Subgroups — C₅×#78571 #14417180

Order 1920.

940 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#909	C₂	1	1	yes	maximal, characteristic
2	C₅×#5523	C₂	1	1	yes	maximal, characteristic
3	C₅×#5516	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5121	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5113	C₂	1	1	yes	maximal, characteristic
7	C₂×C₅×#816	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4716	C₂	1	2	yes	maximal, complemented
9	C₅×#4710	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×Dic₁₂	C₂	1	2	yes	maximal, complemented
11	C₄×C₅×#204	C₂	1	2	yes	maximal, complemented
12	C₅×#2947	—	3	1	no	maximal, Hall
13	C₂×C₅×#235	C₂²	1	1	yes	characteristic
14	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×#117	C₂²	1	1	yes	characteristic
18	C₅×#926	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₅×#909	C₄	1	8	yes	complemented
21	C₂×C₅×Dic₁₂	C₂²	1	2	yes	—
22	C₂×C₅×#204	C₂²	1	2	yes	—
23	C₅×#892	—	2	1	no	—
24	C₅×D₃×C₄⋊C₄	—	2	1	no	—
25	C₅×#887	—	2	1	no	—
26	C₅×#887	—	2	1	no	—
27	C₅×#67⋊C₄	—	2	2	no	—
28	C₅×#877	—	2	2	no	—
29	C₄×C₅×D₁₂	C₂²	1	2	yes	—
30	C₄×C₅×Dic₆	C₂²	1	2	yes	—
31	C₄×C₅×Dic₆	C₂²	1	2	yes	—
32	C₄×C₅×Dic₆	C₂²	1	2	yes	—
33	C₃×C₅×#97	C₂²	1	2	yes	—
34	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
35	C₅×#821	C₂²	1	1	yes	characteristic
36	C₅×#821	C₂²	1	1	yes	characteristic
37	C₅×#818	C₂²	1	2	yes	—
38	C₅×#817	C₂²	1	2	yes	—
39	C₅×#816	C₂²	1	2	yes	—
40	C₅×#816	C₂²	1	1	yes	characteristic
41	C₅×#816	C₂²	1	2	yes	—
42	C₅×#816	C₂²	1	1	yes	characteristic
43	#78571	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
44	C₂×C₅×#137	—	3	1	no	—
45	C₅×#520	—	3	1	no	—
46	C₅×#519	—	3	1	no	—
47	C₅×#441	—	3	2	no	—
48	C₅×#440	—	3	2	no	—
49	C₄×C₅×Q₁₆	—	3	2	no	—
50	C₄×C₅×SD₁₆	—	3	2	no	—
51	C₅×#428	—	3	1	no	—
52	C₅×#416	—	3	1	no	—
53	C₂×C₅×#103	—	3	1	no	—
54	C₅×#405	D₃	1	1	yes	characteristic, complemented
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂×C₅×#67	—	2	1	no	—
57	C₂²×C₅×Dic₃	—	2	1	no	—
58	C₂²×C₅×Dic₃	—	2	1	no	—
59	C₅×#235	—	2	2	no	—
60	C₅×#235	C₂×C₄	1	4	yes	—
61	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
62	C₂×C₄×C₅×D₃	—	2	1	no	—
63	C₂×C₄×C₅×D₃	—	2	2	no	—
64	C₂×C₅×Dic₆	—	2	1	no	—
65	C₂×C₅×Dic₆	—	2	2	no	—
66	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	complemented
67	C₂×C₅×Dic₆	C₂³	1	2	yes	—
68	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
69	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
70	C₂×C₃×C₅×C₈	—	2	2	no	—
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
74	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
