Subgroups — C₃×C₅×#1928 #14274962

Order 1920.

508 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic
5	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#340	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic
8	C₅×#1928	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×C₄²×C₅	—	2	1	no	—
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₃×C₅×#107	—	2	2	no	—
18	C₃×C₅×#103	—	2	2	no	—
19	C₃×C₅×#103	C₄	1	4	yes	complemented
20	C₃×C₅×#95	—	2	1	no	—
21	C₃×C₅×#95	—	2	1	no	—
22	C₃×C₅×#95	—	2	1	no	—
23	C₃×#1928	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic
25	C₂×C₅×#103	C₂×C₃	1	1	yes	characteristic
26	C₂×C₅×#103	C₂×C₃	1	1	yes	characteristic
27	C₅×#391	C₂×C₃	1	1	yes	characteristic
28	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
29	C₅×#340	C₂×C₃	1	1	yes	characteristic
30	C₅×#336	C₂×C₃	1	1	yes	characteristic
31	C₂×C₃×C₅×Q₈	—	2	1	no	—
32	C₂×C₃×C₅×Q₈	—	2	1	no	—
33	C₂×C₃×C₅×Q₈	—	2	1	no	—
34	C₂×C₃×C₅×Q₈	—	2	1	no	—
35	C₂×C₃×C₅×Q₈	—	2	1	no	—
36	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	—	2	1	no	—
39	C₂²×C₃×C₄×C₅	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₂×C₃×C₅×C₈	—	2	1	no	—
49	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
50	C₃×C₅×C₄⋊C₄	—	2	1	no	—
51	C₃×C₅×C₄⋊C₄	—	2	1	no	—
52	C₃×C₅×C₄⋊C₄	—	2	1	no	—
53	C₃×C₅×C₄⋊C₄	—	2	1	no	—
54	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
55	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
56	C₃×C₄²×C₅	—	2	1	no	—
57	C₃×C₄²×C₅	—	2	1	no	—
58	C₃×C₄²×C₅	—	4	2	no	—
59	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic
60	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic
61	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic
62	C₃×#391	C₂×C₅	1	1	yes	characteristic
63	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
64	C₃×#340	C₂×C₅	1	1	yes	characteristic
65	C₃×#336	C₂×C₅	1	1	yes	characteristic
66	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₄²×C₅	—	2	1	no	—
73	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₅×#107	—	2	2	no	—
75	C₅×#103	—	2	2	no	—
76	C₅×#103	C₃×C₄	1	4	yes	complemented
77	C₅×#95	—	2	1	no	—
78	C₅×#95	—	2	1	no	—
79	C₅×#95	—	2	1	no	—
80	#1928	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
81	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
82	C₃×C₅×Q₈	—	2	2	no	—
83	C₃×C₅×Q₈	—	2	2	no	—
84	C₃×C₅×Q₈	—	4	1	no	—
85	C₃×C₅×Q₈	—	4	1	no	—
86	C₂×C₃×C₄×C₅	—	2	1	no	—
87	C₂×C₃×C₄×C₅	—	2	1	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	1	no	—
92	C₂×C₃×C₄×C₅	—	2	1	no	—
93	C₂×C₃×C₄×C₅	—	2	1	no	—
94	C₂×C₃×C₄×C₅	—	4	1	no	—
95	C₂×C₃×C₄×C₅	—	4	1	no	—
96	C₂×C₃×C₄×C₅	—	4	1	no	—
97	C₂×C₃×C₄×C₅	—	4	1	no	—
98	C₂×C₃×C₄×C₅	—	4	1	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	—	4	1	no	—
103	C₂×C₃×C₄×C₅	Q₁₆	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
110	C₃×C₅×C₈	—	2	2	no	—
111	C₃×C₅×C₈	—	4	1	no	—
112	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
113	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
114	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
115	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
116	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
117	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
