Subgroups — C₃×C₅×#1547 #14274581

Order 1920.

520 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#332	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#331	C₂	1	2	yes	maximal, complemented
6	C₅×#1547	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×#41	—	2	1	no	—
8	C₂×C₃×C₅×M₁₆	—	2	1	no	—
9	C₂²×C₃×C₅×C₈	—	2	1	no	—
10	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₃×C₅×#127	C₂²	1	1	yes	characteristic
12	C₃×C₅×#124	—	2	1	no	—
13	C₃×C₅×#121	—	2	1	no	—
14	C₃×C₅×#121	C₄	1	2	yes	—
15	C₃×C₄×C₅×D₄	—	2	1	no	—
16	C₃×C₄×C₅×D₄	C₄	1	2	yes	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₃×C₅×C₄⋊C₈	—	2	1	no	—
19	C₃×C₅×C₄⋊C₈	—	2	1	no	—
20	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
21	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
22	C₃×#1547	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₅×#532	C₂×C₃	1	1	yes	characteristic
24	C₅×#423	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
26	C₅×#332	C₂×C₃	1	2	yes	complemented
27	C₅×#331	C₂×C₃	1	2	yes	complemented
28	C₃×C₅×#41	—	4	2	no	—
29	C₃×C₅×#41	—	4	2	no	—
30	C₂×C₃×C₅×Q₈	—	2	1	no	—
31	C₂×C₃×C₅×D₄	—	2	2	no	—
32	C₂×C₃×C₅×D₄	—	2	1	no	—
33	C₂×C₃×C₅×D₄	—	2	1	no	—
34	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
35	C₂²×C₃×C₄×C₅	—	2	2	no	—
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
39	C₃×C₅×M₁₆	—	4	2	no	—
40	C₂×C₃×C₅×C₈	—	2	2	no	—
41	C₂×C₃×C₅×C₈	—	2	2	no	—
42	C₂×C₃×C₅×C₈	—	4	2	no	—
43	C₃×C₅×C₄⋊C₄	—	2	1	no	—
44	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
45	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
46	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
47	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
48	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
49	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
50	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
51	C₃×#532	C₂×C₅	1	1	yes	characteristic
52	C₃×#423	C₂×C₅	1	1	yes	characteristic, complemented
53	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
54	C₃×#332	C₂×C₅	1	2	yes	complemented
55	C₃×#331	C₂×C₅	1	2	yes	complemented
56	C₂×C₅×#41	—	2	1	no	—
57	C₂×C₅×M₁₆	—	2	1	no	—
58	C₂²×C₅×C₈	—	2	1	no	—
59	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
60	C₅×#127	C₂²×C₃	1	1	yes	characteristic
61	C₅×#124	—	2	1	no	—
62	C₅×#121	—	2	1	no	—
63	C₅×#121	C₃×C₄	1	2	yes	—
64	C₄×C₅×D₄	—	2	1	no	—
65	C₄×C₅×D₄	C₃×C₄	1	2	yes	—
66	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
67	C₅×C₄⋊C₈	—	2	1	no	—
68	C₅×C₄⋊C₈	—	2	1	no	—
69	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
70	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
71	#1547	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
72	C₂³×C₃×C₅	—	2	2	no	—
73	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
74	C₃×C₅×Q₈	—	4	1	no	—
75	C₃×C₅×Q₈	—	4	1	no	—
76	C₃×C₅×D₄	—	4	2	no	—
77	C₃×C₅×D₄	—	4	4	no	—
78	C₃×C₅×D₄	—	4	1	no	—
79	C₃×C₅×D₄	—	4	1	no	—
80	C₃×C₅×D₄	—	4	1	no	—
81	C₃×C₅×D₄	—	4	1	no	—
82	C₂×C₃×C₄×C₅	—	2	1	no	—
83	C₂×C₃×C₄×C₅	—	2	1	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	4	1	no	—
86	C₂×C₃×C₄×C₅	—	4	4	no	—
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	D₈	1	2	yes	—
