Subgroups — C₄×C₅×D₃×D₈ #14415976

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×D₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×D₃×D₄	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×Dic₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅×#213	C₂	1	2	yes	maximal, complemented
6	C₅×D₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4872	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×D₃×#102	C₂	1	2	yes	maximal, complemented
9	C₅×#4756	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₅×D₈	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
14	C₂²×C₄×C₅×D₃	—	2	2	no	—
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
16	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
17	C₅×D₄×Dic₃	C₂²	1	2	yes	complemented
18	C₂×C₅×#213	C₂²	1	2	yes	—
19	C₄×C₅×#67	—	2	2	no	—
20	C₅×D₃×D₈	C₄	1	8	yes	direct product factor
21	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
22	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
24	C₅×#893	C₂²	1	2	yes	complemented
25	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₅×#67⋊C₄	—	2	2	no	—
27	C₅×D₃×C₂²⋊C₄	—	2	2	no	—
28	C₄×C₅×D₁₂	C₂²	1	2	yes	complemented
29	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
30	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×#102	C₂²	1	2	yes	complemented
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
33	C₅×#832	C₂²	1	2	yes	complemented
34	C₅×#821	C₂²	1	2	yes	complemented
35	C₅×#818	C₂²	1	1	yes	characteristic, complemented
36	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
37	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
38	C₅×#809	C₂²	1	2	yes	complemented
39	C₅×#807	C₂²	1	2	yes	complemented
40	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₄×D₃×D₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
42	C₂²×C₅×D₈	—	3	1	no	—
43	C₂×C₄×C₅×D₄	—	3	2	no	—
44	C₄×C₅×D₈	—	3	1	no	—
45	C₄×C₅×D₈	—	3	2	no	—
46	C₄×C₅×D₈	—	3	1	no	—
47	C₄×C₅×D₈	—	3	1	no	—
48	C₄×C₅×D₈	—	3	2	no	—
49	C₄×C₅×D₈	D₃	1	1	yes	characteristic, direct product factor
50	C₂×C₅×#107	—	3	1	no	—
51	C₂×C₅×#102	—	3	2	no	—
52	C₂×C₄×C₅×C₈	—	3	1	no	—
53	C₂³×C₅×D₃	—	2	2	no	—
54	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂×C₅×#67	—	2	2	no	—
57	C₂²×C₅×Dic₃	—	2	2	no	—
58	C₅×D₃×D₄	—	2	4	no	—
59	C₅×D₃×D₄	C₂×C₄	1	8	yes	complemented
60	C₂×C₅×D₁₂	C₂³	1	2	yes	—
61	C₂×C₄×C₅×D₃	—	2	2	no	—
62	C₂×C₄×C₅×D₃	—	2	2	no	—
63	C₂×C₄×C₅×D₃	—	2	2	no	—
64	C₂×C₄×C₅×D₃	—	4	8	no	—
65	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
66	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
67	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
68	C₃×C₅×D₈	C₂×C₄	1	4	yes	complemented
69	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
