Subgroups — C₂×C₅×#5141 #14429292

Order 1920.

936 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#951	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#949	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₅×#204	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5141	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#824	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#823	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#819	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#471	—	3	1	no	maximal, Hall
10	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
11	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
12	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
13	C₃×C₅×#131	—	2	2	no	—
14	C₃×C₅×#131	C₂²	1	4	yes	complemented
15	C₂×C₃×C₅×M₁₆	—	2	1	no	—
16	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₅×C₈	—	2	1	no	—
18	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
19	C₅×#951	—	2	2	no	—
20	C₅×#951	C₂²	1	4	yes	complemented
21	C₅×#949	—	2	2	no	—
22	C₅×#949	C₂²	1	4	yes	—
23	C₂×C₅×#216	—	2	1	no	—
24	C₂×C₅×#215	—	2	1	no	—
25	C₂×C₅×#214	—	2	1	no	—
26	C₂×C₅×#213	—	2	1	no	—
27	C₂×C₅×#208	C₂²	1	1	yes	characteristic
28	C₂×C₅×#208	C₂²	1	1	yes	characteristic
29	C₂×C₅×#204	—	2	1	no	—
30	C₂×C₅×#204	—	2	1	no	—
31	C₂×C₅×#204	—	2	2	no	—
32	C₂×C₅×#204	C₂²	1	4	yes	complemented
33	C₅×#824	C₂²	1	4	yes	complemented
34	C₅×#823	C₂²	1	4	yes	complemented
35	C₅×#819	C₂²	1	4	yes	complemented
36	C₂×#5141	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₂×C₅×#137	—	3	1	no	—
38	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
39	C₂²×C₅×SD₁₆	—	3	1	no	—
40	C₂×C₅×#131	D₃	1	1	yes	characteristic, complemented
41	C₅×#471	—	3	8	no	—
42	C₂×C₅×#108	—	3	1	no	—
43	C₂×C₅×#101	—	3	1	no	—
44	C₂×C₅×#100	—	3	1	no	—
45	C₂³×C₅×D₃	—	2	1	no	—
46	C₃×C₅×#41	—	2	1	no	—
47	C₃×C₅×#41	—	2	1	no	—
48	C₃×C₅×#41	D₄	1	2	yes	—
49	C₃×C₅×#41	C₂³	1	2	yes	—
50	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
51	C₂×C₃×C₅×D₄	—	2	1	no	—
52	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	—	2	1	no	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₅×Dic₃	—	2	1	no	—
56	C₂×C₅×D₁₂	—	2	1	no	—
57	C₂×C₅×D₁₂	—	2	1	no	—
58	C₂×C₅×D₁₂	—	2	1	no	—
59	C₂×C₅×D₁₂	—	2	1	no	—
60	C₂×C₅×D₁₂	—	2	1	no	—
61	C₂×C₅×D₁₂	C₂³	1	2	yes	—
62	C₂×C₅×Dic₆	—	2	1	no	—
63	C₂×C₅×Dic₆	—	2	1	no	—
64	C₂×C₅×Dic₆	—	2	1	no	—
65	C₂×C₅×Dic₆	—	2	1	no	—
66	C₂×C₅×Dic₆	—	2	1	no	—
67	C₂×C₅×Dic₆	C₂³	1	2	yes	—
68	C₃×C₅×M₁₆	—	2	1	no	—
69	C₃×C₅×M₁₆	—	2	4	no	—
70	C₃×C₅×M₁₆	C₂³	1	2	yes	—
71	C₂×C₃×C₅×C₈	—	2	1	no	—
72	C₂×C₃×C₅×C₈	—	2	4	no	—
73	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
