Subgroups — C₅×#78825 #14437776

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5832	C₂	1	1	yes	maximal, characteristic
2	C₅×#5517	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5233	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5113	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5002	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4800	C₂	1	2	yes	maximal, complemented
9	C₅×#4792	C₂	1	2	yes	maximal, complemented
10	C₅×#4768	C₂	1	2	yes	maximal, complemented
11	C₅×#4760	C₂	1	2	yes	maximal, complemented
12	C₅×#3131	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₅×#235	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#117	C₂²	1	1	yes	characteristic
17	C₅×#947	C₂²	1	1	yes	characteristic
18	C₅×#944	C₂²	1	1	yes	characteristic
19	C₅×#940	C₂²	1	1	yes	characteristic
20	C₅×#939	—	2	2	no	—
21	C₅×#936	C₂²	1	1	yes	characteristic
22	C₄×C₅×#67	—	2	2	no	—
23	C₅×#926	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
25	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₅×#890	C₂²	1	2	yes	—
27	C₅×#888	C₂²	1	2	yes	—
28	C₅×#878	—	2	2	no	—
29	C₄×C₅×Dic₆	—	2	2	no	—
30	C₃×C₅×#103	C₂²	1	2	yes	—
31	C₃×C₅×#102	C₂²	1	2	yes	—
32	C₅×#835	C₂²	1	2	yes	—
33	C₅×#832	C₂²	1	2	yes	—
34	C₅×#821	C₂²	1	2	yes	—
35	C₅×#816	C₂²	1	2	yes	—
36	C₅×C₈×Dic₃	C₂²	1	2	yes	—
37	C₅×C₈×Dic₃	C₂²	1	2	yes	—
38	C₅×#810	C₂²	1	2	yes	—
39	C₅×#809	C₂²	1	2	yes	—
40	#78825	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₅×#533	—	3	1	no	—
42	C₅×#532	—	3	1	no	—
43	C₅×#488	—	3	2	no	—
44	C₅×#488	—	3	2	no	—
45	C₅×#487	—	3	2	no	—
46	C₅×#486	—	3	2	no	—
47	C₅×#416	—	3	1	no	—
48	C₅×#416	—	3	1	no	—
49	C₅×#416	—	3	1	no	—
50	C₅×#416	D₃	1	1	yes	characteristic, complemented
51	C₂×C₄×C₅×C₈	—	3	1	no	—
52	C₃×C₅×#41	—	2	2	no	—
53	C₃×C₅×#41	—	2	2	no	—
54	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₅×D₄	—	2	1	no	—
56	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	—	2	1	no	—
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₅×#67	—	2	1	no	—
60	C₂×C₅×#67	—	2	2	no	—
61	C₂²×C₅×Dic₃	D₄	1	2	yes	—
62	C₅×#235	—	2	2	no	—
63	C₅×#235	—	2	2	no	—
64	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
65	C₂×C₄×C₅×D₃	—	2	1	no	—
66	C₂×C₅×Dic₆	—	2	2	no	—
67	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₅×C₈	—	2	2	no	—
69	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
70	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
71	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
72	C₃×C₄²×C₅	—	2	1	no	—
73	C₅×#217	—	2	1	no	—
74	C₅×#217	—	2	2	no	—
75	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
76	C₅×C₄⋊Dic₃	—	2	2	no	—
77	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
78	C₅×Dic₃⋊C₄	—	2	2	no	—
79	C₅×Dic₃⋊C₄	—	2	2	no	—
