Subgroups — C₂⁵×Dic₃ #87575

Order 384.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×C₃	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×Dic₃	C₂	1	62	yes	maximal, direct product factor
3	C₂⁵×C₄	—	3	1	no	maximal, Sylow
4	C₂⁵×C₃	C₄	1	32	yes	complemented
5	C₂⁵×C₃	C₂²	1	31	yes	—
6	C₂³×Dic₃	C₂²	1	620	yes	direct product factor
7	C₂⁶	D₃	1	1	yes	characteristic
8	C₂⁴×C₄	—	3	62	no	—
9	C₂⁴×C₃	C₂×C₄	1	496	yes	complemented
10	C₂⁴×C₃	C₂³	1	155	yes	—
11	C₂²×Dic₃	C₂³	1	1240	yes	direct product factor
12	C₂⁵	Dic₃	1	32	yes	direct product factor
13	C₂⁵	C₂×D₃	1	31	yes	—
14	C₂³×C₄	—	3	620	no	—
15	C₂³×C₃	C₂²×C₄	1	1240	yes	complemented
16	C₂³×C₃	C₂⁴	1	155	yes	—
17	C₂×Dic₃	C₂⁴	1	496	yes	direct product factor
18	C₂⁴	C₂×Dic₃	1	496	yes	direct product factor
19	C₂⁴	C₂²×D₃	1	155	yes	—
20	C₂²×C₄	—	3	1240	no	—
21	C₂²×C₃	C₂³×C₄	1	620	yes	complemented
22	C₂²×C₃	C₂⁵	1	31	yes	—
23	Dic₃	C₂⁵	1	32	yes	direct product factor
24	C₂³	C₂²×Dic₃	1	1240	yes	direct product factor
25	C₂³	C₂³×D₃	1	155	yes	—
26	C₂×C₄	—	3	496	no	—
27	C₂×C₃	C₂⁴×C₄	1	62	yes	complemented
28	C₂×C₃	C₂⁶	1	1	yes	characteristic
29	C₂²	C₂³×Dic₃	1	620	yes	direct product factor
30	C₂²	C₂⁴×D₃	1	31	yes	—
31	C₄	—	3	32	no	—
32	C₃	C₂⁵×C₄	1	1	yes	characteristic, complemented, Sylow
33	C₂	C₂⁴×Dic₃	1	62	yes	direct product factor
34	C₂	C₂⁵×D₃	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.