Subgroups — C₅×D₃×#480 #14431395

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×#121	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#480	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5033	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4967	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4882	C₂	1	2	yes	maximal, complemented
7	C₅×D₃×#107	C₂	1	2	yes	maximal, complemented
8	C₅×#4774	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×#102	C₂	1	2	yes	maximal, complemented
10	C₅×#4736	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#480	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×D₄	—	2	1	no	—
14	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	—	2	1	no	—
16	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
17	C₃×C₅×#121	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
19	C₅×#939	—	2	1	no	—
20	C₅×#938	C₂²	1	1	yes	characteristic
21	C₅×#930	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
24	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
25	C₅×#895	C₂²	1	1	yes	characteristic
26	C₅×D₃×C₄⋊C₄	—	2	1	no	—
27	C₅×D₃×C₄⋊C₄	—	2	1	no	—
28	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
29	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
31	C₅×#884	—	2	1	no	—
32	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
33	C₃×C₅×#107	C₂²	1	2	yes	complemented
34	C₃×C₅×#102	C₂²	1	2	yes	complemented
35	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
36	C₅×#832	C₂²	1	2	yes	complemented
37	C₅×#830	C₂²	1	1	yes	characteristic, complemented
38	C₅×#821	C₂²	1	2	yes	complemented
39	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	complemented
40	C₅×#818	C₂²	1	2	yes	complemented
41	C₅×#809	C₂²	1	2	yes	complemented
42	C₅×#807	C₂²	1	2	yes	complemented
43	C₅×#807	C₂²	1	2	yes	complemented
44	D₃×#480	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×#121	—	3	1	no	—
46	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
47	C₅×#480	—	3	2	no	—
48	C₅×#480	—	3	2	no	—
49	C₅×#480	—	3	1	no	—
50	C₅×#480	—	3	1	no	—
51	C₅×#480	—	3	1	no	—
52	C₅×#480	D₃	1	1	yes	characteristic, direct product factor
53	C₂×C₅×#107	—	3	2	no	—
54	C₂×C₅×#102	—	3	2	no	—
55	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
56	C₂³×C₅×D₃	—	2	1	no	—
57	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
58	C₂×C₃×C₅×D₄	—	2	1	no	—
59	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	—	2	1	no	—
61	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂×C₅×#67	—	2	1	no	—
63	C₂×C₅×#67	—	2	1	no	—
64	C₂×C₅×#67	—	2	1	no	—
65	C₂²×C₅×Dic₃	—	2	1	no	—
66	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
67	C₅×D₃×D₄	—	2	4	no	—
68	C₅×D₃×D₄	—	4	4	no	—
69	C₂×C₅×D₁₂	—	2	1	no	—
70	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
