Subgroups — C₃×C₅×#3062 #14276096

Order 1920.

1008 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#537	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#469	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#468	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#466	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#465	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#428	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3062	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
19	C₃×C₅×#131	—	2	4	no	—
20	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
22	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
24	C₃×C₅×#127	—	2	1	no	—
25	C₃×C₅×#124	—	2	1	no	—
26	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
27	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₃×C₅×#121	—	2	1	no	—
29	C₃×C₅×#121	—	2	2	no	—
30	C₃×C₅×#121	C₂²	1	2	yes	—
31	C₃×C₅×#121	C₂²	1	2	yes	—
32	C₃×C₅×#121	C₂²	1	2	yes	complemented
33	C₃×C₅×#120	—	2	2	no	—
34	C₃×C₅×#117	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₃×C₅×#107	C₂²	1	2	yes	complemented
37	C₃×C₅×#106	C₂²	1	2	yes	complemented
38	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₅×#102	C₂²	1	2	yes	—
41	C₃×C₅×#102	C₂²	1	2	yes	—
42	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
43	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
44	C₃×#3062	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#537	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#535	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#469	C₂×C₃	1	2	yes	complemented
50	C₅×#468	C₂×C₃	1	2	yes	complemented
51	C₅×#466	C₂×C₃	1	2	yes	complemented
52	C₅×#465	C₂×C₃	1	2	yes	complemented
53	C₅×#428	C₂×C₃	1	1	yes	characteristic, complemented
54	C₅×#416	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×C₅×#102	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂⁴×C₃×C₅	—	2	1	no	—
57	C₃×C₅×#41	—	2	2	no	—
58	C₃×C₅×#41	—	2	2	no	—
59	C₃×C₅×#41	—	2	2	no	—
60	C₃×C₅×#41	—	2	2	no	—
61	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
62	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×D₄	—	2	1	no	—
64	C₂×C₃×C₅×D₄	—	2	2	no	—
65	C₂×C₃×C₅×D₄	—	2	2	no	—
66	C₂×C₃×C₅×D₄	—	2	2	no	—
67	C₂×C₃×C₅×D₄	—	2	2	no	—
68	C₂×C₃×C₅×D₄	—	2	1	no	—
69	C₂×C₃×C₅×D₄	—	2	2	no	—
70	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
71	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
72	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
73	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
74	C₂²×C₃×C₄×C₅	—	2	1	no	—
75	C₂²×C₃×C₄×C₅	—	2	1	no	—
76	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₃×C₅×SD₁₆	—	2	4	no	—
79	C₃×C₅×D₈	—	2	4	no	—
80	C₃×C₅×M₁₆	—	2	4	no	—
81	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
82	C₂×C₃×C₅×C₈	—	2	2	no	—
83	C₂×C₃×C₅×C₈	—	2	4	no	—
84	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
87	C₃×C₅×C₄⋊C₄	—	2	1	no	—
88	C₃×C₅×C₄⋊C₄	—	2	2	no	—
89	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
90	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
93	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
94	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
95	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
96	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
97	C₃×C₄²×C₅	—	2	1	no	—
