Subgroups — C₂²×C₅×D₃×SD₁₆ #14509655

Order 1920.

3440 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×#215	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₅×#214	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×D₃×SD₁₆	C₂	1	24	yes	maximal, direct product factor
7	C₂²×C₅×#204	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₅×SD₁₆	—	3	1	no	maximal, Hall
10	C₂⁴×C₅×D₃	—	2	1	no	—
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂²×C₅×#67	—	2	1	no	—
14	C₂×C₅×D₃×Q₈	—	2	6	no	—
15	C₂×C₅×D₃×Q₈	C₂²	1	12	yes	complemented
16	C₂×C₅×D₃×D₄	—	2	6	no	—
17	C₂×C₅×D₃×D₄	C₂²	1	12	yes	—
18	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₅×D₃	—	2	1	no	—
20	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₂²×C₅×Dic₆	—	2	1	no	—
22	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₅×SD₁₆	C₂²	1	12	yes	complemented
24	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₅×#215	C₂²	1	12	yes	complemented
26	C₂×C₅×#214	C₂²	1	12	yes	complemented
27	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
28	C₅×D₃×SD₁₆	C₂²	1	64	yes	direct product factor
29	C₂×C₅×#204	C₂²	1	12	yes	complemented
30	C₂×C₅×D₃×C₈	C₂²	1	12	yes	complemented
31	C₂²×D₃×SD₁₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂³×C₅×Q₈	—	3	1	no	—
33	C₂³×C₅×D₄	—	3	1	no	—
34	C₂²×C₅×SD₁₆	—	3	1	no	—
35	C₂²×C₅×SD₁₆	—	3	1	no	—
36	C₂²×C₅×SD₁₆	—	3	24	no	—
37	C₂²×C₅×SD₁₆	—	3	1	no	—
38	C₂²×C₅×SD₁₆	D₃	1	1	yes	characteristic, direct product factor
39	C₂³×C₅×C₈	—	3	1	no	—
40	C₂⁴×C₃×C₅	—	2	1	no	—
41	C₂³×C₅×D₃	—	2	1	no	—
42	C₂³×C₅×D₃	—	2	12	no	—
43	C₂³×C₅×D₃	—	4	8	no	—
44	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
45	C₂×C₃×C₅×Q₈	—	2	3	no	—
46	C₂×C₃×C₅×Q₈	C₂³	1	6	yes	complemented
47	C₂×C₃×C₅×D₄	—	2	3	no	—
48	C₂×C₃×C₅×D₄	C₂³	1	6	yes	—
49	C₂²×C₃×C₄×C₅	—	2	1	no	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₅×#67	—	2	12	no	—
52	C₂²×C₅×Dic₃	—	2	1	no	—
53	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
54	C₅×D₃×Q₈	—	2	24	no	—
55	C₅×D₃×Q₈	C₂³	1	16	yes	complemented
56	C₅×D₃×D₄	—	2	24	no	—
57	C₅×D₃×D₄	C₂³	1	16	yes	—
58	C₂×C₅×D₁₂	—	2	3	no	—
59	C₂×C₅×D₁₂	C₂³	1	6	yes	—
60	C₂×C₄×C₅×D₃	—	2	12	no	—
61	C₂×C₄×C₅×D₃	D₄	1	6	yes	—
62	C₂×C₄×C₅×D₃	C₂³	1	6	yes	—
63	C₂×C₅×Dic₆	—	2	3	no	—
