Subgroups — C₃×#10601116 #14301520

Order 1920.

888 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4086	C₂	1	1	yes	maximal, characteristic
2	C₃×#65855	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#418	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65504	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3955	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64775	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64752	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601116	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₂²⋊D₅	—	2	2	no	—
11	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₃×C₅×#117	C₂²	1	1	yes	characteristic
14	C₃×#4086	—	2	2	no	—
15	C₃×#4086	C₄	1	4	yes	complemented
16	C₃×#4072	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×#681	C₂²	1	1	yes	characteristic
19	C₃×#4039	—	2	2	no	—
20	C₃×D₅×C₂²⋊C₄	—	2	2	no	—
21	C₃×C₄×D₂₀	—	2	2	no	—
22	C₃×C₅×#102	—	2	2	no	—
23	C₃×#3964	—	2	2	no	—
24	C₃×#3955	—	2	2	no	—
25	C₃×#1887	—	5	1	no	maximal, Hall
26	C₂×#4086	C₂×C₃	1	1	yes	characteristic
27	#65855	C₂×C₃	1	1	yes	characteristic, complemented
28	C₅×#418	C₂×C₃	1	1	yes	characteristic, complemented
29	#65504	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×#3955	C₂×C₃	1	1	yes	characteristic, complemented
31	#64775	C₂×C₃	1	1	yes	characteristic, complemented
32	#64752	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂⁴×C₃×C₅	—	2	1	no	—
34	C₂³×C₃×D₅	D₄	1	2	yes	—
35	C₂×C₃×C₅×D₄	—	2	1	no	—
36	C₂×C₃×C₅×D₄	—	2	1	no	—
37	C₂×C₃×C₅×D₄	—	2	1	no	—
38	C₂×C₃×C₅×D₄	—	2	1	no	—
39	C₂×C₃×C₅×D₄	—	2	1	no	—
40	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	complemented
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
43	C₂×C₃×C₂²⋊D₅	—	4	8	no	—
44	C₂²×C₃×Dic₅	—	2	1	no	—
45	C₂×C₃×D₂₀	—	2	1	no	—
46	C₂×C₃×D₂₀	—	2	1	no	—
47	C₂×C₃×D₂₀	—	2	1	no	—
48	C₂×C₃×D₂₀	—	2	1	no	—
49	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
50	C₂×C₃×D₂₀	D₄	1	2	yes	—
51	C₂×C₃×C₄×D₅	—	2	4	no	—
52	C₃×C₅×M₁₆	—	2	1	no	—
53	C₃×C₅×M₁₆	—	2	1	no	—
54	C₂×C₃×C₅×C₈	—	2	1	no	—
55	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	complemented
56	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
57	C₃×C₄²×C₅	—	2	1	no	—
58	C₃×C₂²⋊Dic₅	—	2	1	no	—
59	C₃×#685	—	2	4	no	—
60	C₃×C₄⋊Dic₅	D₄	1	2	yes	complemented
61	C₃×C₄×Dic₅	—	2	1	no	—
62	C₃×C₄×Dic₅	—	2	1	no	—
63	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	complemented
64	C₃×#681	—	2	1	no	—
65	C₃×#681	—	2	1	no	—
66	C₂×C₃×#168	—	2	1	no	—
67	C₂×C₃×#127	—	5	1	no	—
68	C₃×#518	—	5	1	no	—
69	C₃×#418	—	5	1	no	—
70	C₃×#418	D₅	1	1	yes	characteristic, complemented
71	C₂×C₃×#100	—	5	1	no	—
72	C₃×#339	—	5	1	no	—
73	C₃×#339	—	5	1	no	—
74	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
75	C₂²×C₂²⋊D₅	—	2	2	no	—
76	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
78	C₅×#117	C₂²×C₃	1	1	yes	characteristic
79	#4086	—	2	2	no	—
80	#4086	C₃×C₄	1	4	yes	complemented
81	#4072	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
83	C₂×#681	C₂²×C₃	1	1	yes	characteristic
