Subgroups — C₃×D₅×#576 #14509949

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#576	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66169	C₂	1	2	yes	maximal, complemented
4	C₃×#66108	C₂	1	6	yes	maximal, complemented
5	C₃×D₅×AGL(1,ℤ/8)	C₂	1	6	yes	maximal, complemented
6	C₃×#66103	C₂	1	3	yes	maximal, complemented
7	C₃×D₅×#135	C₂	1	3	yes	maximal, complemented
8	C₃×#66091	C₂	1	3	yes	maximal, complemented
9	C₂×C₃×D₅×D₈	C₂	1	3	yes	maximal, complemented
10	C₃×#66086	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#576	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₅×H(5,𝔽₂)	C₂²	1	2	yes	complemented
14	C₃×#4149	—	2	2	no	—
15	C₃×#4149	C₂²	1	6	yes	complemented
16	C₃×#4149	C₂²	1	2	yes	complemented
17	C₃×D₅×#41	—	2	2	no	—
18	C₃×D₅×#41	C₂²	1	1	yes	characteristic
19	C₃×D₅×#41	C₂²	1	6	yes	complemented
20	C₃×#4144	—	2	6	no	—
21	C₃×#4144	C₂²	1	6	yes	complemented
22	C₂×C₃×D₄×D₅	—	2	6	no	—
23	C₂×C₃×D₄×D₅	C₂²	1	6	yes	complemented
24	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
25	C₃×C₅×#135	C₂²	1	3	yes	complemented
26	C₂×C₃×C₅×D₈	C₂²	1	3	yes	complemented
27	C₃×C₅×#131	C₂²	1	1	yes	characteristic, complemented
28	C₃×#4096	C₂²	1	6	yes	complemented
29	C₃×#4095	C₂²	1	6	yes	complemented
30	C₃×#4094	C₂²	1	1	yes	characteristic, complemented
31	C₃×#4078	C₂²	1	6	yes	complemented
32	C₂×C₃×#686	C₂²	1	6	yes	complemented
33	C₃×#4065	C₂²	1	3	yes	complemented
34	C₃×D₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₃×#4062	C₂²	1	6	yes	complemented
36	C₃×#4060	C₂²	1	12	yes	complemented
37	C₃×D₅×SD₁₆	C₂²	1	6	yes	complemented
38	C₃×#4058	C₂²	1	3	yes	complemented
39	C₃×#4057	C₂²	1	12	yes	complemented
40	C₃×D₅×D₈	C₂²	1	3	yes	complemented
41	C₃×D₅×D₈	C₂²	1	6	yes	complemented
42	C₃×D₅×D₈	C₂²	1	6	yes	complemented
43	C₃×D₅×D₈	C₂²	1	6	yes	complemented
44	C₃×#4054	C₂²	1	6	yes	complemented
45	C₃×#4053	C₂²	1	3	yes	complemented
46	C₃×D₅×M₁₆	C₂²	1	3	yes	complemented
47	C₃×#4050	C₂²	1	3	yes	complemented
48	C₂×C₃×D₄₀	C₂²	1	3	yes	complemented
49	C₃×#4047	C₂²	1	3	yes	complemented
50	C₂×C₃×C₈×D₅	C₂²	1	3	yes	complemented
51	C₂×C₃×#576	—	5	1	no	maximal, Hall
52	D₅×H(5,𝔽₂)	C₂×C₃	1	2	yes	complemented
53	C₅×#576	C₂×C₃	1	1	yes	characteristic, complemented
54	#66169	C₂×C₃	1	2	yes	complemented
55	#66108	C₂×C₃	1	6	yes	complemented
56	D₅×AGL(1,ℤ/8)	C₂×C₃	1	6	yes	complemented
57	#66103	C₂×C₃	1	3	yes	complemented
58	D₅×#135	C₂×C₃	1	3	yes	complemented
59	#66091	C₂×C₃	1	3	yes	complemented
60	C₂×D₅×D₈	C₂×C₃	1	3	yes	complemented
61	#66086	C₂×C₃	1	1	yes	characteristic, complemented
62	D₅×#131	C₂×C₃	1	1	yes	characteristic, complemented
63	C₂³×C₃×D₅	—	2	6	no	—
64	C₃×C₅×#41	—	2	2	no	—
65	C₃×C₅×#41	C₂³	1	1	yes	characteristic
66	C₃×C₅×#41	C₂³	1	6	yes	complemented
67	C₂×C₃×C₅×D₄	—	2	6	no	—
68	C₂×C₃×C₅×D₄	C₂³	1	6	yes	complemented
69	C₂×C₃×C₂²⋊D₅	—	2	12	no	—
70	C₂×C₃×C₂²⋊D₅	—	2	6	no	—
71	C₃×#713	—	2	2	no	—
72	C₃×#713	D₄	1	1	yes	characteristic
73	C₃×#713	C₂³	1	6	yes	complemented
74	C₃×Q₈×D₅	D₄	1	1	yes	characteristic
75	C₃×Q₈×D₅	C₂³	1	2	yes	—
76	C₃×#711	—	2	6	no	—
77	C₃×#711	—	2	6	no	—
78	C₃×#711	D₄	1	3	yes	—
79	C₃×#711	C₂³	1	6	yes	complemented
80	C₃×D₄×D₅	—	2	6	no	—
81	C₃×D₄×D₅	—	2	6	no	—
82	C₃×D₄×D₅	—	2	12	no	—
83	C₃×D₄×D₅	—	2	6	no	—
84	C₃×D₄×D₅	—	2	6	no	—
85	C₃×D₄×D₅	—	2	6	no	—