75	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
76	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
77	C₃×C₄²×C₅	C₂³	1	2	yes	—
78	C₅×#217	—	2	1	no	—
79	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
80	C₅×C₄⋊Dic₃	—	2	1	no	—
81	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
82	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
83	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
84	C₅×Dic₃⋊C₄	—	2	2	no	—
85	C₅×Dic₃⋊C₄	—	2	2	no	—
86	C₅×Dic₃⋊C₄	—	2	2	no	—
87	C₄×C₅×Dic₃	—	2	2	no	—
88	C₄×C₅×Dic₃	—	2	2	no	—
89	C₄×C₅×Dic₃	—	2	2	no	—
90	C₄×C₅×Dic₃	—	2	1	no	—
91	C₅×Dic₁₂	C₂×C₄	1	8	yes	complemented
92	C₅×#204	C₂×C₄	1	8	yes	complemented
93	C₂×#909	C₂×C₅	1	1	yes	characteristic
94	#5523	C₂×C₅	1	1	yes	characteristic
95	#5516	C₂×C₅	1	1	yes	characteristic, complemented
96	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
97	#5121	C₂×C₅	1	1	yes	characteristic, complemented
98	#5113	C₂×C₅	1	1	yes	characteristic
99	C₂×#816	C₂×C₅	1	1	yes	characteristic, complemented
100	#4716	C₂×C₅	1	2	yes	complemented
101	#4710	C₂×C₅	1	2	yes	complemented
102	C₄×Dic₁₂	C₂×C₅	1	2	yes	complemented
103	C₄×#204	C₂×C₅	1	2	yes	complemented
104	C₂×C₅×#41	—	3	1	no	—
105	C₂²×C₅×Q₈	—	3	1	no	—
106	C₅×#137	—	3	8	no	—
107	C₂×C₅×Q₁₆	—	3	2	no	—
108	C₂×C₅×SD₁₆	—	3	2	no	—
109	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
110	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
111	C₄×C₅×Q₈	—	3	2	no	—
112	C₄×C₅×Q₈	—	3	2	no	—
113	C₄×C₅×Q₈	—	3	2	no	—
114	C₄×C₅×Q₈	—	6	1	no	—
115	C₄×C₅×Q₈	—	6	1	no	—
116	C₄×C₅×D₄	—	3	2	no	—
117	C₄×C₅×D₄	—	6	2	no	—
118	C₅×#117	—	3	1	no	—
119	C₅×#117	—	6	1	no	—
120	C₅×#117	—	6	2	no	—
121	C₅×#117	C₂×D₃	1	1	yes	characteristic
122	C₂×C₅×C₄⋊C₄	—	3	1	no	—
123	C₂×C₅×C₄⋊C₄	—	6	1	no	—
124	C₅×#107	—	3	2	no	—
125	C₅×#106	—	3	2	no	—
126	C₅×#103	—	3	2	no	—
127	C₅×#103	—	3	2	no	—
128	C₅×#103	—	3	1	no	—
129	C₅×#103	—	3	1	no	—
130	C₅×#102	—	3	1	no	—
131	C₅×#102	—	3	1	no	—
132	C₅×#97	C₂×D₃	1	2	yes	—
133	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
134	#2947	—	3	1	no	Sylow
135	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₅×D₃	—	2	1	no	—
137	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	#41	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
143	C₅×#67	—	2	4	no	—
144	C₂×C₅×Dic₃	—	2	4	no	—
145	C₂×C₅×Dic₃	—	2	2	no	—
146	C₂×C₅×Dic₃	—	2	1	no	—
147	C₂×C₅×Dic₃	—	2	1	no	—
148	C₂×C₅×Dic₃	—	2	1	no	—
149	C₂×C₅×Dic₃	—	2	2	no	—
150	C₂×C₅×Dic₃	—	8	1	no	—
151	C₅×D₁₂	—	2	1	no	—
152	C₅×D₁₂	C₂²×C₄	1	2	yes	—
153	C₄×C₅×D₃	—	2	4	no	—
154	C₄×C₅×D₃	—	8	2	no	—
