Subgroups — C₂²×C₃×D₅×SD₁₆ #14509656

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×C₃×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₄×D₅	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×#688	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃×#687	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×D₅×SD₁₆	C₂	1	24	yes	maximal, direct product factor
7	C₂²×C₃×#677	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₅×SD₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂⁴×C₃×D₅	—	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×C₃×C₂²⋊D₅	—	2	1	no	—
14	C₂×C₃×Q₈×D₅	—	2	6	no	—
15	C₂×C₃×Q₈×D₅	C₂²	1	12	yes	complemented
16	C₂×C₃×D₄×D₅	—	2	6	no	—
17	C₂×C₃×D₄×D₅	C₂²	1	12	yes	—
18	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×D₅	—	2	1	no	—
20	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
21	C₂²×C₃×Dic₁₀	—	2	1	no	—
22	C₂²×C₃×Dic₁₀	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×C₃×#688	C₂²	1	12	yes	complemented
26	C₂×C₃×#687	C₂²	1	12	yes	complemented
27	C₂²×C₃×#168	C₂²	1	1	yes	characteristic, complemented
28	C₃×D₅×SD₁₆	C₂²	1	64	yes	direct product factor
29	C₂×C₃×#677	C₂²	1	12	yes	complemented
30	C₂×C₃×C₈×D₅	C₂²	1	12	yes	complemented
31	C₂³×C₃×SD₁₆	—	5	1	no	maximal, Hall
32	C₂²×Q₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂²×D₄×D₅	C₂×C₃	1	1	yes	characteristic
34	C₂²×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂²×#688	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂²×#687	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×D₅×SD₁₆	C₂×C₃	1	24	yes	direct product factor
38	C₂²×#677	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂²×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂⁴×C₃×C₅	—	2	1	no	—
41	C₂³×C₃×D₅	—	2	1	no	—
42	C₂³×C₃×D₅	—	2	12	no	—
43	C₂³×C₃×D₅	—	4	8	no	—
44	C₂³×C₃×D₅	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×C₃×C₂²⋊D₅	—	2	12	no	—
52	C₂²×C₃×Dic₅	—	2	1	no	—
53	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
54	C₃×Q₈×D₅	—	2	24	no	—
55	C₃×Q₈×D₅	C₂³	1	16	yes	complemented
56	C₃×D₄×D₅	—	2	24	no	—
57	C₃×D₄×D₅	C₂³	1	16	yes	—
58	C₂×C₃×D₂₀	—	2	3	no	—
