Subgroups — C₃₁×#60768 #21517527

Order 7936.

2268 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3488	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3203	C₂	1	2	yes	maximal, complemented
3	C₃₁×#3199	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3198	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3191	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3188	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3186	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3098	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3096	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3055	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3050	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#466	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3012	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3008	C₂	1	2	yes	maximal, complemented
15	C₂×C₃₁×#408	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	2	yes	complemented
17	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
19	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
21	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
22	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
23	C₃₁×#550	—	2	2	no	—
24	C₃₁×#548	—	2	2	no	—
25	C₃₁×#546	—	2	4	no	—
26	C₃₁×#546	—	2	2	no	—
27	D₄²×C₃₁	—	2	4	no	—
28	D₄²×C₃₁	—	2	2	no	—
29	C₃₁×#537	C₂²	1	2	yes	—
30	C₃₁×#537	C₂²	1	4	yes	complemented
31	C₃₁×#535	C₂²	1	2	yes	—
32	C₃₁×#535	C₂²	1	4	yes	complemented
33	C₃₁×#525	C₂²	1	4	yes	complemented
34	C₃₁×#525	C₂²	1	2	yes	complemented
35	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
36	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
37	C₃₁×#520	C₂²	1	2	yes	complemented
38	C₃₁×#485	C₂²	1	4	yes	complemented
39	C₃₁×#484	C₂²	1	4	yes	complemented
40	C₃₁×#482	C₂²	1	4	yes	complemented
41	C₃₁×#482	C₂²	1	4	yes	complemented
42	C₃₁×#482	C₂²	1	4	yes	complemented
43	C₃₁×#481	C₂²	1	4	yes	complemented
44	C₃₁×#480	C₂²	1	4	yes	complemented
45	C₃₁×#480	C₂²	1	4	yes	complemented
46	C₃₁×#469	C₂²	1	4	yes	complemented
47	C₃₁×#468	C₂²	1	4	yes	complemented
48	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#466	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#466	C₂²	1	4	yes	complemented
52	C₃₁×#466	C₂²	1	2	yes	complemented
53	C₃₁×#466	C₂²	1	2	yes	complemented
54	C₃₁×#466	C₂²	1	2	yes	complemented
55	C₃₁×#466	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#466	C₂²	1	2	yes	complemented
57	C₃₁×#465	C₂²	1	2	yes	complemented
58	C₃₁×#465	C₂²	1	4	yes	complemented
59	C₃₁×#465	C₂²	1	2	yes	complemented
60	C₃₁×#452	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×#449	C₂²	1	4	yes	complemented
65	C₃₁×#447	C₂²	1	4	yes	complemented
66	C₃₁×#447	C₂²	1	4	yes	complemented
67	C₃₁×#447	C₂²	1	4	yes	complemented
68	C₃₁×#428	C₂²	1	2	yes	complemented
69	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#418	C₂²	1	2	yes	complemented
72	C₃₁×#417	C₂²	1	2	yes	complemented
73	C₃₁×#416	C₂²	1	2	yes	complemented
74	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
75	C₃₁×#408	C₂²	1	2	yes	complemented
76	C₃₁×#408	C₂²	1	2	yes	complemented
77	C₃₁×#408	C₂²	1	2	yes	complemented
78	C₃₁×#408	C₂²	1	2	yes	complemented
79	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
80	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
81	C₃₁×H(5,𝔽₂)	—	4	4	no	—
82	C₃₁×H(5,𝔽₂)	—	4	4	no	—
83	C₂×#41×C₃₁	—	2	2	no	—
84	C₂×#41×C₃₁	—	4	2	no	—
85	C₂×#41×C₃₁	—	4	2	no	—
86	C₂×#41×C₃₁	D₄	1	2	yes	—
87	C₂×#41×C₃₁	D₄	1	2	yes	—
88	C₂×#41×C₃₁	C₂³	1	2	yes	—
89	C₂×#41×C₃₁	C₂³	1	4	yes	—
90	C₂×#41×C₃₁	C₂³	1	2	yes	—
91	C₂×#41×C₃₁	C₂³	1	2	yes	—
92	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
93	C₂²×D₄×C₃₁	—	2	2	no	—
94	C₂²×D₄×C₃₁	—	2	4	no	—
