Subgroups — C₄×C₅×C₁₁×C₁₂₈ #72205136

Order 28160.

200 conjugacy classes of subgroups.

The subgroup lattice has 144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₁₁×C₁₂₈	C₂	1	2	yes	maximal
3	C₄×C₅×C₁₁×C₃₂	C₄	1	1	yes	characteristic
4	C₂×C₅×C₁₁×C₆₄	C₄	1	1	yes	characteristic
5	C₂×C₅×C₁₁×C₆₄	C₂²	1	1	yes	characteristic
6	C₅×C₁₁×C₁₂₈	C₄	1	4	yes	direct product factor
7	C₄×C₁₁×C₁₂₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₄×C₅×C₁₁×C₁₆	C₈	1	1	yes	characteristic
9	C₂×C₅×C₁₁×C₃₂	C₈	1	1	yes	characteristic
10	C₂×C₅×C₁₁×C₃₂	C₂×C₄	1	1	yes	characteristic
11	C₅×C₁₁×C₆₄	C₈	1	2	yes	—
12	C₅×C₁₁×C₆₄	C₂×C₄	1	2	yes	—
13	C₄×C₅×C₁₂₈	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₁₁×C₁₂₈	C₂×C₅	1	2	yes	—
15	C₄×C₁₁×C₆₄	C₂×C₅	1	1	yes	characteristic
16	C₂×C₅×C₁₁×C₁₆	C₁₆	1	1	yes	characteristic
17	C₂×C₅×C₁₁×C₁₆	C₂×C₈	1	1	yes	characteristic
18	C₄×C₅×C₈×C₁₁	C₁₆	1	1	yes	characteristic
19	C₅×C₁₁×C₃₂	C₁₆	1	2	yes	—
20	C₅×C₁₁×C₃₂	C₄²	1	1	yes	characteristic
21	C₅×C₁₁×C₃₂	C₂×C₈	1	1	yes	characteristic
22	C₂×C₁₁×C₆₄	C₄×C₅	1	1	yes	characteristic
23	C₂×C₁₁×C₆₄	C₂²×C₅	1	1	yes	characteristic
24	C₄×C₁₁×C₃₂	C₄×C₅	1	1	yes	characteristic
25	C₁₁×C₁₂₈	C₄×C₅	1	4	yes	direct product factor
26	C₂×C₅×C₁₂₈	C₂×C₁₁	1	2	yes	—
27	C₄×C₅×C₆₄	C₂×C₁₁	1	1	yes	characteristic
28	C₂×C₅×C₈×C₁₁	C₃₂	1	1	yes	characteristic
29	C₂×C₅×C₈×C₁₁	C₂×C₁₆	1	1	yes	characteristic
30	C₄²×C₅×C₁₁	C₃₂	1	1	yes	characteristic
31	C₅×C₁₁×C₁₆	C₃₂	1	2	yes	—
32	C₅×C₁₁×C₁₆	C₄×C₈	1	1	yes	characteristic
33	C₅×C₁₁×C₁₆	C₂×C₁₆	1	1	yes	characteristic
34	C₂×C₁₁×C₃₂	C₅×C₈	1	1	yes	characteristic
35	C₂×C₁₁×C₃₂	C₂×C₄×C₅	1	1	yes	characteristic
36	C₄×C₁₁×C₁₆	C₅×C₈	1	1	yes	characteristic
37	C₁₁×C₆₄	C₅×C₈	1	2	yes	—
38	C₁₁×C₆₄	C₂×C₄×C₅	1	2	yes	—
39	C₂×C₅×C₆₄	C₄×C₁₁	1	1	yes	characteristic
40	C₂×C₅×C₆₄	C₂²×C₁₁	1	1	yes	characteristic
41	C₄×C₅×C₃₂	C₄×C₁₁	1	1	yes	characteristic
42	C₅×C₁₂₈	C₄×C₁₁	1	4	yes	direct product factor
43	C₄×C₁₂₈	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×C₄×C₅×C₁₁	C₆₄	1	2	yes	—
45	C₂×C₄×C₅×C₁₁	C₂×C₃₂	1	1	yes	characteristic
46	C₅×C₈×C₁₁	C₆₄	1	2	yes	—
47	C₅×C₈×C₁₁	C₄×C₁₆	1	1	yes	characteristic
48	C₅×C₈×C₁₁	C₂×C₃₂	1	1	yes	characteristic
49	C₂×C₁₁×C₁₆	C₅×C₁₆	1	1	yes	characteristic
50	C₂×C₁₁×C₁₆	C₂×C₅×C₈	1	1	yes	characteristic
51	C₄×C₈×C₁₁	C₅×C₁₆	1	1	yes	characteristic
52	C₁₁×C₃₂	C₅×C₁₆	1	2	yes	—