98	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂×C₃×#131	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#537	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#535	C₂×C₅	1	1	yes	characteristic, complemented
102	C₃×#469	C₂×C₅	1	2	yes	complemented
103	C₃×#468	C₂×C₅	1	2	yes	complemented
104	C₃×#466	C₂×C₅	1	2	yes	complemented
105	C₃×#465	C₂×C₅	1	2	yes	complemented
106	C₃×#428	C₂×C₅	1	1	yes	characteristic, complemented
107	C₃×#416	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂×C₃×#102	C₂×C₅	1	1	yes	characteristic, complemented
109	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
111	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
112	C₅×AGL(1,ℤ/8)	—	2	4	no	—
113	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
114	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
115	C₅×#131	—	2	4	no	—
116	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	complemented
118	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
119	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	complemented
120	C₅×#127	—	2	1	no	—
121	C₅×#124	—	2	1	no	—
122	C₅×C₂²⋊Q₈	—	2	1	no	—
123	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
124	C₅×#121	—	2	1	no	—
125	C₅×#121	—	2	2	no	—
126	C₅×#121	C₂²×C₃	1	2	yes	—
127	C₅×#121	C₂²×C₃	1	2	yes	—
128	C₅×#121	C₂²×C₃	1	2	yes	complemented
129	C₅×#120	—	2	2	no	—
130	C₅×#117	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₅×#107	C₂²×C₃	1	2	yes	complemented
133	C₅×#106	C₂²×C₃	1	2	yes	complemented
134	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
135	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
136	C₅×#102	C₂²×C₃	1	2	yes	—
137	C₅×#102	C₂²×C₃	1	2	yes	—
138	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
139	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
140	#3062	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
141	C₂³×C₃×C₅	—	2	1	no	—
142	C₂³×C₃×C₅	—	2	2	no	—
143	C₂³×C₃×C₅	—	4	2	no	—
144	C₂³×C₃×C₅	—	8	1	no	—
145	C₂³×C₃×C₅	—	8	1	no	—
146	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
147	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
148	C₃×C₅×Q₈	—	2	2	no	—
149	C₃×C₅×Q₈	—	2	1	no	—
150	C₃×C₅×Q₈	—	2	1	no	—
151	C₃×C₅×D₄	—	2	4	no	—
152	C₃×C₅×D₄	—	2	2	no	—
153	C₃×C₅×D₄	—	2	1	no	—
154	C₃×C₅×D₄	—	2	2	no	—
155	C₃×C₅×D₄	—	2	2	no	—
156	C₃×C₅×D₄	—	2	1	no	—
157	C₃×C₅×D₄	—	4	2	no	—
158	C₃×C₅×D₄	—	4	2	no	—
159	C₃×C₅×D₄	—	8	2	no	—
160	C₃×C₅×D₄	—	8	2	no	—
161	C₃×C₅×D₄	—	8	2	no	—
162	C₂×C₃×C₄×C₅	—	2	2	no	—
163	C₂×C₃×C₄×C₅	—	2	2	no	—
164	C₂×C₃×C₄×C₅	—	2	1	no	—
165	C₂×C₃×C₄×C₅	—	2	1	no	—
166	C₂×C₃×C₄×C₅	—	2	2	no	—
167	C₂×C₃×C₄×C₅	—	2	1	no	—
168	C₂×C₃×C₄×C₅	—	4	2	no	—
169	C₂×C₃×C₄×C₅	—	8	1	no	—
170	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
171	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
172	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
173	C₂×C₃×C₄×C₅	#41	1	2	yes	—
174	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
175	C₃×C₅×C₈	—	2	1	no	—
176	C₃×C₅×C₈	—	2	1	no	—
177	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
178	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
179	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
180	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
181	C₃×AGL(1,ℤ/8)	—	2	4	no	—
182	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
183	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
184	C₃×#131	—	2	4	no	—
185	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
