Subgroups — C₃×C₈×#685 #14295146

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×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3952	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#685	C₂	1	1	yes	maximal, characteristic
6	C₃×#64770	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64744	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×#685	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₄×D₅	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×C₃×#685	C₄	1	2	yes	—
14	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
15	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
16	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₈×D₅	—	2	2	no	—
18	C₂×C₃×C₈×D₅	—	2	2	no	—
19	C₂×C₃×C₈×D₅	C₄	1	4	yes	complemented
20	C₃×C₄×C₅×C₈	—	2	2	no	—
21	C₃×#3963	C₄	1	2	yes	—
22	C₃×#3952	C₄	1	4	yes	complemented
23	C₃×C₈×Dic₅	—	2	2	no	—
24	C₃×C₈×C₂²⋊C₄	—	5	1	no	maximal, Hall
25	C₂²×C₈×D₅	C₂×C₃	1	1	yes	characteristic
26	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×#3952	C₂×C₃	1	1	yes	characteristic
28	C₂×C₈×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
29	C₄×#685	C₂×C₃	1	1	yes	characteristic
30	#64770	C₂×C₃	1	1	yes	characteristic, complemented
31	#64744	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂³×C₃×D₅	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×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
37	C₂×C₃×C₄×D₅	—	2	1	no	—
38	C₂×C₃×C₄×D₅	—	2	1	no	—
39	C₂×C₃×C₄×D₅	—	2	1	no	—
40	C₂×C₃×C₄×D₅	—	2	1	no	—
41	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
42	C₂×C₃×C₄×D₅	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	C₂×C₄	1	2	yes	—
46	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
47	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
48	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
49	C₃×C₄²×C₅	—	2	1	no	—
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₃×#685	C₈	1	8	yes	direct product factor
52	C₃×C₄×Dic₅	—	2	1	no	—
53	C₃×C₄×Dic₅	—	2	1	no	—
54	C₂×C₃×#168	—	2	1	no	—
55	C₂×C₃×#168	—	2	1	no	—
56	C₂×C₃×#168	—	2	1	no	—
57	C₂×C₃×#168	—	2	1	no	—
58	C₂×C₃×#168	C₂×C₄	1	2	yes	—
59	C₂×C₃×#168	C₂×C₄	1	2	yes	—
60	C₃×C₈×D₅	—	2	8	no	—
61	C₂³×C₃×C₈	—	5	1	no	—
62	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
63	C₂×C₃×C₄×C₈	—	5	1	no	—
64	C₂×C₃×C₄×C₈	D₅	1	1	yes	characteristic, complemented
65	C₃×C₄×C₂²⋊C₄	—	5	1	no	—
66	C₃×#336	—	5	1	no	—
67	C₃×#336	—	5	1	no	—
68	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
69	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₂×#685	C₃×C₄	1	2	yes	—
73	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
74	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
75	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₈×D₅	—	2	2	no	—
77	C₂×C₈×D₅	—	2	2	no	—
