Subgroups — C₃×D₅×#495 #14438824

Order 1920.

1184 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₅×SD₁₆	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×D₅×D₈	C₂	1	1	yes	maximal, characteristic
4	C₃×D₅×#124	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65480	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65457	C₂	1	2	yes	maximal, complemented
8	C₃×#65444	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65348	C₂	1	2	yes	maximal, complemented
10	C₃×#64985	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#495	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
14	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
15	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
17	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×#124	C₂²	1	2	yes	complemented
19	C₃×#4093	C₂²	1	2	yes	complemented
20	C₂×C₃×#689	C₂²	1	2	yes	complemented
21	C₂×C₃×#688	C₂²	1	2	yes	complemented
22	C₃×#4082	C₂²	1	2	yes	complemented
23	C₂×C₃×#687	C₂²	1	2	yes	complemented
24	C₂×C₃×#686	C₂²	1	2	yes	—
25	C₃×D₅×Q₁₆	—	2	4	no	—
26	C₃×D₅×SD₁₆	—	2	8	no	—
27	C₃×D₅×D₈	—	2	4	no	—
28	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
30	C₂×C₃×#677	C₂²	1	2	yes	complemented
31	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
33	C₃×#4031	—	2	4	no	—
34	C₃×D₅×C₂²⋊C₄	—	2	4	no	—
35	C₃×#4021	C₂²	1	2	yes	complemented
36	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
37	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₄×#168	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃×#495	—	5	1	no	maximal, Hall
42	C₂×D₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×D₅×SD₁₆	C₂×C₃	1	2	yes	complemented
44	C₂×D₅×D₈	C₂×C₃	1	1	yes	characteristic
45	D₅×#124	C₂×C₃	1	2	yes	complemented
46	C₅×#495	C₂×C₃	1	1	yes	characteristic, complemented
47	#65480	C₂×C₃	1	1	yes	characteristic, complemented
48	#65457	C₂×C₃	1	2	yes	complemented
49	#65444	C₂×C₃	1	1	yes	characteristic, complemented
50	#65348	C₂×C₃	1	2	yes	complemented
51	#64985	C₂×C₃	1	1	yes	characteristic, complemented
52	C₄×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂³×C₃×D₅	—	2	2	no	—
54	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
55	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
56	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
57	C₃×Q₈×D₅	—	2	4	no	—
58	C₃×Q₈×D₅	—	2	4	no	—
59	C₃×D₄×D₅	—	2	4	no	—
60	C₃×D₄×D₅	—	2	4	no	—
61	C₂×C₃×D₂₀	C₂³	1	2	yes	—
62	C₂×C₃×C₄×D₅	—	2	2	no	—
63	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
64	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
65	C₂×C₃×Dic₁₀	—	2	2	no	—
66	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
67	C₃×C₅×Q₁₆	—	2	2	no	—
