Subgroups — C₃×#10611056 #14419126

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65813	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65127	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65123	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65120	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65119	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65019	C₂	1	2	yes	maximal, complemented
9	C₃×#65014	C₂	1	2	yes	maximal, complemented
10	C₃×#64998	C₂	1	2	yes	maximal, complemented
11	C₃×#64997	C₂	1	2	yes	maximal, complemented
12	#10611056	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₃×#4076	C₄	1	1	yes	characteristic
15	C₃×#4075	C₄	1	2	yes	—
16	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
17	C₃×#4070	C₄	1	1	yes	characteristic
18	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
19	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
20	C₂×C₃×#676	C₂²	1	2	yes	—
21	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
22	C₃×#4022	C₄	1	2	yes	—
23	C₃×#4021	C₄	1	1	yes	characteristic
24	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
25	C₃×#4018	C₂²	1	2	yes	—
26	C₃×#4016	C₄	1	1	yes	characteristic
27	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
31	C₃×C₅×#97	C₂²	1	2	yes	—
32	C₃×#3952	C₂²	1	2	yes	—
33	C₃×#3952	C₂²	1	2	yes	—
34	C₃×#3947	C₂²	1	2	yes	—
35	C₃×#3946	C₂²	1	2	yes	—
36	C₃×#3946	C₂²	1	2	yes	—
37	C₃×C₈×Dic₅	C₂²	1	2	yes	—
38	C₃×C₄×#168	C₂²	1	1	yes	characteristic
39	C₃×C₄×#168	C₂²	1	1	yes	characteristic
40	C₃×C₄×#168	C₂²	1	1	yes	characteristic
41	C₃×C₄×#168	C₂²	1	1	yes	characteristic
42	C₃×#2966	—	5	1	no	maximal, Hall
43	#65813	C₂×C₃	1	1	yes	characteristic
44	C₅×#432	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×C₄×#168	C₂×C₃	1	1	yes	characteristic, complemented
46	#65127	C₂×C₃	1	1	yes	characteristic, complemented
47	#65123	C₂×C₃	1	1	yes	characteristic, complemented
48	#65120	C₂×C₃	1	1	yes	characteristic, complemented
49	#65119	C₂×C₃	1	1	yes	characteristic, complemented
50	#65019	C₂×C₃	1	2	yes	complemented
51	#65014	C₂×C₃	1	2	yes	complemented
52	#64998	C₂×C₃	1	2	yes	complemented
53	#64997	C₂×C₃	1	2	yes	complemented
54	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
58	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
60	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
62	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
63	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
64	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
65	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
68	C₃×#685	C₂×C₄	1	2	yes	—
69	C₃×#685	C₂×C₄	1	2	yes	—
70	C₃×#685	C₂×C₄	1	2	yes	—
71	C₃×#685	C₂×C₄	1	2	yes	—
72	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
73	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
74	C₃×#683	C₂×C₄	1	2	yes	—
75	C₃×#683	C₂×C₄	1	2	yes	—
76	C₃×#683	C₂×C₄	1	2	yes	—
77	C₃×#683	C₂×C₄	1	2	yes	—
78	C₃×C₄×Dic₅	C₂³	1	2	yes	—
79	C₂×C₃×#168	—	2	2	no	—
80	C₂×C₃×#168	—	2	2	no	—
81	C₂×C₃×#168	C₂³	1	1	yes	characteristic
82	C₂×C₃×#168	C₂³	1	1	yes	characteristic
83	C₂×C₃×#168	C₂³	1	1	yes	characteristic
84	C₂×C₃×#168	C₂³	1	1	yes	characteristic
85	C₃×#676	—	2	4	no	—
86	C₃×C₈×D₅	—	2	4	no	—
87	C₃×#529	—	5	1	no	—
88	C₃×#446	—	5	1	no	—
89	C₃×C₈×Q₈	—	5	1	no	—
90	C₃×#436	—	5	1	no	—
91	C₃×#435	—	5	2	no	—
92	C₃×C₈×D₄	—	5	1	no	—