64	C₂×C₅×Dic₆	—	2	12	no	—
65	C₂×C₅×Dic₆	C₂³	1	6	yes	complemented
66	C₃×C₅×SD₁₆	C₂³	1	16	yes	complemented
67	C₂×C₃×C₅×C₈	C₂³	1	6	yes	complemented
68	C₅×#215	C₂³	1	16	yes	complemented
69	C₅×#214	C₂³	1	16	yes	complemented
70	C₂×C₅×C₃⋊C₈	C₂³	1	6	yes	complemented
71	C₅×#204	C₂³	1	16	yes	complemented
72	C₅×D₃×C₈	C₂³	1	16	yes	complemented
73	C₂²×D₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂²×D₃×D₄	C₂×C₅	1	1	yes	characteristic
75	C₂²×C₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂²×#215	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂²×#214	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂×D₃×SD₁₆	C₂×C₅	1	24	yes	direct product factor
79	C₂²×#204	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂²×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂⁵×C₅	—	6	1	no	—
82	C₂²×C₅×Q₈	—	3	12	no	—
83	C₂²×C₅×Q₈	—	3	1	no	—
84	C₂²×C₅×Q₈	—	6	1	no	—
85	C₂²×C₅×Q₈	—	6	6	no	—
86	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
87	C₂²×C₅×D₄	—	3	12	no	—
88	C₂²×C₅×D₄	—	3	1	no	—
89	C₂²×C₅×D₄	—	6	6	no	—
90	C₂²×C₅×D₄	—	6	1	no	—
91	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
92	C₂³×C₄×C₅	—	3	1	no	—
93	C₂³×C₄×C₅	—	6	1	no	—
94	C₂×C₅×SD₁₆	—	3	12	no	—
95	C₂×C₅×SD₁₆	—	3	12	no	—
96	C₂×C₅×SD₁₆	—	3	64	no	—
97	C₂×C₅×SD₁₆	—	3	12	no	—
98	C₂×C₅×SD₁₆	C₂×D₃	1	12	yes	direct product factor
99	C₂²×C₅×C₈	—	3	1	no	—
100	C₂²×C₅×C₈	—	3	12	no	—
101	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
102	C₂³×SD₁₆	—	3	1	no	Sylow
103	C₂³×C₃×C₅	—	2	6	no	—
104	C₂³×C₃×C₅	—	4	4	no	—
105	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₅×D₃	—	2	6	no	—
107	C₂²×C₅×D₃	—	2	16	no	—
108	C₂²×C₅×D₃	—	4	4	no	—
109	C₂²×C₅×D₃	—	4	48	no	—
110	C₂²×C₅×D₃	SD₁₆	1	8	yes	direct product factor
111	C₂²×C₅×D₃	C₂×D₄	1	6	yes	—
112	C₃×C₅×Q₈	—	2	6	no	—
113	C₃×C₅×Q₈	C₂⁴	1	4	yes	complemented
114	C₃×C₅×D₄	—	2	6	no	—
115	C₃×C₅×D₄	C₂⁴	1	4	yes	—
116	C₂×C₃×C₄×C₅	—	2	6	no	—
117	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
118	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
119	C₅×#67	—	2	16	no	—
120	C₂×C₅×Dic₃	—	2	6	no	—
121	C₂×C₅×Dic₃	C₂×D₄	1	6	yes	—
122	C₅×D₁₂	—	2	6	no	—
123	C₅×D₁₂	C₂⁴	1	4	yes	—
124	C₄×C₅×D₃	—	2	16	no	—
125	C₄×C₅×D₃	C₂×D₄	1	12	yes	—
126	C₄×C₅×D₃	C₂⁴	1	4	yes	—
