Subgroups — C₃₁×#61989 #21518748

Order 7936.

2138 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3308	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3306	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3265	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3264	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3251	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3247	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3213	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3114	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#463	C₂	1	2	yes	maximal, complemented
23	C₃₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₃₁	—	2	1	no	—
25	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
27	C₂²×D₈×C₃₁	C₂²	1	2	yes	—
28	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#555	—	2	1	no	—
31	C₃₁×#551	—	2	2	no	—
32	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
33	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
34	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#548	—	2	1	no	—
36	C₃₁×#548	C₂²	1	2	yes	complemented
37	C₃₁×#547	C₂²	1	1	yes	characteristic
38	C₃₁×#547	C₂²	1	2	yes	complemented
39	C₃₁×#546	—	2	1	no	—
40	C₃₁×#546	—	2	1	no	—
41	C₃₁×#546	—	2	2	no	—
42	C₃₁×#546	C₂²	1	2	yes	complemented
43	D₄²×C₃₁	C₂²	1	1	yes	characteristic
44	D₄²×C₃₁	C₂²	1	2	yes	complemented
45	D₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#542	—	2	1	no	—
47	C₃₁×#538	—	2	2	no	—
48	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#532	C₂²	1	2	yes	complemented
51	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#529	C₂²	1	2	yes	complemented
53	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
54	C₃₁×#525	—	2	2	no	—
55	C₃₁×#525	—	2	1	no	—
56	C₃₁×#518	—	2	1	no	—
57	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
60	C₃₁×#496	C₂²	1	2	yes	complemented
61	C₃₁×#496	C₂²	1	2	yes	complemented
62	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#489	C₂²	1	2	yes	complemented
65	C₃₁×#489	C₂²	1	2	yes	complemented
66	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#483	C₂²	1	2	yes	complemented
70	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#480	C₂²	1	2	yes	complemented
72	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#478	C₂²	1	2	yes	complemented
75	C₃₁×#477	C₂²	1	2	yes	complemented
76	C₃₁×#476	C₂²	1	2	yes	complemented
77	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#469	C₂²	1	2	yes	complemented
80	C₃₁×#468	C₂²	1	2	yes	complemented
81	C₃₁×#466	C₂²	1	2	yes	complemented
82	C₃₁×#466	C₂²	1	2	yes	complemented
83	C₃₁×#465	C₂²	1	2	yes	complemented
84	C₃₁×#465	C₂²	1	2	yes	complemented
85	C₃₁×#463	C₂²	1	1	yes	characteristic
86	C₃₁×#463	C₂²	1	2	yes	—
87	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#463	C₂²	1	2	yes	complemented
89	C₃₁×#463	C₂²	1	2	yes	complemented
90	C₃₁×#463	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×#463	C₂²	1	2	yes	complemented
95	C₃₁×#463	C₂²	1	2	yes	complemented
96	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#460	C₂²	1	2	yes	complemented
99	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#459	C₂²	1	1	yes	characteristic
101	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#459	C₂²	1	2	yes	complemented
103	C₃₁×#459	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×#449	C₂²	1	2	yes	complemented
107	C₃₁×#449	C₂²	1	2	yes	complemented
108	C₃₁×#448	C₂²	1	2	yes	complemented
109	C₃₁×#448	C₂²	1	2	yes	complemented
110	C₃₁×#447	C₂²	1	1	yes	characteristic
111	C₃₁×#447	C₂²	1	2	yes	—
112	C₃₁×#447	C₂²	1	2	yes	complemented
113	C₃₁×#447	C₂²	1	2	yes	complemented
114	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
115	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
116	C₃₁×#442	C₂²	1	2	yes	complemented
117	C₃₁×#442	C₂²	1	2	yes	complemented
118	C₃₁×#440	C₂²	1	2	yes	complemented
119	C₃₁×#440	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
123	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#435	C₂²	1	2	yes	complemented
125	C₃₁×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
127	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
128	C₃₁×#432	C₂²	1	2	yes	complemented
129	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
132	C₃₁×#417	C₂²	1	2	yes	complemented
133	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
134	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	—	2	2	no	—
138	C₂×#41×C₃₁	—	2	2	no	—
139	C₂×#41×C₃₁	—	2	1	no	—
140	C₂×#41×C₃₁	—	4	8	no	—
141	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
142	C₂×#41×C₃₁	C₂³	1	2	yes	—
143	C₂²×Q₈×C₃₁	—	2	1	no	—
144	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
145	C₂²×D₄×C₃₁	—	2	1	no	—
146	C₂²×D₄×C₃₁	—	2	1	no	—
147	C₂²×D₄×C₃₁	—	2	2	no	—
148	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
149	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
150	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
151	C₂³×C₄×C₃₁	—	2	2	no	—
152	C₂³×C₄×C₃₁	—	2	1	no	—
153	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
154	C₂×SD₁₆×C₃₁	—	4	4	no	—
155	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
162	C₂×D₈×C₃₁	—	4	4	no	—
163	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×D₈×C₃₁	C₂³	1	2	yes	—
165	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×D₈×C₃₁	C₂³	1	2	yes	—
167	C₂×D₈×C₃₁	C₂³	1	2	yes	—
168	C₂×D₈×C₃₁	C₂³	1	2	yes	—
169	C₂×D₈×C₃₁	C₂³	1	2	yes	—
170	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
171	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
172	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
173	C₃₁×C₄⋊Q₈	—	2	1	no	—
