Subgroups — #14439863

Order 1920.

712 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11752478	C₂	1	2	yes	maximal
2	#11750781	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic
4	C₃×#64969	C₂	1	1	yes	maximal, characteristic, complemented
5	#11747987	C₂	1	4	yes	maximal, complemented
6	#11747679	C₂	1	4	yes	maximal
7	#11746960	C₂	1	2	yes	maximal, complemented
8	#10610173	—	3	1	no	maximal, Hall
9	#91758	C₂²	1	2	yes	—
10	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
11	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
12	C₃×#4015	C₂²	1	2	yes	—
13	#91381	C₂²	1	4	yes	—
14	#91369	—	2	2	no	—
15	#91365	—	2	2	no	—
16	#91340	—	2	2	no	—
17	#91338	C₂²	1	4	yes	—
18	Dic₃×Dic₁₀	—	2	2	no	—
19	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
20	#91101	C₂²	1	4	yes	—
21	C₅×C₈×Dic₃	C₂²	1	2	yes	—
22	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₃×#3949	C₂²	1	4	yes	—
24	#90990	C₂²	1	8	yes	—
25	#81891	—	5	1	no	maximal, Hall
26	#65804	—	3	2	no	—
27	C₂×C₄×C₅×C₈	—	3	1	no	—
28	#65395	—	3	4	no	—
29	#64972	—	3	4	no	—
30	#64971	—	3	2	no	—
31	#64969	—	3	1	no	—
32	#64969	D₃	1	1	yes	characteristic, complemented
33	C₂×Dic₃₀	—	2	2	no	—
34	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
35	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
36	C₂×C₃×Dic₁₀	—	2	2	no	—
37	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
38	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
39	C₄⋊Dic₁₅	—	2	2	no	—
40	C₄⋊Dic₁₅	C₂³	1	4	yes	—
41	C₄×C₅×Dic₃	D₄	1	2	yes	—
42	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
43	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
44	C₅×D₃×C₈	Q₈	1	8	yes	complemented
45	C₃×C₄⋊Dic₅	—	2	2	no	—
46	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
47	#6669	—	2	4	no	—
48	#6668	—	2	4	no	—
49	(C₂×D₃)⋊Dic₅	—	2	4	no	—
50	Dic₃×Dic₅	—	2	4	no	—
51	#5728	—	5	2	no	—
52	C₃×#498	—	5	1	no	—
53	#5078	—	5	2	no	—
54	#4860	—	5	4	no	—
55	#4858	—	5	4	no	—
56	C₄×D₃×C₈	D₅	1	1	yes	characteristic
57	#4680	—	5	1	no	—
58	C₂²×C₅×C₈	—	3	2	no	—
59	C₂×C₄²×C₅	—	3	1	no	—
60	#4072	—	3	4	no	—
61	#4070	—	6	2	no	—
62	#4070	—	6	2	no	—
63	#4016	—	3	4	no	—
64	#4015	—	3	2	no	—
65	#4015	C₂×D₃	1	2	yes	—
66	C₄×Dic₁₀	—	6	2	no	—
67	C₄×Dic₁₀	—	6	2	no	—
68	C₄×C₅×C₈	—	3	2	no	—
69	C₄×C₅×C₈	—	3	1	no	—
70	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
71	#3950	—	3	8	no	—
72	#3949	—	3	4	no	—
73	#3949	C₂×D₃	1	4	yes	—
74	#3160	—	15	1	no	Sylow
75	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
76	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
77	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
78	C₂×Dic₁₅	—	2	4	no	—
79	Dic₃₀	—	4	4	no	—
80	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
81	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
82	C₄×C₅×D₃	—	2	4	no	—
83	C₄×C₅×D₃	C₂×Q₈	1	4	yes	—
84	C₂×C₃×Dic₅	—	2	4	no	—
85	C₃×Dic₁₀	—	4	4	no	—
86	C₃×C₅×C₈	C₂×Q₈	1	4	yes	—
87	C₅×C₃⋊C₈	C₂×Q₈	1	4	yes	—
88	C₃×C₄⋊Q₈	—	5	2	no	—
89	#946	—	10	2	no	—