91	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₃×C₅×C₈	—	4	2	no	—
96	C₃×C₅×C₈	—	4	2	no	—
97	C₂×C₃×#41	—	2	1	no	—
98	C₂×C₃×M₁₆	—	2	1	no	—
99	C₂²×C₃×C₈	—	2	1	no	—
100	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
101	C₃×#127	C₂²×C₅	1	1	yes	characteristic
102	C₃×#124	—	2	1	no	—
103	C₃×#121	—	2	1	no	—
104	C₃×#121	C₄×C₅	1	2	yes	—
105	C₃×C₄×D₄	—	2	1	no	—
106	C₃×C₄×D₄	C₄×C₅	1	2	yes	—
107	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
108	C₃×C₄⋊C₈	—	2	1	no	—
109	C₃×C₄⋊C₈	—	2	1	no	—
110	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
111	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
112	C₅×#41	—	4	2	no	—
113	C₅×#41	—	4	2	no	—
114	C₂×C₅×Q₈	—	2	1	no	—
115	C₂×C₅×D₄	—	2	2	no	—
116	C₂×C₅×D₄	—	2	1	no	—
117	C₂×C₅×D₄	—	2	1	no	—
118	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
123	C₅×M₁₆	—	4	2	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	4	2	no	—
127	C₅×C₄⋊C₄	—	2	1	no	—
128	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
129	C₅×C₂²⋊C₄	—	2	2	no	—
130	C₅×C₂²⋊C₄	—	2	2	no	—
131	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
132	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
133	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
134	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
135	#532	C₂×C₃×C₅	1	1	yes	characteristic
136	#423	C₂×C₃×C₅	1	1	yes	characteristic, complemented
137	C₂×C₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
138	#332	C₂×C₃×C₅	1	2	yes	complemented
139	#331	C₂×C₃×C₅	1	2	yes	complemented
140	C₂²×C₃×C₅	—	2	1	no	—
141	C₂²×C₃×C₅	—	2	1	no	—
142	C₂²×C₃×C₅	—	4	2	no	—
143	C₂²×C₃×C₅	—	4	2	no	—
144	C₂²×C₃×C₅	—	4	2	no	—
145	C₂²×C₃×C₅	#102	1	2	yes	—
146	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₃×C₄×C₅	—	2	1	no	—
148	C₃×C₄×C₅	—	2	1	no	—
149	C₃×C₄×C₅	—	2	1	no	—
150	C₃×C₄×C₅	—	4	2	no	—
151	C₃×C₄×C₅	#102	1	2	yes	—
152	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
153	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
154	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₃×C₄×C₅	#137	1	1	yes	characteristic
156	C₃×#41	—	4	2	no	—
157	C₃×#41	—	4	2	no	—
158	C₂×C₃×Q₈	—	2	1	no	—
159	C₂×C₃×D₄	—	2	2	no	—
160	C₂×C₃×D₄	—	2	1	no	—
161	C₂×C₃×D₄	—	2	1	no	—
162	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
163	C₂²×C₃×C₄	—	2	2	no	—
164	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
166	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
167	C₃×M₁₆	—	4	2	no	—
168	C₂×C₃×C₈	—	2	2	no	—
169	C₂×C₃×C₈	—	2	2	no	—
170	C₂×C₃×C₈	—	4	2	no	—
171	C₃×C₄⋊C₄	—	2	1	no	—
172	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
173	C₃×C₂²⋊C₄	—	2	2	no	—
174	C₃×C₂²⋊C₄	—	2	2	no	—
175	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
176	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
177	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
178	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
179	C₂³×C₅	—	2	2	no	—
180	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
181	C₅×Q₈	—	4	1	no	—
182	C₅×Q₈	—	4	1	no	—
183	C₅×D₄	—	4	2	no	—
184	C₅×D₄	—	4	4	no	—
185	C₅×D₄	—	4	1	no	—
186	C₅×D₄	—	4	1	no	—
187	C₅×D₄	—	4	1	no	—
188	C₅×D₄	—	4	1	no	—
189	C₂×C₄×C₅	—	2	1	no	—
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	4	1	no	—