127	C₅×Dic₆	—	2	6	no	—
128	C₅×Dic₆	—	2	16	no	—
129	C₅×Dic₆	C₂⁴	1	4	yes	complemented
130	C₃×C₅×C₈	C₂⁴	1	4	yes	complemented
131	C₅×C₃⋊C₈	C₂⁴	1	4	yes	complemented
132	C₂⁴×D₃	—	2	1	no	—
133	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
134	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
135	C₂²×#67	—	2	1	no	—
136	C₂×D₃×Q₈	—	2	6	no	—
137	C₂×D₃×Q₈	C₂²×C₅	1	12	yes	complemented
138	C₂×D₃×D₄	—	2	6	no	—
139	C₂×D₃×D₄	C₂²×C₅	1	12	yes	—
140	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
141	C₂²×C₄×D₃	—	2	1	no	—
142	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
143	C₂²×Dic₆	—	2	1	no	—
144	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
145	C₂×C₃×SD₁₆	C₂²×C₅	1	12	yes	complemented
146	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
147	C₂×#215	C₂²×C₅	1	12	yes	complemented
148	C₂×#214	C₂²×C₅	1	12	yes	complemented
149	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
150	D₃×SD₁₆	C₂²×C₅	1	64	yes	direct product factor
151	C₂×#204	C₂²×C₅	1	12	yes	complemented
152	C₂×D₃×C₈	C₂²×C₅	1	12	yes	complemented
153	C₂⁴×C₅	—	2	1	no	—
154	C₂⁴×C₅	—	3	1	no	—
155	C₂⁴×C₅	—	6	12	no	—
156	C₂⁴×C₅	—	6	1	no	—
157	C₂⁴×C₅	—	12	8	no	—
158	C₂×C₅×Q₈	—	2	3	no	—
159	C₂×C₅×Q₈	—	3	16	no	—
160	C₂×C₅×Q₈	—	3	6	no	—
161	C₂×C₅×Q₈	—	6	12	no	—
162	C₂×C₅×Q₈	—	6	24	no	—
163	C₂×C₅×Q₈	—	6	3	no	—
164	C₂×C₅×Q₈	C₂²×D₃	1	6	yes	complemented
165	C₂×C₅×D₄	—	2	3	no	—
166	C₂×C₅×D₄	—	3	16	no	—
167	C₂×C₅×D₄	—	3	6	no	—
168	C₂×C₅×D₄	—	6	24	no	—
169	C₂×C₅×D₄	—	6	12	no	—
170	C₂×C₅×D₄	—	6	3	no	—
171	C₂×C₅×D₄	C₂²×D₃	1	6	yes	—
172	C₂²×C₄×C₅	—	2	1	no	—
173	C₂²×C₄×C₅	—	3	1	no	—
174	C₂²×C₄×C₅	—	3	6	no	—
175	C₂²×C₄×C₅	—	3	6	no	—
176	C₂²×C₄×C₅	—	6	12	no	—
177	C₂²×C₄×C₅	—	6	1	no	—
178	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
179	C₅×SD₁₆	—	3	16	no	—
180	C₅×SD₁₆	—	3	16	no	—
181	C₅×SD₁₆	—	3	16	no	—
182	C₅×SD₁₆	C₂²×D₃	1	16	yes	direct product factor
183	C₂×C₅×C₈	—	3	6	no	—
184	C₂×C₅×C₈	—	3	16	no	—
185	C₂×C₅×C₈	C₂²×D₃	1	6	yes	complemented
186	C₂³×Q₈	—	3	1	no	—
187	C₂³×D₄	—	3	1	no	—
188	C₂²×SD₁₆	—	3	1	no	—
189	C₂²×SD₁₆	—	3	1	no	—
190	C₂²×SD₁₆	—	3	24	no	—
191	C₂²×SD₁₆	—	3	1	no	—
192	C₂²×SD₁₆	C₅×D₃	1	1	yes	characteristic, direct product factor
193	C₂³×C₈	—	3	1	no	—
194	C₂²×C₃×C₅	—	2	4	no	—