95	C₂²×D₄×C₃₁	—	2	4	no	—
96	C₂²×D₄×C₃₁	—	2	2	no	—
97	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
98	C₂²×D₄×C₃₁	D₄	1	2	yes	—
99	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
100	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
101	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
103	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
104	C₃₁×#135	—	4	2	no	—
105	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
106	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
107	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
108	C₂×D₈×C₃₁	—	4	2	no	—
109	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
110	C₂×D₈×C₃₁	C₂³	1	4	yes	—
111	C₂×D₈×C₃₁	C₂³	1	2	yes	—
112	C₂×D₈×C₃₁	C₂³	1	2	yes	—
113	C₂×M₁₆×C₃₁	—	4	2	no	—
114	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
115	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
116	C₂²×C₈×C₃₁	—	4	2	no	—
117	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
121	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
124	C₃₁×#127	—	2	2	no	—
125	C₃₁×#127	—	2	4	no	—
126	C₃₁×#124	—	2	2	no	—
127	C₃₁×#124	—	2	4	no	—
128	C₃₁×#123	—	2	2	no	—
129	C₃₁×#123	—	2	4	no	—
130	C₃₁×C₂²⋊Q₈	—	2	2	no	—
131	C₃₁×C₂²⋊Q₈	—	2	4	no	—
132	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
133	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
134	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₃₁×#121	—	2	4	no	—
136	C₃₁×#121	—	2	2	no	—
137	C₃₁×#121	—	2	4	no	—
138	C₃₁×#121	—	2	4	no	—
139	C₃₁×#121	—	2	4	no	—
140	C₃₁×#121	—	2	2	no	—
141	C₃₁×#121	—	2	4	no	—
142	C₃₁×#121	—	2	2	no	—
143	C₃₁×#121	—	2	4	no	—
144	C₃₁×#121	C₂³	1	4	yes	—
145	C₃₁×#121	C₂³	1	4	yes	—
146	C₃₁×#121	C₂³	1	4	yes	—
147	C₃₁×#121	C₂³	1	2	yes	—
148	C₃₁×#121	C₂³	1	4	yes	—
149	C₃₁×#121	C₂³	1	2	yes	—
150	C₃₁×#121	C₂³	1	4	yes	—
151	C₃₁×#120	—	2	2	no	—
152	C₃₁×#120	—	2	4	no	—
153	C₃₁×#120	—	2	4	no	—
154	C₃₁×#120	—	2	4	no	—
155	C₃₁×#120	—	2	4	no	—
156	C₄×Q₈×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	—	2	4	no	—
161	C₄×D₄×C₃₁	—	2	2	no	—
162	C₄×D₄×C₃₁	—	2	4	no	—
163	C₃₁×#117	C₂³	1	2	yes	—
164	C₃₁×#117	C₂³	1	4	yes	—
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
167	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
168	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
169	C₃₁×#107	C₂³	1	2	yes	—
170	C₃₁×#107	C₂³	1	2	yes	—
171	C₃₁×#107	C₂³	1	1	yes	characteristic
172	C₃₁×#107	C₂³	1	1	yes	characteristic
173	C₃₁×#107	C₂³	1	4	yes	—
174	C₃₁×#106	C₂³	1	2	yes	—
175	C₃₁×#106	C₂³	1	4	yes	—
176	C₃₁×#103	C₂³	1	2	yes	—
177	C₃₁×#103	C₂³	1	2	yes	—
178	C₃₁×#103	C₂³	1	4	yes	—
179	C₃₁×#102	C₂³	1	4	yes	—
180	C₃₁×#102	C₂³	1	4	yes	—
181	C₃₁×#102	C₂³	1	2	yes	—
182	C₃₁×#102	C₂³	1	2	yes	—
183	C₃₁×#102	C₂³	1	4	yes	—
184	C₃₁×#102	C₂³	1	4	yes	—
185	C₃₁×#102	C₂³	1	4	yes	—
186	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
187	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
188	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
189	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
190	C₂⁴×C₃₁	—	2	4	no	—
191	C₂⁴×C₃₁	—	2	2	no	—
192	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
193	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
194	#41×C₃₁	—	2	4	no	—
195	#41×C₃₁	—	2	4	no	—
196	#41×C₃₁	—	2	4	no	—
197	#41×C₃₁	—	2	4	no	—
198	#41×C₃₁	—	4	2	no	—
199	#41×C₃₁	—	4	2	no	—
200	#41×C₃₁	—	4	4	no	—
201	#41×C₃₁	—	4	4	no	—
202	#41×C₃₁	—	4	4	no	—
203	#41×C₃₁	—	4	4	no	—
204	#41×C₃₁	—	4	8	no	—
205	C₂×Q₈×C₃₁	—	4	2	no	—
206	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
207	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
209	C₂×D₄×C₃₁	—	2	2	no	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	2	4	no	—
