Subgroups — C₂×C₃×Q₈×D₁₃ #11929277

Order 1248.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×Q₈×D₁₃	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₃×C₄×D₁₃	C₂	1	3	yes	maximal
4	C₂×C₃×Dic₂₆	C₂	1	3	yes	maximal, complemented
5	C₂×Q₈×D₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×D₁₃	C₂²	1	1	yes	characteristic
7	C₃×Q₈×C₁₃	C₂²	1	4	yes	complemented
8	C₂×C₃×C₄×C₁₃	C₂²	1	3	yes	—
9	C₂×C₃×Dic₁₃	C₂²	1	3	yes	—
10	C₃×C₄×D₁₃	C₂²	1	12	yes	—
11	C₃×Dic₂₆	C₂²	1	12	yes	complemented
12	C₂×Q₈×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
13	Q₈×D₁₃	C₂×C₃	1	8	yes	direct product factor
14	C₂×C₄×D₁₃	C₂×C₃	1	3	yes	—
15	C₂×Dic₂₆	C₂×C₃	1	3	yes	complemented
16	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
17	C₂×C₃×D₁₃	Q₈	1	4	yes	direct product factor
18	C₂×C₃×D₁₃	C₂³	1	2	yes	—
19	C₃×C₄×C₁₃	C₂³	1	6	yes	—
20	C₃×Dic₁₃	C₂³	1	6	yes	—
21	C₂²×D₁₃	C₂²×C₃	1	1	yes	characteristic
22	Q₈×C₁₃	C₂²×C₃	1	4	yes	complemented
23	C₂×C₄×C₁₃	C₂²×C₃	1	3	yes	—
24	C₂×Dic₁₃	C₂²×C₃	1	3	yes	—
25	C₄×D₁₃	C₂²×C₃	1	12	yes	—
26	Dic₂₆	C₂²×C₃	1	12	yes	complemented
27	C₂²×C₃×Q₈	—	13	1	no	maximal, Hall
28	C₂×C₃×C₁₃	C₂×Q₈	1	2	yes	complemented
29	C₂×C₃×C₁₃	C₂⁴	1	1	yes	characteristic
30	C₃×D₁₃	C₂×Q₈	1	4	yes	direct product factor
31	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
32	C₂×D₁₃	C₃×Q₈	1	4	yes	direct product factor
33	C₂×D₁₃	C₂³×C₃	1	2	yes	—
34	C₄×C₁₃	C₂³×C₃	1	6	yes	—
35	Dic₁₃	C₂³×C₃	1	6	yes	—
36	C₂×C₃×Q₈	—	13	8	no	—
37	C₂×C₃×Q₈	—	13	3	no	—
38	C₂×C₃×Q₈	D₁₃	1	1	yes	characteristic, direct product factor
39	C₂²×C₃×C₄	—	13	3	no	—
40	C₃×C₁₃	C₂²×Q₈	1	1	yes	characteristic, complemented, Hall
41	C₂²×Q₈	—	13	1	no	Sylow
42	C₂×C₁₃	C₂×C₃×Q₈	1	2	yes	complemented
43	C₂×C₁₃	C₂⁴×C₃	1	1	yes	characteristic
44	D₁₃	C₂×C₃×Q₈	1	4	yes	direct product factor
45	C₂³×C₃	—	13	1	no	—
46	C₃×Q₈	—	13	12	no	—
47	C₃×Q₈	C₂×D₁₃	1	4	yes	direct product factor
48	C₂×C₃×C₄	—	13	3	no	—
49	C₂×C₃×C₄	—	13	12	no	—
50	C₂×C₃×C₄	C₂×D₁₃	1	3	yes	—
51	C₂×Q₈	—	13	8	no	—
52	C₂×Q₈	—	13	3	no	—
53	C₂×Q₈	C₃×D₁₃	1	1	yes	characteristic, direct product factor
54	C₂²×C₄	—	13	3	no	—
