Subgroups — C₃×C₅×#3040 #14276074

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 504 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, complemented
2	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#464	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#463	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#419	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#418	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3040	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₃×C₅×#137	—	2	4	no	—
15	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
16	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	complemented
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
19	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
20	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
22	C₃×C₅×#124	—	2	1	no	—
23	C₃×C₅×#124	—	2	1	no	—
24	C₃×C₅×#124	C₂²	1	4	yes	—
25	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
26	C₃×C₄×C₅×D₄	—	2	2	no	—
27	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
28	C₃×C₅×#117	—	2	1	no	—
29	C₃×C₅×#117	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
31	C₂×C₃×C₄²×C₅	—	2	1	no	—
32	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
33	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
34	C₃×C₅×#103	C₂²	1	4	yes	complemented
35	C₃×C₅×#102	C₂²	1	4	yes	—
36	C₃×#3040	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₂×C₅×#137	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic
39	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
40	C₄×C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#464	C₂×C₃	1	4	yes	complemented
42	C₅×#463	C₂×C₃	1	4	yes	complemented
43	C₅×#423	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#419	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#418	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂⁴×C₃×C₅	—	2	1	no	—
47	C₃×C₅×#41	—	2	2	no	—
48	C₃×C₅×#41	D₄	1	4	yes	—
49	C₂×C₃×C₅×Q₈	—	2	1	no	—
50	C₂×C₃×C₅×Q₈	—	2	2	no	—
51	C₂×C₃×C₅×Q₈	—	2	2	no	—
52	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
53	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
54	C₂×C₃×C₅×D₄	—	2	1	no	—
55	C₂×C₃×C₅×D₄	—	2	2	no	—
56	C₂×C₃×C₅×D₄	—	2	1	no	—
57	C₂×C₃×C₅×D₄	—	2	2	no	—
58	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
59	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	—	2	1	no	—
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	—	2	2	no	—
63	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₃×C₅×Q₁₆	—	2	4	no	—
66	C₃×C₅×SD₁₆	—	2	4	no	—
67	C₃×C₅×SD₁₆	—	2	4	no	—
68	C₃×C₅×D₈	—	2	4	no	—
69	C₃×C₅×M₁₆	—	2	2	no	—
70	C₃×C₅×M₁₆	—	2	2	no	—
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
73	C₃×C₅×C₄⋊C₄	—	2	2	no	—
74	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
75	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
76	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
78	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
79	C₃×C₄²×C₅	—	2	1	no	—
80	C₃×C₄²×C₅	—	2	2	no	—
81	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
82	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
83	C₃×C₄²×C₅	C₂³	1	2	yes	—
84	C₂×C₃×#137	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic
86	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
87	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
88	C₃×#464	C₂×C₅	1	4	yes	complemented
89	C₃×#463	C₂×C₅	1	4	yes	complemented
90	C₃×#423	C₂×C₅	1	1	yes	characteristic, complemented
91	C₃×#419	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×#418	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
94	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
95	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
96	C₅×#137	—	2	4	no	—
97	C₅×AGL(1,ℤ/8)	—	2	4	no	—
98	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	complemented
