Subgroups — C₂×C₃×#65021 #14423188

Order 1920.

2096 conjugacy classes of subgroups.

The subgroup lattice has 480 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, complemented
2	C₂×C₃×#4076	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×D₄₀	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3953	C₂	1	2	yes	maximal, complemented
6	C₃×#65021	C₂	1	8	yes	maximal, direct product factor
7	C₂×#65021	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁴×C₃×D₅	—	2	1	no	—
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₂²⋊D₅	—	2	1	no	—
11	C₂²×C₃×D₂₀	—	2	2	no	—
12	C₂²×C₃×D₂₀	—	2	1	no	—
13	C₂²×C₃×D₂₀	—	2	8	no	—
14	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
15	C₂²×C₃×D₂₀	C₂²	1	4	yes	complemented
16	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
18	C₃×#4076	—	2	2	no	—
19	C₃×#4076	C₂²	1	4	yes	complemented
20	C₂×C₃×#685	—	2	1	no	—
21	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×D₄₀	—	2	8	no	—
23	C₂×C₃×D₄₀	C₂²	1	8	yes	complemented
24	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	complemented
25	C₃×#3953	C₂²	1	8	yes	complemented
26	C₂×C₃×#447	—	5	1	no	maximal, Hall
27	C₂³×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×#4076	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂²×D₄₀	C₂×C₃	1	2	yes	complemented
30	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×#3953	C₂×C₃	1	2	yes	complemented
32	#65021	C₂×C₃	1	8	yes	direct product factor
33	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
34	C₂³×C₃×D₅	—	2	8	no	—
35	C₂³×C₃×D₅	—	2	2	no	—
36	C₂³×C₃×D₅	—	2	4	no	—
37	C₂³×C₃×D₅	—	2	1	no	—
38	C₂³×C₃×D₅	—	4	4	no	—
39	C₂³×C₃×D₅	—	4	4	no	—
40	C₂²×C₃×C₄×C₅	—	2	4	no	—
41	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
46	C₂×C₃×C₂²⋊D₅	—	4	4	no	—
47	C₂²×C₃×Dic₅	—	2	1	no	—
48	C₂×C₃×D₂₀	—	2	8	no	—
49	C₂×C₃×D₂₀	—	2	16	no	—
50	C₂×C₃×D₂₀	—	2	2	no	—
51	C₂×C₃×D₂₀	—	2	4	no	—
52	C₂×C₃×D₂₀	—	2	4	no	—
53	C₂×C₃×D₂₀	—	2	16	no	—
54	C₂×C₃×D₂₀	—	2	4	no	—
55	C₂×C₃×D₂₀	—	2	1	no	—
56	C₂×C₃×D₂₀	D₄	1	8	yes	complemented
57	C₂×C₃×D₂₀	C₂³	1	4	yes	—
58	C₂×C₃×D₂₀	C₂³	1	2	yes	complemented
59	C₂×C₃×C₅×C₈	—	2	4	no	—
60	C₂×C₃×C₅×C₈	C₂³	1	4	yes	complemented
61	C₃×#685	—	2	4	no	—
62	C₃×C₄⋊Dic₅	—	2	1	no	—
63	C₃×C₄⋊Dic₅	C₂³	1	2	yes	complemented
64	C₃×D₄₀	—	2	16	no	—
65	C₂³×C₃×D₄	—	5	1	no	—
66	C₂²×C₃×D₈	—	5	2	no	—
67	C₂×C₃×#121	—	5	1	no	—
68	C₃×#447	—	5	8	no	—
69	C₂×C₃×#102	—	5	2	no	—
70	C₂×C₃×C₂²⋊C₈	D₅	1	1	yes	characteristic, complemented
