Subgroups — #430×C₅₂₁ #45686994

Order 33344.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₅₂₁	C₂	1	2	yes	maximal
2	C₂×M₁₆×C₅₂₁	C₂	1	1	yes	maximal, characteristic
3	#108×C₅₂₁	C₂	1	4	yes	maximal, complemented
4	C₂²×C₄×C₅₂₁	C₂²	1	1	yes	characteristic
5	M₁₆×C₅₂₁	—	2	2	no	—
6	M₁₆×C₅₂₁	C₄	1	4	yes	—
7	M₁₆×C₅₂₁	C₂²	1	4	yes	—
8	C₂×C₈×C₅₂₁	—	2	2	no	—
9	C₂×C₈×C₅₂₁	C₂²	1	2	yes	—
10	C₂³×C₅₂₁	Q₈	1	1	yes	characteristic
11	C₂×C₄×C₅₂₁	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₅₂₁	D₄	1	2	yes	—
13	C₂×C₄×C₅₂₁	Q₈	1	1	yes	characteristic
14	C₂×C₄×C₅₂₁	C₂³	1	1	yes	characteristic
15	C₈×C₅₂₁	—	2	4	no	—
16	C₈×C₅₂₁	C₂×C₄	1	4	yes	—
17	C₂²×C₅₂₁	—	4	1	no	—
18	C₂²×C₅₂₁	C₄⋊C₄	1	2	yes	—
19	C₂²×C₅₂₁	C₂×Q₈	1	1	yes	characteristic
20	C₄×C₅₂₁	C₄⋊C₄	1	2	yes	—
21	C₄×C₅₂₁	C₂²×C₄	1	1	yes	characteristic
22	C₄×C₅₂₁	C₂×D₄	1	1	yes	characteristic
23	C₂×C₅₂₁	—	2	2	no	—
24	C₂×C₅₂₁	—	2	1	no	—
25	C₂×C₅₂₁	C₂×C₄⋊C₄	1	1	yes	characteristic
26	C₅₂₁	#430	1	1	yes	characteristic, direct product factor, Sylow
27	#430	C₅₂₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂×M₁₆	C₂×C₅₂₁	1	2	yes	—
29	C₂×M₁₆	C₂×C₅₂₁	1	1	yes	characteristic
30	#108	C₂×C₅₂₁	1	4	yes	complemented
31	C₂²×C₄	C₂²×C₅₂₁	1	1	yes	characteristic
32	M₁₆	—	2	2	no	—
33	M₁₆	C₄×C₅₂₁	1	4	yes	—
34	M₁₆	C₂²×C₅₂₁	1	4	yes	—
35	C₂×C₈	—	2	2	no	—
36	C₂×C₈	C₂²×C₅₂₁	1	2	yes	—
37	C₂³	Q₈×C₅₂₁	1	1	yes	characteristic
38	C₂×C₄	C₂×C₄×C₅₂₁	1	2	yes	—
39	C₂×C₄	D₄×C₅₂₁	1	2	yes	—
40	C₂×C₄	Q₈×C₅₂₁	1	1	yes	characteristic
41	C₂×C₄	C₂³×C₅₂₁	1	1	yes	characteristic
42	C₈	—	2	4	no	—
43	C₈	C₂×C₄×C₅₂₁	1	4	yes	—
44	C₂²	—	4	1	no	—
45	C₂²	C₄⋊C₄×C₅₂₁	1	2	yes	—
46	C₂²	C₂×Q₈×C₅₂₁	1	1	yes	characteristic
47	C₄	C₄⋊C₄×C₅₂₁	1	2	yes	—
48	C₄	C₂²×C₄×C₅₂₁	1	1	yes	characteristic
49	C₄	C₂×D₄×C₅₂₁	1	1	yes	characteristic
50	C₂	—	2	2	no	—
51	C₂	—	2	1	no	—
52	C₂	C₂×C₄⋊C₄×C₅₂₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅₂₁	C₂×D₄
commutator	C₄	C₂²×C₄×C₅₂₁
Frattini, cosocle	C₂×C₄	C₂³×C₅₂₁
socle	C₂×C₅₂₁	C₂×C₄⋊C₄
prime radical	C₂³×C₅₂₁	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅₂₁ ◁ C₂²×C₄×C₅₂₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. #108×C₅₂₁	C₂	semidirect
26. C₅₂₁	#430	direct (N × H)
27. #430	C₅₂₁	direct (N × H)
30. #108	C₂×C₅₂₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×C₅₂₁	2
#108×C₅₂₁	2
#430	521

Subgroups — #430×C521 #45686994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #430×C₅₂₁ #45686994