Subgroups — C₃₁×#60816 #21517575

Order 7936.

2048 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3225	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3223	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3222	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3219	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3216	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3212	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3210	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3156	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3154	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3046	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3045	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3043	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3007	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3005	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3002	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#452	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
32	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
33	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#556	—	2	1	no	—
35	C₃₁×#554	—	2	1	no	—
36	C₃₁×#552	—	2	2	no	—
37	C₃₁×#552	—	2	1	no	—
38	C₃₁×#552	—	2	1	no	—
39	C₃₁×#551	—	2	2	no	—
40	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#542	C₂²	1	2	yes	complemented
42	C₃₁×#541	C₂²	1	2	yes	complemented
43	C₃₁×#537	—	2	1	no	—
44	C₃₁×#537	—	2	1	no	—
45	C₃₁×#536	C₂²	1	1	yes	characteristic
46	C₃₁×#536	C₂²	1	2	yes	—
47	C₃₁×#536	C₂²	1	1	yes	characteristic
48	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#535	C₂²	1	1	yes	characteristic
50	C₃₁×#535	C₂²	1	2	yes	—
51	C₃₁×#535	C₂²	1	1	yes	characteristic
52	C₃₁×#534	—	2	2	no	—
53	C₃₁×#533	C₂²	1	2	yes	complemented
54	C₃₁×#532	C₂²	1	2	yes	—
55	C₃₁×#532	C₂²	1	2	yes	—
56	C₃₁×#529	C₂²	1	2	yes	complemented
57	C₃₁×#525	—	2	1	no	—
58	C₃₁×#525	—	2	2	no	—
59	C₃₁×#525	—	2	1	no	—
60	C₃₁×#525	C₂²	1	1	yes	characteristic
61	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
62	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#519	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
65	C₃₁×#497	C₂²	1	2	yes	complemented
66	C₃₁×#497	C₂²	1	2	yes	complemented
67	C₃₁×#497	C₂²	1	2	yes	complemented
68	C₃₁×#496	C₂²	1	2	yes	complemented
69	C₃₁×#495	C₂²	1	2	yes	complemented
70	C₃₁×#495	C₂²	1	2	yes	complemented
71	C₃₁×#494	C₂²	1	2	yes	complemented
72	C₃₁×#492	C₂²	1	2	yes	complemented
73	C₃₁×#491	C₂²	1	2	yes	complemented
74	C₃₁×#490	C₂²	1	2	yes	complemented
75	C₃₁×#489	C₂²	1	2	yes	complemented
76	C₃₁×#489	C₂²	1	2	yes	complemented
77	C₃₁×#488	C₂²	1	2	yes	complemented
78	C₃₁×#488	C₂²	1	2	yes	complemented
79	C₃₁×#487	C₂²	1	2	yes	complemented
80	C₃₁×#486	C₂²	1	2	yes	complemented
81	C₃₁×#464	C₂²	1	2	yes	complemented
82	C₃₁×#464	C₂²	1	2	yes	complemented
83	C₃₁×#464	C₂²	1	2	yes	complemented
84	C₃₁×#464	C₂²	1	2	yes	complemented
85	C₃₁×#464	C₂²	1	2	yes	complemented
86	C₃₁×#464	C₂²	1	2	yes	complemented
87	C₃₁×#463	C₂²	1	2	yes	complemented
88	C₃₁×#463	C₂²	1	2	yes	complemented
89	C₃₁×#462	C₂²	1	2	yes	complemented
90	C₃₁×#462	C₂²	1	2	yes	complemented
91	C₃₁×#462	C₂²	1	2	yes	complemented
92	C₃₁×#461	C₂²	1	2	yes	complemented
93	C₃₁×#460	C₂²	1	2	yes	complemented
94	C₃₁×#460	C₂²	1	2	yes	complemented
95	C₃₁×#460	C₂²	1	2	yes	complemented
96	C₃₁×#459	C₂²	1	2	yes	complemented
97	C₃₁×#452	C₂²	1	2	yes	—
98	C₃₁×#452	C₂²	1	2	yes	—
99	C₃₁×#452	C₂²	1	2	yes	—
100	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×#452	C₂²	1	2	yes	complemented
102	C₃₁×#452	C₂²	1	2	yes	complemented
103	C₃₁×#452	C₂²	1	2	yes	complemented
104	C₃₁×#452	C₂²	1	2	yes	complemented
105	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#452	C₂²	1	2	yes	complemented
107	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
108	C₃₁×#451	C₂²	1	2	yes	complemented
109	C₃₁×#450	C₂²	1	1	yes	characteristic, complemented
110	C₃₁×#450	C₂²	1	2	yes	complemented
111	C₃₁×#449	C₂²	1	2	yes	—
112	C₃₁×#449	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#449	C₂²	1	2	yes	complemented
114	C₃₁×#449	C₂²	1	1	yes	characteristic, complemented
115	C₃₁×#448	C₂²	1	1	yes	characteristic, complemented
116	C₃₁×#447	C₂²	1	1	yes	characteristic, complemented
117	C₃₁×#433	C₂²	1	2	yes	complemented
118	C₃₁×#433	C₂²	1	2	yes	complemented
119	C₃₁×#432	C₂²	1	2	yes	complemented
120	C₃₁×#431	C₂²	1	2	yes	complemented
121	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#418	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#417	C₂²	1	1	yes	characteristic
126	C₃₁×#417	C₂²	1	1	yes	characteristic
127	C₃₁×#416	C₂²	1	1	yes	characteristic
128	C₃₁×#416	C₂²	1	1	yes	characteristic
129	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#407	C₂²	1	1	yes	characteristic
132	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
133	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
134	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	—	2	1	no	—
138	C₂×#41×C₃₁	—	2	1	no	—
139	C₂×#41×C₃₁	—	4	2	no	—
140	C₂×#41×C₃₁	—	4	2	no	—
141	C₂×#41×C₃₁	—	4	2	no	—
142	C₂×#41×C₃₁	—	4	2	no	—
143	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×#41×C₃₁	C₂³	1	2	yes	—
147	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×#41×C₃₁	C₂³	1	2	yes	—
149	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
151	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
152	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
153	C₂²×D₄×C₃₁	—	2	1	no	—
154	C₂²×D₄×C₃₁	—	2	1	no	—
155	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
156	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
157	C₂³×C₄×C₃₁	—	2	1	no	—
158	C₂³×C₄×C₃₁	—	2	1	no	—
159	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
160	C₃₁×#137	—	4	2	no	—
161	C₃₁×#137	—	4	2	no	—
162	C₃₁×#137	—	4	2	no	—
163	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
164	C₃₁×#135	—	4	2	no	—
165	C₃₁×#135	—	4	2	no	—
166	C₂×Q₁₆×C₃₁	—	4	2	no	—