174	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
175	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
176	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
177	C₃₁×#127	C₂³	1	1	yes	characteristic
178	C₃₁×#127	C₂³	1	1	yes	characteristic
179	C₃₁×#127	C₂³	1	2	yes	—
180	C₃₁×#126	—	2	2	no	—
181	C₃₁×#126	—	2	2	no	—
182	C₃₁×#126	—	2	1	no	—
183	C₃₁×#125	C₂³	1	1	yes	characteristic
184	C₃₁×#124	—	2	1	no	—
185	C₃₁×#124	—	2	2	no	—
186	C₃₁×#124	—	2	2	no	—
187	C₃₁×#124	—	2	2	no	—
188	C₃₁×#124	—	2	1	no	—
189	C₃₁×#124	—	2	2	no	—
190	C₃₁×#124	C₂³	1	1	yes	characteristic
191	C₃₁×#124	C₂³	1	2	yes	—
192	C₃₁×#124	C₂³	1	2	yes	—
193	C₃₁×#124	C₂³	1	2	yes	—
194	C₃₁×#123	—	2	1	no	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×#123	—	2	2	no	—
197	C₃₁×#123	—	2	2	no	—
198	C₃₁×#123	—	2	2	no	—
199	C₃₁×#123	—	2	2	no	—
200	C₃₁×#123	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	—	2	1	no	—
202	C₃₁×C₂²⋊Q₈	—	2	1	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	—	2	1	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	—	2	2	no	—
208	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	1	no	—
214	C₃₁×#121	—	2	1	no	—
215	C₃₁×#121	—	2	1	no	—
216	C₃₁×#121	—	2	2	no	—
217	C₃₁×#121	—	2	1	no	—
218	C₃₁×#121	—	2	2	no	—
219	C₃₁×#121	—	2	1	no	—
220	C₃₁×#121	—	2	2	no	—
221	C₃₁×#121	C₂³	1	2	yes	—
222	C₃₁×#121	C₂³	1	1	yes	characteristic
223	C₃₁×#121	C₂³	1	2	yes	—
224	C₃₁×#121	C₂³	1	2	yes	—
225	C₃₁×#121	C₂³	1	2	yes	—
226	C₃₁×#120	—	2	2	no	—
227	C₃₁×#120	—	2	2	no	—
228	C₃₁×#120	—	2	2	no	—
229	C₃₁×#120	—	2	2	no	—
230	C₃₁×#120	—	2	2	no	—
231	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
232	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
234	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	—	2	2	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	—	2	1	no	—
239	C₄×D₄×C₃₁	—	2	2	no	—
240	C₄×D₄×C₃₁	—	2	2	no	—
241	C₄×D₄×C₃₁	—	2	1	no	—
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	2	no	—
244	C₄×D₄×C₃₁	—	2	1	no	—
245	C₄×D₄×C₃₁	—	2	2	no	—
246	C₄×D₄×C₃₁	—	2	1	no	—
247	C₄×D₄×C₃₁	—	2	1	no	—
248	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
249	C₄×D₄×C₃₁	D₄	1	2	yes	—
250	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₃₁	C₂³	1	2	yes	—
254	C₄×D₄×C₃₁	C₂³	1	2	yes	—
255	C₄×D₄×C₃₁	C₂³	1	2	yes	—
256	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₃₁	C₂³	1	2	yes	—
259	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₃₁	C₂³	1	2	yes	—
261	C₃₁×#117	—	2	1	no	—
262	C₃₁×#117	—	2	1	no	—
263	C₃₁×#117	—	2	2	no	—
264	C₃₁×#117	D₄	1	2	yes	—
265	C₃₁×#117	D₄	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
270	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
272	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
273	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
274	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
275	C₃₁×#107	C₂³	1	1	yes	characteristic
276	C₃₁×#107	C₂³	1	1	yes	characteristic
277	C₃₁×#107	C₂³	1	2	yes	—
278	C₃₁×#106	C₂³	1	1	yes	characteristic
279	C₃₁×#106	C₂³	1	1	yes	characteristic
280	C₃₁×#106	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
285	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	1	yes	characteristic
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	1	yes	characteristic
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	1	yes	characteristic
304	C₃₁×#102	C₂³	1	1	yes	characteristic
305	C₃₁×#102	C₂³	1	2	yes	—
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×#102	C₂³	1	2	yes	—
308	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₃₁×#97	C₂³	1	2	yes	—
313	C₃₁×#97	C₂³	1	2	yes	—
314	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
315	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
316	C₂⁴×C₃₁	—	2	1	no	—
317	C₂⁴×C₃₁	—	2	2	no	—
318	C₂⁴×C₃₁	—	2	2	no	—
319	#41×C₃₁	—	2	4	no	—
320	#41×C₃₁	—	4	8	no	—
321	#41×C₃₁	—	4	4	no	—
322	#41×C₃₁	—	4	2	no	—
323	#41×C₃₁	—	4	2	no	—
324	#41×C₃₁	—	4	8	no	—
325	#41×C₃₁	—	4	4	no	—
326	#41×C₃₁	—	4	4	no	—
327	C₂×Q₈×C₃₁	—	2	2	no	—
328	C₂×Q₈×C₃₁	—	2	1	no	—
329	C₂×Q₈×C₃₁	—	2	2	no	—
330	C₂×Q₈×C₃₁	—	4	2	no	—
331	C₂×Q₈×C₃₁	—	4	2	no	—
332	C₂×Q₈×C₃₁	—	4	4	no	—
333	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
334	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
335	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
336	C₂×D₄×C₃₁	—	2	4	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	—	2	2	no	—
341	C₂×D₄×C₃₁	—	2	2	no	—
342	C₂×D₄×C₃₁	—	2	1	no	—
343	C₂×D₄×C₃₁	—	2	2	no	—
344	C₂×D₄×C₃₁	—	2	1	no	—
345	C₂×D₄×C₃₁	—	2	2	no	—
346	C₂×D₄×C₃₁	—	2	1	no	—
347	C₂×D₄×C₃₁	—	2	2	no	—
348	C₂×D₄×C₃₁	—	2	1	no	—
349	C₂×D₄×C₃₁	—	2	2	no	—
350	C₂×D₄×C₃₁	—	2	1	no	—
351	C₂×D₄×C₃₁	—	2	1	no	—
352	C₂×D₄×C₃₁	—	2	2	no	—
353	C₂×D₄×C₃₁	—	4	2	no	—
354	C₂×D₄×C₃₁	—	4	1	no	—
355	C₂×D₄×C₃₁	—	4	2	no	—
356	C₂×D₄×C₃₁	—	4	2	no	—
357	C₂×D₄×C₃₁	—	4	8	no	—
358	C₂×D₄×C₃₁	—	4	4	no	—
359	C₂×D₄×C₃₁	—	4	4	no	—
360	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
361	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
362	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
363	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
364	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
366	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₃₁	—	2	1	no	—
368	C₂²×C₄×C₃₁	—	2	2	no	—
369	C₂²×C₄×C₃₁	—	2	2	no	—
370	C₂²×C₄×C₃₁	—	2	1	no	—
371	C₂²×C₄×C₃₁	—	2	1	no	—
372	C₂²×C₄×C₃₁	—	2	2	no	—
373	C₂²×C₄×C₃₁	—	2	1	no	—
374	C₂²×C₄×C₃₁	—	2	2	no	—
375	C₂²×C₄×C₃₁	—	2	1	no	—
376	C₂²×C₄×C₃₁	—	2	2	no	—
377	C₂²×C₄×C₃₁	—	2	1	no	—
378	C₂²×C₄×C₃₁	—	2	2	no	—
379	C₂²×C₄×C₃₁	—	2	2	no	—
380	C₂²×C₄×C₃₁	—	4	8	no	—
