Subgroups — C₃₁×#62592 #21519351

Order 7936.

1790 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3361	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3360	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3329	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3326	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3325	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3322	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3240	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3238	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3214	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3213	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3171	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3171	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3141	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3140	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2971	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#559	C₂²	1	1	yes	characteristic
19	C₃₁×#556	—	2	1	no	—
20	C₃₁×#556	C₂²	1	1	yes	characteristic
21	C₃₁×#555	—	2	1	no	—
22	C₃₁×#555	C₂²	1	2	yes	—
23	C₃₁×#554	C₂²	1	2	yes	complemented
24	C₃₁×#553	C₂²	1	4	yes	complemented
25	C₃₁×#551	—	2	2	no	—
26	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#548	—	2	2	no	—
28	C₃₁×#548	C₂²	1	2	yes	—
29	C₃₁×#547	—	2	1	no	—
30	C₃₁×#546	—	2	1	no	—
31	C₃₁×#546	C₂²	1	2	yes	—
32	D₄²×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#542	—	2	1	no	—
34	C₃₁×#542	—	2	2	no	—
35	C₃₁×#538	—	2	2	no	—
36	C₃₁×#537	—	2	1	no	—
37	C₃₁×#533	C₂²	1	2	yes	complemented
38	C₃₁×#532	C₂²	1	1	yes	characteristic
39	C₃₁×#532	C₂²	1	2	yes	complemented
40	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#529	C₂²	1	1	yes	characteristic
43	C₃₁×#529	C₂²	1	2	yes	—
44	C₂×C₃₁×#124	C₂²	1	2	yes	—
45	C₃₁×#520	—	2	1	no	—
46	C₃₁×#518	—	2	1	no	—
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
48	C₃₁×#501	C₂²	1	2	yes	complemented
49	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#496	C₂²	1	1	yes	characteristic
51	C₃₁×#496	C₂²	1	2	yes	complemented
52	C₃₁×#490	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#489	C₂²	1	1	yes	characteristic
54	C₃₁×#489	C₂²	1	2	yes	—
55	C₃₁×#489	C₂²	1	2	yes	complemented
56	C₃₁×#489	C₂²	1	2	yes	complemented
57	C₃₁×#489	C₂²	1	2	yes	complemented
58	C₃₁×#488	C₂²	1	4	yes	—
59	C₃₁×#488	C₂²	1	4	yes	complemented
60	C₃₁×#487	C₂²	1	2	yes	complemented
61	C₃₁×#486	C₂²	1	2	yes	—
62	C₃₁×#485	C₂²	1	4	yes	complemented
63	C₃₁×#483	C₂²	1	2	yes	complemented
64	C₃₁×#482	C₂²	1	4	yes	—
65	C₃₁×#480	C₂²	1	2	yes	—
66	C₃₁×#479	C₂²	1	4	yes	complemented
67	C₃₁×#478	C₂²	1	4	yes	complemented
68	C₃₁×#477	C₂²	1	2	yes	complemented
69	C₃₁×#476	C₂²	1	2	yes	—
70	C₃₁×#469	C₂²	1	2	yes	—
71	C₃₁×#469	C₂²	1	4	yes	—
72	C₃₁×#468	C₂²	1	4	yes	complemented
73	C₃₁×#468	C₂²	1	2	yes	complemented
74	C₃₁×#463	C₂²	1	4	yes	—
75	C₃₁×#463	C₂²	1	4	yes	complemented
76	C₃₁×#461	C₂²	1	2	yes	complemented
77	C₃₁×#459	C₂²	1	2	yes	—
78	C₃₁×#449	C₂²	1	4	yes	complemented
79	C₃₁×#448	C₂²	1	4	yes	complemented
80	C₃₁×#447	C₂²	1	4	yes	—
81	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
82	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
83	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
84	C₄×D₈×C₃₁	C₂²	1	2	yes	—
85	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
86	C₃₁×#436	C₂²	1	2	yes	—
87	C₃₁×#436	C₂²	1	4	yes	complemented
88	C₃₁×#432	C₂²	1	2	yes	complemented
