	characteristic, complemented
427	C₂²×C₃₁	—	2	1	no	—
428	C₂²×C₃₁	—	2	1	no	—
429	C₂²×C₃₁	—	2	2	no	—
430	C₂²×C₃₁	—	2	2	no	—
431	C₂²×C₃₁	—	2	2	no	—
432	C₂²×C₃₁	—	4	4	no	—
433	C₂²×C₃₁	—	4	1	no	—
434	C₂²×C₃₁	—	4	1	no	—
435	C₂²×C₃₁	—	4	4	no	—
436	C₂²×C₃₁	—	4	1	no	—
437	C₂²×C₃₁	—	4	4	no	—
438	C₂²×C₃₁	—	16	4	no	—
439	C₂²×C₃₁	#537	1	2	yes	—
440	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
441	C₄×C₃₁	—	2	1	no	—
442	C₄×C₃₁	—	2	2	no	—
443	C₄×C₃₁	—	2	1	no	—
444	C₄×C₃₁	—	2	2	no	—
445	C₄×C₃₁	—	2	2	no	—
446	C₄×C₃₁	—	2	1	no	—
447	C₄×C₃₁	—	4	2	no	—
448	C₄×C₃₁	—	4	2	no	—
449	C₄×C₃₁	—	4	1	no	—
450	C₄×C₃₁	—	4	1	no	—
451	C₄×C₃₁	—	4	2	no	—
452	C₄×C₃₁	—	4	1	no	—
453	C₄×C₃₁	—	4	2	no	—
454	C₄×C₃₁	#537	1	2	yes	—
455	C₄×C₃₁	#577	1	2	yes	—
456	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
457	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
458	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
459	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
460	C₂×#131	C₂²×C₃₁	1	2	yes	—
461	#559	—	2	1	no	—
462	#559	—	2	1	no	—
463	#550	—	2	1	no	—
464	#550	—	2	1	no	—
465	#546	—	2	2	no	—
466	#546	—	2	2	no	—
467	#544	C₂²×C₃₁	1	1	yes	characteristic
468	#542	—	2	1	no	—
469	#542	C₂²×C₃₁	1	2	yes	complemented
470	#541	—	2	1	no	—
471	#541	C₂²×C₃₁	1	2	yes	complemented
472	#540	C₂²×C₃₁	1	4	yes	—
473	#539	—	2	2	no	—
474	#537	C₂²×C₃₁	1	1	yes	characteristic
475	#536	C₂²×C₃₁	1	1	yes	characteristic
476	#536	C₂²×C₃₁	1	1	yes	characteristic
477	#535	C₂²×C₃₁	1	2	yes	—
478	#533	—	2	1	no	—
479	#533	C₂²×C₃₁	1	1	yes	characteristic
480	#533	C₂²×C₃₁	1	2	yes	complemented
481	#532	C₂²×C₃₁	1	2	yes	—
482	#532	C₂²×C₃₁	1	2	yes	—
483	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
484	#529	—	2	2	no	—
485	#529	—	2	1	no	—
486	#529	C₂²×C₃₁	1	2	yes	complemented
487	#518	C₂²×C₃₁	1	2	yes	—
488	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
489	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
490	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
491	#479	C₂²×C₃₁	1	2	yes	complemented
492	#479	C₂²×C₃₁	1	4	yes	complemented
493	#478	C₂²×C₃₁	1	2	yes	complemented
494	#478	C₂²×C₃₁	1	4	yes	complemented
495	#478	C₂²×C₃₁	1	4	yes	complemented
496	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
497	#477	C₂²×C₃₁	1	2	yes	complemented
498	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
499	#476	C₂²×C₃₁	1	4	yes	complemented
500	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
501	#475	C₂²×C₃₁	1	2	yes	complemented
502	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
503	#474	C₂²×C₃₁	1	4	yes	complemented
504	#469	C₂²×C₃₁	1	4	yes	complemented
505	#468	C₂²×C₃₁	1	4	yes	complemented
506	#468	C₂²×C₃₁	1	4	yes	complemented
507	#468	C₂²×C₃₁	1	4	yes	complemented
508	#466	C₂²×C₃₁	1	4	yes	complemented
509	#465	C₂²×C₃₁	1	4	yes	complemented
510	#465	C₂²×C₃₁	1	4	yes	complemented
511	#465	C₂²×C₃₁	1	4	yes	complemented
512	#463	C₂²×C₃₁	1	4	yes	complemented
513	#463	C₂²×C₃₁	1	4	yes	complemented
514	#461	C₂²×C₃₁	1	4	yes	complemented
515	#461	C₂²×C₃₁	1	4	yes	complemented
516	#460	C₂²×C₃₁	1	2	yes	—
517	#460	C₂²×C₃₁	1	2	yes	—
518	#460	C₂²×C₃₁	1	2	yes	—
519	#460	C₂²×C₃₁	1	4	yes	—
520	#460	C₂²×C₃₁	1	2	yes	—
521	#459	C₂²×C₃₁	1	2	yes	—
522	#459	C₂²×C₃₁	1	2	yes	—
