Subgroups — C₃₁×#61219 #21517978

Order 7936.

2102 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3496	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3315	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3314	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3311	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3310	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3135	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3098	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3063	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3009	C₂	1	2	yes	maximal, complemented
13	C₂×C₃₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2932	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2897	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	2	yes	—
17	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
18	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#131	C₂²	1	2	yes	complemented
20	C₃₁×#559	—	2	1	no	—
21	C₃₁×#557	—	2	1	no	—
22	C₃₁×#556	—	2	2	no	—
23	C₃₁×#556	C₂²	1	2	yes	complemented
24	C₃₁×#554	C₂²	1	2	yes	complemented
25	C₃₁×#552	C₂²	1	4	yes	complemented
26	C₃₁×#547	—	2	1	no	—
27	C₃₁×#547	C₂²	1	2	yes	—
28	C₃₁×#546	—	2	2	no	—
29	C₃₁×#546	C₂²	1	4	yes	—
30	D₄²×C₃₁	—	2	1	no	—
31	D₄²×C₃₁	C₂²	1	2	yes	—
32	C₃₁×#539	—	2	2	no	—
33	C₃₁×#537	C₂²	1	2	yes	—
34	C₃₁×#536	C₂²	1	2	yes	complemented
35	C₃₁×#534	—	2	2	no	—
36	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#532	C₂²	1	1	yes	characteristic
38	C₃₁×#532	C₂²	1	1	yes	characteristic
39	C₃₁×#529	—	2	2	no	—
40	C₂×C₃₁×#121	—	2	2	no	—
41	C₃₁×#520	C₂²	1	2	yes	complemented
42	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#491	C₂²	1	2	yes	complemented
45	C₃₁×#490	C₂²	1	2	yes	complemented
46	C₃₁×#489	C₂²	1	2	yes	complemented
47	C₃₁×#489	C₂²	1	2	yes	complemented
48	C₃₁×#485	C₂²	1	4	yes	complemented
49	C₃₁×#484	C₂²	1	4	yes	complemented
50	C₃₁×#482	C₂²	1	4	yes	complemented
51	C₃₁×#480	C₂²	1	4	yes	complemented
52	C₃₁×#478	C₂²	1	4	yes	complemented
53	C₃₁×#476	C₂²	1	2	yes	complemented
54	C₃₁×#474	C₂²	1	2	yes	complemented
55	C₃₁×#470	C₂²	1	4	yes	complemented
56	C₃₁×#468	C₂²	1	4	yes	complemented
57	C₃₁×#467	C₂²	1	4	yes	complemented
58	C₃₁×#465	C₂²	1	4	yes	complemented
59	C₃₁×#464	C₂²	1	4	yes	complemented
60	C₃₁×#462	C₂²	1	2	yes	complemented
61	C₃₁×#460	C₂²	1	2	yes	complemented
62	C₃₁×#452	C₂²	1	4	yes	complemented
63	C₃₁×#452	C₂²	1	4	yes	complemented
64	C₃₁×#450	C₂²	1	4	yes	complemented
65	C₃₁×#450	C₂²	1	4	yes	complemented
66	C₃₁×#440	C₂²	1	4	yes	complemented
67	C₃₁×#440	C₂²	1	4	yes	complemented
68	C₃₁×#435	C₂²	1	4	yes	complemented
69	C₃₁×#435	C₂²	1	4	yes	complemented
70	C₃₁×#428	C₂²	1	2	yes	complemented
71	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#418	C₂²	1	2	yes	—
74	C₃₁×#418	C₂²	1	4	yes	complemented
75	C₃₁×#417	C₂²	1	2	yes	complemented
76	C₃₁×#417	C₂²	1	4	yes	complemented
77	C₃₁×#416	C₂²	1	2	yes	complemented
78	C₃₁×#416	C₂²	1	2	yes	complemented
79	C₃₁×#416	C₂²	1	4	yes	complemented
80	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
82	C₂×C₃₁×#102	C₂²	1	4	yes	complemented
83	C₃₁×#408	C₂²	1	2	yes	complemented
84	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×H(5,𝔽₂)	—	2	8	no	—
86	C₃₁×H(5,𝔽₂)	—	4	4	no	—
87	C₂×#41×C₃₁	—	2	2	no	—
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	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₃₁	—	2	4	no	—
