Subgroups — C₂×C₃×#65404 #14427685

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4076	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65404	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3953	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#3950	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65404	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₂²⋊D₅	—	2	2	no	—
10	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×C₈	—	2	4	no	—
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	4	yes	complemented
15	C₃×#4076	—	2	4	no	—
16	C₃×#4076	C₂²	1	8	yes	complemented
17	C₂×C₃×#685	—	2	2	no	—
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
19	C₂×C₃×D₄₀	—	2	4	no	—
20	C₂×C₃×D₄₀	C₂²	1	4	yes	complemented
21	C₃×#3953	C₂²	1	8	yes	complemented
22	C₃×#3950	C₂²	1	4	yes	complemented
23	C₂×C₃×#466	—	5	1	no	maximal, Hall
24	C₂³×C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂×#4076	C₂×C₃	1	2	yes	complemented
26	C₂²×D₄₀	C₂×C₃	1	1	yes	characteristic, complemented
27	#65404	C₂×C₃	1	8	yes	direct product factor
28	C₂×#3953	C₂×C₃	1	2	yes	complemented
29	C₂×#3950	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
31	C₂³×C₃×D₅	—	2	2	no	—
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	—	2	2	no	—
34	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
39	C₂×C₃×C₂²⋊D₅	—	4	8	no	—
40	C₂²×C₃×Dic₅	—	2	2	no	—
41	C₂×C₃×D₂₀	—	2	4	no	—
42	C₂×C₃×D₂₀	—	2	4	no	—
43	C₂×C₃×D₂₀	—	2	2	no	—
44	C₂×C₃×D₂₀	C₂³	1	4	yes	—
45	C₂×C₃×C₅×C₈	—	2	2	no	—
46	C₂×C₃×C₅×C₈	—	2	8	no	—
47	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
48	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
49	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
50	C₃×#685	—	2	8	no	—
51	C₃×C₄⋊Dic₅	—	2	2	no	—
52	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
53	C₃×D₄₀	—	2	8	no	—
54	C₂²×C₃×D₈	—	5	1	no	—
55	C₂³×C₃×C₈	D₅	1	1	yes	characteristic, complemented
56	C₂×C₃×#121	—	5	2	no	—
57	C₃×#466	—	5	8	no	—
58	C₂×C₃×#107	—	5	1	no	—
59	C₂×C₃×#102	—	5	2	no	—
60	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
61	C₂²×C₂²⋊D₅	—	2	2	no	—
62	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
63	C₂²×C₅×C₈	—	2	4	no	—
64	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂²×C₃	1	4	yes	complemented
67	#4076	—	2	4	no	—
68	#4076	C₂²×C₃	1	8	yes	complemented
69	C₂×#685	—	2	2	no	—
70	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
71	C₂×D₄₀	—	2	4	no	—
72	C₂×D₄₀	C₂²×C₃	1	4	yes	complemented
73	#3953	C₂²×C₃	1	8	yes	complemented
74	#3950	C₂²×C₃	1	4	yes	complemented
75	C₂×#466	—	5	1	no	Sylow
76	C₂³×C₃×C₅	—	2	2	no	—
77	C₂³×C₃×C₅	—	2	2	no	—
78	C₂³×C₃×C₅	D₈	1	4	yes	complemented
79	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
80	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₃×D₅	—	2	4	no	—
82	C₂²×C₃×D₅	—	4	4	no	—
83	C₂²×C₃×D₅	—	4	4	no	—
