Subgroups — C₂×#102×C₅₂₃ #45689751

Order 33472.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×C₅₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×C₅₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄⋊C₄×C₅₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#102×C₅₂₃	C₂	1	4	yes	maximal, direct product factor
5	C₂⁴×C₅₂₃	—	2	1	no	—
6	C₂×D₄×C₅₂₃	—	2	1	no	—
7	C₂×D₄×C₅₂₃	—	2	2	no	—
8	C₂×D₄×C₅₂₃	C₄	1	4	yes	complemented
9	C₂×D₄×C₅₂₃	C₂²	1	2	yes	—
10	C₂²×C₄×C₅₂₃	—	2	1	no	—
11	C₂²×C₄×C₅₂₃	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₅₂₃	—	2	2	no	—
13	C₂×C₈×C₅₂₃	C₂²	1	2	yes	complemented
14	C₄⋊C₄×C₅₂₃	—	2	1	no	—
15	C₄⋊C₄×C₅₂₃	C₂²	1	2	yes	complemented
16	C₂³×C₅₂₃	—	2	4	no	—
17	C₂³×C₅₂₃	—	2	2	no	—
18	C₂³×C₅₂₃	—	4	2	no	—
19	C₂³×C₅₂₃	—	4	2	no	—
20	C₂³×C₅₂₃	D₄	1	1	yes	characteristic
21	D₄×C₅₂₃	—	2	4	no	—
22	D₄×C₅₂₃	—	2	2	no	—
23	D₄×C₅₂₃	C₂×C₄	1	4	yes	complemented
24	C₂×C₄×C₅₂₃	—	2	2	no	—
25	C₂×C₄×C₅₂₃	—	4	2	no	—
26	C₂×C₄×C₅₂₃	C₂×C₄	1	2	yes	—
27	C₂×C₄×C₅₂₃	D₄	1	1	yes	characteristic
28	C₂×C₄×C₅₂₃	D₄	1	2	yes	—
29	C₂×C₄×C₅₂₃	C₂³	1	1	yes	characteristic
30	C₈×C₅₂₃	—	2	2	no	—
31	C₂²×C₅₂₃	—	2	4	no	—
32	C₂²×C₅₂₃	—	4	8	no	—
33	C₂²×C₅₂₃	—	4	2	no	—
34	C₂²×C₅₂₃	—	4	2	no	—
35	C₂²×C₅₂₃	C₂²⋊C₄	1	2	yes	—
36	C₂²×C₅₂₃	D₈	1	2	yes	—
37	C₂²×C₅₂₃	SD₁₆	1	2	yes	—
38	C₂²×C₅₂₃	C₂×D₄	1	1	yes	characteristic
39	C₄×C₅₂₃	—	4	2	no	—
40	C₄×C₅₂₃	C₂²⋊C₄	1	2	yes	—
41	C₄×C₅₂₃	C₂²×C₄	1	1	yes	characteristic
42	C₄×C₅₂₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₅₂₃	—	4	4	no	—
44	C₂×C₅₂₃	#102	1	4	yes	direct product factor
45	C₂×C₅₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₅₂₃	C₂×D₈	1	1	yes	characteristic
47	C₂×C₅₂₃	C₂×SD₁₆	1	1	yes	characteristic
48	C₅₂₃	C₂×#102	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×#102	C₅₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂²×D₄	C₂×C₅₂₃	1	1	yes	characteristic
51	C₂²×C₈	C₂×C₅₂₃	1	1	yes	characteristic, complemented
52	C₂×C₄⋊C₄	C₂×C₅₂₃	1	1	yes	characteristic, complemented
53	#102	C₂×C₅₂₃	1	4	yes	direct product factor
54	C₂⁴	—	2	1	no	—
55	C₂×D₄	—	2	1	no	—
56	C₂×D₄	—	2	2	no	—
57	C₂×D₄	C₄×C₅₂₃	1	4	yes	complemented
