Subgroups — C₅×#73645 #14327993

Order 1920.

1120 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	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4990	C₂	1	4	yes	maximal, complemented
4	C₅×#4939	C₂	1	2	yes	maximal
5	C₅×#4936	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×C₅×C₄⋊Dic₃	C₂	1	2	yes	maximal, complemented
7	C₅×#4666	C₂	1	2	yes	maximal, complemented
8	C₅×#4664	C₂	1	2	yes	maximal, complemented
9	C₅×#2357	—	3	1	no	maximal, Hall
10	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
16	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
17	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×Dic₃	C₂²	1	4	yes	—
21	C₄×C₅×D₁₂	C₄	1	8	yes	complemented
22	C₃×C₅×#95	C₂²	1	1	yes	characteristic
23	C₃×C₅×#95	C₂²	1	1	yes	characteristic
24	C₅×C₃⋊#95	C₂²	1	2	yes	—
25	C₅×C₃⋊#95	C₂²	1	4	yes	—
26	C₅×C₃⋊#95	C₂²	1	2	yes	—
27	#73645	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₄×C₅×D₄	—	3	1	no	—
29	C₅×#390	—	3	2	no	—
30	C₅×#388	—	3	4	no	—
31	C₅×#382	—	3	1	no	—
32	C₅×#381	—	3	2	no	—
33	C₄×C₅×C₄⋊C₄	—	3	2	no	—
34	C₄×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
35	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
36	C₂³×C₅×D₃	C₂³	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
43	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
44	C₂×C₅×D₁₂	—	2	2	no	—
45	C₂×C₅×D₁₂	—	2	2	no	—
46	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
47	C₂×C₄×C₅×D₃	—	4	4	no	—
48	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	—
49	C₃×C₅×C₄⋊C₄	—	2	4	no	—
50	C₃×C₄²×C₅	—	2	4	no	—
51	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
52	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
53	C₅×(C₂×D₃)⋊C₄	—	4	4	no	—
54	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	—
55	C₅×C₄⋊Dic₃	—	2	4	no	—
56	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	—
57	C₄×C₅×Dic₃	—	4	4	no	—
58	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
59	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
60	#4990	C₂×C₅	1	4	yes	complemented
61	#4939	C₂×C₅	1	2	yes	—
62	#4936	C₂×C₅	1	1	yes	characteristic, complemented
63	C₄×C₄⋊Dic₃	C₂×C₅	1	2	yes	complemented
64	#4666	C₂×C₅	1	2	yes	complemented
65	#4664	C₂×C₅	1	2	yes	complemented
66	C₂²×C₅×D₄	—	3	1	no	—
67	C₂³×C₄×C₅	—	3	2	no	—
68	C₄×C₅×D₄	—	3	8	no	—
69	C₂×C₅×C₄⋊C₄	—	3	1	no	—
70	C₂×C₅×C₄⋊C₄	—	3	2	no	—
71	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
72	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
73	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
74	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
75	C₂×C₄²×C₅	—	3	4	no	—
76	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
77	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
78	C₅×#95	—	3	2	no	—
79	C₅×#95	—	3	4	no	—
80	C₅×#95	—	3	2	no	—
81	C₅×#95	C₂×D₃	1	1	yes	characteristic
82	C₅×#95	C₂×D₃	1	1	yes	characteristic
83	#2357	—	3	1	no	Sylow
84	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
85	C₂²×C₅×D₃	—	2	4	no	—
86	C₂²×C₅×D₃	—	2	2	no	—
87	C₂²×C₅×D₃	—	2	2	no	—
88	C₂²×C₅×D₃	—	2	4	no	—
89	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	#41	1	4	yes	—
101	C₂×C₃×C₄×C₅	#41	1	2	yes	—
102	C₂×C₃×C₄×C₅	#41	1	2	yes	—
103	C₂×C₅×Dic₃	—	2	4	no	—
104	C₂×C₅×Dic₃	—	2	4	no	—
105	C₂×C₅×Dic₃	—	2	4	no	—
