Subgroups — C₃×C₅×#1908 #14274942

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#137	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₅×#101	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#343	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#341	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1908	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₃×C₅×#137	—	2	2	no	—
12	C₃×C₅×#137	C₄	1	4	yes	complemented
13	C₂×C₃×C₅×Q₁₆	—	2	1	no	—
14	C₂×C₃×C₅×SD₁₆	—	2	1	no	—
15	C₃×C₅×#131	—	2	2	no	—
16	C₃×C₅×#131	—	2	2	no	—
17	C₂×C₃×C₅×M₁₆	—	2	1	no	—
18	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₅×C₈	—	2	1	no	—
22	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₃×C₅×#103	—	2	1	no	—
25	C₃×C₅×#103	—	2	1	no	—
26	C₃×C₅×#103	—	2	1	no	—
27	C₃×C₅×#102	—	2	1	no	—
28	C₃×C₅×#101	—	2	2	no	—
29	C₃×#1908	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂×C₅×#137	C₂×C₃	1	1	yes	characteristic
31	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic
32	C₅×#417	C₂×C₃	1	1	yes	characteristic
33	C₂×C₅×#103	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×C₅×#101	C₂×C₃	1	1	yes	characteristic, complemented
35	C₅×#343	C₂×C₃	1	1	yes	characteristic, complemented
36	C₅×#341	C₂×C₃	1	1	yes	characteristic, complemented
37	C₃×C₅×#41	—	2	1	no	—
38	C₃×C₅×#41	—	2	1	no	—
39	C₃×C₅×#41	C₂×C₄	1	2	yes	—
40	C₃×C₅×#41	D₄	1	2	yes	—
41	C₂×C₃×C₅×Q₈	—	2	1	no	—
42	C₂×C₃×C₅×Q₈	—	2	1	no	—
43	C₂×C₃×C₅×Q₈	—	2	1	no	—
44	C₂×C₃×C₅×Q₈	—	2	1	no	—
45	C₂×C₃×C₅×Q₈	—	2	1	no	—
46	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
47	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
48	C₂×C₃×C₅×D₄	—	2	1	no	—
49	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	—	2	1	no	—
51	C₂²×C₃×C₄×C₅	—	2	1	no	—
52	C₂²×C₃×C₄×C₅	—	2	1	no	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₃×C₅×Q₁₆	—	2	4	no	—
55	C₃×C₅×SD₁₆	—	2	4	no	—
56	C₃×C₅×M₁₆	—	2	4	no	—
57	C₃×C₅×M₁₆	—	2	1	no	—
58	C₃×C₅×M₁₆	—	2	1	no	—
59	C₃×C₅×M₁₆	—	2	1	no	—
60	C₃×C₅×M₁₆	—	2	1	no	—
61	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	—
62	C₃×C₅×M₁₆	D₄	1	2	yes	—
63	C₂×C₃×C₅×C₈	—	2	4	no	—
64	C₂×C₃×C₅×C₈	—	2	1	no	—
65	C₂×C₃×C₅×C₈	—	2	1	no	—
66	C₂×C₃×C₅×C₈	—	2	1	no	—
67	C₂×C₃×C₅×C₈	—	2	1	no	—
68	C₂×C₃×C₅×C₈	—	2	1	no	—
69	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
70	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
71	C₃×C₅×C₄⋊C₄	—	2	1	no	—
72	C₃×C₅×C₄⋊C₄	—	2	1	no	—
73	C₂×C₃×#137	C₂×C₅	1	1	yes	characteristic
74	C₂×C₃×#131	C₂×C₅	1	1	yes	characteristic
75	C₃×#417	C₂×C₅	1	1	yes	characteristic
76	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×C₃×#101	C₂×C₅	1	1	yes	characteristic, complemented
78	C₃×#343	C₂×C₅	1	1	yes	characteristic, complemented
79	C₃×#341	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
81	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
82	C₅×#137	—	2	2	no	—
83	C₅×#137	C₃×C₄	1	4	yes	complemented
