Subgroups — C₅×#68647 #14295139

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×C₈×C₂²⋊C₄	—	3	1	no	maximal, Hall
9	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
14	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×D₃×C₈	—	2	2	no	—
18	C₂×C₅×D₃×C₈	—	2	2	no	—
19	C₂×C₅×D₃×C₈	C₄	1	4	yes	complemented
20	C₅×C₃⋊#95	C₄	1	2	yes	—
21	C₅×(C₂×D₃)⋊C₈	C₄	1	4	yes	complemented
22	C₅×C₈×Dic₃	—	2	2	no	—
23	C₄×C₅×C₃⋊C₈	—	2	2	no	—
24	#68647	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂³×C₅×C₈	—	3	1	no	—
26	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
27	C₂×C₄×C₅×C₈	—	3	1	no	—
28	C₂×C₄×C₅×C₈	—	3	1	no	—
29	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
30	C₅×#336	—	3	1	no	—
31	C₅×#336	D₃	1	1	yes	characteristic, complemented
32	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
37	C₂×C₄×C₅×D₃	—	2	1	no	—
38	C₂×C₄×C₅×D₃	—	2	1	no	—
39	C₂×C₄×C₅×D₃	—	2	1	no	—
40	C₂×C₄×C₅×D₃	—	2	1	no	—
41	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
42	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₅×C₈	—	2	1	no	—
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
48	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
49	C₃×C₄²×C₅	—	2	1	no	—
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₅×(C₂×D₃)⋊C₄	C₈	1	8	yes	complemented
52	C₄×C₅×Dic₃	—	2	1	no	—
53	C₄×C₅×Dic₃	—	2	1	no	—
54	C₂×C₅×C₃⋊C₈	—	2	1	no	—
55	C₂×C₅×C₃⋊C₈	—	2	1	no	—
56	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
57	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
58	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
59	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
60	C₅×D₃×C₈	—	2	8	no	—
61	C₂²×D₃×C₈	C₂×C₅	1	1	yes	characteristic
62	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	1	yes	characteristic
63	C₂×C₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
64	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic
65	C₂×C₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
66	C₃×#336	C₂×C₅	1	1	yes	characteristic, complemented
67	#4550	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂³×C₄×C₅	—	3	1	no	—
69	C₂²×C₅×C₈	—	3	1	no	—
70	C₂²×C₅×C₈	—	3	1	no	—
71	C₂²×C₅×C₈	—	3	4	no	—
72	C₂²×C₅×C₈	—	6	2	no	—
73	C₂²×C₅×C₈	—	6	2	no	—
74	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
76	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
77	C₂×C₄²×C₅	—	3	1	no	—
78	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
79	C₅×C₂²⋊C₈	—	3	4	no	—
80	C₄×C₅×C₈	—	6	2	no	—
81	C₄×C₅×C₈	—	6	2	no	—
82	C₅×#95	—	3	2	no	—
83	C₈×C₂²⋊C₄	—	3	1	no	Sylow
84	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₅×D₃	—	2	1	no	—
86	C₂²×C₅×D₃	—	2	1	no	—
87	C₂²×C₅×D₃	—	2	2	no	—
88	C₂²×C₅×D₃	C₄²	1	2	yes	—
89	C₂²×C₅×D₃	C₂×C₈	1	4	yes	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	C₂×C₈	1	4	yes	complemented
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
99	C₂×C₅×Dic₃	—	2	2	no	—
