Subgroups — C₂×C₅×#4525 #14280740

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#830	C₂	1	2	yes	maximal, complemented
3	C₅×#4525	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₅×#323	—	3	1	no	maximal, Hall
5	C₂⁵×C₃×C₅	C₄	1	1	yes	characteristic
6	C₂³×C₃×C₄×C₅	C₄	1	1	yes	characteristic
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
9	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
10	C₂×C₃×C₅×C₂²⋊C₄	C₄	1	2	yes	—
11	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
12	C₂²×C₅×C₃⋊C₈	—	2	2	no	—
13	C₅×#830	—	2	2	no	—
14	C₅×#830	C₂²	1	4	yes	complemented
15	C₂×#4525	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂²×C₅×C₂²⋊C₄	D₃	1	1	yes	characteristic
17	C₂×C₅×C₂²⋊C₈	—	3	2	no	—
18	C₅×#323	—	3	4	no	—
19	C₂⁴×C₃×C₅	—	2	1	no	—
20	C₂⁴×C₃×C₅	—	2	1	no	—
21	C₂⁴×C₃×C₅	—	2	2	no	—
22	C₂⁴×C₃×C₅	—	4	2	no	—
23	C₂⁴×C₃×C₅	—	4	2	no	—
24	C₂⁴×C₃×C₅	C₈	1	4	yes	complemented
25	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
26	C₂⁴×C₃×C₅	C₂×C₄	1	2	yes	—
27	C₂²×C₃×C₄×C₅	—	2	1	no	—
28	C₂²×C₃×C₄×C₅	—	2	1	no	—
29	C₂²×C₃×C₄×C₅	—	4	2	no	—
30	C₂²×C₃×C₄×C₅	—	4	2	no	—
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
37	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
38	C₂×C₅×C₃⋊C₈	—	2	4	no	—
39	C₂×C₅×C₃⋊C₈	—	4	4	no	—
40	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
41	C₂×#830	C₂×C₅	1	2	yes	complemented
42	#4525	C₂×C₅	1	4	yes	direct product factor
43	C₂⁵×C₅	Dic₃	1	1	yes	characteristic
44	C₂³×C₄×C₅	Dic₃	1	1	yes	characteristic
45	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
46	C₂²×C₅×C₈	—	6	2	no	—
47	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
48	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
49	C₂×C₅×C₂²⋊C₄	Dic₃	1	2	yes	—
50	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
51	C₅×C₂²⋊C₈	—	3	4	no	—
52	C₅×C₂²⋊C₈	—	6	2	no	—
53	C₂×#323	—	3	1	no	Sylow
54	C₂³×C₃×C₅	—	2	2	no	—
55	C₂³×C₃×C₅	—	2	2	no	—
56	C₂³×C₃×C₅	—	2	4	no	—
57	C₂³×C₃×C₅	—	2	4	no	—
58	C₂³×C₃×C₅	—	2	2	no	—
59	C₂³×C₃×C₅	—	2	2	no	—
60	C₂³×C₃×C₅	—	4	8	no	—
61	C₂³×C₃×C₅	—	4	2	no	—
62	C₂³×C₃×C₅	—	4	2	no	—
63	C₂³×C₃×C₅	—	4	8	no	—
64	C₂³×C₃×C₅	—	4	2	no	—
65	C₂³×C₃×C₅	—	4	2	no	—
66	C₂³×C₃×C₅	—	4	2	no	—
67	C₂³×C₃×C₅	—	4	2	no	—
68	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
69	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
70	C₂³×C₃×C₅	C₂×C₈	1	2	yes	—
71	C₂³×C₃×C₅	C₂×C₈	1	4	yes	complemented
72	C₂³×C₃×C₅	M₁₆	1	2	yes	—
73	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₃×C₄×C₅	—	2	4	no	—
75	C₂×C₃×C₄×C₅	—	2	2	no	—
76	C₂×C₃×C₄×C₅	—	4	1	no	—
