Subgroups — C₃₁×#62805 #21519564

Order 7936.

7104 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3523	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3520	C₂	1	6	yes	maximal, complemented
3	C₃₁×#3518	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3515	C₂	1	6	yes	maximal, complemented
5	C₃₁×#3511	C₂	1	3	yes	maximal, complemented
6	C₃₁×#3509	C₂	1	3	yes	maximal, complemented
7	C₃₁×#3503	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3499	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3495	C₂	1	6	yes	maximal, complemented
10	C₃₁×#3489	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3482	C₂	1	6	yes	maximal, complemented
12	C₃₁×#3482	C₂	1	2	yes	maximal, complemented
13	Q₈×#41×C₃₁	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3475	C₂	1	6	yes	maximal, complemented
15	C₃₁×#3461	C₂	1	6	yes	maximal, complemented
16	C₃₁×#3444	C₂	1	3	yes	maximal, complemented
17	C₂×C₃₁×#533	C₂	1	3	yes	maximal, complemented
18	C₄×C₃₁×2₋¹⁺⁴	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	2	yes	—
21	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
22	Q₈²×C₃₁	C₂²	1	2	yes	complemented
23	C₃₁×#557	C₂²	1	6	yes	complemented
24	C₃₁×#557	C₂²	1	2	yes	complemented
25	C₃₁×#557	C₂²	1	6	yes	complemented
26	C₃₁×#556	C₂²	1	6	yes	complemented
27	C₃₁×#556	C₂²	1	12	yes	complemented
28	C₃₁×#556	C₂²	1	6	yes	complemented
29	C₃₁×#556	C₂²	1	6	yes	complemented
30	C₃₁×#555	C₂²	1	6	yes	complemented
31	C₃₁×#554	C₂²	1	12	yes	—
32	C₃₁×#554	C₂²	1	6	yes	complemented
33	C₃₁×#554	C₂²	1	6	yes	complemented
34	C₃₁×#553	C₂²	1	12	yes	complemented
35	C₃₁×#552	C₂²	1	12	yes	—
36	C₃₁×#552	C₂²	1	12	yes	complemented
37	C₃₁×#552	C₂²	1	12	yes	complemented
38	C₃₁×#552	C₂²	1	24	yes	complemented
39	C₃₁×#552	C₂²	1	12	yes	complemented
40	C₃₁×#551	C₂²	1	24	yes	—
41	D₄×Q₈×C₃₁	C₂²	1	4	yes	—
42	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
43	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
44	D₄×Q₈×C₃₁	C₂²	1	6	yes	complemented
45	C₃₁×#548	C₂²	1	4	yes	—
46	C₃₁×#548	C₂²	1	12	yes	complemented
47	C₃₁×#547	C₂²	1	12	yes	—
48	C₃₁×#547	C₂²	1	6	yes	complemented
49	C₃₁×#547	C₂²	1	6	yes	complemented
50	C₃₁×#547	C₂²	1	6	yes	complemented
51	C₃₁×#546	C₂²	1	12	yes	—
52	C₃₁×#544	C₂²	1	6	yes	complemented
53	C₃₁×#542	C₂²	1	12	yes	complemented
54	C₃₁×#542	C₂²	1	12	yes	complemented
55	C₃₁×#541	C₂²	1	12	yes	complemented
56	C₃₁×#541	C₂²	1	12	yes	complemented
57	C₃₁×#539	C₂²	1	24	yes	complemented
58	C₃₁×#537	C₂²	1	6	yes	—
59	C₃₁×#536	C₂²	1	6	yes	—
60	C₃₁×#536	C₂²	1	6	yes	complemented
61	C₃₁×#533	C₂²	1	3	yes	—
62	C₃₁×#533	C₂²	1	6	yes	—
63	C₃₁×#533	C₂²	1	6	yes	—
64	C₃₁×#533	C₂²	1	6	yes	—
65	C₃₁×#533	C₂²	1	6	yes	complemented
66	C₃₁×#533	C₂²	1	6	yes	complemented
67	C₃₁×#533	C₂²	1	6	yes	complemented
68	C₃₁×#533	C₂²	1	6	yes	complemented
69	C₃₁×#533	C₂²	1	3	yes	complemented
70	C₃₁×#533	C₂²	1	3	yes	complemented
71	C₃₁×#533	C₂²	1	12	yes	complemented
72	C₃₁×#532	C₂²	1	1	yes	characteristic
73	C₃₁×#532	C₂²	1	3	yes	complemented
74	C₃₁×#532	C₂²	1	3	yes	complemented
75	C₂×C₃₁×C₄⋊Q₈	C₂²	1	3	yes	complemented
76	C₂×C₃₁×C₄⋊Q₈	C₂²	1	3	yes	complemented
77	C₃₁×#529	C₂²	1	6	yes	—
78	C₃₁×#529	C₂²	1	6	yes	—
79	C₃₁×#529	C₂²	1	6	yes	complemented
80	C₃₁×#529	C₂²	1	6	yes	complemented
81	C₃₁×#529	C₂²	1	6	yes	complemented
82	C₃₁×#529	C₂²	1	6	yes	complemented
83	C₃₁×#529	C₂²	1	24	yes	complemented
84	C₃₁×#529	C₂²	1	12	yes	complemented
85	C₂×C₃₁×#125	C₂²	1	6	yes	complemented
86	C₃₁×#525	C₂²	1	6	yes	—
87	C₃₁×#525	C₂²	1	6	yes	—
88	C₃₁×#525	C₂²	1	6	yes	—
89	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	6	yes	—
90	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	6	yes	—
91	C₃₁×#520	C₂²	1	2	yes	—
92	C₃₁×#520	C₂²	1	6	yes	complemented
93	C₃₁×#520	C₂²	1	12	yes	complemented
94	C₃₁×#519	C₂²	1	6	yes	complemented
95	C₃₁×#519	C₂²	1	4	yes	complemented
96	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
97	C₄×#41×C₃₁	C₂²	1	3	yes	—
98	C₄×#41×C₃₁	C₂²	1	3	yes	—
99	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
100	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
101	C₄×#41×C₃₁	C₂²	1	3	yes	—
102	C₄×#41×C₃₁	C₂²	1	3	yes	—
103	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
104	C₄×#41×C₃₁	C₂²	1	6	yes	—
105	C₄×#41×C₃₁	C₂²	1	6	yes	complemented
106	C₄×#41×C₃₁	C₂²	1	12	yes	complemented
107	C₄×#41×C₃₁	C₂²	1	6	yes	complemented
108	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
109	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
110	C₂×C₄×Q₈×C₃₁	C₂²	1	6	yes	complemented
111	C₂×C₄×Q₈×C₃₁	C₂²	1	4	yes	complemented
112	C₂×C₄×Q₈×C₃₁	C₂²	1	6	yes	complemented
113	C₂×C₄×D₄×C₃₁	C₂²	1	3	yes	—
114	C₂×C₄×D₄×C₃₁	C₂²	1	3	yes	—
115	C₂×C₃₁×#117	C₂²	1	3	yes	—
116	C₂×C₃₁×#117	C₂²	1	6	yes	—
117	C₂²×C₄²×C₃₁	C₂²	1	3	yes	—
118	C₃₁×2₋¹⁺⁴	—	2	16	no	—
119	C₂×#41×C₃₁	—	2	8	no	—
120	C₂×#41×C₃₁	C₂³	1	2	yes	—
121	C₂×#41×C₃₁	C₂³	1	3	yes	—
122	C₂×#41×C₃₁	C₂³	1	3	yes	—
123	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
124	C₂×#41×C₃₁	C₂³	1	6	yes	—
125	C₂×#41×C₃₁	C₂³	1	12	yes	—
126	C₂×#41×C₃₁	C₂³	1	6	yes	—
127	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₃₁	C₂³	1	6	yes	—
130	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
