Subgroups — C₂×C₁₃×#239 #11929293

Order 1248.

328 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	C₁₃×#239	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₁₃×D₁₂	C₂	1	3	yes	maximal, complemented
4	C₂×C₄×D₃×C₁₃	C₂	1	3	yes	maximal, complemented
5	C₂×C₁₃×#41	—	3	1	no	maximal, Hall
6	C₂²×D₃×C₁₃	C₂²	1	3	yes	—
7	C₃×Q₈×C₁₃	C₂²	1	4	yes	complemented
8	C₂×C₃×C₄×C₁₃	C₂²	1	3	yes	—
9	C₂×Dic₃×C₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×D₁₂	C₂²	1	12	yes	complemented
11	C₄×D₃×C₁₃	C₂²	1	12	yes	complemented
12	C₁₃×#41	—	3	8	no	—
13	C₂×Q₈×C₁₃	D₃	1	1	yes	characteristic, complemented
14	C₂×D₄×C₁₃	—	3	3	no	—
15	C₂²×C₄×C₁₃	—	3	3	no	—
16	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
17	C₂×D₃×C₁₃	—	2	6	no	—
18	C₂×D₃×C₁₃	C₂³	1	6	yes	—
19	C₃×C₄×C₁₃	C₂³	1	6	yes	—
20	Dic₃×C₁₃	C₂³	1	2	yes	—
21	C₂³×C₁₃	—	3	3	no	—
22	Q₈×C₁₃	C₂×D₃	1	4	yes	complemented
23	D₄×C₁₃	—	3	12	no	—
24	C₂×C₄×C₁₃	—	3	1	no	—
25	C₂×C₄×C₁₃	—	3	12	no	—
26	C₂×C₄×C₁₃	C₂×D₃	1	3	yes	—
27	C₂×#239	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₃×C₁₃	#41	1	2	yes	complemented
29	C₂×C₃×C₁₃	C₂⁴	1	1	yes	characteristic
30	D₃×C₁₃	—	2	6	no	—
31	C₂²×C₁₃	—	3	6	no	—
32	C₂²×C₁₃	—	6	6	no	—
33	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
34	C₄×C₁₃	—	3	2	no	—
35	C₄×C₁₃	C₂²×D₃	1	6	yes	—
36	C₂×C₃×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
37	#239	C₂×C₁₃	1	8	yes	direct product factor
38	C₂×D₁₂	C₂×C₁₃	1	3	yes	complemented
39	C₂×C₄×D₃	C₂×C₁₃	1	3	yes	complemented
40	C₃×C₁₃	C₂×#41	1	1	yes	characteristic, complemented, Hall
41	C₂×#41	—	3	1	no	Sylow
42	C₂×C₁₃	—	6	6	no	—
43	C₂×C₁₃	#239	1	2	yes	direct product factor
44	C₂×C₁₃	C₂³×D₃	1	1	yes	characteristic
45	C₂²×D₃	C₂²×C₁₃	1	3	yes	—
46	C₃×Q₈	C₂²×C₁₃	1	4	yes	complemented
47	C₂×C₃×C₄	C₂²×C₁₃	1	3	yes	—
48	C₂×Dic₃	C₂²×C₁₃	1	1	yes	characteristic
49	D₁₂	C₂²×C₁₃	1	12	yes	complemented
50	C₄×D₃	C₂²×C₁₃	1	12	yes	complemented
51	#41	—	3	8	no	—
52	C₂×Q₈	D₃×C₁₃	1	1	yes	characteristic, complemented
53	C₂×D₄	—	3	3	no	—
54	C₂²×C₄	—	3	3	no	—
55	C₁₃	C₂×#239	1	1	yes	characteristic, direct product factor, Sylow
56	C₂²×C₃	C₂³×C₁₃	1	1	yes	characteristic
57	C₂×D₃	—	2	6	no	—
58	C₂×D₃	C₂³×C₁₃	1	6	yes	—
59	C₃×C₄	C₂³×C₁₃	1	6	yes	—
60	Dic₃	C₂³×C₁₃	1	2	yes	—
61	C₂³	—	3	3	no	—
62	Q₈	C₂×D₃×C₁₃	1	4	yes	complemented
63	D₄	—	3	12	no	—
64	C₂×C₄	—	3	1	no	—
65	C₂×C₄	—	3	12	no	—
66	C₂×C₄	C₂×D₃×C₁₃	1	3	yes	—
67	C₂×C₃	C₁₃×#41	1	2	yes	complemented
68	C₂×C₃	C₂⁴×C₁₃	1	1	yes	characteristic
69	D₃	—	2	6	no	—
70	C₂²	—	3	6	no	—
71	C₂²	—	6	6	no	—
72	C₂²	C₂²×D₃×C₁₃	1	1	yes	characteristic
73	C₄	—	3	2	no	—
74	C₄	C₂²×D₃×C₁₃	1	6	yes	—
75	C₃	C₂×C₁₃×#41	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	6	6	no	—
77	C₂	C₁₃×#239	1	2	yes	direct product factor
78	C₂	C₂³×D₃×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₃	C₂²×D₃
commutator, cosocle	C₂×C₃	C₂⁴×C₁₃
Frattini	C₂	C₂³×D₃×C₁₃
Fitting	C₂×C₃×Q₈×C₁₃	C₂
socle	C₂²×C₃×C₁₃	C₂³
hypercenter	C₂×Q₈×C₁₃	D₃
hypocenter	C₃	C₂×C₁₃×#41
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×Q₈×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×Q₈×C₁₃	C₂	semidirect
2. C₁₃×#239	C₂	direct (N × H)
3. C₂×C₁₃×D₁₂	C₂	semidirect
4. C₂×C₄×D₃×C₁₃	C₂	semidirect
7. C₃×Q₈×C₁₃	C₂²	semidirect
10. C₁₃×D₁₂	C₂²	semidirect
11. C₄×D₃×C₁₃	C₂²	semidirect
13. C₂×Q₈×C₁₃	D₃	semidirect
22. Q₈×C₁₃	C₂×D₃	semidirect
27. C₂×#239	C₁₃	direct (N × H)
28. C₂×C₃×C₁₃	#41	semidirect
36. C₂×C₃×Q₈	C₂×C₁₃	semidirect
37. #239	C₂×C₁₃	direct (N × H)
38. C₂×D₁₂	C₂×C₁₃	semidirect
39. C₂×C₄×D₃	C₂×C₁₃	semidirect
40. C₃×C₁₃	C₂×#41	semidirect
43. C₂×C₁₃	#239	direct (N × H)
46. C₃×Q₈	C₂²×C₁₃	semidirect
49. D₁₂	C₂²×C₁₃	semidirect
50. C₄×D₃	C₂²×C₁₃	semidirect
52. C₂×Q₈	D₃×C₁₃	semidirect
55. C₁₃	C₂×#239	direct (N × H)
62. Q₈	C₂×D₃×C₁₃	semidirect
67. C₂×C₃	C₁₃×#41	semidirect
75. C₃	C₂×C₁₃×#41	semidirect
77. C₂	C₁₃×#239	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
C₁₃×#239	2
C₂×C₁₃×D₁₂	2
C₂×C₄×D₃×C₁₃	2
C₂×C₁₃×#41	3
C₂×#239	13

Subgroups — C2×C13×#239 #11929293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#239 #11929293