Subgroups — C₅×#81023 #14460258

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5732	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5577	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#475	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5088	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅×#216	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4866	C₂	1	2	yes	maximal, complemented
7	C₅×#4864	C₂	1	2	yes	maximal, complemented
8	C₅×#4848	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4834	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4808	C₂	1	2	yes	maximal, complemented
11	C₅×#4804	C₂	1	2	yes	maximal, complemented
12	C₅×#3304	—	3	1	no	maximal, Hall
13	C₂×C₅×#239	C₂²	1	2	yes	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₅×#947	—	2	1	no	—
17	C₅×Q₈×Dic₃	—	2	1	no	—
18	C₂×C₅×#216	C₂²	1	1	yes	characteristic
19	C₂×C₅×#204	C₂²	1	2	yes	—
20	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
21	C₅×#898	—	2	2	no	—
22	C₅×#897	C₂²	1	2	yes	—
23	C₅×#895	—	2	2	no	—
24	C₅×#895	C₂²	1	2	yes	—
25	C₅×#892	C₂²	1	2	yes	—
26	C₅×#874	—	2	1	no	—
27	C₅×#874	C₂²	1	1	yes	characteristic
28	C₄×C₅×D₁₂	—	2	1	no	—
29	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
30	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
31	C₃×C₅×#106	C₂²	1	2	yes	—
32	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₃×C₅×#103	C₂²	1	2	yes	—
34	C₅×#835	C₂²	1	1	yes	characteristic
35	C₅×#821	C₂²	1	2	yes	—
36	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
37	C₅×#810	C₂²	1	1	yes	characteristic
38	C₅×#809	C₂²	1	2	yes	—
39	C₅×#809	C₂²	1	2	yes	—
40	C₅×#807	C₂²	1	1	yes	characteristic
41	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
42	#81023	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#556	—	3	1	no	—
44	C₅×#550	—	3	1	no	—
45	C₅×#486	—	3	1	no	—
46	C₅×#482	—	3	2	no	—
47	C₅×#475	D₃	1	1	yes	characteristic, complemented
48	C₅×#465	—	3	2	no	—
49	C₅×#460	—	3	1	no	—
50	C₅×#452	—	3	2	no	—
51	C₄×C₅×Q₁₆	—	3	1	no	—
52	C₅×C₈×D₄	—	3	1	no	—
53	C₅×#416	—	3	2	no	—
54	C₂×C₃×C₅×Q₈	—	2	1	no	—
55	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
56	C₅×#239	—	2	4	no	—
57	C₅×#239	—	4	2	no	—
58	C₂×C₅×D₁₂	—	2	2	no	—
59	C₂×C₅×D₁₂	—	2	1	no	—
60	C₂×C₅×D₁₂	—	2	2	no	—
61	C₂×C₅×D₁₂	—	2	1	no	—
62	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
63	C₂×C₅×D₁₂	C₂³	1	2	yes	—
64	C₂×C₄×C₅×D₃	—	2	2	no	—
65	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
66	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
68	C₃×C₅×C₄⋊C₄	—	2	1	no	—
69	C₃×C₅×C₄⋊C₄	—	2	1	no	—
70	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
71	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₃×C₄²×C₅	—	2	1	no	—
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₅×#216	—	2	2	no	—
75	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