167	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
168	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
171	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
172	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
173	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
174	C₂×SD₁₆×C₃₁	—	4	2	no	—
175	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
176	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
177	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
178	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
179	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
181	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
182	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
183	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
184	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
185	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
186	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
187	C₂×D₈×C₃₁	C₂³	1	2	yes	—
188	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
189	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
190	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
191	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
192	C₃₁×C₄⋊Q₈	—	2	1	no	—
193	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
194	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
195	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
197	C₃₁×#127	C₂³	1	2	yes	—
198	C₃₁×#127	C₂³	1	2	yes	—
199	C₃₁×#126	—	2	2	no	—
200	C₃₁×#126	—	2	2	no	—
201	C₃₁×#126	—	2	2	no	—
202	C₃₁×#126	—	2	2	no	—
203	C₃₁×#125	—	2	2	no	—
204	C₃₁×#125	—	2	2	no	—
205	C₃₁×#125	—	2	1	no	—
206	C₃₁×#125	—	2	2	no	—
207	C₃₁×#125	C₂³	1	2	yes	—
208	C₃₁×#124	—	2	2	no	—
209	C₃₁×#124	C₂³	1	2	yes	—
210	C₃₁×#124	C₂³	1	2	yes	—
211	C₃₁×#124	C₂³	1	2	yes	—
212	C₃₁×#124	C₂³	1	2	yes	—
213	C₃₁×#124	C₂³	1	2	yes	—
214	C₃₁×#123	—	2	1	no	—
215	C₃₁×#123	—	2	2	no	—
216	C₃₁×#123	—	2	2	no	—
217	C₃₁×#123	—	2	2	no	—
218	C₃₁×#123	—	2	2	no	—
219	C₃₁×#123	—	2	2	no	—
220	C₃₁×#123	—	2	2	no	—
221	C₃₁×#123	—	2	2	no	—
222	C₃₁×C₂²⋊Q₈	—	2	1	no	—
223	C₃₁×C₂²⋊Q₈	—	2	1	no	—
224	C₃₁×C₂²⋊Q₈	—	2	2	no	—
225	C₃₁×C₂²⋊Q₈	—	2	1	no	—
226	C₃₁×C₂²⋊Q₈	—	2	1	no	—
227	C₃₁×C₂²⋊Q₈	—	2	1	no	—
228	C₃₁×C₂²⋊Q₈	—	2	2	no	—
229	C₃₁×C₂²⋊Q₈	—	2	1	no	—
230	C₃₁×C₂²⋊Q₈	—	2	2	no	—
231	C₃₁×C₂²⋊Q₈	—	2	1	no	—
232	C₃₁×C₂²⋊Q₈	—	2	1	no	—
233	C₃₁×C₂²⋊Q₈	—	2	2	no	—
234	C₃₁×C₂²⋊Q₈	—	2	2	no	—
235	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
236	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
237	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
238	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
239	C₃₁×#121	—	2	2	no	—
240	C₃₁×#121	—	2	2	no	—
241	C₃₁×#121	—	2	2	no	—
242	C₃₁×#121	—	2	2	no	—
243	C₃₁×#121	—	2	1	no	—
244	C₃₁×#121	—	2	1	no	—
245	C₃₁×#121	—	2	1	no	—
246	C₃₁×#121	—	2	2	no	—
247	C₃₁×#121	—	2	1	no	—
248	C₃₁×#121	—	2	2	no	—
249	C₃₁×#121	C₂³	1	1	yes	characteristic
250	C₃₁×#121	C₂³	1	1	yes	characteristic
251	C₃₁×#120	—	2	1	no	—
252	C₃₁×#120	—	2	2	no	—
253	C₃₁×#120	—	2	2	no	—
254	C₃₁×#120	—	2	2	no	—
255	C₃₁×#120	—	2	2	no	—
256	C₄×Q₈×C₃₁	—	2	1	no	—
257	C₄×Q₈×C₃₁	—	2	1	no	—
258	C₄×Q₈×C₃₁	—	2	2	no	—
259	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
260	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
261	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
262	C₄×D₄×C₃₁	—	2	1	no	—
263	C₄×D₄×C₃₁	—	2	1	no	—
264	C₄×D₄×C₃₁	—	2	2	no	—
265	C₄×D₄×C₃₁	—	2	2	no	—
266	C₄×D₄×C₃₁	—	2	2	no	—
267	C₄×D₄×C₃₁	—	2	2	no	—
268	C₄×D₄×C₃₁	—	2	2	no	—
269	C₄×D₄×C₃₁	—	2	2	no	—
270	C₄×D₄×C₃₁	C₂³	1	2	yes	—
271	C₃₁×#117	—	2	2	no	—
272	C₃₁×#117	—	2	1	no	—
273	C₃₁×#117	—	2	2	no	—
274	C₃₁×#117	—	2	2	no	—
275	C₃₁×#117	D₄	1	1	yes	characteristic
276	C₃₁×#117	D₄	1	2	yes	—
277	C₃₁×#117	D₄	1	1	yes	characteristic
278	C₃₁×#117	C₂³	1	1	yes	characteristic
279	C₃₁×#117	C₂³	1	1	yes	characteristic
280	C₃₁×#117	C₂³	1	1	yes	characteristic
281	C₃₁×#117	C₂³	1	2	yes	—
282	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
283	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
284	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
285	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
286	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
288	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
289	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
290	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
291	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
292	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
293	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	1	yes	characteristic
297	C₃₁×#103	C₂³	1	1	yes	characteristic
298	C₃₁×#103	C₂³	1	1	yes	characteristic
299	C₃₁×#103	C₂³	1	1	yes	characteristic
300	C₃₁×#103	C₂³	1	2	yes	—
301	C₃₁×#103	C₂³	1	2	yes	—
302	C₃₁×#103	C₂³	1	2	yes	—
303	C₃₁×#103	C₂³	1	2	yes	—
304	C₃₁×#102	C₂³	1	2	yes	—
305	C₃₁×#102	C₂³	1	2	yes	—
306	C₃₁×#102	C₂³	1	1	yes	characteristic
307	C₃₁×#102	C₂³	1	1	yes	characteristic
308	C₃₁×#102	C₂³	1	1	yes	characteristic
309	C₃₁×#102	C₂³	1	1	yes	characteristic
310	C₃₁×#102	C₂³	1	2	yes	—
311	C₃₁×#102	C₂³	1	2	yes	—
312	C₃₁×#102	C₂³	1	2	yes	—
313	C₃₁×#102	C₂³	1	2	yes	—
314	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
315	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
316	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
317	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
318	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
320	C₃₁×#97	C₂³	1	2	yes	—
321	C₃₁×#97	C₂³	1	2	yes	—
322	C₄×C₈×C₃₁	C₂³	1	2	yes	—
323	C₄×C₈×C₃₁	C₂³	1	2	yes	—
324	C₂⁴×C₃₁	—	2	1	no	—
325	C₂⁴×C₃₁	—	2	1	no	—
326	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
327	#41×C₃₁	—	2	2	no	—
328	#41×C₃₁	—	2	2	no	—
329	#41×C₃₁	—	2	2	no	—
330	#41×C₃₁	—	2	2	no	—
331	#41×C₃₁	—	2	2	no	—
332	#41×C₃₁	—	2	2	no	—
333	#41×C₃₁	—	4	2	no	—
334	#41×C₃₁	—	4	2	no	—
335	#41×C₃₁	—	4	2	no	—
336	#41×C₃₁	—	4	1	no	—
337	#41×C₃₁	—	4	1	no	—
