Subgroups — C₄×C₅×#919 #14416215

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#919	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×#239	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×Dic₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅×#215	C₂	1	2	yes	maximal, complemented
6	C₅×#4880	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4872	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4804	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, complemented
11	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₅×#135	—	3	1	no	maximal, Hall
13	C₂×C₅×#239	C₂²	1	2	yes	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
16	C₅×Q₈×Dic₃	C₂²	1	2	yes	—
17	C₂×C₅×#215	C₂²	1	2	yes	—
18	C₅×#919	C₄	1	8	yes	direct product factor
19	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
20	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
22	C₅×#893	—	2	2	no	—
23	C₅×#893	C₂²	1	2	yes	—
24	C₅×#892	—	2	2	no	—
25	C₅×#892	C₂²	1	2	yes	—
26	C₄×C₅×D₁₂	—	2	2	no	—
27	C₄×C₅×D₁₂	C₂²	1	2	yes	—
28	C₄²×C₅×D₃	—	2	2	no	—
29	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
30	C₃×C₅×#107	C₂²	1	1	yes	characteristic
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	2	yes	—
35	C₅×#818	C₂²	1	1	yes	characteristic
36	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
37	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
38	C₅×#809	C₂²	1	2	yes	—
39	C₅×#808	C₂²	1	2	yes	—
40	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
41	C₄×#919	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
42	C₂×C₅×#135	—	3	1	no	—
43	C₄×C₅×#41	—	3	2	no	—
44	C₄×C₅×Q₁₆	—	3	1	no	—
45	C₄×C₅×Q₁₆	D₃	1	1	yes	characteristic, complemented
46	C₄×C₅×SD₁₆	—	3	2	no	—
47	C₄×C₅×SD₁₆	—	3	2	no	—
48	C₄×C₅×D₈	—	3	1	no	—
49	C₄×C₅×D₈	—	3	1	no	—
50	C₅×#427	—	3	1	no	—
51	C₅×#416	—	3	2	no	—
52	C₂×C₄×C₅×C₈	—	3	1	no	—
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	C₅×#239	—	2	4	no	—
55	C₅×#239	C₂×C₄	1	8	yes	complemented
56	C₂×C₅×D₁₂	—	2	2	no	—
57	C₂×C₅×D₁₂	C₂³	1	2	yes	—
58	C₂×C₄×C₅×D₃	—	2	2	no	—
59	C₂×C₄×C₅×D₃	—	2	2	no	—
60	C₂×C₄×C₅×D₃	—	2	2	no	—
61	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
62	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
63	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
64	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	—	2	2	no	—
68	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₃×C₄²×C₅	—	2	2	no	—
70	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₅×#215	C₂×C₄	1	8	yes	complemented
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	C₂³	1	2	yes	—
77	C₄×C₅×Dic₃	—	2	2	no	—
78	C₄×C₅×Dic₃	—	2	2	no	—
79	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
80	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
81	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
82	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
83	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
