Subgroups — C₃×#10605384 #14329455

Order 1920.

1664 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4039	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×#4020	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×D₂₀	C₂	1	2	yes	maximal, complemented
4	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65277	C₂	1	2	yes	maximal, complemented
6	C₃×#65228	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64954	C₂	1	4	yes	maximal, complemented
9	#10605384	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
11	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
12	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
13	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×#685	C₂²	1	4	yes	—
19	C₂×C₃×#685	C₂²	1	4	yes	—
20	C₂×C₃×#685	C₂²	1	4	yes	—
21	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
24	C₃×#4039	—	2	8	no	—
25	C₃×#4020	C₄	1	8	yes	complemented
26	C₃×C₄×D₂₀	—	2	8	no	—
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×#3963	C₂²	1	2	yes	—
29	C₃×#2366	—	5	1	no	maximal, Hall
30	C₂×#4039	C₂×C₃	1	2	yes	complemented
31	C₂×#4020	C₂×C₃	1	1	yes	characteristic
32	C₂×C₄×D₂₀	C₂×C₃	1	2	yes	complemented
33	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
34	#65277	C₂×C₃	1	2	yes	complemented
35	#65228	C₂×C₃	1	2	yes	complemented
36	C₄×C₄⋊Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
37	#64954	C₂×C₃	1	4	yes	complemented
38	C₂³×C₃×D₅	C₂³	1	4	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
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	2	yes	—
45	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
46	C₂×C₃×D₂₀	—	2	4	no	—
47	C₂×C₃×D₂₀	—	2	4	no	—
48	C₂×C₃×D₂₀	—	2	4	no	—
49	C₂×C₃×D₂₀	—	2	4	no	—
50	C₂×C₃×D₂₀	—	4	2	no	—
51	C₂×C₃×D₂₀	—	4	2	no	—
52	C₂×C₃×D₂₀	C₂×C₄	1	8	yes	complemented
53	C₂×C₃×D₂₀	C₂×C₄	1	8	yes	complemented
54	C₂×C₃×D₂₀	C₂×C₄	1	8	yes	complemented
55	C₂×C₃×C₄×D₅	—	2	8	no	—
56	C₂×C₃×C₄×D₅	—	2	8	no	—
57	C₂×C₃×C₄×D₅	—	4	4	no	—
58	C₃×C₅×C₄⋊C₄	—	2	2	no	—
59	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	complemented
60	C₃×C₄²×C₅	—	2	4	no	—
61	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
62	C₃×#685	—	2	8	no	—
63	C₃×#685	—	2	8	no	—
64	C₃×#685	—	4	4	no	—
65	C₃×C₄⋊Dic₅	—	2	2	no	—
66	C₃×C₄⋊Dic₅	D₄	1	4	yes	complemented
67	C₃×C₄×Dic₅	—	2	4	no	—
68	C₂×C₃×#127	—	5	1	no	—
69	C₂×C₃×C₄×D₄	—	5	2	no	—
70	C₂×C₃×C₄×D₄	—	5	2	no	—
71	C₃×#390	—	5	2	no	—
72	C₃×#390	—	5	2	no	—
73	C₃×#386	—	5	4	no	—
74	C₃×C₄×C₄⋊C₄	—	5	1	no	—
75	C₃×C₄×C₄⋊C₄	D₅	1	1	yes	characteristic, complemented
76	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
77	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
78	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
79	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	—
80	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
83	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
