Subgroups — C₃×#10605483 #14320041

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65276	C₂	1	2	yes	maximal
4	C₃×#65266	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×#685	C₂	1	2	yes	maximal
6	C₃×C₄×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65221	C₂	1	2	yes	maximal, complemented
8	C₃×#64953	C₂	1	2	yes	maximal
9	C₃×#64940	C₂	1	2	yes	maximal, complemented
10	#10605483	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×#685	C₂²	1	4	yes	—
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
19	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
20	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
23	C₃×C₄²×D₅	C₄	1	8	yes	complemented
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×#3963	C₂²	1	2	yes	—
26	C₃×#3963	C₂²	1	4	yes	—
27	C₃×#3963	C₂²	1	4	yes	—
28	C₃×#3963	C₂²	1	4	yes	—
29	C₃×#2283	—	5	1	no	maximal, Hall
30	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic
31	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
32	#65276	C₂×C₃	1	2	yes	—
33	#65266	C₂×C₃	1	2	yes	complemented
34	C₄×#685	C₂×C₃	1	2	yes	—
35	C₄×C₄⋊Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
36	#65221	C₂×C₃	1	2	yes	complemented
37	#64953	C₂×C₃	1	2	yes	—
38	#64940	C₂×C₃	1	2	yes	complemented
39	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
45	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
47	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₄×D₅	—	2	4	no	—
49	C₂×C₃×C₄×D₅	—	2	4	no	—
50	C₂×C₃×C₄×D₅	—	2	2	no	—
51	C₂×C₃×C₄×D₅	—	2	2	no	—
52	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
53	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
54	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
55	C₃×C₅×C₄⋊C₄	—	2	4	no	—
56	C₃×C₄²×C₅	—	2	4	no	—
57	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
58	C₃×#685	—	2	8	no	—
59	C₃×C₄⋊Dic₅	—	2	4	no	—
60	C₃×C₄×Dic₅	—	2	4	no	—
61	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
62	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
63	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
64	C₂²×C₃×C₄²	—	5	1	no	—
65	C₃×#383	—	5	2	no	—
66	C₃×#382	—	5	2	no	—
67	C₃×#381	—	5	2	no	—
68	C₃×#380	—	5	2	no	—
69	C₃×C₄×C₄⋊C₄	—	5	1	no	—
70	C₃×C₄×C₄⋊C₄	D₅	1	1	yes	characteristic, complemented
71	C₃×C₄×C₂²⋊C₄	—	5	2	no	—
72	C₃×#376	—	5	2	no	—
73	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
74	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
75	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
77	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
78	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
79	C₂×#685	C₂²×C₃	1	4	yes	—
80	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
81	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
82	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
85	C₄²×D₅	C₃×C₄	1	8	yes	complemented
86	C₅×#95	C₂²×C₃	1	2	yes	—
87	#3963	C₂²×C₃	1	2	yes	—
88	#3963	C₂²×C₃	1	4	yes	—
89	#3963	C₂²×C₃	1	4	yes	—
90	#3963	C₂²×C₃	1	4	yes	—
91	#2283	—	5	1	no	Sylow
92	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
93	C₂²×C₃×D₅	—	2	2	no	—
94	C₂²×C₃×D₅	—	2	1	no	—
95	C₂²×C₃×D₅	—	2	1	no	—
96	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
97	C₂²×C₃×D₅	#41	1	4	yes	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	—	2	4	no	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	#41	1	4	yes	—
106	C₂×C₃×C₄×C₅	#41	1	2	yes	—
107	C₂×C₃×C₄×C₅	#41	1	2	yes	—
108	C₂×C₃×Dic₅	—	2	2	no	—
109	C₂×C₃×Dic₅	—	2	1	no	—
110	C₂×C₃×Dic₅	—	2	1	no	—
111	C₂×C₃×Dic₅	—	2	2	no	—
112	C₂×C₃×Dic₅	—	2	4	no	—
113	C₂×C₃×Dic₅	—	2	4	no	—
114	C₂×C₃×Dic₅	—	2	4	no	—
