Subgroups — C₅×M₁₆×Dic₆ #14418814

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×C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₅×#5118	C₂	1	2	yes	maximal
4	C₅×Dic₃×M₁₆	C₂	1	2	yes	maximal
5	C₅×#4924	C₂	1	1	yes	maximal, characteristic
6	C₅×#4701	C₂	1	4	yes	maximal, complemented
7	C₅×#4679	C₂	1	2	yes	maximal, complemented
8	C₅×C₈×Dic₆	C₂	1	2	yes	maximal, complemented
9	C₅×Q₈×M₁₆	—	3	1	no	maximal, Hall
10	C₂²×C₅×Dic₆	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×C₅×C₄⋊Dic₃	C₄	1	1	yes	characteristic
15	C₂×C₅×Dic₃⋊C₄	C₄	1	2	yes	—
16	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
17	C₂×C₅×#208	C₂²	1	2	yes	—
18	C₄×C₅×Dic₆	C₄	1	1	yes	characteristic
19	C₄×C₅×Dic₆	C₄	1	2	yes	—
20	C₄×C₅×Dic₆	C₄	1	1	yes	characteristic
21	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
22	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
23	C₄×C₅×Dic₆	C₂²	1	2	yes	—
24	C₃×C₅×#97	C₂²	1	2	yes	—
25	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
26	C₅×#815	C₂²	1	4	yes	—
27	C₅×Dic₃⋊C₈	C₂²	1	4	yes	—
28	C₅×Dic₃⋊C₈	C₂²	1	4	yes	—
29	C₅×C₈×Dic₃	C₂²	1	4	yes	—
30	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
31	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
32	M₁₆×Dic₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂×C₄×C₅×Q₈	—	3	1	no	—
34	C₅×#446	—	3	4	no	—
35	C₅×#446	—	3	2	no	—
36	C₅×C₈×Q₈	—	3	2	no	—
37	C₅×#423	—	3	2	no	—
38	C₅×#423	—	3	1	no	—
39	C₄×C₅×M₁₆	—	3	2	no	—
40	C₄×C₅×M₁₆	D₃	1	1	yes	characteristic
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×C₅×Dic₃	C₂×C₄	1	2	yes	—
45	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
46	C₂×C₅×Dic₆	—	2	4	no	—
47	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
48	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
49	C₂×C₅×Dic₆	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	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
59	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
60	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
61	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
62	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
63	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
64	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
65	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
66	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
67	C₄×C₅×Dic₃	C₂³	1	2	yes	—
68	C₄×C₅×Dic₃	C₂³	1	2	yes	—
69	C₅×#208	—	2	4	no	—
70	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
71	C₂×C₄×Dic₆	C₂×C₅	1	1	yes	characteristic
72	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic
73	#5118	C₂×C₅	1	2	yes	—
74	Dic₃×M₁₆	C₂×C₅	1	2	yes	—
75	#4924	C₂×C₅	1	1	yes	characteristic
76	#4701	C₂×C₅	1	4	yes	complemented
77	#4679	C₂×C₅	1	2	yes	complemented
78	C₈×Dic₆	C₂×C₅	1	2	yes	complemented
79	C₂²×C₅×Q₈	—	3	1	no	—
80	C₂×C₅×M₁₆	—	3	2	no	—
81	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
82	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
83	C₄×C₅×Q₈	—	3	1	no	—
84	C₄×C₅×Q₈	—	3	2	no	—
85	C₄×C₅×Q₈	—	3	1	no	—
86	C₄×C₅×Q₈	—	3	1	no	—
87	C₄×C₅×Q₈	—	3	2	no	—
88	C₄×C₅×Q₈	—	3	1	no	—
89	C₂×C₅×C₄⋊C₄	—	3	2	no	—
90	C₂×C₅×C₄⋊C₄	—	3	1	no	—
91	C₂×C₄²×C₅	—	3	2	no	—
92	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
93	C₅×C₄⋊C₈	—	3	4	no	—
94	C₅×C₄⋊C₈	—	3	4	no	—
95	C₅×C₄⋊C₈	—	3	2	no	—
96	C₅×C₄⋊C₈	—	3	2	no	—
97	C₅×#97	—	3	4	no	—
98	C₅×#97	C₂×D₃	1	2	yes	—
99	C₄×C₅×C₈	—	3	4	no	—
100	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
101	Q₈×M₁₆	—	3	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×C₅×Dic₃	—	2	4	no	—
