Subgroups — C₂⁵×Dic₄₇ #20258178

Order 6016.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Dic₄₇	C₂	1	62	yes	maximal, direct product factor
2	C₂⁶×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂³×Dic₄₇	C₂²	1	620	yes	direct product factor
4	C₂⁵×C₄₇	C₄	1	32	yes	complemented
5	C₂⁵×C₄₇	C₂²	1	31	yes	—
6	C₂⁴×C₄₇	C₂×C₄	1	496	yes	complemented
7	C₂⁴×C₄₇	C₂³	1	155	yes	—
8	C₂²×Dic₄₇	C₂³	1	1240	yes	direct product factor
9	C₂³×C₄₇	C₂²×C₄	1	1240	yes	complemented
10	C₂³×C₄₇	C₂⁴	1	155	yes	—
11	C₂×Dic₄₇	C₂⁴	1	496	yes	direct product factor
12	C₂²×C₄₇	C₂³×C₄	1	620	yes	complemented
13	C₂²×C₄₇	C₂⁵	1	31	yes	—
14	Dic₄₇	C₂⁵	1	32	yes	direct product factor
15	C₂⁵×C₄	—	47	1	no	maximal, Sylow
16	C₂×C₄₇	C₂⁴×C₄	1	62	yes	complemented
17	C₂×C₄₇	C₂⁶	1	1	yes	characteristic
18	C₂⁶	D₄₇	1	1	yes	characteristic
19	C₂⁴×C₄	—	47	62	no	—
20	C₄₇	C₂⁵×C₄	1	1	yes	characteristic, complemented, Sylow
21	C₂⁵	Dic₄₇	1	32	yes	direct product factor
22	C₂⁵	C₂×D₄₇	1	31	yes	—
23	C₂³×C₄	—	47	620	no	—
24	C₂⁴	C₂×Dic₄₇	1	496	yes	direct product factor
25	C₂⁴	C₂²×D₄₇	1	155	yes	—
26	C₂²×C₄	—	47	1240	no	—
27	C₂³	C₂²×Dic₄₇	1	1240	yes	direct product factor
28	C₂³	C₂³×D₄₇	1	155	yes	—
29	C₂×C₄	—	47	496	no	—
30	C₂²	C₂³×Dic₄₇	1	620	yes	direct product factor
31	C₂²	C₂⁴×D₄₇	1	31	yes	—
32	C₄	—	47	32	no	—
33	C₂	C₂⁴×Dic₄₇	1	62	yes	direct product factor
34	C₂	C₂⁵×D₄₇	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.