Subgroups — C₃×#10600587 #14305227

Order 1920.

416 conjugacy classes of subgroups.

The subgroup lattice has 248 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×C₃×#3951	C₂	1	1	yes	maximal, characteristic
3	C₃×#65395	C₂	1	1	yes	maximal, characteristic
4	C₃×#65391	C₂	1	2	yes	maximal
5	C₃×#64743	C₂	1	2	yes	maximal
6	#10600587	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₃×#4072	C₂²	1	2	yes	—
11	C₂×C₃×#681	C₂²	1	2	yes	—
12	C₃×C₄×C₅×C₈	—	2	2	no	—
13	C₃×#3951	—	2	2	no	—
14	C₃×#3950	C₄	1	2	yes	complemented
15	C₃×#3949	C₄	1	2	yes	complemented
16	C₃×#3946	—	2	4	no	—
17	C₃×#1945	—	5	1	no	maximal, Hall
18	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic
19	C₂×#3951	C₂×C₃	1	1	yes	characteristic
20	#65395	C₂×C₃	1	1	yes	characteristic
21	#65391	C₂×C₃	1	2	yes	—
22	#64743	C₂×C₃	1	2	yes	—
23	C₂²×C₃×C₄×C₅	—	2	1	no	—
24	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
25	C₂×C₃×C₅×C₈	—	2	1	no	—
26	C₂×C₃×C₅×C₈	—	2	1	no	—
27	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
28	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
29	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
30	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
31	C₂×C₃×C₅×C₈	Q₈	1	2	yes	—
32	C₃×C₄²×C₅	—	2	1	no	—
33	C₃×C₄²×C₅	Q₈	1	2	yes	—
34	C₃×C₂²⋊Dic₅	—	2	2	no	—
35	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	—
36	C₃×C₄×Dic₅	—	2	2	no	—
37	C₃×#681	—	2	2	no	—
38	C₃×#681	—	2	2	no	—
39	C₂×C₃×#168	—	2	2	no	—
40	C₂×C₃×#108	—	5	1	no	—
41	C₃×#427	—	5	1	no	—
42	C₃×#424	—	5	2	no	—
43	C₂×C₃×C₄×C₈	D₅	1	1	yes	characteristic
44	C₃×#339	—	5	2	no	—
45	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
46	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
47	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
48	#4072	C₂²×C₃	1	2	yes	—
49	C₂×#681	C₂²×C₃	1	2	yes	—
50	C₄×C₅×C₈	—	2	2	no	—
51	#3951	—	2	2	no	—
52	#3950	C₃×C₄	1	2	yes	complemented
53	#3949	C₃×C₄	1	2	yes	complemented
54	#3946	—	2	4	no	—
55	#1945	—	5	1	no	Sylow
56	C₂³×C₃×C₅	#41	1	1	yes	characteristic
57	C₂×C₃×C₄×C₅	—	2	4	no	—
58	C₂×C₃×C₄×C₅	—	2	2	no	—
59	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
61	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
62	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
63	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
64	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
65	C₂×C₃×Dic₅	—	2	4	no	—
66	C₃×C₅×C₈	—	2	2	no	—
67	C₃×C₅×C₈	C₄⋊C₄	1	2	yes	—
68	C₃×C₅×C₈	C₄⋊C₄	1	2	yes	—
69	C₃×#168	—	4	2	no	—
70	C₂×C₃×M₁₆	—	5	2	no	—
71	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
72	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
73	C₃×#117	—	5	2	no	—
74	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
75	C₃×#108	—	10	2	no	—
76	C₃×#107	—	5	2	no	—
77	C₃×#106	—	5	2	no	—
78	C₃×C₄⋊C₈	—	10	4	no	—
79	C₃×C₄×C₈	—	2	2	no	—
80	C₂²×C₄×C₅	—	2	1	no	—
81	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
82	C₂×C₅×C₈	—	2	1	no	—
83	C₂×C₅×C₈	—	2	1	no	—
84	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
85	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
86	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
87	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
