Subgroups — C₂×C₃×#65280 #14331529

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#685	C₂	1	2	yes	maximal, complemented
4	C₂²×C₃×#685	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#3963	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65280	C₂	1	8	yes	maximal, direct product factor
7	C₂×#65280	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁴×C₃×D₅	C₂²	1	2	yes	—
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂³×C₃×Dic₅	C₂²	1	2	yes	—
13	C₂²×C₃×D₂₀	—	2	8	no	—
14	C₂²×C₃×D₂₀	—	2	4	no	—
15	C₂²×C₃×D₂₀	C₂²	1	4	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
18	C₂×C₃×#685	—	2	8	no	—
19	C₂×C₃×#685	—	2	8	no	—
20	C₂×C₃×#685	C₂²	1	8	yes	complemented
21	C₂×C₃×#685	C₂²	1	8	yes	complemented
22	C₃×#3963	C₂²	1	4	yes	complemented
23	C₂×C₃×#394	—	5	1	no	maximal, Hall
24	C₂³×D₂₀	C₂×C₃	1	1	yes	characteristic
25	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂²×#685	C₂×C₃	1	2	yes	complemented
27	C₂²×#685	C₂×C₃	1	2	yes	complemented
28	C₂×#3963	C₂×C₃	1	1	yes	characteristic, complemented
29	#65280	C₂×C₃	1	8	yes	direct product factor
30	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
31	C₂³×C₃×D₅	—	2	4	no	—
32	C₂³×C₃×D₅	—	2	4	no	—
33	C₂³×C₃×D₅	—	2	4	no	—
34	C₂³×C₃×D₅	—	2	4	no	—
35	C₂³×C₃×D₅	—	2	4	no	—
36	C₂³×C₃×D₅	—	2	4	no	—
37	C₂³×C₃×D₅	D₄	1	8	yes	—
38	C₂³×C₃×D₅	C₂³	1	4	yes	—
39	C₂²×C₃×C₄×C₅	—	2	4	no	—
40	C₂²×C₃×C₄×C₅	—	2	2	no	—
41	C₂²×C₃×C₄×C₅	—	2	2	no	—
42	C₂²×C₃×C₄×C₅	—	2	2	no	—
43	C₂²×C₃×C₄×C₅	—	2	4	no	—
44	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
45	C₂²×C₃×C₄×C₅	D₄	1	4	yes	complemented
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×Dic₅	—	2	4	no	—
50	C₂²×C₃×Dic₅	—	2	4	no	—
51	C₂²×C₃×Dic₅	—	2	4	no	—
52	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
53	C₂×C₃×D₂₀	—	2	32	no	—
54	C₂×C₃×D₂₀	—	2	16	no	—
55	C₂×C₃×D₂₀	—	2	8	no	—
56	C₃×C₅×C₄⋊C₄	—	2	8	no	—
57	C₃×#685	—	2	16	no	—
58	C₃×#685	—	2	16	no	—
59	C₂³×C₃×D₄	—	5	1	no	—
60	C₂²×C₃×C₄⋊C₄	D₅	1	1	yes	characteristic, complemented
61	C₂²×C₃×C₂²⋊C₄	—	5	2	no	—
62	C₂²×C₃×C₂²⋊C₄	—	5	2	no	—
63	C₃×#394	—	5	8	no	—
64	C₂×C₃×#95	—	5	1	no	—
65	C₂⁴×D₅	C₂²×C₃	1	2	yes	—
66	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
67	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
68	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
69	C₂³×Dic₅	C₂²×C₃	1	2	yes	—
70	C₂²×D₂₀	—	2	8	no	—
71	C₂²×D₂₀	—	2	4	no	—
72	C₂²×D₂₀	C₂²×C₃	1	4	yes	—
73	C₂×C₅×C₄⋊C₄	—	2	4	no	—
74	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
75	C₂×#685	—	2	8	no	—
76	C₂×#685	—	2	8	no	—
77	C₂×#685	C₂²×C₃	1	8	yes	complemented
78	C₂×#685	C₂²×C₃	1	8	yes	complemented
79	#3963	C₂²×C₃	1	4	yes	complemented
80	C₂×#394	—	5	1	no	Sylow