80	C₅×Dic₃⋊C₄	—	2	2	no	—
81	C₄×C₅×Dic₃	—	2	1	no	—
82	C₄×C₅×Dic₃	D₄	1	2	yes	—
83	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
84	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
85	C₂×C₅×C₃⋊C₈	—	2	2	no	—
86	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
87	#5832	C₂×C₅	1	1	yes	characteristic
88	#5517	C₂×C₅	1	1	yes	characteristic, complemented
89	C₃×#416	C₂×C₅	1	1	yes	characteristic, complemented
90	#5233	C₂×C₅	1	1	yes	characteristic, complemented
91	#5113	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂×C₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
93	#5002	C₂×C₅	1	1	yes	characteristic, complemented
94	#4800	C₂×C₅	1	2	yes	complemented
95	#4792	C₂×C₅	1	2	yes	complemented
96	#4768	C₂×C₅	1	2	yes	complemented
97	#4760	C₂×C₅	1	2	yes	complemented
98	C₂×C₅×#41	—	3	1	no	—
99	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
100	C₂²×C₅×C₈	—	3	1	no	—
101	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
102	C₅×C₄⋊Q₈	—	3	2	no	—
103	C₅×C₄⋊Q₈	—	3	1	no	—
104	C₅×#127	—	3	1	no	—
105	C₅×#125	—	3	2	no	—
106	C₅×#124	—	3	1	no	—
107	C₅×#124	—	3	1	no	—
108	C₅×C₂²⋊Q₈	—	6	2	no	—
109	C₅×#121	—	6	2	no	—
110	C₄×C₅×Q₈	—	6	2	no	—
111	C₄×C₅×D₄	—	6	2	no	—
112	C₅×#117	—	3	1	no	—
113	C₅×#117	C₂×D₃	1	1	yes	characteristic
114	C₂×C₄²×C₅	—	3	1	no	—
115	C₅×#103	—	3	2	no	—
116	C₅×#103	—	3	2	no	—
117	C₅×#103	—	3	2	no	—
118	C₅×#103	C₂×D₃	1	2	yes	—
119	C₅×#102	—	3	2	no	—
120	C₅×#102	—	3	2	no	—
121	C₅×#102	—	3	2	no	—
122	C₅×#102	C₂×D₃	1	2	yes	—
123	C₄×C₅×C₈	—	3	2	no	—
124	C₄×C₅×C₈	—	3	2	no	—
125	#3131	—	3	1	no	Sylow
126	C₂³×C₃×C₅	—	2	1	no	—
127	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₅×D₃	—	2	1	no	—
129	C₃×C₅×Q₈	—	2	1	no	—
130	C₃×C₅×Q₈	—	2	1	no	—
131	C₃×C₅×D₄	—	2	1	no	—
132	C₃×C₅×D₄	—	2	1	no	—
133	C₃×C₅×D₄	—	4	2	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
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	#41	1	2	yes	—
139	C₂×C₃×C₄×C₅	#41	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₅×#67	—	4	2	no	—
142	C₅×#67	—	4	4	no	—
143	C₂×C₅×Dic₃	—	2	4	no	—
144	C₂×C₅×Dic₃	—	2	2	no	—
145	C₂×C₅×Dic₃	—	2	1	no	—
146	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
147	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
148	C₅×D₁₂	—	2	1	no	—
149	C₅×D₁₂	—	2	1	no	—
150	C₄×C₅×D₃	—	4	2	no	—
151	C₅×Dic₆	—	2	1	no	—
152	C₅×Dic₆	—	2	1	no	—
153	C₅×Dic₆	—	4	4	no	—
154	C₃×C₅×C₈	—	2	2	no	—
155	C₅×C₃⋊C₈	—	2	2	no	—
156	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
157	C₂×#235	C₂²×C₅	1	1	yes	characteristic
158	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
159	C₃×#117	C₂²×C₅	1	1	yes	characteristic
160	#947	C₂²×C₅	1	1	yes	characteristic
161	#944	C₂²×C₅	1	1	yes	characteristic
