Subgroups — C₃₁×#61217 #21517976

Order 7936.

2064 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3331	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3330	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3329	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3328	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3303	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3302	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3299	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3298	C₂	1	2	yes	maximal, complemented
11	C₂×C₃₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3097	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3063	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3013	C₂	1	2	yes	maximal, complemented
17	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2931	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2898	C₂	1	2	yes	maximal, complemented
20	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	2	yes	—
21	C₂×C₃₁×#137	C₂²	1	2	yes	—
22	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#131	C₂²	1	2	yes	—
24	C₃₁×#556	C₂²	1	2	yes	—
25	C₃₁×#555	C₂²	1	2	yes	—
26	C₃₁×#554	C₂²	1	2	yes	—
27	C₃₁×#553	—	2	2	no	—
28	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
29	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
30	C₃₁×#548	—	2	2	no	—
31	C₃₁×#547	—	2	2	no	—
32	C₃₁×#547	—	2	2	no	—
33	C₃₁×#547	C₂²	1	2	yes	—
34	C₃₁×#547	C₂²	1	2	yes	—
35	C₃₁×#547	C₂²	1	2	yes	—
36	C₃₁×#542	—	2	2	no	—
37	C₃₁×#537	C₂²	1	2	yes	—
38	C₃₁×#536	—	2	2	no	—
39	C₃₁×#536	C₂²	1	2	yes	—
40	C₃₁×#533	—	2	1	no	—
41	C₃₁×#532	—	2	1	no	—
42	C₃₁×#532	—	2	1	no	—
43	C₃₁×#532	C₂²	1	1	yes	characteristic
44	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
45	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
47	C₃₁×#520	C₂²	1	2	yes	—
48	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
49	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
50	C₃₁×#487	C₂²	1	2	yes	—
51	C₃₁×#487	C₂²	1	2	yes	—
52	C₃₁×#487	C₂²	1	2	yes	—
53	C₃₁×#487	C₂²	1	2	yes	—
54	C₃₁×#485	C₂²	1	4	yes	—
55	C₃₁×#485	C₂²	1	4	yes	—
56	C₃₁×#484	C₂²	1	4	yes	—
57	C₃₁×#483	C₂²	1	4	yes	—
58	C₃₁×#477	C₂²	1	2	yes	—
59	C₃₁×#476	C₂²	1	2	yes	—
60	C₃₁×#475	C₂²	1	2	yes	—
61	C₃₁×#474	C₂²	1	2	yes	—
62	C₃₁×#470	C₂²	1	4	yes	—
63	C₃₁×#468	C₂²	1	4	yes	—
64	C₃₁×#467	C₂²	1	4	yes	—
65	C₃₁×#465	C₂²	1	4	yes	—
66	C₃₁×#462	C₂²	1	2	yes	—
67	C₃₁×#462	C₂²	1	2	yes	—
68	C₃₁×#461	C₂²	1	2	yes	—
69	C₃₁×#461	C₂²	1	2	yes	—
70	C₃₁×#452	C₂²	1	4	yes	—
71	C₃₁×#451	C₂²	1	4	yes	—
72	C₃₁×#449	C₂²	1	4	yes	—
73	C₃₁×#448	C₂²	1	4	yes	—
74	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
75	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
76	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
77	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
78	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
79	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
80	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
81	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
82	C₃₁×#436	C₂²	1	2	yes	—
83	C₃₁×#436	C₂²	1	2	yes	—
84	C₈×D₄×C₃₁	C₂²	1	2	yes	—
85	C₈×D₄×C₃₁	C₂²	1	2	yes	—
86	C₃₁×#428	C₂²	1	2	yes	—
87	C₃₁×#427	C₂²	1	1	yes	characteristic
88	C₃₁×#423	C₂²	1	1	yes	characteristic
89	C₃₁×#419	C₂²	1	2	yes	—
90	C₃₁×#419	C₂²	1	4	yes	—
91	C₃₁×#417	C₂²	1	4	yes	—
92	C₃₁×#417	C₂²	1	2	yes	—
93	C₃₁×#416	C₂²	1	1	yes	characteristic
94	C₃₁×#416	C₂²	1	4	yes	—
95	C₃₁×#416	C₂²	1	1	yes	characteristic
96	C₂×C₃₁×#103	C₂²	1	2	yes	—
97	C₂×C₃₁×#103	C₂²	1	2	yes	—
98	C₂×C₃₁×#103	C₂²	1	4	yes	—
99	C₃₁×#408	C₂²	1	2	yes	—
100	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
101	C₃₁×2₋¹⁺⁴	—	2	8	no	—
