Subgroups — C₃×D₅×#509 #14478318

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 608 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, complemented
2	C₂×C₃×D₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#509	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65482	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65436	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65203	C₂	1	2	yes	maximal, complemented
7	C₃×D₅×SD₃₂	C₂	1	2	yes	maximal, complemented
8	C₃×#65200	C₂	1	2	yes	maximal, complemented
9	C₃×D₅×D₁₆	C₂	1	2	yes	maximal, complemented
10	C₃×#65197	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#509	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×D₅×#41	—	2	1	no	—
14	C₂×C₃×D₄×D₅	—	2	1	no	—
15	C₃×C₅×#135	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
17	C₃×#4096	—	2	1	no	—
18	C₂×C₃×#686	—	2	1	no	—
19	C₃×#4065	C₂²	1	1	yes	characteristic, complemented
20	C₃×D₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₃×#4062	—	2	1	no	—
22	C₃×D₅×SD₁₆	—	2	1	no	—
23	C₃×#4058	C₂²	1	1	yes	characteristic, complemented
24	C₃×D₅×D₈	—	2	1	no	—
25	C₃×D₅×D₈	—	2	1	no	—
26	C₃×D₅×D₈	C₂²	1	2	yes	—
27	C₃×D₅×D₈	C₂²	1	2	yes	complemented
28	C₃×D₅×D₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×#4050	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
32	C₃×C₅×SD₃₂	C₂²	1	2	yes	complemented
33	C₃×C₅×D₁₆	C₂²	1	2	yes	complemented
34	C₃×C₅×M₃₂	C₂²	1	1	yes	characteristic, complemented
35	C₃×#3960	C₂²	1	2	yes	complemented
36	C₃×#3959	C₂²	1	2	yes	complemented
37	C₃×#3958	C₂²	1	2	yes	complemented
38	C₃×#3958	C₂²	1	2	yes	complemented
39	C₃×#3944	C₂²	1	1	yes	characteristic, complemented
40	C₃×#3932	C₂²	1	2	yes	complemented
41	C₃×D₈₀	C₂²	1	2	yes	complemented
42	C₃×#3930	C₂²	1	2	yes	complemented
43	C₃×D₅×C₁₆	C₂²	1	2	yes	complemented
44	C₂×C₃×#509	—	5	1	no	maximal, Hall
45	D₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×D₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#509	C₂×C₃	1	1	yes	characteristic, complemented
48	#65482	C₂×C₃	1	1	yes	characteristic, complemented
49	#65436	C₂×C₃	1	1	yes	characteristic, complemented
50	#65203	C₂×C₃	1	2	yes	complemented
51	D₅×SD₃₂	C₂×C₃	1	2	yes	complemented
52	#65200	C₂×C₃	1	2	yes	complemented
53	D₅×D₁₆	C₂×C₃	1	2	yes	complemented
54	#65197	C₂×C₃	1	1	yes	characteristic, complemented
55	D₅×M₃₂	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂³×C₃×D₅	—	4	1	no	—
57	C₃×C₅×#41	—	2	1	no	—
58	C₂×C₃×C₅×D₄	—	2	1	no	—
59	C₂×C₃×C₂²⋊D₅	—	4	1	no	—
60	C₃×#713	—	2	1	no	—
61	C₃×Q₈×D₅	—	2	1	no	—
62	C₃×#711	—	2	1	no	—
63	C₃×#711	—	4	1	no	—
64	C₃×D₄×D₅	—	2	2	no	—
65	C₃×D₄×D₅	—	2	2	no	—
66	C₃×D₄×D₅	—	2	1	no	—
67	C₃×D₄×D₅	—	4	1	no	—
