Subgroups — C₃×#10615523 #14418015

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66156	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#4047	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65525	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65434	C₂	1	4	yes	maximal, complemented
6	C₃×#65433	C₂	1	4	yes	maximal, complemented
7	C₃×#65428	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65413	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65390	C₂	1	1	yes	maximal, characteristic, complemented
10	#10615523	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂×C₃×#709	C₂²	1	1	yes	characteristic
13	C₃×C₅×#131	—	2	1	no	—
14	C₃×C₅×#131	—	2	1	no	—
15	C₃×C₅×#131	C₂²	1	2	yes	complemented
16	C₃×C₅×#131	C₂²	1	2	yes	complemented
17	C₂×C₃×C₅×M₁₆	—	2	1	no	—
18	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×C₈	—	2	1	no	—
20	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₃×#4097	C₄	1	2	yes	complemented
22	C₃×#4096	C₂²	1	4	yes	—
23	C₃×#4095	C₄	1	2	yes	complemented
24	C₃×#4088	C₄	1	2	yes	complemented
25	C₃×#4078	C₄	1	2	yes	complemented
26	C₃×#4072	C₂²	1	1	yes	characteristic
27	C₂×C₃×#681	C₂²	1	1	yes	characteristic
28	C₂×C₃×#681	C₂²	1	1	yes	characteristic
29	C₃×#4047	—	2	1	no	—
30	C₃×#4047	—	2	1	no	—
31	C₃×#4047	C₂²	1	2	yes	complemented
32	C₃×#4047	C₂²	1	2	yes	complemented
33	C₂×C₃×#676	—	2	1	no	—
34	C₂×C₃×C₈×D₅	—	2	1	no	—
35	C₃×#3969	C₂²	1	4	yes	complemented
36	C₃×#3957	C₂²	1	4	yes	complemented
37	C₃×#3954	C₂²	1	4	yes	complemented
38	C₃×#3947	C₂²	1	2	yes	complemented
39	C₃×C₈×Dic₅	C₂²	1	2	yes	complemented
40	C₃×#2955	—	5	1	no	maximal, Hall
41	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic, complemented
42	#66156	C₂×C₃	1	1	yes	characteristic
43	C₂×#4047	C₂×C₃	1	1	yes	characteristic, complemented
44	#65525	C₂×C₃	1	1	yes	characteristic, complemented
45	#65434	C₂×C₃	1	4	yes	complemented
46	#65433	C₂×C₃	1	4	yes	complemented
47	#65428	C₂×C₃	1	1	yes	characteristic, complemented
48	#65413	C₂×C₃	1	1	yes	characteristic, complemented
49	#65390	C₂×C₃	1	1	yes	characteristic, complemented
50	C₃×C₅×#41	—	2	1	no	—
51	C₃×C₅×#41	—	2	1	no	—
52	C₃×C₅×#41	C₂×C₄	1	2	yes	—
53	C₃×C₅×#41	C₂³	1	2	yes	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	C₂×C₃×C₅×D₄	—	2	1	no	—
56	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	—	2	1	no	—
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
60	C₃×#709	—	2	1	no	—
61	C₃×#709	—	2	1	no	—
62	C₃×#709	C₂×C₄	1	2	yes	—
63	C₃×#709	C₂³	1	2	yes	—
64	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
65	C₂×C₃×C₄×D₅	—	2	1	no	—
66	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
67	C₃×C₅×M₁₆	—	2	1	no	—
68	C₃×C₅×M₁₆	—	2	2	no	—
69	C₃×C₅×M₁₆	—	2	2	no	—
70	C₃×C₅×M₁₆	C₂³	1	2	yes	—
71	C₂×C₃×C₅×C₈	—	2	1	no	—
72	C₂×C₃×C₅×C₈	—	2	2	no	—
73	C₂×C₃×C₅×C₈	—	2	2	no	—
74	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
75	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
