Subgroups — C₂³×Q₈×D₁₃ #13129630

Order 1664.

6264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×Q₈×D₁₃	C₂	1	56	yes	maximal, direct product factor
3	C₂³×C₄×D₁₃	C₂	1	3	yes	maximal
4	C₂³×Dic₂₆	C₂	1	3	yes	maximal, complemented
5	C₂⁴×D₁₃	C₂²	1	1	yes	characteristic
6	C₂²×Q₈×C₁₃	C₂²	1	28	yes	complemented
7	C₂³×C₄×C₁₃	C₂²	1	3	yes	—
8	C₂³×Dic₁₃	C₂²	1	3	yes	—
9	C₂×Q₈×D₁₃	C₂²	1	448	yes	direct product factor
10	C₂²×C₄×D₁₃	C₂²	1	84	yes	—
11	C₂²×Dic₂₆	C₂²	1	84	yes	complemented
12	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
13	C₂³×D₁₃	Q₈	1	16	yes	direct product factor
14	C₂³×D₁₃	C₂³	1	14	yes	—
15	C₂×Q₈×C₁₃	C₂³	1	112	yes	complemented
16	C₂²×C₄×C₁₃	C₂³	1	42	yes	—
17	C₂²×Dic₁₃	C₂³	1	42	yes	—
18	Q₈×D₁₃	C₂³	1	512	yes	direct product factor
19	C₂×C₄×D₁₃	C₂³	1	336	yes	—
20	C₂×Dic₂₆	C₂³	1	336	yes	complemented
21	C₂⁴×Q₈	—	13	1	no	maximal, Sylow
22	C₂³×C₁₃	C₂×Q₈	1	8	yes	complemented
23	C₂³×C₁₃	C₂⁴	1	7	yes	—
24	C₂²×D₁₃	C₂×Q₈	1	112	yes	direct product factor
25	C₂²×D₁₃	C₂⁴	1	28	yes	—
26	Q₈×C₁₃	C₂⁴	1	64	yes	complemented
27	C₂×C₄×C₁₃	C₂⁴	1	84	yes	—
28	C₂×Dic₁₃	C₂⁴	1	84	yes	—
29	C₄×D₁₃	C₂⁴	1	192	yes	—
30	Dic₂₆	C₂⁴	1	192	yes	complemented
31	C₂³×Q₈	—	13	56	no	—
32	C₂³×Q₈	—	13	3	no	—
33	C₂³×Q₈	D₁₃	1	1	yes	characteristic, direct product factor
34	C₂⁴×C₄	—	13	3	no	—
35	C₂²×C₁₃	C₂²×Q₈	1	28	yes	complemented
36	C₂²×C₁₃	C₂⁵	1	7	yes	—
37	C₂×D₁₃	C₂²×Q₈	1	112	yes	direct product factor
38	C₂×D₁₃	C₂⁵	1	8	yes	—
39	C₄×C₁₃	C₂⁵	1	24	yes	—
40	Dic₁₃	C₂⁵	1	24	yes	—
41	C₂⁵	—	13	1	no	—
42	C₂²×Q₈	—	13	448	no	—
43	C₂²×Q₈	—	13	84	no	—
44	C₂²×Q₈	C₂×D₁₃	1	28	yes	direct product factor
45	C₂³×C₄	—	13	3	no	—
46	C₂³×C₄	—	13	84	no	—
47	C₂³×C₄	C₂×D₁₃	1	3	yes	—
48	C₂×C₁₃	C₂³×Q₈	1	14	yes	complemented
49	C₂×C₁₃	C₂⁶	1	1	yes	characteristic
50	D₁₃	C₂³×Q₈	1	16	yes	direct product factor
51	C₂⁴	—	13	16	no	—
52	C₂⁴	—	13	14	no	—
53	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
54	C₂×Q₈	—	13	512	no	—
55	C₂×Q₈	—	13	336	no	—
56	C₂×Q₈	C₂²×D₁₃	1	112	yes	direct product factor
57	C₂²×C₄	—	13	42	no	—
58	C₂²×C₄	—	13	336	no	—
59	C₂²×C₄	C₂²×D₁₃	1	42	yes	—
60	C₁₃	C₂⁴×Q₈	1	1	yes	characteristic, complemented, Sylow
61	C₂³	—	13	112	no	—
62	C₂³	—	13	28	no	—
63	C₂³	Q₈×D₁₃	1	8	yes	direct product factor
64	C₂³	C₂³×D₁₃	1	7	yes	—
65	Q₈	—	13	192	no	—
66	Q₈	C₂³×D₁₃	1	64	yes	direct product factor
67	C₂×C₄	—	13	84	no	—
68	C₂×C₄	—	13	192	no	—
69	C₂×C₄	C₂³×D₁₃	1	84	yes	—
70	C₂²	—	13	112	no	—
71	C₂²	—	13	8	no	—
72	C₂²	C₂×Q₈×D₁₃	1	28	yes	direct product factor
73	C₂²	C₂⁴×D₁₃	1	7	yes	—
74	C₄	—	13	24	no	—
75	C₄	C₂⁴×D₁₃	1	24	yes	—
76	C₂	—	13	16	no	—
77	C₂	C₂²×Q₈×D₁₃	1	14	yes	direct product factor
78	C₂	C₂⁵×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂²×D₁₃
commutator, cosocle	C₂×C₁₃	C₂⁶
Frattini	C₂	C₂⁵×D₁₃
Fitting	C₂³×Q₈×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂³
prime radical	C₂⁴×D₁₃	C₂²
hypercenter	C₂³×Q₈	D₁₃
hypocenter	C₁₃	C₂⁴×Q₈
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₈×C₁₃	C₂	semidirect
2. C₂²×Q₈×D₁₃	C₂	direct (N × H)
4. C₂³×Dic₂₆	C₂	semidirect
6. C₂²×Q₈×C₁₃	C₂²	semidirect
9. C₂×Q₈×D₁₃	C₂²	direct (N × H)
11. C₂²×Dic₂₆	C₂²	semidirect
13. C₂³×D₁₃	Q₈	direct (N × H)
15. C₂×Q₈×C₁₃	C₂³	semidirect
18. Q₈×D₁₃	C₂³	direct (N × H)
20. C₂×Dic₂₆	C₂³	semidirect
22. C₂³×C₁₃	C₂×Q₈	semidirect
24. C₂²×D₁₃	C₂×Q₈	direct (N × H)
26. Q₈×C₁₃	C₂⁴	semidirect
30. Dic₂₆	C₂⁴	semidirect
33. C₂³×Q₈	D₁₃	direct (N × H)
35. C₂²×C₁₃	C₂²×Q₈	semidirect
37. C₂×D₁₃	C₂²×Q₈	direct (N × H)
44. C₂²×Q₈	C₂×D₁₃	direct (N × H)
48. C₂×C₁₃	C₂³×Q₈	semidirect
50. D₁₃	C₂³×Q₈	direct (N × H)
56. C₂×Q₈	C₂²×D₁₃	direct (N × H)
60. C₁₃	C₂⁴×Q₈	semidirect
63. C₂³	Q₈×D₁₃	direct (N × H)
66. Q₈	C₂³×D₁₃	direct (N × H)
72. C₂²	C₂×Q₈×D₁₃	direct (N × H)
77. C₂	C₂²×Q₈×D₁₃	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×Q₈×C₁₃	2
C₂²×Q₈×D₁₃	2
C₂³×C₄×D₁₃	2
C₂³×Dic₂₆	2
C₂⁴×Q₈	13

Subgroups — C23×Q8×D13 #13129630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×Q₈×D₁₃ #13129630