Subgroups — C₃₁×#61167 #21517926

Order 7936.

2286 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3484	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3318	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3314	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3310	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3306	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3297	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3296	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3295	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3294	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3092	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3062	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3050	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3045	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3012	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3003	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2946	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2929	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂²×C₃₁×#102	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#554	—	2	1	no	—
32	C₃₁×#554	C₂²	1	2	yes	complemented
33	C₃₁×#553	—	2	1	no	—
34	C₃₁×#553	C₂²	1	2	yes	complemented
35	C₃₁×#552	—	2	1	no	—
36	C₃₁×#552	C₂²	1	2	yes	complemented
37	C₃₁×#547	—	2	1	no	—
38	C₃₁×#547	C₂²	1	2	yes	complemented
39	C₃₁×#546	—	2	1	no	—
40	C₃₁×#546	—	2	1	no	—
41	C₃₁×#546	C₂²	1	2	yes	—
42	C₃₁×#546	C₂²	1	2	yes	—
43	D₄²×C₃₁	—	2	1	no	—
44	D₄²×C₃₁	—	2	1	no	—
45	D₄²×C₃₁	C₂²	1	2	yes	—
46	D₄²×C₃₁	C₂²	1	2	yes	—
47	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#539	—	2	2	no	—
49	C₃₁×#537	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#535	C₂²	1	1	yes	characteristic
51	C₃₁×#535	C₂²	1	1	yes	characteristic
52	C₃₁×#534	—	2	2	no	—
53	C₃₁×#525	—	2	2	no	—
54	C₃₁×#525	C₂²	1	1	yes	characteristic
55	C₃₁×#525	C₂²	1	1	yes	characteristic
56	C₃₁×#525	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₃₁×#120	—	2	2	no	—
58	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#518	C₂²	1	1	yes	characteristic
61	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#490	C₂²	1	2	yes	complemented
63	C₃₁×#489	C₂²	1	2	yes	complemented
64	C₃₁×#488	C₂²	1	2	yes	complemented
65	C₃₁×#486	C₂²	1	2	yes	complemented
66	C₃₁×#484	C₂²	1	2	yes	complemented
67	C₃₁×#483	C₂²	1	2	yes	complemented
68	C₃₁×#482	C₂²	1	2	yes	complemented
69	C₃₁×#482	C₂²	1	2	yes	complemented
70	C₃₁×#481	C₂²	1	2	yes	complemented
71	C₃₁×#481	C₂²	1	2	yes	complemented
72	C₃₁×#480	C₂²	1	2	yes	complemented
73	C₃₁×#480	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	2	yes	complemented
75	C₃₁×#478	C₂²	1	2	yes	complemented
76	C₃₁×#476	C₂²	1	2	yes	complemented
77	C₃₁×#474	C₂²	1	2	yes	complemented
78	C₃₁×#469	C₂²	1	2	yes	complemented
79	C₃₁×#468	C₂²	1	2	yes	complemented
80	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#466	C₂²	1	2	yes	complemented
83	C₃₁×#466	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#466	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#465	C₂²	1	2	yes	complemented
86	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#464	C₂²	1	2	yes	complemented
91	C₃₁×#463	C₂²	1	2	yes	complemented
92	C₃₁×#460	C₂²	1	2	yes	complemented
93	C₃₁×#459	C₂²	1	2	yes	complemented
94	C₃₁×#452	C₂²	1	2	yes	complemented
95	C₃₁×#450	C₂²	1	2	yes	complemented
96	C₃₁×#450	C₂²	1	2	yes	complemented
97	C₃₁×#450	C₂²	1	2	yes	complemented
98	C₃₁×#449	C₂²	1	2	yes	complemented
99	C₃₁×#447	C₂²	1	2	yes	complemented
100	C₃₁×#447	C₂²	1	2	yes	complemented
101	C₃₁×#447	C₂²	1	2	yes	complemented
102	C₃₁×#442	C₂²	1	2	yes	complemented
103	C₃₁×#440	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
105	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
106	C₃₁×#435	C₂²	1	2	yes	complemented
107	C₃₁×#435	C₂²	1	2	yes	complemented
108	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
109	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
110	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
114	C₃₁×#418	C₂²	1	1	yes	characteristic
115	C₃₁×#418	C₂²	1	1	yes	characteristic, complemented
116	C₃₁×#418	C₂²	1	2	yes	complemented
117	C₃₁×#417	C₂²	1	2	yes	complemented
118	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
119	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
120	C₃₁×#416	C₂²	1	2	yes	complemented
121	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
123	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
124	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
125	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic, complemented
126	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
128	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
129	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
130	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
131	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
132	C₃₁×#408	C₂²	1	1	yes	characteristic, complemented
133	C₃₁×#407	C₂²	1	1	yes	characteristic, complemented
134	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
135	C₂⁵×C₃₁	—	2	1	no	—
136	C₃₁×H(5,𝔽₂)	—	2	4	no	—
137	C₃₁×H(5,𝔽₂)	—	4	2	no	—
138	C₂×#41×C₃₁	—	2	1	no	—
139	C₂×#41×C₃₁	—	2	2	no	—
140	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×#41×C₃₁	C₂³	1	2	yes	—
143	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₃₁	—	2	4	no	—
145	C₂²×D₄×C₃₁	—	2	2	no	—
146	C₂²×D₄×C₃₁	—	2	1	no	—
147	C₂²×D₄×C₃₁	—	2	2	no	—
148	C₂²×D₄×C₃₁	—	2	2	no	—
149	C₂²×D₄×C₃₁	—	2	1	no	—
150	C₂²×D₄×C₃₁	—	2	1	no	—
151	C₂²×D₄×C₃₁	—	2	1	no	—
152	C₂²×D₄×C₃₁	—	4	2	no	—
153	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
154	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
155	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
156	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
157	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₂³×C₄×C₃₁	—	2	1	no	—
159	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
160	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
161	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
162	C₃₁×#135	—	4	2	no	—
163	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic, complemented
164	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic, complemented
167	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic, complemented
168	C₂×D₈×C₃₁	C₂³	1	2	yes	—
169	C₂×D₈×C₃₁	C₂³	1	2	yes	—
170	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic, complemented
