Subgroups — #20258974

Order 6084.

112 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	#10621729	—	9	1	no	maximal, Hall
5	C₃×C₁₃²	—	2	2	no	—
6	#90866	—	13	2	no	maximal
7	C₁₃⋊D₁₃	—	9	1	no	—
8	C₃⋊D₃₉	—	13	2	no	—
9	C₃⋊D₃₉	—	26	6	no	—
10	C₁₃²	#157	1	1	yes	characteristic, complemented, Sylow
11	C₃²×C₁₃	—	2	6	no	—
12	C₃²×C₁₃	#261	1	2	yes	complemented
13	D₃₉	—	78	4	no	—
14	D₃₉	—	78	24	no	—
15	#261	—	117	2	no	—
16	C₃×C₁₃	—	2	24	no	—
17	C₃×C₁₃	—	2	4	no	—
18	#157	—	169	1	no	Hall
19	D₁₃	—	117	2	no	—
20	D₁₃	—	234	6	no	—
21	C₃⋊D₃	—	169	1	no	—
22	C₁₃	—	2	6	no	—
23	C₁₃	#90866	1	2	yes	complemented
24	C₃²	#10621729	1	1	yes	characteristic, complemented, Sylow
25	D₃	—	1014	2	no	—
26	C₄	—	1521	1	no	Sylow
27	C₃	—	2	2	no	—
28	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.