Subgroups — C₃×C₅×#1649 #14274683

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#474	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#332	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₅×#1649	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	—	2	1	no	—
10	C₂×C₃×C₅×Q₁₆	—	2	1	no	—
11	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
12	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
15	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
16	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₃×C₄×C₅×D₄	—	2	1	no	—
18	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₃×C₅×#107	—	2	1	no	—
20	C₃×C₅×#107	—	2	2	no	—
21	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×#103	—	2	1	no	—
24	C₃×C₅×#102	—	2	1	no	—
25	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₃×#1649	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×D₄×Q₈	C₂×C₃	1	1	yes	characteristic
28	C₅×#500	C₂×C₃	1	1	yes	characteristic, complemented
29	C₅×#474	C₂×C₃	1	1	yes	characteristic
30	C₅×#462	C₂×C₃	1	1	yes	characteristic, complemented
31	C₅×#332	C₂×C₃	1	1	yes	characteristic, complemented
32	C₅×Q₈⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
33	C₅×D₄⋊C₈	C₂×C₃	1	1	yes	characteristic
34	C₂×C₃×C₅×Q₈	—	2	2	no	—
35	C₂×C₃×C₅×Q₈	—	2	1	no	—
36	C₂×C₃×C₅×Q₈	—	2	1	no	—
37	C₂×C₃×C₅×Q₈	—	4	2	no	—
38	C₂×C₃×C₅×Q₈	—	4	2	no	—
39	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
40	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	—	2	2	no	—
42	C₂²×C₃×C₄×C₅	—	2	1	no	—
43	C₃×C₅×Q₁₆	—	4	2	no	—
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₃×C₅×C₄⋊C₄	—	2	2	no	—
48	C₃×C₅×C₄⋊C₄	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	—	2	1	no	—
51	C₃×C₅×C₄⋊C₄	—	2	1	no	—
52	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
53	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
54	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
55	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
56	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
57	C₃×C₄²×C₅	—	2	1	no	—
58	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₃×D₄×Q₈	C₂×C₅	1	1	yes	characteristic
60	C₃×#500	C₂×C₅	1	1	yes	characteristic, complemented
61	C₃×#474	C₂×C₅	1	1	yes	characteristic
62	C₃×#462	C₂×C₅	1	1	yes	characteristic, complemented
63	C₃×#332	C₂×C₅	1	1	yes	characteristic, complemented
64	C₃×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
65	C₃×D₄⋊C₈	C₂×C₅	1	1	yes	characteristic
66	C₂²×C₅×Q₈	—	2	1	no	—
67	C₂×C₅×Q₁₆	—	2	1	no	—
68	C₅×C₄⋊Q₈	—	2	1	no	—
69	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
70	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
71	C₅×C₂²⋊Q₈	—	2	1	no	—
72	C₅×C₂²⋊Q₈	—	2	2	no	—
73	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
74	C₄×C₅×D₄	—	2	1	no	—
75	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
76	C₅×#107	—	2	1	no	—
77	C₅×#107	—	2	2	no	—
78	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
79	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
80	C₅×#103	—	2	1	no	—
81	C₅×#102	—	2	1	no	—
82	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
83	#1649	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
84	C₂³×C₃×C₅	—	2	1	no	—
