Subgroups — C₅×#81621 #14471612

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5732	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5730	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5083	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4819	C₂	1	2	yes	maximal
7	C₅×#4800	C₂	1	2	yes	maximal, complemented
8	C₅×#4796	C₂	1	2	yes	maximal, complemented
9	C₅×#4788	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×D₂₄	C₂	1	1	yes	maximal, characteristic
11	C₅×C₈×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3360	—	3	1	no	maximal, Hall
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₅×#947	C₂²	1	2	yes	—
16	C₅×#946	—	2	2	no	—
17	C₅×Q₈×Dic₃	C₂²	1	2	yes	—
18	C₂×C₅×#215	C₂²	1	2	yes	—
19	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
20	C₅×#898	—	2	2	no	—
21	C₅×#897	—	2	1	no	—
22	C₅×#897	—	2	1	no	—
23	C₅×#893	C₂²	1	2	yes	—
24	C₅×#892	—	2	1	no	—
25	C₅×D₃×C₄⋊C₄	—	2	1	no	—
26	C₅×#890	C₂²	1	2	yes	—
27	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
28	C₄×C₅×D₁₂	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×#821	C₂²	1	1	yes	characteristic
36	C₅×#818	C₂²	1	1	yes	characteristic
37	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
38	C₅×C₈×Dic₃	C₂²	1	2	yes	—
39	C₅×#809	C₂²	1	2	yes	—
40	C₅×#808	C₂²	1	2	yes	—
41	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
42	#81621	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#556	—	3	1	no	—
44	C₅×#554	—	3	1	no	—
45	C₅×#488	—	3	2	no	—
46	C₅×#487	D₃	1	1	yes	characteristic, complemented
47	C₅×#479	—	3	2	no	—
48	C₅×#476	—	3	1	no	—
49	C₅×#463	—	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×D₈	—	3	1	no	—
54	C₂×C₃×C₅×Q₈	—	2	1	no	—
55	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
56	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
57	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
58	C₂×C₄×C₅×D₃	—	2	1	no	—
59	C₂×C₄×C₅×D₃	—	2	1	no	—
60	C₂×C₄×C₅×D₃	—	2	2	no	—
61	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
62	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₃×C₅×C₄⋊C₄	—	2	1	no	—
65	C₃×C₅×C₄⋊C₄	—	2	1	no	—
66	C₃×C₅×C₄⋊C₄	—	2	1	no	—
67	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₅×#215	—	2	4	no	—
70	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
71	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
72	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
73	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
74	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
75	C₅×C₄⋊Dic₃	—	2	2	no	—
76	C₅×C₄⋊Dic₃	—	2	2	no	—
77	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
78	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
79	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
80	C₅×Dic₃⋊C₄	—	2	2	no	—
81	C₅×Dic₃⋊C₄	D₄	1	2	yes	—
82	C₄×C₅×Dic₃	—	2	2	no	—
83	C₄×C₅×Dic₃	C₂³	1	2	yes	—
84	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
85	C₅×D₂₄	—	2	2	no	—
86	#5732	C₂×C₅	1	1	yes	characteristic, complemented
87	#5730	C₂×C₅	1	1	yes	characteristic, complemented
88	C₃×#487	C₂×C₅	1	1	yes	characteristic, complemented
