Subgroups — C₃₁×#61074 #21517833

Order 7936.

2774 conjugacy classes of subgroups.

The subgroup lattice has 1434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#576	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#575	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3488	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3284	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3280	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3275	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3272	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3269	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3268	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3267	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3264	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3154	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3063	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3055	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3046	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3041	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3012	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3009	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3002	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₃₁×#449	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2933	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#576	—	2	8	no	—
29	C₃₁×#575	—	2	8	no	—
30	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
33	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
36	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
37	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
39	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
41	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
42	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
43	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic, complemented
44	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
45	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
46	C₂²×D₈×C₃₁	C₂²	1	2	yes	complemented
47	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic, complemented
48	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#550	C₂²	1	2	yes	complemented
50	C₃₁×#548	C₂²	1	2	yes	complemented
51	C₃₁×#547	—	2	1	no	—
52	C₃₁×#547	—	2	1	no	—
53	C₃₁×#547	C₂²	1	2	yes	complemented
54	C₃₁×#547	C₂²	1	2	yes	complemented
55	C₃₁×#546	—	2	2	no	—
56	C₃₁×#546	—	2	1	no	—
57	C₃₁×#546	—	2	1	no	—
58	C₃₁×#546	C₂²	1	2	yes	complemented
59	C₃₁×#546	C₂²	1	2	yes	complemented
60	C₃₁×#546	C₂²	1	2	yes	complemented
61	D₄²×C₃₁	—	2	2	no	—
62	D₄²×C₃₁	C₂²	1	2	yes	complemented
63	C₃₁×#537	—	2	1	no	—
64	C₃₁×#537	C₂²	1	1	yes	characteristic
65	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#535	—	2	1	no	—
68	C₃₁×#535	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#534	—	2	2	no	—
70	C₃₁×#525	—	2	1	no	—
71	C₃₁×#525	C₂²	1	1	yes	characteristic
72	C₃₁×#525	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₃₁×#123	—	2	2	no	—
74	C₂×C₃₁×#121	—	2	1	no	—
75	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#518	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#497	C₂²	1	2	yes	complemented
79	C₃₁×#496	C₂²	1	2	yes	complemented
80	C₃₁×#495	C₂²	1	2	yes	complemented
81	C₃₁×#492	C₂²	1	2	yes	complemented
82	C₃₁×#470	C₂²	1	2	yes	complemented
83	C₃₁×#469	C₂²	1	2	yes	complemented
84	C₃₁×#468	C₂²	1	2	yes	complemented
85	C₃₁×#468	C₂²	1	2	yes	complemented
86	C₃₁×#467	C₂²	1	2	yes	complemented
87	C₃₁×#466	C₂²	1	2	yes	complemented
88	C₃₁×#465	C₂²	1	2	yes	complemented
89	C₃₁×#465	C₂²	1	2	yes	complemented
90	C₃₁×#464	C₂²	1	2	yes	complemented
91	C₃₁×#463	C₂²	1	2	yes	complemented
92	C₃₁×#463	C₂²	1	2	yes	complemented
93	C₃₁×#463	C₂²	1	2	yes	complemented
94	C₃₁×#462	C₂²	1	2	yes	complemented
95	C₃₁×#461	C₂²	1	2	yes	complemented
96	C₃₁×#459	C₂²	1	2	yes	complemented
97	C₃₁×#459	C₂²	1	2	yes	complemented
98	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#452	C₂²	1	2	yes	complemented
101	C₃₁×#452	C₂²	1	2	yes	complemented
102	C₃₁×#452	C₂²	1	2	yes	complemented
103	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#450	C₂²	1	1	yes	characteristic, complemented
105	C₃₁×#450	C₂²	1	2	yes	complemented
106	C₃₁×#450	C₂²	1	2	yes	complemented
107	C₃₁×#450	C₂²	1	2	yes	complemented
108	C₃₁×#449	C₂²	1	2	yes	complemented
109	C₃₁×#449	C₂²	1	2	yes	complemented
110	C₃₁×#449	C₂²	1	2	yes	complemented
111	C₃₁×#449	C₂²	1	2	yes	complemented
112	C₃₁×#449	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#449	C₂²	1	1	yes	characteristic, complemented
114	C₃₁×#449	C₂²	1	2	yes	complemented
115	C₃₁×#448	C₂²	1	1	yes	characteristic, complemented
116	C₃₁×#447	C₂²	1	1	yes	characteristic, complemented
117	C₃₁×#447	C₂²	1	2	yes	complemented
118	C₃₁×#442	C₂²	1	2	yes	complemented
119	C₃₁×#440	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
121	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
122	C₃₁×#436	C₂²	1	2	yes	complemented
123	C₃₁×#435	C₂²	1	2	yes	complemented
124	C₃₁×#435	C₂²	1	2	yes	complemented
125	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
126	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
128	C₃₁×#418	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic, complemented
134	C₃₁×#408	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
136	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
137	C₃₁×H(5,𝔽₂)	—	2	4	no	—
138	C₃₁×H(5,𝔽₂)	—	2	4	no	—
139	C₃₁×H(5,𝔽₂)	—	4	2	no	—
140	C₃₁×H(5,𝔽₂)	—	4	2	no	—
141	C₂×#41×C₃₁	—	2	1	no	—
142	C₂×#41×C₃₁	—	2	1	no	—
143	C₂×#41×C₃₁	—	2	1	no	—
144	C₂×#41×C₃₁	—	2	1	no	—
145	C₂×#41×C₃₁	—	2	1	no	—
146	C₂×#41×C₃₁	—	2	1	no	—
147	C₂×#41×C₃₁	—	2	4	no	—
148	C₂×#41×C₃₁	—	2	4	no	—
149	C₂×#41×C₃₁	—	4	2	no	—
150	C₂×#41×C₃₁	—	4	2	no	—
151	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×#41×C₃₁	C₂³	1	2	yes	—
154	C₂×#41×C₃₁	C₂³	1	2	yes	—
155	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×#41×C₃₁	C₂³	1	2	yes	—
157	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×#41×C₃₁	C₂³	1	2	yes	—
159	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
161	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
162	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
163	C₂²×D₄×C₃₁	—	2	1	no	—
164	C₂²×D₄×C₃₁	—	2	1	no	—
165	C₂²×D₄×C₃₁	—	2	1	no	—
166	C₂²×D₄×C₃₁	—	2	1	no	—
167	C₂²×D₄×C₃₁	—	2	2	no	—
168	C₂²×D₄×C₃₁	—	2	2	no	—
169	C₂²×D₄×C₃₁	—	2	1	no	—
170	C₂²×D₄×C₃₁	—	2	2	no	—
171	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
172	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
173	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
174	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
175	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
176	C₂³×C₄×C₃₁	—	2	1	no	—
177	C₂³×C₄×C₃₁	—	2	1	no	—
178	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₃₁×#137	—	2	4	no	—
180	C₃₁×#137	—	2	8	no	—
181	C₃₁×#137	—	2	4	no	—
182	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
183	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
