Subgroups — C₂×Dic₇₅ #10597047

Order 600.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₂₅	C₂	1	1	yes	maximal, characteristic
2	Dic₇₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×Dic₂₅	—	3	1	no	maximal, Hall
4	C₂×C₃×C₂₅	C₄	1	2	yes	complemented
5	C₂×C₃×C₂₅	C₂²	1	1	yes	characteristic
6	C₂×Dic₁₅	—	5	1	no	maximal
7	C₂²×C₂₅	D₃	1	1	yes	characteristic
8	Dic₂₅	—	3	2	no	—
9	C₃×C₂₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
10	C₂²×C₃×C₅	D₅	1	1	yes	characteristic
11	Dic₁₅	—	5	2	no	—
12	C₂×C₂₅	Dic₃	1	2	yes	complemented
13	C₂×C₂₅	C₂×D₃	1	1	yes	characteristic
14	C₂×Dic₅	—	15	1	no	—
15	C₂×C₃×C₅	Dic₅	1	2	yes	—
16	C₂×C₃×C₅	C₂×D₅	1	1	yes	characteristic
17	C₂₅	C₂×Dic₃	1	1	yes	characteristic, complemented, Sylow
18	C₂×Dic₃	—	25	1	no	Hall
19	C₂²×C₅	D₁₅	1	1	yes	characteristic
20	Dic₅	—	15	2	no	—
21	C₃×C₅	C₂×Dic₅	1	1	yes	characteristic
22	C₂²×C₃	D₂₅	1	1	yes	characteristic
23	Dic₃	—	25	2	no	—
24	C₂×C₅	Dic₁₅	1	2	yes	—
25	C₂×C₅	C₂×D₁₅	1	1	yes	characteristic
26	C₂×C₄	—	75	1	no	Sylow
27	C₂×C₃	Dic₂₅	1	2	yes	complemented
28	C₂×C₃	C₂×D₂₅	1	1	yes	characteristic
29	C₅	C₂×Dic₁₅	1	1	yes	characteristic
30	C₂²	D₇₅	1	1	yes	characteristic
31	C₄	—	75	2	no	—
32	C₃	C₂×Dic₂₅	1	1	yes	characteristic, complemented, Sylow
33	C₂	Dic₇₅	1	2	yes	direct product factor
34	C₂	C₂×D₇₅	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.