212	C₂×D₄×C₃₁	—	2	2	no	—
213	C₂×D₄×C₃₁	—	2	4	no	—
214	C₂×D₄×C₃₁	—	2	2	no	—
215	C₂×D₄×C₃₁	—	2	4	no	—
216	C₂×D₄×C₃₁	—	2	4	no	—
217	C₂×D₄×C₃₁	—	2	4	no	—
218	C₂×D₄×C₃₁	—	2	4	no	—
219	C₂×D₄×C₃₁	—	2	2	no	—
220	C₂×D₄×C₃₁	—	2	4	no	—
221	C₂×D₄×C₃₁	—	2	4	no	—
222	C₂×D₄×C₃₁	—	4	2	no	—
223	C₂×D₄×C₃₁	—	4	4	no	—
224	C₂×D₄×C₃₁	—	4	4	no	—
225	C₂×D₄×C₃₁	—	4	4	no	—
226	C₂×D₄×C₃₁	—	4	16	no	—
227	C₂×D₄×C₃₁	—	4	8	no	—
228	C₂×D₄×C₃₁	—	8	4	no	—
229	C₂×D₄×C₃₁	—	8	8	no	—
230	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
231	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
232	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
233	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
234	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
235	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₃₁	—	2	2	no	—
237	C₂²×C₄×C₃₁	—	2	2	no	—
238	C₂²×C₄×C₃₁	—	2	4	no	—
239	C₂²×C₄×C₃₁	—	2	2	no	—
240	C₂²×C₄×C₃₁	—	2	4	no	—
241	C₂²×C₄×C₃₁	—	2	2	no	—
242	C₂²×C₄×C₃₁	—	4	2	no	—
243	C₂²×C₄×C₃₁	—	4	2	no	—
244	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
248	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
249	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
253	Q₁₆×C₃₁	—	4	1	no	—
254	SD₁₆×C₃₁	—	4	2	no	—
255	SD₁₆×C₃₁	—	4	4	no	—
256	D₈×C₃₁	—	4	2	no	—
257	D₈×C₃₁	—	4	2	no	—
258	D₈×C₃₁	—	4	1	no	—
259	D₈×C₃₁	—	4	4	no	—
260	M₁₆×C₃₁	—	2	4	no	—
261	M₁₆×C₃₁	—	4	2	no	—
262	C₂×C₈×C₃₁	—	2	2	no	—
263	C₂×C₈×C₃₁	—	2	2	no	—
264	C₂×C₈×C₃₁	—	4	1	no	—
265	C₂×C₈×C₃₁	—	4	1	no	—
266	C₂×C₈×C₃₁	—	4	1	no	—
267	C₂×C₈×C₃₁	—	4	1	no	—
268	C₂×C₈×C₃₁	—	4	2	no	—
269	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
270	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
271	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
272	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
273	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
274	C₄⋊C₄×C₃₁	—	2	4	no	—
275	C₄⋊C₄×C₃₁	—	2	2	no	—
276	C₄⋊C₄×C₃₁	—	2	2	no	—
277	C₄⋊C₄×C₃₁	—	2	4	no	—
278	C₄⋊C₄×C₃₁	—	2	2	no	—
279	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
281	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
282	C₂²⋊C₄×C₃₁	—	2	4	no	—
283	C₂²⋊C₄×C₃₁	—	2	2	no	—
284	C₂²⋊C₄×C₃₁	—	2	2	no	—
285	C₂²⋊C₄×C₃₁	—	2	4	no	—
286	C₂²⋊C₄×C₃₁	—	2	2	no	—
287	C₂²⋊C₄×C₃₁	—	2	4	no	—
288	C₂²⋊C₄×C₃₁	—	2	2	no	—
289	C₂²⋊C₄×C₃₁	—	2	4	no	—
290	C₂²⋊C₄×C₃₁	—	2	4	no	—
291	C₂²⋊C₄×C₃₁	—	2	4	no	—
292	C₂²⋊C₄×C₃₁	—	2	4	no	—
293	C₂²⋊C₄×C₃₁	—	2	2	no	—
294	C₄²×C₃₁	—	2	4	no	—
295	C₄²×C₃₁	—	2	2	no	—
296	#60768	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
297	C₂³×C₃₁	—	2	2	no	—
298	C₂³×C₃₁	—	2	2	no	—
299	C₂³×C₃₁	—	2	4	no	—
300	C₂³×C₃₁	—	2	4	no	—
301	C₂³×C₃₁	—	2	2	no	—
302	C₂³×C₃₁	—	4	1	no	—
303	C₂³×C₃₁	—	4	2	no	—
304	C₂³×C₃₁	—	4	2	no	—
305	C₂³×C₃₁	—	4	8	no	—
306	C₂³×C₃₁	—	4	4	no	—
307	C₂³×C₃₁	—	8	2	no	—
308	C₂³×C₃₁	—	8	4	no	—
309	C₂³×C₃₁	—	8	2	no	—
310	C₂³×C₃₁	—	8	4	no	—
311	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
312	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
313	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
314	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
315	Q₈×C₃₁	—	2	4	no	—
316	Q₈×C₃₁	—	2	2	no	—
317	Q₈×C₃₁	—	2	2	no	—
318	Q₈×C₃₁	—	4	2	no	—
319	D₄×C₃₁	—	2	8	no	—
320	D₄×C₃₁	—	2	4	no	—
321	D₄×C₃₁	—	2	4	no	—
322	D₄×C₃₁	—	2	2	no	—
323	D₄×C₃₁	—	2	4	no	—
324	D₄×C₃₁	—	2	2	no	—
325	D₄×C₃₁	—	4	2	no	—
326	D₄×C₃₁	—	4	4	no	—
327	D₄×C₃₁	—	4	8	no	—
328	D₄×C₃₁	—	4	8	no	—
329	D₄×C₃₁	—	4	4	no	—
330	D₄×C₃₁	—	4	8	no	—
331	D₄×C₃₁	—	4	4	no	—
332	D₄×C₃₁	—	4	4	no	—
333	D₄×C₃₁	—	8	2	no	—
334	D₄×C₃₁	—	8	4	no	—
335	D₄×C₃₁	—	8	4	no	—
336	D₄×C₃₁	—	8	4	no	—
337	D₄×C₃₁	—	8	4	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	2	2	no	—
340	C₂×C₄×C₃₁	—	2	2	no	—
