Subgroups — D₇₉⋊((C₅⋊D₅)⋊C₃) #37557193

Order 23700.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₉⋊(C₅²⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₅⋊D₅)⋊(C₇₉⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	#26045007	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅⋊D₅×D₇₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₅²⋊(C₇₉⋊C₃)	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅⋊D₃₉₅	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅⋊D₅×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅²×D₇₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅²×C₇₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	D₅×D₇₉	—	15	2	no	—
11	C₂×D₇₉⋊C₃	—	25	1	no	maximal, Hall
12	D₃₉₅	—	15	2	no	—
13	C₅×D₇₉	—	3	2	no	—
14	D₅×C₇₉	—	15	2	no	—
15	C₂×C₇₉⋊C₃	—	25	1	no	—
16	D₇₉⋊C₃	—	25	1	no	—
17	D₇₉⋊C₃	—	50	1	no	—
18	C₅×C₇₉	—	3	2	no	—
19	C₂×D₇₉	—	25	1	no	Hall
20	C₂×(C₅⋊D₅)⋊C₃	—	79	1	no	maximal, Hall
21	C₇₉⋊C₃	—	50	1	no	Hall
22	C₂×C₇₉	—	25	1	no	—
23	D₇₉	—	25	1	no	—
24	D₇₉	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
25	C₂×C₅²⋊C₃	—	79	1	no	—
26	(C₅⋊D₅)⋊C₃	—	79	1	no	—
27	(C₅⋊D₅)⋊C₃	—	158	1	no	—
28	C₂×C₅⋊D₅	—	79	1	no	Hall
29	C₇₉	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	C₅²⋊C₃	—	158	1	no	Hall
31	C₂×C₅²	—	79	1	no	—
32	C₅⋊D₅	—	79	1	no	—
33	C₅⋊D₅	D₇₉⋊C₃	1	1	yes	characteristic, complemented
34	C₅²	C₂×D₇₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
35	C₂×D₅	—	1185	2	no	—
36	C₂²×C₃	—	1975	1	no	Hall
37	C₂×C₅	—	237	2	no	—
38	D₅	—	15	2	no	—
39	D₅	—	1185	2	no	—
40	C₂×C₃	—	3950	1	no	—
41	C₂×C₃	—	3950	1	no	—
42	C₂×C₃	—	1975	1	no	—
43	C₅	—	3	2	no	—
44	C₂²	—	1975	1	no	Sylow
45	C₃	—	7900	1	no	Sylow
46	C₂	—	25	1	no	—
47	C₂	—	79	1	no	—
48	C₂	—	1975	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. D₇₉⋊(C₅²⋊C₃)	C₂	semidirect
2. (C₅⋊D₅)⋊(C₇₉⋊C₃)	C₂	semidirect
3. #26045007	C₂	semidirect
4. C₅⋊D₅×D₇₉	C₃	semidirect
5. C₅²⋊(C₇₉⋊C₃)	C₂²	semidirect
6. C₅⋊D₃₉₅	C₂×C₃	semidirect
7. C₅⋊D₅×C₇₉	C₂×C₃	semidirect
8. C₅²×D₇₉	C₂×C₃	semidirect
9. C₅²×C₇₉	C₂²×C₃	semidirect
24. D₇₉	(C₅⋊D₅)⋊C₃	semidirect
29. C₇₉	C₂×(C₅⋊D₅)⋊C₃	semidirect
33. C₅⋊D₅	D₇₉⋊C₃	semidirect
34. C₅²	C₂×D₇₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
D₇₉⋊(C₅²⋊C₃)	2
(C₅⋊D₅)⋊(C₇₉⋊C₃)	2
#26045007	2
C₅⋊D₅×D₇₉	3
C₂×D₇₉⋊C₃	25
C₂×(C₅⋊D₅)⋊C₃	79

Subgroups — D79⋊((C5⋊D5)⋊C3) #37557193

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇₉⋊((C₅⋊D₅)⋊C₃) #37557193