Subgroups — C₃₁×#60812 #21517571

Order 7936.

2218 conjugacy classes of subgroups.

The subgroup lattice has 982 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	C₂×C₃₁×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3224	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3222	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3217	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3215	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3211	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3208	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3154	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3136	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3045	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3043	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3007	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3003	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3002	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#450	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
21	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
22	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
23	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
24	C₃₁×#556	—	2	1	no	—
25	C₃₁×#554	—	2	1	no	—
26	C₃₁×#552	—	2	2	no	—
27	C₃₁×#552	—	2	1	no	—
28	C₃₁×#552	—	2	1	no	—
29	C₃₁×#551	—	2	2	no	—
30	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#542	C₂²	1	2	yes	complemented
32	C₃₁×#541	C₂²	1	2	yes	complemented
33	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#535	—	2	1	no	—
35	C₃₁×#535	—	2	2	no	—
36	C₃₁×#535	—	2	1	no	—
37	C₃₁×#535	C₂²	1	2	yes	—
38	C₃₁×#535	C₂²	1	4	yes	—
39	C₃₁×#535	C₂²	1	2	yes	—
40	C₃₁×#533	C₂²	1	2	yes	complemented
41	C₂×C₃₁×#127	C₂²	1	2	yes	—
42	C₃₁×#529	C₂²	1	2	yes	complemented
43	C₂×C₃₁×#124	C₂²	1	2	yes	—
44	C₃₁×#525	C₂²	1	1	yes	characteristic
45	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₃₁×#121	—	2	1	no	—
47	C₂×C₃₁×#121	—	2	1	no	—
48	C₂×C₃₁×#120	—	2	2	no	—
49	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#519	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
52	C₃₁×#497	C₂²	1	4	yes	complemented
53	C₃₁×#496	C₂²	1	4	yes	complemented
54	C₃₁×#495	C₂²	1	4	yes	complemented
55	C₃₁×#492	C₂²	1	4	yes	complemented
56	C₃₁×#490	C₂²	1	4	yes	complemented
57	C₃₁×#489	C₂²	1	4	yes	complemented
58	C₃₁×#488	C₂²	1	4	yes	complemented
59	C₃₁×#486	C₂²	1	4	yes	complemented
60	C₃₁×#464	C₂²	1	4	yes	complemented
61	C₃₁×#464	C₂²	1	4	yes	complemented
62	C₃₁×#464	C₂²	1	4	yes	complemented
63	C₃₁×#463	C₂²	1	4	yes	complemented
64	C₃₁×#460	C₂²	1	4	yes	complemented
65	C₃₁×#460	C₂²	1	4	yes	complemented
66	C₃₁×#460	C₂²	1	4	yes	complemented
67	C₃₁×#459	C₂²	1	4	yes	complemented
68	C₃₁×#452	C₂²	1	2	yes	complemented
69	C₃₁×#452	C₂²	1	4	yes	complemented
70	C₃₁×#451	C₂²	1	2	yes	complemented
71	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×#450	C₂²	1	2	yes	—
73	C₃₁×#450	C₂²	1	2	yes	—
74	C₃₁×#450	C₂²	1	2	yes	—
75	C₃₁×#450	C₂²	1	2	yes	complemented
76	C₃₁×#450	C₂²	1	4	yes	complemented
77	C₃₁×#450	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#450	C₂²	1	2	yes	complemented
79	C₃₁×#449	C₂²	1	2	yes	complemented
80	C₃₁×#448	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#447	C₂²	1	2	yes	—
82	C₃₁×#447	C₂²	1	2	yes	complemented
83	C₃₁×#447	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#433	C₂²	1	4	yes	complemented
85	C₃₁×#432	C₂²	1	2	yes	complemented
86	C₃₁×#431	C₂²	1	2	yes	complemented
87	C₃₁×#424	C₂²	1	2	yes	complemented
88	C₃₁×#418	C₂²	1	2	yes	complemented
89	C₃₁×#417	C₂²	1	2	yes	complemented
90	C₃₁×#416	C₂²	1	2	yes	complemented
91	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
92	C₃₁×#407	C₂²	1	1	yes	characteristic
93	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₃₁×#405	C₂²	1	2	yes	complemented
95	C₂⁵×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	1	no	—
97	C₂×#41×C₃₁	—	2	1	no	—
98	C₂×#41×C₃₁	—	4	4	no	—
99	C₂×#41×C₃₁	C₂³	1	2	yes	—
100	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
101	C₂×#41×C₃₁	C₂³	1	2	yes	—
102	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₃₁	—	2	1	no	—
105	C₂²×D₄×C₃₁	—	2	1	no	—
106	C₂²×D₄×C₃₁	—	2	1	no	—
107	C₂²×D₄×C₃₁	—	2	1	no	—
108	C₂²×D₄×C₃₁	—	2	2	no	—
109	C₂²×D₄×C₃₁	—	2	2	no	—
110	C₂²×D₄×C₃₁	—	4	4	no	—
111	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
112	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
113	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
115	C₂³×C₄×C₃₁	—	2	1	no	—
116	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
117	C₃₁×#137	—	4	4	no	—
118	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
