Subgroups — C₂×C₃×#64989 #14417843

Order 1920.

944 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4050	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4047	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3951	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3937	C₂	1	2	yes	maximal, complemented
6	C₃×#64989	C₂	1	8	yes	maximal, direct product factor
7	C₂×#64989	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×#709	C₂²	1	2	yes	—
9	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₃×#681	C₂²	1	2	yes	—
13	C₂×C₃×Dic₂₀	C₄	1	1	yes	characteristic, complemented
14	C₃×#4050	C₄	1	4	yes	complemented
15	C₃×#4050	C₂²	1	4	yes	—
16	C₂×C₃×D₄₀	C₄	1	1	yes	characteristic, complemented
17	C₂×C₃×#677	C₄	1	2	yes	complemented
18	C₃×#4047	—	2	4	no	—
19	C₃×#4047	C₂²	1	8	yes	complemented
20	C₂×C₃×#676	—	2	2	no	—
21	C₂×C₃×C₈×D₅	—	2	2	no	—
22	C₃×C₄×C₅×C₈	C₂²	1	4	yes	complemented
23	C₃×#3951	C₂²	1	4	yes	complemented
24	C₃×#3937	C₂²	1	8	yes	complemented
25	C₂×C₃×#443	—	5	1	no	maximal, Hall
26	C₂×#4050	C₂×C₃	1	1	yes	characteristic
27	C₂×#4047	C₂×C₃	1	2	yes	complemented
28	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×#3951	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×#3937	C₂×C₃	1	2	yes	complemented
31	#64989	C₂×C₃	1	8	yes	direct product factor
32	C₂²×C₃×C₄×C₅	—	2	1	no	—
33	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
35	C₃×#709	—	2	2	no	—
36	C₃×#709	—	2	2	no	—
37	C₃×#709	C₂×C₄	1	4	yes	—
38	C₃×#709	C₂³	1	4	yes	—
39	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
40	C₂×C₃×C₄×D₅	—	2	2	no	—
41	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
42	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
45	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
46	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
47	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
48	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
49	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₃×C₄²×C₅	C₂³	1	2	yes	—
52	C₃×#681	—	2	2	no	—
53	C₃×#681	C₂³	1	4	yes	—
54	C₂×C₃×#168	—	2	2	no	—
55	C₃×Dic₂₀	C₂×C₄	1	4	yes	complemented
56	C₃×D₄₀	C₂×C₄	1	4	yes	complemented
57	C₃×#677	C₂×C₄	1	8	yes	complemented
58	C₃×#676	—	2	8	no	—
59	C₃×C₈×D₅	—	2	8	no	—
60	C₂×C₃×#135	—	5	1	no	—
61	C₂×C₃×#131	—	5	2	no	—
62	C₃×#443	—	5	8	no	—
63	C₂×C₃×#108	—	5	1	no	—
64	C₂×C₃×#104	—	5	2	no	—
65	C₂×C₃×C₄×C₈	D₅	1	1	yes	characteristic, complemented
66	C₂×#709	C₂²×C₃	1	2	yes	—
67	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
70	C₂×#681	C₂²×C₃	1	2	yes	—
71	C₂×Dic₂₀	C₃×C₄	1	1	yes	characteristic, complemented
72	#4050	C₃×C₄	1	4	yes	complemented
73	#4050	C₂²×C₃	1	4	yes	—
74	C₂×D₄₀	C₃×C₄	1	1	yes	characteristic, complemented
75	C₂×#677	C₃×C₄	1	2	yes	complemented
76	#4047	—	2	4	no	—
77	#4047	C₂²×C₃	1	8	yes	complemented
78	C₂×#676	—	2	2	no	—
79	C₂×C₈×D₅	—	2	2	no	—
80	C₄×C₅×C₈	C₂²×C₃	1	4	yes	complemented
81	#3951	C₂²×C₃	1	4	yes	complemented
82	#3937	C₂²×C₃	1	8	yes	complemented
83	C₂×#443	—	5	1	no	Sylow
84	C₂³×C₃×C₅	#41	1	1	yes	characteristic
85	C₂²×C₃×D₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	2	4	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
94	C₃×C₂²⋊D₅	—	2	4	no	—
95	C₃×C₂²⋊D₅	—	2	4	no	—
96	C₂×C₃×Dic₅	—	2	2	no	—
97	C₃×D₂₀	—	2	2	no	—
98	C₃×D₂₀	C₂²×C₄	1	4	yes	—
99	C₃×C₄×D₅	—	2	4	no	—
100	C₃×C₄×D₅	—	2	4	no	—
101	C₃×Dic₁₀	—	2	2	no	—
102	C₃×Dic₁₀	C₂²×C₄	1	4	yes	—
103	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
104	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
105	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
