Subgroups — C₅×#80319 #14471768

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5713	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5543	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#459	C₂	1	1	yes	maximal, characteristic
4	C₅×#5153	C₂	1	2	yes	maximal, complemented
5	C₅×Dic₃×D₈	C₂	1	2	yes	maximal, complemented
6	C₅×#5070	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₅×#214	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4850	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4830	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4768	C₂	1	2	yes	maximal, complemented
11	C₅×#4766	C₂	1	2	yes	maximal, complemented
12	C₅×#3361	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
14	C₃×C₅×#127	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₅×#936	—	2	1	no	—
17	C₅×#936	C₂²	1	2	yes	—
18	C₅×#935	—	2	2	no	—
19	C₅×D₄×Dic₃	—	2	1	no	—
20	C₅×D₄×Dic₃	C₂²	1	2	yes	—
21	C₅×D₄×Dic₃	C₂²	1	2	yes	—
22	C₂×C₅×#214	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
24	C₅×#924	—	2	1	no	—
25	C₅×#890	C₂²	1	2	yes	—
26	C₅×#878	—	2	2	no	—
27	C₅×#869	C₂²	1	1	yes	characteristic
28	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
29	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₃×C₅×#102	C₂²	1	2	yes	—
32	C₅×#832	C₂²	1	1	yes	characteristic
33	C₅×#832	C₂²	1	2	yes	—
34	C₅×#832	C₂²	1	2	yes	—
35	C₅×#818	C₂²	1	2	yes	—
36	C₅×#816	C₂²	1	2	yes	—
37	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
38	C₅×C₈×Dic₃	C₂²	1	2	yes	—
39	C₅×#810	C₂²	1	1	yes	characteristic
40	C₅×#808	C₂²	1	1	yes	characteristic
41	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
42	#80319	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#559	—	3	1	no	—
44	C₅×#554	—	3	1	no	—
45	C₅×#488	—	3	2	no	—
46	C₅×#486	—	3	1	no	—
47	C₅×#478	—	3	2	no	—
48	C₅×#477	—	3	1	no	—
49	C₅×#463	—	3	2	no	—
50	C₅×#459	D₃	1	1	yes	characteristic
51	C₅×C₈×Q₈	—	3	1	no	—
52	C₄×C₅×SD₁₆	—	3	1	no	—
53	C₄×C₅×D₈	—	3	2	no	—
54	C₂×C₃×C₅×D₄	—	2	1	no	—
55	C₂×C₃×C₅×D₄	—	2	1	no	—
56	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
57	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	—	2	1	no	—
59	C₂²×C₅×Dic₃	—	2	2	no	—
60	C₂²×C₅×Dic₃	—	2	2	no	—
61	C₂×C₅×Dic₆	—	2	1	no	—
62	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
63	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
64	C₃×C₅×D₈	—	2	4	no	—
65	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
66	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
68	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₅×#217	—	2	2	no	—
70	C₅×#217	—	2	2	no	—
71	C₅×#217	—	2	2	no	—
72	C₅×#217	—	2	2	no	—
73	C₅×#214	—	2	2	no	—
74	C₅×C₄⋊Dic₃	—	2	1	no	—
75	C₅×C₄⋊Dic₃	—	2	2	no	—