93	C₃×C₈×D₄	—	5	2	no	—
94	C₃×#433	—	5	2	no	—
95	C₃×#432	D₅	1	1	yes	characteristic, complemented
96	C₃×#405	—	5	2	no	—
97	C₂×C₃×C₄×C₈	—	5	1	no	—
98	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
99	#4076	C₃×C₄	1	1	yes	characteristic
100	#4075	C₃×C₄	1	2	yes	—
101	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
102	#4070	C₃×C₄	1	1	yes	characteristic
103	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
104	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
105	C₂×#676	C₂²×C₃	1	2	yes	—
106	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
107	#4022	C₃×C₄	1	2	yes	—
108	#4021	C₃×C₄	1	1	yes	characteristic
109	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
110	#4018	C₂²×C₃	1	2	yes	—
111	#4016	C₃×C₄	1	1	yes	characteristic
112	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
113	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
114	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
115	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
116	C₅×#97	C₂²×C₃	1	2	yes	—
117	#3952	C₂²×C₃	1	2	yes	—
118	#3952	C₂²×C₃	1	2	yes	—
119	#3947	C₂²×C₃	1	2	yes	—
120	#3946	C₂²×C₃	1	2	yes	—
121	#3946	C₂²×C₃	1	2	yes	—
122	C₈×Dic₅	C₂²×C₃	1	2	yes	—
123	C₄×#168	C₂²×C₃	1	1	yes	characteristic
124	C₄×#168	C₂²×C₃	1	1	yes	characteristic
125	C₄×#168	C₂²×C₃	1	1	yes	characteristic
126	C₄×#168	C₂²×C₃	1	1	yes	characteristic
127	#2966	—	5	1	no	Sylow
128	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	1	no	—
133	C₂×C₃×C₄×C₅	—	2	1	no	—
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₃×C₂²⋊D₅	—	2	4	no	—
141	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
142	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
143	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
144	C₃×D₂₀	—	2	2	no	—
145	C₃×C₄×D₅	—	2	2	no	—
146	C₃×C₄×D₅	—	2	2	no	—
147	C₃×Dic₁₀	—	2	2	no	—
148	C₃×C₅×C₈	—	2	2	no	—
149	C₃×C₅×C₈	—	2	2	no	—
150	C₃×#168	—	2	1	no	—
151	C₃×#168	—	2	1	no	—
152	C₃×#168	#41	1	2	yes	—
153	C₃×#168	#41	1	2	yes	—
154	C₂×C₃×M₁₆	—	5	2	no	—
155	C₂²×C₃×C₈	—	5	1	no	—
156	C₂²×C₃×C₈	—	5	1	no	—
157	C₂²×C₃×C₈	—	5	2	no	—
158	C₃×#126	—	5	2	no	—
159	C₃×#125	—	5	1	no	—
160	C₃×#124	—	5	1	no	—
161	C₃×#123	—	5	2	no	—
162	C₃×C₂²⋊Q₈	—	5	1	no	—
163	C₃×#121	—	5	1	no	—
164	C₃×C₄×Q₈	—	5	1	no	—
165	C₃×C₄×D₄	—	5	2	no	—
166	C₃×C₄×D₄	—	5	1	no	—
167	C₃×#117	—	5	2	no	—
168	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
169	C₃×C₄⋊C₈	—	5	2	no	—
170	C₃×C₄⋊C₈	—	5	2	no	—
171	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
172	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
173	C₃×C₂²⋊C₈	—	5	2	no	—
174	C₃×C₂²⋊C₈	—	5	2	no	—
175	C₃×C₂²⋊C₈	C₂×D₅	1	2	yes	—
176	C₃×#97	—	5	2	no	—
177	C₃×#97	C₂×D₅	1	2	yes	—
178	C₃×C₄×C₈	—	5	2	no	—
179	C₃×C₄×C₈	—	5	1	no	—
180	C₃×C₄×C₈	—	5	1	no	—
181	C₃×C₄×C₈	—	5	1	no	—
182	C₃×C₄×C₈	—	5	1	no	—
183	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
186	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
187	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
188	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
189	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
190	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
191	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
192	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
193	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
