Subgroups — C₃×M₁₆×D₂₀ #14415688

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×M₁₆	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65415	C₂	1	2	yes	maximal, complemented
5	C₃×#65213	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64995	C₂	1	4	yes	maximal, complemented
7	C₃×#64977	C₂	1	2	yes	maximal, complemented
8	C₃×C₈×D₂₀	C₂	1	2	yes	maximal, complemented
9	M₁₆×D₂₀	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×D₂₀	C₄	1	1	yes	characteristic
11	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×#685	C₄	1	2	yes	—
16	C₂×C₃×C₄⋊Dic₅	C₄	1	1	yes	characteristic
17	C₂×C₃×#681	C₂²	1	2	yes	—
18	C₃×D₅×M₁₆	—	2	8	no	—
19	C₂×C₃×#676	C₂²	1	4	yes	complemented
20	C₂×C₃×C₈×D₅	C₂²	1	4	yes	complemented
21	C₃×C₄×D₂₀	C₄	1	2	yes	—
22	C₃×C₄×D₂₀	C₄	1	1	yes	characteristic
23	C₃×C₄×D₂₀	C₄	1	1	yes	characteristic
24	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
25	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
26	C₃×C₄×D₂₀	C₂²	1	2	yes	—
27	C₃×C₅×#97	C₂²	1	2	yes	complemented
28	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
29	C₃×#3952	C₂²	1	4	yes	complemented
30	C₃×#3952	C₂²	1	4	yes	complemented
31	C₃×C₄⋊#168	C₂²	1	2	yes	complemented
32	C₃×C₄⋊#168	C₂²	1	2	yes	complemented
33	C₃×D₄×M₁₆	—	5	1	no	maximal, Hall
34	C₂×D₅×M₁₆	C₂×C₃	1	2	yes	complemented
35	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic
36	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
37	#65415	C₂×C₃	1	2	yes	complemented
38	#65213	C₂×C₃	1	1	yes	characteristic, complemented
39	#64995	C₂×C₃	1	4	yes	complemented
40	#64977	C₂×C₃	1	2	yes	complemented
41	C₈×D₂₀	C₂×C₃	1	2	yes	complemented
42	C₂³×C₃×D₅	C₂×C₄	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
47	C₂×C₃×D₂₀	—	2	4	no	—
48	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
49	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₄×D₅	—	2	4	no	—
52	C₂×C₃×C₄×D₅	—	2	4	no	—
53	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
54	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
55	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
56	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
57	C₃×C₅×M₁₆	—	2	2	no	—
58	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
59	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
60	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
61	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
62	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
63	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
64	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
65	C₃×#685	C₂×C₄	1	2	yes	—
66	C₃×#685	C₂×C₄	1	2	yes	—
67	C₃×#685	C₂×C₄	1	2	yes	—
68	C₃×#685	C₂×C₄	1	2	yes	—
69	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
70	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
71	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
72	C₃×#681	—	2	4	no	—
73	C₂×C₃×#168	C₂³	1	4	yes	—
74	C₃×#676	—	2	8	no	—
75	C₃×C₈×D₅	—	2	8	no	—
76	C₂²×C₃×M₁₆	—	5	2	no	—
77	C₂×C₃×C₄×D₄	—	5	1	no	—
78	C₃×#436	—	5	2	no	—
79	C₃×#435	—	5	4	no	—
80	C₃×C₈×D₄	—	5	2	no	—
81	C₃×#423	—	5	1	no	—