89	#5084	C₂×C₅	1	1	yes	characteristic, complemented
90	#5083	C₂×C₅	1	1	yes	characteristic, complemented
91	#4819	C₂×C₅	1	2	yes	—
92	#4800	C₂×C₅	1	2	yes	complemented
93	#4796	C₂×C₅	1	2	yes	complemented
94	#4788	C₂×C₅	1	2	yes	complemented
95	C₄×D₂₄	C₂×C₅	1	1	yes	characteristic
96	C₈×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
97	C₂×C₅×SD₁₆	—	3	2	no	—
98	C₂×C₅×D₈	—	3	1	no	—
99	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
100	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
101	C₅×#126	—	6	2	no	—
102	C₅×#125	—	3	2	no	—
103	C₅×#124	—	3	2	no	—
104	C₅×C₂²⋊Q₈	—	6	1	no	—
105	C₅×C₂²⋊Q₈	—	6	1	no	—
106	C₅×C₂²⋊Q₈	—	6	2	no	—
107	C₄×C₅×Q₈	—	3	1	no	—
108	C₄×C₅×Q₈	—	3	2	no	—
109	C₄×C₅×D₄	—	3	2	no	—
110	C₄×C₅×D₄	—	3	1	no	—
111	C₄×C₅×D₄	—	3	1	no	—
112	C₅×#117	—	6	1	no	—
113	C₂×C₅×C₄⋊C₄	—	6	1	no	—
114	C₅×#107	—	3	1	no	—
115	C₅×#106	—	3	2	no	—
116	C₅×C₄⋊C₈	—	3	2	no	—
117	C₅×C₄⋊C₈	—	3	1	no	—
118	C₅×#103	—	3	2	no	—
119	C₅×#103	C₂×D₃	1	2	yes	—
120	C₅×#103	C₂×D₃	1	2	yes	—
121	C₅×#102	—	3	1	no	—
122	C₅×#102	—	3	1	no	—
123	C₅×#102	—	3	2	no	—
124	C₄×C₅×C₈	—	3	2	no	—
125	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
126	#3360	—	3	1	no	Sylow
127	C₂²×C₅×D₃	—	2	1	no	—
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	—	8	1	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	C₂×D₄	1	2	yes	—
140	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
141	C₅×D₁₂	—	2	1	no	—
142	C₅×D₁₂	—	2	1	no	—
143	C₅×D₁₂	—	2	1	no	—
144	C₅×D₁₂	#41	1	2	yes	—
145	C₄×C₅×D₃	—	4	2	no	—
146	C₄×C₅×D₃	—	4	2	no	—
147	C₄×C₅×D₃	—	8	2	no	—
148	C₅×Dic₆	—	2	2	no	—
149	C₃×C₅×C₈	—	2	1	no	—
150	C₃×C₅×C₈	—	2	1	no	—
151	C₅×C₃⋊C₈	—	2	2	no	—
152	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
153	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
154	#947	C₂²×C₅	1	2	yes	—
155	#946	—	2	2	no	—
156	Q₈×Dic₃	C₂²×C₅	1	2	yes	—
157	C₂×#215	C₂²×C₅	1	2	yes	—
158	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
159	#898	—	2	2	no	—
160	#897	—	2	1	no	—
161	#897	—	2	1	no	—
162	#893	C₂²×C₅	1	2	yes	—
163	#892	—	2	1	no	—
164	D₃×C₄⋊C₄	—	2	1	no	—
165	#890	C₂²×C₅	1	2	yes	—
166	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
167	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
168	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
169	C₃×#103	C₂²×C₅	1	2	yes	—
170	C₃×#103	C₂²×C₅	1	2	yes	—
171	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
172	#835	C₂²×C₅	1	2	yes	—
173	#821	C₂²×C₅	1	1	yes	characteristic
174	#821	C₂²×C₅	1	1	yes	characteristic
175	#818	C₂²×C₅	1	1	yes	characteristic
176	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
177	C₈×Dic₃	C₂²×C₅	1	2	yes	—
178	#809	C₂²×C₅	1	2	yes	—
179	#808	C₂²×C₅	1	2	yes	—
180	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
181	C₂×C₅×Q₈	—	2	1	no	—
182	C₂×C₅×Q₈	—	3	1	no	—
183	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
184	C₂×C₅×D₄	—	3	1	no	—
185	C₂×C₅×D₄	—	3	1	no	—
186	C₂²×C₄×C₅	—	6	2	no	—
187	C₂²×C₄×C₅	—	6	1	no	—
188	C₂²×C₄×C₅	—	6	1	no	—
189	C₅×SD₁₆	—	6	4	no	—
190	C₅×D₈	—	6	2	no	—
