Subgroups — C₃₁×#61789 #21518548

Order 7936.

1718 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3356	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3353	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3342	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3340	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3329	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3328	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3299	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3298	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3230	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3201	C₂	1	4	yes	maximal, complemented
14	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3097	C₂	1	4	yes	maximal, complemented
17	C₃₁×#2979	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#563	—	2	2	no	—
19	C₃₁×#559	—	2	1	no	—
20	Q₈²×C₃₁	—	2	1	no	—
21	C₃₁×#556	C₂²	1	2	yes	—
22	C₃₁×#556	C₂²	1	2	yes	—
23	C₃₁×#556	C₂²	1	2	yes	—
24	C₃₁×#555	C₂²	1	2	yes	—
25	C₃₁×#554	C₂²	1	2	yes	—
26	C₃₁×#553	—	2	2	no	—
27	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
28	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
29	C₃₁×#548	—	2	2	no	—
30	C₃₁×#547	C₂²	1	2	yes	—
31	C₃₁×#542	—	2	2	no	—
32	C₃₁×#542	—	2	2	no	—
33	C₃₁×#542	—	2	2	no	—
34	C₃₁×#537	C₂²	1	2	yes	—
35	C₃₁×#536	C₂²	1	4	yes	—
36	C₃₁×#533	—	2	1	no	—
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₃₁×#533	C₂²	1	1	yes	characteristic
39	C₃₁×#532	—	2	1	no	—
40	C₃₁×#532	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
42	C₃₁×#520	C₂²	1	2	yes	—
43	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#500	C₂²	1	2	yes	—
45	C₃₁×#498	C₂²	1	2	yes	—
46	C₃₁×#487	C₂²	1	2	yes	—
47	C₃₁×#487	C₂²	1	2	yes	—
48	C₃₁×#485	C₂²	1	4	yes	—
49	C₃₁×#485	C₂²	1	4	yes	—
50	C₃₁×#485	C₂²	1	4	yes	—
51	C₃₁×#485	C₂²	1	2	yes	—
52	C₃₁×#485	C₂²	1	2	yes	—
53	C₃₁×#484	C₂²	1	4	yes	—
54	C₃₁×#484	C₂²	1	4	yes	—
55	C₃₁×#483	C₂²	1	4	yes	—
56	C₃₁×#483	C₂²	1	4	yes	—
57	C₃₁×#482	C₂²	1	4	yes	—
58	C₃₁×#477	C₂²	1	2	yes	—
59	C₃₁×#477	C₂²	1	2	yes	—
60	C₃₁×#475	C₂²	1	1	yes	characteristic
61	C₃₁×#475	C₂²	1	2	yes	—
62	C₃₁×#475	C₂²	1	2	yes	—
63	C₃₁×#475	C₂²	1	1	yes	characteristic
64	C₃₁×#474	C₂²	1	1	yes	characteristic
65	C₃₁×#474	C₂²	1	1	yes	characteristic
66	C₃₁×#470	C₂²	1	4	yes	—
67	C₃₁×#468	C₂²	1	4	yes	—
68	C₃₁×#467	C₂²	1	4	yes	—
69	C₃₁×#465	C₂²	1	4	yes	—
70	C₃₁×#462	C₂²	1	1	yes	characteristic
71	C₃₁×#462	C₂²	1	1	yes	characteristic
72	C₃₁×#461	C₂²	1	1	yes	characteristic
73	C₃₁×#461	C₂²	1	1	yes	characteristic
74	C₃₁×#452	C₂²	1	2	yes	—
75	C₃₁×#452	C₂²	1	2	yes	—
76	C₃₁×#451	C₂²	1	4	yes	—
77	C₃₁×#448	C₂²	1	4	yes	—
78	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
79	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
80	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
81	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
82	C₃₁×#436	C₂²	1	2	yes	—
83	C₃₁×#436	C₂²	1	2	yes	—
84	C₈×D₄×C₃₁	C₂²	1	2	yes	—
85	C₈×D₄×C₃₁	C₂²	1	2	yes	—
86	C₃₁×#431	C₂²	1	1	yes	characteristic
87	C₃₁×#431	C₂²	1	1	yes	characteristic