171	C₃₁×#131	—	4	2	no	—
172	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
173	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
174	C₂×M₁₆×C₃₁	C₂³	1	2	yes	complemented
175	C₂²×C₈×C₃₁	—	4	2	no	—
176	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
179	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
181	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
182	C₂²×C₈×C₃₁	C₂³	1	2	yes	complemented
183	C₃₁×C₄⋊Q₈	—	2	1	no	—
184	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	complemented
185	C₃₁×#127	—	2	1	no	—
186	C₃₁×#127	C₂³	1	2	yes	—
187	C₃₁×#126	—	2	2	no	—
188	C₃₁×#126	—	2	2	no	—
189	C₃₁×#125	—	2	2	no	—
190	C₃₁×#125	—	2	2	no	—
191	C₃₁×#125	—	2	1	no	—
192	C₃₁×#125	C₂³	1	2	yes	complemented
193	C₃₁×#124	—	2	1	no	—
194	C₃₁×#124	C₂³	1	2	yes	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×#123	—	2	1	no	—
197	C₃₁×#123	—	2	1	no	—
198	C₃₁×#123	—	2	2	no	—
199	C₃₁×#123	—	2	2	no	—
200	C₃₁×#123	—	2	2	no	—
201	C₃₁×#123	—	2	2	no	—
202	C₃₁×#123	—	2	2	no	—
203	C₃₁×#123	D₄	1	2	yes	—
204	C₃₁×C₂²⋊Q₈	—	2	1	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	—	2	2	no	—
208	C₃₁×C₂²⋊Q₈	—	2	2	no	—
209	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
211	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	complemented
216	C₃₁×#121	—	2	2	no	—
217	C₃₁×#121	—	2	2	no	—
218	C₃₁×#121	—	2	1	no	—
219	C₃₁×#121	—	2	2	no	—
220	C₃₁×#121	—	2	2	no	—
221	C₃₁×#121	—	2	1	no	—
222	C₃₁×#121	—	2	1	no	—
223	C₃₁×#121	—	2	2	no	—
224	C₃₁×#121	—	2	2	no	—
225	C₃₁×#121	D₄	1	1	yes	characteristic
226	C₃₁×#121	D₄	1	1	yes	characteristic
227	C₃₁×#121	C₂³	1	1	yes	characteristic
228	C₃₁×#121	C₂³	1	1	yes	characteristic
229	C₃₁×#121	C₂³	1	1	yes	characteristic
230	C₃₁×#121	C₂³	1	1	yes	characteristic
231	C₃₁×#121	C₂³	1	2	yes	—
232	C₃₁×#121	C₂³	1	2	yes	—
233	C₃₁×#121	C₂³	1	2	yes	complemented
234	C₃₁×#120	—	2	1	no	—
235	C₃₁×#120	—	2	1	no	—
236	C₃₁×#120	—	2	2	no	—
237	C₃₁×#120	—	2	2	no	—
238	C₃₁×#120	—	2	2	no	—
239	C₃₁×#120	—	2	2	no	—
240	C₃₁×#120	—	2	2	no	—
241	C₃₁×#120	—	2	2	no	—
242	C₃₁×#120	—	2	2	no	—
243	C₃₁×#120	—	2	2	no	—
244	C₃₁×#120	D₄	1	2	yes	—
245	C₄×Q₈×C₃₁	—	2	1	no	—
246	C₄×Q₈×C₃₁	C₂³	1	2	yes	complemented
247	C₄×D₄×C₃₁	—	2	2	no	—
248	C₄×D₄×C₃₁	—	2	1	no	—
249	C₄×D₄×C₃₁	—	2	2	no	—
250	C₄×D₄×C₃₁	—	2	1	no	—
251	C₄×D₄×C₃₁	—	2	1	no	—
252	C₄×D₄×C₃₁	—	2	1	no	—
253	C₄×D₄×C₃₁	—	2	1	no	—
254	C₄×D₄×C₃₁	—	2	1	no	—
255	C₄×D₄×C₃₁	—	2	1	no	—
256	C₄×D₄×C₃₁	—	2	2	no	—
257	C₄×D₄×C₃₁	—	2	2	no	—
258	C₄×D₄×C₃₁	C₂³	1	2	yes	—
259	C₄×D₄×C₃₁	C₂³	1	2	yes	—
260	C₄×D₄×C₃₁	C₂³	1	2	yes	—
261	C₄×D₄×C₃₁	C₂³	1	2	yes	—
262	C₄×D₄×C₃₁	C₂³	1	2	yes	complemented
263	C₃₁×#117	—	2	1	no	—
264	C₃₁×#117	—	2	2	no	—
265	C₃₁×#117	C₂³	1	1	yes	characteristic
266	C₃₁×#117	C₂³	1	1	yes	characteristic
267	C₃₁×#117	C₂³	1	1	yes	characteristic
268	C₃₁×#117	C₂³	1	2	yes	complemented
269	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
270	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
271	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
272	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
273	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
276	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
277	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	complemented
278	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
279	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
280	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
281	C₃₁×#107	C₂³	1	1	yes	characteristic, complemented
282	C₃₁×#107	C₂³	1	1	yes	characteristic, complemented
283	C₃₁×#107	C₂³	1	2	yes	complemented
284	C₃₁×#107	C₂³	1	2	yes	complemented
285	C₃₁×#106	C₂³	1	1	yes	characteristic, complemented
286	C₃₁×#106	C₂³	1	1	yes	characteristic, complemented
287	C₃₁×#106	C₂³	1	2	yes	complemented
288	C₃₁×#106	C₂³	1	2	yes	complemented
289	C₃₁×C₄⋊C₈	C₂³	1	2	yes	complemented
290	C₃₁×C₄⋊C₈	C₂³	1	2	yes	complemented
291	C₃₁×#103	C₂³	1	1	yes	characteristic, complemented
292	C₃₁×#103	C₂³	1	2	yes	complemented
293	C₃₁×#103	C₂³	1	1	yes	characteristic, complemented
294	C₃₁×#103	C₂³	1	1	yes	characteristic, complemented
295	C₃₁×#103	C₂³	1	1	yes	characteristic, complemented
296	C₃₁×#103	C₂³	1	2	yes	complemented
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×#102	C₂³	1	2	yes	—
305	C₃₁×#102	C₂³	1	2	yes	—
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×#102	C₂³	1	2	yes	—
308	C₃₁×#102	C₂³	1	2	yes	—
309	C₃₁×#102	C₂³	1	1	yes	characteristic, complemented
310	C₃₁×#102	C₂³	1	2	yes	complemented
311	C₃₁×#102	C₂³	1	1	yes	characteristic, complemented
312	C₃₁×#102	C₂³	1	1	yes	characteristic, complemented
313	C₃₁×#102	C₂³	1	1	yes	characteristic, complemented
314	C₃₁×#102	C₂³	1	2	yes	complemented
315	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
316	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	complemented
318	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	complemented
319	C₃₁×#97	C₂³	1	2	yes	complemented
320	C₄×C₈×C₃₁	C₂³	1	2	yes	complemented
321	C₂⁴×C₃₁	—	2	1	no	—
322	C₂⁴×C₃₁	—	2	2	no	—
323	C₂⁴×C₃₁	—	2	2	no	—
324	C₂⁴×C₃₁	—	2	1	no	—
325	C₂⁴×C₃₁	—	2	2	no	—
326	C₂⁴×C₃₁	—	4	4	no	—
327	C₂⁴×C₃₁	—	8	2	no	—
328	C₂⁴×C₃₁	—	8	2	no	—
329	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
330	#41×C₃₁	—	2	2	no	—
331	#41×C₃₁	—	2	2	no	—
332	#41×C₃₁	—	2	4	no	—
333	#41×C₃₁	—	2	2	no	—
334	#41×C₃₁	—	2	2	no	—
335	#41×C₃₁	—	2	2	no	—
336	#41×C₃₁	—	2	2	no	—
337	#41×C₃₁	—	4	2	no	—
338	#41×C₃₁	—	4	4	no	—
339	#41×C₃₁	—	8	4	no	—
340	C₂×Q₈×C₃₁	—	2	2	no	—
341	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
342	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₃₁	—	2	4	no	—
345	C₂×D₄×C₃₁	—	2	4	no	—
346	C₂×D₄×C₃₁	—	2	4	no	—
347	C₂×D₄×C₃₁	—	2	1	no	—
348	C₂×D₄×C₃₁	—	2	1	no	—
349	C₂×D₄×C₃₁	—	2	1	no	—
350	C₂×D₄×C₃₁	—	2	1	no	—
351	C₂×D₄×C₃₁	—	2	1	no	—
352	C₂×D₄×C₃₁	—	2	1	no	—
353	C₂×D₄×C₃₁	—	2	2	no	—
354	C₂×D₄×C₃₁	—	2	2	no	—
355	C₂×D₄×C₃₁	—	2	2	no	—
356	C₂×D₄×C₃₁	—	2	2	no	—
357	C₂×D₄×C₃₁	—	2	1	no	—
358	C₂×D₄×C₃₁	—	2	2	no	—
359	C₂×D₄×C₃₁	—	2	2	no	—
360	C₂×D₄×C₃₁	—	2	2	no	—
361	C₂×D₄×C₃₁	—	2	1	no	—
362	C₂×D₄×C₃₁	—	2	2	no	—
363	C₂×D₄×C₃₁	—	2	2	no	—
364	C₂×D₄×C₃₁	—	2	2	no	—
365	C₂×D₄×C₃₁	—	2	2	no	—
366	C₂×D₄×C₃₁	—	2	2	no	—
367	C₂×D₄×C₃₁	—	4	2	no	—
368	C₂×D₄×C₃₁	—	4	2	no	—
369	C₂×D₄×C₃₁	—	4	2	no	—
370	C₂×D₄×C₃₁	—	4	4	no	—
371	C₂×D₄×C₃₁	—	4	4	no	—
372	C₂×D₄×C₃₁	—	4	4	no	—
373	C₂×D₄×C₃₁	—	4	4	no	—
374	C₂×D₄×C₃₁	—	4	8	no	—
375	C₂×D₄×C₃₁	—	8	4	no	—
376	C₂×D₄×C₃₁	—	8	4	no	—
377	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
