Subgroups — C₅×#81352 #14435568

Order 1920.

812 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5603	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5521	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#482	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5036	C₂	1	1	yes	maximal, characteristic
5	C₅×#4996	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4890	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4889	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4870	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4852	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4787	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4785	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4756	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4731	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4720	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3118	—	3	1	no	maximal, Hall
17	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
18	C₃×C₅×#121	C₂²	1	1	yes	characteristic
19	C₃×C₅×#117	C₂²	1	1	yes	characteristic
20	C₅×#936	—	2	1	no	—
21	C₅×#936	C₂²	1	1	yes	characteristic, complemented
22	C₅×#935	—	2	1	no	—
23	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₅×#213	C₂²	1	1	yes	characteristic
25	C₂×C₅×#213	C₂²	1	1	yes	characteristic
26	C₅×#926	C₂²	1	1	yes	characteristic
27	C₅×#924	C₂²	1	1	yes	characteristic
28	C₂×C₅×#204	C₂²	1	1	yes	characteristic
29	C₂×C₅×#204	C₂²	1	1	yes	characteristic
30	C₅×#893	C₂²	1	1	yes	characteristic
31	C₅×#893	C₂²	1	1	yes	characteristic
32	C₅×#893	C₂²	1	1	yes	characteristic
33	C₅×#893	C₂²	1	1	yes	characteristic
34	C₅×#888	C₂²	1	1	yes	characteristic, complemented
35	C₅×#887	C₂²	1	1	yes	characteristic, complemented
36	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
37	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
38	C₅×#879	—	2	1	no	—
39	C₅×#878	—	2	1	no	—
40	C₄×C₅×D₁₂	—	2	1	no	—
41	C₄×C₅×D₁₂	—	2	1	no	—
42	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
43	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₅×#830	C₂²	1	1	yes	characteristic
48	C₅×#821	C₂²	1	1	yes	characteristic
49	C₅×#821	C₂²	1	1	yes	characteristic
50	C₅×#815	C₂²	1	1	yes	characteristic, complemented
51	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
54	C₅×#810	C₂²	1	1	yes	characteristic, complemented
55	C₅×#810	C₂²	1	1	yes	characteristic, complemented
56	C₅×#809	C₂²	1	1	yes	characteristic
57	C₅×#809	C₂²	1	1	yes	characteristic
58	C₅×#808	C₂²	1	1	yes	characteristic, complemented
59	C₅×#807	C₂²	1	1	yes	characteristic, complemented
60	#81352	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#542	—	3	1	no	—
62	C₅×#518	—	3	1	no	—
63	C₅×#485	—	3	1	no	—
64	C₅×#482	D₃	1	1	yes	characteristic, complemented
65	C₅×#476	—	3	1	no	—
66	C₅×#474	—	3	1	no	—
67	C₅×#463	—	3	1	no	—
68	C₅×#463	—	3	1	no	—
69	C₅×#450	—	3	1	no	—
70	C₅×#447	—	3	1	no	—
71	C₅×#442	—	3	1	no	—
72	C₅×#440	—	3	1	no	—
73	C₄×C₅×SD₁₆	—	3	1	no	—
74	C₄×C₅×D₈	—	3	1	no	—
75	C₅×#433	—	3	1	no	—
76	C₂³×C₅×D₃	—	2	1	no	—
77	C₂×C₃×C₅×D₄	—	2	1	no	—
78	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₅×Dic₃	—	2	1	no	—
