Subgroups — C₃×C₄×D₅×SD₁₆ #14416041

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×SD₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₄×#688	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×#687	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×D₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×D₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65077	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×D₅×#102	C₂	1	1	yes	maximal, characteristic
13	C₃×#65047	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₄×#677	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×D₅×SD₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×D₅	—	2	1	no	—
20	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×#688	C₂²	1	1	yes	characteristic
25	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×#687	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
28	C₃×D₅×SD₁₆	C₄	1	8	yes	direct product factor
29	C₂×C₃×#677	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
32	C₃×#4039	C₂²	1	1	yes	characteristic
33	C₃×D₅×C₄⋊C₄	—	2	1	no	—
34	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₃×#4033	—	2	1	no	—
37	C₃×#4033	C₂²	1	1	yes	characteristic, complemented
38	C₃×#4027	—	2	1	no	—
39	C₃×D₅×C₂²⋊C₄	—	2	1	no	—
40	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
41	C₃×C₄²×D₅	—	2	1	no	—
42	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
43	C₃×C₄×Dic₁₀	—	2	1	no	—
44	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₅×#102	C₂²	1	1	yes	characteristic
48	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
49	C₃×#3967	C₂²	1	1	yes	characteristic, complemented
50	C₃×#3964	C₂²	1	1	yes	characteristic
51	C₃×#3953	C₂²	1	1	yes	characteristic
52	C₃×#3949	C₂²	1	1	yes	characteristic, complemented
53	C₃×#3948	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
56	C₃×#3942	C₂²	1	1	yes	characteristic, complemented
57	C₃×#3941	C₂²	1	1	yes	characteristic
58	C₃×#3940	C₂²	1	1	yes	characteristic, complemented
59	C₃×#3940	C₂²	1	1	yes	characteristic, complemented
60	C₃×C₄×#168	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₃×C₄×SD₁₆	—	5	1	no	maximal, Hall
62	C₂×D₅×SD₁₆	C₂×C₃	1	1	yes	characteristic
63	C₄×Q₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
64	C₄×D₄×D₅	C₂×C₃	1	1	yes	characteristic
65	C₄×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
66	SD₁₆×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
67	C₄×#688	C₂×C₃	1	1	yes	characteristic, complemented
68	C₄×#687	C₂×C₃	1	1	yes	characteristic, complemented
69	D₅×#106	C₂×C₃	1	1	yes	characteristic, complemented
70	#65141	C₂×C₃	1	1	yes	characteristic, complemented
71	D₅×#103	C₂×C₃	1	1	yes	characteristic, complemented
72	#65077	C₂×C₃	1	1	yes	characteristic, complemented
73	D₅×#102	C₂×C₃	1	1	yes	characteristic
74	#65047	C₂×C₃	1	1	yes	characteristic, complemented
75	C₄×#677	C₂×C₃	1	1	yes	characteristic, complemented
76	C₄×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
77	C₂³×C₃×D₅	—	2	1	no	—
78	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	—	2	1	no	—
81	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
82	C₂²×C₃×Dic₅	—	2	1	no	—
83	C₃×Q₈×D₅	—	2	2	no	—
84	C₃×Q₈×D₅	C₂×C₄	1	4	yes	complemented
85	C₃×D₄×D₅	—	2	2	no	—
86	C₃×D₄×D₅	C₂×C₄	1	4	yes	—
87	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₄×D₅	—	2	1	no	—
89	C₂×C₃×C₄×D₅	—	2	1	no	—
90	C₂×C₃×C₄×D₅	—	2	1	no	—
91	C₂×C₃×C₄×D₅	—	2	1	no	—
92	C₂×C₃×C₄×D₅	—	2	1	no	—
93	C₂×C₃×C₄×D₅	—	4	4	no	—
94	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
