Subgroups — C₂₃×D₁₃×D₂₁ #38737426

Order 25116.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×D₂₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₂₃×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₂₃×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×C₂₃×D₁₃	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂₃×D₉₁	—	3	1	no	—
7	C₁₃×D₇×C₂₃	—	3	1	no	—
8	C₇×C₂₃×D₁₃	D₃	1	1	yes	characteristic, complemented
9	D₃×C₂₃×D₁₃	—	7	1	no	maximal, Hall
10	C₇×C₁₃×C₂₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₂₃×D₂₁	—	13	1	no	maximal, Hall
12	C₂₃×D₃₉	—	7	1	no	—
13	D₃×C₁₃×C₂₃	—	7	1	no	—
14	C₃×C₂₃×D₁₃	D₇	1	1	yes	characteristic, complemented
15	C₂×C₂₃×D₁₃	—	21	1	no	Hall
16	D₁₃×D₂₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₇×C₂₃	—	13	1	no	—
18	C₂₃×D₂₁	—	13	1	no	—
19	C₂₃×D₂₁	D₁₃	1	1	yes	characteristic, direct product factor
20	C₃×C₁₃×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
21	C₂×D₇×C₂₃	—	39	1	no	Hall
22	C₂×C₁₃×C₂₃	—	21	1	no	—
23	C₂₃×D₁₃	—	21	1	no	—
24	C₂₃×D₁₃	D₂₁	1	1	yes	characteristic, direct product factor
25	D₂₇₃	C₂×C₂₃	1	1	yes	characteristic, complemented
26	C₁₃×D₂₁	C₂×C₂₃	1	1	yes	characteristic, complemented
27	C₃×C₇×D₁₃	C₂×C₂₃	1	1	yes	characteristic, complemented
28	C₃×C₇×C₂₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	D₇×D₁₃	—	3	1	no	Hall
30	C₂×C₇×C₂₃	—	13	1	no	—
31	D₇×C₂₃	—	3	1	no	—
32	D₇×C₂₃	—	39	1	no	—
33	C₁₃×C₂₃	C₂×D₂₁	1	1	yes	characteristic, complemented, Hall
34	C₂×D₃×C₂₃	—	91	1	no	Hall
35	C₃×C₇×C₁₃	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
36	D₉₁	—	3	1	no	—
37	C₇×D₁₃	D₃×C₂₃	1	1	yes	characteristic, complemented
38	C₁₃×D₇	—	3	1	no	—
39	C₇×C₂₃	D₃×D₁₃	1	1	yes	characteristic, complemented, Hall
40	D₃×D₁₃	—	7	1	no	Hall
41	C₂×C₃×C₂₃	—	13	1	no	—
42	D₃×C₂₃	—	7	1	no	—
43	D₃×C₂₃	—	91	1	no	—
44	C₂²×C₂₃	—	273	1	no	Hall
45	C₇×C₁₃	C₂×D₃×C₂₃	1	1	yes	characteristic, complemented, Hall
46	C₂×D₂₁	—	13	1	no	Hall
47	D₃₉	—	7	1	no	—
48	C₃×D₁₃	D₇×C₂₃	1	1	yes	characteristic, complemented
49	D₃×C₁₃	—	7	1	no	—
50	C₃×C₂₃	D₇×D₁₃	1	1	yes	characteristic, complemented, Hall
51	C₂×D₁₃	—	21	1	no	Hall
52	C₂×C₂₃	—	13	1	no	—
53	C₂×C₂₃	—	273	1	no	—
54	C₂×C₂₃	—	21	1	no	—
55	C₂×C₃×C₇	—	13	1	no	—
56	D₂₁	—	13	1	no	—
57	D₂₁	C₂₃×D₁₃	1	1	yes	characteristic, direct product factor
58	C₃×C₁₃	C₂×D₇×C₂₃	1	1	yes	characteristic, complemented, Hall
59	C₂×D₇	—	39	1	no	Hall
60	C₂×C₁₃	—	21	1	no	—
61	D₁₃	—	21	1	no	—
62	D₁₃	C₂₃×D₂₁	1	1	yes	characteristic, direct product factor
63	C₂₃	D₁₃×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
64	C₃×C₇	C₂×C₂₃×D₁₃	1	1	yes	characteristic, complemented, Hall
65	C₂×C₇	—	13	1	no	—
66	D₇	—	3	1	no	—
67	D₇	—	39	1	no	—
68	C₁₃	C₂×C₂₃×D₂₁	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₃	—	91	1	no	Hall
70	C₇	D₃×C₂₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	13	1	no	—
72	D₃	—	7	1	no	—
73	D₃	—	91	1	no	—
74	C₂²	—	273	1	no	Sylow
75	C₃	D₇×C₂₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	13	1	no	—
77	C₂	—	273	1	no	—
78	C₂	—	21	1	no	—

	subgroup	G/H
center, hypercenter	C₂₃	D₁₃×D₂₁
commutator, cosocle, hypocenter	C₃×C₇×C₁₃	C₂²×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₂₃	C₂²
LCS	G ▷ C₃×C₇×C₁₃
UCS	C₁ ◁ C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×D₂₇₃	C₂	semidirect
2. C₁₃×C₂₃×D₂₁	C₂	semidirect
3. C₃×C₇×C₂₃×D₁₃	C₂	semidirect
5. C₃×C₇×C₁₃×C₂₃	C₂²	semidirect
8. C₇×C₂₃×D₁₃	D₃	semidirect
10. C₇×C₁₃×C₂₃	C₂×D₃	semidirect
14. C₃×C₂₃×D₁₃	D₇	semidirect
16. D₁₃×D₂₁	C₂₃	direct (N × H)
19. C₂₃×D₂₁	D₁₃	direct (N × H)
20. C₃×C₁₃×C₂₃	C₂×D₇	semidirect
24. C₂₃×D₁₃	D₂₁	direct (N × H)
25. D₂₇₃	C₂×C₂₃	semidirect
26. C₁₃×D₂₁	C₂×C₂₃	semidirect
27. C₃×C₇×D₁₃	C₂×C₂₃	semidirect
28. C₃×C₇×C₂₃	C₂×D₁₃	semidirect
33. C₁₃×C₂₃	C₂×D₂₁	semidirect
35. C₃×C₇×C₁₃	C₂²×C₂₃	semidirect
37. C₇×D₁₃	D₃×C₂₃	semidirect
39. C₇×C₂₃	D₃×D₁₃	semidirect
45. C₇×C₁₃	C₂×D₃×C₂₃	semidirect
48. C₃×D₁₃	D₇×C₂₃	semidirect
50. C₃×C₂₃	D₇×D₁₃	semidirect
57. D₂₁	C₂₃×D₁₃	direct (N × H)
58. C₃×C₁₃	C₂×D₇×C₂₃	semidirect
62. D₁₃	C₂₃×D₂₁	direct (N × H)
63. C₂₃	D₁₃×D₂₁	direct (N × H)
64. C₃×C₇	C₂×C₂₃×D₁₃	semidirect
68. C₁₃	C₂×C₂₃×D₂₁	semidirect
70. C₇	D₃×C₂₃×D₁₃	semidirect
75. C₃	D₇×C₂₃×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×D₂₇₃	2
C₁₃×C₂₃×D₂₁	2
C₃×C₇×C₂₃×D₁₃	2
D₇×C₂₃×D₁₃	3
D₃×C₂₃×D₁₃	7
C₂×C₂₃×D₂₁	13
D₁₃×D₂₁	23

Subgroups — C23×D13×D21 #38737426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×D₁₃×D₂₁ #38737426