Subgroups — C₅×D₃×#495 #14438823

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×C₅×D₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₃×SD₁₆	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×D₃×D₈	C₂	1	1	yes	maximal, characteristic
4	C₅×D₃×#124	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5191	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5168	C₂	1	2	yes	maximal, complemented
8	C₅×#5155	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5059	C₂	1	2	yes	maximal, complemented
10	C₅×#4696	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#495	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
14	C₂×C₅×D₃×D₄	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	C₅×#947	C₂²	1	2	yes	complemented
20	C₂×C₅×#216	C₂²	1	2	yes	complemented
21	C₂×C₅×#215	C₂²	1	2	yes	complemented
22	C₅×#936	C₂²	1	2	yes	complemented
23	C₂×C₅×#214	C₂²	1	2	yes	complemented
24	C₂×C₅×#213	C₂²	1	2	yes	—
25	C₅×D₃×Q₁₆	—	2	4	no	—
26	C₅×D₃×SD₁₆	—	2	8	no	—
27	C₅×D₃×D₈	—	2	4	no	—
28	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
30	C₂×C₅×#204	C₂²	1	2	yes	complemented
31	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
32	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
33	C₅×#885	—	2	4	no	—
34	C₅×D₃×C₂²⋊C₄	—	2	4	no	—
35	C₅×#875	C₂²	1	2	yes	complemented
36	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
37	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
38	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
39	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	D₃×#495	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
42	C₂²×C₅×Q₁₆	—	3	1	no	—
43	C₂²×C₅×SD₁₆	—	3	2	no	—
44	C₂²×C₅×D₈	—	3	1	no	—
45	C₂×C₅×#124	—	3	2	no	—
46	C₅×#495	—	3	1	no	—
47	C₅×#495	—	3	1	no	—
48	C₅×#495	—	3	2	no	—
49	C₅×#495	—	3	1	no	—
50	C₅×#495	—	3	2	no	—
51	C₅×#495	D₃	1	1	yes	characteristic, direct product factor
52	C₂×C₄×C₅×C₈	—	3	1	no	—
53	C₂³×C₅×D₃	—	2	2	no	—
54	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
55	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
56	C₂×C₅×#67	—	2	2	no	—
57	C₅×D₃×Q₈	—	2	4	no	—
58	C₅×D₃×Q₈	—	2	4	no	—
59	C₅×D₃×D₄	—	2	4	no	—
60	C₅×D₃×D₄	—	2	4	no	—
61	C₂×C₅×D₁₂	C₂³	1	2	yes	—
62	C₂×C₄×C₅×D₃	—	2	2	no	—
63	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
64	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
65	C₂×C₅×Dic₆	—	2	2	no	—
66	C₂×C₅×Dic₆	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	C₅×#217	—	2	4	no	—
75	C₅×#216	—	2	4	no	—
76	C₅×#215	—	2	4	no	—
77	C₅×#214	—	2	4	no	—
78	C₅×#213	—	2	4	no	—
79	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
80	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
81	C₄×C₅×Dic₃	D₄	1	2	yes	—
82	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
83	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
84	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
85	C₅×Dic₁₂	—	2	2	no	—
86	C₅×D₂₄	—	2	2	no	—
87	C₅×#204	—	2	4	no	—
88	C₅×D₃×C₈	D₄	1	4	yes	—
89	C₅×D₃×C₈	D₄	1	4	yes	—
90	C₂×D₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×D₃×SD₁₆	C₂×C₅	1	2	yes	complemented