59	C₂×C₃×D₂₀	C₂³	1	6	yes	—
60	C₂×C₃×C₄×D₅	—	2	12	no	—
61	C₂×C₃×C₄×D₅	D₄	1	6	yes	—
62	C₂×C₃×C₄×D₅	C₂³	1	6	yes	—
63	C₂×C₃×Dic₁₀	—	2	3	no	—
64	C₂×C₃×Dic₁₀	—	2	12	no	—
65	C₂×C₃×Dic₁₀	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	C₃×#688	C₂³	1	16	yes	complemented
69	C₃×#687	C₂³	1	16	yes	complemented
70	C₂×C₃×#168	C₂³	1	6	yes	complemented
71	C₃×#677	C₂³	1	16	yes	complemented
72	C₃×C₈×D₅	C₂³	1	16	yes	complemented
73	C₂³×C₃×Q₈	—	5	1	no	—
74	C₂³×C₃×D₄	—	5	1	no	—
75	C₂²×C₃×SD₁₆	—	5	1	no	—
76	C₂²×C₃×SD₁₆	—	5	1	no	—
77	C₂²×C₃×SD₁₆	—	5	24	no	—
78	C₂²×C₃×SD₁₆	—	5	1	no	—
79	C₂²×C₃×SD₁₆	D₅	1	1	yes	characteristic, direct product factor
80	C₂³×C₃×C₈	—	5	1	no	—
81	C₂⁴×D₅	—	2	1	no	—
82	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
83	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
84	C₂²×C₂²⋊D₅	—	2	1	no	—
85	C₂×Q₈×D₅	—	2	6	no	—
86	C₂×Q₈×D₅	C₂²×C₃	1	12	yes	complemented
87	C₂×D₄×D₅	—	2	6	no	—
88	C₂×D₄×D₅	C₂²×C₃	1	12	yes	—
89	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
90	C₂²×C₄×D₅	—	2	1	no	—
91	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
92	C₂²×Dic₁₀	—	2	1	no	—
93	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
94	C₂×C₅×SD₁₆	C₂²×C₃	1	12	yes	complemented
95	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
96	C₂×#688	C₂²×C₃	1	12	yes	complemented
97	C₂×#687	C₂²×C₃	1	12	yes	complemented
98	C₂²×#168	C₂²×C₃	1	1	yes	characteristic, complemented
99	D₅×SD₁₆	C₂²×C₃	1	64	yes	direct product factor
100	C₂×#677	C₂²×C₃	1	12	yes	complemented
101	C₂×C₈×D₅	C₂²×C₃	1	12	yes	complemented
102	C₂³×SD₁₆	—	5	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×C₃×D₅	—	2	6	no	—
107	C₂²×C₃×D₅	—	2	16	no	—
108	C₂²×C₃×D₅	—	4	4	no	—
109	C₂²×C₃×D₅	—	4	48	no	—
110	C₂²×C₃×D₅	SD₁₆	1	8	yes	direct product factor
111	C₂²×C₃×D₅	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	C₃×C₂²⋊D₅	—	2	16	no	—
120	C₂×C₃×Dic₅	—	2	6	no	—
121	C₂×C₃×Dic₅	C₂×D₄	1	6	yes	—
122	C₃×D₂₀	—	2	6	no	—
123	C₃×D₂₀	C₂⁴	1	4	yes	—
124	C₃×C₄×D₅	—	2	16	no	—
125	C₃×C₄×D₅	C₂×D₄	1	12	yes	—
126	C₃×C₄×D₅	C₂⁴	1	4	yes	—
127	C₃×Dic₁₀	—	2	6	no	—
128	C₃×Dic₁₀	—	2	16	no	—
129	C₃×Dic₁₀	C₂⁴	1	4	yes	complemented