119	C₃₁×#135	—	4	4	no	—
120	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	complemented
121	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	complemented
122	C₂×SD₁₆×C₃₁	—	4	4	no	—
123	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
124	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
125	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
126	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	complemented
127	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	complemented
128	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	complemented
129	C₂×D₈×C₃₁	C₂³	1	4	yes	—
130	C₂×D₈×C₃₁	C₂³	1	2	yes	complemented
131	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
132	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
133	C₃₁×C₄⋊Q₈	—	2	1	no	—
134	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	complemented
135	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	complemented
136	C₃₁×#127	—	2	2	no	—
137	C₃₁×#127	—	2	2	no	—
138	C₃₁×#127	C₂³	1	4	yes	—
139	C₃₁×#127	C₂³	1	4	yes	—
140	C₃₁×#126	—	2	2	no	—
141	C₃₁×#126	—	2	2	no	—
142	C₃₁×#126	—	2	2	no	—
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#125	—	2	2	no	—
145	C₃₁×#125	—	2	2	no	—
146	C₃₁×#125	—	2	1	no	—
147	C₃₁×#125	—	2	2	no	—
148	C₃₁×#125	C₂³	1	2	yes	complemented
149	C₃₁×#124	—	2	2	no	—
150	C₃₁×#124	—	2	2	no	—
151	C₃₁×#124	—	2	2	no	—
152	C₃₁×#124	C₂³	1	4	yes	—
153	C₃₁×#124	C₂³	1	4	yes	—
154	C₃₁×#124	C₂³	1	2	yes	complemented
155	C₃₁×#123	—	2	1	no	—
156	C₃₁×#123	—	2	2	no	—
157	C₃₁×#123	—	2	2	no	—
158	C₃₁×#123	—	2	2	no	—
159	C₃₁×C₂²⋊Q₈	—	2	1	no	—
160	C₃₁×C₂²⋊Q₈	—	2	1	no	—
161	C₃₁×C₂²⋊Q₈	—	2	2	no	—
162	C₃₁×C₂²⋊Q₈	—	2	1	no	—
163	C₃₁×C₂²⋊Q₈	—	2	1	no	—
164	C₃₁×C₂²⋊Q₈	—	2	2	no	—
165	C₃₁×C₂²⋊Q₈	—	2	2	no	—
166	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
167	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
168	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
169	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
170	C₃₁×#121	—	2	2	no	—
171	C₃₁×#121	—	2	2	no	—
172	C₃₁×#121	—	2	2	no	—
173	C₃₁×#121	—	2	4	no	—
174	C₃₁×#121	—	2	2	no	—
175	C₃₁×#121	—	2	4	no	—
176	C₃₁×#121	C₂³	1	1	yes	characteristic
177	C₃₁×#121	C₂³	1	1	yes	characteristic
178	C₃₁×#120	—	2	1	no	—
179	C₃₁×#120	—	2	4	no	—
180	C₃₁×#120	—	2	4	no	—
181	C₃₁×#120	—	2	4	no	—
182	C₃₁×#120	—	2	4	no	—
183	C₄×Q₈×C₃₁	—	2	1	no	—
184	C₄×Q₈×C₃₁	—	2	1	no	—
185	C₄×Q₈×C₃₁	—	2	2	no	—
186	C₄×Q₈×C₃₁	C₂³	1	2	yes	complemented
187	C₄×Q₈×C₃₁	C₂³	1	2	yes	complemented
188	C₄×Q₈×C₃₁	C₂³	1	2	yes	complemented
189	C₄×D₄×C₃₁	—	2	1	no	—
190	C₄×D₄×C₃₁	—	2	1	no	—
191	C₄×D₄×C₃₁	—	2	2	no	—
192	C₄×D₄×C₃₁	—	2	2	no	—
193	C₄×D₄×C₃₁	C₂³	1	2	yes	complemented
194	C₃₁×#117	—	2	2	no	—
195	C₃₁×#117	—	2	1	no	—
196	C₃₁×#117	—	2	2	no	—
197	C₃₁×#117	—	2	2	no	—
198	C₃₁×#117	D₄	1	1	yes	characteristic
199	C₃₁×#117	D₄	1	2	yes	—
200	C₃₁×#117	D₄	1	1	yes	characteristic
201	C₃₁×#117	C₂³	1	1	yes	characteristic
202	C₃₁×#117	C₂³	1	1	yes	characteristic
203	C₃₁×#117	C₂³	1	1	yes	characteristic
204	C₃₁×#117	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
206	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
207	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
208	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
209	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
211	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
212	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
213	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
214	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
215	C₃₁×C₄⋊C₈	C₂³	1	4	yes	complemented
216	C₃₁×C₄⋊C₈	C₂³	1	4	yes	complemented
217	C₃₁×#103	C₂³	1	2	yes	complemented
218	C₃₁×#103	C₂³	1	2	yes	complemented
219	C₃₁×#103	C₂³	1	4	yes	complemented
220	C₃₁×#102	C₂³	1	4	yes	—
221	C₃₁×#102	C₂³	1	4	yes	—
222	C₃₁×#102	C₂³	1	4	yes	—
223	C₃₁×#102	C₂³	1	4	yes	—
224	C₃₁×#102	C₂³	1	2	yes	complemented
225	C₃₁×#102	C₂³	1	2	yes	complemented
226	C₃₁×#102	C₂³	1	4	yes	complemented
227	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
229	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
230	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
231	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
232	C₃₁×#97	C₂³	1	4	yes	complemented
233	C₄×C₈×C₃₁	C₂³	1	4	yes	complemented
234	C₂⁴×C₃₁	—	2	2	no	—
235	C₂⁴×C₃₁	—	2	1	no	—
236	C₂⁴×C₃₁	—	2	2	no	—
237	C₂⁴×C₃₁	—	2	2	no	—
238	C₂⁴×C₃₁	—	4	4	no	—
239	C₂⁴×C₃₁	—	8	2	no	—
240	C₂⁴×C₃₁	—	8	2	no	—
241	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
242	#41×C₃₁	—	2	4	no	—
243	#41×C₃₁	—	2	4	no	—
244	#41×C₃₁	—	2	4	no	—
245	#41×C₃₁	—	4	2	no	—
246	#41×C₃₁	—	4	2	no	—
