Subgroups — C₅×#80517 #14471741

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5681	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5539	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#463	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5165	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×Dic₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5150	C₂	1	1	yes	maximal, characteristic
7	C₅×Dic₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5056	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×#213	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4847	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4830	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4800	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4793	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4763	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4760	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3361	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
19	C₃×C₅×#124	C₂²	1	1	yes	characteristic
20	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₅×#947	C₂²	1	1	yes	characteristic
22	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
23	C₅×#940	C₂²	1	1	yes	characteristic
24	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
25	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
26	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
27	C₂×C₅×#213	C₂²	1	1	yes	characteristic
28	C₅×#924	—	2	1	no	—
29	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
30	C₅×#890	C₂²	1	1	yes	characteristic
31	C₅×#888	C₂²	1	1	yes	characteristic
32	C₅×#886	—	2	1	no	—
33	C₅×#885	—	2	1	no	—
34	C₅×#883	—	2	1	no	—
35	C₅×#67⋊C₄	—	2	1	no	—
36	C₅×#878	—	2	1	no	—
37	C₅×#878	—	2	1	no	—
38	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
39	C₅×#870	C₂²	1	1	yes	characteristic
40	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
41	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₃×C₅×#103	C₂²	1	1	yes	characteristic
43	C₃×C₅×#102	C₂²	1	1	yes	characteristic
44	C₅×#835	C₂²	1	1	yes	characteristic
45	C₅×#835	C₂²	1	1	yes	characteristic
46	C₅×#832	C₂²	1	1	yes	characteristic
47	C₅×#832	C₂²	1	1	yes	characteristic
48	C₅×#832	C₂²	1	1	yes	characteristic
49	C₅×#821	C₂²	1	1	yes	characteristic
50	C₅×#821	C₂²	1	1	yes	characteristic
51	C₅×#818	C₂²	1	1	yes	characteristic
52	C₅×#817	C₂²	1	1	yes	characteristic
53	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
54	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
55	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
56	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
57	C₅×#809	C₂²	1	1	yes	characteristic
58	C₅×#807	C₂²	1	1	yes	characteristic
59	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
60	#80517	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#559	—	3	1	no	—
62	C₅×#554	—	3	1	no	—
63	C₅×#488	—	3	1	no	—
64	C₅×#488	—	3	1	no	—
65	C₅×#486	—	3	1	no	—
