Subgroups — C₂×#15692175 #20265163

Order 6464.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄₀₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×#11717579	C₂	1	1	yes	maximal, characteristic, complemented
3	#15692175	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×D₁₀₁	—	2	1	no	—
6	C₂×D₄₀₄	—	2	2	no	—
7	C₂×D₄₀₄	—	2	1	no	—
8	C₂×D₄₀₄	C₄	1	4	yes	complemented
9	C₂×D₄₀₄	C₂²	1	2	yes	—
10	C₂×#11717579	—	2	2	no	—
11	C₂×#11717579	C₂²	1	2	yes	complemented
12	C₂²×C₄×C₁₀₁	—	2	1	no	—
13	C₂²×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₄⋊C₄×C₁₀₁	—	2	1	no	—
15	C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	complemented
16	C₂³×C₁₀₁	D₄	1	1	yes	characteristic
17	C₂²×D₁₀₁	—	2	4	no	—
18	C₂²×D₁₀₁	—	2	2	no	—
19	C₂²×D₁₀₁	—	4	2	no	—
20	C₂²×D₁₀₁	—	4	2	no	—
21	C₂×C₄×C₁₀₁	—	2	2	no	—
22	C₂×C₄×C₁₀₁	—	4	2	no	—
23	C₂×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
24	C₂×C₄×C₁₀₁	D₄	1	2	yes	—
25	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
26	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
27	D₄₀₄	—	2	4	no	—
28	D₄₀₄	—	2	2	no	—
29	D₄₀₄	C₂×C₄	1	4	yes	complemented
30	#11717579	—	2	2	no	—
31	C₂²×C₁₀₁	C₂²⋊C₄	1	2	yes	—
32	C₂²×C₁₀₁	D₈	1	2	yes	—
33	C₂²×C₁₀₁	SD₁₆	1	2	yes	—
34	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
35	C₂×D₁₀₁	—	2	4	no	—
36	C₂×D₁₀₁	—	4	8	no	—
37	C₂×D₁₀₁	—	4	2	no	—
38	C₂×D₁₀₁	—	4	2	no	—
39	C₄×C₁₀₁	—	4	2	no	—
40	C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
41	C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
42	C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
43	C₂×C₁₀₁	#102	1	4	yes	complemented
44	C₂×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₁₀₁	C₂×D₈	1	1	yes	characteristic
46	C₂×C₁₀₁	C₂×SD₁₆	1	1	yes	characteristic
47	D₁₀₁	—	4	4	no	—
48	C₁₀₁	C₂×#102	1	1	yes	characteristic, complemented, Sylow
49	C₂×#102	—	101	1	no	maximal, Sylow
50	C₂²×D₄	—	101	1	no	—
51	C₂²×C₈	—	101	1	no	—
52	C₂×C₄⋊C₄	D₁₀₁	1	1	yes	characteristic, complemented
53	#102	—	101	4	no	—
54	C₂⁴	—	202	1	no	—
55	C₂×D₄	—	101	4	no	—
56	C₂×D₄	—	101	2	no	—
57	C₂×D₄	—	202	2	no	—
58	C₂×D₄	—	202	1	no	—
59	C₂²×C₄	—	2	1	no	—
60	C₂²×C₄	C₂×D₁₀₁	1	1	yes	characteristic
61	C₂×C₈	—	101	2	no	—
62	C₂×C₈	—	202	2	no	—
63	C₄⋊C₄	—	2	1	no	—
64	C₄⋊C₄	C₂×D₁₀₁	1	2	yes	complemented
65	C₂³	—	404	2	no	—
66	C₂³	—	404	2	no	—
67	C₂³	—	202	4	no	—
68	C₂³	—	202	2	no	—
69	C₂³	C₂²⋊D₁₀₁	1	1	yes	characteristic
70	D₄	—	101	4	no	—
71	D₄	—	202	4	no	—
72	D₄	—	202	2	no	—
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	C₄×D₁₀₁	1	2	yes	—
76	C₂×C₄	D₄₀₄	1	2	yes	—
77	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
78	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
79	C₈	—	202	2	no	—
80	C₂²	—	404	8	no	—
81	C₂²	—	404	2	no	—
82	C₂²	—	404	2	no	—
83	C₂²	—	202	4	no	—
84	C₂²	#13108051	1	2	yes	—
85	C₂²	#13108059	1	2	yes	—
86	C₂²	#13108061	1	2	yes	—
87	C₂²	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic
88	C₄	—	4	2	no	—
89	C₄	#13108051	1	2	yes	—
90	C₄	C₂×C₄×D₁₀₁	1	1	yes	characteristic
91	C₄	C₂×D₄₀₄	1	1	yes	characteristic
92	C₂	—	404	4	no	—
93	C₂	#15692175	1	4	yes	direct product factor
94	C₂	C₂×#13108051	1	1	yes	characteristic
95	C₂	C₂×#13108059	1	1	yes	characteristic
96	C₂	C₂×#13108061	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₁₀₁
commutator	C₄×C₁₀₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	C₂×C₄⋊C₄×C₁₀₁	C₂
socle	C₂³×C₁₀₁	D₄
hypercenter	C₂×C₄⋊C₄	D₁₀₁
hypocenter	C₁₀₁	C₂×#102
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×#11717579	C₂	semidirect
3. #15692175	C₂	direct (N × H)
4. C₂×C₄⋊C₄×C₁₀₁	C₂	semidirect
8. C₂×D₄₀₄	C₄	semidirect
11. C₂×#11717579	C₂²	semidirect
15. C₄⋊C₄×C₁₀₁	C₂²	semidirect
29. D₄₀₄	C₂×C₄	semidirect
43. C₂×C₁₀₁	#102	semidirect
48. C₁₀₁	C₂×#102	semidirect
52. C₂×C₄⋊C₄	D₁₀₁	semidirect
64. C₄⋊C₄	C₂×D₁₀₁	semidirect
93. C₂	#15692175	direct (N × H)

Subgroups — C2×#15692175 #20265163

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15692175 #20265163