Subgroups — C₃₁×#61002 #21517761

Order 7936.

1682 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3495	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3250	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3249	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3248	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3243	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3242	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3225	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3223	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3191	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#3190	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3189	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3181	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3170	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3127	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3124	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3121	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3120	C₂	1	2	yes	maximal, complemented
19	C₂×C₃₁×#433	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#556	—	2	2	no	—
21	C₃₁×#554	—	2	2	no	—
22	C₃₁×#552	—	2	2	no	—
23	C₃₁×#552	—	2	2	no	—
24	C₃₁×#552	—	2	2	no	—
25	C₃₁×#552	—	2	2	no	—
26	C₃₁×#551	—	2	2	no	—
27	C₃₁×#551	—	2	2	no	—
28	C₃₁×#544	C₂²	1	2	yes	—
29	C₃₁×#542	C₂²	1	2	yes	—
30	C₃₁×#542	C₂²	1	2	yes	—
31	C₃₁×#541	C₂²	1	2	yes	—
32	C₃₁×#541	C₂²	1	2	yes	—
33	C₃₁×#536	C₂²	1	2	yes	—
34	C₃₁×#533	C₂²	1	2	yes	—
35	C₃₁×#533	C₂²	1	2	yes	—
36	C₃₁×#529	C₂²	1	2	yes	—
37	C₃₁×#529	C₂²	1	2	yes	—
38	C₃₁×#525	C₂²	1	2	yes	—
39	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
40	C₃₁×#520	C₂²	1	2	yes	—
41	C₃₁×#519	C₂²	1	2	yes	—
42	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
43	C₃₁×#501	C₂²	1	2	yes	complemented
44	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#497	C₂²	1	2	yes	complemented
47	C₃₁×#495	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#491	C₂²	1	2	yes	complemented
50	C₃₁×#489	C₂²	1	2	yes	complemented
51	C₃₁×#488	C₂²	1	2	yes	complemented
52	C₃₁×#487	C₂²	1	2	yes	complemented
53	C₃₁×#485	C₂²	1	2	yes	—
54	C₃₁×#485	C₂²	1	2	yes	—
55	C₃₁×#485	C₂²	1	2	yes	—
56	C₃₁×#484	C₂²	1	2	yes	—
57	C₃₁×#484	C₂²	1	2	yes	—
58	C₃₁×#483	C₂²	1	2	yes	—
59	C₃₁×#482	C₂²	1	2	yes	—
60	C₃₁×#480	C₂²	1	2	yes	—
61	C₃₁×#479	C₂²	1	2	yes	complemented
62	C₃₁×#479	C₂²	1	2	yes	complemented
63	C₃₁×#479	C₂²	1	2	yes	complemented
64	C₃₁×#478	C₂²	1	2	yes	complemented
65	C₃₁×#477	C₂²	1	2	yes	complemented
66	C₃₁×#477	C₂²	1	2	yes	complemented
67	C₃₁×#475	C₂²	1	2	yes	complemented
68	C₃₁×#474	C₂²	1	2	yes	complemented
69	C₃₁×#467	C₂²	1	1	yes	characteristic
70	C₃₁×#467	C₂²	1	1	yes	characteristic
71	C₃₁×#467	C₂²	1	2	yes	—
72	C₃₁×#467	C₂²	1	1	yes	characteristic
73	C₃₁×#467	C₂²	1	2	yes	—
74	C₃₁×#467	C₂²	1	2	yes	—
75	C₃₁×#466	C₂²	1	1	yes	characteristic
76	C₃₁×#465	C₂²	1	2	yes	—
77	C₃₁×#465	C₂²	1	2	yes	—
78	C₃₁×#465	C₂²	1	2	yes	—
79	C₃₁×#464	C₂²	1	2	yes	complemented
80	C₃₁×#464	C₂²	1	2	yes	complemented
81	C₃₁×#464	C₂²	1	2	yes	complemented
82	C₃₁×#463	C₂²	1	2	yes	complemented
83	C₃₁×#462	C₂²	1	2	yes	complemented
84	C₃₁×#462	C₂²	1	2	yes	complemented
85	C₃₁×#462	C₂²	1	2	yes	complemented
86	C₃₁×#461	C₂²	1	2	yes	complemented
87	C₃₁×#452	C₂²	1	2	yes	—
88	C₃₁×#452	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×#451	C₂²	1	2	yes	—
93	C₃₁×#449	C₂²	1	2	yes	—
94	C₃₁×#448	C₂²	1	2	yes	—
95	C₃₁×#441	C₂²	1	2	yes	complemented
96	C₃₁×#441	C₂²	1	2	yes	complemented
97	C₃₁×#440	C₂²	1	2	yes	complemented
