Subgroups — C₅×C₁₁⋊(Dic₃₇⋊C₃) #37567508

Order 24420.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₁×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₄₀₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₁₁×C₃₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁⋊(Dic₃₇⋊C₃)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₁×C₃₇	C₂×C₃	1	1	yes	characteristic
6	C₂×C₁₁×C₃₇⋊C₃	C₂×C₅	1	1	yes	characteristic
7	C₅×Dic₃₇⋊C₃	—	11	1	no	maximal, Hall
8	C₅×C₁₁×C₃₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	Dic₄₀₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₁₁×C₃₇⋊C₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×C₃₇⋊C₃	D₁₁	1	1	yes	characteristic
12	C₂×C₁₁×C₃₇	C₂×C₃×C₅	1	1	yes	characteristic
13	C₅×Dic₃₇	—	11	1	no	Hall
14	C₃×C₅×Dic₁₁	—	37	1	no	maximal, Hall
15	C₅×C₃₇⋊C₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
16	Dic₃₇⋊C₃	—	11	1	no	Hall
17	C₁₁×C₃₇	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₃₇	C₃×D₁₁	1	1	yes	characteristic
19	C₂×C₃×C₅×C₁₁	—	37	1	no	—
20	C₂×C₃₇⋊C₃	C₅×D₁₁	1	1	yes	characteristic
21	C₅×Dic₁₁	—	37	1	no	Hall
22	C₅×C₃₇	C₃×Dic₁₁	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₁	—	37	1	no	Hall
24	Dic₃₇	—	11	1	no	Hall
25	C₃×Dic₁₁	—	37	1	no	Hall
26	C₃₇⋊C₃	C₅×Dic₁₁	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅×C₁₁	D₃₇⋊C₃	1	1	yes	characteristic
28	C₂×C₃₇	C₃×C₅×D₁₁	1	1	yes	characteristic
29	C₂×C₃×C₁₁	—	37	1	no	—
30	C₃×C₄×C₅	—	407	1	no	Hall
31	C₅×C₁₁	Dic₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
32	Dic₁₁	—	37	1	no	Hall
33	C₃₇	C₃×C₅×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
34	C₃×C₁₁	—	37	1	no	Hall
35	C₂×C₃×C₅	—	37	1	no	—
36	C₂×C₁₁	C₅×D₃₇⋊C₃	1	1	yes	characteristic
37	C₄×C₅	—	407	1	no	Hall
38	C₃×C₅	—	37	1	no	Hall
39	C₃×C₄	—	407	1	no	Hall
40	C₁₁	C₅×Dic₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	C₁₁⋊(D₃₇⋊C₃)	1	1	yes	characteristic
42	C₂×C₃	—	37	1	no	—
43	C₅	C₁₁⋊(Dic₃₇⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	407	1	no	Sylow
45	C₃	—	37	1	no	Sylow
46	C₂	C₅×C₁₁⋊(D₃₇⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	C₁₁⋊(D₃₇⋊C₃)
commutator, hypocenter	C₁₁×C₃₇	C₃×C₄×C₅
Frattini	C₂	C₅×C₁₁⋊(D₃₇⋊C₃)
Fitting, socle	C₂×C₅×C₁₁×C₃₇	C₂×C₃
prime radical	C₂×C₅×C₁₁×C₃₇⋊C₃	C₂
cosocle	C₂×C₁₁×C₃₇	C₂×C₃×C₅
LCS	G ▷ C₁₁×C₃₇
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×Dic₄₀₇	C₃	semidirect
3. C₅×C₁₁×C₃₇⋊C₃	C₄	semidirect
4. C₁₁⋊(Dic₃₇⋊C₃)	C₅	direct (N × H)
8. C₅×C₁₁×C₃₇	C₃×C₄	semidirect
9. Dic₄₀₇	C₃×C₅	semidirect
10. C₁₁×C₃₇⋊C₃	C₄×C₅	semidirect
15. C₅×C₃₇⋊C₃	Dic₁₁	semidirect
17. C₁₁×C₃₇	C₃×C₄×C₅	semidirect
22. C₅×C₃₇	C₃×Dic₁₁	semidirect
26. C₃₇⋊C₃	C₅×Dic₁₁	semidirect
31. C₅×C₁₁	Dic₃₇⋊C₃	semidirect
33. C₃₇	C₃×C₅×Dic₁₁	semidirect
40. C₁₁	C₅×Dic₃₇⋊C₃	semidirect
43. C₅	C₁₁⋊(Dic₃₇⋊C₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₁₁×C₃₇⋊C₃	2
C₅×Dic₄₀₇	3
C₁₁⋊(Dic₃₇⋊C₃)	5
C₅×Dic₃₇⋊C₃	11
C₃×C₅×Dic₁₁	37

Subgroups — C5×C11⋊(Dic37⋊C3) #37567508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁⋊(Dic₃₇⋊C₃) #37567508