Subgroups — C₂×#16810365 #20273299

Order 6784.

232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133128	C₂	1	2	yes	maximal
2	#16810365	C₂	1	4	yes	maximal, direct product factor
3	C₂×#125×C₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×#88322	—	2	2	no	—
5	#13133128	—	2	2	no	—
6	#13133128	C₂²	1	4	yes	—
7	#125×C₅₃	—	2	2	no	—
8	#125×C₅₃	C₄	1	2	yes	—
9	#125×C₅₃	C₂²	1	2	yes	—
10	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
11	C₂×C₄⋊C₄×C₅₃	C₄	1	2	yes	—
12	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₅₃	—	2	2	no	—
14	C₂²×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₅₃	D₄	1	2	yes	—
16	C₄⋊C₄×C₅₃	—	2	4	no	—
17	C₄⋊C₄×C₅₃	—	2	2	no	—
18	C₄⋊C₄×C₅₃	—	2	4	no	—
19	C₄⋊C₄×C₅₃	C₂×C₄	1	4	yes	—
20	C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
21	C₄²×C₅₃	D₄	1	2	yes	—
22	C₄²×C₅₃	C₂³	1	1	yes	characteristic
23	C₂×#88322	—	2	8	no	—
24	C₂×#88322	—	2	4	no	—
25	C₂³×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₅₃	—	2	2	no	—
27	C₂×C₄×C₅₃	—	2	4	no	—
28	C₂×C₄×C₅₃	—	2	4	no	—
29	C₂×C₄×C₅₃	—	4	4	no	—
30	C₂×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
32	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₅₃	C₂×D₄	1	2	yes	—
34	#88322	—	2	8	no	—
35	C₂²×C₅₃	#101	1	2	yes	—
36	C₂²×C₅₃	#104	1	4	yes	—
37	C₂²×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
38	C₄×C₅₃	—	2	1	no	—
39	C₄×C₅₃	—	2	1	no	—
40	C₄×C₅₃	—	2	2	no	—
41	C₄×C₅₃	—	2	2	no	—
42	C₄×C₅₃	—	4	4	no	—
43	C₂×#330	—	53	1	no	maximal, Sylow
44	C₂×C₅₃	#330	1	4	yes	complemented
45	C₂×C₅₃	C₂×#101	1	1	yes	characteristic
46	C₂×C₅₃	C₂×#104	1	2	yes	—
47	C₂×#125	D₅₃	1	1	yes	characteristic
48	C₂×#97	—	53	2	no	—
49	#330	—	53	4	no	—
50	C₅₃	C₂×#330	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₈	—	106	2	no	—
52	#125	—	2	2	no	—
53	#125	Dic₅₃	1	2	yes	—
54	#125	C₂×D₅₃	1	2	yes	—
55	C₂×C₄⋊C₄	—	2	2	no	—
56	C₂×C₄⋊C₄	Dic₅₃	1	2	yes	—
57	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic
58	#97	—	53	4	no	—
59	#97	—	106	2	no	—
60	C₂²×C₄	—	2	2	no	—
61	C₂²×C₄	C₂×Dic₅₃	1	1	yes	characteristic
62	C₂²×C₄	C₂²⋊D₅₃	1	2	yes	—
63	C₂×C₈	—	106	8	no	—
64	C₂×C₈	—	106	4	no	—
65	C₄⋊C₄	—	2	4	no	—
66	C₄⋊C₄	—	2	4	no	—
67	C₄⋊C₄	—	2	2	no	—
68	C₄⋊C₄	C₂×Dic₅₃	1	4	yes	—
69	C₄²	C₂×Dic₅₃	1	1	yes	characteristic
70	C₄²	C₂²⋊D₅₃	1	2	yes	—
71	C₄²	C₂²×D₅₃	1	1	yes	characteristic
72	C₂³	C₂²⋊Dic₅₃	1	1	yes	characteristic
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	—	2	4	no	—
76	C₂×C₄	—	4	4	no	—
77	C₂×C₄	C₂²⋊Dic₅₃	1	2	yes	—
78	C₂×C₄	C₂²⋊Dic₅₃	1	1	yes	characteristic
79	C₂×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
80	C₂×C₄	C₂×C₂²⋊D₅₃	1	2	yes	—
81	C₈	—	106	8	no	—
82	C₂²	#13133136	1	2	yes	—
83	C₂²	#13133144	1	4	yes	—
84	C₂²	C₂×C₂²⋊Dic₅₃	1	1	yes	characteristic
85	C₄	—	2	1	no	—
86	C₄	—	2	1	no	—
87	C₄	—	2	2	no	—
88	C₄	—	2	2	no	—
89	C₄	—	4	4	no	—
90	C₂	#16810365	1	4	yes	direct product factor
91	C₂	C₂×#13133136	1	1	yes	characteristic
92	C₂	C₂×#13133144	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²⋊Dic₅₃
commutator	C₂×C₄×C₅₃	C₂²×C₄
Frattini	C₄²	C₂²×D₅₃
Fitting	C₂×#125×C₅₃	C₂
socle	C₂³×C₅₃	C₂²⋊C₄
hypercenter	C₂×#125	D₅₃
hypocenter	C₅₃	C₂×#330
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

Complements

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

N	H ≅ G/N	type
2. #16810365	C₂	direct (N × H)
44. C₂×C₅₃	#330	semidirect
50. C₅₃	C₂×#330	semidirect
90. C₂	#16810365	direct (N × H)

Subgroups — C2×#16810365 #20273299

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16810365 #20273299