338	#41×C₃₁	—	4	2	no	—
339	#41×C₃₁	—	4	1	no	—
340	#41×C₃₁	—	4	1	no	—
341	#41×C₃₁	—	4	4	no	—
342	#41×C₃₁	—	4	4	no	—
343	#41×C₃₁	—	4	4	no	—
344	#41×C₃₁	—	4	4	no	—
345	C₂×Q₈×C₃₁	—	2	1	no	—
346	C₂×Q₈×C₃₁	—	2	1	no	—
347	C₂×Q₈×C₃₁	—	2	1	no	—
348	C₂×Q₈×C₃₁	—	2	2	no	—
349	C₂×Q₈×C₃₁	—	2	2	no	—
350	C₂×Q₈×C₃₁	—	2	2	no	—
351	C₂×Q₈×C₃₁	—	2	2	no	—
352	C₂×Q₈×C₃₁	—	2	2	no	—
353	C₂×Q₈×C₃₁	—	4	1	no	—
354	C₂×Q₈×C₃₁	—	4	1	no	—
355	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
356	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
358	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
359	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
360	C₂×D₄×C₃₁	—	2	1	no	—
361	C₂×D₄×C₃₁	—	2	1	no	—
362	C₂×D₄×C₃₁	—	2	2	no	—
363	C₂×D₄×C₃₁	—	2	1	no	—
364	C₂×D₄×C₃₁	—	2	1	no	—
365	C₂×D₄×C₃₁	—	2	1	no	—
366	C₂×D₄×C₃₁	—	2	2	no	—
367	C₂×D₄×C₃₁	—	2	1	no	—
368	C₂×D₄×C₃₁	—	2	1	no	—
369	C₂×D₄×C₃₁	—	2	1	no	—
370	C₂×D₄×C₃₁	—	2	1	no	—
371	C₂×D₄×C₃₁	—	2	2	no	—
372	C₂×D₄×C₃₁	—	2	2	no	—
373	C₂×D₄×C₃₁	—	2	2	no	—
374	C₂×D₄×C₃₁	—	2	2	no	—
375	C₂×D₄×C₃₁	—	2	2	no	—
376	C₂×D₄×C₃₁	—	2	2	no	—
377	C₂×D₄×C₃₁	—	4	1	no	—
378	C₂×D₄×C₃₁	—	4	1	no	—
379	C₂×D₄×C₃₁	—	4	4	no	—
380	C₂×D₄×C₃₁	—	4	4	no	—
381	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
382	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₃₁	—	2	2	no	—
386	C₂²×C₄×C₃₁	—	2	2	no	—
387	C₂²×C₄×C₃₁	—	2	1	no	—
388	C₂²×C₄×C₃₁	—	2	1	no	—
389	C₂²×C₄×C₃₁	—	2	1	no	—
390	C₂²×C₄×C₃₁	—	2	1	no	—
391	C₂²×C₄×C₃₁	—	2	1	no	—
392	C₂²×C₄×C₃₁	—	2	1	no	—
393	C₂²×C₄×C₃₁	—	2	2	no	—
394	C₂²×C₄×C₃₁	—	2	1	no	—
395	C₂²×C₄×C₃₁	—	2	2	no	—
396	C₂²×C₄×C₃₁	—	2	1	no	—
397	C₂²×C₄×C₃₁	—	2	1	no	—
398	C₂²×C₄×C₃₁	—	2	2	no	—
399	C₂²×C₄×C₃₁	—	4	4	no	—
400	C₂²×C₄×C₃₁	—	4	4	no	—
401	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
404	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
405	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
406	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	Q₁₆×C₃₁	—	4	2	no	—
410	Q₁₆×C₃₁	—	4	2	no	—
411	Q₁₆×C₃₁	—	4	1	no	—
412	Q₁₆×C₃₁	—	4	1	no	—
413	Q₁₆×C₃₁	—	4	2	no	—
414	Q₁₆×C₃₁	—	4	2	no	—
415	Q₁₆×C₃₁	—	4	2	no	—
416	SD₁₆×C₃₁	—	4	2	no	—
417	SD₁₆×C₃₁	—	4	2	no	—
418	SD₁₆×C₃₁	—	4	1	no	—
419	SD₁₆×C₃₁	—	4	1	no	—
420	SD₁₆×C₃₁	—	4	1	no	—
421	SD₁₆×C₃₁	—	4	1	no	—
422	SD₁₆×C₃₁	—	4	2	no	—
423	SD₁₆×C₃₁	—	4	2	no	—
424	SD₁₆×C₃₁	—	4	2	no	—
425	SD₁₆×C₃₁	—	4	2	no	—
426	D₈×C₃₁	—	4	1	no	—
427	D₈×C₃₁	—	4	1	no	—
428	D₈×C₃₁	—	4	2	no	—
429	M₁₆×C₃₁	—	2	2	no	—
430	M₁₆×C₃₁	—	2	2	no	—
431	C₂×C₈×C₃₁	—	2	2	no	—
432	C₂×C₈×C₃₁	—	2	2	no	—
433	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
434	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
435	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
436	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
437	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
438	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₃₁	—	2	1	no	—
440	C₄⋊C₄×C₃₁	—	2	2	no	—
441	C₄⋊C₄×C₃₁	—	2	2	no	—
442	C₄⋊C₄×C₃₁	—	2	2	no	—
443	C₄⋊C₄×C₃₁	—	2	2	no	—
444	C₄⋊C₄×C₃₁	—	2	2	no	—
445	C₄⋊C₄×C₃₁	—	2	2	no	—
446	C₄⋊C₄×C₃₁	—	2	2	no	—
447	C₄⋊C₄×C₃₁	—	2	2	no	—
448	C₄⋊C₄×C₃₁	—	2	1	no	—
449	C₄⋊C₄×C₃₁	—	2	2	no	—
450	C₄⋊C₄×C₃₁	—	2	2	no	—
451	C₄⋊C₄×C₃₁	—	2	2	no	—
452	C₄⋊C₄×C₃₁	—	2	2	no	—
453	C₄⋊C₄×C₃₁	—	2	2	no	—
454	C₄⋊C₄×C₃₁	—	2	1	no	—
455	C₄⋊C₄×C₃₁	—	2	2	no	—
456	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
457	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
458	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
459	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
460	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
461	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
462	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
463	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
464	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
465	C₂²⋊C₄×C₃₁	—	2	2	no	—
466	C₂²⋊C₄×C₃₁	—	2	2	no	—
467	C₂²⋊C₄×C₃₁	—	2	1	no	—
468	C₂²⋊C₄×C₃₁	—	2	1	no	—
469	C₂²⋊C₄×C₃₁	—	2	1	no	—
470	C₂²⋊C₄×C₃₁	—	2	1	no	—
471	C₂²⋊C₄×C₃₁	—	2	2	no	—
472	C₂²⋊C₄×C₃₁	—	2	2	no	—
473	C₂²⋊C₄×C₃₁	—	2	2	no	—
474	C₂²⋊C₄×C₃₁	—	2	2	no	—
475	C₂²⋊C₄×C₃₁	—	2	2	no	—
476	C₂²⋊C₄×C₃₁	—	2	2	no	—
477	C₂²⋊C₄×C₃₁	—	2	2	no	—
478	C₂²⋊C₄×C₃₁	—	2	2	no	—
479	C₂²⋊C₄×C₃₁	—	2	2	no	—
480	C₂²⋊C₄×C₃₁	—	2	2	no	—
481	C₂²⋊C₄×C₃₁	—	2	1	no	—
482	C₂²⋊C₄×C₃₁	—	2	2	no	—
483	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
484	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
485	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
486	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
487	C₄²×C₃₁	—	2	2	no	—
488	C₄²×C₃₁	—	2	2	no	—
489	C₄²×C₃₁	—	2	2	no	—
490	C₄²×C₃₁	—	2	1	no	—
491	C₄²×C₃₁	C₂×D₄	1	2	yes	—
492	C₄²×C₃₁	C₂×D₄	1	2	yes	—
493	C₄²×C₃₁	C₂⁴	1	2	yes	—
494	C₄²×C₃₁	C₂⁴	1	2	yes	—
495	#60816	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
496	C₂³×C₃₁	—	2	2	no	—
497	C₂³×C₃₁	—	2	1	no	—
498	C₂³×C₃₁	—	2	2	no	—
499	C₂³×C₃₁	—	2	1	no	—
500	C₂³×C₃₁	—	2	1	no	—
501	C₂³×C₃₁	—	4	1	no	—
502	C₂³×C₃₁	—	4	1	no	—
503	C₂³×C₃₁	—	4	2	no	—
504	C₂³×C₃₁	—	4	2	no	—
505	C₂³×C₃₁	—	8	1	no	—
506	C₂³×C₃₁	—	8	1	no	—
507	C₂³×C₃₁	—	8	1	no	—
508	C₂³×C₃₁	—	8	1	no	—
509	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
510	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
512	Q₈×C₃₁	—	2	2	no	—
513	Q₈×C₃₁	—	2	1	no	—
514	Q₈×C₃₁	—	2	2	no	—
515	Q₈×C₃₁	—	2	1	no	—
516	Q₈×C₃₁	—	2	2	no	—
517	Q₈×C₃₁	—	2	1	no	—
518	Q₈×C₃₁	—	2	1	no	—
519	Q₈×C₃₁	—	2	2	no	—
520	Q₈×C₃₁	—	2	1	no	—
521	Q₈×C₃₁	—	2	1	no	—
522	Q₈×C₃₁	—	4	2	no	—
523	Q₈×C₃₁	—	4	2	no	—
524	Q₈×C₃₁	—	4	2	no	—
525	Q₈×C₃₁	—	8	2	no	—
526	D₄×C₃₁	—	2	1	no	—
527	D₄×C₃₁	—	2	1	no	—
528	D₄×C₃₁	—	2	2	no	—
529	D₄×C₃₁	—	2	1	no	—
530	D₄×C₃₁	—	2	1	no	—
531	D₄×C₃₁	—	2	2	no	—
532	D₄×C₃₁	—	2	1	no	—
533	D₄×C₃₁	—	2	1	no	—
534	D₄×C₃₁	—	4	2	no	—
535	D₄×C₃₁	—	4	2	no	—
536	D₄×C₃₁	—	4	4	no	—
537	D₄×C₃₁	—	4	4	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	—	4	2	no	—
543	D₄×C₃₁	—	4	2	no	—
544	D₄×C₃₁	—	8	2	no	—