81	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
82	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
83	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
84	C₂³×C₃×C₅	#41	1	2	yes	—
85	C₂³×C₃×C₅	#41	1	4	yes	—
86	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
87	C₂²×C₃×D₅	—	2	16	no	—
88	C₂²×C₃×D₅	—	2	16	no	—
89	C₂²×C₃×D₅	—	2	16	no	—
90	C₂²×C₃×D₅	—	2	4	no	—
91	C₂²×C₃×D₅	—	2	4	no	—
92	C₂²×C₃×D₅	—	2	4	no	—
93	C₂²×C₃×D₅	—	2	4	no	—
94	C₂²×C₃×D₅	—	2	4	no	—
95	C₂²×C₃×D₅	—	2	4	no	—
96	C₂²×C₃×D₅	—	4	8	no	—
97	C₂²×C₃×D₅	—	4	8	no	—
98	C₂²×C₃×D₅	—	4	8	no	—
99	C₂²×C₃×D₅	—	4	8	no	—
100	C₂²×C₃×D₅	C₂×D₄	1	8	yes	—
101	C₂×C₃×C₄×C₅	—	2	8	no	—
102	C₂×C₃×C₄×C₅	—	2	8	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	4	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	4	4	no	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	complemented
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	—	4	8	no	—
115	C₃×D₂₀	—	2	32	no	—
116	C₂⁵×C₃	—	5	2	no	—
117	C₂²×C₃×D₄	—	5	4	no	—
118	C₂²×C₃×D₄	—	10	8	no	—
119	C₂²×C₃×D₄	—	10	4	no	—
120	C₂³×C₃×C₄	—	5	2	no	—
121	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
122	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
123	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
124	C₂×C₃×C₄⋊C₄	—	2	4	no	—
125	C₂×C₃×C₄⋊C₄	C₂×D₅	1	4	yes	complemented
126	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
127	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
128	C₂×C₃×C₂²⋊C₄	—	10	8	no	—
129	C₂×C₃×C₂²⋊C₄	—	10	8	no	—
130	C₃×#95	—	5	4	no	—
131	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
132	C₂³×D₅	—	2	4	no	—
133	C₂³×D₅	—	2	4	no	—
134	C₂³×D₅	—	2	4	no	—
135	C₂³×D₅	—	2	4	no	—
136	C₂³×D₅	—	2	4	no	—
137	C₂³×D₅	—	2	4	no	—
138	C₂³×D₅	C₃×D₄	1	8	yes	—
139	C₂³×D₅	C₂³×C₃	1	4	yes	—
140	C₂²×C₄×C₅	—	2	2	no	—
141	C₂²×C₄×C₅	—	2	4	no	—
142	C₂²×C₄×C₅	—	2	2	no	—
143	C₂²×C₄×C₅	—	2	2	no	—
144	C₂²×C₄×C₅	—	2	4	no	—
145	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
146	C₂²×C₄×C₅	C₃×D₄	1	4	yes	complemented
147	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
148	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
149	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
150	C₂²×Dic₅	—	2	4	no	—
151	C₂²×Dic₅	—	2	4	no	—
152	C₂²×Dic₅	—	2	4	no	—
153	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
154	C₂×D₂₀	—	2	32	no	—
155	C₂×D₂₀	—	2	16	no	—
156	C₂×D₂₀	—	2	8	no	—
157	C₅×C₄⋊C₄	—	2	8	no	—
158	#685	—	2	16	no	—
159	#685	—	2	16	no	—
160	C₂³×D₄	—	5	1	no	—
161	C₂²×C₄⋊C₄	C₃×D₅	1	1	yes	characteristic, complemented
162	C₂²×C₂²⋊C₄	—	5	2	no	—
163	C₂²×C₂²⋊C₄	—	5	2	no	—
164	#394	—	5	8	no	—
165	C₂×#95	—	5	1	no	—
166	C₂²×C₃×C₅	#120	1	4	yes	—
167	C₂²×C₃×C₅	#121	1	8	yes	—
168	C₂²×C₃×C₅	#121	1	4	yes	—
