Subgroups — C₃₁×#61010 #21517769

Order 7936.

1700 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3258	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3257	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3233	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3232	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3212	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3211	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3201	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3198	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3183	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3168	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3127	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3126	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3125	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3124	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3123	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3122	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#559	—	2	2	no	—
21	C₃₁×#556	—	2	2	no	—
22	C₃₁×#553	—	2	2	no	—
23	C₃₁×#553	—	2	2	no	—
24	C₃₁×#553	—	2	2	no	—
25	C₃₁×#552	—	2	2	no	—
26	C₃₁×#551	—	2	2	no	—
27	C₃₁×#551	—	2	2	no	—
28	C₃₁×#542	C₂²	1	2	yes	—
29	C₃₁×#542	C₂²	1	2	yes	—
30	C₃₁×#541	C₂²	1	1	yes	characteristic
31	C₃₁×#541	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#540	C₂²	1	1	yes	characteristic
33	C₃₁×#540	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#537	C₂²	1	2	yes	—
35	C₃₁×#536	C₂²	1	1	yes	characteristic
36	C₃₁×#535	C₂²	1	1	yes	characteristic
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#529	C₂²	1	2	yes	—
40	C₃₁×#529	C₂²	1	2	yes	—
41	C₃₁×#529	C₂²	1	2	yes	—
42	C₃₁×#529	C₂²	1	2	yes	complemented
43	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
45	C₃₁×#520	C₂²	1	2	yes	complemented
46	C₃₁×#519	C₂²	1	1	yes	characteristic
47	C₃₁×#518	C₂²	1	1	yes	characteristic
48	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
49	C₃₁×#499	C₂²	1	2	yes	complemented
50	C₃₁×#499	C₂²	1	2	yes	complemented
51	C₃₁×#495	C₂²	1	2	yes	—
52	C₃₁×#495	C₂²	1	2	yes	—
53	C₃₁×#488	C₂²	1	2	yes	—
54	C₃₁×#488	C₂²	1	2	yes	—
55	C₃₁×#488	C₂²	1	2	yes	complemented
56	C₃₁×#488	C₂²	1	2	yes	complemented
57	C₃₁×#485	C₂²	1	2	yes	—
58	C₃₁×#485	C₂²	1	2	yes	—
59	C₃₁×#484	C₂²	1	2	yes	complemented
60	C₃₁×#483	C₂²	1	2	yes	complemented
61	C₃₁×#482	C₂²	1	2	yes	—
62	C₃₁×#482	C₂²	1	2	yes	—
63	C₃₁×#481	C₂²	1	2	yes	—
64	C₃₁×#480	C₂²	1	2	yes	—
65	C₃₁×#479	C₂²	1	2	yes	complemented
66	C₃₁×#479	C₂²	1	2	yes	complemented
67	C₃₁×#478	C₂²	1	2	yes	—
68	C₃₁×#478	C₂²	1	2	yes	—
69	C₃₁×#477	C₂²	1	2	yes	complemented
70	C₃₁×#476	C₂²	1	2	yes	complemented
71	C₃₁×#475	C₂²	1	2	yes	complemented
72	C₃₁×#474	C₂²	1	2	yes	complemented
73	C₃₁×#470	C₂²	1	2	yes	complemented
74	C₃₁×#469	C₂²	1	2	yes	—
75	C₃₁×#468	C₂²	1	2	yes	—
76	C₃₁×#468	C₂²	1	2	yes	complemented
77	C₃₁×#467	C₂²	1	2	yes	complemented
78	C₃₁×#466	C₂²	1	2	yes	—
79	C₃₁×#465	C₂²	1	2	yes	—
80	C₃₁×#465	C₂²	1	2	yes	complemented
81	C₃₁×#464	C₂²	1	2	yes	—
82	C₃₁×#464	C₂²	1	2	yes	—
83	C₃₁×#463	C₂²	1	2	yes	—
84	C₃₁×#463	C₂²	1	2	yes	—
85	C₃₁×#462	C₂²	1	2	yes	complemented
86	C₃₁×#461	C₂²	1	2	yes	—
87	C₃₁×#460	C₂²	1	2	yes	complemented
88	C₃₁×#459	C₂²	1	2	yes	—
89	C₃₁×#452	C₂²	1	2	yes	complemented
90	C₃₁×#452	C₂²	1	2	yes	complemented
91	C₃₁×#451	C₂²	1	2	yes	—
92	C₃₁×#450	C₂²	1	2	yes	—
93	C₃₁×#449	C₂²	1	2	yes	—
94	C₃₁×#449	C₂²	1	2	yes	—
95	C₃₁×#448	C₂²	1	2	yes	—
96	C₃₁×#447	C₂²	1	2	yes	—
97	C₃₁×#442	C₂²	1	2	yes	—
98	C₃₁×#441	C₂²	1	2	yes	complemented
99	C₃₁×#440	C₂²	1	2	yes	—
100	C₃₁×#440	C₂²	1	2	yes	complemented
101	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
103	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
