Subgroups — C₅×D₁₇×D₄₁ #28358296

Order 13940.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₆₉₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₇×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₇×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₇×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₇×D₄₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	D₆₉₇	C₂×C₅	1	1	yes	characteristic, complemented
7	C₁₇×D₄₁	C₂×C₅	1	1	yes	characteristic, complemented
8	D₁₇×C₄₁	C₂×C₅	1	1	yes	characteristic, complemented
9	C₂×C₅×D₄₁	—	17	1	no	maximal, Hall
10	C₁₇×C₄₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×C₄₁	—	17	1	no	—
12	C₅×D₄₁	—	17	1	no	—
13	C₅×D₄₁	D₁₇	1	1	yes	characteristic, direct product factor
14	C₂×C₅×D₁₇	—	41	1	no	maximal, Hall
15	C₅×C₄₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×C₁₇	—	41	1	no	—
17	C₅×D₁₇	—	41	1	no	—
18	C₅×D₁₇	D₄₁	1	1	yes	characteristic, direct product factor
19	C₂×D₄₁	—	17	1	no	Hall
20	C₅×C₁₇	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₄₁	—	17	1	no	—
22	D₄₁	—	17	1	no	—
23	D₄₁	C₅×D₁₇	1	1	yes	characteristic, direct product factor
24	C₂×D₁₇	—	41	1	no	Hall
25	C₄₁	C₂×C₅×D₁₇	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₇	—	41	1	no	—
27	D₁₇	—	41	1	no	—
28	D₁₇	C₅×D₄₁	1	1	yes	characteristic, direct product factor
29	C₂²×C₅	—	697	1	no	Hall
30	C₁₇	C₂×C₅×D₄₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	17	1	no	—
32	C₂×C₅	—	41	1	no	—
33	C₂×C₅	—	697	1	no	—
34	C₅	D₁₇×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²	—	697	1	no	Sylow
36	C₂	—	17	1	no	—
37	C₂	—	41	1	no	—
38	C₂	—	697	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₁₇×D₄₁
commutator, cosocle, hypocenter	C₁₇×C₄₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₇×C₄₁	C₂²
LCS	G ▷ C₁₇×C₄₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₆₉₇	C₂	semidirect
2. C₅×D₁₇×C₄₁	C₂	semidirect
3. C₅×C₁₇×D₄₁	C₂	semidirect
4. C₅×C₁₇×C₄₁	C₂²	semidirect
5. D₁₇×D₄₁	C₅	direct (N × H)
6. D₆₉₇	C₂×C₅	semidirect
7. C₁₇×D₄₁	C₂×C₅	semidirect
8. D₁₇×C₄₁	C₂×C₅	semidirect
10. C₁₇×C₄₁	C₂²×C₅	semidirect
13. C₅×D₄₁	D₁₇	direct (N × H)
15. C₅×C₄₁	C₂×D₁₇	semidirect
18. C₅×D₁₇	D₄₁	direct (N × H)
20. C₅×C₁₇	C₂×D₄₁	semidirect
23. D₄₁	C₅×D₁₇	direct (N × H)
25. C₄₁	C₂×C₅×D₁₇	semidirect
28. D₁₇	C₅×D₄₁	direct (N × H)
30. C₁₇	C₂×C₅×D₄₁	semidirect
34. C₅	D₁₇×D₄₁	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×D₆₉₇	2
C₅×D₁₇×C₄₁	2
C₅×C₁₇×D₄₁	2
D₁₇×D₄₁	5
C₂×C₅×D₄₁	17
C₂×C₅×D₁₇	41

Subgroups — C5×D17×D41 #28358296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₁₇×D₄₁ #28358296