Subgroups — C₂×D₅×D₄₉ #14519939

Order 1960.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₄₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₅×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₄₉	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₅×C₄₉	C₂²	1	1	yes	characteristic, complemented
6	D₂₄₅	C₂²	1	2	yes	complemented
7	C₅×D₄₉	C₂²	1	2	yes	complemented
8	D₅×C₄₉	C₂²	1	2	yes	complemented
9	C₂²×D₄₉	—	5	1	no	maximal, Hall
10	C₂×D₅×D₇	—	7	1	no	maximal
11	C₅×C₄₉	C₂³	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₄₉	—	5	1	no	—
13	C₂×D₄₉	—	5	1	no	—
14	C₂×D₄₉	—	5	4	no	—
15	C₂×D₄₉	D₅	1	1	yes	characteristic, direct product factor
16	C₂×D₃₅	—	7	1	no	—
17	C₂×C₇×D₅	D₇	1	1	yes	characteristic
18	C₂×C₅×D₇	—	7	1	no	—
19	D₅×D₇	—	7	4	no	—
20	C₂×C₄₉	—	5	2	no	—
21	C₂×C₄₉	C₂×D₅	1	1	yes	characteristic, complemented
22	D₄₉	—	5	2	no	—
23	D₄₉	C₂×D₅	1	2	yes	direct product factor
24	C₂×C₅×C₇	C₂×D₇	1	1	yes	characteristic
25	D₃₅	—	7	2	no	—
26	C₅×D₇	—	7	2	no	—
27	C₇×D₅	C₂×D₇	1	2	yes	—
28	C₂²×D₇	—	35	1	no	—
29	C₄₉	C₂²×D₅	1	1	yes	characteristic, complemented, Sylow
30	C₂²×D₅	—	49	1	no	Hall
31	C₅×C₇	C₂²×D₇	1	1	yes	characteristic
32	C₂²×C₇	—	5	1	no	—
33	C₂×D₇	—	7	1	no	—
34	C₂×D₇	—	35	4	no	—
35	C₂×D₇	—	35	1	no	—
36	C₂²×C₅	—	49	1	no	—
37	C₂×D₅	—	49	1	no	—
38	C₂×D₅	—	49	4	no	—
39	C₂×D₅	D₄₉	1	1	yes	characteristic, direct product factor
40	C₂×C₇	—	5	2	no	—
41	C₂×C₇	D₅×D₇	1	1	yes	characteristic
42	D₇	—	7	2	no	—
43	D₇	—	35	2	no	—
44	C₂×C₅	—	49	2	no	—
45	C₂×C₅	C₂×D₄₉	1	1	yes	characteristic, complemented
46	D₅	—	49	2	no	—
47	D₅	C₂×D₄₉	1	2	yes	direct product factor
48	C₂³	—	245	1	no	Sylow
49	C₇	C₂×D₅×D₇	1	1	yes	characteristic
50	C₅	C₂²×D₄₉	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×D₄₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₅×D₄₉
commutator, cosocle, hypocenter	C₅×C₄₉	C₂³
Frattini	C₇	C₂×D₅×D₇
Fitting	C₂×C₅×C₄₉	C₂²
socle	C₂×C₅×C₇	C₂×D₇
LCS	G ▷ C₅×C₄₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×D₂₄₅	C₂	semidirect
2. C₂×D₅×C₄₉	C₂	semidirect
3. C₂×C₅×D₄₉	C₂	semidirect
4. D₅×D₄₉	C₂	direct (N × H)
5. C₂×C₅×C₄₉	C₂²	semidirect
6. D₂₄₅	C₂²	semidirect
7. C₅×D₄₉	C₂²	semidirect
8. D₅×C₄₉	C₂²	semidirect
11. C₅×C₄₉	C₂³	semidirect
15. C₂×D₄₉	D₅	direct (N × H)
21. C₂×C₄₉	C₂×D₅	semidirect
23. D₄₉	C₂×D₅	direct (N × H)
29. C₄₉	C₂²×D₅	semidirect
39. C₂×D₅	D₄₉	direct (N × H)
45. C₂×C₅	C₂×D₄₉	semidirect
47. D₅	C₂×D₄₉	direct (N × H)
50. C₅	C₂²×D₄₉	semidirect
58. C₂	D₅×D₄₉	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×D₂₄₅	2
C₂×D₅×C₄₉	2
C₂×C₅×D₄₉	2
D₅×D₄₉	2
C₂²×D₄₉	5
C₂×D₅×D₇	7

Subgroups — C2×D5×D49 #14519939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×D₄₉ #14519939