Subgroups — C₂²×C₂²⋊#1039 #13107367

Order 1600.

2696 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₅²	C₂	1	1	yes	maximal, characteristic
2	C₂³×#1039	C₂	1	2	yes	maximal, complemented
3	C₂×C₂²⋊#1039	C₂	1	12	yes	maximal, direct product factor
4	C₂⁴×C₅²	—	2	8	no	—
5	C₂⁴×C₅²	C₄	1	8	yes	complemented
6	C₂⁴×C₅²	C₂²	1	6	yes	—
7	C₂⁴×C₅²	C₂²	1	1	yes	characteristic
8	C₂²×#1039	—	2	8	no	—
9	C₂²×#1039	C₂²	1	12	yes	complemented
10	C₂²⋊#1039	C₂²	1	16	yes	direct product factor
11	C₂²×C₂²⋊Dic₅	—	5	6	no	maximal
12	C₂³×C₅²	—	2	32	no	—
13	C₂³×C₅²	—	2	24	no	—
14	C₂³×C₅²	C₂×C₄	1	4	yes	—
15	C₂³×C₅²	C₂×C₄	1	24	yes	complemented
16	C₂³×C₅²	D₄	1	8	yes	—
17	C₂³×C₅²	C₂³	1	4	yes	—
18	C₂³×C₅²	C₂³	1	3	yes	—
19	C₂×#1039	—	2	24	no	—
20	C₂×#1039	C₂³	1	8	yes	complemented
21	C₂⁵×C₅	D₅	1	6	yes	—
22	C₂³×Dic₅	—	5	12	no	—
23	C₂×C₂²⋊Dic₅	—	5	72	no	—
24	C₂²×C₅²	—	2	48	no	—
25	C₂²×C₅²	—	2	8	no	—
26	C₂²×C₅²	C₂²⋊C₄	1	16	yes	complemented
27	C₂²×C₅²	C₂²×C₄	1	6	yes	—
28	C₂²×C₅²	C₂²×C₄	1	8	yes	complemented
29	C₂²×C₅²	C₂×D₄	1	12	yes	—
30	C₂²×C₅²	C₂⁴	1	1	yes	characteristic
31	#1039	—	2	8	no	—
32	C₂⁴×C₅	—	2	48	no	—
33	C₂⁴×C₅	Dic₅	1	48	yes	complemented
34	C₂⁴×C₅	C₂×D₅	1	36	yes	—
35	C₂⁴×C₅	C₂×D₅	1	6	yes	—
36	C₂²×Dic₅	—	5	72	no	—
37	C₂²×Dic₅	—	10	48	no	—
38	C₂²⋊Dic₅	—	5	96	no	—
39	C₂²×C₂²⋊C₄	—	25	1	no	Sylow
40	C₂×C₅²	—	2	8	no	—
41	C₂×C₅²	C₂×C₂²⋊C₄	1	12	yes	complemented
42	C₂×C₅²	C₂³×C₄	1	1	yes	characteristic
43	C₂×C₅²	C₂²×D₄	1	2	yes	—
44	C₂³×C₅	—	2	192	no	—
45	C₂³×C₅	—	2	144	no	—
46	C₂³×C₅	C₂×Dic₅	1	24	yes	—
47	C₂³×C₅	C₂×Dic₅	1	144	yes	complemented
48	C₂³×C₅	C₂²⋊D₅	1	48	yes	—
49	C₂³×C₅	C₂²×D₅	1	24	yes	—
50	C₂³×C₅	C₂²×D₅	1	18	yes	—
51	C₂×Dic₅	—	5	48	no	—
52	C₂×Dic₅	—	10	144	no	—
53	C₂⁵	C₅⋊D₅	1	1	yes	characteristic
54	C₂³×C₄	—	25	2	no	—
55	C₂×C₂²⋊C₄	—	25	12	no	—
56	C₅²	C₂²×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₅	—	2	288	no	—
58	C₂²×C₅	—	2	48	no	—
59	C₂²×C₅	C₂²⋊Dic₅	1	96	yes	complemented
60	C₂²×C₅	C₂²×Dic₅	1	36	yes	—
61	C₂²×C₅	C₂²×Dic₅	1	48	yes	complemented
62	C₂²×C₅	C₂×C₂²⋊D₅	1	72	yes	—
63	C₂²×C₅	C₂³×D₅	1	6	yes	—
64	Dic₅	—	10	48	no	—
65	C₂⁴	—	2	8	no	—
66	C₂⁴	#1039	1	8	yes	complemented
