Subgroups — C₂×#10597155 #11925715

Order 1200.

304 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊#1039	C₂	1	2	yes	maximal
3	#10597155	C₂	1	4	yes	maximal, direct product factor
4	C₂×#6045	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₅²	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₅²	C₂²	1	2	yes	—
7	C₃⋊#1039	C₂²	1	4	yes	—
8	C₂×Dic₃₀	—	5	6	no	maximal
9	C₂×C₄×C₅²	D₃	1	1	yes	characteristic
10	C₂×#1039	—	3	2	no	—
11	#6045	—	3	4	no	—
12	C₂×C₃×C₅²	Q₈	1	2	yes	complemented
13	C₂×C₃×C₅²	C₂³	1	1	yes	characteristic
14	C₂×C₃×C₄×C₅	D₅	1	6	yes	—
15	C₂×Dic₁₅	—	5	12	no	—
16	Dic₃₀	—	5	24	no	—
17	C₂²×C₅²	C₂×D₃	1	1	yes	characteristic
18	C₄×C₅²	C₂×D₃	1	2	yes	—
19	#1039	—	3	4	no	—
20	C₂×Dic₁₀	—	15	6	no	—
21	C₃×C₅²	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
22	C₂²×C₃×C₅	C₂×D₅	1	6	yes	—
23	C₃×C₄×C₅	C₂×D₅	1	12	yes	—
24	Dic₁₅	—	5	24	no	—
25	C₂×C₅²	Dic₆	1	2	yes	complemented
26	C₂×C₅²	C₂²×D₃	1	1	yes	characteristic
27	C₂×Dic₆	—	25	1	no	Hall
28	C₂×C₄×C₅	D₁₅	1	6	yes	—
29	C₂×Dic₅	—	15	12	no	—
30	Dic₁₀	—	15	24	no	—
31	C₂×C₃×C₅	Dic₁₀	1	12	yes	complemented
32	C₂×C₃×C₅	C₂²×D₅	1	6	yes	—
33	C₅²	C₂×Dic₆	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃×C₄	C₅⋊D₅	1	1	yes	characteristic
35	C₂×Dic₃	—	25	2	no	—
36	Dic₆	—	25	4	no	—
37	C₂²×C₅	C₂×D₁₅	1	6	yes	—
38	C₄×C₅	C₂×D₁₅	1	12	yes	—
39	Dic₅	—	15	24	no	—
40	C₂×Q₈	—	75	1	no	Sylow
41	C₃×C₅	C₂×Dic₁₀	1	6	yes	complemented
42	C₂²×C₃	C₂×C₅⋊D₅	1	1	yes	characteristic
43	C₃×C₄	C₂×C₅⋊D₅	1	2	yes	—
44	Dic₃	—	25	4	no	—
45	C₂×C₅	Dic₃₀	1	12	yes	complemented
46	C₂×C₅	C₂²×D₁₅	1	6	yes	—
47	Q₈	—	75	4	no	—
48	C₂×C₄	—	75	2	no	—
49	C₂×C₄	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
50	C₂×C₃	#6045	1	2	yes	complemented
51	C₂×C₃	C₂²×C₅⋊D₅	1	1	yes	characteristic
52	C₅	C₂×Dic₃₀	1	6	yes	complemented
53	C₂²	C₂×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
54	C₄	—	75	4	no	—
55	C₄	C₂×C₃⋊(C₅⋊D₅)	1	2	yes	—
56	C₃	C₂×#6045	1	1	yes	characteristic, complemented, Sylow
57	C₂	#10597155	1	2	yes	direct product factor
58	C₂	C₂²×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₃⋊(C₅⋊D₅)
commutator, cosocle	C₂×C₃×C₅²	C₂³
Frattini	C₂	C₂²×C₃⋊(C₅⋊D₅)
Fitting	C₂×C₃×C₄×C₅²	C₂
socle, prime radical	C₂²×C₃×C₅²	C₂²
hypercenter	C₂×C₄	C₃⋊(C₅⋊D₅)
hypocenter	C₃×C₅²	C₂×Q₈
LCS	G ▷ C₂×C₃×C₅² ▷ C₃×C₅²
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
3. #10597155	C₂	direct (N × H)
12. C₂×C₃×C₅²	Q₈	semidirect
21. C₃×C₅²	C₂×Q₈	semidirect
25. C₂×C₅²	Dic₆	semidirect
31. C₂×C₃×C₅	Dic₁₀	semidirect
33. C₅²	C₂×Dic₆	semidirect
41. C₃×C₅	C₂×Dic₁₀	semidirect
45. C₂×C₅	Dic₃₀	semidirect
50. C₂×C₃	#6045	semidirect
52. C₅	C₂×Dic₃₀	semidirect
56. C₃	C₂×#6045	semidirect
57. C₂	#10597155	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₅²	2
C₂×C₃⋊#1039	2
#10597155	2
C₂×#6045	3
C₂×Dic₃₀	5

Subgroups — C2×#10597155 #11925715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10597155 #11925715