Subgroups — C₃₁×#61083 #21517842

Order 7936.

2674 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#577	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3499	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3270	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3269	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3267	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3266	C₂	1	4	yes	maximal, complemented
9	C₂×C₃₁×#497	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3059	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3057	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3040	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3039	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3011	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3011	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3010	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3009	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2943	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2932	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
24	C₃₁×#578	—	2	8	no	—
25	C₃₁×#577	—	2	8	no	—
26	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#137	C₂²	1	2	yes	—
29	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
30	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
32	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
34	C₂×C₃₁×#135	C₂²	1	2	yes	—
35	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
37	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
38	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
39	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
40	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
41	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
42	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
43	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
44	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic, complemented
45	D₄×Q₈×C₃₁	C₂²	1	4	yes	complemented
46	C₃₁×#548	C₂²	1	4	yes	—
47	C₃₁×#547	—	2	4	no	—
48	C₃₁×#547	C₂²	1	4	yes	complemented
49	C₃₁×#546	—	2	4	no	—
50	C₃₁×#546	C₂²	1	4	yes	—
51	C₃₁×#536	—	2	1	no	—
52	C₃₁×#536	—	2	1	no	—
53	C₃₁×#536	—	2	1	no	—
54	C₃₁×#536	C₂²	1	1	yes	characteristic
55	C₃₁×#536	C₂²	1	1	yes	characteristic
56	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#535	—	2	1	no	—
58	C₃₁×#535	C₂²	1	1	yes	characteristic
59	C₃₁×#532	—	2	1	no	—
60	C₃₁×#532	—	2	1	no	—
61	C₃₁×#532	C₂²	1	1	yes	characteristic
62	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
63	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₃₁×#124	—	2	1	no	—
65	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
66	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
67	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#497	C₂²	1	4	yes	complemented
69	C₃₁×#497	C₂²	1	4	yes	complemented
70	C₃₁×#470	C₂²	1	4	yes	complemented
71	C₃₁×#468	C₂²	1	4	yes	complemented
72	C₃₁×#467	C₂²	1	4	yes	complemented
73	C₃₁×#465	C₂²	1	4	yes	complemented
74	C₃₁×#464	C₂²	1	4	yes	complemented
75	C₃₁×#463	C₂²	1	4	yes	complemented
76	C₃₁×#462	C₂²	1	4	yes	complemented
77	C₃₁×#461	C₂²	1	4	yes	complemented
78	C₃₁×#452	C₂²	1	4	yes	—
79	C₃₁×#452	C₂²	1	4	yes	complemented
80	C₃₁×#452	C₂²	1	4	yes	complemented
81	C₃₁×#451	C₂²	1	4	yes	complemented
82	C₃₁×#451	C₂²	1	4	yes	complemented
83	C₃₁×#450	C₂²	1	4	yes	—
84	C₃₁×#449	C₂²	1	4	yes	complemented
85	C₃₁×#448	C₂²	1	4	yes	complemented
86	C₃₁×#442	C₂²	1	2	yes	complemented
87	C₃₁×#441	C₂²	1	2	yes	complemented
88	C₃₁×#440	C₂²	1	2	yes	complemented
89	C₃₁×#440	C₂²	1	2	yes	complemented
90	C₃₁×#435	C₂²	1	4	yes	complemented
91	C₃₁×#435	C₂²	1	4	yes	complemented
92	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#418	C₂²	1	1	yes	characteristic
98	C₃₁×#416	C₂²	1	1	yes	characteristic
99	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#408	C₂²	1	1	yes	characteristic
101	C₃₁×#408	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×2₋¹⁺⁴	—	2	4	no	—
104	C₃₁×2₋¹⁺⁴	—	2	4	no	—
105	C₃₁×2₋¹⁺⁴	—	2	4	no	—
106	C₃₁×2₋¹⁺⁴	—	4	2	no	—
107	C₃₁×2₋¹⁺⁴	—	4	2	no	—
108	C₃₁×2₋¹⁺⁴	—	4	2	no	—
109	C₃₁×H(5,𝔽₂)	—	2	4	no	—
110	C₃₁×H(5,𝔽₂)	—	4	2	no	—
111	C₂×#41×C₃₁	—	2	1	no	—
112	C₂×#41×C₃₁	—	2	1	no	—
113	C₂×#41×C₃₁	—	2	1	no	—
114	C₂×#41×C₃₁	—	2	1	no	—
115	C₂×#41×C₃₁	—	2	2	no	—
116	C₂×#41×C₃₁	—	2	2	no	—
117	C₂×#41×C₃₁	—	2	2	no	—
118	C₂×#41×C₃₁	C₂³	1	2	yes	—
119	C₂×#41×C₃₁	C₂³	1	2	yes	—
120	C₂×#41×C₃₁	C₂³	1	2	yes	—
121	C₂×#41×C₃₁	C₂³	1	2	yes	—
122	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
123	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
124	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
125	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₃₁	—	2	1	no	—
127	C₂²×Q₈×C₃₁	—	2	1	no	—
128	C₂²×Q₈×C₃₁	—	2	1	no	—
129	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