162	#940	C₂²×C₅	1	1	yes	characteristic
163	#939	—	2	2	no	—
164	#936	C₂²×C₅	1	1	yes	characteristic
165	C₄×#67	—	2	2	no	—
166	#926	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
168	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
169	#890	C₂²×C₅	1	2	yes	—
170	#888	C₂²×C₅	1	2	yes	—
171	#878	—	2	2	no	—
172	C₄×Dic₆	—	2	2	no	—
173	C₃×#103	C₂²×C₅	1	2	yes	—
174	C₃×#102	C₂²×C₅	1	2	yes	—
175	#835	C₂²×C₅	1	2	yes	—
176	#832	C₂²×C₅	1	2	yes	—
177	#821	C₂²×C₅	1	2	yes	—
178	#816	C₂²×C₅	1	2	yes	—
179	C₈×Dic₃	C₂²×C₅	1	2	yes	—
180	C₈×Dic₃	C₂²×C₅	1	2	yes	—
181	#810	C₂²×C₅	1	2	yes	—
182	#809	C₂²×C₅	1	2	yes	—
183	C₅×#41	—	2	2	no	—
184	C₅×#41	—	2	2	no	—
185	C₅×#41	—	6	2	no	—
186	C₅×#41	—	6	2	no	—
187	C₂×C₅×Q₈	—	3	1	no	—
188	C₂×C₅×Q₈	—	6	2	no	—
189	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
190	C₂×C₅×D₄	—	2	1	no	—
191	C₂×C₅×D₄	—	3	1	no	—
192	C₂×C₅×D₄	—	6	2	no	—
193	C₂×C₅×D₄	—	6	1	no	—
194	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
195	C₂²×C₄×C₅	—	2	1	no	—
196	C₂²×C₄×C₅	—	3	2	no	—
197	C₂²×C₄×C₅	—	6	1	no	—
198	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
199	C₂×C₅×C₈	—	2	2	no	—
200	C₂×C₅×C₈	—	3	2	no	—
201	C₂×C₅×C₈	—	6	2	no	—
202	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
203	C₅×C₄⋊C₄	—	3	2	no	—
204	C₅×C₄⋊C₄	—	6	2	no	—
205	C₅×C₄⋊C₄	—	6	2	no	—
206	C₅×C₄⋊C₄	—	6	2	no	—
207	C₅×C₄⋊C₄	—	6	2	no	—
208	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
209	C₅×C₂²⋊C₄	—	2	1	no	—
210	C₅×C₂²⋊C₄	—	6	2	no	—
211	C₅×C₂²⋊C₄	—	6	2	no	—
212	C₅×C₂²⋊C₄	—	6	1	no	—
213	C₄²×C₅	—	2	1	no	—
214	C₄²×C₅	—	3	2	no	—
215	C₄²×C₅	—	3	1	no	—
216	C₄²×C₅	—	3	1	no	—
217	C₄²×C₅	—	6	1	no	—
218	#533	—	3	1	no	—
219	#532	—	3	1	no	—
220	#488	—	3	2	no	—
221	#488	—	3	2	no	—
222	#487	—	3	2	no	—
223	#486	—	3	2	no	—
224	#416	—	3	1	no	—
225	#416	—	3	1	no	—
226	#416	—	3	1	no	—
227	#416	C₅×D₃	1	1	yes	characteristic, complemented
228	C₂×C₄×C₈	—	3	1	no	—
229	C₂²×C₃×C₅	—	2	2	no	—
230	C₂²×C₃×C₅	—	4	1	no	—
231	C₂²×C₃×C₅	—	4	2	no	—
232	C₂²×C₃×C₅	#124	1	2	yes	—
233	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₅×D₃	—	4	1	no	—
235	C₂×C₅×D₃	—	4	2	no	—
236	C₃×C₄×C₅	—	4	1	no	—
237	C₃×C₄×C₅	—	4	2	no	—
238	C₃×C₄×C₅	#124	1	2	yes	—
239	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	C₅×Dic₃	—	2	2	no	—
242	C₅×Dic₃	—	4	1	no	—
243	C₅×Dic₃	—	4	2	no	—
244	C₅×Dic₃	#135	1	4	yes	—
245	C₃×#41	—	2	2	no	—
246	C₃×#41	—	2	2	no	—
247	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
248	C₂×C₃×D₄	—	2	1	no	—
249	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
250	C₂²×C₃×C₄	—	2	1	no	—
251	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
252	C₂×#67	—	2	1	no	—
253	C₂×#67	—	2	2	no	—
254	C₂²×Dic₃	C₅×D₄	1	2	yes	—
255	#235	—	2	2	no	—
