Subgroups — C₃₁×#61050 #21517809

Order 7936.

2870 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#577	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3282	C₂	1	4	yes	maximal, complemented
6	D₄×SD₁₆×C₃₁	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3266	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3265	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3154	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3057	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3050	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3043	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3042	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3010	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3009	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3004	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3003	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2949	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2929	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
22	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
23	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
24	C₃₁×#577	—	2	8	no	—
25	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
28	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
31	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
33	C₂²×SD₁₆×C₃₁	—	2	8	no	—
34	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
35	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
36	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
37	C₂²×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
38	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
39	C₂²×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
40	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
41	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic, complemented
42	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
43	D₄×Q₈×C₃₁	—	2	2	no	—
44	D₄×Q₈×C₃₁	C₂²	1	4	yes	complemented
45	C₃₁×#548	—	2	2	no	—
46	C₃₁×#548	C₂²	1	4	yes	complemented
47	C₃₁×#546	—	2	2	no	—
48	C₃₁×#546	C₂²	1	4	yes	—
49	D₄²×C₃₁	—	2	2	no	—
50	D₄²×C₃₁	C₂²	1	4	yes	—
51	C₃₁×#536	—	2	2	no	—
52	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#535	C₂²	1	1	yes	characteristic
55	C₃₁×#535	C₂²	1	1	yes	characteristic
56	C₃₁×#534	—	2	2	no	—
57	C₃₁×#525	—	2	2	no	—
58	C₃₁×#525	C₂²	1	1	yes	characteristic
59	C₃₁×#525	C₂²	1	1	yes	characteristic
60	C₃₁×#525	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₃₁×#120	—	2	2	no	—
62	C₃₁×#519	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#518	C₂²	1	1	yes	characteristic
64	C₃₁×#497	C₂²	1	2	yes	complemented
65	C₃₁×#496	C₂²	1	2	yes	complemented
66	C₃₁×#495	C₂²	1	2	yes	complemented
67	C₃₁×#492	C₂²	1	2	yes	complemented
68	C₃₁×#468	C₂²	1	4	yes	complemented
69	C₃₁×#467	C₂²	1	2	yes	complemented
70	C₃₁×#466	C₂²	1	2	yes	complemented
71	C₃₁×#465	C₂²	1	4	yes	complemented
72	C₃₁×#465	C₂²	1	2	yes	complemented
73	C₃₁×#465	C₂²	1	2	yes	complemented
74	C₃₁×#464	C₂²	1	4	yes	complemented
75	C₃₁×#463	C₂²	1	4	yes	complemented
76	C₃₁×#461	C₂²	1	4	yes	complemented
77	C₃₁×#460	C₂²	1	4	yes	complemented
78	C₃₁×#452	C₂²	1	4	yes	complemented
79	C₃₁×#451	C₂²	1	4	yes	complemented
80	C₃₁×#450	C₂²	1	4	yes	complemented
81	C₃₁×#450	C₂²	1	4	yes	complemented
82	C₃₁×#449	C₂²	1	4	yes	complemented
83	C₃₁×#448	C₂²	1	4	yes	complemented
84	C₃₁×#448	C₂²	1	4	yes	complemented
85	C₃₁×#447	C₂²	1	4	yes	complemented
86	C₃₁×#440	C₂²	1	4	yes	complemented
87	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
88	C₃₁×#435	C₂²	1	4	yes	complemented
89	C₈×D₄×C₃₁	C₂²	1	4	yes	complemented
90	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#418	C₂²	1	1	yes	characteristic
95	C₃₁×#418	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#408	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#407	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
101	C₂⁵×C₃₁	—	2	1	no	—
102	C₃₁×2₋¹⁺⁴	—	2	4	no	—
103	C₃₁×2₋¹⁺⁴	—	4	2	no	—
104	C₃₁×H(5,𝔽₂)	—	2	4	no	—
105	C₃₁×H(5,𝔽₂)	—	4	2	no	—
106	C₂×#41×C₃₁	—	2	1	no	—
107	C₂×#41×C₃₁	—	2	2	no	—
108	C₂×#41×C₃₁	—	2	1	no	—
109	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
110	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
111	C₂×#41×C₃₁	C₂³	1	2	yes	—
112	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
113	C₂×#41×C₃₁	C₂³	1	2	yes	complemented
114	C₂²×Q₈×C₃₁	—	2	1	no	—
115	C₂²×Q₈×C₃₁	—	2	1	no	—
116	C₂²×Q₈×C₃₁	—	2	2	no	—
117	C₂²×Q₈×C₃₁	—	2	4	no	—
118	C₂²×Q₈×C₃₁	—	4	2	no	—
119	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
120	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
121	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
122	C₂²×Q₈×C₃₁	C₂³	1	2	yes	complemented
123	C₂²×D₄×C₃₁	—	2	4	no	—
124	C₂²×D₄×C₃₁	—	2	2	no	—
125	C₂²×D₄×C₃₁	—	2	1	no	—
126	C₂²×D₄×C₃₁	—	2	4	no	—
127	C₂²×D₄×C₃₁	—	2	1	no	—
128	C₂²×D₄×C₃₁	—	2	2	no	—
129	C₂²×D₄×C₃₁	—	4	2	no	—
130	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
132	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
133	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₃₁	—	2	1	no	—
135	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₃₁×#137	—	2	4	no	—
137	C₃₁×#137	—	2	8	no	—
138	C₃₁×#137	—	4	2	no	—
