Subgroups — D₃×#64883 #14285504

Order 1920.

400 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₄⋊#170	C₂	1	2	yes	maximal
2	D₃×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
3	#11746754	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64883	C₂	1	1	yes	maximal, characteristic, complemented
5	#11746513	C₂	1	2	yes	maximal, complemented
6	C₂×#64883	—	3	1	no	maximal, Hall
7	C₂×D₃×#170	—	2	2	no	—
8	C₂×C₅×D₃×C₈	C₄	1	1	yes	characteristic
9	C₄×D₃×Dic₅	C₂²	1	1	yes	characteristic
10	C₂×D₃×#168	C₄	1	1	yes	characteristic
11	C₄⋊(C₃⋊#170)	C₂²	1	2	yes	—
12	C₃×C₄⋊#170	C₂²	1	2	yes	—
13	Dic₃⋊#170	—	2	2	no	—
14	C₈×Dic₁₅	C₄	1	1	yes	characteristic
15	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
16	#90951	C₄	1	1	yes	characteristic
17	Dic₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
18	D₃×#334	—	5	1	no	maximal, Hall
19	C₂×C₄⋊#170	—	3	2	no	—
20	C₂×C₈×Dic₅	—	3	1	no	—
21	#64883	—	3	2	no	—
22	#64883	—	3	1	no	—
23	#64883	D₃	1	1	yes	characteristic, direct product factor
24	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
25	C₂×D₃×Dic₅	D₄	1	1	yes	characteristic
26	C₂×D₃×Dic₅	Q₈	1	1	yes	characteristic
27	C₂×C₃⋊#170	—	2	2	no	—
28	C₂×C₃×#170	—	2	2	no	—
29	D₃×#170	—	4	4	no	—
30	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
31	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
32	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic
33	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
34	C₅×D₃×C₈	—	2	2	no	—
35	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
36	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
37	Dic₃×Dic₅	D₄	1	1	yes	characteristic
38	Dic₃×Dic₅	Q₈	1	1	yes	characteristic
39	D₃×#168	C₈	1	4	yes	complemented
40	D₃×C₄⋊C₈	—	5	2	no	—
41	C₄×D₃×C₈	—	5	1	no	—
42	C₃×#334	—	5	1	no	—
43	#4480	—	5	2	no	—
44	#4457	—	5	1	no	—
45	C₂²×#170	—	6	2	no	—
46	C₂²×C₅×C₈	—	3	1	no	—
47	C₂×C₄×Dic₅	—	3	1	no	—
48	C₂²×#168	—	3	1	no	—
49	C₄⋊#170	—	3	2	no	—
50	C₄⋊#170	—	6	2	no	—
51	C₄⋊#170	C₂×D₃	1	2	yes	—
52	C₈×Dic₅	—	3	1	no	—
53	C₈×Dic₅	—	3	1	no	—
54	C₈×Dic₅	—	3	1	no	—
55	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
56	C₂×#334	—	15	1	no	Sylow
57	C₂²×C₅×D₃	C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
59	C₂×Dic₁₅	C₄⋊C₄	1	1	yes	characteristic
60	C₂×Dic₁₅	C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₅×Dic₃	C₄⋊C₄	1	1	yes	characteristic
62	C₄×C₅×D₃	C₂×C₈	1	2	yes	—
63	C₄×C₅×D₃	M₁₆	1	2	yes	—
64	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
65	C₂×C₃×Dic₅	C₂×Q₈	1	1	yes	characteristic
66	D₃×Dic₅	—	2	2	no	—
67	D₃×Dic₅	SD₁₆	1	4	yes	—
68	C₃⋊#170	—	4	2	no	—
69	C₃×#170	—	4	2	no	—
70	C₃×C₅×C₈	—	2	1	no	—
71	C₃⋊#168	C₂×C₈	1	2	yes	complemented
72	C₃×#168	C₂×C₈	1	2	yes	complemented
73	C₅×C₃⋊C₈	—	2	1	no	—
74	C₂×D₃×C₈	—	5	1	no	—
75	C₂×D₃×C₈	—	10	2	no	—
76	C₂×D₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
77	C₄²×D₃	—	5	1	no	—
78	C₃×C₄⋊C₈	—	5	2	no	—
79	C₃×C₄×C₈	—	5	1	no	—
80	Dic₃⋊C₈	—	10	2	no	—
81	C₈×Dic₃	—	5	1	no	—
82	C₈×Dic₃	—	5	1	no	—
83	C₄⋊(C₃⋊C₈)	—	5	2	no	—
84	C₄×C₃⋊C₈	—	5	1	no	—
85	C₂²×C₄×C₅	—	3	1	no	—
86	C₂²×Dic₅	—	3	1	no	—