523	#428	C₂²×C₃₁	1	2	yes	—
524	#427	C₂²×C₃₁	1	2	yes	—
525	#424	C₂²×C₃₁	1	2	yes	—
526	#424	C₂²×C₃₁	1	4	yes	complemented
527	#423	C₂²×C₃₁	1	1	yes	characteristic
528	#423	C₂²×C₃₁	1	2	yes	complemented
529	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
530	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
531	#419	C₂²×C₃₁	1	2	yes	—
532	#418	C₂²×C₃₁	1	2	yes	—
533	#416	C₂²×C₃₁	1	2	yes	—
534	C₂×#102	C₂²×C₃₁	1	2	yes	—
535	C₂×C₃₁	—	2	2	no	—
536	C₂×C₃₁	—	4	2	no	—
537	C₂×C₃₁	—	8	1	no	—
538	C₂×C₃₁	—	8	4	no	—
539	C₂×C₃₁	C₂×#537	1	1	yes	characteristic
540	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
541	C₂×C₃₁	#3585	1	1	yes	characteristic
542	C₂×#41	—	2	2	no	—
543	C₂×#41	—	2	2	no	—
544	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
545	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
546	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
547	C₂²×D₄	—	2	1	no	—
548	C₂²×D₄	—	2	1	no	—
549	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
550	AGL(1,ℤ/8)	—	4	4	no	—
551	C₂×SD₁₆	—	4	4	no	—
552	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
553	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
554	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
555	C₂×D₈	C₂³×C₃₁	1	4	yes	—
556	#131	—	4	4	no	—
557	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
558	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
559	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
560	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
561	C₄⋊Q₈	—	2	1	no	—
562	C₄⋊Q₈	—	2	1	no	—
563	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
564	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
565	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
566	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
567	#127	—	2	2	no	—
568	#127	—	2	1	no	—
569	#127	—	2	1	no	—
570	#127	C₂³×C₃₁	1	2	yes	—
571	#127	C₂³×C₃₁	1	2	yes	—
572	#126	—	2	2	no	—
573	#126	—	2	2	no	—
574	#126	—	2	2	no	—
575	#126	—	2	2	no	—
576	#125	—	2	2	no	—
577	#125	—	2	1	no	—
578	#125	—	2	2	no	—
579	#125	—	2	2	no	—
580	#125	C₂³×C₃₁	1	2	yes	—
581	#125	C₂³×C₃₁	1	2	yes	—
582	#124	—	2	2	no	—
583	#124	—	2	1	no	—
584	#124	—	2	2	no	—
585	#124	—	2	2	no	—
586	#124	—	2	2	no	—
587	#124	C₂³×C₃₁	1	2	yes	—
588	#123	—	2	2	no	—
589	#123	—	2	2	no	—
590	#123	—	2	4	no	—
591	#123	—	2	4	no	—
592	#123	—	2	2	no	—
593	#123	—	2	2	no	—
594	C₂²⋊Q₈	—	2	1	no	—
595	C₂²⋊Q₈	—	2	1	no	—
596	C₂²⋊Q₈	—	2	1	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	—	2	1	no	—
599	C₂²⋊Q₈	—	2	1	no	—
600	C₂²⋊Q₈	—	2	2	no	—
601	C₂²⋊Q₈	—	2	2	no	—
602	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
603	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
604	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
605	#121	—	2	2	no	—
606	#121	—	2	1	no	—
607	#121	—	2	2	no	—
608	#121	—	2	2	no	—
609	#121	—	2	4	no	—
610	#121	—	2	4	no	—
611	#121	C₂³×C₃₁	1	2	yes	—
612	#121	C₂³×C₃₁	1	4	yes	—
613	#121	C₂³×C₃₁	1	4	yes	—
614	#120	—	2	4	no	—
615	C₄×Q₈	—	2	1	no	—
616	C₄×Q₈	—	2	1	no	—
617	C₄×Q₈	—	2	2	no	—
618	C₄×Q₈	—	2	1	no	—
619	C₄×Q₈	—	2	1	no	—
620	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
621	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