84	C₅×D₂₄	C₂×C₄	1	4	yes	complemented
85	C₅×D₃×C₈	—	2	2	no	—
86	C₅×D₃×C₈	C₂×C₄	1	4	yes	complemented
87	C₂×#919	C₂×C₅	1	1	yes	characteristic
88	C₄×#239	C₂×C₅	1	2	yes	complemented
89	C₃×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
90	Dic₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
91	C₄×#215	C₂×C₅	1	2	yes	complemented
92	#4880	C₂×C₅	1	1	yes	characteristic, complemented
93	#4872	C₂×C₅	1	1	yes	characteristic, complemented
94	#4804	C₂×C₅	1	2	yes	complemented
95	#4788	C₂×C₅	1	2	yes	complemented
96	C₄×D₂₄	C₂×C₅	1	1	yes	characteristic, complemented
97	C₄×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
98	C₂×C₅×#41	—	3	2	no	—
99	C₅×#135	—	3	8	no	—
100	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
101	C₂×C₅×SD₁₆	—	3	2	no	—
102	C₂×C₅×D₈	—	3	1	no	—
103	C₂²×C₅×C₈	—	3	1	no	—
104	C₂²×C₅×C₈	—	3	1	no	—
105	C₄×C₅×Q₈	—	3	2	no	—
106	C₄×C₅×Q₈	C₂×D₃	1	2	yes	—
107	C₄×C₅×D₄	—	3	2	no	—
108	C₄×C₅×D₄	—	3	2	no	—
109	C₄×C₅×D₄	—	6	2	no	—
110	C₄×C₅×D₄	—	6	2	no	—
111	C₅×#117	—	3	2	no	—
112	C₅×#117	—	6	2	no	—
113	C₂×C₄²×C₅	—	3	1	no	—
114	C₂×C₄²×C₅	—	6	2	no	—
115	C₅×#107	—	3	1	no	—
116	C₅×#107	C₂×D₃	1	1	yes	characteristic
117	C₅×#106	—	3	2	no	—
118	C₅×#103	—	3	2	no	—
119	C₅×#103	C₂×D₃	1	2	yes	—
120	C₅×#102	—	3	2	no	—
121	C₅×#102	—	3	2	no	—
122	C₄×C₅×C₈	—	3	1	no	—
123	C₄×C₅×C₈	—	3	1	no	—
124	C₄×C₅×C₈	—	3	1	no	—
125	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
126	C₄×#135	—	3	1	no	Sylow
127	C₂²×C₅×D₃	—	2	2	no	—
128	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₂×C₅×Dic₃	—	2	2	no	—
137	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
140	C₅×D₁₂	—	2	8	no	—
141	C₅×D₁₂	—	2	2	no	—
142	C₅×D₁₂	C₂²×C₄	1	4	yes	—
143	C₄×C₅×D₃	—	2	2	no	—
144	C₄×C₅×D₃	—	2	8	no	—
145	C₄×C₅×D₃	—	2	2	no	—
146	C₄×C₅×D₃	—	4	4	no	—
147	C₄×C₅×D₃	—	4	4	no	—
148	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
149	C₄×C₅×D₃	#41	1	2	yes	—
150	C₃×C₅×C₈	—	2	1	no	—
151	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
152	C₅×C₃⋊C₈	—	2	1	no	—
153	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
154	C₂×#239	C₂²×C₅	1	2	yes	—
155	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
156	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
157	Q₈×Dic₃	C₂²×C₅	1	2	yes	—
158	C₂×#215	C₂²×C₅	1	2	yes	—
159	#919	C₄×C₅	1	8	yes	direct product factor
160	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
161	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
162	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
163	#893	—	2	2	no	—
164	#893	C₂²×C₅	1	2	yes	—
165	#892	—	2	2	no	—
166	#892	C₂²×C₅	1	2	yes	—
167	C₄×D₁₂	—	2	2	no	—
168	C₄×D₁₂	C₂²×C₅	1	2	yes	—
169	C₄²×D₃	—	2	2	no	—
170	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
171	C₃×#107	C₂²×C₅	1	1	yes	characteristic
172	C₃×#103	C₂²×C₅	1	2	yes	—
173	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
174	#835	C₂²×C₅	1	2	yes	—
175	#821	C₂²×C₅	1	2	yes	—
176	#818	C₂²×C₅	1	1	yes	characteristic