87	C₂²×Dic₅	—	3	1	no	—
88	C₂×#170	—	2	2	no	—
89	C₂×#170	—	6	2	no	—
90	C₂×#170	—	12	4	no	—
91	C₂×C₅×C₈	—	3	1	no	—
92	C₂×C₅×C₈	—	6	2	no	—
93	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
94	C₄×Dic₅	—	3	1	no	—
95	C₄×Dic₅	—	3	1	no	—
96	C₄×Dic₅	—	3	1	no	—
97	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
98	C₂×#168	—	3	1	no	—
99	C₂×#168	—	3	4	no	—
100	C₂×#168	C₄×D₃	1	1	yes	characteristic
101	C₂×C₄⋊C₈	—	15	2	no	—
102	C₂×C₄×C₈	—	15	1	no	—
103	#334	—	5	1	no	—
104	#334	—	15	1	no	—
105	#334	—	15	2	no	—
106	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₅×D₃	C₄⋊C₈	1	2	yes	—
108	C₂×C₅×D₃	#106	1	2	yes	—
109	C₂×C₅×D₃	#108	1	2	yes	—
110	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
111	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
112	Dic₁₅	—	2	1	no	—
113	Dic₁₅	#106	1	2	yes	—
114	C₃×Dic₅	—	2	1	no	—
115	C₃×Dic₅	C₂×SD₁₆	1	2	yes	—
116	C₅×Dic₃	C₄⋊C₈	1	2	yes	—
117	C₂×C₄×D₃	—	5	1	no	—
118	C₂×C₄×D₃	—	5	1	no	—
119	C₂×C₄×D₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
120	C₂×C₃×C₈	—	5	1	no	—
121	C₂×C₃×C₈	—	10	2	no	—
122	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
123	C₃×C₄²	—	5	1	no	—
124	C₄×Dic₃	—	5	1	no	—
125	C₄×Dic₃	—	5	1	no	—
126	C₄×Dic₃	—	5	1	no	—
127	C₂×C₃⋊C₈	—	5	1	no	—
128	C₂×C₃⋊C₈	—	10	2	no	—
129	C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
130	D₃×C₈	—	2	2	no	—
131	D₃×C₈	—	5	4	no	—
132	D₃×C₈	—	20	4	no	—
133	C₂³×C₅	—	3	1	no	—
134	C₂×C₄×C₅	—	3	1	no	—
135	C₂×C₄×C₅	—	3	2	no	—
136	C₂×C₄×C₅	—	3	2	no	—
137	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
138	C₂×Dic₅	—	3	1	no	—
139	C₂×Dic₅	—	3	4	no	—
140	C₂×Dic₅	—	3	1	no	—
141	C₂×Dic₅	—	6	2	no	—
142	C₂×Dic₅	D₃×D₄	1	1	yes	characteristic
143	C₂×Dic₅	D₃×Q₈	1	1	yes	characteristic
144	#170	—	4	2	no	—
145	#170	—	12	2	no	—
146	C₅×C₈	—	2	1	no	—
147	C₅×C₈	—	6	1	no	—
148	#168	—	3	2	no	—
149	#168	D₃×C₈	1	2	yes	complemented
150	C₂²×C₈	—	3	1	no	—
151	C₂²×C₈	—	15	1	no	—
152	C₂²×C₈	—	30	2	no	—
153	C₂×C₄²	—	15	1	no	—
154	C₄⋊C₈	—	5	2	no	—
155	C₄⋊C₈	—	15	2	no	—
156	C₄⋊C₈	—	30	2	no	—
157	C₄×C₈	—	5	1	no	—
158	C₄×C₈	—	15	1	no	—
159	C₄×C₈	—	15	1	no	—
160	C₄×C₈	—	15	1	no	—
161	C₂×C₃×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
162	C₂×C₃×C₅	C₂×#106	1	1	yes	characteristic
163	C₂×C₃×C₅	C₂×#108	1	1	yes	characteristic
164	C₅×D₃	#334	1	4	yes	complemented
165	C₂²×D₃	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
166	C₂×C₃×C₄	—	5	1	no	—
167	C₂×C₃×C₄	—	5	1	no	—
168	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
169	C₂×Dic₃	—	5	1	no	—
170	C₂×Dic₃	—	5	1	no	—
171	C₂×Dic₃	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
172	C₄×D₃	—	5	4	no	—
173	C₄×D₃	—	10	2	no	—
174	C₄×D₃	D₅⋊C₈	1	2	yes	—
175	C₄×D₃	#704	1	2	yes	—
176	C₃×C₈	—	2	1	no	—
177	C₃×C₈	—	5	2	no	—
178	C₃×C₈	—	20	2	no	—
179	C₃⋊C₈	—	2	1	no	—
180	C₃⋊C₈	—	5	2	no	—
181	C₃⋊C₈	—	20	2	no	—
182	C₂²×C₅	—	3	2	no	—
183	C₂²×C₅	—	3	2	no	—
184	C₂²×C₅	—	3	2	no	—
185	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
186	C₄×C₅	—	3	2	no	—
187	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
188	C₄×C₅	D₃×M₁₆	1	1	yes	characteristic
189	Dic₅	—	2	1	no	—