93	C₂²×D₄×C₃₁	—	2	2	no	—
94	C₂²×D₄×C₃₁	—	2	2	no	—
95	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
96	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₃₁	—	2	1	no	—
98	C₃₁×#137	—	4	4	no	—
99	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₃₁	—	2	4	no	—
101	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
103	C₃₁×#131	—	4	4	no	—
104	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
105	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
106	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
109	C₃₁×C₄⋊Q₈	—	2	2	no	—
110	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
111	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₃₁×#127	D₄	1	1	yes	characteristic
115	C₃₁×#127	C₂³	1	1	yes	characteristic
116	C₃₁×#126	—	2	4	no	—
117	C₃₁×#126	—	2	4	no	—
118	C₃₁×#125	—	2	2	no	—
119	C₃₁×#125	—	2	4	no	—
120	C₃₁×#125	C₂³	1	2	yes	—
121	C₃₁×#124	—	2	2	no	—
122	C₃₁×#124	—	2	2	no	—
123	C₃₁×#124	D₄	1	2	yes	—
124	C₃₁×#124	C₂³	1	2	yes	—
125	C₃₁×#123	—	2	4	no	—
126	C₃₁×#123	—	2	4	no	—
127	C₃₁×#123	—	2	4	no	—
128	C₃₁×#123	—	2	4	no	—
129	C₃₁×C₂²⋊Q₈	—	2	2	no	—
130	C₃₁×C₂²⋊Q₈	—	2	1	no	—
131	C₃₁×C₂²⋊Q₈	—	2	1	no	—
132	C₃₁×C₂²⋊Q₈	—	2	4	no	—
133	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₃₁×#121	—	2	4	no	—
137	C₃₁×#121	—	2	2	no	—
138	C₃₁×#121	—	2	2	no	—
139	C₃₁×#121	—	2	1	no	—
140	C₃₁×#121	—	2	1	no	—
141	C₃₁×#121	—	2	2	no	—
142	C₃₁×#121	—	2	4	no	—
143	C₃₁×#121	D₄	1	2	yes	—
144	C₃₁×#121	D₄	1	2	yes	—
145	C₃₁×#121	C₂³	1	4	yes	—
146	C₃₁×#120	—	2	4	no	—
147	C₃₁×#120	—	2	4	no	—
148	C₄×Q₈×C₃₁	—	2	2	no	—
149	C₄×Q₈×C₃₁	—	2	2	no	—
150	C₄×Q₈×C₃₁	—	2	1	no	—
151	C₄×Q₈×C₃₁	—	2	1	no	—
152	C₄×Q₈×C₃₁	—	2	1	no	—
153	C₄×Q₈×C₃₁	—	2	1	no	—
154	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
155	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
156	C₄×D₄×C₃₁	—	2	4	no	—
157	C₄×D₄×C₃₁	—	2	2	no	—
158	C₄×D₄×C₃₁	—	2	2	no	—
159	C₄×D₄×C₃₁	—	2	1	no	—
160	C₄×D₄×C₃₁	—	2	1	no	—
161	C₄×D₄×C₃₁	—	2	1	no	—
162	C₄×D₄×C₃₁	—	2	1	no	—
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	C₄×D₄×C₃₁	C₂³	1	2	yes	—
167	C₃₁×#117	—	2	4	no	—
168	C₃₁×#117	C₂³	1	2	yes	—
169	C₃₁×#117	C₂³	1	4	yes	—
170	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
171	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
172	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
174	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
177	C₂×C₄²×C₃₁	—	2	1	no	—
178	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
179	C₃₁×#107	C₂³	1	4	yes	—
180	C₃₁×#107	C₂³	1	4	yes	—
181	C₃₁×#106	C₂³	1	4	yes	—
182	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
183	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
184	C₃₁×#103	C₂³	1	4	yes	—
185	C₃₁×#103	C₂³	1	2	yes	—
186	C₃₁×#103	C₂³	1	4	yes	—
187	C₃₁×#103	C₂³	1	2	yes	—
188	C₃₁×#103	C₂³	1	2	yes	—
189	C₃₁×#103	C₂³	1	2	yes	—
190	C₃₁×#102	C₂³	1	4	yes	—
191	C₃₁×#102	C₂³	1	2	yes	—
192	C₃₁×#102	C₂³	1	4	yes	—
193	C₃₁×#102	C₂³	1	4	yes	—
194	C₃₁×#102	C₂³	1	4	yes	—
195	C₃₁×#102	C₂³	1	2	yes	—
196	C₃₁×#102	C₂³	1	2	yes	—
197	C₃₁×#102	C₂³	1	2	yes	—
198	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
199	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
200	C₃₁×#97	C₂³	1	2	yes	—
201	C₃₁×#97	C₂³	1	2	yes	—
202	C₂⁴×C₃₁	—	2	1	no	—
203	C₂⁴×C₃₁	—	2	4	no	—
204	#41×C₃₁	—	2	4	no	—
205	#41×C₃₁	—	2	4	no	—