186	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	complemented
187	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
188	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	complemented
189	C₃×#127	—	2	1	no	—
190	C₃×#124	—	2	1	no	—
191	C₃×C₂²⋊Q₈	—	2	1	no	—
192	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
193	C₃×#121	—	2	1	no	—
194	C₃×#121	—	2	2	no	—
195	C₃×#121	C₂²×C₅	1	2	yes	—
196	C₃×#121	C₂²×C₅	1	2	yes	—
197	C₃×#121	C₂²×C₅	1	2	yes	complemented
198	C₃×#120	—	2	2	no	—
199	C₃×#117	C₂²×C₅	1	1	yes	characteristic
200	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
201	C₃×#107	C₂²×C₅	1	2	yes	complemented
202	C₃×#106	C₂²×C₅	1	2	yes	complemented
203	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
204	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
205	C₃×#102	C₂²×C₅	1	2	yes	—
206	C₃×#102	C₂²×C₅	1	2	yes	—
207	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
208	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
209	C₂⁴×C₅	—	2	1	no	—
210	C₅×#41	—	2	2	no	—
211	C₅×#41	—	2	2	no	—
212	C₅×#41	—	2	2	no	—
213	C₅×#41	—	2	2	no	—
214	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
215	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
216	C₂×C₅×D₄	—	2	1	no	—
217	C₂×C₅×D₄	—	2	2	no	—
218	C₂×C₅×D₄	—	2	2	no	—
219	C₂×C₅×D₄	—	2	2	no	—
220	C₂×C₅×D₄	—	2	2	no	—
221	C₂×C₅×D₄	—	2	1	no	—
222	C₂×C₅×D₄	—	2	2	no	—
223	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
224	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
225	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
226	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
227	C₂²×C₄×C₅	—	2	1	no	—
228	C₂²×C₄×C₅	—	2	1	no	—
229	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
230	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
231	C₅×SD₁₆	—	2	4	no	—
232	C₅×D₈	—	2	4	no	—
233	C₅×M₁₆	—	2	4	no	—
234	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
235	C₂×C₅×C₈	—	2	2	no	—
236	C₂×C₅×C₈	—	2	4	no	—
237	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
238	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
239	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
240	C₅×C₄⋊C₄	—	2	1	no	—
241	C₅×C₄⋊C₄	—	2	2	no	—
242	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
243	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
244	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
245	C₅×C₂²⋊C₄	—	2	1	no	—
246	C₅×C₂²⋊C₄	—	2	2	no	—
247	C₅×C₂²⋊C₄	—	2	2	no	—
248	C₅×C₂²⋊C₄	—	2	2	no	—
249	C₅×C₂²⋊C₄	—	2	2	no	—
250	C₄²×C₅	—	2	1	no	—
251	C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	1	1	yes	characteristic, complemented
252	C₂×#131	C₂×C₃×C₅	1	1	yes	characteristic, complemented
253	#537	C₂×C₃×C₅	1	1	yes	characteristic, complemented
254	#535	C₂×C₃×C₅	1	1	yes	characteristic, complemented
255	#469	C₂×C₃×C₅	1	2	yes	complemented
256	#468	C₂×C₃×C₅	1	2	yes	complemented
257	#466	C₂×C₃×C₅	1	2	yes	complemented
258	#465	C₂×C₃×C₅	1	2	yes	complemented
259	#428	C₂×C₃×C₅	1	1	yes	characteristic, complemented
260	#416	C₂×C₃×C₅	1	1	yes	characteristic, complemented
261	C₂×#102	C₂×C₃×C₅	1	1	yes	characteristic, complemented
262	C₂²×C₃×C₅	—	2	1	no	—
263	C₂²×C₃×C₅	—	2	1	no	—
264	C₂²×C₃×C₅	—	2	2	no	—
265	C₂²×C₃×C₅	—	2	2	no	—
266	C₂²×C₃×C₅	—	2	2	no	—
267	C₂²×C₃×C₅	—	4	1	no	—
268	C₂²×C₃×C₅	—	4	2	no	—
269	C₂²×C₃×C₅	—	4	1	no	—
270	C₂²×C₃×C₅	—	4	2	no	—
271	C₂²×C₃×C₅	—	4	2	no	—
