Subgroups — C₂×C₃×#65256 #14431405

Order 1920.

1024 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	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4076	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₂²⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65256	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3941	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#3939	C₂	1	2	yes	maximal, complemented
7	C₂×#65256	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂³×C₃×C₄×C₅	—	2	1	no	—
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₂²⋊D₅	—	2	1	no	—
11	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
13	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
16	C₃×#4076	—	2	2	no	—
17	C₃×#4076	C₂²	1	4	yes	—
18	C₂×C₃×#685	—	2	1	no	—
19	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
20	C₂²×C₃×#168	C₂²	1	2	yes	—
21	C₃×C₂²⋊#168	C₂²	1	4	yes	complemented
22	C₃×#3941	C₂²	1	8	yes	complemented
23	C₃×#3939	C₂²	1	8	yes	complemented
24	C₂×C₃×#480	—	5	1	no	maximal, Hall
25	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×#4076	C₂×C₃	1	1	yes	characteristic
27	C₂×C₂²⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
28	#65256	C₂×C₃	1	8	yes	direct product factor
29	C₂×#3941	C₂×C₃	1	2	yes	complemented
30	C₂×#3939	C₂×C₃	1	2	yes	complemented
31	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
32	C₂³×C₃×D₅	—	2	1	no	—
33	C₂²×C₃×C₄×C₅	—	2	4	no	—
34	C₂²×C₃×C₄×C₅	—	2	2	no	—
35	C₂²×C₃×C₄×C₅	—	2	4	no	—
36	C₂²×C₃×C₄×C₅	—	4	4	no	—
37	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
42	C₂×C₃×C₂²⋊D₅	—	4	4	no	—
43	C₂²×C₃×Dic₅	—	2	1	no	—
44	C₂×C₃×D₂₀	—	2	4	no	—
45	C₂×C₃×D₂₀	—	2	1	no	—
46	C₂×C₃×D₂₀	C₂³	1	2	yes	—
47	C₃×C₅×C₄⋊C₄	—	2	2	no	—
48	C₃×C₅×C₄⋊C₄	—	2	4	no	—
49	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
50	C₃×#685	—	2	4	no	—
51	C₃×C₄⋊Dic₅	—	2	1	no	—
52	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
53	C₂×C₃×#168	—	2	4	no	—
54	C₂×C₃×#168	C₂³	1	4	yes	—
55	C₂×C₃×#121	—	5	1	no	—
56	C₂²×C₃×C₄⋊C₄	D₅	1	1	yes	characteristic, complemented
57	C₃×#480	—	5	8	no	—
58	C₂×C₃×#107	—	5	2	no	—
59	C₂×C₃×#102	—	5	2	no	—
60	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
61	C₂³×C₄×C₅	—	2	1	no	—
62	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
63	C₂²×C₂²⋊D₅	—	2	1	no	—
64	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	—	2	2	no	—
66	C₂×C₅×C₄⋊C₄	—	2	1	no	—
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
68	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
69	#4076	—	2	2	no	—
70	#4076	C₂²×C₃	1	4	yes	—
71	C₂×#685	—	2	1	no	—
72	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
73	C₂²×#168	C₂²×C₃	1	2	yes	—
74	C₂²⋊#168	C₂²×C₃	1	4	yes	complemented
75	#3941	C₂²×C₃	1	8	yes	complemented
76	#3939	C₂²×C₃	1	8	yes	complemented
77	C₂×#480	—	5	1	no	Sylow
78	C₂³×C₃×C₅	—	2	2	no	—
79	C₂³×C₃×C₅	—	2	2	no	—
80	C₂³×C₃×C₅	D₈	1	4	yes	—
81	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
82	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₃×D₅	—	2	2	no	—
84	C₂²×C₃×D₅	—	4	2	no	—
85	C₂²×C₃×D₅	—	4	2	no	—
86	C₂²×C₃×D₅	—	4	2	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	2	4	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	4	8	no	—
92	C₂×C₃×C₄×C₅	—	4	4	no	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	#41	1	4	yes	—
96	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
97	C₃×C₂²⋊D₅	—	4	8	no	—
98	C₂×C₃×Dic₅	—	2	2	no	—
99	C₂×C₃×Dic₅	—	4	2	no	—
