Subgroups — #14439866

Order 1920.

712 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11752466	C₂	1	2	yes	maximal
2	#11750784	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic
4	C₃×#64972	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748029	C₂	1	2	yes	maximal, complemented
6	#11748027	C₂	1	2	yes	maximal, complemented
7	#11747682	C₂	1	2	yes	maximal
8	#11747679	C₂	1	2	yes	maximal
9	#11746950	C₂	1	2	yes	maximal, complemented
10	#10610173	—	3	1	no	maximal, Hall
11	#91759	C₂²	1	2	yes	—
12	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
14	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
15	C₃×#4016	C₂²	1	2	yes	—
16	#91469	C₂²	1	4	yes	—
17	#91352	—	2	4	no	—
18	#91338	C₂²	1	4	yes	—
19	#91324	—	2	4	no	—
20	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
21	#91102	C₂²	1	2	yes	—
22	#91101	C₂²	1	2	yes	—
23	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
24	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
25	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₃×#3950	C₂²	1	2	yes	—
27	C₃×#3949	C₂²	1	2	yes	—
28	#90990	C₂²	1	4	yes	—
29	#90987	C₂²	1	4	yes	—
30	#81916	—	5	1	no	maximal, Hall
31	#65804	—	3	2	no	—
32	C₂×C₄×C₅×C₈	—	3	1	no	—
33	#65395	—	3	2	no	—
34	#65395	—	3	2	no	—
35	#64972	—	3	2	no	—
36	#64972	—	3	1	no	—
37	#64972	D₃	1	1	yes	characteristic, complemented
38	#64971	—	3	2	no	—
39	#64969	—	3	2	no	—
40	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
41	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
42	C₂×#1204	—	2	4	no	—
43	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
44	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
45	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
46	C₄⋊Dic₁₅	C₂³	1	4	yes	—
47	#6712	—	2	4	no	—
48	C₄×C₅×Dic₃	D₄	1	2	yes	—
49	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
50	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
51	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
52	C₅×D₃×C₈	Q₈	1	4	yes	complemented
53	C₅×D₃×C₈	Q₈	1	4	yes	complemented
54	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
55	C₃×#683	—	2	4	no	—
56	Dic₃⋊Dic₅	—	2	4	no	—
57	(C₂×D₃)⋊Dic₅	—	2	4	no	—
58	Dic₃×Dic₅	—	2	4	no	—
59	#5688	—	5	2	no	—
60	C₃×#499	—	5	1	no	—
61	#5065	—	5	2	no	—
62	#4880	—	5	2	no	—
63	#4874	—	5	2	no	—
64	#4860	—	5	2	no	—
65	#4855	—	5	2	no	—
66	C₄×D₃×C₈	D₅	1	1	yes	characteristic
67	#4683	—	5	1	no	—
68	C₂²×C₅×C₈	—	3	1	no	—
69	C₂²×C₅×C₈	—	3	1	no	—
70	C₂×C₄²×C₅	—	3	1	no	—
71	#4072	—	3	4	no	—
72	#4070	—	6	4	no	—
73	#4016	—	3	2	no	—
74	#4016	C₂×D₃	1	2	yes	—
75	#4015	—	3	4	no	—
76	C₄×Dic₁₀	—	6	4	no	—
77	C₄×C₅×C₈	—	3	1	no	—
78	C₄×C₅×C₈	—	3	1	no	—
79	C₄×C₅×C₈	—	3	1	no	—
80	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
81	#3950	—	3	2	no	—
82	#3950	—	3	4	no	—
83	#3950	C₂×D₃	1	2	yes	—
84	#3949	—	3	2	no	—
85	#3949	—	3	4	no	—
86	#3949	C₂×D₃	1	2	yes	—
87	#3160	—	15	1	no	Sylow
88	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
91	C₂×Dic₁₅	—	2	4	no	—
92	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
93	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
94	C₄×C₅×D₃	—	2	4	no	—
95	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
96	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
97	C₂×C₃×Dic₅	—	2	4	no	—
98	#1204	—	4	8	no	—
99	C₃×C₅×C₈	C₂×Q₈	1	2	yes	—
100	C₃×C₅×C₈	C₂×Q₈	1	2	yes	—
101	C₅×C₃⋊C₈	C₂×Q₈	1	2	yes	—
102	C₅×C₃⋊C₈	C₂×Q₈	1	2	yes	—
103	C₃×#125	—	5	2	no	—