89	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#419	C₂²	1	4	yes	complemented
91	C₃₁×#418	C₂²	1	4	yes	—
92	C₃₁×#417	C₂²	1	4	yes	complemented
93	C₄×M₁₆×C₃₁	C₂²	1	2	yes	complemented
94	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	2	no	—
97	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
98	C₂×#41×C₃₁	C₂³	1	2	yes	—
99	C₂²×Q₈×C₃₁	—	2	1	no	—
100	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
101	C₂²×D₄×C₃₁	—	2	1	no	—
102	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
105	C₂×D₈×C₃₁	C₂³	1	2	yes	—
106	C₂×D₈×C₃₁	C₂³	1	4	yes	—
107	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
108	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
109	C₃₁×C₄⋊Q₈	—	2	1	no	—
110	C₃₁×C₄⋊Q₈	—	2	1	no	—
111	C₃₁×C₄⋊Q₈	—	2	1	no	—
112	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₃₁×#127	C₂³	1	1	yes	characteristic
117	C₃₁×#127	C₂³	1	1	yes	characteristic
118	C₃₁×#126	—	2	2	no	—
119	C₃₁×#126	—	2	4	no	—
120	C₃₁×#126	—	2	2	no	—
121	C₃₁×#126	—	2	1	no	—
122	C₃₁×#125	C₂³	1	4	yes	—
123	C₃₁×#125	C₂³	1	1	yes	characteristic
124	C₃₁×#124	—	2	1	no	—
125	C₃₁×#124	—	2	2	no	—
126	C₃₁×#124	—	2	4	no	—
127	C₃₁×#124	—	2	2	no	—
128	C₃₁×#124	—	2	2	no	—
129	C₃₁×#124	—	2	1	no	—
130	C₃₁×#124	—	2	2	no	—
131	C₃₁×#124	C₂³	1	2	yes	—
132	C₃₁×#124	C₂³	1	2	yes	—
133	C₃₁×#124	C₂³	1	1	yes	characteristic
134	C₃₁×#124	C₂³	1	2	yes	—
135	C₃₁×#123	—	2	1	no	—
136	C₃₁×#123	—	2	2	no	—
137	C₃₁×#123	—	2	2	no	—
138	C₃₁×#123	—	2	2	no	—
139	C₃₁×#123	—	2	4	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	2	no	—
144	C₃₁×C₂²⋊Q₈	—	2	4	no	—
145	C₃₁×C₂²⋊Q₈	—	2	2	no	—
146	C₃₁×C₂²⋊Q₈	—	2	2	no	—
147	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
148	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₃₁×#121	—	2	2	no	—
150	C₃₁×#121	—	2	4	no	—
151	C₃₁×#121	—	2	2	no	—
152	C₃₁×#121	—	2	1	no	—
153	C₃₁×#121	—	2	1	no	—
154	C₃₁×#121	—	2	2	no	—
155	C₃₁×#121	—	2	1	no	—
156	C₃₁×#121	—	2	1	no	—
157	C₃₁×#121	—	2	2	no	—
158	C₃₁×#121	C₂³	1	4	yes	—
159	C₃₁×#121	C₂³	1	2	yes	—
160	C₃₁×#121	C₂³	1	1	yes	characteristic
161	C₃₁×#121	C₂³	1	2	yes	—
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×Q₈×C₃₁	C₂³	1	2	yes	—
169	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₃₁	—	2	1	no	—
171	C₄×D₄×C₃₁	—	2	2	no	—
172	C₄×D₄×C₃₁	—	2	1	no	—
173	C₄×D₄×C₃₁	—	2	1	no	—
174	C₄×D₄×C₃₁	—	2	2	no	—
175	C₄×D₄×C₃₁	—	2	4	no	—
176	C₄×D₄×C₃₁	—	2	1	no	—
177	C₄×D₄×C₃₁	—	2	2	no	—
178	C₄×D₄×C₃₁	—	2	1	no	—
179	C₄×D₄×C₃₁	—	2	1	no	—
180	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
181	C₄×D₄×C₃₁	D₄	1	2	yes	—
182	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₃₁	C₂³	1	2	yes	—
184	C₄×D₄×C₃₁	C₂³	1	2	yes	—
185	C₄×D₄×C₃₁	C₂³	1	4	yes	—
186	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₃₁	C₂³	1	2	yes	—
188	C₃₁×#117	—	2	1	no	—
189	C₃₁×#117	—	2	2	no	—
190	C₃₁×#117	—	2	1	no	—
191	C₃₁×#117	—	2	2	no	—
192	C₃₁×#117	D₄	1	1	yes	characteristic
193	C₃₁×#117	D₄	1	2	yes	—
194	C₃₁×#117	C₂³	1	4	yes	—
195	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
196	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
197	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
201	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
203	C₃₁×#107	C₂³	1	2	yes	—
204	C₃₁×#107	C₂³	1	4	yes	—
205	C₃₁×#106	C₂³	1	4	yes	—
206	C₃₁×#106	C₂³	1	2	yes	—
207	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
208	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
209	C₃₁×#103	C₂³	1	4	yes	—
210	C₃₁×#103	C₂³	1	4	yes	—
