Subgroups — C₅×#73617 #14320820

Order 1920.

1304 conjugacy classes of subgroups.

The subgroup lattice has 412 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	C₂×C₅×#872	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4988	C₂	1	2	yes	maximal
5	C₅×#4972	C₂	1	2	yes	maximal, complemented
6	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₄²×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4669	C₂	1	4	yes	maximal, complemented
9	C₅×#2293	—	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	1	yes	characteristic
19	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
20	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
21	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
23	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
24	C₄×C₅×D₁₂	C₄	1	8	yes	complemented
25	C₅×#872	—	2	8	no	—
26	C₃×C₅×#95	C₂²	1	2	yes	—
27	C₅×C₃⋊#95	C₂²	1	4	yes	—
28	#73617	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₄×C₅×D₄	—	3	1	no	—
30	C₂×C₅×#117	—	3	2	no	—
31	C₅×#390	—	3	2	no	—
32	C₅×#389	—	3	2	no	—
33	C₅×#388	—	3	4	no	—
34	C₄×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
35	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
36	C₄³×C₅	—	3	1	no	—
37	C₂³×C₅×D₃	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
43	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
44	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
45	C₂×C₅×D₁₂	—	2	4	no	—
46	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
47	C₂×C₄×C₅×D₃	—	2	4	no	—
48	C₂×C₄×C₅×D₃	—	2	4	no	—
49	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	—
50	C₃×C₅×C₄⋊C₄	—	2	4	no	—
51	C₃×C₄²×C₅	—	2	4	no	—
52	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
53	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
54	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
55	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	—
56	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	—
57	C₅×Dic₃⋊C₄	—	2	8	no	—
58	C₄×C₅×Dic₃	—	2	4	no	—
59	C₄×C₅×Dic₃	—	2	2	no	—
60	C₄×C₅×Dic₃	—	2	4	no	—
61	C₄×C₅×Dic₃	D₄	1	4	yes	complemented
62	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
63	C₂×#872	C₂×C₅	1	2	yes	complemented
64	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
65	#4988	C₂×C₅	1	2	yes	—
66	#4972	C₂×C₅	1	2	yes	complemented
67	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	2	yes	complemented
68	C₄²×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
69	#4669	C₂×C₅	1	4	yes	complemented
70	C₂²×C₅×D₄	—	3	1	no	—
71	C₂³×C₄×C₅	—	3	2	no	—
72	C₄×C₅×D₄	—	3	8	no	—
73	C₅×#117	—	6	8	no	—
74	C₂×C₅×C₄⋊C₄	—	3	1	no	—
75	C₂×C₅×C₄⋊C₄	—	3	4	no	—
76	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
77	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
78	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
79	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
80	C₂×C₄²×C₅	—	3	1	no	—
81	C₂×C₄²×C₅	—	3	2	no	—
82	C₂×C₄²×C₅	—	3	2	no	—
83	C₂×C₄²×C₅	—	3	1	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	C₂×D₃	1	2	yes	—
88	#2293	—	3	1	no	Sylow
89	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
90	C₂²×C₅×D₃	—	2	2	no	—
91	C₂²×C₅×D₃	—	2	4	no	—
92	C₂²×C₅×D₃	—	2	2	no	—
93	C₂²×C₅×D₃	—	2	4	no	—
94	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	4	no	—
97	C₂×C₃×C₄×C₅	—	2	4	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
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	C₂×D₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	#41	1	4	yes	—
104	C₂×C₃×C₄×C₅	#41	1	2	yes	—
105	C₂×C₅×Dic₃	—	2	2	no	—
106	C₂×C₅×Dic₃	—	2	2	no	—
107	C₂×C₅×Dic₃	—	2	2	no	—
108	C₂×C₅×Dic₃	—	2	2	no	—
109	C₂×C₅×Dic₃	—	2	2	no	—
110	C₂×C₅×Dic₃	—	2	2	no	—
111	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
