Subgroups — C₃₁×#60957 #21517716

Order 7936.

1676 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3461	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3262	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3261	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3258	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×#3203	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#3202	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3201	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3172	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×#3108	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3107	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3104	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3102	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#544	C₂²	1	2	yes	—
21	C₃₁×#542	—	2	2	no	—
22	C₃₁×#542	C₂²	1	2	yes	—
23	C₃₁×#542	C₂²	1	2	yes	—
24	C₃₁×#541	—	2	2	no	—
25	C₃₁×#541	C₂²	1	2	yes	—
26	C₃₁×#541	C₂²	1	2	yes	—
27	C₃₁×#539	—	2	2	no	—
28	C₃₁×#539	—	2	2	no	—
29	C₃₁×#537	C₂²	1	2	yes	—
30	C₃₁×#536	C₂²	1	2	yes	—
31	C₃₁×#536	C₂²	1	2	yes	—
32	C₃₁×#533	—	2	2	no	—
33	C₃₁×#533	C₂²	1	2	yes	—
34	C₃₁×#533	C₂²	1	2	yes	—
35	C₃₁×#529	—	2	2	no	—
36	C₃₁×#529	—	2	2	no	—
37	C₃₁×#529	—	2	2	no	—
38	C₃₁×#529	C₂²	1	2	yes	—
39	C₃₁×#529	C₂²	1	2	yes	—
40	C₄×#41×C₃₁	C₂²	1	2	yes	—
41	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
43	C₃₁×#501	C₂²	1	2	yes	—
44	C₃₁×#500	C₂²	1	1	yes	characteristic
45	C₃₁×#499	C₂²	1	1	yes	characteristic
46	C₃₁×#497	C₂²	1	2	yes	—
47	C₃₁×#495	C₂²	1	1	yes	characteristic
48	C₃₁×#494	C₂²	1	1	yes	characteristic
49	C₃₁×#491	C₂²	1	2	yes	—
50	C₃₁×#489	C₂²	1	2	yes	—
51	C₃₁×#488	C₂²	1	2	yes	—
52	C₃₁×#487	C₂²	1	2	yes	—
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	—
62	C₃₁×#479	C₂²	1	2	yes	—
63	C₃₁×#479	C₂²	1	2	yes	—
64	C₃₁×#478	C₂²	1	2	yes	—
65	C₃₁×#477	C₂²	1	2	yes	—
66	C₃₁×#477	C₂²	1	2	yes	—
67	C₃₁×#475	C₂²	1	2	yes	—
68	C₃₁×#474	C₂²	1	2	yes	—
69	C₃₁×#470	C₂²	1	2	yes	—
70	C₃₁×#470	C₂²	1	2	yes	—
71	C₃₁×#468	C₂²	1	2	yes	—
72	C₃₁×#468	C₂²	1	2	yes	—
73	C₃₁×#467	C₂²	1	1	yes	characteristic
74	C₃₁×#467	C₂²	1	2	yes	—
75	C₃₁×#467	C₂²	1	1	yes	characteristic
76	C₃₁×#467	C₂²	1	1	yes	characteristic
77	C₃₁×#466	C₂²	1	1	yes	characteristic
78	C₃₁×#465	C₂²	1	2	yes	—
79	C₃₁×#464	C₂²	1	2	yes	—
80	C₃₁×#464	C₂²	1	2	yes	—
81	C₃₁×#464	C₂²	1	2	yes	—
82	C₃₁×#463	C₂²	1	2	yes	—
83	C₃₁×#462	C₂²	1	2	yes	—
84	C₃₁×#462	C₂²	1	2	yes	—
85	C₃₁×#462	C₂²	1	2	yes	—
86	C₃₁×#461	C₂²	1	2	yes	—
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	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
96	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
97	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
98	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
99	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
100	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
101	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
102	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
103	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
104	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
105	C₃₁×#433	C₂²	1	2	yes	—
106	C₃₁×#433	C₂²	1	2	yes	—
107	C₃₁×#431	C₂²	1	2	yes	—
108	C₃₁×#431	C₂²	1	2	yes	—
109	C₃₁×#424	C₂²	1	1	yes	characteristic
110	C₃₁×#424	C₂²	1	1	yes	characteristic