100	C₃×D₂₀	—	2	4	no	—
101	C₃×D₂₀	—	4	2	no	—
102	C₃×#168	—	2	4	no	—
103	C₂²×C₃×D₄	—	5	1	no	—
104	C₂²×C₃×D₄	—	10	1	no	—
105	C₂³×C₃×C₄	—	2	1	no	—
106	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
107	C₂²×C₃×C₈	—	5	2	no	—
108	C₃×#121	—	5	4	no	—
109	C₃×#121	—	10	2	no	—
110	C₂×C₃×C₄⋊C₄	—	2	2	no	—
111	C₂×C₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₃×C₄⋊C₄	—	5	1	no	—
113	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
114	C₂×C₃×C₄⋊C₄	C₂×D₅	1	4	yes	complemented
115	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
116	C₃×#107	—	5	8	no	—
117	C₃×#102	—	5	8	no	—
118	C₃×C₂²⋊C₈	—	5	4	no	—
119	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
120	C₂³×D₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	4	no	—
122	C₂²×C₄×C₅	—	2	2	no	—
123	C₂²×C₄×C₅	—	2	4	no	—
124	C₂²×C₄×C₅	—	4	4	no	—
125	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
127	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
128	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
129	C₂×C₂²⋊D₅	—	2	4	no	—
130	C₂×C₂²⋊D₅	—	4	4	no	—
131	C₂²×Dic₅	—	2	1	no	—
132	C₂×D₂₀	—	2	4	no	—
133	C₂×D₂₀	—	2	1	no	—
134	C₂×D₂₀	C₂³×C₃	1	2	yes	—
135	C₅×C₄⋊C₄	—	2	2	no	—
136	C₅×C₄⋊C₄	—	2	4	no	—
137	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
138	#685	—	2	4	no	—
139	C₄⋊Dic₅	—	2	1	no	—
140	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
141	C₂×#168	—	2	4	no	—
142	C₂×#168	C₂³×C₃	1	4	yes	—
143	C₂×#121	—	5	1	no	—
144	C₂²×C₄⋊C₄	C₃×D₅	1	1	yes	characteristic, complemented
145	#480	—	5	8	no	—
146	C₂×#107	—	5	2	no	—
147	C₂×#102	—	5	2	no	—
148	C₂×C₂²⋊C₈	—	5	1	no	—
149	C₂²×C₃×C₅	—	2	2	no	—
150	C₂²×C₃×C₅	—	2	2	no	—
151	C₂²×C₃×C₅	—	2	8	no	—
152	C₂²×C₃×C₅	#123	1	2	yes	—
153	C₂²×C₃×C₅	C₂×D₈	1	4	yes	—
154	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
155	C₂²×C₃×C₅	#137	1	2	yes	—
156	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₃×D₅	—	4	2	no	—
158	C₂×C₃×D₅	—	4	2	no	—
159	C₂×C₃×D₅	—	4	2	no	—
160	C₂×C₃×D₅	—	8	4	no	—
161	C₃×C₄×C₅	—	2	2	no	—
162	C₃×C₄×C₅	—	4	4	no	—
163	C₃×C₄×C₅	#123	1	2	yes	—
164	C₃×C₄×C₅	C₂×#41	1	2	yes	—
165	C₃×Dic₅	—	4	2	no	—
166	C₂⁴×C₃	—	10	1	no	—
167	C₂⁴×C₃	C₂²⋊D₅	1	1	yes	characteristic
168	C₂×C₃×D₄	—	5	2	no	—
169	C₂×C₃×D₄	—	10	4	no	—
170	C₂×C₃×D₄	—	10	4	no	—
171	C₂×C₃×D₄	—	10	1	no	—
172	C₂×C₃×D₄	—	20	4	no	—
173	C₂²×C₃×C₄	—	2	4	no	—
174	C₂²×C₃×C₄	—	2	4	no	—
175	C₂²×C₃×C₄	—	2	2	no	—
176	C₂²×C₃×C₄	—	4	4	no	—
177	C₂²×C₃×C₄	—	10	1	no	—
178	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
179	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
181	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
182	C₂×C₃×C₈	—	5	4	no	—
183	C₂×C₃×C₈	—	10	4	no	—
184	C₃×C₄⋊C₄	—	2	2	no	—
185	C₃×C₄⋊C₄	—	2	4	no	—
186	C₃×C₄⋊C₄	—	5	2	no	—
187	C₃×C₄⋊C₄	—	10	1	no	—
188	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
189	C₃×C₂²⋊C₄	—	10	4	no	—
190	C₂³×C₅	—	2	2	no	—
191	C₂³×C₅	—	2	2	no	—
192	C₂³×C₅	C₃×D₈	1	4	yes	—
193	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
194	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
195	C₂²×D₅	—	2	2	no	—
196	C₂²×D₅	—	4	2	no	—
197	C₂²×D₅	—	4	2	no	—
198	C₂²×D₅	—	4	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	4	no	—
201	C₂×C₄×C₅	—	2	4	no	—
202	C₂×C₄×C₅	—	2	4	no	—
203	C₂×C₄×C₅	—	4	8	no	—
204	C₂×C₄×C₅	—	4	4	no	—
205	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
206	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₃×#41	1	4	yes	—
