Subgroups — C₅×#71639 #14281626

Order 1920.

528 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	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₅×#4925	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4535	C₂	1	2	yes	maximal, complemented
5	C₅×D₄⋊(C₃⋊C₈)	C₂	1	2	yes	maximal, complemented
6	C₅×#1477	—	3	1	no	maximal, Hall
7	C₂×C₃×C₅×#41	C₄	1	1	yes	characteristic
8	C₃×C₄×C₅×Q₈	C₄	1	1	yes	characteristic
9	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₃×C₄×C₅×D₄	—	2	1	no	—
11	C₃×C₄×C₅×D₄	—	2	1	no	—
12	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic
13	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₃×C₅×#117	—	2	1	no	—
15	C₃×C₅×#117	C₄	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	—	2	1	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₃⋊C₈	—	2	1	no	—
19	C₅×#830	—	2	1	no	—
20	C₅×C₄⋊(C₃⋊C₈)	—	2	1	no	—
21	C₅×C₄⋊(C₃⋊C₈)	—	2	1	no	—
22	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
23	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
24	#71639	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₄×C₅×#41	D₃	1	1	yes	characteristic
26	C₅×#431	—	3	1	no	—
27	C₂×C₅×C₄⋊C₈	—	3	1	no	—
28	C₅×Q₈⋊C₈	—	3	2	no	—
29	C₅×D₄⋊C₈	—	3	2	no	—
30	C₃×C₅×#41	—	2	2	no	—
31	C₃×C₅×#41	C₈	1	4	yes	complemented
32	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
33	C₂×C₃×C₅×D₄	—	2	1	no	—
34	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	—	2	1	no	—
36	C₂²×C₃×C₄×C₅	—	2	1	no	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
41	C₃×C₅×C₄⋊C₄	—	2	1	no	—
42	C₃×C₅×C₄⋊C₄	—	2	1	no	—
43	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
46	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
48	C₃×C₄²×C₅	—	2	1	no	—
49	C₃×C₄²×C₅	—	2	1	no	—
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₅×C₃⋊C₈	—	2	2	no	—
56	C₂×C₅×C₃⋊C₈	—	2	2	no	—
57	C₂×C₅×C₃⋊C₈	—	4	2	no	—
58	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic
59	#4925	C₂×C₅	1	1	yes	characteristic, complemented
60	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
61	#4535	C₂×C₅	1	2	yes	complemented
62	D₄⋊(C₃⋊C₈)	C₂×C₅	1	2	yes	complemented
63	C₂×C₅×#41	Dic₃	1	1	yes	characteristic
64	C₂²×C₅×C₈	—	6	1	no	—
65	C₄×C₅×Q₈	Dic₃	1	1	yes	characteristic
66	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
67	C₄×C₅×D₄	—	2	1	no	—
68	C₄×C₅×D₄	—	2	1	no	—
69	C₄×C₅×D₄	Dic₃	1	1	yes	characteristic
70	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
71	C₅×#117	—	2	1	no	—
72	C₅×#117	Dic₃	1	1	yes	characteristic
73	C₂×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
75	C₅×C₄⋊C₈	—	3	2	no	—
76	C₅×C₄⋊C₈	—	6	1	no	—
77	C₅×C₄⋊C₈	—	6	1	no	—
78	C₅×C₂²⋊C₈	—	6	1	no	—
79	C₄×C₅×C₈	—	3	2	no	—
80	#1477	—	3	1	no	Sylow
81	C₂³×C₃×C₅	—	2	1	no	—
82	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₃×C₅×Q₈	—	2	1	no	—
84	C₃×C₅×Q₈	C₂×C₈	1	2	yes	complemented
85	C₃×C₅×D₄	—	2	4	no	—
86	C₃×C₅×D₄	—	2	1	no	—
87	C₃×C₅×D₄	C₂×C₈	1	2	yes	complemented
88	C₂×C₃×C₄×C₅	—	2	1	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	1	no	—
91	C₂×C₃×C₄×C₅	—	2	1	no	—
92	C₂×C₃×C₄×C₅	—	2	1	no	—
93	C₂×C₃×C₄×C₅	—	2	1	no	—
94	C₂×C₃×C₄×C₅	—	4	1	no	—
95	C₂×C₃×C₄×C₅	—	4	2	no	—
96	C₂×C₃×C₄×C₅	—	4	1	no	—
97	C₂×C₃×C₄×C₅	—	4	1	no	—
98	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
102	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₅×C₃⋊C₈	—	4	2	no	—
107	C₅×C₃⋊C₈	—	4	2	no	—
108	C₂×C₃×#41	C₄×C₅	1	1	yes	characteristic
109	C₃×C₄×Q₈	C₄×C₅	1	1	yes	characteristic