84	C₂×#685	C₂²×C₃	1	4	yes	—
85	C₂×#685	C₂²×C₃	1	4	yes	—
86	C₂×#685	C₂²×C₃	1	4	yes	—
87	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
90	#4039	—	2	8	no	—
91	#4020	C₃×C₄	1	8	yes	complemented
92	C₄×D₂₀	—	2	8	no	—
93	C₅×#95	C₂²×C₃	1	2	yes	—
94	#3963	C₂²×C₃	1	2	yes	—
95	#2366	—	5	1	no	Sylow
96	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
97	C₂²×C₃×D₅	—	2	4	no	—
98	C₂²×C₃×D₅	—	2	4	no	—
99	C₂²×C₃×D₅	—	2	4	no	—
100	C₂²×C₃×D₅	—	2	4	no	—
101	C₂²×C₃×D₅	—	2	4	no	—
102	C₂²×C₃×D₅	—	2	4	no	—
103	C₂²×C₃×D₅	C₂²×C₄	1	8	yes	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	1	no	—
107	C₂×C₃×C₄×C₅	—	2	1	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	#41	1	2	yes	—
118	C₂×C₃×C₄×C₅	#41	1	2	yes	—
119	C₂×C₃×Dic₅	—	2	2	no	—
120	C₂×C₃×Dic₅	—	2	2	no	—
121	C₂×C₃×Dic₅	—	2	2	no	—
122	C₂×C₃×Dic₅	—	2	2	no	—
123	C₂×C₃×Dic₅	—	2	2	no	—
124	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
125	C₃×D₂₀	—	2	16	no	—
126	C₃×D₂₀	—	2	16	no	—
127	C₃×D₂₀	—	4	8	no	—
128	C₃×C₄×D₅	—	4	16	no	—
129	C₂²×C₃×D₄	—	5	2	no	—
130	C₂²×C₃×D₄	—	5	2	no	—
131	C₂²×C₃×D₄	—	5	2	no	—
132	C₂³×C₃×C₄	—	5	4	no	—
133	C₃×#127	—	5	8	no	—
134	C₃×C₄×D₄	—	10	8	no	—
135	C₃×C₄×D₄	—	10	8	no	—
136	C₂×C₃×C₄⋊C₄	—	5	1	no	—
137	C₂×C₃×C₄⋊C₄	—	5	1	no	—
138	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
139	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
140	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
141	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
142	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
143	C₂×C₃×C₄²	—	5	2	no	—
144	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
145	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
146	C₃×#95	—	5	2	no	—
147	C₃×#95	C₂×D₅	1	2	yes	—
148	C₂³×D₅	C₂³×C₃	1	4	yes	—
149	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
150	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
152	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
154	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
155	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
156	C₂×D₂₀	—	2	4	no	—
157	C₂×D₂₀	—	2	4	no	—
158	C₂×D₂₀	—	2	4	no	—
159	C₂×D₂₀	—	2	4	no	—
160	C₂×D₂₀	—	4	2	no	—
161	C₂×D₂₀	—	4	2	no	—
162	C₂×D₂₀	C₂×C₃×C₄	1	8	yes	complemented
163	C₂×D₂₀	C₂×C₃×C₄	1	8	yes	complemented
164	C₂×D₂₀	C₂×C₃×C₄	1	8	yes	complemented
165	C₂×C₄×D₅	—	2	8	no	—
166	C₂×C₄×D₅	—	2	8	no	—
167	C₂×C₄×D₅	—	4	4	no	—
168	C₅×C₄⋊C₄	—	2	2	no	—
169	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	complemented
170	C₄²×C₅	—	2	4	no	—
171	C₄²×C₅	C₂×C₃×C₄	1	4	yes	complemented
172	#685	—	2	8	no	—
173	#685	—	2	8	no	—
174	#685	—	4	4	no	—
175	C₄⋊Dic₅	—	2	2	no	—
176	C₄⋊Dic₅	C₃×D₄	1	4	yes	complemented
177	C₄×Dic₅	—	2	4	no	—
178	C₂×#127	—	5	1	no	—
179	C₂×C₄×D₄	—	5	2	no	—
180	C₂×C₄×D₄	—	5	2	no	—
181	#390	—	5	2	no	—
182	#390	—	5	2	no	—
183	#386	—	5	4	no	—
