Subgroups — C₃₁×#60771 #21517530

Order 7936.

2254 conjugacy classes of subgroups.

The subgroup lattice has 810 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×#3204	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×#3197	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3194	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3192	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3099	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×#3054	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#469	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	C₃₁×#2879	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	C₂²×M₁₆×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×#483	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×#481	C₂²	1	4	yes	complemented
45	C₃₁×#480	C₂²	1	4	yes	complemented
46	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#469	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#469	C₂²	1	4	yes	complemented
50	C₃₁×#469	C₂²	1	2	yes	complemented
51	C₃₁×#469	C₂²	1	2	yes	complemented
52	C₃₁×#469	C₂²	1	2	yes	complemented
53	C₃₁×#469	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#469	C₂²	1	2	yes	complemented
55	C₃₁×#468	C₂²	1	2	yes	complemented
56	C₃₁×#468	C₂²	1	4	yes	complemented
57	C₃₁×#468	C₂²	1	2	yes	complemented
58	C₃₁×#466	C₂²	1	4	yes	complemented
59	C₃₁×#465	C₂²	1	4	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×#106	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	C₃₁×#407	C₂²	1	2	yes	complemented
80	C₃₁×#407	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	—	4	2	no	—
115	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
116	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
117	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
118	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
119	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
120	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
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	4	yes	—
148	C₃₁×#121	C₂³	1	2	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	4	yes	—
171	C₃₁×#106	C₂³	1	2	yes	—
172	C₃₁×#106	C₂³	1	2	yes	—
173	C₃₁×#106	C₂³	1	1	yes	characteristic
174	C₃₁×#106	C₂³	1	1	yes	characteristic
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	1	no	—
262	M₁₆×C₃₁	—	4	1	no	—
263	M₁₆×C₃₁	—	4	1	no	—
264	M₁₆×C₃₁	—	4	1	no	—
265	M₁₆×C₃₁	—	4	2	no	—
266	C₂×C₈×C₃₁	—	2	2	no	—
267	C₂×C₈×C₃₁	—	2	2	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	4	yes	—
280	C₄⋊C₄×C₃₁	C₂⁴	1	2	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	#60771	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
297	C₂³×C₃₁	—	2	2	no	—
298	C₂³×C₃₁	—	2	4	no	—
299	C₂³×C₃₁	—	2	2	no	—
300	C₂³×C₃₁	—	4	2	no	—
301	C₂³×C₃₁	—	4	2	no	—
302	C₂³×C₃₁	—	4	4	no	—
303	C₂³×C₃₁	—	4	8	no	—
304	C₂³×C₃₁	—	4	4	no	—
305	C₂³×C₃₁	—	8	2	no	—
306	C₂³×C₃₁	—	8	4	no	—
307	C₂³×C₃₁	—	8	2	no	—
308	C₂³×C₃₁	—	8	4	no	—
309	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