208	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
209	C₂²⋊D₅	—	4	8	no	—
210	C₂×Dic₅	—	2	2	no	—
211	C₂×Dic₅	—	4	2	no	—
212	D₂₀	—	2	4	no	—
213	D₂₀	—	4	2	no	—
214	#168	—	2	4	no	—
215	C₂²×D₄	—	5	1	no	—
216	C₂²×D₄	—	10	1	no	—
217	C₂³×C₄	—	2	1	no	—
218	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
219	C₂²×C₈	—	5	2	no	—
220	#121	—	5	4	no	—
221	#121	—	10	2	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	—	2	1	no	—
224	C₂×C₄⋊C₄	—	5	1	no	—
225	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
226	C₂×C₄⋊C₄	C₂×C₃×D₅	1	4	yes	complemented
227	C₂×C₂²⋊C₄	—	10	1	no	—
228	#107	—	5	8	no	—
229	#102	—	5	8	no	—
230	C₂²⋊C₈	—	5	4	no	—
231	C₂×C₃×C₅	—	2	4	no	—
232	C₂×C₃×C₅	#480	1	4	yes	complemented
233	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
234	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
235	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
236	C₃×D₅	—	8	2	no	—
237	C₂³×C₃	—	2	2	no	—
238	C₂³×C₃	—	2	2	no	—
239	C₂³×C₃	—	10	2	no	—
240	C₂³×C₃	—	20	2	no	—
241	C₂³×C₃	—	20	2	no	—
242	C₂³×C₃	—	20	2	no	—
243	C₂³×C₃	#686	1	4	yes	—
244	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
245	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
246	C₃×D₄	—	10	4	no	—
247	C₃×D₄	—	20	8	no	—
248	C₃×D₄	—	20	2	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	2	4	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	2	4	no	—
253	C₂×C₃×C₄	—	4	8	no	—
254	C₂×C₃×C₄	—	4	4	no	—
255	C₂×C₃×C₄	—	10	2	no	—
256	C₂×C₃×C₄	—	20	2	no	—
257	C₂×C₃×C₄	#709	1	4	yes	—
258	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
259	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
261	C₃×C₈	—	10	4	no	—
262	C₂²×C₅	—	2	2	no	—
263	C₂²×C₅	—	2	2	no	—
264	C₂²×C₅	—	2	8	no	—
265	C₂²×C₅	C₃×#123	1	2	yes	—
266	C₂²×C₅	C₂×C₃×D₈	1	4	yes	—
267	C₂²×C₅	C₂×C₃×D₈	1	2	yes	—
268	C₂²×C₅	C₃×#137	1	2	yes	—
269	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
270	C₂×D₅	—	4	2	no	—
271	C₂×D₅	—	4	2	no	—
272	C₂×D₅	—	4	2	no	—
273	C₂×D₅	—	8	4	no	—
274	C₄×C₅	—	2	2	no	—
275	C₄×C₅	—	4	4	no	—
276	C₄×C₅	C₃×#123	1	2	yes	—
277	C₄×C₅	C₂×C₃×#41	1	2	yes	—
278	Dic₅	—	4	2	no	—
279	C₂⁴	—	10	1	no	—
280	C₂⁴	C₃×C₂²⋊D₅	1	1	yes	characteristic
281	C₂×D₄	—	5	2	no	—
282	C₂×D₄	—	10	4	no	—
283	C₂×D₄	—	10	4	no	—
284	C₂×D₄	—	10	1	no	—
285	C₂×D₄	—	20	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	4	4	no	—
290	C₂²×C₄	—	10	1	no	—
291	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
292	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
293	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
294	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
295	C₂×C₈	—	5	4	no	—
296	C₂×C₈	—	10	4	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	5	2	no	—
300	C₄⋊C₄	—	10	1	no	—
301	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
302	C₂²⋊C₄	—	10	4	no	—
303	C₃×C₅	C₂×#480	1	1	yes	characteristic, complemented, Hall
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	2	8	no	—
307	C₂²×C₃	—	20	2	no	—
308	C₂²×C₃	—	20	2	no	—
309	C₂²×C₃	—	20	2	no	—
310	C₂²×C₃	—	40	4	no	—
311	C₂²×C₃	#4075	1	2	yes	—
312	C₂²×C₃	C₂×#686	1	4	yes	—
313	C₂²×C₃	C₂×#686	1	2	yes	—
314	C₂²×C₃	#4088	1	2	yes	—
315	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
316	C₃×C₄	—	2	2	no	—
317	C₃×C₄	—	4	4	no	—
318	C₃×C₄	—	20	2	no	—
319	C₃×C₄	#4075	1	2	yes	—
320	C₃×C₄	C₂×#709	1	2	yes	—
321	C₂×C₅	—	2	4	no	—
322	C₂×C₅	C₃×#480	1	4	yes	complemented
323	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