155	C₅×Dic₆	—	2	4	no	—
156	C₅×Dic₆	—	2	2	no	—
157	C₅×Dic₆	—	2	1	no	—
158	C₅×Dic₆	C₂²×C₄	1	4	yes	—
159	C₅×Dic₆	C₂²×C₄	1	2	yes	—
160	C₃×C₅×C₈	—	2	1	no	—
161	C₃×C₅×C₈	—	2	1	no	—
162	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
163	C₂×#235	C₂²×C₅	1	1	yes	characteristic
164	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
166	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
167	C₃×#117	C₂²×C₅	1	1	yes	characteristic
168	#926	C₂²×C₅	1	1	yes	characteristic
169	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
170	#909	C₄×C₅	1	8	yes	complemented
171	C₂×Dic₁₂	C₂²×C₅	1	2	yes	—
172	C₂×#204	C₂²×C₅	1	2	yes	—
173	#892	—	2	1	no	—
174	D₃×C₄⋊C₄	—	2	1	no	—
175	#887	—	2	1	no	—
176	#887	—	2	1	no	—
177	#67⋊C₄	—	2	2	no	—
178	#877	—	2	2	no	—
179	C₄×D₁₂	C₂²×C₅	1	2	yes	—
180	C₄×Dic₆	C₂²×C₅	1	2	yes	—
181	C₄×Dic₆	C₂²×C₅	1	2	yes	—
182	C₄×Dic₆	C₂²×C₅	1	2	yes	—
183	C₃×#97	C₂²×C₅	1	2	yes	—
184	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
185	#821	C₂²×C₅	1	1	yes	characteristic
186	#821	C₂²×C₅	1	1	yes	characteristic
187	#818	C₂²×C₅	1	2	yes	—
188	#817	C₂²×C₅	1	2	yes	—
189	#816	C₂²×C₅	1	2	yes	—
190	#816	C₂²×C₅	1	1	yes	characteristic
191	#816	C₂²×C₅	1	2	yes	—
192	#816	C₂²×C₅	1	1	yes	characteristic
193	C₅×#41	—	3	4	no	—
194	C₅×#41	—	6	2	no	—
195	C₂×C₅×Q₈	—	3	4	no	—
196	C₂×C₅×Q₈	—	3	2	no	—
197	C₂×C₅×Q₈	—	3	1	no	—
198	C₂×C₅×Q₈	—	6	1	no	—
199	C₂×C₅×Q₈	—	6	2	no	—
200	C₂×C₅×D₄	—	3	1	no	—
201	C₂×C₅×D₄	—	6	1	no	—
202	C₂²×C₄×C₅	—	6	1	no	—
203	C₂²×C₄×C₅	—	6	1	no	—
204	C₂²×C₄×C₅	—	6	1	no	—
205	C₂²×C₄×C₅	—	6	2	no	—
206	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
207	C₅×Q₁₆	—	3	8	no	—
208	C₅×SD₁₆	—	3	8	no	—
209	C₅×M₁₆	C₄×D₃	1	4	yes	complemented
210	C₂×C₅×C₈	—	2	2	no	—
211	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
212	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
213	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
214	C₅×C₄⋊C₄	—	3	2	no	—
215	C₅×C₄⋊C₄	—	3	1	no	—
216	C₅×C₄⋊C₄	—	3	1	no	—
217	C₅×C₄⋊C₄	—	6	1	no	—
218	C₅×C₄⋊C₄	—	6	2	no	—
219	C₅×C₄⋊C₄	—	6	2	no	—
220	C₅×C₄⋊C₄	—	6	2	no	—
221	C₅×C₄⋊C₄	D₁₂	1	1	yes	characteristic
222	C₅×C₄⋊C₄	D₁₂	1	1	yes	characteristic
223	C₅×C₂²⋊C₄	—	6	1	no	—
224	C₅×C₂²⋊C₄	—	6	2	no	—
225	C₅×C₂²⋊C₄	D₁₂	1	2	yes	—
226	C₄²×C₅	—	6	1	no	—
227	C₄²×C₅	—	6	2	no	—
228	C₄²×C₅	—	6	2	no	—
229	C₄²×C₅	—	6	2	no	—
230	C₄²×C₅	C₂²×D₃	1	2	yes	—
231	C₂×#137	—	3	1	no	—
232	#520	—	3	1	no	—
233	#519	—	3	1	no	—
234	#441	—	3	2	no	—
235	#440	—	3	2	no	—
236	C₄×Q₁₆	—	3	2	no	—
237	C₄×SD₁₆	—	3	2	no	—
238	#428	—	3	1	no	—
239	#416	—	3	1	no	—
240	C₂×#103	—	3	1	no	—