310	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
311	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
312	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
313	Q₈×C₃₁	—	2	4	no	—
314	Q₈×C₃₁	—	2	2	no	—
315	Q₈×C₃₁	—	2	2	no	—
316	Q₈×C₃₁	—	4	2	no	—
317	D₄×C₃₁	—	2	8	no	—
318	D₄×C₃₁	—	2	4	no	—
319	D₄×C₃₁	—	2	4	no	—
320	D₄×C₃₁	—	2	2	no	—
321	D₄×C₃₁	—	2	4	no	—
322	D₄×C₃₁	—	2	2	no	—
323	D₄×C₃₁	—	4	2	no	—
324	D₄×C₃₁	—	4	4	no	—
325	D₄×C₃₁	—	4	8	no	—
326	D₄×C₃₁	—	4	8	no	—
327	D₄×C₃₁	—	4	8	no	—
328	D₄×C₃₁	—	4	4	no	—
329	D₄×C₃₁	—	4	4	no	—
330	D₄×C₃₁	—	4	4	no	—
331	D₄×C₃₁	—	8	4	no	—
332	D₄×C₃₁	—	8	2	no	—
333	D₄×C₃₁	—	8	4	no	—
334	D₄×C₃₁	—	8	4	no	—
335	D₄×C₃₁	—	8	4	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	2	1	no	—
340	C₂×C₄×C₃₁	—	2	1	no	—
341	C₂×C₄×C₃₁	—	2	1	no	—
342	C₂×C₄×C₃₁	—	2	1	no	—
343	C₂×C₄×C₃₁	—	2	4	no	—
344	C₂×C₄×C₃₁	—	2	4	no	—
345	C₂×C₄×C₃₁	—	2	2	no	—
346	C₂×C₄×C₃₁	—	2	4	no	—
347	C₂×C₄×C₃₁	—	2	2	no	—
348	C₂×C₄×C₃₁	—	2	2	no	—
349	C₂×C₄×C₃₁	—	4	2	no	—
350	C₂×C₄×C₃₁	—	4	4	no	—
351	C₂×C₄×C₃₁	—	4	8	no	—
352	C₂×C₄×C₃₁	—	4	4	no	—
353	C₂×C₄×C₃₁	—	8	2	no	—
354	C₂×C₄×C₃₁	—	8	4	no	—
355	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
356	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
360	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
361	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
362	C₈×C₃₁	—	2	1	no	—
363	C₈×C₃₁	—	2	1	no	—
364	C₈×C₃₁	—	2	1	no	—
365	C₈×C₃₁	—	2	1	no	—
366	C₈×C₃₁	—	2	4	no	—
367	#3488	C₂×C₃₁	1	2	yes	complemented
368	#3204	C₂×C₃₁	1	2	yes	complemented
369	#3199	C₂×C₃₁	1	2	yes	complemented
370	#3198	C₂×C₃₁	1	4	yes	complemented
371	#3197	C₂×C₃₁	1	2	yes	complemented
372	#3194	C₂×C₃₁	1	4	yes	complemented
373	#3192	C₂×C₃₁	1	2	yes	complemented
374	#3099	C₂×C₃₁	1	2	yes	complemented
375	#3096	C₂×C₃₁	1	2	yes	complemented
376	#3055	C₂×C₃₁	1	2	yes	complemented
377	#3054	C₂×C₃₁	1	1	yes	characteristic, complemented
378	C₂×#469	C₂×C₃₁	1	1	yes	characteristic, complemented
379	#3012	C₂×C₃₁	1	2	yes	complemented
380	#3008	C₂×C₃₁	1	2	yes	complemented
381	#2879	C₂×C₃₁	1	1	yes	characteristic, complemented
382	C₂²×C₃₁	—	2	2	no	—
383	C₂²×C₃₁	—	2	4	no	—
384	C₂²×C₃₁	—	2	2	no	—
385	C₂²×C₃₁	—	2	2	no	—
386	C₂²×C₃₁	—	2	4	no	—
387	C₂²×C₃₁	—	2	1	no	—
388	C₂²×C₃₁	—	2	1	no	—
389	C₂²×C₃₁	—	2	4	no	—
390	C₂²×C₃₁	—	4	4	no	—
391	C₂²×C₃₁	—	4	2	no	—
392	C₂²×C₃₁	—	4	4	no	—
393	C₂²×C₃₁	—	4	2	no	—
394	C₂²×C₃₁	—	4	4	no	—
395	C₂²×C₃₁	—	4	2	no	—
396	C₂²×C₃₁	—	8	2	no	—
397	C₂²×C₃₁	—	8	4	no	—
398	C₂²×C₃₁	—	16	4	no	—
399	C₂²×C₃₁	—	16	8	no	—
400	C₂²×C₃₁	#534	1	2	yes	—
401	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
402	C₄×C₃₁	—	2	1	no	—
403	C₄×C₃₁	—	2	1	no	—
404	C₄×C₃₁	—	2	4	no	—
405	C₄×C₃₁	—	4	4	no	—
406	C₄×C₃₁	—	4	2	no	—
407	C₄×C₃₁	—	4	2	no	—
408	C₄×C₃₁	—	4	2	no	—
409	C₄×C₃₁	#534	1	2	yes	—
410	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
411	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
