Subgroups — C₁₇×#11717962 #28358299

Order 13940.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×D₂₀₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₇×#4223	—	5	1	no	maximal, Hall
4	C₁₇×D₄₁	—	5	1	no	—
5	#11717962	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₇×C₄₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
7	D₂₀₅	C₂×C₁₇	1	1	yes	characteristic
8	C₁₇×AGL(1,𝔽₅)	—	41	1	no	maximal, Hall
9	C₅×C₄₁	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
10	D₅×C₁₇	—	41	1	no	—
11	#4223	—	5	1	no	Hall
12	C₅×C₁₇	#4223	1	1	yes	characteristic, complemented, Hall
13	D₄₁	—	5	1	no	—
14	C₄×C₁₇	—	205	1	no	Hall
15	C₄₁	C₁₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₇	—	205	1	no	—
17	AGL(1,𝔽₅)	—	41	1	no	Hall
18	C₁₇	#11717962	1	1	yes	characteristic, direct product factor, Sylow
19	D₅	—	41	1	no	—
20	C₅	C₁₇×#4223	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	205	1	no	Sylow
22	C₂	—	205	1	no	—

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.