622	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
623	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
624	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
625	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	D₄×C₃₁	1	2	yes	—
634	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
635	C₄×D₄	D₄×C₃₁	1	2	yes	—
636	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
637	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
638	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
639	C₄×D₄	C₂³×C₃₁	1	4	yes	—
640	C₄×D₄	C₂³×C₃₁	1	4	yes	—
641	#117	—	2	2	no	—
642	#117	—	2	1	no	—
643	#117	—	2	2	no	—
644	#117	C₂³×C₃₁	1	1	yes	characteristic
645	#117	C₂³×C₃₁	1	2	yes	—
646	#117	C₂³×C₃₁	1	1	yes	characteristic
647	#117	C₂³×C₃₁	1	2	yes	—
648	C₂×C₄⋊C₄	—	2	1	no	—
649	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	—	2	4	no	—
651	C₂×C₄²	—	2	1	no	—
652	C₂×C₄²	—	2	1	no	—
653	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
655	#107	C₂³×C₃₁	1	2	yes	—
656	#107	C₂³×C₃₁	1	2	yes	—
657	#107	C₂³×C₃₁	1	4	yes	—
658	#106	C₂³×C₃₁	1	2	yes	—
659	#106	C₂³×C₃₁	1	2	yes	—
660	#106	C₂³×C₃₁	1	4	yes	—
661	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
662	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
663	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
664	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
665	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
666	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
667	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
668	#103	C₂³×C₃₁	1	2	yes	—
669	#103	C₂³×C₃₁	1	2	yes	—
670	#103	C₂³×C₃₁	1	4	yes	—
671	#103	C₂³×C₃₁	1	4	yes	—
672	#102	C₂³×C₃₁	1	4	yes	—
673	#102	C₂³×C₃₁	1	4	yes	—
674	#102	C₂³×C₃₁	1	2	yes	—
675	#102	C₂³×C₃₁	1	2	yes	—
676	#102	C₂³×C₃₁	1	4	yes	—
677	#102	C₂³×C₃₁	1	4	yes	—
678	C₃₁	#60924	1	1	yes	characteristic, direct product factor, Sylow
679	C₂⁴	—	2	2	no	—
680	#41	—	2	2	no	—
681	#41	—	2	2	no	—
682	#41	—	2	2	no	—
683	#41	—	2	2	no	—
684	#41	—	8	4	no	—
685	#41	—	8	4	no	—
686	C₂×Q₈	—	2	1	no	—
687	C₂×Q₈	—	2	1	no	—
688	C₂×Q₈	—	2	1	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	—	2	2	no	—
692	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
693	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
694	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	4	no	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	8	2	no	—
707	C₂×D₄	—	8	2	no	—
708	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
709	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
710	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
711	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
721	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
722	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
725	SD₁₆	—	4	4	no	—
726	SD₁₆	—	4	4	no	—
727	SD₁₆	—	4	4	no	—
728	D₈	—	4	4	no	—
729	M₁₆	—	2	4	no	—
730	M₁₆	—	4	4	no	—
731	C₂×C₈	—	2	4	no	—
732	C₂×C₈	—	4	4	no	—
733	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
734	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
735	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
754	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
755	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
