Subgroups — #11925021

Order 1200.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#3874	C₂	1	1	yes	maximal, characteristic
2	#10597081	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#677	—	3	1	no	maximal, Hall
5	C₂×#3874	—	2	1	no	—
6	C₄×C₅²⋊C₃	C₂²	1	1	yes	characteristic
7	#64470	—	2	1	no	—
8	C₅×D₂₀	—	3	1	no	—
9	C₅×Dic₁₀	—	3	1	no	—
10	C₅²×C₈	D₃	1	1	yes	characteristic, complemented
11	C₂×C₅²⋊C₃	D₄	1	1	yes	characteristic
12	#3874	—	4	1	no	—
13	C₂×C₅×D₅	—	6	1	no	—
14	C₄×C₅²	C₂×D₃	1	1	yes	characteristic
15	C₅×Dic₅	—	6	1	no	—
16	C₅×SD₁₆	—	15	1	no	—
17	#677	—	3	1	no	—
18	C₅²⋊C₃	SD₁₆	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅²	D₁₂	1	1	yes	characteristic
20	C₅×D₅	—	12	1	no	—
21	#204	—	25	1	no	maximal, Hall
22	C₅×Q₈	—	15	1	no	—
23	C₅×D₄	—	15	1	no	—
24	D₂₀	—	3	1	no	—
25	Dic₁₀	—	3	1	no	—
26	C₅×C₈	—	3	1	no	—
27	C₅×C₈	—	3	1	no	—
28	C₅²	#204	1	1	yes	characteristic, complemented, Sylow
29	D₁₂	—	25	1	no	—
30	Dic₆	—	25	1	no	—
31	C₃×C₈	—	25	1	no	—
32	C₂²×C₅	—	30	1	no	—
33	C₂×D₅	—	6	1	no	—
34	C₄×C₅	—	3	1	no	—
35	C₄×C₅	—	3	1	no	—
36	C₄×C₅	—	30	1	no	—
37	Dic₅	—	6	1	no	—
38	SD₁₆	—	15	1	no	Sylow
39	C₂×D₃	—	50	1	no	—
40	C₃×C₄	—	25	1	no	—
41	Dic₃	—	50	1	no	—
42	C₂×C₅	—	3	1	no	—
43	C₂×C₅	—	3	1	no	—
44	C₂×C₅	—	60	1	no	—
45	D₅	—	12	1	no	—
46	Q₈	—	15	1	no	—
47	D₄	—	15	1	no	—
48	C₈	#3874	1	1	yes	characteristic, complemented
49	C₂×C₃	—	25	1	no	—
50	D₃	—	100	1	no	—
51	C₅	—	3	1	no	—
52	C₅	—	3	1	no	—
53	C₂²	—	30	1	no	—
54	C₄	—	30	1	no	—
55	C₄	C₂×#3874	1	1	yes	characteristic
56	C₃	—	25	1	no	Sylow
57	C₂	—	60	1	no	—
58	C₂	C₄⋊#3874	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₄⋊#3874
commutator, cosocle	C₄×C₅²⋊C₃	C₂²
Frattini	C₄	C₂×#3874
Fitting	C₅²×C₈	D₃
socle	C₂×C₅²	D₁₂
prime radical	C₄⋊#3874	C₂
hypercenter	C₈	#3874
hypocenter	C₅²⋊C₃	SD₁₆
LCS	G ▷ C₄×C₅²⋊C₃ ▷ C₂×C₅²⋊C₃ ▷ C₅²⋊C₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. #10597081	C₂	semidirect
3. C₈×C₅²⋊C₃	C₂	semidirect
10. C₅²×C₈	D₃	semidirect
18. C₅²⋊C₃	SD₁₆	semidirect
28. C₅²	#204	semidirect
48. C₈	#3874	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#3874	2
#10597081	2
C₈×C₅²⋊C₃	2
C₅×#677	3
#204	25