169	C₂²×C₃×C₅	#123	1	8	yes	—
170	C₂²×C₃×C₅	#124	1	4	yes	—
171	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
172	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
173	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
174	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
175	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
176	C₂×C₃×D₅	—	2	8	no	—
177	C₂×C₃×D₅	—	2	8	no	—
178	C₂×C₃×D₅	—	2	8	no	—
179	C₂×C₃×D₅	—	4	4	no	—
180	C₂×C₃×D₅	—	4	4	no	—
181	C₂×C₃×D₅	—	4	4	no	—
182	C₂×C₃×D₅	—	4	4	no	—
183	C₂×C₃×D₅	—	4	32	no	—
184	C₃×C₄×C₅	—	2	4	no	—
185	C₃×C₄×C₅	—	2	4	no	—
186	C₃×C₄×C₅	—	4	2	no	—
187	C₃×Dic₅	—	4	4	no	—
188	C₂⁴×C₃	—	5	8	no	—
189	C₂⁴×C₃	—	5	4	no	—
190	C₂⁴×C₃	—	10	4	no	—
191	C₂⁴×C₃	—	10	4	no	—
192	C₂⁴×C₃	—	10	4	no	—
193	C₂⁴×C₃	—	10	4	no	—
194	C₂⁴×C₃	—	10	4	no	—
195	C₂⁴×C₃	—	10	4	no	—
196	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
197	C₂×C₃×D₄	—	10	16	no	—
198	C₂×C₃×D₄	—	10	32	no	—
199	C₂×C₃×D₄	—	10	8	no	—
200	C₂²×C₃×C₄	—	2	2	no	—
201	C₂²×C₃×C₄	—	2	4	no	—
202	C₂²×C₃×C₄	—	2	2	no	—
203	C₂²×C₃×C₄	—	2	4	no	—
204	C₂²×C₃×C₄	—	2	2	no	—
205	C₂²×C₃×C₄	—	5	4	no	—
206	C₂²×C₃×C₄	—	10	4	no	—
207	C₂²×C₃×C₄	—	10	4	no	—
208	C₂²×C₃×C₄	—	10	4	no	—
209	C₂²×C₃×C₄	D₂₀	1	4	yes	complemented
210	C₂²×C₃×C₄	C₂²⋊D₅	1	4	yes	—
211	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
212	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
213	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
214	C₃×C₄⋊C₄	—	2	8	no	—
215	C₃×C₂²⋊C₄	—	10	16	no	—
216	C₃×C₂²⋊C₄	—	10	16	no	—
217	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
218	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
219	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
220	C₂³×C₅	C₃×#41	1	2	yes	—
221	C₂³×C₅	C₃×#41	1	4	yes	—
222	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
223	C₂²×D₅	—	2	16	no	—
224	C₂²×D₅	—	2	16	no	—
225	C₂²×D₅	—	2	16	no	—
226	C₂²×D₅	—	2	4	no	—
227	C₂²×D₅	—	2	4	no	—
228	C₂²×D₅	—	2	4	no	—
229	C₂²×D₅	—	2	4	no	—
230	C₂²×D₅	—	2	4	no	—
231	C₂²×D₅	—	2	4	no	—
232	C₂²×D₅	—	4	8	no	—
233	C₂²×D₅	—	4	8	no	—
234	C₂²×D₅	—	4	8	no	—
235	C₂²×D₅	—	4	8	no	—
236	C₂²×D₅	C₂×C₃×D₄	1	8	yes	—
237	C₂×C₄×C₅	—	2	8	no	—
238	C₂×C₄×C₅	—	2	8	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	4	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	4	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	4	4	no	—
245	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
246	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	complemented
247	C₂×Dic₅	—	2	4	no	—
248	C₂×Dic₅	—	2	4	no	—
249	C₂×Dic₅	—	2	4	no	—
250	C₂×Dic₅	—	4	8	no	—
251	D₂₀	—	2	32	no	—
252	C₂⁵	—	5	2	no	—
253	C₂²×D₄	—	5	4	no	—
254	C₂²×D₄	—	10	8	no	—
255	C₂²×D₄	—	10	4	no	—
