Subgroups — C₃×C₅×#3063 #14276097

Order 1920.

944 conjugacy classes of subgroups.

The subgroup lattice has 576 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×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#537	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#470	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#468	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#467	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×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3063	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×Q₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#137	—	2	4	no	—
17	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
19	C₃×C₅×#131	—	2	4	no	—
20	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
21	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
23	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
25	C₃×C₅×#124	—	2	1	no	—
26	C₃×C₅×#123	—	2	2	no	—
27	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
28	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₃×C₅×#121	—	2	1	no	—
32	C₃×C₅×#121	—	2	2	no	—
33	C₃×C₅×#121	C₂²	1	2	yes	—
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	—
37	C₃×C₅×#106	C₂²	1	2	yes	—
38	C₃×C₅×#103	C₂²	1	2	yes	—
39	C₃×C₅×#103	C₂²	1	1	yes	characteristic
40	C₃×C₅×#103	C₂²	1	2	yes	—
41	C₃×C₅×#103	C₂²	1	1	yes	characteristic
42	C₃×C₅×#102	C₂²	1	1	yes	characteristic
43	C₃×C₅×#102	C₂²	1	1	yes	characteristic
44	C₃×#3063	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×#137	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
48	C₅×#536	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#470	C₂×C₃	1	2	yes	complemented
50	C₅×#468	C₂×C₃	1	2	yes	complemented
51	C₅×#467	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×#103	C₂×C₃	1	1	yes	characteristic, complemented
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	—	2	2	no	—
58	C₃×C₅×#41	—	2	2	no	—
59	C₃×C₅×#41	—	2	2	no	—
60	C₂×C₃×C₅×Q₈	—	2	1	no	—
61	C₂×C₃×C₅×Q₈	—	2	2	no	—
62	C₂×C₃×C₅×Q₈	—	2	2	no	—
63	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
64	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
65	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×D₄	—	2	1	no	—
67	C₂×C₃×C₅×D₄	—	2	2	no	—
68	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
69	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
70	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	—	2	1	no	—
72	C₂²×C₃×C₄×C₅	—	2	1	no	—
73	C₂²×C₃×C₄×C₅	—	2	1	no	—
74	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₃×C₅×Q₁₆	—	2	4	no	—
77	C₃×C₅×SD₁₆	—	2	4	no	—
78	C₃×C₅×M₁₆	—	2	4	no	—
79	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
80	C₂×C₃×C₅×C₈	—	2	2	no	—
81	C₂×C₃×C₅×C₈	—	2	4	no	—
82	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
85	C₃×C₅×C₄⋊C₄	—	2	1	no	—
86	C₃×C₅×C₄⋊C₄	—	2	2	no	—
87	C₃×C₅×C₄⋊C₄	—	2	2	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×#137	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
101	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
102	C₃×#470	C₂×C₅	1	2	yes	complemented
103	C₃×#468	C₂×C₅	1	2	yes	complemented
104	C₃×#467	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×#103	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×Q₈	C₂²×C₃	1	1	yes	characteristic
112	C₅×#137	—	2	4	no	—
113	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