378	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
379	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
380	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
381	C₂×D₄×C₃₁	#41	1	4	yes	complemented
382	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
383	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
386	C₂²×C₄×C₃₁	—	2	2	no	—
387	C₂²×C₄×C₃₁	—	2	2	no	—
388	C₂²×C₄×C₃₁	—	2	2	no	—
389	C₂²×C₄×C₃₁	—	2	1	no	—
390	C₂²×C₄×C₃₁	—	2	2	no	—
391	C₂²×C₄×C₃₁	—	2	1	no	—
392	C₂²×C₄×C₃₁	—	2	2	no	—
393	C₂²×C₄×C₃₁	—	2	2	no	—
394	C₂²×C₄×C₃₁	—	2	1	no	—
395	C₂²×C₄×C₃₁	—	2	1	no	—
396	C₂²×C₄×C₃₁	—	2	2	no	—
397	C₂²×C₄×C₃₁	—	2	2	no	—
398	C₂²×C₄×C₃₁	—	2	2	no	—
399	C₂²×C₄×C₃₁	—	8	2	no	—
400	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	Q₁₆×C₃₁	—	4	1	no	—
408	SD₁₆×C₃₁	—	2	4	no	—
409	SD₁₆×C₃₁	—	4	2	no	—
410	SD₁₆×C₃₁	—	4	1	no	—
411	SD₁₆×C₃₁	—	4	1	no	—
412	D₈×C₃₁	—	2	4	no	—
413	D₈×C₃₁	—	4	2	no	—
414	D₈×C₃₁	—	4	1	no	—
415	M₁₆×C₃₁	—	2	2	no	—
416	M₁₆×C₃₁	—	2	2	no	—
417	M₁₆×C₃₁	—	4	2	no	—
418	C₂×C₈×C₃₁	—	2	2	no	—
419	C₂×C₈×C₃₁	—	2	2	no	—
420	C₂×C₈×C₃₁	—	4	1	no	—
421	C₂×C₈×C₃₁	—	4	1	no	—
422	C₂×C₈×C₃₁	—	4	1	no	—
423	C₂×C₈×C₃₁	—	4	1	no	—
424	C₂×C₈×C₃₁	—	4	2	no	—
425	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
426	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
427	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
428	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
429	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
430	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
431	C₄⋊C₄×C₃₁	—	2	1	no	—
432	C₄⋊C₄×C₃₁	—	2	1	no	—
433	C₄⋊C₄×C₃₁	—	2	2	no	—
434	C₄⋊C₄×C₃₁	—	2	2	no	—
435	C₄⋊C₄×C₃₁	—	2	2	no	—
436	C₄⋊C₄×C₃₁	—	2	2	no	—
437	C₄⋊C₄×C₃₁	—	2	2	no	—
438	C₄⋊C₄×C₃₁	—	2	2	no	—
439	C₄⋊C₄×C₃₁	—	2	1	no	—
440	C₄⋊C₄×C₃₁	—	2	1	no	—
441	C₄⋊C₄×C₃₁	—	2	1	no	—
442	C₄⋊C₄×C₃₁	—	2	2	no	—
443	C₄⋊C₄×C₃₁	—	2	2	no	—
444	C₄⋊C₄×C₃₁	—	2	1	no	—
445	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
448	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
449	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
450	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
451	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
453	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
455	C₂²⋊C₄×C₃₁	—	2	1	no	—
456	C₂²⋊C₄×C₃₁	—	2	1	no	—
457	C₂²⋊C₄×C₃₁	—	2	1	no	—
458	C₂²⋊C₄×C₃₁	—	2	1	no	—
459	C₂²⋊C₄×C₃₁	—	2	1	no	—
460	C₂²⋊C₄×C₃₁	—	2	2	no	—
461	C₂²⋊C₄×C₃₁	—	2	1	no	—
462	C₂²⋊C₄×C₃₁	—	2	2	no	—
463	C₂²⋊C₄×C₃₁	—	2	2	no	—
464	C₂²⋊C₄×C₃₁	—	2	2	no	—
465	C₂²⋊C₄×C₃₁	—	2	2	no	—
466	C₂²⋊C₄×C₃₁	—	2	2	no	—
467	C₂²⋊C₄×C₃₁	—	2	2	no	—
468	C₂²⋊C₄×C₃₁	—	2	2	no	—
469	C₂²⋊C₄×C₃₁	—	2	2	no	—
470	C₂²⋊C₄×C₃₁	—	2	1	no	—
471	C₂²⋊C₄×C₃₁	—	2	1	no	—
472	C₂²⋊C₄×C₃₁	—	2	2	no	—
473	C₂²⋊C₄×C₃₁	—	2	1	no	—
474	C₂²⋊C₄×C₃₁	—	2	1	no	—
475	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
476	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
477	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
478	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
479	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
480	C₄²×C₃₁	—	2	2	no	—
481	C₄²×C₃₁	—	2	2	no	—
482	C₄²×C₃₁	—	2	1	no	—
483	C₄²×C₃₁	—	2	1	no	—
484	C₄²×C₃₁	C₂⁴	1	2	yes	—
485	#61167	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
486	C₂³×C₃₁	—	2	2	no	—
487	C₂³×C₃₁	—	2	2	no	—
488	C₂³×C₃₁	—	2	2	no	—
489	C₂³×C₃₁	—	2	2	no	—
490	C₂³×C₃₁	—	2	4	no	—
491	C₂³×C₃₁	—	2	1	no	—
492	C₂³×C₃₁	—	2	2	no	—
493	C₂³×C₃₁	—	2	1	no	—
494	C₂³×C₃₁	—	4	4	no	—
495	C₂³×C₃₁	—	4	4	no	—
496	C₂³×C₃₁	—	4	4	no	—
497	C₂³×C₃₁	—	4	2	no	—
498	C₂³×C₃₁	—	4	4	no	—
499	C₂³×C₃₁	—	4	4	no	—
500	C₂³×C₃₁	—	8	1	no	—
501	C₂³×C₃₁	—	8	2	no	—
502	C₂³×C₃₁	—	8	1	no	—
503	C₂³×C₃₁	—	8	1	no	—
504	C₂³×C₃₁	—	8	2	no	—
505	C₂³×C₃₁	—	8	1	no	—
506	C₂³×C₃₁	—	8	2	no	—
507	C₂³×C₃₁	—	8	2	no	—
508	C₂³×C₃₁	—	8	16	no	—
509	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
510	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
512	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
513	Q₈×C₃₁	—	2	2	no	—
514	Q₈×C₃₁	—	2	1	no	—
515	Q₈×C₃₁	—	2	1	no	—
516	Q₈×C₃₁	—	2	1	no	—
517	Q₈×C₃₁	—	2	1	no	—
518	Q₈×C₃₁	—	8	2	no	—
519	D₄×C₃₁	—	2	4	no	—
520	D₄×C₃₁	—	2	4	no	—
521	D₄×C₃₁	—	2	4	no	—
522	D₄×C₃₁	—	2	4	no	—
523	D₄×C₃₁	—	2	2	no	—
524	D₄×C₃₁	—	2	1	no	—
525	D₄×C₃₁	—	2	2	no	—
526	D₄×C₃₁	—	2	1	no	—
527	D₄×C₃₁	—	2	2	no	—
528	D₄×C₃₁	—	2	1	no	—
529	D₄×C₃₁	—	2	2	no	—
530	D₄×C₃₁	—	2	1	no	—
531	D₄×C₃₁	—	4	4	no	—
532	D₄×C₃₁	—	4	4	no	—
533	D₄×C₃₁	—	4	4	no	—
534	D₄×C₃₁	—	4	4	no	—
535	D₄×C₃₁	—	4	2	no	—
536	D₄×C₃₁	—	4	2	no	—
537	D₄×C₃₁	—	4	2	no	—
538	D₄×C₃₁	—	4	2	no	—
539	D₄×C₃₁	—	4	2	no	—
540	D₄×C₃₁	—	4	2	no	—
541	D₄×C₃₁	—	4	2	no	—
542	D₄×C₃₁	—	8	2	no	—
543	D₄×C₃₁	—	8	2	no	—
544	D₄×C₃₁	—	8	2	no	—
545	D₄×C₃₁	—	8	2	no	—
546	D₄×C₃₁	—	8	2	no	—
547	D₄×C₃₁	C₂×#41	1	4	yes	—
548	C₂×C₄×C₃₁	—	2	2	no	—
549	C₂×C₄×C₃₁	—	2	2	no	—
550	C₂×C₄×C₃₁	—	2	2	no	—
551	C₂×C₄×C₃₁	—	2	1	no	—
552	C₂×C₄×C₃₁	—	2	1	no	—
553	C₂×C₄×C₃₁	—	2	2	no	—
554	C₂×C₄×C₃₁	—	2	1	no	—
555	C₂×C₄×C₃₁	—	2	1	no	—
556	C₂×C₄×C₃₁	—	2	2	no	—
557	C₂×C₄×C₃₁	—	2	1	no	—
558	C₂×C₄×C₃₁	—	2	1	no	—
559	C₂×C₄×C₃₁	—	2	2	no	—
560	C₂×C₄×C₃₁	—	2	1	no	—
561	C₂×C₄×C₃₁	—	2	1	no	—
562	C₂×C₄×C₃₁	—	2	1	no	—
563	C₂×C₄×C₃₁	—	2	1	no	—
564	C₂×C₄×C₃₁	—	2	2	no	—
565	C₂×C₄×C₃₁	—	4	4	no	—
566	C₂×C₄×C₃₁	—	4	4	no	—
567	C₂×C₄×C₃₁	—	4	2	no	—
568	C₂×C₄×C₃₁	—	4	2	no	—
569	C₂×C₄×C₃₁	—	8	2	no	—
570	C₂×C₄×C₃₁	—	8	2	no	—
571	C₂×C₄×C₃₁	—	8	2	no	—
572	C₂×C₄×C₃₁	—	8	1	no	—
573	C₂×C₄×C₃₁	—	8	2	no	—
574	C₂×C₄×C₃₁	—	8	1	no	—
575	C₂×C₄×C₃₁	—	8	2	no	—
576	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
577	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
578	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
579	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
583	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
584	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
585	C₈×C₃₁	—	2	2	no	—
586	C₈×C₃₁	—	2	1	no	—
587	C₈×C₃₁	—	2	1	no	—
588	C₈×C₃₁	—	2	1	no	—
589	C₈×C₃₁	—	2	1	no	—
590	C₈×C₃₁	—	2	2	no	—
591	#3492	C₂×C₃₁	1	1	yes	characteristic, complemented
592	#3484	C₂×C₃₁	1	1	yes	characteristic, complemented
593	#3318	C₂×C₃₁	1	2	yes	complemented
594	#3314	C₂×C₃₁	1	2	yes	complemented
595	#3310	C₂×C₃₁	1	2	yes	complemented
596	#3306	C₂×C₃₁	1	2	yes	complemented
597	#3297	C₂×C₃₁	1	2	yes	complemented
598	#3296	C₂×C₃₁	1	2	yes	complemented
599	#3295	C₂×C₃₁	1	2	yes	complemented
600	#3294	C₂×C₃₁	1	2	yes	complemented
601	#3136	C₂×C₃₁	1	1	yes	characteristic, complemented