77	C₂×C₃×C₄×C₅	—	4	2	no	—
78	C₂×C₃×C₄×C₅	—	4	1	no	—
79	C₂×C₃×C₄×C₅	—	4	2	no	—
80	C₂×C₃×C₄×C₅	—	4	2	no	—
81	C₂×C₃×C₄×C₅	—	4	2	no	—
82	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
83	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
84	C₅×C₃⋊C₈	—	4	4	no	—
85	C₂⁵×C₃	C₄×C₅	1	1	yes	characteristic
86	C₂³×C₃×C₄	C₄×C₅	1	1	yes	characteristic
87	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
88	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
90	C₂×C₃×C₂²⋊C₄	C₄×C₅	1	2	yes	—
91	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
92	C₂²×C₃⋊C₈	—	2	2	no	—
93	#830	—	2	2	no	—
94	#830	C₂²×C₅	1	4	yes	complemented
95	C₂⁴×C₅	—	2	2	no	—
96	C₂⁴×C₅	—	2	1	no	—
97	C₂⁴×C₅	—	2	1	no	—
98	C₂⁴×C₅	—	4	2	no	—
99	C₂⁴×C₅	—	4	2	no	—
100	C₂⁴×C₅	C₃⋊C₈	1	4	yes	complemented
101	C₂⁴×C₅	C₂×Dic₃	1	1	yes	characteristic
102	C₂⁴×C₅	C₂×Dic₃	1	2	yes	—
103	C₂²×C₄×C₅	—	2	1	no	—
104	C₂²×C₄×C₅	—	2	1	no	—
105	C₂²×C₄×C₅	—	4	2	no	—
106	C₂²×C₄×C₅	—	4	2	no	—
107	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
108	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
109	C₂²×C₄×C₅	#67	1	2	yes	—
110	C₂²×C₄×C₅	#67	1	2	yes	—
111	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
112	C₂×C₅×C₈	—	6	4	no	—
113	C₂×C₅×C₈	—	12	4	no	—
114	C₅×C₂²⋊C₄	—	2	4	no	—
115	C₅×C₂²⋊C₄	—	2	4	no	—
116	C₂²×C₂²⋊C₄	C₅×D₃	1	1	yes	characteristic
117	C₂×C₂²⋊C₈	—	3	2	no	—
118	#323	—	3	4	no	—
119	C₂²×C₃×C₅	—	2	4	no	—
120	C₂²×C₃×C₅	—	2	4	no	—
121	C₂²×C₃×C₅	—	2	1	no	—
122	C₂²×C₃×C₅	—	2	1	no	—
123	C₂²×C₃×C₅	—	2	1	no	—
124	C₂²×C₃×C₅	—	2	1	no	—
125	C₂²×C₃×C₅	—	2	4	no	—
126	C₂²×C₃×C₅	—	4	4	no	—
127	C₂²×C₃×C₅	—	4	8	no	—
128	C₂²×C₃×C₅	—	4	4	no	—
129	C₂²×C₃×C₅	—	4	8	no	—
130	C₂²×C₃×C₅	—	4	2	no	—
131	C₂²×C₃×C₅	—	4	2	no	—
132	C₂²×C₃×C₅	C₂²⋊C₈	1	2	yes	—
133	C₂²×C₃×C₅	C₂²⋊C₈	1	2	yes	—
134	C₂²×C₃×C₅	#99	1	2	yes	—
135	C₂²×C₃×C₅	#100	1	2	yes	—
136	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
138	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
139	C₃×C₄×C₅	—	2	2	no	—
140	C₃×C₄×C₅	—	2	2	no	—
141	C₃×C₄×C₅	—	4	2	no	—
142	C₂⁴×C₃	—	2	1	no	—
143	C₂⁴×C₃	—	2	1	no	—
144	C₂⁴×C₃	—	2	2	no	—
145	C₂⁴×C₃	—	4	2	no	—
146	C₂⁴×C₃	—	4	2	no	—
147	C₂⁴×C₃	C₅×C₈	1	4	yes	complemented
148	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
149	C₂⁴×C₃	C₂×C₄×C₅	1	2	yes	—
150	C₂²×C₃×C₄	—	2	1	no	—
151	C₂²×C₃×C₄	—	2	1	no	—
152	C₂²×C₃×C₄	—	4	2	no	—
153	C₂²×C₃×C₄	—	4	2	no	—
154	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
155	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
157	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
