Subgroups — C₂×C₁₃×#216 #11928921

Order 1248.

120 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
2	C₂×C₁₃×Dic₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#216	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×Q₁₆	—	3	1	no	maximal, Hall
6	C₃×Q₈×C₁₃	—	2	1	no	—
7	C₃×Q₈×C₁₃	C₂²	1	2	yes	—
8	C₂×C₃×C₄×C₁₃	—	2	1	no	—
9	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₃×C₁₃	—	2	1	no	—
11	C₁₃×Dic₆	—	2	1	no	—
12	C₁₃×Dic₆	C₂²	1	2	yes	—
13	C₁₃×C₃⋊C₈	C₂²	1	2	yes	—
14	C₂×Q₈×C₁₃	—	3	1	no	—
15	C₂×Q₈×C₁₃	D₃	1	1	yes	characteristic
16	C₁₃×Q₁₆	—	3	4	no	—
17	C₂×C₈×C₁₃	—	3	1	no	—
18	C₂²×C₃×C₁₃	D₄	1	1	yes	characteristic
19	C₃×C₄×C₁₃	—	2	2	no	—
20	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
21	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
22	Dic₃×C₁₃	—	2	2	no	—
23	Q₈×C₁₃	—	2	1	no	—
24	Q₈×C₁₃	—	3	2	no	—
25	Q₈×C₁₃	—	6	1	no	—
26	Q₈×C₁₃	C₂×D₃	1	2	yes	—
27	C₂×C₄×C₁₃	—	2	1	no	—
28	C₂×C₄×C₁₃	—	6	1	no	—
29	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
30	C₈×C₁₃	—	3	2	no	—
31	C₂×#216	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₃×C₁₃	Q₁₆	1	2	yes	complemented
33	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
34	C₂²×C₁₃	#67	1	1	yes	characteristic
35	C₄×C₁₃	—	2	2	no	—
36	C₄×C₁₃	—	6	2	no	—
37	C₄×C₁₃	#67	1	1	yes	characteristic
38	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
39	C₂×C₃×Q₈	C₂×C₁₃	1	1	yes	characteristic
40	C₂×Dic₆	C₂×C₁₃	1	1	yes	characteristic
41	#216	C₂×C₁₃	1	4	yes	direct product factor
42	C₂×C₃⋊C₈	C₂×C₁₃	1	1	yes	characteristic
43	C₃×C₁₃	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
44	C₂×Q₁₆	—	3	1	no	Sylow
45	C₂×C₁₃	#216	1	2	yes	direct product factor
46	C₂×C₁₃	C₂×#67	1	1	yes	characteristic
47	C₃×Q₈	—	2	1	no	—
48	C₃×Q₈	C₂²×C₁₃	1	2	yes	—
49	C₂×C₃×C₄	—	2	1	no	—
50	C₂×C₃×C₄	C₂²×C₁₃	1	1	yes	characteristic
51	C₂×Dic₃	—	2	1	no	—
52	Dic₆	—	2	1	no	—
53	Dic₆	C₂²×C₁₃	1	2	yes	—
54	C₃⋊C₈	C₂²×C₁₃	1	2	yes	—
55	C₂×Q₈	—	3	1	no	—
56	C₂×Q₈	D₃×C₁₃	1	1	yes	characteristic
57	Q₁₆	—	3	4	no	—
58	C₂×C₈	—	3	1	no	—
59	C₁₃	C₂×#216	1	1	yes	characteristic, direct product factor, Sylow
60	C₂²×C₃	D₄×C₁₃	1	1	yes	characteristic
61	C₃×C₄	—	2	2	no	—
62	C₃×C₄	D₄×C₁₃	1	1	yes	characteristic
63	C₃×C₄	C₂³×C₁₃	1	1	yes	characteristic
64	Dic₃	—	2	2	no	—
65	Q₈	—	2	1	no	—
66	Q₈	—	3	2	no	—
67	Q₈	—	6	1	no	—
68	Q₈	C₂×D₃×C₁₃	1	2	yes	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	6	1	no	—
71	C₂×C₄	C₂×D₃×C₁₃	1	1	yes	characteristic
72	C₈	—	3	2	no	—
73	C₂×C₃	C₁₃×Q₁₆	1	2	yes	complemented
74	C₂×C₃	C₂×D₄×C₁₃	1	1	yes	characteristic
75	C₂²	C₁₃×#67	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	6	2	no	—
78	C₄	C₁₃×#67	1	1	yes	characteristic
79	C₄	C₂²×D₃×C₁₃	1	1	yes	characteristic
80	C₃	C₂×C₁₃×Q₁₆	1	1	yes	characteristic, complemented, Sylow
81	C₂	C₁₃×#216	1	2	yes	direct product factor
82	C₂	C₂×C₁₃×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₃	#67
commutator, cosocle	C₃×C₄	C₂³×C₁₃
Frattini	C₄	C₂²×D₃×C₁₃
Fitting	C₂×C₃×Q₈×C₁₃	C₂
socle, prime radical	C₂²×C₃×C₁₃	D₄
hypercenter	C₂×Q₈×C₁₃	D₃
hypocenter	C₃	C₂×C₁₃×Q₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×Q₈×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₁₃×#216	C₂	direct (N × H)
31. C₂×#216	C₁₃	direct (N × H)
32. C₂×C₃×C₁₃	Q₁₆	semidirect
41. #216	C₂×C₁₃	direct (N × H)
43. C₃×C₁₃	C₂×Q₁₆	semidirect
45. C₂×C₁₃	#216	direct (N × H)
59. C₁₃	C₂×#216	direct (N × H)
73. C₂×C₃	C₁₃×Q₁₆	semidirect
80. C₃	C₂×C₁₃×Q₁₆	semidirect
81. C₂	C₁₃×#216	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
C₂×C₁₃×Dic₆	2
C₁₃×#216	2
C₂×C₁₃×C₃⋊C₈	2
C₂×C₁₃×Q₁₆	3
C₂×#216	13

Subgroups — C2×C13×#216 #11928921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#216 #11928921