86	C₃×D₄×D₅	D₄	1	3	yes	—
87	C₃×D₄×D₅	C₂³	1	6	yes	—
88	C₃×D₄×D₅	C₂³	1	12	yes	complemented
89	C₃×#709	—	2	6	no	—
90	C₃×#709	—	2	6	no	—
91	C₃×#709	C₂³	1	3	yes	—
92	C₃×#709	C₂³	1	6	yes	complemented
93	C₂×C₃×D₂₀	—	2	6	no	—
94	C₂×C₃×D₂₀	C₂³	1	6	yes	complemented
95	C₂×C₃×C₄×D₅	—	2	6	no	—
96	C₂×C₃×C₄×D₅	C₂³	1	3	yes	—
97	C₃×C₅×Q₁₆	C₂³	1	1	yes	characteristic, complemented
98	C₃×C₅×SD₁₆	C₂³	1	6	yes	complemented
99	C₃×C₅×D₈	C₂³	1	3	yes	complemented
100	C₃×C₅×D₈	C₂³	1	6	yes	complemented
101	C₃×C₅×M₁₆	C₂³	1	3	yes	complemented
102	C₂×C₃×C₅×C₈	C₂³	1	3	yes	complemented
103	C₃×#689	C₂³	1	2	yes	complemented
104	C₃×#688	C₂³	1	6	yes	complemented
105	C₃×#687	C₂³	1	6	yes	complemented
106	C₃×#686	C₂³	1	6	yes	complemented
107	C₃×#686	C₂³	1	12	yes	complemented
108	C₃×#681	C₂³	1	3	yes	complemented
109	C₂×C₃×#168	C₂³	1	3	yes	complemented
110	C₃×Dic₂₀	C₂³	1	1	yes	characteristic, complemented
111	C₃×D₄₀	C₂³	1	3	yes	complemented
112	C₃×D₄₀	C₂³	1	6	yes	complemented
113	C₃×#677	C₂³	1	6	yes	complemented
114	C₃×#676	C₂³	1	6	yes	complemented
115	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
116	C₃×C₈×D₅	C₂³	1	3	yes	—
117	C₃×C₈×D₅	C₂³	1	3	yes	complemented
118	C₃×C₈×D₅	C₂³	1	3	yes	complemented
119	C₂×C₃×H(5,𝔽₂)	—	5	2	no	—
120	C₃×#576	—	5	2	no	—
121	C₃×#576	—	5	6	no	—
122	C₃×#576	—	5	3	no	—
123	C₃×#576	—	5	3	no	—
124	C₃×#576	—	5	1	no	—
125	C₃×#576	D₅	1	1	yes	characteristic, direct product factor
126	C₂×C₃×AGL(1,ℤ/8)	—	5	6	no	—
127	C₂×C₃×#135	—	5	3	no	—
128	C₂²×C₃×D₈	—	5	3	no	—
129	C₂×C₃×#131	—	5	1	no	—
130	C₅×H(5,𝔽₂)	C₂²×C₃	1	2	yes	complemented
131	#4149	—	2	2	no	—
132	#4149	C₂²×C₃	1	6	yes	complemented
133	#4149	C₂²×C₃	1	2	yes	complemented
134	D₅×#41	—	2	2	no	—
135	D₅×#41	C₂²×C₃	1	1	yes	characteristic
136	D₅×#41	C₂²×C₃	1	6	yes	complemented
137	#4144	—	2	6	no	—
138	#4144	C₂²×C₃	1	6	yes	complemented
139	C₂×D₄×D₅	—	2	6	no	—
140	C₂×D₄×D₅	C₂²×C₃	1	6	yes	complemented
141	C₅×AGL(1,ℤ/8)	C₂²×C₃	1	6	yes	complemented
142	C₅×#135	C₂²×C₃	1	3	yes	complemented
143	C₂×C₅×D₈	C₂²×C₃	1	3	yes	complemented
144	C₅×#131	C₂²×C₃	1	1	yes	characteristic, complemented
145	#4096	C₂²×C₃	1	6	yes	complemented
146	#4095	C₂²×C₃	1	6	yes	complemented
147	#4094	C₂²×C₃	1	1	yes	characteristic, complemented
148	#4078	C₂²×C₃	1	6	yes	complemented
149	C₂×#686	C₂²×C₃	1	6	yes	complemented
150	#4065	C₂²×C₃	1	3	yes	complemented
151	D₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
152	#4062	C₂²×C₃	1	6	yes	complemented
153	#4060	C₂²×C₃	1	12	yes	complemented
154	D₅×SD₁₆	C₂²×C₃	1	6	yes	complemented
155	#4058	C₂²×C₃	1	3	yes	complemented
156	#4057	C₂²×C₃	1	12	yes	complemented
157	D₅×D₈	C₂²×C₃	1	3	yes	complemented
158	D₅×D₈	C₂²×C₃	1	6	yes	complemented
159	D₅×D₈	C₂²×C₃	1	6	yes	complemented
160	D₅×D₈	C₂²×C₃	1	6	yes	complemented
161	#4054	C₂²×C₃	1	6	yes	complemented
162	#4053	C₂²×C₃	1	3	yes	complemented
163	D₅×M₁₆	C₂²×C₃	1	3	yes	complemented
164	#4050	C₂²×C₃	1	3	yes	complemented
165	C₂×D₄₀	C₂²×C₃	1	3	yes	complemented
166	#4047	C₂²×C₃	1	3	yes	complemented
167	C₂×C₈×D₅	C₂²×C₃	1	3	yes	complemented
168	C₂×#576	—	5	1	no	Sylow
169	C₂³×C₃×C₅	—	2	6	no	—
170	C₂²×C₃×D₅	—	2	6	no	—
171	C₂²×C₃×D₅	—	2	6	no	—
172	C₂²×C₃×D₅	—	2	12	no	—
173	C₂²×C₃×D₅	—	8	12	no	—
174	C₂²×C₃×D₅	C₂×D₄	1	3	yes	—