104	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
105	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
106	#896	—	10	4	no	—
107	#892	—	5	4	no	—
108	#888	—	5	4	no	—
109	#887	—	10	4	no	—
110	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
111	#870	—	5	2	no	—
112	C₃×#107	—	5	2	no	—
113	C₃×#106	—	5	2	no	—
114	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
115	#818	—	5	2	no	—
116	#817	—	5	2	no	—
117	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
118	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
119	#808	—	5	4	no	—
120	#807	—	5	4	no	—
121	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
122	C₂²×C₄×C₅	—	3	1	no	—
123	C₂²×C₄×C₅	—	3	2	no	—
124	C₂×Dic₁₀	—	6	4	no	—
125	C₂×C₅×C₈	—	3	1	no	—
126	C₂×C₅×C₈	—	3	1	no	—
127	C₂×C₅×C₈	—	3	4	no	—
128	C₂×C₅×C₈	—	3	4	no	—
129	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
130	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
131	C₄²×C₅	—	3	2	no	—
132	C₄²×C₅	—	3	1	no	—
133	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
134	C₂²⋊Dic₅	—	6	4	no	—
135	C₄⋊Dic₅	—	3	4	no	—
136	C₄⋊Dic₅	—	6	4	no	—
137	C₄⋊Dic₅	C₂²×D₃	1	4	yes	—
138	#683	—	2	4	no	—
139	#683	—	6	4	no	—
140	C₄×Dic₅	—	6	4	no	—
141	#533	—	15	2	no	—
142	#500	—	15	2	no	—
143	#499	—	5	1	no	—
144	#499	—	15	2	no	—
145	#499	—	15	1	no	—
146	#498	—	15	2	no	—
147	#427	—	15	2	no	—
148	#427	—	15	2	no	—
149	C₂×C₄×C₈	—	3	1	no	—
150	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₅×D₃	—	2	2	no	—
152	C₂×C₅×D₃	C₄⋊Q₈	1	2	yes	—
153	C₃×C₄×C₅	—	2	2	no	—
154	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
155	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
156	Dic₁₅	—	4	4	no	—
157	C₃×Dic₅	—	4	4	no	—
158	C₅×Dic₃	C₄⋊Q₈	1	2	yes	—
159	C₅×Dic₃	#135	1	4	yes	—
160	C₂×C₄×D₃	D₂₀	1	2	yes	—
161	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
162	C₂×Dic₆	—	10	4	no	—
163	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
164	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
165	C₃×C₄⋊C₄	—	5	4	no	—
166	C₃×C₄⋊C₄	—	10	4	no	—
167	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
168	(C₂×D₃)⋊C₄	—	10	4	no	—
169	C₄⋊Dic₃	—	5	4	no	—
170	Dic₃⋊C₄	—	10	4	no	—
171	Dic₃⋊C₄	—	10	4	no	—
172	C₄×Dic₃	—	10	4	no	—
173	C₄×Dic₃	D₂₀	1	2	yes	—
174	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
175	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
176	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
177	D₃×C₈	Dic₁₀	1	4	yes	complemented
178	D₃×C₈	Dic₁₀	1	4	yes	complemented
179	C₂³×C₅	—	3	1	no	—
180	C₂×C₄×C₅	—	3	1	no	—
181	C₂×C₄×C₅	—	3	2	no	—
182	C₂×C₄×C₅	—	3	2	no	—
183	C₂×C₄×C₅	—	3	2	no	—
184	C₂×C₄×C₅	—	6	4	no	—
185	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
186	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
187	C₂×Dic₅	—	2	4	no	—
188	C₂×Dic₅	—	6	4	no	—
189	Dic₁₀	—	12	8	no	—
190	C₅×C₈	—	3	2	no	—
191	C₅×C₈	—	3	2	no	—
192	C₅×C₈	D₃×Q₈	1	2	yes	—
193	C₅×C₈	D₃×Q₈	1	2	yes	—
194	C₂²×C₈	—	3	1	no	—
195	C₂²×C₈	—	3	1	no	—
196	C₄⋊Q₈	—	15	4	no	—
197	#125	—	5	2	no	—
198	#125	—	15	2	no	—
199	C₂²⋊Q₈	—	30	4	no	—
200	C₄×Q₈	—	30	4	no	—
201	#117	—	15	4	no	—
202	C₂×C₄²	—	3	1	no	—
203	#107	—	5	2	no	—
204	#107	—	15	4	no	—
205	#107	—	15	2	no	—
206	#106	—	5	2	no	—
207	#106	—	15	4	no	—
208	#106	—	15	2	no	—
209	C₄×C₈	—	3	1	no	—
210	C₄×C₈	—	3	1	no	—
211	C₄×C₈	—	3	1	no	—
212	C₄×C₈	D₃×D₅	1	1	yes	characteristic
213	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
214	C₂×C₃×C₅	C₂×#135	1	2	yes	—
215	C₅×D₃	—	2	2	no	—