88	C₃₁×#428	C₂²	1	4	yes	—
89	C₃₁×#427	C₂²	1	4	yes	—
90	C₃₁×#419	C₂²	1	4	yes	—
91	C₂×C₃₁×#103	C₂²	1	4	yes	—
92	C₃₁×#408	C₂²	1	4	yes	—
93	C₂×#41×C₃₁	—	2	2	no	—
94	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
95	C₂×#41×C₃₁	C₂³	1	2	yes	—
96	C₂²×Q₈×C₃₁	—	2	1	no	—
97	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
98	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
99	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
100	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
101	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
102	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
103	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
104	C₃₁×C₄⋊Q₈	—	2	4	no	—
105	C₃₁×C₄⋊Q₈	—	2	2	no	—
106	C₃₁×C₄⋊Q₈	—	2	2	no	—
107	C₃₁×C₄⋊Q₈	—	2	1	no	—
108	C₃₁×C₄⋊Q₈	—	2	1	no	—
109	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
110	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₃₁×#127	D₄	1	1	yes	characteristic
117	C₃₁×#126	—	2	4	no	—
118	C₃₁×#126	—	2	4	no	—
119	C₃₁×#126	—	2	4	no	—
120	C₃₁×#125	—	2	2	no	—
121	C₃₁×#125	—	2	1	no	—
122	C₃₁×#125	—	2	1	no	—
123	C₃₁×#124	—	2	2	no	—
124	C₃₁×#124	—	2	4	no	—
125	C₃₁×#124	—	2	2	no	—
126	C₃₁×#124	—	2	2	no	—
127	C₃₁×#124	—	2	4	no	—
128	C₃₁×#124	D₄	1	2	yes	—
129	C₃₁×#123	—	2	4	no	—
130	C₃₁×#123	—	2	4	no	—
131	C₃₁×#123	—	2	4	no	—
132	C₃₁×C₂²⋊Q₈	—	2	2	no	—
133	C₃₁×C₂²⋊Q₈	—	2	1	no	—
134	C₃₁×C₂²⋊Q₈	—	2	1	no	—
135	C₃₁×C₂²⋊Q₈	—	2	2	no	—
136	C₃₁×C₂²⋊Q₈	—	2	4	no	—
137	C₃₁×C₂²⋊Q₈	—	2	4	no	—
138	C₃₁×C₂²⋊Q₈	—	2	4	no	—
139	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
140	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
141	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
143	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
144	C₃₁×#121	—	2	2	no	—
145	C₃₁×#121	—	2	2	no	—
146	C₃₁×#121	—	2	4	no	—
147	C₃₁×#121	D₄	1	2	yes	—
148	C₃₁×#121	D₄	1	2	yes	—
149	C₃₁×#121	C₂³	1	4	yes	—
150	C₄×Q₈×C₃₁	—	2	2	no	—
151	C₄×Q₈×C₃₁	—	2	2	no	—
152	C₄×Q₈×C₃₁	—	2	2	no	—
153	C₄×Q₈×C₃₁	—	2	2	no	—
154	C₄×Q₈×C₃₁	—	2	1	no	—
155	C₄×Q₈×C₃₁	—	2	1	no	—
156	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
157	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
158	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
159	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
160	C₄×D₄×C₃₁	—	2	2	no	—
161	C₄×D₄×C₃₁	—	2	4	no	—
162	C₄×D₄×C₃₁	—	2	2	no	—
163	C₄×D₄×C₃₁	—	2	2	no	—
164	C₄×D₄×C₃₁	—	2	2	no	—
165	C₄×D₄×C₃₁	—	2	1	no	—
166	C₄×D₄×C₃₁	—	2	1	no	—
167	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₃₁	C₂³	1	2	yes	—
170	C₄×D₄×C₃₁	C₂³	1	2	yes	—
171	C₃₁×#117	—	2	1	no	—
172	C₃₁×#117	—	2	1	no	—
173	C₃₁×#117	—	2	2	no	—
174	C₃₁×#117	—	2	1	no	—
175	C₃₁×#117	C₂³	1	4	yes	—
176	C₃₁×#117	C₂³	1	4	yes	—
177	C₃₁×#117	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
180	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₄²×C₃₁	—	2	1	no	—
182	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
183	C₃₁×#107	C₂³	1	2	yes	—
184	C₃₁×#107	C₂³	1	4	yes	—
185	C₃₁×#107	C₂³	1	2	yes	—
186	C₃₁×#107	C₂³	1	4	yes	—