104	C₄×D₈×C₃₁	C₂²	1	2	yes	—
105	C₃₁×#433	C₂²	1	1	yes	characteristic
106	C₃₁×#433	C₂²	1	1	yes	characteristic
107	C₃₁×#433	C₂²	1	1	yes	characteristic, complemented
108	C₃₁×#433	C₂²	1	1	yes	characteristic, complemented
109	C₃₁×#431	C₂²	1	2	yes	—
110	C₃₁×#431	C₂²	1	2	yes	complemented
111	C₃₁×#424	C₂²	1	2	yes	complemented
112	C₃₁×#408	C₂²	1	2	yes	—
113	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₃₁	C₂³	1	2	yes	—
116	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
117	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
118	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
119	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
120	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
121	C₂×SD₁₆×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×D₈×C₃₁	C₂³	1	2	yes	—
126	C₂×D₈×C₃₁	C₂³	1	2	yes	—
127	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
128	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
129	C₃₁×C₄⋊Q₈	—	2	1	no	—
130	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
131	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
132	C₃₁×#127	—	2	1	no	—
133	C₃₁×#127	C₂³	1	1	yes	characteristic
134	C₃₁×#126	—	2	2	no	—
135	C₃₁×#126	—	2	2	no	—
136	C₃₁×#126	—	2	2	no	—
137	C₃₁×#126	—	2	2	no	—
138	C₃₁×#126	—	2	2	no	—
139	C₃₁×#126	—	2	2	no	—
140	C₃₁×#126	—	2	2	no	—
141	C₃₁×#126	—	2	2	no	—
142	C₃₁×#125	—	2	2	no	—
143	C₃₁×#125	—	2	2	no	—
144	C₃₁×#125	—	2	2	no	—
145	C₃₁×#125	C₂³	1	1	yes	characteristic
146	C₃₁×#125	C₂³	1	1	yes	characteristic
147	C₃₁×#125	C₂³	1	2	yes	—
148	C₃₁×#125	C₂³	1	2	yes	—
149	C₃₁×#124	—	2	1	no	—
150	C₃₁×#124	—	2	1	no	—
151	C₃₁×#124	—	2	2	no	—
152	C₃₁×#124	—	2	2	no	—
153	C₃₁×#124	—	2	2	no	—
154	C₃₁×#124	C₂³	1	2	yes	—
155	C₃₁×#124	C₂³	1	2	yes	—
156	C₃₁×#124	C₂³	1	2	yes	—
157	C₃₁×#123	—	2	1	no	—
158	C₃₁×#123	—	2	1	no	—
159	C₃₁×#123	—	2	2	no	—
160	C₃₁×#123	—	2	2	no	—
161	C₃₁×#123	—	2	2	no	—
162	C₃₁×#123	—	2	2	no	—
163	C₃₁×#123	—	2	2	no	—
164	C₃₁×#123	—	2	2	no	—
165	C₃₁×#123	—	2	2	no	—
166	C₃₁×#123	—	2	2	no	—
167	C₃₁×C₂²⋊Q₈	—	2	2	no	—
168	C₃₁×C₂²⋊Q₈	—	2	2	no	—
169	C₃₁×C₂²⋊Q₈	—	2	2	no	—
170	C₃₁×C₂²⋊Q₈	—	2	2	no	—
171	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
172	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
173	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
174	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
175	C₃₁×#121	—	2	2	no	—
176	C₃₁×#121	—	2	2	no	—
177	C₃₁×#121	—	2	2	no	—
178	C₃₁×#121	—	2	2	no	—
179	C₃₁×#121	—	2	2	no	—
180	C₃₁×#121	—	2	2	no	—
181	C₃₁×#121	C₂³	1	2	yes	—
182	C₃₁×#121	C₂³	1	2	yes	—
183	C₃₁×#121	C₂³	1	2	yes	—
184	C₃₁×#121	C₂³	1	2	yes	—
185	C₃₁×#120	—	2	1	no	—
186	C₃₁×#120	—	2	1	no	—
187	C₄×Q₈×C₃₁	—	2	2	no	—
188	C₄×Q₈×C₃₁	—	2	2	no	—
189	C₄×Q₈×C₃₁	D₄	1	2	yes	—
190	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
191	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
192	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
193	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
194	C₄×D₄×C₃₁	—	2	2	no	—
195	C₄×D₄×C₃₁	—	2	2	no	—
196	C₄×D₄×C₃₁	—	2	2	no	—
197	C₄×D₄×C₃₁	—	2	2	no	—
198	C₄×D₄×C₃₁	—	2	2	no	—
199	C₄×D₄×C₃₁	—	2	2	no	—
200	C₄×D₄×C₃₁	—	2	2	no	—
201	C₄×D₄×C₃₁	—	2	2	no	—
202	C₄×D₄×C₃₁	D₄	1	2	yes	—
203	C₄×D₄×C₃₁	D₄	1	2	yes	—
204	C₄×D₄×C₃₁	D₄	1	2	yes	—
205	C₄×D₄×C₃₁	C₂³	1	2	yes	—
206	C₄×D₄×C₃₁	C₂³	1	2	yes	—
207	C₄×D₄×C₃₁	C₂³	1	2	yes	—
208	C₄×D₄×C₃₁	C₂³	1	2	yes	—
209	C₃₁×#117	—	2	2	no	—
210	C₃₁×#117	—	2	2	no	—
211	C₃₁×#117	—	2	2	no	—
212	C₃₁×#117	—	2	2	no	—
213	C₃₁×#117	—	2	2	no	—
214	C₃₁×#117	—	2	2	no	—
215	C₃₁×#117	C₂³	1	1	yes	characteristic
216	C₃₁×#117	C₂³	1	1	yes	characteristic
217	C₃₁×#117	C₂³	1	1	yes	characteristic
218	C₃₁×#117	C₂³	1	1	yes	characteristic