111	C₃₁×#408	C₂²	1	1	yes	characteristic
112	C₃₁×#408	C₂²	1	1	yes	characteristic
113	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
114	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
115	C₂×#41×C₃₁	C₂³	1	2	yes	—
116	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
117	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
118	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
119	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
120	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
121	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
122	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
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	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
129	C₂×M₁₆×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	—	2	2	no	—
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×C₄⋊Q₈	C₂³	1	2	yes	—
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×#126	—	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	—	2	2	no	—
153	C₃₁×#125	C₂³	1	2	yes	—
154	C₃₁×#125	C₂³	1	2	yes	—
155	C₃₁×#124	—	2	2	no	—
156	C₃₁×#124	—	2	2	no	—
157	C₃₁×#124	—	2	2	no	—
158	C₃₁×#124	C₂³	1	2	yes	—
159	C₃₁×#124	C₂³	1	2	yes	—
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×#123	—	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	—	2	2	no	—
176	C₃₁×C₂²⋊Q₈	—	2	2	no	—
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×C₂²⋊Q₈	C₂³	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	C₂³	1	2	yes	—
187	C₃₁×#121	C₂³	1	2	yes	—
188	C₄×Q₈×C₃₁	—	2	2	no	—
189	C₄×Q₈×C₃₁	—	2	2	no	—
190	C₄×Q₈×C₃₁	—	2	2	no	—
191	C₄×Q₈×C₃₁	—	2	2	no	—
192	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
193	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
194	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
195	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
196	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
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×D₄×C₃₁	—	2	2	no	—
201	C₄×D₄×C₃₁	—	2	2	no	—
202	C₄×D₄×C₃₁	—	2	2	no	—
203	C₄×D₄×C₃₁	—	2	2	no	—
204	C₄×D₄×C₃₁	D₄	1	2	yes	—
205	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
206	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
207	C₄×D₄×C₃₁	D₄	1	2	yes	—
208	C₄×D₄×C₃₁	C₂³	1	2	yes	—
209	C₄×D₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
216	C₃₁×#117	C₂³	1	1	yes	characteristic
217	C₃₁×#117	C₂³	1	2	yes	—
218	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
219	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
220	C₂×C₄²×C₃₁	—	2	2	no	—
221	C₂×C₄²×C₃₁	—	2	2	no	—
222	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
224	C₃₁×#107	C₂³	1	1	yes	characteristic
225	C₃₁×#107	C₂³	1	1	yes	characteristic
226	C₃₁×#107	C₂³	1	1	yes	characteristic
227	C₃₁×#107	C₂³	1	2	yes	—
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	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
264	#41×C₃₁	—	4	1	no	—
265	#41×C₃₁	—	4	1	no	—
266	#41×C₃₁	—	4	2	no	—
267	#41×C₃₁	—	4	2	no	—
268	C₂×Q₈×C₃₁	—	2	2	no	—
269	C₂×Q₈×C₃₁	—	2	2	no	—
270	C₂×Q₈×C₃₁	—	2	2	no	—
271	C₂×Q₈×C₃₁	—	4	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×Q₈×C₃₁	C₂⁴	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
281	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