187	C₃₁×#106	C₂³	1	2	yes	—
188	C₃₁×#106	C₂³	1	4	yes	—
189	C₃₁×#106	C₂³	1	2	yes	—
190	C₃₁×#106	C₂³	1	4	yes	—
191	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
192	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
194	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
195	C₃₁×#103	C₂³	1	2	yes	—
196	C₃₁×#103	C₂³	1	2	yes	—
197	C₃₁×#103	C₂³	1	4	yes	—
198	C₃₁×#103	C₂³	1	4	yes	—
199	C₃₁×#103	C₂³	1	2	yes	—
200	C₃₁×#103	C₂³	1	2	yes	—
201	C₃₁×#103	C₂³	1	4	yes	—
202	C₃₁×#103	C₂³	1	4	yes	—
203	C₃₁×#103	C₂³	1	2	yes	—
204	C₃₁×#103	C₂³	1	2	yes	—
205	C₃₁×#102	C₂³	1	2	yes	—
206	C₃₁×#102	C₂³	1	2	yes	—
207	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
209	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
210	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
211	C₄×C₈×C₃₁	C₂³	1	2	yes	—
212	C₄×C₈×C₃₁	C₂³	1	2	yes	—
213	#41×C₃₁	—	4	2	no	—
214	#41×C₃₁	—	4	2	no	—
215	#41×C₃₁	—	4	1	no	—
216	#41×C₃₁	—	4	1	no	—
217	#41×C₃₁	—	8	4	no	—
218	C₂×Q₈×C₃₁	—	2	1	no	—
219	C₂×Q₈×C₃₁	—	2	1	no	—
220	C₂×Q₈×C₃₁	—	2	2	no	—
221	C₂×Q₈×C₃₁	—	2	2	no	—
222	C₂×Q₈×C₃₁	—	2	4	no	—
223	C₂×Q₈×C₃₁	—	4	4	no	—
224	C₂×Q₈×C₃₁	—	4	4	no	—
225	C₂×Q₈×C₃₁	—	8	2	no	—
226	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
228	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
229	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
230	C₂×D₄×C₃₁	—	2	1	no	—
231	C₂×D₄×C₃₁	—	2	4	no	—
232	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
233	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
235	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₃₁	—	2	2	no	—
238	C₂²×C₄×C₃₁	—	2	4	no	—
239	C₂²×C₄×C₃₁	—	2	4	no	—
240	C₂²×C₄×C₃₁	—	2	1	no	—
241	C₂²×C₄×C₃₁	—	2	1	no	—
242	C₂²×C₄×C₃₁	—	2	1	no	—
243	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
247	Q₁₆×C₃₁	—	4	2	no	—
248	Q₁₆×C₃₁	—	4	2	no	—
249	SD₁₆×C₃₁	—	4	2	no	—
250	SD₁₆×C₃₁	—	4	2	no	—
251	M₁₆×C₃₁	—	4	4	no	—
252	C₂×C₈×C₃₁	—	4	4	no	—
253	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
254	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
255	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
256	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
257	C₄⋊C₄×C₃₁	—	2	2	no	—
258	C₄⋊C₄×C₃₁	—	2	2	no	—
259	C₄⋊C₄×C₃₁	—	2	2	no	—
260	C₄⋊C₄×C₃₁	—	2	4	no	—
261	C₄⋊C₄×C₃₁	—	2	1	no	—
262	C₄⋊C₄×C₃₁	—	2	1	no	—
263	C₄⋊C₄×C₃₁	—	2	1	no	—
264	C₄⋊C₄×C₃₁	—	2	1	no	—
265	C₄⋊C₄×C₃₁	—	2	1	no	—
266	C₄⋊C₄×C₃₁	—	2	1	no	—
267	C₄⋊C₄×C₃₁	—	2	1	no	—
268	C₄⋊C₄×C₃₁	—	2	1	no	—
269	C₄⋊C₄×C₃₁	—	2	4	no	—
270	C₄⋊C₄×C₃₁	—	2	4	no	—
271	C₄⋊C₄×C₃₁	—	2	4	no	—
272	C₄⋊C₄×C₃₁	—	2	2	no	—
273	C₄⋊C₄×C₃₁	—	2	2	no	—
274	C₄⋊C₄×C₃₁	—	2	2	no	—
275	C₄⋊C₄×C₃₁	—	2	2	no	—
276	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
281	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
282	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
283	C₂²⋊C₄×C₃₁	—	2	2	no	—
284	C₂²⋊C₄×C₃₁	—	2	2	no	—
285	C₂²⋊C₄×C₃₁	—	2	1	no	—
286	C₂²⋊C₄×C₃₁	—	2	4	no	—
287	C₂²⋊C₄×C₃₁	—	2	4	no	—
288	C₂²⋊C₄×C₃₁	—	2	4	no	—
289	C₂²⋊C₄×C₃₁	—	2	4	no	—
290	C₂²⋊C₄×C₃₁	—	2	4	no	—
291	C₂²⋊C₄×C₃₁	—	2	1	no	—
