Subgroups — D₅×#14556419 #37552016

Order 23310.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#14556419	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₅×C₃₇	C₃	1	1	yes	maximal, characteristic
3	C₂×#14556419	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇×C₃₇	C₂×C₃	1	1	yes	characteristic
5	D₅×#66524	—	7	1	no	maximal, Hall
6	C₇×D₅×C₃₇	C₉	1	1	yes	characteristic, complemented, Hall
7	#14556419	D₅	1	1	yes	characteristic, direct product factor, Hall
8	C₅×#66524	—	7	1	no	Hall
9	C₂×C₃×C₇×C₃₇	—	5	1	no	—
10	C₅×C₇×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
11	C₃×D₅×C₃₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
12	C₃×C₇×C₃₇	C₃×D₅	1	1	yes	characteristic
13	C₂×#66524	—	35	1	no	Hall
14	D₅×C₇⋊C₉	—	37	1	no	maximal, Hall
15	C₃×C₅×C₃₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
16	C₂×C₇×C₃₇	—	5	1	no	Hall
17	D₅×C₃₇	C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
18	#66524	—	7	1	no	Hall
19	C₅×C₇⋊C₉	—	37	1	no	Hall
20	C₇×C₃₇	C₉×D₅	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₃₇	—	5	1	no	—
22	C₃×C₇×D₅	C₃₇⋊C₃	1	1	yes	characteristic
23	C₅×C₃₇	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
24	C₂×C₇⋊C₉	—	185	1	no	Hall
25	C₃×C₃₇	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
26	C₃×C₅×C₇	C₂×C₃₇⋊C₃	1	1	yes	characteristic
27	C₉×D₅	—	259	1	no	Hall
28	C₂×C₃₇	—	5	1	no	Hall
29	C₇×D₅	#66524	1	1	yes	characteristic, complemented, Hall
30	C₇⋊C₉	—	37	1	no	Hall
31	C₅×C₉	—	259	1	no	Hall
32	C₂×C₃×C₇	—	5	1	no	—
33	C₃₇	D₅×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
34	C₅×C₇	C₂×#66524	1	1	yes	characteristic, complemented, Hall
35	C₃×D₅	#11715913	1	1	yes	characteristic
36	C₃×C₇	D₅×C₃₇⋊C₃	1	1	yes	characteristic
37	C₂×C₉	—	1295	1	no	Hall
38	C₃×C₅	C₂×#11715913	1	1	yes	characteristic
39	C₂×C₇	—	5	1	no	Hall
40	D₅	#14556419	1	1	yes	characteristic, direct product factor, Hall
41	C₉	—	259	1	no	Sylow
42	C₇	D₅×#66524	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	5	1	no	—
44	C₅	C₂×#14556419	1	1	yes	characteristic, complemented, Sylow
45	C₃	D₅×#11715913	1	1	yes	characteristic
46	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₅×#11715913
commutator, hypocenter	C₅×C₇×C₃₇	C₂×C₉
Fitting, socle, cosocle	C₃×C₅×C₇×C₃₇	C₂×C₃
prime radical	C₃×C₇×D₅×C₃₇	C₃
LCS	G ▷ C₅×C₇×C₃₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₅×#14556419	C₂	semidirect
6. C₇×D₅×C₃₇	C₉	semidirect
7. #14556419	D₅	direct (N × H)
10. C₅×C₇×C₃₇	C₂×C₉	semidirect
17. D₅×C₃₇	C₇⋊C₉	semidirect
20. C₇×C₃₇	C₉×D₅	semidirect
23. C₅×C₃₇	C₂×C₇⋊C₉	semidirect
29. C₇×D₅	#66524	semidirect
33. C₃₇	D₅×C₇⋊C₉	semidirect
34. C₅×C₇	C₂×#66524	semidirect
40. D₅	#14556419	direct (N × H)
42. C₇	D₅×#66524	semidirect
44. C₅	C₂×#14556419	semidirect

Maximal subgroups

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

subgroup	index
C₅×#14556419	2
C₃×C₇×D₅×C₃₇	3
C₂×#14556419	5
D₅×#66524	7
D₅×C₇⋊C₉	37

Subgroups — D5×#14556419 #37552016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#14556419 #37552016