241	#405	C₅×D₃	1	1	yes	characteristic, complemented
242	C₂²×C₃×C₅	—	2	1	no	—
243	C₂²×C₃×C₅	—	2	1	no	—
244	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
245	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₅×D₃	—	2	2	no	—
247	C₂×C₅×D₃	—	4	1	no	—
248	C₂×C₅×D₃	—	4	1	no	—
249	C₃×C₄×C₅	—	2	2	no	—
250	C₃×C₄×C₅	—	2	2	no	—
251	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
252	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
253	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
254	C₅×Dic₃	—	2	4	no	—
255	C₅×Dic₃	—	2	2	no	—
256	C₅×Dic₃	—	4	2	no	—
257	C₅×Dic₃	—	4	1	no	—
258	C₅×Dic₃	—	4	1	no	—
259	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
260	C₂×#67	—	2	1	no	—
261	C₂²×Dic₃	—	2	1	no	—
262	C₂²×Dic₃	—	2	1	no	—
263	#235	—	2	2	no	—
264	#235	C₂×C₄×C₅	1	4	yes	—
265	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
266	C₂×C₄×D₃	—	2	1	no	—
267	C₂×C₄×D₃	—	2	2	no	—
268	C₂×Dic₆	—	2	1	no	—
269	C₂×Dic₆	—	2	2	no	—
270	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	complemented
271	C₂×Dic₆	C₂³×C₅	1	2	yes	—
272	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
273	C₃×M₁₆	C₂×C₄×C₅	1	4	yes	complemented
274	C₂×C₃×C₈	—	2	2	no	—
275	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
276	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
277	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
278	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
279	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
280	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
281	C₃×C₄²	C₂³×C₅	1	2	yes	—
282	#217	—	2	1	no	—
283	(C₂×D₃)⋊C₄	—	2	2	no	—
284	C₄⋊Dic₃	—	2	1	no	—
285	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
286	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
287	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
288	Dic₃⋊C₄	—	2	2	no	—
289	Dic₃⋊C₄	—	2	2	no	—
290	Dic₃⋊C₄	—	2	2	no	—
291	C₄×Dic₃	—	2	2	no	—
292	C₄×Dic₃	—	2	2	no	—
293	C₄×Dic₃	—	2	2	no	—
294	C₄×Dic₃	—	2	1	no	—
295	Dic₁₂	C₂×C₄×C₅	1	8	yes	complemented
296	#204	C₂×C₄×C₅	1	8	yes	complemented
297	C₂³×C₅	—	6	1	no	—
298	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
299	C₅×Q₈	—	3	4	no	—
300	C₅×Q₈	—	3	2	no	—
301	C₅×Q₈	—	6	4	no	—
302	C₅×Q₈	—	6	2	no	—
303	C₅×Q₈	—	6	1	no	—
304	C₅×D₄	—	3	2	no	—
305	C₅×D₄	—	6	4	no	—
306	C₅×D₄	—	6	1	no	—
307	C₂×C₄×C₅	—	6	4	no	—
308	C₂×C₄×C₅	—	6	1	no	—
309	C₂×C₄×C₅	—	6	2	no	—
310	C₂×C₄×C₅	—	6	4	no	—
311	C₂×C₄×C₅	—	6	1	no	—
312	C₂×C₄×C₅	—	6	1	no	—
313	C₂×C₄×C₅	—	6	2	no	—
314	C₂×C₄×C₅	—	24	2	no	—
315	C₂×C₄×C₅	—	24	1	no	—
316	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
