Subgroups — #14563706

Order 2432.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal
2	#11926299	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
5	C₁₉×#117	—	2	4	no	—
6	C₂×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
7	C₂×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
8	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
9	C₂²×C₁₉⋊C₈	C₂²	1	4	yes	—
10	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
11	C₂⁴×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₁₉	—	2	4	no	—
13	C₂²×C₄×C₁₉	C₂×C₄	1	4	yes	—
14	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₁₉	D₄	1	4	yes	—
16	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
17	C₄⋊C₄×C₁₉	—	2	4	no	—
18	C₂²⋊C₄×C₁₉	—	2	4	no	—
19	C₄²×C₁₉	—	2	4	no	—
20	C₂×C₁₉⋊C₈	—	2	4	no	—
21	C₂×C₁₉⋊C₈	—	2	8	no	—
22	C₂³×C₁₉	—	2	2	no	—
23	C₂³×C₁₉	—	2	4	no	—
24	C₂³×C₁₉	C₂²⋊C₄	1	2	yes	—
25	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₉	—	2	2	no	—
27	C₂×C₄×C₁₉	—	2	8	no	—
28	C₂×C₄×C₁₉	—	2	4	no	—
29	C₂×C₄×C₁₉	—	2	8	no	—
30	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
31	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₁₉	#41	1	4	yes	—
33	C₁₉⋊C₈	—	4	4	no	—
34	#1818	—	19	1	no	maximal, Sylow
35	C₂²×C₁₉	—	2	2	no	—
36	C₂²×C₁₉	—	2	4	no	—
37	C₂²×C₁₉	—	4	4	no	—
38	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
39	C₂²×C₁₉	#117	1	2	yes	—
40	C₂²×C₁₉	#131	1	4	yes	—
41	C₄×C₁₉	—	2	2	no	—
42	C₄×C₁₉	—	4	4	no	—
43	C₄×C₁₉	#123	1	4	yes	—
44	C₂×#117	D₁₉	1	1	yes	characteristic
45	C₂×C₂²⋊C₈	—	19	2	no	—
46	#336	—	19	4	no	—
47	C₂×C₁₉	—	4	2	no	—
48	C₂×C₁₉	#381	1	1	yes	characteristic
49	C₂×C₁₉	#408	1	2	yes	—
50	C₂×C₁₉	#433	1	4	yes	—
51	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
52	C₂²×C₈	—	19	4	no	—
53	#117	—	2	4	no	—
54	C₂×C₄⋊C₄	Dic₁₉	1	2	yes	—
55	C₂×C₂²⋊C₄	Dic₁₉	1	2	yes	—
56	C₂×C₄²	C₂×D₁₉	1	2	yes	—
57	C₂²⋊C₈	—	38	4	no	—
58	C₁₉	#1818	1	1	yes	characteristic, complemented, Sylow
59	C₂⁴	C₂×Dic₁₉	1	1	yes	characteristic
60	C₂²×C₄	—	2	4	no	—
61	C₂²×C₄	C₂×Dic₁₉	1	4	yes	—
62	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
63	C₂²×C₄	C₂²⋊D₁₉	1	4	yes	—
64	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
65	C₂×C₈	—	38	8	no	—
66	C₂×C₈	—	38	4	no	—
67	C₄⋊C₄	—	2	4	no	—
68	C₂²⋊C₄	—	2	4	no	—
69	C₄²	—	2	4	no	—
70	C₂³	—	2	4	no	—
71	C₂³	—	2	2	no	—
72	C₂³	C₂²⋊Dic₁₉	1	2	yes	—
73	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	—	2	8	no	—
76	C₂×C₄	—	2	8	no	—
77	C₂×C₄	—	2	4	no	—
78	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
79	C₂×C₄	#64541	1	4	yes	—
80	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
81	C₈	—	76	4	no	—
82	C₂²	—	2	2	no	—
83	C₂²	—	2	4	no	—
84	C₂²	—	4	4	no	—
85	C₂²	#10597372	1	2	yes	—
86	C₂²	#10597394	1	4	yes	—
87	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	4	4	no	—
90	C₄	#10597375	1	4	yes	—
91	C₂	—	4	2	no	—
92	C₂	#11926407	1	1	yes	characteristic
93	C₂	#11926511	1	2	yes	—
94	C₂	#11926605	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₉
commutator, socle	C₂³×C₁₉	C₂²×C₄
Fitting	C₂×C₁₉×#117	C₂
prime radical	C₂⁴×C₁₉	C₂×C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#117	D₁₉
hypocenter	C₁₉	#1818
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
2. #11926299	C₂	semidirect
58. C₁₉	#1818	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂²⋊(C₁₉⋊C₈)	2
#11926299	2
C₂×C₁₉×#117	2
#1818	19