545	D₄×C₃₁	—	8	2	no	—
546	D₄×C₃₁	—	8	2	no	—
547	D₄×C₃₁	—	8	2	no	—
548	D₄×C₃₁	—	8	1	no	—
549	C₂×C₄×C₃₁	—	2	2	no	—
550	C₂×C₄×C₃₁	—	2	2	no	—
551	C₂×C₄×C₃₁	—	2	2	no	—
552	C₂×C₄×C₃₁	—	2	1	no	—
553	C₂×C₄×C₃₁	—	2	1	no	—
554	C₂×C₄×C₃₁	—	2	1	no	—
555	C₂×C₄×C₃₁	—	2	1	no	—
556	C₂×C₄×C₃₁	—	2	1	no	—
557	C₂×C₄×C₃₁	—	2	1	no	—
558	C₂×C₄×C₃₁	—	2	2	no	—
559	C₂×C₄×C₃₁	—	2	1	no	—
560	C₂×C₄×C₃₁	—	2	2	no	—
561	C₂×C₄×C₃₁	—	2	2	no	—
562	C₂×C₄×C₃₁	—	2	1	no	—
563	C₂×C₄×C₃₁	—	2	1	no	—
564	C₂×C₄×C₃₁	—	4	2	no	—
565	C₂×C₄×C₃₁	—	4	2	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	—	4	4	no	—
570	C₂×C₄×C₃₁	—	4	2	no	—
571	C₂×C₄×C₃₁	—	4	2	no	—
572	C₂×C₄×C₃₁	—	4	2	no	—
573	C₂×C₄×C₃₁	—	4	2	no	—
574	C₂×C₄×C₃₁	—	4	2	no	—
575	C₂×C₄×C₃₁	—	4	2	no	—
576	C₂×C₄×C₃₁	—	8	2	no	—
577	C₂×C₄×C₃₁	—	8	1	no	—
578	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
579	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
580	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
582	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
583	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
586	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
587	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
588	C₈×C₃₁	—	2	1	no	—
589	C₈×C₃₁	—	2	1	no	—
590	C₈×C₃₁	—	2	1	no	—
591	C₈×C₃₁	—	2	1	no	—
592	C₈×C₃₁	—	2	2	no	—
593	C₈×C₃₁	—	2	2	no	—
594	#3495	C₂×C₃₁	1	1	yes	characteristic, complemented
595	#3449	C₂×C₃₁	1	1	yes	characteristic, complemented
596	#3225	C₂×C₃₁	1	2	yes	complemented
597	#3224	C₂×C₃₁	1	2	yes	complemented
598	#3223	C₂×C₃₁	1	2	yes	complemented
599	#3222	C₂×C₃₁	1	2	yes	complemented
600	#3219	C₂×C₃₁	1	2	yes	complemented
601	#3216	C₂×C₃₁	1	2	yes	complemented
602	#3212	C₂×C₃₁	1	2	yes	complemented
603	#3210	C₂×C₃₁	1	2	yes	complemented
604	#3156	C₂×C₃₁	1	1	yes	characteristic, complemented
605	#3154	C₂×C₃₁	1	1	yes	characteristic, complemented
606	#3137	C₂×C₃₁	1	1	yes	characteristic, complemented
607	#3136	C₂×C₃₁	1	1	yes	characteristic, complemented
608	#3046	C₂×C₃₁	1	1	yes	characteristic, complemented
609	#3045	C₂×C₃₁	1	1	yes	characteristic, complemented
610	#3044	C₂×C₃₁	1	1	yes	characteristic, complemented
611	#3043	C₂×C₃₁	1	1	yes	characteristic, complemented
612	#3007	C₂×C₃₁	1	1	yes	characteristic, complemented
613	#3005	C₂×C₃₁	1	1	yes	characteristic, complemented
614	#3002	C₂×C₃₁	1	1	yes	characteristic, complemented
615	C₂×#452	C₂×C₃₁	1	1	yes	characteristic, complemented
616	#2924	C₂×C₃₁	1	1	yes	characteristic, complemented
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	1	no	—
622	C₂²×C₃₁	—	2	1	no	—
623	C₂²×C₃₁	—	2	1	no	—
624	C₂²×C₃₁	—	2	1	no	—
625	C₂²×C₃₁	—	4	1	no	—
626	C₂²×C₃₁	—	4	2	no	—
627	C₂²×C₃₁	—	4	1	no	—
628	C₂²×C₃₁	—	4	1	no	—
629	C₂²×C₃₁	—	4	1	no	—
630	C₂²×C₃₁	—	4	2	no	—
631	C₂²×C₃₁	—	4	1	no	—
632	C₂²×C₃₁	—	4	1	no	—
633	C₂²×C₃₁	—	4	2	no	—
634	C₂²×C₃₁	—	4	1	no	—
635	C₂²×C₃₁	—	4	1	no	—
636	C₂²×C₃₁	—	4	1	no	—
637	C₂²×C₃₁	—	8	2	no	—
638	C₂²×C₃₁	—	8	4	no	—
639	C₂²×C₃₁	—	8	4	no	—
640	C₂²×C₃₁	#535	1	2	yes	—
641	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
642	C₄×C₃₁	—	2	2	no	—
643	C₄×C₃₁	—	2	2	no	—
644	C₄×C₃₁	—	2	2	no	—
645	C₄×C₃₁	—	2	2	no	—
646	C₄×C₃₁	—	2	1	no	—
647	C₄×C₃₁	—	2	1	no	—
648	C₄×C₃₁	—	4	2	no	—
649	C₄×C₃₁	—	4	1	no	—
650	C₄×C₃₁	—	4	1	no	—
651	C₄×C₃₁	—	4	2	no	—
652	C₄×C₃₁	—	4	1	no	—
653	C₄×C₃₁	—	4	1	no	—
654	C₄×C₃₁	—	4	1	no	—
655	C₄×C₃₁	—	4	2	no	—
656	C₄×C₃₁	#535	1	2	yes	—
657	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
658	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
659	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
660	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
661	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
662	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
663	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
664	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
666	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
667	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	#556	—	2	1	no	—
670	#554	—	2	1	no	—
671	#552	—	2	2	no	—
672	#552	—	2	1	no	—
673	#552	—	2	1	no	—
674	#551	—	2	2	no	—
675	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
676	#542	C₂²×C₃₁	1	2	yes	complemented
677	#541	C₂²×C₃₁	1	2	yes	complemented
678	#537	—	2	1	no	—
679	#537	—	2	1	no	—
680	#536	C₂²×C₃₁	1	1	yes	characteristic
681	#536	C₂²×C₃₁	1	2	yes	—
682	#536	C₂²×C₃₁	1	1	yes	characteristic
683	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	#535	C₂²×C₃₁	1	1	yes	characteristic
685	#535	C₂²×C₃₁	1	2	yes	—
686	#535	C₂²×C₃₁	1	1	yes	characteristic
687	#534	—	2	2	no	—
688	#533	C₂²×C₃₁	1	2	yes	complemented
689	#532	C₂²×C₃₁	1	2	yes	—
690	#532	C₂²×C₃₁	1	2	yes	—
691	#529	C₂²×C₃₁	1	2	yes	complemented
692	#525	—	2	1	no	—
693	#525	—	2	2	no	—
694	#525	—	2	1	no	—
695	#525	C₂²×C₃₁	1	1	yes	characteristic
696	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
697	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	#519	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
700	#497	C₂²×C₃₁	1	2	yes	complemented
701	#497	C₂²×C₃₁	1	2	yes	complemented
702	#497	C₂²×C₃₁	1	2	yes	complemented
703	#496	C₂²×C₃₁	1	2	yes	complemented
704	#495	C₂²×C₃₁	1	2	yes	complemented
705	#495	C₂²×C₃₁	1	2	yes	complemented
706	#494	C₂²×C₃₁	1	2	yes	complemented
707	#492	C₂²×C₃₁	1	2	yes	complemented
708	#491	C₂²×C₃₁	1	2	yes	complemented
709	#490	C₂²×C₃₁	1	2	yes	complemented
710	#489	C₂²×C₃₁	1	2	yes	complemented
711	#489	C₂²×C₃₁	1	2	yes	complemented
712	#488	C₂²×C₃₁	1	2	yes	complemented
713	#488	C₂²×C₃₁	1	2	yes	complemented
714	#487	C₂²×C₃₁	1	2	yes	complemented
715	#486	C₂²×C₃₁	1	2	yes	complemented
716	#464	C₂²×C₃₁	1	2	yes	complemented
717	#464	C₂²×C₃₁	1	2	yes	complemented
718	#464	C₂²×C₃₁	1	2	yes	complemented
719	#464	C₂²×C₃₁	1	2	yes	complemented
720	#464	C₂²×C₃₁	1	2	yes	complemented
721	#464	C₂²×C₃₁	1	2	yes	complemented
722	#463	C₂²×C₃₁	1	2	yes	complemented
723	#463	C₂²×C₃₁	1	2	yes	complemented