219	C₃₁×#117	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
221	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
222	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
224	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
225	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
228	C₃₁×#107	C₂³	1	2	yes	—
229	C₃₁×#107	C₂³	1	2	yes	—
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×#106	C₂³	1	2	yes	—
235	C₃₁×#106	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×#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×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
260	C₃₁×#97	C₂³	1	1	yes	characteristic
261	C₃₁×#97	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₃₁	C₂³	1	2	yes	—
263	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₃₁	C₂³	1	2	yes	—
266	C₂⁴×C₃₁	—	2	1	no	—
267	#41×C₃₁	—	4	2	no	—
268	#41×C₃₁	—	4	2	no	—
269	#41×C₃₁	—	4	2	no	—
270	C₂×Q₈×C₃₁	—	2	1	no	—
271	C₂×Q₈×C₃₁	—	2	2	no	—
272	C₂×Q₈×C₃₁	—	4	2	no	—
273	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
274	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
275	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
276	C₂×D₄×C₃₁	—	2	2	no	—
277	C₂×D₄×C₃₁	—	2	2	no	—
278	C₂×D₄×C₃₁	—	2	2	no	—
279	C₂×D₄×C₃₁	—	2	2	no	—
280	C₂×D₄×C₃₁	—	2	2	no	—
281	C₂×D₄×C₃₁	—	2	1	no	—
282	C₂×D₄×C₃₁	—	2	2	no	—
283	C₂×D₄×C₃₁	—	4	2	no	—
284	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
285	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
286	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
287	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
288	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₃₁	—	2	1	no	—
290	C₂²×C₄×C₃₁	—	2	2	no	—
291	C₂²×C₄×C₃₁	—	2	2	no	—
292	C₂²×C₄×C₃₁	—	2	2	no	—
293	C₂²×C₄×C₃₁	—	2	2	no	—
294	C₂²×C₄×C₃₁	—	2	2	no	—
295	C₂²×C₄×C₃₁	—	2	2	no	—
296	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
297	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
298	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
299	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
302	Q₁₆×C₃₁	—	4	2	no	—
303	Q₁₆×C₃₁	—	4	2	no	—
304	SD₁₆×C₃₁	—	4	2	no	—
305	SD₁₆×C₃₁	—	4	2	no	—
306	SD₁₆×C₃₁	—	4	2	no	—
307	SD₁₆×C₃₁	—	4	2	no	—
308	D₈×C₃₁	—	4	2	no	—
309	D₈×C₃₁	—	4	2	no	—
310	M₁₆×C₃₁	—	4	2	no	—
311	C₂×C₈×C₃₁	—	4	2	no	—
312	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
313	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
314	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
315	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	—	2	2	no	—
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	C₂⁴	1	2	yes	—
337	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
339	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
340	C₂²⋊C₄×C₃₁	—	2	1	no	—
341	C₂²⋊C₄×C₃₁	—	2	1	no	—
342	C₂²⋊C₄×C₃₁	—	2	2	no	—
343	C₂²⋊C₄×C₃₁	—	2	2	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	—	2	2	no	—
359	C₂²⋊C₄×C₃₁	—	2	2	no	—
360	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
361	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
362	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	1	no	—
368	C₄²×C₃₁	—	2	1	no	—
369	C₄²×C₃₁	C₂×D₄	1	2	yes	—
370	C₄²×C₃₁	C₂×D₄	1	2	yes	—
371	C₄²×C₃₁	C₂×D₄	1	2	yes	—
372	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
375	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
376	#61010	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
377	C₂³×C₃₁	—	2	2	no	—
378	C₂³×C₃₁	—	2	2	no	—
379	C₂³×C₃₁	—	4	2	no	—
380	C₂³×C₃₁	—	8	2	no	—
381	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
382	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
383	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
384	Q₈×C₃₁	—	2	2	no	—
385	Q₈×C₃₁	—	2	2	no	—
386	Q₈×C₃₁	—	2	2	no	—
387	Q₈×C₃₁	—	2	2	no	—
