Subgroups — C₃₁×#61038 #21517797

Order 7936.

2790 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#575	C₂	1	2	yes	maximal, complemented
2	D₄×#41×C₃₁	C₂	1	2	yes	maximal, complemented
3	C₃₁×#3278	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3277	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3276	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3275	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3274	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3273	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3272	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3147	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3054	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3035	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3002	C₂	1	4	yes	maximal, complemented
14	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₃₁	C₂²	1	4	yes	complemented
17	C₃₁×#575	—	2	16	no	—
18	C₂×C₃₁×#137	C₂²	1	4	yes	complemented
19	C₂×C₃₁×#137	C₂²	1	4	yes	complemented
20	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
21	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
22	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
24	C₂×C₃₁×#135	C₂²	1	4	yes	complemented
25	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
26	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	complemented
27	C₃₁×#550	C₂²	1	2	yes	—
28	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
29	C₃₁×#548	C₂²	1	4	yes	complemented
30	C₃₁×#547	—	2	2	no	—
31	C₃₁×#547	C₂²	1	2	yes	—
32	C₃₁×#546	—	2	4	no	—
33	C₃₁×#546	C₂²	1	4	yes	complemented
34	D₄²×C₃₁	—	2	2	no	—
35	D₄²×C₃₁	C₂²	1	2	yes	complemented
36	C₃₁×#532	—	2	2	no	—
37	C₃₁×#532	C₂²	1	2	yes	complemented
38	C₃₁×#525	—	2	4	no	—
39	C₃₁×#525	C₂²	1	4	yes	complemented
40	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
41	C₂×C₄×D₄×C₃₁	—	2	2	no	—
42	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₃₁×#495	C₂²	1	2	yes	complemented
44	C₃₁×#495	C₂²	1	2	yes	complemented
45	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#492	C₂²	1	2	yes	complemented
48	C₃₁×#470	C₂²	1	4	yes	complemented
49	C₃₁×#469	C₂²	1	4	yes	complemented
50	C₃₁×#468	C₂²	1	4	yes	complemented
51	C₃₁×#468	C₂²	1	4	yes	complemented
52	C₃₁×#464	C₂²	1	4	yes	complemented
53	C₃₁×#463	C₂²	1	4	yes	complemented
54	C₃₁×#462	C₂²	1	2	yes	complemented
55	C₃₁×#461	C₂²	1	2	yes	complemented
56	C₃₁×#460	C₂²	1	2	yes	complemented
57	C₃₁×#459	C₂²	1	2	yes	complemented
58	C₃₁×#452	C₂²	1	4	yes	complemented
59	C₃₁×#452	C₂²	1	4	yes	complemented
60	C₃₁×#451	C₂²	1	4	yes	complemented
61	C₃₁×#450	C₂²	1	4	yes	complemented
62	C₃₁×#449	C₂²	1	4	yes	complemented
63	C₃₁×#449	C₂²	1	4	yes	complemented
64	C₃₁×#448	C₂²	1	4	yes	complemented
65	C₃₁×#447	C₂²	1	4	yes	complemented
66	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
67	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
68	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
69	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
70	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
71	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×#436	C₂²	1	2	yes	complemented
73	C₃₁×#436	C₂²	1	2	yes	complemented
74	C₃₁×#436	C₂²	1	2	yes	complemented
75	C₃₁×#436	C₂²	1	2	yes	complemented
76	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
77	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#416	C₂²	1	2	yes	complemented
79	C₃₁×#416	C₂²	1	4	yes	complemented
80	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
81	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
82	C₂×#41×C₃₁	—	2	4	no	—
83	C₂×#41×C₃₁	—	2	4	no	—
84	C₂×#41×C₃₁	—	2	16	no	—
85	C₂×#41×C₃₁	—	4	8	no	—
86	C₂×#41×C₃₁	C₂³	1	4	yes	—
87	C₂×#41×C₃₁	C₂³	1	4	yes	—
88	C₂×#41×C₃₁	C₂³	1	4	yes	—
89	C₂×#41×C₃₁	C₂³	1	2	yes	—
90	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
91	C₂²×D₄×C₃₁	—	2	4	no	—
92	C₂²×D₄×C₃₁	—	2	2	no	—
