Subgroups — C₂×C₂²⋊C₄×C₁₃⋊C₃ #11928720

Order 1248.

264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₁₃⋊C₃	C₂	1	2	yes	maximal, complemented
3	C₂²⋊C₄×C₁₃⋊C₃	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₃×C₂²⋊C₄	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂³×C₁₃⋊C₃	—	2	4	no	—
6	C₂³×C₁₃⋊C₃	C₄	1	4	yes	complemented
7	C₂³×C₁₃⋊C₃	C₂²	1	2	yes	—
8	C₂³×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₁₃⋊C₃	—	2	4	no	—
10	C₂×C₄×C₁₃⋊C₃	C₂²	1	4	yes	complemented
11	C₂⁴×C₁₃	C₂×C₃	1	1	yes	characteristic
12	C₂²×C₄×C₁₃	C₂×C₃	1	2	yes	complemented
13	C₁₃×C₂²⋊C₄	C₂×C₃	1	4	yes	complemented
14	C₂²×C₁₃⋊C₃	—	2	8	no	—
15	C₂²×C₁₃⋊C₃	—	2	4	no	—
16	C₂²×C₁₃⋊C₃	C₂×C₄	1	2	yes	—
17	C₂²×C₁₃⋊C₃	C₂×C₄	1	4	yes	complemented
18	C₂²×C₁₃⋊C₃	D₄	1	4	yes	—
19	C₂²×C₁₃⋊C₃	C₂³	1	1	yes	characteristic
20	C₄×C₁₃⋊C₃	—	2	4	no	—
21	C₂³×C₁₃	—	2	4	no	—
22	C₂³×C₁₃	C₃×C₄	1	4	yes	complemented
23	C₂³×C₁₃	C₂²×C₃	1	2	yes	—
24	C₂³×C₁₃	C₂²×C₃	1	1	yes	characteristic
25	C₂×C₄×C₁₃	—	2	4	no	—
26	C₂×C₄×C₁₃	C₂²×C₃	1	4	yes	complemented
27	C₂×C₃×C₂²⋊C₄	—	13	1	no	maximal, Hall
28	C₂×C₁₃⋊C₃	—	2	4	no	—
29	C₂×C₁₃⋊C₃	C₂²⋊C₄	1	4	yes	direct product factor
30	C₂×C₁₃⋊C₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₁₃⋊C₃	C₂×D₄	1	2	yes	—
32	C₂²×C₁₃	—	2	8	no	—
33	C₂²×C₁₃	—	2	4	no	—
34	C₂²×C₁₃	C₂×C₃×C₄	1	2	yes	—
35	C₂²×C₁₃	C₂×C₃×C₄	1	4	yes	complemented
36	C₂²×C₁₃	C₃×D₄	1	4	yes	—
37	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
38	C₄×C₁₃	—	2	4	no	—
39	C₂⁴×C₃	—	13	1	no	—
40	C₂²×C₃×C₄	—	13	2	no	—
41	C₃×C₂²⋊C₄	—	13	4	no	—
42	C₁₃⋊C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₂²⋊C₄	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×C₁₃	—	2	4	no	—
45	C₂×C₁₃	C₃×C₂²⋊C₄	1	4	yes	complemented
46	C₂×C₁₃	C₂²×C₃×C₄	1	1	yes	characteristic
47	C₂×C₁₃	C₂×C₃×D₄	1	2	yes	—
48	C₂³×C₃	—	13	4	no	—
49	C₂³×C₃	—	13	2	no	—
50	C₂³×C₃	—	13	1	no	—
51	C₂³×C₃	—	26	4	no	—
52	C₂×C₃×C₄	—	13	4	no	—
53	C₂×C₃×C₄	—	26	4	no	—
54	C₂⁴	C₂×C₁₃⋊C₃	1	1	yes	characteristic
55	C₂²×C₄	C₂×C₁₃⋊C₃	1	2	yes	complemented
56	C₂²⋊C₄	C₂×C₁₃⋊C₃	1	4	yes	direct product factor
