Subgroups — C₅×C₈×C₁₉² #72192608

Order 14440.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₁₉²	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₄×C₅×C₁₉²	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₁₉²	C₄	1	1	yes	characteristic
4	C₅×C₁₉²	C₈	1	1	yes	characteristic, direct product factor, Hall
5	C₄×C₁₉²	C₂×C₅	1	1	yes	characteristic
6	C₅×C₈×C₁₉	C₁₉	1	20	yes	maximal, direct product factor
7	C₂×C₁₉²	C₄×C₅	1	1	yes	characteristic
8	C₄×C₅×C₁₉	C₂×C₁₉	1	20	yes	—
9	C₁₉²	C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₅×C₁₉	C₄×C₁₉	1	20	yes	—
11	C₈×C₁₉	C₅×C₁₉	1	20	yes	direct product factor
12	C₅×C₁₉	C₈×C₁₉	1	20	yes	direct product factor
13	C₄×C₁₉	C₂×C₅×C₁₉	1	20	yes	—
14	C₅×C₈	C₁₉²	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₁₉	C₄×C₅×C₁₉	1	20	yes	—
16	C₄×C₅	C₂×C₁₉²	1	1	yes	characteristic
17	C₁₉	C₅×C₈×C₁₉	1	20	yes	direct product factor
18	C₂×C₅	C₄×C₁₉²	1	1	yes	characteristic
19	C₈	C₅×C₁₉²	1	1	yes	characteristic, direct product factor, Sylow
20	C₅	C₈×C₁₉²	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	C₂×C₅×C₁₉²	1	1	yes	characteristic
22	C₂	C₄×C₅×C₁₉²	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.