130	C₃×C₅×C₈	C₂⁴	1	4	yes	complemented
131	C₃×#168	C₂⁴	1	4	yes	complemented
132	C₂⁵×C₃	—	10	1	no	—
133	C₂²×C₃×Q₈	—	5	12	no	—
134	C₂²×C₃×Q₈	—	5	1	no	—
135	C₂²×C₃×Q₈	—	10	1	no	—
136	C₂²×C₃×Q₈	—	10	6	no	—
137	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
138	C₂²×C₃×D₄	—	5	12	no	—
139	C₂²×C₃×D₄	—	5	1	no	—
140	C₂²×C₃×D₄	—	10	6	no	—
141	C₂²×C₃×D₄	—	10	1	no	—
142	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
143	C₂³×C₃×C₄	—	5	1	no	—
144	C₂³×C₃×C₄	—	10	1	no	—
145	C₂×C₃×SD₁₆	—	5	12	no	—
146	C₂×C₃×SD₁₆	—	5	12	no	—
147	C₂×C₃×SD₁₆	—	5	64	no	—
148	C₂×C₃×SD₁₆	—	5	12	no	—
149	C₂×C₃×SD₁₆	C₂×D₅	1	12	yes	direct product factor
150	C₂²×C₃×C₈	—	5	1	no	—
151	C₂²×C₃×C₈	—	5	12	no	—
152	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic, complemented
153	C₂⁴×C₅	—	2	1	no	—
154	C₂³×D₅	—	2	1	no	—
155	C₂³×D₅	—	2	12	no	—
156	C₂³×D₅	—	4	8	no	—
157	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
158	C₂×C₅×Q₈	—	2	3	no	—
159	C₂×C₅×Q₈	C₂³×C₃	1	6	yes	complemented
160	C₂×C₅×D₄	—	2	3	no	—
161	C₂×C₅×D₄	C₂³×C₃	1	6	yes	—
162	C₂²×C₄×C₅	—	2	1	no	—
163	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
164	C₂×C₂²⋊D₅	—	2	12	no	—
165	C₂²×Dic₅	—	2	1	no	—
166	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
167	Q₈×D₅	—	2	24	no	—
168	Q₈×D₅	C₂³×C₃	1	16	yes	complemented
169	D₄×D₅	—	2	24	no	—
170	D₄×D₅	C₂³×C₃	1	16	yes	—
171	C₂×D₂₀	—	2	3	no	—
172	C₂×D₂₀	C₂³×C₃	1	6	yes	—
173	C₂×C₄×D₅	—	2	12	no	—
174	C₂×C₄×D₅	C₃×D₄	1	6	yes	—
175	C₂×C₄×D₅	C₂³×C₃	1	6	yes	—
176	C₂×Dic₁₀	—	2	3	no	—
177	C₂×Dic₁₀	—	2	12	no	—
178	C₂×Dic₁₀	C₂³×C₃	1	6	yes	complemented
179	C₅×SD₁₆	C₂³×C₃	1	16	yes	complemented
180	C₂×C₅×C₈	C₂³×C₃	1	6	yes	complemented
181	#688	C₂³×C₃	1	16	yes	complemented
182	#687	C₂³×C₃	1	16	yes	complemented
183	C₂×#168	C₂³×C₃	1	6	yes	complemented
184	#677	C₂³×C₃	1	16	yes	complemented
185	C₈×D₅	C₂³×C₃	1	16	yes	complemented
186	C₂³×Q₈	—	5	1	no	—
187	C₂³×D₄	—	5	1	no	—
188	C₂²×SD₁₆	—	5	1	no	—
189	C₂²×SD₁₆	—	5	1	no	—
190	C₂²×SD₁₆	—	5	24	no	—
191	C₂²×SD₁₆	—	5	1	no	—
192	C₂²×SD₁₆	C₃×D₅	1	1	yes	characteristic, direct product factor
193	C₂³×C₈	—	5	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×C₃×D₅	—	2	4	no	—
