Subgroups — C₅×#81633 #14471747

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×#5690	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5681	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#488	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5066	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5057	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4819	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4800	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4793	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4788	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4786	C₂	1	1	yes	maximal, characteristic
11	C₅×#4766	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4760	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4756	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×C₈×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3361	—	3	1	no	maximal, Hall
17	C₃×C₅×#125	C₂²	1	1	yes	characteristic
18	C₃×C₅×#124	C₂²	1	1	yes	characteristic
19	C₅×#947	C₂²	1	1	yes	characteristic
20	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₅×#215	C₂²	1	1	yes	characteristic
22	C₅×#940	C₂²	1	1	yes	characteristic
23	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
24	C₂×C₅×#213	C₂²	1	1	yes	characteristic
25	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
26	C₅×#897	—	2	1	no	—
27	C₅×#896	—	2	1	no	—
28	C₅×#896	—	2	1	no	—
29	C₅×#893	C₂²	1	1	yes	characteristic
30	C₅×#893	C₂²	1	1	yes	characteristic
31	C₅×D₃×C₄⋊C₄	—	2	1	no	—
32	C₅×#890	C₂²	1	1	yes	characteristic
33	C₅×#888	C₂²	1	1	yes	characteristic
34	C₅×#886	—	2	1	no	—
35	C₅×#885	—	2	1	no	—
36	C₅×#883	—	2	1	no	—
37	C₅×#67⋊C₄	—	2	1	no	—
38	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
39	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
40	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
41	C₃×C₅×#103	C₂²	1	1	yes	characteristic
42	C₃×C₅×#103	C₂²	1	1	yes	characteristic
43	C₃×C₅×#102	C₂²	1	1	yes	characteristic
44	C₃×C₅×#102	C₂²	1	1	yes	characteristic
45	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
46	C₅×#835	C₂²	1	1	yes	characteristic
47	C₅×#832	C₂²	1	1	yes	characteristic
48	C₅×#821	C₂²	1	1	yes	characteristic
49	C₅×#821	C₂²	1	1	yes	characteristic
50	C₅×#818	C₂²	1	1	yes	characteristic
51	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
52	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
53	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
54	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
55	C₅×#809	C₂²	1	1	yes	characteristic
56	C₅×#809	C₂²	1	1	yes	characteristic
57	C₅×#808	C₂²	1	1	yes	characteristic
58	C₅×#807	C₂²	1	1	yes	characteristic
59	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
60	#81633	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	D₃	1	1	yes	characteristic, complemented
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	—	3	1	no	—
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×C₅×#67	—	2	1	no	—
79	C₂×C₅×#67	—	2	1	no	—
80	C₂²×C₅×Dic₃	—	2	1	no	—
81	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
82	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
83	C₂×C₄×C₅×D₃	—	2	1	no	—
84	C₂×C₄×C₅×D₃	—	2	1	no	—
85	C₂×C₄×C₅×D₃	—	2	1	no	—
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	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
91	C₃×C₅×C₄⋊C₄	—	2	1	no	—
92	C₃×C₅×C₄⋊C₄	—	2	1	no	—
93	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×#215	—	2	2	no	—
100	C₅×#213	—	2	2	no	—
101	C₅×(C₂×D₃)⋊C₄	—	2	1	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×(C₂×D₃)⋊C₄	—	2	1	no	—