388	Q₈×C₃₁	—	4	1	no	—
389	Q₈×C₃₁	—	4	2	no	—
390	Q₈×C₃₁	—	8	2	no	—
391	D₄×C₃₁	—	2	2	no	—
392	D₄×C₃₁	—	2	2	no	—
393	D₄×C₃₁	—	2	2	no	—
394	D₄×C₃₁	—	2	2	no	—
395	D₄×C₃₁	—	4	1	no	—
396	D₄×C₃₁	—	4	1	no	—
397	D₄×C₃₁	—	4	1	no	—
398	D₄×C₃₁	—	4	2	no	—
399	D₄×C₃₁	—	4	4	no	—
400	D₄×C₃₁	—	8	2	no	—
401	D₄×C₃₁	—	8	2	no	—
402	D₄×C₃₁	—	8	2	no	—
403	D₄×C₃₁	—	8	2	no	—
404	D₄×C₃₁	—	8	2	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	2	2	no	—
407	C₂×C₄×C₃₁	—	2	2	no	—
408	C₂×C₄×C₃₁	—	2	2	no	—
409	C₂×C₄×C₃₁	—	2	2	no	—
410	C₂×C₄×C₃₁	—	2	2	no	—
411	C₂×C₄×C₃₁	—	2	2	no	—
412	C₂×C₄×C₃₁	—	2	2	no	—
413	C₂×C₄×C₃₁	—	2	2	no	—
414	C₂×C₄×C₃₁	—	4	2	no	—
415	C₂×C₄×C₃₁	—	4	2	no	—
416	C₂×C₄×C₃₁	—	4	2	no	—
417	C₂×C₄×C₃₁	—	4	4	no	—
418	C₂×C₄×C₃₁	—	4	2	no	—
419	C₂×C₄×C₃₁	—	8	2	no	—
420	C₂×C₄×C₃₁	—	8	2	no	—
421	C₂×C₄×C₃₁	—	8	2	no	—
422	C₂×C₄×C₃₁	—	8	2	no	—
423	C₂×C₄×C₃₁	—	8	2	no	—
424	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
426	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
427	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
428	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
429	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
432	C₈×C₃₁	—	2	2	no	—
433	C₈×C₃₁	—	2	2	no	—
434	C₈×C₃₁	—	2	2	no	—
435	C₈×C₃₁	—	2	2	no	—
436	#3512	C₂×C₃₁	1	1	yes	characteristic, complemented
437	#3510	C₂×C₃₁	1	1	yes	characteristic, complemented
438	#3258	C₂×C₃₁	1	2	yes	complemented
439	#3257	C₂×C₃₁	1	2	yes	complemented
440	#3233	C₂×C₃₁	1	2	yes	complemented
441	#3232	C₂×C₃₁	1	2	yes	complemented
442	#3212	C₂×C₃₁	1	2	yes	complemented
443	#3211	C₂×C₃₁	1	2	yes	complemented
444	#3201	C₂×C₃₁	1	2	yes	complemented
445	#3198	C₂×C₃₁	1	2	yes	complemented
446	#3183	C₂×C₃₁	1	2	yes	complemented
447	#3168	C₂×C₃₁	1	2	yes	complemented
448	#3127	C₂×C₃₁	1	1	yes	characteristic, complemented
449	#3126	C₂×C₃₁	1	1	yes	characteristic, complemented
450	#3125	C₂×C₃₁	1	2	yes	complemented
451	#3124	C₂×C₃₁	1	2	yes	complemented
452	#3123	C₂×C₃₁	1	1	yes	characteristic, complemented
453	#3122	C₂×C₃₁	1	1	yes	characteristic, complemented
454	#2922	C₂×C₃₁	1	1	yes	characteristic, complemented
455	C₂²×C₃₁	—	2	2	no	—
456	C₂²×C₃₁	—	2	2	no	—
457	C₂²×C₃₁	—	2	2	no	—
458	C₂²×C₃₁	—	2	1	no	—
459	C₂²×C₃₁	—	2	1	no	—
460	C₂²×C₃₁	—	2	1	no	—
461	C₂²×C₃₁	—	4	2	no	—
462	C₂²×C₃₁	—	4	2	no	—
463	C₂²×C₃₁	—	4	2	no	—
464	C₂²×C₃₁	—	4	2	no	—
465	C₂²×C₃₁	—	4	2	no	—
466	C₂²×C₃₁	—	4	2	no	—
467	C₂²×C₃₁	—	16	2	no	—
468	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
469	C₄×C₃₁	—	2	2	no	—
470	C₄×C₃₁	—	2	2	no	—
471	C₄×C₃₁	—	2	2	no	—
472	C₄×C₃₁	—	2	2	no	—
473	C₄×C₃₁	—	2	1	no	—
474	C₄×C₃₁	—	2	1	no	—
475	C₄×C₃₁	—	2	1	no	—
476	C₄×C₃₁	—	4	2	no	—
477	C₄×C₃₁	—	4	2	no	—
478	C₄×C₃₁	—	4	2	no	—
479	C₄×C₃₁	—	4	2	no	—
480	C₄×C₃₁	—	4	2	no	—
481	C₄×C₃₁	—	4	2	no	—
482	C₄×C₃₁	#585	1	2	yes	—
483	#559	—	2	2	no	—
484	#556	—	2	2	no	—
485	#553	—	2	2	no	—
486	#553	—	2	2	no	—
487	#553	—	2	2	no	—
488	#552	—	2	2	no	—
489	#551	—	2	2	no	—
490	#551	—	2	2	no	—
491	#542	C₂²×C₃₁	1	2	yes	—
492	#542	C₂²×C₃₁	1	2	yes	—
493	#541	C₂²×C₃₁	1	1	yes	characteristic
494	#541	C₂²×C₃₁	1	1	yes	characteristic, complemented
495	#540	C₂²×C₃₁	1	1	yes	characteristic
496	#540	C₂²×C₃₁	1	1	yes	characteristic, complemented
497	#537	C₂²×C₃₁	1	2	yes	—
498	#536	C₂²×C₃₁	1	1	yes	characteristic
499	#535	C₂²×C₃₁	1	1	yes	characteristic
500	#533	C₂²×C₃₁	1	1	yes	characteristic
501	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
502	#529	C₂²×C₃₁	1	2	yes	—
503	#529	C₂²×C₃₁	1	2	yes	—
504	#529	C₂²×C₃₁	1	2	yes	—
505	#529	C₂²×C₃₁	1	2	yes	complemented
506	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
507	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
508	#520	C₂²×C₃₁	1	2	yes	complemented
509	#519	C₂²×C₃₁	1	1	yes	characteristic
