Subgroups — C₃₁×#61945 #21518704

Order 7936.

1766 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3403	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3401	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3399	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3397	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3371	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3368	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3366	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3222	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3220	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3217	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3123	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3122	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#563	—	2	2	no	—
21	C₃₁×#559	C₂²	1	2	yes	—
22	C₃₁×#559	C₂²	1	2	yes	—
23	C₃₁×#559	C₂²	1	2	yes	complemented
24	C₃₁×#557	C₂²	1	2	yes	complemented
25	C₃₁×#556	C₂²	1	2	yes	complemented
26	C₃₁×#554	C₂²	1	2	yes	complemented
27	C₃₁×#552	—	2	2	no	—
28	C₃₁×#550	C₂²	1	2	yes	—
29	C₃₁×#550	C₂²	1	2	yes	—
30	C₃₁×#546	—	2	2	no	—
31	C₃₁×#546	—	2	2	no	—
32	C₃₁×#542	—	2	2	no	—
33	C₃₁×#542	C₂²	1	2	yes	—
34	C₃₁×#541	C₂²	1	1	yes	characteristic
35	C₃₁×#540	—	2	2	no	—
36	C₃₁×#540	C₂²	1	1	yes	characteristic
37	C₃₁×#539	—	2	2	no	—
38	C₃₁×#535	C₂²	1	1	yes	characteristic
39	C₃₁×#535	C₂²	1	1	yes	characteristic
40	C₃₁×#533	C₂²	1	1	yes	characteristic
41	C₃₁×#532	—	2	2	no	—
42	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
43	C₃₁×#529	C₂²	1	2	yes	—
44	C₃₁×#518	C₂²	1	1	yes	characteristic
45	C₃₁×#518	C₂²	1	1	yes	characteristic
46	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
47	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#496	C₂²	1	2	yes	—
49	C₃₁×#496	C₂²	1	2	yes	—
50	C₃₁×#496	C₂²	1	2	yes	complemented
51	C₃₁×#496	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#495	C₂²	1	2	yes	complemented
53	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#490	C₂²	1	2	yes	—
56	C₃₁×#490	C₂²	1	2	yes	—
57	C₃₁×#490	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#490	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#489	C₂²	1	2	yes	complemented
60	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#486	C₂²	1	2	yes	complemented
63	C₃₁×#485	C₂²	1	2	yes	—
64	C₃₁×#482	C₂²	1	2	yes	—
65	C₃₁×#479	C₂²	1	2	yes	complemented
66	C₃₁×#478	C₂²	1	2	yes	complemented
67	C₃₁×#478	C₂²	1	2	yes	complemented
68	C₃₁×#478	C₂²	1	2	yes	complemented
69	C₃₁×#476	C₂²	1	2	yes	complemented
70	C₃₁×#474	C₂²	1	2	yes	complemented
71	C₃₁×#464	C₂²	1	2	yes	complemented
72	C₃₁×#464	C₂²	1	2	yes	complemented
73	C₃₁×#464	C₂²	1	2	yes	complemented
74	C₃₁×#463	C₂²	1	2	yes	complemented
75	C₃₁×#463	C₂²	1	2	yes	complemented
76	C₃₁×#463	C₂²	1	2	yes	complemented
77	C₃₁×#463	C₂²	1	2	yes	complemented
78	C₃₁×#463	C₂²	1	2	yes	complemented
79	C₃₁×#461	C₂²	1	2	yes	complemented
80	C₃₁×#460	C₂²	1	2	yes	—
81	C₃₁×#460	C₂²	1	2	yes	—
82	C₃₁×#460	C₂²	1	2	yes	complemented
83	C₃₁×#460	C₂²	1	2	yes	complemented
84	C₃₁×#459	C₂²	1	2	yes	—
85	C₃₁×#459	C₂²	1	2	yes	—
86	C₃₁×#459	C₂²	1	2	yes	complemented
87	C₃₁×#459	C₂²	1	2	yes	complemented
88	C₃₁×#459	C₂²	1	2	yes	complemented
89	C₃₁×#452	C₂²	1	2	yes	—
90	C₃₁×#450	C₂²	1	2	yes	—
91	C₃₁×#450	C₂²	1	2	yes	—
92	C₃₁×#449	C₂²	1	2	yes	—
93	C₃₁×#447	C₂²	1	2	yes	—
94	C₃₁×#447	C₂²	1	2	yes	—
95	C₃₁×#446	C₂²	1	2	yes	complemented
96	C₃₁×#446	C₂²	1	2	yes	complemented
97	C₃₁×#446	C₂²	1	2	yes	complemented
98	C₃₁×#446	C₂²	1	2	yes	complemented
99	C₃₁×#442	C₂²	1	2	yes	complemented
100	C₃₁×#442	C₂²	1	2	yes	complemented
101	C₃₁×#442	C₂²	1	2	yes	complemented
102	C₃₁×#441	C₂²	1	2	yes	complemented
103	C₃₁×#440	C₂²	1	2	yes	complemented
104	C₃₁×#440	C₂²	1	2	yes	complemented
105	C₃₁×#440	C₂²	1	2	yes	complemented
106	C₃₁×#440	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
108	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
109	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
110	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
111	C₃₁×#433	C₂²	1	2	yes	—
112	C₃₁×#433	C₂²	1	1	yes	characteristic
113	C₃₁×#433	C₂²	1	1	yes	characteristic
114	C₃₁×#432	C₂²	1	2	yes	—
115	C₂×#41×C₃₁	—	2	2	no	—
116	C₂×#41×C₃₁	—	2	2	no	—