412	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	2	yes	complemented
413	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
414	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
415	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic, complemented
416	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
417	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
418	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
419	#550	—	2	2	no	—
420	#548	—	2	2	no	—
421	#546	—	2	4	no	—
422	#546	—	2	2	no	—
423	D₄²	—	2	4	no	—
424	D₄²	—	2	2	no	—
425	#537	C₂²×C₃₁	1	2	yes	—
426	#537	C₂²×C₃₁	1	4	yes	complemented
427	#535	C₂²×C₃₁	1	2	yes	—
428	#535	C₂²×C₃₁	1	4	yes	complemented
429	#525	C₂²×C₃₁	1	4	yes	complemented
430	#525	C₂²×C₃₁	1	2	yes	complemented
431	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
432	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
433	#520	C₂²×C₃₁	1	2	yes	complemented
434	#485	C₂²×C₃₁	1	4	yes	complemented
435	#483	C₂²×C₃₁	1	4	yes	complemented
436	#482	C₂²×C₃₁	1	4	yes	complemented
437	#482	C₂²×C₃₁	1	4	yes	complemented
438	#482	C₂²×C₃₁	1	4	yes	complemented
439	#481	C₂²×C₃₁	1	4	yes	complemented
440	#481	C₂²×C₃₁	1	4	yes	complemented
441	#480	C₂²×C₃₁	1	4	yes	complemented
442	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
443	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
444	#469	C₂²×C₃₁	1	1	yes	characteristic, complemented
445	#469	C₂²×C₃₁	1	4	yes	complemented
446	#469	C₂²×C₃₁	1	2	yes	complemented
447	#469	C₂²×C₃₁	1	2	yes	complemented
448	#469	C₂²×C₃₁	1	2	yes	complemented
449	#469	C₂²×C₃₁	1	1	yes	characteristic, complemented
450	#469	C₂²×C₃₁	1	2	yes	complemented
451	#468	C₂²×C₃₁	1	2	yes	complemented
452	#468	C₂²×C₃₁	1	4	yes	complemented
453	#468	C₂²×C₃₁	1	2	yes	complemented
454	#466	C₂²×C₃₁	1	4	yes	complemented
455	#465	C₂²×C₃₁	1	4	yes	complemented
456	#452	C₂²×C₃₁	1	4	yes	complemented
457	#450	C₂²×C₃₁	1	4	yes	complemented
458	#449	C₂²×C₃₁	1	4	yes	complemented
459	#449	C₂²×C₃₁	1	4	yes	complemented
460	#449	C₂²×C₃₁	1	4	yes	complemented
461	#447	C₂²×C₃₁	1	4	yes	complemented
462	#447	C₂²×C₃₁	1	4	yes	complemented
463	#447	C₂²×C₃₁	1	4	yes	complemented
464	#428	C₂²×C₃₁	1	2	yes	complemented
465	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
466	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
467	#418	C₂²×C₃₁	1	2	yes	complemented
468	#417	C₂²×C₃₁	1	2	yes	complemented
469	#416	C₂²×C₃₁	1	2	yes	complemented
470	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
471	#408	C₂²×C₃₁	1	2	yes	complemented
472	#408	C₂²×C₃₁	1	2	yes	complemented
473	#408	C₂²×C₃₁	1	2	yes	complemented
474	#408	C₂²×C₃₁	1	2	yes	complemented
475	#407	C₂²×C₃₁	1	2	yes	complemented
476	#407	C₂²×C₃₁	1	2	yes	complemented
477	C₂×C₃₁	—	2	2	no	—
478	C₂×C₃₁	—	4	1	no	—
479	C₂×C₃₁	—	4	1	no	—
480	C₂×C₃₁	—	4	4	no	—
481	C₂×C₃₁	—	8	4	no	—
482	C₂×C₃₁	—	8	2	no	—
483	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
484	C₂×C₃₁	#3585	1	2	yes	—
485	H(5,𝔽₂)	—	4	4	no	—