282	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₃₁	—	2	2	no	—
284	C₂²×C₄×C₃₁	—	2	2	no	—
285	C₂²×C₄×C₃₁	—	2	2	no	—
286	C₂²×C₄×C₃₁	—	2	2	no	—
287	C₂²×C₄×C₃₁	—	2	2	no	—
288	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
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	1	no	—
296	Q₁₆×C₃₁	—	4	2	no	—
297	Q₁₆×C₃₁	—	4	1	no	—
298	Q₁₆×C₃₁	—	4	2	no	—
299	Q₁₆×C₃₁	—	4	2	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	M₁₆×C₃₁	—	4	1	no	—
305	M₁₆×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	1	yes	characteristic
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	1	yes	characteristic
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	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	2	yes	—
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	2	yes	—
376	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
377	#60957	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
378	C₂³×C₃₁	—	2	2	no	—
379	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
380	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
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	1	no	—
388	Q₈×C₃₁	—	4	4	no	—
389	Q₈×C₃₁	—	8	2	no	—
390	Q₈×C₃₁	—	8	2	no	—
391	D₄×C₃₁	—	2	2	no	—
392	D₄×C₃₁	—	2	2	no	—
393	D₄×C₃₁	—	4	2	no	—
394	D₄×C₃₁	—	4	1	no	—
395	D₄×C₃₁	—	4	4	no	—
396	D₄×C₃₁	—	8	2	no	—
397	D₄×C₃₁	—	8	2	no	—
398	C₂×C₄×C₃₁	—	2	4	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	2	no	—
412	C₂×C₄×C₃₁	—	4	1	no	—
413	C₂×C₄×C₃₁	—	4	4	no	—
414	C₂×C₄×C₃₁	—	4	4	no	—
415	C₂×C₄×C₃₁	—	4	4	no	—
416	C₂×C₄×C₃₁	—	8	2	no	—
417	C₂×C₄×C₃₁	—	8	2	no	—
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	1	yes	characteristic
422	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
427	C₈×C₃₁	—	2	1	no	—
428	C₈×C₃₁	—	2	1	no	—
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	#3461	C₂×C₃₁	1	2	yes	complemented
434	#3262	C₂×C₃₁	1	1	yes	characteristic, complemented
435	#3261	C₂×C₃₁	1	1	yes	characteristic, complemented
436	#3258	C₂×C₃₁	1	2	yes	complemented
437	#3243	C₂×C₃₁	1	2	yes	complemented
438	#3242	C₂×C₃₁	1	2	yes	complemented
439	#3225	C₂×C₃₁	1	2	yes	complemented
440	#3223	C₂×C₃₁	1	2	yes	complemented
441	#3203	C₂×C₃₁	1	1	yes	characteristic
442	#3202	C₂×C₃₁	1	1	yes	characteristic, complemented
443	#3201	C₂×C₃₁	1	2	yes	complemented
444	#3172	C₂×C₃₁	1	2	yes	complemented
445	#3170	C₂×C₃₁	1	1	yes	characteristic, complemented
446	#3168	C₂×C₃₁	1	1	yes	characteristic, complemented
447	#3108	C₂×C₃₁	1	2	yes	complemented
448	#3107	C₂×C₃₁	1	2	yes	complemented
449	#3104	C₂×C₃₁	1	2	yes	complemented
450	#3102	C₂×C₃₁	1	2	yes	complemented
451	#2922	C₂×C₃₁	1	1	yes	characteristic, complemented
452	C₂²×C₃₁	—	2	2	no	—
453	C₂²×C₃₁	—	2	1	no	—
454	C₂²×C₃₁	—	2	2	no	—
455	C₂²×C₃₁	—	2	1	no	—
456	C₂²×C₃₁	—	2	1	no	—
457	C₂²×C₃₁	—	2	2	no	—
458	C₂²×C₃₁	—	4	2	no	—
459	C₂²×C₃₁	—	4	2	no	—
460	C₂²×C₃₁	—	4	2	no	—
461	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
462	C₄×C₃₁	—	2	1	no	—
463	C₄×C₃₁	—	2	2	no	—
464	C₄×C₃₁	—	2	1	no	—
465	C₄×C₃₁	—	2	2	no	—
466	C₄×C₃₁	—	2	1	no	—
467	C₄×C₃₁	—	2	2	no	—
468	C₄×C₃₁	—	2	1	no	—
469	C₄×C₃₁	—	4	2	no	—
470	C₄×C₃₁	—	4	2	no	—
471	C₄×C₃₁	—	4	2	no	—
472	C₄×C₃₁	—	4	2	no	—
473	C₄×C₃₁	—	4	2	no	—
474	C₄×C₃₁	—	4	2	no	—
475	C₄×C₃₁	—	4	2	no	—
476	C₄×C₃₁	#578	1	2	yes	—
477	C₄×C₃₁	#585	1	1	yes	characteristic
478	C₄×C₃₁	#585	1	1	yes	characteristic
