Subgroups — C₅×#73752 #14320040

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 428 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×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4987	C₂	1	2	yes	maximal
4	C₅×#4977	C₂	1	2	yes	maximal, complemented
5	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal
6	C₄×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4932	C₂	1	2	yes	maximal, complemented
8	C₅×#4664	C₂	1	2	yes	maximal
9	C₅×#4651	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×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
19	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
20	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
23	C₄²×C₅×D₃	C₄	1	8	yes	complemented
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₅×C₃⋊#95	C₂²	1	2	yes	—
26	C₅×C₃⋊#95	C₂²	1	4	yes	—
27	C₅×C₃⋊#95	C₂²	1	4	yes	—
28	C₅×C₃⋊#95	C₂²	1	4	yes	—
29	#73752	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	1	no	—
36	C₄×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
37	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
38	C₅×#376	—	3	2	no	—
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	2	no	—
51	C₂×C₄×C₅×D₃	—	2	2	no	—
52	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
53	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
54	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
55	C₃×C₅×C₄⋊C₄	—	2	4	no	—
56	C₃×C₄²×C₅	—	2	4	no	—
57	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
58	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
59	C₅×C₄⋊Dic₃	—	2	4	no	—
60	C₄×C₅×Dic₃	—	2	4	no	—
61	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
62	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
63	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
64	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic
65	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
66	#4987	C₂×C₅	1	2	yes	—
67	#4977	C₂×C₅	1	2	yes	complemented
68	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	2	yes	—
69	C₄×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
70	#4932	C₂×C₅	1	2	yes	complemented
71	#4664	C₂×C₅	1	2	yes	—
72	#4651	C₂×C₅	1	2	yes	complemented
73	C₂³×C₄×C₅	—	3	1	no	—
74	C₂³×C₄×C₅	—	3	1	no	—
75	C₂³×C₄×C₅	—	3	1	no	—
76	C₂×C₅×C₄⋊C₄	—	3	2	no	—
77	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
78	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
79	C₂×C₄²×C₅	—	3	1	no	—
80	C₂×C₄²×C₅	—	3	1	no	—
81	C₂×C₄²×C₅	—	3	1	no	—
82	C₂×C₄²×C₅	—	3	8	no	—
83	C₂×C₄²×C₅	—	3	2	no	—
84	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
85	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
86	C₅×#95	—	3	4	no	—
87	C₅×#95	—	3	4	no	—
88	C₅×#95	—	3	4	no	—
89	C₅×#95	—	3	2	no	—
90	C₅×#95	C₂×D₃	1	2	yes	—
91	#2283	—	3	1	no	Sylow
92	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
93	C₂²×C₅×D₃	—	2	2	no	—
94	C₂²×C₅×D₃	—	2	1	no	—
95	C₂²×C₅×D₃	—	2	1	no	—
96	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
97	C₂²×C₅×D₃	#41	1	4	yes	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	—	2	4	no	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	#41	1	4	yes	—
106	C₂×C₃×C₄×C₅	#41	1	2	yes	—
107	C₂×C₃×C₄×C₅	#41	1	2	yes	—
108	C₂×C₅×Dic₃	—	2	2	no	—
109	C₂×C₅×Dic₃	—	2	1	no	—
110	C₂×C₅×Dic₃	—	2	1	no	—
111	C₂×C₅×Dic₃	—	2	2	no	—
112	C₂×C₅×Dic₃	—	2	4	no	—
113	C₂×C₅×Dic₃	—	2	4	no	—
114	C₂×C₅×Dic₃	—	2	4	no	—
115	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
116	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
117	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
118	C₄×C₅×D₃	—	2	8	no	—
119	C₄×C₅×D₃	—	2	8	no	—
120	C₄×C₅×D₃	—	2	8	no	—
