Subgroups — C₃×#10611153 #14415218

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4047	C₂	1	2	yes	maximal, complemented
2	C₃×#65882	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₈×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
5	C₃×#65301	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65127	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65126	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65018	C₂	1	2	yes	maximal, complemented
9	C₃×#65016	C₂	1	2	yes	maximal, complemented
10	C₃×C₈×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611153	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#709	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
15	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₃×#4086	C₄	1	1	yes	characteristic
17	C₃×#4084	C₄	1	1	yes	characteristic
18	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
19	C₂×C₃×#681	C₂²	1	2	yes	—
20	C₃×#4047	—	2	8	no	—
21	C₂×C₃×#676	C₂²	1	2	yes	—
22	C₂×C₃×#676	C₂²	1	2	yes	—
23	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
24	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
26	C₃×#4041	C₄	1	1	yes	characteristic
27	C₃×#4034	C₄	1	1	yes	characteristic
28	C₃×#4031	C₄	1	2	yes	—
29	C₃×#4030	C₄	1	2	yes	—
30	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
31	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
32	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
35	C₃×C₂²⋊#168	C₂²	1	2	yes	—
36	C₃×#3952	C₂²	1	2	yes	—
37	C₃×#3952	C₂²	1	2	yes	—
38	C₃×#3946	C₂²	1	2	yes	—
39	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
40	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
41	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
42	C₃×C₄×#168	C₂²	1	1	yes	characteristic
43	C₃×#2931	—	5	1	no	maximal, Hall
44	C₂×#4047	C₂×C₃	1	2	yes	complemented
45	#65882	C₂×C₃	1	1	yes	characteristic
46	C₅×C₈×D₄	C₂×C₃	1	1	yes	characteristic, complemented
47	C₈×C₂²⋊D₅	C₂×C₃	1	2	yes	complemented
48	#65301	C₂×C₃	1	1	yes	characteristic, complemented
49	#65127	C₂×C₃	1	1	yes	characteristic, complemented
50	#65126	C₂×C₃	1	1	yes	characteristic, complemented
51	#65018	C₂×C₃	1	2	yes	complemented
52	#65016	C₂×C₃	1	2	yes	complemented
53	C₈×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
54	C₄×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
57	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
58	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
59	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
60	C₃×#709	—	2	4	no	—
61	C₃×#709	—	2	4	no	—
62	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
64	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
67	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
68	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
69	C₂×C₃×C₅×C₈	—	2	4	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
75	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
77	C₃×#685	C₂×C₄	1	2	yes	—
78	C₃×#685	C₂×C₄	1	2	yes	—
79	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
80	C₃×#683	C₂×C₄	1	2	yes	—
81	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
82	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
83	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
84	C₃×#681	—	2	4	no	—
85	C₂×C₃×#168	C₂³	1	1	yes	characteristic