95	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
97	C₂×C₃×Dic₁₀	—	2	1	no	—
98	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
99	C₃×C₅×SD₁₆	C₂×C₄	1	4	yes	complemented
100	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
102	C₃×C₅×C₄⋊C₄	—	2	1	no	—
103	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
106	C₃×C₄²×C₅	—	2	1	no	—
107	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
108	C₃×C₂²⋊Dic₅	—	2	1	no	—
109	C₃×#688	C₂×C₄	1	4	yes	complemented
110	C₃×#687	C₂×C₄	1	4	yes	complemented
111	C₃×#685	—	2	1	no	—
112	C₃×#685	—	2	1	no	—
113	C₃×C₄⋊Dic₅	—	2	1	no	—
114	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
115	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
116	C₃×#683	—	2	1	no	—
117	C₃×#683	—	2	1	no	—
118	C₃×#683	—	2	1	no	—
119	C₃×#683	—	2	1	no	—
120	C₃×C₄×Dic₅	—	2	1	no	—
121	C₃×C₄×Dic₅	—	2	1	no	—
122	C₃×C₄×Dic₅	—	2	1	no	—
123	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
124	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
125	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
126	C₂×C₃×#168	C₂³	1	1	yes	characteristic
127	C₂×C₃×#168	C₂³	1	1	yes	characteristic
128	C₃×#677	C₂×C₄	1	4	yes	complemented
129	C₃×C₈×D₅	—	2	2	no	—
130	C₃×C₈×D₅	C₂×C₄	1	4	yes	complemented
131	C₂²×C₃×SD₁₆	—	5	1	no	—
132	C₂×C₃×C₄×Q₈	—	5	1	no	—
133	C₂×C₃×C₄×D₄	—	5	1	no	—
134	C₃×C₄×SD₁₆	—	5	1	no	—
135	C₃×C₄×SD₁₆	—	5	1	no	—
136	C₃×C₄×SD₁₆	—	5	1	no	—
137	C₃×C₄×SD₁₆	—	5	1	no	—
138	C₃×C₄×SD₁₆	—	5	1	no	—
139	C₃×C₄×SD₁₆	—	5	1	no	—
140	C₃×C₄×SD₁₆	—	5	1	no	—
141	C₃×C₄×SD₁₆	D₅	1	1	yes	characteristic, direct product factor
142	C₂×C₃×#106	—	5	1	no	—
143	C₂×C₃×#103	—	5	1	no	—
144	C₂×C₃×#102	—	5	1	no	—
145	C₂×C₃×C₄×C₈	—	5	1	no	—
146	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
147	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
148	C₂²×C₄×D₅	—	2	1	no	—
149	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
150	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
151	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
152	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
153	C₂×#688	C₂²×C₃	1	1	yes	characteristic
154	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
155	C₂×#687	C₂²×C₃	1	1	yes	characteristic
156	C₄×C₂²⋊D₅	—	2	1	no	—
157	D₅×SD₁₆	C₃×C₄	1	8	yes	direct product factor
158	C₂×#677	C₂²×C₃	1	1	yes	characteristic
159	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
160	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
161	#4039	C₂²×C₃	1	1	yes	characteristic
162	D₅×C₄⋊C₄	—	2	1	no	—
163	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
164	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
165	#4033	—	2	1	no	—
166	#4033	C₂²×C₃	1	1	yes	characteristic, complemented
167	#4027	—	2	1	no	—
168	D₅×C₂²⋊C₄	—	2	1	no	—
169	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
170	C₄²×D₅	—	2	1	no	—
171	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
172	C₄×Dic₁₀	—	2	1	no	—
173	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
174	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
175	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
176	C₅×#102	C₂²×C₃	1	1	yes	characteristic
177	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
178	#3967	C₂²×C₃	1	1	yes	characteristic, complemented
179	#3964	C₂²×C₃	1	1	yes	characteristic
180	#3953	C₂²×C₃	1	1	yes	characteristic
181	#3949	C₂²×C₃	1	1	yes	characteristic, complemented
182	#3948	C₂²×C₃	1	1	yes	characteristic, complemented
183	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
184	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
