Subgroups — C₅×#68871 #14298426

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#4987	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#340	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4551	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4529	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4529	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1823	—	3	1	no	maximal, Hall
9	C₂²×C₄×C₅×D₃	—	2	1	no	—
10	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
15	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
18	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₅×D₃×C₄⋊C₄	—	2	2	no	—
20	C₅×D₃×C₄⋊C₄	C₄	1	4	yes	complemented
21	C₅×C₃⋊#95	—	2	1	no	—
22	C₅×(C₂×D₃)⋊C₈	—	2	2	no	—
23	#68871	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
25	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
26	C₅×#380	—	3	1	no	—
27	C₅×#340	—	3	1	no	—
28	C₅×#340	—	3	1	no	—
29	C₅×#340	—	3	1	no	—
30	C₅×#340	D₃	1	1	yes	characteristic, complemented
31	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	—	2	1	no	—
33	C₂²×C₃×C₄×C₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂²×C₅×Dic₃	—	2	1	no	—
36	C₂²×C₅×Dic₃	—	2	1	no	—
37	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
38	C₂×C₄×C₅×D₃	—	2	1	no	—
39	C₂×C₄×C₅×D₃	—	2	1	no	—
40	C₂×C₄×C₅×D₃	—	2	1	no	—
41	C₂×C₄×C₅×D₃	—	2	1	no	—
42	C₂×C₄×C₅×D₃	—	2	4	no	—
43	C₂×C₄×C₅×D₃	—	4	2	no	—
44	C₂×C₄×C₅×D₃	—	4	2	no	—
45	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
46	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₂×C₃×C₅×C₈	—	2	1	no	—
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	—	2	1	no	—
51	C₃×C₅×C₄⋊C₄	—	2	1	no	—
52	C₃×C₅×C₄⋊C₄	—	2	1	no	—
53	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
54	C₅×(C₂×D₃)⋊C₄	—	4	2	no	—
55	C₅×C₄⋊Dic₃	—	2	1	no	—
56	C₅×C₄⋊Dic₃	—	2	1	no	—
57	C₅×C₄⋊Dic₃	—	2	1	no	—
58	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
59	C₅×Dic₃⋊C₄	—	2	4	no	—
60	C₂×C₅×C₃⋊C₈	—	2	1	no	—
61	C₂×C₅×C₃⋊C₈	—	2	1	no	—
62	C₂×C₅×C₃⋊C₈	—	2	1	no	—
63	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
64	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	1	yes	characteristic
65	#4987	C₂×C₅	1	1	yes	characteristic
66	C₃×#340	C₂×C₅	1	1	yes	characteristic, complemented
67	#4551	C₂×C₅	1	1	yes	characteristic, complemented
68	#4529	C₂×C₅	1	1	yes	characteristic, complemented
69	#4529	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂³×C₄×C₅	—	3	1	no	—
71	C₂³×C₄×C₅	—	6	1	no	—
72	C₂²×C₅×C₈	—	3	1	no	—
73	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
74	C₂×C₅×C₄⋊C₄	—	3	1	no	—
75	C₂×C₅×C₄⋊C₄	—	3	4	no	—
76	C₂×C₅×C₄⋊C₄	—	3	1	no	—
77	C₂×C₅×C₄⋊C₄	—	6	2	no	—