88	C₂×C₅×C₈	C₃×Q₈	1	2	yes	—
89	C₄²×C₅	—	2	1	no	—
90	C₄²×C₅	C₃×Q₈	1	2	yes	—
91	C₂²⋊Dic₅	—	2	2	no	—
92	C₄⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
93	C₄×Dic₅	—	2	2	no	—
94	#681	—	2	2	no	—
95	#681	—	2	2	no	—
96	C₂×#168	—	2	2	no	—
97	C₂×#108	—	5	1	no	—
98	#427	—	5	1	no	—
99	#424	—	5	2	no	—
100	C₂×C₄×C₈	C₃×D₅	1	1	yes	characteristic
101	#339	—	5	2	no	—
102	C₂²×C₃×C₅	—	2	2	no	—
103	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
104	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
105	C₂²×C₃×C₅	#125	1	1	yes	characteristic
106	C₃×C₄×C₅	—	2	4	no	—
107	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
108	C₃×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
109	C₃×C₄×C₅	#121	1	1	yes	characteristic
110	C₃×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
111	C₃×Dic₅	—	4	4	no	—
112	C₂²×C₃×C₄	—	2	1	no	—
113	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
114	C₃×M₁₆	—	10	2	no	—
115	C₃×M₁₆	—	10	2	no	—
116	C₂×C₃×C₈	—	2	1	no	—
117	C₂×C₃×C₈	—	2	1	no	—
118	C₂×C₃×C₈	—	10	2	no	—
119	C₂×C₃×C₈	Dic₁₀	1	2	yes	—
120	C₂×C₃×C₈	C₄×D₅	1	1	yes	characteristic
121	C₂×C₃×C₈	C₄×D₅	1	1	yes	characteristic
122	C₂×C₃×C₈	D₂₀	1	2	yes	—
123	C₂×C₃×C₈	C₂²⋊D₅	1	2	yes	—
124	C₃×C₄⋊C₄	—	5	4	no	—
125	C₃×C₂²⋊C₄	—	10	2	no	—
126	C₃×C₄²	—	2	1	no	—
127	C₃×C₄²	—	10	2	no	—
128	C₃×C₄²	Dic₁₀	1	2	yes	—
129	C₂³×C₅	C₃×#41	1	1	yes	characteristic
130	C₂×C₄×C₅	—	2	4	no	—
131	C₂×C₄×C₅	—	2	2	no	—
132	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
133	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
134	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
135	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
136	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
137	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
138	C₂×Dic₅	—	2	4	no	—
139	C₅×C₈	—	2	2	no	—
140	C₅×C₈	C₃×C₄⋊C₄	1	2	yes	—
141	C₅×C₈	C₃×C₄⋊C₄	1	2	yes	—
142	#168	—	4	2	no	—
143	C₂×M₁₆	—	5	2	no	—
144	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
145	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
146	#117	—	5	2	no	—
147	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
148	#108	—	10	2	no	—
149	#107	—	5	2	no	—
150	#106	—	5	2	no	—
151	C₄⋊C₈	—	10	4	no	—
152	C₄×C₈	—	2	2	no	—
153	C₂×C₃×C₅	—	2	1	no	—
154	C₂×C₃×C₅	—	2	1	no	—
155	C₂×C₃×C₅	#389	1	1	yes	characteristic
156	C₂×C₃×C₅	#443	1	2	yes	—
157	C₂³×C₃	#709	1	1	yes	characteristic
158	C₂×C₃×C₄	—	2	4	no	—
159	C₂×C₃×C₄	—	2	2	no	—
160	C₂×C₃×C₄	—	10	4	no	—
161	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
162	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
163	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
164	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
165	C₂×C₃×C₄	#709	1	1	yes	characteristic
166	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
167	C₃×C₈	—	2	2	no	—
168	C₃×C₈	—	20	2	no	—
169	C₃×C₈	#683	1	2	yes	—
170	C₃×C₈	#683	1	2	yes	—
171	C₂²×C₅	—	2	2	no	—
172	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
173	C₂²×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
174	C₂²×C₅	C₃×#125	1	1	yes	characteristic
175	C₄×C₅	—	2	4	no	—
176	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
177	C₄×C₅	C₃×C₄×Q₈	1	1	yes	characteristic