216	C₂²×D₃	C₂×D₂₀	1	1	yes	characteristic
217	C₂×C₃×C₄	—	10	4	no	—
218	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
219	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
220	C₂×Dic₃	—	10	4	no	—
221	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
222	C₂×Dic₃	C₂×D₂₀	1	2	yes	—
223	C₄×D₃	—	2	4	no	—
224	C₄×D₃	C₂×Dic₁₀	1	2	yes	—
225	C₄×D₃	C₂×Dic₁₀	1	2	yes	—
226	Dic₆	—	20	8	no	—
227	C₃×C₈	C₂×Dic₁₀	1	2	yes	—
228	C₃×C₈	C₂×Dic₁₀	1	2	yes	—
229	C₃⋊C₈	C₂×Dic₁₀	1	2	yes	—
230	C₃⋊C₈	C₂×Dic₁₀	1	2	yes	—
231	C₂²×C₅	—	3	2	no	—
232	C₂²×C₅	—	6	2	no	—
233	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
234	C₄×C₅	—	2	2	no	—
235	C₄×C₅	—	3	2	no	—
236	C₄×C₅	—	3	4	no	—
237	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
238	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
239	Dic₅	—	4	4	no	—
240	Dic₅	—	12	4	no	—
241	C₂×Q₈	—	30	4	no	—
242	C₂²×C₄	—	3	1	no	—
243	C₂²×C₄	—	3	2	no	—
244	C₂×C₈	—	3	1	no	—
245	C₂×C₈	—	3	1	no	—
246	C₂×C₈	—	3	4	no	—
247	C₂×C₈	—	3	4	no	—
248	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
249	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
250	C₄⋊C₄	—	5	4	no	—
251	C₄⋊C₄	—	10	4	no	—
252	C₄⋊C₄	—	15	4	no	—
253	C₄⋊C₄	—	30	4	no	—
254	C₄⋊C₄	—	30	4	no	—
255	C₂²⋊C₄	—	30	4	no	—
256	C₄²	—	3	2	no	—
257	C₄²	—	3	1	no	—
258	C₄²	—	30	4	no	—
259	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
260	C₃×C₅	#3160	1	1	yes	characteristic, complemented, Hall
261	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
262	C₂×D₃	—	2	2	no	—
263	C₂×D₃	#4015	1	2	yes	—
264	C₃×C₄	—	2	2	no	—
265	C₃×C₄	—	20	4	no	—
266	C₃×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
267	C₃×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
268	Dic₃	—	20	4	no	—
269	Dic₃	#4015	1	2	yes	—
270	Dic₃	#4050	1	4	yes	—
271	C₂×C₅	—	6	2	no	—
272	C₂×C₅	D₃×C₄⋊Q₈	1	1	yes	characteristic
273	C₂×C₅	D₃×#135	1	2	yes	—
274	C₂³	—	3	1	no	—
275	Q₈	—	60	8	no	—
276	C₂×C₄	—	3	1	no	—
277	C₂×C₄	—	3	2	no	—
278	C₂×C₄	—	3	2	no	—
279	C₂×C₄	—	3	2	no	—
280	C₂×C₄	—	6	4	no	—
281	C₂×C₄	—	10	4	no	—
282	C₂×C₄	—	30	4	no	—
283	C₂×C₄	D₃×D₂₀	1	2	yes	—
284	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
285	C₈	—	3	2	no	—
286	C₈	—	3	2	no	—
287	C₈	D₃×Dic₁₀	1	2	yes	—
288	C₈	D₃×Dic₁₀	1	2	yes	—
289	C₂×C₃	C₂×#4015	1	1	yes	characteristic
290	C₂×C₃	C₂×#4050	1	2	yes	—
291	D₃	—	2	2	no	—
292	C₅	#81916	1	1	yes	characteristic, complemented, Sylow
293	C₂²	—	3	2	no	—
294	C₂²	—	6	2	no	—
295	C₂²	C₂×D₃×D₂₀	1	1	yes	characteristic
296	C₄	—	2	2	no	—
297	C₄	—	3	2	no	—
298	C₄	—	3	4	no	—
299	C₄	—	20	4	no	—
300	C₄	—	60	4	no	—
301	C₄	C₂×D₃×Dic₁₀	1	1	yes	characteristic
302	C₄	C₂×D₃×Dic₁₀	1	1	yes	characteristic
303	C₃	#10610173	1	1	yes	characteristic, complemented, Sylow
304	C₂	—	6	2	no	—
305	C₂	D₃×#4015	1	1	yes	characteristic
306	C₂	D₃×#4050	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. #11750784	C₂	semidirect
4. C₃×#64972	C₂	semidirect
5. #11748029	C₂	semidirect
6. #11748027	C₂	semidirect
9. #11746950	C₂	semidirect
37. #64972	D₃	semidirect
52. C₅×D₃×C₈	Q₈	semidirect
53. C₅×D₃×C₈	Q₈	semidirect
177. D₃×C₈	Dic₁₀	semidirect
178. D₃×C₈	Dic₁₀	semidirect
260. C₃×C₅	#3160	semidirect
292. C₅	#81916	semidirect
303. C₃	#10610173	semidirect

Maximal subgroups

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

subgroup	index
#11752466	2
#11750784	2
C₄×C₅×D₃×C₈	2
C₃×#64972	2
#11748029	2
#11748027	2
#11747682	2
#11747679	2
#11746950	2
#10610173	3
#81916	5