68	C₃×D₄×D₅	—	4	1	no	—
69	C₃×D₄×D₅	—	4	1	no	—
70	C₃×#709	—	2	1	no	—
71	C₃×#709	—	4	1	no	—
72	C₂×C₃×D₂₀	—	2	1	no	—
73	C₂×C₃×C₄×D₅	—	4	1	no	—
74	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
75	C₃×C₅×Q₁₆	C₂³	1	1	yes	characteristic, complemented
76	C₃×C₅×SD₁₆	—	2	1	no	—
77	C₃×C₅×D₈	—	2	1	no	—
78	C₃×C₅×D₈	C₂³	1	2	yes	—
79	C₃×C₅×D₈	C₂³	1	1	yes	characteristic, complemented
80	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
81	C₃×#689	—	2	1	no	—
82	C₃×#688	—	2	1	no	—
83	C₃×#687	—	2	1	no	—
84	C₃×#686	—	2	2	no	—
85	C₃×#686	—	2	2	no	—
86	C₃×#686	—	2	1	no	—
87	C₂×C₃×#168	D₄	1	1	yes	characteristic
88	C₃×Dic₂₀	C₂³	1	1	yes	characteristic, complemented
89	C₃×D₄₀	—	2	1	no	—
90	C₃×D₄₀	C₂³	1	2	yes	—
91	C₃×D₄₀	C₂³	1	1	yes	characteristic, complemented
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	complemented
98	C₃×#672	C₂³	1	2	yes	complemented
99	C₂×C₃×#135	—	5	1	no	—
100	C₂²×C₃×D₈	—	5	1	no	—
101	C₃×#509	—	5	1	no	—
102	C₃×#509	—	5	1	no	—
103	C₃×#509	—	5	2	no	—
104	C₃×#509	—	5	2	no	—
105	C₃×#509	—	5	1	no	—
106	C₃×#509	D₅	1	1	yes	characteristic, direct product factor
107	C₂×C₃×SD₃₂	—	5	2	no	—
108	C₂×C₃×D₁₆	—	5	2	no	—
109	C₂×C₃×M₃₂	—	5	1	no	—
110	D₅×#41	—	2	1	no	—
111	C₂×D₄×D₅	—	2	1	no	—
112	C₅×#135	C₂²×C₃	1	1	yes	characteristic, complemented
113	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
114	#4096	—	2	1	no	—
115	C₂×#686	—	2	1	no	—
116	#4065	C₂²×C₃	1	1	yes	characteristic, complemented
117	D₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
118	#4062	—	2	1	no	—
119	D₅×SD₁₆	—	2	1	no	—
120	#4058	C₂²×C₃	1	1	yes	characteristic, complemented
121	D₅×D₈	—	2	1	no	—
122	D₅×D₈	—	2	1	no	—
123	D₅×D₈	C₂²×C₃	1	2	yes	—
124	D₅×D₈	C₂²×C₃	1	2	yes	complemented
125	D₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
126	#4050	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic, complemented
128	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
129	C₅×SD₃₂	C₂²×C₃	1	2	yes	complemented
130	C₅×D₁₆	C₂²×C₃	1	2	yes	complemented
131	C₅×M₃₂	C₂²×C₃	1	1	yes	characteristic, complemented
132	#3960	C₂²×C₃	1	2	yes	complemented
133	#3959	C₂²×C₃	1	2	yes	complemented
134	#3958	C₂²×C₃	1	2	yes	complemented
135	#3958	C₂²×C₃	1	2	yes	complemented
136	#3944	C₂²×C₃	1	1	yes	characteristic, complemented
137	#3932	C₂²×C₃	1	2	yes	complemented
138	D₈₀	C₂²×C₃	1	2	yes	complemented
139	#3930	C₂²×C₃	1	2	yes	complemented
140	D₅×C₁₆	C₂²×C₃	1	2	yes	complemented
141	C₂×#509	—	5	1	no	Sylow
142	C₂³×C₃×C₅	—	4	1	no	—
143	C₂²×C₃×D₅	—	4	1	no	—
144	C₂²×C₃×D₅	—	4	1	no	—
145	C₂²×C₃×D₅	—	4	2	no	—
146	C₂²×C₃×D₅	—	4	2	no	—
147	C₂²×C₃×D₅	—	8	4	no	—
148	C₂²×C₃×D₅	D₈	1	1	yes	characteristic
149	C₃×C₅×Q₈	—	2	1	no	—
150	C₃×C₅×D₄	—	2	2	no	—