68	C₃×C₅×SD₁₆	—	2	4	no	—
69	C₃×C₅×D₈	—	2	2	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₃×C₂²⋊Dic₅	—	2	4	no	—
75	C₃×#689	—	2	4	no	—
76	C₃×#688	—	2	4	no	—
77	C₃×#687	—	2	4	no	—
78	C₃×#686	—	2	4	no	—
79	C₃×#685	—	2	4	no	—
80	C₃×#685	—	2	4	no	—
81	C₃×C₄×Dic₅	D₄	1	2	yes	—
82	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
83	C₂×C₃×#168	C₂³	1	1	yes	characteristic
84	C₂×C₃×#168	C₂³	1	1	yes	characteristic
85	C₃×Dic₂₀	—	2	2	no	—
86	C₃×D₄₀	—	2	2	no	—
87	C₃×#677	—	2	4	no	—
88	C₃×C₈×D₅	D₄	1	4	yes	—
89	C₃×C₈×D₅	D₄	1	4	yes	—
90	C₂²×C₃×Q₁₆	—	5	1	no	—
91	C₂²×C₃×SD₁₆	—	5	2	no	—
92	C₂²×C₃×D₈	—	5	1	no	—
93	C₂×C₃×#124	—	5	2	no	—
94	C₃×#495	—	5	1	no	—
95	C₃×#495	—	5	2	no	—
96	C₃×#495	—	5	1	no	—
97	C₃×#495	—	5	2	no	—
98	C₃×#495	—	5	1	no	—
99	C₃×#495	D₅	1	1	yes	characteristic, direct product factor
100	C₂×C₃×C₄×C₈	—	5	1	no	—
101	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
102	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
103	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
104	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
105	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
106	C₅×#124	C₂²×C₃	1	2	yes	complemented
107	#4093	C₂²×C₃	1	2	yes	complemented
108	C₂×#689	C₂²×C₃	1	2	yes	complemented
109	C₂×#688	C₂²×C₃	1	2	yes	complemented
110	#4082	C₂²×C₃	1	2	yes	complemented
111	C₂×#687	C₂²×C₃	1	2	yes	complemented
112	C₂×#686	C₂²×C₃	1	2	yes	—
113	D₅×Q₁₆	—	2	4	no	—
114	D₅×SD₁₆	—	2	8	no	—
115	D₅×D₈	—	2	4	no	—
116	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
117	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
118	C₂×#677	C₂²×C₃	1	2	yes	complemented
119	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
121	#4031	—	2	4	no	—
122	D₅×C₂²⋊C₄	—	2	4	no	—
123	#4021	C₂²×C₃	1	2	yes	complemented
124	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
125	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
126	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
128	C₄×#168	C₂²×C₃	1	1	yes	characteristic, complemented
129	C₂×#495	—	5	1	no	Sylow
130	C₂³×C₃×C₅	—	2	2	no	—
131	C₂²×C₃×D₅	—	2	2	no	—
132	C₂²×C₃×D₅	—	4	4	no	—
133	C₂²×C₃×D₅	—	4	8	no	—
134	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
135	C₃×C₅×Q₈	—	2	2	no	—
136	C₃×C₅×Q₈	—	2	2	no	—
137	C₃×C₅×D₄	—	2	2	no	—
138	C₃×C₅×D₄	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
141	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
142	C₃×C₂²⋊D₅	—	4	4	no	—
143	C₂×C₃×Dic₅	—	2	2	no	—
144	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
145	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
146	C₃×D₂₀	—	2	2	no	—
147	C₃×D₂₀	—	2	2	no	—
148	C₃×C₄×D₅	—	2	4	no	—
149	C₃×C₄×D₅	—	4	4	no	—
