Finite Group Databasebeta

← C₅×C₁₇×C₁₁²⋊C₃ #44524809

Subgroups — C₅×C₁₇×C₁₁²⋊C₃ #44524809

Order 30855.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁²×C₁₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×C₁₁²⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁²×C₁₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×C₁₁²⋊C₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₁×C₁₇	—	3	4	no	—
6	C₅×C₁₁²	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
7	C₁₁²⋊C₃	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₅×C₁₇	—	121	1	no	maximal, Hall
9	C₁₁×C₁₇	—	3	4	no	—
10	C₁₁²	C₃×C₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
11	C₅×C₁₇	C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₁₁	—	3	4	no	—
13	C₃×C₁₇	—	121	1	no	Hall
14	C₁₇	C₅×C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₅	—	121	1	no	Hall
16	C₁₁	—	3	4	no	—
17	C₅	C₁₇×C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₃	—	121	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₇	C₁₁²⋊C₃
commutator, cosocle, hypocenter	C₁₁²	C₃×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²×C₁₇	C₃
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₅×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁²×C₁₇	C₃	semidirect
2. C₁₇×C₁₁²⋊C₃	C₅	direct (N × H)
3. C₁₁²×C₁₇	C₃×C₅	semidirect
4. C₅×C₁₁²⋊C₃	C₁₇	direct (N × H)
6. C₅×C₁₁²	C₃×C₁₇	semidirect
7. C₁₁²⋊C₃	C₅×C₁₇	direct (N × H)
10. C₁₁²	C₃×C₅×C₁₇	semidirect
11. C₅×C₁₇	C₁₁²⋊C₃	direct (N × H)
14. C₁₇	C₅×C₁₁²⋊C₃	direct (N × H)
17. C₅	C₁₇×C₁₁²⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₁²×C₁₇	3
C₁₇×C₁₁²⋊C₃	5
C₅×C₁₁²⋊C₃	17
C₃×C₅×C₁₇	121