Subgroups — C₃₁×#62110 #21518869

Order 7936.

2030 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3384	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3366	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3354	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3345	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3325	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3318	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3253	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3245	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3235	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3109	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3077	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₃₁	—	2	1	no	—
19	C₃₁×#556	—	2	1	no	—
20	C₃₁×#555	C₂²	1	2	yes	complemented
21	C₃₁×#554	C₂²	1	2	yes	complemented
22	C₃₁×#553	C₂²	1	4	yes	complemented
23	C₃₁×#550	C₂²	1	1	yes	characteristic
24	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
25	C₃₁×#548	—	2	1	no	—
26	C₃₁×#548	—	2	2	no	—
27	C₃₁×#547	—	2	1	no	—
28	C₃₁×#547	C₂²	1	2	yes	—
29	C₃₁×#547	C₂²	1	1	yes	characteristic
30	C₃₁×#546	—	2	1	no	—
31	C₃₁×#546	—	2	2	no	—
32	D₄²×C₃₁	C₂²	1	2	yes	—
33	D₄²×C₃₁	C₂²	1	1	yes	characteristic
34	C₃₁×#542	—	2	2	no	—
35	C₃₁×#537	—	2	1	no	—
36	C₃₁×#533	C₂²	1	2	yes	complemented
37	C₃₁×#532	C₂²	1	1	yes	characteristic
38	C₃₁×#532	C₂²	1	2	yes	—
39	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#532	C₂²	1	2	yes	complemented
41	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#525	—	2	1	no	—
43	C₃₁×#525	—	2	2	no	—
44	C₃₁×#520	—	2	1	no	—
45	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
47	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
48	C₃₁×#501	C₂²	1	4	yes	complemented
49	C₃₁×#498	C₂²	1	2	yes	complemented
50	C₃₁×#490	C₂²	1	4	yes	complemented
51	C₃₁×#486	C₂²	1	2	yes	complemented
52	C₃₁×#482	C₂²	1	4	yes	complemented
53	C₃₁×#482	C₂²	1	4	yes	complemented
54	C₃₁×#481	C₂²	1	4	yes	complemented
55	C₃₁×#481	C₂²	1	4	yes	complemented
56	C₃₁×#480	C₂²	1	2	yes	complemented
57	C₃₁×#478	C₂²	1	4	yes	—
58	C₃₁×#478	C₂²	1	4	yes	complemented
59	C₃₁×#476	C₂²	1	2	yes	—
60	C₃₁×#476	C₂²	1	2	yes	—
61	C₃₁×#476	C₂²	1	2	yes	complemented
62	C₃₁×#476	C₂²	1	4	yes	complemented
63	C₃₁×#476	C₂²	1	2	yes	complemented
64	C₃₁×#476	C₂²	1	2	yes	complemented
65	C₃₁×#476	C₂²	1	2	yes	complemented
66	C₃₁×#474	C₂²	1	1	yes	characteristic
67	C₃₁×#474	C₂²	1	2	yes	complemented
68	C₃₁×#474	C₂²	1	2	yes	complemented
69	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#469	C₂²	1	4	yes	complemented
71	C₃₁×#469	C₂²	1	4	yes	complemented
72	C₃₁×#466	C₂²	1	4	yes	complemented
73	C₃₁×#459	C₂²	1	1	yes	characteristic
74	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
75	C₃₁×#459	C₂²	1	2	yes	complemented
76	C₃₁×#459	C₂²	1	2	yes	complemented
77	C₃₁×#459	C₂²	1	4	yes	complemented
78	C₃₁×#447	C₂²	1	2	yes	—
79	C₃₁×#447	C₂²	1	4	yes	—
80	C₃₁×#446	C₂²	1	2	yes	complemented
81	C₃₁×#442	C₂²	1	4	yes	—
82	C₃₁×#442	C₂²	1	4	yes	complemented
83	C₄×D₈×C₃₁	C₂²	1	2	yes	—
84	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
85	C₃₁×#436	C₂²	1	2	yes	complemented
86	C₃₁×#435	C₂²	1	4	yes	complemented
87	C₃₁×#432	C₂²	1	2	yes	complemented
88	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#428	C₂²	1	4	yes	complemented
90	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
91	C₃₁×#423	C₂²	1	2	yes	complemented
92	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#418	C₂²	1	4	yes	—
94	C₂×C₃₁×#102	C₂²	1	2	yes	—
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	2	no	—
97	C₂×#41×C₃₁	—	2	1	no	—
98	C₂×#41×C₃₁	—	2	1	no	—
99	C₂×#41×C₃₁	—	2	2	no	—
100	C₂×#41×C₃₁	—	2	1	no	—
101	C₂×#41×C₃₁	—	2	2	no	—
102	C₂×#41×C₃₁	—	4	8	no	—
103	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
104	C₂²×Q₈×C₃₁	—	2	1	no	—
105	C₂²×Q₈×C₃₁	—	2	1	no	—
106	C₂²×D₄×C₃₁	—	2	2	no	—
107	C₂²×D₄×C₃₁	—	2	1	no	—
108	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
110	C₂³×C₄×C₃₁	—	2	2	no	—
111	C₂³×C₄×C₃₁	—	2	1	no	—