74	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
75	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
76	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
77	C₅×#216	—	2	4	no	—
78	C₅×#215	—	2	4	no	—
79	C₅×#214	—	2	4	no	—
80	C₅×#213	—	2	4	no	—
81	C₅×#208	—	2	1	no	—
82	C₅×#208	—	2	1	no	—
83	C₅×#208	C₂³	1	2	yes	—
84	C₅×#208	C₂³	1	2	yes	—
85	C₂×C₅×C₃⋊C₈	—	2	1	no	—
86	C₂×C₅×C₃⋊C₈	—	2	1	no	—
87	C₅×#204	—	2	4	no	—
88	C₅×#204	—	2	4	no	—
89	C₂×C₃×#131	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂×#951	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×#949	C₂×C₅	1	1	yes	characteristic
92	C₂²×#204	C₂×C₅	1	1	yes	characteristic, complemented
93	#5141	C₂×C₅	1	8	yes	direct product factor
94	C₂×#824	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂×#823	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×#819	C₂×C₅	1	1	yes	characteristic, complemented
97	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
98	C₂²×C₅×Q₈	—	3	1	no	—
99	C₂²×C₅×D₄	—	3	1	no	—
100	C₅×#137	—	3	4	no	—
101	C₅×#137	—	6	2	no	—
102	C₅×AGL(1,ℤ/8)	—	3	4	no	—
103	C₅×AGL(1,ℤ/8)	—	6	2	no	—
104	C₂×C₅×Q₁₆	—	6	1	no	—
105	C₂×C₅×SD₁₆	—	3	4	no	—
106	C₂×C₅×SD₁₆	—	6	1	no	—
107	C₂×C₅×SD₁₆	—	6	1	no	—
108	C₂×C₅×SD₁₆	—	6	1	no	—
109	C₂×C₅×SD₁₆	—	6	1	no	—
110	C₂×C₅×SD₁₆	—	6	2	no	—
111	C₂×C₅×D₈	—	6	1	no	—
112	C₅×#131	—	2	2	no	—
113	C₅×#131	C₂×D₃	1	4	yes	complemented
114	C₂×C₅×M₁₆	—	2	1	no	—
115	C₂×C₅×M₁₆	—	3	1	no	—
116	C₂×C₅×M₁₆	—	3	1	no	—
117	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
118	C₂²×C₅×C₈	—	2	1	no	—
119	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
120	C₅×#108	—	3	4	no	—
121	C₅×#101	—	3	4	no	—
122	C₅×#100	—	3	4	no	—
123	C₂×#471	—	3	1	no	Sylow
124	C₂³×C₃×C₅	—	2	1	no	—
125	C₂³×C₃×C₅	#41	1	1	yes	characteristic
126	C₂²×C₅×D₃	—	2	2	no	—
127	C₂²×C₅×D₃	—	4	1	no	—
128	C₂²×C₅×D₃	—	4	1	no	—
129	C₂²×C₅×D₃	—	8	2	no	—
130	C₃×C₅×Q₈	—	2	1	no	—
131	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
132	C₃×C₅×D₄	—	2	2	no	—
133	C₃×C₅×D₄	—	2	2	no	—
134	C₃×C₅×D₄	—	2	1	no	—
135	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
136	C₂×C₃×C₄×C₅	—	2	1	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
144	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₂×C₅×Dic₃	—	2	2	no	—
146	C₂×C₅×Dic₃	—	4	1	no	—
147	C₂×C₅×Dic₃	—	4	1	no	—
148	C₅×D₁₂	—	2	2	no	—
149	C₅×D₁₂	—	2	2	no	—
150	C₅×D₁₂	—	4	1	no	—
151	C₅×D₁₂	—	4	1	no	—
152	C₅×Dic₆	—	2	2	no	—
153	C₅×Dic₆	—	2	2	no	—
154	C₅×Dic₆	—	4	1	no	—
155	C₅×Dic₆	—	4	1	no	—
156	C₃×C₅×C₈	—	2	2	no	—
157	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
158	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
159	C₅×C₃⋊C₈	—	2	2	no	—