72	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₅×#217	—	2	2	no	—
75	C₅×#213	C₂×C₄	1	8	yes	complemented
76	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
77	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
78	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
79	C₅×Dic₃⋊C₄	—	2	2	no	—
80	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
81	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
82	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
83	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
84	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
85	C₅×D₂₄	C₂×C₄	1	4	yes	complemented
86	C₅×D₃×C₈	—	2	2	no	—
87	C₅×D₃×C₈	C₂×C₄	1	4	yes	complemented
88	C₂×D₃×D₈	C₂×C₅	1	1	yes	characteristic
89	C₄×D₃×D₄	C₂×C₅	1	2	yes	complemented
90	C₃×C₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
91	Dic₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
92	C₄×#213	C₂×C₅	1	2	yes	complemented
93	D₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
94	#4872	C₂×C₅	1	1	yes	characteristic, complemented
95	D₃×#102	C₂×C₅	1	2	yes	complemented
96	#4756	C₂×C₅	1	2	yes	complemented
97	C₄×D₂₄	C₂×C₅	1	1	yes	characteristic, complemented
98	C₄×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂²×C₅×D₄	—	3	2	no	—
100	C₂³×C₄×C₅	—	6	2	no	—
101	C₂×C₅×D₈	—	3	2	no	—
102	C₂×C₅×D₈	—	3	8	no	—
103	C₂×C₅×D₈	—	3	1	no	—
104	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
105	C₂²×C₅×C₈	—	3	1	no	—
106	C₂²×C₅×C₈	—	3	1	no	—
107	C₄×C₅×D₄	—	3	2	no	—
108	C₄×C₅×D₄	—	3	2	no	—
109	C₄×C₅×D₄	—	3	2	no	—
110	C₄×C₅×D₄	—	6	2	no	—
111	C₄×C₅×D₄	—	6	2	no	—
112	C₄×C₅×D₄	C₂×D₃	1	2	yes	complemented
113	C₂×C₅×C₄⋊C₄	—	3	2	no	—
114	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
115	C₂×C₄²×C₅	—	3	1	no	—
116	C₅×#107	—	3	1	no	—
117	C₅×#107	—	3	2	no	—
118	C₅×#107	C₂×D₃	1	1	yes	characteristic, complemented
119	C₅×#102	—	3	2	no	—
120	C₅×#102	—	3	2	no	—
121	C₅×#102	—	3	2	no	—
122	C₅×#102	C₂×D₃	1	2	yes	complemented
123	C₄×C₅×C₈	—	3	1	no	—
124	C₄×C₅×C₈	—	3	1	no	—
125	C₄×C₅×C₈	—	3	1	no	—
126	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
127	C₂×C₄×D₈	—	3	1	no	Sylow
128	C₂³×C₃×C₅	—	2	2	no	—
129	C₂²×C₅×D₃	—	2	2	no	—
130	C₂²×C₅×D₃	—	2	8	no	—
131	C₂²×C₅×D₃	—	4	4	no	—
132	C₂²×C₅×D₃	—	4	4	no	—
133	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
134	C₃×C₅×D₄	—	2	2	no	—
135	C₃×C₅×D₄	C₂²×C₄	1	4	yes	complemented
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	4	4	no	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₅×#67	—	2	8	no	—
142	C₂×C₅×Dic₃	—	2	2	no	—
143	C₂×C₅×Dic₃	—	4	4	no	—
144	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
146	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
147	C₅×D₁₂	—	2	2	no	—