117	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
118	C₂²×D₄×C₃₁	—	2	2	no	—
119	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
122	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
128	C₂×D₈×C₃₁	C₂³	1	2	yes	—
129	C₂×D₈×C₃₁	C₂³	1	2	yes	—
130	C₂×D₈×C₃₁	C₂³	1	2	yes	—
131	C₂×D₈×C₃₁	C₂³	1	2	yes	—
132	C₂×D₈×C₃₁	C₂³	1	2	yes	—
133	C₃₁×C₄⋊Q₈	—	2	2	no	—
134	C₃₁×C₄⋊Q₈	D₄	1	2	yes	—
135	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
136	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₃₁×#127	—	2	1	no	—
138	C₃₁×#127	—	2	1	no	—
139	C₃₁×#127	C₂³	1	2	yes	—
140	C₃₁×#127	C₂³	1	2	yes	—
141	C₃₁×#127	C₂³	1	1	yes	characteristic
142	C₃₁×#127	C₂³	1	1	yes	characteristic
143	C₃₁×#127	C₂³	1	2	yes	—
144	C₃₁×#127	C₂³	1	1	yes	characteristic
145	C₃₁×#126	—	2	2	no	—
146	C₃₁×#126	—	2	2	no	—
147	C₃₁×#126	—	2	2	no	—
148	C₃₁×#126	—	2	2	no	—
149	C₃₁×#126	—	2	2	no	—
150	C₃₁×#125	—	2	2	no	—
151	C₃₁×#125	—	2	2	no	—
152	C₃₁×#125	—	2	2	no	—
153	C₃₁×#125	D₄	1	2	yes	—
154	C₃₁×#125	C₂³	1	1	yes	characteristic
155	C₃₁×#125	C₂³	1	1	yes	characteristic
156	C₃₁×#125	C₂³	1	2	yes	—
157	C₃₁×#124	—	2	2	no	—
158	C₃₁×#124	—	2	2	no	—
159	C₃₁×#124	—	2	2	no	—
160	C₃₁×#124	—	2	2	no	—
161	C₃₁×#124	C₂³	1	1	yes	characteristic
162	C₃₁×#124	C₂³	1	2	yes	—
163	C₃₁×#124	C₂³	1	2	yes	—
164	C₃₁×#124	C₂³	1	2	yes	—
165	C₃₁×#124	C₂³	1	1	yes	characteristic
166	C₃₁×#123	—	2	2	no	—
167	C₃₁×#123	—	2	2	no	—
168	C₃₁×#123	—	2	2	no	—
169	C₃₁×#123	—	2	2	no	—
170	C₃₁×#123	—	2	2	no	—
171	C₃₁×#123	—	2	2	no	—
172	C₃₁×#123	—	2	2	no	—
173	C₃₁×#123	—	2	2	no	—
174	C₃₁×#123	—	2	2	no	—
175	C₃₁×C₂²⋊Q₈	—	2	2	no	—
176	C₃₁×C₂²⋊Q₈	—	2	2	no	—
177	C₃₁×C₂²⋊Q₈	—	2	2	no	—
178	C₃₁×C₂²⋊Q₈	—	2	2	no	—
179	C₃₁×C₂²⋊Q₈	—	2	2	no	—
180	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
181	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
182	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
183	C₃₁×#121	—	2	2	no	—
184	C₃₁×#121	—	2	2	no	—
185	C₃₁×#121	—	2	2	no	—
186	C₃₁×#121	—	2	2	no	—
187	C₃₁×#121	—	2	2	no	—
188	C₃₁×#121	—	2	2	no	—
189	C₃₁×#121	—	2	2	no	—
190	C₃₁×#121	—	2	2	no	—
191	C₃₁×#121	—	2	2	no	—
192	C₃₁×#121	C₂³	1	2	yes	—
193	C₃₁×#120	—	2	2	no	—
194	C₃₁×#120	—	2	1	no	—
195	C₃₁×#120	—	2	1	no	—
196	C₄×Q₈×C₃₁	—	2	2	no	—
197	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
198	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
199	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
200	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
201	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
202	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
203	C₄×D₄×C₃₁	—	2	2	no	—
204	C₄×D₄×C₃₁	—	2	2	no	—
205	C₄×D₄×C₃₁	—	2	2	no	—
206	C₄×D₄×C₃₁	—	2	2	no	—
207	C₄×D₄×C₃₁	—	2	2	no	—
208	C₄×D₄×C₃₁	—	2	2	no	—
209	C₄×D₄×C₃₁	—	2	2	no	—
210	C₄×D₄×C₃₁	C₂³	1	2	yes	—
211	C₄×D₄×C₃₁	C₂³	1	2	yes	—
212	C₄×D₄×C₃₁	C₂³	1	2	yes	—
213	C₄×D₄×C₃₁	C₂³	1	2	yes	—
214	C₄×D₄×C₃₁	C₂³	1	2	yes	—
215	C₄×D₄×C₃₁	C₂³	1	2	yes	—
216	C₄×D₄×C₃₁	C₂³	1	2	yes	—
217	C₄×D₄×C₃₁	C₂³	1	2	yes	—
218	C₃₁×#117	—	2	2	no	—
219	C₃₁×#117	—	2	1	no	—
220	C₃₁×#117	—	2	2	no	—
221	C₃₁×#117	C₂³	1	1	yes	characteristic
222	C₃₁×#117	C₂³	1	1	yes	characteristic
223	C₃₁×#117	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
225	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
226	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
227	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
228	C₂×C₄²×C₃₁	—	2	1	no	—
229	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
230	C₃₁×#107	C₂³	1	2	yes	—
231	C₃₁×#107	C₂³	1	2	yes	—
232	C₃₁×#106	C₂³	1	2	yes	—
233	C₃₁×#106	C₂³	1	2	yes	—
234	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
235	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
236	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
237	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
238	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
239	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
240	C₃₁×#103	C₂³	1	2	yes	—
241	C₃₁×#103	C₂³	1	2	yes	—
242	C₃₁×#103	C₂³	1	2	yes	—
243	C₃₁×#103	C₂³	1	2	yes	—
244	C₃₁×#102	C₂³	1	2	yes	—
245	C₃₁×#102	C₂³	1	2	yes	—
246	C₃₁×#102	C₂³	1	2	yes	—
247	C₃₁×#102	C₂³	1	2	yes	—
248	C₃₁×#102	C₂³	1	2	yes	—
249	C₃₁×#102	C₂³	1	2	yes	—
250	C₃₁×#102	C₂³	1	2	yes	—