66	C₅×#478	—	3	1	no	—
67	C₅×#478	—	3	1	no	—
68	C₅×#477	—	3	1	no	—
69	C₅×#463	—	3	1	no	—
70	C₅×#463	D₃	1	1	yes	characteristic, complemented
71	C₅×#459	—	3	1	no	—
72	C₅×C₈×Q₈	—	3	1	no	—
73	C₄×C₅×SD₁₆	—	3	1	no	—
74	C₄×C₅×D₈	—	3	1	no	—
75	C₄×C₅×D₈	—	3	1	no	—
76	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	—	2	1	no	—
80	C₂×C₅×#67	—	2	1	no	—
81	C₂×C₅×#67	—	2	1	no	—
82	C₂²×C₅×Dic₃	—	2	1	no	—
83	C₂²×C₅×Dic₃	—	2	1	no	—
84	C₂²×C₅×Dic₃	—	2	1	no	—
85	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
86	C₂×C₄×C₅×D₃	—	2	1	no	—
87	C₂×C₅×Dic₆	—	2	1	no	—
88	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
89	C₃×C₅×SD₁₆	—	2	2	no	—
90	C₃×C₅×D₈	—	2	2	no	—
91	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
95	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
96	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
97	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
98	C₅×#217	—	2	1	no	—
99	C₅×#217	—	2	1	no	—
100	C₅×#217	—	2	1	no	—
101	C₅×#213	—	2	2	no	—
102	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
103	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
104	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
105	C₅×C₄⋊Dic₃	—	2	1	no	—
106	C₅×C₄⋊Dic₃	—	2	1	no	—
107	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
108	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
109	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
110	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
111	C₅×Dic₃⋊C₄	—	2	1	no	—
112	C₅×Dic₃⋊C₄	—	2	1	no	—
113	C₅×Dic₃⋊C₄	—	2	1	no	—
114	C₅×Dic₃⋊C₄	—	2	1	no	—
115	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
116	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
117	C₄×C₅×Dic₃	—	2	1	no	—
118	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
119	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
120	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
121	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
122	#5681	C₂×C₅	1	1	yes	characteristic, complemented
123	#5539	C₂×C₅	1	1	yes	characteristic, complemented
124	C₃×#463	C₂×C₅	1	1	yes	characteristic, complemented
125	#5165	C₂×C₅	1	1	yes	characteristic, complemented
126	Dic₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
127	#5150	C₂×C₅	1	1	yes	characteristic
128	Dic₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
129	#5056	C₂×C₅	1	1	yes	characteristic, complemented
130	C₄×#213	C₂×C₅	1	1	yes	characteristic, complemented
131	#4847	C₂×C₅	1	1	yes	characteristic, complemented
132	#4830	C₂×C₅	1	1	yes	characteristic, complemented
133	#4800	C₂×C₅	1	1	yes	characteristic, complemented
134	#4793	C₂×C₅	1	1	yes	characteristic, complemented
135	#4763	C₂×C₅	1	1	yes	characteristic, complemented
136	#4760	C₂×C₅	1	1	yes	characteristic, complemented
137	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
138	C₂×C₅×D₈	—	3	1	no	—
139	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
