Subgroups — C₃⋊(C₃⋊#10625191) #20269142

Order 6660.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₁₈₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#10625191	—	3	4	no	maximal
3	C₃²×C₅×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃⋊#3866)	—	5	1	no	maximal, Hall
5	C₃×D₁₈₅	D₃	1	4	yes	—
6	#10625191	—	9	1	no	Hall
7	C₃²×D₃₇	—	5	1	no	—
8	C₃×C₅×C₃₇	Dic₃	1	4	yes	complemented
9	C₃⋊#3866	—	15	4	no	—
10	D₁₈₅	C₃⋊D₃	1	1	yes	characteristic
11	C₃²×C₃₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₃×D₃₇	—	5	4	no	—
13	C₅×C₃₇	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
14	C₃⋊ΓL(1,𝔽₁₆)	—	37	1	no	maximal, Hall
15	#3866	—	45	1	no	Hall
16	C₃×C₃₇	ΓL(1,𝔽₁₆)	1	4	yes	complemented
17	C₃²×D₅	—	37	1	no	—
18	D₃₇	—	5	1	no	—
19	ΓL(1,𝔽₁₆)	—	111	4	no	—
20	C₃²×C₅	#3866	1	1	yes	characteristic, complemented, Hall
21	C₃₇	C₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
22	C₃⋊Dic₃	—	185	1	no	Hall
23	C₃×D₅	—	37	4	no	—
24	AGL(1,𝔽₅)	—	333	1	no	Hall
25	C₂×C₃²	—	185	1	no	—
26	C₃×C₅	C₃⋊#3866	1	4	yes	complemented
27	Dic₃	—	555	4	no	—
28	D₅	—	37	1	no	—
29	C₃²	#10625191	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	—	185	4	no	—
31	C₅	C₃⋊(C₃⋊#3866)	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	1665	1	no	Sylow
33	C₃	C₃⋊#10625191	1	4	yes	complemented
34	C₂	—	185	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₃₇	C₄
LCS	G ▷ C₃²×C₅×C₃₇
UCS	C₁

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