98	C₃₁×#440	C₂²	1	2	yes	complemented
99	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
100	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
101	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
102	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
103	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
104	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
105	C₃₁×#433	C₂²	1	2	yes	—
106	C₃₁×#433	C₂²	1	2	yes	—
107	C₃₁×#433	C₂²	1	2	yes	—
108	C₃₁×#433	C₂²	1	2	yes	—
109	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
110	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
111	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
112	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
113	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
114	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
115	C₂×#41×C₃₁	C₂³	1	2	yes	—
116	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
117	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
118	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
119	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
120	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
121	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
122	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
123	C₂×Q₁₆×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×D₈×C₃₁	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
132	C₃₁×C₄⋊Q₈	—	2	2	no	—
133	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
134	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
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×#126	—	2	2	no	—
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#126	—	2	2	no	—
145	C₃₁×#125	—	2	2	no	—
146	C₃₁×#125	—	2	2	no	—
147	C₃₁×#125	—	2	2	no	—
148	C₃₁×#125	—	2	2	no	—
149	C₃₁×#125	—	2	2	no	—
150	C₃₁×#125	—	2	2	no	—
151	C₃₁×#125	—	2	2	no	—
152	C₃₁×#125	C₂³	1	2	yes	—
153	C₃₁×#125	C₂³	1	2	yes	—
154	C₃₁×#124	—	2	2	no	—
155	C₃₁×#124	—	2	2	no	—
156	C₃₁×#124	C₂³	1	2	yes	—
157	C₃₁×#124	C₂³	1	2	yes	—
158	C₃₁×#123	—	2	2	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×C₂²⋊Q₈	—	2	2	no	—
166	C₃₁×C₂²⋊Q₈	—	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	—	2	2	no	—
172	C₃₁×C₂²⋊Q₈	—	2	2	no	—
173	C₃₁×C₂²⋊Q₈	—	2	2	no	—
174	C₃₁×C₂²⋊Q₈	—	2	2	no	—
175	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
176	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
179	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
180	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
181	C₃₁×#121	C₂³	1	2	yes	—
182	C₃₁×#121	C₂³	1	2	yes	—
183	C₃₁×#120	—	2	2	no	—
184	C₄×Q₈×C₃₁	—	2	2	no	—
185	C₄×Q₈×C₃₁	—	2	2	no	—
186	C₄×Q₈×C₃₁	—	2	2	no	—
187	C₄×Q₈×C₃₁	—	2	2	no	—
188	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
189	C₄×Q₈×C₃₁	C₂³	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	C₂³	1	2	yes	—
201	C₄×D₄×C₃₁	C₂³	1	2	yes	—
202	C₃₁×#117	—	2	2	no	—
203	C₃₁×#117	—	2	2	no	—
204	C₃₁×#117	—	2	2	no	—
205	C₃₁×#117	—	2	2	no	—
206	C₃₁×#117	—	2	2	no	—
207	C₃₁×#117	—	2	2	no	—
208	C₃₁×#117	—	2	2	no	—
209	C₃₁×#117	D₄	1	2	yes	—
210	C₃₁×#117	D₄	1	2	yes	—
211	C₃₁×#117	C₂³	1	2	yes	—
212	C₃₁×#117	C₂³	1	2	yes	—
213	C₃₁×#117	C₂³	1	2	yes	—
214	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
215	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
216	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
217	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
218	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
220	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
