Subgroups — C₅×#13093360⋊C₂ #28414770

Order 14820.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#13093366	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#13093364	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#13093360	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₁₃×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₅×#10625202	C₂²	1	1	yes	characteristic, complemented, Hall
6	#13093360⋊C₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₂₄₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×C₁₉×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₁₃×D₁₉	C₂×C₃	1	1	yes	characteristic, complemented
10	#13093366	C₂×C₅	1	1	yes	characteristic, complemented
11	#13093364	C₂×C₅	1	1	yes	characteristic, complemented
12	#13093360	C₂×C₅	1	1	yes	characteristic, complemented
13	C₅×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×D₁₉⋊C₃	—	13	1	no	maximal, Hall
15	D₁₃×D₁₉	C₃×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×D₁₃⋊C₃	—	19	1	no	maximal, Hall
17	#10625202	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₁₉⋊C₃	—	13	1	no	—
19	C₅×D₁₉⋊C₃	—	13	1	no	—
20	C₅×D₁₉⋊C₃	—	13	1	no	—
21	D₂₄₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
22	C₁₃×D₁₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
23	C₁₉×D₁₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
24	C₂×C₅×C₁₃⋊C₃	—	19	1	no	—
25	C₅×D₁₃⋊C₃	—	19	1	no	—
26	C₅×D₁₃⋊C₃	—	19	1	no	—
27	C₂×C₅×D₁₉	—	13	1	no	Hall
28	C₅×C₁₉⋊C₃	—	13	1	no	Hall
29	C₂×C₅×D₁₃	—	19	1	no	Hall
30	C₁₃×C₁₉	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
31	C₂×D₁₉⋊C₃	—	13	1	no	Hall
32	C₅×C₁₃⋊C₃	—	19	1	no	Hall
33	C₂×C₅×C₁₉	—	13	1	no	—
34	C₅×D₁₉	—	13	1	no	—
35	C₅×D₁₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented
36	C₂×D₁₃⋊C₃	—	19	1	no	Hall
37	C₂×C₅×C₁₃	—	19	1	no	—
38	C₅×D₁₃	—	19	1	no	—
39	C₅×D₁₃	D₁₉⋊C₃	1	1	yes	characteristic, complemented
40	C₂×C₁₉⋊C₃	—	13	1	no	—
41	D₁₉⋊C₃	—	13	1	no	—
42	D₁₉⋊C₃	—	13	1	no	—
43	C₅×C₁₉	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
44	C₂×C₁₃⋊C₃	—	19	1	no	—
45	D₁₃⋊C₃	—	19	1	no	—
46	D₁₃⋊C₃	—	19	1	no	—
47	C₂×D₁₉	—	13	1	no	Hall
48	C₅×C₁₃	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
49	C₂²×C₃×C₅	—	247	1	no	Hall
50	C₁₉⋊C₃	—	13	1	no	Hall
51	C₂×D₁₃	—	19	1	no	Hall
52	C₁₃⋊C₃	—	19	1	no	Hall
53	C₂×C₁₉	—	13	1	no	—
54	D₁₉	—	13	1	no	—
55	D₁₉	C₅×D₁₃⋊C₃	1	1	yes	characteristic, complemented
56	C₂×C₃×C₅	—	247	1	no	—
57	C₂×C₃×C₅	—	247	1	no	—
58	C₂×C₃×C₅	—	247	1	no	—
59	C₂×C₁₃	—	19	1	no	—
60	D₁₃	—	19	1	no	—
61	D₁₃	C₅×D₁₉⋊C₃	1	1	yes	characteristic, complemented
62	C₂²×C₅	—	247	1	no	Hall
63	C₁₉	C₂×C₅×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
64	C₃×C₅	—	247	1	no	Hall
65	C₁₃	C₂×C₅×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₃	—	247	1	no	Hall
67	C₂×C₅	—	13	1	no	—
68	C₂×C₅	—	19	1	no	—
69	C₂×C₅	—	247	1	no	—
70	C₂×C₃	—	247	1	no	—
71	C₂×C₃	—	247	1	no	—
72	C₂×C₃	—	247	1	no	—
73	C₅	#13093360⋊C₂	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	—	247	1	no	Sylow
75	C₃	—	247	1	no	Sylow
76	C₂	—	13	1	no	—
77	C₂	—	19	1	no	—
78	C₂	—	247	1	no	—

	subgroup	G/H
center, hypercenter	C₅	#13093360⋊C₂
commutator, cosocle, hypocenter	C₁₃×C₁₉	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₁₉	C₂²×C₃
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#13093366	C₂	semidirect
2. C₅×#13093364	C₂	semidirect
3. C₅×#13093360	C₂	semidirect
4. C₅×D₁₃×D₁₉	C₃	semidirect
5. C₅×#10625202	C₂²	semidirect
6. #13093360⋊C₂	C₅	direct (N × H)
7. C₅×D₂₄₇	C₂×C₃	semidirect
8. C₅×C₁₉×D₁₃	C₂×C₃	semidirect
9. C₅×C₁₃×D₁₉	C₂×C₃	semidirect
10. #13093366	C₂×C₅	semidirect
11. #13093364	C₂×C₅	semidirect
12. #13093360	C₂×C₅	semidirect
13. C₅×C₁₃×C₁₉	C₂²×C₃	semidirect
15. D₁₃×D₁₉	C₃×C₅	semidirect
17. #10625202	C₂²×C₅	semidirect
21. D₂₄₇	C₂×C₃×C₅	semidirect
22. C₁₃×D₁₉	C₂×C₃×C₅	semidirect
23. C₁₉×D₁₃	C₂×C₃×C₅	semidirect
30. C₁₃×C₁₉	C₂²×C₃×C₅	semidirect
35. C₅×D₁₉	D₁₃⋊C₃	semidirect
39. C₅×D₁₃	D₁₉⋊C₃	semidirect
43. C₅×C₁₉	C₂×D₁₃⋊C₃	semidirect
48. C₅×C₁₃	C₂×D₁₉⋊C₃	semidirect
55. D₁₉	C₅×D₁₃⋊C₃	semidirect
61. D₁₃	C₅×D₁₉⋊C₃	semidirect
63. C₁₉	C₂×C₅×D₁₃⋊C₃	semidirect
65. C₁₃	C₂×C₅×D₁₉⋊C₃	semidirect
73. C₅	#13093360⋊C₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#13093366	2
C₅×#13093364	2
C₅×#13093360	2
C₅×D₁₃×D₁₉	3
#13093360⋊C₂	5
C₂×C₅×D₁₉⋊C₃	13
C₂×C₅×D₁₃⋊C₃	19

Subgroups — C5×#13093360⋊C2 #28414770

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13093360⋊C₂ #28414770