251	C₃₁×#102	C₂³	1	2	yes	—
252	C₃₁×#102	C₂³	1	2	yes	—
253	C₃₁×#102	C₂³	1	2	yes	—
254	C₃₁×#102	C₂³	1	2	yes	—
255	C₃₁×#102	C₂³	1	2	yes	—
256	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₃₁×#97	C₂³	1	2	yes	—
259	C₃₁×#97	C₂³	1	2	yes	—
260	C₃₁×#97	C₂³	1	1	yes	characteristic
261	C₃₁×#97	C₂³	1	2	yes	—
262	C₃₁×#97	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₃₁	C₂³	1	2	yes	—
265	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
266	C₂⁴×C₃₁	—	2	1	no	—
267	C₂⁴×C₃₁	—	2	1	no	—
268	#41×C₃₁	—	4	2	no	—
269	#41×C₃₁	—	8	4	no	—
270	#41×C₃₁	—	8	4	no	—
271	C₂×Q₈×C₃₁	—	2	2	no	—
272	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
273	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
274	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
275	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
276	C₂×D₄×C₃₁	—	2	1	no	—
277	C₂×D₄×C₃₁	—	2	2	no	—
278	C₂×D₄×C₃₁	—	2	1	no	—
279	C₂×D₄×C₃₁	—	2	1	no	—
280	C₂×D₄×C₃₁	—	2	2	no	—
281	C₂×D₄×C₃₁	—	2	2	no	—
282	C₂×D₄×C₃₁	—	2	2	no	—
283	C₂×D₄×C₃₁	—	2	2	no	—
284	C₂×D₄×C₃₁	—	2	2	no	—
285	C₂×D₄×C₃₁	—	2	2	no	—
286	C₂×D₄×C₃₁	—	2	2	no	—
287	C₂×D₄×C₃₁	—	2	2	no	—
288	C₂×D₄×C₃₁	—	2	2	no	—
289	C₂×D₄×C₃₁	—	4	2	no	—
290	C₂×D₄×C₃₁	—	4	2	no	—
291	C₂×D₄×C₃₁	—	8	4	no	—
292	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
293	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
294	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
296	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₃₁	—	2	1	no	—
298	C₂²×C₄×C₃₁	—	2	2	no	—
299	C₂²×C₄×C₃₁	—	2	2	no	—
300	C₂²×C₄×C₃₁	—	2	2	no	—
301	C₂²×C₄×C₃₁	—	2	2	no	—
302	C₂²×C₄×C₃₁	—	2	2	no	—
303	C₂²×C₄×C₃₁	—	2	2	no	—
304	C₂²×C₄×C₃₁	—	2	2	no	—
305	C₂²×C₄×C₃₁	—	2	2	no	—
306	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
307	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
308	Q₁₆×C₃₁	—	4	2	no	—
309	SD₁₆×C₃₁	—	4	2	no	—
310	SD₁₆×C₃₁	—	4	2	no	—
311	SD₁₆×C₃₁	—	4	2	no	—
312	SD₁₆×C₃₁	—	4	2	no	—
313	SD₁₆×C₃₁	—	4	2	no	—
314	SD₁₆×C₃₁	—	4	2	no	—
315	D₈×C₃₁	—	4	2	no	—
316	D₈×C₃₁	—	4	2	no	—
317	D₈×C₃₁	—	4	2	no	—
318	D₈×C₃₁	—	4	2	no	—
319	D₈×C₃₁	—	4	2	no	—
320	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
321	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
322	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
323	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
324	C₄⋊C₄×C₃₁	—	2	2	no	—
325	C₄⋊C₄×C₃₁	—	2	2	no	—
326	C₄⋊C₄×C₃₁	—	2	2	no	—
327	C₄⋊C₄×C₃₁	—	2	2	no	—
328	C₄⋊C₄×C₃₁	—	2	2	no	—
329	C₄⋊C₄×C₃₁	—	2	2	no	—
330	C₄⋊C₄×C₃₁	—	2	2	no	—
331	C₄⋊C₄×C₃₁	—	2	2	no	—
332	C₄⋊C₄×C₃₁	—	2	2	no	—
333	C₄⋊C₄×C₃₁	—	2	2	no	—
334	C₄⋊C₄×C₃₁	—	2	2	no	—
335	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
336	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
337	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
338	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
339	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
340	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
341	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
342	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
343	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
346	C₂²⋊C₄×C₃₁	—	2	1	no	—
347	C₂²⋊C₄×C₃₁	—	2	2	no	—
348	C₂²⋊C₄×C₃₁	—	2	2	no	—
349	C₂²⋊C₄×C₃₁	—	2	2	no	—
350	C₂²⋊C₄×C₃₁	—	2	2	no	—
351	C₂²⋊C₄×C₃₁	—	2	2	no	—
352	C₂²⋊C₄×C₃₁	—	2	2	no	—
353	C₂²⋊C₄×C₃₁	—	2	2	no	—
354	C₂²⋊C₄×C₃₁	—	2	2	no	—
355	C₂²⋊C₄×C₃₁	—	2	2	no	—
356	C₂²⋊C₄×C₃₁	—	2	2	no	—
357	C₂²⋊C₄×C₃₁	—	2	2	no	—
358	C₂²⋊C₄×C₃₁	—	2	2	no	—
359	C₂²⋊C₄×C₃₁	—	2	2	no	—
360	C₂²⋊C₄×C₃₁	—	2	2	no	—
361	C₂²⋊C₄×C₃₁	—	2	2	no	—
362	C₂²⋊C₄×C₃₁	—	2	2	no	—
363	C₂²⋊C₄×C₃₁	—	2	2	no	—
364	C₂²⋊C₄×C₃₁	—	2	2	no	—
365	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
366	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
367	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
368	C₄²×C₃₁	—	2	1	no	—
369	C₄²×C₃₁	—	2	2	no	—
370	C₄²×C₃₁	—	2	2	no	—
371	C₄²×C₃₁	—	2	2	no	—
372	C₄²×C₃₁	—	2	2	no	—
373	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
374	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₄²×C₃₁	C₂⁴	1	2	yes	—
377	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₄²×C₃₁	C₂⁴	1	2	yes	—
379	#61945	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
380	C₂³×C₃₁	—	2	2	no	—
