Subgroups — C₃₁×#61946 #21518705

Order 7936.

1646 conjugacy classes of subgroups.

The subgroup lattice has 912 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×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3402	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3401	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3400	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3398	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3374	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3372	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3225	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3223	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3221	C₂	1	1	yes	maximal, characteristic
14	C₃₁×#3218	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3127	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3126	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3121	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×#557	C₂²	1	2	yes	—
23	C₃₁×#557	C₂²	1	2	yes	—
24	C₃₁×#557	C₂²	1	2	yes	—
25	C₃₁×#556	C₂²	1	2	yes	—
26	C₃₁×#556	C₂²	1	2	yes	—
27	C₃₁×#556	C₂²	1	2	yes	—
28	C₃₁×#554	C₂²	1	2	yes	—
29	C₃₁×#552	—	2	2	no	—
30	C₃₁×#552	—	2	2	no	—
31	C₃₁×#552	—	2	2	no	—
32	C₃₁×#542	—	2	2	no	—
33	C₃₁×#542	C₂²	1	2	yes	—
34	C₃₁×#541	—	2	2	no	—
35	C₃₁×#541	C₂²	1	1	yes	characteristic
36	C₃₁×#540	C₂²	1	1	yes	characteristic
37	C₃₁×#539	—	2	2	no	—
38	C₃₁×#536	C₂²	1	1	yes	characteristic
39	C₃₁×#536	C₂²	1	1	yes	characteristic
40	C₃₁×#533	—	2	2	no	—
41	C₃₁×#533	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
43	C₃₁×#529	C₂²	1	2	yes	—
44	C₃₁×#519	C₂²	1	1	yes	characteristic
45	C₃₁×#519	C₂²	1	1	yes	characteristic
46	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
47	C₃₁×#497	C₂²	1	2	yes	—
48	C₃₁×#497	C₂²	1	2	yes	—
49	C₃₁×#497	C₂²	1	2	yes	—
50	C₃₁×#497	C₂²	1	1	yes	characteristic
51	C₃₁×#496	C₂²	1	1	yes	characteristic
52	C₃₁×#495	C₂²	1	2	yes	—
53	C₃₁×#494	C₂²	1	1	yes	characteristic
54	C₃₁×#492	C₂²	1	1	yes	characteristic
55	C₃₁×#491	C₂²	1	1	yes	characteristic
56	C₃₁×#491	C₂²	1	2	yes	—
57	C₃₁×#491	C₂²	1	1	yes	characteristic
58	C₃₁×#491	C₂²	1	2	yes	—
59	C₃₁×#489	C₂²	1	2	yes	—
60	C₃₁×#488	C₂²	1	1	yes	characteristic
61	C₃₁×#488	C₂²	1	1	yes	characteristic
62	C₃₁×#487	C₂²	1	2	yes	—
63	C₃₁×#485	C₂²	1	2	yes	—
64	C₃₁×#482	C₂²	1	2	yes	—
65	C₃₁×#479	C₂²	1	2	yes	—
66	C₃₁×#479	C₂²	1	2	yes	—
67	C₃₁×#479	C₂²	1	2	yes	—
68	C₃₁×#478	C₂²	1	2	yes	—
69	C₃₁×#477	C₂²	1	2	yes	—
70	C₃₁×#475	C₂²	1	2	yes	—
71	C₃₁×#464	C₂²	1	2	yes	—
72	C₃₁×#464	C₂²	1	2	yes	—
73	C₃₁×#464	C₂²	1	2	yes	—
74	C₃₁×#464	C₂²	1	2	yes	—
75	C₃₁×#464	C₂²	1	2	yes	—
76	C₃₁×#463	C₂²	1	2	yes	—
77	C₃₁×#463	C₂²	1	2	yes	—
78	C₃₁×#463	C₂²	1	2	yes	—
79	C₃₁×#462	C₂²	1	2	yes	—
80	C₃₁×#462	C₂²	1	2	yes	—
81	C₃₁×#462	C₂²	1	2	yes	—
82	C₃₁×#462	C₂²	1	2	yes	—
83	C₃₁×#462	C₂²	1	2	yes	—
84	C₃₁×#461	C₂²	1	2	yes	—
85	C₃₁×#461	C₂²	1	2	yes	—
86	C₃₁×#461	C₂²	1	2	yes	—
87	C₃₁×#461	C₂²	1	2	yes	—
88	C₃₁×#460	C₂²	1	2	yes	—
89	C₃₁×#452	C₂²	1	2	yes	—
90	C₃₁×#451	C₂²	1	2	yes	—
91	C₃₁×#451	C₂²	1	2	yes	—
92	C₃₁×#449	C₂²	1	2	yes	—
93	C₃₁×#448	C₂²	1	2	yes	—
94	C₃₁×#448	C₂²	1	2	yes	—
95	C₃₁×#446	C₂²	1	2	yes	—
96	C₃₁×#446	C₂²	1	2	yes	—
97	C₃₁×#446	C₂²	1	2	yes	—
98	C₃₁×#446	C₂²	1	2	yes	—
99	C₃₁×#442	C₂²	1	2	yes	—
