Subgroups — #18070450

Order 4864.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉⋊C₁₂₈	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₉×C₆₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×C₃₂	C₄	1	1	yes	characteristic
4	C₁₉×C₆₄	C₄	1	1	yes	characteristic
5	C₁₉×C₆₄	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₁₉	C₈	1	1	yes	characteristic
7	C₁₉×C₃₂	C₈	1	1	yes	characteristic
8	C₁₉×C₃₂	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₁₉	C₁₆	1	1	yes	characteristic
10	C₁₆×C₁₉	C₁₆	1	1	yes	characteristic
11	C₁₆×C₁₉	C₂×C₈	1	1	yes	characteristic
12	M₂₅₆	—	19	1	no	maximal, Sylow
13	C₂×C₄×C₁₉	C₃₂	1	1	yes	characteristic
14	C₈×C₁₉	C₃₂	1	1	yes	characteristic
15	C₈×C₁₉	C₂×C₁₆	1	1	yes	characteristic
16	C₂×C₆₄	D₁₉	1	1	yes	characteristic
17	C₁₂₈	—	19	2	no	—
18	C₂²×C₁₉	C₆₄	1	1	yes	characteristic
19	C₄×C₁₉	C₆₄	1	1	yes	characteristic
20	C₄×C₁₉	C₂×C₃₂	1	1	yes	characteristic
21	C₂×C₃₂	Dic₁₉	1	1	yes	characteristic
22	C₆₄	Dic₁₉	1	1	yes	characteristic
23	C₆₄	C₂×D₁₉	1	1	yes	characteristic
24	C₂×C₁₉	—	2	1	no	—
25	C₂×C₁₉	C₂×C₆₄	1	1	yes	characteristic
26	C₂×C₁₆	C₁₉⋊C₈	1	1	yes	characteristic
27	C₃₂	C₁₉⋊C₈	1	1	yes	characteristic
28	C₃₂	C₂×Dic₁₉	1	1	yes	characteristic
29	C₁₉	M₂₅₆	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₈	C₁₉⋊C₁₆	1	1	yes	characteristic
31	C₁₆	C₁₉⋊C₁₆	1	1	yes	characteristic
32	C₁₆	C₂×C₁₉⋊C₈	1	1	yes	characteristic
33	C₂×C₄	C₁₉⋊C₃₂	1	1	yes	characteristic
34	C₈	C₁₉⋊C₃₂	1	1	yes	characteristic
35	C₈	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
36	C₂²	C₁₉⋊C₆₄	1	1	yes	characteristic
37	C₄	C₁₉⋊C₆₄	1	1	yes	characteristic
38	C₄	C₂×C₁₉⋊C₃₂	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	C₂×C₁₉⋊C₆₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₆₄	C₂×D₁₉
commutator, socle	C₂×C₁₉	C₂×C₆₄
Fitting	C₂×C₁₉×C₆₄	C₂
prime radical	C₂²×C₁₉	C₆₄
cosocle	C₁₉×C₆₄	C₂²
hypercenter	C₂×C₆₄	D₁₉
hypocenter	C₁₉	M₂₅₆
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₆₄ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
1. C₁₉⋊C₁₂₈	C₂	semidirect
29. C₁₉	M₂₅₆	semidirect

Maximal subgroups

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

subgroup	index
C₁₉⋊C₁₂₈	2
C₂×C₁₉×C₆₄	2
M₂₅₆	19