106	C₂×C₅×Dic₃	—	2	4	no	—
107	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
108	C₅×D₁₂	—	2	8	no	—
109	C₄×C₅×D₃	—	4	8	no	—
110	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
111	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
112	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
113	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
114	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
115	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
116	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
117	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
118	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
119	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
120	C₂×C₄×Dic₃	C₂²×C₅	1	4	yes	—
121	C₄×D₁₂	C₄×C₅	1	8	yes	complemented
122	C₃×#95	C₂²×C₅	1	1	yes	characteristic
123	C₃×#95	C₂²×C₅	1	1	yes	characteristic
124	C₃⋊#95	C₂²×C₅	1	2	yes	—
125	C₃⋊#95	C₂²×C₅	1	4	yes	—
126	C₃⋊#95	C₂²×C₅	1	2	yes	—
127	C₂⁴×C₅	—	3	2	no	—
128	C₂×C₅×D₄	—	3	4	no	—
129	C₂×C₅×D₄	—	6	2	no	—
130	C₂×C₅×D₄	—	6	2	no	—
131	C₂²×C₄×C₅	—	3	2	no	—
132	C₂²×C₄×C₅	—	3	8	no	—
133	C₂²×C₄×C₅	—	3	4	no	—
134	C₂²×C₄×C₅	—	12	4	no	—
135	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
136	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
139	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
140	C₅×C₄⋊C₄	—	2	4	no	—
141	C₅×C₄⋊C₄	—	3	4	no	—
142	C₅×C₄⋊C₄	—	6	4	no	—
143	C₅×C₂²⋊C₄	—	3	8	no	—
144	C₅×C₂²⋊C₄	—	6	8	no	—
145	C₅×C₂²⋊C₄	—	12	4	no	—
146	C₄²×C₅	—	2	4	no	—
147	C₄²×C₅	—	12	4	no	—
148	C₄²×C₅	C₄×D₃	1	4	yes	—
149	C₂×C₄×D₄	—	3	1	no	—
150	#390	—	3	2	no	—
151	#388	—	3	4	no	—
152	#382	—	3	1	no	—
153	#381	—	3	2	no	—
154	C₄×C₄⋊C₄	—	3	2	no	—
155	C₄×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
156	C₄×C₂²⋊C₄	—	3	2	no	—
157	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
158	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
159	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
160	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
161	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
162	C₂×C₅×D₃	—	2	4	no	—
163	C₂×C₅×D₃	—	2	4	no	—
164	C₂×C₅×D₃	—	2	4	no	—
165	C₂×C₅×D₃	—	4	4	no	—
166	C₂×C₅×D₃	—	4	4	no	—
167	C₃×C₄×C₅	—	2	2	no	—
168	C₃×C₄×C₅	—	2	2	no	—
169	C₃×C₄×C₅	—	2	4	no	—
170	C₃×C₄×C₅	—	4	2	no	—
171	C₃×C₄×C₅	#117	1	4	yes	—
172	C₅×Dic₃	—	2	4	no	—
173	C₅×Dic₃	—	4	4	no	—
174	C₂³×D₃	C₂³×C₅	1	2	yes	—
175	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
176	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
179	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
180	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
181	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
182	C₂×D₁₂	—	2	2	no	—
183	C₂×D₁₂	—	2	2	no	—
184	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
185	C₂×C₄×D₃	—	4	4	no	—
186	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	—
187	C₃×C₄⋊C₄	—	2	4	no	—
188	C₃×C₄²	—	2	4	no	—
189	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
190	(C₂×D₃)⋊C₄	—	2	8	no	—
191	(C₂×D₃)⋊C₄	—	4	4	no	—
192	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	—
193	C₄⋊Dic₃	—	2	4	no	—
194	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	—
195	C₄×Dic₃	—	4	4	no	—
196	C₂³×C₅	—	3	4	no	—