184	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
185	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
186	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
187	C₃₁×AGL(1,ℤ/8)	D₄	1	8	yes	complemented
188	C₃₁×#135	—	2	4	no	—
189	C₃₁×#135	—	2	8	no	—
190	C₃₁×#135	—	2	8	no	—
191	C₃₁×#135	—	2	8	no	—
192	C₃₁×#135	—	4	2	no	—
193	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
194	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
195	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
196	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×SD₁₆×C₃₁	—	4	2	no	—
198	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
199	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
200	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
202	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
203	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
204	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
205	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
207	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
208	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
209	C₂×D₈×C₃₁	—	2	4	no	—
210	C₂×D₈×C₃₁	—	2	8	no	—
211	C₂×D₈×C₃₁	C₂³	1	2	yes	—
212	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×D₈×C₃₁	C₂³	1	2	yes	—
214	C₂×D₈×C₃₁	C₂³	1	2	yes	—
215	C₂×D₈×C₃₁	C₂³	1	2	yes	—
216	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
217	C₂×D₈×C₃₁	C₂³	1	2	yes	—
218	C₃₁×#131	—	2	4	no	—
219	C₂×M₁₆×C₃₁	—	2	4	no	—
220	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
221	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
222	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
223	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
224	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
225	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
227	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
228	C₃₁×C₄⋊Q₈	—	2	1	no	—
229	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
230	C₃₁×#127	—	2	2	no	—
231	C₃₁×#127	C₂³	1	2	yes	—
232	C₃₁×#124	—	2	1	no	—
233	C₃₁×#124	—	2	2	no	—
234	C₃₁×#124	C₂³	1	2	yes	—
235	C₃₁×#124	C₂³	1	2	yes	—
236	C₃₁×#123	—	2	2	no	—
237	C₃₁×#123	—	2	1	no	—
238	C₃₁×#123	—	2	2	no	—
239	C₃₁×#123	—	2	2	no	—
240	C₃₁×#123	—	2	2	no	—
241	C₃₁×#123	—	2	2	no	—
242	C₃₁×#123	—	2	2	no	—
243	C₃₁×#123	—	2	2	no	—
244	C₃₁×#123	—	2	2	no	—
245	C₃₁×#123	—	2	2	no	—
246	C₃₁×#123	D₄	1	2	yes	—
247	C₃₁×C₂²⋊Q₈	—	2	1	no	—
248	C₃₁×C₂²⋊Q₈	—	2	1	no	—
249	C₃₁×C₂²⋊Q₈	—	2	1	no	—
250	C₃₁×C₂²⋊Q₈	—	2	2	no	—
251	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
252	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
253	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
254	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
255	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
256	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
257	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
258	C₃₁×#121	—	2	1	no	—
259	C₃₁×#121	—	2	2	no	—
260	C₃₁×#121	—	2	2	no	—
261	C₃₁×#121	—	2	2	no	—
262	C₃₁×#121	—	2	2	no	—
263	C₃₁×#121	—	2	1	no	—
264	C₃₁×#121	—	2	1	no	—
265	C₃₁×#121	—	2	1	no	—
266	C₃₁×#121	—	2	1	no	—
267	C₃₁×#121	—	2	2	no	—
268	C₃₁×#121	—	2	2	no	—
269	C₃₁×#121	—	2	2	no	—
270	C₃₁×#121	—	2	2	no	—
271	C₃₁×#121	—	2	2	no	—
272	C₃₁×#121	—	2	2	no	—
273	C₃₁×#121	D₄	1	1	yes	characteristic
274	C₃₁×#121	D₄	1	1	yes	characteristic
275	C₃₁×#121	C₂³	1	1	yes	characteristic
276	C₃₁×#121	C₂³	1	2	yes	—
277	C₃₁×#121	C₂³	1	2	yes	—
278	C₃₁×#121	C₂³	1	1	yes	characteristic
279	C₃₁×#121	C₂³	1	2	yes	—
280	C₃₁×#120	—	2	1	no	—
281	C₃₁×#120	—	2	2	no	—
282	C₃₁×#120	—	2	2	no	—
283	C₃₁×#120	—	2	2	no	—
284	C₃₁×#120	—	2	2	no	—
285	C₃₁×#120	—	2	2	no	—
286	C₃₁×#120	—	2	2	no	—
287	C₃₁×#120	D₄	1	2	yes	—
288	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
289	C₄×D₄×C₃₁	—	2	1	no	—
290	C₄×D₄×C₃₁	—	2	1	no	—
291	C₄×D₄×C₃₁	—	2	1	no	—
292	C₄×D₄×C₃₁	—	2	1	no	—
293	C₄×D₄×C₃₁	—	2	2	no	—
294	C₄×D₄×C₃₁	—	2	2	no	—
295	C₄×D₄×C₃₁	—	2	2	no	—
296	C₄×D₄×C₃₁	C₂³	1	2	yes	—
297	C₄×D₄×C₃₁	C₂³	1	2	yes	—
298	C₄×D₄×C₃₁	C₂³	1	2	yes	—
299	C₄×D₄×C₃₁	C₂³	1	2	yes	—
300	C₄×D₄×C₃₁	C₂³	1	2	yes	—
301	C₃₁×#117	—	2	1	no	—
302	C₃₁×#117	C₂³	1	1	yes	characteristic
303	C₃₁×#117	C₂³	1	1	yes	characteristic
304	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
305	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
306	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
307	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
308	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
309	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
310	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
311	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
312	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
313	C₃₁×#107	C₂³	1	2	yes	—
314	C₃₁×#106	C₂³	1	2	yes	—
315	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
316	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
317	C₃₁×#103	C₂³	1	2	yes	—
318	C₃₁×#103	C₂³	1	2	yes	—
319	C₃₁×#103	C₂³	1	1	yes	characteristic
320	C₃₁×#103	C₂³	1	1	yes	characteristic
321	C₃₁×#103	C₂³	1	1	yes	characteristic
322	C₃₁×#103	C₂³	1	1	yes	characteristic
323	C₃₁×#103	C₂³	1	2	yes	—
324	C₃₁×#102	C₂³	1	2	yes	—
325	C₃₁×#102	C₂³	1	2	yes	—
326	C₃₁×#102	C₂³	1	1	yes	characteristic
327	C₃₁×#102	C₂³	1	1	yes	characteristic
328	C₃₁×#102	C₂³	1	1	yes	characteristic
329	C₃₁×#102	C₂³	1	1	yes	characteristic
330	C₃₁×#102	C₂³	1	2	yes	—
331	C₃₁×#102	C₂³	1	2	yes	—
332	C₃₁×#102	C₂³	1	2	yes	—
333	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
334	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
335	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
336	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
337	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
339	C₃₁×#97	C₂³	1	2	yes	—
340	C₄×C₈×C₃₁	C₂³	1	2	yes	—
341	C₂⁴×C₃₁	—	2	1	no	—
342	C₂⁴×C₃₁	—	2	1	no	—
343	C₂⁴×C₃₁	—	2	2	no	—
344	C₂⁴×C₃₁	—	2	2	no	—
345	C₂⁴×C₃₁	—	2	1	no	—
346	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
347	#41×C₃₁	—	2	2	no	—
348	#41×C₃₁	—	2	2	no	—
349	#41×C₃₁	—	2	2	no	—
350	#41×C₃₁	—	2	2	no	—
351	#41×C₃₁	—	2	4	no	—
352	#41×C₃₁	—	2	4	no	—
353	#41×C₃₁	—	2	2	no	—
354	#41×C₃₁	—	2	4	no	—
355	#41×C₃₁	—	2	4	no	—
356	#41×C₃₁	—	2	2	no	—
357	#41×C₃₁	—	2	2	no	—
358	#41×C₃₁	—	2	2	no	—
359	#41×C₃₁	—	2	2	no	—
360	#41×C₃₁	—	4	4	no	—
361	#41×C₃₁	—	4	2	no	—
362	#41×C₃₁	—	4	1	no	—
363	#41×C₃₁	—	4	2	no	—
364	#41×C₃₁	—	4	1	no	—
365	#41×C₃₁	—	4	2	no	—
366	#41×C₃₁	—	4	2	no	—
367	#41×C₃₁	—	4	4	no	—
368	#41×C₃₁	—	4	4	no	—
369	#41×C₃₁	—	4	4	no	—
370	#41×C₃₁	—	4	4	no	—
371	#41×C₃₁	—	4	4	no	—
372	#41×C₃₁	C₂×D₄	1	4	yes	—
373	C₂×Q₈×C₃₁	—	2	1	no	—
374	C₂×Q₈×C₃₁	—	2	1	no	—
375	C₂×Q₈×C₃₁	—	2	2	no	—
376	C₂×Q₈×C₃₁	—	2	2	no	—
377	C₂×Q₈×C₃₁	—	2	2	no	—
378	C₂×Q₈×C₃₁	—	4	1	no	—
379	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
380	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
382	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₂×D₄×C₃₁	—	2	1	no	—
385	C₂×D₄×C₃₁	—	2	4	no	—
