Subgroups — C₃×#10614050 #14320833

Order 1920.

1304 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4072	C₂	1	2	yes	maximal, complemented
3	C₃×#65510	C₂	1	2	yes	maximal
4	C₃×C₄×C₂²⋊Dic₅	C₂	1	2	yes	maximal, complemented
5	C₃×#65274	C₂	1	2	yes	maximal, complemented
6	C₃×#65240	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄²×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
9	#10614050	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
12	C₃×C₄×C₅×D₄	C₄	1	8	yes	complemented
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₂²⋊Dic₅	C₂²	1	4	yes	—
17	C₂×C₃×C₂²⋊Dic₅	C₂²	1	4	yes	—
18	C₃×#4072	—	2	8	no	—
19	C₂×C₃×C₄⋊Dic₅	C₂²	1	4	yes	—
20	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
21	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
22	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
23	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
25	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
26	C₃×#3963	C₂²	1	2	yes	—
27	C₃×#3963	C₂²	1	4	yes	—
28	C₃×#2293	—	5	1	no	maximal, Hall
29	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
30	C₂×#4072	C₂×C₃	1	2	yes	complemented
31	#65510	C₂×C₃	1	2	yes	—
32	C₄×C₂²⋊Dic₅	C₂×C₃	1	2	yes	complemented
33	#65274	C₂×C₃	1	2	yes	complemented
34	#65240	C₂×C₃	1	4	yes	complemented
35	C₄×C₄⋊Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
36	C₄²×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
38	C₂×C₃×C₅×D₄	—	2	4	no	—
39	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
40	C₂²×C₃×C₄×C₅	—	2	4	no	—
41	C₂²×C₃×C₄×C₅	—	2	4	no	—
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	8	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
48	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
49	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
50	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
51	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
52	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
53	C₃×C₂²⋊Dic₅	—	2	8	no	—
54	C₃×C₂²⋊Dic₅	—	2	8	no	—
55	C₃×C₄⋊Dic₅	—	2	4	no	—
56	C₃×C₄⋊Dic₅	—	2	8	no	—
57	C₃×C₄×Dic₅	—	2	4	no	—
58	C₃×C₄×Dic₅	—	2	4	no	—
59	C₃×C₄×Dic₅	—	2	2	no	—
60	C₃×C₄×Dic₅	—	2	4	no	—
61	C₃×C₄×Dic₅	D₄	1	4	yes	complemented
62	C₂×C₃×C₄×D₄	D₅	1	1	yes	characteristic
63	C₂×C₃×#117	—	5	2	no	—
64	C₃×#390	—	5	2	no	—
65	C₃×#389	—	5	2	no	—
66	C₃×#388	—	5	4	no	—
67	C₃×C₄×C₄⋊C₄	—	5	1	no	—
68	C₃×C₄×C₂²⋊C₄	—	5	2	no	—
69	C₃×C₄³	—	5	1	no	—
70	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
71	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
72	C₄×C₅×D₄	C₃×C₄	1	8	yes	complemented
73	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
75	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₂²⋊Dic₅	C₂²×C₃	1	4	yes	—
77	C₂×C₂²⋊Dic₅	C₂²×C₃	1	4	yes	—
78	#4072	—	2	8	no	—
79	C₂×C₄⋊Dic₅	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	2	yes	—
83	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
