Subgroups — C₂×C₁₇×C₃⋊(C₁₃⋊D₁₃) #46828390

Order 34476.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃⋊(C₁₃⋊D₁₃)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₃²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×C₁₃⋊D₁₃	—	3	1	no	maximal, Hall
4	C₃×C₁₃²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₇×C₁₃⋊D₁₃	—	3	2	no	—
6	C₂×C₁₃²×C₁₇	D₃	1	1	yes	characteristic, complemented
7	C₁₃²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₇×D₃₉	—	13	14	no	maximal
9	C₂×C₃⋊(C₁₃⋊D₁₃)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₁₃×C₁₇	D₁₃	1	14	yes	complemented
11	C₁₇×D₃₉	—	13	28	no	—
12	C₂×C₃×C₁₃²	C₂×C₁₇	1	1	yes	characteristic, complemented
13	C₃⋊(C₁₃⋊D₁₃)	C₂×C₁₇	1	2	yes	direct product factor
14	C₂×C₁₇×D₁₃	—	39	14	no	—
15	C₂×C₁₃⋊D₁₃	—	3	1	no	Hall
16	C₃×C₁₃×C₁₇	C₂×D₁₃	1	14	yes	complemented
17	C₃×C₁₃²	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₃×C₁₇	D₃₉	1	14	yes	complemented
19	C₁₇×D₁₃	—	39	28	no	—
20	C₂×C₁₃²	D₃×C₁₇	1	1	yes	characteristic, complemented
21	C₁₃⋊D₁₃	—	3	2	no	—
22	C₁₃×C₁₇	C₂×D₃₉	1	14	yes	complemented
23	C₂×D₃×C₁₇	—	169	1	no	Hall
24	C₁₃²	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
25	C₂×D₃₉	—	13	14	no	—
26	C₂×C₃×C₁₇	C₁₃⋊D₁₃	1	1	yes	characteristic, complemented
27	D₃×C₁₇	—	169	2	no	—
28	C₂×C₃×C₁₃	C₁₇×D₁₃	1	14	yes	complemented
29	D₃₉	—	13	28	no	—
30	C₂²×C₁₇	—	507	1	no	Hall
31	C₂×D₁₃	—	39	14	no	—
32	C₃×C₁₇	C₂×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Hall
33	C₃×C₁₃	C₂×C₁₇×D₁₃	1	14	yes	complemented
34	C₂×C₁₇	—	507	2	no	—
35	C₂×C₁₇	C₃⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic, direct product factor
36	C₂×C₁₃	C₁₇×D₃₉	1	14	yes	complemented
37	D₁₃	—	39	28	no	—
38	C₁₇	C₂×C₃⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic, direct product factor, Sylow
39	C₁₃	C₂×C₁₇×D₃₉	1	14	yes	complemented
40	C₂×D₃	—	169	1	no	Hall
41	C₂×C₃	C₁₇×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented
42	D₃	—	169	2	no	—
43	C₂²	—	507	1	no	Sylow
44	C₃	C₂×C₁₇×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	507	2	no	—
46	C₂	C₁₇×C₃⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	C₃⋊(C₁₃⋊D₁₃)
commutator, cosocle, hypocenter	C₃×C₁₃²	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃²×C₁₇	C₂
LCS	G ▷ C₃×C₁₃²
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₃⋊(C₁₃⋊D₁₃)	C₂	direct (N × H)
2. C₂×C₃×C₁₃²×C₁₇	C₂	semidirect
4. C₃×C₁₃²×C₁₇	C₂²	semidirect
6. C₂×C₁₃²×C₁₇	D₃	semidirect
7. C₁₃²×C₁₇	C₂×D₃	semidirect
9. C₂×C₃⋊(C₁₃⋊D₁₃)	C₁₇	direct (N × H)
10. C₂×C₃×C₁₃×C₁₇	D₁₃	semidirect
12. C₂×C₃×C₁₃²	C₂×C₁₇	semidirect
13. C₃⋊(C₁₃⋊D₁₃)	C₂×C₁₇	direct (N × H)
16. C₃×C₁₃×C₁₇	C₂×D₁₃	semidirect
17. C₃×C₁₃²	C₂²×C₁₇	semidirect
18. C₂×C₁₃×C₁₇	D₃₉	semidirect
20. C₂×C₁₃²	D₃×C₁₇	semidirect
22. C₁₃×C₁₇	C₂×D₃₉	semidirect
24. C₁₃²	C₂×D₃×C₁₇	semidirect
26. C₂×C₃×C₁₇	C₁₃⋊D₁₃	semidirect
28. C₂×C₃×C₁₃	C₁₇×D₁₃	semidirect
32. C₃×C₁₇	C₂×C₁₃⋊D₁₃	semidirect
33. C₃×C₁₃	C₂×C₁₇×D₁₃	semidirect
35. C₂×C₁₇	C₃⋊(C₁₃⋊D₁₃)	direct (N × H)
36. C₂×C₁₃	C₁₇×D₃₉	semidirect
38. C₁₇	C₂×C₃⋊(C₁₃⋊D₁₃)	direct (N × H)
39. C₁₃	C₂×C₁₇×D₃₉	semidirect
41. C₂×C₃	C₁₇×C₁₃⋊D₁₃	semidirect
44. C₃	C₂×C₁₇×C₁₃⋊D₁₃	semidirect
46. C₂	C₁₇×C₃⋊(C₁₃⋊D₁₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×C₃⋊(C₁₃⋊D₁₃)	2
C₂×C₃×C₁₃²×C₁₇	2
C₂×C₁₇×C₁₃⋊D₁₃	3
C₂×C₁₇×D₃₉	13
C₂×C₃⋊(C₁₃⋊D₁₃)	17

Subgroups — C2×C17×C3⋊(C13⋊D13) #46828390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×C₃⋊(C₁₃⋊D₁₃) #46828390