114	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
115	C₅×#131	—	2	4	no	—
116	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
117	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
118	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
119	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
120	C₅×C₄⋊Q₈	—	2	1	no	—
121	C₅×#124	—	2	1	no	—
122	C₅×#123	—	2	2	no	—
123	C₅×C₂²⋊Q₈	—	2	1	no	—
124	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
125	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
126	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
127	C₅×#121	—	2	1	no	—
128	C₅×#121	—	2	2	no	—
129	C₅×#121	C₂²×C₃	1	2	yes	—
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	—
133	C₅×#106	C₂²×C₃	1	2	yes	—
134	C₅×#103	C₂²×C₃	1	2	yes	—
135	C₅×#103	C₂²×C₃	1	2	yes	—
136	C₅×#103	C₂²×C₃	1	1	yes	characteristic
137	C₅×#103	C₂²×C₃	1	1	yes	characteristic
138	C₅×#102	C₂²×C₃	1	1	yes	characteristic
139	C₅×#102	C₂²×C₃	1	1	yes	characteristic
140	#3063	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
141	C₂³×C₃×C₅	—	2	1	no	—
142	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
143	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
144	C₃×C₅×Q₈	—	2	2	no	—
145	C₃×C₅×Q₈	—	2	2	no	—
146	C₃×C₅×Q₈	—	2	1	no	—
147	C₃×C₅×Q₈	—	2	2	no	—
148	C₃×C₅×Q₈	—	2	1	no	—
149	C₃×C₅×Q₈	—	4	2	no	—
150	C₃×C₅×D₄	—	2	4	no	—
151	C₃×C₅×D₄	—	2	2	no	—
152	C₃×C₅×D₄	—	2	1	no	—
153	C₃×C₅×D₄	—	2	1	no	—
154	C₃×C₅×D₄	—	4	2	no	—
155	C₃×C₅×D₄	—	8	2	no	—
156	C₂×C₃×C₄×C₅	—	2	2	no	—
157	C₂×C₃×C₄×C₅	—	2	2	no	—
158	C₂×C₃×C₄×C₅	—	2	1	no	—
159	C₂×C₃×C₄×C₅	—	2	1	no	—
160	C₂×C₃×C₄×C₅	—	2	2	no	—
161	C₂×C₃×C₄×C₅	—	2	1	no	—
162	C₂×C₃×C₄×C₅	—	2	2	no	—
163	C₂×C₃×C₄×C₅	—	4	2	no	—
164	C₂×C₃×C₄×C₅	—	4	2	no	—
165	C₂×C₃×C₄×C₅	—	8	1	no	—
166	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
167	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
168	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
169	C₂×C₃×C₄×C₅	#41	1	2	yes	—
170	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
171	C₃×C₅×C₈	—	2	1	no	—
172	C₃×C₅×C₈	—	2	1	no	—
173	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
174	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
176	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
177	C₃×#137	—	2	4	no	—
178	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
179	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
180	C₃×#131	—	2	4	no	—
181	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
182	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
183	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
184	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
185	C₃×C₄⋊Q₈	—	2	1	no	—
186	C₃×#124	—	2	1	no	—
187	C₃×#123	—	2	2	no	—
188	C₃×C₂²⋊Q₈	—	2	1	no	—
189	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
190	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
191	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
192	C₃×#121	—	2	1	no	—
193	C₃×#121	—	2	2	no	—
194	C₃×#121	C₂²×C₅	1	2	yes	—
195	C₃×#117	C₂²×C₅	1	1	yes	characteristic
196	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
197	C₃×#107	C₂²×C₅	1	2	yes	—
198	C₃×#106	C₂²×C₅	1	2	yes	—
199	C₃×#103	C₂²×C₅	1	2	yes	—
200	C₃×#103	C₂²×C₅	1	2	yes	—
201	C₃×#103	C₂²×C₅	1	1	yes	characteristic
202	C₃×#103	C₂²×C₅	1	1	yes	characteristic
203	C₃×#102	C₂²×C₅	1	1	yes	characteristic
204	C₃×#102	C₂²×C₅	1	1	yes	characteristic