199	C₂×C₃×D₅	—	4	12	no	—
200	C₂×C₃×D₅	—	4	32	no	—
201	C₂×C₃×D₅	C₂×SD₁₆	1	24	yes	direct product factor
202	C₂×C₃×D₅	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	C₃×Dic₅	—	2	4	no	—
207	C₃×Dic₅	C₂²×D₄	1	4	yes	—
208	C₂⁴×C₃	—	2	1	no	—
209	C₂⁴×C₃	—	5	1	no	—
210	C₂⁴×C₃	—	10	12	no	—
211	C₂⁴×C₃	—	10	1	no	—
212	C₂⁴×C₃	—	20	8	no	—
213	C₂×C₃×Q₈	—	2	3	no	—
214	C₂×C₃×Q₈	—	5	16	no	—
215	C₂×C₃×Q₈	—	5	6	no	—
216	C₂×C₃×Q₈	—	10	12	no	—
217	C₂×C₃×Q₈	—	10	24	no	—
218	C₂×C₃×Q₈	—	10	3	no	—
219	C₂×C₃×Q₈	C₂²×D₅	1	6	yes	complemented
220	C₂×C₃×D₄	—	2	3	no	—
221	C₂×C₃×D₄	—	5	16	no	—
222	C₂×C₃×D₄	—	5	6	no	—
223	C₂×C₃×D₄	—	10	24	no	—
224	C₂×C₃×D₄	—	10	12	no	—
225	C₂×C₃×D₄	—	10	3	no	—
226	C₂×C₃×D₄	C₂²×D₅	1	6	yes	—
227	C₂²×C₃×C₄	—	2	1	no	—
228	C₂²×C₃×C₄	—	5	1	no	—
229	C₂²×C₃×C₄	—	5	6	no	—
230	C₂²×C₃×C₄	—	5	6	no	—
231	C₂²×C₃×C₄	—	10	12	no	—
232	C₂²×C₃×C₄	—	10	1	no	—
233	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
234	C₃×SD₁₆	—	5	16	no	—
235	C₃×SD₁₆	—	5	16	no	—
236	C₃×SD₁₆	—	5	16	no	—
237	C₃×SD₁₆	C₂²×D₅	1	16	yes	direct product factor
238	C₂×C₃×C₈	—	5	6	no	—
239	C₂×C₃×C₈	—	5	16	no	—
240	C₂×C₃×C₈	C₂²×D₅	1	6	yes	complemented
241	C₂³×C₅	—	2	6	no	—
242	C₂³×C₅	—	4	4	no	—
243	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
244	C₂²×D₅	—	2	6	no	—
245	C₂²×D₅	—	2	16	no	—
246	C₂²×D₅	—	4	4	no	—
247	C₂²×D₅	—	4	48	no	—
248	C₂²×D₅	C₃×SD₁₆	1	8	yes	direct product factor
249	C₂²×D₅	C₂×C₃×D₄	1	6	yes	—
250	C₅×Q₈	—	2	6	no	—
251	C₅×Q₈	C₂⁴×C₃	1	4	yes	complemented
252	C₅×D₄	—	2	6	no	—
253	C₅×D₄	C₂⁴×C₃	1	4	yes	—
254	C₂×C₄×C₅	—	2	6	no	—
255	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
256	C₂×C₄×C₅	C₂⁴×C₃	1	3	yes	—
257	C₂²⋊D₅	—	2	16	no	—
258	C₂×Dic₅	—	2	6	no	—
259	C₂×Dic₅	C₂×C₃×D₄	1	6	yes	—
260	D₂₀	—	2	6	no	—
261	D₂₀	C₂⁴×C₃	1	4	yes	—
262	C₄×D₅	—	2	16	no	—
263	C₄×D₅	C₂×C₃×D₄	1	12	yes	—
264	C₄×D₅	C₂⁴×C₃	1	4	yes	—
265	Dic₁₀	—	2	6	no	—
266	Dic₁₀	—	2	16	no	—
267	Dic₁₀	C₂⁴×C₃	1	4	yes	complemented
268	C₅×C₈	C₂⁴×C₃	1	4	yes	complemented
269	#168	C₂⁴×C₃	1	4	yes	complemented
270	C₂⁵	—	10	1	no	—
271	C₂²×Q₈	—	5	12	no	—
272	C₂²×Q₈	—	5	1	no	—
273	C₂²×Q₈	—	10	1	no	—
274	C₂²×Q₈	—	10	6	no	—
