Subgroups — C₄×C₅×#821 #14295692

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#821	C₂	1	2	yes	maximal
4	C₄×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4551	C₂	1	2	yes	maximal, complemented
6	C₄×C₅×#102	—	3	1	no	maximal, Hall
7	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₅×D₃	—	2	1	no	—
9	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
12	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
14	C₂×C₄×C₅×Dic₃	—	2	1	no	—
15	C₄×C₅×D₁₂	—	2	2	no	—
16	C₄×C₅×D₁₂	C₄	1	4	yes	complemented
17	C₃×C₄×C₅×C₈	—	2	2	no	—
18	C₅×C₃⋊#95	—	2	1	no	—
19	C₅×#821	C₄	1	8	yes	direct product factor
20	C₄×#821	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₄×C₅×D₄	—	3	1	no	—
22	C₂×C₅×#102	—	3	2	no	—
23	C₂×C₄×C₅×C₈	D₃	1	1	yes	characteristic, complemented
24	C₄×C₅×C₄⋊C₄	—	3	1	no	—
25	C₅×#340	—	3	2	no	—
26	C₂³×C₅×D₃	—	2	1	no	—
27	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
29	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
30	C₂²×C₅×Dic₃	—	2	2	no	—
31	C₂²×C₅×Dic₃	—	2	1	no	—
32	C₂×C₅×D₁₂	—	2	1	no	—
33	C₂×C₅×D₁₂	—	2	2	no	—
34	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
35	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
36	C₂×C₄×C₅×D₃	—	2	4	no	—
37	C₂×C₄×C₅×D₃	—	4	2	no	—
38	C₂×C₄×C₅×D₃	—	4	2	no	—
39	C₂×C₃×C₅×C₈	—	2	2	no	—
40	C₂×C₃×C₅×C₈	—	2	2	no	—
41	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
42	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
43	C₃×C₄²×C₅	D₄	1	2	yes	—
44	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
45	C₅×C₄⋊Dic₃	—	2	1	no	—
46	C₅×C₄⋊Dic₃	—	2	2	no	—
47	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
48	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	complemented
49	C₄×C₅×Dic₃	—	4	2	no	—
50	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
51	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
52	C₂×#821	C₂×C₅	1	2	yes	—
53	C₄×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
54	#4551	C₂×C₅	1	2	yes	complemented
55	C₂²×C₅×D₄	—	3	1	no	—
56	C₂³×C₄×C₅	—	6	1	no	—
57	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
58	C₄×C₅×D₄	—	3	4	no	—
59	C₄×C₅×D₄	—	6	2	no	—
60	C₂×C₅×C₄⋊C₄	—	3	2	no	—
61	C₂×C₅×C₄⋊C₄	—	3	1	no	—
62	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
63	C₂×C₄²×C₅	—	6	1	no	—
64	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
65	C₅×#102	—	3	8	no	—
66	C₄×C₅×C₈	—	2	2	no	—
67	C₅×#95	—	6	1	no	—
68	C₄×#102	—	3	1	no	Sylow
69	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₅×D₃	—	2	2	no	—
71	C₂²×C₅×D₃	—	2	4	no	—
72	C₂²×C₅×D₃	—	4	1	no	—
73	C₂²×C₅×D₃	—	4	1	no	—
74	C₂²×C₅×D₃	—	4	2	no	—
75	C₂×C₃×C₄×C₅	—	2	2	no	—
76	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
77	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
78	C₂×C₃×C₄×C₅	D₈	1	2	yes	—
79	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	—
80	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
82	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂×C₃×C₄×C₅	#41	1	2	yes	—
84	C₂×C₅×Dic₃	—	2	2	no	—
85	C₂×C₅×Dic₃	—	2	4	no	—
86	C₂×C₅×Dic₃	—	4	2	no	—
87	C₂×C₅×Dic₃	—	4	1	no	—
88	C₂×C₅×Dic₃	—	4	1	no	—
89	C₂×C₅×Dic₃	—	4	2	no	—
90	C₅×D₁₂	—	2	2	no	—
91	C₅×D₁₂	—	2	4	no	—
92	C₅×D₁₂	C₄²	1	4	yes	complemented
93	C₄×C₅×D₃	—	4	8	no	—
94	C₃×C₅×C₈	—	2	4	no	—
95	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
96	C₂²×C₄×D₃	—	2	1	no	—
97	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