150	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
151	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
152	C₃×Dic₁₀	—	2	2	no	—
153	C₃×Dic₁₀	—	2	2	no	—
154	C₃×Dic₁₀	—	4	4	no	—
155	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
156	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
157	C₃×#168	C₂×D₄	1	2	yes	—
158	C₃×#168	C₂×D₄	1	2	yes	—
159	C₂²×C₃×Q₈	—	5	2	no	—
160	C₂²×C₃×D₄	—	5	2	no	—
161	C₂×C₃×Q₁₆	—	5	2	no	—
162	C₂×C₃×Q₁₆	—	5	1	no	—
163	C₂×C₃×Q₁₆	—	10	4	no	—
164	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic, complemented
165	C₂×C₃×SD₁₆	—	5	2	no	—
166	C₂×C₃×SD₁₆	—	5	2	no	—
167	C₂×C₃×SD₁₆	—	5	2	no	—
168	C₂×C₃×SD₁₆	—	10	8	no	—
169	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	complemented
170	C₂×C₃×D₈	—	5	2	no	—
171	C₂×C₃×D₈	—	5	1	no	—
172	C₂×C₃×D₈	—	10	4	no	—
173	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
174	C₂²×C₃×C₈	—	5	1	no	—
175	C₂²×C₃×C₈	—	5	1	no	—
176	C₃×#124	—	5	2	no	—
177	C₃×#124	—	5	2	no	—
178	C₃×#124	—	5	2	no	—
179	C₃×#124	—	10	4	no	—
180	C₃×#124	C₂×D₅	1	2	yes	complemented
181	C₂×C₃×C₂²⋊C₄	—	10	4	no	—
182	C₂×C₃×C₄²	—	5	1	no	—
183	C₃×C₄×C₈	—	5	1	no	—
184	C₃×C₄×C₈	—	5	1	no	—
185	C₃×C₄×C₈	—	5	1	no	—
186	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
187	C₂³×D₅	—	2	2	no	—
188	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
189	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
190	C₂×C₂²⋊D₅	—	2	2	no	—
191	Q₈×D₅	—	2	4	no	—
192	Q₈×D₅	—	2	4	no	—
193	D₄×D₅	—	2	4	no	—
194	D₄×D₅	—	2	4	no	—
195	C₂×D₂₀	C₂³×C₃	1	2	yes	—
196	C₂×C₄×D₅	—	2	2	no	—
197	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
198	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
199	C₂×Dic₁₀	—	2	2	no	—
200	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
201	C₅×Q₁₆	—	2	2	no	—
202	C₅×SD₁₆	—	2	4	no	—
203	C₅×D₈	—	2	2	no	—
204	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
205	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
206	C₅×C₂²⋊C₄	—	2	4	no	—
207	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
208	C₂²⋊Dic₅	—	2	4	no	—
209	#689	—	2	4	no	—
210	#688	—	2	4	no	—
211	#687	—	2	4	no	—
212	#686	—	2	4	no	—
213	#685	—	2	4	no	—
214	#685	—	2	4	no	—
215	C₄×Dic₅	C₃×D₄	1	2	yes	—
216	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
217	C₂×#168	C₂³×C₃	1	1	yes	characteristic
218	C₂×#168	C₂³×C₃	1	1	yes	characteristic
219	Dic₂₀	—	2	2	no	—
220	D₄₀	—	2	2	no	—
221	#677	—	2	4	no	—
222	C₈×D₅	C₃×D₄	1	4	yes	—
223	C₈×D₅	C₃×D₄	1	4	yes	—
224	C₂²×Q₁₆	—	5	1	no	—
225	C₂²×SD₁₆	—	5	2	no	—
226	C₂²×D₈	—	5	1	no	—
227	C₂×#124	—	5	2	no	—
228	#495	—	5	1	no	—
229	#495	—	5	2	no	—
230	#495	—	5	1	no	—
231	#495	—	5	2	no	—