112	C₂×D₈×C₃₁	C₂³	1	2	yes	—
113	C₂×D₈×C₃₁	C₂³	1	2	yes	—
114	C₂×D₈×C₃₁	C₂³	1	4	yes	—
115	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
116	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
117	C₃₁×C₄⋊Q₈	—	2	1	no	—
118	C₃₁×C₄⋊Q₈	—	2	1	no	—
119	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
123	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
124	C₃₁×#127	C₂³	1	1	yes	characteristic
125	C₃₁×#127	C₂³	1	1	yes	characteristic
126	C₃₁×#127	C₂³	1	2	yes	—
127	C₃₁×#126	—	2	4	no	—
128	C₃₁×#125	C₂³	1	4	yes	—
129	C₃₁×#124	—	2	4	no	—
130	C₃₁×#124	—	2	1	no	—
131	C₃₁×#124	—	2	2	no	—
132	C₃₁×#124	—	2	1	no	—
133	C₃₁×#124	—	2	2	no	—
134	C₃₁×#123	—	2	2	no	—
135	C₃₁×#123	—	2	2	no	—
136	C₃₁×#123	—	2	2	no	—
137	C₃₁×#123	—	2	4	no	—
138	C₃₁×C₂²⋊Q₈	—	2	2	no	—
139	C₃₁×C₂²⋊Q₈	—	2	2	no	—
140	C₃₁×C₂²⋊Q₈	—	2	2	no	—
141	C₃₁×C₂²⋊Q₈	—	2	1	no	—
142	C₃₁×C₂²⋊Q₈	—	2	2	no	—
143	C₃₁×C₂²⋊Q₈	—	2	1	no	—
144	C₃₁×C₂²⋊Q₈	—	2	2	no	—
145	C₃₁×C₂²⋊Q₈	—	2	4	no	—
146	C₃₁×#121	—	2	2	no	—
147	C₃₁×#121	—	2	4	no	—
148	C₃₁×#121	—	2	1	no	—
149	C₃₁×#121	—	2	2	no	—
150	C₃₁×#121	—	2	2	no	—
151	C₃₁×#121	—	2	1	no	—
152	C₃₁×#121	—	2	1	no	—
153	C₃₁×#121	—	2	2	no	—
154	C₃₁×#121	—	2	1	no	—
155	C₃₁×#121	—	2	2	no	—
156	C₃₁×#121	C₂³	1	2	yes	—
157	C₃₁×#121	C₂³	1	4	yes	—
158	C₃₁×#121	C₂³	1	2	yes	—
159	C₃₁×#121	C₂³	1	2	yes	—
160	C₃₁×#121	C₂³	1	2	yes	—
161	C₃₁×#120	—	2	2	no	—
162	C₃₁×#120	—	2	2	no	—
163	C₃₁×#120	—	2	2	no	—
164	C₄×Q₈×C₃₁	—	2	2	no	—
165	C₄×Q₈×C₃₁	—	2	2	no	—
166	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₃₁	—	2	4	no	—
169	C₄×D₄×C₃₁	—	2	2	no	—
170	C₄×D₄×C₃₁	—	2	1	no	—
171	C₄×D₄×C₃₁	—	2	1	no	—
172	C₄×D₄×C₃₁	—	2	2	no	—
173	C₄×D₄×C₃₁	—	2	2	no	—
174	C₄×D₄×C₃₁	—	2	2	no	—
175	C₄×D₄×C₃₁	—	2	1	no	—
176	C₄×D₄×C₃₁	—	2	1	no	—
177	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
178	C₄×D₄×C₃₁	D₄	1	2	yes	—
179	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₃₁	C₂³	1	2	yes	—
181	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₃₁	C₂³	1	2	yes	—
183	C₄×D₄×C₃₁	C₂³	1	4	yes	—
184	C₄×D₄×C₃₁	C₂³	1	2	yes	—
185	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₃₁	C₂³	1	2	yes	—
188	C₄×D₄×C₃₁	C₂³	1	2	yes	—
189	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₃₁×#117	—	2	2	no	—
191	C₃₁×#117	D₄	1	1	yes	characteristic
192	C₃₁×#117	D₄	1	2	yes	—
193	C₃₁×#117	C₂³	1	4	yes	—
194	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
195	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
196	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
200	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
201	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
203	C₃₁×#107	C₂³	1	2	yes	—
204	C₃₁×#107	C₂³	1	4	yes	—
205	C₃₁×#107	C₂³	1	2	yes	—
206	C₃₁×#106	C₂³	1	4	yes	—
207	C₃₁×#106	C₂³	1	4	yes	—
208	C₃₁×#106	C₂³	1	4	yes	—
209	C₃₁×#106	C₂³	1	4	yes	—
210	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
211	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
212	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
213	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
214	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₃₁×#102	C₂³	1	4	yes	—
216	C₃₁×#102	C₂³	1	4	yes	—
217	C₃₁×#102	C₂³	1	2	yes	—
218	C₃₁×#102	C₂³	1	4	yes	—
219	C₃₁×#102	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	2	yes	—
221	C₃₁×#102	C₂³	1	2	yes	—
222	C₃₁×#102	C₂³	1	2	yes	—
223	C₃₁×#102	C₂³	1	4	yes	—
224	C₃₁×#102	C₂³	1	4	yes	—
225	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₃₁×#97	C₂³	1	4	yes	—
228	C₄×C₈×C₃₁	C₂³	1	2	yes	—
229	C₂⁴×C₃₁	—	2	2	no	—
230	C₂⁴×C₃₁	—	2	1	no	—
231	#41×C₃₁	—	2	4	no	—
232	#41×C₃₁	—	4	8	no	—
233	#41×C₃₁	—	4	8	no	—
234	#41×C₃₁	—	4	4	no	—
235	#41×C₃₁	—	4	4	no	—
236	#41×C₃₁	—	4	4	no	—
237	#41×C₃₁	—	4	4	no	—
238	#41×C₃₁	—	8	4	no	—
239	C₂×Q₈×C₃₁	—	2	1	no	—
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	—	2	2	no	—
242	C₂×Q₈×C₃₁	—	2	1	no	—
243	C₂×Q₈×C₃₁	—	2	2	no	—
244	C₂×Q₈×C₃₁	—	4	4	no	—
245	C₂×Q₈×C₃₁	—	8	2	no	—
246	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