115	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
116	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
117	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
118	C₃×C₄×D₅	—	2	8	no	—
119	C₃×C₄×D₅	—	2	8	no	—
120	C₃×C₄×D₅	—	2	8	no	—
121	C₂³×C₃×C₄	—	5	1	no	—
122	C₂³×C₃×C₄	—	5	1	no	—
123	C₂³×C₃×C₄	—	5	1	no	—
124	C₂×C₃×C₄⋊C₄	—	5	2	no	—
125	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
126	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
127	C₂×C₃×C₄²	—	5	1	no	—
128	C₂×C₃×C₄²	—	5	1	no	—
129	C₂×C₃×C₄²	—	5	1	no	—
130	C₂×C₃×C₄²	—	5	8	no	—
131	C₂×C₃×C₄²	—	5	2	no	—
132	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
133	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
134	C₃×#95	—	5	4	no	—
135	C₃×#95	—	5	4	no	—
136	C₃×#95	—	5	4	no	—
137	C₃×#95	—	5	2	no	—
138	C₃×#95	C₂×D₅	1	2	yes	—
139	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
141	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
144	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
145	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
146	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
147	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
148	C₂×C₄×D₅	—	2	4	no	—
149	C₂×C₄×D₅	—	2	4	no	—
150	C₂×C₄×D₅	—	2	2	no	—
151	C₂×C₄×D₅	—	2	2	no	—
152	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
153	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
154	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
155	C₅×C₄⋊C₄	—	2	4	no	—
156	C₄²×C₅	—	2	4	no	—
157	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
158	#685	—	2	8	no	—
159	C₄⋊Dic₅	—	2	4	no	—
160	C₄×Dic₅	—	2	4	no	—
161	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
162	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
163	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
164	C₂²×C₄²	—	5	1	no	—
165	#383	—	5	2	no	—
166	#382	—	5	2	no	—
167	#381	—	5	2	no	—
168	#380	—	5	2	no	—
169	C₄×C₄⋊C₄	—	5	1	no	—
170	C₄×C₄⋊C₄	C₃×D₅	1	1	yes	characteristic, complemented
171	C₄×C₂²⋊C₄	—	5	2	no	—
172	#376	—	5	2	no	—
173	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
174	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
175	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
176	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
177	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
178	C₂×C₃×D₅	—	2	2	no	—
179	C₂×C₃×D₅	—	2	2	no	—
180	C₂×C₃×D₅	—	2	4	no	—
181	C₂×C₃×D₅	—	2	4	no	—
182	C₂×C₃×D₅	#117	1	4	yes	—
183	C₃×C₄×C₅	—	2	2	no	—
184	C₃×C₄×C₅	—	4	4	no	—
185	C₃×C₄×C₅	#117	1	4	yes	—
186	C₃×C₄×C₅	#117	1	4	yes	—
187	C₃×Dic₅	—	2	2	no	—
188	C₃×Dic₅	—	2	2	no	—
189	C₃×Dic₅	—	2	2	no	—
190	C₃×Dic₅	—	4	4	no	—
191	C₂⁴×C₃	—	5	1	no	—
192	C₂²×C₃×C₄	—	5	1	no	—
193	C₂²×C₃×C₄	—	5	1	no	—
194	C₂²×C₃×C₄	—	5	1	no	—
195	C₂²×C₃×C₄	—	5	4	no	—
196	C₂²×C₃×C₄	—	5	4	no	—
197	C₂²×C₃×C₄	—	5	4	no	—
198	C₂²×C₃×C₄	—	5	4	no	—
199	C₂²×C₃×C₄	—	10	4	no	—
200	C₂²×C₃×C₄	—	10	4	no	—
201	C₂²×C₃×C₄	—	10	2	no	—
202	C₂²×C₃×C₄	—	10	2	no	—
203	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
204	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
207	C₃×C₄⋊C₄	—	2	4	no	—
208	C₃×C₄⋊C₄	—	10	4	no	—
209	C₃×C₂²⋊C₄	—	10	8	no	—
210	C₃×C₄²	—	2	4	no	—
211	C₃×C₄²	—	5	4	no	—
212	C₃×C₄²	—	5	4	no	—
213	C₃×C₄²	—	5	4	no	—
214	C₃×C₄²	—	10	4	no	—
215	C₃×C₄²	C₄×D₅	1	4	yes	—
216	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
217	C₂²×D₅	—	2	2	no	—
218	C₂²×D₅	—	2	1	no	—
219	C₂²×D₅	—	2	1	no	—
220	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
221	C₂²×D₅	C₃×#41	1	4	yes	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	4	no	—
224	C₂×C₄×C₅	—	2	4	no	—