724	#462	C₂²×C₃₁	1	2	yes	complemented
725	#462	C₂²×C₃₁	1	2	yes	complemented
726	#462	C₂²×C₃₁	1	2	yes	complemented
727	#461	C₂²×C₃₁	1	2	yes	complemented
728	#460	C₂²×C₃₁	1	2	yes	complemented
729	#460	C₂²×C₃₁	1	2	yes	complemented
730	#460	C₂²×C₃₁	1	2	yes	complemented
731	#459	C₂²×C₃₁	1	2	yes	complemented
732	#452	C₂²×C₃₁	1	2	yes	—
733	#452	C₂²×C₃₁	1	2	yes	—
734	#452	C₂²×C₃₁	1	2	yes	—
735	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
736	#452	C₂²×C₃₁	1	2	yes	complemented
737	#452	C₂²×C₃₁	1	2	yes	complemented
738	#452	C₂²×C₃₁	1	2	yes	complemented
739	#452	C₂²×C₃₁	1	2	yes	complemented
740	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
741	#452	C₂²×C₃₁	1	2	yes	complemented
742	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
743	#451	C₂²×C₃₁	1	2	yes	complemented
744	#450	C₂²×C₃₁	1	1	yes	characteristic, complemented
745	#450	C₂²×C₃₁	1	2	yes	complemented
746	#449	C₂²×C₃₁	1	2	yes	—
747	#449	C₂²×C₃₁	1	1	yes	characteristic, complemented
748	#449	C₂²×C₃₁	1	2	yes	complemented
749	#449	C₂²×C₃₁	1	1	yes	characteristic, complemented
750	#448	C₂²×C₃₁	1	1	yes	characteristic, complemented
751	#447	C₂²×C₃₁	1	1	yes	characteristic, complemented
752	#433	C₂²×C₃₁	1	2	yes	complemented
753	#433	C₂²×C₃₁	1	2	yes	complemented
754	#432	C₂²×C₃₁	1	2	yes	complemented
755	#431	C₂²×C₃₁	1	2	yes	complemented
756	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
757	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
758	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
759	#418	C₂²×C₃₁	1	1	yes	characteristic, complemented
760	#417	C₂²×C₃₁	1	1	yes	characteristic
761	#417	C₂²×C₃₁	1	1	yes	characteristic
762	#416	C₂²×C₃₁	1	1	yes	characteristic
763	#416	C₂²×C₃₁	1	1	yes	characteristic
764	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
765	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic, complemented
766	#407	C₂²×C₃₁	1	1	yes	characteristic
767	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
768	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
769	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
770	C₂×C₃₁	—	2	2	no	—
771	C₂×C₃₁	—	4	1	no	—
772	C₂×C₃₁	—	4	1	no	—
773	C₂×C₃₁	—	8	1	no	—
774	C₂×C₃₁	—	8	2	no	—
775	C₂×C₃₁	—	8	1	no	—
776	C₂×C₃₁	—	8	1	no	—
777	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
778	C₂×C₃₁	#3584	1	1	yes	characteristic
779	C₂×C₃₁	#3586	1	1	yes	characteristic
780	C₂×#41	—	2	1	no	—
781	C₂×#41	—	2	1	no	—
782	C₂×#41	—	2	1	no	—
783	C₂×#41	—	2	1	no	—
784	C₂×#41	—	4	2	no	—
785	C₂×#41	—	4	2	no	—
786	C₂×#41	—	4	2	no	—
787	C₂×#41	—	4	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	1	yes	characteristic
791	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
792	C₂×#41	C₂³×C₃₁	1	2	yes	—
793	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
794	C₂×#41	C₂³×C₃₁	1	2	yes	—
795	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
796	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
797	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
798	C₂²×D₄	—	2	1	no	—
799	C₂²×D₄	—	2	1	no	—
800	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
801	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
802	C₂³×C₄	—	2	1	no	—
803	C₂³×C₄	—	2	1	no	—
804	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
805	#137	—	4	2	no	—
806	#137	—	4	2	no	—
807	#137	—	4	2	no	—
808	AGL(1,ℤ/8)	—	4	2	no	—
809	#135	—	4	2	no	—
810	#135	—	4	2	no	—
811	C₂×Q₁₆	—	4	2	no	—
812	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
813	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
814	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
815	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
816	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
817	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
818	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
819	C₂×SD₁₆	—	4	2	no	—
820	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
821	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
822	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
823	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
824	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
825	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
826	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
827	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
828	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
829	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
830	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
831	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
832	C₂×D₈	C₂³×C₃₁	1	2	yes	—
833	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
834	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
835	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
836	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
837	C₄⋊Q₈	—	2	1	no	—
838	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
839	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
840	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
841	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
842	#127	C₂³×C₃₁	1	2	yes	—
843	#127	C₂³×C₃₁	1	2	yes	—
844	#126	—	2	2	no	—
845	#126	—	2	2	no	—
846	#126	—	2	2	no	—
847	#126	—	2	2	no	—
848	#125	—	2	2	no	—
849	#125	—	2	2	no	—
850	#125	—	2	1	no	—
851	#125	—	2	2	no	—
852	#125	C₂³×C₃₁	1	2	yes	—
853	#124	—	2	2	no	—
854	#124	C₂³×C₃₁	1	2	yes	—
855	#124	C₂³×C₃₁	1	2	yes	—
856	#124	C₂³×C₃₁	1	2	yes	—
857	#124	C₂³×C₃₁	1	2	yes	—
858	#124	C₂³×C₃₁	1	2	yes	—
859	#123	—	2	1	no	—
860	#123	—	2	2	no	—
861	#123	—	2	2	no	—
862	#123	—	2	2	no	—
863	#123	—	2	2	no	—
864	#123	—	2	2	no	—
865	#123	—	2	2	no	—
866	#123	—	2	2	no	—
867	C₂²⋊Q₈	—	2	1	no	—
868	C₂²⋊Q₈	—	2	1	no	—
869	C₂²⋊Q₈	—	2	2	no	—
870	C₂²⋊Q₈	—	2	1	no	—
871	C₂²⋊Q₈	—	2	1	no	—
872	C₂²⋊Q₈	—	2	1	no	—
873	C₂²⋊Q₈	—	2	2	no	—
874	C₂²⋊Q₈	—	2	1	no	—
875	C₂²⋊Q₈	—	2	2	no	—
876	C₂²⋊Q₈	—	2	1	no	—
877	C₂²⋊Q₈	—	2	1	no	—
878	C₂²⋊Q₈	—	2	2	no	—
879	C₂²⋊Q₈	—	2	2	no	—
