Subgroups — C₁₉⋊C₃×C₁₅₁⋊C₃ #38788871

Order 25821.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22575306	C₃	1	1	yes	maximal, characteristic, complemented
2	#22575305	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₉×C₁₅₁⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₉⋊C₃×C₁₅₁	C₃	1	1	yes	maximal, characteristic, complemented
5	C₁₉×C₁₅₁	C₃²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₅₁⋊C₃	—	19	1	no	maximal, Hall
7	C₃×C₁₅₁	—	19	1	no	—
8	C₁₅₁⋊C₃	—	19	1	no	—
9	C₁₅₁⋊C₃	—	19	1	no	—
10	C₁₅₁⋊C₃	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
11	C₃×C₁₉⋊C₃	—	151	1	no	maximal, Hall
12	C₁₅₁	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₁₉	—	151	1	no	—
14	C₁₉⋊C₃	—	151	1	no	—
15	C₁₉⋊C₃	—	151	1	no	—
16	C₁₉⋊C₃	C₁₅₁⋊C₃	1	1	yes	characteristic, direct product factor
17	C₁₉	C₃×C₁₅₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	C₃²	—	2869	1	no	Sylow
19	C₃	—	19	1	no	—
20	C₃	—	2869	1	no	—
21	C₃	—	2869	1	no	—
22	C₃	—	151	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₉×C₁₅₁	C₃²
LCS	G ▷ C₁₉×C₁₅₁
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.