102	C₃₁×2₋¹⁺⁴	—	4	4	no	—
103	C₂×#41×C₃₁	—	2	2	no	—
104	C₂×#41×C₃₁	—	2	4	no	—
105	C₂×#41×C₃₁	—	2	2	no	—
106	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
107	C₂×#41×C₃₁	C₂³	1	4	yes	—
108	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
109	C₂×#41×C₃₁	C₂³	1	2	yes	—
110	C₂²×Q₈×C₃₁	—	2	2	no	—
111	C₂²×Q₈×C₃₁	—	2	1	no	—
112	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
113	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
114	C₃₁×#137	—	4	4	no	—
115	C₃₁×#135	—	2	4	no	—
116	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
117	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
118	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
119	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
120	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
121	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
122	C₃₁×#131	—	4	4	no	—
123	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
124	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
125	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
127	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
128	C₃₁×C₄⋊Q₈	—	2	2	no	—
129	C₃₁×C₄⋊Q₈	—	2	2	no	—
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	—	2	1	no	—
134	C₃₁×C₄⋊Q₈	—	2	1	no	—
135	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
136	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₃₁×#127	D₄	1	1	yes	characteristic
141	C₃₁×#126	—	2	4	no	—
142	C₃₁×#125	—	2	2	no	—
143	C₃₁×#124	—	2	2	no	—
144	C₃₁×#124	—	2	2	no	—
145	C₃₁×#124	—	2	4	no	—
146	C₃₁×#124	D₄	1	2	yes	—
147	C₃₁×#123	—	2	4	no	—
148	C₃₁×#123	—	2	4	no	—
149	C₃₁×#123	—	2	4	no	—
150	C₃₁×#123	—	2	4	no	—
151	C₃₁×C₂²⋊Q₈	—	2	2	no	—
152	C₃₁×C₂²⋊Q₈	—	2	2	no	—
153	C₃₁×C₂²⋊Q₈	—	2	4	no	—
154	C₃₁×C₂²⋊Q₈	—	2	4	no	—
155	C₃₁×C₂²⋊Q₈	—	2	4	no	—
156	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
157	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
158	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
159	C₃₁×#121	—	2	2	no	—
160	C₃₁×#121	—	2	2	no	—
161	C₃₁×#121	—	2	2	no	—
162	C₃₁×#121	—	2	2	no	—
163	C₃₁×#121	—	2	4	no	—
164	C₃₁×#121	D₄	1	2	yes	—
165	C₃₁×#121	D₄	1	2	yes	—
166	C₃₁×#121	C₂³	1	4	yes	—
167	C₄×Q₈×C₃₁	—	2	2	no	—
168	C₄×Q₈×C₃₁	—	2	2	no	—
169	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₃₁	—	2	2	no	—
174	C₄×D₄×C₃₁	—	2	4	no	—
175	C₄×D₄×C₃₁	—	2	2	no	—
176	C₄×D₄×C₃₁	—	2	2	no	—
177	C₄×D₄×C₃₁	—	2	2	no	—
178	C₄×D₄×C₃₁	—	2	1	no	—
179	C₄×D₄×C₃₁	—	2	1	no	—
180	C₄×D₄×C₃₁	—	2	1	no	—
181	C₄×D₄×C₃₁	—	2	1	no	—
182	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₃₁	C₂³	1	2	yes	—
187	C₄×D₄×C₃₁	C₂³	1	2	yes	—
188	C₃₁×#117	—	2	2	no	—
189	C₃₁×#117	—	2	1	no	—
190	C₃₁×#117	—	2	1	no	—
191	C₃₁×#117	C₂³	1	1	yes	characteristic
192	C₃₁×#117	C₂³	1	4	yes	—
193	C₃₁×#117	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
195	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
196	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
197	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
198	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
199	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
201	C₂×C₄²×C₃₁	—	2	1	no	—
202	C₂×C₄²×C₃₁	—	2	1	no	—
203	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
204	C₃₁×#107	C₂³	1	1	yes	characteristic
205	C₃₁×#107	C₂³	1	1	yes	characteristic
206	C₃₁×#107	C₂³	1	4	yes	—
207	C₃₁×#106	C₂³	1	1	yes	characteristic
208	C₃₁×#106	C₂³	1	1	yes	characteristic
209	C₃₁×#106	C₂³	1	4	yes	—
210	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
211	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
212	C₃₁×#103	C₂³	1	1	yes	characteristic
213	C₃₁×#103	C₂³	1	4	yes	—
214	C₃₁×#103	C₂³	1	4	yes	—