381	C₂²×C₄×C₃₁	—	4	4	no	—
382	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
383	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
385	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
387	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
388	SD₁₆×C₃₁	—	2	2	no	—
389	SD₁₆×C₃₁	—	2	4	no	—
390	SD₁₆×C₃₁	—	4	2	no	—
391	SD₁₆×C₃₁	—	4	2	no	—
392	SD₁₆×C₃₁	—	4	1	no	—
393	SD₁₆×C₃₁	—	4	2	no	—
394	SD₁₆×C₃₁	—	4	2	no	—
395	D₈×C₃₁	—	2	2	no	—
396	D₈×C₃₁	—	2	4	no	—
397	D₈×C₃₁	—	4	2	no	—
398	D₈×C₃₁	—	4	2	no	—
399	D₈×C₃₁	—	4	2	no	—
400	D₈×C₃₁	—	4	1	no	—
401	D₈×C₃₁	—	4	2	no	—
402	M₁₆×C₃₁	—	4	2	no	—
403	C₂×C₈×C₃₁	—	4	2	no	—
404	C₂×C₈×C₃₁	—	4	2	no	—
405	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
407	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
410	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₃₁	—	2	1	no	—
412	C₄⋊C₄×C₃₁	—	2	2	no	—
413	C₄⋊C₄×C₃₁	—	2	1	no	—
414	C₄⋊C₄×C₃₁	—	2	1	no	—
415	C₄⋊C₄×C₃₁	—	2	1	no	—
416	C₄⋊C₄×C₃₁	—	2	1	no	—
417	C₄⋊C₄×C₃₁	—	2	2	no	—
418	C₄⋊C₄×C₃₁	—	2	2	no	—
419	C₄⋊C₄×C₃₁	—	2	1	no	—
420	C₄⋊C₄×C₃₁	—	2	1	no	—
421	C₄⋊C₄×C₃₁	—	2	2	no	—
422	C₄⋊C₄×C₃₁	—	2	1	no	—
423	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
424	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
425	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
426	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
427	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
429	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
430	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
431	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	1	no	—
434	C₂²⋊C₄×C₃₁	—	2	1	no	—
435	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
443	C₂²⋊C₄×C₃₁	—	2	1	no	—
444	C₂²⋊C₄×C₃₁	—	2	2	no	—
445	C₂²⋊C₄×C₃₁	—	2	1	no	—
446	C₂²⋊C₄×C₃₁	—	2	2	no	—
447	C₂²⋊C₄×C₃₁	—	2	1	no	—
448	C₂²⋊C₄×C₃₁	—	2	2	no	—
449	C₂²⋊C₄×C₃₁	—	2	2	no	—
450	C₂²⋊C₄×C₃₁	—	2	2	no	—
451	C₂²⋊C₄×C₃₁	—	2	2	no	—
452	C₂²⋊C₄×C₃₁	—	2	2	no	—
453	C₂²⋊C₄×C₃₁	—	2	2	no	—
454	C₂²⋊C₄×C₃₁	—	2	1	no	—
455	C₂²⋊C₄×C₃₁	—	2	2	no	—
456	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
457	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
458	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
459	C₄²×C₃₁	—	2	2	no	—
460	C₄²×C₃₁	—	2	1	no	—
461	C₄²×C₃₁	C₂×D₄	1	2	yes	—
462	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
463	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
464	C₄²×C₃₁	C₂×D₄	1	2	yes	—
465	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
466	C₄²×C₃₁	C₂⁴	1	2	yes	—
467	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
468	#61989	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
469	C₂³×C₃₁	—	2	1	no	—
470	C₂³×C₃₁	—	2	1	no	—
471	C₂³×C₃₁	—	2	2	no	—
472	C₂³×C₃₁	—	2	2	no	—
473	C₂³×C₃₁	—	2	1	no	—
474	C₂³×C₃₁	—	4	4	no	—
475	C₂³×C₃₁	—	4	2	no	—
476	C₂³×C₃₁	—	4	2	no	—
477	C₂³×C₃₁	—	4	4	no	—
478	C₂³×C₃₁	—	4	4	no	—
479	C₂³×C₃₁	—	8	2	no	—
480	C₂³×C₃₁	—	8	1	no	—
481	C₂³×C₃₁	—	8	2	no	—
482	C₂³×C₃₁	—	8	2	no	—
483	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
484	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
485	Q₈×C₃₁	—	2	2	no	—
486	Q₈×C₃₁	—	2	1	no	—
487	Q₈×C₃₁	—	2	2	no	—
488	Q₈×C₃₁	—	2	1	no	—
489	Q₈×C₃₁	—	2	2	no	—
490	Q₈×C₃₁	—	4	4	no	—
491	Q₈×C₃₁	—	4	2	no	—
492	Q₈×C₃₁	—	8	2	no	—
493	D₄×C₃₁	—	2	4	no	—
494	D₄×C₃₁	—	2	1	no	—
495	D₄×C₃₁	—	2	2	no	—
496	D₄×C₃₁	—	2	2	no	—
497	D₄×C₃₁	—	2	1	no	—
498	D₄×C₃₁	—	2	1	no	—
499	D₄×C₃₁	—	2	2	no	—
500	D₄×C₃₁	—	2	1	no	—
501	D₄×C₃₁	—	2	1	no	—
502	D₄×C₃₁	—	2	2	no	—
503	D₄×C₃₁	—	4	2	no	—
504	D₄×C₃₁	—	4	4	no	—
505	D₄×C₃₁	—	4	4	no	—
506	D₄×C₃₁	—	4	4	no	—
507	D₄×C₃₁	—	4	4	no	—
508	D₄×C₃₁	—	4	4	no	—
509	D₄×C₃₁	—	4	4	no	—
510	D₄×C₃₁	—	4	2	no	—
511	D₄×C₃₁	—	4	2	no	—
512	D₄×C₃₁	—	8	2	no	—
513	D₄×C₃₁	—	8	1	no	—
514	D₄×C₃₁	—	8	1	no	—
515	D₄×C₃₁	—	8	2	no	—
516	D₄×C₃₁	—	8	1	no	—
517	D₄×C₃₁	—	8	2	no	—
518	D₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	complemented
519	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
520	C₂×C₄×C₃₁	—	2	4	no	—
521	C₂×C₄×C₃₁	—	2	2	no	—
522	C₂×C₄×C₃₁	—	2	2	no	—
523	C₂×C₄×C₃₁	—	2	1	no	—
524	C₂×C₄×C₃₁	—	2	2	no	—
525	C₂×C₄×C₃₁	—	2	1	no	—
526	C₂×C₄×C₃₁	—	2	1	no	—
527	C₂×C₄×C₃₁	—	2	1	no	—
528	C₂×C₄×C₃₁	—	2	1	no	—
529	C₂×C₄×C₃₁	—	2	2	no	—
530	C₂×C₄×C₃₁	—	2	1	no	—
531	C₂×C₄×C₃₁	—	2	2	no	—
532	C₂×C₄×C₃₁	—	2	1	no	—
533	C₂×C₄×C₃₁	—	4	2	no	—
534	C₂×C₄×C₃₁	—	4	1	no	—
535	C₂×C₄×C₃₁	—	4	2	no	—
536	C₂×C₄×C₃₁	—	4	4	no	—
537	C₂×C₄×C₃₁	—	4	4	no	—
538	C₂×C₄×C₃₁	—	4	2	no	—
539	C₂×C₄×C₃₁	—	4	4	no	—
540	C₂×C₄×C₃₁	—	4	2	no	—
541	C₂×C₄×C₃₁	—	4	4	no	—
542	C₂×C₄×C₃₁	—	4	2	no	—
543	C₂×C₄×C₃₁	—	4	2	no	—
544	C₂×C₄×C₃₁	—	4	2	no	—
545	C₂×C₄×C₃₁	—	8	2	no	—
546	C₂×C₄×C₃₁	—	8	2	no	—
547	C₂×C₄×C₃₁	—	8	2	no	—
548	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
553	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
555	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
557	C₈×C₃₁	—	2	1	no	—
558	C₈×C₃₁	—	2	1	no	—
559	C₈×C₃₁	—	2	2	no	—
560	C₈×C₃₁	—	2	2	no	—
561	C₈×C₃₁	—	2	1	no	—
562	C₈×C₃₁	—	2	1	no	—
563	#3514	C₂×C₃₁	1	1	yes	characteristic, complemented
564	D₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
565	#3399	C₂×C₃₁	1	1	yes	characteristic, complemented
566	#3397	C₂×C₃₁	1	1	yes	characteristic, complemented
567	#3373	C₂×C₃₁	1	1	yes	characteristic, complemented
568	#3367	C₂×C₃₁	1	1	yes	characteristic, complemented
569	#3308	C₂×C₃₁	1	2	yes	complemented
570	#3306	C₂×C₃₁	1	2	yes	complemented
571	#3298	C₂×C₃₁	1	1	yes	characteristic, complemented
572	#3294	C₂×C₃₁	1	1	yes	characteristic, complemented
573	D₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