486	H(5,𝔽₂)	—	4	4	no	—
487	C₂×#41	—	2	2	no	—
488	C₂×#41	—	4	2	no	—
489	C₂×#41	—	4	2	no	—
490	C₂×#41	D₄×C₃₁	1	2	yes	—
491	C₂×#41	D₄×C₃₁	1	2	yes	—
492	C₂×#41	C₂³×C₃₁	1	2	yes	—
493	C₂×#41	C₂³×C₃₁	1	4	yes	—
494	C₂×#41	C₂³×C₃₁	1	2	yes	—
495	C₂×#41	C₂³×C₃₁	1	2	yes	—
496	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
497	C₂²×D₄	—	2	2	no	—
498	C₂²×D₄	—	2	4	no	—
499	C₂²×D₄	—	2	4	no	—
500	C₂²×D₄	—	2	2	no	—
501	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
502	C₂²×D₄	D₄×C₃₁	1	2	yes	—
503	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
504	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
505	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
507	AGL(1,ℤ/8)	—	4	4	no	—
508	#135	—	4	2	no	—
509	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
510	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
511	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
512	C₂×D₈	—	4	2	no	—
513	C₂×D₈	C₂³×C₃₁	1	2	yes	—
514	C₂×D₈	C₂³×C₃₁	1	2	yes	—
515	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
516	C₂×D₈	C₂³×C₃₁	1	4	yes	—
517	C₂×M₁₆	—	4	2	no	—
518	C₂×M₁₆	—	4	2	no	—
519	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
520	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
521	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
522	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
523	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
524	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
525	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
526	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
527	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
528	#127	—	2	2	no	—
529	#127	—	2	4	no	—
530	#124	—	2	2	no	—
531	#124	—	2	4	no	—
532	#123	—	2	2	no	—
533	#123	—	2	4	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	4	no	—
536	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
537	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
538	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
539	#121	—	2	4	no	—
540	#121	—	2	2	no	—
541	#121	—	2	4	no	—
542	#121	—	2	4	no	—
543	#121	—	2	4	no	—
544	#121	—	2	2	no	—
545	#121	—	2	4	no	—
546	#121	—	2	2	no	—
547	#121	—	2	4	no	—
548	#121	C₂³×C₃₁	1	2	yes	—
549	#121	C₂³×C₃₁	1	4	yes	—
550	#121	C₂³×C₃₁	1	4	yes	—
551	#121	C₂³×C₃₁	1	4	yes	—
552	#121	C₂³×C₃₁	1	4	yes	—
553	#121	C₂³×C₃₁	1	4	yes	—
554	#121	C₂³×C₃₁	1	2	yes	—
555	#120	—	2	2	no	—
556	#120	—	2	4	no	—
557	#120	—	2	4	no	—
558	#120	—	2	4	no	—
559	#120	—	2	4	no	—
560	C₄×Q₈	—	2	2	no	—
561	C₄×D₄	—	2	4	no	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	4	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	4	no	—
567	#117	C₂³×C₃₁	1	2	yes	—
568	#117	C₂³×C₃₁	1	4	yes	—
569	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
571	C₂×C₂²⋊C₄	—	2	2	no	—
572	C₂×C₂²⋊C₄	—	2	4	no	—
573	#107	C₂³×C₃₁	1	2	yes	—
574	#107	C₂³×C₃₁	1	4	yes	—
575	#106	C₂³×C₃₁	1	2	yes	—
576	#106	C₂³×C₃₁	1	2	yes	—
577	#106	C₂³×C₃₁	1	1	yes	characteristic