139	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
140	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
141	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
142	C₃₁×#135	—	2	8	no	—
143	C₃₁×#135	—	2	4	no	—
144	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	complemented
145	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic, complemented
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	complemented
147	C₂×SD₁₆×C₃₁	—	2	4	no	—
148	C₂×SD₁₆×C₃₁	—	2	4	no	—
149	C₂×SD₁₆×C₃₁	—	2	16	no	—
150	C₂×SD₁₆×C₃₁	—	2	16	no	—
151	C₂×SD₁₆×C₃₁	—	2	8	no	—
152	C₂×SD₁₆×C₃₁	—	2	4	no	—
153	C₂×SD₁₆×C₃₁	D₄	1	8	yes	complemented
154	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
155	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
157	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	complemented
163	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic, complemented
164	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic, complemented
165	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	complemented
166	C₂×D₈×C₃₁	C₂³	1	2	yes	—
167	C₂×D₈×C₃₁	C₂³	1	2	yes	—
168	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic, complemented
169	C₃₁×#131	—	2	4	no	—
170	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
172	C₂×M₁₆×C₃₁	C₂³	1	2	yes	complemented
173	C₂²×C₈×C₃₁	—	2	4	no	—
174	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
176	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
177	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₃₁	C₂³	1	2	yes	complemented
179	C₃₁×C₄⋊Q₈	—	2	1	no	—
180	C₃₁×C₄⋊Q₈	—	2	4	no	—
181	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	complemented
182	C₃₁×#127	—	2	1	no	—
183	C₃₁×#127	C₂³	1	2	yes	—
184	C₃₁×#124	—	2	1	no	—
185	C₃₁×#124	—	2	1	no	—
186	C₃₁×#124	—	2	4	no	—
187	C₃₁×#124	C₂³	1	2	yes	—
188	C₃₁×#124	C₂³	1	2	yes	complemented
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	1	no	—
191	C₃₁×#123	—	2	1	no	—
192	C₃₁×#123	—	2	4	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	D₄	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	—	2	4	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	4	no	—
198	C₃₁×C₂²⋊Q₈	—	2	4	no	—
199	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	complemented
203	C₃₁×#121	—	2	4	no	—
204	C₃₁×#121	—	2	4	no	—
205	C₃₁×#121	—	2	2	no	—
206	C₃₁×#121	—	2	4	no	—
207	C₃₁×#121	D₄	1	2	yes	—
208	C₃₁×#121	C₂³	1	2	yes	—
209	C₃₁×#121	C₂³	1	2	yes	—
210	C₃₁×#121	C₂³	1	4	yes	—
211	C₃₁×#120	—	2	1	no	—
212	C₃₁×#120	—	2	1	no	—
213	C₃₁×#120	—	2	2	no	—
214	C₃₁×#120	—	2	4	no	—
215	C₃₁×#120	—	2	2	no	—
216	C₃₁×#120	—	2	4	no	—
217	C₃₁×#120	—	2	4	no	—
218	C₃₁×#120	D₄	1	2	yes	—
219	C₄×Q₈×C₃₁	—	2	2	no	—
220	C₄×Q₈×C₃₁	C₂³	1	4	yes	complemented
221	C₄×D₄×C₃₁	—	2	4	no	—
222	C₄×D₄×C₃₁	—	2	2	no	—
223	C₄×D₄×C₃₁	—	2	2	no	—
224	C₄×D₄×C₃₁	—	2	2	no	—
225	C₄×D₄×C₃₁	—	2	4	no	—
226	C₄×D₄×C₃₁	C₂³	1	4	yes	—
227	C₄×D₄×C₃₁	C₂³	1	4	yes	—
228	C₃₁×#117	—	2	2	no	—
229	C₃₁×#117	C₂³	1	1	yes	characteristic
230	C₃₁×#117	C₂³	1	1	yes	characteristic
231	C₃₁×#117	C₂³	1	1	yes	characteristic
232	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
233	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
234	C₃₁×#107	C₂³	1	2	yes	complemented
235	C₃₁×#106	C₂³	1	2	yes	complemented
236	C₃₁×C₄⋊C₈	C₂³	1	4	yes	complemented
237	C₃₁×#103	C₂³	1	2	yes	complemented
238	C₃₁×#103	C₂³	1	2	yes	complemented
239	C₃₁×#103	C₂³	1	4	yes	complemented
240	C₃₁×#103	C₂³	1	4	yes	complemented
241	C₃₁×#102	C₂³	1	4	yes	—
242	C₃₁×#102	C₂³	1	4	yes	—
243	C₃₁×#102	C₂³	1	2	yes	complemented
244	C₃₁×#102	C₂³	1	2	yes	complemented
245	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
246	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	complemented
247	C₃₁×#97	C₂³	1	2	yes	complemented
248	C₄×C₈×C₃₁	C₂³	1	2	yes	complemented
249	C₂⁴×C₃₁	—	2	1	no	—
250	C₂⁴×C₃₁	—	2	4	no	—
251	C₂⁴×C₃₁	—	2	1	no	—
252	C₂⁴×C₃₁	—	2	2	no	—
253	C₂⁴×C₃₁	—	4	4	no	—
254	C₂⁴×C₃₁	—	8	4	no	—
255	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
256	#41×C₃₁	—	2	2	no	—
257	#41×C₃₁	—	2	2	no	—
258	#41×C₃₁	—	2	4	no	—
259	#41×C₃₁	—	2	4	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	—	4	2	no	—
265	#41×C₃₁	—	4	2	no	—
266	#41×C₃₁	—	4	8	no	—
267	#41×C₃₁	—	4	4	no	—
268	#41×C₃₁	—	4	4	no	—
269	C₂×Q₈×C₃₁	—	2	1	no	—
270	C₂×Q₈×C₃₁	—	2	4	no	—
271	C₂×Q₈×C₃₁	—	2	1	no	—
272	C₂×Q₈×C₃₁	—	2	2	no	—
273	C₂×Q₈×C₃₁	—	2	2	no	—
274	C₂×Q₈×C₃₁	—	2	8	no	—
275	C₂×Q₈×C₃₁	—	2	4	no	—
276	C₂×Q₈×C₃₁	—	2	2	no	—
277	C₂×Q₈×C₃₁	—	2	2	no	—
278	C₂×Q₈×C₃₁	—	4	4	no	—
279	C₂×Q₈×C₃₁	—	4	4	no	—
280	C₂×Q₈×C₃₁	—	4	2	no	—
281	C₂×Q₈×C₃₁	—	4	8	no	—
282	C₂×Q₈×C₃₁	—	4	4	no	—
283	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
284	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	complemented
285	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
286	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
287	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
288	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
289	C₂×D₄×C₃₁	—	2	8	no	—
290	C₂×D₄×C₃₁	—	2	4	no	—
291	C₂×D₄×C₃₁	—	2	2	no	—
292	C₂×D₄×C₃₁	—	2	2	no	—
293	C₂×D₄×C₃₁	—	2	1	no	—
294	C₂×D₄×C₃₁	—	2	2	no	—
295	C₂×D₄×C₃₁	—	2	1	no	—
296	C₂×D₄×C₃₁	—	2	2	no	—
297	C₂×D₄×C₃₁	—	2	4	no	—
298	C₂×D₄×C₃₁	—	2	1	no	—
299	C₂×D₄×C₃₁	—	2	2	no	—
300	C₂×D₄×C₃₁	—	2	2	no	—