222	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
224	C₃₁×#107	C₂³	1	1	yes	characteristic
225	C₃₁×#107	C₂³	1	1	yes	characteristic
226	C₃₁×#107	C₂³	1	2	yes	—
227	C₃₁×#107	C₂³	1	1	yes	characteristic
228	C₃₁×#107	C₂³	1	1	yes	characteristic
229	C₃₁×#107	C₂³	1	2	yes	—
230	C₃₁×#107	C₂³	1	2	yes	—
231	C₃₁×#106	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×#103	C₂³	1	2	yes	—
239	C₃₁×#103	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×#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×C₂²⋊C₈	C₂³	1	2	yes	—
255	C₃₁×C₂²⋊C₈	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	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
264	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
265	#41×C₃₁	—	4	2	no	—
266	#41×C₃₁	—	4	2	no	—
267	C₂×Q₈×C₃₁	—	2	2	no	—
268	C₂×Q₈×C₃₁	—	2	2	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	C₂⁴	1	2	yes	—
273	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
274	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
275	C₂×D₄×C₃₁	—	2	2	no	—
276	C₂×D₄×C₃₁	—	2	2	no	—
277	C₂×D₄×C₃₁	—	2	2	no	—
278	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₃₁	—	2	2	no	—
280	C₂²×C₄×C₃₁	—	2	2	no	—
281	C₂²×C₄×C₃₁	—	2	2	no	—
282	C₂²×C₄×C₃₁	—	2	2	no	—
283	C₂²×C₄×C₃₁	—	2	2	no	—
284	C₂²×C₄×C₃₁	—	4	1	no	—
285	C₂²×C₄×C₃₁	—	4	1	no	—
286	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
291	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
294	Q₁₆×C₃₁	—	4	1	no	—
295	Q₁₆×C₃₁	—	4	2	no	—
296	Q₁₆×C₃₁	—	4	2	no	—
297	Q₁₆×C₃₁	—	4	1	no	—
298	Q₁₆×C₃₁	—	4	2	no	—
299	Q₁₆×C₃₁	—	4	1	no	—
300	SD₁₆×C₃₁	—	4	2	no	—
301	SD₁₆×C₃₁	—	4	2	no	—
302	SD₁₆×C₃₁	—	4	2	no	—
303	D₈×C₃₁	—	4	1	no	—
304	C₂×C₈×C₃₁	—	4	1	no	—
305	C₂×C₈×C₃₁	—	4	1	no	—
306	C₂×C₈×C₃₁	—	4	1	no	—
307	C₂×C₈×C₃₁	—	4	1	no	—
308	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
309	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
311	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
312	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
313	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	—	2	2	no	—
333	C₄⋊C₄×C₃₁	—	2	2	no	—
334	C₄⋊C₄×C₃₁	—	2	2	no	—
335	C₄⋊C₄×C₃₁	—	2	2	no	—
336	C₄⋊C₄×C₃₁	—	2	2	no	—
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	C₂⁴	1	2	yes	—
342	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
343	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
371	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₃₁	C₂×D₄	1	2	yes	—
373	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
374	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
375	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₄²×C₃₁	C₂⁴	1	2	yes	—
377	#61002	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
378	C₂³×C₃₁	—	2	2	no	—
379	C₂³×C₃₁	—	2	2	no	—
380	C₂³×C₃₁	—	4	1	no	—
381	C₂³×C₃₁	—	4	1	no	—
382	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
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	—	2	2	no	—
389	Q₈×C₃₁	—	2	2	no	—
390	Q₈×C₃₁	—	4	4	no	—
391	Q₈×C₃₁	—	8	2	no	—
392	Q₈×C₃₁	—	8	2	no	—
393	D₄×C₃₁	—	2	2	no	—
394	D₄×C₃₁	—	2	2	no	—
395	D₄×C₃₁	—	4	4	no	—
396	D₄×C₃₁	—	4	4	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	1	no	—
401	C₂×C₄×C₃₁	—	2	1	no	—
402	C₂×C₄×C₃₁	—	2	2	no	—
403	C₂×C₄×C₃₁	—	2	2	no	—
404	C₂×C₄×C₃₁	—	2	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	—	4	1	no	—
412	C₂×C₄×C₃₁	—	4	2	no	—
413	C₂×C₄×C₃₁	—	4	1	no	—
414	C₂×C₄×C₃₁	—	4	1	no	—
415	C₂×C₄×C₃₁	—	4	4	no	—
416	C₂×C₄×C₃₁	—	4	4	no	—
417	C₂×C₄×C₃₁	—	8	2	no	—
418	C₂×C₄×C₃₁	—	8	2	no	—
419	C₂×C₄×C₃₁	—	8	2	no	—
