Subgroups — D₃×#64887 #14312817

Order 1920.

544 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×D₃×#674	C₂	1	2	yes	maximal, complemented
3	#11746758	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64887	C₂	1	1	yes	maximal, characteristic, complemented
5	#11746547	C₂	1	2	yes	maximal, complemented
6	C₂×#64887	—	3	1	no	maximal, Hall
7	C₂×C₄×D₃×D₅	C₄	1	1	yes	characteristic
8	C₂×C₈×D₁₅	C₄	1	1	yes	characteristic
9	C₂×C₅×D₃×C₈	C₄	1	1	yes	characteristic
10	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
11	C₂×#6648	C₂²	1	1	yes	characteristic
12	C₂×D₃×#168	C₂²	1	1	yes	characteristic
13	C₂×D₅×C₃⋊C₈	C₄	1	1	yes	characteristic
14	D₃×C₈×D₅	—	2	4	no	—
15	C₂×C₃⋊#674	C₂²	1	2	yes	complemented
16	C₂×C₃×#674	C₂²	1	2	yes	complemented
17	D₃×#674	—	2	4	no	—
18	D₃×C₂²⋊C₁₆	—	5	1	no	maximal, Hall
19	C₂²×C₈×D₅	—	3	1	no	—
20	C₂²×#674	—	3	2	no	—
21	#64887	—	3	1	no	—
22	#64887	—	3	2	no	—
23	#64887	D₃	1	1	yes	characteristic, direct product factor
24	C₂²×D₃×D₅	C₈	1	1	yes	characteristic
25	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
28	C₂×#1200	C₈	1	1	yes	characteristic
29	C₂×D₃×Dic₅	C₈	1	1	yes	characteristic
30	C₂×D₅×Dic₃	C₈	1	1	yes	characteristic
31	C₄×D₃×D₅	—	2	2	no	—
32	C₄×D₃×D₅	—	2	2	no	—
33	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
34	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic
35	C₈×D₁₅	—	2	2	no	—
36	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₅×D₃×C₈	—	2	2	no	—
38	C₂×C₃×#168	C₂³	1	1	yes	characteristic
39	C₃×C₈×D₅	—	2	2	no	—
40	#6648	—	2	2	no	—
41	D₃×#168	D₄	1	4	yes	—
42	D₅×C₃⋊C₈	—	2	2	no	—
43	C₃⋊#674	—	2	2	no	—
44	C₃×#674	—	2	2	no	—
45	C₂²×D₃×C₈	—	5	1	no	—
46	C₂×D₃×C₁₆	—	5	2	no	—
47	C₃×C₂²⋊C₁₆	—	5	1	no	—
48	#4549	—	5	1	no	—
49	(C₂×D₃)⋊C₁₆	—	5	2	no	—
50	C₂²×C₄×D₅	—	3	1	no	—
51	C₂²×C₅×C₈	—	3	1	no	—
52	C₂²×#168	—	3	1	no	—
53	C₂×C₈×D₅	—	3	1	no	—
54	C₂×C₈×D₅	—	3	1	no	—
55	C₂×C₈×D₅	—	3	1	no	—
56	C₂×C₈×D₅	—	6	4	no	—
57	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
58	C₂×#674	—	3	2	no	—
59	C₂×#674	—	6	4	no	—
60	C₂×#674	C₂×D₃	1	2	yes	complemented
61	C₂×C₂²⋊C₁₆	—	15	1	no	Sylow
62	C₂²×D₁₅	C₂×C₈	1	1	yes	characteristic
