Subgroups — C₂×C₄×C₂₃×C₁₇₃ #72208595

Order 31832.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×C₁₇₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₃×C₁₇₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₂₃×C₁₇₃	C₄	1	2	yes	direct product factor
4	C₂×C₂₃×C₁₇₃	C₂²	1	1	yes	characteristic
5	C₂₃×C₁₇₃	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₄×C₁₇₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₁₇₃	C₂×C₂₃	1	1	yes	characteristic
8	C₄×C₁₇₃	C₂×C₂₃	1	2	yes	direct product factor
9	C₂×C₁₇₃	C₄×C₂₃	1	2	yes	direct product factor
10	C₂×C₁₇₃	C₂²×C₂₃	1	1	yes	characteristic
11	C₂×C₄×C₂₃	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₇₃	C₂×C₄×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₂²×C₂₃	C₂×C₁₇₃	1	1	yes	characteristic
14	C₄×C₂₃	C₂×C₁₇₃	1	2	yes	direct product factor
15	C₂×C₂₃	C₄×C₁₇₃	1	2	yes	direct product factor
16	C₂×C₂₃	C₂²×C₁₇₃	1	1	yes	characteristic
17	C₂₃	C₂×C₄×C₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₄	C₂₃×C₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂²	C₂×C₂₃×C₁₇₃	1	1	yes	characteristic
20	C₄	C₂×C₂₃×C₁₇₃	1	2	yes	direct product factor
21	C₂	C₄×C₂₃×C₁₇₃	1	2	yes	direct product factor
22	C₂	C₂²×C₂₃×C₁₇₃	1	1	yes	characteristic

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.