Subgroups — D₃₁×#529 #16858969

Order 3968.

1232 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521586	C₂	1	1	yes	maximal, characteristic, complemented
2	#14521585	C₂	1	1	yes	maximal, characteristic, complemented
3	#14521584	C₂	1	1	yes	maximal, characteristic, complemented
4	#14521583	C₂	1	1	yes	maximal, characteristic, complemented
5	#14521582	C₂	1	2	yes	maximal, complemented
6	#14521581	C₂	1	1	yes	maximal, characteristic, complemented
7	#14521580	C₂	1	1	yes	maximal, characteristic, complemented
8	#14521579	C₂	1	2	yes	maximal, complemented
9	#14521578	C₂	1	1	yes	maximal, characteristic, complemented
10	#14521577	C₂	1	2	yes	maximal, complemented
11	#14521576	C₂	1	2	yes	maximal, complemented
12	#126×D₃₁	C₂	1	2	yes	maximal, complemented
13	#125×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#124×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#123×D₃₁	C₂	1	2	yes	maximal, complemented
16	C₂²⋊Q₈×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
17	#121×D₃₁	C₂	1	1	yes	maximal, characteristic
18	C₄×Q₈×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×D₄×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×D₄×D₃₁	C₂	1	2	yes	maximal, complemented
21	#117×D₃₁	C₂	1	2	yes	maximal, complemented
22	C₂×C₄²×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₃₁	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₃₁	C₂²	1	2	yes	—
26	C₂×D₄×D₃₁	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₃₁	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₃₁	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₃₁	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₃₁	C₂²	1	2	yes	—
31	C₃₁×#126	C₂²	1	2	yes	complemented
32	C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#123	C₂²	1	2	yes	complemented
35	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#121	C₂²	1	1	yes	characteristic
37	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
38	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
39	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#117	C₂²	1	2	yes	complemented
41	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
42	#11758524	C₂²	1	1	yes	characteristic, complemented
43	#11758523	C₂²	1	1	yes	characteristic, complemented
44	Q₈×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
45	#11758516	C₂²	1	2	yes	—
46	#11758515	C₂²	1	1	yes	characteristic
47	#11758513	C₂²	1	1	yes	characteristic, complemented
48	#11758512	C₂²	1	2	yes	complemented
49	D₄×Dic₃₁	C₂²	1	2	yes	complemented
50	D₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
51	#11758507	C₂²	1	1	yes	characteristic
52	#11758506	C₂²	1	2	yes	complemented
53	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
55	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
56	#11758503	C₂²	1	2	yes	complemented
57	#11758501	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
61	#11758475	C₂²	1	2	yes	complemented