205	C₅×#41	—	2	2	no	—
206	C₅×#41	—	2	2	no	—
207	C₅×#41	—	2	2	no	—
208	C₅×#41	—	2	2	no	—
209	C₂×C₅×Q₈	—	2	1	no	—
210	C₂×C₅×Q₈	—	2	2	no	—
211	C₂×C₅×Q₈	—	2	2	no	—
212	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
213	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
214	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
215	C₂×C₅×D₄	—	2	1	no	—
216	C₂×C₅×D₄	—	2	2	no	—
217	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
218	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
219	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
220	C₂²×C₄×C₅	—	2	1	no	—
221	C₂²×C₄×C₅	—	2	1	no	—
222	C₂²×C₄×C₅	—	2	1	no	—
223	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
224	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
225	C₅×Q₁₆	—	2	4	no	—
226	C₅×SD₁₆	—	2	4	no	—
227	C₅×M₁₆	—	2	4	no	—
228	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
229	C₂×C₅×C₈	—	2	2	no	—
230	C₂×C₅×C₈	—	2	4	no	—
231	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
232	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
233	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
234	C₅×C₄⋊C₄	—	2	1	no	—
235	C₅×C₄⋊C₄	—	2	2	no	—
236	C₅×C₄⋊C₄	—	2	2	no	—
237	C₅×C₄⋊C₄	—	2	2	no	—
238	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
239	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
240	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
241	C₅×C₂²⋊C₄	—	2	1	no	—
242	C₅×C₂²⋊C₄	—	2	2	no	—
243	C₅×C₂²⋊C₄	—	2	2	no	—
244	C₅×C₂²⋊C₄	—	2	2	no	—
245	C₅×C₂²⋊C₄	—	2	2	no	—
246	C₄²×C₅	—	2	1	no	—
247	C₂×#137	C₂×C₃×C₅	1	1	yes	characteristic, complemented
248	C₂×#131	C₂×C₃×C₅	1	1	yes	characteristic, complemented
249	#537	C₂×C₃×C₅	1	1	yes	characteristic
250	#536	C₂×C₃×C₅	1	1	yes	characteristic, complemented
251	#470	C₂×C₃×C₅	1	2	yes	complemented
252	#468	C₂×C₃×C₅	1	2	yes	complemented
253	#467	C₂×C₃×C₅	1	2	yes	complemented
254	#465	C₂×C₃×C₅	1	2	yes	complemented
255	#428	C₂×C₃×C₅	1	1	yes	characteristic, complemented
256	#416	C₂×C₃×C₅	1	1	yes	characteristic, complemented
257	C₂×#103	C₂×C₃×C₅	1	1	yes	characteristic, complemented
258	C₂²×C₃×C₅	—	2	1	no	—
259	C₂²×C₃×C₅	—	2	1	no	—
260	C₂²×C₃×C₅	—	2	2	no	—
261	C₂²×C₃×C₅	—	2	2	no	—
262	C₂²×C₃×C₅	—	2	2	no	—
263	C₂²×C₃×C₅	—	4	1	no	—
264	C₂²×C₃×C₅	—	4	1	no	—
265	C₂²×C₃×C₅	—	4	1	no	—
266	C₂²×C₃×C₅	#121	1	2	yes	—
267	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
268	C₃×C₄×C₅	—	2	2	no	—
269	C₃×C₄×C₅	—	4	1	no	—
270	C₃×C₄×C₅	—	4	2	no	—
271	C₃×C₄×C₅	—	4	1	no	—
272	C₃×C₄×C₅	—	4	2	no	—
273	C₃×C₄×C₅	—	4	1	no	—
274	C₃×C₄×C₅	#121	1	2	yes	—
275	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
276	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
277	C₃×#41	—	2	2	no	—
278	C₃×#41	—	2	2	no	—
279	C₃×#41	—	2	2	no	—
280	C₃×#41	—	2	2	no	—
281	C₂×C₃×Q₈	—	2	1	no	—
282	C₂×C₃×Q₈	—	2	2	no	—
283	C₂×C₃×Q₈	—	2	2	no	—
284	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
285	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
286	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
287	C₂×C₃×D₄	—	2	1	no	—
288	C₂×C₃×D₄	—	2	2	no	—
289	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
290	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
291	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
292	C₂²×C₃×C₄	—	2	1	no	—
293	C₂²×C₃×C₄	—	2	1	no	—
294	C₂²×C₃×C₄	—	2	1	no	—
295	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