130	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
133	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
134	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
135	C₂²×D₄×C₃₁	—	2	1	no	—
136	C₂²×D₄×C₃₁	—	2	2	no	—
137	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
139	C₃₁×#137	—	2	4	no	—
140	C₃₁×#137	—	2	4	no	—
141	C₃₁×#137	—	2	4	no	—
142	C₃₁×#137	—	2	8	no	—
143	C₃₁×#137	—	2	8	no	—
144	C₃₁×#137	—	2	8	no	—
145	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
146	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
147	C₃₁×#135	—	2	8	no	—
148	C₃₁×#135	—	2	8	no	—
149	C₃₁×#135	D₄	1	8	yes	complemented
150	C₂×Q₁₆×C₃₁	—	2	8	no	—
151	C₂×Q₁₆×C₃₁	—	2	4	no	—
152	C₂×Q₁₆×C₃₁	—	4	2	no	—
153	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
159	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×SD₁₆×C₃₁	—	2	8	no	—
161	C₂×SD₁₆×C₃₁	—	2	4	no	—
162	C₂×SD₁₆×C₃₁	—	4	2	no	—
163	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
167	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
168	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
169	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
170	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
171	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
172	C₂×D₈×C₃₁	C₂³	1	2	yes	—
173	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
174	C₃₁×#131	—	2	4	no	—
175	C₃₁×#131	—	2	4	no	—
176	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
177	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
179	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
180	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
181	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
182	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
183	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
184	C₃₁×C₄⋊Q₈	—	2	1	no	—
185	C₃₁×C₄⋊Q₈	—	2	1	no	—
186	C₃₁×C₄⋊Q₈	—	2	1	no	—
187	C₃₁×C₄⋊Q₈	—	2	4	no	—
188	C₃₁×C₄⋊Q₈	—	2	1	no	—
189	C₃₁×C₄⋊Q₈	—	2	1	no	—
190	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
191	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
192	C₃₁×#127	—	2	1	no	—
193	C₃₁×#127	D₄	1	1	yes	characteristic
194	C₃₁×#124	—	2	1	no	—
195	C₃₁×#124	—	2	1	no	—
196	C₃₁×#124	—	2	1	no	—
197	C₃₁×#124	—	2	1	no	—
198	C₃₁×#124	—	2	4	no	—
199	C₃₁×#124	—	2	1	no	—
200	C₃₁×#124	—	2	1	no	—
201	C₃₁×#124	D₄	1	1	yes	characteristic
202	C₃₁×#124	D₄	1	1	yes	characteristic
203	C₃₁×#124	C₂³	1	4	yes	—
204	C₃₁×#123	—	2	2	no	—
205	C₃₁×#123	—	2	2	no	—
206	C₃₁×#123	—	2	2	no	—
207	C₃₁×#123	—	2	4	no	—
208	C₃₁×#123	—	2	4	no	—
209	C₃₁×#123	—	2	4	no	—
210	C₃₁×C₂²⋊Q₈	—	2	4	no	—
211	C₃₁×C₂²⋊Q₈	—	2	4	no	—
212	C₃₁×C₂²⋊Q₈	—	2	4	no	—
213	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
214	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
215	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
216	C₃₁×#121	—	2	4	no	—
217	C₃₁×#121	—	2	4	no	—
218	C₃₁×#121	—	2	4	no	—
219	C₃₁×#121	D₄	1	4	yes	—
220	C₃₁×#121	C₂³	1	4	yes	—
221	C₃₁×#120	—	2	4	no	—
222	C₃₁×#120	—	2	2	no	—
223	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
224	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
225	C₄×D₄×C₃₁	—	2	4	no	—
226	C₄×D₄×C₃₁	—	2	2	no	—
227	C₄×D₄×C₃₁	—	2	2	no	—
228	C₄×D₄×C₃₁	—	2	4	no	—
229	C₄×D₄×C₃₁	C₂³	1	2	yes	—
230	C₄×D₄×C₃₁	C₂³	1	2	yes	—
231	C₄×D₄×C₃₁	C₂³	1	4	yes	—
232	C₃₁×#117	—	2	1	no	—
233	C₃₁×#117	—	2	1	no	—
234	C₃₁×#117	C₂³	1	1	yes	characteristic
235	C₃₁×#117	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
237	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
238	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
239	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
240	C₂×C₄²×C₃₁	—	2	1	no	—
241	C₂×C₄²×C₃₁	—	2	1	no	—
242	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
243	C₃₁×#107	C₂³	1	2	yes	—
244	C₃₁×#106	C₂³	1	2	yes	—
245	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
246	C₃₁×#103	C₂³	1	2	yes	—
247	C₃₁×#103	C₂³	1	2	yes	—
248	C₃₁×#103	C₂³	1	4	yes	—
249	C₃₁×#103	C₂³	1	4	yes	—
250	C₃₁×#103	C₂³	1	4	yes	—
251	C₃₁×#102	C₂³	1	2	yes	—
252	C₃₁×#102	C₂³	1	2	yes	—
253	C₃₁×#102	C₂³	1	4	yes	—
254	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
255	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
256	C₃₁×#97	C₂³	1	2	yes	—
257	C₃₁×#97	C₂³	1	2	yes	—
258	C₂⁴×C₃₁	—	2	2	no	—
259	C₂⁴×C₃₁	—	2	1	no	—
260	#41×C₃₁	—	2	2	no	—
261	#41×C₃₁	—	2	2	no	—
262	#41×C₃₁	—	2	2	no	—
263	#41×C₃₁	—	2	2	no	—
264	#41×C₃₁	—	2	2	no	—
265	#41×C₃₁	—	2	2	no	—
266	#41×C₃₁	—	2	4	no	—
267	#41×C₃₁	—	2	4	no	—
268	#41×C₃₁	—	2	4	no	—
269	#41×C₃₁	—	2	4	no	—
270	#41×C₃₁	—	4	2	no	—
271	#41×C₃₁	—	4	2	no	—
272	#41×C₃₁	—	4	2	no	—
273	#41×C₃₁	—	4	2	no	—
274	#41×C₃₁	—	4	4	no	—
275	#41×C₃₁	—	4	4	no	—
276	#41×C₃₁	—	4	4	no	—
277	#41×C₃₁	—	4	4	no	—
278	#41×C₃₁	—	4	8	no	—