86	C₂×C₃×#168	C₂³	1	2	yes	—
87	C₂×C₃×#168	C₂³	1	1	yes	characteristic
88	C₃×#676	—	2	4	no	—
89	C₃×#676	—	2	4	no	—
90	C₃×C₈×D₅	—	2	2	no	—
91	C₃×C₈×D₅	—	2	4	no	—
92	C₃×C₈×D₅	D₄	1	4	yes	complemented
93	C₂×C₃×#131	—	5	2	no	—
94	C₃×#532	—	5	1	no	—
95	C₃×#436	—	5	1	no	—
96	C₃×#436	—	5	1	no	—
97	C₃×#436	—	5	2	no	—
98	C₃×C₈×D₄	—	5	2	no	—
99	C₃×C₈×D₄	—	5	1	no	—
100	C₃×C₈×D₄	D₅	1	1	yes	characteristic, complemented
101	C₃×#423	—	5	1	no	—
102	C₃×#408	—	5	2	no	—
103	C₂×C₃×C₄×C₈	—	5	1	no	—
104	C₂×#709	C₂²×C₃	1	2	yes	—
105	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
106	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
107	#4086	C₃×C₄	1	1	yes	characteristic
108	#4084	C₃×C₄	1	1	yes	characteristic
109	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
110	C₂×#681	C₂²×C₃	1	2	yes	—
111	#4047	—	2	8	no	—
112	C₂×#676	C₂²×C₃	1	2	yes	—
113	C₂×#676	C₂²×C₃	1	2	yes	—
114	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
115	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
117	#4041	C₃×C₄	1	1	yes	characteristic
118	#4034	C₃×C₄	1	1	yes	characteristic
119	#4031	C₃×C₄	1	2	yes	—
120	#4030	C₃×C₄	1	2	yes	—
121	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
122	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
123	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
124	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
125	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
126	C₂²⋊#168	C₂²×C₃	1	2	yes	—
127	#3952	C₂²×C₃	1	2	yes	—
128	#3952	C₂²×C₃	1	2	yes	—
129	#3946	C₂²×C₃	1	2	yes	—
130	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
131	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
132	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
133	C₄×#168	C₂²×C₃	1	1	yes	characteristic
134	#2931	—	5	1	no	Sylow
135	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
136	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
137	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
138	C₃×C₅×D₄	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
143	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₃×C₂²⋊D₅	—	2	4	no	—
146	C₃×C₂²⋊D₅	—	2	4	no	—
147	C₃×C₂²⋊D₅	—	2	4	no	—
148	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
150	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
152	C₃×D₂₀	—	2	4	no	—
153	C₃×D₂₀	—	2	2	no	—
154	C₃×C₄×D₅	—	2	2	no	—
155	C₃×C₄×D₅	—	2	2	no	—
156	C₃×C₄×D₅	—	2	2	no	—
157	C₃×C₄×D₅	—	2	2	no	—
158	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
159	C₃×C₄×D₅	#41	1	2	yes	—
160	C₃×Dic₁₀	—	2	4	no	—
161	C₃×C₅×C₈	—	2	2	no	—
162	C₃×C₅×C₈	—	2	1	no	—
163	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
164	C₃×#168	—	2	2	no	—
165	C₃×#168	—	2	1	no	—
166	C₃×#168	C₂×D₄	1	2	yes	—
167	C₂×C₃×#41	—	5	2	no	—
168	C₃×#131	—	10	8	no	—
169	C₂×C₃×M₁₆	—	5	2	no	—
170	C₂×C₃×M₁₆	—	5	2	no	—
171	C₂×C₃×M₁₆	—	5	2	no	—
172	C₂²×C₃×C₈	—	5	1	no	—
173	C₂²×C₃×C₈	—	5	1	no	—
174	C₂²×C₃×C₈	—	5	2	no	—
175	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
176	C₃×C₄⋊Q₈	—	5	1	no	—
177	C₃×#127	—	5	1	no	—
178	C₃×#124	—	5	2	no	—
179	C₃×#121	—	5	1	no	—
180	C₃×#121	—	5	1	no	—
181	C₃×#121	—	5	2	no	—
182	C₃×C₄×D₄	—	5	2	no	—
183	C₃×C₄×D₄	—	5	1	no	—
184	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
185	C₂×C₃×C₄²	—	5	1	no	—
186	C₃×C₄⋊C₈	—	5	2	no	—
