Subgroups — C₂×D₁₇×C₄₁⋊C₅ #28358288

Order 13940.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇×C₄₁⋊C₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₇×C₄₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×C₄₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₇×C₄₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₁₇×C₄₁	C₂×C₅	1	1	yes	characteristic, complemented
6	D₁₇×C₄₁	C₂×C₅	1	2	yes	complemented
7	C₂²×C₄₁⋊C₅	—	17	1	no	maximal, Hall
8	C₁₇×C₄₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₄₁⋊C₅	—	17	2	no	—
10	C₂×C₄₁⋊C₅	D₁₇	1	1	yes	characteristic, direct product factor
11	C₂×C₅×D₁₇	—	41	1	no	maximal, Hall
12	C₄₁⋊C₅	C₂×D₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₅×C₁₇	—	41	1	no	—
14	C₅×D₁₇	—	41	2	no	—
15	C₂²×C₄₁	—	17	1	no	Hall
16	C₅×C₁₇	—	41	1	no	Hall
17	C₂×C₄₁	—	17	2	no	—
18	C₂×C₄₁	C₅×D₁₇	1	1	yes	characteristic, complemented
19	C₂×D₁₇	C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
20	C₄₁	C₂×C₅×D₁₇	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₁₇	C₂×C₄₁⋊C₅	1	1	yes	characteristic, complemented
22	D₁₇	C₂×C₄₁⋊C₅	1	2	yes	direct product factor
23	C₂²×C₅	—	697	1	no	Hall
24	C₁₇	C₂²×C₄₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅	—	41	1	no	—
26	C₂×C₅	—	697	2	no	—
27	C₅	—	41	1	no	Sylow
28	C₂²	—	17	1	no	Sylow
29	C₂	—	17	2	no	—
30	C₂	D₁₇×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₇×C₄₁⋊C₅
commutator, cosocle, hypocenter	C₁₇×C₄₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₁₇×C₄₁	C₂×C₅
LCS	G ▷ C₁₇×C₄₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₁₇×C₄₁⋊C₅	C₂	direct (N × H)
2. C₂×C₁₇×C₄₁⋊C₅	C₂	semidirect
3. C₁₇×C₄₁⋊C₅	C₂²	semidirect
4. C₂×D₁₇×C₄₁	C₅	semidirect
5. C₂×C₁₇×C₄₁	C₂×C₅	semidirect
6. D₁₇×C₄₁	C₂×C₅	semidirect
8. C₁₇×C₄₁	C₂²×C₅	semidirect
10. C₂×C₄₁⋊C₅	D₁₇	direct (N × H)
12. C₄₁⋊C₅	C₂×D₁₇	direct (N × H)
18. C₂×C₄₁	C₅×D₁₇	semidirect
19. C₂×D₁₇	C₄₁⋊C₅	direct (N × H)
20. C₄₁	C₂×C₅×D₁₇	semidirect
21. C₂×C₁₇	C₂×C₄₁⋊C₅	semidirect
22. D₁₇	C₂×C₄₁⋊C₅	direct (N × H)
24. C₁₇	C₂²×C₄₁⋊C₅	semidirect
30. C₂	D₁₇×C₄₁⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
D₁₇×C₄₁⋊C₅	2
C₂×C₁₇×C₄₁⋊C₅	2
C₂×D₁₇×C₄₁	5
C₂²×C₄₁⋊C₅	17
C₂×C₅×D₁₇	41

Subgroups — C2×D17×C41⋊C5 #28358288

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₇×C₄₁⋊C₅ #28358288