602	#3096	C₂×C₃₁	1	1	yes	characteristic, complemented
603	#3092	C₂×C₃₁	1	1	yes	characteristic, complemented
604	#3081	C₂×C₃₁	1	1	yes	characteristic, complemented
605	#3062	C₂×C₃₁	1	1	yes	characteristic, complemented
606	#3050	C₂×C₃₁	1	1	yes	characteristic, complemented
607	#3045	C₂×C₃₁	1	1	yes	characteristic, complemented
608	#3012	C₂×C₃₁	1	1	yes	characteristic, complemented
609	#3003	C₂×C₃₁	1	1	yes	characteristic, complemented
610	#2946	C₂×C₃₁	1	1	yes	characteristic, complemented
611	#2929	C₂×C₃₁	1	1	yes	characteristic, complemented
612	#2897	C₂×C₃₁	1	1	yes	characteristic, complemented
613	C₂²×#102	C₂×C₃₁	1	1	yes	characteristic, complemented
614	C₂²×C₃₁	—	2	8	no	—
615	C₂²×C₃₁	—	2	1	no	—
616	C₂²×C₃₁	—	2	1	no	—
617	C₂²×C₃₁	—	2	1	no	—
618	C₂²×C₃₁	—	2	1	no	—
619	C₂²×C₃₁	—	2	1	no	—
620	C₂²×C₃₁	—	2	1	no	—
621	C₂²×C₃₁	—	2	2	no	—
622	C₂²×C₃₁	—	2	4	no	—
623	C₂²×C₃₁	—	2	2	no	—
624	C₂²×C₃₁	—	2	2	no	—
625	C₂²×C₃₁	—	4	2	no	—
626	C₂²×C₃₁	—	4	2	no	—
627	C₂²×C₃₁	—	4	1	no	—
628	C₂²×C₃₁	—	4	1	no	—
629	C₂²×C₃₁	—	4	2	no	—
630	C₂²×C₃₁	—	4	1	no	—
631	C₂²×C₃₁	—	4	1	no	—
632	C₂²×C₃₁	—	4	2	no	—
633	C₂²×C₃₁	—	4	1	no	—
634	C₂²×C₃₁	—	4	1	no	—
635	C₂²×C₃₁	—	4	2	no	—
636	C₂²×C₃₁	—	8	4	no	—
637	C₂²×C₃₁	—	8	8	no	—
638	C₂²×C₃₁	—	8	8	no	—
639	C₂²×C₃₁	—	8	4	no	—
640	C₂²×C₃₁	—	16	4	no	—
641	C₂²×C₃₁	#546	1	2	yes	—
642	C₂²×C₃₁	#576	1	2	yes	—
643	C₂²×C₃₁	#577	1	2	yes	—
644	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
645	C₄×C₃₁	—	2	1	no	—
646	C₄×C₃₁	—	2	1	no	—
647	C₄×C₃₁	—	2	2	no	—
648	C₄×C₃₁	—	2	2	no	—
649	C₄×C₃₁	—	2	2	no	—
650	C₄×C₃₁	—	4	1	no	—
651	C₄×C₃₁	—	4	1	no	—
652	C₄×C₃₁	—	4	2	no	—
653	C₄×C₃₁	—	4	2	no	—
654	C₄×C₃₁	—	4	1	no	—
655	C₄×C₃₁	—	4	1	no	—
656	C₄×C₃₁	—	4	1	no	—
657	C₄×C₃₁	—	4	1	no	—
658	C₄×C₃₁	#546	1	2	yes	—
659	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
660	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
661	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
662	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
663	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
664	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#554	—	2	1	no	—
669	#554	C₂²×C₃₁	1	2	yes	complemented
670	#553	—	2	1	no	—
671	#553	C₂²×C₃₁	1	2	yes	complemented
672	#552	—	2	1	no	—
673	#552	C₂²×C₃₁	1	2	yes	complemented
674	#547	—	2	1	no	—
675	#547	C₂²×C₃₁	1	2	yes	complemented
676	#546	—	2	1	no	—
677	#546	—	2	1	no	—
678	#546	C₂²×C₃₁	1	2	yes	—
679	#546	C₂²×C₃₁	1	2	yes	—
680	D₄²	—	2	1	no	—
681	D₄²	—	2	1	no	—
682	D₄²	C₂²×C₃₁	1	2	yes	—
683	D₄²	C₂²×C₃₁	1	2	yes	—
684	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
685	#539	—	2	2	no	—
686	#537	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	#535	C₂²×C₃₁	1	1	yes	characteristic
688	#535	C₂²×C₃₁	1	1	yes	characteristic
689	#534	—	2	2	no	—
690	#525	—	2	2	no	—
691	#525	C₂²×C₃₁	1	1	yes	characteristic
692	#525	C₂²×C₃₁	1	1	yes	characteristic
693	#525	C₂²×C₃₁	1	1	yes	characteristic, complemented
694	C₂×#120	—	2	2	no	—
695	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
696	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
697	#518	C₂²×C₃₁	1	1	yes	characteristic
698	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	#490	C₂²×C₃₁	1	2	yes	complemented
700	#489	C₂²×C₃₁	1	2	yes	complemented
701	#488	C₂²×C₃₁	1	2	yes	complemented
702	#486	C₂²×C₃₁	1	2	yes	complemented
703	#484	C₂²×C₃₁	1	2	yes	complemented
704	#483	C₂²×C₃₁	1	2	yes	complemented
705	#482	C₂²×C₃₁	1	2	yes	complemented
706	#482	C₂²×C₃₁	1	2	yes	complemented
707	#481	C₂²×C₃₁	1	2	yes	complemented
708	#481	C₂²×C₃₁	1	2	yes	complemented
709	#480	C₂²×C₃₁	1	2	yes	complemented
710	#480	C₂²×C₃₁	1	2	yes	complemented
711	#478	C₂²×C₃₁	1	2	yes	complemented
712	#478	C₂²×C₃₁	1	2	yes	complemented
713	#476	C₂²×C₃₁	1	2	yes	complemented
714	#474	C₂²×C₃₁	1	2	yes	complemented
715	#469	C₂²×C₃₁	1	2	yes	complemented
716	#468	C₂²×C₃₁	1	2	yes	complemented
717	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
718	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
719	#466	C₂²×C₃₁	1	2	yes	complemented
720	#466	C₂²×C₃₁	1	1	yes	characteristic, complemented
721	#466	C₂²×C₃₁	1	1	yes	characteristic, complemented
722	#465	C₂²×C₃₁	1	2	yes	complemented
723	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
724	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
725	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
726	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
727	#464	C₂²×C₃₁	1	2	yes	complemented
728	#463	C₂²×C₃₁	1	2	yes	complemented
729	#460	C₂²×C₃₁	1	2	yes	complemented
730	#459	C₂²×C₃₁	1	2	yes	complemented
731	#452	C₂²×C₃₁	1	2	yes	complemented
732	#450	C₂²×C₃₁	1	2	yes	complemented
733	#450	C₂²×C₃₁	1	2	yes	complemented
734	#450	C₂²×C₃₁	1	2	yes	complemented
735	#449	C₂²×C₃₁	1	2	yes	complemented
736	#447	C₂²×C₃₁	1	2	yes	complemented
737	#447	C₂²×C₃₁	1	2	yes	complemented
738	#447	C₂²×C₃₁	1	2	yes	complemented
739	#442	C₂²×C₃₁	1	2	yes	complemented
740	#440	C₂²×C₃₁	1	2	yes	complemented
741	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
742	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
743	#435	C₂²×C₃₁	1	2	yes	complemented
744	#435	C₂²×C₃₁	1	2	yes	complemented
745	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
746	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
747	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
748	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
749	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
750	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
751	#418	C₂²×C₃₁	1	1	yes	characteristic
752	#418	C₂²×C₃₁	1	1	yes	characteristic, complemented
753	#418	C₂²×C₃₁	1	2	yes	complemented
754	#417	C₂²×C₃₁	1	2	yes	complemented
755	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
756	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
757	#416	C₂²×C₃₁	1	2	yes	complemented
758	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
759	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
760	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
761	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
762	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic, complemented
763	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic, complemented
764	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
765	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
766	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
767	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
