Subgroups — C₃×C₅×#1809 #14274843

Order 1920.

632 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#380	C₂	1	2	yes	maximal
5	C₃×C₅×#340	C₂	1	2	yes	maximal, complemented
6	C₅×#1809	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₅×M₁₆	—	2	2	no	—
9	C₂×C₃×C₅×M₁₆	—	2	2	no	—
10	C₂×C₃×C₅×M₁₆	C₄	1	4	yes	complemented
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
16	C₃×C₅×#107	—	2	2	no	—
17	C₃×C₅×#106	—	2	2	no	—
18	C₃×C₅×#95	—	2	2	no	—
19	C₃×#1809	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic
21	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic, complemented
22	C₂×C₅×#106	C₂×C₃	1	1	yes	characteristic, complemented
23	C₅×#380	C₂×C₃	1	2	yes	—
24	C₅×#340	C₂×C₃	1	2	yes	complemented
25	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
26	C₂²×C₃×C₄×C₅	—	2	1	no	—
27	C₂²×C₃×C₄×C₅	—	2	1	no	—
28	C₂²×C₃×C₄×C₅	—	2	1	no	—
29	C₂²×C₃×C₄×C₅	—	2	1	no	—
30	C₂²×C₃×C₄×C₅	—	2	2	no	—
31	C₂²×C₃×C₄×C₅	—	2	2	no	—
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
33	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₃×C₅×M₁₆	—	2	8	no	—
37	C₂×C₃×C₅×C₈	—	2	1	no	—
38	C₂×C₃×C₅×C₈	—	2	1	no	—
39	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
40	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
41	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
42	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
43	C₃×C₅×C₄⋊C₄	—	2	2	no	—
44	C₃×C₅×C₄⋊C₄	—	2	2	no	—
45	C₃×C₅×C₄⋊C₄	—	2	2	no	—
46	C₃×C₅×C₄⋊C₄	—	2	2	no	—
47	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
48	C₂²×C₃×M₁₆	C₂×C₅	1	1	yes	characteristic
49	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
50	C₂×C₃×#106	C₂×C₅	1	1	yes	characteristic, complemented
51	C₃×#380	C₂×C₅	1	2	yes	—
52	C₃×#340	C₂×C₅	1	2	yes	complemented
53	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
54	C₂×C₅×M₁₆	—	2	2	no	—
55	C₂×C₅×M₁₆	—	2	2	no	—
56	C₂×C₅×M₁₆	C₃×C₄	1	4	yes	complemented
57	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
60	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
61	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
62	C₅×#107	—	2	2	no	—
63	C₅×#106	—	2	2	no	—
64	C₅×#95	—	2	2	no	—
65	#1809	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
66	C₂³×C₃×C₅	—	2	1	no	—
67	C₂³×C₃×C₅	—	2	1	no	—
68	C₂³×C₃×C₅	—	2	2	no	—
69	C₂³×C₃×C₅	—	2	2	no	—
70	C₂³×C₃×C₅	C₄⋊C₄	1	2	yes	—
71	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
72	C₂×C₃×C₄×C₅	—	2	1	no	—
73	C₂×C₃×C₄×C₅	—	2	1	no	—
74	C₂×C₃×C₄×C₅	—	2	2	no	—
75	C₂×C₃×C₄×C₅	—	2	2	no	—
76	C₂×C₃×C₄×C₅	—	2	2	no	—
77	C₂×C₃×C₄×C₅	—	2	2	no	—
78	C₂×C₃×C₄×C₅	—	4	2	no	—
79	C₂×C₃×C₄×C₅	—	4	2	no	—
80	C₂×C₃×C₄×C₅	—	4	2	no	—
81	C₂×C₃×C₄×C₅	—	4	2	no	—
82	C₂×C₃×C₄×C₅	—	4	2	no	—
83	C₂×C₃×C₄×C₅	—	4	2	no	—
84	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
85	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
91	C₃×C₅×C₈	—	2	2	no	—
92	C₃×C₅×C₈	C₂²⋊C₄	1	4	yes	complemented
93	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
94	C₂×C₃×M₁₆	—	2	2	no	—
95	C₂×C₃×M₁₆	—	2	2	no	—
96	C₂×C₃×M₁₆	C₄×C₅	1	4	yes	complemented
97	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
98	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
99	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