76	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
77	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
78	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
79	C₅×Dic₃⋊C₄	—	2	1	no	—
80	C₅×Dic₃⋊C₄	—	2	2	no	—
81	C₅×Dic₃⋊C₄	D₄	1	2	yes	—
82	C₄×C₅×Dic₃	—	2	1	no	—
83	C₄×C₅×Dic₃	C₂³	1	2	yes	—
84	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
85	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
86	#5713	C₂×C₅	1	1	yes	characteristic, complemented
87	#5543	C₂×C₅	1	1	yes	characteristic, complemented
88	C₃×#459	C₂×C₅	1	1	yes	characteristic
89	#5153	C₂×C₅	1	2	yes	complemented
90	Dic₃×D₈	C₂×C₅	1	2	yes	complemented
91	#5070	C₂×C₅	1	1	yes	characteristic, complemented
92	C₄×#214	C₂×C₅	1	1	yes	characteristic, complemented
93	#4850	C₂×C₅	1	1	yes	characteristic, complemented
94	#4830	C₂×C₅	1	1	yes	characteristic, complemented
95	#4768	C₂×C₅	1	2	yes	complemented
96	#4766	C₂×C₅	1	2	yes	complemented
97	C₂×C₅×SD₁₆	—	3	1	no	—
98	C₂×C₅×D₈	C₂×D₃	1	2	yes	—
99	C₅×C₄⋊Q₈	—	3	1	no	—
100	C₅×#127	C₂×D₃	1	1	yes	characteristic
101	C₅×#125	—	3	2	no	—
102	C₅×#124	—	3	2	no	—
103	C₅×#124	—	6	1	no	—
104	C₅×#123	—	6	2	no	—
105	C₅×C₂²⋊Q₈	—	6	2	no	—
106	C₅×C₂²⋊Q₈	—	6	1	no	—
107	C₄×C₅×Q₈	—	3	1	no	—
108	C₄×C₅×Q₈	—	3	1	no	—
109	C₄×C₅×D₄	—	3	2	no	—
110	C₄×C₅×D₄	—	3	2	no	—
111	C₄×C₅×D₄	—	6	1	no	—
112	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
113	C₂×C₅×C₄⋊C₄	—	6	1	no	—
114	C₅×#107	—	3	2	no	—
115	C₅×#106	—	3	1	no	—
116	C₅×C₄⋊C₈	—	3	2	no	—
117	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
118	C₅×#103	—	3	2	no	—
119	C₅×#103	—	3	1	no	—
120	C₅×#102	—	3	1	no	—
121	C₅×#102	—	3	2	no	—
122	C₅×#102	—	3	2	no	—
123	C₅×#102	C₂×D₃	1	2	yes	—
124	C₄×C₅×C₈	—	3	2	no	—
125	C₄×C₅×C₈	—	3	1	no	—
126	#3361	—	3	1	no	Sylow
127	C₂³×C₃×C₅	—	2	1	no	—
128	C₂³×C₃×C₅	—	2	2	no	—
129	C₃×C₅×D₄	—	2	2	no	—
130	C₃×C₅×D₄	—	2	1	no	—
131	C₃×C₅×D₄	—	2	2	no	—
132	C₃×C₅×D₄	—	4	2	no	—
133	C₃×C₅×D₄	—	8	1	no	—
134	C₃×C₅×D₄	#41	1	2	yes	—
135	C₂×C₃×C₄×C₅	—	2	1	no	—
136	C₂×C₃×C₄×C₅	—	4	2	no	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₂×C₅×Dic₃	—	2	1	no	—
141	C₂×C₅×Dic₃	—	2	1	no	—
142	C₂×C₅×Dic₃	—	2	2	no	—
143	C₂×C₅×Dic₃	—	8	2	no	—
144	C₂×C₅×Dic₃	—	8	2	no	—
145	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
146	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
147	C₅×Dic₆	—	2	2	no	—
148	C₅×Dic₆	—	2	1	no	—
149	C₅×Dic₆	—	2	1	no	—
150	C₅×Dic₆	—	8	1	no	—
151	C₃×C₅×C₈	—	2	2	no	—
152	C₅×C₃⋊C₈	—	2	1	no	—
153	C₅×C₃⋊C₈	—	2	1	no	—
154	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
155	C₃×#127	C₂²×C₅	1	1	yes	characteristic
156	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
157	#936	—	2	1	no	—
158	#936	C₂²×C₅	1	2	yes	—
159	#935	—	2	2	no	—