100	C₃₁×#441	C₂²	1	2	yes	—
101	C₃₁×#441	C₂²	1	2	yes	—
102	C₃₁×#441	C₂²	1	2	yes	—
103	C₃₁×#440	C₂²	1	2	yes	—
104	C₃₁×#440	C₂²	1	2	yes	—
105	C₃₁×#440	C₂²	1	2	yes	—
106	C₃₁×#440	C₂²	1	2	yes	—
107	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
108	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
109	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
110	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
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	C₂³	1	1	yes	characteristic
116	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
117	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
118	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
119	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
120	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
121	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
122	C₂×Q₁₆×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×SD₁₆×C₃₁	C₂³	1	2	yes	—
129	C₂×D₈×C₃₁	C₂³	1	2	yes	—
130	C₃₁×C₄⋊Q₈	—	2	2	no	—
131	C₃₁×C₄⋊Q₈	—	2	1	no	—
132	C₃₁×C₄⋊Q₈	—	2	1	no	—
133	C₃₁×C₄⋊Q₈	D₄	1	2	yes	—
134	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
135	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₃₁×#127	C₂³	1	1	yes	characteristic
142	C₃₁×#126	—	2	2	no	—
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#126	—	2	2	no	—
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×#126	—	2	2	no	—
151	C₃₁×#125	—	2	2	no	—
152	C₃₁×#125	—	2	2	no	—
153	C₃₁×#125	—	2	2	no	—
154	C₃₁×#125	—	2	2	no	—
155	C₃₁×#125	—	2	2	no	—
156	C₃₁×#125	—	2	2	no	—
157	C₃₁×#125	—	2	2	no	—
158	C₃₁×#125	—	2	2	no	—
159	C₃₁×#125	—	2	2	no	—
160	C₃₁×#125	D₄	1	2	yes	—
161	C₃₁×#125	C₂³	1	2	yes	—
162	C₃₁×#125	C₂³	1	1	yes	characteristic
163	C₃₁×#125	C₂³	1	1	yes	characteristic
164	C₃₁×#124	—	2	2	no	—
165	C₃₁×#124	—	2	2	no	—
166	C₃₁×#124	C₂³	1	1	yes	characteristic
167	C₃₁×#124	C₂³	1	2	yes	—
168	C₃₁×#124	C₂³	1	2	yes	—
169	C₃₁×#124	C₂³	1	1	yes	characteristic
170	C₃₁×#124	C₂³	1	2	yes	—
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×#123	—	2	2	no	—
176	C₃₁×#123	—	2	1	no	—
177	C₃₁×#123	—	2	1	no	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×C₂²⋊Q₈	—	2	2	no	—
180	C₃₁×C₂²⋊Q₈	—	2	2	no	—
181	C₃₁×C₂²⋊Q₈	—	2	2	no	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	2	no	—
184	C₃₁×C₂²⋊Q₈	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
189	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
190	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₃₁×#121	—	2	2	no	—
192	C₃₁×#121	C₂³	1	2	yes	—
193	C₄×Q₈×C₃₁	—	2	2	no	—
194	C₄×Q₈×C₃₁	—	2	2	no	—
195	C₄×Q₈×C₃₁	—	2	2	no	—
196	C₄×Q₈×C₃₁	—	2	2	no	—
197	C₄×Q₈×C₃₁	—	2	2	no	—
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×Q₈×C₃₁	C₂³	1	2	yes	—
204	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
205	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
206	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
207	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
208	C₄×D₄×C₃₁	—	2	2	no	—
209	C₄×D₄×C₃₁	—	2	2	no	—
210	C₄×D₄×C₃₁	—	2	2	no	—
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	C₃₁×#117	—	2	2	no	—
216	C₃₁×#117	—	2	2	no	—
217	C₃₁×#117	—	2	2	no	—
218	C₃₁×#117	—	2	2	no	—
219	C₃₁×#117	—	2	1	no	—
220	C₃₁×#117	—	2	1	no	—
221	C₃₁×#117	—	2	1	no	—