768	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
769	#408	C₂²×C₃₁	1	1	yes	characteristic, complemented
770	#407	C₂²×C₃₁	1	1	yes	characteristic, complemented
771	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
772	C₂×C₃₁	—	2	2	no	—
773	C₂×C₃₁	—	2	2	no	—
774	C₂×C₃₁	—	2	2	no	—
775	C₂×C₃₁	—	4	2	no	—
776	C₂×C₃₁	—	4	4	no	—
777	C₂×C₃₁	—	8	1	no	—
778	C₂×C₃₁	—	8	2	no	—
779	C₂×C₃₁	—	8	1	no	—
780	C₂×C₃₁	C₂×#546	1	1	yes	characteristic
781	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
782	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
783	C₂⁵	—	2	1	no	—
784	H(5,𝔽₂)	—	2	4	no	—
785	H(5,𝔽₂)	—	4	2	no	—
786	C₂×#41	—	2	1	no	—
787	C₂×#41	—	2	2	no	—
788	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
789	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
790	C₂×#41	C₂³×C₃₁	1	2	yes	—
791	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
792	C₂²×D₄	—	2	4	no	—
793	C₂²×D₄	—	2	2	no	—
794	C₂²×D₄	—	2	1	no	—
795	C₂²×D₄	—	2	2	no	—
796	C₂²×D₄	—	2	2	no	—
797	C₂²×D₄	—	2	1	no	—
798	C₂²×D₄	—	2	1	no	—
799	C₂²×D₄	—	2	1	no	—
800	C₂²×D₄	—	4	2	no	—
801	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
802	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
803	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
804	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
805	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
806	C₂³×C₄	—	2	1	no	—
807	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
808	AGL(1,ℤ/8)	—	2	4	no	—
809	AGL(1,ℤ/8)	—	4	2	no	—
810	#135	—	4	2	no	—
811	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic, complemented
812	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
813	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
814	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic, complemented
815	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic, complemented
816	C₂×D₈	C₂³×C₃₁	1	2	yes	—
817	C₂×D₈	C₂³×C₃₁	1	2	yes	—
818	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic, complemented
819	#131	—	4	2	no	—
820	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
821	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
822	C₂×M₁₆	C₂³×C₃₁	1	2	yes	complemented
823	C₂²×C₈	—	4	2	no	—
824	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
825	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
826	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
827	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
828	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
829	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
830	C₂²×C₈	C₂³×C₃₁	1	2	yes	complemented
831	C₄⋊Q₈	—	2	1	no	—
832	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	complemented
833	#127	—	2	1	no	—
834	#127	C₂³×C₃₁	1	2	yes	—
835	#126	—	2	2	no	—
836	#126	—	2	2	no	—
837	#125	—	2	2	no	—
838	#125	—	2	2	no	—
839	#125	—	2	1	no	—
840	#125	C₂³×C₃₁	1	2	yes	complemented
841	#124	—	2	1	no	—
842	#124	C₂³×C₃₁	1	2	yes	—
843	#123	—	2	2	no	—
844	#123	—	2	1	no	—
845	#123	—	2	1	no	—
846	#123	—	2	2	no	—
847	#123	—	2	2	no	—
848	#123	—	2	2	no	—
849	#123	—	2	2	no	—
850	#123	—	2	2	no	—
851	#123	D₄×C₃₁	1	2	yes	—
852	C₂²⋊Q₈	—	2	1	no	—
853	C₂²⋊Q₈	—	2	2	no	—
854	C₂²⋊Q₈	—	2	2	no	—
855	C₂²⋊Q₈	—	2	2	no	—
856	C₂²⋊Q₈	—	2	2	no	—
857	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
858	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
859	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
860	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
861	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
862	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
863	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	complemented
864	#121	—	2	2	no	—
865	#121	—	2	2	no	—
866	#121	—	2	1	no	—
867	#121	—	2	2	no	—
868	#121	—	2	2	no	—
869	#121	—	2	1	no	—
870	#121	—	2	1	no	—
871	#121	—	2	2	no	—
872	#121	—	2	2	no	—
873	#121	D₄×C₃₁	1	1	yes	characteristic
874	#121	D₄×C₃₁	1	1	yes	characteristic
875	#121	C₂³×C₃₁	1	1	yes	characteristic
876	#121	C₂³×C₃₁	1	1	yes	characteristic
877	#121	C₂³×C₃₁	1	1	yes	characteristic
878	#121	C₂³×C₃₁	1	1	yes	characteristic
879	#121	C₂³×C₃₁	1	2	yes	—
880	#121	C₂³×C₃₁	1	2	yes	—
881	#121	C₂³×C₃₁	1	2	yes	complemented
882	#120	—	2	1	no	—
883	#120	—	2	1	no	—
884	#120	—	2	2	no	—
885	#120	—	2	2	no	—
886	#120	—	2	2	no	—
887	#120	—	2	2	no	—
888	#120	—	2	2	no	—
889	#120	—	2	2	no	—
890	#120	—	2	2	no	—
891	#120	—	2	2	no	—
892	#120	D₄×C₃₁	1	2	yes	—
893	C₄×Q₈	—	2	1	no	—
894	C₄×Q₈	C₂³×C₃₁	1	2	yes	complemented
895	C₄×D₄	—	2	2	no	—
896	C₄×D₄	—	2	1	no	—
897	C₄×D₄	—	2	2	no	—
898	C₄×D₄	—	2	1	no	—
899	C₄×D₄	—	2	1	no	—
900	C₄×D₄	—	2	1	no	—
901	C₄×D₄	—	2	1	no	—
902	C₄×D₄	—	2	1	no	—
903	C₄×D₄	—	2	1	no	—
904	C₄×D₄	—	2	2	no	—
905	C₄×D₄	—	2	2	no	—
906	C₄×D₄	C₂³×C₃₁	1	2	yes	—
907	C₄×D₄	C₂³×C₃₁	1	2	yes	—
908	C₄×D₄	C₂³×C₃₁	1	2	yes	—
909	C₄×D₄	C₂³×C₃₁	1	2	yes	—
910	C₄×D₄	C₂³×C₃₁	1	2	yes	complemented
911	#117	—	2	1	no	—
912	#117	—	2	2	no	—
913	#117	C₂³×C₃₁	1	1	yes	characteristic
914	#117	C₂³×C₃₁	1	1	yes	characteristic
915	#117	C₂³×C₃₁	1	1	yes	characteristic
916	#117	C₂³×C₃₁	1	2	yes	complemented
917	C₂×C₄⋊C₄	—	2	1	no	—
918	C₂×C₄⋊C₄	—	2	1	no	—
919	C₂×C₄⋊C₄	—	2	1	no	—
920	C₂×C₄⋊C₄	—	2	1	no	—
921	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
922	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
923	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
924	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
925	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	complemented
926	C₂×C₂²⋊C₄	—	2	2	no	—
927	C₂×C₂²⋊C₄	—	2	2	no	—
928	C₂×C₂²⋊C₄	—	2	2	no	—
929	#107	C₂³×C₃₁	1	1	yes	characteristic, complemented
930	#107	C₂³×C₃₁	1	1	yes	characteristic, complemented
931	#107	C₂³×C₃₁	1	2	yes	complemented
932	#107	C₂³×C₃₁	1	2	yes	complemented
933	#106	C₂³×C₃₁	1	1	yes	characteristic, complemented
934	#106	C₂³×C₃₁	1	1	yes	characteristic, complemented
935	#106	C₂³×C₃₁	1	2	yes	complemented
936	#106	C₂³×C₃₁	1	2	yes	complemented
937	C₄⋊C₈	C₂³×C₃₁	1	2	yes	complemented
938	C₄⋊C₈	C₂³×C₃₁	1	2	yes	complemented
939	#103	C₂³×C₃₁	1	1	yes	characteristic, complemented
940	#103	C₂³×C₃₁	1	2	yes	complemented
941	#103	C₂³×C₃₁	1	1	yes	characteristic, complemented
942	#103	C₂³×C₃₁	1	1	yes	characteristic, complemented
943	#103	C₂³×C₃₁	1	1	yes	characteristic, complemented
944	#103	C₂³×C₃₁	1	2	yes	complemented
945	#102	C₂³×C₃₁	1	2	yes	—
946	#102	C₂³×C₃₁	1	2	yes	—
947	#102	C₂³×C₃₁	1	2	yes	—
948	#102	C₂³×C₃₁	1	2	yes	—
949	#102	C₂³×C₃₁	1	2	yes	—
950	#102	C₂³×C₃₁	1	2	yes	—
