Subgroups — C₁₇×#713 #13062835

Order 1360.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Q₈×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×D₂₀	C₂	1	3	yes	maximal, complemented
3	C₄×D₅×C₁₇	C₂	1	3	yes	maximal, complemented
4	C₂×D₅×C₁₇	C₂²	1	3	yes	—
5	C₄×C₅×C₁₇	C₂²	1	3	yes	—
6	C₁₇×Dic₅	C₂²	1	1	yes	characteristic
7	#41×C₁₇	—	5	1	no	maximal, Hall
8	C₂×C₅×C₁₇	C₂³	1	1	yes	characteristic
9	D₅×C₁₇	—	2	3	no	—
10	Q₈×C₁₇	D₅	1	1	yes	characteristic, complemented
11	D₄×C₁₇	—	5	3	no	—
12	C₂×C₄×C₁₇	—	5	3	no	—
13	C₅×C₁₇	#41	1	1	yes	characteristic, complemented, Hall
14	#713	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂²×C₁₇	—	5	3	no	—
16	C₄×C₁₇	—	5	1	no	—
17	C₄×C₁₇	C₂×D₅	1	3	yes	—
18	C₅×Q₈	C₂×C₁₇	1	1	yes	characteristic, complemented
19	D₂₀	C₂×C₁₇	1	3	yes	complemented
20	C₄×D₅	C₂×C₁₇	1	3	yes	complemented
21	C₂×C₁₇	—	10	3	no	—
22	C₂×C₁₇	C₂²×D₅	1	1	yes	characteristic
23	C₂×D₅	C₂²×C₁₇	1	3	yes	—
24	C₄×C₅	C₂²×C₁₇	1	3	yes	—
25	Dic₅	C₂²×C₁₇	1	1	yes	characteristic
26	C₁₇	#713	1	1	yes	characteristic, direct product factor, Sylow
27	#41	—	5	1	no	Sylow
28	C₂×C₅	C₂³×C₁₇	1	1	yes	characteristic
29	D₅	—	2	3	no	—
30	Q₈	D₅×C₁₇	1	1	yes	characteristic, complemented
31	D₄	—	5	3	no	—
32	C₂×C₄	—	5	3	no	—
33	C₅	#41×C₁₇	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	5	3	no	—
35	C₄	—	5	1	no	—
36	C₄	C₂×D₅×C₁₇	1	3	yes	—
37	C₂	—	10	3	no	—
38	C₂	C₂²×D₅×C₁₇	1	1	yes	characteristic

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

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