Subgroups — C₃×C₅⋊#13095535 #37552080

Order 23310.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#11715913	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊#13095535	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₃₇×D₃₅	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×#13095535	—	5	1	no	maximal, Hall
5	C₅×#11715913	C₂×C₃	1	3	yes	complemented
6	C₃×C₅×C₇×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×D₅×C₃₇⋊C₃	—	7	1	no	maximal, Hall
8	C₃₇×D₃₅	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×#11715913	D₅	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅×C₃₇⋊C₃	—	7	1	no	Hall
11	C₃×D₇×C₃₇	—	5	1	no	—
12	#13095535	—	5	3	no	—
13	C₅×C₇×C₃₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
14	C₃×D₅×C₃₇	—	21	1	no	—
15	D₅×C₃₇⋊C₃	—	7	3	no	—
16	C₃×C₇×C₃₇	C₃×D₅	1	1	yes	characteristic, complemented
17	#11715913	C₃×D₅	1	3	yes	complemented
18	C₂×C₃×C₃₇⋊C₃	—	35	1	no	Hall
19	C₃×C₅⋊AGL(1,𝔽₇)	—	37	1	no	maximal, Hall
20	C₃×C₅×C₃₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
21	C₅×C₃₇⋊C₃	—	7	3	no	—
22	D₇×C₃₇	—	5	1	no	Hall
23	D₅×C₃₇	—	21	1	no	Hall
24	C₃×C₃₇⋊C₃	—	7	1	no	Hall
25	C₃×C₅×ΓL(1,𝔽₈)	—	37	1	no	Hall
26	C₇×C₃₇	C₃²×D₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₃₇	—	105	1	no	—
28	C₂×C₃₇⋊C₃	—	35	3	no	—
29	C₃×D₃₅	C₃₇⋊C₃	1	1	yes	characteristic, complemented
30	C₅⋊AGL(1,𝔽₇)	—	37	3	no	—
31	C₅×C₃₇	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
32	C₃×AGL(1,𝔽₇)	—	185	1	no	Hall
33	C₃×C₃₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
34	C₃₇⋊C₃	—	7	3	no	—
35	C₃×C₅×C₇	C₂×C₃₇⋊C₃	1	1	yes	characteristic, complemented
36	C₅×ΓL(1,𝔽₈)	—	37	3	no	—
37	C₃²×D₅	—	259	1	no	Hall
38	C₂×C₃₇	—	105	1	no	Hall
39	D₃₅	C₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
40	C₃×ΓL(1,𝔽₈)	—	37	1	no	Hall
41	C₃²×C₅	—	259	1	no	Hall
42	C₃×D₇	—	5	1	no	—
43	AGL(1,𝔽₇)	—	185	3	no	—
44	C₃₇	C₃×C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
45	C₅×C₇	C₂×C₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
46	C₃×D₅	—	259	3	no	—
47	C₃×D₅	—	21	1	no	—
48	C₃×C₇	D₅×C₃₇⋊C₃	1	1	yes	characteristic, complemented
49	ΓL(1,𝔽₈)	—	37	3	no	—
50	C₂×C₃²	—	1295	1	no	Hall
51	C₃×C₅	—	259	3	no	—
52	C₃×C₅	#13095535	1	1	yes	characteristic, complemented
53	D₇	—	5	1	no	Hall
54	D₅	—	21	1	no	Hall
55	C₃²	—	259	1	no	Sylow
56	C₇	C₃×D₅×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	—	1295	3	no	—
58	C₂×C₃	—	105	1	no	—
59	C₅	C₃×#13095535	1	1	yes	characteristic, complemented, Sylow
60	C₃	—	259	3	no	—
61	C₃	C₅⋊#13095535	1	1	yes	characteristic, direct product factor
62	C₂	—	105	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₅⋊#13095535
commutator, cosocle, hypocenter	C₅×C₇×C₃₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₃₇	C₂×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. C₃×C₅×#11715913	C₂	semidirect
2. C₅⋊#13095535	C₃	direct (N × H)
3. C₃×C₃₇×D₃₅	C₃	semidirect
5. C₅×#11715913	C₂×C₃	semidirect
6. C₃×C₅×C₇×C₃₇	C₂×C₃	semidirect
8. C₃₇×D₃₅	C₃²	semidirect
9. C₃×#11715913	D₅	semidirect
13. C₅×C₇×C₃₇	C₂×C₃²	semidirect
16. C₃×C₇×C₃₇	C₃×D₅	semidirect
17. #11715913	C₃×D₅	semidirect
20. C₃×C₅×C₃₇	AGL(1,𝔽₇)	semidirect
26. C₇×C₃₇	C₃²×D₅	semidirect
29. C₃×D₃₅	C₃₇⋊C₃	semidirect
31. C₅×C₃₇	C₃×AGL(1,𝔽₇)	semidirect
33. C₃×C₃₇	C₅⋊AGL(1,𝔽₇)	semidirect
35. C₃×C₅×C₇	C₂×C₃₇⋊C₃	semidirect
39. D₃₅	C₃×C₃₇⋊C₃	semidirect
44. C₃₇	C₃×C₅⋊AGL(1,𝔽₇)	semidirect
45. C₅×C₇	C₂×C₃×C₃₇⋊C₃	semidirect
48. C₃×C₇	D₅×C₃₇⋊C₃	semidirect
52. C₃×C₅	#13095535	semidirect
56. C₇	C₃×D₅×C₃₇⋊C₃	semidirect
59. C₅	C₃×#13095535	semidirect
61. C₃	C₅⋊#13095535	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×#11715913	2
C₅⋊#13095535	3
C₃×C₃₇×D₃₅	3
C₃×#13095535	5
C₃×D₅×C₃₇⋊C₃	7
C₃×C₅⋊AGL(1,𝔽₇)	37

Subgroups — C3×C5⋊#13095535 #37552080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅⋊#13095535 #37552080