148	C₅×D₁₂	C₂²×C₄	1	4	yes	complemented
149	C₄×C₅×D₃	—	2	2	no	—
150	C₄×C₅×D₃	—	4	4	no	—
151	C₄×C₅×D₃	—	4	4	no	—
152	C₄×C₅×D₃	—	4	4	no	—
153	C₄×C₅×D₃	D₈	1	4	yes	direct product factor
154	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
155	C₄×C₅×D₃	#41	1	2	yes	—
156	C₃×C₅×C₈	—	2	1	no	—
157	C₃×C₅×C₈	C₂²×C₄	1	2	yes	complemented
158	C₅×C₃⋊C₈	—	2	1	no	—
159	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	complemented
160	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
161	C₂²×C₄×D₃	—	2	2	no	—
162	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
163	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
164	D₄×Dic₃	C₂²×C₅	1	2	yes	complemented
165	C₂×#213	C₂²×C₅	1	2	yes	—
166	C₄×#67	—	2	2	no	—
167	D₃×D₈	C₄×C₅	1	8	yes	direct product factor
168	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
169	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
170	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
171	#893	C₂²×C₅	1	2	yes	complemented
172	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
173	#67⋊C₄	—	2	2	no	—
174	D₃×C₂²⋊C₄	—	2	2	no	—
175	C₄×D₁₂	C₂²×C₅	1	2	yes	complemented
176	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
177	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
178	C₃×#102	C₂²×C₅	1	2	yes	complemented
179	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
180	#832	C₂²×C₅	1	2	yes	complemented
181	#821	C₂²×C₅	1	2	yes	complemented
182	#818	C₂²×C₅	1	1	yes	characteristic, complemented
183	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
184	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
185	#809	C₂²×C₅	1	2	yes	complemented
186	#807	C₂²×C₅	1	2	yes	complemented
187	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
188	C₂⁴×C₅	—	6	2	no	—
189	C₂×C₅×D₄	—	3	8	no	—
190	C₂×C₅×D₄	—	3	2	no	—
191	C₂×C₅×D₄	—	6	4	no	—
192	C₂×C₅×D₄	—	6	2	no	—
193	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
194	C₂²×C₄×C₅	—	2	2	no	—
195	C₂²×C₄×C₅	—	3	1	no	—
196	C₂²×C₄×C₅	—	3	1	no	—
197	C₂²×C₄×C₅	—	3	1	no	—
198	C₂²×C₄×C₅	—	6	2	no	—
199	C₂²×C₄×C₅	—	6	2	no	—
200	C₂²×C₄×C₅	—	6	2	no	—
201	C₂²×C₄×C₅	—	6	2	no	—
202	C₂²×C₄×C₅	—	12	8	no	—
203	C₅×D₈	—	3	8	no	—
204	C₅×D₈	—	3	4	no	—
205	C₅×D₈	C₄×D₃	1	4	yes	direct product factor
206	C₂×C₅×C₈	—	3	1	no	—
207	C₂×C₅×C₈	—	3	4	no	—
208	C₂×C₅×C₈	—	3	1	no	—
209	C₂×C₅×C₈	—	6	2	no	—
210	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
211	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
212	C₅×C₄⋊C₄	—	3	2	no	—
213	C₅×C₄⋊C₄	—	6	2	no	—
214	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
215	C₅×C₂²⋊C₄	—	2	2	no	—
216	C₅×C₂²⋊C₄	—	6	2	no	—
217	C₅×C₂²⋊C₄	—	6	2	no	—
218	C₅×C₂²⋊C₄	—	6	2	no	—
219	C₄²×C₅	—	3	1	no	—
220	C₄²×C₅	—	3	1	no	—