292	C₂²⋊C₄×C₃₁	—	2	1	no	—
293	C₂²⋊C₄×C₃₁	—	2	4	no	—
294	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
295	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
296	C₄²×C₃₁	—	2	1	no	—
297	C₄²×C₃₁	—	2	1	no	—
298	C₄²×C₃₁	—	2	1	no	—
299	C₄²×C₃₁	—	2	4	no	—
300	C₄²×C₃₁	—	2	2	no	—
301	C₄²×C₃₁	—	2	2	no	—
302	C₄²×C₃₁	—	2	4	no	—
303	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
307	#61789	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
308	C₂³×C₃₁	—	2	1	no	—
309	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
310	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
311	Q₈×C₃₁	—	2	2	no	—
312	Q₈×C₃₁	—	2	2	no	—
313	Q₈×C₃₁	—	2	1	no	—
314	Q₈×C₃₁	—	2	1	no	—
315	Q₈×C₃₁	—	2	2	no	—
316	Q₈×C₃₁	—	2	2	no	—
317	Q₈×C₃₁	—	4	2	no	—
318	Q₈×C₃₁	—	4	2	no	—
319	Q₈×C₃₁	—	4	4	no	—
320	Q₈×C₃₁	—	4	2	no	—
321	Q₈×C₃₁	—	8	4	no	—
322	Q₈×C₃₁	—	8	2	no	—
323	D₄×C₃₁	—	2	4	no	—
324	D₄×C₃₁	—	2	4	no	—
325	D₄×C₃₁	—	2	1	no	—
326	D₄×C₃₁	—	2	1	no	—
327	D₄×C₃₁	—	4	2	no	—
328	D₄×C₃₁	—	4	4	no	—
329	D₄×C₃₁	—	4	2	no	—
330	D₄×C₃₁	—	8	4	no	—
331	C₂×C₄×C₃₁	—	2	2	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	4	no	—
334	C₂×C₄×C₃₁	—	2	4	no	—
335	C₂×C₄×C₃₁	—	2	1	no	—
336	C₂×C₄×C₃₁	—	2	1	no	—
337	C₂×C₄×C₃₁	—	2	1	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	2	2	no	—
340	C₂×C₄×C₃₁	—	2	1	no	—
341	C₂×C₄×C₃₁	—	2	1	no	—
342	C₂×C₄×C₃₁	—	2	2	no	—
343	C₂×C₄×C₃₁	—	2	2	no	—
344	C₂×C₄×C₃₁	—	2	4	no	—
345	C₂×C₄×C₃₁	—	4	2	no	—
346	C₂×C₄×C₃₁	—	4	2	no	—
347	C₂×C₄×C₃₁	—	4	2	no	—
348	C₂×C₄×C₃₁	—	8	4	no	—
349	C₂×C₄×C₃₁	—	8	2	no	—
350	C₂×C₄×C₃₁	—	8	4	no	—
351	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
352	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
358	C₈×C₃₁	—	2	2	no	—
359	C₈×C₃₁	—	2	2	no	—
360	C₈×C₃₁	—	2	2	no	—
361	C₈×C₃₁	—	2	2	no	—
362	#3550	C₂×C₃₁	1	1	yes	characteristic, complemented
363	#3511	C₂×C₃₁	1	1	yes	characteristic
364	#3356	C₂×C₃₁	1	2	yes	complemented
365	#3353	C₂×C₃₁	1	2	yes	complemented
366	#3342	C₂×C₃₁	1	2	yes	complemented
367	#3340	C₂×C₃₁	1	2	yes	complemented
368	#3329	C₂×C₃₁	1	2	yes	complemented
369	#3328	C₂×C₃₁	1	2	yes	complemented
370	#3299	C₂×C₃₁	1	2	yes	complemented
371	#3298	C₂×C₃₁	1	2	yes	complemented
372	#3230	C₂×C₃₁	1	1	yes	characteristic, complemented
373	#3229	C₂×C₃₁	1	1	yes	characteristic, complemented
374	#3201	C₂×C₃₁	1	4	yes	complemented
375	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
376	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
377	#3097	C₂×C₃₁	1	4	yes	complemented
378	#2979	C₂×C₃₁	1	1	yes	characteristic, complemented
379	C₂²×C₃₁	—	2	4	no	—
380	C₂²×C₃₁	—	2	1	no	—
381	C₂²×C₃₁	—	2	1	no	—
382	C₂²×C₃₁	—	2	4	no	—
383	C₂²×C₃₁	—	2	1	no	—
384	C₂²×C₃₁	—	2	4	no	—
385	C₂²×C₃₁	—	4	1	no	—
386	C₂²×C₃₁	—	4	1	no	—
387	C₂²×C₃₁	—	4	1	no	—
388	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
389	C₄×C₃₁	—	2	1	no	—
390	C₄×C₃₁	—	2	4	no	—
391	C₄×C₃₁	—	2	1	no	—
392	C₄×C₃₁	—	2	1	no	—
393	C₄×C₃₁	—	4	1	no	—
394	C₄×C₃₁	—	4	2	no	—
395	C₄×C₃₁	—	4	2	no	—
396	C₄×C₃₁	—	4	1	no	—
397	C₄×C₃₁	—	4	4	no	—
398	C₄×C₃₁	—	4	2	no	—
