Subgroups — C₄×C₅×#812 #14312584

Order 1920.

392 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#812	C₂	1	2	yes	maximal
3	C₅×#4461	C₂	1	2	yes	maximal, complemented
4	C₄×C₅×C₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
5	C₄×C₅×M₃₂	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₅×C₈	C₄	1	1	yes	characteristic
7	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄²×C₅	C₄	1	1	yes	characteristic
9	C₃×C₄×C₅×C₈	C₄	1	1	yes	characteristic
10	C₃×C₄×C₅×C₈	C₄	1	1	yes	characteristic
11	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₅×#812	C₄	1	8	yes	direct product factor
14	C₂×C₅×C₃⋊C₁₆	C₂²	1	4	yes	—
15	C₄×#812	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₅×M₃₂	—	3	2	no	—
17	C₂×C₄×C₅×C₈	D₃	1	1	yes	characteristic
18	C₅×#346	—	3	2	no	—
19	C₄×C₅×C₁₆	—	3	2	no	—
20	C₂²×C₃×C₄×C₅	C₈	1	2	yes	—
21	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
22	C₂×C₃×C₅×C₈	C₈	1	4	yes	—
23	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
24	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	—
25	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
26	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
27	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
28	C₃×C₄²×C₅	C₈	1	2	yes	—
29	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
30	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
31	C₅×C₃⋊C₁₆	C₂×C₄	1	8	yes	complemented
32	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic
33	C₂×#812	C₂×C₅	1	2	yes	—
34	#4461	C₂×C₅	1	2	yes	complemented
35	C₄×C₃⋊C₁₆	C₂×C₅	1	2	yes	complemented
36	C₂²×C₅×C₈	Dic₃	1	1	yes	characteristic
37	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
38	C₂×C₄²×C₅	Dic₃	1	1	yes	characteristic
39	C₅×M₃₂	—	3	8	no	—
40	C₂×C₅×C₁₆	—	3	4	no	—
41	C₄×C₅×C₈	Dic₃	1	1	yes	characteristic
42	C₄×C₅×C₈	Dic₃	1	1	yes	characteristic
43	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
44	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
45	C₄×M₃₂	—	3	1	no	Sylow
46	C₂³×C₃×C₅	C₂×C₈	1	1	yes	characteristic
47	C₂×C₃×C₄×C₅	—	2	4	no	—
48	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
49	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
50	C₂×C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
51	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
52	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
53	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
54	C₃×C₅×C₈	C₄²	1	2	yes	—
55	C₃×C₅×C₈	C₂×C₈	1	2	yes	—
56	C₃×C₅×C₈	C₂×C₈	1	2	yes	—
57	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
58	C₂²×C₃×C₈	C₄×C₅	1	1	yes	characteristic
59	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
60	C₂×C₃×C₄²	C₄×C₅	1	1	yes	characteristic
61	C₃×C₄×C₈	C₄×C₅	1	1	yes	characteristic
62	C₃×C₄×C₈	C₄×C₅	1	1	yes	characteristic
63	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
64	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
65	#812	C₄×C₅	1	8	yes	direct product factor
66	C₂×C₃⋊C₁₆	C₂²×C₅	1	4	yes	—
67	C₂²×C₄×C₅	C₃⋊C₈	1	2	yes	—
68	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
69	C₂×C₅×C₈	C₃⋊C₈	1	4	yes	—
70	C₂×C₅×C₈	C₄×D₃	1	4	yes	—
71	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
72	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
73	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
74	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
75	C₄²×C₅	C₃⋊C₈	1	2	yes	—
76	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
77	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
78	C₅×C₁₆	—	3	8	no	—
79	C₂×M₃₂	—	3	2	no	—
80	C₂×C₄×C₈	C₅×D₃	1	1	yes	characteristic
81	#346	—	3	2	no	—
82	C₄×C₁₆	—	3	2	no	—
83	C₂²×C₃×C₅	—	2	2	no	—
84	C₂²×C₃×C₅	C₄×C₈	1	2	yes	—
85	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
86	C₃×C₄×C₅	—	2	2	no	—
87	C₃×C₄×C₅	C₄×C₈	1	2	yes	—
88	C₃×C₄×C₅	M₃₂	1	4	yes	complemented
89	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
90	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
91	C₂²×C₃×C₄	C₅×C₈	1	2	yes	—
92	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
93	C₂×C₃×C₈	C₅×C₈	1	4	yes	—
94	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	—