160	C₅×C₃⋊C₈	—	2	2	no	—
161	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
162	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
163	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
164	C₃×#131	—	2	2	no	—
165	C₃×#131	C₂²×C₅	1	4	yes	complemented
166	C₂×C₃×M₁₆	—	2	1	no	—
167	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
168	C₂²×C₃×C₈	—	2	1	no	—
169	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
170	#951	—	2	2	no	—
171	#951	C₂²×C₅	1	4	yes	complemented
172	#949	—	2	2	no	—
173	#949	C₂²×C₅	1	4	yes	—
174	C₂×#216	—	2	1	no	—
175	C₂×#215	—	2	1	no	—
176	C₂×#214	—	2	1	no	—
177	C₂×#213	—	2	1	no	—
178	C₂×#208	C₂²×C₅	1	1	yes	characteristic
179	C₂×#208	C₂²×C₅	1	1	yes	characteristic
180	C₂×#204	—	2	1	no	—
181	C₂×#204	—	2	1	no	—
182	C₂×#204	—	2	2	no	—
183	C₂×#204	C₂²×C₅	1	4	yes	complemented
184	#824	C₂²×C₅	1	4	yes	complemented
185	#823	C₂²×C₅	1	4	yes	complemented
186	#819	C₂²×C₅	1	4	yes	complemented
187	C₂⁴×C₅	—	6	1	no	—
188	C₅×#41	—	2	1	no	—
189	C₅×#41	—	2	1	no	—
190	C₅×#41	D₁₂	1	2	yes	—
191	C₅×#41	C₂²×D₃	1	2	yes	—
192	C₂×C₅×Q₈	—	3	2	no	—
193	C₂×C₅×Q₈	—	6	1	no	—
194	C₂×C₅×Q₈	—	6	1	no	—
195	C₂×C₅×Q₈	—	6	1	no	—
196	C₂×C₅×Q₈	—	6	1	no	—
197	C₂×C₅×Q₈	—	6	1	no	—
198	C₂×C₅×Q₈	D₁₂	1	1	yes	characteristic
199	C₂×C₅×D₄	—	2	1	no	—
200	C₂×C₅×D₄	—	3	2	no	—
201	C₂×C₅×D₄	—	6	1	no	—
202	C₂×C₅×D₄	—	6	1	no	—
203	C₂×C₅×D₄	—	6	1	no	—
204	C₂×C₅×D₄	—	6	1	no	—
205	C₂×C₅×D₄	—	6	1	no	—
206	C₂×C₅×D₄	D₁₂	1	1	yes	characteristic
207	C₂²×C₄×C₅	—	2	1	no	—
208	C₂²×C₄×C₅	—	6	1	no	—
209	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
210	C₅×Q₁₆	—	6	4	no	—
211	C₅×SD₁₆	—	6	4	no	—
212	C₅×SD₁₆	—	6	4	no	—
213	C₅×SD₁₆	—	6	4	no	—
214	C₅×SD₁₆	—	6	4	no	—
215	C₅×D₈	—	6	4	no	—
216	C₅×M₁₆	—	2	1	no	—
217	C₅×M₁₆	—	2	4	no	—
218	C₅×M₁₆	—	3	2	no	—
219	C₅×M₁₆	—	3	2	no	—
220	C₅×M₁₆	—	6	1	no	—
221	C₅×M₁₆	—	6	1	no	—
222	C₅×M₁₆	C₂²×D₃	1	2	yes	—
223	C₂×C₅×C₈	—	2	1	no	—
224	C₂×C₅×C₈	—	2	4	no	—
225	C₂×C₅×C₈	—	6	1	no	—
226	C₂×C₅×C₈	—	6	1	no	—
227	C₂×C₅×C₈	#67	1	1	yes	characteristic
228	C₂×C₅×C₈	#67	1	1	yes	characteristic
229	C₂×C₅×C₈	#67	1	2	yes	—
230	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
231	C₂×#137	—	3	1	no	—
232	C₂×AGL(1,ℤ/8)	—	3	1	no	—
233	C₂²×SD₁₆	—	3	1	no	—
234	C₂×#131	C₅×D₃	1	1	yes	characteristic, complemented
235	#471	—	3	8	no	—
236	C₂×#108	—	3	1	no	—
237	C₂×#101	—	3	1	no	—
238	C₂×#100	—	3	1	no	—
239	C₂²×C₃×C₅	—	2	2	no	—
240	C₂²×C₃×C₅	—	2	2	no	—
241	C₂²×C₃×C₅	—	4	2	no	—
242	C₂²×C₃×C₅	#121	1	1	yes	characteristic
243	C₂²×C₃×C₅	#121	1	1	yes	characteristic
244	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
245	C₂×C₅×D₃	—	4	2	no	—
246	C₂×C₅×D₃	—	8	2	no	—
247	C₂×C₅×D₃	—	8	2	no	—