67	C₂⁴	C₂×C₅⋊D₅	1	6	yes	—
68	C₂⁴	C₂×C₅⋊D₅	1	1	yes	characteristic
69	C₂²×C₄	—	25	12	no	—
70	C₂²×C₄	—	50	8	no	—
71	C₂²⋊C₄	—	25	16	no	—
72	C₂×C₅	—	2	48	no	—
73	C₂×C₅	C₂×C₂²⋊Dic₅	1	72	yes	complemented
74	C₂×C₅	C₂³×Dic₅	1	6	yes	—
75	C₂×C₅	C₂²×C₂²⋊D₅	1	12	yes	—
76	C₂³	—	2	32	no	—
77	C₂³	—	2	24	no	—
78	C₂³	C₂×#1039	1	4	yes	—
79	C₂³	C₂×#1039	1	24	yes	complemented
80	C₂³	C₂²⋊(C₅⋊D₅)	1	8	yes	—
81	C₂³	C₂²×C₅⋊D₅	1	4	yes	—
82	C₂³	C₂²×C₅⋊D₅	1	3	yes	—
83	C₂×C₄	—	25	8	no	—
84	C₂×C₄	—	50	24	no	—
85	C₅	C₂²×C₂²⋊Dic₅	1	6	yes	complemented
86	C₂²	—	2	8	no	—
87	C₂²	—	2	48	no	—
88	C₂²	C₂²⋊#1039	1	16	yes	direct product factor
89	C₂²	C₂²×#1039	1	6	yes	—
90	C₂²	C₂²×#1039	1	8	yes	complemented
91	C₂²	C₂×C₂²⋊(C₅⋊D₅)	1	12	yes	—
92	C₂²	C₂³×C₅⋊D₅	1	1	yes	characteristic
93	C₄	—	50	8	no	—
94	C₂	—	2	8	no	—
95	C₂	C₂×C₂²⋊#1039	1	12	yes	direct product factor
96	C₂	C₂³×#1039	1	1	yes	characteristic
97	C₂	C₂²×C₂²⋊(C₅⋊D₅)	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×C₅⋊D₅
commutator	C₂×C₅²	C₂³×C₄
Frattini	C₂²	C₂³×C₅⋊D₅
Fitting, prime radical	C₂⁵×C₅²	C₂
socle	C₂⁴×C₅²	C₂²
cosocle	C₂²×C₅²	C₂⁴
hypercenter	C₂⁵	C₅⋊D₅
hypocenter	C₅²	C₂²×C₂²⋊C₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂⁴ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
2. C₂³×#1039	C₂	semidirect
3. C₂×C₂²⋊#1039	C₂	direct (N × H)
5. C₂⁴×C₅²	C₄	semidirect
9. C₂²×#1039	C₂²	semidirect
10. C₂²⋊#1039	C₂²	direct (N × H)
15. C₂³×C₅²	C₂×C₄	semidirect
20. C₂×#1039	C₂³	semidirect
26. C₂²×C₅²	C₂²⋊C₄	semidirect
28. C₂²×C₅²	C₂²×C₄	semidirect
33. C₂⁴×C₅	Dic₅	semidirect
41. C₂×C₅²	C₂×C₂²⋊C₄	semidirect
47. C₂³×C₅	C₂×Dic₅	semidirect
56. C₅²	C₂²×C₂²⋊C₄	semidirect
59. C₂²×C₅	C₂²⋊Dic₅	semidirect
61. C₂²×C₅	C₂²×Dic₅	semidirect
66. C₂⁴	#1039	semidirect
73. C₂×C₅	C₂×C₂²⋊Dic₅	semidirect
79. C₂³	C₂×#1039	semidirect
85. C₅	C₂²×C₂²⋊Dic₅	semidirect
88. C₂²	C₂²⋊#1039	direct (N × H)
90. C₂²	C₂²×#1039	semidirect
95. C₂	C₂×C₂²⋊#1039	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₅²	2
C₂³×#1039	2
C₂×C₂²⋊#1039	2
C₂²×C₂²⋊Dic₅	5

Subgroups — C22×C22⋊#1039 #13107367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂²⋊#1039 #13107367