110	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
111	C₃×C₄×D₄	—	2	1	no	—
112	C₃×C₄×D₄	—	2	1	no	—
113	C₃×C₄×D₄	C₄×C₅	1	1	yes	characteristic
114	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
115	C₃×#117	—	2	1	no	—
116	C₃×#117	C₄×C₅	1	1	yes	characteristic
117	C₂×C₃×C₄²	—	2	1	no	—
118	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
119	C₂²×C₃⋊C₈	—	2	1	no	—
120	#830	—	2	1	no	—
121	C₄⋊(C₃⋊C₈)	—	2	1	no	—
122	C₄⋊(C₃⋊C₈)	—	2	1	no	—
123	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
124	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
125	C₅×#41	—	2	2	no	—
126	C₅×#41	C₃⋊C₈	1	4	yes	complemented
127	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
128	C₂×C₅×D₄	—	2	1	no	—
129	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	—	2	1	no	—
132	C₂²×C₄×C₅	—	2	1	no	—
133	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
134	C₂²×C₄×C₅	#67	1	1	yes	characteristic
135	C₂²×C₄×C₅	#67	1	1	yes	characteristic
136	C₂×C₅×C₈	—	6	2	no	—
137	C₂×C₅×C₈	—	6	2	no	—
138	C₂×C₅×C₈	—	12	2	no	—
139	C₅×C₄⋊C₄	—	2	1	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
142	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
143	C₅×C₂²⋊C₄	—	2	1	no	—
144	C₅×C₂²⋊C₄	—	2	1	no	—
145	C₅×C₂²⋊C₄	—	2	1	no	—
146	C₄²×C₅	—	2	1	no	—
147	C₄²×C₅	—	2	1	no	—
148	C₄²×C₅	—	2	1	no	—
149	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
150	C₄²×C₅	#67	1	1	yes	characteristic
151	C₄²×C₅	#67	1	1	yes	characteristic
152	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
153	C₄×#41	C₅×D₃	1	1	yes	characteristic
154	#431	—	3	1	no	—
155	C₂×C₄⋊C₈	—	3	1	no	—
156	Q₈⋊C₈	—	3	2	no	—
157	D₄⋊C₈	—	3	2	no	—
158	C₂²×C₃×C₅	—	2	1	no	—
159	C₂²×C₃×C₅	—	2	1	no	—
160	C₂²×C₃×C₅	—	2	2	no	—
161	C₂²×C₃×C₅	—	4	1	no	—
162	C₂²×C₃×C₅	—	4	1	no	—
163	C₂²×C₃×C₅	C₂²⋊C₈	1	2	yes	—
164	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₃×C₄×C₅	—	2	2	no	—
166	C₃×C₄×C₅	—	2	1	no	—
167	C₃×C₄×C₅	—	2	1	no	—
168	C₃×C₄×C₅	—	2	1	no	—
169	C₃×C₄×C₅	—	4	1	no	—
170	C₃×C₄×C₅	—	4	1	no	—
171	C₃×C₄×C₅	C₂²⋊C₈	1	2	yes	—
172	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
173	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
174	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₃×C₄×C₅	#137	1	1	yes	characteristic
176	C₃×#41	—	2	2	no	—
177	C₃×#41	C₅×C₈	1	4	yes	complemented
178	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
179	C₂×C₃×D₄	—	2	1	no	—
180	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
181	C₂²×C₃×C₄	—	2	1	no	—
182	C₂²×C₃×C₄	—	2	1	no	—
183	C₂²×C₃×C₄	—	2	1	no	—
184	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
187	C₃×C₄⋊C₄	—	2	1	no	—
188	C₃×C₄⋊C₄	—	2	1	no	—
189	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
190	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
191	C₃×C₂²⋊C₄	—	2	1	no	—
192	C₃×C₂²⋊C₄	—	2	1	no	—
193	C₃×C₂²⋊C₄	—	2	1	no	—
194	C₃×C₄²	—	2	1	no	—
195	C₃×C₄²	—	2	1	no	—
196	C₃×C₄²	—	2	1	no	—
197	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
198	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
199	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
200	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
201	C₂×C₃⋊C₈	—	2	2	no	—
202	C₂×C₃⋊C₈	—	2	2	no	—
203	C₂×C₃⋊C₈	—	4	2	no	—
204	C₂³×C₅	—	2	1	no	—
205	C₂³×C₅	#217	1	1	yes	characteristic
206	C₅×Q₈	—	2	1	no	—
207	C₅×Q₈	C₂×C₃⋊C₈	1	2	yes	complemented
208	C₅×D₄	—	2	4	no	—
209	C₅×D₄	—	2	1	no	—
210	C₅×D₄	C₂×C₃⋊C₈	1	2	yes	complemented