211	C₃₁×#103	C₂³	1	2	yes	—
212	C₃₁×#103	C₂³	1	4	yes	—
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	2	yes	—
217	C₃₁×#102	C₂³	1	4	yes	—
218	C₃₁×#102	C₂³	1	4	yes	—
219	C₃₁×#102	C₂³	1	2	yes	—
220	C₃₁×#102	C₂³	1	2	yes	—
221	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
222	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₃₁×#97	C₂³	1	1	yes	characteristic
224	C₃₁×#97	C₂³	1	2	yes	—
225	C₃₁×#97	C₂³	1	1	yes	characteristic
226	C₄×C₈×C₃₁	C₂³	1	2	yes	—
227	C₄×C₈×C₃₁	C₂³	1	4	yes	—
228	C₂⁴×C₃₁	—	2	2	no	—
229	#41×C₃₁	—	4	2	no	—
230	#41×C₃₁	—	4	4	no	—
231	#41×C₃₁	—	4	4	no	—
232	#41×C₃₁	—	8	4	no	—
233	C₂×Q₈×C₃₁	—	2	1	no	—
234	C₂×Q₈×C₃₁	—	2	2	no	—
235	C₂×Q₈×C₃₁	—	2	2	no	—
236	C₂×Q₈×C₃₁	—	2	2	no	—
237	C₂×Q₈×C₃₁	—	4	4	no	—
238	C₂×Q₈×C₃₁	—	8	2	no	—
239	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
241	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
242	C₂×D₄×C₃₁	—	2	2	no	—
243	C₂×D₄×C₃₁	—	2	2	no	—
244	C₂×D₄×C₃₁	—	2	1	no	—
245	C₂×D₄×C₃₁	—	2	2	no	—
246	C₂×D₄×C₃₁	—	2	4	no	—
247	C₂×D₄×C₃₁	—	2	1	no	—
248	C₂×D₄×C₃₁	—	2	1	no	—
249	C₂×D₄×C₃₁	—	2	1	no	—
250	C₂×D₄×C₃₁	—	2	1	no	—
251	C₂×D₄×C₃₁	—	2	2	no	—
252	C₂×D₄×C₃₁	—	4	4	no	—
253	C₂×D₄×C₃₁	—	4	4	no	—
254	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
256	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
258	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₃₁	—	2	2	no	—
260	C₂²×C₄×C₃₁	—	2	2	no	—
261	C₂²×C₄×C₃₁	—	2	2	no	—
262	C₂²×C₄×C₃₁	—	2	1	no	—
263	C₂²×C₄×C₃₁	—	2	2	no	—
264	C₂²×C₄×C₃₁	—	2	2	no	—
265	C₂²×C₄×C₃₁	—	2	4	no	—
266	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
272	SD₁₆×C₃₁	—	4	2	no	—
273	SD₁₆×C₃₁	—	4	4	no	—
274	D₈×C₃₁	—	4	4	no	—
275	D₈×C₃₁	—	4	2	no	—
276	M₁₆×C₃₁	—	4	4	no	—
277	M₁₆×C₃₁	—	4	2	no	—
278	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
279	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
280	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
281	C₄⋊C₄×C₃₁	—	2	2	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	4	no	—
284	C₄⋊C₄×C₃₁	—	2	2	no	—
285	C₄⋊C₄×C₃₁	—	2	1	no	—
286	C₄⋊C₄×C₃₁	—	2	1	no	—
287	C₄⋊C₄×C₃₁	—	2	1	no	—
288	C₄⋊C₄×C₃₁	—	2	1	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	4	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	1	no	—
295	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
296	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
300	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
303	C₂²⋊C₄×C₃₁	—	2	2	no	—
304	C₂²⋊C₄×C₃₁	—	2	4	no	—
305	C₂²⋊C₄×C₃₁	—	2	1	no	—
306	C₂²⋊C₄×C₃₁	—	2	2	no	—
307	C₂²⋊C₄×C₃₁	—	2	1	no	—
308	C₂²⋊C₄×C₃₁	—	2	1	no	—
309	C₂²⋊C₄×C₃₁	—	2	1	no	—
310	C₂²⋊C₄×C₃₁	—	2	2	no	—
311	C₂²⋊C₄×C₃₁	—	2	2	no	—
312	C₂²⋊C₄×C₃₁	—	2	2	no	—
313	C₂²⋊C₄×C₃₁	—	2	2	no	—
314	C₂²⋊C₄×C₃₁	—	2	2	no	—
315	C₂²⋊C₄×C₃₁	—	2	4	no	—
316	C₂²⋊C₄×C₃₁	—	2	2	no	—
317	C₂²⋊C₄×C₃₁	—	2	2	no	—
318	C₂²⋊C₄×C₃₁	—	2	1	no	—
319	C₂²⋊C₄×C₃₁	—	2	2	no	—
320	C₂²⋊C₄×C₃₁	—	2	4	no	—
321	C₂²⋊C₄×C₃₁	—	2	2	no	—
322	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
324	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
325	C₄²×C₃₁	—	2	2	no	—
326	C₄²×C₃₁	—	2	4	no	—
327	C₄²×C₃₁	—	2	1	no	—
328	C₄²×C₃₁	C₂×D₄	1	2	yes	—
329	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₃₁	C₂×D₄	1	2	yes	—
332	C₄²×C₃₁	C₂⁴	1	2	yes	—
333	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
335	#62592	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂³×C₃₁	—	2	1	no	—
337	C₂³×C₃₁	—	2	2	no	—
338	C₂³×C₃₁	—	2	2	no	—
