Subgroups — C₂₃×#12895 #19160521

Order 5888.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#1726	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1374	C₂	1	6	yes	maximal
3	C₂²×C₁₆×C₂₃	C₂²	1	4	yes	—
4	C₂×C₂₃×#97	C₄	1	3	yes	—
5	C₂×C₄×C₈×C₂₃	C₂²	1	3	yes	—
6	C₂₃×#376	C₄	1	1	yes	characteristic
7	C₂²×C₈×C₂₃	C₂×C₄	1	3	yes	—
8	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
9	C₂×C₄²×C₂₃	C₂×C₄	1	3	yes	—
10	C₂×C₁₆×C₂₃	—	2	12	no	—
11	C₂₃×#97	—	2	6	no	—
12	C₄×C₈×C₂₃	—	2	6	no	—
13	C₂₃×#95	C₈	1	4	yes	—
14	C₂²×C₄×C₂₃	C₂×C₈	1	6	yes	—
15	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₈×C₂₃	—	2	3	no	—
17	C₂×C₈×C₂₃	—	2	3	no	—
18	C₂×C₈×C₂₃	M₁₆	1	6	yes	—
19	C₂×C₈×C₂₃	#41	1	6	yes	—
20	C₄²×C₂₃	—	2	3	no	—
21	C₄²×C₂₃	—	2	3	no	—
22	C₁₆×C₂₃	—	4	4	no	—
23	#12895	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂³×C₂₃	C₂²×C₈	1	1	yes	characteristic
25	C₂×C₄×C₂₃	—	2	6	no	—
26	C₂×C₄×C₂₃	—	2	12	no	—
27	C₂×C₄×C₂₃	#117	1	3	yes	—
28	C₂×C₄×C₂₃	C₂×M₁₆	1	3	yes	—
29	C₈×C₂₃	—	2	6	no	—
30	C₈×C₂₃	#126	1	4	yes	—
31	#1726	C₂×C₂₃	1	1	yes	characteristic
32	#1374	C₂×C₂₃	1	6	yes	—
33	C₂²×C₂₃	#431	1	3	yes	—
34	C₂²×C₂₃	#504	1	4	yes	—
35	C₄×C₂₃	—	4	6	no	—
36	C₄×C₂₃	#383	1	1	yes	characteristic
37	C₄×C₂₃	#432	1	3	yes	—
38	C₂²×C₁₆	C₂²×C₂₃	1	4	yes	—
39	C₂×#97	C₄×C₂₃	1	3	yes	—
40	C₂×C₄×C₈	C₂²×C₂₃	1	3	yes	—
41	#376	C₄×C₂₃	1	1	yes	characteristic
42	C₂×C₂₃	#1839	1	1	yes	characteristic
43	C₂×C₂₃	#2164	1	6	yes	—
44	C₂²×C₈	C₂×C₄×C₂₃	1	3	yes	—
45	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
46	C₂×C₄²	C₂×C₄×C₂₃	1	3	yes	—
47	C₂×C₁₆	—	2	12	no	—
48	#97	—	2	6	no	—
49	C₄×C₈	—	2	6	no	—
50	#95	C₈×C₂₃	1	4	yes	—
51	C₂₃	#12895	1	1	yes	characteristic, direct product factor, Sylow
52	C₂²×C₄	C₂×C₈×C₂₃	1	6	yes	—
53	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
54	C₂×C₈	—	2	3	no	—
55	C₂×C₈	—	2	3	no	—
56	C₂×C₈	M₁₆×C₂₃	1	6	yes	—
57	C₂×C₈	#41×C₂₃	1	6	yes	—
58	C₄²	—	2	3	no	—
59	C₄²	—	2	3	no	—
60	C₁₆	—	4	4	no	—
61	C₂³	C₂²×C₈×C₂₃	1	1	yes	characteristic
62	C₂×C₄	—	2	6	no	—
63	C₂×C₄	—	2	12	no	—
64	C₂×C₄	C₂₃×#117	1	3	yes	—
65	C₂×C₄	C₂×M₁₆×C₂₃	1	3	yes	—
66	C₈	—	2	6	no	—
67	C₈	C₂₃×#126	1	4	yes	—
68	C₂²	C₂₃×#431	1	3	yes	—
69	C₂²	C₂₃×#504	1	4	yes	—
70	C₄	—	4	6	no	—
71	C₄	C₂₃×#383	1	1	yes	characteristic
72	C₄	C₂₃×#432	1	3	yes	—
73	C₂	C₂₃×#1839	1	1	yes	characteristic
74	C₂	C₂₃×#2164	1	6	yes	—

	subgroup	G/H
center	C₂²×C₈×C₂₃	C₂³
commutator	C₂³	C₂²×C₈×C₂₃
Frattini, cosocle	C₂²×C₈	C₂³×C₂₃
socle, prime radical	C₂³×C₂₃	C₂²×C₈
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
23. #12895	C₂₃	direct (N × H)
51. C₂₃	#12895	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#1726	2
C₂₃×#1374	2
#12895	23

Subgroups — C23×#12895 #19160521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#12895 #19160521