Subgroups — C₄×C₁₃⋊C₃×C₁₆₇ #39907513

Order 26052.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃⋊C₃×C₁₆₇	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×C₁₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃⋊C₃×C₁₆₇	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₃×C₁₆₇	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₁₆₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×C₄×C₁₆₇	—	13	1	no	maximal, Hall
7	C₂×C₃×C₁₆₇	—	13	1	no	—
8	C₄×C₁₆₇	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₆₇	—	13	1	no	Hall
10	C₂×C₁₆₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic
11	C₁₆₇	C₄×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₄×C₁₃⋊C₃	C₁₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₁₃⋊C₃	C₂×C₁₆₇	1	1	yes	characteristic
14	C₄×C₁₃	C₃×C₁₆₇	1	1	yes	characteristic, complemented, Hall
15	C₁₃⋊C₃	C₄×C₁₆₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₃	C₂×C₃×C₁₆₇	1	1	yes	characteristic
17	C₁₃	C₃×C₄×C₁₆₇	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	13	1	no	Hall
19	C₂×C₃	—	13	1	no	—
20	C₄	C₁₃⋊C₃×C₁₆₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	—	13	1	no	Sylow
22	C₂	C₂×C₁₃⋊C₃×C₁₆₇	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.