Subgroups — C₂×C₅×#5016 #14425929

Order 1920.

1128 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×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#214	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#213	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#875	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5016	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#810	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#463	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	—	2	1	no	—
12	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
13	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
14	C₃×C₄×C₅×D₄	—	2	2	no	—
15	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₅×#214	—	2	4	no	—
20	C₂×C₅×#214	C₂²	1	4	yes	complemented
21	C₂×C₅×#213	—	2	4	no	—
22	C₂×C₅×#213	C₂²	1	4	yes	—
23	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
24	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
25	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
27	C₅×#875	—	2	2	no	—
28	C₅×#875	C₂²	1	4	yes	complemented
29	C₅×#810	C₂²	1	4	yes	complemented
30	C₅×#809	C₂²	1	4	yes	complemented
31	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
32	C₂×#5016	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂²×C₅×SD₁₆	—	3	1	no	—
34	C₂²×C₅×D₈	—	3	1	no	—
35	C₂×C₅×#124	—	3	1	no	—
36	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic, complemented
37	C₅×#463	—	3	8	no	—
38	C₂×C₅×C₄⋊C₈	—	3	1	no	—
39	C₂×C₅×#103	—	3	1	no	—
40	C₂×C₅×#102	—	3	1	no	—
41	C₂⁴×C₃×C₅	—	2	1	no	—
42	C₂³×C₅×D₃	—	2	1	no	—
43	C₂×C₃×C₅×D₄	—	2	1	no	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	D₄	1	4	yes	—
46	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	—	2	1	no	—
48	C₂²×C₃×C₄×C₅	—	2	4	no	—
49	C₂²×C₃×C₄×C₅	—	4	4	no	—
50	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₅×Dic₃	—	2	1	no	—
54	C₂×C₅×D₁₂	—	2	2	no	—
55	C₂×C₅×D₁₂	—	2	2	no	—
56	C₂×C₅×D₁₂	—	2	1	no	—
57	C₂×C₅×D₁₂	C₂³	1	2	yes	—
58	C₂×C₅×Dic₆	—	2	2	no	—
59	C₂×C₅×Dic₆	—	2	2	no	—
60	C₂×C₅×Dic₆	—	2	1	no	—
61	C₂×C₅×Dic₆	C₂³	1	2	yes	—
62	C₃×C₅×C₄⋊C₄	—	2	1	no	—
63	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
65	C₃×C₄²×C₅	D₄	1	2	yes	—
66	C₃×C₄²×C₅	C₂³	1	2	yes	—
67	C₅×#214	—	2	8	no	—
68	C₅×#213	—	2	8	no	—
69	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
70	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
71	C₂×C₅×C₃⋊C₈	—	2	2	no	—
72	C₂×C₅×C₃⋊C₈	—	2	2	no	—
73	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
74	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
75	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂²×#214	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂²×#213	C₂×C₅	1	1	yes	characteristic
78	C₂×#875	C₂×C₅	1	1	yes	characteristic, complemented
79	#5016	C₂×C₅	1	8	yes	direct product factor
