Subgroups — D₃×#64988 #14438813

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×Dic₂₀	C₂	1	4	yes	maximal
2	D₃×#4015	C₂	1	2	yes	maximal
3	#11750800	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic
5	C₃×#64988	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748033	C₂	1	4	yes	maximal, complemented
7	#11747100	C₂	1	2	yes	maximal, complemented
8	C₂×#64988	—	3	1	no	maximal, Hall
9	C₂×D₃×Dic₁₀	C₂²	1	4	yes	—
10	C₂×Dic₆₀	C₂²	1	4	yes	—
11	#91758	C₂²	1	2	yes	—
12	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
13	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₂×C₃×Dic₂₀	C₂²	1	4	yes	—
15	C₃×#4015	C₂²	1	2	yes	—
16	#91469	—	2	4	no	—
17	D₃×C₄⋊Dic₅	—	2	4	no	—
18	#91389	C₂²	1	4	yes	—
19	C₂×#6662	C₂²	1	8	yes	—
20	D₃×Dic₂₀	—	2	16	no	—
21	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₅×C₈×Dic₃	C₂²	1	2	yes	—
23	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
24	D₃×#494	—	5	1	no	maximal, Hall
25	C₂²×Dic₂₀	—	3	4	no	—
26	C₂×#4015	—	3	2	no	—
27	C₂×C₄×C₅×C₈	—	3	1	no	—
28	#64988	—	3	4	no	—
29	#64988	—	3	2	no	—
30	#64988	—	3	1	no	—
31	#64988	D₃	1	1	yes	characteristic, direct product factor
32	C₂×Dic₃₀	C₂³	1	4	yes	—
33	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
34	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
35	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
36	C₂×#1204	—	2	4	no	—
37	C₂×D₃×Dic₅	—	2	4	no	—
38	D₃×Dic₁₀	—	2	16	no	—
39	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
40	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
41	C₄⋊Dic₁₅	—	2	4	no	—
42	Dic₆₀	—	2	8	no	—
43	C₄×C₅×Dic₃	D₄	1	2	yes	—
44	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
45	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
46	C₅×D₃×C₈	D₄	1	8	yes	—
47	C₃×C₄⋊Dic₅	—	2	4	no	—
48	C₃×Dic₂₀	—	2	8	no	—
49	Dic₃⋊Dic₅	—	2	8	no	—
50	#6662	—	2	16	no	—
51	C₂×D₃×Q₁₆	—	5	4	no	—
52	D₃×C₄⋊Q₈	—	5	2	no	—
53	C₃×#494	—	5	1	no	—
54	#5183	—	5	4	no	—
55	#5092	—	5	2	no	—
56	#4699	—	5	1	no	—
57	C₄×D₃×C₈	D₅	1	1	yes	characteristic
58	C₂²×Dic₁₀	—	3	4	no	—
59	C₂²×C₅×C₈	—	3	2	no	—
60	C₂×C₄²×C₅	—	3	1	no	—
61	C₂×C₄⋊Dic₅	—	6	4	no	—
62	C₂×Dic₂₀	—	3	8	no	—
63	C₂×Dic₂₀	—	3	4	no	—
64	C₂×Dic₂₀	—	6	16	no	—
65	C₂×Dic₂₀	C₂×D₃	1	4	yes	—
66	#4015	—	3	4	no	—
67	#4015	—	3	2	no	—
68	#4015	—	6	4	no	—
69	#4015	C₂×D₃	1	2	yes	—
70	C₄×C₅×C₈	—	3	2	no	—
71	C₄×C₅×C₈	—	3	1	no	—
72	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
73	C₂×#494	—	15	1	no	Sylow
74	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
75	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
76	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
77	C₂×Dic₁₅	—	2	4	no	—
78	Dic₃₀	—	2	8	no	—
79	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
80	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
81	C₄×C₅×D₃	Q₁₆	1	8	yes	complemented
82	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
83	C₂×C₃×Dic₅	—	2	4	no	—
84	C₃×Dic₁₀	—	2	8	no	—
85	#1204	—	4	8	no	—
86	D₃×Dic₅	—	4	8	no	—
87	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
88	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
89	C₂×D₃×Q₈	—	5	4	no	—
90	C₂×C₃×Q₁₆	—	5	4	no	—
91	C₃×C₄⋊Q₈	—	5	2	no	—
92	#944	—	5	4	no	—
93	C₂×#216	—	5	8	no	—
94	D₃×Q₁₆	—	10	16	no	—