78	C₂×C₅×C₄⋊C₄	—	6	1	no	—
79	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
80	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
81	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
82	C₅×C₂²⋊C₈	—	6	2	no	—
83	C₅×#95	—	6	1	no	—
84	#1823	—	3	1	no	Sylow
85	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₅×D₃	—	2	1	no	—
87	C₂²×C₅×D₃	—	2	1	no	—
88	C₂²×C₅×D₃	—	2	1	no	—
89	C₂²×C₅×D₃	—	2	1	no	—
90	C₂²×C₅×D₃	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₅×D₃	D₈	1	2	yes	—
92	C₂²×C₅×D₃	SD₁₆	1	2	yes	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	—	4	1	no	—
95	C₂×C₃×C₄×C₅	—	4	1	no	—
96	C₂×C₃×C₄×C₅	—	4	1	no	—
97	C₂×C₃×C₄×C₅	—	4	1	no	—
98	C₂×C₃×C₄×C₅	—	4	1	no	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
105	C₂×C₅×Dic₃	—	2	1	no	—
106	C₂×C₅×Dic₃	—	2	1	no	—
107	C₂×C₅×Dic₃	—	2	2	no	—
108	C₂×C₅×Dic₃	—	4	1	no	—
109	C₂×C₅×Dic₃	—	4	1	no	—
110	C₂×C₅×Dic₃	—	4	1	no	—
111	C₂×C₅×Dic₃	—	4	1	no	—
112	C₂×C₅×Dic₃	—	4	1	no	—
113	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
114	C₄×C₅×D₃	—	2	2	no	—
115	C₄×C₅×D₃	—	2	2	no	—
116	C₄×C₅×D₃	—	2	2	no	—
117	C₄×C₅×D₃	—	2	2	no	—
118	C₄×C₅×D₃	—	4	8	no	—
119	C₃×C₅×C₈	—	4	1	no	—
120	C₅×C₃⋊C₈	—	4	1	no	—
121	C₂²×C₄×D₃	—	2	1	no	—
122	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
123	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
124	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
125	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
126	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
127	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
129	C₂×Dic₃⋊C₄	—	2	1	no	—
130	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
131	D₃×C₄⋊C₄	—	2	2	no	—
132	D₃×C₄⋊C₄	C₄×C₅	1	4	yes	complemented
133	C₃⋊#95	—	2	1	no	—
134	(C₂×D₃)⋊C₈	—	2	2	no	—
135	C₂⁴×C₅	—	3	1	no	—
136	C₂²×C₄×C₅	—	2	1	no	—
137	C₂²×C₄×C₅	—	2	1	no	—
138	C₂²×C₄×C₅	—	3	1	no	—
139	C₂²×C₄×C₅	—	3	2	no	—
140	C₂²×C₄×C₅	—	3	2	no	—
141	C₂²×C₄×C₅	—	6	4	no	—
142	C₂²×C₄×C₅	—	6	1	no	—
143	C₂²×C₄×C₅	—	6	1	no	—
144	C₂²×C₄×C₅	—	6	1	no	—
145	C₂²×C₄×C₅	—	6	1	no	—
146	C₂²×C₄×C₅	—	6	1	no	—
147	C₂²×C₄×C₅	—	6	1	no	—
148	C₂²×C₄×C₅	—	12	2	no	—
149	C₂²×C₄×C₅	—	12	2	no	—
150	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	2	1	no	—
153	C₂×C₅×C₈	—	2	1	no	—
154	C₂×C₅×C₈	—	6	1	no	—
155	C₂×C₅×C₈	—	6	1	no	—
156	C₂×C₅×C₈	—	6	1	no	—
157	C₅×C₄⋊C₄	—	2	1	no	—
158	C₅×C₄⋊C₄	—	2	1	no	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	3	2	no	—
161	C₅×C₄⋊C₄	—	6	4	no	—
162	C₅×C₄⋊C₄	—	6	1	no	—
163	C₅×C₄⋊C₄	—	6	1	no	—
164	C₅×C₄⋊C₄	—	6	1	no	—
165	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
166	C₅×C₂²⋊C₄	—	12	2	no	—
