Subgroups — C₂×#1039⋊C₃ #10597089

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
2	#1039⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×#1039	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₅²⋊C₃	C₄	1	2	yes	complemented
5	C₂×C₅²⋊C₃	C₂²	1	1	yes	characteristic
6	C₂²×C₅²	C₂×C₃	1	1	yes	characteristic
7	#1039	C₂×C₃	1	2	yes	complemented
8	C₅²⋊C₃	C₂×C₄	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅²	C₃×C₄	1	2	yes	complemented
10	C₂×C₅²	C₂²×C₃	1	1	yes	characteristic
11	C₂×Dic₅	—	15	2	no	—
12	C₅²	C₂×C₃×C₄	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₃×C₄	—	25	1	no	maximal, Hall
14	C₂²×C₅	—	3	2	no	—
15	Dic₅	—	15	4	no	—
16	C₂²×C₃	—	25	1	no	—
17	C₃×C₄	—	25	2	no	—
18	C₂×C₅	—	3	4	no	—
19	C₂×C₅	—	3	2	no	—
20	C₂×C₄	—	25	1	no	Sylow
21	C₂×C₃	—	25	2	no	—
22	C₂×C₃	—	25	1	no	—
23	C₅	—	3	2	no	—
24	C₂²	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
25	C₄	—	25	2	no	—
26	C₃	—	25	1	no	Sylow
27	C₂	#1039⋊C₃	1	2	yes	direct product factor
28	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.