Subgroups — C₃×C₅×#1942 #14274976

Order 1920.

496 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#389	C₂	1	2	yes	maximal
5	C₃×C₅×#340	C₂	1	2	yes	maximal
6	C₅×#1942	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
10	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₅×#107	—	2	2	no	—
14	C₃×C₅×#107	C₄	1	4	yes	complemented
15	C₃×C₄×C₅×C₈	—	2	2	no	—
16	C₃×C₅×#95	—	2	2	no	—
17	C₃×#1942	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic
19	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic
20	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic
21	C₅×#389	C₂×C₃	1	2	yes	—
22	C₅×#340	C₂×C₃	1	2	yes	—
23	C₂²×C₃×C₄×C₅	—	2	2	no	—
24	C₂²×C₃×C₄×C₅	—	2	2	no	—
25	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
26	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
27	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
28	C₂×C₃×C₅×C₈	—	2	1	no	—
29	C₂×C₃×C₅×C₈	—	2	1	no	—
30	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
31	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
32	C₂×C₃×C₅×C₈	Q₈	1	2	yes	—
33	C₂×C₃×C₅×C₈	Q₈	1	2	yes	—
34	C₃×C₅×C₄⋊C₄	—	2	2	no	—
35	C₃×C₅×C₄⋊C₄	—	2	2	no	—
36	C₃×C₅×C₄⋊C₄	—	2	2	no	—
37	C₃×C₅×C₄⋊C₄	—	4	4	no	—
38	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
39	C₃×C₄²×C₅	—	2	1	no	—
40	C₃×C₄²×C₅	—	2	1	no	—
41	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic
42	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic
43	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic
44	C₃×#389	C₂×C₅	1	2	yes	—
45	C₃×#340	C₂×C₅	1	2	yes	—
46	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
48	C₂×C₅×C₄⋊C₄	—	2	2	no	—
49	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
50	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
51	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
52	C₅×#107	—	2	2	no	—
53	C₅×#107	C₃×C₄	1	4	yes	complemented
54	C₄×C₅×C₈	—	2	2	no	—
55	C₅×#95	—	2	2	no	—
56	#1942	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
57	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
58	C₂×C₃×C₄×C₅	—	2	1	no	—
59	C₂×C₃×C₄×C₅	—	2	1	no	—
60	C₂×C₃×C₄×C₅	—	2	1	no	—
61	C₂×C₃×C₄×C₅	—	2	1	no	—
62	C₂×C₃×C₄×C₅	—	2	4	no	—
63	C₂×C₃×C₄×C₅	—	4	2	no	—
64	C₂×C₃×C₄×C₅	—	4	2	no	—
65	C₂×C₃×C₄×C₅	—	4	2	no	—
66	C₂×C₃×C₄×C₅	—	4	2	no	—
67	C₂×C₃×C₄×C₅	—	4	2	no	—
68	C₂×C₃×C₄×C₅	D₈	1	2	yes	—
69	C₂×C₃×C₄×C₅	Q₁₆	1	2	yes	—
70	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
72	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
73	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
74	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
75	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
76	C₃×C₅×C₈	—	2	2	no	—
77	C₃×C₅×C₈	C₄⋊C₄	1	4	yes	complemented
78	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
79	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
80	C₂×C₃×C₄⋊C₄	—	2	2	no	—
81	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
82	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
83	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
84	C₃×#107	—	2	2	no	—
85	C₃×#107	C₄×C₅	1	4	yes	complemented
