Subgroups — C₄²×C₁₉×C₄₁ #72190811

Order 12464.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₉×C₄₁	C₂	1	3	yes	maximal
2	C₂²×C₁₉×C₄₁	C₂²	1	1	yes	characteristic
3	C₄×C₁₉×C₄₁	C₄	1	6	yes	direct product factor
4	C₂×C₁₉×C₄₁	C₂×C₄	1	3	yes	—
5	C₁₉×C₄₁	C₄²	1	1	yes	characteristic, direct product factor, Hall
6	C₄²×C₄₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₄×C₄₁	C₂×C₁₉	1	3	yes	—
8	C₄²×C₁₉	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₄₁	C₂²×C₁₉	1	1	yes	characteristic
10	C₄×C₄₁	C₄×C₁₉	1	6	yes	direct product factor
11	C₂×C₄×C₁₉	C₂×C₄₁	1	3	yes	—
12	C₂×C₄₁	C₂×C₄×C₁₉	1	3	yes	—
13	C₂²×C₁₉	C₂²×C₄₁	1	1	yes	characteristic
14	C₄×C₁₉	C₄×C₄₁	1	6	yes	direct product factor
15	C₄₁	C₄²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₁₉	C₂×C₄×C₄₁	1	3	yes	—
17	C₁₉	C₄²×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₄²	C₁₉×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₄	C₂×C₁₉×C₄₁	1	3	yes	—
20	C₂²	C₂²×C₁₉×C₄₁	1	1	yes	characteristic
21	C₄	C₄×C₁₉×C₄₁	1	6	yes	direct product factor
22	C₂	C₂×C₄×C₁₉×C₄₁	1	3	yes	—

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.