99	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
100	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
101	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
102	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
104	C₅×#124	—	2	1	no	—
105	C₅×#124	—	2	1	no	—
106	C₅×#124	C₂²×C₃	1	4	yes	—
107	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
108	C₄×C₅×D₄	—	2	2	no	—
109	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
110	C₅×#117	—	2	1	no	—
111	C₅×#117	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₄²×C₅	—	2	1	no	—
114	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
115	C₅×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
116	C₅×#103	C₂²×C₃	1	4	yes	complemented
117	C₅×#102	C₂²×C₃	1	4	yes	—
118	#3040	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
119	C₂³×C₃×C₅	—	2	1	no	—
120	C₂³×C₃×C₅	—	2	2	no	—
121	C₂³×C₃×C₅	—	4	4	no	—
122	C₂³×C₃×C₅	—	4	2	no	—
123	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
124	C₃×C₅×Q₈	—	2	1	no	—
125	C₃×C₅×Q₈	—	2	2	no	—
126	C₃×C₅×Q₈	—	2	2	no	—
127	C₃×C₅×Q₈	—	4	2	no	—
128	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
129	C₃×C₅×D₄	—	2	4	no	—
130	C₃×C₅×D₄	—	2	2	no	—
131	C₃×C₅×D₄	—	2	1	no	—
132	C₃×C₅×D₄	—	2	2	no	—
133	C₃×C₅×D₄	—	4	2	no	—
134	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	—	2	1	no	—
136	C₂×C₃×C₄×C₅	—	2	4	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	4	2	no	—
140	C₂×C₃×C₄×C₅	—	4	4	no	—
141	C₂×C₃×C₄×C₅	—	4	2	no	—
142	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
143	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
146	C₂×C₃×C₄×C₅	#41	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₃×C₅×C₈	—	2	2	no	—
149	C₃×C₅×C₈	—	2	2	no	—
150	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
151	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
152	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
153	C₃×#137	—	2	4	no	—
154	C₃×AGL(1,ℤ/8)	—	2	4	no	—
155	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	complemented
156	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
157	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
158	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
159	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
160	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
161	C₃×#124	—	2	1	no	—
162	C₃×#124	—	2	1	no	—
163	C₃×#124	C₂²×C₅	1	4	yes	—
164	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
165	C₃×C₄×D₄	—	2	2	no	—
166	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
167	C₃×#117	—	2	1	no	—
168	C₃×#117	C₂²×C₅	1	1	yes	characteristic
169	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
170	C₂×C₃×C₄²	—	2	1	no	—
171	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
172	C₃×C₄⋊C₈	C₂²×C₅	1	4	yes	complemented
173	C₃×#103	C₂²×C₅	1	4	yes	complemented
174	C₃×#102	C₂²×C₅	1	4	yes	—
175	C₂⁴×C₅	—	2	1	no	—
176	C₅×#41	—	2	2	no	—
177	C₅×#41	C₃×D₄	1	4	yes	—
178	C₂×C₅×Q₈	—	2	1	no	—
179	C₂×C₅×Q₈	—	2	2	no	—
180	C₂×C₅×Q₈	—	2	2	no	—
181	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
182	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
183	C₂×C₅×D₄	—	2	1	no	—
184	C₂×C₅×D₄	—	2	2	no	—
185	C₂×C₅×D₄	—	2	1	no	—
186	C₂×C₅×D₄	—	2	2	no	—
187	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
188	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
189	C₂²×C₄×C₅	—	2	1	no	—
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	2	2	no	—
192	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
193	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
194	C₅×Q₁₆	—	2	4	no	—
195	C₅×SD₁₆	—	2	4	no	—
196	C₅×SD₁₆	—	2	4	no	—
197	C₅×D₈	—	2	4	no	—
198	C₅×M₁₆	—	2	2	no	—
199	C₅×M₁₆	—	2	2	no	—
200	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
201	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
202	C₅×C₄⋊C₄	—	2	2	no	—
203	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