158	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
159	C₃×C₂²⋊C₄	—	2	4	no	—
160	C₃×C₂²⋊C₄	—	2	4	no	—
161	C₂×C₃⋊C₈	—	2	4	no	—
162	C₂×C₃⋊C₈	—	4	4	no	—
163	C₂³×C₅	—	2	2	no	—
164	C₂³×C₅	—	2	2	no	—
165	C₂³×C₅	—	2	4	no	—
166	C₂³×C₅	—	2	4	no	—
167	C₂³×C₅	—	2	2	no	—
168	C₂³×C₅	—	2	2	no	—
169	C₂³×C₅	—	4	8	no	—
170	C₂³×C₅	—	4	2	no	—
171	C₂³×C₅	—	4	2	no	—
172	C₂³×C₅	—	4	2	no	—
173	C₂³×C₅	—	4	2	no	—
174	C₂³×C₅	—	4	8	no	—
175	C₂³×C₅	—	4	2	no	—
176	C₂³×C₅	—	4	2	no	—
177	C₂³×C₅	C₂×C₃⋊C₈	1	2	yes	—
178	C₂³×C₅	C₂×C₃⋊C₈	1	4	yes	complemented
179	C₂³×C₅	#208	1	2	yes	—
180	C₂³×C₅	#217	1	1	yes	characteristic
181	C₂³×C₅	#217	1	1	yes	characteristic
182	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
183	C₂×C₄×C₅	—	2	4	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	4	1	no	—
186	C₂×C₄×C₅	—	4	2	no	—
187	C₂×C₄×C₅	—	4	1	no	—
188	C₂×C₄×C₅	—	4	2	no	—
189	C₂×C₄×C₅	—	4	2	no	—
190	C₂×C₄×C₅	—	4	2	no	—
191	C₂×C₄×C₅	#217	1	2	yes	—
192	C₂×C₄×C₅	C₂×#67	1	2	yes	—
193	C₅×C₈	—	12	4	no	—
194	C₂⁵	C₅×Dic₃	1	1	yes	characteristic
195	C₂³×C₄	C₅×Dic₃	1	1	yes	characteristic
196	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
197	C₂²×C₈	—	6	2	no	—
198	C₂×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₂²⋊C₄	C₅×Dic₃	1	2	yes	—
201	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
202	C₂²⋊C₈	—	3	4	no	—
203	C₂²⋊C₈	—	6	2	no	—
204	C₂×C₃×C₅	—	2	2	no	—
205	C₂×C₃×C₅	—	2	1	no	—
206	C₂×C₃×C₅	—	2	1	no	—
207	C₂×C₃×C₅	—	4	4	no	—
208	C₂×C₃×C₅	#323	1	4	yes	complemented
209	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
210	C₂×C₃×C₅	C₂×#99	1	1	yes	characteristic
211	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
212	C₂³×C₃	—	2	2	no	—
213	C₂³×C₃	—	2	2	no	—
214	C₂³×C₃	—	2	2	no	—
215	C₂³×C₃	—	2	2	no	—
216	C₂³×C₃	—	2	4	no	—
217	C₂³×C₃	—	2	4	no	—
218	C₂³×C₃	—	4	8	no	—
219	C₂³×C₃	—	4	2	no	—
220	C₂³×C₃	—	4	2	no	—
221	C₂³×C₃	—	4	8	no	—
222	C₂³×C₃	—	4	2	no	—
223	C₂³×C₃	—	4	2	no	—
224	C₂³×C₃	—	4	2	no	—
225	C₂³×C₃	—	4	2	no	—
226	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
227	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
228	C₂³×C₃	C₂×C₅×C₈	1	2	yes	—
229	C₂³×C₃	C₂×C₅×C₈	1	4	yes	complemented
230	C₂³×C₃	C₅×M₁₆	1	2	yes	—
231	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
232	C₂×C₃×C₄	—	2	4	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	4	1	no	—
235	C₂×C₃×C₄	—	4	2	no	—
236	C₂×C₃×C₄	—	4	1	no	—
237	C₂×C₃×C₄	—	4	2	no	—
238	C₂×C₃×C₄	—	4	2	no	—
239	C₂×C₃×C₄	—	4	2	no	—
240	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