479	#544	C₂²×C₃₁	1	2	yes	—
480	#542	—	2	2	no	—
481	#542	C₂²×C₃₁	1	2	yes	—
482	#542	C₂²×C₃₁	1	2	yes	—
483	#541	—	2	2	no	—
484	#541	C₂²×C₃₁	1	2	yes	—
485	#541	C₂²×C₃₁	1	2	yes	—
486	#539	—	2	2	no	—
487	#539	—	2	2	no	—
488	#537	C₂²×C₃₁	1	2	yes	—
489	#536	C₂²×C₃₁	1	2	yes	—
490	#536	C₂²×C₃₁	1	2	yes	—
491	#533	—	2	2	no	—
492	#533	C₂²×C₃₁	1	2	yes	—
493	#533	C₂²×C₃₁	1	2	yes	—
494	#529	—	2	2	no	—
495	#529	—	2	2	no	—
496	#529	—	2	2	no	—
497	#529	C₂²×C₃₁	1	2	yes	—
498	#529	C₂²×C₃₁	1	2	yes	—
499	C₄×#41	C₂²×C₃₁	1	2	yes	—
500	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
501	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
502	#501	C₂²×C₃₁	1	2	yes	—
503	#500	C₂²×C₃₁	1	1	yes	characteristic
504	#499	C₂²×C₃₁	1	1	yes	characteristic
505	#497	C₂²×C₃₁	1	2	yes	—
506	#495	C₂²×C₃₁	1	1	yes	characteristic
507	#494	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	2	yes	—
511	#487	C₂²×C₃₁	1	2	yes	—
512	#485	C₂²×C₃₁	1	2	yes	—
513	#485	C₂²×C₃₁	1	2	yes	—
514	#485	C₂²×C₃₁	1	2	yes	—
515	#484	C₂²×C₃₁	1	2	yes	—
516	#484	C₂²×C₃₁	1	2	yes	—
517	#483	C₂²×C₃₁	1	2	yes	—
518	#482	C₂²×C₃₁	1	2	yes	—
519	#480	C₂²×C₃₁	1	2	yes	—
520	#479	C₂²×C₃₁	1	2	yes	—
521	#479	C₂²×C₃₁	1	2	yes	—
522	#479	C₂²×C₃₁	1	2	yes	—
523	#478	C₂²×C₃₁	1	2	yes	—
524	#477	C₂²×C₃₁	1	2	yes	—
525	#477	C₂²×C₃₁	1	2	yes	—
526	#475	C₂²×C₃₁	1	2	yes	—
527	#474	C₂²×C₃₁	1	2	yes	—
528	#470	C₂²×C₃₁	1	2	yes	—
529	#470	C₂²×C₃₁	1	2	yes	—
530	#468	C₂²×C₃₁	1	2	yes	—
531	#468	C₂²×C₃₁	1	2	yes	—
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	1	yes	characteristic
536	#466	C₂²×C₃₁	1	1	yes	characteristic
537	#465	C₂²×C₃₁	1	2	yes	—
538	#464	C₂²×C₃₁	1	2	yes	—
539	#464	C₂²×C₃₁	1	2	yes	—
540	#464	C₂²×C₃₁	1	2	yes	—
541	#463	C₂²×C₃₁	1	2	yes	—
542	#462	C₂²×C₃₁	1	2	yes	—
543	#462	C₂²×C₃₁	1	2	yes	—
544	#462	C₂²×C₃₁	1	2	yes	—
545	#461	C₂²×C₃₁	1	2	yes	—
546	#452	C₂²×C₃₁	1	2	yes	—
547	#452	C₂²×C₃₁	1	2	yes	—
548	#452	C₂²×C₃₁	1	2	yes	—
549	#451	C₂²×C₃₁	1	2	yes	—
550	#451	C₂²×C₃₁	1	2	yes	—
551	#451	C₂²×C₃₁	1	2	yes	—
552	#449	C₂²×C₃₁	1	2	yes	—
553	#448	C₂²×C₃₁	1	2	yes	—
554	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
555	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
556	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
557	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
558	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
559	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
560	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
561	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
562	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
563	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
564	#433	C₂²×C₃₁	1	2	yes	—
565	#433	C₂²×C₃₁	1	2	yes	—
566	#431	C₂²×C₃₁	1	2	yes	—
567	#431	C₂²×C₃₁	1	2	yes	—
568	#424	C₂²×C₃₁	1	1	yes	characteristic
569	#424	C₂²×C₃₁	1	1	yes	characteristic
570	#408	C₂²×C₃₁	1	1	yes	characteristic
571	#408	C₂²×C₃₁	1	1	yes	characteristic
572	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
573	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
574	C₂×C₃₁	—	4	2	no	—
575	C₂×C₃₁	—	4	1	no	—
576	C₂×C₃₁	—	8	2	no	—
577	C₂×C₃₁	#3449	1	1	yes	characteristic
578	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
579	C₂×C₃₁	#3584	1	1	yes	characteristic
580	C₂×#41	C₂³×C₃₁	1	2	yes	—
581	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