167	C₂²×C₄⋊C₄	—	3	1	no	—
168	C₂×C₂²⋊C₈	—	3	1	no	—
169	#380	—	3	1	no	—
170	#340	—	3	1	no	—
171	#340	—	3	1	no	—
172	#340	—	3	1	no	—
173	#340	C₅×D₃	1	1	yes	characteristic, complemented
174	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂²×C₃×C₅	#123	1	1	yes	characteristic
176	C₂²×C₃×C₅	#123	1	1	yes	characteristic
177	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
178	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
179	C₂²×C₃×C₅	#137	1	1	yes	characteristic
180	C₂²×C₃×C₅	#137	1	1	yes	characteristic
181	C₂×C₅×D₃	—	2	2	no	—
182	C₂×C₅×D₃	—	2	2	no	—
183	C₂×C₅×D₃	—	2	2	no	—
184	C₂×C₅×D₃	—	2	2	no	—
185	C₂×C₅×D₃	—	2	2	no	—
186	C₂×C₅×D₃	—	2	2	no	—
187	C₂×C₅×D₃	#102	1	4	yes	—
188	C₃×C₄×C₅	—	4	2	no	—
189	C₃×C₄×C₅	—	8	1	no	—
190	C₃×C₄×C₅	#117	1	1	yes	characteristic
191	C₃×C₄×C₅	#117	1	1	yes	characteristic
192	C₃×C₄×C₅	#123	1	1	yes	characteristic
193	C₃×C₄×C₅	#123	1	1	yes	characteristic
194	C₅×Dic₃	—	2	2	no	—
195	C₅×Dic₃	—	4	2	no	—
196	C₅×Dic₃	—	8	1	no	—
197	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
198	C₂²×C₃×C₄	—	2	1	no	—
199	C₂²×C₃×C₄	—	2	1	no	—
200	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
201	C₂²×Dic₃	—	2	1	no	—
202	C₂²×Dic₃	—	2	1	no	—
203	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
204	C₂×C₄×D₃	—	2	1	no	—
205	C₂×C₄×D₃	—	2	1	no	—
206	C₂×C₄×D₃	—	2	1	no	—
207	C₂×C₄×D₃	—	2	1	no	—
208	C₂×C₄×D₃	—	2	4	no	—
209	C₂×C₄×D₃	—	4	2	no	—
210	C₂×C₄×D₃	—	4	2	no	—
211	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
212	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
213	C₂×C₃×C₈	—	2	1	no	—
214	C₂×C₃×C₈	—	2	1	no	—
215	C₂×C₃×C₈	—	2	1	no	—
216	C₃×C₄⋊C₄	—	2	1	no	—
217	C₃×C₄⋊C₄	—	2	1	no	—
218	C₃×C₄⋊C₄	—	2	1	no	—
219	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
220	(C₂×D₃)⋊C₄	—	4	2	no	—
221	C₄⋊Dic₃	—	2	1	no	—
222	C₄⋊Dic₃	—	2	1	no	—
223	C₄⋊Dic₃	—	2	1	no	—
224	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
225	Dic₃⋊C₄	—	2	4	no	—
226	C₂×C₃⋊C₈	—	2	1	no	—
227	C₂×C₃⋊C₈	—	2	1	no	—
228	C₂×C₃⋊C₈	—	2	1	no	—
229	C₂³×C₅	—	3	2	no	—
230	C₂³×C₅	—	3	2	no	—
231	C₂³×C₅	—	3	2	no	—
232	C₂³×C₅	—	6	1	no	—
233	C₂³×C₅	—	6	1	no	—
234	C₂³×C₅	—	6	1	no	—
235	C₂³×C₅	—	6	1	no	—
236	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	3	2	no	—
239	C₂×C₄×C₅	—	4	1	no	—
240	C₂×C₄×C₅	—	4	1	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	4	1	no	—
243	C₂×C₄×C₅	—	4	1	no	—
244	C₂×C₄×C₅	—	6	1	no	—
245	C₂×C₄×C₅	—	6	1	no	—
246	C₂×C₄×C₅	—	6	2	no	—
247	C₂×C₄×C₅	—	6	2	no	—
248	C₂×C₄×C₅	—	6	2	no	—
249	C₂×C₄×C₅	—	6	2	no	—
250	C₂×C₄×C₅	—	6	2	no	—
251	C₂×C₄×C₅	—	12	8	no	—
252	C₂×C₄×C₅	—	12	1	no	—
253	C₂×C₄×C₅	—	12	1	no	—
254	C₂×C₄×C₅	—	12	1	no	—
