Subgroups — C₂×D₅×Dic₇ #10587954

Order 560.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×Dic₇	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₅×C₇	C₂²	1	1	yes	characteristic
6	C₂×C₇×D₅	C₄	1	4	yes	complemented
7	C₂×C₇×D₅	C₂²	1	2	yes	—
8	Dic₃₅	C₂²	1	2	yes	complemented
9	C₅×Dic₇	C₂²	1	2	yes	complemented
10	C₂²×Dic₇	—	5	1	no	maximal, Hall
11	C₂×C₄×D₅	—	7	1	no	maximal, Hall
12	C₂×C₅×C₇	C₂×C₄	1	2	yes	complemented
13	C₂×C₅×C₇	C₂³	1	1	yes	characteristic
14	C₇×D₅	C₂×C₄	1	4	yes	complemented
15	C₂³×C₇	—	5	1	no	—
16	C₂×Dic₇	—	5	1	no	—
17	C₂×Dic₇	—	5	4	no	—
18	C₂×Dic₇	D₅	1	1	yes	characteristic, direct product factor
19	C₂²×D₅	D₇	1	1	yes	characteristic
20	C₂×C₄×C₅	—	7	1	no	—
21	C₂×Dic₅	—	7	1	no	—
22	C₄×D₅	—	7	4	no	—
23	C₅×C₇	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₇	—	5	4	no	—
25	C₂²×C₇	—	5	2	no	—
26	C₂²×C₇	C₂×D₅	1	1	yes	characteristic
27	Dic₇	—	5	2	no	—
28	Dic₇	C₂×D₅	1	2	yes	direct product factor
29	C₂²×C₅	C₂×D₇	1	1	yes	characteristic
30	C₂×D₅	Dic₇	1	4	yes	direct product factor
31	C₂×D₅	C₂×D₇	1	2	yes	—
32	C₄×C₅	—	7	2	no	—
33	Dic₅	—	7	2	no	—
34	C₂²×C₄	—	35	1	no	Sylow
35	C₂×C₇	—	5	4	no	—
36	C₂×C₇	C₄×D₅	1	2	yes	complemented
37	C₂×C₇	C₂²×D₅	1	1	yes	characteristic
38	C₂×C₅	C₂×Dic₇	1	2	yes	complemented
39	C₂×C₅	C₂²×D₇	1	1	yes	characteristic
40	D₅	C₂×Dic₇	1	4	yes	direct product factor
41	C₂³	—	5	1	no	—
42	C₂×C₄	—	7	1	no	—
43	C₂×C₄	—	35	4	no	—
44	C₂×C₄	—	35	1	no	—
45	C₇	C₂×C₄×D₅	1	1	yes	characteristic, complemented, Sylow
46	C₅	C₂²×Dic₇	1	1	yes	characteristic, complemented, Sylow
47	C₂²	—	5	4	no	—
48	C₂²	—	5	2	no	—
49	C₂²	D₅×D₇	1	1	yes	characteristic
50	C₄	—	7	2	no	—
51	C₄	—	35	2	no	—
52	C₂	—	5	4	no	—
53	C₂	D₅×Dic₇	1	2	yes	direct product factor
54	C₂	C₂×D₅×D₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₅×D₇
commutator, hypocenter	C₅×C₇	C₂²×C₄
Frattini	C₂	C₂×D₅×D₇
Fitting, socle	C₂²×C₅×C₇	C₂²
prime radical	C₂²×C₇×D₅	C₂
cosocle	C₂×C₅×C₇	C₂³
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₃₅	C₂	semidirect
3. C₂×C₅×Dic₇	C₂	semidirect
4. D₅×Dic₇	C₂	direct (N × H)
6. C₂×C₇×D₅	C₄	semidirect
8. Dic₃₅	C₂²	semidirect
9. C₅×Dic₇	C₂²	semidirect
12. C₂×C₅×C₇	C₂×C₄	semidirect
14. C₇×D₅	C₂×C₄	semidirect
18. C₂×Dic₇	D₅	direct (N × H)
23. C₅×C₇	C₂²×C₄	semidirect
28. Dic₇	C₂×D₅	direct (N × H)
30. C₂×D₅	Dic₇	direct (N × H)
36. C₂×C₇	C₄×D₅	semidirect
38. C₂×C₅	C₂×Dic₇	semidirect
40. D₅	C₂×Dic₇	direct (N × H)
45. C₇	C₂×C₄×D₅	semidirect
46. C₅	C₂²×Dic₇	semidirect
53. C₂	D₅×Dic₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₇×D₅	2
C₂×Dic₃₅	2
C₂×C₅×Dic₇	2
D₅×Dic₇	2
C₂²×Dic₇	5
C₂×C₄×D₅	7

Subgroups — C2×D5×Dic7 #10587954

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×Dic₇ #10587954