106	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
107	C₅×C₄⋊Dic₃	—	2	1	no	—
108	C₅×C₄⋊Dic₃	—	2	1	no	—
109	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
110	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
111	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
112	C₅×Dic₃⋊C₄	—	2	1	no	—
113	C₅×Dic₃⋊C₄	—	2	1	no	—
114	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
115	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
116	C₄×C₅×Dic₃	—	2	1	no	—
117	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
118	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
119	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
120	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
121	C₅×D₂₄	—	2	2	no	—
122	#5690	C₂×C₅	1	1	yes	characteristic, complemented
123	#5681	C₂×C₅	1	1	yes	characteristic, complemented
124	C₃×#488	C₂×C₅	1	1	yes	characteristic, complemented
125	#5066	C₂×C₅	1	1	yes	characteristic, complemented
126	#5057	C₂×C₅	1	1	yes	characteristic, complemented
127	#4819	C₂×C₅	1	1	yes	characteristic, complemented
128	#4800	C₂×C₅	1	1	yes	characteristic, complemented
129	#4793	C₂×C₅	1	1	yes	characteristic, complemented
130	#4788	C₂×C₅	1	1	yes	characteristic, complemented
131	#4786	C₂×C₅	1	1	yes	characteristic
132	#4766	C₂×C₅	1	1	yes	characteristic, complemented
133	#4760	C₂×C₅	1	1	yes	characteristic, complemented
134	#4756	C₂×C₅	1	1	yes	characteristic, complemented
135	C₄×D₂₄	C₂×C₅	1	1	yes	characteristic, complemented
136	C₈×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
137	C₂×C₅×SD₁₆	—	3	1	no	—
138	C₂×C₅×D₈	—	3	1	no	—
139	C₂×C₅×D₈	—	3	1	no	—
140	C₅×C₄⋊Q₈	—	3	1	no	—
141	C₅×#127	—	3	1	no	—
142	C₅×#125	—	3	1	no	—
143	C₅×#125	C₂×D₃	1	1	yes	characteristic
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	—	3	1	no	—
159	C₄×C₅×D₄	—	6	1	no	—
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	—	3	1	no	—
167	C₅×#103	—	3	1	no	—
168	C₅×#103	C₂×D₃	1	1	yes	characteristic
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	C₂×D₃	1	1	yes	characteristic
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	C₂×D₃	1	1	yes	characteristic
180	#3361	—	3	1	no	Sylow
181	C₂³×C₃×C₅	—	2	1	no	—
182	C₂²×C₅×D₃	—	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	C₂×C₃×C₄×C₅	—	2	1	no	—
189	C₂×C₃×C₄×C₅	—	2	1	no	—
190	C₂×C₃×C₄×C₅	—	2	1	no	—
191	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
192	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
193	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
194	C₅×#67	—	4	2	no	—
195	C₅×#67	—	8	1	no	—
196	C₂×C₅×Dic₃	—	2	1	no	—
197	C₂×C₅×Dic₃	—	2	1	no	—
198	C₂×C₅×Dic₃	—	8	1	no	—
199	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
200	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
201	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
202	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
203	C₅×D₁₂	—	2	1	no	—
204	C₅×D₁₂	—	2	1	no	—
205	C₅×D₁₂	—	2	1	no	—
206	C₅×D₁₂	#41	1	2	yes	—
207	C₄×C₅×D₃	—	4	2	no	—
208	C₄×C₅×D₃	—	8	1	no	—
209	C₄×C₅×D₃	—	8	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	C₃×#125	C₂²×C₅	1	1	yes	characteristic
218	C₃×#124	C₂²×C₅	1	1	yes	characteristic
219	#947	C₂²×C₅	1	1	yes	characteristic
220	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
221	C₂×#215	C₂²×C₅	1	1	yes	characteristic
222	#940	C₂²×C₅	1	1	yes	characteristic
223	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
224	C₂×#213	C₂²×C₅	1	1	yes	characteristic
225	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