121	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
122	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
123	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
124	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
125	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
126	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
127	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
128	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
129	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
130	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
132	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
133	C₄²×D₃	C₄×C₅	1	8	yes	complemented
134	C₃×#95	C₂²×C₅	1	2	yes	—
135	C₃⋊#95	C₂²×C₅	1	2	yes	—
136	C₃⋊#95	C₂²×C₅	1	4	yes	—
137	C₃⋊#95	C₂²×C₅	1	4	yes	—
138	C₃⋊#95	C₂²×C₅	1	4	yes	—
139	C₂⁴×C₅	—	3	1	no	—
140	C₂²×C₄×C₅	—	3	1	no	—
141	C₂²×C₄×C₅	—	3	1	no	—
142	C₂²×C₄×C₅	—	3	1	no	—
143	C₂²×C₄×C₅	—	3	4	no	—
144	C₂²×C₄×C₅	—	3	4	no	—
145	C₂²×C₄×C₅	—	3	4	no	—
146	C₂²×C₄×C₅	—	3	4	no	—
147	C₂²×C₄×C₅	—	6	4	no	—
148	C₂²×C₄×C₅	—	6	4	no	—
149	C₂²×C₄×C₅	—	6	2	no	—
150	C₂²×C₄×C₅	—	6	2	no	—
151	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
152	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
155	C₅×C₄⋊C₄	—	2	4	no	—
156	C₅×C₄⋊C₄	—	6	4	no	—
157	C₅×C₂²⋊C₄	—	6	8	no	—
158	C₄²×C₅	—	2	4	no	—
159	C₄²×C₅	—	3	4	no	—
160	C₄²×C₅	—	3	4	no	—
161	C₄²×C₅	—	3	4	no	—
162	C₄²×C₅	—	6	4	no	—
163	C₄²×C₅	C₄×D₃	1	4	yes	—
164	C₂²×C₄²	—	3	1	no	—
165	#383	—	3	2	no	—
166	#382	—	3	2	no	—
167	#381	—	3	2	no	—
168	#380	—	3	2	no	—
169	C₄×C₄⋊C₄	—	3	1	no	—
170	C₄×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
171	C₄×C₂²⋊C₄	—	3	2	no	—
172	#376	—	3	2	no	—
173	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
174	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
175	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
176	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
177	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
178	C₂×C₅×D₃	—	2	2	no	—
179	C₂×C₅×D₃	—	2	2	no	—
180	C₂×C₅×D₃	—	2	4	no	—
181	C₂×C₅×D₃	—	2	4	no	—
182	C₂×C₅×D₃	#117	1	4	yes	—
183	C₃×C₄×C₅	—	2	2	no	—
184	C₃×C₄×C₅	—	4	4	no	—
185	C₃×C₄×C₅	#117	1	4	yes	—
186	C₃×C₄×C₅	#117	1	4	yes	—
187	C₅×Dic₃	—	2	2	no	—
188	C₅×Dic₃	—	2	2	no	—
189	C₅×Dic₃	—	2	2	no	—
190	C₅×Dic₃	—	4	4	no	—
191	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
192	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
193	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
195	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
196	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
197	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
198	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
199	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
200	C₂×C₄×D₃	—	2	4	no	—
201	C₂×C₄×D₃	—	2	4	no	—
202	C₂×C₄×D₃	—	2	2	no	—
203	C₂×C₄×D₃	—	2	2	no	—
204	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
205	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
206	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
207	C₃×C₄⋊C₄	—	2	4	no	—
208	C₃×C₄²	—	2	4	no	—
209	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
210	(C₂×D₃)⋊C₄	—	2	8	no	—
211	C₄⋊Dic₃	—	2	4	no	—
212	C₄×Dic₃	—	2	4	no	—
213	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
214	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
215	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
216	C₂³×C₅	—	3	2	no	—
217	C₂³×C₅	—	3	4	no	—
218	C₂³×C₅	—	6	2	no	—
219	C₂³×C₅	—	6	1	no	—
220	C₂³×C₅	—	6	1	no	—
221	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	4	no	—
224	C₂×C₄×C₅	—	2	4	no	—
