Subgroups — C₅×#70446 #14299038

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₃⋊C₈	C₂	1	4	yes	maximal
3	C₅×#4932	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
5	C₅×#1843	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
7	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
9	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
10	C₃×C₅×C₄⋊C₈	—	2	2	no	—
11	C₅×C₃⋊#95	C₄	1	2	yes	—
12	C₅×C₃⋊#95	C₄	1	2	yes	—
13	C₅×Dic₃⋊C₈	—	2	8	no	—
14	C₅×C₄⋊(C₃⋊C₈)	—	2	2	no	—
15	#70446	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₅×C₄⋊C₈	—	3	4	no	—
17	C₂×C₅×C₄⋊C₈	—	3	1	no	—
18	C₂×C₅×C₄⋊C₈	D₃	1	1	yes	characteristic
19	C₅×#376	—	3	1	no	—
20	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
23	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
24	C₂×C₃×C₅×C₈	—	2	4	no	—
25	C₂×C₃×C₅×C₈	—	2	2	no	—
26	C₃×C₄²×C₅	D₄	1	2	yes	—
27	C₃×C₄²×C₅	Q₈	1	2	yes	—
28	C₄×C₅×Dic₃	D₄	1	4	yes	—
29	C₄×C₅×Dic₃	Q₈	1	4	yes	—
30	C₂×C₅×C₃⋊C₈	—	2	2	no	—
31	C₂×C₅×C₃⋊C₈	—	2	4	no	—
32	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
33	C₂×Dic₃⋊C₈	C₂×C₅	1	4	yes	—
34	#4932	C₂×C₅	1	1	yes	characteristic
35	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic
36	C₂²×C₅×C₈	—	3	2	no	—
37	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
38	C₂×C₄²×C₅	—	3	2	no	—
39	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
40	C₅×C₄⋊C₈	—	2	2	no	—
41	C₅×C₄⋊C₈	—	6	8	no	—
42	C₅×C₄⋊C₈	—	6	2	no	—
43	C₅×#95	—	3	2	no	—
44	C₅×#95	—	3	2	no	—
45	#1843	—	3	1	no	Sylow
46	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₃×C₄×C₅	—	2	2	no	—
48	C₂×C₃×C₄×C₅	—	2	2	no	—
49	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
50	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
51	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
52	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
53	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
54	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
55	C₂×C₅×Dic₃	—	2	4	no	—
56	C₂×C₅×Dic₃	—	2	4	no	—
57	C₂×C₅×Dic₃	C₄⋊C₄	1	8	yes	—
58	C₃×C₅×C₈	—	4	2	no	—
59	C₅×C₃⋊C₈	—	4	2	no	—
60	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
61	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
62	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
63	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
64	C₃×C₄⋊C₈	—	2	2	no	—
65	C₃⋊#95	C₄×C₅	1	2	yes	—
66	C₃⋊#95	C₄×C₅	1	2	yes	—
67	Dic₃⋊C₈	—	2	8	no	—
68	C₄⋊(C₃⋊C₈)	—	2	2	no	—
69	C₂²×C₄×C₅	—	3	4	no	—
70	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
71	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
72	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
73	C₂×C₅×C₈	—	2	4	no	—
74	C₂×C₅×C₈	—	2	2	no	—
75	C₂×C₅×C₈	—	6	4	no	—
76	C₂×C₅×C₈	—	6	2	no	—
77	C₄²×C₅	—	3	4	no	—
78	C₄²×C₅	—	3	4	no	—
79	C₄²×C₅	Dic₆	1	2	yes	—
80	C₄²×C₅	#67	1	2	yes	—
81	C₂×C₄⋊C₈	—	3	4	no	—
82	C₂×C₄⋊C₈	—	3	1	no	—
83	C₂×C₄⋊C₈	C₅×D₃	1	1	yes	characteristic
84	#376	—	3	1	no	—
85	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
86	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₃×C₅	#131	1	2	yes	—
88	C₂²×C₃×C₅	#131	1	2	yes	—
89	C₃×C₄×C₅	—	2	2	no	—
90	C₃×C₄×C₅	—	2	2	no	—
91	C₃×C₄×C₅	#127	1	1	yes	characteristic
92	C₃×C₄×C₅	C₄⋊Q₈	1	2	yes	—
93	C₃×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
94	C₅×Dic₃	—	2	8	no	—
95	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
96	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
97	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
98	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	—
99	C₂×C₃×C₈	—	2	4	no	—
100	C₂×C₃×C₈	—	2	2	no	—
101	C₃×C₄²	C₅×D₄	1	2	yes	—
102	C₃×C₄²	C₅×Q₈	1	2	yes	—
103	C₄×Dic₃	C₅×D₄	1	4	yes	—
104	C₄×Dic₃	C₅×Q₈	1	4	yes	—
105	C₂×C₃⋊C₈	—	2	2	no	—
106	C₂×C₃⋊C₈	—	2	4	no	—
107	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
108	C₂×C₄×C₅	—	2	2	no	—
109	C₂×C₄×C₅	—	2	2	no	—
110	C₂×C₄×C₅	—	3	8	no	—
111	C₂×C₄×C₅	—	6	4	no	—
112	C₂×C₄×C₅	—	6	4	no	—
113	C₂×C₄×C₅	Dic₃⋊C₄	1	2	yes	—
114	C₂×C₄×C₅	Dic₃⋊C₄	1	2	yes	—
115	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