85	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
86	#3963	C₂²×C₃	1	2	yes	—
87	#3963	C₂²×C₃	1	4	yes	—
88	#2293	—	5	1	no	Sylow
89	C₂³×C₃×C₅	—	2	2	no	—
90	C₂³×C₃×C₅	—	2	4	no	—
91	C₂³×C₃×C₅	—	2	2	no	—
92	C₂³×C₃×C₅	—	2	4	no	—
93	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
94	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
95	C₃×C₅×D₄	—	2	8	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	16	no	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
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	C₂×D₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	#41	1	4	yes	—
106	C₂×C₃×C₄×C₅	#41	1	2	yes	—
107	C₂×C₃×Dic₅	—	2	2	no	—
108	C₂×C₃×Dic₅	—	2	2	no	—
109	C₂×C₃×Dic₅	—	2	2	no	—
110	C₂×C₃×Dic₅	—	2	2	no	—
111	C₂×C₃×Dic₅	—	2	4	no	—
112	C₂×C₃×Dic₅	—	2	4	no	—
113	C₂×C₃×Dic₅	—	2	4	no	—
114	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
115	C₂×C₃×Dic₅	#41	1	4	yes	—
116	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
117	C₂³×C₃×C₄	C₂×D₅	1	2	yes	—
118	C₃×C₄×D₄	Dic₅	1	8	yes	complemented
119	C₃×#117	—	10	8	no	—
120	C₂×C₃×C₄⋊C₄	—	5	2	no	—
121	C₂×C₃×C₄⋊C₄	—	5	4	no	—
122	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
123	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
124	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
125	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
126	C₂×C₃×C₄²	—	5	1	no	—
127	C₂×C₃×C₄²	—	5	2	no	—
128	C₂×C₃×C₄²	—	5	2	no	—
129	C₂×C₃×C₄²	—	5	1	no	—
130	C₂×C₃×C₄²	—	5	2	no	—
131	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
132	C₃×#95	—	5	4	no	—
133	C₃×#95	—	5	2	no	—
134	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
135	C₂×C₅×D₄	—	2	4	no	—
136	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
137	C₂²×C₄×C₅	—	2	4	no	—
138	C₂²×C₄×C₅	—	2	4	no	—
139	C₂²×C₄×C₅	C₂×C₃×C₄	1	8	yes	—
140	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
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	2	yes	—
146	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
147	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
148	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
149	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
150	C₂²⋊Dic₅	—	2	8	no	—
151	C₂²⋊Dic₅	—	2	8	no	—
152	C₄⋊Dic₅	—	2	4	no	—
153	C₄⋊Dic₅	—	2	8	no	—
154	C₄×Dic₅	—	2	4	no	—
155	C₄×Dic₅	—	2	4	no	—
156	C₄×Dic₅	—	2	2	no	—
157	C₄×Dic₅	—	2	4	no	—
158	C₄×Dic₅	C₃×D₄	1	4	yes	complemented
159	C₂×C₄×D₄	C₃×D₅	1	1	yes	characteristic
160	C₂×#117	—	5	2	no	—
161	#390	—	5	2	no	—
162	#389	—	5	2	no	—
163	#388	—	5	4	no	—
164	C₄×C₄⋊C₄	—	5	1	no	—
165	C₄×C₂²⋊C₄	—	5	2	no	—
166	C₄³	—	5	1	no	—
167	C₂²×C₃×C₅	—	2	4	no	—
168	C₂²×C₃×C₅	—	2	4	no	—
169	C₂²×C₃×C₅	—	2	4	no	—
170	C₂²×C₃×C₅	—	4	4	no	—
171	C₂²×C₃×C₅	—	4	4	no	—
172	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
173	C₂²×C₃×C₅	C₂²×D₄	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	2	yes	—