62	#11758475	C₂²	1	2	yes	complemented
63	#11758475	C₂²	1	2	yes	complemented
64	#11758474	C₂²	1	1	yes	characteristic, complemented
65	#11758473	C₂²	1	2	yes	complemented
66	#11758472	C₂²	1	1	yes	characteristic
67	#11758471	C₂²	1	2	yes	complemented
68	#11758471	C₂²	1	2	yes	complemented
69	#11758470	C₂²	1	2	yes	complemented
70	#11758470	C₂²	1	1	yes	characteristic, complemented
71	#11758469	C₂²	1	2	yes	complemented
72	#11758469	C₂²	1	2	yes	complemented
73	C₄⋊C₄×D₃₁	C₂²	1	2	yes	—
74	C₄⋊C₄×D₃₁	C₂²	1	2	yes	—
75	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
76	C₄⋊C₄×D₃₁	C₂²	1	2	yes	—
77	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
78	C₄⋊C₄×D₃₁	C₂²	1	2	yes	—
79	#11758467	C₂²	1	1	yes	characteristic, complemented
80	#11758467	C₂²	1	1	yes	characteristic, complemented
81	#11758466	C₂²	1	2	yes	complemented
82	#11758466	C₂²	1	2	yes	complemented
83	#11758464	C₂²	1	2	yes	complemented
84	#11758464	C₂²	1	1	yes	characteristic, complemented
85	#11758463	C₂²	1	2	yes	complemented
86	#11758462	C₂²	1	2	yes	complemented
87	#11758462	C₂²	1	2	yes	complemented
88	#11758461	C₂²	1	2	yes	—
89	#11758460	C₂²	1	2	yes	complemented
90	#11758460	C₂²	1	2	yes	complemented
91	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	complemented
92	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	complemented
93	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	—
95	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	—
96	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	—
97	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	—
98	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	—
99	#11758456	C₂²	1	2	yes	complemented
100	#11758456	C₂²	1	2	yes	complemented
101	#11758456	C₂²	1	2	yes	complemented
102	#11758455	C₂²	1	2	yes	complemented
103	#11758454	C₂²	1	2	yes	complemented
104	#11758454	C₂²	1	2	yes	complemented
105	#11758453	C₂²	1	2	yes	complemented
106	#11758452	C₂²	1	1	yes	characteristic, complemented
107	C₄×D₁₂₄	C₂²	1	2	yes	complemented
108	C₄×D₁₂₄	C₂²	1	1	yes	characteristic, complemented
109	#11758449	C₂²	1	2	yes	complemented
110	#11758449	C₂²	1	2	yes	complemented
111	C₄²×D₃₁	C₂²	1	1	yes	characteristic
112	C₄²×D₃₁	C₂²	1	1	yes	characteristic
113	C₄²×D₃₁	C₂²	1	1	yes	characteristic
114	C₄²×D₃₁	C₂²	1	1	yes	characteristic
115	C₄²×D₃₁	C₂²	1	2	yes	—
116	C₄²×D₃₁	C₂²	1	1	yes	characteristic, complemented
117	C₄²×D₃₁	C₂²	1	1	yes	characteristic, complemented
118	C₄²×D₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₄²×D₃₁	C₂²	1	1	yes	characteristic, complemented
120	#11758447	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₆₂	C₂²	1	2	yes	complemented
122	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₃₁	C₂³	1	2	yes	—
124	C₂³×D₃₁	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₃₁	C₂³	1	2	yes	—
127	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