55	C₁₃	C₂²×C₃×Q₈	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₃	—	13	4	no	—
57	C₂²×C₃	—	13	2	no	—
58	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
59	C₃×C₄	—	13	6	no	—
60	C₃×C₄	C₂²×D₁₃	1	6	yes	—
61	C₂³	—	13	1	no	—
62	Q₈	—	13	12	no	—
63	Q₈	C₂×C₃×D₁₃	1	4	yes	direct product factor
64	C₂×C₄	—	13	3	no	—
65	C₂×C₄	—	13	12	no	—
66	C₂×C₄	C₂×C₃×D₁₃	1	3	yes	—
67	C₂×C₃	—	13	4	no	—
68	C₂×C₃	Q₈×D₁₃	1	2	yes	direct product factor
69	C₂×C₃	C₂³×D₁₃	1	1	yes	characteristic
70	C₂²	—	13	4	no	—
71	C₂²	—	13	2	no	—
72	C₂²	C₂²×C₃×D₁₃	1	1	yes	characteristic
73	C₄	—	13	6	no	—
74	C₄	C₂²×C₃×D₁₃	1	6	yes	—
75	C₃	C₂×Q₈×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	13	4	no	—
77	C₂	C₃×Q₈×D₁₃	1	2	yes	direct product factor
78	C₂	C₂³×C₃×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₃
commutator, cosocle	C₂×C₁₃	C₂⁴×C₃
Frattini	C₂	C₂³×C₃×D₁₃
Fitting	C₂×C₃×Q₈×C₁₃	C₂
socle	C₂²×C₃×C₁₃	C₂³
prime radical	C₂²×C₃×D₁₃	C₂²
hypercenter	C₂×C₃×Q₈	D₁₃
hypocenter	C₁₃	C₂²×C₃×Q₈
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×Q₈×C₁₃	C₂	semidirect
2. C₃×Q₈×D₁₃	C₂	direct (N × H)
4. C₂×C₃×Dic₂₆	C₂	semidirect
5. C₂×Q₈×D₁₃	C₃	direct (N × H)
7. C₃×Q₈×C₁₃	C₂²	semidirect
11. C₃×Dic₂₆	C₂²	semidirect
12. C₂×Q₈×C₁₃	C₂×C₃	semidirect
13. Q₈×D₁₃	C₂×C₃	direct (N × H)
15. C₂×Dic₂₆	C₂×C₃	semidirect
17. C₂×C₃×D₁₃	Q₈	direct (N × H)
22. Q₈×C₁₃	C₂²×C₃	semidirect
26. Dic₂₆	C₂²×C₃	semidirect
28. C₂×C₃×C₁₃	C₂×Q₈	semidirect
30. C₃×D₁₃	C₂×Q₈	direct (N × H)
32. C₂×D₁₃	C₃×Q₈	direct (N × H)
38. C₂×C₃×Q₈	D₁₃	direct (N × H)
40. C₃×C₁₃	C₂²×Q₈	semidirect
42. C₂×C₁₃	C₂×C₃×Q₈	semidirect
44. D₁₃	C₂×C₃×Q₈	direct (N × H)
47. C₃×Q₈	C₂×D₁₃	direct (N × H)
53. C₂×Q₈	C₃×D₁₃	direct (N × H)
55. C₁₃	C₂²×C₃×Q₈	semidirect
63. Q₈	C₂×C₃×D₁₃	direct (N × H)
68. C₂×C₃	Q₈×D₁₃	direct (N × H)
75. C₃	C₂×Q₈×D₁₃	direct (N × H)
77. C₂	C₃×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
C₂×C₃×Q₈×C₁₃	2
C₃×Q₈×D₁₃	2
C₂×C₃×C₄×D₁₃	2
C₂×C₃×Dic₂₆	2
C₂×Q₈×D₁₃	3
C₂²×C₃×Q₈	13

Subgroups — C2×C3×Q8×D13 #11929277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×Q₈×D₁₃ #11929277