53	C₁₁×C₃₂	C₄²×C₅	1	1	yes	characteristic
54	C₁₁×C₃₂	C₂×C₅×C₈	1	1	yes	characteristic
55	C₂×C₅×C₃₂	C₈×C₁₁	1	1	yes	characteristic
56	C₂×C₅×C₃₂	C₂×C₄×C₁₁	1	1	yes	characteristic
57	C₄×C₅×C₁₆	C₈×C₁₁	1	1	yes	characteristic
58	C₅×C₆₄	C₈×C₁₁	1	2	yes	—
59	C₅×C₆₄	C₂×C₄×C₁₁	1	2	yes	—
60	C₂×C₁₂₈	C₂×C₅×C₁₁	1	2	yes	—
61	C₄×C₆₄	C₂×C₅×C₁₁	1	1	yes	characteristic
62	C₂²×C₅×C₁₁	C₂×C₆₄	1	1	yes	characteristic
63	C₄×C₅×C₁₁	C₁₂₈	1	4	yes	direct product factor
64	C₄×C₅×C₁₁	C₄×C₃₂	1	1	yes	characteristic
65	C₄×C₅×C₁₁	C₂×C₆₄	1	1	yes	characteristic
66	C₂×C₈×C₁₁	C₅×C₃₂	1	1	yes	characteristic
67	C₂×C₈×C₁₁	C₂×C₅×C₁₆	1	1	yes	characteristic
68	C₄²×C₁₁	C₅×C₃₂	1	1	yes	characteristic
69	C₁₁×C₁₆	C₅×C₃₂	1	2	yes	—
70	C₁₁×C₁₆	C₄×C₅×C₈	1	1	yes	characteristic
71	C₁₁×C₁₆	C₂×C₅×C₁₆	1	1	yes	characteristic
72	C₂×C₅×C₁₆	C₁₁×C₁₆	1	1	yes	characteristic
73	C₂×C₅×C₁₆	C₂×C₈×C₁₁	1	1	yes	characteristic
74	C₄×C₅×C₈	C₁₁×C₁₆	1	1	yes	characteristic
75	C₅×C₃₂	C₁₁×C₁₆	1	2	yes	—
76	C₅×C₃₂	C₄²×C₁₁	1	1	yes	characteristic
77	C₅×C₃₂	C₂×C₈×C₁₁	1	1	yes	characteristic
78	C₂×C₆₄	C₄×C₅×C₁₁	1	1	yes	characteristic
79	C₂×C₆₄	C₂²×C₅×C₁₁	1	1	yes	characteristic
80	C₄×C₃₂	C₄×C₅×C₁₁	1	1	yes	characteristic
81	C₁₂₈	C₄×C₅×C₁₁	1	4	yes	direct product factor
82	C₂×C₅×C₁₁	C₄×C₆₄	1	1	yes	characteristic
83	C₂×C₅×C₁₁	C₂×C₁₂₈	1	2	yes	—
84	C₂×C₄×C₁₁	C₅×C₆₄	1	2	yes	—
85	C₂×C₄×C₁₁	C₂×C₅×C₃₂	1	1	yes	characteristic
86	C₈×C₁₁	C₅×C₆₄	1	2	yes	—
87	C₈×C₁₁	C₄×C₅×C₁₆	1	1	yes	characteristic
88	C₈×C₁₁	C₂×C₅×C₃₂	1	1	yes	characteristic
89	C₂×C₅×C₈	C₁₁×C₃₂	1	1	yes	characteristic
90	C₂×C₅×C₈	C₂×C₁₁×C₁₆	1	1	yes	characteristic
91	C₄²×C₅	C₁₁×C₃₂	1	1	yes	characteristic
92	C₅×C₁₆	C₁₁×C₃₂	1	2	yes	—
93	C₅×C₁₆	C₄×C₈×C₁₁	1	1	yes	characteristic
94	C₅×C₁₆	C₂×C₁₁×C₁₆	1	1	yes	characteristic
95	C₂×C₃₂	C₅×C₈×C₁₁	1	1	yes	characteristic
96	C₂×C₃₂	C₂×C₄×C₅×C₁₁	1	1	yes	characteristic
97	C₄×C₁₆	C₅×C₈×C₁₁	1	1	yes	characteristic
98	C₆₄	C₅×C₈×C₁₁	1	2	yes	—
99	C₆₄	C₂×C₄×C₅×C₁₁	1	2	yes	—
100	C₅×C₁₁	C₄×C₁₂₈	1	1	yes	characteristic, direct product factor, Hall
101	C₂²×C₁₁	C₂×C₅×C₆₄	1	1	yes	characteristic
102	C₄×C₁₁	C₅×C₁₂₈	1	4	yes	direct product factor
103	C₄×C₁₁	C₄×C₅×C₃₂	1	1	yes	characteristic
104	C₄×C₁₁	C₂×C₅×C₆₄	1	1	yes	characteristic
105	C₂×C₄×C₅	C₁₁×C₆₄	1	2	yes	—
106	C₂×C₄×C₅	C₂×C₁₁×C₃₂	1	1	yes	characteristic
107	C₅×C₈	C₁₁×C₆₄	1	2	yes	—
108	C₅×C₈	C₄×C₁₁×C₁₆	1	1	yes	characteristic