84	C₂×C₅×Q₁₆	—	2	1	no	—
85	C₂×C₅×SD₁₆	—	2	1	no	—
86	C₅×#131	—	2	2	no	—
87	C₅×#131	—	2	2	no	—
88	C₂×C₅×M₁₆	—	2	1	no	—
89	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
92	C₂²×C₅×C₈	—	2	1	no	—
93	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
95	C₅×#103	—	2	1	no	—
96	C₅×#103	—	2	1	no	—
97	C₅×#103	—	2	1	no	—
98	C₅×#102	—	2	1	no	—
99	C₅×#101	—	2	2	no	—
100	#1908	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
101	C₂³×C₃×C₅	—	2	1	no	—
102	C₂³×C₃×C₅	#41	1	1	yes	characteristic
103	C₃×C₅×Q₈	—	2	1	no	—
104	C₃×C₅×Q₈	—	2	2	no	—
105	C₃×C₅×Q₈	—	2	2	no	—
106	C₃×C₅×Q₈	—	4	1	no	—
107	C₃×C₅×Q₈	—	4	1	no	—
108	C₃×C₅×Q₈	C₂²⋊C₄	1	2	yes	—
109	C₃×C₅×D₄	—	2	2	no	—
110	C₃×C₅×D₄	—	2	2	no	—
111	C₃×C₅×D₄	—	2	1	no	—
112	C₃×C₅×D₄	C₂²⋊C₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	—	2	1	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	4	1	no	—
118	C₂×C₃×C₄×C₅	—	4	1	no	—
119	C₂×C₃×C₄×C₅	—	4	1	no	—
120	C₂×C₃×C₄×C₅	—	8	1	no	—
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
127	C₃×C₅×C₈	—	2	2	no	—
128	C₃×C₅×C₈	—	2	1	no	—
129	C₃×C₅×C₈	—	2	2	no	—
130	C₃×C₅×C₈	—	2	1	no	—
131	C₃×C₅×C₈	—	4	1	no	—
132	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
133	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
134	C₃×#137	—	2	2	no	—
135	C₃×#137	C₄×C₅	1	4	yes	complemented
136	C₂×C₃×Q₁₆	—	2	1	no	—
137	C₂×C₃×SD₁₆	—	2	1	no	—
138	C₃×#131	—	2	2	no	—
139	C₃×#131	—	2	2	no	—
140	C₂×C₃×M₁₆	—	2	1	no	—
141	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
142	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
143	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
144	C₂²×C₃×C₈	—	2	1	no	—
145	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
147	C₃×#103	—	2	1	no	—
148	C₃×#103	—	2	1	no	—
149	C₃×#103	—	2	1	no	—
150	C₃×#102	—	2	1	no	—
151	C₃×#101	—	2	2	no	—
152	C₅×#41	—	2	1	no	—
153	C₅×#41	—	2	1	no	—
154	C₅×#41	C₂×C₃×C₄	1	2	yes	—
155	C₅×#41	C₃×D₄	1	2	yes	—
156	C₂×C₅×Q₈	—	2	1	no	—
157	C₂×C₅×Q₈	—	2	1	no	—
158	C₂×C₅×Q₈	—	2	1	no	—
159	C₂×C₅×Q₈	—	2	1	no	—
160	C₂×C₅×Q₈	—	2	1	no	—
161	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
162	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
163	C₂×C₅×D₄	—	2	1	no	—
164	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂²×C₄×C₅	—	2	1	no	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
169	C₅×Q₁₆	—	2	4	no	—
170	C₅×SD₁₆	—	2	4	no	—
171	C₅×M₁₆	—	2	4	no	—
172	C₅×M₁₆	—	2	1	no	—
173	C₅×M₁₆	—	2	1	no	—
174	C₅×M₁₆	—	2	1	no	—
175	C₅×M₁₆	—	2	1	no	—
176	C₅×M₁₆	C₂×C₃×C₄	1	2	yes	—
177	C₅×M₁₆	C₃×D₄	1	2	yes	—
178	C₂×C₅×C₈	—	2	4	no	—
179	C₂×C₅×C₈	—	2	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
185	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
186	C₅×C₄⋊C₄	—	2	1	no	—
187	C₅×C₄⋊C₄	—	2	1	no	—
188	C₂×#137	C₂×C₃×C₅	1	1	yes	characteristic
189	C₂×#131	C₂×C₃×C₅	1	1	yes	characteristic
190	#417	C₂×C₃×C₅	1	1	yes	characteristic