106	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
107	C₃×#168	—	2	4	no	—
108	C₂×C₃×#41	—	5	2	no	—
109	C₃×#135	—	5	4	no	—
110	C₃×#135	—	5	4	no	—
111	C₂×C₃×Q₁₆	—	5	1	no	—
112	C₂×C₃×SD₁₆	—	5	2	no	—
113	C₂×C₃×D₈	—	5	1	no	—
114	C₃×#131	—	5	8	no	—
115	C₃×#131	—	10	4	no	—
116	C₂×C₃×M₁₆	—	5	2	no	—
117	C₂×C₃×M₁₆	—	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×C₄²	C₂×D₅	1	1	yes	characteristic
122	C₃×#108	—	5	4	no	—
123	C₃×#104	—	5	8	no	—
124	C₃×C₄×C₈	C₂×D₅	1	4	yes	complemented
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
127	C₂×C₂²⋊D₅	—	2	2	no	—
128	#709	—	2	2	no	—
129	#709	—	2	2	no	—
130	#709	C₂×C₃×C₄	1	4	yes	—
131	#709	C₂³×C₃	1	4	yes	—
132	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
133	C₂×C₄×D₅	—	2	2	no	—
134	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
135	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
136	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
137	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
138	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
139	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
140	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
141	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
142	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
143	C₄²×C₅	—	2	1	no	—
144	C₄²×C₅	C₂³×C₃	1	2	yes	—
145	#681	—	2	2	no	—
146	#681	C₂³×C₃	1	4	yes	—
147	C₂×#168	—	2	2	no	—
148	Dic₂₀	C₂×C₃×C₄	1	4	yes	complemented
149	D₄₀	C₂×C₃×C₄	1	4	yes	complemented
150	#677	C₂×C₃×C₄	1	8	yes	complemented
151	#676	—	2	8	no	—
152	C₈×D₅	—	2	8	no	—
153	C₂×#135	—	5	1	no	—
154	C₂×#131	—	5	2	no	—
155	#443	—	5	8	no	—
156	C₂×#108	—	5	1	no	—
157	C₂×#104	—	5	2	no	—
158	C₂×C₄×C₈	C₃×D₅	1	1	yes	characteristic, complemented
159	C₂²×C₃×C₅	—	2	2	no	—
160	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
161	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
162	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
163	C₂×C₃×D₅	—	2	4	no	—
164	C₂×C₃×D₅	—	4	4	no	—
165	C₃×C₄×C₅	—	2	4	no	—
166	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
167	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
168	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
169	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
170	C₃×Dic₅	—	2	4	no	—
171	C₃×#41	—	5	4	no	—
172	C₃×#41	—	5	4	no	—
173	C₃×#41	—	10	2	no	—
174	C₃×#41	—	10	2	no	—
175	C₂×C₃×Q₈	—	5	2	no	—
176	C₂×C₃×D₄	—	5	2	no	—
177	C₂×C₃×D₄	—	10	2	no	—
178	C₂²×C₃×C₄	—	2	1	no	—
179	C₂²×C₃×C₄	—	10	2	no	—
180	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
181	C₃×Q₁₆	—	5	4	no	—
182	C₃×SD₁₆	—	5	8	no	—
183	C₃×D₈	—	5	4	no	—
184	C₃×M₁₆	—	5	4	no	—
185	C₃×M₁₆	—	10	2	no	—
186	C₃×M₁₆	—	10	8	no	—
187	C₂×C₃×C₈	—	10	2	no	—
188	C₂×C₃×C₈	—	10	8	no	—
189	C₂×C₃×C₈	C₄×D₅	1	1	yes	characteristic
190	C₂×C₃×C₈	C₄×D₅	1	1	yes	characteristic
191	C₂×C₃×C₈	C₄×D₅	1	2	yes	—
192	C₂×C₃×C₈	D₂₀	1	1	yes	characteristic
193	C₂×C₃×C₈	D₂₀	1	2	yes	—
194	C₂×C₃×C₈	D₂₀	1	1	yes	characteristic
195	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
196	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
197	C₃×C₄²	—	2	1	no	—
198	C₃×C₄²	C₂²×D₅	1	2	yes	—
199	C₂³×C₅	C₃×#41	1	1	yes	characteristic
200	C₂²×D₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	4	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
209	C₂²⋊D₅	—	2	4	no	—
210	C₂²⋊D₅	—	2	4	no	—
211	C₂×Dic₅	—	2	2	no	—
212	D₂₀	—	2	2	no	—
213	D₂₀	C₂²×C₃×C₄	1	4	yes	—
214	C₄×D₅	—	2	4	no	—
215	C₄×D₅	—	2	4	no	—
216	Dic₁₀	—	2	2	no	—
217	Dic₁₀	C₂²×C₃×C₄	1	4	yes	—
218	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
