Subgroups — C₃⋊#16809859 #23758679

Order 10092.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×D₂₉	C₂	1	1	yes	maximal, characteristic
2	#16809859	—	3	1	no	maximal, Hall
3	C₃×C₂₉²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂₉×D₂₉	D₃	1	1	yes	characteristic
5	C₂₉²	Dic₃	1	1	yes	characteristic, complemented, Sylow
6	C₃⋊#1181	—	29	1	no	maximal
7	Dic₈₇	—	29	1	no	maximal
8	C₂×C₃×C₂₉	—	29	1	no	—
9	C₃×D₂₉	D₂₉	1	1	yes	characteristic
10	#1181	—	87	1	no	—
11	Dic₂₉	—	87	1	no	—
12	C₃×C₂₉	—	4	7	no	—
13	C₃×C₂₉	Dic₂₉	1	1	yes	characteristic, complemented
14	C₃×C₂₉	#1181	1	1	yes	characteristic, complemented
15	C₂×C₂₉	—	29	1	no	—
16	D₂₉	D₈₇	1	1	yes	characteristic
17	C₂₉	—	4	7	no	—
18	C₂₉	Dic₈₇	1	1	yes	characteristic, complemented
19	C₂₉	C₃⋊#1181	1	1	yes	characteristic, complemented
20	Dic₃	—	841	1	no	Hall
21	C₂×C₃	—	29	1	no	—
22	C₄	—	2523	1	no	Sylow
23	C₃	#16809859	1	1	yes	characteristic, complemented, Sylow
24	C₂	—	29	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₂₉²	C₄
prime radical, cosocle	C₃×C₂₉×D₂₉	C₂
LCS	G ▷ C₃×C₂₉²
UCS	C₁

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