339	C₂³×C₃₁	—	4	4	no	—
340	C₂³×C₃₁	—	8	2	no	—
341	C₂³×C₃₁	—	8	2	no	—
342	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
343	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
344	Q₈×C₃₁	—	2	2	no	—
345	Q₈×C₃₁	—	2	2	no	—
346	Q₈×C₃₁	—	2	4	no	—
347	Q₈×C₃₁	—	4	4	no	—
348	Q₈×C₃₁	—	4	2	no	—
349	Q₈×C₃₁	—	8	2	no	—
350	Q₈×C₃₁	—	8	2	no	—
351	D₄×C₃₁	—	2	2	no	—
352	D₄×C₃₁	—	2	2	no	—
353	D₄×C₃₁	—	2	2	no	—
354	D₄×C₃₁	—	2	2	no	—
355	D₄×C₃₁	—	2	4	no	—
356	D₄×C₃₁	—	4	2	no	—
357	D₄×C₃₁	—	4	2	no	—
358	D₄×C₃₁	—	4	2	no	—
359	D₄×C₃₁	—	4	4	no	—
360	D₄×C₃₁	—	4	4	no	—
361	D₄×C₃₁	—	4	2	no	—
362	D₄×C₃₁	—	8	1	no	—
363	D₄×C₃₁	—	8	2	no	—
364	D₄×C₃₁	—	8	1	no	—
365	D₄×C₃₁	—	8	2	no	—
366	D₄×C₃₁	—	8	4	no	—
367	C₂×C₄×C₃₁	—	2	2	no	—
368	C₂×C₄×C₃₁	—	2	4	no	—
369	C₂×C₄×C₃₁	—	2	2	no	—
370	C₂×C₄×C₃₁	—	2	1	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	2	no	—
375	C₂×C₄×C₃₁	—	2	4	no	—
376	C₂×C₄×C₃₁	—	4	1	no	—
377	C₂×C₄×C₃₁	—	4	2	no	—
378	C₂×C₄×C₃₁	—	4	2	no	—
379	C₂×C₄×C₃₁	—	4	2	no	—
380	C₂×C₄×C₃₁	—	4	4	no	—
381	C₂×C₄×C₃₁	—	8	2	no	—
382	C₂×C₄×C₃₁	—	8	2	no	—
383	C₂×C₄×C₃₁	—	8	4	no	—
384	C₂×C₄×C₃₁	—	8	2	no	—
385	C₂×C₄×C₃₁	—	8	2	no	—
386	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₃₁	C₂²×D₄	1	2	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	1	yes	characteristic
391	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
395	C₈×C₃₁	—	2	2	no	—
396	C₈×C₃₁	—	2	2	no	—
397	C₈×C₃₁	—	2	4	no	—
398	#3514	C₂×C₃₁	1	1	yes	characteristic, complemented
399	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
400	#3361	C₂×C₃₁	1	2	yes	complemented
401	#3360	C₂×C₃₁	1	2	yes	complemented
402	#3329	C₂×C₃₁	1	2	yes	complemented
403	#3326	C₂×C₃₁	1	4	yes	complemented
404	#3325	C₂×C₃₁	1	2	yes	complemented
405	#3322	C₂×C₃₁	1	4	yes	complemented
406	#3240	C₂×C₃₁	1	2	yes	complemented
407	#3238	C₂×C₃₁	1	1	yes	characteristic, complemented
408	#3214	C₂×C₃₁	1	1	yes	characteristic, complemented
409	#3213	C₂×C₃₁	1	2	yes	complemented
410	#3171	C₂×C₃₁	1	1	yes	characteristic, complemented
411	#3171	C₂×C₃₁	1	2	yes	complemented
412	#3141	C₂×C₃₁	1	1	yes	characteristic, complemented
413	#3140	C₂×C₃₁	1	2	yes	complemented
414	#2971	C₂×C₃₁	1	1	yes	characteristic, complemented
415	C₂²×C₃₁	—	2	1	no	—
416	C₂²×C₃₁	—	2	2	no	—
417	C₂²×C₃₁	—	2	2	no	—
418	C₂²×C₃₁	—	2	1	no	—
419	C₂²×C₃₁	—	2	1	no	—
420	C₂²×C₃₁	—	2	2	no	—
421	C₂²×C₃₁	—	4	2	no	—
422	C₂²×C₃₁	—	4	2	no	—
423	C₂²×C₃₁	—	4	1	no	—
424	C₂²×C₃₁	—	4	2	no	—
425	C₂²×C₃₁	—	4	1	no	—
426	C₂²×C₃₁	—	4	2	no	—
427	C₂²×C₃₁	—	4	2	no	—
428	C₂²×C₃₁	—	4	1	no	—
429	C₂²×C₃₁	—	4	2	no	—
430	C₂²×C₃₁	—	16	4	no	—
431	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
432	C₄×C₃₁	—	2	1	no	—
433	C₄×C₃₁	—	2	2	no	—
434	C₄×C₃₁	—	2	1	no	—
435	C₄×C₃₁	—	2	1	no	—
436	C₄×C₃₁	—	2	2	no	—
437	C₄×C₃₁	—	2	1	no	—
438	C₄×C₃₁	—	2	2	no	—
439	C₄×C₃₁	—	4	1	no	—
440	C₄×C₃₁	—	4	4	no	—
441	C₄×C₃₁	—	4	2	no	—
442	C₄×C₃₁	—	4	1	no	—
443	C₄×C₃₁	—	4	1	no	—
444	C₄×C₃₁	—	4	2	no	—
445	C₄×C₃₁	#575	1	2	yes	—
446	C₄×C₃₁	#585	1	2	yes	—
447	#559	C₂²×C₃₁	1	1	yes	characteristic
448	#556	—	2	1	no	—
449	#556	C₂²×C₃₁	1	1	yes	characteristic
450	#555	—	2	1	no	—
451	#555	C₂²×C₃₁	1	2	yes	—
452	#554	C₂²×C₃₁	1	2	yes	complemented
453	#553	C₂²×C₃₁	1	4	yes	complemented
454	#551	—	2	2	no	—
455	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
456	#548	—	2	2	no	—
457	#548	C₂²×C₃₁	1	2	yes	—
458	#547	—	2	1	no	—
459	#546	—	2	1	no	—
460	#546	C₂²×C₃₁	1	2	yes	—
461	D₄²	C₂²×C₃₁	1	1	yes	characteristic
462	#542	—	2	1	no	—