140	C₅×C₄⋊Q₈	—	3	1	no	—
141	C₅×#127	—	3	1	no	—
142	C₅×#125	—	3	1	no	—
143	C₅×#125	—	3	1	no	—
144	C₅×#124	—	3	1	no	—
145	C₅×#124	—	6	1	no	—
146	C₅×#124	C₂×D₃	1	1	yes	characteristic
147	C₅×#123	—	6	1	no	—
148	C₅×#123	—	6	1	no	—
149	C₅×C₂²⋊Q₈	—	6	1	no	—
150	C₅×C₂²⋊Q₈	—	6	1	no	—
151	C₅×C₂²⋊Q₈	—	6	1	no	—
152	C₄×C₅×Q₈	—	3	1	no	—
153	C₄×C₅×Q₈	—	3	1	no	—
154	C₄×C₅×D₄	—	3	1	no	—
155	C₄×C₅×D₄	—	3	1	no	—
156	C₄×C₅×D₄	—	3	1	no	—
157	C₄×C₅×D₄	—	3	1	no	—
158	C₄×C₅×D₄	—	6	1	no	—
159	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
160	C₂×C₅×C₄⋊C₄	—	6	1	no	—
161	C₅×#107	—	3	1	no	—
162	C₅×#107	—	3	1	no	—
163	C₅×#106	—	3	1	no	—
164	C₅×C₄⋊C₈	—	3	1	no	—
165	C₅×C₄⋊C₈	—	3	1	no	—
166	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
167	C₅×#103	—	3	1	no	—
168	C₅×#103	—	3	1	no	—
169	C₅×#103	C₂×D₃	1	1	yes	characteristic
170	C₅×#102	—	3	1	no	—
171	C₅×#102	—	3	1	no	—
172	C₅×#102	—	3	1	no	—
173	C₅×#102	—	3	1	no	—
174	C₅×#102	—	3	1	no	—
175	C₅×#102	—	3	1	no	—
176	C₅×#102	C₂×D₃	1	1	yes	characteristic
177	C₄×C₅×C₈	—	3	1	no	—
178	C₄×C₅×C₈	—	3	1	no	—
179	C₄×C₅×C₈	—	3	1	no	—
180	#3361	—	3	1	no	Sylow
181	C₂³×C₃×C₅	—	2	1	no	—
182	C₂³×C₃×C₅	—	2	1	no	—
183	C₂²×C₅×D₃	—	2	1	no	—
184	C₃×C₅×Q₈	—	2	1	no	—
185	C₃×C₅×Q₈	—	2	1	no	—
186	C₃×C₅×D₄	—	2	1	no	—
187	C₃×C₅×D₄	—	2	1	no	—
188	C₃×C₅×D₄	—	2	1	no	—
189	C₃×C₅×D₄	#41	1	2	yes	—
190	C₂×C₃×C₄×C₅	—	2	1	no	—
191	C₂×C₃×C₄×C₅	—	2	1	no	—
192	C₂×C₃×C₄×C₅	—	8	1	no	—
193	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
194	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
195	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
196	C₅×#67	—	4	2	no	—
197	C₅×#67	—	8	1	no	—
198	C₂×C₅×Dic₃	—	2	1	no	—
199	C₂×C₅×Dic₃	—	2	1	no	—
200	C₂×C₅×Dic₃	—	2	1	no	—
201	C₂×C₅×Dic₃	—	4	2	no	—
202	C₂×C₅×Dic₃	—	8	1	no	—
203	C₂×C₅×Dic₃	—	8	1	no	—
204	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
205	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
206	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
207	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
208	C₅×D₁₂	—	2	1	no	—
209	C₅×D₁₂	—	2	1	no	—
210	C₄×C₅×D₃	—	8	1	no	—
211	C₅×Dic₆	—	2	2	no	—
212	C₅×Dic₆	—	8	1	no	—
213	C₃×C₅×C₈	—	2	1	no	—
214	C₃×C₅×C₈	—	2	1	no	—
215	C₅×C₃⋊C₈	—	2	1	no	—
216	C₅×C₃⋊C₈	—	2	1	no	—
217	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
218	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
219	C₃×#124	C₂²×C₅	1	1	yes	characteristic
220	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
221	#947	C₂²×C₅	1	1	yes	characteristic
222	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
223	#940	C₂²×C₅	1	1	yes	characteristic
224	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
225	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
226	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
227	C₂×#213	C₂²×C₅	1	1	yes	characteristic
228	#924	—	2	1	no	—
229	C₂×Dic₃⋊C₄	—	2	1	no	—
230	#890	C₂²×C₅	1	1	yes	characteristic
231	#888	C₂²×C₅	1	1	yes	characteristic