58	C₂×D₄	C₂²×C₅₂₃	1	2	yes	—
59	C₂²×C₄	—	2	1	no	—
60	C₂²×C₄	C₂²×C₅₂₃	1	1	yes	characteristic
61	C₂×C₈	—	2	2	no	—
62	C₂×C₈	C₂²×C₅₂₃	1	2	yes	complemented
63	C₄⋊C₄	—	2	1	no	—
64	C₄⋊C₄	C₂²×C₅₂₃	1	2	yes	complemented
65	C₂³	—	2	4	no	—
66	C₂³	—	2	2	no	—
67	C₂³	—	4	2	no	—
68	C₂³	—	4	2	no	—
69	C₂³	D₄×C₅₂₃	1	1	yes	characteristic
70	D₄	—	2	4	no	—
71	D₄	—	2	2	no	—
72	D₄	C₂×C₄×C₅₂₃	1	4	yes	complemented
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	C₂×C₄×C₅₂₃	1	2	yes	—
76	C₂×C₄	D₄×C₅₂₃	1	1	yes	characteristic
77	C₂×C₄	D₄×C₅₂₃	1	2	yes	—
78	C₂×C₄	C₂³×C₅₂₃	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₂²	—	2	4	no	—
81	C₂²	—	4	8	no	—
82	C₂²	—	4	2	no	—
83	C₂²	—	4	2	no	—
84	C₂²	C₂²⋊C₄×C₅₂₃	1	2	yes	—
85	C₂²	D₈×C₅₂₃	1	2	yes	—
86	C₂²	SD₁₆×C₅₂₃	1	2	yes	—
87	C₂²	C₂×D₄×C₅₂₃	1	1	yes	characteristic
88	C₄	—	4	2	no	—
89	C₄	C₂²⋊C₄×C₅₂₃	1	2	yes	—
90	C₄	C₂²×C₄×C₅₂₃	1	1	yes	characteristic
91	C₄	C₂×D₄×C₅₂₃	1	1	yes	characteristic
92	C₂	—	4	4	no	—
93	C₂	#102×C₅₂₃	1	4	yes	direct product factor
94	C₂	C₂×C₂²⋊C₄×C₅₂₃	1	1	yes	characteristic
95	C₂	C₂×D₈×C₅₂₃	1	1	yes	characteristic
96	C₂	C₂×SD₁₆×C₅₂₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₂₃	D₄
commutator	C₄	C₂²×C₄×C₅₂₃
Frattini, cosocle	C₂×C₄	C₂³×C₅₂₃
prime radical	C₂²×D₄×C₅₂₃	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₂₃ ◁ C₂²×C₄×C₅₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₈×C₅₂₃	C₂	semidirect
3. C₂×C₄⋊C₄×C₅₂₃	C₂	semidirect
4. #102×C₅₂₃	C₂	direct (N × H)
8. C₂×D₄×C₅₂₃	C₄	semidirect
13. C₂×C₈×C₅₂₃	C₂²	semidirect
15. C₄⋊C₄×C₅₂₃	C₂²	semidirect
23. D₄×C₅₂₃	C₂×C₄	semidirect
44. C₂×C₅₂₃	#102	direct (N × H)
48. C₅₂₃	C₂×#102	direct (N × H)
49. C₂×#102	C₅₂₃	direct (N × H)
51. C₂²×C₈	C₂×C₅₂₃	semidirect
52. C₂×C₄⋊C₄	C₂×C₅₂₃	semidirect
53. #102	C₂×C₅₂₃	direct (N × H)
57. C₂×D₄	C₄×C₅₂₃	semidirect
62. C₂×C₈	C₂²×C₅₂₃	semidirect
64. C₄⋊C₄	C₂²×C₅₂₃	semidirect
72. D₄	C₂×C₄×C₅₂₃	semidirect
93. C₂	#102×C₅₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₄×C₅₂₃	2
C₂²×C₈×C₅₂₃	2
C₂×C₄⋊C₄×C₅₂₃	2
#102×C₅₂₃	2
C₂×#102	523

Subgroups — C2×#102×C523 #45689751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#102×C₅₂₃ #45689751