Subgroups — C₂×C₃⋊(C₅⋊D₃₉₅) #37557281

Order 23700.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₅⋊D₃₉₅)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅²×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅⋊D₃₉₅	—	3	1	no	maximal, Hall
4	C₃×C₅²×C₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₁₈₅	—	5	6	no	maximal
6	C₅⋊D₃₉₅	—	3	2	no	—
7	C₂×C₅²×C₇₉	D₃	1	1	yes	characteristic, complemented
8	D₁₁₈₅	—	5	12	no	—
9	C₂×C₃×C₅×C₇₉	D₅	1	6	yes	complemented
10	C₅²×C₇₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₃₉₅	—	15	6	no	—
12	C₃×C₅×C₇₉	C₂×D₅	1	6	yes	complemented
13	C₂×D₂₃₇	—	25	1	no	Hall
14	C₂×C₅×C₇₉	D₁₅	1	6	yes	complemented
15	D₃₉₅	—	15	12	no	—
16	C₂×C₃×C₇₉	C₅⋊D₅	1	1	yes	characteristic, complemented
17	D₂₃₇	—	25	2	no	—
18	C₅×C₇₉	C₂×D₁₅	1	6	yes	complemented
19	C₂×D₇₉	—	75	1	no	Hall
20	C₂×C₃⋊(C₅⋊D₅)	—	79	1	no	maximal, Hall
21	C₃×C₇₉	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇₉	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented
23	D₇₉	—	75	2	no	—
24	C₂×C₃×C₅²	D₇₉	1	1	yes	characteristic, complemented
25	C₃⋊(C₅⋊D₅)	—	79	2	no	—
26	C₂×C₅⋊D₅	—	237	1	no	Hall
27	C₇₉	C₂×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented, Sylow
28	C₃×C₅²	C₂×D₇₉	1	1	yes	characteristic, complemented, Hall
29	C₂×D₁₅	—	395	6	no	—
30	C₂×C₅²	D₂₃₇	1	1	yes	characteristic, complemented
31	C₅⋊D₅	—	237	2	no	—
32	C₂×C₃×C₅	D₃₉₅	1	6	yes	complemented
33	D₁₅	—	395	12	no	—
34	C₅²	C₂×D₂₃₇	1	1	yes	characteristic, complemented, Sylow
35	C₂×D₅	—	1185	6	no	—
36	C₃×C₅	C₂×D₃₉₅	1	6	yes	complemented
37	C₂×D₃	—	1975	1	no	Hall
38	C₂×C₅	D₁₁₈₅	1	6	yes	complemented
39	D₅	—	1185	12	no	—
40	C₂×C₃	C₅⋊D₃₉₅	1	1	yes	characteristic, complemented
41	D₃	—	1975	2	no	—
42	C₅	C₂×D₁₁₈₅	1	6	yes	complemented
43	C₂²	—	5925	1	no	Sylow
44	C₃	C₂×C₅⋊D₃₉₅	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	5925	2	no	—
46	C₂	C₃⋊(C₅⋊D₃₉₅)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊(C₅⋊D₃₉₅)
commutator, cosocle, hypocenter	C₃×C₅²×C₇₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₇₉	C₂
LCS	G ▷ C₃×C₅²×C₇₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₅⋊D₃₉₅)	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₇₉	C₂	semidirect
4. C₃×C₅²×C₇₉	C₂²	semidirect
7. C₂×C₅²×C₇₉	D₃	semidirect
9. C₂×C₃×C₅×C₇₉	D₅	semidirect
10. C₅²×C₇₉	C₂×D₃	semidirect
12. C₃×C₅×C₇₉	C₂×D₅	semidirect
14. C₂×C₅×C₇₉	D₁₅	semidirect
16. C₂×C₃×C₇₉	C₅⋊D₅	semidirect
18. C₅×C₇₉	C₂×D₁₅	semidirect
21. C₃×C₇₉	C₂×C₅⋊D₅	semidirect
22. C₂×C₇₉	C₃⋊(C₅⋊D₅)	semidirect
24. C₂×C₃×C₅²	D₇₉	semidirect
27. C₇₉	C₂×C₃⋊(C₅⋊D₅)	semidirect
28. C₃×C₅²	C₂×D₇₉	semidirect
30. C₂×C₅²	D₂₃₇	semidirect
32. C₂×C₃×C₅	D₃₉₅	semidirect
34. C₅²	C₂×D₂₃₇	semidirect
36. C₃×C₅	C₂×D₃₉₅	semidirect
38. C₂×C₅	D₁₁₈₅	semidirect
40. C₂×C₃	C₅⋊D₃₉₅	semidirect
42. C₅	C₂×D₁₁₈₅	semidirect
44. C₃	C₂×C₅⋊D₃₉₅	semidirect
46. C₂	C₃⋊(C₅⋊D₃₉₅)	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⋊(C₅⋊D₃₉₅)	2
C₂×C₃×C₅²×C₇₉	2
C₂×C₅⋊D₃₉₅	3
C₂×D₁₁₈₅	5
C₂×C₃⋊(C₅⋊D₅)	79

Subgroups — C2×C3⋊(C5⋊D395) #37557281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊(C₅⋊D₃₉₅) #37557281