90	Q₈×Dic₃	—	10	2	no	—
91	C₂×D₃×C₈	C₂×D₅	1	2	yes	—
92	#897	—	10	2	no	—
93	#892	—	5	4	no	—
94	#890	—	5	4	no	—
95	#887	—	10	2	no	—
96	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
97	#869	—	5	2	no	—
98	C₃×#106	—	5	4	no	—
99	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
100	#817	—	5	4	no	—
101	C₈×Dic₃	C₂×D₅	1	2	yes	—
102	#807	—	5	8	no	—
103	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
104	C₂²×C₄×C₅	—	3	1	no	—
105	C₂²×C₄×C₅	—	3	2	no	—
106	C₂×Dic₁₀	—	2	2	no	—
107	C₂×Dic₁₀	—	6	2	no	—
108	C₂×C₅×C₈	—	3	2	no	—
109	C₂×C₅×C₈	—	3	8	no	—
110	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
111	C₄²×C₅	—	3	2	no	—
112	C₄²×C₅	—	3	1	no	—
113	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
114	C₂²⋊Dic₅	—	6	4	no	—
115	C₄⋊Dic₅	—	2	2	no	—
116	C₄⋊Dic₅	—	3	4	no	—
117	C₄⋊Dic₅	—	6	2	no	—
118	C₄⋊Dic₅	C₂²×D₃	1	4	yes	—
119	#683	—	6	4	no	—
120	#683	—	6	4	no	—
121	C₄×Dic₅	—	6	4	no	—
122	#533	—	15	2	no	—
123	#500	—	15	2	no	—
124	#499	—	15	4	no	—
125	#498	—	5	1	no	—
126	#498	—	15	1	no	—
127	#427	—	15	4	no	—
128	C₂×C₄×C₈	—	3	1	no	—
129	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
130	C₂×C₅×D₃	—	2	2	no	—
131	C₂×C₅×D₃	C₄⋊Q₈	1	2	yes	—
132	C₃×C₄×C₅	#135	1	4	yes	—
133	C₃×C₄×C₅	C₂²×Q₈	1	2	yes	—
134	Dic₁₅	—	4	4	no	—
135	C₃×Dic₅	—	4	4	no	—
136	C₅×Dic₃	—	2	2	no	—
137	C₅×Dic₃	C₄⋊Q₈	1	2	yes	—
138	C₂×C₃×Q₈	—	10	2	no	—
139	C₂×C₄×D₃	D₂₀	1	2	yes	—
140	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
141	C₂×Dic₆	—	10	2	no	—
142	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
143	C₃×C₄⋊C₄	—	5	4	no	—
144	C₃×C₄⋊C₄	—	10	2	no	—
145	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
146	(C₂×D₃)⋊C₄	—	10	4	no	—
147	C₄⋊Dic₃	—	5	4	no	—
148	C₄⋊Dic₃	—	10	2	no	—
149	C₄⋊Dic₃	—	10	4	no	—
150	Dic₃⋊C₄	—	10	4	no	—
151	C₄×Dic₃	—	10	4	no	—
152	C₄×Dic₃	D₂₀	1	2	yes	—
153	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
154	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
155	D₃×C₈	Dic₁₀	1	8	yes	complemented
156	C₂³×C₅	—	3	1	no	—
157	C₂×C₄×C₅	—	3	1	no	—
158	C₂×C₄×C₅	—	3	4	no	—
159	C₂×C₄×C₅	—	3	2	no	—
160	C₂×C₄×C₅	—	6	4	no	—
161	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
162	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
163	C₂×Dic₅	—	2	4	no	—
164	C₂×Dic₅	—	6	4	no	—
165	Dic₁₀	—	4	4	no	—
166	Dic₁₀	—	12	4	no	—
167	C₅×C₈	—	3	4	no	—
168	C₅×C₈	D₃×Q₈	1	4	yes	—
169	C₂²×C₈	—	3	2	no	—
170	C₄⋊Q₈	—	5	2	no	—
171	C₄⋊Q₈	—	15	2	no	—
172	#125	—	15	4	no	—
173	C₂²⋊Q₈	—	30	2	no	—
174	C₂²⋊Q₈	—	30	2	no	—
175	C₄×Q₈	—	30	2	no	—
176	C₄×Q₈	—	30	2	no	—
177	#117	—	15	4	no	—
178	C₂×C₄²	—	3	1	no	—
179	#107	—	15	8	no	—
180	#106	—	5	4	no	—
181	#106	—	15	4	no	—
182	C₄×C₈	—	3	2	no	—
183	C₄×C₈	—	3	1	no	—
184	C₄×C₈	D₃×D₅	1	1	yes	characteristic
185	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
186	C₂×C₃×C₅	C₂×#135	1	2	yes	—
187	C₅×D₃	—	2	2	no	—
188	C₂²×D₃	C₂×D₂₀	1	1	yes	characteristic
189	C₃×Q₈	—	20	4	no	—
190	C₂×C₃×C₄	—	10	4	no	—
191	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