80	C₂×#810	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂×#809	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂²×C₅×Q₈	—	3	1	no	—
84	C₂²×C₅×D₄	—	3	1	no	—
85	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
86	C₂³×C₄×C₅	—	2	1	no	—
87	C₂×C₅×SD₁₆	—	3	4	no	—
88	C₂×C₅×SD₁₆	—	6	4	no	—
89	C₂×C₅×D₈	—	3	4	no	—
90	C₂×C₅×D₈	—	6	4	no	—
91	C₂²×C₅×C₈	—	3	1	no	—
92	C₂²×C₅×C₈	—	3	1	no	—
93	C₅×#124	—	3	4	no	—
94	C₅×#124	—	6	2	no	—
95	C₄×C₅×D₄	—	2	2	no	—
96	C₄×C₅×D₄	C₂×D₃	1	4	yes	complemented
97	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
98	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
100	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
101	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
102	C₅×C₄⋊C₈	—	3	4	no	—
103	C₅×#103	—	3	4	no	—
104	C₅×#102	—	3	4	no	—
105	C₂×#463	—	3	1	no	Sylow
106	C₂³×C₃×C₅	—	2	4	no	—
107	C₂³×C₃×C₅	—	2	2	no	—
108	C₂³×C₃×C₅	—	4	2	no	—
109	C₂³×C₃×C₅	—	4	2	no	—
110	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₅×D₃	—	2	2	no	—
112	C₂²×C₅×D₃	—	4	2	no	—
113	C₂²×C₅×D₃	—	4	2	no	—
114	C₂²×C₅×D₃	—	4	2	no	—
115	C₃×C₅×D₄	—	2	4	no	—
116	C₃×C₅×D₄	—	2	2	no	—
117	C₃×C₅×D₄	C₂×D₄	1	4	yes	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	4	8	no	—
122	C₂×C₃×C₄×C₅	—	4	2	no	—
123	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
125	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	#41	1	2	yes	—
128	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
129	C₂×C₅×Dic₃	—	2	2	no	—
130	C₂×C₅×Dic₃	—	4	2	no	—
131	C₅×D₁₂	—	2	2	no	—
132	C₅×D₁₂	—	2	2	no	—
133	C₅×D₁₂	—	4	2	no	—
134	C₅×Dic₆	—	2	2	no	—
135	C₅×Dic₆	—	2	2	no	—
136	C₅×Dic₆	—	4	2	no	—
137	C₅×C₃⋊C₈	—	2	2	no	—
138	C₅×C₃⋊C₈	—	2	2	no	—
139	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
140	C₂³×C₃×C₄	—	2	1	no	—
141	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
142	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
143	C₃×C₄×D₄	—	2	2	no	—
144	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
145	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
147	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
148	C₂×#214	—	2	4	no	—
149	C₂×#214	C₂²×C₅	1	4	yes	complemented
150	C₂×#213	—	2	4	no	—
151	C₂×#213	C₂²×C₅	1	4	yes	—
152	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
153	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
154	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
155	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
156	#875	—	2	2	no	—
157	#875	C₂²×C₅	1	4	yes	complemented
158	#810	C₂²×C₅	1	4	yes	complemented
159	#809	C₂²×C₅	1	4	yes	complemented
160	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	4	yes	complemented
161	C₂⁴×C₅	—	2	1	no	—
162	C₂⁴×C₅	—	6	1	no	—
163	C₂×C₅×Q₈	—	3	2	no	—
164	C₂×C₅×Q₈	—	6	1	no	—
165	C₂×C₅×Q₈	—	6	2	no	—
