Subgroups — C₂×#64470 #10597084

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	#64470	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×Dic₅	—	3	1	no	maximal, Hall
4	C₂×C₅²⋊C₃	C₄	1	2	yes	complemented
5	C₂×C₅²⋊C₃	C₂²	1	1	yes	characteristic
6	C₂²×C₅²	D₃	1	1	yes	characteristic
7	C₅×Dic₅	—	3	2	no	—
8	C₅²⋊C₃	C₂×C₄	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅²	Dic₃	1	2	yes	complemented
10	C₂×C₅²	C₂×D₃	1	1	yes	characteristic
11	C₂×C₄×C₅	—	15	1	no	—
12	C₂×Dic₅	—	3	1	no	—
13	C₅²	C₂×Dic₃	1	1	yes	characteristic, complemented, Sylow
14	C₂×Dic₃	—	25	1	no	maximal, Hall
15	C₂²×C₅	—	3	1	no	—
16	C₂²×C₅	—	3	1	no	—
17	C₄×C₅	—	15	2	no	—
18	Dic₅	—	3	2	no	—
19	C₂²×C₃	—	25	1	no	—
20	Dic₃	—	25	2	no	—
21	C₂×C₅	—	3	2	no	—
22	C₂×C₅	—	3	2	no	—
23	C₂×C₅	—	3	1	no	—
24	C₂×C₅	—	3	1	no	—
25	C₂×C₄	—	15	1	no	Sylow
26	C₂×C₃	—	25	2	no	—
27	C₂×C₃	—	25	1	no	—
28	C₅	—	3	1	no	—
29	C₅	—	3	1	no	—
30	C₂²	#3874	1	1	yes	characteristic
31	C₄	—	15	2	no	—
32	C₃	—	25	1	no	Sylow
33	C₂	#64470	1	2	yes	direct product factor
34	C₂	C₂×#3874	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.