71	C₂⁴×D₅	—	2	1	no	—
72	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₂²⋊D₅	—	2	1	no	—
74	C₂²×D₂₀	—	2	2	no	—
75	C₂²×D₂₀	—	2	1	no	—
76	C₂²×D₂₀	—	2	8	no	—
77	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
78	C₂²×D₂₀	C₂²×C₃	1	4	yes	complemented
79	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
80	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	complemented
81	#4076	—	2	2	no	—
82	#4076	C₂²×C₃	1	4	yes	complemented
83	C₂×#685	—	2	1	no	—
84	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
85	C₂×D₄₀	—	2	8	no	—
86	C₂×D₄₀	C₂²×C₃	1	8	yes	complemented
87	C₅×C₂²⋊C₈	C₂²×C₃	1	4	yes	complemented
88	#3953	C₂²×C₃	1	8	yes	complemented
89	C₂×#447	—	5	1	no	Sylow
90	C₂³×C₃×C₅	—	2	2	no	—
91	C₂³×C₃×C₅	—	2	2	no	—
92	C₂³×C₃×C₅	D₈	1	4	yes	complemented
93	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
94	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₃×D₅	—	2	16	no	—
96	C₂²×C₃×D₅	—	2	8	no	—
97	C₂²×C₃×D₅	—	2	4	no	—
98	C₂²×C₃×D₅	—	2	2	no	—
99	C₂²×C₃×D₅	—	4	8	no	—
100	C₂²×C₃×D₅	—	4	32	no	—
101	C₂²×C₃×D₅	—	4	4	no	—
102	C₂²×C₃×D₅	—	4	8	no	—
103	C₂²×C₃×D₅	—	4	4	no	—
104	C₂²×C₃×D₅	—	4	2	no	—
105	C₂²×C₃×D₅	—	4	2	no	—
106	C₂²×C₃×D₅	—	4	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	4	no	—
109	C₂×C₃×C₄×C₅	—	2	4	no	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
113	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
114	C₃×C₂²⋊D₅	—	4	8	no	—
115	C₂×C₃×Dic₅	—	2	2	no	—
116	C₂×C₃×Dic₅	—	4	2	no	—
117	C₃×D₂₀	—	2	16	no	—
118	C₃×D₂₀	—	2	8	no	—
119	C₃×D₂₀	—	2	4	no	—
120	C₃×D₂₀	—	2	4	no	—
121	C₃×D₂₀	—	4	2	no	—
122	C₃×D₂₀	C₂×D₄	1	8	yes	complemented
123	C₃×C₅×C₈	—	2	4	no	—
124	C₂⁵×C₃	—	10	1	no	—
125	C₂²×C₃×D₄	—	5	2	no	—
126	C₂²×C₃×D₄	—	5	1	no	—
127	C₂²×C₃×D₄	—	5	4	no	—
128	C₂²×C₃×D₄	—	10	8	no	—
129	C₂²×C₃×D₄	—	10	1	no	—
130	C₂²×C₃×D₄	—	10	2	no	—
131	C₂²×C₃×D₄	—	10	1	no	—
132	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
133	C₂×C₃×D₈	—	5	8	no	—
134	C₂×C₃×D₈	—	10	8	no	—
135	C₂²×C₃×C₈	C₂×D₅	1	2	yes	complemented
136	C₃×#121	—	5	4	no	—
137	C₃×#121	—	10	2	no	—
138	C₂×C₃×C₄⋊C₄	—	5	1	no	—
139	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
140	C₃×#102	—	5	8	no	—
141	C₃×C₂²⋊C₈	C₂×D₅	1	4	yes	complemented
142	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
143	C₂³×D₅	—	2	8	no	—
144	C₂³×D₅	—	2	2	no	—
145	C₂³×D₅	—	2	4	no	—
146	C₂³×D₅	—	2	1	no	—
147	C₂³×D₅	—	4	4	no	—
148	C₂³×D₅	—	4	4	no	—
149	C₂²×C₄×C₅	—	2	4	no	—
