Subgroups — C₃×#88180 #11928816

Order 1248.

152 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	C₃×C₂²⋊Dic₁₃	C₂	1	2	yes	maximal
3	C₃×C₄⋊Dic₁₃	C₂	1	2	yes	maximal, complemented
4	C₃×C₄×Dic₁₃	C₂	1	2	yes	maximal, complemented
5	#88180	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₃×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄×C₁₃	C₄	1	4	yes	complemented
8	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₃×Dic₁₃	C₂²	1	4	yes	—
11	C₂²×C₄×C₁₃	C₂×C₃	1	1	yes	characteristic
12	C₂²⋊Dic₁₃	C₂×C₃	1	2	yes	—
13	C₄⋊Dic₁₃	C₂×C₃	1	2	yes	complemented
14	C₄×Dic₁₃	C₂×C₃	1	2	yes	complemented
15	C₂²×C₃×C₁₃	—	2	2	no	—
16	C₂²×C₃×C₁₃	C₂×C₄	1	2	yes	—
17	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
18	C₃×C₄×C₁₃	C₂×C₄	1	2	yes	—
19	C₃×C₄×C₁₃	C₂×C₄	1	2	yes	—
20	C₃×Dic₁₃	—	2	4	no	—
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	1	yes	characteristic
24	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
25	C₂×Dic₁₃	C₂²×C₃	1	4	yes	—
26	C₃×#117	—	13	1	no	maximal, Hall
27	C₂×C₃×C₁₃	—	2	2	no	—
28	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₃×C₁₃	#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	C₂×C₃×C₄	1	2	yes	—
34	C₄×C₁₃	C₂×C₃×C₄	1	2	yes	—
35	Dic₁₃	—	2	4	no	—
36	C₂²×C₃×C₄	D₁₃	1	1	yes	characteristic
37	C₃×C₄⋊C₄	—	13	2	no	—
38	C₃×C₂²⋊C₄	—	13	2	no	—
39	C₃×C₄²	—	13	2	no	—
40	C₃×C₁₃	#117	1	1	yes	characteristic, complemented, Hall
41	#117	—	13	1	no	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	C₂×D₁₃	1	1	yes	characteristic
46	C₂×C₃×C₄	—	13	4	no	—
47	C₂×C₃×C₄	Dic₁₃	1	4	yes	complemented
48	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
49	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
50	C₂²×C₄	C₃×D₁₃	1	1	yes	characteristic
51	C₄⋊C₄	—	13	2	no	—
52	C₂²⋊C₄	—	13	2	no	—
53	C₄²	—	13	2	no	—
54	C₁₃	C₃×#117	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₃	—	2	2	no	—
56	C₂²×C₃	C₂×Dic₁₃	1	2	yes	—
57	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
58	C₃×C₄	—	26	4	no	—
59	C₃×C₄	C₂×Dic₁₃	1	2	yes	—
60	C₃×C₄	C₂×Dic₁₃	1	2	yes	—
61	C₂³	C₂×C₃×D₁₃	1	1	yes	characteristic
62	C₂×C₄	—	13	4	no	—
63	C₂×C₄	C₃×Dic₁₃	1	4	yes	complemented
64	C₂×C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
65	C₂×C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
66	C₂×C₃	—	2	2	no	—
67	C₂×C₃	#6127	1	2	yes	—
68	C₂×C₃	C₂²×Dic₁₃	1	1	yes	characteristic
69	C₂²	—	2	2	no	—
70	C₂²	C₂×C₃×Dic₁₃	1	2	yes	—
71	C₂²	C₂²×C₃×D₁₃	1	1	yes	characteristic
72	C₄	—	26	4	no	—
73	C₄	C₂×C₃×Dic₁₃	1	2	yes	—
74	C₄	C₂×C₃×Dic₁₃	1	2	yes	—
75	C₃	#88180	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	2	2	no	—
77	C₂	C₃×#6127	1	2	yes	—
78	C₂	C₂²×C₃×Dic₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₁₃
commutator	C₂×C₁₃	C₂²×C₃×C₄
Frattini	C₂²	C₂²×C₃×D₁₃
Fitting	C₂²×C₃×C₄×C₁₃	C₂
socle	C₂²×C₃×C₁₃	C₂³
prime radical	C₂³×C₃×C₁₃	C₂²
cosocle	C₂²×C₁₃	C₂³×C₃
hypercenter	C₂²×C₃×C₄	D₁₃
hypocenter	C₁₃	C₃×#117
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄

Complements

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

N	H ≅ G/N	type
3. C₃×C₄⋊Dic₁₃	C₂	semidirect
4. C₃×C₄×Dic₁₃	C₂	semidirect
5. #88180	C₃	direct (N × H)
7. C₂×C₃×C₄×C₁₃	C₄	semidirect
13. C₄⋊Dic₁₃	C₂×C₃	semidirect
14. C₄×Dic₁₃	C₂×C₃	semidirect
22. C₂×C₄×C₁₃	C₃×C₄	semidirect
40. C₃×C₁₃	#117	semidirect
47. C₂×C₃×C₄	Dic₁₃	semidirect
54. C₁₃	C₃×#117	semidirect
63. C₂×C₄	C₃×Dic₁₃	semidirect
75. C₃	#88180	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
C₃×C₂²⋊Dic₁₃	2
C₃×C₄⋊Dic₁₃	2
C₃×C₄×Dic₁₃	2
#88180	3
C₃×#117	13

Subgroups — C3×#88180 #11928816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88180 #11928816