135	C₂²×Dic₃₁	C₂³	1	2	yes	—
136	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
137	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
138	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
139	Q₈×D₃₁	—	2	4	no	—
140	D₄×D₃₁	—	2	8	no	—
141	D₄×D₃₁	—	2	4	no	—
142	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
143	C₂×D₁₂₄	C₂³	1	2	yes	—
144	C₂×C₄×D₃₁	—	2	4	no	—
145	C₂×C₄×D₃₁	—	2	4	no	—
146	C₂×C₄×D₃₁	—	2	8	no	—
147	C₂×C₄×D₃₁	—	2	4	no	—
148	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₃₁	C₂³	1	2	yes	—
153	C₂×C₄×D₃₁	C₂³	1	2	yes	—
154	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₃₁	C₂³	1	2	yes	—
161	C₂×C₄×D₃₁	C₂³	1	2	yes	—
162	C₂×C₄×D₃₁	C₂³	1	2	yes	—
163	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
165	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
166	C₂×Dic₆₂	C₂³	1	2	yes	—
167	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₄²×C₃₁	C₂³	1	1	yes	characteristic
179	C₄²×C₃₁	C₂³	1	2	yes	—
180	C₄²×C₃₁	C₂³	1	1	yes	characteristic
181	C₄²×C₃₁	C₂³	1	1	yes	characteristic
182	C₄²×C₃₁	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
184	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
185	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
186	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
187	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
188	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
198	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₃₁	C₂³	1	2	yes	—
200	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₃₁	C₂³	1	2	yes	—
202	C₄⋊Dic₃₁	C₂³	1	2	yes	—
203	C₄⋊Dic₃₁	C₂³	1	2	yes	—
204	Dic₃₁⋊C₄	C₂³	1	2	yes	—
205	Dic₃₁⋊C₄	C₂³	1	2	yes	—
206	Dic₃₁⋊C₄	C₂³	1	2	yes	—
207	Dic₃₁⋊C₄	C₂³	1	2	yes	—
208	Dic₃₁⋊C₄	C₂³	1	2	yes	—
209	Dic₃₁⋊C₄	C₂³	1	2	yes	—
210	Dic₃₁⋊C₄	C₂³	1	2	yes	—
211	Dic₃₁⋊C₄	C₂³	1	2	yes	—
212	Dic₃₁⋊C₄	C₂³	1	2	yes	—
213	Dic₃₁⋊C₄	C₂³	1	2	yes	—
214	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
215	C₄×Dic₃₁	C₂³	1	2	yes	—
216	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
217	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
218	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
219	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
220	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
221	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
222	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
223	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
224	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
225	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
226	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
227	C₄×Dic₃₁	C₂³	1	2	yes	—
228	C₄×Dic₃₁	C₂³	1	2	yes	—
229	C₂³×C₃₁	C₂⁴	1	2	yes	—
230	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
231	C₂²×D₃₁	—	2	2	no	—
232	C₂²×D₃₁	—	2	2	no	—
233	C₂²×D₃₁	—	2	4	no	—
234	C₂²×D₃₁	—	2	4	no	—
235	C₂²×D₃₁	—	2	4	no	—
236	C₂²×D₃₁	#41	1	4	yes	—