386	C₂×D₄×C₃₁	—	2	4	no	—
387	C₂×D₄×C₃₁	—	2	2	no	—
388	C₂×D₄×C₃₁	—	2	2	no	—
389	C₂×D₄×C₃₁	—	2	1	no	—
390	C₂×D₄×C₃₁	—	2	1	no	—
391	C₂×D₄×C₃₁	—	2	2	no	—
392	C₂×D₄×C₃₁	—	2	2	no	—
393	C₂×D₄×C₃₁	—	2	1	no	—
394	C₂×D₄×C₃₁	—	2	2	no	—
395	C₂×D₄×C₃₁	—	2	2	no	—
396	C₂×D₄×C₃₁	—	2	1	no	—
397	C₂×D₄×C₃₁	—	2	1	no	—
398	C₂×D₄×C₃₁	—	2	1	no	—
399	C₂×D₄×C₃₁	—	2	2	no	—
400	C₂×D₄×C₃₁	—	2	2	no	—
401	C₂×D₄×C₃₁	—	2	1	no	—
402	C₂×D₄×C₃₁	—	2	2	no	—
403	C₂×D₄×C₃₁	—	2	1	no	—
404	C₂×D₄×C₃₁	—	2	2	no	—
405	C₂×D₄×C₃₁	—	2	1	no	—
406	C₂×D₄×C₃₁	—	2	2	no	—
407	C₂×D₄×C₃₁	—	2	2	no	—
408	C₂×D₄×C₃₁	—	2	2	no	—
409	C₂×D₄×C₃₁	—	2	2	no	—
410	C₂×D₄×C₃₁	—	2	2	no	—
411	C₂×D₄×C₃₁	—	4	1	no	—
412	C₂×D₄×C₃₁	—	4	2	no	—
413	C₂×D₄×C₃₁	—	4	2	no	—
414	C₂×D₄×C₃₁	—	4	4	no	—
415	C₂×D₄×C₃₁	—	4	8	no	—
416	C₂×D₄×C₃₁	—	4	4	no	—
417	C₂×D₄×C₃₁	—	4	4	no	—
418	C₂×D₄×C₃₁	—	4	8	no	—
419	C₂×D₄×C₃₁	—	4	4	no	—
420	C₂×D₄×C₃₁	—	8	4	no	—
421	C₂×D₄×C₃₁	—	8	2	no	—
422	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
423	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
424	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
425	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
426	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	complemented
427	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
428	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
429	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
430	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
431	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
432	C₂²×C₄×C₃₁	—	2	1	no	—
433	C₂²×C₄×C₃₁	—	2	2	no	—
434	C₂²×C₄×C₃₁	—	2	2	no	—
435	C₂²×C₄×C₃₁	—	2	1	no	—
436	C₂²×C₄×C₃₁	—	2	1	no	—
437	C₂²×C₄×C₃₁	—	2	1	no	—
438	C₂²×C₄×C₃₁	—	2	1	no	—
439	C₂²×C₄×C₃₁	—	2	2	no	—
440	C₂²×C₄×C₃₁	—	2	2	no	—
441	C₂²×C₄×C₃₁	—	2	2	no	—
442	C₂²×C₄×C₃₁	—	2	1	no	—
443	C₂²×C₄×C₃₁	—	2	2	no	—
444	C₂²×C₄×C₃₁	—	2	1	no	—
445	C₂²×C₄×C₃₁	—	2	1	no	—
446	C₂²×C₄×C₃₁	—	2	2	no	—
447	C₂²×C₄×C₃₁	—	2	2	no	—
448	C₂²×C₄×C₃₁	—	2	2	no	—
449	C₂²×C₄×C₃₁	—	4	4	no	—
450	C₂²×C₄×C₃₁	—	4	4	no	—
451	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
452	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
453	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
454	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
455	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
456	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
457	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
458	Q₁₆×C₃₁	—	2	2	no	—
459	Q₁₆×C₃₁	—	2	4	no	—
460	Q₁₆×C₃₁	—	2	4	no	—
461	Q₁₆×C₃₁	—	4	1	no	—
462	SD₁₆×C₃₁	—	2	2	no	—
463	SD₁₆×C₃₁	—	2	2	no	—
464	SD₁₆×C₃₁	—	2	4	no	—
465	SD₁₆×C₃₁	—	2	4	no	—
466	SD₁₆×C₃₁	—	2	4	no	—
467	SD₁₆×C₃₁	—	2	4	no	—
468	SD₁₆×C₃₁	—	4	2	no	—
469	SD₁₆×C₃₁	—	4	2	no	—
470	SD₁₆×C₃₁	—	4	1	no	—
471	SD₁₆×C₃₁	—	4	1	no	—
472	SD₁₆×C₃₁	C₂×D₄	1	8	yes	complemented
473	D₈×C₃₁	—	2	4	no	—
474	D₈×C₃₁	—	2	2	no	—
475	D₈×C₃₁	—	2	4	no	—
476	D₈×C₃₁	—	2	4	no	—
477	D₈×C₃₁	—	2	4	no	—
478	D₈×C₃₁	—	4	1	no	—
479	D₈×C₃₁	C₂×D₄	1	8	yes	complemented
480	M₁₆×C₃₁	—	2	2	no	—
481	M₁₆×C₃₁	—	2	4	no	—
482	M₁₆×C₃₁	—	2	4	no	—
483	M₁₆×C₃₁	C₂×D₄	1	4	yes	complemented
484	C₂×C₈×C₃₁	—	2	2	no	—
485	C₂×C₈×C₃₁	—	2	2	no	—
486	C₂×C₈×C₃₁	—	2	4	no	—
487	C₂×C₈×C₃₁	—	2	4	no	—
488	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
489	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
490	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
491	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
492	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
493	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
494	C₄⋊C₄×C₃₁	—	2	1	no	—
495	C₄⋊C₄×C₃₁	—	2	1	no	—
496	C₄⋊C₄×C₃₁	—	2	1	no	—
497	C₄⋊C₄×C₃₁	—	2	2	no	—
498	C₄⋊C₄×C₃₁	—	2	2	no	—
499	C₄⋊C₄×C₃₁	—	2	2	no	—
500	C₄⋊C₄×C₃₁	—	2	2	no	—
501	C₄⋊C₄×C₃₁	—	2	2	no	—
502	C₄⋊C₄×C₃₁	—	2	2	no	—
503	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
504	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
505	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
506	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
507	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
508	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
509	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
510	C₂²⋊C₄×C₃₁	—	2	1	no	—
511	C₂²⋊C₄×C₃₁	—	2	2	no	—
512	C₂²⋊C₄×C₃₁	—	2	2	no	—
513	C₂²⋊C₄×C₃₁	—	2	2	no	—
514	C₂²⋊C₄×C₃₁	—	2	1	no	—
515	C₂²⋊C₄×C₃₁	—	2	1	no	—
516	C₂²⋊C₄×C₃₁	—	2	2	no	—
517	C₂²⋊C₄×C₃₁	—	2	1	no	—
518	C₂²⋊C₄×C₃₁	—	2	1	no	—
519	C₂²⋊C₄×C₃₁	—	2	2	no	—
520	C₂²⋊C₄×C₃₁	—	2	2	no	—
521	C₂²⋊C₄×C₃₁	—	2	2	no	—
522	C₂²⋊C₄×C₃₁	—	2	2	no	—
523	C₂²⋊C₄×C₃₁	—	2	2	no	—
524	C₂²⋊C₄×C₃₁	—	2	2	no	—
525	C₂²⋊C₄×C₃₁	—	2	2	no	—
526	C₂²⋊C₄×C₃₁	—	2	2	no	—
527	C₂²⋊C₄×C₃₁	—	2	2	no	—
528	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
529	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
530	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
531	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
532	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
533	C₄²×C₃₁	—	2	2	no	—
534	C₄²×C₃₁	—	2	1	no	—
535	C₄²×C₃₁	C₂⁴	1	2	yes	—
536	#61074	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
537	C₂³×C₃₁	—	2	2	no	—
538	C₂³×C₃₁	—	2	1	no	—
539	C₂³×C₃₁	—	2	2	no	—
540	C₂³×C₃₁	—	2	4	no	—
541	C₂³×C₃₁	—	2	1	no	—
542	C₂³×C₃₁	—	2	2	no	—
543	C₂³×C₃₁	—	2	1	no	—
544	C₂³×C₃₁	—	4	1	no	—
545	C₂³×C₃₁	—	4	1	no	—
546	C₂³×C₃₁	—	4	2	no	—
547	C₂³×C₃₁	—	4	4	no	—
548	C₂³×C₃₁	—	4	4	no	—
549	C₂³×C₃₁	—	4	2	no	—
550	C₂³×C₃₁	—	4	2	no	—
551	C₂³×C₃₁	—	8	1	no	—
552	C₂³×C₃₁	—	8	1	no	—
553	C₂³×C₃₁	—	8	1	no	—
554	C₂³×C₃₁	—	8	1	no	—
555	C₂³×C₃₁	—	8	2	no	—
556	C₂³×C₃₁	—	8	1	no	—
557	C₂³×C₃₁	—	8	2	no	—
558	C₂³×C₃₁	—	8	2	no	—
559	C₂³×C₃₁	—	8	2	no	—
560	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
561	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
562	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
563	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
564	Q₈×C₃₁	—	2	2	no	—
565	Q₈×C₃₁	—	2	1	no	—
566	Q₈×C₃₁	—	2	1	no	—
567	Q₈×C₃₁	—	2	1	no	—
568	Q₈×C₃₁	—	2	2	no	—
569	Q₈×C₃₁	—	2	2	no	—
570	Q₈×C₃₁	—	2	1	no	—
571	Q₈×C₃₁	—	2	1	no	—
572	Q₈×C₃₁	—	4	2	no	—
573	Q₈×C₃₁	—	4	2	no	—
574	Q₈×C₃₁	C₂²×D₄	1	2	yes	—
575	D₄×C₃₁	—	2	4	no	—
576	D₄×C₃₁	—	2	4	no	—
577	D₄×C₃₁	—	2	4	no	—
578	D₄×C₃₁	—	2	2	no	—
579	D₄×C₃₁	—	2	2	no	—
580	D₄×C₃₁	—	2	1	no	—
581	D₄×C₃₁	—	2	1	no	—
582	D₄×C₃₁	—	2	2	no	—
583	D₄×C₃₁	—	2	1	no	—
584	D₄×C₃₁	—	2	1	no	—
585	D₄×C₃₁	—	2	1	no	—
586	D₄×C₃₁	—	2	2	no	—
587	D₄×C₃₁	—	4	2	no	—
588	D₄×C₃₁	—	4	2	no	—
589	D₄×C₃₁	—	4	4	no	—
590	D₄×C₃₁	—	4	4	no	—
591	D₄×C₃₁	—	4	2	no	—
592	D₄×C₃₁	—	4	4	no	—
593	D₄×C₃₁	—	4	2	no	—
594	D₄×C₃₁	—	4	4	no	—
595	D₄×C₃₁	—	4	4	no	—
596	D₄×C₃₁	—	4	2	no	—
597	D₄×C₃₁	—	4	4	no	—
598	D₄×C₃₁	—	4	4	no	—
599	D₄×C₃₁	—	4	2	no	—
600	D₄×C₃₁	—	4	2	no	—
601	D₄×C₃₁	—	4	2	no	—
602	D₄×C₃₁	—	8	2	no	—
603	D₄×C₃₁	—	8	2	no	—
604	D₄×C₃₁	—	8	1	no	—
605	D₄×C₃₁	—	8	1	no	—
606	D₄×C₃₁	—	8	2	no	—
607	D₄×C₃₁	—	8	2	no	—
608	D₄×C₃₁	C₂²×D₄	1	4	yes	—
609	D₄×C₃₁	C₂²×D₄	1	2	yes	—
610	C₂×C₄×C₃₁	—	2	2	no	—
611	C₂×C₄×C₃₁	—	2	1	no	—
612	C₂×C₄×C₃₁	—	2	2	no	—
