Subgroups — C₁₇×(C₁₃₉⋊C₃)⋊C₄ #43248574

Order 28356.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×C₁₃₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₇×Dic₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇×C₁₃₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₇×C₁₃₉	C₂×C₃	1	1	yes	characteristic
5	C₁₇×C₁₃₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	(C₁₃₉⋊C₃)⋊C₄	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₃₉⋊C₃	C₂×C₁₇	1	1	yes	characteristic
8	Dic₁₃₉	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
9	C₁₃₉⋊C₃	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₃₉	C₂×C₃×C₁₇	1	1	yes	characteristic
11	C₃×C₄×C₁₇	—	139	1	no	maximal, Hall
12	C₁₃₉	C₃×C₄×C₁₇	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₃×C₁₇	—	139	1	no	—
14	C₄×C₁₇	—	139	1	no	Hall
15	C₃×C₁₇	—	139	1	no	Hall
16	C₂×C₁₇	D₁₃₉⋊C₃	1	1	yes	characteristic
17	C₁₇	(C₁₃₉⋊C₃)⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₄	—	139	1	no	Hall
19	C₂×C₃	—	139	1	no	—
20	C₄	—	139	1	no	Sylow
21	C₃	—	139	1	no	Sylow
22	C₂	C₁₇×D₁₃₉⋊C₃	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.