275	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
276	C₂²×D₄	—	5	12	no	—
277	C₂²×D₄	—	5	1	no	—
278	C₂²×D₄	—	10	6	no	—
279	C₂²×D₄	—	10	1	no	—
280	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
281	C₂³×C₄	—	5	1	no	—
282	C₂³×C₄	—	10	1	no	—
283	C₂×SD₁₆	—	5	12	no	—
284	C₂×SD₁₆	—	5	12	no	—
285	C₂×SD₁₆	—	5	64	no	—
286	C₂×SD₁₆	—	5	12	no	—
287	C₂×SD₁₆	C₂×C₃×D₅	1	12	yes	direct product factor
288	C₂²×C₈	—	5	1	no	—
289	C₂²×C₈	—	5	12	no	—
290	C₂²×C₈	C₂×C₃×D₅	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	C₃×D₅	—	4	4	no	—
295	C₃×D₅	C₂²×SD₁₆	1	8	yes	direct product factor
296	C₂³×C₃	—	2	6	no	—
297	C₂³×C₃	—	4	4	no	—
298	C₂³×C₃	—	5	6	no	—
299	C₂³×C₃	—	5	8	no	—
300	C₂³×C₃	—	10	16	no	—
301	C₂³×C₃	—	10	6	no	—
302	C₂³×C₃	—	20	48	no	—
303	C₂³×C₃	—	20	4	no	—
304	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
305	C₃×Q₈	—	2	6	no	—
306	C₃×Q₈	—	5	4	no	—
307	C₃×Q₈	—	10	16	no	—
308	C₃×Q₈	—	10	6	no	—
309	C₃×Q₈	C₂³×D₅	1	4	yes	complemented
310	C₃×D₄	—	2	6	no	—
311	C₃×D₄	—	5	4	no	—
312	C₃×D₄	—	10	16	no	—
313	C₃×D₄	—	10	6	no	—
314	C₃×D₄	C₂³×D₅	1	4	yes	—
315	C₂×C₃×C₄	—	2	6	no	—
316	C₂×C₃×C₄	—	5	6	no	—
317	C₂×C₃×C₄	—	5	12	no	—
318	C₂×C₃×C₄	—	5	4	no	—
319	C₂×C₃×C₄	—	10	16	no	—
320	C₂×C₃×C₄	—	10	6	no	—
321	C₂×C₃×C₄	D₄×D₅	1	3	yes	—
322	C₂×C₃×C₄	C₂³×D₅	1	3	yes	—
323	C₃×C₈	—	5	4	no	—
324	C₃×C₈	C₂³×D₅	1	4	yes	complemented
325	C₂²×C₅	—	2	4	no	—
326	C₂²×C₅	—	4	12	no	—
327	C₂²×C₅	C₂×C₃×SD₁₆	1	4	yes	complemented
328	C₂²×C₅	C₂²×C₃×D₄	1	3	yes	—
329	C₂×D₅	—	2	4	no	—
330	C₂×D₅	—	4	12	no	—
331	C₂×D₅	—	4	32	no	—
332	C₂×D₅	C₂×C₃×SD₁₆	1	24	yes	direct product factor
333	C₂×D₅	C₂²×C₃×D₄	1	4	yes	—
334	C₄×C₅	—	2	4	no	—
335	C₄×C₅	C₂²×C₃×D₄	1	3	yes	—
336	C₄×C₅	C₂⁵×C₃	1	1	yes	characteristic
337	Dic₅	—	2	4	no	—
338	Dic₅	C₂²×C₃×D₄	1	4	yes	—
339	C₂⁴	—	2	1	no	—
340	C₂⁴	—	5	1	no	—
341	C₂⁴	—	10	12	no	—
342	C₂⁴	—	10	1	no	—
343	C₂⁴	—	20	8	no	—
344	C₂×Q₈	—	2	3	no	—
345	C₂×Q₈	—	5	16	no	—
346	C₂×Q₈	—	5	6	no	—
347	C₂×Q₈	—	10	12	no	—
348	C₂×Q₈	—	10	24	no	—
349	C₂×Q₈	—	10	3	no	—
350	C₂×Q₈	C₂²×C₃×D₅	1	6	yes	complemented
351	C₂×D₄	—	2	3	no	—
352	C₂×D₄	—	5	16	no	—
353	C₂×D₄	—	5	6	no	—
354	C₂×D₄	—	10	24	no	—