175	C₃×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
176	C₃×C₅×Q₈	C₂⁴	1	2	yes	—
177	C₃×C₅×D₄	—	2	6	no	—
178	C₃×C₅×D₄	—	2	6	no	—
179	C₃×C₅×D₄	C₂×D₄	1	3	yes	—
180	C₃×C₅×D₄	C₂⁴	1	6	yes	—
181	C₂×C₃×C₄×C₅	—	2	6	no	—
182	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
183	C₃×C₂²⋊D₅	—	2	6	no	—
184	C₃×C₂²⋊D₅	—	2	6	no	—
185	C₃×C₂²⋊D₅	—	2	6	no	—
186	C₃×C₂²⋊D₅	—	2	12	no	—
187	C₃×C₂²⋊D₅	C₂×D₄	1	6	yes	—
188	C₂×C₃×Dic₅	—	2	6	no	—
189	C₂×C₃×Dic₅	C₂×D₄	1	3	yes	—
190	C₃×D₂₀	—	2	6	no	—
191	C₃×D₂₀	—	2	6	no	—
192	C₃×D₂₀	C₂×D₄	1	3	yes	—
193	C₃×D₂₀	C₂⁴	1	6	yes	—
194	C₃×C₄×D₅	—	2	2	no	—
195	C₃×C₄×D₅	—	2	6	no	—
196	C₃×C₄×D₅	—	2	6	no	—
197	C₃×C₄×D₅	C₂×D₄	1	3	yes	—
198	C₃×C₄×D₅	C₂×D₄	1	3	yes	—
199	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
200	C₃×C₄×D₅	C₂⁴	1	3	yes	—
201	C₃×Dic₁₀	—	2	2	no	—
202	C₃×Dic₁₀	C₂×D₄	1	3	yes	—
203	C₃×Dic₁₀	C₂⁴	1	2	yes	—
204	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
205	C₃×C₅×C₈	C₂⁴	1	3	yes	—
206	C₃×#168	C₂⁴	1	1	yes	characteristic
207	C₃×#168	C₂⁴	1	3	yes	—
208	C₃×H(5,𝔽₂)	—	5	2	no	—
209	C₃×H(5,𝔽₂)	—	5	6	no	—
210	C₃×H(5,𝔽₂)	—	5	6	no	—
211	C₃×H(5,𝔽₂)	—	10	6	no	—
212	C₃×H(5,𝔽₂)	—	10	2	no	—
213	C₃×H(5,𝔽₂)	C₂×D₅	1	2	yes	complemented
214	C₂×C₃×#41	—	5	1	no	—
215	C₂×C₃×#41	—	5	6	no	—
216	C₂×C₃×#41	—	10	2	no	—
217	C₂²×C₃×D₄	—	5	6	no	—
218	C₂²×C₃×D₄	—	10	6	no	—
219	C₃×AGL(1,ℤ/8)	—	5	6	no	—
220	C₃×AGL(1,ℤ/8)	—	5	6	no	—
221	C₃×AGL(1,ℤ/8)	—	5	12	no	—
222	C₃×AGL(1,ℤ/8)	—	5	12	no	—
223	C₃×AGL(1,ℤ/8)	—	5	6	no	—
224	C₃×AGL(1,ℤ/8)	C₂×D₅	1	6	yes	complemented
225	C₃×#135	—	5	6	no	—
226	C₃×#135	—	5	3	no	—
227	C₃×#135	—	5	6	no	—
228	C₃×#135	—	5	3	no	—
229	C₃×#135	—	5	3	no	—
230	C₃×#135	C₂×D₅	1	3	yes	complemented
231	C₂×C₃×Q₁₆	—	5	1	no	—
232	C₂×C₃×SD₁₆	—	5	6	no	—
233	C₂×C₃×D₈	—	5	6	no	—
234	C₂×C₃×D₈	—	5	3	no	—
235	C₂×C₃×D₈	—	5	6	no	—
236	C₂×C₃×D₈	—	5	6	no	—
237	C₂×C₃×D₈	—	5	6	no	—
238	C₂×C₃×D₈	—	5	3	no	—
239	C₂×C₃×D₈	C₂×D₅	1	3	yes	complemented
240	C₃×#131	—	5	1	no	—
241	C₃×#131	—	5	3	no	—
242	C₃×#131	—	5	3	no	—
243	C₃×#131	C₂×D₅	1	1	yes	characteristic, complemented
244	C₂×C₃×M₁₆	—	5	3	no	—
245	C₂²×C₃×C₈	—	5	3	no	—
246	C₂³×D₅	—	2	6	no	—
247	C₅×#41	—	2	2	no	—
248	C₅×#41	C₂³×C₃	1	1	yes	characteristic
249	C₅×#41	C₂³×C₃	1	6	yes	complemented
250	C₂×C₅×D₄	—	2	6	no	—
251	C₂×C₅×D₄	C₂³×C₃	1	6	yes	complemented
252	C₂×C₂²⋊D₅	—	2	12	no	—
253	C₂×C₂²⋊D₅	—	2	6	no	—
254	#713	—	2	2	no	—
255	#713	C₃×D₄	1	1	yes	characteristic
256	#713	C₂³×C₃	1	6	yes	complemented
257	Q₈×D₅	C₃×D₄	1	1	yes	characteristic
258	Q₈×D₅	C₂³×C₃	1	2	yes	—
259	#711	—	2	6	no	—
260	#711	—	2	6	no	—
261	#711	C₃×D₄	1	3	yes	—
262	#711	C₂³×C₃	1	6	yes	complemented
263	D₄×D₅	—	2	6	no	—
264	D₄×D₅	—	2	6	no	—
265	D₄×D₅	—	2	12	no	—
266	D₄×D₅	—	2	6	no	—
267	D₄×D₅	—	2	6	no	—
268	D₄×D₅	—	2	6	no	—
269	D₄×D₅	C₃×D₄	1	3	yes	—
270	D₄×D₅	C₂³×C₃	1	6	yes	—
271	D₄×D₅	C₂³×C₃	1	12	yes	complemented
272	#709	—	2	6	no	—
273	#709	—	2	6	no	—
274	#709	C₂³×C₃	1	3	yes	—
275	#709	C₂³×C₃	1	6	yes	complemented
276	C₂×D₂₀	—	2	6	no	—
277	C₂×D₂₀	C₂³×C₃	1	6	yes	complemented
278	C₂×C₄×D₅	—	2	6	no	—
279	C₂×C₄×D₅	C₂³×C₃	1	3	yes	—
280	C₅×Q₁₆	C₂³×C₃	1	1	yes	characteristic, complemented
281	C₅×SD₁₆	C₂³×C₃	1	6	yes	complemented
282	C₅×D₈	C₂³×C₃	1	3	yes	complemented
283	C₅×D₈	C₂³×C₃	1	6	yes	complemented
284	C₅×M₁₆	C₂³×C₃	1	3	yes	complemented