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	4	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	4	1	no	—
218	C₂×C₄×C₅	—	4	2	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	C₂×C₃⋊C₈	1	2	yes	—
222	C₂×C₄×C₅	#208	1	2	yes	—
223	C₂×C₄×C₅	#217	1	1	yes	characteristic
224	C₂×C₄×C₅	#217	1	1	yes	characteristic
225	C₂×C₄×C₅	#217	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
229	C₅×C₈	—	12	2	no	—
230	C₅×C₈	—	12	2	no	—
231	C₂×#41	C₅×Dic₃	1	1	yes	characteristic
232	C₂²×C₈	—	6	1	no	—
233	C₄×Q₈	C₅×Dic₃	1	1	yes	characteristic
234	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	C₅×Dic₃	1	1	yes	characteristic
238	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
239	#117	—	2	1	no	—
240	#117	C₅×Dic₃	1	1	yes	characteristic
241	C₂×C₄²	—	2	1	no	—
242	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
243	C₄⋊C₈	—	3	2	no	—
244	C₄⋊C₈	—	6	1	no	—
245	C₄⋊C₈	—	6	1	no	—
246	C₂²⋊C₈	—	6	1	no	—
247	C₄×C₈	—	3	2	no	—
248	C₂×C₃×C₅	—	2	2	no	—
249	C₂×C₃×C₅	—	4	2	no	—
250	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
251	C₂×C₃×C₅	#417	1	1	yes	characteristic
252	C₂×C₃×C₅	#421	1	1	yes	characteristic
253	C₂³×C₃	—	2	1	no	—
254	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
255	C₃×Q₈	—	2	1	no	—
256	C₃×Q₈	C₂×C₅×C₈	1	2	yes	complemented
257	C₃×D₄	—	2	4	no	—
258	C₃×D₄	—	2	1	no	—
259	C₃×D₄	C₂×C₅×C₈	1	2	yes	complemented
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	1	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	4	1	no	—
267	C₂×C₃×C₄	—	4	2	no	—
268	C₂×C₃×C₄	—	4	1	no	—
269	C₂×C₃×C₄	—	4	1	no	—
270	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂×C₅×C₈	1	2	yes	—
274	C₂×C₃×C₄	C₅×M₁₆	1	2	yes	—
275	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
278	C₃⋊C₈	—	4	2	no	—
279	C₃⋊C₈	—	4	2	no	—
280	C₂²×C₅	—	2	1	no	—
281	C₂²×C₅	—	2	1	no	—
282	C₂²×C₅	—	2	2	no	—
283	C₂²×C₅	—	4	1	no	—
284	C₂²×C₅	—	4	1	no	—
285	C₂²×C₅	#830	1	2	yes	—
286	C₂²×C₅	C₂×#217	1	1	yes	characteristic
287	C₄×C₅	—	2	2	no	—
288	C₄×C₅	—	2	1	no	—
289	C₄×C₅	—	2	1	no	—
290	C₄×C₅	—	2	1	no	—
291	C₄×C₅	—	4	1	no	—
292	C₄×C₅	—	4	1	no	—
293	C₄×C₅	#830	1	2	yes	—
294	C₄×C₅	C₂²×C₃⋊C₈	1	1	yes	characteristic
295	C₄×C₅	C₂×#208	1	1	yes	characteristic
296	C₄×C₅	#949	1	1	yes	characteristic
297	C₄×C₅	#951	1	1	yes	characteristic
298	#41	—	2	2	no	—
299	#41	C₅×C₃⋊C₈	1	4	yes	complemented
300	C₂×Q₈	C₂×C₅×Dic₃	1	1	yes	characteristic
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	C₂×C₅×Dic₃	1	1	yes	characteristic
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
307	C₂²×C₄	C₅×#67	1	1	yes	characteristic
308	C₂²×C₄	C₅×#67	1	1	yes	characteristic
309	C₂×C₈	—	6	2	no	—
310	C₂×C₈	—	6	2	no	—
311	C₂×C₈	—	12	2	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
315	C₄⋊C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
316	C₂²⋊C₄	—	2	1	no	—
317	C₂²⋊C₄	—	2	1	no	—
318	C₂²⋊C₄	—	2	1	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	2	1	no	—
322	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
323	C₄²	C₅×#67	1	1	yes	characteristic
324	C₄²	C₅×#67	1	1	yes	characteristic
325	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
326	C₃×C₅	#1477	1	1	yes	characteristic, complemented, Hall
327	C₂²×C₃	—	2	1	no	—
328	C₂²×C₃	—	2	1	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	4	1	no	—
331	C₂²×C₃	—	4	1	no	—
332	C₂²×C₃	C₅×C₂²⋊C₈	1	2	yes	—
333	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
334	C₃×C₄	—	2	2	no	—
335	C₃×C₄	—	2	1	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	4	1	no	—
