Subgroups — C₅×Dic₅×C₄₉⋊C₃ #28412866

Order 14700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₄₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₅×C₄₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₄₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄×C₅×C₄₉⋊C₃	—	5	1	no	maximal
5	Dic₅×C₄₉⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₅²×C₄₉	C₂×C₃	1	1	yes	characteristic
7	C₅×Dic₅×ΓL(1,𝔽₈)	—	7	1	no	maximal
8	C₂×C₅×C₄₉⋊C₃	—	2	2	no	—
9	C₂×C₅×C₄₉⋊C₃	D₅	1	1	yes	characteristic
10	C₂×C₅×C₄₉⋊C₃	C₂×C₅	1	1	yes	characteristic
11	C₅²×C₄₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅²×ΓL(1,𝔽₈)	—	7	1	no	—
13	C₄×C₅×C₄₉	—	5	1	no	—
14	Dic₅×C₄₉	C₃×C₅	1	1	yes	characteristic, complemented
15	C₅×C₄₉⋊C₃	—	2	2	no	—
16	C₅×C₄₉⋊C₃	Dic₅	1	1	yes	characteristic, direct product factor
17	C₅×C₄₉⋊C₃	C₄×C₅	1	1	yes	characteristic, complemented
18	C₅×C₇×Dic₅	ΓL(1,𝔽₈)	1	1	yes	characteristic
19	C₄×C₄₉⋊C₃	—	5	1	no	Hall
20	C₅²×ΓL(1,𝔽₈)	—	7	1	no	—
21	C₂×C₅×C₄₉	—	2	2	no	—
22	C₂×C₅×C₄₉	C₃×D₅	1	1	yes	characteristic
23	C₂×C₅×C₄₉	C₂×C₃×C₅	1	1	yes	characteristic
24	C₄×C₅×ΓL(1,𝔽₈)	—	35	1	no	—
25	Dic₅×ΓL(1,𝔽₈)	—	7	1	no	—
26	C₂×C₅²×C₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
27	C₃×C₅×Dic₅	—	49	1	no	Hall
28	C₂×C₄₉⋊C₃	C₅×D₅	1	1	yes	characteristic
29	C₅×C₄₉	—	2	2	no	—
30	C₅×C₄₉	C₃×Dic₅	1	1	yes	characteristic, complemented
31	C₅×C₄₉	C₃×C₄×C₅	1	1	yes	characteristic, complemented
32	C₂×C₅×ΓL(1,𝔽₈)	—	7	1	no	—
33	C₂×C₅×ΓL(1,𝔽₈)	—	7	1	no	—
34	C₂×C₅×ΓL(1,𝔽₈)	—	14	2	no	—
35	C₄×C₄₉	—	5	1	no	Hall
36	C₅²×C₇	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
37	C₂×C₃×C₅²	—	49	1	no	—
38	C₄₉⋊C₃	C₅×Dic₅	1	1	yes	characteristic, direct product factor, Hall
39	C₄×C₅×C₇	—	5	1	no	—
40	C₇×Dic₅	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
41	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
42	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
43	C₅×ΓL(1,𝔽₈)	—	14	2	no	—
44	C₅×Dic₅	C₄₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
45	C₂×C₄₉	C₃×C₅×D₅	1	1	yes	characteristic
46	C₄×ΓL(1,𝔽₈)	—	35	1	no	—
47	C₃×C₅²	—	49	1	no	Hall
48	C₂×C₅×C₇	—	2	2	no	—
49	C₂×C₅×C₇	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
50	C₂×C₅×C₇	C₂×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
51	C₃×C₄×C₅	—	245	1	no	—
52	C₃×Dic₅	—	49	1	no	—
53	C₂×C₅²	C₂×C₄₉⋊C₃	1	1	yes	characteristic
54	C₄₉	C₃×C₅×Dic₅	1	1	yes	characteristic, complemented, Sylow
55	C₂×ΓL(1,𝔽₈)	—	7	1	no	—
56	C₅×C₇	—	2	2	no	—
57	C₅×C₇	Dic₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
58	C₅×C₇	C₄×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
59	C₂×C₃×C₅	—	49	1	no	—
60	C₂×C₃×C₅	—	49	1	no	—
61	C₂×C₃×C₅	—	98	2	no	—
62	C₄×C₇	—	5	1	no	—
63	C₅²	C₄×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
64	ΓL(1,𝔽₈)	—	7	1	no	—
65	C₄×C₅	—	5	1	no	—
66	Dic₅	C₅×C₄₉⋊C₃	1	1	yes	characteristic, direct product factor
67	C₃×C₅	—	49	1	no	—
68	C₃×C₅	—	49	1	no	—
69	C₃×C₅	—	98	2	no	—
70	C₂×C₇	C₅×D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
71	C₃×C₄	—	245	1	no	Hall
72	C₂×C₅	—	2	2	no	—
73	C₂×C₅	D₅×C₄₉⋊C₃	1	1	yes	characteristic
74	C₂×C₅	C₂×C₅×C₄₉⋊C₃	1	1	yes	characteristic
75	C₇	C₅×Dic₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
76	C₂×C₃	—	49	1	no	—
77	C₅	—	2	2	no	—
78	C₅	Dic₅×C₄₉⋊C₃	1	1	yes	characteristic, direct product factor
79	C₅	C₄×C₅×C₄₉⋊C₃	1	1	yes	characteristic, complemented
80	C₄	—	5	1	no	Sylow
81	C₃	—	49	1	no	Sylow
82	C₂	C₅×D₅×C₄₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	D₅×C₄₉⋊C₃
commutator, hypocenter	C₅×C₄₉	C₃×C₄×C₅
Frattini	C₂×C₇	C₅×D₅×ΓL(1,𝔽₈)
Fitting	C₂×C₅²×C₄₉	C₂×C₃
socle	C₂×C₅²×C₇	C₂×ΓL(1,𝔽₈)
prime radical	C₂×C₅²×C₄₉⋊C₃	C₂
cosocle	C₂×C₅×C₄₉	C₂×C₃×C₅
LCS	G ▷ C₅×C₄₉
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×Dic₅×C₄₉	C₃	semidirect
3. C₅²×C₄₉⋊C₃	C₄	semidirect
5. Dic₅×C₄₉⋊C₃	C₅	direct (N × H)
11. C₅²×C₄₉	C₃×C₄	semidirect
14. Dic₅×C₄₉	C₃×C₅	semidirect
16. C₅×C₄₉⋊C₃	Dic₅	direct (N × H)
17. C₅×C₄₉⋊C₃	C₄×C₅	semidirect
30. C₅×C₄₉	C₃×Dic₅	semidirect
31. C₅×C₄₉	C₃×C₄×C₅	semidirect
38. C₄₉⋊C₃	C₅×Dic₅	direct (N × H)
44. C₅×Dic₅	C₄₉⋊C₃	direct (N × H)
54. C₄₉	C₃×C₅×Dic₅	semidirect
63. C₅²	C₄×C₄₉⋊C₃	semidirect
66. Dic₅	C₅×C₄₉⋊C₃	direct (N × H)
78. C₅	Dic₅×C₄₉⋊C₃	direct (N × H)
79. C₅	C₄×C₅×C₄₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅²×C₄₉⋊C₃	2
C₅×Dic₅×C₄₉	3
C₄×C₅×C₄₉⋊C₃	5
Dic₅×C₄₉⋊C₃	5
C₅×Dic₅×ΓL(1,𝔽₈)	7

Subgroups — C5×Dic5×C49⋊C3 #28412866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Dic₅×C₄₉⋊C₃ #28412866