247	C₂×D₄×C₃₁	—	2	2	no	—
248	C₂×D₄×C₃₁	—	2	4	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	2	no	—
253	C₂×D₄×C₃₁	—	2	4	no	—
254	C₂×D₄×C₃₁	—	2	2	no	—
255	C₂×D₄×C₃₁	—	2	1	no	—
256	C₂×D₄×C₃₁	—	2	1	no	—
257	C₂×D₄×C₃₁	—	2	1	no	—
258	C₂×D₄×C₃₁	—	2	2	no	—
259	C₂×D₄×C₃₁	—	2	1	no	—
260	C₂×D₄×C₃₁	—	2	1	no	—
261	C₂×D₄×C₃₁	—	2	2	no	—
262	C₂×D₄×C₃₁	—	4	1	no	—
263	C₂×D₄×C₃₁	—	4	2	no	—
264	C₂×D₄×C₃₁	—	4	8	no	—
265	C₂×D₄×C₃₁	—	4	4	no	—
266	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
267	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
268	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
269	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
270	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
271	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₃₁	—	2	2	no	—
273	C₂²×C₄×C₃₁	—	2	1	no	—
274	C₂²×C₄×C₃₁	—	2	2	no	—
275	C₂²×C₄×C₃₁	—	2	2	no	—
276	C₂²×C₄×C₃₁	—	2	1	no	—
277	C₂²×C₄×C₃₁	—	2	2	no	—
278	C₂²×C₄×C₃₁	—	2	1	no	—
279	C₂²×C₄×C₃₁	—	2	2	no	—
280	C₂²×C₄×C₃₁	—	2	1	no	—
281	C₂²×C₄×C₃₁	—	2	2	no	—
282	C₂²×C₄×C₃₁	—	2	1	no	—
283	C₂²×C₄×C₃₁	—	2	4	no	—
284	C₂²×C₄×C₃₁	—	4	8	no	—
285	C₂²×C₄×C₃₁	—	4	4	no	—
286	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
289	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
292	D₈×C₃₁	—	2	4	no	—
293	D₈×C₃₁	—	4	4	no	—
294	D₈×C₃₁	—	4	2	no	—
295	M₁₆×C₃₁	—	4	4	no	—
296	C₂×C₈×C₃₁	—	4	2	no	—
297	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
298	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
299	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
300	C₄⋊C₄×C₃₁	—	2	2	no	—
301	C₄⋊C₄×C₃₁	—	2	2	no	—
302	C₄⋊C₄×C₃₁	—	2	4	no	—
303	C₄⋊C₄×C₃₁	—	2	2	no	—
304	C₄⋊C₄×C₃₁	—	2	1	no	—
305	C₄⋊C₄×C₃₁	—	2	2	no	—
306	C₄⋊C₄×C₃₁	—	2	1	no	—
307	C₄⋊C₄×C₃₁	—	2	1	no	—
308	C₄⋊C₄×C₃₁	—	2	2	no	—
309	C₄⋊C₄×C₃₁	—	2	4	no	—
310	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
311	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
312	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
313	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
314	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
315	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
316	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
317	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
318	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
319	C₂²⋊C₄×C₃₁	—	2	4	no	—
320	C₂²⋊C₄×C₃₁	—	2	1	no	—
321	C₂²⋊C₄×C₃₁	—	2	1	no	—
322	C₂²⋊C₄×C₃₁	—	2	2	no	—
323	C₂²⋊C₄×C₃₁	—	2	1	no	—
324	C₂²⋊C₄×C₃₁	—	2	2	no	—
325	C₂²⋊C₄×C₃₁	—	2	1	no	—
326	C₂²⋊C₄×C₃₁	—	2	2	no	—
327	C₂²⋊C₄×C₃₁	—	2	4	no	—
328	C₂²⋊C₄×C₃₁	—	2	2	no	—
329	C₂²⋊C₄×C₃₁	—	2	2	no	—
330	C₂²⋊C₄×C₃₁	—	2	2	no	—
331	C₂²⋊C₄×C₃₁	—	2	2	no	—
332	C₂²⋊C₄×C₃₁	—	2	4	no	—
333	C₂²⋊C₄×C₃₁	—	2	2	no	—
334	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
335	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
336	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
337	C₄²×C₃₁	—	2	4	no	—
338	C₄²×C₃₁	C₂×D₄	1	2	yes	—
339	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₃₁	C₂×D₄	1	2	yes	—
342	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₄²×C₃₁	C₂⁴	1	2	yes	—
344	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
345	#62110	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
346	C₂³×C₃₁	—	2	1	no	—
347	C₂³×C₃₁	—	2	2	no	—
348	C₂³×C₃₁	—	2	2	no	—
349	C₂³×C₃₁	—	2	1	no	—
350	C₂³×C₃₁	—	4	2	no	—
351	C₂³×C₃₁	—	4	4	no	—
352	C₂³×C₃₁	—	4	4	no	—
353	C₂³×C₃₁	—	4	2	no	—
354	C₂³×C₃₁	—	8	1	no	—
355	C₂³×C₃₁	—	8	2	no	—
356	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
357	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
358	Q₈×C₃₁	—	2	2	no	—
359	Q₈×C₃₁	—	4	4	no	—
360	Q₈×C₃₁	—	4	4	no	—
361	Q₈×C₃₁	—	4	2	no	—
362	Q₈×C₃₁	—	4	2	no	—
363	Q₈×C₃₁	—	8	2	no	—
364	D₄×C₃₁	—	2	4	no	—
365	D₄×C₃₁	—	2	2	no	—
366	D₄×C₃₁	—	2	2	no	—
367	D₄×C₃₁	—	2	1	no	—
368	D₄×C₃₁	—	2	2	no	—
369	D₄×C₃₁	—	2	1	no	—
370	D₄×C₃₁	—	2	2	no	—
371	D₄×C₃₁	—	2	2	no	—
372	D₄×C₃₁	—	2	1	no	—
373	D₄×C₃₁	—	4	2	no	—
374	D₄×C₃₁	—	4	4	no	—
