Subgroups — C₄²×C₅×C₃₀₇ #72201800

Order 24560.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₃₀₇	C₂	1	3	yes	maximal
2	C₂²×C₅×C₃₀₇	C₂²	1	1	yes	characteristic
3	C₄×C₅×C₃₀₇	C₄	1	6	yes	direct product factor
4	C₄²×C₃₀₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₃₀₇	C₂×C₄	1	3	yes	—
6	C₂×C₄×C₃₀₇	C₂×C₅	1	3	yes	—
7	C₅×C₃₀₇	C₄²	1	1	yes	characteristic, direct product factor, Hall
8	C₂²×C₃₀₇	C₂²×C₅	1	1	yes	characteristic
9	C₄×C₃₀₇	C₄×C₅	1	6	yes	direct product factor
10	C₂×C₃₀₇	C₂×C₄×C₅	1	3	yes	—
11	C₃₀₇	C₄²×C₅	1	1	yes	characteristic, direct product factor, Sylow
12	C₄²×C₅	C₃₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₄×C₅	C₂×C₃₀₇	1	3	yes	—
14	C₂²×C₅	C₂²×C₃₀₇	1	1	yes	characteristic
15	C₄×C₅	C₄×C₃₀₇	1	6	yes	direct product factor
16	C₄²	C₅×C₃₀₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₅	C₂×C₄×C₃₀₇	1	3	yes	—
18	C₂×C₄	C₂×C₅×C₃₀₇	1	3	yes	—
19	C₅	C₄²×C₃₀₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂²	C₂²×C₅×C₃₀₇	1	1	yes	characteristic
21	C₄	C₄×C₅×C₃₀₇	1	6	yes	direct product factor
22	C₂	C₂×C₄×C₅×C₃₀₇	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.