Subgroups — C₂×#10625124 #13092903

Order 1472.

662 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊D₂₃	C₂	1	3	yes	maximal, complemented
3	#10625124	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₂²⋊Dic₂₃	C₂	1	3	yes	maximal, complemented
5	C₂⁴×C₂₃	—	2	12	no	—
6	C₂⁴×C₂₃	C₂²	1	3	yes	—
7	C₂⁴×C₂₃	C₂²	1	4	yes	complemented
8	C₂³×D₂₃	C₂²	1	1	yes	characteristic, complemented
9	C₂×C₂²⋊D₂₃	—	2	12	no	—
10	C₂×C₂²⋊D₂₃	C₂²	1	12	yes	complemented
11	C₂²×Dic₂₃	C₂²	1	3	yes	complemented
12	C₂²⋊Dic₂₃	C₂²	1	12	yes	complemented
13	C₂³×C₂₃	—	2	32	no	—
14	C₂³×C₂₃	—	2	12	no	—
15	C₂³×C₂₃	—	2	24	no	—
16	C₂³×C₂₃	D₄	1	12	yes	complemented
17	C₂³×C₂₃	C₂³	1	6	yes	—
18	C₂³×C₂₃	C₂³	1	1	yes	characteristic
19	C₂²×D₂₃	—	2	6	no	—
20	C₂²×D₂₃	C₂³	1	2	yes	complemented
21	C₂²⋊D₂₃	—	2	24	no	—
22	C₂×Dic₂₃	—	2	6	no	—
23	C₂×Dic₂₃	C₂³	1	6	yes	complemented
24	C₂²×C₂₃	—	2	32	no	—
25	C₂²×C₂₃	—	2	24	no	—
26	C₂²×C₂₃	—	2	12	no	—
27	C₂²×C₂₃	C₂×D₄	1	6	yes	—
28	C₂²×C₂₃	C₂×D₄	1	12	yes	complemented
29	C₂²×C₂₃	C₂⁴	1	1	yes	characteristic
30	C₂×D₂₃	—	2	6	no	—
31	C₂×D₂₃	—	4	4	no	—
32	Dic₂₃	—	2	6	no	—
33	C₂×#120	—	23	1	no	maximal, Sylow
34	C₂×C₂₃	—	2	12	no	—
35	C₂×C₂₃	#120	1	4	yes	complemented
36	C₂×C₂₃	C₂²×D₄	1	3	yes	—
37	D₂₃	—	4	2	no	—
38	C₂⁵	D₂₃	1	1	yes	characteristic, complemented
39	C₂²×D₄	—	23	3	no	—
40	#120	—	23	8	no	—
41	C₂×C₂²⋊C₄	—	23	3	no	—
42	C₂₃	C₂×#120	1	1	yes	characteristic, complemented, Sylow
43	C₂⁴	—	2	12	no	—
44	C₂⁴	—	23	1	no	—
45	C₂⁴	C₂×D₂₃	1	3	yes	—
46	C₂⁴	C₂×D₂₃	1	4	yes	complemented
47	C₂×D₄	—	23	12	no	—
48	C₂×D₄	—	46	12	no	—
49	C₂²×C₄	—	23	3	no	—
50	C₂²⋊C₄	—	23	12	no	—
51	C₂³	—	2	32	no	—
52	C₂³	—	2	12	no	—
53	C₂³	—	2	24	no	—
54	C₂³	—	23	2	no	—
55	C₂³	—	46	6	no	—
56	C₂³	C₂²⋊D₂₃	1	12	yes	complemented
57	C₂³	C₂²×D₂₃	1	6	yes	—
58	C₂³	C₂²×D₂₃	1	1	yes	characteristic
59	D₄	—	46	24	no	—
60	C₂×C₄	—	23	6	no	—
61	C₂×C₄	—	46	6	no	—
62	C₂²	—	2	32	no	—
63	C₂²	—	2	24	no	—
64	C₂²	—	2	12	no	—
65	C₂²	—	46	6	no	—
66	C₂²	—	92	4	no	—
67	C₂²	C₂×C₂²⋊D₂₃	1	6	yes	—
68	C₂²	C₂×C₂²⋊D₂₃	1	12	yes	complemented
69	C₂²	C₂³×D₂₃	1	1	yes	characteristic
70	C₄	—	46	6	no	—
71	C₂	—	2	12	no	—
72	C₂	—	92	2	no	—
73	C₂	#10625124	1	4	yes	direct product factor
74	C₂	C₂²×C₂²⋊D₂₃	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₂₃
commutator, cosocle	C₂²×C₂₃	C₂⁴
Frattini	C₂²	C₂³×D₂₃
Fitting	C₂⁵×C₂₃	C₂
socle	C₂³×C₂₃	C₂³
hypercenter	C₂⁵	D₂₃
hypocenter	C₂₃	C₂×#120
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂⁵×C₂₃	C₂	semidirect
2. C₂²×C₂²⋊D₂₃	C₂	semidirect
3. #10625124	C₂	direct (N × H)
4. C₂×C₂²⋊Dic₂₃	C₂	semidirect
7. C₂⁴×C₂₃	C₂²	semidirect
8. C₂³×D₂₃	C₂²	semidirect
10. C₂×C₂²⋊D₂₃	C₂²	semidirect
11. C₂²×Dic₂₃	C₂²	semidirect
12. C₂²⋊Dic₂₃	C₂²	semidirect
16. C₂³×C₂₃	D₄	semidirect
20. C₂²×D₂₃	C₂³	semidirect
23. C₂×Dic₂₃	C₂³	semidirect
28. C₂²×C₂₃	C₂×D₄	semidirect
35. C₂×C₂₃	#120	semidirect
38. C₂⁵	D₂₃	semidirect
42. C₂₃	C₂×#120	semidirect
46. C₂⁴	C₂×D₂₃	semidirect
56. C₂³	C₂²⋊D₂₃	semidirect
68. C₂²	C₂×C₂²⋊D₂₃	semidirect
73. C₂	#10625124	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×C₂₃	2
C₂²×C₂²⋊D₂₃	2
#10625124	2
C₂×C₂²⋊Dic₂₃	2
C₂×#120	23

Subgroups — C2×#10625124 #13092903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10625124 #13092903