160	D₄×Dic₃	—	2	1	no	—
161	D₄×Dic₃	C₂²×C₅	1	2	yes	—
162	D₄×Dic₃	C₂²×C₅	1	2	yes	—
163	C₂×#214	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₄⋊Dic₃	—	2	1	no	—
165	#924	—	2	1	no	—
166	#890	C₂²×C₅	1	2	yes	—
167	#878	—	2	2	no	—
168	#869	C₂²×C₅	1	1	yes	characteristic
169	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
170	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
171	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
172	C₃×#102	C₂²×C₅	1	2	yes	—
173	#832	C₂²×C₅	1	1	yes	characteristic
174	#832	C₂²×C₅	1	2	yes	—
175	#832	C₂²×C₅	1	2	yes	—
176	#818	C₂²×C₅	1	2	yes	—
177	#816	C₂²×C₅	1	2	yes	—
178	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
179	C₈×Dic₃	C₂²×C₅	1	2	yes	—
180	#810	C₂²×C₅	1	1	yes	characteristic
181	#808	C₂²×C₅	1	1	yes	characteristic
182	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₅×Q₈	—	3	1	no	—
184	C₂×C₅×Q₈	—	3	1	no	—
185	C₂×C₅×Q₈	—	6	1	no	—
186	C₂×C₅×D₄	—	2	1	no	—
187	C₂×C₅×D₄	—	2	1	no	—
188	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
189	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	6	2	no	—
192	C₂²×C₄×C₅	—	6	2	no	—
193	C₅×SD₁₆	—	6	2	no	—
194	C₅×D₈	—	2	4	no	—
195	C₂×C₅×C₈	—	3	1	no	—
196	C₂×C₅×C₈	—	3	1	no	—
197	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
198	C₅×C₄⋊C₄	—	3	1	no	—
199	C₅×C₄⋊C₄	—	3	2	no	—
200	C₅×C₄⋊C₄	—	3	1	no	—
201	C₅×C₄⋊C₄	—	3	2	no	—
202	C₅×C₄⋊C₄	—	6	2	no	—
203	C₅×C₄⋊C₄	—	6	2	no	—
204	C₅×C₄⋊C₄	—	6	1	no	—
205	C₅×C₄⋊C₄	—	6	1	no	—
206	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
207	C₅×C₂²⋊C₄	—	2	1	no	—
208	C₅×C₂²⋊C₄	—	6	2	no	—
209	C₅×C₂²⋊C₄	—	6	2	no	—
210	C₅×C₂²⋊C₄	—	6	2	no	—
211	C₅×C₂²⋊C₄	—	6	2	no	—
212	C₄²×C₅	—	3	2	no	—
213	C₄²×C₅	—	6	1	no	—
214	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
215	#559	—	3	1	no	—
216	#554	—	3	1	no	—
217	#488	—	3	2	no	—
218	#486	—	3	1	no	—
219	#478	—	3	2	no	—
220	#477	—	3	1	no	—
221	#463	—	3	2	no	—
222	#459	C₅×D₃	1	1	yes	characteristic
223	C₈×Q₈	—	3	1	no	—
224	C₄×SD₁₆	—	3	1	no	—
225	C₄×D₈	—	3	2	no	—
226	C₂²×C₃×C₅	—	2	2	no	—
227	C₂²×C₃×C₅	—	4	1	no	—
228	C₂²×C₃×C₅	—	4	1	no	—
229	C₂²×C₃×C₅	—	4	2	no	—
230	C₂²×C₃×C₅	—	4	2	no	—
231	C₂²×C₃×C₅	—	4	2	no	—
232	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
233	C₃×C₄×C₅	—	2	1	no	—
234	C₃×C₄×C₅	—	4	1	no	—
235	C₃×C₄×C₅	#135	1	2	yes	—
236	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
237	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
238	C₅×Dic₃	—	2	2	no	—
239	C₅×Dic₃	—	2	2	no	—
240	C₅×Dic₃	—	4	1	no	—
241	C₅×Dic₃	—	4	2	no	—
242	C₅×Dic₃	—	4	1	no	—
243	C₂×C₃×D₄	—	2	1	no	—
244	C₂×C₃×D₄	—	2	1	no	—
245	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
246	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
