Subgroups — C₁₇×D₁₃⋊(C₅²⋊C₃) #45684145

Order 33150.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₁₃⋊(C₅²⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×C₁₇×D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₇×C₅²⋊C₃	—	13	1	no	maximal, Hall
5	C₅×C₁₇×D₁₃	—	3	2	no	—
6	D₁₃⋊(C₅²⋊C₃)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₇×D₁₃⋊C₃	—	25	1	no	maximal, Hall
8	C₁₇×C₅²⋊C₃	—	13	1	no	Hall
9	C₅×C₁₃×C₁₇	—	3	2	no	—
10	C₁₃⋊(C₅²⋊C₃)	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅²×C₁₇	—	13	1	no	Hall
12	C₁₇×C₁₃⋊C₃	—	25	1	no	Hall
13	C₅²×D₁₃	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₁₇×D₁₃	C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₅²×C₁₇	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
16	C₅²×C₁₃	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
17	C₁₃×C₁₇	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₁₇	—	39	2	no	—
19	C₂×C₅²⋊C₃	—	13	1	no	Hall
20	C₅×D₁₃	—	3	2	no	—
21	C₂×C₃×C₁₇	—	325	1	no	Hall
22	C₅×C₁₇	—	3	2	no	—
23	D₁₃⋊C₃	—	25	1	no	Hall
24	C₅²⋊C₃	—	13	1	no	Hall
25	C₅×C₁₃	—	3	2	no	—
26	C₃×C₁₇	—	325	1	no	Hall
27	C₂×C₅²	—	13	1	no	Hall
28	C₁₃⋊C₃	—	25	1	no	Hall
29	C₂×C₁₇	—	13	1	no	Hall
30	D₁₃	C₁₇×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₅²	C₁₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
32	C₁₇	D₁₃⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
33	C₁₃	C₂×C₁₇×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₅	—	39	2	no	—
35	C₂×C₃	—	325	1	no	Hall
36	C₅	—	3	2	no	—
37	C₃	—	325	1	no	Sylow
38	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	D₁₃⋊(C₅²⋊C₃)
commutator, cosocle, hypocenter	C₅²×C₁₃	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₅²×C₁₃×C₁₇	C₂×C₃
LCS	G ▷ C₅²×C₁₃
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₁₃⋊(C₅²⋊C₃)	C₂	semidirect
2. C₅²×C₁₇×D₁₃	C₃	semidirect
3. C₅²×C₁₃×C₁₇	C₂×C₃	semidirect
6. D₁₃⋊(C₅²⋊C₃)	C₁₇	direct (N × H)
10. C₁₃⋊(C₅²⋊C₃)	C₂×C₁₇	semidirect
13. C₅²×D₁₃	C₃×C₁₇	semidirect
14. C₁₇×D₁₃	C₅²⋊C₃	semidirect
15. C₅²×C₁₇	D₁₃⋊C₃	semidirect
16. C₅²×C₁₃	C₂×C₃×C₁₇	semidirect
17. C₁₃×C₁₇	C₂×C₅²⋊C₃	semidirect
30. D₁₃	C₁₇×C₅²⋊C₃	semidirect
31. C₅²	C₁₇×D₁₃⋊C₃	semidirect
32. C₁₇	D₁₃⋊(C₅²⋊C₃)	direct (N × H)
33. C₁₃	C₂×C₁₇×C₅²⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×C₁₃⋊(C₅²⋊C₃)	2
C₅²×C₁₇×D₁₃	3
C₂×C₁₇×C₅²⋊C₃	13
D₁₃⋊(C₅²⋊C₃)	17
C₁₇×D₁₃⋊C₃	25

Subgroups — C17×D13⋊(C52⋊C3) #45684145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×D₁₃⋊(C₅²⋊C₃) #45684145