951	#102	C₂³×C₃₁	1	2	yes	—
952	#102	C₂³×C₃₁	1	2	yes	—
953	#102	C₂³×C₃₁	1	2	yes	—
954	#102	C₂³×C₃₁	1	2	yes	—
955	#102	C₂³×C₃₁	1	2	yes	—
956	#102	C₂³×C₃₁	1	2	yes	—
957	#102	C₂³×C₃₁	1	1	yes	characteristic, complemented
958	#102	C₂³×C₃₁	1	2	yes	complemented
959	#102	C₂³×C₃₁	1	1	yes	characteristic, complemented
960	#102	C₂³×C₃₁	1	1	yes	characteristic, complemented
961	#102	C₂³×C₃₁	1	1	yes	characteristic, complemented
962	#102	C₂³×C₃₁	1	2	yes	complemented
963	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
964	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
965	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	complemented
966	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	complemented
967	#97	C₂³×C₃₁	1	2	yes	complemented
968	C₄×C₈	C₂³×C₃₁	1	2	yes	complemented
969	C₃₁	#61167	1	1	yes	characteristic, direct product factor, Sylow
970	C₂⁴	—	2	1	no	—
971	C₂⁴	—	2	2	no	—
972	C₂⁴	—	2	2	no	—
973	C₂⁴	—	2	1	no	—
974	C₂⁴	—	2	2	no	—
975	C₂⁴	—	4	4	no	—
976	C₂⁴	—	8	2	no	—
977	C₂⁴	—	8	2	no	—
978	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
979	#41	—	2	2	no	—
980	#41	—	2	2	no	—
981	#41	—	2	4	no	—
982	#41	—	2	2	no	—
983	#41	—	2	2	no	—
984	#41	—	2	2	no	—
985	#41	—	2	2	no	—
986	#41	—	4	2	no	—
987	#41	—	4	4	no	—
988	#41	—	8	4	no	—
989	C₂×Q₈	—	2	2	no	—
990	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
991	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
992	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
993	C₂×D₄	—	2	4	no	—
994	C₂×D₄	—	2	4	no	—
995	C₂×D₄	—	2	4	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	1	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	1	no	—
1000	C₂×D₄	—	2	1	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	2	2	no	—
1003	C₂×D₄	—	2	2	no	—
1004	C₂×D₄	—	2	2	no	—
1005	C₂×D₄	—	2	2	no	—
1006	C₂×D₄	—	2	1	no	—
1007	C₂×D₄	—	2	2	no	—
1008	C₂×D₄	—	2	2	no	—
1009	C₂×D₄	—	2	2	no	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	2	no	—
1012	C₂×D₄	—	2	2	no	—
1013	C₂×D₄	—	2	2	no	—
1014	C₂×D₄	—	2	2	no	—
1015	C₂×D₄	—	2	2	no	—
1016	C₂×D₄	—	4	2	no	—
1017	C₂×D₄	—	4	2	no	—
1018	C₂×D₄	—	4	2	no	—
1019	C₂×D₄	—	4	4	no	—
1020	C₂×D₄	—	4	4	no	—
1021	C₂×D₄	—	4	4	no	—
1022	C₂×D₄	—	4	4	no	—
1023	C₂×D₄	—	4	8	no	—
1024	C₂×D₄	—	8	4	no	—
1025	C₂×D₄	—	8	4	no	—
1026	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1027	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1028	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1029	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1030	C₂×D₄	#41×C₃₁	1	4	yes	complemented
1031	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1032	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1033	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1034	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1035	C₂²×C₄	—	2	2	no	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	2	2	no	—
1038	C₂²×C₄	—	2	1	no	—
1039	C₂²×C₄	—	2	2	no	—
1040	C₂²×C₄	—	2	1	no	—
1041	C₂²×C₄	—	2	2	no	—
1042	C₂²×C₄	—	2	2	no	—
1043	C₂²×C₄	—	2	1	no	—
1044	C₂²×C₄	—	2	1	no	—
1045	C₂²×C₄	—	2	2	no	—
1046	C₂²×C₄	—	2	2	no	—
1047	C₂²×C₄	—	2	2	no	—
1048	C₂²×C₄	—	8	2	no	—
1049	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1050	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1051	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1052	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1053	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1054	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1055	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1056	Q₁₆	—	4	1	no	—
1057	SD₁₆	—	2	4	no	—
1058	SD₁₆	—	4	2	no	—
1059	SD₁₆	—	4	1	no	—
1060	SD₁₆	—	4	1	no	—
1061	D₈	—	2	4	no	—
1062	D₈	—	4	2	no	—
1063	D₈	—	4	1	no	—
1064	M₁₆	—	2	2	no	—
1065	M₁₆	—	2	2	no	—
1066	M₁₆	—	4	2	no	—
1067	C₂×C₈	—	2	2	no	—
1068	C₂×C₈	—	2	2	no	—
1069	C₂×C₈	—	4	1	no	—
1070	C₂×C₈	—	4	1	no	—
1071	C₂×C₈	—	4	1	no	—
1072	C₂×C₈	—	4	1	no	—
1073	C₂×C₈	—	4	2	no	—
1074	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1075	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1076	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1077	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1078	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1079	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1080	C₄⋊C₄	—	2	1	no	—
1081	C₄⋊C₄	—	2	1	no	—
1082	C₄⋊C₄	—	2	2	no	—
1083	C₄⋊C₄	—	2	2	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	2	no	—
1087	C₄⋊C₄	—	2	2	no	—
1088	C₄⋊C₄	—	2	1	no	—
1089	C₄⋊C₄	—	2	1	no	—
1090	C₄⋊C₄	—	2	1	no	—
1091	C₄⋊C₄	—	2	2	no	—
1092	C₄⋊C₄	—	2	2	no	—
1093	C₄⋊C₄	—	2	1	no	—
1094	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1095	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1096	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1097	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1098	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1099	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1100	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1101	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1102	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1103	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	—	2	2	no	—
1110	C₂²⋊C₄	—	2	1	no	—
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	2	no	—
1113	C₂²⋊C₄	—	2	2	no	—
1114	C₂²⋊C₄	—	2	2	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	—	2	2	no	—
1117	C₂²⋊C₄	—	2	2	no	—
1118	C₂²⋊C₄	—	2	2	no	—
1119	C₂²⋊C₄	—	2	1	no	—
1120	C₂²⋊C₄	—	2	1	no	—
1121	C₂²⋊C₄	—	2	2	no	—
1122	C₂²⋊C₄	—	2	1	no	—
1123	C₂²⋊C₄	—	2	1	no	—
1124	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1125	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1126	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1127	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1128	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1129	C₄²	—	2	2	no	—
1130	C₄²	—	2	2	no	—
1131	C₄²	—	2	1	no	—
1132	C₄²	—	2	1	no	—
1133	C₄²	C₂⁴×C₃₁	1	2	yes	—
1134	C₂³	—	2	2	no	—
1135	C₂³	—	2	2	no	—
1136	C₂³	—	2	2	no	—
1137	C₂³	—	2	2	no	—
1138	C₂³	—	2	4	no	—
1139	C₂³	—	2	1	no	—
1140	C₂³	—	2	2	no	—
1141	C₂³	—	2	1	no	—
1142	C₂³	—	4	4	no	—
1143	C₂³	—	4	4	no	—
1144	C₂³	—	4	4	no	—
1145	C₂³	—	4	2	no	—
1146	C₂³	—	4	4	no	—
1147	C₂³	—	4	4	no	—
1148	C₂³	—	8	1	no	—
1149	C₂³	—	8	2	no	—
1150	C₂³	—	8	1	no	—
1151	C₂³	—	8	1	no	—
1152	C₂³	—	8	2	no	—
1153	C₂³	—	8	1	no	—
1154	C₂³	—	8	2	no	—
1155	C₂³	—	8	2	no	—
1156	C₂³	—	8	16	no	—