226	#897	—	2	1	no	—
227	#896	—	2	1	no	—
228	#896	—	2	1	no	—
229	#893	C₂²×C₅	1	1	yes	characteristic
230	#893	C₂²×C₅	1	1	yes	characteristic
231	D₃×C₄⋊C₄	—	2	1	no	—
232	#890	C₂²×C₅	1	1	yes	characteristic
233	#888	C₂²×C₅	1	1	yes	characteristic
234	#886	—	2	1	no	—
235	#885	—	2	1	no	—
236	#883	—	2	1	no	—
237	#67⋊C₄	—	2	1	no	—
238	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
239	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
240	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
241	C₃×#103	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	C₃×#102	C₂²×C₅	1	1	yes	characteristic
245	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
246	#835	C₂²×C₅	1	1	yes	characteristic
247	#832	C₂²×C₅	1	1	yes	characteristic
248	#821	C₂²×C₅	1	1	yes	characteristic
249	#821	C₂²×C₅	1	1	yes	characteristic
250	#818	C₂²×C₅	1	1	yes	characteristic
251	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
252	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
253	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
254	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
255	#809	C₂²×C₅	1	1	yes	characteristic
256	#809	C₂²×C₅	1	1	yes	characteristic
257	#808	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	—	3	1	no	—
265	C₂×C₅×D₄	—	6	1	no	—
266	C₂×C₅×D₄	—	6	1	no	—
267	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
268	C₂²×C₄×C₅	—	6	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	—	6	2	no	—
274	C₅×D₈	—	6	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	—	2	1	no	—
281	C₅×C₄⋊C₄	—	2	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	—	3	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	C₂²×D₃	1	1	yes	characteristic
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	—	6	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	C₅×D₃	1	1	yes	characteristic, complemented
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	—	3	1	no	—
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	—	4	1	no	—
322	C₂²×C₃×C₅	—	4	1	no	—
323	C₂²×C₃×C₅	—	4	1	no	—
324	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₅×D₃	—	2	2	no	—
326	C₂×C₅×D₃	—	4	1	no	—
327	C₂×C₅×D₃	—	4	1	no	—
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	—	4	1	no	—
336	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
337	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
338	C₅×Dic₃	—	2	1	no	—
339	C₅×Dic₃	—	2	1	no	—
340	C₅×Dic₃	—	2	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×#67	—	2	1	no	—
347	C₂×#67	—	2	1	no	—
348	C₂²×Dic₃	—	2	1	no	—
349	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
350	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
351	C₂×C₄×D₃	—	2	1	no	—
352	C₂×C₄×D₃	—	2	1	no	—
353	C₂×C₄×D₃	—	2	1	no	—
354	C₂×C₄×D₃	—	2	1	no	—
355	C₂×Dic₆	—	2	1	no	—
356	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
357	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
358	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
359	C₃×C₄⋊C₄	—	2	1	no	—
360	C₃×C₄⋊C₄	—	2	1	no	—
361	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
362	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	#215	—	2	2	no	—
368	#213	—	2	2	no	—
369	(C₂×D₃)⋊C₄	—	2	1	no	—
370	(C₂×D₃)⋊C₄	—	2	1	no	—
371	(C₂×D₃)⋊C₄	—	2	1	no	—
372	(C₂×D₃)⋊C₄	—	2	1	no	—
373	(C₂×D₃)⋊C₄	—	2	1	no	—
374	(C₂×D₃)⋊C₄	—	2	1	no	—
375	C₄⋊Dic₃	—	2	1	no	—
376	C₄⋊Dic₃	—	2	1	no	—
377	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
378	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
379	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
