Subgroups — D₃×#64971 #14439821

Order 1920.

848 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×#4015	C₂	1	2	yes	maximal
2	#11750783	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic
4	C₃×#64971	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748029	C₂	1	4	yes	maximal, complemented
6	D₃×#3950	C₂	1	4	yes	maximal
7	#11746960	C₂	1	2	yes	maximal, complemented
8	C₂×#64971	—	3	1	no	maximal, Hall
9	C₂×D₃×Dic₁₀	—	2	2	no	—
10	#91758	C₂²	1	2	yes	—
11	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
12	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
13	C₃×#4015	C₂²	1	2	yes	—
14	#91469	—	2	2	no	—
15	#91469	C₂²	1	4	yes	—
16	D₃×C₄⋊Dic₅	—	2	2	no	—
17	D₃×C₄⋊Dic₅	C₂²	1	4	yes	—
18	#91389	—	2	2	no	—
19	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
20	#91102	C₂²	1	4	yes	—
21	C₅×C₈×Dic₃	C₂²	1	2	yes	—
22	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₃×#3950	C₂²	1	4	yes	—
24	#90990	C₂²	1	8	yes	—
25	D₃×#500	—	5	1	no	maximal, Hall
26	C₂×#4015	—	3	2	no	—
27	C₂×C₄×C₅×C₈	—	3	1	no	—
28	C₂×#3950	—	3	4	no	—
29	#64971	—	3	2	no	—
30	#64971	—	3	1	no	—
31	#64971	—	3	4	no	—
32	#64971	D₃	1	1	yes	characteristic, direct product factor
33	C₂×Dic₃₀	—	2	2	no	—
34	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
35	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
36	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
37	C₂×C₃×Dic₁₀	—	2	2	no	—
38	C₂×#1204	—	2	4	no	—
39	C₂×D₃×Dic₅	—	2	4	no	—
40	D₃×Dic₁₀	—	4	8	no	—
41	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
42	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
43	C₄⋊Dic₁₅	—	2	2	no	—
44	C₄⋊Dic₁₅	C₂³	1	4	yes	—
45	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
46	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
47	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
48	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
49	C₅×D₃×C₈	Q₈	1	8	yes	complemented
50	C₃×C₄⋊Dic₅	—	2	2	no	—
51	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
52	Dic₃⋊Dic₅	—	2	4	no	—
53	Dic₃⋊Dic₅	—	2	4	no	—
54	D₃×C₄⋊Q₈	—	5	2	no	—
55	C₃×#500	—	5	1	no	—
56	#5078	—	5	2	no	—
57	D₃×#107	—	5	4	no	—
58	#4874	—	5	4	no	—
59	C₄×D₃×C₈	D₅	1	1	yes	characteristic
60	#4682	—	5	1	no	—
61	C₂²×Dic₁₀	—	6	2	no	—
62	C₂²×C₅×C₈	—	3	2	no	—
63	C₂×C₄²×C₅	—	3	1	no	—
64	C₂×C₄⋊Dic₅	—	3	4	no	—
65	C₂×C₄⋊Dic₅	—	6	2	no	—
66	#4015	—	3	2	no	—
67	#4015	—	3	4	no	—
68	#4015	—	6	2	no	—
69	#4015	—	6	2	no	—
70	#4015	C₂×D₃	1	2	yes	—
71	C₄×C₅×C₈	—	3	2	no	—
72	C₄×C₅×C₈	—	3	1	no	—
73	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
74	#3950	—	3	4	no	—
75	#3950	—	3	8	no	—
76	#3950	C₂×D₃	1	4	yes	—
77	C₂×#500	—	15	1	no	Sylow
78	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
79	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
82	C₂×Dic₁₅	—	2	4	no	—
83	Dic₃₀	—	4	4	no	—
84	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
85	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
86	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
87	C₄×C₅×D₃	D₈	1	4	yes	—
88	C₄×C₅×D₃	Q₁₆	1	4	yes	—
89	C₄×C₅×D₃	C₂×Q₈	1	4	yes	—
90	C₂×C₃×Dic₅	—	2	4	no	—
91	C₃×Dic₁₀	—	4	4	no	—
92	#1204	—	4	8	no	—
93	D₃×Dic₅	—	4	8	no	—
94	C₃×C₅×C₈	C₂×Q₈	1	4	yes	complemented
95	C₅×C₃⋊C₈	C₂×Q₈	1	4	yes	complemented
96	C₂×D₃×Q₈	—	10	2	no	—
97	C₃×C₄⋊Q₈	—	5	2	no	—
98	#944	—	10	2	no	—
99	C₂×D₃×C₈	C₂×D₅	1	2	yes	—