151	C₃×C₅×D₄	—	2	1	no	—
152	C₃×C₅×D₄	—	4	1	no	—
153	C₃×C₅×D₄	—	4	1	no	—
154	C₂×C₃×C₄×C₅	—	4	1	no	—
155	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₃×C₂²⋊D₅	—	4	1	no	—
157	C₃×C₂²⋊D₅	—	4	1	no	—
158	C₃×C₂²⋊D₅	—	4	1	no	—
159	C₃×C₂²⋊D₅	—	4	2	no	—
160	C₃×C₂²⋊D₅	—	4	2	no	—
161	C₂×C₃×Dic₅	—	4	1	no	—
162	C₂×C₃×Dic₅	D₈	1	1	yes	characteristic
163	C₃×D₂₀	—	2	1	no	—
164	C₃×D₂₀	—	2	2	no	—
165	C₃×D₂₀	—	4	1	no	—
166	C₃×D₂₀	—	4	1	no	—
167	C₃×C₄×D₅	—	4	1	no	—
168	C₃×C₄×D₅	—	4	1	no	—
169	C₃×C₄×D₅	—	4	1	no	—
170	C₃×C₄×D₅	D₈	1	1	yes	characteristic
171	C₃×C₄×D₅	D₈	1	1	yes	characteristic
172	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
173	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
174	C₃×Dic₁₀	—	2	1	no	—
175	C₃×Dic₁₀	—	4	1	no	—
176	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
177	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
178	C₃×#168	C₂×D₄	1	1	yes	characteristic
179	C₃×#168	C₂×D₄	1	1	yes	characteristic
180	C₂×C₃×#41	—	10	1	no	—
181	C₂²×C₃×D₄	—	10	1	no	—
182	C₃×#135	—	5	1	no	—
183	C₃×#135	—	5	1	no	—
184	C₃×#135	—	5	1	no	—
185	C₃×#135	—	10	1	no	—
186	C₃×#135	—	10	1	no	—
187	C₃×#135	C₂×D₅	1	1	yes	characteristic, complemented
188	C₂×C₃×Q₁₆	—	5	1	no	—
189	C₂×C₃×SD₁₆	—	10	1	no	—
190	C₂×C₃×D₈	—	5	2	no	—
191	C₂×C₃×D₈	—	5	2	no	—
192	C₂×C₃×D₈	—	5	1	no	—
193	C₂×C₃×D₈	—	5	1	no	—
194	C₂×C₃×D₈	—	10	1	no	—
195	C₂×C₃×D₈	—	10	1	no	—
196	C₂×C₃×D₈	—	10	1	no	—
197	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic, complemented
198	C₂²×C₃×C₈	—	5	1	no	—
199	C₃×SD₃₂	—	5	2	no	—
200	C₃×SD₃₂	—	5	2	no	—
201	C₃×SD₃₂	—	5	2	no	—
202	C₃×SD₃₂	C₂×D₅	1	2	yes	complemented
203	C₃×D₁₆	—	5	2	no	—
204	C₃×D₁₆	—	5	2	no	—
205	C₃×D₁₆	—	5	2	no	—
206	C₃×D₁₆	C₂×D₅	1	2	yes	complemented
207	C₃×M₃₂	—	5	1	no	—
208	C₃×M₃₂	—	5	2	no	—
209	C₃×M₃₂	C₂×D₅	1	1	yes	characteristic, complemented
210	C₂×C₃×C₁₆	—	5	2	no	—
211	C₂³×D₅	—	4	1	no	—
212	C₅×#41	—	2	1	no	—
213	C₂×C₅×D₄	—	2	1	no	—
214	C₂×C₂²⋊D₅	—	4	1	no	—
215	#713	—	2	1	no	—
216	Q₈×D₅	—	2	1	no	—
217	#711	—	2	1	no	—
218	#711	—	4	1	no	—
219	D₄×D₅	—	2	2	no	—
220	D₄×D₅	—	2	2	no	—
221	D₄×D₅	—	2	1	no	—
222	D₄×D₅	—	4	1	no	—
223	D₄×D₅	—	4	1	no	—
224	D₄×D₅	—	4	1	no	—
225	#709	—	2	1	no	—
226	#709	—	4	1	no	—
227	C₂×D₂₀	—	2	1	no	—
228	C₂×C₄×D₅	—	4	1	no	—
229	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
230	C₅×Q₁₆	C₂³×C₃	1	1	yes	characteristic, complemented
231	C₅×SD₁₆	—	2	1	no	—
232	C₅×D₈	—	2	1	no	—
233	C₅×D₈	C₂³×C₃	1	2	yes	—
234	C₅×D₈	C₂³×C₃	1	1	yes	characteristic, complemented
235	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
236	#689	—	2	1	no	—
237	#688	—	2	1	no	—
238	#687	—	2	1	no	—
239	#686	—	2	1	no	—
240	#686	—	2	2	no	—
241	#686	—	2	2	no	—
