Subgroups — C₅×#71530 #14297426

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#830	C₂	1	2	yes	maximal
3	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	2	yes	maximal, complemented
4	C₅×#4524	C₂	1	2	yes	maximal, complemented
5	C₅×#1797	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₄×C₅	C₄	1	1	yes	characteristic
7	C₂³×C₃×C₄×C₅	C₄	1	1	yes	characteristic
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄²×C₅	—	2	4	no	—
10	C₂×C₃×C₄²×C₅	C₄	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₄	1	1	yes	characteristic
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂²×C₅×C₃⋊C₈	C₂²	1	4	yes	—
15	C₅×#830	—	2	4	no	—
16	C₅×C₄⋊(C₃⋊C₈)	—	2	4	no	—
17	#71530	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂²×C₄²×C₅	D₃	1	1	yes	characteristic
19	C₂×C₅×C₄⋊C₈	—	3	2	no	—
20	C₂×C₅×C₂²⋊C₈	—	3	2	no	—
21	C₅×#336	—	3	2	no	—
22	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₃×C₄×C₅	—	2	2	no	—
24	C₂²×C₃×C₄×C₅	—	2	2	no	—
25	C₂²×C₃×C₄×C₅	—	2	2	no	—
26	C₂²×C₃×C₄×C₅	—	2	2	no	—
27	C₂²×C₃×C₄×C₅	—	2	2	no	—
28	C₂²×C₃×C₄×C₅	—	2	2	no	—
29	C₂²×C₃×C₄×C₅	—	2	2	no	—
30	C₂²×C₃×C₄×C₅	C₈	1	4	yes	complemented
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
37	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₃×C₄²×C₅	—	2	2	no	—
40	C₃×C₄²×C₅	—	2	2	no	—
41	C₃×C₄²×C₅	—	2	2	no	—
42	C₃×C₄²×C₅	D₄	1	4	yes	—
43	C₂×C₅×C₃⋊C₈	—	2	4	no	—
44	C₂×C₅×C₃⋊C₈	—	2	4	no	—
45	C₂×C₅×C₃⋊C₈	—	2	4	no	—
46	C₂²×C₃×C₄²	C₂×C₅	1	1	yes	characteristic
47	C₂×#830	C₂×C₅	1	2	yes	—
48	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	2	yes	complemented
49	#4524	C₂×C₅	1	2	yes	complemented
50	C₂³×C₄×C₅	Dic₃	1	1	yes	characteristic
51	C₂³×C₄×C₅	Dic₃	1	1	yes	characteristic
52	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
53	C₂²×C₅×C₈	—	3	4	no	—
54	C₂×C₄²×C₅	—	2	4	no	—
55	C₂×C₄²×C₅	Dic₃	1	1	yes	characteristic
56	C₂×C₄²×C₅	Dic₃	1	1	yes	characteristic
57	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
58	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
59	C₅×C₄⋊C₈	—	6	4	no	—
60	C₅×C₂²⋊C₈	—	6	4	no	—
61	#1797	—	3	1	no	Sylow
62	C₂³×C₃×C₅	—	2	1	no	—
63	C₂³×C₃×C₅	—	2	1	no	—
64	C₂³×C₃×C₅	—	2	1	no	—
65	C₂³×C₃×C₅	—	2	1	no	—
66	C₂³×C₃×C₅	C₄⋊C₄	1	2	yes	—
67	C₂³×C₃×C₅	C₂×C₈	1	2	yes	—
68	C₂³×C₃×C₅	M₁₆	1	2	yes	—
69	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₃×C₄×C₅	—	2	8	no	—
71	C₂×C₃×C₄×C₅	—	2	1	no	—
72	C₂×C₃×C₄×C₅	—	2	1	no	—
73	C₂×C₃×C₄×C₅	—	2	1	no	—
74	C₂×C₃×C₄×C₅	—	2	1	no	—
75	C₂×C₃×C₄×C₅	—	2	1	no	—
76	C₂×C₃×C₄×C₅	—	2	1	no	—
77	C₂×C₃×C₄×C₅	—	2	1	no	—
78	C₂×C₃×C₄×C₅	—	2	1	no	—
79	C₂×C₃×C₄×C₅	—	2	8	no	—
80	C₂×C₃×C₄×C₅	—	2	4	no	—
81	C₂×C₃×C₄×C₅	—	2	4	no	—
82	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
83	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