221	C₄²×C₅	—	3	1	no	—
222	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
223	C₂²×D₈	—	3	1	no	—
224	C₂×C₄×D₄	—	3	2	no	—
225	C₄×D₈	—	3	1	no	—
226	C₄×D₈	—	3	2	no	—
227	C₄×D₈	—	3	1	no	—
228	C₄×D₈	—	3	2	no	—
229	C₄×D₈	—	3	1	no	—
230	C₄×D₈	C₅×D₃	1	1	yes	characteristic, direct product factor
231	C₂×#107	—	3	1	no	—
232	C₂×#102	—	3	2	no	—
233	C₂×C₄×C₈	—	3	1	no	—
234	C₂²×C₃×C₅	—	2	4	no	—
235	C₂²×C₃×C₅	—	4	2	no	—
236	C₂²×C₃×C₅	—	4	2	no	—
237	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₅×D₃	—	2	4	no	—
239	C₂×C₅×D₃	—	4	2	no	—
240	C₂×C₅×D₃	—	4	2	no	—
241	C₂×C₅×D₃	—	4	16	no	—
242	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
243	C₂×C₅×D₃	C₂×D₈	1	2	yes	—
244	C₂×C₅×D₃	#135	1	2	yes	—
245	C₃×C₄×C₅	—	2	1	no	—
246	C₃×C₄×C₅	—	4	2	no	—
247	C₃×C₄×C₅	C₂×D₈	1	2	yes	complemented
248	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
249	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
250	C₅×Dic₃	—	2	1	no	—
251	C₅×Dic₃	—	4	2	no	—
252	C₅×Dic₃	C₄×D₄	1	2	yes	—
253	C₅×Dic₃	C₂×D₈	1	2	yes	complemented
254	C₂³×D₃	—	2	2	no	—
255	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
256	C₂²×C₃×C₄	—	2	2	no	—
257	C₂×#67	—	2	2	no	—
258	C₂²×Dic₃	—	2	2	no	—
259	D₃×D₄	—	2	4	no	—
260	D₃×D₄	C₂×C₄×C₅	1	8	yes	complemented
261	C₂×D₁₂	C₂³×C₅	1	2	yes	—
262	C₂×C₄×D₃	—	2	2	no	—
263	C₂×C₄×D₃	—	2	2	no	—
264	C₂×C₄×D₃	—	2	2	no	—
265	C₂×C₄×D₃	—	4	8	no	—
266	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
267	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
268	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
269	C₃×D₈	C₂×C₄×C₅	1	4	yes	complemented
270	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
271	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
272	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
273	C₃×C₂²⋊C₄	—	2	2	no	—
274	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
275	#217	—	2	2	no	—
276	#213	C₂×C₄×C₅	1	8	yes	complemented
277	(C₂×D₃)⋊C₄	—	2	2	no	—
278	(C₂×D₃)⋊C₄	—	2	2	no	—
279	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
280	Dic₃⋊C₄	—	2	2	no	—
281	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
282	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
283	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
284	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
285	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
286	D₂₄	C₂×C₄×C₅	1	4	yes	complemented
287	D₃×C₈	—	2	2	no	—
288	D₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
289	C₂³×C₅	—	2	2	no	—
290	C₂³×C₅	—	3	1	no	—
291	C₂³×C₅	—	6	8	no	—
292	C₂³×C₅	—	6	2	no	—
293	C₂³×C₅	—	12	4	no	—
294	C₂³×C₅	—	12	4	no	—
295	C₅×D₄	—	2	2	no	—
296	C₅×D₄	—	3	4	no	—
297	C₅×D₄	—	6	8	no	—
298	C₅×D₄	—	6	2	no	—