114	C₂×C₅×Dic₃	—	4	2	no	—
115	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
116	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
117	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
118	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
119	C₅×Dic₆	—	2	2	no	—
120	C₅×Dic₆	—	2	4	no	—
121	C₅×Dic₆	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	C₅×C₃⋊C₈	—	2	4	no	—
125	C₂²×Dic₆	C₄×C₅	1	1	yes	characteristic
126	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₄⋊Dic₃	C₄×C₅	1	1	yes	characteristic
130	C₂×Dic₃⋊C₄	C₄×C₅	1	2	yes	—
131	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
132	C₂×#208	C₂²×C₅	1	2	yes	—
133	C₄×Dic₆	C₄×C₅	1	1	yes	characteristic
134	C₄×Dic₆	C₄×C₅	1	2	yes	—
135	C₄×Dic₆	C₄×C₅	1	1	yes	characteristic
136	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
137	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
138	C₄×Dic₆	C₂²×C₅	1	2	yes	—
139	C₃×#97	C₂²×C₅	1	2	yes	—
140	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
141	#815	C₂²×C₅	1	4	yes	—
142	Dic₃⋊C₈	C₂²×C₅	1	4	yes	—
143	Dic₃⋊C₈	C₂²×C₅	1	4	yes	—
144	C₈×Dic₃	C₂²×C₅	1	4	yes	—
145	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
146	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
147	C₂×C₅×Q₈	—	3	1	no	—
148	C₂×C₅×Q₈	—	3	2	no	—
149	C₂×C₅×Q₈	—	3	1	no	—
150	C₂×C₅×Q₈	—	6	4	no	—
151	C₂²×C₄×C₅	—	3	2	no	—
152	C₂²×C₄×C₅	—	3	2	no	—
153	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
156	C₅×M₁₆	—	2	2	no	—
157	C₅×M₁₆	—	6	4	no	—
158	C₅×M₁₆	Dic₆	1	4	yes	direct product factor
159	C₂×C₅×C₈	—	3	4	no	—
160	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
161	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
162	C₅×C₄⋊C₄	—	3	2	no	—
163	C₅×C₄⋊C₄	—	3	2	no	—
164	C₅×C₄⋊C₄	—	3	2	no	—
165	C₅×C₄⋊C₄	—	3	2	no	—
166	C₅×C₄⋊C₄	—	3	2	no	—
167	C₅×C₄⋊C₄	—	3	1	no	—
168	C₅×C₄⋊C₄	—	3	1	no	—
169	C₄²×C₅	—	3	2	no	—
170	C₄²×C₅	—	3	2	no	—
171	C₄²×C₅	—	3	2	no	—
172	C₄²×C₅	—	3	2	no	—
173	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
174	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
175	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
176	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
177	C₂×C₄×Q₈	—	3	1	no	—
178	#446	—	3	4	no	—
179	#446	—	3	2	no	—
180	C₈×Q₈	—	3	2	no	—
181	#423	—	3	2	no	—
182	#423	—	3	1	no	—
183	C₄×M₁₆	—	3	2	no	—
184	C₄×M₁₆	C₅×D₃	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	C₅×Dic₃	—	2	2	no	—
197	C₅×Dic₃	—	2	2	no	—
198	C₅×Dic₃	—	2	2	no	—
199	C₅×Dic₃	C₂×M₁₆	1	4	yes	—
200	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
201	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
202	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
203	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
204	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
205	C₂×Dic₆	—	2	4	no	—
206	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
207	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
208	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
209	C₃×M₁₆	—	2	2	no	—
210	C₃×M₁₆	C₅×Q₈	1	4	yes	complemented
211	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
212	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
213	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
214	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
215	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
216	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
217	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
218	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