375	D₄×C₃₁	—	4	4	no	—
376	D₄×C₃₁	—	4	2	no	—
377	D₄×C₃₁	—	4	4	no	—
378	D₄×C₃₁	—	4	4	no	—
379	D₄×C₃₁	—	4	4	no	—
380	D₄×C₃₁	—	4	4	no	—
381	D₄×C₃₁	—	4	2	no	—
382	D₄×C₃₁	—	4	2	no	—
383	D₄×C₃₁	—	8	2	no	—
384	D₄×C₃₁	—	8	1	no	—
385	D₄×C₃₁	—	8	4	no	—
386	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
387	C₂×C₄×C₃₁	—	2	4	no	—
388	C₂×C₄×C₃₁	—	2	1	no	—
389	C₂×C₄×C₃₁	—	2	2	no	—
390	C₂×C₄×C₃₁	—	2	1	no	—
391	C₂×C₄×C₃₁	—	2	2	no	—
392	C₂×C₄×C₃₁	—	2	2	no	—
393	C₂×C₄×C₃₁	—	2	4	no	—
394	C₂×C₄×C₃₁	—	2	1	no	—
395	C₂×C₄×C₃₁	—	2	2	no	—
396	C₂×C₄×C₃₁	—	2	1	no	—
397	C₂×C₄×C₃₁	—	4	1	no	—
398	C₂×C₄×C₃₁	—	4	2	no	—
399	C₂×C₄×C₃₁	—	4	4	no	—
400	C₂×C₄×C₃₁	—	4	4	no	—
401	C₂×C₄×C₃₁	—	4	4	no	—
402	C₂×C₄×C₃₁	—	4	2	no	—
403	C₂×C₄×C₃₁	—	4	2	no	—
404	C₂×C₄×C₃₁	—	4	2	no	—
405	C₂×C₄×C₃₁	—	4	2	no	—
406	C₂×C₄×C₃₁	—	4	4	no	—
407	C₂×C₄×C₃₁	—	4	2	no	—
408	C₂×C₄×C₃₁	—	4	4	no	—
409	C₂×C₄×C₃₁	—	8	4	no	—
410	C₂×C₄×C₃₁	—	8	2	no	—
411	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
412	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
421	C₈×C₃₁	—	2	2	no	—
422	C₈×C₃₁	—	2	4	no	—
423	C₈×C₃₁	—	2	2	no	—
424	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
425	D₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
426	#3384	C₂×C₃₁	1	2	yes	complemented
427	#3366	C₂×C₃₁	1	2	yes	complemented
428	#3354	C₂×C₃₁	1	2	yes	complemented
429	#3345	C₂×C₃₁	1	4	yes	complemented
430	#3325	C₂×C₃₁	1	2	yes	complemented
431	#3318	C₂×C₃₁	1	4	yes	complemented
432	#3253	C₂×C₃₁	1	2	yes	complemented
433	#3245	C₂×C₃₁	1	1	yes	characteristic, complemented
434	#3235	C₂×C₃₁	1	2	yes	complemented
435	#3227	C₂×C₃₁	1	1	yes	characteristic, complemented
436	#3109	C₂×C₃₁	1	2	yes	complemented
437	#3100	C₂×C₃₁	1	1	yes	characteristic, complemented
438	#3077	C₂×C₃₁	1	2	yes	complemented
439	C₂×#476	C₂×C₃₁	1	1	yes	characteristic, complemented
440	#2989	C₂×C₃₁	1	1	yes	characteristic, complemented
441	C₂²×C₃₁	—	2	1	no	—
442	C₂²×C₃₁	—	2	1	no	—
443	C₂²×C₃₁	—	2	2	no	—
444	C₂²×C₃₁	—	2	2	no	—
445	C₂²×C₃₁	—	2	2	no	—
446	C₂²×C₃₁	—	2	2	no	—
447	C₂²×C₃₁	—	4	1	no	—
448	C₂²×C₃₁	—	4	1	no	—
449	C₂²×C₃₁	—	4	2	no	—
450	C₂²×C₃₁	—	4	1	no	—
451	C₂²×C₃₁	—	4	2	no	—
452	C₂²×C₃₁	—	4	1	no	—
453	C₂²×C₃₁	—	4	2	no	—
454	C₂²×C₃₁	—	4	2	no	—
455	C₂²×C₃₁	—	4	2	no	—
456	C₂²×C₃₁	—	4	1	no	—
457	C₂²×C₃₁	—	4	2	no	—
458	C₂²×C₃₁	—	8	4	no	—
459	C₂²×C₃₁	—	8	8	no	—
460	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
461	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
462	C₄×C₃₁	—	2	1	no	—
463	C₄×C₃₁	—	2	2	no	—
464	C₄×C₃₁	—	2	1	no	—
465	C₄×C₃₁	—	2	1	no	—
466	C₄×C₃₁	—	2	2	no	—
467	C₄×C₃₁	—	2	2	no	—
468	C₄×C₃₁	—	4	4	no	—
469	C₄×C₃₁	—	4	1	no	—
470	C₄×C₃₁	—	4	2	no	—
471	C₄×C₃₁	—	4	1	no	—
472	C₄×C₃₁	—	4	2	no	—
473	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
474	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
475	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
476	C₄×C₃₁	#585	1	1	yes	characteristic
477	C₂²×#41	—	2	1	no	—
478	#556	—	2	1	no	—
479	#555	C₂²×C₃₁	1	2	yes	complemented
480	#554	C₂²×C₃₁	1	2	yes	complemented
481	#553	C₂²×C₃₁	1	4	yes	complemented
482	#550	C₂²×C₃₁	1	1	yes	characteristic
483	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
484	#548	—	2	1	no	—
485	#548	—	2	2	no	—
486	#547	—	2	1	no	—
487	#547	C₂²×C₃₁	1	2	yes	—
488	#547	C₂²×C₃₁	1	1	yes	characteristic
489	#546	—	2	1	no	—
490	#546	—	2	2	no	—
491	D₄²	C₂²×C₃₁	1	2	yes	—
492	D₄²	C₂²×C₃₁	1	1	yes	characteristic
493	#542	—	2	2	no	—
494	#537	—	2	1	no	—
495	#533	C₂²×C₃₁	1	2	yes	complemented
496	#532	C₂²×C₃₁	1	1	yes	characteristic
497	#532	C₂²×C₃₁	1	2	yes	—
498	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
499	#532	C₂²×C₃₁	1	2	yes	complemented
500	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
501	#525	—	2	1	no	—
502	#525	—	2	2	no	—
503	#520	—	2	1	no	—
504	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
505	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
506	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
507	#501	C₂²×C₃₁	1	4	yes	complemented