225	C₂×C₄×C₅	—	2	4	no	—
226	C₂×C₄×C₅	—	3	2	no	—
227	C₂×C₄×C₅	—	3	2	no	—
228	C₂×C₄×C₅	—	3	2	no	—
229	C₂×C₄×C₅	—	6	8	no	—
230	C₂×C₄×C₅	—	6	2	no	—
231	C₂×C₄×C₅	—	6	1	no	—
232	C₂×C₄×C₅	—	6	1	no	—
233	C₂×C₄×C₅	—	6	2	no	—
234	C₂×C₄×C₅	—	6	8	no	—
235	C₂×C₄×C₅	—	6	8	no	—
236	C₂×C₄×C₅	—	6	4	no	—
237	C₂×C₄×C₅	—	6	4	no	—
238	C₂×C₄×C₅	—	6	4	no	—
239	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
240	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
241	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
242	C₂×C₄×C₅	#235	1	4	yes	—
243	C₂×C₄×C₅	#237	1	2	yes	—
244	C₂×C₄×C₅	#239	1	2	yes	—
245	C₂³×C₄	—	3	1	no	—
246	C₂³×C₄	—	3	1	no	—
247	C₂³×C₄	—	3	1	no	—
248	C₂×C₄⋊C₄	—	3	2	no	—
249	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
250	C₂×C₂²⋊C₄	—	3	4	no	—
251	C₂×C₄²	—	3	1	no	—
252	C₂×C₄²	—	3	1	no	—
253	C₂×C₄²	—	3	1	no	—
254	C₂×C₄²	—	3	8	no	—
255	C₂×C₄²	—	3	2	no	—
256	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
257	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
258	#95	—	3	4	no	—
259	#95	—	3	4	no	—
260	#95	—	3	4	no	—
261	#95	—	3	2	no	—
262	#95	C₂×C₅×D₃	1	2	yes	—
263	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
264	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
265	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
266	C₂×C₃×C₅	#529	1	2	yes	—
267	C₂×C₃×C₅	#529	1	2	yes	—
268	C₅×D₃	—	2	4	no	—
269	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
270	C₂²×D₃	—	2	2	no	—
271	C₂²×D₃	—	2	1	no	—
272	C₂²×D₃	—	2	1	no	—
273	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
274	C₂²×D₃	C₅×#41	1	4	yes	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	4	no	—
277	C₂×C₃×C₄	—	2	4	no	—
278	C₂×C₃×C₄	—	2	4	no	—
279	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
280	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
281	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
282	C₂×C₃×C₄	C₅×#41	1	4	yes	—
283	C₂×C₃×C₄	C₅×#41	1	2	yes	—
284	C₂×C₃×C₄	C₅×#41	1	2	yes	—
285	C₂×Dic₃	—	2	2	no	—
286	C₂×Dic₃	—	2	1	no	—
287	C₂×Dic₃	—	2	1	no	—
288	C₂×Dic₃	—	2	2	no	—
289	C₂×Dic₃	—	2	4	no	—
290	C₂×Dic₃	—	2	4	no	—
291	C₂×Dic₃	—	2	4	no	—
292	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
293	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
294	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
295	C₄×D₃	—	2	8	no	—
296	C₄×D₃	—	2	8	no	—
297	C₄×D₃	—	2	8	no	—
298	C₂²×C₅	—	3	4	no	—
299	C₂²×C₅	—	6	2	no	—
300	C₂²×C₅	—	6	2	no	—
301	C₂²×C₅	—	6	4	no	—
302	C₂²×C₅	—	6	4	no	—
303	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
304	C₂²×C₅	C₂×#235	1	2	yes	—
305	C₂²×C₅	C₂×#237	1	1	yes	characteristic
306	C₂²×C₅	C₂×#239	1	1	yes	characteristic
307	C₂²×C₅	D₃×#41	1	2	yes	—
308	C₄×C₅	—	2	2	no	—
309	C₄×C₅	—	4	4	no	—
310	C₄×C₅	—	6	2	no	—
311	C₄×C₅	—	6	2	no	—
312	C₄×C₅	—	6	2	no	—
313	C₄×C₅	—	12	4	no	—
314	C₄×C₅	#872	1	4	yes	—
315	C₄×C₅	#892	1	4	yes	—
316	C₂⁴	—	3	1	no	—
317	C₂²×C₄	—	3	1	no	—
318	C₂²×C₄	—	3	1	no	—
319	C₂²×C₄	—	3	1	no	—
320	C₂²×C₄	—	3	4	no	—
321	C₂²×C₄	—	3	4	no	—
322	C₂²×C₄	—	3	4	no	—
323	C₂²×C₄	—	3	4	no	—
324	C₂²×C₄	—	6	4	no	—
325	C₂²×C₄	—	6	4	no	—
326	C₂²×C₄	—	6	2	no	—
327	C₂²×C₄	—	6	2	no	—
328	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
329	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
330	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
331	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	6	4	no	—
334	C₂²⋊C₄	—	6	8	no	—
335	C₄²	—	2	4	no	—
336	C₄²	—	3	4	no	—
337	C₄²	—	3	4	no	—
338	C₄²	—	3	4	no	—
339	C₄²	—	6	4	no	—
340	C₄²	C₄×C₅×D₃	1	4	yes	—
341	C₃×C₅	#2283	1	1	yes	characteristic, complemented, Hall
342	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