195	C₂²×C₃×C₅	—	4	12	no	—
196	C₂²×C₃×C₅	C₂×SD₁₆	1	4	yes	complemented
197	C₂²×C₃×C₅	C₂²×D₄	1	3	yes	—
198	C₂×C₅×D₃	—	2	4	no	—
199	C₂×C₅×D₃	—	4	12	no	—
200	C₂×C₅×D₃	—	4	32	no	—
201	C₂×C₅×D₃	C₂×SD₁₆	1	24	yes	direct product factor
202	C₂×C₅×D₃	C₂²×D₄	1	4	yes	—
203	C₃×C₄×C₅	—	2	4	no	—
204	C₃×C₄×C₅	C₂²×D₄	1	3	yes	—
205	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
206	C₅×Dic₃	—	2	4	no	—
207	C₅×Dic₃	C₂²×D₄	1	4	yes	—
208	C₂⁴×C₃	—	2	1	no	—
209	C₂³×D₃	—	2	1	no	—
210	C₂³×D₃	—	2	12	no	—
211	C₂³×D₃	—	4	8	no	—
212	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
213	C₂×C₃×Q₈	—	2	3	no	—
214	C₂×C₃×Q₈	C₂³×C₅	1	6	yes	complemented
215	C₂×C₃×D₄	—	2	3	no	—
216	C₂×C₃×D₄	C₂³×C₅	1	6	yes	—
217	C₂²×C₃×C₄	—	2	1	no	—
218	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
219	C₂×#67	—	2	12	no	—
220	C₂²×Dic₃	—	2	1	no	—
221	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
222	D₃×Q₈	—	2	24	no	—
223	D₃×Q₈	C₂³×C₅	1	16	yes	complemented
224	D₃×D₄	—	2	24	no	—
225	D₃×D₄	C₂³×C₅	1	16	yes	—
226	C₂×D₁₂	—	2	3	no	—
227	C₂×D₁₂	C₂³×C₅	1	6	yes	—
228	C₂×C₄×D₃	—	2	12	no	—
229	C₂×C₄×D₃	C₅×D₄	1	6	yes	—
230	C₂×C₄×D₃	C₂³×C₅	1	6	yes	—
231	C₂×Dic₆	—	2	3	no	—
232	C₂×Dic₆	—	2	12	no	—
233	C₂×Dic₆	C₂³×C₅	1	6	yes	complemented
234	C₃×SD₁₆	C₂³×C₅	1	16	yes	complemented
235	C₂×C₃×C₈	C₂³×C₅	1	6	yes	complemented
236	#215	C₂³×C₅	1	16	yes	complemented
237	#214	C₂³×C₅	1	16	yes	complemented
238	C₂×C₃⋊C₈	C₂³×C₅	1	6	yes	complemented
239	#204	C₂³×C₅	1	16	yes	complemented
240	D₃×C₈	C₂³×C₅	1	16	yes	complemented
241	C₂³×C₅	—	2	6	no	—
242	C₂³×C₅	—	3	8	no	—
243	C₂³×C₅	—	3	6	no	—
244	C₂³×C₅	—	4	4	no	—
245	C₂³×C₅	—	6	16	no	—
246	C₂³×C₅	—	6	6	no	—
247	C₂³×C₅	—	12	48	no	—
248	C₂³×C₅	—	12	4	no	—
249	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
250	C₅×Q₈	—	2	6	no	—
251	C₅×Q₈	—	3	4	no	—
252	C₅×Q₈	—	6	16	no	—
253	C₅×Q₈	—	6	6	no	—
254	C₅×Q₈	C₂³×D₃	1	4	yes	complemented
255	C₅×D₄	—	2	6	no	—
256	C₅×D₄	—	3	4	no	—
257	C₅×D₄	—	6	16	no	—
258	C₅×D₄	—	6	6	no	—
259	C₅×D₄	C₂³×D₃	1	4	yes	—
260	C₂×C₄×C₅	—	2	6	no	—
261	C₂×C₄×C₅	—	3	6	no	—
262	C₂×C₄×C₅	—	3	12	no	—
263	C₂×C₄×C₅	—	3	4	no	—
264	C₂×C₄×C₅	—	6	16	no	—
265	C₂×C₄×C₅	—	6	6	no	—
266	C₂×C₄×C₅	D₃×D₄	1	3	yes	—
267	C₂×C₄×C₅	C₂³×D₃	1	3	yes	—
268	C₅×C₈	—	3	4	no	—