95	C₂×Dic₁₂	—	5	4	no	—
96	C₂×D₃×C₈	C₂×D₅	1	2	yes	—
97	D₃×C₄⋊C₄	—	10	4	no	—
98	#888	—	10	4	no	—
99	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
100	#869	—	5	2	no	—
101	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
102	C₈×Dic₃	C₂×D₅	1	2	yes	—
103	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
104	C₂²×C₄×C₅	—	3	2	no	—
105	C₂²×C₄×C₅	—	3	1	no	—
106	C₂²×Dic₅	—	6	4	no	—
107	C₂×Dic₁₀	—	3	4	no	—
108	C₂×Dic₁₀	—	6	16	no	—
109	C₂×Dic₁₀	—	6	4	no	—
110	C₂×Dic₁₀	C₂²×D₃	1	4	yes	—
111	C₂×C₅×C₈	—	3	2	no	—
112	C₂×C₅×C₈	—	3	8	no	—
113	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
114	C₄²×C₅	—	3	2	no	—
115	C₄²×C₅	—	3	1	no	—
116	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
117	C₄⋊Dic₅	—	2	4	no	—
118	C₄⋊Dic₅	—	6	8	no	—
119	C₄⋊Dic₅	—	6	4	no	—
120	Dic₂₀	—	2	8	no	—
121	Dic₂₀	—	6	16	no	—
122	Dic₂₀	—	6	8	no	—
123	C₂²×Q₁₆	—	15	4	no	—
124	C₂×C₄⋊Q₈	—	15	2	no	—
125	#494	—	5	1	no	—
126	#494	—	15	2	no	—
127	#494	—	15	4	no	—
128	#494	—	15	1	no	—
129	C₂×C₄×C₈	—	3	1	no	—
130	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₅×D₃	#127	1	2	yes	—
132	C₂×C₅×D₃	C₂×Q₁₆	1	4	yes	—
133	C₃×C₄×C₅	C₂×Q₁₆	1	4	yes	complemented
134	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
135	Dic₁₅	—	4	4	no	—
136	C₃×Dic₅	—	4	4	no	—
137	C₅×Dic₃	#127	1	2	yes	—
138	C₅×Dic₃	C₂×Q₁₆	1	4	yes	complemented
139	C₂×C₃×Q₈	—	5	4	no	—
140	D₃×Q₈	—	10	16	no	—
141	C₂×C₄×D₃	—	10	4	no	—
142	C₂×C₄×D₃	D₂₀	1	2	yes	—
143	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
144	C₂×Dic₆	—	5	4	no	—
145	C₂×Dic₆	—	10	4	no	—
146	C₃×Q₁₆	—	10	8	no	—
147	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
148	C₃×C₄⋊C₄	—	10	4	no	—
149	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
150	#216	—	10	16	no	—
151	C₄⋊Dic₃	—	10	4	no	—
152	Dic₃⋊C₄	—	10	8	no	—
153	C₄×Dic₃	D₂₀	1	2	yes	—
154	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
155	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
156	Dic₁₂	—	10	8	no	—
157	D₃×C₈	D₂₀	1	8	yes	—
158	C₂³×C₅	—	3	1	no	—
159	C₂×C₄×C₅	—	3	2	no	—
160	C₂×C₄×C₅	—	3	1	no	—
161	C₂×C₄×C₅	—	3	8	no	—
162	C₂×C₄×C₅	—	3	4	no	—
163	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
164	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
165	C₂×Dic₅	—	2	4	no	—
166	C₂×Dic₅	—	6	4	no	—
167	C₂×Dic₅	—	12	8	no	—
168	Dic₁₀	—	2	8	no	—
169	Dic₁₀	—	6	8	no	—
170	Dic₁₀	—	12	8	no	—
171	C₅×C₈	—	3	4	no	—
172	C₅×C₈	D₃×D₄	1	4	yes	—
173	C₂²×Q₈	—	15	4	no	—
174	C₂×Q₁₆	—	5	4	no	—
175	C₂×Q₁₆	—	15	8	no	—
176	C₂×Q₁₆	—	15	4	no	—
177	C₂×Q₁₆	—	30	16	no	—
178	C₂²×C₈	—	3	2	no	—
179	C₄⋊Q₈	—	5	2	no	—
180	C₄⋊Q₈	—	15	4	no	—
181	C₄⋊Q₈	—	15	2	no	—
182	C₄⋊Q₈	—	30	4	no	—
183	C₂×C₄⋊C₄	—	30	4	no	—
184	C₂×C₄²	—	3	1	no	—
185	C₄×C₈	—	3	2	no	—
186	C₄×C₈	—	3	1	no	—
187	C₄×C₈	D₃×D₅	1	1	yes	characteristic
188	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
189	C₂×C₃×C₅	C₂²×Q₁₆	1	2	yes	—
190	C₅×D₃	#494	1	4	yes	complemented
191	C₂²×D₃	C₂×D₂₀	1	1	yes	characteristic
192	C₃×Q₈	—	10	8	no	—
193	C₂×C₃×C₄	—	10	4	no	—
194	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
195	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
196	C₂×Dic₃	—	10	4	no	—
197	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
198	C₂×Dic₃	C₂×D₂₀	1	2	yes	—