191	C₂×#103	C₂×C₃×C₅	1	1	yes	characteristic, complemented
192	C₂×#101	C₂×C₃×C₅	1	1	yes	characteristic, complemented
193	#343	C₂×C₃×C₅	1	1	yes	characteristic, complemented
194	#341	C₂×C₃×C₅	1	1	yes	characteristic, complemented
195	C₂²×C₃×C₅	—	2	1	no	—
196	C₂²×C₃×C₅	—	2	1	no	—
197	C₂²×C₃×C₅	—	2	2	no	—
198	C₂²×C₃×C₅	—	4	1	no	—
199	C₂²×C₃×C₅	—	4	1	no	—
200	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
201	C₂²×C₃×C₅	#121	1	1	yes	characteristic
202	C₂²×C₃×C₅	#123	1	1	yes	characteristic
203	C₃×C₄×C₅	—	2	2	no	—
204	C₃×C₄×C₅	—	4	2	no	—
205	C₃×C₄×C₅	—	8	1	no	—
206	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
208	C₃×C₄×C₅	#120	1	1	yes	characteristic
209	C₃×C₄×C₅	#121	1	1	yes	characteristic
210	C₃×#41	—	2	1	no	—
211	C₃×#41	—	2	1	no	—
212	C₃×#41	C₂×C₄×C₅	1	2	yes	—
213	C₃×#41	C₅×D₄	1	2	yes	—
214	C₂×C₃×Q₈	—	2	1	no	—
215	C₂×C₃×Q₈	—	2	1	no	—
216	C₂×C₃×Q₈	—	2	1	no	—
217	C₂×C₃×Q₈	—	2	1	no	—
218	C₂×C₃×Q₈	—	2	1	no	—
219	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
220	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
221	C₂×C₃×D₄	—	2	1	no	—
222	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
223	C₂²×C₃×C₄	—	2	1	no	—
224	C₂²×C₃×C₄	—	2	1	no	—
225	C₂²×C₃×C₄	—	2	1	no	—
226	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
227	C₃×Q₁₆	—	2	4	no	—
228	C₃×SD₁₆	—	2	4	no	—
229	C₃×M₁₆	—	2	4	no	—
230	C₃×M₁₆	—	2	1	no	—
231	C₃×M₁₆	—	2	1	no	—
232	C₃×M₁₆	—	2	1	no	—
233	C₃×M₁₆	—	2	1	no	—
234	C₃×M₁₆	C₂×C₄×C₅	1	2	yes	—
235	C₃×M₁₆	C₅×D₄	1	2	yes	—
236	C₂×C₃×C₈	—	2	4	no	—
237	C₂×C₃×C₈	—	2	1	no	—
238	C₂×C₃×C₈	—	2	1	no	—
239	C₂×C₃×C₈	—	2	1	no	—
240	C₂×C₃×C₈	—	2	1	no	—
241	C₂×C₃×C₈	—	2	1	no	—
242	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
243	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
244	C₃×C₄⋊C₄	—	2	1	no	—
245	C₃×C₄⋊C₄	—	2	1	no	—
246	C₂³×C₅	—	2	1	no	—
247	C₂³×C₅	C₃×#41	1	1	yes	characteristic
248	C₅×Q₈	—	2	1	no	—
249	C₅×Q₈	—	2	2	no	—
250	C₅×Q₈	—	2	2	no	—
251	C₅×Q₈	—	4	1	no	—
252	C₅×Q₈	—	4	1	no	—
253	C₅×Q₈	C₃×C₂²⋊C₄	1	2	yes	—
254	C₅×D₄	—	2	2	no	—
255	C₅×D₄	—	2	2	no	—
256	C₅×D₄	—	2	1	no	—
257	C₅×D₄	C₃×C₂²⋊C₄	1	2	yes	—
258	C₂×C₄×C₅	—	2	1	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	4	1	no	—
263	C₂×C₄×C₅	—	4	1	no	—
264	C₂×C₄×C₅	—	4	1	no	—
265	C₂×C₄×C₅	—	8	1	no	—
266	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
271	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
272	C₅×C₈	—	2	2	no	—
273	C₅×C₈	—	2	1	no	—
274	C₅×C₈	—	2	2	no	—
275	C₅×C₈	—	2	1	no	—
276	C₅×C₈	—	4	1	no	—
277	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
278	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
279	#137	—	2	2	no	—
280	#137	C₃×C₄×C₅	1	4	yes	complemented
281	C₂×Q₁₆	—	2	1	no	—
282	C₂×SD₁₆	—	2	1	no	—
283	#131	—	2	2	no	—
284	#131	—	2	2	no	—
285	C₂×M₁₆	—	2	1	no	—
286	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
287	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