82	C₃×#407	—	5	2	no	—
83	C₃×C₄×M₁₆	D₅	1	1	yes	characteristic, complemented
84	C₂²×D₂₀	C₃×C₄	1	1	yes	characteristic
85	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
86	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
89	C₂×#685	C₃×C₄	1	2	yes	—
90	C₂×C₄⋊Dic₅	C₃×C₄	1	1	yes	characteristic
91	C₂×#681	C₂²×C₃	1	2	yes	—
92	D₅×M₁₆	—	2	8	no	—
93	C₂×#676	C₂²×C₃	1	4	yes	complemented
94	C₂×C₈×D₅	C₂²×C₃	1	4	yes	complemented
95	C₄×D₂₀	C₃×C₄	1	2	yes	—
96	C₄×D₂₀	C₃×C₄	1	1	yes	characteristic
97	C₄×D₂₀	C₃×C₄	1	1	yes	characteristic
98	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
99	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
100	C₄×D₂₀	C₂²×C₃	1	2	yes	—
101	C₅×#97	C₂²×C₃	1	2	yes	complemented
102	C₄×C₅×C₈	C₂²×C₃	1	2	yes	complemented
103	#3952	C₂²×C₃	1	4	yes	complemented
104	#3952	C₂²×C₃	1	4	yes	complemented
105	C₄⋊#168	C₂²×C₃	1	2	yes	complemented
106	C₄⋊#168	C₂²×C₃	1	2	yes	complemented
107	D₄×M₁₆	—	5	1	no	Sylow
108	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₃×D₅	—	2	4	no	—
110	C₂²×C₃×D₅	—	2	4	no	—
111	C₂²×C₃×D₅	—	4	2	no	—
112	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
113	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	4	1	no	—
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	#41	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
124	C₂×C₃×Dic₅	—	2	4	no	—
125	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
126	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
127	C₃×D₂₀	—	2	4	no	—
128	C₃×D₂₀	—	2	2	no	—
129	C₃×D₂₀	M₁₆	1	4	yes	direct product factor
130	C₃×C₄×D₅	—	2	4	no	—
131	C₃×C₄×D₅	—	2	4	no	—
132	C₃×C₄×D₅	—	2	2	no	—
133	C₃×C₄×D₅	—	2	2	no	—
134	C₃×C₄×D₅	—	2	2	no	—
135	C₃×C₄×D₅	—	2	2	no	—
136	C₃×C₅×C₈	—	2	2	no	—
137	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
138	C₃×#168	—	2	4	no	—
139	C₂²×C₃×D₄	—	5	1	no	—
140	C₂³×C₃×C₄	—	5	2	no	—
141	C₂×C₃×M₁₆	—	5	2	no	—
142	C₂×C₃×M₁₆	—	5	4	no	—
143	C₂×C₃×M₁₆	—	10	8	no	—
144	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
145	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
146	C₂²×C₃×C₈	—	5	4	no	—
147	C₃×C₄×D₄	—	5	1	no	—
148	C₃×C₄×D₄	—	5	2	no	—
149	C₃×C₄×D₄	—	5	1	no	—
150	C₃×C₄×D₄	—	5	1	no	—
151	C₃×C₄×D₄	—	5	2	no	—
152	C₃×C₄×D₄	—	5	1	no	—
153	C₂×C₃×C₄⋊C₄	—	5	1	no	—
154	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
155	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
156	C₃×C₄⋊C₈	—	5	2	no	—
157	C₃×C₄⋊C₈	—	5	2	no	—
158	C₃×C₂²⋊C₈	—	5	4	no	—
159	C₃×C₂²⋊C₈	—	5	4	no	—
160	C₃×#97	C₂×D₅	1	2	yes	complemented
161	C₃×C₄×C₈	C₂×D₅	1	2	yes	complemented
162	C₂³×D₅	C₂×C₃×C₄	1	2	yes	—
163	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
166	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
167	C₂×D₂₀	—	2	4	no	—
168	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
169	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
170	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
171	C₂×C₄×D₅	—	2	4	no	—
172	C₂×C₄×D₅	—	2	4	no	—
173	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
174	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