166	C₂×C₅×Q₈	—	6	2	no	—
167	C₂×C₅×D₄	—	2	2	no	—
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	—	3	2	no	—
170	C₂×C₅×D₄	—	6	2	no	—
171	C₂×C₅×D₄	—	6	2	no	—
172	C₂×C₅×D₄	—	6	1	no	—
173	C₂×C₅×D₄	D₁₂	1	4	yes	—
174	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	2	4	no	—
177	C₂²×C₄×C₅	—	4	4	no	—
178	C₂²×C₄×C₅	—	6	1	no	—
179	C₂²×C₄×C₅	#67	1	1	yes	characteristic
180	C₂²×C₄×C₅	#67	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
182	C₅×SD₁₆	—	6	8	no	—
183	C₅×D₈	—	6	8	no	—
184	C₂×C₅×C₈	—	3	2	no	—
185	C₂×C₅×C₈	—	3	2	no	—
186	C₂×C₅×C₈	—	6	2	no	—
187	C₂×C₅×C₈	—	6	2	no	—
188	C₅×C₄⋊C₄	—	2	1	no	—
189	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
190	C₅×C₂²⋊C₄	—	2	4	no	—
191	C₅×C₂²⋊C₄	—	6	4	no	—
192	C₅×C₂²⋊C₄	—	6	4	no	—
193	C₄²×C₅	#67	1	2	yes	—
194	C₄²×C₅	C₂²×D₃	1	2	yes	—
195	C₂²×SD₁₆	—	3	1	no	—
196	C₂²×D₈	—	3	1	no	—
197	C₂×#124	—	3	1	no	—
198	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic, complemented
199	#463	—	3	8	no	—
200	C₂×C₄⋊C₈	—	3	1	no	—
201	C₂×#103	—	3	1	no	—
202	C₂×#102	—	3	1	no	—
203	C₂²×C₃×C₅	—	2	4	no	—
204	C₂²×C₃×C₅	—	4	2	no	—
205	C₂²×C₃×C₅	—	4	2	no	—
206	C₂²×C₃×C₅	—	4	8	no	—
207	C₂²×C₃×C₅	#121	1	2	yes	—
208	C₂²×C₃×C₅	#135	1	2	yes	—
209	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
210	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₅×D₃	—	4	2	no	—
212	C₂×C₅×D₃	—	4	2	no	—
213	C₂×C₅×D₃	—	4	2	no	—
214	C₂×C₅×D₃	—	8	4	no	—
215	C₃×C₄×C₅	—	2	2	no	—
216	C₃×C₄×C₅	—	2	2	no	—
217	C₃×C₄×C₅	—	4	2	no	—
218	C₃×C₄×C₅	#121	1	2	yes	—
219	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
220	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
221	C₅×Dic₃	—	4	2	no	—
222	C₂⁴×C₃	—	2	1	no	—
223	C₂³×D₃	—	2	1	no	—
224	C₂×C₃×D₄	—	2	1	no	—
225	C₂×C₃×D₄	—	2	2	no	—
226	C₂×C₃×D₄	C₅×D₄	1	4	yes	—
227	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
228	C₂²×C₃×C₄	—	2	1	no	—
229	C₂²×C₃×C₄	—	2	4	no	—
230	C₂²×C₃×C₄	—	4	4	no	—
231	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
232	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
233	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
234	C₂²×Dic₃	—	2	1	no	—
235	C₂×D₁₂	—	2	2	no	—
236	C₂×D₁₂	—	2	2	no	—
237	C₂×D₁₂	—	2	1	no	—
238	C₂×D₁₂	C₂³×C₅	1	2	yes	—
239	C₂×Dic₆	—	2	2	no	—
240	C₂×Dic₆	—	2	2	no	—
241	C₂×Dic₆	—	2	1	no	—
242	C₂×Dic₆	C₂³×C₅	1	2	yes	—
243	C₃×C₄⋊C₄	—	2	1	no	—
244	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
245	C₃×C₂²⋊C₄	—	2	4	no	—
246	C₃×C₄²	C₅×D₄	1	2	yes	—
247	C₃×C₄²	C₂³×C₅	1	2	yes	—
248	#214	—	2	8	no	—
249	#213	—	2	8	no	—
250	(C₂×D₃)⋊C₄	—	2	4	no	—
251	(C₂×D₃)⋊C₄	—	2	4	no	—
252	C₂×C₃⋊C₈	—	2	2	no	—
253	C₂×C₃⋊C₈	—	2	2	no	—
254	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
255	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
256	C₂³×C₅	—	2	4	no	—
257	C₂³×C₅	—	2	2	no	—
