Subgroups — #11924861

Order 1200.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#6014	C₂	1	2	yes	maximal, complemented
3	#87716	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₂₅	C₄	1	1	yes	characteristic
5	C₃×C₄×C₂₅	C₄	1	1	yes	characteristic
6	C₃×C₄×C₂₅	C₂²	1	1	yes	characteristic
7	#6710	—	5	1	no	maximal
8	C₂×C₄×C₂₅	D₃	1	1	yes	characteristic
9	#6014	—	3	2	no	—
10	C₂×C₃×C₂₅	—	2	1	no	—
11	C₂×C₃×C₂₅	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×C₄×C₅	D₅	1	1	yes	characteristic
13	C₃⋊#168	—	5	2	no	—
14	C₂²×C₂₅	Dic₃	1	1	yes	characteristic
15	C₄×C₂₅	Dic₃	1	1	yes	characteristic
16	C₄×C₂₅	C₂×D₃	1	1	yes	characteristic
17	#681	—	15	1	no	—
18	C₃×C₂₅	M₁₆	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₃×C₅	Dic₅	1	1	yes	characteristic
20	C₃×C₄×C₅	Dic₅	1	1	yes	characteristic
21	C₃×C₄×C₅	C₂×D₅	1	1	yes	characteristic
22	C₂×C₂₅	—	2	1	no	—
23	C₂×C₂₅	C₂×Dic₃	1	1	yes	characteristic
24	#208	—	25	1	no	Hall
25	C₂×C₄×C₅	D₁₅	1	1	yes	characteristic
26	#168	—	15	2	no	—
27	C₂×C₃×C₅	—	2	1	no	—
28	C₂×C₃×C₅	C₂×Dic₅	1	1	yes	characteristic
29	C₂₅	#208	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃×C₄	D₂₅	1	1	yes	characteristic
31	C₃⋊C₈	—	25	2	no	—
32	C₂²×C₅	Dic₁₅	1	1	yes	characteristic
33	C₄×C₅	Dic₁₅	1	1	yes	characteristic
34	C₄×C₅	C₂×D₁₅	1	1	yes	characteristic
35	M₁₆	—	75	1	no	Sylow
36	C₃×C₅	#681	1	1	yes	characteristic
37	C₂²×C₃	Dic₂₅	1	1	yes	characteristic
38	C₃×C₄	Dic₂₅	1	1	yes	characteristic
39	C₃×C₄	C₂×D₂₅	1	1	yes	characteristic
40	C₂×C₅	—	2	1	no	—
41	C₂×C₅	C₂×Dic₁₅	1	1	yes	characteristic
42	C₂×C₄	D₇₅	1	1	yes	characteristic
43	C₈	—	75	2	no	—
44	C₂×C₃	—	2	1	no	—
45	C₂×C₃	C₂×Dic₂₅	1	1	yes	characteristic
46	C₅	#6710	1	1	yes	characteristic
47	C₂²	Dic₇₅	1	1	yes	characteristic
48	C₄	Dic₇₅	1	1	yes	characteristic
49	C₄	C₂×D₇₅	1	1	yes	characteristic
50	C₃	#87716	1	1	yes	characteristic, complemented, Sylow
51	C₂	—	2	1	no	—
52	C₂	C₂×Dic₇₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₇₅
commutator	C₂×C₃×C₂₅	C₂×C₄
Frattini	C₄×C₅	C₂×D₁₅
Fitting	C₂×C₃×C₄×C₂₅	C₂
socle	C₂×C₃×C₅	C₂×Dic₅
prime radical	C₂²×C₃×C₅	Dic₅
cosocle	C₃×C₄×C₂₅	C₂²
hypercenter	C₂×C₄	D₇₅
hypocenter	C₃×C₂₅	M₁₆
LCS	G ▷ C₂×C₃×C₂₅ ▷ C₃×C₂₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₃⋊#6014	C₂	semidirect
18. C₃×C₂₅	M₁₆	semidirect
29. C₂₅	#208	semidirect
50. C₃	#87716	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₂₅	2
C₃⋊#6014	2
#87716	3
#6710	5