Subgroups — #11924813

Order 1200.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₆×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₅₀	C₂	1	1	yes	maximal, characteristic
3	C₃⋊#6014	C₂	1	1	yes	maximal, characteristic
4	#87723	—	3	1	no	maximal, Hall
5	C₃×C₄×C₂₅	C₂²	1	1	yes	characteristic
6	C₃×Dic₂₅	—	2	1	no	—
7	Dic₃×C₂₅	—	2	1	no	—
8	#6661	—	5	1	no	maximal
9	Q₈×C₂₅	—	3	1	no	—
10	Dic₅₀	D₃	1	1	yes	characteristic
11	#6014	—	3	1	no	—
12	C₂×C₃×C₂₅	D₄	1	1	yes	characteristic
13	C₅×Dic₆	D₅	1	1	yes	characteristic
14	C₃×Dic₁₀	—	5	1	no	—
15	C₃⋊#168	—	5	1	no	—
16	C₄×C₂₅	—	6	1	no	—
17	C₄×C₂₅	C₂×D₃	1	1	yes	characteristic
18	Dic₂₅	—	2	1	no	—
19	#689	—	15	1	no	—
20	C₃×C₂₅	Q₁₆	1	1	yes	characteristic, complemented, Hall
21	C₃×C₄×C₅	C₂×D₅	1	1	yes	characteristic
22	C₃×Dic₅	—	10	1	no	—
23	C₅×Dic₃	—	2	1	no	—
24	C₂×C₂₅	#67	1	1	yes	characteristic
25	#216	—	25	1	no	Hall
26	C₅×Q₈	—	3	1	no	—
27	Dic₁₀	—	5	1	no	—
28	#168	—	15	1	no	—
29	C₂×C₃×C₅	C₂²⋊D₅	1	1	yes	characteristic
30	C₂₅	#216	1	1	yes	characteristic, complemented, Sylow
31	C₃×Q₈	—	25	1	no	—
32	Dic₆	D₂₅	1	1	yes	characteristic
33	C₃⋊C₈	—	25	1	no	—
34	C₄×C₅	—	6	1	no	—
35	C₄×C₅	D₃×D₅	1	1	yes	characteristic
36	Dic₅	—	10	1	no	—
37	Q₁₆	—	75	1	no	Sylow
38	C₃×C₅	#689	1	1	yes	characteristic
39	C₃×C₄	—	50	1	no	—
40	C₃×C₄	C₂×D₂₅	1	1	yes	characteristic
41	Dic₃	—	2	1	no	—
42	C₂×C₅	#1201	1	1	yes	characteristic
43	Q₈	—	3	1	no	—
44	Q₈	—	25	1	no	—
45	C₈	—	75	1	no	—
46	C₂×C₃	C₂²⋊D₂₅	1	1	yes	characteristic
47	C₅	#6661	1	1	yes	characteristic
48	C₄	—	6	1	no	—
49	C₄	—	50	1	no	—
50	C₄	D₃×D₂₅	1	1	yes	characteristic
51	C₃	#87723	1	1	yes	characteristic, complemented, Sylow
52	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, prime radical	C₂×C₃×C₅	C₂²⋊D₅
hypercenter	C₄	D₃×D₂₅
hypocenter	C₃×C₂₅	Q₁₆
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
20. C₃×C₂₅	Q₁₆	semidirect
30. C₂₅	#216	semidirect
51. C₃	#87723	semidirect

Maximal subgroups

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

subgroup	index
Dic₆×C₂₅	2
C₃×Dic₅₀	2
C₃⋊#6014	2
#87723	3
#6661	5