Subgroups — #339×C₅₀₃ #44565752

Order 32192.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₅₀₃	C₂	1	1	yes	maximal, characteristic
2	#117×C₅₀₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₅₀₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₅₀₃	—	2	1	no	—
5	C₂²×C₄×C₅₀₃	C₂²	1	1	yes	characteristic
6	M₁₆×C₅₀₃	—	2	1	no	—
7	M₁₆×C₅₀₃	C₄	1	2	yes	complemented
8	C₂×C₈×C₅₀₃	—	2	1	no	—
9	C₄⋊C₄×C₅₀₃	C₄	1	2	yes	complemented
10	C₂²⋊C₄×C₅₀₃	—	2	1	no	—
11	C₄²×C₅₀₃	—	2	1	no	—
12	C₄²×C₅₀₃	—	2	1	no	—
13	C₄²×C₅₀₃	C₄	1	2	yes	complemented
14	C₂³×C₅₀₃	D₄	1	1	yes	characteristic
15	C₂×C₄×C₅₀₃	—	2	4	no	—
16	C₂×C₄×C₅₀₃	—	2	2	no	—
17	C₂×C₄×C₅₀₃	—	2	2	no	—
18	C₂×C₄×C₅₀₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₅₀₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₅₀₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₅₀₃	D₄	1	1	yes	characteristic
22	C₂×C₄×C₅₀₃	D₄	1	1	yes	characteristic
23	C₂×C₄×C₅₀₃	Q₈	1	1	yes	characteristic
24	C₈×C₅₀₃	—	2	2	no	—
25	C₂²×C₅₀₃	—	2	2	no	—
26	C₂²×C₅₀₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₅₀₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂²×C₅₀₃	C₄⋊C₄	1	1	yes	characteristic
29	C₄×C₅₀₃	—	2	4	no	—
30	C₄×C₅₀₃	—	4	2	no	—
31	C₄×C₅₀₃	C₄²	1	1	yes	characteristic
32	C₄×C₅₀₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₄×C₅₀₃	C₄⋊C₄	1	1	yes	characteristic
34	C₄×C₅₀₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₅₀₃	—	2	1	no	—
36	C₂×C₅₀₃	—	2	1	no	—
37	C₂×C₅₀₃	#95	1	1	yes	characteristic
38	C₂×C₅₀₃	#104	1	2	yes	—
39	C₅₀₃	#339	1	1	yes	characteristic, direct product factor, Sylow
40	#339	C₅₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂×M₁₆	C₂×C₅₀₃	1	1	yes	characteristic
42	#117	C₂×C₅₀₃	1	1	yes	characteristic
43	C₂×C₄²	C₂×C₅₀₃	1	1	yes	characteristic
44	C₂²×C₄	—	2	1	no	—
45	C₂²×C₄	C₂²×C₅₀₃	1	1	yes	characteristic
46	M₁₆	—	2	1	no	—
47	M₁₆	C₄×C₅₀₃	1	2	yes	complemented
48	C₂×C₈	—	2	1	no	—
49	C₄⋊C₄	C₄×C₅₀₃	1	2	yes	complemented
50	C₂²⋊C₄	—	2	1	no	—
51	C₄²	—	2	1	no	—
52	C₄²	—	2	1	no	—
53	C₄²	C₄×C₅₀₃	1	2	yes	complemented
54	C₂³	D₄×C₅₀₃	1	1	yes	characteristic
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	C₂×C₄×C₅₀₃	1	1	yes	characteristic
59	C₂×C₄	C₂×C₄×C₅₀₃	1	1	yes	characteristic
60	C₂×C₄	C₂×C₄×C₅₀₃	1	1	yes	characteristic
61	C₂×C₄	D₄×C₅₀₃	1	1	yes	characteristic
62	C₂×C₄	D₄×C₅₀₃	1	1	yes	characteristic
63	C₂×C₄	Q₈×C₅₀₃	1	1	yes	characteristic
64	C₈	—	2	2	no	—
65	C₂²	—	2	2	no	—
66	C₂²	C₂²⋊C₄×C₅₀₃	1	1	yes	characteristic
67	C₂²	C₂²⋊C₄×C₅₀₃	1	1	yes	characteristic
68	C₂²	C₄⋊C₄×C₅₀₃	1	1	yes	characteristic
69	C₄	—	2	4	no	—
70	C₄	—	4	2	no	—
71	C₄	C₄²×C₅₀₃	1	1	yes	characteristic
72	C₄	C₂²⋊C₄×C₅₀₃	1	1	yes	characteristic
73	C₄	C₄⋊C₄×C₅₀₃	1	1	yes	characteristic
74	C₄	C₄⋊C₄×C₅₀₃	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	2	1	no	—
77	C₂	#95×C₅₀₃	1	1	yes	characteristic
78	C₂	#104×C₅₀₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅₀₃	D₄
commutator	C₄	C₄²×C₅₀₃
Frattini, cosocle	C₂²×C₄	C₂²×C₅₀₃
socle	C₂²×C₅₀₃	C₂²⋊C₄
prime radical	C₂³×C₅₀₃	D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₀₃ ◁ C₂²×C₄×C₅₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
7. M₁₆×C₅₀₃	C₄	semidirect
9. C₄⋊C₄×C₅₀₃	C₄	semidirect
13. C₄²×C₅₀₃	C₄	semidirect
39. C₅₀₃	#339	direct (N × H)
40. #339	C₅₀₃	direct (N × H)
47. M₁₆	C₄×C₅₀₃	semidirect
49. C₄⋊C₄	C₄×C₅₀₃	semidirect
53. C₄²	C₄×C₅₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×C₅₀₃	2
#117×C₅₀₃	2
C₂×C₄²×C₅₀₃	2
#339	503

Subgroups — #339×C503 #44565752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #339×C₅₀₃ #44565752