296	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
297	C₃×Q₁₆	—	2	4	no	—
298	C₃×SD₁₆	—	2	4	no	—
299	C₃×M₁₆	—	2	4	no	—
300	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
301	C₂×C₃×C₈	—	2	2	no	—
302	C₂×C₃×C₈	—	2	4	no	—
303	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
304	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
305	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
306	C₃×C₄⋊C₄	—	2	1	no	—
307	C₃×C₄⋊C₄	—	2	2	no	—
308	C₃×C₄⋊C₄	—	2	2	no	—
309	C₃×C₄⋊C₄	—	2	2	no	—
310	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
311	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
312	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
313	C₃×C₂²⋊C₄	—	2	1	no	—
314	C₃×C₂²⋊C₄	—	2	2	no	—
315	C₃×C₂²⋊C₄	—	2	2	no	—
316	C₃×C₂²⋊C₄	—	2	2	no	—
317	C₃×C₂²⋊C₄	—	2	2	no	—
318	C₃×C₄²	—	2	1	no	—
319	C₂³×C₅	—	2	1	no	—
320	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
321	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
322	C₅×Q₈	—	2	2	no	—
323	C₅×Q₈	—	2	2	no	—
324	C₅×Q₈	—	2	1	no	—
325	C₅×Q₈	—	2	2	no	—
326	C₅×Q₈	—	2	1	no	—
327	C₅×Q₈	—	4	2	no	—
328	C₅×D₄	—	2	4	no	—
329	C₅×D₄	—	2	2	no	—
330	C₅×D₄	—	2	1	no	—
331	C₅×D₄	—	2	1	no	—
332	C₅×D₄	—	4	2	no	—
333	C₅×D₄	—	8	2	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	—	2	2	no	—
336	C₂×C₄×C₅	—	2	1	no	—
337	C₂×C₄×C₅	—	2	1	no	—
338	C₂×C₄×C₅	—	2	2	no	—
339	C₂×C₄×C₅	—	2	1	no	—
340	C₂×C₄×C₅	—	2	2	no	—
341	C₂×C₄×C₅	—	4	2	no	—
342	C₂×C₄×C₅	—	4	2	no	—
343	C₂×C₄×C₅	—	8	1	no	—
344	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
345	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
346	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
347	C₂×C₄×C₅	C₃×#41	1	2	yes	—
348	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
349	C₅×C₈	—	2	1	no	—
350	C₅×C₈	—	2	1	no	—
351	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
352	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
353	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
354	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
355	#137	—	2	4	no	—
356	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
357	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
358	#131	—	2	4	no	—
359	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
360	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
361	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
362	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
363	C₄⋊Q₈	—	2	1	no	—
364	#124	—	2	1	no	—
365	#123	—	2	2	no	—
366	C₂²⋊Q₈	—	2	1	no	—
367	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
368	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
369	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
370	#121	—	2	1	no	—
371	#121	—	2	2	no	—
372	#121	C₂²×C₃×C₅	1	2	yes	—
373	#117	C₂²×C₃×C₅	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
375	#107	C₂²×C₃×C₅	1	2	yes	—
376	#106	C₂²×C₃×C₅	1	2	yes	—
377	#103	C₂²×C₃×C₅	1	2	yes	—
378	#103	C₂²×C₃×C₅	1	2	yes	—
379	#103	C₂²×C₃×C₅	1	1	yes	characteristic
380	#103	C₂²×C₃×C₅	1	1	yes	characteristic
381	#102	C₂²×C₃×C₅	1	1	yes	characteristic
382	#102	C₂²×C₃×C₅	1	1	yes	characteristic
383	C₂×C₃×C₅	—	2	2	no	—
384	C₂×C₃×C₅	—	4	2	no	—
385	C₂×C₃×C₅	—	8	1	no	—
386	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
387	C₂×C₃×C₅	#577	1	1	yes	characteristic
388	C₂×C₃×C₅	#578	1	1	yes	characteristic
389	C₂³×C₃	—	2	1	no	—
