Subgroups — D₃×#64882 #14285531

Order 1920.

400 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	D₃×C₄⋊#170	C₂	1	2	yes	maximal
2	D₃×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
3	#11746753	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64882	C₂	1	1	yes	maximal, characteristic, complemented
5	#11746514	C₂	1	2	yes	maximal, complemented
6	C₂×#64882	—	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×#335	—	5	1	no	maximal, Hall
19	C₂×C₄⋊#170	—	3	2	no	—
20	C₂×C₈×Dic₅	—	3	1	no	—
21	#64882	—	3	2	no	—
22	#64882	—	3	1	no	—
23	#64882	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	C₈	1	4	yes	complemented
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	—	2	2	no	—
40	D₃×C₄⋊C₈	—	5	2	no	—
41	C₄×D₃×C₈	—	5	1	no	—
42	C₃×#335	—	5	1	no	—
43	#4479	—	5	2	no	—
44	#4458	—	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×#335	—	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	D₈	1	2	yes	—
68	D₃×Dic₅	Q₁₆	1	2	yes	—
69	C₃⋊#170	—	4	2	no	—
70	C₃×#170	—	4	2	no	—
71	C₃×C₅×C₈	C₂×C₈	1	2	yes	complemented
72	C₃⋊#168	—	2	1	no	—
73	C₃×#168	—	2	1	no	—
74	C₅×C₃⋊C₈	C₂×C₈	1	2	yes	complemented
75	C₂×D₃×C₈	—	5	1	no	—
76	C₂×D₃×C₈	—	10	2	no	—
77	C₂×D₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
78	C₄²×D₃	—	5	1	no	—
79	C₃×C₄⋊C₈	—	5	2	no	—
80	C₃×C₄×C₈	—	5	1	no	—
81	Dic₃⋊C₈	—	10	2	no	—
82	C₈×Dic₃	—	5	1	no	—
83	C₈×Dic₃	—	5	1	no	—
84	C₄⋊(C₃⋊C₈)	—	5	2	no	—
85	C₄×C₃⋊C₈	—	5	1	no	—
86	C₂²×C₄×C₅	—	3	1	no	—
87	C₂²×Dic₅	—	3	1	no	—
88	C₂²×Dic₅	—	3	1	no	—
89	C₂×#170	—	2	2	no	—
90	C₂×#170	—	6	2	no	—
91	C₂×#170	—	12	4	no	—
92	C₂×C₅×C₈	—	3	1	no	—
93	C₂×C₅×C₈	—	3	4	no	—
94	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
95	C₄×Dic₅	—	3	1	no	—
96	C₄×Dic₅	—	3	1	no	—
97	C₄×Dic₅	—	3	1	no	—
98	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
99	C₂×#168	—	3	1	no	—
100	C₂×#168	—	6	2	no	—
101	C₂×#168	C₄×D₃	1	1	yes	characteristic
102	C₂×C₄⋊C₈	—	15	2	no	—
103	C₂×C₄×C₈	—	15	1	no	—
104	#335	—	5	1	no	—
105	#335	—	15	1	no	—
106	#335	—	15	2	no	—
107	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₅×D₃	C₄⋊C₈	1	2	yes	—
109	C₂×C₅×D₃	#107	1	2	yes	—
110	C₂×C₅×D₃	#108	1	2	yes	—
111	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
112	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
113	Dic₁₅	—	2	1	no	—
114	Dic₁₅	#107	1	2	yes	—
115	C₃×Dic₅	—	2	1	no	—
116	C₃×Dic₅	C₂×D₈	1	1	yes	characteristic
117	C₃×Dic₅	C₂×Q₁₆	1	1	yes	characteristic
118	C₅×Dic₃	C₄⋊C₈	1	2	yes	—
119	C₂×C₄×D₃	—	5	1	no	—
120	C₂×C₄×D₃	—	5	1	no	—
121	C₂×C₄×D₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
122	C₂×C₃×C₈	—	5	1	no	—