84	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
85	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
86	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
87	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
88	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	#41	1	2	yes	—
93	C₅×C₃⋊C₈	—	4	4	no	—
94	C₂³×C₃×C₄	C₄×C₅	1	1	yes	characteristic
95	C₂³×C₃×C₄	C₄×C₅	1	1	yes	characteristic
96	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
97	C₂×C₃×C₄²	—	2	4	no	—
98	C₂×C₃×C₄²	C₄×C₅	1	1	yes	characteristic
99	C₂×C₃×C₄²	C₄×C₅	1	1	yes	characteristic
100	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
101	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
102	C₂²×C₃⋊C₈	C₂²×C₅	1	4	yes	—
103	#830	—	2	4	no	—
104	C₄⋊(C₃⋊C₈)	—	2	4	no	—
105	C₂⁴×C₅	C₂×Dic₃	1	1	yes	characteristic
106	C₂²×C₄×C₅	—	2	2	no	—
107	C₂²×C₄×C₅	—	2	2	no	—
108	C₂²×C₄×C₅	—	2	2	no	—
109	C₂²×C₄×C₅	—	2	2	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	C₃⋊C₈	1	4	yes	complemented
114	C₂²×C₄×C₅	Dic₆	1	2	yes	—
115	C₂²×C₄×C₅	D₁₂	1	2	yes	—
116	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
122	C₂×C₅×C₈	—	6	4	no	—
123	C₂×C₅×C₈	—	6	4	no	—
124	C₂×C₅×C₈	—	6	4	no	—
125	C₄²×C₅	—	2	2	no	—
126	C₄²×C₅	—	2	2	no	—
127	C₄²×C₅	—	2	2	no	—
128	C₄²×C₅	#67	1	4	yes	—
129	C₂²×C₄²	C₅×D₃	1	1	yes	characteristic
130	C₂×C₄⋊C₈	—	3	2	no	—
131	C₂×C₂²⋊C₈	—	3	2	no	—
132	#336	—	3	2	no	—
133	C₂²×C₃×C₅	—	2	2	no	—
134	C₂²×C₃×C₅	—	2	2	no	—
135	C₂²×C₃×C₅	—	2	2	no	—
136	C₂²×C₃×C₅	—	2	2	no	—
137	C₂²×C₃×C₅	—	2	2	no	—
138	C₂²×C₃×C₅	—	2	2	no	—
139	C₂²×C₃×C₅	C₄⋊C₈	1	4	yes	complemented
140	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂²×C₃×C₅	#117	1	1	yes	characteristic
143	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
144	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
145	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
146	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
147	C₃×C₄×C₅	—	2	2	no	—
148	C₃×C₄×C₅	—	2	2	no	—
149	C₃×C₄×C₅	—	2	2	no	—
150	C₃×C₄×C₅	—	2	2	no	—
151	C₃×C₄×C₅	C₂²⋊C₈	1	4	yes	complemented
152	C₃×C₄×C₅	#121	1	2	yes	—
153	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
154	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
155	C₂²×C₃×C₄	—	2	2	no	—
156	C₂²×C₃×C₄	—	2	2	no	—
157	C₂²×C₃×C₄	—	2	2	no	—
158	C₂²×C₃×C₄	—	2	2	no	—
159	C₂²×C₃×C₄	—	2	2	no	—
160	C₂²×C₃×C₄	—	2	2	no	—
161	C₂²×C₃×C₄	—	2	2	no	—
162	C₂²×C₃×C₄	C₅×C₈	1	4	yes	complemented
163	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
164	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
166	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
169	C₂²×C₃×C₄	C₅×Q₈	1	2	yes	—
170	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
