Subgroups — C₃×M₁₆×Dic₁₀ #14418815

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃×#65407	C₂	1	2	yes	maximal
4	C₃×M₁₆×Dic₅	C₂	1	2	yes	maximal
5	C₃×#65213	C₂	1	1	yes	maximal, characteristic
6	C₃×#64990	C₂	1	4	yes	maximal, complemented
7	C₃×#64968	C₂	1	2	yes	maximal, complemented
8	C₃×C₈×Dic₁₀	C₂	1	2	yes	maximal, complemented
9	M₁₆×Dic₁₀	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×Dic₁₀	C₄	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄⋊Dic₅	C₄	1	1	yes	characteristic
15	C₂×C₃×#683	C₄	1	2	yes	—
16	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
17	C₂×C₃×#681	C₂²	1	2	yes	—
18	C₃×C₄×Dic₁₀	C₄	1	1	yes	characteristic
19	C₃×C₄×Dic₁₀	C₄	1	2	yes	—
20	C₃×C₄×Dic₁₀	C₄	1	1	yes	characteristic
21	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
22	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
23	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
24	C₃×C₅×#97	C₂²	1	2	yes	—
25	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
26	C₃×#3947	C₂²	1	4	yes	—
27	C₃×#3946	C₂²	1	4	yes	—
28	C₃×#3946	C₂²	1	4	yes	—
29	C₃×C₈×Dic₅	C₂²	1	4	yes	—
30	C₃×C₄⋊#168	C₂²	1	2	yes	—
31	C₃×C₄⋊#168	C₂²	1	2	yes	—
32	C₃×Q₈×M₁₆	—	5	1	no	maximal, Hall
33	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic
34	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic
35	#65407	C₂×C₃	1	2	yes	—
36	M₁₆×Dic₅	C₂×C₃	1	2	yes	—
37	#65213	C₂×C₃	1	1	yes	characteristic
38	#64990	C₂×C₃	1	4	yes	complemented
39	#64968	C₂×C₃	1	2	yes	complemented
40	C₈×Dic₁₀	C₂×C₃	1	2	yes	complemented
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
45	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
46	C₂×C₃×Dic₁₀	—	2	4	no	—
47	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
49	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
50	C₃×C₅×M₁₆	—	2	2	no	—
51	C₃×C₅×M₁₆	Q₈	1	4	yes	complemented
52	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
53	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
54	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
55	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
56	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
57	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
58	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
59	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
60	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
61	C₃×#683	C₂×C₄	1	2	yes	—
62	C₃×#683	C₂×C₄	1	2	yes	—
63	C₃×#683	C₂×C₄	1	2	yes	—
64	C₃×#683	C₂×C₄	1	2	yes	—
65	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
66	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
67	C₃×C₄×Dic₅	C₂³	1	2	yes	—
68	C₃×C₄×Dic₅	C₂³	1	2	yes	—
69	C₃×#681	—	2	4	no	—
70	C₂×C₃×#168	C₂³	1	4	yes	—
71	C₂×C₃×C₄×Q₈	—	5	1	no	—
72	C₃×#446	—	5	4	no	—
73	C₃×#446	—	5	2	no	—
74	C₃×C₈×Q₈	—	5	2	no	—
75	C₃×#423	—	5	2	no	—
76	C₃×#423	—	5	1	no	—
77	C₃×C₄×M₁₆	—	5	2	no	—
78	C₃×C₄×M₁₆	D₅	1	1	yes	characteristic
79	C₂²×Dic₁₀	C₃×C₄	1	1	yes	characteristic
80	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₄⋊Dic₅	C₃×C₄	1	1	yes	characteristic
84	C₂×#683	C₃×C₄	1	2	yes	—
85	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
86	C₂×#681	C₂²×C₃	1	2	yes	—
87	C₄×Dic₁₀	C₃×C₄	1	1	yes	characteristic
88	C₄×Dic₁₀	C₃×C₄	1	2	yes	—
89	C₄×Dic₁₀	C₃×C₄	1	1	yes	characteristic
90	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
91	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
92	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
93	C₅×#97	C₂²×C₃	1	2	yes	—
94	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
95	#3947	C₂²×C₃	1	4	yes	—
96	#3946	C₂²×C₃	1	4	yes	—
97	#3946	C₂²×C₃	1	4	yes	—
98	C₈×Dic₅	C₂²×C₃	1	4	yes	—
99	C₄⋊#168	C₂²×C₃	1	2	yes	—
100	C₄⋊#168	C₂²×C₃	1	2	yes	—
101	Q₈×M₁₆	—	5	1	no	Sylow