613	C₂×C₄×C₃₁	—	2	2	no	—
614	C₂×C₄×C₃₁	—	2	4	no	—
615	C₂×C₄×C₃₁	—	2	1	no	—
616	C₂×C₄×C₃₁	—	2	2	no	—
617	C₂×C₄×C₃₁	—	2	1	no	—
618	C₂×C₄×C₃₁	—	2	1	no	—
619	C₂×C₄×C₃₁	—	2	1	no	—
620	C₂×C₄×C₃₁	—	2	2	no	—
621	C₂×C₄×C₃₁	—	2	1	no	—
622	C₂×C₄×C₃₁	—	2	1	no	—
623	C₂×C₄×C₃₁	—	2	2	no	—
624	C₂×C₄×C₃₁	—	2	1	no	—
625	C₂×C₄×C₃₁	—	2	2	no	—
626	C₂×C₄×C₃₁	—	2	1	no	—
627	C₂×C₄×C₃₁	—	4	2	no	—
628	C₂×C₄×C₃₁	—	4	4	no	—
629	C₂×C₄×C₃₁	—	4	2	no	—
630	C₂×C₄×C₃₁	—	4	2	no	—
631	C₂×C₄×C₃₁	—	4	4	no	—
632	C₂×C₄×C₃₁	—	4	4	no	—
633	C₂×C₄×C₃₁	—	4	4	no	—
634	C₂×C₄×C₃₁	—	4	2	no	—
635	C₂×C₄×C₃₁	—	4	2	no	—
636	C₂×C₄×C₃₁	—	4	2	no	—
637	C₂×C₄×C₃₁	—	8	2	no	—
638	C₂×C₄×C₃₁	—	8	2	no	—
639	C₂×C₄×C₃₁	—	8	2	no	—
640	C₂×C₄×C₃₁	—	8	1	no	—
641	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
642	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
643	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
644	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
645	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
646	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
647	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
648	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
649	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
650	C₈×C₃₁	—	2	1	no	—
651	C₈×C₃₁	—	2	1	no	—
652	C₈×C₃₁	—	2	2	no	—
653	C₈×C₃₁	—	2	1	no	—
654	C₈×C₃₁	—	2	1	no	—
655	C₈×C₃₁	C₂²×D₄	1	4	yes	—
656	C₂×#576	C₂×C₃₁	1	1	yes	characteristic, complemented
657	C₂×#575	C₂×C₃₁	1	1	yes	characteristic, complemented
658	#3488	C₂×C₃₁	1	1	yes	characteristic, complemented
659	#3485	C₂×C₃₁	1	1	yes	characteristic, complemented
660	#3284	C₂×C₃₁	1	2	yes	complemented
661	#3280	C₂×C₃₁	1	2	yes	complemented
662	#3275	C₂×C₃₁	1	2	yes	complemented
663	#3272	C₂×C₃₁	1	2	yes	complemented
664	#3269	C₂×C₃₁	1	2	yes	complemented
665	#3268	C₂×C₃₁	1	2	yes	complemented
666	#3267	C₂×C₃₁	1	2	yes	complemented
667	#3264	C₂×C₃₁	1	2	yes	complemented
668	#3154	C₂×C₃₁	1	1	yes	characteristic, complemented
669	#3063	C₂×C₃₁	1	1	yes	characteristic, complemented
670	#3055	C₂×C₃₁	1	1	yes	characteristic, complemented
671	#3046	C₂×C₃₁	1	1	yes	characteristic, complemented
672	#3041	C₂×C₃₁	1	1	yes	characteristic, complemented
673	#3012	C₂×C₃₁	1	1	yes	characteristic, complemented
674	#3009	C₂×C₃₁	1	1	yes	characteristic, complemented
675	#3002	C₂×C₃₁	1	1	yes	characteristic, complemented
676	C₂×#449	C₂×C₃₁	1	1	yes	characteristic, complemented
677	#2946	C₂×C₃₁	1	1	yes	characteristic, complemented
678	#2933	C₂×C₃₁	1	1	yes	characteristic, complemented
679	C₂²×C₃₁	—	2	1	no	—
680	C₂²×C₃₁	—	2	1	no	—
681	C₂²×C₃₁	—	2	1	no	—
682	C₂²×C₃₁	—	2	2	no	—
683	C₂²×C₃₁	—	2	1	no	—
684	C₂²×C₃₁	—	2	1	no	—
685	C₂²×C₃₁	—	2	2	no	—
686	C₂²×C₃₁	—	2	1	no	—
687	C₂²×C₃₁	—	2	1	no	—
688	C₂²×C₃₁	—	2	1	no	—
689	C₂²×C₃₁	—	2	2	no	—
690	C₂²×C₃₁	—	2	2	no	—
691	C₂²×C₃₁	—	2	4	no	—
692	C₂²×C₃₁	—	4	2	no	—
693	C₂²×C₃₁	—	4	1	no	—
694	C₂²×C₃₁	—	4	1	no	—
695	C₂²×C₃₁	—	4	2	no	—
696	C₂²×C₃₁	—	4	1	no	—
697	C₂²×C₃₁	—	4	2	no	—
698	C₂²×C₃₁	—	4	1	no	—
699	C₂²×C₃₁	—	4	2	no	—
700	C₂²×C₃₁	—	4	1	no	—
701	C₂²×C₃₁	—	4	1	no	—
702	C₂²×C₃₁	—	4	1	no	—
703	C₂²×C₃₁	—	4	2	no	—
704	C₂²×C₃₁	—	4	1	no	—
705	C₂²×C₃₁	—	8	2	no	—
706	C₂²×C₃₁	—	8	4	no	—
707	C₂²×C₃₁	—	8	4	no	—
708	C₂²×C₃₁	—	16	2	no	—
709	C₂²×C₃₁	—	16	4	no	—
710	C₂²×C₃₁	—	16	4	no	—
711	C₂²×C₃₁	D₄²	1	2	yes	—
712	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
713	C₄×C₃₁	—	2	2	no	—
714	C₄×C₃₁	—	2	2	no	—
715	C₄×C₃₁	—	2	1	no	—
716	C₄×C₃₁	—	2	1	no	—
717	C₄×C₃₁	—	2	2	no	—
718	C₄×C₃₁	—	2	2	no	—
719	C₄×C₃₁	—	4	1	no	—
720	C₄×C₃₁	—	4	2	no	—
721	C₄×C₃₁	—	4	1	no	—
722	C₄×C₃₁	—	4	1	no	—
723	C₄×C₃₁	—	4	1	no	—
724	C₄×C₃₁	—	4	2	no	—
725	C₄×C₃₁	D₄²	1	2	yes	—
726	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
727	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
728	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
729	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic, complemented
730	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
731	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
732	#576	—	2	8	no	—
733	#575	—	2	8	no	—
734	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
735	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
736	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
737	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
738	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic, complemented
739	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
740	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
741	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic, complemented
742	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
743	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
744	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
745	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
746	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
747	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic, complemented
748	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
749	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
750	C₂²×D₈	C₂²×C₃₁	1	2	yes	complemented
751	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic, complemented
752	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
753	#550	C₂²×C₃₁	1	2	yes	complemented
754	#548	C₂²×C₃₁	1	2	yes	complemented
755	#547	—	2	1	no	—
756	#547	—	2	1	no	—
757	#547	C₂²×C₃₁	1	2	yes	complemented
758	#547	C₂²×C₃₁	1	2	yes	complemented
759	#546	—	2	2	no	—
760	#546	—	2	1	no	—
761	#546	—	2	1	no	—
762	#546	C₂²×C₃₁	1	2	yes	complemented
763	#546	C₂²×C₃₁	1	2	yes	complemented
764	#546	C₂²×C₃₁	1	2	yes	complemented
765	D₄²	—	2	2	no	—
766	D₄²	C₂²×C₃₁	1	2	yes	complemented
767	#537	—	2	1	no	—
768	#537	C₂²×C₃₁	1	1	yes	characteristic
769	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
770	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
771	#535	—	2	1	no	—
772	#535	C₂²×C₃₁	1	1	yes	characteristic, complemented
773	#534	—	2	2	no	—
774	#525	—	2	1	no	—
775	#525	C₂²×C₃₁	1	1	yes	characteristic
776	#525	C₂²×C₃₁	1	1	yes	characteristic, complemented
777	C₂×#123	—	2	2	no	—
778	C₂×#121	—	2	1	no	—
779	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
780	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
781	#518	C₂²×C₃₁	1	1	yes	characteristic, complemented
782	#497	C₂²×C₃₁	1	2	yes	complemented
783	#496	C₂²×C₃₁	1	2	yes	complemented
784	#495	C₂²×C₃₁	1	2	yes	complemented
785	#492	C₂²×C₃₁	1	2	yes	complemented
786	#470	C₂²×C₃₁	1	2	yes	complemented
787	#469	C₂²×C₃₁	1	2	yes	complemented
788	#468	C₂²×C₃₁	1	2	yes	complemented
789	#468	C₂²×C₃₁	1	2	yes	complemented
790	#467	C₂²×C₃₁	1	2	yes	complemented
791	#466	C₂²×C₃₁	1	2	yes	complemented
792	#465	C₂²×C₃₁	1	2	yes	complemented
793	#465	C₂²×C₃₁	1	2	yes	complemented
794	#464	C₂²×C₃₁	1	2	yes	complemented
795	#463	C₂²×C₃₁	1	2	yes	complemented
796	#463	C₂²×C₃₁	1	2	yes	complemented
797	#463	C₂²×C₃₁	1	2	yes	complemented
798	#462	C₂²×C₃₁	1	2	yes	complemented
799	#461	C₂²×C₃₁	1	2	yes	complemented