185	#3942	C₂²×C₃	1	1	yes	characteristic, complemented
186	#3941	C₂²×C₃	1	1	yes	characteristic
187	#3940	C₂²×C₃	1	1	yes	characteristic, complemented
188	#3940	C₂²×C₃	1	1	yes	characteristic, complemented
189	C₄×#168	C₂²×C₃	1	1	yes	characteristic, complemented
190	C₂×C₄×SD₁₆	—	5	1	no	Sylow
191	C₂³×C₃×C₅	—	2	1	no	—
192	C₂²×C₃×D₅	—	2	1	no	—
193	C₂²×C₃×D₅	—	2	4	no	—
194	C₂²×C₃×D₅	—	4	2	no	—
195	C₂²×C₃×D₅	—	4	2	no	—
196	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
197	C₃×C₅×Q₈	—	2	1	no	—
198	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	complemented
199	C₃×C₅×D₄	—	2	1	no	—
200	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
201	C₂×C₃×C₄×C₅	—	2	1	no	—
202	C₂×C₃×C₄×C₅	—	2	1	no	—
203	C₂×C₃×C₄×C₅	—	2	1	no	—
204	C₂×C₃×C₄×C₅	—	4	2	no	—
205	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
206	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
207	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
208	C₃×C₂²⋊D₅	—	2	4	no	—
209	C₂×C₃×Dic₅	—	2	1	no	—
210	C₂×C₃×Dic₅	—	2	1	no	—
211	C₂×C₃×Dic₅	—	2	1	no	—
212	C₂×C₃×Dic₅	—	4	2	no	—
213	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
214	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
215	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
216	C₃×D₂₀	—	2	1	no	—
217	C₃×D₂₀	C₂²×C₄	1	2	yes	—
218	C₃×C₄×D₅	—	2	4	no	—
219	C₃×C₄×D₅	—	2	2	no	—
220	C₃×C₄×D₅	—	4	2	no	—
221	C₃×C₄×D₅	—	4	2	no	—
222	C₃×C₄×D₅	—	4	2	no	—
223	C₃×C₄×D₅	—	4	2	no	—
224	C₃×C₄×D₅	SD₁₆	1	4	yes	direct product factor
225	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
226	C₃×C₄×D₅	#41	1	2	yes	—
227	C₃×Dic₁₀	—	2	1	no	—
228	C₃×Dic₁₀	—	2	4	no	—
229	C₃×Dic₁₀	C₂²×C₄	1	2	yes	complemented
230	C₃×C₅×C₈	—	2	1	no	—
231	C₃×C₅×C₈	C₂²×C₄	1	2	yes	complemented
232	C₃×#168	—	2	1	no	—
233	C₃×#168	C₂²×C₄	1	2	yes	complemented
234	C₂²×C₃×Q₈	—	5	1	no	—
235	C₂²×C₃×D₄	—	5	1	no	—
236	C₂³×C₃×C₄	—	10	1	no	—
237	C₂×C₃×SD₁₆	—	5	1	no	—
238	C₂×C₃×SD₁₆	—	5	1	no	—
239	C₂×C₃×SD₁₆	—	5	8	no	—
240	C₂×C₃×SD₁₆	—	5	1	no	—
241	C₂×C₃×SD₁₆	C₂×D₅	1	1	yes	characteristic
242	C₂²×C₃×C₈	—	5	1	no	—
243	C₂²×C₃×C₈	—	5	1	no	—
244	C₃×C₄×Q₈	—	5	1	no	—
245	C₃×C₄×Q₈	—	5	1	no	—
246	C₃×C₄×Q₈	—	5	1	no	—
247	C₃×C₄×Q₈	—	10	1	no	—
248	C₃×C₄×Q₈	—	10	1	no	—
249	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
250	C₃×C₄×D₄	—	5	1	no	—
251	C₃×C₄×D₄	—	5	1	no	—
252	C₃×C₄×D₄	—	5	1	no	—
253	C₃×C₄×D₄	—	10	1	no	—
254	C₃×C₄×D₄	—	10	1	no	—
255	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
256	C₂×C₃×C₄⋊C₄	—	5	1	no	—
257	C₂×C₃×C₄⋊C₄	—	5	1	no	—
258	C₂×C₃×C₄⋊C₄	—	10	1	no	—
259	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
260	C₂×C₃×C₄²	—	5	1	no	—
261	C₂×C₃×C₄²	—	10	1	no	—
262	C₃×#106	—	5	1	no	—
263	C₃×#106	—	5	1	no	—
264	C₃×#106	—	5	1	no	—
265	C₃×#106	C₂×D₅	1	1	yes	characteristic, complemented
266	C₃×#103	—	5	1	no	—
267	C₃×#103	—	5	1	no	—
268	C₃×#103	—	5	1	no	—
269	C₃×#103	C₂×D₅	1	1	yes	characteristic, complemented
270	C₃×#102	—	5	1	no	—
271	C₃×#102	—	5	1	no	—
272	C₃×#102	—	5	1	no	—
273	C₃×#102	C₂×D₅	1	1	yes	characteristic
274	C₃×C₄×C₈	—	5	1	no	—
275	C₃×C₄×C₈	—	5	1	no	—
276	C₃×C₄×C₈	—	5	1	no	—
277	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
278	C₂³×D₅	—	2	1	no	—
279	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
280	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
281	C₂²×C₄×C₅	—	2	1	no	—
282	C₂×C₂²⋊D₅	—	2	1	no	—
283	C₂²×Dic₅	—	2	1	no	—
284	Q₈×D₅	—	2	2	no	—
285	Q₈×D₅	C₂×C₃×C₄	1	4	yes	complemented
286	D₄×D₅	—	2	2	no	—
287	D₄×D₅	C₂×C₃×C₄	1	4	yes	—
288	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