510	#518	C₂²×C₃₁	1	1	yes	characteristic
511	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
512	#499	C₂²×C₃₁	1	2	yes	complemented
513	#499	C₂²×C₃₁	1	2	yes	complemented
514	#495	C₂²×C₃₁	1	2	yes	—
515	#495	C₂²×C₃₁	1	2	yes	—
516	#488	C₂²×C₃₁	1	2	yes	—
517	#488	C₂²×C₃₁	1	2	yes	—
518	#488	C₂²×C₃₁	1	2	yes	complemented
519	#488	C₂²×C₃₁	1	2	yes	complemented
520	#485	C₂²×C₃₁	1	2	yes	—
521	#485	C₂²×C₃₁	1	2	yes	—
522	#484	C₂²×C₃₁	1	2	yes	complemented
523	#483	C₂²×C₃₁	1	2	yes	complemented
524	#482	C₂²×C₃₁	1	2	yes	—
525	#482	C₂²×C₃₁	1	2	yes	—
526	#481	C₂²×C₃₁	1	2	yes	—
527	#480	C₂²×C₃₁	1	2	yes	—
528	#479	C₂²×C₃₁	1	2	yes	complemented
529	#479	C₂²×C₃₁	1	2	yes	complemented
530	#478	C₂²×C₃₁	1	2	yes	—
531	#478	C₂²×C₃₁	1	2	yes	—
532	#477	C₂²×C₃₁	1	2	yes	complemented
533	#476	C₂²×C₃₁	1	2	yes	complemented
534	#475	C₂²×C₃₁	1	2	yes	complemented
535	#474	C₂²×C₃₁	1	2	yes	complemented
536	#470	C₂²×C₃₁	1	2	yes	complemented
537	#469	C₂²×C₃₁	1	2	yes	—
538	#468	C₂²×C₃₁	1	2	yes	—
539	#468	C₂²×C₃₁	1	2	yes	complemented
540	#467	C₂²×C₃₁	1	2	yes	complemented
541	#466	C₂²×C₃₁	1	2	yes	—
542	#465	C₂²×C₃₁	1	2	yes	—
543	#465	C₂²×C₃₁	1	2	yes	complemented
544	#464	C₂²×C₃₁	1	2	yes	—
545	#464	C₂²×C₃₁	1	2	yes	—
546	#463	C₂²×C₃₁	1	2	yes	—
547	#463	C₂²×C₃₁	1	2	yes	—
548	#462	C₂²×C₃₁	1	2	yes	complemented
549	#461	C₂²×C₃₁	1	2	yes	—
550	#460	C₂²×C₃₁	1	2	yes	complemented
551	#459	C₂²×C₃₁	1	2	yes	—
552	#452	C₂²×C₃₁	1	2	yes	complemented
553	#452	C₂²×C₃₁	1	2	yes	complemented
554	#451	C₂²×C₃₁	1	2	yes	—
555	#450	C₂²×C₃₁	1	2	yes	—
556	#449	C₂²×C₃₁	1	2	yes	—
557	#449	C₂²×C₃₁	1	2	yes	—
558	#448	C₂²×C₃₁	1	2	yes	—
559	#447	C₂²×C₃₁	1	2	yes	—
560	#442	C₂²×C₃₁	1	2	yes	—
561	#441	C₂²×C₃₁	1	2	yes	complemented
562	#440	C₂²×C₃₁	1	2	yes	—
563	#440	C₂²×C₃₁	1	2	yes	complemented
564	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
565	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
566	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
567	C₄×D₈	C₂²×C₃₁	1	2	yes	—
568	#433	C₂²×C₃₁	1	1	yes	characteristic
569	#433	C₂²×C₃₁	1	1	yes	characteristic
570	#433	C₂²×C₃₁	1	1	yes	characteristic, complemented
571	#433	C₂²×C₃₁	1	1	yes	characteristic, complemented
572	#431	C₂²×C₃₁	1	2	yes	—
573	#431	C₂²×C₃₁	1	2	yes	complemented
574	#424	C₂²×C₃₁	1	2	yes	complemented
575	#408	C₂²×C₃₁	1	2	yes	—
576	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
577	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
578	C₂×C₃₁	—	4	1	no	—
579	C₂×C₃₁	—	4	1	no	—
580	C₂×C₃₁	—	4	1	no	—
581	C₂×C₃₁	—	8	2	no	—
582	C₂×C₃₁	—	8	2	no	—
583	C₂×C₃₁	#3449	1	1	yes	characteristic
584	C₂×C₃₁	#3584	1	2	yes	—
585	C₂×#41	C₂³×C₃₁	1	2	yes	—
586	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
587	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
588	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
589	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
590	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
591	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
592	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
593	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
594	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
595	C₂×D₈	C₂³×C₃₁	1	2	yes	—
596	C₂×D₈	C₂³×C₃₁	1	2	yes	—
597	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
598	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
599	C₄⋊Q₈	—	2	1	no	—
600	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
601	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
602	#127	—	2	1	no	—
603	#127	C₂³×C₃₁	1	1	yes	characteristic
604	#126	—	2	2	no	—
605	#126	—	2	2	no	—
606	#126	—	2	2	no	—
607	#126	—	2	2	no	—
608	#126	—	2	2	no	—
609	#126	—	2	2	no	—
610	#126	—	2	2	no	—
611	#126	—	2	2	no	—
612	#125	—	2	2	no	—
