Subgroups — C₅×D₃×#380 #14319819

Order 1920.

2464 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	2	yes	maximal
4	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5212	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4987	C₂	1	2	yes	maximal, complemented
7	C₅×#4942	C₂	1	2	yes	maximal, complemented
8	C₅×#4667	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×#95	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#380	—	3	1	no	maximal, Hall
11	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₅×D₃	—	2	8	no	—
15	C₂²×C₄×C₅×D₃	C₄	1	8	yes	complemented
16	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
17	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₅×#217	C₂²	1	2	yes	—
24	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
25	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
26	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	complemented
27	C₅×D₃×C₄⋊C₄	—	2	8	no	—
28	C₅×D₃×C₂²⋊C₄	—	2	8	no	—
29	C₃×C₅×#95	C₂²	1	2	yes	complemented
30	C₅×C₃⋊#95	C₂²	1	2	yes	complemented
31	C₅×C₃⋊#95	C₂²	1	4	yes	complemented
32	D₃×#380	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂⁴×C₄×C₅	—	3	1	no	—
34	C₂²×C₅×C₄⋊C₄	—	3	2	no	—
35	C₂²×C₅×C₂²⋊C₄	—	3	2	no	—
36	C₅×#380	—	3	2	no	—
37	C₅×#380	—	3	1	no	—
38	C₅×#380	—	3	2	no	—
39	C₅×#380	—	3	2	no	—
40	C₅×#380	D₃	1	1	yes	characteristic, direct product factor
41	C₂×C₅×#95	—	3	2	no	—
42	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
43	C₂³×C₅×D₃	—	2	4	no	—
44	C₂³×C₅×D₃	—	2	4	no	—
45	C₂³×C₅×D₃	C₂×C₄	1	4	yes	—
46	C₂³×C₅×D₃	D₄	1	4	yes	—
47	C₂³×C₅×D₃	Q₈	1	4	yes	—
48	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
49	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	—	2	4	no	—
51	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	complemented
52	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₅×Dic₃	—	2	4	no	—
56	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
57	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
58	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
59	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
60	C₂×C₄×C₅×D₃	—	2	4	no	—
61	C₂×C₄×C₅×D₃	—	2	4	no	—
62	C₂×C₄×C₅×D₃	—	2	4	no	—
63	C₂×C₄×C₅×D₃	—	2	32	no	—
64	C₂×C₄×C₅×D₃	—	2	8	no	—
65	C₂×C₄×C₅×D₃	—	2	8	no	—
66	C₂×C₄×C₅×D₃	—	2	8	no	—
67	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
68	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
69	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	complemented
70	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	complemented
71	C₂×C₄×C₅×D₃	D₄	1	8	yes	—
72	C₃×C₅×C₄⋊C₄	—	2	4	no	—
73	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
74	C₅×#217	—	2	4	no	—
75	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
76	C₅×C₄⋊Dic₃	—	2	4	no	—
77	C₅×Dic₃⋊C₄	—	2	8	no	—
78	C₂³×C₄×D₃	C₂×C₅	1	1	yes	characteristic
79	C₂×D₃×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
80	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	2	yes	—
81	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
82	#5212	C₂×C₅	1	1	yes	characteristic, complemented
83	#4987	C₂×C₅	1	2	yes	complemented
84	#4942	C₂×C₅	1	2	yes	complemented
85	#4667	C₂×C₅	1	2	yes	complemented
86	D₃×#95	C₂×C₅	1	2	yes	complemented