93	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
94	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
95	C₂³×C₄×C₃₁	—	2	4	no	—
96	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
97	C₃₁×#137	—	2	16	no	—
98	C₃₁×#137	—	2	16	no	—
99	C₃₁×AGL(1,ℤ/8)	—	2	16	no	—
100	C₃₁×AGL(1,ℤ/8)	—	2	16	no	—
101	C₃₁×#135	—	2	16	no	—
102	C₃₁×#135	—	2	8	no	—
103	C₃₁×#135	—	4	4	no	—
104	C₃₁×#135	D₄	1	8	yes	complemented
105	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
106	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
107	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
108	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
109	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
114	C₂×D₈×C₃₁	C₂³	1	4	yes	—
115	C₂×D₈×C₃₁	C₂³	1	2	yes	—
116	C₂×D₈×C₃₁	C₂³	1	2	yes	—
117	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₃₁	—	2	8	no	—
119	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
120	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
121	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
123	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
124	C₃₁×C₄⋊Q₈	—	2	2	no	—
125	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
126	C₃₁×#127	—	2	2	no	—
127	C₃₁×#127	C₂³	1	2	yes	—
128	C₃₁×#124	—	2	4	no	—
129	C₃₁×#124	C₂³	1	4	yes	—
130	C₃₁×#123	—	2	4	no	—
131	C₃₁×#123	—	2	4	no	—
132	C₃₁×#123	—	2	4	no	—
133	C₃₁×C₂²⋊Q₈	—	2	4	no	—
134	C₃₁×C₂²⋊Q₈	—	2	4	no	—
135	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
137	C₃₁×#121	—	2	4	no	—
138	C₃₁×#121	—	2	2	no	—
139	C₃₁×#121	—	2	2	no	—
140	C₃₁×#121	—	2	2	no	—
141	C₃₁×#121	—	2	2	no	—
142	C₃₁×#121	—	2	4	no	—
143	C₃₁×#121	—	2	4	no	—
144	C₃₁×#121	C₂³	1	4	yes	—
145	C₃₁×#121	C₂³	1	4	yes	—
146	C₃₁×#120	—	2	4	no	—
147	C₃₁×#120	—	2	4	no	—
148	C₃₁×#120	—	2	4	no	—
149	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
150	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
151	C₄×D₄×C₃₁	—	2	2	no	—
152	C₄×D₄×C₃₁	—	2	4	no	—
153	C₄×D₄×C₃₁	—	2	2	no	—
154	C₄×D₄×C₃₁	—	2	2	no	—
155	C₄×D₄×C₃₁	—	2	4	no	—
156	C₄×D₄×C₃₁	—	2	2	no	—
157	C₄×D₄×C₃₁	—	2	4	no	—
158	C₄×D₄×C₃₁	—	2	2	no	—
159	C₄×D₄×C₃₁	—	2	2	no	—
160	C₄×D₄×C₃₁	D₄	1	2	yes	—
161	C₄×D₄×C₃₁	D₄	1	2	yes	—
162	C₄×D₄×C₃₁	C₂³	1	2	yes	—
163	C₄×D₄×C₃₁	C₂³	1	2	yes	—
164	C₄×D₄×C₃₁	C₂³	1	2	yes	—
165	C₄×D₄×C₃₁	C₂³	1	2	yes	—
166	C₃₁×#117	—	2	2	no	—
167	C₃₁×#117	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
169	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
171	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
172	C₂×C₄²×C₃₁	—	2	2	no	—
173	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
174	C₃₁×#107	C₂³	1	1	yes	characteristic
175	C₃₁×#107	C₂³	1	1	yes	characteristic
176	C₃₁×#106	C₂³	1	2	yes	—
177	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
178	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
179	C₃₁×#103	C₂³	1	2	yes	—
180	C₃₁×#103	C₂³	1	2	yes	—
181	C₃₁×#103	C₂³	1	4	yes	—
182	C₃₁×#103	C₂³	1	4	yes	—
183	C₃₁×#102	C₂³	1	2	yes	—
184	C₃₁×#102	C₂³	1	2	yes	—
185	C₃₁×#102	C₂³	1	4	yes	—
186	C₃₁×#102	C₂³	1	4	yes	—
187	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
188	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
189	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
190	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
191	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
192	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
193	C₂⁴×C₃₁	—	2	4	no	—
194	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
195	#41×C₃₁	—	2	4	no	—
196	#41×C₃₁	—	2	8	no	—
197	#41×C₃₁	—	2	8	no	—
198	#41×C₃₁	—	2	8	no	—
199	#41×C₃₁	—	2	8	no	—
200	#41×C₃₁	—	4	16	no	—
201	#41×C₃₁	—	4	4	no	—
202	#41×C₃₁	—	4	4	no	—
203	#41×C₃₁	—	4	16	no	—
204	#41×C₃₁	C₂×D₄	1	8	yes	complemented
205	C₂×Q₈×C₃₁	—	2	4	no	—
206	C₂×Q₈×C₃₁	—	2	8	no	—
207	C₂×Q₈×C₃₁	—	4	4	no	—
208	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