242	C₂×#168	C₃×D₄	1	1	yes	characteristic
243	Dic₂₀	C₂³×C₃	1	1	yes	characteristic, complemented
244	D₄₀	—	2	1	no	—
245	D₄₀	C₂³×C₃	1	2	yes	—
246	D₄₀	C₂³×C₃	1	1	yes	characteristic, complemented
247	#677	—	2	1	no	—
248	C₈×D₅	C₃×D₄	1	1	yes	characteristic
249	C₈×D₅	C₃×D₄	1	1	yes	characteristic
250	C₈×D₅	C₂³×C₃	1	1	yes	characteristic
251	C₈×D₅	C₂³×C₃	1	1	yes	characteristic
252	C₅×C₁₆	C₂³×C₃	1	2	yes	complemented
253	#672	C₂³×C₃	1	2	yes	complemented
254	C₂×#135	—	5	1	no	—
255	C₂²×D₈	—	5	1	no	—
256	#509	—	5	1	no	—
257	#509	—	5	1	no	—
258	#509	—	5	2	no	—
259	#509	—	5	2	no	—
260	#509	—	5	1	no	—
261	#509	C₃×D₅	1	1	yes	characteristic, direct product factor
262	C₂×SD₃₂	—	5	2	no	—
263	C₂×D₁₆	—	5	2	no	—
264	C₂×M₃₂	—	5	1	no	—
265	C₂²×C₃×C₅	—	4	1	no	—
266	C₂²×C₃×C₅	—	4	2	no	—
267	C₂²×C₃×C₅	—	8	2	no	—
268	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
269	C₂×C₃×D₅	—	2	2	no	—
270	C₂×C₃×D₅	—	4	1	no	—
271	C₂×C₃×D₅	—	4	2	no	—
272	C₂×C₃×D₅	—	8	4	no	—
273	C₂×C₃×D₅	—	8	2	no	—
274	C₂×C₃×D₅	—	8	2	no	—
275	C₂×C₃×D₅	—	8	4	no	—
276	C₂×C₃×D₅	C₂×D₈	1	1	yes	characteristic
277	C₂×C₃×D₅	C₂×D₈	1	1	yes	characteristic
278	C₃×C₄×C₅	—	4	1	no	—
279	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
280	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
281	C₃×Dic₅	—	4	1	no	—
282	C₃×Dic₅	C₂×D₈	1	1	yes	characteristic
283	C₃×Dic₅	C₂×D₈	1	1	yes	characteristic
284	C₂⁴×C₃	—	20	1	no	—
285	C₃×#41	—	2	1	no	—
286	C₃×#41	—	10	1	no	—
287	C₃×#41	—	10	1	no	—
288	C₃×#41	—	10	1	no	—
289	C₃×#41	—	20	1	no	—
290	C₃×#41	—	20	1	no	—
291	C₂×C₃×Q₈	—	10	1	no	—
292	C₂×C₃×D₄	—	2	1	no	—
293	C₂×C₃×D₄	—	10	2	no	—
294	C₂×C₃×D₄	—	10	2	no	—
295	C₂×C₃×D₄	—	10	1	no	—
296	C₂×C₃×D₄	—	10	1	no	—
297	C₂×C₃×D₄	—	20	1	no	—
298	C₂×C₃×D₄	—	20	1	no	—
299	C₂×C₃×D₄	—	20	1	no	—
300	C₂×C₃×D₄	—	20	1	no	—
301	C₂²×C₃×C₄	—	5	1	no	—
302	C₂²×C₃×C₄	—	20	1	no	—
303	C₃×Q₁₆	—	5	1	no	—
304	C₃×Q₁₆	—	10	1	no	—
305	C₃×Q₁₆	C₂²×D₅	1	1	yes	characteristic, complemented
306	C₃×SD₁₆	—	2	1	no	—
307	C₃×SD₁₆	—	10	1	no	—
308	C₃×SD₁₆	—	10	1	no	—
309	C₃×SD₁₆	—	10	1	no	—
310	C₃×D₈	—	2	1	no	—
311	C₃×D₈	—	5	2	no	—
312	C₃×D₈	—	5	1	no	—
313	C₃×D₈	—	10	2	no	—
314	C₃×D₈	—	10	2	no	—
315	C₃×D₈	—	10	1	no	—
316	C₃×D₈	—	10	1	no	—
317	C₃×D₈	C₂²×D₅	1	2	yes	—
318	C₃×D₈	C₂²×D₅	1	1	yes	characteristic, complemented
319	C₂×C₃×C₈	—	5	1	no	—
320	C₂×C₃×C₈	—	5	1	no	—
321	C₂×C₃×C₈	—	5	1	no	—
322	C₂×C₃×C₈	—	5	1	no	—
323	C₂×C₃×C₈	—	5	1	no	—
324	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
325	C₃×C₁₆	—	5	2	no	—
326	C₃×C₁₆	C₂²×D₅	1	2	yes	complemented
327	C₂³×C₅	—	4	1	no	—
328	C₂²×D₅	—	4	1	no	—
329	C₂²×D₅	—	4	1	no	—
330	C₂²×D₅	—	4	2	no	—
331	C₂²×D₅	—	4	2	no	—
332	C₂²×D₅	—	8	4	no	—