87	C₂⁵×C₅	—	3	1	no	—
88	C₂³×C₄×C₅	—	3	1	no	—
89	C₂³×C₄×C₅	—	3	1	no	—
90	C₂³×C₄×C₅	—	3	8	no	—
91	C₂³×C₄×C₅	—	3	1	no	—
92	C₂³×C₄×C₅	—	3	1	no	—
93	C₂³×C₄×C₅	—	3	1	no	—
94	C₂³×C₄×C₅	—	3	4	no	—
95	C₂³×C₄×C₅	—	6	8	no	—
96	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
97	C₂×C₅×C₄⋊C₄	—	3	4	no	—
98	C₂×C₅×C₄⋊C₄	—	3	2	no	—
99	C₂×C₅×C₄⋊C₄	—	6	8	no	—
100	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
101	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
102	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
103	C₂×C₅×C₂²⋊C₄	—	6	8	no	—
104	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
105	C₅×#95	—	3	4	no	—
106	C₅×#95	—	3	2	no	—
107	C₅×#95	C₂×D₃	1	2	yes	complemented
108	C₂×#380	—	3	1	no	Sylow
109	C₂³×C₃×C₅	—	2	2	no	—
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
112	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
113	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
114	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
115	C₂²×C₅×D₃	—	2	2	no	—
116	C₂²×C₅×D₃	—	2	2	no	—
117	C₂²×C₅×D₃	—	2	8	no	—
118	C₂²×C₅×D₃	—	2	8	no	—
119	C₂²×C₅×D₃	—	2	16	no	—
120	C₂²×C₅×D₃	—	2	16	no	—
121	C₂²×C₅×D₃	C₄⋊C₄	1	16	yes	complemented
122	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
123	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
124	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
125	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
126	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
127	C₂²×C₅×D₃	C₂×Q₈	1	2	yes	—
128	C₂²×C₅×D₃	C₂×Q₈	1	2	yes	—
129	C₂²×C₅×D₃	#41	1	4	yes	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	8	no	—
132	C₂×C₃×C₄×C₅	—	2	4	no	—
133	C₂×C₃×C₄×C₅	—	2	4	no	—
134	C₂×C₃×C₄×C₅	—	2	4	no	—
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
136	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
138	C₂×C₅×Dic₃	—	2	2	no	—
139	C₂×C₅×Dic₃	—	2	8	no	—
140	C₂×C₅×Dic₃	—	2	4	no	—
141	C₂×C₅×Dic₃	—	2	4	no	—
142	C₂×C₅×Dic₃	—	2	4	no	—
143	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
144	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
145	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
146	C₄×C₅×D₃	—	2	8	no	—
147	C₄×C₅×D₃	—	2	8	no	—
148	C₄×C₅×D₃	—	2	8	no	—
149	C₄×C₅×D₃	—	4	16	no	—
150	C₄×C₅×D₃	C₂²⋊C₄	1	16	yes	complemented
151	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
152	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
153	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
154	C₂²×C₄×D₃	—	2	8	no	—
155	C₂²×C₄×D₃	C₄×C₅	1	8	yes	complemented
156	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
157	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
158	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
159	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
160	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
162	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
163	C₂×#217	C₂²×C₅	1	2	yes	—
164	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
165	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
166	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	complemented
167	D₃×C₄⋊C₄	—	2	8	no	—
168	D₃×C₂²⋊C₄	—	2	8	no	—
169	C₃×#95	C₂²×C₅	1	2	yes	complemented
170	C₃⋊#95	C₂²×C₅	1	2	yes	complemented
