Subgroups — C₄³×C₇×C₅₃ #72201064

Order 23744.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₇×C₅₃	C₂	1	7	yes	maximal
2	C₂²×C₄×C₇×C₅₃	C₂²	1	7	yes	—
3	C₄²×C₇×C₅₃	C₄	1	28	yes	direct product factor
4	C₂³×C₇×C₅₃	C₂³	1	1	yes	characteristic
5	C₂×C₄×C₇×C₅₃	C₂×C₄	1	42	yes	—
6	C₄³×C₅₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₄²×C₅₃	C₂×C₇	1	7	yes	—
8	C₂²×C₇×C₅₃	C₂²×C₄	1	7	yes	—
9	C₄×C₇×C₅₃	C₄²	1	28	yes	direct product factor
10	C₂²×C₄×C₅₃	C₂²×C₇	1	7	yes	—
11	C₄²×C₅₃	C₄×C₇	1	28	yes	direct product factor
12	C₂×C₇×C₅₃	C₂×C₄²	1	7	yes	—
13	C₄³×C₇	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂³×C₅₃	C₂³×C₇	1	1	yes	characteristic
15	C₂×C₄×C₅₃	C₂×C₄×C₇	1	42	yes	—
16	C₇×C₅₃	C₄³	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₄²×C₇	C₂×C₅₃	1	7	yes	—
18	C₂²×C₅₃	C₂²×C₄×C₇	1	7	yes	—
19	C₄×C₅₃	C₄²×C₇	1	28	yes	direct product factor
20	C₂²×C₄×C₇	C₂²×C₅₃	1	7	yes	—
21	C₄²×C₇	C₄×C₅₃	1	28	yes	direct product factor
22	C₂×C₅₃	C₂×C₄²×C₇	1	7	yes	—
23	C₄³	C₇×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂³×C₇	C₂³×C₅₃	1	1	yes	characteristic
25	C₂×C₄×C₇	C₂×C₄×C₅₃	1	42	yes	—
26	C₅₃	C₄³×C₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₄²	C₂×C₇×C₅₃	1	7	yes	—
28	C₂²×C₇	C₂²×C₄×C₅₃	1	7	yes	—
29	C₄×C₇	C₄²×C₅₃	1	28	yes	direct product factor
30	C₂²×C₄	C₂²×C₇×C₅₃	1	7	yes	—
31	C₄²	C₄×C₇×C₅₃	1	28	yes	direct product factor
32	C₂×C₇	C₂×C₄²×C₅₃	1	7	yes	—
33	C₂³	C₂³×C₇×C₅₃	1	1	yes	characteristic
34	C₂×C₄	C₂×C₄×C₇×C₅₃	1	42	yes	—
35	C₇	C₄³×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²	C₂²×C₄×C₇×C₅₃	1	7	yes	—
37	C₄	C₄²×C₇×C₅₃	1	28	yes	direct product factor
38	C₂	C₂×C₄²×C₇×C₅₃	1	7	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³	C₂³×C₇×C₅₃
socle, prime radical	C₂³×C₇×C₅₃	C₂³
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄²×C₇×C₅₃	C₄	direct (N × H)
6. C₄³×C₅₃	C₇	direct (N × H)
9. C₄×C₇×C₅₃	C₄²	direct (N × H)
11. C₄²×C₅₃	C₄×C₇	direct (N × H)
13. C₄³×C₇	C₅₃	direct (N × H)
16. C₇×C₅₃	C₄³	direct (N × H)
19. C₄×C₅₃	C₄²×C₇	direct (N × H)
21. C₄²×C₇	C₄×C₅₃	direct (N × H)
23. C₄³	C₇×C₅₃	direct (N × H)
26. C₅₃	C₄³×C₇	direct (N × H)
29. C₄×C₇	C₄²×C₅₃	direct (N × H)
31. C₄²	C₄×C₇×C₅₃	direct (N × H)
35. C₇	C₄³×C₅₃	direct (N × H)
37. C₄	C₄²×C₇×C₅₃	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×C₄²×C₇×C₅₃	2
C₄³×C₅₃	7
C₄³×C₇	53

Subgroups — C43×C7×C53 #72201064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄³×C₇×C₅₃ #72201064