613	#125	—	2	2	no	—
614	#125	—	2	2	no	—
615	#125	C₂³×C₃₁	1	2	yes	—
616	#125	C₂³×C₃₁	1	1	yes	characteristic
617	#125	C₂³×C₃₁	1	1	yes	characteristic
618	#125	C₂³×C₃₁	1	2	yes	—
619	#124	—	2	1	no	—
620	#124	—	2	1	no	—
621	#124	—	2	2	no	—
622	#124	—	2	2	no	—
623	#124	—	2	2	no	—
624	#124	C₂³×C₃₁	1	2	yes	—
625	#124	C₂³×C₃₁	1	2	yes	—
626	#124	C₂³×C₃₁	1	2	yes	—
627	#123	—	2	1	no	—
628	#123	—	2	1	no	—
629	#123	—	2	2	no	—
630	#123	—	2	2	no	—
631	#123	—	2	2	no	—
632	#123	—	2	2	no	—
633	#123	—	2	2	no	—
634	#123	—	2	2	no	—
635	#123	—	2	2	no	—
636	#123	—	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	C₂³×C₃₁	1	2	yes	—
642	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
643	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
644	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
645	#121	—	2	2	no	—
646	#121	—	2	2	no	—
647	#121	—	2	2	no	—
648	#121	—	2	2	no	—
649	#121	—	2	2	no	—
650	#121	—	2	2	no	—
651	#121	C₂³×C₃₁	1	2	yes	—
652	#121	C₂³×C₃₁	1	2	yes	—
653	#121	C₂³×C₃₁	1	2	yes	—
654	#121	C₂³×C₃₁	1	2	yes	—
655	#120	—	2	1	no	—
656	#120	—	2	1	no	—
657	C₄×Q₈	—	2	2	no	—
658	C₄×Q₈	—	2	2	no	—
659	C₄×Q₈	D₄×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×Q₈	C₂³×C₃₁	1	2	yes	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	D₄×C₃₁	1	2	yes	—
673	C₄×D₄	D₄×C₃₁	1	2	yes	—
674	C₄×D₄	D₄×C₃₁	1	2	yes	—
675	C₄×D₄	C₂³×C₃₁	1	2	yes	—
676	C₄×D₄	C₂³×C₃₁	1	2	yes	—
677	C₄×D₄	C₂³×C₃₁	1	2	yes	—
678	C₄×D₄	C₂³×C₃₁	1	2	yes	—
679	#117	—	2	2	no	—
680	#117	—	2	2	no	—
681	#117	—	2	2	no	—
682	#117	—	2	2	no	—
683	#117	—	2	2	no	—
684	#117	—	2	2	no	—
685	#117	C₂³×C₃₁	1	1	yes	characteristic
686	#117	C₂³×C₃₁	1	1	yes	characteristic
687	#117	C₂³×C₃₁	1	1	yes	characteristic
688	#117	C₂³×C₃₁	1	1	yes	characteristic
689	#117	C₂³×C₃₁	1	1	yes	characteristic
690	C₂×C₄⋊C₄	—	2	2	no	—
691	C₂×C₄⋊C₄	—	2	2	no	—
692	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
693	C₂×C₂²⋊C₄	—	2	2	no	—
694	C₂×C₂²⋊C₄	—	2	2	no	—
695	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
698	#107	C₂³×C₃₁	1	2	yes	—
699	#107	C₂³×C₃₁	1	2	yes	—
700	#107	C₂³×C₃₁	1	2	yes	—
701	#107	C₂³×C₃₁	1	2	yes	—
702	#106	C₂³×C₃₁	1	2	yes	—
703	#106	C₂³×C₃₁	1	2	yes	—
704	#106	C₂³×C₃₁	1	2	yes	—
705	#106	C₂³×C₃₁	1	2	yes	—
706	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
707	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
708	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
709	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
710	#103	C₂³×C₃₁	1	2	yes	—
711	#103	C₂³×C₃₁	1	2	yes	—
712	#103	C₂³×C₃₁	1	2	yes	—
713	#103	C₂³×C₃₁	1	2	yes	—
714	#103	C₂³×C₃₁	1	2	yes	—
715	#103	C₂³×C₃₁	1	2	yes	—
716	#103	C₂³×C₃₁	1	2	yes	—
717	#103	C₂³×C₃₁	1	2	yes	—
718	#102	C₂³×C₃₁	1	2	yes	—
719	#102	C₂³×C₃₁	1	2	yes	—
720	#102	C₂³×C₃₁	1	2	yes	—
721	#102	C₂³×C₃₁	1	2	yes	—
722	#102	C₂³×C₃₁	1	2	yes	—
723	#102	C₂³×C₃₁	1	2	yes	—
724	#102	C₂³×C₃₁	1	2	yes	—
725	#102	C₂³×C₃₁	1	2	yes	—
726	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
727	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
728	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
729	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
730	#97	C₂³×C₃₁	1	1	yes	characteristic
731	#97	C₂³×C₃₁	1	1	yes	characteristic
732	C₄×C₈	C₂³×C₃₁	1	2	yes	—
733	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
734	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
735	C₄×C₈	C₂³×C₃₁	1	2	yes	—
736	C₃₁	#61010	1	1	yes	characteristic, direct product factor, Sylow
737	C₂⁴	—	2	1	no	—
738	#41	—	4	2	no	—
739	#41	—	4	2	no	—
740	#41	—	4	2	no	—
741	C₂×Q₈	—	2	1	no	—
742	C₂×Q₈	—	2	2	no	—
743	C₂×Q₈	—	4	2	no	—
744	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
745	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