232	#886	—	2	1	no	—
233	#885	—	2	1	no	—
234	#883	—	2	1	no	—
235	#67⋊C₄	—	2	1	no	—
236	#878	—	2	1	no	—
237	#878	—	2	1	no	—
238	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
239	#870	C₂²×C₅	1	1	yes	characteristic
240	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
241	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
242	C₃×#103	C₂²×C₅	1	1	yes	characteristic
243	C₃×#102	C₂²×C₅	1	1	yes	characteristic
244	#835	C₂²×C₅	1	1	yes	characteristic
245	#835	C₂²×C₅	1	1	yes	characteristic
246	#832	C₂²×C₅	1	1	yes	characteristic
247	#832	C₂²×C₅	1	1	yes	characteristic
248	#832	C₂²×C₅	1	1	yes	characteristic
249	#821	C₂²×C₅	1	1	yes	characteristic
250	#821	C₂²×C₅	1	1	yes	characteristic
251	#818	C₂²×C₅	1	1	yes	characteristic
252	#817	C₂²×C₅	1	1	yes	characteristic
253	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
254	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
255	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
256	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
257	#809	C₂²×C₅	1	1	yes	characteristic
258	#807	C₂²×C₅	1	1	yes	characteristic
259	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₅×Q₈	—	3	1	no	—
261	C₂×C₅×Q₈	—	6	1	no	—
262	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
263	C₂×C₅×D₄	—	3	1	no	—
264	C₂×C₅×D₄	—	6	1	no	—
265	C₂×C₅×D₄	—	6	1	no	—
266	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
267	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
268	C₂²×C₄×C₅	—	2	1	no	—
269	C₂²×C₄×C₅	—	6	1	no	—
270	C₂²×C₄×C₅	—	6	1	no	—
271	C₂²×C₄×C₅	—	6	1	no	—
272	C₂²×C₄×C₅	—	6	1	no	—
273	C₅×SD₁₆	—	2	2	no	—
274	C₅×D₈	—	2	2	no	—
275	C₅×D₈	—	6	2	no	—
276	C₂×C₅×C₈	—	3	1	no	—
277	C₂×C₅×C₈	—	3	1	no	—
278	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
279	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
280	C₅×C₄⋊C₄	—	3	1	no	—
281	C₅×C₄⋊C₄	—	3	1	no	—
282	C₅×C₄⋊C₄	—	3	1	no	—
283	C₅×C₄⋊C₄	—	3	1	no	—
284	C₅×C₄⋊C₄	—	3	1	no	—
285	C₅×C₄⋊C₄	—	3	1	no	—
286	C₅×C₄⋊C₄	—	6	1	no	—
287	C₅×C₄⋊C₄	—	6	1	no	—
288	C₅×C₄⋊C₄	—	6	1	no	—
289	C₅×C₄⋊C₄	—	6	1	no	—
290	C₅×C₄⋊C₄	—	6	1	no	—
291	C₅×C₄⋊C₄	—	6	1	no	—
292	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
293	C₅×C₂²⋊C₄	—	2	1	no	—
294	C₅×C₂²⋊C₄	—	2	1	no	—
295	C₅×C₂²⋊C₄	—	2	1	no	—
296	C₅×C₂²⋊C₄	—	6	1	no	—
297	C₅×C₂²⋊C₄	—	6	1	no	—
298	C₅×C₂²⋊C₄	—	6	1	no	—
299	C₅×C₂²⋊C₄	—	6	1	no	—
300	C₅×C₂²⋊C₄	—	6	1	no	—
301	C₅×C₂²⋊C₄	—	6	1	no	—
302	C₄²×C₅	—	3	1	no	—
303	C₄²×C₅	—	3	1	no	—
304	C₄²×C₅	—	6	1	no	—
305	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
306	#559	—	3	1	no	—
307	#554	—	3	1	no	—
308	#488	—	3	1	no	—
309	#488	—	3	1	no	—
310	#486	—	3	1	no	—
311	#478	—	3	1	no	—
312	#478	—	3	1	no	—
313	#477	—	3	1	no	—
314	#463	—	3	1	no	—
315	#463	C₅×D₃	1	1	yes	characteristic, complemented
316	#459	—	3	1	no	—
317	C₈×Q₈	—	3	1	no	—
318	C₄×SD₁₆	—	3	1	no	—
319	C₄×D₈	—	3	1	no	—
320	C₄×D₈	—	3	1	no	—
321	C₂²×C₃×C₅	—	2	2	no	—
322	C₂²×C₃×C₅	—	4	1	no	—
