Subgroups — C₃×C₅×#1922 #14274956

Order 1920.

372 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#427	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#341	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#339	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#339	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic
8	C₅×#1922	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₅×#117	C₂²	1	1	yes	characteristic
14	C₃×C₅×#117	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₅×#107	C₄	1	1	yes	characteristic, complemented
17	C₃×C₅×#107	C₄	1	1	yes	characteristic, complemented
18	C₃×C₅×#106	C₄	1	1	yes	characteristic, complemented
19	C₃×C₅×#106	C₄	1	1	yes	characteristic, complemented
20	C₃×C₅×C₄⋊C₈	—	2	1	no	—
21	C₃×C₅×C₄⋊C₈	—	2	1	no	—
22	C₃×C₅×#97	—	2	1	no	—
23	C₃×C₄×C₅×C₈	—	2	1	no	—
24	C₃×#1922	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₅×#427	C₂×C₃	1	1	yes	characteristic
26	C₅×#424	C₂×C₃	1	1	yes	characteristic
27	C₅×#405	C₂×C₃	1	1	yes	characteristic
28	C₅×#341	C₂×C₃	1	1	yes	characteristic
29	C₅×#339	C₂×C₃	1	1	yes	characteristic
30	C₅×#339	C₂×C₃	1	1	yes	characteristic
31	C₅×#336	C₂×C₃	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	—	2	1	no	—
33	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₃×C₅×M₁₆	—	2	1	no	—
35	C₃×C₅×M₁₆	—	2	1	no	—
36	C₃×C₅×M₁₆	—	2	1	no	—
37	C₃×C₅×M₁₆	Q₈	1	2	yes	—
38	C₂×C₃×C₅×C₈	—	2	1	no	—
39	C₂×C₃×C₅×C₈	—	2	1	no	—
40	C₂×C₃×C₅×C₈	—	2	1	no	—
41	C₂×C₃×C₅×C₈	—	2	1	no	—
42	C₂×C₃×C₅×C₈	—	2	1	no	—
43	C₂×C₃×C₅×C₈	—	2	1	no	—
44	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
45	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
47	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
48	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
53	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
54	C₃×C₄²×C₅	—	2	1	no	—
55	C₃×C₄²×C₅	—	2	1	no	—
56	C₃×C₄²×C₅	—	2	1	no	—
57	C₃×C₄²×C₅	—	2	1	no	—
58	C₃×#427	C₂×C₅	1	1	yes	characteristic
59	C₃×#424	C₂×C₅	1	1	yes	characteristic
60	C₃×#405	C₂×C₅	1	1	yes	characteristic
61	C₃×#341	C₂×C₅	1	1	yes	characteristic
62	C₃×#339	C₂×C₅	1	1	yes	characteristic
63	C₃×#339	C₂×C₅	1	1	yes	characteristic
64	C₃×#336	C₂×C₅	1	1	yes	characteristic
65	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
69	C₅×#117	C₂²×C₃	1	1	yes	characteristic
70	C₅×#117	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₅×#107	C₃×C₄	1	1	yes	characteristic, complemented
73	C₅×#107	C₃×C₄	1	1	yes	characteristic, complemented
74	C₅×#106	C₃×C₄	1	1	yes	characteristic, complemented
75	C₅×#106	C₃×C₄	1	1	yes	characteristic, complemented
76	C₅×C₄⋊C₈	—	2	1	no	—
77	C₅×C₄⋊C₈	—	2	1	no	—
78	C₅×#97	—	2	1	no	—
79	C₄×C₅×C₈	—	2	1	no	—
80	#1922	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
81	C₂³×C₃×C₅	#41	1	1	yes	characteristic
82	C₂×C₃×C₄×C₅	—	2	2	no	—
83	C₂×C₃×C₄×C₅	—	2	1	no	—
84	C₂×C₃×C₄×C₅	—	2	1	no	—
85	C₂×C₃×C₄×C₅	—	2	1	no	—
86	C₂×C₃×C₄×C₅	—	2	1	no	—
87	C₂×C₃×C₄×C₅	—	4	1	no	—
88	C₂×C₃×C₄×C₅	—	4	1	no	—
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
95	C₃×C₅×C₈	—	2	1	no	—
96	C₃×C₅×C₈	—	2	1	no	—
97	C₃×C₅×C₈	—	2	2	no	—
98	C₃×C₅×C₈	—	2	1	no	—
99	C₃×C₅×C₈	—	2	1	no	—
100	C₃×C₅×C₈	—	4	1	no	—
101	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
102	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