131	C₂²×Q₈×C₃₁	C₂³	1	6	yes	—
132	C₂²×D₄×C₃₁	C₂³	1	3	yes	—
133	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
134	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
135	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
136	C₃₁×C₄⋊Q₈	C₂³	1	3	yes	—
137	C₃₁×C₄⋊Q₈	C₂³	1	3	yes	—
138	C₃₁×C₄⋊Q₈	C₂³	1	6	yes	—
139	C₃₁×C₄⋊Q₈	C₂³	1	6	yes	—
140	C₃₁×C₄⋊Q₈	C₂³	1	6	yes	—
141	C₃₁×C₄⋊Q₈	C₂³	1	6	yes	—
142	C₃₁×C₄⋊Q₈	C₂³	1	6	yes	—
143	C₃₁×C₄⋊Q₈	C₂³	1	6	yes	—
144	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
145	C₃₁×C₄⋊Q₈	C₂³	1	12	yes	—
146	C₃₁×C₄⋊Q₈	C₂³	1	12	yes	—
147	C₃₁×#127	C₂³	1	1	yes	characteristic
148	C₃₁×#126	C₂³	1	12	yes	—
149	C₃₁×#126	C₂³	1	12	yes	—
150	C₃₁×#126	C₂³	1	24	yes	—
151	C₃₁×#126	C₂³	1	24	yes	—
152	C₃₁×#126	C₂³	1	24	yes	—
153	C₃₁×#125	C₂³	1	6	yes	—
154	C₃₁×#125	C₂³	1	12	yes	—
155	C₃₁×#125	C₂³	1	12	yes	—
156	C₃₁×#125	C₂³	1	12	yes	—
157	C₃₁×#125	C₂³	1	6	yes	—
158	C₃₁×#125	C₂³	1	6	yes	—
159	C₃₁×#125	C₂³	1	24	yes	—
160	C₃₁×#125	C₂³	1	12	yes	—
161	C₃₁×#125	C₂³	1	24	yes	—
162	C₃₁×#124	C₂³	1	6	yes	—
163	C₃₁×#124	C₂³	1	6	yes	—
164	C₃₁×#124	C₂³	1	2	yes	—
165	C₃₁×#124	C₂³	1	12	yes	—
166	C₃₁×#124	C₂³	1	24	yes	—
167	C₃₁×#123	C₂³	1	12	yes	—
168	C₃₁×#123	C₂³	1	12	yes	—
169	C₃₁×#123	C₂³	1	12	yes	—
170	C₃₁×#123	C₂³	1	24	yes	—
171	C₃₁×#123	C₂³	1	24	yes	—
172	C₃₁×#123	C₂³	1	24	yes	—
173	C₃₁×C₂²⋊Q₈	C₂³	1	6	yes	—
174	C₃₁×C₂²⋊Q₈	C₂³	1	6	yes	—
175	C₃₁×C₂²⋊Q₈	C₂³	1	12	yes	—
176	C₃₁×C₂²⋊Q₈	C₂³	1	12	yes	—
177	C₃₁×C₂²⋊Q₈	C₂³	1	12	yes	—
178	C₃₁×C₂²⋊Q₈	C₂³	1	12	yes	—
179	C₃₁×C₂²⋊Q₈	C₂³	1	12	yes	—
180	C₃₁×C₂²⋊Q₈	C₂³	1	12	yes	—
181	C₃₁×C₂²⋊Q₈	C₂³	1	6	yes	—
182	C₃₁×C₂²⋊Q₈	C₂³	1	6	yes	—
183	C₃₁×C₂²⋊Q₈	C₂³	1	6	yes	—
184	C₃₁×C₂²⋊Q₈	C₂³	1	6	yes	—
185	C₃₁×C₂²⋊Q₈	C₂³	1	12	yes	—
186	C₃₁×C₂²⋊Q₈	C₂³	1	24	yes	—
187	C₃₁×C₂²⋊Q₈	C₂³	1	12	yes	—
188	C₃₁×C₂²⋊Q₈	C₂³	1	12	yes	—
189	C₃₁×C₂²⋊Q₈	C₂³	1	24	yes	—
190	C₃₁×#121	C₂³	1	2	yes	—
191	C₃₁×#121	C₂³	1	2	yes	—
192	C₃₁×#121	C₂³	1	6	yes	—
193	C₃₁×#121	C₂³	1	6	yes	—
194	C₃₁×#121	C₂³	1	6	yes	—
195	C₃₁×#121	C₂³	1	6	yes	—
196	C₃₁×#121	C₂³	1	24	yes	—
197	C₃₁×#121	C₂³	1	12	yes	—
198	C₃₁×#120	C₂³	1	12	yes	—
199	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
200	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
201	C₄×Q₈×C₃₁	C₂³	1	3	yes	—
202	C₄×Q₈×C₃₁	C₂³	1	3	yes	—
203	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
204	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
205	C₄×Q₈×C₃₁	C₂³	1	3	yes	—
206	C₄×Q₈×C₃₁	C₂³	1	3	yes	—
207	C₄×Q₈×C₃₁	C₂³	1	6	yes	—
208	C₄×Q₈×C₃₁	C₂³	1	12	yes	—
209	C₄×Q₈×C₃₁	C₂³	1	6	yes	—
210	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
211	C₄×Q₈×C₃₁	C₂³	1	12	yes	—
212	C₄×Q₈×C₃₁	C₂³	1	12	yes	—
213	C₄×Q₈×C₃₁	C₂³	1	12	yes	—
214	C₄×Q₈×C₃₁	C₂³	1	12	yes	—
215	C₄×Q₈×C₃₁	C₂³	1	12	yes	—
216	C₄×Q₈×C₃₁	C₂³	1	12	yes	—
217	C₄×Q₈×C₃₁	C₂³	1	6	yes	—
218	C₄×Q₈×C₃₁	C₂³	1	6	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	6	yes	—
220	C₄×Q₈×C₃₁	C₂³	1	12	yes	—
221	C₄×Q₈×C₃₁	C₂³	1	6	yes	—
222	C₄×D₄×C₃₁	C₂³	1	3	yes	—
223	C₄×D₄×C₃₁	C₂³	1	3	yes	—
224	C₄×D₄×C₃₁	C₂³	1	3	yes	—
225	C₄×D₄×C₃₁	C₂³	1	6	yes	—
226	C₄×D₄×C₃₁	C₂³	1	6	yes	—
227	C₄×D₄×C₃₁	C₂³	1	3	yes	—
228	C₄×D₄×C₃₁	C₂³	1	3	yes	—
229	C₄×D₄×C₃₁	C₂³	1	3	yes	—
230	C₄×D₄×C₃₁	C₂³	1	3	yes	—
231	C₄×D₄×C₃₁	C₂³	1	6	yes	—
232	C₄×D₄×C₃₁	C₂³	1	6	yes	—
233	C₄×D₄×C₃₁	C₂³	1	3	yes	—
234	C₄×D₄×C₃₁	C₂³	1	12	yes	—
235	C₄×D₄×C₃₁	C₂³	1	12	yes	—
236	C₄×D₄×C₃₁	C₂³	1	6	yes	—
237	C₄×D₄×C₃₁	C₂³	1	6	yes	—
238	C₄×D₄×C₃₁	C₂³	1	12	yes	—
239	C₄×D₄×C₃₁	C₂³	1	2	yes	—
240	C₄×D₄×C₃₁	C₂³	1	2	yes	—
241	C₄×D₄×C₃₁	C₂³	1	12	yes	—
242	C₄×D₄×C₃₁	C₂³	1	12	yes	—
243	C₄×D₄×C₃₁	C₂³	1	6	yes	—
244	C₄×D₄×C₃₁	C₂³	1	24	yes	—
245	C₄×D₄×C₃₁	C₂³	1	12	yes	—
246	C₄×D₄×C₃₁	C₂³	1	12	yes	—
247	C₄×D₄×C₃₁	C₂³	1	6	yes	—
248	C₃₁×#117	C₂³	1	6	yes	—
249	C₃₁×#117	C₂³	1	3	yes	—
250	C₃₁×#117	C₂³	1	3	yes	—
251	C₃₁×#117	C₂³	1	6	yes	—
252	C₃₁×#117	C₂³	1	3	yes	—
253	C₃₁×#117	C₂³	1	6	yes	—
254	C₃₁×#117	C₂³	1	3	yes	—
255	C₃₁×#117	C₂³	1	12	yes	—
256	C₃₁×#117	C₂³	1	12	yes	—
257	C₃₁×#117	C₂³	1	12	yes	—
258	C₃₁×#117	C₂³	1	12	yes	—
259	C₃₁×#117	C₂³	1	6	yes	—
260	C₃₁×#117	C₂³	1	12	yes	—
261	C₃₁×#117	C₂³	1	24	yes	—
262	C₃₁×#117	C₂³	1	12	yes	—
263	C₃₁×#117	C₂³	1	6	yes	—
264	C₃₁×#117	C₂³	1	12	yes	—
265	C₂×C₄⋊C₄×C₃₁	C₂³	1	3	yes	—
266	C₂×C₄⋊C₄×C₃₁	C₂³	1	3	yes	—
267	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
268	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
269	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
270	C₂×C₄⋊C₄×C₃₁	C₂³	1	12	yes	—
271	C₂×C₄⋊C₄×C₃₁	C₂³	1	12	yes	—
272	C₂×C₄⋊C₄×C₃₁	C₂³	1	12	yes	—
273	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
274	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
275	C₂×C₂²⋊C₄×C₃₁	C₂³	1	12	yes	—
276	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
277	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
278	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
279	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
280	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
281	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
282	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
283	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