355	C₂×D₄	—	10	12	no	—
356	C₂×D₄	—	10	3	no	—
357	C₂×D₄	C₂²×C₃×D₅	1	6	yes	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	5	1	no	—
360	C₂²×C₄	—	5	6	no	—
361	C₂²×C₄	—	5	6	no	—
362	C₂²×C₄	—	10	12	no	—
363	C₂²×C₄	—	10	1	no	—
364	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
365	SD₁₆	—	5	16	no	—
366	SD₁₆	—	5	16	no	—
367	SD₁₆	—	5	16	no	—
368	SD₁₆	C₂²×C₃×D₅	1	16	yes	direct product factor
369	C₂×C₈	—	5	6	no	—
370	C₂×C₈	—	5	16	no	—
371	C₂×C₈	C₂²×C₃×D₅	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	—	5	24	no	—
376	C₂²×C₃	—	5	4	no	—
377	C₂²×C₃	—	10	4	no	—
378	C₂²×C₃	—	20	32	no	—
379	C₂²×C₃	—	20	12	no	—
380	C₂²×C₃	D₅×SD₁₆	1	4	yes	direct product factor
381	C₂²×C₃	C₂×D₄×D₅	1	3	yes	—
382	C₃×C₄	—	2	4	no	—
383	C₃×C₄	—	5	4	no	—
384	C₃×C₄	—	10	4	no	—
385	C₃×C₄	C₂×D₄×D₅	1	3	yes	—
386	C₃×C₄	C₂⁴×D₅	1	1	yes	characteristic
387	C₂×C₅	—	4	4	no	—
388	C₂×C₅	C₂²×C₃×SD₁₆	1	6	yes	complemented
389	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
390	D₅	—	4	4	no	—
391	D₅	C₂²×C₃×SD₁₆	1	8	yes	direct product factor
392	C₂³	—	2	6	no	—
393	C₂³	—	4	4	no	—
394	C₂³	—	5	6	no	—
395	C₂³	—	5	8	no	—
396	C₂³	—	10	16	no	—
397	C₂³	—	10	6	no	—
398	C₂³	—	20	48	no	—
399	C₂³	—	20	4	no	—
400	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
401	Q₈	—	2	6	no	—
402	Q₈	—	5	4	no	—
403	Q₈	—	10	16	no	—
404	Q₈	—	10	6	no	—
405	Q₈	C₂³×C₃×D₅	1	4	yes	complemented
406	D₄	—	2	6	no	—
407	D₄	—	5	4	no	—
408	D₄	—	10	16	no	—
409	D₄	—	10	6	no	—
410	D₄	C₂³×C₃×D₅	1	4	yes	—
411	C₂×C₄	—	2	6	no	—
412	C₂×C₄	—	5	6	no	—
413	C₂×C₄	—	5	12	no	—
414	C₂×C₄	—	5	4	no	—
415	C₂×C₄	—	10	16	no	—
416	C₂×C₄	—	10	6	no	—
417	C₂×C₄	C₃×D₄×D₅	1	3	yes	—
418	C₂×C₄	C₂³×C₃×D₅	1	3	yes	—
419	C₈	—	5	4	no	—
420	C₈	C₂³×C₃×D₅	1	4	yes	complemented
421	C₂×C₃	—	4	4	no	—
422	C₂×C₃	—	5	8	no	—
423	C₂×C₃	—	20	4	no	—
424	C₂×C₃	C₂×D₅×SD₁₆	1	6	yes	direct product factor
425	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
426	C₅	C₂³×C₃×SD₁₆	1	1	yes	characteristic, complemented, Sylow
427	C₂²	—	2	4	no	—
428	C₂²	—	4	12	no	—
429	C₂²	—	5	4	no	—
430	C₂²	—	5	24	no	—
431	C₂²	—	10	4	no	—
432	C₂²	—	20	32	no	—
433	C₂²	—	20	12	no	—