756	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
757	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
758	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
759	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
760	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
761	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	1	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	1	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
777	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
778	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	1	no	—
781	C₄²	—	2	1	no	—
782	C₄²	—	2	1	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
786	C₄²	C₂×D₄×C₃₁	1	2	yes	—
787	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
788	C₄²	C₂×D₄×C₃₁	1	2	yes	—
789	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
790	C₄²	C₂⁴×C₃₁	1	2	yes	—
791	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
792	C₂³	—	2	1	no	—
793	C₂³	—	2	4	no	—
794	C₂³	—	4	4	no	—
795	C₂³	—	8	2	no	—
796	C₂³	—	8	2	no	—
797	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
798	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
799	Q₈	—	2	2	no	—
800	Q₈	—	2	2	no	—
801	Q₈	—	2	1	no	—
802	Q₈	—	2	2	no	—
803	Q₈	—	2	1	no	—
804	Q₈	—	4	2	no	—
805	Q₈	—	4	2	no	—
806	Q₈	—	4	2	no	—
807	Q₈	—	8	2	no	—
808	D₄	—	2	4	no	—
809	D₄	—	2	2	no	—
810	D₄	—	2	1	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	4	no	—
813	D₄	—	2	1	no	—
814	D₄	—	4	4	no	—
815	D₄	—	4	2	no	—
816	D₄	—	4	4	no	—
817	D₄	—	4	4	no	—
818	D₄	—	8	2	no	—
819	D₄	—	8	2	no	—
820	D₄	—	8	2	no	—
821	D₄	—	8	4	no	—
822	D₄	—	8	4	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	4	2	no	—
837	C₂×C₄	—	4	2	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	8	1	no	—
840	C₂×C₄	—	8	4	no	—
841	C₂×C₄	—	8	4	no	—
842	C₂×C₄	—	8	1	no	—
843	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
848	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
849	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
850	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
851	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
852	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
853	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
854	C₈	—	2	2	no	—
855	C₈	—	2	2	no	—
856	C₈	—	2	4	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	4	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	4	no	—
866	C₂²	—	4	4	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	16	4	no	—
869	C₂²	C₃₁×#537	1	2	yes	—
870	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
871	C₄	—	2	2	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	2	no	—
876	C₄	—	2	1	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	1	no	—
884	C₄	C₃₁×#537	1	2	yes	—
885	C₄	C₃₁×#577	1	2	yes	—
886	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
887	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
888	C₂	—	2	2	no	—
889	C₂	—	4	2	no	—
890	C₂	—	8	4	no	—
891	C₂	—	8	1	no	—
892	C₂	C₂×C₃₁×#537	1	1	yes	characteristic
893	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
894	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3508	C₂	semidirect
2. C₃₁×#3461	C₂	semidirect
3. C₃₁×#3260	C₂	semidirect
4. C₃₁×#3257	C₂	semidirect