71	C₂×C₄×C₅×D₃	—	2	4	no	—
72	C₂×C₄×C₅×D₃	—	2	1	no	—
73	C₂×C₄×C₅×D₃	—	2	2	no	—
74	C₂×C₄×C₅×D₃	—	2	2	no	—
75	C₂×C₄×C₅×D₃	—	4	4	no	—
76	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
77	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
78	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
79	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
81	C₃×C₅×C₄⋊C₄	—	2	1	no	—
82	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
83	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
85	C₅×#217	—	2	1	no	—
86	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
87	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
88	C₅×C₄⋊Dic₃	—	2	1	no	—
89	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
90	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
91	C₅×Dic₃⋊C₄	—	2	1	no	—
92	C₅×Dic₃⋊C₄	—	2	2	no	—
93	C₅×Dic₃⋊C₄	—	2	2	no	—
94	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
95	C₅×D₃×C₈	—	2	4	no	—
96	D₃×#121	C₂×C₅	1	1	yes	characteristic
97	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#480	C₂×C₅	1	1	yes	characteristic, complemented
99	#5033	C₂×C₅	1	1	yes	characteristic, complemented
100	#4967	C₂×C₅	1	1	yes	characteristic, complemented
101	#4882	C₂×C₅	1	2	yes	complemented
102	D₃×#107	C₂×C₅	1	2	yes	complemented
103	#4774	C₂×C₅	1	2	yes	complemented
104	D₃×#102	C₂×C₅	1	2	yes	complemented
105	#4736	C₂×C₅	1	1	yes	characteristic, complemented
106	D₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
107	C₂²×C₅×D₄	—	3	1	no	—
108	C₂²×C₅×D₄	—	6	1	no	—
109	C₂³×C₄×C₅	—	3	1	no	—
110	C₂³×C₄×C₅	—	6	1	no	—
111	C₂²×C₅×C₈	—	3	2	no	—
112	C₅×#121	—	3	1	no	—
113	C₅×#121	—	3	1	no	—
114	C₅×#121	—	3	1	no	—
115	C₅×#121	—	6	1	no	—
116	C₅×#121	—	6	1	no	—
117	C₅×#121	C₂×D₃	1	1	yes	characteristic
118	C₂×C₅×C₄⋊C₄	—	3	1	no	—
119	C₂×C₅×C₄⋊C₄	—	3	2	no	—
120	C₂×C₅×C₄⋊C₄	—	3	1	no	—
121	C₂×C₅×C₄⋊C₄	—	3	2	no	—
122	C₂×C₅×C₄⋊C₄	—	6	1	no	—
123	C₂×C₅×C₄⋊C₄	—	6	1	no	—
124	C₂×C₅×C₄⋊C₄	—	6	1	no	—
125	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
126	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
127	C₅×#107	—	3	2	no	—
128	C₅×#107	—	3	2	no	—
129	C₅×#107	—	3	2	no	—
130	C₅×#107	C₂×D₃	1	2	yes	complemented
131	C₅×#102	—	3	2	no	—
132	C₅×#102	—	3	2	no	—
133	C₅×#102	—	3	2	no	—
134	C₅×#102	C₂×D₃	1	2	yes	complemented
135	C₅×C₂²⋊C₈	—	3	1	no	—
136	C₅×C₂²⋊C₈	—	3	2	no	—
137	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
138	C₂×#480	—	3	1	no	Sylow
139	C₂³×C₃×C₅	—	2	1	no	—
140	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₅×D₃	—	2	2	no	—
142	C₂²×C₅×D₃	—	2	2	no	—
143	C₂²×C₅×D₃	—	2	1	no	—
144	C₂²×C₅×D₃	—	4	2	no	—
145	C₂²×C₅×D₃	—	4	2	no	—
146	C₂²×C₅×D₃	—	4	2	no	—
147	C₂²×C₅×D₃	D₈	1	4	yes	—
148	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