184	C₄×C₄⋊C₄	—	5	1	no	—
185	C₄×C₄⋊C₄	C₃×D₅	1	1	yes	characteristic, complemented
186	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
187	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
189	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
190	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
191	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂×C₃×D₅	—	2	8	no	—
194	C₂×C₃×D₅	—	2	8	no	—
195	C₂×C₃×D₅	—	2	8	no	—
196	C₂×C₃×D₅	—	4	4	no	—
197	C₂×C₃×D₅	—	4	4	no	—
198	C₂×C₃×D₅	—	4	4	no	—
199	C₂×C₃×D₅	—	4	4	no	—
200	C₃×C₄×C₅	—	2	2	no	—
201	C₃×C₄×C₅	—	2	4	no	—
202	C₃×C₄×C₅	—	4	2	no	—
203	C₃×C₄×C₅	C₄×D₄	1	4	yes	complemented
204	C₃×C₄×C₅	C₄×D₄	1	4	yes	complemented
205	C₃×Dic₅	—	2	4	no	—
206	C₃×Dic₅	—	4	2	no	—
207	C₂⁴×C₃	—	5	4	no	—
208	C₂×C₃×D₄	—	5	8	no	—
209	C₂×C₃×D₄	—	5	8	no	—
210	C₂×C₃×D₄	—	5	8	no	—
211	C₂×C₃×D₄	—	10	4	no	—
212	C₂×C₃×D₄	—	10	4	no	—
213	C₂×C₃×D₄	—	10	4	no	—
214	C₂×C₃×D₄	—	10	4	no	—
215	C₂×C₃×D₄	—	20	2	no	—
216	C₂×C₃×D₄	—	20	2	no	—
217	C₂²×C₃×C₄	—	5	2	no	—
218	C₂²×C₃×C₄	—	5	2	no	—
219	C₂²×C₃×C₄	—	10	8	no	—
220	C₂²×C₃×C₄	—	10	8	no	—
221	C₂²×C₃×C₄	—	20	4	no	—
222	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
223	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
225	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
227	C₃×C₄⋊C₄	—	2	2	no	—
228	C₃×C₄⋊C₄	—	5	4	no	—
229	C₃×C₄⋊C₄	—	10	2	no	—
230	C₃×C₄⋊C₄	D₂₀	1	4	yes	complemented
231	C₃×C₂²⋊C₄	—	10	8	no	—
232	C₃×C₂²⋊C₄	—	10	8	no	—
233	C₃×C₂²⋊C₄	—	20	4	no	—
234	C₃×C₄²	—	2	4	no	—
235	C₃×C₄²	—	10	4	no	—
236	C₃×C₄²	C₄×D₅	1	4	yes	complemented
237	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
238	C₂²×D₅	—	2	4	no	—
239	C₂²×D₅	—	2	4	no	—
240	C₂²×D₅	—	2	4	no	—
241	C₂²×D₅	—	2	4	no	—
242	C₂²×D₅	—	2	4	no	—
243	C₂²×D₅	—	2	4	no	—
244	C₂²×D₅	C₂²×C₃×C₄	1	8	yes	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	2	1	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
253	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
254	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
255	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
256	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
257	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
258	C₂×C₄×C₅	C₃×#41	1	2	yes	—
259	C₂×C₄×C₅	C₃×#41	1	2	yes	—
260	C₂×Dic₅	—	2	2	no	—
261	C₂×Dic₅	—	2	2	no	—
262	C₂×Dic₅	—	2	2	no	—
263	C₂×Dic₅	—	2	2	no	—
264	C₂×Dic₅	—	2	2	no	—
265	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
266	D₂₀	—	2	16	no	—
267	D₂₀	—	2	16	no	—
268	D₂₀	—	4	8	no	—
269	C₄×D₅	—	4	16	no	—
270	C₂²×D₄	—	5	2	no	—
271	C₂²×D₄	—	5	2	no	—
272	C₂²×D₄	—	5	2	no	—
273	C₂³×C₄	—	5	4	no	—
274	#127	—	5	8	no	—
275	C₄×D₄	—	10	8	no	—
276	C₄×D₄	—	10	8	no	—
277	C₂×C₄⋊C₄	—	5	1	no	—
278	C₂×C₄⋊C₄	—	5	1	no	—
279	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	—	5	4	no	—
282	C₂×C₂²⋊C₄	—	5	4	no	—