197	C₂³×C₅	—	6	4	no	—
198	C₂³×C₅	—	6	2	no	—
199	C₂³×C₅	—	6	2	no	—
200	C₂³×C₅	—	6	4	no	—
201	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
202	C₅×D₄	—	6	8	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	3	4	no	—
211	C₂×C₄×C₅	—	6	4	no	—
212	C₂×C₄×C₅	—	6	4	no	—
213	C₂×C₄×C₅	—	6	4	no	—
214	C₂×C₄×C₅	—	6	4	no	—
215	C₂×C₄×C₅	—	12	8	no	—
216	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
217	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
218	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
219	C₂×C₄×C₅	#235	1	4	yes	—
220	C₂×C₄×C₅	#237	1	2	yes	—
221	C₂×C₄×C₅	#239	1	2	yes	—
222	C₂²×D₄	—	3	1	no	—
223	C₂³×C₄	—	3	2	no	—
224	C₄×D₄	—	3	8	no	—
225	C₂×C₄⋊C₄	—	3	1	no	—
226	C₂×C₄⋊C₄	—	3	2	no	—
227	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
228	C₂×C₂²⋊C₄	—	3	2	no	—
229	C₂×C₂²⋊C₄	—	3	4	no	—
230	C₂×C₂²⋊C₄	—	3	4	no	—
231	C₂×C₄²	—	3	4	no	—
232	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
233	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
234	#95	—	3	2	no	—
235	#95	—	3	4	no	—
236	#95	—	3	2	no	—
237	#95	C₂×C₅×D₃	1	1	yes	characteristic
238	#95	C₂×C₅×D₃	1	1	yes	characteristic
239	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
240	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
241	C₂×C₃×C₅	#518	1	1	yes	characteristic
242	C₂×C₃×C₅	#553	1	2	yes	—
243	C₂×C₃×C₅	#559	1	2	yes	—
244	C₅×D₃	—	4	4	no	—
245	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
246	C₂²×D₃	—	2	4	no	—
247	C₂²×D₃	—	2	2	no	—
248	C₂²×D₃	—	2	2	no	—
249	C₂²×D₃	—	2	4	no	—
250	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
259	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
260	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
261	C₂×C₃×C₄	C₅×#41	1	4	yes	—
262	C₂×C₃×C₄	C₅×#41	1	2	yes	—
263	C₂×C₃×C₄	C₅×#41	1	2	yes	—
264	C₂×Dic₃	—	2	4	no	—
265	C₂×Dic₃	—	2	4	no	—
266	C₂×Dic₃	—	2	4	no	—
267	C₂×Dic₃	—	2	4	no	—
268	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
269	D₁₂	—	2	8	no	—
270	C₄×D₃	—	4	8	no	—
271	C₂²×C₅	—	6	4	no	—
272	C₂²×C₅	—	6	4	no	—
273	C₂²×C₅	—	6	4	no	—
274	C₂²×C₅	—	12	4	no	—
275	C₂²×C₅	—	12	4	no	—
276	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
277	C₂²×C₅	C₂×#235	1	2	yes	—
278	C₂²×C₅	C₂×#237	1	1	yes	characteristic
279	C₂²×C₅	C₂×#239	1	1	yes	characteristic
280	C₂²×C₅	#1009	1	2	yes	—
281	C₄×C₅	—	2	2	no	—
282	C₄×C₅	—	2	2	no	—
283	C₄×C₅	—	2	4	no	—
284	C₄×C₅	—	4	2	no	—
285	C₄×C₅	—	6	4	no	—
286	C₄×C₅	—	12	4	no	—
287	C₄×C₅	#892	1	4	yes	—
288	C₂⁴	—	3	2	no	—
289	C₂×D₄	—	3	4	no	—
290	C₂×D₄	—	6	2	no	—
291	C₂×D₄	—	6	2	no	—
292	C₂²×C₄	—	3	2	no	—
293	C₂²×C₄	—	3	8	no	—
294	C₂²×C₄	—	3	4	no	—
295	C₂²×C₄	—	12	4	no	—
296	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
297	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
298	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
300	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	3	4	no	—
303	C₄⋊C₄	—	6	4	no	—
304	C₂²⋊C₄	—	3	8	no	—
305	C₂²⋊C₄	—	6	8	no	—
306	C₂²⋊C₄	—	12	4	no	—
307	C₄²	—	2	4	no	—
308	C₄²	—	12	4	no	—
309	C₄²	C₄×C₅×D₃	1	4	yes	—
310	C₃×C₅	#2357	1	1	yes	characteristic, complemented, Hall
311	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
312	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
313	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