98	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
99	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
100	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
101	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
102	C₂×C₄×Dic₃	—	2	1	no	—
103	C₄×D₁₂	—	2	2	no	—
104	C₄×D₁₂	C₄×C₅	1	4	yes	complemented
105	C₃×C₄×C₈	—	2	2	no	—
106	C₃⋊#95	—	2	1	no	—
107	#821	C₄×C₅	1	8	yes	direct product factor
108	C₂⁴×C₅	—	6	1	no	—
109	C₂×C₅×D₄	—	3	2	no	—
110	C₂×C₅×D₄	—	3	4	no	—
111	C₂×C₅×D₄	—	6	2	no	—
112	C₂×C₅×D₄	—	6	1	no	—
113	C₂²×C₄×C₅	—	6	2	no	—
114	C₂²×C₄×C₅	—	6	1	no	—
115	C₂²×C₄×C₅	—	6	4	no	—
116	C₂²×C₄×C₅	—	12	2	no	—
117	C₂²×C₄×C₅	—	12	2	no	—
118	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
119	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	C₄×D₃	1	4	yes	complemented
124	C₅×C₄⋊C₄	—	3	2	no	—
125	C₅×C₄⋊C₄	—	3	4	no	—
126	C₅×C₄⋊C₄	—	6	2	no	—
127	C₅×C₄⋊C₄	—	6	1	no	—
128	C₅×C₂²⋊C₄	—	6	4	no	—
129	C₄²×C₅	—	12	2	no	—
130	C₄²×C₅	C₄×D₃	1	2	yes	—
131	C₄²×C₅	#67	1	2	yes	—
132	C₂×C₄×D₄	—	3	1	no	—
133	C₂×#102	—	3	2	no	—
134	C₂×C₄×C₈	C₅×D₃	1	1	yes	characteristic, complemented
135	C₄×C₄⋊C₄	—	3	1	no	—
136	#340	—	3	2	no	—
137	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
139	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
140	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
141	C₂²×C₃×C₅	#135	1	2	yes	—
142	C₂×C₅×D₃	—	2	4	no	—
143	C₂×C₅×D₃	—	4	2	no	—
144	C₂×C₅×D₃	—	4	2	no	—
145	C₂×C₅×D₃	—	4	4	no	—
146	C₂×C₅×D₃	—	4	4	no	—
147	C₃×C₄×C₅	—	2	2	no	—
148	C₃×C₄×C₅	#102	1	4	yes	complemented
149	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
150	C₃×C₄×C₅	#117	1	1	yes	characteristic
151	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
152	C₅×Dic₃	—	4	2	no	—
153	C₅×Dic₃	—	4	4	no	—
154	C₂³×D₃	—	2	1	no	—
155	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
158	C₂²×Dic₃	—	2	2	no	—
159	C₂²×Dic₃	—	2	1	no	—
160	C₂×D₁₂	—	2	1	no	—
161	C₂×D₁₂	—	2	2	no	—
162	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
163	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
164	C₂×C₄×D₃	—	2	4	no	—
165	C₂×C₄×D₃	—	4	2	no	—
166	C₂×C₄×D₃	—	4	2	no	—
167	C₂×C₃×C₈	—	2	2	no	—
168	C₂×C₃×C₈	—	2	2	no	—
169	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
170	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
171	C₃×C₄²	C₅×D₄	1	2	yes	—
172	(C₂×D₃)⋊C₄	—	2	4	no	—
173	C₄⋊Dic₃	—	2	1	no	—
174	C₄⋊Dic₃	—	2	2	no	—
175	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
176	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	complemented
177	C₄×Dic₃	—	4	2	no	—
178	C₂³×C₅	—	6	4	no	—
179	C₂³×C₅	—	6	2	no	—
180	C₂³×C₅	—	12	1	no	—
181	C₂³×C₅	—	12	1	no	—
182	C₂³×C₅	—	12	2	no	—
183	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
184	C₅×D₄	—	3	4	no	—
185	C₅×D₄	—	6	2	no	—
186	C₅×D₄	—	6	4	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	6	4	no	—
189	C₂×C₄×C₅	—	6	2	no	—
190	C₂×C₄×C₅	—	12	1	no	—
191	C₂×C₄×C₅	—	12	2	no	—
192	C₂×C₄×C₅	—	12	1	no	—
193	C₂×C₄×C₅	—	12	2	no	—
194	C₂×C₄×C₅	—	12	8	no	—
195	C₂×C₄×C₅	#204	1	2	yes	—
196	C₂×C₄×C₅	D₂₄	1	2	yes	—
197	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
198	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
199	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
200	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
201	C₂×C₄×C₅	#235	1	2	yes	—
202	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