333	C₂²×D₅	C₃×D₈	1	1	yes	characteristic
334	C₅×Q₈	—	2	1	no	—
335	C₅×D₄	—	2	2	no	—
336	C₅×D₄	—	2	1	no	—
337	C₅×D₄	—	4	1	no	—
338	C₅×D₄	—	4	1	no	—
339	C₂×C₄×C₅	—	4	1	no	—
340	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
341	C₂²⋊D₅	—	4	1	no	—
342	C₂²⋊D₅	—	4	1	no	—
343	C₂²⋊D₅	—	4	1	no	—
344	C₂²⋊D₅	—	4	2	no	—
345	C₂²⋊D₅	—	4	2	no	—
346	C₂×Dic₅	—	4	1	no	—
347	C₂×Dic₅	C₃×D₈	1	1	yes	characteristic
348	D₂₀	—	2	1	no	—
349	D₂₀	—	2	2	no	—
350	D₂₀	—	4	1	no	—
351	D₂₀	—	4	1	no	—
352	C₄×D₅	—	4	1	no	—
353	C₄×D₅	—	4	1	no	—
354	C₄×D₅	—	4	1	no	—
355	C₄×D₅	C₃×D₈	1	1	yes	characteristic
356	C₄×D₅	C₃×D₈	1	1	yes	characteristic
357	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
358	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
359	Dic₁₀	—	2	1	no	—
360	Dic₁₀	—	4	1	no	—
361	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
362	C₅×C₈	C₂⁴×C₃	1	1	yes	characteristic
363	#168	C₂×C₃×D₄	1	1	yes	characteristic
364	#168	C₂×C₃×D₄	1	1	yes	characteristic
365	C₂×#41	—	10	1	no	—
366	C₂²×D₄	—	10	1	no	—
367	#135	—	5	1	no	—
368	#135	—	5	1	no	—
369	#135	—	5	1	no	—
370	#135	—	10	1	no	—
371	#135	—	10	1	no	—
372	#135	C₂×C₃×D₅	1	1	yes	characteristic, complemented
373	C₂×Q₁₆	—	5	1	no	—
374	C₂×SD₁₆	—	10	1	no	—
375	C₂×D₈	—	5	2	no	—
376	C₂×D₈	—	5	2	no	—
377	C₂×D₈	—	5	1	no	—
378	C₂×D₈	—	5	1	no	—
379	C₂×D₈	—	10	1	no	—
380	C₂×D₈	—	10	1	no	—
381	C₂×D₈	—	10	1	no	—
382	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
383	C₂²×C₈	—	5	1	no	—
384	SD₃₂	—	5	2	no	—
385	SD₃₂	—	5	2	no	—
386	SD₃₂	—	5	2	no	—
387	SD₃₂	C₂×C₃×D₅	1	2	yes	complemented
388	D₁₆	—	5	2	no	—
389	D₁₆	—	5	2	no	—
390	D₁₆	—	5	2	no	—
391	D₁₆	C₂×C₃×D₅	1	2	yes	complemented
392	M₃₂	—	5	1	no	—
393	M₃₂	—	5	2	no	—
394	M₃₂	C₂×C₃×D₅	1	1	yes	characteristic, complemented
395	C₂×C₁₆	—	5	2	no	—
396	C₂×C₃×C₅	—	2	1	no	—
397	C₂×C₃×C₅	—	8	2	no	—
398	C₂×C₃×C₅	—	8	1	no	—
399	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
400	C₃×D₅	—	2	1	no	—
401	C₃×D₅	—	8	1	no	—
402	C₃×D₅	—	8	2	no	—
403	C₃×D₅	#509	1	2	yes	direct product factor
404	C₂³×C₃	—	4	1	no	—
405	C₂³×C₃	—	5	1	no	—
406	C₂³×C₃	—	20	1	no	—
407	C₂³×C₃	—	20	2	no	—
408	C₂³×C₃	—	20	2	no	—
409	C₂³×C₃	—	20	1	no	—
410	C₂³×C₃	—	40	4	no	—
411	C₃×Q₈	—	2	1	no	—
412	C₃×Q₈	—	10	1	no	—
413	C₃×Q₈	—	20	1	no	—
414	C₃×D₄	—	2	2	no	—
415	C₃×D₄	—	2	1	no	—
416	C₃×D₄	—	4	1	no	—
417	C₃×D₄	—	4	1	no	—
418	C₃×D₄	—	10	2	no	—
419	C₃×D₄	—	10	1	no	—
420	C₃×D₄	—	20	1	no	—
421	C₃×D₄	—	20	2	no	—
422	C₃×D₄	—	20	2	no	—
423	C₃×D₄	—	20	1	no	—
424	C₃×D₄	—	20	1	no	—
425	C₃×D₄	—	20	1	no	—
426	C₃×D₄	—	20	1	no	—
427	C₂×C₃×C₄	—	4	1	no	—
428	C₂×C₃×C₄	—	5	1	no	—
429	C₂×C₃×C₄	—	5	1	no	—
430	C₂×C₃×C₄	—	5	1	no	—
431	C₂×C₃×C₄	—	5	1	no	—
432	C₂×C₃×C₄	—	5	1	no	—
433	C₂×C₃×C₄	—	20	1	no	—