225	C₂×C₄×C₅	—	2	4	no	—
226	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
227	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
228	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
229	C₂×C₄×C₅	C₃×#41	1	4	yes	—
230	C₂×C₄×C₅	C₃×#41	1	2	yes	—
231	C₂×C₄×C₅	C₃×#41	1	2	yes	—
232	C₂×Dic₅	—	2	2	no	—
233	C₂×Dic₅	—	2	1	no	—
234	C₂×Dic₅	—	2	1	no	—
235	C₂×Dic₅	—	2	2	no	—
236	C₂×Dic₅	—	2	4	no	—
237	C₂×Dic₅	—	2	4	no	—
238	C₂×Dic₅	—	2	4	no	—
239	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
240	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
241	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
242	C₄×D₅	—	2	8	no	—
243	C₄×D₅	—	2	8	no	—
244	C₄×D₅	—	2	8	no	—
245	C₂³×C₄	—	5	1	no	—
246	C₂³×C₄	—	5	1	no	—
247	C₂³×C₄	—	5	1	no	—
248	C₂×C₄⋊C₄	—	5	2	no	—
249	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
250	C₂×C₂²⋊C₄	—	5	4	no	—
251	C₂×C₄²	—	5	1	no	—
252	C₂×C₄²	—	5	1	no	—
253	C₂×C₄²	—	5	1	no	—
254	C₂×C₄²	—	5	8	no	—
255	C₂×C₄²	—	5	2	no	—
256	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
257	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
258	#95	—	5	4	no	—
259	#95	—	5	4	no	—
260	#95	—	5	4	no	—
261	#95	—	5	2	no	—
262	#95	C₂×C₃×D₅	1	2	yes	—
263	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
264	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
265	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
266	C₂×C₃×C₅	#529	1	2	yes	—
267	C₂×C₃×C₅	#529	1	2	yes	—
268	C₃×D₅	—	2	4	no	—
269	C₂³×C₃	—	5	2	no	—
270	C₂³×C₃	—	5	4	no	—
271	C₂³×C₃	—	10	2	no	—
272	C₂³×C₃	—	10	1	no	—
273	C₂³×C₃	—	10	1	no	—
274	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	4	no	—
277	C₂×C₃×C₄	—	2	4	no	—
278	C₂×C₃×C₄	—	2	4	no	—
279	C₂×C₃×C₄	—	5	2	no	—
280	C₂×C₃×C₄	—	5	2	no	—
281	C₂×C₃×C₄	—	5	2	no	—
282	C₂×C₃×C₄	—	10	8	no	—
283	C₂×C₃×C₄	—	10	2	no	—
284	C₂×C₃×C₄	—	10	1	no	—
285	C₂×C₃×C₄	—	10	1	no	—
286	C₂×C₃×C₄	—	10	2	no	—
287	C₂×C₃×C₄	—	10	8	no	—
288	C₂×C₃×C₄	—	10	8	no	—
289	C₂×C₃×C₄	—	10	4	no	—
290	C₂×C₃×C₄	—	10	4	no	—
291	C₂×C₃×C₄	—	10	4	no	—
292	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
293	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
294	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
295	C₂×C₃×C₄	#709	1	4	yes	—
296	C₂×C₃×C₄	#711	1	2	yes	—
297	C₂×C₃×C₄	#713	1	2	yes	—
298	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
299	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
300	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
301	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
302	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
303	C₂×D₅	—	2	2	no	—
304	C₂×D₅	—	2	2	no	—
305	C₂×D₅	—	2	4	no	—
306	C₂×D₅	—	2	4	no	—
307	C₂×D₅	C₃×#117	1	4	yes	—
308	C₄×C₅	—	2	2	no	—
309	C₄×C₅	—	4	4	no	—
310	C₄×C₅	C₃×#117	1	4	yes	—
311	C₄×C₅	C₃×#117	1	4	yes	—
312	Dic₅	—	2	2	no	—
313	Dic₅	—	2	2	no	—
314	Dic₅	—	2	2	no	—
315	Dic₅	—	4	4	no	—
316	C₂⁴	—	5	1	no	—
317	C₂²×C₄	—	5	1	no	—
318	C₂²×C₄	—	5	1	no	—
319	C₂²×C₄	—	5	1	no	—
320	C₂²×C₄	—	5	4	no	—
321	C₂²×C₄	—	5	4	no	—
322	C₂²×C₄	—	5	4	no	—
323	C₂²×C₄	—	5	4	no	—
324	C₂²×C₄	—	10	4	no	—
325	C₂²×C₄	—	10	4	no	—
326	C₂²×C₄	—	10	2	no	—
327	C₂²×C₄	—	10	2	no	—
328	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
329	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
330	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
331	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	10	4	no	—
334	C₂²⋊C₄	—	10	8	no	—
335	C₄²	—	2	4	no	—
336	C₄²	—	5	4	no	—
337	C₄²	—	5	4	no	—
338	C₄²	—	5	4	no	—
339	C₄²	—	10	4	no	—
340	C₄²	C₃×C₄×D₅	1	4	yes	—
341	C₃×C₅	#2283	1	1	yes	characteristic, complemented, Hall