279	#41×C₃₁	—	4	8	no	—
280	#41×C₃₁	—	4	8	no	—
281	#41×C₃₁	C₂×D₄	1	4	yes	—
282	#41×C₃₁	C₂×D₄	1	4	yes	—
283	C₂×Q₈×C₃₁	—	2	2	no	—
284	C₂×Q₈×C₃₁	—	2	2	no	—
285	C₂×Q₈×C₃₁	—	2	2	no	—
286	C₂×Q₈×C₃₁	—	2	1	no	—
287	C₂×Q₈×C₃₁	—	2	1	no	—
288	C₂×Q₈×C₃₁	—	2	1	no	—
289	C₂×Q₈×C₃₁	—	2	4	no	—
290	C₂×Q₈×C₃₁	—	2	4	no	—
291	C₂×Q₈×C₃₁	—	2	4	no	—
292	C₂×Q₈×C₃₁	—	2	2	no	—
293	C₂×Q₈×C₃₁	—	2	2	no	—
294	C₂×Q₈×C₃₁	—	2	2	no	—
295	C₂×Q₈×C₃₁	—	2	2	no	—
296	C₂×Q₈×C₃₁	—	2	2	no	—
297	C₂×Q₈×C₃₁	—	2	2	no	—
298	C₂×Q₈×C₃₁	—	4	2	no	—
299	C₂×Q₈×C₃₁	—	4	2	no	—
300	C₂×Q₈×C₃₁	—	4	2	no	—
301	C₂×Q₈×C₃₁	—	4	4	no	—
302	C₂×Q₈×C₃₁	—	4	4	no	—
303	C₂×Q₈×C₃₁	—	4	4	no	—
304	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
305	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
306	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
307	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
308	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
309	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
311	C₂×D₄×C₃₁	—	2	1	no	—
312	C₂×D₄×C₃₁	—	2	1	no	—
313	C₂×D₄×C₃₁	—	2	4	no	—
314	C₂×D₄×C₃₁	—	2	2	no	—
315	C₂×D₄×C₃₁	—	2	2	no	—
316	C₂×D₄×C₃₁	—	2	2	no	—
317	C₂×D₄×C₃₁	—	2	2	no	—
318	C₂×D₄×C₃₁	—	2	4	no	—
319	C₂×D₄×C₃₁	—	2	2	no	—
320	C₂×D₄×C₃₁	—	2	2	no	—
321	C₂×D₄×C₃₁	—	2	1	no	—
322	C₂×D₄×C₃₁	—	2	2	no	—
323	C₂×D₄×C₃₁	—	4	2	no	—
324	C₂×D₄×C₃₁	—	4	4	no	—
325	C₂×D₄×C₃₁	—	4	8	no	—
326	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
327	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
328	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
329	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
330	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
331	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
332	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₃₁	—	2	1	no	—
335	C₂²×C₄×C₃₁	—	2	1	no	—
336	C₂²×C₄×C₃₁	—	2	1	no	—
337	C₂²×C₄×C₃₁	—	2	1	no	—
338	C₂²×C₄×C₃₁	—	2	1	no	—
339	C₂²×C₄×C₃₁	—	2	2	no	—
340	C₂²×C₄×C₃₁	—	2	2	no	—
341	C₂²×C₄×C₃₁	—	2	2	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	C₂×D₄	1	2	yes	—
349	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
352	Q₁₆×C₃₁	—	2	4	no	—
353	Q₁₆×C₃₁	—	2	4	no	—
354	Q₁₆×C₃₁	—	2	4	no	—
355	Q₁₆×C₃₁	—	2	4	no	—
356	Q₁₆×C₃₁	—	2	4	no	—
357	Q₁₆×C₃₁	—	4	4	no	—
358	Q₁₆×C₃₁	C₂×D₄	1	4	yes	—
359	SD₁₆×C₃₁	—	2	4	no	—
360	SD₁₆×C₃₁	—	2	4	no	—
361	SD₁₆×C₃₁	—	2	4	no	—
362	SD₁₆×C₃₁	—	2	4	no	—
363	SD₁₆×C₃₁	—	2	4	no	—
364	SD₁₆×C₃₁	—	2	4	no	—
365	SD₁₆×C₃₁	—	4	4	no	—
366	SD₁₆×C₃₁	C₂×D₄	1	4	yes	—
367	SD₁₆×C₃₁	C₂×D₄	1	4	yes	—
368	D₈×C₃₁	—	2	4	no	—
369	D₈×C₃₁	C₂×D₄	1	4	yes	—
370	M₁₆×C₃₁	—	2	2	no	—
371	M₁₆×C₃₁	—	2	2	no	—
372	M₁₆×C₃₁	—	2	4	no	—
373	M₁₆×C₃₁	—	2	4	no	—
374	C₂×C₈×C₃₁	—	2	2	no	—
375	C₂×C₈×C₃₁	—	2	4	no	—
376	C₂×C₈×C₃₁	—	2	4	no	—
377	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
378	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
379	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
380	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
381	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₃₁	—	2	4	no	—
384	C₄⋊C₄×C₃₁	—	2	4	no	—
385	C₄⋊C₄×C₃₁	—	2	4	no	—
386	C₄⋊C₄×C₃₁	—	2	4	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	4	no	—
390	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
391	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
392	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
393	C₂²⋊C₄×C₃₁	—	2	4	no	—
394	C₂²⋊C₄×C₃₁	—	2	1	no	—
395	C₂²⋊C₄×C₃₁	—	2	1	no	—
396	C₂²⋊C₄×C₃₁	—	2	4	no	—
397	C₂²⋊C₄×C₃₁	—	2	4	no	—
398	C₂²⋊C₄×C₃₁	—	2	4	no	—
399	C₂²⋊C₄×C₃₁	—	2	4	no	—
400	C₂²⋊C₄×C₃₁	—	2	4	no	—
401	C₂²⋊C₄×C₃₁	—	2	2	no	—
402	C₂²⋊C₄×C₃₁	—	2	2	no	—
403	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
404	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
405	C₄²×C₃₁	—	2	1	no	—
406	C₄²×C₃₁	—	2	1	no	—
407	C₄²×C₃₁	—	2	2	no	—
408	C₄²×C₃₁	—	2	2	no	—
409	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
410	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
411	C₄²×C₃₁	C₂⁴	1	2	yes	—
412	#61083	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
413	C₂³×C₃₁	—	2	1	no	—
414	C₂³×C₃₁	—	2	1	no	—
415	C₂³×C₃₁	—	2	2	no	—
416	C₂³×C₃₁	—	4	4	no	—
417	C₂³×C₃₁	—	4	2	no	—
418	C₂³×C₃₁	—	8	2	no	—
419	C₂³×C₃₁	—	8	4	no	—
420	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
421	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
422	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
423	Q₈×C₃₁	—	2	2	no	—
424	Q₈×C₃₁	—	2	2	no	—
425	Q₈×C₃₁	—	2	1	no	—
426	Q₈×C₃₁	—	2	1	no	—
427	Q₈×C₃₁	—	2	2	no	—
428	Q₈×C₃₁	—	2	2	no	—
429	Q₈×C₃₁	—	2	2	no	—
430	Q₈×C₃₁	—	2	2	no	—
431	Q₈×C₃₁	—	2	2	no	—
432	Q₈×C₃₁	—	2	2	no	—
433	Q₈×C₃₁	—	4	4	no	—
434	Q₈×C₃₁	—	4	4	no	—
435	Q₈×C₃₁	—	4	4	no	—
436	Q₈×C₃₁	—	4	2	no	—
437	Q₈×C₃₁	—	4	2	no	—
438	Q₈×C₃₁	—	4	2	no	—
439	Q₈×C₃₁	C₂²×D₄	1	2	yes	—
440	Q₈×C₃₁	C₂²×D₄	1	2	yes	—
441	D₄×C₃₁	—	2	4	no	—
