Subgroups — C₁₃×C₄₁×D₂₁ #36375596

Order 22386.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₇×C₄₁	—	3	1	no	maximal, Hall
3	C₇×C₁₃×C₄₁	D₃	1	1	yes	characteristic, complemented, Hall
4	D₃×C₁₃×C₄₁	—	7	1	no	maximal, Hall
5	C₄₁×D₂₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₁₃×C₄₁	D₇	1	1	yes	characteristic, complemented, Hall
7	C₂×C₁₃×C₄₁	—	21	1	no	Hall
8	C₃×C₇×C₄₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
9	D₇×C₄₁	—	3	1	no	Hall
10	C₁₃×D₂₁	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₃×C₄₁	D₂₁	1	1	yes	characteristic, direct product factor, Hall
12	C₇×C₄₁	D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₇×C₁₃	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
14	D₃×C₄₁	—	7	1	no	Hall
15	C₁₃×D₇	—	3	1	no	Hall
16	C₃×C₄₁	C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
17	C₇×C₁₃	D₃×C₄₁	1	1	yes	characteristic, complemented, Hall
18	C₂×C₄₁	—	21	1	no	Hall
19	D₃×C₁₃	—	7	1	no	Hall
20	D₂₁	C₁₃×C₄₁	1	1	yes	characteristic, direct product factor, Hall
21	C₄₁	C₁₃×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₃×C₁₃	D₇×C₄₁	1	1	yes	characteristic, complemented, Hall
23	C₂×C₁₃	—	21	1	no	Hall
24	C₃×C₇	C₂×C₁₃×C₄₁	1	1	yes	characteristic, complemented, Hall
25	D₇	—	3	1	no	Hall
26	C₁₃	C₄₁×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	D₃×C₁₃×C₄₁	1	1	yes	characteristic, complemented, Sylow
28	D₃	—	7	1	no	Hall
29	C₃	C₁₃×D₇×C₄₁	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₄₁	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₁₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₄₁	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₁₃×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₃×C₄₁	C₂	semidirect
3. C₇×C₁₃×C₄₁	D₃	semidirect
5. C₄₁×D₂₁	C₁₃	direct (N × H)
6. C₃×C₁₃×C₄₁	D₇	semidirect
8. C₃×C₇×C₄₁	C₂×C₁₃	semidirect
10. C₁₃×D₂₁	C₄₁	direct (N × H)
11. C₁₃×C₄₁	D₂₁	direct (N × H)
12. C₇×C₄₁	D₃×C₁₃	semidirect
13. C₃×C₇×C₁₃	C₂×C₄₁	semidirect
16. C₃×C₄₁	C₁₃×D₇	semidirect
17. C₇×C₁₃	D₃×C₄₁	semidirect
20. D₂₁	C₁₃×C₄₁	direct (N × H)
21. C₄₁	C₁₃×D₂₁	direct (N × H)
22. C₃×C₁₃	D₇×C₄₁	semidirect
24. C₃×C₇	C₂×C₁₃×C₄₁	semidirect
26. C₁₃	C₄₁×D₂₁	direct (N × H)
27. C₇	D₃×C₁₃×C₄₁	semidirect
29. C₃	C₁₃×D₇×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₃×C₄₁	2
C₁₃×D₇×C₄₁	3
D₃×C₁₃×C₄₁	7
C₄₁×D₂₁	13
C₁₃×D₂₁	41

Subgroups — C13×C41×D21 #36375596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₄₁×D₂₁ #36375596