Subgroups — C₅×#73413 #14320028

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal
4	C₅×#4932	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅×Dic₃⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₅×#4667	C₂	1	2	yes	maximal
7	C₅×#4664	C₂	1	2	yes	maximal
8	C₅×#4651	C₂	1	2	yes	maximal, complemented
9	C₅×#4650	C₂	1	2	yes	maximal, complemented
10	C₅×#2283	—	3	1	no	maximal, Hall
11	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
17	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
18	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
19	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
22	C₄²×C₅×D₃	C₄	1	8	yes	complemented
23	C₃×C₅×#95	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₅×C₃⋊#95	C₂²	1	4	yes	—
26	C₅×C₃⋊#95	C₂²	1	2	yes	—
27	C₅×C₃⋊#95	C₂²	1	4	yes	—
28	C₅×C₃⋊#95	C₂²	1	2	yes	—
29	#73413	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂²×C₄²×C₅	—	3	1	no	—
31	C₅×#383	—	3	2	no	—
32	C₅×#382	—	3	2	no	—
33	C₅×#381	—	3	2	no	—
34	C₅×#380	—	3	2	no	—
35	C₄×C₅×C₄⋊C₄	—	3	2	no	—
36	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
37	C₅×#376	—	3	1	no	—
38	C₅×#376	D₃	1	1	yes	characteristic, complemented
39	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
45	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
46	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
47	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
48	C₂×C₄×C₅×D₃	—	2	4	no	—
49	C₂×C₄×C₅×D₃	—	2	4	no	—
50	C₂×C₄×C₅×D₃	—	2	4	no	—
51	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
52	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
53	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
54	C₃×C₄²×C₅	—	2	4	no	—
55	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
56	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
57	C₅×Dic₃⋊C₄	—	2	8	no	—
58	C₄×C₅×Dic₃	—	2	4	no	—
59	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
60	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
61	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
62	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic
63	C₃×#376	C₂×C₅	1	1	yes	characteristic, complemented
64	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	2	yes	—
65	#4932	C₂×C₅	1	1	yes	characteristic, complemented
66	C₄×Dic₃⋊C₄	C₂×C₅	1	2	yes	complemented
67	#4667	C₂×C₅	1	2	yes	—
68	#4664	C₂×C₅	1	2	yes	—
69	#4651	C₂×C₅	1	2	yes	complemented
70	#4650	C₂×C₅	1	2	yes	complemented
71	C₂³×C₄×C₅	—	3	1	no	—
72	C₂³×C₄×C₅	—	3	1	no	—
73	C₂³×C₄×C₅	—	3	1	no	—
74	C₂×C₅×C₄⋊C₄	—	3	4	no	—
75	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
76	C₂×C₄²×C₅	—	3	1	no	—
77	C₂×C₄²×C₅	—	3	1	no	—
78	C₂×C₄²×C₅	—	3	1	no	—
79	C₂×C₄²×C₅	—	3	8	no	—
80	C₂×C₄²×C₅	—	3	2	no	—
81	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
82	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
83	C₅×#95	—	3	2	no	—
84	C₅×#95	—	3	2	no	—
85	C₅×#95	—	3	4	no	—
86	C₅×#95	—	3	4	no	—
87	C₅×#95	C₂×D₃	1	2	yes	—
88	C₅×#95	C₂×D₃	1	2	yes	—
89	#2283	—	3	1	no	Sylow
90	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
91	C₂²×C₅×D₃	—	2	2	no	—
92	C₂²×C₅×D₃	—	2	2	no	—
93	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
94	C₂²×C₅×D₃	#41	1	4	yes	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	4	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	#41	1	4	yes	—
104	C₂×C₅×Dic₃	—	2	2	no	—
105	C₂×C₅×Dic₃	—	2	2	no	—
