Subgroups — C₃×C₄×#3955 #14295420

Order 1920.

720 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	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3955	C₂	1	2	yes	maximal
4	C₃×C₄×#681	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64774	C₂	1	2	yes	maximal, complemented
6	C₄×#3955	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₄×D₅	C₄	1	2	yes	—
9	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂×C₃×#685	C₄	1	2	yes	—
12	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
13	C₂×C₃×#681	C₂²	1	2	yes	—
14	C₃×C₄×D₂₀	—	2	1	no	—
15	C₃×C₄×D₂₀	—	2	1	no	—
16	C₃×C₄×D₂₀	—	2	1	no	—
17	C₃×C₄×D₂₀	—	2	1	no	—
18	C₃×C₅×#97	—	2	1	no	—
19	C₃×C₄×C₅×C₈	—	2	1	no	—
20	C₃×#3955	C₄	1	8	yes	direct product factor
21	C₃×#3935	—	2	1	no	—
22	C₃×C₄×#168	—	2	1	no	—
23	C₃×C₄×#100	—	5	1	no	maximal, Hall
24	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic
25	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×#3955	C₂×C₃	1	2	yes	—
27	C₄×#681	C₂×C₃	1	1	yes	characteristic, complemented
28	#64774	C₂×C₃	1	2	yes	complemented
29	C₂³×C₃×D₅	C₂×C₄	1	2	yes	—
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
33	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
34	C₂×C₃×D₂₀	—	2	1	no	—
35	C₂×C₃×D₂₀	—	2	1	no	—
36	C₂×C₃×D₂₀	—	2	2	no	—
37	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	—
38	C₂×C₃×C₄×D₅	—	2	2	no	—
39	C₂×C₃×C₄×D₅	—	2	2	no	—
40	C₂×C₃×C₄×D₅	—	4	4	no	—
41	C₃×C₅×M₁₆	—	2	2	no	—
42	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
43	C₂×C₃×C₅×C₈	—	2	2	no	—
44	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
45	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
46	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
47	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
48	C₃×#685	—	2	2	no	—
49	C₃×#685	—	2	2	no	—
50	C₃×C₄⋊Dic₅	—	2	1	no	—
51	C₃×C₄⋊Dic₅	—	2	1	no	—
52	C₃×#681	—	2	2	no	—
53	C₃×#681	C₂×C₄	1	4	yes	complemented
54	C₂×C₃×#168	—	2	2	no	—
55	C₂×C₃×C₄×D₄	—	5	1	no	—
56	C₂×C₃×#100	—	5	2	no	—
57	C₃×C₄×M₁₆	—	5	1	no	—
58	C₃×C₄×M₁₆	D₅	1	1	yes	characteristic, complemented
59	C₃×#343	—	5	2	no	—
60	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
61	C₂²×C₄×D₅	C₃×C₄	1	2	yes	—
62	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
63	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
64	C₂×#685	C₃×C₄	1	2	yes	—
65	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
66	C₂×#681	C₂²×C₃	1	2	yes	—
67	C₄×D₂₀	—	2	1	no	—
68	C₄×D₂₀	—	2	1	no	—
69	C₄×D₂₀	—	2	1	no	—
70	C₄×D₂₀	—	2	1	no	—
71	C₅×#97	—	2	1	no	—
72	C₄×C₅×C₈	—	2	1	no	—
73	#3955	C₃×C₄	1	8	yes	direct product factor
74	#3935	—	2	1	no	—
75	C₄×#168	—	2	1	no	—
76	C₄×#100	—	5	1	no	Sylow
77	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₃×D₅	—	2	2	no	—
79	C₂²×C₃×D₅	—	2	2	no	—
80	C₂²×C₃×D₅	—	4	2	no	—
81	C₂²×C₃×D₅	—	4	2	no	—
82	C₂²×C₃×D₅	C₄²	1	4	yes	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	4	1	no	—
85	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
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	2	yes	—
93	C₂×C₃×Dic₅	—	2	2	no	—
94	C₂×C₃×Dic₅	—	4	2	no	—
95	C₃×D₂₀	—	2	4	no	—
96	C₃×D₂₀	—	2	4	no	—
97	C₃×C₄×D₅	—	4	4	no	—
98	C₃×C₄×D₅	—	4	4	no	—
99	C₃×C₅×C₈	—	2	4	no	—
100	C₃×#168	—	2	4	no	—
101	C₂²×C₃×D₄	—	5	1	no	—
102	C₂³×C₃×C₄	—	5	2	no	—
