Subgroups — C₂×C₅×D₁₇₉₉ #49112682

Order 35980.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₇₉₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇×C₂₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×C₂₅₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₇₉₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×D₂₅₇	—	7	1	no	maximal, Hall
6	C₂×C₇×C₂₅₇	C₂×C₅	1	1	yes	characteristic, complemented
7	D₁₇₉₉	C₂×C₅	1	2	yes	direct product factor
8	C₂×C₅×C₂₅₇	D₇	1	1	yes	characteristic, complemented
9	C₅×D₂₅₇	—	7	2	no	—
10	C₇×C₂₅₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₂₅₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
12	C₂×D₂₅₇	—	7	1	no	Hall
13	C₂×C₂₅₇	C₅×D₇	1	1	yes	characteristic, complemented
14	D₂₅₇	—	7	2	no	—
15	C₂₅₇	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₅×D₇	—	257	1	no	maximal, Hall
17	C₂×C₅×C₇	D₂₅₇	1	1	yes	characteristic, complemented
18	C₅×D₇	—	257	2	no	—
19	C₅×C₇	C₂×D₂₅₇	1	1	yes	characteristic, complemented, Hall
20	C₂×D₇	—	257	1	no	Hall
21	C₂²×C₅	—	1799	1	no	Hall
22	C₂×C₇	C₅×D₂₅₇	1	1	yes	characteristic, complemented
23	D₇	—	257	2	no	—
24	C₂×C₅	—	1799	2	no	—
25	C₂×C₅	D₁₇₉₉	1	1	yes	characteristic, direct product factor
26	C₇	C₂×C₅×D₂₅₇	1	1	yes	characteristic, complemented, Sylow
27	C₅	C₂×D₁₇₉₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	1799	1	no	Sylow
29	C₂	—	1799	2	no	—
30	C₂	C₅×D₁₇₉₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₇₉₉
commutator, cosocle, hypocenter	C₇×C₂₅₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₂₅₇	C₂
LCS	G ▷ C₇×C₂₅₇
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₇₉₉	C₂	direct (N × H)
2. C₂×C₅×C₇×C₂₅₇	C₂	semidirect
3. C₅×C₇×C₂₅₇	C₂²	semidirect
4. C₂×D₁₇₉₉	C₅	direct (N × H)
6. C₂×C₇×C₂₅₇	C₂×C₅	semidirect
7. D₁₇₉₉	C₂×C₅	direct (N × H)
8. C₂×C₅×C₂₅₇	D₇	semidirect
10. C₇×C₂₅₇	C₂²×C₅	semidirect
11. C₅×C₂₅₇	C₂×D₇	semidirect
13. C₂×C₂₅₇	C₅×D₇	semidirect
15. C₂₅₇	C₂×C₅×D₇	semidirect
17. C₂×C₅×C₇	D₂₅₇	semidirect
19. C₅×C₇	C₂×D₂₅₇	semidirect
22. C₂×C₇	C₅×D₂₅₇	semidirect
25. C₂×C₅	D₁₇₉₉	direct (N × H)
26. C₇	C₂×C₅×D₂₅₇	semidirect
27. C₅	C₂×D₁₇₉₉	direct (N × H)
30. C₂	C₅×D₁₇₉₉	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×D₁₇₉₉	2
C₂×C₅×C₇×C₂₅₇	2
C₂×D₁₇₉₉	5
C₂×C₅×D₂₅₇	7
C₂×C₅×D₇	257

Subgroups — C2×C5×D1799 #49112682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₁₇₉₉ #49112682