103	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
104	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
105	C₃×#117	C₂²×C₅	1	1	yes	characteristic
106	C₃×#117	C₂²×C₅	1	1	yes	characteristic
107	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
108	C₃×#107	C₄×C₅	1	1	yes	characteristic, complemented
109	C₃×#107	C₄×C₅	1	1	yes	characteristic, complemented
110	C₃×#106	C₄×C₅	1	1	yes	characteristic, complemented
111	C₃×#106	C₄×C₅	1	1	yes	characteristic, complemented
112	C₃×C₄⋊C₈	—	2	1	no	—
113	C₃×C₄⋊C₈	—	2	1	no	—
114	C₃×#97	—	2	1	no	—
115	C₃×C₄×C₈	—	2	1	no	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
118	C₅×M₁₆	—	2	1	no	—
119	C₅×M₁₆	—	2	1	no	—
120	C₅×M₁₆	—	2	1	no	—
121	C₅×M₁₆	C₃×Q₈	1	2	yes	—
122	C₂×C₅×C₈	—	2	1	no	—
123	C₂×C₅×C₈	—	2	1	no	—
124	C₂×C₅×C₈	—	2	1	no	—
125	C₂×C₅×C₈	—	2	1	no	—
126	C₂×C₅×C₈	—	2	1	no	—
127	C₂×C₅×C₈	—	2	1	no	—
128	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
129	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
130	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
131	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
132	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
133	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
134	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
135	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
136	C₅×C₂²⋊C₄	—	2	1	no	—
137	C₅×C₂²⋊C₄	—	2	1	no	—
138	C₄²×C₅	—	2	1	no	—
139	C₄²×C₅	—	2	1	no	—
140	C₄²×C₅	—	2	1	no	—
141	C₄²×C₅	—	2	1	no	—
142	#427	C₂×C₃×C₅	1	1	yes	characteristic
143	#424	C₂×C₃×C₅	1	1	yes	characteristic
144	#405	C₂×C₃×C₅	1	1	yes	characteristic
145	#341	C₂×C₃×C₅	1	1	yes	characteristic
146	#339	C₂×C₃×C₅	1	1	yes	characteristic
147	#339	C₂×C₃×C₅	1	1	yes	characteristic
148	#336	C₂×C₃×C₅	1	1	yes	characteristic
149	C₂²×C₃×C₅	—	2	1	no	—
150	C₂²×C₃×C₅	—	2	1	no	—
151	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
152	C₂²×C₃×C₅	#125	1	1	yes	characteristic
153	C₂²×C₃×C₅	#126	1	1	yes	characteristic
154	C₃×C₄×C₅	—	4	2	no	—
155	C₃×C₄×C₅	—	4	1	no	—
156	C₃×C₄×C₅	—	4	1	no	—
157	C₃×C₄×C₅	—	4	1	no	—
158	C₃×C₄×C₅	—	4	1	no	—
159	C₃×C₄×C₅	#117	1	1	yes	characteristic
160	C₃×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
161	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
162	C₃×C₄×C₅	#123	1	1	yes	characteristic
163	C₂²×C₃×C₄	—	2	1	no	—
164	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
165	C₃×M₁₆	—	2	1	no	—
166	C₃×M₁₆	—	2	1	no	—
167	C₃×M₁₆	—	2	1	no	—
168	C₃×M₁₆	C₅×Q₈	1	2	yes	—
169	C₂×C₃×C₈	—	2	1	no	—
170	C₂×C₃×C₈	—	2	1	no	—
171	C₂×C₃×C₈	—	2	1	no	—
172	C₂×C₃×C₈	—	2	1	no	—
173	C₂×C₃×C₈	—	2	1	no	—
174	C₂×C₃×C₈	—	2	1	no	—
175	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
176	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
177	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
178	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
179	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
180	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
181	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
182	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
183	C₃×C₂²⋊C₄	—	2	1	no	—
184	C₃×C₂²⋊C₄	—	2	1	no	—
185	C₃×C₄²	—	2	1	no	—
186	C₃×C₄²	—	2	1	no	—
187	C₃×C₄²	—	2	1	no	—
188	C₃×C₄²	—	2	1	no	—
189	C₂³×C₅	C₃×#41	1	1	yes	characteristic
