Subgroups — C₂²×#595 #63265

Order 272.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#595	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₁₇	C₄	1	1	yes	characteristic, complemented
4	C₂×D₁₇	C₄	1	3	yes	complemented
5	C₂×D₁₇	C₂²	1	3	yes	—
6	#595	C₂²	1	4	yes	direct product factor
7	C₂×C₁₇	C₂×C₄	1	3	yes	complemented
8	D₁₇	C₂×C₄	1	3	yes	complemented
9	D₁₇	C₂³	1	1	yes	characteristic
10	C₁₇	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
11	C₂²×C₄	—	17	1	no	maximal, Sylow
12	C₂³	—	17	1	no	—
13	C₂×C₄	—	17	6	no	—
14	C₂²	—	17	3	no	—
15	C₂²	—	17	3	no	—
16	C₂²	#595	1	1	yes	characteristic, direct product factor
17	C₄	—	17	4	no	—
18	C₂	—	17	1	no	—
19	C₂	—	17	3	no	—
20	C₂	C₂×#595	1	3	yes	direct product factor

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.