Subgroups — #14555574⋊C₅ #24926767

Order 10980.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃⋊(D₆₁⋊C₅))	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₆₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	#14555574	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃⋊(D₆₁⋊C₅)	—	6	2	no	—
5	#6923⋊C₅	—	9	1	no	maximal, Hall
6	C₃⋊D₁₈₃	C₂×C₅	1	1	yes	characteristic
7	C₃×C₆₁⋊C₅	—	2	2	no	—
8	D₆₁⋊C₅	—	9	1	no	—
9	C₃²×C₆₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
10	D₁₈₃	—	6	2	no	—
11	C₆₁⋊C₅	#157	1	1	yes	characteristic, complemented, Hall
12	#6923	—	9	1	no	Hall
13	C₃×C₆₁	—	2	2	no	—
14	C₅×#157	—	61	1	no	maximal, Hall
15	D₆₁	—	9	1	no	—
16	C₅×C₃⋊D₃	—	61	1	no	—
17	C₆₁	C₅×#157	1	1	yes	characteristic, complemented, Sylow
18	C₃²×C₅	—	61	1	no	Hall
19	#157	—	61	1	no	Hall
20	C₅×D₃	—	366	2	no	—
21	C₄×C₅	—	549	1	no	Hall
22	C₃⋊D₃	—	61	1	no	—
23	C₃×C₅	—	122	2	no	—
24	C₂×C₅	—	549	1	no	—
25	C₃²	#6923⋊C₅	1	1	yes	characteristic, complemented, Sylow
26	D₃	—	366	2	no	—
27	C₅	—	61	1	no	Sylow
28	C₄	—	549	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	549	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₆₁	C₄×C₅
prime radical	C₃⋊(C₃⋊(D₆₁⋊C₅))	C₂
cosocle	C₃⋊D₁₈₃	C₂×C₅
LCS	G ▷ C₃²×C₆₁
UCS	C₁

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.