285	C₂×C₅×C₈	C₂³×C₃	1	3	yes	complemented
286	#689	C₂³×C₃	1	2	yes	complemented
287	#688	C₂³×C₃	1	6	yes	complemented
288	#687	C₂³×C₃	1	6	yes	complemented
289	#686	C₂³×C₃	1	6	yes	complemented
290	#686	C₂³×C₃	1	12	yes	complemented
291	#681	C₂³×C₃	1	3	yes	complemented
292	C₂×#168	C₂³×C₃	1	3	yes	complemented
293	Dic₂₀	C₂³×C₃	1	1	yes	characteristic, complemented
294	D₄₀	C₂³×C₃	1	3	yes	complemented
295	D₄₀	C₂³×C₃	1	6	yes	complemented
296	#677	C₂³×C₃	1	6	yes	complemented
297	#676	C₂³×C₃	1	6	yes	complemented
298	C₈×D₅	C₂³×C₃	1	1	yes	characteristic
299	C₈×D₅	C₂³×C₃	1	3	yes	—
300	C₈×D₅	C₂³×C₃	1	3	yes	complemented
301	C₈×D₅	C₂³×C₃	1	3	yes	complemented
302	C₂×H(5,𝔽₂)	—	5	2	no	—
303	#576	—	5	2	no	—
304	#576	—	5	6	no	—
305	#576	—	5	3	no	—
306	#576	—	5	3	no	—
307	#576	—	5	1	no	—
308	#576	C₃×D₅	1	1	yes	characteristic, direct product factor
309	C₂×AGL(1,ℤ/8)	—	5	6	no	—
310	C₂×#135	—	5	3	no	—
311	C₂²×D₈	—	5	3	no	—
312	C₂×#131	—	5	1	no	—
313	C₂²×C₃×C₅	—	2	6	no	—
314	C₂²×C₃×C₅	—	8	6	no	—
315	C₂²×C₃×C₅	C₂²×D₄	1	3	yes	—
316	C₂×C₃×D₅	—	2	6	no	—
317	C₂×C₃×D₅	—	2	6	no	—
318	C₂×C₃×D₅	—	4	12	no	—
319	C₂×C₃×D₅	—	8	12	no	—
320	C₂×C₃×D₅	—	8	6	no	—
321	C₂×C₃×D₅	C₂²×D₄	1	3	yes	—
322	C₂×C₃×D₅	C₂²×D₄	1	1	yes	characteristic
323	C₃×C₄×C₅	—	2	2	no	—
324	C₃×C₄×C₅	C₂²×D₄	1	3	yes	—
325	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
326	C₃×Dic₅	—	2	2	no	—
327	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
328	C₃×Dic₅	C₂²×D₄	1	3	yes	—
329	C₂⁴×C₃	—	10	6	no	—
330	C₃×#41	—	2	2	no	—
331	C₃×#41	—	5	1	no	—
332	C₃×#41	—	5	3	no	—
333	C₃×#41	—	5	3	no	—
334	C₃×#41	—	5	6	no	—
335	C₃×#41	—	5	6	no	—
336	C₃×#41	—	5	6	no	—
337	C₃×#41	—	10	6	no	—
338	C₃×#41	—	10	6	no	—
339	C₃×#41	—	10	6	no	—
340	C₃×#41	—	10	6	no	—
341	C₃×#41	—	10	2	no	—
342	C₃×#41	C₂²×D₅	1	1	yes	characteristic
343	C₃×#41	C₂²×D₅	1	6	yes	complemented
344	C₂×C₃×Q₈	—	5	1	no	—
345	C₂×C₃×Q₈	—	5	2	no	—
346	C₂×C₃×D₄	—	2	6	no	—
347	C₂×C₃×D₄	—	5	3	no	—
348	C₂×C₃×D₄	—	5	6	no	—
349	C₂×C₃×D₄	—	5	12	no	—
350	C₂×C₃×D₄	—	5	6	no	—
351	C₂×C₃×D₄	—	10	6	no	—
352	C₂×C₃×D₄	—	10	6	no	—
353	C₂×C₃×D₄	—	10	6	no	—
354	C₂×C₃×D₄	—	10	6	no	—
355	C₂×C₃×D₄	—	10	12	no	—
356	C₂×C₃×D₄	—	10	6	no	—
357	C₂×C₃×D₄	—	10	6	no	—
358	C₂×C₃×D₄	—	10	12	no	—
359	C₂×C₃×D₄	—	10	6	no	—
360	C₂×C₃×D₄	C₂²×D₅	1	6	yes	complemented
361	C₂²×C₃×C₄	—	5	3	no	—
362	C₂²×C₃×C₄	—	10	6	no	—
363	C₃×Q₁₆	—	5	2	no	—
364	C₃×Q₁₆	—	5	1	no	—
365	C₃×Q₁₆	C₂²×D₅	1	1	yes	characteristic, complemented
366	C₃×SD₁₆	—	5	6	no	—
367	C₃×SD₁₆	—	5	6	no	—
368	C₃×SD₁₆	—	5	6	no	—
369	C₃×SD₁₆	C₂²×D₅	1	6	yes	complemented
370	C₃×D₈	—	5	6	no	—
371	C₃×D₈	—	5	12	no	—
372	C₃×D₈	—	5	3	no	—
373	C₃×D₈	—	5	6	no	—
374	C₃×D₈	C₂²×D₅	1	3	yes	complemented
375	C₃×D₈	C₂²×D₅	1	6	yes	complemented
376	C₃×M₁₆	—	5	3	no	—
377	C₃×M₁₆	—	5	6	no	—
378	C₃×M₁₆	C₂²×D₅	1	3	yes	complemented
379	C₂×C₃×C₈	—	5	3	no	—
380	C₂×C₃×C₈	—	5	1	no	—
381	C₂×C₃×C₈	—	5	3	no	—
382	C₂×C₃×C₈	—	5	3	no	—
383	C₂×C₃×C₈	—	5	3	no	—
384	C₂×C₃×C₈	C₂²×D₅	1	3	yes	complemented
385	C₂³×C₅	—	2	6	no	—
386	C₂²×D₅	—	2	6	no	—
387	C₂²×D₅	—	2	6	no	—
388	C₂²×D₅	—	2	12	no	—
389	C₂²×D₅	—	8	12	no	—
390	C₂²×D₅	C₂×C₃×D₄	1	3	yes	—
391	C₅×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
392	C₅×Q₈	C₂⁴×C₃	1	2	yes	—
393	C₅×D₄	—	2	6	no	—
394	C₅×D₄	—	2	6	no	—