150	C₃×C₅×D₄	—	2	2	no	—
151	C₃×C₅×D₄	—	4	2	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	2	1	no	—
155	C₂×C₃×C₄×C₅	—	4	2	no	—
156	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
158	C₅×#67	—	4	2	no	—
159	C₅×#67	—	4	2	no	—
160	C₅×#67	—	4	2	no	—
161	C₂×C₅×Dic₃	—	2	2	no	—
162	C₂×C₅×Dic₃	—	2	2	no	—
163	C₂×C₅×Dic₃	—	2	1	no	—
164	C₂×C₅×Dic₃	—	4	2	no	—
165	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
166	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
167	C₅×D₁₂	—	2	2	no	—
168	C₅×D₁₂	—	4	2	no	—
169	C₄×C₅×D₃	—	2	2	no	—
170	C₄×C₅×D₃	—	2	2	no	—
171	C₄×C₅×D₃	—	2	2	no	—
172	C₄×C₅×D₃	—	4	4	no	—
173	C₄×C₅×D₃	—	4	4	no	—
174	C₄×C₅×D₃	—	4	2	no	—
175	C₄×C₅×D₃	#41	1	4	yes	—
176	C₃×C₅×C₈	—	2	2	no	—
177	C₅×C₃⋊C₈	—	2	2	no	—
178	C₂×D₃×D₄	—	2	1	no	—
179	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
180	C₂²×C₄×D₃	—	2	1	no	—
181	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
182	C₃×#121	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
184	#939	—	2	1	no	—
185	#938	C₂²×C₅	1	1	yes	characteristic
186	#930	C₂²×C₅	1	1	yes	characteristic
187	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
188	C₂×Dic₃⋊C₄	—	2	1	no	—
189	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
190	#895	C₂²×C₅	1	1	yes	characteristic
191	D₃×C₄⋊C₄	—	2	1	no	—
192	D₃×C₄⋊C₄	—	2	1	no	—
193	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
194	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
195	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
196	#884	—	2	1	no	—
197	D₃×C₂²⋊C₄	—	2	1	no	—
198	C₃×#107	C₂²×C₅	1	2	yes	complemented
199	C₃×#102	C₂²×C₅	1	2	yes	complemented
200	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
201	#832	C₂²×C₅	1	2	yes	complemented
202	#830	C₂²×C₅	1	1	yes	characteristic, complemented
203	#821	C₂²×C₅	1	2	yes	complemented
204	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	complemented
205	#818	C₂²×C₅	1	2	yes	complemented
206	#809	C₂²×C₅	1	2	yes	complemented
207	#807	C₂²×C₅	1	2	yes	complemented
208	#807	C₂²×C₅	1	2	yes	complemented
209	C₂⁴×C₅	—	3	1	no	—
210	C₂⁴×C₅	—	6	1	no	—
211	C₂×C₅×D₄	—	2	1	no	—
212	C₂×C₅×D₄	—	3	1	no	—
213	C₂×C₅×D₄	—	6	1	no	—
214	C₂×C₅×D₄	—	6	4	no	—
215	C₂×C₅×D₄	—	6	1	no	—
216	C₂×C₅×D₄	—	6	1	no	—
217	C₂×C₅×D₄	—	6	1	no	—
218	C₂×C₅×D₄	—	12	4	no	—
219	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
220	C₂²×C₄×C₅	—	2	1	no	—
221	C₂²×C₄×C₅	—	3	1	no	—
222	C₂²×C₄×C₅	—	3	1	no	—
223	C₂²×C₄×C₅	—	3	1	no	—
224	C₂²×C₄×C₅	—	3	1	no	—
225	C₂²×C₄×C₅	—	3	1	no	—
226	C₂²×C₄×C₅	—	6	4	no	—
227	C₂²×C₄×C₅	—	6	1	no	—
228	C₂²×C₄×C₅	—	6	2	no	—
229	C₂²×C₄×C₅	—	6	2	no	—
230	C₂²×C₄×C₅	—	6	1	no	—
231	C₂²×C₄×C₅	—	12	4	no	—
232	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
233	C₂×C₅×C₈	—	3	2	no	—
