Subgroups — C₂×Dic₃₀ #6814

Order 240.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₅	C₂	1	2	yes	maximal
3	Dic₃₀	C₂	1	4	yes	maximal, direct product factor
4	C₂×Dic₁₀	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₅	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₅	C₂²	1	2	yes	—
7	Dic₁₅	C₂²	1	4	yes	—
8	C₂×Dic₆	—	5	1	no	maximal, Hall
9	C₂×C₄×C₅	D₃	1	1	yes	characteristic
10	C₂×Dic₅	—	3	2	no	—
11	Dic₁₀	—	3	4	no	—
12	C₂×C₃×C₅	Q₈	1	2	yes	complemented
13	C₂×C₃×C₅	C₂³	1	1	yes	characteristic
14	C₂×C₃×C₄	D₅	1	1	yes	characteristic
15	C₂×Dic₃	—	5	2	no	—
16	Dic₆	—	5	4	no	—
17	C₂²×C₅	C₂×D₃	1	1	yes	characteristic
18	C₄×C₅	C₂×D₃	1	2	yes	—
19	Dic₅	—	3	4	no	—
20	C₂×Q₈	—	15	1	no	Sylow
21	C₃×C₅	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
22	C₂²×C₃	C₂×D₅	1	1	yes	characteristic
23	C₃×C₄	C₂×D₅	1	2	yes	—
24	Dic₃	—	5	4	no	—
25	C₂×C₅	Dic₆	1	2	yes	complemented
26	C₂×C₅	C₂²×D₃	1	1	yes	characteristic
27	Q₈	—	15	4	no	—
28	C₂×C₄	—	15	2	no	—
29	C₂×C₄	D₁₅	1	1	yes	characteristic
30	C₂×C₃	Dic₁₀	1	2	yes	complemented
31	C₂×C₃	C₂²×D₅	1	1	yes	characteristic
32	C₅	C₂×Dic₆	1	1	yes	characteristic, complemented, Sylow
33	C₂²	C₂×D₁₅	1	1	yes	characteristic
34	C₄	—	15	4	no	—
35	C₄	C₂×D₁₅	1	2	yes	—
36	C₃	C₂×Dic₁₀	1	1	yes	characteristic, complemented, Sylow
37	C₂	Dic₃₀	1	2	yes	direct product factor
38	C₂	C₂²×D₁₅	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.