Subgroups — C₁₉⋊#13184070 #46799052

Order 33820.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉×D₈₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₉×C₈₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉⋊#67063	—	5	1	no	maximal, Hall
4	C₁₉×D₈₉	D₅	1	1	yes	characteristic
5	#13184070	—	19	1	no	maximal, Hall
6	C₁₉×C₈₉	Dic₅	1	1	yes	characteristic, complemented, Hall
7	C₅×D₈₉	D₁₉	1	1	yes	characteristic
8	C₅×C₈₉	Dic₁₉	1	1	yes	characteristic, complemented, Hall
9	Dic₉₅	—	89	1	no	maximal, Hall
10	#67063	—	95	1	no	Hall
11	C₂×C₅×C₁₉	—	89	1	no	—
12	D₈₉	D₉₅	1	1	yes	characteristic
13	C₅×C₁₉	#67063	1	1	yes	characteristic, complemented, Hall
14	C₈₉	Dic₉₅	1	1	yes	characteristic, complemented, Sylow
15	Dic₁₉	—	445	1	no	Hall
16	C₂×C₁₉	—	89	1	no	—
17	Dic₅	—	1691	1	no	Hall
18	C₁₉	#13184070	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	—	89	1	no	—
20	C₅	C₁₉⋊#67063	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	8455	1	no	Sylow
22	C₂	—	89	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₉×C₈₉	C₄
prime radical, cosocle	C₅×C₁₉×D₈₉	C₂
LCS	G ▷ C₅×C₁₉×C₈₉
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.