219	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
220	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
221	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
222	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
223	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
224	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
225	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
226	C₄×Dic₃	C₂³×C₅	1	2	yes	—
227	C₄×Dic₃	C₂³×C₅	1	2	yes	—
228	#208	—	2	4	no	—
229	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
230	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
231	C₅×Q₈	—	3	4	no	—
232	C₅×Q₈	—	6	4	no	—
233	C₅×Q₈	—	6	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	3	2	no	—
236	C₂×C₄×C₅	—	3	2	no	—
237	C₂×C₄×C₅	—	3	2	no	—
238	C₂×C₄×C₅	—	3	2	no	—
239	C₂×C₄×C₅	—	4	1	no	—
240	C₂×C₄×C₅	—	6	4	no	—
241	C₂×C₄×C₅	—	12	2	no	—
242	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
243	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
248	C₂×C₄×C₅	#235	1	2	yes	—
249	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
250	C₅×C₈	—	2	2	no	—
251	C₅×C₈	—	6	4	no	—
252	C₅×C₈	C₂×Dic₆	1	4	yes	complemented
253	C₂²×Q₈	—	3	1	no	—
254	C₂×M₁₆	—	3	2	no	—
255	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
256	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
257	C₄×Q₈	—	3	1	no	—
258	C₄×Q₈	—	3	2	no	—
259	C₄×Q₈	—	3	1	no	—
260	C₄×Q₈	—	3	1	no	—
261	C₄×Q₈	—	3	2	no	—
262	C₄×Q₈	—	3	1	no	—
263	C₂×C₄⋊C₄	—	3	2	no	—
264	C₂×C₄⋊C₄	—	3	1	no	—
265	C₂×C₄²	—	3	2	no	—
266	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
267	C₄⋊C₈	—	3	4	no	—
268	C₄⋊C₈	—	3	4	no	—
269	C₄⋊C₈	—	3	2	no	—
270	C₄⋊C₈	—	3	2	no	—
271	#97	—	3	4	no	—
272	#97	C₂×C₅×D₃	1	2	yes	—
273	C₄×C₈	—	3	4	no	—
274	C₄×C₈	C₂×C₅×D₃	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	C₂²×C₄×C₅	1	1	yes	characteristic
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	4	1	no	—
282	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
288	C₂×C₃×C₄	C₅×#41	1	2	yes	—
289	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
290	C₂×Dic₃	—	2	4	no	—
291	C₂×Dic₃	—	4	2	no	—
292	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
293	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
294	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
295	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
296	Dic₆	—	2	2	no	—
297	Dic₆	—	2	4	no	—
298	Dic₆	C₅×M₁₆	1	4	yes	direct product factor
299	C₃×C₈	—	2	2	no	—
300	C₃×C₈	C₂×C₅×Q₈	1	4	yes	complemented
301	C₃⋊C₈	—	2	4	no	—
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	—	2	1	no	—
304	C₂²×C₅	C₄×Dic₆	1	2	yes	—
305	C₂²×C₅	C₂²×C₄×D₃	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	—	3	4	no	—
310	C₄×C₅	—	6	2	no	—
311	C₄×C₅	—	6	2	no	—
312	C₄×C₅	—	6	2	no	—
313	C₄×C₅	C₄×Dic₆	1	2	yes	—
314	C₄×C₅	D₃×M₁₆	1	2	yes	—
315	C₄×C₅	C₂²×Dic₆	1	1	yes	characteristic
316	C₄×C₅	C₂×#235	1	1	yes	characteristic
317	C₂×Q₈	—	3	1	no	—
318	C₂×Q₈	—	3	2	no	—
319	C₂×Q₈	—	3	1	no	—
320	C₂×Q₈	—	6	4	no	—
321	C₂²×C₄	—	3	2	no	—
322	C₂²×C₄	—	3	2	no	—
323	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
324	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
325	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
326	M₁₆	—	2	2	no	—
327	M₁₆	—	6	4	no	—
328	M₁₆	C₅×Dic₆	1	4	yes	direct product factor
329	C₂×C₈	—	3	4	no	—
330	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
331	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
332	C₄⋊C₄	—	3	2	no	—
333	C₄⋊C₄	—	3	2	no	—
334	C₄⋊C₄	—	3	2	no	—
335	C₄⋊C₄	—	3	2	no	—
336	C₄⋊C₄	—	3	2	no	—