222	C₃₁×#117	—	2	2	no	—
223	C₃₁×#117	C₂³	1	1	yes	characteristic
224	C₃₁×#117	C₂³	1	1	yes	characteristic
225	C₃₁×#117	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
227	C₂×C₄⋊C₄×C₃₁	—	2	2	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×#103	C₂³	1	2	yes	—
245	C₃₁×#103	C₂³	1	2	yes	—
246	C₃₁×#103	C₂³	1	2	yes	—
247	C₃₁×#103	C₂³	1	2	yes	—
248	C₃₁×#103	C₂³	1	2	yes	—
249	C₃₁×#103	C₂³	1	2	yes	—
250	C₃₁×#103	C₂³	1	2	yes	—
251	C₃₁×#103	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	#41×C₃₁	—	4	2	no	—
267	C₂×Q₈×C₃₁	—	2	1	no	—
268	C₂×Q₈×C₃₁	—	2	1	no	—
269	C₂×Q₈×C₃₁	—	2	2	no	—
270	C₂×Q₈×C₃₁	—	4	2	no	—
271	C₂×Q₈×C₃₁	—	4	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	2	yes	—
275	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
276	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
277	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
278	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
283	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₃₁	—	2	1	no	—
285	C₂²×C₄×C₃₁	—	2	1	no	—
286	C₂²×C₄×C₃₁	—	2	2	no	—
287	C₂²×C₄×C₃₁	—	2	1	no	—
288	C₂²×C₄×C₃₁	—	2	2	no	—
289	C₂²×C₄×C₃₁	—	2	2	no	—
290	C₂²×C₄×C₃₁	—	2	2	no	—
291	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
292	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
293	Q₁₆×C₃₁	—	4	2	no	—
294	Q₁₆×C₃₁	—	4	2	no	—
295	Q₁₆×C₃₁	—	4	2	no	—
296	Q₁₆×C₃₁	—	4	2	no	—
297	Q₁₆×C₃₁	—	4	2	no	—
298	SD₁₆×C₃₁	—	4	2	no	—
299	SD₁₆×C₃₁	—	4	2	no	—
300	SD₁₆×C₃₁	—	4	2	no	—
301	SD₁₆×C₃₁	—	4	2	no	—
302	SD₁₆×C₃₁	—	4	2	no	—
303	SD₁₆×C₃₁	—	4	2	no	—
304	D₈×C₃₁	—	4	2	no	—
305	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
306	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
307	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
308	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
309	C₄⋊C₄×C₃₁	—	2	2	no	—
310	C₄⋊C₄×C₃₁	—	2	2	no	—
311	C₄⋊C₄×C₃₁	—	2	2	no	—
312	C₄⋊C₄×C₃₁	—	2	2	no	—
313	C₄⋊C₄×C₃₁	—	2	2	no	—
314	C₄⋊C₄×C₃₁	—	2	2	no	—
315	C₄⋊C₄×C₃₁	—	2	2	no	—
316	C₄⋊C₄×C₃₁	—	2	2	no	—
317	C₄⋊C₄×C₃₁	—	2	2	no	—
318	C₄⋊C₄×C₃₁	—	2	2	no	—
319	C₄⋊C₄×C₃₁	—	2	2	no	—
320	C₄⋊C₄×C₃₁	—	2	2	no	—
321	C₄⋊C₄×C₃₁	—	2	2	no	—
322	C₄⋊C₄×C₃₁	—	2	2	no	—
323	C₄⋊C₄×C₃₁	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
333	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
334	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	C₂⁴	1	2	yes	—
341	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
342	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
343	C₂²⋊C₄×C₃₁	—	2	1	no	—
344	C₂²⋊C₄×C₃₁	—	2	2	no	—
345	C₂²⋊C₄×C₃₁	—	2	2	no	—
346	C₂²⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	2	yes	—
359	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
360	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
361	C₄²×C₃₁	—	2	1	no	—
362	C₄²×C₃₁	—	2	2	no	—
363	C₄²×C₃₁	—	2	2	no	—
364	C₄²×C₃₁	—	2	2	no	—
365	C₄²×C₃₁	—	2	2	no	—
366	C₄²×C₃₁	—	2	2	no	—
367	C₄²×C₃₁	—	2	2	no	—
368	C₄²×C₃₁	—	2	2	no	—
369	C₄²×C₃₁	—	2	2	no	—
370	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
371	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₄²×C₃₁	C₂⁴	1	2	yes	—
374	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
375	C₄²×C₃₁	C₂⁴	1	2	yes	—
376	#61946	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
