Subgroups — C₃⋊(C₇⋊#13184069) #49153192

Order 37380.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₅×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₇⋊#13184069	—	3	1	no	maximal, Hall
3	C₃×C₅×C₇×C₈₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₈₆₉	—	5	1	no	maximal, Hall
5	C₇×D₅×C₈₉	D₃	1	1	yes	characteristic
6	C₃⋊#13184069	—	7	1	no	maximal, Hall
7	C₂×C₃×C₇×C₈₉	—	5	1	no	—
8	C₅×C₇×C₈₉	Dic₃	1	1	yes	characteristic, complemented, Hall
9	C₃×D₅×C₈₉	D₇	1	1	yes	characteristic
10	Dic₆₂₃	—	15	1	no	Hall
11	C₃×C₇×C₈₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	#13184069	—	21	1	no	Hall
13	C₃×C₅×C₈₉	Dic₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇×C₈₉	—	5	1	no	—
15	Dic₂₆₇	—	35	1	no	Hall
16	D₅×C₈₉	D₂₁	1	1	yes	characteristic
17	C₇×C₈₉	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₈₉	—	5	1	no	—
19	C₅×C₈₉	Dic₂₁	1	1	yes	characteristic, complemented, Hall
20	C₃⋊(C₇⋊AGL(1,𝔽₅))	—	89	1	no	maximal, Hall
21	Dic₈₉	—	105	1	no	Hall
22	C₃×C₈₉	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇×D₅	D₈₉	1	1	yes	characteristic
24	C₂×C₈₉	—	5	1	no	—
25	C₇⋊AGL(1,𝔽₅)	—	267	1	no	Hall
26	C₃×C₅×C₇	Dic₈₉	1	1	yes	characteristic, complemented, Hall
27	C₈₉	C₃⋊(C₇⋊AGL(1,𝔽₅))	1	1	yes	characteristic, complemented, Sylow
28	Dic₂₁	—	445	1	no	Hall
29	C₇×D₅	D₂₆₇	1	1	yes	characteristic
30	ΓL(1,𝔽₁₆)	—	623	1	no	Hall
31	C₂×C₃×C₇	—	5	1	no	—
32	C₅×C₇	Dic₂₆₇	1	1	yes	characteristic, complemented, Hall
33	C₃×D₅	D₆₂₃	1	1	yes	characteristic
34	Dic₇	—	1335	1	no	Hall
35	C₃×C₇	#13184069	1	1	yes	characteristic, complemented, Hall
36	AGL(1,𝔽₅)	—	1869	1	no	Hall
37	C₃×C₅	Dic₆₂₃	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇	—	5	1	no	—
39	Dic₃	—	3115	1	no	Hall
40	D₅	D₁₈₆₉	1	1	yes	characteristic
41	C₇	C₃⋊#13184069	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃	—	5	1	no	—
43	C₅	Dic₁₈₆₉	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	9345	1	no	Sylow
45	C₃	C₇⋊#13184069	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅×C₇×C₈₉	C₄
prime radical, cosocle	C₃×C₇×D₅×C₈₉	C₂
LCS	G ▷ C₃×C₅×C₇×C₈₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₇×C₈₉	C₄	semidirect
8. C₅×C₇×C₈₉	Dic₃	semidirect
11. C₃×C₇×C₈₉	AGL(1,𝔽₅)	semidirect
13. C₃×C₅×C₈₉	Dic₇	semidirect
17. C₇×C₈₉	ΓL(1,𝔽₁₆)	semidirect
19. C₅×C₈₉	Dic₂₁	semidirect
22. C₃×C₈₉	C₇⋊AGL(1,𝔽₅)	semidirect
26. C₃×C₅×C₇	Dic₈₉	semidirect
27. C₈₉	C₃⋊(C₇⋊AGL(1,𝔽₅))	semidirect
32. C₅×C₇	Dic₂₆₇	semidirect
35. C₃×C₇	#13184069	semidirect
37. C₃×C₅	Dic₆₂₃	semidirect
41. C₇	C₃⋊#13184069	semidirect
43. C₅	Dic₁₈₆₉	semidirect
45. C₃	C₇⋊#13184069	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×D₅×C₈₉	2
C₇⋊#13184069	3
Dic₁₈₆₉	5
C₃⋊#13184069	7
C₃⋊(C₇⋊AGL(1,𝔽₅))	89

Subgroups — C3⋊(C7⋊#13184069) #49153192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₇⋊#13184069) #49153192