Subgroups — C₃×C₅×D₄×Q₁₆ #14276320

Order 1920.

944 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×Q₁₆	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×D₄×Q₈	C₂	1	2	yes	maximal
3	C₃×C₅×#494	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#467	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#462	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#451	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic
9	C₅×D₄×Q₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	4	yes	—
11	C₂×C₃×C₅×Q₁₆	—	2	8	no	—
12	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	—
13	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
17	C₃×C₅×C₄⋊Q₈	—	2	2	no	—
18	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
20	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
21	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
22	C₃×C₄×C₅×D₄	—	2	2	no	—
23	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
24	C₃×C₅×#107	C₂²	1	1	yes	characteristic
25	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₃×C₅×#103	C₂²	1	2	yes	—
27	C₃×C₅×#103	C₂²	1	4	yes	—
28	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
30	C₃×D₄×Q₁₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂²×C₅×Q₁₆	C₂×C₃	1	2	yes	complemented
32	C₅×D₄×Q₈	C₂×C₃	1	2	yes	—
33	C₅×#494	C₂×C₃	1	1	yes	characteristic, complemented
34	C₅×#467	C₂×C₃	1	2	yes	complemented
35	C₅×#462	C₂×C₃	1	2	yes	complemented
36	C₅×#451	C₂×C₃	1	4	yes	complemented
37	C₄×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×C₈×D₄	C₂×C₃	1	1	yes	characteristic
39	C₂×C₃×C₅×Q₈	—	2	4	no	—
40	C₂×C₃×C₅×Q₈	—	2	8	no	—
41	C₂×C₃×C₅×Q₈	—	4	4	no	—
42	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
43	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
44	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	—	2	4	no	—
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₃×C₅×Q₁₆	—	2	8	no	—
48	C₃×C₅×Q₁₆	—	2	4	no	—
49	C₃×C₅×Q₁₆	—	4	2	no	—
50	C₃×C₅×Q₁₆	D₄	1	4	yes	direct product factor
51	C₂×C₃×C₅×C₈	—	2	4	no	—
52	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
53	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
54	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₃×C₅×C₄⋊C₄	—	2	2	no	—
56	C₃×C₅×C₄⋊C₄	—	2	2	no	—
57	C₃×C₅×C₄⋊C₄	—	2	2	no	—
58	C₃×C₅×C₄⋊C₄	—	2	4	no	—
59	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
60	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
62	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
63	C₃×C₄²×C₅	—	2	2	no	—
64	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
65	C₂²×C₃×Q₁₆	C₂×C₅	1	2	yes	complemented
66	C₃×D₄×Q₈	C₂×C₅	1	2	yes	—
67	C₃×#494	C₂×C₅	1	1	yes	characteristic, complemented
68	C₃×#467	C₂×C₅	1	2	yes	complemented
69	C₃×#462	C₂×C₅	1	2	yes	complemented
70	C₃×#451	C₂×C₅	1	4	yes	complemented
71	C₃×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
72	C₃×C₈×D₄	C₂×C₅	1	1	yes	characteristic
73	C₂²×C₅×Q₈	C₂²×C₃	1	4	yes	—
74	C₂×C₅×Q₁₆	—	2	8	no	—
75	C₂×C₅×Q₁₆	C₂²×C₃	1	4	yes	—
76	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
77	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
78	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
79	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
80	C₅×C₄⋊Q₈	—	2	2	no	—
81	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
82	C₅×C₂²⋊Q₈	—	2	4	no	—
83	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
84	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
85	C₄×C₅×D₄	—	2	2	no	—
86	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
87	C₅×#107	C₂²×C₃	1	1	yes	characteristic
88	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
89	C₅×#103	C₂²×C₃	1	2	yes	—
90	C₅×#103	C₂²×C₃	1	4	yes	—
91	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
92	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