256	C₂³×C₄	—	5	2	no	—
257	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
258	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
259	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
260	C₂×C₄⋊C₄	—	2	4	no	—
261	C₂×C₄⋊C₄	C₂×C₃×D₅	1	4	yes	complemented
262	C₂×C₂²⋊C₄	—	5	8	no	—
263	C₂×C₂²⋊C₄	—	5	8	no	—
264	C₂×C₂²⋊C₄	—	10	8	no	—
265	C₂×C₂²⋊C₄	—	10	8	no	—
266	#95	—	5	4	no	—
267	C₂×C₃×C₅	#394	1	8	yes	complemented
268	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
269	C₂×C₃×C₅	C₂×#121	1	2	yes	—
270	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
271	C₂×C₃×C₅	C₂×#123	1	2	yes	—
272	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
273	C₃×D₅	—	4	8	no	—
274	C₂³×C₃	—	5	8	no	—
275	C₂³×C₃	—	10	4	no	—
276	C₂³×C₃	—	10	4	no	—
277	C₂³×C₃	—	10	4	no	—
278	C₂³×C₃	—	10	4	no	—
279	C₂³×C₃	—	10	4	no	—
280	C₂³×C₃	—	10	4	no	—
281	C₂³×C₃	—	10	16	no	—
282	C₂³×C₃	—	10	16	no	—
283	C₂³×C₃	—	10	16	no	—
284	C₂³×C₃	—	20	8	no	—
285	C₂³×C₃	—	20	8	no	—
286	C₂³×C₃	—	20	8	no	—
287	C₂³×C₃	—	20	8	no	—
288	C₂³×C₃	C₂×D₂₀	1	2	yes	—
289	C₂³×C₃	#709	1	2	yes	—
290	C₂³×C₃	D₄×D₅	1	4	yes	—
291	C₂³×C₃	#713	1	4	yes	—
292	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
293	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
294	C₃×D₄	—	10	32	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	4	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	8	no	—
299	C₂×C₃×C₄	—	2	8	no	—
300	C₂×C₃×C₄	—	2	4	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	4	4	no	—
303	C₂×C₃×C₄	—	10	4	no	—
304	C₂×C₃×C₄	—	10	4	no	—
305	C₂×C₃×C₄	—	10	4	no	—
306	C₂×C₃×C₄	—	20	8	no	—
307	C₂×C₃×C₄	C₂×D₂₀	1	4	yes	complemented
308	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
309	C₂²×C₅	C₃×#120	1	4	yes	—
310	C₂²×C₅	C₃×#121	1	8	yes	—
311	C₂²×C₅	C₃×#121	1	4	yes	—
312	C₂²×C₅	C₃×#123	1	8	yes	—
313	C₂²×C₅	C₃×#124	1	4	yes	—
314	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
315	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
316	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
317	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
318	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
319	C₂×D₅	—	2	8	no	—
320	C₂×D₅	—	2	8	no	—
321	C₂×D₅	—	2	8	no	—
322	C₂×D₅	—	4	32	no	—
323	C₂×D₅	—	4	4	no	—
324	C₂×D₅	—	4	4	no	—
325	C₂×D₅	—	4	4	no	—
326	C₂×D₅	—	4	4	no	—
327	C₄×C₅	—	2	4	no	—
328	C₄×C₅	—	2	4	no	—
329	C₄×C₅	—	4	2	no	—
330	Dic₅	—	4	4	no	—
331	C₂⁴	—	5	8	no	—
332	C₂⁴	—	5	4	no	—
333	C₂⁴	—	10	4	no	—
334	C₂⁴	—	10	4	no	—
335	C₂⁴	—	10	4	no	—
336	C₂⁴	—	10	4	no	—
337	C₂⁴	—	10	4	no	—
338	C₂⁴	—	10	4	no	—
339	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
340	C₂×D₄	—	10	16	no	—
341	C₂×D₄	—	10	32	no	—