301	C₂×D₄×C₃₁	—	2	4	no	—
302	C₂×D₄×C₃₁	—	2	1	no	—
303	C₂×D₄×C₃₁	—	2	4	no	—
304	C₂×D₄×C₃₁	—	2	2	no	—
305	C₂×D₄×C₃₁	—	2	2	no	—
306	C₂×D₄×C₃₁	—	4	4	no	—
307	C₂×D₄×C₃₁	—	4	2	no	—
308	C₂×D₄×C₃₁	—	4	8	no	—
309	C₂×D₄×C₃₁	—	4	4	no	—
310	C₂×D₄×C₃₁	—	4	4	no	—
311	C₂×D₄×C₃₁	—	4	8	no	—
312	C₂×D₄×C₃₁	—	8	8	no	—
313	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
314	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
315	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
316	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
317	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
318	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
319	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
320	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₃₁	—	2	1	no	—
322	C₂²×C₄×C₃₁	—	2	2	no	—
323	C₂²×C₄×C₃₁	—	2	2	no	—
324	C₂²×C₄×C₃₁	—	2	4	no	—
325	C₂²×C₄×C₃₁	—	2	2	no	—
326	C₂²×C₄×C₃₁	—	2	1	no	—
327	C₂²×C₄×C₃₁	—	2	2	no	—
328	C₂²×C₄×C₃₁	—	2	1	no	—
329	C₂²×C₄×C₃₁	—	2	1	no	—
330	C₂²×C₄×C₃₁	—	2	2	no	—
331	C₂²×C₄×C₃₁	—	2	4	no	—
332	C₂²×C₄×C₃₁	—	4	4	no	—
333	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
334	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
338	Q₁₆×C₃₁	—	2	4	no	—
339	Q₁₆×C₃₁	—	2	2	no	—
340	Q₁₆×C₃₁	—	4	2	no	—
341	SD₁₆×C₃₁	—	2	8	no	—
342	SD₁₆×C₃₁	—	2	4	no	—
343	SD₁₆×C₃₁	—	2	8	no	—
344	SD₁₆×C₃₁	—	2	4	no	—
345	SD₁₆×C₃₁	—	2	4	no	—
346	SD₁₆×C₃₁	—	2	4	no	—
347	SD₁₆×C₃₁	—	2	2	no	—
348	SD₁₆×C₃₁	—	2	2	no	—
349	SD₁₆×C₃₁	—	4	2	no	—
350	SD₁₆×C₃₁	—	4	2	no	—
351	SD₁₆×C₃₁	C₂×D₄	1	8	yes	complemented
352	SD₁₆×C₃₁	C₂×D₄	1	8	yes	complemented
353	D₈×C₃₁	—	2	4	no	—
354	D₈×C₃₁	—	2	2	no	—
355	D₈×C₃₁	—	4	2	no	—
356	M₁₆×C₃₁	—	2	2	no	—
357	M₁₆×C₃₁	—	2	2	no	—
358	M₁₆×C₃₁	—	2	4	no	—
359	C₂×C₈×C₃₁	—	2	2	no	—
360	C₂×C₈×C₃₁	—	2	4	no	—
361	C₂×C₈×C₃₁	—	2	4	no	—
362	C₂×C₈×C₃₁	—	2	4	no	—
363	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	complemented
364	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
365	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
366	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
367	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₃₁	—	2	4	no	—
370	C₄⋊C₄×C₃₁	—	2	2	no	—
371	C₄⋊C₄×C₃₁	—	2	4	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	—	2	4	no	—
374	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
375	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
376	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
377	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
378	C₂²⋊C₄×C₃₁	—	2	1	no	—
379	C₂²⋊C₄×C₃₁	—	2	2	no	—
380	C₂²⋊C₄×C₃₁	—	2	1	no	—
381	C₂²⋊C₄×C₃₁	—	2	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	4	no	—
383	C₂²⋊C₄×C₃₁	—	2	4	no	—
384	C₂²⋊C₄×C₃₁	—	2	4	no	—
385	C₂²⋊C₄×C₃₁	—	2	4	no	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	—	2	4	no	—
388	C₂²⋊C₄×C₃₁	—	2	2	no	—
389	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
391	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
392	C₄²×C₃₁	—	2	4	no	—
393	C₄²×C₃₁	—	2	1	no	—
394	C₄²×C₃₁	—	2	1	no	—
395	C₄²×C₃₁	C₂⁴	1	2	yes	—
396	#61050	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
397	C₂³×C₃₁	—	2	2	no	—
398	C₂³×C₃₁	—	2	4	no	—
399	C₂³×C₃₁	—	2	2	no	—
400	C₂³×C₃₁	—	2	4	no	—
401	C₂³×C₃₁	—	2	1	no	—
402	C₂³×C₃₁	—	2	2	no	—
403	C₂³×C₃₁	—	2	1	no	—
404	C₂³×C₃₁	—	4	8	no	—
405	C₂³×C₃₁	—	4	4	no	—
406	C₂³×C₃₁	—	4	2	no	—
407	C₂³×C₃₁	—	4	8	no	—
408	C₂³×C₃₁	—	8	2	no	—
409	C₂³×C₃₁	—	8	4	no	—
410	C₂³×C₃₁	—	8	2	no	—
411	C₂³×C₃₁	—	8	4	no	—
412	C₂³×C₃₁	—	8	16	no	—
413	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
414	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
415	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
416	Q₈×C₃₁	—	2	4	no	—
417	Q₈×C₃₁	—	2	2	no	—
418	Q₈×C₃₁	—	2	2	no	—
419	Q₈×C₃₁	—	2	2	no	—
420	Q₈×C₃₁	—	2	1	no	—
421	Q₈×C₃₁	—	2	1	no	—
422	Q₈×C₃₁	—	2	1	no	—
423	Q₈×C₃₁	—	2	2	no	—
424	Q₈×C₃₁	—	2	1	no	—
425	Q₈×C₃₁	—	4	8	no	—
426	Q₈×C₃₁	—	4	4	no	—
427	Q₈×C₃₁	—	4	2	no	—
428	Q₈×C₃₁	C₂²×D₄	1	4	yes	—
429	D₄×C₃₁	—	2	4	no	—
430	D₄×C₃₁	—	2	8	no	—
431	D₄×C₃₁	—	2	4	no	—
432	D₄×C₃₁	—	2	2	no	—
433	D₄×C₃₁	—	2	1	no	—
434	D₄×C₃₁	—	2	1	no	—
435	D₄×C₃₁	—	2	2	no	—
436	D₄×C₃₁	—	2	2	no	—
437	D₄×C₃₁	—	2	1	no	—
438	D₄×C₃₁	—	2	2	no	—
439	D₄×C₃₁	—	2	1	no	—
440	D₄×C₃₁	—	4	8	no	—
441	D₄×C₃₁	—	4	4	no	—
442	D₄×C₃₁	—	4	4	no	—
443	D₄×C₃₁	—	4	4	no	—
444	D₄×C₃₁	—	4	2	no	—
445	D₄×C₃₁	—	4	2	no	—
446	D₄×C₃₁	—	4	4	no	—
447	D₄×C₃₁	—	4	4	no	—
448	D₄×C₃₁	—	4	2	no	—
449	D₄×C₃₁	—	8	4	no	—
450	D₄×C₃₁	—	8	4	no	—
451	D₄×C₃₁	C₂²×D₄	1	4	yes	—
452	C₂×C₄×C₃₁	—	2	2	no	—
453	C₂×C₄×C₃₁	—	2	4	no	—
454	C₂×C₄×C₃₁	—	2	2	no	—
455	C₂×C₄×C₃₁	—	2	4	no	—
456	C₂×C₄×C₃₁	—	2	2	no	—
457	C₂×C₄×C₃₁	—	2	2	no	—
458	C₂×C₄×C₃₁	—	2	2	no	—
459	C₂×C₄×C₃₁	—	2	2	no	—
460	C₂×C₄×C₃₁	—	2	2	no	—
461	C₂×C₄×C₃₁	—	2	2	no	—
462	C₂×C₄×C₃₁	—	2	1	no	—
463	C₂×C₄×C₃₁	—	2	2	no	—
464	C₂×C₄×C₃₁	—	2	1	no	—
465	C₂×C₄×C₃₁	—	4	4	no	—
466	C₂×C₄×C₃₁	—	4	8	no	—
467	C₂×C₄×C₃₁	—	4	4	no	—
468	C₂×C₄×C₃₁	—	4	4	no	—
469	C₂×C₄×C₃₁	—	4	2	no	—
470	C₂×C₄×C₃₁	—	4	2	no	—
471	C₂×C₄×C₃₁	—	4	2	no	—
472	C₂×C₄×C₃₁	—	8	4	no	—
473	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
474	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
476	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