463	#542	—	2	2	no	—
464	#538	—	2	2	no	—
465	#537	—	2	1	no	—
466	#533	C₂²×C₃₁	1	2	yes	complemented
467	#532	C₂²×C₃₁	1	1	yes	characteristic
468	#532	C₂²×C₃₁	1	2	yes	complemented
469	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
470	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
471	#529	C₂²×C₃₁	1	1	yes	characteristic
472	#529	C₂²×C₃₁	1	2	yes	—
473	C₂×#124	C₂²×C₃₁	1	2	yes	—
474	#520	—	2	1	no	—
475	#518	—	2	1	no	—
476	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
477	#501	C₂²×C₃₁	1	2	yes	complemented
478	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
479	#496	C₂²×C₃₁	1	1	yes	characteristic
480	#496	C₂²×C₃₁	1	2	yes	complemented
481	#490	C₂²×C₃₁	1	1	yes	characteristic, complemented
482	#489	C₂²×C₃₁	1	1	yes	characteristic
483	#489	C₂²×C₃₁	1	2	yes	—
484	#489	C₂²×C₃₁	1	2	yes	complemented
485	#489	C₂²×C₃₁	1	2	yes	complemented
486	#489	C₂²×C₃₁	1	2	yes	complemented
487	#488	C₂²×C₃₁	1	4	yes	—
488	#488	C₂²×C₃₁	1	4	yes	complemented
489	#487	C₂²×C₃₁	1	2	yes	complemented
490	#486	C₂²×C₃₁	1	2	yes	—
491	#485	C₂²×C₃₁	1	4	yes	complemented
492	#483	C₂²×C₃₁	1	2	yes	complemented
493	#482	C₂²×C₃₁	1	4	yes	—
494	#480	C₂²×C₃₁	1	2	yes	—
495	#479	C₂²×C₃₁	1	4	yes	complemented
496	#478	C₂²×C₃₁	1	4	yes	complemented
497	#477	C₂²×C₃₁	1	2	yes	complemented
498	#476	C₂²×C₃₁	1	2	yes	—
499	#469	C₂²×C₃₁	1	2	yes	—
500	#469	C₂²×C₃₁	1	4	yes	—
501	#468	C₂²×C₃₁	1	4	yes	complemented
502	#468	C₂²×C₃₁	1	2	yes	complemented
503	#463	C₂²×C₃₁	1	4	yes	—
504	#463	C₂²×C₃₁	1	4	yes	complemented
505	#461	C₂²×C₃₁	1	2	yes	complemented
506	#459	C₂²×C₃₁	1	2	yes	—
507	#449	C₂²×C₃₁	1	4	yes	complemented
508	#448	C₂²×C₃₁	1	4	yes	complemented
509	#447	C₂²×C₃₁	1	4	yes	—
510	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
511	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
512	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
513	C₄×D₈	C₂²×C₃₁	1	2	yes	—
514	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
515	#436	C₂²×C₃₁	1	2	yes	—
516	#436	C₂²×C₃₁	1	4	yes	complemented
517	#432	C₂²×C₃₁	1	2	yes	complemented
518	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
519	#419	C₂²×C₃₁	1	4	yes	complemented
520	#418	C₂²×C₃₁	1	4	yes	—
521	#417	C₂²×C₃₁	1	4	yes	complemented
522	C₄×M₁₆	C₂²×C₃₁	1	2	yes	complemented
523	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
524	C₂×C₃₁	—	4	1	no	—
525	C₂×C₃₁	—	4	2	no	—
526	C₂×C₃₁	—	8	2	no	—
527	C₂×C₃₁	—	8	2	no	—
528	C₂×C₃₁	—	8	1	no	—
529	C₂×C₃₁	#3500	1	1	yes	characteristic
530	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
531	C₂×C₃₁	#3585	1	1	yes	characteristic
532	C₂×#41	—	2	1	no	—
533	C₂×#41	—	2	2	no	—
534	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
535	C₂×#41	C₂³×C₃₁	1	2	yes	—
536	C₂²×Q₈	—	2	1	no	—
537	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
538	C₂²×D₄	—	2	1	no	—
539	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
540	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
541	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
542	C₂×D₈	C₂³×C₃₁	1	2	yes	—
543	C₂×D₈	C₂³×C₃₁	1	4	yes	—
544	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
545	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
546	C₄⋊Q₈	—	2	1	no	—
547	C₄⋊Q₈	—	2	1	no	—
548	C₄⋊Q₈	—	2	1	no	—
549	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
550	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
551	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
552	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