219	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
220	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
221	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
222	#168	—	2	4	no	—
223	C₂×#41	—	5	2	no	—
224	#135	—	5	4	no	—
225	#135	—	5	4	no	—
226	C₂×Q₁₆	—	5	1	no	—
227	C₂×SD₁₆	—	5	2	no	—
228	C₂×D₈	—	5	1	no	—
229	#131	—	5	8	no	—
230	#131	—	10	4	no	—
231	C₂×M₁₆	—	5	2	no	—
232	C₂×M₁₆	—	10	2	no	—
233	C₂²×C₈	—	10	2	no	—
234	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
235	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
236	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
237	#108	—	5	4	no	—
238	#104	—	5	8	no	—
239	C₄×C₈	C₂×C₃×D₅	1	4	yes	complemented
240	C₂×C₃×C₅	—	2	1	no	—
241	C₂×C₃×C₅	—	2	1	no	—
242	C₂×C₃×C₅	#443	1	2	yes	complemented
243	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
244	C₃×D₅	—	4	4	no	—
245	C₂³×C₃	—	10	2	no	—
246	C₂³×C₃	#709	1	1	yes	characteristic
247	C₃×Q₈	—	5	4	no	—
248	C₃×Q₈	—	10	2	no	—
249	C₃×D₄	—	5	4	no	—
250	C₃×D₄	—	10	4	no	—
251	C₃×D₄	—	10	4	no	—
252	C₃×D₄	—	10	2	no	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	10	2	no	—
256	C₂×C₃×C₄	—	10	4	no	—
257	C₂×C₃×C₄	—	10	4	no	—
258	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
262	C₂×C₃×C₄	#709	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
264	C₃×C₈	—	10	4	no	—
265	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
266	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
267	C₃×C₈	C₂×D₂₀	1	2	yes	—
268	C₃×C₈	C₂×D₂₀	1	2	yes	—
269	C₂²×C₅	—	2	2	no	—
270	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
271	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
272	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
273	C₂×D₅	—	2	4	no	—
274	C₂×D₅	—	4	4	no	—
275	C₄×C₅	—	2	4	no	—
276	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
277	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
278	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
279	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
280	Dic₅	—	2	4	no	—
281	#41	—	5	4	no	—
282	#41	—	5	4	no	—
283	#41	—	10	2	no	—
284	#41	—	10	2	no	—
285	C₂×Q₈	—	5	2	no	—
286	C₂×D₄	—	5	2	no	—
287	C₂×D₄	—	10	2	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	10	2	no	—
290	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
291	Q₁₆	—	5	4	no	—
292	SD₁₆	—	5	8	no	—
293	D₈	—	5	4	no	—
294	M₁₆	—	5	4	no	—
295	M₁₆	—	10	2	no	—
296	M₁₆	—	10	8	no	—
297	C₂×C₈	—	10	2	no	—
298	C₂×C₈	—	10	8	no	—
299	C₂×C₈	C₃×C₄×D₅	1	1	yes	characteristic
300	C₂×C₈	C₃×C₄×D₅	1	1	yes	characteristic
301	C₂×C₈	C₃×C₄×D₅	1	2	yes	—
302	C₂×C₈	C₃×D₂₀	1	1	yes	characteristic
303	C₂×C₈	C₃×D₂₀	1	1	yes	characteristic
304	C₂×C₈	C₃×D₂₀	1	2	yes	—
305	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
306	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
307	C₄²	—	2	1	no	—
308	C₄²	C₂²×C₃×D₅	1	2	yes	—
309	C₃×C₅	C₂×#443	1	1	yes	characteristic, complemented, Hall
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	—	10	4	no	—
312	C₂²×C₃	—	20	4	no	—
313	C₂²×C₃	C₄×D₂₀	1	1	yes	characteristic
314	C₂²×C₃	C₄×D₂₀	1	1	yes	characteristic
315	C₂²×C₃	C₂×#709	1	1	yes	characteristic
316	C₃×C₄	—	2	4	no	—
317	C₃×C₄	—	10	4	no	—
318	C₃×C₄	C₄×D₂₀	1	1	yes	characteristic
319	C₃×C₄	C₄×D₂₀	1	1	yes	characteristic
320	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
321	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
322	C₂×C₅	—	2	1	no	—
323	C₂×C₅	—	2	1	no	—
324	C₂×C₅	C₃×#443	1	2	yes	complemented
325	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
326	D₅	—	4	4	no	—
327	C₂³	—	10	2	no	—
328	C₂³	C₃×#709	1	1	yes	characteristic
329	Q₈	—	5	4	no	—