248	C₂×C₅×D₃	—	8	2	no	—
249	C₃×C₄×C₅	—	2	2	no	—
250	C₃×C₄×C₅	#121	1	1	yes	characteristic
251	C₃×C₄×C₅	#121	1	1	yes	characteristic
252	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
253	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
254	C₅×Dic₃	—	4	2	no	—
255	C₂³×D₃	—	2	1	no	—
256	C₃×#41	—	2	1	no	—
257	C₃×#41	—	2	1	no	—
258	C₃×#41	C₅×D₄	1	2	yes	—
259	C₃×#41	C₂³×C₅	1	2	yes	—
260	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
261	C₂×C₃×D₄	—	2	1	no	—
262	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
263	C₂²×C₃×C₄	—	2	1	no	—
264	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
265	C₂²×Dic₃	—	2	1	no	—
266	C₂×D₁₂	—	2	1	no	—
267	C₂×D₁₂	—	2	1	no	—
268	C₂×D₁₂	—	2	1	no	—
269	C₂×D₁₂	—	2	1	no	—
270	C₂×D₁₂	—	2	1	no	—
271	C₂×D₁₂	C₂³×C₅	1	2	yes	—
272	C₂×Dic₆	—	2	1	no	—
273	C₂×Dic₆	—	2	1	no	—
274	C₂×Dic₆	—	2	1	no	—
275	C₂×Dic₆	—	2	1	no	—
276	C₂×Dic₆	—	2	1	no	—
277	C₂×Dic₆	C₂³×C₅	1	2	yes	—
278	C₃×M₁₆	—	2	1	no	—
279	C₃×M₁₆	—	2	4	no	—
280	C₃×M₁₆	C₂³×C₅	1	2	yes	—
281	C₂×C₃×C₈	—	2	1	no	—
282	C₂×C₃×C₈	—	2	4	no	—
283	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
284	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
285	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
286	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
287	#216	—	2	4	no	—
288	#215	—	2	4	no	—
289	#214	—	2	4	no	—
290	#213	—	2	4	no	—
291	#208	—	2	1	no	—
292	#208	—	2	1	no	—
293	#208	C₂³×C₅	1	2	yes	—
294	#208	C₂³×C₅	1	2	yes	—
295	C₂×C₃⋊C₈	—	2	1	no	—
296	C₂×C₃⋊C₈	—	2	1	no	—
297	#204	—	2	4	no	—
298	#204	—	2	4	no	—
299	C₂³×C₅	—	2	1	no	—
300	C₂³×C₅	—	6	2	no	—
301	C₂³×C₅	—	12	1	no	—
302	C₂³×C₅	—	12	1	no	—
303	C₂³×C₅	—	24	2	no	—
304	C₂³×C₅	#235	1	1	yes	characteristic
305	C₅×Q₈	—	2	1	no	—
306	C₅×Q₈	—	6	2	no	—
307	C₅×Q₈	—	6	2	no	—
308	C₅×Q₈	—	12	1	no	—
309	C₅×Q₈	—	12	1	no	—
310	C₅×Q₈	C₂×D₁₂	1	2	yes	—
311	C₅×D₄	—	2	2	no	—
312	C₅×D₄	—	2	2	no	—
313	C₅×D₄	—	2	1	no	—
314	C₅×D₄	—	6	2	no	—
315	C₅×D₄	—	6	2	no	—
316	C₅×D₄	—	12	1	no	—
317	C₅×D₄	—	12	1	no	—
318	C₅×D₄	C₂×D₁₂	1	2	yes	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	6	2	no	—
323	C₂×C₄×C₅	—	12	1	no	—
324	C₂×C₄×C₅	—	12	1	no	—
325	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
326	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
327	C₂×C₄×C₅	#235	1	1	yes	characteristic
328	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
329	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
330	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
331	C₅×C₈	—	2	2	no	—
332	C₅×C₈	—	6	2	no	—
333	C₅×C₈	—	6	2	no	—
334	C₅×C₈	C₂×#67	1	2	yes	—
335	C₅×C₈	C₂×#67	1	2	yes	—
336	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