86	C₃×C₄×C₈	—	2	2	no	—
87	C₃×#95	—	2	2	no	—
88	C₂²×C₄×C₅	—	2	2	no	—
89	C₂²×C₄×C₅	—	2	2	no	—
90	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
93	C₂×C₅×C₈	—	2	1	no	—
94	C₂×C₅×C₈	—	2	1	no	—
95	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
96	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
97	C₂×C₅×C₈	C₃×Q₈	1	2	yes	—
98	C₂×C₅×C₈	C₃×Q₈	1	2	yes	—
99	C₅×C₄⋊C₄	—	2	2	no	—
100	C₅×C₄⋊C₄	—	2	2	no	—
101	C₅×C₄⋊C₄	—	2	2	no	—
102	C₅×C₄⋊C₄	—	4	4	no	—
103	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
104	C₄²×C₅	—	2	1	no	—
105	C₄²×C₅	—	2	1	no	—
106	C₂×#107	C₂×C₃×C₅	1	1	yes	characteristic
107	C₂×#107	C₂×C₃×C₅	1	1	yes	characteristic
108	C₂×C₄×C₈	C₂×C₃×C₅	1	1	yes	characteristic
109	#389	C₂×C₃×C₅	1	2	yes	—
110	#340	C₂×C₃×C₅	1	2	yes	—
111	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
112	C₂²×C₃×C₅	#121	1	1	yes	characteristic
113	C₂²×C₃×C₅	C₄⋊Q₈	1	1	yes	characteristic
114	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
115	C₂²×C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic
116	C₂²×C₃×C₅	#135	1	1	yes	characteristic
117	C₂²×C₃×C₅	#135	1	1	yes	characteristic
118	C₃×C₄×C₅	—	2	2	no	—
119	C₃×C₄×C₅	—	2	2	no	—
120	C₃×C₄×C₅	—	4	4	no	—
121	C₃×C₄×C₅	—	8	2	no	—
122	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₃×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
124	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
125	C₃×C₄×C₅	#125	1	1	yes	characteristic
126	C₂²×C₃×C₄	—	2	2	no	—
127	C₂²×C₃×C₄	—	2	2	no	—
128	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
129	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
130	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
131	C₂×C₃×C₈	—	2	1	no	—
132	C₂×C₃×C₈	—	2	1	no	—
133	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
134	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
135	C₂×C₃×C₈	C₅×Q₈	1	2	yes	—
136	C₂×C₃×C₈	C₅×Q₈	1	2	yes	—
137	C₃×C₄⋊C₄	—	2	2	no	—
138	C₃×C₄⋊C₄	—	2	2	no	—
139	C₃×C₄⋊C₄	—	2	2	no	—
140	C₃×C₄⋊C₄	—	4	4	no	—
141	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
142	C₃×C₄²	—	2	1	no	—
143	C₃×C₄²	—	2	1	no	—
144	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
145	C₂×C₄×C₅	—	2	1	no	—
146	C₂×C₄×C₅	—	2	1	no	—
147	C₂×C₄×C₅	—	2	1	no	—
148	C₂×C₄×C₅	—	2	1	no	—
149	C₂×C₄×C₅	—	2	4	no	—
150	C₂×C₄×C₅	—	4	2	no	—
151	C₂×C₄×C₅	—	4	2	no	—
152	C₂×C₄×C₅	—	4	2	no	—
153	C₂×C₄×C₅	—	4	2	no	—
154	C₂×C₄×C₅	—	4	2	no	—
155	C₂×C₄×C₅	C₃×D₈	1	2	yes	—
156	C₂×C₄×C₅	C₃×Q₁₆	1	2	yes	—
157	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
158	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
159	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
162	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
163	C₅×C₈	—	2	2	no	—
164	C₅×C₈	C₃×C₄⋊C₄	1	4	yes	complemented
165	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
166	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
167	C₂×C₄⋊C₄	—	2	2	no	—
168	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
169	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
170	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
