Subgroups — C₃×C₅×#2088 #14275122

Order 1920.

448 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#106	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#340	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#340	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#340	C₂	1	1	yes	maximal, characteristic
8	C₅×#2088	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
12	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₃×C₅×#106	—	2	2	no	—
19	C₃×C₅×C₄⋊C₈	—	2	2	no	—
20	C₃×C₅×#95	—	2	1	no	—
21	C₃×C₅×#95	—	2	1	no	—
22	C₃×#2088	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂×C₅×#106	C₂×C₃	1	1	yes	characteristic
24	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
25	C₅×#389	C₂×C₃	1	1	yes	characteristic
26	C₅×#389	C₂×C₃	1	1	yes	characteristic
27	C₅×#340	C₂×C₃	1	1	yes	characteristic
28	C₅×#340	C₂×C₃	1	1	yes	characteristic
29	C₅×#340	C₂×C₃	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	—	2	1	no	—
31	C₂²×C₃×C₄×C₅	—	2	1	no	—
32	C₂²×C₃×C₄×C₅	—	2	1	no	—
33	C₂²×C₃×C₄×C₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₃×C₅×C₈	—	2	1	no	—
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	D₄	1	2	yes	—
43	C₃×C₅×C₄⋊C₄	—	2	1	no	—
44	C₃×C₅×C₄⋊C₄	—	2	1	no	—
45	C₃×C₅×C₄⋊C₄	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	—	2	1	no	—
47	C₃×C₅×C₄⋊C₄	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	—	4	2	no	—
50	C₃×C₅×C₄⋊C₄	—	4	2	no	—
51	C₃×C₅×C₄⋊C₄	Q₈	1	2	yes	—
52	C₃×C₅×C₄⋊C₄	Q₈	1	2	yes	—
53	C₃×C₄²×C₅	—	2	1	no	—
54	C₃×C₄²×C₅	—	2	1	no	—
55	C₂×C₃×#106	C₂×C₅	1	1	yes	characteristic
56	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
57	C₃×#389	C₂×C₅	1	1	yes	characteristic
58	C₃×#389	C₂×C₅	1	1	yes	characteristic
59	C₃×#340	C₂×C₅	1	1	yes	characteristic
60	C₃×#340	C₂×C₅	1	1	yes	characteristic
61	C₃×#340	C₂×C₅	1	1	yes	characteristic
62	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
63	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	—	2	1	no	—
65	C₂×C₅×C₄⋊C₄	—	2	1	no	—
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
71	C₅×#106	—	2	2	no	—
72	C₅×C₄⋊C₈	—	2	2	no	—
73	C₅×#95	—	2	1	no	—
74	C₅×#95	—	2	1	no	—
75	#2088	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
76	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
77	C₂×C₃×C₄×C₅	—	2	1	no	—
78	C₂×C₃×C₄×C₅	—	2	1	no	—
79	C₂×C₃×C₄×C₅	—	2	1	no	—
80	C₂×C₃×C₄×C₅	—	2	2	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	2	1	no	—
83	C₂×C₃×C₄×C₅	—	2	1	no	—
84	C₂×C₃×C₄×C₅	—	4	1	no	—
85	C₂×C₃×C₄×C₅	—	4	1	no	—
86	C₂×C₃×C₄×C₅	—	4	1	no	—
87	C₂×C₃×C₄×C₅	—	4	1	no	—
88	C₂×C₃×C₄×C₅	—	4	1	no	—
89	C₂×C₃×C₄×C₅	—	4	1	no	—
90	C₂×C₃×C₄×C₅	—	4	1	no	—
91	C₂×C₃×C₄×C₅	—	4	1	no	—
92	C₂×C₃×C₄×C₅	—	4	1	no	—
93	C₂×C₃×C₄×C₅	—	4	1	no	—
94	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
101	C₃×C₅×C₈	—	2	2	no	—
102	C₃×C₅×C₈	—	4	1	no	—
103	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
104	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
105	C₂×C₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
108	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
109	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
110	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
111	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
112	C₃×#106	—	2	2	no	—
113	C₃×C₄⋊C₈	—	2	2	no	—
114	C₃×#95	—	2	1	no	—
115	C₃×#95	—	2	1	no	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	1	no	—
118	C₂²×C₄×C₅	—	2	1	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
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	C₃×D₄	1	2	yes	—
129	C₅×C₄⋊C₄	—	2	1	no	—
130	C₅×C₄⋊C₄	—	2	1	no	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	2	1	no	—
133	C₅×C₄⋊C₄	—	2	1	no	—
134	C₅×C₄⋊C₄	—	2	1	no	—
135	C₅×C₄⋊C₄	—	4	2	no	—
136	C₅×C₄⋊C₄	—	4	2	no	—
137	C₅×C₄⋊C₄	C₃×Q₈	1	2	yes	—
138	C₅×C₄⋊C₄	C₃×Q₈	1	2	yes	—
139	C₄²×C₅	—	2	1	no	—
140	C₄²×C₅	—	2	1	no	—
141	C₂×#106	C₂×C₃×C₅	1	1	yes	characteristic
142	C₂×C₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic
143	#389	C₂×C₃×C₅	1	1	yes	characteristic