395	C₅×D₄	C₂×C₃×D₄	1	3	yes	—
396	C₅×D₄	C₂⁴×C₃	1	6	yes	—
397	C₂×C₄×C₅	—	2	6	no	—
398	C₂×C₄×C₅	C₂⁴×C₃	1	3	yes	—
399	C₂²⋊D₅	—	2	6	no	—
400	C₂²⋊D₅	—	2	6	no	—
401	C₂²⋊D₅	—	2	6	no	—
402	C₂²⋊D₅	—	2	12	no	—
403	C₂²⋊D₅	C₂×C₃×D₄	1	6	yes	—
404	C₂×Dic₅	—	2	6	no	—
405	C₂×Dic₅	C₂×C₃×D₄	1	3	yes	—
406	D₂₀	—	2	6	no	—
407	D₂₀	—	2	6	no	—
408	D₂₀	C₂×C₃×D₄	1	3	yes	—
409	D₂₀	C₂⁴×C₃	1	6	yes	—
410	C₄×D₅	—	2	2	no	—
411	C₄×D₅	—	2	6	no	—
412	C₄×D₅	—	2	6	no	—
413	C₄×D₅	C₂×C₃×D₄	1	3	yes	—
414	C₄×D₅	C₂×C₃×D₄	1	3	yes	—
415	C₄×D₅	C₂⁴×C₃	1	1	yes	characteristic
416	C₄×D₅	C₂⁴×C₃	1	3	yes	—
417	Dic₁₀	—	2	2	no	—
418	Dic₁₀	C₂×C₃×D₄	1	3	yes	—
419	Dic₁₀	C₂⁴×C₃	1	2	yes	—
420	C₅×C₈	C₂⁴×C₃	1	1	yes	characteristic
421	C₅×C₈	C₂⁴×C₃	1	3	yes	—
422	#168	C₂⁴×C₃	1	1	yes	characteristic
423	#168	C₂⁴×C₃	1	3	yes	—
424	H(5,𝔽₂)	—	5	2	no	—
425	H(5,𝔽₂)	—	5	6	no	—
426	H(5,𝔽₂)	—	5	6	no	—
427	H(5,𝔽₂)	—	10	6	no	—
428	H(5,𝔽₂)	—	10	2	no	—
429	H(5,𝔽₂)	C₂×C₃×D₅	1	2	yes	complemented
430	C₂×#41	—	5	1	no	—
431	C₂×#41	—	5	6	no	—
432	C₂×#41	—	10	2	no	—
433	C₂²×D₄	—	5	6	no	—
434	C₂²×D₄	—	10	6	no	—
435	AGL(1,ℤ/8)	—	5	6	no	—
436	AGL(1,ℤ/8)	—	5	6	no	—
437	AGL(1,ℤ/8)	—	5	12	no	—
438	AGL(1,ℤ/8)	—	5	12	no	—
439	AGL(1,ℤ/8)	—	5	6	no	—
440	AGL(1,ℤ/8)	C₂×C₃×D₅	1	6	yes	complemented
441	#135	—	5	6	no	—
442	#135	—	5	3	no	—
443	#135	—	5	6	no	—
444	#135	—	5	3	no	—
445	#135	—	5	3	no	—
446	#135	C₂×C₃×D₅	1	3	yes	complemented
447	C₂×Q₁₆	—	5	1	no	—
448	C₂×SD₁₆	—	5	6	no	—
449	C₂×D₈	—	5	6	no	—
450	C₂×D₈	—	5	3	no	—
451	C₂×D₈	—	5	6	no	—
452	C₂×D₈	—	5	6	no	—
453	C₂×D₈	—	5	6	no	—
454	C₂×D₈	—	5	3	no	—
455	C₂×D₈	C₂×C₃×D₅	1	3	yes	complemented
456	#131	—	5	1	no	—
457	#131	—	5	3	no	—
458	#131	—	5	3	no	—
459	#131	C₂×C₃×D₅	1	1	yes	characteristic, complemented
460	C₂×M₁₆	—	5	3	no	—
461	C₂²×C₈	—	5	3	no	—
462	C₂×C₃×C₅	—	2	3	no	—
463	C₂×C₃×C₅	—	4	6	no	—
464	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
465	C₃×D₅	—	2	3	no	—
466	C₃×D₅	—	4	6	no	—
467	C₃×D₅	#576	1	2	yes	direct product factor
468	C₂³×C₃	—	2	6	no	—
469	C₂³×C₃	—	5	3	no	—
470	C₂³×C₃	—	10	6	no	—
471	C₂³×C₃	—	10	12	no	—
472	C₂³×C₃	—	10	6	no	—
473	C₂³×C₃	—	40	12	no	—
474	C₃×Q₈	—	5	3	no	—
475	C₃×Q₈	—	5	2	no	—
476	C₃×Q₈	—	10	2	no	—
477	C₃×Q₈	D₄×D₅	1	1	yes	characteristic
478	C₃×Q₈	C₂³×D₅	1	2	yes	—
479	C₃×D₄	—	2	6	no	—
480	C₃×D₄	—	2	6	no	—
481	C₃×D₄	—	5	6	no	—
482	C₃×D₄	—	5	3	no	—
483	C₃×D₄	—	5	6	no	—
484	C₃×D₄	—	10	6	no	—
485	C₃×D₄	—	10	6	no	—
486	C₃×D₄	—	10	12	no	—
487	C₃×D₄	—	10	6	no	—
488	C₃×D₄	—	10	6	no	—
489	C₃×D₄	—	10	6	no	—
490	C₃×D₄	D₄×D₅	1	3	yes	—
491	C₃×D₄	C₂³×D₅	1	6	yes	—
492	C₂×C₃×C₄	—	2	6	no	—
493	C₂×C₃×C₄	—	5	3	no	—
494	C₂×C₃×C₄	—	5	3	no	—
495	C₂×C₃×C₄	—	5	3	no	—
496	C₂×C₃×C₄	—	5	1	no	—
497	C₂×C₃×C₄	—	5	3	no	—
498	C₂×C₃×C₄	—	10	6	no	—
499	C₂×C₃×C₄	—	10	2	no	—
500	C₂×C₃×C₄	—	10	6	no	—
501	C₂×C₃×C₄	—	10	6	no	—
502	C₂×C₃×C₄	C₂³×D₅	1	3	yes	—
503	C₃×C₈	—	5	1	no	—
504	C₃×C₈	—	5	3	no	—
505	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
506	C₃×C₈	C₂³×D₅	1	3	yes	—
507	C₂²×C₅	—	2	6	no	—
508	C₂²×C₅	—	8	6	no	—
509	C₂²×C₅	C₂²×C₃×D₄	1	3	yes	—
510	C₂×D₅	—	2	6	no	—
511	C₂×D₅	—	2	6	no	—
512	C₂×D₅	—	4	12	no	—
513	C₂×D₅	—	8	12	no	—
514	C₂×D₅	—	8	6	no	—
515	C₂×D₅	C₂²×C₃×D₄	1	3	yes	—
516	C₂×D₅	C₂²×C₃×D₄	1	1	yes	characteristic
517	C₄×C₅	—	2	2	no	—
518	C₄×C₅	C₂²×C₃×D₄	1	3	yes	—