100	C₂×C₅×Dic₃	—	2	1	no	—
101	C₂×C₅×Dic₃	—	2	1	no	—
102	C₂×C₅×Dic₃	—	2	2	no	—
103	C₂×C₅×Dic₃	C₄²	1	2	yes	—
104	C₂×C₅×Dic₃	C₂×C₈	1	4	yes	complemented
105	C₄×C₅×D₃	—	2	2	no	—
106	C₄×C₅×D₃	—	2	2	no	—
107	C₄×C₅×D₃	—	2	2	no	—
108	C₄×C₅×D₃	—	2	2	no	—
109	C₃×C₅×C₈	—	2	2	no	—
110	C₃×C₅×C₈	—	2	2	no	—
111	C₅×C₃⋊C₈	—	2	2	no	—
112	C₅×C₃⋊C₈	C₂²⋊C₄	1	4	yes	complemented
113	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
114	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
115	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
116	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
117	C₂×(C₂×D₃)⋊C₄	C₄×C₅	1	2	yes	—
118	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
119	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
120	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
121	C₂×D₃×C₈	—	2	2	no	—
122	C₂×D₃×C₈	—	2	2	no	—
123	C₂×D₃×C₈	C₄×C₅	1	4	yes	complemented
124	C₃⋊#95	C₄×C₅	1	2	yes	—
125	(C₂×D₃)⋊C₈	C₄×C₅	1	4	yes	complemented
126	C₈×Dic₃	—	2	2	no	—
127	C₄×C₃⋊C₈	—	2	2	no	—
128	C₂⁴×C₅	—	3	1	no	—
129	C₂²×C₄×C₅	—	3	2	no	—
130	C₂²×C₄×C₅	—	3	1	no	—
131	C₂²×C₄×C₅	—	3	2	no	—
132	C₂²×C₄×C₅	—	3	2	no	—
133	C₂²×C₄×C₅	—	6	1	no	—
134	C₂²×C₄×C₅	—	6	1	no	—
135	C₂²×C₄×C₅	—	6	1	no	—
136	C₂²×C₄×C₅	—	6	1	no	—
137	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
138	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	3	2	no	—
144	C₂×C₅×C₈	—	3	2	no	—
145	C₂×C₅×C₈	—	3	2	no	—
146	C₂×C₅×C₈	—	3	2	no	—
147	C₂×C₅×C₈	—	6	8	no	—
148	C₂×C₅×C₈	—	6	1	no	—
149	C₂×C₅×C₈	—	6	1	no	—
150	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
151	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
152	C₅×C₂²⋊C₄	—	3	8	no	—
153	C₄²×C₅	—	2	1	no	—
154	C₄²×C₅	—	2	1	no	—
155	C₄²×C₅	—	6	1	no	—
156	C₄²×C₅	—	6	1	no	—
157	C₂³×C₈	—	3	1	no	—
158	C₂×C₂²⋊C₈	—	3	1	no	—
159	C₂×C₄×C₈	—	3	1	no	—
160	C₂×C₄×C₈	—	3	1	no	—
161	C₄×C₂²⋊C₄	—	3	1	no	—
162	#336	—	3	1	no	—
163	#336	C₅×D₃	1	1	yes	characteristic, complemented
164	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
165	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
166	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
167	C₂²×C₃×C₅	C₂²×C₈	1	2	yes	—
168	C₂²×C₃×C₅	#131	1	2	yes	—
169	C₂×C₅×D₃	—	2	2	no	—
170	C₂×C₅×D₃	—	2	2	no	—
171	C₂×C₅×D₃	—	2	4	no	—
172	C₂×C₅×D₃	—	2	4	no	—
173	C₂×C₅×D₃	C₄×C₈	1	4	yes	complemented
174	C₃×C₄×C₅	—	2	4	no	—
175	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₃×C₄×C₅	#117	1	1	yes	characteristic
177	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
178	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
179	C₅×Dic₃	—	2	2	no	—
180	C₅×Dic₃	—	2	4	no	—
181	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
183	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
184	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
185	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
186	C₂×C₄×D₃	—	2	1	no	—
187	C₂×C₄×D₃	—	2	1	no	—