234	C₂×C₅×C₈	—	6	4	no	—
235	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
236	C₅×C₄⋊C₄	—	2	1	no	—
237	C₅×C₄⋊C₄	—	3	2	no	—
238	C₅×C₄⋊C₄	—	3	1	no	—
239	C₅×C₄⋊C₄	—	6	2	no	—
240	C₅×C₄⋊C₄	—	6	2	no	—
241	C₅×C₄⋊C₄	—	6	1	no	—
242	C₅×C₄⋊C₄	—	6	1	no	—
243	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
244	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
245	C₅×C₂²⋊C₄	—	2	1	no	—
246	C₅×C₂²⋊C₄	—	6	1	no	—
247	C₅×C₂²⋊C₄	—	6	1	no	—
248	C₅×C₂²⋊C₄	—	6	1	no	—
249	C₂×#121	—	3	1	no	—
250	C₂²×C₄⋊C₄	—	3	1	no	—
251	#480	—	3	1	no	—
252	#480	—	3	1	no	—
253	#480	—	3	2	no	—
254	#480	—	3	2	no	—
255	#480	—	3	1	no	—
256	#480	C₅×D₃	1	1	yes	characteristic, direct product factor
257	C₂×#107	—	3	2	no	—
258	C₂×#102	—	3	2	no	—
259	C₂×C₂²⋊C₈	—	3	1	no	—
260	C₂²×C₃×C₅	—	2	1	no	—
261	C₂²×C₃×C₅	—	2	1	no	—
262	C₂²×C₃×C₅	—	4	1	no	—
263	C₂²×C₃×C₅	—	4	1	no	—
264	C₂²×C₃×C₅	—	4	1	no	—
265	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
266	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₅×D₃	—	2	1	no	—
268	C₂×C₅×D₃	—	2	1	no	—
269	C₂×C₅×D₃	—	2	8	no	—
270	C₂×C₅×D₃	—	4	1	no	—
271	C₂×C₅×D₃	—	4	1	no	—
272	C₂×C₅×D₃	—	4	1	no	—
273	C₂×C₅×D₃	—	8	4	no	—
274	C₂×C₅×D₃	#123	1	2	yes	—
275	C₂×C₅×D₃	C₂×D₈	1	2	yes	—
276	C₂×C₅×D₃	C₂×D₈	1	2	yes	—
277	C₂×C₅×D₃	#137	1	2	yes	—
278	C₃×C₄×C₅	—	2	1	no	—
279	C₃×C₄×C₅	—	4	2	no	—
280	C₃×C₄×C₅	—	4	1	no	—
281	C₃×C₄×C₅	C₂×#41	1	2	yes	—
282	C₅×Dic₃	—	2	1	no	—
283	C₅×Dic₃	—	4	2	no	—
284	C₅×Dic₃	—	4	1	no	—
285	C₅×Dic₃	#123	1	2	yes	—
286	C₂³×D₃	—	2	1	no	—
287	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
288	C₂×C₃×D₄	—	2	1	no	—
289	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
290	C₂²×C₃×C₄	—	2	1	no	—
291	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
292	C₂×#67	—	2	1	no	—
293	C₂×#67	—	2	1	no	—
294	C₂×#67	—	2	1	no	—
295	C₂²×Dic₃	—	2	1	no	—
296	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
297	D₃×D₄	—	2	4	no	—
298	D₃×D₄	—	4	4	no	—
299	C₂×D₁₂	—	2	1	no	—
300	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
301	C₂×C₄×D₃	—	2	4	no	—
302	C₂×C₄×D₃	—	2	1	no	—
303	C₂×C₄×D₃	—	2	2	no	—
304	C₂×C₄×D₃	—	2	2	no	—
305	C₂×C₄×D₃	—	4	4	no	—
306	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
307	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
308	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
309	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
310	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
311	C₃×C₄⋊C₄	—	2	1	no	—
312	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
313	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
314	C₃×C₂²⋊C₄	—	2	1	no	—
315	#217	—	2	1	no	—
316	(C₂×D₃)⋊C₄	—	2	1	no	—
317	(C₂×D₃)⋊C₄	—	2	1	no	—
318	C₄⋊Dic₃	—	2	1	no	—
319	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