288	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
292	#103	—	2	1	no	—
293	#103	—	2	1	no	—
294	#103	—	2	1	no	—
295	#102	—	2	1	no	—
296	#101	—	2	2	no	—
297	C₂×C₃×C₅	—	2	1	no	—
298	C₂×C₃×C₅	—	2	1	no	—
299	C₂×C₃×C₅	—	4	2	no	—
300	C₂×C₃×C₅	#386	1	1	yes	characteristic
301	C₂×C₃×C₅	#471	1	1	yes	characteristic
302	C₂×C₃×C₅	#473	1	1	yes	characteristic
303	C₂³×C₃	—	2	1	no	—
304	C₂³×C₃	C₅×#41	1	1	yes	characteristic
305	C₃×Q₈	—	2	1	no	—
306	C₃×Q₈	—	2	2	no	—
307	C₃×Q₈	—	2	2	no	—
308	C₃×Q₈	—	4	1	no	—
309	C₃×Q₈	—	4	1	no	—
310	C₃×Q₈	C₅×C₂²⋊C₄	1	2	yes	—
311	C₃×D₄	—	2	2	no	—
312	C₃×D₄	—	2	2	no	—
313	C₃×D₄	—	2	1	no	—
314	C₃×D₄	C₅×C₂²⋊C₄	1	2	yes	—
315	C₂×C₃×C₄	—	2	1	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	4	1	no	—
320	C₂×C₃×C₄	—	4	1	no	—
321	C₂×C₃×C₄	—	4	1	no	—
322	C₂×C₃×C₄	—	8	1	no	—
323	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
328	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
329	C₃×C₈	—	2	2	no	—
330	C₃×C₈	—	2	1	no	—
331	C₃×C₈	—	2	2	no	—
332	C₃×C₈	—	2	1	no	—
333	C₃×C₈	—	4	1	no	—
334	C₂²×C₅	—	2	1	no	—
335	C₂²×C₅	—	2	1	no	—
336	C₂²×C₅	—	2	2	no	—
337	C₂²×C₅	—	4	1	no	—
338	C₂²×C₅	—	4	1	no	—
339	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
340	C₂²×C₅	C₃×#121	1	1	yes	characteristic
341	C₂²×C₅	C₃×#123	1	1	yes	characteristic
342	C₄×C₅	—	2	2	no	—
343	C₄×C₅	—	4	2	no	—
344	C₄×C₅	—	8	1	no	—
345	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
346	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
347	C₄×C₅	C₃×#120	1	1	yes	characteristic
348	C₄×C₅	C₃×#121	1	1	yes	characteristic
349	#41	—	2	1	no	—
350	#41	—	2	1	no	—
351	#41	C₂×C₃×C₄×C₅	1	2	yes	—
352	#41	C₃×C₅×D₄	1	2	yes	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	C₂×C₃×C₄×C₅	1	2	yes	—
359	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
366	Q₁₆	—	2	4	no	—
367	SD₁₆	—	2	4	no	—
368	M₁₆	—	2	4	no	—
369	M₁₆	—	2	1	no	—
370	M₁₆	—	2	1	no	—
371	M₁₆	—	2	1	no	—
372	M₁₆	—	2	1	no	—
373	M₁₆	C₂×C₃×C₄×C₅	1	2	yes	—
374	M₁₆	C₃×C₅×D₄	1	2	yes	—
375	C₂×C₈	—	2	4	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
382	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₃×C₅	#1908	1	1	yes	characteristic, direct product factor, Hall
386	C₂²×C₃	—	2	1	no	—
387	C₂²×C₃	—	2	1	no	—
388	C₂²×C₃	—	2	2	no	—
389	C₂²×C₃	—	4	1	no	—
390	C₂²×C₃	—	4	1	no	—
391	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
392	C₂²×C₃	C₅×#121	1	1	yes	characteristic
393	C₂²×C₃	C₅×#123	1	1	yes	characteristic
394	C₃×C₄	—	2	2	no	—
395	C₃×C₄	—	4	2	no	—
396	C₃×C₄	—	8	1	no	—
397	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
398	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
399	C₃×C₄	C₅×#120	1	1	yes	characteristic
400	C₃×C₄	C₅×#121	1	1	yes	characteristic
401	C₂×C₅	—	2	1	no	—
402	C₂×C₅	—	2	1	no	—
403	C₂×C₅	—	4	2	no	—
404	C₂×C₅	C₃×#386	1	1	yes	characteristic
405	C₂×C₅	C₃×#471	1	1	yes	characteristic
406	C₂×C₅	C₃×#473	1	1	yes	characteristic
407	C₂³	—	2	1	no	—