381	C₂³×C₃₁	—	2	2	no	—
382	C₂³×C₃₁	—	2	1	no	—
383	C₂³×C₃₁	—	2	1	no	—
384	C₂³×C₃₁	—	2	1	no	—
385	C₂³×C₃₁	—	4	2	no	—
386	C₂³×C₃₁	—	4	2	no	—
387	C₂³×C₃₁	—	8	2	no	—
388	C₂³×C₃₁	—	8	2	no	—
389	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
390	Q₈×C₃₁	—	2	2	no	—
391	Q₈×C₃₁	—	2	2	no	—
392	Q₈×C₃₁	—	2	2	no	—
393	Q₈×C₃₁	—	4	2	no	—
394	Q₈×C₃₁	—	4	2	no	—
395	Q₈×C₃₁	—	8	2	no	—
396	D₄×C₃₁	—	2	2	no	—
397	D₄×C₃₁	—	2	2	no	—
398	D₄×C₃₁	—	2	2	no	—
399	D₄×C₃₁	—	2	2	no	—
400	D₄×C₃₁	—	2	2	no	—
401	D₄×C₃₁	—	2	2	no	—
402	D₄×C₃₁	—	2	2	no	—
403	D₄×C₃₁	—	4	2	no	—
404	D₄×C₃₁	—	4	2	no	—
405	D₄×C₃₁	—	4	4	no	—
406	D₄×C₃₁	—	4	4	no	—
407	D₄×C₃₁	—	4	2	no	—
408	D₄×C₃₁	—	8	2	no	—
409	D₄×C₃₁	—	8	2	no	—
410	D₄×C₃₁	—	8	2	no	—
411	D₄×C₃₁	—	8	2	no	—
412	D₄×C₃₁	—	8	2	no	—
413	D₄×C₃₁	—	8	2	no	—
414	D₄×C₃₁	—	8	2	no	—
415	D₄×C₃₁	—	8	2	no	—
416	C₂×C₄×C₃₁	—	2	2	no	—
417	C₂×C₄×C₃₁	—	2	2	no	—
418	C₂×C₄×C₃₁	—	2	1	no	—
419	C₂×C₄×C₃₁	—	2	2	no	—
420	C₂×C₄×C₃₁	—	2	2	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	4	2	no	—
423	C₂×C₄×C₃₁	—	4	2	no	—
424	C₂×C₄×C₃₁	—	4	4	no	—
425	C₂×C₄×C₃₁	—	8	2	no	—
426	C₂×C₄×C₃₁	—	8	2	no	—
427	C₂×C₄×C₃₁	—	8	2	no	—
428	C₂×C₄×C₃₁	—	8	2	no	—
429	C₂×C₄×C₃₁	—	8	2	no	—
430	C₂×C₄×C₃₁	—	8	2	no	—
431	C₂×C₄×C₃₁	—	8	2	no	—
432	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
437	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
438	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
439	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
440	C₈×C₃₁	—	2	2	no	—
441	C₈×C₃₁	—	2	2	no	—
442	C₈×C₃₁	—	2	2	no	—
443	C₈×C₃₁	—	2	2	no	—
444	#3557	C₂×C₃₁	1	1	yes	characteristic, complemented
445	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
446	#3403	C₂×C₃₁	1	2	yes	complemented
447	#3401	C₂×C₃₁	1	2	yes	complemented
448	#3399	C₂×C₃₁	1	2	yes	complemented
449	#3397	C₂×C₃₁	1	2	yes	complemented
450	#3371	C₂×C₃₁	1	2	yes	complemented
451	#3370	C₂×C₃₁	1	2	yes	complemented
452	#3368	C₂×C₃₁	1	2	yes	complemented
453	#3366	C₂×C₃₁	1	2	yes	complemented
454	#3224	C₂×C₃₁	1	2	yes	complemented
455	#3222	C₂×C₃₁	1	1	yes	characteristic, complemented
456	#3220	C₂×C₃₁	1	1	yes	characteristic, complemented
457	#3217	C₂×C₃₁	1	2	yes	complemented
458	#3123	C₂×C₃₁	1	1	yes	characteristic, complemented
459	#3122	C₂×C₃₁	1	1	yes	characteristic, complemented
460	#3118	C₂×C₃₁	1	2	yes	complemented
461	#3111	C₂×C₃₁	1	2	yes	complemented
462	#2987	C₂×C₃₁	1	1	yes	characteristic, complemented
463	C₂²×C₃₁	—	2	2	no	—
464	C₂²×C₃₁	—	2	1	no	—
465	C₂²×C₃₁	—	4	2	no	—
466	C₂²×C₃₁	—	4	2	no	—
467	C₂²×C₃₁	—	4	2	no	—
468	C₂²×C₃₁	—	4	2	no	—
469	C₂²×C₃₁	—	4	2	no	—
470	C₂²×C₃₁	—	4	2	no	—
471	C₂²×C₃₁	—	4	2	no	—
472	C₂²×C₃₁	—	4	1	no	—
473	C₂²×C₃₁	—	4	2	no	—
474	C₂²×C₃₁	—	4	1	no	—
475	C₂²×C₃₁	—	4	1	no	—
476	C₂²×C₃₁	—	4	2	no	—
477	C₂²×C₃₁	—	16	2	no	—
478	C₂²×C₃₁	—	16	2	no	—
479	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
480	C₄×C₃₁	—	2	2	no	—
481	C₄×C₃₁	—	2	2	no	—
482	C₄×C₃₁	—	2	2	no	—
483	C₄×C₃₁	—	2	2	no	—
484	C₄×C₃₁	—	2	2	no	—
485	C₄×C₃₁	—	2	2	no	—
486	C₄×C₃₁	—	2	1	no	—
487	C₄×C₃₁	—	4	2	no	—
488	C₄×C₃₁	—	4	2	no	—
489	C₄×C₃₁	—	4	2	no	—
490	C₄×C₃₁	—	4	1	no	—
491	C₄×C₃₁	—	4	2	no	—
492	C₄×C₃₁	#585	1	2	yes	—
493	#563	—	2	2	no	—
494	#559	C₂²×C₃₁	1	2	yes	—
495	#559	C₂²×C₃₁	1	2	yes	—
496	#559	C₂²×C₃₁	1	2	yes	complemented
497	#557	C₂²×C₃₁	1	2	yes	complemented
498	#556	C₂²×C₃₁	1	2	yes	complemented
499	#554	C₂²×C₃₁	1	2	yes	complemented
500	#552	—	2	2	no	—
501	#550	C₂²×C₃₁	1	2	yes	—
502	#550	C₂²×C₃₁	1	2	yes	—
503	#546	—	2	2	no	—
504	#546	—	2	2	no	—
505	#542	—	2	2	no	—
506	#542	C₂²×C₃₁	1	2	yes	—
507	#541	C₂²×C₃₁	1	1	yes	characteristic
508	#540	—	2	2	no	—
509	#540	C₂²×C₃₁	1	1	yes	characteristic
510	#539	—	2	2	no	—
511	#535	C₂²×C₃₁	1	1	yes	characteristic
512	#535	C₂²×C₃₁	1	1	yes	characteristic
513	#533	C₂²×C₃₁	1	1	yes	characteristic
514	#532	—	2	2	no	—
515	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
516	#529	C₂²×C₃₁	1	2	yes	—
517	#518	C₂²×C₃₁	1	1	yes	characteristic
518	#518	C₂²×C₃₁	1	1	yes	characteristic
519	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
520	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
521	#496	C₂²×C₃₁	1	2	yes	—
522	#496	C₂²×C₃₁	1	2	yes	—
523	#496	C₂²×C₃₁	1	2	yes	complemented
524	#496	C₂²×C₃₁	1	1	yes	characteristic, complemented