800	#459	C₂²×C₃₁	1	2	yes	complemented
801	#459	C₂²×C₃₁	1	2	yes	complemented
802	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
803	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
804	#452	C₂²×C₃₁	1	2	yes	complemented
805	#452	C₂²×C₃₁	1	2	yes	complemented
806	#452	C₂²×C₃₁	1	2	yes	complemented
807	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
808	#450	C₂²×C₃₁	1	1	yes	characteristic, complemented
809	#450	C₂²×C₃₁	1	2	yes	complemented
810	#450	C₂²×C₃₁	1	2	yes	complemented
811	#450	C₂²×C₃₁	1	2	yes	complemented
812	#449	C₂²×C₃₁	1	2	yes	complemented
813	#449	C₂²×C₃₁	1	2	yes	complemented
814	#449	C₂²×C₃₁	1	2	yes	complemented
815	#449	C₂²×C₃₁	1	2	yes	complemented
816	#449	C₂²×C₃₁	1	1	yes	characteristic, complemented
817	#449	C₂²×C₃₁	1	1	yes	characteristic, complemented
818	#449	C₂²×C₃₁	1	2	yes	complemented
819	#448	C₂²×C₃₁	1	1	yes	characteristic, complemented
820	#447	C₂²×C₃₁	1	1	yes	characteristic, complemented
821	#447	C₂²×C₃₁	1	2	yes	complemented
822	#442	C₂²×C₃₁	1	2	yes	complemented
823	#440	C₂²×C₃₁	1	2	yes	complemented
824	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
825	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
826	#436	C₂²×C₃₁	1	2	yes	complemented
827	#435	C₂²×C₃₁	1	2	yes	complemented
828	#435	C₂²×C₃₁	1	2	yes	complemented
829	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
830	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
831	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
832	#418	C₂²×C₃₁	1	1	yes	characteristic, complemented
833	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
834	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
835	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
836	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
837	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic, complemented
838	#408	C₂²×C₃₁	1	1	yes	characteristic, complemented
839	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
840	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
841	C₂×C₃₁	—	2	2	no	—
842	C₂×C₃₁	—	4	1	no	—
843	C₂×C₃₁	—	4	1	no	—
844	C₂×C₃₁	—	4	2	no	—
845	C₂×C₃₁	—	4	4	no	—
846	C₂×C₃₁	—	4	2	no	—
847	C₂×C₃₁	—	8	1	no	—
848	C₂×C₃₁	—	8	2	no	—
849	C₂×C₃₁	—	8	1	no	—
850	C₂×C₃₁	C₂×D₄²	1	1	yes	characteristic
851	C₂×C₃₁	#3584	1	1	yes	characteristic
852	C₂×C₃₁	#3585	1	1	yes	characteristic
853	H(5,𝔽₂)	—	2	4	no	—
854	H(5,𝔽₂)	—	2	4	no	—
855	H(5,𝔽₂)	—	4	2	no	—
856	H(5,𝔽₂)	—	4	2	no	—
857	C₂×#41	—	2	1	no	—
858	C₂×#41	—	2	1	no	—
859	C₂×#41	—	2	1	no	—
860	C₂×#41	—	2	1	no	—
861	C₂×#41	—	2	1	no	—
862	C₂×#41	—	2	1	no	—
863	C₂×#41	—	2	4	no	—
864	C₂×#41	—	2	4	no	—
865	C₂×#41	—	4	2	no	—
866	C₂×#41	—	4	2	no	—
867	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
868	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
869	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
870	C₂×#41	C₂³×C₃₁	1	2	yes	—
871	C₂×#41	C₂³×C₃₁	1	2	yes	—
872	C₂×#41	C₂³×C₃₁	1	2	yes	—
873	C₂×#41	C₂³×C₃₁	1	2	yes	—
874	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
875	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
876	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
877	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
878	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
879	C₂²×D₄	—	2	1	no	—
880	C₂²×D₄	—	2	1	no	—
881	C₂²×D₄	—	2	1	no	—
882	C₂²×D₄	—	2	1	no	—
883	C₂²×D₄	—	2	2	no	—
884	C₂²×D₄	—	2	2	no	—
885	C₂²×D₄	—	2	1	no	—
886	C₂²×D₄	—	2	2	no	—
887	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
888	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
889	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
890	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
891	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
892	C₂³×C₄	—	2	1	no	—
893	C₂³×C₄	—	2	1	no	—
894	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
895	#137	—	2	4	no	—
896	#137	—	2	8	no	—
897	#137	—	2	4	no	—
898	AGL(1,ℤ/8)	—	2	4	no	—
899	AGL(1,ℤ/8)	—	2	8	no	—
900	AGL(1,ℤ/8)	—	2	8	no	—
901	AGL(1,ℤ/8)	—	2	8	no	—
902	AGL(1,ℤ/8)	—	2	4	no	—
903	AGL(1,ℤ/8)	D₄×C₃₁	1	8	yes	complemented
904	#135	—	2	4	no	—
905	#135	—	2	8	no	—
906	#135	—	2	8	no	—
907	#135	—	2	8	no	—
908	#135	—	4	2	no	—
909	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
910	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
911	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
912	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
913	C₂×SD₁₆	—	4	2	no	—
914	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
915	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
916	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
917	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
918	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
919	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
920	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
921	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
922	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
923	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
924	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
925	C₂×D₈	—	2	4	no	—
926	C₂×D₈	—	2	8	no	—
927	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
928	C₂×D₈	C₂³×C₃₁	1	2	yes	—
929	C₂×D₈	C₂³×C₃₁	1	2	yes	—
930	C₂×D₈	C₂³×C₃₁	1	2	yes	—
931	C₂×D₈	C₂³×C₃₁	1	2	yes	—
932	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
933	C₂×D₈	C₂³×C₃₁	1	2	yes	—
934	#131	—	2	4	no	—
935	C₂×M₁₆	—	2	4	no	—
936	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
937	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
938	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
939	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
940	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
941	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
942	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
943	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
944	C₄⋊Q₈	—	2	1	no	—
945	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
946	#127	—	2	2	no	—
947	#127	C₂³×C₃₁	1	2	yes	—
948	#124	—	2	1	no	—
949	#124	—	2	2	no	—
950	#124	C₂³×C₃₁	1	2	yes	—
951	#124	C₂³×C₃₁	1	2	yes	—
952	#123	—	2	2	no	—
953	#123	—	2	1	no	—
954	#123	—	2	2	no	—
955	#123	—	2	2	no	—
956	#123	—	2	2	no	—
957	#123	—	2	2	no	—
958	#123	—	2	2	no	—
959	#123	—	2	2	no	—
960	#123	—	2	2	no	—
961	#123	—	2	2	no	—
962	#123	D₄×C₃₁	1	2	yes	—
963	C₂²⋊Q₈	—	2	1	no	—
964	C₂²⋊Q₈	—	2	1	no	—
965	C₂²⋊Q₈	—	2	1	no	—
966	C₂²⋊Q₈	—	2	2	no	—
967	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
968	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
969	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
970	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
971	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
972	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
973	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
974	#121	—	2	1	no	—
975	#121	—	2	2	no	—
976	#121	—	2	2	no	—
977	#121	—	2	2	no	—
978	#121	—	2	2	no	—
979	#121	—	2	1	no	—
980	#121	—	2	1	no	—
981	#121	—	2	1	no	—
