Subgroups — C₂×C₁₉×D₂₄₅ #32916005

Order 18620.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×D₂₄₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₉×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₉×C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₉×D₄₉	—	5	1	no	maximal, Hall
5	C₂×C₁₉×D₃₅	—	7	1	no	maximal
6	C₂×C₁₉×C₄₉	D₅	1	1	yes	characteristic, complemented
7	C₁₉×D₄₉	—	5	2	no	—
8	C₂×C₅×C₇×C₁₉	D₇	1	1	yes	characteristic
9	C₁₉×D₃₅	—	7	2	no	—
10	C₂×D₂₄₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₉×C₄₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
12	C₅×C₇×C₁₉	C₂×D₇	1	1	yes	characteristic
13	C₂×D₇×C₁₉	—	35	1	no	—
14	C₂×C₅×C₄₉	C₂×C₁₉	1	1	yes	characteristic, complemented
15	D₂₄₅	C₂×C₁₉	1	2	yes	direct product factor
16	C₂×D₅×C₁₉	—	49	1	no	Hall
17	C₂×C₇×C₁₉	D₃₅	1	1	yes	characteristic
18	D₇×C₁₉	—	35	2	no	—
19	C₅×C₄₉	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
20	C₂×D₄₉	—	5	1	no	Hall
21	C₂×C₅×C₁₉	D₄₉	1	1	yes	characteristic, complemented
22	D₅×C₁₉	—	49	2	no	—
23	C₂×D₃₅	—	7	1	no	—
24	C₇×C₁₉	C₂×D₃₅	1	1	yes	characteristic
25	C₂×C₄₉	D₅×C₁₉	1	1	yes	characteristic, complemented
26	D₄₉	—	5	2	no	—
27	C₅×C₁₉	C₂×D₄₉	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₁₉	—	245	1	no	Hall
29	C₂×C₅×C₇	D₇×C₁₉	1	1	yes	characteristic
30	D₃₅	—	7	2	no	—
31	C₄₉	C₂×D₅×C₁₉	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₁₉	—	245	2	no	—
33	C₂×C₁₉	D₂₄₅	1	1	yes	characteristic, direct product factor
34	C₅×C₇	C₂×D₇×C₁₉	1	1	yes	characteristic
35	C₂×D₇	—	35	1	no	—
36	C₂×D₅	—	49	1	no	Hall
37	C₁₉	C₂×D₂₄₅	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₇	C₁₉×D₃₅	1	1	yes	characteristic
39	D₇	—	35	2	no	—
40	C₂×C₅	C₁₉×D₄₉	1	1	yes	characteristic, complemented
41	D₅	—	49	2	no	—
42	C₇	C₂×C₁₉×D₃₅	1	1	yes	characteristic
43	C₅	C₂×C₁₉×D₄₉	1	1	yes	characteristic, complemented, Sylow
44	C₂²	—	245	1	no	Sylow
45	C₂	—	245	2	no	—
46	C₂	C₁₉×D₂₄₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₂₄₅
commutator, cosocle, hypocenter	C₅×C₄₉	C₂²×C₁₉
Frattini	C₇	C₂×C₁₉×D₃₅
Fitting	C₂×C₅×C₁₉×C₄₉	C₂
socle	C₂×C₅×C₇×C₁₉	D₇
LCS	G ▷ C₅×C₄₉
UCS	C₁ ◁ C₂×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×D₂₄₅	C₂	direct (N × H)
2. C₂×C₅×C₁₉×C₄₉	C₂	semidirect
3. C₅×C₁₉×C₄₉	C₂²	semidirect
6. C₂×C₁₉×C₄₉	D₅	semidirect
10. C₂×D₂₄₅	C₁₉	direct (N × H)
11. C₁₉×C₄₉	C₂×D₅	semidirect
14. C₂×C₅×C₄₉	C₂×C₁₉	semidirect
15. D₂₄₅	C₂×C₁₉	direct (N × H)
19. C₅×C₄₉	C₂²×C₁₉	semidirect
21. C₂×C₅×C₁₉	D₄₉	semidirect
25. C₂×C₄₉	D₅×C₁₉	semidirect
27. C₅×C₁₉	C₂×D₄₉	semidirect
31. C₄₉	C₂×D₅×C₁₉	semidirect
33. C₂×C₁₉	D₂₄₅	direct (N × H)
37. C₁₉	C₂×D₂₄₅	direct (N × H)
40. C₂×C₅	C₁₉×D₄₉	semidirect
43. C₅	C₂×C₁₉×D₄₉	semidirect
46. C₂	C₁₉×D₂₄₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×D₂₄₅	2
C₂×C₅×C₁₉×C₄₉	2
C₂×C₁₉×D₄₉	5
C₂×C₁₉×D₃₅	7
C₂×D₂₄₅	19

Subgroups — C2×C19×D245 #32916005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×D₂₄₅ #32916005