57	C₁₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₃	—	13	2	no	—
59	C₂²×C₃	—	13	4	no	—
60	C₂²×C₃	—	13	4	no	—
61	C₂²×C₃	—	13	1	no	—
62	C₂²×C₃	—	26	4	no	—
63	C₂²×C₃	—	26	8	no	—
64	C₃×C₄	—	26	4	no	—
65	C₂³	—	2	4	no	—
66	C₂³	C₄×C₁₃⋊C₃	1	4	yes	complemented
67	C₂³	C₂²×C₁₃⋊C₃	1	2	yes	—
68	C₂³	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
69	C₂×C₄	—	2	4	no	—
70	C₂×C₄	C₂²×C₁₃⋊C₃	1	4	yes	complemented
71	C₂×C₃	—	13	1	no	—
72	C₂×C₃	—	13	2	no	—
73	C₂×C₃	—	13	4	no	—
74	C₂×C₃	—	26	4	no	—
75	C₂²	—	2	4	no	—
76	C₂²	—	2	8	no	—
77	C₂²	C₂×C₄×C₁₃⋊C₃	1	2	yes	—
78	C₂²	C₂×C₄×C₁₃⋊C₃	1	4	yes	complemented
79	C₂²	D₄×C₁₃⋊C₃	1	4	yes	—
80	C₂²	C₂³×C₁₃⋊C₃	1	1	yes	characteristic
81	C₄	—	2	4	no	—
82	C₃	—	13	1	no	Sylow
83	C₂	—	2	4	no	—
84	C₂	C₂²⋊C₄×C₁₃⋊C₃	1	4	yes	direct product factor
85	C₂	C₂²×C₄×C₁₃⋊C₃	1	1	yes	characteristic
86	C₂	C₂×D₄×C₁₃⋊C₃	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×C₁₃⋊C₃
commutator	C₂×C₁₃	C₂²×C₃×C₄
Frattini	C₂²	C₂³×C₁₃⋊C₃
Fitting	C₂×C₁₃×C₂²⋊C₄	C₃
socle	C₂³×C₁₃	C₂²×C₃
prime radical	C₂⁴×C₁₃⋊C₃	C₂
cosocle	C₂²×C₁₃	C₂³×C₃
hypercenter	C₂×C₂²⋊C₄	C₁₃⋊C₃
hypocenter	C₁₃	C₂×C₃×C₂²⋊C₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₁₃⋊C₃	C₂	semidirect
3. C₂²⋊C₄×C₁₃⋊C₃	C₂	direct (N × H)
4. C₂×C₁₃×C₂²⋊C₄	C₃	semidirect
6. C₂³×C₁₃⋊C₃	C₄	semidirect
10. C₂×C₄×C₁₃⋊C₃	C₂²	semidirect
12. C₂²×C₄×C₁₃	C₂×C₃	semidirect
13. C₁₃×C₂²⋊C₄	C₂×C₃	semidirect
17. C₂²×C₁₃⋊C₃	C₂×C₄	semidirect
22. C₂³×C₁₃	C₃×C₄	semidirect
26. C₂×C₄×C₁₃	C₂²×C₃	semidirect
29. C₂×C₁₃⋊C₃	C₂²⋊C₄	direct (N × H)
35. C₂²×C₁₃	C₂×C₃×C₄	semidirect
42. C₁₃⋊C₃	C₂×C₂²⋊C₄	direct (N × H)
43. C₂×C₂²⋊C₄	C₁₃⋊C₃	direct (N × H)
45. C₂×C₁₃	C₃×C₂²⋊C₄	semidirect
55. C₂²×C₄	C₂×C₁₃⋊C₃	semidirect
56. C₂²⋊C₄	C₂×C₁₃⋊C₃	direct (N × H)
57. C₁₃	C₂×C₃×C₂²⋊C₄	semidirect
66. C₂³	C₄×C₁₃⋊C₃	semidirect
70. C₂×C₄	C₂²×C₁₃⋊C₃	semidirect
78. C₂²	C₂×C₄×C₁₃⋊C₃	semidirect
84. C₂	C₂²⋊C₄×C₁₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₁₃⋊C₃	2
C₂²×C₄×C₁₃⋊C₃	2
C₂²⋊C₄×C₁₃⋊C₃	2
C₂×C₁₃×C₂²⋊C₄	3
C₂×C₃×C₂²⋊C₄	13

Subgroups — C2×C22⋊C4×C13⋊C3 #11928720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂²⋊C₄×C₁₃⋊C₃ #11928720