269	C₅×C₈	C₂³×D₃	1	4	yes	complemented
270	C₂⁵	—	6	1	no	—
271	C₂²×Q₈	—	3	12	no	—
272	C₂²×Q₈	—	3	1	no	—
273	C₂²×Q₈	—	6	1	no	—
274	C₂²×Q₈	—	6	6	no	—
275	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
276	C₂²×D₄	—	3	12	no	—
277	C₂²×D₄	—	3	1	no	—
278	C₂²×D₄	—	6	6	no	—
279	C₂²×D₄	—	6	1	no	—
280	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
281	C₂³×C₄	—	3	1	no	—
282	C₂³×C₄	—	6	1	no	—
283	C₂×SD₁₆	—	3	12	no	—
284	C₂×SD₁₆	—	3	12	no	—
285	C₂×SD₁₆	—	3	64	no	—
286	C₂×SD₁₆	—	3	12	no	—
287	C₂×SD₁₆	C₂×C₅×D₃	1	12	yes	direct product factor
288	C₂²×C₈	—	3	1	no	—
289	C₂²×C₈	—	3	12	no	—
290	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
291	C₂×C₃×C₅	—	4	4	no	—
292	C₂×C₃×C₅	C₂²×SD₁₆	1	6	yes	complemented
293	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
294	C₅×D₃	—	4	4	no	—
295	C₅×D₃	C₂²×SD₁₆	1	8	yes	direct product factor
296	C₂³×C₃	—	2	6	no	—
297	C₂³×C₃	—	4	4	no	—
298	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
299	C₂²×D₃	—	2	6	no	—
300	C₂²×D₃	—	2	16	no	—
301	C₂²×D₃	—	4	4	no	—
302	C₂²×D₃	—	4	48	no	—
303	C₂²×D₃	C₅×SD₁₆	1	8	yes	direct product factor
304	C₂²×D₃	C₂×C₅×D₄	1	6	yes	—
305	C₃×Q₈	—	2	6	no	—
306	C₃×Q₈	C₂⁴×C₅	1	4	yes	complemented
307	C₃×D₄	—	2	6	no	—
308	C₃×D₄	C₂⁴×C₅	1	4	yes	—
309	C₂×C₃×C₄	—	2	6	no	—
310	C₂×C₃×C₄	C₂×C₅×D₄	1	3	yes	—
311	C₂×C₃×C₄	C₂⁴×C₅	1	3	yes	—
312	#67	—	2	16	no	—
313	C₂×Dic₃	—	2	6	no	—
314	C₂×Dic₃	C₂×C₅×D₄	1	6	yes	—
315	D₁₂	—	2	6	no	—
316	D₁₂	C₂⁴×C₅	1	4	yes	—
317	C₄×D₃	—	2	16	no	—
318	C₄×D₃	C₂×C₅×D₄	1	12	yes	—
319	C₄×D₃	C₂⁴×C₅	1	4	yes	—
320	Dic₆	—	2	6	no	—
321	Dic₆	—	2	16	no	—
322	Dic₆	C₂⁴×C₅	1	4	yes	complemented
323	C₃×C₈	C₂⁴×C₅	1	4	yes	complemented
324	C₃⋊C₈	C₂⁴×C₅	1	4	yes	complemented
325	C₂²×C₅	—	2	4	no	—
326	C₂²×C₅	—	3	4	no	—
327	C₂²×C₅	—	3	24	no	—
328	C₂²×C₅	—	4	12	no	—
329	C₂²×C₅	—	6	4	no	—
330	C₂²×C₅	—	12	32	no	—
331	C₂²×C₅	—	12	12	no	—
332	C₂²×C₅	D₃×SD₁₆	1	4	yes	direct product factor
333	C₂²×C₅	C₂×D₃×D₄	1	3	yes	—
334	C₄×C₅	—	2	4	no	—
335	C₄×C₅	—	3	4	no	—
336	C₄×C₅	—	6	4	no	—
337	C₄×C₅	C₂×D₃×D₄	1	3	yes	—
338	C₄×C₅	C₂⁴×D₃	1	1	yes	characteristic
339	C₂⁴	—	2	1	no	—
340	C₂⁴	—	3	1	no	—
341	C₂⁴	—	6	12	no	—
342	C₂⁴	—	6	1	no	—
343	C₂⁴	—	12	8	no	—
344	C₂×Q₈	—	2	3	no	—
345	C₂×Q₈	—	3	16	no	—
346	C₂×Q₈	—	3	6	no	—