880	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
881	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
882	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
883	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
884	#121	—	2	2	no	—
885	#121	—	2	2	no	—
886	#121	—	2	2	no	—
887	#121	—	2	2	no	—
888	#121	—	2	1	no	—
889	#121	—	2	1	no	—
890	#121	—	2	1	no	—
891	#121	—	2	2	no	—
892	#121	—	2	1	no	—
893	#121	—	2	2	no	—
894	#121	C₂³×C₃₁	1	1	yes	characteristic
895	#121	C₂³×C₃₁	1	1	yes	characteristic
896	#120	—	2	1	no	—
897	#120	—	2	2	no	—
898	#120	—	2	2	no	—
899	#120	—	2	2	no	—
900	#120	—	2	2	no	—
901	C₄×Q₈	—	2	1	no	—
902	C₄×Q₈	—	2	1	no	—
903	C₄×Q₈	—	2	2	no	—
904	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
905	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
906	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
907	C₄×D₄	—	2	1	no	—
908	C₄×D₄	—	2	1	no	—
909	C₄×D₄	—	2	2	no	—
910	C₄×D₄	—	2	2	no	—
911	C₄×D₄	—	2	2	no	—
912	C₄×D₄	—	2	2	no	—
913	C₄×D₄	—	2	2	no	—
914	C₄×D₄	—	2	2	no	—
915	C₄×D₄	C₂³×C₃₁	1	2	yes	—
916	#117	—	2	2	no	—
917	#117	—	2	1	no	—
918	#117	—	2	2	no	—
919	#117	—	2	2	no	—
920	#117	D₄×C₃₁	1	1	yes	characteristic
921	#117	D₄×C₃₁	1	2	yes	—
922	#117	D₄×C₃₁	1	1	yes	characteristic
923	#117	C₂³×C₃₁	1	1	yes	characteristic
924	#117	C₂³×C₃₁	1	1	yes	characteristic
925	#117	C₂³×C₃₁	1	1	yes	characteristic
926	#117	C₂³×C₃₁	1	2	yes	—
927	C₂×C₄⋊C₄	—	2	1	no	—
928	C₂×C₄⋊C₄	—	2	1	no	—
929	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
930	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
931	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
932	C₂×C₂²⋊C₄	—	2	1	no	—
933	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
934	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
935	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
936	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
937	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
938	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
939	#103	C₂³×C₃₁	1	2	yes	—
940	#103	C₂³×C₃₁	1	2	yes	—
941	#103	C₂³×C₃₁	1	1	yes	characteristic
942	#103	C₂³×C₃₁	1	1	yes	characteristic
943	#103	C₂³×C₃₁	1	1	yes	characteristic
944	#103	C₂³×C₃₁	1	1	yes	characteristic
945	#103	C₂³×C₃₁	1	2	yes	—
946	#103	C₂³×C₃₁	1	2	yes	—
947	#103	C₂³×C₃₁	1	2	yes	—
948	#103	C₂³×C₃₁	1	2	yes	—
949	#102	C₂³×C₃₁	1	2	yes	—
950	#102	C₂³×C₃₁	1	2	yes	—
951	#102	C₂³×C₃₁	1	1	yes	characteristic
952	#102	C₂³×C₃₁	1	1	yes	characteristic
953	#102	C₂³×C₃₁	1	1	yes	characteristic
954	#102	C₂³×C₃₁	1	1	yes	characteristic
955	#102	C₂³×C₃₁	1	2	yes	—
956	#102	C₂³×C₃₁	1	2	yes	—
957	#102	C₂³×C₃₁	1	2	yes	—
958	#102	C₂³×C₃₁	1	2	yes	—
959	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
960	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
961	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
962	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
963	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
964	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
965	#97	C₂³×C₃₁	1	2	yes	—
966	#97	C₂³×C₃₁	1	2	yes	—
967	C₄×C₈	C₂³×C₃₁	1	2	yes	—
968	C₄×C₈	C₂³×C₃₁	1	2	yes	—
969	C₃₁	#60816	1	1	yes	characteristic, direct product factor, Sylow
970	C₂⁴	—	2	1	no	—
971	C₂⁴	—	2	1	no	—
972	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
973	#41	—	2	2	no	—
974	#41	—	2	2	no	—
975	#41	—	2	2	no	—
976	#41	—	2	2	no	—
977	#41	—	2	2	no	—
978	#41	—	2	2	no	—
979	#41	—	4	2	no	—
980	#41	—	4	2	no	—
981	#41	—	4	2	no	—
982	#41	—	4	1	no	—
983	#41	—	4	1	no	—
984	#41	—	4	2	no	—
985	#41	—	4	1	no	—
986	#41	—	4	1	no	—
987	#41	—	4	4	no	—
988	#41	—	4	4	no	—
989	#41	—	4	4	no	—
990	#41	—	4	4	no	—
991	C₂×Q₈	—	2	1	no	—
992	C₂×Q₈	—	2	1	no	—
993	C₂×Q₈	—	2	1	no	—
994	C₂×Q₈	—	2	2	no	—
995	C₂×Q₈	—	2	2	no	—
996	C₂×Q₈	—	2	2	no	—
997	C₂×Q₈	—	2	2	no	—
998	C₂×Q₈	—	2	2	no	—
999	C₂×Q₈	—	4	1	no	—
1000	C₂×Q₈	—	4	1	no	—
1001	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1002	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1003	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1004	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1005	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1006	C₂×D₄	—	2	1	no	—
1007	C₂×D₄	—	2	1	no	—
1008	C₂×D₄	—	2	2	no	—
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	1	no	—
1012	C₂×D₄	—	2	2	no	—
1013	C₂×D₄	—	2	1	no	—
1014	C₂×D₄	—	2	1	no	—
1015	C₂×D₄	—	2	1	no	—
1016	C₂×D₄	—	2	1	no	—
1017	C₂×D₄	—	2	2	no	—
1018	C₂×D₄	—	2	2	no	—
1019	C₂×D₄	—	2	2	no	—
1020	C₂×D₄	—	2	2	no	—
1021	C₂×D₄	—	2	2	no	—
1022	C₂×D₄	—	2	2	no	—
1023	C₂×D₄	—	4	1	no	—
1024	C₂×D₄	—	4	1	no	—
1025	C₂×D₄	—	4	4	no	—
1026	C₂×D₄	—	4	4	no	—
1027	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1028	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1029	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1030	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1031	C₂²×C₄	—	2	2	no	—
1032	C₂²×C₄	—	2	2	no	—
1033	C₂²×C₄	—	2	1	no	—
1034	C₂²×C₄	—	2	1	no	—
1035	C₂²×C₄	—	2	1	no	—
1036	C₂²×C₄	—	2	1	no	—
1037	C₂²×C₄	—	2	1	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	1	no	—
1043	C₂²×C₄	—	2	1	no	—
1044	C₂²×C₄	—	2	2	no	—
1045	C₂²×C₄	—	4	4	no	—
1046	C₂²×C₄	—	4	4	no	—
1047	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1048	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1049	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1050	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
1051	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
1052	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1053	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1054	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1055	Q₁₆	—	4	2	no	—
1056	Q₁₆	—	4	2	no	—
1057	Q₁₆	—	4	1	no	—
1058	Q₁₆	—	4	1	no	—
1059	Q₁₆	—	4	2	no	—
1060	Q₁₆	—	4	2	no	—
1061	Q₁₆	—	4	2	no	—
1062	SD₁₆	—	4	2	no	—
1063	SD₁₆	—	4	2	no	—
1064	SD₁₆	—	4	1	no	—
1065	SD₁₆	—	4	1	no	—
1066	SD₁₆	—	4	1	no	—
1067	SD₁₆	—	4	1	no	—
