Subgroups — C₃×D₅×#510 #14478375

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×D₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#510	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65468	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65207	C₂	1	2	yes	maximal, complemented
7	C₃×D₅×Q₃₂	C₂	1	2	yes	maximal, complemented
8	C₃×#65204	C₂	1	2	yes	maximal, complemented
9	C₃×D₅×SD₃₂	C₂	1	2	yes	maximal, complemented
10	C₃×#65198	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#510	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×D₅×#41	—	2	1	no	—
14	C₂×C₃×Q₈×D₅	—	2	1	no	—
15	C₃×C₅×#135	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
17	C₃×#4096	—	2	1	no	—
18	C₂×C₃×#689	—	2	1	no	—
19	C₃×#4065	C₂²	1	1	yes	characteristic
20	C₃×D₅×Q₁₆	—	2	1	no	—
21	C₃×D₅×Q₁₆	—	2	1	no	—
22	C₃×D₅×Q₁₆	C₂²	1	1	yes	characteristic
23	C₃×D₅×Q₁₆	C₂²	1	2	yes	—
24	C₃×D₅×Q₁₆	C₂²	1	2	yes	complemented
25	C₃×#4062	—	2	1	no	—
26	C₃×D₅×SD₁₆	—	2	1	no	—
27	C₃×#4058	C₂²	1	1	yes	characteristic
28	C₃×D₅×D₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
30	C₃×#4050	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
32	C₃×C₅×Q₃₂	C₂²	1	2	yes	complemented
33	C₃×C₅×SD₃₂	C₂²	1	2	yes	complemented
34	C₃×C₅×M₃₂	C₂²	1	1	yes	characteristic, complemented
35	C₃×#3961	C₂²	1	2	yes	complemented
36	C₃×#3961	C₂²	1	2	yes	complemented
37	C₃×#3960	C₂²	1	2	yes	complemented
38	C₃×#3959	C₂²	1	2	yes	complemented
39	C₃×#3944	C₂²	1	1	yes	characteristic, complemented
40	C₃×Dic₄₀	C₂²	1	2	yes	complemented
41	C₃×#3932	C₂²	1	2	yes	complemented
42	C₃×#3930	C₂²	1	2	yes	complemented
43	C₃×D₅×C₁₆	C₂²	1	2	yes	—
44	C₂×C₃×#510	—	5	1	no	maximal, Hall
45	D₅×#135	C₂×C₃	1	1	yes	characteristic
46	C₂×D₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#510	C₂×C₃	1	1	yes	characteristic, complemented
48	#65484	C₂×C₃	1	1	yes	characteristic, complemented
49	#65468	C₂×C₃	1	1	yes	characteristic, complemented
50	#65207	C₂×C₃	1	2	yes	complemented
51	D₅×Q₃₂	C₂×C₃	1	2	yes	complemented
52	#65204	C₂×C₃	1	2	yes	complemented
53	D₅×SD₃₂	C₂×C₃	1	2	yes	complemented
54	#65198	C₂×C₃	1	1	yes	characteristic, complemented
55	D₅×M₃₂	C₂×C₃	1	1	yes	characteristic, complemented
56	C₃×C₅×#41	—	2	1	no	—
57	C₂×C₃×C₅×Q₈	—	2	1	no	—
58	C₃×#713	—	2	1	no	—
59	C₃×Q₈×D₅	—	2	2	no	—
60	C₃×Q₈×D₅	—	2	2	no	—
61	C₃×Q₈×D₅	—	2	1	no	—
62	C₃×Q₈×D₅	—	4	1	no	—
63	C₃×Q₈×D₅	—	4	1	no	—
64	C₃×#711	—	2	1	no	—
65	C₃×#711	—	4	1	no	—
66	C₃×D₄×D₅	—	2	1	no	—