420	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
425	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
429	C₈×C₃₁	—	2	1	no	—
430	C₈×C₃₁	—	2	1	no	—
431	C₈×C₃₁	—	2	2	no	—
432	C₈×C₃₁	—	2	2	no	—
433	C₈×C₃₁	—	2	1	no	—
434	C₈×C₃₁	—	2	1	no	—
435	#3495	C₂×C₃₁	1	2	yes	complemented
436	#3250	C₂×C₃₁	1	1	yes	characteristic, complemented
437	#3249	C₂×C₃₁	1	1	yes	characteristic, complemented
438	#3248	C₂×C₃₁	1	2	yes	complemented
439	#3243	C₂×C₃₁	1	2	yes	complemented
440	#3242	C₂×C₃₁	1	2	yes	complemented
441	#3225	C₂×C₃₁	1	2	yes	complemented
442	#3223	C₂×C₃₁	1	2	yes	complemented
443	#3191	C₂×C₃₁	1	1	yes	characteristic
444	#3190	C₂×C₃₁	1	2	yes	complemented
445	#3189	C₂×C₃₁	1	1	yes	characteristic, complemented
446	#3181	C₂×C₃₁	1	2	yes	complemented
447	#3170	C₂×C₃₁	1	1	yes	characteristic, complemented
448	#3168	C₂×C₃₁	1	1	yes	characteristic, complemented
449	#3127	C₂×C₃₁	1	2	yes	complemented
450	#3124	C₂×C₃₁	1	2	yes	complemented
451	#3121	C₂×C₃₁	1	2	yes	complemented
452	#3120	C₂×C₃₁	1	2	yes	complemented
453	C₂×#433	C₂×C₃₁	1	1	yes	characteristic, complemented
454	C₂²×C₃₁	—	2	1	no	—
455	C₂²×C₃₁	—	2	1	no	—
456	C₂²×C₃₁	—	2	2	no	—
457	C₂²×C₃₁	—	2	2	no	—
458	C₂²×C₃₁	—	2	2	no	—
459	C₂²×C₃₁	—	4	2	no	—
460	C₂²×C₃₁	—	4	2	no	—
461	C₂²×C₃₁	—	4	2	no	—
462	C₂²×C₃₁	—	8	2	no	—
463	C₂²×C₃₁	#578	1	2	yes	—
464	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
465	C₄×C₃₁	—	2	1	no	—
466	C₄×C₃₁	—	2	2	no	—
467	C₄×C₃₁	—	2	1	no	—
468	C₄×C₃₁	—	2	2	no	—
469	C₄×C₃₁	—	2	1	no	—
470	C₄×C₃₁	—	2	1	no	—
471	C₄×C₃₁	—	2	2	no	—
472	C₄×C₃₁	—	2	1	no	—
473	C₄×C₃₁	—	4	2	no	—
474	C₄×C₃₁	—	4	2	no	—
475	C₄×C₃₁	—	4	2	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	#585	1	1	yes	characteristic
481	C₄×C₃₁	#585	1	1	yes	characteristic
482	#556	—	2	2	no	—
483	#554	—	2	2	no	—
484	#552	—	2	2	no	—
485	#552	—	2	2	no	—
486	#552	—	2	2	no	—
487	#552	—	2	2	no	—
488	#551	—	2	2	no	—
489	#551	—	2	2	no	—
490	#544	C₂²×C₃₁	1	2	yes	—
491	#542	C₂²×C₃₁	1	2	yes	—
492	#542	C₂²×C₃₁	1	2	yes	—
493	#541	C₂²×C₃₁	1	2	yes	—
494	#541	C₂²×C₃₁	1	2	yes	—
495	#536	C₂²×C₃₁	1	2	yes	—
496	#533	C₂²×C₃₁	1	2	yes	—
497	#533	C₂²×C₃₁	1	2	yes	—
498	#529	C₂²×C₃₁	1	2	yes	—
499	#529	C₂²×C₃₁	1	2	yes	—
500	#525	C₂²×C₃₁	1	2	yes	—
501	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
502	#520	C₂²×C₃₁	1	2	yes	—
503	#519	C₂²×C₃₁	1	2	yes	—
504	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
505	#501	C₂²×C₃₁	1	2	yes	complemented
506	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
507	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
508	#497	C₂²×C₃₁	1	2	yes	complemented
509	#495	C₂²×C₃₁	1	1	yes	characteristic, complemented
510	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
511	#491	C₂²×C₃₁	1	2	yes	complemented
512	#489	C₂²×C₃₁	1	2	yes	complemented
513	#488	C₂²×C₃₁	1	2	yes	complemented
514	#487	C₂²×C₃₁	1	2	yes	complemented
515	#485	C₂²×C₃₁	1	2	yes	—
516	#485	C₂²×C₃₁	1	2	yes	—
517	#485	C₂²×C₃₁	1	2	yes	—
518	#484	C₂²×C₃₁	1	2	yes	—
519	#484	C₂²×C₃₁	1	2	yes	—
520	#483	C₂²×C₃₁	1	2	yes	—
521	#482	C₂²×C₃₁	1	2	yes	—
522	#480	C₂²×C₃₁	1	2	yes	—
523	#479	C₂²×C₃₁	1	2	yes	complemented
524	#479	C₂²×C₃₁	1	2	yes	complemented
525	#479	C₂²×C₃₁	1	2	yes	complemented
526	#478	C₂²×C₃₁	1	2	yes	complemented
527	#477	C₂²×C₃₁	1	2	yes	complemented
528	#477	C₂²×C₃₁	1	2	yes	complemented
529	#475	C₂²×C₃₁	1	2	yes	complemented
530	#474	C₂²×C₃₁	1	2	yes	complemented
531	#467	C₂²×C₃₁	1	1	yes	characteristic
532	#467	C₂²×C₃₁	1	1	yes	characteristic
533	#467	C₂²×C₃₁	1	2	yes	—
534	#467	C₂²×C₃₁	1	1	yes	characteristic
