Subgroups — #11924809

Order 1200.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₂×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₅₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊#6014	C₂	1	1	yes	maximal, characteristic, complemented
4	#87721	—	3	1	no	maximal, Hall
5	C₂×D₃×C₂₅	—	2	1	no	—
6	C₃×C₄×C₂₅	C₂²	1	1	yes	characteristic
7	C₃×Dic₂₅	—	2	1	no	—
8	#6656	—	5	1	no	maximal
9	D₄×C₂₅	—	3	1	no	—
10	Dic₅₀	D₃	1	1	yes	characteristic, complemented
11	#6014	—	3	1	no	—
12	C₂×C₃×C₂₅	D₄	1	1	yes	characteristic
13	D₃×C₂₅	—	4	1	no	—
14	C₅×D₁₂	D₅	1	1	yes	characteristic
15	C₃×Dic₁₀	—	5	1	no	—
16	C₃⋊#168	—	5	1	no	—
17	C₂²×C₂₅	—	6	1	no	—
18	C₄×C₂₅	C₂×D₃	1	1	yes	characteristic
19	Dic₂₅	—	2	1	no	—
20	#687	—	15	1	no	—
21	C₃×C₂₅	SD₁₆	1	1	yes	characteristic, complemented, Hall
22	C₂×C₅×D₃	—	2	1	no	—
23	C₃×C₄×C₅	C₂×D₅	1	1	yes	characteristic
24	C₃×Dic₅	—	10	1	no	—
25	C₂×C₂₅	—	12	1	no	—
26	C₂×C₂₅	#67	1	1	yes	characteristic
27	#215	—	25	1	no	Hall
28	C₅×D₄	—	3	1	no	—
29	Dic₁₀	—	5	1	no	—
30	#168	—	15	1	no	—
31	C₂×C₃×C₅	C₂²⋊D₅	1	1	yes	characteristic
32	C₅×D₃	—	4	1	no	—
33	C₂₅	#215	1	1	yes	characteristic, complemented, Sylow
34	C₃×Q₈	—	25	1	no	—
35	D₁₂	D₂₅	1	1	yes	characteristic
36	C₃⋊C₈	—	25	1	no	—
37	C₂²×C₅	—	6	1	no	—
38	C₄×C₅	D₃×D₅	1	1	yes	characteristic
39	Dic₅	—	10	1	no	—
40	SD₁₆	—	75	1	no	Sylow
41	C₃×C₅	#687	1	1	yes	characteristic
42	C₂×D₃	—	2	1	no	—
43	C₃×C₄	—	50	1	no	—
44	C₃×C₄	C₂×D₂₅	1	1	yes	characteristic
45	C₂×C₅	—	12	1	no	—
46	C₂×C₅	#1201	1	1	yes	characteristic
47	Q₈	—	25	1	no	—
48	D₄	—	3	1	no	—
49	C₈	—	75	1	no	—
50	C₂×C₃	C₂²⋊D₂₅	1	1	yes	characteristic
51	D₃	—	4	1	no	—
52	C₅	#6656	1	1	yes	characteristic
53	C₂²	—	6	1	no	—
54	C₄	—	50	1	no	—
55	C₄	D₃×D₂₅	1	1	yes	characteristic
56	C₃	#87721	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	12	1	no	—
58	C₂	#10597031	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10597031
commutator, Fitting, cosocle	C₃×C₄×C₂₅	C₂²
Frattini	C₄×C₅	D₃×D₅
socle	C₂×C₃×C₅	C₂²⋊D₅
prime radical	C₅×D₁₂	D₅
hypercenter	C₄	D₃×D₂₅
hypocenter	C₃×C₂₅	SD₁₆
LCS	G ▷ C₃×C₄×C₂₅ ▷ C₂×C₃×C₂₅ ▷ C₃×C₂₅
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₃×Dic₅₀	C₂	semidirect
3. C₃⋊#6014	C₂	semidirect
10. Dic₅₀	D₃	semidirect
21. C₃×C₂₅	SD₁₆	semidirect
33. C₂₅	#215	semidirect
56. C₃	#87721	semidirect

Maximal subgroups

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

subgroup	index
D₁₂×C₂₅	2
C₃×Dic₅₀	2
C₃⋊#6014	2
#87721	3
#6656	5