337	C₂²×Q₈	—	3	1	no	—
338	C₂²×D₄	—	3	1	no	—
339	#137	—	3	4	no	—
340	#137	—	6	2	no	—
341	AGL(1,ℤ/8)	—	3	4	no	—
342	AGL(1,ℤ/8)	—	6	2	no	—
343	C₂×Q₁₆	—	6	1	no	—
344	C₂×SD₁₆	—	3	4	no	—
345	C₂×SD₁₆	—	6	1	no	—
346	C₂×SD₁₆	—	6	1	no	—
347	C₂×SD₁₆	—	6	1	no	—
348	C₂×SD₁₆	—	6	1	no	—
349	C₂×SD₁₆	—	6	2	no	—
350	C₂×D₈	—	6	1	no	—
351	#131	—	2	2	no	—
352	#131	C₂×C₅×D₃	1	4	yes	complemented
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	3	1	no	—
355	C₂×M₁₆	—	3	1	no	—
356	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
357	C₂²×C₈	—	2	1	no	—
358	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
359	#108	—	3	4	no	—
360	#101	—	3	4	no	—
361	#100	—	3	4	no	—
362	C₂×C₃×C₅	—	2	1	no	—
363	C₂×C₃×C₅	—	2	1	no	—
364	C₂×C₃×C₅	—	4	2	no	—
365	C₂×C₃×C₅	#471	1	2	yes	complemented
366	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
367	C₅×D₃	—	8	2	no	—
368	C₂³×C₃	—	2	1	no	—
369	C₂³×C₃	C₅×#41	1	1	yes	characteristic
370	C₂²×D₃	—	2	2	no	—
371	C₂²×D₃	—	4	1	no	—
372	C₂²×D₃	—	4	1	no	—
373	C₂²×D₃	—	8	2	no	—
374	C₃×Q₈	—	2	1	no	—
375	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
376	C₃×D₄	—	2	2	no	—
377	C₃×D₄	—	2	2	no	—
378	C₃×D₄	—	2	1	no	—
379	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	2	2	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
384	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
386	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
387	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
389	C₂×Dic₃	—	2	2	no	—
390	C₂×Dic₃	—	4	1	no	—
391	C₂×Dic₃	—	4	1	no	—
392	D₁₂	—	2	2	no	—
393	D₁₂	—	2	2	no	—
394	D₁₂	—	4	1	no	—
395	D₁₂	—	4	1	no	—
396	Dic₆	—	2	2	no	—
397	Dic₆	—	2	2	no	—
398	Dic₆	—	4	1	no	—
399	Dic₆	—	4	1	no	—
400	C₃×C₈	—	2	2	no	—
401	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
402	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
403	C₃⋊C₈	—	2	2	no	—
404	C₃⋊C₈	—	2	2	no	—
405	C₂²×C₅	—	2	2	no	—
406	C₂²×C₅	—	2	2	no	—
407	C₂²×C₅	—	4	2	no	—
408	C₂²×C₅	—	12	2	no	—
409	C₂²×C₅	—	24	2	no	—
410	C₂²×C₅	—	24	2	no	—
411	C₂²×C₅	—	24	2	no	—
412	C₂²×C₅	#930	1	1	yes	characteristic
413	C₂²×C₅	#930	1	1	yes	characteristic
414	C₂²×C₅	C₂×#235	1	1	yes	characteristic
415	C₄×C₅	—	2	2	no	—
416	C₄×C₅	—	12	2	no	—
417	C₄×C₅	#930	1	1	yes	characteristic
418	C₄×C₅	#930	1	1	yes	characteristic
419	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
420	C₄×C₅	C₂²×#67	1	1	yes	characteristic
421	C₂⁴	—	6	1	no	—
422	#41	—	2	1	no	—
423	#41	—	2	1	no	—
424	#41	C₅×D₁₂	1	2	yes	—
425	#41	C₂²×C₅×D₃	1	2	yes	—
426	C₂×Q₈	—	3	2	no	—
427	C₂×Q₈	—	6	1	no	—
428	C₂×Q₈	—	6	1	no	—
429	C₂×Q₈	—	6	1	no	—
430	C₂×Q₈	—	6	1	no	—
431	C₂×Q₈	—	6	1	no	—
