Subgroups — C₄²×C₂₉×C₃₁ #72192529

Order 14384.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂₉×C₃₁	C₂	1	3	yes	maximal
2	C₂²×C₂₉×C₃₁	C₂²	1	1	yes	characteristic
3	C₄×C₂₉×C₃₁	C₄	1	6	yes	direct product factor
4	C₂×C₂₉×C₃₁	C₂×C₄	1	3	yes	—
5	C₂₉×C₃₁	C₄²	1	1	yes	characteristic, direct product factor, Hall
6	C₄²×C₃₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₄²×C₂₉	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₄×C₃₁	C₂×C₂₉	1	3	yes	—
9	C₂×C₄×C₂₉	C₂×C₃₁	1	3	yes	—
10	C₂²×C₃₁	C₂²×C₂₉	1	1	yes	characteristic
11	C₄×C₃₁	C₄×C₂₉	1	6	yes	direct product factor
12	C₂²×C₂₉	C₂²×C₃₁	1	1	yes	characteristic
13	C₄×C₂₉	C₄×C₃₁	1	6	yes	direct product factor
14	C₂×C₃₁	C₂×C₄×C₂₉	1	3	yes	—
15	C₂×C₂₉	C₂×C₄×C₃₁	1	3	yes	—
16	C₃₁	C₄²×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₂₉	C₄²×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₄²	C₂₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₄	C₂×C₂₉×C₃₁	1	3	yes	—
20	C₂²	C₂²×C₂₉×C₃₁	1	1	yes	characteristic
21	C₄	C₄×C₂₉×C₃₁	1	6	yes	direct product factor
22	C₂	C₂×C₄×C₂₉×C₃₁	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.