478	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
479	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
480	C₈×C₃₁	—	2	2	no	—
481	C₈×C₃₁	—	2	2	no	—
482	C₈×C₃₁	—	2	2	no	—
483	C₈×C₃₁	C₂²×D₄	1	2	yes	—
484	C₈×C₃₁	C₂²×D₄	1	2	yes	—
485	C₂×#577	C₂×C₃₁	1	1	yes	characteristic, complemented
486	C₂³×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
487	#3486	C₂×C₃₁	1	1	yes	characteristic, complemented
488	#3484	C₂×C₃₁	1	1	yes	characteristic, complemented
489	#3282	C₂×C₃₁	1	4	yes	complemented
490	D₄×SD₁₆	C₂×C₃₁	1	4	yes	complemented
491	#3266	C₂×C₃₁	1	4	yes	complemented
492	#3265	C₂×C₃₁	1	4	yes	complemented
493	#3154	C₂×C₃₁	1	1	yes	characteristic, complemented
494	#3057	C₂×C₃₁	1	1	yes	characteristic, complemented
495	#3050	C₂×C₃₁	1	1	yes	characteristic, complemented
496	#3043	C₂×C₃₁	1	1	yes	characteristic, complemented
497	#3042	C₂×C₃₁	1	1	yes	characteristic, complemented
498	#3010	C₂×C₃₁	1	1	yes	characteristic, complemented
499	#3009	C₂×C₃₁	1	1	yes	characteristic, complemented
500	#3004	C₂×C₃₁	1	1	yes	characteristic, complemented
501	#3003	C₂×C₃₁	1	1	yes	characteristic, complemented
502	#2949	C₂×C₃₁	1	1	yes	characteristic, complemented
503	#2929	C₂×C₃₁	1	1	yes	characteristic, complemented
504	C₂²×C₃₁	—	2	8	no	—
505	C₂²×C₃₁	—	2	2	no	—
506	C₂²×C₃₁	—	2	2	no	—
507	C₂²×C₃₁	—	2	2	no	—
508	C₂²×C₃₁	—	2	2	no	—
509	C₂²×C₃₁	—	2	4	no	—
510	C₂²×C₃₁	—	2	4	no	—
511	C₂²×C₃₁	—	4	4	no	—
512	C₂²×C₃₁	—	4	1	no	—
513	C₂²×C₃₁	—	4	1	no	—
514	C₂²×C₃₁	—	4	2	no	—
515	C₂²×C₃₁	—	4	2	no	—
516	C₂²×C₃₁	—	4	2	no	—
517	C₂²×C₃₁	—	4	4	no	—
518	C₂²×C₃₁	—	8	4	no	—
519	C₂²×C₃₁	—	8	16	no	—
520	C₂²×C₃₁	—	8	4	no	—
521	C₂²×C₃₁	—	16	4	no	—
522	C₂²×C₃₁	D₄²	1	2	yes	—
523	C₂²×C₃₁	#577	1	4	yes	complemented
524	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
525	C₄×C₃₁	—	2	2	no	—
526	C₄×C₃₁	—	2	4	no	—
527	C₄×C₃₁	—	2	2	no	—
528	C₄×C₃₁	—	2	4	no	—
529	C₄×C₃₁	—	4	1	no	—
530	C₄×C₃₁	—	4	1	no	—
531	C₄×C₃₁	—	4	2	no	—
532	C₄×C₃₁	—	4	2	no	—
533	C₄×C₃₁	—	4	2	no	—
534	C₄×C₃₁	D₄²	1	2	yes	—
535	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
536	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
537	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic, complemented
538	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
539	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
540	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
541	#577	—	2	8	no	—
542	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
543	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
544	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
545	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
546	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic, complemented
547	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
548	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic, complemented
549	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
550	C₂²×SD₁₆	—	2	8	no	—
551	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
552	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
553	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
554	C₂²×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
555	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
556	C₂²×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
557	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
558	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic, complemented
559	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
560	D₄×Q₈	—	2	2	no	—
561	D₄×Q₈	C₂²×C₃₁	1	4	yes	complemented
562	#548	—	2	2	no	—
563	#548	C₂²×C₃₁	1	4	yes	complemented
564	#546	—	2	2	no	—
565	#546	C₂²×C₃₁	1	4	yes	—
566	D₄²	—	2	2	no	—
567	D₄²	C₂²×C₃₁	1	4	yes	—
568	#536	—	2	2	no	—
569	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
570	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
571	#535	C₂²×C₃₁	1	1	yes	characteristic
572	#535	C₂²×C₃₁	1	1	yes	characteristic
573	#534	—	2	2	no	—
574	#525	—	2	2	no	—
575	#525	C₂²×C₃₁	1	1	yes	characteristic
576	#525	C₂²×C₃₁	1	1	yes	characteristic
577	#525	C₂²×C₃₁	1	1	yes	characteristic, complemented
578	C₂×#120	—	2	2	no	—
579	#519	C₂²×C₃₁	1	1	yes	characteristic, complemented
580	#518	C₂²×C₃₁	1	1	yes	characteristic
581	#497	C₂²×C₃₁	1	2	yes	complemented
582	#496	C₂²×C₃₁	1	2	yes	complemented
583	#495	C₂²×C₃₁	1	2	yes	complemented
584	#492	C₂²×C₃₁	1	2	yes	complemented
585	#468	C₂²×C₃₁	1	4	yes	complemented
586	#467	C₂²×C₃₁	1	2	yes	complemented
587	#466	C₂²×C₃₁	1	2	yes	complemented
588	#465	C₂²×C₃₁	1	4	yes	complemented
589	#465	C₂²×C₃₁	1	2	yes	complemented
590	#465	C₂²×C₃₁	1	2	yes	complemented
591	#464	C₂²×C₃₁	1	4	yes	complemented
592	#463	C₂²×C₃₁	1	4	yes	complemented
593	#461	C₂²×C₃₁	1	4	yes	complemented
594	#460	C₂²×C₃₁	1	4	yes	complemented
595	#452	C₂²×C₃₁	1	4	yes	complemented
596	#451	C₂²×C₃₁	1	4	yes	complemented
597	#450	C₂²×C₃₁	1	4	yes	complemented
598	#450	C₂²×C₃₁	1	4	yes	complemented
599	#449	C₂²×C₃₁	1	4	yes	complemented
600	#448	C₂²×C₃₁	1	4	yes	complemented
601	#448	C₂²×C₃₁	1	4	yes	complemented
602	#447	C₂²×C₃₁	1	4	yes	complemented
603	#440	C₂²×C₃₁	1	4	yes	complemented
604	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
605	#435	C₂²×C₃₁	1	4	yes	complemented
606	C₈×D₄	C₂²×C₃₁	1	4	yes	complemented
