Subgroups — #20258976

Order 6084.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₁₃²	—	6	2	no	—
4	#10621725	—	9	1	no	maximal, Hall
5	C₃×C₁₃²	—	2	2	no	—
6	#90865	—	13	14	no	maximal
7	C₂×C₁₃²	—	9	1	no	—
8	C₁₃×C₃⋊D₃	D₁₃	1	14	yes	—
9	C₁₃²	#157	1	1	yes	characteristic, complemented, Sylow
10	C₃²×C₁₃	Dic₁₃	1	14	yes	complemented
11	D₃×C₁₃	—	6	28	no	—
12	Dic₁₃	—	117	14	no	—
13	C₃×C₁₃	—	2	28	no	—
14	#157	—	169	1	no	Hall
15	C₂×C₁₃	—	9	14	no	—
16	C₃⋊D₃	C₁₃⋊D₁₃	1	1	yes	characteristic
17	C₁₃	#90865	1	14	yes	complemented
18	C₃²	#10621725	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	6	2	no	—
20	C₄	—	1521	1	no	Sylow
21	C₃	—	2	2	no	—
22	C₂	—	9	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.