Subgroups — C₂×C₃₇×D₂₃₅ #46852014

Order 34780.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃₇	D₂₃₅
commutator, cosocle, hypocenter	C₅×C₄₇	C₂²×C₃₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₃₇×C₄₇	C₂
LCS	G ▷ C₅×C₄₇
UCS	C₁ ◁ C₂×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₃₇×D₂₃₅	C₂	direct (N × H)
2. C₂×C₅×C₃₇×C₄₇	C₂	semidirect
3. C₅×C₃₇×C₄₇	C₂²	semidirect
5. C₂×C₃₇×C₄₇	D₅	semidirect
7. C₃₇×C₄₇	C₂×D₅	semidirect
8. C₂×D₂₃₅	C₃₇	direct (N × H)
10. C₂×C₅×C₄₇	C₂×C₃₇	semidirect
11. D₂₃₅	C₂×C₃₇	direct (N × H)
12. C₂×C₅×C₃₇	D₄₇	semidirect
14. C₅×C₄₇	C₂²×C₃₇	semidirect
16. C₅×C₃₇	C₂×D₄₇	semidirect
18. C₂×C₄₇	D₅×C₃₇	semidirect
21. C₂×C₃₇	D₂₃₅	direct (N × H)
22. C₄₇	C₂×D₅×C₃₇	semidirect
23. C₃₇	C₂×D₂₃₅	direct (N × H)
25. C₂×C₅	C₃₇×D₄₇	semidirect
27. C₅	C₂×C₃₇×D₄₇	semidirect
30. C₂	C₃₇×D₂₃₅	direct (N × H)

Maximal subgroups

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

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

Subgroups — C2×C37×D235 #46852014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₇×D₂₃₅ #46852014