Subgroups — C₂×D₅×C₇⋊D₇ #14520039

Order 1960.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇²×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×C₇⋊D₇	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₅×C₇²	C₂²	1	1	yes	characteristic, complemented
6	C₅⋊(C₇⋊D₇)	C₂²	1	2	yes	complemented
7	C₇²×D₅	C₂²	1	2	yes	complemented
8	C₅×C₇⋊D₇	C₂²	1	2	yes	complemented
9	C₂²×C₇⋊D₇	—	5	1	no	maximal, Hall
10	C₂×D₅×D₇	—	7	8	no	maximal
11	C₅×C₇²	C₂³	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₇²	—	5	1	no	—
13	C₂×C₇⋊D₇	—	5	1	no	—
14	C₂×C₇⋊D₇	—	5	4	no	—
15	C₂×C₇⋊D₇	D₅	1	1	yes	characteristic, direct product factor
16	C₂×D₃₅	—	7	8	no	—
17	C₂×C₇×D₅	D₇	1	8	yes	complemented
18	C₂×C₅×D₇	—	7	8	no	—
19	D₅×D₇	—	7	32	no	—
20	C₂×C₇²	—	5	2	no	—
21	C₂×C₇²	C₂×D₅	1	1	yes	characteristic, complemented
22	C₇⋊D₇	—	5	2	no	—
23	C₇⋊D₇	C₂×D₅	1	2	yes	direct product factor
24	C₂×C₅×C₇	C₂×D₇	1	8	yes	complemented
25	D₃₅	—	7	16	no	—
26	C₅×D₇	—	7	16	no	—
27	C₇×D₅	C₂×D₇	1	16	yes	complemented
28	C₂²×D₇	—	35	8	no	—
29	C₇²	C₂²×D₅	1	1	yes	characteristic, complemented, Sylow
30	C₂²×D₅	—	49	1	no	Hall
31	C₅×C₇	C₂²×D₇	1	8	yes	complemented
32	C₂²×C₇	—	5	8	no	—
33	C₂×D₇	—	7	8	no	—
34	C₂×D₇	—	35	32	no	—
35	C₂×D₇	—	35	8	no	—
36	C₂²×C₅	—	49	1	no	—
37	C₂×D₅	—	49	1	no	—
38	C₂×D₅	—	49	4	no	—
39	C₂×D₅	C₇⋊D₇	1	1	yes	characteristic, direct product factor
40	C₂×C₇	—	5	16	no	—
41	C₂×C₇	D₅×D₇	1	8	yes	complemented
42	D₇	—	7	16	no	—
43	D₇	—	35	16	no	—
44	C₂×C₅	—	49	2	no	—
45	C₂×C₅	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented
46	D₅	—	49	2	no	—
47	D₅	C₂×C₇⋊D₇	1	2	yes	direct product factor
48	C₂³	—	245	1	no	Sylow
49	C₇	C₂×D₅×D₇	1	8	yes	complemented
50	C₅	C₂²×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
51	C₂²	—	5	1	no	—
52	C₂²	—	49	1	no	—
53	C₂²	—	245	4	no	—
54	C₂²	—	245	1	no	—
55	C₂	—	5	2	no	—
56	C₂	—	49	2	no	—
57	C₂	—	245	2	no	—
58	C₂	D₅×C₇⋊D₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₅×C₇⋊D₇
commutator, cosocle, hypocenter	C₅×C₇²	C₂³
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²	C₂²
LCS	G ▷ C₅×C₇²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₅⋊(C₇⋊D₇)	C₂	semidirect
2. C₂×C₇²×D₅	C₂	semidirect
3. C₂×C₅×C₇⋊D₇	C₂	semidirect
4. D₅×C₇⋊D₇	C₂	direct (N × H)
5. C₂×C₅×C₇²	C₂²	semidirect
6. C₅⋊(C₇⋊D₇)	C₂²	semidirect
7. C₇²×D₅	C₂²	semidirect
8. C₅×C₇⋊D₇	C₂²	semidirect
11. C₅×C₇²	C₂³	semidirect
15. C₂×C₇⋊D₇	D₅	direct (N × H)
17. C₂×C₇×D₅	D₇	semidirect
21. C₂×C₇²	C₂×D₅	semidirect
23. C₇⋊D₇	C₂×D₅	direct (N × H)
24. C₂×C₅×C₇	C₂×D₇	semidirect
27. C₇×D₅	C₂×D₇	semidirect
29. C₇²	C₂²×D₅	semidirect
31. C₅×C₇	C₂²×D₇	semidirect
39. C₂×D₅	C₇⋊D₇	direct (N × H)
41. C₂×C₇	D₅×D₇	semidirect
45. C₂×C₅	C₂×C₇⋊D₇	semidirect
47. D₅	C₂×C₇⋊D₇	direct (N × H)
49. C₇	C₂×D₅×D₇	semidirect
50. C₅	C₂²×C₇⋊D₇	semidirect
58. C₂	D₅×C₇⋊D₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅⋊(C₇⋊D₇)	2
C₂×C₇²×D₅	2
C₂×C₅×C₇⋊D₇	2
D₅×C₇⋊D₇	2
C₂²×C₇⋊D₇	5
C₂×D₅×D₇	7

Subgroups — C2×D5×C7⋊D7 #14520039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×C₇⋊D₇ #14520039