377	C₂³×C₃₁	—	2	1	no	—
378	C₂³×C₃₁	—	2	2	no	—
379	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
380	Q₈×C₃₁	—	2	2	no	—
381	Q₈×C₃₁	—	2	2	no	—
382	Q₈×C₃₁	—	2	2	no	—
383	Q₈×C₃₁	—	2	2	no	—
384	Q₈×C₃₁	—	2	2	no	—
385	Q₈×C₃₁	—	2	2	no	—
386	Q₈×C₃₁	—	2	2	no	—
387	Q₈×C₃₁	—	4	2	no	—
388	Q₈×C₃₁	—	4	2	no	—
389	Q₈×C₃₁	—	4	2	no	—
390	Q₈×C₃₁	—	4	2	no	—
391	Q₈×C₃₁	—	8	2	no	—
392	D₄×C₃₁	—	2	2	no	—
393	D₄×C₃₁	—	2	2	no	—
394	D₄×C₃₁	—	2	2	no	—
395	D₄×C₃₁	—	4	2	no	—
396	D₄×C₃₁	—	8	2	no	—
397	D₄×C₃₁	—	8	2	no	—
398	C₂×C₄×C₃₁	—	2	2	no	—
399	C₂×C₄×C₃₁	—	2	2	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	2	2	no	—
402	C₂×C₄×C₃₁	—	2	1	no	—
403	C₂×C₄×C₃₁	—	2	1	no	—
404	C₂×C₄×C₃₁	—	2	2	no	—
405	C₂×C₄×C₃₁	—	2	1	no	—
406	C₂×C₄×C₃₁	—	2	2	no	—
407	C₂×C₄×C₃₁	—	4	2	no	—
408	C₂×C₄×C₃₁	—	4	4	no	—
409	C₂×C₄×C₃₁	—	4	2	no	—
410	C₂×C₄×C₃₁	—	4	2	no	—
411	C₂×C₄×C₃₁	—	4	2	no	—
412	C₂×C₄×C₃₁	—	8	2	no	—
413	C₂×C₄×C₃₁	—	8	2	no	—
414	C₂×C₄×C₃₁	—	8	2	no	—
415	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
423	C₈×C₃₁	—	2	2	no	—
424	C₈×C₃₁	—	2	2	no	—
425	C₈×C₃₁	—	2	2	no	—
426	C₈×C₃₁	—	2	2	no	—
427	#3557	C₂×C₃₁	1	1	yes	characteristic, complemented
428	#3509	C₂×C₃₁	1	1	yes	characteristic, complemented
429	#3402	C₂×C₃₁	1	2	yes	complemented
430	#3401	C₂×C₃₁	1	2	yes	complemented
431	#3400	C₂×C₃₁	1	2	yes	complemented
432	#3398	C₂×C₃₁	1	2	yes	complemented
433	#3377	C₂×C₃₁	1	2	yes	complemented
434	#3376	C₂×C₃₁	1	2	yes	complemented
435	#3374	C₂×C₃₁	1	2	yes	complemented
436	#3372	C₂×C₃₁	1	2	yes	complemented
437	#3225	C₂×C₃₁	1	2	yes	complemented
438	#3223	C₂×C₃₁	1	1	yes	characteristic, complemented
439	#3221	C₂×C₃₁	1	1	yes	characteristic
440	#3218	C₂×C₃₁	1	2	yes	complemented
441	#3127	C₂×C₃₁	1	1	yes	characteristic, complemented
442	#3126	C₂×C₃₁	1	1	yes	characteristic, complemented
443	#3121	C₂×C₃₁	1	2	yes	complemented
444	#3111	C₂×C₃₁	1	2	yes	complemented
445	#2987	C₂×C₃₁	1	1	yes	characteristic, complemented
446	C₂²×C₃₁	—	2	2	no	—
447	C₂²×C₃₁	—	2	1	no	—
448	C₂²×C₃₁	—	4	2	no	—
449	C₂²×C₃₁	—	4	2	no	—
450	C₂²×C₃₁	—	4	2	no	—
451	C₂²×C₃₁	—	4	1	no	—
452	C₂²×C₃₁	—	4	2	no	—
453	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
454	C₄×C₃₁	—	2	2	no	—
455	C₄×C₃₁	—	2	2	no	—
456	C₄×C₃₁	—	2	2	no	—
457	C₄×C₃₁	—	2	2	no	—
458	C₄×C₃₁	—	2	2	no	—
459	C₄×C₃₁	—	2	2	no	—
460	C₄×C₃₁	—	2	1	no	—
461	C₄×C₃₁	—	4	2	no	—
462	C₄×C₃₁	—	4	2	no	—
463	C₄×C₃₁	—	4	2	no	—
464	C₄×C₃₁	—	4	1	no	—
465	C₄×C₃₁	—	4	2	no	—
466	C₄×C₃₁	—	4	1	no	—
467	C₄×C₃₁	—	4	1	no	—
468	C₄×C₃₁	—	4	2	no	—
469	C₄×C₃₁	#585	1	2	yes	—
470	#563	—	2	2	no	—
471	#559	C₂²×C₃₁	1	2	yes	—
472	#557	C₂²×C₃₁	1	2	yes	—
473	#557	C₂²×C₃₁	1	2	yes	—
474	#557	C₂²×C₃₁	1	2	yes	—
475	#556	C₂²×C₃₁	1	2	yes	—
476	#556	C₂²×C₃₁	1	2	yes	—
477	#556	C₂²×C₃₁	1	2	yes	—
478	#554	C₂²×C₃₁	1	2	yes	—
479	#552	—	2	2	no	—
480	#552	—	2	2	no	—
481	#552	—	2	2	no	—
482	#542	—	2	2	no	—
483	#542	C₂²×C₃₁	1	2	yes	—
484	#541	—	2	2	no	—
485	#541	C₂²×C₃₁	1	1	yes	characteristic
486	#540	C₂²×C₃₁	1	1	yes	characteristic
487	#539	—	2	2	no	—
488	#536	C₂²×C₃₁	1	1	yes	characteristic
489	#536	C₂²×C₃₁	1	1	yes	characteristic
490	#533	—	2	2	no	—
491	#533	C₂²×C₃₁	1	1	yes	characteristic
492	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
493	#529	C₂²×C₃₁	1	2	yes	—
494	#519	C₂²×C₃₁	1	1	yes	characteristic