95	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
96	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
97	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
98	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
99	C₃×C₄²	C₅×C₈	1	2	yes	—
100	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
101	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
102	C₃⋊C₁₆	C₂×C₄×C₅	1	8	yes	complemented
103	C₂³×C₅	C₂×C₃⋊C₈	1	1	yes	characteristic
104	C₂×C₄×C₅	—	2	4	no	—
105	C₂×C₄×C₅	C₂×C₃⋊C₈	1	2	yes	—
106	C₂×C₄×C₅	C₂×C₃⋊C₈	1	1	yes	characteristic
107	C₂×C₄×C₅	C₂×C₃⋊C₈	1	2	yes	—
108	C₂×C₄×C₅	C₂×C₃⋊C₈	1	2	yes	—
109	C₂×C₄×C₅	C₄×Dic₃	1	2	yes	—
110	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
111	C₅×C₈	C₂×C₃⋊C₈	1	2	yes	—
112	C₅×C₈	C₂×C₃⋊C₈	1	2	yes	—
113	C₅×C₈	C₄×Dic₃	1	2	yes	—
114	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
115	C₂²×C₈	C₅×Dic₃	1	1	yes	characteristic
116	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
117	C₂×C₄²	C₅×Dic₃	1	1	yes	characteristic
118	M₃₂	—	3	8	no	—
119	C₂×C₁₆	—	3	4	no	—
120	C₄×C₈	C₅×Dic₃	1	1	yes	characteristic
121	C₄×C₈	C₅×Dic₃	1	1	yes	characteristic
122	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
123	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
124	C₂×C₃×C₅	—	2	2	no	—
125	C₂×C₃×C₅	C₂×C₄×C₈	1	1	yes	characteristic
126	C₂×C₃×C₅	C₂×M₃₂	1	2	yes	—
127	C₂³×C₃	C₂×C₅×C₈	1	1	yes	characteristic
128	C₂×C₃×C₄	—	2	4	no	—
129	C₂×C₃×C₄	C₄²×C₅	1	2	yes	—
130	C₂×C₃×C₄	C₂×C₅×C₈	1	2	yes	—
131	C₂×C₃×C₄	C₂×C₅×C₈	1	2	yes	—
132	C₂×C₃×C₄	C₂×C₅×C₈	1	1	yes	characteristic
133	C₂×C₃×C₄	C₂×C₅×C₈	1	2	yes	—
134	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
135	C₃×C₈	C₄²×C₅	1	2	yes	—
136	C₃×C₈	C₂×C₅×C₈	1	2	yes	—
137	C₃×C₈	C₂×C₅×C₈	1	2	yes	—
138	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
139	C₂²×C₅	—	2	2	no	—
140	C₂²×C₅	C₄×C₃⋊C₈	1	2	yes	—
141	C₂²×C₅	C₂²×C₃⋊C₈	1	1	yes	characteristic
142	C₄×C₅	—	2	2	no	—
143	C₄×C₅	C₄×C₃⋊C₈	1	2	yes	—
144	C₄×C₅	#812	1	4	yes	direct product factor
145	C₄×C₅	C₂²×C₃⋊C₈	1	1	yes	characteristic
146	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
147	C₂²×C₄	C₅×C₃⋊C₈	1	2	yes	—
148	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
149	C₂×C₈	C₅×C₃⋊C₈	1	4	yes	—
150	C₂×C₈	C₄×C₅×D₃	1	4	yes	—
151	C₂×C₈	C₂×C₅×Dic₃	1	1	yes	characteristic
152	C₂×C₈	C₂×C₅×Dic₃	1	1	yes	characteristic
153	C₂×C₈	C₂×C₅×Dic₃	1	1	yes	characteristic
154	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
155	C₄²	C₅×C₃⋊C₈	1	2	yes	—
156	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
157	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
158	C₁₆	—	3	8	no	—
159	C₃×C₅	C₄×M₃₂	1	1	yes	characteristic, complemented, Hall
160	C₂²×C₃	—	2	2	no	—
161	C₂²×C₃	C₄×C₅×C₈	1	2	yes	—
162	C₂²×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
163	C₃×C₄	—	2	2	no	—
164	C₃×C₄	C₄×C₅×C₈	1	2	yes	—
165	C₃×C₄	C₅×M₃₂	1	4	yes	complemented
166	C₃×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
167	C₃×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
168	C₂×C₅	—	2	2	no	—
169	C₂×C₅	C₂×C₄×C₃⋊C₈	1	1	yes	characteristic
170	C₂×C₅	C₂×#812	1	2	yes	—
171	C₂³	C₂×C₅×C₃⋊C₈	1	1	yes	characteristic
172	C₂×C₄	—	2	4	no	—
173	C₂×C₄	C₂×C₅×C₃⋊C₈	1	2	yes	—
174	C₂×C₄	C₂×C₅×C₃⋊C₈	1	2	yes	—
175	C₂×C₄	C₂×C₅×C₃⋊C₈	1	1	yes	characteristic
176	C₂×C₄	C₂×C₅×C₃⋊C₈	1	2	yes	—
177	C₂×C₄	C₄×C₅×Dic₃	1	2	yes	—
178	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
179	C₈	C₂×C₅×C₃⋊C₈	1	2	yes	—
180	C₈	C₂×C₅×C₃⋊C₈	1	2	yes	—
181	C₈	C₄×C₅×Dic₃	1	2	yes	—
182	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
183	C₂×C₃	—	2	2	no	—
184	C₂×C₃	C₂×C₄×C₅×C₈	1	1	yes	characteristic
185	C₂×C₃	C₂×C₅×M₃₂	1	2	yes	—
186	C₅	C₄×#812	1	1	yes	characteristic, direct product factor, Sylow
187	C₂²	—	2	2	no	—
188	C₂²	C₄×C₅×C₃⋊C₈	1	2	yes	—
189	C₂²	C₂²×C₅×C₃⋊C₈	1	1	yes	characteristic
190	C₄	—	2	2	no	—
191	C₄	C₄×C₅×C₃⋊C₈	1	2	yes	—
192	C₄	C₅×#812	1	4	yes	direct product factor
193	C₄	C₂²×C₅×C₃⋊C₈	1	1	yes	characteristic
194	C₄	C₂×C₄×C₅×Dic₃	1	1	yes	characteristic
195	C₃	C₄×C₅×M₃₂	1	1	yes	characteristic, complemented, Sylow
196	C₂	—	2	2	no	—
197	C₂	C₂×C₄×C₅×C₃⋊C₈	1	1	yes	characteristic
198	C₂	C₂×C₅×#812	1	2	yes	—