150	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
152	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
153	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
154	C₂×C₂²⋊D₅	—	2	4	no	—
155	C₂×C₂²⋊D₅	—	4	4	no	—
156	C₂²×Dic₅	—	2	1	no	—
157	C₂×D₂₀	—	2	8	no	—
158	C₂×D₂₀	—	2	16	no	—
159	C₂×D₂₀	—	2	2	no	—
160	C₂×D₂₀	—	2	4	no	—
161	C₂×D₂₀	—	2	4	no	—
162	C₂×D₂₀	—	2	16	no	—
163	C₂×D₂₀	—	2	4	no	—
164	C₂×D₂₀	—	2	1	no	—
165	C₂×D₂₀	C₃×D₄	1	8	yes	complemented
166	C₂×D₂₀	C₂³×C₃	1	4	yes	—
167	C₂×D₂₀	C₂³×C₃	1	2	yes	complemented
168	C₂×C₅×C₈	—	2	4	no	—
169	C₂×C₅×C₈	C₂³×C₃	1	4	yes	complemented
170	#685	—	2	4	no	—
171	C₄⋊Dic₅	—	2	1	no	—
172	C₄⋊Dic₅	C₂³×C₃	1	2	yes	complemented
173	D₄₀	—	2	16	no	—
174	C₂³×D₄	—	5	1	no	—
175	C₂²×D₈	—	5	2	no	—
176	C₂×#121	—	5	1	no	—
177	#447	—	5	8	no	—
178	C₂×#102	—	5	2	no	—
179	C₂×C₂²⋊C₈	C₃×D₅	1	1	yes	characteristic, complemented
180	C₂²×C₃×C₅	—	2	2	no	—
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	—	2	8	no	—
183	C₂²×C₃×C₅	#120	1	2	yes	—
184	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
185	C₂²×C₃×C₅	C₂×D₈	1	4	yes	complemented
186	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
187	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₃×D₅	—	2	8	no	—
189	C₂×C₃×D₅	—	4	32	no	—
190	C₂×C₃×D₅	—	4	4	no	—
191	C₂×C₃×D₅	—	4	4	no	—
192	C₂×C₃×D₅	—	4	16	no	—
193	C₂×C₃×D₅	—	4	2	no	—
194	C₂×C₃×D₅	—	4	2	no	—
195	C₂×C₃×D₅	—	4	2	no	—
196	C₂×C₃×D₅	—	8	4	no	—
197	C₃×C₄×C₅	—	2	2	no	—
198	C₃×C₄×C₅	#120	1	2	yes	—
199	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
200	C₃×Dic₅	—	4	2	no	—
201	C₂⁴×C₃	—	10	8	no	—
202	C₂⁴×C₃	—	10	4	no	—
203	C₂⁴×C₃	—	10	2	no	—
204	C₂⁴×C₃	—	10	1	no	—
205	C₂⁴×C₃	—	20	4	no	—
206	C₂⁴×C₃	—	20	4	no	—
207	C₂⁴×C₃	D₂₀	1	1	yes	characteristic
208	C₂×C₃×D₄	—	5	8	no	—
209	C₂×C₃×D₄	—	5	4	no	—
210	C₂×C₃×D₄	—	5	2	no	—
211	C₂×C₃×D₄	—	10	16	no	—
212	C₂×C₃×D₄	—	10	8	no	—
213	C₂×C₃×D₄	—	10	16	no	—
214	C₂×C₃×D₄	—	10	4	no	—
215	C₂×C₃×D₄	—	10	4	no	—
216	C₂×C₃×D₄	—	10	2	no	—
217	C₂×C₃×D₄	—	10	1	no	—
218	C₂×C₃×D₄	—	10	4	no	—
219	C₂×C₃×D₄	—	10	4	no	—
220	C₂×C₃×D₄	—	20	4	no	—
221	C₂²×C₃×C₄	—	2	4	no	—
222	C₂²×C₃×C₄	—	10	1	no	—
223	C₂²×C₃×C₄	D₂₀	1	2	yes	—
224	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
226	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
227	C₃×D₈	—	10	16	no	—
228	C₂×C₃×C₈	—	2	4	no	—
229	C₂×C₃×C₈	C₂²×D₅	1	4	yes	complemented
230	C₃×C₄⋊C₄	—	5	2	no	—
231	C₃×C₄⋊C₄	—	10	1	no	—