215	C₃₁×#103	C₂³	1	4	yes	—
216	C₃₁×#103	C₂³	1	4	yes	—
217	C₃₁×#103	C₂³	1	4	yes	—
218	C₃₁×#103	C₂³	1	4	yes	—
219	C₃₁×#103	C₂³	1	1	yes	characteristic
220	C₃₁×#103	C₂³	1	4	yes	—
221	C₃₁×#103	C₂³	1	1	yes	characteristic
222	C₃₁×#103	C₂³	1	1	yes	characteristic
223	C₃₁×#102	C₂³	1	1	yes	characteristic
224	C₃₁×#102	C₂³	1	1	yes	characteristic
225	C₃₁×#102	C₂³	1	4	yes	—
226	C₃₁×#102	C₂³	1	1	yes	characteristic
227	C₃₁×#102	C₂³	1	1	yes	characteristic
228	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
230	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
231	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
234	#41×C₃₁	—	2	4	no	—
235	#41×C₃₁	—	2	4	no	—
236	#41×C₃₁	—	2	2	no	—
237	#41×C₃₁	—	2	8	no	—
238	#41×C₃₁	—	2	2	no	—
239	#41×C₃₁	—	2	2	no	—
240	#41×C₃₁	—	4	4	no	—
241	#41×C₃₁	—	4	8	no	—
242	#41×C₃₁	—	4	16	no	—
243	#41×C₃₁	—	8	4	no	—
244	#41×C₃₁	#41	1	4	yes	complemented
245	C₂×Q₈×C₃₁	—	2	2	no	—
246	C₂×Q₈×C₃₁	—	2	4	no	—
247	C₂×Q₈×C₃₁	—	2	2	no	—
248	C₂×Q₈×C₃₁	—	2	2	no	—
249	C₂×Q₈×C₃₁	—	2	8	no	—
250	C₂×Q₈×C₃₁	—	2	4	no	—
251	C₂×Q₈×C₃₁	—	2	4	no	—
252	C₂×Q₈×C₃₁	—	4	4	no	—
253	C₂×Q₈×C₃₁	—	4	8	no	—
254	C₂×Q₈×C₃₁	—	8	2	no	—
255	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
256	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
257	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
258	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
259	C₂×D₄×C₃₁	—	2	1	no	—
260	C₂×D₄×C₃₁	—	2	1	no	—
261	C₂×D₄×C₃₁	—	2	4	no	—
262	C₂×D₄×C₃₁	—	2	4	no	—
263	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
264	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
265	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
266	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
267	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
268	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₃₁	—	2	1	no	—
270	C₂²×C₄×C₃₁	—	2	2	no	—
271	C₂²×C₄×C₃₁	—	2	4	no	—
272	C₂²×C₄×C₃₁	—	2	2	no	—
273	C₂²×C₄×C₃₁	—	2	4	no	—
274	C₂²×C₄×C₃₁	—	2	1	no	—
275	C₂²×C₄×C₃₁	—	2	1	no	—
276	C₂²×C₄×C₃₁	—	2	1	no	—
277	C₂²×C₄×C₃₁	—	2	1	no	—
278	C₂²×C₄×C₃₁	—	2	1	no	—
279	C₂²×C₄×C₃₁	—	2	4	no	—
280	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
283	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
284	Q₁₆×C₃₁	—	2	2	no	—
285	Q₁₆×C₃₁	—	4	4	no	—
286	SD₁₆×C₃₁	—	2	2	no	—
287	SD₁₆×C₃₁	—	2	2	no	—
288	SD₁₆×C₃₁	—	4	4	no	—
289	D₈×C₃₁	—	2	2	no	—
290	M₁₆×C₃₁	—	2	4	no	—
291	M₁₆×C₃₁	—	4	4	no	—
292	C₂×C₈×C₃₁	—	2	2	no	—
293	C₂×C₈×C₃₁	—	2	2	no	—
294	C₂×C₈×C₃₁	—	4	4	no	—
295	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
296	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
297	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
298	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
299	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
300	C₄⋊C₄×C₃₁	—	2	2	no	—
301	C₄⋊C₄×C₃₁	—	2	2	no	—
302	C₄⋊C₄×C₃₁	—	2	2	no	—
303	C₄⋊C₄×C₃₁	—	2	2	no	—
304	C₄⋊C₄×C₃₁	—	2	2	no	—
305	C₄⋊C₄×C₃₁	—	2	4	no	—
306	C₄⋊C₄×C₃₁	—	2	4	no	—
307	C₄⋊C₄×C₃₁	—	2	2	no	—
308	C₄⋊C₄×C₃₁	—	2	2	no	—
309	C₄⋊C₄×C₃₁	—	2	4	no	—
310	C₄⋊C₄×C₃₁	—	2	1	no	—
311	C₄⋊C₄×C₃₁	—	2	1	no	—
312	C₄⋊C₄×C₃₁	—	2	1	no	—
313	C₄⋊C₄×C₃₁	—	2	1	no	—
314	C₄⋊C₄×C₃₁	—	2	4	no	—
315	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
316	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
317	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
318	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
319	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
320	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
321	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
322	C₂²⋊C₄×C₃₁	—	2	1	no	—
323	C₂²⋊C₄×C₃₁	—	2	4	no	—