194	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
195	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
196	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
197	#685	C₂×C₃×C₄	1	2	yes	—
198	#685	C₂×C₃×C₄	1	2	yes	—
199	#685	C₂×C₃×C₄	1	2	yes	—
200	#685	C₂×C₃×C₄	1	2	yes	—
201	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
202	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
203	#683	C₂×C₃×C₄	1	2	yes	—
204	#683	C₂×C₃×C₄	1	2	yes	—
205	#683	C₂×C₃×C₄	1	2	yes	—
206	#683	C₂×C₃×C₄	1	2	yes	—
207	C₄×Dic₅	C₂³×C₃	1	2	yes	—
208	C₂×#168	—	2	2	no	—
209	C₂×#168	—	2	2	no	—
210	C₂×#168	C₂³×C₃	1	1	yes	characteristic
211	C₂×#168	C₂³×C₃	1	1	yes	characteristic
212	C₂×#168	C₂³×C₃	1	1	yes	characteristic
213	C₂×#168	C₂³×C₃	1	1	yes	characteristic
214	#676	—	2	4	no	—
215	C₈×D₅	—	2	4	no	—
216	#529	—	5	1	no	—
217	#446	—	5	1	no	—
218	C₈×Q₈	—	5	1	no	—
219	#436	—	5	1	no	—
220	#435	—	5	2	no	—
221	C₈×D₄	—	5	1	no	—
222	C₈×D₄	—	5	2	no	—
223	#433	—	5	2	no	—
224	#432	C₃×D₅	1	1	yes	characteristic, complemented
225	#405	—	5	2	no	—
226	C₂×C₄×C₈	—	5	1	no	—
227	C₂²×C₃×C₅	—	2	1	no	—
228	C₂²×C₃×C₅	—	2	1	no	—
229	C₂²×C₃×C₅	#131	1	2	yes	—
230	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₃×D₅	—	2	2	no	—
232	C₂×C₃×D₅	—	2	2	no	—
233	C₂×C₃×D₅	—	2	2	no	—
234	C₃×C₄×C₅	—	2	1	no	—
235	C₃×C₄×C₅	—	2	1	no	—
236	C₃×C₄×C₅	—	2	1	no	—
237	C₃×C₄×C₅	—	2	1	no	—
238	C₃×C₄×C₅	#131	1	2	yes	—
239	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	C₃×Dic₅	—	2	2	no	—
242	C₃×Dic₅	—	2	2	no	—
243	C₃×Dic₅	—	2	2	no	—
244	C₂×C₃×Q₈	—	5	1	no	—
245	C₂×C₃×D₄	—	5	2	no	—
246	C₂×C₃×D₄	—	5	1	no	—
247	C₂²×C₃×C₄	—	5	2	no	—
248	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
249	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
250	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
251	C₃×M₁₆	—	10	4	no	—
252	C₂×C₃×C₈	—	5	1	no	—
253	C₂×C₃×C₈	—	5	1	no	—
254	C₂×C₃×C₈	—	5	1	no	—
255	C₂×C₃×C₈	—	5	1	no	—
256	C₂×C₃×C₈	—	10	4	no	—
257	C₂×C₃×C₈	—	10	2	no	—
258	C₂×C₃×C₈	—	10	2	no	—
259	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
260	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
261	C₃×C₄⋊C₄	—	5	2	no	—
262	C₃×C₄⋊C₄	—	5	2	no	—
263	C₃×C₄⋊C₄	—	5	2	no	—
264	C₃×C₄⋊C₄	—	5	2	no	—
265	C₃×C₄⋊C₄	—	5	1	no	—
266	C₃×C₄⋊C₄	—	5	1	no	—
267	C₃×C₂²⋊C₄	—	5	2	no	—
268	C₃×C₂²⋊C₄	—	5	2	no	—
269	C₃×C₂²⋊C₄	—	5	2	no	—
270	C₃×C₂²⋊C₄	—	5	2	no	—
271	C₃×C₂²⋊C₄	—	5	2	no	—
272	C₃×C₄²	—	5	2	no	—
273	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
274	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
275	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
276	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
277	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
278	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
288	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
289	C₂²⋊D₅	—	2	4	no	—
290	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
291	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
292	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
293	D₂₀	—	2	2	no	—
294	C₄×D₅	—	2	2	no	—
295	C₄×D₅	—	2	2	no	—
296	Dic₁₀	—	2	2	no	—
297	C₅×C₈	—	2	2	no	—
298	C₅×C₈	—	2	2	no	—
299	#168	—	2	1	no	—
300	#168	—	2	1	no	—
301	#168	C₃×#41	1	2	yes	—
302	#168	C₃×#41	1	2	yes	—
303	C₂×M₁₆	—	5	2	no	—
304	C₂²×C₈	—	5	1	no	—
305	C₂²×C₈	—	5	1	no	—
306	C₂²×C₈	—	5	2	no	—