106	C₂×C₅×Dic₃	—	2	4	no	—
107	C₂×C₅×Dic₃	—	2	4	no	—
108	C₂×C₅×Dic₃	—	2	4	no	—
109	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
110	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
111	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
112	C₂×C₅×Dic₃	#41	1	4	yes	—
113	C₄×C₅×D₃	—	2	8	no	—
114	C₄×C₅×D₃	—	2	8	no	—
115	C₄×C₅×D₃	—	2	8	no	—
116	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
117	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
118	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
119	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
120	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
121	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
122	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
123	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
124	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
125	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
127	C₄²×D₃	C₄×C₅	1	8	yes	complemented
128	C₃×#95	C₂²×C₅	1	2	yes	—
129	C₃×#95	C₂²×C₅	1	2	yes	—
130	C₃⋊#95	C₂²×C₅	1	4	yes	—
131	C₃⋊#95	C₂²×C₅	1	2	yes	—
132	C₃⋊#95	C₂²×C₅	1	4	yes	—
133	C₃⋊#95	C₂²×C₅	1	2	yes	—
134	C₂⁴×C₅	—	3	1	no	—
135	C₂²×C₄×C₅	—	3	1	no	—
136	C₂²×C₄×C₅	—	3	1	no	—
137	C₂²×C₄×C₅	—	3	1	no	—
138	C₂²×C₄×C₅	—	3	4	no	—
139	C₂²×C₄×C₅	—	3	4	no	—
140	C₂²×C₄×C₅	—	3	4	no	—
141	C₂²×C₄×C₅	—	3	4	no	—
142	C₂²×C₄×C₅	—	6	4	no	—
143	C₂²×C₄×C₅	—	6	4	no	—
144	C₂²×C₄×C₅	—	6	4	no	—
145	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
146	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
149	C₅×C₄⋊C₄	—	6	8	no	—
150	C₅×C₂²⋊C₄	—	6	8	no	—
151	C₄²×C₅	—	2	4	no	—
152	C₄²×C₅	—	3	4	no	—
153	C₄²×C₅	—	3	4	no	—
154	C₄²×C₅	—	3	4	no	—
155	C₄²×C₅	—	6	4	no	—
156	C₄²×C₅	C₄×D₃	1	4	yes	—
157	C₂²×C₄²	—	3	1	no	—
158	#383	—	3	2	no	—
159	#382	—	3	2	no	—
160	#381	—	3	2	no	—
161	#380	—	3	2	no	—
162	C₄×C₄⋊C₄	—	3	2	no	—
163	C₄×C₂²⋊C₄	—	3	2	no	—
164	#376	—	3	1	no	—
165	#376	C₅×D₃	1	1	yes	characteristic, complemented
166	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
167	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
168	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
169	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
170	C₂×C₅×D₃	—	2	2	no	—
171	C₂×C₅×D₃	—	2	2	no	—
172	C₂×C₅×D₃	—	2	8	no	—
173	C₂×C₅×D₃	#117	1	4	yes	—
174	C₃×C₄×C₅	—	2	2	no	—
175	C₃×C₄×C₅	—	2	2	no	—
176	C₃×C₄×C₅	—	4	4	no	—
177	C₃×C₄×C₅	#117	1	4	yes	—
178	C₅×Dic₃	—	2	2	no	—
179	C₅×Dic₃	—	2	2	no	—
180	C₅×Dic₃	—	4	4	no	—
181	C₅×Dic₃	#117	1	4	yes	—
182	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
184	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
187	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
188	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
189	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
190	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
191	C₂×C₄×D₃	—	2	4	no	—
192	C₂×C₄×D₃	—	2	4	no	—
193	C₂×C₄×D₃	—	2	4	no	—
194	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
195	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
196	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
197	C₃×C₄²	—	2	4	no	—
198	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
199	(C₂×D₃)⋊C₄	—	2	8	no	—
200	Dic₃⋊C₄	—	2	8	no	—
201	C₄×Dic₃	—	2	4	no	—
202	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