232	#495	—	5	1	no	—
233	#495	C₃×D₅	1	1	yes	characteristic, direct product factor
234	C₂×C₄×C₈	—	5	1	no	—
235	C₂²×C₃×C₅	—	4	2	no	—
236	C₂²×C₃×C₅	—	4	4	no	—
237	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₃×D₅	—	4	2	no	—
239	C₂×C₃×D₅	—	4	4	no	—
240	C₂×C₃×D₅	—	8	8	no	—
241	C₂×C₃×D₅	#127	1	2	yes	—
242	C₂×C₃×D₅	#135	1	4	yes	—
243	C₃×C₄×C₅	—	2	2	no	—
244	C₃×C₄×C₅	—	4	2	no	—
245	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
246	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
247	C₃×Dic₅	—	2	2	no	—
248	C₃×Dic₅	—	4	2	no	—
249	C₃×Dic₅	#127	1	2	yes	—
250	C₂⁴×C₃	—	10	2	no	—
251	C₂×C₃×Q₈	—	5	2	no	—
252	C₂×C₃×Q₈	—	10	2	no	—
253	C₂×C₃×Q₈	—	10	4	no	—
254	C₂×C₃×Q₈	—	10	4	no	—
255	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
256	C₂×C₃×D₄	—	5	2	no	—
257	C₂×C₃×D₄	—	10	4	no	—
258	C₂×C₃×D₄	—	10	4	no	—
259	C₂×C₃×D₄	—	10	2	no	—
260	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
261	C₂²×C₃×C₄	—	5	1	no	—
262	C₂²×C₃×C₄	—	5	2	no	—
263	C₂²×C₃×C₄	—	10	2	no	—
264	C₃×Q₁₆	—	2	2	no	—
265	C₃×Q₁₆	—	10	4	no	—
266	C₃×Q₁₆	—	10	2	no	—
267	C₃×SD₁₆	—	2	4	no	—
268	C₃×SD₁₆	—	10	4	no	—
269	C₃×SD₁₆	—	10	4	no	—
270	C₃×SD₁₆	—	10	4	no	—
271	C₃×D₈	—	2	2	no	—
272	C₃×D₈	—	10	4	no	—
273	C₃×D₈	—	10	2	no	—
274	C₂×C₃×C₈	—	5	1	no	—
275	C₂×C₃×C₈	—	5	1	no	—
276	C₂×C₃×C₈	—	5	4	no	—
277	C₂×C₃×C₈	—	5	4	no	—
278	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
279	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
280	C₃×C₂²⋊C₄	—	2	4	no	—
281	C₃×C₂²⋊C₄	—	10	4	no	—
282	C₃×C₂²⋊C₄	—	10	4	no	—
283	C₃×C₂²⋊C₄	—	10	4	no	—
284	C₃×C₄²	—	5	2	no	—
285	C₃×C₄²	—	5	1	no	—
286	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
287	C₂³×C₅	—	2	2	no	—
288	C₂²×D₅	—	2	2	no	—
289	C₂²×D₅	—	4	4	no	—
290	C₂²×D₅	—	4	8	no	—
291	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
292	C₅×Q₈	—	2	2	no	—
293	C₅×Q₈	—	2	2	no	—
294	C₅×D₄	—	2	2	no	—
295	C₅×D₄	—	2	2	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
298	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
299	C₂²⋊D₅	—	4	4	no	—
300	C₂×Dic₅	—	2	2	no	—
301	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
302	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
303	D₂₀	—	2	2	no	—
304	D₂₀	—	2	2	no	—
305	C₄×D₅	—	2	4	no	—
306	C₄×D₅	—	4	4	no	—
307	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
308	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
309	Dic₁₀	—	2	2	no	—
310	Dic₁₀	—	2	2	no	—
311	Dic₁₀	—	4	4	no	—
312	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
313	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
314	#168	C₂×C₃×D₄	1	2	yes	—
315	#168	C₂×C₃×D₄	1	2	yes	—
316	C₂²×Q₈	—	5	2	no	—
317	C₂²×D₄	—	5	2	no	—
318	C₂×Q₁₆	—	5	2	no	—