256	#235	—	2	2	no	—
257	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
258	C₂×C₄×D₃	—	2	1	no	—
259	C₂×Dic₆	—	2	2	no	—
260	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
261	C₂×C₃×C₈	—	2	2	no	—
262	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
263	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
264	C₃×C₂²⋊C₄	—	2	1	no	—
265	C₃×C₄²	—	2	1	no	—
266	#217	—	2	1	no	—
267	#217	—	2	2	no	—
268	(C₂×D₃)⋊C₄	—	2	2	no	—
269	C₄⋊Dic₃	—	2	2	no	—
270	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
271	Dic₃⋊C₄	—	2	2	no	—
272	Dic₃⋊C₄	—	2	2	no	—
273	Dic₃⋊C₄	—	2	2	no	—
274	C₄×Dic₃	—	2	1	no	—
275	C₄×Dic₃	C₅×D₄	1	2	yes	—
276	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
277	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₃⋊C₈	—	2	2	no	—
279	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
280	C₂³×C₅	—	2	1	no	—
281	C₂³×C₅	—	6	1	no	—
282	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
283	C₅×Q₈	—	2	1	no	—
284	C₅×Q₈	—	2	1	no	—
285	C₅×Q₈	—	6	1	no	—
286	C₅×Q₈	—	6	1	no	—
287	C₅×Q₈	—	12	4	no	—
288	C₅×D₄	—	2	1	no	—
289	C₅×D₄	—	2	1	no	—
290	C₅×D₄	—	4	2	no	—
291	C₅×D₄	—	6	1	no	—
292	C₅×D₄	—	6	1	no	—
293	C₅×D₄	—	12	4	no	—
294	C₅×D₄	—	12	2	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	3	2	no	—
298	C₂×C₄×C₅	—	3	2	no	—
299	C₂×C₄×C₅	—	4	2	no	—
300	C₂×C₄×C₅	—	6	4	no	—
301	C₂×C₄×C₅	—	6	2	no	—
302	C₂×C₄×C₅	—	6	1	no	—
303	C₂×C₄×C₅	—	12	2	no	—
304	C₂×C₄×C₅	#235	1	2	yes	—
305	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
306	C₂×C₄×C₅	#237	1	2	yes	—
307	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
308	C₅×C₈	—	2	2	no	—
309	C₅×C₈	—	6	2	no	—
310	C₂×#41	—	3	1	no	—
311	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
312	C₂²×C₈	—	3	1	no	—
313	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
314	C₄⋊Q₈	—	3	2	no	—
315	C₄⋊Q₈	—	3	1	no	—
316	#127	—	3	1	no	—
317	#125	—	3	2	no	—
318	#124	—	3	1	no	—
319	#124	—	3	1	no	—
320	C₂²⋊Q₈	—	6	2	no	—
321	#121	—	6	2	no	—
322	C₄×Q₈	—	6	2	no	—
323	C₄×D₄	—	6	2	no	—
324	#117	—	3	1	no	—
325	#117	C₂×C₅×D₃	1	1	yes	characteristic
326	C₂×C₄²	—	3	1	no	—
327	#103	—	3	2	no	—
328	#103	—	3	2	no	—
329	#103	—	3	2	no	—
330	#103	C₂×C₅×D₃	1	2	yes	—
331	#102	—	3	2	no	—
332	#102	—	3	2	no	—
333	#102	—	3	2	no	—
334	#102	C₂×C₅×D₃	1	2	yes	—
335	C₄×C₈	—	3	2	no	—
336	C₄×C₈	—	3	2	no	—
337	C₂×C₃×C₅	—	2	2	no	—
338	C₂×C₃×C₅	—	8	1	no	—
339	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
340	C₂×C₃×C₅	C₂×#135	1	2	yes	—
341	C₅×D₃	—	8	1	no	—
342	C₂³×C₃	—	2	1	no	—
343	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
344	C₂²×D₃	—	2	1	no	—
345	C₃×Q₈	—	2	1	no	—
346	C₃×Q₈	—	2	1	no	—
347	C₃×D₄	—	2	1	no	—
348	C₃×D₄	—	2	1	no	—
349	C₃×D₄	—	4	2	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	2	1	no	—