84	#4039	—	2	2	no	—
85	D₅×C₂²⋊C₄	—	2	2	no	—
86	C₄×D₂₀	—	2	2	no	—
87	C₅×#102	—	2	2	no	—
88	#3964	—	2	2	no	—
89	#3955	—	2	2	no	—
90	#1887	—	5	1	no	Sylow
91	C₂³×C₃×C₅	—	2	2	no	—
92	C₂³×C₃×C₅	—	4	4	no	—
93	C₂³×C₃×C₅	—	4	1	no	—
94	C₂³×C₃×C₅	—	4	1	no	—
95	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₃×D₅	—	2	2	no	—
97	C₂²×C₃×D₅	—	2	2	no	—
98	C₂²×C₃×D₅	—	4	4	no	—
99	C₂²×C₃×D₅	C₂²⋊C₄	1	4	yes	—
100	C₃×C₅×D₄	—	2	2	no	—
101	C₃×C₅×D₄	—	2	2	no	—
102	C₃×C₅×D₄	—	4	1	no	—
103	C₃×C₅×D₄	—	4	1	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
111	C₃×C₂²⋊D₅	—	4	16	no	—
112	C₂×C₃×Dic₅	—	2	4	no	—
113	C₂×C₃×Dic₅	—	2	2	no	—
114	C₂×C₃×Dic₅	—	2	2	no	—
115	C₃×D₂₀	—	2	2	no	—
116	C₃×D₂₀	—	2	2	no	—
117	C₃×D₂₀	—	2	2	no	—
118	C₃×D₂₀	—	2	2	no	—
119	C₃×C₄×D₅	—	8	4	no	—
120	C₃×C₅×C₈	—	4	1	no	—
121	C₃×#168	—	4	1	no	—
122	C₂²×C₃×D₄	—	5	1	no	—
123	C₂²×C₃×D₄	—	10	2	no	—
124	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
125	C₂×C₃×M₁₆	—	5	1	no	—
126	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
127	C₃×#127	—	5	4	no	—
128	C₃×#127	—	10	2	no	—
129	C₃×C₄×D₄	—	10	2	no	—
130	C₃×C₄×D₄	—	10	2	no	—
131	C₃×#117	—	5	1	no	—
132	C₃×#117	C₂×D₅	1	1	yes	characteristic
133	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
134	C₂×C₃×C₄²	—	5	1	no	—
135	C₃×#102	—	2	2	no	—
136	C₃×#102	—	10	2	no	—
137	C₃×#100	—	10	2	no	—
138	C₂⁴×C₅	—	2	1	no	—
139	C₂³×D₅	C₃×D₄	1	2	yes	—
140	C₂×C₅×D₄	—	2	1	no	—
141	C₂×C₅×D₄	—	2	1	no	—
142	C₂×C₅×D₄	—	2	1	no	—
143	C₂×C₅×D₄	—	2	1	no	—
144	C₂×C₅×D₄	—	2	1	no	—
145	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	complemented
146	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
147	C₂×C₂²⋊D₅	—	2	8	no	—
148	C₂×C₂²⋊D₅	—	4	8	no	—
149	C₂²×Dic₅	—	2	1	no	—
150	C₂×D₂₀	—	2	1	no	—
151	C₂×D₂₀	—	2	1	no	—
152	C₂×D₂₀	—	2	1	no	—
153	C₂×D₂₀	—	2	1	no	—
154	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
155	C₂×D₂₀	C₃×D₄	1	2	yes	—
156	C₂×C₄×D₅	—	2	4	no	—
157	C₅×M₁₆	—	2	1	no	—
158	C₅×M₁₆	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	complemented
161	C₅×C₂²⋊C₄	—	2	1	no	—
162	C₄²×C₅	—	2	1	no	—
163	C₂²⋊Dic₅	—	2	1	no	—
164	#685	—	2	4	no	—
165	C₄⋊Dic₅	C₃×D₄	1	2	yes	complemented
166	C₄×Dic₅	—	2	1	no	—
167	C₄×Dic₅	—	2	1	no	—
168	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	complemented
169	#681	—	2	1	no	—
170	#681	—	2	1	no	—
171	C₂×#168	—	2	1	no	—
172	C₂×#127	—	5	1	no	—
173	#518	—	5	1	no	—
174	#418	—	5	1	no	—
175	#418	C₃×D₅	1	1	yes	characteristic, complemented
176	C₂×#100	—	5	1	no	—
177	#339	—	5	1	no	—
178	#339	—	5	1	no	—
179	C₂²×C₃×C₅	—	2	2	no	—
180	C₂²×C₃×C₅	—	4	4	no	—
181	C₂²×C₃×C₅	—	4	2	no	—
182	C₂²×C₃×C₅	—	8	2	no	—
183	C₂²×C₃×C₅	—	8	2	no	—
184	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂²×C₃×C₅	#120	1	1	yes	characteristic
186	C₂²×C₃×C₅	#123	1	1	yes	characteristic
187	C₂×C₃×D₅	—	2	4	no	—
188	C₂×C₃×D₅	—	4	4	no	—
189	C₂×C₃×D₅	—	4	4	no	—
190	C₂×C₃×D₅	—	8	2	no	—
191	C₃×C₄×C₅	—	4	2	no	—
192	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
193	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