607	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
608	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
609	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
610	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
611	#418	C₂²×C₃₁	1	1	yes	characteristic
612	#418	C₂²×C₃₁	1	1	yes	characteristic, complemented
613	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
614	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
615	#408	C₂²×C₃₁	1	1	yes	characteristic, complemented
616	#407	C₂²×C₃₁	1	1	yes	characteristic, complemented
617	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
618	C₂×C₃₁	—	2	2	no	—
619	C₂×C₃₁	—	2	4	no	—
620	C₂×C₃₁	—	4	2	no	—
621	C₂×C₃₁	—	4	4	no	—
622	C₂×C₃₁	—	8	1	no	—
623	C₂×C₃₁	—	8	2	no	—
624	C₂×C₃₁	—	8	1	no	—
625	C₂×C₃₁	C₂×D₄²	1	1	yes	characteristic
626	C₂×C₃₁	C₂×#577	1	2	yes	—
627	C₂⁵	—	2	1	no	—
628	2₋¹⁺⁴	—	2	4	no	—
629	2₋¹⁺⁴	—	4	2	no	—
630	H(5,𝔽₂)	—	2	4	no	—
631	H(5,𝔽₂)	—	4	2	no	—
632	C₂×#41	—	2	1	no	—
633	C₂×#41	—	2	2	no	—
634	C₂×#41	—	2	1	no	—
635	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
636	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
637	C₂×#41	C₂³×C₃₁	1	2	yes	—
638	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
639	C₂×#41	C₂³×C₃₁	1	2	yes	complemented
640	C₂²×Q₈	—	2	1	no	—
641	C₂²×Q₈	—	2	1	no	—
642	C₂²×Q₈	—	2	2	no	—
643	C₂²×Q₈	—	2	4	no	—
644	C₂²×Q₈	—	4	2	no	—
645	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
646	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
647	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
648	C₂²×Q₈	C₂³×C₃₁	1	2	yes	complemented
649	C₂²×D₄	—	2	4	no	—
650	C₂²×D₄	—	2	2	no	—
651	C₂²×D₄	—	2	1	no	—
652	C₂²×D₄	—	2	4	no	—
653	C₂²×D₄	—	2	1	no	—
654	C₂²×D₄	—	2	2	no	—
655	C₂²×D₄	—	4	2	no	—
656	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
657	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
658	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
659	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
660	C₂³×C₄	—	2	1	no	—
661	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
662	#137	—	2	4	no	—
663	#137	—	2	8	no	—
664	#137	—	4	2	no	—
665	AGL(1,ℤ/8)	—	2	4	no	—
666	AGL(1,ℤ/8)	—	2	8	no	—
667	AGL(1,ℤ/8)	—	4	2	no	—
668	#135	—	2	8	no	—
669	#135	—	2	4	no	—
670	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	complemented
671	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic, complemented
672	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	complemented
673	C₂×SD₁₆	—	2	4	no	—
674	C₂×SD₁₆	—	2	4	no	—
675	C₂×SD₁₆	—	2	16	no	—
676	C₂×SD₁₆	—	2	16	no	—
677	C₂×SD₁₆	—	2	8	no	—
678	C₂×SD₁₆	—	2	4	no	—
679	C₂×SD₁₆	D₄×C₃₁	1	8	yes	complemented
680	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
681	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
682	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
683	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
684	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
685	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
686	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
687	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
688	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic, complemented
689	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	complemented
690	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic, complemented
691	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	complemented
692	C₂×D₈	C₂³×C₃₁	1	2	yes	—
693	C₂×D₈	C₂³×C₃₁	1	2	yes	—
694	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic, complemented
695	#131	—	2	4	no	—
696	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
697	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
698	C₂×M₁₆	C₂³×C₃₁	1	2	yes	complemented
699	C₂²×C₈	—	2	4	no	—
700	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
701	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
702	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
703	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
704	C₂²×C₈	C₂³×C₃₁	1	2	yes	complemented
705	C₄⋊Q₈	—	2	1	no	—
706	C₄⋊Q₈	—	2	4	no	—
707	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	complemented
708	#127	—	2	1	no	—
709	#127	C₂³×C₃₁	1	2	yes	—
710	#124	—	2	1	no	—
711	#124	—	2	1	no	—
712	#124	—	2	4	no	—
713	#124	C₂³×C₃₁	1	2	yes	—
714	#124	C₂³×C₃₁	1	2	yes	complemented
715	#123	—	2	2	no	—
716	#123	—	2	1	no	—
717	#123	—	2	1	no	—
718	#123	—	2	4	no	—
719	#123	—	2	2	no	—
720	#123	D₄×C₃₁	1	2	yes	—
721	C₂²⋊Q₈	—	2	4	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	—	2	4	no	—
724	C₂²⋊Q₈	—	2	4	no	—
725	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
726	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
727	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
728	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	complemented
729	#121	—	2	4	no	—
730	#121	—	2	4	no	—
731	#121	—	2	2	no	—
732	#121	—	2	4	no	—
733	#121	D₄×C₃₁	1	2	yes	—
734	#121	C₂³×C₃₁	1	2	yes	—
735	#121	C₂³×C₃₁	1	2	yes	—
736	#121	C₂³×C₃₁	1	4	yes	—
737	#120	—	2	1	no	—
738	#120	—	2	1	no	—
739	#120	—	2	2	no	—
740	#120	—	2	4	no	—
741	#120	—	2	2	no	—
742	#120	—	2	4	no	—
743	#120	—	2	4	no	—
744	#120	D₄×C₃₁	1	2	yes	—
745	C₄×Q₈	—	2	2	no	—
746	C₄×Q₈	C₂³×C₃₁	1	4	yes	complemented
