Subgroups — C₂₃×#10597479 #28381069

Order 14076.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₃⋊D₅₁	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₇×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₂₃×D₅₁	—	6	2	no	—
4	C₂₃×#595	—	9	1	no	maximal, Hall
5	C₃×C₁₇×C₂₃	—	2	2	no	—
6	C₂₃×#157	—	17	1	no	maximal, Hall
7	C₂₃×D₁₇	—	9	1	no	—
8	#10597479	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃⋊D₃×C₂₃	—	17	1	no	—
10	C₁₇×C₂₃	#157	1	1	yes	characteristic, complemented, Hall
11	C₃⋊D₅₁	C₂×C₂₃	1	1	yes	characteristic
12	C₃²×C₂₃	#595	1	1	yes	characteristic, complemented, Hall
13	C₃²×C₁₇	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
14	D₃×C₂₃	—	102	2	no	—
15	D₅₁	—	6	2	no	—
16	C₄×C₂₃	—	153	1	no	Hall
17	C₃×C₂₃	—	2	2	no	—
18	#595	—	9	1	no	Hall
19	C₃×C₁₇	—	2	2	no	—
20	C₂×C₂₃	—	153	1	no	—
21	#157	—	17	1	no	Hall
22	D₁₇	—	9	1	no	—
23	C₂₃	#10597479	1	1	yes	characteristic, direct product factor, Sylow
24	C₃⋊D₃	—	17	1	no	—
25	C₁₇	C₂₃×#157	1	1	yes	characteristic, complemented, Sylow
26	C₃²	C₂₃×#595	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	102	2	no	—
28	C₄	—	153	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	153	1	no	—

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.