194	C₃×C₄×C₅	#121	1	1	yes	characteristic
195	C₃×C₄×C₅	#121	1	1	yes	characteristic
196	C₃×Dic₅	—	2	4	no	—
197	C₃×Dic₅	—	4	2	no	—
198	C₂⁴×C₃	—	2	1	no	—
199	C₂⁴×C₃	—	5	2	no	—
200	C₂×C₃×D₄	—	2	1	no	—
201	C₂×C₃×D₄	—	2	1	no	—
202	C₂×C₃×D₄	—	2	1	no	—
203	C₂×C₃×D₄	—	2	1	no	—
204	C₂×C₃×D₄	—	2	1	no	—
205	C₂×C₃×D₄	—	5	2	no	—
206	C₂×C₃×D₄	—	5	2	no	—
207	C₂×C₃×D₄	—	10	8	no	—
208	C₂×C₃×D₄	—	10	1	no	—
209	C₂×C₃×D₄	—	10	1	no	—
210	C₂×C₃×D₄	—	10	1	no	—
211	C₂×C₃×D₄	—	10	1	no	—
212	C₂×C₃×D₄	—	20	8	no	—
213	C₂×C₃×D₄	C₄×D₅	1	2	yes	complemented
214	C₂²×C₃×C₄	—	10	4	no	—
215	C₂²×C₃×C₄	—	10	1	no	—
216	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
217	C₃×M₁₆	—	2	1	no	—
218	C₃×M₁₆	—	2	1	no	—
219	C₃×M₁₆	—	10	1	no	—
220	C₃×M₁₆	—	10	1	no	—
221	C₂×C₃×C₈	—	2	1	no	—
222	C₂×C₃×C₈	—	10	1	no	—
223	C₃×C₄⋊C₄	—	5	2	no	—
224	C₃×C₄⋊C₄	C₂²⋊D₅	1	2	yes	complemented
225	C₃×C₂²⋊C₄	—	2	1	no	—
226	C₃×C₂²⋊C₄	—	10	4	no	—
227	C₃×C₂²⋊C₄	—	10	1	no	—
228	C₃×C₄²	—	2	1	no	—
229	C₃×C₄²	—	5	2	no	—
230	C₃×C₄²	—	10	1	no	—
231	C₃×C₄²	—	10	1	no	—
232	C₂³×C₅	—	2	2	no	—
233	C₂³×C₅	—	4	4	no	—
234	C₂³×C₅	—	4	1	no	—
235	C₂³×C₅	—	4	1	no	—
236	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
237	C₂²×D₅	—	2	2	no	—
238	C₂²×D₅	—	2	2	no	—
239	C₂²×D₅	—	4	4	no	—
240	C₂²×D₅	C₃×C₂²⋊C₄	1	4	yes	—
241	C₅×D₄	—	2	2	no	—
242	C₅×D₄	—	2	2	no	—
243	C₅×D₄	—	4	1	no	—
244	C₅×D₄	—	4	1	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
250	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
251	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
252	C₂²⋊D₅	—	4	16	no	—
253	C₂×Dic₅	—	2	4	no	—
254	C₂×Dic₅	—	2	2	no	—
255	C₂×Dic₅	—	2	2	no	—
256	D₂₀	—	2	2	no	—
257	D₂₀	—	2	2	no	—
258	D₂₀	—	2	2	no	—
259	D₂₀	—	2	2	no	—
260	C₄×D₅	—	8	4	no	—
261	C₅×C₈	—	4	1	no	—
262	#168	—	4	1	no	—
263	C₂²×D₄	—	5	1	no	—
264	C₂²×D₄	—	10	2	no	—
265	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
266	C₂×M₁₆	—	5	1	no	—
267	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
268	#127	—	5	4	no	—
269	#127	—	10	2	no	—
270	C₄×D₄	—	10	2	no	—
271	C₄×D₄	—	10	2	no	—
272	#117	—	5	1	no	—
273	#117	C₂×C₃×D₅	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	—	10	2	no	—
275	C₂×C₄²	—	5	1	no	—
276	#102	—	2	2	no	—
277	#102	—	10	2	no	—
278	#100	—	10	2	no	—
279	C₂×C₃×C₅	—	2	1	no	—
280	C₂×C₃×C₅	—	2	1	no	—
281	C₂×C₃×C₅	—	8	2	no	—
282	C₂×C₃×C₅	#386	1	1	yes	characteristic
283	C₂×C₃×C₅	#453	1	2	yes	—
284	C₃×D₅	—	4	4	no	—
285	C₂³×C₃	—	2	2	no	—
286	C₂³×C₃	—	4	4	no	—
287	C₂³×C₃	—	4	1	no	—
288	C₂³×C₃	—	4	1	no	—
289	C₂³×C₃	—	5	4	no	—
290	C₂³×C₃	—	10	2	no	—
291	C₂³×C₃	—	10	2	no	—
292	C₂³×C₃	—	20	4	no	—
293	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
294	C₃×D₄	—	2	2	no	—
295	C₃×D₄	—	2	2	no	—
296	C₃×D₄	—	4	1	no	—
297	C₃×D₄	—	4	1	no	—
298	C₃×D₄	—	10	2	no	—
299	C₃×D₄	—	10	2	no	—
300	C₃×D₄	—	10	2	no	—
301	C₃×D₄	—	10	2	no	—
302	C₃×D₄	—	20	16	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	10	4	no	—
305	C₂×C₃×C₄	—	10	2	no	—
306	C₂×C₃×C₄	—	10	2	no	—
307	C₂×C₃×C₄	—	40	4	no	—
308	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