171	#107	—	2	2	no	—
172	#107	C₃×C₄×C₅	1	4	yes	complemented
173	C₄×C₈	—	2	2	no	—
174	#95	—	2	2	no	—
175	C₂×C₃×C₅	#389	1	1	yes	characteristic
176	C₂×C₃×C₅	C₄×D₈	1	1	yes	characteristic
177	C₂×C₃×C₅	C₄×Q₁₆	1	1	yes	characteristic
178	C₂×C₃×C₅	#466	1	1	yes	characteristic
179	C₂×C₃×C₅	#467	1	1	yes	characteristic
180	C₂×C₃×C₅	#499	1	1	yes	characteristic
181	C₂×C₃×C₅	#500	1	1	yes	characteristic
182	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
183	C₂×C₃×C₄	—	2	1	no	—
184	C₂×C₃×C₄	—	2	1	no	—
185	C₂×C₃×C₄	—	2	1	no	—
186	C₂×C₃×C₄	—	2	1	no	—
187	C₂×C₃×C₄	—	2	4	no	—
188	C₂×C₃×C₄	—	4	2	no	—
189	C₂×C₃×C₄	—	4	2	no	—
190	C₂×C₃×C₄	—	4	2	no	—
191	C₂×C₃×C₄	—	4	2	no	—
192	C₂×C₃×C₄	—	4	2	no	—
193	C₂×C₃×C₄	C₅×D₈	1	2	yes	—
194	C₂×C₃×C₄	C₅×Q₁₆	1	2	yes	—
195	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
196	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
197	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
198	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
199	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
200	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
201	C₃×C₈	—	2	2	no	—
202	C₃×C₈	C₅×C₄⋊C₄	1	4	yes	complemented
203	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
204	C₂²×C₅	C₃×#121	1	1	yes	characteristic
205	C₂²×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
206	C₂²×C₅	C₂×C₃×D₈	1	1	yes	characteristic
207	C₂²×C₅	C₂×C₃×Q₁₆	1	1	yes	characteristic
208	C₂²×C₅	C₃×#135	1	1	yes	characteristic
209	C₂²×C₅	C₃×#135	1	1	yes	characteristic
210	C₄×C₅	—	2	2	no	—
211	C₄×C₅	—	2	2	no	—
212	C₄×C₅	—	4	4	no	—
213	C₄×C₅	—	8	2	no	—
214	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
215	C₄×C₅	C₃×C₄×Q₈	1	1	yes	characteristic
216	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
217	C₄×C₅	C₃×#125	1	1	yes	characteristic
218	C₂²×C₄	—	2	2	no	—
219	C₂²×C₄	—	2	2	no	—
220	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
221	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
222	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
223	C₂×C₈	—	2	1	no	—
224	C₂×C₈	—	2	1	no	—
225	C₂×C₈	C₂×C₃×C₄×C₅	1	2	yes	—
226	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
227	C₂×C₈	C₃×C₅×Q₈	1	2	yes	—
228	C₂×C₈	C₃×C₅×Q₈	1	2	yes	—
229	C₄⋊C₄	—	2	2	no	—
230	C₄⋊C₄	—	2	2	no	—
231	C₄⋊C₄	—	2	2	no	—
232	C₄⋊C₄	—	4	4	no	—
233	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
234	C₄²	—	2	1	no	—
235	C₄²	—	2	1	no	—
236	C₃×C₅	#1942	1	1	yes	characteristic, direct product factor, Hall
237	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
238	C₂²×C₃	C₅×#121	1	1	yes	characteristic
239	C₂²×C₃	C₅×C₄⋊Q₈	1	1	yes	characteristic
240	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
241	C₂²×C₃	C₂×C₅×Q₁₆	1	1	yes	characteristic
242	C₂²×C₃	C₅×#135	1	1	yes	characteristic
243	C₂²×C₃	C₅×#135	1	1	yes	characteristic
244	C₃×C₄	—	2	2	no	—
245	C₃×C₄	—	2	2	no	—
246	C₃×C₄	—	4	4	no	—
247	C₃×C₄	—	8	2	no	—
248	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
249	C₃×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
250	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