317	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
318	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
319	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
320	C₂×C₄×C₅	#235	1	2	yes	—
321	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
322	C₅×C₈	—	2	1	no	—
323	C₅×C₈	—	2	1	no	—
324	C₅×C₈	C₂×C₄×D₃	1	4	yes	—
325	C₂×#41	—	3	1	no	—
326	C₂²×Q₈	—	3	1	no	—
327	#137	—	3	8	no	—
328	C₂×Q₁₆	—	3	2	no	—
329	C₂×SD₁₆	—	3	2	no	—
330	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
331	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
332	C₄×Q₈	—	3	2	no	—
333	C₄×Q₈	—	3	2	no	—
334	C₄×Q₈	—	3	2	no	—
335	C₄×Q₈	—	6	1	no	—
336	C₄×Q₈	—	6	1	no	—
337	C₄×D₄	—	3	2	no	—
338	C₄×D₄	—	6	2	no	—
339	#117	—	3	1	no	—
340	#117	—	6	1	no	—
341	#117	—	6	2	no	—
342	#117	C₂×C₅×D₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	—	3	1	no	—
344	C₂×C₄⋊C₄	—	6	1	no	—
345	#107	—	3	2	no	—
346	#106	—	3	2	no	—
347	#103	—	3	2	no	—
348	#103	—	3	2	no	—
349	#103	—	3	1	no	—
350	#103	—	3	1	no	—
351	#102	—	3	1	no	—
352	#102	—	3	1	no	—
353	#97	C₂×C₅×D₃	1	2	yes	—
354	C₄×C₈	C₂×C₅×D₃	1	2	yes	—
355	C₂×C₃×C₅	—	2	2	no	—
356	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
357	C₂×C₃×C₅	#577	1	1	yes	characteristic
358	C₂×C₃×C₅	#578	1	1	yes	characteristic
359	C₅×D₃	—	4	2	no	—
360	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
361	C₂²×D₃	—	2	1	no	—
362	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
363	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
364	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
365	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
366	C₂×C₃×C₄	C₅×#41	1	2	yes	—
367	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
368	#67	—	2	4	no	—
369	C₂×Dic₃	—	2	4	no	—
370	C₂×Dic₃	—	2	2	no	—
371	C₂×Dic₃	—	2	1	no	—
372	C₂×Dic₃	—	2	1	no	—
373	C₂×Dic₃	—	2	1	no	—
374	C₂×Dic₃	—	2	2	no	—
375	C₂×Dic₃	—	8	1	no	—
376	D₁₂	—	2	1	no	—
377	D₁₂	C₂²×C₄×C₅	1	2	yes	—
378	C₄×D₃	—	2	4	no	—
379	C₄×D₃	—	8	2	no	—
380	Dic₆	—	2	4	no	—
381	Dic₆	—	2	2	no	—
382	Dic₆	—	2	1	no	—
383	Dic₆	C₂²×C₄×C₅	1	4	yes	—
384	Dic₆	C₂²×C₄×C₅	1	2	yes	—
385	C₃×C₈	—	2	1	no	—
386	C₃×C₈	—	2	1	no	—
387	C₃×C₈	C₂²×C₄×C₅	1	4	yes	—
388	C₂²×C₅	—	2	1	no	—
389	C₂²×C₅	—	2	1	no	—
390	C₂²×C₅	—	6	2	no	—
391	C₂²×C₅	—	12	1	no	—
392	C₂²×C₅	—	12	1	no	—
393	C₂²×C₅	C₄×D₁₂	1	2	yes	—
394	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
395	C₄×C₅	—	2	2	no	—
396	C₄×C₅	—	2	2	no	—
397	C₄×C₅	—	6	2	no	—
398	C₄×C₅	—	6	4	no	—
399	C₄×C₅	—	12	1	no	—
400	C₄×C₅	—	12	2	no	—
401	C₄×C₅	—	12	1	no	—
402	C₄×C₅	C₄×D₁₂	1	2	yes	—