76	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
77	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
78	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₃×C₂²⋊Dic₅	—	2	1	no	—
81	C₃×#689	C₂×C₄	1	4	yes	—
82	C₃×#688	C₂×C₄	1	4	yes	—
83	C₃×#687	C₂×C₄	1	4	yes	—
84	C₃×#686	C₂×C₄	1	4	yes	—
85	C₃×C₄⋊Dic₅	—	2	1	no	—
86	C₃×C₄×Dic₅	C₂³	1	2	yes	—
87	C₃×#681	—	2	1	no	—
88	C₃×#681	C₂×C₄	1	2	yes	—
89	C₃×#681	C₂×C₄	1	2	yes	—
90	C₃×#681	C₂³	1	2	yes	—
91	C₂×C₃×#168	—	2	1	no	—
92	C₂×C₃×#168	C₂³	1	2	yes	—
93	C₃×#676	—	2	2	no	—
94	C₃×#676	—	2	2	no	—
95	C₃×C₈×D₅	—	2	2	no	—
96	C₃×C₈×D₅	—	2	2	no	—
97	C₃×#575	—	5	1	no	—
98	C₂×C₃×#131	—	5	1	no	—
99	C₂×C₃×#131	D₅	1	1	yes	characteristic, complemented
100	C₃×#444	—	5	4	no	—
101	C₃×#443	—	5	4	no	—
102	C₃×#430	—	5	1	no	—
103	C₃×#421	—	5	1	no	—
104	C₃×#421	—	5	1	no	—
105	C₃×#405	—	5	1	no	—
106	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
107	C₂×#709	C₂²×C₃	1	1	yes	characteristic
108	C₅×#131	—	2	1	no	—
109	C₅×#131	—	2	1	no	—
110	C₅×#131	C₂²×C₃	1	2	yes	complemented
111	C₅×#131	C₂²×C₃	1	2	yes	complemented
112	C₂×C₅×M₁₆	—	2	1	no	—
113	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
114	C₂²×C₅×C₈	—	2	1	no	—
115	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
116	#4097	C₃×C₄	1	2	yes	complemented
117	#4096	C₂²×C₃	1	4	yes	—
118	#4095	C₃×C₄	1	2	yes	complemented
119	#4088	C₃×C₄	1	2	yes	complemented
120	#4078	C₃×C₄	1	2	yes	complemented
121	#4072	C₂²×C₃	1	1	yes	characteristic
122	C₂×#681	C₂²×C₃	1	1	yes	characteristic
123	C₂×#681	C₂²×C₃	1	1	yes	characteristic
124	#4047	—	2	1	no	—
125	#4047	—	2	1	no	—
126	#4047	C₂²×C₃	1	2	yes	complemented
127	#4047	C₂²×C₃	1	2	yes	complemented
128	C₂×#676	—	2	1	no	—
129	C₂×C₈×D₅	—	2	1	no	—
130	#3969	C₂²×C₃	1	4	yes	complemented
131	#3957	C₂²×C₃	1	4	yes	complemented
132	#3954	C₂²×C₃	1	4	yes	complemented
133	#3947	C₂²×C₃	1	2	yes	complemented
134	C₈×Dic₅	C₂²×C₃	1	2	yes	complemented
135	#2955	—	5	1	no	Sylow
136	C₂³×C₃×C₅	—	2	1	no	—
137	C₂³×C₃×C₅	#41	1	1	yes	characteristic
138	C₂²×C₃×D₅	—	2	1	no	—
139	C₃×C₅×Q₈	—	2	1	no	—
140	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
141	C₃×C₅×D₄	—	2	2	no	—
142	C₃×C₅×D₄	—	2	2	no	—
143	C₃×C₅×D₄	—	2	1	no	—
144	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₃×C₂²⋊D₅	—	2	2	no	—
155	C₃×C₂²⋊D₅	—	2	2	no	—
156	C₂×C₃×Dic₅	—	2	1	no	—
157	C₂×C₃×Dic₅	—	2	2	no	—
158	C₃×D₂₀	—	2	1	no	—
159	C₃×D₂₀	C₂²×C₄	1	2	yes	—
160	C₃×C₄×D₅	—	2	2	no	—
161	C₃×C₄×D₅	—	2	2	no	—
162	C₃×Dic₁₀	—	2	1	no	—
163	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
164	C₃×C₅×C₈	—	2	2	no	—
165	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
166	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
167	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
168	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
169	C₃×#168	—	2	2	no	—
170	C₃×#168	C₂²×C₄	1	4	yes	—
171	C₂×C₃×#41	—	5	1	no	—
172	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
173	C₃×#137	—	5	2	no	—
