Subgroups — C₁₃×D₂₁×D₂₃ #38737422

Order 25116.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₄₈₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₂₃×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₁₃×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×D₇×D₂₃	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₃×D₁₆₁	—	3	1	no	—
7	C₁₃×D₇×C₂₃	—	3	1	no	—
8	C₇×C₁₃×D₂₃	D₃	1	1	yes	characteristic, complemented
9	D₃×C₁₃×D₂₃	—	7	1	no	maximal, Hall
10	C₇×C₁₃×C₂₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₂₁×D₂₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₃×D₆₉	—	7	1	no	—
13	D₃×C₁₃×C₂₃	—	7	1	no	—
14	C₃×C₁₃×D₂₃	D₇	1	1	yes	characteristic, complemented
15	C₂×C₁₃×D₂₃	—	21	1	no	Hall
16	C₂×C₁₃×D₂₁	—	23	1	no	maximal, Hall
17	D₄₈₃	C₂×C₁₃	1	1	yes	characteristic, complemented
18	C₂₃×D₂₁	C₂×C₁₃	1	1	yes	characteristic, complemented
19	C₃×C₇×D₂₃	C₂×C₁₃	1	1	yes	characteristic, complemented
20	C₃×C₁₃×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
21	D₇×D₂₃	—	3	1	no	Hall
22	C₂×C₁₃×C₂₃	—	21	1	no	—
23	C₁₃×D₂₃	—	21	1	no	—
24	C₁₃×D₂₃	D₂₁	1	1	yes	characteristic, direct product factor
25	C₂×C₃×C₇×C₁₃	—	23	1	no	—
26	C₁₃×D₂₁	—	23	1	no	—
27	C₁₃×D₂₁	D₂₃	1	1	yes	characteristic, direct product factor
28	C₃×C₇×C₂₃	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
29	C₂×C₁₃×D₇	—	69	1	no	Hall
30	D₁₆₁	—	3	1	no	—
31	C₇×D₂₃	D₃×C₁₃	1	1	yes	characteristic, complemented
32	D₇×C₂₃	—	3	1	no	—
33	C₁₃×C₂₃	C₂×D₂₁	1	1	yes	characteristic, complemented, Hall
34	D₃×D₂₃	—	7	1	no	Hall
35	C₃×C₇×C₁₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
36	C₂×C₇×C₁₃	—	23	1	no	—
37	C₁₃×D₇	—	3	1	no	—
38	C₁₃×D₇	—	69	1	no	—
39	C₇×C₂₃	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
40	C₂×D₃×C₁₃	—	161	1	no	Hall
41	D₆₉	—	7	1	no	—
42	C₃×D₂₃	C₁₃×D₇	1	1	yes	characteristic, complemented
43	D₃×C₂₃	—	7	1	no	—
44	C₂×D₂₃	—	21	1	no	Hall
45	C₇×C₁₃	D₃×D₂₃	1	1	yes	characteristic, complemented, Hall
46	C₂×D₂₁	—	23	1	no	Hall
47	C₂×C₃×C₁₃	—	23	1	no	—
48	D₃×C₁₃	—	7	1	no	—
49	D₃×C₁₃	—	161	1	no	—
50	C₃×C₂₃	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
51	C₂²×C₁₃	—	483	1	no	Hall
52	C₂×C₂₃	—	21	1	no	—
53	D₂₃	—	21	1	no	—
54	D₂₃	C₁₃×D₂₁	1	1	yes	characteristic, direct product factor
55	C₂×C₃×C₇	—	23	1	no	—
56	D₂₁	—	23	1	no	—
57	D₂₁	C₁₃×D₂₃	1	1	yes	characteristic, direct product factor
58	C₃×C₁₃	D₇×D₂₃	1	1	yes	characteristic, complemented, Hall
59	C₂×D₇	—	69	1	no	Hall
60	C₂×C₁₃	—	21	1	no	—
61	C₂×C₁₃	—	23	1	no	—
62	C₂×C₁₃	—	483	1	no	—
63	C₂₃	C₂×C₁₃×D₂₁	1	1	yes	characteristic, complemented, Sylow
64	C₃×C₇	C₂×C₁₃×D₂₃	1	1	yes	characteristic, complemented, Hall
65	C₂×C₇	—	23	1	no	—
66	D₇	—	3	1	no	—
67	D₇	—	69	1	no	—
68	C₁₃	D₂₁×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
69	C₂×D₃	—	161	1	no	Hall
70	C₇	D₃×C₁₃×D₂₃	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	23	1	no	—
72	D₃	—	7	1	no	—
73	D₃	—	161	1	no	—
74	C₂²	—	483	1	no	Sylow
75	C₃	C₁₃×D₇×D₂₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	21	1	no	—
77	C₂	—	23	1	no	—
78	C₂	—	483	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₂₁×D₂₃
commutator, cosocle, hypocenter	C₃×C₇×C₂₃	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₂₃	C₂²
LCS	G ▷ C₃×C₇×C₂₃
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₄₈₃	C₂	semidirect
2. C₁₃×C₂₃×D₂₁	C₂	semidirect
3. C₃×C₇×C₁₃×D₂₃	C₂	semidirect
5. C₃×C₇×C₁₃×C₂₃	C₂²	semidirect
8. C₇×C₁₃×D₂₃	D₃	semidirect
10. C₇×C₁₃×C₂₃	C₂×D₃	semidirect
11. D₂₁×D₂₃	C₁₃	direct (N × H)
14. C₃×C₁₃×D₂₃	D₇	semidirect
17. D₄₈₃	C₂×C₁₃	semidirect
18. C₂₃×D₂₁	C₂×C₁₃	semidirect
19. C₃×C₇×D₂₃	C₂×C₁₃	semidirect
20. C₃×C₁₃×C₂₃	C₂×D₇	semidirect
24. C₁₃×D₂₃	D₂₁	direct (N × H)
27. C₁₃×D₂₁	D₂₃	direct (N × H)
28. C₃×C₇×C₂₃	C₂²×C₁₃	semidirect
31. C₇×D₂₃	D₃×C₁₃	semidirect
33. C₁₃×C₂₃	C₂×D₂₁	semidirect
35. C₃×C₇×C₁₃	C₂×D₂₃	semidirect
39. C₇×C₂₃	C₂×D₃×C₁₃	semidirect
42. C₃×D₂₃	C₁₃×D₇	semidirect
45. C₇×C₁₃	D₃×D₂₃	semidirect
50. C₃×C₂₃	C₂×C₁₃×D₇	semidirect
54. D₂₃	C₁₃×D₂₁	direct (N × H)
57. D₂₁	C₁₃×D₂₃	direct (N × H)
58. C₃×C₁₃	D₇×D₂₃	semidirect
63. C₂₃	C₂×C₁₃×D₂₁	semidirect
64. C₃×C₇	C₂×C₁₃×D₂₃	semidirect
68. C₁₃	D₂₁×D₂₃	direct (N × H)
70. C₇	D₃×C₁₃×D₂₃	semidirect
75. C₃	C₁₃×D₇×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×D₄₈₃	2
C₁₃×C₂₃×D₂₁	2
C₃×C₇×C₁₃×D₂₃	2
C₁₃×D₇×D₂₃	3
D₃×C₁₃×D₂₃	7
D₂₁×D₂₃	13
C₂×C₁₃×D₂₁	23

Subgroups — C13×D21×D23 #38737422

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×D₂₁×D₂₃ #38737422