203	C₅×C₈	—	2	4	no	—
204	C₂²×D₄	—	3	1	no	—
205	C₂³×C₄	—	6	1	no	—
206	C₂²×C₈	C₂×C₅×D₃	1	2	yes	—
207	C₄×D₄	—	3	4	no	—
208	C₄×D₄	—	6	2	no	—
209	C₂×C₄⋊C₄	—	3	1	no	—
210	C₂×C₄⋊C₄	—	3	2	no	—
211	C₂×C₂²⋊C₄	—	6	1	no	—
212	C₂×C₄²	—	6	1	no	—
213	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
214	#102	—	3	8	no	—
215	C₄×C₈	—	2	2	no	—
216	#95	—	6	1	no	—
217	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
219	C₂×C₃×C₅	#416	1	1	yes	characteristic
220	C₂×C₃×C₅	C₄×D₈	1	2	yes	—
221	C₂×C₃×C₅	C₄×SD₁₆	1	2	yes	—
222	C₅×D₃	—	4	4	no	—
223	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
224	C₂²×D₃	—	2	2	no	—
225	C₂²×D₃	—	2	4	no	—
226	C₂²×D₃	—	4	1	no	—
227	C₂²×D₃	—	4	1	no	—
228	C₂²×D₃	—	4	2	no	—
229	C₂×C₃×C₄	—	2	2	no	—
230	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
231	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
232	C₂×C₃×C₄	C₅×D₈	1	2	yes	—
233	C₂×C₃×C₄	C₅×SD₁₆	1	2	yes	—
234	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
235	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
236	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
237	C₂×C₃×C₄	C₅×#41	1	2	yes	—
238	C₂×Dic₃	—	2	2	no	—
239	C₂×Dic₃	—	2	4	no	—
240	C₂×Dic₃	—	4	2	no	—
241	C₂×Dic₃	—	4	1	no	—
242	C₂×Dic₃	—	4	1	no	—
243	C₂×Dic₃	—	4	2	no	—
244	D₁₂	—	2	2	no	—
245	D₁₂	—	2	4	no	—
246	D₁₂	C₄²×C₅	1	4	yes	complemented
247	C₄×D₃	—	4	8	no	—
248	C₃×C₈	—	2	4	no	—
249	C₂²×C₅	—	6	4	no	—
250	C₂²×C₅	—	12	4	no	—
251	C₂²×C₅	—	12	4	no	—
252	C₂²×C₅	—	12	2	no	—
253	C₂²×C₅	—	12	2	no	—
254	C₂²×C₅	C₄×D₁₂	1	2	yes	—
255	C₂²×C₅	C₂×#204	1	1	yes	characteristic
256	C₂²×C₅	C₂×D₂₄	1	1	yes	characteristic
257	C₂²×C₅	#904	1	2	yes	—
258	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
259	C₄×C₅	—	2	2	no	—
260	C₄×C₅	—	12	4	no	—
261	C₄×C₅	—	12	2	no	—
262	C₄×C₅	#821	1	4	yes	direct product factor
263	C₄×C₅	C₄²×D₃	1	1	yes	characteristic
264	C₄×C₅	#872	1	1	yes	characteristic
265	C₄×C₅	C₄×#67	1	2	yes	—
266	C₂⁴	—	6	1	no	—
267	C₂×D₄	—	3	4	no	—
268	C₂×D₄	—	3	2	no	—
269	C₂×D₄	—	6	2	no	—
270	C₂×D₄	—	6	1	no	—
271	C₂²×C₄	—	6	2	no	—
272	C₂²×C₄	—	6	1	no	—
273	C₂²×C₄	—	6	4	no	—
274	C₂²×C₄	—	12	2	no	—
275	C₂²×C₄	—	12	2	no	—
276	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
277	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
278	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	C₄×C₅×D₃	1	4	yes	complemented
282	C₄⋊C₄	—	3	4	no	—
283	C₄⋊C₄	—	3	2	no	—
284	C₄⋊C₄	—	6	2	no	—
285	C₄⋊C₄	—	6	1	no	—
286	C₂²⋊C₄	—	6	4	no	—
287	C₄²	—	12	2	no	—
288	C₄²	C₄×C₅×D₃	1	2	yes	—
289	C₄²	C₅×#67	1	2	yes	—
290	C₃×C₅	C₄×#102	1	1	yes	characteristic, complemented, Hall
291	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
292	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
293	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
294	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
295	C₂²×C₃	C₅×#135	1	2	yes	—
296	C₂×D₃	—	2	4	no	—
297	C₂×D₃	—	4	2	no	—
298	C₂×D₃	—	4	2	no	—
299	C₂×D₃	—	4	4	no	—
300	C₂×D₃	—	4	4	no	—
301	C₃×C₄	—	2	2	no	—
302	C₃×C₄	C₅×#102	1	4	yes	complemented
303	C₃×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
304	C₃×C₄	C₅×#117	1	1	yes	characteristic
305	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
306	Dic₃	—	4	2	no	—
307	Dic₃	—	4	4	no	—
308	C₂×C₅	—	12	4	no	—
309	C₂×C₅	C₄×#204	1	2	yes	—
310	C₂×C₅	C₄×D₂₄	1	2	yes	—
311	C₂×C₅	C₄×(C₂×D₃)⋊C₄	1	1	yes	characteristic
312	C₂×C₅	C₂×#821	1	1	yes	characteristic
