Subgroups — C₅×C₁₇²×C₃⋊D₃ #39907255

Order 26010.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₇²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₃×C₁₇²	—	3	4	no	maximal
3	C₁₇²×C₃⋊D₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₇²	D₃	1	4	yes	complemented
5	C₂×C₅×C₁₇²	—	9	1	no	Hall
6	C₃²×C₁₇²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	D₃×C₁₇²	—	3	4	no	—
8	C₅×C₁₇×C₃⋊D₃	C₁₇	1	18	yes	maximal, direct product factor
9	C₅×C₁₇²	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₁₇²	C₅×D₃	1	4	yes	complemented
11	C₃²×C₅×C₁₇	C₂×C₁₇	1	18	yes	complemented
12	C₂×C₁₇²	—	9	1	no	Hall
13	C₅×D₃×C₁₇	—	3	72	no	—
14	C₁₇×C₃⋊D₃	C₅×C₁₇	1	18	yes	direct product factor
15	C₁₇²	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₃×C₅×C₁₇	D₃×C₁₇	1	72	yes	complemented
17	C₂×C₅×C₁₇	—	9	18	no	—
18	C₃²×C₁₇	C₂×C₅×C₁₇	1	18	yes	complemented
19	D₃×C₁₇	—	3	72	no	—
20	C₅×C₃⋊D₃	C₁₇²	1	1	yes	characteristic, direct product factor, Hall
21	C₅×C₁₇	C₁₇×C₃⋊D₃	1	18	yes	direct product factor
22	C₃×C₁₇	C₅×D₃×C₁₇	1	72	yes	complemented
23	C₃²×C₅	C₂×C₁₇²	1	1	yes	characteristic, complemented, Hall
24	C₂×C₁₇	—	9	18	no	—
25	C₅×D₃	—	3	4	no	—
26	C₃⋊D₃	C₅×C₁₇²	1	1	yes	characteristic, direct product factor, Hall
27	C₁₇	C₅×C₁₇×C₃⋊D₃	1	18	yes	direct product factor
28	C₃×C₅	D₃×C₁₇²	1	4	yes	complemented
29	C₂×C₅	—	9	1	no	Hall
30	C₃²	C₂×C₅×C₁₇²	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	3	4	no	—
32	C₅	C₁₇²×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₅×D₃×C₁₇²	1	4	yes	complemented
34	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₇²	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₅×C₁₇²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₇²	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅×C₁₇²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₇²	C₂	semidirect
3. C₁₇²×C₃⋊D₃	C₅	direct (N × H)
4. C₃×C₅×C₁₇²	D₃	semidirect
6. C₃²×C₁₇²	C₂×C₅	semidirect
8. C₅×C₁₇×C₃⋊D₃	C₁₇	direct (N × H)
9. C₅×C₁₇²	C₃⋊D₃	direct (N × H)
10. C₃×C₁₇²	C₅×D₃	semidirect
11. C₃²×C₅×C₁₇	C₂×C₁₇	semidirect
14. C₁₇×C₃⋊D₃	C₅×C₁₇	direct (N × H)
15. C₁₇²	C₅×C₃⋊D₃	direct (N × H)
16. C₃×C₅×C₁₇	D₃×C₁₇	semidirect
18. C₃²×C₁₇	C₂×C₅×C₁₇	semidirect
20. C₅×C₃⋊D₃	C₁₇²	direct (N × H)
21. C₅×C₁₇	C₁₇×C₃⋊D₃	direct (N × H)
22. C₃×C₁₇	C₅×D₃×C₁₇	semidirect
23. C₃²×C₅	C₂×C₁₇²	semidirect
26. C₃⋊D₃	C₅×C₁₇²	direct (N × H)
27. C₁₇	C₅×C₁₇×C₃⋊D₃	direct (N × H)
28. C₃×C₅	D₃×C₁₇²	semidirect
30. C₃²	C₂×C₅×C₁₇²	semidirect
32. C₅	C₁₇²×C₃⋊D₃	direct (N × H)
33. C₃	C₅×D₃×C₁₇²	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₁₇²	2
C₅×D₃×C₁₇²	3
C₁₇²×C₃⋊D₃	5
C₅×C₁₇×C₃⋊D₃	17

Subgroups — C5×C172×C3⋊D3 #39907255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₇²×C₃⋊D₃ #39907255