84	C₂²×C₃×D₅	—	4	4	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	2	4	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
92	C₂×C₃×C₄×C₅	#41	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
94	C₃×C₂²⋊D₅	—	4	16	no	—
95	C₂×C₃×Dic₅	—	2	4	no	—
96	C₂×C₃×Dic₅	—	4	4	no	—
97	C₃×D₂₀	—	2	4	no	—
98	C₃×D₂₀	—	2	4	no	—
99	C₃×D₂₀	—	4	4	no	—
100	C₃×C₅×C₈	—	2	2	no	—
101	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
102	C₂²×C₃×D₄	—	5	2	no	—
103	C₂²×C₃×D₄	—	10	2	no	—
104	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
105	C₂×C₃×D₈	—	5	4	no	—
106	C₂×C₃×D₈	—	10	4	no	—
107	C₂²×C₃×C₈	—	2	4	no	—
108	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
109	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
110	C₂²×C₃×C₈	C₂×D₅	1	4	yes	complemented
111	C₃×#121	—	5	8	no	—
112	C₃×#121	—	10	4	no	—
113	C₂×C₃×C₄⋊C₄	—	5	2	no	—
114	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
115	C₃×#107	—	5	4	no	—
116	C₃×#102	—	5	8	no	—
117	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
118	C₂³×D₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
123	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
124	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
125	C₂×C₂²⋊D₅	—	2	8	no	—
126	C₂×C₂²⋊D₅	—	4	8	no	—
127	C₂²×Dic₅	—	2	2	no	—
128	C₂×D₂₀	—	2	4	no	—
129	C₂×D₂₀	—	2	4	no	—
130	C₂×D₂₀	—	2	2	no	—
131	C₂×D₂₀	C₂³×C₃	1	4	yes	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	2	8	no	—
134	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
135	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
136	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
137	#685	—	2	8	no	—
138	C₄⋊Dic₅	—	2	2	no	—
139	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
140	D₄₀	—	2	8	no	—
141	C₂²×D₈	—	5	1	no	—
142	C₂³×C₈	C₃×D₅	1	1	yes	characteristic, complemented
143	C₂×#121	—	5	2	no	—
144	#466	—	5	8	no	—
145	C₂×#107	—	5	1	no	—
146	C₂×#102	—	5	2	no	—
147	C₂²×C₃×C₅	—	2	2	no	—
148	C₂²×C₃×C₅	—	2	2	no	—
149	C₂²×C₃×C₅	—	2	8	no	—
150	C₂²×C₃×C₅	#121	1	2	yes	—
151	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
152	C₂²×C₃×C₅	C₂×D₈	1	4	yes	complemented
153	C₂²×C₃×C₅	#135	1	2	yes	—
154	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₃×D₅	—	4	4	no	—
156	C₂×C₃×D₅	—	4	4	no	—
157	C₂×C₃×D₅	—	4	4	no	—
158	C₂×C₃×D₅	—	8	8	no	—
159	C₃×C₄×C₅	—	2	2	no	—
160	C₃×C₄×C₅	#121	1	2	yes	—
161	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
162	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
163	C₃×Dic₅	—	4	4	no	—
164	C₂⁴×C₃	—	10	2	no	—
165	C₂⁴×C₃	D₂₀	1	1	yes	characteristic
166	C₂×C₃×D₄	—	5	4	no	—
167	C₂×C₃×D₄	—	10	8	no	—
168	C₂×C₃×D₄	—	10	2	no	—
169	C₂×C₃×D₄	—	10	4	no	—
170	C₂×C₃×D₄	—	10	4	no	—
171	C₂×C₃×D₄	—	20	8	no	—
172	C₂²×C₃×C₄	—	2	2	no	—
173	C₂²×C₃×C₄	—	2	2	no	—
174	C₂²×C₃×C₄	—	10	2	no	—
175	C₂²×C₃×C₄	D₂₀	1	2	yes	—
176	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
