Subgroups — C₂²×C₁₃×#564 #15749031

Order 3328.

6374 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#564	C₂	1	48	yes	maximal, direct product factor
2	C₂²×C₁₃×#125	C₂	1	15	yes	maximal
3	C₁₃×#564	C₂²	1	256	yes	direct product factor
4	C₂×C₁₃×#125	C₂²	1	360	yes	—
5	C₂²×C₁₃×C₄⋊C₄	C₂²	1	30	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	5	yes	—
7	C₂³×C₄×C₁₃	C₂³	1	15	yes	—
8	C₁₃×#125	C₂³	1	960	yes	—
9	C₂×C₁₃×C₄⋊C₄	C₂³	1	360	yes	—
10	C₂×C₄²×C₁₃	C₂³	1	60	yes	—
11	C₂²×#564	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
13	C₂²×C₄×C₁₃	—	2	60	no	—
14	C₂²×C₄×C₁₃	C₂⁴	1	90	yes	—
15	C₁₃×C₄⋊C₄	C₂⁴	1	480	yes	—
16	C₄²×C₁₃	C₂⁴	1	80	yes	—
17	C₂×#564	C₂×C₁₃	1	48	yes	direct product factor
18	C₂²×#125	C₂×C₁₃	1	15	yes	—
19	C₂³×C₁₃	2₋¹⁺⁴	1	12	yes	—
20	C₂³×C₁₃	C₂⁵	1	3	yes	—
21	C₂×C₄×C₁₃	—	2	180	no	—
22	C₂×C₄×C₁₃	C₂⁵	1	60	yes	—
23	#564	C₂²×C₁₃	1	256	yes	direct product factor
24	C₂×#125	C₂²×C₁₃	1	360	yes	—
25	C₂²×C₄⋊C₄	C₂²×C₁₃	1	30	yes	—
26	C₂²×C₄²	C₂²×C₁₃	1	5	yes	—
27	C₂²×C₁₃	#564	1	16	yes	direct product factor
28	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	18	yes	—
29	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
30	C₄×C₁₃	—	2	60	no	—
31	C₂³×C₄	C₂³×C₁₃	1	15	yes	—
32	#125	C₂³×C₁₃	1	960	yes	—
33	C₂×C₄⋊C₄	C₂³×C₁₃	1	360	yes	—
34	C₂×C₄²	C₂³×C₁₃	1	60	yes	—
35	C₂×C₁₃	C₂×#564	1	12	yes	direct product factor
36	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	3	yes	—
37	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
38	C₂²×C₄	—	2	60	no	—
39	C₂²×C₄	C₂⁴×C₁₃	1	90	yes	—
40	C₄⋊C₄	C₂⁴×C₁₃	1	480	yes	—
41	C₄²	C₂⁴×C₁₃	1	80	yes	—
42	C₁₃	C₂²×#564	1	1	yes	characteristic, direct product factor, Sylow
43	C₂³	C₁₃×2₋¹⁺⁴	1	12	yes	—
44	C₂³	C₂⁵×C₁₃	1	3	yes	—
45	C₂×C₄	—	2	180	no	—
46	C₂×C₄	C₂⁵×C₁₃	1	60	yes	—
47	C₂²	C₁₃×#564	1	16	yes	direct product factor
48	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	18	yes	—
49	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
50	C₄	—	2	60	no	—
51	C₂	C₂×C₁₃×#564	1	12	yes	direct product factor
52	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#564	C₂	direct (N × H)
3. C₁₃×#564	C₂²	direct (N × H)
11. C₂²×#564	C₁₃	direct (N × H)
17. C₂×#564	C₂×C₁₃	direct (N × H)
23. #564	C₂²×C₁₃	direct (N × H)
27. C₂²×C₁₃	#564	direct (N × H)
35. C₂×C₁₃	C₂×#564	direct (N × H)
42. C₁₃	C₂²×#564	direct (N × H)
47. C₂²	C₁₃×#564	direct (N × H)
51. C₂	C₂×C₁₃×#564	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#564	2
C₂²×C₁₃×#125	2
C₂²×#564	13

Subgroups — C22×C13×#564 #15749031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×#564 #15749031