347	C₂×Q₈	—	6	12	no	—
348	C₂×Q₈	—	6	24	no	—
349	C₂×Q₈	—	6	3	no	—
350	C₂×Q₈	C₂²×C₅×D₃	1	6	yes	complemented
351	C₂×D₄	—	2	3	no	—
352	C₂×D₄	—	3	16	no	—
353	C₂×D₄	—	3	6	no	—
354	C₂×D₄	—	6	24	no	—
355	C₂×D₄	—	6	12	no	—
356	C₂×D₄	—	6	3	no	—
357	C₂×D₄	C₂²×C₅×D₃	1	6	yes	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	3	1	no	—
360	C₂²×C₄	—	3	6	no	—
361	C₂²×C₄	—	3	6	no	—
362	C₂²×C₄	—	6	12	no	—
363	C₂²×C₄	—	6	1	no	—
364	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
365	SD₁₆	—	3	16	no	—
366	SD₁₆	—	3	16	no	—
367	SD₁₆	—	3	16	no	—
368	SD₁₆	C₂²×C₅×D₃	1	16	yes	direct product factor
369	C₂×C₈	—	3	6	no	—
370	C₂×C₈	—	3	16	no	—
371	C₂×C₈	C₂²×C₅×D₃	1	6	yes	complemented
372	C₃×C₅	C₂³×SD₁₆	1	1	yes	characteristic, complemented, Hall
373	C₂²×C₃	—	2	4	no	—
374	C₂²×C₃	—	4	12	no	—
375	C₂²×C₃	C₂×C₅×SD₁₆	1	4	yes	complemented
376	C₂²×C₃	C₂²×C₅×D₄	1	3	yes	—
377	C₂×D₃	—	2	4	no	—
378	C₂×D₃	—	4	12	no	—
379	C₂×D₃	—	4	32	no	—
380	C₂×D₃	C₂×C₅×SD₁₆	1	24	yes	direct product factor
381	C₂×D₃	C₂²×C₅×D₄	1	4	yes	—
382	C₃×C₄	—	2	4	no	—
383	C₃×C₄	C₂²×C₅×D₄	1	3	yes	—
384	C₃×C₄	C₂⁵×C₅	1	1	yes	characteristic
385	Dic₃	—	2	4	no	—
386	Dic₃	C₂²×C₅×D₄	1	4	yes	—
387	C₂×C₅	—	3	8	no	—
388	C₂×C₅	—	4	4	no	—
389	C₂×C₅	—	12	4	no	—
390	C₂×C₅	C₂×D₃×SD₁₆	1	6	yes	direct product factor
391	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
392	C₂³	—	2	6	no	—
393	C₂³	—	3	8	no	—
394	C₂³	—	3	6	no	—
395	C₂³	—	4	4	no	—
396	C₂³	—	6	16	no	—
397	C₂³	—	6	6	no	—
398	C₂³	—	12	48	no	—
399	C₂³	—	12	4	no	—
400	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
401	Q₈	—	2	6	no	—
402	Q₈	—	3	4	no	—
403	Q₈	—	6	16	no	—
404	Q₈	—	6	6	no	—
405	Q₈	C₂³×C₅×D₃	1	4	yes	complemented
406	D₄	—	2	6	no	—
407	D₄	—	3	4	no	—
408	D₄	—	6	16	no	—
409	D₄	—	6	6	no	—
410	D₄	C₂³×C₅×D₃	1	4	yes	—
411	C₂×C₄	—	2	6	no	—
412	C₂×C₄	—	3	6	no	—
413	C₂×C₄	—	3	12	no	—
414	C₂×C₄	—	3	4	no	—
415	C₂×C₄	—	6	16	no	—
416	C₂×C₄	—	6	6	no	—
417	C₂×C₄	C₅×D₃×D₄	1	3	yes	—
418	C₂×C₄	C₂³×C₅×D₃	1	3	yes	—
419	C₈	—	3	4	no	—
420	C₈	C₂³×C₅×D₃	1	4	yes	complemented
421	C₂×C₃	—	4	4	no	—
422	C₂×C₃	C₂²×C₅×SD₁₆	1	6	yes	complemented
423	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
424	D₃	—	4	4	no	—
425	D₃	C₂²×C₅×SD₁₆	1	8	yes	direct product factor