284	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
285	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
286	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
287	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
288	C₂×C₄²×C₃₁	C₂³	1	12	yes	—
289	C₂×C₄²×C₃₁	C₂³	1	12	yes	—
290	C₂⁴×C₃₁	C₂⁴	1	3	yes	—
291	#41×C₃₁	—	2	4	no	—
292	#41×C₃₁	—	2	12	no	—
293	#41×C₃₁	—	2	48	no	—
294	#41×C₃₁	—	2	12	no	—
295	#41×C₃₁	—	2	24	no	—
296	#41×C₃₁	—	2	8	no	—
297	#41×C₃₁	—	4	12	no	—
298	#41×C₃₁	#41	1	8	yes	complemented
299	C₂×Q₈×C₃₁	—	2	4	no	—
300	C₂×Q₈×C₃₁	—	2	16	no	—
301	C₂×Q₈×C₃₁	—	2	24	no	—
302	C₂×Q₈×C₃₁	—	4	12	no	—
303	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
304	C₂×Q₈×C₃₁	C₂⁴	1	6	yes	—
305	C₂×Q₈×C₃₁	C₂⁴	1	12	yes	—
306	C₂×Q₈×C₃₁	C₂⁴	1	6	yes	—
307	C₂×Q₈×C₃₁	C₂⁴	1	3	yes	—
308	C₂×Q₈×C₃₁	C₂⁴	1	12	yes	—
309	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₂×D₄×C₃₁	—	2	12	no	—
311	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
312	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
313	C₂×D₄×C₃₁	C₂⁴	1	12	yes	—
314	C₂×D₄×C₃₁	C₂⁴	1	6	yes	—
315	C₂×D₄×C₃₁	C₂⁴	1	3	yes	—
316	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
317	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
318	C₂×D₄×C₃₁	C₂⁴	1	12	yes	—
319	C₂×D₄×C₃₁	C₂⁴	1	3	yes	—
320	C₂²×C₄×C₃₁	—	2	12	no	—
321	C₂²×C₄×C₃₁	—	2	12	no	—
322	C₂²×C₄×C₃₁	—	4	6	no	—
323	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
326	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
327	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
328	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
329	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
330	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
331	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
332	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
333	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
334	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
335	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
336	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
337	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
338	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
339	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
340	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
341	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
342	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
343	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
344	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
345	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
346	C₄⋊C₄×C₃₁	C₂⁴	1	3	yes	—
347	C₄⋊C₄×C₃₁	C₂⁴	1	6	yes	—
348	C₄⋊C₄×C₃₁	C₂⁴	1	6	yes	—
349	C₄⋊C₄×C₃₁	C₂⁴	1	6	yes	—
350	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
351	C₄⋊C₄×C₃₁	C₂⁴	1	6	yes	—
352	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
353	C₄⋊C₄×C₃₁	C₂⁴	1	24	yes	—
354	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
355	C₄⋊C₄×C₃₁	C₂⁴	1	3	yes	—
356	C₄⋊C₄×C₃₁	C₂⁴	1	6	yes	—
357	C₄⋊C₄×C₃₁	C₂⁴	1	3	yes	—
358	C₄⋊C₄×C₃₁	C₂⁴	1	3	yes	—
359	C₄⋊C₄×C₃₁	C₂⁴	1	6	yes	—
360	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
361	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
362	C₄⋊C₄×C₃₁	C₂⁴	1	24	yes	—
363	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
364	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
367	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
368	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
369	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
370	C₂²⋊C₄×C₃₁	C₂⁴	1	12	yes	—
371	C₂²⋊C₄×C₃₁	C₂⁴	1	6	yes	—
372	C₂²⋊C₄×C₃₁	C₂⁴	1	6	yes	—
373	C₂²⋊C₄×C₃₁	C₂⁴	1	6	yes	—
374	C₂²⋊C₄×C₃₁	C₂⁴	1	6	yes	—
375	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
376	C₂²⋊C₄×C₃₁	C₂⁴	1	12	yes	—
377	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
378	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
379	C₂²⋊C₄×C₃₁	C₂⁴	1	12	yes	—
380	C₂²⋊C₄×C₃₁	C₂⁴	1	12	yes	—
381	C₂²⋊C₄×C₃₁	C₂⁴	1	12	yes	—
382	C₂²⋊C₄×C₃₁	C₂⁴	1	12	yes	—
383	C₂²⋊C₄×C₃₁	C₂⁴	1	12	yes	—
384	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
386	C₄²×C₃₁	C₂⁴	1	3	yes	—
387	C₄²×C₃₁	C₂⁴	1	3	yes	—
388	C₄²×C₃₁	C₂⁴	1	3	yes	—
389	C₄²×C₃₁	C₂⁴	1	3	yes	—
390	C₄²×C₃₁	C₂⁴	1	3	yes	—
391	C₄²×C₃₁	C₂⁴	1	3	yes	—
392	C₄²×C₃₁	C₂⁴	1	3	yes	—
393	C₄²×C₃₁	C₂⁴	1	3	yes	—
394	C₄²×C₃₁	C₂⁴	1	3	yes	—
395	C₄²×C₃₁	C₂⁴	1	3	yes	—
396	C₄²×C₃₁	C₂⁴	1	12	yes	—
397	C₄²×C₃₁	C₂⁴	1	24	yes	—
398	C₄²×C₃₁	C₂⁴	1	12	yes	—
399	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₄²×C₃₁	C₂⁴	1	3	yes	—
401	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
402	C₄²×C₃₁	C₂⁴	1	3	yes	—
403	C₄²×C₃₁	C₂⁴	1	12	yes	—
404	#62805	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
405	C₂³×C₃₁	—	2	6	no	—
406	C₂³×C₃₁	—	2	6	no	—
407	C₂³×C₃₁	—	4	3	no	—
408	C₂³×C₃₁	C₂⁵	1	3	yes	—
409	C₂³×C₃₁	C₂⁵	1	4	yes	—
410	C₂³×C₃₁	C₂⁵	1	3	yes	—
411	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
412	Q₈×C₃₁	—	2	24	no	—
413	Q₈×C₃₁	—	2	12	no	—
414	Q₈×C₃₁	—	2	6	no	—
415	Q₈×C₃₁	—	2	4	no	—
416	Q₈×C₃₁	—	2	12	no	—
417	Q₈×C₃₁	—	4	12	no	—
418	Q₈×C₃₁	C₂×#41	1	4	yes	—
419	D₄×C₃₁	—	2	12	no	—
420	D₄×C₃₁	—	2	24	no	—