247	#41×C₃₁	—	4	4	no	—
248	#41×C₃₁	—	4	4	no	—
249	C₂×Q₈×C₃₁	—	2	1	no	—
250	C₂×Q₈×C₃₁	—	2	1	no	—
251	C₂×Q₈×C₃₁	—	2	2	no	—
252	C₂×Q₈×C₃₁	—	2	4	no	—
253	C₂×Q₈×C₃₁	—	4	2	no	—
254	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
255	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
256	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₂×D₄×C₃₁	—	2	1	no	—
258	C₂×D₄×C₃₁	—	2	1	no	—
259	C₂×D₄×C₃₁	—	2	2	no	—
260	C₂×D₄×C₃₁	—	2	2	no	—
261	C₂×D₄×C₃₁	—	2	1	no	—
262	C₂×D₄×C₃₁	—	2	2	no	—
263	C₂×D₄×C₃₁	—	2	2	no	—
264	C₂×D₄×C₃₁	—	2	2	no	—
265	C₂×D₄×C₃₁	—	2	1	no	—
266	C₂×D₄×C₃₁	—	2	4	no	—
267	C₂×D₄×C₃₁	—	2	4	no	—
268	C₂×D₄×C₃₁	—	2	4	no	—
269	C₂×D₄×C₃₁	—	2	4	no	—
270	C₂×D₄×C₃₁	—	2	4	no	—
271	C₂×D₄×C₃₁	—	2	4	no	—
272	C₂×D₄×C₃₁	—	4	4	no	—
273	C₂×D₄×C₃₁	—	4	4	no	—
274	C₂×D₄×C₃₁	—	4	2	no	—
275	C₂×D₄×C₃₁	—	4	4	no	—
276	C₂×D₄×C₃₁	—	4	4	no	—
277	C₂×D₄×C₃₁	—	4	4	no	—
278	C₂×D₄×C₃₁	—	4	4	no	—
279	C₂×D₄×C₃₁	—	8	4	no	—
280	C₂×D₄×C₃₁	—	8	4	no	—
281	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
282	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
283	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₃₁	—	2	4	no	—
285	C₂²×C₄×C₃₁	—	2	1	no	—
286	C₂²×C₄×C₃₁	—	2	1	no	—
287	C₂²×C₄×C₃₁	—	2	1	no	—
288	C₂²×C₄×C₃₁	—	2	1	no	—
289	C₂²×C₄×C₃₁	—	2	2	no	—
290	C₂²×C₄×C₃₁	—	2	2	no	—
291	C₂²×C₄×C₃₁	—	2	2	no	—
292	C₂²×C₄×C₃₁	—	4	4	no	—
293	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
294	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
298	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
301	Q₁₆×C₃₁	—	4	2	no	—
302	Q₁₆×C₃₁	—	4	4	no	—
303	SD₁₆×C₃₁	—	4	4	no	—
304	SD₁₆×C₃₁	—	4	4	no	—
305	SD₁₆×C₃₁	—	4	4	no	—
306	SD₁₆×C₃₁	—	4	2	no	—
307	SD₁₆×C₃₁	—	4	2	no	—
308	SD₁₆×C₃₁	—	4	4	no	—
309	D₈×C₃₁	—	4	4	no	—
310	D₈×C₃₁	—	4	2	no	—
311	M₁₆×C₃₁	—	2	4	no	—
312	C₂×C₈×C₃₁	—	2	4	no	—
313	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
314	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
315	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
316	C₄⋊C₄×C₃₁	—	2	1	no	—
317	C₄⋊C₄×C₃₁	—	2	2	no	—
318	C₄⋊C₄×C₃₁	—	2	2	no	—
319	C₄⋊C₄×C₃₁	—	2	2	no	—
320	C₄⋊C₄×C₃₁	—	2	2	no	—
321	C₄⋊C₄×C₃₁	—	2	2	no	—
322	C₄⋊C₄×C₃₁	—	2	2	no	—
323	C₄⋊C₄×C₃₁	—	2	2	no	—
324	C₄⋊C₄×C₃₁	—	2	2	no	—
325	C₄⋊C₄×C₃₁	—	2	1	no	—
326	C₄⋊C₄×C₃₁	—	2	2	no	—
327	C₄⋊C₄×C₃₁	—	2	1	no	—
328	C₄⋊C₄×C₃₁	—	2	2	no	—
329	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
330	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
331	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
332	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
333	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
334	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
335	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
336	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
337	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
338	C₂²⋊C₄×C₃₁	—	2	2	no	—
339	C₂²⋊C₄×C₃₁	—	2	2	no	—
340	C₂²⋊C₄×C₃₁	—	2	1	no	—
341	C₂²⋊C₄×C₃₁	—	2	1	no	—
342	C₂²⋊C₄×C₃₁	—	2	1	no	—
343	C₂²⋊C₄×C₃₁	—	2	4	no	—
344	C₂²⋊C₄×C₃₁	—	2	4	no	—
345	C₂²⋊C₄×C₃₁	—	2	4	no	—
346	C₂²⋊C₄×C₃₁	—	2	4	no	—
347	C₂²⋊C₄×C₃₁	—	2	1	no	—
348	C₂²⋊C₄×C₃₁	—	2	2	no	—
349	C₂²⋊C₄×C₃₁	—	2	2	no	—
350	C₂²⋊C₄×C₃₁	—	2	1	no	—
351	C₂²⋊C₄×C₃₁	—	2	2	no	—
352	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
353	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
354	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
355	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
356	C₄²×C₃₁	—	2	2	no	—
357	C₄²×C₃₁	—	2	2	no	—
358	C₄²×C₃₁	—	2	2	no	—
359	C₄²×C₃₁	—	2	1	no	—
360	C₄²×C₃₁	C₂×D₄	1	2	yes	—
361	C₄²×C₃₁	C₂×D₄	1	2	yes	—
362	C₄²×C₃₁	C₂⁴	1	2	yes	—
363	C₄²×C₃₁	C₂⁴	1	2	yes	—
364	#60812	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
365	C₂³×C₃₁	—	2	2	no	—
366	C₂³×C₃₁	—	2	2	no	—
367	C₂³×C₃₁	—	2	1	no	—
368	C₂³×C₃₁	—	2	4	no	—
369	C₂³×C₃₁	—	2	2	no	—
370	C₂³×C₃₁	—	4	1	no	—
371	C₂³×C₃₁	—	4	2	no	—
372	C₂³×C₃₁	—	4	4	no	—
373	C₂³×C₃₁	—	4	4	no	—
374	C₂³×C₃₁	—	4	2	no	—
375	C₂³×C₃₁	—	4	4	no	—
376	C₂³×C₃₁	—	4	4	no	—
377	C₂³×C₃₁	—	4	2	no	—
378	C₂³×C₃₁	—	4	4	no	—
379	C₂³×C₃₁	—	8	2	no	—
380	C₂³×C₃₁	—	8	2	no	—
381	C₂³×C₃₁	—	8	2	no	—
382	C₂³×C₃₁	—	8	2	no	—
383	C₂³×C₃₁	—	8	16	no	—
384	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
385	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
386	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
387	Q₈×C₃₁	—	2	4	no	—
388	Q₈×C₃₁	—	2	2	no	—
389	Q₈×C₃₁	—	2	2	no	—
390	Q₈×C₃₁	—	2	2	no	—
391	Q₈×C₃₁	—	4	2	no	—
392	Q₈×C₃₁	—	4	2	no	—
393	Q₈×C₃₁	—	8	2	no	—
394	D₄×C₃₁	—	2	2	no	—
395	D₄×C₃₁	—	2	4	no	—
396	D₄×C₃₁	—	2	2	no	—
397	D₄×C₃₁	—	2	4	no	—
