Subgroups — C₁₃×#816 #11928092

Order 1248.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×Dic₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#103	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×Dic₃×C₁₃	—	2	1	no	—
7	C₂×Dic₃×C₁₃	—	2	1	no	—
8	C₁₃×Dic₆	—	2	1	no	—
9	C₁₃×Dic₆	C₄	1	2	yes	complemented
10	C₃×C₈×C₁₃	—	2	1	no	—
11	C₂×Q₈×C₁₃	—	3	1	no	—
12	C₂×C₈×C₁₃	D₃	1	1	yes	characteristic
13	C₁₃×C₄⋊C₄	—	3	1	no	—
14	C₂²×C₃×C₁₃	D₄	1	1	yes	characteristic
15	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
17	Dic₃×C₁₃	—	2	2	no	—
18	Dic₃×C₁₃	—	4	1	no	—
19	Q₈×C₁₃	—	3	2	no	—
20	Q₈×C₁₃	—	6	1	no	—
21	C₂×C₄×C₁₃	—	6	1	no	—
22	C₂×C₄×C₁₃	—	6	1	no	—
23	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
24	C₈×C₁₃	—	2	1	no	—
25	#816	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₃×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₃×C₁₃	SD₁₆	1	1	yes	characteristic
28	C₂×C₃×C₁₃	Q₁₆	1	1	yes	characteristic
29	C₂²×C₁₃	D₁₂	1	1	yes	characteristic
30	C₄×C₁₃	—	6	2	no	—
31	C₄×C₁₃	—	12	1	no	—
32	C₄×C₁₃	C₄×D₃	1	1	yes	characteristic
33	C₄×C₁₃	#67	1	1	yes	characteristic
34	C₂×Dic₆	C₂×C₁₃	1	1	yes	characteristic
35	C₂×C₃×C₈	C₂×C₁₃	1	1	yes	characteristic
36	C₄⋊Dic₃	C₂×C₁₃	1	1	yes	characteristic
37	C₃×C₁₃	#103	1	1	yes	characteristic, complemented, Hall
38	#103	—	3	1	no	Sylow
39	C₂×C₁₃	#204	1	1	yes	characteristic
40	C₂×C₁₃	Dic₁₂	1	1	yes	characteristic
41	C₂×C₁₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
42	C₂×C₃×C₄	C₂²×C₁₃	1	1	yes	characteristic
43	C₂×Dic₃	—	2	1	no	—
44	C₂×Dic₃	—	2	1	no	—
45	Dic₆	—	2	1	no	—
46	Dic₆	C₄×C₁₃	1	2	yes	complemented
47	C₃×C₈	—	2	1	no	—
48	C₂×Q₈	—	3	1	no	—
49	C₂×C₈	D₃×C₁₃	1	1	yes	characteristic
50	C₄⋊C₄	—	3	1	no	—
51	C₁₃	#816	1	1	yes	characteristic, direct product factor, Sylow
52	C₂²×C₃	D₄×C₁₃	1	1	yes	characteristic
53	C₃×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
54	C₃×C₄	D₄×C₁₃	1	1	yes	characteristic
55	Dic₃	—	2	2	no	—
56	Dic₃	—	4	1	no	—
57	Q₈	—	3	2	no	—
58	Q₈	—	6	1	no	—
59	C₂×C₄	—	6	1	no	—
60	C₂×C₄	—	6	1	no	—
61	C₂×C₄	C₂×D₃×C₁₃	1	1	yes	characteristic
62	C₈	—	2	1	no	—
63	C₂×C₃	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₃	C₁₃×SD₁₆	1	1	yes	characteristic
65	C₂×C₃	C₁₃×Q₁₆	1	1	yes	characteristic
66	C₂²	C₁₃×D₁₂	1	1	yes	characteristic
67	C₄	—	6	2	no	—
68	C₄	—	12	1	no	—
69	C₄	C₄×D₃×C₁₃	1	1	yes	characteristic
70	C₄	C₁₃×#67	1	1	yes	characteristic
71	C₃	C₁₃×#103	1	1	yes	characteristic, complemented, Sylow
72	C₂	C₁₃×#204	1	1	yes	characteristic
73	C₂	C₁₃×Dic₁₂	1	1	yes	characteristic
74	C₂	C₁₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₃	D₁₂
commutator	C₃×C₄	C₂×C₄×C₁₃
Frattini	C₂×C₄	C₂×D₃×C₁₃
Fitting	C₂×C₃×C₈×C₁₃	C₂
socle, prime radical	C₂²×C₃×C₁₃	D₄
cosocle	C₂×C₃×C₄	C₂²×C₁₃
hypercenter	C₂×C₈×C₁₃	D₃
hypocenter	C₃	C₁₃×#103
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₈×C₁₃

Complements

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

N	H ≅ G/N	type
9. C₁₃×Dic₆	C₄	semidirect
25. #816	C₁₃	direct (N × H)
37. C₃×C₁₃	#103	semidirect
46. Dic₆	C₄×C₁₃	semidirect
51. C₁₃	#816	direct (N × H)
71. C₃	C₁₃×#103	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
C₂×C₃×C₈×C₁₃	2
C₁₃×C₄⋊Dic₃	2
C₁₃×#103	3
#816	13

Subgroups — C13×#816 #11928092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#816 #11928092