Subgroups — C₅×C₈×#106 #11931000

Order 1280.

446 conjugacy classes of subgroups.

The subgroup lattice has 202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#106	C₂	1	1	yes	maximal, characteristic
2	C₅×C₈×C₄⋊C₄	C₂	1	2	yes	maximal
3	C₂×C₅×#334	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₈²	C₂	1	1	yes	maximal, characteristic
5	C₅×#1279	C₂	1	2	yes	maximal
6	C₂×C₅×#106	C₄	1	2	yes	—
7	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
8	C₂×C₄×C₅×C₈	—	2	2	no	—
9	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₅×#340	C₄	1	2	yes	—
14	C₅×#336	—	2	2	no	—
15	C₅×#334	C₄	1	4	yes	complemented
16	C₅×C₈²	C₄	1	4	yes	complemented
17	C₈×#106	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂²×C₅×C₈	—	2	1	no	—
19	C₂²×C₅×C₈	—	2	2	no	—
20	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
23	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
24	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
25	C₂×C₄²×C₅	—	2	2	no	—
26	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
27	C₅×#106	C₈	1	8	yes	direct product factor
28	C₅×C₄⋊C₈	—	2	2	no	—
29	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
30	C₄×C₅×C₈	—	2	1	no	—
31	C₄×C₅×C₈	—	4	4	no	—
32	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
33	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
34	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
35	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
36	C₄×C₅×C₈	Q₈	1	2	yes	—
37	C₅×#95	—	2	2	no	—
38	C₄×#106	C₂×C₅	1	1	yes	characteristic
39	C₈×C₄⋊C₄	C₂×C₅	1	2	yes	—
40	C₂×#334	C₂×C₅	1	1	yes	characteristic
41	C₂×C₈²	C₂×C₅	1	1	yes	characteristic
42	#1279	C₂×C₅	1	2	yes	—
43	C₂²×C₄×C₅	—	2	4	no	—
44	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
45	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₅	#41	1	1	yes	characteristic
47	C₂×C₅×C₈	—	2	4	no	—
48	C₂×C₅×C₈	—	2	2	no	—
49	C₂×C₅×C₈	—	2	2	no	—
50	C₂×C₅×C₈	—	2	2	no	—
51	C₂×C₅×C₈	—	2	4	no	—
52	C₂×C₅×C₈	—	4	2	no	—
53	C₂×C₅×C₈	—	4	2	no	—
54	C₂×C₅×C₈	C₄²	1	2	yes	—
55	C₂×C₅×C₈	C₄²	1	2	yes	—
56	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
57	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
58	C₂×C₅×C₈	C₂×C₈	1	4	yes	—
59	C₂×C₅×C₈	SD₁₆	1	4	yes	—
60	C₅×C₄⋊C₄	—	2	4	no	—
61	C₅×C₄⋊C₄	C₂×C₈	1	8	yes	—
62	C₄²×C₅	—	4	2	no	—
63	C₄²×C₅	—	4	2	no	—
64	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
65	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
66	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
67	C₄²×C₅	#41	1	1	yes	characteristic
68	C₂×#106	C₄×C₅	1	2	yes	—
69	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
70	C₂×C₄×C₈	—	2	2	no	—
71	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
72	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
73	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
74	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
75	#340	C₄×C₅	1	2	yes	—
76	#336	—	2	2	no	—
77	#334	C₄×C₅	1	4	yes	complemented
78	C₈²	C₄×C₅	1	4	yes	complemented
79	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
80	C₂×C₄×C₅	—	2	2	no	—
81	C₂×C₄×C₅	—	2	8	no	—
82	C₂×C₄×C₅	—	4	4	no	—
83	C₂×C₄×C₅	—	4	4	no	—
84	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
85	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₅	#117	1	1	yes	characteristic
87	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
88	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
89	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
90	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
91	C₂×C₄×C₅	#131	1	2	yes	—
92	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
93	C₂×C₄×C₅	#135	1	2	yes	—
94	C₅×C₈	—	2	4	no	—
95	C₅×C₈	—	2	2	no	—
96	C₅×C₈	—	2	2	no	—
97	C₅×C₈	—	4	4	no	—
98	C₅×C₈	C₄×C₈	1	4	yes	complemented
99	C₅×C₈	#106	1	4	yes	direct product factor
100	C₂²×C₈	—	2	1	no	—
101	C₂²×C₈	—	2	2	no	—
102	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
103	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
104	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
105	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
106	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
107	C₂×C₄²	—	2	2	no	—
108	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