209	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
210	C₂×D₄×C₃₁	—	2	2	no	—
211	C₂×D₄×C₃₁	—	2	8	no	—
212	C₂×D₄×C₃₁	—	2	4	no	—
213	C₂×D₄×C₃₁	—	2	4	no	—
214	C₂×D₄×C₃₁	—	2	4	no	—
215	C₂×D₄×C₃₁	—	2	4	no	—
216	C₂×D₄×C₃₁	—	2	4	no	—
217	C₂×D₄×C₃₁	—	2	2	no	—
218	C₂×D₄×C₃₁	—	2	4	no	—
219	C₂×D₄×C₃₁	—	2	2	no	—
220	C₂×D₄×C₃₁	—	4	2	no	—
221	C₂×D₄×C₃₁	—	4	4	no	—
222	C₂×D₄×C₃₁	—	4	16	no	—
223	C₂×D₄×C₃₁	—	4	8	no	—
224	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
225	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
226	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
227	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₃₁	—	2	4	no	—
229	C₂²×C₄×C₃₁	—	2	2	no	—
230	C₂²×C₄×C₃₁	—	2	4	no	—
231	C₂²×C₄×C₃₁	—	2	4	no	—
232	C₂²×C₄×C₃₁	—	2	2	no	—
233	C₂²×C₄×C₃₁	—	2	4	no	—
234	C₂²×C₄×C₃₁	—	2	4	no	—
235	C₂²×C₄×C₃₁	—	2	4	no	—
236	C₂²×C₄×C₃₁	—	2	2	no	—
237	C₂²×C₄×C₃₁	—	4	16	no	—
238	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
240	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
241	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
243	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
244	Q₁₆×C₃₁	—	2	8	no	—
245	Q₁₆×C₃₁	—	2	4	no	—
246	Q₁₆×C₃₁	—	4	2	no	—
247	Q₁₆×C₃₁	C₂×D₄	1	4	yes	complemented
248	SD₁₆×C₃₁	—	2	8	no	—
249	SD₁₆×C₃₁	—	2	8	no	—
250	SD₁₆×C₃₁	—	2	8	no	—
251	SD₁₆×C₃₁	—	4	4	no	—
252	SD₁₆×C₃₁	C₂×D₄	1	8	yes	complemented
253	D₈×C₃₁	—	2	8	no	—
254	D₈×C₃₁	—	2	4	no	—
255	D₈×C₃₁	—	4	2	no	—
256	D₈×C₃₁	C₂×D₄	1	4	yes	complemented
257	M₁₆×C₃₁	—	2	8	no	—
258	M₁₆×C₃₁	—	2	8	no	—
259	C₂×C₈×C₃₁	—	2	4	no	—
260	C₂×C₈×C₃₁	—	2	2	no	—
261	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	complemented
262	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
263	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
264	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
265	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
266	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
267	C₄⋊C₄×C₃₁	—	2	2	no	—
268	C₄⋊C₄×C₃₁	—	2	4	no	—
269	C₄⋊C₄×C₃₁	—	2	2	no	—
270	C₄⋊C₄×C₃₁	—	2	2	no	—
271	C₄⋊C₄×C₃₁	—	2	2	no	—
272	C₄⋊C₄×C₃₁	—	2	4	no	—
273	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
274	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
275	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
276	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
277	C₂²⋊C₄×C₃₁	—	2	4	no	—
278	C₂²⋊C₄×C₃₁	—	2	2	no	—
279	C₂²⋊C₄×C₃₁	—	2	4	no	—
280	C₂²⋊C₄×C₃₁	—	2	4	no	—
281	C₂²⋊C₄×C₃₁	—	2	4	no	—
282	C₂²⋊C₄×C₃₁	—	2	2	no	—
283	C₂²⋊C₄×C₃₁	—	2	2	no	—
284	C₂²⋊C₄×C₃₁	—	2	4	no	—
285	C₂²⋊C₄×C₃₁	—	2	4	no	—
286	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
287	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
288	C₄²×C₃₁	—	2	2	no	—
289	C₄²×C₃₁	—	2	2	no	—
290	C₄²×C₃₁	—	2	2	no	—
291	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
292	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
293	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
294	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
295	#61038	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
296	C₂³×C₃₁	—	2	2	no	—
297	C₂³×C₃₁	—	2	4	no	—
298	C₂³×C₃₁	—	2	4	no	—
299	C₂³×C₃₁	—	4	2	no	—
300	C₂³×C₃₁	—	4	2	no	—
301	C₂³×C₃₁	—	4	8	no	—
302	C₂³×C₃₁	—	4	8	no	—
303	C₂³×C₃₁	—	8	4	no	—
304	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
305	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
306	Q₈×C₃₁	—	2	2	no	—
307	Q₈×C₃₁	—	2	4	no	—
308	Q₈×C₃₁	—	2	4	no	—
309	Q₈×C₃₁	—	4	8	no	—
310	Q₈×C₃₁	C₂²×D₄	1	4	yes	—
311	D₄×C₃₁	—	2	8	no	—
312	D₄×C₃₁	—	2	4	no	—
313	D₄×C₃₁	—	2	4	no	—
314	D₄×C₃₁	—	2	2	no	—
315	D₄×C₃₁	—	2	4	no	—
316	D₄×C₃₁	—	4	2	no	—
317	D₄×C₃₁	—	4	8	no	—
318	D₄×C₃₁	—	4	8	no	—
319	D₄×C₃₁	—	4	8	no	—
320	D₄×C₃₁	—	4	8	no	—
321	D₄×C₃₁	—	4	8	no	—
322	D₄×C₃₁	—	4	4	no	—
323	D₄×C₃₁	—	8	2	no	—
324	D₄×C₃₁	—	8	4	no	—
325	D₄×C₃₁	C₂²×D₄	1	4	yes	—