390	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
391	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
392	C₃×Q₈	—	2	2	no	—
393	C₃×Q₈	—	2	2	no	—
394	C₃×Q₈	—	2	1	no	—
395	C₃×Q₈	—	2	2	no	—
396	C₃×Q₈	—	2	1	no	—
397	C₃×Q₈	—	4	2	no	—
398	C₃×D₄	—	2	4	no	—
399	C₃×D₄	—	2	2	no	—
400	C₃×D₄	—	2	1	no	—
401	C₃×D₄	—	2	1	no	—
402	C₃×D₄	—	4	2	no	—
403	C₃×D₄	—	8	2	no	—
404	C₂×C₃×C₄	—	2	2	no	—
405	C₂×C₃×C₄	—	2	2	no	—
406	C₂×C₃×C₄	—	2	1	no	—
407	C₂×C₃×C₄	—	2	1	no	—
408	C₂×C₃×C₄	—	2	2	no	—
409	C₂×C₃×C₄	—	2	1	no	—
410	C₂×C₃×C₄	—	2	2	no	—
411	C₂×C₃×C₄	—	4	2	no	—
412	C₂×C₃×C₄	—	4	2	no	—
413	C₂×C₃×C₄	—	8	1	no	—
414	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
415	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
416	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
417	C₂×C₃×C₄	C₅×#41	1	2	yes	—
418	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
419	C₃×C₈	—	2	1	no	—
420	C₃×C₈	—	2	1	no	—
421	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
422	C₂²×C₅	—	2	1	no	—
423	C₂²×C₅	—	2	1	no	—
424	C₂²×C₅	—	2	2	no	—
425	C₂²×C₅	—	2	2	no	—
426	C₂²×C₅	—	2	2	no	—
427	C₂²×C₅	—	4	1	no	—
428	C₂²×C₅	—	4	1	no	—
429	C₂²×C₅	—	4	1	no	—
430	C₂²×C₅	C₃×#121	1	2	yes	—
431	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
432	C₄×C₅	—	2	2	no	—
433	C₄×C₅	—	4	1	no	—
434	C₄×C₅	—	4	2	no	—
435	C₄×C₅	—	4	1	no	—
436	C₄×C₅	—	4	1	no	—
437	C₄×C₅	—	4	2	no	—
438	C₄×C₅	C₃×#121	1	2	yes	—
439	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
440	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
441	#41	—	2	2	no	—
442	#41	—	2	2	no	—
443	#41	—	2	2	no	—
444	#41	—	2	2	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
449	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
450	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
454	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
455	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
460	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
461	Q₁₆	—	2	4	no	—
462	SD₁₆	—	2	4	no	—
463	M₁₆	—	2	4	no	—
464	M₁₆	C₃×C₅×D₄	1	4	yes	complemented
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	4	no	—
467	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
468	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
469	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
475	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
476	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₄²	—	2	1	no	—
483	C₃×C₅	#3063	1	1	yes	characteristic, direct product factor, Hall
484	C₂²×C₃	—	2	1	no	—
485	C₂²×C₃	—	2	1	no	—
486	C₂²×C₃	—	2	2	no	—
487	C₂²×C₃	—	2	2	no	—
488	C₂²×C₃	—	2	2	no	—
489	C₂²×C₃	—	4	1	no	—
490	C₂²×C₃	—	4	1	no	—
491	C₂²×C₃	—	4	1	no	—
492	C₂²×C₃	C₅×#121	1	2	yes	—
493	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
494	C₃×C₄	—	2	2	no	—
495	C₃×C₄	—	4	1	no	—
496	C₃×C₄	—	4	2	no	—
497	C₃×C₄	—	4	1	no	—
498	C₃×C₄	—	4	2	no	—
499	C₃×C₄	—	4	1	no	—
500	C₃×C₄	C₅×#121	1	2	yes	—
501	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
502	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
503	C₂×C₅	—	2	2	no	—
504	C₂×C₅	—	4	2	no	—
505	C₂×C₅	—	8	1	no	—
506	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
507	C₂×C₅	C₃×#577	1	1	yes	characteristic
508	C₂×C₅	C₃×#578	1	1	yes	characteristic
509	C₂³	—	2	1	no	—
510	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
511	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