123	C₂×C₃×C₈	—	10	2	no	—
124	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
125	C₃×C₄²	—	5	1	no	—
126	C₄×Dic₃	—	5	1	no	—
127	C₄×Dic₃	—	5	1	no	—
128	C₄×Dic₃	—	5	1	no	—
129	C₂×C₃⋊C₈	—	5	1	no	—
130	C₂×C₃⋊C₈	—	10	2	no	—
131	C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
132	D₃×C₈	—	10	2	no	—
133	D₃×C₈	—	20	4	no	—
134	D₃×C₈	#170	1	4	yes	complemented
135	C₂³×C₅	—	3	1	no	—
136	C₂×C₄×C₅	—	3	1	no	—
137	C₂×C₄×C₅	—	3	2	no	—
138	C₂×C₄×C₅	—	3	2	no	—
139	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
140	C₂×Dic₅	—	3	1	no	—
141	C₂×Dic₅	—	3	2	no	—
142	C₂×Dic₅	—	3	2	no	—
143	C₂×Dic₅	—	3	1	no	—
144	C₂×Dic₅	—	6	2	no	—
145	C₂×Dic₅	D₃×D₄	1	1	yes	characteristic
146	C₂×Dic₅	D₃×Q₈	1	1	yes	characteristic
147	#170	—	4	2	no	—
148	#170	—	12	2	no	—
149	C₅×C₈	—	3	2	no	—
150	C₅×C₈	D₃×C₈	1	2	yes	complemented
151	#168	—	2	1	no	—
152	#168	—	6	1	no	—
153	C₂²×C₈	—	3	1	no	—
154	C₂²×C₈	—	15	1	no	—
155	C₂²×C₈	—	30	2	no	—
156	C₂×C₄²	—	15	1	no	—
157	C₄⋊C₈	—	5	2	no	—
158	C₄⋊C₈	—	15	2	no	—
159	C₄⋊C₈	—	30	2	no	—
160	C₄×C₈	—	5	1	no	—
161	C₄×C₈	—	15	1	no	—
162	C₄×C₈	—	15	1	no	—
163	C₄×C₈	—	15	1	no	—
164	C₂×C₃×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
165	C₂×C₃×C₅	C₂×#107	1	1	yes	characteristic
166	C₂×C₃×C₅	C₂×#108	1	1	yes	characteristic
167	C₅×D₃	#335	1	4	yes	complemented
168	C₂²×D₃	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
169	C₂×C₃×C₄	—	5	1	no	—
170	C₂×C₃×C₄	—	5	1	no	—
171	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
172	C₂×Dic₃	—	5	1	no	—
173	C₂×Dic₃	—	5	1	no	—
174	C₂×Dic₃	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
175	C₄×D₃	—	5	2	no	—
176	C₄×D₃	—	5	2	no	—
177	C₄×D₃	—	10	2	no	—
178	C₄×D₃	#700	1	2	yes	—
179	C₄×D₃	C₂×#170	1	2	yes	—
180	C₃×C₈	—	10	1	no	—
181	C₃×C₈	—	20	2	no	—
182	C₃×C₈	C₂×#170	1	2	yes	complemented
183	C₃⋊C₈	—	10	1	no	—
184	C₃⋊C₈	—	20	2	no	—
185	C₃⋊C₈	C₂×#170	1	2	yes	complemented
186	C₂²×C₅	—	3	2	no	—
187	C₂²×C₅	—	3	2	no	—
188	C₂²×C₅	—	3	2	no	—
189	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
190	C₄×C₅	—	3	2	no	—
191	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
192	C₄×C₅	D₃×M₁₆	1	1	yes	characteristic
193	Dic₅	—	2	1	no	—
194	Dic₅	—	3	2	no	—
195	Dic₅	—	6	1	no	—
196	Dic₅	D₃×D₈	1	1	yes	characteristic
197	Dic₅	D₃×Q₁₆	1	1	yes	characteristic
198	C₂²×C₄	—	3	1	no	—
199	C₂²×C₄	—	15	1	no	—
200	C₂²×C₄	—	15	1	no	—
201	C₂×C₈	—	3	1	no	—
202	C₂×C₈	—	3	4	no	—
203	C₂×C₈	—	5	1	no	—
204	C₂×C₈	—	10	2	no	—
205	C₂×C₈	—	15	1	no	—
206	C₂×C₈	—	30	2	no	—
207	C₂×C₈	—	30	2	no	—
208	C₂×C₈	—	60	4	no	—
209	C₂×C₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
210	C₄²	—	5	1	no	—