255	C₂×C₄×C₅	—	12	1	no	—
256	C₂×C₄×C₅	—	12	1	no	—
257	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
258	C₂×C₄×C₅	#235	1	1	yes	characteristic
259	C₂×C₄×C₅	#235	1	1	yes	characteristic
260	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
261	C₂×C₄×C₅	#237	1	1	yes	characteristic
262	C₂×C₄×C₅	#239	1	1	yes	characteristic
263	C₅×C₈	—	4	1	no	—
264	C₅×C₈	—	12	1	no	—
265	C₂³×C₄	—	3	1	no	—
266	C₂³×C₄	—	6	1	no	—
267	C₂²×C₈	—	3	1	no	—
268	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
269	C₂×C₄⋊C₄	—	3	1	no	—
270	C₂×C₄⋊C₄	—	3	4	no	—
271	C₂×C₄⋊C₄	—	3	1	no	—
272	C₂×C₄⋊C₄	—	6	2	no	—
273	C₂×C₄⋊C₄	—	6	1	no	—
274	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	—	6	1	no	—
277	C₂²⋊C₈	—	6	2	no	—
278	#95	—	6	1	no	—
279	C₂×C₃×C₅	#381	1	1	yes	characteristic
280	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
281	C₂×C₃×C₅	#419	1	1	yes	characteristic
282	C₂×C₃×C₅	#480	1	1	yes	characteristic
283	C₂×C₃×C₅	#480	1	1	yes	characteristic
284	C₂×C₃×C₅	#483	1	1	yes	characteristic
285	C₂×C₃×C₅	#483	1	1	yes	characteristic
286	C₅×D₃	—	2	4	no	—
287	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
288	C₂²×D₃	—	2	1	no	—
289	C₂²×D₃	—	2	1	no	—
290	C₂²×D₃	—	2	1	no	—
291	C₂²×D₃	—	2	1	no	—
292	C₂²×D₃	C₅×C₂²⋊C₄	1	2	yes	—
293	C₂²×D₃	C₅×D₈	1	2	yes	—
294	C₂²×D₃	C₅×SD₁₆	1	2	yes	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	4	1	no	—
297	C₂×C₃×C₄	—	4	1	no	—
298	C₂×C₃×C₄	—	4	1	no	—
299	C₂×C₃×C₄	—	4	1	no	—
300	C₂×C₃×C₄	—	4	1	no	—
301	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
303	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
304	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
305	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
306	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
307	C₂×Dic₃	—	2	1	no	—
308	C₂×Dic₃	—	2	1	no	—
309	C₂×Dic₃	—	2	2	no	—
310	C₂×Dic₃	—	4	1	no	—
311	C₂×Dic₃	—	4	1	no	—
312	C₂×Dic₃	—	4	1	no	—
313	C₂×Dic₃	—	4	1	no	—
314	C₂×Dic₃	—	4	1	no	—
315	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
316	C₄×D₃	—	2	2	no	—
317	C₄×D₃	—	2	2	no	—
318	C₄×D₃	—	2	2	no	—
319	C₄×D₃	—	2	2	no	—
320	C₄×D₃	—	4	8	no	—
321	C₃×C₈	—	4	1	no	—
322	C₃⋊C₈	—	4	1	no	—
323	C₂²×C₅	—	3	4	no	—
324	C₂²×C₅	—	6	2	no	—
325	C₂²×C₅	—	6	2	no	—
326	C₂²×C₅	—	6	2	no	—
327	C₂²×C₅	—	6	2	no	—
328	C₂²×C₅	—	6	2	no	—
329	C₂²×C₅	—	6	2	no	—
330	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
331	C₂²×C₅	#883	1	1	yes	characteristic
332	C₂²×C₅	#894	1	1	yes	characteristic
333	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
334	C₂²×C₅	D₃×SD₁₆	1	1	yes	characteristic
335	C₂²×C₅	#915	1	1	yes	characteristic
336	C₂²×C₅	#918	1	1	yes	characteristic