326	C₂×C₄×C₃₁	—	2	4	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	8	no	—
329	C₂×C₄×C₃₁	—	2	8	no	—
330	C₂×C₄×C₃₁	—	2	2	no	—
331	C₂×C₄×C₃₁	—	2	4	no	—
332	C₂×C₄×C₃₁	—	2	4	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	2	no	—
335	C₂×C₄×C₃₁	—	2	4	no	—
336	C₂×C₄×C₃₁	—	4	1	no	—
337	C₂×C₄×C₃₁	—	4	8	no	—
338	C₂×C₄×C₃₁	—	4	8	no	—
339	C₂×C₄×C₃₁	—	4	8	no	—
340	C₂×C₄×C₃₁	—	4	8	no	—
341	C₂×C₄×C₃₁	—	4	4	no	—
342	C₂×C₄×C₃₁	—	8	2	no	—
343	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
347	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
348	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
351	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
352	C₈×C₃₁	—	2	4	no	—
353	C₈×C₃₁	—	2	1	no	—
354	C₈×C₃₁	—	2	1	no	—
355	C₈×C₃₁	C₂²×D₄	1	2	yes	—
356	C₈×C₃₁	C₂²×D₄	1	2	yes	—
357	C₂×#575	C₂×C₃₁	1	2	yes	complemented
358	D₄×#41	C₂×C₃₁	1	2	yes	complemented
359	#3278	C₂×C₃₁	1	2	yes	complemented
360	#3277	C₂×C₃₁	1	2	yes	complemented
361	#3276	C₂×C₃₁	1	2	yes	complemented
362	#3275	C₂×C₃₁	1	4	yes	complemented
363	#3274	C₂×C₃₁	1	2	yes	complemented
364	#3273	C₂×C₃₁	1	2	yes	complemented
365	#3272	C₂×C₃₁	1	2	yes	complemented
366	#3147	C₂×C₃₁	1	1	yes	characteristic, complemented
367	#3054	C₂×C₃₁	1	2	yes	complemented
368	#3035	C₂×C₃₁	1	2	yes	complemented
369	#3002	C₂×C₃₁	1	4	yes	complemented
370	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
371	C₂×#436	C₂×C₃₁	1	1	yes	characteristic, complemented
372	C₂²×C₃₁	—	2	1	no	—
373	C₂²×C₃₁	—	2	1	no	—
374	C₂²×C₃₁	—	2	4	no	—
375	C₂²×C₃₁	—	2	4	no	—
376	C₂²×C₃₁	—	2	4	no	—
377	C₂²×C₃₁	—	2	4	no	—
378	C₂²×C₃₁	—	4	2	no	—
379	C₂²×C₃₁	—	4	2	no	—
380	C₂²×C₃₁	—	4	4	no	—
381	C₂²×C₃₁	—	4	4	no	—
382	C₂²×C₃₁	—	4	4	no	—
383	C₂²×C₃₁	—	8	4	no	—
384	C₂²×C₃₁	—	8	16	no	—
385	C₂²×C₃₁	D₄²	1	2	yes	—
386	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
387	C₄×C₃₁	—	2	1	no	—
388	C₄×C₃₁	—	2	1	no	—
389	C₄×C₃₁	—	2	4	no	—
390	C₄×C₃₁	—	2	4	no	—
391	C₄×C₃₁	—	2	1	no	—
392	C₄×C₃₁	—	4	2	no	—
393	C₄×C₃₁	—	4	4	no	—
394	C₄×C₃₁	—	4	2	no	—
395	C₄×C₃₁	D₄²	1	2	yes	—
396	C₄×C₃₁	#575	1	2	yes	complemented
397	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
398	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
399	C₂²×#41	C₂²×C₃₁	1	4	yes	complemented
400	#575	—	2	16	no	—
401	C₂×#137	C₂²×C₃₁	1	4	yes	complemented
402	C₂×#137	C₂²×C₃₁	1	4	yes	complemented
403	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	4	yes	complemented
404	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	4	yes	complemented
405	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
406	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
407	C₂×#135	C₂²×C₃₁	1	4	yes	complemented
408	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
409	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	complemented
410	#550	C₂²×C₃₁	1	2	yes	—
411	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
412	#548	C₂²×C₃₁	1	4	yes	complemented
413	#547	—	2	2	no	—
414	#547	C₂²×C₃₁	1	2	yes	—
415	#546	—	2	4	no	—
416	#546	C₂²×C₃₁	1	4	yes	complemented
417	D₄²	—	2	2	no	—
418	D₄²	C₂²×C₃₁	1	2	yes	complemented
419	#532	—	2	2	no	—
420	#532	C₂²×C₃₁	1	2	yes	complemented
421	#525	—	2	4	no	—
422	#525	C₂²×C₃₁	1	4	yes	complemented
423	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
424	C₂×C₄×D₄	—	2	2	no	—
425	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
426	#495	C₂²×C₃₁	1	2	yes	complemented
427	#495	C₂²×C₃₁	1	2	yes	complemented
428	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
429	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
430	#492	C₂²×C₃₁	1	2	yes	complemented
431	#470	C₂²×C₃₁	1	4	yes	complemented
432	#469	C₂²×C₃₁	1	4	yes	complemented
433	#468	C₂²×C₃₁	1	4	yes	complemented
434	#468	C₂²×C₃₁	1	4	yes	complemented
435	#464	C₂²×C₃₁	1	4	yes	complemented
436	#463	C₂²×C₃₁	1	4	yes	complemented
437	#462	C₂²×C₃₁	1	2	yes	complemented
438	#461	C₂²×C₃₁	1	2	yes	complemented