380	Dic₃⋊C₄	—	2	1	no	—
381	Dic₃⋊C₄	—	2	1	no	—
382	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
383	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
384	C₄×Dic₃	—	2	1	no	—
385	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
386	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
387	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
388	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
389	D₂₄	—	2	2	no	—
390	C₂³×C₅	—	2	1	no	—
391	C₂³×C₅	—	6	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	—	3	2	no	—
400	C₅×D₄	—	6	1	no	—
401	C₅×D₄	—	6	1	no	—
402	C₅×D₄	—	6	1	no	—
403	C₅×D₄	—	12	2	no	—
404	C₅×D₄	—	24	1	no	—
405	C₂×C₄×C₅	—	2	1	no	—
406	C₂×C₄×C₅	—	2	1	no	—
407	C₂×C₄×C₅	—	2	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	—	3	1	no	—
412	C₂×C₄×C₅	—	6	1	no	—
413	C₂×C₄×C₅	—	6	1	no	—
414	C₂×C₄×C₅	—	12	2	no	—
415	C₂×C₄×C₅	—	24	1	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	—	3	1	no	—
427	C₂×D₈	—	3	1	no	—
428	C₂×D₈	—	3	1	no	—
429	C₄⋊Q₈	—	3	1	no	—
430	#127	—	3	1	no	—
431	#125	—	3	1	no	—
432	#125	C₂×C₅×D₃	1	1	yes	characteristic
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	—	3	1	no	—
448	C₄×D₄	—	6	1	no	—
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	—	3	1	no	—
456	#103	—	3	1	no	—
457	#103	C₂×C₅×D₃	1	1	yes	characteristic
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	C₂×C₅×D₃	1	1	yes	characteristic
465	#102	C₂×C₅×D₃	1	1	yes	characteristic
466	C₄×C₈	—	3	1	no	—
467	C₄×C₈	—	3	1	no	—
468	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
469	C₂×C₃×C₅	—	8	1	no	—
470	C₂×C₃×C₅	#548	1	1	yes	characteristic
471	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
472	C₂×C₃×C₅	#576	1	1	yes	characteristic
473	C₅×D₃	—	4	2	no	—
474	C₅×D₃	—	8	1	no	—
475	C₂³×C₃	—	2	1	no	—
476	C₂²×D₃	—	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	C₂×C₃×C₄	—	2	1	no	—
483	C₂×C₃×C₄	—	2	1	no	—
484	C₂×C₃×C₄	—	2	1	no	—
485	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
486	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
487	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
488	#67	—	4	2	no	—
489	#67	—	8	1	no	—
490	C₂×Dic₃	—	2	1	no	—
491	C₂×Dic₃	—	2	1	no	—
492	C₂×Dic₃	—	8	1	no	—
493	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
494	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
495	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
496	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
497	D₁₂	—	2	1	no	—
498	D₁₂	—	2	1	no	—
499	D₁₂	—	2	1	no	—
500	D₁₂	C₅×#41	1	2	yes	—
501	C₄×D₃	—	4	2	no	—
502	C₄×D₃	—	8	1	no	—
503	C₄×D₃	—	8	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	—	4	1	no	—
512	C₂²×C₅	—	4	1	no	—
513	C₂²×C₅	—	4	1	no	—
514	C₂²×C₅	—	6	2	no	—
515	C₂²×C₅	—	12	1	no	—
516	C₂²×C₅	—	12	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	—	4	1	no	—
527	C₄×C₅	—	6	1	no	—
528	C₄×C₅	—	6	1	no	—
529	C₄×C₅	—	6	1	no	—
530	C₄×C₅	—	12	1	no	—
531	C₄×C₅	—	12	1	no	—
532	C₄×C₅	D₃×#41	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	—	3	1	no	—
539	C₂×D₄	—	6	1	no	—
540	C₂×D₄	—	6	1	no	—
541	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
542	C₂²×C₄	—	6	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	—	6	2	no	—
548	D₈	—	6	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	—	2	1	no	—
555	C₄⋊C₄	—	2	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	—	3	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	C₂²×C₅×D₃	1	1	yes	characteristic
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	—	6	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	—	4	1	no	—