323	C₂²×C₃×C₅	—	4	1	no	—
324	C₂²×C₃×C₅	—	4	1	no	—
325	C₂²×C₃×C₅	—	4	1	no	—
326	C₂²×C₃×C₅	—	4	1	no	—
327	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₅×D₃	—	4	1	no	—
329	C₂×C₅×D₃	—	4	1	no	—
330	C₂×C₅×D₃	—	4	1	no	—
331	C₃×C₄×C₅	—	2	1	no	—
332	C₃×C₄×C₅	—	2	1	no	—
333	C₃×C₄×C₅	—	4	1	no	—
334	C₃×C₄×C₅	—	4	1	no	—
335	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
336	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
337	C₅×Dic₃	—	2	1	no	—
338	C₅×Dic₃	—	2	1	no	—
339	C₅×Dic₃	—	2	1	no	—
340	C₅×Dic₃	—	4	1	no	—
341	C₅×Dic₃	—	4	1	no	—
342	C₅×Dic₃	—	4	1	no	—
343	C₅×Dic₃	#135	1	2	yes	—
344	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
345	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
346	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
347	C₂²×C₃×C₄	—	2	1	no	—
348	C₂×#67	—	2	1	no	—
349	C₂×#67	—	2	1	no	—
350	C₂²×Dic₃	—	2	1	no	—
351	C₂²×Dic₃	—	2	1	no	—
352	C₂²×Dic₃	—	2	1	no	—
353	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
354	C₂×C₄×D₃	—	2	1	no	—
355	C₂×Dic₆	—	2	1	no	—
356	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
357	C₃×SD₁₆	—	2	2	no	—
358	C₃×D₈	—	2	2	no	—
359	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
360	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
361	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
362	C₃×C₂²⋊C₄	—	2	1	no	—
363	C₃×C₂²⋊C₄	—	2	1	no	—
364	C₃×C₂²⋊C₄	—	2	1	no	—
365	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
366	#217	—	2	1	no	—
367	#217	—	2	1	no	—
368	#217	—	2	1	no	—
369	#213	—	2	2	no	—
370	(C₂×D₃)⋊C₄	—	2	1	no	—
371	(C₂×D₃)⋊C₄	—	2	1	no	—
372	(C₂×D₃)⋊C₄	—	2	1	no	—
373	C₄⋊Dic₃	—	2	1	no	—
374	C₄⋊Dic₃	—	2	1	no	—
375	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
376	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
377	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
378	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
379	Dic₃⋊C₄	—	2	1	no	—
380	Dic₃⋊C₄	—	2	1	no	—
381	Dic₃⋊C₄	—	2	1	no	—
382	Dic₃⋊C₄	—	2	1	no	—
383	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
384	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
385	C₄×Dic₃	—	2	1	no	—
386	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
387	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
388	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
389	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
390	C₂³×C₅	—	2	1	no	—
391	C₂³×C₅	—	2	1	no	—
392	C₂³×C₅	—	6	1	no	—
393	C₅×Q₈	—	2	1	no	—
394	C₅×Q₈	—	2	1	no	—
395	C₅×Q₈	—	6	2	no	—
396	C₅×Q₈	—	24	1	no	—
397	C₅×D₄	—	2	1	no	—
398	C₅×D₄	—	2	1	no	—
399	C₅×D₄	—	2	1	no	—
400	C₅×D₄	—	6	1	no	—
401	C₅×D₄	—	6	1	no	—
402	C₅×D₄	—	12	2	no	—
403	C₅×D₄	—	24	1	no	—
404	C₅×D₄	#237	1	2	yes	—
405	C₂×C₄×C₅	—	2	1	no	—
406	C₂×C₄×C₅	—	2	1	no	—
407	C₂×C₄×C₅	—	3	1	no	—
408	C₂×C₄×C₅	—	3	1	no	—
409	C₂×C₄×C₅	—	3	1	no	—
410	C₂×C₄×C₅	—	3	1	no	—
411	C₂×C₄×C₅	—	6	1	no	—
412	C₂×C₄×C₅	—	6	1	no	—
413	C₂×C₄×C₅	—	6	1	no	—
414	C₂×C₄×C₅	—	8	1	no	—