525	#495	C₂²×C₃₁	1	2	yes	complemented
526	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
527	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
528	#490	C₂²×C₃₁	1	2	yes	—
529	#490	C₂²×C₃₁	1	2	yes	—
530	#490	C₂²×C₃₁	1	1	yes	characteristic, complemented
531	#490	C₂²×C₃₁	1	1	yes	characteristic, complemented
532	#489	C₂²×C₃₁	1	2	yes	complemented
533	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
534	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
535	#486	C₂²×C₃₁	1	2	yes	complemented
536	#485	C₂²×C₃₁	1	2	yes	—
537	#482	C₂²×C₃₁	1	2	yes	—
538	#479	C₂²×C₃₁	1	2	yes	complemented
539	#478	C₂²×C₃₁	1	2	yes	complemented
540	#478	C₂²×C₃₁	1	2	yes	complemented
541	#478	C₂²×C₃₁	1	2	yes	complemented
542	#476	C₂²×C₃₁	1	2	yes	complemented
543	#474	C₂²×C₃₁	1	2	yes	complemented
544	#464	C₂²×C₃₁	1	2	yes	complemented
545	#464	C₂²×C₃₁	1	2	yes	complemented
546	#464	C₂²×C₃₁	1	2	yes	complemented
547	#463	C₂²×C₃₁	1	2	yes	complemented
548	#463	C₂²×C₃₁	1	2	yes	complemented
549	#463	C₂²×C₃₁	1	2	yes	complemented
550	#463	C₂²×C₃₁	1	2	yes	complemented
551	#463	C₂²×C₃₁	1	2	yes	complemented
552	#461	C₂²×C₃₁	1	2	yes	complemented
553	#460	C₂²×C₃₁	1	2	yes	—
554	#460	C₂²×C₃₁	1	2	yes	—
555	#460	C₂²×C₃₁	1	2	yes	complemented
556	#460	C₂²×C₃₁	1	2	yes	complemented
557	#459	C₂²×C₃₁	1	2	yes	—
558	#459	C₂²×C₃₁	1	2	yes	—
559	#459	C₂²×C₃₁	1	2	yes	complemented
560	#459	C₂²×C₃₁	1	2	yes	complemented
561	#459	C₂²×C₃₁	1	2	yes	complemented
562	#452	C₂²×C₃₁	1	2	yes	—
563	#450	C₂²×C₃₁	1	2	yes	—
564	#450	C₂²×C₃₁	1	2	yes	—
565	#449	C₂²×C₃₁	1	2	yes	—
566	#447	C₂²×C₃₁	1	2	yes	—
567	#447	C₂²×C₃₁	1	2	yes	—
568	#446	C₂²×C₃₁	1	2	yes	complemented
569	#446	C₂²×C₃₁	1	2	yes	complemented
570	#446	C₂²×C₃₁	1	2	yes	complemented
571	#446	C₂²×C₃₁	1	2	yes	complemented
572	#442	C₂²×C₃₁	1	2	yes	complemented
573	#442	C₂²×C₃₁	1	2	yes	complemented
574	#442	C₂²×C₃₁	1	2	yes	complemented
575	#441	C₂²×C₃₁	1	2	yes	complemented
576	#440	C₂²×C₃₁	1	2	yes	complemented
577	#440	C₂²×C₃₁	1	2	yes	complemented
578	#440	C₂²×C₃₁	1	2	yes	complemented
579	#440	C₂²×C₃₁	1	2	yes	complemented
580	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
581	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
582	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
583	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
584	#433	C₂²×C₃₁	1	2	yes	—
585	#433	C₂²×C₃₁	1	1	yes	characteristic
586	#433	C₂²×C₃₁	1	1	yes	characteristic
587	#432	C₂²×C₃₁	1	2	yes	—
588	C₂×C₃₁	—	4	1	no	—
589	C₂×C₃₁	—	8	1	no	—
590	C₂×C₃₁	—	8	2	no	—
591	C₂×C₃₁	—	8	2	no	—
592	C₂×C₃₁	—	8	1	no	—
593	C₂×C₃₁	—	8	1	no	—
594	C₂×C₃₁	#3487	1	1	yes	characteristic
595	C₂×C₃₁	#3585	1	2	yes	—
596	C₂×#41	—	2	2	no	—
597	C₂×#41	—	2	2	no	—
598	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
599	C₂²×D₄	—	2	2	no	—
600	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
601	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
602	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
603	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
604	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
605	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
606	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
607	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
608	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
609	C₂×D₈	C₂³×C₃₁	1	2	yes	—
610	C₂×D₈	C₂³×C₃₁	1	2	yes	—
611	C₂×D₈	C₂³×C₃₁	1	2	yes	—
612	C₂×D₈	C₂³×C₃₁	1	2	yes	—
613	C₂×D₈	C₂³×C₃₁	1	2	yes	—
614	C₄⋊Q₈	—	2	2	no	—
615	C₄⋊Q₈	D₄×C₃₁	1	2	yes	—
616	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
617	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
618	#127	—	2	1	no	—
619	#127	—	2	1	no	—
620	#127	C₂³×C₃₁	1	2	yes	—
621	#127	C₂³×C₃₁	1	2	yes	—
622	#127	C₂³×C₃₁	1	1	yes	characteristic
623	#127	C₂³×C₃₁	1	2	yes	—
624	#127	C₂³×C₃₁	1	1	yes	characteristic
625	#127	C₂³×C₃₁	1	1	yes	characteristic
626	#126	—	2	2	no	—
627	#126	—	2	2	no	—
628	#126	—	2	2	no	—
629	#126	—	2	2	no	—
630	#126	—	2	2	no	—
631	#125	—	2	2	no	—
632	#125	—	2	2	no	—
633	#125	—	2	2	no	—
634	#125	D₄×C₃₁	1	2	yes	—
635	#125	C₂³×C₃₁	1	2	yes	—
636	#125	C₂³×C₃₁	1	1	yes	characteristic
637	#125	C₂³×C₃₁	1	1	yes	characteristic
638	#124	—	2	2	no	—
639	#124	—	2	2	no	—