232	C₃×C₂²⋊C₄	—	10	4	no	—
233	C₂³×C₅	—	2	2	no	—
234	C₂³×C₅	—	2	2	no	—
235	C₂³×C₅	C₃×D₈	1	4	yes	complemented
236	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
237	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
238	C₂²×D₅	—	2	16	no	—
239	C₂²×D₅	—	2	8	no	—
240	C₂²×D₅	—	2	4	no	—
241	C₂²×D₅	—	2	2	no	—
242	C₂²×D₅	—	4	8	no	—
243	C₂²×D₅	—	4	32	no	—
244	C₂²×D₅	—	4	4	no	—
245	C₂²×D₅	—	4	8	no	—
246	C₂²×D₅	—	4	4	no	—
247	C₂²×D₅	—	4	2	no	—
248	C₂²×D₅	—	4	2	no	—
249	C₂²×D₅	—	4	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	2	4	no	—
252	C₂×C₄×C₅	—	2	4	no	—
253	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
254	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
256	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
257	C₂²⋊D₅	—	4	8	no	—
258	C₂×Dic₅	—	2	2	no	—
259	C₂×Dic₅	—	4	2	no	—
260	D₂₀	—	2	16	no	—
261	D₂₀	—	2	8	no	—
262	D₂₀	—	2	4	no	—
263	D₂₀	—	2	4	no	—
264	D₂₀	—	4	2	no	—
265	D₂₀	C₂×C₃×D₄	1	8	yes	complemented
266	C₅×C₈	—	2	4	no	—
267	C₂⁵	—	10	1	no	—
268	C₂²×D₄	—	5	2	no	—
269	C₂²×D₄	—	5	1	no	—
270	C₂²×D₄	—	5	4	no	—
271	C₂²×D₄	—	10	8	no	—
272	C₂²×D₄	—	10	1	no	—
273	C₂²×D₄	—	10	1	no	—
274	C₂²×D₄	—	10	2	no	—
275	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
276	C₂×D₈	—	5	8	no	—
277	C₂×D₈	—	10	8	no	—
278	C₂²×C₈	C₂×C₃×D₅	1	2	yes	complemented
279	#121	—	5	4	no	—
280	#121	—	10	2	no	—
281	C₂×C₄⋊C₄	—	5	1	no	—
282	C₂×C₂²⋊C₄	—	10	1	no	—
283	#102	—	5	8	no	—
284	C₂²⋊C₈	C₂×C₃×D₅	1	4	yes	complemented
285	C₂×C₃×C₅	—	2	4	no	—
286	C₂×C₃×C₅	#447	1	4	yes	complemented
287	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
288	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
289	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
290	C₃×D₅	—	4	8	no	—
291	C₃×D₅	—	8	2	no	—
292	C₂³×C₃	—	2	2	no	—
293	C₂³×C₃	—	2	2	no	—
294	C₂³×C₃	—	10	16	no	—
295	C₂³×C₃	—	10	4	no	—
296	C₂³×C₃	—	10	8	no	—
297	C₂³×C₃	—	10	2	no	—
298	C₂³×C₃	—	20	8	no	—
299	C₂³×C₃	—	20	32	no	—
300	C₂³×C₃	—	20	4	no	—
301	C₂³×C₃	—	20	8	no	—
302	C₂³×C₃	—	20	4	no	—
303	C₂³×C₃	—	20	2	no	—
304	C₂³×C₃	—	20	2	no	—
305	C₂³×C₃	—	20	2	no	—
306	C₂³×C₃	D₄₀	1	4	yes	complemented
307	C₂³×C₃	C₂×D₂₀	1	2	yes	—
308	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
309	C₃×D₄	—	5	8	no	—
310	C₃×D₄	—	10	16	no	—
311	C₃×D₄	—	10	4	no	—
312	C₃×D₄	—	10	4	no	—
313	C₃×D₄	—	10	8	no	—
314	C₃×D₄	—	20	8	no	—
315	C₃×D₄	—	20	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	4	no	—