177	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
178	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
179	#809	C₂²×C₅	1	2	yes	—
180	#808	C₂²×C₅	1	2	yes	—
181	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
182	C₅×#41	—	3	8	no	—
183	C₅×#41	—	6	4	no	—
184	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
185	C₂×C₅×D₄	—	3	2	no	—
186	C₂×C₅×D₄	—	6	2	no	—
187	C₂²×C₄×C₅	—	3	1	no	—
188	C₂²×C₄×C₅	—	3	1	no	—
189	C₂²×C₄×C₅	—	3	1	no	—
190	C₂²×C₄×C₅	—	6	2	no	—
191	C₂²×C₄×C₅	—	6	2	no	—
192	C₂²×C₄×C₅	—	6	2	no	—
193	C₅×Q₁₆	C₄×D₃	1	4	yes	complemented
194	C₅×SD₁₆	—	3	8	no	—
195	C₅×D₈	—	3	4	no	—
196	C₂×C₅×C₈	—	3	1	no	—
197	C₂×C₅×C₈	—	3	4	no	—
198	C₂×C₅×C₈	—	3	1	no	—
199	C₂×C₅×C₈	—	6	2	no	—
200	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
201	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
202	C₅×C₄⋊C₄	—	2	2	no	—
203	C₅×C₄⋊C₄	—	3	2	no	—
204	C₅×C₄⋊C₄	—	6	2	no	—
205	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
206	C₅×C₂²⋊C₄	—	6	2	no	—
207	C₅×C₂²⋊C₄	—	6	2	no	—
208	C₅×C₂²⋊C₄	—	6	2	no	—
209	C₄²×C₅	—	2	2	no	—
210	C₄²×C₅	—	3	1	no	—
211	C₄²×C₅	—	3	1	no	—
212	C₄²×C₅	—	3	1	no	—
213	C₄²×C₅	—	6	2	no	—
214	C₄²×C₅	—	6	2	no	—
215	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
216	C₂×#135	—	3	1	no	—
217	C₄×#41	—	3	2	no	—
218	C₄×Q₁₆	—	3	1	no	—
219	C₄×Q₁₆	C₅×D₃	1	1	yes	characteristic, complemented
220	C₄×SD₁₆	—	3	2	no	—
221	C₄×SD₁₆	—	3	2	no	—
222	C₄×D₈	—	3	1	no	—
223	C₄×D₈	—	3	1	no	—
224	#427	—	3	1	no	—
225	#416	—	3	2	no	—
226	C₂×C₄×C₈	—	3	1	no	—
227	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₅×D₃	—	2	1	no	—
229	C₂×C₅×D₃	—	2	1	no	—
230	C₂×C₅×D₃	—	2	4	no	—
231	C₂×C₅×D₃	—	4	2	no	—
232	C₂×C₅×D₃	—	4	2	no	—
233	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
234	C₃×C₄×C₅	—	2	4	no	—
235	C₃×C₄×C₅	—	2	1	no	—
236	C₃×C₄×C₅	—	4	2	no	—
237	C₃×C₄×C₅	#135	1	2	yes	complemented
238	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
239	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	C₅×Dic₃	—	2	1	no	—
241	C₅×Dic₃	—	4	2	no	—
242	C₅×Dic₃	C₄×D₄	1	2	yes	—
243	C₅×Dic₃	#135	1	2	yes	complemented
244	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
245	#239	—	2	4	no	—
246	#239	C₂×C₄×C₅	1	8	yes	complemented
247	C₂×D₁₂	—	2	2	no	—
248	C₂×D₁₂	C₂³×C₅	1	2	yes	—
249	C₂×C₄×D₃	—	2	2	no	—
250	C₂×C₄×D₃	—	2	2	no	—
251	C₂×C₄×D₃	—	2	2	no	—
252	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
253	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
254	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
255	C₃×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
256	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
258	C₃×C₄⋊C₄	—	2	2	no	—
259	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
260	C₃×C₄²	—	2	2	no	—
261	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
262	#215	C₂×C₄×C₅	1	8	yes	complemented
263	(C₂×D₃)⋊C₄	—	2	2	no	—
264	(C₂×D₃)⋊C₄	—	2	2	no	—
265	(C₂×D₃)⋊C₄	—	2	2	no	—
266	C₄⋊Dic₃	—	2	2	no	—