421	D₄×C₃₁	—	2	8	no	—
422	D₄×C₃₁	—	2	6	no	—
423	D₄×C₃₁	—	2	4	no	—
424	D₄×C₃₁	—	2	4	no	—
425	D₄×C₃₁	—	2	4	no	—
426	D₄×C₃₁	—	4	12	no	—
427	D₄×C₃₁	C₂×#41	1	12	yes	—
428	C₂×C₄×C₃₁	—	2	6	no	—
429	C₂×C₄×C₃₁	—	2	24	no	—
430	C₂×C₄×C₃₁	—	2	6	no	—
431	C₂×C₄×C₃₁	—	2	2	no	—
432	C₂×C₄×C₃₁	—	2	6	no	—
433	C₂×C₄×C₃₁	—	2	6	no	—
434	C₂×C₄×C₃₁	—	2	6	no	—
435	C₂×C₄×C₃₁	—	2	24	no	—
436	C₂×C₄×C₃₁	—	2	6	no	—
437	C₂×C₄×C₃₁	—	2	6	no	—
438	C₂×C₄×C₃₁	—	2	6	no	—
439	C₂×C₄×C₃₁	—	2	6	no	—
440	C₂×C₄×C₃₁	—	2	8	no	—
441	C₂×C₄×C₃₁	—	2	2	no	—
442	C₂×C₄×C₃₁	—	2	6	no	—
443	C₂×C₄×C₃₁	—	2	6	no	—
444	C₂×C₄×C₃₁	—	4	3	no	—
445	C₂×C₄×C₃₁	—	4	3	no	—
446	C₂×C₄×C₃₁	—	4	3	no	—
447	C₂×C₄×C₃₁	—	4	12	no	—
448	C₂×C₄×C₃₁	—	4	12	no	—
449	C₂×C₄×C₃₁	C₂×#41	1	12	yes	—
450	C₂×C₄×C₃₁	2₋¹⁺⁴	1	4	yes	complemented
451	C₂×C₄×C₃₁	C₂⁵	1	3	yes	—
452	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
453	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
454	C₂×C₄×C₃₁	C₂⁵	1	3	yes	—
455	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
456	C₂×C₄×C₃₁	C₂⁵	1	3	yes	—
457	C₂×C₄×C₃₁	C₂⁵	1	3	yes	—
458	C₂×C₄×C₃₁	C₂⁵	1	12	yes	—
459	C₂×C₄×C₃₁	C₂⁵	1	12	yes	—
460	C₂×C₄×C₃₁	C₂⁵	1	3	yes	—
461	C₂×C₄×C₃₁	C₂⁵	1	3	yes	—
462	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
463	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
464	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
465	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
466	#3523	C₂×C₃₁	1	2	yes	complemented
467	#3520	C₂×C₃₁	1	6	yes	complemented
468	#3518	C₂×C₃₁	1	2	yes	complemented
469	#3515	C₂×C₃₁	1	6	yes	complemented
470	#3511	C₂×C₃₁	1	3	yes	complemented
471	#3509	C₂×C₃₁	1	3	yes	complemented
472	#3503	C₂×C₃₁	1	1	yes	characteristic, complemented
473	#3499	C₂×C₃₁	1	1	yes	characteristic, complemented
474	#3495	C₂×C₃₁	1	6	yes	complemented
475	#3489	C₂×C₃₁	1	2	yes	complemented
476	#3482	C₂×C₃₁	1	6	yes	complemented
477	#3482	C₂×C₃₁	1	2	yes	complemented
478	Q₈×#41	C₂×C₃₁	1	2	yes	complemented
479	#3475	C₂×C₃₁	1	6	yes	complemented
480	#3461	C₂×C₃₁	1	6	yes	complemented
481	#3444	C₂×C₃₁	1	3	yes	complemented
482	C₂×#533	C₂×C₃₁	1	3	yes	complemented
483	C₄×2₋¹⁺⁴	C₂×C₃₁	1	2	yes	complemented
484	C₂×C₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
485	C₂²×C₃₁	—	2	1	no	—
486	C₂²×C₃₁	—	2	3	no	—
487	C₂²×C₃₁	—	2	3	no	—
488	C₂²×C₃₁	—	2	1	no	—
489	C₂²×C₃₁	—	2	4	no	—
490	C₂²×C₃₁	—	2	3	no	—
491	C₂²×C₃₁	—	2	3	no	—
492	C₂²×C₃₁	—	2	4	no	—
493	C₂²×C₃₁	—	2	3	no	—
494	C₂²×C₃₁	—	2	4	no	—
495	C₂²×C₃₁	—	4	12	no	—
496	C₂²×C₃₁	C₂²×#41	1	6	yes	—
497	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
498	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
499	C₄×C₃₁	—	2	1	no	—
500	C₄×C₃₁	—	2	3	no	—
501	C₄×C₃₁	—	2	12	no	—
502	C₄×C₃₁	—	2	3	no	—
503	C₄×C₃₁	—	2	3	no	—
504	C₄×C₃₁	—	2	4	no	—
505	C₄×C₃₁	—	2	1	no	—
506	C₄×C₃₁	—	2	3	no	—
507	C₄×C₃₁	—	2	3	no	—
508	C₄×C₃₁	—	2	12	no	—
509	C₄×C₃₁	C₂²×#41	1	6	yes	—
510	C₄×C₃₁	C₂²×#41	1	2	yes	—
511	C₄×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
512	C₄×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
513	C₄×C₃₁	#585	1	2	yes	—
514	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	2	yes	—
515	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
516	Q₈²	C₂²×C₃₁	1	2	yes	complemented
517	#557	C₂²×C₃₁	1	6	yes	complemented
518	#557	C₂²×C₃₁	1	2	yes	complemented
519	#557	C₂²×C₃₁	1	6	yes	complemented
520	#556	C₂²×C₃₁	1	6	yes	complemented
521	#556	C₂²×C₃₁	1	12	yes	complemented
522	#556	C₂²×C₃₁	1	6	yes	complemented
523	#556	C₂²×C₃₁	1	6	yes	complemented
524	#555	C₂²×C₃₁	1	6	yes	complemented
525	#554	C₂²×C₃₁	1	12	yes	—
526	#554	C₂²×C₃₁	1	6	yes	complemented
527	#554	C₂²×C₃₁	1	6	yes	complemented
528	#553	C₂²×C₃₁	1	12	yes	complemented
529	#552	C₂²×C₃₁	1	12	yes	—
530	#552	C₂²×C₃₁	1	12	yes	complemented
531	#552	C₂²×C₃₁	1	12	yes	complemented
532	#552	C₂²×C₃₁	1	24	yes	complemented
533	#552	C₂²×C₃₁	1	12	yes	complemented
534	#551	C₂²×C₃₁	1	24	yes	—
535	D₄×Q₈	C₂²×C₃₁	1	4	yes	—
536	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
537	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
538	D₄×Q₈	C₂²×C₃₁	1	6	yes	complemented
539	#548	C₂²×C₃₁	1	4	yes	—
540	#548	C₂²×C₃₁	1	12	yes	complemented
541	#547	C₂²×C₃₁	1	12	yes	—
542	#547	C₂²×C₃₁	1	6	yes	complemented
543	#547	C₂²×C₃₁	1	6	yes	complemented
544	#547	C₂²×C₃₁	1	6	yes	complemented
545	#546	C₂²×C₃₁	1	12	yes	—
546	#544	C₂²×C₃₁	1	6	yes	complemented
547	#542	C₂²×C₃₁	1	12	yes	complemented
548	#542	C₂²×C₃₁	1	12	yes	complemented
549	#541	C₂²×C₃₁	1	12	yes	complemented
550	#541	C₂²×C₃₁	1	12	yes	complemented
551	#539	C₂²×C₃₁	1	24	yes	complemented
552	#537	C₂²×C₃₁	1	6	yes	—
553	#536	C₂²×C₃₁	1	6	yes	—
554	#536	C₂²×C₃₁	1	6	yes	complemented
555	#533	C₂²×C₃₁	1	3	yes	—
556	#533	C₂²×C₃₁	1	6	yes	—
557	#533	C₂²×C₃₁	1	6	yes	—
558	#533	C₂²×C₃₁	1	6	yes	—
559	#533	C₂²×C₃₁	1	6	yes	complemented
560	#533	C₂²×C₃₁	1	6	yes	complemented
561	#533	C₂²×C₃₁	1	6	yes	complemented
562	#533	C₂²×C₃₁	1	6	yes	complemented
563	#533	C₂²×C₃₁	1	3	yes	complemented
564	#533	C₂²×C₃₁	1	3	yes	complemented
565	#533	C₂²×C₃₁	1	12	yes	complemented
566	#532	C₂²×C₃₁	1	1	yes	characteristic
567	#532	C₂²×C₃₁	1	3	yes	complemented
568	#532	C₂²×C₃₁	1	3	yes	complemented