93	D₄×Q₁₆	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
94	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
95	C₃×C₅×Q₈	—	2	2	no	—
96	C₃×C₅×Q₈	—	2	4	no	—
97	C₃×C₅×Q₈	—	2	4	no	—
98	C₃×C₅×Q₈	—	4	8	no	—
99	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
100	C₃×C₅×D₄	Q₁₆	1	4	yes	direct product factor
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	4	no	—
106	C₂×C₃×C₄×C₅	—	4	8	no	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
111	C₃×C₅×C₈	—	2	2	no	—
112	C₃×C₅×C₈	—	2	1	no	—
113	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
114	C₂²×C₃×Q₈	C₂²×C₅	1	4	yes	—
115	C₂×C₃×Q₁₆	—	2	8	no	—
116	C₂×C₃×Q₁₆	C₂²×C₅	1	4	yes	—
117	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
118	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
119	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
120	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
121	C₃×C₄⋊Q₈	—	2	2	no	—
122	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
123	C₃×C₂²⋊Q₈	—	2	4	no	—
124	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
125	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
126	C₃×C₄×D₄	—	2	2	no	—
127	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
128	C₃×#107	C₂²×C₅	1	1	yes	characteristic
129	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
130	C₃×#103	C₂²×C₅	1	2	yes	—
131	C₃×#103	C₂²×C₅	1	4	yes	—
132	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
133	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₅×Q₈	—	2	4	no	—
135	C₂×C₅×Q₈	—	2	8	no	—
136	C₂×C₅×Q₈	—	4	4	no	—
137	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
138	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
139	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	—	2	4	no	—
141	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
142	C₅×Q₁₆	—	2	8	no	—
143	C₅×Q₁₆	—	2	4	no	—
144	C₅×Q₁₆	—	4	2	no	—
145	C₅×Q₁₆	C₃×D₄	1	4	yes	direct product factor
146	C₂×C₅×C₈	—	2	4	no	—
147	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
148	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
149	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
150	C₅×C₄⋊C₄	—	2	2	no	—
151	C₅×C₄⋊C₄	—	2	2	no	—
152	C₅×C₄⋊C₄	—	2	2	no	—
153	C₅×C₄⋊C₄	—	2	4	no	—
154	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
155	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
156	C₅×C₂²⋊C₄	—	2	4	no	—
157	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
158	C₄²×C₅	—	2	2	no	—
159	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
160	C₂²×Q₁₆	C₂×C₃×C₅	1	2	yes	complemented
161	D₄×Q₈	C₂×C₃×C₅	1	2	yes	—
162	#494	C₂×C₃×C₅	1	1	yes	characteristic, complemented
163	#467	C₂×C₃×C₅	1	2	yes	complemented
164	#462	C₂×C₃×C₅	1	2	yes	complemented
165	#451	C₂×C₃×C₅	1	4	yes	complemented
166	C₄×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
167	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic
168	C₂²×C₃×C₅	—	2	2	no	—
169	C₂²×C₃×C₅	—	2	2	no	—
170	C₂²×C₃×C₅	C₂×Q₁₆	1	4	yes	complemented
171	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
172	C₃×C₄×C₅	—	2	2	no	—
173	C₃×C₄×C₅	—	2	4	no	—
174	C₃×C₄×C₅	—	2	1	no	—
175	C₃×C₄×C₅	—	4	4	no	—
176	C₃×C₄×C₅	—	4	2	no	—
177	C₃×C₄×C₅	C₂×Q₁₆	1	2	yes	complemented
178	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
179	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
180	C₂×C₃×Q₈	—	2	4	no	—
181	C₂×C₃×Q₈	—	2	8	no	—
182	C₂×C₃×Q₈	—	4	4	no	—
183	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
184	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
185	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
186	C₂²×C₃×C₄	—	2	4	no	—
187	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
188	C₃×Q₁₆	—	2	8	no	—
189	C₃×Q₁₆	—	2	4	no	—
190	C₃×Q₁₆	—	4	2	no	—
191	C₃×Q₁₆	C₅×D₄	1	4	yes	direct product factor
192	C₂×C₃×C₈	—	2	4	no	—
193	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