299	C₅×D₄	C₂×C₄×D₃	1	4	yes	complemented
300	C₂×C₄×C₅	—	2	2	no	—
301	C₂×C₄×C₅	—	3	1	no	—
302	C₂×C₄×C₅	—	3	1	no	—
303	C₂×C₄×C₅	—	3	4	no	—
304	C₂×C₄×C₅	—	3	2	no	—
305	C₂×C₄×C₅	—	3	2	no	—
306	C₂×C₄×C₅	—	3	1	no	—
307	C₂×C₄×C₅	—	4	4	no	—
308	C₂×C₄×C₅	—	6	2	no	—
309	C₂×C₄×C₅	—	6	2	no	—
310	C₂×C₄×C₅	—	12	4	no	—
311	C₂×C₄×C₅	—	12	4	no	—
312	C₂×C₄×C₅	—	12	4	no	—
313	C₂×C₄×C₅	—	12	4	no	—
314	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
315	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
316	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
317	C₅×C₈	—	2	1	no	—
318	C₅×C₈	—	3	2	no	—
319	C₅×C₈	—	6	1	no	—
320	C₅×C₈	C₂×C₄×D₃	1	2	yes	complemented
321	C₂²×D₄	—	3	2	no	—
322	C₂³×C₄	—	6	2	no	—
323	C₂×D₈	—	3	2	no	—
324	C₂×D₈	—	3	8	no	—
325	C₂×D₈	—	3	1	no	—
326	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
327	C₂²×C₈	—	3	1	no	—
328	C₂²×C₈	—	3	1	no	—
329	C₄×D₄	—	3	2	no	—
330	C₄×D₄	—	3	2	no	—
331	C₄×D₄	—	3	2	no	—
332	C₄×D₄	—	6	2	no	—
333	C₄×D₄	—	6	2	no	—
334	C₄×D₄	C₂×C₅×D₃	1	2	yes	complemented
335	C₂×C₄⋊C₄	—	3	2	no	—
336	C₂×C₂²⋊C₄	—	6	2	no	—
337	C₂×C₄²	—	3	1	no	—
338	#107	—	3	1	no	—
339	#107	—	3	2	no	—
340	#107	C₂×C₅×D₃	1	1	yes	characteristic, complemented
341	#102	—	3	2	no	—
342	#102	—	3	2	no	—
343	#102	—	3	2	no	—
344	#102	C₂×C₅×D₃	1	2	yes	complemented
345	C₄×C₈	—	3	1	no	—
346	C₄×C₈	—	3	1	no	—
347	C₄×C₈	—	3	1	no	—
348	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
349	C₂×C₃×C₅	—	4	4	no	—
350	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
351	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
352	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
353	C₅×D₃	—	4	4	no	—
354	C₅×D₃	C₄×D₈	1	4	yes	direct product factor
355	C₂³×C₃	—	2	2	no	—
356	C₂²×D₃	—	2	2	no	—
357	C₂²×D₃	—	2	8	no	—
358	C₂²×D₃	—	4	4	no	—
359	C₂²×D₃	—	4	4	no	—
360	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
361	C₃×D₄	—	2	2	no	—
362	C₃×D₄	C₂²×C₄×C₅	1	4	yes	complemented
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	4	4	no	—
365	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
366	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
367	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
368	#67	—	2	8	no	—
369	C₂×Dic₃	—	2	2	no	—
370	C₂×Dic₃	—	4	4	no	—
371	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
372	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
373	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
374	D₁₂	—	2	2	no	—
375	D₁₂	C₂²×C₄×C₅	1	4	yes	complemented
376	C₄×D₃	—	2	2	no	—
377	C₄×D₃	—	4	4	no	—
378	C₄×D₃	—	4	4	no	—
379	C₄×D₃	—	4	4	no	—
380	C₄×D₃	C₅×D₈	1	4	yes	direct product factor
381	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
382	C₄×D₃	C₅×#41	1	2	yes	—
383	C₃×C₈	—	2	1	no	—
