Subgroups — D₅×C₁₁×C₆₇⋊C₃ #36348643

Order 22110.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×C₁₁×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₁₁×C₆₇⋊C₃	—	5	1	no	maximal, Hall
4	C₅×C₁₁×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₁×C₆₇⋊C₃	D₅	1	1	yes	characteristic, direct product factor, Hall
6	D₅×C₆₇⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₁×C₆₇	—	5	1	no	Hall
8	C₅×C₆₇⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₆₇	C₃×D₅	1	1	yes	characteristic, complemented, Hall
10	D₅×C₆₇	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
11	C₂×C₆₇⋊C₃	—	5	1	no	Hall
12	C₅×C₆₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₃×D₅×C₁₁	—	67	1	no	maximal, Hall
14	C₆₇⋊C₃	D₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅×C₁₁	—	67	1	no	Hall
16	C₂×C₆₇	—	5	1	no	Hall
17	D₅×C₁₁	C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
18	C₆₇	C₃×D₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃×C₁₁	—	335	1	no	Hall
20	C₅×C₁₁	C₂×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁	—	67	1	no	Hall
22	C₃×D₅	—	67	1	no	Hall
23	C₂×C₁₁	—	5	1	no	Hall
24	C₃×C₅	—	67	1	no	Hall
25	C₁₁	D₅×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
26	D₅	C₁₁×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₃	—	335	1	no	Hall
28	C₅	C₂×C₁₁×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
29	C₃	—	67	1	no	Sylow
30	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	D₅×C₆₇⋊C₃
commutator, cosocle, hypocenter	C₅×C₆₇	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₆₇	C₂×C₃
LCS	G ▷ C₅×C₆₇
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×C₆₇⋊C₃	C₂	semidirect
2. D₅×C₁₁×C₆₇	C₃	semidirect
4. C₅×C₁₁×C₆₇	C₂×C₃	semidirect
5. C₁₁×C₆₇⋊C₃	D₅	direct (N × H)
6. D₅×C₆₇⋊C₃	C₁₁	direct (N × H)
8. C₅×C₆₇⋊C₃	C₂×C₁₁	semidirect
9. C₁₁×C₆₇	C₃×D₅	semidirect
10. D₅×C₆₇	C₃×C₁₁	semidirect
12. C₅×C₆₇	C₂×C₃×C₁₁	semidirect
14. C₆₇⋊C₃	D₅×C₁₁	direct (N × H)
17. D₅×C₁₁	C₆₇⋊C₃	direct (N × H)
18. C₆₇	C₃×D₅×C₁₁	semidirect
20. C₅×C₁₁	C₂×C₆₇⋊C₃	semidirect
25. C₁₁	D₅×C₆₇⋊C₃	direct (N × H)
26. D₅	C₁₁×C₆₇⋊C₃	direct (N × H)
28. C₅	C₂×C₁₁×C₆₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₁×C₆₇⋊C₃	2
D₅×C₁₁×C₆₇	3
C₂×C₁₁×C₆₇⋊C₃	5
D₅×C₆₇⋊C₃	11
C₃×D₅×C₁₁	67

Subgroups — D5×C11×C67⋊C3 #36348643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₁×C₆₇⋊C₃ #36348643