324	C₂²⋊C₄×C₃₁	—	2	1	no	—
325	C₂²⋊C₄×C₃₁	—	2	4	no	—
326	C₂²⋊C₄×C₃₁	—	2	4	no	—
327	C₂²⋊C₄×C₃₁	—	2	4	no	—
328	C₂²⋊C₄×C₃₁	—	2	1	no	—
329	C₂²⋊C₄×C₃₁	—	2	1	no	—
330	C₂²⋊C₄×C₃₁	—	2	1	no	—
331	C₂²⋊C₄×C₃₁	—	2	1	no	—
332	C₂²⋊C₄×C₃₁	—	2	4	no	—
333	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
334	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
335	C₄²×C₃₁	—	2	1	no	—
336	C₄²×C₃₁	—	2	1	no	—
337	C₄²×C₃₁	—	2	1	no	—
338	C₄²×C₃₁	—	2	1	no	—
339	C₄²×C₃₁	—	2	1	no	—
340	C₄²×C₃₁	—	2	1	no	—
341	C₄²×C₃₁	—	2	4	no	—
342	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
343	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
344	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
345	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
346	#61217	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
347	C₂³×C₃₁	—	2	1	no	—
348	C₂³×C₃₁	—	2	1	no	—
349	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
350	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
351	Q₈×C₃₁	—	2	4	no	—
352	Q₈×C₃₁	—	2	1	no	—
353	Q₈×C₃₁	—	2	1	no	—
354	Q₈×C₃₁	—	2	4	no	—
355	Q₈×C₃₁	—	2	4	no	—
356	Q₈×C₃₁	—	2	1	no	—
357	Q₈×C₃₁	—	4	8	no	—
358	Q₈×C₃₁	—	4	4	no	—
359	Q₈×C₃₁	—	4	4	no	—
360	Q₈×C₃₁	—	8	2	no	—
361	Q₈×C₃₁	C₂×#41	1	2	yes	—
362	D₄×C₃₁	—	2	4	no	—
363	D₄×C₃₁	—	2	8	no	—
364	D₄×C₃₁	—	2	4	no	—
365	D₄×C₃₁	—	2	4	no	—
366	D₄×C₃₁	—	2	4	no	—
367	D₄×C₃₁	—	2	1	no	—
368	D₄×C₃₁	—	2	1	no	—
369	D₄×C₃₁	—	2	1	no	—
370	D₄×C₃₁	—	4	8	no	—
371	D₄×C₃₁	—	4	2	no	—
372	D₄×C₃₁	—	8	4	no	—
373	D₄×C₃₁	C₂×#41	1	2	yes	—
374	C₂×C₄×C₃₁	—	2	1	no	—
375	C₂×C₄×C₃₁	—	2	4	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	2	4	no	—
379	C₂×C₄×C₃₁	—	2	4	no	—
380	C₂×C₄×C₃₁	—	2	1	no	—
381	C₂×C₄×C₃₁	—	2	1	no	—
382	C₂×C₄×C₃₁	—	2	1	no	—
383	C₂×C₄×C₃₁	—	2	1	no	—
384	C₂×C₄×C₃₁	—	2	1	no	—
385	C₂×C₄×C₃₁	—	2	4	no	—
386	C₂×C₄×C₃₁	—	2	4	no	—
387	C₂×C₄×C₃₁	—	4	8	no	—
388	C₂×C₄×C₃₁	—	4	8	no	—
389	C₂×C₄×C₃₁	—	4	4	no	—
390	C₂×C₄×C₃₁	—	4	2	no	—
391	C₂×C₄×C₃₁	—	4	2	no	—
392	C₂×C₄×C₃₁	—	4	2	no	—
393	C₂×C₄×C₃₁	—	4	2	no	—
394	C₂×C₄×C₃₁	—	4	2	no	—
395	C₂×C₄×C₃₁	—	8	2	no	—
396	C₂×C₄×C₃₁	—	8	4	no	—
397	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
398	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
404	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
405	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
406	C₈×C₃₁	—	2	1	no	—
407	C₈×C₃₁	—	2	1	no	—
408	C₈×C₃₁	—	2	1	no	—
409	C₈×C₃₁	—	2	1	no	—
410	C₈×C₃₁	—	2	4	no	—
411	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
412	#3499	C₂×C₃₁	1	1	yes	characteristic, complemented
413	#3331	C₂×C₃₁	1	2	yes	complemented
414	#3330	C₂×C₃₁	1	2	yes	complemented
415	#3329	C₂×C₃₁	1	2	yes	complemented
416	#3328	C₂×C₃₁	1	2	yes	complemented
417	#3303	C₂×C₃₁	1	2	yes	complemented
418	#3302	C₂×C₃₁	1	2	yes	complemented
419	#3299	C₂×C₃₁	1	2	yes	complemented
420	#3298	C₂×C₃₁	1	2	yes	complemented
421	C₂×#487	C₂×C₃₁	1	1	yes	characteristic, complemented
422	#3097	C₂×C₃₁	1	2	yes	complemented
423	#3079	C₂×C₃₁	1	1	yes	characteristic, complemented
424	#3063	C₂×C₃₁	1	2	yes	complemented
425	#3039	C₂×C₃₁	1	1	yes	characteristic, complemented
426	#3013	C₂×C₃₁	1	2	yes	complemented
427	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
428	#2931	C₂×C₃₁	1	1	yes	characteristic, complemented
429	#2898	C₂×C₃₁	1	2	yes	complemented
430	C₂²×C₃₁	—	2	1	no	—
431	C₂²×C₃₁	—	2	1	no	—
432	C₂²×C₃₁	—	2	2	no	—
433	C₂²×C₃₁	—	2	4	no	—
434	C₂²×C₃₁	—	2	4	no	—
435	C₂²×C₃₁	—	2	4	no	—
436	C₂²×C₃₁	—	4	1	no	—
437	C₂²×C₃₁	—	4	1	no	—
438	C₂²×C₃₁	—	4	1	no	—
439	C₂²×C₃₁	—	4	1	no	—
440	C₂²×C₃₁	—	4	1	no	—
441	C₂²×C₃₁	#546	1	2	yes	—
442	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
443	C₄×C₃₁	—	2	2	no	—
444	C₄×C₃₁	—	2	4	no	—