100	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
101	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
102	C₃×#107	—	2	2	no	—
103	C₃×#106	—	2	2	no	—
104	C₃×#95	—	2	2	no	—
105	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	—	2	1	no	—
107	C₂²×C₄×C₅	—	2	1	no	—
108	C₂²×C₄×C₅	—	2	1	no	—
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
113	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₃×Q₈	1	2	yes	—
115	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
116	C₅×M₁₆	—	2	8	no	—
117	C₂×C₅×C₈	—	2	1	no	—
118	C₂×C₅×C₈	—	2	1	no	—
119	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
120	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
121	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
122	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
123	C₅×C₄⋊C₄	—	2	2	no	—
124	C₅×C₄⋊C₄	—	2	2	no	—
125	C₅×C₄⋊C₄	—	2	2	no	—
126	C₅×C₄⋊C₄	—	2	2	no	—
127	C₅×C₂²⋊C₄	—	4	4	no	—
128	C₂²×M₁₆	C₂×C₃×C₅	1	1	yes	characteristic
129	C₂×#107	C₂×C₃×C₅	1	1	yes	characteristic, complemented
130	C₂×#106	C₂×C₃×C₅	1	1	yes	characteristic, complemented
131	#380	C₂×C₃×C₅	1	2	yes	—
132	#340	C₂×C₃×C₅	1	2	yes	complemented
133	C₂²×C₃×C₅	—	2	2	no	—
134	C₂²×C₃×C₅	—	2	4	no	—
135	C₂²×C₃×C₅	—	4	2	no	—
136	C₂²×C₃×C₅	—	4	1	no	—
137	C₂²×C₃×C₅	—	4	1	no	—
138	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂²×C₃×C₅	#121	1	1	yes	characteristic
140	C₂²×C₃×C₅	#121	1	1	yes	characteristic
141	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
142	C₂²×C₃×C₅	#137	1	2	yes	—
143	C₃×C₄×C₅	—	2	2	no	—
144	C₃×C₄×C₅	—	8	2	no	—
145	C₃×C₄×C₅	—	8	2	no	—
146	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₃×C₄×C₅	#117	1	1	yes	characteristic
148	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
149	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
151	C₂²×C₃×C₄	—	2	1	no	—
152	C₂²×C₃×C₄	—	2	1	no	—
153	C₂²×C₃×C₄	—	2	1	no	—
154	C₂²×C₃×C₄	—	2	1	no	—
155	C₂²×C₃×C₄	—	2	2	no	—
156	C₂²×C₃×C₄	—	2	2	no	—
157	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
158	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₅×Q₈	1	2	yes	—
160	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
161	C₃×M₁₆	—	2	8	no	—
162	C₂×C₃×C₈	—	2	1	no	—
163	C₂×C₃×C₈	—	2	1	no	—
164	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
165	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
166	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
167	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
168	C₃×C₄⋊C₄	—	2	2	no	—
169	C₃×C₄⋊C₄	—	2	2	no	—
170	C₃×C₄⋊C₄	—	2	2	no	—
171	C₃×C₄⋊C₄	—	2	2	no	—
172	C₃×C₂²⋊C₄	—	4	4	no	—
173	C₂³×C₅	—	2	1	no	—
174	C₂³×C₅	—	2	1	no	—
175	C₂³×C₅	—	2	2	no	—
176	C₂³×C₅	—	2	2	no	—
177	C₂³×C₅	C₃×C₄⋊C₄	1	2	yes	—
178	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
179	C₂×C₄×C₅	—	2	1	no	—
180	C₂×C₄×C₅	—	2	1	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	4	2	no	—
186	C₂×C₄×C₅	—	4	2	no	—
187	C₂×C₄×C₅	—	4	2	no	—
188	C₂×C₄×C₅	—	4	2	no	—
189	C₂×C₄×C₅	—	4	2	no	—
190	C₂×C₄×C₅	—	4	2	no	—
191	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
192	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
197	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
198	C₅×C₈	—	2	2	no	—
199	C₅×C₈	C₃×C₂²⋊C₄	1	4	yes	complemented