267	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
268	C₄×Dic₃	—	2	2	no	—
269	C₄×Dic₃	—	2	2	no	—
270	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
271	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
272	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
273	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
274	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
275	D₂₄	C₂×C₄×C₅	1	4	yes	complemented
276	D₃×C₈	—	2	2	no	—
277	D₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
278	C₂³×C₅	—	3	1	no	—
279	C₂³×C₅	—	6	2	no	—
280	C₅×Q₈	—	2	2	no	—
281	C₅×Q₈	C₂×C₄×D₃	1	4	yes	—
282	C₅×D₄	—	3	4	no	—
283	C₅×D₄	—	6	8	no	—
284	C₅×D₄	—	6	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	3	1	no	—
288	C₂×C₄×C₅	—	3	1	no	—
289	C₂×C₄×C₅	—	3	2	no	—
290	C₂×C₄×C₅	—	3	2	no	—
291	C₂×C₄×C₅	—	3	1	no	—
292	C₂×C₄×C₅	—	6	2	no	—
293	C₂×C₄×C₅	—	6	8	no	—
294	C₂×C₄×C₅	—	6	2	no	—
295	C₂×C₄×C₅	—	6	2	no	—
296	C₂×C₄×C₅	—	12	4	no	—
297	C₂×C₄×C₅	—	12	4	no	—
298	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
299	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
301	C₅×C₈	—	2	1	no	—
302	C₅×C₈	—	3	2	no	—
303	C₅×C₈	—	6	1	no	—
304	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
305	C₂×#41	—	3	2	no	—
306	#135	—	3	8	no	—
307	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
308	C₂×SD₁₆	—	3	2	no	—
309	C₂×D₈	—	3	1	no	—
310	C₂²×C₈	—	3	1	no	—
311	C₂²×C₈	—	3	1	no	—
312	C₄×Q₈	—	3	2	no	—
313	C₄×Q₈	C₂×C₅×D₃	1	2	yes	—
314	C₄×D₄	—	3	2	no	—
315	C₄×D₄	—	3	2	no	—
316	C₄×D₄	—	6	2	no	—
317	C₄×D₄	—	6	2	no	—
318	#117	—	3	2	no	—
319	#117	—	6	2	no	—
320	C₂×C₄²	—	3	1	no	—
321	C₂×C₄²	—	6	2	no	—
322	#107	—	3	1	no	—
323	#107	C₂×C₅×D₃	1	1	yes	characteristic
324	#106	—	3	2	no	—
325	#103	—	3	2	no	—
326	#103	C₂×C₅×D₃	1	2	yes	—
327	#102	—	3	2	no	—
328	#102	—	3	2	no	—
329	C₄×C₈	—	3	1	no	—
330	C₄×C₈	—	3	1	no	—
331	C₄×C₈	—	3	1	no	—
332	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
333	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
334	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
335	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
336	C₅×D₃	—	2	2	no	—
337	C₅×D₃	—	4	4	no	—
338	C₂²×D₃	—	2	2	no	—
339	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
340	C₃×Q₈	—	2	2	no	—
341	C₃×Q₈	C₂²×C₄×C₅	1	4	yes	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	2	2	no	—
344	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
347	C₂×Dic₃	—	2	2	no	—
348	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
349	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
350	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
351	D₁₂	—	2	8	no	—
352	D₁₂	—	2	2	no	—
353	D₁₂	C₂²×C₄×C₅	1	4	yes	—
354	C₄×D₃	—	2	2	no	—
355	C₄×D₃	—	2	8	no	—
356	C₄×D₃	—	2	2	no	—
357	C₄×D₃	—	4	4	no	—
358	C₄×D₃	—	4	4	no	—
359	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
360	C₄×D₃	C₅×#41	1	2	yes	—
361	C₃×C₈	—	2	1	no	—