352	C₂×C₃×C₄	—	4	2	no	—
353	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
354	C₂×C₃×C₄	C₅×#41	1	2	yes	—
355	C₂×C₃×C₄	C₅×#41	1	2	yes	—
356	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
357	#67	—	4	2	no	—
358	#67	—	4	4	no	—
359	C₂×Dic₃	—	2	4	no	—
360	C₂×Dic₃	—	2	2	no	—
361	C₂×Dic₃	—	2	1	no	—
362	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
363	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
364	D₁₂	—	2	1	no	—
365	D₁₂	—	2	1	no	—
366	C₄×D₃	—	4	2	no	—
367	Dic₆	—	2	1	no	—
368	Dic₆	—	2	1	no	—
369	Dic₆	—	4	4	no	—
370	C₃×C₈	—	2	2	no	—
371	C₃⋊C₈	—	2	2	no	—
372	C₂²×C₅	—	2	2	no	—
373	C₂²×C₅	—	4	1	no	—
374	C₂²×C₅	—	4	2	no	—
375	C₂²×C₅	—	12	1	no	—
376	C₂²×C₅	—	12	2	no	—
377	C₂²×C₅	#885	1	2	yes	—
378	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
379	C₄×C₅	—	3	4	no	—
380	C₄×C₅	—	4	1	no	—
381	C₄×C₅	—	4	2	no	—
382	C₄×C₅	—	6	2	no	—
383	C₄×C₅	—	12	1	no	—
384	C₄×C₅	—	12	2	no	—
385	C₄×C₅	#885	1	2	yes	—
386	C₄×C₅	C₂×#235	1	1	yes	characteristic
387	C₄×C₅	C₂×#237	1	1	yes	characteristic
388	#41	—	2	2	no	—
389	#41	—	2	2	no	—
390	#41	—	6	2	no	—
391	#41	—	6	2	no	—
392	C₂×Q₈	—	3	1	no	—
393	C₂×Q₈	—	6	2	no	—
394	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	3	1	no	—
397	C₂×D₄	—	6	2	no	—
398	C₂×D₄	—	6	1	no	—
399	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	3	2	no	—
402	C₂²×C₄	—	6	1	no	—
403	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	3	2	no	—
406	C₂×C₈	—	6	2	no	—
407	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
408	C₄⋊C₄	—	3	2	no	—
409	C₄⋊C₄	—	6	2	no	—
410	C₄⋊C₄	—	6	2	no	—
411	C₄⋊C₄	—	6	2	no	—
412	C₄⋊C₄	—	6	2	no	—
413	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	6	2	no	—
416	C₂²⋊C₄	—	6	2	no	—
417	C₂²⋊C₄	—	6	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	3	2	no	—
420	C₄²	—	3	1	no	—
421	C₄²	—	3	1	no	—
422	C₄²	—	6	1	no	—
423	C₃×C₅	#3131	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	—	2	2	no	—
425	C₂²×C₃	—	4	1	no	—
426	C₂²×C₃	—	4	2	no	—
427	C₂²×C₃	C₅×#124	1	2	yes	—
428	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
429	C₂×D₃	—	4	1	no	—
430	C₂×D₃	—	4	2	no	—
431	C₃×C₄	—	4	1	no	—
432	C₃×C₄	—	4	2	no	—
433	C₃×C₄	C₅×#124	1	2	yes	—
434	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
435	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
436	Dic₃	—	2	2	no	—
437	Dic₃	—	4	1	no	—
438	Dic₃	—	4	2	no	—
439	Dic₃	C₅×#135	1	4	yes	—
440	C₂×C₅	—	2	2	no	—
441	C₂×C₅	—	8	1	no	—
442	C₂×C₅	—	24	1	no	—
443	C₂×C₅	C₂×#885	1	1	yes	characteristic
444	C₂×C₅	D₃×#135	1	2	yes	—
445	C₂³	—	2	1	no	—
446	C₂³	—	6	1	no	—
447	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
448	Q₈	—	2	1	no	—
449	Q₈	—	2	1	no	—
450	Q₈	—	6	1	no	—
451	Q₈	—	6	1	no	—
