Subgroups — C₂×C₅×#11924781 #26046151

Order 11970.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#11924781	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₇×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₂×#11924781	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
5	C₂×C₅×#4296	—	7	1	no	maximal, Hall
6	C₂×C₅×C₇×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
7	#11924781	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
8	C₅×#4296	—	7	1	no	Hall
9	C₂×C₇×C₁₉⋊C₃	C₃×C₅	1	1	yes	characteristic
10	C₅×C₇×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×C₇⋊C₉	—	19	1	no	maximal, Hall
12	C₂×C₅×C₁₉⋊C₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
13	C₇×C₁₉⋊C₃	C₂×C₃×C₅	1	1	yes	characteristic
14	C₂×#4296	—	7	1	no	Hall
15	C₅×C₇⋊C₉	—	19	1	no	Hall
16	C₅×C₁₉⋊C₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
17	C₂×C₇×C₁₉	C₅×C₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₅×C₇	—	19	1	no	—
19	C₂×C₅×C₁₉	C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
20	#4296	—	7	1	no	Hall
21	C₇×C₁₉	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇⋊C₉	—	19	1	no	Hall
23	C₂×C₁₉⋊C₃	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
24	C₃×C₅×C₇	—	19	1	no	—
25	C₅×C₁₉	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅×C₉	—	133	1	no	Hall
27	C₂×C₅×C₇	#4296	1	1	yes	characteristic, complemented, Hall
28	C₇⋊C₉	—	19	1	no	Hall
29	C₁₉⋊C₃	C₂×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
30	C₅×C₉	—	133	1	no	Hall
31	C₂×C₃×C₇	—	19	1	no	—
32	C₂×C₁₉	C₅×C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
33	C₅×C₇	C₂×#4296	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×C₅	—	19	1	no	—
35	C₃×C₇	—	19	1	no	—
36	C₁₉	C₂×C₅×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₉	—	133	1	no	Hall
38	C₃×C₅	—	19	1	no	—
39	C₂×C₇	C₅×#4296	1	1	yes	characteristic, complemented, Hall
40	C₂×C₅	#11924781	1	1	yes	characteristic, direct product factor, Hall
41	C₉	—	133	1	no	Sylow
42	C₇	C₂×C₅×#4296	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	19	1	no	—
44	C₅	C₂×#11924781	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	19	1	no	—
46	C₂	C₅×#11924781	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₅	#11924781
commutator, hypocenter	C₇×C₁₉	C₂×C₅×C₉
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₁₉	C₉
prime radical	C₂×C₅×C₇×C₁₉⋊C₃	C₃
cosocle	C₇×C₁₉⋊C₃	C₂×C₃×C₅
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#11924781	C₂	direct (N × H)
3. C₂×#11924781	C₅	direct (N × H)
6. C₂×C₅×C₇×C₁₉	C₉	semidirect
7. #11924781	C₂×C₅	direct (N × H)
10. C₅×C₇×C₁₉	C₂×C₉	semidirect
17. C₂×C₇×C₁₉	C₅×C₉	semidirect
19. C₂×C₅×C₁₉	C₇⋊C₉	semidirect
21. C₇×C₁₉	C₂×C₅×C₉	semidirect
25. C₅×C₁₉	C₂×C₇⋊C₉	semidirect
27. C₂×C₅×C₇	#4296	semidirect
32. C₂×C₁₉	C₅×C₇⋊C₉	semidirect
33. C₅×C₇	C₂×#4296	semidirect
36. C₁₉	C₂×C₅×C₇⋊C₉	semidirect
39. C₂×C₇	C₅×#4296	semidirect
40. C₂×C₅	#11924781	direct (N × H)
42. C₇	C₂×C₅×#4296	semidirect
44. C₅	C₂×#11924781	direct (N × H)
46. C₂	C₅×#11924781	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#11924781	2
C₂×C₅×C₇×C₁₉⋊C₃	3
C₂×#11924781	5
C₂×C₅×#4296	7
C₂×C₅×C₇⋊C₉	19

Subgroups — C2×C5×#11924781 #26046151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#11924781 #26046151