144	#389	C₂×C₃×C₅	1	1	yes	characteristic
145	#340	C₂×C₃×C₅	1	1	yes	characteristic
146	#340	C₂×C₃×C₅	1	1	yes	characteristic
147	#340	C₂×C₃×C₅	1	1	yes	characteristic
148	C₂²×C₃×C₅	#121	1	1	yes	characteristic
149	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
152	C₂²×C₃×C₅	#135	1	1	yes	characteristic
153	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂²×C₃×C₅	#137	1	1	yes	characteristic
155	C₃×C₄×C₅	—	2	2	no	—
156	C₃×C₄×C₅	—	4	1	no	—
157	C₃×C₄×C₅	—	4	2	no	—
158	C₃×C₄×C₅	—	4	2	no	—
159	C₃×C₄×C₅	—	8	1	no	—
160	C₃×C₄×C₅	—	8	1	no	—
161	C₃×C₄×C₅	#123	1	1	yes	characteristic
162	C₃×C₄×C₅	#125	1	1	yes	characteristic
163	C₃×C₄×C₅	#125	1	1	yes	characteristic
164	C₃×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
165	C₂²×C₃×C₄	—	2	1	no	—
166	C₂²×C₃×C₄	—	2	1	no	—
167	C₂²×C₃×C₄	—	2	1	no	—
168	C₂²×C₃×C₄	—	2	1	no	—
169	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
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	—	2	1	no	—
176	C₂×C₃×C₈	—	2	1	no	—
177	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
178	C₃×C₄⋊C₄	—	2	1	no	—
179	C₃×C₄⋊C₄	—	2	1	no	—
180	C₃×C₄⋊C₄	—	2	1	no	—
181	C₃×C₄⋊C₄	—	2	1	no	—
182	C₃×C₄⋊C₄	—	2	1	no	—
183	C₃×C₄⋊C₄	—	2	1	no	—
184	C₃×C₄⋊C₄	—	4	2	no	—
185	C₃×C₄⋊C₄	—	4	2	no	—
186	C₃×C₄⋊C₄	C₅×Q₈	1	2	yes	—
187	C₃×C₄⋊C₄	C₅×Q₈	1	2	yes	—
188	C₃×C₄²	—	2	1	no	—
189	C₃×C₄²	—	2	1	no	—
190	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
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	2	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	1	no	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	4	1	no	—
199	C₂×C₄×C₅	—	4	1	no	—
200	C₂×C₄×C₅	—	4	1	no	—
201	C₂×C₄×C₅	—	4	1	no	—
202	C₂×C₄×C₅	—	4	1	no	—
203	C₂×C₄×C₅	—	4	1	no	—
204	C₂×C₄×C₅	—	4	1	no	—
205	C₂×C₄×C₅	—	4	1	no	—
206	C₂×C₄×C₅	—	4	1	no	—
207	C₂×C₄×C₅	—	4	1	no	—
208	C₂×C₄×C₅	C₃×SD₁₆	1	2	yes	—
209	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
212	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
213	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
214	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
215	C₅×C₈	—	2	2	no	—
216	C₅×C₈	—	4	1	no	—
217	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
218	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
219	C₂×C₄⋊C₄	—	2	1	no	—
220	C₂×C₄⋊C₄	—	2	1	no	—
221	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
222	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
223	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
225	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
226	#106	—	2	2	no	—
227	C₄⋊C₈	—	2	2	no	—
228	#95	—	2	1	no	—
229	#95	—	2	1	no	—
230	C₂×C₃×C₅	#398	1	1	yes	characteristic
231	C₂×C₃×C₅	#465	1	1	yes	characteristic
232	C₂×C₃×C₅	#468	1	1	yes	characteristic
233	C₂×C₃×C₅	#475	1	1	yes	characteristic
234	C₂×C₃×C₅	#476	1	1	yes	characteristic
235	C₂×C₃×C₅	#478	1	1	yes	characteristic
236	C₂×C₃×C₅	#479	1	1	yes	characteristic
237	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	4	1	no	—
246	C₂×C₃×C₄	—	4	1	no	—
247	C₂×C₃×C₄	—	4	1	no	—
248	C₂×C₃×C₄	—	4	1	no	—
249	C₂×C₃×C₄	—	4	1	no	—
250	C₂×C₃×C₄	—	4	1	no	—
251	C₂×C₃×C₄	—	4	1	no	—
252	C₂×C₃×C₄	—	4	1	no	—
253	C₂×C₃×C₄	—	4	1	no	—
254	C₂×C₃×C₄	—	4	1	no	—
255	C₂×C₃×C₄	C₅×SD₁₆	1	2	yes	—
256	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
259	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
260	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
261	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
262	C₃×C₈	—	2	2	no	—
263	C₃×C₈	—	4	1	no	—
264	C₂²×C₅	C₃×#121	1	1	yes	characteristic
265	C₂²×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
266	C₂²×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
267	C₂²×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
268	C₂²×C₅	C₃×#135	1	1	yes	characteristic
269	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
270	C₂²×C₅	C₃×#137	1	1	yes	characteristic
271	C₄×C₅	—	2	2	no	—
272	C₄×C₅	—	4	1	no	—
273	C₄×C₅	—	4	2	no	—
274	C₄×C₅	—	4	2	no	—
