Subgroups — C₃×D₅×#491 #14437948

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×D₅×#125	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#491	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65371	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65358	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×D₅×#103	C₂	1	4	yes	maximal
7	C₃×#65086	C₂	1	4	yes	maximal, complemented
8	C₃×D₅×#97	C₂	1	1	yes	maximal, characteristic
9	C₃×#64992	C₂	1	1	yes	maximal, characteristic, complemented
10	D₅×#491	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
12	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₃×C₅×#125	C₂²	1	1	yes	characteristic
14	C₃×#4090	C₂²	1	2	yes	—
15	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
16	C₃×D₅×C₄⋊C₄	—	2	2	no	—
17	C₃×D₅×C₄⋊C₄	—	2	2	no	—
18	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₃×#4036	C₂²	1	2	yes	—
20	C₃×#4035	—	2	2	no	—
21	C₃×#4034	—	2	2	no	—
22	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
23	C₃×#4016	C₂²	1	1	yes	characteristic
24	C₃×#4015	C₂²	1	1	yes	characteristic
25	C₃×C₅×#103	C₂²	1	4	yes	—
26	C₃×C₅×#97	C₂²	1	1	yes	characteristic
27	C₃×#3967	C₂²	1	4	yes	—
28	C₃×#3948	C₂²	1	4	yes	—
29	C₃×#3947	C₂²	1	2	yes	—
30	C₃×#3942	C₂²	1	4	yes	—
31	C₃×#3935	C₂²	1	1	yes	characteristic
32	C₂×C₃×#491	—	5	1	no	maximal, Hall
33	D₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
34	D₅×#125	C₂×C₃	1	1	yes	characteristic
35	C₅×#491	C₂×C₃	1	1	yes	characteristic, complemented
36	#65371	C₂×C₃	1	1	yes	characteristic, complemented
37	#65358	C₂×C₃	1	1	yes	characteristic, complemented
38	D₅×#103	C₂×C₃	1	4	yes	—
39	#65086	C₂×C₃	1	4	yes	complemented
40	D₅×#97	C₂×C₃	1	1	yes	characteristic
41	#64992	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
43	C₃×Q₈×D₅	—	2	8	no	—
44	C₂×C₃×C₄×D₅	—	2	2	no	—
45	C₂×C₃×C₄×D₅	—	2	2	no	—
46	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
47	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
48	C₂×C₃×Dic₁₀	—	2	2	no	—
49	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
50	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
51	C₃×C₅×C₄⋊C₄	—	2	2	no	—
52	C₃×C₅×C₄⋊C₄	—	2	2	no	—
53	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₃×C₄⋊Dic₅	—	2	2	no	—
56	C₃×C₄⋊Dic₅	—	2	2	no	—
57	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
58	C₃×#683	—	2	2	no	—
59	C₃×#683	—	2	4	no	—
60	C₃×#683	—	2	2	no	—
61	C₃×#683	—	2	2	no	—
62	C₃×C₄×Dic₅	D₄	1	2	yes	—
63	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
64	C₂×C₃×#168	C₂³	1	2	yes	—
65	C₃×C₈×D₅	—	2	4	no	—
66	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
67	C₂×C₃×#125	—	5	1	no	—
68	C₃×#491	—	5	1	no	—
69	C₃×#491	—	5	1	no	—
70	C₃×#491	—	5	4	no	—
71	C₃×#491	—	5	1	no	—
72	C₃×#491	D₅	1	1	yes	characteristic, direct product factor
73	C₂×C₃×#103	—	5	4	no	—
74	C₂×C₃×#97	—	5	1	no	—
75	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
76	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
77	C₅×#125	C₂²×C₃	1	1	yes	characteristic
