Subgroups — #14572331

Order 2432.

520 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597347	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927056	C₂	1	1	yes	maximal, characteristic
4	#11926617	C₂	1	4	yes	maximal, complemented
5	C₈×D₇₆	C₂	1	4	yes	maximal, complemented
6	#11926571	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926512	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926507	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#64541	C₂²	1	1	yes	characteristic
11	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
12	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂×#64520	C₂²	1	1	yes	characteristic
16	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	#10597347	—	2	4	no	—
18	C₂×#64515	C₂²	1	2	yes	complemented
19	C₂×C₈×D₁₉	—	2	4	no	—
20	C₂×C₈×D₁₉	C₂²	1	2	yes	—
21	C₂×C₈×D₁₉	C₂²	1	2	yes	—
22	C₂×C₈×D₁₉	C₂²	1	2	yes	complemented
23	#10597343	C₄	1	2	yes	—
24	#10597341	C₄	1	2	yes	—
25	#10597332	C₄	1	2	yes	—
26	#10597328	C₄	1	2	yes	—
27	C₄×D₇₆	C₂²	1	4	yes	—
28	C₁₉×#97	C₂²	1	2	yes	complemented
29	C₄×C₈×C₁₉	C₂²	1	2	yes	complemented
30	(C₂×D₁₉)⋊C₈	C₂²	1	4	yes	—
31	(C₂×D₁₉)⋊C₈	C₂²	1	4	yes	complemented
32	C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	complemented
33	C₂³×D₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×C₂²⋊D₁₉	C₂×C₄	1	2	yes	—
36	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
37	#64541	—	2	2	no	—
38	#64541	—	2	2	no	—
39	C₂×D₇₆	C₂×C₄	1	1	yes	characteristic
40	C₂×D₇₆	C₂×C₄	1	4	yes	—
41	C₂×C₄×D₁₉	—	2	2	no	—
42	C₂×C₄×D₁₉	—	2	2	no	—
43	C₂×C₄×D₁₉	C₂×C₄	1	2	yes	—
44	C₂×C₄×D₁₉	C₂³	1	2	yes	—
45	C₂×C₄×D₁₉	C₂³	1	2	yes	—
46	C₂×Dic₃₈	C₂×C₄	1	1	yes	characteristic
47	M₁₆×C₁₉	—	2	2	no	—
48	C₂×C₈×C₁₉	D₄	1	4	yes	complemented
49	C₂×C₈×C₁₉	C₂³	1	2	yes	—
50	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
51	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
52	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
53	C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
54	C₄²×C₁₉	C₂³	1	2	yes	—
55	(C₂×D₁₉)⋊C₄	C₂×C₄	1	4	yes	—
56	(C₂×D₁₉)⋊C₄	C₂×C₄	1	4	yes	—
57	C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
58	#64520	—	2	2	no	—
59	C₂×C₁₉⋊C₈	—	2	2	no	—
60	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
61	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
62	#64515	—	2	4	no	—
63	C₈×D₁₉	—	2	4	no	—
64	C₈×D₁₉	—	2	4	no	—
65	C₈×D₁₉	—	2	4	no	—
66	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
67	C₂²×D₁₉	—	2	2	no	—
68	C₂²×D₁₉	—	2	4	no	—
69	C₂²×D₁₉	C₂²×C₄	1	2	yes	—
70	C₂²×D₁₉	C₂²×C₄	1	2	yes	—
71	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