116	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
117	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
118	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
119	C₅×C₈	—	4	2	no	—
120	C₅×C₈	—	12	2	no	—
121	C₂²×C₈	—	3	2	no	—
122	C₂²×C₈	C₂×C₅×D₃	1	2	yes	—
123	C₂×C₄²	—	3	2	no	—
124	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
125	C₄⋊C₈	—	2	2	no	—
126	C₄⋊C₈	—	6	8	no	—
127	C₄⋊C₈	—	6	2	no	—
128	#95	—	3	2	no	—
129	#95	—	3	2	no	—
130	C₂×C₃×C₅	#384	1	1	yes	characteristic
131	C₂×C₃×C₅	#424	1	4	yes	—
132	C₂×C₃×C₅	#424	1	1	yes	characteristic
133	C₂×C₃×C₅	#424	1	1	yes	characteristic
134	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
135	C₂×C₃×C₄	—	2	2	no	—
136	C₂×C₃×C₄	—	2	2	no	—
137	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
138	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
139	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
140	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
141	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
142	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
143	C₂×Dic₃	—	2	4	no	—
144	C₂×Dic₃	—	2	4	no	—
145	C₂×Dic₃	C₅×C₄⋊C₄	1	8	yes	—
146	C₃×C₈	—	4	2	no	—
147	C₃⋊C₈	—	4	2	no	—
148	C₂²×C₅	D₃×C₄⋊C₄	1	2	yes	—
149	C₂²×C₅	#901	1	2	yes	—
150	C₂²×C₅	#907	1	2	yes	—
151	C₂²×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
152	C₄×C₅	—	2	2	no	—
153	C₄×C₅	—	2	2	no	—
154	C₄×C₅	—	6	8	no	—
155	C₄×C₅	#888	1	2	yes	—
156	C₄×C₅	#940	1	1	yes	characteristic
157	C₄×C₅	#944	1	1	yes	characteristic
158	C₂²×C₄	—	3	4	no	—
159	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
160	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
161	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
162	C₂×C₈	—	2	4	no	—
163	C₂×C₈	—	2	2	no	—
164	C₂×C₈	—	6	4	no	—
165	C₂×C₈	—	6	2	no	—
166	C₄²	—	3	4	no	—
167	C₄²	—	3	4	no	—
168	C₄²	C₅×Dic₆	1	2	yes	—
169	C₄²	C₅×#67	1	2	yes	—
170	C₃×C₅	#1843	1	1	yes	characteristic, complemented, Hall
171	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
172	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×C₃	C₅×#131	1	2	yes	—
174	C₂²×C₃	C₅×#131	1	2	yes	—
175	C₃×C₄	—	2	2	no	—
176	C₃×C₄	—	2	2	no	—
177	C₃×C₄	C₅×#127	1	1	yes	characteristic
178	C₃×C₄	C₅×C₄⋊Q₈	1	2	yes	—
179	C₃×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
180	Dic₃	—	2	8	no	—
181	C₂×C₅	#4839	1	4	yes	—
182	C₂×C₅	#4975	1	1	yes	characteristic
183	C₂×C₅	#5102	1	1	yes	characteristic
184	C₂×C₅	#5119	1	1	yes	characteristic
185	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	3	8	no	—
189	C₂×C₄	—	6	4	no	—
190	C₂×C₄	—	6	4	no	—
191	C₂×C₄	C₅×Dic₃⋊C₄	1	2	yes	—
192	C₂×C₄	C₅×Dic₃⋊C₄	1	2	yes	—
193	C₂×C₄	C₂×C₅×Dic₆	1	1	yes	characteristic
194	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
195	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
196	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
197	C₈	—	4	2	no	—
198	C₈	—	12	2	no	—
199	C₂×C₃	C₅×#384	1	1	yes	characteristic
200	C₂×C₃	C₅×#424	1	4	yes	—
201	C₂×C₃	C₅×#424	1	1	yes	characteristic
202	C₂×C₃	C₅×#424	1	1	yes	characteristic
203	C₅	#70446	1	1	yes	characteristic, direct product factor, Sylow
204	C₂²	C₅×D₃×C₄⋊C₄	1	2	yes	—
205	C₂²	C₅×#901	1	2	yes	—
206	C₂²	C₅×#907	1	2	yes	—
207	C₂²	C₂×C₅×Dic₃⋊C₄	1	1	yes	characteristic
208	C₄	—	2	2	no	—
209	C₄	—	2	2	no	—
210	C₄	—	6	8	no	—
211	C₄	C₅×#888	1	2	yes	—
212	C₄	C₅×#940	1	1	yes	characteristic
213	C₄	C₅×#944	1	1	yes	characteristic
214	C₃	C₅×#1843	1	1	yes	characteristic, complemented, Sylow
215	C₂	C₅×#4839	1	4	yes	—
216	C₂	C₅×#4975	1	1	yes	characteristic
217	C₂	C₅×#5102	1	1	yes	characteristic
218	C₂	C₅×#5119	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×C₄⋊C₈	D₃
hypocenter	C₃	C₅×#1843
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
15. #70446	C₅	direct (N × H)
170. C₃×C₅	#1843	semidirect
203. C₅	#70446	direct (N × H)
214. C₃	C₅×#1843	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₅×Dic₃⋊C₈	2
C₅×#4932	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₅×#1843	3
#70446	5

Subgroups — C5×#70446 #14299038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70446 #14299038