Subgroups — C₁₉×Dic₅×C₆₇ #38764262

Order 25460.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₉×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₉×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄×C₁₉×C₆₇	—	5	1	no	maximal, Hall
4	C₂×C₁₉×C₆₇	D₅	1	1	yes	characteristic
5	Dic₅×C₆₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₉×C₆₇	Dic₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅×C₆₇	C₂×C₁₉	1	1	yes	characteristic
8	C₁₉×Dic₅	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₆₇	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
10	C₄×C₆₇	—	5	1	no	Hall
11	C₂×C₅×C₁₉	C₂×C₆₇	1	1	yes	characteristic
12	C₂×C₆₇	D₅×C₁₉	1	1	yes	characteristic
13	C₅×C₁₉	C₄×C₆₇	1	1	yes	characteristic, complemented, Hall
14	C₄×C₁₉	—	5	1	no	Hall
15	C₆₇	C₁₉×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₁₉	D₅×C₆₇	1	1	yes	characteristic
17	Dic₅	C₁₉×C₆₇	1	1	yes	characteristic, direct product factor, Hall
18	C₁₉	Dic₅×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	C₂×C₁₉×C₆₇	1	1	yes	characteristic
20	C₅	C₄×C₁₉×C₆₇	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	5	1	no	Sylow
22	C₂	D₅×C₁₉×C₆₇	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.