320	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
321	Dic₃⋊C₄	—	2	1	no	—
322	Dic₃⋊C₄	—	2	2	no	—
323	Dic₃⋊C₄	—	2	2	no	—
324	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
325	D₃×C₈	—	2	4	no	—
326	C₂³×C₅	—	2	1	no	—
327	C₂³×C₅	—	3	1	no	—
328	C₂³×C₅	—	3	4	no	—
329	C₂³×C₅	—	3	1	no	—
330	C₂³×C₅	—	6	2	no	—
331	C₂³×C₅	—	6	2	no	—
332	C₂³×C₅	—	6	1	no	—
333	C₂³×C₅	—	12	2	no	—
334	C₂³×C₅	—	12	2	no	—
335	C₂³×C₅	—	12	2	no	—
336	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
337	C₅×D₄	—	2	2	no	—
338	C₅×D₄	—	4	2	no	—
339	C₅×D₄	—	6	2	no	—
340	C₅×D₄	—	12	2	no	—
341	C₅×D₄	—	12	2	no	—
342	C₅×D₄	—	12	2	no	—
343	C₅×D₄	—	12	2	no	—
344	C₂×C₄×C₅	—	2	2	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	2	no	—
347	C₂×C₄×C₅	—	3	1	no	—
348	C₂×C₄×C₅	—	3	4	no	—
349	C₂×C₄×C₅	—	3	1	no	—
350	C₂×C₄×C₅	—	4	2	no	—
351	C₂×C₄×C₅	—	6	2	no	—
352	C₂×C₄×C₅	—	6	2	no	—
353	C₂×C₄×C₅	—	6	2	no	—
354	C₂×C₄×C₅	—	6	2	no	—
355	C₂×C₄×C₅	—	6	1	no	—
356	C₂×C₄×C₅	—	6	2	no	—
357	C₂×C₄×C₅	—	12	4	no	—
358	C₂×C₄×C₅	—	12	4	no	—
359	C₂×C₄×C₅	—	12	2	no	—
360	C₂×C₄×C₅	—	12	2	no	—
361	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
362	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
363	C₅×C₈	—	2	2	no	—
364	C₅×C₈	—	6	2	no	—
365	C₂²×D₄	—	3	1	no	—
366	C₂²×D₄	—	6	1	no	—
367	C₂³×C₄	—	3	1	no	—
368	C₂³×C₄	—	6	1	no	—
369	C₂²×C₈	—	3	2	no	—
370	#121	—	3	1	no	—
371	#121	—	3	1	no	—
372	#121	—	3	1	no	—
373	#121	—	6	1	no	—
374	#121	—	6	1	no	—
375	#121	C₂×C₅×D₃	1	1	yes	characteristic
376	C₂×C₄⋊C₄	—	3	1	no	—
377	C₂×C₄⋊C₄	—	3	2	no	—
378	C₂×C₄⋊C₄	—	3	2	no	—
379	C₂×C₄⋊C₄	—	3	1	no	—
380	C₂×C₄⋊C₄	—	6	1	no	—
381	C₂×C₄⋊C₄	—	6	1	no	—
382	C₂×C₄⋊C₄	—	6	1	no	—
383	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
384	C₂×C₂²⋊C₄	—	6	1	no	—
385	#107	—	3	2	no	—
386	#107	—	3	2	no	—
387	#107	—	3	2	no	—
388	#107	C₂×C₅×D₃	1	2	yes	complemented
389	#102	—	3	2	no	—
390	#102	—	3	2	no	—
391	#102	—	3	2	no	—
392	#102	C₂×C₅×D₃	1	2	yes	complemented
393	C₂²⋊C₈	—	3	1	no	—
394	C₂²⋊C₈	—	3	2	no	—
395	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
396	C₂×C₃×C₅	—	2	2	no	—
397	C₂×C₃×C₅	—	8	1	no	—
398	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
399	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
400	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
401	C₅×D₃	—	2	2	no	—
402	C₅×D₃	—	8	1	no	—
403	C₅×D₃	#480	1	4	yes	direct product factor
404	C₂³×C₃	—	2	1	no	—
405	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
406	C₂²×D₃	—	2	2	no	—
407	C₂²×D₃	—	2	2	no	—
408	C₂²×D₃	—	2	1	no	—
409	C₂²×D₃	—	4	2	no	—
410	C₂²×D₃	—	4	2	no	—
411	C₂²×D₃	—	4	2	no	—
412	C₂²×D₃	C₅×D₈	1	4	yes	—
413	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
414	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