178	C₄×C₅	C₃×#121	1	1	yes	characteristic
179	C₄×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
180	Dic₅	—	4	4	no	—
181	C₂²×C₄	—	2	1	no	—
182	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
183	M₁₆	—	10	2	no	—
184	M₁₆	—	10	2	no	—
185	C₂×C₈	—	2	1	no	—
186	C₂×C₈	—	2	1	no	—
187	C₂×C₈	—	10	2	no	—
188	C₂×C₈	C₃×Dic₁₀	1	2	yes	—
189	C₂×C₈	C₃×C₄×D₅	1	1	yes	characteristic
190	C₂×C₈	C₃×C₄×D₅	1	1	yes	characteristic
191	C₂×C₈	C₃×D₂₀	1	2	yes	—
192	C₂×C₈	C₃×C₂²⋊D₅	1	2	yes	—
193	C₄⋊C₄	—	5	4	no	—
194	C₂²⋊C₄	—	10	2	no	—
195	C₄²	—	2	1	no	—
196	C₄²	—	10	2	no	—
197	C₄²	C₃×Dic₁₀	1	2	yes	—
198	C₃×C₅	#1945	1	1	yes	characteristic, complemented, Hall
199	C₂²×C₃	—	2	2	no	—
200	C₂²×C₃	#4016	1	1	yes	characteristic
201	C₂²×C₃	C₄×D₂₀	1	1	yes	characteristic
202	C₂²×C₃	#4070	1	1	yes	characteristic
203	C₃×C₄	—	2	4	no	—
204	C₃×C₄	—	20	4	no	—
205	C₃×C₄	C₄×Dic₁₀	1	1	yes	characteristic
206	C₃×C₄	#4015	1	1	yes	characteristic
207	C₃×C₄	C₂×#683	1	1	yes	characteristic
208	C₃×C₄	#4076	1	1	yes	characteristic
209	C₂×C₅	—	2	1	no	—
210	C₂×C₅	—	2	1	no	—
211	C₂×C₅	C₃×#389	1	1	yes	characteristic
212	C₂×C₅	C₃×#443	1	2	yes	—
213	C₂³	C₃×#709	1	1	yes	characteristic
214	C₂×C₄	—	2	4	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	10	4	no	—
217	C₂×C₄	C₂×C₃×Dic₁₀	1	1	yes	characteristic
218	C₂×C₄	C₂×C₃×Dic₁₀	1	1	yes	characteristic
219	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
220	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
221	C₂×C₄	C₃×#709	1	1	yes	characteristic
222	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
223	C₈	—	2	2	no	—
224	C₈	—	20	2	no	—
225	C₈	C₃×#683	1	2	yes	—
226	C₈	C₃×#683	1	2	yes	—
227	C₂×C₃	—	2	1	no	—
228	C₂×C₃	—	2	1	no	—
229	C₂×C₃	#64989	1	2	yes	—
230	C₂×C₃	#65217	1	1	yes	characteristic
231	C₅	C₃×#1945	1	1	yes	characteristic, complemented, Sylow
232	C₂²	—	2	2	no	—
233	C₂²	C₃×#4016	1	1	yes	characteristic
234	C₂²	C₃×C₄×D₂₀	1	1	yes	characteristic
235	C₂²	C₃×#4070	1	1	yes	characteristic
236	C₄	—	2	4	no	—
237	C₄	—	20	4	no	—
238	C₄	C₃×C₄×Dic₁₀	1	1	yes	characteristic
239	C₄	C₃×#4015	1	1	yes	characteristic
240	C₄	C₂×C₃×#683	1	1	yes	characteristic
241	C₄	C₃×#4076	1	1	yes	characteristic
242	C₃	#10600587	1	1	yes	characteristic, direct product factor, Sylow
243	C₂	—	2	1	no	—
244	C₂	—	2	1	no	—
245	C₂	C₃×#64989	1	2	yes	—
246	C₂	C₃×#65217	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₂₀
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×C₈	C₂
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂³×C₃×C₅	#41
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂×C₃×C₄×C₈	D₅
hypocenter	C₅	C₃×#1945
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₈ ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
6. #10600587	C₃	direct (N × H)
14. C₃×#3950	C₄	semidirect
15. C₃×#3949	C₄	semidirect
52. #3950	C₃×C₄	semidirect
53. #3949	C₃×C₄	semidirect
198. C₃×C₅	#1945	semidirect
231. C₅	C₃×#1945	semidirect
242. C₃	#10600587	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×C₃×C₄×C₅×C₈	2
C₂×C₃×#3951	2
C₃×#65395	2
C₃×#65391	2
C₃×#64743	2
#10600587	3
C₃×#1945	5

Subgroups — C3×#10600587 #14305227

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10600587 #14305227