Subgroups — C₃×C₅⋊D₅×D₇₉ #37557233

Order 23700.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅⋊D₅×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅⋊D₃₉₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅⋊D₅×D₇₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅²×C₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₅×D₇₉	—	5	6	no	maximal
7	C₅⋊D₃₉₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅⋊D₅×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅²×D₇₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₃₉₅	—	5	6	no	—
11	C₃×D₅×C₇₉	—	5	6	no	—
12	C₃×C₅×D₇₉	D₅	1	6	yes	complemented
13	C₅²×C₇₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	D₅×D₇₉	—	5	6	no	—
15	C₃×C₅×C₇₉	C₂×D₅	1	6	yes	complemented
16	C₂×C₃×D₇₉	—	25	1	no	Hall
17	D₃₉₅	—	5	6	no	—
18	C₅×D₇₉	C₃×D₅	1	6	yes	complemented
19	D₅×C₇₉	—	5	6	no	—
20	C₂×C₃×C₇₉	—	25	1	no	—
21	C₃×D₇₉	—	25	1	no	—
22	C₃×D₇₉	C₅⋊D₅	1	1	yes	characteristic, direct product factor
23	C₅×C₇₉	C₂×C₃×D₅	1	6	yes	complemented
24	C₂×D₇₉	—	25	1	no	Hall
25	C₂×C₃×C₅⋊D₅	—	79	1	no	maximal, Hall
26	C₃×C₇₉	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₇₉	—	25	1	no	—
28	D₇₉	—	25	1	no	—
29	D₇₉	C₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor
30	C₂×C₃×C₅²	—	79	1	no	—
31	C₃×C₅⋊D₅	—	79	1	no	—
32	C₃×C₅⋊D₅	D₇₉	1	1	yes	characteristic, direct product factor
33	C₂×C₅⋊D₅	—	79	1	no	Hall
34	C₇₉	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
35	C₃×C₅²	C₂×D₇₉	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×D₅	—	395	6	no	—
37	C₂×C₅²	—	79	1	no	—
38	C₅⋊D₅	—	79	1	no	—
39	C₅⋊D₅	C₃×D₇₉	1	1	yes	characteristic, direct product factor
40	C₂×C₃×C₅	—	79	6	no	—
41	C₃×D₅	—	5	6	no	—
42	C₃×D₅	—	395	6	no	—
43	C₅²	C₂×C₃×D₇₉	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₅	—	395	6	no	—
45	C₃×C₅	D₅×D₇₉	1	6	yes	complemented
46	C₂²×C₃	—	1975	1	no	Hall
47	C₂×C₅	—	79	6	no	—
48	D₅	—	5	6	no	—
49	D₅	—	395	6	no	—
50	C₂×C₃	—	25	1	no	—
51	C₂×C₃	—	79	1	no	—
52	C₂×C₃	—	1975	1	no	—
53	C₅	C₃×D₅×D₇₉	1	6	yes	complemented
54	C₂²	—	1975	1	no	Sylow
55	C₃	C₅⋊D₅×D₇₉	1	1	yes	characteristic, direct product factor, Sylow
56	C₂	—	25	1	no	—
57	C₂	—	79	1	no	—
58	C₂	—	1975	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₅⋊D₅×D₇₉
commutator, cosocle, hypocenter	C₅²×C₇₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇₉	C₂²
LCS	G ▷ C₅²×C₇₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×D₇₉	C₂	semidirect
2. C₃×C₅⋊D₅×C₇₉	C₂	semidirect
3. C₃×C₅⋊D₃₉₅	C₂	semidirect
4. C₅⋊D₅×D₇₉	C₃	direct (N × H)
5. C₃×C₅²×C₇₉	C₂²	semidirect
7. C₅⋊D₃₉₅	C₂×C₃	semidirect
8. C₅⋊D₅×C₇₉	C₂×C₃	semidirect
9. C₅²×D₇₉	C₂×C₃	semidirect
12. C₃×C₅×D₇₉	D₅	semidirect
13. C₅²×C₇₉	C₂²×C₃	semidirect
15. C₃×C₅×C₇₉	C₂×D₅	semidirect
18. C₅×D₇₉	C₃×D₅	semidirect
22. C₃×D₇₉	C₅⋊D₅	direct (N × H)
23. C₅×C₇₉	C₂×C₃×D₅	semidirect
26. C₃×C₇₉	C₂×C₅⋊D₅	semidirect
29. D₇₉	C₃×C₅⋊D₅	direct (N × H)
32. C₃×C₅⋊D₅	D₇₉	direct (N × H)
34. C₇₉	C₂×C₃×C₅⋊D₅	semidirect
35. C₃×C₅²	C₂×D₇₉	semidirect
39. C₅⋊D₅	C₃×D₇₉	direct (N × H)
43. C₅²	C₂×C₃×D₇₉	semidirect
45. C₃×C₅	D₅×D₇₉	semidirect
53. C₅	C₃×D₅×D₇₉	semidirect
55. C₃	C₅⋊D₅×D₇₉	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×C₅²×D₇₉	2
C₃×C₅⋊D₅×C₇₉	2
C₃×C₅⋊D₃₉₅	2
C₅⋊D₅×D₇₉	3
C₃×D₅×D₇₉	5
C₂×C₃×C₅⋊D₅	79

Subgroups — C3×C5⋊D5×D79 #37557233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅⋊D₅×D₇₉ #37557233