85	C₃×C₅×Q₈	—	2	1	no	—
86	C₃×C₅×Q₈	—	4	4	no	—
87	C₃×C₅×Q₈	—	4	1	no	—
88	C₃×C₅×Q₈	—	4	1	no	—
89	C₃×C₅×Q₈	—	4	1	no	—
90	C₃×C₅×Q₈	—	4	1	no	—
91	C₃×C₅×Q₈	D₈	1	2	yes	—
92	C₃×C₅×D₄	—	2	1	no	—
93	C₃×C₅×D₄	Q₁₆	1	2	yes	complemented
94	C₂×C₃×C₄×C₅	—	2	1	no	—
95	C₂×C₃×C₄×C₅	—	2	1	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	—	4	4	no	—
99	C₂×C₃×C₄×C₅	—	4	1	no	—
100	C₂×C₃×C₄×C₅	—	4	1	no	—
101	C₂×C₃×C₄×C₅	—	4	1	no	—
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₃×C₅×C₈	—	2	2	no	—
106	C₃×C₅×C₈	—	4	1	no	—
107	C₃×C₅×C₈	—	4	1	no	—
108	C₂²×C₃×Q₈	—	2	1	no	—
109	C₂×C₃×Q₁₆	—	2	1	no	—
110	C₃×C₄⋊Q₈	—	2	1	no	—
111	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
112	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
113	C₃×C₂²⋊Q₈	—	2	1	no	—
114	C₃×C₂²⋊Q₈	—	2	2	no	—
115	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
116	C₃×C₄×D₄	—	2	1	no	—
117	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
118	C₃×#107	—	2	1	no	—
119	C₃×#107	—	2	2	no	—
120	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
121	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
122	C₃×#103	—	2	1	no	—
123	C₃×#102	—	2	1	no	—
124	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
125	C₂×C₅×Q₈	—	2	2	no	—
126	C₂×C₅×Q₈	—	2	1	no	—
127	C₂×C₅×Q₈	—	2	1	no	—
128	C₂×C₅×Q₈	—	4	2	no	—
129	C₂×C₅×Q₈	—	4	2	no	—
130	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
131	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	—	2	2	no	—
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₅×Q₁₆	—	4	2	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	2	1	no	—
137	C₂×C₅×C₈	—	2	1	no	—
138	C₅×C₄⋊C₄	—	2	2	no	—
139	C₅×C₄⋊C₄	—	2	1	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₄⋊C₄	—	2	1	no	—
143	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
144	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
145	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
146	C₅×C₂²⋊C₄	—	2	2	no	—
147	C₅×C₂²⋊C₄	—	2	1	no	—
148	C₄²×C₅	—	2	1	no	—
149	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
150	D₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
151	#500	C₂×C₃×C₅	1	1	yes	characteristic, complemented
152	#474	C₂×C₃×C₅	1	1	yes	characteristic
153	#462	C₂×C₃×C₅	1	1	yes	characteristic, complemented
154	#332	C₂×C₃×C₅	1	1	yes	characteristic, complemented
155	Q₈⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
156	D₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic
157	C₂²×C₃×C₅	—	2	2	no	—
158	C₂²×C₃×C₅	—	4	1	no	—
159	C₂²×C₃×C₅	—	4	1	no	—
160	C₂²×C₃×C₅	#120	1	1	yes	characteristic
161	C₃×C₄×C₅	—	2	2	no	—
162	C₃×C₄×C₅	—	2	1	no	—
163	C₃×C₄×C₅	—	4	2	no	—
164	C₃×C₄×C₅	—	4	1	no	—
165	C₃×C₄×C₅	—	4	1	no	—
166	C₃×C₄×C₅	—	8	1	no	—
167	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
168	C₃×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
169	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₃×C₄×C₅	#137	1	1	yes	characteristic
171	C₂×C₃×Q₈	—	2	2	no	—
172	C₂×C₃×Q₈	—	2	1	no	—
173	C₂×C₃×Q₈	—	2	1	no	—
174	C₂×C₃×Q₈	—	4	2	no	—
175	C₂×C₃×Q₈	—	4	2	no	—
176	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
177	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
178	C₂²×C₃×C₄	—	2	2	no	—
179	C₂²×C₃×C₄	—	2	1	no	—