578	#106	C₂³×C₃₁	1	1	yes	characteristic
579	#106	C₂³×C₃₁	1	4	yes	—
580	#103	C₂³×C₃₁	1	2	yes	—
581	#103	C₂³×C₃₁	1	2	yes	—
582	#103	C₂³×C₃₁	1	4	yes	—
583	#102	C₂³×C₃₁	1	4	yes	—
584	#102	C₂³×C₃₁	1	4	yes	—
585	#102	C₂³×C₃₁	1	2	yes	—
586	#102	C₂³×C₃₁	1	2	yes	—
587	#102	C₂³×C₃₁	1	4	yes	—
588	#102	C₂³×C₃₁	1	4	yes	—
589	#102	C₂³×C₃₁	1	4	yes	—
590	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
591	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
592	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
593	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
594	C₃₁	#60771	1	1	yes	characteristic, direct product factor, Sylow
595	C₂⁴	—	2	4	no	—
596	C₂⁴	—	2	2	no	—
597	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
598	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
599	#41	—	2	4	no	—
600	#41	—	2	4	no	—
601	#41	—	2	4	no	—
602	#41	—	2	4	no	—
603	#41	—	4	2	no	—
604	#41	—	4	2	no	—
605	#41	—	4	4	no	—
606	#41	—	4	4	no	—
607	#41	—	4	4	no	—
608	#41	—	4	4	no	—
609	#41	—	4	8	no	—
610	C₂×Q₈	—	4	2	no	—
611	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
612	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
613	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂×D₄	—	4	4	no	—
629	C₂×D₄	—	4	4	no	—
630	C₂×D₄	—	4	4	no	—
631	C₂×D₄	—	4	16	no	—
632	C₂×D₄	—	4	8	no	—
633	C₂×D₄	—	8	4	no	—
634	C₂×D₄	—	8	8	no	—
635	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
636	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
637	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
638	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
639	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
640	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
653	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
655	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
658	Q₁₆	—	4	1	no	—
659	SD₁₆	—	4	2	no	—
660	SD₁₆	—	4	4	no	—
661	D₈	—	4	2	no	—
662	D₈	—	4	2	no	—
663	D₈	—	4	1	no	—
664	D₈	—	4	4	no	—
665	M₁₆	—	2	4	no	—
666	M₁₆	—	4	1	no	—
667	M₁₆	—	4	1	no	—
668	M₁₆	—	4	1	no	—
669	M₁₆	—	4	1	no	—
670	M₁₆	—	4	2	no	—
671	C₂×C₈	—	2	2	no	—
672	C₂×C₈	—	2	2	no	—
673	C₂×C₈	—	4	2	no	—
674	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
675	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
676	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
677	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
678	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
685	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
686	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₄²	—	2	4	no	—
700	C₄²	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	4	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	4	2	no	—
705	C₂³	—	4	2	no	—
706	C₂³	—	4	4	no	—
707	C₂³	—	4	8	no	—
708	C₂³	—	4	4	no	—
709	C₂³	—	8	2	no	—
710	C₂³	—	8	4	no	—
711	C₂³	—	8	2	no	—
712	C₂³	—	8	4	no	—
713	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
714	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