553	#127	C₂³×C₃₁	1	1	yes	characteristic
554	#127	C₂³×C₃₁	1	1	yes	characteristic
555	#126	—	2	2	no	—
556	#126	—	2	4	no	—
557	#126	—	2	2	no	—
558	#126	—	2	1	no	—
559	#125	C₂³×C₃₁	1	1	yes	characteristic
560	#125	C₂³×C₃₁	1	4	yes	—
561	#124	—	2	1	no	—
562	#124	—	2	2	no	—
563	#124	—	2	4	no	—
564	#124	—	2	2	no	—
565	#124	—	2	2	no	—
566	#124	—	2	1	no	—
567	#124	—	2	2	no	—
568	#124	C₂³×C₃₁	1	1	yes	characteristic
569	#124	C₂³×C₃₁	1	2	yes	—
570	#124	C₂³×C₃₁	1	2	yes	—
571	#124	C₂³×C₃₁	1	2	yes	—
572	#123	—	2	1	no	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	#123	—	2	2	no	—
576	#123	—	2	4	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	4	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
585	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
586	#121	—	2	2	no	—
587	#121	—	2	4	no	—
588	#121	—	2	2	no	—
589	#121	—	2	1	no	—
590	#121	—	2	1	no	—
591	#121	—	2	2	no	—
592	#121	—	2	1	no	—
593	#121	—	2	1	no	—
594	#121	—	2	2	no	—
595	#121	C₂³×C₃₁	1	2	yes	—
596	#121	C₂³×C₃₁	1	1	yes	characteristic
597	#121	C₂³×C₃₁	1	2	yes	—
598	#121	C₂³×C₃₁	1	4	yes	—
599	#120	—	2	2	no	—
600	#120	—	2	2	no	—
601	C₄×Q₈	—	2	2	no	—
602	C₄×Q₈	—	2	2	no	—
603	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
604	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
605	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
606	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	4	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
618	C₄×D₄	D₄×C₃₁	1	2	yes	—
619	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
620	C₄×D₄	C₂³×C₃₁	1	2	yes	—
621	C₄×D₄	C₂³×C₃₁	1	4	yes	—
622	C₄×D₄	C₂³×C₃₁	1	2	yes	—
623	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
624	C₄×D₄	C₂³×C₃₁	1	2	yes	—
625	#117	—	2	1	no	—
626	#117	—	2	2	no	—
627	#117	—	2	1	no	—
628	#117	—	2	2	no	—
629	#117	D₄×C₃₁	1	1	yes	characteristic
630	#117	D₄×C₃₁	1	2	yes	—
631	#117	C₂³×C₃₁	1	4	yes	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	2	no	—
634	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
635	C₂×C₂²⋊C₄	—	2	2	no	—
636	C₂×C₂²⋊C₄	—	2	2	no	—
637	C₂×C₂²⋊C₄	—	2	2	no	—
638	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
639	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
640	#107	C₂³×C₃₁	1	2	yes	—
641	#107	C₂³×C₃₁	1	4	yes	—
642	#106	C₂³×C₃₁	1	4	yes	—
643	#106	C₂³×C₃₁	1	2	yes	—
644	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
645	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
646	#103	C₂³×C₃₁	1	4	yes	—
647	#103	C₂³×C₃₁	1	4	yes	—
648	#103	C₂³×C₃₁	1	2	yes	—
649	#103	C₂³×C₃₁	1	4	yes	—
650	#103	C₂³×C₃₁	1	4	yes	—
651	#102	C₂³×C₃₁	1	4	yes	—
652	#102	C₂³×C₃₁	1	4	yes	—
653	#102	C₂³×C₃₁	1	2	yes	—
654	#102	C₂³×C₃₁	1	4	yes	—
655	#102	C₂³×C₃₁	1	4	yes	—
656	#102	C₂³×C₃₁	1	2	yes	—
657	#102	C₂³×C₃₁	1	2	yes	—
658	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
659	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
660	#97	C₂³×C₃₁	1	1	yes	characteristic
661	#97	C₂³×C₃₁	1	2	yes	—
662	#97	C₂³×C₃₁	1	1	yes	characteristic
663	C₄×C₈	C₂³×C₃₁	1	2	yes	—
664	C₄×C₈	C₂³×C₃₁	1	4	yes	—
665	C₃₁	#62592	1	1	yes	characteristic, direct product factor, Sylow
666	C₂⁴	—	2	2	no	—
667	#41	—	4	2	no	—
668	#41	—	4	4	no	—
669	#41	—	4	4	no	—
670	#41	—	8	4	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	4	4	no	—
676	C₂×Q₈	—	8	2	no	—
677	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
678	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