103	C₂×C₃×M₁₆	—	5	2	no	—
104	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	—
105	C₃×C₄×D₄	—	10	1	no	—
106	C₃×C₄×D₄	—	10	1	no	—
107	C₃×C₄×D₄	—	10	1	no	—
108	C₃×C₄×D₄	—	10	1	no	—
109	C₂×C₃×C₄⋊C₄	—	5	1	no	—
110	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
111	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
112	C₃×#100	—	5	8	no	—
113	C₃×#97	—	2	1	no	—
114	C₃×#97	—	10	1	no	—
115	C₃×C₄×C₈	—	2	1	no	—
116	C₃×C₄×C₈	—	10	1	no	—
117	C₂³×D₅	C₂×C₃×C₄	1	2	yes	—
118	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
121	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
122	C₂×D₂₀	—	2	1	no	—
123	C₂×D₂₀	—	2	1	no	—
124	C₂×D₂₀	—	2	2	no	—
125	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	—
126	C₂×C₄×D₅	—	2	2	no	—
127	C₂×C₄×D₅	—	2	2	no	—
128	C₂×C₄×D₅	—	4	4	no	—
129	C₅×M₁₆	—	2	2	no	—
130	C₅×M₁₆	C₂×C₃×C₄	1	4	yes	complemented
131	C₂×C₅×C₈	—	2	2	no	—
132	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
133	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
134	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
135	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
136	#685	—	2	2	no	—
137	#685	—	2	2	no	—
138	C₄⋊Dic₅	—	2	1	no	—
139	C₄⋊Dic₅	—	2	1	no	—
140	#681	—	2	2	no	—
141	#681	C₂×C₃×C₄	1	4	yes	complemented
142	C₂×#168	—	2	2	no	—
143	C₂×C₄×D₄	—	5	1	no	—
144	C₂×#100	—	5	2	no	—
145	C₄×M₁₆	—	5	1	no	—
146	C₄×M₁₆	C₃×D₅	1	1	yes	characteristic, complemented
147	#343	—	5	2	no	—
148	C₂²×C₃×C₅	—	2	1	no	—
149	C₂²×C₃×C₅	—	2	1	no	—
150	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
151	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₃×C₅	#117	1	1	yes	characteristic
153	C₂×C₃×D₅	—	2	4	no	—
154	C₂×C₃×D₅	—	4	4	no	—
155	C₂×C₃×D₅	—	4	2	no	—
156	C₂×C₃×D₅	—	4	2	no	—
157	C₂×C₃×D₅	—	4	4	no	—
158	C₃×C₄×C₅	—	2	1	no	—
159	C₃×C₄×C₅	—	2	1	no	—
160	C₃×C₄×C₅	—	2	1	no	—
161	C₃×C₄×C₅	#100	1	2	yes	complemented
162	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
163	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
164	C₃×Dic₅	—	4	2	no	—
165	C₂⁴×C₃	—	5	2	no	—
166	C₂×C₃×D₄	—	5	4	no	—
167	C₂×C₃×D₄	—	10	1	no	—
168	C₂×C₃×D₄	—	10	2	no	—
169	C₂×C₃×D₄	—	10	1	no	—
170	C₂²×C₃×C₄	—	5	2	no	—
171	C₂²×C₃×C₄	—	10	2	no	—
172	C₂²×C₃×C₄	—	10	2	no	—
173	C₂²×C₃×C₄	—	20	4	no	—
174	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
177	C₃×M₁₆	—	2	2	no	—
178	C₃×M₁₆	—	5	4	no	—
179	C₃×M₁₆	—	10	2	no	—
180	C₃×M₁₆	C₄×D₅	1	4	yes	complemented
181	C₂×C₃×C₈	—	2	2	no	—
182	C₂×C₃×C₈	—	10	2	no	—
183	C₃×C₄⋊C₄	—	10	1	no	—
184	C₃×C₄⋊C₄	—	10	1	no	—
185	C₃×C₂²⋊C₄	—	10	2	no	—
186	C₃×C₂²⋊C₄	—	10	2	no	—
187	C₃×C₄²	D₂₀	1	1	yes	characteristic
188	C₃×C₄²	D₂₀	1	1	yes	characteristic
189	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
190	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
191	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
192	C₂²×D₅	—	2	2	no	—
193	C₂²×D₅	—	2	2	no	—
194	C₂²×D₅	—	4	2	no	—
195	C₂²×D₅	—	4	2	no	—
196	C₂²×D₅	C₃×C₄²	1	4	yes	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	4	1	no	—
199	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
204	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
206	C₂×C₄×C₅	C₃×#41	1	2	yes	—
207	C₂×Dic₅	—	2	2	no	—
208	C₂×Dic₅	—	4	2	no	—
209	D₂₀	—	2	4	no	—
210	D₂₀	—	2	4	no	—
211	C₄×D₅	—	4	4	no	—