171	C₃×C₄²	—	2	2	no	—
172	C₃×C₄²	—	2	2	no	—
173	C₃×C₄²	—	2	2	no	—
174	C₃×C₄²	C₅×D₄	1	4	yes	—
175	C₂×C₃⋊C₈	—	2	4	no	—
176	C₂×C₃⋊C₈	—	2	4	no	—
177	C₂×C₃⋊C₈	—	2	4	no	—
178	C₂³×C₅	—	2	1	no	—
179	C₂³×C₅	—	2	1	no	—
180	C₂³×C₅	—	2	1	no	—
181	C₂³×C₅	—	2	1	no	—
182	C₂³×C₅	C₂×C₃⋊C₈	1	2	yes	—
183	C₂³×C₅	#208	1	2	yes	—
184	C₂³×C₅	C₄⋊Dic₃	1	2	yes	—
185	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
186	C₂×C₄×C₅	—	2	8	no	—
187	C₂×C₄×C₅	—	2	1	no	—
188	C₂×C₄×C₅	—	2	1	no	—
189	C₂×C₄×C₅	—	2	1	no	—
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	2	1	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	8	no	—
196	C₂×C₄×C₅	—	2	4	no	—
197	C₂×C₄×C₅	—	2	4	no	—
198	C₂×C₄×C₅	C₂×C₃⋊C₈	1	2	yes	—
199	C₂×C₄×C₅	C₂×C₃⋊C₈	1	2	yes	—
200	C₂×C₄×C₅	#208	1	2	yes	—
201	C₂×C₄×C₅	#208	1	2	yes	—
202	C₂×C₄×C₅	C₄⋊Dic₃	1	2	yes	—
203	C₂×C₄×C₅	#217	1	2	yes	—
204	C₂×C₄×C₅	#217	1	2	yes	—
205	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
207	C₂×C₄×C₅	#235	1	2	yes	—
208	C₂×C₄×C₅	C₂×#67	1	2	yes	—
209	C₅×C₈	—	12	4	no	—
210	C₂³×C₄	C₅×Dic₃	1	1	yes	characteristic
211	C₂³×C₄	C₅×Dic₃	1	1	yes	characteristic
212	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
213	C₂²×C₈	—	3	4	no	—
214	C₂×C₄²	—	2	4	no	—
215	C₂×C₄²	C₅×Dic₃	1	1	yes	characteristic
216	C₂×C₄²	C₅×Dic₃	1	1	yes	characteristic
217	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
218	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
219	C₄⋊C₈	—	6	4	no	—
220	C₂²⋊C₈	—	6	4	no	—
221	C₂×C₃×C₅	—	2	4	no	—
222	C₂×C₃×C₅	#380	1	1	yes	characteristic
223	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
224	C₂×C₃×C₅	#407	1	1	yes	characteristic
225	C₂×C₃×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
226	C₂×C₃×C₅	#423	1	1	yes	characteristic
227	C₂×C₃×C₅	#431	1	1	yes	characteristic
228	C₂×C₃×C₅	#432	1	1	yes	characteristic
229	C₂³×C₃	—	2	1	no	—
230	C₂³×C₃	—	2	1	no	—
231	C₂³×C₃	—	2	1	no	—
232	C₂³×C₃	—	2	1	no	—
233	C₂³×C₃	C₅×C₄⋊C₄	1	2	yes	—
234	C₂³×C₃	C₂×C₅×C₈	1	2	yes	—
235	C₂³×C₃	C₅×M₁₆	1	2	yes	—
236	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
237	C₂×C₃×C₄	—	2	8	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	4	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	8	no	—
249	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
250	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
251	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
252	C₂×C₃×C₄	C₂×C₅×C₈	1	2	yes	—
253	C₂×C₃×C₄	C₂×C₅×C₈	1	2	yes	—
254	C₂×C₃×C₄	C₅×M₁₆	1	2	yes	—
255	C₂×C₃×C₄	C₅×M₁₆	1	2	yes	—
256	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
258	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
259	C₂×C₃×C₄	C₅×#41	1	2	yes	—
260	C₃⋊C₈	—	4	4	no	—
261	C₂²×C₅	—	2	2	no	—
262	C₂²×C₅	—	2	2	no	—
