Subgroups — C₅×#81620 #14471509

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5727	C₂	1	1	yes	maximal, characteristic
2	C₅×#5721	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5094	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5083	C₂	1	1	yes	maximal, characteristic
6	C₅×#4818	C₂	1	2	yes	maximal
7	C₅×#4792	C₂	1	2	yes	maximal, complemented
8	C₅×#4791	C₂	1	2	yes	maximal, complemented
9	C₅×#4788	C₂	1	2	yes	maximal
10	C₄×C₅×#204	C₂	1	1	yes	maximal, characteristic
11	C₅×C₈×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3359	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×Q₈	—	2	1	no	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₅×#946	—	2	1	no	—
17	C₅×Q₈×Dic₃	C₂²	1	2	yes	—
18	C₅×#944	C₂²	1	2	yes	—
19	C₂×C₅×#215	C₂²	1	2	yes	—
20	C₂×C₅×#204	C₂²	1	1	yes	characteristic
21	C₅×#896	—	2	2	no	—
22	C₅×#893	C₂²	1	2	yes	—
23	C₅×#890	—	2	1	no	—
24	C₅×#889	—	2	2	no	—
25	C₅×#888	C₂²	1	2	yes	—
26	C₅×#887	—	2	1	no	—
27	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
28	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
29	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
30	C₃×C₅×#103	C₂²	1	2	yes	—
31	C₃×C₅×#103	C₂²	1	2	yes	—
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₅×#835	C₂²	1	2	yes	—
34	C₅×#821	C₂²	1	1	yes	characteristic
35	C₅×#817	C₂²	1	1	yes	characteristic
36	C₅×#816	C₂²	1	1	yes	characteristic
37	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
38	C₅×C₈×Dic₃	C₂²	1	2	yes	—
39	C₅×#810	C₂²	1	2	yes	—
40	C₅×#808	C₂²	1	2	yes	—
41	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
42	#81620	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#557	—	3	1	no	—
44	C₅×D₄×Q₈	—	3	1	no	—
45	C₅×#487	—	3	2	no	—
46	C₅×#487	D₃	1	1	yes	characteristic, complemented
47	C₅×#475	—	3	2	no	—
48	C₅×#475	—	3	1	no	—
49	C₅×#461	—	3	2	no	—
50	C₅×#461	—	3	1	no	—
51	C₅×C₈×Q₈	—	3	1	no	—
52	C₄×C₅×SD₁₆	—	3	2	no	—
53	C₄×C₅×SD₁₆	—	3	1	no	—
54	C₂×C₃×C₅×Q₈	—	2	1	no	—
55	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
56	C₅×D₃×Q₈	—	4	4	no	—
57	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
58	C₂×C₄×C₅×D₃	—	2	1	no	—
59	C₂×C₄×C₅×D₃	—	2	2	no	—
60	C₂×C₅×Dic₆	—	2	2	no	—
61	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
62	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₃×C₅×C₄⋊C₄	—	2	1	no	—
66	C₃×C₅×C₄⋊C₄	—	2	1	no	—
67	C₃×C₅×C₄⋊C₄	—	2	1	no	—
68	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₅×#215	—	2	4	no	—
71	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
72	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
73	C₅×C₄⋊Dic₃	—	2	2	no	—
74	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
75	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
76	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
77	C₅×Dic₃⋊C₄	—	2	1	no	—
78	C₅×Dic₃⋊C₄	—	2	2	no	—
79	C₅×Dic₃⋊C₄	—	2	2	no	—
80	C₅×Dic₃⋊C₄	—	2	2	no	—
81	C₅×Dic₃⋊C₄	D₄	1	2	yes	—
82	C₄×C₅×Dic₃	—	2	1	no	—
83	C₄×C₅×Dic₃	—	2	2	no	—
84	C₄×C₅×Dic₃	C₂³	1	2	yes	—
85	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
86	C₅×#204	—	2	2	no	—
87	#5727	C₂×C₅	1	1	yes	characteristic