175	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
176	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
177	C₅×M₁₆	—	2	2	no	—
178	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
179	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
180	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
181	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
182	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
183	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
184	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
185	#685	C₂×C₃×C₄	1	2	yes	—
186	#685	C₂×C₃×C₄	1	2	yes	—
187	#685	C₂×C₃×C₄	1	2	yes	—
188	#685	C₂×C₃×C₄	1	2	yes	—
189	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
190	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
191	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
192	#681	—	2	4	no	—
193	C₂×#168	C₂³×C₃	1	4	yes	—
194	#676	—	2	8	no	—
195	C₈×D₅	—	2	8	no	—
196	C₂²×M₁₆	—	5	2	no	—
197	C₂×C₄×D₄	—	5	1	no	—
198	#436	—	5	2	no	—
199	#435	—	5	4	no	—
200	C₈×D₄	—	5	2	no	—
201	#423	—	5	1	no	—
202	#407	—	5	2	no	—
203	C₄×M₁₆	C₃×D₅	1	1	yes	characteristic, complemented
204	C₂²×C₃×C₅	—	2	1	no	—
205	C₂²×C₃×C₅	—	2	1	no	—
206	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
207	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₃×D₅	—	2	2	no	—
209	C₂×C₃×D₅	—	2	2	no	—
210	C₂×C₃×D₅	—	2	2	no	—
211	C₂×C₃×D₅	—	2	2	no	—
212	C₂×C₃×D₅	—	2	2	no	—
213	C₂×C₃×D₅	—	4	8	no	—
214	C₂×C₃×D₅	C₂×M₁₆	1	4	yes	complemented
215	C₃×C₄×C₅	—	2	1	no	—
216	C₃×C₄×C₅	—	2	1	no	—
217	C₃×C₄×C₅	—	2	1	no	—
218	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
219	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	complemented
220	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
221	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
222	C₃×Dic₅	—	2	2	no	—
223	C₃×Dic₅	—	2	2	no	—
224	C₂⁴×C₃	—	5	2	no	—
225	C₂×C₃×D₄	—	5	1	no	—
226	C₂×C₃×D₄	—	5	2	no	—
227	C₂×C₃×D₄	—	5	1	no	—
228	C₂×C₃×D₄	—	10	4	no	—
229	C₂²×C₃×C₄	—	5	2	no	—
230	C₂²×C₃×C₄	—	5	2	no	—
231	C₂²×C₃×C₄	—	5	2	no	—
232	C₂²×C₃×C₄	—	5	2	no	—
233	C₂²×C₃×C₄	—	5	2	no	—
234	C₂²×C₃×C₄	—	10	4	no	—
235	C₂²×C₃×C₄	—	10	4	no	—
236	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
237	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
238	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
239	C₃×M₁₆	—	2	2	no	—
240	C₃×M₁₆	—	10	4	no	—
241	C₃×M₁₆	—	10	8	no	—
242	C₃×M₁₆	D₂₀	1	4	yes	direct product factor
243	C₂×C₃×C₈	—	5	4	no	—
244	C₂×C₃×C₈	—	10	8	no	—
245	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
246	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
247	C₃×C₄⋊C₄	—	5	2	no	—
248	C₃×C₄⋊C₄	—	5	1	no	—
249	C₃×C₄⋊C₄	—	5	1	no	—
250	C₃×C₂²⋊C₄	—	5	2	no	—
251	C₃×C₂²⋊C₄	—	5	2	no	—
252	C₃×C₂²⋊C₄	—	5	2	no	—
253	C₃×C₂²⋊C₄	—	5	2	no	—
254	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
255	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
256	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
257	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
258	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