415	C₂×C₄×C₅	—	12	2	no	—
416	C₂×C₄×C₅	—	24	1	no	—
417	C₂×C₄×C₅	—	24	1	no	—
418	C₂×C₄×C₅	—	24	1	no	—
419	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
420	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
421	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
422	C₅×C₈	—	2	1	no	—
423	C₅×C₈	—	2	1	no	—
424	C₅×C₈	—	6	1	no	—
425	C₅×C₈	—	6	1	no	—
426	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
427	C₂×D₈	—	3	1	no	—
428	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
429	C₄⋊Q₈	—	3	1	no	—
430	#127	—	3	1	no	—
431	#125	—	3	1	no	—
432	#125	—	3	1	no	—
433	#124	—	3	1	no	—
434	#124	—	6	1	no	—
435	#124	C₂×C₅×D₃	1	1	yes	characteristic
436	#123	—	6	1	no	—
437	#123	—	6	1	no	—
438	C₂²⋊Q₈	—	6	1	no	—
439	C₂²⋊Q₈	—	6	1	no	—
440	C₂²⋊Q₈	—	6	1	no	—
441	C₄×Q₈	—	3	1	no	—
442	C₄×Q₈	—	3	1	no	—
443	C₄×D₄	—	3	1	no	—
444	C₄×D₄	—	3	1	no	—
445	C₄×D₄	—	3	1	no	—
446	C₄×D₄	—	3	1	no	—
447	C₄×D₄	—	6	1	no	—
448	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
449	C₂×C₄⋊C₄	—	6	1	no	—
450	#107	—	3	1	no	—
451	#107	—	3	1	no	—
452	#106	—	3	1	no	—
453	C₄⋊C₈	—	3	1	no	—
454	C₄⋊C₈	—	3	1	no	—
455	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
456	#103	—	3	1	no	—
457	#103	—	3	1	no	—
458	#103	C₂×C₅×D₃	1	1	yes	characteristic
459	#102	—	3	1	no	—
460	#102	—	3	1	no	—
461	#102	—	3	1	no	—
462	#102	—	3	1	no	—
463	#102	—	3	1	no	—
464	#102	—	3	1	no	—
465	#102	C₂×C₅×D₃	1	1	yes	characteristic
466	C₄×C₈	—	3	1	no	—
467	C₄×C₈	—	3	1	no	—
468	C₄×C₈	—	3	1	no	—
469	C₂×C₃×C₅	—	4	2	no	—
470	C₂×C₃×C₅	—	8	1	no	—
471	C₂×C₃×C₅	#548	1	1	yes	characteristic
472	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
473	C₂×C₃×C₅	#576	1	1	yes	characteristic
474	C₅×D₃	—	8	1	no	—
475	C₂³×C₃	—	2	1	no	—
476	C₂³×C₃	—	2	1	no	—
477	C₂²×D₃	—	2	1	no	—
478	C₃×Q₈	—	2	1	no	—
479	C₃×Q₈	—	2	1	no	—
480	C₃×D₄	—	2	1	no	—
481	C₃×D₄	—	2	1	no	—
482	C₃×D₄	—	2	1	no	—
483	C₃×D₄	C₅×#41	1	2	yes	—
484	C₂×C₃×C₄	—	2	1	no	—
485	C₂×C₃×C₄	—	2	1	no	—
486	C₂×C₃×C₄	—	8	1	no	—
487	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
488	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
489	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
490	#67	—	4	2	no	—
491	#67	—	8	1	no	—
492	C₂×Dic₃	—	2	1	no	—
493	C₂×Dic₃	—	2	1	no	—
494	C₂×Dic₃	—	2	1	no	—
495	C₂×Dic₃	—	4	2	no	—
496	C₂×Dic₃	—	8	1	no	—
497	C₂×Dic₃	—	8	1	no	—
498	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
499	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
500	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
501	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
502	D₁₂	—	2	1	no	—
503	D₁₂	—	2	1	no	—
504	C₄×D₃	—	8	1	no	—
505	Dic₆	—	2	2	no	—
506	Dic₆	—	8	1	no	—
507	C₃×C₈	—	2	1	no	—
508	C₃×C₈	—	2	1	no	—
509	C₃⋊C₈	—	2	1	no	—
510	C₃⋊C₈	—	2	1	no	—
511	C₂²×C₅	—	2	2	no	—
512	C₂²×C₅	—	4	1	no	—
513	C₂²×C₅	—	4	1	no	—
514	C₂²×C₅	—	4	1	no	—
515	C₂²×C₅	—	4	1	no	—
516	C₂²×C₅	—	4	1	no	—
517	C₂²×C₅	—	12	1	no	—
518	C₂²×C₅	—	12	1	no	—
