Subgroups — (C₅⋊(D₇₉⋊C₃))⋊D₅ #37557205

Order 23700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₅×C₇₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₅⋊(D₇₉⋊C₃)	C₂	1	2	yes	maximal, complemented
3	(C₅⋊D₅)⋊D₇₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅²×C₇₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×D₇₉⋊C₃	—	5	2	no	maximal
6	C₅⋊D₅×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×D₃₉₅	C₂×C₃	1	2	yes	complemented
8	C₅⋊(D₇₉⋊C₃)	D₅	1	2	yes	complemented
9	D₅×C₇₉⋊C₃	—	5	2	no	—
10	D₅×C₇₉⋊C₃	—	10	2	no	—
11	C₅×D₇₉⋊C₃	—	5	2	no	—
12	C₅²×C₇₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
13	D₅×D₇₉	—	5	2	no	—
14	C₅×C₇₉⋊C₃	—	2	2	no	—
15	C₅×C₇₉⋊C₃	C₂×D₅	1	2	yes	complemented
16	C₂×D₇₉⋊C₃	—	25	1	no	Hall
17	D₃₉₅	C₃×D₅	1	2	yes	complemented
18	C₅×D₇₉	—	5	2	no	—
19	D₅×C₇₉	—	5	2	no	—
20	D₅×C₇₉	—	10	2	no	—
21	C₂×C₇₉⋊C₃	—	25	1	no	—
22	D₇₉⋊C₃	—	5	2	no	—
23	C₅×C₇₉	—	2	2	no	—
24	C₅×C₇₉	C₂×C₃×D₅	1	2	yes	complemented
25	C₂×D₇₉	—	25	1	no	Hall
26	C₃×D₅²	—	79	1	no	maximal, Hall
27	C₇₉⋊C₃	D₅²	1	1	yes	characteristic, complemented, Hall
28	C₂×C₇₉	—	25	1	no	—
29	D₇₉	—	5	2	no	—
30	C₃×C₅⋊D₅	—	158	1	no	—
31	C₃×C₅×D₅	—	79	2	no	—
32	D₅²	—	79	1	no	Hall
33	C₇₉	C₃×D₅²	1	1	yes	characteristic, complemented, Sylow
34	C₃×C₅²	—	158	1	no	Hall
35	C₂×C₃×D₅	—	395	2	no	—
36	C₅⋊D₅	D₇₉⋊C₃	1	1	yes	characteristic, complemented
37	C₅×D₅	—	79	2	no	—
38	C₂×C₃×C₅	—	395	2	no	—
39	C₃×D₅	—	790	2	no	—
40	C₃×D₅	—	790	2	no	—
41	C₃×D₅	—	79	2	no	—
42	C₅²	C₂×D₇₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₅	—	395	2	no	—
44	C₃×C₅	—	158	2	no	—
45	C₃×C₅	—	158	2	no	—
46	C₂²×C₃	—	1975	1	no	Hall
47	C₂×C₅	—	395	2	no	—
48	D₅	—	5	2	no	—
49	D₅	—	10	2	no	—
50	D₅	—	79	2	no	—
51	C₂×C₃	—	3950	1	no	—
52	C₂×C₃	—	395	2	no	—
53	C₅	—	2	2	no	—
54	C₅	D₅×D₇₉⋊C₃	1	2	yes	complemented
55	C₂²	—	1975	1	no	Sylow
56	C₃	—	158	1	no	Sylow
57	C₂	—	25	1	no	—
58	C₂	—	395	2	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. C₅⋊D₅×C₇₉⋊C₃	C₂	semidirect
2. C₅×C₅⋊(D₇₉⋊C₃)	C₂	semidirect
3. (C₅⋊D₅)⋊D₇₉	C₃	semidirect
4. C₅²×C₇₉⋊C₃	C₂²	semidirect
6. C₅⋊D₅×C₇₉	C₂×C₃	semidirect
7. C₅×D₃₉₅	C₂×C₃	semidirect
8. C₅⋊(D₇₉⋊C₃)	D₅	semidirect
12. C₅²×C₇₉	C₂²×C₃	semidirect
15. C₅×C₇₉⋊C₃	C₂×D₅	semidirect
17. D₃₉₅	C₃×D₅	semidirect
24. C₅×C₇₉	C₂×C₃×D₅	semidirect
27. C₇₉⋊C₃	D₅²	semidirect
33. C₇₉	C₃×D₅²	semidirect
36. C₅⋊D₅	D₇₉⋊C₃	semidirect
42. C₅²	C₂×D₇₉⋊C₃	semidirect
54. C₅	D₅×D₇₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₅⋊D₅×C₇₉⋊C₃	2
C₅×C₅⋊(D₇₉⋊C₃)	2
(C₅⋊D₅)⋊D₇₉	3
D₅×D₇₉⋊C₃	5
C₃×D₅²	79

Subgroups — (C5⋊(D79⋊C3))⋊D5 #37557205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₅⋊(D₇₉⋊C₃))⋊D₅ #37557205