Subgroups — C₃×C₁₁×#168 #13050302

Order 1320.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#168	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₅×C₁₁	C₄	1	1	yes	characteristic
4	C₃×C₈×C₁₁	—	5	1	no	maximal, Hall
5	C₄×C₅×C₁₁	C₂×C₃	1	1	yes	characteristic
6	C₃×C₅×C₁₁	C₈	1	1	yes	characteristic, complemented, Hall
7	C₃×C₄×C₁₁	D₅	1	1	yes	characteristic
8	C₃×#168	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₅×C₁₁	C₃×C₄	1	1	yes	characteristic
10	C₈×C₁₁	—	5	1	no	Hall
11	C₂×C₃×C₁₁	Dic₅	1	1	yes	characteristic
12	C₃×C₄×C₅	C₂×C₁₁	1	1	yes	characteristic
13	C₅×C₁₁	C₃×C₈	1	1	yes	characteristic, complemented, Hall
14	C₄×C₁₁	C₃×D₅	1	1	yes	characteristic
15	#168	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₁	#168	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₅	C₄×C₁₁	1	1	yes	characteristic
18	C₃×C₈	—	5	1	no	Hall
19	C₂×C₁₁	C₃×Dic₅	1	1	yes	characteristic
20	C₄×C₅	C₂×C₃×C₁₁	1	1	yes	characteristic
21	C₃×C₅	C₈×C₁₁	1	1	yes	characteristic, complemented, Hall
22	C₃×C₄	D₅×C₁₁	1	1	yes	characteristic
23	C₁₁	C₃×#168	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₅	C₃×C₄×C₁₁	1	1	yes	characteristic
25	C₈	—	5	1	no	Sylow
26	C₂×C₃	C₁₁×Dic₅	1	1	yes	characteristic
27	C₅	C₃×C₈×C₁₁	1	1	yes	characteristic, complemented, Sylow
28	C₄	C₃×D₅×C₁₁	1	1	yes	characteristic
29	C₃	C₁₁×#168	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	C₃×C₁₁×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄×C₁₁	D₅
commutator, hypocenter	C₅	C₃×C₈×C₁₁
Frattini	C₄	C₃×D₅×C₁₁
Fitting	C₃×C₄×C₅×C₁₁	C₂
socle, prime radical	C₂×C₃×C₅×C₁₁	C₄
cosocle	C₄×C₅	C₂×C₃×C₁₁
LCS	G ▷ C₅
UCS	C₁ ◁ C₃×C₄×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₁₁×#168	C₃	direct (N × H)
6. C₃×C₅×C₁₁	C₈	semidirect
8. C₃×#168	C₁₁	direct (N × H)
13. C₅×C₁₁	C₃×C₈	semidirect
15. #168	C₃×C₁₁	direct (N × H)
16. C₃×C₁₁	#168	direct (N × H)
21. C₃×C₅	C₈×C₁₁	semidirect
23. C₁₁	C₃×#168	direct (N × H)
27. C₅	C₃×C₈×C₁₁	semidirect
29. C₃	C₁₁×#168	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₄×C₅×C₁₁	2
C₁₁×#168	3
C₃×C₈×C₁₁	5
C₃×#168	11

Subgroups — C3×C11×#168 #13050302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×#168 #13050302