204	C₅×C₂²⋊C₄	—	2	1	no	—
205	C₅×C₂²⋊C₄	—	2	4	no	—
206	C₅×C₂²⋊C₄	—	2	4	no	—
207	C₅×C₂²⋊C₄	—	2	2	no	—
208	C₄²×C₅	—	2	1	no	—
209	C₄²×C₅	—	2	2	no	—
210	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
211	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
212	C₄²×C₅	C₂³×C₃	1	2	yes	—
213	C₂×#137	C₂×C₃×C₅	1	1	yes	characteristic, complemented
214	C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	1	1	yes	characteristic
215	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic, complemented
216	C₄×#41	C₂×C₃×C₅	1	1	yes	characteristic, complemented
217	#464	C₂×C₃×C₅	1	4	yes	complemented
218	#463	C₂×C₃×C₅	1	4	yes	complemented
219	#423	C₂×C₃×C₅	1	1	yes	characteristic, complemented
220	#419	C₂×C₃×C₅	1	1	yes	characteristic, complemented
221	#418	C₂×C₃×C₅	1	1	yes	characteristic, complemented
222	C₂²×C₃×C₅	—	2	2	no	—
223	C₂²×C₃×C₅	—	2	2	no	—
224	C₂²×C₃×C₅	—	4	2	no	—
225	C₂²×C₃×C₅	—	4	2	no	—
226	C₂²×C₃×C₅	—	4	4	no	—
227	C₂²×C₃×C₅	—	8	4	no	—
228	C₂²×C₃×C₅	#121	1	2	yes	—
229	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
230	C₃×C₄×C₅	—	2	2	no	—
231	C₃×C₄×C₅	—	2	2	no	—
232	C₃×C₄×C₅	—	2	2	no	—
233	C₃×C₄×C₅	—	4	2	no	—
234	C₃×C₄×C₅	—	4	2	no	—
235	C₃×C₄×C₅	#121	1	2	yes	—
236	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
237	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
238	C₂⁴×C₃	—	2	1	no	—
239	C₃×#41	—	2	2	no	—
240	C₃×#41	C₅×D₄	1	4	yes	—
241	C₂×C₃×Q₈	—	2	1	no	—
242	C₂×C₃×Q₈	—	2	2	no	—
243	C₂×C₃×Q₈	—	2	2	no	—
244	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
245	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
246	C₂×C₃×D₄	—	2	1	no	—
247	C₂×C₃×D₄	—	2	2	no	—
248	C₂×C₃×D₄	—	2	1	no	—
249	C₂×C₃×D₄	—	2	2	no	—
250	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
251	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
252	C₂²×C₃×C₄	—	2	1	no	—
253	C₂²×C₃×C₄	—	2	1	no	—
254	C₂²×C₃×C₄	—	2	2	no	—
255	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
256	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
257	C₃×Q₁₆	—	2	4	no	—
258	C₃×SD₁₆	—	2	4	no	—
259	C₃×SD₁₆	—	2	4	no	—
260	C₃×D₈	—	2	4	no	—
261	C₃×M₁₆	—	2	2	no	—
262	C₃×M₁₆	—	2	2	no	—
263	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
264	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
265	C₃×C₄⋊C₄	—	2	2	no	—
266	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
267	C₃×C₂²⋊C₄	—	2	1	no	—
268	C₃×C₂²⋊C₄	—	2	4	no	—
269	C₃×C₂²⋊C₄	—	2	4	no	—
270	C₃×C₂²⋊C₄	—	2	2	no	—
271	C₃×C₄²	—	2	1	no	—
272	C₃×C₄²	—	2	2	no	—
273	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
274	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
275	C₃×C₄²	C₂³×C₅	1	2	yes	—
276	C₂³×C₅	—	2	1	no	—
277	C₂³×C₅	—	2	2	no	—
278	C₂³×C₅	—	4	4	no	—
279	C₂³×C₅	—	4	2	no	—
280	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
281	C₅×Q₈	—	2	1	no	—
282	C₅×Q₈	—	2	2	no	—
283	C₅×Q₈	—	2	2	no	—
284	C₅×Q₈	—	4	2	no	—
285	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
286	C₅×D₄	—	2	4	no	—
287	C₅×D₄	—	2	2	no	—
288	C₅×D₄	—	2	1	no	—
289	C₅×D₄	—	2	2	no	—
290	C₅×D₄	—	4	2	no	—
291	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	4	no	—
294	C₂×C₄×C₅	—	2	2	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	4	2	no	—
297	C₂×C₄×C₅	—	4	4	no	—
298	C₂×C₄×C₅	—	4	2	no	—
299	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
300	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
301	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
303	C₂×C₄×C₅	C₃×#41	1	2	yes	—
304	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
305	C₅×C₈	—	2	2	no	—
306	C₅×C₈	—	2	2	no	—
307	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
308	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
309	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
310	#137	—	2	4	no	—
311	AGL(1,ℤ/8)	—	2	4	no	—
312	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	complemented