88	#5721	C₂×C₅	1	1	yes	characteristic, complemented
89	C₃×#487	C₂×C₅	1	1	yes	characteristic, complemented
90	#5094	C₂×C₅	1	1	yes	characteristic, complemented
91	#5083	C₂×C₅	1	1	yes	characteristic
92	#4818	C₂×C₅	1	2	yes	—
93	#4792	C₂×C₅	1	2	yes	complemented
94	#4791	C₂×C₅	1	2	yes	complemented
95	#4788	C₂×C₅	1	2	yes	—
96	C₄×#204	C₂×C₅	1	1	yes	characteristic
97	C₈×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
98	C₂²×C₅×Q₈	—	6	1	no	—
99	C₂×C₅×SD₁₆	—	3	2	no	—
100	C₂×C₅×SD₁₆	—	3	1	no	—
101	C₅×C₄⋊Q₈	—	3	2	no	—
102	C₅×C₄⋊Q₈	—	3	2	no	—
103	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
104	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
105	C₅×#125	—	6	2	no	—
106	C₅×#125	—	6	1	no	—
107	C₅×C₂²⋊Q₈	—	6	2	no	—
108	C₅×C₂²⋊Q₈	—	6	1	no	—
109	C₄×C₅×Q₈	—	3	1	no	—
110	C₄×C₅×Q₈	—	3	2	no	—
111	C₄×C₅×Q₈	—	3	1	no	—
112	C₄×C₅×Q₈	—	6	1	no	—
113	C₄×C₅×D₄	—	3	2	no	—
114	C₄×C₅×D₄	—	3	1	no	—
115	C₅×#106	—	3	1	no	—
116	C₅×#106	—	3	2	no	—
117	C₅×C₄⋊C₈	—	3	2	no	—
118	C₅×C₄⋊C₈	—	3	1	no	—
119	C₅×#103	—	3	2	no	—
120	C₅×#103	—	3	1	no	—
121	C₅×#103	—	3	2	no	—
122	C₅×#103	C₂×D₃	1	2	yes	—
123	C₅×#103	C₂×D₃	1	2	yes	—
124	C₅×#102	—	3	1	no	—
125	C₄×C₅×C₈	—	3	2	no	—
126	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
127	#3359	—	3	1	no	Sylow
128	C₂²×C₅×D₃	—	2	1	no	—
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₃×C₅×Q₈	—	2	2	no	—
131	C₃×C₅×Q₈	—	4	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
137	C₂×C₅×Dic₃	—	2	1	no	—
138	C₂×C₅×Dic₃	—	2	1	no	—
139	C₂×C₅×Dic₃	—	2	1	no	—
140	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
141	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
142	C₅×D₁₂	—	2	1	no	—
143	C₅×D₁₂	#41	1	2	yes	—
144	C₄×C₅×D₃	—	4	2	no	—
145	C₄×C₅×D₃	—	4	4	no	—
146	C₅×Dic₆	—	2	1	no	—
147	C₅×Dic₆	—	2	1	no	—
148	C₅×Dic₆	—	4	4	no	—
149	C₅×Dic₆	SD₁₆	1	4	yes	complemented
150	C₃×C₅×C₈	—	2	1	no	—
151	C₃×C₅×C₈	—	2	1	no	—
152	C₅×C₃⋊C₈	—	2	2	no	—
153	C₂×D₃×Q₈	—	2	1	no	—
154	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
155	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
156	#946	—	2	1	no	—
157	Q₈×Dic₃	C₂²×C₅	1	2	yes	—
158	#944	C₂²×C₅	1	2	yes	—
159	C₂×#215	C₂²×C₅	1	2	yes	—
160	C₂×#204	C₂²×C₅	1	1	yes	characteristic
161	#896	—	2	2	no	—
162	#893	C₂²×C₅	1	2	yes	—
163	#890	—	2	1	no	—
164	#889	—	2	2	no	—
165	#888	C₂²×C₅	1	2	yes	—
166	#887	—	2	1	no	—
167	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
168	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
169	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
170	C₃×#103	C₂²×C₅	1	2	yes	—
171	C₃×#103	C₂²×C₅	1	2	yes	—
172	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
173	#835	C₂²×C₅	1	2	yes	—
174	#821	C₂²×C₅	1	1	yes	characteristic
175	#817	C₂²×C₅	1	1	yes	characteristic
176	#816	C₂²×C₅	1	1	yes	characteristic
177	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
178	C₈×Dic₃	C₂²×C₅	1	2	yes	—
179	#810	C₂²×C₅	1	2	yes	—
180	#808	C₂²×C₅	1	2	yes	—
181	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
182	C₂×C₅×Q₈	—	2	1	no	—
183	C₂×C₅×Q₈	—	3	1	no	—
184	C₂×C₅×Q₈	—	3	1	no	—
185	C₂×C₅×Q₈	—	6	2	no	—
186	C₂×C₅×Q₈	—	12	4	no	—