342	C₂×D₄	—	10	8	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	5	4	no	—
349	C₂²×C₄	—	10	4	no	—
350	C₂²×C₄	—	10	4	no	—
351	C₂²×C₄	—	10	4	no	—
352	C₂²×C₄	C₃×D₂₀	1	4	yes	complemented
353	C₂²×C₄	C₃×C₂²⋊D₅	1	4	yes	—
354	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
355	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
356	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
357	C₄⋊C₄	—	2	8	no	—
358	C₂²⋊C₄	—	10	16	no	—
359	C₂²⋊C₄	—	10	16	no	—
360	C₃×C₅	C₂×#394	1	1	yes	characteristic, complemented, Hall
361	C₂²×C₃	—	10	8	no	—
362	C₂²×C₃	—	10	8	no	—
363	C₂²×C₃	—	10	8	no	—
364	C₂²×C₃	—	20	32	no	—
365	C₂²×C₃	—	20	4	no	—
366	C₂²×C₃	—	20	4	no	—
367	C₂²×C₃	—	20	4	no	—
368	C₂²×C₃	—	20	4	no	—
369	C₂²×C₃	#4040	1	8	yes	—
370	C₂²×C₃	#4041	1	8	yes	—
371	C₂²×C₃	#4076	1	4	yes	—
372	C₂²×C₃	#4083	1	4	yes	—
373	C₂²×C₃	#4093	1	4	yes	—
374	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
375	C₂²×C₃	C₂×#709	1	1	yes	characteristic
376	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
377	C₂²×C₃	C₂×#713	1	2	yes	—
378	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
379	C₃×C₄	—	2	4	no	—
380	C₃×C₄	—	2	4	no	—
381	C₃×C₄	—	4	2	no	—
382	C₃×C₄	—	20	4	no	—
383	C₂×C₅	C₃×#394	1	8	yes	complemented
384	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
385	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
386	C₂×C₅	C₂×C₃×#121	1	2	yes	—
387	C₂×C₅	C₂×C₃×#123	1	2	yes	—
388	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
389	D₅	—	4	8	no	—
390	C₂³	—	5	8	no	—
391	C₂³	—	10	16	no	—
392	C₂³	—	10	4	no	—
393	C₂³	—	10	4	no	—
394	C₂³	—	10	4	no	—
395	C₂³	—	10	4	no	—
396	C₂³	—	10	4	no	—
397	C₂³	—	10	4	no	—
398	C₂³	—	10	16	no	—
399	C₂³	—	10	16	no	—
400	C₂³	—	20	8	no	—
401	C₂³	—	20	8	no	—
402	C₂³	—	20	8	no	—
403	C₂³	—	20	8	no	—
404	C₂³	C₂×C₃×D₂₀	1	2	yes	—
405	C₂³	C₃×#709	1	2	yes	—
406	C₂³	C₃×D₄×D₅	1	4	yes	—
407	C₂³	C₃×#713	1	4	yes	—
408	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
409	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
410	D₄	—	10	32	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	10	4	no	—
420	C₂×C₄	—	10	4	no	—
421	C₂×C₄	—	10	4	no	—
422	C₂×C₄	—	20	8	no	—
423	C₂×C₄	C₂×C₃×D₂₀	1	4	yes	complemented
424	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
425	C₂×C₃	—	20	8	no	—
426	C₂×C₃	#65280	1	8	yes	direct product factor
427	C₂×C₃	C₂×#4040	1	2	yes	—
428	C₂×C₃	C₂×#4041	1	2	yes	—
429	C₂×C₃	C₂×#4076	1	1	yes	characteristic
430	C₂×C₃	C₂×#4083	1	1	yes	characteristic
431	C₂×C₃	C₂×#4093	1	1	yes	characteristic
432	C₅	C₂×C₃×#394	1	1	yes	characteristic, complemented, Sylow
433	C₂²	—	10	8	no	—
434	C₂²	—	10	8	no	—
435	C₂²	—	10	8	no	—
436	C₂²	—	20	32	no	—
437	C₂²	—	20	4	no	—
438	C₂²	—	20	4	no	—
439	C₂²	—	20	4	no	—
440	C₂²	—	20	4	no	—