341	C₂×C₄×C₃₁	—	2	1	no	—
342	C₂×C₄×C₃₁	—	2	1	no	—
343	C₂×C₄×C₃₁	—	2	1	no	—
344	C₂×C₄×C₃₁	—	2	1	no	—
345	C₂×C₄×C₃₁	—	2	4	no	—
346	C₂×C₄×C₃₁	—	2	4	no	—
347	C₂×C₄×C₃₁	—	2	2	no	—
348	C₂×C₄×C₃₁	—	2	4	no	—
349	C₂×C₄×C₃₁	—	2	2	no	—
350	C₂×C₄×C₃₁	—	2	2	no	—
351	C₂×C₄×C₃₁	—	4	2	no	—
352	C₂×C₄×C₃₁	—	4	4	no	—
353	C₂×C₄×C₃₁	—	4	8	no	—
354	C₂×C₄×C₃₁	—	4	4	no	—
355	C₂×C₄×C₃₁	—	8	2	no	—
356	C₂×C₄×C₃₁	—	8	4	no	—
357	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
358	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
362	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
363	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
364	C₈×C₃₁	—	2	1	no	—
365	C₈×C₃₁	—	2	1	no	—
366	C₈×C₃₁	—	2	1	no	—
367	C₈×C₃₁	—	2	1	no	—
368	C₈×C₃₁	—	2	4	no	—
369	#3488	C₂×C₃₁	1	2	yes	complemented
370	#3203	C₂×C₃₁	1	2	yes	complemented
371	#3199	C₂×C₃₁	1	2	yes	complemented
372	#3198	C₂×C₃₁	1	4	yes	complemented
373	#3191	C₂×C₃₁	1	2	yes	complemented
374	#3188	C₂×C₃₁	1	4	yes	complemented
375	#3186	C₂×C₃₁	1	2	yes	complemented
376	#3098	C₂×C₃₁	1	2	yes	complemented
377	#3096	C₂×C₃₁	1	2	yes	complemented
378	#3055	C₂×C₃₁	1	2	yes	complemented
379	#3050	C₂×C₃₁	1	1	yes	characteristic, complemented
380	C₂×#466	C₂×C₃₁	1	1	yes	characteristic, complemented
381	#3012	C₂×C₃₁	1	2	yes	complemented
382	#3008	C₂×C₃₁	1	2	yes	complemented
383	C₂×#408	C₂×C₃₁	1	1	yes	characteristic, complemented
384	C₂²×C₃₁	—	2	1	no	—
385	C₂²×C₃₁	—	2	1	no	—
386	C₂²×C₃₁	—	2	1	no	—
387	C₂²×C₃₁	—	2	1	no	—
388	C₂²×C₃₁	—	2	1	no	—
389	C₂²×C₃₁	—	2	4	no	—
390	C₂²×C₃₁	—	2	1	no	—
391	C₂²×C₃₁	—	2	4	no	—
392	C₂²×C₃₁	—	2	4	no	—
393	C₂²×C₃₁	—	2	1	no	—
394	C₂²×C₃₁	—	4	4	no	—
395	C₂²×C₃₁	—	4	4	no	—
396	C₂²×C₃₁	—	4	2	no	—
397	C₂²×C₃₁	—	4	4	no	—
398	C₂²×C₃₁	—	4	2	no	—
399	C₂²×C₃₁	—	4	4	no	—
400	C₂²×C₃₁	—	4	2	no	—
401	C₂²×C₃₁	—	8	4	no	—
402	C₂²×C₃₁	—	16	4	no	—
403	C₂²×C₃₁	—	16	8	no	—
404	C₂²×C₃₁	#534	1	2	yes	—
405	C₂²×C₃₁	#576	1	2	yes	—
406	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
407	C₄×C₃₁	—	2	1	no	—
408	C₄×C₃₁	—	2	1	no	—
409	C₄×C₃₁	—	2	4	no	—
410	C₄×C₃₁	—	4	2	no	—
411	C₄×C₃₁	—	4	2	no	—
412	C₄×C₃₁	—	4	4	no	—
413	C₄×C₃₁	—	4	2	no	—
414	C₄×C₃₁	#534	1	2	yes	—
415	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
416	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
417	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	2	yes	complemented
418	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
419	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
420	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic, complemented
421	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
422	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
423	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
424	#550	—	2	2	no	—
425	#548	—	2	2	no	—
426	#546	—	2	4	no	—
427	#546	—	2	2	no	—
428	D₄²	—	2	4	no	—
429	D₄²	—	2	2	no	—
430	#537	C₂²×C₃₁	1	2	yes	—
431	#537	C₂²×C₃₁	1	4	yes	complemented
432	#535	C₂²×C₃₁	1	2	yes	—
433	#535	C₂²×C₃₁	1	4	yes	complemented
434	#525	C₂²×C₃₁	1	4	yes	complemented
435	#525	C₂²×C₃₁	1	2	yes	complemented
436	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
437	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
438	#520	C₂²×C₃₁	1	2	yes	complemented
439	#485	C₂²×C₃₁	1	4	yes	complemented
440	#484	C₂²×C₃₁	1	4	yes	complemented
441	#482	C₂²×C₃₁	1	4	yes	complemented
442	#482	C₂²×C₃₁	1	4	yes	complemented
443	#482	C₂²×C₃₁	1	4	yes	complemented
444	#481	C₂²×C₃₁	1	4	yes	complemented
445	#480	C₂²×C₃₁	1	4	yes	complemented
446	#480	C₂²×C₃₁	1	4	yes	complemented
447	#469	C₂²×C₃₁	1	4	yes	complemented
448	#468	C₂²×C₃₁	1	4	yes	complemented
449	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
450	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