283	C₂×C₂²⋊C₄	—	5	4	no	—
284	C₂×C₄²	—	5	2	no	—
285	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
286	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
287	#95	—	5	2	no	—
288	#95	C₂×C₃×D₅	1	2	yes	—
289	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
290	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
291	C₂×C₃×C₅	#518	1	1	yes	characteristic
292	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
293	C₂×C₃×C₅	#550	1	1	yes	characteristic
294	C₂×C₃×C₅	#550	1	1	yes	characteristic
295	C₂×C₃×C₅	#559	1	1	yes	characteristic
296	C₃×D₅	—	4	8	no	—
297	C₂³×C₃	—	5	8	no	—
298	C₂³×C₃	—	10	4	no	—
299	C₂³×C₃	—	10	4	no	—
300	C₂³×C₃	—	10	4	no	—
301	C₂³×C₃	—	10	4	no	—
302	C₂³×C₃	—	10	4	no	—
303	C₂³×C₃	—	10	4	no	—
304	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
305	C₃×D₄	—	10	16	no	—
306	C₃×D₄	—	10	16	no	—
307	C₃×D₄	—	20	8	no	—
308	C₂×C₃×C₄	—	2	2	no	—
309	C₂×C₃×C₄	—	2	2	no	—
310	C₂×C₃×C₄	—	2	1	no	—
311	C₂×C₃×C₄	—	2	1	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	5	4	no	—
316	C₂×C₃×C₄	—	10	2	no	—
317	C₂×C₃×C₄	—	10	2	no	—
318	C₂×C₃×C₄	—	10	2	no	—
319	C₂×C₃×C₄	—	10	2	no	—
320	C₂×C₃×C₄	—	10	2	no	—
321	C₂×C₃×C₄	—	20	16	no	—
322	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
323	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
324	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
325	C₂×C₃×C₄	C₂×D₂₀	1	4	yes	—
326	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
327	C₂×C₃×C₄	#709	1	2	yes	—
328	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
329	C₂×C₃×C₄	#713	1	2	yes	—
330	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
331	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
332	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
333	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
334	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
335	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
336	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
337	C₂×D₅	—	2	8	no	—
338	C₂×D₅	—	2	8	no	—
339	C₂×D₅	—	2	8	no	—
340	C₂×D₅	—	4	4	no	—
341	C₂×D₅	—	4	4	no	—
342	C₂×D₅	—	4	4	no	—
343	C₂×D₅	—	4	4	no	—
344	C₄×C₅	—	2	2	no	—
345	C₄×C₅	—	2	4	no	—
346	C₄×C₅	—	4	2	no	—
347	C₄×C₅	C₃×C₄×D₄	1	4	yes	complemented
348	C₄×C₅	C₃×C₄×D₄	1	4	yes	complemented
349	Dic₅	—	2	4	no	—
350	Dic₅	—	4	2	no	—
351	C₂⁴	—	5	4	no	—
352	C₂×D₄	—	5	8	no	—
353	C₂×D₄	—	5	8	no	—
354	C₂×D₄	—	5	8	no	—
355	C₂×D₄	—	10	4	no	—
356	C₂×D₄	—	10	4	no	—
357	C₂×D₄	—	10	4	no	—
358	C₂×D₄	—	10	4	no	—
359	C₂×D₄	—	20	2	no	—
360	C₂×D₄	—	20	2	no	—
361	C₂²×C₄	—	5	2	no	—
362	C₂²×C₄	—	5	2	no	—
363	C₂²×C₄	—	10	8	no	—
364	C₂²×C₄	—	10	8	no	—
365	C₂²×C₄	—	20	4	no	—
366	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
367	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
368	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