439	#460	C₂²×C₃₁	1	2	yes	complemented
440	#459	C₂²×C₃₁	1	2	yes	complemented
441	#452	C₂²×C₃₁	1	4	yes	complemented
442	#452	C₂²×C₃₁	1	4	yes	complemented
443	#451	C₂²×C₃₁	1	4	yes	complemented
444	#450	C₂²×C₃₁	1	4	yes	complemented
445	#449	C₂²×C₃₁	1	4	yes	complemented
446	#449	C₂²×C₃₁	1	4	yes	complemented
447	#448	C₂²×C₃₁	1	4	yes	complemented
448	#447	C₂²×C₃₁	1	4	yes	complemented
449	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
450	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
451	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
452	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
453	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
454	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
455	#436	C₂²×C₃₁	1	2	yes	complemented
456	#436	C₂²×C₃₁	1	2	yes	complemented
457	#436	C₂²×C₃₁	1	2	yes	complemented
458	#436	C₂²×C₃₁	1	2	yes	complemented
459	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
460	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
461	#416	C₂²×C₃₁	1	2	yes	complemented
462	#416	C₂²×C₃₁	1	4	yes	complemented
463	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	complemented
464	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
465	C₂×C₃₁	—	2	2	no	—
466	C₂×C₃₁	—	4	4	no	—
467	C₂×C₃₁	—	4	4	no	—
468	C₂×C₃₁	—	8	4	no	—
469	C₂×C₃₁	C₂×D₄²	1	1	yes	characteristic
470	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
471	C₂×C₃₁	#3584	1	1	yes	characteristic
472	C₂×#41	—	2	4	no	—
473	C₂×#41	—	2	4	no	—
474	C₂×#41	—	2	16	no	—
475	C₂×#41	—	4	8	no	—
476	C₂×#41	C₂³×C₃₁	1	4	yes	—
477	C₂×#41	C₂³×C₃₁	1	4	yes	—
478	C₂×#41	C₂³×C₃₁	1	4	yes	—
479	C₂×#41	C₂³×C₃₁	1	2	yes	—
480	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
481	C₂²×D₄	—	2	4	no	—
482	C₂²×D₄	—	2	2	no	—
483	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
484	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
485	C₂³×C₄	—	2	4	no	—
486	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
487	#137	—	2	16	no	—
488	#137	—	2	16	no	—
489	AGL(1,ℤ/8)	—	2	16	no	—
490	AGL(1,ℤ/8)	—	2	16	no	—
491	#135	—	2	16	no	—
492	#135	—	2	8	no	—
493	#135	—	4	4	no	—
494	#135	D₄×C₃₁	1	8	yes	complemented
495	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
496	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
497	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
498	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
499	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
500	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
501	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
502	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
503	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
504	C₂×D₈	C₂³×C₃₁	1	4	yes	—
505	C₂×D₈	C₂³×C₃₁	1	2	yes	—
506	C₂×D₈	C₂³×C₃₁	1	2	yes	—
507	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
508	C₂×M₁₆	—	2	8	no	—
509	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
510	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
511	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
512	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
513	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
514	C₄⋊Q₈	—	2	2	no	—
515	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
516	#127	—	2	2	no	—
517	#127	C₂³×C₃₁	1	2	yes	—
518	#124	—	2	4	no	—
519	#124	C₂³×C₃₁	1	4	yes	—
520	#123	—	2	4	no	—
521	#123	—	2	4	no	—
522	#123	—	2	4	no	—
523	C₂²⋊Q₈	—	2	4	no	—
524	C₂²⋊Q₈	—	2	4	no	—
525	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
526	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
527	#121	—	2	4	no	—
528	#121	—	2	2	no	—
529	#121	—	2	2	no	—
530	#121	—	2	2	no	—
531	#121	—	2	2	no	—
532	#121	—	2	4	no	—
533	#121	—	2	4	no	—
534	#121	C₂³×C₃₁	1	4	yes	—
535	#121	C₂³×C₃₁	1	4	yes	—
536	#120	—	2	4	no	—
537	#120	—	2	4	no	—
538	#120	—	2	4	no	—
539	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
