Subgroups — C₂×C₂₅×D₇₉⋊C₃ #37557134

Order 23700.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×D₇₉⋊C₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₂₅×C₇₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₅×D₇₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂₅×C₇₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×D₇₉⋊C₃	C₅	1	1	yes	maximal, characteristic
6	C₂₅×D₇₉	C₂×C₃	1	2	yes	complemented
7	C₂×C₂₅×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×D₇₉⋊C₃	C₂×C₅	1	2	yes	—
9	C₂×C₅×C₇₉⋊C₃	C₂×C₅	1	1	yes	characteristic
10	C₂₅×C₇₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×D₇₉	C₃×C₅	1	1	yes	characteristic
12	C₅×C₇₉⋊C₃	C₂²×C₅	1	1	yes	characteristic
13	C₂×D₇₉⋊C₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅×C₇₉	C₂×C₃×C₅	1	1	yes	characteristic
15	C₅×D₇₉	C₂×C₃×C₅	1	2	yes	—
16	C₂×C₇₉⋊C₃	C₂×C₂₅	1	1	yes	characteristic, complemented
17	D₇₉⋊C₃	C₂×C₂₅	1	2	yes	direct product factor
18	C₅×C₇₉	C₂²×C₃×C₅	1	1	yes	characteristic
19	C₂×D₇₉	C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₃×C₂₅	—	79	1	no	maximal, Hall
21	C₇₉⋊C₃	C₂²×C₂₅	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇₉	C₂×C₃×C₂₅	1	1	yes	characteristic, complemented
23	D₇₉	C₂×C₃×C₂₅	1	2	yes	complemented
24	C₂×C₃×C₂₅	—	79	2	no	—
25	C₂×C₃×C₂₅	—	79	1	no	—
26	C₂²×C₂₅	—	79	1	no	Hall
27	C₇₉	C₂²×C₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
28	C₃×C₂₅	—	79	1	no	Hall
29	C₂²×C₃×C₅	—	79	1	no	—
30	C₂×C₂₅	—	79	2	no	—
31	C₂×C₂₅	D₇₉⋊C₃	1	1	yes	characteristic, direct product factor
32	C₂×C₃×C₅	—	79	2	no	—
33	C₂×C₃×C₅	—	79	1	no	—
34	C₂₅	C₂×D₇₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²×C₅	—	79	1	no	—
36	C₃×C₅	—	79	1	no	—
37	C₂²×C₃	—	79	1	no	Hall
38	C₂×C₅	—	79	2	no	—
39	C₂×C₅	C₅×D₇₉⋊C₃	1	1	yes	characteristic
40	C₂×C₃	—	79	2	no	—
41	C₂×C₃	—	79	1	no	—
42	C₅	C₂×C₅×D₇₉⋊C₃	1	1	yes	characteristic
43	C₂²	—	79	1	no	Sylow
44	C₃	—	79	1	no	Sylow
45	C₂	—	79	2	no	—
46	C₂	C₂₅×D₇₉⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₅	D₇₉⋊C₃
commutator, hypocenter	C₇₉	C₂²×C₃×C₂₅
Frattini	C₅	C₂×C₅×D₇₉⋊C₃
Fitting	C₂×C₂₅×C₇₉	C₂×C₃
socle	C₂×C₅×C₇₉	C₂×C₃×C₅
prime radical	C₂×C₅×D₇₉⋊C₃	C₅
cosocle	C₅×C₇₉	C₂²×C₃×C₅
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₂×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₂₅×D₇₉⋊C₃	C₂	direct (N × H)
2. C₂×C₂₅×C₇₉⋊C₃	C₂	semidirect
3. C₂×C₂₅×D₇₉	C₃	semidirect
4. C₂₅×C₇₉⋊C₃	C₂²	semidirect
6. C₂₅×D₇₉	C₂×C₃	semidirect
7. C₂×C₂₅×C₇₉	C₂×C₃	semidirect
10. C₂₅×C₇₉	C₂²×C₃	semidirect
13. C₂×D₇₉⋊C₃	C₂₅	direct (N × H)
16. C₂×C₇₉⋊C₃	C₂×C₂₅	semidirect
17. D₇₉⋊C₃	C₂×C₂₅	direct (N × H)
19. C₂×D₇₉	C₃×C₂₅	semidirect
21. C₇₉⋊C₃	C₂²×C₂₅	semidirect
22. C₂×C₇₉	C₂×C₃×C₂₅	semidirect
23. D₇₉	C₂×C₃×C₂₅	semidirect
27. C₇₉	C₂²×C₃×C₂₅	semidirect
31. C₂×C₂₅	D₇₉⋊C₃	direct (N × H)
34. C₂₅	C₂×D₇₉⋊C₃	direct (N × H)
46. C₂	C₂₅×D₇₉⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₅×D₇₉⋊C₃	2
C₂×C₂₅×C₇₉⋊C₃	2
C₂×C₂₅×D₇₉	3
C₂×C₅×D₇₉⋊C₃	5
C₂²×C₃×C₂₅	79

Subgroups — C2×C25×D79⋊C3 #37557134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₅×D₇₉⋊C₃ #37557134