188	C₂×C₄×D₃	—	2	1	no	—
189	C₂×C₄×D₃	—	2	1	no	—
190	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
191	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
192	C₂×C₃×C₈	—	2	1	no	—
193	C₂×C₃×C₈	—	2	1	no	—
194	C₂×C₃×C₈	—	2	1	no	—
195	C₂×C₃×C₈	—	2	1	no	—
196	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
197	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
198	C₃×C₄²	—	2	1	no	—
199	C₃×C₄²	—	2	1	no	—
200	(C₂×D₃)⋊C₄	C₅×C₈	1	8	yes	complemented
201	C₄×Dic₃	—	2	1	no	—
202	C₄×Dic₃	—	2	1	no	—
203	C₂×C₃⋊C₈	—	2	1	no	—
204	C₂×C₃⋊C₈	—	2	1	no	—
205	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
206	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
207	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
208	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
209	D₃×C₈	—	2	8	no	—
210	C₂³×C₅	—	3	2	no	—
211	C₂³×C₅	—	3	4	no	—
212	C₂³×C₅	—	6	1	no	—
213	C₂³×C₅	—	6	1	no	—
214	C₂³×C₅	—	6	2	no	—
215	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	3	2	no	—
219	C₂×C₄×C₅	—	3	4	no	—
220	C₂×C₄×C₅	—	6	1	no	—
221	C₂×C₄×C₅	—	6	2	no	—
222	C₂×C₄×C₅	—	6	1	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	D₃×C₈	1	4	yes	complemented
229	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
231	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
232	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
233	C₂×C₄×C₅	#237	1	1	yes	characteristic
234	C₂×C₄×C₅	#239	1	1	yes	characteristic
235	C₅×C₈	—	2	2	no	—
236	C₅×C₈	—	2	2	no	—
237	C₅×C₈	—	3	4	no	—
238	C₅×C₈	—	6	2	no	—
239	C₂³×C₄	—	3	1	no	—
240	C₂²×C₈	—	3	1	no	—
241	C₂²×C₈	—	3	1	no	—
242	C₂²×C₈	—	3	4	no	—
243	C₂²×C₈	—	6	2	no	—
244	C₂²×C₈	—	6	2	no	—
245	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
246	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	—	3	2	no	—
248	C₂×C₄²	—	3	1	no	—
249	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
250	C₂²⋊C₈	—	3	4	no	—
251	C₄×C₈	—	6	2	no	—
252	C₄×C₈	—	6	2	no	—
253	#95	—	3	2	no	—
254	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₃×C₅	C₂×C₄×C₈	1	1	yes	characteristic
256	C₂×C₃×C₅	#405	1	1	yes	characteristic
257	C₂×C₃×C₅	C₈×D₄	1	2	yes	—
258	C₂×C₃×C₅	C₈×D₄	1	2	yes	—
259	C₅×D₃	—	2	4	no	—
260	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
261	C₂²×D₃	—	2	1	no	—
262	C₂²×D₃	—	2	1	no	—
263	C₂²×D₃	—	2	2	no	—
264	C₂²×D₃	C₄²×C₅	1	2	yes	—
265	C₂²×D₃	C₂×C₅×C₈	1	4	yes	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	C₂×C₅×C₈	1	4	yes	complemented
269	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
271	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
273	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
274	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
275	C₂×Dic₃	—	2	2	no	—
276	C₂×Dic₃	—	2	1	no	—
277	C₂×Dic₃	—	2	1	no	—
278	C₂×Dic₃	—	2	2	no	—
279	C₂×Dic₃	C₄²×C₅	1	2	yes	—
280	C₂×Dic₃	C₂×C₅×C₈	1	4	yes	complemented
281	C₄×D₃	—	2	2	no	—
282	C₄×D₃	—	2	2	no	—
283	C₄×D₃	—	2	2	no	—