747	C₄×D₄	—	2	4	no	—
748	C₄×D₄	—	2	2	no	—
749	C₄×D₄	—	2	2	no	—
750	C₄×D₄	—	2	2	no	—
751	C₄×D₄	—	2	4	no	—
752	C₄×D₄	C₂³×C₃₁	1	4	yes	—
753	C₄×D₄	C₂³×C₃₁	1	4	yes	—
754	#117	—	2	2	no	—
755	#117	C₂³×C₃₁	1	1	yes	characteristic
756	#117	C₂³×C₃₁	1	1	yes	characteristic
757	#117	C₂³×C₃₁	1	1	yes	characteristic
758	C₂×C₂²⋊C₄	—	2	2	no	—
759	C₂×C₂²⋊C₄	—	2	4	no	—
760	#107	C₂³×C₃₁	1	2	yes	complemented
761	#106	C₂³×C₃₁	1	2	yes	complemented
762	C₄⋊C₈	C₂³×C₃₁	1	4	yes	complemented
763	#103	C₂³×C₃₁	1	2	yes	complemented
764	#103	C₂³×C₃₁	1	2	yes	complemented
765	#103	C₂³×C₃₁	1	4	yes	complemented
766	#103	C₂³×C₃₁	1	4	yes	complemented
767	#102	C₂³×C₃₁	1	4	yes	—
768	#102	C₂³×C₃₁	1	4	yes	—
769	#102	C₂³×C₃₁	1	2	yes	complemented
770	#102	C₂³×C₃₁	1	2	yes	complemented
771	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
772	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	complemented
773	#97	C₂³×C₃₁	1	2	yes	complemented
774	C₄×C₈	C₂³×C₃₁	1	2	yes	complemented
775	C₃₁	#61050	1	1	yes	characteristic, direct product factor, Sylow
776	C₂⁴	—	2	1	no	—
777	C₂⁴	—	2	4	no	—
778	C₂⁴	—	2	1	no	—
779	C₂⁴	—	2	2	no	—
780	C₂⁴	—	4	4	no	—
781	C₂⁴	—	8	4	no	—
782	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
783	#41	—	2	2	no	—
784	#41	—	2	2	no	—
785	#41	—	2	4	no	—
786	#41	—	2	4	no	—
787	#41	—	2	2	no	—
788	#41	—	2	2	no	—
789	#41	—	2	2	no	—
790	#41	—	2	2	no	—
791	#41	—	4	2	no	—
792	#41	—	4	2	no	—
793	#41	—	4	8	no	—
794	#41	—	4	4	no	—
795	#41	—	4	4	no	—
796	C₂×Q₈	—	2	1	no	—
797	C₂×Q₈	—	2	4	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	2	2	no	—
800	C₂×Q₈	—	2	2	no	—
801	C₂×Q₈	—	2	8	no	—
802	C₂×Q₈	—	2	4	no	—
803	C₂×Q₈	—	2	2	no	—
804	C₂×Q₈	—	2	2	no	—
805	C₂×Q₈	—	4	4	no	—
806	C₂×Q₈	—	4	4	no	—
807	C₂×Q₈	—	4	2	no	—
808	C₂×Q₈	—	4	8	no	—
809	C₂×Q₈	—	4	4	no	—
810	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
811	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	complemented
812	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
813	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
814	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
815	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
816	C₂×D₄	—	2	8	no	—
817	C₂×D₄	—	2	4	no	—
818	C₂×D₄	—	2	2	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	1	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	2	1	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	4	no	—
825	C₂×D₄	—	2	1	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	4	no	—
829	C₂×D₄	—	2	1	no	—
830	C₂×D₄	—	2	4	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	4	4	no	—
834	C₂×D₄	—	4	2	no	—
835	C₂×D₄	—	4	8	no	—
836	C₂×D₄	—	4	4	no	—
837	C₂×D₄	—	4	4	no	—
838	C₂×D₄	—	4	8	no	—
839	C₂×D₄	—	8	8	no	—
840	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
841	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
842	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
843	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
844	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
845	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
846	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
847	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	4	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	4	no	—
859	C₂²×C₄	—	4	4	no	—
860	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
861	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
862	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
863	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
864	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
865	Q₁₆	—	2	4	no	—
866	Q₁₆	—	2	2	no	—
867	Q₁₆	—	4	2	no	—
868	SD₁₆	—	2	8	no	—
869	SD₁₆	—	2	4	no	—
870	SD₁₆	—	2	8	no	—
871	SD₁₆	—	2	4	no	—
872	SD₁₆	—	2	4	no	—
873	SD₁₆	—	2	4	no	—
874	SD₁₆	—	2	2	no	—
875	SD₁₆	—	2	2	no	—
876	SD₁₆	—	4	2	no	—
877	SD₁₆	—	4	2	no	—
878	SD₁₆	C₂×D₄×C₃₁	1	8	yes	complemented
879	SD₁₆	C₂×D₄×C₃₁	1	8	yes	complemented
880	D₈	—	2	4	no	—
881	D₈	—	2	2	no	—
882	D₈	—	4	2	no	—
883	M₁₆	—	2	2	no	—
884	M₁₆	—	2	2	no	—
885	M₁₆	—	2	4	no	—
886	C₂×C₈	—	2	2	no	—
887	C₂×C₈	—	2	4	no	—
888	C₂×C₈	—	2	4	no	—
889	C₂×C₈	—	2	4	no	—
890	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	complemented
891	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
892	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
893	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
894	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
895	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
896	C₄⋊C₄	—	2	4	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	4	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	4	no	—
901	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
902	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
903	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
904	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
905	C₂²⋊C₄	—	2	1	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	1	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	4	no	—
910	C₂²⋊C₄	—	2	4	no	—
911	C₂²⋊C₄	—	2	4	no	—
912	C₂²⋊C₄	—	2	4	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	4	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
917	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