78	#4090	C₂²×C₃	1	2	yes	—
79	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
80	D₅×C₄⋊C₄	—	2	2	no	—
81	D₅×C₄⋊C₄	—	2	2	no	—
82	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
83	#4036	C₂²×C₃	1	2	yes	—
84	#4035	—	2	2	no	—
85	#4034	—	2	2	no	—
86	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
87	#4016	C₂²×C₃	1	1	yes	characteristic
88	#4015	C₂²×C₃	1	1	yes	characteristic
89	C₅×#103	C₂²×C₃	1	4	yes	—
90	C₅×#97	C₂²×C₃	1	1	yes	characteristic
91	#3967	C₂²×C₃	1	4	yes	—
92	#3948	C₂²×C₃	1	4	yes	—
93	#3947	C₂²×C₃	1	2	yes	—
94	#3942	C₂²×C₃	1	4	yes	—
95	#3935	C₂²×C₃	1	1	yes	characteristic
96	C₂×#491	—	5	1	no	Sylow
97	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
98	C₃×C₅×Q₈	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
103	C₂×C₃×Dic₅	—	2	2	no	—
104	C₂×C₃×Dic₅	—	2	2	no	—
105	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
106	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
107	C₃×C₄×D₅	—	2	4	no	—
108	C₃×C₄×D₅	—	4	4	no	—
109	C₃×C₄×D₅	—	4	4	no	—
110	C₃×C₄×D₅	#41	1	4	yes	—
111	C₃×Dic₁₀	—	2	4	no	—
112	C₃×Dic₁₀	—	4	4	no	—
113	C₃×C₅×C₈	—	2	2	no	—
114	C₃×#168	—	2	2	no	—
115	C₂²×C₃×Q₈	—	5	2	no	—
116	C₂²×C₃×C₈	—	5	2	no	—
117	C₃×C₄⋊Q₈	—	5	2	no	—
118	C₃×C₄⋊Q₈	—	5	1	no	—
119	C₃×C₄⋊Q₈	—	10	2	no	—
120	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
121	C₃×#125	—	5	2	no	—
122	C₃×#125	—	5	1	no	—
123	C₃×#125	—	10	2	no	—
124	C₃×#125	C₂×D₅	1	1	yes	characteristic
125	C₂×C₃×C₄⋊C₄	—	5	2	no	—
126	C₂×C₃×C₄⋊C₄	—	10	2	no	—
127	C₂×C₃×C₄⋊C₄	—	10	2	no	—
128	C₂×C₃×C₄²	—	5	1	no	—
129	C₃×#103	—	5	4	no	—
130	C₃×#103	—	5	4	no	—
131	C₃×#103	—	5	4	no	—
132	C₃×#103	C₂×D₅	1	4	yes	—
133	C₃×#97	—	5	2	no	—
134	C₃×#97	—	5	1	no	—
135	C₃×#97	C₂×D₅	1	1	yes	characteristic
136	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
137	Q₈×D₅	—	2	8	no	—
138	C₂×C₄×D₅	—	2	2	no	—
139	C₂×C₄×D₅	—	2	2	no	—
140	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
141	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
142	C₂×Dic₁₀	—	2	2	no	—
143	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
144	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
148	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
149	C₄⋊Dic₅	—	2	2	no	—
150	C₄⋊Dic₅	—	2	2	no	—
151	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
152	#683	—	2	2	no	—
153	#683	—	2	4	no	—
154	#683	—	2	2	no	—
155	#683	—	2	2	no	—
156	C₄×Dic₅	C₃×D₄	1	2	yes	—
157	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
158	C₂×#168	C₂³×C₃	1	2	yes	—
159	C₈×D₅	—	2	4	no	—
160	C₂×C₄⋊Q₈	—	5	1	no	—
161	C₂×#125	—	5	1	no	—
162	#491	—	5	1	no	—
163	#491	—	5	1	no	—
164	#491	—	5	4	no	—
165	#491	—	5	1	no	—
166	#491	C₃×D₅	1	1	yes	characteristic, direct product factor
167	C₂×#103	—	5	4	no	—
168	C₂×#97	—	5	1	no	—
169	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₃×D₅	#124	1	2	yes	—
171	C₂×C₃×D₅	#137	1	4	yes	—
172	C₃×C₄×C₅	—	2	2	no	—
173	C₃×C₄×C₅	—	4	2	no	—
174	C₃×C₄×C₅	—	4	2	no	—
175	C₃×C₄×C₅	C₂×#41	1	2	yes	—
176	C₃×Dic₅	—	2	2	no	—
177	C₃×Dic₅	—	4	2	no	—
