Subgroups — D₃₅×D₂₅₇ #49112675

Order 35980.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₉₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃₅×C₂₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×D₂₅₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇×C₂₅₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₇×D₂₅₇	—	5	1	no	maximal, Hall
6	D₅×D₂₅₇	—	7	1	no	maximal, Hall
7	D₁₇₉₉	—	5	1	no	—
8	C₇×D₂₅₇	D₅	1	1	yes	characteristic, complemented
9	D₇×C₂₅₇	—	5	1	no	—
10	D₁₂₈₅	—	7	1	no	—
11	C₅×D₂₅₇	D₇	1	1	yes	characteristic, complemented
12	D₅×C₂₅₇	—	7	1	no	—
13	C₇×C₂₅₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₂₅₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
15	C₂×D₂₅₇	—	35	1	no	Hall
16	C₂×C₂₅₇	—	35	1	no	—
17	D₂₅₇	—	35	1	no	—
18	D₂₅₇	D₃₅	1	1	yes	characteristic, direct product factor
19	C₂₅₇	C₂×D₃₅	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₃₅	—	257	1	no	maximal, Hall
21	C₂×C₅×C₇	—	257	1	no	—
22	D₃₅	—	257	1	no	—
23	D₃₅	D₂₅₇	1	1	yes	characteristic, direct product factor
24	C₅×C₇	C₂×D₂₅₇	1	1	yes	characteristic, complemented, Hall
25	C₂×D₇	—	1285	1	no	Hall
26	C₂×D₅	—	1799	1	no	Hall
27	C₂×C₇	—	257	1	no	—
28	D₇	—	5	1	no	—
29	D₇	—	1285	1	no	—
30	C₂×C₅	—	257	1	no	—
31	D₅	—	7	1	no	—
32	D₅	—	1799	1	no	—
33	C₇	D₅×D₂₅₇	1	1	yes	characteristic, complemented, Sylow
34	C₅	D₇×D₂₅₇	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	8995	1	no	Sylow
36	C₂	—	257	1	no	—
37	C₂	—	35	1	no	—
38	C₂	—	8995	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. D₈₉₉₅	C₂	semidirect
2. D₃₅×C₂₅₇	C₂	semidirect
3. C₅×C₇×D₂₅₇	C₂	semidirect
4. C₅×C₇×C₂₅₇	C₂²	semidirect
8. C₇×D₂₅₇	D₅	semidirect
11. C₅×D₂₅₇	D₇	semidirect
13. C₇×C₂₅₇	C₂×D₅	semidirect
14. C₅×C₂₅₇	C₂×D₇	semidirect
18. D₂₅₇	D₃₅	direct (N × H)
19. C₂₅₇	C₂×D₃₅	semidirect
23. D₃₅	D₂₅₇	direct (N × H)
24. C₅×C₇	C₂×D₂₅₇	semidirect
33. C₇	D₅×D₂₅₇	semidirect
34. C₅	D₇×D₂₅₇	semidirect

Maximal subgroups

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

subgroup	index
D₈₉₉₅	2
D₃₅×C₂₅₇	2
C₅×C₇×D₂₅₇	2
D₇×D₂₅₇	5
D₅×D₂₅₇	7
C₂×D₃₅	257

Subgroups — D35×D257 #49112675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₅×D₂₅₇ #49112675