284	C₄×D₃	—	2	2	no	—
285	C₃×C₈	—	2	2	no	—
286	C₃×C₈	—	2	2	no	—
287	C₃⋊C₈	—	2	2	no	—
288	C₃⋊C₈	C₅×C₂²⋊C₄	1	4	yes	complemented
289	C₂²×C₅	—	3	4	no	—
290	C₂²×C₅	—	6	2	no	—
291	C₂²×C₅	—	6	2	no	—
292	C₂²×C₅	—	6	4	no	—
293	C₂²×C₅	—	6	4	no	—
294	C₂²×C₅	C₄²×D₃	1	1	yes	characteristic
295	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
296	C₂²×C₅	#893	1	1	yes	characteristic
297	C₂²×C₅	C₂×D₃×C₈	1	2	yes	—
298	C₂²×C₅	#907	1	2	yes	—
299	C₄×C₅	—	2	4	no	—
300	C₄×C₅	—	6	2	no	—
301	C₄×C₅	—	6	4	no	—
302	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
303	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
304	C₄×C₅	#892	1	1	yes	characteristic
305	C₄×C₅	#893	1	1	yes	characteristic
306	C₂⁴	—	3	1	no	—
307	C₂²×C₄	—	3	1	no	—
308	C₂²×C₄	—	3	2	no	—
309	C₂²×C₄	—	3	2	no	—
310	C₂²×C₄	—	3	2	no	—
311	C₂²×C₄	—	6	1	no	—
312	C₂²×C₄	—	6	1	no	—
313	C₂²×C₄	—	6	1	no	—
314	C₂²×C₄	—	6	1	no	—
315	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
316	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	3	2	no	—
322	C₂×C₈	—	3	2	no	—
323	C₂×C₈	—	3	2	no	—
324	C₂×C₈	—	3	2	no	—
325	C₂×C₈	—	6	8	no	—
326	C₂×C₈	—	6	1	no	—
327	C₂×C₈	—	6	1	no	—
328	C₂×C₈	C₄×C₅×D₃	1	2	yes	—
329	C₂×C₈	C₄×C₅×D₃	1	2	yes	—
330	C₂²⋊C₄	—	3	8	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	6	1	no	—
334	C₄²	—	6	1	no	—
335	C₃×C₅	C₈×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
336	C₂²×C₃	C₂×C₄²×C₅	1	1	yes	characteristic
337	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
338	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
339	C₂²×C₃	C₂²×C₅×C₈	1	2	yes	—
340	C₂²×C₃	C₅×#131	1	2	yes	—
341	C₂×D₃	—	2	2	no	—
342	C₂×D₃	—	2	2	no	—
343	C₂×D₃	—	2	4	no	—
344	C₂×D₃	—	2	4	no	—
345	C₂×D₃	C₄×C₅×C₈	1	4	yes	complemented
346	C₃×C₄	—	2	4	no	—
347	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
348	C₃×C₄	C₅×#117	1	1	yes	characteristic
349	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
350	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
351	Dic₃	—	2	2	no	—
352	Dic₃	—	2	4	no	—
353	C₂×C₅	—	6	4	no	—
354	C₂×C₅	#4666	1	1	yes	characteristic
355	C₂×C₅	C₄×D₃×C₈	1	1	yes	characteristic
356	C₂×C₅	#4708	1	1	yes	characteristic
357	C₂×C₅	#67⋊C₈	1	2	yes	—
358	C₂×C₅	#4834	1	2	yes	—
359	C₂³	—	3	2	no	—
360	C₂³	—	3	4	no	—
361	C₂³	—	6	1	no	—
362	C₂³	—	6	1	no	—
363	C₂³	—	6	2	no	—
364	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	3	2	no	—
368	C₂×C₄	—	3	4	no	—
369	C₂×C₄	—	6	1	no	—
370	C₂×C₄	—	6	2	no	—
371	C₂×C₄	—	6	1	no	—
372	C₂×C₄	—	6	2	no	—
373	C₂×C₄	—	6	2	no	—
374	C₂×C₄	—	6	2	no	—
375	C₂×C₄	—	6	2	no	—
376	C₂×C₄	—	6	2	no	—
377	C₂×C₄	C₅×D₃×C₈	1	4	yes	complemented
378	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
379	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
380	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
381	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
382	C₂×C₄	C₅×#237	1	1	yes	characteristic