679	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	4	4	no	—
691	C₂×D₄	—	4	4	no	—
692	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
693	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
694	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
695	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
696	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
706	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
707	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
710	SD₁₆	—	4	2	no	—
711	SD₁₆	—	4	4	no	—
712	D₈	—	4	4	no	—
713	D₈	—	4	2	no	—
714	M₁₆	—	4	4	no	—
715	M₁₆	—	4	2	no	—
716	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
717	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
718	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
734	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
735	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
736	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
738	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
739	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
740	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
761	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
762	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	4	no	—
765	C₄²	—	2	1	no	—
766	C₄²	C₂×D₄×C₃₁	1	2	yes	—
767	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
769	C₄²	C₂×D₄×C₃₁	1	2	yes	—
770	C₄²	C₂⁴×C₃₁	1	2	yes	—
771	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
772	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
773	C₂³	—	2	1	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	4	4	no	—
777	C₂³	—	8	2	no	—
778	C₂³	—	8	2	no	—
779	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
780	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
781	Q₈	—	2	2	no	—
782	Q₈	—	2	2	no	—
783	Q₈	—	2	4	no	—
784	Q₈	—	4	4	no	—
785	Q₈	—	4	2	no	—
786	Q₈	—	8	2	no	—
787	Q₈	—	8	2	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	2	no	—
790	D₄	—	2	2	no	—
791	D₄	—	2	2	no	—
792	D₄	—	2	4	no	—
793	D₄	—	4	2	no	—
794	D₄	—	4	2	no	—
795	D₄	—	4	2	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	2	no	—
799	D₄	—	8	1	no	—
800	D₄	—	8	2	no	—
801	D₄	—	8	1	no	—
802	D₄	—	8	2	no	—
803	D₄	—	8	4	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	4	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	8	2	no	—
819	C₂×C₄	—	8	2	no	—
820	C₂×C₄	—	8	4	no	—
821	C₂×C₄	—	8	2	no	—
822	C₂×C₄	—	8	2	no	—
823	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
825	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
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	2	yes	—
829	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
831	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
832	C₈	—	2	2	no	—
833	C₈	—	2	2	no	—
834	C₈	—	2	4	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	16	4	no	—
851	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
852	C₄	—	2	1	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	2	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	1	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	4	no	—
864	C₄	—	4	1	no	—
865	C₄	C₃₁×#575	1	2	yes	—
866	C₄	C₃₁×#585	1	2	yes	—
867	C₂	—	4	2	no	—
868	C₂	—	4	1	no	—
869	C₂	—	8	1	no	—
870	C₂	—	8	2	no	—
871	C₂	—	8	2	no	—
872	C₂	C₃₁×#3500	1	1	yes	characteristic
873	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
874	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×#3514	C₂	semidirect
2. C₃₁×#3511	C₂	semidirect