67	C₃×D₄×D₅	—	4	1	no	—
68	C₃×#709	—	2	1	no	—
69	C₃×#709	—	4	1	no	—
70	C₂×C₃×C₄×D₅	—	4	1	no	—
71	C₂×C₃×C₄×D₅	—	4	1	no	—
72	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
73	C₂×C₃×Dic₁₀	—	2	1	no	—
74	C₂×C₃×Dic₁₀	—	4	1	no	—
75	C₃×C₅×Q₁₆	—	2	1	no	—
76	C₃×C₅×Q₁₆	C₂³	1	2	yes	—
77	C₃×C₅×Q₁₆	C₂³	1	1	yes	characteristic
78	C₃×C₅×SD₁₆	—	2	1	no	—
79	C₃×C₅×D₈	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
81	C₃×#689	—	2	2	no	—
82	C₃×#689	—	2	2	no	—
83	C₃×#689	—	2	1	no	—
84	C₃×#688	—	2	1	no	—
85	C₃×#687	—	2	1	no	—
86	C₃×#686	—	2	1	no	—
87	C₂×C₃×#168	D₄	1	1	yes	characteristic
88	C₃×Dic₂₀	—	2	1	no	—
89	C₃×Dic₂₀	C₂³	1	2	yes	—
90	C₃×Dic₂₀	C₂³	1	1	yes	characteristic
91	C₃×D₄₀	C₂³	1	1	yes	characteristic
92	C₃×#677	—	2	1	no	—
93	C₃×C₈×D₅	D₄	1	1	yes	characteristic
94	C₃×C₈×D₅	D₄	1	1	yes	characteristic
95	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
96	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
97	C₃×C₅×C₁₆	C₂³	1	2	yes	—
98	C₃×#672	C₂³	1	2	yes	—
99	C₂×C₃×#135	—	5	1	no	—
100	C₂²×C₃×Q₁₆	—	5	1	no	—
101	C₃×#510	—	5	1	no	—
102	C₃×#510	—	5	1	no	—
103	C₃×#510	—	5	2	no	—
104	C₃×#510	—	5	2	no	—
105	C₃×#510	—	5	1	no	—
106	C₃×#510	D₅	1	1	yes	characteristic, direct product factor
107	C₂×C₃×Q₃₂	—	5	2	no	—
108	C₂×C₃×SD₃₂	—	5	2	no	—
109	C₂×C₃×M₃₂	—	5	1	no	—
110	D₅×#41	—	2	1	no	—
111	C₂×Q₈×D₅	—	2	1	no	—
112	C₅×#135	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
114	#4096	—	2	1	no	—
115	C₂×#689	—	2	1	no	—
116	#4065	C₂²×C₃	1	1	yes	characteristic
117	D₅×Q₁₆	—	2	1	no	—
118	D₅×Q₁₆	—	2	1	no	—
119	D₅×Q₁₆	C₂²×C₃	1	2	yes	—
120	D₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
121	D₅×Q₁₆	C₂²×C₃	1	2	yes	complemented
122	#4062	—	2	1	no	—
123	D₅×SD₁₆	—	2	1	no	—
124	#4058	C₂²×C₃	1	1	yes	characteristic
125	D₅×D₈	C₂²×C₃	1	1	yes	characteristic
126	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
127	#4050	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
129	C₅×Q₃₂	C₂²×C₃	1	2	yes	complemented
130	C₅×SD₃₂	C₂²×C₃	1	2	yes	complemented
131	C₅×M₃₂	C₂²×C₃	1	1	yes	characteristic, complemented
132	#3961	C₂²×C₃	1	2	yes	complemented
133	#3961	C₂²×C₃	1	2	yes	complemented
134	#3960	C₂²×C₃	1	2	yes	complemented
135	#3959	C₂²×C₃	1	2	yes	complemented
136	#3944	C₂²×C₃	1	1	yes	characteristic, complemented
137	Dic₄₀	C₂²×C₃	1	2	yes	complemented
138	#3932	C₂²×C₃	1	2	yes	complemented
139	#3930	C₂²×C₃	1	2	yes	complemented
140	D₅×C₁₆	C₂²×C₃	1	2	yes	—
141	C₂×#510	—	5	1	no	Sylow