171	C₃⋊#95	C₂²×C₅	1	4	yes	complemented
172	C₂⁴×C₅	—	3	1	no	—
173	C₂⁴×C₅	—	3	4	no	—
174	C₂⁴×C₅	—	3	4	no	—
175	C₂⁴×C₅	—	3	4	no	—
176	C₂⁴×C₅	—	3	1	no	—
177	C₂⁴×C₅	—	6	4	no	—
178	C₂⁴×C₅	—	6	4	no	—
179	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
180	C₂²×C₄×C₅	—	2	4	no	—
181	C₂²×C₄×C₅	—	3	1	no	—
182	C₂²×C₄×C₅	—	3	4	no	—
183	C₂²×C₄×C₅	—	3	8	no	—
184	C₂²×C₄×C₅	—	3	4	no	—
185	C₂²×C₄×C₅	—	3	1	no	—
186	C₂²×C₄×C₅	—	3	4	no	—
187	C₂²×C₄×C₅	—	3	4	no	—
188	C₂²×C₄×C₅	—	3	4	no	—
189	C₂²×C₄×C₅	—	3	4	no	—
190	C₂²×C₄×C₅	—	6	4	no	—
191	C₂²×C₄×C₅	—	6	32	no	—
192	C₂²×C₄×C₅	—	6	4	no	—
193	C₂²×C₄×C₅	—	6	8	no	—
194	C₂²×C₄×C₅	—	6	8	no	—
195	C₂²×C₄×C₅	—	6	8	no	—
196	C₂²×C₄×C₅	—	6	4	no	—
197	C₂²×C₄×C₅	—	6	4	no	—
198	C₂²×C₄×C₅	C₄×D₃	1	4	yes	complemented
199	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
200	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
201	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
202	C₅×C₄⋊C₄	—	2	4	no	—
203	C₅×C₄⋊C₄	—	6	8	no	—
204	C₅×C₄⋊C₄	—	6	4	no	—
205	C₅×C₂²⋊C₄	—	2	4	no	—
206	C₅×C₂²⋊C₄	—	6	8	no	—
207	C₅×C₂²⋊C₄	—	6	4	no	—
208	C₂⁴×C₄	—	3	1	no	—
209	C₂²×C₄⋊C₄	—	3	2	no	—
210	C₂²×C₂²⋊C₄	—	3	2	no	—
211	#380	—	3	1	no	—
212	#380	—	3	2	no	—
213	#380	—	3	2	no	—
214	#380	—	3	2	no	—
215	#380	C₅×D₃	1	1	yes	characteristic, direct product factor
216	C₂×#95	—	3	2	no	—
217	C₂²×C₃×C₅	—	2	2	no	—
218	C₂²×C₃×C₅	—	2	2	no	—
219	C₂²×C₃×C₅	—	2	4	no	—
220	C₂²×C₃×C₅	—	2	4	no	—
221	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	4	yes	complemented
222	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
223	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
224	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
225	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
226	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
227	C₂×C₅×D₃	—	2	2	no	—
228	C₂×C₅×D₃	—	2	2	no	—
229	C₂×C₅×D₃	—	2	4	no	—
230	C₂×C₅×D₃	—	2	4	no	—
231	C₂×C₅×D₃	—	2	32	no	—
232	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	4	yes	—
233	C₂×C₅×D₃	C₂×C₄⋊C₄	1	4	yes	—
234	C₂×C₅×D₃	C₂×C₄⋊C₄	1	4	yes	complemented
235	C₂×C₅×D₃	#117	1	4	yes	—
236	C₂×C₅×D₃	#121	1	8	yes	—
237	C₂×C₅×D₃	C₂²⋊Q₈	1	8	yes	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	—	4	4	no	—
240	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	complemented
241	C₅×Dic₃	—	2	2	no	—
242	C₅×Dic₃	—	4	4	no	—
243	C₅×Dic₃	C₂×C₂²⋊C₄	1	4	yes	complemented
244	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
245	C₂³×D₃	—	2	4	no	—
246	C₂³×D₃	—	2	4	no	—
247	C₂³×D₃	C₂×C₄×C₅	1	4	yes	—
248	C₂³×D₃	C₅×D₄	1	4	yes	—
249	C₂³×D₃	C₅×Q₈	1	4	yes	—
250	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
251	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
252	C₂²×C₃×C₄	—	2	4	no	—
253	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	complemented
254	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
255	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
256	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
257	C₂²×Dic₃	—	2	4	no	—
258	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
259	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
260	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
261	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