1157	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1158	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1159	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1160	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1161	Q₈	—	2	2	no	—
1162	Q₈	—	2	1	no	—
1163	Q₈	—	2	1	no	—
1164	Q₈	—	2	1	no	—
1165	Q₈	—	2	1	no	—
1166	Q₈	—	8	2	no	—
1167	D₄	—	2	4	no	—
1168	D₄	—	2	4	no	—
1169	D₄	—	2	4	no	—
1170	D₄	—	2	4	no	—
1171	D₄	—	2	2	no	—
1172	D₄	—	2	1	no	—
1173	D₄	—	2	2	no	—
1174	D₄	—	2	1	no	—
1175	D₄	—	2	2	no	—
1176	D₄	—	2	1	no	—
1177	D₄	—	2	2	no	—
1178	D₄	—	2	1	no	—
1179	D₄	—	4	4	no	—
1180	D₄	—	4	4	no	—
1181	D₄	—	4	4	no	—
1182	D₄	—	4	4	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	4	2	no	—
1186	D₄	—	4	2	no	—
1187	D₄	—	4	2	no	—
1188	D₄	—	4	2	no	—
1189	D₄	—	4	2	no	—
1190	D₄	—	8	2	no	—
1191	D₄	—	8	2	no	—
1192	D₄	—	8	2	no	—
1193	D₄	—	8	2	no	—
1194	D₄	—	8	2	no	—
1195	D₄	C₂×#41×C₃₁	1	4	yes	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	2	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	1	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	2	no	—
1213	C₂×C₄	—	4	4	no	—
1214	C₂×C₄	—	4	4	no	—
1215	C₂×C₄	—	4	2	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	8	2	no	—
1218	C₂×C₄	—	8	2	no	—
1219	C₂×C₄	—	8	2	no	—
1220	C₂×C₄	—	8	1	no	—
1221	C₂×C₄	—	8	2	no	—
1222	C₂×C₄	—	8	1	no	—
1223	C₂×C₄	—	8	2	no	—
1224	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1225	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1226	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1227	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1228	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1229	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1230	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1231	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1232	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1233	C₈	—	2	2	no	—
1234	C₈	—	2	1	no	—
1235	C₈	—	2	1	no	—
1236	C₈	—	2	1	no	—
1237	C₈	—	2	1	no	—
1238	C₈	—	2	2	no	—
1239	C₂²	—	2	8	no	—
1240	C₂²	—	2	1	no	—
1241	C₂²	—	2	1	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	1	no	—
1245	C₂²	—	2	1	no	—
1246	C₂²	—	2	2	no	—
1247	C₂²	—	2	4	no	—
1248	C₂²	—	2	2	no	—
1249	C₂²	—	2	2	no	—
1250	C₂²	—	4	2	no	—
1251	C₂²	—	4	2	no	—
1252	C₂²	—	4	1	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	2	no	—
1255	C₂²	—	4	1	no	—
1256	C₂²	—	4	1	no	—
1257	C₂²	—	4	2	no	—
1258	C₂²	—	4	1	no	—
1259	C₂²	—	4	1	no	—
1260	C₂²	—	4	2	no	—
1261	C₂²	—	8	4	no	—
1262	C₂²	—	8	8	no	—
1263	C₂²	—	8	8	no	—
1264	C₂²	—	8	4	no	—
1265	C₂²	—	16	4	no	—
1266	C₂²	C₃₁×#546	1	2	yes	—
1267	C₂²	C₃₁×#576	1	2	yes	—
1268	C₂²	C₃₁×#577	1	2	yes	—
1269	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1270	C₄	—	2	1	no	—
1271	C₄	—	2	1	no	—
1272	C₄	—	2	2	no	—
1273	C₄	—	2	2	no	—
1274	C₄	—	2	2	no	—
1275	C₄	—	4	1	no	—
1276	C₄	—	4	1	no	—
1277	C₄	—	4	2	no	—
1278	C₄	—	4	2	no	—
1279	C₄	—	4	1	no	—
1280	C₄	—	4	1	no	—
1281	C₄	—	4	1	no	—
1282	C₄	—	4	1	no	—
1283	C₄	C₃₁×#546	1	2	yes	—
1284	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1285	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1286	C₂	—	2	2	no	—
1287	C₂	—	2	2	no	—
1288	C₂	—	2	2	no	—
1289	C₂	—	4	2	no	—
1290	C₂	—	4	4	no	—
1291	C₂	—	8	2	no	—
1292	C₂	—	8	1	no	—
1293	C₂	—	8	1	no	—
1294	C₂	C₂×C₃₁×#546	1	1	yes	characteristic
1295	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1296	C₂	C₂×C₃₁×#577	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 ◁ C₃₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3492	C₂	semidirect
2. C₃₁×#3484	C₂	semidirect
3. C₃₁×#3318	C₂	semidirect
4. C₃₁×#3314	C₂	semidirect
5. C₃₁×#3310	C₂	semidirect
6. C₃₁×#3306	C₂	semidirect
7. C₃₁×#3297	C₂	semidirect
8. C₃₁×#3296	C₂	semidirect
9. C₃₁×#3295	C₂	semidirect
10. C₃₁×#3294	C₂	semidirect
11. C₃₁×#3136	C₂	semidirect
12. C₃₁×#3096	C₂	semidirect
13. C₃₁×#3092	C₂	semidirect
14. C₃₁×#3081	C₂	semidirect
15. C₃₁×#3062	C₂	semidirect
16. C₃₁×#3050	C₂	semidirect
17. C₃₁×#3045	C₂	semidirect
18. C₃₁×#3012	C₂	semidirect
19. C₃₁×#3003	C₂	semidirect
20. C₃₁×#2946	C₂	semidirect
21. C₃₁×#2929	C₂	semidirect
22. C₃₁×#2897	C₂	semidirect
23. C₂²×C₃₁×#102	C₂	semidirect
27. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂×C₃₁×#135	C₂²	semidirect
29. C₂×C₃₁×#131	C₂²	semidirect
30. C₂³×C₈×C₃₁	C₂²	semidirect
32. C₃₁×#554	C₂²	semidirect
34. C₃₁×#553	C₂²	semidirect
36. C₃₁×#552	C₂²	semidirect
38. C₃₁×#547	C₂²	semidirect
47. C₃₁×#544	C₂²	semidirect
49. C₃₁×#537	C₂²	semidirect
56. C₃₁×#525	C₂²	semidirect
58. C₃₁×#520	C₂²	semidirect
59. C₃₁×#520	C₂²	semidirect
61. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
62. C₃₁×#490	C₂²	semidirect
63. C₃₁×#489	C₂²	semidirect
64. C₃₁×#488	C₂²	semidirect
65. C₃₁×#486	C₂²	semidirect
66. C₃₁×#484	C₂²	semidirect
67. C₃₁×#483	C₂²	semidirect
68. C₃₁×#482	C₂²	semidirect
69. C₃₁×#482	C₂²	semidirect
70. C₃₁×#481	C₂²	semidirect
71. C₃₁×#481	C₂²	semidirect
72. C₃₁×#480	C₂²	semidirect
73. C₃₁×#480	C₂²	semidirect
74. C₃₁×#478	C₂²	semidirect
75. C₃₁×#478	C₂²	semidirect
76. C₃₁×#476	C₂²	semidirect
77. C₃₁×#474	C₂²	semidirect
78. C₃₁×#469	C₂²	semidirect
79. C₃₁×#468	C₂²	semidirect
80. C₃₁×#467	C₂²	semidirect
81. C₃₁×#467	C₂²	semidirect
82. C₃₁×#466	C₂²	semidirect
83. C₃₁×#466	C₂²	semidirect
84. C₃₁×#466	C₂²	semidirect
85. C₃₁×#465	C₂²	semidirect
86. C₃₁×#465	C₂²	semidirect
87. C₃₁×#465	C₂²	semidirect
88. C₃₁×#465	C₂²	semidirect
89. C₃₁×#465	C₂²	semidirect
90. C₃₁×#464	C₂²	semidirect
91. C₃₁×#463	C₂²	semidirect
92. C₃₁×#460	C₂²	semidirect
93. C₃₁×#459	C₂²	semidirect
94. C₃₁×#452	C₂²	semidirect
95. C₃₁×#450	C₂²	semidirect
96. C₃₁×#450	C₂²	semidirect
97. C₃₁×#450	C₂²	semidirect
98. C₃₁×#449	C₂²	semidirect
99. C₃₁×#447	C₂²	semidirect
100. C₃₁×#447	C₂²	semidirect
101. C₃₁×#447	C₂²	semidirect
102. C₃₁×#442	C₂²	semidirect
103. C₃₁×#440	C₂²	semidirect
104. C₄×SD₁₆×C₃₁	C₂²	semidirect
105. C₄×D₈×C₃₁	C₂²	semidirect
106. C₃₁×#435	C₂²	semidirect
107. C₃₁×#435	C₂²	semidirect
108. C₈×D₄×C₃₁	C₂²	semidirect
109. C₈×D₄×C₃₁	C₂²	semidirect
110. C₃₁×#428	C₂²	semidirect
111. C₃₁×#428	C₂²	semidirect
112. C₃₁×#427	C₂²	semidirect
113. C₃₁×#424	C₂²	semidirect
115. C₃₁×#418	C₂²	semidirect
116. C₃₁×#418	C₂²	semidirect
117. C₃₁×#417	C₂²	semidirect
118. C₃₁×#417	C₂²	semidirect
119. C₃₁×#417	C₂²	semidirect
120. C₃₁×#416	C₂²	semidirect
121. C₃₁×#416	C₂²	semidirect
122. C₃₁×#416	C₂²	semidirect
125. C₂×C₃₁×#102	C₂²	semidirect
126. C₂×C₃₁×#102	C₂²	semidirect
127. C₂×C₃₁×#102	C₂²	semidirect
128. C₂×C₃₁×#102	C₂²	semidirect