384	C₃×C₈	C₂²×C₄×C₅	1	2	yes	complemented
385	C₃⋊C₈	—	2	1	no	—
386	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	complemented
387	C₂²×C₅	—	2	4	no	—
388	C₂²×C₅	—	3	2	no	—
389	C₂²×C₅	—	3	2	no	—
390	C₂²×C₅	—	3	2	no	—
391	C₂²×C₅	—	4	2	no	—
392	C₂²×C₅	—	4	2	no	—
393	C₂²×C₅	—	6	4	no	—
394	C₂²×C₅	—	12	16	no	—
395	C₂²×C₅	—	12	2	no	—
396	C₂²×C₅	—	12	2	no	—
397	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
398	C₄×C₅	—	2	1	no	—
399	C₄×C₅	—	3	2	no	—
400	C₄×C₅	—	3	2	no	—
401	C₄×C₅	—	4	2	no	—
402	C₄×C₅	—	6	1	no	—
403	C₄×C₅	—	12	2	no	—
404	C₄×C₅	D₃×D₈	1	2	yes	direct product factor
405	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
406	C₄×C₅	D₃×#41	1	1	yes	characteristic
407	C₂⁴	—	6	2	no	—
408	C₂×D₄	—	3	8	no	—
409	C₂×D₄	—	3	2	no	—
410	C₂×D₄	—	6	4	no	—
411	C₂×D₄	—	6	2	no	—
412	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	3	1	no	—
415	C₂²×C₄	—	3	1	no	—
416	C₂²×C₄	—	3	1	no	—
417	C₂²×C₄	—	6	2	no	—
418	C₂²×C₄	—	6	2	no	—
419	C₂²×C₄	—	6	2	no	—
420	C₂²×C₄	—	6	2	no	—
421	C₂²×C₄	—	12	8	no	—
422	D₈	—	3	8	no	—
423	D₈	—	3	4	no	—
424	D₈	C₄×C₅×D₃	1	4	yes	direct product factor
425	C₂×C₈	—	3	1	no	—
426	C₂×C₈	—	3	4	no	—
427	C₂×C₈	—	3	1	no	—
428	C₂×C₈	—	6	2	no	—
429	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
430	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
431	C₄⋊C₄	—	3	2	no	—
432	C₄⋊C₄	—	6	2	no	—
433	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	6	2	no	—
436	C₂²⋊C₄	—	6	2	no	—
437	C₂²⋊C₄	—	6	2	no	—
438	C₄²	—	3	1	no	—
439	C₄²	—	3	1	no	—
440	C₄²	—	3	1	no	—
441	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
442	C₃×C₅	C₂×C₄×D₈	1	1	yes	characteristic, complemented, Hall
443	C₂²×C₃	—	2	4	no	—
444	C₂²×C₃	—	4	2	no	—
445	C₂²×C₃	—	4	2	no	—
446	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
447	C₂×D₃	—	2	4	no	—
448	C₂×D₃	—	4	2	no	—
449	C₂×D₃	—	4	2	no	—
450	C₂×D₃	—	4	16	no	—
451	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
452	C₂×D₃	C₂×C₅×D₈	1	2	yes	—
453	C₂×D₃	C₅×#135	1	2	yes	—
454	C₃×C₄	—	2	1	no	—
455	C₃×C₄	—	4	2	no	—
456	C₃×C₄	C₂×C₅×D₈	1	2	yes	complemented
457	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
458	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
459	Dic₃	—	2	1	no	—
460	Dic₃	—	4	2	no	—
461	Dic₃	C₄×C₅×D₄	1	2	yes	—
462	Dic₃	C₂×C₅×D₈	1	2	yes	complemented
463	C₂×C₅	—	3	4	no	—
464	C₂×C₅	—	4	4	no	—
465	C₂×C₅	—	12	4	no	—
466	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
467	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
468	C₂×C₅	D₃×#135	1	1	yes	characteristic
469	C₂³	—	2	2	no	—
470	C₂³	—	3	1	no	—
471	C₂³	—	6	8	no	—
472	C₂³	—	6	2	no	—
473	C₂³	—	12	4	no	—
474	C₂³	—	12	4	no	—
475	D₄	—	2	2	no	—
476	D₄	—	3	4	no	—
477	D₄	—	6	8	no	—
478	D₄	—	6	2	no	—