72	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
74	C₂×C₄×C₁₉	#41	1	2	yes	—
75	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
76	C₂²⋊D₁₉	—	2	4	no	—
77	C₂×Dic₁₉	—	2	2	no	—
78	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
79	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
80	D₇₆	—	2	8	no	—
81	D₇₆	—	2	2	no	—
82	C₄×D₁₉	—	2	4	no	—
83	C₄×D₁₉	—	2	2	no	—
84	C₄×D₁₉	—	2	2	no	—
85	C₄×D₁₉	—	2	2	no	—
86	C₄×D₁₉	—	2	2	no	—
87	Dic₃₈	—	2	2	no	—
88	C₈×C₁₉	—	2	2	no	—
89	C₈×C₁₉	C₂×D₄	1	2	yes	—
90	C₈×C₁₉	C₂×D₄	1	2	yes	—
91	C₁₉⋊C₈	—	2	2	no	—
92	C₁₉⋊C₈	—	2	2	no	—
93	#2929	—	19	1	no	maximal, Sylow
94	C₂²×C₁₉	—	2	2	no	—
95	C₂²×C₁₉	C₄×D₄	1	2	yes	—
96	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
97	C₂×D₁₉	—	2	8	no	—
98	C₂×D₁₉	—	2	2	no	—
99	C₂×D₁₉	—	2	2	no	—
100	C₂×D₁₉	—	2	2	no	—
101	C₂×D₁₉	—	2	4	no	—
102	C₂×D₁₉	#131	1	4	yes	complemented
103	C₄×C₁₉	—	2	4	no	—
104	C₄×C₁₉	C₄×D₄	1	2	yes	—
105	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
106	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
107	Dic₁₉	—	2	2	no	—
108	Dic₁₉	—	2	2	no	—
109	C₂×#131	—	19	1	no	—
110	C₂³×C₈	—	19	1	no	—
111	#525	—	19	1	no	—
112	#435	—	19	4	no	—
113	C₈×D₄	—	19	4	no	—
114	#424	—	19	1	no	—
115	#408	—	19	1	no	—
116	#407	—	19	1	no	—
117	#405	D₁₉	1	1	yes	characteristic, complemented
118	C₂×C₁₉	—	2	2	no	—
119	C₂×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
120	C₂×C₁₉	C₂×#131	1	2	yes	—
121	D₁₉	—	2	4	no	—
122	D₁₉	—	4	2	no	—
123	C₂×#41	—	19	1	no	—
124	C₂³×C₄	—	19	1	no	—
125	#131	—	38	4	no	—
126	C₂×M₁₆	—	19	1	no	—
127	C₂×M₁₆	—	19	2	no	—
128	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
129	C₂²×C₈	—	19	1	no	—
130	C₂²×C₈	—	19	2	no	—
131	C₂²×C₈	—	19	2	no	—
132	C₂²×C₈	—	19	2	no	—
133	C₂²×C₈	—	38	4	no	—
134	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
135	#123	—	19	2	no	—
136	C₂²⋊Q₈	—	19	2	no	—
137	#121	—	19	2	no	—
138	#120	—	19	2	no	—
139	C₄×D₄	—	19	4	no	—
140	#117	C₂×D₁₉	1	1	yes	characteristic
141	C₄⋊C₈	—	19	4	no	—
142	C₂²⋊C₈	—	19	4	no	—
143	C₂²⋊C₈	—	19	4	no	—
144	#97	C₂×D₁₉	1	2	yes	complemented
145	C₄×C₈	C₂×D₁₉	1	2	yes	complemented
146	C₁₉	#2929	1	1	yes	characteristic, complemented, Sylow
147	C₂⁴	—	19	1	no	—
148	#41	—	38	2	no	—
149	#41	—	38	2	no	—
150	C₂×Q₈	—	19	1	no	—
151	C₂×D₄	—	19	2	no	—
152	C₂×D₄	—	19	4	no	—
153	C₂×D₄	—	19	1	no	—
154	C₂²×C₄	—	19	1	no	—
155	C₂²×C₄	—	19	2	no	—
156	C₂²×C₄	—	19	2	no	—
157	C₂²×C₄	—	19	2	no	—
158	C₂²×C₄	—	38	2	no	—
159	C₂²×C₄	—	38	2	no	—
160	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
161	M₁₆	—	2	2	no	—
162	M₁₆	—	38	2	no	—
163	M₁₆	—	38	4	no	—
164	C₂×C₈	—	19	2	no	—
165	C₂×C₈	—	19	2	no	—
166	C₂×C₈	—	38	2	no	—
