Subgroups — C₁₃×#825 #11928096

Order 1248.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#235	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#104	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	C₁₃×#67	—	2	1	no	—
7	C₂×Dic₃×C₁₃	—	2	1	no	—
8	C₁₃×D₁₂	C₄	1	1	yes	characteristic, complemented
9	C₄×D₃×C₁₃	—	2	1	no	—
10	C₁₃×Dic₆	C₄	1	1	yes	characteristic, complemented
11	C₃×C₈×C₁₃	—	2	1	no	—
12	C₁₃×#41	—	3	1	no	—
13	C₁₃×M₁₆	D₃	1	1	yes	characteristic, complemented
14	C₄²×C₁₃	—	3	1	no	—
15	C₂²×C₃×C₁₃	D₄	1	1	yes	characteristic
16	C₂×D₃×C₁₃	—	2	1	no	—
17	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
19	Dic₃×C₁₃	—	2	2	no	—
20	Dic₃×C₁₃	—	2	1	no	—
21	Q₈×C₁₃	—	3	1	no	—
22	D₄×C₁₃	—	3	1	no	—
23	D₄×C₁₃	—	6	1	no	—
24	C₂×C₄×C₁₃	—	6	1	no	—
25	C₂×C₄×C₁₃	—	6	1	no	—
26	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
27	C₈×C₁₃	—	2	1	no	—
28	#825	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₃×C₁₃	—	2	1	no	—
30	C₂×C₃×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
31	D₃×C₁₃	—	4	1	no	—
32	C₂²×C₁₃	—	6	1	no	—
33	C₂²×C₁₃	D₁₂	1	1	yes	characteristic
34	C₄×C₁₃	—	6	2	no	—
35	C₄×C₁₃	—	6	1	no	—
36	C₄×C₁₃	C₄×D₃	1	1	yes	characteristic
37	C₄×C₁₃	#67	1	1	yes	characteristic
38	#235	C₂×C₁₃	1	1	yes	characteristic
39	C₃×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
40	C₄×Dic₃	C₂×C₁₃	1	1	yes	characteristic, complemented
41	C₃×C₁₃	#104	1	1	yes	characteristic, complemented, Hall
42	#104	—	3	1	no	Sylow
43	C₂×C₁₃	—	2	1	no	—
44	C₂×C₁₃	—	12	1	no	—
45	C₂×C₁₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
46	C₂×C₃×C₄	C₂²×C₁₃	1	1	yes	characteristic
47	#67	—	2	1	no	—
48	C₂×Dic₃	—	2	1	no	—
49	D₁₂	C₄×C₁₃	1	1	yes	characteristic, complemented
50	C₄×D₃	—	2	1	no	—
51	Dic₆	C₄×C₁₃	1	1	yes	characteristic, complemented
52	C₃×C₈	—	2	1	no	—
53	#41	—	3	1	no	—
54	M₁₆	D₃×C₁₃	1	1	yes	characteristic, complemented
55	C₄²	—	3	1	no	—
56	C₁₃	#825	1	1	yes	characteristic, direct product factor, Sylow
57	C₂²×C₃	D₄×C₁₃	1	1	yes	characteristic
58	C₂×D₃	—	2	1	no	—
59	C₃×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
60	C₃×C₄	D₄×C₁₃	1	1	yes	characteristic
61	Dic₃	—	2	2	no	—
62	Dic₃	—	2	1	no	—
63	Q₈	—	3	1	no	—
64	D₄	—	3	1	no	—
65	D₄	—	6	1	no	—
66	C₂×C₄	—	6	1	no	—
67	C₂×C₄	—	6	1	no	—
68	C₂×C₄	C₂×D₃×C₁₃	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₂×C₃	—	2	1	no	—
71	C₂×C₃	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
72	D₃	—	4	1	no	—
73	C₂²	—	6	1	no	—
74	C₂²	C₁₃×D₁₂	1	1	yes	characteristic
75	C₄	—	6	2	no	—
76	C₄	—	6	1	no	—
77	C₄	C₄×D₃×C₁₃	1	1	yes	characteristic
78	C₄	C₁₃×#67	1	1	yes	characteristic
79	C₃	C₁₃×#104	1	1	yes	characteristic, complemented, Sylow
80	C₂	—	2	1	no	—
81	C₂	—	12	1	no	—
82	C₂	C₁₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	#67
commutator	C₃×C₄	C₂×C₄×C₁₃
Frattini	C₂×C₄	C₂×D₃×C₁₃
Fitting	C₃×C₁₃×M₁₆	C₂
socle	C₂×C₃×C₁₃	C₂²⋊C₄
prime radical	C₁₃×#235	C₂
cosocle	C₂×C₃×C₄	C₂²×C₁₃
hypercenter	C₁₃×M₁₆	D₃
hypocenter	C₃	C₁₃×#104
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₁₃×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₃×M₁₆	C₂	semidirect
3. C₄×Dic₃×C₁₃	C₂	semidirect
8. C₁₃×D₁₂	C₄	semidirect
10. C₁₃×Dic₆	C₄	semidirect
13. C₁₃×M₁₆	D₃	semidirect
28. #825	C₁₃	direct (N × H)
39. C₃×M₁₆	C₂×C₁₃	semidirect
40. C₄×Dic₃	C₂×C₁₃	semidirect
41. C₃×C₁₃	#104	semidirect
49. D₁₂	C₄×C₁₃	semidirect
51. Dic₆	C₄×C₁₃	semidirect
54. M₁₆	D₃×C₁₃	semidirect
56. C₁₃	#825	direct (N × H)
79. C₃	C₁₃×#104	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#235	2
C₃×C₁₃×M₁₆	2
C₄×Dic₃×C₁₃	2
C₁₃×#104	3
#825	13

Subgroups — C13×#825 #11928096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#825 #11928096