508	#498	C₂²×C₃₁	1	2	yes	complemented
509	#490	C₂²×C₃₁	1	4	yes	complemented
510	#486	C₂²×C₃₁	1	2	yes	complemented
511	#482	C₂²×C₃₁	1	4	yes	complemented
512	#482	C₂²×C₃₁	1	4	yes	complemented
513	#481	C₂²×C₃₁	1	4	yes	complemented
514	#481	C₂²×C₃₁	1	4	yes	complemented
515	#480	C₂²×C₃₁	1	2	yes	complemented
516	#478	C₂²×C₃₁	1	4	yes	—
517	#478	C₂²×C₃₁	1	4	yes	complemented
518	#476	C₂²×C₃₁	1	2	yes	—
519	#476	C₂²×C₃₁	1	2	yes	—
520	#476	C₂²×C₃₁	1	2	yes	complemented
521	#476	C₂²×C₃₁	1	4	yes	complemented
522	#476	C₂²×C₃₁	1	2	yes	complemented
523	#476	C₂²×C₃₁	1	2	yes	complemented
524	#476	C₂²×C₃₁	1	2	yes	complemented
525	#474	C₂²×C₃₁	1	1	yes	characteristic
526	#474	C₂²×C₃₁	1	2	yes	complemented
527	#474	C₂²×C₃₁	1	2	yes	complemented
528	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
529	#469	C₂²×C₃₁	1	4	yes	complemented
530	#469	C₂²×C₃₁	1	4	yes	complemented
531	#466	C₂²×C₃₁	1	4	yes	complemented
532	#459	C₂²×C₃₁	1	1	yes	characteristic
533	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
534	#459	C₂²×C₃₁	1	2	yes	complemented
535	#459	C₂²×C₃₁	1	2	yes	complemented
536	#459	C₂²×C₃₁	1	4	yes	complemented
537	#447	C₂²×C₃₁	1	2	yes	—
538	#447	C₂²×C₃₁	1	4	yes	—
539	#446	C₂²×C₃₁	1	2	yes	complemented
540	#442	C₂²×C₃₁	1	4	yes	—
541	#442	C₂²×C₃₁	1	4	yes	complemented
542	C₄×D₈	C₂²×C₃₁	1	2	yes	—
543	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
544	#436	C₂²×C₃₁	1	2	yes	complemented
545	#435	C₂²×C₃₁	1	4	yes	complemented
546	#432	C₂²×C₃₁	1	2	yes	complemented
547	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
548	#428	C₂²×C₃₁	1	4	yes	complemented
549	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
550	#423	C₂²×C₃₁	1	2	yes	complemented
551	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
552	#418	C₂²×C₃₁	1	4	yes	—
553	C₂×#102	C₂²×C₃₁	1	2	yes	—
554	C₂×C₃₁	—	2	2	no	—
555	C₂×C₃₁	—	4	2	no	—
556	C₂×C₃₁	—	4	2	no	—
557	C₂×C₃₁	—	8	2	no	—
558	C₂×C₃₁	—	8	1	no	—
559	C₂×C₃₁	—	8	2	no	—
560	C₂×C₃₁	#3489	1	1	yes	characteristic
561	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
562	C₂×C₃₁	#3585	1	1	yes	characteristic
563	C₂×#41	—	2	1	no	—
564	C₂×#41	—	2	2	no	—
565	C₂×#41	—	2	1	no	—
566	C₂×#41	—	2	1	no	—
567	C₂×#41	—	2	2	no	—
568	C₂×#41	—	2	1	no	—
569	C₂×#41	—	2	2	no	—
570	C₂×#41	—	4	8	no	—
571	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
572	C₂²×Q₈	—	2	1	no	—
573	C₂²×Q₈	—	2	1	no	—
574	C₂²×D₄	—	2	2	no	—
575	C₂²×D₄	—	2	1	no	—
576	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
577	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
578	C₂³×C₄	—	2	2	no	—
579	C₂³×C₄	—	2	1	no	—
580	C₂×D₈	C₂³×C₃₁	1	2	yes	—
581	C₂×D₈	C₂³×C₃₁	1	2	yes	—
582	C₂×D₈	C₂³×C₃₁	1	4	yes	—
583	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
584	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
585	C₄⋊Q₈	—	2	1	no	—
586	C₄⋊Q₈	—	2	1	no	—
587	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
588	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
589	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
590	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
591	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
592	#127	C₂³×C₃₁	1	1	yes	characteristic
593	#127	C₂³×C₃₁	1	2	yes	—
594	#127	C₂³×C₃₁	1	1	yes	characteristic
595	#126	—	2	4	no	—
596	#125	C₂³×C₃₁	1	4	yes	—
597	#124	—	2	4	no	—
598	#124	—	2	1	no	—
599	#124	—	2	2	no	—
600	#124	—	2	1	no	—
601	#124	—	2	2	no	—
602	#123	—	2	2	no	—
603	#123	—	2	2	no	—
604	#123	—	2	2	no	—
605	#123	—	2	4	no	—
606	C₂²⋊Q₈	—	2	2	no	—
607	C₂²⋊Q₈	—	2	2	no	—
608	C₂²⋊Q₈	—	2	2	no	—
609	C₂²⋊Q₈	—	2	1	no	—
610	C₂²⋊Q₈	—	2	2	no	—
611	C₂²⋊Q₈	—	2	1	no	—
612	C₂²⋊Q₈	—	2	2	no	—
613	C₂²⋊Q₈	—	2	4	no	—
614	#121	—	2	2	no	—
615	#121	—	2	4	no	—
616	#121	—	2	1	no	—
617	#121	—	2	2	no	—
618	#121	—	2	2	no	—
619	#121	—	2	1	no	—
620	#121	—	2	1	no	—
621	#121	—	2	2	no	—
622	#121	—	2	1	no	—
623	#121	—	2	2	no	—
624	#121	C₂³×C₃₁	1	2	yes	—
625	#121	C₂³×C₃₁	1	2	yes	—
626	#121	C₂³×C₃₁	1	2	yes	—
627	#121	C₂³×C₃₁	1	2	yes	—
628	#121	C₂³×C₃₁	1	4	yes	—
629	#120	—	2	2	no	—
