Subgroups — D₅×C₃₇×D₄₇ #46852002

Order 34780.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×D₂₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₃₇×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃₇×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₃₇×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃₇×D₄₇	—	5	1	no	maximal, Hall
6	C₂×C₃₇×C₄₇	—	5	1	no	—
7	C₃₇×D₄₇	—	5	1	no	—
8	C₃₇×D₄₇	D₅	1	1	yes	characteristic, direct product factor
9	C₃₇×C₄₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
10	D₅×D₄₇	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×D₅×C₃₇	—	47	1	no	maximal, Hall
12	D₂₃₅	C₂×C₃₇	1	1	yes	characteristic, complemented
13	C₅×D₄₇	C₂×C₃₇	1	1	yes	characteristic, complemented
14	D₅×C₄₇	C₂×C₃₇	1	1	yes	characteristic, complemented
15	C₂×C₅×C₃₇	—	47	1	no	—
16	D₅×C₃₇	—	47	1	no	—
17	D₅×C₃₇	D₄₇	1	1	yes	characteristic, direct product factor
18	C₅×C₄₇	C₂²×C₃₇	1	1	yes	characteristic, complemented, Hall
19	C₂×D₄₇	—	5	1	no	Hall
20	C₅×C₃₇	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₃₇	—	235	1	no	Hall
22	C₂×C₄₇	—	5	1	no	—
23	D₄₇	—	5	1	no	—
24	D₄₇	D₅×C₃₇	1	1	yes	characteristic, direct product factor
25	C₂×C₃₇	—	5	1	no	—
26	C₂×C₃₇	—	47	1	no	—
27	C₂×C₃₇	—	235	1	no	—
28	C₄₇	C₂×D₅×C₃₇	1	1	yes	characteristic, complemented, Sylow
29	C₃₇	D₅×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×D₅	—	47	1	no	Hall
31	C₂×C₅	—	47	1	no	—
32	D₅	—	47	1	no	—
33	D₅	C₃₇×D₄₇	1	1	yes	characteristic, direct product factor
34	C₅	C₂×C₃₇×D₄₇	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	235	1	no	Sylow
36	C₂	—	5	1	no	—
37	C₂	—	47	1	no	—
38	C₂	—	235	1	no	—

	subgroup	G/H
center, hypercenter	C₃₇	D₅×D₄₇
commutator, cosocle, hypocenter	C₅×C₄₇	C₂²×C₃₇
Frattini	C₁	G
Fitting, socle	C₅×C₃₇×C₄₇	C₂²
LCS	G ▷ C₅×C₄₇
UCS	C₁ ◁ C₃₇

Complements

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

N	H ≅ G/N	type
1. C₃₇×D₂₃₅	C₂	semidirect
2. D₅×C₃₇×C₄₇	C₂	semidirect
3. C₅×C₃₇×D₄₇	C₂	semidirect
4. C₅×C₃₇×C₄₇	C₂²	semidirect
8. C₃₇×D₄₇	D₅	direct (N × H)
9. C₃₇×C₄₇	C₂×D₅	semidirect
10. D₅×D₄₇	C₃₇	direct (N × H)
12. D₂₃₅	C₂×C₃₇	semidirect
13. C₅×D₄₇	C₂×C₃₇	semidirect
14. D₅×C₄₇	C₂×C₃₇	semidirect
17. D₅×C₃₇	D₄₇	direct (N × H)
18. C₅×C₄₇	C₂²×C₃₇	semidirect
20. C₅×C₃₇	C₂×D₄₇	semidirect
24. D₄₇	D₅×C₃₇	direct (N × H)
28. C₄₇	C₂×D₅×C₃₇	semidirect
29. C₃₇	D₅×D₄₇	direct (N × H)
33. D₅	C₃₇×D₄₇	direct (N × H)
34. C₅	C₂×C₃₇×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×D₂₃₅	2
D₅×C₃₇×C₄₇	2
C₅×C₃₇×D₄₇	2
C₂×C₃₇×D₄₇	5
D₅×D₄₇	37
C₂×D₅×C₃₇	47

Subgroups — D5×C37×D47 #46852002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₃₇×D₄₇ #46852002