Subgroups — C₃⋊#16813380 #24925314

Order 10830.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉²⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#16813380	—	3	1	no	maximal, Hall
3	C₁₉×D₅₇	—	5	1	no	maximal, Hall
4	C₁₉²⋊C₅	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉²	D₅	1	1	yes	characteristic, complemented, Hall
6	C₁₉×D₁₉	—	15	1	no	Hall
7	C₁₉²	D₁₅	1	1	yes	characteristic, complemented, Sylow
8	D₅₇	—	5	1	no	—
9	D₃×C₁₉	—	95	1	no	—
10	C₃×C₁₉	—	5	1	no	—
11	C₃×C₁₉	—	5	1	no	—
12	C₃×C₁₉	—	10	1	no	—
13	C₂×C₁₉	—	285	1	no	—
14	D₁₉	—	15	1	no	—
15	D₁₅	—	361	1	no	maximal, Hall
16	C₁₉	—	5	1	no	—
17	C₁₉	—	5	1	no	—
18	C₁₉	—	10	1	no	—
19	C₃×C₅	—	361	1	no	Hall
20	D₅	—	1083	1	no	Hall
21	D₃	—	95	1	no	Hall
22	C₅	—	361	1	no	Sylow
23	C₃	#16813380	1	1	yes	characteristic, complemented, Sylow
24	C₂	—	285	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃×C₁₉²⋊C₅	C₂
Fitting, socle	C₃×C₁₉²	D₅
LCS	G ▷ C₃×C₁₉²⋊C₅
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.