512	Q₈	—	2	2	no	—
513	Q₈	—	2	2	no	—
514	Q₈	—	2	1	no	—
515	Q₈	—	2	2	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	4	2	no	—
518	D₄	—	2	4	no	—
519	D₄	—	2	1	no	—
520	D₄	—	2	2	no	—
521	D₄	—	2	1	no	—
522	D₄	—	4	2	no	—
523	D₄	—	8	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	8	1	no	—
534	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
535	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
536	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
537	C₂×C₄	C₃×C₅×#41	1	2	yes	—
538	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	C₂×C₃×C₅×D₄	1	4	yes	—
542	C₂×C₃	—	2	2	no	—
543	C₂×C₃	—	4	2	no	—
544	C₂×C₃	—	8	1	no	—
545	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
546	C₂×C₃	C₅×#577	1	1	yes	characteristic
547	C₂×C₃	C₅×#578	1	1	yes	characteristic
548	C₅	C₃×#3063	1	1	yes	characteristic, direct product factor, Sylow
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	C₃×C₅×#121	1	2	yes	—
558	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
559	C₄	—	2	2	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	C₃×C₅×#121	1	2	yes	—
566	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
567	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
568	C₃	C₅×#3063	1	1	yes	characteristic, direct product factor, Sylow
569	C₂	—	2	2	no	—
570	C₂	—	4	2	no	—
571	C₂	—	8	1	no	—
572	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
573	C₂	C₃×C₅×#577	1	1	yes	characteristic
574	C₂	C₃×C₅×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#537	C₂
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×#137	C₂	semidirect
2. C₂×C₃×C₅×#131	C₂	semidirect
4. C₃×C₅×#536	C₂	semidirect
5. C₃×C₅×#470	C₂	semidirect
6. C₃×C₅×#468	C₂	semidirect
7. C₃×C₅×#467	C₂	semidirect
8. C₃×C₅×#465	C₂	semidirect
9. C₃×C₅×#428	C₂	semidirect
10. C₃×C₅×#416	C₂	semidirect
11. C₂×C₃×C₅×#103	C₂	semidirect
12. C₅×#3063	C₃	direct (N × H)
44. C₃×#3063	C₅	direct (N × H)
45. C₂×C₅×#137	C₂×C₃	semidirect
46. C₂×C₅×#131	C₂×C₃	semidirect
48. C₅×#536	C₂×C₃	semidirect
49. C₅×#470	C₂×C₃	semidirect
50. C₅×#468	C₂×C₃	semidirect
51. C₅×#467	C₂×C₃	semidirect
52. C₅×#465	C₂×C₃	semidirect
53. C₅×#428	C₂×C₃	semidirect
54. C₅×#416	C₂×C₃	semidirect
55. C₂×C₅×#103	C₂×C₃	semidirect
79. C₃×C₅×M₁₆	D₄	semidirect
98. C₂×C₃×#137	C₂×C₅	semidirect
99. C₂×C₃×#131	C₂×C₅	semidirect
101. C₃×#536	C₂×C₅	semidirect
102. C₃×#470	C₂×C₅	semidirect
103. C₃×#468	C₂×C₅	semidirect
104. C₃×#467	C₂×C₅	semidirect
105. C₃×#465	C₂×C₅	semidirect
106. C₃×#428	C₂×C₅	semidirect
107. C₃×#416	C₂×C₅	semidirect
108. C₂×C₃×#103	C₂×C₅	semidirect
140. #3063	C₃×C₅	direct (N × H)
228. C₅×M₁₆	C₃×D₄	semidirect
247. C₂×#137	C₂×C₃×C₅	semidirect
248. C₂×#131	C₂×C₃×C₅	semidirect
250. #536	C₂×C₃×C₅	semidirect
251. #470	C₂×C₃×C₅	semidirect
252. #468	C₂×C₃×C₅	semidirect
253. #467	C₂×C₃×C₅	semidirect
254. #465	C₂×C₃×C₅	semidirect
255. #428	C₂×C₃×C₅	semidirect
256. #416	C₂×C₃×C₅	semidirect
257. C₂×#103	C₂×C₃×C₅	semidirect
300. C₃×M₁₆	C₅×D₄	semidirect
464. M₁₆	C₃×C₅×D₄	semidirect
483. C₃×C₅	#3063	direct (N × H)
548. C₅	C₃×#3063	direct (N × H)
568. C₃	C₅×#3063	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×#537	2
C₃×C₅×#536	2
C₃×C₅×#470	2
C₃×C₅×#468	2
C₃×C₅×#467	2
C₃×C₅×#465	2
C₃×C₅×#428	2
C₃×C₅×#416	2
C₂×C₃×C₅×#103	2
C₅×#3063	3
C₃×#3063	5

Subgroups — C3×C5×#3063 #14276097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3063 #14276097