445	C₄×C₃₁	—	2	1	no	—
446	C₄×C₃₁	—	2	1	no	—
447	C₄×C₃₁	—	4	4	no	—
448	C₄×C₃₁	—	4	1	no	—
449	C₄×C₃₁	—	4	1	no	—
450	C₄×C₃₁	—	4	1	no	—
451	C₄×C₃₁	—	4	4	no	—
452	C₄×C₃₁	—	4	1	no	—
453	C₄×C₃₁	—	4	1	no	—
454	C₄×C₃₁	#546	1	2	yes	—
455	C₄×C₃₁	#577	1	2	yes	—
456	C₄×C₃₁	#578	1	2	yes	—
457	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
458	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	2	yes	—
460	C₂×#137	C₂²×C₃₁	1	2	yes	—
461	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
462	C₂×#131	C₂²×C₃₁	1	2	yes	—
463	#556	C₂²×C₃₁	1	2	yes	—
464	#555	C₂²×C₃₁	1	2	yes	—
465	#554	C₂²×C₃₁	1	2	yes	—
466	#553	—	2	2	no	—
467	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
468	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
469	#548	—	2	2	no	—
470	#547	—	2	2	no	—
471	#547	—	2	2	no	—
472	#547	C₂²×C₃₁	1	2	yes	—
473	#547	C₂²×C₃₁	1	2	yes	—
474	#547	C₂²×C₃₁	1	2	yes	—
475	#542	—	2	2	no	—
476	#537	C₂²×C₃₁	1	2	yes	—
477	#536	—	2	2	no	—
478	#536	C₂²×C₃₁	1	2	yes	—
479	#533	—	2	1	no	—
480	#532	—	2	1	no	—
481	#532	—	2	1	no	—
482	#532	C₂²×C₃₁	1	1	yes	characteristic
483	C₂×C₄⋊Q₈	—	2	1	no	—
484	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
485	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
486	#520	C₂²×C₃₁	1	2	yes	—
487	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
488	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
489	#487	C₂²×C₃₁	1	2	yes	—
490	#487	C₂²×C₃₁	1	2	yes	—
491	#487	C₂²×C₃₁	1	2	yes	—
492	#487	C₂²×C₃₁	1	2	yes	—
493	#485	C₂²×C₃₁	1	4	yes	—
494	#485	C₂²×C₃₁	1	4	yes	—
495	#484	C₂²×C₃₁	1	4	yes	—
496	#483	C₂²×C₃₁	1	4	yes	—
497	#477	C₂²×C₃₁	1	2	yes	—
498	#476	C₂²×C₃₁	1	2	yes	—
499	#475	C₂²×C₃₁	1	2	yes	—
500	#474	C₂²×C₃₁	1	2	yes	—
501	#470	C₂²×C₃₁	1	4	yes	—
502	#468	C₂²×C₃₁	1	4	yes	—
503	#467	C₂²×C₃₁	1	4	yes	—
504	#465	C₂²×C₃₁	1	4	yes	—
505	#462	C₂²×C₃₁	1	2	yes	—
506	#462	C₂²×C₃₁	1	2	yes	—
507	#461	C₂²×C₃₁	1	2	yes	—
508	#461	C₂²×C₃₁	1	2	yes	—
509	#452	C₂²×C₃₁	1	4	yes	—
510	#451	C₂²×C₃₁	1	4	yes	—
511	#449	C₂²×C₃₁	1	4	yes	—
512	#448	C₂²×C₃₁	1	4	yes	—
513	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
514	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
515	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
516	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
517	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
518	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
519	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
520	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
521	#436	C₂²×C₃₁	1	2	yes	—
522	#436	C₂²×C₃₁	1	2	yes	—
523	C₈×D₄	C₂²×C₃₁	1	2	yes	—
524	C₈×D₄	C₂²×C₃₁	1	2	yes	—
525	#428	C₂²×C₃₁	1	2	yes	—
526	#427	C₂²×C₃₁	1	1	yes	characteristic
527	#423	C₂²×C₃₁	1	1	yes	characteristic
528	#419	C₂²×C₃₁	1	4	yes	—
529	#419	C₂²×C₃₁	1	2	yes	—
530	#417	C₂²×C₃₁	1	4	yes	—
531	#417	C₂²×C₃₁	1	2	yes	—
532	#416	C₂²×C₃₁	1	1	yes	characteristic
533	#416	C₂²×C₃₁	1	4	yes	—
534	#416	C₂²×C₃₁	1	1	yes	characteristic
535	C₂×#103	C₂²×C₃₁	1	2	yes	—
536	C₂×#103	C₂²×C₃₁	1	2	yes	—
537	C₂×#103	C₂²×C₃₁	1	4	yes	—
538	#408	C₂²×C₃₁	1	2	yes	—
539	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
540	C₂×C₃₁	—	2	2	no	—
541	C₂×C₃₁	—	4	4	no	—
542	C₂×C₃₁	—	4	2	no	—
543	C₂×C₃₁	—	8	1	no	—
544	C₂×C₃₁	C₂×#546	1	1	yes	characteristic
545	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
546	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
547	2₋¹⁺⁴	—	2	8	no	—
548	2₋¹⁺⁴	—	4	4	no	—
549	C₂×#41	—	2	2	no	—
550	C₂×#41	—	2	4	no	—
551	C₂×#41	—	2	2	no	—
552	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
553	C₂×#41	C₂³×C₃₁	1	4	yes	—
554	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
555	C₂×#41	C₂³×C₃₁	1	2	yes	—
