Subgroups — C₃⋊(C₃⋊(C₁₉⋊#261)) #22580359

Order 8892.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₉×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₁₉⋊#261)	—	3	4	no	maximal
3	C₃²×C₁₃×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₉×D₁₃	D₃	1	4	yes	—
5	C₁₉⋊#261	—	9	1	no	Hall
6	C₃×C₁₃×C₁₉	Dic₃	1	4	yes	complemented
7	C₃⋊Dic₅₇	—	13	1	no	maximal, Hall
8	C₁₉×D₁₃	C₃⋊D₃	1	1	yes	characteristic
9	C₃⋊(C₃⋊#261)	—	19	1	no	maximal, Hall
10	C₂×C₃²×C₁₉	—	13	1	no	—
11	C₁₃×C₁₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
12	C₃²×D₁₃	D₁₉	1	1	yes	characteristic
13	Dic₅₇	—	39	4	no	—
14	C₃²×C₁₉	#261	1	1	yes	characteristic, complemented, Hall
15	C₃⋊#261	—	57	4	no	—
16	C₃²×C₁₃	Dic₁₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₉	—	13	4	no	—
18	C₃×D₁₃	D₅₇	1	4	yes	—
19	Dic₁₉	—	117	1	no	Hall
20	C₃×C₁₉	C₃⋊#261	1	4	yes	complemented
21	#261	—	171	1	no	Hall
22	C₃×C₁₃	Dic₅₇	1	4	yes	complemented
23	C₂×C₁₉	—	13	1	no	—
24	C₃⋊Dic₃	—	247	1	no	Hall
25	D₁₃	C₃⋊D₅₇	1	1	yes	characteristic
26	C₁₉	C₃⋊(C₃⋊#261)	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃²	—	13	1	no	—
28	C₁₃	C₃⋊Dic₅₇	1	1	yes	characteristic, complemented, Sylow
29	Dic₃	—	741	4	no	—
30	C₃²	C₁₉⋊#261	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	13	4	no	—
32	C₄	—	2223	1	no	Sylow
33	C₃	C₃⋊(C₁₉⋊#261)	1	4	yes	complemented
34	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₃×C₁₉	C₄
LCS	G ▷ C₃²×C₁₃×C₁₉
UCS	C₁

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