251	C₃×C₄	C₅×#125	1	1	yes	characteristic
252	C₂×C₅	C₃×#389	1	1	yes	characteristic
253	C₂×C₅	C₃×C₄×D₈	1	1	yes	characteristic
254	C₂×C₅	C₃×C₄×Q₁₆	1	1	yes	characteristic
255	C₂×C₅	C₃×#466	1	1	yes	characteristic
256	C₂×C₅	C₃×#467	1	1	yes	characteristic
257	C₂×C₅	C₃×#499	1	1	yes	characteristic
258	C₂×C₅	C₃×#500	1	1	yes	characteristic
259	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
260	C₂×C₄	—	2	1	no	—
261	C₂×C₄	—	2	1	no	—
262	C₂×C₄	—	2	1	no	—
263	C₂×C₄	—	2	1	no	—
264	C₂×C₄	—	2	4	no	—
265	C₂×C₄	—	4	2	no	—
266	C₂×C₄	—	4	2	no	—
267	C₂×C₄	—	4	2	no	—
268	C₂×C₄	—	4	2	no	—
269	C₂×C₄	—	4	2	no	—
270	C₂×C₄	C₃×C₅×D₈	1	2	yes	—
271	C₂×C₄	C₃×C₅×Q₁₆	1	2	yes	—
272	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
273	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
274	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
275	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
276	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
277	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
278	C₈	—	2	2	no	—
279	C₈	C₃×C₅×C₄⋊C₄	1	4	yes	complemented
280	C₂×C₃	C₅×#389	1	1	yes	characteristic
281	C₂×C₃	C₄×C₅×D₈	1	1	yes	characteristic
282	C₂×C₃	C₄×C₅×Q₁₆	1	1	yes	characteristic
283	C₂×C₃	C₅×#466	1	1	yes	characteristic
284	C₂×C₃	C₅×#467	1	1	yes	characteristic
285	C₂×C₃	C₅×#499	1	1	yes	characteristic
286	C₂×C₃	C₅×#500	1	1	yes	characteristic
287	C₅	C₃×#1942	1	1	yes	characteristic, direct product factor, Sylow
288	C₂²	C₃×C₄×C₅×D₄	1	1	yes	characteristic
289	C₂²	C₃×C₅×#121	1	1	yes	characteristic
290	C₂²	C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
291	C₂²	C₂×C₃×C₅×D₈	1	1	yes	characteristic
292	C₂²	C₂×C₃×C₅×Q₁₆	1	1	yes	characteristic
293	C₂²	C₃×C₅×#135	1	1	yes	characteristic
294	C₂²	C₃×C₅×#135	1	1	yes	characteristic
295	C₄	—	2	2	no	—
296	C₄	—	2	2	no	—
297	C₄	—	4	4	no	—
298	C₄	—	8	2	no	—
299	C₄	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
300	C₄	C₃×C₄×C₅×Q₈	1	1	yes	characteristic
301	C₄	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
302	C₄	C₃×C₅×#125	1	1	yes	characteristic
303	C₃	C₅×#1942	1	1	yes	characteristic, direct product factor, Sylow
304	C₂	C₃×C₅×#389	1	1	yes	characteristic
305	C₂	C₃×C₄×C₅×D₈	1	1	yes	characteristic
306	C₂	C₃×C₄×C₅×Q₁₆	1	1	yes	characteristic
307	C₂	C₃×C₅×#466	1	1	yes	characteristic
308	C₂	C₃×C₅×#467	1	1	yes	characteristic
309	C₂	C₃×C₅×#499	1	1	yes	characteristic
310	C₂	C₃×C₅×#500	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₅×#1942	C₃	direct (N × H)
14. C₃×C₅×#107	C₄	semidirect
17. C₃×#1942	C₅	direct (N × H)
53. C₅×#107	C₃×C₄	semidirect
56. #1942	C₃×C₅	direct (N × H)
77. C₃×C₅×C₈	C₄⋊C₄	semidirect
85. C₃×#107	C₄×C₅	semidirect
164. C₅×C₈	C₃×C₄⋊C₄	semidirect
172. #107	C₃×C₄×C₅	semidirect
202. C₃×C₈	C₅×C₄⋊C₄	semidirect
236. C₃×C₅	#1942	direct (N × H)
279. C₈	C₃×C₅×C₄⋊C₄	semidirect
287. C₅	C₃×#1942	direct (N × H)
303. C₃	C₅×#1942	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#107	2
C₂×C₃×C₄×C₅×C₈	2
C₃×C₅×#389	2
C₃×C₅×#340	2
C₅×#1942	3
C₃×#1942	5

Subgroups — C3×C5×#1942 #14274976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1942 #14274976