398	D₄×C₃₁	—	2	2	no	—
399	D₄×C₃₁	—	4	4	no	—
400	D₄×C₃₁	—	4	4	no	—
401	D₄×C₃₁	—	4	2	no	—
402	D₄×C₃₁	—	4	4	no	—
403	D₄×C₃₁	—	4	4	no	—
404	D₄×C₃₁	—	4	2	no	—
405	D₄×C₃₁	—	4	2	no	—
406	D₄×C₃₁	—	4	4	no	—
407	D₄×C₃₁	—	8	4	no	—
408	D₄×C₃₁	—	8	4	no	—
409	D₄×C₃₁	—	8	4	no	—
410	D₄×C₃₁	—	8	4	no	—
411	D₄×C₃₁	—	8	1	no	—
412	C₂×C₄×C₃₁	—	2	2	no	—
413	C₂×C₄×C₃₁	—	2	4	no	—
414	C₂×C₄×C₃₁	—	2	2	no	—
415	C₂×C₄×C₃₁	—	2	2	no	—
416	C₂×C₄×C₃₁	—	2	2	no	—
417	C₂×C₄×C₃₁	—	2	2	no	—
418	C₂×C₄×C₃₁	—	2	1	no	—
419	C₂×C₄×C₃₁	—	2	1	no	—
420	C₂×C₄×C₃₁	—	2	2	no	—
421	C₂×C₄×C₃₁	—	2	1	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	2	2	no	—
424	C₂×C₄×C₃₁	—	4	2	no	—
425	C₂×C₄×C₃₁	—	4	4	no	—
426	C₂×C₄×C₃₁	—	4	2	no	—
427	C₂×C₄×C₃₁	—	4	2	no	—
428	C₂×C₄×C₃₁	—	4	4	no	—
429	C₂×C₄×C₃₁	—	4	2	no	—
430	C₂×C₄×C₃₁	—	8	2	no	—
431	C₂×C₄×C₃₁	—	8	1	no	—
432	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
437	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
440	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
441	C₈×C₃₁	—	2	2	no	—
442	C₈×C₃₁	—	2	2	no	—
443	C₈×C₃₁	—	2	4	no	—
444	#3495	C₂×C₃₁	1	1	yes	characteristic, complemented
445	C₂×#535	C₂×C₃₁	1	1	yes	characteristic, complemented
446	#3224	C₂×C₃₁	1	4	yes	complemented
447	#3222	C₂×C₃₁	1	4	yes	complemented
448	#3217	C₂×C₃₁	1	2	yes	complemented
449	#3215	C₂×C₃₁	1	2	yes	complemented
450	#3211	C₂×C₃₁	1	2	yes	complemented
451	#3208	C₂×C₃₁	1	2	yes	complemented
452	#3154	C₂×C₃₁	1	2	yes	complemented
453	#3136	C₂×C₃₁	1	2	yes	complemented
454	#3045	C₂×C₃₁	1	2	yes	complemented
455	#3043	C₂×C₃₁	1	2	yes	complemented
456	#3007	C₂×C₃₁	1	1	yes	characteristic, complemented
457	#3003	C₂×C₃₁	1	1	yes	characteristic, complemented
458	#3002	C₂×C₃₁	1	1	yes	characteristic, complemented
459	C₂×#450	C₂×C₃₁	1	1	yes	characteristic, complemented
460	#2924	C₂×C₃₁	1	1	yes	characteristic, complemented
461	C₂²×C₃₁	—	2	1	no	—
462	C₂²×C₃₁	—	2	1	no	—
463	C₂²×C₃₁	—	2	1	no	—
464	C₂²×C₃₁	—	2	1	no	—
465	C₂²×C₃₁	—	2	1	no	—
466	C₂²×C₃₁	—	2	1	no	—
467	C₂²×C₃₁	—	2	1	no	—
468	C₂²×C₃₁	—	4	4	no	—
469	C₂²×C₃₁	—	4	1	no	—
470	C₂²×C₃₁	—	4	2	no	—
471	C₂²×C₃₁	—	4	4	no	—
472	C₂²×C₃₁	—	4	2	no	—
473	C₂²×C₃₁	—	4	1	no	—
474	C₂²×C₃₁	—	4	4	no	—
475	C₂²×C₃₁	—	4	1	no	—
476	C₂²×C₃₁	—	4	2	no	—
477	C₂²×C₃₁	—	4	4	no	—
478	C₂²×C₃₁	—	8	4	no	—
479	C₂²×C₃₁	—	8	8	no	—
480	C₂²×C₃₁	—	8	8	no	—
481	C₂²×C₃₁	—	8	8	no	—
482	C₂²×C₃₁	#535	1	2	yes	—
483	C₂²×C₃₁	#577	1	2	yes	—
484	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
485	C₄×C₃₁	—	2	2	no	—
486	C₄×C₃₁	—	2	2	no	—
487	C₄×C₃₁	—	2	1	no	—
488	C₄×C₃₁	—	2	1	no	—
489	C₄×C₃₁	—	2	2	no	—
490	C₄×C₃₁	—	2	2	no	—
491	C₄×C₃₁	—	4	2	no	—
492	C₄×C₃₁	—	4	1	no	—
493	C₄×C₃₁	—	4	2	no	—
494	C₄×C₃₁	—	4	1	no	—
495	C₄×C₃₁	—	4	2	no	—
496	C₄×C₃₁	—	4	1	no	—
497	C₄×C₃₁	#535	1	2	yes	—
498	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
499	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
500	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
501	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
502	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
503	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
504	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
505	#556	—	2	1	no	—
506	#554	—	2	1	no	—
507	#552	—	2	2	no	—
508	#552	—	2	1	no	—
509	#552	—	2	1	no	—
510	#551	—	2	2	no	—
511	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
512	#542	C₂²×C₃₁	1	2	yes	complemented
513	#541	C₂²×C₃₁	1	2	yes	complemented
514	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
515	#535	—	2	1	no	—
516	#535	—	2	2	no	—
517	#535	—	2	1	no	—
518	#535	C₂²×C₃₁	1	2	yes	—
519	#535	C₂²×C₃₁	1	4	yes	—
520	#535	C₂²×C₃₁	1	2	yes	—
521	#533	C₂²×C₃₁	1	2	yes	complemented
522	C₂×#127	C₂²×C₃₁	1	2	yes	—
523	#529	C₂²×C₃₁	1	2	yes	complemented
524	C₂×#124	C₂²×C₃₁	1	2	yes	—
525	#525	C₂²×C₃₁	1	1	yes	characteristic
526	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
527	C₂×#121	—	2	1	no	—
528	C₂×#121	—	2	1	no	—
529	C₂×#120	—	2	2	no	—
530	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
531	#519	C₂²×C₃₁	1	1	yes	characteristic, complemented
532	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
533	#497	C₂²×C₃₁	1	4	yes	complemented
534	#496	C₂²×C₃₁	1	4	yes	complemented
535	#495	C₂²×C₃₁	1	4	yes	complemented
536	#492	C₂²×C₃₁	1	4	yes	complemented
537	#490	C₂²×C₃₁	1	4	yes	complemented
538	#489	C₂²×C₃₁	1	4	yes	complemented
539	#488	C₂²×C₃₁	1	4	yes	complemented
540	#486	C₂²×C₃₁	1	4	yes	complemented
541	#464	C₂²×C₃₁	1	4	yes	complemented
542	#464	C₂²×C₃₁	1	4	yes	complemented
543	#464	C₂²×C₃₁	1	4	yes	complemented
544	#463	C₂²×C₃₁	1	4	yes	complemented
545	#460	C₂²×C₃₁	1	4	yes	complemented