109	C₅×C₈	C₂×C₁₁×C₃₂	1	1	yes	characteristic
110	C₂×C₁₆	C₅×C₁₁×C₁₆	1	1	yes	characteristic
111	C₂×C₁₆	C₂×C₅×C₈×C₁₁	1	1	yes	characteristic
112	C₄×C₈	C₅×C₁₁×C₁₆	1	1	yes	characteristic
113	C₃₂	C₅×C₁₁×C₁₆	1	2	yes	—
114	C₃₂	C₄²×C₅×C₁₁	1	1	yes	characteristic
115	C₃₂	C₂×C₅×C₈×C₁₁	1	1	yes	characteristic
116	C₂×C₁₁	C₄×C₅×C₆₄	1	1	yes	characteristic
117	C₂×C₁₁	C₂×C₅×C₁₂₈	1	2	yes	—
118	C₂²×C₅	C₂×C₁₁×C₆₄	1	1	yes	characteristic
119	C₄×C₅	C₁₁×C₁₂₈	1	4	yes	direct product factor
120	C₄×C₅	C₄×C₁₁×C₃₂	1	1	yes	characteristic
121	C₄×C₅	C₂×C₁₁×C₆₄	1	1	yes	characteristic
122	C₂×C₈	C₅×C₁₁×C₃₂	1	1	yes	characteristic
123	C₂×C₈	C₂×C₅×C₁₁×C₁₆	1	1	yes	characteristic
124	C₄²	C₅×C₁₁×C₃₂	1	1	yes	characteristic
125	C₁₆	C₅×C₁₁×C₃₂	1	2	yes	—
126	C₁₆	C₄×C₅×C₈×C₁₁	1	1	yes	characteristic
127	C₁₆	C₂×C₅×C₁₁×C₁₆	1	1	yes	characteristic
128	C₁₁	C₄×C₅×C₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
129	C₂×C₅	C₄×C₁₁×C₆₄	1	1	yes	characteristic
130	C₂×C₅	C₂×C₁₁×C₁₂₈	1	2	yes	—
131	C₂×C₄	C₅×C₁₁×C₆₄	1	2	yes	—
132	C₂×C₄	C₂×C₅×C₁₁×C₃₂	1	1	yes	characteristic
133	C₈	C₅×C₁₁×C₆₄	1	2	yes	—
134	C₈	C₂×C₅×C₁₁×C₃₂	1	1	yes	characteristic
135	C₈	C₄×C₅×C₁₁×C₁₆	1	1	yes	characteristic
136	C₅	C₄×C₁₁×C₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
137	C₂²	C₂×C₅×C₁₁×C₆₄	1	1	yes	characteristic
138	C₄	C₅×C₁₁×C₁₂₈	1	4	yes	direct product factor
139	C₄	C₂×C₅×C₁₁×C₆₄	1	1	yes	characteristic
140	C₄	C₄×C₅×C₁₁×C₃₂	1	1	yes	characteristic
141	C₂	C₂×C₅×C₁₁×C₁₂₈	1	2	yes	—
142	C₂	C₄×C₅×C₁₁×C₆₄	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₆₄	C₂²×C₅×C₁₁
socle, prime radical	C₂²×C₅×C₁₁	C₂×C₆₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₅×C₁₁×C₁₂₈	C₄	direct (N × H)
7. C₄×C₁₁×C₁₂₈	C₅	direct (N × H)
13. C₄×C₅×C₁₂₈	C₁₁	direct (N × H)
25. C₁₁×C₁₂₈	C₄×C₅	direct (N × H)
42. C₅×C₁₂₈	C₄×C₁₁	direct (N × H)
43. C₄×C₁₂₈	C₅×C₁₁	direct (N × H)
63. C₄×C₅×C₁₁	C₁₂₈	direct (N × H)
81. C₁₂₈	C₄×C₅×C₁₁	direct (N × H)
100. C₅×C₁₁	C₄×C₁₂₈	direct (N × H)
102. C₄×C₁₁	C₅×C₁₂₈	direct (N × H)
119. C₄×C₅	C₁₁×C₁₂₈	direct (N × H)
128. C₁₁	C₄×C₅×C₁₂₈	direct (N × H)
136. C₅	C₄×C₁₁×C₁₂₈	direct (N × H)
138. C₄	C₅×C₁₁×C₁₂₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×C₁₁×C₆₄	2
C₂×C₅×C₁₁×C₁₂₈	2
C₄×C₁₁×C₁₂₈	5
C₄×C₅×C₁₂₈	11

Subgroups — C4×C5×C11×C128 #72205136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×C₁₁×C₁₂₈ #72205136