540	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	4	no	—
543	C₄×D₄	—	2	2	no	—
544	C₄×D₄	—	2	2	no	—
545	C₄×D₄	—	2	4	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	4	no	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	D₄×C₃₁	1	2	yes	—
551	C₄×D₄	D₄×C₃₁	1	2	yes	—
552	C₄×D₄	C₂³×C₃₁	1	2	yes	—
553	C₄×D₄	C₂³×C₃₁	1	2	yes	—
554	C₄×D₄	C₂³×C₃₁	1	2	yes	—
555	C₄×D₄	C₂³×C₃₁	1	2	yes	—
556	#117	—	2	2	no	—
557	#117	C₂³×C₃₁	1	2	yes	—
558	C₂×C₄⋊C₄	—	2	2	no	—
559	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
560	C₂×C₂²⋊C₄	—	2	4	no	—
561	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
562	C₂×C₄²	—	2	2	no	—
563	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
564	#107	C₂³×C₃₁	1	1	yes	characteristic
565	#107	C₂³×C₃₁	1	1	yes	characteristic
566	#106	C₂³×C₃₁	1	2	yes	—
567	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
568	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
569	#103	C₂³×C₃₁	1	2	yes	—
570	#103	C₂³×C₃₁	1	2	yes	—
571	#103	C₂³×C₃₁	1	4	yes	—
572	#103	C₂³×C₃₁	1	4	yes	—
573	#102	C₂³×C₃₁	1	2	yes	—
574	#102	C₂³×C₃₁	1	2	yes	—
575	#102	C₂³×C₃₁	1	4	yes	—
576	#102	C₂³×C₃₁	1	4	yes	—
577	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
578	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
579	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
580	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
581	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
582	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
583	C₃₁	#61038	1	1	yes	characteristic, direct product factor, Sylow
584	C₂⁴	—	2	4	no	—
585	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
586	#41	—	2	4	no	—
587	#41	—	2	8	no	—
588	#41	—	2	8	no	—
589	#41	—	2	8	no	—
590	#41	—	2	8	no	—
591	#41	—	4	16	no	—
592	#41	—	4	4	no	—
593	#41	—	4	4	no	—
594	#41	—	4	16	no	—
595	#41	C₂×D₄×C₃₁	1	8	yes	complemented
596	C₂×Q₈	—	2	4	no	—
597	C₂×Q₈	—	2	8	no	—
598	C₂×Q₈	—	4	4	no	—
599	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
600	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	8	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	4	2	no	—
612	C₂×D₄	—	4	4	no	—
613	C₂×D₄	—	4	16	no	—
614	C₂×D₄	—	4	8	no	—
615	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
616	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
617	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
618	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	4	16	no	—
629	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
630	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
631	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
632	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
634	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
635	Q₁₆	—	2	8	no	—
636	Q₁₆	—	2	4	no	—
637	Q₁₆	—	4	2	no	—
638	Q₁₆	C₂×D₄×C₃₁	1	4	yes	complemented
639	SD₁₆	—	2	8	no	—
640	SD₁₆	—	2	8	no	—
641	SD₁₆	—	2	8	no	—
642	SD₁₆	—	4	4	no	—
643	SD₁₆	C₂×D₄×C₃₁	1	8	yes	complemented
644	D₈	—	2	8	no	—
645	D₈	—	2	4	no	—
646	D₈	—	4	2	no	—
647	D₈	C₂×D₄×C₃₁	1	4	yes	complemented
648	M₁₆	—	2	8	no	—
649	M₁₆	—	2	8	no	—
650	C₂×C₈	—	2	4	no	—
651	C₂×C₈	—	2	2	no	—
652	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	complemented
653	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
654	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
655	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
656	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
657	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
665	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
666	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
667	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
678	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
679	C₄²	—	2	2	no	—
680	C₄²	—	2	2	no	—
681	C₄²	—	2	2	no	—
682	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
683	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