263	C₂²×C₅	—	2	2	no	—
264	C₂²×C₅	—	2	2	no	—
265	C₂²×C₅	—	2	2	no	—
266	C₂²×C₅	—	2	2	no	—
267	C₂²×C₅	C₄⋊(C₃⋊C₈)	1	4	yes	complemented
268	C₂²×C₅	C₂²×C₃⋊C₈	1	1	yes	characteristic
269	C₂²×C₅	C₂×#208	1	1	yes	characteristic
270	C₂²×C₅	C₂×#208	1	1	yes	characteristic
271	C₂²×C₅	C₂×#208	1	1	yes	characteristic
272	C₂²×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
273	C₂²×C₅	#926	1	1	yes	characteristic
274	C₂²×C₅	C₂×#217	1	1	yes	characteristic
275	C₄×C₅	—	2	2	no	—
276	C₄×C₅	—	2	2	no	—
277	C₄×C₅	—	2	2	no	—
278	C₄×C₅	—	2	2	no	—
279	C₄×C₅	#830	1	4	yes	complemented
280	C₄×C₅	#924	1	2	yes	—
281	C₄×C₅	#930	1	2	yes	—
282	C₂⁴	C₂×C₅×Dic₃	1	1	yes	characteristic
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	C₅×C₃⋊C₈	1	4	yes	complemented
291	C₂²×C₄	C₅×Dic₆	1	2	yes	—
292	C₂²×C₄	C₅×D₁₂	1	2	yes	—
293	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
298	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
299	C₂×C₈	—	6	4	no	—
300	C₂×C₈	—	6	4	no	—
301	C₂×C₈	—	6	4	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	C₅×#67	1	4	yes	—
306	C₃×C₅	#1797	1	1	yes	characteristic, complemented, Hall
307	C₂²×C₃	—	2	2	no	—
308	C₂²×C₃	—	2	2	no	—
309	C₂²×C₃	—	2	2	no	—
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	—	2	2	no	—
312	C₂²×C₃	—	2	2	no	—
313	C₂²×C₃	C₅×C₄⋊C₈	1	4	yes	complemented
314	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
315	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
316	C₂²×C₃	C₅×#117	1	1	yes	characteristic
317	C₂²×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
318	C₂²×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
319	C₂²×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
320	C₂²×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
321	C₃×C₄	—	2	2	no	—
322	C₃×C₄	—	2	2	no	—
323	C₃×C₄	—	2	2	no	—
324	C₃×C₄	—	2	2	no	—
325	C₃×C₄	C₅×C₂²⋊C₈	1	4	yes	complemented
326	C₃×C₄	C₅×#121	1	2	yes	—
327	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
328	C₂×C₅	—	2	4	no	—
329	C₂×C₅	C₂×C₄⋊(C₃⋊C₈)	1	1	yes	characteristic
330	C₂×C₅	#4924	1	1	yes	characteristic
331	C₂×C₅	#4925	1	1	yes	characteristic
332	C₂×C₅	#4926	1	1	yes	characteristic
333	C₂×C₅	C₂×#830	1	1	yes	characteristic
334	C₂×C₅	#5207	1	1	yes	characteristic
335	C₂×C₅	#5212	1	1	yes	characteristic
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	C₂×C₅×C₃⋊C₈	1	2	yes	—
341	C₂³	C₅×#208	1	2	yes	—
342	C₂³	C₅×C₄⋊Dic₃	1	2	yes	—
343	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	C₂×C₅×C₃⋊C₈	1	2	yes	—
357	C₂×C₄	C₂×C₅×C₃⋊C₈	1	2	yes	—
358	C₂×C₄	C₅×#208	1	2	yes	—
359	C₂×C₄	C₅×#208	1	2	yes	—
360	C₂×C₄	C₅×C₄⋊Dic₃	1	2	yes	—
361	C₂×C₄	C₅×#217	1	2	yes	—
362	C₂×C₄	C₅×#217	1	2	yes	—
363	C₂×C₄	C₂×C₅×Dic₆	1	1	yes	characteristic