206	#41×C₃₁	—	2	8	no	—
207	#41×C₃₁	—	2	4	no	—
208	#41×C₃₁	—	2	4	no	—
209	#41×C₃₁	—	4	4	no	—
210	#41×C₃₁	—	4	8	no	—
211	C₂×Q₈×C₃₁	—	2	1	no	—
212	C₂×Q₈×C₃₁	—	2	1	no	—
213	C₂×Q₈×C₃₁	—	2	1	no	—
214	C₂×Q₈×C₃₁	—	2	2	no	—
215	C₂×Q₈×C₃₁	—	2	2	no	—
216	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
217	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
218	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
219	C₂×D₄×C₃₁	—	2	8	no	—
220	C₂×D₄×C₃₁	—	2	4	no	—
221	C₂×D₄×C₃₁	—	2	2	no	—
222	C₂×D₄×C₃₁	—	2	4	no	—
223	C₂×D₄×C₃₁	—	2	1	no	—
224	C₂×D₄×C₃₁	—	2	1	no	—
225	C₂×D₄×C₃₁	—	2	4	no	—
226	C₂×D₄×C₃₁	—	2	1	no	—
227	C₂×D₄×C₃₁	—	2	2	no	—
228	C₂×D₄×C₃₁	—	4	4	no	—
229	C₂×D₄×C₃₁	—	4	8	no	—
230	C₂×D₄×C₃₁	—	4	16	no	—
231	C₂×D₄×C₃₁	—	8	4	no	—
232	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
233	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₃₁	#41	1	4	yes	—
237	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
238	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₃₁	—	2	1	no	—
240	C₂²×C₄×C₃₁	—	2	1	no	—
241	C₂²×C₄×C₃₁	—	2	1	no	—
242	C₂²×C₄×C₃₁	—	2	4	no	—
243	C₂²×C₄×C₃₁	—	2	4	no	—
244	C₂²×C₄×C₃₁	—	2	2	no	—
245	C₂²×C₄×C₃₁	—	2	2	no	—
246	C₂²×C₄×C₃₁	—	2	2	no	—
247	C₂²×C₄×C₃₁	—	8	2	no	—
248	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
252	Q₁₆×C₃₁	—	4	4	no	—
253	SD₁₆×C₃₁	—	2	8	no	—
254	SD₁₆×C₃₁	—	4	4	no	—
255	M₁₆×C₃₁	—	2	4	no	—
256	M₁₆×C₃₁	—	4	4	no	—
257	C₂×C₈×C₃₁	—	2	2	no	—
258	C₂×C₈×C₃₁	—	2	2	no	—
259	C₂×C₈×C₃₁	—	4	4	no	—
260	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
261	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
262	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
263	C₄⋊C₄×C₃₁	—	2	1	no	—
264	C₄⋊C₄×C₃₁	—	2	2	no	—
265	C₄⋊C₄×C₃₁	—	2	2	no	—
266	C₄⋊C₄×C₃₁	—	2	4	no	—
267	C₄⋊C₄×C₃₁	—	2	1	no	—
268	C₄⋊C₄×C₃₁	—	2	1	no	—
269	C₄⋊C₄×C₃₁	—	2	4	no	—
270	C₄⋊C₄×C₃₁	—	2	2	no	—
271	C₄⋊C₄×C₃₁	—	2	4	no	—
272	C₄⋊C₄×C₃₁	—	2	1	no	—
273	C₄⋊C₄×C₃₁	—	2	1	no	—
274	C₄⋊C₄×C₃₁	—	2	2	no	—
275	C₄⋊C₄×C₃₁	—	2	1	no	—
276	C₄⋊C₄×C₃₁	—	2	4	no	—
277	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
283	C₂²⋊C₄×C₃₁	—	2	4	no	—
284	C₂²⋊C₄×C₃₁	—	2	4	no	—
285	C₂²⋊C₄×C₃₁	—	2	2	no	—
286	C₂²⋊C₄×C₃₁	—	2	4	no	—
287	C₂²⋊C₄×C₃₁	—	2	4	no	—
288	C₂²⋊C₄×C₃₁	—	2	2	no	—
289	C₂²⋊C₄×C₃₁	—	2	2	no	—
290	C₂²⋊C₄×C₃₁	—	2	2	no	—
291	C₂²⋊C₄×C₃₁	—	2	4	no	—
292	C₂²⋊C₄×C₃₁	—	2	2	no	—
293	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
294	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
295	C₄²×C₃₁	—	2	2	no	—
296	C₄²×C₃₁	—	2	2	no	—
297	C₄²×C₃₁	—	2	4	no	—
298	C₄²×C₃₁	—	2	2	no	—
299	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
302	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
303	#61219	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
304	C₂³×C₃₁	—	2	2	no	—
305	C₂³×C₃₁	—	2	4	no	—
306	C₂³×C₃₁	—	2	2	no	—
307	C₂³×C₃₁	—	4	8	no	—
308	C₂³×C₃₁	—	8	1	no	—
309	C₂³×C₃₁	—	8	1	no	—
310	C₂³×C₃₁	—	8	4	no	—
311	C₂³×C₃₁	—	8	4	no	—
312	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
313	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
314	Q₈×C₃₁	—	2	4	no	—
315	Q₈×C₃₁	—	2	2	no	—
316	Q₈×C₃₁	—	2	2	no	—
317	Q₈×C₃₁	—	2	2	no	—
318	Q₈×C₃₁	—	2	2	no	—
319	Q₈×C₃₁	—	4	2	no	—
320	Q₈×C₃₁	—	4	2	no	—
321	Q₈×C₃₁	—	8	1	no	—
322	D₄×C₃₁	—	2	8	no	—
323	D₄×C₃₁	—	2	4	no	—
324	D₄×C₃₁	—	2	4	no	—
325	D₄×C₃₁	—	2	2	no	—
326	D₄×C₃₁	—	2	2	no	—
327	D₄×C₃₁	—	2	2	no	—