403	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
404	C₄×C₅	C₂×#235	1	1	yes	characteristic
405	#41	—	3	4	no	—
406	#41	—	6	2	no	—
407	C₂×Q₈	—	3	4	no	—
408	C₂×Q₈	—	3	2	no	—
409	C₂×Q₈	—	3	1	no	—
410	C₂×Q₈	—	6	1	no	—
411	C₂×Q₈	—	6	2	no	—
412	C₂×D₄	—	3	1	no	—
413	C₂×D₄	—	6	1	no	—
414	C₂²×C₄	—	6	1	no	—
415	C₂²×C₄	—	6	1	no	—
416	C₂²×C₄	—	6	1	no	—
417	C₂²×C₄	—	6	2	no	—
418	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
419	Q₁₆	—	3	8	no	—
420	SD₁₆	—	3	8	no	—
421	M₁₆	C₄×C₅×D₃	1	4	yes	complemented
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
424	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
425	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
426	C₄⋊C₄	—	3	1	no	—
427	C₄⋊C₄	—	3	1	no	—
428	C₄⋊C₄	—	3	2	no	—
429	C₄⋊C₄	—	6	1	no	—
430	C₄⋊C₄	—	6	2	no	—
431	C₄⋊C₄	—	6	2	no	—
432	C₄⋊C₄	—	6	2	no	—
433	C₄⋊C₄	C₅×D₁₂	1	1	yes	characteristic
434	C₄⋊C₄	C₅×D₁₂	1	1	yes	characteristic
435	C₂²⋊C₄	—	6	1	no	—
436	C₂²⋊C₄	—	6	2	no	—
437	C₂²⋊C₄	C₅×D₁₂	1	2	yes	—
438	C₄²	—	6	1	no	—
439	C₄²	—	6	2	no	—
440	C₄²	—	6	2	no	—
441	C₄²	—	6	2	no	—
442	C₄²	C₂²×C₅×D₃	1	2	yes	—
443	C₃×C₅	#2947	1	1	yes	characteristic, complemented, Hall
444	C₂²×C₃	—	2	1	no	—
445	C₂²×C₃	—	2	1	no	—
446	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
447	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
448	C₂×D₃	—	2	2	no	—
449	C₂×D₃	—	4	1	no	—
450	C₂×D₃	—	4	1	no	—
451	C₃×C₄	—	2	2	no	—
452	C₃×C₄	—	2	2	no	—
453	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
454	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
455	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
456	Dic₃	—	2	4	no	—
457	Dic₃	—	2	2	no	—
458	Dic₃	—	4	2	no	—
459	Dic₃	—	4	1	no	—
460	Dic₃	—	4	1	no	—
461	C₂×C₅	—	2	2	no	—
462	C₂×C₅	—	12	2	no	—
463	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
464	C₂×C₅	#5751	1	1	yes	characteristic
465	C₂×C₅	#5753	1	1	yes	characteristic
466	C₂³	—	6	1	no	—
467	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
468	Q₈	—	3	4	no	—
469	Q₈	—	3	2	no	—
470	Q₈	—	6	4	no	—
471	Q₈	—	6	2	no	—
472	Q₈	—	6	1	no	—
473	D₄	—	3	2	no	—
474	D₄	—	6	4	no	—
475	D₄	—	6	1	no	—
476	C₂×C₄	—	6	4	no	—
477	C₂×C₄	—	6	1	no	—
478	C₂×C₄	—	6	2	no	—
479	C₂×C₄	—	6	4	no	—
480	C₂×C₄	—	6	1	no	—
481	C₂×C₄	—	6	1	no	—
482	C₂×C₄	—	6	2	no	—
483	C₂×C₄	—	24	2	no	—
484	C₂×C₄	—	24	1	no	—
485	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
486	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
487	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
488	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
489	C₂×C₄	C₅×#235	1	2	yes	—