495	#519	C₂²×C₃₁	1	1	yes	characteristic
496	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
497	#497	C₂²×C₃₁	1	2	yes	—
498	#497	C₂²×C₃₁	1	2	yes	—
499	#497	C₂²×C₃₁	1	2	yes	—
500	#497	C₂²×C₃₁	1	1	yes	characteristic
501	#496	C₂²×C₃₁	1	1	yes	characteristic
502	#495	C₂²×C₃₁	1	2	yes	—
503	#494	C₂²×C₃₁	1	1	yes	characteristic
504	#492	C₂²×C₃₁	1	1	yes	characteristic
505	#491	C₂²×C₃₁	1	1	yes	characteristic
506	#491	C₂²×C₃₁	1	2	yes	—
507	#491	C₂²×C₃₁	1	1	yes	characteristic
508	#491	C₂²×C₃₁	1	2	yes	—
509	#489	C₂²×C₃₁	1	2	yes	—
510	#488	C₂²×C₃₁	1	1	yes	characteristic
511	#488	C₂²×C₃₁	1	1	yes	characteristic
512	#487	C₂²×C₃₁	1	2	yes	—
513	#485	C₂²×C₃₁	1	2	yes	—
514	#482	C₂²×C₃₁	1	2	yes	—
515	#479	C₂²×C₃₁	1	2	yes	—
516	#479	C₂²×C₃₁	1	2	yes	—
517	#479	C₂²×C₃₁	1	2	yes	—
518	#478	C₂²×C₃₁	1	2	yes	—
519	#477	C₂²×C₃₁	1	2	yes	—
520	#475	C₂²×C₃₁	1	2	yes	—
521	#464	C₂²×C₃₁	1	2	yes	—
522	#464	C₂²×C₃₁	1	2	yes	—
523	#464	C₂²×C₃₁	1	2	yes	—
524	#464	C₂²×C₃₁	1	2	yes	—
525	#464	C₂²×C₃₁	1	2	yes	—
526	#463	C₂²×C₃₁	1	2	yes	—
527	#463	C₂²×C₃₁	1	2	yes	—
528	#463	C₂²×C₃₁	1	2	yes	—
529	#462	C₂²×C₃₁	1	2	yes	—
530	#462	C₂²×C₃₁	1	2	yes	—
531	#462	C₂²×C₃₁	1	2	yes	—
532	#462	C₂²×C₃₁	1	2	yes	—
533	#462	C₂²×C₃₁	1	2	yes	—
534	#461	C₂²×C₃₁	1	2	yes	—
535	#461	C₂²×C₃₁	1	2	yes	—
536	#461	C₂²×C₃₁	1	2	yes	—
537	#461	C₂²×C₃₁	1	2	yes	—
538	#460	C₂²×C₃₁	1	2	yes	—
539	#452	C₂²×C₃₁	1	2	yes	—
540	#451	C₂²×C₃₁	1	2	yes	—
541	#451	C₂²×C₃₁	1	2	yes	—
542	#449	C₂²×C₃₁	1	2	yes	—
543	#448	C₂²×C₃₁	1	2	yes	—
544	#448	C₂²×C₃₁	1	2	yes	—
545	#446	C₂²×C₃₁	1	2	yes	—
546	#446	C₂²×C₃₁	1	2	yes	—
547	#446	C₂²×C₃₁	1	2	yes	—
548	#446	C₂²×C₃₁	1	2	yes	—
549	#442	C₂²×C₃₁	1	2	yes	—
550	#441	C₂²×C₃₁	1	2	yes	—
551	#441	C₂²×C₃₁	1	2	yes	—
552	#441	C₂²×C₃₁	1	2	yes	—
553	#440	C₂²×C₃₁	1	2	yes	—
554	#440	C₂²×C₃₁	1	2	yes	—
555	#440	C₂²×C₃₁	1	2	yes	—
556	#440	C₂²×C₃₁	1	2	yes	—
557	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
558	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
559	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
560	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
561	#433	C₂²×C₃₁	1	2	yes	—
562	#433	C₂²×C₃₁	1	1	yes	characteristic
563	#433	C₂²×C₃₁	1	1	yes	characteristic
564	#432	C₂²×C₃₁	1	2	yes	—
565	C₂×C₃₁	—	4	1	no	—
566	C₂×C₃₁	—	8	1	no	—
567	C₂×C₃₁	—	8	2	no	—
568	C₂×C₃₁	#3487	1	1	yes	characteristic
569	C₂×C₃₁	#3586	1	2	yes	—
570	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
571	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
572	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
573	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
574	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
575	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
576	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
577	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
578	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
579	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
580	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
581	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
582	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
583	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
584	C₂×D₈	C₂³×C₃₁	1	2	yes	—
585	C₄⋊Q₈	—	2	2	no	—