918	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
919	C₄²	—	2	4	no	—
920	C₄²	—	2	1	no	—
921	C₄²	—	2	1	no	—
922	C₄²	C₂⁴×C₃₁	1	2	yes	—
923	C₂³	—	2	2	no	—
924	C₂³	—	2	4	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	4	no	—
927	C₂³	—	2	1	no	—
928	C₂³	—	2	2	no	—
929	C₂³	—	2	1	no	—
930	C₂³	—	4	8	no	—
931	C₂³	—	4	4	no	—
932	C₂³	—	4	2	no	—
933	C₂³	—	4	8	no	—
934	C₂³	—	8	2	no	—
935	C₂³	—	8	4	no	—
936	C₂³	—	8	2	no	—
937	C₂³	—	8	4	no	—
938	C₂³	—	8	16	no	—
939	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
940	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
941	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
942	Q₈	—	2	4	no	—
943	Q₈	—	2	2	no	—
944	Q₈	—	2	2	no	—
945	Q₈	—	2	2	no	—
946	Q₈	—	2	1	no	—
947	Q₈	—	2	1	no	—
948	Q₈	—	2	1	no	—
949	Q₈	—	2	2	no	—
950	Q₈	—	2	1	no	—
951	Q₈	—	4	8	no	—
952	Q₈	—	4	4	no	—
953	Q₈	—	4	2	no	—
954	Q₈	C₂²×D₄×C₃₁	1	4	yes	—
955	D₄	—	2	4	no	—
956	D₄	—	2	8	no	—
957	D₄	—	2	4	no	—
958	D₄	—	2	2	no	—
959	D₄	—	2	1	no	—
960	D₄	—	2	1	no	—
961	D₄	—	2	2	no	—
962	D₄	—	2	2	no	—
963	D₄	—	2	1	no	—
964	D₄	—	2	2	no	—
965	D₄	—	2	1	no	—
966	D₄	—	4	8	no	—
967	D₄	—	4	4	no	—
968	D₄	—	4	4	no	—
969	D₄	—	4	4	no	—
970	D₄	—	4	2	no	—
971	D₄	—	4	2	no	—
972	D₄	—	4	4	no	—
973	D₄	—	4	4	no	—
974	D₄	—	4	2	no	—
975	D₄	—	8	4	no	—
976	D₄	—	8	4	no	—
977	D₄	C₂²×D₄×C₃₁	1	4	yes	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	4	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	4	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	4	4	no	—
992	C₂×C₄	—	4	8	no	—
993	C₂×C₄	—	4	4	no	—
994	C₂×C₄	—	4	4	no	—
995	C₂×C₄	—	4	2	no	—
996	C₂×C₄	—	4	2	no	—
997	C₂×C₄	—	4	2	no	—
998	C₂×C₄	—	8	4	no	—
999	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
1000	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1001	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1002	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1003	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1004	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1005	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1006	C₈	—	2	2	no	—
1007	C₈	—	2	2	no	—
1008	C₈	—	2	2	no	—
1009	C₈	C₂²×D₄×C₃₁	1	2	yes	—
1010	C₈	C₂²×D₄×C₃₁	1	2	yes	—
1011	C₂²	—	2	8	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	2	4	no	—
1017	C₂²	—	2	4	no	—
1018	C₂²	—	4	4	no	—
1019	C₂²	—	4	1	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	2	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	4	no	—
1025	C₂²	—	8	4	no	—
1026	C₂²	—	8	16	no	—
1027	C₂²	—	8	4	no	—
1028	C₂²	—	16	4	no	—
1029	C₂²	D₄²×C₃₁	1	2	yes	—
1030	C₂²	C₃₁×#577	1	4	yes	complemented
1031	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1032	C₄	—	2	2	no	—
1033	C₄	—	2	4	no	—
1034	C₄	—	2	2	no	—
1035	C₄	—	2	4	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	1	no	—
1038	C₄	—	4	2	no	—
1039	C₄	—	4	2	no	—
1040	C₄	—	4	2	no	—
1041	C₄	D₄²×C₃₁	1	2	yes	—
1042	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
1043	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1044	C₂	—	2	2	no	—
1045	C₂	—	2	4	no	—
1046	C₂	—	4	2	no	—
1047	C₂	—	4	4	no	—
1048	C₂	—	8	2	no	—
1049	C₂	—	8	1	no	—
1050	C₂	—	8	1	no	—
1051	C₂	C₂×D₄²×C₃₁	1	1	yes	characteristic
1052	C₂	C₂×C₃₁×#577	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#577	C₂	semidirect
2. C₂³×SD₁₆×C₃₁	C₂	semidirect
3. C₃₁×#3486	C₂	semidirect
4. C₃₁×#3484	C₂	semidirect
5. C₃₁×#3282	C₂	semidirect
6. D₄×SD₁₆×C₃₁	C₂	semidirect
7. C₃₁×#3266	C₂	semidirect
8. C₃₁×#3265	C₂	semidirect
9. C₃₁×#3154	C₂	semidirect
10. C₃₁×#3057	C₂	semidirect
11. C₃₁×#3050	C₂	semidirect
12. C₃₁×#3043	C₂	semidirect
13. C₃₁×#3042	C₂	semidirect
14. C₃₁×#3010	C₂	semidirect
15. C₃₁×#3009	C₂	semidirect
16. C₃₁×#3004	C₂	semidirect
17. C₃₁×#3003	C₂	semidirect
18. C₃₁×#2949	C₂	semidirect
19. C₃₁×#2929	C₂	semidirect
20. C₂×C₃₁×2₋¹⁺⁴	C₂²	semidirect
22. C₂³×Q₈×C₃₁	C₂²	semidirect
25. C₂×C₃₁×#137	C₂²	semidirect
26. C₂×C₃₁×#137	C₂²	semidirect
27. C₂×C₃₁×#137	C₂²	semidirect
29. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
30. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
31. C₂×C₃₁×#135	C₂²	semidirect
32. C₂×C₃₁×#135	C₂²	semidirect
36. C₂²×SD₁₆×C₃₁	C₂²	semidirect
37. C₂²×SD₁₆×C₃₁	C₂²	semidirect
38. C₂²×SD₁₆×C₃₁	C₂²	semidirect
39. C₂²×SD₁₆×C₃₁	C₂²	semidirect
40. C₂²×SD₁₆×C₃₁	C₂²	semidirect
41. C₂×C₃₁×#131	C₂²	semidirect
42. C₂³×C₈×C₃₁	C₂²	semidirect
44. D₄×Q₈×C₃₁	C₂²	semidirect
46. C₃₁×#548	C₂²	semidirect
52. C₃₁×#536	C₂²	semidirect
53. C₃₁×#536	C₂²	semidirect
60. C₃₁×#525	C₂²	semidirect
62. C₃₁×#519	C₂²	semidirect
64. C₃₁×#497	C₂²	semidirect
65. C₃₁×#496	C₂²	semidirect
66. C₃₁×#495	C₂²	semidirect
67. C₃₁×#492	C₂²	semidirect
68. C₃₁×#468	C₂²	semidirect
69. C₃₁×#467	C₂²	semidirect
70. C₃₁×#466	C₂²	semidirect
71. C₃₁×#465	C₂²	semidirect
72. C₃₁×#465	C₂²	semidirect
73. C₃₁×#465	C₂²	semidirect
74. C₃₁×#464	C₂²	semidirect
75. C₃₁×#463	C₂²	semidirect
76. C₃₁×#461	C₂²	semidirect
77. C₃₁×#460	C₂²	semidirect
78. C₃₁×#452	C₂²	semidirect
79. C₃₁×#451	C₂²	semidirect
80. C₃₁×#450	C₂²	semidirect
81. C₃₁×#450	C₂²	semidirect
82. C₃₁×#449	C₂²	semidirect
83. C₃₁×#448	C₂²	semidirect
84. C₃₁×#448	C₂²	semidirect
85. C₃₁×#447	C₂²	semidirect
86. C₃₁×#440	C₂²	semidirect
87. C₄×SD₁₆×C₃₁	C₂²	semidirect
88. C₃₁×#435	C₂²	semidirect
89. C₈×D₄×C₃₁	C₂²	semidirect