479	D₄	C₂×C₄×C₅×D₃	1	4	yes	complemented
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	3	1	no	—
482	C₂×C₄	—	3	1	no	—
483	C₂×C₄	—	3	4	no	—
484	C₂×C₄	—	3	2	no	—
485	C₂×C₄	—	3	2	no	—
486	C₂×C₄	—	3	1	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	6	2	no	—
489	C₂×C₄	—	6	2	no	—
490	C₂×C₄	—	12	4	no	—
491	C₂×C₄	—	12	4	no	—
492	C₂×C₄	—	12	4	no	—
493	C₂×C₄	—	12	4	no	—
494	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
495	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
496	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
497	C₈	—	2	1	no	—
498	C₈	—	3	2	no	—
499	C₈	—	6	1	no	—
500	C₈	C₂×C₄×C₅×D₃	1	2	yes	complemented
501	C₂×C₃	—	4	4	no	—
502	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
503	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
504	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
505	D₃	—	4	4	no	—
506	D₃	C₄×C₅×D₈	1	4	yes	direct product factor
507	C₅	C₄×D₃×D₈	1	1	yes	characteristic, direct product factor, Sylow
508	C₂²	—	2	4	no	—
509	C₂²	—	3	2	no	—
510	C₂²	—	3	2	no	—
511	C₂²	—	3	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	6	4	no	—
515	C₂²	—	12	16	no	—
516	C₂²	—	12	2	no	—
517	C₂²	—	12	2	no	—
518	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
519	C₄	—	2	1	no	—
520	C₄	—	3	2	no	—
521	C₄	—	3	2	no	—
522	C₄	—	4	2	no	—
523	C₄	—	6	1	no	—
524	C₄	—	12	2	no	—
525	C₄	C₅×D₃×D₈	1	2	yes	direct product factor
526	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
527	C₄	C₅×D₃×#41	1	1	yes	characteristic
528	C₃	C₂×C₄×C₅×D₈	1	1	yes	characteristic, complemented, Sylow
529	C₂	—	3	4	no	—
530	C₂	—	4	4	no	—
531	C₂	—	12	4	no	—
532	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
533	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic
534	C₂	C₅×D₃×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×D₈	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×D₃×D₈	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₄×C₅×D₈	D₃
hypocenter	C₃	C₂×C₄×C₅×D₈
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×D₈

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×D₃×D₄	C₂	semidirect
3. C₃×C₄×C₅×D₈	C₂	semidirect
4. C₅×Dic₃×D₈	C₂	semidirect
5. C₄×C₅×#213	C₂	semidirect
6. C₅×D₃×#107	C₂	semidirect
7. C₅×#4872	C₂	semidirect
8. C₅×D₃×#102	C₂	semidirect
9. C₅×#4756	C₂	semidirect
10. C₄×C₅×D₂₄	C₂	semidirect
11. C₄×C₅×D₃×C₈	C₂	semidirect
16. C₃×C₄×C₅×D₄	C₂²	semidirect
17. C₅×D₄×Dic₃	C₂²	semidirect
20. C₅×D₃×D₈	C₄	direct (N × H)
24. C₅×#893	C₂²	semidirect
28. C₄×C₅×D₁₂	C₂²	semidirect
30. C₃×C₅×#107	C₂²	semidirect
31. C₃×C₅×#102	C₂²	semidirect
32. C₃×C₄×C₅×C₈	C₂²	semidirect
33. C₅×#832	C₂²	semidirect
34. C₅×#821	C₂²	semidirect
35. C₅×#818	C₂²	semidirect
36. C₅×C₈×Dic₃	C₂²	semidirect