237	C₂²×D₃₁	C₂⁴	1	2	yes	—
238	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
239	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
240	Q₈×C₃₁	—	2	2	no	—
241	D₄×C₃₁	—	2	4	no	—
242	D₄×C₃₁	—	2	2	no	—
243	C₂×C₄×C₃₁	—	2	2	no	—
244	C₂×C₄×C₃₁	—	2	2	no	—
245	C₂×C₄×C₃₁	—	2	2	no	—
246	C₂×C₄×C₃₁	—	2	4	no	—
247	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
252	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
253	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
254	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂²⋊D₃₁	—	2	4	no	—
257	C₂²⋊D₃₁	—	2	4	no	—
258	C₂²⋊D₃₁	—	2	4	no	—
259	C₂×Dic₃₁	—	2	2	no	—
260	C₂×Dic₃₁	—	2	2	no	—
261	C₂×Dic₃₁	—	2	2	no	—
262	C₂×Dic₃₁	—	2	4	no	—
263	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₃₁	C₂⁴	1	2	yes	—
268	C₂×Dic₃₁	C₂⁴	1	2	yes	—
269	C₂×Dic₃₁	C₂⁴	1	2	yes	—
270	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
272	D₁₂₄	—	2	4	no	—
273	D₁₂₄	—	2	2	no	—
274	C₄×D₃₁	—	2	2	no	—
275	C₄×D₃₁	—	2	2	no	—
276	C₄×D₃₁	—	2	2	no	—
277	C₄×D₃₁	—	2	2	no	—
278	C₄×D₃₁	—	2	2	no	—
279	C₄×D₃₁	—	2	2	no	—
280	C₄×D₃₁	—	2	4	no	—
281	C₄×D₃₁	—	2	4	no	—
282	C₄×D₃₁	—	2	4	no	—
283	C₄×D₃₁	—	2	2	no	—
284	C₄×D₃₁	—	2	2	no	—
285	C₄×D₃₁	—	2	4	no	—
286	C₄×D₃₁	—	2	2	no	—
287	C₄×D₃₁	—	2	2	no	—
288	C₄×D₃₁	—	2	4	no	—
289	C₄×D₃₁	#41	1	4	yes	—
290	C₄×D₃₁	#41	1	4	yes	—
291	Dic₆₂	—	2	2	no	—
292	Dic₆₂	—	2	4	no	—
293	C₂×#529	—	31	1	no	maximal, Sylow
294	C₂²×C₃₁	—	2	1	no	—
295	C₂²×C₃₁	—	2	1	no	—
296	C₂²×C₃₁	—	2	2	no	—
297	C₂²×C₃₁	—	2	2	no	—
298	C₂²×C₃₁	—	2	2	no	—
299	C₂²×C₃₁	C₂×#41	1	2	yes	—
300	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
301	C₂×D₃₁	—	2	1	no	—
302	C₂×D₃₁	—	2	1	no	—
303	C₂×D₃₁	—	2	8	no	—
304	C₂×D₃₁	—	2	2	no	—
305	C₂×D₃₁	—	2	2	no	—
306	C₂×D₃₁	—	2	2	no	—
307	C₂×D₃₁	—	4	8	no	—
308	C₂×D₃₁	C₂×#41	1	2	yes	—
309	C₂×D₃₁	C₂×#41	1	2	yes	—
310	C₂×D₃₁	C₂×#41	1	2	yes	—
311	C₂×D₃₁	C₂×#41	1	2	yes	—
312	C₄×C₃₁	—	2	2	no	—
313	C₄×C₃₁	—	2	1	no	—
314	C₄×C₃₁	—	2	1	no	—
315	C₄×C₃₁	—	2	1	no	—
316	C₄×C₃₁	—	2	1	no	—
317	C₄×C₃₁	—	2	2	no	—
318	C₄×C₃₁	—	2	2	no	—
319	C₄×C₃₁	C₂×#41	1	2	yes	—
320	C₄×C₃₁	C₂×#41	1	2	yes	—
321	Dic₃₁	—	2	2	no	—
322	Dic₃₁	—	2	1	no	—
323	Dic₃₁	—	2	1	no	—
324	Dic₃₁	—	2	1	no	—
325	Dic₃₁	—	2	1	no	—
326	Dic₃₁	—	2	2	no	—
327	Dic₃₁	—	2	2	no	—
328	Dic₃₁	C₂×#41	1	2	yes	—
329	Dic₃₁	C₂×#41	1	2	yes	—
330	#529	—	31	2	no	—
331	#529	—	31	1	no	—
332	#529	—	31	1	no	—
333	#529	—	31	2	no	—
334	#529	—	31	1	no	—
335	#529	—	31	1	no	—
336	#529	—	31	1	no	—
337	#529	—	31	2	no	—
338	#529	—	31	1	no	—
339	#529	—	31	2	no	—
340	#529	—	31	1	no	—
341	#529	D₃₁	1	1	yes	characteristic, direct product factor
342	C₂×#126	—	31	2	no	—
343	C₂×#125	—	31	1	no	—
344	C₂×#124	—	31	1	no	—
345	C₂×#123	—	31	2	no	—
346	C₂×C₂²⋊Q₈	—	31	1	no	—
347	C₂×#121	—	31	1	no	—
348	C₂×C₄×Q₈	—	31	1	no	—
349	C₂×C₄×D₄	—	31	2	no	—
350	C₂×C₄×D₄	—	31	1	no	—
351	C₂×#117	—	31	2	no	—
352	C₂²×C₄²	—	31	1	no	—