519	C₄×C₅	C₂⁵×C₃	1	1	yes	characteristic
520	Dic₅	—	2	2	no	—
521	Dic₅	C₂²×C₃×D₄	1	1	yes	characteristic
522	Dic₅	C₂²×C₃×D₄	1	3	yes	—
523	C₂⁴	—	10	6	no	—
524	#41	—	2	2	no	—
525	#41	—	5	1	no	—
526	#41	—	5	3	no	—
527	#41	—	5	3	no	—
528	#41	—	5	6	no	—
529	#41	—	5	6	no	—
530	#41	—	5	6	no	—
531	#41	—	10	6	no	—
532	#41	—	10	6	no	—
533	#41	—	10	6	no	—
534	#41	—	10	6	no	—
535	#41	—	10	2	no	—
536	#41	C₂²×C₃×D₅	1	1	yes	characteristic
537	#41	C₂²×C₃×D₅	1	6	yes	complemented
538	C₂×Q₈	—	5	1	no	—
539	C₂×Q₈	—	5	2	no	—
540	C₂×D₄	—	2	6	no	—
541	C₂×D₄	—	5	3	no	—
542	C₂×D₄	—	5	6	no	—
543	C₂×D₄	—	5	12	no	—
544	C₂×D₄	—	5	6	no	—
545	C₂×D₄	—	10	6	no	—
546	C₂×D₄	—	10	6	no	—
547	C₂×D₄	—	10	6	no	—
548	C₂×D₄	—	10	6	no	—
549	C₂×D₄	—	10	12	no	—
550	C₂×D₄	—	10	6	no	—
551	C₂×D₄	—	10	6	no	—
552	C₂×D₄	—	10	12	no	—
553	C₂×D₄	—	10	6	no	—
554	C₂×D₄	C₂²×C₃×D₅	1	6	yes	complemented
555	C₂²×C₄	—	5	3	no	—
556	C₂²×C₄	—	10	6	no	—
557	Q₁₆	—	5	2	no	—
558	Q₁₆	—	5	1	no	—
559	Q₁₆	C₂²×C₃×D₅	1	1	yes	characteristic, complemented
560	SD₁₆	—	5	6	no	—
561	SD₁₆	—	5	6	no	—
562	SD₁₆	—	5	6	no	—
563	SD₁₆	C₂²×C₃×D₅	1	6	yes	complemented
564	D₈	—	5	6	no	—
565	D₈	—	5	12	no	—
566	D₈	—	5	3	no	—
567	D₈	—	5	6	no	—
568	D₈	C₂²×C₃×D₅	1	3	yes	complemented
569	D₈	C₂²×C₃×D₅	1	6	yes	complemented
570	M₁₆	—	5	3	no	—
571	M₁₆	—	5	6	no	—
572	M₁₆	C₂²×C₃×D₅	1	3	yes	complemented
573	C₂×C₈	—	5	3	no	—
574	C₂×C₈	—	5	1	no	—
575	C₂×C₈	—	5	3	no	—
576	C₂×C₈	—	5	3	no	—
577	C₂×C₈	—	5	3	no	—
578	C₂×C₈	C₂²×C₃×D₅	1	3	yes	complemented
579	C₃×C₅	C₂×#576	1	1	yes	characteristic, complemented, Hall
580	C₂²×C₃	—	2	6	no	—
581	C₂²×C₃	—	5	1	no	—
582	C₂²×C₃	—	5	3	no	—
583	C₂²×C₃	—	8	6	no	—
584	C₂²×C₃	—	10	6	no	—
585	C₂²×C₃	—	10	6	no	—
586	C₂²×C₃	—	20	12	no	—
587	C₂²×C₃	—	40	6	no	—
588	C₂²×C₃	—	40	12	no	—
589	C₂²×C₃	C₂×D₄×D₅	1	3	yes	—
590	C₃×C₄	—	2	2	no	—
591	C₃×C₄	—	5	1	no	—
592	C₃×C₄	—	5	3	no	—
593	C₃×C₄	—	10	2	no	—
594	C₃×C₄	C₂×D₄×D₅	1	3	yes	—
595	C₃×C₄	C₂⁴×D₅	1	1	yes	characteristic
596	C₂×C₅	—	2	3	no	—
597	C₂×C₅	—	4	6	no	—
598	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
599	D₅	—	2	3	no	—
600	D₅	—	4	6	no	—
601	D₅	C₃×#576	1	2	yes	direct product factor
602	C₂³	—	2	6	no	—
603	C₂³	—	5	3	no	—
604	C₂³	—	10	6	no	—
605	C₂³	—	10	12	no	—
606	C₂³	—	10	6	no	—
607	C₂³	—	40	12	no	—
608	Q₈	—	5	3	no	—
609	Q₈	—	5	2	no	—
610	Q₈	—	10	2	no	—
611	Q₈	C₃×D₄×D₅	1	1	yes	characteristic
612	Q₈	C₂³×C₃×D₅	1	2	yes	—
613	D₄	—	2	6	no	—
614	D₄	—	2	6	no	—
615	D₄	—	5	6	no	—
616	D₄	—	5	3	no	—
617	D₄	—	5	6	no	—
618	D₄	—	10	6	no	—
619	D₄	—	10	6	no	—
620	D₄	—	10	12	no	—
621	D₄	—	10	6	no	—
622	D₄	—	10	6	no	—
623	D₄	—	10	6	no	—
624	D₄	C₃×D₄×D₅	1	3	yes	—
625	D₄	C₂³×C₃×D₅	1	6	yes	—
626	C₂×C₄	—	2	6	no	—
627	C₂×C₄	—	5	3	no	—
628	C₂×C₄	—	5	3	no	—
629	C₂×C₄	—	5	3	no	—
630	C₂×C₄	—	5	1	no	—
631	C₂×C₄	—	5	3	no	—
632	C₂×C₄	—	10	6	no	—
633	C₂×C₄	—	10	2	no	—
634	C₂×C₄	—	10	6	no	—
635	C₂×C₄	—	10	6	no	—
636	C₂×C₄	C₂³×C₃×D₅	1	3	yes	—
637	C₈	—	5	1	no	—
638	C₈	—	5	3	no	—
639	C₈	C₂³×C₃×D₅	1	1	yes	characteristic
640	C₈	C₂³×C₃×D₅	1	3	yes	—
641	C₂×C₃	—	2	3	no	—
642	C₂×C₃	—	4	6	no	—
643	C₂×C₃	—	5	2	no	—
644	C₂×C₃	—	10	3	no	—
645	C₂×C₃	—	20	6	no	—
646	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
647	C₅	C₂×C₃×#576	1	1	yes	characteristic, complemented, Sylow
648	C₂²	—	2	6	no	—
649	C₂²	—	5	1	no	—