174	C₃×#137	—	5	2	no	—
175	C₃×AGL(1,ℤ/8)	—	5	2	no	—
176	C₃×AGL(1,ℤ/8)	—	5	2	no	—
177	C₃×#135	—	5	4	no	—
178	C₃×#131	—	2	1	no	—
179	C₃×#131	—	2	1	no	—
180	C₃×#131	—	5	2	no	—
181	C₃×#131	—	5	2	no	—
182	C₃×#131	—	10	1	no	—
183	C₃×#131	—	10	1	no	—
184	C₃×#131	C₂×D₅	1	2	yes	complemented
185	C₃×#131	C₂×D₅	1	2	yes	complemented
186	C₂×C₃×M₁₆	—	2	1	no	—
187	C₂×C₃×M₁₆	—	5	1	no	—
188	C₂×C₃×M₁₆	—	5	1	no	—
189	C₂×C₃×M₁₆	—	10	1	no	—
190	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
191	C₂²×C₃×C₈	—	2	1	no	—
192	C₂²×C₃×C₈	—	10	1	no	—
193	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
194	C₃×#117	—	5	1	no	—
195	C₃×#108	—	5	4	no	—
196	C₃×#104	—	5	4	no	—
197	C₃×#104	—	5	4	no	—
198	C₃×#97	—	5	2	no	—
199	C₃×C₄×C₈	—	5	2	no	—
200	C₅×#41	—	2	1	no	—
201	C₅×#41	—	2	1	no	—
202	C₅×#41	C₂×C₃×C₄	1	2	yes	—
203	C₅×#41	C₂³×C₃	1	2	yes	—
204	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
205	C₂×C₅×D₄	—	2	1	no	—
206	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₅	—	2	1	no	—
208	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₂²⋊D₅	—	2	1	no	—
210	#709	—	2	1	no	—
211	#709	—	2	1	no	—
212	#709	C₂×C₃×C₄	1	2	yes	—
213	#709	C₂³×C₃	1	2	yes	—
214	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
215	C₂×C₄×D₅	—	2	1	no	—
216	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
217	C₅×M₁₆	—	2	1	no	—
218	C₅×M₁₆	—	2	2	no	—
219	C₅×M₁₆	—	2	2	no	—
220	C₅×M₁₆	C₂³×C₃	1	2	yes	—
221	C₂×C₅×C₈	—	2	1	no	—
222	C₂×C₅×C₈	—	2	2	no	—
223	C₂×C₅×C₈	—	2	2	no	—
224	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
225	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
226	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
227	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
228	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
229	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
230	C₂²⋊Dic₅	—	2	1	no	—
231	#689	C₂×C₃×C₄	1	4	yes	—
232	#688	C₂×C₃×C₄	1	4	yes	—
233	#687	C₂×C₃×C₄	1	4	yes	—
234	#686	C₂×C₃×C₄	1	4	yes	—
235	C₄⋊Dic₅	—	2	1	no	—
236	C₄×Dic₅	C₂³×C₃	1	2	yes	—
237	#681	—	2	1	no	—
238	#681	C₂×C₃×C₄	1	2	yes	—
239	#681	C₂×C₃×C₄	1	2	yes	—
240	#681	C₂³×C₃	1	2	yes	—
241	C₂×#168	—	2	1	no	—
242	C₂×#168	C₂³×C₃	1	2	yes	—
243	#676	—	2	2	no	—
244	#676	—	2	2	no	—
245	C₈×D₅	—	2	2	no	—
246	C₈×D₅	—	2	2	no	—
247	#575	—	5	1	no	—
248	C₂×#131	—	5	1	no	—
249	C₂×#131	C₃×D₅	1	1	yes	characteristic, complemented
250	#444	—	5	4	no	—
251	#443	—	5	4	no	—
252	#430	—	5	1	no	—
253	#421	—	5	1	no	—
254	#421	—	5	1	no	—
255	#405	—	5	1	no	—
256	C₂²×C₃×C₅	—	2	2	no	—
257	C₂²×C₃×C₅	—	4	1	no	—
258	C₂²×C₃×C₅	—	4	2	no	—
259	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
260	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
261	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
262	C₂×C₃×D₅	—	2	2	no	—
263	C₂×C₃×D₅	—	4	2	no	—
264	C₃×C₄×C₅	—	2	2	no	—
265	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
266	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