451	#466	C₂²×C₃₁	1	1	yes	characteristic, complemented
452	#466	C₂²×C₃₁	1	4	yes	complemented
453	#466	C₂²×C₃₁	1	2	yes	complemented
454	#466	C₂²×C₃₁	1	2	yes	complemented
455	#466	C₂²×C₃₁	1	2	yes	complemented
456	#466	C₂²×C₃₁	1	1	yes	characteristic, complemented
457	#466	C₂²×C₃₁	1	2	yes	complemented
458	#465	C₂²×C₃₁	1	2	yes	complemented
459	#465	C₂²×C₃₁	1	4	yes	complemented
460	#465	C₂²×C₃₁	1	2	yes	complemented
461	#452	C₂²×C₃₁	1	4	yes	complemented
462	#450	C₂²×C₃₁	1	4	yes	complemented
463	#449	C₂²×C₃₁	1	4	yes	complemented
464	#449	C₂²×C₃₁	1	4	yes	complemented
465	#449	C₂²×C₃₁	1	4	yes	complemented
466	#447	C₂²×C₃₁	1	4	yes	complemented
467	#447	C₂²×C₃₁	1	4	yes	complemented
468	#447	C₂²×C₃₁	1	4	yes	complemented
469	#428	C₂²×C₃₁	1	2	yes	complemented
470	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
471	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
472	#418	C₂²×C₃₁	1	2	yes	complemented
473	#417	C₂²×C₃₁	1	2	yes	complemented
474	#416	C₂²×C₃₁	1	2	yes	complemented
475	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
476	#408	C₂²×C₃₁	1	2	yes	complemented
477	#408	C₂²×C₃₁	1	2	yes	complemented
478	#408	C₂²×C₃₁	1	2	yes	complemented
479	#408	C₂²×C₃₁	1	2	yes	complemented
480	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	complemented
481	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	complemented
482	C₂×C₃₁	—	2	2	no	—
483	C₂×C₃₁	—	2	2	no	—
484	C₂×C₃₁	—	4	1	no	—
485	C₂×C₃₁	—	4	4	no	—
486	C₂×C₃₁	—	8	4	no	—
487	C₂×C₃₁	—	8	2	no	—
488	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
489	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
490	C₂×C₃₁	#3584	1	1	yes	characteristic
491	H(5,𝔽₂)	—	4	4	no	—
492	H(5,𝔽₂)	—	4	4	no	—
493	C₂×#41	—	2	2	no	—
494	C₂×#41	—	4	2	no	—
495	C₂×#41	—	4	2	no	—
496	C₂×#41	D₄×C₃₁	1	2	yes	—
497	C₂×#41	D₄×C₃₁	1	2	yes	—
498	C₂×#41	C₂³×C₃₁	1	2	yes	—
499	C₂×#41	C₂³×C₃₁	1	4	yes	—
500	C₂×#41	C₂³×C₃₁	1	2	yes	—
501	C₂×#41	C₂³×C₃₁	1	2	yes	—
502	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
503	C₂²×D₄	—	2	2	no	—
504	C₂²×D₄	—	2	4	no	—
505	C₂²×D₄	—	2	4	no	—
506	C₂²×D₄	—	2	2	no	—
507	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
508	C₂²×D₄	D₄×C₃₁	1	2	yes	—
509	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
510	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
511	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
513	AGL(1,ℤ/8)	—	4	4	no	—
514	#135	—	4	2	no	—
515	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
516	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
517	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
518	C₂×D₈	—	4	2	no	—
519	C₂×D₈	C₂³×C₃₁	1	2	yes	—
520	C₂×D₈	C₂³×C₃₁	1	2	yes	—
521	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
522	C₂×D₈	C₂³×C₃₁	1	4	yes	—
523	C₂×M₁₆	—	4	2	no	—
524	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
525	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
526	C₂²×C₈	—	4	2	no	—
527	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
528	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
529	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
530	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
531	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
532	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
533	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
534	#127	—	2	2	no	—
535	#127	—	2	4	no	—
536	#124	—	2	2	no	—
537	#124	—	2	4	no	—
538	#123	—	2	2	no	—
539	#123	—	2	4	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	2	4	no	—
542	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
543	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
544	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