650	C₂²	—	5	3	no	—
651	C₂²	—	8	6	no	—
652	C₂²	—	10	6	no	—
653	C₂²	—	10	6	no	—
654	C₂²	—	20	12	no	—
655	C₂²	—	40	6	no	—
656	C₂²	—	40	12	no	—
657	C₂²	C₂×C₃×D₄×D₅	1	3	yes	—
658	C₄	—	2	2	no	—
659	C₄	—	5	1	no	—
660	C₄	—	5	3	no	—
661	C₄	—	10	2	no	—
662	C₄	C₂×C₃×D₄×D₅	1	3	yes	—
663	C₄	C₂⁴×C₃×D₅	1	1	yes	characteristic
664	C₃	D₅×#576	1	1	yes	characteristic, direct product factor, Sylow
665	C₂	—	2	3	no	—
666	C₂	—	4	6	no	—
667	C₂	—	5	2	no	—
668	C₂	—	10	3	no	—
669	C₂	—	20	6	no	—
670	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²×D₄×D₅
commutator, cosocle	C₄×C₅	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#576	C₂
socle	C₂×C₃×C₅	C₂³×D₄
hypercenter	C₃×#576	D₅
hypocenter	C₅	C₂×C₃×#576
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×#41 ◁ C₃×#576

Complements

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

N	H ≅ G/N	type
1. C₃×D₅×H(5,𝔽₂)	C₂	semidirect
2. C₃×C₅×#576	C₂	semidirect
3. C₃×#66169	C₂	semidirect
4. C₃×#66108	C₂	semidirect
5. C₃×D₅×AGL(1,ℤ/8)	C₂	semidirect
6. C₃×#66103	C₂	semidirect
7. C₃×D₅×#135	C₂	semidirect
8. C₃×#66091	C₂	semidirect
9. C₂×C₃×D₅×D₈	C₂	semidirect
10. C₃×#66086	C₂	semidirect
11. C₃×D₅×#131	C₂	semidirect
12. D₅×#576	C₃	direct (N × H)
13. C₃×C₅×H(5,𝔽₂)	C₂²	semidirect
15. C₃×#4149	C₂²	semidirect
16. C₃×#4149	C₂²	semidirect
19. C₃×D₅×#41	C₂²	semidirect
21. C₃×#4144	C₂²	semidirect
23. C₂×C₃×D₄×D₅	C₂²	semidirect
24. C₃×C₅×AGL(1,ℤ/8)	C₂²	semidirect
25. C₃×C₅×#135	C₂²	semidirect
26. C₂×C₃×C₅×D₈	C₂²	semidirect
27. C₃×C₅×#131	C₂²	semidirect
28. C₃×#4096	C₂²	semidirect
29. C₃×#4095	C₂²	semidirect
30. C₃×#4094	C₂²	semidirect
31. C₃×#4078	C₂²	semidirect
32. C₂×C₃×#686	C₂²	semidirect
33. C₃×#4065	C₂²	semidirect
34. C₃×D₅×Q₁₆	C₂²	semidirect
35. C₃×#4062	C₂²	semidirect
36. C₃×#4060	C₂²	semidirect
37. C₃×D₅×SD₁₆	C₂²	semidirect
38. C₃×#4058	C₂²	semidirect
39. C₃×#4057	C₂²	semidirect
40. C₃×D₅×D₈	C₂²	semidirect
41. C₃×D₅×D₈	C₂²	semidirect
42. C₃×D₅×D₈	C₂²	semidirect
43. C₃×D₅×D₈	C₂²	semidirect
44. C₃×#4054	C₂²	semidirect
45. C₃×#4053	C₂²	semidirect
46. C₃×D₅×M₁₆	C₂²	semidirect
47. C₃×#4050	C₂²	semidirect
48. C₂×C₃×D₄₀	C₂²	semidirect
49. C₃×#4047	C₂²	semidirect
50. C₂×C₃×C₈×D₅	C₂²	semidirect
52. D₅×H(5,𝔽₂)	C₂×C₃	semidirect
53. C₅×#576	C₂×C₃	semidirect
54. #66169	C₂×C₃	semidirect
55. #66108	C₂×C₃	semidirect
56. D₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
57. #66103	C₂×C₃	semidirect
58. D₅×#135	C₂×C₃	semidirect
59. #66091	C₂×C₃	semidirect
60. C₂×D₅×D₈	C₂×C₃	semidirect
61. #66086	C₂×C₃	semidirect
62. D₅×#131	C₂×C₃	semidirect
66. C₃×C₅×#41	C₂³	semidirect
68. C₂×C₃×C₅×D₄	C₂³	semidirect
73. C₃×#713	C₂³	semidirect
79. C₃×#711	C₂³	semidirect
88. C₃×D₄×D₅	C₂³	semidirect
92. C₃×#709	C₂³	semidirect
94. C₂×C₃×D₂₀	C₂³	semidirect
97. C₃×C₅×Q₁₆	C₂³	semidirect
98. C₃×C₅×SD₁₆	C₂³	semidirect
99. C₃×C₅×D₈	C₂³	semidirect
100. C₃×C₅×D₈	C₂³	semidirect
101. C₃×C₅×M₁₆	C₂³	semidirect
102. C₂×C₃×C₅×C₈	C₂³	semidirect
103. C₃×#689	C₂³	semidirect
104. C₃×#688	C₂³	semidirect
105. C₃×#687	C₂³	semidirect
106. C₃×#686	C₂³	semidirect
107. C₃×#686	C₂³	semidirect
108. C₃×#681	C₂³	semidirect
109. C₂×C₃×#168	C₂³	semidirect
110. C₃×Dic₂₀	C₂³	semidirect
111. C₃×D₄₀	C₂³	semidirect
112. C₃×D₄₀	C₂³	semidirect
113. C₃×#677	C₂³	semidirect