187	C₃×C₄⋊C₈	—	5	1	no	—
188	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
189	C₃×C₂²⋊C₈	—	5	2	no	—
190	C₃×C₂²⋊C₈	—	5	2	no	—
191	C₃×C₂²⋊C₈	—	5	2	no	—
192	C₃×C₂²⋊C₈	C₂×D₅	1	2	yes	—
193	C₃×C₄×C₈	—	5	1	no	—
194	C₃×C₄×C₈	—	5	1	no	—
195	C₃×C₄×C₈	—	5	1	no	—
196	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
197	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
199	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
200	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
201	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
202	#709	—	2	4	no	—
203	#709	—	2	4	no	—
204	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
205	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
206	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
207	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
208	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
209	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
210	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
211	C₂×C₅×C₈	—	2	4	no	—
212	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
213	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
214	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
215	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
216	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
217	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
218	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
219	#685	C₂×C₃×C₄	1	2	yes	—
220	#685	C₂×C₃×C₄	1	2	yes	—
221	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
222	#683	C₂×C₃×C₄	1	2	yes	—
223	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
224	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
225	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
226	#681	—	2	4	no	—
227	C₂×#168	C₂³×C₃	1	1	yes	characteristic
228	C₂×#168	C₂³×C₃	1	2	yes	—
229	C₂×#168	C₂³×C₃	1	1	yes	characteristic
230	#676	—	2	4	no	—
231	#676	—	2	4	no	—
232	C₈×D₅	—	2	2	no	—
233	C₈×D₅	—	2	4	no	—
234	C₈×D₅	C₃×D₄	1	4	yes	complemented
235	C₂×#131	—	5	2	no	—
236	#532	—	5	1	no	—
237	#436	—	5	1	no	—
238	#436	—	5	1	no	—
239	#436	—	5	2	no	—
240	C₈×D₄	—	5	2	no	—
241	C₈×D₄	—	5	1	no	—
242	C₈×D₄	C₃×D₅	1	1	yes	characteristic, complemented
243	#423	—	5	1	no	—
244	#408	—	5	2	no	—
245	C₂×C₄×C₈	—	5	1	no	—
246	C₂²×C₃×C₅	—	2	2	no	—
247	C₂²×C₃×C₅	—	2	2	no	—
248	C₂²×C₃×C₅	—	2	2	no	—
249	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
250	C₂×C₃×D₅	—	2	1	no	—
251	C₂×C₃×D₅	—	2	1	no	—
252	C₂×C₃×D₅	—	2	2	no	—
253	C₂×C₃×D₅	—	2	2	no	—
254	C₂×C₃×D₅	—	2	2	no	—
255	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
256	C₃×C₄×C₅	—	2	2	no	—
257	C₃×C₄×C₅	—	2	1	no	—
258	C₃×C₄×C₅	#131	1	2	yes	complemented
259	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
260	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
261	C₃×Dic₅	—	2	2	no	—
262	C₃×Dic₅	—	2	1	no	—
263	C₃×Dic₅	C₄×D₄	1	2	yes	—
264	C₃×Dic₅	#131	1	2	yes	complemented
265	C₃×#41	—	10	4	no	—
266	C₃×#41	—	10	4	no	—
267	C₂×C₃×Q₈	—	5	2	no	—
268	C₂×C₃×D₄	—	5	2	no	—
269	C₂×C₃×D₄	—	5	2	no	—
270	C₂×C₃×D₄	—	5	2	no	—
271	C₂×C₃×D₄	—	5	1	no	—
272	C₂×C₃×D₄	—	5	2	no	—
273	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
274	C₂²×C₃×C₄	—	5	1	no	—
275	C₂²×C₃×C₄	—	5	1	no	—
276	C₂²×C₃×C₄	—	5	1	no	—
