Subgroups — C₂⁵×C₁₇×C₂₃ #72190860

Order 12512.

1496 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₁₇×C₂₃	C₂	1	31	yes	maximal, direct product factor
2	C₂³×C₁₇×C₂₃	C₂²	1	155	yes	direct product factor
3	C₂²×C₁₇×C₂₃	C₂³	1	155	yes	direct product factor
4	C₂×C₁₇×C₂₃	C₂⁴	1	31	yes	direct product factor
5	C₂⁵×C₂₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂⁵×C₁₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₇×C₂₃	C₂⁵	1	1	yes	characteristic, direct product factor, Hall
8	C₂⁴×C₂₃	C₂×C₁₇	1	31	yes	direct product factor
9	C₂⁴×C₁₇	C₂×C₂₃	1	31	yes	direct product factor
10	C₂³×C₂₃	C₂²×C₁₇	1	155	yes	direct product factor
11	C₂³×C₁₇	C₂²×C₂₃	1	155	yes	direct product factor
12	C₂²×C₂₃	C₂³×C₁₇	1	155	yes	direct product factor
13	C₂²×C₁₇	C₂³×C₂₃	1	155	yes	direct product factor
14	C₂×C₂₃	C₂⁴×C₁₇	1	31	yes	direct product factor
15	C₂×C₁₇	C₂⁴×C₂₃	1	31	yes	direct product factor
16	C₂⁵	C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₂₃	C₂⁵×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₁₇	C₂⁵×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂⁴	C₂×C₁₇×C₂₃	1	31	yes	direct product factor
20	C₂³	C₂²×C₁₇×C₂₃	1	155	yes	direct product factor
21	C₂²	C₂³×C₁₇×C₂₃	1	155	yes	direct product factor
22	C₂	C₂⁴×C₁₇×C₂₃	1	31	yes	direct product factor

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.