63	C₂²×C₅×D₃	C₂×C₈	1	1	yes	characteristic
64	C₂²×C₃×D₅	C₂×C₈	1	1	yes	characteristic
65	C₂×D₃×D₅	—	2	2	no	—
66	C₂×D₃×D₅	—	2	2	no	—
67	C₂×D₃×D₅	C₁₆	1	4	yes	complemented
68	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
69	C₂×Dic₁₅	C₂×C₈	1	1	yes	characteristic
70	C₄×D₁₅	—	2	1	no	—
71	C₄×D₁₅	—	2	1	no	—
72	C₂×C₅×Dic₃	C₂×C₈	1	1	yes	characteristic
73	C₄×C₅×D₃	C₂²⋊C₄	1	2	yes	—
74	C₄×C₅×D₃	M₁₆	1	2	yes	—
75	C₂×C₃×Dic₅	C₂×C₈	1	1	yes	characteristic
76	C₃×C₄×D₅	—	2	1	no	—
77	C₃×C₄×D₅	—	2	1	no	—
78	#1200	—	2	2	no	—
79	D₃×Dic₅	—	2	2	no	—
80	D₅×Dic₃	—	2	2	no	—
81	C₃×C₅×C₈	—	2	1	no	—
82	C₃⋊#168	C₂²⋊C₄	1	2	yes	—
83	C₃×#168	C₂×D₄	1	2	yes	—
84	C₅×C₃⋊C₈	—	2	1	no	—
85	C₂²×C₄×D₃	—	5	1	no	—
86	C₂²×C₃×C₈	—	5	1	no	—
87	C₂²×C₃⋊C₈	—	5	1	no	—
88	C₂×D₃×C₈	—	5	1	no	—
89	C₂×D₃×C₈	—	5	1	no	—
90	C₂×D₃×C₈	—	5	1	no	—
91	C₂×D₃×C₈	—	10	4	no	—
92	C₂×D₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
93	C₂×C₃×C₁₆	—	5	2	no	—
94	C₂×C₃⋊C₁₆	—	5	2	no	—
95	D₃×C₁₆	—	10	4	no	—
96	C₂³×D₅	—	3	1	no	—
97	C₂²×C₄×C₅	—	3	1	no	—
98	C₂²×Dic₅	—	3	1	no	—
99	C₂×C₄×D₅	—	3	1	no	—
100	C₂×C₄×D₅	—	3	1	no	—
101	C₂×C₄×D₅	—	3	1	no	—
102	C₂×C₄×D₅	—	6	2	no	—
103	C₂×C₄×D₅	—	6	2	no	—
104	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
105	C₂×C₅×C₈	—	3	1	no	—
106	C₂×C₅×C₈	—	6	2	no	—
107	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
108	C₂×#168	—	3	1	no	—
109	C₂×#168	—	3	4	no	—
110	C₂×#168	C₂²×D₃	1	1	yes	characteristic
111	C₈×D₅	—	2	2	no	—
112	C₈×D₅	—	6	2	no	—
113	C₈×D₅	—	6	2	no	—
114	C₈×D₅	—	6	2	no	—
115	#674	—	2	2	no	—
116	#674	—	6	2	no	—
117	C₂³×C₈	—	15	1	no	—
118	C₂²×C₁₆	—	15	2	no	—
119	C₂²⋊C₁₆	—	5	1	no	—
120	C₂²⋊C₁₆	—	15	2	no	—
121	C₂²⋊C₁₆	—	15	1	no	—
122	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
123	C₂×D₁₅	—	2	1	no	—
124	C₂×D₁₅	—	2	1	no	—
125	C₂×D₁₅	C₂×C₁₆	1	2	yes	complemented
126	C₂×C₅×D₃	C₂²⋊C₈	1	2	yes	—
127	C₂×C₅×D₃	C₂×C₁₆	1	2	yes	—
128	C₂×C₅×D₃	M₃₂	1	2	yes	—
129	C₂×C₃×D₅	—	2	1	no	—
130	C₂×C₃×D₅	—	2	1	no	—
131	C₂×C₃×D₅	C₂×C₁₆	1	2	yes	complemented
132	D₃×D₅	—	2	8	no	—
133	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
135	Dic₁₅	—	2	1	no	—
136	C₃×Dic₅	—	2	1	no	—
137	C₅×Dic₃	C₂²⋊C₈	1	2	yes	—
138	C₂³×D₃	—	5	1	no	—
