Subgroups — C₂₃×#10691 #19158317

Order 5888.

372 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#1304	C₂	1	7	yes	maximal
2	C₂₃×#379	C₂²	1	7	yes	—
3	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
4	C₂×C₂²⋊C₄×C₂₃	—	2	21	no	—
5	C₂⁴×C₂₃	—	8	3	no	—
6	C₂⁴×C₂₃	#41	1	7	yes	—
7	C₂²×C₄×C₂₃	—	4	7	no	—
8	C₂²⋊C₄×C₂₃	—	8	21	no	—
9	#10691	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂³×C₂₃	—	4	21	no	—
11	C₂³×C₂₃	—	8	8	no	—
12	C₂³×C₂₃	#126	1	7	yes	—
13	C₂×C₄×C₂₃	—	8	21	no	—
14	#1304	C₂×C₂₃	1	7	yes	—
15	C₂²×C₂₃	—	2	21	no	—
16	C₂²×C₂₃	—	8	14	no	—
17	C₂²×C₂₃	#401	1	1	yes	characteristic
18	C₄×C₂₃	—	16	7	no	—
19	#379	C₂²×C₂₃	1	7	yes	—
20	C₂×C₂₃	—	4	7	no	—
21	C₂×C₂₃	#2104	1	3	yes	—
22	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
23	C₂×C₂²⋊C₄	—	2	21	no	—
24	C₂₃	#10691	1	1	yes	characteristic, direct product factor, Sylow
25	C₂⁴	—	8	3	no	—
26	C₂⁴	#41×C₂₃	1	7	yes	—
27	C₂²×C₄	—	4	7	no	—
28	C₂²⋊C₄	—	8	21	no	—
29	C₂³	—	4	21	no	—
30	C₂³	—	8	8	no	—
31	C₂³	C₂₃×#126	1	7	yes	—
32	C₂×C₄	—	8	21	no	—
33	C₂²	—	2	21	no	—
34	C₂²	—	8	14	no	—
35	C₂²	C₂₃×#401	1	1	yes	characteristic
36	C₄	—	16	7	no	—
37	C₂	—	4	7	no	—
38	C₂	C₂₃×#2104	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	#401
commutator, Frattini, cosocle	C₂⁵	C₂³×C₂₃
prime radical	C₂⁵×C₂₃	C₂³
LCS	G ▷ C₂⁵ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂⁵×C₂₃ ◁ G

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
9. #10691	C₂₃	direct (N × H)
24. C₂₃	#10691	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#1304	2
#10691	23