187	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
188	C₂×C₅×D₄	—	3	1	no	—
189	C₂²×C₄×C₅	—	6	2	no	—
190	C₂²×C₄×C₅	—	6	1	no	—
191	C₅×SD₁₆	—	6	2	no	—
192	C₅×SD₁₆	—	6	4	no	—
193	C₂×C₅×C₈	—	3	2	no	—
194	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
195	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	1	no	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	—	3	2	no	—
200	C₅×C₄⋊C₄	—	3	1	no	—
201	C₅×C₄⋊C₄	—	3	1	no	—
202	C₅×C₄⋊C₄	—	3	1	no	—
203	C₅×C₄⋊C₄	—	6	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	1	no	—
208	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
209	C₅×C₂²⋊C₄	—	6	2	no	—
210	C₅×C₂²⋊C₄	—	6	1	no	—
211	C₄²×C₅	—	3	2	no	—
212	C₄²×C₅	—	6	2	no	—
213	C₄²×C₅	—	6	1	no	—
214	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
215	#557	—	3	1	no	—
216	D₄×Q₈	—	3	1	no	—
217	#487	—	3	2	no	—
218	#487	C₅×D₃	1	1	yes	characteristic, complemented
219	#475	—	3	1	no	—
220	#475	—	3	2	no	—
221	#461	—	3	1	no	—
222	#461	—	3	2	no	—
223	C₈×Q₈	—	3	1	no	—
224	C₄×SD₁₆	—	3	2	no	—
225	C₄×SD₁₆	—	3	1	no	—
226	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₅×D₃	—	2	2	no	—
228	C₂×C₅×D₃	—	4	1	no	—
229	C₂×C₅×D₃	—	4	1	no	—
230	C₃×C₄×C₅	—	2	1	no	—
231	C₃×C₄×C₅	—	4	2	no	—
232	C₃×C₄×C₅	—	4	2	no	—
233	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
234	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
235	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
236	C₅×Dic₃	—	2	2	no	—
237	C₅×Dic₃	—	4	1	no	—
238	C₅×Dic₃	—	4	1	no	—
239	C₅×Dic₃	—	4	1	no	—
240	C₅×Dic₃	C₂×SD₁₆	1	4	yes	—
241	C₂×C₃×Q₈	—	2	1	no	—
242	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
243	D₃×Q₈	—	4	4	no	—
244	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
245	C₂×C₄×D₃	—	2	1	no	—
246	C₂×C₄×D₃	—	2	2	no	—
247	C₂×Dic₆	—	2	2	no	—
248	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
249	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
250	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
251	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
252	C₃×C₄⋊C₄	—	2	1	no	—
253	C₃×C₄⋊C₄	—	2	1	no	—
254	C₃×C₄⋊C₄	—	2	1	no	—
255	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
256	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
257	#215	—	2	4	no	—
258	(C₂×D₃)⋊C₄	—	2	1	no	—
259	(C₂×D₃)⋊C₄	—	2	2	no	—
260	C₄⋊Dic₃	—	2	2	no	—
261	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
262	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
263	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
264	Dic₃⋊C₄	—	2	1	no	—
265	Dic₃⋊C₄	—	2	2	no	—
266	Dic₃⋊C₄	—	2	2	no	—
267	Dic₃⋊C₄	—	2	2	no	—
268	Dic₃⋊C₄	C₅×D₄	1	2	yes	—
269	C₄×Dic₃	—	2	1	no	—
270	C₄×Dic₃	—	2	2	no	—
271	C₄×Dic₃	C₂³×C₅	1	2	yes	—
272	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
273	#204	—	2	2	no	—
274	C₂³×C₅	—	6	1	no	—
275	C₅×Q₈	—	2	2	no	—
276	C₅×Q₈	—	2	2	no	—
277	C₅×Q₈	—	3	4	no	—
278	C₅×Q₈	—	4	2	no	—
279	C₅×Q₈	—	6	1	no	—
280	C₅×Q₈	—	6	1	no	—
281	C₅×Q₈	—	12	4	no	—
282	C₅×D₄	—	3	2	no	—
283	C₅×D₄	—	6	1	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	3	2	no	—
287	C₂×C₄×C₅	—	3	2	no	—
288	C₂×C₄×C₅	—	6	1	no	—
289	C₂×C₄×C₅	—	6	1	no	—
