Subgroups — C₁₃×#888 #11928865

Order 1248.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×Dic₆	C₂	1	2	yes	maximal
2	C₃×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₁₃×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₁₃×Dic₃⋊C₄	C₂	1	2	yes	maximal
5	C₄×Dic₃×C₁₃	C₂	1	1	yes	maximal, characteristic
6	C₁₃×C₄⋊Q₈	—	3	1	no	maximal, Hall
7	C₂×C₃×C₄×C₁₃	C₂²	1	2	yes	—
8	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₃×C₁₃	C₂²	1	2	yes	—
10	C₂×Dic₃×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₃×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×Dic₆	—	2	4	no	—
13	C₂×Q₈×C₁₃	—	3	2	no	—
14	C₁₃×C₄⋊C₄	—	3	2	no	—
15	C₁₃×C₄⋊C₄	—	3	1	no	—
16	C₁₃×C₄⋊C₄	D₃	1	1	yes	characteristic
17	C₄²×C₁₃	—	3	1	no	—
18	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
19	C₃×C₄×C₁₃	—	2	2	no	—
20	C₃×C₄×C₁₃	Q₈	1	2	yes	complemented
21	Dic₃×C₁₃	—	2	2	no	—
22	Dic₃×C₁₃	D₄	1	2	yes	—
23	Dic₃×C₁₃	Q₈	1	2	yes	complemented
24	Q₈×C₁₃	—	6	4	no	—
25	C₂×C₄×C₁₃	—	3	1	no	—
26	C₂×C₄×C₁₃	—	3	1	no	—
27	C₂×C₄×C₁₃	—	3	2	no	—
28	C₂×C₄×C₁₃	C₂×D₃	1	2	yes	—
29	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
30	#888	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic
34	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
35	C₄×C₁₃	—	2	2	no	—
36	C₄×C₁₃	—	3	2	no	—
37	C₄×C₁₃	—	3	2	no	—
38	C₄×C₁₃	—	6	2	no	—
39	C₄×C₁₃	Dic₆	1	2	yes	complemented
40	C₂×Dic₆	C₂×C₁₃	1	2	yes	—
41	C₃×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
42	C₄⋊Dic₃	C₂×C₁₃	1	1	yes	characteristic
43	Dic₃⋊C₄	C₂×C₁₃	1	2	yes	—
44	C₄×Dic₃	C₂×C₁₃	1	1	yes	characteristic
45	C₃×C₁₃	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
46	C₄⋊Q₈	—	3	1	no	Sylow
47	C₂×C₁₃	C₂×Dic₆	1	1	yes	characteristic
48	C₂×C₁₃	D₃×D₄	1	1	yes	characteristic
49	C₂×C₁₃	D₃×Q₈	1	1	yes	characteristic
50	C₂×C₃×C₄	C₂²×C₁₃	1	2	yes	—
51	C₂×C₃×C₄	C₂²×C₁₃	1	1	yes	characteristic
52	C₂×Dic₃	C₂²×C₁₃	1	2	yes	—
53	C₂×Dic₃	C₂²×C₁₃	1	1	yes	characteristic
54	C₂×Dic₃	C₂²×C₁₃	1	1	yes	characteristic
55	Dic₆	—	2	4	no	—
56	C₂×Q₈	—	3	2	no	—
57	C₄⋊C₄	—	3	2	no	—
58	C₄⋊C₄	—	3	1	no	—
59	C₄⋊C₄	D₃×C₁₃	1	1	yes	characteristic
60	C₄²	—	3	1	no	—
61	C₁₃	#888	1	1	yes	characteristic, direct product factor, Sylow
62	C₂²×C₃	C₂³×C₁₃	1	1	yes	characteristic
63	C₃×C₄	—	2	2	no	—
64	C₃×C₄	Q₈×C₁₃	1	2	yes	complemented
65	Dic₃	—	2	2	no	—
66	Dic₃	D₄×C₁₃	1	2	yes	—
67	Dic₃	Q₈×C₁₃	1	2	yes	complemented
68	Q₈	—	6	4	no	—
69	C₂×C₄	—	3	1	no	—
70	C₂×C₄	—	3	1	no	—
71	C₂×C₄	—	3	2	no	—
72	C₂×C₄	C₂×D₃×C₁₃	1	2	yes	—
73	C₂×C₄	C₂×D₃×C₁₃	1	1	yes	characteristic
74	C₂×C₃	C₂×D₄×C₁₃	1	1	yes	characteristic
75	C₂×C₃	C₂×Q₈×C₁₃	1	1	yes	characteristic
76	C₂×C₃	C₂×Q₈×C₁₃	1	1	yes	characteristic
77	C₂²	C₂²×D₃×C₁₃	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	3	2	no	—
80	C₄	—	3	2	no	—
81	C₄	—	6	2	no	—
82	C₄	C₁₃×Dic₆	1	2	yes	complemented
83	C₃	C₁₃×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
84	C₂	C₂×C₁₃×Dic₆	1	1	yes	characteristic
85	C₂	D₃×D₄×C₁₃	1	1	yes	characteristic
86	C₂	D₃×Q₈×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₃	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₁₃
Frattini	C₂²	C₂²×D₃×C₁₃
Fitting	C₃×C₁₃×C₄⋊C₄	C₂
socle, prime radical	C₂²×C₃×C₁₃	C₂³
hypercenter	C₁₃×C₄⋊C₄	D₃
hypocenter	C₃	C₁₃×C₄⋊Q₈
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
20. C₃×C₄×C₁₃	Q₈	semidirect
23. Dic₃×C₁₃	Q₈	semidirect
30. #888	C₁₃	direct (N × H)
39. C₄×C₁₃	Dic₆	semidirect
45. C₃×C₁₃	C₄⋊Q₈	semidirect
61. C₁₃	#888	direct (N × H)
64. C₃×C₄	Q₈×C₁₃	semidirect
67. Dic₃	Q₈×C₁₃	semidirect
82. C₄	C₁₃×Dic₆	semidirect
83. C₃	C₁₃×C₄⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×Dic₆	2
C₃×C₁₃×C₄⋊C₄	2
C₁₃×C₄⋊Dic₃	2
C₁₃×Dic₃⋊C₄	2
C₄×Dic₃×C₁₃	2
C₁₃×C₄⋊Q₈	3
#888	13

Subgroups — C13×#888 #11928865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#888 #11928865