81	C₂×C₅×D₁₂	—	2	1	no	—
82	C₂×C₅×D₁₂	—	2	2	no	—
83	C₂×C₅×D₁₂	—	2	2	no	—
84	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
85	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
86	C₂×C₄×C₅×D₃	—	2	1	no	—
87	C₂×C₄×C₅×D₃	—	2	1	no	—
88	C₂×C₄×C₅×D₃	—	2	1	no	—
89	C₂×C₄×C₅×D₃	—	2	1	no	—
90	C₂×C₅×Dic₆	—	2	1	no	—
91	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
94	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
98	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
99	C₃×C₄²×C₅	—	2	1	no	—
100	C₅×#217	—	2	1	no	—
101	C₅×#217	—	2	1	no	—
102	C₅×#217	—	2	1	no	—
103	C₅×#217	—	2	1	no	—
104	C₅×#217	D₄	1	1	yes	characteristic
105	C₅×#217	D₄	1	1	yes	characteristic
106	C₅×#213	—	2	2	no	—
107	C₅×#213	—	2	2	no	—
108	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
109	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
110	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
111	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
112	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
113	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
114	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
115	C₅×Dic₃⋊C₄	—	2	1	no	—
116	C₅×Dic₃⋊C₄	—	2	1	no	—
117	C₅×Dic₃⋊C₄	—	2	1	no	—
118	C₄×C₅×Dic₃	—	2	1	no	—
119	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
120	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
121	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
122	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
123	C₅×#204	—	2	2	no	—
124	C₅×#204	—	2	2	no	—
125	#5603	C₂×C₅	1	1	yes	characteristic, complemented
126	#5521	C₂×C₅	1	1	yes	characteristic, complemented
127	C₃×#482	C₂×C₅	1	1	yes	characteristic, complemented
128	#5036	C₂×C₅	1	1	yes	characteristic
129	#4996	C₂×C₅	1	1	yes	characteristic, complemented
130	#4890	C₂×C₅	1	1	yes	characteristic, complemented
131	#4889	C₂×C₅	1	1	yes	characteristic, complemented
132	#4870	C₂×C₅	1	1	yes	characteristic, complemented
133	#4852	C₂×C₅	1	1	yes	characteristic, complemented
134	#4787	C₂×C₅	1	1	yes	characteristic, complemented
135	#4787	C₂×C₅	1	1	yes	characteristic, complemented
136	#4785	C₂×C₅	1	1	yes	characteristic, complemented
137	#4756	C₂×C₅	1	1	yes	characteristic, complemented
138	#4731	C₂×C₅	1	1	yes	characteristic, complemented
139	#4720	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂²×C₅×D₄	—	3	1	no	—
141	C₂×C₅×SD₁₆	—	3	1	no	—
142	C₂×C₅×SD₁₆	—	3	1	no	—
143	C₂×C₅×D₈	—	3	1	no	—
144	C₂×C₅×D₈	—	3	1	no	—
145	C₅×C₄⋊Q₈	—	3	1	no	—
146	C₅×#126	—	6	1	no	—
147	C₅×#124	—	3	1	no	—
148	C₅×#124	—	6	1	no	—
149	C₅×#123	—	6	1	no	—
150	C₅×C₂²⋊Q₈	—	3	1	no	—
151	C₅×C₂²⋊Q₈	—	6	1	no	—
152	C₅×#121	C₂×D₃	1	1	yes	characteristic
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	C₄×C₅×D₄	—	6	1	no	—
161	C₅×#117	—	3	1	no	—
162	C₅×#117	C₂×D₃	1	1	yes	characteristic
163	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
164	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
165	C₅×#107	—	3	1	no	—
166	C₅×#107	C₂×D₃	1	1	yes	characteristic, complemented
167	C₅×#106	—	3	1	no	—
168	C₅×#106	C₂×D₃	1	1	yes	characteristic, complemented
