Subgroups — C₂²×C₃⋊#1044 #11925813

Order 1200.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊#1044	C₂	1	6	yes	maximal, direct product factor
3	C₂²×#1044	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₅²	C₄	1	1	yes	characteristic, complemented
5	C₂×C₃×C₅⋊D₅	C₄	1	3	yes	complemented
6	C₂×C₃×C₅⋊D₅	C₂²	1	3	yes	—
7	C₃⋊#1044	C₂²	1	4	yes	direct product factor
8	C₂²×ΓL(1,𝔽₁₆)	—	5	2	no	maximal
9	C₂²×C₅⋊D₅	D₃	1	1	yes	characteristic
10	C₂×#1044	—	3	6	no	—
11	C₂×C₃×C₅²	C₂×C₄	1	3	yes	complemented
12	C₃×C₅⋊D₅	C₂×C₄	1	3	yes	complemented
13	C₃×C₅⋊D₅	C₂³	1	1	yes	characteristic
14	C₂²×C₃×D₅	—	5	2	no	—
15	C₂²×C₃×D₅	—	10	2	no	—
16	C₂×ΓL(1,𝔽₁₆)	—	5	12	no	—
17	C₂²×C₅²	Dic₃	1	1	yes	characteristic, complemented
18	C₂×C₅⋊D₅	Dic₃	1	3	yes	complemented
19	C₂×C₅⋊D₅	C₂×D₃	1	3	yes	—
20	#1044	—	3	4	no	—
21	C₂²×AGL(1,𝔽₅)	—	15	2	no	—
22	C₃×C₅²	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
23	C₂²×C₃×C₅	—	2	2	no	—
24	C₂²×C₃×C₅	AGL(1,𝔽₅)	1	2	yes	complemented
25	C₂×C₃×D₅	—	5	6	no	—
26	C₂×C₃×D₅	—	5	6	no	—
27	C₂×C₃×D₅	—	10	6	no	—
28	C₂×C₃×D₅	—	10	6	no	—
29	ΓL(1,𝔽₁₆)	—	5	8	no	—
30	C₂×C₅²	C₂×Dic₃	1	3	yes	complemented
31	C₅⋊D₅	C₂×Dic₃	1	3	yes	complemented
32	C₅⋊D₅	C₂²×D₃	1	1	yes	characteristic
33	C₂²×Dic₃	—	25	1	no	Hall
34	C₂²×D₅	—	5	2	no	—
35	C₂²×D₅	—	10	2	no	—
36	C₂×AGL(1,𝔽₅)	—	15	12	no	—
37	C₂×C₃×C₅	—	2	6	no	—
38	C₂×C₃×C₅	C₂×AGL(1,𝔽₅)	1	6	yes	complemented
39	C₃×D₅	—	5	6	no	—
40	C₃×D₅	—	5	2	no	—
41	C₃×D₅	—	10	6	no	—
42	C₃×D₅	—	10	2	no	—
43	C₅²	C₂²×Dic₃	1	1	yes	characteristic, complemented, Sylow
44	C₂³×C₃	—	25	1	no	—
45	C₂×Dic₃	—	25	6	no	—
46	C₂²×C₅	—	2	2	no	—
47	C₂²×C₅	ΓL(1,𝔽₁₆)	1	2	yes	complemented
48	C₂×D₅	—	5	6	no	—
49	C₂×D₅	—	5	6	no	—
50	C₂×D₅	—	10	6	no	—
51	C₂×D₅	—	10	6	no	—
52	AGL(1,𝔽₅)	—	15	8	no	—
53	C₂²×C₄	—	75	1	no	Sylow
54	C₃×C₅	—	2	2	no	—
55	C₃×C₅	C₂²×AGL(1,𝔽₅)	1	2	yes	complemented
56	C₂²×C₃	—	25	3	no	—
57	C₂²×C₃	—	25	3	no	—
58	C₂²×C₃	#1044	1	1	yes	characteristic, complemented
59	Dic₃	—	25	4	no	—
60	C₂×C₅	—	2	6	no	—
61	C₂×C₅	C₂×ΓL(1,𝔽₁₆)	1	6	yes	complemented
62	D₅	—	5	6	no	—
63	D₅	—	5	2	no	—
64	D₅	—	10	6	no	—
65	D₅	—	10	2	no	—
66	C₂³	—	25	1	no	—
67	C₂×C₄	—	75	6	no	—
68	C₂×C₃	—	25	1	no	—
69	C₂×C₃	—	25	3	no	—
70	C₂×C₃	C₂×#1044	1	3	yes	complemented
71	C₅	—	2	2	no	—
72	C₅	C₂²×ΓL(1,𝔽₁₆)	1	2	yes	complemented
73	C₂²	—	25	3	no	—
74	C₂²	—	25	3	no	—
75	C₂²	C₃⋊#1044	1	1	yes	characteristic, direct product factor
76	C₄	—	75	4	no	—
77	C₃	C₂²×#1044	1	1	yes	characteristic, complemented, Sylow
78	C₂	—	25	1	no	—
79	C₂	—	25	3	no	—
80	C₂	C₂×C₃⋊#1044	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	C₃⋊#1044
commutator, hypocenter	C₃×C₅²	C₂²×C₄
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₅²	C₄
prime radical	C₂²×C₃×C₅⋊D₅	C₂
cosocle	C₃×C₅⋊D₅	C₂³
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. C₂×C₃⋊#1044	C₂	direct (N × H)
4. C₂²×C₃×C₅²	C₄	semidirect
5. C₂×C₃×C₅⋊D₅	C₄	semidirect
7. C₃⋊#1044	C₂²	direct (N × H)
11. C₂×C₃×C₅²	C₂×C₄	semidirect
12. C₃×C₅⋊D₅	C₂×C₄	semidirect
17. C₂²×C₅²	Dic₃	semidirect
18. C₂×C₅⋊D₅	Dic₃	semidirect
22. C₃×C₅²	C₂²×C₄	semidirect
24. C₂²×C₃×C₅	AGL(1,𝔽₅)	semidirect
30. C₂×C₅²	C₂×Dic₃	semidirect
31. C₅⋊D₅	C₂×Dic₃	semidirect
38. C₂×C₃×C₅	C₂×AGL(1,𝔽₅)	semidirect
43. C₅²	C₂²×Dic₃	semidirect
47. C₂²×C₅	ΓL(1,𝔽₁₆)	semidirect
55. C₃×C₅	C₂²×AGL(1,𝔽₅)	semidirect
58. C₂²×C₃	#1044	semidirect
61. C₂×C₅	C₂×ΓL(1,𝔽₁₆)	semidirect
70. C₂×C₃	C₂×#1044	semidirect
72. C₅	C₂²×ΓL(1,𝔽₁₆)	semidirect
75. C₂²	C₃⋊#1044	direct (N × H)
77. C₃	C₂²×#1044	semidirect
80. C₂	C₂×C₃⋊#1044	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×C₅⋊D₅	2
C₂×C₃⋊#1044	2
C₂²×#1044	3
C₂²×ΓL(1,𝔽₁₆)	5

Subgroups — C22×C3⋊#1044 #11925813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃⋊#1044 #11925813