118	C₂×C₃×C₄²	—	2	1	no	—
119	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
120	C₃×#107	—	2	2	no	—
121	C₃×#103	—	2	2	no	—
122	C₃×#103	C₄×C₅	1	4	yes	complemented
123	C₃×#95	—	2	1	no	—
124	C₃×#95	—	2	1	no	—
125	C₃×#95	—	2	1	no	—
126	C₂×C₅×Q₈	—	2	1	no	—
127	C₂×C₅×Q₈	—	2	1	no	—
128	C₂×C₅×Q₈	—	2	1	no	—
129	C₂×C₅×Q₈	—	2	1	no	—
130	C₂×C₅×Q₈	—	2	1	no	—
131	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
132	C₂²×C₄×C₅	—	2	1	no	—
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₂²×C₄×C₅	—	2	1	no	—
135	C₂²×C₄×C₅	—	2	1	no	—
136	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	2	1	no	—
144	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
145	C₅×C₄⋊C₄	—	2	1	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
150	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
151	C₄²×C₅	—	2	1	no	—
152	C₄²×C₅	—	2	1	no	—
153	C₄²×C₅	—	4	2	no	—
154	C₂×#107	C₂×C₃×C₅	1	1	yes	characteristic
155	C₂×#103	C₂×C₃×C₅	1	1	yes	characteristic
156	C₂×#103	C₂×C₃×C₅	1	1	yes	characteristic
157	#391	C₂×C₃×C₅	1	1	yes	characteristic
158	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
159	#340	C₂×C₃×C₅	1	1	yes	characteristic
160	#336	C₂×C₃×C₅	1	1	yes	characteristic
161	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
162	C₂²×C₃×C₅	#121	1	1	yes	characteristic
163	C₂²×C₃×C₅	#123	1	1	yes	characteristic
164	C₂²×C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic
165	C₂²×C₃×C₅	#135	1	1	yes	characteristic
166	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₂²×C₃×C₅	#137	1	1	yes	characteristic
168	C₃×C₄×C₅	—	2	2	no	—
169	C₃×C₄×C₅	—	4	2	no	—
170	C₃×C₄×C₅	—	4	2	no	—
171	C₃×C₄×C₅	—	4	2	no	—
172	C₃×C₄×C₅	—	4	1	no	—
173	C₃×C₄×C₅	—	8	1	no	—
174	C₃×C₄×C₅	#117	1	1	yes	characteristic
175	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
176	C₃×C₄×C₅	#124	1	1	yes	characteristic
177	C₃×C₄×C₅	#126	1	1	yes	characteristic
178	C₂×C₃×Q₈	—	2	1	no	—
179	C₂×C₃×Q₈	—	2	1	no	—
180	C₂×C₃×Q₈	—	2	1	no	—
181	C₂×C₃×Q₈	—	2	1	no	—
182	C₂×C₃×Q₈	—	2	1	no	—
183	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
184	C₂²×C₃×C₄	—	2	1	no	—
185	C₂²×C₃×C₄	—	2	1	no	—
186	C₂²×C₃×C₄	—	2	1	no	—
187	C₂²×C₃×C₄	—	2	1	no	—
188	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
190	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
191	C₂×C₃×C₈	—	2	1	no	—
192	C₂×C₃×C₈	—	2	1	no	—
193	C₂×C₃×C₈	—	2	1	no	—
194	C₂×C₃×C₈	—	2	1	no	—
195	C₂×C₃×C₈	—	2	1	no	—
196	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
197	C₃×C₄⋊C₄	—	2	1	no	—
198	C₃×C₄⋊C₄	—	2	1	no	—
199	C₃×C₄⋊C₄	—	2	1	no	—
200	C₃×C₄⋊C₄	—	2	1	no	—
201	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
202	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
203	C₃×C₄²	—	2	1	no	—
204	C₃×C₄²	—	2	1	no	—
205	C₃×C₄²	—	4	2	no	—
206	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
207	C₅×Q₈	—	2	2	no	—
208	C₅×Q₈	—	2	2	no	—
209	C₅×Q₈	—	4	1	no	—
210	C₅×Q₈	—	4	1	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	1	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	—	4	1	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	—	4	1	no	—
226	C₂×C₄×C₅	—	4	1	no	—
227	C₂×C₄×C₅	—	4	1	no	—
228	C₂×C₄×C₅	C₃×Q₁₆	1	2	yes	—
229	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