746	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	1	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
756	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
757	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
758	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
759	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
768	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
769	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
773	Q₁₆	—	4	2	no	—
774	Q₁₆	—	4	2	no	—
775	SD₁₆	—	4	2	no	—
776	SD₁₆	—	4	2	no	—
777	SD₁₆	—	4	2	no	—
778	SD₁₆	—	4	2	no	—
779	D₈	—	4	2	no	—
780	D₈	—	4	2	no	—
781	M₁₆	—	4	2	no	—
782	C₂×C₈	—	4	2	no	—
783	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
784	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
785	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
786	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
805	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
806	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
807	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
808	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
809	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
810	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
811	C₂²⋊C₄	—	2	1	no	—
812	C₂²⋊C₄	—	2	1	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
832	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
833	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	1	no	—
839	C₄²	—	2	1	no	—
840	C₄²	C₂×D₄×C₃₁	1	2	yes	—
841	C₄²	C₂×D₄×C₃₁	1	2	yes	—
842	C₄²	C₂×D₄×C₃₁	1	2	yes	—
843	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
844	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
845	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
846	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	4	2	no	—
850	C₂³	—	8	2	no	—
851	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
852	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
853	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
854	Q₈	—	2	2	no	—
855	Q₈	—	2	2	no	—
856	Q₈	—	2	2	no	—
857	Q₈	—	2	2	no	—
858	Q₈	—	4	1	no	—
859	Q₈	—	4	2	no	—
860	Q₈	—	8	2	no	—
861	D₄	—	2	2	no	—
862	D₄	—	2	2	no	—
863	D₄	—	2	2	no	—
864	D₄	—	2	2	no	—
865	D₄	—	4	1	no	—
866	D₄	—	4	1	no	—
867	D₄	—	4	1	no	—
868	D₄	—	4	2	no	—
869	D₄	—	4	4	no	—
870	D₄	—	8	2	no	—
871	D₄	—	8	2	no	—
872	D₄	—	8	2	no	—
873	D₄	—	8	2	no	—
874	D₄	—	8	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	4	2	no	—
885	C₂×C₄	—	4	2	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	4	4	no	—
888	C₂×C₄	—	4	2	no	—
889	C₂×C₄	—	8	2	no	—
890	C₂×C₄	—	8	2	no	—
891	C₂×C₄	—	8	2	no	—
892	C₂×C₄	—	8	2	no	—
893	C₂×C₄	—	8	2	no	—
894	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
895	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
896	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
897	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
898	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
899	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
901	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
902	C₈	—	2	2	no	—
903	C₈	—	2	2	no	—
904	C₈	—	2	2	no	—
905	C₈	—	2	2	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	1	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	2	no	—
910	C₂²	—	2	2	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	2	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	16	2	no	—
919	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	2	no	—
924	C₄	—	2	2	no	—
925	C₄	—	2	2	no	—
926	C₄	—	2	2	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	C₃₁×#585	1	2	yes	—
934	C₂	—	4	1	no	—
935	C₂	—	4	1	no	—
936	C₂	—	4	1	no	—
937	C₂	—	8	2	no	—
938	C₂	—	8	2	no	—
939	C₂	C₃₁×#3449	1	1	yes	characteristic
