Subgroups — C₁₇×D₁₃×D₄₁ #49136166

Order 36244.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×D₅₃₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×D₁₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₁₇×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×C₁₇×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₇×D₄₁	—	13	1	no	maximal, Hall
6	D₁₃×D₄₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₇×C₄₁	—	13	1	no	—
8	C₁₇×D₄₁	—	13	1	no	—
9	C₁₇×D₄₁	D₁₃	1	1	yes	characteristic, direct product factor
10	D₅₃₃	C₂×C₁₇	1	1	yes	characteristic, complemented
11	C₁₃×D₄₁	C₂×C₁₇	1	1	yes	characteristic, complemented
12	D₁₃×C₄₁	C₂×C₁₇	1	1	yes	characteristic, complemented
13	C₂×C₁₇×D₁₃	—	41	1	no	maximal, Hall
14	C₁₇×C₄₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₁₃×C₄₁	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃×C₁₇	—	41	1	no	—
17	C₁₇×D₁₃	—	41	1	no	—
18	C₁₇×D₁₃	D₄₁	1	1	yes	characteristic, direct product factor
19	C₁₃×C₁₇	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
20	C₂×D₄₁	—	13	1	no	Hall
21	C₂×C₄₁	—	13	1	no	—
22	D₄₁	—	13	1	no	—
23	D₄₁	C₁₇×D₁₃	1	1	yes	characteristic, direct product factor
24	C₂²×C₁₇	—	533	1	no	Hall
25	C₂×D₁₃	—	41	1	no	Hall
26	C₄₁	C₂×C₁₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₇	—	13	1	no	—
28	C₂×C₁₇	—	533	1	no	—
29	C₂×C₁₇	—	41	1	no	—
30	C₂×C₁₃	—	41	1	no	—
31	D₁₃	—	41	1	no	—
32	D₁₃	C₁₇×D₄₁	1	1	yes	characteristic, direct product factor
33	C₁₇	D₁₃×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
34	C₁₃	C₂×C₁₇×D₄₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	533	1	no	Sylow
36	C₂	—	13	1	no	—
37	C₂	—	533	1	no	—
38	C₂	—	41	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	D₁₃×D₄₁
commutator, cosocle, hypocenter	C₁₃×C₄₁	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₇×C₄₁	C₂²
LCS	G ▷ C₁₃×C₄₁
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×D₅₃₃	C₂	semidirect
2. C₁₇×D₁₃×C₄₁	C₂	semidirect
3. C₁₃×C₁₇×D₄₁	C₂	semidirect
4. C₁₃×C₁₇×C₄₁	C₂²	semidirect
6. D₁₃×D₄₁	C₁₇	direct (N × H)
9. C₁₇×D₄₁	D₁₃	direct (N × H)
10. D₅₃₃	C₂×C₁₇	semidirect
11. C₁₃×D₄₁	C₂×C₁₇	semidirect
12. D₁₃×C₄₁	C₂×C₁₇	semidirect
14. C₁₇×C₄₁	C₂×D₁₃	semidirect
15. C₁₃×C₄₁	C₂²×C₁₇	semidirect
18. C₁₇×D₁₃	D₄₁	direct (N × H)
19. C₁₃×C₁₇	C₂×D₄₁	semidirect
23. D₄₁	C₁₇×D₁₃	direct (N × H)
26. C₄₁	C₂×C₁₇×D₁₃	semidirect
32. D₁₃	C₁₇×D₄₁	direct (N × H)
33. C₁₇	D₁₃×D₄₁	direct (N × H)
34. C₁₃	C₂×C₁₇×D₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×D₅₃₃	2
C₁₇×D₁₃×C₄₁	2
C₁₃×C₁₇×D₄₁	2
C₂×C₁₇×D₄₁	13
D₁₃×D₄₁	17
C₂×C₁₇×D₁₃	41

Subgroups — C17×D13×D41 #49136166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×D₁₃×D₄₁ #49136166