277	C₂²×C₃×C₄	—	5	2	no	—
278	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
279	C₃×M₁₆	—	10	4	no	—
280	C₃×M₁₆	—	10	4	no	—
281	C₃×M₁₆	—	10	4	no	—
282	C₂×C₃×C₈	—	2	4	no	—
283	C₂×C₃×C₈	—	5	1	no	—
284	C₂×C₃×C₈	—	5	4	no	—
285	C₂×C₃×C₈	—	5	1	no	—
286	C₂×C₃×C₈	—	5	2	no	—
287	C₂×C₃×C₈	—	10	2	no	—
288	C₂×C₃×C₈	—	10	4	no	—
289	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
290	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
291	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
292	C₃×C₄⋊C₄	—	5	2	no	—
293	C₃×C₄⋊C₄	—	5	1	no	—
294	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
295	C₃×C₂²⋊C₄	—	5	2	no	—
296	C₃×C₂²⋊C₄	—	5	2	no	—
297	C₃×C₂²⋊C₄	—	5	2	no	—
298	C₃×C₂²⋊C₄	C₄×D₅	1	2	yes	—
299	C₃×C₄²	—	5	1	no	—
300	C₃×C₄²	—	5	1	no	—
301	C₃×C₄²	—	5	1	no	—
302	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
303	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
304	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
305	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
306	C₅×D₄	—	2	2	no	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
311	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
313	C₂²⋊D₅	—	2	4	no	—
314	C₂²⋊D₅	—	2	4	no	—
315	C₂²⋊D₅	—	2	4	no	—
316	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
317	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
318	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
319	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
320	D₂₀	—	2	4	no	—
321	D₂₀	—	2	2	no	—
322	C₄×D₅	—	2	2	no	—
323	C₄×D₅	—	2	2	no	—
324	C₄×D₅	—	2	2	no	—
325	C₄×D₅	—	2	2	no	—
326	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
327	C₄×D₅	C₃×#41	1	2	yes	—
328	Dic₁₀	—	2	4	no	—
329	C₅×C₈	—	2	2	no	—
330	C₅×C₈	—	2	1	no	—
331	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
332	#168	—	2	2	no	—
333	#168	—	2	1	no	—
334	#168	C₂×C₃×D₄	1	2	yes	—
335	C₂×#41	—	5	2	no	—
336	#131	—	10	8	no	—
337	C₂×M₁₆	—	5	2	no	—
338	C₂×M₁₆	—	5	2	no	—
339	C₂×M₁₆	—	5	2	no	—
340	C₂²×C₈	—	5	1	no	—
341	C₂²×C₈	—	5	2	no	—
342	C₂²×C₈	—	5	1	no	—
343	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
344	C₄⋊Q₈	—	5	1	no	—
345	#127	—	5	1	no	—
346	#124	—	5	2	no	—
347	#121	—	5	1	no	—
348	#121	—	5	1	no	—
349	#121	—	5	2	no	—
350	C₄×D₄	—	5	2	no	—
351	C₄×D₄	—	5	1	no	—
352	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
353	C₂×C₄²	—	5	1	no	—
354	C₄⋊C₈	—	5	2	no	—
355	C₄⋊C₈	—	5	1	no	—
356	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
357	C₂²⋊C₈	—	5	2	no	—
358	C₂²⋊C₈	—	5	2	no	—
359	C₂²⋊C₈	—	5	2	no	—
360	C₂²⋊C₈	C₂×C₃×D₅	1	2	yes	—
361	C₄×C₈	—	5	1	no	—
362	C₄×C₈	—	5	1	no	—
363	C₄×C₈	—	5	1	no	—
364	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
365	C₂×C₃×C₅	—	4	2	no	—
366	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
367	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
368	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
369	C₃×D₅	—	2	2	no	—
370	C₃×D₅	—	4	2	no	—
371	C₂³×C₃	—	5	1	no	—
372	C₂³×C₃	—	5	2	no	—
373	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
374	C₃×Q₈	—	10	4	no	—
375	C₃×D₄	—	2	2	no	—
376	C₃×D₄	—	10	4	no	—
377	C₃×D₄	—	10	4	no	—
378	C₃×D₄	—	10	4	no	—
379	C₃×D₄	—	10	4	no	—
380	C₃×D₄	—	10	2	no	—
381	C₂×C₃×C₄	—	2	2	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	5	1	no	—
384	C₂×C₃×C₄	—	5	1	no	—