339	C₃×C₄	—	4	1	no	—
340	C₃×C₄	C₅×C₂²⋊C₈	1	2	yes	—
341	C₃×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
342	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
343	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
344	C₃×C₄	C₅×#137	1	1	yes	characteristic
345	C₂×C₅	—	2	2	no	—
346	C₂×C₅	—	4	2	no	—
347	C₂×C₅	C₂×#830	1	1	yes	characteristic
348	C₂×C₅	#5232	1	1	yes	characteristic
349	C₂×C₅	#5236	1	1	yes	characteristic
350	C₂³	—	2	1	no	—
351	C₂³	C₅×#217	1	1	yes	characteristic
352	Q₈	—	2	1	no	—
353	Q₈	C₂×C₅×C₃⋊C₈	1	2	yes	complemented
354	D₄	—	2	4	no	—
355	D₄	—	2	1	no	—
356	D₄	C₂×C₅×C₃⋊C₈	1	2	yes	complemented
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	C₂×C₅×C₃⋊C₈	1	2	yes	—
368	C₂×C₄	C₅×#208	1	2	yes	—
369	C₂×C₄	C₅×#217	1	1	yes	characteristic
370	C₂×C₄	C₅×#217	1	1	yes	characteristic
371	C₂×C₄	C₅×#217	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
373	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
374	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
375	C₈	—	12	2	no	—
376	C₈	—	12	2	no	—
377	C₂×C₃	—	2	2	no	—
378	C₂×C₃	—	4	2	no	—
379	C₂×C₃	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
380	C₂×C₃	C₅×#417	1	1	yes	characteristic
381	C₂×C₃	C₅×#421	1	1	yes	characteristic
382	C₅	#71639	1	1	yes	characteristic, direct product factor, Sylow
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	C₅×#830	1	2	yes	—
389	C₂²	C₂×C₅×#217	1	1	yes	characteristic
390	C₄	—	2	2	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	1	no	—
396	C₄	C₅×#830	1	2	yes	—
397	C₄	C₂²×C₅×C₃⋊C₈	1	1	yes	characteristic
398	C₄	C₂×C₅×#208	1	1	yes	characteristic
399	C₄	C₅×#949	1	1	yes	characteristic
400	C₄	C₅×#951	1	1	yes	characteristic
401	C₃	C₅×#1477	1	1	yes	characteristic, complemented, Sylow
402	C₂	—	2	2	no	—
403	C₂	—	4	2	no	—
404	C₂	C₂×C₅×#830	1	1	yes	characteristic
405	C₂	C₅×#5232	1	1	yes	characteristic
406	C₂	C₅×#5236	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×#67
commutator	C₃×C₄	C₂²×C₅×C₈
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₄×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×C₅×#41	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₄×C₅×#41	D₃
hypocenter	C₃	C₅×#1477
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₄×C₅×#41

Complements

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

N	H ≅ G/N	type
2. C₅×#4925	C₂	semidirect
3. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
4. C₅×#4535	C₂	semidirect
5. C₅×D₄⋊(C₃⋊C₈)	C₂	semidirect
24. #71639	C₅	direct (N × H)
31. C₃×C₅×#41	C₈	semidirect
59. #4925	C₂×C₅	semidirect
60. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
61. #4535	C₂×C₅	semidirect
62. D₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
84. C₃×C₅×Q₈	C₂×C₈	semidirect
87. C₃×C₅×D₄	C₂×C₈	semidirect
126. C₅×#41	C₃⋊C₈	semidirect
177. C₃×#41	C₅×C₈	semidirect
207. C₅×Q₈	C₂×C₃⋊C₈	semidirect
210. C₅×D₄	C₂×C₃⋊C₈	semidirect
256. C₃×Q₈	C₂×C₅×C₈	semidirect
259. C₃×D₄	C₂×C₅×C₈	semidirect
299. #41	C₅×C₃⋊C₈	semidirect
326. C₃×C₅	#1477	semidirect
353. Q₈	C₂×C₅×C₃⋊C₈	semidirect
356. D₄	C₂×C₅×C₃⋊C₈	semidirect
382. C₅	#71639	direct (N × H)
401. C₃	C₅×#1477	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₅×#41	2
C₅×#4925	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₅×#4535	2
C₅×D₄⋊(C₃⋊C₈)	2
C₅×#1477	3
#71639	5

Subgroups — C5×#71639 #14281626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71639 #14281626