328	D₄×C₃₁	—	4	2	no	—
329	D₄×C₃₁	—	4	2	no	—
330	D₄×C₃₁	—	4	8	no	—
331	D₄×C₃₁	—	4	2	no	—
332	D₄×C₃₁	—	4	8	no	—
333	D₄×C₃₁	—	4	4	no	—
334	D₄×C₃₁	—	8	1	no	—
335	D₄×C₃₁	—	8	4	no	—
336	D₄×C₃₁	C₂×#41	1	4	yes	—
337	C₂×C₄×C₃₁	—	2	4	no	—
338	C₂×C₄×C₃₁	—	2	4	no	—
339	C₂×C₄×C₃₁	—	2	2	no	—
340	C₂×C₄×C₃₁	—	2	2	no	—
341	C₂×C₄×C₃₁	—	2	2	no	—
342	C₂×C₄×C₃₁	—	2	2	no	—
343	C₂×C₄×C₃₁	—	2	2	no	—
344	C₂×C₄×C₃₁	—	2	2	no	—
345	C₂×C₄×C₃₁	—	4	1	no	—
346	C₂×C₄×C₃₁	—	4	1	no	—
347	C₂×C₄×C₃₁	—	4	8	no	—
348	C₂×C₄×C₃₁	—	4	4	no	—
349	C₂×C₄×C₃₁	—	4	2	no	—
350	C₂×C₄×C₃₁	—	4	4	no	—
351	C₂×C₄×C₃₁	—	8	2	no	—
352	C₂×C₄×C₃₁	—	8	1	no	—
353	C₂×C₄×C₃₁	—	8	4	no	—
354	C₂×C₄×C₃₁	—	8	1	no	—
355	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	C₂×#41	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	2	no	—
365	C₈×C₃₁	—	2	2	no	—
366	C₈×C₃₁	—	2	4	no	—
367	#3507	C₂×C₃₁	1	1	yes	characteristic, complemented
368	#3496	C₂×C₃₁	1	1	yes	characteristic
369	#3315	C₂×C₃₁	1	4	yes	complemented
370	#3314	C₂×C₃₁	1	4	yes	complemented
371	#3311	C₂×C₃₁	1	4	yes	complemented
372	#3310	C₂×C₃₁	1	4	yes	complemented
373	#3135	C₂×C₃₁	1	1	yes	characteristic, complemented
374	#3098	C₂×C₃₁	1	2	yes	complemented
375	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
376	#3063	C₂×C₃₁	1	2	yes	complemented
377	#3037	C₂×C₃₁	1	1	yes	characteristic, complemented
378	#3009	C₂×C₃₁	1	2	yes	complemented
379	C₂×#440	C₂×C₃₁	1	1	yes	characteristic, complemented
380	#2932	C₂×C₃₁	1	1	yes	characteristic, complemented
381	#2897	C₂×C₃₁	1	2	yes	complemented
382	C₂²×C₃₁	—	2	1	no	—
383	C₂²×C₃₁	—	2	1	no	—
384	C₂²×C₃₁	—	2	4	no	—
385	C₂²×C₃₁	—	2	4	no	—
386	C₂²×C₃₁	—	2	4	no	—
387	C₂²×C₃₁	—	2	4	no	—
388	C₂²×C₃₁	—	4	2	no	—
389	C₂²×C₃₁	—	4	2	no	—
390	C₂²×C₃₁	—	4	2	no	—
391	C₂²×C₃₁	—	4	2	no	—
392	C₂²×C₃₁	—	4	2	no	—
393	C₂²×C₃₁	—	8	4	no	—
394	C₂²×C₃₁	—	16	8	no	—
395	C₂²×C₃₁	#546	1	2	yes	—
396	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
397	C₄×C₃₁	—	2	1	no	—
398	C₄×C₃₁	—	2	1	no	—
399	C₄×C₃₁	—	2	1	no	—
400	C₄×C₃₁	—	2	1	no	—
401	C₄×C₃₁	—	2	4	no	—
402	C₄×C₃₁	—	4	2	no	—
403	C₄×C₃₁	—	4	2	no	—
404	C₄×C₃₁	—	4	2	no	—
405	C₄×C₃₁	—	4	2	no	—
406	C₄×C₃₁	—	4	2	no	—
407	C₄×C₃₁	—	4	2	no	—
408	C₄×C₃₁	#546	1	2	yes	—
409	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
410	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
411	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	2	yes	—
412	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
413	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
414	C₂×#131	C₂²×C₃₁	1	2	yes	complemented
415	#559	—	2	1	no	—
416	#557	—	2	1	no	—
417	#556	—	2	2	no	—
418	#556	C₂²×C₃₁	1	2	yes	complemented
419	#554	C₂²×C₃₁	1	2	yes	complemented
420	#552	C₂²×C₃₁	1	4	yes	complemented
421	#547	—	2	1	no	—
422	#547	C₂²×C₃₁	1	2	yes	—
423	#546	—	2	2	no	—
424	#546	C₂²×C₃₁	1	4	yes	—
425	D₄²	—	2	1	no	—
426	D₄²	C₂²×C₃₁	1	2	yes	—
427	#539	—	2	2	no	—
428	#537	C₂²×C₃₁	1	2	yes	—
429	#536	C₂²×C₃₁	1	2	yes	complemented
430	#534	—	2	2	no	—
431	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
432	#532	C₂²×C₃₁	1	1	yes	characteristic
433	#532	C₂²×C₃₁	1	1	yes	characteristic
434	#529	—	2	2	no	—
435	C₂×#121	—	2	2	no	—
436	#520	C₂²×C₃₁	1	2	yes	complemented
437	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
438	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
439	#491	C₂²×C₃₁	1	2	yes	complemented