169	C₅×C₄⋊C₈	—	3	1	no	—
170	C₅×C₄⋊C₈	—	3	1	no	—
171	C₅×#103	—	3	1	no	—
172	C₅×#103	—	3	1	no	—
173	C₅×#102	—	3	1	no	—
174	C₅×#102	—	3	1	no	—
175	C₅×#102	—	3	1	no	—
176	C₅×#102	—	3	1	no	—
177	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
178	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
179	C₅×C₂²⋊C₈	—	3	1	no	—
180	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
181	C₅×#97	—	3	1	no	—
182	C₄×C₅×C₈	—	3	1	no	—
183	#3118	—	3	1	no	Sylow
184	C₂³×C₃×C₅	—	2	1	no	—
185	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₅×D₃	—	2	1	no	—
187	C₂²×C₅×D₃	—	2	1	no	—
188	C₂²×C₅×D₃	—	2	4	no	—
189	C₂²×C₅×D₃	—	8	1	no	—
190	C₂²×C₅×D₃	—	8	1	no	—
191	C₃×C₅×D₄	—	2	1	no	—
192	C₃×C₅×D₄	—	2	1	no	—
193	C₃×C₅×D₄	—	8	1	no	—
194	C₂×C₃×C₄×C₅	—	2	1	no	—
195	C₂×C₃×C₄×C₅	—	2	1	no	—
196	C₂×C₃×C₄×C₅	—	2	1	no	—
197	C₂×C₃×C₄×C₅	—	2	1	no	—
198	C₂×C₃×C₄×C₅	—	2	1	no	—
199	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
200	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
201	C₂×C₅×Dic₃	—	2	1	no	—
202	C₂×C₅×Dic₃	—	2	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	4	no	—
209	C₅×D₁₂	—	2	1	no	—
210	C₅×D₁₂	—	2	1	no	—
211	C₅×D₁₂	#41	1	2	yes	—
212	C₅×D₁₂	#41	1	2	yes	—
213	C₄×C₅×D₃	—	8	1	no	—
214	C₄×C₅×D₃	—	8	1	no	—
215	C₄×C₅×D₃	—	8	1	no	—
216	C₄×C₅×D₃	—	8	1	no	—
217	C₅×Dic₆	—	2	1	no	—
218	C₅×Dic₆	—	2	1	no	—
219	C₅×Dic₆	—	8	1	no	—
220	C₃×C₅×C₈	—	2	1	no	—
221	C₃×C₅×C₈	—	2	1	no	—
222	C₅×C₃⋊C₈	—	2	1	no	—
223	C₅×C₃⋊C₈	—	2	1	no	—
224	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
225	C₃×#121	C₂²×C₅	1	1	yes	characteristic
226	C₃×#117	C₂²×C₅	1	1	yes	characteristic
227	#936	—	2	1	no	—
228	#936	C₂²×C₅	1	1	yes	characteristic, complemented
229	#935	—	2	1	no	—
230	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
231	C₂×#213	C₂²×C₅	1	1	yes	characteristic
232	C₂×#213	C₂²×C₅	1	1	yes	characteristic
233	#926	C₂²×C₅	1	1	yes	characteristic
234	#924	C₂²×C₅	1	1	yes	characteristic
235	C₂×#204	C₂²×C₅	1	1	yes	characteristic
236	C₂×#204	C₂²×C₅	1	1	yes	characteristic
237	#893	C₂²×C₅	1	1	yes	characteristic
238	#893	C₂²×C₅	1	1	yes	characteristic
239	#893	C₂²×C₅	1	1	yes	characteristic
240	#893	C₂²×C₅	1	1	yes	characteristic
241	#888	C₂²×C₅	1	1	yes	characteristic, complemented
242	#887	C₂²×C₅	1	1	yes	characteristic, complemented
243	D₃×C₂²⋊C₄	—	2	1	no	—
244	D₃×C₂²⋊C₄	—	2	1	no	—
245	#879	—	2	1	no	—
246	#878	—	2	1	no	—
247	C₄×D₁₂	—	2	1	no	—
248	C₄×D₁₂	—	2	1	no	—
249	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
250	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
251	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
252	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
253	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
254	#830	C₂²×C₅	1	1	yes	characteristic
255	#821	C₂²×C₅	1	1	yes	characteristic
256	#821	C₂²×C₅	1	1	yes	characteristic
257	#815	C₂²×C₅	1	1	yes	characteristic, complemented
258	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
259	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
261	#810	C₂²×C₅	1	1	yes	characteristic, complemented
262	#810	C₂²×C₅	1	1	yes	characteristic, complemented