415	C₃×D₄	—	2	2	no	—
416	C₃×D₄	—	4	2	no	—
417	C₂×C₃×C₄	—	2	2	no	—
418	C₂×C₃×C₄	—	2	2	no	—
419	C₂×C₃×C₄	—	2	1	no	—
420	C₂×C₃×C₄	—	4	2	no	—
421	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
422	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
423	#67	—	4	2	no	—
424	#67	—	4	2	no	—
425	#67	—	4	2	no	—
426	C₂×Dic₃	—	2	2	no	—
427	C₂×Dic₃	—	2	2	no	—
428	C₂×Dic₃	—	2	1	no	—
429	C₂×Dic₃	—	4	2	no	—
430	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
431	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
432	D₁₂	—	2	2	no	—
433	D₁₂	—	4	2	no	—
434	C₄×D₃	—	2	2	no	—
435	C₄×D₃	—	2	2	no	—
436	C₄×D₃	—	2	2	no	—
437	C₄×D₃	—	4	4	no	—
438	C₄×D₃	—	4	4	no	—
439	C₄×D₃	—	4	2	no	—
440	C₄×D₃	C₅×#41	1	4	yes	—
441	C₃×C₈	—	2	2	no	—
442	C₃⋊C₈	—	2	2	no	—
443	C₂²×C₅	—	2	1	no	—
444	C₂²×C₅	—	2	1	no	—
445	C₂²×C₅	—	3	2	no	—
446	C₂²×C₅	—	3	2	no	—
447	C₂²×C₅	—	3	2	no	—
448	C₂²×C₅	—	3	2	no	—
449	C₂²×C₅	—	4	1	no	—
450	C₂²×C₅	—	4	1	no	—
451	C₂²×C₅	—	4	1	no	—
452	C₂²×C₅	—	6	8	no	—
453	C₂²×C₅	—	6	1	no	—
454	C₂²×C₅	—	6	1	no	—
455	C₂²×C₅	—	12	1	no	—
456	C₂²×C₅	—	12	1	no	—
457	C₂²×C₅	—	12	1	no	—
458	C₂²×C₅	—	24	4	no	—
459	C₂²×C₅	D₃×D₈	1	2	yes	—
460	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
461	C₄×C₅	—	2	1	no	—
462	C₄×C₅	—	3	2	no	—
463	C₄×C₅	—	4	2	no	—
464	C₄×C₅	—	4	1	no	—
465	C₄×C₅	—	6	1	no	—
466	C₄×C₅	—	12	2	no	—
467	C₄×C₅	—	12	1	no	—
468	C₄×C₅	D₃×#41	1	2	yes	—
469	C₂⁴	—	3	1	no	—
470	C₂⁴	—	6	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	3	1	no	—
473	C₂×D₄	—	6	1	no	—
474	C₂×D₄	—	6	4	no	—
475	C₂×D₄	—	6	1	no	—
476	C₂×D₄	—	6	1	no	—
477	C₂×D₄	—	6	1	no	—
478	C₂×D₄	—	12	4	no	—
479	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	3	1	no	—
482	C₂²×C₄	—	3	1	no	—
483	C₂²×C₄	—	3	1	no	—
484	C₂²×C₄	—	3	1	no	—
485	C₂²×C₄	—	3	1	no	—
486	C₂²×C₄	—	6	4	no	—
487	C₂²×C₄	—	6	1	no	—
488	C₂²×C₄	—	6	2	no	—
489	C₂²×C₄	—	6	2	no	—
490	C₂²×C₄	—	6	1	no	—
491	C₂²×C₄	—	12	4	no	—
492	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
493	C₂×C₈	—	3	2	no	—
494	C₂×C₈	—	6	4	no	—
495	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	3	2	no	—
498	C₄⋊C₄	—	3	1	no	—
499	C₄⋊C₄	—	6	2	no	—
500	C₄⋊C₄	—	6	2	no	—
501	C₄⋊C₄	—	6	1	no	—
502	C₄⋊C₄	—	6	1	no	—
503	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
504	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	6	1	no	—
507	C₂²⋊C₄	—	6	1	no	—
508	C₂²⋊C₄	—	6	1	no	—
509	C₃×C₅	C₂×#480	1	1	yes	characteristic, complemented, Hall
510	C₂²×C₃	—	2	1	no	—
511	C₂²×C₃	—	2	1	no	—
512	C₂²×C₃	—	4	1	no	—
513	C₂²×C₃	—	4	1	no	—
514	C₂²×C₃	—	4	1	no	—
515	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
516	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
517	C₂×D₃	—	2	1	no	—
518	C₂×D₃	—	2	1	no	—
519	C₂×D₃	—	2	8	no	—
520	C₂×D₃	—	4	1	no	—