318	C₂×C₃×C₄	—	2	4	no	—
319	C₂×C₃×C₄	—	10	2	no	—
320	C₂×C₃×C₄	—	20	2	no	—
321	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
322	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
323	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
324	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
325	C₃×C₈	—	2	4	no	—
326	C₂²×C₅	—	2	2	no	—
327	C₂²×C₅	—	2	8	no	—
328	C₂²×C₅	—	2	2	no	—
329	C₂²×C₅	C₃×#120	1	2	yes	—
330	C₂²×C₅	C₂×C₃×D₈	1	2	yes	—
331	C₂²×C₅	C₂×C₃×D₈	1	4	yes	complemented
332	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
333	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
334	C₂×D₅	—	2	8	no	—
335	C₂×D₅	—	4	32	no	—
336	C₂×D₅	—	4	4	no	—
337	C₂×D₅	—	4	4	no	—
338	C₂×D₅	—	4	16	no	—
339	C₂×D₅	—	4	2	no	—
340	C₂×D₅	—	4	2	no	—
341	C₂×D₅	—	4	2	no	—
342	C₂×D₅	—	8	4	no	—
343	C₄×C₅	—	2	2	no	—
344	C₄×C₅	C₃×#120	1	2	yes	—
345	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
346	Dic₅	—	4	2	no	—
347	C₂⁴	—	10	8	no	—
348	C₂⁴	—	10	4	no	—
349	C₂⁴	—	10	2	no	—
350	C₂⁴	—	10	1	no	—
351	C₂⁴	—	20	4	no	—
352	C₂⁴	—	20	4	no	—
353	C₂⁴	C₃×D₂₀	1	1	yes	characteristic
354	C₂×D₄	—	5	8	no	—
355	C₂×D₄	—	5	4	no	—
356	C₂×D₄	—	5	2	no	—
357	C₂×D₄	—	10	16	no	—
358	C₂×D₄	—	10	8	no	—
359	C₂×D₄	—	10	16	no	—
360	C₂×D₄	—	10	4	no	—
361	C₂×D₄	—	10	4	no	—
362	C₂×D₄	—	10	2	no	—
363	C₂×D₄	—	10	1	no	—
364	C₂×D₄	—	10	4	no	—
365	C₂×D₄	—	10	4	no	—
366	C₂×D₄	—	20	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	10	1	no	—
369	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
370	C₂²×C₄	C₃×D₂₀	1	2	yes	—
371	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
372	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
373	D₈	—	10	16	no	—
374	C₂×C₈	—	2	4	no	—
375	C₂×C₈	C₂²×C₃×D₅	1	4	yes	complemented
376	C₄⋊C₄	—	5	2	no	—
377	C₄⋊C₄	—	10	1	no	—
378	C₂²⋊C₄	—	10	4	no	—
379	C₃×C₅	C₂×#447	1	1	yes	characteristic, complemented, Hall
380	C₂²×C₃	—	2	2	no	—
381	C₂²×C₃	—	2	2	no	—
382	C₂²×C₃	—	2	8	no	—
383	C₂²×C₃	—	10	8	no	—
384	C₂²×C₃	—	20	32	no	—
385	C₂²×C₃	—	20	4	no	—
386	C₂²×C₃	—	20	4	no	—
387	C₂²×C₃	—	20	16	no	—
388	C₂²×C₃	—	20	2	no	—
389	C₂²×C₃	—	20	2	no	—
390	C₂²×C₃	—	20	2	no	—
391	C₂²×C₃	—	40	4	no	—
392	C₂²×C₃	#4028	1	2	yes	—
393	C₂²×C₃	C₂×D₄₀	1	2	yes	—
394	C₂²×C₃	C₂×D₄₀	1	4	yes	complemented
395	C₂²×C₃	#4054	1	2	yes	—
396	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	—	20	2	no	—
399	C₃×C₄	#4028	1	2	yes	—
400	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