307	#126	—	5	2	no	—
308	#125	—	5	1	no	—
309	#124	—	5	1	no	—
310	#123	—	5	2	no	—
311	C₂²⋊Q₈	—	5	1	no	—
312	#121	—	5	1	no	—
313	C₄×Q₈	—	5	1	no	—
314	C₄×D₄	—	5	2	no	—
315	C₄×D₄	—	5	1	no	—
316	#117	—	5	2	no	—
317	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
318	C₄⋊C₈	—	5	2	no	—
319	C₄⋊C₈	—	5	2	no	—
320	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
321	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
322	C₂²⋊C₈	—	5	2	no	—
323	C₂²⋊C₈	—	5	2	no	—
324	C₂²⋊C₈	C₂×C₃×D₅	1	2	yes	—
325	#97	—	5	2	no	—
326	#97	C₂×C₃×D₅	1	2	yes	—
327	C₄×C₈	—	5	2	no	—
328	C₄×C₈	—	5	1	no	—
329	C₄×C₈	—	5	1	no	—
330	C₄×C₈	—	5	1	no	—
331	C₄×C₈	—	5	1	no	—
332	C₂×C₃×C₅	—	2	2	no	—
333	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
334	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
335	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
336	C₃×D₅	—	4	2	no	—
337	C₂³×C₃	—	5	2	no	—
338	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
339	C₃×Q₈	—	10	2	no	—
340	C₃×D₄	—	10	4	no	—
341	C₃×D₄	—	10	2	no	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	2	1	no	—
344	C₂×C₃×C₄	—	2	1	no	—
345	C₂×C₃×C₄	—	2	2	no	—
346	C₂×C₃×C₄	—	5	2	no	—
347	C₂×C₃×C₄	—	5	2	no	—
348	C₂×C₃×C₄	—	5	2	no	—
349	C₂×C₃×C₄	—	10	2	no	—
350	C₂×C₃×C₄	—	10	2	no	—
351	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
355	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
356	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
357	C₃×C₈	—	2	2	no	—
358	C₃×C₈	—	2	2	no	—
359	C₃×C₈	—	5	2	no	—
360	C₃×C₈	—	5	2	no	—
361	C₃×C₈	—	10	1	no	—
362	C₃×C₈	—	10	1	no	—
363	C₂²×C₅	—	2	1	no	—
364	C₂²×C₅	—	2	1	no	—
365	C₂²×C₅	C₃×#131	1	2	yes	—
366	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
367	C₂×D₅	—	2	2	no	—
368	C₂×D₅	—	2	2	no	—
369	C₂×D₅	—	2	2	no	—
370	C₄×C₅	—	2	1	no	—
371	C₄×C₅	—	2	1	no	—
372	C₄×C₅	—	2	1	no	—
373	C₄×C₅	—	2	1	no	—
374	C₄×C₅	C₃×#131	1	2	yes	—
375	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
376	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
377	Dic₅	—	2	2	no	—
378	Dic₅	—	2	2	no	—
379	Dic₅	—	2	2	no	—
380	C₂×Q₈	—	5	1	no	—
381	C₂×D₄	—	5	2	no	—
382	C₂×D₄	—	5	1	no	—
383	C₂²×C₄	—	5	2	no	—
384	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
385	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
387	M₁₆	—	10	4	no	—
388	C₂×C₈	—	5	1	no	—
389	C₂×C₈	—	5	1	no	—
390	C₂×C₈	—	5	1	no	—
391	C₂×C₈	—	5	1	no	—
392	C₂×C₈	—	10	4	no	—
393	C₂×C₈	—	10	2	no	—
394	C₂×C₈	—	10	2	no	—
395	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
396	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
397	C₄⋊C₄	—	5	2	no	—
398	C₄⋊C₄	—	5	2	no	—
399	C₄⋊C₄	—	5	1	no	—
400	C₄⋊C₄	—	5	2	no	—
401	C₄⋊C₄	—	5	1	no	—
402	C₄⋊C₄	—	5	2	no	—
403	C₂²⋊C₄	—	5	2	no	—
404	C₂²⋊C₄	—	5	2	no	—
405	C₂²⋊C₄	—	5	2	no	—
406	C₂²⋊C₄	—	5	2	no	—
407	C₂²⋊C₄	—	5	2	no	—
408	C₄²	—	5	2	no	—
409	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
410	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
411	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
412	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
413	C₃×C₅	#2966	1	1	yes	characteristic, complemented, Hall
414	C₂²×C₃	—	2	1	no	—
415	C₂²×C₃	—	2	1	no	—
416	C₂²×C₃	—	10	2	no	—
417	C₂²×C₃	—	10	2	no	—
418	C₂²×C₃	—	10	2	no	—
419	C₂²×C₃	#4053	1	2	yes	—
420	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
421	C₃×C₄	—	2	1	no	—