289	C₂×C₄×D₅	—	2	1	no	—
290	C₂×C₄×D₅	—	2	1	no	—
291	C₂×C₄×D₅	—	2	1	no	—
292	C₂×C₄×D₅	—	2	1	no	—
293	C₂×C₄×D₅	—	2	1	no	—
294	C₂×C₄×D₅	—	4	4	no	—
295	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
296	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
297	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
298	C₂×Dic₁₀	—	2	1	no	—
299	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
300	C₅×SD₁₆	C₂×C₃×C₄	1	4	yes	complemented
301	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
302	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
303	C₅×C₄⋊C₄	—	2	1	no	—
304	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
305	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
306	C₅×C₂²⋊C₄	—	2	1	no	—
307	C₄²×C₅	—	2	1	no	—
308	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
309	C₂²⋊Dic₅	—	2	1	no	—
310	#688	C₂×C₃×C₄	1	4	yes	complemented
311	#687	C₂×C₃×C₄	1	4	yes	complemented
312	#685	—	2	1	no	—
313	#685	—	2	1	no	—
314	C₄⋊Dic₅	—	2	1	no	—
315	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
316	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
317	#683	—	2	1	no	—
318	#683	—	2	1	no	—
319	#683	—	2	1	no	—
320	#683	—	2	1	no	—
321	C₄×Dic₅	—	2	1	no	—
322	C₄×Dic₅	—	2	1	no	—
323	C₄×Dic₅	—	2	1	no	—
324	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
325	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
326	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
327	C₂×#168	C₂³×C₃	1	1	yes	characteristic
328	C₂×#168	C₂³×C₃	1	1	yes	characteristic
329	#677	C₂×C₃×C₄	1	4	yes	complemented
330	C₈×D₅	—	2	2	no	—
331	C₈×D₅	C₂×C₃×C₄	1	4	yes	complemented
332	C₂²×SD₁₆	—	5	1	no	—
333	C₂×C₄×Q₈	—	5	1	no	—
334	C₂×C₄×D₄	—	5	1	no	—
335	C₄×SD₁₆	—	5	1	no	—
336	C₄×SD₁₆	—	5	1	no	—
337	C₄×SD₁₆	—	5	1	no	—
338	C₄×SD₁₆	—	5	1	no	—
339	C₄×SD₁₆	—	5	1	no	—
340	C₄×SD₁₆	—	5	1	no	—
341	C₄×SD₁₆	—	5	1	no	—
342	C₄×SD₁₆	C₃×D₅	1	1	yes	characteristic, direct product factor
343	C₂×#106	—	5	1	no	—
344	C₂×#103	—	5	1	no	—
345	C₂×#102	—	5	1	no	—
346	C₂×C₄×C₈	—	5	1	no	—
347	C₂²×C₃×C₅	—	2	2	no	—
348	C₂²×C₃×C₅	—	4	1	no	—
349	C₂²×C₃×C₅	—	4	1	no	—
350	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₃×D₅	—	2	2	no	—
352	C₂×C₃×D₅	—	4	1	no	—
353	C₂×C₃×D₅	—	4	1	no	—
354	C₂×C₃×D₅	—	4	8	no	—
355	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
356	C₂×C₃×D₅	C₂×SD₁₆	1	2	yes	—
357	C₂×C₃×D₅	#135	1	2	yes	—
358	C₃×C₄×C₅	—	2	2	no	—
359	C₃×C₄×C₅	—	2	1	no	—
360	C₃×C₄×C₅	—	4	1	no	—
361	C₃×C₄×C₅	—	4	1	no	—
362	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	complemented
363	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
364	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
365	C₃×Dic₅	—	2	2	no	—
366	C₃×Dic₅	—	2	1	no	—
367	C₃×Dic₅	—	4	1	no	—
368	C₃×Dic₅	—	4	1	no	—
369	C₃×Dic₅	C₄×D₄	1	2	yes	—
370	C₃×Dic₅	C₂×SD₁₆	1	2	yes	complemented
371	C₂⁴×C₃	—	10	1	no	—
372	C₂×C₃×Q₈	—	5	4	no	—
373	C₂×C₃×Q₈	—	5	1	no	—
374	C₂×C₃×Q₈	—	10	1	no	—
375	C₂×C₃×Q₈	—	10	2	no	—
376	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
377	C₂×C₃×D₄	—	5	4	no	—
378	C₂×C₃×D₄	—	5	1	no	—
379	C₂×C₃×D₄	—	10	2	no	—
380	C₂×C₃×D₄	—	10	1	no	—
381	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
382	C₂²×C₃×C₄	—	2	1	no	—
383	C₂²×C₃×C₄	—	5	1	no	—
384	C₂²×C₃×C₄	—	5	1	no	—
385	C₂²×C₃×C₄	—	5	1	no	—
386	C₂²×C₃×C₄	—	10	1	no	—
387	C₂²×C₃×C₄	—	10	1	no	—
388	C₂²×C₃×C₄	—	10	1	no	—
389	C₂²×C₃×C₄	—	10	1	no	—
390	C₂²×C₃×C₄	—	10	1	no	—
391	C₂²×C₃×C₄	—	10	1	no	—
392	C₂²×C₃×C₄	—	20	4	no	—
393	C₃×SD₁₆	—	5	4	no	—
394	C₃×SD₁₆	—	5	4	no	—
395	C₃×SD₁₆	—	5	4	no	—