142	C₂²×C₃×D₅	—	4	1	no	—
143	C₂²×C₃×D₅	D₈	1	1	yes	characteristic
144	C₃×C₅×Q₈	—	2	1	no	—
145	C₃×C₅×Q₈	—	2	2	no	—
146	C₃×C₅×Q₈	—	4	1	no	—
147	C₃×C₅×D₄	—	2	1	no	—
148	C₃×C₅×D₄	—	4	1	no	—
149	C₂×C₃×C₄×C₅	—	4	1	no	—
150	C₂×C₃×C₄×C₅	—	4	1	no	—
151	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₃×C₂²⋊D₅	—	4	1	no	—
153	C₃×C₂²⋊D₅	—	4	1	no	—
154	C₃×C₂²⋊D₅	—	4	1	no	—
155	C₂×C₃×Dic₅	—	4	1	no	—
156	C₂×C₃×Dic₅	—	4	1	no	—
157	C₂×C₃×Dic₅	D₈	1	1	yes	characteristic
158	C₃×D₂₀	—	2	1	no	—
159	C₃×D₂₀	—	4	1	no	—
160	C₃×C₄×D₅	—	4	1	no	—
161	C₃×C₄×D₅	—	4	2	no	—
162	C₃×C₄×D₅	—	4	2	no	—
163	C₃×C₄×D₅	—	4	1	no	—
164	C₃×C₄×D₅	—	4	1	no	—
165	C₃×C₄×D₅	D₈	1	1	yes	characteristic
166	C₃×C₄×D₅	D₈	1	1	yes	characteristic
167	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
168	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
169	C₃×Dic₁₀	—	2	1	no	—
170	C₃×Dic₁₀	—	2	2	no	—
171	C₃×Dic₁₀	—	4	1	no	—
172	C₃×Dic₁₀	—	4	2	no	—
173	C₃×Dic₁₀	—	4	2	no	—
174	C₃×Dic₁₀	—	4	1	no	—
175	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
176	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
177	C₃×#168	C₂×D₄	1	1	yes	characteristic
178	C₃×#168	C₂×D₄	1	1	yes	characteristic
179	C₂×C₃×#41	—	10	1	no	—
180	C₂²×C₃×Q₈	—	10	1	no	—
181	C₃×#135	—	5	1	no	—
182	C₃×#135	—	5	1	no	—
183	C₃×#135	—	5	1	no	—
184	C₃×#135	—	10	1	no	—
185	C₃×#135	—	10	1	no	—
186	C₃×#135	C₂×D₅	1	1	yes	characteristic
187	C₂×C₃×Q₁₆	—	5	2	no	—
188	C₂×C₃×Q₁₆	—	5	1	no	—
189	C₂×C₃×Q₁₆	—	5	2	no	—
190	C₂×C₃×Q₁₆	—	5	1	no	—
191	C₂×C₃×Q₁₆	—	10	1	no	—
192	C₂×C₃×Q₁₆	—	10	1	no	—
193	C₂×C₃×Q₁₆	—	10	1	no	—
194	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic, complemented
195	C₂×C₃×SD₁₆	—	10	1	no	—
196	C₂×C₃×D₈	—	5	1	no	—
197	C₂²×C₃×C₈	—	5	1	no	—
198	C₃×Q₃₂	—	5	2	no	—
199	C₃×Q₃₂	—	5	2	no	—
200	C₃×Q₃₂	—	5	2	no	—
201	C₃×Q₃₂	C₂×D₅	1	2	yes	complemented
202	C₃×SD₃₂	—	5	2	no	—
203	C₃×SD₃₂	—	5	2	no	—
204	C₃×SD₃₂	—	5	2	no	—
205	C₃×SD₃₂	C₂×D₅	1	2	yes	complemented
206	C₃×M₃₂	—	5	1	no	—
207	C₃×M₃₂	—	5	2	no	—
208	C₃×M₃₂	C₂×D₅	1	1	yes	characteristic, complemented
209	C₂×C₃×C₁₆	—	5	2	no	—
210	C₅×#41	—	2	1	no	—
211	C₂×C₅×Q₈	—	2	1	no	—
212	#713	—	2	1	no	—
213	Q₈×D₅	—	2	2	no	—
214	Q₈×D₅	—	2	2	no	—
215	Q₈×D₅	—	2	1	no	—
216	Q₈×D₅	—	4	1	no	—
217	Q₈×D₅	—	4	1	no	—
218	#711	—	2	1	no	—
219	#711	—	4	1	no	—
220	D₄×D₅	—	2	1	no	—
221	D₄×D₅	—	4	1	no	—
222	#709	—	2	1	no	—
223	#709	—	4	1	no	—
224	C₂×C₄×D₅	—	4	1	no	—
225	C₂×C₄×D₅	—	4	1	no	—