263	#809	C₂²×C₅	1	1	yes	characteristic
264	#809	C₂²×C₅	1	1	yes	characteristic
265	#808	C₂²×C₅	1	1	yes	characteristic, complemented
266	#807	C₂²×C₅	1	1	yes	characteristic, complemented
267	C₂⁴×C₅	—	6	1	no	—
268	C₂×C₅×Q₈	—	3	1	no	—
269	C₂×C₅×Q₈	—	6	1	no	—
270	C₂×C₅×D₄	—	2	1	no	—
271	C₂×C₅×D₄	—	3	1	no	—
272	C₂×C₅×D₄	—	3	1	no	—
273	C₂×C₅×D₄	—	6	2	no	—
274	C₂×C₅×D₄	—	6	2	no	—
275	C₂×C₅×D₄	—	6	1	no	—
276	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
277	C₂²×C₄×C₅	—	6	1	no	—
278	C₂²×C₄×C₅	—	6	1	no	—
279	C₂²×C₄×C₅	—	6	1	no	—
280	C₂²×C₄×C₅	—	6	1	no	—
281	C₂²×C₄×C₅	—	6	1	no	—
282	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
283	C₅×SD₁₆	—	6	2	no	—
284	C₅×SD₁₆	—	6	2	no	—
285	C₅×D₈	—	6	2	no	—
286	C₅×D₈	—	6	2	no	—
287	C₂×C₅×C₈	—	3	1	no	—
288	C₂×C₅×C₈	—	3	1	no	—
289	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
290	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
291	C₅×C₄⋊C₄	—	3	1	no	—
292	C₅×C₄⋊C₄	—	3	1	no	—
293	C₅×C₄⋊C₄	—	3	1	no	—
294	C₅×C₄⋊C₄	—	6	1	no	—
295	C₅×C₄⋊C₄	—	6	1	no	—
296	C₅×C₄⋊C₄	—	6	1	no	—
297	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
298	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
299	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
300	C₅×C₂²⋊C₄	—	2	1	no	—
301	C₅×C₂²⋊C₄	—	2	1	no	—
302	C₅×C₂²⋊C₄	—	3	1	no	—
303	C₅×C₂²⋊C₄	—	3	1	no	—
304	C₅×C₂²⋊C₄	—	6	1	no	—
305	C₅×C₂²⋊C₄	—	6	1	no	—
306	C₅×C₂²⋊C₄	—	6	1	no	—
307	C₅×C₂²⋊C₄	—	6	1	no	—
308	C₅×C₂²⋊C₄	—	6	1	no	—
309	C₅×C₂²⋊C₄	—	6	1	no	—
310	C₅×C₂²⋊C₄	—	6	1	no	—
311	C₅×C₂²⋊C₄	—	6	1	no	—
312	C₄²×C₅	—	2	1	no	—
313	C₄²×C₅	—	3	1	no	—
314	C₄²×C₅	—	3	1	no	—
315	C₄²×C₅	—	6	1	no	—
316	#542	—	3	1	no	—
317	#518	—	3	1	no	—
318	#485	—	3	1	no	—
319	#482	C₅×D₃	1	1	yes	characteristic, complemented
320	#476	—	3	1	no	—
321	#474	—	3	1	no	—
322	#463	—	3	1	no	—
323	#463	—	3	1	no	—
324	#450	—	3	1	no	—
325	#447	—	3	1	no	—
326	#442	—	3	1	no	—
327	#440	—	3	1	no	—
328	C₄×SD₁₆	—	3	1	no	—
329	C₄×D₈	—	3	1	no	—
330	#433	—	3	1	no	—
331	C₂²×C₃×C₅	—	2	1	no	—
332	C₂²×C₃×C₅	—	2	1	no	—
333	C₂²×C₃×C₅	—	2	1	no	—
334	C₂²×C₃×C₅	—	4	1	no	—
335	C₂²×C₃×C₅	—	4	1	no	—
336	C₂²×C₃×C₅	—	4	1	no	—
337	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₅×D₃	—	2	2	no	—
339	C₂×C₅×D₃	—	2	2	no	—
340	C₂×C₅×D₃	—	4	1	no	—
341	C₂×C₅×D₃	—	4	1	no	—
342	C₂×C₅×D₃	—	4	1	no	—
343	C₂×C₅×D₃	—	4	1	no	—
344	C₂×C₅×D₃	—	8	4	no	—
345	C₃×C₄×C₅	—	2	1	no	—
346	C₃×C₄×C₅	—	4	1	no	—
347	C₃×C₄×C₅	—	4	1	no	—
348	C₃×C₄×C₅	—	4	1	no	—
349	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
350	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
351	C₅×Dic₃	—	2	1	no	—
352	C₅×Dic₃	—	2	1	no	—
353	C₅×Dic₃	—	2	1	no	—
354	C₅×Dic₃	—	2	1	no	—
355	C₅×Dic₃	—	4	1	no	—
356	C₅×Dic₃	—	4	1	no	—
357	C₂³×D₃	—	2	1	no	—
358	C₂×C₃×D₄	—	2	1	no	—
359	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
360	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
361	C₂²×Dic₃	—	2	1	no	—
362	C₂×D₁₂	—	2	1	no	—
363	C₂×D₁₂	—	2	2	no	—
364	C₂×D₁₂	—	2	2	no	—
365	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
366	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
367	C₂×C₄×D₃	—	2	1	no	—
368	C₂×C₄×D₃	—	2	1	no	—