267	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
268	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
269	C₃×Dic₅	—	2	2	no	—
270	C₃×Dic₅	—	4	2	no	—
271	C₃×#41	—	2	1	no	—
272	C₃×#41	—	2	1	no	—
273	C₃×#41	—	5	2	no	—
274	C₃×#41	—	5	2	no	—
275	C₃×#41	—	10	1	no	—
276	C₃×#41	—	10	1	no	—
277	C₃×#41	C₄×D₅	1	2	yes	—
278	C₃×#41	C₂²×D₅	1	2	yes	—
279	C₂×C₃×Q₈	—	5	1	no	—
280	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
281	C₂×C₃×D₄	—	2	1	no	—
282	C₂×C₃×D₄	—	5	1	no	—
283	C₂×C₃×D₄	—	10	1	no	—
284	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
285	C₂²×C₃×C₄	—	2	1	no	—
286	C₂²×C₃×C₄	—	10	1	no	—
287	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
288	C₃×Q₁₆	—	5	4	no	—
289	C₃×SD₁₆	—	5	4	no	—
290	C₃×SD₁₆	—	5	4	no	—
291	C₃×D₈	—	5	4	no	—
292	C₃×M₁₆	—	2	1	no	—
293	C₃×M₁₆	—	2	2	no	—
294	C₃×M₁₆	—	2	2	no	—
295	C₃×M₁₆	—	5	2	no	—
296	C₃×M₁₆	—	5	2	no	—
297	C₃×M₁₆	—	5	2	no	—
298	C₃×M₁₆	—	10	1	no	—
299	C₃×M₁₆	—	10	2	no	—
300	C₃×M₁₆	—	10	2	no	—
301	C₃×M₁₆	C₂²×D₅	1	2	yes	—
302	C₂×C₃×C₈	—	2	1	no	—
303	C₂×C₃×C₈	—	2	2	no	—
304	C₂×C₃×C₈	—	2	2	no	—
305	C₂×C₃×C₈	—	5	2	no	—
306	C₂×C₃×C₈	—	10	1	no	—
307	C₂×C₃×C₈	—	10	2	no	—
308	C₂×C₃×C₈	—	10	2	no	—
309	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
310	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
311	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
312	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
313	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
314	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
315	C₃×C₄⋊C₄	—	10	1	no	—
316	C₃×C₂²⋊C₄	—	10	1	no	—
317	C₃×C₄²	—	5	2	no	—
318	C₂³×C₅	—	2	1	no	—
319	C₂³×C₅	C₃×#41	1	1	yes	characteristic
320	C₂²×D₅	—	2	1	no	—
321	C₅×Q₈	—	2	1	no	—
322	C₅×Q₈	C₂²×C₃×C₄	1	2	yes	—
323	C₅×D₄	—	2	2	no	—
324	C₅×D₄	—	2	2	no	—
325	C₅×D₄	—	2	1	no	—
326	C₅×D₄	C₂²×C₃×C₄	1	2	yes	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
331	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
333	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
334	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
335	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
336	C₂²⋊D₅	—	2	2	no	—
337	C₂²⋊D₅	—	2	2	no	—
338	C₂×Dic₅	—	2	1	no	—
339	C₂×Dic₅	—	2	2	no	—
340	D₂₀	—	2	1	no	—
341	D₂₀	C₂²×C₃×C₄	1	2	yes	—
342	C₄×D₅	—	2	2	no	—
343	C₄×D₅	—	2	2	no	—
344	Dic₁₀	—	2	1	no	—
345	Dic₁₀	C₂²×C₃×C₄	1	2	yes	—
346	C₅×C₈	—	2	2	no	—
347	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
348	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
349	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
350	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
351	#168	—	2	2	no	—
352	#168	C₂²×C₃×C₄	1	4	yes	—
353	C₂×#41	—	5	1	no	—
354	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
355	#137	—	5	2	no	—
356	#137	—	5	2	no	—
357	AGL(1,ℤ/8)	—	5	2	no	—
358	AGL(1,ℤ/8)	—	5	2	no	—
359	#135	—	5	4	no	—
360	#131	—	2	1	no	—
361	#131	—	2	1	no	—
362	#131	—	5	2	no	—
363	#131	—	5	2	no	—