353	C₂×C₃₁	—	2	2	no	—
354	C₂×C₃₁	—	4	2	no	—
355	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
356	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
357	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
358	D₃₁	—	2	2	no	—
359	D₃₁	—	4	2	no	—
360	D₃₁	#529	1	4	yes	direct product factor
361	C₂²×Q₈	—	31	1	no	—
362	C₂²×D₄	—	31	2	no	—
363	C₂²×D₄	—	31	1	no	—
364	C₂³×C₄	—	31	2	no	—
365	C₂³×C₄	—	31	1	no	—
366	C₂³×C₄	—	31	1	no	—
367	C₂³×C₄	—	31	1	no	—
368	#126	—	31	2	no	—
369	#126	—	31	2	no	—
370	#126	—	31	2	no	—
371	#126	—	31	2	no	—
372	#126	—	31	2	no	—
373	#126	—	31	2	no	—
374	#126	—	31	2	no	—
375	#126	C₂×D₃₁	1	2	yes	complemented
376	#125	—	31	2	no	—
377	#125	—	31	2	no	—
378	#125	—	31	1	no	—
379	#125	—	31	1	no	—
380	#125	—	31	1	no	—
381	#125	C₂×D₃₁	1	1	yes	characteristic, complemented
382	#124	—	31	1	no	—
383	#124	—	31	1	no	—
384	#124	—	31	2	no	—
385	#124	—	31	2	no	—
386	#124	—	31	1	no	—
387	#124	C₂×D₃₁	1	1	yes	characteristic, complemented
388	#123	—	31	2	no	—
389	#123	—	31	2	no	—
390	#123	—	31	2	no	—
391	#123	—	31	2	no	—
392	#123	—	31	2	no	—
393	#123	—	31	2	no	—
394	#123	—	31	2	no	—
395	#123	C₂×D₃₁	1	2	yes	complemented
396	C₂²⋊Q₈	—	31	1	no	—
397	C₂²⋊Q₈	—	31	1	no	—
398	C₂²⋊Q₈	—	31	2	no	—
399	C₂²⋊Q₈	—	31	1	no	—
400	C₂²⋊Q₈	—	31	2	no	—
401	C₂²⋊Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
402	#121	—	31	1	no	—
403	#121	—	31	2	no	—
404	#121	—	31	1	no	—
405	#121	—	31	1	no	—
406	#121	—	31	2	no	—
407	#121	C₂×D₃₁	1	1	yes	characteristic
408	C₄×Q₈	—	31	1	no	—
409	C₄×Q₈	—	31	2	no	—
410	C₄×Q₈	—	31	1	no	—
411	C₄×Q₈	—	31	2	no	—
412	C₄×Q₈	—	31	1	no	—
413	C₄×Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
414	C₄×D₄	—	31	1	no	—
415	C₄×D₄	—	31	2	no	—
416	C₄×D₄	—	31	2	no	—
417	C₄×D₄	—	31	2	no	—
418	C₄×D₄	—	31	2	no	—
419	C₄×D₄	—	31	1	no	—
420	C₄×D₄	—	31	2	no	—
421	C₄×D₄	—	31	2	no	—
422	C₄×D₄	—	31	2	no	—
423	C₄×D₄	—	31	2	no	—
424	C₄×D₄	—	31	1	no	—
425	C₄×D₄	—	31	2	no	—
426	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic, complemented
427	C₄×D₄	C₂×D₃₁	1	2	yes	complemented
428	#117	—	31	2	no	—
429	#117	—	31	2	no	—
430	#117	—	31	2	no	—
431	#117	—	31	2	no	—
432	#117	—	31	2	no	—
433	#117	—	31	2	no	—
434	#117	—	31	2	no	—
435	#117	C₂×D₃₁	1	2	yes	complemented
436	C₂×C₄⋊C₄	—	31	2	no	—
437	C₂×C₄⋊C₄	—	31	2	no	—
438	C₂×C₄⋊C₄	—	31	1	no	—
439	C₂×C₄⋊C₄	—	31	2	no	—
440	C₂×C₄⋊C₄	—	31	1	no	—
441	C₂×C₄⋊C₄	—	31	2	no	—
442	C₂×C₂²⋊C₄	—	31	2	no	—
443	C₂×C₂²⋊C₄	—	31	2	no	—
444	C₂×C₂²⋊C₄	—	31	2	no	—
445	C₂×C₂²⋊C₄	—	31	2	no	—
446	C₂×C₂²⋊C₄	—	31	2	no	—
447	C₂×C₄²	—	31	1	no	—
448	C₂×C₄²	—	31	1	no	—
449	C₂×C₄²	—	31	1	no	—
450	C₂×C₄²	—	31	1	no	—
451	C₂×C₄²	—	31	2	no	—
452	C₂×C₄²	—	31	1	no	—
453	C₂×C₄²	—	31	1	no	—
454	C₂×C₄²	—	31	1	no	—
455	C₂×C₄²	—	31	1	no	—
456	C₂×C₄²	—	31	1	no	—
457	C₂×C₄²	—	31	1	no	—
458	C₂×C₄²	—	31	1	no	—
459	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic, complemented