940	C₂	C₃₁×#3584	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3512	C₂	semidirect
2. C₃₁×#3510	C₂	semidirect
3. C₃₁×#3258	C₂	semidirect
4. C₃₁×#3257	C₂	semidirect
5. C₃₁×#3233	C₂	semidirect
6. C₃₁×#3232	C₂	semidirect
7. C₃₁×#3212	C₂	semidirect
8. C₃₁×#3211	C₂	semidirect
9. C₃₁×#3201	C₂	semidirect
10. C₃₁×#3198	C₂	semidirect
11. C₃₁×#3183	C₂	semidirect
12. C₃₁×#3168	C₂	semidirect
13. C₃₁×#3127	C₂	semidirect
14. C₃₁×#3126	C₂	semidirect
15. C₃₁×#3125	C₂	semidirect
16. C₃₁×#3124	C₂	semidirect
17. C₃₁×#3123	C₂	semidirect
18. C₃₁×#3122	C₂	semidirect
19. C₃₁×#2922	C₂	semidirect
31. C₃₁×#541	C₂²	semidirect
33. C₃₁×#540	C₂²	semidirect
38. C₃₁×#532	C₂²	semidirect
42. C₃₁×#529	C₂²	semidirect
43. C₂×C₃₁×#125	C₂²	semidirect
45. C₃₁×#520	C₂²	semidirect
49. C₃₁×#499	C₂²	semidirect
50. C₃₁×#499	C₂²	semidirect
55. C₃₁×#488	C₂²	semidirect
56. C₃₁×#488	C₂²	semidirect
59. C₃₁×#484	C₂²	semidirect
60. C₃₁×#483	C₂²	semidirect
65. C₃₁×#479	C₂²	semidirect
66. C₃₁×#479	C₂²	semidirect
69. C₃₁×#477	C₂²	semidirect
70. C₃₁×#476	C₂²	semidirect
71. C₃₁×#475	C₂²	semidirect
72. C₃₁×#474	C₂²	semidirect
73. C₃₁×#470	C₂²	semidirect
76. C₃₁×#468	C₂²	semidirect
77. C₃₁×#467	C₂²	semidirect
80. C₃₁×#465	C₂²	semidirect
85. C₃₁×#462	C₂²	semidirect
87. C₃₁×#460	C₂²	semidirect
89. C₃₁×#452	C₂²	semidirect
90. C₃₁×#452	C₂²	semidirect
98. C₃₁×#441	C₂²	semidirect
100. C₃₁×#440	C₂²	semidirect
101. C₄×Q₁₆×C₃₁	C₂²	semidirect
103. C₄×SD₁₆×C₃₁	C₂²	semidirect
107. C₃₁×#433	C₂²	semidirect
108. C₃₁×#433	C₂²	semidirect
110. C₃₁×#431	C₂²	semidirect
111. C₃₁×#424	C₂²	semidirect
113. C₄×M₁₆×C₃₁	C₂²	semidirect
114. C₂×C₄×C₈×C₃₁	C₂²	semidirect
376. #61010	C₃₁	direct (N × H)
436. #3512	C₂×C₃₁	semidirect
437. #3510	C₂×C₃₁	semidirect
438. #3258	C₂×C₃₁	semidirect
439. #3257	C₂×C₃₁	semidirect
440. #3233	C₂×C₃₁	semidirect
441. #3232	C₂×C₃₁	semidirect
442. #3212	C₂×C₃₁	semidirect
443. #3211	C₂×C₃₁	semidirect
444. #3201	C₂×C₃₁	semidirect
445. #3198	C₂×C₃₁	semidirect
446. #3183	C₂×C₃₁	semidirect
447. #3168	C₂×C₃₁	semidirect
448. #3127	C₂×C₃₁	semidirect
449. #3126	C₂×C₃₁	semidirect
450. #3125	C₂×C₃₁	semidirect
451. #3124	C₂×C₃₁	semidirect
452. #3123	C₂×C₃₁	semidirect
453. #3122	C₂×C₃₁	semidirect
454. #2922	C₂×C₃₁	semidirect
494. #541	C₂²×C₃₁	semidirect
496. #540	C₂²×C₃₁	semidirect
501. #532	C₂²×C₃₁	semidirect
505. #529	C₂²×C₃₁	semidirect
506. C₂×#125	C₂²×C₃₁	semidirect
508. #520	C₂²×C₃₁	semidirect
512. #499	C₂²×C₃₁	semidirect
513. #499	C₂²×C₃₁	semidirect
518. #488	C₂²×C₃₁	semidirect
519. #488	C₂²×C₃₁	semidirect
522. #484	C₂²×C₃₁	semidirect
523. #483	C₂²×C₃₁	semidirect
528. #479	C₂²×C₃₁	semidirect
529. #479	C₂²×C₃₁	semidirect
532. #477	C₂²×C₃₁	semidirect
533. #476	C₂²×C₃₁	semidirect
534. #475	C₂²×C₃₁	semidirect
535. #474	C₂²×C₃₁	semidirect
536. #470	C₂²×C₃₁	semidirect
539. #468	C₂²×C₃₁	semidirect
540. #467	C₂²×C₃₁	semidirect
543. #465	C₂²×C₃₁	semidirect
548. #462	C₂²×C₃₁	semidirect
550. #460	C₂²×C₃₁	semidirect
552. #452	C₂²×C₃₁	semidirect
553. #452	C₂²×C₃₁	semidirect
561. #441	C₂²×C₃₁	semidirect
563. #440	C₂²×C₃₁	semidirect
564. C₄×Q₁₆	C₂²×C₃₁	semidirect
566. C₄×SD₁₆	C₂²×C₃₁	semidirect
570. #433	C₂²×C₃₁	semidirect
571. #433	C₂²×C₃₁	semidirect
573. #431	C₂²×C₃₁	semidirect
574. #424	C₂²×C₃₁	semidirect
576. C₄×M₁₆	C₂²×C₃₁	semidirect
577. C₂×C₄×C₈	C₂²×C₃₁	semidirect
736. C₃₁	#61010	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×#3512	2
C₃₁×#3510	2
C₃₁×#3258	2
C₃₁×#3257	2
C₃₁×#3233	2
C₃₁×#3232	2
C₃₁×#3212	2
C₃₁×#3211	2
C₃₁×#3201	2
C₃₁×#3198	2
C₃₁×#3183	2
C₃₁×#3168	2
C₃₁×#3127	2
C₃₁×#3126	2
C₃₁×#3125	2
C₃₁×#3124	2
C₃₁×#3123	2
C₃₁×#3122	2
C₃₁×#2922	2
#61010	31

Subgroups — C31×#61010 #21517769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61010 #21517769