574	D₄×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
575	#3265	C₂×C₃₁	1	2	yes	complemented
576	#3264	C₂×C₃₁	1	2	yes	complemented
577	#3251	C₂×C₃₁	1	1	yes	characteristic, complemented
578	#3247	C₂×C₃₁	1	2	yes	complemented
579	#3213	C₂×C₃₁	1	2	yes	complemented
580	#3207	C₂×C₃₁	1	1	yes	characteristic, complemented
581	#3114	C₂×C₃₁	1	2	yes	complemented
582	#3105	C₂×C₃₁	1	1	yes	characteristic, complemented
583	#3036	C₂×C₃₁	1	1	yes	characteristic, complemented
584	C₂×#463	C₂×C₃₁	1	2	yes	complemented
585	#2990	C₂×C₃₁	1	1	yes	characteristic, complemented
586	C₂²×C₃₁	—	2	2	no	—
587	C₂²×C₃₁	—	2	2	no	—
588	C₂²×C₃₁	—	2	1	no	—
589	C₂²×C₃₁	—	2	1	no	—
590	C₂²×C₃₁	—	2	2	no	—
591	C₂²×C₃₁	—	2	1	no	—
592	C₂²×C₃₁	—	4	1	no	—
593	C₂²×C₃₁	—	4	1	no	—
594	C₂²×C₃₁	—	4	2	no	—
595	C₂²×C₃₁	—	4	2	no	—
596	C₂²×C₃₁	—	4	1	no	—
597	C₂²×C₃₁	—	4	1	no	—
598	C₂²×C₃₁	—	4	2	no	—
599	C₂²×C₃₁	—	4	2	no	—
600	C₂²×C₃₁	—	4	1	no	—
601	C₂²×C₃₁	—	4	1	no	—
602	C₂²×C₃₁	—	4	2	no	—
603	C₂²×C₃₁	—	4	1	no	—
604	C₂²×C₃₁	—	4	1	no	—
605	C₂²×C₃₁	—	4	2	no	—
606	C₂²×C₃₁	—	8	8	no	—
607	C₂²×C₃₁	—	8	4	no	—
608	C₂²×C₃₁	—	16	4	no	—
609	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
610	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
611	C₄×C₃₁	—	2	1	no	—
612	C₄×C₃₁	—	2	2	no	—
613	C₄×C₃₁	—	2	1	no	—
614	C₄×C₃₁	—	2	1	no	—
615	C₄×C₃₁	—	2	2	no	—
616	C₄×C₃₁	—	2	1	no	—
617	C₄×C₃₁	—	2	2	no	—
618	C₄×C₃₁	—	4	1	no	—
619	C₄×C₃₁	—	4	2	no	—
620	C₄×C₃₁	—	4	1	no	—
621	C₄×C₃₁	—	4	1	no	—
622	C₄×C₃₁	—	4	2	no	—
623	C₄×C₃₁	—	4	1	no	—
624	C₄×C₃₁	—	4	1	no	—
625	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
626	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
627	C₄×C₃₁	#585	1	1	yes	characteristic
628	C₂²×#41	—	2	1	no	—
629	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
630	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
631	C₂²×D₈	C₂²×C₃₁	1	2	yes	—
632	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
633	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	#555	—	2	1	no	—
635	#551	—	2	2	no	—
636	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
637	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
639	#548	—	2	1	no	—
640	#548	C₂²×C₃₁	1	2	yes	complemented
641	#547	C₂²×C₃₁	1	1	yes	characteristic
642	#547	C₂²×C₃₁	1	2	yes	complemented
643	#546	—	2	1	no	—
644	#546	—	2	1	no	—
645	#546	—	2	2	no	—
646	#546	C₂²×C₃₁	1	2	yes	complemented
647	D₄²	C₂²×C₃₁	1	1	yes	characteristic
648	D₄²	C₂²×C₃₁	1	2	yes	complemented
649	D₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#542	—	2	1	no	—
651	#538	—	2	2	no	—
652	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
653	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	#532	C₂²×C₃₁	1	2	yes	complemented
655	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	#529	C₂²×C₃₁	1	2	yes	complemented
657	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
658	#525	—	2	2	no	—
659	#525	—	2	1	no	—
660	#518	—	2	1	no	—
661	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
662	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
663	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
664	#496	C₂²×C₃₁	1	2	yes	complemented
665	#496	C₂²×C₃₁	1	2	yes	complemented
666	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#489	C₂²×C₃₁	1	2	yes	complemented
669	#489	C₂²×C₃₁	1	2	yes	complemented
670	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
671	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
672	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	#483	C₂²×C₃₁	1	2	yes	complemented
674	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
675	#480	C₂²×C₃₁	1	2	yes	complemented
676	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
677	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
678	#478	C₂²×C₃₁	1	2	yes	complemented
679	#477	C₂²×C₃₁	1	2	yes	complemented
680	#476	C₂²×C₃₁	1	2	yes	complemented
681	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
682	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
683	#469	C₂²×C₃₁	1	2	yes	complemented
684	#468	C₂²×C₃₁	1	2	yes	complemented
685	#466	C₂²×C₃₁	1	2	yes	complemented
686	#466	C₂²×C₃₁	1	2	yes	complemented
687	#465	C₂²×C₃₁	1	2	yes	complemented
688	#465	C₂²×C₃₁	1	2	yes	complemented
689	#463	C₂²×C₃₁	1	1	yes	characteristic
690	#463	C₂²×C₃₁	1	2	yes	—
691	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
692	#463	C₂²×C₃₁	1	2	yes	complemented
693	#463	C₂²×C₃₁	1	2	yes	complemented
694	#463	C₂²×C₃₁	1	2	yes	complemented
695	#463	C₂²×C₃₁	1	2	yes	complemented
696	#463	C₂²×C₃₁	1	2	yes	complemented
697	#463	C₂²×C₃₁	1	2	yes	complemented
698	#463	C₂²×C₃₁	1	2	yes	complemented
699	#463	C₂²×C₃₁	1	2	yes	complemented
700	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
702	#460	C₂²×C₃₁	1	2	yes	complemented
703	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
704	#459	C₂²×C₃₁	1	1	yes	characteristic
705	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	#459	C₂²×C₃₁	1	2	yes	complemented
707	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
708	#450	C₂²×C₃₁	1	1	yes	characteristic, complemented
709	#450	C₂²×C₃₁	1	2	yes	complemented
710	#449	C₂²×C₃₁	1	2	yes	complemented
711	#449	C₂²×C₃₁	1	2	yes	complemented
712	#448	C₂²×C₃₁	1	2	yes	complemented
713	#448	C₂²×C₃₁	1	2	yes	complemented
714	#447	C₂²×C₃₁	1	1	yes	characteristic
715	#447	C₂²×C₃₁	1	2	yes	—
716	#447	C₂²×C₃₁	1	2	yes	complemented
717	#447	C₂²×C₃₁	1	2	yes	complemented
718	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
719	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
720	#442	C₂²×C₃₁	1	2	yes	complemented