385	C₂×C₃×C₄	—	5	2	no	—
386	C₂×C₃×C₄	—	5	2	no	—
387	C₂×C₃×C₄	—	5	1	no	—
388	C₂×C₃×C₄	—	5	2	no	—
389	C₂×C₃×C₄	—	10	2	no	—
390	C₂×C₃×C₄	—	10	2	no	—
391	C₂×C₃×C₄	—	10	2	no	—
392	C₂×C₃×C₄	—	10	2	no	—
393	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
394	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
395	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
396	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
397	C₃×C₈	—	2	2	no	—
398	C₃×C₈	—	2	1	no	—
399	C₃×C₈	—	5	2	no	—
400	C₃×C₈	—	10	2	no	—
401	C₃×C₈	—	10	1	no	—
402	C₃×C₈	D₄×D₅	1	2	yes	—
403	C₂²×C₅	—	2	2	no	—
404	C₂²×C₅	—	2	2	no	—
405	C₂²×C₅	—	2	2	no	—
406	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
407	C₂×D₅	—	2	1	no	—
408	C₂×D₅	—	2	1	no	—
409	C₂×D₅	—	2	2	no	—
410	C₂×D₅	—	2	2	no	—
411	C₂×D₅	—	2	2	no	—
412	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
413	C₄×C₅	—	2	1	no	—
414	C₄×C₅	—	2	2	no	—
415	C₄×C₅	C₃×#131	1	2	yes	complemented
416	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
417	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
418	Dic₅	—	2	1	no	—
419	Dic₅	—	2	2	no	—
420	Dic₅	C₃×C₄×D₄	1	2	yes	—
421	Dic₅	C₃×#131	1	2	yes	complemented
422	#41	—	10	4	no	—
423	#41	—	10	4	no	—
424	C₂×Q₈	—	5	2	no	—
425	C₂×D₄	—	5	2	no	—
426	C₂×D₄	—	5	2	no	—
427	C₂×D₄	—	5	2	no	—
428	C₂×D₄	—	5	1	no	—
429	C₂×D₄	—	5	2	no	—
430	C₂×D₄	C₃×C₄×D₅	1	1	yes	characteristic
431	C₂²×C₄	—	5	1	no	—
432	C₂²×C₄	—	5	1	no	—
433	C₂²×C₄	—	5	1	no	—
434	C₂²×C₄	—	5	2	no	—
435	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
436	M₁₆	—	10	4	no	—
437	M₁₆	—	10	4	no	—
438	M₁₆	—	10	4	no	—
439	C₂×C₈	—	2	4	no	—
440	C₂×C₈	—	5	1	no	—
441	C₂×C₈	—	5	4	no	—
442	C₂×C₈	—	5	1	no	—
443	C₂×C₈	—	5	2	no	—
444	C₂×C₈	—	10	2	no	—
445	C₂×C₈	—	10	4	no	—
446	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
447	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
448	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
449	C₄⋊C₄	—	5	2	no	—
450	C₄⋊C₄	—	5	1	no	—
451	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
452	C₂²⋊C₄	—	5	2	no	—
453	C₂²⋊C₄	—	5	2	no	—
454	C₂²⋊C₄	—	5	2	no	—
455	C₂²⋊C₄	C₃×C₄×D₅	1	2	yes	—
456	C₄²	—	5	1	no	—
457	C₄²	—	5	1	no	—
458	C₄²	—	5	1	no	—
459	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
460	C₃×C₅	#2931	1	1	yes	characteristic, complemented, Hall
461	C₂²×C₃	—	2	2	no	—
462	C₂²×C₃	—	2	2	no	—
463	C₂²×C₃	—	2	2	no	—
464	C₂²×C₃	—	5	2	no	—
465	C₂²×C₃	—	10	1	no	—
466	C₂²×C₃	—	10	1	no	—
467	C₂²×C₃	—	10	2	no	—
468	C₂²×C₃	—	10	2	no	—
469	C₂²×C₃	—	10	2	no	—
470	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
471	C₃×C₄	—	2	1	no	—
472	C₃×C₄	—	2	2	no	—
473	C₃×C₄	—	5	2	no	—
474	C₃×C₄	—	5	2	no	—
475	C₃×C₄	—	10	1	no	—
476	C₃×C₄	—	10	2	no	—
477	C₃×C₄	#4047	1	2	yes	complemented
478	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
479	C₃×C₄	D₅×#41	1	1	yes	characteristic
480	C₂×C₅	—	4	2	no	—
481	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
482	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
483	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
484	D₅	—	2	2	no	—
485	D₅	—	4	2	no	—
486	C₂³	—	5	1	no	—
487	C₂³	—	5	2	no	—
488	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
489	Q₈	—	10	4	no	—
490	D₄	—	2	2	no	—
491	D₄	—	10	4	no	—
492	D₄	—	10	4	no	—
493	D₄	—	10	4	no	—
494	D₄	—	10	4	no	—