247	C₂²×C₃×C₄	—	2	1	no	—
248	C₂²×Dic₃	—	2	2	no	—
249	C₂²×Dic₃	—	2	2	no	—
250	C₂×Dic₆	—	2	1	no	—
251	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
252	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
253	C₃×D₈	—	2	4	no	—
254	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
255	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
256	C₃×C₂²⋊C₄	—	2	1	no	—
257	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
258	#217	—	2	2	no	—
259	#217	—	2	2	no	—
260	#217	—	2	2	no	—
261	#217	—	2	2	no	—
262	#214	—	2	2	no	—
263	C₄⋊Dic₃	—	2	1	no	—
264	C₄⋊Dic₃	—	2	2	no	—
265	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
266	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
267	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
268	Dic₃⋊C₄	—	2	1	no	—
269	Dic₃⋊C₄	—	2	2	no	—
270	Dic₃⋊C₄	C₅×D₄	1	2	yes	—
271	C₄×Dic₃	—	2	1	no	—
272	C₄×Dic₃	C₂³×C₅	1	2	yes	—
273	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
274	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
275	C₂³×C₅	—	2	1	no	—
276	C₂³×C₅	—	2	2	no	—
277	C₅×Q₈	—	6	2	no	—
278	C₅×Q₈	—	6	1	no	—
279	C₅×Q₈	—	6	1	no	—
280	C₅×Q₈	—	24	1	no	—
281	C₅×D₄	—	2	2	no	—
282	C₅×D₄	—	2	1	no	—
283	C₅×D₄	—	2	2	no	—
284	C₅×D₄	—	4	2	no	—
285	C₅×D₄	—	8	1	no	—
286	C₅×D₄	#237	1	2	yes	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	3	2	no	—
289	C₂×C₄×C₅	—	3	2	no	—
290	C₂×C₄×C₅	—	4	2	no	—
291	C₂×C₄×C₅	—	6	1	no	—
292	C₂×C₄×C₅	—	6	1	no	—
293	C₂×C₄×C₅	—	6	2	no	—
294	C₂×C₄×C₅	—	24	2	no	—
295	C₂×C₄×C₅	—	24	2	no	—
296	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
297	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
298	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
299	C₅×C₈	—	2	2	no	—
300	C₅×C₈	—	6	1	no	—
301	C₅×C₈	—	6	1	no	—
302	C₂×SD₁₆	—	3	1	no	—
303	C₂×D₈	C₂×C₅×D₃	1	2	yes	—
304	C₄⋊Q₈	—	3	1	no	—
305	#127	C₂×C₅×D₃	1	1	yes	characteristic
306	#125	—	3	2	no	—
307	#124	—	3	2	no	—
308	#124	—	6	1	no	—
309	#123	—	6	2	no	—
310	C₂²⋊Q₈	—	6	2	no	—
311	C₂²⋊Q₈	—	6	1	no	—
312	C₄×Q₈	—	3	1	no	—
313	C₄×Q₈	—	3	1	no	—
314	C₄×D₄	—	3	2	no	—
315	C₄×D₄	—	3	2	no	—
316	C₄×D₄	—	6	1	no	—
317	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
318	C₂×C₄⋊C₄	—	6	1	no	—
319	#107	—	3	2	no	—
320	#106	—	3	1	no	—
321	C₄⋊C₈	—	3	2	no	—
322	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
323	#103	—	3	2	no	—
324	#103	—	3	1	no	—
325	#102	—	3	1	no	—
326	#102	—	3	2	no	—
327	#102	—	3	2	no	—
328	#102	C₂×C₅×D₃	1	2	yes	—
329	C₄×C₈	—	3	2	no	—
330	C₄×C₈	—	3	1	no	—
331	C₂×C₃×C₅	—	4	2	no	—
332	C₂×C₃×C₅	—	8	2	no	—
333	C₂×C₃×C₅	#548	1	1	yes	characteristic
334	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
335	C₂×C₃×C₅	#576	1	1	yes	characteristic
336	C₂³×C₃	—	2	1	no	—