364	#131	—	10	1	no	—
365	#131	—	10	1	no	—
366	#131	C₂×C₃×D₅	1	2	yes	complemented
367	#131	C₂×C₃×D₅	1	2	yes	complemented
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	5	1	no	—
370	C₂×M₁₆	—	5	1	no	—
371	C₂×M₁₆	—	10	1	no	—
372	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	—	10	1	no	—
375	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
376	#117	—	5	1	no	—
377	#108	—	5	4	no	—
378	#104	—	5	4	no	—
379	#104	—	5	4	no	—
380	#97	—	5	2	no	—
381	C₄×C₈	—	5	2	no	—
382	C₂×C₃×C₅	—	2	1	no	—
383	C₂×C₃×C₅	—	2	1	no	—
384	C₂×C₃×C₅	—	2	1	no	—
385	C₂×C₃×C₅	—	4	2	no	—
386	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
387	C₃×D₅	—	4	2	no	—
388	C₂³×C₃	—	2	1	no	—
389	C₂³×C₃	—	10	1	no	—
390	C₂³×C₃	#709	1	1	yes	characteristic
391	C₃×Q₈	—	2	1	no	—
392	C₃×Q₈	—	5	2	no	—
393	C₃×Q₈	—	10	1	no	—
394	C₃×Q₈	C₂×C₄×D₅	1	2	yes	—
395	C₃×D₄	—	2	2	no	—
396	C₃×D₄	—	2	2	no	—
397	C₃×D₄	—	2	1	no	—
398	C₃×D₄	—	5	2	no	—
399	C₃×D₄	—	10	2	no	—
400	C₃×D₄	—	10	2	no	—
401	C₃×D₄	—	10	1	no	—
402	C₃×D₄	C₂×C₄×D₅	1	2	yes	—
403	C₂×C₃×C₄	—	2	1	no	—
404	C₂×C₃×C₄	—	2	2	no	—
405	C₂×C₃×C₄	—	2	2	no	—
406	C₂×C₃×C₄	—	10	1	no	—
407	C₂×C₃×C₄	—	10	2	no	—
408	C₂×C₃×C₄	—	10	2	no	—
409	C₂×C₃×C₄	—	10	2	no	—
410	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
411	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
412	C₂×C₃×C₄	#709	1	1	yes	characteristic
413	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
414	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
415	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
416	C₃×C₈	—	2	2	no	—
417	C₃×C₈	—	5	4	no	—
418	C₃×C₈	—	10	2	no	—
419	C₃×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
420	C₃×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
421	C₃×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
422	C₃×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
423	C₂²×C₅	—	2	2	no	—
424	C₂²×C₅	—	4	1	no	—
425	C₂²×C₅	—	4	2	no	—
426	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
427	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
428	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
429	C₂×D₅	—	2	2	no	—
430	C₂×D₅	—	4	2	no	—
431	C₄×C₅	—	2	2	no	—
432	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
433	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
434	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
435	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
436	Dic₅	—	2	2	no	—
437	Dic₅	—	4	2	no	—
438	#41	—	2	1	no	—
439	#41	—	2	1	no	—
440	#41	—	5	2	no	—
441	#41	—	5	2	no	—
442	#41	—	10	1	no	—
443	#41	—	10	1	no	—
444	#41	C₃×C₄×D₅	1	2	yes	—
445	#41	C₂²×C₃×D₅	1	2	yes	—
446	C₂×Q₈	—	5	1	no	—
447	C₂×Q₈	C₃×C₄×D₅	1	1	yes	characteristic
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	5	1	no	—
450	C₂×D₄	—	10	1	no	—
451	C₂×D₄	C₃×C₄×D₅	1	1	yes	characteristic
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	10	1	no	—
454	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
455	Q₁₆	—	5	4	no	—