684	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
685	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
686	C₂³	—	2	2	no	—
687	C₂³	—	2	4	no	—
688	C₂³	—	2	4	no	—
689	C₂³	—	4	2	no	—
690	C₂³	—	4	2	no	—
691	C₂³	—	4	8	no	—
692	C₂³	—	4	8	no	—
693	C₂³	—	8	4	no	—
694	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
695	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
696	Q₈	—	2	2	no	—
697	Q₈	—	2	4	no	—
698	Q₈	—	2	4	no	—
699	Q₈	—	4	8	no	—
700	Q₈	C₂²×D₄×C₃₁	1	4	yes	—
701	D₄	—	2	8	no	—
702	D₄	—	2	4	no	—
703	D₄	—	2	4	no	—
704	D₄	—	2	2	no	—
705	D₄	—	2	4	no	—
706	D₄	—	4	2	no	—
707	D₄	—	4	8	no	—
708	D₄	—	4	8	no	—
709	D₄	—	4	8	no	—
710	D₄	—	4	8	no	—
711	D₄	—	4	8	no	—
712	D₄	—	4	4	no	—
713	D₄	—	8	2	no	—
714	D₄	—	8	4	no	—
715	D₄	C₂²×D₄×C₃₁	1	4	yes	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	8	no	—
719	C₂×C₄	—	2	8	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	8	no	—
728	C₂×C₄	—	4	8	no	—
729	C₂×C₄	—	4	8	no	—
730	C₂×C₄	—	4	8	no	—
731	C₂×C₄	—	4	4	no	—
732	C₂×C₄	—	8	2	no	—
733	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
734	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
735	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
736	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
737	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
738	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
739	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
740	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
741	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
742	C₈	—	2	4	no	—
743	C₈	—	2	1	no	—
744	C₈	—	2	1	no	—
745	C₈	C₂²×D₄×C₃₁	1	2	yes	—
746	C₈	C₂²×D₄×C₃₁	1	2	yes	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	1	no	—
749	C₂²	—	2	4	no	—
750	C₂²	—	2	4	no	—
751	C₂²	—	2	4	no	—
752	C₂²	—	2	4	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	4	no	—
756	C₂²	—	4	4	no	—
757	C₂²	—	4	4	no	—
758	C₂²	—	8	4	no	—
759	C₂²	—	8	16	no	—
760	C₂²	D₄²×C₃₁	1	2	yes	—
761	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
762	C₄	—	2	4	no	—
763	C₄	—	2	4	no	—
764	C₄	—	2	1	no	—
765	C₄	—	2	1	no	—
766	C₄	—	2	1	no	—
767	C₄	—	4	4	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	D₄²×C₃₁	1	2	yes	—
771	C₄	C₃₁×#575	1	2	yes	complemented
772	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
773	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
774	C₂	—	2	2	no	—
775	C₂	—	4	4	no	—
776	C₂	—	4	4	no	—
777	C₂	—	8	4	no	—
778	C₂	C₂×D₄²×C₃₁	1	1	yes	characteristic
779	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
780	C₂	C₃₁×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#575	C₂	semidirect
2. D₄×#41×C₃₁	C₂	semidirect
3. C₃₁×#3278	C₂	semidirect
4. C₃₁×#3277	C₂	semidirect
5. C₃₁×#3276	C₂	semidirect
6. C₃₁×#3275	C₂	semidirect
7. C₃₁×#3274	C₂	semidirect
8. C₃₁×#3273	C₂	semidirect
9. C₃₁×#3272	C₂	semidirect
10. C₃₁×#3147	C₂	semidirect
11. C₃₁×#3054	C₂	semidirect
12. C₃₁×#3035	C₂	semidirect
13. C₃₁×#3002	C₂	semidirect
14. C₄×C₃₁×#135	C₂	semidirect
15. C₂×C₃₁×#436	C₂	semidirect
16. C₂²×#41×C₃₁	C₂²	semidirect
18. C₂×C₃₁×#137	C₂²	semidirect
19. C₂×C₃₁×#137	C₂²	semidirect
20. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₃₁×#135	C₂²	semidirect
24. C₂×C₃₁×#135	C₂²	semidirect
25. C₂×C₃₁×#135	C₂²	semidirect
26. C₂²×M₁₆×C₃₁	C₂²	semidirect
28. D₄×Q₈×C₃₁	C₂²	semidirect
29. C₃₁×#548	C₂²	semidirect
33. C₃₁×#546	C₂²	semidirect
35. D₄²×C₃₁	C₂²	semidirect
37. C₃₁×#532	C₂²	semidirect
39. C₃₁×#525	C₂²	semidirect
40. C₄×#41×C₃₁	C₂²	semidirect
43. C₃₁×#495	C₂²	semidirect
44. C₃₁×#495	C₂²	semidirect
45. C₃₁×#494	C₂²	semidirect
46. C₃₁×#493	C₂²	semidirect
47. C₃₁×#492	C₂²	semidirect
48. C₃₁×#470	C₂²	semidirect
49. C₃₁×#469	C₂²	semidirect
50. C₃₁×#468	C₂²	semidirect
51. C₃₁×#468	C₂²	semidirect
52. C₃₁×#464	C₂²	semidirect
53. C₃₁×#463	C₂²	semidirect
54. C₃₁×#462	C₂²	semidirect
55. C₃₁×#461	C₂²	semidirect