569	C₂×C₄⋊Q₈	C₂²×C₃₁	1	3	yes	complemented
570	C₂×C₄⋊Q₈	C₂²×C₃₁	1	3	yes	complemented
571	#529	C₂²×C₃₁	1	6	yes	—
572	#529	C₂²×C₃₁	1	6	yes	—
573	#529	C₂²×C₃₁	1	6	yes	complemented
574	#529	C₂²×C₃₁	1	6	yes	complemented
575	#529	C₂²×C₃₁	1	6	yes	complemented
576	#529	C₂²×C₃₁	1	6	yes	complemented
577	#529	C₂²×C₃₁	1	24	yes	complemented
578	#529	C₂²×C₃₁	1	12	yes	complemented
579	C₂×#125	C₂²×C₃₁	1	6	yes	complemented
580	#525	C₂²×C₃₁	1	6	yes	—
581	#525	C₂²×C₃₁	1	6	yes	—
582	#525	C₂²×C₃₁	1	6	yes	—
583	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	6	yes	—
584	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	6	yes	—
585	#520	C₂²×C₃₁	1	2	yes	—
586	#520	C₂²×C₃₁	1	6	yes	complemented
587	#520	C₂²×C₃₁	1	12	yes	complemented
588	#519	C₂²×C₃₁	1	6	yes	complemented
589	#519	C₂²×C₃₁	1	4	yes	complemented
590	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
591	C₄×#41	C₂²×C₃₁	1	3	yes	—
592	C₄×#41	C₂²×C₃₁	1	3	yes	—
593	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
594	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
595	C₄×#41	C₂²×C₃₁	1	3	yes	—
596	C₄×#41	C₂²×C₃₁	1	3	yes	—
597	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
598	C₄×#41	C₂²×C₃₁	1	6	yes	—
599	C₄×#41	C₂²×C₃₁	1	6	yes	complemented
600	C₄×#41	C₂²×C₃₁	1	12	yes	complemented
601	C₄×#41	C₂²×C₃₁	1	6	yes	complemented
602	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
603	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
604	C₂×C₄×Q₈	C₂²×C₃₁	1	6	yes	complemented
605	C₂×C₄×Q₈	C₂²×C₃₁	1	4	yes	complemented
606	C₂×C₄×Q₈	C₂²×C₃₁	1	6	yes	complemented
607	C₂×C₄×D₄	C₂²×C₃₁	1	3	yes	—
608	C₂×C₄×D₄	C₂²×C₃₁	1	3	yes	—
609	C₂×#117	C₂²×C₃₁	1	3	yes	—
610	C₂×#117	C₂²×C₃₁	1	6	yes	—
611	C₂²×C₄²	C₂²×C₃₁	1	3	yes	—
612	C₂×C₃₁	—	2	2	no	—
613	C₂×C₃₁	—	2	6	no	—
614	C₂×C₃₁	—	4	4	no	—
615	C₂×C₃₁	—	4	3	no	—
616	C₂×C₃₁	C₂³×#41	1	1	yes	characteristic
617	C₂×C₃₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
618	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
619	2₋¹⁺⁴	—	2	16	no	—
620	C₂×#41	—	2	8	no	—
621	C₂×#41	C₂³×C₃₁	1	2	yes	—
622	C₂×#41	C₂³×C₃₁	1	3	yes	—
623	C₂×#41	C₂³×C₃₁	1	3	yes	—
624	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
625	C₂×#41	C₂³×C₃₁	1	6	yes	—
626	C₂×#41	C₂³×C₃₁	1	12	yes	—
627	C₂×#41	C₂³×C₃₁	1	6	yes	—
628	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
629	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
630	C₂²×Q₈	C₂³×C₃₁	1	6	yes	—
631	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
632	C₂²×Q₈	C₂³×C₃₁	1	6	yes	—
633	C₂²×D₄	C₂³×C₃₁	1	3	yes	—
634	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
635	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
636	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
637	C₄⋊Q₈	C₂³×C₃₁	1	3	yes	—
638	C₄⋊Q₈	C₂³×C₃₁	1	3	yes	—
639	C₄⋊Q₈	C₂³×C₃₁	1	6	yes	—
640	C₄⋊Q₈	C₂³×C₃₁	1	6	yes	—
641	C₄⋊Q₈	C₂³×C₃₁	1	6	yes	—
642	C₄⋊Q₈	C₂³×C₃₁	1	6	yes	—
643	C₄⋊Q₈	C₂³×C₃₁	1	6	yes	—
644	C₄⋊Q₈	C₂³×C₃₁	1	6	yes	—
645	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
646	C₄⋊Q₈	C₂³×C₃₁	1	12	yes	—
647	C₄⋊Q₈	C₂³×C₃₁	1	12	yes	—
648	#127	C₂³×C₃₁	1	1	yes	characteristic
649	#126	C₂³×C₃₁	1	12	yes	—
650	#126	C₂³×C₃₁	1	12	yes	—
651	#126	C₂³×C₃₁	1	24	yes	—
652	#126	C₂³×C₃₁	1	24	yes	—
653	#126	C₂³×C₃₁	1	24	yes	—
654	#125	C₂³×C₃₁	1	6	yes	—
655	#125	C₂³×C₃₁	1	12	yes	—
656	#125	C₂³×C₃₁	1	12	yes	—
657	#125	C₂³×C₃₁	1	12	yes	—
658	#125	C₂³×C₃₁	1	6	yes	—
659	#125	C₂³×C₃₁	1	6	yes	—
660	#125	C₂³×C₃₁	1	24	yes	—
661	#125	C₂³×C₃₁	1	12	yes	—
662	#125	C₂³×C₃₁	1	24	yes	—
663	#124	C₂³×C₃₁	1	6	yes	—
664	#124	C₂³×C₃₁	1	6	yes	—
665	#124	C₂³×C₃₁	1	2	yes	—
666	#124	C₂³×C₃₁	1	12	yes	—
667	#124	C₂³×C₃₁	1	24	yes	—
668	#123	C₂³×C₃₁	1	12	yes	—
669	#123	C₂³×C₃₁	1	12	yes	—
670	#123	C₂³×C₃₁	1	12	yes	—
671	#123	C₂³×C₃₁	1	24	yes	—
672	#123	C₂³×C₃₁	1	24	yes	—
673	#123	C₂³×C₃₁	1	24	yes	—
674	C₂²⋊Q₈	C₂³×C₃₁	1	6	yes	—
675	C₂²⋊Q₈	C₂³×C₃₁	1	6	yes	—
676	C₂²⋊Q₈	C₂³×C₃₁	1	12	yes	—
677	C₂²⋊Q₈	C₂³×C₃₁	1	12	yes	—
678	C₂²⋊Q₈	C₂³×C₃₁	1	12	yes	—
679	C₂²⋊Q₈	C₂³×C₃₁	1	12	yes	—
680	C₂²⋊Q₈	C₂³×C₃₁	1	12	yes	—
681	C₂²⋊Q₈	C₂³×C₃₁	1	12	yes	—
682	C₂²⋊Q₈	C₂³×C₃₁	1	6	yes	—
683	C₂²⋊Q₈	C₂³×C₃₁	1	6	yes	—
684	C₂²⋊Q₈	C₂³×C₃₁	1	6	yes	—
685	C₂²⋊Q₈	C₂³×C₃₁	1	6	yes	—
686	C₂²⋊Q₈	C₂³×C₃₁	1	12	yes	—
687	C₂²⋊Q₈	C₂³×C₃₁	1	24	yes	—
688	C₂²⋊Q₈	C₂³×C₃₁	1	12	yes	—
689	C₂²⋊Q₈	C₂³×C₃₁	1	12	yes	—
690	C₂²⋊Q₈	C₂³×C₃₁	1	24	yes	—
691	#121	C₂³×C₃₁	1	2	yes	—
692	#121	C₂³×C₃₁	1	2	yes	—
693	#121	C₂³×C₃₁	1	6	yes	—
694	#121	C₂³×C₃₁	1	6	yes	—
695	#121	C₂³×C₃₁	1	6	yes	—
696	#121	C₂³×C₃₁	1	6	yes	—
697	#121	C₂³×C₃₁	1	24	yes	—
698	#121	C₂³×C₃₁	1	12	yes	—
699	#120	C₂³×C₃₁	1	12	yes	—
700	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
701	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
702	C₄×Q₈	C₂³×C₃₁	1	3	yes	—
703	C₄×Q₈	C₂³×C₃₁	1	3	yes	—
704	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
705	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
706	C₄×Q₈	C₂³×C₃₁	1	3	yes	—
707	C₄×Q₈	C₂³×C₃₁	1	3	yes	—
708	C₄×Q₈	C₂³×C₃₁	1	6	yes	—
709	C₄×Q₈	C₂³×C₃₁	1	12	yes	—
710	C₄×Q₈	C₂³×C₃₁	1	6	yes	—
711	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
712	C₄×Q₈	C₂³×C₃₁	1	12	yes	—
713	C₄×Q₈	C₂³×C₃₁	1	12	yes	—