192	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
193	C₂×Dic₃	—	10	4	no	—
194	C₂×Dic₃	C₂×D₂₀	1	2	yes	—
195	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
196	C₄×D₃	—	2	4	no	—
197	C₄×D₃	C₂×Dic₁₀	1	4	yes	—
198	Dic₆	—	20	4	no	—
199	C₃×C₈	C₂×Dic₁₀	1	4	yes	—
200	C₃⋊C₈	C₂×Dic₁₀	1	4	yes	—
201	C₂²×C₅	—	3	2	no	—
202	C₂²×C₅	—	6	2	no	—
203	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
204	C₄×C₅	—	3	2	no	—
205	C₄×C₅	—	6	2	no	—
206	C₄×C₅	#916	1	4	yes	—
207	C₄×C₅	C₂×D₃×Q₈	1	2	yes	—
208	Dic₅	—	4	4	no	—
209	Dic₅	—	12	4	no	—
210	C₂×Q₈	—	10	2	no	—
211	C₂×Q₈	—	30	2	no	—
212	C₂²×C₄	—	3	1	no	—
213	C₂²×C₄	—	3	2	no	—
214	C₂×C₈	—	3	2	no	—
215	C₂×C₈	—	3	8	no	—
216	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
217	C₄⋊C₄	—	5	4	no	—
218	C₄⋊C₄	—	10	2	no	—
219	C₄⋊C₄	—	15	4	no	—
220	C₄⋊C₄	—	30	4	no	—
221	C₄⋊C₄	—	30	4	no	—
222	C₄⋊C₄	—	30	2	no	—
223	C₂²⋊C₄	—	30	4	no	—
224	C₄²	—	3	2	no	—
225	C₄²	—	3	1	no	—
226	C₄²	—	30	4	no	—
227	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
228	C₃×C₅	#3160	1	1	yes	characteristic, complemented, Hall
229	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
230	C₂×D₃	—	2	2	no	—
231	C₂×D₃	#4015	1	2	yes	—
232	C₃×C₄	—	20	4	no	—
233	C₃×C₄	#4050	1	4	yes	—
234	C₃×C₄	C₂²×Dic₁₀	1	2	yes	—
235	Dic₃	—	2	2	no	—
236	Dic₃	—	20	4	no	—
237	Dic₃	#4015	1	2	yes	—
238	C₂×C₅	—	6	2	no	—
239	C₂×C₅	D₃×C₄⋊Q₈	1	1	yes	characteristic
240	C₂×C₅	C₂×#916	1	2	yes	—
241	C₂³	—	3	1	no	—
242	Q₈	—	20	4	no	—
243	Q₈	—	60	4	no	—
244	C₂×C₄	—	3	1	no	—
245	C₂×C₄	—	3	4	no	—
246	C₂×C₄	—	3	2	no	—
247	C₂×C₄	—	6	4	no	—
248	C₂×C₄	—	10	4	no	—
249	C₂×C₄	—	30	4	no	—
250	C₂×C₄	D₃×D₂₀	1	2	yes	—
251	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
252	C₈	—	3	4	no	—
253	C₈	D₃×Dic₁₀	1	4	yes	—
254	C₂×C₃	C₂×#4015	1	1	yes	characteristic
255	C₂×C₃	C₂×#4050	1	2	yes	—
256	D₃	—	2	2	no	—
257	C₅	#81891	1	1	yes	characteristic, complemented, Sylow
258	C₂²	—	3	2	no	—
259	C₂²	—	6	2	no	—
260	C₂²	C₂×D₃×D₂₀	1	1	yes	characteristic
261	C₄	—	3	2	no	—
262	C₄	—	6	2	no	—
263	C₄	—	20	4	no	—
264	C₄	—	60	4	no	—
265	C₄	#91272	1	4	yes	—
266	C₄	C₂×D₃×Dic₁₀	1	2	yes	—
267	C₃	#10610173	1	1	yes	characteristic, complemented, Sylow
268	C₂	—	6	2	no	—
269	C₂	D₃×#4015	1	1	yes	characteristic
270	C₂	C₂×#91272	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₃×D₂₀
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₅×D₃	C₂×D₄
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	#3160
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #11750781	C₂	semidirect
4. C₃×#64969	C₂	semidirect
5. #11747987	C₂	semidirect
7. #11746960	C₂	semidirect
32. #64969	D₃	semidirect
44. C₅×D₃×C₈	Q₈	semidirect
155. D₃×C₈	Dic₁₀	semidirect
228. C₃×C₅	#3160	semidirect
257. C₅	#81891	semidirect
267. C₃	#10610173	semidirect

Maximal subgroups

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

subgroup	index
#11752478	2
#11750781	2
C₄×C₅×D₃×C₈	2
C₃×#64969	2
#11747987	2
#11747679	2
#11746960	2
#10610173	3
#81891	5