546	#460	C₂²×C₃₁	1	4	yes	complemented
547	#460	C₂²×C₃₁	1	4	yes	complemented
548	#459	C₂²×C₃₁	1	4	yes	complemented
549	#452	C₂²×C₃₁	1	2	yes	complemented
550	#452	C₂²×C₃₁	1	4	yes	complemented
551	#451	C₂²×C₃₁	1	2	yes	complemented
552	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
553	#450	C₂²×C₃₁	1	2	yes	—
554	#450	C₂²×C₃₁	1	2	yes	—
555	#450	C₂²×C₃₁	1	2	yes	—
556	#450	C₂²×C₃₁	1	2	yes	complemented
557	#450	C₂²×C₃₁	1	4	yes	complemented
558	#450	C₂²×C₃₁	1	1	yes	characteristic, complemented
559	#450	C₂²×C₃₁	1	2	yes	complemented
560	#449	C₂²×C₃₁	1	2	yes	complemented
561	#448	C₂²×C₃₁	1	1	yes	characteristic, complemented
562	#447	C₂²×C₃₁	1	2	yes	—
563	#447	C₂²×C₃₁	1	2	yes	complemented
564	#447	C₂²×C₃₁	1	1	yes	characteristic, complemented
565	#433	C₂²×C₃₁	1	4	yes	complemented
566	#432	C₂²×C₃₁	1	2	yes	complemented
567	#431	C₂²×C₃₁	1	2	yes	complemented
568	#424	C₂²×C₃₁	1	2	yes	complemented
569	#418	C₂²×C₃₁	1	2	yes	complemented
570	#417	C₂²×C₃₁	1	2	yes	complemented
571	#416	C₂²×C₃₁	1	2	yes	complemented
572	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
573	#407	C₂²×C₃₁	1	1	yes	characteristic
574	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
575	#405	C₂²×C₃₁	1	2	yes	complemented
576	C₂×C₃₁	—	2	2	no	—
577	C₂×C₃₁	—	2	2	no	—
578	C₂×C₃₁	—	4	1	no	—
579	C₂×C₃₁	—	8	1	no	—
580	C₂×C₃₁	—	8	2	no	—
581	C₂×C₃₁	—	8	4	no	—
582	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
583	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
584	C₂×C₃₁	#3585	1	1	yes	characteristic
585	C₂⁵	—	2	1	no	—
586	C₂×#41	—	2	1	no	—
587	C₂×#41	—	2	1	no	—
588	C₂×#41	—	4	4	no	—
589	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
590	C₂×#41	C₂³×C₃₁	1	2	yes	—
591	C₂×#41	C₂³×C₃₁	1	2	yes	—
592	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
593	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
594	C₂²×D₄	—	2	1	no	—
595	C₂²×D₄	—	2	1	no	—
596	C₂²×D₄	—	2	1	no	—
597	C₂²×D₄	—	2	1	no	—
598	C₂²×D₄	—	2	2	no	—
599	C₂²×D₄	—	2	2	no	—
600	C₂²×D₄	—	4	4	no	—
601	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
602	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
603	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
604	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
605	C₂³×C₄	—	2	1	no	—
606	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
607	#137	—	4	4	no	—
608	AGL(1,ℤ/8)	—	4	4	no	—
609	#135	—	4	4	no	—
610	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	complemented
611	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	complemented
612	C₂×SD₁₆	—	4	4	no	—
613	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
614	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
615	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
616	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	complemented
617	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	complemented
618	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	complemented
619	C₂×D₈	C₂³×C₃₁	1	4	yes	—
620	C₂×D₈	C₂³×C₃₁	1	2	yes	complemented
621	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
622	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
623	C₄⋊Q₈	—	2	1	no	—
624	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	complemented
625	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	complemented
626	#127	—	2	2	no	—
627	#127	—	2	2	no	—
628	#127	C₂³×C₃₁	1	4	yes	—
629	#127	C₂³×C₃₁	1	4	yes	—
630	#126	—	2	2	no	—
631	#126	—	2	2	no	—
632	#126	—	2	2	no	—
633	#126	—	2	2	no	—
634	#125	—	2	2	no	—
635	#125	—	2	2	no	—
636	#125	—	2	1	no	—
637	#125	—	2	2	no	—
638	#125	C₂³×C₃₁	1	2	yes	complemented
639	#124	—	2	2	no	—
640	#124	—	2	2	no	—
641	#124	—	2	2	no	—
642	#124	C₂³×C₃₁	1	4	yes	—
643	#124	C₂³×C₃₁	1	4	yes	—
644	#124	C₂³×C₃₁	1	2	yes	complemented
645	#123	—	2	1	no	—
646	#123	—	2	2	no	—
647	#123	—	2	2	no	—
648	#123	—	2	2	no	—
649	C₂²⋊Q₈	—	2	1	no	—
650	C₂²⋊Q₈	—	2	1	no	—
651	C₂²⋊Q₈	—	2	2	no	—
652	C₂²⋊Q₈	—	2	1	no	—
653	C₂²⋊Q₈	—	2	1	no	—
654	C₂²⋊Q₈	—	2	2	no	—
655	C₂²⋊Q₈	—	2	2	no	—
656	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
657	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
658	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
659	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
660	#121	—	2	2	no	—
661	#121	—	2	2	no	—
662	#121	—	2	2	no	—
663	#121	—	2	4	no	—
664	#121	—	2	2	no	—
665	#121	—	2	4	no	—
666	#121	C₂³×C₃₁	1	1	yes	characteristic
667	#121	C₂³×C₃₁	1	1	yes	characteristic
668	#120	—	2	1	no	—
669	#120	—	2	4	no	—
670	#120	—	2	4	no	—
671	#120	—	2	4	no	—
672	#120	—	2	4	no	—
673	C₄×Q₈	—	2	1	no	—
674	C₄×Q₈	—	2	1	no	—
675	C₄×Q₈	—	2	2	no	—
676	C₄×Q₈	C₂³×C₃₁	1	2	yes	complemented