364	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
365	C₂×C₄	C₅×#235	1	2	yes	—
366	C₂×C₄	C₂×C₅×#67	1	2	yes	—
367	C₈	—	12	4	no	—
368	C₂×C₃	—	2	4	no	—
369	C₂×C₃	C₅×#380	1	1	yes	characteristic
370	C₂×C₃	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
371	C₂×C₃	C₅×#407	1	1	yes	characteristic
372	C₂×C₃	C₂×C₅×C₄⋊C₈	1	1	yes	characteristic
373	C₂×C₃	C₅×#423	1	1	yes	characteristic
374	C₂×C₃	C₅×#431	1	1	yes	characteristic
375	C₂×C₃	C₅×#432	1	1	yes	characteristic
376	C₅	#71530	1	1	yes	characteristic, direct product factor, Sylow
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	C₅×C₄⋊(C₃⋊C₈)	1	4	yes	complemented
384	C₂²	C₂²×C₅×C₃⋊C₈	1	1	yes	characteristic
385	C₂²	C₂×C₅×#208	1	1	yes	characteristic
386	C₂²	C₂×C₅×#208	1	1	yes	characteristic
387	C₂²	C₂×C₅×#208	1	1	yes	characteristic
388	C₂²	C₂×C₅×C₄⋊Dic₃	1	1	yes	characteristic
389	C₂²	C₅×#926	1	1	yes	characteristic
390	C₂²	C₂×C₅×#217	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	C₅×#830	1	4	yes	complemented
396	C₄	C₅×#924	1	2	yes	—
397	C₄	C₅×#930	1	2	yes	—
398	C₃	C₅×#1797	1	1	yes	characteristic, complemented, Sylow
399	C₂	—	2	4	no	—
400	C₂	C₂×C₅×C₄⋊(C₃⋊C₈)	1	1	yes	characteristic
401	C₂	C₅×#4924	1	1	yes	characteristic
402	C₂	C₅×#4925	1	1	yes	characteristic
403	C₂	C₅×#4926	1	1	yes	characteristic
404	C₂	C₂×C₅×#830	1	1	yes	characteristic
405	C₂	C₅×#5207	1	1	yes	characteristic
406	C₂	C₅×#5212	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₅×C₈
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂²×C₃×C₄²×C₅	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂⁴×C₃×C₅	C₂×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂²×C₄²×C₅	D₃
hypocenter	C₃	C₅×#1797
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂²×C₄²×C₅

Complements

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

N	H ≅ G/N	type
3. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
4. C₅×#4524	C₂	semidirect
17. #71530	C₅	direct (N × H)
30. C₂²×C₃×C₄×C₅	C₈	semidirect
48. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
49. #4524	C₂×C₅	semidirect
113. C₂²×C₄×C₅	C₃⋊C₈	semidirect
139. C₂²×C₃×C₅	C₄⋊C₈	semidirect
151. C₃×C₄×C₅	C₂²⋊C₈	semidirect
162. C₂²×C₃×C₄	C₅×C₈	semidirect
267. C₂²×C₅	C₄⋊(C₃⋊C₈)	semidirect
279. C₄×C₅	#830	semidirect
290. C₂²×C₄	C₅×C₃⋊C₈	semidirect
306. C₃×C₅	#1797	semidirect
313. C₂²×C₃	C₅×C₄⋊C₈	semidirect
325. C₃×C₄	C₅×C₂²⋊C₈	semidirect
376. C₅	#71530	direct (N × H)
383. C₂²	C₅×C₄⋊(C₃⋊C₈)	semidirect
395. C₄	C₅×#830	semidirect
398. C₃	C₅×#1797	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄²×C₅	2
C₂×C₅×#830	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₅×#4524	2
C₅×#1797	3
#71530	5

Subgroups — C5×#71530 #14297426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71530 #14297426