193	C₂×C₄×C₅	—	4	4	no	—
194	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₅	C₃×D₈	1	2	yes	—
198	C₂×C₄×C₅	C₃×SD₁₆	1	2	yes	—
199	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
200	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
201	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
202	C₅×C₈	—	4	2	no	—
203	C₅×C₈	—	4	2	no	—
204	C₂×#41	—	2	1	no	—
205	C₂×M₁₆	—	2	1	no	—
206	C₂²×C₈	—	2	1	no	—
207	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
208	#127	C₂²×C₃×C₅	1	1	yes	characteristic
209	#124	—	2	1	no	—
210	#121	—	2	1	no	—
211	#121	C₃×C₄×C₅	1	2	yes	—
212	C₄×D₄	—	2	1	no	—
213	C₄×D₄	C₃×C₄×C₅	1	2	yes	—
214	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
215	C₄⋊C₈	—	2	1	no	—
216	C₄⋊C₈	—	2	1	no	—
217	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
218	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
219	C₂×C₃×C₅	—	2	2	no	—
220	C₂×C₃×C₅	—	8	2	no	—
221	C₂×C₃×C₅	#413	1	1	yes	characteristic
222	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
223	C₂×C₃×C₅	#417	1	1	yes	characteristic
224	C₂³×C₃	—	2	2	no	—
225	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
226	C₃×Q₈	—	4	1	no	—
227	C₃×Q₈	—	4	1	no	—
228	C₃×D₄	—	4	2	no	—
229	C₃×D₄	—	4	4	no	—
230	C₃×D₄	—	4	1	no	—
231	C₃×D₄	—	4	1	no	—
232	C₃×D₄	—	4	1	no	—
233	C₃×D₄	—	4	1	no	—
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	4	1	no	—
238	C₂×C₃×C₄	—	4	4	no	—
239	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₃×C₄	C₅×D₈	1	2	yes	—
243	C₂×C₃×C₄	C₅×SD₁₆	1	2	yes	—
244	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
246	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
247	C₃×C₈	—	4	2	no	—
248	C₃×C₈	—	4	2	no	—
249	C₂²×C₅	—	2	1	no	—
250	C₂²×C₅	—	2	1	no	—
251	C₂²×C₅	—	4	2	no	—
252	C₂²×C₅	—	4	2	no	—
253	C₂²×C₅	—	4	2	no	—
254	C₂²×C₅	C₃×#102	1	2	yes	—
255	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
256	C₄×C₅	—	2	1	no	—
257	C₄×C₅	—	2	1	no	—
258	C₄×C₅	—	2	1	no	—
259	C₄×C₅	—	4	2	no	—
260	C₄×C₅	C₃×#102	1	2	yes	—
261	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
262	C₄×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
263	C₄×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
264	C₄×C₅	C₃×#137	1	1	yes	characteristic
265	#41	—	4	2	no	—
266	#41	—	4	2	no	—
267	C₂×Q₈	—	2	1	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	1	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	C₂×C₃×C₄×C₅	1	2	yes	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
274	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
275	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
276	M₁₆	—	4	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	4	2	no	—
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	C₂×C₃×C₄×C₅	1	2	yes	—
282	C₂²⋊C₄	—	2	2	no	—
283	C₂²⋊C₄	—	2	2	no	—
284	C₄²	C₂×C₃×C₄×C₅	1	1	yes	characteristic
285	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
286	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
287	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
288	C₃×C₅	#1547	1	1	yes	characteristic, direct product factor, Hall
289	C₂²×C₃	—	2	1	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	4	2	no	—
292	C₂²×C₃	—	4	2	no	—
293	C₂²×C₃	—	4	2	no	—