337	C₂³×C₃	—	2	2	no	—
338	C₃×D₄	—	2	2	no	—
339	C₃×D₄	—	2	1	no	—
340	C₃×D₄	—	2	2	no	—
341	C₃×D₄	—	4	2	no	—
342	C₃×D₄	—	8	1	no	—
343	C₃×D₄	C₅×#41	1	2	yes	—
344	C₂×C₃×C₄	—	2	1	no	—
345	C₂×C₃×C₄	—	4	2	no	—
346	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
347	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
348	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
349	C₂×Dic₃	—	2	1	no	—
350	C₂×Dic₃	—	2	1	no	—
351	C₂×Dic₃	—	2	2	no	—
352	C₂×Dic₃	—	8	2	no	—
353	C₂×Dic₃	—	8	2	no	—
354	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
355	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
356	Dic₆	—	2	2	no	—
357	Dic₆	—	2	1	no	—
358	Dic₆	—	2	1	no	—
359	Dic₆	—	8	1	no	—
360	C₃×C₈	—	2	2	no	—
361	C₃⋊C₈	—	2	1	no	—
362	C₃⋊C₈	—	2	1	no	—
363	C₂²×C₅	—	2	2	no	—
364	C₂²×C₅	—	4	1	no	—
365	C₂²×C₅	—	4	1	no	—
366	C₂²×C₅	—	4	2	no	—
367	C₂²×C₅	—	4	2	no	—
368	C₂²×C₅	—	4	2	no	—
369	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
370	C₄×C₅	—	2	1	no	—
371	C₄×C₅	—	4	1	no	—
372	C₄×C₅	—	6	2	no	—
373	C₄×C₅	—	6	2	no	—
374	C₄×C₅	—	12	1	no	—
375	C₄×C₅	—	12	2	no	—
376	C₄×C₅	—	12	1	no	—
377	C₄×C₅	#912	1	2	yes	—
378	C₄×C₅	C₂×#237	1	1	yes	characteristic
379	C₄×C₅	#1010	1	1	yes	characteristic
380	C₂×Q₈	—	3	1	no	—
381	C₂×Q₈	—	3	1	no	—
382	C₂×Q₈	—	6	1	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
386	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	6	2	no	—
389	C₂²×C₄	—	6	2	no	—
390	SD₁₆	—	6	2	no	—
391	D₈	—	2	4	no	—
392	C₂×C₈	—	3	1	no	—
393	C₂×C₈	—	3	1	no	—
394	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
395	C₄⋊C₄	—	3	1	no	—
396	C₄⋊C₄	—	3	2	no	—
397	C₄⋊C₄	—	3	2	no	—
398	C₄⋊C₄	—	3	1	no	—
399	C₄⋊C₄	—	6	2	no	—
400	C₄⋊C₄	—	6	2	no	—
401	C₄⋊C₄	—	6	1	no	—
402	C₄⋊C₄	—	6	1	no	—
403	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
404	C₂²⋊C₄	—	2	1	no	—
405	C₂²⋊C₄	—	6	2	no	—
406	C₂²⋊C₄	—	6	2	no	—
407	C₂²⋊C₄	—	6	2	no	—
408	C₂²⋊C₄	—	6	2	no	—
409	C₄²	—	3	2	no	—
410	C₄²	—	6	1	no	—
411	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
412	C₃×C₅	#3361	1	1	yes	characteristic, complemented, Hall
413	C₂²×C₃	—	2	2	no	—
414	C₂²×C₃	—	4	1	no	—
415	C₂²×C₃	—	4	1	no	—
416	C₂²×C₃	—	4	2	no	—
417	C₂²×C₃	—	4	2	no	—
418	C₂²×C₃	—	4	2	no	—
419	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
420	C₃×C₄	—	2	1	no	—
421	C₃×C₄	—	4	1	no	—
422	C₃×C₄	C₅×#135	1	2	yes	—
423	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
424	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
425	Dic₃	—	2	2	no	—
426	Dic₃	—	2	2	no	—
427	Dic₃	—	4	1	no	—
428	Dic₃	—	4	2	no	—
429	Dic₃	—	4	1	no	—
430	C₂×C₅	—	4	2	no	—
431	C₂×C₅	—	8	2	no	—
432	C₂×C₅	#5598	1	1	yes	characteristic
433	C₂×C₅	C₂×#912	1	1	yes	characteristic
434	C₂×C₅	#5774	1	1	yes	characteristic