226	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
227	C₂×Dic₁₀	—	2	1	no	—
228	C₂×Dic₁₀	—	4	1	no	—
229	C₅×Q₁₆	—	2	1	no	—
230	C₅×Q₁₆	C₂³×C₃	1	2	yes	—
231	C₅×Q₁₆	C₂³×C₃	1	1	yes	characteristic
232	C₅×SD₁₆	—	2	1	no	—
233	C₅×D₈	C₂³×C₃	1	1	yes	characteristic
234	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
235	#689	—	2	1	no	—
236	#689	—	2	2	no	—
237	#689	—	2	2	no	—
238	#688	—	2	1	no	—
239	#687	—	2	1	no	—
240	#686	—	2	1	no	—
241	C₂×#168	C₃×D₄	1	1	yes	characteristic
242	Dic₂₀	—	2	1	no	—
243	Dic₂₀	C₂³×C₃	1	2	yes	—
244	Dic₂₀	C₂³×C₃	1	1	yes	characteristic
245	D₄₀	C₂³×C₃	1	1	yes	characteristic
246	#677	—	2	1	no	—
247	C₈×D₅	C₃×D₄	1	1	yes	characteristic
248	C₈×D₅	C₃×D₄	1	1	yes	characteristic
249	C₈×D₅	C₂³×C₃	1	1	yes	characteristic
250	C₈×D₅	C₂³×C₃	1	1	yes	characteristic
251	C₅×C₁₆	C₂³×C₃	1	2	yes	—
252	#672	C₂³×C₃	1	2	yes	—
253	C₂×#135	—	5	1	no	—
254	C₂²×Q₁₆	—	5	1	no	—
255	#510	—	5	1	no	—
256	#510	—	5	1	no	—
257	#510	—	5	2	no	—
258	#510	—	5	2	no	—
259	#510	—	5	1	no	—
260	#510	C₃×D₅	1	1	yes	characteristic, direct product factor
261	C₂×Q₃₂	—	5	2	no	—
262	C₂×SD₃₂	—	5	2	no	—
263	C₂×M₃₂	—	5	1	no	—
264	C₂²×C₃×C₅	—	4	1	no	—
265	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
266	C₂×C₃×D₅	—	2	2	no	—
267	C₂×C₃×D₅	—	4	1	no	—
268	C₂×C₃×D₅	—	8	2	no	—
269	C₂×C₃×D₅	C₂×D₈	1	1	yes	characteristic
270	C₂×C₃×D₅	C₂×D₈	1	1	yes	characteristic
271	C₃×C₄×C₅	—	4	2	no	—
272	C₃×C₄×C₅	—	4	1	no	—
273	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
274	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
275	C₃×Dic₅	—	4	2	no	—
276	C₃×Dic₅	—	4	1	no	—
277	C₃×Dic₅	C₂×D₈	1	1	yes	characteristic
278	C₃×Dic₅	C₂×D₈	1	1	yes	characteristic
279	C₃×#41	—	2	1	no	—
280	C₃×#41	—	10	1	no	—
281	C₃×#41	—	10	1	no	—
282	C₃×#41	—	10	1	no	—
283	C₃×#41	—	20	1	no	—
284	C₃×#41	—	20	1	no	—
285	C₂×C₃×Q₈	—	2	1	no	—
286	C₂×C₃×Q₈	—	10	1	no	—
287	C₂×C₃×Q₈	—	10	2	no	—
288	C₂×C₃×Q₈	—	10	2	no	—
289	C₂×C₃×Q₈	—	10	1	no	—
290	C₂×C₃×Q₈	—	20	1	no	—
291	C₂×C₃×Q₈	—	20	1	no	—
292	C₂×C₃×Q₈	—	20	1	no	—
293	C₂×C₃×D₄	—	10	1	no	—
294	C₂×C₃×D₄	—	20	1	no	—
295	C₂²×C₃×C₄	—	5	1	no	—
296	C₂²×C₃×C₄	—	20	1	no	—
297	C₂²×C₃×C₄	—	20	1	no	—
298	C₃×Q₁₆	—	2	1	no	—
299	C₃×Q₁₆	—	5	2	no	—
300	C₃×Q₁₆	—	5	1	no	—
301	C₃×Q₁₆	—	10	2	no	—
302	C₃×Q₁₆	—	10	2	no	—
303	C₃×Q₁₆	—	10	1	no	—
304	C₃×Q₁₆	—	10	1	no	—
305	C₃×Q₁₆	C₂²×D₅	1	2	yes	—
306	C₃×Q₁₆	C₂²×D₅	1	1	yes	characteristic
307	C₃×SD₁₆	—	2	1	no	—
308	C₃×SD₁₆	—	10	1	no	—
309	C₃×SD₁₆	—	10	1	no	—
