Subgroups — C₄²×C₁₇×C₅₃ #72192589

Order 14416.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₇×C₅₃	C₂	1	3	yes	maximal
2	C₂²×C₁₇×C₅₃	C₂²	1	1	yes	characteristic
3	C₄×C₁₇×C₅₃	C₄	1	6	yes	direct product factor
4	C₂×C₁₇×C₅₃	C₂×C₄	1	3	yes	—
5	C₁₇×C₅₃	C₄²	1	1	yes	characteristic, direct product factor, Hall
6	C₄²×C₅₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₄×C₅₃	C₂×C₁₇	1	3	yes	—
8	C₄²×C₁₇	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₅₃	C₂²×C₁₇	1	1	yes	characteristic
10	C₄×C₅₃	C₄×C₁₇	1	6	yes	direct product factor
11	C₂×C₄×C₁₇	C₂×C₅₃	1	3	yes	—
12	C₂×C₅₃	C₂×C₄×C₁₇	1	3	yes	—
13	C₂²×C₁₇	C₂²×C₅₃	1	1	yes	characteristic
14	C₄×C₁₇	C₄×C₅₃	1	6	yes	direct product factor
15	C₅₃	C₄²×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₁₇	C₂×C₄×C₅₃	1	3	yes	—
17	C₁₇	C₄²×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₄²	C₁₇×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₄	C₂×C₁₇×C₅₃	1	3	yes	—
20	C₂²	C₂²×C₁₇×C₅₃	1	1	yes	characteristic
21	C₄	C₄×C₁₇×C₅₃	1	6	yes	direct product factor
22	C₂	C₂×C₄×C₁₇×C₅₃	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.