630	#120	—	2	2	no	—
631	#120	—	2	2	no	—
632	C₄×Q₈	—	2	2	no	—
633	C₄×Q₈	—	2	2	no	—
634	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
635	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
636	C₄×D₄	—	2	4	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	1	no	—
639	C₄×D₄	—	2	1	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	2	no	—
643	C₄×D₄	—	2	1	no	—
644	C₄×D₄	—	2	1	no	—
645	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
646	C₄×D₄	D₄×C₃₁	1	2	yes	—
647	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
648	C₄×D₄	C₂³×C₃₁	1	2	yes	—
649	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
650	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
651	C₄×D₄	C₂³×C₃₁	1	2	yes	—
652	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
653	C₄×D₄	C₂³×C₃₁	1	2	yes	—
654	C₄×D₄	C₂³×C₃₁	1	4	yes	—
655	C₄×D₄	C₂³×C₃₁	1	2	yes	—
656	C₄×D₄	C₂³×C₃₁	1	2	yes	—
657	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
658	#117	—	2	2	no	—
659	#117	D₄×C₃₁	1	1	yes	characteristic
660	#117	D₄×C₃₁	1	2	yes	—
661	#117	C₂³×C₃₁	1	4	yes	—
662	C₂×C₄⋊C₄	—	2	1	no	—
663	C₂×C₄⋊C₄	—	2	2	no	—
664	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
667	C₂×C₂²⋊C₄	—	2	1	no	—
668	C₂×C₂²⋊C₄	—	2	2	no	—
669	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
670	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
671	#107	C₂³×C₃₁	1	2	yes	—
672	#107	C₂³×C₃₁	1	4	yes	—
673	#107	C₂³×C₃₁	1	2	yes	—
674	#106	C₂³×C₃₁	1	4	yes	—
675	#106	C₂³×C₃₁	1	4	yes	—
676	#106	C₂³×C₃₁	1	4	yes	—
677	#106	C₂³×C₃₁	1	4	yes	—
678	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
679	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
680	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
681	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
682	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
683	#102	C₂³×C₃₁	1	4	yes	—
684	#102	C₂³×C₃₁	1	4	yes	—
685	#102	C₂³×C₃₁	1	2	yes	—
686	#102	C₂³×C₃₁	1	4	yes	—
687	#102	C₂³×C₃₁	1	4	yes	—
688	#102	C₂³×C₃₁	1	2	yes	—
689	#102	C₂³×C₃₁	1	2	yes	—
690	#102	C₂³×C₃₁	1	2	yes	—
691	#102	C₂³×C₃₁	1	4	yes	—
692	#102	C₂³×C₃₁	1	4	yes	—
693	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
694	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
695	#97	C₂³×C₃₁	1	4	yes	—
696	C₄×C₈	C₂³×C₃₁	1	2	yes	—
697	C₃₁	#62110	1	1	yes	characteristic, direct product factor, Sylow
698	C₂⁴	—	2	2	no	—
699	C₂⁴	—	2	1	no	—
700	#41	—	2	4	no	—
701	#41	—	4	8	no	—
702	#41	—	4	8	no	—
703	#41	—	4	4	no	—
704	#41	—	4	4	no	—
705	#41	—	4	4	no	—
706	#41	—	4	4	no	—
707	#41	—	8	4	no	—
708	C₂×Q₈	—	2	1	no	—
709	C₂×Q₈	—	2	2	no	—
710	C₂×Q₈	—	2	2	no	—
711	C₂×Q₈	—	2	1	no	—
712	C₂×Q₈	—	2	2	no	—
713	C₂×Q₈	—	4	4	no	—
714	C₂×Q₈	—	8	2	no	—
715	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	1	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	4	1	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	8	no	—
734	C₂×D₄	—	4	4	no	—
735	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
736	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
737	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
738	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
739	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
740	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	1	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	—	4	8	no	—
754	C₂²×C₄	—	4	4	no	—
755	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
756	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
757	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
758	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
761	D₈	—	2	4	no	—
762	D₈	—	4	4	no	—
763	D₈	—	4	2	no	—
764	M₁₆	—	4	4	no	—
765	C₂×C₈	—	4	2	no	—
766	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
767	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
768	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	4	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	1	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	1	no	—