982	#121	—	2	1	no	—
983	#121	—	2	2	no	—
984	#121	—	2	2	no	—
985	#121	—	2	2	no	—
986	#121	—	2	2	no	—
987	#121	—	2	2	no	—
988	#121	—	2	2	no	—
989	#121	D₄×C₃₁	1	1	yes	characteristic
990	#121	D₄×C₃₁	1	1	yes	characteristic
991	#121	C₂³×C₃₁	1	2	yes	—
992	#121	C₂³×C₃₁	1	2	yes	—
993	#121	C₂³×C₃₁	1	1	yes	characteristic
994	#121	C₂³×C₃₁	1	1	yes	characteristic
995	#121	C₂³×C₃₁	1	2	yes	—
996	#120	—	2	1	no	—
997	#120	—	2	2	no	—
998	#120	—	2	2	no	—
999	#120	—	2	2	no	—
1000	#120	—	2	2	no	—
1001	#120	—	2	2	no	—
1002	#120	—	2	2	no	—
1003	#120	D₄×C₃₁	1	2	yes	—
1004	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
1005	C₄×D₄	—	2	1	no	—
1006	C₄×D₄	—	2	1	no	—
1007	C₄×D₄	—	2	1	no	—
1008	C₄×D₄	—	2	1	no	—
1009	C₄×D₄	—	2	2	no	—
1010	C₄×D₄	—	2	2	no	—
1011	C₄×D₄	—	2	2	no	—
1012	C₄×D₄	C₂³×C₃₁	1	2	yes	—
1013	C₄×D₄	C₂³×C₃₁	1	2	yes	—
1014	C₄×D₄	C₂³×C₃₁	1	2	yes	—
1015	C₄×D₄	C₂³×C₃₁	1	2	yes	—
1016	C₄×D₄	C₂³×C₃₁	1	2	yes	—
1017	#117	—	2	1	no	—
1018	#117	C₂³×C₃₁	1	1	yes	characteristic
1019	#117	C₂³×C₃₁	1	1	yes	characteristic
1020	C₂×C₄⋊C₄	—	2	1	no	—
1021	C₂×C₄⋊C₄	—	2	2	no	—
1022	C₂×C₄⋊C₄	—	2	2	no	—
1023	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1024	C₂×C₂²⋊C₄	—	2	1	no	—
1025	C₂×C₂²⋊C₄	—	2	2	no	—
1026	C₂×C₂²⋊C₄	—	2	2	no	—
1027	C₂×C₂²⋊C₄	—	2	2	no	—
1028	C₂×C₂²⋊C₄	—	2	2	no	—
1029	#107	C₂³×C₃₁	1	2	yes	—
1030	#106	C₂³×C₃₁	1	2	yes	—
1031	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
1032	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
1033	#103	C₂³×C₃₁	1	2	yes	—
1034	#103	C₂³×C₃₁	1	2	yes	—
1035	#103	C₂³×C₃₁	1	1	yes	characteristic
1036	#103	C₂³×C₃₁	1	1	yes	characteristic
1037	#103	C₂³×C₃₁	1	1	yes	characteristic
1038	#103	C₂³×C₃₁	1	1	yes	characteristic
1039	#103	C₂³×C₃₁	1	2	yes	—
1040	#102	C₂³×C₃₁	1	2	yes	—
1041	#102	C₂³×C₃₁	1	2	yes	—
1042	#102	C₂³×C₃₁	1	1	yes	characteristic
1043	#102	C₂³×C₃₁	1	1	yes	characteristic
1044	#102	C₂³×C₃₁	1	1	yes	characteristic
1045	#102	C₂³×C₃₁	1	1	yes	characteristic
1046	#102	C₂³×C₃₁	1	2	yes	—
1047	#102	C₂³×C₃₁	1	2	yes	—
1048	#102	C₂³×C₃₁	1	2	yes	—
1049	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1050	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1051	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1052	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1053	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
1054	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
1055	#97	C₂³×C₃₁	1	2	yes	—
1056	C₄×C₈	C₂³×C₃₁	1	2	yes	—
1057	C₃₁	#61074	1	1	yes	characteristic, direct product factor, Sylow
1058	C₂⁴	—	2	1	no	—
1059	C₂⁴	—	2	1	no	—
1060	C₂⁴	—	2	2	no	—
1061	C₂⁴	—	2	2	no	—
1062	C₂⁴	—	2	1	no	—
1063	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
1064	#41	—	2	2	no	—
1065	#41	—	2	2	no	—
1066	#41	—	2	2	no	—
1067	#41	—	2	2	no	—
1068	#41	—	2	4	no	—
1069	#41	—	2	4	no	—
1070	#41	—	2	2	no	—
1071	#41	—	2	4	no	—
1072	#41	—	2	4	no	—
1073	#41	—	2	2	no	—
1074	#41	—	2	2	no	—
1075	#41	—	2	2	no	—
1076	#41	—	2	2	no	—
1077	#41	—	4	4	no	—
1078	#41	—	4	2	no	—
1079	#41	—	4	1	no	—
1080	#41	—	4	2	no	—
1081	#41	—	4	1	no	—
1082	#41	—	4	2	no	—
1083	#41	—	4	2	no	—
1084	#41	—	4	4	no	—
1085	#41	—	4	4	no	—
1086	#41	—	4	4	no	—
1087	#41	—	4	4	no	—
1088	#41	—	4	4	no	—
1089	#41	C₂×D₄×C₃₁	1	4	yes	—
1090	C₂×Q₈	—	2	1	no	—
1091	C₂×Q₈	—	2	1	no	—
1092	C₂×Q₈	—	2	2	no	—
1093	C₂×Q₈	—	2	2	no	—
1094	C₂×Q₈	—	2	2	no	—
1095	C₂×Q₈	—	4	1	no	—
1096	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1097	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1098	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1099	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1100	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1101	C₂×D₄	—	2	1	no	—
1102	C₂×D₄	—	2	4	no	—
1103	C₂×D₄	—	2	4	no	—
1104	C₂×D₄	—	2	2	no	—
1105	C₂×D₄	—	2	2	no	—
1106	C₂×D₄	—	2	1	no	—
1107	C₂×D₄	—	2	1	no	—
1108	C₂×D₄	—	2	2	no	—
1109	C₂×D₄	—	2	2	no	—
1110	C₂×D₄	—	2	1	no	—
1111	C₂×D₄	—	2	2	no	—
1112	C₂×D₄	—	2	2	no	—
1113	C₂×D₄	—	2	1	no	—
1114	C₂×D₄	—	2	1	no	—
1115	C₂×D₄	—	2	1	no	—
1116	C₂×D₄	—	2	2	no	—
1117	C₂×D₄	—	2	2	no	—
1118	C₂×D₄	—	2	1	no	—
1119	C₂×D₄	—	2	2	no	—
1120	C₂×D₄	—	2	1	no	—
1121	C₂×D₄	—	2	2	no	—
1122	C₂×D₄	—	2	1	no	—
1123	C₂×D₄	—	2	2	no	—
1124	C₂×D₄	—	2	2	no	—
1125	C₂×D₄	—	2	2	no	—
1126	C₂×D₄	—	2	2	no	—
1127	C₂×D₄	—	2	2	no	—
1128	C₂×D₄	—	4	1	no	—
1129	C₂×D₄	—	4	2	no	—
1130	C₂×D₄	—	4	2	no	—
1131	C₂×D₄	—	4	4	no	—
1132	C₂×D₄	—	4	8	no	—
1133	C₂×D₄	—	4	4	no	—
1134	C₂×D₄	—	4	4	no	—
1135	C₂×D₄	—	4	8	no	—
1136	C₂×D₄	—	4	4	no	—
1137	C₂×D₄	—	8	4	no	—
1138	C₂×D₄	—	8	2	no	—
1139	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1140	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1141	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1142	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1143	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	complemented
1144	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1145	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1146	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1147	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1148	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1149	C₂²×C₄	—	2	1	no	—
1150	C₂²×C₄	—	2	2	no	—
1151	C₂²×C₄	—	2	2	no	—
1152	C₂²×C₄	—	2	1	no	—
1153	C₂²×C₄	—	2	1	no	—
1154	C₂²×C₄	—	2	1	no	—
1155	C₂²×C₄	—	2	1	no	—
1156	C₂²×C₄	—	2	2	no	—
1157	C₂²×C₄	—	2	2	no	—
1158	C₂²×C₄	—	2	2	no	—
1159	C₂²×C₄	—	2	1	no	—
1160	C₂²×C₄	—	2	2	no	—
1161	C₂²×C₄	—	2	1	no	—
1162	C₂²×C₄	—	2	1	no	—
1163	C₂²×C₄	—	2	2	no	—
1164	C₂²×C₄	—	2	2	no	—
1165	C₂²×C₄	—	2	2	no	—
1166	C₂²×C₄	—	4	4	no	—
1167	C₂²×C₄	—	4	4	no	—
1168	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1169	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1170	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1171	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1172	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1173	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1174	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1175	Q₁₆	—	2	2	no	—
1176	Q₁₆	—	2	4	no	—
1177	Q₁₆	—	2	4	no	—
1178	Q₁₆	—	4	1	no	—
1179	SD₁₆	—	2	2	no	—
1180	SD₁₆	—	2	2	no	—
1181	SD₁₆	—	2	4	no	—
1182	SD₁₆	—	2	4	no	—
1183	SD₁₆	—	2	4	no	—
1184	SD₁₆	—	2	4	no	—
1185	SD₁₆	—	4	2	no	—
1186	SD₁₆	—	4	2	no	—
1187	SD₁₆	—	4	1	no	—
1188	SD₁₆	—	4	1	no	—
1189	SD₁₆	C₂×D₄×C₃₁	1	8	yes	complemented
1190	D₈	—	2	4	no	—
1191	D₈	—	2	2	no	—
1192	D₈	—	2	4	no	—
1193	D₈	—	2	4	no	—
1194	D₈	—	2	4	no	—
1195	D₈	—	4	1	no	—
1196	D₈	C₂×D₄×C₃₁	1	8	yes	complemented
1197	M₁₆	—	2	2	no	—
1198	M₁₆	—	2	4	no	—
1199	M₁₆	—	2	4	no	—
1200	M₁₆	C₂×D₄×C₃₁	1	4	yes	complemented
1201	C₂×C₈	—	2	2	no	—
1202	C₂×C₈	—	2	2	no	—
1203	C₂×C₈	—	2	4	no	—
1204	C₂×C₈	—	2	4	no	—
1205	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1206	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1207	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1208	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1209	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1210	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1211	C₄⋊C₄	—	2	1	no	—