272	C₂²×C₃×C₅	—	4	1	no	—
273	C₂²×C₃×C₅	—	8	4	no	—
274	C₂²×C₃×C₅	#121	1	2	yes	—
275	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
276	C₃×C₄×C₅	—	2	2	no	—
277	C₃×C₄×C₅	—	4	1	no	—
278	C₃×C₄×C₅	—	4	2	no	—
279	C₃×C₄×C₅	—	4	1	no	—
280	C₃×C₄×C₅	—	4	1	no	—
281	C₃×C₄×C₅	#121	1	2	yes	—
282	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
283	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
284	C₂⁴×C₃	—	2	1	no	—
285	C₃×#41	—	2	2	no	—
286	C₃×#41	—	2	2	no	—
287	C₃×#41	—	2	2	no	—
288	C₃×#41	—	2	2	no	—
289	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
290	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
291	C₂×C₃×D₄	—	2	1	no	—
292	C₂×C₃×D₄	—	2	2	no	—
293	C₂×C₃×D₄	—	2	2	no	—
294	C₂×C₃×D₄	—	2	2	no	—
295	C₂×C₃×D₄	—	2	2	no	—
296	C₂×C₃×D₄	—	2	1	no	—
297	C₂×C₃×D₄	—	2	2	no	—
298	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
299	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
300	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
301	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
302	C₂²×C₃×C₄	—	2	1	no	—
303	C₂²×C₃×C₄	—	2	1	no	—
304	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
305	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
306	C₃×SD₁₆	—	2	4	no	—
307	C₃×D₈	—	2	4	no	—
308	C₃×M₁₆	—	2	4	no	—
309	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
310	C₂×C₃×C₈	—	2	2	no	—
311	C₂×C₃×C₈	—	2	4	no	—
312	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
313	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
314	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
315	C₃×C₄⋊C₄	—	2	1	no	—
316	C₃×C₄⋊C₄	—	2	2	no	—
317	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
318	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
319	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
320	C₃×C₂²⋊C₄	—	2	1	no	—
321	C₃×C₂²⋊C₄	—	2	2	no	—
322	C₃×C₂²⋊C₄	—	2	2	no	—
323	C₃×C₂²⋊C₄	—	2	2	no	—
324	C₃×C₂²⋊C₄	—	2	2	no	—
325	C₃×C₄²	—	2	1	no	—
326	C₂³×C₅	—	2	1	no	—
327	C₂³×C₅	—	2	2	no	—
328	C₂³×C₅	—	4	2	no	—
329	C₂³×C₅	—	8	1	no	—
330	C₂³×C₅	—	8	1	no	—
331	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
332	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
333	C₅×Q₈	—	2	2	no	—
334	C₅×Q₈	—	2	1	no	—
335	C₅×Q₈	—	2	1	no	—
336	C₅×D₄	—	2	4	no	—
337	C₅×D₄	—	2	2	no	—
338	C₅×D₄	—	2	1	no	—
339	C₅×D₄	—	2	2	no	—
340	C₅×D₄	—	2	2	no	—
341	C₅×D₄	—	2	1	no	—
342	C₅×D₄	—	4	2	no	—
343	C₅×D₄	—	4	2	no	—
344	C₅×D₄	—	8	2	no	—
345	C₅×D₄	—	8	2	no	—
346	C₅×D₄	—	8	2	no	—
347	C₂×C₄×C₅	—	2	2	no	—
348	C₂×C₄×C₅	—	2	2	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	1	no	—
351	C₂×C₄×C₅	—	2	2	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	4	2	no	—
354	C₂×C₄×C₅	—	8	1	no	—
355	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
356	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
357	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
358	C₂×C₄×C₅	C₃×#41	1	2	yes	—
359	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
360	C₅×C₈	—	2	1	no	—
361	C₅×C₈	—	2	1	no	—
362	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
363	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
364	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
365	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
366	AGL(1,ℤ/8)	—	2	4	no	—
367	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
368	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