776	C₄⋊C₄	—	2	1	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
780	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
781	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
782	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
783	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
784	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
785	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
786	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
787	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	1	no	—
790	C₂²⋊C₄	—	2	1	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	1	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
804	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
805	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
806	C₄²	—	2	4	no	—
807	C₄²	C₂×D₄×C₃₁	1	2	yes	—
808	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
809	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
810	C₄²	C₂×D₄×C₃₁	1	2	yes	—
811	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
812	C₄²	C₂⁴×C₃₁	1	2	yes	—
813	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
814	C₂³	—	2	1	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	4	2	no	—
819	C₂³	—	4	4	no	—
820	C₂³	—	4	4	no	—
821	C₂³	—	4	2	no	—
822	C₂³	—	8	1	no	—
823	C₂³	—	8	2	no	—
824	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
825	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
826	Q₈	—	2	2	no	—
827	Q₈	—	4	4	no	—
828	Q₈	—	4	4	no	—
829	Q₈	—	4	2	no	—
830	Q₈	—	4	2	no	—
831	Q₈	—	8	2	no	—
832	D₄	—	2	4	no	—
833	D₄	—	2	2	no	—
834	D₄	—	2	2	no	—
835	D₄	—	2	1	no	—
836	D₄	—	2	2	no	—
837	D₄	—	2	1	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	2	no	—
840	D₄	—	2	1	no	—
841	D₄	—	4	2	no	—
842	D₄	—	4	4	no	—
843	D₄	—	4	4	no	—
844	D₄	—	4	2	no	—
845	D₄	—	4	4	no	—
846	D₄	—	4	4	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	2	no	—
850	D₄	—	4	2	no	—
851	D₄	—	8	2	no	—
852	D₄	—	8	1	no	—
853	D₄	—	8	4	no	—
854	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	4	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	2	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	—	4	2	no	—
873	C₂×C₄	—	4	2	no	—
874	C₂×C₄	—	4	4	no	—
875	C₂×C₄	—	4	2	no	—
876	C₂×C₄	—	4	4	no	—
877	C₂×C₄	—	8	4	no	—
878	C₂×C₄	—	8	2	no	—
879	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
880	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
881	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
882	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
883	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
884	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
885	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
886	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
887	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
888	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
889	C₈	—	2	2	no	—
890	C₈	—	2	4	no	—
891	C₈	—	2	2	no	—
892	C₂²	—	2	1	no	—
893	C₂²	—	2	1	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	4	1	no	—
899	C₂²	—	4	1	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	1	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	1	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	8	4	no	—
910	C₂²	—	8	8	no	—
911	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
912	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
913	C₄	—	2	1	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	1	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	4	no	—
924	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
925	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
926	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
927	C₄	C₃₁×#585	1	1	yes	characteristic
928	C₂	—	2	2	no	—
929	C₂	—	4	2	no	—
930	C₂	—	4	2	no	—
931	C₂	—	8	1	no	—
932	C₂	—	8	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₃₁×#3489	1	1	yes	characteristic
935	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
936	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×#3511	C₂	semidirect