199	C₄×D₃	—	20	8	no	—
200	C₄×D₃	Dic₂₀	1	8	yes	complemented
201	C₄×D₃	C₂×D₂₀	1	4	yes	—
202	Dic₆	—	10	8	no	—
203	Dic₆	—	20	8	no	—
204	C₃×C₈	C₂×D₂₀	1	4	yes	—
205	C₃⋊C₈	C₂×D₂₀	1	4	yes	—
206	C₂²×C₅	—	3	2	no	—
207	C₂²×C₅	—	3	4	no	—
208	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
209	C₄×C₅	—	3	2	no	—
210	C₄×C₅	—	3	4	no	—
211	C₄×C₅	D₃×Q₁₆	1	4	yes	complemented
212	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
213	Dic₅	—	4	4	no	—
214	Dic₅	—	12	4	no	—
215	C₂×Q₈	—	5	4	no	—
216	C₂×Q₈	—	15	4	no	—
217	C₂×Q₈	—	30	4	no	—
218	C₂×Q₈	—	30	16	no	—
219	C₂²×C₄	—	3	2	no	—
220	C₂²×C₄	—	3	1	no	—
221	C₂²×C₄	—	30	4	no	—
222	Q₁₆	—	10	8	no	—
223	Q₁₆	—	30	16	no	—
224	Q₁₆	—	30	8	no	—
225	C₂×C₈	—	3	2	no	—
226	C₂×C₈	—	3	8	no	—
227	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
228	C₄⋊C₄	—	10	4	no	—
229	C₄⋊C₄	—	30	8	no	—
230	C₄⋊C₄	—	30	4	no	—
231	C₄²	—	3	2	no	—
232	C₄²	—	3	1	no	—
233	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
234	C₃×C₅	C₂×#494	1	1	yes	characteristic, complemented, Hall
235	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
236	C₂×D₃	#4020	1	2	yes	—
237	C₂×D₃	C₂×Dic₂₀	1	4	yes	—
238	C₃×C₄	—	20	4	no	—
239	C₃×C₄	C₂×Dic₂₀	1	4	yes	complemented
240	C₃×C₄	C₂²×D₂₀	1	2	yes	—
241	Dic₃	—	20	4	no	—
242	Dic₃	#4020	1	2	yes	—
243	Dic₃	C₂×Dic₂₀	1	4	yes	complemented
244	C₂×C₅	—	3	4	no	—
245	C₂×C₅	D₃×#127	1	1	yes	characteristic
246	C₂×C₅	C₂×D₃×Q₁₆	1	2	yes	—
247	C₂³	—	3	1	no	—
248	Q₈	—	10	8	no	—
249	Q₈	—	30	8	no	—
250	Q₈	—	60	8	no	—
251	C₂×C₄	—	3	2	no	—
252	C₂×C₄	—	3	1	no	—
253	C₂×C₄	—	3	4	no	—
254	C₂×C₄	—	3	8	no	—
255	C₂×C₄	—	10	4	no	—
256	C₂×C₄	—	30	4	no	—
257	C₂×C₄	—	60	8	no	—
258	C₂×C₄	D₃×D₂₀	1	2	yes	—
259	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
260	C₈	—	3	4	no	—
261	C₈	D₃×D₂₀	1	4	yes	—
262	C₂×C₃	C₂×#4020	1	1	yes	characteristic
263	C₂×C₃	C₂²×Dic₂₀	1	2	yes	—
264	D₃	#64988	1	4	yes	direct product factor
265	C₅	D₃×#494	1	1	yes	characteristic, complemented, Sylow
266	C₂²	—	3	4	no	—
267	C₂²	—	3	2	no	—
268	C₂²	C₂×D₃×D₂₀	1	1	yes	characteristic
269	C₄	—	3	4	no	—
270	C₄	—	3	2	no	—
271	C₄	—	20	4	no	—
272	C₄	—	60	4	no	—
273	C₄	D₃×Dic₂₀	1	4	yes	complemented
274	C₄	C₂×D₃×D₂₀	1	2	yes	—
275	C₃	C₂×#64988	1	1	yes	characteristic, complemented, Sylow
276	C₂	—	3	4	no	—
277	C₂	D₃×#4020	1	1	yes	characteristic
278	C₂	C₂×D₃×Dic₂₀	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	C₂×#494
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
3. #11750800	C₂	semidirect
5. C₃×#64988	C₂	semidirect
6. #11748033	C₂	semidirect
7. #11747100	C₂	semidirect
31. #64988	D₃	direct (N × H)
81. C₄×C₅×D₃	Q₁₆	semidirect
133. C₃×C₄×C₅	C₂×Q₁₆	semidirect
138. C₅×Dic₃	C₂×Q₁₆	semidirect
190. C₅×D₃	#494	semidirect
200. C₄×D₃	Dic₂₀	semidirect
211. C₄×C₅	D₃×Q₁₆	semidirect
234. C₃×C₅	C₂×#494	semidirect
239. C₃×C₄	C₂×Dic₂₀	semidirect
243. Dic₃	C₂×Dic₂₀	semidirect
264. D₃	#64988	direct (N × H)
265. C₅	D₃×#494	semidirect
273. C₄	D₃×Dic₂₀	semidirect
275. C₃	C₂×#64988	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×Dic₂₀	2
D₃×#4015	2
#11750800	2
C₄×C₅×D₃×C₈	2
C₃×#64988	2
#11748033	2
#11747100	2
C₂×#64988	3
D₃×#494	5

Subgroups — D3×#64988 #14438813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#64988 #14438813