112	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
113	C₂×C₅×Dic₃	#41	1	4	yes	—
114	C₅×D₁₂	—	2	8	no	—
115	C₄×C₅×D₃	—	2	16	no	—
116	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
117	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
118	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
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×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
123	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
124	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
125	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
126	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
127	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
129	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
130	C₄×D₁₂	C₄×C₅	1	8	yes	complemented
131	#872	—	2	8	no	—
132	C₃×#95	C₂²×C₅	1	2	yes	—
133	C₃⋊#95	C₂²×C₅	1	4	yes	—
134	C₂⁴×C₅	—	3	2	no	—
135	C₂×C₅×D₄	—	3	4	no	—
136	C₂×C₅×D₄	—	6	4	no	—
137	C₂²×C₄×C₅	—	3	2	no	—
138	C₂²×C₄×C₅	—	3	2	no	—
139	C₂²×C₄×C₅	—	3	2	no	—
140	C₂²×C₄×C₅	—	3	8	no	—
141	C₂²×C₄×C₅	—	6	4	no	—
142	C₂²×C₄×C₅	—	6	4	no	—
143	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
144	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
147	C₅×C₄⋊C₄	—	2	4	no	—
148	C₅×C₄⋊C₄	—	3	4	no	—
149	C₅×C₄⋊C₄	—	6	8	no	—
150	C₅×C₂²⋊C₄	—	3	8	no	—
151	C₅×C₂²⋊C₄	—	6	8	no	—
152	C₅×C₂²⋊C₄	—	6	8	no	—
153	C₄²×C₅	—	2	4	no	—
154	C₄²×C₅	—	3	4	no	—
155	C₄²×C₅	—	6	4	no	—
156	C₄²×C₅	—	6	4	no	—
157	C₄²×C₅	—	6	2	no	—
158	C₄²×C₅	C₄×D₃	1	4	yes	—
159	C₂×C₄×D₄	—	3	1	no	—
160	C₂×#117	—	3	2	no	—
161	#390	—	3	2	no	—
162	#389	—	3	2	no	—
163	#388	—	3	4	no	—
164	C₄×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
165	C₄×C₂²⋊C₄	—	3	2	no	—
166	C₄³	—	3	1	no	—
167	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
168	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
169	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
170	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
171	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
172	C₂×C₅×D₃	—	2	4	no	—
173	C₂×C₅×D₃	—	2	4	no	—
174	C₂×C₅×D₃	—	2	4	no	—
175	C₂×C₅×D₃	—	4	4	no	—
176	C₂×C₅×D₃	—	4	4	no	—
177	C₃×C₄×C₅	—	2	2	no	—
178	C₃×C₄×C₅	—	4	4	no	—
179	C₃×C₄×C₅	#117	1	4	yes	complemented
180	C₃×C₄×C₅	C₄×D₄	1	4	yes	—
181	C₅×Dic₃	—	2	4	no	—
182	C₅×Dic₃	—	2	4	no	—
183	C₅×Dic₃	—	2	4	no	—
184	C₂³×D₃	C₂³×C₅	1	2	yes	—
185	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
186	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
187	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
188	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
189	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
190	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
191	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
192	C₂×D₁₂	—	2	4	no	—
193	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
194	C₂×C₄×D₃	—	2	4	no	—
195	C₂×C₄×D₃	—	2	4	no	—
196	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	—
197	C₃×C₄⋊C₄	—	2	4	no	—
198	C₃×C₄²	—	2	4	no	—
199	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
200	(C₂×D₃)⋊C₄	—	2	8	no	—
201	(C₂×D₃)⋊C₄	—	2	8	no	—
202	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	—
203	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	—
204	Dic₃⋊C₄	—	2	8	no	—
205	C₄×Dic₃	—	2	4	no	—
206	C₄×Dic₃	—	2	2	no	—
207	C₄×Dic₃	—	2	4	no	—
208	C₄×Dic₃	C₅×D₄	1	4	yes	complemented
209	C₂³×C₅	—	3	4	no	—
210	C₂³×C₅	—	6	4	no	—
211	C₂³×C₅	—	6	2	no	—
212	C₂³×C₅	—	6	2	no	—
213	C₂³×C₅	—	6	4	no	—
214	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
215	C₅×D₄	—	6	8	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	4	no	—
218	C₂×C₄×C₅	—	2	4	no	—
219	C₂×C₄×C₅	—	2	4	no	—