677	C₄×Q₈	C₂³×C₃₁	1	2	yes	complemented
678	C₄×Q₈	C₂³×C₃₁	1	2	yes	complemented
679	C₄×D₄	—	2	1	no	—
680	C₄×D₄	—	2	1	no	—
681	C₄×D₄	—	2	2	no	—
682	C₄×D₄	—	2	2	no	—
683	C₄×D₄	C₂³×C₃₁	1	2	yes	complemented
684	#117	—	2	2	no	—
685	#117	—	2	1	no	—
686	#117	—	2	2	no	—
687	#117	—	2	2	no	—
688	#117	D₄×C₃₁	1	1	yes	characteristic
689	#117	D₄×C₃₁	1	2	yes	—
690	#117	D₄×C₃₁	1	1	yes	characteristic
691	#117	C₂³×C₃₁	1	1	yes	characteristic
692	#117	C₂³×C₃₁	1	1	yes	characteristic
693	#117	C₂³×C₃₁	1	1	yes	characteristic
694	#117	C₂³×C₃₁	1	2	yes	—
695	C₂×C₄⋊C₄	—	2	1	no	—
696	C₂×C₄⋊C₄	—	2	1	no	—
697	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
698	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
699	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	—	2	1	no	—
701	C₂×C₂²⋊C₄	—	2	2	no	—
702	C₂×C₂²⋊C₄	—	2	2	no	—
703	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
704	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
705	C₄⋊C₈	C₂³×C₃₁	1	4	yes	complemented
706	C₄⋊C₈	C₂³×C₃₁	1	4	yes	complemented
707	#103	C₂³×C₃₁	1	2	yes	complemented
708	#103	C₂³×C₃₁	1	2	yes	complemented
709	#103	C₂³×C₃₁	1	4	yes	complemented
710	#102	C₂³×C₃₁	1	4	yes	—
711	#102	C₂³×C₃₁	1	4	yes	—
712	#102	C₂³×C₃₁	1	4	yes	—
713	#102	C₂³×C₃₁	1	4	yes	—
714	#102	C₂³×C₃₁	1	2	yes	complemented
715	#102	C₂³×C₃₁	1	2	yes	complemented
716	#102	C₂³×C₃₁	1	4	yes	complemented
717	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
718	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
719	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
720	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
721	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
722	#97	C₂³×C₃₁	1	4	yes	complemented
723	C₄×C₈	C₂³×C₃₁	1	4	yes	complemented
724	C₃₁	#60812	1	1	yes	characteristic, direct product factor, Sylow
725	C₂⁴	—	2	2	no	—
726	C₂⁴	—	2	1	no	—
727	C₂⁴	—	2	2	no	—
728	C₂⁴	—	2	2	no	—
729	C₂⁴	—	4	4	no	—
730	C₂⁴	—	8	2	no	—
731	C₂⁴	—	8	2	no	—
732	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
733	#41	—	2	4	no	—
734	#41	—	2	4	no	—
735	#41	—	2	4	no	—
736	#41	—	4	2	no	—
737	#41	—	4	2	no	—
738	#41	—	4	4	no	—
739	#41	—	4	4	no	—
740	C₂×Q₈	—	2	1	no	—
741	C₂×Q₈	—	2	1	no	—
742	C₂×Q₈	—	2	2	no	—
743	C₂×Q₈	—	2	4	no	—
744	C₂×Q₈	—	4	2	no	—
745	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
746	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
747	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
748	C₂×D₄	—	2	1	no	—
749	C₂×D₄	—	2	1	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	1	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	1	no	—
757	C₂×D₄	—	2	4	no	—
758	C₂×D₄	—	2	4	no	—
759	C₂×D₄	—	2	4	no	—
760	C₂×D₄	—	2	4	no	—
761	C₂×D₄	—	2	4	no	—
762	C₂×D₄	—	2	4	no	—
763	C₂×D₄	—	4	4	no	—
764	C₂×D₄	—	4	4	no	—
765	C₂×D₄	—	4	2	no	—
766	C₂×D₄	—	4	4	no	—
767	C₂×D₄	—	4	4	no	—
768	C₂×D₄	—	4	4	no	—
769	C₂×D₄	—	4	4	no	—
770	C₂×D₄	—	8	4	no	—
771	C₂×D₄	—	8	4	no	—
772	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
773	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
774	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
775	C₂²×C₄	—	2	4	no	—
776	C₂²×C₄	—	2	1	no	—
777	C₂²×C₄	—	2	1	no	—
778	C₂²×C₄	—	2	1	no	—
779	C₂²×C₄	—	2	1	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	4	4	no	—
784	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
785	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
786	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
787	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
788	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
792	Q₁₆	—	4	2	no	—
793	Q₁₆	—	4	4	no	—
794	SD₁₆	—	4	4	no	—
795	SD₁₆	—	4	4	no	—
796	SD₁₆	—	4	4	no	—
797	SD₁₆	—	4	2	no	—
798	SD₁₆	—	4	2	no	—
799	SD₁₆	—	4	4	no	—
800	D₈	—	4	4	no	—
801	D₈	—	4	2	no	—
802	M₁₆	—	2	4	no	—
803	C₂×C₈	—	2	4	no	—
804	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
805	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
806	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
807	C₄⋊C₄	—	2	1	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	1	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
821	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
822	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
823	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
824	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
825	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
827	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
828	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	1	no	—
832	C₂²⋊C₄	—	2	1	no	—
833	C₂²⋊C₄	—	2	1	no	—
834	C₂²⋊C₄	—	2	4	no	—
835	C₂²⋊C₄	—	2	4	no	—
836	C₂²⋊C₄	—	2	4	no	—