556	C₂²×Q₈	—	2	2	no	—
557	C₂²×Q₈	—	2	1	no	—
558	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
559	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
560	#137	—	4	4	no	—
561	#135	—	2	4	no	—
562	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
563	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
564	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
565	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
566	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
567	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
568	#131	—	4	4	no	—
569	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
570	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
571	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
572	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
573	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
574	C₄⋊Q₈	—	2	2	no	—
575	C₄⋊Q₈	—	2	2	no	—
576	C₄⋊Q₈	—	2	2	no	—
577	C₄⋊Q₈	—	2	1	no	—
578	C₄⋊Q₈	—	2	1	no	—
579	C₄⋊Q₈	—	2	1	no	—
580	C₄⋊Q₈	—	2	1	no	—
581	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
582	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
583	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
584	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
585	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
586	#127	D₄×C₃₁	1	1	yes	characteristic
587	#126	—	2	4	no	—
588	#125	—	2	2	no	—
589	#124	—	2	2	no	—
590	#124	—	2	2	no	—
591	#124	—	2	4	no	—
592	#124	D₄×C₃₁	1	2	yes	—
593	#123	—	2	4	no	—
594	#123	—	2	4	no	—
595	#123	—	2	4	no	—
596	#123	—	2	4	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	—	2	4	no	—
600	C₂²⋊Q₈	—	2	4	no	—
601	C₂²⋊Q₈	—	2	4	no	—
602	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
603	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
604	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
605	#121	—	2	2	no	—
606	#121	—	2	2	no	—
607	#121	—	2	2	no	—
608	#121	—	2	2	no	—
609	#121	—	2	4	no	—
610	#121	D₄×C₃₁	1	2	yes	—
611	#121	D₄×C₃₁	1	2	yes	—
612	#121	C₂³×C₃₁	1	4	yes	—
613	C₄×Q₈	—	2	2	no	—
614	C₄×Q₈	—	2	2	no	—
615	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
616	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
617	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
618	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	4	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
629	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
630	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
631	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
632	C₄×D₄	C₂³×C₃₁	1	2	yes	—
633	C₄×D₄	C₂³×C₃₁	1	2	yes	—
634	#117	—	2	2	no	—
635	#117	—	2	1	no	—
636	#117	—	2	1	no	—
637	#117	C₂³×C₃₁	1	1	yes	characteristic
638	#117	C₂³×C₃₁	1	1	yes	characteristic
639	#117	C₂³×C₃₁	1	4	yes	—
640	C₂×C₄⋊C₄	—	2	1	no	—
641	C₂×C₄⋊C₄	—	2	1	no	—
642	C₂×C₄⋊C₄	—	2	1	no	—
643	C₂×C₄⋊C₄	—	2	2	no	—
644	C₂×C₄⋊C₄	—	2	2	no	—
645	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
647	C₂×C₄²	—	2	1	no	—
648	C₂×C₄²	—	2	1	no	—
649	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
650	#107	C₂³×C₃₁	1	1	yes	characteristic
651	#107	C₂³×C₃₁	1	1	yes	characteristic
652	#107	C₂³×C₃₁	1	4	yes	—
653	#106	C₂³×C₃₁	1	1	yes	characteristic
654	#106	C₂³×C₃₁	1	1	yes	characteristic
655	#106	C₂³×C₃₁	1	4	yes	—
656	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
657	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
658	#103	C₂³×C₃₁	1	1	yes	characteristic
659	#103	C₂³×C₃₁	1	4	yes	—
660	#103	C₂³×C₃₁	1	4	yes	—
661	#103	C₂³×C₃₁	1	4	yes	—
662	#103	C₂³×C₃₁	1	4	yes	—
663	#103	C₂³×C₃₁	1	4	yes	—
664	#103	C₂³×C₃₁	1	4	yes	—
665	#103	C₂³×C₃₁	1	1	yes	characteristic