369	C₂×C₄×D₃	—	2	1	no	—
370	C₂×C₄×D₃	—	2	1	no	—
371	C₂×Dic₆	—	2	1	no	—
372	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
373	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
374	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
375	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
376	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
377	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
378	C₃×C₂²⋊C₄	—	2	1	no	—
379	C₃×C₂²⋊C₄	—	2	1	no	—
380	C₃×C₄²	—	2	1	no	—
381	#217	—	2	1	no	—
382	#217	—	2	1	no	—
383	#217	—	2	1	no	—
384	#217	—	2	1	no	—
385	#217	C₅×D₄	1	1	yes	characteristic
386	#217	C₅×D₄	1	1	yes	characteristic
387	#213	—	2	2	no	—
388	#213	—	2	2	no	—
389	(C₂×D₃)⋊C₄	—	2	1	no	—
390	(C₂×D₃)⋊C₄	—	2	1	no	—
391	(C₂×D₃)⋊C₄	—	2	1	no	—
392	(C₂×D₃)⋊C₄	—	2	1	no	—
393	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
394	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
395	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
396	Dic₃⋊C₄	—	2	1	no	—
397	Dic₃⋊C₄	—	2	1	no	—
398	Dic₃⋊C₄	—	2	1	no	—
399	C₄×Dic₃	—	2	1	no	—
400	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
401	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
402	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
403	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
404	#204	—	2	2	no	—
405	#204	—	2	2	no	—
406	C₂³×C₅	—	2	1	no	—
407	C₂³×C₅	—	6	4	no	—
408	C₂³×C₅	—	6	1	no	—
409	C₂³×C₅	—	6	1	no	—
410	C₂³×C₅	—	24	1	no	—
411	C₂³×C₅	—	24	1	no	—
412	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
413	C₅×Q₈	—	6	1	no	—
414	C₅×Q₈	—	6	1	no	—
415	C₅×Q₈	—	24	1	no	—
416	C₅×D₄	—	2	1	no	—
417	C₅×D₄	—	2	1	no	—
418	C₅×D₄	—	3	2	no	—
419	C₅×D₄	—	3	2	no	—
420	C₅×D₄	—	6	4	no	—
421	C₅×D₄	—	6	1	no	—
422	C₅×D₄	—	6	1	no	—
423	C₅×D₄	—	8	1	no	—
424	C₂×C₄×C₅	—	2	1	no	—
425	C₂×C₄×C₅	—	2	1	no	—
426	C₂×C₄×C₅	—	2	1	no	—
427	C₂×C₄×C₅	—	2	1	no	—
428	C₂×C₄×C₅	—	2	1	no	—
429	C₂×C₄×C₅	—	3	1	no	—
430	C₂×C₄×C₅	—	3	1	no	—
431	C₂×C₄×C₅	—	3	1	no	—
432	C₂×C₄×C₅	—	3	1	no	—
433	C₂×C₄×C₅	—	6	1	no	—
434	C₂×C₄×C₅	—	6	1	no	—
435	C₂×C₄×C₅	—	24	1	no	—
436	C₂×C₄×C₅	—	24	1	no	—
437	C₂×C₄×C₅	—	24	1	no	—
438	C₂×C₄×C₅	—	24	1	no	—
439	C₂×C₄×C₅	—	24	1	no	—
440	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
441	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
442	C₅×C₈	—	2	1	no	—
443	C₅×C₈	—	2	1	no	—
444	C₅×C₈	—	6	1	no	—
445	C₅×C₈	—	6	1	no	—
446	C₂²×D₄	—	3	1	no	—
447	C₂×SD₁₆	—	3	1	no	—
448	C₂×SD₁₆	—	3	1	no	—
449	C₂×D₈	—	3	1	no	—
450	C₂×D₈	—	3	1	no	—
451	C₄⋊Q₈	—	3	1	no	—
452	#126	—	6	1	no	—
453	#124	—	3	1	no	—
454	#124	—	6	1	no	—
455	#123	—	6	1	no	—
456	C₂²⋊Q₈	—	3	1	no	—
457	C₂²⋊Q₈	—	6	1	no	—
458	#121	C₂×C₅×D₃	1	1	yes	characteristic
459	C₄×Q₈	—	3	1	no	—
460	C₄×D₄	—	3	1	no	—
461	C₄×D₄	—	3	1	no	—
462	C₄×D₄	—	3	1	no	—
463	C₄×D₄	—	3	1	no	—
464	C₄×D₄	—	3	1	no	—
465	C₄×D₄	—	6	1	no	—
466	C₄×D₄	—	6	1	no	—
467	#117	—	3	1	no	—
468	#117	C₂×C₅×D₃	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	—	6	1	no	—
470	C₂×C₂²⋊C₄	—	6	1	no	—
471	#107	—	3	1	no	—
472	#107	C₂×C₅×D₃	1	1	yes	characteristic, complemented
473	#106	—	3	1	no	—