178	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
179	C₃×D₈	—	10	8	no	—
180	C₂×C₃×C₈	—	2	2	no	—
181	C₂×C₃×C₈	—	2	8	no	—
182	C₂×C₃×C₈	C₂²⋊D₅	1	4	yes	complemented
183	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
184	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
185	C₃×C₄⋊C₄	—	5	4	no	—
186	C₃×C₄⋊C₄	—	10	2	no	—
187	C₃×C₂²⋊C₄	—	10	8	no	—
188	C₂³×C₅	—	2	2	no	—
189	C₂³×C₅	—	2	2	no	—
190	C₂³×C₅	C₃×D₈	1	4	yes	complemented
191	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
192	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
193	C₂²×D₅	—	2	4	no	—
194	C₂²×D₅	—	4	4	no	—
195	C₂²×D₅	—	4	4	no	—
196	C₂²×D₅	—	4	4	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	4	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
202	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
204	C₂×C₄×C₅	C₃×#41	1	2	yes	—
205	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
206	C₂²⋊D₅	—	4	16	no	—
207	C₂×Dic₅	—	2	4	no	—
208	C₂×Dic₅	—	4	4	no	—
209	D₂₀	—	2	4	no	—
210	D₂₀	—	2	4	no	—
211	D₂₀	—	4	4	no	—
212	C₅×C₈	—	2	2	no	—
213	C₅×C₈	C₂×C₃×D₄	1	4	yes	complemented
214	C₂²×D₄	—	5	2	no	—
215	C₂²×D₄	—	10	2	no	—
216	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
217	C₂×D₈	—	5	4	no	—
218	C₂×D₈	—	10	4	no	—
219	C₂²×C₈	—	2	4	no	—
220	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
221	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
222	C₂²×C₈	C₂×C₃×D₅	1	4	yes	complemented
223	#121	—	5	8	no	—
224	#121	—	10	4	no	—
225	C₂×C₄⋊C₄	—	5	2	no	—
226	C₂×C₂²⋊C₄	—	10	2	no	—
227	#107	—	5	4	no	—
228	#102	—	5	8	no	—
229	C₂×C₃×C₅	—	2	4	no	—
230	C₂×C₃×C₅	#466	1	4	yes	complemented
231	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
232	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
233	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
234	C₃×D₅	—	8	4	no	—
235	C₂³×C₃	—	2	2	no	—
236	C₂³×C₃	—	2	2	no	—
237	C₂³×C₃	—	10	4	no	—
238	C₂³×C₃	—	20	4	no	—
239	C₂³×C₃	—	20	4	no	—
240	C₂³×C₃	—	20	4	no	—
241	C₂³×C₃	D₄₀	1	4	yes	complemented
242	C₂³×C₃	C₂×D₂₀	1	2	yes	—
243	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
244	C₃×D₄	—	10	4	no	—
245	C₃×D₄	—	10	4	no	—
246	C₃×D₄	—	20	16	no	—
247	C₃×D₄	—	20	4	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	10	4	no	—
253	C₂×C₃×C₄	—	20	4	no	—
254	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
255	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
256	C₂×C₃×C₄	#709	1	2	yes	—
257	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
258	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
259	C₃×C₈	—	2	2	no	—
260	C₃×C₈	C₂×C₂²⋊D₅	1	4	yes	complemented
261	C₂²×C₅	—	2	2	no	—
262	C₂²×C₅	—	2	8	no	—
263	C₂²×C₅	—	2	2	no	—
264	C₂²×C₅	C₃×#121	1	2	yes	—
265	C₂²×C₅	C₂×C₃×D₈	1	2	yes	—
266	C₂²×C₅	C₂×C₃×D₈	1	4	yes	complemented
267	C₂²×C₅	C₃×#135	1	2	yes	—
268	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