102	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	4	1	no	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
111	C₂×C₃×C₄×C₅	#41	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
113	C₂×C₃×Dic₅	—	2	4	no	—
114	C₂×C₃×Dic₅	—	4	2	no	—
115	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
116	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
117	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
118	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
119	C₃×Dic₁₀	—	2	2	no	—
120	C₃×Dic₁₀	—	2	4	no	—
121	C₃×Dic₁₀	M₁₆	1	4	yes	direct product factor
122	C₃×C₅×C₈	—	2	2	no	—
123	C₃×C₅×C₈	C₂×Q₈	1	4	yes	complemented
124	C₃×#168	—	2	4	no	—
125	C₂²×C₃×Q₈	—	5	1	no	—
126	C₂×C₃×M₁₆	—	5	2	no	—
127	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
128	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
129	C₃×C₄×Q₈	—	5	1	no	—
130	C₃×C₄×Q₈	—	5	2	no	—
131	C₃×C₄×Q₈	—	5	1	no	—
132	C₃×C₄×Q₈	—	5	1	no	—
133	C₃×C₄×Q₈	—	5	2	no	—
134	C₃×C₄×Q₈	—	5	1	no	—
135	C₂×C₃×C₄⋊C₄	—	5	2	no	—
136	C₂×C₃×C₄⋊C₄	—	5	1	no	—
137	C₂×C₃×C₄²	—	5	2	no	—
138	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
139	C₃×C₄⋊C₈	—	5	4	no	—
140	C₃×C₄⋊C₈	—	5	4	no	—
141	C₃×C₄⋊C₈	—	5	2	no	—
142	C₃×C₄⋊C₈	—	5	2	no	—
143	C₃×#97	—	5	4	no	—
144	C₃×#97	C₂×D₅	1	2	yes	—
145	C₃×C₄×C₈	—	5	4	no	—
146	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
147	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
150	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
151	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
152	C₂×Dic₁₀	—	2	4	no	—
153	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
154	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
155	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
156	C₅×M₁₆	—	2	2	no	—
157	C₅×M₁₆	C₃×Q₈	1	4	yes	complemented
158	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
159	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
160	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
161	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
162	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
163	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
164	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
165	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
166	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
167	#683	C₂×C₃×C₄	1	2	yes	—
168	#683	C₂×C₃×C₄	1	2	yes	—
169	#683	C₂×C₃×C₄	1	2	yes	—
170	#683	C₂×C₃×C₄	1	2	yes	—
171	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
172	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
173	C₄×Dic₅	C₂³×C₃	1	2	yes	—
174	C₄×Dic₅	C₂³×C₃	1	2	yes	—
175	#681	—	2	4	no	—
176	C₂×#168	C₂³×C₃	1	4	yes	—
177	C₂×C₄×Q₈	—	5	1	no	—
178	#446	—	5	4	no	—
179	#446	—	5	2	no	—
180	C₈×Q₈	—	5	2	no	—
181	#423	—	5	2	no	—
182	#423	—	5	1	no	—
183	C₄×M₁₆	—	5	2	no	—
184	C₄×M₁₆	C₃×D₅	1	1	yes	characteristic
185	C₂²×C₃×C₅	—	2	1	no	—
186	C₂²×C₃×C₅	—	2	1	no	—
187	C₂²×C₃×C₅	C₄×Q₈	1	2	yes	—
188	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
189	C₃×C₄×C₅	—	2	1	no	—
190	C₃×C₄×C₅	—	2	1	no	—
191	C₃×C₄×C₅	—	2	1	no	—
192	C₃×C₄×C₅	C₄×Q₈	1	2	yes	—
193	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
194	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
195	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
196	C₃×Dic₅	—	2	2	no	—
197	C₃×Dic₅	—	2	2	no	—
198	C₃×Dic₅	—	2	2	no	—
199	C₃×Dic₅	C₂×M₁₆	1	4	yes	—
200	C₂×C₃×Q₈	—	5	1	no	—
201	C₂×C₃×Q₈	—	5	2	no	—
202	C₂×C₃×Q₈	—	5	1	no	—
203	C₂×C₃×Q₈	—	10	4	no	—
204	C₂²×C₃×C₄	—	5	2	no	—
205	C₂²×C₃×C₄	—	5	2	no	—
206	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
208	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
209	C₃×M₁₆	—	2	2	no	—
210	C₃×M₁₆	—	10	4	no	—