582	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
583	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
584	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
585	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
586	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
587	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
588	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
589	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
590	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
591	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
592	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
593	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
594	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
595	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
596	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
597	C₄⋊Q₈	—	2	2	no	—
598	C₄⋊Q₈	—	2	2	no	—
599	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
600	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
601	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
602	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
603	#126	—	2	2	no	—
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	#125	—	2	2	no	—
612	#125	—	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	C₂³×C₃₁	1	2	yes	—
619	#125	C₂³×C₃₁	1	2	yes	—
620	#124	—	2	2	no	—
621	#124	—	2	2	no	—
622	#124	—	2	2	no	—
623	#124	C₂³×C₃₁	1	2	yes	—
624	#124	C₂³×C₃₁	1	2	yes	—
625	#123	—	2	2	no	—
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	C₂³×C₃₁	1	2	yes	—
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	#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	C₄×Q₈	—	2	2	no	—
654	C₄×Q₈	—	2	2	no	—
655	C₄×Q₈	—	2	2	no	—
656	C₄×Q₈	—	2	2	no	—
657	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
658	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
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×Q₈	C₂³×C₃₁	1	2	yes	—
664	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
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	D₄×C₃₁	1	2	yes	—
670	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
671	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
672	C₄×D₄	D₄×C₃₁	1	2	yes	—
673	C₄×D₄	C₂³×C₃₁	1	2	yes	—
674	C₄×D₄	C₂³×C₃₁	1	2	yes	—
675	#117	—	2	2	no	—
676	#117	—	2	2	no	—
677	#117	—	2	2	no	—
678	#117	—	2	2	no	—
679	#117	—	2	2	no	—
680	#117	C₂³×C₃₁	1	2	yes	—
681	#117	C₂³×C₃₁	1	2	yes	—
682	#117	C₂³×C₃₁	1	1	yes	characteristic
683	C₂×C₄⋊C₄	—	2	2	no	—
684	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
685	C₂×C₄²	—	2	2	no	—
686	C₂×C₄²	—	2	2	no	—
687	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
688	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
689	#107	C₂³×C₃₁	1	1	yes	characteristic
690	#107	C₂³×C₃₁	1	1	yes	characteristic
691	#107	C₂³×C₃₁	1	1	yes	characteristic
692	#107	C₂³×C₃₁	1	2	yes	—
693	#107	C₂³×C₃₁	1	1	yes	characteristic
694	#107	C₂³×C₃₁	1	2	yes	—
695	#107	C₂³×C₃₁	1	2	yes	—
696	#106	C₂³×C₃₁	1	2	yes	—
697	#106	C₂³×C₃₁	1	2	yes	—
698	#106	C₂³×C₃₁	1	2	yes	—
699	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
700	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
701	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