258	C₂³×C₅	—	4	2	no	—
259	C₂³×C₅	—	4	2	no	—
260	C₂³×C₅	—	6	2	no	—
261	C₂³×C₅	—	12	2	no	—
262	C₂³×C₅	—	12	2	no	—
263	C₂³×C₅	—	12	2	no	—
264	C₂³×C₅	C₂×#67	1	1	yes	characteristic
265	C₅×Q₈	—	6	2	no	—
266	C₅×Q₈	—	6	2	no	—
267	C₅×Q₈	—	12	2	no	—
268	C₅×D₄	—	2	4	no	—
269	C₅×D₄	—	2	2	no	—
270	C₅×D₄	—	6	2	no	—
271	C₅×D₄	—	6	2	no	—
272	C₅×D₄	—	12	2	no	—
273	C₅×D₄	C₂×D₁₂	1	4	yes	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	4	8	no	—
278	C₂×C₄×C₅	—	4	2	no	—
279	C₂×C₄×C₅	—	6	2	no	—
280	C₂×C₄×C₅	—	12	2	no	—
281	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
282	C₂×C₄×C₅	#235	1	2	yes	—
283	C₂×C₄×C₅	C₂×#67	1	2	yes	—
284	C₂×C₄×C₅	C₂×#67	1	2	yes	—
285	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
287	C₅×C₈	—	6	2	no	—
288	C₅×C₈	—	6	2	no	—
289	C₂²×Q₈	—	3	1	no	—
290	C₂²×D₄	—	3	1	no	—
291	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
292	C₂³×C₄	—	2	1	no	—
293	C₂×SD₁₆	—	3	4	no	—
294	C₂×SD₁₆	—	6	4	no	—
295	C₂×D₈	—	3	4	no	—
296	C₂×D₈	—	6	4	no	—
297	C₂²×C₈	—	3	1	no	—
298	C₂²×C₈	—	3	1	no	—
299	#124	—	3	4	no	—
300	#124	—	6	2	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	C₂×C₅×D₃	1	4	yes	complemented
303	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	6	1	no	—
306	C₂×C₂²⋊C₄	—	6	1	no	—
307	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
308	C₄⋊C₈	—	3	4	no	—
309	#103	—	3	4	no	—
310	#102	—	3	4	no	—
311	C₂×C₃×C₅	—	4	4	no	—
312	C₂×C₃×C₅	#463	1	4	yes	complemented
313	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
314	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
315	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
316	C₅×D₃	—	8	2	no	—
317	C₂³×C₃	—	2	4	no	—
318	C₂³×C₃	—	2	2	no	—
319	C₂³×C₃	—	4	2	no	—
320	C₂³×C₃	—	4	2	no	—
321	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂²×D₃	—	2	2	no	—
323	C₂²×D₃	—	4	2	no	—
324	C₂²×D₃	—	4	2	no	—
325	C₂²×D₃	—	4	2	no	—
326	C₃×D₄	—	2	4	no	—
327	C₃×D₄	—	2	2	no	—
328	C₃×D₄	C₂×C₅×D₄	1	4	yes	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	4	8	no	—
333	C₂×C₃×C₄	—	4	2	no	—
334	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
335	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
336	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
337	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
338	C₂×C₃×C₄	C₅×#41	1	2	yes	—
339	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
340	C₂×Dic₃	—	2	2	no	—
341	C₂×Dic₃	—	4	2	no	—
342	D₁₂	—	2	2	no	—
343	D₁₂	—	2	2	no	—
344	D₁₂	—	4	2	no	—
345	Dic₆	—	2	2	no	—
346	Dic₆	—	2	2	no	—
347	Dic₆	—	4	2	no	—
348	C₃⋊C₈	—	2	2	no	—
349	C₃⋊C₈	—	2	2	no	—
350	C₂²×C₅	—	2	4	no	—
351	C₂²×C₅	—	4	8	no	—
352	C₂²×C₅	—	4	2	no	—
353	C₂²×C₅	—	4	2	no	—
354	C₂²×C₅	—	12	2	no	—
355	C₂²×C₅	—	12	2	no	—
356	C₂²×C₅	—	12	2	no	—
357	C₂²×C₅	—	24	4	no	—
358	C₂²×C₅	#930	1	2	yes	—
359	C₂²×C₅	#932	1	2	yes	—
