Subgroups — #18070449

Order 4864.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, Frattini	C₆₄	C₂×D₁₉
commutator, socle	C₂×C₁₉	C₂×C₆₄
Fitting	C₁₉×C₁₂₈	C₂
prime radical	C₂×D₁₉	C₆₄
cosocle	C₁₉×C₆₄	C₂²
hypercenter	C₁₂₈	D₁₉
hypocenter	C₁₉	M₂₅₆
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₆₄ ◁ C₁₂₈

Complements

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

N	H ≅ G/N	type
2. C₁₉⋊C₁₂₈	C₂	semidirect
3. C₁₉×C₁₂₈	C₂	semidirect
19. C₁₂₈	D₁₉	semidirect
31. C₁₉	M₂₅₆	semidirect

Maximal subgroups

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

subgroup	index
D₁₉×C₆₄	2
C₁₉⋊C₁₂₈	2
C₁₉×C₁₂₈	2
M₂₅₆	19