369	#131	—	2	4	no	—
370	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
371	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	complemented
372	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
373	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	complemented
374	#127	—	2	1	no	—
375	#124	—	2	1	no	—
376	C₂²⋊Q₈	—	2	1	no	—
377	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
378	#121	—	2	1	no	—
379	#121	—	2	2	no	—
380	#121	C₂²×C₃×C₅	1	2	yes	—
381	#121	C₂²×C₃×C₅	1	2	yes	—
382	#121	C₂²×C₃×C₅	1	2	yes	complemented
383	#120	—	2	2	no	—
384	#117	C₂²×C₃×C₅	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
386	#107	C₂²×C₃×C₅	1	2	yes	complemented
387	#106	C₂²×C₃×C₅	1	2	yes	complemented
388	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
389	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
390	#102	C₂²×C₃×C₅	1	2	yes	—
391	#102	C₂²×C₃×C₅	1	2	yes	—
392	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
393	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
394	C₂×C₃×C₅	—	2	2	no	—
395	C₂×C₃×C₅	—	4	2	no	—
396	C₂×C₃×C₅	—	8	1	no	—
397	C₂×C₃×C₅	—	8	2	no	—
398	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
399	C₂×C₃×C₅	#576	1	1	yes	characteristic
400	C₂×C₃×C₅	#577	1	1	yes	characteristic
401	C₂³×C₃	—	2	1	no	—
402	C₂³×C₃	—	2	2	no	—
403	C₂³×C₃	—	4	2	no	—
404	C₂³×C₃	—	8	1	no	—
405	C₂³×C₃	—	8	1	no	—
406	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
407	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
408	C₃×Q₈	—	2	2	no	—
409	C₃×Q₈	—	2	1	no	—
410	C₃×Q₈	—	2	1	no	—
411	C₃×D₄	—	2	4	no	—
412	C₃×D₄	—	2	2	no	—
413	C₃×D₄	—	2	1	no	—
414	C₃×D₄	—	2	2	no	—
415	C₃×D₄	—	2	2	no	—
416	C₃×D₄	—	2	1	no	—
417	C₃×D₄	—	4	2	no	—
418	C₃×D₄	—	4	2	no	—
419	C₃×D₄	—	8	2	no	—
420	C₃×D₄	—	8	2	no	—
421	C₃×D₄	—	8	2	no	—
422	C₂×C₃×C₄	—	2	2	no	—
423	C₂×C₃×C₄	—	2	2	no	—
424	C₂×C₃×C₄	—	2	1	no	—
425	C₂×C₃×C₄	—	2	1	no	—
426	C₂×C₃×C₄	—	2	2	no	—
427	C₂×C₃×C₄	—	2	1	no	—
428	C₂×C₃×C₄	—	4	2	no	—
429	C₂×C₃×C₄	—	8	1	no	—
430	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
431	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
432	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
433	C₂×C₃×C₄	C₅×#41	1	2	yes	—
434	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
435	C₃×C₈	—	2	1	no	—
436	C₃×C₈	—	2	1	no	—
437	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
438	C₂²×C₅	—	2	1	no	—
439	C₂²×C₅	—	2	1	no	—
440	C₂²×C₅	—	2	2	no	—
441	C₂²×C₅	—	2	2	no	—
442	C₂²×C₅	—	2	2	no	—
443	C₂²×C₅	—	4	1	no	—
444	C₂²×C₅	—	4	2	no	—
445	C₂²×C₅	—	4	2	no	—
446	C₂²×C₅	—	4	1	no	—
447	C₂²×C₅	—	4	1	no	—
448	C₂²×C₅	—	4	2	no	—
449	C₂²×C₅	—	8	4	no	—
450	C₂²×C₅	C₃×#121	1	2	yes	—
451	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
452	C₄×C₅	—	2	2	no	—
453	C₄×C₅	—	4	2	no	—
454	C₄×C₅	—	4	1	no	—
455	C₄×C₅	—	4	1	no	—
456	C₄×C₅	—	4	1	no	—
457	C₄×C₅	C₃×#121	1	2	yes	—
458	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
459	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
460	C₂⁴	—	2	1	no	—
461	#41	—	2	2	no	—
462	#41	—	2	2	no	—
463	#41	—	2	2	no	—
464	#41	—	2	2	no	—
465	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
466	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
475	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
476	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
477	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
