Subgroups — #14561775

Order 2432.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926378	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₉×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₁₉	C₄	1	1	yes	characteristic
4	C₁₉×M₃₂	—	2	2	no	—
5	C₂×C₁₆×C₁₉	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉⋊C₃₂	—	2	2	no	—
8	C₂²×C₄×C₁₉	C₈	1	1	yes	characteristic
9	C₂×C₈×C₁₉	—	2	1	no	—
10	C₂×C₈×C₁₉	—	2	1	no	—
11	C₂×C₈×C₁₉	C₈	1	1	yes	characteristic
12	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₁₉	—	2	1	no	—
14	C₁₆×C₁₉	D₄	1	2	yes	—
15	C₂³×C₁₉	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₁₉	—	2	1	no	—
17	C₂×C₄×C₁₉	—	2	1	no	—
18	C₂×C₄×C₁₉	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
20	C₈×C₁₉	—	2	1	no	—
21	C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₁₉	M₁₆	1	1	yes	characteristic
23	#1400	—	19	1	no	maximal, Sylow
24	C₂²×C₁₉	—	2	1	no	—
25	C₂²×C₁₉	—	4	1	no	—
26	C₂²×C₁₉	C₂×C₁₆	1	1	yes	characteristic
27	C₄×C₁₉	—	2	1	no	—
28	C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
29	C₄×C₁₉	M₃₂	1	1	yes	characteristic
30	C₂×M₃₂	D₁₉	1	1	yes	characteristic
31	M₆₄	—	19	2	no	—
32	C₂×C₁₉	—	2	1	no	—
33	C₂×C₁₉	—	4	1	no	—
34	C₂×C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic
35	C₂²×C₈	Dic₁₉	1	1	yes	characteristic
36	M₃₂	—	2	2	no	—
37	C₂×C₁₆	Dic₁₉	1	1	yes	characteristic
38	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
39	C₃₂	—	38	2	no	—
40	C₁₉	#1400	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₄	C₁₉⋊C₈	1	1	yes	characteristic
42	C₂×C₈	—	2	1	no	—
43	C₂×C₈	—	2	1	no	—
44	C₂×C₈	C₁₉⋊C₈	1	1	yes	characteristic
45	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
46	C₁₆	—	2	1	no	—
47	C₁₆	C₂²⋊D₁₉	1	2	yes	—
48	C₂³	C₁₉⋊C₁₆	1	1	yes	characteristic
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	C₁₉⋊C₁₆	1	1	yes	characteristic
52	C₂×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	#64520	1	1	yes	characteristic
55	C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
56	C₂²	—	2	1	no	—
57	C₂²	—	4	1	no	—
58	C₂²	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	#10597269	1	1	yes	characteristic
61	C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	4	1	no	—
64	C₂	C₂²⋊(C₁₉⋊C₁₆)	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊Dic₁₉
commutator	C₂²×C₁₉	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₁₉
Fitting	C₂×C₁₉×M₃₂	C₂
socle	C₂×C₁₉	C₂²⋊C₁₆
prime radical	C₂³×C₁₉	C₁₆
cosocle	C₂×C₁₆×C₁₉	C₂²
hypercenter	C₂×M₃₂	D₁₉
hypocenter	C₁₉	#1400
LCS	G ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
1. #11926378	C₂	semidirect
40. C₁₉	#1400	semidirect

Maximal subgroups

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

subgroup	index
#11926378	2
C₂×C₁₉×M₃₂	2
#1400	19