399	C₄×C₃₁	—	4	1	no	—
400	C₄×C₃₁	—	4	2	no	—
401	C₄×C₃₁	#577	1	2	yes	—
402	C₄×C₃₁	#578	1	2	yes	—
403	C₄×C₃₁	#585	1	1	yes	characteristic
404	C₄×C₃₁	#585	1	1	yes	characteristic
405	#563	—	2	2	no	—
406	#559	—	2	1	no	—
407	Q₈²	—	2	1	no	—
408	#556	C₂²×C₃₁	1	2	yes	—
409	#556	C₂²×C₃₁	1	2	yes	—
410	#556	C₂²×C₃₁	1	2	yes	—
411	#555	C₂²×C₃₁	1	2	yes	—
412	#554	C₂²×C₃₁	1	2	yes	—
413	#553	—	2	2	no	—
414	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
415	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
416	#548	—	2	2	no	—
417	#547	C₂²×C₃₁	1	2	yes	—
418	#542	—	2	2	no	—
419	#542	—	2	2	no	—
420	#542	—	2	2	no	—
421	#537	C₂²×C₃₁	1	2	yes	—
422	#536	C₂²×C₃₁	1	4	yes	—
423	#533	—	2	1	no	—
424	#533	C₂²×C₃₁	1	1	yes	characteristic
425	#533	C₂²×C₃₁	1	1	yes	characteristic
426	#532	—	2	1	no	—
427	#532	C₂²×C₃₁	1	1	yes	characteristic
428	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
429	#520	C₂²×C₃₁	1	2	yes	—
430	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
431	#500	C₂²×C₃₁	1	2	yes	—
432	#498	C₂²×C₃₁	1	2	yes	—
433	#487	C₂²×C₃₁	1	2	yes	—
434	#487	C₂²×C₃₁	1	2	yes	—
435	#485	C₂²×C₃₁	1	4	yes	—
436	#485	C₂²×C₃₁	1	4	yes	—
437	#485	C₂²×C₃₁	1	4	yes	—
438	#485	C₂²×C₃₁	1	2	yes	—
439	#485	C₂²×C₃₁	1	2	yes	—
440	#484	C₂²×C₃₁	1	4	yes	—
441	#484	C₂²×C₃₁	1	4	yes	—
442	#483	C₂²×C₃₁	1	4	yes	—
443	#483	C₂²×C₃₁	1	4	yes	—
444	#482	C₂²×C₃₁	1	4	yes	—
445	#477	C₂²×C₃₁	1	2	yes	—
446	#477	C₂²×C₃₁	1	2	yes	—
447	#475	C₂²×C₃₁	1	2	yes	—
448	#475	C₂²×C₃₁	1	1	yes	characteristic
449	#475	C₂²×C₃₁	1	2	yes	—
450	#475	C₂²×C₃₁	1	1	yes	characteristic
451	#474	C₂²×C₃₁	1	1	yes	characteristic
452	#474	C₂²×C₃₁	1	1	yes	characteristic
453	#470	C₂²×C₃₁	1	4	yes	—
454	#468	C₂²×C₃₁	1	4	yes	—
455	#467	C₂²×C₃₁	1	4	yes	—
456	#465	C₂²×C₃₁	1	4	yes	—
457	#462	C₂²×C₃₁	1	1	yes	characteristic
458	#462	C₂²×C₃₁	1	1	yes	characteristic
459	#461	C₂²×C₃₁	1	1	yes	characteristic
460	#461	C₂²×C₃₁	1	1	yes	characteristic
461	#452	C₂²×C₃₁	1	2	yes	—
462	#452	C₂²×C₃₁	1	2	yes	—
463	#451	C₂²×C₃₁	1	4	yes	—
464	#448	C₂²×C₃₁	1	4	yes	—
465	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
466	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
467	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
468	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
469	#436	C₂²×C₃₁	1	2	yes	—
470	#436	C₂²×C₃₁	1	2	yes	—
471	C₈×D₄	C₂²×C₃₁	1	2	yes	—
472	C₈×D₄	C₂²×C₃₁	1	2	yes	—
473	#431	C₂²×C₃₁	1	1	yes	characteristic
474	#431	C₂²×C₃₁	1	1	yes	characteristic
475	#428	C₂²×C₃₁	1	4	yes	—
476	#427	C₂²×C₃₁	1	4	yes	—
477	#419	C₂²×C₃₁	1	4	yes	—
478	C₂×#103	C₂²×C₃₁	1	4	yes	—
479	#408	C₂²×C₃₁	1	4	yes	—
480	C₂×C₃₁	—	4	4	no	—
481	C₂×C₃₁	—	4	1	no	—
482	C₂×C₃₁	—	8	1	no	—
483	C₂×C₃₁	#3485	1	1	yes	characteristic
484	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
485	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
486	C₂×#41	—	2	2	no	—
487	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
488	C₂×#41	C₂³×C₃₁	1	2	yes	—
489	C₂²×Q₈	—	2	1	no	—
490	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
491	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