714	C₄×Q₈	C₂³×C₃₁	1	12	yes	—
715	C₄×Q₈	C₂³×C₃₁	1	12	yes	—
716	C₄×Q₈	C₂³×C₃₁	1	12	yes	—
717	C₄×Q₈	C₂³×C₃₁	1	12	yes	—
718	C₄×Q₈	C₂³×C₃₁	1	6	yes	—
719	C₄×Q₈	C₂³×C₃₁	1	6	yes	—
720	C₄×Q₈	C₂³×C₃₁	1	6	yes	—
721	C₄×Q₈	C₂³×C₃₁	1	12	yes	—
722	C₄×Q₈	C₂³×C₃₁	1	6	yes	—
723	C₄×D₄	C₂³×C₃₁	1	3	yes	—
724	C₄×D₄	C₂³×C₃₁	1	3	yes	—
725	C₄×D₄	C₂³×C₃₁	1	3	yes	—
726	C₄×D₄	C₂³×C₃₁	1	6	yes	—
727	C₄×D₄	C₂³×C₃₁	1	6	yes	—
728	C₄×D₄	C₂³×C₃₁	1	3	yes	—
729	C₄×D₄	C₂³×C₃₁	1	3	yes	—
730	C₄×D₄	C₂³×C₃₁	1	3	yes	—
731	C₄×D₄	C₂³×C₃₁	1	3	yes	—
732	C₄×D₄	C₂³×C₃₁	1	6	yes	—
733	C₄×D₄	C₂³×C₃₁	1	6	yes	—
734	C₄×D₄	C₂³×C₃₁	1	3	yes	—
735	C₄×D₄	C₂³×C₃₁	1	12	yes	—
736	C₄×D₄	C₂³×C₃₁	1	12	yes	—
737	C₄×D₄	C₂³×C₃₁	1	6	yes	—
738	C₄×D₄	C₂³×C₃₁	1	6	yes	—
739	C₄×D₄	C₂³×C₃₁	1	12	yes	—
740	C₄×D₄	C₂³×C₃₁	1	2	yes	—
741	C₄×D₄	C₂³×C₃₁	1	2	yes	—
742	C₄×D₄	C₂³×C₃₁	1	12	yes	—
743	C₄×D₄	C₂³×C₃₁	1	12	yes	—
744	C₄×D₄	C₂³×C₃₁	1	6	yes	—
745	C₄×D₄	C₂³×C₃₁	1	24	yes	—
746	C₄×D₄	C₂³×C₃₁	1	12	yes	—
747	C₄×D₄	C₂³×C₃₁	1	12	yes	—
748	C₄×D₄	C₂³×C₃₁	1	6	yes	—
749	#117	C₂³×C₃₁	1	6	yes	—
750	#117	C₂³×C₃₁	1	3	yes	—
751	#117	C₂³×C₃₁	1	3	yes	—
752	#117	C₂³×C₃₁	1	6	yes	—
753	#117	C₂³×C₃₁	1	3	yes	—
754	#117	C₂³×C₃₁	1	6	yes	—
755	#117	C₂³×C₃₁	1	3	yes	—
756	#117	C₂³×C₃₁	1	12	yes	—
757	#117	C₂³×C₃₁	1	12	yes	—
758	#117	C₂³×C₃₁	1	12	yes	—
759	#117	C₂³×C₃₁	1	12	yes	—
760	#117	C₂³×C₃₁	1	6	yes	—
761	#117	C₂³×C₃₁	1	12	yes	—
762	#117	C₂³×C₃₁	1	24	yes	—
763	#117	C₂³×C₃₁	1	12	yes	—
764	#117	C₂³×C₃₁	1	6	yes	—
765	#117	C₂³×C₃₁	1	12	yes	—
766	C₂×C₄⋊C₄	C₂³×C₃₁	1	3	yes	—
767	C₂×C₄⋊C₄	C₂³×C₃₁	1	3	yes	—
768	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
769	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
770	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
771	C₂×C₄⋊C₄	C₂³×C₃₁	1	12	yes	—
772	C₂×C₄⋊C₄	C₂³×C₃₁	1	12	yes	—
773	C₂×C₄⋊C₄	C₂³×C₃₁	1	12	yes	—
774	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₃₁	1	12	yes	—
777	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
778	C₂×C₄²	C₂³×C₃₁	1	12	yes	—
779	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
780	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
781	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
782	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
783	C₂×C₄²	C₂³×C₃₁	1	12	yes	—
784	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
785	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
786	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
787	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
788	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
789	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
790	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
791	C₃₁	#62805	1	1	yes	characteristic, direct product factor, Sylow
792	C₂⁴	C₂⁴×C₃₁	1	3	yes	—
793	#41	—	2	4	no	—
794	#41	—	2	12	no	—
795	#41	—	2	48	no	—
796	#41	—	2	12	no	—
797	#41	—	2	24	no	—
798	#41	—	2	8	no	—
799	#41	—	4	12	no	—
800	#41	#41×C₃₁	1	8	yes	complemented
801	C₂×Q₈	—	2	4	no	—
802	C₂×Q₈	—	2	16	no	—
803	C₂×Q₈	—	2	24	no	—
804	C₂×Q₈	—	4	12	no	—
805	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
806	C₂×Q₈	C₂⁴×C₃₁	1	6	yes	—
807	C₂×Q₈	C₂⁴×C₃₁	1	12	yes	—
808	C₂×Q₈	C₂⁴×C₃₁	1	6	yes	—
809	C₂×Q₈	C₂⁴×C₃₁	1	3	yes	—
810	C₂×Q₈	C₂⁴×C₃₁	1	12	yes	—
811	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
812	C₂×D₄	—	2	12	no	—
813	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
814	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
815	C₂×D₄	C₂⁴×C₃₁	1	12	yes	—
816	C₂×D₄	C₂⁴×C₃₁	1	6	yes	—
817	C₂×D₄	C₂⁴×C₃₁	1	3	yes	—
818	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
819	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
820	C₂×D₄	C₂⁴×C₃₁	1	12	yes	—
821	C₂×D₄	C₂⁴×C₃₁	1	3	yes	—
822	C₂²×C₄	—	2	12	no	—
823	C₂²×C₄	—	2	12	no	—
824	C₂²×C₄	—	4	6	no	—
825	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
826	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
829	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
830	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
831	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
832	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
833	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
834	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
835	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
836	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
837	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
838	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
839	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
840	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
841	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
842	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
843	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
844	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
845	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
846	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
847	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
848	C₄⋊C₄	C₂⁴×C₃₁	1	3	yes	—
849	C₄⋊C₄	C₂⁴×C₃₁	1	6	yes	—
850	C₄⋊C₄	C₂⁴×C₃₁	1	6	yes	—
851	C₄⋊C₄	C₂⁴×C₃₁	1	6	yes	—