90. C₃₁×#427	C₂²	semidirect
91. C₃₁×#424	C₂²	semidirect
92. C₃₁×#419	C₂²	semidirect
93. C₃₁×#419	C₂²	semidirect
95. C₃₁×#418	C₂²	semidirect
96. C₃₁×#416	C₂²	semidirect
97. C₃₁×#416	C₂²	semidirect
98. C₃₁×#408	C₂²	semidirect
99. C₃₁×#407	C₂²	semidirect
100. C₃₁×#405	C₂²	semidirect
113. C₂×#41×C₃₁	C₂³	semidirect
122. C₂²×Q₈×C₃₁	C₂³	semidirect
144. C₂×Q₁₆×C₃₁	C₂³	semidirect
145. C₂×Q₁₆×C₃₁	C₂³	semidirect
146. C₂×Q₁₆×C₃₁	C₂³	semidirect
153. C₂×SD₁₆×C₃₁	D₄	semidirect
162. C₂×SD₁₆×C₃₁	C₂³	semidirect
163. C₂×SD₁₆×C₃₁	C₂³	semidirect
164. C₂×SD₁₆×C₃₁	C₂³	semidirect
165. C₂×SD₁₆×C₃₁	C₂³	semidirect
168. C₂×D₈×C₃₁	C₂³	semidirect
172. C₂×M₁₆×C₃₁	C₂³	semidirect
178. C₂²×C₈×C₃₁	C₂³	semidirect
181. C₃₁×C₄⋊Q₈	C₂³	semidirect
188. C₃₁×#124	C₂³	semidirect
202. C₃₁×C₂²⋊Q₈	C₂³	semidirect
220. C₄×Q₈×C₃₁	C₂³	semidirect
234. C₃₁×#107	C₂³	semidirect
235. C₃₁×#106	C₂³	semidirect
236. C₃₁×C₄⋊C₈	C₂³	semidirect
237. C₃₁×#103	C₂³	semidirect
238. C₃₁×#103	C₂³	semidirect
239. C₃₁×#103	C₂³	semidirect
240. C₃₁×#103	C₂³	semidirect
243. C₃₁×#102	C₂³	semidirect
244. C₃₁×#102	C₂³	semidirect
246. C₃₁×C₂²⋊C₈	C₂³	semidirect
247. C₃₁×#97	C₂³	semidirect
248. C₄×C₈×C₃₁	C₂³	semidirect
284. C₂×Q₈×C₃₁	C₂×D₄	semidirect
351. SD₁₆×C₃₁	C₂×D₄	semidirect
352. SD₁₆×C₃₁	C₂×D₄	semidirect
363. C₂×C₈×C₃₁	C₂×D₄	semidirect
396. #61050	C₃₁	direct (N × H)
485. C₂×#577	C₂×C₃₁	semidirect
486. C₂³×SD₁₆	C₂×C₃₁	semidirect
487. #3486	C₂×C₃₁	semidirect
488. #3484	C₂×C₃₁	semidirect
489. #3282	C₂×C₃₁	semidirect
490. D₄×SD₁₆	C₂×C₃₁	semidirect
491. #3266	C₂×C₃₁	semidirect
492. #3265	C₂×C₃₁	semidirect
493. #3154	C₂×C₃₁	semidirect
494. #3057	C₂×C₃₁	semidirect
495. #3050	C₂×C₃₁	semidirect
496. #3043	C₂×C₃₁	semidirect
497. #3042	C₂×C₃₁	semidirect
498. #3010	C₂×C₃₁	semidirect
499. #3009	C₂×C₃₁	semidirect
500. #3004	C₂×C₃₁	semidirect
501. #3003	C₂×C₃₁	semidirect
502. #2949	C₂×C₃₁	semidirect
503. #2929	C₂×C₃₁	semidirect
523. C₂²×C₃₁	#577	semidirect
537. C₂×2₋¹⁺⁴	C₂²×C₃₁	semidirect
539. C₂³×Q₈	C₂²×C₃₁	semidirect
542. C₂×#137	C₂²×C₃₁	semidirect
543. C₂×#137	C₂²×C₃₁	semidirect
544. C₂×#137	C₂²×C₃₁	semidirect
546. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
547. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
548. C₂×#135	C₂²×C₃₁	semidirect
549. C₂×#135	C₂²×C₃₁	semidirect
553. C₂²×SD₁₆	C₂²×C₃₁	semidirect
554. C₂²×SD₁₆	C₂²×C₃₁	semidirect
555. C₂²×SD₁₆	C₂²×C₃₁	semidirect
556. C₂²×SD₁₆	C₂²×C₃₁	semidirect
557. C₂²×SD₁₆	C₂²×C₃₁	semidirect
558. C₂×#131	C₂²×C₃₁	semidirect
559. C₂³×C₈	C₂²×C₃₁	semidirect
561. D₄×Q₈	C₂²×C₃₁	semidirect
563. #548	C₂²×C₃₁	semidirect
569. #536	C₂²×C₃₁	semidirect
570. #536	C₂²×C₃₁	semidirect
577. #525	C₂²×C₃₁	semidirect
579. #519	C₂²×C₃₁	semidirect
581. #497	C₂²×C₃₁	semidirect
582. #496	C₂²×C₃₁	semidirect
583. #495	C₂²×C₃₁	semidirect
584. #492	C₂²×C₃₁	semidirect
585. #468	C₂²×C₃₁	semidirect
586. #467	C₂²×C₃₁	semidirect
587. #466	C₂²×C₃₁	semidirect
588. #465	C₂²×C₃₁	semidirect
589. #465	C₂²×C₃₁	semidirect
590. #465	C₂²×C₃₁	semidirect
591. #464	C₂²×C₃₁	semidirect
592. #463	C₂²×C₃₁	semidirect
593. #461	C₂²×C₃₁	semidirect
594. #460	C₂²×C₃₁	semidirect
595. #452	C₂²×C₃₁	semidirect
596. #451	C₂²×C₃₁	semidirect
597. #450	C₂²×C₃₁	semidirect
598. #450	C₂²×C₃₁	semidirect
599. #449	C₂²×C₃₁	semidirect
600. #448	C₂²×C₃₁	semidirect
601. #448	C₂²×C₃₁	semidirect
602. #447	C₂²×C₃₁	semidirect
603. #440	C₂²×C₃₁	semidirect
604. C₄×SD₁₆	C₂²×C₃₁	semidirect
605. #435	C₂²×C₃₁	semidirect
606. C₈×D₄	C₂²×C₃₁	semidirect
607. #427	C₂²×C₃₁	semidirect
608. #424	C₂²×C₃₁	semidirect
609. #419	C₂²×C₃₁	semidirect
610. #419	C₂²×C₃₁	semidirect
612. #418	C₂²×C₃₁	semidirect
613. #416	C₂²×C₃₁	semidirect
614. #416	C₂²×C₃₁	semidirect
615. #408	C₂²×C₃₁	semidirect
616. #407	C₂²×C₃₁	semidirect
617. #405	C₂²×C₃₁	semidirect
639. C₂×#41	C₂³×C₃₁	semidirect
648. C₂²×Q₈	C₂³×C₃₁	semidirect
670. C₂×Q₁₆	C₂³×C₃₁	semidirect
671. C₂×Q₁₆	C₂³×C₃₁	semidirect
672. C₂×Q₁₆	C₂³×C₃₁	semidirect
679. C₂×SD₁₆	D₄×C₃₁	semidirect
688. C₂×SD₁₆	C₂³×C₃₁	semidirect
689. C₂×SD₁₆	C₂³×C₃₁	semidirect
690. C₂×SD₁₆	C₂³×C₃₁	semidirect
691. C₂×SD₁₆	C₂³×C₃₁	semidirect
694. C₂×D₈	C₂³×C₃₁	semidirect
698. C₂×M₁₆	C₂³×C₃₁	semidirect
704. C₂²×C₈	C₂³×C₃₁	semidirect
707. C₄⋊Q₈	C₂³×C₃₁	semidirect
714. #124	C₂³×C₃₁	semidirect
728. C₂²⋊Q₈	C₂³×C₃₁	semidirect
746. C₄×Q₈	C₂³×C₃₁	semidirect
760. #107	C₂³×C₃₁	semidirect
761. #106	C₂³×C₃₁	semidirect
762. C₄⋊C₈	C₂³×C₃₁	semidirect
763. #103	C₂³×C₃₁	semidirect
764. #103	C₂³×C₃₁	semidirect
765. #103	C₂³×C₃₁	semidirect
766. #103	C₂³×C₃₁	semidirect
769. #102	C₂³×C₃₁	semidirect
770. #102	C₂³×C₃₁	semidirect
772. C₂²⋊C₈	C₂³×C₃₁	semidirect
773. #97	C₂³×C₃₁	semidirect
774. C₄×C₈	C₂³×C₃₁	semidirect
775. C₃₁	#61050	direct (N × H)
811. C₂×Q₈	C₂×D₄×C₃₁	semidirect
878. SD₁₆	C₂×D₄×C₃₁	semidirect
879. SD₁₆	C₂×D₄×C₃₁	semidirect
890. C₂×C₈	C₂×D₄×C₃₁	semidirect
1030. C₂²	C₃₁×#577	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#577	2
C₂³×SD₁₆×C₃₁	2
C₃₁×#3486	2
C₃₁×#3484	2
C₃₁×#3282	2
D₄×SD₁₆×C₃₁	2
C₃₁×#3266	2
C₃₁×#3265	2
C₃₁×#3154	2
C₃₁×#3057	2
C₃₁×#3050	2
C₃₁×#3043	2
C₃₁×#3042	2
C₃₁×#3010	2
C₃₁×#3009	2
C₃₁×#3004	2
C₃₁×#3003	2
C₃₁×#2949	2
C₃₁×#2929	2
#61050	31

Subgroups — C31×#61050 #21517809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61050 #21517809