Subgroups — C₂×C₅×C₁₇×D₇₉ #41001719

Order 26860.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₇×D₇₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₇×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₇×C₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₇×D₇₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₇×C₇₉	C₂×C₅	1	1	yes	characteristic, complemented
6	C₁₇×D₇₉	C₂×C₅	1	2	yes	direct product factor
7	C₂×C₅×D₇₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₇₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₇₉	C₂×C₁₇	1	1	yes	characteristic, complemented
10	C₅×D₇₉	C₂×C₁₇	1	2	yes	direct product factor
11	C₅×C₇₉	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₅×C₁₇	—	79	1	no	maximal, Hall
13	C₂×D₇₉	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅×C₁₇	—	79	2	no	—
15	C₂×C₅×C₁₇	D₇₉	1	1	yes	characteristic, direct product factor
16	C₂×C₇₉	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented
17	D₇₉	C₂×C₅×C₁₇	1	2	yes	direct product factor
18	C₅×C₁₇	C₂×D₇₉	1	1	yes	characteristic, direct product factor, Hall
19	C₇₉	C₂²×C₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
20	C₂²×C₁₇	—	79	1	no	Hall
21	C₂×C₁₇	—	79	2	no	—
22	C₂×C₁₇	C₅×D₇₉	1	1	yes	characteristic, direct product factor
23	C₂²×C₅	—	79	1	no	Hall
24	C₁₇	C₂×C₅×D₇₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₅	—	79	2	no	—
26	C₂×C₅	C₁₇×D₇₉	1	1	yes	characteristic, direct product factor
27	C₅	C₂×C₁₇×D₇₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	79	1	no	Sylow
29	C₂	—	79	2	no	—
30	C₂	C₅×C₁₇×D₇₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₇	D₇₉
commutator, cosocle, hypocenter	C₇₉	C₂²×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₇×C₇₉	C₂
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₂×C₅×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₇×D₇₉	C₂	direct (N × H)
2. C₂×C₅×C₁₇×C₇₉	C₂	semidirect
3. C₅×C₁₇×C₇₉	C₂²	semidirect
4. C₂×C₁₇×D₇₉	C₅	direct (N × H)
5. C₂×C₁₇×C₇₉	C₂×C₅	semidirect
6. C₁₇×D₇₉	C₂×C₅	direct (N × H)
7. C₂×C₅×D₇₉	C₁₇	direct (N × H)
8. C₁₇×C₇₉	C₂²×C₅	semidirect
9. C₂×C₅×C₇₉	C₂×C₁₇	semidirect
10. C₅×D₇₉	C₂×C₁₇	direct (N × H)
11. C₅×C₇₉	C₂²×C₁₇	semidirect
13. C₂×D₇₉	C₅×C₁₇	direct (N × H)
15. C₂×C₅×C₁₇	D₇₉	direct (N × H)
16. C₂×C₇₉	C₂×C₅×C₁₇	semidirect
17. D₇₉	C₂×C₅×C₁₇	direct (N × H)
18. C₅×C₁₇	C₂×D₇₉	direct (N × H)
19. C₇₉	C₂²×C₅×C₁₇	semidirect
22. C₂×C₁₇	C₅×D₇₉	direct (N × H)
24. C₁₇	C₂×C₅×D₇₉	direct (N × H)
26. C₂×C₅	C₁₇×D₇₉	direct (N × H)
27. C₅	C₂×C₁₇×D₇₉	direct (N × H)
30. C₂	C₅×C₁₇×D₇₉	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×C₁₇×D₇₉	2
C₂×C₅×C₁₇×C₇₉	2
C₂×C₁₇×D₇₉	5
C₂×C₅×D₇₉	17
C₂²×C₅×C₁₇	79

Subgroups — C2×C5×C17×D79 #41001719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₇×D₇₉ #41001719