422	C₃×C₄	—	2	1	no	—
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	2	1	no	—
425	C₃×C₄	—	10	2	no	—
426	C₃×C₄	—	10	2	no	—
427	C₃×C₄	—	10	2	no	—
428	C₃×C₄	#4053	1	2	yes	—
429	C₃×C₄	D₅×#41	1	1	yes	characteristic
430	C₃×C₄	D₅×#41	1	1	yes	characteristic
431	C₂×C₅	—	2	2	no	—
432	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
433	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
434	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
435	D₅	—	4	2	no	—
436	C₂³	—	5	2	no	—
437	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
438	Q₈	—	10	2	no	—
439	D₄	—	10	4	no	—
440	D₄	—	10	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	5	2	no	—
446	C₂×C₄	—	5	2	no	—
447	C₂×C₄	—	5	2	no	—
448	C₂×C₄	—	10	2	no	—
449	C₂×C₄	—	10	2	no	—
450	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
451	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
452	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
453	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
454	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
455	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
456	C₈	—	2	2	no	—
457	C₈	—	2	2	no	—
458	C₈	—	5	2	no	—
459	C₈	—	5	2	no	—
460	C₈	—	10	1	no	—
461	C₈	—	10	1	no	—
462	C₂×C₃	—	2	2	no	—
463	C₂×C₃	—	20	2	no	—
464	C₂×C₃	#65856	1	1	yes	characteristic
465	C₂×C₃	C₂×#4053	1	1	yes	characteristic
466	C₂×C₃	C₂×#4053	1	1	yes	characteristic
467	C₅	C₃×#2966	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	10	2	no	—
471	C₂²	—	10	2	no	—
472	C₂²	—	10	2	no	—
473	C₂²	C₃×#4053	1	2	yes	—
474	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	10	2	no	—
480	C₄	—	10	2	no	—
481	C₄	—	10	2	no	—
482	C₄	C₃×#4053	1	2	yes	—
483	C₄	C₃×D₅×#41	1	1	yes	characteristic
484	C₄	C₃×D₅×#41	1	1	yes	characteristic
485	C₃	#10611056	1	1	yes	characteristic, direct product factor, Sylow
486	C₂	—	2	2	no	—
487	C₂	—	20	2	no	—
488	C₂	C₃×#65856	1	1	yes	characteristic
489	C₂	C₂×C₃×#4053	1	1	yes	characteristic
490	C₂	C₂×C₃×#4053	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#432	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#4076	C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#432	D₅
hypocenter	C₅	C₃×#2966
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#432

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#432	C₂	semidirect
3. C₂×C₃×C₄×#168	C₂	semidirect
4. C₃×#65127	C₂	semidirect
5. C₃×#65123	C₂	semidirect
6. C₃×#65120	C₂	semidirect
7. C₃×#65119	C₂	semidirect
8. C₃×#65019	C₂	semidirect
9. C₃×#65014	C₂	semidirect
10. C₃×#64998	C₂	semidirect
11. C₃×#64997	C₂	semidirect
12. #10611056	C₃	direct (N × H)
44. C₅×#432	C₂×C₃	semidirect
45. C₂×C₄×#168	C₂×C₃	semidirect
46. #65127	C₂×C₃	semidirect
47. #65123	C₂×C₃	semidirect
48. #65120	C₂×C₃	semidirect
49. #65119	C₂×C₃	semidirect
50. #65019	C₂×C₃	semidirect
51. #65014	C₂×C₃	semidirect
52. #64998	C₂×C₃	semidirect
53. #64997	C₂×C₃	semidirect
95. C₃×#432	D₅	semidirect
224. #432	C₃×D₅	semidirect
413. C₃×C₅	#2966	semidirect
467. C₅	C₃×#2966	semidirect
485. C₃	#10611056	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#65813	2
C₃×C₅×#432	2
C₂×C₃×C₄×#168	2
C₃×#65127	2
C₃×#65123	2
C₃×#65120	2
C₃×#65119	2
C₃×#65019	2
C₃×#65014	2
C₃×#64998	2
C₃×#64997	2
#10611056	3
C₃×#2966	5

Subgroups — C3×#10611056 #14419126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611056 #14419126