259	C₂²×D₅	—	2	4	no	—
260	C₂²×D₅	—	2	4	no	—
261	C₂²×D₅	—	4	2	no	—
262	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
263	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	4	1	no	—
266	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
272	C₂×C₄×C₅	C₃×#41	1	2	yes	—
273	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
274	C₂×Dic₅	—	2	4	no	—
275	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
276	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
277	D₂₀	—	2	4	no	—
278	D₂₀	—	2	2	no	—
279	D₂₀	C₃×M₁₆	1	4	yes	direct product factor
280	C₄×D₅	—	2	4	no	—
281	C₄×D₅	—	2	4	no	—
282	C₄×D₅	—	2	2	no	—
283	C₄×D₅	—	2	2	no	—
284	C₄×D₅	—	2	2	no	—
285	C₄×D₅	—	2	2	no	—
286	C₅×C₈	—	2	2	no	—
287	C₅×C₈	C₂×C₃×D₄	1	4	yes	complemented
288	#168	—	2	4	no	—
289	C₂²×D₄	—	5	1	no	—
290	C₂³×C₄	—	5	2	no	—
291	C₂×M₁₆	—	5	2	no	—
292	C₂×M₁₆	—	5	4	no	—
293	C₂×M₁₆	—	10	8	no	—
294	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
295	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
296	C₂²×C₈	—	5	4	no	—
297	C₄×D₄	—	5	1	no	—
298	C₄×D₄	—	5	2	no	—
299	C₄×D₄	—	5	1	no	—
300	C₄×D₄	—	5	1	no	—
301	C₄×D₄	—	5	2	no	—
302	C₄×D₄	—	5	1	no	—
303	C₂×C₄⋊C₄	—	5	1	no	—
304	C₂×C₂²⋊C₄	—	5	2	no	—
305	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
306	C₄⋊C₈	—	5	2	no	—
307	C₄⋊C₈	—	5	2	no	—
308	C₂²⋊C₈	—	5	4	no	—
309	C₂²⋊C₈	—	5	4	no	—
310	#97	C₂×C₃×D₅	1	2	yes	complemented
311	C₄×C₈	C₂×C₃×D₅	1	2	yes	complemented
312	C₂×C₃×C₅	—	2	2	no	—
313	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
314	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
315	C₂×C₃×C₅	#568	1	1	yes	characteristic
316	C₃×D₅	—	2	4	no	—
317	C₃×D₅	—	4	2	no	—
318	C₂³×C₃	—	5	2	no	—
319	C₂³×C₃	—	5	2	no	—
320	C₂³×C₃	—	10	4	no	—
321	C₂³×C₃	—	10	4	no	—
322	C₂³×C₃	—	20	2	no	—
323	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
324	C₃×D₄	—	5	4	no	—
325	C₃×D₄	—	10	4	no	—
326	C₃×D₄	—	10	2	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	4	1	no	—
329	C₂×C₃×C₄	—	5	2	no	—
330	C₂×C₃×C₄	—	5	2	no	—
331	C₂×C₃×C₄	—	10	4	no	—
332	C₂×C₃×C₄	—	10	2	no	—
333	C₂×C₃×C₄	—	10	2	no	—
334	C₂×C₃×C₄	—	10	2	no	—
335	C₂×C₃×C₄	—	10	2	no	—
336	C₂×C₃×C₄	—	10	4	no	—
337	C₂×C₃×C₄	—	10	4	no	—
338	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
341	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
343	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
344	C₂×C₃×C₄	#709	1	2	yes	—
345	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
346	C₃×C₈	—	2	2	no	—
347	C₃×C₈	—	10	4	no	—
348	C₃×C₈	C₂×D₂₀	1	4	yes	complemented
349	C₂²×C₅	—	2	1	no	—
350	C₂²×C₅	—	2	1	no	—
351	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
352	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
353	C₂×D₅	—	2	2	no	—
354	C₂×D₅	—	2	2	no	—
355	C₂×D₅	—	2	2	no	—
356	C₂×D₅	—	2	2	no	—
357	C₂×D₅	—	2	2	no	—
358	C₂×D₅	—	4	8	no	—
359	C₂×D₅	C₂×C₃×M₁₆	1	4	yes	complemented
360	C₄×C₅	—	2	1	no	—
361	C₄×C₅	—	2	1	no	—
362	C₄×C₅	—	2	1	no	—
363	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
364	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	complemented