460	C₃₁	C₂×#529	1	1	yes	characteristic, complemented, Sylow
461	C₂⁴	—	31	1	no	—
462	C₂⁴	—	31	2	no	—
463	C₂×Q₈	—	31	2	no	—
464	C₂×Q₈	—	31	1	no	—
465	C₂×Q₈	—	62	4	no	—
466	C₂×Q₈	C₂²×D₃₁	1	1	yes	characteristic
467	C₂×D₄	—	31	2	no	—
468	C₂×D₄	—	31	2	no	—
469	C₂×D₄	—	31	2	no	—
470	C₂×D₄	—	31	2	no	—
471	C₂×D₄	—	31	1	no	—
472	C₂×D₄	—	62	4	no	—
473	C₂×D₄	—	62	8	no	—
474	C₂×D₄	C₂²×D₃₁	1	2	yes	—
475	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
476	C₂²×C₄	—	31	1	no	—
477	C₂²×C₄	—	31	1	no	—
478	C₂²×C₄	—	31	1	no	—
479	C₂²×C₄	—	31	1	no	—
480	C₂²×C₄	—	31	1	no	—
481	C₂²×C₄	—	31	2	no	—
482	C₂²×C₄	—	31	1	no	—
483	C₂²×C₄	—	31	1	no	—
484	C₂²×C₄	—	31	1	no	—
485	C₂²×C₄	—	31	1	no	—
486	C₂²×C₄	—	31	1	no	—
487	C₂²×C₄	—	31	1	no	—
488	C₂²×C₄	—	31	1	no	—
489	C₂²×C₄	—	31	1	no	—
490	C₂²×C₄	—	31	1	no	—
491	C₂²×C₄	—	31	2	no	—
492	C₂²×C₄	—	31	2	no	—
493	C₂²×C₄	—	31	2	no	—
494	C₂²×C₄	—	31	2	no	—
495	C₂²×C₄	—	31	1	no	—
496	C₂²×C₄	—	31	2	no	—
497	C₂²×C₄	—	62	4	no	—
498	C₂²×C₄	—	62	8	no	—
499	C₂²×C₄	—	62	4	no	—
500	C₂²×C₄	—	62	4	no	—
501	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
503	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
504	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
505	C₄⋊C₄	—	31	2	no	—
506	C₄⋊C₄	—	31	2	no	—
507	C₄⋊C₄	—	31	2	no	—
508	C₄⋊C₄	—	31	2	no	—
509	C₄⋊C₄	—	31	2	no	—
510	C₄⋊C₄	—	31	2	no	—
511	C₄⋊C₄	—	31	2	no	—
512	C₄⋊C₄	—	31	2	no	—
513	C₄⋊C₄	—	31	2	no	—
514	C₄⋊C₄	—	31	2	no	—
515	C₄⋊C₄	—	31	2	no	—
516	C₄⋊C₄	—	31	2	no	—
517	C₄⋊C₄	—	31	1	no	—
518	C₄⋊C₄	—	31	2	no	—
519	C₄⋊C₄	—	31	1	no	—
520	C₄⋊C₄	—	31	2	no	—
521	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
522	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
523	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
525	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
527	C₂²⋊C₄	—	31	2	no	—
528	C₂²⋊C₄	—	31	2	no	—
529	C₂²⋊C₄	—	31	2	no	—
530	C₂²⋊C₄	—	31	2	no	—
531	C₂²⋊C₄	—	31	2	no	—
532	C₂²⋊C₄	—	31	2	no	—
533	C₂²⋊C₄	—	31	2	no	—
534	C₂²⋊C₄	—	31	2	no	—
535	C₂²⋊C₄	—	31	2	no	—
536	C₂²⋊C₄	—	31	2	no	—
537	C₂²⋊C₄	—	31	2	no	—
538	C₂²⋊C₄	—	31	2	no	—
539	C₂²⋊C₄	—	31	2	no	—
540	C₂²⋊C₄	—	31	2	no	—
541	C₂²⋊C₄	—	31	2	no	—
542	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
547	C₄²	—	31	1	no	—
548	C₄²	—	31	1	no	—
549	C₄²	—	31	1	no	—
550	C₄²	—	31	1	no	—
551	C₄²	—	31	1	no	—
552	C₄²	—	31	1	no	—
553	C₄²	—	31	1	no	—
554	C₄²	—	31	1	no	—
555	C₄²	—	31	1	no	—
556	C₄²	—	31	1	no	—
557	C₄²	—	31	2	no	—
558	C₄²	—	31	2	no	—
559	C₄²	—	31	1	no	—
560	C₄²	—	31	1	no	—
561	C₄²	—	31	2	no	—
562	C₄²	C₂²×D₃₁	1	1	yes	characteristic
563	C₄²	C₂²×D₃₁	1	1	yes	characteristic
564	C₄²	C₂²×D₃₁	1	1	yes	characteristic
565	C₄²	C₂²×D₃₁	1	1	yes	characteristic
566	C₄²	C₂²×D₃₁	1	2	yes	—
567	C₂³	—	31	1	no	—
568	C₂³	—	31	4	no	—
569	C₂³	—	31	1	no	—
570	C₂³	—	31	2	no	—
571	C₂³	—	62	2	no	—
572	C₂³	—	62	2	no	—
573	C₂³	—	62	4	no	—
574	C₂³	—	62	4	no	—