	subgroup	G/H
center	C₄×C₅×C₈	C₂×D₃
commutator	C₂×C₃	C₂×C₄×C₅×C₈
Frattini	C₂×C₈	C₂²×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×C₈	C₂
socle	C₂²×C₃×C₅	C₂²×C₈
prime radical	C₂³×C₃×C₅	C₂×C₈
cosocle	C₂×C₃×C₈	C₂³×C₅
hypercenter	C₂×C₄×C₅×C₈	D₃
hypocenter	C₃	C₄×C₅×M₃₂
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅×C₈ ◁ C₂×C₄×C₅×C₈

Complements

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

N	H ≅ G/N	type
3. C₅×#4461	C₂	semidirect
4. C₄×C₅×C₃⋊C₁₆	C₂	semidirect
13. C₅×#812	C₄	direct (N × H)
15. C₄×#812	C₅	direct (N × H)
31. C₅×C₃⋊C₁₆	C₂×C₄	semidirect
34. #4461	C₂×C₅	semidirect
35. C₄×C₃⋊C₁₆	C₂×C₅	semidirect
65. #812	C₄×C₅	direct (N × H)
88. C₃×C₄×C₅	M₃₂	semidirect
102. C₃⋊C₁₆	C₂×C₄×C₅	semidirect
144. C₄×C₅	#812	direct (N × H)
159. C₃×C₅	C₄×M₃₂	semidirect
165. C₃×C₄	C₅×M₃₂	semidirect
186. C₅	C₄×#812	direct (N × H)
192. C₄	C₅×#812	direct (N × H)
195. C₃	C₄×C₅×M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₅×C₈	2
C₂×C₅×#812	2
C₅×#4461	2
C₄×C₅×C₃⋊C₁₆	2
C₄×C₅×M₃₂	3
C₄×#812	5

Subgroups — C4×C5×#812 #14312584

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#812 #14312584