492	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
493	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
494	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
495	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
496	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
497	C₄⋊Q₈	—	2	4	no	—
498	C₄⋊Q₈	—	2	2	no	—
499	C₄⋊Q₈	—	2	2	no	—
500	C₄⋊Q₈	—	2	1	no	—
501	C₄⋊Q₈	—	2	1	no	—
502	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
503	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
504	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
506	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
507	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
508	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
509	#127	D₄×C₃₁	1	1	yes	characteristic
510	#126	—	2	4	no	—
511	#126	—	2	4	no	—
512	#126	—	2	4	no	—
513	#125	—	2	2	no	—
514	#125	—	2	1	no	—
515	#125	—	2	1	no	—
516	#124	—	2	2	no	—
517	#124	—	2	4	no	—
518	#124	—	2	2	no	—
519	#124	—	2	2	no	—
520	#124	—	2	4	no	—
521	#124	D₄×C₃₁	1	2	yes	—
522	#123	—	2	4	no	—
523	#123	—	2	4	no	—
524	#123	—	2	4	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	—	2	1	no	—
527	C₂²⋊Q₈	—	2	1	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	—	2	4	no	—
531	C₂²⋊Q₈	—	2	4	no	—
532	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
533	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
534	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
535	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
536	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
537	#121	—	2	2	no	—
538	#121	—	2	2	no	—
539	#121	—	2	4	no	—
540	#121	D₄×C₃₁	1	2	yes	—
541	#121	D₄×C₃₁	1	2	yes	—
542	#121	C₂³×C₃₁	1	4	yes	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	—	2	2	no	—
547	C₄×Q₈	—	2	1	no	—
548	C₄×Q₈	—	2	1	no	—
549	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
550	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
551	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
552	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	4	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	2	no	—
557	C₄×D₄	—	2	2	no	—
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
561	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
562	C₄×D₄	C₂³×C₃₁	1	2	yes	—
563	C₄×D₄	C₂³×C₃₁	1	2	yes	—
564	#117	—	2	1	no	—
565	#117	—	2	1	no	—
566	#117	—	2	2	no	—
567	#117	—	2	1	no	—
568	#117	C₂³×C₃₁	1	1	yes	characteristic
569	#117	C₂³×C₃₁	1	4	yes	—
570	#117	C₂³×C₃₁	1	4	yes	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
574	C₂×C₄²	—	2	1	no	—
575	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
576	#107	C₂³×C₃₁	1	2	yes	—
577	#107	C₂³×C₃₁	1	4	yes	—
578	#107	C₂³×C₃₁	1	2	yes	—
579	#107	C₂³×C₃₁	1	4	yes	—
580	#106	C₂³×C₃₁	1	2	yes	—
581	#106	C₂³×C₃₁	1	4	yes	—
582	#106	C₂³×C₃₁	1	2	yes	—
583	#106	C₂³×C₃₁	1	4	yes	—
584	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
585	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
586	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