92	C₂×D₃×D₈	C₂×C₅	1	1	yes	characteristic
93	D₃×#124	C₂×C₅	1	2	yes	complemented
94	C₃×#495	C₂×C₅	1	1	yes	characteristic, complemented
95	#5191	C₂×C₅	1	1	yes	characteristic, complemented
96	#5168	C₂×C₅	1	2	yes	complemented
97	#5155	C₂×C₅	1	1	yes	characteristic, complemented
98	#5059	C₂×C₅	1	2	yes	complemented
99	#4696	C₂×C₅	1	1	yes	characteristic, complemented
100	C₄×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂²×C₅×Q₈	—	3	2	no	—
102	C₂²×C₅×D₄	—	3	2	no	—
103	C₂×C₅×Q₁₆	—	3	2	no	—
104	C₂×C₅×Q₁₆	—	3	1	no	—
105	C₂×C₅×Q₁₆	—	6	4	no	—
106	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
107	C₂×C₅×SD₁₆	—	3	2	no	—
108	C₂×C₅×SD₁₆	—	3	2	no	—
109	C₂×C₅×SD₁₆	—	3	2	no	—
110	C₂×C₅×SD₁₆	—	6	8	no	—
111	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	complemented
112	C₂×C₅×D₈	—	3	2	no	—
113	C₂×C₅×D₈	—	3	1	no	—
114	C₂×C₅×D₈	—	6	4	no	—
115	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
116	C₂²×C₅×C₈	—	3	1	no	—
117	C₂²×C₅×C₈	—	3	1	no	—
118	C₅×#124	—	3	2	no	—
119	C₅×#124	—	3	2	no	—
120	C₅×#124	—	3	2	no	—
121	C₅×#124	—	6	4	no	—
122	C₅×#124	C₂×D₃	1	2	yes	complemented
123	C₂×C₅×C₂²⋊C₄	—	6	4	no	—
124	C₂×C₄²×C₅	—	3	1	no	—
125	C₄×C₅×C₈	—	3	1	no	—
126	C₄×C₅×C₈	—	3	1	no	—
127	C₄×C₅×C₈	—	3	1	no	—
128	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
129	C₂×#495	—	3	1	no	Sylow
130	C₂³×C₃×C₅	—	2	2	no	—
131	C₂²×C₅×D₃	—	2	2	no	—
132	C₂²×C₅×D₃	—	4	4	no	—
133	C₂²×C₅×D₃	—	4	8	no	—
134	C₂²×C₅×D₃	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	C₅×#67	—	4	4	no	—
143	C₂×C₅×Dic₃	—	2	2	no	—
144	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
145	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
146	C₅×D₁₂	—	2	2	no	—
147	C₅×D₁₂	—	2	2	no	—
148	C₄×C₅×D₃	—	2	4	no	—
149	C₄×C₅×D₃	—	4	4	no	—
150	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
151	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
152	C₅×Dic₆	—	2	2	no	—
153	C₅×Dic₆	—	2	2	no	—
154	C₅×Dic₆	—	4	4	no	—
155	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
156	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
157	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
158	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
159	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
160	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
161	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
162	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
163	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
164	C₃×#124	C₂²×C₅	1	2	yes	complemented
165	#947	C₂²×C₅	1	2	yes	complemented
166	C₂×#216	C₂²×C₅	1	2	yes	complemented
167	C₂×#215	C₂²×C₅	1	2	yes	complemented
168	#936	C₂²×C₅	1	2	yes	complemented
169	C₂×#214	C₂²×C₅	1	2	yes	complemented
170	C₂×#213	C₂²×C₅	1	2	yes	—
171	D₃×Q₁₆	—	2	4	no	—
172	D₃×SD₁₆	—	2	8	no	—
173	D₃×D₈	—	2	4	no	—
174	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
175	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
176	C₂×#204	C₂²×C₅	1	2	yes	complemented
177	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