442	D₄×C₃₁	—	2	4	no	—
443	D₄×C₃₁	—	2	4	no	—
444	D₄×C₃₁	—	2	4	no	—
445	D₄×C₃₁	—	2	2	no	—
446	D₄×C₃₁	—	2	2	no	—
447	D₄×C₃₁	—	2	2	no	—
448	D₄×C₃₁	—	2	1	no	—
449	D₄×C₃₁	—	2	1	no	—
450	D₄×C₃₁	—	2	2	no	—
451	D₄×C₃₁	—	4	4	no	—
452	D₄×C₃₁	—	4	4	no	—
453	D₄×C₃₁	—	4	4	no	—
454	D₄×C₃₁	—	4	4	no	—
455	D₄×C₃₁	—	4	4	no	—
456	D₄×C₃₁	—	4	4	no	—
457	D₄×C₃₁	—	4	2	no	—
458	D₄×C₃₁	—	8	4	no	—
459	D₄×C₃₁	C₂²×D₄	1	2	yes	—
460	D₄×C₃₁	C₂²×D₄	1	2	yes	—
461	C₂×C₄×C₃₁	—	2	1	no	—
462	C₂×C₄×C₃₁	—	2	1	no	—
463	C₂×C₄×C₃₁	—	2	4	no	—
464	C₂×C₄×C₃₁	—	2	4	no	—
465	C₂×C₄×C₃₁	—	2	2	no	—
466	C₂×C₄×C₃₁	—	2	2	no	—
467	C₂×C₄×C₃₁	—	2	2	no	—
468	C₂×C₄×C₃₁	—	2	2	no	—
469	C₂×C₄×C₃₁	—	2	2	no	—
470	C₂×C₄×C₃₁	—	2	2	no	—
471	C₂×C₄×C₃₁	—	2	2	no	—
472	C₂×C₄×C₃₁	—	2	2	no	—
473	C₂×C₄×C₃₁	—	2	2	no	—
474	C₂×C₄×C₃₁	—	4	2	no	—
475	C₂×C₄×C₃₁	—	4	4	no	—
476	C₂×C₄×C₃₁	—	4	4	no	—
477	C₂×C₄×C₃₁	—	4	4	no	—
478	C₂×C₄×C₃₁	—	4	4	no	—
479	C₂×C₄×C₃₁	—	4	4	no	—
480	C₂×C₄×C₃₁	—	4	4	no	—
481	C₂×C₄×C₃₁	—	4	4	no	—
482	C₂×C₄×C₃₁	—	4	4	no	—
483	C₂×C₄×C₃₁	—	4	2	no	—
484	C₂×C₄×C₃₁	—	4	2	no	—
485	C₂×C₄×C₃₁	—	4	2	no	—
486	C₂×C₄×C₃₁	—	8	2	no	—
487	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
494	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
495	C₈×C₃₁	—	2	2	no	—
496	C₈×C₃₁	—	2	2	no	—
497	C₈×C₃₁	—	2	2	no	—
498	C₈×C₃₁	C₂²×D₄	1	2	yes	—
499	C₈×C₃₁	C₂²×D₄	1	2	yes	—
500	C₂×#578	C₂×C₃₁	1	1	yes	characteristic, complemented
501	C₂×#577	C₂×C₃₁	1	1	yes	characteristic, complemented
502	#3500	C₂×C₃₁	1	1	yes	characteristic, complemented
503	#3499	C₂×C₃₁	1	1	yes	characteristic, complemented
504	#3270	C₂×C₃₁	1	4	yes	complemented
505	#3269	C₂×C₃₁	1	4	yes	complemented
506	#3267	C₂×C₃₁	1	4	yes	complemented
507	#3266	C₂×C₃₁	1	4	yes	complemented
508	C₂×#497	C₂×C₃₁	1	1	yes	characteristic, complemented
509	#3059	C₂×C₃₁	1	1	yes	characteristic, complemented
510	#3057	C₂×C₃₁	1	1	yes	characteristic, complemented
511	#3040	C₂×C₃₁	1	1	yes	characteristic, complemented
512	#3039	C₂×C₃₁	1	1	yes	characteristic, complemented
513	#3011	C₂×C₃₁	1	1	yes	characteristic, complemented
514	#3011	C₂×C₃₁	1	1	yes	characteristic, complemented
515	#3010	C₂×C₃₁	1	1	yes	characteristic, complemented
516	#3009	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#2943	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#2932	C₂×C₃₁	1	1	yes	characteristic, complemented
519	C₂²×C₃₁	—	2	2	no	—
520	C₂²×C₃₁	—	2	4	no	—
521	C₂²×C₃₁	—	2	4	no	—
522	C₂²×C₃₁	—	2	2	no	—
523	C₂²×C₃₁	—	2	2	no	—
524	C₂²×C₃₁	—	2	2	no	—
525	C₂²×C₃₁	—	2	2	no	—
526	C₂²×C₃₁	—	4	2	no	—
527	C₂²×C₃₁	—	4	2	no	—
528	C₂²×C₃₁	—	4	4	no	—
529	C₂²×C₃₁	—	4	2	no	—
530	C₂²×C₃₁	—	16	2	no	—
531	C₂²×C₃₁	—	16	4	no	—
532	C₂²×C₃₁	D₄²	1	2	yes	—
533	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
534	C₄×C₃₁	—	2	2	no	—
535	C₄×C₃₁	—	2	2	no	—
536	C₄×C₃₁	—	2	2	no	—
537	C₄×C₃₁	—	2	2	no	—
538	C₄×C₃₁	—	2	2	no	—
539	C₄×C₃₁	—	2	2	no	—
540	C₄×C₃₁	—	4	2	no	—
541	C₄×C₃₁	—	4	2	no	—
542	C₄×C₃₁	—	4	2	no	—
543	C₄×C₃₁	—	4	2	no	—
544	C₄×C₃₁	—	4	2	no	—
545	C₄×C₃₁	D₄²	1	2	yes	—
546	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
547	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
548	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic
549	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic
550	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic, complemented
551	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
552	#578	—	2	8	no	—
553	#577	—	2	8	no	—
554	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
555	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
556	C₂×#137	C₂²×C₃₁	1	2	yes	—
557	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
558	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
559	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
560	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
561	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
562	C₂×#135	C₂²×C₃₁	1	2	yes	—
563	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
564	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
565	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
566	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
567	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
568	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
569	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
570	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
571	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
572	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic, complemented
573	D₄×Q₈	C₂²×C₃₁	1	4	yes	complemented
574	#548	C₂²×C₃₁	1	4	yes	—
575	#547	—	2	4	no	—
576	#547	C₂²×C₃₁	1	4	yes	complemented
577	#546	—	2	4	no	—
578	#546	C₂²×C₃₁	1	4	yes	—
579	#536	—	2	1	no	—
580	#536	—	2	1	no	—
581	#536	—	2	1	no	—
582	#536	C₂²×C₃₁	1	1	yes	characteristic