211	C₃×M₁₆	Dic₁₀	1	4	yes	direct product factor
212	C₂×C₃×C₈	—	5	4	no	—
213	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
214	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
215	C₃×C₄⋊C₄	—	5	2	no	—
216	C₃×C₄⋊C₄	—	5	2	no	—
217	C₃×C₄⋊C₄	—	5	2	no	—
218	C₃×C₄⋊C₄	—	5	2	no	—
219	C₃×C₄⋊C₄	—	5	2	no	—
220	C₃×C₄⋊C₄	—	5	1	no	—
221	C₃×C₄⋊C₄	—	5	1	no	—
222	C₃×C₄²	—	5	2	no	—
223	C₃×C₄²	—	5	2	no	—
224	C₃×C₄²	—	5	2	no	—
225	C₃×C₄²	—	5	2	no	—
226	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
227	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
228	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
229	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
230	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
239	C₂×C₄×C₅	C₃×#41	1	2	yes	—
240	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
241	C₂×Dic₅	—	2	4	no	—
242	C₂×Dic₅	—	4	2	no	—
243	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
244	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
245	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
246	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
247	Dic₁₀	—	2	2	no	—
248	Dic₁₀	—	2	4	no	—
249	Dic₁₀	C₃×M₁₆	1	4	yes	direct product factor
250	C₅×C₈	—	2	2	no	—
251	C₅×C₈	C₂×C₃×Q₈	1	4	yes	complemented
252	#168	—	2	4	no	—
253	C₂²×Q₈	—	5	1	no	—
254	C₂×M₁₆	—	5	2	no	—
255	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
256	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
257	C₄×Q₈	—	5	1	no	—
258	C₄×Q₈	—	5	2	no	—
259	C₄×Q₈	—	5	1	no	—
260	C₄×Q₈	—	5	1	no	—
261	C₄×Q₈	—	5	2	no	—
262	C₄×Q₈	—	5	1	no	—
263	C₂×C₄⋊C₄	—	5	2	no	—
264	C₂×C₄⋊C₄	—	5	1	no	—
265	C₂×C₄²	—	5	2	no	—
266	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
267	C₄⋊C₈	—	5	4	no	—
268	C₄⋊C₈	—	5	4	no	—
269	C₄⋊C₈	—	5	2	no	—
270	C₄⋊C₈	—	5	2	no	—
271	#97	—	5	4	no	—
272	#97	C₂×C₃×D₅	1	2	yes	—
273	C₄×C₈	—	5	4	no	—
274	C₄×C₈	C₂×C₃×D₅	1	2	yes	—
275	C₂×C₃×C₅	—	2	2	no	—
276	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
277	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
278	C₂×C₃×C₅	#568	1	1	yes	characteristic
279	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
280	C₃×Q₈	—	5	4	no	—
281	C₃×Q₈	—	10	4	no	—
282	C₃×Q₈	—	10	2	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	4	1	no	—
285	C₂×C₃×C₄	—	5	2	no	—
286	C₂×C₃×C₄	—	5	2	no	—
287	C₂×C₃×C₄	—	5	2	no	—
288	C₂×C₃×C₄	—	5	2	no	—
289	C₂×C₃×C₄	—	10	4	no	—
290	C₂×C₃×C₄	—	20	2	no	—
291	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
292	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
297	C₂×C₃×C₄	#709	1	2	yes	—
298	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
299	C₃×C₈	—	2	2	no	—
300	C₃×C₈	—	10	4	no	—
301	C₃×C₈	C₂×Dic₁₀	1	4	yes	complemented
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	—	2	1	no	—
304	C₂²×C₅	C₃×C₄×Q₈	1	2	yes	—
305	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
306	C₄×C₅	—	2	1	no	—
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	C₃×C₄×Q₈	1	2	yes	—
310	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	—
311	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
312	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
313	Dic₅	—	2	2	no	—
314	Dic₅	—	2	2	no	—
315	Dic₅	—	2	2	no	—
316	Dic₅	C₂×C₃×M₁₆	1	4	yes	—
317	C₂×Q₈	—	5	1	no	—
318	C₂×Q₈	—	5	2	no	—
319	C₂×Q₈	—	5	1	no	—
320	C₂×Q₈	—	10	4	no	—
321	C₂²×C₄	—	5	2	no	—
322	C₂²×C₄	—	5	2	no	—
323	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
324	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
325	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
326	M₁₆	—	2	2	no	—
327	M₁₆	—	10	4	no	—
328	M₁₆	C₃×Dic₁₀	1	4	yes	direct product factor
329	C₂×C₈	—	5	4	no	—
330	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
