Finite Group Databasebeta

← C₉×C₁₉₉⋊C₃ #19129012

Subgroups — C₉×C₁₉₉⋊C₃ #19129012

Order 5373.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉₉⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₉₉	C₃	1	1	yes	maximal, characteristic, complemented
3	#13184224	C₃	1	2	yes	maximal, complemented
4	C₃×C₁₉₉	C₃²	1	1	yes	characteristic
5	C₁₉₉⋊C₃	C₉	1	3	yes	direct product factor
6	C₁₉₉	C₃×C₉	1	1	yes	characteristic, complemented, Sylow
7	C₃×C₉	—	199	1	no	maximal, Sylow
8	C₃²	—	199	1	no	—
9	C₉	—	199	2	no	—
10	C₉	C₁₉₉⋊C₃	1	1	yes	characteristic, direct product factor
11	C₃	—	199	3	no	—
12	C₃	C₃×C₁₉₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₉	C₁₉₉⋊C₃
commutator, hypocenter	C₁₉₉	C₃×C₉
Frattini	C₃	C₃×C₁₉₉⋊C₃
Fitting	C₉×C₁₉₉	C₃
socle	C₃×C₁₉₉	C₃²
LCS	G ▷ C₁₉₉
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
2. C₉×C₁₉₉	C₃	semidirect
3. #13184224	C₃	semidirect
5. C₁₉₉⋊C₃	C₉	direct (N × H)
6. C₁₉₉	C₃×C₉	semidirect
10. C₉	C₁₉₉⋊C₃	direct (N × H)