440	#490	C₂²×C₃₁	1	2	yes	complemented
441	#489	C₂²×C₃₁	1	2	yes	complemented
442	#489	C₂²×C₃₁	1	2	yes	complemented
443	#485	C₂²×C₃₁	1	4	yes	complemented
444	#484	C₂²×C₃₁	1	4	yes	complemented
445	#482	C₂²×C₃₁	1	4	yes	complemented
446	#480	C₂²×C₃₁	1	4	yes	complemented
447	#478	C₂²×C₃₁	1	4	yes	complemented
448	#476	C₂²×C₃₁	1	2	yes	complemented
449	#474	C₂²×C₃₁	1	2	yes	complemented
450	#470	C₂²×C₃₁	1	4	yes	complemented
451	#468	C₂²×C₃₁	1	4	yes	complemented
452	#467	C₂²×C₃₁	1	4	yes	complemented
453	#465	C₂²×C₃₁	1	4	yes	complemented
454	#464	C₂²×C₃₁	1	4	yes	complemented
455	#462	C₂²×C₃₁	1	2	yes	complemented
456	#460	C₂²×C₃₁	1	2	yes	complemented
457	#452	C₂²×C₃₁	1	4	yes	complemented
458	#452	C₂²×C₃₁	1	4	yes	complemented
459	#450	C₂²×C₃₁	1	4	yes	complemented
460	#450	C₂²×C₃₁	1	4	yes	complemented
461	#440	C₂²×C₃₁	1	4	yes	complemented
462	#440	C₂²×C₃₁	1	4	yes	complemented
463	#435	C₂²×C₃₁	1	4	yes	complemented
464	#435	C₂²×C₃₁	1	4	yes	complemented
465	#428	C₂²×C₃₁	1	2	yes	complemented
466	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
467	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
468	#418	C₂²×C₃₁	1	2	yes	—
469	#418	C₂²×C₃₁	1	4	yes	complemented
470	#417	C₂²×C₃₁	1	2	yes	complemented
471	#417	C₂²×C₃₁	1	4	yes	complemented
472	#416	C₂²×C₃₁	1	2	yes	complemented
473	#416	C₂²×C₃₁	1	2	yes	complemented
474	#416	C₂²×C₃₁	1	4	yes	complemented
475	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
476	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
477	C₂×#102	C₂²×C₃₁	1	4	yes	complemented
478	#408	C₂²×C₃₁	1	2	yes	complemented
479	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic, complemented
480	C₂×C₃₁	—	2	2	no	—
481	C₂×C₃₁	—	4	4	no	—
482	C₂×C₃₁	—	4	4	no	—
483	C₂×C₃₁	—	8	2	no	—
484	C₂×C₃₁	C₂×#546	1	1	yes	characteristic
485	C₂×C₃₁	#3585	1	1	yes	characteristic
486	C₂×C₃₁	#3586	1	1	yes	characteristic
487	H(5,𝔽₂)	—	2	8	no	—
488	H(5,𝔽₂)	—	4	4	no	—
489	C₂×#41	—	2	2	no	—
490	C₂×#41	C₂³×C₃₁	1	2	yes	—
491	C₂×#41	C₂³×C₃₁	1	4	yes	—
492	C₂×#41	C₂³×C₃₁	1	2	yes	—
493	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
494	C₂²×D₄	—	2	4	no	—
495	C₂²×D₄	—	2	2	no	—
496	C₂²×D₄	—	2	2	no	—
497	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
498	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
499	C₂³×C₄	—	2	1	no	—
500	#137	—	4	4	no	—
501	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
502	C₂×SD₁₆	—	2	4	no	—
503	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
504	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
505	#131	—	4	4	no	—
506	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
507	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
508	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
509	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
510	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
511	C₄⋊Q₈	—	2	2	no	—
512	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
513	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
516	#127	D₄×C₃₁	1	1	yes	characteristic
517	#127	C₂³×C₃₁	1	1	yes	characteristic
518	#126	—	2	4	no	—
519	#126	—	2	4	no	—
520	#125	—	2	2	no	—
521	#125	—	2	4	no	—
522	#125	C₂³×C₃₁	1	2	yes	—
523	#124	—	2	2	no	—
524	#124	—	2	2	no	—
525	#124	D₄×C₃₁	1	2	yes	—
526	#124	C₂³×C₃₁	1	2	yes	—
527	#123	—	2	4	no	—
528	#123	—	2	4	no	—
529	#123	—	2	4	no	—