294	C₂²×C₃	C₅×#102	1	2	yes	—
295	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
296	C₃×C₄	—	2	1	no	—
297	C₃×C₄	—	2	1	no	—
298	C₃×C₄	—	2	1	no	—
299	C₃×C₄	—	4	2	no	—
300	C₃×C₄	C₅×#102	1	2	yes	—
301	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
302	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
303	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
304	C₃×C₄	C₅×#137	1	1	yes	characteristic
305	C₂×C₅	—	2	2	no	—
306	C₂×C₅	—	8	2	no	—
307	C₂×C₅	C₃×#413	1	1	yes	characteristic
308	C₂×C₅	C₂×C₃×#102	1	1	yes	characteristic
309	C₂×C₅	C₃×#417	1	1	yes	characteristic
310	C₂³	—	2	2	no	—
311	C₂³	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
312	Q₈	—	4	1	no	—
313	Q₈	—	4	1	no	—
314	D₄	—	4	2	no	—
315	D₄	—	4	4	no	—
316	D₄	—	4	1	no	—
317	D₄	—	4	1	no	—
318	D₄	—	4	1	no	—
319	D₄	—	4	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
326	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
327	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
328	C₂×C₄	C₃×C₅×D₈	1	2	yes	—
329	C₂×C₄	C₃×C₅×SD₁₆	1	2	yes	—
330	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
331	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
332	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
333	C₈	—	4	2	no	—
334	C₈	—	4	2	no	—
335	C₂×C₃	—	2	2	no	—
336	C₂×C₃	—	8	2	no	—
337	C₂×C₃	C₅×#413	1	1	yes	characteristic
338	C₂×C₃	C₂×C₅×#102	1	1	yes	characteristic
339	C₂×C₃	C₅×#417	1	1	yes	characteristic
340	C₅	C₃×#1547	1	1	yes	characteristic, direct product factor, Sylow
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	2	no	—
346	C₂²	C₃×C₅×#102	1	2	yes	—
347	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	4	2	no	—
352	C₄	C₃×C₅×#102	1	2	yes	—
353	C₄	C₂×C₃×C₅×D₈	1	1	yes	characteristic
354	C₄	C₂×C₃×C₅×SD₁₆	1	1	yes	characteristic
355	C₄	C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
356	C₄	C₃×C₅×#137	1	1	yes	characteristic
357	C₃	C₅×#1547	1	1	yes	characteristic, direct product factor, Sylow
358	C₂	—	2	2	no	—
359	C₂	—	8	2	no	—
360	C₂	C₃×C₅×#413	1	1	yes	characteristic
361	C₂	C₂×C₃×C₅×#102	1	1	yes	characteristic
362	C₂	C₃×C₅×#417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₄²	C₂³×C₃×C₅
prime radical	C₃×C₅×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#423	C₂	semidirect
3. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
4. C₃×C₅×#332	C₂	semidirect
5. C₃×C₅×#331	C₂	semidirect
6. C₅×#1547	C₃	direct (N × H)
22. C₃×#1547	C₅	direct (N × H)
24. C₅×#423	C₂×C₃	semidirect
25. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
26. C₅×#332	C₂×C₃	semidirect
27. C₅×#331	C₂×C₃	semidirect
52. C₃×#423	C₂×C₅	semidirect
53. C₂×C₃×C₄⋊C₈	C₂×C₅	semidirect
54. C₃×#332	C₂×C₅	semidirect
55. C₃×#331	C₂×C₅	semidirect
71. #1547	C₃×C₅	direct (N × H)
136. #423	C₂×C₃×C₅	semidirect
137. C₂×C₄⋊C₈	C₂×C₃×C₅	semidirect
138. #332	C₂×C₃×C₅	semidirect
139. #331	C₂×C₃×C₅	semidirect
288. C₃×C₅	#1547	direct (N × H)
340. C₅	C₃×#1547	direct (N × H)
357. C₃	C₅×#1547	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×#532	2
C₃×C₅×#423	2
C₂×C₃×C₅×C₄⋊C₈	2
C₃×C₅×#332	2
C₃×C₅×#331	2
C₅×#1547	3
C₃×#1547	5

Subgroups — C3×C5×#1547 #14274581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1547 #14274581