582	C₂²×C₃	—	4	1	no	—
583	C₂²×C₃	—	4	1	no	—
584	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
585	C₂×D₃	—	2	2	no	—
586	C₂×D₃	—	4	1	no	—
587	C₂×D₃	—	4	1	no	—
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	—	4	1	no	—
596	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
597	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
598	Dic₃	—	2	1	no	—
599	Dic₃	—	2	1	no	—
600	Dic₃	—	2	1	no	—
601	Dic₃	—	4	1	no	—
602	Dic₃	—	4	1	no	—
603	Dic₃	C₅×#135	1	2	yes	—
604	C₂×C₅	—	8	1	no	—
605	C₂×C₅	—	12	2	no	—
606	C₂×C₅	—	24	1	no	—
607	C₂×C₅	#5677	1	1	yes	characteristic
608	C₂×C₅	D₃×#135	1	1	yes	characteristic
609	C₂×C₅	#5769	1	1	yes	characteristic
610	C₂³	—	2	1	no	—
611	C₂³	—	6	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	—	3	2	no	—
620	D₄	—	6	1	no	—
621	D₄	—	6	1	no	—
622	D₄	—	6	1	no	—
623	D₄	—	12	2	no	—
624	D₄	—	24	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	3	1	no	—
629	C₂×C₄	—	3	1	no	—
630	C₂×C₄	—	3	1	no	—
631	C₂×C₄	—	3	1	no	—
632	C₂×C₄	—	6	1	no	—
633	C₂×C₄	—	6	1	no	—
634	C₂×C₄	—	12	2	no	—
635	C₂×C₄	—	24	1	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	—	8	1	no	—
647	C₂×C₃	C₅×#548	1	1	yes	characteristic
648	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
649	C₂×C₃	C₅×#576	1	1	yes	characteristic
650	D₃	—	4	2	no	—
651	D₃	—	8	1	no	—
652	C₅	#81633	1	1	yes	characteristic, direct product factor, Sylow
653	C₂²	—	4	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	6	2	no	—
657	C₂²	—	12	1	no	—
658	C₂²	—	12	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	—	4	1	no	—
669	C₄	—	6	1	no	—
670	C₄	—	6	1	no	—
671	C₄	—	6	1	no	—
672	C₄	—	12	1	no	—
673	C₄	—	12	1	no	—
674	C₄	C₅×D₃×#41	1	1	yes	characteristic
675	C₄	C₅×#1010	1	1	yes	characteristic
676	C₃	C₅×#3361	1	1	yes	characteristic, complemented, Sylow
677	C₂	—	8	1	no	—
678	C₂	—	12	2	no	—
679	C₂	—	24	1	no	—
680	C₂	C₅×#5677	1	1	yes	characteristic
681	C₂	C₅×D₃×#135	1	1	yes	characteristic
682	C₂	C₅×#5769	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×#488	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#4786	C₂
hypercenter	C₅×#488	D₃
hypocenter	C₃	C₅×#3361
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#488

Complements

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

N	H ≅ G/N	type
1. C₅×#5690	C₂	semidirect
2. C₅×#5681	C₂	semidirect
3. C₃×C₅×#488	C₂	semidirect
4. C₅×#5066	C₂	semidirect
5. C₅×#5057	C₂	semidirect
6. C₅×#4819	C₂	semidirect
7. C₅×#4800	C₂	semidirect
8. C₅×#4793	C₂	semidirect
9. C₅×#4788	C₂	semidirect
11. C₅×#4766	C₂	semidirect
12. C₅×#4760	C₂	semidirect
13. C₅×#4756	C₂	semidirect
14. C₄×C₅×D₂₄	C₂	semidirect
15. C₅×C₈×Dic₆	C₂	semidirect
60. #81633	C₅	direct (N × H)
64. C₅×#488	D₃	semidirect
122. #5690	C₂×C₅	semidirect
123. #5681	C₂×C₅	semidirect
124. C₃×#488	C₂×C₅	semidirect
125. #5066	C₂×C₅	semidirect
126. #5057	C₂×C₅	semidirect
127. #4819	C₂×C₅	semidirect
128. #4800	C₂×C₅	semidirect
129. #4793	C₂×C₅	semidirect
130. #4788	C₂×C₅	semidirect
132. #4766	C₂×C₅	semidirect
133. #4760	C₂×C₅	semidirect
134. #4756	C₂×C₅	semidirect
135. C₄×D₂₄	C₂×C₅	semidirect
136. C₈×Dic₆	C₂×C₅	semidirect
309. #488	C₅×D₃	semidirect
580. C₃×C₅	#3361	semidirect
652. C₅	#81633	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×#5690	2
C₅×#5681	2
C₃×C₅×#488	2
C₅×#5066	2
C₅×#5057	2
C₅×#4819	2
C₅×#4800	2
C₅×#4793	2
C₅×#4788	2
C₅×#4786	2
C₅×#4766	2
C₅×#4760	2
C₅×#4756	2
C₄×C₅×D₂₄	2
C₅×C₈×Dic₆	2
C₅×#3361	3
#81633	5

Subgroups — C5×#81633 #14471747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81633 #14471747