269	C₂×D₅	—	4	4	no	—
270	C₂×D₅	—	4	4	no	—
271	C₂×D₅	—	4	4	no	—
272	C₂×D₅	—	8	8	no	—
273	C₄×C₅	—	2	2	no	—
274	C₄×C₅	C₃×#121	1	2	yes	—
275	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
276	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
277	Dic₅	—	4	4	no	—
278	C₂⁴	—	10	2	no	—
279	C₂⁴	C₃×D₂₀	1	1	yes	characteristic
280	C₂×D₄	—	5	4	no	—
281	C₂×D₄	—	10	8	no	—
282	C₂×D₄	—	10	2	no	—
283	C₂×D₄	—	10	4	no	—
284	C₂×D₄	—	10	4	no	—
285	C₂×D₄	—	20	8	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	10	2	no	—
289	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
290	C₂²×C₄	C₃×D₂₀	1	2	yes	—
291	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
292	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
293	D₈	—	10	8	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	8	no	—
296	C₂×C₈	C₃×C₂²⋊D₅	1	4	yes	complemented
297	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
298	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
299	C₄⋊C₄	—	5	4	no	—
300	C₄⋊C₄	—	10	2	no	—
301	C₂²⋊C₄	—	10	8	no	—
302	C₃×C₅	C₂×#466	1	1	yes	characteristic, complemented, Hall
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	2	8	no	—
306	C₂²×C₃	—	20	4	no	—
307	C₂²×C₃	—	20	4	no	—
308	C₂²×C₃	—	20	4	no	—
309	C₂²×C₃	—	40	8	no	—
310	C₂²×C₃	C₂×D₄₀	1	2	yes	—
311	C₂²×C₃	C₂×D₄₀	1	4	yes	complemented
312	C₂²×C₃	#4050	1	2	yes	—
313	C₂²×C₃	#4076	1	2	yes	—
314	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
315	C₃×C₄	—	2	2	no	—
316	C₃×C₄	—	20	4	no	—
317	C₃×C₄	#4076	1	2	yes	—
318	C₃×C₄	C₂×#709	1	1	yes	characteristic
319	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
320	C₂×C₅	—	2	4	no	—
321	C₂×C₅	C₃×#466	1	4	yes	complemented
322	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
323	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
324	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
325	D₅	—	8	4	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	10	4	no	—
329	C₂³	—	20	4	no	—
330	C₂³	—	20	4	no	—
331	C₂³	—	20	4	no	—
332	C₂³	C₃×D₄₀	1	4	yes	complemented
333	C₂³	C₂×C₃×D₂₀	1	2	yes	—
334	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
335	D₄	—	10	4	no	—
336	D₄	—	10	4	no	—
337	D₄	—	20	16	no	—
338	D₄	—	20	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	10	4	no	—
344	C₂×C₄	—	20	4	no	—
345	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
346	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
347	C₂×C₄	C₃×#709	1	2	yes	—
348	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
349	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
350	C₈	—	2	2	no	—
351	C₈	C₂×C₃×C₂²⋊D₅	1	4	yes	complemented
352	C₂×C₃	—	2	4	no	—
353	C₂×C₃	—	40	4	no	—
354	C₂×C₃	#65404	1	4	yes	direct product factor
355	C₂×C₃	C₂²×D₄₀	1	1	yes	characteristic
356	C₂×C₃	C₂×#4050	1	1	yes	characteristic
357	C₂×C₃	C₂×#4076	1	1	yes	characteristic