324	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
325	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
326	D₅	—	8	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	10	2	no	—
330	C₂³	—	20	2	no	—
331	C₂³	—	20	2	no	—
332	C₂³	—	20	2	no	—
333	C₂³	C₃×#686	1	4	yes	—
334	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
335	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
336	D₄	—	10	4	no	—
337	D₄	—	20	8	no	—
338	D₄	—	20	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	4	8	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	10	2	no	—
346	C₂×C₄	—	20	2	no	—
347	C₂×C₄	C₃×#709	1	4	yes	—
348	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
349	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
350	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
351	C₈	—	10	4	no	—
352	C₂×C₃	—	2	4	no	—
353	C₂×C₃	—	40	2	no	—
354	C₂×C₃	#65256	1	4	yes	direct product factor
355	C₂×C₃	C₂×#4075	1	1	yes	characteristic
356	C₂×C₃	C₂²×#686	1	1	yes	characteristic
357	C₂×C₃	C₂×#4088	1	1	yes	characteristic
358	C₅	C₂×C₃×#480	1	1	yes	characteristic, complemented, Sylow
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	8	no	—
362	C₂²	—	20	2	no	—
363	C₂²	—	20	2	no	—
364	C₂²	—	20	2	no	—
365	C₂²	—	40	4	no	—
366	C₂²	C₃×#4075	1	2	yes	—
367	C₂²	C₂×C₃×#686	1	4	yes	—
368	C₂²	C₂×C₃×#686	1	2	yes	—
369	C₂²	C₃×#4088	1	2	yes	—
370	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
371	C₄	—	2	2	no	—
372	C₄	—	4	4	no	—
373	C₄	—	20	2	no	—
374	C₄	C₃×#4075	1	2	yes	—
375	C₄	C₂×C₃×#709	1	2	yes	—
376	C₃	C₂×#65256	1	1	yes	characteristic, direct product factor, Sylow
377	C₂	—	2	4	no	—
378	C₂	—	40	2	no	—
379	C₂	C₃×#65256	1	4	yes	direct product factor
380	C₂	C₂×C₃×#4075	1	1	yes	characteristic
381	C₂	C₂²×C₃×#686	1	1	yes	characteristic
382	C₂	C₂×C₃×#4088	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂²×C₃×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂×C₃×#4076	C₂
hypercenter	C₂²×C₃×C₄⋊C₄	D₅
hypocenter	C₅	C₂×C₃×#480
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×C₄ ◁ C₂²×C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×C₄⋊C₄	C₂	semidirect
3. C₂×C₃×C₂²⋊#168	C₂	semidirect
4. C₃×#65256	C₂	direct (N × H)
5. C₂×C₃×#3941	C₂	semidirect
6. C₂×C₃×#3939	C₂	semidirect
7. C₂×#65256	C₃	direct (N × H)
15. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
21. C₃×C₂²⋊#168	C₂²	semidirect
22. C₃×#3941	C₂²	semidirect
23. C₃×#3939	C₂²	semidirect
25. C₂²×C₅×C₄⋊C₄	C₂×C₃	semidirect
27. C₂×C₂²⋊#168	C₂×C₃	semidirect
28. #65256	C₂×C₃	direct (N × H)
29. C₂×#3941	C₂×C₃	semidirect
30. C₂×#3939	C₂×C₃	semidirect
56. C₂²×C₃×C₄⋊C₄	D₅	semidirect
68. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
74. C₂²⋊#168	C₂²×C₃	semidirect
75. #3941	C₂²×C₃	semidirect
76. #3939	C₂²×C₃	semidirect
114. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
144. C₂²×C₄⋊C₄	C₃×D₅	semidirect
226. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
232. C₂×C₃×C₅	#480	semidirect
303. C₃×C₅	C₂×#480	semidirect
322. C₂×C₅	C₃×#480	semidirect
354. C₂×C₃	#65256	direct (N × H)
358. C₅	C₂×C₃×#480	semidirect
376. C₃	C₂×#65256	direct (N × H)
379. C₂	C₃×#65256	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×C₅×C₄⋊C₄	2
C₂×C₃×#4076	2
C₂×C₃×C₂²⋊#168	2
C₃×#65256	2
C₂×C₃×#3941	2
C₂×C₃×#3939	2
C₂×#65256	3
C₂×C₃×#480	5

Subgroups — C2×C3×#65256 #14431405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65256 #14431405