100	D₃×C₄⋊C₄	—	5	4	no	—
101	D₃×C₄⋊C₄	—	10	2	no	—
102	#888	—	5	4	no	—
103	#888	—	10	2	no	—
104	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
105	#869	—	5	2	no	—
106	C₃×#107	—	5	4	no	—
107	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
108	#818	—	5	4	no	—
109	C₈×Dic₃	C₂×D₅	1	2	yes	—
110	#807	—	5	8	no	—
111	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
112	C₂²×C₄×C₅	—	3	1	no	—
113	C₂²×C₄×C₅	—	3	1	no	—
114	C₂²×C₄×C₅	—	3	1	no	—
115	C₂²×Dic₅	—	6	4	no	—
116	C₂×Dic₁₀	—	2	2	no	—
117	C₂×Dic₁₀	—	6	4	no	—
118	C₂×Dic₁₀	—	6	2	no	—
119	C₂×Dic₁₀	—	12	8	no	—
120	C₂×C₅×C₈	—	3	2	no	—
121	C₂×C₅×C₈	—	3	8	no	—
122	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
123	C₄²×C₅	—	3	1	no	—
124	C₄²×C₅	—	3	1	no	—
125	C₄²×C₅	—	3	1	no	—
126	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
127	C₄⋊Dic₅	—	2	2	no	—
128	C₄⋊Dic₅	—	3	4	no	—
129	C₄⋊Dic₅	—	6	4	no	—
130	C₄⋊Dic₅	—	6	4	no	—
131	C₄⋊Dic₅	—	6	2	no	—
132	C₄⋊Dic₅	C₂²×D₃	1	4	yes	—
133	C₂×C₄⋊Q₈	—	15	2	no	—
134	#500	—	5	1	no	—
135	#500	—	15	4	no	—
136	#500	—	15	2	no	—
137	#500	—	15	1	no	—
138	C₂×#107	—	15	4	no	—
139	C₂×C₄×C₈	—	3	1	no	—
140	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₅×D₃	C₄⋊Q₈	1	2	yes	—
142	C₂×C₅×D₃	C₂×D₈	1	2	yes	—
143	C₂×C₅×D₃	C₂×Q₁₆	1	2	yes	—
144	C₃×C₄×C₅	C₂×D₈	1	2	yes	—
145	C₃×C₄×C₅	C₂×Q₁₆	1	2	yes	—
146	C₃×C₄×C₅	C₂²×Q₈	1	2	yes	—
147	Dic₁₅	—	4	4	no	—
148	C₃×Dic₅	—	4	4	no	—
149	C₅×Dic₃	C₄⋊Q₈	1	2	yes	—
150	C₅×Dic₃	C₂×D₈	1	2	yes	—
151	C₅×Dic₃	C₂×Q₁₆	1	2	yes	—
152	C₂×C₃×Q₈	—	10	2	no	—
153	D₃×Q₈	—	20	8	no	—
154	C₂×C₄×D₃	—	10	4	no	—
155	C₂×C₄×D₃	D₂₀	1	1	yes	characteristic
156	C₂×C₄×D₃	D₂₀	1	1	yes	characteristic
157	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
158	C₂×Dic₆	—	10	2	no	—
159	C₂×Dic₆	—	10	4	no	—
160	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
161	C₃×C₄⋊C₄	—	5	4	no	—
162	C₃×C₄⋊C₄	—	10	2	no	—
163	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
164	C₄⋊Dic₃	—	5	4	no	—
165	C₄⋊Dic₃	—	10	2	no	—
166	Dic₃⋊C₄	—	10	4	no	—
167	Dic₃⋊C₄	—	10	4	no	—
168	C₄×Dic₃	D₂₀	1	1	yes	characteristic
169	C₄×Dic₃	D₂₀	1	1	yes	characteristic
170	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
171	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
172	D₃×C₈	Dic₁₀	1	8	yes	complemented
173	C₂³×C₅	—	3	1	no	—
174	C₂×C₄×C₅	—	3	1	no	—
175	C₂×C₄×C₅	—	3	1	no	—
176	C₂×C₄×C₅	—	3	1	no	—
177	C₂×C₄×C₅	—	3	4	no	—
178	C₂×C₄×C₅	—	3	4	no	—
179	C₂×C₄×C₅	—	3	4	no	—
180	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
181	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
183	C₂×Dic₅	—	2	4	no	—
184	C₂×Dic₅	—	6	4	no	—
185	C₂×Dic₅	—	12	8	no	—
186	Dic₁₀	—	4	4	no	—
187	Dic₁₀	—	12	8	no	—
188	Dic₁₀	—	12	4	no	—
189	C₅×C₈	—	3	4	no	—
190	C₅×C₈	D₃×Q₈	1	4	yes	complemented
191	C₂²×Q₈	—	30	2	no	—
192	C₂²×C₈	—	3	2	no	—
193	C₄⋊Q₈	—	5	2	no	—
194	C₄⋊Q₈	—	15	4	no	—
195	C₄⋊Q₈	—	15	2	no	—
196	C₄⋊Q₈	—	30	2	no	—
197	C₄⋊Q₈	—	30	2	no	—
198	C₂×C₄⋊C₄	—	15	4	no	—
199	C₂×C₄⋊C₄	—	30	2	no	—
200	C₂×C₄²	—	3	1	no	—
201	#107	—	5	4	no	—
202	#107	—	15	8	no	—
203	#107	—	15	4	no	—
204	C₄×C₈	—	3	2	no	—
205	C₄×C₈	—	3	1	no	—
206	C₄×C₈	D₃×D₅	1	1	yes	characteristic
207	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
208	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
209	C₂×C₃×C₅	C₂²×Q₁₆	1	1	yes	characteristic
210	C₅×D₃	#500	1	4	yes	complemented