220	C₂×C₄×C₅	—	3	4	no	—
221	C₂×C₄×C₅	—	3	4	no	—
222	C₂×C₄×C₅	—	3	4	no	—
223	C₂×C₄×C₅	—	6	2	no	—
224	C₂×C₄×C₅	—	6	2	no	—
225	C₂×C₄×C₅	—	6	2	no	—
226	C₂×C₄×C₅	—	6	2	no	—
227	C₂×C₄×C₅	—	6	2	no	—
228	C₂×C₄×C₅	—	6	2	no	—
229	C₂×C₄×C₅	—	6	16	no	—
230	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
231	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
232	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
233	C₂×C₄×C₅	#235	1	4	yes	—
234	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
235	C₂×C₄×C₅	#239	1	2	yes	—
236	C₂²×D₄	—	3	1	no	—
237	C₂³×C₄	—	3	2	no	—
238	C₄×D₄	—	3	8	no	—
239	#117	—	6	8	no	—
240	C₂×C₄⋊C₄	—	3	1	no	—
241	C₂×C₄⋊C₄	—	3	4	no	—
242	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
243	C₂×C₂²⋊C₄	—	3	2	no	—
244	C₂×C₂²⋊C₄	—	3	4	no	—
245	C₂×C₂²⋊C₄	—	3	4	no	—
246	C₂×C₄²	—	3	1	no	—
247	C₂×C₄²	—	3	1	no	—
248	C₂×C₄²	—	3	2	no	—
249	C₂×C₄²	—	3	2	no	—
250	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
251	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
252	#95	—	3	4	no	—
253	#95	C₂×C₅×D₃	1	2	yes	—
254	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
255	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
256	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
257	C₂×C₃×C₅	#529	1	2	yes	—
258	C₂×C₃×C₅	#532	1	2	yes	—
259	C₅×D₃	—	4	4	no	—
260	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
261	C₂²×D₃	—	2	2	no	—
262	C₂²×D₃	—	2	4	no	—
263	C₂²×D₃	—	2	2	no	—
264	C₂²×D₃	—	2	4	no	—
265	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	4	no	—
268	C₂×C₃×C₄	—	2	4	no	—
269	C₂×C₃×C₄	—	2	4	no	—
270	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
271	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
272	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
273	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
274	C₂×C₃×C₄	C₅×#41	1	4	yes	—
275	C₂×C₃×C₄	C₅×#41	1	2	yes	—
276	C₂×Dic₃	—	2	2	no	—
277	C₂×Dic₃	—	2	2	no	—
278	C₂×Dic₃	—	2	2	no	—
279	C₂×Dic₃	—	2	2	no	—
280	C₂×Dic₃	—	2	2	no	—
281	C₂×Dic₃	—	2	2	no	—
282	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
283	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
284	C₂×Dic₃	C₅×#41	1	4	yes	—
285	D₁₂	—	2	8	no	—
286	C₄×D₃	—	2	16	no	—
287	C₂²×C₅	—	6	4	no	—
288	C₂²×C₅	—	6	4	no	—
289	C₂²×C₅	—	6	4	no	—
290	C₂²×C₅	—	12	4	no	—
291	C₂²×C₅	—	12	4	no	—
292	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
293	C₂²×C₅	C₂×#235	1	2	yes	—
294	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
295	C₂²×C₅	C₂×#239	1	1	yes	characteristic
296	C₂²×C₅	D₃×#41	1	2	yes	—
297	C₄×C₅	—	2	2	no	—
298	C₄×C₅	—	4	4	no	—
299	C₄×C₅	—	6	4	no	—
300	C₄×C₅	—	6	4	no	—
301	C₄×C₅	—	6	4	no	—
302	C₄×C₅	#872	1	4	yes	complemented
303	C₄×C₅	#893	1	4	yes	—
304	C₂⁴	—	3	2	no	—
305	C₂×D₄	—	3	4	no	—
306	C₂×D₄	—	6	4	no	—
307	C₂²×C₄	—	3	2	no	—
308	C₂²×C₄	—	3	2	no	—
309	C₂²×C₄	—	3	2	no	—
310	C₂²×C₄	—	3	8	no	—
311	C₂²×C₄	—	6	4	no	—
312	C₂²×C₄	—	6	4	no	—
313	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
314	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
315	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
316	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	3	4	no	—
319	C₄⋊C₄	—	6	8	no	—
320	C₂²⋊C₄	—	3	8	no	—
321	C₂²⋊C₄	—	6	8	no	—
322	C₂²⋊C₄	—	6	8	no	—
323	C₄²	—	2	4	no	—
324	C₄²	—	3	4	no	—
325	C₄²	—	6	4	no	—
326	C₄²	—	6	4	no	—
327	C₄²	—	6	2	no	—
328	C₄²	C₄×C₅×D₃	1	4	yes	—
329	C₃×C₅	#2293	1	1	yes	characteristic, complemented, Hall
330	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
331	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
332	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
333	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