109	#106	C₅×C₈	1	8	yes	direct product factor
110	C₄⋊C₈	—	2	2	no	—
111	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
112	C₄×C₈	—	2	1	no	—
113	C₄×C₈	—	4	4	no	—
114	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
115	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
116	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
117	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
118	C₄×C₈	C₅×Q₈	1	2	yes	—
119	#95	—	2	2	no	—
120	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
121	C₂²×C₅	C₈×D₄	1	2	yes	—
122	C₂²×C₅	C₄×SD₁₆	1	2	yes	—
123	C₂²×C₅	#443	1	2	yes	—
124	C₄×C₅	—	2	1	no	—
125	C₄×C₅	—	2	1	no	—
126	C₄×C₅	—	4	8	no	—
127	C₄×C₅	C₂×C₄×C₈	1	1	yes	characteristic
128	C₄×C₅	#405	1	1	yes	characteristic
129	C₄×C₅	C₂×#106	1	1	yes	characteristic
130	C₄×C₅	#427	1	1	yes	characteristic
131	C₄×C₅	C₄×SD₁₆	1	2	yes	—
132	C₄×C₅	C₈×Q₈	1	2	yes	—
133	C₂²×C₄	—	2	4	no	—
134	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
135	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
136	C₂²×C₄	C₅×#41	1	1	yes	characteristic
137	C₂×C₈	—	2	4	no	—
138	C₂×C₈	—	2	2	no	—
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	—	2	2	no	—
141	C₂×C₈	—	2	4	no	—
142	C₂×C₈	—	4	2	no	—
143	C₂×C₈	—	4	2	no	—
144	C₂×C₈	C₄²×C₅	1	2	yes	—
145	C₂×C₈	C₄²×C₅	1	2	yes	—
146	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
147	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
148	C₂×C₈	C₂×C₅×C₈	1	4	yes	—
149	C₂×C₈	C₅×SD₁₆	1	4	yes	—
150	C₄⋊C₄	—	2	4	no	—
151	C₄⋊C₄	C₂×C₅×C₈	1	8	yes	—
152	C₄²	—	4	2	no	—
153	C₄²	—	4	2	no	—
154	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
155	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
156	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
157	C₄²	C₅×#41	1	1	yes	characteristic
158	C₂×C₅	C₈×SD₁₆	1	4	yes	—
159	C₂×C₅	C₈×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₅	#1772	1	1	yes	characteristic
161	C₂×C₅	C₄×#106	1	1	yes	characteristic
162	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	8	no	—
165	C₂×C₄	—	4	4	no	—
166	C₂×C₄	—	4	4	no	—
167	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
168	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄	C₅×#117	1	1	yes	characteristic
170	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
171	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
172	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
173	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
174	C₂×C₄	C₅×#131	1	2	yes	—
175	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
176	C₂×C₄	C₅×#135	1	2	yes	—
177	C₈	—	2	4	no	—
178	C₈	—	2	2	no	—
179	C₈	—	2	2	no	—
180	C₈	—	4	4	no	—
181	C₈	C₄×C₅×C₈	1	4	yes	complemented
182	C₈	C₅×#106	1	4	yes	direct product factor
183	C₅	C₈×#106	1	1	yes	characteristic, direct product factor, Sylow
184	C₂²	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
185	C₂²	C₅×C₈×D₄	1	2	yes	—
186	C₂²	C₄×C₅×SD₁₆	1	2	yes	—
187	C₂²	C₅×#443	1	2	yes	—
188	C₄	—	2	1	no	—
189	C₄	—	2	1	no	—
190	C₄	—	4	8	no	—
191	C₄	C₂×C₄×C₅×C₈	1	1	yes	characteristic
192	C₄	C₅×#405	1	1	yes	characteristic
193	C₄	C₂×C₅×#106	1	1	yes	characteristic
194	C₄	C₅×#427	1	1	yes	characteristic
195	C₄	C₄×C₅×SD₁₆	1	2	yes	—
196	C₄	C₅×C₈×Q₈	1	2	yes	—
197	C₂	C₅×C₈×SD₁₆	1	4	yes	—
198	C₂	C₅×C₈×C₄⋊C₄	1	1	yes	characteristic
199	C₂	C₅×#1772	1	1	yes	characteristic
200	C₂	C₄×C₅×#106	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅×C₈	D₄
commutator	C₄	C₂×C₄×C₅×C₈
Frattini, cosocle	C₂×C₄²	C₂³×C₅
socle, prime radical	C₂³×C₅	C₄×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅×C₈ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₅×#334	C₄	semidirect
16. C₅×C₈²	C₄	semidirect
17. C₈×#106	C₅	direct (N × H)
27. C₅×#106	C₈	direct (N × H)
77. #334	C₄×C₅	semidirect
78. C₈²	C₄×C₅	semidirect
98. C₅×C₈	C₄×C₈	semidirect
99. C₅×C₈	#106	direct (N × H)
109. #106	C₅×C₈	direct (N × H)
181. C₈	C₄×C₅×C₈	semidirect
182. C₈	C₅×#106	direct (N × H)
183. C₅	C₈×#106	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×#106	2
C₅×C₈×C₄⋊C₄	2
C₂×C₅×#334	2
C₂×C₅×C₈²	2
C₅×#1279	2
C₈×#106	5

Subgroups — C5×C8×#106 #11931000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₈×#106 #11931000