211	C₂²×D₃	C₂×D₂₀	1	1	yes	characteristic
212	C₃×Q₈	—	20	4	no	—
213	C₂×C₃×C₄	—	10	4	no	—
214	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
215	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
216	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
217	C₂×Dic₃	—	10	4	no	—
218	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
219	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
220	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
221	C₄×D₃	—	20	8	no	—
222	C₄×D₃	D₄₀	1	4	yes	—
223	C₄×D₃	Dic₂₀	1	4	yes	—
224	C₄×D₃	C₂×Dic₁₀	1	4	yes	—
225	Dic₆	—	20	4	no	—
226	Dic₆	—	20	8	no	—
227	C₃×C₈	C₂×Dic₁₀	1	4	yes	complemented
228	C₃⋊C₈	C₂×Dic₁₀	1	4	yes	complemented
229	C₂²×C₅	—	3	2	no	—
230	C₂²×C₅	—	3	2	no	—
231	C₂²×C₅	—	3	2	no	—
232	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
233	C₄×C₅	—	3	2	no	—
234	C₄×C₅	—	3	2	no	—
235	C₄×C₅	—	3	2	no	—
236	C₄×C₅	D₃×D₈	1	2	yes	—
237	C₄×C₅	D₃×Q₁₆	1	2	yes	—
238	C₄×C₅	C₂×D₃×Q₈	1	2	yes	—
239	Dic₅	—	4	4	no	—
240	Dic₅	—	12	4	no	—
241	C₂×Q₈	—	10	2	no	—
242	C₂×Q₈	—	30	4	no	—
243	C₂×Q₈	—	30	2	no	—
244	C₂×Q₈	—	60	8	no	—
245	C₂²×C₄	—	3	1	no	—
246	C₂²×C₄	—	3	1	no	—
247	C₂²×C₄	—	3	1	no	—
248	C₂²×C₄	—	30	4	no	—
249	C₂×C₈	—	3	2	no	—
250	C₂×C₈	—	3	8	no	—
251	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
252	C₄⋊C₄	—	5	4	no	—
253	C₄⋊C₄	—	10	2	no	—
254	C₄⋊C₄	—	15	4	no	—
255	C₄⋊C₄	—	30	4	no	—
256	C₄⋊C₄	—	30	4	no	—
257	C₄⋊C₄	—	30	2	no	—
258	C₄²	—	3	1	no	—
259	C₄²	—	3	1	no	—
260	C₄²	—	3	1	no	—
261	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
262	C₃×C₅	C₂×#500	1	1	yes	characteristic, complemented, Hall
263	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
264	C₂×D₃	#4015	1	2	yes	—
265	C₂×D₃	C₂×D₄₀	1	2	yes	—
266	C₂×D₃	C₂×Dic₂₀	1	2	yes	—
267	C₃×C₄	—	20	4	no	—
268	C₃×C₄	C₂×D₄₀	1	2	yes	—
269	C₃×C₄	C₂×Dic₂₀	1	2	yes	—
270	C₃×C₄	C₂²×Dic₁₀	1	2	yes	—
271	Dic₃	—	20	4	no	—
272	Dic₃	#4015	1	2	yes	—
273	Dic₃	C₂×D₄₀	1	2	yes	—
274	Dic₃	C₂×Dic₂₀	1	2	yes	—
275	C₂×C₅	—	3	4	no	—
276	C₂×C₅	D₃×C₄⋊Q₈	1	1	yes	characteristic
277	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
278	C₂×C₅	C₂×D₃×Q₁₆	1	1	yes	characteristic
279	C₂³	—	3	1	no	—
280	Q₈	—	20	4	no	—
281	Q₈	—	60	8	no	—
282	Q₈	—	60	4	no	—
283	C₂×C₄	—	3	1	no	—
284	C₂×C₄	—	3	1	no	—
285	C₂×C₄	—	3	1	no	—
286	C₂×C₄	—	3	4	no	—
287	C₂×C₄	—	3	4	no	—
288	C₂×C₄	—	3	4	no	—
289	C₂×C₄	—	10	4	no	—
290	C₂×C₄	—	30	4	no	—
291	C₂×C₄	—	60	8	no	—
292	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
293	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
294	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
295	C₈	—	3	4	no	—
296	C₈	D₃×Dic₁₀	1	4	yes	complemented
297	C₂×C₃	C₂×#4015	1	1	yes	characteristic
298	C₂×C₃	C₂²×D₄₀	1	1	yes	characteristic
299	C₂×C₃	C₂²×Dic₂₀	1	1	yes	characteristic
300	D₃	#64971	1	4	yes	direct product factor
301	C₅	D₃×#500	1	1	yes	characteristic, complemented, Sylow
302	C₂²	—	3	2	no	—
303	C₂²	—	3	2	no	—
304	C₂²	—	3	2	no	—
305	C₂²	C₂×D₃×D₂₀	1	1	yes	characteristic
306	C₄	—	3	2	no	—
307	C₄	—	3	2	no	—
308	C₄	—	3	2	no	—
309	C₄	—	20	4	no	—
310	C₄	—	60	4	no	—
311	C₄	D₃×D₄₀	1	2	yes	—
312	C₄	D₃×Dic₂₀	1	2	yes	—
313	C₄	C₂×D₃×Dic₁₀	1	2	yes	—
314	C₃	C₂×#64971	1	1	yes	characteristic, complemented, Sylow
315	C₂	—	3	4	no	—
316	C₂	D₃×#4015	1	1	yes	characteristic
317	C₂	C₂×D₃×D₄₀	1	1	yes	characteristic
318	C₂	C₂×D₃×Dic₂₀	1	1	yes	characteristic

