Subgroups — C₂²×C₅×Dic₁₇ #13062826

Order 1360.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₁₇	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₅×C₁₇	C₄	1	4	yes	complemented
4	C₂²×C₅×C₁₇	C₂²	1	3	yes	—
5	C₅×Dic₁₇	C₂²	1	4	yes	direct product factor
6	C₂²×Dic₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₁₇	C₂×C₄	1	6	yes	complemented
8	C₂×C₅×C₁₇	C₂³	1	1	yes	characteristic
9	C₂³×C₁₇	C₂×C₅	1	1	yes	characteristic
10	C₂×Dic₁₇	C₂×C₅	1	6	yes	direct product factor
11	C₅×C₁₇	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₄×C₅	—	17	1	no	maximal, Hall
13	C₂²×C₁₇	C₄×C₅	1	4	yes	complemented
14	C₂²×C₁₇	C₂²×C₅	1	3	yes	—
15	Dic₁₇	C₂²×C₅	1	4	yes	direct product factor
16	C₂³×C₅	D₁₇	1	1	yes	characteristic
17	C₂×C₄×C₅	—	17	6	no	—
18	C₂×C₁₇	C₂×C₄×C₅	1	6	yes	complemented
19	C₂×C₁₇	C₂³×C₅	1	1	yes	characteristic
20	C₂²×C₅	Dic₁₇	1	4	yes	direct product factor
21	C₂²×C₅	C₂×D₁₇	1	3	yes	—
22	C₄×C₅	—	17	4	no	—
23	C₁₇	C₂²×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₄	—	17	1	no	Sylow
25	C₂×C₅	C₂×Dic₁₇	1	6	yes	direct product factor
26	C₂×C₅	C₂²×D₁₇	1	1	yes	characteristic
27	C₂³	C₅×D₁₇	1	1	yes	characteristic
28	C₂×C₄	—	17	6	no	—
29	C₅	C₂²×Dic₁₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²	C₅×Dic₁₇	1	4	yes	direct product factor
31	C₂²	C₂×C₅×D₁₇	1	3	yes	—
32	C₄	—	17	4	no	—
33	C₂	C₂×C₅×Dic₁₇	1	6	yes	direct product factor
34	C₂	C₂²×C₅×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₅	D₁₇
commutator, hypocenter	C₁₇	C₂²×C₄×C₅
Frattini	C₂	C₂²×C₅×D₁₇
Fitting, socle, prime radical	C₂³×C₅×C₁₇	C₂
cosocle	C₂×C₁₇	C₂³×C₅
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂³×C₅

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×Dic₁₇	C₂	direct (N × H)
3. C₂²×C₅×C₁₇	C₄	semidirect
5. C₅×Dic₁₇	C₂²	direct (N × H)
6. C₂²×Dic₁₇	C₅	direct (N × H)
7. C₂×C₅×C₁₇	C₂×C₄	semidirect
10. C₂×Dic₁₇	C₂×C₅	direct (N × H)
11. C₅×C₁₇	C₂²×C₄	semidirect
13. C₂²×C₁₇	C₄×C₅	semidirect
15. Dic₁₇	C₂²×C₅	direct (N × H)
18. C₂×C₁₇	C₂×C₄×C₅	semidirect
20. C₂²×C₅	Dic₁₇	direct (N × H)
23. C₁₇	C₂²×C₄×C₅	semidirect
25. C₂×C₅	C₂×Dic₁₇	direct (N × H)
29. C₅	C₂²×Dic₁₇	direct (N × H)
30. C₂²	C₅×Dic₁₇	direct (N × H)
33. C₂	C₂×C₅×Dic₁₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₅×C₁₇	2
C₂×C₅×Dic₁₇	2
C₂²×Dic₁₇	5
C₂²×C₄×C₅	17

Subgroups — C22×C5×Dic17 #13062826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×Dic₁₇ #13062826