530	#123	—	2	4	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	2	1	no	—
533	C₂²⋊Q₈	—	2	1	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
536	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
537	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
538	#121	—	2	4	no	—
539	#121	—	2	2	no	—
540	#121	—	2	2	no	—
541	#121	—	2	1	no	—
542	#121	—	2	1	no	—
543	#121	—	2	2	no	—
544	#121	—	2	4	no	—
545	#121	D₄×C₃₁	1	2	yes	—
546	#121	D₄×C₃₁	1	2	yes	—
547	#121	C₂³×C₃₁	1	4	yes	—
548	#120	—	2	4	no	—
549	#120	—	2	4	no	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	1	no	—
553	C₄×Q₈	—	2	1	no	—
554	C₄×Q₈	—	2	1	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
557	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
558	C₄×D₄	—	2	4	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	1	no	—
562	C₄×D₄	—	2	1	no	—
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	C₂³×C₃₁	1	2	yes	—
566	C₄×D₄	C₂³×C₃₁	1	2	yes	—
567	C₄×D₄	C₂³×C₃₁	1	2	yes	—
568	C₄×D₄	C₂³×C₃₁	1	2	yes	—
569	#117	—	2	4	no	—
570	#117	C₂³×C₃₁	1	2	yes	—
571	#117	C₂³×C₃₁	1	4	yes	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	2	no	—
574	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	C₂×C₂²⋊C₄	—	2	4	no	—
579	C₂×C₄²	—	2	1	no	—
580	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
581	#107	C₂³×C₃₁	1	4	yes	—
582	#107	C₂³×C₃₁	1	4	yes	—
583	#106	C₂³×C₃₁	1	4	yes	—
584	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
585	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
586	#103	C₂³×C₃₁	1	4	yes	—
587	#103	C₂³×C₃₁	1	2	yes	—
588	#103	C₂³×C₃₁	1	4	yes	—
589	#103	C₂³×C₃₁	1	2	yes	—
590	#103	C₂³×C₃₁	1	2	yes	—
591	#103	C₂³×C₃₁	1	2	yes	—
592	#102	C₂³×C₃₁	1	4	yes	—
593	#102	C₂³×C₃₁	1	2	yes	—
594	#102	C₂³×C₃₁	1	4	yes	—
595	#102	C₂³×C₃₁	1	4	yes	—
596	#102	C₂³×C₃₁	1	4	yes	—
597	#102	C₂³×C₃₁	1	2	yes	—
598	#102	C₂³×C₃₁	1	2	yes	—
599	#102	C₂³×C₃₁	1	2	yes	—
600	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
601	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
602	#97	C₂³×C₃₁	1	2	yes	—
603	#97	C₂³×C₃₁	1	2	yes	—
604	C₃₁	#61219	1	1	yes	characteristic, direct product factor, Sylow
605	C₂⁴	—	2	1	no	—
606	C₂⁴	—	2	4	no	—
607	#41	—	2	4	no	—
608	#41	—	2	4	no	—
609	#41	—	2	8	no	—
610	#41	—	2	4	no	—
611	#41	—	2	4	no	—
612	#41	—	4	4	no	—
613	#41	—	4	8	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	2	no	—
618	C₂×Q₈	—	2	2	no	—
619	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
620	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
621	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
622	C₂×D₄	—	2	8	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	4	4	no	—
632	C₂×D₄	—	4	8	no	—
633	C₂×D₄	—	4	16	no	—
634	C₂×D₄	—	8	4	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	2	yes	—
639	C₂×D₄	#41×C₃₁	1	4	yes	—
640	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
641	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	8	2	no	—
651	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
654	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
655	Q₁₆	—	4	4	no	—
656	SD₁₆	—	2	8	no	—
657	SD₁₆	—	4	4	no	—
658	M₁₆	—	2	4	no	—
659	M₁₆	—	4	4	no	—
660	C₂×C₈	—	2	2	no	—
661	C₂×C₈	—	2	2	no	—
662	C₂×C₈	—	4	4	no	—
663	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
664	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
665	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