78	C₂×C₈×D₅	C₃×C₄	1	4	yes	complemented
79	C₄×C₅×C₈	—	2	2	no	—
80	#3963	C₃×C₄	1	2	yes	—
81	#3952	C₃×C₄	1	4	yes	complemented
82	C₈×Dic₅	—	2	2	no	—
83	C₈×C₂²⋊C₄	—	5	1	no	Sylow
84	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₃×D₅	—	2	1	no	—
86	C₂²×C₃×D₅	—	2	1	no	—
87	C₂²×C₃×D₅	—	2	2	no	—
88	C₂²×C₃×D₅	C₄²	1	2	yes	—
89	C₂²×C₃×D₅	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×C₃×Dic₅	—	2	2	no	—
100	C₂×C₃×Dic₅	—	2	1	no	—
101	C₂×C₃×Dic₅	—	2	1	no	—
102	C₂×C₃×Dic₅	—	2	2	no	—
103	C₂×C₃×Dic₅	C₄²	1	2	yes	—
104	C₂×C₃×Dic₅	C₂×C₈	1	4	yes	complemented
105	C₃×C₄×D₅	—	2	2	no	—
106	C₃×C₄×D₅	—	2	2	no	—
107	C₃×C₄×D₅	—	2	2	no	—
108	C₃×C₄×D₅	—	2	2	no	—
109	C₃×C₅×C₈	—	2	2	no	—
110	C₃×C₅×C₈	C₂²⋊C₄	1	4	yes	complemented
111	C₃×#168	—	2	2	no	—
112	C₃×#168	—	2	2	no	—
113	C₂³×C₃×C₄	—	5	1	no	—
114	C₂²×C₃×C₈	—	5	1	no	—
115	C₂²×C₃×C₈	—	5	1	no	—
116	C₂²×C₃×C₈	—	5	4	no	—
117	C₂²×C₃×C₈	—	10	2	no	—
118	C₂²×C₃×C₈	—	10	2	no	—
119	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
120	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
121	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
122	C₂×C₃×C₄²	—	5	1	no	—
123	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
124	C₃×C₂²⋊C₈	—	5	4	no	—
125	C₃×C₄×C₈	—	2	2	no	—
126	C₃×C₄×C₈	—	10	2	no	—
127	C₃×#95	—	5	2	no	—
128	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
130	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
131	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
132	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
133	C₂×C₄×D₅	—	2	1	no	—
134	C₂×C₄×D₅	—	2	1	no	—
135	C₂×C₄×D₅	—	2	1	no	—
136	C₂×C₄×D₅	—	2	1	no	—
137	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
138	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
142	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
143	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
144	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
145	C₄²×C₅	—	2	1	no	—
146	C₄²×C₅	—	2	1	no	—
147	#685	C₃×C₈	1	8	yes	direct product factor
148	C₄×Dic₅	—	2	1	no	—
149	C₄×Dic₅	—	2	1	no	—
150	C₂×#168	—	2	1	no	—
151	C₂×#168	—	2	1	no	—
152	C₂×#168	—	2	1	no	—
153	C₂×#168	—	2	1	no	—
154	C₂×#168	C₂×C₃×C₄	1	2	yes	—
155	C₂×#168	C₂×C₃×C₄	1	2	yes	—
156	C₈×D₅	—	2	8	no	—
157	C₂³×C₈	—	5	1	no	—
158	C₂×C₂²⋊C₈	—	5	1	no	—
159	C₂×C₄×C₈	—	5	1	no	—
160	C₂×C₄×C₈	C₃×D₅	1	1	yes	characteristic, complemented
161	C₄×C₂²⋊C₄	—	5	1	no	—
162	#336	—	5	1	no	—
163	#336	—	5	1	no	—
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×C₃×D₅	—	2	2	no	—
170	C₂×C₃×D₅	—	2	2	no	—
171	C₂×C₃×D₅	—	2	4	no	—
172	C₂×C₃×D₅	—	2	4	no	—
173	C₂×C₃×D₅	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	C₃×Dic₅	—	2	2	no	—
180	C₃×Dic₅	—	2	4	no	—
181	C₂⁴×C₃	—	5	1	no	—
182	C₂²×C₃×C₄	—	5	1	no	—
183	C₂²×C₃×C₄	—	5	2	no	—
184	C₂²×C₃×C₄	—	5	2	no	—