200	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
201	C₂×M₁₆	—	2	2	no	—
202	C₂×M₁₆	—	2	2	no	—
203	C₂×M₁₆	C₃×C₄×C₅	1	4	yes	complemented
204	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
205	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
207	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
208	C₂×C₂²⋊C₄	—	2	2	no	—
209	#107	—	2	2	no	—
210	#106	—	2	2	no	—
211	#95	—	2	2	no	—
212	C₂×C₃×C₅	—	4	2	no	—
213	C₂×C₃×C₅	#380	1	1	yes	characteristic
214	C₂×C₃×C₅	#428	1	2	yes	—
215	C₂×C₃×C₅	#468	1	2	yes	—
216	C₂×C₃×C₅	#469	1	1	yes	characteristic
217	C₂×C₃×C₅	#470	1	1	yes	characteristic
218	C₂³×C₃	—	2	1	no	—
219	C₂³×C₃	—	2	1	no	—
220	C₂³×C₃	—	2	2	no	—
221	C₂³×C₃	—	2	2	no	—
222	C₂³×C₃	C₅×C₄⋊C₄	1	2	yes	—
223	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
224	C₂×C₃×C₄	—	2	1	no	—
225	C₂×C₃×C₄	—	2	1	no	—
226	C₂×C₃×C₄	—	2	2	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	2	2	no	—
230	C₂×C₃×C₄	—	4	2	no	—
231	C₂×C₃×C₄	—	4	2	no	—
232	C₂×C₃×C₄	—	4	2	no	—
233	C₂×C₃×C₄	—	4	2	no	—
234	C₂×C₃×C₄	—	4	2	no	—
235	C₂×C₃×C₄	—	4	2	no	—
236	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
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×D₄	1	1	yes	characteristic
240	C₂×C₃×C₄	C₂×C₅×Q₈	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	2	no	—
244	C₃×C₈	C₅×C₂²⋊C₄	1	4	yes	complemented
245	C₂²×C₅	—	2	2	no	—
246	C₂²×C₅	—	2	4	no	—
247	C₂²×C₅	—	4	2	no	—
248	C₂²×C₅	—	4	1	no	—
249	C₂²×C₅	—	4	1	no	—
250	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
251	C₂²×C₅	C₃×#121	1	1	yes	characteristic
252	C₂²×C₅	C₃×#121	1	1	yes	characteristic
253	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
254	C₂²×C₅	C₃×#137	1	2	yes	—
255	C₄×C₅	—	2	2	no	—
256	C₄×C₅	—	8	2	no	—
257	C₄×C₅	—	8	2	no	—
258	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
259	C₄×C₅	C₃×#117	1	1	yes	characteristic
260	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
261	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
262	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	C₂×C₃×C₄×C₅	1	2	yes	—
270	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
271	C₂²×C₄	C₃×C₅×Q₈	1	2	yes	—
272	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
273	M₁₆	—	2	8	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	—	2	1	no	—
276	C₂×C₈	C₂×C₃×C₄×C₅	1	2	yes	—
277	C₂×C₈	C₂×C₃×C₄×C₅	1	2	yes	—
278	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
279	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
280	C₄⋊C₄	—	2	2	no	—
281	C₄⋊C₄	—	2	2	no	—
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₂²⋊C₄	—	4	4	no	—
285	C₃×C₅	#1809	1	1	yes	characteristic, direct product factor, Hall
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	—	2	4	no	—
288	C₂²×C₃	—	4	2	no	—
289	C₂²×C₃	—	4	1	no	—
290	C₂²×C₃	—	4	1	no	—
291	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
292	C₂²×C₃	C₅×#121	1	1	yes	characteristic
293	C₂²×C₃	C₅×#121	1	1	yes	characteristic
294	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
295	C₂²×C₃	C₅×#137	1	2	yes	—
296	C₃×C₄	—	2	2	no	—
297	C₃×C₄	—	8	2	no	—
298	C₃×C₄	—	8	2	no	—
299	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
300	C₃×C₄	C₅×#117	1	1	yes	characteristic
301	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