178	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
179	#885	—	2	4	no	—
180	D₃×C₂²⋊C₄	—	2	4	no	—
181	#875	C₂²×C₅	1	2	yes	complemented
182	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
183	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
184	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
185	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
186	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
187	C₂⁴×C₅	—	6	2	no	—
188	C₂×C₅×Q₈	—	3	2	no	—
189	C₂×C₅×Q₈	—	6	2	no	—
190	C₂×C₅×Q₈	—	6	4	no	—
191	C₂×C₅×Q₈	—	6	4	no	—
192	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
193	C₂×C₅×D₄	—	3	2	no	—
194	C₂×C₅×D₄	—	6	4	no	—
195	C₂×C₅×D₄	—	6	4	no	—
196	C₂×C₅×D₄	—	6	2	no	—
197	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
198	C₂²×C₄×C₅	—	3	1	no	—
199	C₂²×C₄×C₅	—	3	2	no	—
200	C₂²×C₄×C₅	—	6	2	no	—
201	C₅×Q₁₆	—	2	2	no	—
202	C₅×Q₁₆	—	6	4	no	—
203	C₅×Q₁₆	—	6	2	no	—
204	C₅×SD₁₆	—	2	4	no	—
205	C₅×SD₁₆	—	6	4	no	—
206	C₅×SD₁₆	—	6	4	no	—
207	C₅×SD₁₆	—	6	4	no	—
208	C₅×D₈	—	2	2	no	—
209	C₅×D₈	—	6	4	no	—
210	C₅×D₈	—	6	2	no	—
211	C₂×C₅×C₈	—	3	1	no	—
212	C₂×C₅×C₈	—	3	1	no	—
213	C₂×C₅×C₈	—	3	4	no	—
214	C₂×C₅×C₈	—	3	4	no	—
215	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
216	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
217	C₅×C₂²⋊C₄	—	2	4	no	—
218	C₅×C₂²⋊C₄	—	6	4	no	—
219	C₅×C₂²⋊C₄	—	6	4	no	—
220	C₅×C₂²⋊C₄	—	6	4	no	—
221	C₄²×C₅	—	3	2	no	—
222	C₄²×C₅	—	3	1	no	—
223	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
224	C₂²×Q₁₆	—	3	1	no	—
225	C₂²×SD₁₆	—	3	2	no	—
226	C₂²×D₈	—	3	1	no	—
227	C₂×#124	—	3	2	no	—
228	#495	—	3	1	no	—
229	#495	—	3	2	no	—
230	#495	—	3	1	no	—
231	#495	—	3	2	no	—
232	#495	—	3	1	no	—
233	#495	C₅×D₃	1	1	yes	characteristic, direct product factor
234	C₂×C₄×C₈	—	3	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×C₅×D₃	—	4	2	no	—
239	C₂×C₅×D₃	—	4	4	no	—
240	C₂×C₅×D₃	—	8	8	no	—
241	C₂×C₅×D₃	#127	1	2	yes	—
242	C₂×C₅×D₃	#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	C₅×Dic₃	—	2	2	no	—
248	C₅×Dic₃	—	4	2	no	—
249	C₅×Dic₃	#127	1	2	yes	—
250	C₂³×D₃	—	2	2	no	—
251	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
252	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
253	C₂×#67	—	2	2	no	—
254	D₃×Q₈	—	2	4	no	—
255	D₃×Q₈	—	2	4	no	—
256	D₃×D₄	—	2	4	no	—
257	D₃×D₄	—	2	4	no	—
258	C₂×D₁₂	C₂³×C₅	1	2	yes	—
259	C₂×C₄×D₃	—	2	2	no	—
260	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
261	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
262	C₂×Dic₆	—	2	2	no	—
263	C₂×Dic₆	C₂³×C₅	1	2	yes	—
264	C₃×Q₁₆	—	2	2	no	—
265	C₃×SD₁₆	—	2	4	no	—
266	C₃×D₈	—	2	2	no	—
267	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
268	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
269	C₃×C₂²⋊C₄	—	2	4	no	—
270	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
271	#217	—	2	4	no	—
272	#216	—	2	4	no	—
273	#215	—	2	4	no	—
274	#214	—	2	4	no	—
275	#213	—	2	4	no	—
276	(C₂×D₃)⋊C₄	—	2	4	no	—
277	(C₂×D₃)⋊C₄	—	2	4	no	—
278	C₄×Dic₃	C₅×D₄	1	2	yes	—