37. C₅×C₈×Dic₃	C₂²	semidirect
38. C₅×#809	C₂²	semidirect
39. C₅×#807	C₂²	semidirect
40. C₄×C₅×C₃⋊C₈	C₂²	semidirect
41. C₄×D₃×D₈	C₅	direct (N × H)
49. C₄×C₅×D₈	D₃	direct (N × H)
59. C₅×D₃×D₄	C₂×C₄	semidirect
68. C₃×C₅×D₈	C₂×C₄	semidirect
75. C₅×#213	C₂×C₄	semidirect
85. C₅×D₂₄	C₂×C₄	semidirect
87. C₅×D₃×C₈	C₂×C₄	semidirect
89. C₄×D₃×D₄	C₂×C₅	semidirect
90. C₃×C₄×D₈	C₂×C₅	semidirect
91. Dic₃×D₈	C₂×C₅	semidirect
92. C₄×#213	C₂×C₅	semidirect
93. D₃×#107	C₂×C₅	semidirect
94. #4872	C₂×C₅	semidirect
95. D₃×#102	C₂×C₅	semidirect
96. #4756	C₂×C₅	semidirect
97. C₄×D₂₄	C₂×C₅	semidirect
98. C₄×D₃×C₈	C₂×C₅	semidirect
112. C₄×C₅×D₄	C₂×D₃	semidirect
118. C₅×#107	C₂×D₃	semidirect
122. C₅×#102	C₂×D₃	semidirect
126. C₄×C₅×C₈	C₂×D₃	semidirect
135. C₃×C₅×D₄	C₂²×C₄	semidirect
148. C₅×D₁₂	C₂²×C₄	semidirect
153. C₄×C₅×D₃	D₈	direct (N × H)
157. C₃×C₅×C₈	C₂²×C₄	semidirect
159. C₅×C₃⋊C₈	C₂²×C₄	semidirect
163. C₃×C₄×D₄	C₂²×C₅	semidirect
164. D₄×Dic₃	C₂²×C₅	semidirect
167. D₃×D₈	C₄×C₅	direct (N × H)
171. #893	C₂²×C₅	semidirect
175. C₄×D₁₂	C₂²×C₅	semidirect
177. C₃×#107	C₂²×C₅	semidirect
178. C₃×#102	C₂²×C₅	semidirect
179. C₃×C₄×C₈	C₂²×C₅	semidirect
180. #832	C₂²×C₅	semidirect
181. #821	C₂²×C₅	semidirect
182. #818	C₂²×C₅	semidirect
183. C₈×Dic₃	C₂²×C₅	semidirect
184. C₈×Dic₃	C₂²×C₅	semidirect
185. #809	C₂²×C₅	semidirect
186. #807	C₂²×C₅	semidirect
187. C₄×C₃⋊C₈	C₂²×C₅	semidirect
205. C₅×D₈	C₄×D₃	direct (N × H)
230. C₄×D₈	C₅×D₃	direct (N × H)
247. C₃×C₄×C₅	C₂×D₈	semidirect
253. C₅×Dic₃	C₂×D₈	semidirect
260. D₃×D₄	C₂×C₄×C₅	semidirect
269. C₃×D₈	C₂×C₄×C₅	semidirect
276. #213	C₂×C₄×C₅	semidirect
286. D₂₄	C₂×C₄×C₅	semidirect
288. D₃×C₈	C₂×C₄×C₅	semidirect
299. C₅×D₄	C₂×C₄×D₃	semidirect
320. C₅×C₈	C₂×C₄×D₃	semidirect
334. C₄×D₄	C₂×C₅×D₃	semidirect
340. #107	C₂×C₅×D₃	semidirect
344. #102	C₂×C₅×D₃	semidirect
348. C₄×C₈	C₂×C₅×D₃	semidirect
354. C₅×D₃	C₄×D₈	direct (N × H)
362. C₃×D₄	C₂²×C₄×C₅	semidirect
375. D₁₂	C₂²×C₄×C₅	semidirect
380. C₄×D₃	C₅×D₈	direct (N × H)
384. C₃×C₈	C₂²×C₄×C₅	semidirect
386. C₃⋊C₈	C₂²×C₄×C₅	semidirect
404. C₄×C₅	D₃×D₈	direct (N × H)
424. D₈	C₄×C₅×D₃	direct (N × H)
442. C₃×C₅	C₂×C₄×D₈	semidirect
456. C₃×C₄	C₂×C₅×D₈	semidirect
462. Dic₃	C₂×C₅×D₈	semidirect
479. D₄	C₂×C₄×C₅×D₃	semidirect
500. C₈	C₂×C₄×C₅×D₃	semidirect
506. D₃	C₄×C₅×D₈	direct (N × H)
507. C₅	C₄×D₃×D₈	direct (N × H)
525. C₄	C₅×D₃×D₈	direct (N × H)
528. C₃	C₂×C₄×C₅×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×D₈	2
C₄×C₅×D₃×D₄	2
C₃×C₄×C₅×D₈	2
C₅×Dic₃×D₈	2
C₄×C₅×#213	2
C₅×D₃×#107	2
C₅×#4872	2
C₅×D₃×#102	2
C₅×#4756	2
C₄×C₅×D₂₄	2
C₄×C₅×D₃×C₈	2
C₂×C₄×C₅×D₈	3
C₄×D₃×D₈	5

Subgroups — C4×C5×D3×D8 #14415976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×D₃×D₈ #14415976