852	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
853	C₄⋊C₄	C₂⁴×C₃₁	1	6	yes	—
854	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
855	C₄⋊C₄	C₂⁴×C₃₁	1	24	yes	—
856	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
857	C₄⋊C₄	C₂⁴×C₃₁	1	3	yes	—
858	C₄⋊C₄	C₂⁴×C₃₁	1	6	yes	—
859	C₄⋊C₄	C₂⁴×C₃₁	1	3	yes	—
860	C₄⋊C₄	C₂⁴×C₃₁	1	3	yes	—
861	C₄⋊C₄	C₂⁴×C₃₁	1	6	yes	—
862	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
863	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
864	C₄⋊C₄	C₂⁴×C₃₁	1	24	yes	—
865	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
866	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
867	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
868	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
869	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
870	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
871	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
872	C₂²⋊C₄	C₂⁴×C₃₁	1	12	yes	—
873	C₂²⋊C₄	C₂⁴×C₃₁	1	6	yes	—
874	C₂²⋊C₄	C₂⁴×C₃₁	1	6	yes	—
875	C₂²⋊C₄	C₂⁴×C₃₁	1	6	yes	—
876	C₂²⋊C₄	C₂⁴×C₃₁	1	6	yes	—
877	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
878	C₂²⋊C₄	C₂⁴×C₃₁	1	12	yes	—
879	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
880	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
881	C₂²⋊C₄	C₂⁴×C₃₁	1	12	yes	—
882	C₂²⋊C₄	C₂⁴×C₃₁	1	12	yes	—
883	C₂²⋊C₄	C₂⁴×C₃₁	1	12	yes	—
884	C₂²⋊C₄	C₂⁴×C₃₁	1	12	yes	—
885	C₂²⋊C₄	C₂⁴×C₃₁	1	12	yes	—
886	C₄²	C₂⁴×C₃₁	1	3	yes	—
887	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
888	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
889	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
890	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
891	C₄²	C₂⁴×C₃₁	1	3	yes	—
892	C₄²	C₂⁴×C₃₁	1	3	yes	—
893	C₄²	C₂⁴×C₃₁	1	3	yes	—
894	C₄²	C₂⁴×C₃₁	1	3	yes	—
895	C₄²	C₂⁴×C₃₁	1	12	yes	—
896	C₄²	C₂⁴×C₃₁	1	3	yes	—
897	C₄²	C₂⁴×C₃₁	1	3	yes	—
898	C₄²	C₂⁴×C₃₁	1	3	yes	—
899	C₄²	C₂⁴×C₃₁	1	3	yes	—
900	C₄²	C₂⁴×C₃₁	1	3	yes	—
901	C₄²	C₂⁴×C₃₁	1	3	yes	—
902	C₄²	C₂⁴×C₃₁	1	3	yes	—
903	C₄²	C₂⁴×C₃₁	1	12	yes	—
904	C₄²	C₂⁴×C₃₁	1	24	yes	—
905	C₄²	C₂⁴×C₃₁	1	12	yes	—
906	C₂³	—	2	6	no	—
907	C₂³	—	2	6	no	—
908	C₂³	—	4	3	no	—
909	C₂³	C₂⁵×C₃₁	1	3	yes	—
910	C₂³	C₂⁵×C₃₁	1	4	yes	—
911	C₂³	C₂⁵×C₃₁	1	3	yes	—
912	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
913	Q₈	—	2	24	no	—
914	Q₈	—	2	12	no	—
915	Q₈	—	2	6	no	—
916	Q₈	—	2	4	no	—
917	Q₈	—	2	12	no	—
918	Q₈	—	4	12	no	—
919	Q₈	C₂×#41×C₃₁	1	4	yes	—
920	D₄	—	2	12	no	—
921	D₄	—	2	24	no	—
922	D₄	—	2	8	no	—
923	D₄	—	2	6	no	—
924	D₄	—	2	4	no	—
925	D₄	—	2	4	no	—
926	D₄	—	2	4	no	—
927	D₄	—	4	12	no	—
928	D₄	C₂×#41×C₃₁	1	12	yes	—
929	C₂×C₄	—	2	6	no	—
930	C₂×C₄	—	2	24	no	—
931	C₂×C₄	—	2	6	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	6	no	—
934	C₂×C₄	—	2	6	no	—
935	C₂×C₄	—	2	6	no	—
936	C₂×C₄	—	2	24	no	—
937	C₂×C₄	—	2	6	no	—
938	C₂×C₄	—	2	6	no	—
939	C₂×C₄	—	2	6	no	—
940	C₂×C₄	—	2	6	no	—
941	C₂×C₄	—	2	8	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	6	no	—
944	C₂×C₄	—	2	6	no	—
945	C₂×C₄	—	4	3	no	—
946	C₂×C₄	—	4	3	no	—
947	C₂×C₄	—	4	3	no	—
948	C₂×C₄	—	4	12	no	—
949	C₂×C₄	—	4	12	no	—
950	C₂×C₄	C₂×#41×C₃₁	1	12	yes	—
951	C₂×C₄	C₃₁×2₋¹⁺⁴	1	4	yes	complemented
952	C₂×C₄	C₂⁵×C₃₁	1	3	yes	—
953	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
954	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
955	C₂×C₄	C₂⁵×C₃₁	1	3	yes	—
956	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
957	C₂×C₄	C₂⁵×C₃₁	1	3	yes	—
958	C₂×C₄	C₂⁵×C₃₁	1	3	yes	—
959	C₂×C₄	C₂⁵×C₃₁	1	12	yes	—
960	C₂×C₄	C₂⁵×C₃₁	1	12	yes	—
961	C₂×C₄	C₂⁵×C₃₁	1	3	yes	—
962	C₂×C₄	C₂⁵×C₃₁	1	3	yes	—
963	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
964	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
965	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
966	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
967	C₂²	—	2	1	no	—
968	C₂²	—	2	3	no	—
969	C₂²	—	2	3	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	4	no	—
972	C₂²	—	2	3	no	—
973	C₂²	—	2	3	no	—
974	C₂²	—	2	4	no	—
975	C₂²	—	2	3	no	—
976	C₂²	—	2	4	no	—
977	C₂²	—	4	12	no	—
978	C₂²	C₂²×#41×C₃₁	1	6	yes	—
979	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
980	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
981	C₄	—	2	1	no	—
982	C₄	—	2	3	no	—
983	C₄	—	2	12	no	—
984	C₄	—	2	3	no	—
985	C₄	—	2	3	no	—
986	C₄	—	2	4	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	3	no	—
989	C₄	—	2	3	no	—
990	C₄	—	2	12	no	—
991	C₄	C₂²×#41×C₃₁	1	6	yes	—
992	C₄	C₂²×#41×C₃₁	1	2	yes	—
993	C₄	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
994	C₄	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
995	C₄	C₃₁×#585	1	2	yes	—
996	C₂	—	2	2	no	—
997	C₂	—	2	6	no	—
998	C₂	—	4	3	no	—
999	C₂	—	4	4	no	—
1000	C₂	C₂³×#41×C₃₁	1	1	yes	characteristic
1001	C₂	C₂²×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1002	C₂	C₂×C₃₁×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
socle	C₂²×C₃₁	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3523	C₂	semidirect
2. C₃₁×#3520	C₂	semidirect
3. C₃₁×#3518	C₂	semidirect
4. C₃₁×#3515	C₂	semidirect
5. C₃₁×#3511	C₂	semidirect
6. C₃₁×#3509	C₂	semidirect
7. C₃₁×#3503	C₂	semidirect
8. C₃₁×#3499	C₂	semidirect