203	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
204	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
205	C₂³×C₅	—	3	2	no	—
206	C₂³×C₅	—	3	4	no	—
207	C₂³×C₅	—	6	2	no	—
208	C₂³×C₅	—	6	2	no	—
209	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	4	no	—
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	—	2	4	no	—
215	C₂×C₄×C₅	—	3	2	no	—
216	C₂×C₄×C₅	—	3	4	no	—
217	C₂×C₄×C₅	—	3	2	no	—
218	C₂×C₄×C₅	—	3	2	no	—
219	C₂×C₄×C₅	—	6	8	no	—
220	C₂×C₄×C₅	—	6	8	no	—
221	C₂×C₄×C₅	—	6	2	no	—
222	C₂×C₄×C₅	—	6	2	no	—
223	C₂×C₄×C₅	—	6	8	no	—
224	C₂×C₄×C₅	—	6	4	no	—
225	C₂×C₄×C₅	—	6	4	no	—
226	C₂×C₄×C₅	—	6	4	no	—
227	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
228	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
229	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
230	C₂×C₄×C₅	#235	1	4	yes	—
231	C₂³×C₄	—	3	1	no	—
232	C₂³×C₄	—	3	1	no	—
233	C₂³×C₄	—	3	1	no	—
234	C₂×C₄⋊C₄	—	3	4	no	—
235	C₂×C₂²⋊C₄	—	3	4	no	—
236	C₂×C₄²	—	3	1	no	—
237	C₂×C₄²	—	3	1	no	—
238	C₂×C₄²	—	3	1	no	—
239	C₂×C₄²	—	3	8	no	—
240	C₂×C₄²	—	3	2	no	—
241	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
242	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
243	#95	—	3	2	no	—
244	#95	—	3	2	no	—
245	#95	—	3	4	no	—
246	#95	—	3	4	no	—
247	#95	C₂×C₅×D₃	1	2	yes	—
248	#95	C₂×C₅×D₃	1	2	yes	—
249	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
250	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
251	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
252	C₂×C₃×C₅	#529	1	4	yes	—
253	C₅×D₃	—	2	4	no	—
254	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
255	C₂²×D₃	—	2	2	no	—
256	C₂²×D₃	—	2	2	no	—
257	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
258	C₂²×D₃	C₅×#41	1	4	yes	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
265	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
266	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
267	C₂×C₃×C₄	C₅×#41	1	4	yes	—
268	C₂×Dic₃	—	2	2	no	—
269	C₂×Dic₃	—	2	2	no	—
270	C₂×Dic₃	—	2	4	no	—
271	C₂×Dic₃	—	2	4	no	—
272	C₂×Dic₃	—	2	4	no	—
273	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
274	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
275	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
276	C₂×Dic₃	C₅×#41	1	4	yes	—
277	C₄×D₃	—	2	8	no	—
278	C₄×D₃	—	2	8	no	—
279	C₄×D₃	—	2	8	no	—
280	C₂²×C₅	—	3	4	no	—
281	C₂²×C₅	—	6	2	no	—
282	C₂²×C₅	—	6	2	no	—
283	C₂²×C₅	—	6	8	no	—
284	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
285	C₂²×C₅	C₂×#235	1	2	yes	—
286	C₂²×C₅	D₃×#41	1	2	yes	—
287	C₂²×C₅	D₃×#41	1	2	yes	—
288	C₄×C₅	—	2	2	no	—
289	C₄×C₅	—	2	2	no	—
290	C₄×C₅	—	3	4	no	—
291	C₄×C₅	—	4	4	no	—
292	C₄×C₅	—	6	2	no	—
293	C₄×C₅	—	6	2	no	—
294	C₄×C₅	—	12	4	no	—
295	C₄×C₅	#872	1	4	yes	—
296	C₂⁴	—	3	1	no	—
297	C₂²×C₄	—	3	1	no	—
298	C₂²×C₄	—	3	1	no	—
299	C₂²×C₄	—	3	1	no	—
300	C₂²×C₄	—	3	4	no	—
301	C₂²×C₄	—	3	4	no	—
302	C₂²×C₄	—	3	4	no	—
303	C₂²×C₄	—	3	4	no	—
304	C₂²×C₄	—	6	4	no	—
305	C₂²×C₄	—	6	4	no	—
306	C₂²×C₄	—	6	4	no	—
307	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
308	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
309	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
311	C₄⋊C₄	—	6	8	no	—
312	C₂²⋊C₄	—	6	8	no	—
313	C₄²	—	2	4	no	—
314	C₄²	—	3	4	no	—
315	C₄²	—	3	4	no	—
316	C₄²	—	3	4	no	—
317	C₄²	—	6	4	no	—
318	C₄²	C₄×C₅×D₃	1	4	yes	—