	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	C₂×#500
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. #11750783	C₂	semidirect
4. C₃×#64971	C₂	semidirect
5. #11748029	C₂	semidirect
7. #11746960	C₂	semidirect
32. #64971	D₃	direct (N × H)
49. C₅×D₃×C₈	Q₈	semidirect
94. C₃×C₅×C₈	C₂×Q₈	semidirect
95. C₅×C₃⋊C₈	C₂×Q₈	semidirect
172. D₃×C₈	Dic₁₀	semidirect
190. C₅×C₈	D₃×Q₈	semidirect
210. C₅×D₃	#500	semidirect
227. C₃×C₈	C₂×Dic₁₀	semidirect
228. C₃⋊C₈	C₂×Dic₁₀	semidirect
262. C₃×C₅	C₂×#500	semidirect
296. C₈	D₃×Dic₁₀	semidirect
300. D₃	#64971	direct (N × H)
301. C₅	D₃×#500	semidirect
314. C₃	C₂×#64971	semidirect

Maximal subgroups

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

subgroup	index
D₃×#4015	2
#11750783	2
C₄×C₅×D₃×C₈	2
C₃×#64971	2
#11748029	2
D₃×#3950	2
#11746960	2
C₂×#64971	3
D₃×#500	5

Subgroups — D3×#64971 #14439821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#64971 #14439821