302	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
303	C₂×C₅	—	4	2	no	—
304	C₂×C₅	C₃×#380	1	1	yes	characteristic
305	C₂×C₅	C₃×#428	1	2	yes	—
306	C₂×C₅	C₃×#468	1	2	yes	—
307	C₂×C₅	C₃×#469	1	1	yes	characteristic
308	C₂×C₅	C₃×#470	1	1	yes	characteristic
309	C₂³	—	2	1	no	—
310	C₂³	—	2	1	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	C₃×C₅×C₄⋊C₄	1	2	yes	—
314	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	C₃×C₅×C₄⋊C₄	1	2	yes	—
328	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
329	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
330	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
331	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
332	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
333	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
334	C₈	—	2	2	no	—
335	C₈	C₃×C₅×C₂²⋊C₄	1	4	yes	complemented
336	C₂×C₃	—	4	2	no	—
337	C₂×C₃	C₅×#380	1	1	yes	characteristic
338	C₂×C₃	C₅×#428	1	2	yes	—
339	C₂×C₃	C₅×#468	1	2	yes	—
340	C₂×C₃	C₅×#469	1	1	yes	characteristic
341	C₂×C₃	C₅×#470	1	1	yes	characteristic
342	C₅	C₃×#1809	1	1	yes	characteristic, direct product factor, Sylow
343	C₂²	—	2	2	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	4	2	no	—
346	C₂²	—	4	1	no	—
347	C₂²	—	4	1	no	—
348	C₂²	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
349	C₂²	C₃×C₅×#121	1	1	yes	characteristic
350	C₂²	C₃×C₅×#121	1	1	yes	characteristic
351	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
352	C₂²	C₃×C₅×#137	1	2	yes	—
353	C₄	—	2	2	no	—
354	C₄	—	8	2	no	—
355	C₄	—	8	2	no	—
356	C₄	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
357	C₄	C₃×C₅×#117	1	1	yes	characteristic
358	C₄	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
359	C₄	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
360	C₃	C₅×#1809	1	1	yes	characteristic, direct product factor, Sylow
361	C₂	—	4	2	no	—
362	C₂	C₃×C₅×#380	1	1	yes	characteristic
363	C₂	C₃×C₅×#428	1	2	yes	—
364	C₂	C₃×C₅×#468	1	2	yes	—
365	C₂	C₃×C₅×#469	1	1	yes	characteristic
366	C₂	C₃×C₅×#470	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂⁴×C₃×C₅	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂³×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#107	C₂	semidirect
3. C₂×C₃×C₅×#106	C₂	semidirect
5. C₃×C₅×#340	C₂	semidirect
6. C₅×#1809	C₃	direct (N × H)
10. C₂×C₃×C₅×M₁₆	C₄	semidirect
19. C₃×#1809	C₅	direct (N × H)
21. C₂×C₅×#107	C₂×C₃	semidirect
22. C₂×C₅×#106	C₂×C₃	semidirect
24. C₅×#340	C₂×C₃	semidirect
49. C₂×C₃×#107	C₂×C₅	semidirect
50. C₂×C₃×#106	C₂×C₅	semidirect
52. C₃×#340	C₂×C₅	semidirect
56. C₂×C₅×M₁₆	C₃×C₄	semidirect
65. #1809	C₃×C₅	direct (N × H)
92. C₃×C₅×C₈	C₂²⋊C₄	semidirect
96. C₂×C₃×M₁₆	C₄×C₅	semidirect
129. C₂×#107	C₂×C₃×C₅	semidirect
130. C₂×#106	C₂×C₃×C₅	semidirect
132. #340	C₂×C₃×C₅	semidirect
199. C₅×C₈	C₃×C₂²⋊C₄	semidirect
203. C₂×M₁₆	C₃×C₄×C₅	semidirect
244. C₃×C₈	C₅×C₂²⋊C₄	semidirect
285. C₃×C₅	#1809	direct (N × H)
335. C₈	C₃×C₅×C₂²⋊C₄	semidirect
342. C₅	C₃×#1809	direct (N × H)
360. C₃	C₅×#1809	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×M₁₆	2
C₂×C₃×C₅×#107	2
C₂×C₃×C₅×#106	2
C₃×C₅×#380	2
C₃×C₅×#340	2
C₅×#1809	3
C₃×#1809	5

Subgroups — C3×C5×#1809 #14274843

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1809 #14274843