Subgroups — C₅×#63256 #13062825

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	C₅×D₆₈	C₂	1	3	yes	maximal, complemented
3	C₄×C₅×D₁₇	C₂	1	3	yes	maximal, complemented
4	C₂×C₅×D₁₇	C₂²	1	3	yes	—
5	C₄×C₅×C₁₇	C₂²	1	3	yes	—
6	C₅×Dic₁₇	C₂²	1	1	yes	characteristic
7	#63256	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₁₇	C₂³	1	1	yes	characteristic
9	C₅×D₁₇	—	2	3	no	—
10	Q₈×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented
11	D₆₈	C₂×C₅	1	3	yes	complemented
12	C₄×D₁₇	C₂×C₅	1	3	yes	complemented
13	C₅×C₁₇	#41	1	1	yes	characteristic, complemented, Hall
14	C₅×#41	—	17	1	no	maximal, Hall
15	C₂×D₁₇	C₂²×C₅	1	3	yes	—
16	C₄×C₁₇	C₂²×C₅	1	3	yes	—
17	Dic₁₇	C₂²×C₅	1	1	yes	characteristic
18	C₅×Q₈	D₁₇	1	1	yes	characteristic, complemented
19	C₅×D₄	—	17	3	no	—
20	C₂×C₄×C₅	—	17	3	no	—
21	C₂×C₁₇	C₂³×C₅	1	1	yes	characteristic
22	D₁₇	—	2	3	no	—
23	C₂²×C₅	—	17	3	no	—
24	C₄×C₅	—	17	1	no	—
25	C₄×C₅	C₂×D₁₇	1	3	yes	—
26	C₁₇	C₅×#41	1	1	yes	characteristic, complemented, Sylow
27	#41	—	17	1	no	Sylow
28	C₂×C₅	—	34	3	no	—
29	C₂×C₅	C₂²×D₁₇	1	1	yes	characteristic
30	Q₈	C₅×D₁₇	1	1	yes	characteristic, complemented
31	D₄	—	17	3	no	—
32	C₂×C₄	—	17	3	no	—
33	C₅	#63256	1	1	yes	characteristic, direct product factor, Sylow
34	C₂²	—	17	3	no	—
35	C₄	—	17	1	no	—
36	C₄	C₂×C₅×D₁₇	1	3	yes	—
37	C₂	—	34	3	no	—
38	C₂	C₂²×C₅×D₁₇	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.