Subgroups — C₂⁵×A₄ #87591

Order 384.

10984 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×A₄	C₂	1	31	yes	maximal, direct product factor
2	C₂⁷	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₂⁵×C₃	—	4	1	no	maximal
4	C₂³×A₄	C₂²	1	155	yes	direct product factor
5	C₂⁶	—	3	31	no	—
6	C₂⁶	—	3	1	no	—
7	C₂⁶	C₂×C₃	1	31	yes	complemented
8	C₂⁴×C₃	—	4	31	no	—
9	C₂²×A₄	C₂³	1	155	yes	direct product factor
10	C₂⁵	—	3	465	no	—
11	C₂⁵	—	3	310	no	—
12	C₂⁵	—	3	31	no	—
13	C₂⁵	—	3	31	no	—
14	C₂⁵	A₄	1	1	yes	characteristic, direct product factor
15	C₂⁵	C₂²×C₃	1	155	yes	complemented
16	C₂³×C₃	—	4	155	no	—
17	C₂×A₄	C₂⁴	1	31	yes	direct product factor
18	C₂⁴	—	3	1085	no	—
19	C₂⁴	—	3	2170	no	—
20	C₂⁴	—	3	465	no	—
21	C₂⁴	—	3	155	no	—
22	C₂⁴	C₂×A₄	1	31	yes	direct product factor
23	C₂⁴	C₂³×C₃	1	155	yes	complemented
24	C₂²×C₃	—	4	155	no	—
25	A₄	C₂⁵	1	1	yes	characteristic, direct product factor
26	C₂³	—	3	465	no	—
27	C₂³	—	3	2170	no	—
28	C₂³	—	3	1085	no	—
29	C₂³	—	3	155	no	—
30	C₂³	C₂²×A₄	1	155	yes	direct product factor
31	C₂³	C₂⁴×C₃	1	31	yes	complemented
32	C₂×C₃	—	4	31	no	—
33	C₂²	—	3	31	no	—
34	C₂²	—	3	310	no	—
35	C₂²	—	3	465	no	—
36	C₂²	—	3	31	no	—
37	C₂²	C₂³×A₄	1	155	yes	direct product factor
38	C₂²	C₂⁵×C₃	1	1	yes	characteristic, complemented
39	C₃	—	4	1	no	Sylow
40	C₂	—	3	31	no	—
41	C₂	—	3	1	no	—
42	C₂	C₂⁴×A₄	1	31	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁵	A₄
commutator, cosocle, hypocenter	C₂²	C₂⁵×C₃
Frattini	C₁	G
Fitting, socle	C₂⁷	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂⁵

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.