Subgroups — C₄×C₂₃×#564 #19181981

Order 5888.

1800 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#564	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2382	C₂	1	15	yes	maximal
3	C₄×C₂₃×#125	C₂	1	15	yes	maximal
4	C₂₃×#564	C₄	1	16	yes	direct product factor
5	C₂×C₂₃×#125	C₂²	1	15	yes	—
6	C₂₃×#389	C₂²	1	30	yes	—
7	C₂₃×#387	C₂²	1	60	yes	—
8	C₂₃×#382	C₂²	1	15	yes	—
9	C₄×C₄⋊C₄×C₂₃	C₂²	1	30	yes	—
10	C₄³×C₂₃	C₂²	1	5	yes	—
11	C₂₃×#125	C₂×C₄	1	120	yes	—
12	C₂×C₄⋊C₄×C₂₃	C₂³	1	30	yes	—
13	C₂×C₄⋊C₄×C₂₃	C₂³	1	30	yes	—
14	C₂×C₄²×C₂₃	C₂³	1	15	yes	—
15	C₂×C₄²×C₂₃	C₂³	1	15	yes	—
16	C₂×C₄²×C₂₃	C₂³	1	5	yes	—
17	C₂₃×#95	C₂³	1	60	yes	—
18	C₂²×C₄×C₂₃	C₂⁴	1	15	yes	—
19	C₂²×C₄×C₂₃	C₂⁴	1	15	yes	—
20	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
21	C₄⋊C₄×C₂₃	—	4	30	no	—
22	C₄⋊C₄×C₂₃	C₂²×C₄	1	120	yes	—
23	C₄²×C₂₃	—	2	30	no	—
24	C₄²×C₂₃	—	4	15	no	—
25	C₄²×C₂₃	C₂²×C₄	1	20	yes	—
26	C₄×#564	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
28	C₂×C₄×C₂₃	—	2	15	no	—
29	C₂×C₄×C₂₃	—	2	15	no	—
30	C₂×C₄×C₂₃	—	2	15	no	—
31	C₂×C₄×C₂₃	—	2	30	no	—
32	C₂×C₄×C₂₃	C₂³×C₄	1	30	yes	—
33	C₂×C₄×C₂₃	2₋¹⁺⁴	1	6	yes	—
34	C₂×#564	C₂×C₂₃	1	1	yes	characteristic
35	#2382	C₂×C₂₃	1	15	yes	—
36	C₄×#125	C₂×C₂₃	1	15	yes	—
37	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
38	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	3	yes	—
39	C₂²×C₂₃	#585	1	3	yes	—
40	C₄×C₂₃	—	2	30	no	—
41	C₄×C₂₃	—	4	15	no	—
42	C₄×C₂₃	#564	1	4	yes	direct product factor
43	#564	C₄×C₂₃	1	16	yes	direct product factor
44	C₂×#125	C₂²×C₂₃	1	15	yes	—
45	#389	C₂²×C₂₃	1	30	yes	—
46	#387	C₂²×C₂₃	1	60	yes	—
47	#382	C₂²×C₂₃	1	15	yes	—
48	C₄×C₄⋊C₄	C₂²×C₂₃	1	30	yes	—
49	C₄³	C₂²×C₂₃	1	5	yes	—
50	C₂×C₂₃	C₄×2₋¹⁺⁴	1	3	yes	—
51	C₂×C₂₃	C₂×#564	1	1	yes	characteristic
52	C₂×C₂₃	#3531	1	3	yes	—
53	#125	C₂×C₄×C₂₃	1	120	yes	—
54	C₂×C₄⋊C₄	C₂³×C₂₃	1	30	yes	—
55	C₂×C₄⋊C₄	C₂³×C₂₃	1	30	yes	—
56	C₂×C₄²	C₂³×C₂₃	1	15	yes	—
57	C₂×C₄²	C₂³×C₂₃	1	15	yes	—
58	C₂×C₄²	C₂³×C₂₃	1	5	yes	—
59	#95	C₂³×C₂₃	1	60	yes	—
60	C₂₃	C₄×#564	1	1	yes	characteristic, direct product factor, Sylow
61	C₂²×C₄	C₂⁴×C₂₃	1	15	yes	—
62	C₂²×C₄	C₂⁴×C₂₃	1	15	yes	—
63	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
64	C₄⋊C₄	—	4	30	no	—
65	C₄⋊C₄	C₂²×C₄×C₂₃	1	120	yes	—
66	C₄²	—	2	30	no	—
67	C₄²	—	4	15	no	—
68	C₄²	C₂²×C₄×C₂₃	1	20	yes	—
69	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
70	C₂×C₄	—	2	15	no	—
71	C₂×C₄	—	2	15	no	—
72	C₂×C₄	—	2	15	no	—
73	C₂×C₄	—	2	30	no	—
74	C₂×C₄	C₂³×C₄×C₂₃	1	30	yes	—
75	C₂×C₄	C₂₃×2₋¹⁺⁴	1	6	yes	—
76	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
77	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	3	yes	—
78	C₂²	C₂₃×#585	1	3	yes	—
79	C₄	—	2	30	no	—
80	C₄	—	4	15	no	—
81	C₄	C₂₃×#564	1	4	yes	direct product factor
82	C₂	C₄×C₂₃×2₋¹⁺⁴	1	3	yes	—
83	C₂	C₂×C₂₃×#564	1	1	yes	characteristic
84	C₂	C₂₃×#3531	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
socle, prime radical	C₂³×C₂₃	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₃×#564	C₄	direct (N × H)
26. C₄×#564	C₂₃	direct (N × H)
42. C₄×C₂₃	#564	direct (N × H)
43. #564	C₄×C₂₃	direct (N × H)
60. C₂₃	C₄×#564	direct (N × H)
81. C₄	C₂₃×#564	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#564	2
C₂₃×#2382	2
C₄×C₂₃×#125	2
C₄×#564	23

Subgroups — C4×C23×#564 #19181981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₃×#564 #19181981