583	#536	C₂²×C₃₁	1	1	yes	characteristic
584	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
585	#535	—	2	1	no	—
586	#535	C₂²×C₃₁	1	1	yes	characteristic
587	#532	—	2	1	no	—
588	#532	—	2	1	no	—
589	#532	C₂²×C₃₁	1	1	yes	characteristic
590	C₂×C₄⋊Q₈	—	2	1	no	—
591	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
592	C₂×#124	—	2	1	no	—
593	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
594	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
595	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
596	#497	C₂²×C₃₁	1	4	yes	complemented
597	#497	C₂²×C₃₁	1	4	yes	complemented
598	#470	C₂²×C₃₁	1	4	yes	complemented
599	#468	C₂²×C₃₁	1	4	yes	complemented
600	#467	C₂²×C₃₁	1	4	yes	complemented
601	#465	C₂²×C₃₁	1	4	yes	complemented
602	#464	C₂²×C₃₁	1	4	yes	complemented
603	#463	C₂²×C₃₁	1	4	yes	complemented
604	#462	C₂²×C₃₁	1	4	yes	complemented
605	#461	C₂²×C₃₁	1	4	yes	complemented
606	#452	C₂²×C₃₁	1	4	yes	—
607	#452	C₂²×C₃₁	1	4	yes	complemented
608	#452	C₂²×C₃₁	1	4	yes	complemented
609	#451	C₂²×C₃₁	1	4	yes	complemented
610	#451	C₂²×C₃₁	1	4	yes	complemented
611	#450	C₂²×C₃₁	1	4	yes	—
612	#449	C₂²×C₃₁	1	4	yes	complemented
613	#448	C₂²×C₃₁	1	4	yes	complemented
614	#442	C₂²×C₃₁	1	2	yes	complemented
615	#441	C₂²×C₃₁	1	2	yes	complemented
616	#440	C₂²×C₃₁	1	2	yes	complemented
617	#440	C₂²×C₃₁	1	2	yes	complemented
618	#435	C₂²×C₃₁	1	4	yes	complemented
619	#435	C₂²×C₃₁	1	4	yes	complemented
620	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
621	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
622	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
623	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
624	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
625	#418	C₂²×C₃₁	1	1	yes	characteristic
626	#416	C₂²×C₃₁	1	1	yes	characteristic
627	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
628	#408	C₂²×C₃₁	1	1	yes	characteristic
629	#408	C₂²×C₃₁	1	1	yes	characteristic, complemented
630	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic, complemented
631	C₂×C₃₁	—	2	2	no	—
632	C₂×C₃₁	—	4	2	no	—
633	C₂×C₃₁	—	4	2	no	—
634	C₂×C₃₁	—	4	2	no	—
635	C₂×C₃₁	—	4	2	no	—
636	C₂×C₃₁	—	8	2	no	—
637	C₂×C₃₁	C₂×D₄²	1	1	yes	characteristic
638	C₂×C₃₁	#3586	1	2	yes	—
639	2₋¹⁺⁴	—	2	4	no	—
640	2₋¹⁺⁴	—	2	4	no	—
641	2₋¹⁺⁴	—	2	4	no	—
642	2₋¹⁺⁴	—	4	2	no	—
643	2₋¹⁺⁴	—	4	2	no	—
644	2₋¹⁺⁴	—	4	2	no	—
645	H(5,𝔽₂)	—	2	4	no	—
646	H(5,𝔽₂)	—	4	2	no	—
647	C₂×#41	—	2	1	no	—
648	C₂×#41	—	2	1	no	—
649	C₂×#41	—	2	1	no	—
650	C₂×#41	—	2	1	no	—
651	C₂×#41	—	2	2	no	—
652	C₂×#41	—	2	2	no	—
653	C₂×#41	—	2	2	no	—
654	C₂×#41	C₂³×C₃₁	1	2	yes	—
655	C₂×#41	C₂³×C₃₁	1	2	yes	—
656	C₂×#41	C₂³×C₃₁	1	2	yes	—
657	C₂×#41	C₂³×C₃₁	1	2	yes	—
658	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
659	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
660	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
661	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
662	C₂²×Q₈	—	2	1	no	—
663	C₂²×Q₈	—	2	1	no	—
664	C₂²×Q₈	—	2	1	no	—
665	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
666	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
667	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
668	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
669	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
670	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
671	C₂²×D₄	—	2	1	no	—
672	C₂²×D₄	—	2	2	no	—
673	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
674	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
675	#137	—	2	4	no	—
676	#137	—	2	4	no	—
677	#137	—	2	4	no	—
678	#137	—	2	8	no	—
679	#137	—	2	8	no	—
680	#137	—	2	8	no	—
681	AGL(1,ℤ/8)	—	2	4	no	—
682	AGL(1,ℤ/8)	—	2	8	no	—
683	#135	—	2	8	no	—
684	#135	—	2	8	no	—
685	#135	D₄×C₃₁	1	8	yes	complemented
686	C₂×Q₁₆	—	2	8	no	—
687	C₂×Q₁₆	—	2	4	no	—
688	C₂×Q₁₆	—	4	2	no	—
689	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
690	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
691	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
692	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
693	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
694	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
695	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
696	C₂×SD₁₆	—	2	8	no	—
697	C₂×SD₁₆	—	2	4	no	—
698	C₂×SD₁₆	—	4	2	no	—
699	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
700	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
701	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
702	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
703	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
704	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
705	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
706	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
708	C₂×D₈	C₂³×C₃₁	1	2	yes	—