262	C₂×C₄×D₃	—	2	4	no	—
263	C₂×C₄×D₃	—	2	4	no	—
264	C₂×C₄×D₃	—	2	4	no	—
265	C₂×C₄×D₃	—	2	32	no	—
266	C₂×C₄×D₃	—	2	8	no	—
267	C₂×C₄×D₃	—	2	8	no	—
268	C₂×C₄×D₃	—	2	8	no	—
269	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
270	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
271	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	complemented
272	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	complemented
273	C₂×C₄×D₃	C₅×D₄	1	8	yes	—
274	C₃×C₄⋊C₄	—	2	4	no	—
275	C₃×C₂²⋊C₄	—	2	4	no	—
276	#217	—	2	4	no	—
277	(C₂×D₃)⋊C₄	—	2	8	no	—
278	C₄⋊Dic₃	—	2	4	no	—
279	Dic₃⋊C₄	—	2	8	no	—
280	C₂³×C₅	—	2	2	no	—
281	C₂³×C₅	—	2	2	no	—
282	C₂³×C₅	—	3	2	no	—
283	C₂³×C₅	—	3	4	no	—
284	C₂³×C₅	—	3	2	no	—
285	C₂³×C₅	—	3	2	no	—
286	C₂³×C₅	—	3	4	no	—
287	C₂³×C₅	—	3	16	no	—
288	C₂³×C₅	—	3	2	no	—
289	C₂³×C₅	—	3	2	no	—
290	C₂³×C₅	—	3	2	no	—
291	C₂³×C₅	—	6	8	no	—
292	C₂³×C₅	—	6	8	no	—
293	C₂³×C₅	—	6	16	no	—
294	C₂³×C₅	—	6	16	no	—
295	C₂³×C₅	—	6	2	no	—
296	C₂³×C₅	—	6	2	no	—
297	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
298	C₂³×C₅	D₃×D₄	1	2	yes	—
299	C₂³×C₅	D₃×Q₈	1	2	yes	—
300	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	8	no	—
303	C₂×C₄×C₅	—	2	4	no	—
304	C₂×C₄×C₅	—	2	4	no	—
305	C₂×C₄×C₅	—	2	4	no	—
306	C₂×C₄×C₅	—	3	2	no	—
307	C₂×C₄×C₅	—	3	4	no	—
308	C₂×C₄×C₅	—	3	16	no	—
309	C₂×C₄×C₅	—	3	2	no	—
310	C₂×C₄×C₅	—	6	8	no	—
311	C₂×C₄×C₅	—	6	8	no	—
312	C₂×C₄×C₅	—	6	8	no	—
313	C₂×C₄×C₅	—	6	2	no	—
314	C₂×C₄×C₅	—	6	8	no	—
315	C₂×C₄×C₅	—	6	4	no	—
316	C₂×C₄×C₅	—	6	4	no	—
317	C₂×C₄×C₅	—	6	4	no	—
318	C₂×C₄×C₅	—	12	16	no	—
319	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
320	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
321	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
322	C₂⁵	—	3	1	no	—
323	C₂³×C₄	—	3	1	no	—
324	C₂³×C₄	—	3	1	no	—
325	C₂³×C₄	—	3	8	no	—
326	C₂³×C₄	—	3	1	no	—
327	C₂³×C₄	—	3	1	no	—
328	C₂³×C₄	—	3	1	no	—
329	C₂³×C₄	—	3	4	no	—
330	C₂³×C₄	—	6	8	no	—
331	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
332	C₂×C₄⋊C₄	—	3	4	no	—
333	C₂×C₄⋊C₄	—	3	2	no	—
334	C₂×C₄⋊C₄	—	6	8	no	—
335	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
336	C₂×C₂²⋊C₄	—	3	2	no	—
337	C₂×C₂²⋊C₄	—	3	4	no	—
338	C₂×C₂²⋊C₄	—	6	8	no	—
339	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
340	#95	—	3	4	no	—
341	#95	—	3	2	no	—
342	#95	C₂×C₅×D₃	1	2	yes	complemented
343	C₂×C₃×C₅	—	2	4	no	—
344	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
345	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
346	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
347	C₂×C₃×C₅	C₂×#121	1	2	yes	—
348	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	2	yes	—
349	C₅×D₃	—	2	4	no	—
350	C₅×D₃	#380	1	8	yes	direct product factor
351	C₂³×C₃	—	2	2	no	—
352	C₂³×C₃	—	2	2	no	—
353	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
354	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
355	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
356	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
357	C₂²×D₃	—	2	2	no	—
358	C₂²×D₃	—	2	2	no	—
359	C₂²×D₃	—	2	8	no	—
360	C₂²×D₃	—	2	8	no	—
361	C₂²×D₃	—	2	16	no	—
362	C₂²×D₃	—	2	16	no	—
363	C₂²×D₃	C₅×C₄⋊C₄	1	16	yes	complemented
364	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