681	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
682	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
683	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
684	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
685	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
697	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
698	C₄²	—	2	2	no	—
699	C₄²	—	2	2	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	2	no	—
702	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
703	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
704	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
705	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
706	C₂³	—	2	2	no	—
707	C₂³	—	2	4	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	4	8	no	—
710	C₂³	—	8	1	no	—
711	C₂³	—	8	1	no	—
712	C₂³	—	8	4	no	—
713	C₂³	—	8	4	no	—
714	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
715	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
716	Q₈	—	2	4	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	—	4	2	no	—
722	Q₈	—	4	2	no	—
723	Q₈	—	8	1	no	—
724	D₄	—	2	8	no	—
725	D₄	—	2	4	no	—
726	D₄	—	2	4	no	—
727	D₄	—	2	2	no	—
728	D₄	—	2	2	no	—
729	D₄	—	2	2	no	—
730	D₄	—	4	2	no	—
731	D₄	—	4	2	no	—
732	D₄	—	4	8	no	—
733	D₄	—	4	2	no	—
734	D₄	—	4	8	no	—
735	D₄	—	4	4	no	—
736	D₄	—	8	1	no	—
737	D₄	—	8	4	no	—
738	D₄	C₂×#41×C₃₁	1	4	yes	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	8	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	4	2	no	—
752	C₂×C₄	—	4	4	no	—
753	C₂×C₄	—	8	2	no	—
754	C₂×C₄	—	8	1	no	—
755	C₂×C₄	—	8	4	no	—
756	C₂×C₄	—	8	1	no	—
757	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
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	C₂×#41×C₃₁	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	2	no	—
767	C₈	—	2	2	no	—
768	C₈	—	2	4	no	—
769	C₂²	—	2	1	no	—
770	C₂²	—	2	1	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	2	4	no	—
773	C₂²	—	2	4	no	—
774	C₂²	—	2	4	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	8	4	no	—
781	C₂²	—	16	8	no	—
782	C₂²	C₃₁×#546	1	2	yes	—
783	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
784	C₄	—	2	4	no	—
785	C₄	—	2	1	no	—
786	C₄	—	2	1	no	—
787	C₄	—	2	1	no	—
788	C₄	—	2	1	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	C₃₁×#546	1	2	yes	—
796	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
797	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
798	C₂	—	2	2	no	—
799	C₂	—	4	4	no	—
800	C₂	—	4	4	no	—
801	C₂	—	8	2	no	—
802	C₂	C₂×C₃₁×#546	1	1	yes	characteristic
803	C₂	C₃₁×#3585	1	1	yes	characteristic
804	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3507	C₂	semidirect
3. C₃₁×#3315	C₂	semidirect
4. C₃₁×#3314	C₂	semidirect
5. C₃₁×#3311	C₂	semidirect
6. C₃₁×#3310	C₂	semidirect
7. C₃₁×#3135	C₂	semidirect
8. C₃₁×#3098	C₂	semidirect
9. C₃₁×#3077	C₂	semidirect
10. C₃₁×#3063	C₂	semidirect
11. C₃₁×#3037	C₂	semidirect
12. C₃₁×#3009	C₂	semidirect
13. C₂×C₃₁×#440	C₂	semidirect
14. C₃₁×#2932	C₂	semidirect
15. C₃₁×#2897	C₂	semidirect
17. C₂×C₃₁×#137	C₂²	semidirect
19. C₂×C₃₁×#131	C₂²	semidirect
23. C₃₁×#556	C₂²	semidirect
24. C₃₁×#554	C₂²	semidirect
25. C₃₁×#552	C₂²	semidirect
34. C₃₁×#536	C₂²	semidirect
36. C₃₁×#533	C₂²	semidirect
41. C₃₁×#520	C₂²	semidirect
42. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
44. C₃₁×#491	C₂²	semidirect
45. C₃₁×#490	C₂²	semidirect
