Subgroups — #117×C₁₃⋊C₃ #11928722

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×C₁₃⋊C₃	C₂	1	2	yes	maximal, complemented
3	C₂²⋊C₄×C₁₃⋊C₃	C₂	1	2	yes	maximal
4	C₄²×C₁₃⋊C₃	C₂	1	2	yes	maximal, complemented
5	C₁₃×#117	C₃	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂³×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₁₃⋊C₃	C₄	1	4	yes	complemented
8	C₂×C₄×C₁₃⋊C₃	C₂²	1	4	yes	—
9	C₂×C₄×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₁₃	C₂×C₃	1	1	yes	characteristic
12	C₁₃×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
13	C₁₃×C₂²⋊C₄	C₂×C₃	1	2	yes	—
14	C₄²×C₁₃	C₂×C₃	1	2	yes	complemented
15	C₂²×C₁₃⋊C₃	—	2	2	no	—
16	C₂²×C₁₃⋊C₃	C₂×C₄	1	2	yes	—
17	C₂²×C₁₃⋊C₃	C₂³	1	1	yes	characteristic
18	C₄×C₁₃⋊C₃	—	2	4	no	—
19	C₄×C₁₃⋊C₃	C₂×C₄	1	2	yes	—
20	C₄×C₁₃⋊C₃	C₂×C₄	1	2	yes	—
21	C₂³×C₁₃	C₂²×C₃	1	1	yes	characteristic
22	C₂×C₄×C₁₃	C₃×C₄	1	4	yes	complemented
23	C₂×C₄×C₁₃	C₂²×C₃	1	4	yes	—
24	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
25	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
26	C₃×#117	—	13	1	no	maximal, Hall
27	C₂×C₁₃⋊C₃	—	2	2	no	—
28	C₂×C₁₃⋊C₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₁₃⋊C₃	#41	1	2	yes	—
30	C₂²×C₁₃	—	2	2	no	—
31	C₂²×C₁₃	C₂×C₃×C₄	1	2	yes	—
32	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
33	C₄×C₁₃	—	2	4	no	—
34	C₄×C₁₃	C₂×C₃×C₄	1	2	yes	—
35	C₄×C₁₃	C₂×C₃×C₄	1	2	yes	—
36	C₂²×C₃×C₄	—	13	1	no	—
37	C₃×C₄⋊C₄	—	13	2	no	—
38	C₃×C₂²⋊C₄	—	13	2	no	—
39	C₃×C₄²	—	13	2	no	—
40	C₁₃⋊C₃	#117	1	1	yes	characteristic, direct product factor, Hall
41	#117	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₁₃	—	2	2	no	—
43	C₂×C₁₃	C₂²×C₃×C₄	1	1	yes	characteristic
44	C₂×C₁₃	C₃×#41	1	2	yes	—
45	C₂³×C₃	—	13	1	no	—
46	C₂×C₃×C₄	—	13	4	no	—
47	C₂×C₃×C₄	—	13	1	no	—
48	C₂×C₃×C₄	—	13	4	no	—
49	C₂×C₃×C₄	—	13	1	no	—
50	C₂²×C₄	C₂×C₁₃⋊C₃	1	1	yes	characteristic
51	C₄⋊C₄	C₂×C₁₃⋊C₃	1	2	yes	complemented
52	C₂²⋊C₄	C₂×C₁₃⋊C₃	1	2	yes	—
53	C₄²	C₂×C₁₃⋊C₃	1	2	yes	complemented
54	C₁₃	C₃×#117	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₃	—	13	2	no	—
56	C₂²×C₃	—	13	1	no	—
57	C₂²×C₃	—	26	2	no	—
58	C₃×C₄	—	13	2	no	—
59	C₃×C₄	—	13	2	no	—
60	C₃×C₄	—	26	4	no	—
61	C₂³	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
62	C₂×C₄	C₄×C₁₃⋊C₃	1	4	yes	complemented
63	C₂×C₄	C₂²×C₁₃⋊C₃	1	4	yes	—
64	C₂×C₄	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
65	C₂×C₄	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
66	C₂×C₃	—	13	1	no	—
67	C₂×C₃	—	13	2	no	—
68	C₂×C₃	—	26	2	no	—
69	C₂²	—	2	2	no	—
70	C₂²	C₂×C₄×C₁₃⋊C₃	1	2	yes	—
71	C₂²	C₂³×C₁₃⋊C₃	1	1	yes	characteristic
72	C₄	—	2	4	no	—
73	C₄	C₂×C₄×C₁₃⋊C₃	1	2	yes	—
74	C₄	C₂×C₄×C₁₃⋊C₃	1	2	yes	—
75	C₃	—	13	1	no	Sylow
76	C₂	—	2	2	no	—
77	C₂	C₂²×C₄×C₁₃⋊C₃	1	1	yes	characteristic
78	C₂	#41×C₁₃⋊C₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×C₁₃⋊C₃
commutator	C₂×C₁₃	C₂²×C₃×C₄
Frattini	C₂²	C₂³×C₁₃⋊C₃
Fitting	C₁₃×#117	C₃
socle, cosocle	C₂²×C₁₃	C₂³×C₃
prime radical	C₂³×C₁₃⋊C₃	C₂²
hypercenter	#117	C₁₃⋊C₃
hypocenter	C₁₃	C₃×#117
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
2. C₄⋊C₄×C₁₃⋊C₃	C₂	semidirect
4. C₄²×C₁₃⋊C₃	C₂	semidirect
5. C₁₃×#117	C₃	semidirect
7. C₂×C₄×C₁₃⋊C₃	C₄	semidirect
12. C₁₃×C₄⋊C₄	C₂×C₃	semidirect
14. C₄²×C₁₃	C₂×C₃	semidirect
22. C₂×C₄×C₁₃	C₃×C₄	semidirect
40. C₁₃⋊C₃	#117	direct (N × H)
41. #117	C₁₃⋊C₃	direct (N × H)
51. C₄⋊C₄	C₂×C₁₃⋊C₃	semidirect
53. C₄²	C₂×C₁₃⋊C₃	semidirect
54. C₁₃	C₃×#117	semidirect
62. C₂×C₄	C₄×C₁₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₁₃⋊C₃	2
C₄⋊C₄×C₁₃⋊C₃	2
C₂²⋊C₄×C₁₃⋊C₃	2
C₄²×C₁₃⋊C₃	2
C₁₃×#117	3
C₃×#117	13

Subgroups — #117×C13⋊C3 #11928722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #117×C₁₃⋊C₃ #11928722