456	SD₁₆	—	5	4	no	—
457	SD₁₆	—	5	4	no	—
458	D₈	—	5	4	no	—
459	M₁₆	—	2	1	no	—
460	M₁₆	—	2	2	no	—
461	M₁₆	—	2	2	no	—
462	M₁₆	—	5	2	no	—
463	M₁₆	—	5	2	no	—
464	M₁₆	—	5	2	no	—
465	M₁₆	—	10	1	no	—
466	M₁₆	—	10	2	no	—
467	M₁₆	—	10	2	no	—
468	M₁₆	C₂²×C₃×D₅	1	2	yes	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	5	2	no	—
473	C₂×C₈	—	10	1	no	—
474	C₂×C₈	—	10	2	no	—
475	C₂×C₈	—	10	2	no	—
476	C₂×C₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
477	C₂×C₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
478	C₂×C₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
479	C₂×C₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
480	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
481	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
482	C₄⋊C₄	—	10	1	no	—
483	C₂²⋊C₄	—	10	1	no	—
484	C₄²	—	5	2	no	—
485	C₃×C₅	#2955	1	1	yes	characteristic, complemented, Hall
486	C₂²×C₃	—	2	2	no	—
487	C₂²×C₃	—	4	1	no	—
488	C₂²×C₃	—	4	2	no	—
489	C₂²×C₃	—	10	2	no	—
490	C₂²×C₃	—	20	2	no	—
491	C₂²×C₃	C₄×C₂²⋊D₅	1	1	yes	characteristic
492	C₂²×C₃	C₄×C₂²⋊D₅	1	1	yes	characteristic
493	C₂²×C₃	C₂×#709	1	1	yes	characteristic
494	C₃×C₄	—	2	2	no	—
495	C₃×C₄	—	10	2	no	—
496	C₃×C₄	—	20	2	no	—
497	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
498	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
499	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
500	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
501	C₂×C₅	—	2	1	no	—
502	C₂×C₅	—	2	1	no	—
503	C₂×C₅	—	2	1	no	—
504	C₂×C₅	—	4	2	no	—
505	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
506	D₅	—	4	2	no	—
507	C₂³	—	2	1	no	—
508	C₂³	—	10	1	no	—
509	C₂³	C₃×#709	1	1	yes	characteristic
510	Q₈	—	2	1	no	—
511	Q₈	—	5	2	no	—
512	Q₈	—	10	1	no	—
513	Q₈	C₂×C₃×C₄×D₅	1	2	yes	—
514	D₄	—	2	2	no	—
515	D₄	—	2	2	no	—
516	D₄	—	2	1	no	—
517	D₄	—	5	2	no	—
518	D₄	—	10	2	no	—
519	D₄	—	10	2	no	—
520	D₄	—	10	1	no	—
521	D₄	C₂×C₃×C₄×D₅	1	2	yes	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	10	1	no	—
526	C₂×C₄	—	10	2	no	—
527	C₂×C₄	—	10	2	no	—
528	C₂×C₄	—	10	2	no	—
529	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
530	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
531	C₂×C₄	C₃×#709	1	1	yes	characteristic
532	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
533	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
534	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
535	C₈	—	2	2	no	—
536	C₈	—	5	4	no	—
537	C₈	—	10	2	no	—
538	C₈	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
539	C₈	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
540	C₈	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
541	C₈	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
542	C₂×C₃	—	2	1	no	—
543	C₂×C₃	—	2	1	no	—
544	C₂×C₃	—	2	1	no	—
545	C₂×C₃	—	4	2	no	—
546	C₂×C₃	—	20	2	no	—
547	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
548	C₅	C₃×#2955	1	1	yes	characteristic, complemented, Sylow