178	C₃×Dic₅	—	4	2	no	—
179	C₃×Dic₅	#124	1	2	yes	—
180	C₂×C₃×Q₈	—	5	2	no	—
181	C₂×C₃×Q₈	—	10	2	no	—
182	C₂×C₃×Q₈	—	10	8	no	—
183	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
184	C₂²×C₃×C₄	—	5	1	no	—
185	C₂²×C₃×C₄	—	5	2	no	—
186	C₂²×C₃×C₄	—	10	2	no	—
187	C₂²×C₃×C₄	—	10	2	no	—
188	C₂×C₃×C₈	—	5	2	no	—
189	C₂×C₃×C₈	—	10	4	no	—
190	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
191	C₃×C₄⋊C₄	—	2	2	no	—
192	C₃×C₄⋊C₄	—	2	2	no	—
193	C₃×C₄⋊C₄	—	5	2	no	—
194	C₃×C₄⋊C₄	—	10	2	no	—
195	C₃×C₄⋊C₄	—	10	2	no	—
196	C₃×C₄⋊C₄	—	10	4	no	—
197	C₃×C₄⋊C₄	—	10	2	no	—
198	C₃×C₄⋊C₄	—	10	2	no	—
199	C₃×C₄⋊C₄	—	10	2	no	—
200	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
201	C₃×C₄²	—	5	2	no	—
202	C₃×C₄²	—	5	1	no	—
203	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
204	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
205	C₅×Q₈	—	2	4	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
209	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
210	C₂×Dic₅	—	2	2	no	—
211	C₂×Dic₅	—	2	2	no	—
212	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
213	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
214	C₄×D₅	—	2	4	no	—
215	C₄×D₅	—	4	4	no	—
216	C₄×D₅	—	4	4	no	—
217	C₄×D₅	C₃×#41	1	4	yes	—
218	Dic₁₀	—	2	4	no	—
219	Dic₁₀	—	4	4	no	—
220	C₅×C₈	—	2	2	no	—
221	#168	—	2	2	no	—
222	C₂²×Q₈	—	5	2	no	—
223	C₂²×C₈	—	5	2	no	—
224	C₄⋊Q₈	—	5	2	no	—
225	C₄⋊Q₈	—	5	1	no	—
226	C₄⋊Q₈	—	10	2	no	—
227	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
228	#125	—	5	2	no	—
229	#125	—	5	1	no	—
230	#125	—	10	2	no	—
231	#125	C₂×C₃×D₅	1	1	yes	characteristic
232	C₂×C₄⋊C₄	—	5	2	no	—
233	C₂×C₄⋊C₄	—	10	2	no	—
234	C₂×C₄⋊C₄	—	10	2	no	—
235	C₂×C₄²	—	5	1	no	—
236	#103	—	5	4	no	—
237	#103	—	5	4	no	—
238	#103	—	5	4	no	—
239	#103	C₂×C₃×D₅	1	4	yes	—
240	#97	—	5	2	no	—
241	#97	—	5	1	no	—
242	#97	C₂×C₃×D₅	1	1	yes	characteristic
243	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
244	C₂×C₃×C₅	C₂×#137	1	2	yes	—
245	C₃×D₅	#491	1	4	yes	direct product factor
246	C₂³×C₃	—	5	1	no	—
247	C₃×Q₈	—	2	4	no	—
248	C₃×Q₈	—	10	4	no	—
249	C₃×Q₈	—	20	4	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	5	1	no	—
253	C₂×C₃×C₄	—	5	4	no	—
254	C₂×C₃×C₄	—	5	2	no	—
255	C₂×C₃×C₄	—	10	4	no	—
256	C₂×C₃×C₄	—	10	2	no	—
257	C₂×C₃×C₄	—	10	2	no	—
258	C₂×C₃×C₄	—	20	4	no	—
259	C₂×C₃×C₄	—	20	4	no	—
260	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
261	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
262	C₃×C₈	—	2	2	no	—
263	C₃×C₈	—	10	2	no	—
264	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
265	C₂×D₅	C₃×#124	1	2	yes	—
266	C₂×D₅	C₃×#137	1	4	yes	—
267	C₄×C₅	—	2	2	no	—
268	C₄×C₅	—	4	2	no	—
269	C₄×C₅	—	4	2	no	—
270	C₄×C₅	C₂×C₃×#41	1	2	yes	—
271	Dic₅	—	2	2	no	—
272	Dic₅	—	4	2	no	—
273	Dic₅	—	4	2	no	—
274	Dic₅	C₃×#124	1	2	yes	—
275	C₂×Q₈	—	5	2	no	—
276	C₂×Q₈	—	10	2	no	—
277	C₂×Q₈	—	10	8	no	—
278	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
279	C₂²×C₄	—	5	1	no	—
280	C₂²×C₄	—	5	2	no	—
281	C₂²×C₄	—	10	2	no	—
282	C₂²×C₄	—	10	2	no	—