185	C₂²×C₃×C₄	—	5	2	no	—
186	C₂²×C₃×C₄	—	10	1	no	—
187	C₂²×C₃×C₄	—	10	1	no	—
188	C₂²×C₃×C₄	—	10	1	no	—
189	C₂²×C₃×C₄	—	10	1	no	—
190	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
191	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
192	C₂×C₃×C₈	—	2	1	no	—
193	C₂×C₃×C₈	—	2	1	no	—
194	C₂×C₃×C₈	—	5	2	no	—
195	C₂×C₃×C₈	—	5	2	no	—
196	C₂×C₃×C₈	—	10	1	no	—
197	C₂×C₃×C₈	—	10	1	no	—
198	C₂×C₃×C₈	—	10	1	no	—
199	C₂×C₃×C₈	—	10	1	no	—
200	C₂×C₃×C₈	—	10	8	no	—
201	C₂×C₃×C₈	C₄×D₅	1	2	yes	—
202	C₂×C₃×C₈	C₄×D₅	1	2	yes	—
203	C₂×C₃×C₈	D₂₀	1	2	yes	—
204	C₂×C₃×C₈	C₂²⋊D₅	1	2	yes	—
205	C₃×C₂²⋊C₄	—	5	8	no	—
206	C₃×C₄²	—	2	1	no	—
207	C₃×C₄²	—	2	1	no	—
208	C₃×C₄²	—	10	1	no	—
209	C₃×C₄²	—	10	1	no	—
210	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
211	C₂²×D₅	—	2	1	no	—
212	C₂²×D₅	—	2	1	no	—
213	C₂²×D₅	—	2	2	no	—
214	C₂²×D₅	C₃×C₄²	1	2	yes	—
215	C₂²×D₅	C₂×C₃×C₈	1	4	yes	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	C₂×C₃×C₈	1	4	yes	complemented
219	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
224	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
225	C₂×Dic₅	—	2	2	no	—
226	C₂×Dic₅	—	2	1	no	—
227	C₂×Dic₅	—	2	1	no	—
228	C₂×Dic₅	—	2	2	no	—
229	C₂×Dic₅	C₃×C₄²	1	2	yes	—
230	C₂×Dic₅	C₂×C₃×C₈	1	4	yes	complemented
231	C₄×D₅	—	2	2	no	—
232	C₄×D₅	—	2	2	no	—
233	C₄×D₅	—	2	2	no	—
234	C₄×D₅	—	2	2	no	—
235	C₅×C₈	—	2	2	no	—
236	C₅×C₈	C₃×C₂²⋊C₄	1	4	yes	complemented
237	#168	—	2	2	no	—
238	#168	—	2	2	no	—
239	C₂³×C₄	—	5	1	no	—
240	C₂²×C₈	—	5	1	no	—
241	C₂²×C₈	—	5	1	no	—
242	C₂²×C₈	—	5	4	no	—
243	C₂²×C₈	—	10	2	no	—
244	C₂²×C₈	—	10	2	no	—
245	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
246	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	—	5	2	no	—
248	C₂×C₄²	—	5	1	no	—
249	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
250	C₂²⋊C₈	—	5	4	no	—
251	C₄×C₈	—	2	2	no	—
252	C₄×C₈	—	10	2	no	—
253	#95	—	5	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	C₃×D₅	—	2	4	no	—
260	C₂³×C₃	—	5	2	no	—
261	C₂³×C₃	—	5	4	no	—
262	C₂³×C₃	—	10	1	no	—
263	C₂³×C₃	—	10	2	no	—
264	C₂³×C₃	—	10	1	no	—
265	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	5	2	no	—
269	C₂×C₃×C₄	—	5	4	no	—
270	C₂×C₃×C₄	—	10	2	no	—
271	C₂×C₃×C₄	—	10	1	no	—
272	C₂×C₃×C₄	—	10	2	no	—
273	C₂×C₃×C₄	—	10	1	no	—
274	C₂×C₃×C₄	—	10	2	no	—
275	C₂×C₃×C₄	—	10	2	no	—
276	C₂×C₃×C₄	—	10	2	no	—
277	C₂×C₃×C₄	—	10	2	no	—
278	C₂×C₃×C₄	C₈×D₅	1	4	yes	complemented
279	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
282	C₂×C₃×C₄	#709	1	1	yes	characteristic
283	C₂×C₃×C₄	#709	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
285	C₃×C₈	—	2	2	no	—
286	C₃×C₈	—	10	2	no	—
287	C₃×C₈	—	10	2	no	—
288	C₃×C₈	#685	1	4	yes	direct product factor
289	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