331	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
332	C₄⋊C₄	—	5	2	no	—
333	C₄⋊C₄	—	5	2	no	—
334	C₄⋊C₄	—	5	2	no	—
335	C₄⋊C₄	—	5	2	no	—
336	C₄⋊C₄	—	5	2	no	—
337	C₄⋊C₄	—	5	1	no	—
338	C₄⋊C₄	—	5	1	no	—
339	C₄²	—	5	2	no	—
340	C₄²	—	5	2	no	—
341	C₄²	—	5	2	no	—
342	C₄²	—	5	2	no	—
343	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
344	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
345	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
346	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
347	C₃×C₅	Q₈×M₁₆	1	1	yes	characteristic, complemented, Hall
348	C₂²×C₃	—	2	1	no	—
349	C₂²×C₃	—	2	1	no	—
350	C₂²×C₃	C₄×Dic₁₀	1	2	yes	—
351	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	5	4	no	—
356	C₃×C₄	—	10	2	no	—
357	C₃×C₄	—	10	2	no	—
358	C₃×C₄	—	10	2	no	—
359	C₃×C₄	C₄×Dic₁₀	1	2	yes	—
360	C₃×C₄	D₅×M₁₆	1	2	yes	—
361	C₃×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
362	C₃×C₄	C₂×#709	1	1	yes	characteristic
363	C₂×C₅	—	2	2	no	—
364	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
365	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
366	C₂×C₅	C₃×#568	1	1	yes	characteristic
367	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
368	Q₈	—	5	4	no	—
369	Q₈	—	10	4	no	—
370	Q₈	—	10	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	5	2	no	—
374	C₂×C₄	—	5	2	no	—
375	C₂×C₄	—	5	2	no	—
376	C₂×C₄	—	5	2	no	—
377	C₂×C₄	—	10	4	no	—
378	C₂×C₄	—	20	2	no	—
379	C₂×C₄	C₂×C₃×Dic₁₀	1	2	yes	—
380	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
381	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
382	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
383	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
384	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
385	C₂×C₄	C₃×#709	1	2	yes	—
386	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	10	4	no	—
389	C₈	C₂×C₃×Dic₁₀	1	4	yes	complemented
390	C₂×C₃	—	2	2	no	—
391	C₂×C₃	C₂×C₄×Dic₁₀	1	1	yes	characteristic
392	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
393	C₂×C₃	#66079	1	1	yes	characteristic
394	C₅	C₃×Q₈×M₁₆	1	1	yes	characteristic, complemented, Sylow
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	C₃×C₄×Dic₁₀	1	2	yes	—
398	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	5	4	no	—
403	C₄	—	10	2	no	—
404	C₄	—	10	2	no	—
405	C₄	—	10	2	no	—
406	C₄	C₃×C₄×Dic₁₀	1	2	yes	—
407	C₄	C₃×D₅×M₁₆	1	2	yes	—
408	C₄	C₂²×C₃×Dic₁₀	1	1	yes	characteristic
409	C₄	C₂×C₃×#709	1	1	yes	characteristic
410	C₃	M₁₆×Dic₁₀	1	1	yes	characteristic, direct product factor, Sylow
411	C₂	—	2	2	no	—
412	C₂	C₂×C₃×C₄×Dic₁₀	1	1	yes	characteristic
413	C₂	C₂×C₃×D₅×M₁₆	1	1	yes	characteristic
414	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	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×M₁₆	D₅
hypocenter	C₅	C₃×Q₈×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
6. C₃×#64990	C₂	semidirect
7. C₃×#64968	C₂	semidirect
8. C₃×C₈×Dic₁₀	C₂	semidirect
9. M₁₆×Dic₁₀	C₃	direct (N × H)
38. #64990	C₂×C₃	semidirect
39. #64968	C₂×C₃	semidirect
40. C₈×Dic₁₀	C₂×C₃	semidirect
51. C₃×C₅×M₁₆	Q₈	semidirect
121. C₃×Dic₁₀	M₁₆	direct (N × H)
123. C₃×C₅×C₈	C₂×Q₈	semidirect
157. C₅×M₁₆	C₃×Q₈	semidirect
211. C₃×M₁₆	Dic₁₀	direct (N × H)
249. Dic₁₀	C₃×M₁₆	direct (N × H)
251. C₅×C₈	C₂×C₃×Q₈	semidirect
301. C₃×C₈	C₂×Dic₁₀	semidirect
328. M₁₆	C₃×Dic₁₀	direct (N × H)
347. C₃×C₅	Q₈×M₁₆	semidirect
389. C₈	C₂×C₃×Dic₁₀	semidirect
394. C₅	C₃×Q₈×M₁₆	semidirect
410. C₃	M₁₆×Dic₁₀	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×Dic₁₀	2
C₃×C₄×C₅×M₁₆	2
C₃×#65407	2
C₃×M₁₆×Dic₅	2
C₃×#65213	2
C₃×#64990	2
C₃×#64968	2
C₃×C₈×Dic₁₀	2
M₁₆×Dic₁₀	3
C₃×Q₈×M₁₆	5

Subgroups — C3×M16×Dic10 #14418815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×M₁₆×Dic₁₀ #14418815