275	C₄×C₅	—	8	1	no	—
276	C₄×C₅	—	8	1	no	—
277	C₄×C₅	C₃×#123	1	1	yes	characteristic
278	C₄×C₅	C₃×#125	1	1	yes	characteristic
279	C₄×C₅	C₃×#125	1	1	yes	characteristic
280	C₄×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
286	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
287	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	—	2	1	no	—
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	4	2	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₄⋊C₄	C₃×C₅×Q₈	1	2	yes	—
303	C₄⋊C₄	C₃×C₅×Q₈	1	2	yes	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	1	no	—
306	C₃×C₅	#2088	1	1	yes	characteristic, direct product factor, Hall
307	C₂²×C₃	C₅×#121	1	1	yes	characteristic
308	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
309	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
310	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
311	C₂²×C₃	C₅×#135	1	1	yes	characteristic
312	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
313	C₂²×C₃	C₅×#137	1	1	yes	characteristic
314	C₃×C₄	—	2	2	no	—
315	C₃×C₄	—	4	1	no	—
316	C₃×C₄	—	4	2	no	—
317	C₃×C₄	—	4	2	no	—
318	C₃×C₄	—	8	1	no	—
319	C₃×C₄	—	8	1	no	—
320	C₃×C₄	C₅×#123	1	1	yes	characteristic
321	C₃×C₄	C₅×#125	1	1	yes	characteristic
322	C₃×C₄	C₅×#125	1	1	yes	characteristic
323	C₃×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
324	C₂×C₅	C₃×#398	1	1	yes	characteristic
325	C₂×C₅	C₃×#465	1	1	yes	characteristic
326	C₂×C₅	C₃×#468	1	1	yes	characteristic
327	C₂×C₅	C₃×#475	1	1	yes	characteristic
328	C₂×C₅	C₃×#476	1	1	yes	characteristic
329	C₂×C₅	C₃×#478	1	1	yes	characteristic
330	C₂×C₅	C₃×#479	1	1	yes	characteristic
331	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	C₃×C₅×SD₁₆	1	2	yes	—
350	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
351	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
352	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
353	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
354	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
355	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
356	C₈	—	2	2	no	—
357	C₈	—	4	1	no	—
358	C₂×C₃	C₅×#398	1	1	yes	characteristic
359	C₂×C₃	C₅×#465	1	1	yes	characteristic
360	C₂×C₃	C₅×#468	1	1	yes	characteristic
361	C₂×C₃	C₅×#475	1	1	yes	characteristic
362	C₂×C₃	C₅×#476	1	1	yes	characteristic
363	C₂×C₃	C₅×#478	1	1	yes	characteristic
364	C₂×C₃	C₅×#479	1	1	yes	characteristic
365	C₅	C₃×#2088	1	1	yes	characteristic, direct product factor, Sylow
366	C₂²	C₃×C₅×#121	1	1	yes	characteristic
367	C₂²	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
368	C₂²	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
369	C₂²	C₂×C₃×C₅×SD₁₆	1	1	yes	characteristic
370	C₂²	C₃×C₅×#135	1	1	yes	characteristic
371	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
372	C₂²	C₃×C₅×#137	1	1	yes	characteristic
373	C₄	—	2	2	no	—
374	C₄	—	4	1	no	—
375	C₄	—	4	2	no	—
376	C₄	—	4	2	no	—
377	C₄	—	8	1	no	—
378	C₄	—	8	1	no	—
379	C₄	C₃×C₅×#123	1	1	yes	characteristic
380	C₄	C₃×C₅×#125	1	1	yes	characteristic
381	C₄	C₃×C₅×#125	1	1	yes	characteristic
382	C₄	C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
383	C₃	C₅×#2088	1	1	yes	characteristic, direct product factor, Sylow
384	C₂	C₃×C₅×#398	1	1	yes	characteristic
385	C₂	C₃×C₅×#465	1	1	yes	characteristic
386	C₂	C₃×C₅×#468	1	1	yes	characteristic
387	C₂	C₃×C₅×#475	1	1	yes	characteristic
388	C₂	C₃×C₅×#476	1	1	yes	characteristic
389	C₂	C₃×C₅×#478	1	1	yes	characteristic
390	C₂	C₃×C₅×#479	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
LCS	G ▷ C₂²×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
8. C₅×#2088	C₃	direct (N × H)
22. C₃×#2088	C₅	direct (N × H)
75. #2088	C₃×C₅	direct (N × H)
306. C₃×C₅	#2088	direct (N × H)
365. C₅	C₃×#2088	direct (N × H)
383. C₃	C₅×#2088	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×#106	2
C₂×C₃×C₅×C₄⋊C₈	2
C₃×C₅×#389	2
C₃×C₅×#340	2
C₅×#2088	3
C₃×#2088	5

Subgroups — C3×C5×#2088 #14275122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2088 #14275122