Subgroups — D₃₇×D₂₃₅ #46852007

Order 34780.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₆₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×D₂₃₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₄₇×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₃₇×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃₇×D₄₇	—	5	1	no	maximal, Hall
6	D₁₇₃₉	—	5	1	no	—
7	C₃₇×D₄₇	—	5	1	no	—
8	C₄₇×D₃₇	D₅	1	1	yes	characteristic, complemented
9	C₃₇×C₄₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
10	C₂×D₂₃₅	—	37	1	no	maximal, Hall
11	D₅×D₃₇	—	47	1	no	maximal, Hall
12	C₂×C₅×C₄₇	—	37	1	no	—
13	D₂₃₅	—	37	1	no	—
14	D₂₃₅	D₃₇	1	1	yes	characteristic, direct product factor
15	D₁₈₅	—	47	1	no	—
16	C₅×D₃₇	D₄₇	1	1	yes	characteristic, complemented
17	D₅×C₃₇	—	47	1	no	—
18	C₅×C₄₇	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
19	C₂×D₄₇	—	185	1	no	Hall
20	C₅×C₃₇	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
21	C₂×D₃₇	—	235	1	no	Hall
22	C₂×C₄₇	—	37	1	no	—
23	D₄₇	—	5	1	no	—
24	D₄₇	—	185	1	no	—
25	C₂×C₃₇	—	235	1	no	—
26	D₃₇	—	235	1	no	—
27	D₃₇	D₂₃₅	1	1	yes	characteristic, direct product factor
28	C₄₇	D₅×D₃₇	1	1	yes	characteristic, complemented, Sylow
29	C₃₇	C₂×D₂₃₅	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₅	—	1739	1	no	Hall
31	C₂×C₅	—	37	1	no	—
32	D₅	—	47	1	no	—
33	D₅	—	1739	1	no	—
34	C₅	D₃₇×D₄₇	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	8695	1	no	Sylow
36	C₂	—	37	1	no	—
37	C₂	—	235	1	no	—
38	C₂	—	8695	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. D₈₆₉₅	C₂	semidirect
2. C₃₇×D₂₃₅	C₂	semidirect
3. C₅×C₄₇×D₃₇	C₂	semidirect
4. C₅×C₃₇×C₄₇	C₂²	semidirect
8. C₄₇×D₃₇	D₅	semidirect
9. C₃₇×C₄₇	C₂×D₅	semidirect
14. D₂₃₅	D₃₇	direct (N × H)
16. C₅×D₃₇	D₄₇	semidirect
18. C₅×C₄₇	C₂×D₃₇	semidirect
20. C₅×C₃₇	C₂×D₄₇	semidirect
27. D₃₇	D₂₃₅	direct (N × H)
28. C₄₇	D₅×D₃₇	semidirect
29. C₃₇	C₂×D₂₃₅	semidirect
34. C₅	D₃₇×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
D₈₆₉₅	2
C₃₇×D₂₃₅	2
C₅×C₄₇×D₃₇	2
D₃₇×D₄₇	5
C₂×D₂₃₅	37
D₅×D₃₇	47

Subgroups — D37×D235 #46852007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₇×D₂₃₅ #46852007