139	C₂²×C₃×C₄	—	5	1	no	—
140	C₂²×Dic₃	—	5	1	no	—
141	C₂×C₄×D₃	—	5	1	no	—
142	C₂×C₄×D₃	—	5	1	no	—
143	C₂×C₄×D₃	—	5	1	no	—
144	C₂×C₄×D₃	—	10	2	no	—
145	C₂×C₄×D₃	—	10	2	no	—
146	C₂×C₄×D₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
147	C₂×C₃×C₈	—	5	1	no	—
148	C₂×C₃×C₈	—	10	2	no	—
149	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
150	C₂×C₃⋊C₈	—	5	1	no	—
151	C₂×C₃⋊C₈	—	10	2	no	—
152	C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
153	D₃×C₈	—	2	2	no	—
154	D₃×C₈	—	5	4	no	—
155	D₃×C₈	—	10	2	no	—
156	D₃×C₈	—	10	2	no	—
157	C₃×C₁₆	—	10	2	no	—
158	C₃⋊C₁₆	—	10	2	no	—
159	C₂³×C₅	—	3	1	no	—
160	C₂²×D₅	—	3	1	no	—
161	C₂²×D₅	—	3	4	no	—
162	C₂²×D₅	—	6	2	no	—
163	C₂²×D₅	—	6	2	no	—
164	C₂²×D₅	D₃×C₈	1	1	yes	characteristic
165	C₂×C₄×C₅	—	3	1	no	—
166	C₂×C₄×C₅	—	3	2	no	—
167	C₂×C₄×C₅	—	3	2	no	—
168	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
169	C₂×Dic₅	—	3	1	no	—
170	C₂×Dic₅	—	6	2	no	—
171	C₂×Dic₅	D₃×C₈	1	1	yes	characteristic
172	C₄×D₅	—	2	1	no	—
173	C₄×D₅	—	2	1	no	—
174	C₄×D₅	—	6	2	no	—
175	C₄×D₅	—	6	2	no	—
176	C₄×D₅	—	6	1	no	—
177	C₄×D₅	—	6	1	no	—
178	C₅×C₈	—	2	1	no	—
179	C₅×C₈	—	6	1	no	—
180	#168	—	3	2	no	—
181	#168	D₃×D₄	1	2	yes	—
182	C₂³×C₄	—	15	1	no	—
183	C₂²×C₈	—	3	1	no	—
184	C₂²×C₈	—	5	1	no	—
185	C₂²×C₈	—	15	1	no	—
186	C₂²×C₈	—	15	1	no	—
187	C₂²×C₈	—	15	1	no	—
188	C₂²×C₈	—	15	1	no	—
189	C₂²×C₈	—	30	4	no	—
190	C₂×C₁₆	—	5	2	no	—
191	C₂×C₁₆	—	15	2	no	—
192	C₂×C₁₆	—	30	4	no	—
193	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
194	C₂×C₃×C₅	C₂²×C₁₆	1	1	yes	characteristic
195	C₂×C₃×C₅	C₂×M₃₂	1	1	yes	characteristic
196	D₁₅	—	2	2	no	—
197	C₃×D₅	—	2	2	no	—
198	C₅×D₃	C₂²⋊C₁₆	1	4	yes	complemented
199	C₂³×C₃	—	5	1	no	—
200	C₂²×D₃	—	5	1	no	—
201	C₂²×D₃	—	5	4	no	—
202	C₂²×D₃	—	10	2	no	—
203	C₂²×D₃	—	10	2	no	—
204	C₂²×D₃	D₅⋊C₈	1	1	yes	characteristic
205	C₂×C₃×C₄	—	5	1	no	—
206	C₂×C₃×C₄	—	10	1	no	—
207	C₂×C₃×C₄	—	10	1	no	—
208	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
209	C₂×Dic₃	—	5	1	no	—
210	C₂×Dic₃	—	10	2	no	—
211	C₂×Dic₃	D₅⋊C₈	1	1	yes	characteristic
212	C₄×D₃	—	10	2	no	—
213	C₄×D₃	—	10	1	no	—
214	C₄×D₃	—	10	1	no	—
215	C₄×D₃	—	10	2	no	—