231	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
232	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
233	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
234	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
235	C₅×C₈	—	2	2	no	—
236	C₅×C₈	—	4	1	no	—
237	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
238	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
239	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
243	C₂×C₄²	—	2	1	no	—
244	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
245	#107	—	2	2	no	—
246	#103	—	2	2	no	—
247	#103	C₃×C₄×C₅	1	4	yes	complemented
248	#95	—	2	1	no	—
249	#95	—	2	1	no	—
250	#95	—	2	1	no	—
251	C₂×C₃×C₅	#388	1	1	yes	characteristic
252	C₂×C₃×C₅	C₄×Q₁₆	1	1	yes	characteristic
253	C₂×C₃×C₅	#440	1	1	yes	characteristic
254	C₂×C₃×C₅	#462	1	1	yes	characteristic
255	C₂×C₃×C₅	#463	1	1	yes	characteristic
256	C₂×C₃×C₅	#484	1	1	yes	characteristic
257	C₂×C₃×C₅	#485	1	1	yes	characteristic
258	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
259	C₃×Q₈	—	2	2	no	—
260	C₃×Q₈	—	2	2	no	—
261	C₃×Q₈	—	4	1	no	—
262	C₃×Q₈	—	4	1	no	—
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	2	1	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	4	1	no	—
272	C₂×C₃×C₄	—	4	1	no	—
273	C₂×C₃×C₄	—	4	1	no	—
274	C₂×C₃×C₄	—	4	1	no	—
275	C₂×C₃×C₄	—	4	1	no	—
276	C₂×C₃×C₄	—	4	1	no	—
277	C₂×C₃×C₄	—	4	1	no	—
278	C₂×C₃×C₄	—	4	1	no	—
279	C₂×C₃×C₄	—	4	1	no	—
280	C₂×C₃×C₄	C₅×Q₁₆	1	2	yes	—
281	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
283	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
284	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
285	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
286	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
287	C₃×C₈	—	2	2	no	—
288	C₃×C₈	—	4	1	no	—
289	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
290	C₂²×C₅	C₃×#121	1	1	yes	characteristic
291	C₂²×C₅	C₃×#123	1	1	yes	characteristic
292	C₂²×C₅	C₂×C₃×Q₁₆	1	1	yes	characteristic
293	C₂²×C₅	C₃×#135	1	1	yes	characteristic
294	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
295	C₂²×C₅	C₃×#137	1	1	yes	characteristic
296	C₄×C₅	—	2	2	no	—
297	C₄×C₅	—	4	2	no	—
298	C₄×C₅	—	4	2	no	—
299	C₄×C₅	—	4	2	no	—
300	C₄×C₅	—	4	1	no	—
301	C₄×C₅	—	8	1	no	—
302	C₄×C₅	C₃×#117	1	1	yes	characteristic
303	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
304	C₄×C₅	C₃×#124	1	1	yes	characteristic
305	C₄×C₅	C₃×#126	1	1	yes	characteristic
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	C₂×C₃×C₄×C₅	1	2	yes	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
317	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
318	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	C₂×C₃×C₄×C₅	1	2	yes	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	C₂×C₃×C₄×C₅	1	2	yes	—
330	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	4	2	no	—
334	C₃×C₅	#1928	1	1	yes	characteristic, direct product factor, Hall
335	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
336	C₂²×C₃	C₅×#121	1	1	yes	characteristic
337	C₂²×C₃	C₅×#123	1	1	yes	characteristic
338	C₂²×C₃	C₂×C₅×Q₁₆	1	1	yes	characteristic
339	C₂²×C₃	C₅×#135	1	1	yes	characteristic
340	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