401	C₂×C₅	—	2	4	no	—
402	C₂×C₅	C₃×#447	1	4	yes	complemented
403	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
404	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
405	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
406	D₅	—	4	8	no	—
407	D₅	—	8	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	10	16	no	—
411	C₂³	—	10	4	no	—
412	C₂³	—	10	8	no	—
413	C₂³	—	10	2	no	—
414	C₂³	—	20	8	no	—
415	C₂³	—	20	32	no	—
416	C₂³	—	20	4	no	—
417	C₂³	—	20	8	no	—
418	C₂³	—	20	4	no	—
419	C₂³	—	20	2	no	—
420	C₂³	—	20	2	no	—
421	C₂³	—	20	2	no	—
422	C₂³	C₃×D₄₀	1	4	yes	complemented
423	C₂³	C₂×C₃×D₂₀	1	2	yes	—
424	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
425	D₄	—	5	8	no	—
426	D₄	—	10	16	no	—
427	D₄	—	10	4	no	—
428	D₄	—	10	4	no	—
429	D₄	—	10	8	no	—
430	D₄	—	20	8	no	—
431	D₄	—	20	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	10	2	no	—
436	C₂×C₄	—	20	2	no	—
437	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
438	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
439	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
440	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
441	C₈	—	2	4	no	—
442	C₂×C₃	—	2	4	no	—
443	C₂×C₃	—	20	8	no	—
444	C₂×C₃	—	40	2	no	—
445	C₂×C₃	#65021	1	4	yes	direct product factor
446	C₂×C₃	C₂×#4028	1	1	yes	characteristic
447	C₂×C₃	C₂²×D₄₀	1	1	yes	characteristic
448	C₂×C₃	C₂×#4054	1	1	yes	characteristic
449	C₅	C₂×C₃×#447	1	1	yes	characteristic, complemented, Sylow
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	8	no	—
453	C₂²	—	10	8	no	—
454	C₂²	—	20	32	no	—
455	C₂²	—	20	4	no	—
456	C₂²	—	20	4	no	—
457	C₂²	—	20	16	no	—
458	C₂²	—	20	2	no	—
459	C₂²	—	20	2	no	—
460	C₂²	—	20	2	no	—
461	C₂²	—	40	4	no	—
462	C₂²	C₃×#4028	1	2	yes	—
463	C₂²	C₂×C₃×D₄₀	1	2	yes	—
464	C₂²	C₂×C₃×D₄₀	1	4	yes	complemented
465	C₂²	C₃×#4054	1	2	yes	—
466	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
467	C₄	—	2	2	no	—
468	C₄	—	20	2	no	—
469	C₄	C₃×#4028	1	2	yes	—
470	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
471	C₃	C₂×#65021	1	1	yes	characteristic, direct product factor, Sylow
472	C₂	—	2	4	no	—
473	C₂	—	20	8	no	—
474	C₂	—	40	2	no	—
475	C₂	C₃×#65021	1	4	yes	direct product factor
476	C₂	C₂×C₃×#4028	1	1	yes	characteristic
477	C₂	C₂²×C₃×D₄₀	1	1	yes	characteristic
478	C₂	C₂×C₃×#4054	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×C₂²⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₃×C₂²⋊C₈	D₅