666	#103	C₂³×C₃₁	1	4	yes	—
667	#103	C₂³×C₃₁	1	1	yes	characteristic
668	#103	C₂³×C₃₁	1	1	yes	characteristic
669	#102	C₂³×C₃₁	1	1	yes	characteristic
670	#102	C₂³×C₃₁	1	1	yes	characteristic
671	#102	C₂³×C₃₁	1	4	yes	—
672	#102	C₂³×C₃₁	1	1	yes	characteristic
673	#102	C₂³×C₃₁	1	1	yes	characteristic
674	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
675	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
676	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
677	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
678	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
679	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
680	C₃₁	#61217	1	1	yes	characteristic, direct product factor, Sylow
681	#41	—	2	4	no	—
682	#41	—	2	4	no	—
683	#41	—	2	2	no	—
684	#41	—	2	8	no	—
685	#41	—	2	2	no	—
686	#41	—	2	2	no	—
687	#41	—	4	4	no	—
688	#41	—	4	8	no	—
689	#41	—	4	16	no	—
690	#41	—	8	4	no	—
691	#41	#41×C₃₁	1	4	yes	complemented
692	C₂×Q₈	—	2	2	no	—
693	C₂×Q₈	—	2	4	no	—
694	C₂×Q₈	—	2	2	no	—
695	C₂×Q₈	—	2	2	no	—
696	C₂×Q₈	—	2	8	no	—
697	C₂×Q₈	—	2	4	no	—
698	C₂×Q₈	—	2	4	no	—
699	C₂×Q₈	—	4	4	no	—
700	C₂×Q₈	—	4	8	no	—
701	C₂×Q₈	—	8	2	no	—
702	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
703	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
704	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
705	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	1	no	—
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	2	4	no	—
710	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
711	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
712	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
713	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
714	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
715	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
728	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
730	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
731	Q₁₆	—	2	2	no	—
732	Q₁₆	—	4	4	no	—
733	SD₁₆	—	2	2	no	—
734	SD₁₆	—	2	2	no	—
735	SD₁₆	—	4	4	no	—
736	D₈	—	2	2	no	—
737	M₁₆	—	2	4	no	—
738	M₁₆	—	4	4	no	—
739	C₂×C₈	—	2	2	no	—
740	C₂×C₈	—	2	2	no	—
741	C₂×C₈	—	4	4	no	—
742	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
743	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
744	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
745	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
746	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
763	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
764	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
765	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
766	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
767	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
768	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	1	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	—	2	1	no	—
777	C₂²⋊C₄	—	2	1	no	—
778	C₂²⋊C₄	—	2	1	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
781	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
782	C₄²	—	2	1	no	—
783	C₄²	—	2	1	no	—
784	C₄²	—	2	1	no	—
785	C₄²	—	2	1	no	—
786	C₄²	—	2	1	no	—
787	C₄²	—	2	1	no	—
788	C₄²	—	2	4	no	—
789	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
790	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
791	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
792	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
793	C₂³	—	2	1	no	—
794	C₂³	—	2	1	no	—
795	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
796	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
797	Q₈	—	2	4	no	—
798	Q₈	—	2	1	no	—
799	Q₈	—	2	1	no	—
800	Q₈	—	2	4	no	—
801	Q₈	—	2	4	no	—