177	C₃×C₄×C₅	—	2	4	no	—
178	C₃×C₄×C₅	—	2	2	no	—
179	C₃×C₄×C₅	#117	1	4	yes	complemented
180	C₃×C₄×C₅	C₄×D₄	1	4	yes	—
181	C₃×Dic₅	—	2	4	no	—
182	C₃×Dic₅	—	2	4	no	—
183	C₃×Dic₅	—	4	4	no	—
184	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
185	C₂×C₃×D₄	—	2	4	no	—
186	C₂×C₃×D₄	C₂×Dic₅	1	4	yes	—
187	C₂²×C₃×C₄	—	2	4	no	—
188	C₂²×C₃×C₄	—	2	4	no	—
189	C₂²×C₃×C₄	—	5	2	no	—
190	C₂²×C₃×C₄	—	5	2	no	—
191	C₂²×C₃×C₄	—	5	4	no	—
192	C₂²×C₃×C₄	C₂×Dic₅	1	8	yes	—
193	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
195	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
196	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
197	C₃×C₄⋊C₄	—	10	8	no	—
198	C₃×C₄⋊C₄	—	10	4	no	—
199	C₃×C₄⋊C₄	C₂×Dic₅	1	4	yes	—
200	C₃×C₂²⋊C₄	—	10	8	no	—
201	C₃×C₂²⋊C₄	—	10	8	no	—
202	C₃×C₂²⋊C₄	C₂×Dic₅	1	8	yes	—
203	C₃×C₄²	—	5	4	no	—
204	C₃×C₄²	—	10	4	no	—
205	C₃×C₄²	—	10	4	no	—
206	C₃×C₄²	—	10	4	no	—
207	C₃×C₄²	—	10	2	no	—
208	C₃×C₄²	C₂×Dic₅	1	4	yes	—
209	C₂³×C₅	—	2	2	no	—
210	C₂³×C₅	—	2	4	no	—
211	C₂³×C₅	—	2	2	no	—
212	C₂³×C₅	—	2	4	no	—
213	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
214	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
215	C₅×D₄	—	2	8	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	16	no	—
220	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
221	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
222	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
223	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
224	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
225	C₂×C₄×C₅	C₃×#41	1	4	yes	—
226	C₂×C₄×C₅	C₃×#41	1	2	yes	—
227	C₂×Dic₅	—	2	2	no	—
228	C₂×Dic₅	—	2	2	no	—
229	C₂×Dic₅	—	2	2	no	—
230	C₂×Dic₅	—	2	2	no	—
231	C₂×Dic₅	—	2	4	no	—
232	C₂×Dic₅	—	2	4	no	—
233	C₂×Dic₅	—	2	4	no	—
234	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
235	C₂×Dic₅	C₃×#41	1	4	yes	—
236	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
237	C₂³×C₄	C₂×C₃×D₅	1	2	yes	—
238	C₄×D₄	C₃×Dic₅	1	8	yes	complemented
239	#117	—	10	8	no	—
240	C₂×C₄⋊C₄	—	5	4	no	—
241	C₂×C₄⋊C₄	—	5	2	no	—
242	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
243	C₂×C₂²⋊C₄	—	5	4	no	—
244	C₂×C₂²⋊C₄	—	5	4	no	—
245	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
246	C₂×C₄²	—	5	1	no	—
247	C₂×C₄²	—	5	2	no	—
248	C₂×C₄²	—	5	1	no	—
249	C₂×C₄²	—	5	2	no	—
250	C₂×C₄²	—	5	2	no	—
251	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
252	#95	—	5	4	no	—
253	#95	—	5	2	no	—
254	C₂×C₃×C₅	—	4	4	no	—
255	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
256	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
257	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
258	C₂×C₃×C₅	#529	1	2	yes	—
259	C₂×C₃×C₅	#532	1	2	yes	—
260	C₂³×C₃	—	2	4	no	—
261	C₂³×C₃	—	2	2	no	—
262	C₂³×C₃	—	2	2	no	—
263	C₂³×C₃	—	2	4	no	—
264	C₂³×C₃	C₂²×Dic₅	1	4	yes	—
265	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