434	C₂²	C₃×D₅×SD₁₆	1	4	yes	direct product factor
435	C₂²	C₂×C₃×D₄×D₅	1	3	yes	—
436	C₄	—	2	4	no	—
437	C₄	—	5	4	no	—
438	C₄	—	10	4	no	—
439	C₄	C₂×C₃×D₄×D₅	1	3	yes	—
440	C₄	C₂⁴×C₃×D₅	1	1	yes	characteristic
441	C₃	C₂²×D₅×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
442	C₂	—	4	4	no	—
443	C₂	—	5	8	no	—
444	C₂	—	20	4	no	—
445	C₂	C₂×C₃×D₅×SD₁₆	1	6	yes	direct product factor
446	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₄×D₅
commutator, cosocle	C₄×C₅	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×D₅
Fitting	C₂²×C₃×C₅×SD₁₆	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×D₄×D₅	C₂
hypercenter	C₂²×C₃×SD₁₆	D₅
hypocenter	C₅	C₂³×C₃×SD₁₆
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×Q₈×D₅	C₂	semidirect
3. C₂²×C₃×C₅×SD₁₆	C₂	semidirect
4. C₂²×C₃×#688	C₂	semidirect
5. C₂²×C₃×#687	C₂	semidirect
6. C₂×C₃×D₅×SD₁₆	C₂	direct (N × H)
7. C₂²×C₃×#677	C₂	semidirect
8. C₂²×C₃×C₈×D₅	C₂	semidirect
9. C₂²×D₅×SD₁₆	C₃	direct (N × H)
11. C₂²×C₃×C₅×Q₈	C₂²	semidirect
15. C₂×C₃×Q₈×D₅	C₂²	semidirect
22. C₂²×C₃×Dic₁₀	C₂²	semidirect
23. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
24. C₂²×C₃×C₅×C₈	C₂²	semidirect
25. C₂×C₃×#688	C₂²	semidirect
26. C₂×C₃×#687	C₂²	semidirect
27. C₂²×C₃×#168	C₂²	semidirect
28. C₃×D₅×SD₁₆	C₂²	direct (N × H)
29. C₂×C₃×#677	C₂²	semidirect
30. C₂×C₃×C₈×D₅	C₂²	semidirect
32. C₂²×Q₈×D₅	C₂×C₃	semidirect
34. C₂²×C₅×SD₁₆	C₂×C₃	semidirect
35. C₂²×#688	C₂×C₃	semidirect
36. C₂²×#687	C₂×C₃	semidirect
37. C₂×D₅×SD₁₆	C₂×C₃	direct (N × H)
38. C₂²×#677	C₂×C₃	semidirect
39. C₂²×C₈×D₅	C₂×C₃	semidirect
46. C₂×C₃×C₅×Q₈	C₂³	semidirect
55. C₃×Q₈×D₅	C₂³	semidirect
65. C₂×C₃×Dic₁₀	C₂³	semidirect
66. C₃×C₅×SD₁₆	C₂³	semidirect
67. C₂×C₃×C₅×C₈	C₂³	semidirect
68. C₃×#688	C₂³	semidirect
69. C₃×#687	C₂³	semidirect
70. C₂×C₃×#168	C₂³	semidirect
71. C₃×#677	C₂³	semidirect
72. C₃×C₈×D₅	C₂³	semidirect
79. C₂²×C₃×SD₁₆	D₅	direct (N × H)
82. C₂²×C₅×Q₈	C₂²×C₃	semidirect
86. C₂×Q₈×D₅	C₂²×C₃	semidirect
93. C₂²×Dic₁₀	C₂²×C₃	semidirect
94. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
95. C₂²×C₅×C₈	C₂²×C₃	semidirect
96. C₂×#688	C₂²×C₃	semidirect
97. C₂×#687	C₂²×C₃	semidirect