640	#124	—	2	2	no	—
641	#124	—	2	2	no	—
642	#124	C₂³×C₃₁	1	2	yes	—
643	#124	C₂³×C₃₁	1	1	yes	characteristic
644	#124	C₂³×C₃₁	1	2	yes	—
645	#124	C₂³×C₃₁	1	1	yes	characteristic
646	#124	C₂³×C₃₁	1	2	yes	—
647	#123	—	2	2	no	—
648	#123	—	2	2	no	—
649	#123	—	2	2	no	—
650	#123	—	2	2	no	—
651	#123	—	2	2	no	—
652	#123	—	2	2	no	—
653	#123	—	2	2	no	—
654	#123	—	2	2	no	—
655	#123	—	2	2	no	—
656	C₂²⋊Q₈	—	2	2	no	—
657	C₂²⋊Q₈	—	2	2	no	—
658	C₂²⋊Q₈	—	2	2	no	—
659	C₂²⋊Q₈	—	2	2	no	—
660	C₂²⋊Q₈	—	2	2	no	—
661	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
662	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
663	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
664	#121	—	2	2	no	—
665	#121	—	2	2	no	—
666	#121	—	2	2	no	—
667	#121	—	2	2	no	—
668	#121	—	2	2	no	—
669	#121	—	2	2	no	—
670	#121	—	2	2	no	—
671	#121	—	2	2	no	—
672	#121	—	2	2	no	—
673	#121	C₂³×C₃₁	1	2	yes	—
674	#120	—	2	2	no	—
675	#120	—	2	1	no	—
676	#120	—	2	1	no	—
677	C₄×Q₈	—	2	2	no	—
678	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
679	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
680	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
681	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
682	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
683	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
684	C₄×D₄	—	2	2	no	—
685	C₄×D₄	—	2	2	no	—
686	C₄×D₄	—	2	2	no	—
687	C₄×D₄	—	2	2	no	—
688	C₄×D₄	—	2	2	no	—
689	C₄×D₄	—	2	2	no	—
690	C₄×D₄	—	2	2	no	—
691	C₄×D₄	C₂³×C₃₁	1	2	yes	—
692	C₄×D₄	C₂³×C₃₁	1	2	yes	—
693	C₄×D₄	C₂³×C₃₁	1	2	yes	—
694	C₄×D₄	C₂³×C₃₁	1	2	yes	—
695	C₄×D₄	C₂³×C₃₁	1	2	yes	—
696	C₄×D₄	C₂³×C₃₁	1	2	yes	—
697	C₄×D₄	C₂³×C₃₁	1	2	yes	—
698	C₄×D₄	C₂³×C₃₁	1	2	yes	—
699	#117	—	2	2	no	—
700	#117	—	2	1	no	—
701	#117	—	2	2	no	—
702	#117	C₂³×C₃₁	1	1	yes	characteristic
703	#117	C₂³×C₃₁	1	1	yes	characteristic
704	#117	C₂³×C₃₁	1	1	yes	characteristic
705	C₂×C₄⋊C₄	—	2	2	no	—
706	C₂×C₂²⋊C₄	—	2	2	no	—
707	C₂×C₂²⋊C₄	—	2	1	no	—
708	C₂×C₂²⋊C₄	—	2	1	no	—
709	C₂×C₄²	—	2	1	no	—
710	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
711	#107	C₂³×C₃₁	1	2	yes	—
712	#107	C₂³×C₃₁	1	2	yes	—
713	#106	C₂³×C₃₁	1	2	yes	—
714	#106	C₂³×C₃₁	1	2	yes	—
715	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
716	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
717	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
718	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
719	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
720	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
721	#103	C₂³×C₃₁	1	2	yes	—
722	#103	C₂³×C₃₁	1	2	yes	—
723	#103	C₂³×C₃₁	1	2	yes	—
724	#103	C₂³×C₃₁	1	2	yes	—
725	#102	C₂³×C₃₁	1	2	yes	—
726	#102	C₂³×C₃₁	1	2	yes	—
727	#102	C₂³×C₃₁	1	2	yes	—
728	#102	C₂³×C₃₁	1	2	yes	—
729	#102	C₂³×C₃₁	1	2	yes	—
730	#102	C₂³×C₃₁	1	2	yes	—
731	#102	C₂³×C₃₁	1	2	yes	—
732	#102	C₂³×C₃₁	1	2	yes	—
733	#102	C₂³×C₃₁	1	2	yes	—
734	#102	C₂³×C₃₁	1	2	yes	—
735	#102	C₂³×C₃₁	1	2	yes	—
736	#102	C₂³×C₃₁	1	2	yes	—
737	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
738	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
739	#97	C₂³×C₃₁	1	2	yes	—
740	#97	C₂³×C₃₁	1	2	yes	—
741	#97	C₂³×C₃₁	1	1	yes	characteristic
742	#97	C₂³×C₃₁	1	2	yes	—
743	#97	C₂³×C₃₁	1	1	yes	characteristic
744	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
745	C₄×C₈	C₂³×C₃₁	1	2	yes	—
746	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
747	C₃₁	#61945	1	1	yes	characteristic, direct product factor, Sylow
748	C₂⁴	—	2	1	no	—
749	C₂⁴	—	2	1	no	—
750	#41	—	4	2	no	—
751	#41	—	8	4	no	—
752	#41	—	8	4	no	—
753	C₂×Q₈	—	2	2	no	—
754	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
755	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
756	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
757	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
758	C₂×D₄	—	2	1	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	1	no	—
761	C₂×D₄	—	2	1	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	4	2	no	—
772	C₂×D₄	—	4	2	no	—
773	C₂×D₄	—	8	4	no	—
774	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
775	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
776	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
777	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