241	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
242	C₃⋊C₈	—	4	4	no	—
243	C₂²×C₅	—	2	1	no	—
244	C₂²×C₅	—	2	1	no	—
245	C₂²×C₅	—	2	1	no	—
246	C₂²×C₅	—	2	1	no	—
247	C₂²×C₅	—	2	4	no	—
248	C₂²×C₅	—	2	4	no	—
249	C₂²×C₅	—	2	4	no	—
250	C₂²×C₅	—	4	4	no	—
251	C₂²×C₅	—	4	8	no	—
252	C₂²×C₅	—	4	4	no	—
253	C₂²×C₅	—	4	2	no	—
254	C₂²×C₅	—	4	2	no	—
255	C₂²×C₅	—	4	8	no	—
256	C₂²×C₅	#830	1	2	yes	—
257	C₂²×C₅	#830	1	2	yes	—
258	C₂²×C₅	#833	1	2	yes	—
259	C₂²×C₅	#834	1	2	yes	—
260	C₂²×C₅	C₂²×C₃⋊C₈	1	1	yes	characteristic
261	C₂²×C₅	C₂×#208	1	1	yes	characteristic
262	C₂²×C₅	C₂×#217	1	1	yes	characteristic
263	C₄×C₅	—	2	2	no	—
264	C₄×C₅	—	2	2	no	—
265	C₄×C₅	—	4	2	no	—
266	C₂⁴	—	2	2	no	—
267	C₂⁴	—	2	1	no	—
268	C₂⁴	—	2	1	no	—
269	C₂⁴	—	4	2	no	—
270	C₂⁴	—	4	2	no	—
271	C₂⁴	C₅×C₃⋊C₈	1	4	yes	complemented
272	C₂⁴	C₂×C₅×Dic₃	1	1	yes	characteristic
273	C₂⁴	C₂×C₅×Dic₃	1	2	yes	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
279	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
280	C₂²×C₄	C₅×#67	1	2	yes	—
281	C₂²×C₄	C₅×#67	1	2	yes	—
282	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
283	C₂×C₈	—	6	4	no	—
284	C₂×C₈	—	12	4	no	—
285	C₂²⋊C₄	—	2	4	no	—
286	C₂²⋊C₄	—	2	4	no	—
287	C₃×C₅	C₂×#323	1	1	yes	characteristic, complemented, Hall
288	C₂²×C₃	—	2	4	no	—
289	C₂²×C₃	—	2	4	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	—	2	1	no	—
293	C₂²×C₃	—	2	1	no	—
294	C₂²×C₃	—	2	4	no	—
295	C₂²×C₃	—	4	4	no	—
296	C₂²×C₃	—	4	4	no	—
297	C₂²×C₃	—	4	8	no	—
298	C₂²×C₃	—	4	8	no	—
299	C₂²×C₃	—	4	2	no	—
300	C₂²×C₃	—	4	2	no	—
301	C₂²×C₃	C₅×C₂²⋊C₈	1	2	yes	—
302	C₂²×C₃	C₅×C₂²⋊C₈	1	2	yes	—
303	C₂²×C₃	C₅×#99	1	2	yes	—
304	C₂²×C₃	C₅×#100	1	2	yes	—
305	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
306	C₂²×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
307	C₂²×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
308	C₃×C₄	—	2	2	no	—
309	C₃×C₄	—	2	2	no	—
310	C₃×C₄	—	4	2	no	—
311	C₂×C₅	—	2	2	no	—
312	C₂×C₅	—	2	1	no	—
313	C₂×C₅	—	2	1	no	—
314	C₂×C₅	—	4	4	no	—
315	C₂×C₅	#4525	1	4	yes	direct product factor
316	C₂×C₅	C₂×#830	1	1	yes	characteristic
317	C₂×C₅	C₂×#833	1	1	yes	characteristic
318	C₂×C₅	C₂×#834	1	1	yes	characteristic
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	2	4	no	—
324	C₂³	—	2	4	no	—
325	C₂³	—	4	8	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	8	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	C₂×C₅×C₃⋊C₈	1	2	yes	—
334	C₂³	C₂×C₅×C₃⋊C₈	1	4	yes	complemented
335	C₂³	C₅×#208	1	2	yes	—
336	C₂³	C₅×#217	1	1	yes	characteristic
337	C₂³	C₅×#217	1	1	yes	characteristic
