Subgroups — C₁₇⋊((C₅⋊D₅)⋊(C₁₃⋊C₃)) #45684159

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	C₁₃×C₅⋊D₈₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₇⋊((C₅⋊D₅)⋊C₃)	—	13	1	no	maximal, Hall
5	C₁₃×D₈₅	—	15	2	no	—
6	(C₅⋊D₅)⋊(C₁₃⋊C₃)	—	17	1	no	maximal, Hall
7	D₁₇×C₁₃⋊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)	D₁₇	1	1	yes	characteristic, complemented, Hall
11	C₅⋊D₈₅	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
12	C₁₇×C₁₃⋊C₃	—	25	1	no	Hall
13	C₁₃×C₅⋊D₅	—	17	1	no	Hall
14	C₁₃×D₁₇	—	25	1	no	Hall
15	C₅²×C₁₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
16	C₅²×C₁₃	C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
17	C₁₃×C₁₇	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Hall
18	D₈₅	—	15	2	no	—
19	(C₅⋊D₅)⋊C₃	—	221	1	no	Hall
20	D₅×C₁₃	—	255	2	no	—
21	C₃×D₁₇	—	325	1	no	Hall
22	C₅×C₁₇	—	3	2	no	—
23	C₂×C₁₃⋊C₃	—	425	1	no	Hall
24	C₅²⋊C₃	—	13	1	no	Hall
25	C₅×C₁₃	—	3	2	no	—
26	C₃×C₁₇	—	325	1	no	Hall
27	C₅⋊D₅	—	17	1	no	Hall
28	C₁₃⋊C₃	—	25	1	no	Hall
29	D₁₇	—	25	1	no	Hall
30	C₂×C₁₃	—	425	1	no	Hall
31	C₅²	D₁₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
32	C₁₇	(C₅⋊D₅)⋊(C₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
33	C₁₃	C₁₇⋊((C₅⋊D₅)⋊C₃)	1	1	yes	characteristic, complemented, Sylow
34	D₅	—	255	2	no	—
35	C₂×C₃	—	5525	1	no	Hall
36	C₅	—	3	2	no	—
37	C₃	—	325	1	no	Sylow
38	C₂	—	425	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₁₃⋊(C₅²⋊C₃)	C₂	semidirect
2. C₁₃×C₅⋊D₈₅	C₃	semidirect
3. C₅²×C₁₃×C₁₇	C₂×C₃	semidirect
10. C₁₃⋊(C₅²⋊C₃)	D₁₇	semidirect
11. C₅⋊D₈₅	C₁₃⋊C₃	semidirect
15. C₅²×C₁₇	C₂×C₁₃⋊C₃	semidirect
16. C₅²×C₁₃	C₃×D₁₇	semidirect
17. C₁₃×C₁₇	(C₅⋊D₅)⋊C₃	semidirect
31. C₅²	D₁₇×C₁₃⋊C₃	semidirect
32. C₁₇	(C₅⋊D₅)⋊(C₁₃⋊C₃)	semidirect
33. C₁₃	C₁₇⋊((C₅⋊D₅)⋊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
C₁₃×C₅⋊D₈₅	3
C₁₇⋊((C₅⋊D₅)⋊C₃)	13
(C₅⋊D₅)⋊(C₁₃⋊C₃)	17
D₁₇×C₁₃⋊C₃	25

Subgroups — C17⋊((C5⋊D5)⋊(C13⋊C3)) #45684159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇⋊((C₅⋊D₅)⋊(C₁₃⋊C₃)) #45684159