452	Q₈	—	12	4	no	—
453	D₄	—	2	1	no	—
454	D₄	—	2	1	no	—
455	D₄	—	4	2	no	—
456	D₄	—	6	1	no	—
457	D₄	—	6	1	no	—
458	D₄	—	12	4	no	—
459	D₄	—	12	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	3	2	no	—
463	C₂×C₄	—	3	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	6	4	no	—
466	C₂×C₄	—	6	2	no	—
467	C₂×C₄	—	6	1	no	—
468	C₂×C₄	—	12	2	no	—
469	C₂×C₄	C₅×#235	1	2	yes	—
470	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
471	C₂×C₄	C₅×#237	1	2	yes	—
472	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
473	C₈	—	2	2	no	—
474	C₈	—	6	2	no	—
475	C₂×C₃	—	2	2	no	—
476	C₂×C₃	—	8	1	no	—
477	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
478	C₂×C₃	C₂×C₅×#135	1	2	yes	—
479	D₃	—	8	1	no	—
480	C₅	#78825	1	1	yes	characteristic, direct product factor, Sylow
481	C₂²	—	2	2	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	12	1	no	—
485	C₂²	—	12	2	no	—
486	C₂²	C₅×#885	1	2	yes	—
487	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
488	C₄	—	3	4	no	—
489	C₄	—	4	1	no	—
490	C₄	—	4	2	no	—
491	C₄	—	6	2	no	—
492	C₄	—	12	1	no	—
493	C₄	—	12	2	no	—
494	C₄	C₅×#885	1	2	yes	—
495	C₄	C₂×C₅×#235	1	1	yes	characteristic
496	C₄	C₂×C₅×#237	1	1	yes	characteristic
497	C₃	C₅×#3131	1	1	yes	characteristic, complemented, Sylow
498	C₂	—	2	2	no	—
499	C₂	—	8	1	no	—
500	C₂	—	24	1	no	—
501	C₂	C₂×C₅×#885	1	1	yes	characteristic
502	C₂	C₅×D₃×#135	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#416	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5832	C₂
hypercenter	C₅×#416	D₃
hypocenter	C₃	C₅×#3131
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#416

Complements

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

N	H ≅ G/N	type
2. C₅×#5517	C₂	semidirect
3. C₃×C₅×#416	C₂	semidirect
4. C₅×#5233	C₂	semidirect
5. C₅×#5113	C₂	semidirect
6. C₂×C₅×C₈×Dic₃	C₂	semidirect
7. C₅×#5002	C₂	semidirect
8. C₅×#4800	C₂	semidirect
9. C₅×#4792	C₂	semidirect
10. C₅×#4768	C₂	semidirect
11. C₅×#4760	C₂	semidirect
40. #78825	C₅	direct (N × H)
50. C₅×#416	D₃	semidirect
88. #5517	C₂×C₅	semidirect
89. C₃×#416	C₂×C₅	semidirect
90. #5233	C₂×C₅	semidirect
91. #5113	C₂×C₅	semidirect
92. C₂×C₈×Dic₃	C₂×C₅	semidirect
93. #5002	C₂×C₅	semidirect
94. #4800	C₂×C₅	semidirect
95. #4792	C₂×C₅	semidirect
96. #4768	C₂×C₅	semidirect
97. #4760	C₂×C₅	semidirect
227. #416	C₅×D₃	semidirect
423. C₃×C₅	#3131	semidirect
480. C₅	#78825	direct (N × H)
497. C₃	C₅×#3131	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5832	2
C₅×#5517	2
C₃×C₅×#416	2
C₅×#5233	2
C₅×#5113	2
C₂×C₅×C₈×Dic₃	2
C₅×#5002	2
C₅×#4800	2
C₅×#4792	2
C₅×#4768	2
C₅×#4760	2
C₅×#3131	3
#78825	5

Subgroups — C5×#78825 #14437776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78825 #14437776