587	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
588	#103	C₂³×C₃₁	1	2	yes	—
589	#103	C₂³×C₃₁	1	2	yes	—
590	#103	C₂³×C₃₁	1	4	yes	—
591	#103	C₂³×C₃₁	1	4	yes	—
592	#103	C₂³×C₃₁	1	2	yes	—
593	#103	C₂³×C₃₁	1	2	yes	—
594	#103	C₂³×C₃₁	1	4	yes	—
595	#103	C₂³×C₃₁	1	4	yes	—
596	#103	C₂³×C₃₁	1	2	yes	—
597	#103	C₂³×C₃₁	1	2	yes	—
598	#102	C₂³×C₃₁	1	2	yes	—
599	#102	C₂³×C₃₁	1	2	yes	—
600	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
601	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
602	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
603	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
604	C₄×C₈	C₂³×C₃₁	1	2	yes	—
605	C₄×C₈	C₂³×C₃₁	1	2	yes	—
606	C₃₁	#61789	1	1	yes	characteristic, direct product factor, Sylow
607	#41	—	4	2	no	—
608	#41	—	4	2	no	—
609	#41	—	4	1	no	—
610	#41	—	4	1	no	—
611	#41	—	8	4	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	2	no	—
615	C₂×Q₈	—	2	2	no	—
616	C₂×Q₈	—	2	4	no	—
617	C₂×Q₈	—	4	4	no	—
618	C₂×Q₈	—	4	4	no	—
619	C₂×Q₈	—	8	2	no	—
620	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
621	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
622	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
623	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
627	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
628	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
629	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
630	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
638	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
641	Q₁₆	—	4	2	no	—
642	Q₁₆	—	4	2	no	—
643	SD₁₆	—	4	2	no	—
644	SD₁₆	—	4	2	no	—
645	M₁₆	—	4	4	no	—
646	C₂×C₈	—	4	4	no	—
647	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
648	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
649	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
650	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
671	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
672	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
673	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
674	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
675	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
676	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	2	1	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	1	no	—
686	C₂²⋊C₄	—	2	1	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
689	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
690	C₄²	—	2	1	no	—
691	C₄²	—	2	1	no	—
692	C₄²	—	2	1	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	2	no	—
695	C₄²	—	2	2	no	—
696	C₄²	—	2	4	no	—
697	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
698	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
699	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
700	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
701	C₂³	—	2	1	no	—
702	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
703	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
704	Q₈	—	2	2	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	1	no	—