319	C₂×Q₁₆	—	5	1	no	—
320	C₂×Q₁₆	—	10	4	no	—
321	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
322	C₂×SD₁₆	—	5	2	no	—
323	C₂×SD₁₆	—	5	2	no	—
324	C₂×SD₁₆	—	5	2	no	—
325	C₂×SD₁₆	—	10	8	no	—
326	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	complemented
327	C₂×D₈	—	5	2	no	—
328	C₂×D₈	—	5	1	no	—
329	C₂×D₈	—	10	4	no	—
330	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
331	C₂²×C₈	—	5	1	no	—
332	C₂²×C₈	—	5	1	no	—
333	#124	—	5	2	no	—
334	#124	—	5	2	no	—
335	#124	—	5	2	no	—
336	#124	—	10	4	no	—
337	#124	C₂×C₃×D₅	1	2	yes	complemented
338	C₂×C₂²⋊C₄	—	10	4	no	—
339	C₂×C₄²	—	5	1	no	—
340	C₄×C₈	—	5	1	no	—
341	C₄×C₈	—	5	1	no	—
342	C₄×C₈	—	5	1	no	—
343	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
344	C₂×C₃×C₅	—	8	2	no	—
345	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
346	C₂×C₃×C₅	C₂×#135	1	2	yes	—
347	C₃×D₅	—	8	2	no	—
348	C₃×D₅	#495	1	4	yes	direct product factor
349	C₂³×C₃	—	2	2	no	—
350	C₂³×C₃	—	5	1	no	—
351	C₂³×C₃	—	10	2	no	—
352	C₂³×C₃	—	20	4	no	—
353	C₂³×C₃	—	20	8	no	—
354	C₃×Q₈	—	2	2	no	—
355	C₃×Q₈	—	2	2	no	—
356	C₃×Q₈	—	10	2	no	—
357	C₃×Q₈	—	10	2	no	—
358	C₃×Q₈	—	20	4	no	—
359	C₃×D₄	—	2	2	no	—
360	C₃×D₄	—	2	2	no	—
361	C₃×D₄	—	10	2	no	—
362	C₃×D₄	—	10	2	no	—
363	C₃×D₄	—	20	4	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	5	1	no	—
366	C₂×C₃×C₄	—	5	2	no	—
367	C₂×C₃×C₄	—	5	2	no	—
368	C₂×C₃×C₄	—	5	2	no	—
369	C₂×C₃×C₄	—	10	4	no	—
370	C₂×C₃×C₄	—	10	2	no	—
371	C₂×C₃×C₄	—	20	4	no	—
372	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
373	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
374	C₃×C₈	—	5	2	no	—
375	C₃×C₈	—	5	2	no	—
376	C₃×C₈	D₄×D₅	1	2	yes	—
377	C₃×C₈	D₄×D₅	1	2	yes	—
378	C₂²×C₅	—	4	4	no	—
379	C₂²×C₅	—	4	2	no	—
380	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
381	C₂×D₅	—	4	4	no	—
382	C₂×D₅	—	4	2	no	—
383	C₂×D₅	—	8	8	no	—
384	C₂×D₅	C₃×#127	1	2	yes	—
385	C₂×D₅	C₃×#135	1	4	yes	—
386	C₄×C₅	—	2	2	no	—
387	C₄×C₅	—	4	2	no	—
388	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
389	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
390	Dic₅	—	2	2	no	—
391	Dic₅	—	4	2	no	—
392	Dic₅	C₃×#127	1	2	yes	—
393	C₂⁴	—	10	2	no	—
394	C₂×Q₈	—	5	2	no	—
395	C₂×Q₈	—	10	2	no	—
396	C₂×Q₈	—	10	4	no	—
397	C₂×Q₈	—	10	4	no	—
398	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
399	C₂×D₄	—	5	2	no	—
400	C₂×D₄	—	10	4	no	—
401	C₂×D₄	—	10	4	no	—
402	C₂×D₄	—	10	2	no	—
403	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
404	C₂²×C₄	—	5	1	no	—
405	C₂²×C₄	—	5	2	no	—
406	C₂²×C₄	—	10	2	no	—
407	Q₁₆	—	2	2	no	—
408	Q₁₆	—	10	4	no	—
409	Q₁₆	—	10	2	no	—
410	SD₁₆	—	2	4	no	—
411	SD₁₆	—	10	4	no	—
412	SD₁₆	—	10	4	no	—
413	SD₁₆	—	10	4	no	—