545	#121	—	2	4	no	—
546	#121	—	2	2	no	—
547	#121	—	2	4	no	—
548	#121	—	2	4	no	—
549	#121	—	2	4	no	—
550	#121	—	2	2	no	—
551	#121	—	2	4	no	—
552	#121	—	2	2	no	—
553	#121	—	2	4	no	—
554	#121	C₂³×C₃₁	1	2	yes	—
555	#121	C₂³×C₃₁	1	4	yes	—
556	#121	C₂³×C₃₁	1	4	yes	—
557	#121	C₂³×C₃₁	1	4	yes	—
558	#121	C₂³×C₃₁	1	4	yes	—
559	#121	C₂³×C₃₁	1	4	yes	—
560	#121	C₂³×C₃₁	1	2	yes	—
561	#120	—	2	2	no	—
562	#120	—	2	4	no	—
563	#120	—	2	4	no	—
564	#120	—	2	4	no	—
565	#120	—	2	4	no	—
566	C₄×Q₈	—	2	2	no	—
567	C₄×D₄	—	2	4	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	4	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	4	no	—
573	#117	C₂³×C₃₁	1	2	yes	—
574	#117	C₂³×C₃₁	1	4	yes	—
575	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
577	C₂×C₂²⋊C₄	—	2	2	no	—
578	C₂×C₂²⋊C₄	—	2	4	no	—
579	#107	C₂³×C₃₁	1	2	yes	—
580	#107	C₂³×C₃₁	1	2	yes	—
581	#107	C₂³×C₃₁	1	1	yes	characteristic
582	#107	C₂³×C₃₁	1	1	yes	characteristic
583	#107	C₂³×C₃₁	1	4	yes	—
584	#106	C₂³×C₃₁	1	2	yes	—
585	#106	C₂³×C₃₁	1	4	yes	—
586	#103	C₂³×C₃₁	1	2	yes	—
587	#103	C₂³×C₃₁	1	2	yes	—
588	#103	C₂³×C₃₁	1	4	yes	—
589	#102	C₂³×C₃₁	1	4	yes	—
590	#102	C₂³×C₃₁	1	4	yes	—
591	#102	C₂³×C₃₁	1	2	yes	—
592	#102	C₂³×C₃₁	1	2	yes	—
593	#102	C₂³×C₃₁	1	4	yes	—
594	#102	C₂³×C₃₁	1	4	yes	—
595	#102	C₂³×C₃₁	1	4	yes	—
596	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
597	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
598	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
599	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
600	C₃₁	#60768	1	1	yes	characteristic, direct product factor, Sylow
601	C₂⁴	—	2	4	no	—
602	C₂⁴	—	2	2	no	—
603	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
604	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
605	#41	—	2	4	no	—
606	#41	—	2	4	no	—
607	#41	—	2	4	no	—
608	#41	—	2	4	no	—
609	#41	—	4	2	no	—
610	#41	—	4	2	no	—
611	#41	—	4	4	no	—
612	#41	—	4	4	no	—
613	#41	—	4	4	no	—
614	#41	—	4	4	no	—
615	#41	—	4	8	no	—
616	C₂×Q₈	—	4	2	no	—
617	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
618	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
619	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	4	2	no	—
634	C₂×D₄	—	4	4	no	—
635	C₂×D₄	—	4	4	no	—
636	C₂×D₄	—	4	4	no	—
637	C₂×D₄	—	4	16	no	—
638	C₂×D₄	—	4	8	no	—
639	C₂×D₄	—	8	4	no	—
640	C₂×D₄	—	8	8	no	—
641	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
642	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
643	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
644	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
645	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
646	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
659	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
661	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
664	Q₁₆	—	4	1	no	—
665	SD₁₆	—	4	2	no	—
666	SD₁₆	—	4	4	no	—
667	D₈	—	4	2	no	—
668	D₈	—	4	2	no	—
669	D₈	—	4	1	no	—
670	D₈	—	4	4	no	—
671	M₁₆	—	2	4	no	—
672	M₁₆	—	4	2	no	—
673	C₂×C₈	—	2	2	no	—
674	C₂×C₈	—	2	2	no	—
675	C₂×C₈	—	4	1	no	—
676	C₂×C₈	—	4	1	no	—
677	C₂×C₈	—	4	1	no	—
678	C₂×C₈	—	4	1	no	—
679	C₂×C₈	—	4	2	no	—
680	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
681	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
682	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
683	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
684	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
691	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
692	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₄²	—	2	4	no	—
706	C₄²	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	4	no	—
710	C₂³	—	2	4	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	2	no	—