432	C₂×Q₈	C₅×D₁₂	1	1	yes	characteristic
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	3	2	no	—
435	C₂×D₄	—	6	1	no	—
436	C₂×D₄	—	6	1	no	—
437	C₂×D₄	—	6	1	no	—
438	C₂×D₄	—	6	1	no	—
439	C₂×D₄	—	6	1	no	—
440	C₂×D₄	C₅×D₁₂	1	1	yes	characteristic
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	6	1	no	—
443	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
444	Q₁₆	—	6	4	no	—
445	SD₁₆	—	6	4	no	—
446	SD₁₆	—	6	4	no	—
447	SD₁₆	—	6	4	no	—
448	SD₁₆	—	6	4	no	—
449	D₈	—	6	4	no	—
450	M₁₆	—	2	1	no	—
451	M₁₆	—	2	4	no	—
452	M₁₆	—	3	2	no	—
453	M₁₆	—	3	2	no	—
454	M₁₆	—	6	1	no	—
455	M₁₆	—	6	1	no	—
456	M₁₆	C₂²×C₅×D₃	1	2	yes	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	4	no	—
459	C₂×C₈	—	6	1	no	—
460	C₂×C₈	—	6	1	no	—
461	C₂×C₈	C₅×#67	1	1	yes	characteristic
462	C₂×C₈	C₅×#67	1	1	yes	characteristic
463	C₂×C₈	C₅×#67	1	2	yes	—
464	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
465	C₃×C₅	C₂×#471	1	1	yes	characteristic, complemented, Hall
466	C₂²×C₃	—	2	2	no	—
467	C₂²×C₃	—	2	2	no	—
468	C₂²×C₃	—	4	2	no	—
469	C₂²×C₃	C₅×#121	1	1	yes	characteristic
470	C₂²×C₃	C₅×#121	1	1	yes	characteristic
471	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
472	C₂×D₃	—	4	2	no	—
473	C₂×D₃	—	8	2	no	—
474	C₂×D₃	—	8	2	no	—
475	C₂×D₃	—	8	2	no	—
476	C₃×C₄	—	2	2	no	—
477	C₃×C₄	C₅×#121	1	1	yes	characteristic
478	C₃×C₄	C₅×#121	1	1	yes	characteristic
479	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
480	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
481	Dic₃	—	4	2	no	—
482	C₂×C₅	—	2	1	no	—
483	C₂×C₅	—	2	1	no	—
484	C₂×C₅	—	4	2	no	—
485	C₂×C₅	—	24	2	no	—
486	C₂×C₅	#5141	1	2	yes	direct product factor
487	C₂×C₅	C₂×#930	1	1	yes	characteristic
488	C₂³	—	2	1	no	—
489	C₂³	—	6	2	no	—
490	C₂³	—	12	1	no	—
491	C₂³	—	12	1	no	—
492	C₂³	—	24	2	no	—
493	C₂³	C₅×#235	1	1	yes	characteristic
494	Q₈	—	2	1	no	—
495	Q₈	—	6	2	no	—
496	Q₈	—	6	2	no	—
497	Q₈	—	12	1	no	—
498	Q₈	—	12	1	no	—
499	Q₈	C₂×C₅×D₁₂	1	2	yes	—
500	D₄	—	2	2	no	—
501	D₄	—	2	2	no	—
502	D₄	—	2	1	no	—
503	D₄	—	6	2	no	—
504	D₄	—	6	2	no	—
505	D₄	—	12	1	no	—
506	D₄	—	12	1	no	—
507	D₄	C₂×C₅×D₁₂	1	2	yes	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	6	2	no	—
512	C₂×C₄	—	12	1	no	—
513	C₂×C₄	—	12	1	no	—
514	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
515	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
516	C₂×C₄	C₅×#235	1	1	yes	characteristic
517	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
518	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
519	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
520	C₈	—	2	2	no	—
521	C₈	—	6	2	no	—
522	C₈	—	6	2	no	—
523	C₈	C₂×C₅×#67	1	2	yes	—
524	C₈	C₂×C₅×#67	1	2	yes	—