360	C₂²×C₅	#950	1	2	yes	—
361	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
362	C₄×C₅	—	2	2	no	—
363	C₄×C₅	—	2	2	no	—
364	C₄×C₅	—	4	2	no	—
365	C₄×C₅	—	12	2	no	—
366	C₄×C₅	#930	1	2	yes	—
367	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
368	C₄×C₅	C₂×#235	1	1	yes	characteristic
369	C₂⁴	—	2	1	no	—
370	C₂⁴	—	6	1	no	—
371	C₂×Q₈	—	3	2	no	—
372	C₂×Q₈	—	6	1	no	—
373	C₂×Q₈	—	6	2	no	—
374	C₂×Q₈	—	6	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	3	2	no	—
378	C₂×D₄	—	6	2	no	—
379	C₂×D₄	—	6	2	no	—
380	C₂×D₄	—	6	1	no	—
381	C₂×D₄	C₅×D₁₂	1	4	yes	—
382	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	4	4	no	—
386	C₂²×C₄	—	6	1	no	—
387	C₂²×C₄	C₅×#67	1	1	yes	characteristic
388	C₂²×C₄	C₅×#67	1	1	yes	characteristic
389	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
390	SD₁₆	—	6	8	no	—
391	D₈	—	6	8	no	—
392	C₂×C₈	—	3	2	no	—
393	C₂×C₈	—	3	2	no	—
394	C₂×C₈	—	6	2	no	—
395	C₂×C₈	—	6	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	6	4	no	—
400	C₂²⋊C₄	—	6	4	no	—
401	C₄²	C₅×#67	1	2	yes	—
402	C₄²	C₂²×C₅×D₃	1	2	yes	—
403	C₃×C₅	C₂×#463	1	1	yes	characteristic, complemented, Hall
404	C₂²×C₃	—	2	4	no	—
405	C₂²×C₃	—	4	8	no	—
406	C₂²×C₃	—	4	2	no	—
407	C₂²×C₃	—	4	2	no	—
408	C₂²×C₃	C₅×#121	1	2	yes	—
409	C₂²×C₃	C₅×#135	1	2	yes	—
410	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
411	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
412	C₂×D₃	—	4	2	no	—
413	C₂×D₃	—	4	2	no	—
414	C₂×D₃	—	4	2	no	—
415	C₂×D₃	—	8	4	no	—
416	C₃×C₄	—	2	2	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	4	2	no	—
419	C₃×C₄	C₅×#121	1	2	yes	—
420	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
421	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
422	Dic₃	—	4	2	no	—
423	C₂×C₅	—	4	4	no	—
424	C₂×C₅	—	24	2	no	—
425	C₂×C₅	#5016	1	4	yes	direct product factor
426	C₂×C₅	C₂×#930	1	1	yes	characteristic
427	C₂×C₅	C₂×#932	1	1	yes	characteristic
428	C₂×C₅	C₂×#950	1	1	yes	characteristic
429	C₂³	—	2	4	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	6	2	no	—
434	C₂³	—	12	2	no	—
435	C₂³	—	12	2	no	—
436	C₂³	—	12	2	no	—
437	C₂³	C₂×C₅×#67	1	1	yes	characteristic
438	Q₈	—	6	2	no	—
439	Q₈	—	6	2	no	—
440	Q₈	—	12	2	no	—
441	D₄	—	2	4	no	—
442	D₄	—	2	2	no	—
443	D₄	—	6	2	no	—
444	D₄	—	6	2	no	—
445	D₄	—	12	2	no	—
446	D₄	C₂×C₅×D₁₂	1	4	yes	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	4	8	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	6	2	no	—
453	C₂×C₄	—	12	2	no	—
454	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
455	C₂×C₄	C₅×#235	1	2	yes	—
456	C₂×C₄	C₂×C₅×#67	1	2	yes	—
457	C₂×C₄	C₂×C₅×#67	1	2	yes	—
458	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
459	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
460	C₈	—	6	2	no	—
461	C₈	—	6	2	no	—
462	C₂×C₃	—	4	4	no	—