190	Dic₅	—	3	2	no	—
191	Dic₅	—	6	1	no	—
192	Dic₅	D₃×SD₁₆	1	2	yes	—
193	C₂²×C₄	—	3	1	no	—
194	C₂²×C₄	—	15	1	no	—
195	C₂²×C₄	—	15	1	no	—
196	C₂×C₈	—	3	1	no	—
197	C₂×C₈	—	5	1	no	—
198	C₂×C₈	—	6	2	no	—
199	C₂×C₈	—	10	2	no	—
200	C₂×C₈	—	15	4	no	—
201	C₂×C₈	—	15	1	no	—
202	C₂×C₈	—	30	2	no	—
203	C₂×C₈	—	60	4	no	—
204	C₂×C₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
205	C₄²	—	5	1	no	—
206	C₄²	—	15	1	no	—
207	C₄²	—	15	1	no	—
208	C₄²	—	15	1	no	—
209	C₃×C₅	C₂×#334	1	1	yes	characteristic, complemented, Hall
210	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
211	C₂×D₃	#3993	1	2	yes	—
212	C₂×D₃	#3996	1	2	yes	—
213	C₂×D₃	#4004	1	2	yes	—
214	C₃×C₄	—	5	2	no	—
215	C₃×C₄	—	10	1	no	—
216	C₃×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
217	C₃×C₄	C₂×#704	1	1	yes	characteristic
218	Dic₃	—	5	2	no	—
219	Dic₃	—	10	1	no	—
220	Dic₃	#4004	1	2	yes	—
221	C₂×C₅	—	3	4	no	—
222	C₂×C₅	D₃×C₄⋊C₈	1	1	yes	characteristic
223	C₂×C₅	D₃×#106	1	1	yes	characteristic
224	C₂×C₅	D₃×#108	1	1	yes	characteristic
225	C₂³	—	3	1	no	—
226	C₂×C₄	—	3	1	no	—
227	C₂×C₄	—	3	2	no	—
228	C₂×C₄	—	3	2	no	—
229	C₂×C₄	—	5	1	no	—
230	C₂×C₄	—	5	1	no	—
231	C₂×C₄	—	15	4	no	—
232	C₂×C₄	—	15	1	no	—
233	C₂×C₄	—	15	1	no	—
234	C₂×C₄	—	30	2	no	—
235	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
236	C₈	—	2	1	no	—
237	C₈	—	5	2	no	—
238	C₈	—	6	1	no	—
239	C₈	—	15	2	no	—
240	C₈	—	20	2	no	—
241	C₈	—	60	2	no	—
242	C₂×C₃	C₂×#3993	1	1	yes	characteristic
243	C₂×C₃	C₂×#3996	1	1	yes	characteristic
244	C₂×C₃	C₂×#4004	1	1	yes	characteristic
245	D₃	#64883	1	4	yes	direct product factor
246	C₅	D₃×#334	1	1	yes	characteristic, complemented, Sylow
247	C₂²	—	3	2	no	—
248	C₂²	—	3	2	no	—
249	C₂²	—	3	2	no	—
250	C₂²	D₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
251	C₄	—	3	2	no	—
252	C₄	—	5	2	no	—
253	C₄	—	10	1	no	—
254	C₄	—	15	2	no	—
255	C₄	—	30	1	no	—
256	C₄	D₃×D₅⋊C₈	1	1	yes	characteristic
257	C₄	D₃×#704	1	1	yes	characteristic
258	C₃	C₂×#64883	1	1	yes	characteristic, complemented, Sylow
259	C₂	—	3	4	no	—
260	C₂	D₃×#3993	1	1	yes	characteristic
261	C₂	D₃×#3996	1	1	yes	characteristic
262	C₂	D₃×#4004	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×C₄⋊AGL(1,𝔽₅)
commutator	C₃×C₄×C₅	C₂²×C₈
Frattini	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂²×C₅×D₃	C₄⋊C₄
cosocle	C₃×C₄×Dic₅	C₂³
hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₂×#334
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
3. #11746754	C₂	semidirect
4. C₃×#64883	C₂	semidirect
5. #11746513	C₂	semidirect
23. #64883	D₃	direct (N × H)
39. D₃×#168	C₈	semidirect
71. C₃⋊#168	C₂×C₈	semidirect
72. C₃×#168	C₂×C₈	semidirect
149. #168	D₃×C₈	semidirect
164. C₅×D₃	#334	semidirect
209. C₃×C₅	C₂×#334	semidirect
245. D₃	#64883	direct (N × H)
246. C₅	D₃×#334	semidirect
258. C₃	C₂×#64883	semidirect

Maximal subgroups

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

subgroup	index
D₃×C₄⋊#170	2
D₃×C₈×Dic₅	2
#11746754	2
C₃×#64883	2
#11746513	2
C₂×#64883	3
D₃×#334	5

Subgroups — D3×#64883 #14285504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#64883 #14285504