714	C₂³	—	4	2	no	—
715	C₂³	—	4	8	no	—
716	C₂³	—	4	4	no	—
717	C₂³	—	8	2	no	—
718	C₂³	—	8	4	no	—
719	C₂³	—	8	2	no	—
720	C₂³	—	8	4	no	—
721	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
722	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
723	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
724	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
725	Q₈	—	2	4	no	—
726	Q₈	—	2	2	no	—
727	Q₈	—	2	2	no	—
728	Q₈	—	4	2	no	—
729	D₄	—	2	8	no	—
730	D₄	—	2	4	no	—
731	D₄	—	2	4	no	—
732	D₄	—	2	2	no	—
733	D₄	—	2	4	no	—
734	D₄	—	2	2	no	—
735	D₄	—	4	2	no	—
736	D₄	—	4	4	no	—
737	D₄	—	4	8	no	—
738	D₄	—	4	8	no	—
739	D₄	—	4	4	no	—
740	D₄	—	4	8	no	—
741	D₄	—	4	4	no	—
742	D₄	—	4	4	no	—
743	D₄	—	8	2	no	—
744	D₄	—	8	4	no	—
745	D₄	—	8	4	no	—
746	D₄	—	8	4	no	—
747	D₄	—	8	4	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	4	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	—	4	4	no	—
763	C₂×C₄	—	4	8	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	8	2	no	—
766	C₂×C₄	—	8	4	no	—
767	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
768	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
769	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
770	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
771	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
772	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
773	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
774	C₈	—	2	1	no	—
775	C₈	—	2	1	no	—
776	C₈	—	2	1	no	—
777	C₈	—	2	1	no	—
778	C₈	—	2	4	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	2	1	no	—
781	C₂²	—	2	1	no	—
782	C₂²	—	2	1	no	—
783	C₂²	—	2	1	no	—
784	C₂²	—	2	4	no	—
785	C₂²	—	2	4	no	—
786	C₂²	—	2	1	no	—
787	C₂²	—	2	1	no	—
788	C₂²	—	2	4	no	—
789	C₂²	—	4	4	no	—
790	C₂²	—	4	4	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	4	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	4	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	8	4	no	—
797	C₂²	—	16	4	no	—
798	C₂²	—	16	8	no	—
799	C₂²	C₃₁×#534	1	2	yes	—
800	C₂²	C₃₁×#576	1	2	yes	—
801	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	2	4	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	4	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	C₃₁×#534	1	2	yes	—
810	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
811	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
812	C₂	—	2	2	no	—
813	C₂	—	2	2	no	—
814	C₂	—	4	1	no	—
815	C₂	—	4	4	no	—
816	C₂	—	8	4	no	—
817	C₂	—	8	2	no	—
818	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
819	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
820	C₂	C₃₁×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3488	C₂	semidirect
2. C₃₁×#3203	C₂	semidirect
3. C₃₁×#3199	C₂	semidirect
4. C₃₁×#3198	C₂	semidirect
5. C₃₁×#3191	C₂	semidirect
6. C₃₁×#3188	C₂	semidirect
7. C₃₁×#3186	C₂	semidirect
8. C₃₁×#3098	C₂	semidirect
9. C₃₁×#3096	C₂	semidirect
10. C₃₁×#3055	C₂	semidirect
11. C₃₁×#3050	C₂	semidirect
12. C₂×C₃₁×#466	C₂	semidirect
13. C₃₁×#3012	C₂	semidirect
14. C₃₁×#3008	C₂	semidirect
15. C₂×C₃₁×#408	C₂	semidirect
16. C₂×C₃₁×H(5,𝔽₂)	C₂²	semidirect
18. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
19. C₂×C₃₁×#135	C₂²	semidirect
20. C₂²×D₈×C₃₁	C₂²	semidirect
21. C₂²×M₁₆×C₃₁	C₂²	semidirect
22. C₂³×C₈×C₃₁	C₂²	semidirect
30. C₃₁×#537	C₂²	semidirect
32. C₃₁×#535	C₂²	semidirect
33. C₃₁×#525	C₂²	semidirect
34. C₃₁×#525	C₂²	semidirect
35. C₂×C₃₁×#121	C₂²	semidirect
36. C₂×C₃₁×#121	C₂²	semidirect
37. C₃₁×#520	C₂²	semidirect
38. C₃₁×#485	C₂²	semidirect
39. C₃₁×#484	C₂²	semidirect
40. C₃₁×#482	C₂²	semidirect
41. C₃₁×#482	C₂²	semidirect
42. C₃₁×#482	C₂²	semidirect
43. C₃₁×#481	C₂²	semidirect
44. C₃₁×#480	C₂²	semidirect