337	C₄×C₅	—	4	2	no	—
338	C₄×C₅	—	6	2	no	—
339	C₄×C₅	—	8	1	no	—
340	C₄×C₅	—	12	2	no	—
341	C₄×C₅	—	24	1	no	—
342	C₄×C₅	#872	1	1	yes	characteristic
343	C₄×C₅	#883	1	1	yes	characteristic
344	C₄×C₅	#892	1	1	yes	characteristic
345	C₄×C₅	#894	1	1	yes	characteristic
346	C₂⁴	—	3	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	3	1	no	—
350	C₂²×C₄	—	3	2	no	—
351	C₂²×C₄	—	3	2	no	—
352	C₂²×C₄	—	6	4	no	—
353	C₂²×C₄	—	6	1	no	—
354	C₂²×C₄	—	6	1	no	—
355	C₂²×C₄	—	6	1	no	—
356	C₂²×C₄	—	6	1	no	—
357	C₂²×C₄	—	6	1	no	—
358	C₂²×C₄	—	6	1	no	—
359	C₂²×C₄	—	12	2	no	—
360	C₂²×C₄	—	12	2	no	—
361	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	6	1	no	—
366	C₂×C₈	—	6	1	no	—
367	C₂×C₈	—	6	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	3	2	no	—
372	C₄⋊C₄	—	6	4	no	—
373	C₄⋊C₄	—	6	1	no	—
374	C₄⋊C₄	—	6	1	no	—
375	C₄⋊C₄	—	6	1	no	—
376	C₄⋊C₄	C₄×C₅×D₃	1	2	yes	—
377	C₂²⋊C₄	—	12	2	no	—
378	C₃×C₅	#1823	1	1	yes	characteristic, complemented, Hall
379	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
380	C₂²×C₃	C₅×#123	1	1	yes	characteristic
381	C₂²×C₃	C₅×#123	1	1	yes	characteristic
382	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
383	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
384	C₂²×C₃	C₅×#137	1	1	yes	characteristic
385	C₂²×C₃	C₅×#137	1	1	yes	characteristic
386	C₂×D₃	—	2	2	no	—
387	C₂×D₃	—	2	2	no	—
388	C₂×D₃	—	2	2	no	—
389	C₂×D₃	—	2	2	no	—
390	C₂×D₃	—	2	2	no	—
391	C₂×D₃	—	2	2	no	—
392	C₂×D₃	C₅×#102	1	4	yes	—
393	C₃×C₄	—	4	2	no	—
394	C₃×C₄	—	8	1	no	—
395	C₃×C₄	C₅×#117	1	1	yes	characteristic
396	C₃×C₄	C₅×#117	1	1	yes	characteristic
397	C₃×C₄	C₅×#123	1	1	yes	characteristic
398	C₃×C₄	C₅×#123	1	1	yes	characteristic
399	Dic₃	—	2	2	no	—
400	Dic₃	—	4	2	no	—
401	Dic₃	—	8	1	no	—
402	C₂×C₅	—	6	4	no	—
403	C₂×C₅	#4664	1	1	yes	characteristic
404	C₂×C₅	D₃×#102	1	1	yes	characteristic
405	C₂×C₅	#4774	1	1	yes	characteristic
406	C₂×C₅	#4802	1	1	yes	characteristic
407	C₂×C₅	#4805	1	1	yes	characteristic
408	C₂×C₅	#4862	1	1	yes	characteristic
409	C₂×C₅	#4882	1	1	yes	characteristic
410	C₂³	—	3	2	no	—
411	C₂³	—	3	2	no	—
412	C₂³	—	3	2	no	—
413	C₂³	—	6	1	no	—
414	C₂³	—	6	1	no	—
415	C₂³	—	6	1	no	—
416	C₂³	—	6	1	no	—
417	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	3	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	6	1	no	—
426	C₂×C₄	—	6	1	no	—
427	C₂×C₄	—	6	2	no	—
428	C₂×C₄	—	6	2	no	—
429	C₂×C₄	—	6	2	no	—
430	C₂×C₄	—	6	2	no	—
431	C₂×C₄	—	6	2	no	—
432	C₂×C₄	—	12	8	no	—
433	C₂×C₄	—	12	1	no	—
434	C₂×C₄	—	12	1	no	—
435	C₂×C₄	—	12	1	no	—
436	C₂×C₄	—	12	1	no	—
437	C₂×C₄	—	12	1	no	—
438	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