365	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
366	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
367	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
368	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
369	C₂²×D₃	C₂×C₅×Q₈	1	2	yes	—
370	C₂²×D₃	C₂×C₅×Q₈	1	2	yes	—
371	C₂²×D₃	C₅×#41	1	4	yes	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	8	no	—
374	C₂×C₃×C₄	—	2	4	no	—
375	C₂×C₃×C₄	—	2	4	no	—
376	C₂×C₃×C₄	—	2	4	no	—
377	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
378	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
379	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
380	C₂×Dic₃	—	2	2	no	—
381	C₂×Dic₃	—	2	8	no	—
382	C₂×Dic₃	—	2	4	no	—
383	C₂×Dic₃	—	2	4	no	—
384	C₂×Dic₃	—	2	4	no	—
385	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
386	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
387	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
388	C₄×D₃	—	2	8	no	—
389	C₄×D₃	—	2	8	no	—
390	C₄×D₃	—	2	8	no	—
391	C₄×D₃	—	4	16	no	—
392	C₄×D₃	C₅×C₂²⋊C₄	1	16	yes	complemented
393	C₂²×C₅	—	2	2	no	—
394	C₂²×C₅	—	2	2	no	—
395	C₂²×C₅	—	2	4	no	—
396	C₂²×C₅	—	2	4	no	—
397	C₂²×C₅	—	3	4	no	—
398	C₂²×C₅	—	3	4	no	—
399	C₂²×C₅	—	3	4	no	—
400	C₂²×C₅	—	3	8	no	—
401	C₂²×C₅	—	3	8	no	—
402	C₂²×C₅	—	3	4	no	—
403	C₂²×C₅	—	6	32	no	—
404	C₂²×C₅	—	6	2	no	—
405	C₂²×C₅	—	6	2	no	—
406	C₂²×C₅	—	6	4	no	—
407	C₂²×C₅	—	6	4	no	—
408	C₂²×C₅	D₃×C₄⋊C₄	1	4	yes	complemented
409	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
410	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
411	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
412	C₂²×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
413	C₂²×C₅	D₃×#41	1	2	yes	—
414	C₄×C₅	—	2	2	no	—
415	C₄×C₅	—	3	4	no	—
416	C₄×C₅	—	4	4	no	—
417	C₄×C₅	—	6	2	no	—
418	C₄×C₅	—	12	4	no	—
419	C₄×C₅	D₃×C₂²⋊C₄	1	4	yes	complemented
420	C₂⁴	—	3	1	no	—
421	C₂⁴	—	3	4	no	—
422	C₂⁴	—	3	4	no	—
423	C₂⁴	—	3	4	no	—
424	C₂⁴	—	3	1	no	—
425	C₂⁴	—	6	4	no	—
426	C₂⁴	—	6	4	no	—
427	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	3	1	no	—
430	C₂²×C₄	—	3	4	no	—
431	C₂²×C₄	—	3	8	no	—
432	C₂²×C₄	—	3	4	no	—
433	C₂²×C₄	—	3	1	no	—
434	C₂²×C₄	—	3	4	no	—
435	C₂²×C₄	—	3	4	no	—
436	C₂²×C₄	—	3	4	no	—
437	C₂²×C₄	—	3	4	no	—
438	C₂²×C₄	—	6	4	no	—
439	C₂²×C₄	—	6	32	no	—
440	C₂²×C₄	—	6	4	no	—
441	C₂²×C₄	—	6	8	no	—
442	C₂²×C₄	—	6	8	no	—
443	C₂²×C₄	—	6	8	no	—
444	C₂²×C₄	—	6	4	no	—
445	C₂²×C₄	—	6	4	no	—
446	C₂²×C₄	C₄×C₅×D₃	1	4	yes	complemented
447	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
448	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
449	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	6	8	no	—
452	C₄⋊C₄	—	6	4	no	—
453	C₂²⋊C₄	—	2	4	no	—
454	C₂²⋊C₄	—	6	8	no	—
455	C₂²⋊C₄	—	6	4	no	—
456	C₃×C₅	C₂×#380	1	1	yes	characteristic, complemented, Hall
457	C₂²×C₃	—	2	2	no	—
458	C₂²×C₃	—	2	2	no	—
459	C₂²×C₃	—	2	4	no	—
460	C₂²×C₃	—	2	4	no	—
461	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	4	yes	complemented
462	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
463	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
464	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
465	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