216	C₄×D₃	#700	1	2	yes	—
217	C₄×D₃	C₂²⋊AGL(1,𝔽₅)	1	2	yes	—
218	C₃×C₈	—	2	1	no	—
219	C₃×C₈	—	5	2	no	—
220	C₃⋊C₈	—	2	1	no	—
221	C₃⋊C₈	—	5	2	no	—
222	C₂²×C₅	—	3	2	no	—
223	C₂²×C₅	—	3	2	no	—
224	C₂²×C₅	—	3	2	no	—
225	C₂²×C₅	C₂×D₃×C₈	1	1	yes	characteristic
226	C₂×D₅	—	2	1	no	—
227	C₂×D₅	—	2	1	no	—
228	C₂×D₅	—	3	2	no	—
229	C₂×D₅	—	6	8	no	—
230	C₂×D₅	—	6	1	no	—
231	C₂×D₅	—	6	1	no	—
232	C₂×D₅	D₃×C₁₆	1	2	yes	complemented
233	C₄×C₅	—	3	2	no	—
234	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
235	C₄×C₅	D₃×M₁₆	1	1	yes	characteristic
236	Dic₅	—	2	1	no	—
237	Dic₅	—	6	1	no	—
238	C₂⁴	—	15	1	no	—
239	C₂²×C₄	—	3	1	no	—
240	C₂²×C₄	—	5	1	no	—
241	C₂²×C₄	—	15	1	no	—
242	C₂²×C₄	—	15	1	no	—
243	C₂²×C₄	—	15	1	no	—
244	C₂²×C₄	—	15	1	no	—
245	C₂²×C₄	—	30	2	no	—
246	C₂²×C₄	—	30	2	no	—
247	C₂×C₈	—	3	1	no	—
248	C₂×C₈	—	5	1	no	—
249	C₂×C₈	—	6	2	no	—
250	C₂×C₈	—	10	2	no	—
251	C₂×C₈	—	15	4	no	—
252	C₂×C₈	—	15	1	no	—
253	C₂×C₈	—	30	2	no	—
254	C₂×C₈	—	30	2	no	—
255	C₂×C₈	—	30	2	no	—
256	C₂×C₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
257	C₁₆	—	10	2	no	—
258	C₁₆	—	30	2	no	—
259	C₃×C₅	C₂×C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Hall
260	C₂²×C₃	—	5	2	no	—
261	C₂²×C₃	—	10	1	no	—
262	C₂²×C₃	—	10	1	no	—
263	C₂²×C₃	C₂×D₅⋊C₈	1	1	yes	characteristic
264	C₂×D₃	—	5	2	no	—
265	C₂×D₃	—	10	1	no	—
266	C₂×D₃	—	10	1	no	—
267	C₂×D₃	—	10	8	no	—
268	C₂×D₃	D₅⋊C₁₆	1	2	yes	—
269	C₂×D₃	#3990	1	2	yes	—
270	C₂×D₃	#4003	1	2	yes	—
271	C₃×C₄	—	10	1	no	—
272	C₃×C₄	C₂×#700	1	1	yes	characteristic
273	C₃×C₄	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
274	Dic₃	—	10	1	no	—
275	Dic₃	#4003	1	2	yes	—
276	C₂×C₅	—	3	4	no	—
277	C₂×C₅	D₃×C₂²⋊C₈	1	1	yes	characteristic
278	C₂×C₅	C₂×D₃×C₁₆	1	1	yes	characteristic
279	C₂×C₅	D₃×M₃₂	1	1	yes	characteristic
280	D₅	—	2	2	no	—
281	D₅	—	6	2	no	—
282	C₂³	—	3	1	no	—
283	C₂³	—	5	1	no	—
284	C₂³	—	15	4	no	—
285	C₂³	—	15	1	no	—
286	C₂³	—	30	2	no	—
287	C₂³	—	30	2	no	—
288	C₂×C₄	—	3	1	no	—
289	C₂×C₄	—	3	2	no	—
290	C₂×C₄	—	3	2	no	—
291	C₂×C₄	—	5	1	no	—
292	C₂×C₄	—	10	1	no	—
293	C₂×C₄	—	10	1	no	—
294	C₂×C₄	—	15	1	no	—
295	C₂×C₄	—	30	2	no	—
296	C₂×C₄	—	30	2	no	—
297	C₂×C₄	—	30	2	no	—