330	Q₈	—	10	2	no	—
331	D₄	—	5	4	no	—
332	D₄	—	10	4	no	—
333	D₄	—	10	4	no	—
334	D₄	—	10	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	10	2	no	—
338	C₂×C₄	—	10	4	no	—
339	C₂×C₄	—	10	4	no	—
340	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
341	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
342	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
343	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
344	C₂×C₄	C₃×#709	1	1	yes	characteristic
345	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
346	C₈	—	10	4	no	—
347	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
348	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
349	C₈	C₂×C₃×D₂₀	1	2	yes	—
350	C₈	C₂×C₃×D₂₀	1	2	yes	—
351	C₂×C₃	—	2	1	no	—
352	C₂×C₃	—	2	1	no	—
353	C₂×C₃	—	20	4	no	—
354	C₂×C₃	#64989	1	2	yes	direct product factor
355	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
356	C₅	C₂×C₃×#443	1	1	yes	characteristic, complemented, Sylow
357	C₂²	—	2	2	no	—
358	C₂²	—	10	4	no	—
359	C₂²	—	20	4	no	—
360	C₂²	C₃×C₄×D₂₀	1	1	yes	characteristic
361	C₂²	C₃×C₄×D₂₀	1	1	yes	characteristic
362	C₂²	C₂×C₃×#709	1	1	yes	characteristic
363	C₄	—	2	4	no	—
364	C₄	—	10	4	no	—
365	C₄	C₃×C₄×D₂₀	1	1	yes	characteristic
366	C₄	C₃×C₄×D₂₀	1	1	yes	characteristic
367	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
368	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
369	C₃	C₂×#64989	1	1	yes	characteristic, direct product factor, Sylow
370	C₂	—	2	1	no	—
371	C₂	—	2	1	no	—
372	C₂	—	20	4	no	—
373	C₂	C₃×#64989	1	2	yes	direct product factor
374	C₂	C₂×C₃×C₄×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₈	D₂₀
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×C₈	C₂
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₃×#4050	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₄×C₈	D₅
hypocenter	C₅	C₂×C₃×#443
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₈ ◁ 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×#4047	C₂	semidirect
3. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
4. C₂×C₃×#3951	C₂	semidirect
5. C₂×C₃×#3937	C₂	semidirect
6. C₃×#64989	C₂	direct (N × H)
7. C₂×#64989	C₃	direct (N × H)
13. C₂×C₃×Dic₂₀	C₄	semidirect
14. C₃×#4050	C₄	semidirect
16. C₂×C₃×D₄₀	C₄	semidirect
17. C₂×C₃×#677	C₄	semidirect
19. C₃×#4047	C₂²	semidirect
22. C₃×C₄×C₅×C₈	C₂²	semidirect
23. C₃×#3951	C₂²	semidirect
24. C₃×#3937	C₂²	semidirect
27. C₂×#4047	C₂×C₃	semidirect
28. C₂×C₄×C₅×C₈	C₂×C₃	semidirect
29. C₂×#3951	C₂×C₃	semidirect
30. C₂×#3937	C₂×C₃	semidirect
31. #64989	C₂×C₃	direct (N × H)
55. C₃×Dic₂₀	C₂×C₄	semidirect
56. C₃×D₄₀	C₂×C₄	semidirect
57. C₃×#677	C₂×C₄	semidirect
65. C₂×C₃×C₄×C₈	D₅	semidirect
71. C₂×Dic₂₀	C₃×C₄	semidirect
72. #4050	C₃×C₄	semidirect
74. C₂×D₄₀	C₃×C₄	semidirect
75. C₂×#677	C₃×C₄	semidirect
77. #4047	C₂²×C₃	semidirect
80. C₄×C₅×C₈	C₂²×C₃	semidirect
81. #3951	C₂²×C₃	semidirect
82. #3937	C₂²×C₃	semidirect
124. C₃×C₄×C₈	C₂×D₅	semidirect
148. Dic₂₀	C₂×C₃×C₄	semidirect
149. D₄₀	C₂×C₃×C₄	semidirect
150. #677	C₂×C₃×C₄	semidirect
158. C₂×C₄×C₈	C₃×D₅	semidirect
239. C₄×C₈	C₂×C₃×D₅	semidirect
242. C₂×C₃×C₅	#443	semidirect
309. C₃×C₅	C₂×#443	semidirect
324. C₂×C₅	C₃×#443	semidirect
354. C₂×C₃	#64989	direct (N × H)
356. C₅	C₂×C₃×#443	semidirect
369. C₃	C₂×#64989	direct (N × H)
373. C₂	C₃×#64989	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#4050	2
C₂×C₃×#4047	2
C₂×C₃×C₄×C₅×C₈	2
C₂×C₃×#3951	2
C₂×C₃×#3937	2
C₃×#64989	2
C₂×#64989	3
C₂×C₃×#443	5

Subgroups — C2×C3×#64989 #14417843

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64989 #14417843