434	C₂×C₃×C₄	—	20	1	no	—
435	C₂×C₃×C₄	—	20	1	no	—
436	C₂×C₃×C₄	—	20	1	no	—
437	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
438	C₃×C₈	—	5	1	no	—
439	C₃×C₈	—	5	1	no	—
440	C₃×C₈	D₄×D₅	1	1	yes	characteristic
441	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
442	C₂²×C₅	—	4	1	no	—
443	C₂²×C₅	—	4	2	no	—
444	C₂²×C₅	—	8	2	no	—
445	C₂²×C₅	C₂×C₃×D₈	1	1	yes	characteristic
446	C₂×D₅	—	2	2	no	—
447	C₂×D₅	—	4	1	no	—
448	C₂×D₅	—	4	2	no	—
449	C₂×D₅	—	8	4	no	—
450	C₂×D₅	—	8	2	no	—
451	C₂×D₅	—	8	2	no	—
452	C₂×D₅	—	8	4	no	—
453	C₂×D₅	C₂×C₃×D₈	1	1	yes	characteristic
454	C₂×D₅	C₂×C₃×D₈	1	1	yes	characteristic
455	C₄×C₅	—	4	1	no	—
456	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
457	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
458	Dic₅	—	4	1	no	—
459	Dic₅	C₂×C₃×D₈	1	1	yes	characteristic
460	Dic₅	C₂×C₃×D₈	1	1	yes	characteristic
461	C₂⁴	—	20	1	no	—
462	#41	—	2	1	no	—
463	#41	—	10	1	no	—
464	#41	—	10	1	no	—
465	#41	—	10	1	no	—
466	#41	—	20	1	no	—
467	#41	—	20	1	no	—
468	C₂×Q₈	—	10	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	10	2	no	—
471	C₂×D₄	—	10	2	no	—
472	C₂×D₄	—	10	1	no	—
473	C₂×D₄	—	10	1	no	—
474	C₂×D₄	—	20	1	no	—
475	C₂×D₄	—	20	1	no	—
476	C₂×D₄	—	20	1	no	—
477	C₂×D₄	—	20	1	no	—
478	C₂²×C₄	—	5	1	no	—
479	C₂²×C₄	—	20	1	no	—
480	Q₁₆	—	5	1	no	—
481	Q₁₆	—	10	1	no	—
482	Q₁₆	C₂²×C₃×D₅	1	1	yes	characteristic, complemented
483	SD₁₆	—	2	1	no	—
484	SD₁₆	—	10	1	no	—
485	SD₁₆	—	10	1	no	—
486	SD₁₆	—	10	1	no	—
487	D₈	—	2	1	no	—
488	D₈	—	5	1	no	—
489	D₈	—	5	2	no	—
490	D₈	—	10	2	no	—
491	D₈	—	10	2	no	—
492	D₈	—	10	1	no	—
493	D₈	—	10	1	no	—
494	D₈	C₂²×C₃×D₅	1	2	yes	—
495	D₈	C₂²×C₃×D₅	1	1	yes	characteristic, complemented
496	C₂×C₈	—	5	1	no	—
497	C₂×C₈	—	5	1	no	—
498	C₂×C₈	—	5	1	no	—
499	C₂×C₈	—	5	1	no	—
500	C₂×C₈	—	5	1	no	—
501	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
502	C₁₆	—	5	2	no	—
503	C₁₆	C₂²×C₃×D₅	1	2	yes	complemented
504	C₃×C₅	C₂×#509	1	1	yes	characteristic, complemented, Hall
505	C₂²×C₃	—	4	1	no	—
506	C₂²×C₃	—	4	2	no	—
507	C₂²×C₃	—	5	1	no	—
508	C₂²×C₃	—	5	1	no	—
509	C₂²×C₃	—	8	2	no	—
510	C₂²×C₃	—	10	2	no	—
511	C₂²×C₃	—	20	1	no	—
512	C₂²×C₃	—	20	2	no	—
513	C₂²×C₃	—	40	2	no	—
514	C₂²×C₃	—	40	2	no	—
515	C₂²×C₃	—	40	4	no	—
516	C₂²×C₃	—	40	4	no	—
517	C₂²×C₃	D₅×D₈	1	1	yes	characteristic
518	C₃×C₄	—	4	1	no	—
519	C₃×C₄	—	5	1	no	—
520	C₃×C₄	—	5	1	no	—
521	C₃×C₄	—	20	1	no	—
522	C₃×C₄	D₅×D₈	1	1	yes	characteristic
523	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
524	C₂×C₅	—	2	1	no	—
525	C₂×C₅	—	8	2	no	—
526	C₂×C₅	—	8	1	no	—
527	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
528	D₅	—	2	1	no	—
529	D₅	—	8	2	no	—
530	D₅	—	8	1	no	—