46. C₃₁×#489	C₂²	semidirect
47. C₃₁×#489	C₂²	semidirect
48. C₃₁×#485	C₂²	semidirect
49. C₃₁×#484	C₂²	semidirect
50. C₃₁×#482	C₂²	semidirect
51. C₃₁×#480	C₂²	semidirect
52. C₃₁×#478	C₂²	semidirect
53. C₃₁×#476	C₂²	semidirect
54. C₃₁×#474	C₂²	semidirect
55. C₃₁×#470	C₂²	semidirect
56. C₃₁×#468	C₂²	semidirect
57. C₃₁×#467	C₂²	semidirect
58. C₃₁×#465	C₂²	semidirect
59. C₃₁×#464	C₂²	semidirect
60. C₃₁×#462	C₂²	semidirect
61. C₃₁×#460	C₂²	semidirect
62. C₃₁×#452	C₂²	semidirect
63. C₃₁×#452	C₂²	semidirect
64. C₃₁×#450	C₂²	semidirect
65. C₃₁×#450	C₂²	semidirect
66. C₃₁×#440	C₂²	semidirect
67. C₃₁×#440	C₂²	semidirect
68. C₃₁×#435	C₂²	semidirect
69. C₃₁×#435	C₂²	semidirect
70. C₃₁×#428	C₂²	semidirect
71. C₂×C₃₁×#107	C₂²	semidirect
72. C₃₁×#423	C₂²	semidirect
74. C₃₁×#418	C₂²	semidirect
75. C₃₁×#417	C₂²	semidirect
76. C₃₁×#417	C₂²	semidirect
77. C₃₁×#416	C₂²	semidirect
78. C₃₁×#416	C₂²	semidirect
79. C₃₁×#416	C₂²	semidirect
80. C₂×C₃₁×#103	C₂²	semidirect
82. C₂×C₃₁×#102	C₂²	semidirect
83. C₃₁×#408	C₂²	semidirect
84. C₂×C₃₁×#97	C₂²	semidirect
303. #61219	C₃₁	direct (N × H)
367. #3507	C₂×C₃₁	semidirect
369. #3315	C₂×C₃₁	semidirect
370. #3314	C₂×C₃₁	semidirect
371. #3311	C₂×C₃₁	semidirect
372. #3310	C₂×C₃₁	semidirect
373. #3135	C₂×C₃₁	semidirect
374. #3098	C₂×C₃₁	semidirect
375. #3077	C₂×C₃₁	semidirect
376. #3063	C₂×C₃₁	semidirect
377. #3037	C₂×C₃₁	semidirect
378. #3009	C₂×C₃₁	semidirect
379. C₂×#440	C₂×C₃₁	semidirect
380. #2932	C₂×C₃₁	semidirect
381. #2897	C₂×C₃₁	semidirect
412. C₂×#137	C₂²×C₃₁	semidirect
414. C₂×#131	C₂²×C₃₁	semidirect
418. #556	C₂²×C₃₁	semidirect
419. #554	C₂²×C₃₁	semidirect
420. #552	C₂²×C₃₁	semidirect
429. #536	C₂²×C₃₁	semidirect
431. #533	C₂²×C₃₁	semidirect
436. #520	C₂²×C₃₁	semidirect
437. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
439. #491	C₂²×C₃₁	semidirect
440. #490	C₂²×C₃₁	semidirect
441. #489	C₂²×C₃₁	semidirect
442. #489	C₂²×C₃₁	semidirect
443. #485	C₂²×C₃₁	semidirect
444. #484	C₂²×C₃₁	semidirect
445. #482	C₂²×C₃₁	semidirect
446. #480	C₂²×C₃₁	semidirect
447. #478	C₂²×C₃₁	semidirect
448. #476	C₂²×C₃₁	semidirect
449. #474	C₂²×C₃₁	semidirect
450. #470	C₂²×C₃₁	semidirect
451. #468	C₂²×C₃₁	semidirect
452. #467	C₂²×C₃₁	semidirect
453. #465	C₂²×C₃₁	semidirect
454. #464	C₂²×C₃₁	semidirect
455. #462	C₂²×C₃₁	semidirect
456. #460	C₂²×C₃₁	semidirect
457. #452	C₂²×C₃₁	semidirect
458. #452	C₂²×C₃₁	semidirect
459. #450	C₂²×C₃₁	semidirect
460. #450	C₂²×C₃₁	semidirect
461. #440	C₂²×C₃₁	semidirect
462. #440	C₂²×C₃₁	semidirect
463. #435	C₂²×C₃₁	semidirect
464. #435	C₂²×C₃₁	semidirect
465. #428	C₂²×C₃₁	semidirect
466. C₂×#107	C₂²×C₃₁	semidirect
467. #423	C₂²×C₃₁	semidirect
469. #418	C₂²×C₃₁	semidirect
470. #417	C₂²×C₃₁	semidirect
471. #417	C₂²×C₃₁	semidirect
472. #416	C₂²×C₃₁	semidirect
473. #416	C₂²×C₃₁	semidirect
474. #416	C₂²×C₃₁	semidirect
475. C₂×#103	C₂²×C₃₁	semidirect
477. C₂×#102	C₂²×C₃₁	semidirect
478. #408	C₂²×C₃₁	semidirect
479. C₂×#97	C₂²×C₃₁	semidirect
604. C₃₁	#61219	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×#3507	2
C₃₁×#3496	2
C₃₁×#3315	2
C₃₁×#3314	2
C₃₁×#3311	2
C₃₁×#3310	2
C₃₁×#3135	2
C₃₁×#3098	2
C₃₁×#3077	2
C₃₁×#3063	2
C₃₁×#3037	2
C₃₁×#3009	2
C₂×C₃₁×#440	2
C₃₁×#2932	2
C₃₁×#2897	2
#61219	31

Subgroups — C31×#61219 #21517978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61219 #21517978