338	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	C₅×#217	1	2	yes	—
348	C₂×C₄	C₂×C₅×#67	1	2	yes	—
349	C₈	—	12	4	no	—
350	C₂×C₃	—	2	1	no	—
351	C₂×C₃	—	2	1	no	—
352	C₂×C₃	—	2	2	no	—
353	C₂×C₃	—	4	4	no	—
354	C₂×C₃	C₅×#323	1	4	yes	complemented
355	C₂×C₃	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
356	C₂×C₃	C₂×C₅×#99	1	1	yes	characteristic
357	C₂×C₃	C₂×C₅×#100	1	1	yes	characteristic
358	C₅	C₂×#4525	1	1	yes	characteristic, direct product factor, Sylow
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	4	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	8	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	8	no	—
372	C₂²	C₅×#830	1	2	yes	—
373	C₂²	C₅×#830	1	2	yes	—
374	C₂²	C₅×#833	1	2	yes	—
375	C₂²	C₅×#834	1	2	yes	—
376	C₂²	C₂²×C₅×C₃⋊C₈	1	1	yes	characteristic
377	C₂²	C₂×C₅×#208	1	1	yes	characteristic
378	C₂²	C₂×C₅×#217	1	1	yes	characteristic
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	4	2	no	—
382	C₃	C₂×C₅×#323	1	1	yes	characteristic, complemented, Sylow
383	C₂	—	2	1	no	—
384	C₂	—	2	1	no	—
385	C₂	—	2	2	no	—
386	C₂	—	4	4	no	—
387	C₂	C₅×#4525	1	4	yes	direct product factor
388	C₂	C₂×C₅×#830	1	1	yes	characteristic
389	C₂	C₂×C₅×#833	1	1	yes	characteristic
390	C₂	C₂×C₅×#834	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	#217
commutator	C₂²×C₃	C₂²×C₅×C₈
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂²×C₃×C₅×C₂²⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂²⋊C₄
prime radical	C₂⁵×C₃×C₅	C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂²×C₅×C₂²⋊C₄	D₃
hypocenter	C₃	C₂×C₅×#323
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂²×C₅×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#830	C₂	semidirect
3. C₅×#4525	C₂	direct (N × H)
14. C₅×#830	C₂²	semidirect
15. C₂×#4525	C₅	direct (N × H)
24. C₂⁴×C₃×C₅	C₈	semidirect
41. C₂×#830	C₂×C₅	semidirect
42. #4525	C₂×C₅	direct (N × H)
71. C₂³×C₃×C₅	C₂×C₈	semidirect
94. #830	C₂²×C₅	semidirect
100. C₂⁴×C₅	C₃⋊C₈	semidirect
147. C₂⁴×C₃	C₅×C₈	semidirect
178. C₂³×C₅	C₂×C₃⋊C₈	semidirect
208. C₂×C₃×C₅	#323	semidirect
229. C₂³×C₃	C₂×C₅×C₈	semidirect
271. C₂⁴	C₅×C₃⋊C₈	semidirect
287. C₃×C₅	C₂×#323	semidirect
315. C₂×C₅	#4525	direct (N × H)
334. C₂³	C₂×C₅×C₃⋊C₈	semidirect
354. C₂×C₃	C₅×#323	semidirect
358. C₅	C₂×#4525	direct (N × H)
382. C₃	C₂×C₅×#323	semidirect
387. C₂	C₅×#4525	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×C₂²⋊C₄	2
C₂×C₅×#830	2
C₅×#4525	2
C₂×C₅×#323	3
C₂×#4525	5

Subgroups — C2×C5×#4525 #14280740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4525 #14280740