3. C₃₁×#3361	C₂	semidirect
4. C₃₁×#3360	C₂	semidirect
5. C₃₁×#3329	C₂	semidirect
6. C₃₁×#3326	C₂	semidirect
7. C₃₁×#3325	C₂	semidirect
8. C₃₁×#3322	C₂	semidirect
9. C₃₁×#3240	C₂	semidirect
10. C₃₁×#3238	C₂	semidirect
11. C₃₁×#3214	C₂	semidirect
12. C₃₁×#3213	C₂	semidirect
13. C₃₁×#3171	C₂	semidirect
14. C₃₁×#3171	C₂	semidirect
15. C₃₁×#3141	C₂	semidirect
16. C₃₁×#3140	C₂	semidirect
17. C₃₁×#2971	C₂	semidirect
23. C₃₁×#554	C₂²	semidirect
24. C₃₁×#553	C₂²	semidirect
37. 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×#501	C₂²	semidirect
51. C₃₁×#496	C₂²	semidirect
52. C₃₁×#490	C₂²	semidirect
55. C₃₁×#489	C₂²	semidirect
56. C₃₁×#489	C₂²	semidirect
57. C₃₁×#489	C₂²	semidirect
59. C₃₁×#488	C₂²	semidirect
60. C₃₁×#487	C₂²	semidirect
62. C₃₁×#485	C₂²	semidirect
63. C₃₁×#483	C₂²	semidirect
66. C₃₁×#479	C₂²	semidirect
67. C₃₁×#478	C₂²	semidirect
68. C₃₁×#477	C₂²	semidirect
72. C₃₁×#468	C₂²	semidirect
73. C₃₁×#468	C₂²	semidirect
75. C₃₁×#463	C₂²	semidirect
76. C₃₁×#461	C₂²	semidirect
78. C₃₁×#449	C₂²	semidirect
79. C₃₁×#448	C₂²	semidirect
81. C₈×Q₈×C₃₁	C₂²	semidirect
82. C₄×SD₁₆×C₃₁	C₂²	semidirect
83. C₄×SD₁₆×C₃₁	C₂²	semidirect
85. C₄×D₈×C₃₁	C₂²	semidirect
87. C₃₁×#436	C₂²	semidirect
88. C₃₁×#432	C₂²	semidirect
89. C₃₁×#432	C₂²	semidirect
90. C₃₁×#419	C₂²	semidirect
92. C₃₁×#417	C₂²	semidirect
93. C₄×M₁₆×C₃₁	C₂²	semidirect
94. C₄×M₁₆×C₃₁	C₂²	semidirect
335. #62592	C₃₁	direct (N × H)
398. #3514	C₂×C₃₁	semidirect
399. #3511	C₂×C₃₁	semidirect
400. #3361	C₂×C₃₁	semidirect
401. #3360	C₂×C₃₁	semidirect
402. #3329	C₂×C₃₁	semidirect
403. #3326	C₂×C₃₁	semidirect
404. #3325	C₂×C₃₁	semidirect
405. #3322	C₂×C₃₁	semidirect
406. #3240	C₂×C₃₁	semidirect
407. #3238	C₂×C₃₁	semidirect
408. #3214	C₂×C₃₁	semidirect
409. #3213	C₂×C₃₁	semidirect
410. #3171	C₂×C₃₁	semidirect
411. #3171	C₂×C₃₁	semidirect
412. #3141	C₂×C₃₁	semidirect
413. #3140	C₂×C₃₁	semidirect
414. #2971	C₂×C₃₁	semidirect
452. #554	C₂²×C₃₁	semidirect
453. #553	C₂²×C₃₁	semidirect
466. #533	C₂²×C₃₁	semidirect
468. #532	C₂²×C₃₁	semidirect
469. #532	C₂²×C₃₁	semidirect
470. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
477. #501	C₂²×C₃₁	semidirect
478. #501	C₂²×C₃₁	semidirect
480. #496	C₂²×C₃₁	semidirect
481. #490	C₂²×C₃₁	semidirect
484. #489	C₂²×C₃₁	semidirect
485. #489	C₂²×C₃₁	semidirect
486. #489	C₂²×C₃₁	semidirect
488. #488	C₂²×C₃₁	semidirect
489. #487	C₂²×C₃₁	semidirect
491. #485	C₂²×C₃₁	semidirect
492. #483	C₂²×C₃₁	semidirect
495. #479	C₂²×C₃₁	semidirect
496. #478	C₂²×C₃₁	semidirect
497. #477	C₂²×C₃₁	semidirect
501. #468	C₂²×C₃₁	semidirect
502. #468	C₂²×C₃₁	semidirect
504. #463	C₂²×C₃₁	semidirect
505. #461	C₂²×C₃₁	semidirect
507. #449	C₂²×C₃₁	semidirect
508. #448	C₂²×C₃₁	semidirect
510. C₈×Q₈	C₂²×C₃₁	semidirect
511. C₄×SD₁₆	C₂²×C₃₁	semidirect
512. C₄×SD₁₆	C₂²×C₃₁	semidirect
514. C₄×D₈	C₂²×C₃₁	semidirect
516. #436	C₂²×C₃₁	semidirect
517. #432	C₂²×C₃₁	semidirect
518. #432	C₂²×C₃₁	semidirect
519. #419	C₂²×C₃₁	semidirect
521. #417	C₂²×C₃₁	semidirect
522. C₄×M₁₆	C₂²×C₃₁	semidirect
523. C₄×M₁₆	C₂²×C₃₁	semidirect
665. C₃₁	#62592	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×#3514	2
C₃₁×#3511	2
C₃₁×#3361	2
C₃₁×#3360	2
C₃₁×#3329	2
C₃₁×#3326	2
C₃₁×#3325	2
C₃₁×#3322	2
C₃₁×#3240	2
C₃₁×#3238	2
C₃₁×#3214	2
C₃₁×#3213	2
C₃₁×#3171	2
C₃₁×#3141	2
C₃₁×#3140	2
C₃₁×#2971	2
#62592	31

Subgroups — C31×#62592 #21519351

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62592 #21519351