535	#467	C₂²×C₃₁	1	2	yes	—
536	#467	C₂²×C₃₁	1	2	yes	—
537	#466	C₂²×C₃₁	1	1	yes	characteristic
538	#465	C₂²×C₃₁	1	2	yes	—
539	#465	C₂²×C₃₁	1	2	yes	—
540	#465	C₂²×C₃₁	1	2	yes	—
541	#464	C₂²×C₃₁	1	2	yes	complemented
542	#464	C₂²×C₃₁	1	2	yes	complemented
543	#464	C₂²×C₃₁	1	2	yes	complemented
544	#463	C₂²×C₃₁	1	2	yes	complemented
545	#462	C₂²×C₃₁	1	2	yes	complemented
546	#462	C₂²×C₃₁	1	2	yes	complemented
547	#462	C₂²×C₃₁	1	2	yes	complemented
548	#461	C₂²×C₃₁	1	2	yes	complemented
549	#452	C₂²×C₃₁	1	2	yes	—
550	#452	C₂²×C₃₁	1	2	yes	—
551	#452	C₂²×C₃₁	1	2	yes	—
552	#451	C₂²×C₃₁	1	2	yes	—
553	#451	C₂²×C₃₁	1	2	yes	—
554	#451	C₂²×C₃₁	1	2	yes	—
555	#449	C₂²×C₃₁	1	2	yes	—
556	#448	C₂²×C₃₁	1	2	yes	—
557	#441	C₂²×C₃₁	1	2	yes	complemented
558	#441	C₂²×C₃₁	1	2	yes	complemented
559	#440	C₂²×C₃₁	1	2	yes	complemented
560	#440	C₂²×C₃₁	1	2	yes	complemented
561	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
562	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
563	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
564	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
565	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
566	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
567	#433	C₂²×C₃₁	1	2	yes	—
568	#433	C₂²×C₃₁	1	2	yes	—
569	#433	C₂²×C₃₁	1	2	yes	—
570	#433	C₂²×C₃₁	1	2	yes	—
571	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
572	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
573	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
574	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
575	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
576	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
577	C₂×C₃₁	—	2	2	no	—
578	C₂×C₃₁	—	4	2	no	—
579	C₂×C₃₁	—	8	2	no	—
580	C₂×C₃₁	#3449	1	1	yes	characteristic
581	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
582	C₂×C₃₁	#3584	1	1	yes	characteristic
583	C₂×#41	C₂³×C₃₁	1	2	yes	—
584	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
585	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
586	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
587	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
588	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
589	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
590	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
591	C₂×Q₁₆	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	1	yes	characteristic
596	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
597	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
598	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
599	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
600	C₄⋊Q₈	—	2	2	no	—
601	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
602	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
603	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
604	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
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	#126	—	2	2	no	—
613	#125	—	2	2	no	—
614	#125	—	2	2	no	—
615	#125	—	2	2	no	—
616	#125	—	2	2	no	—
617	#125	—	2	2	no	—
618	#125	—	2	2	no	—
619	#125	—	2	2	no	—
620	#125	C₂³×C₃₁	1	2	yes	—
621	#125	C₂³×C₃₁	1	2	yes	—
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	#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	2	no	—
632	#123	—	2	2	no	—
633	C₂²⋊Q₈	—	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	C₂³×C₃₁	1	2	yes	—
644	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
645	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
