Subgroups — #20258973

Order 6084.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃⋊(C₁₃⋊D₁₃))	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃⋊(C₁₃⋊D₁₃)	—	6	2	no	—
4	#10621728	—	9	1	no	maximal, Hall
5	C₃×C₁₃²	—	2	2	no	—
6	#90866	—	13	14	no	maximal
7	C₁₃⋊D₁₃	—	9	1	no	—
8	C₃⋊D₃₉	—	13	14	no	—
9	C₁₃²	#157	1	1	yes	characteristic, complemented, Sylow
10	C₃²×C₁₃	#261	1	14	yes	complemented
11	D₃₉	—	78	28	no	—
12	#261	—	117	14	no	—
13	C₃×C₁₃	—	2	28	no	—
14	#157	—	169	1	no	Hall
15	D₁₃	—	117	14	no	—
16	C₃⋊D₃	—	169	1	no	—
17	C₁₃	#90866	1	14	yes	complemented
18	C₃²	#10621728	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	1014	2	no	—
20	C₄	—	1521	1	no	Sylow
21	C₃	—	2	2	no	—
22	C₂	—	1521	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₃²	C₄
LCS	G ▷ C₃²×C₁₃²
UCS	C₁

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