211	C₄²	—	15	1	no	—
212	C₄²	—	15	1	no	—
213	C₄²	—	15	1	no	—
214	C₃×C₅	C₂×#335	1	1	yes	characteristic, complemented, Hall
215	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
216	C₂×D₃	#3994	1	2	yes	—
217	C₂×D₃	#3996	1	2	yes	—
218	C₂×D₃	C₄⋊#170	1	2	yes	—
219	C₃×C₄	—	5	1	no	—
220	C₃×C₄	—	5	1	no	—
221	C₃×C₄	—	10	1	no	—
222	C₃×C₄	C₂×#700	1	1	yes	characteristic
223	C₃×C₄	C₂²×#170	1	1	yes	characteristic
224	Dic₃	—	5	2	no	—
225	Dic₃	—	10	1	no	—
226	Dic₃	C₄⋊#170	1	2	yes	—
227	C₂×C₅	—	3	4	no	—
228	C₂×C₅	D₃×C₄⋊C₈	1	1	yes	characteristic
229	C₂×C₅	D₃×#107	1	1	yes	characteristic
230	C₂×C₅	D₃×#108	1	1	yes	characteristic
231	C₂³	—	3	1	no	—
232	C₂×C₄	—	3	1	no	—
233	C₂×C₄	—	3	2	no	—
234	C₂×C₄	—	3	2	no	—
235	C₂×C₄	—	5	1	no	—
236	C₂×C₄	—	5	1	no	—
237	C₂×C₄	—	15	2	no	—
238	C₂×C₄	—	15	2	no	—
239	C₂×C₄	—	15	1	no	—
240	C₂×C₄	—	15	1	no	—
241	C₂×C₄	—	30	2	no	—
242	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
243	C₈	—	3	2	no	—
244	C₈	—	10	1	no	—
245	C₈	—	20	2	no	—
246	C₈	—	30	1	no	—
247	C₈	—	60	2	no	—
248	C₈	D₃×#170	1	2	yes	complemented
249	C₂×C₃	C₂×#3994	1	1	yes	characteristic
250	C₂×C₃	C₂×#3996	1	1	yes	characteristic
251	C₂×C₃	C₂×C₄⋊#170	1	1	yes	characteristic
252	D₃	#64882	1	4	yes	direct product factor
253	C₅	D₃×#335	1	1	yes	characteristic, complemented, Sylow
254	C₂²	—	3	2	no	—
255	C₂²	—	3	2	no	—
256	C₂²	—	3	2	no	—
257	C₂²	D₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
258	C₄	—	3	2	no	—
259	C₄	—	5	1	no	—
260	C₄	—	5	1	no	—
261	C₄	—	10	1	no	—
262	C₄	—	15	2	no	—
263	C₄	—	30	1	no	—
264	C₄	D₃×#700	1	1	yes	characteristic
265	C₄	C₂×D₃×#170	1	1	yes	characteristic
266	C₃	C₂×#64882	1	1	yes	characteristic, complemented, Sylow
267	C₂	—	3	4	no	—
268	C₂	D₃×#3994	1	1	yes	characteristic
269	C₂	D₃×#3996	1	1	yes	characteristic
270	C₂	D₃×C₄⋊#170	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×#335
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. #11746753	C₂	semidirect
4. C₃×#64882	C₂	semidirect
5. #11746514	C₂	semidirect
23. #64882	D₃	direct (N × H)
34. C₅×D₃×C₈	C₈	semidirect
71. C₃×C₅×C₈	C₂×C₈	semidirect
74. C₅×C₃⋊C₈	C₂×C₈	semidirect
134. D₃×C₈	#170	semidirect
150. C₅×C₈	D₃×C₈	semidirect
167. C₅×D₃	#335	semidirect
182. C₃×C₈	C₂×#170	semidirect
185. C₃⋊C₈	C₂×#170	semidirect
214. C₃×C₅	C₂×#335	semidirect
248. C₈	D₃×#170	semidirect
252. D₃	#64882	direct (N × H)
253. C₅	D₃×#335	semidirect
266. C₃	C₂×#64882	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
#11746753	2
C₃×#64882	2
#11746514	2
C₂×#64882	3
D₃×#335	5

Subgroups — D3×#64882 #14285531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#64882 #14285531