290	C₂×C₄×C₅	—	6	1	no	—
291	C₂×C₄×C₅	—	12	4	no	—
292	C₂×C₄×C₅	—	12	2	no	—
293	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
294	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
296	C₅×C₈	—	2	1	no	—
297	C₅×C₈	—	2	1	no	—
298	C₅×C₈	—	6	2	no	—
299	C₂²×Q₈	—	6	1	no	—
300	C₂×SD₁₆	—	3	2	no	—
301	C₂×SD₁₆	—	3	1	no	—
302	C₄⋊Q₈	—	3	2	no	—
303	C₄⋊Q₈	—	3	2	no	—
304	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
305	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
306	#125	—	6	2	no	—
307	#125	—	6	1	no	—
308	C₂²⋊Q₈	—	6	2	no	—
309	C₂²⋊Q₈	—	6	1	no	—
310	C₄×Q₈	—	3	1	no	—
311	C₄×Q₈	—	3	2	no	—
312	C₄×Q₈	—	3	1	no	—
313	C₄×Q₈	—	6	1	no	—
314	C₄×D₄	—	3	2	no	—
315	C₄×D₄	—	3	1	no	—
316	#106	—	3	1	no	—
317	#106	—	3	2	no	—
318	C₄⋊C₈	—	3	2	no	—
319	C₄⋊C₈	—	3	1	no	—
320	#103	—	3	2	no	—
321	#103	—	3	1	no	—
322	#103	—	3	2	no	—
323	#103	C₂×C₅×D₃	1	2	yes	—
324	#103	C₂×C₅×D₃	1	2	yes	—
325	#102	—	3	1	no	—
326	C₄×C₈	—	3	2	no	—
327	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
328	C₂×C₃×C₅	#548	1	1	yes	characteristic
329	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
330	C₂×C₃×C₅	#578	1	1	yes	characteristic
331	C₅×D₃	—	4	2	no	—
332	C₂²×D₃	—	2	1	no	—
333	C₃×Q₈	—	2	2	no	—
334	C₃×Q₈	—	2	2	no	—
335	C₃×Q₈	—	4	2	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
341	C₂×Dic₃	—	2	1	no	—
342	C₂×Dic₃	—	2	1	no	—
343	C₂×Dic₃	—	2	1	no	—
344	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
345	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
346	D₁₂	—	2	1	no	—
347	D₁₂	C₅×#41	1	2	yes	—
348	C₄×D₃	—	4	2	no	—
349	C₄×D₃	—	4	4	no	—
350	Dic₆	—	2	1	no	—
351	Dic₆	—	2	1	no	—
352	Dic₆	—	4	4	no	—
353	Dic₆	C₅×SD₁₆	1	4	yes	complemented
354	C₃×C₈	—	2	1	no	—
355	C₃×C₈	—	2	1	no	—
356	C₃⋊C₈	—	2	2	no	—
357	C₂²×C₅	—	6	2	no	—
358	C₂²×C₅	—	12	1	no	—
359	C₂²×C₅	—	12	1	no	—
360	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
361	C₄×C₅	—	2	1	no	—
362	C₄×C₅	—	3	4	no	—
363	C₄×C₅	—	4	2	no	—
364	C₄×C₅	—	4	2	no	—
365	C₄×C₅	—	6	2	no	—
366	C₄×C₅	—	12	1	no	—
367	C₄×C₅	—	12	1	no	—
368	C₄×C₅	—	12	1	no	—
369	C₄×C₅	D₃×SD₁₆	1	2	yes	—
370	C₄×C₅	D₃×#41	1	1	yes	characteristic
371	C₄×C₅	#1010	1	1	yes	characteristic
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	3	1	no	—
374	C₂×Q₈	—	3	1	no	—
375	C₂×Q₈	—	6	2	no	—
376	C₂×Q₈	—	12	4	no	—
377	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
378	C₂×D₄	—	3	1	no	—
379	C₂²×C₄	—	6	2	no	—
380	C₂²×C₄	—	6	1	no	—
381	SD₁₆	—	6	2	no	—
382	SD₁₆	—	6	4	no	—
383	C₂×C₈	—	3	2	no	—
384	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
385	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	3	2	no	—
390	C₄⋊C₄	—	3	1	no	—
391	C₄⋊C₄	—	3	1	no	—
392	C₄⋊C₄	—	3	1	no	—
393	C₄⋊C₄	—	6	2	no	—
394	C₄⋊C₄	—	6	2	no	—
395	C₄⋊C₄	—	6	2	no	—
396	C₄⋊C₄	—	6	2	no	—
397	C₄⋊C₄	—	6	1	no	—
398	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
399	C₂²⋊C₄	—	6	2	no	—
400	C₂²⋊C₄	—	6	1	no	—
401	C₄²	—	3	2	no	—
402	C₄²	—	6	2	no	—
403	C₄²	—	6	1	no	—
404	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
405	C₃×C₅	#3359	1	1	yes	characteristic, complemented, Hall
406	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