76	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
77	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
78	C₅×(C₂×D₃)⋊C₄	D₄	1	2	yes	—
79	C₅×C₄⋊Dic₃	—	2	2	no	—
80	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
81	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
82	C₅×Dic₃⋊C₄	—	2	1	no	—
83	C₄×C₅×Dic₃	—	2	1	no	—
84	C₄×C₅×Dic₃	—	2	2	no	—
85	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
86	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
87	C₅×#204	—	4	2	no	—
88	C₅×D₃×C₈	—	4	2	no	—
89	#5732	C₂×C₅	1	1	yes	characteristic, complemented
90	#5577	C₂×C₅	1	1	yes	characteristic
91	C₃×#475	C₂×C₅	1	1	yes	characteristic, complemented
92	#5088	C₂×C₅	1	1	yes	characteristic, complemented
93	C₄×#216	C₂×C₅	1	1	yes	characteristic, complemented
94	#4866	C₂×C₅	1	2	yes	complemented
95	#4864	C₂×C₅	1	2	yes	complemented
96	#4848	C₂×C₅	1	1	yes	characteristic, complemented
97	#4834	C₂×C₅	1	1	yes	characteristic, complemented
98	#4808	C₂×C₅	1	2	yes	complemented
99	#4804	C₂×C₅	1	2	yes	complemented
100	C₂×C₅×#41	—	3	2	no	—
101	C₂×C₅×Q₁₆	—	3	1	no	—
102	C₂×C₅×SD₁₆	—	3	2	no	—
103	C₂²×C₅×C₈	—	3	2	no	—
104	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
105	C₅×#127	—	3	1	no	—
106	C₅×#127	—	6	1	no	—
107	C₅×#126	—	6	2	no	—
108	C₅×#124	—	6	1	no	—
109	C₅×C₂²⋊Q₈	—	3	2	no	—
110	C₅×#121	—	3	2	no	—
111	C₅×#121	—	6	2	no	—
112	C₄×C₅×Q₈	—	3	1	no	—
113	C₄×C₅×Q₈	—	6	1	no	—
114	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
115	C₄×C₅×D₄	—	3	1	no	—
116	C₄×C₅×D₄	—	6	1	no	—
117	C₅×#117	—	3	2	no	—
118	C₅×#107	—	3	1	no	—
119	C₅×#106	C₂×D₃	1	2	yes	—
120	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
121	C₅×#103	—	3	1	no	—
122	C₅×#103	—	3	1	no	—
123	C₅×#103	C₂×D₃	1	2	yes	—
124	C₅×#102	—	3	2	no	—
125	C₅×#102	—	3	2	no	—
126	C₅×#102	—	3	2	no	—
127	C₅×C₂²⋊C₈	—	3	2	no	—
128	C₄×C₅×C₈	—	3	1	no	—
129	#3304	—	3	1	no	Sylow
130	C₂²×C₅×D₃	—	2	2	no	—
131	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
132	C₃×C₅×Q₈	—	2	1	no	—
133	C₃×C₅×Q₈	—	4	2	no	—
134	C₃×C₅×Q₈	#41	1	2	yes	—
135	C₂×C₃×C₄×C₅	—	2	1	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	1	no	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₂×C₅×Dic₃	—	2	1	no	—
142	C₂×C₅×Dic₃	—	2	1	no	—
143	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
144	C₅×D₁₂	—	2	2	no	—
145	C₅×D₁₂	—	2	2	no	—
146	C₅×D₁₂	—	2	2	no	—
147	C₅×D₁₂	—	4	4	no	—
148	C₅×D₁₂	—	4	2	no	—
149	C₅×D₁₂	—	8	1	no	—
150	C₅×D₁₂	—	8	2	no	—
151	C₄×C₅×D₃	—	2	2	no	—
152	C₄×C₅×D₃	—	2	2	no	—
153	C₄×C₅×D₃	—	4	4	no	—
154	C₅×Dic₆	—	2	1	no	—
155	C₅×Dic₆	—	2	1	no	—
156	C₃×C₅×C₈	—	2	2	no	—
157	C₅×C₃⋊C₈	—	2	1	no	—
158	C₅×C₃⋊C₈	—	2	1	no	—
159	C₂×#239	C₂²×C₅	1	2	yes	—
160	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
161	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
162	#947	—	2	1	no	—
163	Q₈×Dic₃	—	2	1	no	—
164	C₂×#216	C₂²×C₅	1	1	yes	characteristic