2. D₄×#41×C₃₁	C₂	semidirect
3. C₃₁×#3384	C₂	semidirect
4. C₃₁×#3366	C₂	semidirect
5. C₃₁×#3354	C₂	semidirect
6. C₃₁×#3345	C₂	semidirect
7. C₃₁×#3325	C₂	semidirect
8. C₃₁×#3318	C₂	semidirect
9. C₃₁×#3253	C₂	semidirect
10. C₃₁×#3245	C₂	semidirect
11. C₃₁×#3235	C₂	semidirect
12. C₃₁×#3227	C₂	semidirect
13. C₃₁×#3109	C₂	semidirect
14. C₃₁×#3100	C₂	semidirect
15. C₃₁×#3077	C₂	semidirect
16. C₂×C₃₁×#476	C₂	semidirect
17. C₃₁×#2989	C₂	semidirect
20. C₃₁×#555	C₂²	semidirect
21. C₃₁×#554	C₂²	semidirect
22. C₃₁×#553	C₂²	semidirect
36. C₃₁×#533	C₂²	semidirect
39. C₃₁×#532	C₂²	semidirect
40. C₃₁×#532	C₂²	semidirect
41. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
48. C₃₁×#501	C₂²	semidirect
49. C₃₁×#498	C₂²	semidirect
50. C₃₁×#490	C₂²	semidirect
51. C₃₁×#486	C₂²	semidirect
52. C₃₁×#482	C₂²	semidirect
53. C₃₁×#482	C₂²	semidirect
54. C₃₁×#481	C₂²	semidirect
55. C₃₁×#481	C₂²	semidirect
56. C₃₁×#480	C₂²	semidirect
58. C₃₁×#478	C₂²	semidirect
61. C₃₁×#476	C₂²	semidirect
62. C₃₁×#476	C₂²	semidirect
63. C₃₁×#476	C₂²	semidirect
64. C₃₁×#476	C₂²	semidirect
65. C₃₁×#476	C₂²	semidirect
67. C₃₁×#474	C₂²	semidirect
68. C₃₁×#474	C₂²	semidirect
69. C₃₁×#474	C₂²	semidirect
70. C₃₁×#469	C₂²	semidirect
71. C₃₁×#469	C₂²	semidirect
72. C₃₁×#466	C₂²	semidirect
74. C₃₁×#459	C₂²	semidirect
75. C₃₁×#459	C₂²	semidirect
76. C₃₁×#459	C₂²	semidirect
77. C₃₁×#459	C₂²	semidirect
80. C₃₁×#446	C₂²	semidirect
82. C₃₁×#442	C₂²	semidirect
84. C₄×D₈×C₃₁	C₂²	semidirect
85. C₃₁×#436	C₂²	semidirect
86. C₃₁×#435	C₂²	semidirect
87. C₃₁×#432	C₂²	semidirect
88. C₃₁×#431	C₂²	semidirect
89. C₃₁×#428	C₂²	semidirect
90. C₂×C₃₁×#106	C₂²	semidirect
91. C₃₁×#423	C₂²	semidirect
92. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
345. #62110	C₃₁	direct (N × H)
424. #3511	C₂×C₃₁	semidirect
425. D₄×#41	C₂×C₃₁	semidirect
426. #3384	C₂×C₃₁	semidirect
427. #3366	C₂×C₃₁	semidirect
428. #3354	C₂×C₃₁	semidirect
429. #3345	C₂×C₃₁	semidirect
430. #3325	C₂×C₃₁	semidirect
431. #3318	C₂×C₃₁	semidirect
432. #3253	C₂×C₃₁	semidirect
433. #3245	C₂×C₃₁	semidirect
434. #3235	C₂×C₃₁	semidirect
435. #3227	C₂×C₃₁	semidirect
436. #3109	C₂×C₃₁	semidirect
437. #3100	C₂×C₃₁	semidirect
438. #3077	C₂×C₃₁	semidirect
439. C₂×#476	C₂×C₃₁	semidirect
440. #2989	C₂×C₃₁	semidirect
479. #555	C₂²×C₃₁	semidirect
480. #554	C₂²×C₃₁	semidirect
481. #553	C₂²×C₃₁	semidirect
495. #533	C₂²×C₃₁	semidirect
498. #532	C₂²×C₃₁	semidirect
499. #532	C₂²×C₃₁	semidirect
500. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
507. #501	C₂²×C₃₁	semidirect
508. #498	C₂²×C₃₁	semidirect
509. #490	C₂²×C₃₁	semidirect
510. #486	C₂²×C₃₁	semidirect
511. #482	C₂²×C₃₁	semidirect
512. #482	C₂²×C₃₁	semidirect
513. #481	C₂²×C₃₁	semidirect
514. #481	C₂²×C₃₁	semidirect
515. #480	C₂²×C₃₁	semidirect
517. #478	C₂²×C₃₁	semidirect
520. #476	C₂²×C₃₁	semidirect
521. #476	C₂²×C₃₁	semidirect
522. #476	C₂²×C₃₁	semidirect
523. #476	C₂²×C₃₁	semidirect
524. #476	C₂²×C₃₁	semidirect
526. #474	C₂²×C₃₁	semidirect
527. #474	C₂²×C₃₁	semidirect
528. #474	C₂²×C₃₁	semidirect
529. #469	C₂²×C₃₁	semidirect
530. #469	C₂²×C₃₁	semidirect
531. #466	C₂²×C₃₁	semidirect
533. #459	C₂²×C₃₁	semidirect
534. #459	C₂²×C₃₁	semidirect
535. #459	C₂²×C₃₁	semidirect
536. #459	C₂²×C₃₁	semidirect
539. #446	C₂²×C₃₁	semidirect
541. #442	C₂²×C₃₁	semidirect
543. C₄×D₈	C₂²×C₃₁	semidirect
544. #436	C₂²×C₃₁	semidirect
545. #435	C₂²×C₃₁	semidirect
546. #432	C₂²×C₃₁	semidirect
547. #431	C₂²×C₃₁	semidirect
548. #428	C₂²×C₃₁	semidirect
549. C₂×#106	C₂²×C₃₁	semidirect
550. #423	C₂²×C₃₁	semidirect
551. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
697. C₃₁	#62110	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×#3511	2
D₄×#41×C₃₁	2
C₃₁×#3384	2
C₃₁×#3366	2
C₃₁×#3354	2
C₃₁×#3345	2
C₃₁×#3325	2
C₃₁×#3318	2
C₃₁×#3253	2
C₃₁×#3245	2
C₃₁×#3235	2
C₃₁×#3227	2
C₃₁×#3109	2
C₃₁×#3100	2
C₃₁×#3077	2
C₂×C₃₁×#476	2
C₃₁×#2989	2
#62110	31

Subgroups — C31×#62110 #21518869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62110 #21518869