426	C₅	C₂²×D₃×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
427	C₂²	—	2	4	no	—
428	C₂²	—	3	4	no	—
429	C₂²	—	3	24	no	—
430	C₂²	—	4	12	no	—
431	C₂²	—	6	4	no	—
432	C₂²	—	12	32	no	—
433	C₂²	—	12	12	no	—
434	C₂²	C₅×D₃×SD₁₆	1	4	yes	direct product factor
435	C₂²	C₂×C₅×D₃×D₄	1	3	yes	—
436	C₄	—	2	4	no	—
437	C₄	—	3	4	no	—
438	C₄	—	6	4	no	—
439	C₄	C₂×C₅×D₃×D₄	1	3	yes	—
440	C₄	C₂⁴×C₅×D₃	1	1	yes	characteristic
441	C₃	C₂³×C₅×SD₁₆	1	1	yes	characteristic, complemented, Sylow
442	C₂	—	3	8	no	—
443	C₂	—	4	4	no	—
444	C₂	—	12	4	no	—
445	C₂	C₂×C₅×D₃×SD₁₆	1	6	yes	direct product factor
446	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁵×C₅
Frattini	C₄	C₂⁴×C₅×D₃
Fitting	C₂²×C₃×C₅×SD₁₆	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₃×D₄	C₂
hypercenter	C₂²×C₅×SD₁₆	D₃
hypocenter	C₃	C₂³×C₅×SD₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×D₃×Q₈	C₂	semidirect
3. C₂²×C₃×C₅×SD₁₆	C₂	semidirect
4. C₂²×C₅×#215	C₂	semidirect
5. C₂²×C₅×#214	C₂	semidirect
6. C₂×C₅×D₃×SD₁₆	C₂	direct (N × H)
7. C₂²×C₅×#204	C₂	semidirect
8. C₂²×C₅×D₃×C₈	C₂	semidirect
11. C₂²×C₃×C₅×Q₈	C₂²	semidirect
15. C₂×C₅×D₃×Q₈	C₂²	semidirect
22. C₂²×C₅×Dic₆	C₂²	semidirect
23. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
24. C₂²×C₃×C₅×C₈	C₂²	semidirect
25. C₂×C₅×#215	C₂²	semidirect
26. C₂×C₅×#214	C₂²	semidirect
27. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
28. C₅×D₃×SD₁₆	C₂²	direct (N × H)
29. C₂×C₅×#204	C₂²	semidirect
30. C₂×C₅×D₃×C₈	C₂²	semidirect
31. C₂²×D₃×SD₁₆	C₅	direct (N × H)
38. C₂²×C₅×SD₁₆	D₃	direct (N × H)
46. C₂×C₃×C₅×Q₈	C₂³	semidirect
55. C₅×D₃×Q₈	C₂³	semidirect
65. C₂×C₅×Dic₆	C₂³	semidirect
66. C₃×C₅×SD₁₆	C₂³	semidirect
67. C₂×C₃×C₅×C₈	C₂³	semidirect
68. C₅×#215	C₂³	semidirect
69. C₅×#214	C₂³	semidirect
70. C₂×C₅×C₃⋊C₈	C₂³	semidirect
71. C₅×#204	C₂³	semidirect
72. C₅×D₃×C₈	C₂³	semidirect
73. C₂²×D₃×Q₈	C₂×C₅	semidirect
75. C₂²×C₃×SD₁₆	C₂×C₅	semidirect
76. C₂²×#215	C₂×C₅	semidirect
77. C₂²×#214	C₂×C₅	semidirect
78. C₂×D₃×SD₁₆	C₂×C₅	direct (N × H)
79. C₂²×#204	C₂×C₅	semidirect
80. C₂²×D₃×C₈	C₂×C₅	semidirect
86. C₂²×C₅×Q₈	C₂×D₃	semidirect
98. C₂×C₅×SD₁₆	C₂×D₃	direct (N × H)
101. C₂²×C₅×C₈	C₂×D₃	semidirect
110. C₂²×C₅×D₃	SD₁₆	direct (N × H)
113. C₃×C₅×Q₈	C₂⁴	semidirect
129. C₅×Dic₆	C₂⁴	semidirect