586	C₄⋊Q₈	—	2	1	no	—
587	C₄⋊Q₈	—	2	1	no	—
588	C₄⋊Q₈	D₄×C₃₁	1	2	yes	—
589	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
590	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
591	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
592	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
593	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
594	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
595	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
596	#127	C₂³×C₃₁	1	1	yes	characteristic
597	#126	—	2	2	no	—
598	#126	—	2	2	no	—
599	#126	—	2	2	no	—
600	#126	—	2	2	no	—
601	#126	—	2	2	no	—
602	#126	—	2	2	no	—
603	#126	—	2	2	no	—
604	#126	—	2	2	no	—
605	#126	—	2	2	no	—
606	#125	—	2	2	no	—
607	#125	—	2	2	no	—
608	#125	—	2	2	no	—
609	#125	—	2	2	no	—
610	#125	—	2	2	no	—
611	#125	—	2	2	no	—
612	#125	—	2	2	no	—
613	#125	—	2	2	no	—
614	#125	—	2	2	no	—
615	#125	D₄×C₃₁	1	2	yes	—
616	#125	C₂³×C₃₁	1	2	yes	—
617	#125	C₂³×C₃₁	1	1	yes	characteristic
618	#125	C₂³×C₃₁	1	1	yes	characteristic
619	#124	—	2	2	no	—
620	#124	—	2	2	no	—
621	#124	C₂³×C₃₁	1	2	yes	—
622	#124	C₂³×C₃₁	1	1	yes	characteristic
623	#124	C₂³×C₃₁	1	2	yes	—
624	#124	C₂³×C₃₁	1	1	yes	characteristic
625	#124	C₂³×C₃₁	1	2	yes	—
626	#123	—	2	2	no	—
627	#123	—	2	2	no	—
628	#123	—	2	2	no	—
629	#123	—	2	2	no	—
630	#123	—	2	2	no	—
631	#123	—	2	1	no	—
632	#123	—	2	1	no	—
633	#123	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	—	2	2	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
644	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
645	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
646	#121	—	2	2	no	—
647	#121	C₂³×C₃₁	1	2	yes	—
648	C₄×Q₈	—	2	2	no	—
649	C₄×Q₈	—	2	2	no	—
650	C₄×Q₈	—	2	2	no	—
651	C₄×Q₈	—	2	2	no	—
652	C₄×Q₈	—	2	2	no	—
653	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
654	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
655	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
656	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
657	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
658	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
659	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
660	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
661	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
662	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
663	C₄×D₄	—	2	2	no	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	C₂³×C₃₁	1	2	yes	—
667	C₄×D₄	C₂³×C₃₁	1	2	yes	—
668	C₄×D₄	C₂³×C₃₁	1	2	yes	—
669	C₄×D₄	C₂³×C₃₁	1	2	yes	—
670	#117	—	2	2	no	—
671	#117	—	2	2	no	—
672	#117	—	2	2	no	—
673	#117	—	2	2	no	—
674	#117	—	2	1	no	—
675	#117	—	2	1	no	—
676	#117	—	2	1	no	—
677	#117	—	2	2	no	—
678	#117	C₂³×C₃₁	1	1	yes	characteristic
679	#117	C₂³×C₃₁	1	1	yes	characteristic
680	#117	C₂³×C₃₁	1	1	yes	characteristic
681	C₂×C₄⋊C₄	—	2	2	no	—
682	C₂×C₄⋊C₄	—	2	2	no	—
683	C₂×C₄²	—	2	1	no	—
684	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
685	#107	C₂³×C₃₁	1	2	yes	—
686	#107	C₂³×C₃₁	1	2	yes	—
687	#106	C₂³×C₃₁	1	2	yes	—
688	#106	C₂³×C₃₁	1	2	yes	—
689	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
690	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
691	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