279	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
280	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
281	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
282	Dic₁₂	—	2	2	no	—
283	D₂₄	—	2	2	no	—
284	#204	—	2	4	no	—
285	D₃×C₈	C₅×D₄	1	4	yes	—
286	D₃×C₈	C₅×D₄	1	4	yes	—
287	C₂³×C₅	—	2	2	no	—
288	C₂³×C₅	—	3	1	no	—
289	C₂³×C₅	—	6	2	no	—
290	C₂³×C₅	—	12	4	no	—
291	C₂³×C₅	—	12	8	no	—
292	C₅×Q₈	—	2	2	no	—
293	C₅×Q₈	—	2	2	no	—
294	C₅×Q₈	—	6	2	no	—
295	C₅×Q₈	—	6	2	no	—
296	C₅×Q₈	—	12	4	no	—
297	C₅×D₄	—	2	2	no	—
298	C₅×D₄	—	2	2	no	—
299	C₅×D₄	—	6	2	no	—
300	C₅×D₄	—	6	2	no	—
301	C₅×D₄	—	12	4	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	3	1	no	—
304	C₂×C₄×C₅	—	3	2	no	—
305	C₂×C₄×C₅	—	3	2	no	—
306	C₂×C₄×C₅	—	3	2	no	—
307	C₂×C₄×C₅	—	6	4	no	—
308	C₂×C₄×C₅	—	6	2	no	—
309	C₂×C₄×C₅	—	12	4	no	—
310	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
311	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
312	C₅×C₈	—	3	2	no	—
313	C₅×C₈	—	3	2	no	—
314	C₅×C₈	D₃×D₄	1	2	yes	—
315	C₅×C₈	D₃×D₄	1	2	yes	—
316	C₂²×Q₈	—	3	2	no	—
317	C₂²×D₄	—	3	2	no	—
318	C₂×Q₁₆	—	3	2	no	—
319	C₂×Q₁₆	—	3	1	no	—
320	C₂×Q₁₆	—	6	4	no	—
321	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
322	C₂×SD₁₆	—	3	2	no	—
323	C₂×SD₁₆	—	3	2	no	—
324	C₂×SD₁₆	—	3	2	no	—
325	C₂×SD₁₆	—	6	8	no	—
326	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	complemented
327	C₂×D₈	—	3	2	no	—
328	C₂×D₈	—	3	1	no	—
329	C₂×D₈	—	6	4	no	—
330	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
331	C₂²×C₈	—	3	1	no	—
332	C₂²×C₈	—	3	1	no	—
333	#124	—	3	2	no	—
334	#124	—	3	2	no	—
335	#124	—	3	2	no	—
336	#124	—	6	4	no	—
337	#124	C₂×C₅×D₃	1	2	yes	complemented
338	C₂×C₂²⋊C₄	—	6	4	no	—
339	C₂×C₄²	—	3	1	no	—
340	C₄×C₈	—	3	1	no	—
341	C₄×C₈	—	3	1	no	—
342	C₄×C₈	—	3	1	no	—
343	C₄×C₈	C₂×C₅×D₃	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	C₅×D₃	—	8	2	no	—
348	C₅×D₃	#495	1	4	yes	direct product factor
349	C₂³×C₃	—	2	2	no	—
350	C₂²×D₃	—	2	2	no	—
351	C₂²×D₃	—	4	4	no	—
352	C₂²×D₃	—	4	8	no	—
353	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
354	C₃×Q₈	—	2	2	no	—
355	C₃×Q₈	—	2	2	no	—
356	C₃×D₄	—	2	2	no	—
357	C₃×D₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	2	no	—
359	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
360	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
361	#67	—	4	4	no	—
362	C₂×Dic₃	—	2	2	no	—
363	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
364	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
365	D₁₂	—	2	2	no	—
366	D₁₂	—	2	2	no	—
367	C₄×D₃	—	2	4	no	—
368	C₄×D₃	—	4	4	no	—
369	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
370	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
371	Dic₆	—	2	2	no	—
372	Dic₆	—	2	2	no	—
373	Dic₆	—	4	4	no	—
374	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
375	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
376	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
377	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
378	C₂²×C₅	—	3	2	no	—
379	C₂²×C₅	—	3	4	no	—
380	C₂²×C₅	—	4	2	no	—
381	C₂²×C₅	—	4	4	no	—