165	C₂×#204	C₂²×C₅	1	2	yes	—
166	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
167	#898	—	2	2	no	—
168	#897	C₂²×C₅	1	2	yes	—
169	#895	—	2	2	no	—
170	#895	C₂²×C₅	1	2	yes	—
171	#892	C₂²×C₅	1	2	yes	—
172	#874	—	2	1	no	—
173	#874	C₂²×C₅	1	1	yes	characteristic
174	C₄×D₁₂	—	2	1	no	—
175	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
176	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
177	C₃×#106	C₂²×C₅	1	2	yes	—
178	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
179	C₃×#103	C₂²×C₅	1	2	yes	—
180	#835	C₂²×C₅	1	1	yes	characteristic
181	#821	C₂²×C₅	1	2	yes	—
182	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	—
183	#810	C₂²×C₅	1	1	yes	characteristic
184	#809	C₂²×C₅	1	2	yes	—
185	#809	C₂²×C₅	1	2	yes	—
186	#807	C₂²×C₅	1	1	yes	characteristic
187	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
188	C₅×#41	—	6	4	no	—
189	C₅×#41	—	12	2	no	—
190	C₂×C₅×Q₈	—	2	1	no	—
191	C₂×C₅×Q₈	—	3	1	no	—
192	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
193	C₂×C₅×D₄	—	3	1	no	—
194	C₂×C₅×D₄	—	3	2	no	—
195	C₂×C₅×D₄	—	6	2	no	—
196	C₂×C₅×D₄	—	6	2	no	—
197	C₂×C₅×D₄	—	6	1	no	—
198	C₂×C₅×D₄	—	6	1	no	—
199	C₂²×C₄×C₅	—	3	2	no	—
200	C₂²×C₄×C₅	—	6	2	no	—
201	C₅×Q₁₆	—	6	2	no	—
202	C₅×SD₁₆	—	12	2	no	—
203	C₂×C₅×C₈	—	3	1	no	—
204	C₂×C₅×C₈	—	3	1	no	—
205	C₂×C₅×C₈	—	12	2	no	—
206	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
207	C₅×C₄⋊C₄	—	2	1	no	—
208	C₅×C₄⋊C₄	—	2	1	no	—
209	C₅×C₄⋊C₄	—	3	1	no	—
210	C₅×C₄⋊C₄	—	3	1	no	—
211	C₅×C₄⋊C₄	—	6	2	no	—
212	C₅×C₄⋊C₄	—	6	1	no	—
213	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
214	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
215	C₅×C₂²⋊C₄	—	3	2	no	—
216	C₅×C₂²⋊C₄	—	6	2	no	—
217	C₅×C₂²⋊C₄	—	6	2	no	—
218	C₅×C₂²⋊C₄	—	6	2	no	—
219	C₄²×C₅	—	2	1	no	—
220	C₄²×C₅	—	6	2	no	—
221	C₄²×C₅	—	6	1	no	—
222	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
223	#556	—	3	1	no	—
224	#550	—	3	1	no	—
225	#486	—	3	1	no	—
226	#482	—	3	2	no	—
227	#475	C₅×D₃	1	1	yes	characteristic, complemented
228	#465	—	3	2	no	—
229	#460	—	3	1	no	—
230	#452	—	3	2	no	—
231	C₄×Q₁₆	—	3	1	no	—
232	C₈×D₄	—	3	1	no	—
233	#416	—	3	2	no	—
234	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₅×D₃	—	2	2	no	—
236	C₂×C₅×D₃	—	2	2	no	—
237	C₂×C₅×D₃	—	2	2	no	—
238	C₂×C₅×D₃	—	4	2	no	—
239	C₂×C₅×D₃	—	4	2	no	—
240	C₂×C₅×D₃	—	4	2	no	—
241	C₃×C₄×C₅	—	2	2	no	—
242	C₃×C₄×C₅	—	2	1	no	—
243	C₃×C₄×C₅	—	4	2	no	—
244	C₃×C₄×C₅	—	4	1	no	—
245	C₃×C₄×C₅	#135	1	2	yes	—
246	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
247	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
248	C₅×Dic₃	—	2	2	no	—
249	C₅×Dic₃	—	4	1	no	—
250	C₅×Dic₃	—	4	1	no	—
251	C₂×C₃×Q₈	—	2	1	no	—
252	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
253	#239	—	2	4	no	—
254	#239	—	4	2	no	—
255	C₂×D₁₂	—	2	2	no	—
256	C₂×D₁₂	—	2	1	no	—
