Subgroups — C₃×C₄₉⋊#1044 #28412969

Order 14700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₄₉⋊#1044	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₄₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₄₉⋊AGL(1,𝔽₅)	—	5	2	no	maximal
5	C₄₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	C₃×C₇⋊#1044	—	7	1	no	maximal
7	C₃×D₅×C₄₉	—	5	2	no	—
8	C₃×D₅×C₄₉	—	10	2	no	—
9	C₅²×C₄₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
10	C₃×C₇×C₅⋊D₅	D₇	1	1	yes	characteristic
11	C₄₉⋊AGL(1,𝔽₅)	—	5	2	no	—
12	C₃×C₅×C₄₉	—	2	2	no	—
13	C₃×C₅×C₄₉	AGL(1,𝔽₅)	1	2	yes	complemented
14	C₇⋊#1044	—	7	1	no	—
15	C₃×Dic₄₉	—	25	1	no	Hall
16	C₃×C₅²×C₇	Dic₇	1	1	yes	characteristic
17	D₅×C₄₉	—	5	2	no	—
18	D₅×C₄₉	—	10	2	no	—
19	C₃×C₇⋊AGL(1,𝔽₅)	—	35	2	no	—
20	C₇×C₅⋊D₅	C₃×D₇	1	1	yes	characteristic
21	C₃×#1044	—	49	1	no	Hall
22	C₂×C₃×C₄₉	—	25	1	no	—
23	C₅×C₄₉	—	2	2	no	—
24	C₅×C₄₉	C₃×AGL(1,𝔽₅)	1	2	yes	complemented
25	C₃×C₇×D₅	—	5	2	no	—
26	C₃×C₇×D₅	—	10	2	no	—
27	Dic₄₉	—	25	1	no	Hall
28	C₅²×C₇	C₃×Dic₇	1	1	yes	characteristic
29	C₃×C₅⋊D₅	D₄₉	1	1	yes	characteristic
30	C₃×C₄₉	#1044	1	1	yes	characteristic, complemented, Hall
31	C₇⋊AGL(1,𝔽₅)	—	35	2	no	—
32	C₃×C₅×C₇	—	2	2	no	—
33	C₃×C₅×C₇	C₇⋊AGL(1,𝔽₅)	1	2	yes	—
34	#1044	—	49	1	no	Hall
35	C₂×C₄₉	—	25	1	no	—
36	C₃×Dic₇	—	175	1	no	—
37	C₃×C₅²	Dic₄₉	1	1	yes	characteristic, complemented, Hall
38	C₇×D₅	—	5	2	no	—
39	C₇×D₅	—	10	2	no	—
40	C₃×AGL(1,𝔽₅)	—	245	2	no	—
41	C₅⋊D₅	C₃×D₄₉	1	1	yes	characteristic
42	C₄₉	C₃×#1044	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃×C₇	—	25	1	no	—
44	C₅×C₇	—	2	2	no	—
45	C₅×C₇	C₃×C₇⋊AGL(1,𝔽₅)	1	2	yes	—
46	C₃×D₅	—	5	2	no	—
47	C₃×D₅	—	10	2	no	—
48	Dic₇	—	175	1	no	—
49	C₅²	C₃×Dic₄₉	1	1	yes	characteristic, complemented, Sylow
50	C₃×C₇	C₇⋊#1044	1	1	yes	characteristic
51	AGL(1,𝔽₅)	—	245	2	no	—
52	C₃×C₅	—	2	2	no	—
53	C₃×C₅	C₄₉⋊AGL(1,𝔽₅)	1	2	yes	complemented
54	C₂×C₇	—	25	1	no	—
55	C₃×C₄	—	1225	1	no	Hall
56	D₅	—	5	2	no	—
57	D₅	—	10	2	no	—
58	C₇	C₃×C₇⋊#1044	1	1	yes	characteristic
59	C₂×C₃	—	25	1	no	—
60	C₅	—	2	2	no	—
61	C₅	C₃×C₄₉⋊AGL(1,𝔽₅)	1	2	yes	complemented
62	C₄	—	1225	1	no	Sylow
63	C₃	C₄₉⋊#1044	1	1	yes	characteristic, direct product factor, Sylow
64	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₄₉⋊#1044
commutator, hypocenter	C₅²×C₄₉	C₃×C₄
Frattini	C₇	C₃×C₇⋊#1044
Fitting	C₃×C₅²×C₄₉	C₄
socle	C₃×C₅²×C₇	Dic₇
prime radical	C₃×C₇×C₅⋊D₅	D₇
cosocle	C₄₉×C₅⋊D₅	C₂×C₃
LCS	G ▷ C₅²×C₄₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₄₉⋊#1044	C₃	direct (N × H)
3. C₃×C₅²×C₄₉	C₄	semidirect
9. C₅²×C₄₉	C₃×C₄	semidirect
13. C₃×C₅×C₄₉	AGL(1,𝔽₅)	semidirect
24. C₅×C₄₉	C₃×AGL(1,𝔽₅)	semidirect
30. C₃×C₄₉	#1044	semidirect
37. C₃×C₅²	Dic₄₉	semidirect
42. C₄₉	C₃×#1044	semidirect
49. C₅²	C₃×Dic₄₉	semidirect
53. C₃×C₅	C₄₉⋊AGL(1,𝔽₅)	semidirect
61. C₅	C₃×C₄₉⋊AGL(1,𝔽₅)	semidirect
63. C₃	C₄₉⋊#1044	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄₉×C₅⋊D₅	2
C₄₉⋊#1044	3
C₃×C₄₉⋊AGL(1,𝔽₅)	5
C₃×C₇⋊#1044	7

Subgroups — C3×C49⋊#1044 #28412969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₉⋊#1044 #28412969