441	C₂²	C₃×#4040	1	8	yes	—
442	C₂²	C₃×#4041	1	8	yes	—
443	C₂²	C₃×#4076	1	4	yes	—
444	C₂²	C₃×#4083	1	4	yes	—
445	C₂²	C₃×#4093	1	4	yes	—
446	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
447	C₂²	C₂×C₃×#709	1	1	yes	characteristic
448	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
449	C₂²	C₂×C₃×#713	1	2	yes	—
450	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
451	C₄	—	2	4	no	—
452	C₄	—	2	4	no	—
453	C₄	—	4	2	no	—
454	C₄	—	20	4	no	—
455	C₃	C₂×#65280	1	1	yes	characteristic, direct product factor, Sylow
456	C₂	—	20	8	no	—
457	C₂	C₃×#65280	1	8	yes	direct product factor
458	C₂	C₂×C₃×#4040	1	2	yes	—
459	C₂	C₂×C₃×#4041	1	2	yes	—
460	C₂	C₂×C₃×#4076	1	1	yes	characteristic
461	C₂	C₂×C₃×#4083	1	1	yes	characteristic
462	C₂	C₂×C₃×#4093	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₃	C₂²×D₅
commutator, cosocle	C₂³×C₅	C₂⁴×C₃
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₂²×C₃×C₅×C₄⋊C₄	C₂
socle	C₂⁴×C₃×C₅	C₂³
prime radical	C₂³×C₃×D₂₀	C₂
hypercenter	C₂²×C₃×C₄⋊C₄	D₅
hypocenter	C₅	C₂×C₃×#394
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂²×C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₅×C₄⋊C₄	C₂	semidirect
3. C₂²×C₃×#685	C₂	semidirect
4. C₂²×C₃×#685	C₂	semidirect
5. C₂×C₃×#3963	C₂	semidirect
6. C₃×#65280	C₂	direct (N × H)
7. C₂×#65280	C₃	direct (N × H)
17. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
20. C₂×C₃×#685	C₂²	semidirect
21. C₂×C₃×#685	C₂²	semidirect
22. C₃×#3963	C₂²	semidirect
25. C₂²×C₅×C₄⋊C₄	C₂×C₃	semidirect
26. C₂²×#685	C₂×C₃	semidirect
27. C₂²×#685	C₂×C₃	semidirect
28. C₂×#3963	C₂×C₃	semidirect
29. #65280	C₂×C₃	direct (N × H)
45. C₂²×C₃×C₄×C₅	D₄	semidirect
60. C₂²×C₃×C₄⋊C₄	D₅	semidirect
74. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
77. C₂×#685	C₂²×C₃	semidirect
78. C₂×#685	C₂²×C₃	semidirect
79. #3963	C₂²×C₃	semidirect
110. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
125. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
146. C₂²×C₄×C₅	C₃×D₄	semidirect
161. C₂²×C₄⋊C₄	C₃×D₅	semidirect
209. C₂²×C₃×C₄	D₂₀	semidirect
246. C₂×C₄×C₅	C₂×C₃×D₄	semidirect
261. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
267. C₂×C₃×C₅	#394	semidirect
307. C₂×C₃×C₄	C₂×D₂₀	semidirect
352. C₂²×C₄	C₃×D₂₀	semidirect
360. C₃×C₅	C₂×#394	semidirect
383. C₂×C₅	C₃×#394	semidirect
423. C₂×C₄	C₂×C₃×D₂₀	semidirect
426. C₂×C₃	#65280	direct (N × H)
432. C₅	C₂×C₃×#394	semidirect
455. C₃	C₂×#65280	direct (N × H)
457. C₂	C₃×#65280	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×D₂₀	2
C₂²×C₃×C₅×C₄⋊C₄	2
C₂²×C₃×#685	2
C₂×C₃×#3963	2
C₃×#65280	2
C₂×#65280	3
C₂×C₃×#394	5

Subgroups — C2×C3×#65280 #14331529

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65280 #14331529