474	#106	C₂×C₅×D₃	1	1	yes	characteristic, complemented
475	C₄⋊C₈	—	3	1	no	—
476	C₄⋊C₈	—	3	1	no	—
477	#103	—	3	1	no	—
478	#103	—	3	1	no	—
479	#102	—	3	1	no	—
480	#102	—	3	1	no	—
481	#102	—	3	1	no	—
482	#102	—	3	1	no	—
483	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
484	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
485	C₂²⋊C₈	—	3	1	no	—
486	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
487	#97	—	3	1	no	—
488	C₄×C₈	—	3	1	no	—
489	C₂×C₃×C₅	—	4	1	no	—
490	C₂×C₃×C₅	—	8	1	no	—
491	C₂×C₃×C₅	#525	1	1	yes	characteristic
492	C₂×C₃×C₅	#576	1	1	yes	characteristic
493	C₂×C₃×C₅	#577	1	1	yes	characteristic
494	C₅×D₃	—	4	2	no	—
495	C₅×D₃	—	4	2	no	—
496	C₂³×C₃	—	2	1	no	—
497	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
498	C₂²×D₃	—	2	1	no	—
499	C₂²×D₃	—	2	1	no	—
500	C₂²×D₃	—	2	4	no	—
501	C₂²×D₃	—	8	1	no	—
502	C₂²×D₃	—	8	1	no	—
503	C₃×D₄	—	2	1	no	—
504	C₃×D₄	—	2	1	no	—
505	C₃×D₄	—	8	1	no	—
506	C₂×C₃×C₄	—	2	1	no	—
507	C₂×C₃×C₄	—	2	1	no	—
508	C₂×C₃×C₄	—	2	1	no	—
509	C₂×C₃×C₄	—	2	1	no	—
510	C₂×C₃×C₄	—	2	1	no	—
511	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
512	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
513	C₂×Dic₃	—	2	1	no	—
514	C₂×Dic₃	—	2	1	no	—
515	C₂×Dic₃	—	8	1	no	—
516	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
517	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
518	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
519	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
520	D₁₂	—	2	4	no	—
521	D₁₂	—	2	1	no	—
522	D₁₂	—	2	1	no	—
523	D₁₂	C₅×#41	1	2	yes	—
524	D₁₂	C₅×#41	1	2	yes	—
525	C₄×D₃	—	8	1	no	—
526	C₄×D₃	—	8	1	no	—
527	C₄×D₃	—	8	1	no	—
528	C₄×D₃	—	8	1	no	—
529	Dic₆	—	2	1	no	—
530	Dic₆	—	2	1	no	—
531	Dic₆	—	8	1	no	—
532	C₃×C₈	—	2	1	no	—
533	C₃×C₈	—	2	1	no	—
534	C₃⋊C₈	—	2	1	no	—
535	C₃⋊C₈	—	2	1	no	—
536	C₂²×C₅	—	2	1	no	—
537	C₂²×C₅	—	2	1	no	—
538	C₂²×C₅	—	2	1	no	—
539	C₂²×C₅	—	4	1	no	—
540	C₂²×C₅	—	4	1	no	—
541	C₂²×C₅	—	4	1	no	—
542	C₂²×C₅	—	6	2	no	—
543	C₂²×C₅	—	6	2	no	—
544	C₂²×C₅	—	12	1	no	—
545	C₂²×C₅	—	12	1	no	—
546	C₂²×C₅	—	12	1	no	—
547	C₂²×C₅	—	12	1	no	—
548	C₂²×C₅	—	24	4	no	—
549	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
550	C₄×C₅	—	2	1	no	—
551	C₄×C₅	—	4	1	no	—
552	C₄×C₅	—	4	1	no	—
553	C₄×C₅	—	4	1	no	—
554	C₄×C₅	—	6	1	no	—
555	C₄×C₅	—	6	1	no	—
556	C₄×C₅	—	6	1	no	—
557	C₄×C₅	—	6	1	no	—
558	C₄×C₅	—	12	1	no	—
559	C₄×C₅	—	12	1	no	—
560	C₄×C₅	D₃×#41	1	1	yes	characteristic
561	C₄×C₅	D₃×#41	1	1	yes	characteristic
562	C₂⁴	—	6	1	no	—
563	C₂×Q₈	—	3	1	no	—
564	C₂×Q₈	—	6	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	3	1	no	—
567	C₂×D₄	—	3	1	no	—
568	C₂×D₄	—	6	2	no	—
569	C₂×D₄	—	6	2	no	—
570	C₂×D₄	—	6	1	no	—
571	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
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	C₂²×C₄	—	6	1	no	—
577	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
578	SD₁₆	—	6	2	no	—
579	SD₁₆	—	6	2	no	—
580	D₈	—	6	2	no	—
581	D₈	—	6	2	no	—
582	C₂×C₈	—	3	1	no	—
583	C₂×C₈	—	3	1	no	—
584	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
585	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
586	C₄⋊C₄	—	3	1	no	—