309	C₂×C₃×C₄	#709	1	1	yes	characteristic
310	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
311	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
312	C₂×C₃×C₄	#711	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
314	C₃×C₈	—	4	1	no	—
315	C₃×C₈	—	20	1	no	—
316	C₂²×C₅	—	2	2	no	—
317	C₂²×C₅	—	4	4	no	—
318	C₂²×C₅	—	4	2	no	—
319	C₂²×C₅	—	8	2	no	—
320	C₂²×C₅	—	8	2	no	—
321	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
322	C₂²×C₅	C₃×#120	1	1	yes	characteristic
323	C₂²×C₅	C₃×#123	1	1	yes	characteristic
324	C₂×D₅	—	2	4	no	—
325	C₂×D₅	—	4	4	no	—
326	C₂×D₅	—	4	4	no	—
327	C₂×D₅	—	8	2	no	—
328	C₄×C₅	—	4	2	no	—
329	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
330	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
331	C₄×C₅	C₃×#121	1	1	yes	characteristic
332	C₄×C₅	C₃×#121	1	1	yes	characteristic
333	Dic₅	—	2	4	no	—
334	Dic₅	—	4	2	no	—
335	C₂⁴	—	2	1	no	—
336	C₂⁴	—	5	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	5	2	no	—
343	C₂×D₄	—	5	2	no	—
344	C₂×D₄	—	10	8	no	—
345	C₂×D₄	—	10	1	no	—
346	C₂×D₄	—	10	1	no	—
347	C₂×D₄	—	10	1	no	—
348	C₂×D₄	—	10	1	no	—
349	C₂×D₄	—	20	8	no	—
350	C₂×D₄	C₃×C₄×D₅	1	2	yes	complemented
351	C₂²×C₄	—	10	4	no	—
352	C₂²×C₄	—	10	1	no	—
353	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
354	M₁₆	—	2	1	no	—
355	M₁₆	—	2	1	no	—
356	M₁₆	—	10	1	no	—
357	M₁₆	—	10	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	10	1	no	—
360	C₄⋊C₄	—	5	2	no	—
361	C₄⋊C₄	C₃×C₂²⋊D₅	1	2	yes	complemented
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	10	4	no	—
364	C₂²⋊C₄	—	10	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	5	2	no	—
367	C₄²	—	10	1	no	—
368	C₄²	—	10	1	no	—
369	C₃×C₅	#1887	1	1	yes	characteristic, complemented, Hall
370	C₂²×C₃	—	2	2	no	—
371	C₂²×C₃	—	4	4	no	—
372	C₂²×C₃	—	4	2	no	—
373	C₂²×C₃	—	8	2	no	—
374	C₂²×C₃	—	8	2	no	—
375	C₂²×C₃	—	10	4	no	—
376	C₂²×C₃	—	20	4	no	—
377	C₂²×C₃	—	20	4	no	—
378	C₂²×C₃	—	40	2	no	—
379	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
380	C₂²×C₃	#4029	1	1	yes	characteristic
381	C₂²×C₃	#4083	1	1	yes	characteristic
382	C₃×C₄	—	4	2	no	—
383	C₃×C₄	—	10	4	no	—
384	C₃×C₄	—	20	2	no	—
385	C₃×C₄	#4027	1	1	yes	characteristic
386	C₃×C₄	#4030	1	1	yes	characteristic
387	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
388	C₃×C₄	#4084	1	1	yes	characteristic
389	C₂×C₅	—	2	1	no	—
390	C₂×C₅	—	2	1	no	—
391	C₂×C₅	—	8	2	no	—
392	C₂×C₅	C₃×#386	1	1	yes	characteristic
393	C₂×C₅	C₃×#453	1	2	yes	—
394	D₅	—	4	4	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	4	4	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	5	4	no	—
400	C₂³	—	10	2	no	—
401	C₂³	—	10	2	no	—
402	C₂³	—	20	4	no	—
403	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
404	D₄	—	2	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	4	1	no	—
407	D₄	—	4	1	no	—
408	D₄	—	10	2	no	—
409	D₄	—	10	2	no	—
410	D₄	—	10	2	no	—
411	D₄	—	10	2	no	—
412	D₄	—	20	16	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	10	4	no	—
415	C₂×C₄	—	10	2	no	—
416	C₂×C₄	—	10	2	no	—
417	C₂×C₄	—	40	4	no	—