167	C₂×C₈	—	38	4	no	—
168	C₂×C₈	—	38	4	no	—
169	C₂×C₈	—	38	4	no	—
170	C₂×C₈	D₇₆	1	4	yes	complemented
171	C₂×C₈	C₂²×D₁₉	1	2	yes	—
172	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
173	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
174	C₄⋊C₄	—	19	4	no	—
175	C₄⋊C₄	C₄×D₁₉	1	2	yes	—
176	C₂²⋊C₄	—	19	4	no	—
177	C₂²⋊C₄	—	19	4	no	—
178	C₂²⋊C₄	C₄×D₁₉	1	2	yes	—
179	C₄²	C₂²×D₁₉	1	2	yes	—
180	C₂³	—	19	2	no	—
181	C₂³	—	19	2	no	—
182	C₂³	—	38	4	no	—
183	C₂³	—	38	2	no	—
184	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
185	Q₈	—	38	2	no	—
186	D₄	—	38	8	no	—
187	D₄	—	38	4	no	—
188	D₄	—	38	2	no	—
189	C₂×C₄	—	19	2	no	—
190	C₂×C₄	—	19	2	no	—
191	C₂×C₄	—	38	2	no	—
192	C₂×C₄	—	38	2	no	—
193	C₂×C₄	—	38	2	no	—
194	C₂×C₄	—	38	2	no	—
195	C₂×C₄	—	38	2	no	—
196	C₂×C₄	—	38	4	no	—
197	C₂×C₄	C₂×C₄×D₁₉	1	4	yes	—
198	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
199	C₂×C₄	C₂×D₇₆	1	2	yes	—
200	C₂×C₄	#64541	1	2	yes	—
201	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
202	C₈	—	2	2	no	—
203	C₈	—	38	2	no	—
204	C₈	—	38	2	no	—
205	C₈	C₂×D₇₆	1	2	yes	—
206	C₈	C₂×D₇₆	1	2	yes	—
207	C₂²	—	2	2	no	—
208	C₂²	—	19	4	no	—
209	C₂²	—	38	8	no	—
210	C₂²	—	38	2	no	—
211	C₂²	—	38	2	no	—
212	C₂²	—	38	4	no	—
213	C₂²	—	38	2	no	—
214	C₂²	C₄×D₇₆	1	2	yes	—
215	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
216	C₄	—	2	4	no	—
217	C₄	—	38	2	no	—
218	C₄	—	38	2	no	—
219	C₄	C₄×D₇₆	1	2	yes	—
220	C₄	C₂²×D₇₆	1	1	yes	characteristic
221	C₄	C₂×#64541	1	1	yes	characteristic
222	C₂	—	2	2	no	—
223	C₂	—	38	4	no	—
224	C₂	—	76	2	no	—
225	C₂	C₂×C₄×D₇₆	1	1	yes	characteristic
226	C₂	#131×D₁₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂²×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#405	C₂
prime radical	#11927056	C₂
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#405	D₁₉
hypocenter	C₁₉	#2929
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
1. C₂×#10597347	C₂	semidirect
2. C₂²×C₈×D₁₉	C₂	semidirect
4. #11926617	C₂	semidirect
5. C₈×D₇₆	C₂	semidirect
6. #11926571	C₂	semidirect
7. #11926512	C₂	semidirect
8. #11926507	C₂	semidirect
9. C₁₉×#405	C₂	semidirect
18. C₂×#64515	C₂²	semidirect
22. C₂×C₈×D₁₉	C₂²	semidirect
28. C₁₉×#97	C₂²	semidirect
29. C₄×C₈×C₁₉	C₂²	semidirect
31. (C₂×D₁₉)⋊C₈	C₂²	semidirect
32. C₄⋊(C₁₉⋊C₈)	C₂²	semidirect
48. C₂×C₈×C₁₉	D₄	semidirect
102. C₂×D₁₉	#131	semidirect
117. #405	D₁₉	semidirect
144. #97	C₂×D₁₉	semidirect
145. C₄×C₈	C₂×D₁₉	semidirect
146. C₁₉	#2929	semidirect
170. C₂×C₈	D₇₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597347	2
C₂²×C₈×D₁₉	2
#11927056	2
#11926617	2
C₈×D₇₆	2
#11926571	2
#11926512	2
#11926507	2
C₁₉×#405	2
#2929	19