310	C₃×SD₁₆	—	10	1	no	—
311	C₃×D₈	—	5	1	no	—
312	C₃×D₈	—	10	1	no	—
313	C₃×D₈	C₂²×D₅	1	1	yes	characteristic
314	C₂×C₃×C₈	—	5	1	no	—
315	C₂×C₃×C₈	—	5	1	no	—
316	C₂×C₃×C₈	—	5	1	no	—
317	C₂×C₃×C₈	—	5	1	no	—
318	C₂×C₃×C₈	—	5	1	no	—
319	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
320	C₃×C₁₆	—	5	2	no	—
321	C₃×C₁₆	C₂²×D₅	1	2	yes	—
322	C₂²×D₅	—	4	1	no	—
323	C₂²×D₅	C₃×D₈	1	1	yes	characteristic
324	C₅×Q₈	—	2	1	no	—
325	C₅×Q₈	—	2	2	no	—
326	C₅×Q₈	—	4	1	no	—
327	C₅×D₄	—	2	1	no	—
328	C₅×D₄	—	4	1	no	—
329	C₂×C₄×C₅	—	4	1	no	—
330	C₂×C₄×C₅	—	4	1	no	—
331	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
332	C₂²⋊D₅	—	4	1	no	—
333	C₂²⋊D₅	—	4	1	no	—
334	C₂²⋊D₅	—	4	1	no	—
335	C₂×Dic₅	—	4	1	no	—
336	C₂×Dic₅	—	4	1	no	—
337	C₂×Dic₅	C₃×D₈	1	1	yes	characteristic
338	D₂₀	—	2	1	no	—
339	D₂₀	—	4	1	no	—
340	C₄×D₅	—	4	1	no	—
341	C₄×D₅	—	4	2	no	—
342	C₄×D₅	—	4	2	no	—
343	C₄×D₅	—	4	1	no	—
344	C₄×D₅	—	4	1	no	—
345	C₄×D₅	C₃×D₈	1	1	yes	characteristic
346	C₄×D₅	C₃×D₈	1	1	yes	characteristic
347	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
348	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
349	Dic₁₀	—	2	1	no	—
350	Dic₁₀	—	2	2	no	—
351	Dic₁₀	—	4	1	no	—
352	Dic₁₀	—	4	2	no	—
353	Dic₁₀	—	4	2	no	—
354	Dic₁₀	—	4	1	no	—
355	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
356	C₅×C₈	C₂⁴×C₃	1	1	yes	characteristic
357	#168	C₂×C₃×D₄	1	1	yes	characteristic
358	#168	C₂×C₃×D₄	1	1	yes	characteristic
359	C₂×#41	—	10	1	no	—
360	C₂²×Q₈	—	10	1	no	—
361	#135	—	5	1	no	—
362	#135	—	5	1	no	—
363	#135	—	5	1	no	—
364	#135	—	10	1	no	—
365	#135	—	10	1	no	—
366	#135	C₂×C₃×D₅	1	1	yes	characteristic
367	C₂×Q₁₆	—	5	2	no	—
368	C₂×Q₁₆	—	5	2	no	—
369	C₂×Q₁₆	—	5	1	no	—
370	C₂×Q₁₆	—	5	1	no	—
371	C₂×Q₁₆	—	10	1	no	—
372	C₂×Q₁₆	—	10	1	no	—
373	C₂×Q₁₆	—	10	1	no	—
374	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
375	C₂×SD₁₆	—	10	1	no	—
376	C₂×D₈	—	5	1	no	—
377	C₂²×C₈	—	5	1	no	—
378	Q₃₂	—	5	2	no	—
379	Q₃₂	—	5	2	no	—
380	Q₃₂	—	5	2	no	—
381	Q₃₂	C₂×C₃×D₅	1	2	yes	complemented
382	SD₃₂	—	5	2	no	—
383	SD₃₂	—	5	2	no	—
384	SD₃₂	—	5	2	no	—
385	SD₃₂	C₂×C₃×D₅	1	2	yes	complemented
386	M₃₂	—	5	1	no	—
387	M₃₂	—	5	2	no	—
388	M₃₂	C₂×C₃×D₅	1	1	yes	characteristic, complemented
389	C₂×C₁₆	—	5	2	no	—
390	C₂×C₃×C₅	—	2	1	no	—
391	C₂×C₃×C₅	—	8	1	no	—
392	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
393	C₃×D₅	—	2	1	no	—
394	C₃×D₅	—	8	1	no	—
395	C₃×D₅	#510	1	2	yes	direct product factor
