Subgroups — #383×D₅₃ #20277103

Order 6784.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#16810491	C₂	1	1	yes	maximal, characteristic, complemented
3	#16810490	C₂	1	6	yes	maximal, complemented
4	#95×D₅₃	C₂	1	6	yes	maximal
5	C₅₃×#383	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₅₃	C₂²	1	4	yes	—
7	C₂²×C₄×D₅₃	C₂²	1	3	yes	—
8	C₂×C₄×Dic₅₃	C₂²	1	3	yes	—
9	C₄²×D₅₃	C₄	1	8	yes	complemented
10	#13133124	C₂²	1	12	yes	—
11	#13133124	C₂²	1	6	yes	—
12	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic
13	#95×C₅₃	C₂²	1	6	yes	—
14	C₂³×D₅₃	C₂³	1	1	yes	characteristic
15	C₂²×C₄×C₅₃	C₂³	1	4	yes	—
16	C₂²×C₄×C₅₃	C₂³	1	3	yes	—
17	C₂²×Dic₅₃	C₂³	1	4	yes	—
18	C₂²×Dic₅₃	C₂³	1	3	yes	—
19	C₂×C₄×D₅₃	—	2	12	no	—
20	C₂×C₄×D₅₃	—	2	24	no	—
21	C₂×C₄×D₅₃	C₂×C₄	1	12	yes	—
22	C₄²×C₅₃	C₂×C₄	1	4	yes	complemented
23	C₄×Dic₅₃	C₂×C₄	1	12	yes	complemented
24	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
25	C₂²×D₅₃	C₂²×C₄	1	2	yes	—
26	C₂²×D₅₃	#41	1	12	yes	—
27	C₂×C₄×C₅₃	—	2	6	no	—
28	C₂×C₄×C₅₃	—	2	12	no	—
29	C₂×C₄×C₅₃	C₂²×C₄	1	6	yes	—
30	C₂×Dic₅₃	—	2	6	no	—
31	C₂×Dic₅₃	—	2	12	no	—
32	C₂×Dic₅₃	C₂²×C₄	1	6	yes	—
33	C₄×D₅₃	—	2	24	no	—
34	C₄×D₅₃	—	4	16	no	—
35	C₂²×C₅₃	C₂³×C₄	1	1	yes	characteristic
36	C₂²×C₅₃	C₂×#41	1	6	yes	—
37	C₂×D₅₃	#117	1	12	yes	—
38	C₂×D₅₃	#126	1	16	yes	—
39	C₄×C₅₃	—	2	6	no	—
40	C₄×C₅₃	—	4	4	no	—
41	Dic₅₃	—	2	6	no	—
42	Dic₅₃	—	4	4	no	—
43	C₂×#383	—	53	1	no	maximal, Sylow
44	C₂×C₅₃	C₂×#117	1	3	yes	—
45	C₂×C₅₃	C₂×#126	1	4	yes	—
46	D₅₃	#383	1	8	yes	direct product factor
47	C₂²×C₄²	—	53	1	no	—
48	#383	—	53	1	no	—
49	#383	—	53	6	no	—
50	#383	D₅₃	1	1	yes	characteristic, direct product factor
51	C₂×#95	—	53	6	no	—
52	C₅₃	C₂×#383	1	1	yes	characteristic, complemented, Sylow
53	C₂³×C₄	—	53	3	no	—
54	C₂³×C₄	—	53	4	no	—
55	C₂×C₄²	—	53	3	no	—
56	C₂×C₄²	—	53	8	no	—
57	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic
58	#95	—	53	12	no	—
59	#95	—	53	6	no	—
60	#95	C₂×D₅₃	1	6	yes	—
61	C₂⁴	—	53	1	no	—
62	C₂²×C₄	—	53	3	no	—
63	C₂²×C₄	—	53	12	no	—
64	C₂²×C₄	—	53	4	no	—
65	C₂²×C₄	—	106	12	no	—
66	C₂²×C₄	—	106	24	no	—
67	C₂²×C₄	C₂²×D₅₃	1	4	yes	—
68	C₂²×C₄	C₂²×D₅₃	1	3	yes	—
69	C₄²	—	53	12	no	—
70	C₄²	C₄×D₅₃	1	4	yes	complemented
71	C₂³	—	53	2	no	—
72	C₂³	—	53	12	no	—
73	C₂³	C₂³×D₅₃	1	1	yes	characteristic
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	—	2	12	no	—
76	C₂×C₄	—	53	6	no	—
77	C₂×C₄	—	106	24	no	—
78	C₂×C₄	—	106	6	no	—
79	C₂×C₄	—	106	12	no	—
80	C₂×C₄	—	212	16	no	—
81	C₂×C₄	C₂×C₄×D₅₃	1	6	yes	—
82	C₂²	—	53	12	no	—
83	C₂²	—	53	16	no	—
84	C₂²	C₂²×C₄×D₅₃	1	1	yes	characteristic
85	C₂²	#41×D₅₃	1	6	yes	—
86	C₄	—	2	6	no	—
87	C₄	—	4	4	no	—
88	C₄	—	106	6	no	—
89	C₄	—	212	4	no	—
90	C₂	—	53	8	no	—
91	C₂	#117×D₅₃	1	3	yes	—
92	C₂	#126×D₅₃	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₅₃
commutator	C₂²×C₅₃	C₂³×C₄
Fitting	C₅₃×#383	C₂
socle	C₂³×C₅₃	C₂⁴
hypercenter	#383	D₅₃
hypocenter	C₅₃	C₂×#383
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #383

Complements

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

N	H ≅ G/N	type
2. #16810491	C₂	semidirect
3. #16810490	C₂	semidirect
5. C₅₃×#383	C₂	semidirect
9. C₄²×D₅₃	C₄	semidirect
22. C₄²×C₅₃	C₂×C₄	semidirect
23. C₄×Dic₅₃	C₂×C₄	semidirect
46. D₅₃	#383	direct (N × H)
50. #383	D₅₃	direct (N × H)
52. C₅₃	C₂×#383	semidirect
70. C₄²	C₄×D₅₃	semidirect

Subgroups — #383×D53 #20277103

Conjugacy classes of subgroups

Complements

Subgroups — #383×D₅₃ #20277103