Subgroups — (C₂²⋊(C₅⋊D₅))⋊C₃ #10597090

Order 600.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#1039⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊(C₅⋊D₅)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₅²⋊C₃	—	2	1	no	—
6	C₂×C₅²⋊C₃	C₂²	1	1	yes	characteristic
7	(C₅⋊D₅)⋊C₃	—	2	1	no	—
8	C₂²×C₅²	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
10	#1039	C₂×C₃	1	1	yes	characteristic, complemented
11	C₅²⋊C₃	D₄	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅²	—	2	1	no	—
13	C₂×C₅²	C₂²×C₃	1	1	yes	characteristic
14	C₅⋊D₅	—	2	1	no	—
15	C₂²⋊D₅	—	15	2	no	—
16	C₅²	C₃×D₄	1	1	yes	characteristic, complemented, Sylow
17	C₃×D₄	—	25	1	no	maximal, Hall
18	C₂²×C₅	—	3	2	no	—
19	C₂×D₅	—	15	2	no	—
20	Dic₅	—	15	2	no	—
21	C₂²×C₃	—	25	1	no	—
22	C₂²×C₃	—	25	1	no	—
23	C₃×C₄	—	25	1	no	—
24	C₂×C₅	—	3	2	no	—
25	C₂×C₅	—	6	2	no	—
26	D₅	—	30	2	no	—
27	D₄	—	25	1	no	Sylow
28	C₂×C₃	—	25	1	no	—
29	C₂×C₃	—	50	1	no	—
30	C₂×C₃	—	50	1	no	—
31	C₅	—	3	2	no	—
32	C₂²	—	25	1	no	—
33	C₂²	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
34	C₄	—	25	1	no	—
35	C₃	—	25	1	no	Sylow
36	C₂	—	2	1	no	—
37	C₂	—	50	1	no	—
38	C₂	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic

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

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