319	C₃×C₅	#2283	1	1	yes	characteristic, complemented, Hall
320	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
321	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
322	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
323	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
324	C₂×D₃	—	2	2	no	—
325	C₂×D₃	—	2	2	no	—
326	C₂×D₃	—	2	8	no	—
327	C₂×D₃	C₅×#117	1	4	yes	—
328	C₃×C₄	—	2	2	no	—
329	C₃×C₄	—	2	2	no	—
330	C₃×C₄	—	4	4	no	—
331	C₃×C₄	C₅×#117	1	4	yes	—
332	Dic₃	—	2	2	no	—
333	Dic₃	—	2	2	no	—
334	Dic₃	—	4	4	no	—
335	Dic₃	C₅×#117	1	4	yes	—
336	C₂×C₅	—	6	4	no	—
337	C₂×C₅	C₂×#872	1	1	yes	characteristic
338	C₂×C₅	D₃×#117	1	1	yes	characteristic
339	C₂×C₅	D₃×#117	1	1	yes	characteristic
340	C₂×C₅	#5528	1	4	yes	—
341	C₂³	—	3	2	no	—
342	C₂³	—	3	4	no	—
343	C₂³	—	6	2	no	—
344	C₂³	—	6	2	no	—
345	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	3	2	no	—
352	C₂×C₄	—	3	4	no	—
353	C₂×C₄	—	3	2	no	—
354	C₂×C₄	—	3	2	no	—
355	C₂×C₄	—	6	8	no	—
356	C₂×C₄	—	6	8	no	—
357	C₂×C₄	—	6	2	no	—
358	C₂×C₄	—	6	2	no	—
359	C₂×C₄	—	6	8	no	—
360	C₂×C₄	—	6	4	no	—
361	C₂×C₄	—	6	4	no	—
362	C₂×C₄	—	6	4	no	—
363	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
364	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
365	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
366	C₂×C₄	C₅×#235	1	4	yes	—
367	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
368	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
369	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
370	C₂×C₃	C₅×#529	1	4	yes	—
371	D₃	—	2	4	no	—
372	C₅	#73413	1	1	yes	characteristic, direct product factor, Sylow
373	C₂²	—	3	4	no	—
374	C₂²	—	6	2	no	—
375	C₂²	—	6	2	no	—
376	C₂²	—	6	8	no	—
377	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
378	C₂²	C₂×C₅×#235	1	2	yes	—
379	C₂²	C₅×D₃×#41	1	2	yes	—
380	C₂²	C₅×D₃×#41	1	2	yes	—
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	3	4	no	—
384	C₄	—	4	4	no	—
385	C₄	—	6	2	no	—
386	C₄	—	6	2	no	—
387	C₄	—	12	4	no	—
388	C₄	C₅×#872	1	4	yes	—
389	C₃	C₅×#2283	1	1	yes	characteristic, complemented, Sylow
390	C₂	—	6	4	no	—
391	C₂	C₂×C₅×#872	1	1	yes	characteristic
392	C₂	C₅×D₃×#117	1	1	yes	characteristic
393	C₂	C₅×D₃×#117	1	1	yes	characteristic
394	C₂	C₅×#5528	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#376	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₅×D₃	C₂³
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#376	D₃
hypocenter	C₃	C₅×#2283
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₅×#376

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#376	C₂	semidirect
4. C₅×#4932	C₂	semidirect
5. C₄×C₅×Dic₃⋊C₄	C₂	semidirect
8. C₅×#4651	C₂	semidirect
9. C₅×#4650	C₂	semidirect
22. C₄²×C₅×D₃	C₄	semidirect
29. #73413	C₅	direct (N × H)
38. C₅×#376	D₃	semidirect
63. C₃×#376	C₂×C₅	semidirect
65. #4932	C₂×C₅	semidirect
66. C₄×Dic₃⋊C₄	C₂×C₅	semidirect
69. #4651	C₂×C₅	semidirect
70. #4650	C₂×C₅	semidirect
127. C₄²×D₃	C₄×C₅	semidirect
165. #376	C₅×D₃	semidirect
319. C₃×C₅	#2283	semidirect
372. C₅	#73413	direct (N × H)
389. C₃	C₅×#2283	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×C₅×D₃	2
C₃×C₅×#376	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₅×#4932	2
C₄×C₅×Dic₃⋊C₄	2
C₅×#4667	2
C₅×#4664	2
C₅×#4651	2
C₅×#4650	2
C₅×#2283	3
#73413	5

Subgroups — C5×#73413 #14320028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73413 #14320028