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	2	1	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	4	1	no	—
196	C₂×C₄×C₅	—	4	1	no	—
197	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
199	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
200	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
201	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
202	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
203	C₅×C₈	—	2	1	no	—
204	C₅×C₈	—	2	1	no	—
205	C₅×C₈	—	2	2	no	—
206	C₅×C₈	—	2	1	no	—
207	C₅×C₈	—	2	1	no	—
208	C₅×C₈	—	4	1	no	—
209	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
210	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
211	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
212	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
213	#117	C₂²×C₃×C₅	1	1	yes	characteristic
214	#117	C₂²×C₃×C₅	1	1	yes	characteristic
215	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
216	#107	C₃×C₄×C₅	1	1	yes	characteristic, complemented
217	#107	C₃×C₄×C₅	1	1	yes	characteristic, complemented
218	#106	C₃×C₄×C₅	1	1	yes	characteristic, complemented
219	#106	C₃×C₄×C₅	1	1	yes	characteristic, complemented
220	C₄⋊C₈	—	2	1	no	—
221	C₄⋊C₈	—	2	1	no	—
222	#97	—	2	1	no	—
223	C₄×C₈	—	2	1	no	—
224	C₂×C₃×C₅	—	2	1	no	—
225	C₂×C₃×C₅	—	2	1	no	—
226	C₂×C₃×C₅	#387	1	1	yes	characteristic
227	C₂×C₃×C₅	#443	1	1	yes	characteristic
228	C₂×C₃×C₅	#444	1	1	yes	characteristic
229	C₂³×C₃	C₅×#41	1	1	yes	characteristic
230	C₂×C₃×C₄	—	2	2	no	—
231	C₂×C₃×C₄	—	2	1	no	—
232	C₂×C₃×C₄	—	2	1	no	—
233	C₂×C₃×C₄	—	2	1	no	—
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	4	1	no	—
236	C₂×C₃×C₄	—	4	1	no	—
237	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
238	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
240	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
241	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
242	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
243	C₃×C₈	—	2	1	no	—
244	C₃×C₈	—	2	1	no	—
245	C₃×C₈	—	2	2	no	—
246	C₃×C₈	—	2	1	no	—
247	C₃×C₈	—	2	1	no	—
248	C₃×C₈	—	4	1	no	—
249	C₂²×C₅	—	2	1	no	—
250	C₂²×C₅	—	2	1	no	—
251	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
252	C₂²×C₅	C₃×#125	1	1	yes	characteristic
253	C₂²×C₅	C₃×#126	1	1	yes	characteristic
254	C₄×C₅	—	4	2	no	—
255	C₄×C₅	—	4	1	no	—
256	C₄×C₅	—	4	1	no	—
257	C₄×C₅	—	4	1	no	—
258	C₄×C₅	—	4	1	no	—
259	C₄×C₅	C₃×#117	1	1	yes	characteristic
260	C₄×C₅	C₃×C₄×Q₈	1	1	yes	characteristic
261	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
262	C₄×C₅	C₃×#123	1	1	yes	characteristic
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
265	M₁₆	—	2	1	no	—
266	M₁₆	—	2	1	no	—
267	M₁₆	—	2	1	no	—
268	M₁₆	C₃×C₅×Q₈	1	2	yes	—
269	C₂×C₈	—	2	1	no	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	2	1	no	—
272	C₂×C₈	—	2	1	no	—
273	C₂×C₈	—	2	1	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
276	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
277	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
278	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
279	C₄⋊C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
280	C₄⋊C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
281	C₄⋊C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
282	C₄⋊C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
283	C₂²⋊C₄	—	2	1	no	—
284	C₂²⋊C₄	—	2	1	no	—