396	C₃×SD₁₆	C₄×D₅	1	4	yes	direct product factor
397	C₂×C₃×C₈	—	5	1	no	—
398	C₂×C₃×C₈	—	5	4	no	—
399	C₂×C₃×C₈	—	5	1	no	—
400	C₂×C₃×C₈	—	10	2	no	—
401	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
402	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
403	C₃×C₄⋊C₄	—	2	1	no	—
404	C₃×C₄⋊C₄	—	5	1	no	—
405	C₃×C₄⋊C₄	—	5	1	no	—
406	C₃×C₄⋊C₄	—	10	1	no	—
407	C₃×C₄⋊C₄	—	10	1	no	—
408	C₃×C₄⋊C₄	—	10	1	no	—
409	C₃×C₄⋊C₄	—	10	1	no	—
410	C₃×C₄⋊C₄	—	10	1	no	—
411	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
412	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
413	C₃×C₂²⋊C₄	—	2	1	no	—
414	C₃×C₂²⋊C₄	—	10	1	no	—
415	C₃×C₂²⋊C₄	—	10	1	no	—
416	C₃×C₂²⋊C₄	—	10	1	no	—
417	C₃×C₄²	—	2	1	no	—
418	C₃×C₄²	—	5	1	no	—
419	C₃×C₄²	—	5	1	no	—
420	C₃×C₄²	—	5	1	no	—
421	C₃×C₄²	—	10	1	no	—
422	C₃×C₄²	—	10	1	no	—
423	C₃×C₄²	—	10	1	no	—
424	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
425	C₂³×C₅	—	2	1	no	—
426	C₂²×D₅	—	2	1	no	—
427	C₂²×D₅	—	2	4	no	—
428	C₂²×D₅	—	4	2	no	—
429	C₂²×D₅	—	4	2	no	—
430	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
431	C₅×Q₈	—	2	1	no	—
432	C₅×Q₈	C₂²×C₃×C₄	1	2	yes	complemented
433	C₅×D₄	—	2	1	no	—
434	C₅×D₄	C₂²×C₃×C₄	1	2	yes	—
435	C₂×C₄×C₅	—	2	1	no	—
436	C₂×C₄×C₅	—	2	1	no	—
437	C₂×C₄×C₅	—	2	1	no	—
438	C₂×C₄×C₅	—	4	2	no	—
439	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
440	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
441	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
442	C₂²⋊D₅	—	2	4	no	—
443	C₂×Dic₅	—	2	1	no	—
444	C₂×Dic₅	—	2	1	no	—
445	C₂×Dic₅	—	2	1	no	—
446	C₂×Dic₅	—	4	2	no	—
447	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
448	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
449	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
450	D₂₀	—	2	1	no	—
451	D₂₀	C₂²×C₃×C₄	1	2	yes	—
452	C₄×D₅	—	2	4	no	—
453	C₄×D₅	—	2	2	no	—
454	C₄×D₅	—	4	2	no	—
455	C₄×D₅	—	4	2	no	—
456	C₄×D₅	—	4	2	no	—
457	C₄×D₅	—	4	2	no	—
458	C₄×D₅	C₃×SD₁₆	1	4	yes	direct product factor
459	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
460	C₄×D₅	C₃×#41	1	2	yes	—
461	Dic₁₀	—	2	1	no	—
462	Dic₁₀	—	2	4	no	—
463	Dic₁₀	C₂²×C₃×C₄	1	2	yes	complemented
464	C₅×C₈	—	2	1	no	—
465	C₅×C₈	C₂²×C₃×C₄	1	2	yes	complemented
466	#168	—	2	1	no	—
467	#168	C₂²×C₃×C₄	1	2	yes	complemented
468	C₂²×Q₈	—	5	1	no	—
469	C₂²×D₄	—	5	1	no	—
470	C₂³×C₄	—	10	1	no	—
471	C₂×SD₁₆	—	5	1	no	—
472	C₂×SD₁₆	—	5	1	no	—
473	C₂×SD₁₆	—	5	8	no	—
474	C₂×SD₁₆	—	5	1	no	—
475	C₂×SD₁₆	C₂×C₃×D₅	1	1	yes	characteristic
476	C₂²×C₈	—	5	1	no	—
477	C₂²×C₈	—	5	1	no	—
478	C₄×Q₈	—	5	1	no	—
479	C₄×Q₈	—	5	1	no	—
480	C₄×Q₈	—	5	1	no	—
481	C₄×Q₈	—	10	1	no	—
482	C₄×Q₈	—	10	1	no	—
483	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
484	C₄×D₄	—	5	1	no	—
485	C₄×D₄	—	5	1	no	—
486	C₄×D₄	—	5	1	no	—
487	C₄×D₄	—	10	1	no	—
488	C₄×D₄	—	10	1	no	—
489	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
490	C₂×C₄⋊C₄	—	5	1	no	—
491	C₂×C₄⋊C₄	—	5	1	no	—
492	C₂×C₄⋊C₄	—	10	1	no	—
493	C₂×C₂²⋊C₄	—	10	1	no	—
494	C₂×C₄²	—	5	1	no	—
495	C₂×C₄²	—	10	1	no	—
496	#106	—	5	1	no	—
497	#106	—	5	1	no	—
498	#106	—	5	1	no	—
499	#106	C₂×C₃×D₅	1	1	yes	characteristic, complemented
500	#103	—	5	1	no	—
501	#103	—	5	1	no	—
502	#103	—	5	1	no	—
503	#103	C₂×C₃×D₅	1	1	yes	characteristic, complemented
504	#102	—	5	1	no	—
505	#102	—	5	1	no	—
506	#102	—	5	1	no	—
507	#102	C₂×C₃×D₅	1	1	yes	characteristic
508	C₄×C₈	—	5	1	no	—
509	C₄×C₈	—	5	1	no	—
510	C₄×C₈	—	5	1	no	—
511	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
512	C₂×C₃×C₅	—	4	2	no	—
513	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