587	C₄⋊C₄	—	3	1	no	—
588	C₄⋊C₄	—	3	1	no	—
589	C₄⋊C₄	—	6	1	no	—
590	C₄⋊C₄	—	6	1	no	—
591	C₄⋊C₄	—	6	1	no	—
592	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
593	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
594	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
595	C₂²⋊C₄	—	2	1	no	—
596	C₂²⋊C₄	—	2	1	no	—
597	C₂²⋊C₄	—	3	1	no	—
598	C₂²⋊C₄	—	3	1	no	—
599	C₂²⋊C₄	—	6	1	no	—
600	C₂²⋊C₄	—	6	1	no	—
601	C₂²⋊C₄	—	6	1	no	—
602	C₂²⋊C₄	—	6	1	no	—
603	C₂²⋊C₄	—	6	1	no	—
604	C₂²⋊C₄	—	6	1	no	—
605	C₂²⋊C₄	—	6	1	no	—
606	C₂²⋊C₄	—	6	1	no	—
607	C₄²	—	2	1	no	—
608	C₄²	—	3	1	no	—
609	C₄²	—	3	1	no	—
610	C₄²	—	6	1	no	—
611	C₃×C₅	#3118	1	1	yes	characteristic, complemented, Hall
612	C₂²×C₃	—	2	1	no	—
613	C₂²×C₃	—	2	1	no	—
614	C₂²×C₃	—	2	1	no	—
615	C₂²×C₃	—	4	1	no	—
616	C₂²×C₃	—	4	1	no	—
617	C₂²×C₃	—	4	1	no	—
618	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
619	C₂×D₃	—	2	2	no	—
620	C₂×D₃	—	2	2	no	—
621	C₂×D₃	—	4	1	no	—
622	C₂×D₃	—	4	1	no	—
623	C₂×D₃	—	4	1	no	—
624	C₂×D₃	—	4	1	no	—
625	C₂×D₃	—	8	4	no	—
626	C₃×C₄	—	2	1	no	—
627	C₃×C₄	—	4	1	no	—
628	C₃×C₄	—	4	1	no	—
629	C₃×C₄	—	4	1	no	—
630	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
631	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
632	Dic₃	—	2	1	no	—
633	Dic₃	—	2	1	no	—
634	Dic₃	—	2	1	no	—
635	Dic₃	—	2	1	no	—
636	Dic₃	—	4	1	no	—
637	Dic₃	—	4	1	no	—
638	C₂×C₅	—	4	1	no	—
639	C₂×C₅	—	8	1	no	—
640	C₂×C₅	—	12	2	no	—
641	C₂×C₅	—	12	2	no	—
642	C₂×C₅	#5656	1	1	yes	characteristic
643	C₂×C₅	#5770	1	1	yes	characteristic
644	C₂×C₅	#5774	1	1	yes	characteristic
645	C₂³	—	2	1	no	—
646	C₂³	—	6	4	no	—
647	C₂³	—	6	1	no	—
648	C₂³	—	6	1	no	—
649	C₂³	—	24	1	no	—
650	C₂³	—	24	1	no	—
651	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
652	Q₈	—	6	1	no	—
653	Q₈	—	6	1	no	—
654	Q₈	—	24	1	no	—
655	D₄	—	2	1	no	—
656	D₄	—	2	1	no	—
657	D₄	—	3	2	no	—
658	D₄	—	3	2	no	—
659	D₄	—	6	4	no	—
660	D₄	—	6	1	no	—
661	D₄	—	6	1	no	—
662	D₄	—	8	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	3	1	no	—
669	C₂×C₄	—	3	1	no	—
670	C₂×C₄	—	3	1	no	—
671	C₂×C₄	—	3	1	no	—
672	C₂×C₄	—	6	1	no	—
673	C₂×C₄	—	6	1	no	—
674	C₂×C₄	—	24	1	no	—
675	C₂×C₄	—	24	1	no	—
676	C₂×C₄	—	24	1	no	—
677	C₂×C₄	—	24	1	no	—
678	C₂×C₄	—	24	1	no	—
679	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
680	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
681	C₈	—	2	1	no	—
682	C₈	—	2	1	no	—
683	C₈	—	6	1	no	—
684	C₈	—	6	1	no	—
685	C₂×C₃	—	4	1	no	—
686	C₂×C₃	—	8	1	no	—
687	C₂×C₃	C₅×#525	1	1	yes	characteristic
688	C₂×C₃	C₅×#576	1	1	yes	characteristic
689	C₂×C₃	C₅×#577	1	1	yes	characteristic
690	D₃	—	4	2	no	—
691	D₃	—	4	2	no	—
692	C₅	#81352	1	1	yes	characteristic, direct product factor, Sylow
693	C₂²	—	2	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	6	2	no	—
700	C₂²	—	6	2	no	—
701	C₂²	—	12	1	no	—
702	C₂²	—	12	1	no	—
703	C₂²	—	12	1	no	—
704	C₂²	—	12	1	no	—
705	C₂²	—	24	4	no	—
706	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
707	C₄	—	2	1	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	1	no	—
710	C₄	—	4	1	no	—
711	C₄	—	6	1	no	—
712	C₄	—	6	1	no	—
713	C₄	—	6	1	no	—
714	C₄	—	6	1	no	—