382	C₂²×C₅	—	12	2	no	—
383	C₂²×C₅	—	12	4	no	—
384	C₂²×C₅	—	24	8	no	—
385	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
386	C₄×C₅	—	2	2	no	—
387	C₄×C₅	—	3	2	no	—
388	C₄×C₅	—	4	2	no	—
389	C₄×C₅	—	6	2	no	—
390	C₄×C₅	—	12	2	no	—
391	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
392	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
393	C₂⁴	—	6	2	no	—
394	C₂×Q₈	—	3	2	no	—
395	C₂×Q₈	—	6	2	no	—
396	C₂×Q₈	—	6	4	no	—
397	C₂×Q₈	—	6	4	no	—
398	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
399	C₂×D₄	—	3	2	no	—
400	C₂×D₄	—	6	4	no	—
401	C₂×D₄	—	6	4	no	—
402	C₂×D₄	—	6	2	no	—
403	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
404	C₂²×C₄	—	3	1	no	—
405	C₂²×C₄	—	3	2	no	—
406	C₂²×C₄	—	6	2	no	—
407	Q₁₆	—	2	2	no	—
408	Q₁₆	—	6	4	no	—
409	Q₁₆	—	6	2	no	—
410	SD₁₆	—	2	4	no	—
411	SD₁₆	—	6	4	no	—
412	SD₁₆	—	6	4	no	—
413	SD₁₆	—	6	4	no	—
414	D₈	—	2	2	no	—
415	D₈	—	6	4	no	—
416	D₈	—	6	2	no	—
417	C₂×C₈	—	3	1	no	—
418	C₂×C₈	—	3	1	no	—
419	C₂×C₈	—	3	4	no	—
420	C₂×C₈	—	3	4	no	—
421	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
422	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
423	C₂²⋊C₄	—	2	4	no	—
424	C₂²⋊C₄	—	6	4	no	—
425	C₂²⋊C₄	—	6	4	no	—
426	C₂²⋊C₄	—	6	4	no	—
427	C₄²	—	3	2	no	—
428	C₄²	—	3	1	no	—
429	C₄²	C₂²×C₅×D₃	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	C₂²×C₅×D₄	1	1	yes	characteristic
434	C₂×D₃	—	4	2	no	—
435	C₂×D₃	—	4	4	no	—
436	C₂×D₃	—	8	8	no	—
437	C₂×D₃	C₅×#127	1	2	yes	—
438	C₂×D₃	C₅×#135	1	4	yes	—
439	C₃×C₄	—	2	2	no	—
440	C₃×C₄	—	4	2	no	—
441	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
442	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
443	Dic₃	—	2	2	no	—
444	Dic₃	—	4	2	no	—
445	Dic₃	C₅×#127	1	2	yes	—
446	C₂×C₅	—	3	4	no	—
447	C₂×C₅	—	8	2	no	—
448	C₂×C₅	—	24	2	no	—
449	C₂×C₅	D₃×#127	1	1	yes	characteristic
450	C₂×C₅	D₃×#135	1	2	yes	—
451	C₂³	—	2	2	no	—
452	C₂³	—	3	1	no	—
453	C₂³	—	6	2	no	—
454	C₂³	—	12	4	no	—
455	C₂³	—	12	8	no	—
456	Q₈	—	2	2	no	—
457	Q₈	—	2	2	no	—
458	Q₈	—	6	2	no	—
459	Q₈	—	6	2	no	—
460	Q₈	—	12	4	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	2	no	—
463	D₄	—	6	2	no	—
464	D₄	—	6	2	no	—
465	D₄	—	12	4	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	3	1	no	—
468	C₂×C₄	—	3	2	no	—
469	C₂×C₄	—	3	2	no	—
470	C₂×C₄	—	3	2	no	—
471	C₂×C₄	—	6	4	no	—
472	C₂×C₄	—	6	2	no	—
473	C₂×C₄	—	12	4	no	—
474	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
475	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
476	C₈	—	3	2	no	—
477	C₈	—	3	2	no	—
478	C₈	C₅×D₃×D₄	1	2	yes	—
479	C₈	C₅×D₃×D₄	1	2	yes	—
480	C₂×C₃	—	8	2	no	—
481	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
482	C₂×C₃	C₂×C₅×#135	1	2	yes	—
483	D₃	—	8	2	no	—
484	D₃	C₅×#495	1	4	yes	direct product factor
485	C₅	D₃×#495	1	1	yes	characteristic, direct product factor, Sylow
486	C₂²	—	3	2	no	—
487	C₂²	—	3	4	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	12	2	no	—
491	C₂²	—	12	4	no	—
492	C₂²	—	24	8	no	—
493	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	3	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	6	2	no	—
