Subgroups — #87799⋊C₃ #11925035

Order 1200.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₈×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#6029⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#87799	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×(C₅⋊D₅)⋊C₃	C₄	1	1	yes	characteristic
6	C₄×C₅²⋊C₃	C₂²	1	1	yes	characteristic
7	#1039⋊C₃	C₄	1	1	yes	characteristic
8	C₄×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
9	C₅²×C₈	C₂×C₃	1	1	yes	characteristic, complemented
10	#6029	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₅²⋊C₃	C₂×C₄	1	1	yes	characteristic
12	(C₅⋊D₅)⋊C₃	—	2	1	no	—
13	C₂×C₅⋊D₅	C₃×C₄	1	1	yes	characteristic
14	C₄×C₅²	C₂²×C₃	1	1	yes	characteristic
15	#1039	C₃×C₄	1	1	yes	characteristic
16	#676	—	15	2	no	—
17	C₅²⋊C₃	M₁₆	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅²	C₂×C₃×C₄	1	1	yes	characteristic
19	C₅⋊D₅	—	2	1	no	—
20	C₃×M₁₆	—	25	1	no	maximal, Hall
21	C₄×D₅	—	15	2	no	—
22	C₅×C₈	—	3	2	no	—
23	#168	—	15	2	no	—
24	C₅²	C₃×M₁₆	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃×C₄	—	25	1	no	—
26	C₃×C₈	—	25	1	no	—
27	C₃×C₈	—	25	1	no	—
28	C₂×D₅	—	15	2	no	—
29	C₄×C₅	—	3	2	no	—
30	Dic₅	—	15	2	no	—
31	M₁₆	—	25	1	no	Sylow
32	C₂²×C₃	—	25	1	no	—
33	C₃×C₄	—	25	1	no	—
34	C₃×C₄	—	25	1	no	—
35	C₂×C₅	—	3	2	no	—
36	D₅	—	30	2	no	—
37	C₂×C₄	—	25	1	no	—
38	C₈	—	25	1	no	—
39	C₈	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
40	C₂×C₃	—	25	1	no	—
41	C₂×C₃	—	50	1	no	—
42	C₅	—	3	2	no	—
43	C₂²	—	25	1	no	—
44	C₄	—	25	1	no	—
45	C₄	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
46	C₃	—	25	1	no	Sylow
47	C₂	—	50	1	no	—
48	C₂	C₄×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂×(C₅⋊D₅)⋊C₃
commutator, socle	C₂×C₅²	C₂×C₃×C₄
Fitting	C₅²×C₈	C₂×C₃
prime radical	C₂×(C₅⋊D₅)⋊C₃	C₄
cosocle	C₄×C₅²	C₂²×C₃
hypercenter	C₈	(C₅⋊D₅)⋊C₃
hypocenter	C₅²	C₃×M₁₆
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. C₈×C₅²⋊C₃	C₂	semidirect
3. #6029⋊C₃	C₂	semidirect
4. #87799	C₃	semidirect
9. C₅²×C₈	C₂×C₃	semidirect
10. #6029	C₂×C₃	semidirect
17. C₅²⋊C₃	M₁₆	semidirect
24. C₅²	C₃×M₁₆	semidirect
39. C₈	(C₅⋊D₅)⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×(C₅⋊D₅)⋊C₃	2
C₈×C₅²⋊C₃	2
#6029⋊C₃	2
#87799	3
C₃×M₁₆	25

Subgroups — #87799⋊C3 #11925035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #87799⋊C₃ #11925035