466	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
467	C₂×D₃	—	2	2	no	—
468	C₂×D₃	—	2	2	no	—
469	C₂×D₃	—	2	4	no	—
470	C₂×D₃	—	2	4	no	—
471	C₂×D₃	—	2	32	no	—
472	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
473	C₂×D₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
474	C₂×D₃	C₂×C₅×C₄⋊C₄	1	4	yes	complemented
475	C₂×D₃	C₅×#117	1	4	yes	—
476	C₂×D₃	C₅×#121	1	8	yes	—
477	C₂×D₃	C₅×C₂²⋊Q₈	1	8	yes	—
478	C₃×C₄	—	2	2	no	—
479	C₃×C₄	—	4	4	no	—
480	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	complemented
481	Dic₃	—	2	2	no	—
482	Dic₃	—	4	4	no	—
483	Dic₃	C₂×C₅×C₂²⋊C₄	1	4	yes	complemented
484	C₂×C₅	—	2	4	no	—
485	C₂×C₅	—	3	8	no	—
486	C₂×C₅	—	6	4	no	—
487	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
488	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
489	C₂×C₅	D₃×#117	1	1	yes	characteristic
490	C₂×C₅	D₃×#121	1	2	yes	—
491	C₂×C₅	D₃×C₂²⋊Q₈	1	2	yes	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	3	2	no	—
495	C₂³	—	3	4	no	—
496	C₂³	—	3	2	no	—
497	C₂³	—	3	2	no	—
498	C₂³	—	3	4	no	—
499	C₂³	—	3	16	no	—
500	C₂³	—	3	2	no	—
501	C₂³	—	3	2	no	—
502	C₂³	—	3	2	no	—
503	C₂³	—	6	8	no	—
504	C₂³	—	6	8	no	—
505	C₂³	—	6	16	no	—
506	C₂³	—	6	16	no	—
507	C₂³	—	6	2	no	—
508	C₂³	—	6	2	no	—
509	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
510	C₂³	C₅×D₃×D₄	1	2	yes	—
511	C₂³	C₅×D₃×Q₈	1	2	yes	—
512	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	8	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	3	2	no	—
519	C₂×C₄	—	3	4	no	—
520	C₂×C₄	—	3	16	no	—
521	C₂×C₄	—	3	2	no	—
522	C₂×C₄	—	6	8	no	—
523	C₂×C₄	—	6	8	no	—
524	C₂×C₄	—	6	8	no	—
525	C₂×C₄	—	6	2	no	—
526	C₂×C₄	—	6	8	no	—
527	C₂×C₄	—	6	4	no	—
528	C₂×C₄	—	6	4	no	—
529	C₂×C₄	—	6	4	no	—
530	C₂×C₄	—	12	16	no	—
531	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
532	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
533	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
534	C₂×C₃	—	2	4	no	—
535	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
536	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
537	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
538	C₂×C₃	C₂×C₅×#121	1	2	yes	—
539	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	2	yes	—
540	D₃	—	2	4	no	—
541	D₃	C₅×#380	1	8	yes	direct product factor
542	C₅	D₃×#380	1	1	yes	characteristic, direct product factor, Sylow
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	4	no	—
546	C₂²	—	2	4	no	—
547	C₂²	—	3	4	no	—
548	C₂²	—	3	4	no	—
549	C₂²	—	3	4	no	—
550	C₂²	—	3	8	no	—
551	C₂²	—	3	8	no	—
552	C₂²	—	3	4	no	—
553	C₂²	—	6	32	no	—
554	C₂²	—	6	2	no	—
555	C₂²	—	6	2	no	—
556	C₂²	—	6	4	no	—
557	C₂²	—	6	4	no	—
558	C₂²	C₅×D₃×C₄⋊C₄	1	4	yes	complemented
559	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
560	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
561	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
562	C₂²	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
563	C₂²	C₅×D₃×#41	1	2	yes	—
564	C₄	—	2	2	no	—
565	C₄	—	3	4	no	—
566	C₄	—	4	4	no	—
567	C₄	—	6	2	no	—
568	C₄	—	12	4	no	—
569	C₄	C₅×D₃×C₂²⋊C₄	1	4	yes	complemented
570	C₃	C₂×C₅×#380	1	1	yes	characteristic, complemented, Sylow
571	C₂	—	2	4	no	—
572	C₂	—	3	8	no	—
573	C₂	—	6	4	no	—
574	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
