Subgroups — C₅×C₁₇×#4223 #28358290

Order 13940.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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