191	C₂×C₅×C₈	—	3	2	no	—
192	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₄⋊C₄	—	3	1	no	—
198	C₅×C₄⋊C₄	—	3	2	no	—
199	C₅×C₄⋊C₄	—	3	1	no	—
200	C₅×C₄⋊C₄	—	3	1	no	—
201	C₅×C₄⋊C₄	—	6	2	no	—
202	C₅×C₄⋊C₄	—	6	2	no	—
203	C₅×C₄⋊C₄	—	6	2	no	—
204	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
205	C₅×C₂²⋊C₄	—	6	2	no	—
206	C₅×C₂²⋊C₄	—	6	2	no	—
207	C₅×C₂²⋊C₄	—	6	2	no	—
208	C₅×C₂²⋊C₄	—	6	1	no	—
209	C₅×C₂²⋊C₄	—	6	1	no	—
210	C₄²×C₅	—	3	2	no	—
211	C₄²×C₅	—	6	2	no	—
212	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
213	#556	—	3	1	no	—
214	#554	—	3	1	no	—
215	#488	—	3	2	no	—
216	#487	C₅×D₃	1	1	yes	characteristic, complemented
217	#479	—	3	2	no	—
218	#476	—	3	1	no	—
219	#463	—	3	2	no	—
220	#461	—	3	1	no	—
221	C₈×Q₈	—	3	1	no	—
222	C₄×SD₁₆	—	3	2	no	—
223	C₄×D₈	—	3	1	no	—
224	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₅×D₃	—	2	2	no	—
226	C₂×C₅×D₃	—	4	1	no	—
227	C₂×C₅×D₃	—	4	1	no	—
228	C₂×C₅×D₃	—	4	1	no	—
229	C₂×C₅×D₃	—	4	1	no	—
230	C₂×C₅×D₃	—	4	1	no	—
231	C₃×C₄×C₅	—	2	1	no	—
232	C₃×C₄×C₅	—	4	2	no	—
233	C₃×C₄×C₅	—	4	2	no	—
234	C₃×C₄×C₅	#135	1	2	yes	—
235	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
236	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
237	C₅×Dic₃	—	2	2	no	—
238	C₅×Dic₃	—	2	2	no	—
239	C₅×Dic₃	—	4	1	no	—
240	C₅×Dic₃	—	4	1	no	—
241	C₂×C₃×Q₈	—	2	1	no	—
242	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
243	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
244	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
245	C₂×C₄×D₃	—	2	1	no	—
246	C₂×C₄×D₃	—	2	1	no	—
247	C₂×C₄×D₃	—	2	2	no	—
248	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
249	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
250	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
251	C₃×C₄⋊C₄	—	2	1	no	—
252	C₃×C₄⋊C₄	—	2	1	no	—
253	C₃×C₄⋊C₄	—	2	1	no	—
254	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
255	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
256	#215	—	2	4	no	—
257	(C₂×D₃)⋊C₄	—	2	1	no	—
258	(C₂×D₃)⋊C₄	—	2	1	no	—
259	(C₂×D₃)⋊C₄	—	2	2	no	—
260	(C₂×D₃)⋊C₄	—	2	2	no	—
261	(C₂×D₃)⋊C₄	—	2	2	no	—
262	C₄⋊Dic₃	—	2	2	no	—
263	C₄⋊Dic₃	—	2	2	no	—
264	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
265	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
266	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
267	Dic₃⋊C₄	—	2	2	no	—
268	Dic₃⋊C₄	C₅×D₄	1	2	yes	—
269	C₄×Dic₃	—	2	2	no	—
270	C₄×Dic₃	C₂³×C₅	1	2	yes	—
271	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
272	D₂₄	—	2	2	no	—
273	C₂³×C₅	—	6	1	no	—
274	C₂³×C₅	—	6	1	no	—
275	C₅×Q₈	—	2	2	no	—
276	C₅×Q₈	—	2	2	no	—
277	C₅×Q₈	—	6	2	no	—
278	C₅×Q₈	—	8	1	no	—
279	C₅×D₄	—	3	2	no	—
280	C₅×D₄	—	6	1	no	—
281	C₅×D₄	—	6	1	no	—
282	C₅×D₄	—	6	1	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	3	2	no	—
286	C₂×C₄×C₅	—	3	2	no	—
287	C₂×C₄×C₅	—	6	1	no	—
288	C₂×C₄×C₅	—	6	1	no	—
289	C₂×C₄×C₅	—	12	2	no	—
290	C₂×C₄×C₅	—	12	2	no	—
291	C₂×C₄×C₅	—	24	2	no	—
292	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
293	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