463	C₂×C₃	C₅×#463	1	4	yes	complemented
464	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
465	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
466	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
467	D₃	—	8	2	no	—
468	C₅	C₂×#5016	1	1	yes	characteristic, direct product factor, Sylow
469	C₂²	—	2	4	no	—
470	C₂²	—	4	8	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	12	2	no	—
474	C₂²	—	12	2	no	—
475	C₂²	—	12	2	no	—
476	C₂²	—	24	4	no	—
477	C₂²	C₅×#930	1	2	yes	—
478	C₂²	C₅×#932	1	2	yes	—
479	C₂²	C₅×#950	1	2	yes	—
480	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
481	C₄	—	2	2	no	—
482	C₄	—	2	2	no	—
483	C₄	—	4	2	no	—
484	C₄	—	12	2	no	—
485	C₄	C₅×#930	1	2	yes	—
486	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
487	C₄	C₂×C₅×#235	1	1	yes	characteristic
488	C₃	C₂×C₅×#463	1	1	yes	characteristic, complemented, Sylow
489	C₂	—	4	4	no	—
490	C₂	—	24	2	no	—
491	C₂	C₅×#5016	1	4	yes	direct product factor
492	C₂	C₂×C₅×#930	1	1	yes	characteristic
493	C₂	C₂×C₅×#932	1	1	yes	characteristic
494	C₂	C₂×C₅×#950	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×#213	C₂
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₂×C₅×#463
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
2. C₂²×C₅×#214	C₂	semidirect
4. C₂×C₅×#875	C₂	semidirect
5. C₅×#5016	C₂	direct (N × H)
6. C₂×C₅×#810	C₂	semidirect
7. C₂×C₅×#809	C₂	semidirect
8. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
15. C₃×C₄×C₅×D₄	C₂²	semidirect
20. C₂×C₅×#214	C₂²	semidirect
28. C₅×#875	C₂²	semidirect
29. C₅×#810	C₂²	semidirect
30. C₅×#809	C₂²	semidirect
31. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
32. C₂×#5016	C₅	direct (N × H)
36. C₂×C₄×C₅×D₄	D₃	semidirect
75. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
76. C₂²×#214	C₂×C₅	semidirect
78. C₂×#875	C₂×C₅	semidirect
79. #5016	C₂×C₅	direct (N × H)
80. C₂×#810	C₂×C₅	semidirect
81. C₂×#809	C₂×C₅	semidirect
82. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
96. C₄×C₅×D₄	C₂×D₃	semidirect
144. C₃×C₄×D₄	C₂²×C₅	semidirect
149. C₂×#214	C₂²×C₅	semidirect
157. #875	C₂²×C₅	semidirect
158. #810	C₂²×C₅	semidirect
159. #809	C₂²×C₅	semidirect
160. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
198. C₂×C₄×D₄	C₅×D₃	semidirect
302. C₄×D₄	C₂×C₅×D₃	semidirect
312. C₂×C₃×C₅	#463	semidirect
403. C₃×C₅	C₂×#463	semidirect
425. C₂×C₅	#5016	direct (N × H)
463. C₂×C₃	C₅×#463	semidirect
468. C₅	C₂×#5016	direct (N × H)
488. C₃	C₂×C₅×#463	semidirect
491. C₂	C₅×#5016	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×C₄×C₅×D₄	2
C₂²×C₅×#214	2
C₂²×C₅×#213	2
C₂×C₅×#875	2
C₅×#5016	2
C₂×C₅×#810	2
C₂×C₅×#809	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₂×C₅×#463	3
C₂×#5016	5

Subgroups — C2×C5×#5016 #14425929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5016 #14425929