290	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
291	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
292	C₂²×C₅	C₂²×C₃×C₈	1	2	yes	—
293	C₂²×C₅	C₃×#131	1	2	yes	—
294	C₂×D₅	—	2	2	no	—
295	C₂×D₅	—	2	2	no	—
296	C₂×D₅	—	2	4	no	—
297	C₂×D₅	—	2	4	no	—
298	C₂×D₅	C₃×C₄×C₈	1	4	yes	complemented
299	C₄×C₅	—	2	4	no	—
300	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
301	C₄×C₅	C₃×#117	1	1	yes	characteristic
302	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
303	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
304	Dic₅	—	2	2	no	—
305	Dic₅	—	2	4	no	—
306	C₂⁴	—	5	1	no	—
307	C₂²×C₄	—	5	1	no	—
308	C₂²×C₄	—	5	2	no	—
309	C₂²×C₄	—	5	2	no	—
310	C₂²×C₄	—	5	2	no	—
311	C₂²×C₄	—	10	1	no	—
312	C₂²×C₄	—	10	1	no	—
313	C₂²×C₄	—	10	1	no	—
314	C₂²×C₄	—	10	1	no	—
315	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
316	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	5	2	no	—
320	C₂×C₈	—	5	2	no	—
321	C₂×C₈	—	10	1	no	—
322	C₂×C₈	—	10	1	no	—
323	C₂×C₈	—	10	1	no	—
324	C₂×C₈	—	10	1	no	—
325	C₂×C₈	—	10	8	no	—
326	C₂×C₈	C₃×C₄×D₅	1	2	yes	—
327	C₂×C₈	C₃×C₄×D₅	1	2	yes	—
328	C₂×C₈	C₃×D₂₀	1	2	yes	—
329	C₂×C₈	C₃×C₂²⋊D₅	1	2	yes	—
330	C₂²⋊C₄	—	5	8	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	10	1	no	—
334	C₄²	—	10	1	no	—
335	C₃×C₅	C₈×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
336	C₂²×C₃	—	5	4	no	—
337	C₂²×C₃	—	10	4	no	—
338	C₂²×C₃	—	10	2	no	—
339	C₂²×C₃	—	10	4	no	—
340	C₂²×C₃	—	10	2	no	—
341	C₂²×C₃	C₄²×D₅	1	1	yes	characteristic
342	C₂²×C₃	C₄×D₂₀	1	1	yes	characteristic
343	C₂²×C₃	C₂×C₈×D₅	1	2	yes	—
344	C₂²×C₃	#4047	1	2	yes	—
345	C₂²×C₃	C₄×C₂²⋊D₅	1	1	yes	characteristic
346	C₃×C₄	—	2	4	no	—
347	C₃×C₄	—	10	2	no	—
348	C₃×C₄	—	10	4	no	—
349	C₃×C₄	#4018	1	1	yes	characteristic
350	C₃×C₄	C₄×D₂₀	1	1	yes	characteristic
351	C₃×C₄	C₂×#685	1	1	yes	characteristic
352	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
353	C₂×C₅	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
354	C₂×C₅	C₂×C₃×C₄×C₈	1	1	yes	characteristic
355	C₂×C₅	C₃×#405	1	1	yes	characteristic
356	C₂×C₅	C₃×C₈×D₄	1	2	yes	—
357	C₂×C₅	C₃×C₈×D₄	1	2	yes	—
358	D₅	—	2	4	no	—
359	C₂³	—	5	2	no	—
360	C₂³	—	5	4	no	—
361	C₂³	—	10	1	no	—
362	C₂³	—	10	2	no	—
363	C₂³	—	10	1	no	—
364	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	5	2	no	—
368	C₂×C₄	—	5	4	no	—
369	C₂×C₄	—	10	2	no	—
370	C₂×C₄	—	10	1	no	—
371	C₂×C₄	—	10	2	no	—
372	C₂×C₄	—	10	1	no	—
373	C₂×C₄	—	10	2	no	—
374	C₂×C₄	—	10	2	no	—
375	C₂×C₄	—	10	2	no	—
376	C₂×C₄	—	10	2	no	—
377	C₂×C₄	C₃×C₈×D₅	1	4	yes	complemented
378	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
379	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
380	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
381	C₂×C₄	C₃×#709	1	1	yes	characteristic
382	C₂×C₄	C₃×#709	1	1	yes	characteristic