709	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
710	#131	—	2	4	no	—
711	#131	—	2	4	no	—
712	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
713	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
714	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
715	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
716	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
717	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
718	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
719	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
720	C₄⋊Q₈	—	2	1	no	—
721	C₄⋊Q₈	—	2	1	no	—
722	C₄⋊Q₈	—	2	1	no	—
723	C₄⋊Q₈	—	2	4	no	—
724	C₄⋊Q₈	—	2	1	no	—
725	C₄⋊Q₈	—	2	1	no	—
726	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
727	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
728	#127	—	2	1	no	—
729	#127	D₄×C₃₁	1	1	yes	characteristic
730	#124	—	2	1	no	—
731	#124	—	2	1	no	—
732	#124	—	2	1	no	—
733	#124	—	2	1	no	—
734	#124	—	2	4	no	—
735	#124	—	2	1	no	—
736	#124	—	2	1	no	—
737	#124	D₄×C₃₁	1	1	yes	characteristic
738	#124	D₄×C₃₁	1	1	yes	characteristic
739	#124	C₂³×C₃₁	1	4	yes	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	4	no	—
744	#123	—	2	4	no	—
745	#123	—	2	4	no	—
746	C₂²⋊Q₈	—	2	4	no	—
747	C₂²⋊Q₈	—	2	4	no	—
748	C₂²⋊Q₈	—	2	4	no	—
749	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
750	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
751	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
752	#121	—	2	4	no	—
753	#121	—	2	4	no	—
754	#121	—	2	4	no	—
755	#121	D₄×C₃₁	1	4	yes	—
756	#121	C₂³×C₃₁	1	4	yes	—
757	#120	—	2	4	no	—
758	#120	—	2	2	no	—
759	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
760	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
761	C₄×D₄	—	2	4	no	—
762	C₄×D₄	—	2	2	no	—
763	C₄×D₄	—	2	2	no	—
764	C₄×D₄	—	2	4	no	—
765	C₄×D₄	C₂³×C₃₁	1	2	yes	—
766	C₄×D₄	C₂³×C₃₁	1	2	yes	—
767	C₄×D₄	C₂³×C₃₁	1	4	yes	—
768	#117	—	2	1	no	—
769	#117	—	2	1	no	—
770	#117	C₂³×C₃₁	1	1	yes	characteristic
771	#117	C₂³×C₃₁	1	1	yes	characteristic
772	C₂×C₄⋊C₄	—	2	2	no	—
773	C₂×C₄⋊C₄	—	2	4	no	—
774	C₂×C₂²⋊C₄	—	2	2	no	—
775	C₂×C₂²⋊C₄	—	2	4	no	—
776	C₂×C₄²	—	2	1	no	—
777	C₂×C₄²	—	2	1	no	—
778	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
779	#107	C₂³×C₃₁	1	2	yes	—
780	#106	C₂³×C₃₁	1	2	yes	—
781	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
782	#103	C₂³×C₃₁	1	2	yes	—
783	#103	C₂³×C₃₁	1	2	yes	—
784	#103	C₂³×C₃₁	1	4	yes	—
785	#103	C₂³×C₃₁	1	4	yes	—
786	#103	C₂³×C₃₁	1	4	yes	—
787	#102	C₂³×C₃₁	1	2	yes	—
788	#102	C₂³×C₃₁	1	2	yes	—
789	#102	C₂³×C₃₁	1	4	yes	—
790	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
791	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
792	#97	C₂³×C₃₁	1	2	yes	—
793	#97	C₂³×C₃₁	1	2	yes	—
794	C₃₁	#61083	1	1	yes	characteristic, direct product factor, Sylow
795	C₂⁴	—	2	2	no	—
796	C₂⁴	—	2	1	no	—
797	#41	—	2	2	no	—
798	#41	—	2	2	no	—
799	#41	—	2	2	no	—
800	#41	—	2	2	no	—
801	#41	—	2	2	no	—
802	#41	—	2	2	no	—
803	#41	—	2	4	no	—
804	#41	—	2	4	no	—
805	#41	—	2	4	no	—
806	#41	—	2	4	no	—
807	#41	—	4	2	no	—
808	#41	—	4	2	no	—
809	#41	—	4	2	no	—
810	#41	—	4	2	no	—
811	#41	—	4	4	no	—
812	#41	—	4	4	no	—
813	#41	—	4	4	no	—
814	#41	—	4	4	no	—
815	#41	—	4	8	no	—
816	#41	—	4	8	no	—
817	#41	—	4	8	no	—
818	#41	C₂×D₄×C₃₁	1	4	yes	—
819	#41	C₂×D₄×C₃₁	1	4	yes	—
820	C₂×Q₈	—	2	2	no	—
821	C₂×Q₈	—	2	2	no	—
822	C₂×Q₈	—	2	2	no	—
823	C₂×Q₈	—	2	1	no	—
824	C₂×Q₈	—	2	1	no	—
825	C₂×Q₈	—	2	1	no	—
826	C₂×Q₈	—	2	4	no	—
827	C₂×Q₈	—	2	4	no	—
828	C₂×Q₈	—	2	4	no	—
829	C₂×Q₈	—	2	2	no	—
830	C₂×Q₈	—	2	2	no	—
831	C₂×Q₈	—	2	2	no	—
832	C₂×Q₈	—	2	2	no	—
833	C₂×Q₈	—	2	2	no	—
834	C₂×Q₈	—	2	2	no	—
835	C₂×Q₈	—	4	2	no	—
836	C₂×Q₈	—	4	2	no	—
837	C₂×Q₈	—	4	2	no	—
838	C₂×Q₈	—	4	4	no	—
839	C₂×Q₈	—	4	4	no	—
840	C₂×Q₈	—	4	4	no	—
841	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
842	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
843	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
844	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
845	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
846	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
847	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
848	C₂×D₄	—	2	1	no	—
849	C₂×D₄	—	2	1	no	—
850	C₂×D₄	—	2	4	no	—
851	C₂×D₄	—	2	2	no	—
852	C₂×D₄	—	2	2	no	—
853	C₂×D₄	—	2	2	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	—	2	4	no	—
856	C₂×D₄	—	2	2	no	—
857	C₂×D₄	—	2	2	no	—
858	C₂×D₄	—	2	1	no	—
859	C₂×D₄	—	2	2	no	—
860	C₂×D₄	—	4	2	no	—
861	C₂×D₄	—	4	4	no	—
862	C₂×D₄	—	4	8	no	—
863	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
864	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
865	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
866	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