294	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
295	C₅×C₈	—	2	1	no	—
296	C₅×C₈	—	2	1	no	—
297	C₅×C₈	—	6	2	no	—
298	C₂×SD₁₆	—	3	2	no	—
299	C₂×D₈	—	3	1	no	—
300	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
301	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
302	#126	—	6	2	no	—
303	#125	—	3	2	no	—
304	#124	—	3	2	no	—
305	C₂²⋊Q₈	—	6	1	no	—
306	C₂²⋊Q₈	—	6	1	no	—
307	C₂²⋊Q₈	—	6	2	no	—
308	C₄×Q₈	—	3	1	no	—
309	C₄×Q₈	—	3	2	no	—
310	C₄×D₄	—	3	2	no	—
311	C₄×D₄	—	3	1	no	—
312	C₄×D₄	—	3	1	no	—
313	#117	—	6	1	no	—
314	C₂×C₄⋊C₄	—	6	1	no	—
315	#107	—	3	1	no	—
316	#106	—	3	2	no	—
317	C₄⋊C₈	—	3	2	no	—
318	C₄⋊C₈	—	3	1	no	—
319	#103	—	3	2	no	—
320	#103	C₂×C₅×D₃	1	2	yes	—
321	#103	C₂×C₅×D₃	1	2	yes	—
322	#102	—	3	1	no	—
323	#102	—	3	1	no	—
324	#102	—	3	2	no	—
325	C₄×C₈	—	3	2	no	—
326	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
327	C₂×C₃×C₅	#548	1	1	yes	characteristic
328	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
329	C₂×C₃×C₅	#577	1	1	yes	characteristic
330	C₅×D₃	—	4	2	no	—
331	C₅×D₃	—	8	1	no	—
332	C₂²×D₃	—	2	1	no	—
333	C₂²×D₃	—	2	1	no	—
334	C₃×Q₈	—	2	2	no	—
335	C₃×Q₈	—	2	2	no	—
336	C₃×Q₈	—	8	1	no	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	—	2	2	no	—
339	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
341	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
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	—	2	1	no	—
348	D₁₂	—	2	1	no	—
349	D₁₂	C₅×#41	1	2	yes	—
350	C₄×D₃	—	4	2	no	—
351	C₄×D₃	—	4	2	no	—
352	C₄×D₃	—	8	2	no	—
353	Dic₆	—	2	2	no	—
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	—	12	1	no	—
361	C₂²×C₅	—	12	1	no	—
362	C₂²×C₅	—	12	1	no	—
363	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
364	C₄×C₅	—	2	1	no	—
365	C₄×C₅	—	4	2	no	—
366	C₄×C₅	—	4	2	no	—
367	C₄×C₅	—	6	2	no	—
368	C₄×C₅	—	6	2	no	—
369	C₄×C₅	—	12	1	no	—
370	C₄×C₅	—	12	1	no	—
371	C₄×C₅	#919	1	2	yes	—
372	C₄×C₅	D₃×#41	1	1	yes	characteristic
373	C₄×C₅	#1010	1	1	yes	characteristic
374	C₂×Q₈	—	2	1	no	—
375	C₂×Q₈	—	3	1	no	—
376	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
377	C₂×D₄	—	3	1	no	—
378	C₂×D₄	—	3	1	no	—
379	C₂²×C₄	—	6	2	no	—
380	C₂²×C₄	—	6	1	no	—
381	C₂²×C₄	—	6	1	no	—
382	SD₁₆	—	6	4	no	—
383	D₈	—	6	2	no	—
384	C₂×C₈	—	3	2	no	—
385	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
386	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	3	1	no	—
391	C₄⋊C₄	—	3	2	no	—
392	C₄⋊C₄	—	3	1	no	—
393	C₄⋊C₄	—	3	1	no	—
394	C₄⋊C₄	—	6	2	no	—
395	C₄⋊C₄	—	6	2	no	—
396	C₄⋊C₄	—	6	2	no	—
397	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
398	C₂²⋊C₄	—	6	2	no	—
399	C₂²⋊C₄	—	6	2	no	—
400	C₂²⋊C₄	—	6	2	no	—
401	C₂²⋊C₄	—	6	1	no	—
402	C₂²⋊C₄	—	6	1	no	—
403	C₄²	—	3	2	no	—
404	C₄²	—	6	2	no	—
405	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
406	C₃×C₅	#3360	1	1	yes	characteristic, complemented, Hall
407	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
408	C₂×D₃	—	2	2	no	—
409	C₂×D₃	—	4	1	no	—
410	C₂×D₃	—	4	1	no	—
411	C₂×D₃	—	4	1	no	—
412	C₂×D₃	—	4	1	no	—
413	C₂×D₃	—	4	1	no	—
414	C₃×C₄	—	2	1	no	—