778	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
779	C₂²×C₄	—	2	1	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
790	Q₁₆	—	4	2	no	—
791	SD₁₆	—	4	2	no	—
792	SD₁₆	—	4	2	no	—
793	SD₁₆	—	4	2	no	—
794	SD₁₆	—	4	2	no	—
795	SD₁₆	—	4	2	no	—
796	SD₁₆	—	4	2	no	—
797	D₈	—	4	2	no	—
798	D₈	—	4	2	no	—
799	D₈	—	4	2	no	—
800	D₈	—	4	2	no	—
801	D₈	—	4	2	no	—
802	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
803	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
804	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
805	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
818	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
819	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
820	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
821	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
822	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
823	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
824	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
825	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
827	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
828	C₂²⋊C₄	—	2	1	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
848	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
849	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
850	C₄²	—	2	1	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	2	no	—
855	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
856	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
857	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
858	C₄²	C₂⁴×C₃₁	1	2	yes	—
859	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
860	C₄²	C₂⁴×C₃₁	1	2	yes	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	2	1	no	—
866	C₂³	—	4	2	no	—
867	C₂³	—	4	2	no	—
868	C₂³	—	8	2	no	—
869	C₂³	—	8	2	no	—
870	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
871	Q₈	—	2	2	no	—
872	Q₈	—	2	2	no	—
873	Q₈	—	2	2	no	—
874	Q₈	—	4	2	no	—
875	Q₈	—	4	2	no	—
876	Q₈	—	8	2	no	—
877	D₄	—	2	2	no	—
878	D₄	—	2	2	no	—
879	D₄	—	2	2	no	—
880	D₄	—	2	2	no	—
881	D₄	—	2	2	no	—
882	D₄	—	2	2	no	—
883	D₄	—	2	2	no	—
884	D₄	—	4	2	no	—
885	D₄	—	4	2	no	—
886	D₄	—	4	4	no	—
887	D₄	—	4	4	no	—
888	D₄	—	4	2	no	—
889	D₄	—	8	2	no	—
890	D₄	—	8	2	no	—
891	D₄	—	8	2	no	—
892	D₄	—	8	2	no	—
893	D₄	—	8	2	no	—
894	D₄	—	8	2	no	—
895	D₄	—	8	2	no	—
896	D₄	—	8	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	4	2	no	—
904	C₂×C₄	—	4	2	no	—
905	C₂×C₄	—	4	4	no	—
906	C₂×C₄	—	8	2	no	—
907	C₂×C₄	—	8	2	no	—
908	C₂×C₄	—	8	2	no	—
909	C₂×C₄	—	8	2	no	—
910	C₂×C₄	—	8	2	no	—
911	C₂×C₄	—	8	2	no	—
912	C₂×C₄	—	8	2	no	—
913	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
914	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
915	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
916	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
917	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
918	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
919	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
920	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
921	C₈	—	2	2	no	—
922	C₈	—	2	2	no	—
923	C₈	—	2	2	no	—
924	C₈	—	2	2	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	1	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	2	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	16	2	no	—
940	C₂²	—	16	2	no	—
941	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
942	C₄	—	2	1	no	—
943	C₄	—	2	2	no	—
944	C₄	—	2	2	no	—
945	C₄	—	2	2	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	2	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	2	no	—
954	C₄	C₃₁×#585	1	2	yes	—
955	C₂	—	4	1	no	—
956	C₂	—	8	2	no	—
957	C₂	—	8	1	no	—
958	C₂	—	8	1	no	—
959	C₂	—	8	1	no	—
960	C₂	—	8	2	no	—
961	C₂	C₃₁×#3487	1	1	yes	characteristic
962	C₂	C₃₁×#3585	1	2	yes	—

	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×#3557	C₂	semidirect
2. C₃₁×#3508	C₂	semidirect
3. C₃₁×#3403	C₂	semidirect
4. C₃₁×#3401	C₂	semidirect
5. C₃₁×#3399	C₂	semidirect
6. C₃₁×#3397	C₂	semidirect
7. C₃₁×#3371	C₂	semidirect
8. C₃₁×#3370	C₂	semidirect
9. C₃₁×#3368	C₂	semidirect
10. C₃₁×#3366	C₂	semidirect
11. C₃₁×#3224	C₂	semidirect
12. C₃₁×#3222	C₂	semidirect
13. C₃₁×#3220	C₂	semidirect