525	C₂×C₃	—	2	1	no	—
526	C₂×C₃	—	2	1	no	—
527	C₂×C₃	—	4	2	no	—
528	C₂×C₃	C₅×#471	1	2	yes	complemented
529	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
530	D₃	—	8	2	no	—
531	C₅	C₂×#5141	1	1	yes	characteristic, direct product factor, Sylow
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	12	2	no	—
536	C₂²	—	24	2	no	—
537	C₂²	—	24	2	no	—
538	C₂²	—	24	2	no	—
539	C₂²	C₅×#930	1	1	yes	characteristic
540	C₂²	C₅×#930	1	1	yes	characteristic
541	C₂²	C₂×C₅×#235	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	12	2	no	—
544	C₄	C₅×#930	1	1	yes	characteristic
545	C₄	C₅×#930	1	1	yes	characteristic
546	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
547	C₄	C₂²×C₅×#67	1	1	yes	characteristic
548	C₃	C₂×C₅×#471	1	1	yes	characteristic, complemented, Sylow
549	C₂	—	2	1	no	—
550	C₂	—	2	1	no	—
551	C₂	—	4	2	no	—
552	C₂	—	24	2	no	—
553	C₂	C₅×#5141	1	2	yes	direct product factor
554	C₂	C₂×C₅×#930	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#930
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#131	C₂
socle	C₂²×C₃×C₅	#121
prime radical	C₂×C₅×#949	C₂
hypercenter	C₂×C₅×#131	D₃
hypocenter	C₃	C₂×C₅×#471
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#131

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#131	C₂	semidirect
2. C₂×C₅×#951	C₂	semidirect
4. C₂²×C₅×#204	C₂	semidirect
5. C₅×#5141	C₂	direct (N × H)
6. C₂×C₅×#824	C₂	semidirect
7. C₂×C₅×#823	C₂	semidirect
8. C₂×C₅×#819	C₂	semidirect
14. C₃×C₅×#131	C₂²	semidirect
20. C₅×#951	C₂²	semidirect
32. C₂×C₅×#204	C₂²	semidirect
33. C₅×#824	C₂²	semidirect
34. C₅×#823	C₂²	semidirect
35. C₅×#819	C₂²	semidirect
36. C₂×#5141	C₅	direct (N × H)
40. C₂×C₅×#131	D₃	semidirect
89. C₂×C₃×#131	C₂×C₅	semidirect
90. C₂×#951	C₂×C₅	semidirect
92. C₂²×#204	C₂×C₅	semidirect
93. #5141	C₂×C₅	direct (N × H)
94. C₂×#824	C₂×C₅	semidirect
95. C₂×#823	C₂×C₅	semidirect
96. C₂×#819	C₂×C₅	semidirect
113. C₅×#131	C₂×D₃	semidirect
165. C₃×#131	C₂²×C₅	semidirect
171. #951	C₂²×C₅	semidirect
183. C₂×#204	C₂²×C₅	semidirect
184. #824	C₂²×C₅	semidirect
185. #823	C₂²×C₅	semidirect
186. #819	C₂²×C₅	semidirect
234. C₂×#131	C₅×D₃	semidirect
352. #131	C₂×C₅×D₃	semidirect
365. C₂×C₃×C₅	#471	semidirect
465. C₃×C₅	C₂×#471	semidirect
486. C₂×C₅	#5141	direct (N × H)
528. C₂×C₃	C₅×#471	semidirect
531. C₅	C₂×#5141	direct (N × H)
548. C₃	C₂×C₅×#471	semidirect
553. C₂	C₅×#5141	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#131	2
C₂×C₅×#951	2
C₂×C₅×#949	2
C₂²×C₅×#204	2
C₅×#5141	2
C₂×C₅×#824	2
C₂×C₅×#823	2
C₂×C₅×#819	2
C₂×C₅×#471	3
C₂×#5141	5

Subgroups — C2×C5×#5141 #14429292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5141 #14429292