Subgroups — #20283102

Order 6784.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16810521	C₂	1	4	yes	maximal
2	#16810507	C₂	1	8	yes	maximal
3	#16810489	C₂	1	2	yes	maximal
4	C₄³×C₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊Dic₅₃	C₂²	1	4	yes	—
6	C₂×#11719919	C₂²	1	8	yes	—
7	#13133124	C₂²	1	8	yes	—
8	#13133124	C₂²	1	8	yes	—
9	C₂×C₄²×C₅₃	C₂²	1	4	yes	—
10	C₂×C₄²×C₅₃	C₂²	1	2	yes	—
11	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
13	C₂²×C₄×C₅₃	C₂³	1	4	yes	—
14	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
15	C₂²×Dic₅₃	C₂³	1	8	yes	—
16	C₄²×C₅₃	—	2	8	no	—
17	C₄²×C₅₃	—	2	4	no	—
18	C₄²×C₅₃	Q₈	1	4	yes	—
19	C₄⋊Dic₅₃	—	2	8	no	—
20	#11719919	—	2	16	no	—
21	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
22	C₂×C₄×C₅₃	—	2	4	no	—
23	C₂×C₄×C₅₃	—	2	4	no	—
24	C₂×C₄×C₅₃	—	2	4	no	—
25	C₂×C₄×C₅₃	C₂×Q₈	1	4	yes	—
26	C₂×C₄×C₅₃	C₂×Q₈	1	2	yes	—
27	C₂×C₄×C₅₃	#41	1	8	yes	—
28	C₂×C₄×C₅₃	#41	1	4	yes	—
29	C₂×Dic₅₃	—	2	16	no	—
30	C₂×Dic₅₃	—	2	8	no	—
31	C₂²×C₅₃	C₂²×Q₈	1	1	yes	characteristic
32	C₂²×C₅₃	C₂×#41	1	2	yes	—
33	C₂²×C₅₃	C₂×#41	1	4	yes	—
34	C₄×C₅₃	—	2	8	no	—
35	C₄×C₅₃	—	2	4	no	—
36	C₄×C₅₃	#125	1	4	yes	—
37	Dic₅₃	—	4	8	no	—
38	#2864	—	53	1	no	maximal, Sylow
39	C₂×C₅₃	C₂×#125	1	1	yes	characteristic
40	C₂×C₅₃	#529	1	4	yes	—
41	C₂×C₅₃	#533	1	2	yes	—
42	#389	—	53	4	no	—
43	#387	—	53	8	no	—
44	#382	—	53	2	no	—
45	C₄³	D₅₃	1	1	yes	characteristic
46	C₅₃	#2864	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₄⋊C₄	—	53	8	no	—
48	C₂×C₄⋊C₄	—	53	4	no	—
49	C₂×C₄²	C₂×D₅₃	1	4	yes	—
50	C₂×C₄²	C₂×D₅₃	1	2	yes	—
51	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic
52	#95	—	53	8	no	—
53	#95	—	53	8	no	—
54	C₂²×C₄	—	53	8	no	—
55	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
56	C₂²×C₄	C₂²×D₅₃	1	4	yes	—
57	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
58	C₄⋊C₄	—	106	16	no	—
59	C₄⋊C₄	—	106	8	no	—
60	C₄²	—	2	8	no	—
61	C₄²	—	2	4	no	—
62	C₄²	Dic₁₀₆	1	4	yes	—
63	C₂³	C₂³×D₅₃	1	1	yes	characteristic
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	2	4	no	—
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	106	8	no	—
68	C₂×C₄	—	106	16	no	—
69	C₂×C₄	C₂×Dic₁₀₆	1	4	yes	—
70	C₂×C₄	C₂×Dic₁₀₆	1	2	yes	—
71	C₂×C₄	#11719945	1	8	yes	—
72	C₂×C₄	#11719945	1	4	yes	—
73	C₂²	C₂²×Dic₁₀₆	1	1	yes	characteristic
74	C₂²	C₂×#11719945	1	2	yes	—
75	C₂²	C₂×#11719945	1	4	yes	—
76	C₄	—	2	8	no	—
77	C₄	—	2	4	no	—
78	C₄	—	212	8	no	—
79	C₄	#13133209	1	4	yes	—
80	C₂	C₂×#13133209	1	1	yes	characteristic
81	C₂	#16811157	1	4	yes	—
82	C₂	#16811180	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₅₃
commutator, socle	C₂³×C₅₃	C₂⁴
Fitting	C₄³×C₅₃	C₂
hypercenter	C₄³	D₅₃
hypocenter	C₅₃	#2864
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
46. C₅₃	#2864	semidirect