212	C₄×D₅	—	4	4	no	—
213	C₅×C₈	—	2	4	no	—
214	#168	—	2	4	no	—
215	C₂²×D₄	—	5	1	no	—
216	C₂³×C₄	—	5	2	no	—
217	C₂×M₁₆	—	5	2	no	—
218	C₂×M₁₆	C₂×C₃×D₅	1	2	yes	—
219	C₄×D₄	—	10	1	no	—
220	C₄×D₄	—	10	1	no	—
221	C₄×D₄	—	10	1	no	—
222	C₄×D₄	—	10	1	no	—
223	C₂×C₄⋊C₄	—	5	1	no	—
224	C₂×C₂²⋊C₄	—	5	2	no	—
225	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
226	#100	—	5	8	no	—
227	#97	—	2	1	no	—
228	#97	—	10	1	no	—
229	C₄×C₈	—	2	1	no	—
230	C₄×C₈	—	10	1	no	—
231	C₂×C₃×C₅	—	2	1	no	—
232	C₂×C₃×C₅	—	2	1	no	—
233	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
235	C₂×C₃×C₅	#413	1	1	yes	characteristic
236	C₃×D₅	—	4	4	no	—
237	C₂³×C₃	—	5	4	no	—
238	C₂³×C₃	—	10	2	no	—
239	C₂³×C₃	—	10	2	no	—
240	C₂³×C₃	—	20	2	no	—
241	C₂³×C₃	—	20	2	no	—
242	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
243	C₃×D₄	—	10	4	no	—
244	C₃×D₄	—	10	4	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	4	1	no	—
247	C₂×C₃×C₄	—	10	2	no	—
248	C₂×C₃×C₄	—	20	4	no	—
249	C₂×C₃×C₄	—	20	4	no	—
250	C₂×C₃×C₄	—	20	2	no	—
251	C₂×C₃×C₄	#685	1	1	yes	characteristic
252	C₂×C₃×C₄	#685	1	1	yes	characteristic
253	C₂×C₃×C₄	#685	1	1	yes	characteristic
254	C₂×C₃×C₄	#685	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
256	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
257	C₂×C₃×C₄	#709	1	2	yes	—
258	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
259	C₃×C₈	—	2	4	no	—
260	C₃×C₈	—	10	4	no	—
261	C₂²×C₅	—	2	1	no	—
262	C₂²×C₅	—	2	1	no	—
263	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
264	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
265	C₂²×C₅	C₃×#117	1	1	yes	characteristic
266	C₂×D₅	—	2	4	no	—
267	C₂×D₅	—	4	4	no	—
268	C₂×D₅	—	4	2	no	—
269	C₂×D₅	—	4	2	no	—
270	C₂×D₅	—	4	4	no	—
271	C₄×C₅	—	2	1	no	—
272	C₄×C₅	—	2	1	no	—
273	C₄×C₅	—	2	1	no	—
274	C₄×C₅	C₃×#100	1	2	yes	complemented
275	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
276	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
277	Dic₅	—	4	2	no	—
278	C₂⁴	—	5	2	no	—
279	C₂×D₄	—	5	4	no	—
280	C₂×D₄	—	10	1	no	—
281	C₂×D₄	—	10	2	no	—
282	C₂×D₄	—	10	1	no	—
283	C₂²×C₄	—	5	2	no	—
284	C₂²×C₄	—	10	2	no	—
285	C₂²×C₄	—	10	2	no	—
286	C₂²×C₄	—	20	4	no	—
287	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
288	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
289	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
290	M₁₆	—	2	2	no	—
291	M₁₆	—	5	4	no	—
292	M₁₆	—	10	2	no	—
293	M₁₆	C₃×C₄×D₅	1	4	yes	complemented
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	10	2	no	—
296	C₄⋊C₄	—	10	1	no	—
297	C₄⋊C₄	—	10	1	no	—
298	C₂²⋊C₄	—	10	2	no	—
299	C₂²⋊C₄	—	10	2	no	—
300	C₄²	C₃×D₂₀	1	1	yes	characteristic
301	C₄²	C₃×D₂₀	1	1	yes	characteristic
302	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
303	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
304	C₃×C₅	C₄×#100	1	1	yes	characteristic, complemented, Hall
305	C₂²×C₃	—	2	1	no	—
306	C₂²×C₃	—	2	1	no	—
307	C₂²×C₃	—	10	4	no	—
308	C₂²×C₃	—	20	4	no	—
309	C₂²×C₃	—	20	4	no	—
310	C₂²×C₃	—	20	2	no	—
311	C₂²×C₃	—	20	2	no	—
312	C₂²×C₃	C₄²×D₅	1	1	yes	characteristic
313	C₂²×C₃	#4018	1	1	yes	characteristic
314	C₂²×C₃	C₂×#685	1	1	yes	characteristic
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	20	2	no	—
319	C₃×C₄	#3955	1	2	yes	direct product factor