867	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
868	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
869	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
870	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	1	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	2	no	—
877	C₂²×C₄	—	2	2	no	—
878	C₂²×C₄	—	2	2	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
886	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
887	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
888	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
889	Q₁₆	—	2	4	no	—
890	Q₁₆	—	2	4	no	—
891	Q₁₆	—	2	4	no	—
892	Q₁₆	—	2	4	no	—
893	Q₁₆	—	2	4	no	—
894	Q₁₆	—	4	4	no	—
895	Q₁₆	C₂×D₄×C₃₁	1	4	yes	—
896	SD₁₆	—	2	4	no	—
897	SD₁₆	—	2	4	no	—
898	SD₁₆	—	2	4	no	—
899	SD₁₆	—	2	4	no	—
900	SD₁₆	—	2	4	no	—
901	SD₁₆	—	2	4	no	—
902	SD₁₆	—	4	4	no	—
903	SD₁₆	C₂×D₄×C₃₁	1	4	yes	—
904	SD₁₆	C₂×D₄×C₃₁	1	4	yes	—
905	D₈	—	2	4	no	—
906	D₈	C₂×D₄×C₃₁	1	4	yes	—
907	M₁₆	—	2	2	no	—
908	M₁₆	—	2	2	no	—
909	M₁₆	—	2	4	no	—
910	M₁₆	—	2	4	no	—
911	C₂×C₈	—	2	2	no	—
912	C₂×C₈	—	2	4	no	—
913	C₂×C₈	—	2	4	no	—
914	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
915	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
916	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
917	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
918	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
919	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
920	C₄⋊C₄	—	2	4	no	—
921	C₄⋊C₄	—	2	4	no	—
922	C₄⋊C₄	—	2	4	no	—
923	C₄⋊C₄	—	2	4	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	4	no	—
927	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
928	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
929	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
930	C₂²⋊C₄	—	2	4	no	—
931	C₂²⋊C₄	—	2	1	no	—
932	C₂²⋊C₄	—	2	1	no	—
933	C₂²⋊C₄	—	2	4	no	—
934	C₂²⋊C₄	—	2	4	no	—
935	C₂²⋊C₄	—	2	4	no	—
936	C₂²⋊C₄	—	2	4	no	—
937	C₂²⋊C₄	—	2	4	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
941	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
942	C₄²	—	2	1	no	—
943	C₄²	—	2	1	no	—
944	C₄²	—	2	2	no	—
945	C₄²	—	2	2	no	—
946	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
947	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
948	C₄²	C₂⁴×C₃₁	1	2	yes	—
949	C₂³	—	2	1	no	—
950	C₂³	—	2	1	no	—
951	C₂³	—	2	2	no	—
952	C₂³	—	4	4	no	—
953	C₂³	—	4	2	no	—
954	C₂³	—	8	2	no	—
955	C₂³	—	8	4	no	—
956	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
957	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
958	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
959	Q₈	—	2	2	no	—
960	Q₈	—	2	2	no	—
961	Q₈	—	2	1	no	—
962	Q₈	—	2	1	no	—
963	Q₈	—	2	2	no	—
964	Q₈	—	2	2	no	—
965	Q₈	—	2	2	no	—
966	Q₈	—	2	2	no	—
967	Q₈	—	2	2	no	—
968	Q₈	—	2	2	no	—
969	Q₈	—	4	4	no	—
970	Q₈	—	4	4	no	—
971	Q₈	—	4	4	no	—
972	Q₈	—	4	2	no	—
973	Q₈	—	4	2	no	—
974	Q₈	—	4	2	no	—
975	Q₈	C₂²×D₄×C₃₁	1	2	yes	—
976	Q₈	C₂²×D₄×C₃₁	1	2	yes	—
977	D₄	—	2	4	no	—
978	D₄	—	2	4	no	—
979	D₄	—	2	4	no	—
980	D₄	—	2	4	no	—
981	D₄	—	2	2	no	—
982	D₄	—	2	2	no	—
983	D₄	—	2	2	no	—
984	D₄	—	2	1	no	—
985	D₄	—	2	1	no	—
986	D₄	—	2	2	no	—
987	D₄	—	4	4	no	—
988	D₄	—	4	4	no	—
989	D₄	—	4	4	no	—
990	D₄	—	4	4	no	—
991	D₄	—	4	4	no	—
992	D₄	—	4	4	no	—
993	D₄	—	4	2	no	—
994	D₄	—	8	4	no	—
995	D₄	C₂²×D₄×C₃₁	1	2	yes	—
996	D₄	C₂²×D₄×C₃₁	1	2	yes	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	4	no	—
1000	C₂×C₄	—	2	4	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	4	2	no	—
1011	C₂×C₄	—	4	4	no	—
1012	C₂×C₄	—	4	4	no	—
1013	C₂×C₄	—	4	4	no	—
1014	C₂×C₄	—	4	4	no	—
1015	C₂×C₄	—	4	4	no	—
1016	C₂×C₄	—	4	4	no	—
1017	C₂×C₄	—	4	4	no	—
1018	C₂×C₄	—	4	4	no	—
1019	C₂×C₄	—	4	2	no	—
1020	C₂×C₄	—	4	2	no	—
1021	C₂×C₄	—	4	2	no	—
1022	C₂×C₄	—	8	2	no	—
1023	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1024	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1025	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1026	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1027	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1028	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1029	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1030	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1031	C₈	—	2	2	no	—
1032	C₈	—	2	2	no	—
1033	C₈	—	2	2	no	—
1034	C₈	C₂²×D₄×C₃₁	1	2	yes	—
1035	C₈	C₂²×D₄×C₃₁	1	2	yes	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	2	2	no	—
1041	C₂²	—	2	4	no	—
1042	C₂²	—	2	4	no	—
1043	C₂²	—	4	2	no	—
1044	C₂²	—	4	2	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	4	no	—
1047	C₂²	—	16	2	no	—
1048	C₂²	—	16	4	no	—
1049	C₂²	D₄²×C₃₁	1	2	yes	—
1050	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1051	C₄	—	2	2	no	—
1052	C₄	—	2	2	no	—
1053	C₄	—	2	2	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	2	2	no	—