418	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
419	C₂×C₄	C₃×#709	1	1	yes	characteristic
420	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
421	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
422	C₂×C₄	C₃×#711	1	1	yes	characteristic
423	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
424	C₈	—	4	1	no	—
425	C₈	—	20	1	no	—
426	C₂×C₃	—	2	1	no	—
427	C₂×C₃	—	2	1	no	—
428	C₂×C₃	—	8	2	no	—
429	C₂×C₃	—	20	4	no	—
430	C₂×C₃	#65245	1	1	yes	characteristic
431	C₂×C₃	#65487	1	2	yes	—
432	C₅	C₃×#1887	1	1	yes	characteristic, complemented, Sylow
433	C₂²	—	2	2	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	2	no	—
438	C₂²	—	10	4	no	—
439	C₂²	—	20	4	no	—
440	C₂²	—	20	4	no	—
441	C₂²	—	40	2	no	—
442	C₂²	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
443	C₂²	C₃×#4029	1	1	yes	characteristic
444	C₂²	C₃×#4083	1	1	yes	characteristic
445	C₄	—	4	2	no	—
446	C₄	—	10	4	no	—
447	C₄	—	20	2	no	—
448	C₄	C₃×#4027	1	1	yes	characteristic
449	C₄	C₃×#4030	1	1	yes	characteristic
450	C₄	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
451	C₄	C₃×#4084	1	1	yes	characteristic
452	C₃	#10601116	1	1	yes	characteristic, direct product factor, Sylow
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	8	2	no	—
456	C₂	—	20	4	no	—
457	C₂	C₃×#65245	1	1	yes	characteristic
458	C₂	C₃×#65487	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	#4083
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₃×C₅×#418	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₂×C₃×#4086	C₂
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₃×#418	D₅
hypocenter	C₅	C₃×#1887
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#418

Complements

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

N	H ≅ G/N	type
2. C₃×#65855	C₂	semidirect
3. C₃×C₅×#418	C₂	semidirect
4. C₃×#65504	C₂	semidirect
5. C₂×C₃×#3955	C₂	semidirect
6. C₃×#64775	C₂	semidirect
7. C₃×#64752	C₂	semidirect
8. #10601116	C₃	direct (N × H)
15. C₃×#4086	C₄	semidirect
27. #65855	C₂×C₃	semidirect
28. C₅×#418	C₂×C₃	semidirect
29. #65504	C₂×C₃	semidirect
30. C₂×#3955	C₂×C₃	semidirect
31. #64775	C₂×C₃	semidirect
32. #64752	C₂×C₃	semidirect
40. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
55. C₃×C₅×C₄⋊C₄	D₄	semidirect
60. C₃×C₄⋊Dic₅	D₄	semidirect
63. C₃×C₄×Dic₅	C₂×C₄	semidirect
70. C₃×#418	D₅	semidirect
80. #4086	C₃×C₄	semidirect
145. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
160. C₅×C₄⋊C₄	C₃×D₄	semidirect
165. C₄⋊Dic₅	C₃×D₄	semidirect
168. C₄×Dic₅	C₂×C₃×C₄	semidirect
175. #418	C₃×D₅	semidirect
213. C₂×C₃×D₄	C₄×D₅	semidirect
224. C₃×C₄⋊C₄	C₂²⋊D₅	semidirect
350. C₂×D₄	C₃×C₄×D₅	semidirect
361. C₄⋊C₄	C₃×C₂²⋊D₅	semidirect
369. C₃×C₅	#1887	semidirect
432. C₅	C₃×#1887	semidirect
452. C₃	#10601116	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×#4086	2
C₃×#65855	2
C₃×C₅×#418	2
C₃×#65504	2
C₂×C₃×#3955	2
C₃×#64775	2
C₃×#64752	2
#10601116	3
C₃×#1887	5

Subgroups — C3×#10601116 #14301520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10601116 #14301520