114. C₃×#676	C₂³	semidirect
117. C₃×C₈×D₅	C₂³	semidirect
118. C₃×C₈×D₅	C₂³	semidirect
125. C₃×#576	D₅	direct (N × H)
130. C₅×H(5,𝔽₂)	C₂²×C₃	semidirect
132. #4149	C₂²×C₃	semidirect
133. #4149	C₂²×C₃	semidirect
136. D₅×#41	C₂²×C₃	semidirect
138. #4144	C₂²×C₃	semidirect
140. C₂×D₄×D₅	C₂²×C₃	semidirect
141. C₅×AGL(1,ℤ/8)	C₂²×C₃	semidirect
142. C₅×#135	C₂²×C₃	semidirect
143. C₂×C₅×D₈	C₂²×C₃	semidirect
144. C₅×#131	C₂²×C₃	semidirect
145. #4096	C₂²×C₃	semidirect
146. #4095	C₂²×C₃	semidirect
147. #4094	C₂²×C₃	semidirect
148. #4078	C₂²×C₃	semidirect
149. C₂×#686	C₂²×C₃	semidirect
150. #4065	C₂²×C₃	semidirect
151. D₅×Q₁₆	C₂²×C₃	semidirect
152. #4062	C₂²×C₃	semidirect
153. #4060	C₂²×C₃	semidirect
154. D₅×SD₁₆	C₂²×C₃	semidirect
155. #4058	C₂²×C₃	semidirect
156. #4057	C₂²×C₃	semidirect
157. D₅×D₈	C₂²×C₃	semidirect
158. D₅×D₈	C₂²×C₃	semidirect
159. D₅×D₈	C₂²×C₃	semidirect
160. D₅×D₈	C₂²×C₃	semidirect
161. #4054	C₂²×C₃	semidirect
162. #4053	C₂²×C₃	semidirect
163. D₅×M₁₆	C₂²×C₃	semidirect
164. #4050	C₂²×C₃	semidirect
165. C₂×D₄₀	C₂²×C₃	semidirect
166. #4047	C₂²×C₃	semidirect
167. C₂×C₈×D₅	C₂²×C₃	semidirect
213. C₃×H(5,𝔽₂)	C₂×D₅	semidirect
224. C₃×AGL(1,ℤ/8)	C₂×D₅	semidirect
230. C₃×#135	C₂×D₅	semidirect
239. C₂×C₃×D₈	C₂×D₅	semidirect
243. C₃×#131	C₂×D₅	semidirect
249. C₅×#41	C₂³×C₃	semidirect
251. C₂×C₅×D₄	C₂³×C₃	semidirect
256. #713	C₂³×C₃	semidirect
262. #711	C₂³×C₃	semidirect
271. D₄×D₅	C₂³×C₃	semidirect
275. #709	C₂³×C₃	semidirect
277. C₂×D₂₀	C₂³×C₃	semidirect
280. C₅×Q₁₆	C₂³×C₃	semidirect
281. C₅×SD₁₆	C₂³×C₃	semidirect
282. C₅×D₈	C₂³×C₃	semidirect
283. C₅×D₈	C₂³×C₃	semidirect
284. C₅×M₁₆	C₂³×C₃	semidirect
285. C₂×C₅×C₈	C₂³×C₃	semidirect
286. #689	C₂³×C₃	semidirect
287. #688	C₂³×C₃	semidirect
288. #687	C₂³×C₃	semidirect
289. #686	C₂³×C₃	semidirect
290. #686	C₂³×C₃	semidirect
291. #681	C₂³×C₃	semidirect
292. C₂×#168	C₂³×C₃	semidirect
293. Dic₂₀	C₂³×C₃	semidirect
294. D₄₀	C₂³×C₃	semidirect
295. D₄₀	C₂³×C₃	semidirect
296. #677	C₂³×C₃	semidirect
297. #676	C₂³×C₃	semidirect
300. C₈×D₅	C₂³×C₃	semidirect
301. C₈×D₅	C₂³×C₃	semidirect
308. #576	C₃×D₅	direct (N × H)
343. C₃×#41	C₂²×D₅	semidirect
360. C₂×C₃×D₄	C₂²×D₅	semidirect
365. C₃×Q₁₆	C₂²×D₅	semidirect
369. C₃×SD₁₆	C₂²×D₅	semidirect
374. C₃×D₈	C₂²×D₅	semidirect
375. C₃×D₈	C₂²×D₅	semidirect
378. C₃×M₁₆	C₂²×D₅	semidirect
384. C₂×C₃×C₈	C₂²×D₅	semidirect
429. H(5,𝔽₂)	C₂×C₃×D₅	semidirect
440. AGL(1,ℤ/8)	C₂×C₃×D₅	semidirect
446. #135	C₂×C₃×D₅	semidirect
455. C₂×D₈	C₂×C₃×D₅	semidirect
459. #131	C₂×C₃×D₅	semidirect
467. C₃×D₅	#576	direct (N × H)
537. #41	C₂²×C₃×D₅	semidirect
554. C₂×D₄	C₂²×C₃×D₅	semidirect
559. Q₁₆	C₂²×C₃×D₅	semidirect
563. SD₁₆	C₂²×C₃×D₅	semidirect
568. D₈	C₂²×C₃×D₅	semidirect
569. D₈	C₂²×C₃×D₅	semidirect
572. M₁₆	C₂²×C₃×D₅	semidirect
578. C₂×C₈	C₂²×C₃×D₅	semidirect
579. C₃×C₅	C₂×#576	semidirect
601. D₅	C₃×#576	direct (N × H)
647. C₅	C₂×C₃×#576	semidirect
664. C₃	D₅×#576	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₅×H(5,𝔽₂)	2
C₃×C₅×#576	2
C₃×#66169	2
C₃×#66108	2
C₃×D₅×AGL(1,ℤ/8)	2
C₃×#66103	2
C₃×D₅×#135	2
C₃×#66091	2
C₂×C₃×D₅×D₈	2
C₃×#66086	2
C₃×D₅×#131	2
D₅×#576	3
C₂×C₃×#576	5

Subgroups — C3×D5×#576 #14509949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#576 #14509949