439	C₂×C₄	C₅×#235	1	1	yes	characteristic
440	C₂×C₄	C₅×#235	1	1	yes	characteristic
441	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
442	C₂×C₄	C₅×#237	1	1	yes	characteristic
443	C₂×C₄	C₅×#239	1	1	yes	characteristic
444	C₈	—	4	1	no	—
445	C₈	—	12	1	no	—
446	C₂×C₃	C₅×#381	1	1	yes	characteristic
447	C₂×C₃	C₂×C₅×#102	1	1	yes	characteristic
448	C₂×C₃	C₅×#419	1	1	yes	characteristic
449	C₂×C₃	C₅×#480	1	1	yes	characteristic
450	C₂×C₃	C₅×#480	1	1	yes	characteristic
451	C₂×C₃	C₅×#483	1	1	yes	characteristic
452	C₂×C₃	C₅×#483	1	1	yes	characteristic
453	D₃	—	2	4	no	—
454	C₅	#68871	1	1	yes	characteristic, direct product factor, Sylow
455	C₂²	—	3	4	no	—
456	C₂²	—	6	2	no	—
457	C₂²	—	6	2	no	—
458	C₂²	—	6	2	no	—
459	C₂²	—	6	2	no	—
460	C₂²	—	6	2	no	—
461	C₂²	—	6	2	no	—
462	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
463	C₂²	C₅×#883	1	1	yes	characteristic
464	C₂²	C₅×#894	1	1	yes	characteristic
465	C₂²	C₅×D₃×D₈	1	1	yes	characteristic
466	C₂²	C₅×D₃×SD₁₆	1	1	yes	characteristic
467	C₂²	C₅×#915	1	1	yes	characteristic
468	C₂²	C₅×#918	1	1	yes	characteristic
469	C₄	—	4	2	no	—
470	C₄	—	6	2	no	—
471	C₄	—	8	1	no	—
472	C₄	—	12	2	no	—
473	C₄	—	24	1	no	—
474	C₄	C₅×#872	1	1	yes	characteristic
475	C₄	C₅×#883	1	1	yes	characteristic
476	C₄	C₅×#892	1	1	yes	characteristic
477	C₄	C₅×#894	1	1	yes	characteristic
478	C₃	C₅×#1823	1	1	yes	characteristic, complemented, Sylow
479	C₂	—	6	4	no	—
480	C₂	C₅×#4664	1	1	yes	characteristic
481	C₂	C₅×D₃×#102	1	1	yes	characteristic
482	C₂	C₅×#4774	1	1	yes	characteristic
483	C₂	C₅×#4802	1	1	yes	characteristic
484	C₂	C₅×#4805	1	1	yes	characteristic
485	C₂	C₅×#4862	1	1	yes	characteristic
486	C₂	C₅×#4882	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#340	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂³×C₅×D₃	D₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#340	D₃
hypocenter	C₃	C₅×#1823
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#340

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#340	C₂	semidirect
5. C₅×#4551	C₂	semidirect
6. C₅×#4529	C₂	semidirect
7. C₅×#4529	C₂	semidirect
20. C₅×D₃×C₄⋊C₄	C₄	semidirect
23. #68871	C₅	direct (N × H)
30. C₅×#340	D₃	semidirect
66. C₃×#340	C₂×C₅	semidirect
67. #4551	C₂×C₅	semidirect
68. #4529	C₂×C₅	semidirect
69. #4529	C₂×C₅	semidirect
132. D₃×C₄⋊C₄	C₄×C₅	semidirect
173. #340	C₅×D₃	semidirect
378. C₃×C₅	#1823	semidirect
454. C₅	#68871	direct (N × H)
478. C₃	C₅×#1823	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₅×#4987	2
C₃×C₅×#340	2
C₅×#4551	2
C₅×#4529	2
C₅×#1823	3
#68871	5

Subgroups — C5×#68871 #14298426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68871 #14298426