396	C₂³×C₃	—	5	1	no	—
397	C₂³×C₃	—	20	1	no	—
398	C₃×Q₈	—	2	1	no	—
399	C₃×Q₈	—	2	2	no	—
400	C₃×Q₈	—	4	1	no	—
401	C₃×Q₈	—	10	1	no	—
402	C₃×Q₈	—	10	2	no	—
403	C₃×Q₈	—	20	2	no	—
404	C₃×Q₈	—	20	2	no	—
405	C₃×Q₈	—	20	1	no	—
406	C₃×Q₈	—	20	1	no	—
407	C₃×D₄	—	2	1	no	—
408	C₃×D₄	—	4	1	no	—
409	C₃×D₄	—	10	1	no	—
410	C₃×D₄	—	20	1	no	—
411	C₃×D₄	—	20	1	no	—
412	C₃×D₄	—	20	1	no	—
413	C₃×D₄	—	20	1	no	—
414	C₂×C₃×C₄	—	4	1	no	—
415	C₂×C₃×C₄	—	4	1	no	—
416	C₂×C₃×C₄	—	5	1	no	—
417	C₂×C₃×C₄	—	5	1	no	—
418	C₂×C₃×C₄	—	5	1	no	—
419	C₂×C₃×C₄	—	5	1	no	—
420	C₂×C₃×C₄	—	5	1	no	—
421	C₂×C₃×C₄	—	20	1	no	—
422	C₂×C₃×C₄	—	20	1	no	—
423	C₂×C₃×C₄	—	20	2	no	—
424	C₂×C₃×C₄	—	20	2	no	—
425	C₂×C₃×C₄	—	20	1	no	—
426	C₂×C₃×C₄	—	20	1	no	—
427	C₂×C₃×C₄	—	20	1	no	—
428	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
429	C₃×C₈	—	5	1	no	—
430	C₃×C₈	—	5	1	no	—
431	C₃×C₈	D₄×D₅	1	1	yes	characteristic
432	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
433	C₂²×C₅	—	4	1	no	—
434	C₂²×C₅	C₂×C₃×D₈	1	1	yes	characteristic
435	C₂×D₅	—	2	2	no	—
436	C₂×D₅	—	4	1	no	—
437	C₂×D₅	—	8	2	no	—
438	C₂×D₅	C₂×C₃×D₈	1	1	yes	characteristic
439	C₂×D₅	C₂×C₃×D₈	1	1	yes	characteristic
440	C₄×C₅	—	4	2	no	—
441	C₄×C₅	—	4	1	no	—
442	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
443	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
444	Dic₅	—	4	2	no	—
445	Dic₅	—	4	1	no	—
446	Dic₅	C₂×C₃×D₈	1	1	yes	characteristic
447	Dic₅	C₂×C₃×D₈	1	1	yes	characteristic
448	#41	—	2	1	no	—
449	#41	—	10	1	no	—
450	#41	—	10	1	no	—
451	#41	—	10	1	no	—
452	#41	—	20	1	no	—
453	#41	—	20	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	10	1	no	—
456	C₂×Q₈	—	10	2	no	—
457	C₂×Q₈	—	10	2	no	—
458	C₂×Q₈	—	10	1	no	—
459	C₂×Q₈	—	20	1	no	—
460	C₂×Q₈	—	20	1	no	—
461	C₂×Q₈	—	20	1	no	—
462	C₂×D₄	—	10	1	no	—
463	C₂×D₄	—	20	1	no	—
464	C₂²×C₄	—	5	1	no	—
465	C₂²×C₄	—	20	1	no	—
466	C₂²×C₄	—	20	1	no	—
467	Q₁₆	—	2	1	no	—
468	Q₁₆	—	5	2	no	—
469	Q₁₆	—	5	1	no	—
470	Q₁₆	—	10	2	no	—
471	Q₁₆	—	10	2	no	—
472	Q₁₆	—	10	1	no	—
473	Q₁₆	—	10	1	no	—
474	Q₁₆	C₂²×C₃×D₅	1	2	yes	—
475	Q₁₆	C₂²×C₃×D₅	1	1	yes	characteristic
476	SD₁₆	—	2	1	no	—
477	SD₁₆	—	10	1	no	—
478	SD₁₆	—	10	1	no	—
479	SD₁₆	—	10	1	no	—
480	D₈	—	5	1	no	—
481	D₈	—	10	1	no	—
482	D₈	C₂²×C₃×D₅	1	1	yes	characteristic
483	C₂×C₈	—	5	1	no	—
484	C₂×C₈	—	5	1	no	—
485	C₂×C₈	—	5	1	no	—
486	C₂×C₈	—	5	1	no	—
487	C₂×C₈	—	5	1	no	—
488	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
489	C₁₆	—	5	2	no	—