369	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
370	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	5	4	no	—
373	C₄⋊C₄	—	10	2	no	—
374	C₄⋊C₄	C₃×D₂₀	1	4	yes	complemented
375	C₂²⋊C₄	—	10	8	no	—
376	C₂²⋊C₄	—	10	8	no	—
377	C₂²⋊C₄	—	20	4	no	—
378	C₄²	—	2	4	no	—
379	C₄²	—	10	4	no	—
380	C₄²	C₃×C₄×D₅	1	4	yes	complemented
381	C₃×C₅	#2366	1	1	yes	characteristic, complemented, Hall
382	C₂²×C₃	—	10	8	no	—
383	C₂²×C₃	—	10	8	no	—
384	C₂²×C₃	—	10	8	no	—
385	C₂²×C₃	—	20	4	no	—
386	C₂²×C₃	—	20	4	no	—
387	C₂²×C₃	—	20	4	no	—
388	C₂²×C₃	—	20	4	no	—
389	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
390	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
391	C₂²×C₃	C₂×#709	1	1	yes	characteristic
392	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
393	C₂²×C₃	C₂×#713	1	1	yes	characteristic
394	C₂²×C₃	#4149	1	1	yes	characteristic
395	C₂²×C₃	#4149	1	1	yes	characteristic
396	C₃×C₄	—	2	2	no	—
397	C₃×C₄	—	2	4	no	—
398	C₃×C₄	—	4	2	no	—
399	C₃×C₄	—	10	4	no	—
400	C₃×C₄	—	20	2	no	—
401	C₃×C₄	C₄×D₂₀	1	4	yes	complemented
402	C₃×C₄	#4039	1	4	yes	complemented
403	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
404	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
405	C₂×C₅	C₃×#518	1	1	yes	characteristic
406	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
407	C₂×C₅	C₃×#550	1	1	yes	characteristic
408	C₂×C₅	C₃×#550	1	1	yes	characteristic
409	C₂×C₅	C₃×#559	1	1	yes	characteristic
410	D₅	—	4	8	no	—
411	C₂³	—	5	8	no	—
412	C₂³	—	10	4	no	—
413	C₂³	—	10	4	no	—
414	C₂³	—	10	4	no	—
415	C₂³	—	10	4	no	—
416	C₂³	—	10	4	no	—
417	C₂³	—	10	4	no	—
418	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
419	D₄	—	10	16	no	—
420	D₄	—	10	16	no	—
421	D₄	—	20	8	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	5	4	no	—
430	C₂×C₄	—	10	2	no	—
431	C₂×C₄	—	10	2	no	—
432	C₂×C₄	—	10	2	no	—
433	C₂×C₄	—	10	2	no	—
434	C₂×C₄	—	10	2	no	—
435	C₂×C₄	—	20	16	no	—
436	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
437	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
438	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
439	C₂×C₄	C₂×C₃×D₂₀	1	4	yes	—
440	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
441	C₂×C₄	C₃×#709	1	2	yes	—
442	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
443	C₂×C₄	C₃×#713	1	2	yes	—
444	C₂×C₃	—	20	8	no	—
445	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
446	C₂×C₃	C₂×#4039	1	1	yes	characteristic
447	C₂×C₃	#65855	1	1	yes	characteristic
448	C₂×C₃	D₄×D₂₀	1	1	yes	characteristic
449	C₂×C₃	#65887	1	1	yes	characteristic
450	C₂×C₃	#65911	1	1	yes	characteristic
451	C₂×C₃	#65919	1	1	yes	characteristic
452	C₅	C₃×#2366	1	1	yes	characteristic, complemented, Sylow
453	C₂²	—	10	8	no	—
454	C₂²	—	10	8	no	—
455	C₂²	—	10	8	no	—
456	C₂²	—	20	4	no	—
457	C₂²	—	20	4	no	—
458	C₂²	—	20	4	no	—
459	C₂²	—	20	4	no	—
460	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