180	C₃×Q₁₆	—	4	2	no	—
181	C₂×C₃×C₈	—	2	1	no	—
182	C₂×C₃×C₈	—	2	1	no	—
183	C₂×C₃×C₈	—	2	1	no	—
184	C₃×C₄⋊C₄	—	2	2	no	—
185	C₃×C₄⋊C₄	—	2	1	no	—
186	C₃×C₄⋊C₄	—	2	1	no	—
187	C₃×C₄⋊C₄	—	2	1	no	—
188	C₃×C₄⋊C₄	—	2	1	no	—
189	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
190	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
191	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
192	C₃×C₂²⋊C₄	—	2	2	no	—
193	C₃×C₂²⋊C₄	—	2	1	no	—
194	C₃×C₄²	—	2	1	no	—
195	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
196	C₂³×C₅	—	2	1	no	—
197	C₅×Q₈	—	2	1	no	—
198	C₅×Q₈	—	4	4	no	—
199	C₅×Q₈	—	4	1	no	—
200	C₅×Q₈	—	4	1	no	—
201	C₅×Q₈	—	4	1	no	—
202	C₅×Q₈	—	4	1	no	—
203	C₅×Q₈	C₃×D₈	1	2	yes	—
204	C₅×D₄	—	2	1	no	—
205	C₅×D₄	C₃×Q₁₆	1	2	yes	complemented
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	4	4	no	—
211	C₂×C₄×C₅	—	4	1	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
217	C₅×C₈	—	2	2	no	—
218	C₅×C₈	—	4	1	no	—
219	C₅×C₈	—	4	1	no	—
220	C₂²×Q₈	—	2	1	no	—
221	C₂×Q₁₆	—	2	1	no	—
222	C₄⋊Q₈	—	2	1	no	—
223	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
224	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
225	C₂²⋊Q₈	—	2	1	no	—
226	C₂²⋊Q₈	—	2	2	no	—
227	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
230	#107	—	2	1	no	—
231	#107	—	2	2	no	—
232	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
233	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
234	#103	—	2	1	no	—
235	#102	—	2	1	no	—
236	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
237	C₂×C₃×C₅	—	4	2	no	—
238	C₂×C₃×C₅	#447	1	1	yes	characteristic
239	C₂×C₃×C₅	#451	1	1	yes	characteristic
240	C₂×C₃×C₅	#456	1	1	yes	characteristic
241	C₂³×C₃	—	2	1	no	—
242	C₃×Q₈	—	2	1	no	—
243	C₃×Q₈	—	4	4	no	—
244	C₃×Q₈	—	4	1	no	—
245	C₃×Q₈	—	4	1	no	—
246	C₃×Q₈	—	4	1	no	—
247	C₃×Q₈	—	4	1	no	—
248	C₃×Q₈	C₅×D₈	1	2	yes	—
249	C₃×D₄	—	2	1	no	—
250	C₃×D₄	C₅×Q₁₆	1	2	yes	complemented
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	4	4	no	—
256	C₂×C₃×C₄	—	4	1	no	—
257	C₂×C₃×C₄	—	4	1	no	—
258	C₂×C₃×C₄	—	4	1	no	—
259	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
262	C₃×C₈	—	2	2	no	—
263	C₃×C₈	—	4	1	no	—
264	C₃×C₈	—	4	1	no	—
265	C₂²×C₅	—	2	2	no	—
266	C₂²×C₅	—	4	1	no	—
267	C₂²×C₅	—	4	1	no	—
268	C₂²×C₅	C₃×#120	1	1	yes	characteristic
269	C₄×C₅	—	2	2	no	—
270	C₄×C₅	—	2	1	no	—
271	C₄×C₅	—	4	2	no	—
272	C₄×C₅	—	4	1	no	—
273	C₄×C₅	—	4	1	no	—
274	C₄×C₅	—	8	1	no	—
275	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
276	C₄×C₅	C₂×C₃×Q₁₆	1	1	yes	characteristic
277	C₄×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
278	C₄×C₅	C₃×#137	1	1	yes	characteristic
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	4	2	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
285	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	1	no	—
288	Q₁₆	—	4	2	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	1	no	—
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	—	2	1	no	—
297	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
298	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
299	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
300	C₂²⋊C₄	—	2	2	no	—
301	C₂²⋊C₄	—	2	1	no	—
302	C₄²	—	2	1	no	—