337	C₄⋊C₄	—	3	1	no	—
338	C₄⋊C₄	—	3	1	no	—
339	C₄²	—	3	2	no	—
340	C₄²	—	3	2	no	—
341	C₄²	—	3	2	no	—
342	C₄²	—	3	2	no	—
343	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
344	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
345	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
346	C₄²	C₂²×C₅×D₃	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×C₅×Q₈	1	2	yes	—
351	C₂²×C₃	C₂³×C₄×C₅	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	C₄×C₅×Q₈	1	2	yes	—
356	C₃×C₄	C₂×C₅×M₁₆	1	2	yes	—
357	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
358	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
359	Dic₃	—	2	2	no	—
360	Dic₃	—	2	2	no	—
361	Dic₃	—	2	2	no	—
362	Dic₃	C₂×C₅×M₁₆	1	4	yes	—
363	C₂×C₅	—	2	2	no	—
364	C₂×C₅	C₂×C₄×Dic₆	1	1	yes	characteristic
365	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
366	C₂×C₅	#5745	1	1	yes	characteristic
367	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
368	Q₈	—	3	4	no	—
369	Q₈	—	6	4	no	—
370	Q₈	—	6	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	3	2	no	—
373	C₂×C₄	—	3	2	no	—
374	C₂×C₄	—	3	2	no	—
375	C₂×C₄	—	3	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	6	4	no	—
378	C₂×C₄	—	12	2	no	—
379	C₂×C₄	C₂×C₅×Dic₆	1	2	yes	—
380	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
381	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
382	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
383	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
384	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
385	C₂×C₄	C₅×#235	1	2	yes	—
386	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	6	4	no	—
389	C₈	C₂×C₅×Dic₆	1	4	yes	complemented
390	C₂×C₃	—	2	2	no	—
391	C₂×C₃	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
392	C₂×C₃	C₂²×C₅×M₁₆	1	1	yes	characteristic
393	C₂×C₃	C₅×#568	1	1	yes	characteristic
394	C₅	M₁₆×Dic₆	1	1	yes	characteristic, direct product factor, Sylow
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	C₄×C₅×Dic₆	1	2	yes	—
398	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	3	4	no	—
403	C₄	—	6	2	no	—
404	C₄	—	6	2	no	—
405	C₄	—	6	2	no	—
406	C₄	C₄×C₅×Dic₆	1	2	yes	—
407	C₄	C₅×D₃×M₁₆	1	2	yes	—
408	C₄	C₂²×C₅×Dic₆	1	1	yes	characteristic
409	C₄	C₂×C₅×#235	1	1	yes	characteristic
410	C₃	C₅×Q₈×M₁₆	1	1	yes	characteristic, complemented, Sylow
411	C₂	—	2	2	no	—
412	C₂	C₂×C₄×C₅×Dic₆	1	1	yes	characteristic
413	C₂	C₂×C₅×D₃×M₁₆	1	1	yes	characteristic
414	C₂	C₅×#5745	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₄×C₅×M₁₆	D₃
hypocenter	C₃	C₅×Q₈×M₁₆
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄×C₅×M₁₆

Complements

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

N	H ≅ G/N	type
6. C₅×#4701	C₂	semidirect
7. C₅×#4679	C₂	semidirect
8. C₅×C₈×Dic₆	C₂	semidirect
32. M₁₆×Dic₆	C₅	direct (N × H)
51. C₃×C₅×M₁₆	Q₈	semidirect
76. #4701	C₂×C₅	semidirect
77. #4679	C₂×C₅	semidirect
78. C₈×Dic₆	C₂×C₅	semidirect
121. C₅×Dic₆	M₁₆	direct (N × H)
123. C₃×C₅×C₈	C₂×Q₈	semidirect
158. C₅×M₁₆	Dic₆	direct (N × H)
210. C₃×M₁₆	C₅×Q₈	semidirect
252. C₅×C₈	C₂×Dic₆	semidirect
298. Dic₆	C₅×M₁₆	direct (N × H)
300. C₃×C₈	C₂×C₅×Q₈	semidirect
328. M₁₆	C₅×Dic₆	direct (N × H)
347. C₃×C₅	Q₈×M₁₆	semidirect
389. C₈	C₂×C₅×Dic₆	semidirect
394. C₅	M₁₆×Dic₆	direct (N × H)
410. C₃	C₅×Q₈×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×Dic₆	2
C₃×C₄×C₅×M₁₆	2
C₅×#5118	2
C₅×Dic₃×M₁₆	2
C₅×#4924	2
C₅×#4701	2
C₅×#4679	2
C₅×C₈×Dic₆	2
C₅×Q₈×M₁₆	3
M₁₆×Dic₆	5

Subgroups — C5×M16×Dic6 #14418814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×M₁₆×Dic₆ #14418814