414	D₈	—	2	2	no	—
415	D₈	—	10	4	no	—
416	D₈	—	10	2	no	—
417	C₂×C₈	—	5	1	no	—
418	C₂×C₈	—	5	1	no	—
419	C₂×C₈	—	5	4	no	—
420	C₂×C₈	—	5	4	no	—
421	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
422	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
423	C₂²⋊C₄	—	2	4	no	—
424	C₂²⋊C₄	—	10	4	no	—
425	C₂²⋊C₄	—	10	4	no	—
426	C₂²⋊C₄	—	10	4	no	—
427	C₄²	—	5	2	no	—
428	C₄²	—	5	1	no	—
429	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
430	C₃×C₅	C₂×#495	1	1	yes	characteristic, complemented, Hall
431	C₂²×C₃	—	4	2	no	—
432	C₂²×C₃	—	4	4	no	—
433	C₂²×C₃	—	5	2	no	—
434	C₂²×C₃	—	5	4	no	—
435	C₂²×C₃	—	20	2	no	—
436	C₂²×C₃	—	20	4	no	—
437	C₂²×C₃	—	40	8	no	—
438	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
439	C₃×C₄	—	2	2	no	—
440	C₃×C₄	—	4	2	no	—
441	C₃×C₄	—	5	2	no	—
442	C₃×C₄	—	10	2	no	—
443	C₃×C₄	—	20	2	no	—
444	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
445	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
446	C₂×C₅	—	8	2	no	—
447	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
448	C₂×C₅	C₂×C₃×#135	1	2	yes	—
449	D₅	—	8	2	no	—
450	D₅	C₃×#495	1	4	yes	direct product factor
451	C₂³	—	2	2	no	—
452	C₂³	—	5	1	no	—
453	C₂³	—	10	2	no	—
454	C₂³	—	20	4	no	—
455	C₂³	—	20	8	no	—
456	Q₈	—	2	2	no	—
457	Q₈	—	2	2	no	—
458	Q₈	—	10	2	no	—
459	Q₈	—	10	2	no	—
460	Q₈	—	20	4	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	2	no	—
463	D₄	—	10	2	no	—
464	D₄	—	10	2	no	—
465	D₄	—	20	4	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	5	1	no	—
468	C₂×C₄	—	5	2	no	—
469	C₂×C₄	—	5	2	no	—
470	C₂×C₄	—	5	2	no	—
471	C₂×C₄	—	10	4	no	—
472	C₂×C₄	—	10	2	no	—
473	C₂×C₄	—	20	4	no	—
474	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
475	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
476	C₈	—	5	2	no	—
477	C₈	—	5	2	no	—
478	C₈	C₃×D₄×D₅	1	2	yes	—
479	C₈	C₃×D₄×D₅	1	2	yes	—
480	C₂×C₃	—	5	4	no	—
481	C₂×C₃	—	8	2	no	—
482	C₂×C₃	—	40	2	no	—
483	C₂×C₃	D₅×#127	1	1	yes	characteristic
484	C₂×C₃	D₅×#135	1	2	yes	—
485	C₅	C₂×C₃×#495	1	1	yes	characteristic, complemented, Sylow
486	C₂²	—	4	4	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	5	4	no	—
489	C₂²	—	5	2	no	—
490	C₂²	—	20	4	no	—
491	C₂²	—	20	2	no	—
492	C₂²	—	40	8	no	—
493	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	5	2	no	—
497	C₄	—	10	2	no	—
498	C₄	—	20	2	no	—
499	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
500	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
501	C₃	D₅×#495	1	1	yes	characteristic, direct product factor, Sylow
502	C₂	—	5	4	no	—
503	C₂	—	8	2	no	—
504	C₂	—	40	2	no	—
505	C₂	C₃×D₅×#127	1	1	yes	characteristic