365	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
366	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
367	Dic₅	—	2	2	no	—
368	Dic₅	—	2	2	no	—
369	C₂⁴	—	5	2	no	—
370	C₂×D₄	—	5	1	no	—
371	C₂×D₄	—	5	2	no	—
372	C₂×D₄	—	5	1	no	—
373	C₂×D₄	—	10	4	no	—
374	C₂²×C₄	—	5	2	no	—
375	C₂²×C₄	—	5	2	no	—
376	C₂²×C₄	—	5	2	no	—
377	C₂²×C₄	—	5	2	no	—
378	C₂²×C₄	—	5	2	no	—
379	C₂²×C₄	—	10	4	no	—
380	C₂²×C₄	—	10	4	no	—
381	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
382	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
383	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
384	M₁₆	—	2	2	no	—
385	M₁₆	—	10	4	no	—
386	M₁₆	—	10	8	no	—
387	M₁₆	C₃×D₂₀	1	4	yes	direct product factor
388	C₂×C₈	—	5	4	no	—
389	C₂×C₈	—	10	8	no	—
390	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
391	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
392	C₄⋊C₄	—	5	2	no	—
393	C₄⋊C₄	—	5	1	no	—
394	C₄⋊C₄	—	5	1	no	—
395	C₂²⋊C₄	—	5	2	no	—
396	C₂²⋊C₄	—	5	2	no	—
397	C₂²⋊C₄	—	5	2	no	—
398	C₂²⋊C₄	—	5	2	no	—
399	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
400	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
401	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
402	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
403	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
404	C₂²×C₃	—	2	1	no	—
405	C₂²×C₃	—	2	1	no	—
406	C₂²×C₃	—	5	4	no	—
407	C₂²×C₃	—	10	2	no	—
408	C₂²×C₃	—	10	2	no	—
409	C₂²×C₃	—	10	2	no	—
410	C₂²×C₃	—	10	2	no	—
411	C₂²×C₃	—	10	2	no	—
412	C₂²×C₃	—	20	8	no	—
413	C₂²×C₃	C₄×D₂₀	1	2	yes	—
414	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	2	1	no	—
417	C₃×C₄	—	2	1	no	—
418	C₃×C₄	—	10	2	no	—
419	C₃×C₄	—	10	2	no	—
420	C₃×C₄	C₄×D₂₀	1	2	yes	—
421	C₃×C₄	D₅×M₁₆	1	2	yes	complemented
422	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
423	C₃×C₄	C₂×#709	1	1	yes	characteristic
424	C₂×C₅	—	2	2	no	—
425	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
426	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
427	C₂×C₅	C₃×#568	1	1	yes	characteristic
428	D₅	—	2	4	no	—
429	D₅	—	4	2	no	—
430	C₂³	—	5	2	no	—
431	C₂³	—	5	2	no	—
432	C₂³	—	10	4	no	—
433	C₂³	—	10	4	no	—
434	C₂³	—	20	2	no	—
435	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
436	D₄	—	5	4	no	—
437	D₄	—	10	4	no	—
438	D₄	—	10	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	5	2	no	—
442	C₂×C₄	—	5	2	no	—
443	C₂×C₄	—	10	4	no	—
444	C₂×C₄	—	10	2	no	—
445	C₂×C₄	—	10	2	no	—
446	C₂×C₄	—	10	2	no	—
447	C₂×C₄	—	10	2	no	—
448	C₂×C₄	—	10	4	no	—
449	C₂×C₄	—	10	4	no	—
450	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
451	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
452	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
453	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
454	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
455	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
456	C₂×C₄	C₃×#709	1	2	yes	—
457	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
458	C₈	—	2	2	no	—
459	C₈	—	10	4	no	—
460	C₈	C₂×C₃×D₂₀	1	4	yes	complemented
461	C₂×C₃	—	2	2	no	—
