Subgroups — D₅×C₇⋊D₂₅₉ #49136452

Order 36260.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇⋊D₂₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇²×D₅×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅⋊(C₇⋊D₂₅₉)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇²×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇⋊D₂₅₉	—	5	1	no	maximal, Hall
6	D₅×D₂₅₉	—	7	8	no	maximal
7	C₇⋊D₂₅₉	—	5	1	no	—
8	C₇⋊D₂₅₉	D₅	1	1	yes	characteristic, direct product factor
9	C₂×C₇²×C₃₇	—	5	1	no	—
10	D₁₂₉₅	—	7	8	no	—
11	C₇×D₅×C₃₇	D₇	1	8	yes	complemented
12	C₅×D₂₅₉	—	7	8	no	—
13	C₇²×C₃₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₇×C₃₇	C₂×D₇	1	8	yes	complemented
15	C₂×D₂₅₉	—	35	8	no	—
16	D₅×C₇⋊D₇	—	37	1	no	maximal, Hall
17	D₅×D₃₇	—	49	1	no	Hall
18	C₂×C₇×C₃₇	—	5	8	no	—
19	D₂₅₉	—	7	8	no	—
20	D₂₅₉	—	35	8	no	—
21	C₅⋊(C₇⋊D₇)	—	37	1	no	—
22	C₇²×D₅	D₃₇	1	1	yes	characteristic, complemented
23	C₅×C₇⋊D₇	—	37	1	no	—
24	D₁₈₅	—	49	1	no	—
25	C₅×D₃₇	—	49	1	no	—
26	D₅×C₃₇	C₇⋊D₇	1	1	yes	characteristic, complemented
27	C₇×C₃₇	D₅×D₇	1	8	yes	complemented
28	C₅×C₇²	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
29	C₂×C₇⋊D₇	—	185	1	no	Hall
30	C₅×C₃₇	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
31	C₂×D₃₇	—	245	1	no	Hall
32	D₅×D₇	—	259	8	no	—
33	C₂×C₇²	—	5	1	no	—
34	C₇⋊D₇	—	37	1	no	—
35	C₇⋊D₇	—	185	1	no	—
36	C₂×C₃₇	—	5	1	no	—
37	D₃₇	—	49	1	no	—
38	D₃₇	—	245	1	no	—
39	D₃₅	—	259	8	no	—
40	C₅×D₇	—	259	8	no	—
41	C₇×D₅	D₂₅₉	1	8	yes	complemented
42	C₇²	D₅×D₃₇	1	1	yes	characteristic, complemented, Sylow
43	C₃₇	D₅×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
44	C₅×C₇	C₂×D₂₅₉	1	8	yes	complemented
45	C₂×D₇	—	1295	8	no	—
46	C₂×D₅	—	1813	1	no	Hall
47	C₂×C₇	—	5	8	no	—
48	D₇	—	259	8	no	—
49	D₇	—	1295	8	no	—
50	C₂×C₅	—	1813	1	no	—
51	D₅	—	1813	1	no	—
52	D₅	C₇⋊D₂₅₉	1	1	yes	characteristic, direct product factor
53	C₇	D₅×D₂₅₉	1	8	yes	complemented
54	C₅	C₂×C₇⋊D₂₅₉	1	1	yes	characteristic, complemented, Sylow
55	C₂²	—	9065	1	no	Sylow
56	C₂	—	5	1	no	—
57	C₂	—	1813	1	no	—
58	C₂	—	9065	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇²×C₃₇	C₂²
LCS	G ▷ C₅×C₇²×C₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₇⋊D₂₅₉	C₂	semidirect
2. C₇²×D₅×C₃₇	C₂	semidirect
3. C₅⋊(C₇⋊D₂₅₉)	C₂	semidirect
4. C₅×C₇²×C₃₇	C₂²	semidirect
8. C₇⋊D₂₅₉	D₅	direct (N × H)
11. C₇×D₅×C₃₇	D₇	semidirect
13. C₇²×C₃₇	C₂×D₅	semidirect
14. C₅×C₇×C₃₇	C₂×D₇	semidirect
22. C₇²×D₅	D₃₇	semidirect
26. D₅×C₃₇	C₇⋊D₇	semidirect
27. C₇×C₃₇	D₅×D₇	semidirect
28. C₅×C₇²	C₂×D₃₇	semidirect
30. C₅×C₃₇	C₂×C₇⋊D₇	semidirect
41. C₇×D₅	D₂₅₉	semidirect
42. C₇²	D₅×D₃₇	semidirect
43. C₃₇	D₅×C₇⋊D₇	semidirect
44. C₅×C₇	C₂×D₂₅₉	semidirect
52. D₅	C₇⋊D₂₅₉	direct (N × H)
53. C₇	D₅×D₂₅₉	semidirect
54. C₅	C₂×C₇⋊D₂₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇⋊D₂₅₉	2
C₇²×D₅×C₃₇	2
C₅⋊(C₇⋊D₂₅₉)	2
C₂×C₇⋊D₂₅₉	5
D₅×D₂₅₉	7
D₅×C₇⋊D₇	37

Subgroups — D5×C7⋊D259 #49136452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₇⋊D₂₅₉ #49136452