45. C₃₁×#480	C₂²	semidirect
46. C₃₁×#469	C₂²	semidirect
47. C₃₁×#468	C₂²	semidirect
48. C₃₁×#467	C₂²	semidirect
49. C₃₁×#467	C₂²	semidirect
50. C₃₁×#466	C₂²	semidirect
51. C₃₁×#466	C₂²	semidirect
52. C₃₁×#466	C₂²	semidirect
53. C₃₁×#466	C₂²	semidirect
54. C₃₁×#466	C₂²	semidirect
55. C₃₁×#466	C₂²	semidirect
56. C₃₁×#466	C₂²	semidirect
57. C₃₁×#465	C₂²	semidirect
58. C₃₁×#465	C₂²	semidirect
59. C₃₁×#465	C₂²	semidirect
60. C₃₁×#452	C₂²	semidirect
61. C₃₁×#450	C₂²	semidirect
62. C₃₁×#449	C₂²	semidirect
63. C₃₁×#449	C₂²	semidirect
64. C₃₁×#449	C₂²	semidirect
65. C₃₁×#447	C₂²	semidirect
66. C₃₁×#447	C₂²	semidirect
67. C₃₁×#447	C₂²	semidirect
68. C₃₁×#428	C₂²	semidirect
69. C₃₁×#427	C₂²	semidirect
70. C₂×C₃₁×#107	C₂²	semidirect
71. C₃₁×#418	C₂²	semidirect
72. C₃₁×#417	C₂²	semidirect
73. C₃₁×#416	C₂²	semidirect
74. C₂×C₃₁×#102	C₂²	semidirect
75. C₃₁×#408	C₂²	semidirect
76. C₃₁×#408	C₂²	semidirect
77. C₃₁×#408	C₂²	semidirect
78. C₃₁×#408	C₂²	semidirect
79. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
80. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
296. #60768	C₃₁	direct (N × H)
369. #3488	C₂×C₃₁	semidirect
370. #3203	C₂×C₃₁	semidirect
371. #3199	C₂×C₃₁	semidirect
372. #3198	C₂×C₃₁	semidirect
373. #3191	C₂×C₃₁	semidirect
374. #3188	C₂×C₃₁	semidirect
375. #3186	C₂×C₃₁	semidirect
376. #3098	C₂×C₃₁	semidirect
377. #3096	C₂×C₃₁	semidirect
378. #3055	C₂×C₃₁	semidirect
379. #3050	C₂×C₃₁	semidirect
380. C₂×#466	C₂×C₃₁	semidirect
381. #3012	C₂×C₃₁	semidirect
382. #3008	C₂×C₃₁	semidirect
383. C₂×#408	C₂×C₃₁	semidirect
417. C₂×H(5,𝔽₂)	C₂²×C₃₁	semidirect
419. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
420. C₂×#135	C₂²×C₃₁	semidirect
421. C₂²×D₈	C₂²×C₃₁	semidirect
422. C₂²×M₁₆	C₂²×C₃₁	semidirect
423. C₂³×C₈	C₂²×C₃₁	semidirect
431. #537	C₂²×C₃₁	semidirect
433. #535	C₂²×C₃₁	semidirect
434. #525	C₂²×C₃₁	semidirect
435. #525	C₂²×C₃₁	semidirect
436. C₂×#121	C₂²×C₃₁	semidirect
437. C₂×#121	C₂²×C₃₁	semidirect
438. #520	C₂²×C₃₁	semidirect
439. #485	C₂²×C₃₁	semidirect
440. #484	C₂²×C₃₁	semidirect
441. #482	C₂²×C₃₁	semidirect
442. #482	C₂²×C₃₁	semidirect
443. #482	C₂²×C₃₁	semidirect
444. #481	C₂²×C₃₁	semidirect
445. #480	C₂²×C₃₁	semidirect
446. #480	C₂²×C₃₁	semidirect
447. #469	C₂²×C₃₁	semidirect
448. #468	C₂²×C₃₁	semidirect
449. #467	C₂²×C₃₁	semidirect
450. #467	C₂²×C₃₁	semidirect
451. #466	C₂²×C₃₁	semidirect
452. #466	C₂²×C₃₁	semidirect
453. #466	C₂²×C₃₁	semidirect
454. #466	C₂²×C₃₁	semidirect
455. #466	C₂²×C₃₁	semidirect
456. #466	C₂²×C₃₁	semidirect
457. #466	C₂²×C₃₁	semidirect
458. #465	C₂²×C₃₁	semidirect
459. #465	C₂²×C₃₁	semidirect
460. #465	C₂²×C₃₁	semidirect
461. #452	C₂²×C₃₁	semidirect
462. #450	C₂²×C₃₁	semidirect
463. #449	C₂²×C₃₁	semidirect
464. #449	C₂²×C₃₁	semidirect
465. #449	C₂²×C₃₁	semidirect
466. #447	C₂²×C₃₁	semidirect
467. #447	C₂²×C₃₁	semidirect
468. #447	C₂²×C₃₁	semidirect
469. #428	C₂²×C₃₁	semidirect
470. #427	C₂²×C₃₁	semidirect
471. C₂×#107	C₂²×C₃₁	semidirect
472. #418	C₂²×C₃₁	semidirect
473. #417	C₂²×C₃₁	semidirect
474. #416	C₂²×C₃₁	semidirect
475. C₂×#102	C₂²×C₃₁	semidirect
476. #408	C₂²×C₃₁	semidirect
477. #408	C₂²×C₃₁	semidirect
478. #408	C₂²×C₃₁	semidirect
479. #408	C₂²×C₃₁	semidirect
480. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
481. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
600. C₃₁	#60768	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3488	2
C₃₁×#3203	2
C₃₁×#3199	2
C₃₁×#3198	2
C₃₁×#3191	2
C₃₁×#3188	2
C₃₁×#3186	2
C₃₁×#3098	2
C₃₁×#3096	2
C₃₁×#3055	2
C₃₁×#3050	2
C₂×C₃₁×#466	2
C₃₁×#3012	2
C₃₁×#3008	2
C₂×C₃₁×#408	2
#60768	31

Subgroups — C31×#60768 #21517527

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60768 #21517527