1212	C₄⋊C₄	—	2	1	no	—
1213	C₄⋊C₄	—	2	1	no	—
1214	C₄⋊C₄	—	2	2	no	—
1215	C₄⋊C₄	—	2	2	no	—
1216	C₄⋊C₄	—	2	2	no	—
1217	C₄⋊C₄	—	2	2	no	—
1218	C₄⋊C₄	—	2	2	no	—
1219	C₄⋊C₄	—	2	2	no	—
1220	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1221	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1222	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1223	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1224	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1225	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1226	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1227	C₂²⋊C₄	—	2	1	no	—
1228	C₂²⋊C₄	—	2	2	no	—
1229	C₂²⋊C₄	—	2	2	no	—
1230	C₂²⋊C₄	—	2	2	no	—
1231	C₂²⋊C₄	—	2	1	no	—
1232	C₂²⋊C₄	—	2	1	no	—
1233	C₂²⋊C₄	—	2	2	no	—
1234	C₂²⋊C₄	—	2	1	no	—
1235	C₂²⋊C₄	—	2	1	no	—
1236	C₂²⋊C₄	—	2	2	no	—
1237	C₂²⋊C₄	—	2	2	no	—
1238	C₂²⋊C₄	—	2	2	no	—
1239	C₂²⋊C₄	—	2	2	no	—
1240	C₂²⋊C₄	—	2	2	no	—
1241	C₂²⋊C₄	—	2	2	no	—
1242	C₂²⋊C₄	—	2	2	no	—
1243	C₂²⋊C₄	—	2	2	no	—
1244	C₂²⋊C₄	—	2	2	no	—
1245	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1246	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1247	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1248	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1249	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1250	C₄²	—	2	2	no	—
1251	C₄²	—	2	1	no	—
1252	C₄²	C₂⁴×C₃₁	1	2	yes	—
1253	C₂³	—	2	2	no	—
1254	C₂³	—	2	1	no	—
1255	C₂³	—	2	2	no	—
1256	C₂³	—	2	4	no	—
1257	C₂³	—	2	1	no	—
1258	C₂³	—	2	2	no	—
1259	C₂³	—	2	1	no	—
1260	C₂³	—	4	1	no	—
1261	C₂³	—	4	1	no	—
1262	C₂³	—	4	2	no	—
1263	C₂³	—	4	4	no	—
1264	C₂³	—	4	4	no	—
1265	C₂³	—	4	2	no	—
1266	C₂³	—	4	2	no	—
1267	C₂³	—	8	1	no	—
1268	C₂³	—	8	1	no	—
1269	C₂³	—	8	1	no	—
1270	C₂³	—	8	1	no	—
1271	C₂³	—	8	2	no	—
1272	C₂³	—	8	1	no	—
1273	C₂³	—	8	2	no	—
1274	C₂³	—	8	2	no	—
1275	C₂³	—	8	2	no	—
1276	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1277	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1278	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1279	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1280	Q₈	—	2	2	no	—
1281	Q₈	—	2	1	no	—
1282	Q₈	—	2	1	no	—
1283	Q₈	—	2	1	no	—
1284	Q₈	—	2	2	no	—
1285	Q₈	—	2	2	no	—
1286	Q₈	—	2	1	no	—
1287	Q₈	—	2	1	no	—
1288	Q₈	—	4	2	no	—
1289	Q₈	—	4	2	no	—
1290	Q₈	C₂²×D₄×C₃₁	1	2	yes	—
1291	D₄	—	2	4	no	—
1292	D₄	—	2	4	no	—
1293	D₄	—	2	4	no	—
1294	D₄	—	2	2	no	—
1295	D₄	—	2	2	no	—
1296	D₄	—	2	1	no	—
1297	D₄	—	2	1	no	—
1298	D₄	—	2	2	no	—
1299	D₄	—	2	1	no	—
1300	D₄	—	2	1	no	—
1301	D₄	—	2	1	no	—
1302	D₄	—	2	2	no	—
1303	D₄	—	4	2	no	—
1304	D₄	—	4	2	no	—
1305	D₄	—	4	4	no	—
1306	D₄	—	4	4	no	—
1307	D₄	—	4	2	no	—
1308	D₄	—	4	4	no	—
1309	D₄	—	4	2	no	—
1310	D₄	—	4	4	no	—
1311	D₄	—	4	4	no	—
1312	D₄	—	4	2	no	—
1313	D₄	—	4	4	no	—
1314	D₄	—	4	4	no	—
1315	D₄	—	4	2	no	—
1316	D₄	—	4	2	no	—
1317	D₄	—	4	2	no	—
1318	D₄	—	8	2	no	—
1319	D₄	—	8	2	no	—
1320	D₄	—	8	1	no	—
1321	D₄	—	8	1	no	—
1322	D₄	—	8	2	no	—
1323	D₄	—	8	2	no	—
1324	D₄	C₂²×D₄×C₃₁	1	4	yes	—
1325	D₄	C₂²×D₄×C₃₁	1	2	yes	—
1326	C₂×C₄	—	2	2	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	2	2	no	—
1329	C₂×C₄	—	2	2	no	—
1330	C₂×C₄	—	2	4	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	2	no	—
1333	C₂×C₄	—	2	1	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	1	no	—
1336	C₂×C₄	—	2	2	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	2	no	—
1340	C₂×C₄	—	2	1	no	—
1341	C₂×C₄	—	2	2	no	—
1342	C₂×C₄	—	2	1	no	—
1343	C₂×C₄	—	4	2	no	—
1344	C₂×C₄	—	4	4	no	—
1345	C₂×C₄	—	4	2	no	—
1346	C₂×C₄	—	4	2	no	—
1347	C₂×C₄	—	4	4	no	—
1348	C₂×C₄	—	4	4	no	—
1349	C₂×C₄	—	4	4	no	—
1350	C₂×C₄	—	4	2	no	—
1351	C₂×C₄	—	4	2	no	—
1352	C₂×C₄	—	4	2	no	—
1353	C₂×C₄	—	8	2	no	—
1354	C₂×C₄	—	8	2	no	—
1355	C₂×C₄	—	8	2	no	—
1356	C₂×C₄	—	8	1	no	—
1357	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1358	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1359	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1360	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1361	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1362	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1363	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1364	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1365	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1366	C₈	—	2	1	no	—
1367	C₈	—	2	1	no	—
1368	C₈	—	2	2	no	—
1369	C₈	—	2	1	no	—
1370	C₈	—	2	1	no	—
1371	C₈	C₂²×D₄×C₃₁	1	4	yes	—
1372	C₂²	—	2	1	no	—
1373	C₂²	—	2	1	no	—
1374	C₂²	—	2	1	no	—
1375	C₂²	—	2	1	no	—
1376	C₂²	—	2	2	no	—
1377	C₂²	—	2	2	no	—
1378	C₂²	—	2	4	no	—
1379	C₂²	—	2	1	no	—
1380	C₂²	—	2	2	no	—
1381	C₂²	—	2	1	no	—
1382	C₂²	—	2	1	no	—
1383	C₂²	—	2	2	no	—
1384	C₂²	—	2	1	no	—
1385	C₂²	—	4	2	no	—
1386	C₂²	—	4	1	no	—
1387	C₂²	—	4	1	no	—
1388	C₂²	—	4	2	no	—
1389	C₂²	—	4	1	no	—
1390	C₂²	—	4	2	no	—
1391	C₂²	—	4	1	no	—
1392	C₂²	—	4	1	no	—
1393	C₂²	—	4	2	no	—
1394	C₂²	—	4	1	no	—
1395	C₂²	—	4	2	no	—
1396	C₂²	—	4	1	no	—
1397	C₂²	—	4	1	no	—
1398	C₂²	—	8	2	no	—
1399	C₂²	—	8	4	no	—
1400	C₂²	—	8	4	no	—
1401	C₂²	—	16	2	no	—
1402	C₂²	—	16	4	no	—
1403	C₂²	—	16	4	no	—
1404	C₂²	D₄²×C₃₁	1	2	yes	—
1405	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1406	C₄	—	2	1	no	—
1407	C₄	—	2	1	no	—
1408	C₄	—	2	2	no	—
1409	C₄	—	2	2	no	—
1410	C₄	—	2	2	no	—
1411	C₄	—	2	2	no	—
1412	C₄	—	4	1	no	—
1413	C₄	—	4	1	no	—
1414	C₄	—	4	2	no	—
1415	C₄	—	4	1	no	—
1416	C₄	—	4	2	no	—
1417	C₄	—	4	1	no	—
1418	C₄	D₄²×C₃₁	1	2	yes	—
1419	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
1420	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1421	C₂	—	2	2	no	—
1422	C₂	—	4	1	no	—
1423	C₂	—	4	1	no	—
1424	C₂	—	4	2	no	—
1425	C₂	—	4	2	no	—
1426	C₂	—	4	4	no	—
1427	C₂	—	8	1	no	—
1428	C₂	—	8	2	no	—
1429	C₂	—	8	1	no	—
1430	C₂	C₂×D₄²×C₃₁	1	1	yes	characteristic
1431	C₂	C₃₁×#3584	1	1	yes	characteristic
1432	C₂	C₃₁×#3585	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. C₂×C₃₁×#576	C₂	semidirect
2. C₂×C₃₁×#575	C₂	semidirect
3. C₃₁×#3488	C₂	semidirect
4. C₃₁×#3485	C₂	semidirect
5. C₃₁×#3284	C₂	semidirect
6. C₃₁×#3280	C₂	semidirect
7. C₃₁×#3275	C₂	semidirect
8. C₃₁×#3272	C₂	semidirect
9. C₃₁×#3269	C₂	semidirect
10. C₃₁×#3268	C₂	semidirect
11. C₃₁×#3267	C₂	semidirect
12. C₃₁×#3264	C₂	semidirect
13. C₃₁×#3154	C₂	semidirect
14. C₃₁×#3063	C₂	semidirect
15. C₃₁×#3055	C₂	semidirect
16. C₃₁×#3046	C₂	semidirect
17. C₃₁×#3041	C₂	semidirect
18. C₃₁×#3012	C₂	semidirect
19. C₃₁×#3009	C₂	semidirect
20. C₃₁×#3002	C₂	semidirect
21. C₂×C₃₁×#449	C₂	semidirect
22. C₃₁×#2946	C₂	semidirect
23. C₃₁×#2933	C₂	semidirect
25. C₂×C₃₁×H(5,𝔽₂)	C₂²	semidirect
26. C₂²×#41×C₃₁	C₂²	semidirect
27. C₂²×#41×C₃₁	C₂²	semidirect
30. C₂×C₃₁×#137	C₂²	semidirect
31. C₂×C₃₁×#137	C₂²	semidirect
32. C₂×C₃₁×#137	C₂²	semidirect
34. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
35. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
36. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
37. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
38. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