514	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
515	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
516	C₃×D₅	—	4	2	no	—
517	C₃×D₅	C₄×SD₁₆	1	4	yes	direct product factor
518	C₂³×C₃	—	2	1	no	—
519	C₂³×C₃	—	5	1	no	—
520	C₂³×C₃	—	10	4	no	—
521	C₂³×C₃	—	10	1	no	—
522	C₂³×C₃	—	20	2	no	—
523	C₂³×C₃	—	20	2	no	—
524	C₃×Q₈	—	2	1	no	—
525	C₃×Q₈	—	5	2	no	—
526	C₃×Q₈	—	10	4	no	—
527	C₃×Q₈	—	10	1	no	—
528	C₃×Q₈	C₂×C₄×D₅	1	2	yes	complemented
529	C₃×D₄	—	2	1	no	—
530	C₃×D₄	—	5	2	no	—
531	C₃×D₄	—	10	4	no	—
532	C₃×D₄	—	10	1	no	—
533	C₃×D₄	C₂×C₄×D₅	1	2	yes	—
534	C₂×C₃×C₄	—	2	1	no	—
535	C₂×C₃×C₄	—	2	1	no	—
536	C₂×C₃×C₄	—	2	1	no	—
537	C₂×C₃×C₄	—	4	2	no	—
538	C₂×C₃×C₄	—	5	1	no	—
539	C₂×C₃×C₄	—	5	1	no	—
540	C₂×C₃×C₄	—	5	2	no	—
541	C₂×C₃×C₄	—	5	2	no	—
542	C₂×C₃×C₄	—	5	4	no	—
543	C₂×C₃×C₄	—	5	1	no	—
544	C₂×C₃×C₄	—	10	2	no	—
545	C₂×C₃×C₄	—	10	4	no	—
546	C₂×C₃×C₄	—	10	1	no	—
547	C₂×C₃×C₄	—	10	1	no	—
548	C₂×C₃×C₄	—	10	1	no	—
549	C₂×C₃×C₄	—	20	2	no	—
550	C₂×C₃×C₄	—	20	2	no	—
551	C₂×C₃×C₄	—	20	2	no	—
552	C₂×C₃×C₄	—	20	2	no	—
553	C₂×C₃×C₄	—	20	2	no	—
554	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
555	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
556	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
557	C₃×C₈	—	2	1	no	—
558	C₃×C₈	—	5	2	no	—
559	C₃×C₈	—	10	1	no	—
560	C₃×C₈	C₂×C₄×D₅	1	2	yes	complemented
561	C₂²×C₅	—	2	2	no	—
562	C₂²×C₅	—	4	1	no	—
563	C₂²×C₅	—	4	1	no	—
564	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
565	C₂×D₅	—	2	2	no	—
566	C₂×D₅	—	4	1	no	—
567	C₂×D₅	—	4	1	no	—
568	C₂×D₅	—	4	8	no	—
569	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
570	C₂×D₅	C₂×C₃×SD₁₆	1	2	yes	—
571	C₂×D₅	C₃×#135	1	2	yes	—
572	C₄×C₅	—	2	1	no	—
573	C₄×C₅	—	2	2	no	—
574	C₄×C₅	—	4	1	no	—
575	C₄×C₅	—	4	1	no	—
576	C₄×C₅	C₂×C₃×SD₁₆	1	2	yes	complemented
577	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
578	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
579	Dic₅	—	2	1	no	—
580	Dic₅	—	2	2	no	—
581	Dic₅	—	4	1	no	—
582	Dic₅	—	4	1	no	—
583	Dic₅	C₃×C₄×D₄	1	2	yes	—
584	Dic₅	C₂×C₃×SD₁₆	1	2	yes	complemented
585	C₂⁴	—	10	1	no	—
586	C₂×Q₈	—	5	4	no	—
587	C₂×Q₈	—	5	1	no	—
588	C₂×Q₈	—	10	1	no	—
589	C₂×Q₈	—	10	2	no	—
590	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
591	C₂×D₄	—	5	4	no	—
592	C₂×D₄	—	5	1	no	—
593	C₂×D₄	—	10	2	no	—
594	C₂×D₄	—	10	1	no	—
595	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	5	1	no	—
598	C₂²×C₄	—	5	1	no	—
599	C₂²×C₄	—	5	1	no	—
600	C₂²×C₄	—	10	1	no	—
601	C₂²×C₄	—	10	1	no	—
602	C₂²×C₄	—	10	1	no	—
603	C₂²×C₄	—	10	1	no	—
604	C₂²×C₄	—	10	1	no	—
605	C₂²×C₄	—	10	1	no	—
606	C₂²×C₄	—	20	4	no	—
607	SD₁₆	—	5	4	no	—
608	SD₁₆	—	5	4	no	—
609	SD₁₆	—	5	4	no	—
610	SD₁₆	C₃×C₄×D₅	1	4	yes	direct product factor
611	C₂×C₈	—	5	1	no	—
612	C₂×C₈	—	5	4	no	—
613	C₂×C₈	—	5	1	no	—
614	C₂×C₈	—	10	2	no	—
615	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
616	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	5	1	no	—
619	C₄⋊C₄	—	5	1	no	—
620	C₄⋊C₄	—	10	1	no	—
621	C₄⋊C₄	—	10	1	no	—
622	C₄⋊C₄	—	10	1	no	—
623	C₄⋊C₄	—	10	1	no	—
624	C₄⋊C₄	—	10	1	no	—
625	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
626	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	10	1	no	—
629	C₂²⋊C₄	—	10	1	no	—
630	C₂²⋊C₄	—	10	1	no	—
631	C₄²	—	2	1	no	—
632	C₄²	—	5	1	no	—
633	C₄²	—	5	1	no	—
634	C₄²	—	5	1	no	—
635	C₄²	—	10	1	no	—
636	C₄²	—	10	1	no	—
637	C₄²	—	10	1	no	—
638	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
639	C₃×C₅	C₂×C₄×SD₁₆	1	1	yes	characteristic, complemented, Hall
640	C₂²×C₃	—	2	2	no	—