519	C₂²×C₅	—	12	1	no	—
520	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
521	C₄×C₅	—	2	1	no	—
522	C₄×C₅	—	2	1	no	—
523	C₄×C₅	—	3	2	no	—
524	C₄×C₅	—	4	1	no	—
525	C₄×C₅	—	4	1	no	—
526	C₄×C₅	—	6	1	no	—
527	C₄×C₅	—	6	1	no	—
528	C₄×C₅	—	6	1	no	—
529	C₄×C₅	—	12	1	no	—
530	C₄×C₅	—	12	1	no	—
531	C₄×C₅	—	12	1	no	—
532	C₄×C₅	C₂×#237	1	1	yes	characteristic
533	C₄×C₅	#1010	1	1	yes	characteristic
534	C₂×Q₈	—	3	1	no	—
535	C₂×Q₈	—	6	1	no	—
536	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
537	C₂×D₄	—	3	1	no	—
538	C₂×D₄	—	6	1	no	—
539	C₂×D₄	—	6	1	no	—
540	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
541	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	6	1	no	—
544	C₂²×C₄	—	6	1	no	—
545	C₂²×C₄	—	6	1	no	—
546	C₂²×C₄	—	6	1	no	—
547	SD₁₆	—	2	2	no	—
548	D₈	—	2	2	no	—
549	D₈	—	6	2	no	—
550	C₂×C₈	—	3	1	no	—
551	C₂×C₈	—	3	1	no	—
552	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
553	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
554	C₄⋊C₄	—	3	1	no	—
555	C₄⋊C₄	—	3	1	no	—
556	C₄⋊C₄	—	3	1	no	—
557	C₄⋊C₄	—	3	1	no	—
558	C₄⋊C₄	—	3	1	no	—
559	C₄⋊C₄	—	3	1	no	—
560	C₄⋊C₄	—	6	1	no	—
561	C₄⋊C₄	—	6	1	no	—
562	C₄⋊C₄	—	6	1	no	—
563	C₄⋊C₄	—	6	1	no	—
564	C₄⋊C₄	—	6	1	no	—
565	C₄⋊C₄	—	6	1	no	—
566	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
567	C₂²⋊C₄	—	2	1	no	—
568	C₂²⋊C₄	—	2	1	no	—
569	C₂²⋊C₄	—	2	1	no	—
570	C₂²⋊C₄	—	6	1	no	—
571	C₂²⋊C₄	—	6	1	no	—
572	C₂²⋊C₄	—	6	1	no	—
573	C₂²⋊C₄	—	6	1	no	—
574	C₂²⋊C₄	—	6	1	no	—
575	C₂²⋊C₄	—	6	1	no	—
576	C₄²	—	3	1	no	—
577	C₄²	—	3	1	no	—
578	C₄²	—	6	1	no	—
579	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
580	C₃×C₅	#3361	1	1	yes	characteristic, complemented, Hall
581	C₂²×C₃	—	2	2	no	—
582	C₂²×C₃	—	4	1	no	—
583	C₂²×C₃	—	4	1	no	—
584	C₂²×C₃	—	4	1	no	—
585	C₂²×C₃	—	4	1	no	—
586	C₂²×C₃	—	4	1	no	—
587	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
588	C₂×D₃	—	4	1	no	—
589	C₂×D₃	—	4	1	no	—
590	C₂×D₃	—	4	1	no	—
591	C₃×C₄	—	2	1	no	—
592	C₃×C₄	—	2	1	no	—
593	C₃×C₄	—	4	1	no	—
594	C₃×C₄	—	4	1	no	—
595	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
596	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
597	Dic₃	—	2	1	no	—
598	Dic₃	—	2	1	no	—
599	Dic₃	—	2	1	no	—
600	Dic₃	—	4	1	no	—
601	Dic₃	—	4	1	no	—
602	Dic₃	—	4	1	no	—
603	Dic₃	C₅×#135	1	2	yes	—
604	C₂×C₅	—	4	2	no	—
605	C₂×C₅	—	8	1	no	—
606	C₂×C₅	—	24	1	no	—
607	C₂×C₅	#5598	1	1	yes	characteristic
608	C₂×C₅	D₃×#135	1	1	yes	characteristic
609	C₂×C₅	#5774	1	1	yes	characteristic
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	6	1	no	—
613	Q₈	—	2	1	no	—
614	Q₈	—	2	1	no	—
615	Q₈	—	6	2	no	—
616	Q₈	—	24	1	no	—
617	D₄	—	2	1	no	—
618	D₄	—	2	1	no	—
619	D₄	—	2	1	no	—
620	D₄	—	6	1	no	—
621	D₄	—	6	1	no	—
622	D₄	—	12	2	no	—
623	D₄	—	24	1	no	—
624	D₄	C₅×#237	1	2	yes	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	3	1	no	—
628	C₂×C₄	—	3	1	no	—
629	C₂×C₄	—	3	1	no	—
630	C₂×C₄	—	3	1	no	—
631	C₂×C₄	—	6	1	no	—