1068	SD₁₆	—	4	2	no	—
1069	SD₁₆	—	4	2	no	—
1070	SD₁₆	—	4	2	no	—
1071	SD₁₆	—	4	2	no	—
1072	D₈	—	4	1	no	—
1073	D₈	—	4	1	no	—
1074	D₈	—	4	2	no	—
1075	M₁₆	—	2	2	no	—
1076	M₁₆	—	2	2	no	—
1077	C₂×C₈	—	2	2	no	—
1078	C₂×C₈	—	2	2	no	—
1079	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1080	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1081	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1082	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1083	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1084	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1085	C₄⋊C₄	—	2	1	no	—
1086	C₄⋊C₄	—	2	2	no	—
1087	C₄⋊C₄	—	2	2	no	—
1088	C₄⋊C₄	—	2	2	no	—
1089	C₄⋊C₄	—	2	2	no	—
1090	C₄⋊C₄	—	2	2	no	—
1091	C₄⋊C₄	—	2	2	no	—
1092	C₄⋊C₄	—	2	2	no	—
1093	C₄⋊C₄	—	2	2	no	—
1094	C₄⋊C₄	—	2	1	no	—
1095	C₄⋊C₄	—	2	2	no	—
1096	C₄⋊C₄	—	2	2	no	—
1097	C₄⋊C₄	—	2	2	no	—
1098	C₄⋊C₄	—	2	2	no	—
1099	C₄⋊C₄	—	2	2	no	—
1100	C₄⋊C₄	—	2	1	no	—
1101	C₄⋊C₄	—	2	2	no	—
1102	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1103	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1104	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1105	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1106	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1107	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1108	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1109	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1110	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	2	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	1	no	—
1115	C₂²⋊C₄	—	2	1	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	2	no	—
1118	C₂²⋊C₄	—	2	2	no	—
1119	C₂²⋊C₄	—	2	2	no	—
1120	C₂²⋊C₄	—	2	2	no	—
1121	C₂²⋊C₄	—	2	2	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	2	no	—
1124	C₂²⋊C₄	—	2	2	no	—
1125	C₂²⋊C₄	—	2	2	no	—
1126	C₂²⋊C₄	—	2	2	no	—
1127	C₂²⋊C₄	—	2	1	no	—
1128	C₂²⋊C₄	—	2	2	no	—
1129	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1130	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1131	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1132	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1133	C₄²	—	2	2	no	—
1134	C₄²	—	2	2	no	—
1135	C₄²	—	2	2	no	—
1136	C₄²	—	2	1	no	—
1137	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1138	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1139	C₄²	C₂⁴×C₃₁	1	2	yes	—
1140	C₄²	C₂⁴×C₃₁	1	2	yes	—
1141	C₂³	—	2	2	no	—
1142	C₂³	—	2	1	no	—
1143	C₂³	—	2	2	no	—
1144	C₂³	—	2	1	no	—
1145	C₂³	—	2	1	no	—
1146	C₂³	—	4	1	no	—
1147	C₂³	—	4	1	no	—
1148	C₂³	—	4	2	no	—
1149	C₂³	—	4	2	no	—
1150	C₂³	—	8	1	no	—
1151	C₂³	—	8	1	no	—
1152	C₂³	—	8	1	no	—
1153	C₂³	—	8	1	no	—
1154	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1155	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1156	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1157	Q₈	—	2	2	no	—
1158	Q₈	—	2	1	no	—
1159	Q₈	—	2	2	no	—
1160	Q₈	—	2	1	no	—
1161	Q₈	—	2	2	no	—
1162	Q₈	—	2	1	no	—
1163	Q₈	—	2	1	no	—
1164	Q₈	—	2	2	no	—
1165	Q₈	—	2	1	no	—
1166	Q₈	—	2	1	no	—
1167	Q₈	—	4	2	no	—
1168	Q₈	—	4	2	no	—
1169	Q₈	—	4	2	no	—
1170	Q₈	—	8	2	no	—
1171	D₄	—	2	1	no	—
1172	D₄	—	2	1	no	—
1173	D₄	—	2	2	no	—
1174	D₄	—	2	1	no	—
1175	D₄	—	2	1	no	—
1176	D₄	—	2	2	no	—
1177	D₄	—	2	1	no	—
1178	D₄	—	2	1	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	4	2	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	—	8	2	no	—
1190	D₄	—	8	2	no	—
1191	D₄	—	8	2	no	—
1192	D₄	—	8	2	no	—
1193	D₄	—	8	1	no	—
1194	C₂×C₄	—	2	2	no	—
1195	C₂×C₄	—	2	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	2	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	2	no	—
1206	C₂×C₄	—	2	2	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	4	2	no	—
1210	C₂×C₄	—	4	2	no	—
1211	C₂×C₄	—	4	4	no	—
1212	C₂×C₄	—	4	2	no	—
1213	C₂×C₄	—	4	2	no	—
1214	C₂×C₄	—	4	4	no	—
1215	C₂×C₄	—	4	2	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	4	2	no	—
1219	C₂×C₄	—	4	2	no	—
1220	C₂×C₄	—	4	2	no	—
1221	C₂×C₄	—	8	2	no	—
1222	C₂×C₄	—	8	1	no	—
1223	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1224	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1225	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1226	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1227	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1228	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1229	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1230	C₂×C₄	C₃₁×H(5,𝔽₂)	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	1	no	—
1234	C₈	—	2	1	no	—
1235	C₈	—	2	1	no	—
1236	C₈	—	2	1	no	—
1237	C₈	—	2	2	no	—
1238	C₈	—	2	2	no	—
1239	C₂²	—	2	1	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	1	no	—
1247	C₂²	—	4	2	no	—
1248	C₂²	—	4	1	no	—
1249	C₂²	—	4	1	no	—
1250	C₂²	—	4	1	no	—
1251	C₂²	—	4	1	no	—
1252	C₂²	—	4	2	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	1	no	—
1255	C₂²	—	4	1	no	—
1256	C₂²	—	4	2	no	—
1257	C₂²	—	4	1	no	—
1258	C₂²	—	4	1	no	—
1259	C₂²	—	8	2	no	—
1260	C₂²	—	8	4	no	—
1261	C₂²	—	8	4	no	—
1262	C₂²	C₃₁×#535	1	2	yes	—
1263	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1264	C₄	—	2	1	no	—
1265	C₄	—	2	1	no	—
1266	C₄	—	2	2	no	—
1267	C₄	—	2	2	no	—
1268	C₄	—	2	2	no	—
1269	C₄	—	2	2	no	—
1270	C₄	—	4	2	no	—
1271	C₄	—	4	1	no	—
1272	C₄	—	4	1	no	—
1273	C₄	—	4	1	no	—
1274	C₄	—	4	2	no	—
1275	C₄	—	4	2	no	—
1276	C₄	—	4	1	no	—
1277	C₄	—	4	1	no	—
1278	C₄	C₃₁×#535	1	2	yes	—
1279	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1280	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1281	C₂	—	2	2	no	—
1282	C₂	—	4	1	no	—
1283	C₂	—	4	1	no	—
1284	C₂	—	8	2	no	—
1285	C₂	—	8	1	no	—
1286	C₂	—	8	1	no	—
1287	C₂	—	8	1	no	—
1288	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
1289	C₂	C₃₁×#3584	1	1	yes	characteristic
1290	C₂	C₃₁×#3586	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 ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3495	C₂	semidirect
2. C₃₁×#3449	C₂	semidirect
3. C₃₁×#3225	C₂	semidirect