481	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
482	SD₁₆	—	2	4	no	—
483	D₈	—	2	4	no	—
484	M₁₆	—	2	4	no	—
485	M₁₆	C₃×C₅×D₄	1	4	yes	complemented
486	C₂×C₈	—	2	2	no	—
487	C₂×C₈	—	2	4	no	—
488	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
489	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
490	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
494	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
495	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
496	C₂²⋊C₄	—	2	1	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₄²	—	2	1	no	—
502	C₃×C₅	#3062	1	1	yes	characteristic, direct product factor, Hall
503	C₂²×C₃	—	2	1	no	—
504	C₂²×C₃	—	2	1	no	—
505	C₂²×C₃	—	2	2	no	—
506	C₂²×C₃	—	2	2	no	—
507	C₂²×C₃	—	2	2	no	—
508	C₂²×C₃	—	4	1	no	—
509	C₂²×C₃	—	4	2	no	—
510	C₂²×C₃	—	4	1	no	—
511	C₂²×C₃	—	4	2	no	—
512	C₂²×C₃	—	4	2	no	—
513	C₂²×C₃	—	4	1	no	—
514	C₂²×C₃	—	8	4	no	—
515	C₂²×C₃	C₅×#121	1	2	yes	—
516	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
517	C₃×C₄	—	2	2	no	—
518	C₃×C₄	—	4	1	no	—
519	C₃×C₄	—	4	2	no	—
520	C₃×C₄	—	4	1	no	—
521	C₃×C₄	—	4	1	no	—
522	C₃×C₄	C₅×#121	1	2	yes	—
523	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
524	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
525	C₂×C₅	—	2	2	no	—
526	C₂×C₅	—	4	2	no	—
527	C₂×C₅	—	8	2	no	—
528	C₂×C₅	—	8	1	no	—
529	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
530	C₂×C₅	C₃×#576	1	1	yes	characteristic
531	C₂×C₅	C₃×#577	1	1	yes	characteristic
532	C₂³	—	2	1	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	4	2	no	—
535	C₂³	—	8	1	no	—
536	C₂³	—	8	1	no	—
537	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
538	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
539	Q₈	—	2	2	no	—
540	Q₈	—	2	1	no	—
541	Q₈	—	2	1	no	—
542	D₄	—	2	4	no	—
543	D₄	—	2	1	no	—
544	D₄	—	2	2	no	—
545	D₄	—	2	2	no	—
546	D₄	—	2	2	no	—
547	D₄	—	2	1	no	—
548	D₄	—	4	2	no	—
549	D₄	—	4	2	no	—
550	D₄	—	8	2	no	—
551	D₄	—	8	2	no	—
552	D₄	—	8	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	8	1	no	—
561	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
562	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
563	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
564	C₂×C₄	C₃×C₅×#41	1	2	yes	—
565	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
566	C₈	—	2	1	no	—
567	C₈	—	2	1	no	—
568	C₈	C₂×C₃×C₅×D₄	1	4	yes	—
569	C₂×C₃	—	2	2	no	—
570	C₂×C₃	—	4	2	no	—
571	C₂×C₃	—	8	2	no	—
572	C₂×C₃	—	8	1	no	—
573	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
574	C₂×C₃	C₅×#576	1	1	yes	characteristic
575	C₂×C₃	C₅×#577	1	1	yes	characteristic
576	C₅	C₃×#3062	1	1	yes	characteristic, direct product factor, Sylow
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	8	4	no	—
589	C₂²	C₃×C₅×#121	1	2	yes	—
590	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
591	C₄	—	2	2	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	C₃×C₅×#121	1	2	yes	—
597	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
598	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
599	C₃	C₅×#3062	1	1	yes	characteristic, direct product factor, Sylow
600	C₂	—	2	2	no	—
601	C₂	—	4	2	no	—
602	C₂	—	8	2	no	—
603	C₂	—	8	1	no	—
604	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
605	C₂	C₃×C₅×#576	1	1	yes	characteristic
606	C₂	C₃×C₅×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₃×C₅×#131	C₂	semidirect