343	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
344	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
345	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
346	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
347	C₂×D₃	—	2	2	no	—
348	C₂×D₃	—	2	2	no	—
349	C₂×D₃	—	2	4	no	—
350	C₂×D₃	—	2	4	no	—
351	C₂×D₃	C₅×#117	1	4	yes	—
352	C₃×C₄	—	2	2	no	—
353	C₃×C₄	—	4	4	no	—
354	C₃×C₄	C₅×#117	1	4	yes	—
355	C₃×C₄	C₅×#117	1	4	yes	—
356	Dic₃	—	2	2	no	—
357	Dic₃	—	2	2	no	—
358	Dic₃	—	2	2	no	—
359	Dic₃	—	4	4	no	—
360	C₂×C₅	—	6	4	no	—
361	C₂×C₅	C₂×#872	1	1	yes	characteristic
362	C₂×C₅	C₂×#892	1	1	yes	characteristic
363	C₂×C₅	D₃×#117	1	1	yes	characteristic
364	C₂×C₅	#5557	1	2	yes	—
365	C₂×C₅	#5580	1	2	yes	—
366	C₂³	—	3	2	no	—
367	C₂³	—	3	4	no	—
368	C₂³	—	6	2	no	—
369	C₂³	—	6	1	no	—
370	C₂³	—	6	1	no	—
371	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	3	2	no	—
377	C₂×C₄	—	3	2	no	—
378	C₂×C₄	—	3	2	no	—
379	C₂×C₄	—	6	8	no	—
380	C₂×C₄	—	6	2	no	—
381	C₂×C₄	—	6	1	no	—
382	C₂×C₄	—	6	1	no	—
383	C₂×C₄	—	6	2	no	—
384	C₂×C₄	—	6	8	no	—
385	C₂×C₄	—	6	8	no	—
386	C₂×C₄	—	6	4	no	—
387	C₂×C₄	—	6	4	no	—
388	C₂×C₄	—	6	4	no	—
389	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
390	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
391	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
392	C₂×C₄	C₅×#235	1	4	yes	—
393	C₂×C₄	C₅×#237	1	2	yes	—
394	C₂×C₄	C₅×#239	1	2	yes	—
395	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
396	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
397	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
398	C₂×C₃	C₅×#529	1	2	yes	—
399	C₂×C₃	C₅×#529	1	2	yes	—
400	D₃	—	2	4	no	—
401	C₅	#73752	1	1	yes	characteristic, direct product factor, Sylow
402	C₂²	—	3	4	no	—
403	C₂²	—	6	2	no	—
404	C₂²	—	6	2	no	—
405	C₂²	—	6	4	no	—
406	C₂²	—	6	4	no	—
407	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
408	C₂²	C₂×C₅×#235	1	2	yes	—
409	C₂²	C₂×C₅×#237	1	1	yes	characteristic
410	C₂²	C₂×C₅×#239	1	1	yes	characteristic
411	C₂²	C₅×D₃×#41	1	2	yes	—
412	C₄	—	2	2	no	—
413	C₄	—	4	4	no	—
414	C₄	—	6	2	no	—
415	C₄	—	6	2	no	—
416	C₄	—	6	2	no	—
417	C₄	—	12	4	no	—
418	C₄	C₅×#872	1	4	yes	—
419	C₄	C₅×#892	1	4	yes	—
420	C₃	C₅×#2283	1	1	yes	characteristic, complemented, Sylow
421	C₂	—	6	4	no	—
422	C₂	C₂×C₅×#872	1	1	yes	characteristic
423	C₂	C₂×C₅×#892	1	1	yes	characteristic
424	C₂	C₅×D₃×#117	1	1	yes	characteristic
425	C₂	C₅×#5557	1	2	yes	—
426	C₂	C₅×#5580	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×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	C₂³×C₅×D₃	C₂³
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₄×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₅×#2283
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×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
4. C₅×#4977	C₂	semidirect
6. C₄×C₅×C₄⋊Dic₃	C₂	semidirect
7. C₅×#4932	C₂	semidirect
9. C₅×#4651	C₂	semidirect
23. C₄²×C₅×D₃	C₄	semidirect
29. #73752	C₅	direct (N × H)
36. C₄×C₅×C₄⋊C₄	D₃	semidirect
65. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
67. #4977	C₂×C₅	semidirect
69. C₄×C₄⋊Dic₃	C₂×C₅	semidirect
70. #4932	C₂×C₅	semidirect
72. #4651	C₂×C₅	semidirect
133. C₄²×D₃	C₄×C₅	semidirect
170. C₄×C₄⋊C₄	C₅×D₃	semidirect
341. C₃×C₅	#2283	semidirect
401. C₅	#73752	direct (N × H)
420. 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×C₄×C₅×C₄⋊C₄	2
C₅×#4987	2
C₅×#4977	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₄×C₅×C₄⋊Dic₃	2
C₅×#4932	2
C₅×#4664	2
C₅×#4651	2
C₅×#2283	3
#73752	5

Subgroups — C5×#73752 #14320040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73752 #14320040