Subgroups — C₂×C₅×D₁₇₃₉ #46852012

Order 34780.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₇₃₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₃₇×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃₇×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₇₃₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃₇×C₄₇	C₂×C₅	1	1	yes	characteristic, complemented
6	D₁₇₃₉	C₂×C₅	1	2	yes	direct product factor
7	C₃₇×C₄₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅×D₄₇	—	37	1	no	maximal, Hall
9	C₂×C₅×D₃₇	—	47	1	no	maximal, Hall
10	C₂×C₅×C₄₇	D₃₇	1	1	yes	characteristic, complemented
11	C₅×D₄₇	—	37	2	no	—
12	C₂×C₅×C₃₇	D₄₇	1	1	yes	characteristic, complemented
13	C₅×D₃₇	—	47	2	no	—
14	C₅×C₄₇	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
15	C₂×D₄₇	—	37	1	no	Hall
16	C₅×C₃₇	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
17	C₂×D₃₇	—	47	1	no	Hall
18	C₂×C₄₇	C₅×D₃₇	1	1	yes	characteristic, complemented
19	D₄₇	—	37	2	no	—
20	C₂×C₃₇	C₅×D₄₇	1	1	yes	characteristic, complemented
21	D₃₇	—	47	2	no	—
22	C₄₇	C₂×C₅×D₃₇	1	1	yes	characteristic, complemented, Sylow
23	C₃₇	C₂×C₅×D₄₇	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₅	—	1739	1	no	Hall
25	C₂×C₅	—	1739	2	no	—
26	C₂×C₅	D₁₇₃₉	1	1	yes	characteristic, direct product factor
27	C₅	C₂×D₁₇₃₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	1739	1	no	Sylow
29	C₂	—	1739	2	no	—
30	C₂	C₅×D₁₇₃₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₇₃₉
commutator, cosocle, hypocenter	C₃₇×C₄₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₃₇×C₄₇	C₂
LCS	G ▷ C₃₇×C₄₇
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₇₃₉	C₂	direct (N × H)
2. C₂×C₅×C₃₇×C₄₇	C₂	semidirect
3. C₅×C₃₇×C₄₇	C₂²	semidirect
4. C₂×D₁₇₃₉	C₅	direct (N × H)
5. C₂×C₃₇×C₄₇	C₂×C₅	semidirect
6. D₁₇₃₉	C₂×C₅	direct (N × H)
7. C₃₇×C₄₇	C₂²×C₅	semidirect
10. C₂×C₅×C₄₇	D₃₇	semidirect
12. C₂×C₅×C₃₇	D₄₇	semidirect
14. C₅×C₄₇	C₂×D₃₇	semidirect
16. C₅×C₃₇	C₂×D₄₇	semidirect
18. C₂×C₄₇	C₅×D₃₇	semidirect
20. C₂×C₃₇	C₅×D₄₇	semidirect
22. C₄₇	C₂×C₅×D₃₇	semidirect
23. C₃₇	C₂×C₅×D₄₇	semidirect
26. C₂×C₅	D₁₇₃₉	direct (N × H)
27. C₅	C₂×D₁₇₃₉	direct (N × H)
30. C₂	C₅×D₁₇₃₉	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×D₁₇₃₉	2
C₂×C₅×C₃₇×C₄₇	2
C₂×D₁₇₃₉	5
C₂×C₅×D₄₇	37
C₂×C₅×D₃₇	47

Subgroups — C2×C5×D1739 #46852012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₁₇₃₉ #46852012