531	D₅	C₃×#509	1	2	yes	direct product factor
532	C₂³	—	4	1	no	—
533	C₂³	—	5	1	no	—
534	C₂³	—	20	1	no	—
535	C₂³	—	20	2	no	—
536	C₂³	—	20	2	no	—
537	C₂³	—	20	1	no	—
538	C₂³	—	40	4	no	—
539	Q₈	—	2	1	no	—
540	Q₈	—	10	1	no	—
541	Q₈	—	20	1	no	—
542	D₄	—	2	2	no	—
543	D₄	—	2	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	10	2	no	—
547	D₄	—	10	1	no	—
548	D₄	—	20	1	no	—
549	D₄	—	20	2	no	—
550	D₄	—	20	2	no	—
551	D₄	—	20	1	no	—
552	D₄	—	20	1	no	—
553	D₄	—	20	1	no	—
554	D₄	—	20	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	5	1	no	—
557	C₂×C₄	—	5	1	no	—
558	C₂×C₄	—	5	1	no	—
559	C₂×C₄	—	5	1	no	—
560	C₂×C₄	—	5	1	no	—
561	C₂×C₄	—	20	1	no	—
562	C₂×C₄	—	20	1	no	—
563	C₂×C₄	—	20	1	no	—
564	C₂×C₄	—	20	1	no	—
565	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
566	C₈	—	5	1	no	—
567	C₈	—	5	1	no	—
568	C₈	C₃×D₄×D₅	1	1	yes	characteristic
569	C₈	C₂³×C₃×D₅	1	1	yes	characteristic
570	C₂×C₃	—	2	1	no	—
571	C₂×C₃	—	5	2	no	—
572	C₂×C₃	—	8	2	no	—
573	C₂×C₃	—	8	1	no	—
574	C₂×C₃	—	10	1	no	—
575	C₂×C₃	—	40	2	no	—
576	C₂×C₃	—	40	1	no	—
577	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
578	C₅	C₂×C₃×#509	1	1	yes	characteristic, complemented, Sylow
579	C₂²	—	4	1	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	5	1	no	—
582	C₂²	—	5	1	no	—
583	C₂²	—	8	2	no	—
584	C₂²	—	10	2	no	—
585	C₂²	—	20	1	no	—
586	C₂²	—	20	2	no	—
587	C₂²	—	40	2	no	—
588	C₂²	—	40	4	no	—
589	C₂²	—	40	2	no	—
590	C₂²	—	40	4	no	—
591	C₂²	C₃×D₅×D₈	1	1	yes	characteristic
592	C₄	—	4	1	no	—
593	C₄	—	5	1	no	—
594	C₄	—	5	1	no	—
595	C₄	—	20	1	no	—
596	C₄	C₃×D₅×D₈	1	1	yes	characteristic
597	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
598	C₃	D₅×#509	1	1	yes	characteristic, direct product factor, Sylow
599	C₂	—	2	1	no	—
600	C₂	—	5	2	no	—
601	C₂	—	8	2	no	—
602	C₂	—	8	1	no	—
603	C₂	—	10	1	no	—
604	C₂	—	40	2	no	—
605	C₂	—	40	1	no	—
606	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×#509	C₂
socle	C₂×C₃×C₅	C₂²×D₈
hypercenter	C₃×#509	D₅
hypocenter	C₅	C₂×C₃×#509
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₃×#509

Complements

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

N	H ≅ G/N	type
1. C₃×D₅×#135	C₂	semidirect
2. C₂×C₃×D₅×D₈	C₂	semidirect
3. C₃×C₅×#509	C₂	semidirect
4. C₃×#65482	C₂	semidirect
5. C₃×#65436	C₂	semidirect
6. C₃×#65203	C₂	semidirect
7. C₃×D₅×SD₃₂	C₂	semidirect
8. C₃×#65200	C₂	semidirect
9. C₃×D₅×D₁₆	C₂	semidirect
10. C₃×#65197	C₂	semidirect
11. C₃×D₅×M₃₂	C₂	semidirect
12. D₅×#509	C₃	direct (N × H)
15. C₃×C₅×#135	C₂²	semidirect
16. C₂×C₃×C₅×D₈	C₂²	semidirect
19. C₃×#4065	C₂²	semidirect
20. C₃×D₅×Q₁₆	C₂²	semidirect
23. C₃×#4058	C₂²	semidirect
27. C₃×D₅×D₈	C₂²	semidirect
28. C₃×D₅×D₈	C₂²	semidirect