802	Q₈	—	2	1	no	—
803	Q₈	—	4	8	no	—
804	Q₈	—	4	4	no	—
805	Q₈	—	4	4	no	—
806	Q₈	—	8	2	no	—
807	Q₈	C₂×#41×C₃₁	1	2	yes	—
808	D₄	—	2	4	no	—
809	D₄	—	2	8	no	—
810	D₄	—	2	4	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	4	no	—
813	D₄	—	2	1	no	—
814	D₄	—	2	1	no	—
815	D₄	—	2	1	no	—
816	D₄	—	4	8	no	—
817	D₄	—	4	2	no	—
818	D₄	—	8	4	no	—
819	D₄	C₂×#41×C₃₁	1	2	yes	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	4	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	4	8	no	—
834	C₂×C₄	—	4	8	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	4	2	no	—
837	C₂×C₄	—	4	2	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	4	2	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	8	2	no	—
842	C₂×C₄	—	8	4	no	—
843	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
844	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
847	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
849	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
850	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
851	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
852	C₈	—	2	1	no	—
853	C₈	—	2	1	no	—
854	C₈	—	2	1	no	—
855	C₈	—	2	1	no	—
856	C₈	—	2	4	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	4	no	—
861	C₂²	—	2	4	no	—
862	C₂²	—	2	4	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	1	no	—
868	C₂²	C₃₁×#546	1	2	yes	—
869	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
870	C₄	—	2	2	no	—
871	C₄	—	2	4	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	4	4	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	4	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	1	no	—
881	C₄	C₃₁×#546	1	2	yes	—
882	C₄	C₃₁×#577	1	2	yes	—
883	C₄	C₃₁×#578	1	2	yes	—
884	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
885	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
886	C₂	—	2	2	no	—
887	C₂	—	4	4	no	—
888	C₂	—	4	2	no	—
889	C₂	—	8	1	no	—
890	C₂	C₂×C₃₁×#546	1	1	yes	characteristic
891	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
892	C₂	C₂×C₃₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3511	C₂	semidirect
2. C₃₁×#3499	C₂	semidirect
3. C₃₁×#3331	C₂	semidirect
4. C₃₁×#3330	C₂	semidirect
5. C₃₁×#3329	C₂	semidirect
6. C₃₁×#3328	C₂	semidirect
7. C₃₁×#3303	C₂	semidirect
8. C₃₁×#3302	C₂	semidirect
9. C₃₁×#3299	C₂	semidirect
10. C₃₁×#3298	C₂	semidirect
11. C₂×C₃₁×#487	C₂	semidirect
12. C₃₁×#3097	C₂	semidirect
13. C₃₁×#3079	C₂	semidirect
14. C₃₁×#3063	C₂	semidirect
15. C₃₁×#3039	C₂	semidirect
16. C₃₁×#3013	C₂	semidirect
17. C₄×C₃₁×#135	C₂	semidirect
18. C₃₁×#2931	C₂	semidirect
19. C₃₁×#2898	C₂	semidirect
244. #41×C₃₁	#41	semidirect
346. #61217	C₃₁	direct (N × H)
411. #3511	C₂×C₃₁	semidirect
412. #3499	C₂×C₃₁	semidirect
413. #3331	C₂×C₃₁	semidirect
414. #3330	C₂×C₃₁	semidirect
415. #3329	C₂×C₃₁	semidirect
416. #3328	C₂×C₃₁	semidirect
417. #3303	C₂×C₃₁	semidirect
418. #3302	C₂×C₃₁	semidirect
419. #3299	C₂×C₃₁	semidirect
420. #3298	C₂×C₃₁	semidirect
421. C₂×#487	C₂×C₃₁	semidirect
422. #3097	C₂×C₃₁	semidirect
423. #3079	C₂×C₃₁	semidirect
424. #3063	C₂×C₃₁	semidirect
425. #3039	C₂×C₃₁	semidirect
426. #3013	C₂×C₃₁	semidirect
427. C₄×#135	C₂×C₃₁	semidirect
428. #2931	C₂×C₃₁	semidirect
429. #2898	C₂×C₃₁	semidirect
680. C₃₁	#61217	direct (N × H)
691. #41	#41×C₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3511	2
C₃₁×#3499	2
C₃₁×#3331	2
C₃₁×#3330	2
C₃₁×#3329	2
C₃₁×#3328	2
C₃₁×#3303	2
C₃₁×#3302	2
C₃₁×#3299	2
C₃₁×#3298	2
C₂×C₃₁×#487	2
C₃₁×#3097	2
C₃₁×#3079	2
C₃₁×#3063	2
C₃₁×#3039	2
C₃₁×#3013	2
C₄×C₃₁×#135	2
C₃₁×#2931	2
C₃₁×#2898	2
#61217	31

Subgroups — C31×#61217 #21517976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61217 #21517976