495	D₄	—	10	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	5	1	no	—
499	C₂×C₄	—	5	1	no	—
500	C₂×C₄	—	5	2	no	—
501	C₂×C₄	—	5	2	no	—
502	C₂×C₄	—	5	1	no	—
503	C₂×C₄	—	5	2	no	—
504	C₂×C₄	—	10	2	no	—
505	C₂×C₄	—	10	2	no	—
506	C₂×C₄	—	10	2	no	—
507	C₂×C₄	—	10	2	no	—
508	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
509	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
510	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
511	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
512	C₈	—	2	2	no	—
513	C₈	—	2	1	no	—
514	C₈	—	5	2	no	—
515	C₈	—	10	2	no	—
516	C₈	—	10	1	no	—
517	C₈	C₃×D₄×D₅	1	2	yes	—
518	C₂×C₃	—	4	2	no	—
519	C₂×C₃	—	10	2	no	—
520	C₂×C₃	—	20	2	no	—
521	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
522	C₂×C₃	C₂×#4047	1	1	yes	characteristic
523	C₂×C₃	D₅×#131	1	1	yes	characteristic
524	C₅	C₃×#2931	1	1	yes	characteristic, complemented, Sylow
525	C₂²	—	2	2	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	5	2	no	—
529	C₂²	—	10	1	no	—
530	C₂²	—	10	1	no	—
531	C₂²	—	10	2	no	—
532	C₂²	—	10	2	no	—
533	C₂²	—	10	2	no	—
534	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
535	C₄	—	2	2	no	—
536	C₄	—	2	1	no	—
537	C₄	—	5	2	no	—
538	C₄	—	5	2	no	—
539	C₄	—	10	2	no	—
540	C₄	—	10	1	no	—
541	C₄	C₃×#4047	1	2	yes	complemented
542	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
543	C₄	C₃×D₅×#41	1	1	yes	characteristic
544	C₃	#10611153	1	1	yes	characteristic, direct product factor, Sylow
545	C₂	—	4	2	no	—
546	C₂	—	10	2	no	—
547	C₂	—	20	2	no	—
548	C₂	C₃×C₄×D₄×D₅	1	1	yes	characteristic
549	C₂	C₂×C₃×#4047	1	1	yes	characteristic
550	C₂	C₃×D₅×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₈	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×C₈×D₄	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#65882	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×C₈×D₄	D₅
hypocenter	C₅	C₃×#2931
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₈ ◁ C₃×C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4047	C₂	semidirect
3. C₃×C₅×C₈×D₄	C₂	semidirect
4. C₃×C₈×C₂²⋊D₅	C₂	semidirect
5. C₃×#65301	C₂	semidirect
6. C₃×#65127	C₂	semidirect
7. C₃×#65126	C₂	semidirect
8. C₃×#65018	C₂	semidirect
9. C₃×#65016	C₂	semidirect
10. C₃×C₈×D₂₀	C₂	semidirect
11. C₃×C₄×C₈×D₅	C₂	semidirect
12. #10611153	C₃	direct (N × H)
44. C₂×#4047	C₂×C₃	semidirect
46. C₅×C₈×D₄	C₂×C₃	semidirect
47. C₈×C₂²⋊D₅	C₂×C₃	semidirect
48. #65301	C₂×C₃	semidirect
49. #65127	C₂×C₃	semidirect
50. #65126	C₂×C₃	semidirect
51. #65018	C₂×C₃	semidirect
52. #65016	C₂×C₃	semidirect
53. C₈×D₂₀	C₂×C₃	semidirect
54. C₄×C₈×D₅	C₂×C₃	semidirect
92. C₃×C₈×D₅	D₄	semidirect
100. C₃×C₈×D₄	D₅	semidirect
234. C₈×D₅	C₃×D₄	semidirect
242. C₈×D₄	C₃×D₅	semidirect
258. C₃×C₄×C₅	#131	semidirect
264. C₃×Dic₅	#131	semidirect
415. C₄×C₅	C₃×#131	semidirect
421. Dic₅	C₃×#131	semidirect
460. C₃×C₅	#2931	semidirect
477. C₃×C₄	#4047	semidirect
524. C₅	C₃×#2931	semidirect
541. C₄	C₃×#4047	semidirect
544. C₃	#10611153	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×#4047	2
C₃×#65882	2
C₃×C₅×C₈×D₄	2
C₃×C₈×C₂²⋊D₅	2
C₃×#65301	2
C₃×#65127	2
C₃×#65126	2
C₃×#65018	2
C₃×#65016	2
C₃×C₈×D₂₀	2
C₃×C₄×C₈×D₅	2
#10611153	3
C₃×#2931	5

Subgroups — C3×#10611153 #14415218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611153 #14415218