Subgroups — C₅×Dic₁₅×C₇₉ #37557178

Order 23700.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅²×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₅×C₇₉	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₇₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₅×C₇₉	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×Dic₃×C₇₉	—	5	1	no	maximal
6	C₂×C₅²×C₇₉	D₃	1	1	yes	characteristic
7	C₂×C₃×C₅×C₇₉	—	2	2	no	—
8	C₂×C₃×C₅×C₇₉	D₅	1	1	yes	characteristic
9	C₂×C₃×C₅×C₇₉	C₂×C₅	1	1	yes	characteristic
10	C₅²×C₇₉	Dic₃	1	1	yes	characteristic, complemented, Hall
11	C₄×C₅×C₇₉	—	15	1	no	—
12	Dic₅×C₇₉	—	3	1	no	—
13	C₃×C₅×C₇₉	—	2	2	no	—
14	C₃×C₅×C₇₉	Dic₅	1	1	yes	characteristic, complemented
15	C₃×C₅×C₇₉	C₄×C₅	1	1	yes	characteristic, complemented
16	Dic₃×C₇₉	—	5	1	no	Hall
17	C₂×C₅×C₇₉	—	2	2	no	—
18	C₂×C₅×C₇₉	C₅×D₃	1	1	yes	characteristic
19	C₂×C₅×C₇₉	D₁₅	1	1	yes	characteristic
20	C₂×C₃×C₇₉	C₅×D₅	1	1	yes	characteristic
21	C₅×C₇₉	—	2	2	no	—
22	C₅×C₇₉	C₅×Dic₃	1	1	yes	characteristic, complemented
23	C₅×C₇₉	Dic₁₅	1	1	yes	characteristic, direct product factor
24	C₄×C₇₉	—	15	1	no	Hall
25	C₅×Dic₁₅	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₃×C₇₉	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₇₉	C₅×D₁₅	1	1	yes	characteristic
28	C₂×C₃×C₅²	C₂×C₇₉	1	1	yes	characteristic
29	C₅×Dic₅	—	3	1	no	Hall
30	C₇₉	C₅×Dic₁₅	1	1	yes	characteristic, direct product factor, Sylow
31	C₃×C₅²	C₄×C₇₉	1	1	yes	characteristic, complemented, Hall
32	Dic₁₅	C₅×C₇₉	1	1	yes	characteristic, direct product factor
33	C₅×Dic₃	—	5	1	no	—
34	C₂×C₅²	D₃×C₇₉	1	1	yes	characteristic
35	C₂×C₃×C₅	—	2	2	no	—
36	C₂×C₃×C₅	D₅×C₇₉	1	1	yes	characteristic
37	C₂×C₃×C₅	C₂×C₅×C₇₉	1	1	yes	characteristic
38	C₅²	Dic₃×C₇₉	1	1	yes	characteristic, complemented, Sylow
39	C₄×C₅	—	15	1	no	—
40	Dic₅	—	3	1	no	—
41	C₃×C₅	—	2	2	no	—
42	C₃×C₅	Dic₅×C₇₉	1	1	yes	characteristic, complemented
43	C₃×C₅	C₄×C₅×C₇₉	1	1	yes	characteristic, complemented
44	Dic₃	—	5	1	no	Hall
45	C₂×C₅	—	2	2	no	—
46	C₂×C₅	C₅×D₃×C₇₉	1	1	yes	characteristic
47	C₂×C₅	D₁₅×C₇₉	1	1	yes	characteristic
48	C₂×C₃	C₅×D₅×C₇₉	1	1	yes	characteristic
49	C₅	—	2	2	no	—
50	C₅	C₅×Dic₃×C₇₉	1	1	yes	characteristic, complemented
51	C₅	Dic₁₅×C₇₉	1	1	yes	characteristic, direct product factor
52	C₄	—	15	1	no	Sylow
53	C₃	C₅×Dic₅×C₇₉	1	1	yes	characteristic, complemented, Sylow
54	C₂	C₅×D₁₅×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇₉	D₁₅
commutator, hypocenter	C₃×C₅	C₄×C₅×C₇₉
Frattini	C₂	C₅×D₁₅×C₇₉
Fitting, socle, prime radical	C₂×C₃×C₅²×C₇₉	C₂
cosocle	C₂×C₃×C₅	C₂×C₅×C₇₉
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₅×C₇₉

Complements

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

N	H ≅ G/N	type
3. C₃×C₅²×C₇₉	C₄	semidirect
4. Dic₁₅×C₇₉	C₅	direct (N × H)
10. C₅²×C₇₉	Dic₃	semidirect
14. C₃×C₅×C₇₉	Dic₅	semidirect
15. C₃×C₅×C₇₉	C₄×C₅	semidirect
22. C₅×C₇₉	C₅×Dic₃	semidirect
23. C₅×C₇₉	Dic₁₅	direct (N × H)
25. C₅×Dic₁₅	C₇₉	direct (N × H)
26. C₃×C₇₉	C₅×Dic₅	semidirect
30. C₇₉	C₅×Dic₁₅	direct (N × H)
31. C₃×C₅²	C₄×C₇₉	semidirect
32. Dic₁₅	C₅×C₇₉	direct (N × H)
38. C₅²	Dic₃×C₇₉	semidirect
42. C₃×C₅	Dic₅×C₇₉	semidirect
43. C₃×C₅	C₄×C₅×C₇₉	semidirect
50. C₅	C₅×Dic₃×C₇₉	semidirect
51. C₅	Dic₁₅×C₇₉	direct (N × H)
53. C₃	C₅×Dic₅×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅²×C₇₉	2
C₅×Dic₅×C₇₉	3
Dic₁₅×C₇₉	5
C₅×Dic₃×C₇₉	5
C₅×Dic₁₅	79

Subgroups — C5×Dic15×C79 #37557178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Dic₁₅×C₇₉ #37557178