490	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
491	C₈	—	2	1	no	—
492	C₈	—	2	1	no	—
493	C₈	C₂×C₄×C₅×D₃	1	4	yes	—
494	C₂×C₃	—	2	2	no	—
495	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
496	C₂×C₃	C₅×#577	1	1	yes	characteristic
497	C₂×C₃	C₅×#578	1	1	yes	characteristic
498	D₃	—	4	2	no	—
499	C₅	#78571	1	1	yes	characteristic, direct product factor, Sylow
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	6	2	no	—
503	C₂²	—	12	1	no	—
504	C₂²	—	12	1	no	—
505	C₂²	C₄×C₅×D₁₂	1	2	yes	—
506	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	6	2	no	—
510	C₄	—	6	4	no	—
511	C₄	—	12	2	no	—
512	C₄	—	12	1	no	—
513	C₄	—	12	1	no	—
514	C₄	C₄×C₅×D₁₂	1	2	yes	—
515	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
516	C₄	C₂×C₅×#235	1	1	yes	characteristic
517	C₃	C₅×#2947	1	1	yes	characteristic, complemented, Sylow
518	C₂	—	2	2	no	—
519	C₂	—	12	2	no	—
520	C₂	C₂×C₄×C₅×D₁₂	1	1	yes	characteristic
521	C₂	C₅×#5751	1	1	yes	characteristic
522	C₂	C₅×#5753	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×D₁₂
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#405	D₃
hypocenter	C₃	C₅×#2947
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#117 ◁ C₅×#405

Complements

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

N	H ≅ G/N	type
3. C₅×#5516	C₂	semidirect
4. C₃×C₅×#405	C₂	semidirect
5. C₅×#5121	C₂	semidirect
7. C₂×C₅×#816	C₂	semidirect
8. C₅×#4716	C₂	semidirect
9. C₅×#4710	C₂	semidirect
10. C₄×C₅×Dic₁₂	C₂	semidirect
11. C₄×C₅×#204	C₂	semidirect
20. C₅×#909	C₄	semidirect
43. #78571	C₅	direct (N × H)
54. C₅×#405	D₃	semidirect
66. C₂×C₅×Dic₆	C₂×C₄	semidirect
69. C₃×C₅×M₁₆	C₂×C₄	semidirect
91. C₅×Dic₁₂	C₂×C₄	semidirect
92. C₅×#204	C₂×C₄	semidirect
95. #5516	C₂×C₅	semidirect
96. C₃×#405	C₂×C₅	semidirect
97. #5121	C₂×C₅	semidirect
99. C₂×#816	C₂×C₅	semidirect
100. #4716	C₂×C₅	semidirect
101. #4710	C₂×C₅	semidirect
102. C₄×Dic₁₂	C₂×C₅	semidirect
103. C₄×#204	C₂×C₅	semidirect
170. #909	C₄×C₅	semidirect
209. C₅×M₁₆	C₄×D₃	semidirect
241. #405	C₅×D₃	semidirect
270. C₂×Dic₆	C₂×C₄×C₅	semidirect
273. C₃×M₁₆	C₂×C₄×C₅	semidirect
295. Dic₁₂	C₂×C₄×C₅	semidirect
296. #204	C₂×C₄×C₅	semidirect
421. M₁₆	C₄×C₅×D₃	semidirect
443. C₃×C₅	#2947	semidirect
499. C₅	#78571	direct (N × H)
517. C₃	C₅×#2947	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#909	2
C₅×#5523	2
C₅×#5516	2
C₃×C₅×#405	2
C₅×#5121	2
C₅×#5113	2
C₂×C₅×#816	2
C₅×#4716	2
C₅×#4710	2
C₄×C₅×Dic₁₂	2
C₄×C₅×#204	2
C₅×#2947	3
#78571	5

Subgroups — C5×#78571 #14417180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78571 #14417180