715	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
716	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
717	Q₈	—	2	4	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	4	2	no	—
721	D₄	—	2	8	no	—
722	D₄	—	2	4	no	—
723	D₄	—	2	4	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	4	no	—
726	D₄	—	2	2	no	—
727	D₄	—	4	2	no	—
728	D₄	—	4	4	no	—
729	D₄	—	4	8	no	—
730	D₄	—	4	8	no	—
731	D₄	—	4	8	no	—
732	D₄	—	4	4	no	—
733	D₄	—	4	4	no	—
734	D₄	—	4	4	no	—
735	D₄	—	8	4	no	—
736	D₄	—	8	2	no	—
737	D₄	—	8	4	no	—
738	D₄	—	8	4	no	—
739	D₄	—	8	4	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	4	4	no	—
755	C₂×C₄	—	4	8	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	—	8	2	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
760	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
763	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
764	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
765	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
766	C₈	—	2	1	no	—
767	C₈	—	2	1	no	—
768	C₈	—	2	1	no	—
769	C₈	—	2	1	no	—
770	C₈	—	2	4	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	1	no	—
773	C₂²	—	2	1	no	—
774	C₂²	—	2	4	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	4	no	—
779	C₂²	—	4	4	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	4	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	4	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	8	2	no	—
786	C₂²	—	8	4	no	—
787	C₂²	—	16	4	no	—
788	C₂²	—	16	8	no	—
789	C₂²	C₃₁×#534	1	2	yes	—
790	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
791	C₄	—	2	1	no	—
792	C₄	—	2	1	no	—
793	C₄	—	2	4	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	4	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	C₃₁×#534	1	2	yes	—
799	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
800	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
801	C₂	—	2	2	no	—
802	C₂	—	4	1	no	—
803	C₂	—	4	4	no	—
804	C₂	—	4	1	no	—
805	C₂	—	8	4	no	—
806	C₂	—	8	2	no	—
807	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
808	C₂	C₃₁×#3585	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 ◁ 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×#3204	C₂	semidirect
3. C₃₁×#3199	C₂	semidirect
4. C₃₁×#3198	C₂	semidirect
5. C₃₁×#3197	C₂	semidirect
6. C₃₁×#3194	C₂	semidirect
7. C₃₁×#3192	C₂	semidirect
8. C₃₁×#3099	C₂	semidirect
9. C₃₁×#3096	C₂	semidirect
10. C₃₁×#3055	C₂	semidirect
11. C₃₁×#3054	C₂	semidirect
12. C₂×C₃₁×#469	C₂	semidirect
13. C₃₁×#3012	C₂	semidirect
14. C₃₁×#3008	C₂	semidirect
15. C₃₁×#2879	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. C₂²×M₁₆×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×#483	C₂²	semidirect
40. C₃₁×#482	C₂²	semidirect
41. C₃₁×#482	C₂²	semidirect
42. C₃₁×#482	C₂²	semidirect
43. C₃₁×#481	C₂²	semidirect
44. C₃₁×#481	C₂²	semidirect
45. C₃₁×#480	C₂²	semidirect
46. C₃₁×#470	C₂²	semidirect
47. C₃₁×#470	C₂²	semidirect
48. C₃₁×#469	C₂²	semidirect
49. C₃₁×#469	C₂²	semidirect