549	C₂²	—	2	2	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	10	2	no	—
553	C₂²	—	20	2	no	—
554	C₂²	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
555	C₂²	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
556	C₂²	C₂×C₃×#709	1	1	yes	characteristic
557	C₄	—	2	2	no	—
558	C₄	—	10	2	no	—
559	C₄	—	20	2	no	—
560	C₄	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
561	C₄	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
562	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
563	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
564	C₃	#10615523	1	1	yes	characteristic, direct product factor, Sylow
565	C₂	—	2	1	no	—
566	C₂	—	2	1	no	—
567	C₂	—	2	1	no	—
568	C₂	—	4	2	no	—
569	C₂	—	20	2	no	—
570	C₂	C₂×C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₈	C₂×C₂²⋊D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#131	C₂
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₃×#66156	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×#131	D₅
hypocenter	C₅	C₃×#2955
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₈ ◁ C₂²×C₃×C₈ ◁ C₂×C₃×#131

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#131	C₂	semidirect
3. C₂×C₃×#4047	C₂	semidirect
4. C₃×#65525	C₂	semidirect
5. C₃×#65434	C₂	semidirect
6. C₃×#65433	C₂	semidirect
7. C₃×#65428	C₂	semidirect
8. C₃×#65413	C₂	semidirect
9. C₃×#65390	C₂	semidirect
10. #10615523	C₃	direct (N × H)
15. C₃×C₅×#131	C₂²	semidirect
16. C₃×C₅×#131	C₂²	semidirect
21. C₃×#4097	C₄	semidirect
23. C₃×#4095	C₄	semidirect
24. C₃×#4088	C₄	semidirect
25. C₃×#4078	C₄	semidirect
31. C₃×#4047	C₂²	semidirect
32. C₃×#4047	C₂²	semidirect
35. C₃×#3969	C₂²	semidirect
36. C₃×#3957	C₂²	semidirect
37. C₃×#3954	C₂²	semidirect
38. C₃×#3947	C₂²	semidirect
39. C₃×C₈×Dic₅	C₂²	semidirect
41. C₂×C₅×#131	C₂×C₃	semidirect
43. C₂×#4047	C₂×C₃	semidirect
44. #65525	C₂×C₃	semidirect
45. #65434	C₂×C₃	semidirect
46. #65433	C₂×C₃	semidirect
47. #65428	C₂×C₃	semidirect
48. #65413	C₂×C₃	semidirect
49. #65390	C₂×C₃	semidirect
99. C₂×C₃×#131	D₅	semidirect
110. C₅×#131	C₂²×C₃	semidirect
111. C₅×#131	C₂²×C₃	semidirect
116. #4097	C₃×C₄	semidirect
118. #4095	C₃×C₄	semidirect
119. #4088	C₃×C₄	semidirect
120. #4078	C₃×C₄	semidirect
126. #4047	C₂²×C₃	semidirect
127. #4047	C₂²×C₃	semidirect
130. #3969	C₂²×C₃	semidirect
131. #3957	C₂²×C₃	semidirect
132. #3954	C₂²×C₃	semidirect
133. #3947	C₂²×C₃	semidirect
134. C₈×Dic₅	C₂²×C₃	semidirect
184. C₃×#131	C₂×D₅	semidirect
185. C₃×#131	C₂×D₅	semidirect
249. C₂×#131	C₃×D₅	semidirect
366. #131	C₂×C₃×D₅	semidirect
367. #131	C₂×C₃×D₅	semidirect
485. C₃×C₅	#2955	semidirect
548. C₅	C₃×#2955	semidirect
564. C₃	#10615523	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×#131	2
C₃×#66156	2
C₂×C₃×#4047	2
C₃×#65525	2
C₃×#65434	2
C₃×#65433	2
C₃×#65428	2
C₃×#65413	2
C₃×#65390	2
#10615523	3
C₃×#2955	5

Subgroups — C3×#10615523 #14418015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615523 #14418015