Subgroups — #20301653

Order 7380.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₆₁₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	#13093287	—	5	1	no	maximal, Hall
4	D₆₁₅	—	6	2	no	—
5	#11717961	—	9	1	no	maximal, Hall
6	C₃⋊D₁₂₃	—	5	1	no	—
7	C₃×C₅×C₄₁	—	2	2	no	—
8	D₂₀₅	—	9	1	no	—
9	C₃²×C₄₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
10	D₁₂₃	—	30	2	no	—
11	C₅×C₄₁	#157	1	1	yes	characteristic, complemented, Hall
12	#4380	—	41	1	no	maximal, Hall
13	#4223	—	45	1	no	Hall
14	C₃×C₄₁	—	2	2	no	—
15	C₃⋊D₁₅	—	41	1	no	—
16	D₄₁	—	45	1	no	—
17	C₃²×C₅	#4223	1	1	yes	characteristic, complemented, Hall
18	C₄₁	#4380	1	1	yes	characteristic, complemented, Sylow
19	#157	—	205	1	no	Hall
20	D₁₅	—	246	2	no	—
21	AGL(1,𝔽₅)	—	369	1	no	Hall
22	C₃⋊D₃	—	205	1	no	—
23	C₃×C₅	—	2	2	no	—
24	D₅	—	369	1	no	—
25	C₃²	#11717961	1	1	yes	characteristic, complemented, Sylow
26	D₃	—	1230	2	no	—
27	C₅	#13093287	1	1	yes	characteristic, complemented, Sylow
28	C₄	—	1845	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	1845	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₄₁	C₄
LCS	G ▷ C₃²×C₅×C₄₁
UCS	C₁

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