715	C₄	—	12	1	no	—
716	C₄	—	12	1	no	—
717	C₄	C₅×D₃×#41	1	1	yes	characteristic
718	C₄	C₅×D₃×#41	1	1	yes	characteristic
719	C₃	C₅×#3118	1	1	yes	characteristic, complemented, Sylow
720	C₂	—	4	1	no	—
721	C₂	—	8	1	no	—
722	C₂	—	12	2	no	—
723	C₂	—	12	2	no	—
724	C₂	C₅×#5656	1	1	yes	characteristic
725	C₂	C₅×#5770	1	1	yes	characteristic
726	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×#482	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5036	C₂
hypercenter	C₅×#482	D₃
hypocenter	C₃	C₅×#3118
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#482

Complements

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

N	H ≅ G/N	type
1. C₅×#5603	C₂	semidirect
2. C₅×#5521	C₂	semidirect
3. C₃×C₅×#482	C₂	semidirect
5. C₅×#4996	C₂	semidirect
6. C₅×#4890	C₂	semidirect
7. C₅×#4889	C₂	semidirect
8. C₅×#4870	C₂	semidirect
9. C₅×#4852	C₂	semidirect
10. C₅×#4787	C₂	semidirect
11. C₅×#4787	C₂	semidirect
12. C₅×#4785	C₂	semidirect
13. C₅×#4756	C₂	semidirect
14. C₅×#4731	C₂	semidirect
15. C₅×#4720	C₂	semidirect
21. C₅×#936	C₂²	semidirect
23. C₅×D₄×Dic₃	C₂²	semidirect
34. C₅×#888	C₂²	semidirect
35. C₅×#887	C₂²	semidirect
42. C₃×C₅×#107	C₂²	semidirect
43. C₃×C₅×#106	C₂²	semidirect
44. C₃×C₅×#102	C₂²	semidirect
45. C₃×C₅×#102	C₂²	semidirect
50. C₅×#815	C₂²	semidirect
51. C₅×Dic₃⋊C₈	C₂²	semidirect
52. C₅×Dic₃⋊C₈	C₂²	semidirect
53. C₅×C₈×Dic₃	C₂²	semidirect
54. C₅×#810	C₂²	semidirect
55. C₅×#810	C₂²	semidirect
58. C₅×#808	C₂²	semidirect
59. C₅×#807	C₂²	semidirect
60. #81352	C₅	direct (N × H)
64. C₅×#482	D₃	semidirect
125. #5603	C₂×C₅	semidirect
126. #5521	C₂×C₅	semidirect
127. C₃×#482	C₂×C₅	semidirect
129. #4996	C₂×C₅	semidirect
130. #4890	C₂×C₅	semidirect
131. #4889	C₂×C₅	semidirect
132. #4870	C₂×C₅	semidirect
133. #4852	C₂×C₅	semidirect
134. #4787	C₂×C₅	semidirect
135. #4787	C₂×C₅	semidirect
136. #4785	C₂×C₅	semidirect
137. #4756	C₂×C₅	semidirect
138. #4731	C₂×C₅	semidirect
139. #4720	C₂×C₅	semidirect
166. C₅×#107	C₂×D₃	semidirect
168. C₅×#106	C₂×D₃	semidirect
177. C₅×#102	C₂×D₃	semidirect
178. C₅×#102	C₂×D₃	semidirect
228. #936	C₂²×C₅	semidirect
230. D₄×Dic₃	C₂²×C₅	semidirect
241. #888	C₂²×C₅	semidirect
242. #887	C₂²×C₅	semidirect
249. C₃×#107	C₂²×C₅	semidirect
250. C₃×#106	C₂²×C₅	semidirect
251. C₃×#102	C₂²×C₅	semidirect
252. C₃×#102	C₂²×C₅	semidirect
257. #815	C₂²×C₅	semidirect
258. Dic₃⋊C₈	C₂²×C₅	semidirect
259. Dic₃⋊C₈	C₂²×C₅	semidirect
260. C₈×Dic₃	C₂²×C₅	semidirect
261. #810	C₂²×C₅	semidirect
262. #810	C₂²×C₅	semidirect
265. #808	C₂²×C₅	semidirect
266. #807	C₂²×C₅	semidirect
319. #482	C₅×D₃	semidirect
472. #107	C₂×C₅×D₃	semidirect
474. #106	C₂×C₅×D₃	semidirect
483. #102	C₂×C₅×D₃	semidirect
484. #102	C₂×C₅×D₃	semidirect
611. C₃×C₅	#3118	semidirect
692. C₅	#81352	direct (N × H)
719. C₃	C₅×#3118	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5603	2
C₅×#5521	2
C₃×C₅×#482	2
C₅×#5036	2
C₅×#4996	2
C₅×#4890	2
C₅×#4889	2
C₅×#4870	2
C₅×#4852	2
C₅×#4787	2
C₅×#4785	2
C₅×#4756	2
C₅×#4731	2
C₅×#4720	2
C₅×#3118	3
#81352	5

Subgroups — C5×#81352 #14435568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81352 #14435568