383	C₂×C₄	C₅×#239	1	1	yes	characteristic
384	C₈	—	2	2	no	—
385	C₈	—	2	2	no	—
386	C₈	—	3	4	no	—
387	C₈	—	6	2	no	—
388	C₂×C₃	C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
389	C₂×C₃	C₂×C₄×C₅×C₈	1	1	yes	characteristic
390	C₂×C₃	C₅×#405	1	1	yes	characteristic
391	C₂×C₃	C₅×C₈×D₄	1	2	yes	—
392	C₂×C₃	C₅×C₈×D₄	1	2	yes	—
393	D₃	—	2	4	no	—
394	C₅	#68647	1	1	yes	characteristic, direct product factor, Sylow
395	C₂²	—	3	4	no	—
396	C₂²	—	6	2	no	—
397	C₂²	—	6	2	no	—
398	C₂²	—	6	4	no	—
399	C₂²	—	6	4	no	—
400	C₂²	C₄²×C₅×D₃	1	1	yes	characteristic
401	C₂²	C₅×#67⋊C₄	1	1	yes	characteristic
402	C₂²	C₅×#893	1	1	yes	characteristic
403	C₂²	C₂×C₅×D₃×C₈	1	2	yes	—
404	C₂²	C₅×#907	1	2	yes	—
405	C₄	—	2	4	no	—
406	C₄	—	6	2	no	—
407	C₄	—	6	4	no	—
408	C₄	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
409	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
410	C₄	C₅×#892	1	1	yes	characteristic
411	C₄	C₅×#893	1	1	yes	characteristic
412	C₃	C₅×C₈×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
413	C₂	—	6	4	no	—
414	C₂	C₅×#4666	1	1	yes	characteristic
415	C₂	C₄×C₅×D₃×C₈	1	1	yes	characteristic
416	C₂	C₅×#4708	1	1	yes	characteristic
417	C₂	C₅×#67⋊C₈	1	2	yes	—
418	C₂	C₅×#4834	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂×C₃	C₂×C₄×C₅×C₈
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#336	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×C₅×D₃	C₂×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#336	D₃
hypocenter	C₃	C₅×C₈×C₂²⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₅×#336

Complements

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

N	H ≅ G/N	type
3. C₂×C₅×C₈×Dic₃	C₂	semidirect
5. C₂×C₄×C₅×C₃⋊C₈	C₂	semidirect
6. C₃×C₅×#336	C₂	semidirect
7. C₅×#4550	C₂	semidirect
19. C₂×C₅×D₃×C₈	C₄	semidirect
21. C₅×(C₂×D₃)⋊C₈	C₄	semidirect
24. #68647	C₅	direct (N × H)
31. C₅×#336	D₃	semidirect
51. C₅×(C₂×D₃)⋊C₄	C₈	semidirect
63. C₂×C₈×Dic₃	C₂×C₅	semidirect
65. C₂×C₄×C₃⋊C₈	C₂×C₅	semidirect
66. C₃×#336	C₂×C₅	semidirect
67. #4550	C₂×C₅	semidirect
92. C₂×C₃×C₄×C₅	C₂×C₈	semidirect
104. C₂×C₅×Dic₃	C₂×C₈	semidirect
112. C₅×C₃⋊C₈	C₂²⋊C₄	semidirect
123. C₂×D₃×C₈	C₄×C₅	semidirect
125. (C₂×D₃)⋊C₈	C₄×C₅	semidirect
163. #336	C₅×D₃	semidirect
173. C₂×C₅×D₃	C₄×C₈	semidirect
200. (C₂×D₃)⋊C₄	C₅×C₈	semidirect
228. C₂×C₄×C₅	D₃×C₈	semidirect
268. C₂×C₃×C₄	C₂×C₅×C₈	semidirect
280. C₂×Dic₃	C₂×C₅×C₈	semidirect
288. C₃⋊C₈	C₅×C₂²⋊C₄	semidirect
335. C₃×C₅	C₈×C₂²⋊C₄	semidirect
345. C₂×D₃	C₄×C₅×C₈	semidirect
377. C₂×C₄	C₅×D₃×C₈	semidirect
394. C₅	#68647	direct (N × H)
412. C₃	C₅×C₈×C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×D₃×C₈	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₂×C₅×C₈×Dic₃	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₂×C₄×C₅×C₃⋊C₈	2
C₃×C₅×#336	2
C₅×#4550	2
C₅×C₈×C₂²⋊C₄	3
#68647	5

Subgroups — C5×#68647 #14295139

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68647 #14295139