303	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
304	C₃×C₅	#1649	1	1	yes	characteristic, direct product factor, Hall
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	4	1	no	—
307	C₂²×C₃	—	4	1	no	—
308	C₂²×C₃	C₅×#120	1	1	yes	characteristic
309	C₃×C₄	—	2	2	no	—
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	—	4	2	no	—
312	C₃×C₄	—	4	1	no	—
313	C₃×C₄	—	4	1	no	—
314	C₃×C₄	—	8	1	no	—
315	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
316	C₃×C₄	C₂×C₅×Q₁₆	1	1	yes	characteristic
317	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
318	C₃×C₄	C₅×#137	1	1	yes	characteristic
319	C₂×C₅	—	4	2	no	—
320	C₂×C₅	C₃×#447	1	1	yes	characteristic
321	C₂×C₅	C₃×#451	1	1	yes	characteristic
322	C₂×C₅	C₃×#456	1	1	yes	characteristic
323	C₂³	—	2	1	no	—
324	Q₈	—	2	1	no	—
325	Q₈	—	4	4	no	—
326	Q₈	—	4	1	no	—
327	Q₈	—	4	1	no	—
328	Q₈	—	4	1	no	—
329	Q₈	—	4	1	no	—
330	Q₈	C₃×C₅×D₈	1	2	yes	—
331	D₄	—	2	1	no	—
332	D₄	C₃×C₅×Q₁₆	1	2	yes	complemented
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
342	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
343	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
344	C₈	—	2	2	no	—
345	C₈	—	4	1	no	—
346	C₈	—	4	1	no	—
347	C₂×C₃	—	4	2	no	—
348	C₂×C₃	C₅×#447	1	1	yes	characteristic
349	C₂×C₃	C₅×#451	1	1	yes	characteristic
350	C₂×C₃	C₅×#456	1	1	yes	characteristic
351	C₅	C₃×#1649	1	1	yes	characteristic, direct product factor, Sylow
352	C₂²	—	2	2	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	1	no	—
355	C₂²	C₃×C₅×#120	1	1	yes	characteristic
356	C₄	—	2	1	no	—
357	C₄	—	2	2	no	—
358	C₄	—	4	1	no	—
359	C₄	—	4	2	no	—
360	C₄	—	4	1	no	—
361	C₄	—	8	1	no	—
362	C₄	C₂×C₃×C₅×D₈	1	1	yes	characteristic
363	C₄	C₂×C₃×C₅×Q₁₆	1	1	yes	characteristic
364	C₄	C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
365	C₄	C₃×C₅×#137	1	1	yes	characteristic
366	C₃	C₅×#1649	1	1	yes	characteristic, direct product factor, Sylow
367	C₂	—	4	2	no	—
368	C₂	C₃×C₅×#447	1	1	yes	characteristic
369	C₂	C₃×C₅×#451	1	1	yes	characteristic
370	C₂	C₃×C₅×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₃×C₅
prime radical	C₂×C₃×C₅×D₄	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#500	C₂	semidirect
4. C₃×C₅×#462	C₂	semidirect
5. C₃×C₅×#332	C₂	semidirect
6. C₃×C₅×Q₈⋊C₈	C₂	semidirect
8. C₅×#1649	C₃	direct (N × H)
26. C₃×#1649	C₅	direct (N × H)
28. C₅×#500	C₂×C₃	semidirect
30. C₅×#462	C₂×C₃	semidirect
31. C₅×#332	C₂×C₃	semidirect
32. C₅×Q₈⋊C₈	C₂×C₃	semidirect
60. C₃×#500	C₂×C₅	semidirect
62. C₃×#462	C₂×C₅	semidirect
63. C₃×#332	C₂×C₅	semidirect
64. C₃×Q₈⋊C₈	C₂×C₅	semidirect
83. #1649	C₃×C₅	direct (N × H)
93. C₃×C₅×D₄	Q₁₆	semidirect
151. #500	C₂×C₃×C₅	semidirect
153. #462	C₂×C₃×C₅	semidirect
154. #332	C₂×C₃×C₅	semidirect
155. Q₈⋊C₈	C₂×C₃×C₅	semidirect
205. C₅×D₄	C₃×Q₁₆	semidirect
250. C₃×D₄	C₅×Q₁₆	semidirect
304. C₃×C₅	#1649	direct (N × H)
332. D₄	C₃×C₅×Q₁₆	semidirect
351. C₅	C₃×#1649	direct (N × H)
366. C₃	C₅×#1649	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×D₄×Q₈	2
C₃×C₅×#500	2
C₃×C₅×#474	2
C₃×C₅×#462	2
C₃×C₅×#332	2
C₃×C₅×Q₈⋊C₈	2
C₃×C₅×D₄⋊C₈	2
C₅×#1649	3
C₃×#1649	5

Subgroups — C3×C5×#1649 #14274683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1649 #14274683