341	C₂²×C₃	C₅×#137	1	1	yes	characteristic
342	C₃×C₄	—	2	2	no	—
343	C₃×C₄	—	4	2	no	—
344	C₃×C₄	—	4	2	no	—
345	C₃×C₄	—	4	2	no	—
346	C₃×C₄	—	4	1	no	—
347	C₃×C₄	—	8	1	no	—
348	C₃×C₄	C₅×#117	1	1	yes	characteristic
349	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
350	C₃×C₄	C₅×#124	1	1	yes	characteristic
351	C₃×C₄	C₅×#126	1	1	yes	characteristic
352	C₂×C₅	C₃×#388	1	1	yes	characteristic
353	C₂×C₅	C₃×C₄×Q₁₆	1	1	yes	characteristic
354	C₂×C₅	C₃×#440	1	1	yes	characteristic
355	C₂×C₅	C₃×#462	1	1	yes	characteristic
356	C₂×C₅	C₃×#463	1	1	yes	characteristic
357	C₂×C₅	C₃×#484	1	1	yes	characteristic
358	C₂×C₅	C₃×#485	1	1	yes	characteristic
359	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	Q₈	—	2	2	no	—
362	Q₈	—	4	1	no	—
363	Q₈	—	4	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	C₃×C₅×Q₁₆	1	2	yes	—
382	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
383	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
384	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
385	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
386	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
387	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
388	C₈	—	2	2	no	—
389	C₈	—	4	1	no	—
390	C₂×C₃	C₅×#388	1	1	yes	characteristic
391	C₂×C₃	C₄×C₅×Q₁₆	1	1	yes	characteristic
392	C₂×C₃	C₅×#440	1	1	yes	characteristic
393	C₂×C₃	C₅×#462	1	1	yes	characteristic
394	C₂×C₃	C₅×#463	1	1	yes	characteristic
395	C₂×C₃	C₅×#484	1	1	yes	characteristic
396	C₂×C₃	C₅×#485	1	1	yes	characteristic
397	C₅	C₃×#1928	1	1	yes	characteristic, direct product factor, Sylow
398	C₂²	C₃×C₄×C₅×D₄	1	1	yes	characteristic
399	C₂²	C₃×C₅×#121	1	1	yes	characteristic
400	C₂²	C₃×C₅×#123	1	1	yes	characteristic
401	C₂²	C₂×C₃×C₅×Q₁₆	1	1	yes	characteristic
402	C₂²	C₃×C₅×#135	1	1	yes	characteristic
403	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
404	C₂²	C₃×C₅×#137	1	1	yes	characteristic
405	C₄	—	2	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	8	1	no	—
411	C₄	C₃×C₅×#117	1	1	yes	characteristic
412	C₄	C₃×C₄×C₅×D₄	1	1	yes	characteristic
413	C₄	C₃×C₅×#124	1	1	yes	characteristic
414	C₄	C₃×C₅×#126	1	1	yes	characteristic
415	C₃	C₅×#1928	1	1	yes	characteristic, direct product factor, Sylow
416	C₂	C₃×C₅×#388	1	1	yes	characteristic
417	C₂	C₃×C₄×C₅×Q₁₆	1	1	yes	characteristic
418	C₂	C₃×C₅×#440	1	1	yes	characteristic
419	C₂	C₃×C₅×#462	1	1	yes	characteristic
420	C₂	C₃×C₅×#463	1	1	yes	characteristic
421	C₂	C₃×C₅×#484	1	1	yes	characteristic
422	C₂	C₃×C₅×#485	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
LCS	G ▷ C₂×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×#1928	C₃	direct (N × H)
19. C₃×C₅×#103	C₄	semidirect
23. C₃×#1928	C₅	direct (N × H)
76. C₅×#103	C₃×C₄	semidirect
80. #1928	C₃×C₅	direct (N × H)
122. C₃×#103	C₄×C₅	semidirect
247. #103	C₃×C₄×C₅	semidirect
334. C₃×C₅	#1928	direct (N × H)
397. C₅	C₃×#1928	direct (N × H)
415. C₃	C₅×#1928	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×#107	2
C₂×C₃×C₅×#103	2
C₃×C₅×#391	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₅×#340	2
C₃×C₅×#336	2
C₅×#1928	3
C₃×#1928	5

Subgroups — C3×C5×#1928 #14274962

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1928 #14274962