641	C₂²×C₃	—	4	1	no	—
642	C₂²×C₃	—	4	1	no	—
643	C₂²×C₃	—	5	2	no	—
644	C₂²×C₃	—	5	2	no	—
645	C₂²×C₃	—	5	2	no	—
646	C₂²×C₃	—	10	2	no	—
647	C₂²×C₃	—	20	8	no	—
648	C₂²×C₃	—	20	1	no	—
649	C₂²×C₃	—	20	1	no	—
650	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
651	C₃×C₄	—	2	1	no	—
652	C₃×C₄	—	2	2	no	—
653	C₃×C₄	—	4	1	no	—
654	C₃×C₄	—	4	1	no	—
655	C₃×C₄	—	5	2	no	—
656	C₃×C₄	—	5	2	no	—
657	C₃×C₄	—	10	1	no	—
658	C₃×C₄	—	10	2	no	—
659	C₃×C₄	—	20	1	no	—
660	C₃×C₄	—	20	1	no	—
661	C₃×C₄	D₅×SD₁₆	1	2	yes	direct product factor
662	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
663	C₃×C₄	D₅×#41	1	1	yes	characteristic
664	C₂×C₅	—	4	2	no	—
665	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
666	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
667	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
668	D₅	—	4	2	no	—
669	D₅	C₃×C₄×SD₁₆	1	4	yes	direct product factor
670	C₂³	—	2	1	no	—
671	C₂³	—	5	1	no	—
672	C₂³	—	10	4	no	—
673	C₂³	—	10	1	no	—
674	C₂³	—	20	2	no	—
675	C₂³	—	20	2	no	—
676	Q₈	—	2	1	no	—
677	Q₈	—	5	2	no	—
678	Q₈	—	10	4	no	—
679	Q₈	—	10	1	no	—
680	Q₈	C₂×C₃×C₄×D₅	1	2	yes	complemented
681	D₄	—	2	1	no	—
682	D₄	—	5	2	no	—
683	D₄	—	10	4	no	—
684	D₄	—	10	1	no	—
685	D₄	C₂×C₃×C₄×D₅	1	2	yes	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	5	1	no	—
691	C₂×C₄	—	5	1	no	—
692	C₂×C₄	—	5	2	no	—
693	C₂×C₄	—	5	2	no	—
694	C₂×C₄	—	5	4	no	—
695	C₂×C₄	—	5	1	no	—
696	C₂×C₄	—	10	2	no	—
697	C₂×C₄	—	10	4	no	—
698	C₂×C₄	—	10	1	no	—
699	C₂×C₄	—	10	1	no	—
700	C₂×C₄	—	10	1	no	—
701	C₂×C₄	—	20	2	no	—
702	C₂×C₄	—	20	2	no	—
703	C₂×C₄	—	20	2	no	—
704	C₂×C₄	—	20	2	no	—
705	C₂×C₄	—	20	2	no	—
706	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
707	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
708	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
709	C₈	—	2	1	no	—
710	C₈	—	5	2	no	—
711	C₈	—	10	1	no	—
712	C₈	C₂×C₃×C₄×D₅	1	2	yes	complemented
713	C₂×C₃	—	4	2	no	—
714	C₂×C₃	—	5	4	no	—
715	C₂×C₃	—	20	2	no	—
716	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
717	C₂×C₃	C₂×D₅×SD₁₆	1	1	yes	characteristic
718	C₂×C₃	D₅×#135	1	1	yes	characteristic
719	C₅	C₂×C₃×C₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
720	C₂²	—	2	2	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	5	2	no	—
724	C₂²	—	5	2	no	—
725	C₂²	—	5	2	no	—
726	C₂²	—	10	2	no	—
727	C₂²	—	20	8	no	—
728	C₂²	—	20	1	no	—
729	C₂²	—	20	1	no	—
730	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
731	C₄	—	2	1	no	—
732	C₄	—	2	2	no	—
733	C₄	—	4	1	no	—
734	C₄	—	4	1	no	—
735	C₄	—	5	2	no	—
736	C₄	—	5	2	no	—
737	C₄	—	10	1	no	—
738	C₄	—	10	2	no	—
739	C₄	—	20	1	no	—
740	C₄	—	20	1	no	—
741	C₄	C₃×D₅×SD₁₆	1	2	yes	direct product factor
742	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
743	C₄	C₃×D₅×#41	1	1	yes	characteristic
744	C₃	C₄×D₅×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
745	C₂	—	4	2	no	—
746	C₂	—	5	4	no	—
747	C₂	—	20	2	no	—
748	C₂	C₃×C₄×D₄×D₅	1	1	yes	characteristic
749	C₂	C₂×C₃×D₅×SD₁₆	1	1	yes	characteristic
750	C₂	C₃×D₅×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×SD₁₆	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×D₄×D₅	C₂²
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×SD₁₆	D₅
hypocenter	C₅	C₂×C₃×C₄×SD₁₆
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄² ◁ C₃×C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×Q₈×D₅	C₂	semidirect
4. C₃×C₄×C₅×SD₁₆	C₂	semidirect
5. C₃×SD₁₆×Dic₅	C₂	semidirect
6. C₃×C₄×#688	C₂	semidirect
7. C₃×C₄×#687	C₂	semidirect
8. C₃×D₅×#106	C₂	semidirect
9. C₃×#65141	C₂	semidirect