646	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
647	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
648	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
649	#121	C₂³×C₃₁	1	2	yes	—
650	#121	C₂³×C₃₁	1	2	yes	—
651	#120	—	2	2	no	—
652	C₄×Q₈	—	2	2	no	—
653	C₄×Q₈	—	2	2	no	—
654	C₄×Q₈	—	2	2	no	—
655	C₄×Q₈	—	2	2	no	—
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×D₄	—	2	2	no	—
663	C₄×D₄	—	2	2	no	—
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	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	2	no	—
675	#117	—	2	2	no	—
676	#117	—	2	2	no	—
677	#117	D₄×C₃₁	1	2	yes	—
678	#117	D₄×C₃₁	1	2	yes	—
679	#117	C₂³×C₃₁	1	2	yes	—
680	#117	C₂³×C₃₁	1	2	yes	—
681	#117	C₂³×C₃₁	1	2	yes	—
682	C₂×C₄⋊C₄	—	2	2	no	—
683	C₂×C₄⋊C₄	—	2	2	no	—
684	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
685	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
686	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
687	C₂×C₂²⋊C₄	—	2	2	no	—
688	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
689	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
692	#107	C₂³×C₃₁	1	1	yes	characteristic
693	#107	C₂³×C₃₁	1	1	yes	characteristic
694	#107	C₂³×C₃₁	1	2	yes	—
695	#107	C₂³×C₃₁	1	1	yes	characteristic
696	#107	C₂³×C₃₁	1	1	yes	characteristic
697	#107	C₂³×C₃₁	1	2	yes	—
698	#107	C₂³×C₃₁	1	2	yes	—
699	#106	C₂³×C₃₁	1	2	yes	—
700	#106	C₂³×C₃₁	1	2	yes	—
701	#106	C₂³×C₃₁	1	2	yes	—
702	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
703	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
704	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
705	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
706	#103	C₂³×C₃₁	1	2	yes	—
707	#103	C₂³×C₃₁	1	2	yes	—
708	#103	C₂³×C₃₁	1	2	yes	—
709	#103	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	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
723	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
724	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
725	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
726	#97	C₂³×C₃₁	1	2	yes	—
727	#97	C₂³×C₃₁	1	2	yes	—
728	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
729	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
730	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
731	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
732	C₃₁	#61002	1	1	yes	characteristic, direct product factor, Sylow
733	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
734	#41	—	4	2	no	—
735	#41	—	4	2	no	—
736	C₂×Q₈	—	2	2	no	—
737	C₂×Q₈	—	2	2	no	—
738	C₂×Q₈	—	2	2	no	—
739	C₂×Q₈	—	4	2	no	—
740	C₂×Q₈	—	4	2	no	—
741	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
742	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
743	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
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	—	4	1	no	—
754	C₂²×C₄	—	4	1	no	—
755	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
756	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
757	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
758	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
759	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
760	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
763	Q₁₆	—	4	1	no	—
764	Q₁₆	—	4	2	no	—
765	Q₁₆	—	4	2	no	—
766	Q₁₆	—	4	1	no	—
767	Q₁₆	—	4	2	no	—
768	Q₁₆	—	4	1	no	—
769	SD₁₆	—	4	2	no	—
770	SD₁₆	—	4	2	no	—
771	SD₁₆	—	4	2	no	—
772	D₈	—	4	1	no	—
773	C₂×C₈	—	4	1	no	—
774	C₂×C₈	—	4	1	no	—
775	C₂×C₈	—	4	1	no	—
776	C₂×C₈	—	4	1	no	—
777	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