692	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
693	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
694	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
695	#103	C₂³×C₃₁	1	2	yes	—
696	#103	C₂³×C₃₁	1	2	yes	—
697	#103	C₂³×C₃₁	1	2	yes	—
698	#103	C₂³×C₃₁	1	2	yes	—
699	#103	C₂³×C₃₁	1	2	yes	—
700	#103	C₂³×C₃₁	1	2	yes	—
701	#103	C₂³×C₃₁	1	2	yes	—
702	#103	C₂³×C₃₁	1	2	yes	—
703	#103	C₂³×C₃₁	1	2	yes	—
704	#103	C₂³×C₃₁	1	2	yes	—
705	#103	C₂³×C₃₁	1	2	yes	—
706	#103	C₂³×C₃₁	1	2	yes	—
707	#102	C₂³×C₃₁	1	2	yes	—
708	#102	C₂³×C₃₁	1	2	yes	—
709	#102	C₂³×C₃₁	1	2	yes	—
710	#102	C₂³×C₃₁	1	2	yes	—
711	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
712	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
713	#97	C₂³×C₃₁	1	2	yes	—
714	#97	C₂³×C₃₁	1	2	yes	—
715	#97	C₂³×C₃₁	1	1	yes	characteristic
716	#97	C₂³×C₃₁	1	2	yes	—
717	#97	C₂³×C₃₁	1	1	yes	characteristic
718	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
719	C₄×C₈	C₂³×C₃₁	1	2	yes	—
720	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
721	C₃₁	#61946	1	1	yes	characteristic, direct product factor, Sylow
722	#41	—	4	2	no	—
723	C₂×Q₈	—	2	1	no	—
724	C₂×Q₈	—	2	1	no	—
725	C₂×Q₈	—	2	2	no	—
726	C₂×Q₈	—	4	2	no	—
727	C₂×Q₈	—	4	2	no	—
728	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
729	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
730	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
731	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
732	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
733	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
734	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
735	C₂×D₄	—	2	1	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
739	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
740	C₂²×C₄	—	2	1	no	—
741	C₂²×C₄	—	2	1	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	1	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
749	Q₁₆	—	4	2	no	—
750	Q₁₆	—	4	2	no	—
751	Q₁₆	—	4	2	no	—
752	Q₁₆	—	4	2	no	—
753	Q₁₆	—	4	2	no	—
754	SD₁₆	—	4	2	no	—
755	SD₁₆	—	4	2	no	—
756	SD₁₆	—	4	2	no	—
757	SD₁₆	—	4	2	no	—
758	SD₁₆	—	4	2	no	—
759	SD₁₆	—	4	2	no	—
760	D₈	—	4	2	no	—
761	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
762	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
763	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
764	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
789	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
790	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
791	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
792	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
793	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
794	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
795	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
796	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
797	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
798	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
799	C₂²⋊C₄	—	2	1	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
815	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
816	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
817	C₄²	—	2	1	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	2	no	—