721	#442	C₂²×C₃₁	1	2	yes	complemented
722	#440	C₂²×C₃₁	1	2	yes	complemented
723	#440	C₂²×C₃₁	1	2	yes	complemented
724	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
725	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
726	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
727	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
728	#435	C₂²×C₃₁	1	2	yes	complemented
729	#435	C₂²×C₃₁	1	2	yes	complemented
730	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
731	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
732	#432	C₂²×C₃₁	1	2	yes	complemented
733	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
734	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
735	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
736	#417	C₂²×C₃₁	1	2	yes	complemented
737	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
738	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
739	C₂×C₃₁	—	2	4	no	—
740	C₂×C₃₁	—	4	1	no	—
741	C₂×C₃₁	—	4	2	no	—
742	C₂×C₃₁	—	8	2	no	—
743	C₂×C₃₁	—	8	1	no	—
744	C₂×C₃₁	—	8	2	no	—
745	C₂×C₃₁	—	8	1	no	—
746	C₂×C₃₁	#3488	1	1	yes	characteristic
747	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
748	C₂×C₃₁	#3584	1	1	yes	characteristic
749	C₂×#41	—	2	1	no	—
750	C₂×#41	—	2	1	no	—
751	C₂×#41	—	2	2	no	—
752	C₂×#41	—	2	2	no	—
753	C₂×#41	—	2	1	no	—
754	C₂×#41	—	4	8	no	—
755	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
756	C₂×#41	C₂³×C₃₁	1	2	yes	—
757	C₂²×Q₈	—	2	1	no	—
758	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
759	C₂²×D₄	—	2	1	no	—
760	C₂²×D₄	—	2	1	no	—
761	C₂²×D₄	—	2	2	no	—
762	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
763	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
764	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
765	C₂³×C₄	—	2	2	no	—
766	C₂³×C₄	—	2	1	no	—
767	AGL(1,ℤ/8)	—	4	4	no	—
768	C₂×SD₁₆	—	4	4	no	—
769	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
770	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
771	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
772	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
773	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
774	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
775	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
776	C₂×D₈	—	4	4	no	—
777	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
778	C₂×D₈	C₂³×C₃₁	1	2	yes	—
779	C₂×D₈	C₂³×C₃₁	1	2	yes	—
780	C₂×D₈	C₂³×C₃₁	1	2	yes	—
781	C₂×D₈	C₂³×C₃₁	1	2	yes	—
782	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
783	C₂×D₈	C₂³×C₃₁	1	2	yes	—
784	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
785	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
786	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
787	C₄⋊Q₈	—	2	1	no	—
788	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
789	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
790	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
791	#127	C₂³×C₃₁	1	1	yes	characteristic
792	#127	C₂³×C₃₁	1	2	yes	—
793	#127	C₂³×C₃₁	1	1	yes	characteristic
794	#126	—	2	2	no	—
795	#126	—	2	2	no	—
796	#126	—	2	1	no	—
797	#125	C₂³×C₃₁	1	1	yes	characteristic
798	#124	—	2	1	no	—
799	#124	—	2	2	no	—
800	#124	—	2	2	no	—
801	#124	—	2	2	no	—
802	#124	—	2	1	no	—
803	#124	—	2	2	no	—
804	#124	C₂³×C₃₁	1	1	yes	characteristic
805	#124	C₂³×C₃₁	1	2	yes	—
806	#124	C₂³×C₃₁	1	2	yes	—
807	#124	C₂³×C₃₁	1	2	yes	—
808	#123	—	2	1	no	—
809	#123	—	2	2	no	—
810	#123	—	2	2	no	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	C₂²⋊Q₈	—	2	1	no	—
816	C₂²⋊Q₈	—	2	1	no	—
817	C₂²⋊Q₈	—	2	2	no	—
818	C₂²⋊Q₈	—	2	1	no	—
819	C₂²⋊Q₈	—	2	2	no	—
820	C₂²⋊Q₈	—	2	2	no	—
821	C₂²⋊Q₈	—	2	2	no	—
822	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
823	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
824	#121	—	2	2	no	—
825	#121	—	2	1	no	—
826	#121	—	2	2	no	—
827	#121	—	2	1	no	—
828	#121	—	2	1	no	—
829	#121	—	2	1	no	—
830	#121	—	2	2	no	—
831	#121	—	2	1	no	—
832	#121	—	2	2	no	—
833	#121	—	2	1	no	—
834	#121	—	2	2	no	—
835	#121	C₂³×C₃₁	1	2	yes	—
836	#121	C₂³×C₃₁	1	1	yes	characteristic
837	#121	C₂³×C₃₁	1	2	yes	—
838	#121	C₂³×C₃₁	1	2	yes	—
839	#121	C₂³×C₃₁	1	2	yes	—
840	#120	—	2	2	no	—
841	#120	—	2	2	no	—
842	#120	—	2	2	no	—
843	#120	—	2	2	no	—
844	#120	—	2	2	no	—
845	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
846	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
847	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
848	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	2	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	2	no	—
854	C₄×D₄	—	2	2	no	—
855	C₄×D₄	—	2	1	no	—
856	C₄×D₄	—	2	1	no	—
857	C₄×D₄	—	2	2	no	—
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	2	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	1	no	—
862	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
863	C₄×D₄	D₄×C₃₁	1	2	yes	—
864	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
865	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
866	C₄×D₄	C₂³×C₃₁	1	2	yes	—
867	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
868	C₄×D₄	C₂³×C₃₁	1	2	yes	—
869	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
870	C₄×D₄	C₂³×C₃₁	1	2	yes	—
871	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
872	C₄×D₄	C₂³×C₃₁	1	2	yes	—
873	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
874	C₄×D₄	C₂³×C₃₁	1	2	yes	—
875	#117	—	2	1	no	—
876	#117	—	2	1	no	—
877	#117	—	2	2	no	—
878	#117	D₄×C₃₁	1	2	yes	—
879	#117	D₄×C₃₁	1	1	yes	characteristic
880	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
881	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