313	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
314	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
315	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
316	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
317	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
318	#124	—	2	1	no	—
319	#124	—	2	1	no	—
320	#124	C₂²×C₃×C₅	1	4	yes	—
321	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
324	#117	—	2	1	no	—
325	#117	C₂²×C₃×C₅	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
329	C₄⋊C₈	C₂²×C₃×C₅	1	4	yes	complemented
330	#103	C₂²×C₃×C₅	1	4	yes	complemented
331	#102	C₂²×C₃×C₅	1	4	yes	—
332	C₂×C₃×C₅	—	2	2	no	—
333	C₂×C₃×C₅	—	4	2	no	—
334	C₂×C₃×C₅	—	8	2	no	—
335	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
336	C₂×C₃×C₅	#575	1	2	yes	—
337	C₂³×C₃	—	2	1	no	—
338	C₂³×C₃	—	2	2	no	—
339	C₂³×C₃	—	4	4	no	—
340	C₂³×C₃	—	4	2	no	—
341	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
342	C₃×Q₈	—	2	1	no	—
343	C₃×Q₈	—	2	2	no	—
344	C₃×Q₈	—	2	2	no	—
345	C₃×Q₈	—	4	2	no	—
346	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
347	C₃×D₄	—	2	4	no	—
348	C₃×D₄	—	2	2	no	—
349	C₃×D₄	—	2	1	no	—
350	C₃×D₄	—	2	2	no	—
351	C₃×D₄	—	4	2	no	—
352	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
353	C₂×C₃×C₄	—	2	1	no	—
354	C₂×C₃×C₄	—	2	4	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	4	2	no	—
358	C₂×C₃×C₄	—	4	4	no	—
359	C₂×C₃×C₄	—	4	2	no	—
360	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
361	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
362	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
363	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
364	C₂×C₃×C₄	C₅×#41	1	2	yes	—
365	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
366	C₃×C₈	—	2	2	no	—
367	C₃×C₈	—	2	2	no	—
368	C₂²×C₅	—	2	2	no	—
369	C₂²×C₅	—	2	2	no	—
370	C₂²×C₅	—	4	2	no	—
371	C₂²×C₅	—	4	4	no	—
372	C₂²×C₅	—	4	2	no	—
373	C₂²×C₅	—	8	4	no	—
374	C₂²×C₅	C₃×#121	1	2	yes	—
375	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
376	C₄×C₅	—	2	2	no	—
377	C₄×C₅	—	2	2	no	—
378	C₄×C₅	—	2	2	no	—
379	C₄×C₅	—	4	2	no	—
380	C₄×C₅	—	4	2	no	—
381	C₄×C₅	C₃×#121	1	2	yes	—
382	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
383	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
384	C₂⁴	—	2	1	no	—
385	#41	—	2	2	no	—
386	#41	C₃×C₅×D₄	1	4	yes	—
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
391	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
397	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
402	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
403	Q₁₆	—	2	4	no	—
404	SD₁₆	—	2	4	no	—
405	SD₁₆	—	2	4	no	—
406	D₈	—	2	4	no	—
407	M₁₆	—	2	2	no	—
408	M₁₆	—	2	2	no	—
409	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
410	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	2	no	—
419	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
420	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
421	C₄²	C₂³×C₃×C₅	1	2	yes	—
422	C₃×C₅	#3040	1	1	yes	characteristic, direct product factor, Hall
423	C₂²×C₃	—	2	2	no	—
424	C₂²×C₃	—	2	2	no	—
425	C₂²×C₃	—	4	2	no	—
426	C₂²×C₃	—	4	2	no	—
427	C₂²×C₃	—	4	4	no	—
428	C₂²×C₃	—	8	4	no	—
429	C₂²×C₃	C₅×#121	1	2	yes	—
430	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
431	C₃×C₄	—	2	2	no	—
432	C₃×C₄	—	2	2	no	—
433	C₃×C₄	—	2	2	no	—
434	C₃×C₄	—	4	2	no	—
435	C₃×C₄	—	4	2	no	—
436	C₃×C₄	C₅×#121	1	2	yes	—
437	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
438	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
439	C₂×C₅	—	2	2	no	—
440	C₂×C₅	—	4	2	no	—
441	C₂×C₅	—	8	2	no	—
442	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
443	C₂×C₅	C₃×#575	1	2	yes	—
444	C₂³	—	2	1	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	4	4	no	—
447	C₂³	—	4	2	no	—
448	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
449	Q₈	—	2	1	no	—
450	Q₈	—	2	2	no	—