283	C₂×C₈	—	5	2	no	—
284	C₂×C₈	—	10	4	no	—
285	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	5	2	no	—
289	C₄⋊C₄	—	10	2	no	—
290	C₄⋊C₄	—	10	2	no	—
291	C₄⋊C₄	—	10	2	no	—
292	C₄⋊C₄	—	10	4	no	—
293	C₄⋊C₄	—	10	2	no	—
294	C₄⋊C₄	—	10	2	no	—
295	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
296	C₄²	—	5	2	no	—
297	C₄²	—	5	1	no	—
298	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
299	C₃×C₅	C₂×#491	1	1	yes	characteristic, complemented, Hall
300	C₂²×C₃	—	5	4	no	—
301	C₂²×C₃	—	5	2	no	—
302	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
303	C₃×C₄	—	2	2	no	—
304	C₃×C₄	—	4	2	no	—
305	C₃×C₄	—	4	2	no	—
306	C₃×C₄	—	5	2	no	—
307	C₃×C₄	—	10	2	no	—
308	C₃×C₄	—	20	2	no	—
309	C₃×C₄	—	20	2	no	—
310	C₃×C₄	D₅×#41	1	2	yes	—
311	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
312	C₂×C₅	C₂×C₃×#137	1	2	yes	—
313	D₅	C₃×#491	1	4	yes	direct product factor
314	C₂³	—	5	1	no	—
315	Q₈	—	2	4	no	—
316	Q₈	—	10	4	no	—
317	Q₈	—	20	4	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	5	1	no	—
321	C₂×C₄	—	5	4	no	—
322	C₂×C₄	—	5	2	no	—
323	C₂×C₄	—	10	4	no	—
324	C₂×C₄	—	10	2	no	—
325	C₂×C₄	—	10	2	no	—
326	C₂×C₄	—	20	4	no	—
327	C₂×C₄	—	20	4	no	—
328	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
329	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
330	C₈	—	2	2	no	—
331	C₈	—	10	2	no	—
332	C₂×C₃	—	5	4	no	—
333	C₂×C₃	D₅×#124	1	1	yes	characteristic
334	C₂×C₃	D₅×#137	1	2	yes	—
335	C₅	C₂×C₃×#491	1	1	yes	characteristic, complemented, Sylow
336	C₂²	—	5	4	no	—
337	C₂²	—	5	2	no	—
338	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
339	C₄	—	2	2	no	—
340	C₄	—	4	2	no	—
341	C₄	—	4	2	no	—
342	C₄	—	5	2	no	—
343	C₄	—	10	2	no	—
344	C₄	—	20	2	no	—
345	C₄	—	20	2	no	—
346	C₄	C₃×D₅×#41	1	2	yes	—
347	C₃	D₅×#491	1	1	yes	characteristic, direct product factor, Sylow
348	C₂	—	5	4	no	—
349	C₂	C₃×D₅×#124	1	1	yes	characteristic
350	C₂	C₃×D₅×#137	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#491	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₃×D₅	C₂×D₄
hypercenter	C₃×#491	D₅
hypocenter	C₅	C₂×C₃×#491
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#491

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#491	C₂	semidirect
4. C₃×#65371	C₂	semidirect
5. C₃×#65358	C₂	semidirect
7. C₃×#65086	C₂	semidirect
9. C₃×#64992	C₂	semidirect
10. D₅×#491	C₃	direct (N × H)
35. C₅×#491	C₂×C₃	semidirect
36. #65371	C₂×C₃	semidirect
37. #65358	C₂×C₃	semidirect
39. #65086	C₂×C₃	semidirect
41. #64992	C₂×C₃	semidirect
72. C₃×#491	D₅	direct (N × H)
166. #491	C₃×D₅	direct (N × H)
245. C₃×D₅	#491	direct (N × H)
299. C₃×C₅	C₂×#491	semidirect
313. D₅	C₃×#491	direct (N × H)
335. C₅	C₂×C₃×#491	semidirect
347. C₃	D₅×#491	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₅×C₄⋊Q₈	2
C₃×D₅×#125	2
C₃×C₅×#491	2
C₃×#65371	2
C₃×#65358	2
C₃×D₅×#103	2
C₃×#65086	2
C₃×D₅×#97	2
C₃×#64992	2
D₅×#491	3
C₂×C₃×#491	5

Subgroups — C3×D5×#491 #14437948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#491 #14437948