882	C₂×C₂²⋊C₄	—	2	2	no	—
883	C₂×C₂²⋊C₄	—	2	1	no	—
884	C₂×C₂²⋊C₄	—	2	2	no	—
885	C₂×C₂²⋊C₄	—	2	2	no	—
886	C₂×C₂²⋊C₄	—	2	2	no	—
887	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
888	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
889	#107	C₂³×C₃₁	1	1	yes	characteristic
890	#107	C₂³×C₃₁	1	1	yes	characteristic
891	#107	C₂³×C₃₁	1	2	yes	—
892	#106	C₂³×C₃₁	1	1	yes	characteristic
893	#106	C₂³×C₃₁	1	1	yes	characteristic
894	#106	C₂³×C₃₁	1	2	yes	—
895	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
896	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
897	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
898	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
899	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
900	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
901	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
902	#103	C₂³×C₃₁	1	1	yes	characteristic
903	#103	C₂³×C₃₁	1	2	yes	—
904	#103	C₂³×C₃₁	1	2	yes	—
905	#103	C₂³×C₃₁	1	2	yes	—
906	#103	C₂³×C₃₁	1	2	yes	—
907	#103	C₂³×C₃₁	1	1	yes	characteristic
908	#103	C₂³×C₃₁	1	2	yes	—
909	#102	C₂³×C₃₁	1	1	yes	characteristic
910	#102	C₂³×C₃₁	1	2	yes	—
911	#102	C₂³×C₃₁	1	2	yes	—
912	#102	C₂³×C₃₁	1	2	yes	—
913	#102	C₂³×C₃₁	1	2	yes	—
914	#102	C₂³×C₃₁	1	1	yes	characteristic
915	#102	C₂³×C₃₁	1	1	yes	characteristic
916	#102	C₂³×C₃₁	1	1	yes	characteristic
917	#102	C₂³×C₃₁	1	1	yes	characteristic
918	#102	C₂³×C₃₁	1	1	yes	characteristic
919	#102	C₂³×C₃₁	1	2	yes	—
920	#102	C₂³×C₃₁	1	2	yes	—
921	#102	C₂³×C₃₁	1	2	yes	—
922	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
923	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
924	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
925	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
926	#97	C₂³×C₃₁	1	2	yes	—
927	#97	C₂³×C₃₁	1	2	yes	—
928	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
929	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
930	C₃₁	#61989	1	1	yes	characteristic, direct product factor, Sylow
931	C₂⁴	—	2	1	no	—
932	C₂⁴	—	2	2	no	—
933	C₂⁴	—	2	2	no	—
934	#41	—	2	4	no	—
935	#41	—	4	8	no	—
936	#41	—	4	4	no	—
937	#41	—	4	2	no	—
938	#41	—	4	2	no	—
939	#41	—	4	8	no	—
940	#41	—	4	4	no	—
941	#41	—	4	4	no	—
942	C₂×Q₈	—	2	2	no	—
943	C₂×Q₈	—	2	1	no	—
944	C₂×Q₈	—	2	2	no	—
945	C₂×Q₈	—	4	2	no	—
946	C₂×Q₈	—	4	2	no	—
947	C₂×Q₈	—	4	4	no	—
948	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
949	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
950	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
951	C₂×D₄	—	2	4	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	1	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	1	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	1	no	—
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	—	4	2	no	—
969	C₂×D₄	—	4	1	no	—
970	C₂×D₄	—	4	2	no	—
971	C₂×D₄	—	4	2	no	—
972	C₂×D₄	—	4	8	no	—
973	C₂×D₄	—	4	4	no	—
974	C₂×D₄	—	4	4	no	—
975	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
976	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
977	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
978	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
979	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
980	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
981	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
982	C₂²×C₄	—	2	1	no	—
983	C₂²×C₄	—	2	2	no	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	2	1	no	—
986	C₂²×C₄	—	2	1	no	—
987	C₂²×C₄	—	2	2	no	—
988	C₂²×C₄	—	2	1	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	1	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	4	8	no	—
996	C₂²×C₄	—	4	4	no	—
997	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
998	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
999	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
1000	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1001	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1002	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1003	SD₁₆	—	2	2	no	—
1004	SD₁₆	—	2	4	no	—
1005	SD₁₆	—	4	2	no	—
1006	SD₁₆	—	4	2	no	—
1007	SD₁₆	—	4	1	no	—
1008	SD₁₆	—	4	2	no	—
1009	SD₁₆	—	4	2	no	—
1010	D₈	—	2	2	no	—
1011	D₈	—	2	4	no	—
1012	D₈	—	4	2	no	—
1013	D₈	—	4	2	no	—
1014	D₈	—	4	2	no	—
1015	D₈	—	4	1	no	—
1016	D₈	—	4	2	no	—
1017	M₁₆	—	4	2	no	—
1018	C₂×C₈	—	4	2	no	—
1019	C₂×C₈	—	4	2	no	—
1020	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1021	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1022	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1023	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1024	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1025	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1039	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1040	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1041	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1042	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1043	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1044	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1045	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1046	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	1	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	1	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1072	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1073	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1074	C₄²	—	2	2	no	—
1075	C₄²	—	2	1	no	—