462	C₂×C₃	—	10	4	no	—
463	C₂×C₃	—	20	2	no	—
464	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
465	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
466	C₂×C₃	#66079	1	1	yes	characteristic
467	C₅	C₃×D₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	5	4	no	—
471	C₂²	—	10	2	no	—
472	C₂²	—	10	2	no	—
473	C₂²	—	10	2	no	—
474	C₂²	—	10	2	no	—
475	C₂²	—	10	2	no	—
476	C₂²	—	20	8	no	—
477	C₂²	C₃×C₄×D₂₀	1	2	yes	—
478	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	10	2	no	—
483	C₄	—	10	2	no	—
484	C₄	C₃×C₄×D₂₀	1	2	yes	—
485	C₄	C₃×D₅×M₁₆	1	2	yes	complemented
486	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
487	C₄	C₂×C₃×#709	1	1	yes	characteristic
488	C₃	M₁₆×D₂₀	1	1	yes	characteristic, direct product factor, Sylow
489	C₂	—	2	2	no	—
490	C₂	—	10	4	no	—
491	C₂	—	20	2	no	—
492	C₂	C₂×C₃×C₄×D₂₀	1	1	yes	characteristic
493	C₂	C₂×C₃×D₅×M₁₆	1	1	yes	characteristic
494	C₂	C₃×#66079	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×C₃×D₂₀	C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×M₁₆	D₅
hypocenter	C₅	C₃×D₄×M₁₆
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅×M₁₆	C₂	semidirect
3. C₃×C₄×C₅×M₁₆	C₂	semidirect
4. C₃×#65415	C₂	semidirect
5. C₃×#65213	C₂	semidirect
6. C₃×#64995	C₂	semidirect
7. C₃×#64977	C₂	semidirect
8. C₃×C₈×D₂₀	C₂	semidirect
9. M₁₆×D₂₀	C₃	direct (N × H)
19. C₂×C₃×#676	C₂²	semidirect
20. C₂×C₃×C₈×D₅	C₂²	semidirect
27. C₃×C₅×#97	C₂²	semidirect
28. C₃×C₄×C₅×C₈	C₂²	semidirect
29. C₃×#3952	C₂²	semidirect
30. C₃×#3952	C₂²	semidirect
31. C₃×C₄⋊#168	C₂²	semidirect
32. C₃×C₄⋊#168	C₂²	semidirect
34. C₂×D₅×M₁₆	C₂×C₃	semidirect
36. C₄×C₅×M₁₆	C₂×C₃	semidirect
37. #65415	C₂×C₃	semidirect
38. #65213	C₂×C₃	semidirect
39. #64995	C₂×C₃	semidirect
40. #64977	C₂×C₃	semidirect
41. C₈×D₂₀	C₂×C₃	semidirect
58. C₃×C₅×M₁₆	D₄	semidirect
83. C₃×C₄×M₁₆	D₅	semidirect
93. C₂×#676	C₂²×C₃	semidirect
94. C₂×C₈×D₅	C₂²×C₃	semidirect
101. C₅×#97	C₂²×C₃	semidirect
102. C₄×C₅×C₈	C₂²×C₃	semidirect
103. #3952	C₂²×C₃	semidirect
104. #3952	C₂²×C₃	semidirect
105. C₄⋊#168	C₂²×C₃	semidirect
106. C₄⋊#168	C₂²×C₃	semidirect
129. C₃×D₂₀	M₁₆	direct (N × H)
137. C₃×C₅×C₈	C₂×D₄	semidirect
160. C₃×#97	C₂×D₅	semidirect
161. C₃×C₄×C₈	C₂×D₅	semidirect
178. C₅×M₁₆	C₃×D₄	semidirect
203. C₄×M₁₆	C₃×D₅	semidirect
214. C₂×C₃×D₅	C₂×M₁₆	semidirect
219. C₃×C₄×C₅	C₂×M₁₆	semidirect
242. C₃×M₁₆	D₂₀	direct (N × H)
279. D₂₀	C₃×M₁₆	direct (N × H)
287. C₅×C₈	C₂×C₃×D₄	semidirect
310. #97	C₂×C₃×D₅	semidirect
311. C₄×C₈	C₂×C₃×D₅	semidirect
348. C₃×C₈	C₂×D₂₀	semidirect
359. C₂×D₅	C₂×C₃×M₁₆	semidirect
364. C₄×C₅	C₂×C₃×M₁₆	semidirect
387. M₁₆	C₃×D₂₀	direct (N × H)
403. C₃×C₅	D₄×M₁₆	semidirect
421. C₃×C₄	D₅×M₁₆	semidirect
460. C₈	C₂×C₃×D₂₀	semidirect
467. C₅	C₃×D₄×M₁₆	semidirect
485. C₄	C₃×D₅×M₁₆	semidirect
488. C₃	M₁₆×D₂₀	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×D₅×M₁₆	2
C₂×C₃×C₄×D₂₀	2
C₃×C₄×C₅×M₁₆	2
C₃×#65415	2
C₃×#65213	2
C₃×#64995	2
C₃×#64977	2
C₃×C₈×D₂₀	2
M₁₆×D₂₀	3
C₃×D₄×M₁₆	5

Subgroups — C3×M16×D20 #14415688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×M₁₆×D₂₀ #14415688