194	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
195	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
196	C₃×C₄⋊C₄	—	2	2	no	—
197	C₃×C₄⋊C₄	—	2	2	no	—
198	C₃×C₄⋊C₄	—	2	2	no	—
199	C₃×C₄⋊C₄	—	2	4	no	—
200	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
201	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
202	C₃×C₂²⋊C₄	—	2	4	no	—
203	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
204	C₃×C₄²	—	2	2	no	—
205	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
206	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
207	C₅×Q₈	—	2	2	no	—
208	C₅×Q₈	—	2	4	no	—
209	C₅×Q₈	—	2	4	no	—
210	C₅×Q₈	—	4	8	no	—
211	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
212	C₅×D₄	C₃×Q₁₆	1	4	yes	direct product factor
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	4	no	—
218	C₂×C₄×C₅	—	4	8	no	—
219	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
221	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
223	C₅×C₈	—	2	2	no	—
224	C₅×C₈	—	2	1	no	—
225	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
226	C₂²×Q₈	C₂²×C₃×C₅	1	4	yes	—
227	C₂×Q₁₆	—	2	8	no	—
228	C₂×Q₁₆	C₂²×C₃×C₅	1	4	yes	—
229	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
230	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
231	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
232	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
233	C₄⋊Q₈	—	2	2	no	—
234	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
235	C₂²⋊Q₈	—	2	4	no	—
236	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
237	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
240	#107	C₂²×C₃×C₅	1	1	yes	characteristic
241	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
242	#103	C₂²×C₃×C₅	1	2	yes	—
243	#103	C₂²×C₃×C₅	1	4	yes	—
244	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
245	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
246	C₂×C₃×C₅	—	2	4	no	—
247	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
248	C₂×C₃×C₅	C₂²×Q₁₆	1	1	yes	characteristic
249	C₂×C₃×C₅	#578	1	1	yes	characteristic
250	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
251	C₃×Q₈	—	2	2	no	—
252	C₃×Q₈	—	2	4	no	—
253	C₃×Q₈	—	2	4	no	—
254	C₃×Q₈	—	4	8	no	—
255	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
256	C₃×D₄	C₅×Q₁₆	1	4	yes	direct product factor
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	4	8	no	—
263	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
265	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
267	C₃×C₈	—	2	2	no	—
268	C₃×C₈	—	2	1	no	—
269	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
270	C₂²×C₅	—	2	2	no	—
271	C₂²×C₅	—	2	2	no	—
272	C₂²×C₅	C₂×C₃×Q₁₆	1	4	yes	complemented
273	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
274	C₄×C₅	—	2	1	no	—
275	C₄×C₅	—	2	2	no	—
276	C₄×C₅	—	2	4	no	—
277	C₄×C₅	—	4	2	no	—
278	C₄×C₅	—	4	4	no	—
279	C₄×C₅	C₂×C₃×Q₁₆	1	2	yes	complemented
280	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
281	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
282	C₂×Q₈	—	2	4	no	—
283	C₂×Q₈	—	2	8	no	—
284	C₂×Q₈	—	4	4	no	—
285	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
286	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
287	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
290	Q₁₆	—	2	8	no	—
291	Q₁₆	—	2	4	no	—
292	Q₁₆	—	4	2	no	—
293	Q₁₆	C₃×C₅×D₄	1	4	yes	direct product factor
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
296	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
297	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
303	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
304	C₂²⋊C₄	—	2	4	no	—
305	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
306	C₄²	—	2	2	no	—
307	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
308	C₃×C₅	D₄×Q₁₆	1	1	yes	characteristic, direct product factor, Hall