778	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
779	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
780	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
781	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
782	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
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	—	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	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
807	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
808	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
809	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
810	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
811	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
812	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
813	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
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	C₂×D₄×C₃₁	1	2	yes	—
830	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
831	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
832	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
841	C₄²	C₂×D₄×C₃₁	1	2	yes	—
842	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
843	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
844	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
845	C₄²	C₂⁴×C₃₁	1	2	yes	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	4	1	no	—
849	C₂³	—	4	1	no	—
850	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
851	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
852	Q₈	—	2	2	no	—
853	Q₈	—	2	2	no	—
854	Q₈	—	2	2	no	—
855	Q₈	—	2	2	no	—
856	Q₈	—	2	2	no	—
857	Q₈	—	2	2	no	—
858	Q₈	—	4	4	no	—
859	Q₈	—	8	2	no	—
860	Q₈	—	8	2	no	—
861	D₄	—	2	2	no	—
862	D₄	—	2	2	no	—
863	D₄	—	4	4	no	—
864	D₄	—	4	4	no	—
865	D₄	—	8	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	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	—	4	1	no	—
880	C₂×C₄	—	4	2	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	4	1	no	—
883	C₂×C₄	—	4	4	no	—
884	C₂×C₄	—	4	4	no	—
885	C₂×C₄	—	8	2	no	—
886	C₂×C₄	—	8	2	no	—
887	C₂×C₄	—	8	2	no	—
888	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
889	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
890	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
891	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
892	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
893	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
894	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
895	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
896	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
897	C₈	—	2	1	no	—
898	C₈	—	2	1	no	—
899	C₈	—	2	2	no	—
900	C₈	—	2	2	no	—
901	C₈	—	2	1	no	—
902	C₈	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	2	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	8	2	no	—
912	C₂²	C₃₁×#578	1	2	yes	—
913	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
914	C₄	—	2	2	no	—
915	C₄	—	2	1	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	2	no	—
921	C₄	—	2	1	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	C₃₁×#585	1	1	yes	characteristic
930	C₄	C₃₁×#585	1	1	yes	characteristic
931	C₂	—	2	2	no	—
932	C₂	—	4	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₃₁×#3449	1	1	yes	characteristic
935	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
936	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3191	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3495	C₂	semidirect
2. C₃₁×#3250	C₂	semidirect