285	C₄²	—	2	1	no	—
286	C₄²	—	2	1	no	—
287	C₄²	—	2	1	no	—
288	C₄²	—	2	1	no	—
289	C₃×C₅	#1922	1	1	yes	characteristic, direct product factor, Hall
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
293	C₂²×C₃	C₅×#125	1	1	yes	characteristic
294	C₂²×C₃	C₅×#126	1	1	yes	characteristic
295	C₃×C₄	—	4	2	no	—
296	C₃×C₄	—	4	1	no	—
297	C₃×C₄	—	4	1	no	—
298	C₃×C₄	—	4	1	no	—
299	C₃×C₄	—	4	1	no	—
300	C₃×C₄	C₅×#117	1	1	yes	characteristic
301	C₃×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
302	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
303	C₃×C₄	C₅×#123	1	1	yes	characteristic
304	C₂×C₅	—	2	1	no	—
305	C₂×C₅	—	2	1	no	—
306	C₂×C₅	C₃×#387	1	1	yes	characteristic
307	C₂×C₅	C₃×#443	1	1	yes	characteristic
308	C₂×C₅	C₃×#444	1	1	yes	characteristic
309	C₂³	C₃×C₅×#41	1	1	yes	characteristic
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
318	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
319	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
320	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
321	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
322	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
323	C₈	—	2	1	no	—
324	C₈	—	2	1	no	—
325	C₈	—	2	2	no	—
326	C₈	—	2	1	no	—
327	C₈	—	2	1	no	—
328	C₈	—	4	1	no	—
329	C₂×C₃	—	2	1	no	—
330	C₂×C₃	—	2	1	no	—
331	C₂×C₃	C₅×#387	1	1	yes	characteristic
332	C₂×C₃	C₅×#443	1	1	yes	characteristic
333	C₂×C₃	C₅×#444	1	1	yes	characteristic
334	C₅	C₃×#1922	1	1	yes	characteristic, direct product factor, Sylow
335	C₂²	—	2	1	no	—
336	C₂²	—	2	1	no	—
337	C₂²	C₃×C₄×C₅×D₄	1	1	yes	characteristic
338	C₂²	C₃×C₅×#125	1	1	yes	characteristic
339	C₂²	C₃×C₅×#126	1	1	yes	characteristic
340	C₄	—	4	2	no	—
341	C₄	—	4	1	no	—
342	C₄	—	4	1	no	—
343	C₄	—	4	1	no	—
344	C₄	—	4	1	no	—
345	C₄	C₃×C₅×#117	1	1	yes	characteristic
346	C₄	C₃×C₄×C₅×Q₈	1	1	yes	characteristic
347	C₄	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
348	C₄	C₃×C₅×#123	1	1	yes	characteristic
349	C₃	C₅×#1922	1	1	yes	characteristic, direct product factor, Sylow
350	C₂	—	2	1	no	—
351	C₂	—	2	1	no	—
352	C₂	C₃×C₅×#387	1	1	yes	characteristic
353	C₂	C₃×C₅×#443	1	1	yes	characteristic
354	C₂	C₃×C₅×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄×C₅	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂³×C₃×C₅	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄×C₅ ◁ C₂²×C₃×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₅×#1922	C₃	direct (N × H)
16. C₃×C₅×#107	C₄	semidirect
17. C₃×C₅×#107	C₄	semidirect
18. C₃×C₅×#106	C₄	semidirect
19. C₃×C₅×#106	C₄	semidirect
24. C₃×#1922	C₅	direct (N × H)
72. C₅×#107	C₃×C₄	semidirect
73. C₅×#107	C₃×C₄	semidirect
74. C₅×#106	C₃×C₄	semidirect
75. C₅×#106	C₃×C₄	semidirect
80. #1922	C₃×C₅	direct (N × H)
108. C₃×#107	C₄×C₅	semidirect
109. C₃×#107	C₄×C₅	semidirect
110. C₃×#106	C₄×C₅	semidirect
111. C₃×#106	C₄×C₅	semidirect
216. #107	C₃×C₄×C₅	semidirect
217. #107	C₃×C₄×C₅	semidirect
218. #106	C₃×C₄×C₅	semidirect
219. #106	C₃×C₄×C₅	semidirect
289. C₃×C₅	#1922	direct (N × H)
334. C₅	C₃×#1922	direct (N × H)
349. C₃	C₅×#1922	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×C₅×#427	2
C₃×C₅×#424	2
C₃×C₅×#405	2
C₃×C₅×#341	2
C₃×C₅×#339	2
C₃×C₅×#336	2
C₅×#1922	3
C₃×#1922	5

Subgroups — C3×C5×#1922 #14274956

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1922 #14274956