130. C₃×C₅×C₈	C₂⁴	semidirect
131. C₅×C₃⋊C₈	C₂⁴	semidirect
133. C₂²×C₃×Q₈	C₂²×C₅	semidirect
137. C₂×D₃×Q₈	C₂²×C₅	semidirect
144. C₂²×Dic₆	C₂²×C₅	semidirect
145. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
146. C₂²×C₃×C₈	C₂²×C₅	semidirect
147. C₂×#215	C₂²×C₅	semidirect
148. C₂×#214	C₂²×C₅	semidirect
149. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
150. D₃×SD₁₆	C₂²×C₅	direct (N × H)
151. C₂×#204	C₂²×C₅	semidirect
152. C₂×D₃×C₈	C₂²×C₅	semidirect
164. C₂×C₅×Q₈	C₂²×D₃	semidirect
182. C₅×SD₁₆	C₂²×D₃	direct (N × H)
185. C₂×C₅×C₈	C₂²×D₃	semidirect
192. C₂²×SD₁₆	C₅×D₃	direct (N × H)
196. C₂²×C₃×C₅	C₂×SD₁₆	semidirect
201. C₂×C₅×D₃	C₂×SD₁₆	direct (N × H)
214. C₂×C₃×Q₈	C₂³×C₅	semidirect
223. D₃×Q₈	C₂³×C₅	semidirect
233. C₂×Dic₆	C₂³×C₅	semidirect
234. C₃×SD₁₆	C₂³×C₅	semidirect
235. C₂×C₃×C₈	C₂³×C₅	semidirect
236. #215	C₂³×C₅	semidirect
237. #214	C₂³×C₅	semidirect
238. C₂×C₃⋊C₈	C₂³×C₅	semidirect
239. #204	C₂³×C₅	semidirect
240. D₃×C₈	C₂³×C₅	semidirect
254. C₅×Q₈	C₂³×D₃	semidirect
269. C₅×C₈	C₂³×D₃	semidirect
275. C₂²×Q₈	C₂×C₅×D₃	semidirect
287. C₂×SD₁₆	C₂×C₅×D₃	direct (N × H)
290. C₂²×C₈	C₂×C₅×D₃	semidirect
292. C₂×C₃×C₅	C₂²×SD₁₆	semidirect
295. C₅×D₃	C₂²×SD₁₆	direct (N × H)
303. C₂²×D₃	C₅×SD₁₆	direct (N × H)
306. C₃×Q₈	C₂⁴×C₅	semidirect
322. Dic₆	C₂⁴×C₅	semidirect
323. C₃×C₈	C₂⁴×C₅	semidirect
324. C₃⋊C₈	C₂⁴×C₅	semidirect
332. C₂²×C₅	D₃×SD₁₆	direct (N × H)
350. C₂×Q₈	C₂²×C₅×D₃	semidirect
368. SD₁₆	C₂²×C₅×D₃	direct (N × H)
371. C₂×C₈	C₂²×C₅×D₃	semidirect
372. C₃×C₅	C₂³×SD₁₆	semidirect
375. C₂²×C₃	C₂×C₅×SD₁₆	semidirect
380. C₂×D₃	C₂×C₅×SD₁₆	direct (N × H)
390. C₂×C₅	C₂×D₃×SD₁₆	direct (N × H)
405. Q₈	C₂³×C₅×D₃	semidirect
420. C₈	C₂³×C₅×D₃	semidirect
422. C₂×C₃	C₂²×C₅×SD₁₆	semidirect
425. D₃	C₂²×C₅×SD₁₆	direct (N × H)
426. C₅	C₂²×D₃×SD₁₆	direct (N × H)
434. C₂²	C₅×D₃×SD₁₆	direct (N × H)
441. C₃	C₂³×C₅×SD₁₆	semidirect
445. C₂	C₂×C₅×D₃×SD₁₆	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×C₅×D₃×Q₈	2
C₂²×C₅×D₃×D₄	2
C₂²×C₃×C₅×SD₁₆	2
C₂²×C₅×#215	2
C₂²×C₅×#214	2
C₂×C₅×D₃×SD₁₆	2
C₂²×C₅×#204	2
C₂²×C₅×D₃×C₈	2
C₂³×C₅×SD₁₆	3
C₂²×D₃×SD₁₆	5

Subgroups — C22×C5×D3×SD16 #14509655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×D₃×SD₁₆ #14509655