266	C₃×D₄	—	2	8	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	16	no	—
271	C₂×C₃×C₄	—	5	4	no	—
272	C₂×C₃×C₄	—	5	4	no	—
273	C₂×C₃×C₄	—	10	2	no	—
274	C₂×C₃×C₄	—	10	2	no	—
275	C₂×C₃×C₄	—	10	2	no	—
276	C₂×C₃×C₄	—	10	2	no	—
277	C₂×C₃×C₄	—	10	4	no	—
278	C₂×C₃×C₄	—	10	4	no	—
279	C₂×C₃×C₄	—	10	4	no	—
280	C₂×C₃×C₄	#709	1	4	yes	—
281	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
282	C₂×C₃×C₄	#711	1	2	yes	—
283	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
284	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
285	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
286	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
287	C₂²×C₅	—	2	4	no	—
288	C₂²×C₅	—	2	4	no	—
289	C₂²×C₅	—	2	4	no	—
290	C₂²×C₅	—	4	4	no	—
291	C₂²×C₅	—	4	4	no	—
292	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
293	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
294	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
295	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
296	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
297	C₄×C₅	—	2	4	no	—
298	C₄×C₅	—	2	2	no	—
299	C₄×C₅	C₃×#117	1	4	yes	complemented
300	C₄×C₅	C₃×C₄×D₄	1	4	yes	—
301	Dic₅	—	2	4	no	—
302	Dic₅	—	2	4	no	—
303	Dic₅	—	4	4	no	—
304	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	C₂×C₃×Dic₅	1	4	yes	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	5	2	no	—
310	C₂²×C₄	—	5	2	no	—
311	C₂²×C₄	—	5	4	no	—
312	C₂²×C₄	C₂×C₃×Dic₅	1	8	yes	—
313	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
314	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
315	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
316	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
317	C₄⋊C₄	—	10	8	no	—
318	C₄⋊C₄	—	10	4	no	—
319	C₄⋊C₄	C₂×C₃×Dic₅	1	4	yes	—
320	C₂²⋊C₄	—	10	8	no	—
321	C₂²⋊C₄	—	10	8	no	—
322	C₂²⋊C₄	C₂×C₃×Dic₅	1	8	yes	—
323	C₄²	—	5	4	no	—
324	C₄²	—	10	4	no	—
325	C₄²	—	10	4	no	—
326	C₄²	—	10	4	no	—
327	C₄²	—	10	2	no	—
328	C₄²	C₂×C₃×Dic₅	1	4	yes	—
329	C₃×C₅	#2293	1	1	yes	characteristic, complemented, Hall
330	C₂²×C₃	—	2	4	no	—
331	C₂²×C₃	—	2	4	no	—
332	C₂²×C₃	—	2	4	no	—
333	C₂²×C₃	—	4	4	no	—
334	C₂²×C₃	—	4	4	no	—
335	C₂²×C₃	C₂×#709	1	2	yes	—
336	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
337	C₂²×C₃	C₂×#711	1	1	yes	characteristic
338	C₂²×C₃	D₅×#41	1	2	yes	—
339	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
340	C₃×C₄	—	2	4	no	—
341	C₃×C₄	—	2	2	no	—
342	C₃×C₄	—	10	4	no	—
343	C₃×C₄	—	10	4	no	—
344	C₃×C₄	—	20	4	no	—
345	C₃×C₄	#4072	1	4	yes	complemented
346	C₃×C₄	D₄×Dic₅	1	4	yes	—
347	C₂×C₅	—	4	4	no	—
348	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
349	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
350	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
351	C₂×C₅	C₃×#529	1	2	yes	—
352	C₂×C₅	C₃×#532	1	2	yes	—
353	C₂³	—	2	4	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	4	no	—
357	C₂³	C₂²×C₃×Dic₅	1	4	yes	—