257	C₂×D₁₂	—	2	2	no	—
258	C₂×D₁₂	—	2	1	no	—
259	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
260	C₂×D₁₂	C₂³×C₅	1	2	yes	—
261	C₂×C₄×D₃	—	2	2	no	—
262	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
263	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
264	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
265	C₃×C₄⋊C₄	—	2	1	no	—
266	C₃×C₄⋊C₄	—	2	1	no	—
267	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
268	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
269	C₃×C₄²	—	2	1	no	—
270	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
271	#216	—	2	2	no	—
272	(C₂×D₃)⋊C₄	—	2	2	no	—
273	(C₂×D₃)⋊C₄	—	2	2	no	—
274	(C₂×D₃)⋊C₄	—	2	2	no	—
275	(C₂×D₃)⋊C₄	C₅×D₄	1	2	yes	—
276	C₄⋊Dic₃	—	2	2	no	—
277	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
278	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
279	Dic₃⋊C₄	—	2	1	no	—
280	C₄×Dic₃	—	2	1	no	—
281	C₄×Dic₃	—	2	2	no	—
282	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
283	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
284	#204	—	4	2	no	—
285	D₃×C₈	—	4	2	no	—
286	C₂³×C₅	—	3	2	no	—
287	C₂³×C₅	—	6	2	no	—
288	C₅×Q₈	—	2	1	no	—
289	C₅×Q₈	—	4	2	no	—
290	C₅×Q₈	—	6	1	no	—
291	C₅×Q₈	—	6	1	no	—
292	C₅×Q₈	#239	1	2	yes	—
293	C₅×D₄	—	6	2	no	—
294	C₅×D₄	—	6	2	no	—
295	C₅×D₄	—	6	2	no	—
296	C₅×D₄	—	12	4	no	—
297	C₅×D₄	—	12	2	no	—
298	C₅×D₄	—	24	1	no	—
299	C₅×D₄	—	24	2	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	3	2	no	—
304	C₂×C₄×C₅	—	6	2	no	—
305	C₂×C₄×C₅	—	6	2	no	—
306	C₂×C₄×C₅	—	6	1	no	—
307	C₂×C₄×C₅	—	6	1	no	—
308	C₂×C₄×C₅	—	12	4	no	—
309	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
310	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
312	C₅×C₈	—	2	2	no	—
313	C₅×C₈	—	6	1	no	—
314	C₅×C₈	—	6	1	no	—
315	C₂×#41	—	3	2	no	—
316	C₂×Q₁₆	—	3	1	no	—
317	C₂×SD₁₆	—	3	2	no	—
318	C₂²×C₈	—	3	2	no	—
319	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
320	#127	—	3	1	no	—
321	#127	—	6	1	no	—
322	#126	—	6	2	no	—
323	#124	—	6	1	no	—
324	C₂²⋊Q₈	—	3	2	no	—
325	#121	—	3	2	no	—
326	#121	—	6	2	no	—
327	C₄×Q₈	—	3	1	no	—
328	C₄×Q₈	—	6	1	no	—
329	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
330	C₄×D₄	—	3	1	no	—
331	C₄×D₄	—	6	1	no	—
332	#117	—	3	2	no	—
333	#107	—	3	1	no	—
334	#106	C₂×C₅×D₃	1	2	yes	—
335	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
336	#103	—	3	1	no	—
337	#103	—	3	1	no	—
338	#103	C₂×C₅×D₃	1	2	yes	—
339	#102	—	3	2	no	—
340	#102	—	3	2	no	—
341	#102	—	3	2	no	—
342	C₂²⋊C₈	—	3	2	no	—
343	C₄×C₈	—	3	1	no	—
344	C₂×C₃×C₅	#546	1	1	yes	characteristic
345	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
346	C₂×C₃×C₅	#577	1	1	yes	characteristic
347	C₅×D₃	—	4	2	no	—
348	C₅×D₃	—	8	2	no	—
349	C₂²×D₃	—	2	2	no	—
350	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
351	C₃×Q₈	—	2	1	no	—
352	C₃×Q₈	—	4	2	no	—
353	C₃×Q₈	C₅×#41	1	2	yes	—