506	C₂	C₃×D₅×#135	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#495	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×D₅×D₈	C₂
hypercenter	C₃×#495	D₅
hypocenter	C₅	C₂×C₃×#495
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#495

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅×Q₁₆	C₂	semidirect
2. C₂×C₃×D₅×SD₁₆	C₂	semidirect
4. C₃×D₅×#124	C₂	semidirect
5. C₃×C₅×#495	C₂	semidirect
6. C₃×#65480	C₂	semidirect
7. C₃×#65457	C₂	semidirect
8. C₃×#65444	C₂	semidirect
9. C₃×#65348	C₂	semidirect
10. C₃×#64985	C₂	semidirect
11. C₃×C₄×C₈×D₅	C₂	semidirect
12. D₅×#495	C₃	direct (N × H)
15. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
16. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
18. C₃×C₅×#124	C₂²	semidirect
19. C₃×#4093	C₂²	semidirect
20. C₂×C₃×#689	C₂²	semidirect
21. C₂×C₃×#688	C₂²	semidirect
22. C₃×#4082	C₂²	semidirect
23. C₂×C₃×#687	C₂²	semidirect
28. C₂×C₃×Dic₂₀	C₂²	semidirect
30. C₂×C₃×#677	C₂²	semidirect
35. C₃×#4021	C₂²	semidirect
37. C₃×C₄×C₅×C₈	C₂²	semidirect
38. C₃×C₈×Dic₅	C₂²	semidirect
39. C₃×C₈×Dic₅	C₂²	semidirect
40. C₃×C₄×#168	C₂²	semidirect
42. C₂×D₅×Q₁₆	C₂×C₃	semidirect
43. C₂×D₅×SD₁₆	C₂×C₃	semidirect
45. D₅×#124	C₂×C₃	semidirect
46. C₅×#495	C₂×C₃	semidirect
47. #65480	C₂×C₃	semidirect
48. #65457	C₂×C₃	semidirect
49. #65444	C₂×C₃	semidirect
50. #65348	C₂×C₃	semidirect
51. #64985	C₂×C₃	semidirect
52. C₄×C₈×D₅	C₂×C₃	semidirect
99. C₃×#495	D₅	direct (N × H)
103. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
104. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
106. C₅×#124	C₂²×C₃	semidirect
107. #4093	C₂²×C₃	semidirect
108. C₂×#689	C₂²×C₃	semidirect
109. C₂×#688	C₂²×C₃	semidirect
110. #4082	C₂²×C₃	semidirect
111. C₂×#687	C₂²×C₃	semidirect
116. C₂×Dic₂₀	C₂²×C₃	semidirect
118. C₂×#677	C₂²×C₃	semidirect
123. #4021	C₂²×C₃	semidirect
125. C₄×C₅×C₈	C₂²×C₃	semidirect
126. C₈×Dic₅	C₂²×C₃	semidirect
127. C₈×Dic₅	C₂²×C₃	semidirect
128. C₄×#168	C₂²×C₃	semidirect
164. C₂×C₃×Q₁₆	C₂×D₅	semidirect
169. C₂×C₃×SD₁₆	C₂×D₅	semidirect
180. C₃×#124	C₂×D₅	semidirect
186. C₃×C₄×C₈	C₂×D₅	semidirect
233. #495	C₃×D₅	direct (N × H)
321. C₂×Q₁₆	C₂×C₃×D₅	semidirect
326. C₂×SD₁₆	C₂×C₃×D₅	semidirect
337. #124	C₂×C₃×D₅	semidirect
343. C₄×C₈	C₂×C₃×D₅	semidirect
348. C₃×D₅	#495	direct (N × H)
430. C₃×C₅	C₂×#495	semidirect
450. D₅	C₃×#495	direct (N × H)
485. C₅	C₂×C₃×#495	semidirect
501. C₃	D₅×#495	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×Q₁₆	2
C₂×C₃×D₅×SD₁₆	2
C₂×C₃×D₅×D₈	2
C₃×D₅×#124	2
C₃×C₅×#495	2
C₃×#65480	2
C₃×#65457	2
C₃×#65444	2
C₃×#65348	2
C₃×#64985	2
C₃×C₄×C₈×D₅	2
D₅×#495	3
C₂×C₃×#495	5

Subgroups — C3×D5×#495 #14438824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#495 #14438824