129. C₂×C₃₁×#102	C₂²	semidirect
130. C₂×C₃₁×#102	C₂²	semidirect
131. C₂×C₃₁×#102	C₂²	semidirect
132. C₃₁×#408	C₂²	semidirect
133. C₃₁×#407	C₂²	semidirect
134. C₃₁×#405	C₂²	semidirect
163. C₂×Q₁₆×C₃₁	C₂³	semidirect
166. C₂×SD₁₆×C₃₁	C₂³	semidirect
167. C₂×SD₁₆×C₃₁	C₂³	semidirect
170. C₂×D₈×C₃₁	C₂³	semidirect
174. C₂×M₁₆×C₃₁	C₂³	semidirect
182. C₂²×C₈×C₃₁	C₂³	semidirect
184. C₃₁×C₄⋊Q₈	C₂³	semidirect
192. C₃₁×#125	C₂³	semidirect
215. C₃₁×C₂²⋊Q₈	C₂³	semidirect
233. C₃₁×#121	C₂³	semidirect
246. C₄×Q₈×C₃₁	C₂³	semidirect
262. C₄×D₄×C₃₁	C₂³	semidirect
268. C₃₁×#117	C₂³	semidirect
277. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
281. C₃₁×#107	C₂³	semidirect
282. C₃₁×#107	C₂³	semidirect
283. C₃₁×#107	C₂³	semidirect
284. C₃₁×#107	C₂³	semidirect
285. C₃₁×#106	C₂³	semidirect
286. C₃₁×#106	C₂³	semidirect
287. C₃₁×#106	C₂³	semidirect
288. C₃₁×#106	C₂³	semidirect
289. C₃₁×C₄⋊C₈	C₂³	semidirect
290. C₃₁×C₄⋊C₈	C₂³	semidirect
291. C₃₁×#103	C₂³	semidirect
292. C₃₁×#103	C₂³	semidirect
293. C₃₁×#103	C₂³	semidirect
294. C₃₁×#103	C₂³	semidirect
295. C₃₁×#103	C₂³	semidirect
296. C₃₁×#103	C₂³	semidirect
309. C₃₁×#102	C₂³	semidirect
310. C₃₁×#102	C₂³	semidirect
311. C₃₁×#102	C₂³	semidirect
312. C₃₁×#102	C₂³	semidirect
313. C₃₁×#102	C₂³	semidirect
314. C₃₁×#102	C₂³	semidirect
317. C₃₁×C₂²⋊C₈	C₂³	semidirect
318. C₃₁×C₂²⋊C₈	C₂³	semidirect
319. C₃₁×#97	C₂³	semidirect
320. C₄×C₈×C₃₁	C₂³	semidirect
381. C₂×D₄×C₃₁	#41	semidirect
485. #61167	C₃₁	direct (N × H)
591. #3492	C₂×C₃₁	semidirect
592. #3484	C₂×C₃₁	semidirect
593. #3318	C₂×C₃₁	semidirect
594. #3314	C₂×C₃₁	semidirect
595. #3310	C₂×C₃₁	semidirect
596. #3306	C₂×C₃₁	semidirect
597. #3297	C₂×C₃₁	semidirect
598. #3296	C₂×C₃₁	semidirect
599. #3295	C₂×C₃₁	semidirect
600. #3294	C₂×C₃₁	semidirect
601. #3136	C₂×C₃₁	semidirect
602. #3096	C₂×C₃₁	semidirect
603. #3092	C₂×C₃₁	semidirect
604. #3081	C₂×C₃₁	semidirect
605. #3062	C₂×C₃₁	semidirect
606. #3050	C₂×C₃₁	semidirect
607. #3045	C₂×C₃₁	semidirect
608. #3012	C₂×C₃₁	semidirect
609. #3003	C₂×C₃₁	semidirect
610. #2946	C₂×C₃₁	semidirect
611. #2929	C₂×C₃₁	semidirect
612. #2897	C₂×C₃₁	semidirect
613. C₂²×#102	C₂×C₃₁	semidirect
664. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
665. C₂×#135	C₂²×C₃₁	semidirect
666. C₂×#131	C₂²×C₃₁	semidirect
667. C₂³×C₈	C₂²×C₃₁	semidirect
669. #554	C₂²×C₃₁	semidirect
671. #553	C₂²×C₃₁	semidirect
673. #552	C₂²×C₃₁	semidirect
675. #547	C₂²×C₃₁	semidirect
684. #544	C₂²×C₃₁	semidirect
686. #537	C₂²×C₃₁	semidirect
693. #525	C₂²×C₃₁	semidirect
695. #520	C₂²×C₃₁	semidirect
696. #520	C₂²×C₃₁	semidirect
698. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
699. #490	C₂²×C₃₁	semidirect
700. #489	C₂²×C₃₁	semidirect
701. #488	C₂²×C₃₁	semidirect
702. #486	C₂²×C₃₁	semidirect
703. #484	C₂²×C₃₁	semidirect
704. #483	C₂²×C₃₁	semidirect
705. #482	C₂²×C₃₁	semidirect
706. #482	C₂²×C₃₁	semidirect
707. #481	C₂²×C₃₁	semidirect
708. #481	C₂²×C₃₁	semidirect
709. #480	C₂²×C₃₁	semidirect
710. #480	C₂²×C₃₁	semidirect
711. #478	C₂²×C₃₁	semidirect
712. #478	C₂²×C₃₁	semidirect
713. #476	C₂²×C₃₁	semidirect
714. #474	C₂²×C₃₁	semidirect
715. #469	C₂²×C₃₁	semidirect
716. #468	C₂²×C₃₁	semidirect
717. #467	C₂²×C₃₁	semidirect
718. #467	C₂²×C₃₁	semidirect
719. #466	C₂²×C₃₁	semidirect
720. #466	C₂²×C₃₁	semidirect
721. #466	C₂²×C₃₁	semidirect
722. #465	C₂²×C₃₁	semidirect
723. #465	C₂²×C₃₁	semidirect
724. #465	C₂²×C₃₁	semidirect
725. #465	C₂²×C₃₁	semidirect
726. #465	C₂²×C₃₁	semidirect
727. #464	C₂²×C₃₁	semidirect
728. #463	C₂²×C₃₁	semidirect
729. #460	C₂²×C₃₁	semidirect
730. #459	C₂²×C₃₁	semidirect
731. #452	C₂²×C₃₁	semidirect
732. #450	C₂²×C₃₁	semidirect
733. #450	C₂²×C₃₁	semidirect
734. #450	C₂²×C₃₁	semidirect
735. #449	C₂²×C₃₁	semidirect
736. #447	C₂²×C₃₁	semidirect
737. #447	C₂²×C₃₁	semidirect
738. #447	C₂²×C₃₁	semidirect
739. #442	C₂²×C₃₁	semidirect
740. #440	C₂²×C₃₁	semidirect
741. C₄×SD₁₆	C₂²×C₃₁	semidirect
742. C₄×D₈	C₂²×C₃₁	semidirect
743. #435	C₂²×C₃₁	semidirect
744. #435	C₂²×C₃₁	semidirect
745. C₈×D₄	C₂²×C₃₁	semidirect
746. C₈×D₄	C₂²×C₃₁	semidirect
747. #428	C₂²×C₃₁	semidirect
748. #428	C₂²×C₃₁	semidirect
749. #427	C₂²×C₃₁	semidirect
750. #424	C₂²×C₃₁	semidirect
752. #418	C₂²×C₃₁	semidirect
753. #418	C₂²×C₃₁	semidirect
754. #417	C₂²×C₃₁	semidirect
755. #417	C₂²×C₃₁	semidirect
756. #417	C₂²×C₃₁	semidirect
757. #416	C₂²×C₃₁	semidirect
758. #416	C₂²×C₃₁	semidirect
759. #416	C₂²×C₃₁	semidirect
762. C₂×#102	C₂²×C₃₁	semidirect
763. C₂×#102	C₂²×C₃₁	semidirect
764. C₂×#102	C₂²×C₃₁	semidirect
765. C₂×#102	C₂²×C₃₁	semidirect
766. C₂×#102	C₂²×C₃₁	semidirect
767. C₂×#102	C₂²×C₃₁	semidirect
768. C₂×#102	C₂²×C₃₁	semidirect
769. #408	C₂²×C₃₁	semidirect
770. #407	C₂²×C₃₁	semidirect
771. #405	C₂²×C₃₁	semidirect
811. C₂×Q₁₆	C₂³×C₃₁	semidirect
814. C₂×SD₁₆	C₂³×C₃₁	semidirect
815. C₂×SD₁₆	C₂³×C₃₁	semidirect
818. C₂×D₈	C₂³×C₃₁	semidirect
822. C₂×M₁₆	C₂³×C₃₁	semidirect
830. C₂²×C₈	C₂³×C₃₁	semidirect
832. C₄⋊Q₈	C₂³×C₃₁	semidirect
840. #125	C₂³×C₃₁	semidirect
863. C₂²⋊Q₈	C₂³×C₃₁	semidirect
881. #121	C₂³×C₃₁	semidirect
894. C₄×Q₈	C₂³×C₃₁	semidirect
910. C₄×D₄	C₂³×C₃₁	semidirect
916. #117	C₂³×C₃₁	semidirect
925. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
929. #107	C₂³×C₃₁	semidirect
930. #107	C₂³×C₃₁	semidirect
931. #107	C₂³×C₃₁	semidirect
932. #107	C₂³×C₃₁	semidirect
933. #106	C₂³×C₃₁	semidirect
934. #106	C₂³×C₃₁	semidirect
935. #106	C₂³×C₃₁	semidirect
936. #106	C₂³×C₃₁	semidirect
937. C₄⋊C₈	C₂³×C₃₁	semidirect
938. C₄⋊C₈	C₂³×C₃₁	semidirect
939. #103	C₂³×C₃₁	semidirect
940. #103	C₂³×C₃₁	semidirect
941. #103	C₂³×C₃₁	semidirect
942. #103	C₂³×C₃₁	semidirect
943. #103	C₂³×C₃₁	semidirect
944. #103	C₂³×C₃₁	semidirect
957. #102	C₂³×C₃₁	semidirect
958. #102	C₂³×C₃₁	semidirect
959. #102	C₂³×C₃₁	semidirect
960. #102	C₂³×C₃₁	semidirect
961. #102	C₂³×C₃₁	semidirect
962. #102	C₂³×C₃₁	semidirect
965. C₂²⋊C₈	C₂³×C₃₁	semidirect
966. C₂²⋊C₈	C₂³×C₃₁	semidirect
967. #97	C₂³×C₃₁	semidirect
968. C₄×C₈	C₂³×C₃₁	semidirect
969. C₃₁	#61167	direct (N × H)
1030. C₂×D₄	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3492	2
C₃₁×#3484	2
C₃₁×#3318	2
C₃₁×#3314	2
C₃₁×#3310	2
C₃₁×#3306	2
C₃₁×#3297	2
C₃₁×#3296	2
C₃₁×#3295	2
C₃₁×#3294	2
C₃₁×#3136	2
C₃₁×#3096	2
C₃₁×#3092	2
C₃₁×#3081	2
C₃₁×#3062	2
C₃₁×#3050	2
C₃₁×#3045	2
C₃₁×#3012	2
C₃₁×#3003	2
C₃₁×#2946	2
C₃₁×#2929	2
C₃₁×#2897	2
C₂²×C₃₁×#102	2
#61167	31

Subgroups — C31×#61167 #21517926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61167 #21517926