354	C₂×C₃×C₄	—	2	1	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	2	1	no	—
357	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
358	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
359	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
360	C₂×Dic₃	—	2	1	no	—
361	C₂×Dic₃	—	2	1	no	—
362	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
363	D₁₂	—	2	2	no	—
364	D₁₂	—	2	2	no	—
365	D₁₂	—	2	2	no	—
366	D₁₂	—	4	4	no	—
367	D₁₂	—	4	2	no	—
368	D₁₂	—	8	1	no	—
369	D₁₂	—	8	2	no	—
370	C₄×D₃	—	2	2	no	—
371	C₄×D₃	—	2	2	no	—
372	C₄×D₃	—	4	4	no	—
373	Dic₆	—	2	1	no	—
374	Dic₆	—	2	1	no	—
375	C₃×C₈	—	2	2	no	—
376	C₃⋊C₈	—	2	1	no	—
377	C₃⋊C₈	—	2	1	no	—
378	C₂²×C₅	—	6	2	no	—
379	C₂²×C₅	—	6	2	no	—
380	C₂²×C₅	—	6	2	no	—
381	C₂²×C₅	—	12	2	no	—
382	C₂²×C₅	—	12	2	no	—
383	C₂²×C₅	—	12	2	no	—
384	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
385	C₄×C₅	—	2	1	no	—
386	C₄×C₅	—	2	2	no	—
387	C₄×C₅	—	4	2	no	—
388	C₄×C₅	—	4	1	no	—
389	C₄×C₅	—	6	2	no	—
390	C₄×C₅	—	12	1	no	—
391	C₄×C₅	—	12	1	no	—
392	C₄×C₅	#916	1	2	yes	—
393	C₄×C₅	C₂×#239	1	1	yes	characteristic
394	C₄×C₅	#1009	1	1	yes	characteristic
395	#41	—	6	4	no	—
396	#41	—	12	2	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	3	1	no	—
399	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
400	C₂×D₄	—	3	1	no	—
401	C₂×D₄	—	3	2	no	—
402	C₂×D₄	—	6	2	no	—
403	C₂×D₄	—	6	2	no	—
404	C₂×D₄	—	6	1	no	—
405	C₂×D₄	—	6	1	no	—
406	C₂²×C₄	—	3	2	no	—
407	C₂²×C₄	—	6	2	no	—
408	Q₁₆	—	6	2	no	—
409	SD₁₆	—	12	2	no	—
410	C₂×C₈	—	3	1	no	—
411	C₂×C₈	—	3	1	no	—
412	C₂×C₈	—	12	2	no	—
413	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	3	1	no	—
417	C₄⋊C₄	—	3	1	no	—
418	C₄⋊C₄	—	6	2	no	—
419	C₄⋊C₄	—	6	1	no	—
420	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
421	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
422	C₂²⋊C₄	—	3	2	no	—
423	C₂²⋊C₄	—	6	2	no	—
424	C₂²⋊C₄	—	6	2	no	—
425	C₂²⋊C₄	—	6	2	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	6	2	no	—
428	C₄²	—	6	1	no	—
429	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
430	C₃×C₅	#3304	1	1	yes	characteristic, complemented, Hall
431	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
432	C₂×D₃	—	2	2	no	—
433	C₂×D₃	—	2	2	no	—
434	C₂×D₃	—	2	2	no	—
435	C₂×D₃	—	4	2	no	—
436	C₂×D₃	—	4	2	no	—
437	C₂×D₃	—	4	2	no	—
438	C₃×C₄	—	2	2	no	—
439	C₃×C₄	—	2	1	no	—
440	C₃×C₄	—	4	2	no	—
441	C₃×C₄	—	4	1	no	—
442	C₃×C₄	C₅×#135	1	2	yes	—
443	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
444	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
445	Dic₃	—	2	2	no	—
446	Dic₃	—	4	1	no	—
447	Dic₃	—	4	1	no	—
448	C₂×C₅	—	12	2	no	—
449	C₂×C₅	—	24	2	no	—
450	C₂×C₅	#5630	1	1	yes	characteristic
451	C₂×C₅	C₂×#916	1	1	yes	characteristic
452	C₂×C₅	#5778	1	1	yes	characteristic
453	C₂³	—	3	2	no	—
454	C₂³	—	6	2	no	—