362	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
363	C₃⋊C₈	—	2	1	no	—
364	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
365	C₂²×C₅	—	3	2	no	—
366	C₂²×C₅	—	6	1	no	—
367	C₂²×C₅	—	6	1	no	—
368	C₂²×C₅	—	6	4	no	—
369	C₂²×C₅	—	12	2	no	—
370	C₂²×C₅	—	12	2	no	—
371	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
372	C₄×C₅	—	2	1	no	—
373	C₄×C₅	—	2	4	no	—
374	C₄×C₅	—	3	2	no	—
375	C₄×C₅	—	3	2	no	—
376	C₄×C₅	—	4	2	no	—
377	C₄×C₅	—	6	1	no	—
378	C₄×C₅	—	12	2	no	—
379	C₄×C₅	#919	1	2	yes	direct product factor
380	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
381	C₄×C₅	D₃×#41	1	1	yes	characteristic
382	#41	—	3	8	no	—
383	#41	—	6	4	no	—
384	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
385	C₂×D₄	—	3	2	no	—
386	C₂×D₄	—	6	2	no	—
387	C₂²×C₄	—	3	1	no	—
388	C₂²×C₄	—	3	1	no	—
389	C₂²×C₄	—	3	1	no	—
390	C₂²×C₄	—	6	2	no	—
391	C₂²×C₄	—	6	2	no	—
392	C₂²×C₄	—	6	2	no	—
393	Q₁₆	C₄×C₅×D₃	1	4	yes	complemented
394	SD₁₆	—	3	8	no	—
395	D₈	—	3	4	no	—
396	C₂×C₈	—	3	1	no	—
397	C₂×C₈	—	3	4	no	—
398	C₂×C₈	—	3	1	no	—
399	C₂×C₈	—	6	2	no	—
400	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
401	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	3	2	no	—
404	C₄⋊C₄	—	6	2	no	—
405	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
406	C₂²⋊C₄	—	6	2	no	—
407	C₂²⋊C₄	—	6	2	no	—
408	C₂²⋊C₄	—	6	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	3	1	no	—
411	C₄²	—	3	1	no	—
412	C₄²	—	3	1	no	—
413	C₄²	—	6	2	no	—
414	C₄²	—	6	2	no	—
415	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
416	C₃×C₅	C₄×#135	1	1	yes	characteristic, complemented, Hall
417	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
418	C₂×D₃	—	2	1	no	—
419	C₂×D₃	—	2	1	no	—
420	C₂×D₃	—	2	4	no	—
421	C₂×D₃	—	4	2	no	—
422	C₂×D₃	—	4	2	no	—
423	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
424	C₃×C₄	—	2	4	no	—
425	C₃×C₄	—	2	1	no	—
426	C₃×C₄	—	4	2	no	—
427	C₃×C₄	C₅×#135	1	2	yes	complemented
428	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
429	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
430	Dic₃	—	2	1	no	—
431	Dic₃	—	4	2	no	—
432	Dic₃	C₄×C₅×D₄	1	2	yes	—
433	Dic₃	C₅×#135	1	2	yes	complemented
434	C₂×C₅	—	6	2	no	—
435	C₂×C₅	—	12	4	no	—
436	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
437	C₂×C₅	C₂×#919	1	1	yes	characteristic
438	C₂×C₅	D₃×#135	1	1	yes	characteristic
439	C₂³	—	3	1	no	—
440	C₂³	—	6	2	no	—
441	Q₈	—	2	2	no	—
442	Q₈	C₂×C₄×C₅×D₃	1	4	yes	—
443	D₄	—	3	4	no	—
444	D₄	—	6	8	no	—
445	D₄	—	6	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	3	1	no	—
449	C₂×C₄	—	3	1	no	—
450	C₂×C₄	—	3	2	no	—
451	C₂×C₄	—	3	2	no	—
452	C₂×C₄	—	3	1	no	—
453	C₂×C₄	—	6	2	no	—
454	C₂×C₄	—	6	8	no	—
455	C₂×C₄	—	6	2	no	—
456	C₂×C₄	—	6	2	no	—
457	C₂×C₄	—	12	4	no	—
458	C₂×C₄	—	12	4	no	—
459	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
460	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
461	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
462	C₈	—	2	1	no	—