29. C₃×#4050	C₂²	semidirect
30. C₂×C₃×D₄₀	C₂²	semidirect
32. C₃×C₅×SD₃₂	C₂²	semidirect
33. C₃×C₅×D₁₆	C₂²	semidirect
34. C₃×C₅×M₃₂	C₂²	semidirect
35. C₃×#3960	C₂²	semidirect
36. C₃×#3959	C₂²	semidirect
37. C₃×#3958	C₂²	semidirect
38. C₃×#3958	C₂²	semidirect
39. C₃×#3944	C₂²	semidirect
40. C₃×#3932	C₂²	semidirect
41. C₃×D₈₀	C₂²	semidirect
42. C₃×#3930	C₂²	semidirect
43. C₃×D₅×C₁₆	C₂²	semidirect
45. D₅×#135	C₂×C₃	semidirect
46. C₂×D₅×D₈	C₂×C₃	semidirect
47. C₅×#509	C₂×C₃	semidirect
48. #65482	C₂×C₃	semidirect
49. #65436	C₂×C₃	semidirect
50. #65203	C₂×C₃	semidirect
51. D₅×SD₃₂	C₂×C₃	semidirect
52. #65200	C₂×C₃	semidirect
53. D₅×D₁₆	C₂×C₃	semidirect
54. #65197	C₂×C₃	semidirect
55. D₅×M₃₂	C₂×C₃	semidirect
75. C₃×C₅×Q₁₆	C₂³	semidirect
79. C₃×C₅×D₈	C₂³	semidirect
88. C₃×Dic₂₀	C₂³	semidirect
91. C₃×D₄₀	C₂³	semidirect
97. C₃×C₅×C₁₆	C₂³	semidirect
98. C₃×#672	C₂³	semidirect
106. C₃×#509	D₅	direct (N × H)
112. C₅×#135	C₂²×C₃	semidirect
113. C₂×C₅×D₈	C₂²×C₃	semidirect
116. #4065	C₂²×C₃	semidirect
117. D₅×Q₁₆	C₂²×C₃	semidirect
120. #4058	C₂²×C₃	semidirect
124. D₅×D₈	C₂²×C₃	semidirect
125. D₅×D₈	C₂²×C₃	semidirect
126. #4050	C₂²×C₃	semidirect
127. C₂×D₄₀	C₂²×C₃	semidirect
129. C₅×SD₃₂	C₂²×C₃	semidirect
130. C₅×D₁₆	C₂²×C₃	semidirect
131. C₅×M₃₂	C₂²×C₃	semidirect
132. #3960	C₂²×C₃	semidirect
133. #3959	C₂²×C₃	semidirect
134. #3958	C₂²×C₃	semidirect
135. #3958	C₂²×C₃	semidirect
136. #3944	C₂²×C₃	semidirect
137. #3932	C₂²×C₃	semidirect
138. D₈₀	C₂²×C₃	semidirect
139. #3930	C₂²×C₃	semidirect
140. D₅×C₁₆	C₂²×C₃	semidirect
187. C₃×#135	C₂×D₅	semidirect
197. C₂×C₃×D₈	C₂×D₅	semidirect
202. C₃×SD₃₂	C₂×D₅	semidirect
206. C₃×D₁₆	C₂×D₅	semidirect
209. C₃×M₃₂	C₂×D₅	semidirect
230. C₅×Q₁₆	C₂³×C₃	semidirect
234. C₅×D₈	C₂³×C₃	semidirect
243. Dic₂₀	C₂³×C₃	semidirect
246. D₄₀	C₂³×C₃	semidirect
252. C₅×C₁₆	C₂³×C₃	semidirect
253. #672	C₂³×C₃	semidirect
261. #509	C₃×D₅	direct (N × H)
305. C₃×Q₁₆	C₂²×D₅	semidirect
318. C₃×D₈	C₂²×D₅	semidirect
326. C₃×C₁₆	C₂²×D₅	semidirect
372. #135	C₂×C₃×D₅	semidirect
382. C₂×D₈	C₂×C₃×D₅	semidirect
387. SD₃₂	C₂×C₃×D₅	semidirect
391. D₁₆	C₂×C₃×D₅	semidirect
394. M₃₂	C₂×C₃×D₅	semidirect
403. C₃×D₅	#509	direct (N × H)
482. Q₁₆	C₂²×C₃×D₅	semidirect
495. D₈	C₂²×C₃×D₅	semidirect
503. C₁₆	C₂²×C₃×D₅	semidirect
504. C₃×C₅	C₂×#509	semidirect
531. D₅	C₃×#509	direct (N × H)
578. C₅	C₂×C₃×#509	semidirect
598. C₃	D₅×#509	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×D₈	2
C₃×C₅×#509	2
C₃×#65482	2
C₃×#65436	2
C₃×#65203	2
C₃×D₅×SD₃₂	2
C₃×#65200	2
C₃×D₅×D₁₆	2
C₃×#65197	2
C₃×D₅×M₃₂	2
D₅×#509	3
C₂×C₃×#509	5

Subgroups — C3×D5×#509 #14478318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#509 #14478318