435	C₂³	—	2	1	no	—
436	C₂³	—	2	2	no	—
437	Q₈	—	6	2	no	—
438	Q₈	—	6	1	no	—
439	Q₈	—	6	1	no	—
440	Q₈	—	24	1	no	—
441	D₄	—	2	2	no	—
442	D₄	—	2	1	no	—
443	D₄	—	2	2	no	—
444	D₄	—	4	2	no	—
445	D₄	—	8	1	no	—
446	D₄	C₅×#237	1	2	yes	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	3	2	no	—
449	C₂×C₄	—	3	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	6	1	no	—
452	C₂×C₄	—	6	1	no	—
453	C₂×C₄	—	6	2	no	—
454	C₂×C₄	—	24	2	no	—
455	C₂×C₄	—	24	2	no	—
456	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
457	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
458	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
459	C₈	—	2	2	no	—
460	C₈	—	6	1	no	—
461	C₈	—	6	1	no	—
462	C₂×C₃	—	4	2	no	—
463	C₂×C₃	—	8	2	no	—
464	C₂×C₃	C₅×#548	1	1	yes	characteristic
465	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
466	C₂×C₃	C₅×#576	1	1	yes	characteristic
467	C₅	#80319	1	1	yes	characteristic, direct product factor, Sylow
468	C₂²	—	2	2	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	4	1	no	—
477	C₄	—	6	2	no	—
478	C₄	—	6	2	no	—
479	C₄	—	12	1	no	—
480	C₄	—	12	2	no	—
481	C₄	—	12	1	no	—
482	C₄	C₅×#912	1	2	yes	—
483	C₄	C₂×C₅×#237	1	1	yes	characteristic
484	C₄	C₅×#1010	1	1	yes	characteristic
485	C₃	C₅×#3361	1	1	yes	characteristic, complemented, Sylow
486	C₂	—	4	2	no	—
487	C₂	—	8	2	no	—
488	C₂	C₅×#5598	1	1	yes	characteristic
489	C₂	C₂×C₅×#912	1	1	yes	characteristic
490	C₂	C₅×#5774	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting, prime radical	C₃×C₅×#459	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#459	D₃
hypocenter	C₃	C₅×#3361
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#459

Complements

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

N	H ≅ G/N	type
1. C₅×#5713	C₂	semidirect
2. C₅×#5543	C₂	semidirect
4. C₅×#5153	C₂	semidirect
5. C₅×Dic₃×D₈	C₂	semidirect
6. C₅×#5070	C₂	semidirect
7. C₄×C₅×#214	C₂	semidirect
8. C₅×#4850	C₂	semidirect
9. C₅×#4830	C₂	semidirect
10. C₅×#4768	C₂	semidirect
11. C₅×#4766	C₂	semidirect
42. #80319	C₅	direct (N × H)
86. #5713	C₂×C₅	semidirect
87. #5543	C₂×C₅	semidirect
89. #5153	C₂×C₅	semidirect
90. Dic₃×D₈	C₂×C₅	semidirect
91. #5070	C₂×C₅	semidirect
92. C₄×#214	C₂×C₅	semidirect
93. #4850	C₂×C₅	semidirect
94. #4830	C₂×C₅	semidirect
95. #4768	C₂×C₅	semidirect
96. #4766	C₂×C₅	semidirect
412. C₃×C₅	#3361	semidirect
467. C₅	#80319	direct (N × H)
485. C₃	C₅×#3361	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5713	2
C₅×#5543	2
C₃×C₅×#459	2
C₅×#5153	2
C₅×Dic₃×D₈	2
C₅×#5070	2
C₄×C₅×#214	2
C₅×#4850	2
C₅×#4830	2
C₅×#4768	2
C₅×#4766	2
C₅×#3361	3
#80319	5

Subgroups — C5×#80319 #14471768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80319 #14471768