463	C₈	—	3	2	no	—
464	C₈	—	6	1	no	—
465	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
466	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
467	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
468	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
469	D₃	—	2	2	no	—
470	D₃	—	4	4	no	—
471	C₅	C₄×#919	1	1	yes	characteristic, direct product factor, Sylow
472	C₂²	—	3	2	no	—
473	C₂²	—	6	1	no	—
474	C₂²	—	6	1	no	—
475	C₂²	—	6	4	no	—
476	C₂²	—	12	2	no	—
477	C₂²	—	12	2	no	—
478	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	4	no	—
481	C₄	—	3	2	no	—
482	C₄	—	3	2	no	—
483	C₄	—	4	2	no	—
484	C₄	—	6	1	no	—
485	C₄	—	12	2	no	—
486	C₄	C₅×#919	1	2	yes	direct product factor
487	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
488	C₄	C₅×D₃×#41	1	1	yes	characteristic
489	C₃	C₄×C₅×#135	1	1	yes	characteristic, complemented, Sylow
490	C₂	—	6	2	no	—
491	C₂	—	12	4	no	—
492	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
493	C₂	C₂×C₅×#919	1	1	yes	characteristic
494	C₂	C₅×D₃×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×Q₁₆	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#919	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₄×C₅×Q₁₆	D₃
hypocenter	C₃	C₄×C₅×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×#239	C₂	semidirect
3. C₃×C₄×C₅×Q₁₆	C₂	semidirect
4. C₅×Dic₃×Q₁₆	C₂	semidirect
5. C₄×C₅×#215	C₂	semidirect
6. C₅×#4880	C₂	semidirect
7. C₅×#4872	C₂	semidirect
8. C₅×#4804	C₂	semidirect
9. C₅×#4788	C₂	semidirect
10. C₄×C₅×D₂₄	C₂	semidirect
11. C₄×C₅×D₃×C₈	C₂	semidirect
18. C₅×#919	C₄	direct (N × H)
41. C₄×#919	C₅	direct (N × H)
45. C₄×C₅×Q₁₆	D₃	semidirect
55. C₅×#239	C₂×C₄	semidirect
64. C₃×C₅×Q₁₆	C₂×C₄	semidirect
71. C₅×#215	C₂×C₄	semidirect
84. C₅×D₂₄	C₂×C₄	semidirect
86. C₅×D₃×C₈	C₂×C₄	semidirect
88. C₄×#239	C₂×C₅	semidirect
89. C₃×C₄×Q₁₆	C₂×C₅	semidirect
90. Dic₃×Q₁₆	C₂×C₅	semidirect
91. C₄×#215	C₂×C₅	semidirect
92. #4880	C₂×C₅	semidirect
93. #4872	C₂×C₅	semidirect
94. #4804	C₂×C₅	semidirect
95. #4788	C₂×C₅	semidirect
96. C₄×D₂₄	C₂×C₅	semidirect
97. C₄×D₃×C₈	C₂×C₅	semidirect
159. #919	C₄×C₅	direct (N × H)
193. C₅×Q₁₆	C₄×D₃	semidirect
219. C₄×Q₁₆	C₅×D₃	semidirect
237. C₃×C₄×C₅	#135	semidirect
243. C₅×Dic₃	#135	semidirect
246. #239	C₂×C₄×C₅	semidirect
255. C₃×Q₁₆	C₂×C₄×C₅	semidirect
262. #215	C₂×C₄×C₅	semidirect
275. D₂₄	C₂×C₄×C₅	semidirect
277. D₃×C₈	C₂×C₄×C₅	semidirect
379. C₄×C₅	#919	direct (N × H)
393. Q₁₆	C₄×C₅×D₃	semidirect
416. C₃×C₅	C₄×#135	semidirect
427. C₃×C₄	C₅×#135	semidirect
433. Dic₃	C₅×#135	semidirect
471. C₅	C₄×#919	direct (N × H)
486. C₄	C₅×#919	direct (N × H)
489. C₃	C₄×C₅×#135	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#919	2
C₄×C₅×#239	2
C₃×C₄×C₅×Q₁₆	2
C₅×Dic₃×Q₁₆	2
C₄×C₅×#215	2
C₅×#4880	2
C₅×#4872	2
C₅×#4804	2
C₅×#4788	2
C₄×C₅×D₂₄	2
C₄×C₅×D₃×C₈	2
C₄×C₅×#135	3
C₄×#919	5

Subgroups — C4×C5×#919 #14416215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#919 #14416215