Subgroups — C₂×C₅×Dic₃₄ #13062818

Order 1360.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₁₇	C₂	1	2	yes	maximal
3	C₅×Dic₃₄	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₅×C₁₇	C₂²	1	1	yes	characteristic
5	C₄×C₅×C₁₇	C₂²	1	2	yes	—
6	C₅×Dic₁₇	C₂²	1	4	yes	—
7	C₂×Dic₃₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₁₇	Q₈	1	2	yes	complemented
9	C₂×C₅×C₁₇	C₂³	1	1	yes	characteristic
10	C₂×C₄×C₁₇	C₂×C₅	1	1	yes	characteristic
11	C₂×Dic₁₇	C₂×C₅	1	2	yes	—
12	Dic₃₄	C₂×C₅	1	4	yes	direct product factor
13	C₅×C₁₇	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×Q₈	—	17	1	no	maximal, Hall
15	C₂²×C₁₇	C₂²×C₅	1	1	yes	characteristic
16	C₄×C₁₇	C₂²×C₅	1	2	yes	—
17	Dic₁₇	C₂²×C₅	1	4	yes	—
18	C₅×Q₈	—	17	4	no	—
19	C₂×C₄×C₅	—	17	2	no	—
20	C₂×C₄×C₅	D₁₇	1	1	yes	characteristic
21	C₂×C₁₇	C₅×Q₈	1	2	yes	complemented
22	C₂×C₁₇	C₂³×C₅	1	1	yes	characteristic
23	C₂²×C₅	C₂×D₁₇	1	1	yes	characteristic
24	C₄×C₅	—	17	4	no	—
25	C₄×C₅	C₂×D₁₇	1	2	yes	—
26	C₁₇	C₂×C₅×Q₈	1	1	yes	characteristic, complemented, Sylow
27	C₂×Q₈	—	17	1	no	Sylow
28	C₂×C₅	Dic₃₄	1	2	yes	direct product factor
29	C₂×C₅	C₂²×D₁₇	1	1	yes	characteristic
30	Q₈	—	17	4	no	—
31	C₂×C₄	—	17	2	no	—
32	C₂×C₄	C₅×D₁₇	1	1	yes	characteristic
33	C₅	C₂×Dic₃₄	1	1	yes	characteristic, direct product factor, Sylow
34	C₂²	C₂×C₅×D₁₇	1	1	yes	characteristic
35	C₄	—	17	4	no	—
36	C₄	C₂×C₅×D₁₇	1	2	yes	—
37	C₂	C₅×Dic₃₄	1	2	yes	direct product factor
38	C₂	C₂²×C₅×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₁₇
commutator, cosocle	C₂×C₁₇	C₂³×C₅
Frattini	C₂	C₂²×C₅×D₁₇
Fitting	C₂×C₄×C₅×C₁₇	C₂
socle, prime radical	C₂²×C₅×C₁₇	C₂²
hypercenter	C₂×C₄×C₅	D₁₇
hypocenter	C₁₇	C₂×C₅×Q₈
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅

Complements

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

N	H ≅ G/N	type
3. C₅×Dic₃₄	C₂	direct (N × H)
7. C₂×Dic₃₄	C₅	direct (N × H)
8. C₂×C₅×C₁₇	Q₈	semidirect
12. Dic₃₄	C₂×C₅	direct (N × H)
13. C₅×C₁₇	C₂×Q₈	semidirect
21. C₂×C₁₇	C₅×Q₈	semidirect
26. C₁₇	C₂×C₅×Q₈	semidirect
28. C₂×C₅	Dic₃₄	direct (N × H)
33. C₅	C₂×Dic₃₄	direct (N × H)
37. C₂	C₅×Dic₃₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×C₁₇	2
C₂×C₅×Dic₁₇	2
C₅×Dic₃₄	2
C₂×Dic₃₄	5
C₂×C₅×Q₈	17

Subgroups — C2×C5×Dic34 #13062818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×Dic₃₄ #13062818