407	C₂×D₃	—	2	2	no	—
408	C₂×D₃	—	4	1	no	—
409	C₂×D₃	—	4	1	no	—
410	C₃×C₄	—	2	1	no	—
411	C₃×C₄	—	4	2	no	—
412	C₃×C₄	—	4	2	no	—
413	C₃×C₄	C₂×C₅×SD₁₆	1	2	yes	—
414	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
415	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
416	Dic₃	—	2	2	no	—
417	Dic₃	—	4	1	no	—
418	Dic₃	—	4	1	no	—
419	Dic₃	—	4	1	no	—
420	Dic₃	C₂×C₅×SD₁₆	1	4	yes	—
421	C₂×C₅	—	12	2	no	—
422	C₂×C₅	#5677	1	1	yes	characteristic
423	C₂×C₅	C₂×D₃×SD₁₆	1	1	yes	characteristic
424	C₂×C₅	#5766	1	1	yes	characteristic
425	C₂³	—	6	1	no	—
426	Q₈	—	2	2	no	—
427	Q₈	—	2	2	no	—
428	Q₈	—	3	4	no	—
429	Q₈	—	4	2	no	—
430	Q₈	—	6	1	no	—
431	Q₈	—	6	1	no	—
432	Q₈	—	12	4	no	—
433	D₄	—	3	2	no	—
434	D₄	—	6	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	3	2	no	—
438	C₂×C₄	—	3	2	no	—
439	C₂×C₄	—	6	1	no	—
440	C₂×C₄	—	6	1	no	—
441	C₂×C₄	—	6	1	no	—
442	C₂×C₄	—	12	4	no	—
443	C₂×C₄	—	12	2	no	—
444	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
445	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
446	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
447	C₈	—	2	1	no	—
448	C₈	—	2	1	no	—
449	C₈	—	6	2	no	—
450	C₂×C₃	C₅×#548	1	1	yes	characteristic
451	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
452	C₂×C₃	C₅×#578	1	1	yes	characteristic
453	D₃	—	4	2	no	—
454	C₅	#81620	1	1	yes	characteristic, direct product factor, Sylow
455	C₂²	—	6	2	no	—
456	C₂²	—	12	1	no	—
457	C₂²	—	12	1	no	—
458	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	3	4	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	6	2	no	—
464	C₄	—	12	1	no	—
465	C₄	—	12	1	no	—
466	C₄	—	12	1	no	—
467	C₄	C₅×D₃×SD₁₆	1	2	yes	—
468	C₄	C₅×D₃×#41	1	1	yes	characteristic
469	C₄	C₅×#1010	1	1	yes	characteristic
470	C₃	C₅×#3359	1	1	yes	characteristic, complemented, Sylow
471	C₂	—	12	2	no	—
472	C₂	C₅×#5677	1	1	yes	characteristic
473	C₂	C₂×C₅×D₃×SD₁₆	1	1	yes	characteristic
474	C₂	C₅×#5766	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×#487	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×D₁₂	C₂³
hypercenter	C₅×#487	D₃
hypocenter	C₃	C₅×#3359
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#487

Complements

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

N	H ≅ G/N	type
2. C₅×#5721	C₂	semidirect
3. C₃×C₅×#487	C₂	semidirect
4. C₅×#5094	C₂	semidirect
7. C₅×#4792	C₂	semidirect
8. C₅×#4791	C₂	semidirect
11. C₅×C₈×Dic₆	C₂	semidirect
42. #81620	C₅	direct (N × H)
46. C₅×#487	D₃	semidirect
88. #5721	C₂×C₅	semidirect
89. C₃×#487	C₂×C₅	semidirect
90. #5094	C₂×C₅	semidirect
93. #4792	C₂×C₅	semidirect
94. #4791	C₂×C₅	semidirect
97. C₈×Dic₆	C₂×C₅	semidirect
149. C₅×Dic₆	SD₁₆	semidirect
218. #487	C₅×D₃	semidirect
353. Dic₆	C₅×SD₁₆	semidirect
405. C₃×C₅	#3359	semidirect
454. C₅	#81620	direct (N × H)
470. C₃	C₅×#3359	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5727	2
C₅×#5721	2
C₃×C₅×#487	2
C₅×#5094	2
C₅×#5083	2
C₅×#4818	2
C₅×#4792	2
C₅×#4791	2
C₅×#4788	2
C₄×C₅×#204	2
C₅×C₈×Dic₆	2
C₅×#3359	3
#81620	5

Subgroups — C5×#81620 #14471509

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81620 #14471509