3. C₃×C₅×#537	C₂	semidirect
4. C₃×C₅×#535	C₂	semidirect
5. C₃×C₅×#469	C₂	semidirect
6. C₃×C₅×#468	C₂	semidirect
7. C₃×C₅×#466	C₂	semidirect
8. C₃×C₅×#465	C₂	semidirect
9. C₃×C₅×#428	C₂	semidirect
10. C₃×C₅×#416	C₂	semidirect
11. C₂×C₃×C₅×#102	C₂	semidirect
12. C₅×#3062	C₃	direct (N × H)
21. C₂×C₃×C₅×M₁₆	C₂²	semidirect
23. C₂²×C₃×C₅×C₈	C₂²	semidirect
27. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
32. C₃×C₅×#121	C₂²	semidirect
36. C₃×C₅×#107	C₂²	semidirect
37. C₃×C₅×#106	C₂²	semidirect
38. C₃×C₅×#103	C₂²	semidirect
39. C₃×C₅×#103	C₂²	semidirect
42. C₃×C₅×#102	C₂²	semidirect
43. C₃×C₅×#102	C₂²	semidirect
44. C₃×#3062	C₅	direct (N × H)
45. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
46. C₂×C₅×#131	C₂×C₃	semidirect
47. C₅×#537	C₂×C₃	semidirect
48. C₅×#535	C₂×C₃	semidirect
49. C₅×#469	C₂×C₃	semidirect
50. C₅×#468	C₂×C₃	semidirect
51. C₅×#466	C₂×C₃	semidirect
52. C₅×#465	C₂×C₃	semidirect
53. C₅×#428	C₂×C₃	semidirect
54. C₅×#416	C₂×C₃	semidirect
55. C₂×C₅×#102	C₂×C₃	semidirect
81. C₃×C₅×M₁₆	D₄	semidirect
98. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
99. C₂×C₃×#131	C₂×C₅	semidirect
100. C₃×#537	C₂×C₅	semidirect
101. C₃×#535	C₂×C₅	semidirect
102. C₃×#469	C₂×C₅	semidirect
103. C₃×#468	C₂×C₅	semidirect
104. C₃×#466	C₂×C₅	semidirect
105. C₃×#465	C₂×C₅	semidirect
106. C₃×#428	C₂×C₅	semidirect
107. C₃×#416	C₂×C₅	semidirect
108. C₂×C₃×#102	C₂×C₅	semidirect
117. C₂×C₅×M₁₆	C₂²×C₃	semidirect
119. C₂²×C₅×C₈	C₂²×C₃	semidirect
123. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
128. C₅×#121	C₂²×C₃	semidirect
132. C₅×#107	C₂²×C₃	semidirect
133. C₅×#106	C₂²×C₃	semidirect
134. C₅×#103	C₂²×C₃	semidirect
135. C₅×#103	C₂²×C₃	semidirect
138. C₅×#102	C₂²×C₃	semidirect
139. C₅×#102	C₂²×C₃	semidirect
140. #3062	C₃×C₅	direct (N × H)
186. C₂×C₃×M₁₆	C₂²×C₅	semidirect
188. C₂²×C₃×C₈	C₂²×C₅	semidirect
192. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
197. C₃×#121	C₂²×C₅	semidirect
201. C₃×#107	C₂²×C₅	semidirect
202. C₃×#106	C₂²×C₅	semidirect
203. C₃×#103	C₂²×C₅	semidirect
204. C₃×#103	C₂²×C₅	semidirect
207. C₃×#102	C₂²×C₅	semidirect
208. C₃×#102	C₂²×C₅	semidirect
234. C₅×M₁₆	C₃×D₄	semidirect
251. C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	semidirect
252. C₂×#131	C₂×C₃×C₅	semidirect
253. #537	C₂×C₃×C₅	semidirect
254. #535	C₂×C₃×C₅	semidirect
255. #469	C₂×C₃×C₅	semidirect
256. #468	C₂×C₃×C₅	semidirect
257. #466	C₂×C₃×C₅	semidirect
258. #465	C₂×C₃×C₅	semidirect
259. #428	C₂×C₃×C₅	semidirect
260. #416	C₂×C₃×C₅	semidirect
261. C₂×#102	C₂×C₃×C₅	semidirect
309. C₃×M₁₆	C₅×D₄	semidirect
371. C₂×M₁₆	C₂²×C₃×C₅	semidirect
373. C₂²×C₈	C₂²×C₃×C₅	semidirect
377. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
382. #121	C₂²×C₃×C₅	semidirect
386. #107	C₂²×C₃×C₅	semidirect
387. #106	C₂²×C₃×C₅	semidirect
388. #103	C₂²×C₃×C₅	semidirect
389. #103	C₂²×C₃×C₅	semidirect
392. #102	C₂²×C₃×C₅	semidirect
393. #102	C₂²×C₃×C₅	semidirect
485. M₁₆	C₃×C₅×D₄	semidirect
502. C₃×C₅	#3062	direct (N × H)
576. C₅	C₃×#3062	direct (N × H)
599. C₃	C₅×#3062	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×AGL(1,ℤ/8)	2
C₂×C₃×C₅×#131	2
C₃×C₅×#537	2
C₃×C₅×#535	2
C₃×C₅×#469	2
C₃×C₅×#468	2
C₃×C₅×#466	2
C₃×C₅×#465	2
C₃×C₅×#428	2
C₃×C₅×#416	2
C₂×C₃×C₅×#102	2
C₅×#3062	3
C₃×#3062	5

Subgroups — C3×C5×#3062 #14276096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3062 #14276096