837	C₂²⋊C₄	—	2	4	no	—
838	C₂²⋊C₄	—	2	1	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	1	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
844	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
845	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
846	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	1	no	—
851	C₄²	C₂×D₄×C₃₁	1	2	yes	—
852	C₄²	C₂×D₄×C₃₁	1	2	yes	—
853	C₄²	C₂⁴×C₃₁	1	2	yes	—
854	C₄²	C₂⁴×C₃₁	1	2	yes	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	4	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	4	1	no	—
861	C₂³	—	4	2	no	—
862	C₂³	—	4	4	no	—
863	C₂³	—	4	4	no	—
864	C₂³	—	4	2	no	—
865	C₂³	—	4	4	no	—
866	C₂³	—	4	4	no	—
867	C₂³	—	4	2	no	—
868	C₂³	—	4	4	no	—
869	C₂³	—	8	2	no	—
870	C₂³	—	8	2	no	—
871	C₂³	—	8	2	no	—
872	C₂³	—	8	2	no	—
873	C₂³	—	8	16	no	—
874	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
875	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
876	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
877	Q₈	—	2	4	no	—
878	Q₈	—	2	2	no	—
879	Q₈	—	2	2	no	—
880	Q₈	—	2	2	no	—
881	Q₈	—	4	2	no	—
882	Q₈	—	4	2	no	—
883	Q₈	—	8	2	no	—
884	D₄	—	2	2	no	—
885	D₄	—	2	4	no	—
886	D₄	—	2	2	no	—
887	D₄	—	2	4	no	—
888	D₄	—	2	2	no	—
889	D₄	—	4	4	no	—
890	D₄	—	4	4	no	—
891	D₄	—	4	2	no	—
892	D₄	—	4	4	no	—
893	D₄	—	4	4	no	—
894	D₄	—	4	2	no	—
895	D₄	—	4	2	no	—
896	D₄	—	4	4	no	—
897	D₄	—	8	4	no	—
898	D₄	—	8	4	no	—
899	D₄	—	8	4	no	—
900	D₄	—	8	4	no	—
901	D₄	—	8	1	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	4	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	4	2	no	—
915	C₂×C₄	—	4	4	no	—
916	C₂×C₄	—	4	2	no	—
917	C₂×C₄	—	4	2	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	—	4	2	no	—
920	C₂×C₄	—	8	2	no	—
921	C₂×C₄	—	8	1	no	—
922	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
923	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
924	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
925	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
926	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
927	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
928	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
929	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
930	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
931	C₈	—	2	2	no	—
932	C₈	—	2	2	no	—
933	C₈	—	2	4	no	—
934	C₂²	—	2	1	no	—
935	C₂²	—	2	1	no	—
936	C₂²	—	2	1	no	—
937	C₂²	—	2	1	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	1	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	4	4	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	4	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	4	no	—
948	C₂²	—	4	1	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	4	no	—
951	C₂²	—	8	8	no	—
952	C₂²	—	8	4	no	—
953	C₂²	—	8	8	no	—
954	C₂²	—	8	8	no	—
955	C₂²	C₃₁×#535	1	2	yes	—
956	C₂²	C₃₁×#577	1	2	yes	—
957	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
958	C₄	—	2	1	no	—
959	C₄	—	2	1	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	1	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	1	no	—
970	C₄	C₃₁×#535	1	2	yes	—
971	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
972	C₂	—	2	2	no	—
973	C₂	—	2	2	no	—
974	C₂	—	4	1	no	—
975	C₂	—	8	4	no	—
976	C₂	—	8	2	no	—
977	C₂	—	8	1	no	—
978	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
979	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
980	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 ◁ 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. C₂×C₃₁×#535	C₂	semidirect
3. C₃₁×#3224	C₂	semidirect
4. C₃₁×#3222	C₂	semidirect
5. C₃₁×#3217	C₂	semidirect
6. C₃₁×#3215	C₂	semidirect
7. C₃₁×#3211	C₂	semidirect
8. C₃₁×#3208	C₂	semidirect
9. C₃₁×#3154	C₂	semidirect
10. C₃₁×#3136	C₂	semidirect
11. C₃₁×#3045	C₂	semidirect
12. C₃₁×#3043	C₂	semidirect
13. C₃₁×#3007	C₂	semidirect
14. C₃₁×#3003	C₂	semidirect
15. C₃₁×#3002	C₂	semidirect
16. C₂×C₃₁×#450	C₂	semidirect
17. C₃₁×#2924	C₂	semidirect
20. C₂×C₃₁×#137	C₂²	semidirect
21. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₃₁×#135	C₂²	semidirect
23. C₂²×SD₁₆×C₃₁	C₂²	semidirect
30. C₃₁×#544	C₂²	semidirect
31. C₃₁×#542	C₂²	semidirect
32. C₃₁×#541	C₂²	semidirect
33. C₃₁×#536	C₂²	semidirect
40. C₃₁×#533	C₂²	semidirect
42. C₃₁×#529	C₂²	semidirect
49. C₃₁×#520	C₂²	semidirect
50. C₃₁×#519	C₂²	semidirect
52. C₃₁×#497	C₂²	semidirect
53. C₃₁×#496	C₂²	semidirect
54. C₃₁×#495	C₂²	semidirect
55. C₃₁×#492	C₂²	semidirect
56. C₃₁×#490	C₂²	semidirect
57. C₃₁×#489	C₂²	semidirect
58. C₃₁×#488	C₂²	semidirect
59. C₃₁×#486	C₂²	semidirect
60. C₃₁×#464	C₂²	semidirect
61. C₃₁×#464	C₂²	semidirect
62. C₃₁×#464	C₂²	semidirect