415	C₃×C₄	—	4	2	no	—
416	C₃×C₄	—	4	2	no	—
417	C₃×C₄	C₅×#135	1	2	yes	—
418	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
419	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
420	Dic₃	—	2	2	no	—
421	Dic₃	—	2	2	no	—
422	Dic₃	—	4	1	no	—
423	Dic₃	—	4	1	no	—
424	C₂×C₅	—	12	2	no	—
425	C₂×C₅	—	24	1	no	—
426	C₂×C₅	#5677	1	1	yes	characteristic
427	C₂×C₅	#5762	1	1	yes	characteristic
428	C₂×C₅	C₂×#919	1	1	yes	characteristic
429	C₂³	—	6	1	no	—
430	C₂³	—	6	1	no	—
431	Q₈	—	2	2	no	—
432	Q₈	—	2	2	no	—
433	Q₈	—	6	2	no	—
434	Q₈	—	8	1	no	—
435	D₄	—	3	2	no	—
436	D₄	—	6	1	no	—
437	D₄	—	6	1	no	—
438	D₄	—	6	1	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	3	2	no	—
442	C₂×C₄	—	3	2	no	—
443	C₂×C₄	—	6	1	no	—
444	C₂×C₄	—	6	1	no	—
445	C₂×C₄	—	12	2	no	—
446	C₂×C₄	—	12	2	no	—
447	C₂×C₄	—	24	2	no	—
448	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
449	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
450	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
451	C₈	—	2	1	no	—
452	C₈	—	2	1	no	—
453	C₈	—	6	2	no	—
454	C₂×C₃	C₅×#548	1	1	yes	characteristic
455	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
456	C₂×C₃	C₅×#577	1	1	yes	characteristic
457	D₃	—	4	2	no	—
458	D₃	—	8	1	no	—
459	C₅	#81621	1	1	yes	characteristic, direct product factor, Sylow
460	C₂²	—	6	2	no	—
461	C₂²	—	12	1	no	—
462	C₂²	—	12	1	no	—
463	C₂²	—	12	1	no	—
464	C₂²	—	12	1	no	—
465	C₂²	—	12	1	no	—
466	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
467	C₄	—	2	1	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	6	2	no	—
471	C₄	—	6	2	no	—
472	C₄	—	12	1	no	—
473	C₄	—	12	1	no	—
474	C₄	C₅×#919	1	2	yes	—
475	C₄	C₅×D₃×#41	1	1	yes	characteristic
476	C₄	C₅×#1010	1	1	yes	characteristic
477	C₃	C₅×#3360	1	1	yes	characteristic, complemented, Sylow
478	C₂	—	12	2	no	—
479	C₂	—	24	1	no	—
480	C₂	C₅×#5677	1	1	yes	characteristic
481	C₂	C₅×#5762	1	1	yes	characteristic
482	C₂	C₂×C₅×#919	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×D₂₄	C₂²
hypercenter	C₅×#487	D₃
hypocenter	C₃	C₅×#3360
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
1. C₅×#5732	C₂	semidirect
2. C₅×#5730	C₂	semidirect
3. C₃×C₅×#487	C₂	semidirect
4. C₅×#5084	C₂	semidirect
5. C₅×#5083	C₂	semidirect
7. C₅×#4800	C₂	semidirect
8. C₅×#4796	C₂	semidirect
9. C₅×#4788	C₂	semidirect
11. C₅×C₈×Dic₆	C₂	semidirect
42. #81621	C₅	direct (N × H)
46. C₅×#487	D₃	semidirect
86. #5732	C₂×C₅	semidirect
87. #5730	C₂×C₅	semidirect
88. C₃×#487	C₂×C₅	semidirect
89. #5084	C₂×C₅	semidirect
90. #5083	C₂×C₅	semidirect
92. #4800	C₂×C₅	semidirect
93. #4796	C₂×C₅	semidirect
94. #4788	C₂×C₅	semidirect
96. C₈×Dic₆	C₂×C₅	semidirect
216. #487	C₅×D₃	semidirect
406. C₃×C₅	#3360	semidirect
459. C₅	#81621	direct (N × H)
477. C₃	C₅×#3360	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5732	2
C₅×#5730	2
C₃×C₅×#487	2
C₅×#5084	2
C₅×#5083	2
C₅×#4819	2
C₅×#4800	2
C₅×#4796	2
C₅×#4788	2
C₄×C₅×D₂₄	2
C₅×C₈×Dic₆	2
C₅×#3360	3
#81621	5

Subgroups — C5×#81621 #14471612

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81621 #14471612