314	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
315	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
316	C₂×D₃	—	2	4	no	—
317	C₂×D₃	—	2	4	no	—
318	C₂×D₃	—	2	4	no	—
319	C₂×D₃	—	4	4	no	—
320	C₂×D₃	—	4	4	no	—
321	C₃×C₄	—	2	2	no	—
322	C₃×C₄	—	2	2	no	—
323	C₃×C₄	—	2	4	no	—
324	C₃×C₄	—	4	2	no	—
325	C₃×C₄	C₅×#117	1	4	yes	—
326	Dic₃	—	2	4	no	—
327	Dic₃	—	4	4	no	—
328	C₂×C₅	—	12	4	no	—
329	C₂×C₅	C₄×#235	1	1	yes	characteristic
330	C₂×C₅	C₂×#892	1	1	yes	characteristic
331	C₂×C₅	#5521	1	1	yes	characteristic
332	C₂×C₅	#5565	1	2	yes	—
333	C₂×C₅	#5585	1	2	yes	—
334	C₂³	—	3	4	no	—
335	C₂³	—	6	4	no	—
336	C₂³	—	6	2	no	—
337	C₂³	—	6	2	no	—
338	C₂³	—	6	4	no	—
339	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
340	D₄	—	6	8	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	3	4	no	—
349	C₂×C₄	—	6	4	no	—
350	C₂×C₄	—	6	4	no	—
351	C₂×C₄	—	6	4	no	—
352	C₂×C₄	—	6	4	no	—
353	C₂×C₄	—	12	8	no	—
354	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
355	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
356	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
357	C₂×C₄	C₅×#235	1	4	yes	—
358	C₂×C₄	C₅×#237	1	2	yes	—
359	C₂×C₄	C₅×#239	1	2	yes	—
360	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
361	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
362	C₂×C₃	C₅×#518	1	1	yes	characteristic
363	C₂×C₃	C₅×#553	1	2	yes	—
364	C₂×C₃	C₅×#559	1	2	yes	—
365	D₃	—	4	4	no	—
366	C₅	#73645	1	1	yes	characteristic, direct product factor, Sylow
367	C₂²	—	6	4	no	—
368	C₂²	—	6	4	no	—
369	C₂²	—	6	4	no	—
370	C₂²	—	12	4	no	—
371	C₂²	—	12	4	no	—
372	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
373	C₂²	C₂×C₅×#235	1	2	yes	—
374	C₂²	C₂×C₅×#237	1	1	yes	characteristic
375	C₂²	C₂×C₅×#239	1	1	yes	characteristic
376	C₂²	C₅×#1009	1	2	yes	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	4	no	—
380	C₄	—	4	2	no	—
381	C₄	—	6	4	no	—
382	C₄	—	12	4	no	—
383	C₄	C₅×#892	1	4	yes	—
384	C₃	C₅×#2357	1	1	yes	characteristic, complemented, Sylow
385	C₂	—	12	4	no	—
386	C₂	C₄×C₅×#235	1	1	yes	characteristic
387	C₂	C₂×C₅×#892	1	1	yes	characteristic
388	C₂	C₅×#5521	1	1	yes	characteristic
389	C₂	C₅×#5565	1	2	yes	—
390	C₂	C₅×#5585	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₄×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₅×#2357
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
3. C₅×#4990	C₂	semidirect
5. C₅×#4936	C₂	semidirect
6. C₄×C₅×C₄⋊Dic₃	C₂	semidirect
7. C₅×#4666	C₂	semidirect
8. C₅×#4664	C₂	semidirect
21. C₄×C₅×D₁₂	C₄	semidirect
27. #73645	C₅	direct (N × H)
34. C₄×C₅×C₄⋊C₄	D₃	semidirect
59. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
60. #4990	C₂×C₅	semidirect
62. #4936	C₂×C₅	semidirect
63. C₄×C₄⋊Dic₃	C₂×C₅	semidirect
64. #4666	C₂×C₅	semidirect
65. #4664	C₂×C₅	semidirect
121. C₄×D₁₂	C₄×C₅	semidirect
155. C₄×C₄⋊C₄	C₅×D₃	semidirect
310. C₃×C₅	#2357	semidirect
366. C₅	#73645	direct (N × H)
384. C₃	C₅×#2357	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×D₁₂	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#4990	2
C₅×#4939	2
C₅×#4936	2
C₄×C₅×C₄⋊Dic₃	2
C₅×#4666	2
C₅×#4664	2
C₅×#2357	3
#73645	5

Subgroups — C5×#73645 #14327993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73645 #14327993