50. C₃₁×#469	C₂²	semidirect
51. C₃₁×#469	C₂²	semidirect
52. C₃₁×#469	C₂²	semidirect
53. C₃₁×#469	C₂²	semidirect
54. C₃₁×#469	C₂²	semidirect
55. C₃₁×#468	C₂²	semidirect
56. C₃₁×#468	C₂²	semidirect
57. C₃₁×#468	C₂²	semidirect
58. C₃₁×#466	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×#106	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. C₃₁×#407	C₂²	semidirect
80. C₃₁×#407	C₂²	semidirect
296. #60771	C₃₁	direct (N × H)
367. #3488	C₂×C₃₁	semidirect
368. #3204	C₂×C₃₁	semidirect
369. #3199	C₂×C₃₁	semidirect
370. #3198	C₂×C₃₁	semidirect
371. #3197	C₂×C₃₁	semidirect
372. #3194	C₂×C₃₁	semidirect
373. #3192	C₂×C₃₁	semidirect
374. #3099	C₂×C₃₁	semidirect
375. #3096	C₂×C₃₁	semidirect
376. #3055	C₂×C₃₁	semidirect
377. #3054	C₂×C₃₁	semidirect
378. C₂×#469	C₂×C₃₁	semidirect
379. #3012	C₂×C₃₁	semidirect
380. #3008	C₂×C₃₁	semidirect
381. #2879	C₂×C₃₁	semidirect
412. C₂×H(5,𝔽₂)	C₂²×C₃₁	semidirect
414. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
415. C₂×#135	C₂²×C₃₁	semidirect
416. C₂²×D₈	C₂²×C₃₁	semidirect
417. C₂²×M₁₆	C₂²×C₃₁	semidirect
418. C₂²×M₁₆	C₂²×C₃₁	semidirect
426. #537	C₂²×C₃₁	semidirect
428. #535	C₂²×C₃₁	semidirect
429. #525	C₂²×C₃₁	semidirect
430. #525	C₂²×C₃₁	semidirect
431. C₂×#121	C₂²×C₃₁	semidirect
432. C₂×#121	C₂²×C₃₁	semidirect
433. #520	C₂²×C₃₁	semidirect
434. #485	C₂²×C₃₁	semidirect
435. #483	C₂²×C₃₁	semidirect
436. #482	C₂²×C₃₁	semidirect
437. #482	C₂²×C₃₁	semidirect
438. #482	C₂²×C₃₁	semidirect
439. #481	C₂²×C₃₁	semidirect
440. #481	C₂²×C₃₁	semidirect
441. #480	C₂²×C₃₁	semidirect
442. #470	C₂²×C₃₁	semidirect
443. #470	C₂²×C₃₁	semidirect
444. #469	C₂²×C₃₁	semidirect
445. #469	C₂²×C₃₁	semidirect
446. #469	C₂²×C₃₁	semidirect
447. #469	C₂²×C₃₁	semidirect
448. #469	C₂²×C₃₁	semidirect
449. #469	C₂²×C₃₁	semidirect
450. #469	C₂²×C₃₁	semidirect
451. #468	C₂²×C₃₁	semidirect
452. #468	C₂²×C₃₁	semidirect
453. #468	C₂²×C₃₁	semidirect
454. #466	C₂²×C₃₁	semidirect
455. #465	C₂²×C₃₁	semidirect
456. #452	C₂²×C₃₁	semidirect
457. #450	C₂²×C₃₁	semidirect
458. #449	C₂²×C₃₁	semidirect
459. #449	C₂²×C₃₁	semidirect
460. #449	C₂²×C₃₁	semidirect
461. #447	C₂²×C₃₁	semidirect
462. #447	C₂²×C₃₁	semidirect
463. #447	C₂²×C₃₁	semidirect
464. #428	C₂²×C₃₁	semidirect
465. #427	C₂²×C₃₁	semidirect
466. C₂×#106	C₂²×C₃₁	semidirect
467. #418	C₂²×C₃₁	semidirect
468. #417	C₂²×C₃₁	semidirect
469. #416	C₂²×C₃₁	semidirect
470. C₂×#102	C₂²×C₃₁	semidirect
471. #408	C₂²×C₃₁	semidirect
472. #408	C₂²×C₃₁	semidirect
473. #408	C₂²×C₃₁	semidirect
474. #408	C₂²×C₃₁	semidirect
475. #407	C₂²×C₃₁	semidirect
476. #407	C₂²×C₃₁	semidirect
594. C₃₁	#60771	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×#3204	2
C₃₁×#3199	2
C₃₁×#3198	2
C₃₁×#3197	2
C₃₁×#3194	2
C₃₁×#3192	2
C₃₁×#3099	2
C₃₁×#3096	2
C₃₁×#3055	2
C₃₁×#3054	2
C₂×C₃₁×#469	2
C₃₁×#3012	2
C₃₁×#3008	2
C₃₁×#2879	2
#60771	31

Subgroups — C31×#60771 #21517530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60771 #21517530