1076	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1077	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1078	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1079	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1080	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1081	C₄²	C₂⁴×C₃₁	1	2	yes	—
1082	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1083	C₂³	—	2	1	no	—
1084	C₂³	—	2	1	no	—
1085	C₂³	—	2	2	no	—
1086	C₂³	—	2	2	no	—
1087	C₂³	—	2	1	no	—
1088	C₂³	—	4	4	no	—
1089	C₂³	—	4	2	no	—
1090	C₂³	—	4	2	no	—
1091	C₂³	—	4	4	no	—
1092	C₂³	—	4	4	no	—
1093	C₂³	—	8	2	no	—
1094	C₂³	—	8	1	no	—
1095	C₂³	—	8	2	no	—
1096	C₂³	—	8	2	no	—
1097	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1098	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1099	Q₈	—	2	2	no	—
1100	Q₈	—	2	1	no	—
1101	Q₈	—	2	2	no	—
1102	Q₈	—	2	1	no	—
1103	Q₈	—	2	2	no	—
1104	Q₈	—	4	4	no	—
1105	Q₈	—	4	2	no	—
1106	Q₈	—	8	2	no	—
1107	D₄	—	2	4	no	—
1108	D₄	—	2	1	no	—
1109	D₄	—	2	2	no	—
1110	D₄	—	2	2	no	—
1111	D₄	—	2	1	no	—
1112	D₄	—	2	1	no	—
1113	D₄	—	2	2	no	—
1114	D₄	—	2	1	no	—
1115	D₄	—	2	1	no	—
1116	D₄	—	2	2	no	—
1117	D₄	—	4	2	no	—
1118	D₄	—	4	4	no	—
1119	D₄	—	4	4	no	—
1120	D₄	—	4	4	no	—
1121	D₄	—	4	4	no	—
1122	D₄	—	4	4	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	2	no	—
1125	D₄	—	4	2	no	—
1126	D₄	—	8	2	no	—
1127	D₄	—	8	1	no	—
1128	D₄	—	8	1	no	—
1129	D₄	—	8	2	no	—
1130	D₄	—	8	1	no	—
1131	D₄	—	8	2	no	—
1132	D₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	complemented
1133	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1134	C₂×C₄	—	2	4	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	4	2	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	2	no	—
1150	C₂×C₄	—	4	4	no	—
1151	C₂×C₄	—	4	4	no	—
1152	C₂×C₄	—	4	2	no	—
1153	C₂×C₄	—	4	4	no	—
1154	C₂×C₄	—	4	2	no	—
1155	C₂×C₄	—	4	4	no	—
1156	C₂×C₄	—	4	2	no	—
1157	C₂×C₄	—	4	2	no	—
1158	C₂×C₄	—	4	2	no	—
1159	C₂×C₄	—	8	2	no	—
1160	C₂×C₄	—	8	2	no	—
1161	C₂×C₄	—	8	2	no	—
1162	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1163	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1164	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1165	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1166	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1167	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1168	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1169	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1170	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1171	C₈	—	2	1	no	—
1172	C₈	—	2	1	no	—
1173	C₈	—	2	2	no	—
1174	C₈	—	2	2	no	—
1175	C₈	—	2	1	no	—
1176	C₈	—	2	1	no	—
1177	C₂²	—	2	2	no	—
1178	C₂²	—	2	2	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	2	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	4	1	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	2	no	—
1186	C₂²	—	4	2	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	2	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	2	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	4	2	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	8	8	no	—
1198	C₂²	—	8	4	no	—
1199	C₂²	—	16	4	no	—
1200	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	4	yes	—
1201	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1202	C₄	—	2	1	no	—
1203	C₄	—	2	2	no	—
1204	C₄	—	2	1	no	—
1205	C₄	—	2	2	no	—
1206	C₄	—	2	1	no	—
1207	C₄	—	2	2	no	—
1208	C₄	—	2	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	2	no	—
1213	C₄	—	4	1	no	—
1214	C₄	—	4	1	no	—
1215	C₄	—	4	1	no	—
1216	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
1217	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1218	C₄	C₃₁×#585	1	1	yes	characteristic
1219	C₂	—	2	4	no	—
1220	C₂	—	4	1	no	—
1221	C₂	—	4	2	no	—
1222	C₂	—	8	2	no	—
1223	C₂	—	8	1	no	—
1224	C₂	—	8	1	no	—
1225	C₂	—	8	2	no	—
1226	C₂	C₃₁×#3488	1	1	yes	characteristic
1227	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
1228	C₂	C₃₁×#3584	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3514	C₂	semidirect
2. D₄×#41×C₃₁	C₂	semidirect
3. C₃₁×#3399	C₂	semidirect
4. C₃₁×#3397	C₂	semidirect
5. C₃₁×#3373	C₂	semidirect
6. C₃₁×#3367	C₂	semidirect
7. C₃₁×#3308	C₂	semidirect
8. C₃₁×#3306	C₂	semidirect
9. C₃₁×#3298	C₂	semidirect
10. C₃₁×#3294	C₂	semidirect
11. D₄×SD₁₆×C₃₁	C₂	semidirect
12. D₄×D₈×C₃₁	C₂	semidirect
13. C₃₁×#3265	C₂	semidirect
14. C₃₁×#3264	C₂	semidirect
15. C₃₁×#3251	C₂	semidirect
16. C₃₁×#3247	C₂	semidirect
17. C₃₁×#3213	C₂	semidirect
18. C₃₁×#3207	C₂	semidirect
19. C₃₁×#3114	C₂	semidirect
20. C₃₁×#3105	C₂	semidirect
21. C₃₁×#3036	C₂	semidirect
22. C₂×C₃₁×#463	C₂	semidirect
23. C₃₁×#2990	C₂	semidirect
25. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂²×SD₁₆×C₃₁	C₂²	semidirect
28. C₃₁×#559	C₂²	semidirect
29. C₃₁×#556	C₂²	semidirect
32. C₃₁×#550	C₂²	semidirect
33. D₄×Q₈×C₃₁	C₂²	semidirect
34. D₄×Q₈×C₃₁	C₂²	semidirect
36. C₃₁×#548	C₂²	semidirect
38. C₃₁×#547	C₂²	semidirect
42. C₃₁×#546	C₂²	semidirect
44. D₄²×C₃₁	C₂²	semidirect
45. D₄²×C₃₁	C₂²	semidirect
48. C₃₁×#532	C₂²	semidirect
49. C₃₁×#532	C₂²	semidirect
50. C₃₁×#532	C₂²	semidirect
51. C₃₁×#529	C₂²	semidirect
52. C₃₁×#529	C₂²	semidirect
53. C₂×C₃₁×#124	C₂²	semidirect
58. C₂×C₄×D₄×C₃₁	C₂²	semidirect
59. C₂×C₄×D₄×C₃₁	C₂²	semidirect
60. C₃₁×#496	C₂²	semidirect
61. C₃₁×#496	C₂²	semidirect
62. C₃₁×#493	C₂²	semidirect
63. C₃₁×#492	C₂²	semidirect
64. C₃₁×#489	C₂²	semidirect
65. C₃₁×#489	C₂²	semidirect
66. C₃₁×#487	C₂²	semidirect
67. C₃₁×#486	C₂²	semidirect
68. C₃₁×#484	C₂²	semidirect
69. C₃₁×#483	C₂²	semidirect
70. C₃₁×#481	C₂²	semidirect
71. C₃₁×#480	C₂²	semidirect
72. C₃₁×#478	C₂²	semidirect
73. C₃₁×#478	C₂²	semidirect
74. C₃₁×#478	C₂²	semidirect
