Subgroups — #14519913

Order 1960.

48 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×C₅×D₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₅×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₄₉	C₂²	1	1	yes	characteristic
5	D₂₄₅	—	2	1	no	—
6	C₅×D₄₉	—	2	1	no	—
7	D₁₉₆	—	5	1	no	maximal, Hall
8	#63306	—	7	1	no	maximal
9	C₅×C₄₉	D₄	1	1	yes	characteristic, complemented, Hall
10	C₂×D₄₉	—	5	1	no	—
11	C₂×D₄₉	D₅	1	1	yes	characteristic, complemented
12	C₄×C₄₉	—	5	1	no	—
13	C₂×D₃₅	—	7	1	no	—
14	C₂×C₅×D₇	—	7	1	no	—
15	C₇×Dic₅	D₇	1	1	yes	characteristic
16	C₂×C₄₉	C₂×D₅	1	1	yes	characteristic
17	D₄₉	—	2	1	no	—
18	D₄₉	—	10	1	no	—
19	C₂×C₅×C₇	C₂×D₇	1	1	yes	characteristic
20	D₃₅	—	14	1	no	—
21	C₅×D₇	—	14	1	no	—
22	D₂₈	—	35	1	no	—
23	C₄₉	C₂²⋊D₅	1	1	yes	characteristic, complemented, Sylow
24	C₂²⋊D₅	—	49	1	no	Hall
25	C₅×C₇	D₂₈	1	1	yes	characteristic
26	C₂×D₇	—	7	1	no	—
27	C₂×D₇	—	35	1	no	—
28	C₄×C₇	—	5	1	no	—
29	C₂²×C₅	—	49	1	no	—
30	C₂×D₅	—	49	1	no	—
31	Dic₅	D₄₉	1	1	yes	characteristic, complemented
32	C₂×C₇	D₅×D₇	1	1	yes	characteristic
33	D₇	—	14	1	no	—
34	D₇	—	70	1	no	—
35	C₂×C₅	—	98	1	no	—
36	C₂×C₅	C₂×D₄₉	1	1	yes	characteristic
37	D₅	—	98	1	no	—
38	D₄	—	245	1	no	Sylow
39	C₇	#63306	1	1	yes	characteristic
40	C₅	D₁₉₆	1	1	yes	characteristic, complemented, Sylow
41	C₂²	—	49	1	no	—
42	C₂²	—	245	1	no	—
43	C₄	—	5	1	no	—
44	C₂	—	98	1	no	—
45	C₂	—	490	1	no	—
46	C₂	D₅×D₄₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₅×D₄₉
commutator, Fitting, cosocle	C₂×C₅×C₄₉	C₂²
Frattini	C₂×C₇	D₅×D₇
socle	C₂×C₅×C₇	C₂×D₇
hypocenter	C₅×C₄₉	D₄
LCS	G ▷ C₂×C₅×C₄₉ ▷ 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×C₅×D₄₉	C₂	semidirect
3. Dic₅×C₄₉	C₂	semidirect
9. C₅×C₄₉	D₄	semidirect
11. C₂×D₄₉	D₅	semidirect
23. C₄₉	C₂²⋊D₅	semidirect
31. Dic₅	D₄₉	semidirect
40. C₅	D₁₉₆	semidirect

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×C₅×D₄₉	2
Dic₅×C₄₉	2
D₁₉₆	5
#63306	7