702	C₄⋊C₈	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	#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	#102	C₂³×C₃₁	1	2	yes	—
716	#102	C₂³×C₃₁	1	2	yes	—
717	#102	C₂³×C₃₁	1	2	yes	—
718	#102	C₂³×C₃₁	1	2	yes	—
719	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
720	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
721	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
722	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
723	#97	C₂³×C₃₁	1	2	yes	—
724	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
725	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
726	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
727	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
728	C₄×C₈	C₂³×C₃₁	1	2	yes	—
729	C₃₁	#60957	1	1	yes	characteristic, direct product factor, Sylow
730	#41	—	4	1	no	—
731	#41	—	4	1	no	—
732	#41	—	4	2	no	—
733	#41	—	4	2	no	—
734	C₂×Q₈	—	2	2	no	—
735	C₂×Q₈	—	2	2	no	—
736	C₂×Q₈	—	2	2	no	—
737	C₂×Q₈	—	4	2	no	—
738	C₂×Q₈	—	4	2	no	—
739	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
740	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
741	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
742	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
747	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
748	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
755	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
756	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
757	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
760	Q₁₆	—	4	1	no	—
761	Q₁₆	—	4	1	no	—
762	Q₁₆	—	4	2	no	—
763	Q₁₆	—	4	1	no	—
764	Q₁₆	—	4	2	no	—
765	Q₁₆	—	4	2	no	—
766	SD₁₆	—	4	2	no	—
767	SD₁₆	—	4	2	no	—
768	SD₁₆	—	4	2	no	—
769	D₈	—	4	1	no	—
770	M₁₆	—	4	1	no	—
771	M₁₆	—	4	1	no	—
772	C₂×C₈	—	4	1	no	—
773	C₂×C₈	—	4	1	no	—
774	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
775	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
776	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
777	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
778	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
779	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
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	—	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	C₂×D₄×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
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	2	no	—
812	C₂²⋊C₄	—	2	2	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	C₂×D₄×C₃₁	1	2	yes	—
827	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
828	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	C₂×D₄×C₃₁	1	2	yes	—
837	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
838	C₄²	C₂×D₄×C₃₁	1	2	yes	—
839	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
840	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
841	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
842	C₄²	C₂⁴×C₃₁	1	2	yes	—
843	C₂³	—	2	2	no	—
844	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
845	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
846	Q₈	—	2	2	no	—
847	Q₈	—	2	2	no	—
848	Q₈	—	2	2	no	—
849	Q₈	—	2	2	no	—
850	Q₈	—	2	2	no	—
851	Q₈	—	2	2	no	—
852	Q₈	—	4	1	no	—
853	Q₈	—	4	4	no	—
854	Q₈	—	8	2	no	—
855	Q₈	—	8	2	no	—
856	D₄	—	2	2	no	—
857	D₄	—	2	2	no	—
858	D₄	—	4	2	no	—
859	D₄	—	4	1	no	—
860	D₄	—	4	4	no	—
861	D₄	—	8	2	no	—