575	C₂³	—	62	4	no	—
576	C₂³	C₂³×D₃₁	1	2	yes	—
577	C₂³	C₂³×D₃₁	1	1	yes	characteristic
578	Q₈	—	2	2	no	—
579	Q₈	—	62	4	no	—
580	Q₈	—	62	2	no	—
581	D₄	—	2	4	no	—
582	D₄	—	2	2	no	—
583	D₄	—	62	4	no	—
584	D₄	—	62	4	no	—
585	D₄	—	62	4	no	—
586	D₄	—	62	4	no	—
587	D₄	—	62	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	31	1	no	—
593	C₂×C₄	—	31	1	no	—
594	C₂×C₄	—	31	4	no	—
595	C₂×C₄	—	31	4	no	—
596	C₂×C₄	—	31	1	no	—
597	C₂×C₄	—	31	1	no	—
598	C₂×C₄	—	31	1	no	—
599	C₂×C₄	—	31	1	no	—
600	C₂×C₄	—	31	2	no	—
601	C₂×C₄	—	31	2	no	—
602	C₂×C₄	—	31	2	no	—
603	C₂×C₄	—	62	2	no	—
604	C₂×C₄	—	62	4	no	—
605	C₂×C₄	—	62	2	no	—
606	C₂×C₄	—	62	2	no	—
607	C₂×C₄	—	62	2	no	—
608	C₂×C₄	—	62	4	no	—
609	C₂×C₄	—	62	2	no	—
610	C₂×C₄	—	62	2	no	—
611	C₂×C₄	—	62	2	no	—
612	C₂×C₄	—	62	2	no	—
613	C₂×C₄	—	62	4	no	—
614	C₂×C₄	—	62	4	no	—
615	C₂×C₄	—	62	2	no	—
616	C₂×C₄	—	62	4	no	—
617	C₂×C₄	—	62	2	no	—
618	C₂×C₄	—	62	2	no	—
619	C₂×C₄	—	62	2	no	—
620	C₂×C₄	—	62	4	no	—
621	C₂×C₄	—	62	2	no	—
622	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₃₁	1	2	yes	—
627	C₂×C₄	C₂³×D₃₁	1	2	yes	—
628	C₂×C₄	C₂³×D₃₁	1	2	yes	—
629	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	31	2	no	—
637	C₂²	—	31	2	no	—
638	C₂²	—	31	2	no	—
639	C₂²	—	31	2	no	—
640	C₂²	—	62	8	no	—
641	C₂²	—	62	1	no	—
642	C₂²	—	62	1	no	—
643	C₂²	—	62	2	no	—
644	C₂²	—	62	2	no	—
645	C₂²	—	62	2	no	—
646	C₂²	—	124	8	no	—
647	C₂²	#41×D₃₁	1	2	yes	—
648	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	31	2	no	—
657	C₄	—	31	2	no	—
658	C₄	—	62	1	no	—
659	C₄	—	62	1	no	—
660	C₄	—	62	1	no	—
661	C₄	—	62	1	no	—
662	C₄	—	62	2	no	—
663	C₄	—	62	2	no	—
664	C₄	—	62	2	no	—
665	C₄	#41×D₃₁	1	2	yes	—
666	C₄	#41×D₃₁	1	2	yes	—
667	C₂	—	2	2	no	—
668	C₂	—	4	2	no	—
669	C₂	—	31	4	no	—
670	C₂	—	62	2	no	—
671	C₂	—	124	2	no	—
672	C₂	C₂×#41×D₃₁	1	1	yes	characteristic
673	C₂	C₂×#41×D₃₁	1	1	yes	characteristic
674	C₂	C₂×#41×D₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₃₁
commutator, socle, cosocle	C₂²×C₃₁	C₂⁵
Frattini	C₂²	C₂⁴×D₃₁
Fitting	C₃₁×#529	C₂
prime radical	#121×D₃₁	C₂
hypercenter	#529	D₃₁
hypocenter	C₃₁	C₂×#529
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. #14521586	C₂	semidirect
2. #14521585	C₂	semidirect
3. #14521584	C₂	semidirect
4. #14521583	C₂	semidirect
5. #14521582	C₂	semidirect
6. #14521581	C₂	semidirect
7. #14521580	C₂	semidirect
8. #14521579	C₂	semidirect
9. #14521578	C₂	semidirect
10. #14521577	C₂	semidirect
11. #14521576	C₂	semidirect
12. #126×D₃₁	C₂	semidirect
13. #125×D₃₁	C₂	semidirect
14. #124×D₃₁	C₂	semidirect
15. #123×D₃₁	C₂	semidirect
16. C₂²⋊Q₈×D₃₁	C₂	semidirect
18. C₄×Q₈×D₃₁	C₂	semidirect
19. C₄×D₄×D₃₁	C₂	semidirect
20. C₄×D₄×D₃₁	C₂	semidirect
21. #117×D₃₁	C₂	semidirect
22. C₂×C₄²×D₃₁	C₂	semidirect
23. C₃₁×#529	C₂	semidirect
31. C₃₁×#126	C₂²	semidirect
32. C₃₁×#125	C₂²	semidirect
33. C₃₁×#124	C₂²	semidirect
34. C₃₁×#123	C₂²	semidirect