14. C₃₁×#3217	C₂	semidirect
15. C₃₁×#3123	C₂	semidirect
16. C₃₁×#3122	C₂	semidirect
17. C₃₁×#3118	C₂	semidirect
18. C₃₁×#3111	C₂	semidirect
19. C₃₁×#2987	C₂	semidirect
23. C₃₁×#559	C₂²	semidirect
24. C₃₁×#557	C₂²	semidirect
25. C₃₁×#556	C₂²	semidirect
26. C₃₁×#554	C₂²	semidirect
47. C₃₁×#497	C₂²	semidirect
50. C₃₁×#496	C₂²	semidirect
51. C₃₁×#496	C₂²	semidirect
52. C₃₁×#495	C₂²	semidirect
53. C₃₁×#493	C₂²	semidirect
54. C₃₁×#492	C₂²	semidirect
57. C₃₁×#490	C₂²	semidirect
58. C₃₁×#490	C₂²	semidirect
59. C₃₁×#489	C₂²	semidirect
60. C₃₁×#488	C₂²	semidirect
61. C₃₁×#488	C₂²	semidirect
62. C₃₁×#486	C₂²	semidirect
65. C₃₁×#479	C₂²	semidirect
66. C₃₁×#478	C₂²	semidirect
67. C₃₁×#478	C₂²	semidirect
68. C₃₁×#478	C₂²	semidirect
69. C₃₁×#476	C₂²	semidirect
70. C₃₁×#474	C₂²	semidirect
71. C₃₁×#464	C₂²	semidirect
72. C₃₁×#464	C₂²	semidirect
73. C₃₁×#464	C₂²	semidirect
74. C₃₁×#463	C₂²	semidirect
75. C₃₁×#463	C₂²	semidirect
76. C₃₁×#463	C₂²	semidirect
77. C₃₁×#463	C₂²	semidirect
78. C₃₁×#463	C₂²	semidirect
79. C₃₁×#461	C₂²	semidirect
82. C₃₁×#460	C₂²	semidirect
83. C₃₁×#460	C₂²	semidirect
86. C₃₁×#459	C₂²	semidirect
87. C₃₁×#459	C₂²	semidirect
88. C₃₁×#459	C₂²	semidirect
95. C₃₁×#446	C₂²	semidirect
96. C₃₁×#446	C₂²	semidirect
97. C₃₁×#446	C₂²	semidirect
98. C₃₁×#446	C₂²	semidirect
99. C₃₁×#442	C₂²	semidirect
100. C₃₁×#442	C₂²	semidirect
101. C₃₁×#442	C₂²	semidirect
102. C₃₁×#441	C₂²	semidirect
103. C₃₁×#440	C₂²	semidirect
104. C₃₁×#440	C₂²	semidirect
105. C₃₁×#440	C₂²	semidirect
106. C₃₁×#440	C₂²	semidirect
107. C₄×SD₁₆×C₃₁	C₂²	semidirect
108. C₄×SD₁₆×C₃₁	C₂²	semidirect
109. C₄×D₈×C₃₁	C₂²	semidirect
110. C₄×D₈×C₃₁	C₂²	semidirect
379. #61945	C₃₁	direct (N × H)
444. #3557	C₂×C₃₁	semidirect
445. #3508	C₂×C₃₁	semidirect
446. #3403	C₂×C₃₁	semidirect
447. #3401	C₂×C₃₁	semidirect
448. #3399	C₂×C₃₁	semidirect
449. #3397	C₂×C₃₁	semidirect
450. #3371	C₂×C₃₁	semidirect
451. #3370	C₂×C₃₁	semidirect
452. #3368	C₂×C₃₁	semidirect
453. #3366	C₂×C₃₁	semidirect
454. #3224	C₂×C₃₁	semidirect
455. #3222	C₂×C₃₁	semidirect
456. #3220	C₂×C₃₁	semidirect
457. #3217	C₂×C₃₁	semidirect
458. #3123	C₂×C₃₁	semidirect
459. #3122	C₂×C₃₁	semidirect
460. #3118	C₂×C₃₁	semidirect
461. #3111	C₂×C₃₁	semidirect
462. #2987	C₂×C₃₁	semidirect
496. #559	C₂²×C₃₁	semidirect
497. #557	C₂²×C₃₁	semidirect
498. #556	C₂²×C₃₁	semidirect
499. #554	C₂²×C₃₁	semidirect
520. #497	C₂²×C₃₁	semidirect
523. #496	C₂²×C₃₁	semidirect
524. #496	C₂²×C₃₁	semidirect
525. #495	C₂²×C₃₁	semidirect
526. #493	C₂²×C₃₁	semidirect
527. #492	C₂²×C₃₁	semidirect
530. #490	C₂²×C₃₁	semidirect
531. #490	C₂²×C₃₁	semidirect
532. #489	C₂²×C₃₁	semidirect
533. #488	C₂²×C₃₁	semidirect
534. #488	C₂²×C₃₁	semidirect
535. #486	C₂²×C₃₁	semidirect
538. #479	C₂²×C₃₁	semidirect
539. #478	C₂²×C₃₁	semidirect
540. #478	C₂²×C₃₁	semidirect
541. #478	C₂²×C₃₁	semidirect
542. #476	C₂²×C₃₁	semidirect
543. #474	C₂²×C₃₁	semidirect
544. #464	C₂²×C₃₁	semidirect
545. #464	C₂²×C₃₁	semidirect
546. #464	C₂²×C₃₁	semidirect
547. #463	C₂²×C₃₁	semidirect
548. #463	C₂²×C₃₁	semidirect
549. #463	C₂²×C₃₁	semidirect
550. #463	C₂²×C₃₁	semidirect
551. #463	C₂²×C₃₁	semidirect
552. #461	C₂²×C₃₁	semidirect
555. #460	C₂²×C₃₁	semidirect
556. #460	C₂²×C₃₁	semidirect
559. #459	C₂²×C₃₁	semidirect
560. #459	C₂²×C₃₁	semidirect
561. #459	C₂²×C₃₁	semidirect
568. #446	C₂²×C₃₁	semidirect
569. #446	C₂²×C₃₁	semidirect
570. #446	C₂²×C₃₁	semidirect
571. #446	C₂²×C₃₁	semidirect
572. #442	C₂²×C₃₁	semidirect
573. #442	C₂²×C₃₁	semidirect
574. #442	C₂²×C₃₁	semidirect
575. #441	C₂²×C₃₁	semidirect
576. #440	C₂²×C₃₁	semidirect
577. #440	C₂²×C₃₁	semidirect
578. #440	C₂²×C₃₁	semidirect
579. #440	C₂²×C₃₁	semidirect
580. C₄×SD₁₆	C₂²×C₃₁	semidirect
581. C₄×SD₁₆	C₂²×C₃₁	semidirect
582. C₄×D₈	C₂²×C₃₁	semidirect
583. C₄×D₈	C₂²×C₃₁	semidirect
747. C₃₁	#61945	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×#3557	2
C₃₁×#3508	2
C₃₁×#3403	2
C₃₁×#3401	2
C₃₁×#3399	2
C₃₁×#3397	2
C₃₁×#3371	2
C₃₁×#3370	2
C₃₁×#3368	2
C₃₁×#3366	2
C₃₁×#3224	2
C₃₁×#3222	2
C₃₁×#3220	2
C₃₁×#3217	2
C₃₁×#3123	2
C₃₁×#3122	2
C₃₁×#3118	2
C₃₁×#3111	2
C₃₁×#2987	2
#61945	31

Subgroups — C31×#61945 #21518704

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61945 #21518704