342	C₂²×C₃	—	5	4	no	—
343	C₂²×C₃	—	10	2	no	—
344	C₂²×C₃	—	10	2	no	—
345	C₂²×C₃	—	10	4	no	—
346	C₂²×C₃	—	10	4	no	—
347	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
348	C₂²×C₃	C₂×#709	1	2	yes	—
349	C₂²×C₃	C₂×#711	1	1	yes	characteristic
350	C₂²×C₃	C₂×#713	1	1	yes	characteristic
351	C₂²×C₃	D₅×#41	1	2	yes	—
352	C₃×C₄	—	2	2	no	—
353	C₃×C₄	—	4	4	no	—
354	C₃×C₄	—	10	2	no	—
355	C₃×C₄	—	10	2	no	—
356	C₃×C₄	—	10	2	no	—
357	C₃×C₄	—	20	4	no	—
358	C₃×C₄	#4018	1	4	yes	—
359	C₃×C₄	#4038	1	4	yes	—
360	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
361	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
362	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
363	C₂×C₅	C₃×#529	1	2	yes	—
364	C₂×C₅	C₃×#529	1	2	yes	—
365	D₅	—	2	4	no	—
366	C₂³	—	5	2	no	—
367	C₂³	—	5	4	no	—
368	C₂³	—	10	2	no	—
369	C₂³	—	10	1	no	—
370	C₂³	—	10	1	no	—
371	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	5	2	no	—
377	C₂×C₄	—	5	2	no	—
378	C₂×C₄	—	5	2	no	—
379	C₂×C₄	—	10	8	no	—
380	C₂×C₄	—	10	2	no	—
381	C₂×C₄	—	10	1	no	—
382	C₂×C₄	—	10	1	no	—
383	C₂×C₄	—	10	2	no	—
384	C₂×C₄	—	10	8	no	—
385	C₂×C₄	—	10	8	no	—
386	C₂×C₄	—	10	4	no	—
387	C₂×C₄	—	10	4	no	—
388	C₂×C₄	—	10	4	no	—
389	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
390	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
391	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
392	C₂×C₄	C₃×#709	1	4	yes	—
393	C₂×C₄	C₃×#711	1	2	yes	—
394	C₂×C₄	C₃×#713	1	2	yes	—
395	C₂×C₃	—	10	4	no	—
396	C₂×C₃	C₂×#4018	1	1	yes	characteristic
397	C₂×C₃	C₂×#4038	1	1	yes	characteristic
398	C₂×C₃	D₅×#117	1	1	yes	characteristic
399	C₂×C₃	#65891	1	2	yes	—
400	C₂×C₃	#65914	1	2	yes	—
401	C₅	C₃×#2283	1	1	yes	characteristic, complemented, Sylow
402	C₂²	—	5	4	no	—
403	C₂²	—	10	4	no	—
404	C₂²	—	10	4	no	—
405	C₂²	—	10	2	no	—
406	C₂²	—	10	2	no	—
407	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
408	C₂²	C₂×C₃×#709	1	2	yes	—
409	C₂²	C₂×C₃×#711	1	1	yes	characteristic
410	C₂²	C₂×C₃×#713	1	1	yes	characteristic
411	C₂²	C₃×D₅×#41	1	2	yes	—
412	C₄	—	2	2	no	—
413	C₄	—	4	4	no	—
414	C₄	—	10	2	no	—
415	C₄	—	10	2	no	—
416	C₄	—	10	2	no	—
417	C₄	—	20	4	no	—
418	C₄	C₃×#4018	1	4	yes	—
419	C₄	C₃×#4038	1	4	yes	—
420	C₃	#10605483	1	1	yes	characteristic, direct product factor, Sylow
421	C₂	—	10	4	no	—
422	C₂	C₂×C₃×#4018	1	1	yes	characteristic
423	C₂	C₂×C₃×#4038	1	1	yes	characteristic
424	C₂	C₃×D₅×#117	1	1	yes	characteristic
425	C₂	C₃×#65891	1	2	yes	—
426	C₂	C₃×#65914	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₃×D₅	C₂³
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×C₄⋊C₄	D₅
hypocenter	C₅	C₃×#2283
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₃×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
4. C₃×#65266	C₂	semidirect
6. C₃×C₄×C₄⋊Dic₅	C₂	semidirect
7. C₃×#65221	C₂	semidirect
9. C₃×#64940	C₂	semidirect
10. #10605483	C₃	direct (N × H)
23. C₃×C₄²×D₅	C₄	semidirect
31. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
33. #65266	C₂×C₃	semidirect
35. C₄×C₄⋊Dic₅	C₂×C₃	semidirect
36. #65221	C₂×C₃	semidirect
38. #64940	C₂×C₃	semidirect
70. C₃×C₄×C₄⋊C₄	D₅	semidirect
85. C₄²×D₅	C₃×C₄	semidirect
170. C₄×C₄⋊C₄	C₃×D₅	semidirect
341. C₃×C₅	#2283	semidirect
401. C₅	C₃×#2283	semidirect
420. C₃	#10605483	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×C₄²×D₅	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×#65276	2
C₃×#65266	2
C₃×C₄×#685	2
C₃×C₄×C₄⋊Dic₅	2
C₃×#65221	2
C₃×#64953	2
C₃×#64940	2
#10605483	3
C₃×#2283	5

Subgroups — C3×#10605483 #14320041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10605483 #14320041