10. C₃×D₅×#103	C₂	semidirect
11. C₃×#65077	C₂	semidirect
13. C₃×#65047	C₂	semidirect
14. C₃×C₄×#677	C₂	semidirect
15. C₃×C₄×C₈×D₅	C₂	semidirect
16. C₄×D₅×SD₁₆	C₃	direct (N × H)
21. C₃×C₄×C₅×Q₈	C₂²	semidirect
23. C₃×Q₈×Dic₅	C₂²	semidirect
28. C₃×D₅×SD₁₆	C₄	direct (N × H)
37. C₃×#4033	C₂²	semidirect
44. C₃×C₄×Dic₁₀	C₂²	semidirect
45. C₃×C₅×#106	C₂²	semidirect
46. C₃×C₅×#103	C₂²	semidirect
48. C₃×C₄×C₅×C₈	C₂²	semidirect
49. C₃×#3967	C₂²	semidirect
52. C₃×#3949	C₂²	semidirect
53. C₃×#3948	C₂²	semidirect
54. C₃×C₈×Dic₅	C₂²	semidirect
55. C₃×C₈×Dic₅	C₂²	semidirect
56. C₃×#3942	C₂²	semidirect
58. C₃×#3940	C₂²	semidirect
59. C₃×#3940	C₂²	semidirect
60. C₃×C₄×#168	C₂²	semidirect
63. C₄×Q₈×D₅	C₂×C₃	semidirect
65. C₄×C₅×SD₁₆	C₂×C₃	semidirect
66. SD₁₆×Dic₅	C₂×C₃	semidirect
67. C₄×#688	C₂×C₃	semidirect
68. C₄×#687	C₂×C₃	semidirect
69. D₅×#106	C₂×C₃	semidirect
70. #65141	C₂×C₃	semidirect
71. D₅×#103	C₂×C₃	semidirect
72. #65077	C₂×C₃	semidirect
74. #65047	C₂×C₃	semidirect
75. C₄×#677	C₂×C₃	semidirect
76. C₄×C₈×D₅	C₂×C₃	semidirect
84. C₃×Q₈×D₅	C₂×C₄	semidirect
99. C₃×C₅×SD₁₆	C₂×C₄	semidirect
109. C₃×#688	C₂×C₄	semidirect
110. C₃×#687	C₂×C₄	semidirect
128. C₃×#677	C₂×C₄	semidirect
130. C₃×C₈×D₅	C₂×C₄	semidirect
141. C₃×C₄×SD₁₆	D₅	direct (N × H)
150. C₄×C₅×Q₈	C₂²×C₃	semidirect
152. Q₈×Dic₅	C₂²×C₃	semidirect
157. D₅×SD₁₆	C₃×C₄	direct (N × H)
166. #4033	C₂²×C₃	semidirect
173. C₄×Dic₁₀	C₂²×C₃	semidirect
174. C₅×#106	C₂²×C₃	semidirect
175. C₅×#103	C₂²×C₃	semidirect
177. C₄×C₅×C₈	C₂²×C₃	semidirect
178. #3967	C₂²×C₃	semidirect
181. #3949	C₂²×C₃	semidirect
182. #3948	C₂²×C₃	semidirect
183. C₈×Dic₅	C₂²×C₃	semidirect
184. C₈×Dic₅	C₂²×C₃	semidirect
185. #3942	C₂²×C₃	semidirect
187. #3940	C₂²×C₃	semidirect
188. #3940	C₂²×C₃	semidirect
189. C₄×#168	C₂²×C₃	semidirect
198. C₃×C₅×Q₈	C₂²×C₄	semidirect
224. C₃×C₄×D₅	SD₁₆	direct (N × H)
229. C₃×Dic₁₀	C₂²×C₄	semidirect
231. C₃×C₅×C₈	C₂²×C₄	semidirect
233. C₃×#168	C₂²×C₄	semidirect
249. C₃×C₄×Q₈	C₂×D₅	semidirect
265. C₃×#106	C₂×D₅	semidirect
269. C₃×#103	C₂×D₅	semidirect
277. C₃×C₄×C₈	C₂×D₅	semidirect
285. Q₈×D₅	C₂×C₃×C₄	semidirect
300. C₅×SD₁₆	C₂×C₃×C₄	semidirect
310. #688	C₂×C₃×C₄	semidirect
311. #687	C₂×C₃×C₄	semidirect
329. #677	C₂×C₃×C₄	semidirect
331. C₈×D₅	C₂×C₃×C₄	semidirect
342. C₄×SD₁₆	C₃×D₅	direct (N × H)
362. C₃×C₄×C₅	C₂×SD₁₆	semidirect
370. C₃×Dic₅	C₂×SD₁₆	semidirect
396. C₃×SD₁₆	C₄×D₅	direct (N × H)
432. C₅×Q₈	C₂²×C₃×C₄	semidirect
458. C₄×D₅	C₃×SD₁₆	direct (N × H)
463. Dic₁₀	C₂²×C₃×C₄	semidirect
465. C₅×C₈	C₂²×C₃×C₄	semidirect
467. #168	C₂²×C₃×C₄	semidirect
483. C₄×Q₈	C₂×C₃×D₅	semidirect
499. #106	C₂×C₃×D₅	semidirect
503. #103	C₂×C₃×D₅	semidirect
511. C₄×C₈	C₂×C₃×D₅	semidirect
517. C₃×D₅	C₄×SD₁₆	direct (N × H)
528. C₃×Q₈	C₂×C₄×D₅	semidirect
560. C₃×C₈	C₂×C₄×D₅	semidirect
576. C₄×C₅	C₂×C₃×SD₁₆	semidirect
584. Dic₅	C₂×C₃×SD₁₆	semidirect
610. SD₁₆	C₃×C₄×D₅	direct (N × H)
639. C₃×C₅	C₂×C₄×SD₁₆	semidirect
661. C₃×C₄	D₅×SD₁₆	direct (N × H)
669. D₅	C₃×C₄×SD₁₆	direct (N × H)
680. Q₈	C₂×C₃×C₄×D₅	semidirect
712. C₈	C₂×C₃×C₄×D₅	semidirect
719. C₅	C₂×C₃×C₄×SD₁₆	semidirect
741. C₄	C₃×D₅×SD₁₆	direct (N × H)
744. C₃	C₄×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
C₂×C₃×D₅×SD₁₆	2
C₃×C₄×Q₈×D₅	2
C₃×C₄×D₄×D₅	2
C₃×C₄×C₅×SD₁₆	2
C₃×SD₁₆×Dic₅	2
C₃×C₄×#688	2
C₃×C₄×#687	2
C₃×D₅×#106	2
C₃×#65141	2
C₃×D₅×#103	2
C₃×#65077	2
C₃×D₅×#102	2
C₃×#65047	2
C₃×C₄×#677	2
C₃×C₄×C₈×D₅	2
C₄×D₅×SD₁₆	3
C₂×C₃×C₄×SD₁₆	5

Subgroups — C3×C4×D5×SD16 #14416041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×D₅×SD₁₆ #14416041