5. C₃₁×#3254	C₂	semidirect
6. C₃₁×#3251	C₂	semidirect
7. C₃₁×#3247	C₂	semidirect
8. C₃₁×#3246	C₂	semidirect
9. C₃₁×#3081	C₂	semidirect
10. C₃₁×#3078	C₂	semidirect
11. C₃₁×#3076	C₂	semidirect
12. C₃₁×#3062	C₂	semidirect
13. C₃₁×#3057	C₂	semidirect
14. C₃₁×#3042	C₂	semidirect
15. C₃₁×#3038	C₂	semidirect
16. C₂×C₃₁×#460	C₂	semidirect
17. C₃₁×#2906	C₂	semidirect
29. C₃₁×#542	C₂²	semidirect
31. C₃₁×#541	C₂²	semidirect
40. C₃₁×#533	C₂²	semidirect
46. C₃₁×#529	C₂²	semidirect
51. C₃₁×#479	C₂²	semidirect
52. C₃₁×#479	C₂²	semidirect
53. C₃₁×#478	C₂²	semidirect
54. C₃₁×#478	C₂²	semidirect
55. C₃₁×#478	C₂²	semidirect
56. C₃₁×#477	C₂²	semidirect
57. C₃₁×#477	C₂²	semidirect
58. C₃₁×#476	C₂²	semidirect
59. C₃₁×#476	C₂²	semidirect
60. C₃₁×#475	C₂²	semidirect
61. C₃₁×#475	C₂²	semidirect
62. C₃₁×#474	C₂²	semidirect
63. C₃₁×#474	C₂²	semidirect
64. C₃₁×#469	C₂²	semidirect
65. C₃₁×#468	C₂²	semidirect
66. C₃₁×#468	C₂²	semidirect
67. C₃₁×#468	C₂²	semidirect
68. C₃₁×#466	C₂²	semidirect
69. C₃₁×#465	C₂²	semidirect
70. C₃₁×#465	C₂²	semidirect
71. C₃₁×#465	C₂²	semidirect
72. C₃₁×#463	C₂²	semidirect
73. C₃₁×#463	C₂²	semidirect
74. C₃₁×#461	C₂²	semidirect
75. C₃₁×#461	C₂²	semidirect
86. C₃₁×#424	C₂²	semidirect
88. C₃₁×#423	C₂²	semidirect
90. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
344. #60924	C₃₁	direct (N × H)
410. #3508	C₂×C₃₁	semidirect
411. #3461	C₂×C₃₁	semidirect
412. #3260	C₂×C₃₁	semidirect
413. #3257	C₂×C₃₁	semidirect
414. #3254	C₂×C₃₁	semidirect
415. #3251	C₂×C₃₁	semidirect
416. #3247	C₂×C₃₁	semidirect
417. #3246	C₂×C₃₁	semidirect
418. #3081	C₂×C₃₁	semidirect
419. #3078	C₂×C₃₁	semidirect
420. #3076	C₂×C₃₁	semidirect
421. #3062	C₂×C₃₁	semidirect
422. #3057	C₂×C₃₁	semidirect
423. #3042	C₂×C₃₁	semidirect
424. #3038	C₂×C₃₁	semidirect
425. C₂×#460	C₂×C₃₁	semidirect
426. #2906	C₂×C₃₁	semidirect
469. #542	C₂²×C₃₁	semidirect
471. #541	C₂²×C₃₁	semidirect
480. #533	C₂²×C₃₁	semidirect
486. #529	C₂²×C₃₁	semidirect
491. #479	C₂²×C₃₁	semidirect
492. #479	C₂²×C₃₁	semidirect
493. #478	C₂²×C₃₁	semidirect
494. #478	C₂²×C₃₁	semidirect
495. #478	C₂²×C₃₁	semidirect
496. #477	C₂²×C₃₁	semidirect
497. #477	C₂²×C₃₁	semidirect
498. #476	C₂²×C₃₁	semidirect
499. #476	C₂²×C₃₁	semidirect
500. #475	C₂²×C₃₁	semidirect
501. #475	C₂²×C₃₁	semidirect
502. #474	C₂²×C₃₁	semidirect
503. #474	C₂²×C₃₁	semidirect
504. #469	C₂²×C₃₁	semidirect
505. #468	C₂²×C₃₁	semidirect
506. #468	C₂²×C₃₁	semidirect
507. #468	C₂²×C₃₁	semidirect
508. #466	C₂²×C₃₁	semidirect
509. #465	C₂²×C₃₁	semidirect
510. #465	C₂²×C₃₁	semidirect
511. #465	C₂²×C₃₁	semidirect
512. #463	C₂²×C₃₁	semidirect
513. #463	C₂²×C₃₁	semidirect
514. #461	C₂²×C₃₁	semidirect
515. #461	C₂²×C₃₁	semidirect
526. #424	C₂²×C₃₁	semidirect
528. #423	C₂²×C₃₁	semidirect
530. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
678. C₃₁	#60924	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×#3508	2
C₃₁×#3461	2
C₃₁×#3260	2
C₃₁×#3257	2
C₃₁×#3254	2
C₃₁×#3251	2
C₃₁×#3247	2
C₃₁×#3246	2
C₃₁×#3081	2
C₃₁×#3078	2
C₃₁×#3076	2
C₃₁×#3062	2
C₃₁×#3057	2
C₃₁×#3042	2
C₃₁×#3038	2
C₂×C₃₁×#460	2
C₃₁×#2906	2
#60924	31

Subgroups — C31×#60924 #21517683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60924 #21517683