383	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
384	C₈	—	2	2	no	—
385	C₈	—	10	2	no	—
386	C₈	—	10	2	no	—
387	C₈	C₃×#685	1	4	yes	direct product factor
388	C₂×C₃	—	10	4	no	—
389	C₂×C₃	C₄×C₈×D₅	1	1	yes	characteristic
390	C₂×C₃	C₈×D₂₀	1	2	yes	—
391	C₂×C₃	#64978	1	1	yes	characteristic
392	C₂×C₃	C₄×#685	1	1	yes	characteristic
393	C₂×C₃	C₈×C₂²⋊D₅	1	2	yes	—
394	C₅	C₃×C₈×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
395	C₂²	—	5	4	no	—
396	C₂²	—	10	4	no	—
397	C₂²	—	10	2	no	—
398	C₂²	—	10	4	no	—
399	C₂²	—	10	2	no	—
400	C₂²	C₃×C₄²×D₅	1	1	yes	characteristic
401	C₂²	C₃×C₄×D₂₀	1	1	yes	characteristic
402	C₂²	C₂×C₃×C₈×D₅	1	2	yes	—
403	C₂²	C₃×#4047	1	2	yes	—
404	C₂²	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
405	C₄	—	2	4	no	—
406	C₄	—	10	2	no	—
407	C₄	—	10	4	no	—
408	C₄	C₃×#4018	1	1	yes	characteristic
409	C₄	C₃×C₄×D₂₀	1	1	yes	characteristic
410	C₄	C₂×C₃×#685	1	1	yes	characteristic
411	C₄	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
412	C₃	C₈×#685	1	1	yes	characteristic, direct product factor, Sylow
413	C₂	—	10	4	no	—
414	C₂	C₃×C₄×C₈×D₅	1	1	yes	characteristic
415	C₂	C₃×C₈×D₂₀	1	2	yes	—
416	C₂	C₃×#64978	1	1	yes	characteristic
417	C₂	C₃×C₄×#685	1	1	yes	characteristic
418	C₂	C₃×C₈×C₂²⋊D₅	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₈	C₂×D₅
commutator	C₂×C₅	C₂×C₃×C₄×C₈
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂×C₃×C₄×C₈	D₅
hypocenter	C₅	C₃×C₈×C₂²⋊C₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₈ ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
4. C₂×C₃×C₈×Dic₅	C₂	semidirect
6. C₃×#64770	C₂	semidirect
7. C₃×#64744	C₂	semidirect
8. C₈×#685	C₃	direct (N × H)
19. C₂×C₃×C₈×D₅	C₄	semidirect
22. C₃×#3952	C₄	semidirect
26. C₂×C₄×C₅×C₈	C₂×C₃	semidirect
28. C₂×C₈×Dic₅	C₂×C₃	semidirect
30. #64770	C₂×C₃	semidirect
31. #64744	C₂×C₃	semidirect
51. C₃×#685	C₈	direct (N × H)
64. C₂×C₃×C₄×C₈	D₅	semidirect
78. C₂×C₈×D₅	C₃×C₄	semidirect
81. #3952	C₃×C₄	semidirect
92. C₂×C₃×C₄×C₅	C₂×C₈	semidirect
104. C₂×C₃×Dic₅	C₂×C₈	semidirect
110. C₃×C₅×C₈	C₂²⋊C₄	semidirect
147. #685	C₃×C₈	direct (N × H)
160. C₂×C₄×C₈	C₃×D₅	semidirect
173. C₂×C₃×D₅	C₄×C₈	semidirect
218. C₂×C₄×C₅	C₂×C₃×C₈	semidirect
230. C₂×Dic₅	C₂×C₃×C₈	semidirect
236. C₅×C₈	C₃×C₂²⋊C₄	semidirect
278. C₂×C₃×C₄	C₈×D₅	semidirect
288. C₃×C₈	#685	direct (N × H)
298. C₂×D₅	C₃×C₄×C₈	semidirect
335. C₃×C₅	C₈×C₂²⋊C₄	semidirect
377. C₂×C₄	C₃×C₈×D₅	semidirect
387. C₈	C₃×#685	direct (N × H)
394. C₅	C₃×C₈×C₂²⋊C₄	semidirect
412. C₃	C₈×#685	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₈×D₅	2
C₂×C₃×C₄×C₅×C₈	2
C₂×C₃×#3952	2
C₂×C₃×C₈×Dic₅	2
C₃×C₄×#685	2
C₃×#64770	2
C₃×#64744	2
C₈×#685	3
C₃×C₈×C₂²⋊C₄	5

Subgroups — C3×C8×#685 #14295146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈×#685 #14295146