521	C₂×D₃	—	4	1	no	—
522	C₂×D₃	—	4	1	no	—
523	C₂×D₃	—	8	4	no	—
524	C₂×D₃	C₅×#123	1	2	yes	—
525	C₂×D₃	C₂×C₅×D₈	1	2	yes	—
526	C₂×D₃	C₂×C₅×D₈	1	2	yes	—
527	C₂×D₃	C₅×#137	1	2	yes	—
528	C₃×C₄	—	2	1	no	—
529	C₃×C₄	—	4	2	no	—
530	C₃×C₄	—	4	1	no	—
531	C₃×C₄	C₂×C₅×#41	1	2	yes	—
532	Dic₃	—	2	1	no	—
533	Dic₃	—	4	2	no	—
534	Dic₃	—	4	1	no	—
535	Dic₃	C₅×#123	1	2	yes	—
536	C₂×C₅	—	2	2	no	—
537	C₂×C₅	—	3	4	no	—
538	C₂×C₅	—	6	2	no	—
539	C₂×C₅	—	8	1	no	—
540	C₂×C₅	—	24	1	no	—
541	C₂×C₅	D₃×#123	1	1	yes	characteristic
542	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
543	C₂×C₅	D₃×#137	1	1	yes	characteristic
544	C₂³	—	2	1	no	—
545	C₂³	—	3	1	no	—
546	C₂³	—	3	4	no	—
547	C₂³	—	3	1	no	—
548	C₂³	—	6	2	no	—
549	C₂³	—	6	2	no	—
550	C₂³	—	6	1	no	—
551	C₂³	—	12	2	no	—
552	C₂³	—	12	2	no	—
553	C₂³	—	12	2	no	—
554	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
555	D₄	—	2	2	no	—
556	D₄	—	4	2	no	—
557	D₄	—	6	2	no	—
558	D₄	—	12	2	no	—
559	D₄	—	12	2	no	—
560	D₄	—	12	2	no	—
561	D₄	—	12	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	3	1	no	—
566	C₂×C₄	—	3	4	no	—
567	C₂×C₄	—	3	1	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	6	2	no	—
570	C₂×C₄	—	6	2	no	—
571	C₂×C₄	—	6	2	no	—
572	C₂×C₄	—	6	2	no	—
573	C₂×C₄	—	6	1	no	—
574	C₂×C₄	—	6	2	no	—
575	C₂×C₄	—	12	4	no	—
576	C₂×C₄	—	12	4	no	—
577	C₂×C₄	—	12	2	no	—
578	C₂×C₄	—	12	2	no	—
579	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
580	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
581	C₈	—	2	2	no	—
582	C₈	—	6	2	no	—
583	C₂×C₃	—	2	2	no	—
584	C₂×C₃	—	8	1	no	—
585	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
586	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
587	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
588	D₃	—	2	2	no	—
589	D₃	—	8	1	no	—
590	D₃	C₅×#480	1	4	yes	direct product factor
591	C₅	D₃×#480	1	1	yes	characteristic, direct product factor, Sylow
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	3	2	no	—
595	C₂²	—	3	2	no	—
596	C₂²	—	3	2	no	—
597	C₂²	—	3	2	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	6	8	no	—
602	C₂²	—	6	1	no	—
603	C₂²	—	6	1	no	—
604	C₂²	—	12	1	no	—
605	C₂²	—	12	1	no	—
606	C₂²	—	12	1	no	—
607	C₂²	—	24	4	no	—
608	C₂²	C₅×D₃×D₈	1	2	yes	—
609	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
610	C₄	—	2	1	no	—
611	C₄	—	3	2	no	—
612	C₄	—	4	2	no	—
613	C₄	—	4	1	no	—
614	C₄	—	6	1	no	—
615	C₄	—	12	2	no	—
616	C₄	—	12	1	no	—
617	C₄	C₅×D₃×#41	1	2	yes	—
618	C₃	C₂×C₅×#480	1	1	yes	characteristic, complemented, Sylow
619	C₂	—	2	2	no	—
620	C₂	—	3	4	no	—
621	C₂	—	6	2	no	—
622	C₂	—	8	1	no	—
623	C₂	—	24	1	no	—
624	C₂	C₅×D₃×#123	1	1	yes	characteristic
625	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic
626	C₂	C₅×D₃×#137	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#480	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×D₃×#121	C₂
hypercenter	C₅×#480	D₃
hypocenter	C₃	C₂×C₅×#480
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#480

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
3. C₃×C₅×#480	C₂	semidirect
4. C₅×#5033	C₂	semidirect
5. C₅×#4967	C₂	semidirect
6. C₅×#4882	C₂	semidirect
7. C₅×D₃×#107	C₂	semidirect
8. C₅×#4774	C₂	semidirect
9. C₅×D₃×#102	C₂	semidirect
10. C₅×#4736	C₂	semidirect
11. C₅×D₃×C₂²⋊C₈	C₂	semidirect
18. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
22. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
30. C₅×D₃×C₄⋊C₄	C₂²	semidirect
33. C₃×C₅×#107	C₂²	semidirect
34. C₃×C₅×#102	C₂²	semidirect
35. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
36. C₅×#832	C₂²	semidirect
37. C₅×#830	C₂²	semidirect
38. C₅×#821	C₂²	semidirect
39. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
40. C₅×#818	C₂²	semidirect
41. C₅×#809	C₂²	semidirect
42. C₅×#807	C₂²	semidirect
43. C₅×#807	C₂²	semidirect
44. D₃×#480	C₅	direct (N × H)
52. C₅×#480	D₃	direct (N × H)
97. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
98. C₃×#480	C₂×C₅	semidirect
99. #5033	C₂×C₅	semidirect
100. #4967	C₂×C₅	semidirect
101. #4882	C₂×C₅	semidirect
102. D₃×#107	C₂×C₅	semidirect
103. #4774	C₂×C₅	semidirect
104. D₃×#102	C₂×C₅	semidirect
105. #4736	C₂×C₅	semidirect
106. D₃×C₂²⋊C₈	C₂×C₅	semidirect
125. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
130. C₅×#107	C₂×D₃	semidirect
134. C₅×#102	C₂×D₃	semidirect
137. C₅×C₂²⋊C₈	C₂×D₃	semidirect
183. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
187. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
195. D₃×C₄⋊C₄	C₂²×C₅	semidirect
198. C₃×#107	C₂²×C₅	semidirect
199. C₃×#102	C₂²×C₅	semidirect
200. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
201. #832	C₂²×C₅	semidirect
202. #830	C₂²×C₅	semidirect
203. #821	C₂²×C₅	semidirect
204. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
205. #818	C₂²×C₅	semidirect
206. #809	C₂²×C₅	semidirect
207. #807	C₂²×C₅	semidirect
208. #807	C₂²×C₅	semidirect
256. #480	C₅×D₃	direct (N × H)
383. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
388. #107	C₂×C₅×D₃	semidirect
392. #102	C₂×C₅×D₃	semidirect
395. C₂²⋊C₈	C₂×C₅×D₃	semidirect
403. C₅×D₃	#480	direct (N × H)
509. C₃×C₅	C₂×#480	semidirect
590. D₃	C₅×#480	direct (N × H)
591. C₅	D₃×#480	direct (N × H)
618. C₃	C₂×C₅×#480	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×#121	2
C₂×C₅×D₃×C₄⋊C₄	2
C₃×C₅×#480	2
C₅×#5033	2
C₅×#4967	2
C₅×#4882	2
C₅×D₃×#107	2
C₅×#4774	2
C₅×D₃×#102	2
C₅×#4736	2
C₅×D₃×C₂²⋊C₈	2
C₂×C₅×#480	3
D₃×#480	5

Subgroups — C5×D3×#480 #14431395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#480 #14431395