862	D₄	—	8	2	no	—
863	C₂×C₄	—	2	4	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	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	—	4	2	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	4	no	—
879	C₂×C₄	—	4	4	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	8	2	no	—
882	C₂×C₄	—	8	2	no	—
883	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
884	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
885	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
886	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
887	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
888	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
889	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
890	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
891	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
892	C₈	—	2	1	no	—
893	C₈	—	2	1	no	—
894	C₈	—	2	1	no	—
895	C₈	—	2	1	no	—
896	C₈	—	2	2	no	—
897	C₈	—	2	2	no	—
898	C₂²	—	2	2	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	2	no	—
902	C₂²	—	2	2	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
908	C₄	—	2	2	no	—
909	C₄	—	2	1	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	1	no	—
912	C₄	—	2	1	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	1	no	—
915	C₄	—	4	2	no	—
916	C₄	—	4	2	no	—
917	C₄	—	4	2	no	—
918	C₄	—	4	2	no	—
919	C₄	—	4	2	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	2	no	—
922	C₄	C₃₁×#578	1	2	yes	—
923	C₄	C₃₁×#585	1	1	yes	characteristic
924	C₄	C₃₁×#585	1	1	yes	characteristic
925	C₂	—	4	2	no	—
926	C₂	—	4	1	no	—
927	C₂	—	8	2	no	—
928	C₂	C₃₁×#3449	1	1	yes	characteristic
929	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
930	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
socle	C₂²×C₃₁	C₂³×D₄
prime radical	C₃₁×#3203	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3461	C₂	semidirect
2. C₃₁×#3262	C₂	semidirect
3. C₃₁×#3261	C₂	semidirect
4. C₃₁×#3258	C₂	semidirect
5. C₃₁×#3243	C₂	semidirect
6. C₃₁×#3242	C₂	semidirect
7. C₃₁×#3225	C₂	semidirect
8. C₃₁×#3223	C₂	semidirect
10. C₃₁×#3202	C₂	semidirect
11. C₃₁×#3201	C₂	semidirect
12. C₃₁×#3172	C₂	semidirect
13. C₃₁×#3170	C₂	semidirect
14. C₃₁×#3168	C₂	semidirect
15. C₃₁×#3108	C₂	semidirect
16. C₃₁×#3107	C₂	semidirect
17. C₃₁×#3104	C₂	semidirect
18. C₃₁×#3102	C₂	semidirect
19. C₃₁×#2922	C₂	semidirect
377. #60957	C₃₁	direct (N × H)
433. #3461	C₂×C₃₁	semidirect
434. #3262	C₂×C₃₁	semidirect
435. #3261	C₂×C₃₁	semidirect
436. #3258	C₂×C₃₁	semidirect
437. #3243	C₂×C₃₁	semidirect
438. #3242	C₂×C₃₁	semidirect
439. #3225	C₂×C₃₁	semidirect
440. #3223	C₂×C₃₁	semidirect
442. #3202	C₂×C₃₁	semidirect
443. #3201	C₂×C₃₁	semidirect
444. #3172	C₂×C₃₁	semidirect
445. #3170	C₂×C₃₁	semidirect
446. #3168	C₂×C₃₁	semidirect
447. #3108	C₂×C₃₁	semidirect
448. #3107	C₂×C₃₁	semidirect
449. #3104	C₂×C₃₁	semidirect
450. #3102	C₂×C₃₁	semidirect
451. #2922	C₂×C₃₁	semidirect
729. C₃₁	#60957	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×#3461	2
C₃₁×#3262	2
C₃₁×#3261	2
C₃₁×#3258	2
C₃₁×#3243	2
C₃₁×#3242	2
C₃₁×#3225	2
C₃₁×#3223	2
C₃₁×#3203	2
C₃₁×#3202	2
C₃₁×#3201	2
C₃₁×#3172	2
C₃₁×#3170	2
C₃₁×#3168	2
C₃₁×#3108	2
C₃₁×#3107	2
C₃₁×#3104	2
C₃₁×#3102	2
C₃₁×#2922	2
#60957	31

Subgroups — C31×#60957 #21517716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60957 #21517716