Subgroups — C₃×#87712 #11924825

Order 1200.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#6014	C₂	1	1	yes	maximal, characteristic, complemented
4	#87712	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×D₂₅	C₄	1	1	yes	characteristic
6	C₃×C₄×C₂₅	C₂²	1	1	yes	characteristic
7	C₃×Dic₂₅	C₄	1	1	yes	characteristic
8	C₃×#676	—	5	1	no	maximal
9	C₄×D₂₅	C₂×C₃	1	1	yes	characteristic
10	C₈×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
11	#6014	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×C₃×C₂₅	C₂×C₄	1	1	yes	characteristic
13	C₃×D₂₅	—	2	1	no	—
14	C₃×C₄×D₅	—	5	1	no	—
15	C₃×C₅×C₈	D₅	1	1	yes	characteristic
16	C₃×#168	—	5	1	no	—
17	C₂×D₂₅	C₃×C₄	1	1	yes	characteristic
18	C₄×C₂₅	C₂²×C₃	1	1	yes	characteristic
19	Dic₂₅	C₃×C₄	1	1	yes	characteristic
20	#676	—	5	1	no	—
21	C₃×C₂₅	M₁₆	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×D₅	—	5	1	no	—
23	C₃×C₄×C₅	C₂×D₅	1	1	yes	characteristic
24	C₃×Dic₅	—	5	1	no	—
25	C₂×C₂₅	C₂×C₃×C₄	1	1	yes	characteristic
26	D₂₅	—	2	1	no	—
27	C₃×M₁₆	—	25	1	no	Hall
28	C₄×D₅	—	5	1	no	—
29	C₅×C₈	C₃×D₅	1	1	yes	characteristic
30	#168	—	5	1	no	—
31	C₂×C₃×C₅	C₄×D₅	1	1	yes	characteristic
32	C₃×D₅	—	10	1	no	—
33	C₂₅	C₃×M₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃×C₄	—	25	1	no	—
35	C₃×C₈	—	25	1	no	—
36	C₃×C₈	D₂₅	1	1	yes	characteristic, complemented
37	C₂×D₅	—	5	1	no	—
38	C₄×C₅	C₂×C₃×D₅	1	1	yes	characteristic
39	Dic₅	—	5	1	no	—
40	M₁₆	—	25	1	no	Sylow
41	C₃×C₅	#676	1	1	yes	characteristic
42	C₂²×C₃	—	25	1	no	—
43	C₃×C₄	—	25	1	no	—
44	C₃×C₄	C₂×D₂₅	1	1	yes	characteristic
45	C₂×C₅	C₃×C₄×D₅	1	1	yes	characteristic
46	D₅	—	10	1	no	—
47	C₂×C₄	—	25	1	no	—
48	C₈	—	25	1	no	—
49	C₈	C₃×D₂₅	1	1	yes	characteristic, complemented
50	C₂×C₃	—	50	1	no	—
51	C₂×C₃	C₄×D₂₅	1	1	yes	characteristic
52	C₅	C₃×#676	1	1	yes	characteristic
53	C₂²	—	25	1	no	—
54	C₄	—	25	1	no	—
55	C₄	C₂×C₃×D₂₅	1	1	yes	characteristic
56	C₃	#87712	1	1	yes	characteristic, direct product factor, Sylow
57	C₂	—	50	1	no	—
58	C₂	C₃×C₄×D₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×D₂₅
commutator	C₂×C₂₅	C₂×C₃×C₄
Frattini	C₄×C₅	C₂×C₃×D₅
Fitting	C₃×C₈×C₂₅	C₂
socle	C₂×C₃×C₅	C₄×D₅
prime radical	C₂×C₃×D₂₅	C₄
cosocle	C₄×C₂₅	C₂²×C₃
hypercenter	C₃×C₈	D₂₅
hypocenter	C₂₅	C₃×M₁₆
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₃×C₄ ◁ C₃×C₈

Complements

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

N	H ≅ G/N	type
2. C₃×C₈×C₂₅	C₂	semidirect
3. C₃×#6014	C₂	semidirect
4. #87712	C₃	direct (N × H)
10. C₈×C₂₅	C₂×C₃	semidirect
11. #6014	C₂×C₃	semidirect
21. C₃×C₂₅	M₁₆	semidirect
33. C₂₅	C₃×M₁₆	semidirect
36. C₃×C₈	D₂₅	semidirect
49. C₈	C₃×D₂₅	semidirect
56. C₃	#87712	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×D₂₅	2
C₃×C₈×C₂₅	2
C₃×#6014	2
#87712	3
C₃×#676	5

Subgroups — C3×#87712 #11924825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#87712 #11924825