40. C₂×C₃₁×#135	C₂²	semidirect
41. C₂×C₃₁×#135	C₂²	semidirect
42. C₂×C₃₁×#135	C₂²	semidirect
43. C₂×C₃₁×#135	C₂²	semidirect
44. C₂²×SD₁₆×C₃₁	C₂²	semidirect
45. C₂²×D₈×C₃₁	C₂²	semidirect
46. C₂²×D₈×C₃₁	C₂²	semidirect
47. C₂×C₃₁×#131	C₂²	semidirect
48. C₂²×M₁₆×C₃₁	C₂²	semidirect
49. C₃₁×#550	C₂²	semidirect
50. C₃₁×#548	C₂²	semidirect
53. C₃₁×#547	C₂²	semidirect
54. C₃₁×#547	C₂²	semidirect
58. C₃₁×#546	C₂²	semidirect
59. C₃₁×#546	C₂²	semidirect
60. C₃₁×#546	C₂²	semidirect
62. D₄²×C₃₁	C₂²	semidirect
65. C₃₁×#536	C₂²	semidirect
66. C₃₁×#536	C₂²	semidirect
68. C₃₁×#535	C₂²	semidirect
72. C₃₁×#525	C₂²	semidirect
75. C₂×C₃₁×#121	C₂²	semidirect
76. C₃₁×#520	C₂²	semidirect
77. C₃₁×#518	C₂²	semidirect
78. C₃₁×#497	C₂²	semidirect
79. C₃₁×#496	C₂²	semidirect
80. C₃₁×#495	C₂²	semidirect
81. C₃₁×#492	C₂²	semidirect
82. C₃₁×#470	C₂²	semidirect
83. C₃₁×#469	C₂²	semidirect
84. C₃₁×#468	C₂²	semidirect
85. C₃₁×#468	C₂²	semidirect
86. C₃₁×#467	C₂²	semidirect
87. C₃₁×#466	C₂²	semidirect
88. C₃₁×#465	C₂²	semidirect
89. C₃₁×#465	C₂²	semidirect
90. C₃₁×#464	C₂²	semidirect
91. C₃₁×#463	C₂²	semidirect
92. C₃₁×#463	C₂²	semidirect
93. C₃₁×#463	C₂²	semidirect
94. C₃₁×#462	C₂²	semidirect
95. C₃₁×#461	C₂²	semidirect
96. C₃₁×#459	C₂²	semidirect
97. C₃₁×#459	C₂²	semidirect
98. C₃₁×#452	C₂²	semidirect
99. C₃₁×#452	C₂²	semidirect
100. C₃₁×#452	C₂²	semidirect
101. C₃₁×#452	C₂²	semidirect
102. C₃₁×#452	C₂²	semidirect
103. C₃₁×#451	C₂²	semidirect
104. C₃₁×#450	C₂²	semidirect
105. C₃₁×#450	C₂²	semidirect
106. C₃₁×#450	C₂²	semidirect
107. C₃₁×#450	C₂²	semidirect
108. C₃₁×#449	C₂²	semidirect
109. C₃₁×#449	C₂²	semidirect
110. C₃₁×#449	C₂²	semidirect
111. C₃₁×#449	C₂²	semidirect
112. C₃₁×#449	C₂²	semidirect
113. C₃₁×#449	C₂²	semidirect
114. C₃₁×#449	C₂²	semidirect
115. C₃₁×#448	C₂²	semidirect
116. C₃₁×#447	C₂²	semidirect
117. C₃₁×#447	C₂²	semidirect
118. C₃₁×#442	C₂²	semidirect
119. C₃₁×#440	C₂²	semidirect
120. C₄×SD₁₆×C₃₁	C₂²	semidirect
121. C₄×D₈×C₃₁	C₂²	semidirect
122. C₃₁×#436	C₂²	semidirect
123. C₃₁×#435	C₂²	semidirect
124. C₃₁×#435	C₂²	semidirect
125. C₈×D₄×C₃₁	C₂²	semidirect
126. C₃₁×#428	C₂²	semidirect
127. C₃₁×#424	C₂²	semidirect
128. C₃₁×#418	C₂²	semidirect
129. C₃₁×#417	C₂²	semidirect
130. C₃₁×#416	C₂²	semidirect
131. C₃₁×#416	C₂²	semidirect
132. C₂×C₃₁×#103	C₂²	semidirect
133. C₂×C₃₁×#102	C₂²	semidirect
134. C₃₁×#408	C₂²	semidirect
135. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
136. C₃₁×#405	C₂²	semidirect
187. C₃₁×AGL(1,ℤ/8)	D₄	semidirect
426. C₂×D₄×C₃₁	C₂×D₄	semidirect
472. SD₁₆×C₃₁	C₂×D₄	semidirect
479. D₈×C₃₁	C₂×D₄	semidirect
483. M₁₆×C₃₁	C₂×D₄	semidirect
536. #61074	C₃₁	direct (N × H)
656. C₂×#576	C₂×C₃₁	semidirect
657. C₂×#575	C₂×C₃₁	semidirect
658. #3488	C₂×C₃₁	semidirect
659. #3485	C₂×C₃₁	semidirect
660. #3284	C₂×C₃₁	semidirect
661. #3280	C₂×C₃₁	semidirect
662. #3275	C₂×C₃₁	semidirect
663. #3272	C₂×C₃₁	semidirect
664. #3269	C₂×C₃₁	semidirect
665. #3268	C₂×C₃₁	semidirect
666. #3267	C₂×C₃₁	semidirect
667. #3264	C₂×C₃₁	semidirect
668. #3154	C₂×C₃₁	semidirect
669. #3063	C₂×C₃₁	semidirect
670. #3055	C₂×C₃₁	semidirect
671. #3046	C₂×C₃₁	semidirect
672. #3041	C₂×C₃₁	semidirect
673. #3012	C₂×C₃₁	semidirect
674. #3009	C₂×C₃₁	semidirect
675. #3002	C₂×C₃₁	semidirect
676. C₂×#449	C₂×C₃₁	semidirect
677. #2946	C₂×C₃₁	semidirect
678. #2933	C₂×C₃₁	semidirect
729. C₂×H(5,𝔽₂)	C₂²×C₃₁	semidirect
730. C₂²×#41	C₂²×C₃₁	semidirect
731. C₂²×#41	C₂²×C₃₁	semidirect
734. C₂×#137	C₂²×C₃₁	semidirect
735. C₂×#137	C₂²×C₃₁	semidirect
736. C₂×#137	C₂²×C₃₁	semidirect
738. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
739. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
740. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
741. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
742. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
744. C₂×#135	C₂²×C₃₁	semidirect
745. C₂×#135	C₂²×C₃₁	semidirect
746. C₂×#135	C₂²×C₃₁	semidirect
747. C₂×#135	C₂²×C₃₁	semidirect
748. C₂²×SD₁₆	C₂²×C₃₁	semidirect
749. C₂²×D₈	C₂²×C₃₁	semidirect
750. C₂²×D₈	C₂²×C₃₁	semidirect
751. C₂×#131	C₂²×C₃₁	semidirect
752. C₂²×M₁₆	C₂²×C₃₁	semidirect
753. #550	C₂²×C₃₁	semidirect
754. #548	C₂²×C₃₁	semidirect
757. #547	C₂²×C₃₁	semidirect
758. #547	C₂²×C₃₁	semidirect
762. #546	C₂²×C₃₁	semidirect
763. #546	C₂²×C₃₁	semidirect
764. #546	C₂²×C₃₁	semidirect
766. D₄²	C₂²×C₃₁	semidirect
769. #536	C₂²×C₃₁	semidirect
770. #536	C₂²×C₃₁	semidirect
772. #535	C₂²×C₃₁	semidirect
776. #525	C₂²×C₃₁	semidirect
779. C₂×#121	C₂²×C₃₁	semidirect
780. #520	C₂²×C₃₁	semidirect
781. #518	C₂²×C₃₁	semidirect
782. #497	C₂²×C₃₁	semidirect
783. #496	C₂²×C₃₁	semidirect
784. #495	C₂²×C₃₁	semidirect
785. #492	C₂²×C₃₁	semidirect
786. #470	C₂²×C₃₁	semidirect
787. #469	C₂²×C₃₁	semidirect
788. #468	C₂²×C₃₁	semidirect
789. #468	C₂²×C₃₁	semidirect
790. #467	C₂²×C₃₁	semidirect
791. #466	C₂²×C₃₁	semidirect
792. #465	C₂²×C₃₁	semidirect
793. #465	C₂²×C₃₁	semidirect
794. #464	C₂²×C₃₁	semidirect
795. #463	C₂²×C₃₁	semidirect
796. #463	C₂²×C₃₁	semidirect
797. #463	C₂²×C₃₁	semidirect
798. #462	C₂²×C₃₁	semidirect
799. #461	C₂²×C₃₁	semidirect
800. #459	C₂²×C₃₁	semidirect
801. #459	C₂²×C₃₁	semidirect
802. #452	C₂²×C₃₁	semidirect
803. #452	C₂²×C₃₁	semidirect
804. #452	C₂²×C₃₁	semidirect
805. #452	C₂²×C₃₁	semidirect
806. #452	C₂²×C₃₁	semidirect
807. #451	C₂²×C₃₁	semidirect
808. #450	C₂²×C₃₁	semidirect
809. #450	C₂²×C₃₁	semidirect
810. #450	C₂²×C₃₁	semidirect
811. #450	C₂²×C₃₁	semidirect
812. #449	C₂²×C₃₁	semidirect
813. #449	C₂²×C₃₁	semidirect
814. #449	C₂²×C₃₁	semidirect
815. #449	C₂²×C₃₁	semidirect
816. #449	C₂²×C₃₁	semidirect
817. #449	C₂²×C₃₁	semidirect
818. #449	C₂²×C₃₁	semidirect
819. #448	C₂²×C₃₁	semidirect
820. #447	C₂²×C₃₁	semidirect
821. #447	C₂²×C₃₁	semidirect
822. #442	C₂²×C₃₁	semidirect
823. #440	C₂²×C₃₁	semidirect
824. C₄×SD₁₆	C₂²×C₃₁	semidirect
825. C₄×D₈	C₂²×C₃₁	semidirect
826. #436	C₂²×C₃₁	semidirect
827. #435	C₂²×C₃₁	semidirect
828. #435	C₂²×C₃₁	semidirect
829. C₈×D₄	C₂²×C₃₁	semidirect
830. #428	C₂²×C₃₁	semidirect
831. #424	C₂²×C₃₁	semidirect
832. #418	C₂²×C₃₁	semidirect
833. #417	C₂²×C₃₁	semidirect
834. #416	C₂²×C₃₁	semidirect
835. #416	C₂²×C₃₁	semidirect
836. C₂×#103	C₂²×C₃₁	semidirect
837. C₂×#102	C₂²×C₃₁	semidirect
838. #408	C₂²×C₃₁	semidirect
839. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
840. #405	C₂²×C₃₁	semidirect
903. AGL(1,ℤ/8)	D₄×C₃₁	semidirect
1057. C₃₁	#61074	direct (N × H)
1143. C₂×D₄	C₂×D₄×C₃₁	semidirect
1189. SD₁₆	C₂×D₄×C₃₁	semidirect
1196. D₈	C₂×D₄×C₃₁	semidirect
1200. M₁₆	C₂×D₄×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#576	2
C₂×C₃₁×#575	2
C₃₁×#3488	2
C₃₁×#3485	2
C₃₁×#3284	2
C₃₁×#3280	2
C₃₁×#3275	2
C₃₁×#3272	2
C₃₁×#3269	2
C₃₁×#3268	2
C₃₁×#3267	2
C₃₁×#3264	2
C₃₁×#3154	2
C₃₁×#3063	2
C₃₁×#3055	2
C₃₁×#3046	2
C₃₁×#3041	2
C₃₁×#3012	2
C₃₁×#3009	2
C₃₁×#3002	2
C₂×C₃₁×#449	2
C₃₁×#2946	2
C₃₁×#2933	2
#61074	31

Subgroups — C31×#61074 #21517833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61074 #21517833