490	C₁₆	C₂²×C₃×D₅	1	2	yes	—
491	C₃×C₅	C₂×#510	1	1	yes	characteristic, complemented, Hall
492	C₂²×C₃	—	4	1	no	—
493	C₂²×C₃	—	5	1	no	—
494	C₂²×C₃	—	5	1	no	—
495	C₂²×C₃	—	10	2	no	—
496	C₂²×C₃	—	20	1	no	—
497	C₂²×C₃	—	40	2	no	—
498	C₂²×C₃	D₅×D₈	1	1	yes	characteristic
499	C₃×C₄	—	4	1	no	—
500	C₃×C₄	—	4	2	no	—
501	C₃×C₄	—	5	1	no	—
502	C₃×C₄	—	5	1	no	—
503	C₃×C₄	—	20	1	no	—
504	C₃×C₄	—	20	2	no	—
505	C₃×C₄	D₅×D₈	1	1	yes	characteristic
506	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
507	C₂×C₅	—	2	1	no	—
508	C₂×C₅	—	8	1	no	—
509	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
510	D₅	—	2	1	no	—
511	D₅	—	8	1	no	—
512	D₅	C₃×#510	1	2	yes	direct product factor
513	C₂³	—	5	1	no	—
514	C₂³	—	20	1	no	—
515	Q₈	—	2	1	no	—
516	Q₈	—	2	2	no	—
517	Q₈	—	4	1	no	—
518	Q₈	—	10	1	no	—
519	Q₈	—	10	2	no	—
520	Q₈	—	20	2	no	—
521	Q₈	—	20	2	no	—
522	Q₈	—	20	1	no	—
523	Q₈	—	20	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	10	1	no	—
527	D₄	—	20	1	no	—
528	D₄	—	20	1	no	—
529	D₄	—	20	1	no	—
530	D₄	—	20	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	5	1	no	—
534	C₂×C₄	—	5	1	no	—
535	C₂×C₄	—	5	1	no	—
536	C₂×C₄	—	5	1	no	—
537	C₂×C₄	—	5	1	no	—
538	C₂×C₄	—	20	1	no	—
539	C₂×C₄	—	20	1	no	—
540	C₂×C₄	—	20	2	no	—
541	C₂×C₄	—	20	2	no	—
542	C₂×C₄	—	20	1	no	—
543	C₂×C₄	—	20	1	no	—
544	C₂×C₄	—	20	1	no	—
545	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
546	C₈	—	5	1	no	—
547	C₈	—	5	1	no	—
548	C₈	C₃×D₄×D₅	1	1	yes	characteristic
549	C₈	C₂³×C₃×D₅	1	1	yes	characteristic
550	C₂×C₃	—	2	1	no	—
551	C₂×C₃	—	5	2	no	—
552	C₂×C₃	—	8	1	no	—
553	C₂×C₃	—	10	1	no	—
554	C₂×C₃	—	40	1	no	—
555	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
556	C₅	C₂×C₃×#510	1	1	yes	characteristic, complemented, Sylow
557	C₂²	—	4	1	no	—
558	C₂²	—	5	1	no	—
559	C₂²	—	5	1	no	—
560	C₂²	—	10	2	no	—
561	C₂²	—	20	1	no	—
562	C₂²	—	40	2	no	—
563	C₂²	C₃×D₅×D₈	1	1	yes	characteristic
564	C₄	—	4	1	no	—
565	C₄	—	4	2	no	—
566	C₄	—	5	1	no	—
567	C₄	—	5	1	no	—
568	C₄	—	20	1	no	—
569	C₄	—	20	2	no	—
570	C₄	C₃×D₅×D₈	1	1	yes	characteristic
571	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
572	C₃	D₅×#510	1	1	yes	characteristic, direct product factor, Sylow
573	C₂	—	2	1	no	—
574	C₂	—	5	2	no	—
575	C₂	—	8	1	no	—
576	C₂	—	10	1	no	—
577	C₂	—	40	1	no	—
578	C₂	C₂×C₃×D₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₅×D₈
commutator, cosocle	C₅×C₈	C₂⁴×C₃
Frattini	C₈	C₂³×C₃×D₅
Fitting	C₃×C₅×#510	C₂
socle	C₂×C₃×C₅	C₂²×D₈