98. C₂²×#168	C₂²×C₃	semidirect
99. D₅×SD₁₆	C₂²×C₃	direct (N × H)
100. C₂×#677	C₂²×C₃	semidirect
101. C₂×C₈×D₅	C₂²×C₃	semidirect
110. C₂²×C₃×D₅	SD₁₆	direct (N × H)
113. C₃×C₅×Q₈	C₂⁴	semidirect
129. C₃×Dic₁₀	C₂⁴	semidirect
130. C₃×C₅×C₈	C₂⁴	semidirect
131. C₃×#168	C₂⁴	semidirect
137. C₂²×C₃×Q₈	C₂×D₅	semidirect
149. C₂×C₃×SD₁₆	C₂×D₅	direct (N × H)
152. C₂²×C₃×C₈	C₂×D₅	semidirect
159. C₂×C₅×Q₈	C₂³×C₃	semidirect
168. Q₈×D₅	C₂³×C₃	semidirect
178. C₂×Dic₁₀	C₂³×C₃	semidirect
179. C₅×SD₁₆	C₂³×C₃	semidirect
180. C₂×C₅×C₈	C₂³×C₃	semidirect
181. #688	C₂³×C₃	semidirect
182. #687	C₂³×C₃	semidirect
183. C₂×#168	C₂³×C₃	semidirect
184. #677	C₂³×C₃	semidirect
185. C₈×D₅	C₂³×C₃	semidirect
192. C₂²×SD₁₆	C₃×D₅	direct (N × H)
196. C₂²×C₃×C₅	C₂×SD₁₆	semidirect
201. C₂×C₃×D₅	C₂×SD₁₆	direct (N × H)
219. C₂×C₃×Q₈	C₂²×D₅	semidirect
237. C₃×SD₁₆	C₂²×D₅	direct (N × H)
240. C₂×C₃×C₈	C₂²×D₅	semidirect
248. C₂²×D₅	C₃×SD₁₆	direct (N × H)
251. C₅×Q₈	C₂⁴×C₃	semidirect
267. Dic₁₀	C₂⁴×C₃	semidirect
268. C₅×C₈	C₂⁴×C₃	semidirect
269. #168	C₂⁴×C₃	semidirect
275. C₂²×Q₈	C₂×C₃×D₅	semidirect
287. C₂×SD₁₆	C₂×C₃×D₅	direct (N × H)
290. C₂²×C₈	C₂×C₃×D₅	semidirect
292. C₂×C₃×C₅	C₂²×SD₁₆	semidirect
295. C₃×D₅	C₂²×SD₁₆	direct (N × H)
309. C₃×Q₈	C₂³×D₅	semidirect
324. C₃×C₈	C₂³×D₅	semidirect
327. C₂²×C₅	C₂×C₃×SD₁₆	semidirect
332. C₂×D₅	C₂×C₃×SD₁₆	direct (N × H)
350. C₂×Q₈	C₂²×C₃×D₅	semidirect
368. SD₁₆	C₂²×C₃×D₅	direct (N × H)
371. C₂×C₈	C₂²×C₃×D₅	semidirect
372. C₃×C₅	C₂³×SD₁₆	semidirect
380. C₂²×C₃	D₅×SD₁₆	direct (N × H)
388. C₂×C₅	C₂²×C₃×SD₁₆	semidirect
391. D₅	C₂²×C₃×SD₁₆	direct (N × H)
405. Q₈	C₂³×C₃×D₅	semidirect
420. C₈	C₂³×C₃×D₅	semidirect
424. C₂×C₃	C₂×D₅×SD₁₆	direct (N × H)
426. C₅	C₂³×C₃×SD₁₆	semidirect
434. C₂²	C₃×D₅×SD₁₆	direct (N × H)
441. C₃	C₂²×D₅×SD₁₆	direct (N × H)
445. C₂	C₂×C₃×D₅×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×C₃×Q₈×D₅	2
C₂²×C₃×D₄×D₅	2
C₂²×C₃×C₅×SD₁₆	2
C₂²×C₃×#688	2
C₂²×C₃×#687	2
C₂×C₃×D₅×SD₁₆	2
C₂²×C₃×#677	2
C₂²×C₃×C₈×D₅	2
C₂²×D₅×SD₁₆	3
C₂³×C₃×SD₁₆	5

Subgroups — C22×C3×D5×SD16 #14509656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×D₅×SD₁₆ #14509656