Subgroups — C₂⁵×C₁₉×C₃₇ #72199913

Order 22496.

1496 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₁₉×C₃₇	C₂	1	31	yes	maximal, direct product factor
2	C₂³×C₁₉×C₃₇	C₂²	1	155	yes	direct product factor
3	C₂²×C₁₉×C₃₇	C₂³	1	155	yes	direct product factor
4	C₂×C₁₉×C₃₇	C₂⁴	1	31	yes	direct product factor
5	C₂⁵×C₃₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₉×C₃₇	C₂⁵	1	1	yes	characteristic, direct product factor, Hall
7	C₂⁵×C₁₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁴×C₃₇	C₂×C₁₉	1	31	yes	direct product factor
9	C₂⁴×C₁₉	C₂×C₃₇	1	31	yes	direct product factor
10	C₂³×C₃₇	C₂²×C₁₉	1	155	yes	direct product factor
11	C₂³×C₁₉	C₂²×C₃₇	1	155	yes	direct product factor
12	C₂²×C₃₇	C₂³×C₁₉	1	155	yes	direct product factor
13	C₂²×C₁₉	C₂³×C₃₇	1	155	yes	direct product factor
14	C₂×C₃₇	C₂⁴×C₁₉	1	31	yes	direct product factor
15	C₂×C₁₉	C₂⁴×C₃₇	1	31	yes	direct product factor
16	C₃₇	C₂⁵×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₂⁵	C₁₉×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₁₉	C₂⁵×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₂⁴	C₂×C₁₉×C₃₇	1	31	yes	direct product factor
20	C₂³	C₂²×C₁₉×C₃₇	1	155	yes	direct product factor
21	C₂²	C₂³×C₁₉×C₃₇	1	155	yes	direct product factor
22	C₂	C₂⁴×C₁₉×C₃₇	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.