prime radical	C₃×D₅×#135	C₂
hypercenter	C₃×#510	D₅
hypocenter	C₅	C₂×C₃×#510
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₃×#510

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×D₅×Q₁₆	C₂	semidirect
3. C₃×C₅×#510	C₂	semidirect
4. C₃×#65484	C₂	semidirect
5. C₃×#65468	C₂	semidirect
6. C₃×#65207	C₂	semidirect
7. C₃×D₅×Q₃₂	C₂	semidirect
8. C₃×#65204	C₂	semidirect
9. C₃×D₅×SD₃₂	C₂	semidirect
10. C₃×#65198	C₂	semidirect
11. C₃×D₅×M₃₂	C₂	semidirect
12. D₅×#510	C₃	direct (N × H)
16. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
24. C₃×D₅×Q₁₆	C₂²	semidirect
29. C₂×C₃×Dic₂₀	C₂²	semidirect
32. C₃×C₅×Q₃₂	C₂²	semidirect
33. C₃×C₅×SD₃₂	C₂²	semidirect
34. C₃×C₅×M₃₂	C₂²	semidirect
35. C₃×#3961	C₂²	semidirect
36. C₃×#3961	C₂²	semidirect
37. C₃×#3960	C₂²	semidirect
38. C₃×#3959	C₂²	semidirect
39. C₃×#3944	C₂²	semidirect
40. C₃×Dic₄₀	C₂²	semidirect
41. C₃×#3932	C₂²	semidirect
42. C₃×#3930	C₂²	semidirect
46. C₂×D₅×Q₁₆	C₂×C₃	semidirect
47. C₅×#510	C₂×C₃	semidirect
48. #65484	C₂×C₃	semidirect
49. #65468	C₂×C₃	semidirect
50. #65207	C₂×C₃	semidirect
51. D₅×Q₃₂	C₂×C₃	semidirect
52. #65204	C₂×C₃	semidirect
53. D₅×SD₃₂	C₂×C₃	semidirect
54. #65198	C₂×C₃	semidirect
55. D₅×M₃₂	C₂×C₃	semidirect
106. C₃×#510	D₅	direct (N × H)
113. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
121. D₅×Q₁₆	C₂²×C₃	semidirect
126. C₂×Dic₂₀	C₂²×C₃	semidirect
129. C₅×Q₃₂	C₂²×C₃	semidirect
130. C₅×SD₃₂	C₂²×C₃	semidirect
131. C₅×M₃₂	C₂²×C₃	semidirect
132. #3961	C₂²×C₃	semidirect
133. #3961	C₂²×C₃	semidirect
134. #3960	C₂²×C₃	semidirect
135. #3959	C₂²×C₃	semidirect
136. #3944	C₂²×C₃	semidirect
137. Dic₄₀	C₂²×C₃	semidirect
138. #3932	C₂²×C₃	semidirect
139. #3930	C₂²×C₃	semidirect
194. C₂×C₃×Q₁₆	C₂×D₅	semidirect
201. C₃×Q₃₂	C₂×D₅	semidirect
205. C₃×SD₃₂	C₂×D₅	semidirect
208. C₃×M₃₂	C₂×D₅	semidirect
260. #510	C₃×D₅	direct (N × H)
374. C₂×Q₁₆	C₂×C₃×D₅	semidirect
381. Q₃₂	C₂×C₃×D₅	semidirect
385. SD₃₂	C₂×C₃×D₅	semidirect
388. M₃₂	C₂×C₃×D₅	semidirect
395. C₃×D₅	#510	direct (N × H)
491. C₃×C₅	C₂×#510	semidirect
512. D₅	C₃×#510	direct (N × H)
556. C₅	C₂×C₃×#510	semidirect
572. C₃	D₅×#510	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×#135	2
C₂×C₃×D₅×Q₁₆	2
C₃×C₅×#510	2
C₃×#65484	2
C₃×#65468	2
C₃×#65207	2
C₃×D₅×Q₃₂	2
C₃×#65204	2
C₃×D₅×SD₃₂	2
C₃×#65198	2
C₃×D₅×M₃₂	2
D₅×#510	3
C₂×C₃×#510	5

Subgroups — C3×D5×#510 #14478375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#510 #14478375