575	C₂	C₂×C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
576	C₂	C₅×D₃×#117	1	1	yes	characteristic
577	C₂	C₅×D₃×#121	1	2	yes	—
578	C₂	C₅×D₃×C₂²⋊Q₈	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#380	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₅×D₃	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#380	D₃
hypocenter	C₃	C₂×C₅×#380
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#380

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
4. C₃×C₅×#380	C₂	semidirect
5. C₅×#5212	C₂	semidirect
6. C₅×#4987	C₂	semidirect
7. C₅×#4942	C₂	semidirect
8. C₅×#4667	C₂	semidirect
9. C₅×D₃×#95	C₂	semidirect
15. C₂²×C₄×C₅×D₃	C₄	semidirect
21. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
25. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
26. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
29. C₃×C₅×#95	C₂²	semidirect
30. C₅×C₃⋊#95	C₂²	semidirect
31. C₅×C₃⋊#95	C₂²	semidirect
32. D₃×#380	C₅	direct (N × H)
40. C₅×#380	D₃	direct (N × H)
51. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
56. C₂²×C₅×Dic₃	C₂×C₄	semidirect
69. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
70. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
79. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
81. C₃×#380	C₂×C₅	semidirect
82. #5212	C₂×C₅	semidirect
83. #4987	C₂×C₅	semidirect
84. #4942	C₂×C₅	semidirect
85. #4667	C₂×C₅	semidirect
86. D₃×#95	C₂×C₅	semidirect
100. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
107. C₅×#95	C₂×D₃	semidirect
121. C₂²×C₅×D₃	C₄⋊C₄	semidirect
150. C₄×C₅×D₃	C₂²⋊C₄	semidirect
155. C₂²×C₄×D₃	C₄×C₅	semidirect
161. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
165. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
166. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
169. C₃×#95	C₂²×C₅	semidirect
170. C₃⋊#95	C₂²×C₅	semidirect
171. C₃⋊#95	C₂²×C₅	semidirect
198. C₂²×C₄×C₅	C₄×D₃	semidirect
215. #380	C₅×D₃	direct (N × H)
221. C₂²×C₃×C₅	C₂×C₄⋊C₄	semidirect
234. C₂×C₅×D₃	C₂×C₄⋊C₄	semidirect
240. C₃×C₄×C₅	C₂×C₂²⋊C₄	semidirect
243. C₅×Dic₃	C₂×C₂²⋊C₄	semidirect
253. C₂²×C₃×C₄	C₂×C₄×C₅	semidirect
258. C₂²×Dic₃	C₂×C₄×C₅	semidirect
271. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
272. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
335. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
342. #95	C₂×C₅×D₃	semidirect
350. C₅×D₃	#380	direct (N × H)
363. C₂²×D₃	C₅×C₄⋊C₄	semidirect
392. C₄×D₃	C₅×C₂²⋊C₄	semidirect
408. C₂²×C₅	D₃×C₄⋊C₄	semidirect
419. C₄×C₅	D₃×C₂²⋊C₄	semidirect
446. C₂²×C₄	C₄×C₅×D₃	semidirect
456. C₃×C₅	C₂×#380	semidirect
461. C₂²×C₃	C₂×C₅×C₄⋊C₄	semidirect
474. C₂×D₃	C₂×C₅×C₄⋊C₄	semidirect
480. C₃×C₄	C₂×C₅×C₂²⋊C₄	semidirect
483. Dic₃	C₂×C₅×C₂²⋊C₄	semidirect
541. D₃	C₅×#380	direct (N × H)
542. C₅	D₃×#380	direct (N × H)
558. C₂²	C₅×D₃×C₄⋊C₄	semidirect
569. C₄	C₅×D₃×C₂²⋊C₄	semidirect
570. C₃	C₂×C₅×#380	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₅×D₃	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₅×D₃×C₂²⋊C₄	2
C₃×C₅×#380	2
C₅×#5212	2
C₅×#4987	2
C₅×#4942	2
C₅×#4667	2
C₅×D₃×#95	2
C₂×C₅×#380	3
D₃×#380	5

Subgroups — C5×D3×#380 #14319819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#380 #14319819