1056	C₄	—	2	2	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	2	no	—
1059	C₄	—	4	2	no	—
1060	C₄	—	4	2	no	—
1061	C₄	—	4	2	no	—
1062	C₄	D₄²×C₃₁	1	2	yes	—
1063	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
1064	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1065	C₂	—	2	2	no	—
1066	C₂	—	4	2	no	—
1067	C₂	—	4	2	no	—
1068	C₂	—	4	2	no	—
1069	C₂	—	4	2	no	—
1070	C₂	—	8	2	no	—
1071	C₂	C₂×D₄²×C₃₁	1	1	yes	characteristic
1072	C₂	C₃₁×#3586	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 ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#578	C₂	semidirect
2. C₂×C₃₁×#577	C₂	semidirect
3. C₃₁×#3500	C₂	semidirect
4. C₃₁×#3499	C₂	semidirect
5. C₃₁×#3270	C₂	semidirect
6. C₃₁×#3269	C₂	semidirect
7. C₃₁×#3267	C₂	semidirect
8. C₃₁×#3266	C₂	semidirect
9. C₂×C₃₁×#497	C₂	semidirect
10. C₃₁×#3059	C₂	semidirect
11. C₃₁×#3057	C₂	semidirect
12. C₃₁×#3040	C₂	semidirect
13. C₃₁×#3039	C₂	semidirect
14. C₃₁×#3011	C₂	semidirect
15. C₃₁×#3011	C₂	semidirect
16. C₃₁×#3010	C₂	semidirect
17. C₃₁×#3009	C₂	semidirect
18. C₃₁×#2943	C₂	semidirect
19. C₃₁×#2932	C₂	semidirect
22. C₂×C₃₁×2₋¹⁺⁴	C₂²	semidirect
29. C₂×C₃₁×#137	C₂²	semidirect
30. C₂×C₃₁×#137	C₂²	semidirect
31. C₂×C₃₁×#137	C₂²	semidirect
36. C₂×C₃₁×#135	C₂²	semidirect
37. C₂²×Q₁₆×C₃₁	C₂²	semidirect
38. C₂²×Q₁₆×C₃₁	C₂²	semidirect
39. C₂²×Q₁₆×C₃₁	C₂²	semidirect
44. C₂×C₃₁×#131	C₂²	semidirect
45. D₄×Q₈×C₃₁	C₂²	semidirect
48. C₃₁×#547	C₂²	semidirect
56. C₃₁×#536	C₂²	semidirect
63. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
67. C₄×#41×C₃₁	C₂²	semidirect
68. C₃₁×#497	C₂²	semidirect
69. C₃₁×#497	C₂²	semidirect
70. C₃₁×#470	C₂²	semidirect
71. C₃₁×#468	C₂²	semidirect
72. C₃₁×#467	C₂²	semidirect
73. C₃₁×#465	C₂²	semidirect
74. C₃₁×#464	C₂²	semidirect
75. C₃₁×#463	C₂²	semidirect
76. C₃₁×#462	C₂²	semidirect
77. C₃₁×#461	C₂²	semidirect
79. C₃₁×#452	C₂²	semidirect
80. C₃₁×#452	C₂²	semidirect
81. C₃₁×#451	C₂²	semidirect
82. C₃₁×#451	C₂²	semidirect
84. C₃₁×#449	C₂²	semidirect
85. C₃₁×#448	C₂²	semidirect
86. C₃₁×#442	C₂²	semidirect
87. C₃₁×#441	C₂²	semidirect
88. C₃₁×#440	C₂²	semidirect
89. C₃₁×#440	C₂²	semidirect
90. C₃₁×#435	C₂²	semidirect
91. C₃₁×#435	C₂²	semidirect
92. C₃₁×#427	C₂²	semidirect
93. C₃₁×#423	C₂²	semidirect
94. C₃₁×#419	C₂²	semidirect
95. C₃₁×#419	C₂²	semidirect
96. C₃₁×#419	C₂²	semidirect
99. C₃₁×#416	C₂²	semidirect
101. C₃₁×#408	C₂²	semidirect
102. C₂×C₃₁×#97	C₂²	semidirect
149. C₃₁×#135	D₄	semidirect
412. #61083	C₃₁	direct (N × H)
500. C₂×#578	C₂×C₃₁	semidirect
501. C₂×#577	C₂×C₃₁	semidirect
502. #3500	C₂×C₃₁	semidirect
503. #3499	C₂×C₃₁	semidirect
504. #3270	C₂×C₃₁	semidirect
505. #3269	C₂×C₃₁	semidirect
506. #3267	C₂×C₃₁	semidirect
507. #3266	C₂×C₃₁	semidirect
508. C₂×#497	C₂×C₃₁	semidirect
509. #3059	C₂×C₃₁	semidirect
510. #3057	C₂×C₃₁	semidirect
511. #3040	C₂×C₃₁	semidirect
512. #3039	C₂×C₃₁	semidirect
513. #3011	C₂×C₃₁	semidirect
514. #3011	C₂×C₃₁	semidirect
515. #3010	C₂×C₃₁	semidirect
516. #3009	C₂×C₃₁	semidirect
517. #2943	C₂×C₃₁	semidirect
518. #2932	C₂×C₃₁	semidirect
550. C₂×2₋¹⁺⁴	C₂²×C₃₁	semidirect
557. C₂×#137	C₂²×C₃₁	semidirect
558. C₂×#137	C₂²×C₃₁	semidirect
559. C₂×#137	C₂²×C₃₁	semidirect
564. C₂×#135	C₂²×C₃₁	semidirect
565. C₂²×Q₁₆	C₂²×C₃₁	semidirect
566. C₂²×Q₁₆	C₂²×C₃₁	semidirect
567. C₂²×Q₁₆	C₂²×C₃₁	semidirect
572. C₂×#131	C₂²×C₃₁	semidirect
573. D₄×Q₈	C₂²×C₃₁	semidirect
576. #547	C₂²×C₃₁	semidirect
584. #536	C₂²×C₃₁	semidirect
591. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
595. C₄×#41	C₂²×C₃₁	semidirect
596. #497	C₂²×C₃₁	semidirect
597. #497	C₂²×C₃₁	semidirect
598. #470	C₂²×C₃₁	semidirect
599. #468	C₂²×C₃₁	semidirect
600. #467	C₂²×C₃₁	semidirect
601. #465	C₂²×C₃₁	semidirect
602. #464	C₂²×C₃₁	semidirect
603. #463	C₂²×C₃₁	semidirect
604. #462	C₂²×C₃₁	semidirect
605. #461	C₂²×C₃₁	semidirect
607. #452	C₂²×C₃₁	semidirect
608. #452	C₂²×C₃₁	semidirect
609. #451	C₂²×C₃₁	semidirect
610. #451	C₂²×C₃₁	semidirect
612. #449	C₂²×C₃₁	semidirect
613. #448	C₂²×C₃₁	semidirect
614. #442	C₂²×C₃₁	semidirect
615. #441	C₂²×C₃₁	semidirect
616. #440	C₂²×C₃₁	semidirect
617. #440	C₂²×C₃₁	semidirect
618. #435	C₂²×C₃₁	semidirect
619. #435	C₂²×C₃₁	semidirect
620. #427	C₂²×C₃₁	semidirect
621. #423	C₂²×C₃₁	semidirect
622. #419	C₂²×C₃₁	semidirect
623. #419	C₂²×C₃₁	semidirect
624. #419	C₂²×C₃₁	semidirect
627. #416	C₂²×C₃₁	semidirect
629. #408	C₂²×C₃₁	semidirect
630. C₂×#97	C₂²×C₃₁	semidirect
685. #135	D₄×C₃₁	semidirect
794. C₃₁	#61083	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#578	2
C₂×C₃₁×#577	2
C₃₁×#3500	2
C₃₁×#3499	2
C₃₁×#3270	2
C₃₁×#3269	2
C₃₁×#3267	2
C₃₁×#3266	2
C₂×C₃₁×#497	2
C₃₁×#3059	2
C₃₁×#3057	2
C₃₁×#3040	2
C₃₁×#3039	2
C₃₁×#3011	2
C₃₁×#3010	2
C₃₁×#3009	2
C₃₁×#2943	2
C₃₁×#2932	2
#61083	31

Subgroups — C31×#61083 #21517842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61083 #21517842