320	C₃×C₄	C₄×D₂₀	1	2	yes	—
321	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
322	C₂×C₅	—	2	1	no	—
323	C₂×C₅	—	2	1	no	—
324	C₂×C₅	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
325	C₂×C₅	C₂×C₃×#100	1	1	yes	characteristic
326	C₂×C₅	C₃×#413	1	1	yes	characteristic
327	D₅	—	4	4	no	—
328	C₂³	—	5	4	no	—
329	C₂³	—	10	2	no	—
330	C₂³	—	10	2	no	—
331	C₂³	—	20	2	no	—
332	C₂³	—	20	2	no	—
333	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
334	D₄	—	10	4	no	—
335	D₄	—	10	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	10	2	no	—
339	C₂×C₄	—	20	4	no	—
340	C₂×C₄	—	20	4	no	—
341	C₂×C₄	—	20	2	no	—
342	C₂×C₄	C₃×#685	1	1	yes	characteristic
343	C₂×C₄	C₃×#685	1	1	yes	characteristic
344	C₂×C₄	C₃×#685	1	1	yes	characteristic
345	C₂×C₄	C₃×#685	1	1	yes	characteristic
346	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
347	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
348	C₂×C₄	C₃×#709	1	2	yes	—
349	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
350	C₈	—	2	4	no	—
351	C₈	—	10	4	no	—
352	C₂×C₃	—	2	1	no	—
353	C₂×C₃	—	2	1	no	—
354	C₂×C₃	—	20	4	no	—
355	C₂×C₃	C₄×#685	1	1	yes	characteristic
356	C₂×C₃	C₂×#3955	1	1	yes	characteristic
357	C₂×C₃	#65421	1	1	yes	characteristic
358	C₅	C₃×C₄×#100	1	1	yes	characteristic, complemented, Sylow
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	10	4	no	—
362	C₂²	—	20	4	no	—
363	C₂²	—	20	4	no	—
364	C₂²	—	20	2	no	—
365	C₂²	—	20	2	no	—
366	C₂²	C₃×C₄²×D₅	1	1	yes	characteristic
367	C₂²	C₃×#4018	1	1	yes	characteristic
368	C₂²	C₂×C₃×#685	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	20	2	no	—
373	C₄	C₃×#3955	1	2	yes	direct product factor
374	C₄	C₃×C₄×D₂₀	1	2	yes	—
375	C₄	C₃×C₄×C₂²⋊D₅	1	2	yes	—
376	C₃	C₄×#3955	1	1	yes	characteristic, direct product factor, Sylow
377	C₂	—	2	1	no	—
378	C₂	—	2	1	no	—
379	C₂	—	20	4	no	—
380	C₂	C₃×C₄×#685	1	1	yes	characteristic
381	C₂	C₂×C₃×#3955	1	1	yes	characteristic
382	C₂	C₃×#65421	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	#685
commutator	C₂²×C₅	C₂×C₃×C₄²
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₃×C₄×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂²×C₃×D₂₀	C₂²
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₃×C₄×M₁₆	D₅
hypocenter	C₅	C₃×C₄×#100
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×M₁₆	C₂	semidirect
4. C₃×C₄×#681	C₂	semidirect
5. C₃×#64774	C₂	semidirect
6. C₄×#3955	C₃	direct (N × H)
20. C₃×#3955	C₄	direct (N × H)
25. C₄×C₅×M₁₆	C₂×C₃	semidirect
27. C₄×#681	C₂×C₃	semidirect
28. #64774	C₂×C₃	semidirect
42. C₃×C₅×M₁₆	C₂×C₄	semidirect
53. C₃×#681	C₂×C₄	semidirect
58. C₃×C₄×M₁₆	D₅	semidirect
73. #3955	C₃×C₄	direct (N × H)
130. C₅×M₁₆	C₂×C₃×C₄	semidirect
141. #681	C₂×C₃×C₄	semidirect
146. C₄×M₁₆	C₃×D₅	semidirect
161. C₃×C₄×C₅	#100	semidirect
180. C₃×M₁₆	C₄×D₅	semidirect
274. C₄×C₅	C₃×#100	semidirect
293. M₁₆	C₃×C₄×D₅	semidirect
304. C₃×C₅	C₄×#100	semidirect
319. C₃×C₄	#3955	direct (N × H)
358. C₅	C₃×C₄×#100	semidirect
373. C₄	C₃×#3955	direct (N × H)
376. C₃	C₄×#3955	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×C₄×D₂₀	2
C₃×C₄×C₅×M₁₆	2
C₂×C₃×#3955	2
C₃×C₄×#681	2
C₃×#64774	2
C₄×#3955	3
C₃×C₄×#100	5

Subgroups — C3×C4×#3955 #14295420

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#3955 #14295420