826	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
827	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
828	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
829	C₄²	C₂⁴×C₃₁	1	2	yes	—
830	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
831	C₄²	C₂⁴×C₃₁	1	2	yes	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	2	no	—
834	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
835	Q₈	—	2	2	no	—
836	Q₈	—	2	2	no	—
837	Q₈	—	2	2	no	—
838	Q₈	—	2	2	no	—
839	Q₈	—	2	2	no	—
840	Q₈	—	2	2	no	—
841	Q₈	—	2	2	no	—
842	Q₈	—	4	2	no	—
843	Q₈	—	4	2	no	—
844	Q₈	—	4	2	no	—
845	Q₈	—	4	2	no	—
846	Q₈	—	8	2	no	—
847	D₄	—	2	2	no	—
848	D₄	—	2	2	no	—
849	D₄	—	2	2	no	—
850	D₄	—	4	2	no	—
851	D₄	—	8	2	no	—
852	D₄	—	8	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	4	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	—	4	2	no	—
867	C₂×C₄	—	8	2	no	—
868	C₂×C₄	—	8	2	no	—
869	C₂×C₄	—	8	2	no	—
870	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
872	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
873	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
874	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
875	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
876	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
877	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
878	C₈	—	2	2	no	—
879	C₈	—	2	2	no	—
880	C₈	—	2	2	no	—
881	C₈	—	2	2	no	—
882	C₂²	—	2	1	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
890	C₄	—	2	1	no	—
891	C₄	—	2	2	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	2	no	—
905	C₄	C₃₁×#585	1	2	yes	—
906	C₂	—	4	1	no	—
907	C₂	—	8	1	no	—
908	C₂	—	8	2	no	—
909	C₂	C₃₁×#3487	1	1	yes	characteristic
910	C₂	C₃₁×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3221	C₂
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×#3509	C₂	semidirect
3. C₃₁×#3402	C₂	semidirect
4. C₃₁×#3401	C₂	semidirect
5. C₃₁×#3400	C₂	semidirect
6. C₃₁×#3398	C₂	semidirect
7. C₃₁×#3377	C₂	semidirect
8. C₃₁×#3376	C₂	semidirect
9. C₃₁×#3374	C₂	semidirect
10. C₃₁×#3372	C₂	semidirect
11. C₃₁×#3225	C₂	semidirect
12. C₃₁×#3223	C₂	semidirect
14. C₃₁×#3218	C₂	semidirect
15. C₃₁×#3127	C₂	semidirect
16. C₃₁×#3126	C₂	semidirect
17. C₃₁×#3121	C₂	semidirect
18. C₃₁×#3111	C₂	semidirect
19. C₃₁×#2987	C₂	semidirect
376. #61946	C₃₁	direct (N × H)
427. #3557	C₂×C₃₁	semidirect
428. #3509	C₂×C₃₁	semidirect
429. #3402	C₂×C₃₁	semidirect
430. #3401	C₂×C₃₁	semidirect
431. #3400	C₂×C₃₁	semidirect
432. #3398	C₂×C₃₁	semidirect
433. #3377	C₂×C₃₁	semidirect
434. #3376	C₂×C₃₁	semidirect
435. #3374	C₂×C₃₁	semidirect
436. #3372	C₂×C₃₁	semidirect
437. #3225	C₂×C₃₁	semidirect
438. #3223	C₂×C₃₁	semidirect
440. #3218	C₂×C₃₁	semidirect
441. #3127	C₂×C₃₁	semidirect
442. #3126	C₂×C₃₁	semidirect
443. #3121	C₂×C₃₁	semidirect
444. #3111	C₂×C₃₁	semidirect
445. #2987	C₂×C₃₁	semidirect
721. C₃₁	#61946	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×#3509	2
C₃₁×#3402	2
C₃₁×#3401	2
C₃₁×#3400	2
C₃₁×#3398	2
C₃₁×#3377	2
C₃₁×#3376	2
C₃₁×#3374	2
C₃₁×#3372	2
C₃₁×#3225	2
C₃₁×#3223	2
C₃₁×#3221	2
C₃₁×#3218	2
C₃₁×#3127	2
C₃₁×#3126	2
C₃₁×#3121	2
C₃₁×#3111	2
C₃₁×#2987	2
#61946	31

Subgroups — C31×#61946 #21518705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61946 #21518705