358	C₅	C₂×C₃×#466	1	1	yes	characteristic, complemented, Sylow
359	C₂²	—	2	2	no	—
360	C₂²	—	2	8	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	20	4	no	—
363	C₂²	—	20	4	no	—
364	C₂²	—	20	4	no	—
365	C₂²	—	40	8	no	—
366	C₂²	C₂×C₃×D₄₀	1	2	yes	—
367	C₂²	C₂×C₃×D₄₀	1	4	yes	complemented
368	C₂²	C₃×#4050	1	2	yes	—
369	C₂²	C₃×#4076	1	2	yes	—
370	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
371	C₄	—	2	2	no	—
372	C₄	—	20	4	no	—
373	C₄	C₃×#4076	1	2	yes	—
374	C₄	C₂×C₃×#709	1	1	yes	characteristic
375	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
376	C₃	C₂×#65404	1	1	yes	characteristic, direct product factor, Sylow
377	C₂	—	2	4	no	—
378	C₂	—	40	4	no	—
379	C₂	C₃×#65404	1	4	yes	direct product factor
380	C₂	C₂²×C₃×D₄₀	1	1	yes	characteristic
381	C₂	C₂×C₃×#4050	1	1	yes	characteristic
382	C₂	C₂×C₃×#4076	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂³×C₃×C₅×C₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂³×C₃×C₈	D₅
hypocenter	C₅	C₂×C₃×#466
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×C₄ ◁ C₂³×C₃×C₈

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×C₈	C₂	semidirect
2. C₂×C₃×#4076	C₂	semidirect
3. C₂²×C₃×D₄₀	C₂	semidirect
4. C₃×#65404	C₂	direct (N × H)
5. C₂×C₃×#3953	C₂	semidirect
6. C₂×C₃×#3950	C₂	semidirect
7. C₂×#65404	C₃	direct (N × H)
14. C₂²×C₃×C₅×C₈	C₂²	semidirect
16. C₃×#4076	C₂²	semidirect
20. C₂×C₃×D₄₀	C₂²	semidirect
21. C₃×#3953	C₂²	semidirect
22. C₃×#3950	C₂²	semidirect
24. C₂³×C₅×C₈	C₂×C₃	semidirect
25. C₂×#4076	C₂×C₃	semidirect
26. C₂²×D₄₀	C₂×C₃	semidirect
27. #65404	C₂×C₃	direct (N × H)
28. C₂×#3953	C₂×C₃	semidirect
29. C₂×#3950	C₂×C₃	semidirect
47. C₂×C₃×C₅×C₈	D₄	semidirect
55. C₂³×C₃×C₈	D₅	semidirect
66. C₂²×C₅×C₈	C₂²×C₃	semidirect
68. #4076	C₂²×C₃	semidirect
72. C₂×D₄₀	C₂²×C₃	semidirect
73. #3953	C₂²×C₃	semidirect
74. #3950	C₂²×C₃	semidirect
78. C₂³×C₃×C₅	D₈	semidirect
101. C₃×C₅×C₈	C₂×D₄	semidirect
110. C₂²×C₃×C₈	C₂×D₅	semidirect
134. C₂×C₅×C₈	C₃×D₄	semidirect
142. C₂³×C₈	C₃×D₅	semidirect
152. C₂²×C₃×C₅	C₂×D₈	semidirect
182. C₂×C₃×C₈	C₂²⋊D₅	semidirect
190. C₂³×C₅	C₃×D₈	semidirect
213. C₅×C₈	C₂×C₃×D₄	semidirect
222. C₂²×C₈	C₂×C₃×D₅	semidirect
230. C₂×C₃×C₅	#466	semidirect
241. C₂³×C₃	D₄₀	semidirect
260. C₃×C₈	C₂×C₂²⋊D₅	semidirect
266. C₂²×C₅	C₂×C₃×D₈	semidirect
296. C₂×C₈	C₃×C₂²⋊D₅	semidirect
302. C₃×C₅	C₂×#466	semidirect
311. C₂²×C₃	C₂×D₄₀	semidirect
321. C₂×C₅	C₃×#466	semidirect
332. C₂³	C₃×D₄₀	semidirect
351. C₈	C₂×C₃×C₂²⋊D₅	semidirect
354. C₂×C₃	#65404	direct (N × H)
358. C₅	C₂×C₃×#466	semidirect
367. C₂²	C₂×C₃×D₄₀	semidirect
376. C₃	C₂×#65404	direct (N × H)
379. C₂	C₃×#65404	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅×C₈	2
C₂×C₃×#4076	2
C₂²×C₃×D₄₀	2
C₃×#65404	2
C₂×C₃×#3953	2
C₂×C₃×#3950	2
C₂×#65404	3
C₂×C₃×#466	5

Subgroups — C2×C3×#65404 #14427685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65404 #14427685