632	C₂×C₄	—	6	1	no	—
633	C₂×C₄	—	6	1	no	—
634	C₂×C₄	—	8	1	no	—
635	C₂×C₄	—	12	2	no	—
636	C₂×C₄	—	24	1	no	—
637	C₂×C₄	—	24	1	no	—
638	C₂×C₄	—	24	1	no	—
639	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
640	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
641	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
642	C₈	—	2	1	no	—
643	C₈	—	2	1	no	—
644	C₈	—	6	1	no	—
645	C₈	—	6	1	no	—
646	C₂×C₃	—	4	2	no	—
647	C₂×C₃	—	8	1	no	—
648	C₂×C₃	C₅×#548	1	1	yes	characteristic
649	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
650	C₂×C₃	C₅×#576	1	1	yes	characteristic
651	D₃	—	8	1	no	—
652	C₅	#80517	1	1	yes	characteristic, direct product factor, Sylow
653	C₂²	—	2	2	no	—
654	C₂²	—	4	1	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	12	1	no	—
660	C₂²	—	12	1	no	—
661	C₂²	—	12	1	no	—
662	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	3	2	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	6	1	no	—
669	C₄	—	6	1	no	—
670	C₄	—	6	1	no	—
671	C₄	—	12	1	no	—
672	C₄	—	12	1	no	—
673	C₄	—	12	1	no	—
674	C₄	C₂×C₅×#237	1	1	yes	characteristic
675	C₄	C₅×#1010	1	1	yes	characteristic
676	C₃	C₅×#3361	1	1	yes	characteristic, complemented, Sylow
677	C₂	—	4	2	no	—
678	C₂	—	8	1	no	—
679	C₂	—	24	1	no	—
680	C₂	C₅×#5598	1	1	yes	characteristic
681	C₂	C₅×D₃×#135	1	1	yes	characteristic
682	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	C₃×C₅×#463	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5150	C₂
hypercenter	C₅×#463	D₃
hypocenter	C₃	C₅×#3361
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#463

Complements

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

N	H ≅ G/N	type
1. C₅×#5681	C₂	semidirect
2. C₅×#5539	C₂	semidirect
3. C₃×C₅×#463	C₂	semidirect
4. C₅×#5165	C₂	semidirect
5. C₅×Dic₃×SD₁₆	C₂	semidirect
7. C₅×Dic₃×D₈	C₂	semidirect
8. C₅×#5056	C₂	semidirect
9. C₄×C₅×#213	C₂	semidirect
10. C₅×#4847	C₂	semidirect
11. C₅×#4830	C₂	semidirect
12. C₅×#4800	C₂	semidirect
13. C₅×#4793	C₂	semidirect
14. C₅×#4763	C₂	semidirect
15. C₅×#4760	C₂	semidirect
60. #80517	C₅	direct (N × H)
70. C₅×#463	D₃	semidirect
122. #5681	C₂×C₅	semidirect
123. #5539	C₂×C₅	semidirect
124. C₃×#463	C₂×C₅	semidirect
125. #5165	C₂×C₅	semidirect
126. Dic₃×SD₁₆	C₂×C₅	semidirect
128. Dic₃×D₈	C₂×C₅	semidirect
129. #5056	C₂×C₅	semidirect
130. C₄×#213	C₂×C₅	semidirect
131. #4847	C₂×C₅	semidirect
132. #4830	C₂×C₅	semidirect
133. #4800	C₂×C₅	semidirect
134. #4793	C₂×C₅	semidirect
135. #4763	C₂×C₅	semidirect
136. #4760	C₂×C₅	semidirect
315. #463	C₅×D₃	semidirect
580. C₃×C₅	#3361	semidirect
652. C₅	#80517	direct (N × H)
676. 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×#5681	2
C₅×#5539	2
C₃×C₅×#463	2
C₅×#5165	2
C₅×Dic₃×SD₁₆	2
C₅×#5150	2
C₅×Dic₃×D₈	2
C₅×#5056	2
C₄×C₅×#213	2
C₅×#4847	2
C₅×#4830	2
C₅×#4800	2
C₅×#4793	2
C₅×#4763	2
C₅×#4760	2
C₅×#3361	3
#80517	5

Subgroups — C5×#80517 #14471741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80517 #14471741