35. C₃₁×C₂²⋊Q₈	C₂²	semidirect
37. C₄×Q₈×C₃₁	C₂²	semidirect
38. C₄×D₄×C₃₁	C₂²	semidirect
39. C₄×D₄×C₃₁	C₂²	semidirect
40. C₃₁×#117	C₂²	semidirect
41. C₂×C₄²×C₃₁	C₂²	semidirect
42. #11758524	C₂²	semidirect
43. #11758523	C₂²	semidirect
44. Q₈×Dic₃₁	C₂²	semidirect
47. #11758513	C₂²	semidirect
48. #11758512	C₂²	semidirect
49. D₄×Dic₃₁	C₂²	semidirect
50. D₄×Dic₃₁	C₂²	semidirect
52. #11758506	C₂²	semidirect
53. C₄×C₂²⋊D₃₁	C₂²	semidirect
54. C₄×C₂²⋊D₃₁	C₂²	semidirect
55. C₄×C₂²⋊D₃₁	C₂²	semidirect
56. #11758503	C₂²	semidirect
57. #11758501	C₂²	semidirect
58. C₂×C₄×Dic₃₁	C₂²	semidirect
59. C₂×C₄×Dic₃₁	C₂²	semidirect
60. C₂×C₄×Dic₃₁	C₂²	semidirect
61. #11758475	C₂²	semidirect
62. #11758475	C₂²	semidirect
63. #11758475	C₂²	semidirect
64. #11758474	C₂²	semidirect
65. #11758473	C₂²	semidirect
67. #11758471	C₂²	semidirect
68. #11758471	C₂²	semidirect
69. #11758470	C₂²	semidirect
70. #11758470	C₂²	semidirect
71. #11758469	C₂²	semidirect
72. #11758469	C₂²	semidirect
79. #11758467	C₂²	semidirect
80. #11758467	C₂²	semidirect
81. #11758466	C₂²	semidirect
82. #11758466	C₂²	semidirect
83. #11758464	C₂²	semidirect
84. #11758464	C₂²	semidirect
85. #11758463	C₂²	semidirect
86. #11758462	C₂²	semidirect
87. #11758462	C₂²	semidirect
89. #11758460	C₂²	semidirect
90. #11758460	C₂²	semidirect
91. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
92. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
93. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
99. #11758456	C₂²	semidirect
100. #11758456	C₂²	semidirect
101. #11758456	C₂²	semidirect
102. #11758455	C₂²	semidirect
103. #11758454	C₂²	semidirect
104. #11758454	C₂²	semidirect
105. #11758453	C₂²	semidirect
106. #11758452	C₂²	semidirect
107. C₄×D₁₂₄	C₂²	semidirect
108. C₄×D₁₂₄	C₂²	semidirect
109. #11758449	C₂²	semidirect
110. #11758449	C₂²	semidirect
116. C₄²×D₃₁	C₂²	semidirect
117. C₄²×D₃₁	C₂²	semidirect
118. C₄²×D₃₁	C₂²	semidirect
119. C₄²×D₃₁	C₂²	semidirect
120. #11758447	C₂²	semidirect
121. C₄×Dic₆₂	C₂²	semidirect
122. C₄×Dic₆₂	C₂²	semidirect
341. #529	D₃₁	direct (N × H)
360. D₃₁	#529	direct (N × H)
375. #126	C₂×D₃₁	semidirect
381. #125	C₂×D₃₁	semidirect
387. #124	C₂×D₃₁	semidirect
395. #123	C₂×D₃₁	semidirect
401. C₂²⋊Q₈	C₂×D₃₁	semidirect
413. C₄×Q₈	C₂×D₃₁	semidirect
426. C₄×D₄	C₂×D₃₁	semidirect
427. C₄×D₄	C₂×D₃₁	semidirect
435. #117	C₂×D₃₁	semidirect
459. C₂×C₄²	C₂×D₃₁	semidirect
460. C₃₁	C₂×#529	semidirect

Maximal subgroups

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

subgroup	index
#14521586	2
#14521585	2
#14521584	2
#14521583	2
#14521582	2
#14521581	2
#14521580	2
#14521579	2
#14521578	2
#14521577	2
#14521576	2
#126×D₃₁	2
#125×D₃₁	2
#124×D₃₁	2
#123×D₃₁	2
C₂²⋊Q₈×D₃₁	2
#121×D₃₁	2
C₄×Q₈×D₃₁	2
C₄×D₄×D₃₁	2
#117×D₃₁	2
C₂×C₄²×D₃₁	2
C₃₁×#529	2
C₂×#529	31

Subgroups — D31×#529 #16858969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₁×#529 #16858969