498	C₄	—	12	2	no	—
499	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
500	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
501	C₃	C₂×C₅×#495	1	1	yes	characteristic, complemented, Sylow
502	C₂	—	3	4	no	—
503	C₂	—	8	2	no	—
504	C₂	—	24	2	no	—
505	C₂	C₅×D₃×#127	1	1	yes	characteristic
506	C₂	C₅×D₃×#135	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#495	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×D₃×D₈	C₂
hypercenter	C₅×#495	D₃
hypocenter	C₃	C₂×C₅×#495
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#495

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×Q₁₆	C₂	semidirect
2. C₂×C₅×D₃×SD₁₆	C₂	semidirect
4. C₅×D₃×#124	C₂	semidirect
5. C₃×C₅×#495	C₂	semidirect
6. C₅×#5191	C₂	semidirect
7. C₅×#5168	C₂	semidirect
8. C₅×#5155	C₂	semidirect
9. C₅×#5059	C₂	semidirect
10. C₅×#4696	C₂	semidirect
11. C₄×C₅×D₃×C₈	C₂	semidirect
15. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
16. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
18. C₃×C₅×#124	C₂²	semidirect
19. C₅×#947	C₂²	semidirect
20. C₂×C₅×#216	C₂²	semidirect
21. C₂×C₅×#215	C₂²	semidirect
22. C₅×#936	C₂²	semidirect
23. C₂×C₅×#214	C₂²	semidirect
28. C₂×C₅×Dic₁₂	C₂²	semidirect
30. C₂×C₅×#204	C₂²	semidirect
35. C₅×#875	C₂²	semidirect
37. C₃×C₄×C₅×C₈	C₂²	semidirect
38. C₅×C₈×Dic₃	C₂²	semidirect
39. C₅×C₈×Dic₃	C₂²	semidirect
40. C₄×C₅×C₃⋊C₈	C₂²	semidirect
41. D₃×#495	C₅	direct (N × H)
51. C₅×#495	D₃	direct (N × H)
90. C₂×D₃×Q₁₆	C₂×C₅	semidirect
91. C₂×D₃×SD₁₆	C₂×C₅	semidirect
93. D₃×#124	C₂×C₅	semidirect
94. C₃×#495	C₂×C₅	semidirect
95. #5191	C₂×C₅	semidirect
96. #5168	C₂×C₅	semidirect
97. #5155	C₂×C₅	semidirect
98. #5059	C₂×C₅	semidirect
99. #4696	C₂×C₅	semidirect
100. C₄×D₃×C₈	C₂×C₅	semidirect
106. C₂×C₅×Q₁₆	C₂×D₃	semidirect
111. C₂×C₅×SD₁₆	C₂×D₃	semidirect
122. C₅×#124	C₂×D₃	semidirect
128. C₄×C₅×C₈	C₂×D₃	semidirect
161. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
162. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
164. C₃×#124	C₂²×C₅	semidirect
165. #947	C₂²×C₅	semidirect
166. C₂×#216	C₂²×C₅	semidirect
167. C₂×#215	C₂²×C₅	semidirect
168. #936	C₂²×C₅	semidirect
169. C₂×#214	C₂²×C₅	semidirect
174. C₂×Dic₁₂	C₂²×C₅	semidirect
176. C₂×#204	C₂²×C₅	semidirect
181. #875	C₂²×C₅	semidirect
183. C₃×C₄×C₈	C₂²×C₅	semidirect
184. C₈×Dic₃	C₂²×C₅	semidirect
185. C₈×Dic₃	C₂²×C₅	semidirect
186. C₄×C₃⋊C₈	C₂²×C₅	semidirect
233. #495	C₅×D₃	direct (N × H)
321. C₂×Q₁₆	C₂×C₅×D₃	semidirect
326. C₂×SD₁₆	C₂×C₅×D₃	semidirect
337. #124	C₂×C₅×D₃	semidirect
343. C₄×C₈	C₂×C₅×D₃	semidirect
348. C₅×D₃	#495	direct (N × H)
430. C₃×C₅	C₂×#495	semidirect
484. D₃	C₅×#495	direct (N × H)
485. C₅	D₃×#495	direct (N × H)
501. C₃	C₂×C₅×#495	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×Q₁₆	2
C₂×C₅×D₃×SD₁₆	2
C₂×C₅×D₃×D₈	2
C₅×D₃×#124	2
C₃×C₅×#495	2
C₅×#5191	2
C₅×#5168	2
C₅×#5155	2
C₅×#5059	2
C₅×#4696	2
C₄×C₅×D₃×C₈	2
C₂×C₅×#495	3
D₃×#495	5

Subgroups — C5×D3×#495 #14438823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#495 #14438823