4. C₃₁×#3224	C₂	semidirect
5. C₃₁×#3223	C₂	semidirect
6. C₃₁×#3222	C₂	semidirect
7. C₃₁×#3219	C₂	semidirect
8. C₃₁×#3216	C₂	semidirect
9. C₃₁×#3212	C₂	semidirect
10. C₃₁×#3210	C₂	semidirect
11. C₃₁×#3156	C₂	semidirect
12. C₃₁×#3154	C₂	semidirect
13. C₃₁×#3137	C₂	semidirect
14. C₃₁×#3136	C₂	semidirect
15. C₃₁×#3046	C₂	semidirect
16. C₃₁×#3045	C₂	semidirect
17. C₃₁×#3044	C₂	semidirect
18. C₃₁×#3043	C₂	semidirect
19. C₃₁×#3007	C₂	semidirect
20. C₃₁×#3005	C₂	semidirect
21. C₃₁×#3002	C₂	semidirect
22. C₂×C₃₁×#452	C₂	semidirect
23. C₃₁×#2924	C₂	semidirect
28. C₂×C₃₁×#137	C₂²	semidirect
29. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
32. C₂²×Q₁₆×C₃₁	C₂²	semidirect
33. C₂²×SD₁₆×C₃₁	C₂²	semidirect
40. C₃₁×#544	C₂²	semidirect
41. C₃₁×#542	C₂²	semidirect
42. C₃₁×#541	C₂²	semidirect
48. C₃₁×#536	C₂²	semidirect
53. C₃₁×#533	C₂²	semidirect
56. C₃₁×#529	C₂²	semidirect
62. C₃₁×#520	C₂²	semidirect
63. C₃₁×#519	C₂²	semidirect
65. C₃₁×#497	C₂²	semidirect
66. C₃₁×#497	C₂²	semidirect
67. C₃₁×#497	C₂²	semidirect
68. C₃₁×#496	C₂²	semidirect
69. C₃₁×#495	C₂²	semidirect
70. C₃₁×#495	C₂²	semidirect
71. C₃₁×#494	C₂²	semidirect
72. C₃₁×#492	C₂²	semidirect
73. C₃₁×#491	C₂²	semidirect
74. C₃₁×#490	C₂²	semidirect
75. C₃₁×#489	C₂²	semidirect
76. C₃₁×#489	C₂²	semidirect
77. C₃₁×#488	C₂²	semidirect
78. C₃₁×#488	C₂²	semidirect
79. C₃₁×#487	C₂²	semidirect
80. C₃₁×#486	C₂²	semidirect
81. C₃₁×#464	C₂²	semidirect
82. C₃₁×#464	C₂²	semidirect
83. C₃₁×#464	C₂²	semidirect
84. C₃₁×#464	C₂²	semidirect
85. C₃₁×#464	C₂²	semidirect
86. C₃₁×#464	C₂²	semidirect
87. C₃₁×#463	C₂²	semidirect
88. C₃₁×#463	C₂²	semidirect
89. C₃₁×#462	C₂²	semidirect
90. C₃₁×#462	C₂²	semidirect
91. C₃₁×#462	C₂²	semidirect
92. C₃₁×#461	C₂²	semidirect
93. C₃₁×#460	C₂²	semidirect
94. C₃₁×#460	C₂²	semidirect
95. C₃₁×#460	C₂²	semidirect
96. C₃₁×#459	C₂²	semidirect
100. C₃₁×#452	C₂²	semidirect
101. C₃₁×#452	C₂²	semidirect
102. C₃₁×#452	C₂²	semidirect
103. C₃₁×#452	C₂²	semidirect
104. C₃₁×#452	C₂²	semidirect
105. C₃₁×#452	C₂²	semidirect
106. C₃₁×#452	C₂²	semidirect
107. C₃₁×#451	C₂²	semidirect
108. C₃₁×#451	C₂²	semidirect
109. C₃₁×#450	C₂²	semidirect
110. C₃₁×#450	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×#433	C₂²	semidirect
118. C₃₁×#433	C₂²	semidirect
119. C₃₁×#432	C₂²	semidirect
120. C₃₁×#431	C₂²	semidirect
121. C₃₁×#424	C₂²	semidirect
122. C₃₁×#424	C₂²	semidirect
123. C₃₁×#419	C₂²	semidirect
124. C₃₁×#418	C₂²	semidirect
129. C₂×C₃₁×#103	C₂²	semidirect
130. C₂×C₃₁×#102	C₂²	semidirect
133. C₃₁×#405	C₂²	semidirect
134. C₃₁×#405	C₂²	semidirect
495. #60816	C₃₁	direct (N × H)
594. #3495	C₂×C₃₁	semidirect
595. #3449	C₂×C₃₁	semidirect
596. #3225	C₂×C₃₁	semidirect
597. #3224	C₂×C₃₁	semidirect
598. #3223	C₂×C₃₁	semidirect
599. #3222	C₂×C₃₁	semidirect
600. #3219	C₂×C₃₁	semidirect
601. #3216	C₂×C₃₁	semidirect
602. #3212	C₂×C₃₁	semidirect
603. #3210	C₂×C₃₁	semidirect
604. #3156	C₂×C₃₁	semidirect
605. #3154	C₂×C₃₁	semidirect
606. #3137	C₂×C₃₁	semidirect
607. #3136	C₂×C₃₁	semidirect
608. #3046	C₂×C₃₁	semidirect
609. #3045	C₂×C₃₁	semidirect
610. #3044	C₂×C₃₁	semidirect
611. #3043	C₂×C₃₁	semidirect
612. #3007	C₂×C₃₁	semidirect
613. #3005	C₂×C₃₁	semidirect
614. #3002	C₂×C₃₁	semidirect
615. C₂×#452	C₂×C₃₁	semidirect
616. #2924	C₂×C₃₁	semidirect
663. C₂×#137	C₂²×C₃₁	semidirect
664. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
667. C₂²×Q₁₆	C₂²×C₃₁	semidirect
668. C₂²×SD₁₆	C₂²×C₃₁	semidirect
675. #544	C₂²×C₃₁	semidirect
676. #542	C₂²×C₃₁	semidirect
677. #541	C₂²×C₃₁	semidirect
683. #536	C₂²×C₃₁	semidirect
688. #533	C₂²×C₃₁	semidirect
691. #529	C₂²×C₃₁	semidirect
697. #520	C₂²×C₃₁	semidirect
698. #519	C₂²×C₃₁	semidirect
700. #497	C₂²×C₃₁	semidirect
701. #497	C₂²×C₃₁	semidirect
702. #497	C₂²×C₃₁	semidirect
703. #496	C₂²×C₃₁	semidirect
704. #495	C₂²×C₃₁	semidirect
705. #495	C₂²×C₃₁	semidirect
706. #494	C₂²×C₃₁	semidirect
707. #492	C₂²×C₃₁	semidirect
708. #491	C₂²×C₃₁	semidirect
709. #490	C₂²×C₃₁	semidirect
710. #489	C₂²×C₃₁	semidirect
711. #489	C₂²×C₃₁	semidirect
712. #488	C₂²×C₃₁	semidirect
713. #488	C₂²×C₃₁	semidirect
714. #487	C₂²×C₃₁	semidirect
715. #486	C₂²×C₃₁	semidirect
716. #464	C₂²×C₃₁	semidirect
717. #464	C₂²×C₃₁	semidirect
718. #464	C₂²×C₃₁	semidirect
719. #464	C₂²×C₃₁	semidirect
720. #464	C₂²×C₃₁	semidirect
721. #464	C₂²×C₃₁	semidirect
722. #463	C₂²×C₃₁	semidirect
723. #463	C₂²×C₃₁	semidirect
724. #462	C₂²×C₃₁	semidirect
725. #462	C₂²×C₃₁	semidirect
726. #462	C₂²×C₃₁	semidirect
727. #461	C₂²×C₃₁	semidirect
728. #460	C₂²×C₃₁	semidirect
729. #460	C₂²×C₃₁	semidirect
730. #460	C₂²×C₃₁	semidirect
731. #459	C₂²×C₃₁	semidirect
735. #452	C₂²×C₃₁	semidirect
736. #452	C₂²×C₃₁	semidirect
737. #452	C₂²×C₃₁	semidirect
738. #452	C₂²×C₃₁	semidirect
739. #452	C₂²×C₃₁	semidirect
740. #452	C₂²×C₃₁	semidirect
741. #452	C₂²×C₃₁	semidirect
742. #451	C₂²×C₃₁	semidirect
743. #451	C₂²×C₃₁	semidirect
744. #450	C₂²×C₃₁	semidirect
745. #450	C₂²×C₃₁	semidirect
747. #449	C₂²×C₃₁	semidirect
748. #449	C₂²×C₃₁	semidirect
749. #449	C₂²×C₃₁	semidirect
750. #448	C₂²×C₃₁	semidirect
751. #447	C₂²×C₃₁	semidirect
752. #433	C₂²×C₃₁	semidirect
753. #433	C₂²×C₃₁	semidirect
754. #432	C₂²×C₃₁	semidirect
755. #431	C₂²×C₃₁	semidirect
756. #424	C₂²×C₃₁	semidirect
757. #424	C₂²×C₃₁	semidirect
758. #419	C₂²×C₃₁	semidirect
759. #418	C₂²×C₃₁	semidirect
764. C₂×#103	C₂²×C₃₁	semidirect
765. C₂×#102	C₂²×C₃₁	semidirect
768. #405	C₂²×C₃₁	semidirect
769. #405	C₂²×C₃₁	semidirect
969. C₃₁	#60816	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3495	2
C₃₁×#3449	2
C₃₁×#3225	2
C₃₁×#3224	2
C₃₁×#3223	2
C₃₁×#3222	2
C₃₁×#3219	2
C₃₁×#3216	2
C₃₁×#3212	2
C₃₁×#3210	2
C₃₁×#3156	2
C₃₁×#3154	2
C₃₁×#3137	2
C₃₁×#3136	2
C₃₁×#3046	2
C₃₁×#3045	2
C₃₁×#3044	2
C₃₁×#3043	2
C₃₁×#3007	2
C₃₁×#3005	2
C₃₁×#3002	2
C₂×C₃₁×#452	2
C₃₁×#2924	2
#60816	31

Subgroups — C31×#60816 #21517575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60816 #21517575