408	C₂³	C₃×C₅×#41	1	1	yes	characteristic
409	Q₈	—	2	1	no	—
410	Q₈	—	2	2	no	—
411	Q₈	—	2	2	no	—
412	Q₈	—	4	1	no	—
413	Q₈	—	4	1	no	—
414	Q₈	C₃×C₅×C₂²⋊C₄	1	2	yes	—
415	D₄	—	2	2	no	—
416	D₄	—	2	2	no	—
417	D₄	—	2	1	no	—
418	D₄	C₃×C₅×C₂²⋊C₄	1	2	yes	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	8	1	no	—
427	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
428	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
429	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
430	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
431	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
432	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	2	1	no	—
435	C₈	—	2	2	no	—
436	C₈	—	2	1	no	—
437	C₈	—	4	1	no	—
438	C₂×C₃	—	2	1	no	—
439	C₂×C₃	—	2	1	no	—
440	C₂×C₃	—	4	2	no	—
441	C₂×C₃	C₅×#386	1	1	yes	characteristic
442	C₂×C₃	C₅×#471	1	1	yes	characteristic
443	C₂×C₃	C₅×#473	1	1	yes	characteristic
444	C₅	C₃×#1908	1	1	yes	characteristic, direct product factor, Sylow
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	C₃×C₄×C₅×D₄	1	1	yes	characteristic
451	C₂²	C₃×C₅×#121	1	1	yes	characteristic
452	C₂²	C₃×C₅×#123	1	1	yes	characteristic
453	C₄	—	2	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	8	1	no	—
456	C₄	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
457	C₄	C₃×C₄×C₅×D₄	1	1	yes	characteristic
458	C₄	C₃×C₅×#120	1	1	yes	characteristic
459	C₄	C₃×C₅×#121	1	1	yes	characteristic
460	C₃	C₅×#1908	1	1	yes	characteristic, direct product factor, Sylow
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	4	2	no	—
464	C₂	C₃×C₅×#386	1	1	yes	characteristic
465	C₂	C₃×C₅×#471	1	1	yes	characteristic
466	C₂	C₃×C₅×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#121
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂×C₃×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₃×C₅×#103	C₂	semidirect
5. C₂×C₃×C₅×#101	C₂	semidirect
6. C₃×C₅×#343	C₂	semidirect
7. C₃×C₅×#341	C₂	semidirect
8. C₅×#1908	C₃	direct (N × H)
12. C₃×C₅×#137	C₄	semidirect
29. C₃×#1908	C₅	direct (N × H)
33. C₂×C₅×#103	C₂×C₃	semidirect
34. C₂×C₅×#101	C₂×C₃	semidirect
35. C₅×#343	C₂×C₃	semidirect
36. C₅×#341	C₂×C₃	semidirect
76. C₂×C₃×#103	C₂×C₅	semidirect
77. C₂×C₃×#101	C₂×C₅	semidirect
78. C₃×#343	C₂×C₅	semidirect
79. C₃×#341	C₂×C₅	semidirect
83. C₅×#137	C₃×C₄	semidirect
100. #1908	C₃×C₅	direct (N × H)
135. C₃×#137	C₄×C₅	semidirect
191. C₂×#103	C₂×C₃×C₅	semidirect
192. C₂×#101	C₂×C₃×C₅	semidirect
193. #343	C₂×C₃×C₅	semidirect
194. #341	C₂×C₃×C₅	semidirect
280. #137	C₃×C₄×C₅	semidirect
385. C₃×C₅	#1908	direct (N × H)
444. C₅	C₃×#1908	direct (N × H)
460. C₃	C₅×#1908	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×#137	2
C₂×C₃×C₅×#131	2
C₃×C₅×#417	2
C₂×C₃×C₅×#103	2
C₂×C₃×C₅×#101	2
C₃×C₅×#343	2
C₃×C₅×#341	2
C₅×#1908	3
C₃×#1908	5

Subgroups — C3×C5×#1908 #14274942

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1908 #14274942