707	Q₈	—	2	1	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	2	2	no	—
710	Q₈	—	4	2	no	—
711	Q₈	—	4	2	no	—
712	Q₈	—	4	4	no	—
713	Q₈	—	4	2	no	—
714	Q₈	—	8	4	no	—
715	Q₈	—	8	2	no	—
716	D₄	—	2	4	no	—
717	D₄	—	2	4	no	—
718	D₄	—	2	1	no	—
719	D₄	—	2	1	no	—
720	D₄	—	4	2	no	—
721	D₄	—	4	4	no	—
722	D₄	—	4	2	no	—
723	D₄	—	8	4	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	4	no	—
738	C₂×C₄	—	4	2	no	—
739	C₂×C₄	—	4	2	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	8	4	no	—
742	C₂×C₄	—	8	2	no	—
743	C₂×C₄	—	8	4	no	—
744	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
745	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
746	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
747	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
748	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
750	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
751	C₈	—	2	2	no	—
752	C₈	—	2	2	no	—
753	C₈	—	2	2	no	—
754	C₈	—	2	2	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	4	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
765	C₄	—	2	1	no	—
766	C₄	—	2	4	no	—
767	C₄	—	2	1	no	—
768	C₄	—	2	1	no	—
769	C₄	—	4	1	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	1	no	—
773	C₄	—	4	4	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	1	no	—
776	C₄	—	4	2	no	—
777	C₄	C₃₁×#577	1	2	yes	—
778	C₄	C₃₁×#578	1	2	yes	—
779	C₄	C₃₁×#585	1	1	yes	characteristic
780	C₄	C₃₁×#585	1	1	yes	characteristic
781	C₂	—	4	4	no	—
782	C₂	—	4	1	no	—
783	C₂	—	8	1	no	—
784	C₂	C₃₁×#3485	1	1	yes	characteristic
785	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
786	C₂	C₂×C₃₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3511	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3550	C₂	semidirect
3. C₃₁×#3356	C₂	semidirect
4. C₃₁×#3353	C₂	semidirect
5. C₃₁×#3342	C₂	semidirect
6. C₃₁×#3340	C₂	semidirect
7. C₃₁×#3329	C₂	semidirect
8. C₃₁×#3328	C₂	semidirect
9. C₃₁×#3299	C₂	semidirect
10. C₃₁×#3298	C₂	semidirect
11. C₃₁×#3230	C₂	semidirect
12. C₃₁×#3229	C₂	semidirect
13. C₃₁×#3201	C₂	semidirect
14. C₃₁×#3107	C₂	semidirect
15. C₃₁×#3107	C₂	semidirect
16. C₃₁×#3097	C₂	semidirect
17. C₃₁×#2979	C₂	semidirect
307. #61789	C₃₁	direct (N × H)
362. #3550	C₂×C₃₁	semidirect
364. #3356	C₂×C₃₁	semidirect
365. #3353	C₂×C₃₁	semidirect
366. #3342	C₂×C₃₁	semidirect
367. #3340	C₂×C₃₁	semidirect
368. #3329	C₂×C₃₁	semidirect
369. #3328	C₂×C₃₁	semidirect
370. #3299	C₂×C₃₁	semidirect
371. #3298	C₂×C₃₁	semidirect
372. #3230	C₂×C₃₁	semidirect
373. #3229	C₂×C₃₁	semidirect
374. #3201	C₂×C₃₁	semidirect
375. #3107	C₂×C₃₁	semidirect
376. #3107	C₂×C₃₁	semidirect
377. #3097	C₂×C₃₁	semidirect
378. #2979	C₂×C₃₁	semidirect
606. C₃₁	#61789	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×#3550	2
C₃₁×#3511	2
C₃₁×#3356	2
C₃₁×#3353	2
C₃₁×#3342	2
C₃₁×#3340	2
C₃₁×#3329	2
C₃₁×#3328	2
C₃₁×#3299	2
C₃₁×#3298	2
C₃₁×#3230	2
C₃₁×#3229	2
C₃₁×#3201	2
C₃₁×#3107	2
C₃₁×#3097	2
C₃₁×#2979	2
#61789	31

Subgroups — C31×#61789 #21518548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61789 #21518548