334	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
335	C₂×D₃	—	2	4	no	—
336	C₂×D₃	—	2	4	no	—
337	C₂×D₃	—	2	4	no	—
338	C₂×D₃	—	4	4	no	—
339	C₂×D₃	—	4	4	no	—
340	C₃×C₄	—	2	2	no	—
341	C₃×C₄	—	4	4	no	—
342	C₃×C₄	C₅×#117	1	4	yes	complemented
343	C₃×C₄	C₄×C₅×D₄	1	4	yes	—
344	Dic₃	—	2	4	no	—
345	Dic₃	—	2	4	no	—
346	Dic₃	—	2	4	no	—
347	C₂×C₅	—	12	4	no	—
348	C₂×C₅	C₂×#872	1	1	yes	characteristic
349	C₂×C₅	C₂×#893	1	1	yes	characteristic
350	C₂×C₅	#5522	1	1	yes	characteristic
351	C₂×C₅	#5548	1	2	yes	—
352	C₂×C₅	#5580	1	2	yes	—
353	C₂³	—	3	4	no	—
354	C₂³	—	6	4	no	—
355	C₂³	—	6	2	no	—
356	C₂³	—	6	2	no	—
357	C₂³	—	6	4	no	—
358	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
359	D₄	—	6	8	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	3	4	no	—
365	C₂×C₄	—	3	4	no	—
366	C₂×C₄	—	3	4	no	—
367	C₂×C₄	—	6	2	no	—
368	C₂×C₄	—	6	2	no	—
369	C₂×C₄	—	6	2	no	—
370	C₂×C₄	—	6	2	no	—
371	C₂×C₄	—	6	2	no	—
372	C₂×C₄	—	6	2	no	—
373	C₂×C₄	—	6	16	no	—
374	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
375	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
376	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
377	C₂×C₄	C₅×#235	1	4	yes	—
378	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
379	C₂×C₄	C₅×#239	1	2	yes	—
380	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
381	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
382	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
383	C₂×C₃	C₅×#529	1	2	yes	—
384	C₂×C₃	C₅×#532	1	2	yes	—
385	D₃	—	4	4	no	—
386	C₅	#73617	1	1	yes	characteristic, direct product factor, Sylow
387	C₂²	—	6	4	no	—
388	C₂²	—	6	4	no	—
389	C₂²	—	6	4	no	—
390	C₂²	—	12	4	no	—
391	C₂²	—	12	4	no	—
392	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
393	C₂²	C₂×C₅×#235	1	2	yes	—
394	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
395	C₂²	C₂×C₅×#239	1	1	yes	characteristic
396	C₂²	C₅×D₃×#41	1	2	yes	—
397	C₄	—	2	2	no	—
398	C₄	—	4	4	no	—
399	C₄	—	6	4	no	—
400	C₄	—	6	4	no	—
401	C₄	—	6	4	no	—
402	C₄	C₅×#872	1	4	yes	complemented
403	C₄	C₅×#893	1	4	yes	—
404	C₃	C₅×#2293	1	1	yes	characteristic, complemented, Sylow
405	C₂	—	12	4	no	—
406	C₂	C₂×C₅×#872	1	1	yes	characteristic
407	C₂	C₂×C₅×#893	1	1	yes	characteristic
408	C₂	C₅×#5522	1	1	yes	characteristic
409	C₂	C₅×#5548	1	2	yes	—
410	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	C₂²×C₅×D₁₂	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₄×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₅×#2293
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. C₂×C₅×#872	C₂	semidirect
3. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
5. C₅×#4972	C₂	semidirect
6. C₄×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
7. C₄²×C₅×Dic₃	C₂	semidirect
8. C₅×#4669	C₂	semidirect
24. C₄×C₅×D₁₂	C₄	semidirect
28. #73617	C₅	direct (N × H)
34. C₄×C₅×C₄⋊C₄	D₃	semidirect
61. C₄×C₅×Dic₃	D₄	semidirect
63. C₂×#872	C₂×C₅	semidirect
64. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
66. #4972	C₂×C₅	semidirect
67. C₄×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
68. C₄²×Dic₃	C₂×C₅	semidirect
69. #4669	C₂×C₅	semidirect
130. C₄×D₁₂	C₄×C₅	semidirect
164. C₄×C₄⋊C₄	C₅×D₃	semidirect
179. C₃×C₄×C₅	#117	semidirect
208. C₄×Dic₃	C₅×D₄	semidirect
302. C₄×C₅	#872	semidirect
329. C₃×C₅	#2293	semidirect
342. C₃×C₄	C₅×#117	semidirect
386. C₅	#73617	direct (N × H)
402. C₄	C₅×#872	semidirect
404. C₃	C₅×#2293	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
C₂×C₅×#872	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#4988	2
C₅×#4972	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₄²×C₅×Dic₃	2
C₅×#4669	2
C₅×#2293	3
#73617	5

Subgroups — C5×#73617 #14320820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73617 #14320820