Subgroups — C₂×C₁₃×#208 #11928897

Order 1248.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#208	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₃×C₃⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×M₁₆	—	3	1	no	maximal, Hall
5	C₂³×C₃×C₁₃	C₄	1	1	yes	characteristic
6	C₂×C₃×C₄×C₁₃	C₄	1	2	yes	—
7	C₂×C₃×C₄×C₁₃	C₄	1	1	yes	characteristic
8	C₂×C₃×C₄×C₁₃	C₂²	1	2	yes	—
9	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×C₃⋊C₈	C₂²	1	4	yes	complemented
11	C₂²×C₄×C₁₃	D₃	1	1	yes	characteristic
12	C₁₃×M₁₆	—	3	4	no	—
13	C₂×C₈×C₁₃	—	3	2	no	—
14	C₂²×C₃×C₁₃	—	2	2	no	—
15	C₂²×C₃×C₁₃	C₂×C₄	1	2	yes	—
16	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₃×C₄×C₁₃	C₂×C₄	1	2	yes	—
18	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
20	C₂³×C₁₃	Dic₃	1	1	yes	characteristic
21	C₂×C₄×C₁₃	Dic₃	1	1	yes	characteristic
22	C₂×C₄×C₁₃	Dic₃	1	2	yes	—
23	C₂×C₄×C₁₃	C₂×D₃	1	2	yes	—
24	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
25	C₈×C₁₃	—	3	4	no	—
26	C₂×#208	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₃×C₁₃	—	2	2	no	—
28	C₂×C₃×C₁₃	M₁₆	1	2	yes	complemented
29	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₁₃	—	2	2	no	—
31	C₂²×C₁₃	C₂×Dic₃	1	2	yes	—
32	C₂²×C₁₃	C₂×Dic₃	1	1	yes	characteristic
33	C₄×C₁₃	C₂×Dic₃	1	2	yes	—
34	C₄×C₁₃	C₂×Dic₃	1	1	yes	characteristic
35	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
36	C₂²×C₃×C₄	C₂×C₁₃	1	1	yes	characteristic
37	#208	C₂×C₁₃	1	4	yes	direct product factor
38	C₂×C₃⋊C₈	C₂×C₁₃	1	2	yes	complemented
39	C₃×C₁₃	C₂×M₁₆	1	1	yes	characteristic, complemented, Hall
40	C₂×M₁₆	—	3	1	no	Sylow
41	C₂×C₁₃	—	2	2	no	—
42	C₂×C₁₃	#208	1	2	yes	direct product factor
43	C₂×C₁₃	C₂²×Dic₃	1	1	yes	characteristic
44	C₂³×C₃	C₄×C₁₃	1	1	yes	characteristic
45	C₂×C₃×C₄	C₄×C₁₃	1	2	yes	—
46	C₂×C₃×C₄	C₄×C₁₃	1	1	yes	characteristic
47	C₂×C₃×C₄	C₂²×C₁₃	1	1	yes	characteristic
48	C₂×C₃×C₄	C₂²×C₁₃	1	2	yes	—
49	C₃⋊C₈	C₂²×C₁₃	1	4	yes	complemented
50	C₂²×C₄	D₃×C₁₃	1	1	yes	characteristic
51	M₁₆	—	3	4	no	—
52	C₂×C₈	—	3	2	no	—
53	C₁₃	C₂×#208	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²×C₃	—	2	2	no	—
55	C₂²×C₃	C₂×C₄×C₁₃	1	2	yes	—
56	C₂²×C₃	C₂×C₄×C₁₃	1	1	yes	characteristic
57	C₃×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
58	C₃×C₄	C₂×C₄×C₁₃	1	2	yes	—
59	C₃×C₄	C₂³×C₁₃	1	1	yes	characteristic
60	C₂³	Dic₃×C₁₃	1	1	yes	characteristic
61	C₂×C₄	Dic₃×C₁₃	1	2	yes	—
62	C₂×C₄	Dic₃×C₁₃	1	1	yes	characteristic
63	C₂×C₄	C₂×D₃×C₁₃	1	1	yes	characteristic
64	C₂×C₄	C₂×D₃×C₁₃	1	2	yes	—
65	C₈	—	3	4	no	—
66	C₂×C₃	—	2	2	no	—
67	C₂×C₃	C₁₃×M₁₆	1	2	yes	complemented
68	C₂×C₃	C₂²×C₄×C₁₃	1	1	yes	characteristic
69	C₂²	—	2	2	no	—
70	C₂²	C₂×Dic₃×C₁₃	1	2	yes	—
71	C₂²	C₂×Dic₃×C₁₃	1	1	yes	characteristic
72	C₄	C₂×Dic₃×C₁₃	1	2	yes	—
73	C₄	C₂×Dic₃×C₁₃	1	1	yes	characteristic
74	C₄	C₂²×D₃×C₁₃	1	1	yes	characteristic
75	C₃	C₂×C₁₃×M₁₆	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	2	2	no	—
77	C₂	C₁₃×#208	1	2	yes	direct product factor
78	C₂	C₂²×Dic₃×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₃
commutator	C₂×C₃	C₂²×C₄×C₁₃
Frattini	C₄	C₂²×D₃×C₁₃
Fitting	C₂²×C₃×C₄×C₁₃	C₂
socle	C₂²×C₃×C₁₃	C₂×C₄
prime radical	C₂³×C₃×C₁₃	C₄
cosocle	C₃×C₄	C₂³×C₁₃
hypercenter	C₂²×C₄×C₁₃	D₃
hypocenter	C₃	C₂×C₁₃×M₁₆
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₁₃×#208	C₂	direct (N × H)
3. C₂×C₁₃×C₃⋊C₈	C₂	semidirect
10. C₁₃×C₃⋊C₈	C₂²	semidirect
26. C₂×#208	C₁₃	direct (N × H)
28. C₂×C₃×C₁₃	M₁₆	semidirect
37. #208	C₂×C₁₃	direct (N × H)
38. C₂×C₃⋊C₈	C₂×C₁₃	semidirect
39. C₃×C₁₃	C₂×M₁₆	semidirect
42. C₂×C₁₃	#208	direct (N × H)
49. C₃⋊C₈	C₂²×C₁₃	semidirect
53. C₁₃	C₂×#208	direct (N × H)
67. C₂×C₃	C₁₃×M₁₆	semidirect
75. C₃	C₂×C₁₃×M₁₆	semidirect
77. C₂	C₁₃×#208	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄×C₁₃	2
C₁₃×#208	2
C₂×C₁₃×C₃⋊C₈	2
C₂×C₁₃×M₁₆	3
C₂×#208	13

Subgroups — C2×C13×#208 #11928897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#208 #11928897