313	C₂×C₅	#5113	1	1	yes	characteristic
314	C₂³	—	6	4	no	—
315	C₂³	—	6	2	no	—
316	C₂³	—	12	1	no	—
317	C₂³	—	12	1	no	—
318	C₂³	—	12	2	no	—
319	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
320	D₄	—	3	4	no	—
321	D₄	—	6	2	no	—
322	D₄	—	6	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	6	4	no	—
325	C₂×C₄	—	6	2	no	—
326	C₂×C₄	—	12	1	no	—
327	C₂×C₄	—	12	2	no	—
328	C₂×C₄	—	12	1	no	—
329	C₂×C₄	—	12	2	no	—
330	C₂×C₄	—	12	8	no	—
331	C₂×C₄	C₅×#204	1	2	yes	—
332	C₂×C₄	C₅×D₂₄	1	2	yes	—
333	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
334	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
335	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
336	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
337	C₂×C₄	C₅×#235	1	2	yes	—
338	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
339	C₈	—	2	4	no	—
340	C₂×C₃	C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
341	C₂×C₃	C₂×C₅×#102	1	1	yes	characteristic
342	C₂×C₃	C₅×#416	1	1	yes	characteristic
343	C₂×C₃	C₄×C₅×D₈	1	2	yes	—
344	C₂×C₃	C₄×C₅×SD₁₆	1	2	yes	—
345	D₃	—	4	4	no	—
346	C₅	C₄×#821	1	1	yes	characteristic, direct product factor, Sylow
347	C₂²	—	6	4	no	—
348	C₂²	—	12	4	no	—
349	C₂²	—	12	4	no	—
350	C₂²	—	12	2	no	—
351	C₂²	—	12	2	no	—
352	C₂²	C₄×C₅×D₁₂	1	2	yes	—
353	C₂²	C₂×C₅×#204	1	1	yes	characteristic
354	C₂²	C₂×C₅×D₂₄	1	1	yes	characteristic
355	C₂²	C₅×#904	1	2	yes	—
356	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
357	C₄	—	2	2	no	—
358	C₄	—	12	4	no	—
359	C₄	—	12	2	no	—
360	C₄	C₅×#821	1	4	yes	direct product factor
361	C₄	C₄²×C₅×D₃	1	1	yes	characteristic
362	C₄	C₅×#872	1	1	yes	characteristic
363	C₄	C₄×C₅×#67	1	2	yes	—
364	C₃	C₄×C₅×#102	1	1	yes	characteristic, complemented, Sylow
365	C₂	—	12	4	no	—
366	C₂	C₄×C₅×#204	1	2	yes	—
367	C₂	C₄×C₅×D₂₄	1	2	yes	—
368	C₂	C₄×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
369	C₂	C₂×C₅×#821	1	1	yes	characteristic
370	C₂	C₅×#5113	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	D₁₂
commutator	C₃×C₄	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×C₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₄×C₅×C₈	D₃
hypocenter	C₃	C₄×C₅×#102
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×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. C₄×C₅×C₄⋊Dic₃	C₂	semidirect
5. C₅×#4551	C₂	semidirect
16. C₄×C₅×D₁₂	C₄	semidirect
19. C₅×#821	C₄	direct (N × H)
20. C₄×#821	C₅	direct (N × H)
23. C₂×C₄×C₅×C₈	D₃	semidirect
41. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
48. C₅×C₄⋊Dic₃	C₂×C₄	semidirect
51. C₂×C₃×C₄×C₈	C₂×C₅	semidirect
53. C₄×C₄⋊Dic₃	C₂×C₅	semidirect
54. #4551	C₂×C₅	semidirect
92. C₅×D₁₂	C₄²	semidirect
104. C₄×D₁₂	C₄×C₅	semidirect
107. #821	C₄×C₅	direct (N × H)
123. C₂×C₅×C₈	C₄×D₃	semidirect
134. C₂×C₄×C₈	C₅×D₃	semidirect
148. C₃×C₄×C₅	#102	semidirect
169. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
176. C₄⋊Dic₃	C₂×C₄×C₅	semidirect
246. D₁₂	C₄²×C₅	semidirect
262. C₄×C₅	#821	direct (N × H)
281. C₂×C₈	C₄×C₅×D₃	semidirect
290. C₃×C₅	C₄×#102	semidirect
302. C₃×C₄	C₅×#102	semidirect
346. C₅	C₄×#821	direct (N × H)
360. C₄	C₅×#821	direct (N × H)
364. C₃	C₄×C₅×#102	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×D₁₂	2
C₂×C₃×C₄×C₅×C₈	2
C₂×C₅×#821	2
C₄×C₅×C₄⋊Dic₃	2
C₅×#4551	2
C₄×C₅×#102	3
C₄×#821	5

Subgroups — C4×C5×#821 #14295692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#821 #14295692