63. C₃₁×#463	C₂²	semidirect
64. C₃₁×#460	C₂²	semidirect
65. C₃₁×#460	C₂²	semidirect
66. C₃₁×#460	C₂²	semidirect
67. C₃₁×#459	C₂²	semidirect
68. C₃₁×#452	C₂²	semidirect
69. C₃₁×#452	C₂²	semidirect
70. C₃₁×#451	C₂²	semidirect
71. C₃₁×#451	C₂²	semidirect
75. C₃₁×#450	C₂²	semidirect
76. C₃₁×#450	C₂²	semidirect
77. C₃₁×#450	C₂²	semidirect
78. C₃₁×#450	C₂²	semidirect
79. C₃₁×#449	C₂²	semidirect
80. C₃₁×#448	C₂²	semidirect
82. C₃₁×#447	C₂²	semidirect
83. C₃₁×#447	C₂²	semidirect
84. C₃₁×#433	C₂²	semidirect
85. C₃₁×#432	C₂²	semidirect
86. C₃₁×#431	C₂²	semidirect
87. C₃₁×#424	C₂²	semidirect
88. C₃₁×#418	C₂²	semidirect
89. C₃₁×#417	C₂²	semidirect
90. C₃₁×#416	C₂²	semidirect
91. C₂×C₃₁×#102	C₂²	semidirect
94. C₃₁×#405	C₂²	semidirect
120. C₂×Q₁₆×C₃₁	C₂³	semidirect
121. C₂×Q₁₆×C₃₁	C₂³	semidirect
126. C₂×SD₁₆×C₃₁	C₂³	semidirect
127. C₂×SD₁₆×C₃₁	C₂³	semidirect
128. C₂×SD₁₆×C₃₁	C₂³	semidirect
130. C₂×D₈×C₃₁	C₂³	semidirect
134. C₃₁×C₄⋊Q₈	C₂³	semidirect
135. C₃₁×C₄⋊Q₈	C₂³	semidirect
148. C₃₁×#125	C₂³	semidirect
154. C₃₁×#124	C₂³	semidirect
186. C₄×Q₈×C₃₁	C₂³	semidirect
187. C₄×Q₈×C₃₁	C₂³	semidirect
188. C₄×Q₈×C₃₁	C₂³	semidirect
193. C₄×D₄×C₃₁	C₂³	semidirect
215. C₃₁×C₄⋊C₈	C₂³	semidirect
216. C₃₁×C₄⋊C₈	C₂³	semidirect
217. C₃₁×#103	C₂³	semidirect
218. C₃₁×#103	C₂³	semidirect
219. C₃₁×#103	C₂³	semidirect
224. C₃₁×#102	C₂³	semidirect
225. C₃₁×#102	C₂³	semidirect
226. C₃₁×#102	C₂³	semidirect
232. C₃₁×#97	C₂³	semidirect
233. C₄×C₈×C₃₁	C₂³	semidirect
364. #60812	C₃₁	direct (N × H)
444. #3495	C₂×C₃₁	semidirect
445. C₂×#535	C₂×C₃₁	semidirect
446. #3224	C₂×C₃₁	semidirect
447. #3222	C₂×C₃₁	semidirect
448. #3217	C₂×C₃₁	semidirect
449. #3215	C₂×C₃₁	semidirect
450. #3211	C₂×C₃₁	semidirect
451. #3208	C₂×C₃₁	semidirect
452. #3154	C₂×C₃₁	semidirect
453. #3136	C₂×C₃₁	semidirect
454. #3045	C₂×C₃₁	semidirect
455. #3043	C₂×C₃₁	semidirect
456. #3007	C₂×C₃₁	semidirect
457. #3003	C₂×C₃₁	semidirect
458. #3002	C₂×C₃₁	semidirect
459. C₂×#450	C₂×C₃₁	semidirect
460. #2924	C₂×C₃₁	semidirect
501. C₂×#137	C₂²×C₃₁	semidirect
502. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
503. C₂×#135	C₂²×C₃₁	semidirect
504. C₂²×SD₁₆	C₂²×C₃₁	semidirect
511. #544	C₂²×C₃₁	semidirect
512. #542	C₂²×C₃₁	semidirect
513. #541	C₂²×C₃₁	semidirect
514. #536	C₂²×C₃₁	semidirect
521. #533	C₂²×C₃₁	semidirect
523. #529	C₂²×C₃₁	semidirect
530. #520	C₂²×C₃₁	semidirect
531. #519	C₂²×C₃₁	semidirect
533. #497	C₂²×C₃₁	semidirect
534. #496	C₂²×C₃₁	semidirect
535. #495	C₂²×C₃₁	semidirect
536. #492	C₂²×C₃₁	semidirect
537. #490	C₂²×C₃₁	semidirect
538. #489	C₂²×C₃₁	semidirect
539. #488	C₂²×C₃₁	semidirect
540. #486	C₂²×C₃₁	semidirect
541. #464	C₂²×C₃₁	semidirect
542. #464	C₂²×C₃₁	semidirect
543. #464	C₂²×C₃₁	semidirect
544. #463	C₂²×C₃₁	semidirect
545. #460	C₂²×C₃₁	semidirect
546. #460	C₂²×C₃₁	semidirect
547. #460	C₂²×C₃₁	semidirect
548. #459	C₂²×C₃₁	semidirect
549. #452	C₂²×C₃₁	semidirect
550. #452	C₂²×C₃₁	semidirect
551. #451	C₂²×C₃₁	semidirect
552. #451	C₂²×C₃₁	semidirect
556. #450	C₂²×C₃₁	semidirect
557. #450	C₂²×C₃₁	semidirect
558. #450	C₂²×C₃₁	semidirect
559. #450	C₂²×C₃₁	semidirect
560. #449	C₂²×C₃₁	semidirect
561. #448	C₂²×C₃₁	semidirect
563. #447	C₂²×C₃₁	semidirect
564. #447	C₂²×C₃₁	semidirect
565. #433	C₂²×C₃₁	semidirect
566. #432	C₂²×C₃₁	semidirect
567. #431	C₂²×C₃₁	semidirect
568. #424	C₂²×C₃₁	semidirect
569. #418	C₂²×C₃₁	semidirect
570. #417	C₂²×C₃₁	semidirect
571. #416	C₂²×C₃₁	semidirect
572. C₂×#102	C₂²×C₃₁	semidirect
575. #405	C₂²×C₃₁	semidirect
610. C₂×Q₁₆	C₂³×C₃₁	semidirect
611. C₂×Q₁₆	C₂³×C₃₁	semidirect
616. C₂×SD₁₆	C₂³×C₃₁	semidirect
617. C₂×SD₁₆	C₂³×C₃₁	semidirect
618. C₂×SD₁₆	C₂³×C₃₁	semidirect
620. C₂×D₈	C₂³×C₃₁	semidirect
624. C₄⋊Q₈	C₂³×C₃₁	semidirect
625. C₄⋊Q₈	C₂³×C₃₁	semidirect
638. #125	C₂³×C₃₁	semidirect
644. #124	C₂³×C₃₁	semidirect
676. C₄×Q₈	C₂³×C₃₁	semidirect
677. C₄×Q₈	C₂³×C₃₁	semidirect
678. C₄×Q₈	C₂³×C₃₁	semidirect
683. C₄×D₄	C₂³×C₃₁	semidirect
705. C₄⋊C₈	C₂³×C₃₁	semidirect
706. C₄⋊C₈	C₂³×C₃₁	semidirect
707. #103	C₂³×C₃₁	semidirect
708. #103	C₂³×C₃₁	semidirect
709. #103	C₂³×C₃₁	semidirect
714. #102	C₂³×C₃₁	semidirect
715. #102	C₂³×C₃₁	semidirect
716. #102	C₂³×C₃₁	semidirect
722. #97	C₂³×C₃₁	semidirect
723. C₄×C₈	C₂³×C₃₁	semidirect
724. C₃₁	#60812	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
C₂×C₃₁×#535	2
C₃₁×#3224	2
C₃₁×#3222	2
C₃₁×#3217	2
C₃₁×#3215	2
C₃₁×#3211	2
C₃₁×#3208	2
C₃₁×#3154	2
C₃₁×#3136	2
C₃₁×#3045	2
C₃₁×#3043	2
C₃₁×#3007	2
C₃₁×#3003	2
C₃₁×#3002	2
C₂×C₃₁×#450	2
C₃₁×#2924	2
#60812	31

Subgroups — C31×#60812 #21517571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60812 #21517571