3. C₃₁×#3249	C₂	semidirect
4. C₃₁×#3248	C₂	semidirect
5. C₃₁×#3243	C₂	semidirect
6. C₃₁×#3242	C₂	semidirect
7. C₃₁×#3225	C₂	semidirect
8. C₃₁×#3223	C₂	semidirect
10. C₃₁×#3190	C₂	semidirect
11. C₃₁×#3189	C₂	semidirect
12. C₃₁×#3181	C₂	semidirect
13. C₃₁×#3170	C₂	semidirect
14. C₃₁×#3168	C₂	semidirect
15. C₃₁×#3127	C₂	semidirect
16. C₃₁×#3124	C₂	semidirect
17. C₃₁×#3121	C₂	semidirect
18. C₃₁×#3120	C₂	semidirect
19. C₂×C₃₁×#433	C₂	semidirect
43. C₃₁×#501	C₂²	semidirect
44. C₃₁×#500	C₂²	semidirect
45. C₃₁×#499	C₂²	semidirect
46. C₃₁×#497	C₂²	semidirect
47. C₃₁×#495	C₂²	semidirect
48. C₃₁×#494	C₂²	semidirect
49. C₃₁×#491	C₂²	semidirect
50. C₃₁×#489	C₂²	semidirect
51. C₃₁×#488	C₂²	semidirect
52. C₃₁×#487	C₂²	semidirect
61. C₃₁×#479	C₂²	semidirect
62. C₃₁×#479	C₂²	semidirect
63. C₃₁×#479	C₂²	semidirect
64. C₃₁×#478	C₂²	semidirect
65. C₃₁×#477	C₂²	semidirect
66. C₃₁×#477	C₂²	semidirect
67. C₃₁×#475	C₂²	semidirect
68. C₃₁×#474	C₂²	semidirect
79. C₃₁×#464	C₂²	semidirect
80. C₃₁×#464	C₂²	semidirect
81. C₃₁×#464	C₂²	semidirect
82. C₃₁×#463	C₂²	semidirect
83. C₃₁×#462	C₂²	semidirect
84. C₃₁×#462	C₂²	semidirect
85. C₃₁×#462	C₂²	semidirect
86. C₃₁×#461	C₂²	semidirect
95. C₃₁×#441	C₂²	semidirect
96. C₃₁×#441	C₂²	semidirect
97. C₃₁×#440	C₂²	semidirect
98. C₃₁×#440	C₂²	semidirect
99. C₄×Q₁₆×C₃₁	C₂²	semidirect
100. C₄×Q₁₆×C₃₁	C₂²	semidirect
101. C₄×Q₁₆×C₃₁	C₂²	semidirect
102. C₄×Q₁₆×C₃₁	C₂²	semidirect
103. C₄×SD₁₆×C₃₁	C₂²	semidirect
104. C₄×D₈×C₃₁	C₂²	semidirect
377. #61002	C₃₁	direct (N × H)
435. #3495	C₂×C₃₁	semidirect
436. #3250	C₂×C₃₁	semidirect
437. #3249	C₂×C₃₁	semidirect
438. #3248	C₂×C₃₁	semidirect
439. #3243	C₂×C₃₁	semidirect
440. #3242	C₂×C₃₁	semidirect
441. #3225	C₂×C₃₁	semidirect
442. #3223	C₂×C₃₁	semidirect
444. #3190	C₂×C₃₁	semidirect
445. #3189	C₂×C₃₁	semidirect
446. #3181	C₂×C₃₁	semidirect
447. #3170	C₂×C₃₁	semidirect
448. #3168	C₂×C₃₁	semidirect
449. #3127	C₂×C₃₁	semidirect
450. #3124	C₂×C₃₁	semidirect
451. #3121	C₂×C₃₁	semidirect
452. #3120	C₂×C₃₁	semidirect
453. C₂×#433	C₂×C₃₁	semidirect
505. #501	C₂²×C₃₁	semidirect
506. #500	C₂²×C₃₁	semidirect
507. #499	C₂²×C₃₁	semidirect
508. #497	C₂²×C₃₁	semidirect
509. #495	C₂²×C₃₁	semidirect
510. #494	C₂²×C₃₁	semidirect
511. #491	C₂²×C₃₁	semidirect
512. #489	C₂²×C₃₁	semidirect
513. #488	C₂²×C₃₁	semidirect
514. #487	C₂²×C₃₁	semidirect
523. #479	C₂²×C₃₁	semidirect
524. #479	C₂²×C₃₁	semidirect
525. #479	C₂²×C₃₁	semidirect
526. #478	C₂²×C₃₁	semidirect
527. #477	C₂²×C₃₁	semidirect
528. #477	C₂²×C₃₁	semidirect
529. #475	C₂²×C₃₁	semidirect
530. #474	C₂²×C₃₁	semidirect
541. #464	C₂²×C₃₁	semidirect
542. #464	C₂²×C₃₁	semidirect
543. #464	C₂²×C₃₁	semidirect
544. #463	C₂²×C₃₁	semidirect
545. #462	C₂²×C₃₁	semidirect
546. #462	C₂²×C₃₁	semidirect
547. #462	C₂²×C₃₁	semidirect
548. #461	C₂²×C₃₁	semidirect
557. #441	C₂²×C₃₁	semidirect
558. #441	C₂²×C₃₁	semidirect
559. #440	C₂²×C₃₁	semidirect
560. #440	C₂²×C₃₁	semidirect
561. C₄×Q₁₆	C₂²×C₃₁	semidirect
562. C₄×Q₁₆	C₂²×C₃₁	semidirect
563. C₄×Q₁₆	C₂²×C₃₁	semidirect
564. C₄×Q₁₆	C₂²×C₃₁	semidirect
565. C₄×SD₁₆	C₂²×C₃₁	semidirect
566. C₄×D₈	C₂²×C₃₁	semidirect
732. C₃₁	#61002	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×#3495	2
C₃₁×#3250	2
C₃₁×#3249	2
C₃₁×#3248	2
C₃₁×#3243	2
C₃₁×#3242	2
C₃₁×#3225	2
C₃₁×#3223	2
C₃₁×#3191	2
C₃₁×#3190	2
C₃₁×#3189	2
C₃₁×#3181	2
C₃₁×#3170	2
C₃₁×#3168	2
C₃₁×#3127	2
C₃₁×#3124	2
C₃₁×#3121	2
C₃₁×#3120	2
C₂×C₃₁×#433	2
#61002	31

Subgroups — C31×#61002 #21517761

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61002 #21517761