9. C₃₁×#3495	C₂	semidirect
10. C₃₁×#3489	C₂	semidirect
11. C₃₁×#3482	C₂	semidirect
12. C₃₁×#3482	C₂	semidirect
13. Q₈×#41×C₃₁	C₂	semidirect
14. C₃₁×#3475	C₂	semidirect
15. C₃₁×#3461	C₂	semidirect
16. C₃₁×#3444	C₂	semidirect
17. C₂×C₃₁×#533	C₂	semidirect
18. C₄×C₃₁×2₋¹⁺⁴	C₂	semidirect
19. C₂×C₄×#41×C₃₁	C₂	semidirect
22. Q₈²×C₃₁	C₂²	semidirect
23. C₃₁×#557	C₂²	semidirect
24. C₃₁×#557	C₂²	semidirect
25. C₃₁×#557	C₂²	semidirect
26. C₃₁×#556	C₂²	semidirect
27. C₃₁×#556	C₂²	semidirect
28. C₃₁×#556	C₂²	semidirect
29. C₃₁×#556	C₂²	semidirect
30. C₃₁×#555	C₂²	semidirect
32. C₃₁×#554	C₂²	semidirect
33. C₃₁×#554	C₂²	semidirect
34. C₃₁×#553	C₂²	semidirect
36. C₃₁×#552	C₂²	semidirect
37. C₃₁×#552	C₂²	semidirect
38. C₃₁×#552	C₂²	semidirect
39. C₃₁×#552	C₂²	semidirect
42. D₄×Q₈×C₃₁	C₂²	semidirect
43. D₄×Q₈×C₃₁	C₂²	semidirect
44. D₄×Q₈×C₃₁	C₂²	semidirect
46. C₃₁×#548	C₂²	semidirect
48. C₃₁×#547	C₂²	semidirect
49. C₃₁×#547	C₂²	semidirect
50. C₃₁×#547	C₂²	semidirect
52. C₃₁×#544	C₂²	semidirect
53. C₃₁×#542	C₂²	semidirect
54. C₃₁×#542	C₂²	semidirect
55. C₃₁×#541	C₂²	semidirect
56. C₃₁×#541	C₂²	semidirect
57. C₃₁×#539	C₂²	semidirect
60. C₃₁×#536	C₂²	semidirect
65. C₃₁×#533	C₂²	semidirect
66. C₃₁×#533	C₂²	semidirect
67. C₃₁×#533	C₂²	semidirect
68. C₃₁×#533	C₂²	semidirect
69. C₃₁×#533	C₂²	semidirect
70. C₃₁×#533	C₂²	semidirect
71. C₃₁×#533	C₂²	semidirect
73. C₃₁×#532	C₂²	semidirect
74. C₃₁×#532	C₂²	semidirect
75. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
76. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
79. C₃₁×#529	C₂²	semidirect
80. C₃₁×#529	C₂²	semidirect
81. C₃₁×#529	C₂²	semidirect
82. C₃₁×#529	C₂²	semidirect
83. C₃₁×#529	C₂²	semidirect
84. C₃₁×#529	C₂²	semidirect
85. C₂×C₃₁×#125	C₂²	semidirect
92. C₃₁×#520	C₂²	semidirect
93. C₃₁×#520	C₂²	semidirect
94. C₃₁×#519	C₂²	semidirect
95. C₃₁×#519	C₂²	semidirect
105. C₄×#41×C₃₁	C₂²	semidirect
106. C₄×#41×C₃₁	C₂²	semidirect
107. C₄×#41×C₃₁	C₂²	semidirect
110. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
111. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
112. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
298. #41×C₃₁	#41	semidirect
404. #62805	C₃₁	direct (N × H)
450. C₂×C₄×C₃₁	2₋¹⁺⁴	semidirect
466. #3523	C₂×C₃₁	semidirect
467. #3520	C₂×C₃₁	semidirect
468. #3518	C₂×C₃₁	semidirect
469. #3515	C₂×C₃₁	semidirect
470. #3511	C₂×C₃₁	semidirect
471. #3509	C₂×C₃₁	semidirect
472. #3503	C₂×C₃₁	semidirect
473. #3499	C₂×C₃₁	semidirect
474. #3495	C₂×C₃₁	semidirect
475. #3489	C₂×C₃₁	semidirect
476. #3482	C₂×C₃₁	semidirect
477. #3482	C₂×C₃₁	semidirect
478. Q₈×#41	C₂×C₃₁	semidirect
479. #3475	C₂×C₃₁	semidirect
480. #3461	C₂×C₃₁	semidirect
481. #3444	C₂×C₃₁	semidirect
482. C₂×#533	C₂×C₃₁	semidirect
483. C₄×2₋¹⁺⁴	C₂×C₃₁	semidirect
484. C₂×C₄×#41	C₂×C₃₁	semidirect
516. Q₈²	C₂²×C₃₁	semidirect
517. #557	C₂²×C₃₁	semidirect
518. #557	C₂²×C₃₁	semidirect
519. #557	C₂²×C₃₁	semidirect
520. #556	C₂²×C₃₁	semidirect
521. #556	C₂²×C₃₁	semidirect
522. #556	C₂²×C₃₁	semidirect
523. #556	C₂²×C₃₁	semidirect
524. #555	C₂²×C₃₁	semidirect
526. #554	C₂²×C₃₁	semidirect
527. #554	C₂²×C₃₁	semidirect
528. #553	C₂²×C₃₁	semidirect
530. #552	C₂²×C₃₁	semidirect
531. #552	C₂²×C₃₁	semidirect
532. #552	C₂²×C₃₁	semidirect
533. #552	C₂²×C₃₁	semidirect
536. D₄×Q₈	C₂²×C₃₁	semidirect
537. D₄×Q₈	C₂²×C₃₁	semidirect
538. D₄×Q₈	C₂²×C₃₁	semidirect
540. #548	C₂²×C₃₁	semidirect
542. #547	C₂²×C₃₁	semidirect
543. #547	C₂²×C₃₁	semidirect
544. #547	C₂²×C₃₁	semidirect
546. #544	C₂²×C₃₁	semidirect
547. #542	C₂²×C₃₁	semidirect
548. #542	C₂²×C₃₁	semidirect
549. #541	C₂²×C₃₁	semidirect
550. #541	C₂²×C₃₁	semidirect
551. #539	C₂²×C₃₁	semidirect
554. #536	C₂²×C₃₁	semidirect
559. #533	C₂²×C₃₁	semidirect
560. #533	C₂²×C₃₁	semidirect
561. #533	C₂²×C₃₁	semidirect
562. #533	C₂²×C₃₁	semidirect
563. #533	C₂²×C₃₁	semidirect
564. #533	C₂²×C₃₁	semidirect
565. #533	C₂²×C₃₁	semidirect
567. #532	C₂²×C₃₁	semidirect
568. #532	C₂²×C₃₁	semidirect
569. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
570. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
573. #529	C₂²×C₃₁	semidirect
574. #529	C₂²×C₃₁	semidirect
575. #529	C₂²×C₃₁	semidirect
576. #529	C₂²×C₃₁	semidirect
577. #529	C₂²×C₃₁	semidirect
578. #529	C₂²×C₃₁	semidirect
579. C₂×#125	C₂²×C₃₁	semidirect
586. #520	C₂²×C₃₁	semidirect
587. #520	C₂²×C₃₁	semidirect
588. #519	C₂²×C₃₁	semidirect
589. #519	C₂²×C₃₁	semidirect
599. C₄×#41	C₂²×C₃₁	semidirect
600. C₄×#41	C₂²×C₃₁	semidirect
601. C₄×#41	C₂²×C₃₁	semidirect
604. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
605. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
606. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
791. C₃₁	#62805	direct (N × H)
800. #41	#41×C₃₁	semidirect
951. C₂×C₄	C₃₁×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3523	2
C₃₁×#3520	2
C₃₁×#3518	2
C₃₁×#3515	2
C₃₁×#3511	2
C₃₁×#3509	2
C₃₁×#3503	2
C₃₁×#3499	2
C₃₁×#3495	2
C₃₁×#3489	2
C₃₁×#3482	2
Q₈×#41×C₃₁	2
C₃₁×#3475	2
C₃₁×#3461	2
C₃₁×#3444	2
C₂×C₃₁×#533	2
C₄×C₃₁×2₋¹⁺⁴	2
C₂×C₄×#41×C₃₁	2
#62805	31

Subgroups — C31×#62805 #21519564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62805 #21519564