56. C₃₁×#460	C₂²	semidirect
57. C₃₁×#459	C₂²	semidirect
58. C₃₁×#452	C₂²	semidirect
59. C₃₁×#452	C₂²	semidirect
60. C₃₁×#451	C₂²	semidirect
61. C₃₁×#450	C₂²	semidirect
62. C₃₁×#449	C₂²	semidirect
63. C₃₁×#449	C₂²	semidirect
64. C₃₁×#448	C₂²	semidirect
65. C₃₁×#447	C₂²	semidirect
66. C₄×Q₁₆×C₃₁	C₂²	semidirect
67. C₄×Q₁₆×C₃₁	C₂²	semidirect
68. C₄×SD₁₆×C₃₁	C₂²	semidirect
69. C₄×SD₁₆×C₃₁	C₂²	semidirect
70. C₄×D₈×C₃₁	C₂²	semidirect
71. C₄×D₈×C₃₁	C₂²	semidirect
72. C₃₁×#436	C₂²	semidirect
73. C₃₁×#436	C₂²	semidirect
74. C₃₁×#436	C₂²	semidirect
75. C₃₁×#436	C₂²	semidirect
76. C₃₁×#427	C₂²	semidirect
77. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
78. C₃₁×#416	C₂²	semidirect
79. C₃₁×#416	C₂²	semidirect
80. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
81. C₂×C₄×C₈×C₃₁	C₂²	semidirect
104. C₃₁×#135	D₄	semidirect
204. #41×C₃₁	C₂×D₄	semidirect
247. Q₁₆×C₃₁	C₂×D₄	semidirect
252. SD₁₆×C₃₁	C₂×D₄	semidirect
256. D₈×C₃₁	C₂×D₄	semidirect
261. C₂×C₈×C₃₁	C₂×D₄	semidirect
295. #61038	C₃₁	direct (N × H)
357. C₂×#575	C₂×C₃₁	semidirect
358. D₄×#41	C₂×C₃₁	semidirect
359. #3278	C₂×C₃₁	semidirect
360. #3277	C₂×C₃₁	semidirect
361. #3276	C₂×C₃₁	semidirect
362. #3275	C₂×C₃₁	semidirect
363. #3274	C₂×C₃₁	semidirect
364. #3273	C₂×C₃₁	semidirect
365. #3272	C₂×C₃₁	semidirect
366. #3147	C₂×C₃₁	semidirect
367. #3054	C₂×C₃₁	semidirect
368. #3035	C₂×C₃₁	semidirect
369. #3002	C₂×C₃₁	semidirect
370. C₄×#135	C₂×C₃₁	semidirect
371. C₂×#436	C₂×C₃₁	semidirect
396. C₄×C₃₁	#575	semidirect
399. C₂²×#41	C₂²×C₃₁	semidirect
401. C₂×#137	C₂²×C₃₁	semidirect
402. C₂×#137	C₂²×C₃₁	semidirect
403. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
404. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
406. C₂×#135	C₂²×C₃₁	semidirect
407. C₂×#135	C₂²×C₃₁	semidirect
408. C₂×#135	C₂²×C₃₁	semidirect
409. C₂²×M₁₆	C₂²×C₃₁	semidirect
411. D₄×Q₈	C₂²×C₃₁	semidirect
412. #548	C₂²×C₃₁	semidirect
416. #546	C₂²×C₃₁	semidirect
418. D₄²	C₂²×C₃₁	semidirect
420. #532	C₂²×C₃₁	semidirect
422. #525	C₂²×C₃₁	semidirect
423. C₄×#41	C₂²×C₃₁	semidirect
426. #495	C₂²×C₃₁	semidirect
427. #495	C₂²×C₃₁	semidirect
428. #494	C₂²×C₃₁	semidirect
429. #493	C₂²×C₃₁	semidirect
430. #492	C₂²×C₃₁	semidirect
431. #470	C₂²×C₃₁	semidirect
432. #469	C₂²×C₃₁	semidirect
433. #468	C₂²×C₃₁	semidirect
434. #468	C₂²×C₃₁	semidirect
435. #464	C₂²×C₃₁	semidirect
436. #463	C₂²×C₃₁	semidirect
437. #462	C₂²×C₃₁	semidirect
438. #461	C₂²×C₃₁	semidirect
439. #460	C₂²×C₃₁	semidirect
440. #459	C₂²×C₃₁	semidirect
441. #452	C₂²×C₃₁	semidirect
442. #452	C₂²×C₃₁	semidirect
443. #451	C₂²×C₃₁	semidirect
444. #450	C₂²×C₃₁	semidirect
445. #449	C₂²×C₃₁	semidirect
446. #449	C₂²×C₃₁	semidirect
447. #448	C₂²×C₃₁	semidirect
448. #447	C₂²×C₃₁	semidirect
449. C₄×Q₁₆	C₂²×C₃₁	semidirect
450. C₄×Q₁₆	C₂²×C₃₁	semidirect
451. C₄×SD₁₆	C₂²×C₃₁	semidirect
452. C₄×SD₁₆	C₂²×C₃₁	semidirect
453. C₄×D₈	C₂²×C₃₁	semidirect
454. C₄×D₈	C₂²×C₃₁	semidirect
455. #436	C₂²×C₃₁	semidirect
456. #436	C₂²×C₃₁	semidirect
457. #436	C₂²×C₃₁	semidirect
458. #436	C₂²×C₃₁	semidirect
459. #427	C₂²×C₃₁	semidirect
460. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
461. #416	C₂²×C₃₁	semidirect
462. #416	C₂²×C₃₁	semidirect
463. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
464. C₂×C₄×C₈	C₂²×C₃₁	semidirect
494. #135	D₄×C₃₁	semidirect
583. C₃₁	#61038	direct (N × H)
595. #41	C₂×D₄×C₃₁	semidirect
638. Q₁₆	C₂×D₄×C₃₁	semidirect
643. SD₁₆	C₂×D₄×C₃₁	semidirect
647. D₈	C₂×D₄×C₃₁	semidirect
652. C₂×C₈	C₂×D₄×C₃₁	semidirect
771. C₄	C₃₁×#575	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#575	2
D₄×#41×C₃₁	2
C₃₁×#3278	2
C₃₁×#3277	2
C₃₁×#3276	2
C₃₁×#3275	2
C₃₁×#3274	2
C₃₁×#3273	2
C₃₁×#3272	2
C₃₁×#3147	2
C₃₁×#3054	2
C₃₁×#3035	2
C₃₁×#3002	2
C₄×C₃₁×#135	2
C₂×C₃₁×#436	2
#61038	31

Subgroups — C31×#61038 #21517797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61038 #21517797