hypocenter	C₅	C₂×C₃×#447
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×C₄ ◁ C₂×C₃×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×D₂₀	C₂	semidirect
2. C₂×C₃×#4076	C₂	semidirect
3. C₂²×C₃×D₄₀	C₂	semidirect
4. C₂×C₃×C₅×C₂²⋊C₈	C₂	semidirect
5. C₂×C₃×#3953	C₂	semidirect
6. C₃×#65021	C₂	direct (N × H)
7. C₂×#65021	C₃	direct (N × H)
15. C₂²×C₃×D₂₀	C₂²	semidirect
16. C₂²×C₃×D₂₀	C₂²	semidirect
17. C₂²×C₃×C₅×C₈	C₂²	semidirect
19. C₃×#4076	C₂²	semidirect
21. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
23. C₂×C₃×D₄₀	C₂²	semidirect
24. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
25. C₃×#3953	C₂²	semidirect
27. C₂³×D₂₀	C₂×C₃	semidirect
28. C₂×#4076	C₂×C₃	semidirect
29. C₂²×D₄₀	C₂×C₃	semidirect
30. C₂×C₅×C₂²⋊C₈	C₂×C₃	semidirect
31. C₂×#3953	C₂×C₃	semidirect
32. #65021	C₂×C₃	direct (N × H)
56. C₂×C₃×D₂₀	D₄	semidirect
58. C₂×C₃×D₂₀	C₂³	semidirect
60. C₂×C₃×C₅×C₈	C₂³	semidirect
63. C₃×C₄⋊Dic₅	C₂³	semidirect
70. C₂×C₃×C₂²⋊C₈	D₅	semidirect
78. C₂²×D₂₀	C₂²×C₃	semidirect
79. C₂²×D₂₀	C₂²×C₃	semidirect
80. C₂²×C₅×C₈	C₂²×C₃	semidirect
82. #4076	C₂²×C₃	semidirect
84. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
86. C₂×D₄₀	C₂²×C₃	semidirect
87. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
88. #3953	C₂²×C₃	semidirect
92. C₂³×C₃×C₅	D₈	semidirect
122. C₃×D₂₀	C₂×D₄	semidirect
135. C₂²×C₃×C₈	C₂×D₅	semidirect
141. C₃×C₂²⋊C₈	C₂×D₅	semidirect
165. C₂×D₂₀	C₃×D₄	semidirect
167. C₂×D₂₀	C₂³×C₃	semidirect
169. C₂×C₅×C₈	C₂³×C₃	semidirect
172. C₄⋊Dic₅	C₂³×C₃	semidirect
179. C₂×C₂²⋊C₈	C₃×D₅	semidirect
185. C₂²×C₃×C₅	C₂×D₈	semidirect
229. C₂×C₃×C₈	C₂²×D₅	semidirect
235. C₂³×C₅	C₃×D₈	semidirect
265. D₂₀	C₂×C₃×D₄	semidirect
278. C₂²×C₈	C₂×C₃×D₅	semidirect
284. C₂²⋊C₈	C₂×C₃×D₅	semidirect
286. C₂×C₃×C₅	#447	semidirect
306. C₂³×C₃	D₄₀	semidirect
331. C₂²×C₅	C₂×C₃×D₈	semidirect
375. C₂×C₈	C₂²×C₃×D₅	semidirect
379. C₃×C₅	C₂×#447	semidirect
394. C₂²×C₃	C₂×D₄₀	semidirect
402. C₂×C₅	C₃×#447	semidirect
422. C₂³	C₃×D₄₀	semidirect
445. C₂×C₃	#65021	direct (N × H)
449. C₅	C₂×C₃×#447	semidirect
464. C₂²	C₂×C₃×D₄₀	semidirect
471. C₃	C₂×#65021	direct (N × H)
475. C₂	C₃×#65021	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
C₂×C₃×#4076	2
C₂²×C₃×D₄₀	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₂×C₃×#3953	2
C₃×#65021	2
C₂×#65021	3
C₂×C₃×#447	5

Subgroups — C2×C3×#65021 #14423188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65021 #14423188