455	Q₈	—	2	1	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	6	1	no	—
458	Q₈	—	6	1	no	—
459	Q₈	C₅×#239	1	2	yes	—
460	D₄	—	6	2	no	—
461	D₄	—	6	2	no	—
462	D₄	—	6	2	no	—
463	D₄	—	12	4	no	—
464	D₄	—	12	2	no	—
465	D₄	—	24	1	no	—
466	D₄	—	24	2	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	3	2	no	—
471	C₂×C₄	—	6	2	no	—
472	C₂×C₄	—	6	2	no	—
473	C₂×C₄	—	6	1	no	—
474	C₂×C₄	—	6	1	no	—
475	C₂×C₄	—	12	4	no	—
476	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
477	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
478	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
479	C₈	—	2	2	no	—
480	C₈	—	6	1	no	—
481	C₈	—	6	1	no	—
482	C₂×C₃	C₅×#546	1	1	yes	characteristic
483	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
484	C₂×C₃	C₅×#577	1	1	yes	characteristic
485	D₃	—	4	2	no	—
486	D₃	—	8	2	no	—
487	C₅	#81023	1	1	yes	characteristic, direct product factor, Sylow
488	C₂²	—	6	2	no	—
489	C₂²	—	6	2	no	—
490	C₂²	—	6	2	no	—
491	C₂²	—	12	2	no	—
492	C₂²	—	12	2	no	—
493	C₂²	—	12	2	no	—
494	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
495	C₄	—	2	1	no	—
496	C₄	—	2	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	1	no	—
499	C₄	—	6	2	no	—
500	C₄	—	12	1	no	—
501	C₄	—	12	1	no	—
502	C₄	C₅×#916	1	2	yes	—
503	C₄	C₂×C₅×#239	1	1	yes	characteristic
504	C₄	C₅×#1009	1	1	yes	characteristic
505	C₃	C₅×#3304	1	1	yes	characteristic, complemented, Sylow
506	C₂	—	12	2	no	—
507	C₂	—	24	2	no	—
508	C₂	C₅×#5630	1	1	yes	characteristic
509	C₂	C₂×C₅×#916	1	1	yes	characteristic
510	C₂	C₅×#5778	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	C₃×C₅×#475	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5577	C₂
hypercenter	C₅×#475	D₃
hypocenter	C₃	C₅×#3304
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#475

Complements

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

N	H ≅ G/N	type
1. C₅×#5732	C₂	semidirect
3. C₃×C₅×#475	C₂	semidirect
4. C₅×#5088	C₂	semidirect
5. C₄×C₅×#216	C₂	semidirect
6. C₅×#4866	C₂	semidirect
7. C₅×#4864	C₂	semidirect
8. C₅×#4848	C₂	semidirect
9. C₅×#4834	C₂	semidirect
10. C₅×#4808	C₂	semidirect
11. C₅×#4804	C₂	semidirect
42. #81023	C₅	direct (N × H)
47. C₅×#475	D₃	semidirect
89. #5732	C₂×C₅	semidirect
91. C₃×#475	C₂×C₅	semidirect
92. #5088	C₂×C₅	semidirect
93. C₄×#216	C₂×C₅	semidirect
94. #4866	C₂×C₅	semidirect
95. #4864	C₂×C₅	semidirect
96. #4848	C₂×C₅	semidirect
97. #4834	C₂×C₅	semidirect
98. #4808	C₂×C₅	semidirect
99. #4804	C₂×C₅	semidirect
227. #475	C₅×D₃	semidirect
430. C₃×C₅	#3304	semidirect
487. C₅	#81023	direct (N × H)
505. C₃	C₅×#3304	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5732	2
C₅×#5577	2
C₃×C₅×#475	2
C₅×#5088	2
C₄×C₅×#216	2
C₅×#4866	2
C₅×#4864	2
C₅×#4848	2
C₅×#4834	2
C₅×#4808	2
C₅×#4804	2
C₅×#3304	3
#81023	5

Subgroups — C5×#81023 #14460258

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81023 #14460258