451	Q₈	—	2	2	no	—
452	Q₈	—	4	2	no	—
453	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
454	D₄	—	2	4	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	1	no	—
457	D₄	—	2	2	no	—
458	D₄	—	4	2	no	—
459	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
468	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
469	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
470	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
471	C₂×C₄	C₃×C₅×#41	1	2	yes	—
472	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
473	C₈	—	2	2	no	—
474	C₈	—	2	2	no	—
475	C₂×C₃	—	2	2	no	—
476	C₂×C₃	—	4	2	no	—
477	C₂×C₃	—	8	2	no	—
478	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
479	C₂×C₃	C₅×#575	1	2	yes	—
480	C₅	C₃×#3040	1	1	yes	characteristic, direct product factor, Sylow
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	8	4	no	—
487	C₂²	C₃×C₅×#121	1	2	yes	—
488	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
489	C₄	—	2	2	no	—
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	2	no	—
494	C₄	C₃×C₅×#121	1	2	yes	—
495	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
496	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
497	C₃	C₅×#3040	1	1	yes	characteristic, direct product factor, Sylow
498	C₂	—	2	2	no	—
499	C₂	—	4	2	no	—
500	C₂	—	8	2	no	—
501	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
502	C₂	C₃×C₅×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#137	C₂	semidirect
3. C₂×C₃×C₅×#124	C₂	semidirect
4. C₃×C₄×C₅×#41	C₂	semidirect
5. C₃×C₅×#464	C₂	semidirect
6. C₃×C₅×#463	C₂	semidirect
7. C₃×C₅×#423	C₂	semidirect
8. C₃×C₅×#419	C₂	semidirect
9. C₃×C₅×#418	C₂	semidirect
10. C₅×#3040	C₃	direct (N × H)
16. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
18. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
25. C₃×C₄×C₅×Q₈	C₂²	semidirect
27. C₃×C₄×C₅×D₄	C₂²	semidirect
33. C₃×C₅×C₄⋊C₈	C₂²	semidirect
34. C₃×C₅×#103	C₂²	semidirect
36. C₃×#3040	C₅	direct (N × H)
37. C₂×C₅×#137	C₂×C₃	semidirect
39. C₂×C₅×#124	C₂×C₃	semidirect
40. C₄×C₅×#41	C₂×C₃	semidirect
41. C₅×#464	C₂×C₃	semidirect
42. C₅×#463	C₂×C₃	semidirect
43. C₅×#423	C₂×C₃	semidirect
44. C₅×#419	C₂×C₃	semidirect
45. C₅×#418	C₂×C₃	semidirect
84. C₂×C₃×#137	C₂×C₅	semidirect
86. C₂×C₃×#124	C₂×C₅	semidirect
87. C₃×C₄×#41	C₂×C₅	semidirect
88. C₃×#464	C₂×C₅	semidirect
89. C₃×#463	C₂×C₅	semidirect
90. C₃×#423	C₂×C₅	semidirect
91. C₃×#419	C₂×C₅	semidirect
92. C₃×#418	C₂×C₅	semidirect
98. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
100. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
107. C₄×C₅×Q₈	C₂²×C₃	semidirect
109. C₄×C₅×D₄	C₂²×C₃	semidirect
115. C₅×C₄⋊C₈	C₂²×C₃	semidirect
116. C₅×#103	C₂²×C₃	semidirect
118. #3040	C₃×C₅	direct (N × H)
155. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
157. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
164. C₃×C₄×Q₈	C₂²×C₅	semidirect
166. C₃×C₄×D₄	C₂²×C₅	semidirect
172. C₃×C₄⋊C₈	C₂²×C₅	semidirect
173. C₃×#103	C₂²×C₅	semidirect
213. C₂×#137	C₂×C₃×C₅	semidirect
215. C₂×#124	C₂×C₃×C₅	semidirect
216. C₄×#41	C₂×C₃×C₅	semidirect
217. #464	C₂×C₃×C₅	semidirect
218. #463	C₂×C₃×C₅	semidirect
219. #423	C₂×C₃×C₅	semidirect
220. #419	C₂×C₃×C₅	semidirect
221. #418	C₂×C₃×C₅	semidirect
312. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
314. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
321. C₄×Q₈	C₂²×C₃×C₅	semidirect
323. C₄×D₄	C₂²×C₃×C₅	semidirect
329. C₄⋊C₈	C₂²×C₃×C₅	semidirect
330. #103	C₂²×C₃×C₅	semidirect
422. C₃×C₅	#3040	direct (N × H)
480. C₅	C₃×#3040	direct (N × H)
497. C₃	C₅×#3040	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×AGL(1,ℤ/8)	2
C₂×C₃×C₅×#124	2
C₃×C₄×C₅×#41	2
C₃×C₅×#464	2
C₃×C₅×#463	2
C₃×C₅×#423	2
C₃×C₅×#419	2
C₃×C₅×#418	2
C₅×#3040	3
C₃×#3040	5

Subgroups — C3×C5×#3040 #14276074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3040 #14276074