Subgroups — C₂³×#125 #62661

Order 256.

4207 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#125	C₂	1	56	yes	maximal, direct product factor
2	C₂³×C₄⋊C₄	C₂	1	4	yes	maximal
3	C₂³×C₄⋊C₄	C₂	1	2	yes	maximal
4	C₂³×C₄²	C₂	1	1	yes	maximal, characteristic
5	C₂⁴×C₄	C₂²	1	2	yes	—
6	C₂⁴×C₄	C₂²	1	4	yes	—
7	C₂⁴×C₄	C₂²	1	1	yes	characteristic
8	C₂×#125	C₂²	1	448	yes	direct product factor
9	C₂²×C₄⋊C₄	C₂²	1	112	yes	—
10	C₂²×C₄⋊C₄	C₂²	1	56	yes	—
11	C₂²×C₄²	C₂²	1	28	yes	—
12	C₂⁵	C₂³	1	1	yes	characteristic
13	C₂³×C₄	—	2	16	no	—
14	C₂³×C₄	—	2	32	no	—
15	C₂³×C₄	Q₈	1	16	yes	—
16	C₂³×C₄	C₂³	1	56	yes	—
17	C₂³×C₄	C₂³	1	28	yes	—
18	C₂³×C₄	C₂³	1	14	yes	—
19	#125	C₂³	1	512	yes	direct product factor
20	C₂×C₄⋊C₄	C₂³	1	448	yes	—
21	C₂×C₄⋊C₄	C₂³	1	224	yes	—
22	C₂×C₄²	C₂³	1	112	yes	—
23	C₂⁴	C₂×Q₈	1	8	yes	—
24	C₂⁴	#41	1	16	yes	—
25	C₂⁴	C₂⁴	1	7	yes	—
26	C₂²×C₄	—	2	224	no	—
27	C₂²×C₄	—	2	112	no	—
28	C₂²×C₄	C₂×Q₈	1	112	yes	—
29	C₂²×C₄	C₂⁴	1	56	yes	—
30	C₂²×C₄	C₂⁴	1	112	yes	—
31	C₂²×C₄	C₂⁴	1	28	yes	—
32	C₄⋊C₄	C₂⁴	1	256	yes	—
33	C₄⋊C₄	C₂⁴	1	128	yes	—
34	C₄²	C₂⁴	1	64	yes	—
35	C₂³	#125	1	64	yes	direct product factor
36	C₂³	C₂²×Q₈	1	28	yes	—
37	C₂³	C₂×#41	1	56	yes	—
38	C₂³	C₂⁵	1	7	yes	—
39	C₂×C₄	—	2	112	no	—
40	C₂×C₄	—	2	224	no	—
41	C₂×C₄	C₂²×Q₈	1	112	yes	—
42	C₂×C₄	C₂⁵	1	16	yes	—
43	C₂×C₄	C₂⁵	1	32	yes	—
44	C₂×C₄	C₂⁵	1	8	yes	—
45	C₂²	C₂×#125	1	112	yes	direct product factor
46	C₂²	C₂³×Q₈	1	14	yes	—
47	C₂²	C₂²×#41	1	28	yes	—
48	C₂²	C₂⁶	1	1	yes	characteristic
49	C₄	—	2	16	no	—
50	C₄	—	2	32	no	—
51	C₄	C₂³×Q₈	1	16	yes	—
52	C₂	C₂²×#125	1	28	yes	direct product factor
53	C₂	C₂⁴×Q₈	1	1	yes	characteristic
54	C₂	C₂³×#41	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁵	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂²×#125	C₂	direct (N × H)
8. C₂×#125	C₂²	direct (N × H)
19. #125	C₂³	direct (N × H)
35. C₂³	#125	direct (N × H)
45. C₂²	C₂×#125	direct (N × H)
52. C₂	C₂²×#125	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#125	2
C₂³×C₄⋊C₄	2
C₂³×C₄²	2

Subgroups — C23×#125 #62661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#125 #62661