461	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
462	C₂²	C₂×C₃×#709	1	1	yes	characteristic
463	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
464	C₂²	C₂×C₃×#713	1	1	yes	characteristic
465	C₂²	C₃×#4149	1	1	yes	characteristic
466	C₂²	C₃×#4149	1	1	yes	characteristic
467	C₄	—	2	2	no	—
468	C₄	—	2	4	no	—
469	C₄	—	4	2	no	—
470	C₄	—	10	4	no	—
471	C₄	—	20	2	no	—
472	C₄	C₃×C₄×D₂₀	1	4	yes	complemented
473	C₄	C₃×#4039	1	4	yes	complemented
474	C₃	#10605384	1	1	yes	characteristic, direct product factor, Sylow
475	C₂	—	20	8	no	—
476	C₂	C₂×C₃×C₄×D₂₀	1	1	yes	characteristic
477	C₂	C₂×C₃×#4039	1	1	yes	characteristic
478	C₂	C₃×#65855	1	1	yes	characteristic
479	C₂	C₃×D₄×D₂₀	1	1	yes	characteristic
480	C₂	C₃×#65887	1	1	yes	characteristic
481	C₂	C₃×#65911	1	1	yes	characteristic
482	C₂	C₃×#65919	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×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	C₂×C₃×#4020	C₂
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×C₄⋊C₄	D₅
hypocenter	C₅	C₃×#2366
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4039	C₂	semidirect
3. C₂×C₃×C₄×D₂₀	C₂	semidirect
4. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
5. C₃×#65277	C₂	semidirect
6. C₃×#65228	C₂	semidirect
7. C₃×C₄×C₄⋊Dic₅	C₂	semidirect
8. C₃×#64954	C₂	semidirect
9. #10605384	C₃	direct (N × H)
25. C₃×#4020	C₄	semidirect
30. C₂×#4039	C₂×C₃	semidirect
32. C₂×C₄×D₂₀	C₂×C₃	semidirect
33. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
34. #65277	C₂×C₃	semidirect
35. #65228	C₂×C₃	semidirect
36. C₄×C₄⋊Dic₅	C₂×C₃	semidirect
37. #64954	C₂×C₃	semidirect
52. C₂×C₃×D₂₀	C₂×C₄	semidirect
53. C₂×C₃×D₂₀	C₂×C₄	semidirect
54. C₂×C₃×D₂₀	C₂×C₄	semidirect
59. C₃×C₅×C₄⋊C₄	D₄	semidirect
61. C₃×C₄²×C₅	C₂×C₄	semidirect
66. C₃×C₄⋊Dic₅	D₄	semidirect
75. C₃×C₄×C₄⋊C₄	D₅	semidirect
91. #4020	C₃×C₄	semidirect
162. C₂×D₂₀	C₂×C₃×C₄	semidirect
163. C₂×D₂₀	C₂×C₃×C₄	semidirect
164. C₂×D₂₀	C₂×C₃×C₄	semidirect
169. C₅×C₄⋊C₄	C₃×D₄	semidirect
171. C₄²×C₅	C₂×C₃×C₄	semidirect
176. C₄⋊Dic₅	C₃×D₄	semidirect
185. C₄×C₄⋊C₄	C₃×D₅	semidirect
203. C₃×C₄×C₅	C₄×D₄	semidirect
204. C₃×C₄×C₅	C₄×D₄	semidirect
230. C₃×C₄⋊C₄	D₂₀	semidirect
236. C₃×C₄²	C₄×D₅	semidirect
347. C₄×C₅	C₃×C₄×D₄	semidirect
348. C₄×C₅	C₃×C₄×D₄	semidirect
374. C₄⋊C₄	C₃×D₂₀	semidirect
380. C₄²	C₃×C₄×D₅	semidirect
381. C₃×C₅	#2366	semidirect
401. C₃×C₄	C₄×D₂₀	semidirect
402. C₃×C₄	#4039	semidirect
452. C₅	C₃×#2366	semidirect
472. C₄	C₃×C₄×D₂₀	semidirect
473. C₄	C₃×#4039	semidirect
474. C₃	#10605384	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×#4039	2
C₂×C₃×#4020	2
C₂×C₃×C₄×D₂₀	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×#65277	2
C₃×#65228	2
C₃×C₄×C₄⋊Dic₅	2
C₃×#64954	2
#10605384	3
C₃×#2366	5

Subgroups — C3×#10605384 #14329455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10605384 #14329455