298	C₂×C₄	—	30	1	no	—
299	C₂×C₄	—	30	1	no	—
300	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
301	C₈	—	2	1	no	—
302	C₈	—	5	2	no	—
303	C₈	—	6	1	no	—
304	C₈	—	15	2	no	—
305	C₂×C₃	—	10	2	no	—
306	C₂×C₃	C₂×D₅⋊C₁₆	1	1	yes	characteristic
307	C₂×C₃	C₂×#3990	1	1	yes	characteristic
308	C₂×C₃	C₂×#4003	1	1	yes	characteristic
309	D₃	—	10	2	no	—
310	D₃	#64887	1	4	yes	direct product factor
311	C₅	D₃×C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
312	C₂²	—	3	2	no	—
313	C₂²	—	3	2	no	—
314	C₂²	—	3	2	no	—
315	C₂²	—	5	2	no	—
316	C₂²	—	10	1	no	—
317	C₂²	—	10	1	no	—
318	C₂²	—	15	2	no	—
319	C₂²	—	30	8	no	—
320	C₂²	—	30	1	no	—
321	C₂²	—	30	1	no	—
322	C₂²	D₃×D₅⋊C₈	1	1	yes	characteristic
323	C₄	—	3	2	no	—
324	C₄	—	10	1	no	—
325	C₄	—	30	1	no	—
326	C₄	D₃×#700	1	1	yes	characteristic
327	C₄	D₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
328	C₃	C₂×#64887	1	1	yes	characteristic, complemented, Sylow
329	C₂	—	3	4	no	—
330	C₂	—	10	2	no	—
331	C₂	—	30	2	no	—
332	C₂	D₃×D₅⋊C₁₆	1	1	yes	characteristic
333	C₂	D₃×#3990	1	1	yes	characteristic
334	C₂	D₃×#4003	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)
commutator	C₂×C₃×C₅	C₂²×C₁₆
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
socle	C₂²×C₃×C₅	C₂²×C₈
prime radical	C₂²×D₃×D₅	C₈
cosocle	C₂×C₃×#168	C₂³
hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₂×C₂²⋊C₁₆
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×D₃×#674	C₂	semidirect
3. #11746758	C₂	semidirect
4. C₃×#64887	C₂	semidirect
5. #11746547	C₂	semidirect
15. C₂×C₃⋊#674	C₂²	semidirect
16. C₂×C₃×#674	C₂²	semidirect
23. #64887	D₃	direct (N × H)
60. C₂×#674	C₂×D₃	semidirect
67. C₂×D₃×D₅	C₁₆	semidirect
125. C₂×D₁₅	C₂×C₁₆	semidirect
131. C₂×C₃×D₅	C₂×C₁₆	semidirect
198. C₅×D₃	C₂²⋊C₁₆	semidirect
232. C₂×D₅	D₃×C₁₆	semidirect
259. C₃×C₅	C₂×C₂²⋊C₁₆	semidirect
310. D₃	#64887	direct (N × H)
311. C₅	D₃×C₂²⋊C₁₆	semidirect
328. C₃	C₂×#64887	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×C₈×D₅	2
C₂×D₃×#674	2
#11746758	2
C₃×#64887	2
#11746547	2
C₂×#64887	3
D₃×C₂²⋊C₁₆	5

Subgroups — D3×#64887 #14312817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#64887 #14312817