358	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
359	D₄	—	2	8	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	16	no	—
364	C₂×C₄	—	5	4	no	—
365	C₂×C₄	—	5	4	no	—
366	C₂×C₄	—	10	2	no	—
367	C₂×C₄	—	10	2	no	—
368	C₂×C₄	—	10	2	no	—
369	C₂×C₄	—	10	2	no	—
370	C₂×C₄	—	10	4	no	—
371	C₂×C₄	—	10	4	no	—
372	C₂×C₄	—	10	4	no	—
373	C₂×C₄	C₃×#709	1	4	yes	—
374	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
375	C₂×C₄	C₃×#711	1	2	yes	—
376	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
377	C₂×C₄	C₂²×C₃×Dic₅	1	4	yes	—
378	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
379	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
380	C₂×C₃	—	4	4	no	—
381	C₂×C₃	#65882	1	2	yes	—
382	C₂×C₃	#65891	1	2	yes	—
383	C₂×C₃	C₂×#4072	1	1	yes	characteristic
384	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
385	C₂×C₃	#41×Dic₅	1	1	yes	characteristic
386	C₅	C₃×#2293	1	1	yes	characteristic, complemented, Sylow
387	C₂²	—	2	4	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	4	no	—
392	C₂²	C₂×C₃×#709	1	2	yes	—
393	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
394	C₂²	C₂×C₃×#711	1	1	yes	characteristic
395	C₂²	C₃×D₅×#41	1	2	yes	—
396	C₂²	C₂³×C₃×Dic₅	1	1	yes	characteristic
397	C₄	—	2	4	no	—
398	C₄	—	2	2	no	—
399	C₄	—	10	4	no	—
400	C₄	—	10	4	no	—
401	C₄	—	20	4	no	—
402	C₄	C₃×#4072	1	4	yes	complemented
403	C₄	C₃×D₄×Dic₅	1	4	yes	—
404	C₃	#10614050	1	1	yes	characteristic, direct product factor, Sylow
405	C₂	—	4	4	no	—
406	C₂	C₃×#65882	1	2	yes	—
407	C₂	C₃×#65891	1	2	yes	—
408	C₂	C₂×C₃×#4072	1	1	yes	characteristic
409	C₂	C₂×C₃×D₄×Dic₅	1	1	yes	characteristic
410	C₂	C₃×#41×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₃×C₅×D₄	C₂²
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₄×D₄	D₅
hypocenter	C₅	C₃×#2293
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4072	C₂	semidirect
4. C₃×C₄×C₂²⋊Dic₅	C₂	semidirect
5. C₃×#65274	C₂	semidirect
6. C₃×#65240	C₂	semidirect
7. C₃×C₄×C₄⋊Dic₅	C₂	semidirect
8. C₃×C₄²×Dic₅	C₂	semidirect
9. #10614050	C₃	direct (N × H)
12. C₃×C₄×C₅×D₄	C₄	semidirect
30. C₂×#4072	C₂×C₃	semidirect
32. C₄×C₂²⋊Dic₅	C₂×C₃	semidirect
33. #65274	C₂×C₃	semidirect
34. #65240	C₂×C₃	semidirect
35. C₄×C₄⋊Dic₅	C₂×C₃	semidirect
36. C₄²×Dic₅	C₂×C₃	semidirect
61. C₃×C₄×Dic₅	D₄	semidirect
72. C₄×C₅×D₄	C₃×C₄	semidirect
118. C₃×C₄×D₄	Dic₅	semidirect
158. C₄×Dic₅	C₃×D₄	semidirect
179. C₃×C₄×C₅	#117	semidirect
238. C₄×D₄	C₃×Dic₅	semidirect
299. C₄×C₅	C₃×#117	semidirect
329. C₃×C₅	#2293	semidirect
345. C₃×C₄	#4072	semidirect
386. C₅	C₃×#2293	semidirect
402. C₄	C₃×#4072	semidirect
404. C₃	#10614050	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×C₄×C₅×D₄	2
C₂×C₃×#4072	2
C₃×#65510	2
C₃×C₄×C₂²⋊Dic₅	2
C₃×#65274	2
C₃×#65240	2
C₃×C₄×C₄⋊Dic₅	2
C₃×C₄²×Dic₅	2
#10614050	3
C₃×#2293	5

Subgroups — C3×#10614050 #14320833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10614050 #14320833