309	C₂²×C₃	—	2	2	no	—
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	C₂×C₅×Q₁₆	1	4	yes	complemented
312	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
313	C₃×C₄	—	2	2	no	—
314	C₃×C₄	—	2	4	no	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	4	4	no	—
317	C₃×C₄	—	4	2	no	—
318	C₃×C₄	C₂×C₅×Q₁₆	1	2	yes	complemented
319	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
320	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
321	C₂×C₅	—	2	4	no	—
322	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
323	C₂×C₅	C₂²×C₃×Q₁₆	1	1	yes	characteristic
324	C₂×C₅	C₃×#578	1	1	yes	characteristic
325	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
326	Q₈	—	2	2	no	—
327	Q₈	—	2	4	no	—
328	Q₈	—	2	4	no	—
329	Q₈	—	4	8	no	—
330	Q₈	C₂×C₃×C₅×D₄	1	4	yes	—
331	D₄	C₃×C₅×Q₁₆	1	4	yes	direct product factor
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	4	8	no	—
338	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
339	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
340	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
341	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
342	C₈	—	2	2	no	—
343	C₈	—	2	1	no	—
344	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
345	C₂×C₃	—	2	4	no	—
346	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
347	C₂×C₃	C₂²×C₅×Q₁₆	1	1	yes	characteristic
348	C₂×C₃	C₅×#578	1	1	yes	characteristic
349	C₅	C₃×D₄×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	C₂×C₃×C₅×Q₁₆	1	4	yes	complemented
353	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	4	no	—
356	C₄	—	2	1	no	—
357	C₄	—	4	4	no	—
358	C₄	—	4	2	no	—
359	C₄	C₂×C₃×C₅×Q₁₆	1	2	yes	complemented
360	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
361	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
362	C₃	C₅×D₄×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
363	C₂	—	2	4	no	—
364	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
365	C₂	C₂²×C₃×C₅×Q₁₆	1	1	yes	characteristic
366	C₂	C₃×C₅×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×D₄	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×Q₁₆	C₂	semidirect
3. C₃×C₅×#494	C₂	semidirect
4. C₃×C₅×#467	C₂	semidirect
5. C₃×C₅×#462	C₂	semidirect
6. C₃×C₅×#451	C₂	semidirect
7. C₃×C₄×C₅×Q₁₆	C₂	semidirect
9. C₅×D₄×Q₁₆	C₃	direct (N × H)
30. C₃×D₄×Q₁₆	C₅	direct (N × H)
31. C₂²×C₅×Q₁₆	C₂×C₃	semidirect
33. C₅×#494	C₂×C₃	semidirect
34. C₅×#467	C₂×C₃	semidirect
35. C₅×#462	C₂×C₃	semidirect
36. C₅×#451	C₂×C₃	semidirect
37. C₄×C₅×Q₁₆	C₂×C₃	semidirect
50. C₃×C₅×Q₁₆	D₄	direct (N × H)
65. C₂²×C₃×Q₁₆	C₂×C₅	semidirect
67. C₃×#494	C₂×C₅	semidirect
68. C₃×#467	C₂×C₅	semidirect
69. C₃×#462	C₂×C₅	semidirect
70. C₃×#451	C₂×C₅	semidirect
71. C₃×C₄×Q₁₆	C₂×C₅	semidirect
93. D₄×Q₁₆	C₃×C₅	direct (N × H)
100. C₃×C₅×D₄	Q₁₆	direct (N × H)
145. C₅×Q₁₆	C₃×D₄	direct (N × H)
160. C₂²×Q₁₆	C₂×C₃×C₅	semidirect
162. #494	C₂×C₃×C₅	semidirect
163. #467	C₂×C₃×C₅	semidirect
164. #462	C₂×C₃×C₅	semidirect
165. #451	C₂×C₃×C₅	semidirect
166. C₄×Q₁₆	C₂×C₃×C₅	semidirect
170. C₂²×C₃×C₅	C₂×Q₁₆	semidirect
177. C₃×C₄×C₅	C₂×Q₁₆	semidirect
191. C₃×Q₁₆	C₅×D₄	direct (N × H)
212. C₅×D₄	C₃×Q₁₆	direct (N × H)
256. C₃×D₄	C₅×Q₁₆	direct (N × H)
272. C₂²×C₅	C₂×C₃×Q₁₆	semidirect
279. C₄×C₅	C₂×C₃×Q₁₆	semidirect
293. Q₁₆	C₃×C₅×D₄	direct (N × H)
308. C₃×C₅	D₄×Q₁₆	direct (N × H)
311. C₂²×C₃	C₂×C₅×Q₁₆	semidirect
318. C₃×C₄	C₂×C₅×Q₁₆	semidirect
331. D₄	C₃×C₅×Q₁₆	direct (N × H)
349. C₅	C₃×D₄×Q₁₆	direct (N × H)
352. C₂²	C₂×C₃×C₅×Q₁₆	semidirect
359. C₄	C₂×C₃×C₅×Q₁₆	semidirect
362. C₃	C₅×D₄×Q₁₆	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×C₅×Q₁₆	2
C₃×C₅×D₄×Q₈	2
C₃×C₅×#494	2
C₃×C₅×#467	2
C₃×C₅×#462	2
C₃×C₅×#451	2
C₃×C₄×C₅×Q₁₆	2
C₃×C₅×C₈×D₄	2
C₅×D₄×Q₁₆	3
C₃×D₄×Q₁₆	5

Subgroups — C3×C5×D4×Q16 #14276320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₄×Q₁₆ #14276320