Subgroups — C₅×Dic₇₄₁ #28414730

Order 14820.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₂₄₇	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₃×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₇₄₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₃×C₁₉	D₃	1	1	yes	characteristic
6	C₂×C₃×C₁₃×C₁₉	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₃×C₁₉	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₅×Dic₅₇	—	13	1	no	maximal, Hall
9	Dic₂₄₇	—	3	1	no	Hall
10	C₅×Dic₃₉	—	19	1	no	maximal, Hall
11	C₃×C₁₃×C₁₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×C₁₉	D₁₃	1	1	yes	characteristic
13	C₂×C₁₃×C₁₉	C₅×D₃	1	1	yes	characteristic
14	C₂×C₃×C₅×C₁₃	D₁₉	1	1	yes	characteristic
15	C₅×Dic₁₉	—	39	1	no	Hall
16	C₃×C₅×C₁₉	Dic₁₃	1	1	yes	characteristic, complemented, Hall
17	C₅×Dic₁₃	—	57	1	no	Hall
18	C₁₃×C₁₉	C₅×Dic₃	1	1	yes	characteristic, complemented, Hall
19	Dic₅₇	—	13	1	no	Hall
20	C₃×C₅×C₁₃	Dic₁₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×C₁₉	D₃₉	1	1	yes	characteristic
22	Dic₃₉	—	19	1	no	Hall
23	C₂×C₅×C₁₃	D₅₇	1	1	yes	characteristic
24	C₂×C₃×C₁₉	C₅×D₁₃	1	1	yes	characteristic
25	C₅×C₁₉	Dic₃₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₁₃	C₅×D₁₉	1	1	yes	characteristic
27	Dic₁₉	—	39	1	no	Hall
28	C₅×C₁₃	Dic₅₇	1	1	yes	characteristic, complemented, Hall
29	C₅×Dic₃	—	247	1	no	Hall
30	C₃×C₁₉	C₅×Dic₁₃	1	1	yes	characteristic, complemented, Hall
31	Dic₁₃	—	57	1	no	Hall
32	C₃×C₁₃	C₅×Dic₁₉	1	1	yes	characteristic, complemented, Hall
33	C₂×C₁₉	C₅×D₃₉	1	1	yes	characteristic
34	C₂×C₃×C₅	D₂₄₇	1	1	yes	characteristic
35	C₂×C₁₃	C₅×D₅₇	1	1	yes	characteristic
36	C₄×C₅	—	741	1	no	Hall
37	C₁₉	C₅×Dic₃₉	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₅	Dic₂₄₇	1	1	yes	characteristic, complemented, Hall
39	C₁₃	C₅×Dic₅₇	1	1	yes	characteristic, complemented, Sylow
40	Dic₃	—	247	1	no	Hall
41	C₂×C₅	D₇₄₁	1	1	yes	characteristic
42	C₂×C₃	C₅×D₂₄₇	1	1	yes	characteristic
43	C₅	Dic₇₄₁	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	741	1	no	Sylow
45	C₃	C₅×Dic₂₄₇	1	1	yes	characteristic, complemented, Sylow
46	C₂	C₅×D₇₄₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	D₇₄₁
commutator, hypocenter	C₃×C₁₃×C₁₉	C₄×C₅
Frattini	C₂	C₅×D₇₄₁
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₃×C₁₉	C₂
cosocle	C₂×C₃×C₁₃×C₁₉	C₂×C₅
LCS	G ▷ C₃×C₁₃×C₁₉
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₃×C₁₉	C₄	semidirect
4. Dic₇₄₁	C₅	direct (N × H)
7. C₅×C₁₃×C₁₉	Dic₃	semidirect
11. C₃×C₁₃×C₁₉	C₄×C₅	semidirect
16. C₃×C₅×C₁₉	Dic₁₃	semidirect
18. C₁₃×C₁₉	C₅×Dic₃	semidirect
20. C₃×C₅×C₁₃	Dic₁₉	semidirect
25. C₅×C₁₉	Dic₃₉	semidirect
28. C₅×C₁₃	Dic₅₇	semidirect
30. C₃×C₁₉	C₅×Dic₁₃	semidirect
32. C₃×C₁₃	C₅×Dic₁₉	semidirect
37. C₁₉	C₅×Dic₃₉	semidirect
38. C₃×C₅	Dic₂₄₇	semidirect
39. C₁₃	C₅×Dic₅₇	semidirect
43. C₅	Dic₇₄₁	direct (N × H)
45. C₃	C₅×Dic₂₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₁₃×C₁₉	2
C₅×Dic₂₄₇	3
Dic₇₄₁	5
C₅×Dic₅₇	13
C₅×Dic₃₉	19

Subgroups — C5×Dic741 #28414730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Dic₇₄₁ #28414730