75. C₃₁×#477	C₂²	semidirect
76. C₃₁×#476	C₂²	semidirect
77. C₃₁×#475	C₂²	semidirect
78. C₃₁×#474	C₂²	semidirect
79. C₃₁×#469	C₂²	semidirect
80. C₃₁×#468	C₂²	semidirect
81. C₃₁×#466	C₂²	semidirect
82. C₃₁×#466	C₂²	semidirect
83. C₃₁×#465	C₂²	semidirect
84. C₃₁×#465	C₂²	semidirect
87. C₃₁×#463	C₂²	semidirect
88. C₃₁×#463	C₂²	semidirect
89. C₃₁×#463	C₂²	semidirect
90. C₃₁×#463	C₂²	semidirect
91. C₃₁×#463	C₂²	semidirect
92. C₃₁×#463	C₂²	semidirect
93. C₃₁×#463	C₂²	semidirect
94. C₃₁×#463	C₂²	semidirect
95. C₃₁×#463	C₂²	semidirect
96. C₃₁×#461	C₂²	semidirect
97. C₃₁×#461	C₂²	semidirect
98. C₃₁×#460	C₂²	semidirect
99. C₃₁×#460	C₂²	semidirect
101. C₃₁×#459	C₂²	semidirect
102. C₃₁×#459	C₂²	semidirect
103. C₃₁×#459	C₂²	semidirect
104. C₃₁×#450	C₂²	semidirect
105. C₃₁×#450	C₂²	semidirect
106. C₃₁×#449	C₂²	semidirect
107. C₃₁×#449	C₂²	semidirect
108. C₃₁×#448	C₂²	semidirect
109. C₃₁×#448	C₂²	semidirect
112. C₃₁×#447	C₂²	semidirect
113. C₃₁×#447	C₂²	semidirect
114. C₃₁×#446	C₂²	semidirect
115. C₃₁×#446	C₂²	semidirect
116. C₃₁×#442	C₂²	semidirect
117. C₃₁×#442	C₂²	semidirect
118. C₃₁×#440	C₂²	semidirect
119. C₃₁×#440	C₂²	semidirect
120. C₄×SD₁₆×C₃₁	C₂²	semidirect
121. C₄×SD₁₆×C₃₁	C₂²	semidirect
123. C₄×D₈×C₃₁	C₂²	semidirect
124. C₃₁×#435	C₂²	semidirect
125. C₃₁×#435	C₂²	semidirect
126. C₈×D₄×C₃₁	C₂²	semidirect
127. C₈×D₄×C₃₁	C₂²	semidirect
128. C₃₁×#432	C₂²	semidirect
129. C₃₁×#431	C₂²	semidirect
130. C₃₁×#423	C₂²	semidirect
131. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
132. C₃₁×#417	C₂²	semidirect
133. C₂×C₃₁×#103	C₂²	semidirect
134. C₂×C₃₁×#102	C₂²	semidirect
468. #61989	C₃₁	direct (N × H)
518. D₄×C₃₁	AGL(1,ℤ/8)	semidirect
563. #3514	C₂×C₃₁	semidirect
564. D₄×#41	C₂×C₃₁	semidirect
565. #3399	C₂×C₃₁	semidirect
566. #3397	C₂×C₃₁	semidirect
567. #3373	C₂×C₃₁	semidirect
568. #3367	C₂×C₃₁	semidirect
569. #3308	C₂×C₃₁	semidirect
570. #3306	C₂×C₃₁	semidirect
571. #3298	C₂×C₃₁	semidirect
572. #3294	C₂×C₃₁	semidirect
573. D₄×SD₁₆	C₂×C₃₁	semidirect
574. D₄×D₈	C₂×C₃₁	semidirect
575. #3265	C₂×C₃₁	semidirect
576. #3264	C₂×C₃₁	semidirect
577. #3251	C₂×C₃₁	semidirect
578. #3247	C₂×C₃₁	semidirect
579. #3213	C₂×C₃₁	semidirect
580. #3207	C₂×C₃₁	semidirect
581. #3114	C₂×C₃₁	semidirect
582. #3105	C₂×C₃₁	semidirect
583. #3036	C₂×C₃₁	semidirect
584. C₂×#463	C₂×C₃₁	semidirect
585. #2990	C₂×C₃₁	semidirect
629. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
630. C₂²×SD₁₆	C₂²×C₃₁	semidirect
632. #559	C₂²×C₃₁	semidirect
633. #556	C₂²×C₃₁	semidirect
636. #550	C₂²×C₃₁	semidirect
637. D₄×Q₈	C₂²×C₃₁	semidirect
638. D₄×Q₈	C₂²×C₃₁	semidirect
640. #548	C₂²×C₃₁	semidirect
642. #547	C₂²×C₃₁	semidirect
646. #546	C₂²×C₃₁	semidirect
648. D₄²	C₂²×C₃₁	semidirect
649. D₄²	C₂²×C₃₁	semidirect
652. #532	C₂²×C₃₁	semidirect
653. #532	C₂²×C₃₁	semidirect
654. #532	C₂²×C₃₁	semidirect
655. #529	C₂²×C₃₁	semidirect
656. #529	C₂²×C₃₁	semidirect
657. C₂×#124	C₂²×C₃₁	semidirect
662. C₂×C₄×D₄	C₂²×C₃₁	semidirect
663. C₂×C₄×D₄	C₂²×C₃₁	semidirect
664. #496	C₂²×C₃₁	semidirect
665. #496	C₂²×C₃₁	semidirect
666. #493	C₂²×C₃₁	semidirect
667. #492	C₂²×C₃₁	semidirect
668. #489	C₂²×C₃₁	semidirect
669. #489	C₂²×C₃₁	semidirect
670. #487	C₂²×C₃₁	semidirect
671. #486	C₂²×C₃₁	semidirect
672. #484	C₂²×C₃₁	semidirect
673. #483	C₂²×C₃₁	semidirect
674. #481	C₂²×C₃₁	semidirect
675. #480	C₂²×C₃₁	semidirect
676. #478	C₂²×C₃₁	semidirect
677. #478	C₂²×C₃₁	semidirect
678. #478	C₂²×C₃₁	semidirect
679. #477	C₂²×C₃₁	semidirect
680. #476	C₂²×C₃₁	semidirect
681. #475	C₂²×C₃₁	semidirect
682. #474	C₂²×C₃₁	semidirect
683. #469	C₂²×C₃₁	semidirect
684. #468	C₂²×C₃₁	semidirect
685. #466	C₂²×C₃₁	semidirect
686. #466	C₂²×C₃₁	semidirect
687. #465	C₂²×C₃₁	semidirect
688. #465	C₂²×C₃₁	semidirect
691. #463	C₂²×C₃₁	semidirect
692. #463	C₂²×C₃₁	semidirect
693. #463	C₂²×C₃₁	semidirect
694. #463	C₂²×C₃₁	semidirect
695. #463	C₂²×C₃₁	semidirect
696. #463	C₂²×C₃₁	semidirect
697. #463	C₂²×C₃₁	semidirect
698. #463	C₂²×C₃₁	semidirect
699. #463	C₂²×C₃₁	semidirect
700. #461	C₂²×C₃₁	semidirect
701. #461	C₂²×C₃₁	semidirect
702. #460	C₂²×C₃₁	semidirect
703. #460	C₂²×C₃₁	semidirect
705. #459	C₂²×C₃₁	semidirect
706. #459	C₂²×C₃₁	semidirect
707. #459	C₂²×C₃₁	semidirect
708. #450	C₂²×C₃₁	semidirect
709. #450	C₂²×C₃₁	semidirect
710. #449	C₂²×C₃₁	semidirect
711. #449	C₂²×C₃₁	semidirect
712. #448	C₂²×C₃₁	semidirect
713. #448	C₂²×C₃₁	semidirect
716. #447	C₂²×C₃₁	semidirect
717. #447	C₂²×C₃₁	semidirect
718. #446	C₂²×C₃₁	semidirect
719. #446	C₂²×C₃₁	semidirect
720. #442	C₂²×C₃₁	semidirect
721. #442	C₂²×C₃₁	semidirect
722. #440	C₂²×C₃₁	semidirect
723. #440	C₂²×C₃₁	semidirect
724. C₄×SD₁₆	C₂²×C₃₁	semidirect
725. C₄×SD₁₆	C₂²×C₃₁	semidirect
727. C₄×D₈	C₂²×C₃₁	semidirect
728. #435	C₂²×C₃₁	semidirect
729. #435	C₂²×C₃₁	semidirect
730. C₈×D₄	C₂²×C₃₁	semidirect
731. C₈×D₄	C₂²×C₃₁	semidirect
732. #432	C₂²×C₃₁	semidirect
733. #431	C₂²×C₃₁	semidirect
734. #423	C₂²×C₃₁	semidirect
735. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
736. #417	C₂²×C₃₁	semidirect
737. C₂×#103	C₂²×C₃₁	semidirect
738. C₂×#102	C₂²×C₃₁	semidirect
930. C₃₁	#61989	direct (N × H)
1132. D₄	C₃₁×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3514	2
D₄×#41×C₃₁	2
C₃₁×#3399	2
C₃₁×#3397	2
C₃₁×#3373	2
C₃₁×#3367	2
C₃₁×#3308	2
C₃₁×#3306	2
C₃₁×#3298	2
C₃₁×#3294	2
D₄×SD₁₆×C₃₁	2
D₄×D₈×C₃₁	2
C₃₁×#3265	2
C₃₁×#3264	2
C₃₁×#3251	2
C₃₁×#3247	2
C₃₁×#3213	2
C₃₁×#3207	2
C₃₁×#3114	2
C₃₁×#3105	2
C₃₁×#3036	2
C₂×C₃₁×#463	2
C₃₁×#2990	2
#61989	31

Subgroups — C31×#61989 #21518748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61989 #21518748