Subgroups — C₂×C₅×#5047 #14423493

Order 1920.

1520 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#216	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×#215	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#830	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5047	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#810	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#452	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂²×C₅×#67	—	2	1	no	—
13	C₂×C₅×#235	—	2	2	no	—
14	C₂×C₅×#235	—	2	4	no	—
15	C₂×C₅×#235	—	2	4	no	—
16	C₂×C₅×#235	C₂²	1	4	yes	—
17	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	—	2	1	no	—
19	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
21	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
22	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
25	C₂×C₅×#216	—	2	4	no	—
26	C₂×C₅×#216	C₂²	1	4	yes	complemented
27	C₂×C₅×#215	—	2	4	no	—
28	C₂×C₅×#215	C₂²	1	4	yes	complemented
29	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
30	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
31	C₅×#830	C₂²	1	4	yes	complemented
32	C₅×#810	C₂²	1	4	yes	complemented
33	C₅×#809	C₂²	1	4	yes	complemented
34	C₂×#5047	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂²×C₅×#41	—	3	1	no	—
36	C₂²×C₅×Q₁₆	—	3	1	no	—
37	C₂²×C₅×SD₁₆	—	3	1	no	—
38	C₂×C₅×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
39	C₅×#452	—	3	8	no	—
40	C₂×C₅×#103	—	3	1	no	—
41	C₂×C₅×#102	—	3	1	no	—
42	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
43	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
44	C₂³×C₅×D₃	—	2	1	no	—
45	C₂×C₃×C₅×Q₈	—	2	1	no	—
46	C₂×C₃×C₅×Q₈	—	2	2	no	—
47	C₂×C₃×C₅×Q₈	—	2	2	no	—
48	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	—	2	2	no	—
50	C₂²×C₃×C₄×C₅	—	2	2	no	—
51	C₂²×C₃×C₄×C₅	—	2	1	no	—
52	C₂²×C₃×C₄×C₅	—	2	1	no	—
53	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂×C₅×#67	—	2	8	no	—
58	C₂×C₅×#67	—	2	4	no	—
59	C₂²×C₅×Dic₃	—	2	1	no	—
60	C₅×#235	—	2	16	no	—
61	C₅×#235	—	2	8	no	—
62	C₅×#235	—	2	8	no	—
63	C₂×C₅×D₁₂	—	2	1	no	—
64	C₂×C₅×D₁₂	—	2	2	no	—
65	C₂×C₅×D₁₂	D₄	1	4	yes	—
66	C₂×C₅×D₁₂	C₂³	1	2	yes	—
67	C₂×C₄×C₅×D₃	—	2	8	no	—
68	C₂×C₄×C₅×D₃	—	2	4	no	—
69	C₂×C₅×Dic₆	—	2	1	no	—
70	C₂×C₅×Dic₆	—	2	2	no	—
71	C₂×C₅×Dic₆	D₄	1	4	yes	—
72	C₂×C₅×Dic₆	C₂³	1	2	yes	—
73	C₃×C₅×C₄⋊C₄	—	2	4	no	—
74	C₃×C₅×C₄⋊C₄	—	2	1	no	—
75	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
76	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
77	C₅×#216	—	2	8	no	—
78	C₅×#215	—	2	8	no	—
79	C₂×C₅×C₃⋊C₈	—	2	2	no	—
80	C₂×C₅×C₃⋊C₈	—	2	2	no	—
81	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
82	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
83	C₂²×#235	C₂×C₅	1	1	yes	characteristic
84	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂²×#216	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂²×#215	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂×#830	C₂×C₅	1	1	yes	characteristic, complemented
88	#5047	C₂×C₅	1	8	yes	direct product factor
89	C₂×#810	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂×#809	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×C₅×#41	—	3	4	no	—
92	C₂×C₅×#41	—	6	4	no	—
93	C₂×C₅×#41	—	6	4	no	—
94	C₂×C₅×#41	—	6	2	no	—
95	C₂²×C₅×Q₈	—	3	1	no	—
96	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
97	C₂²×C₅×D₄	—	3	1	no	—
98	C₂²×C₅×D₄	—	6	1	no	—
99	C₂³×C₄×C₅	—	6	1	no	—
100	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
101	C₂×C₅×Q₁₆	—	3	4	no	—
102	C₂×C₅×Q₁₆	—	6	4	no	—
103	C₂×C₅×SD₁₆	—	3	4	no	—
104	C₂×C₅×SD₁₆	—	6	4	no	—
105	C₂²×C₅×C₈	—	3	1	no	—
106	C₂²×C₅×C₈	—	3	1	no	—
107	C₅×C₂²⋊Q₈	—	2	2	no	—
108	C₅×C₂²⋊Q₈	C₂×D₃	1	4	yes	complemented
109	C₂×C₅×C₄⋊C₄	—	2	1	no	—
110	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
111	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
112	C₅×#103	—	3	4	no	—
113	C₅×#102	—	3	4	no	—
114	C₅×C₂²⋊C₈	—	3	4	no	—
115	C₂×#452	—	3	1	no	Sylow
116	C₂³×C₃×C₅	—	2	2	no	—
117	C₂³×C₃×C₅	—	2	2	no	—
118	C₂³×C₃×C₅	—	2	2	no	—
119	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
120	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₅×D₃	—	2	4	no	—
122	C₂²×C₅×D₃	—	2	2	no	—
123	C₂²×C₅×D₃	—	4	2	no	—
124	C₂²×C₅×D₃	—	4	2	no	—
125	C₃×C₅×Q₈	—	2	2	no	—
126	C₃×C₅×Q₈	—	2	2	no	—
127	C₃×C₅×Q₈	—	4	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	4	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	4	2	no	—
135	C₂×C₃×C₄×C₅	—	4	2	no	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₅×#67	—	2	16	no	—
142	C₂×C₅×Dic₃	—	2	4	no	—
143	C₂×C₅×Dic₃	—	2	2	no	—
144	C₅×D₁₂	—	2	4	no	—
145	C₅×D₁₂	—	2	2	no	—
146	C₅×D₁₂	C₂×D₄	1	4	yes	—
147	C₄×C₅×D₃	—	2	16	no	—
148	C₅×Dic₆	—	2	4	no	—
149	C₅×Dic₆	—	2	2	no	—
150	C₅×Dic₆	C₂×D₄	1	4	yes	—
151	C₅×C₃⋊C₈	—	2	2	no	—
152	C₅×C₃⋊C₈	—	2	2	no	—
153	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
154	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
155	C₂²×#67	—	2	1	no	—
156	C₂×#235	—	2	2	no	—
157	C₂×#235	—	2	4	no	—
158	C₂×#235	—	2	4	no	—
159	C₂×#235	C₂²×C₅	1	4	yes	—
160	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
161	C₂²×C₄×D₃	—	2	1	no	—
162	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
163	C₃×C₂²⋊Q₈	—	2	2	no	—
164	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
165	C₂×C₃×C₄⋊C₄	—	2	1	no	—
166	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
168	C₂×#216	—	2	4	no	—
169	C₂×#216	C₂²×C₅	1	4	yes	complemented
170	C₂×#215	—	2	4	no	—
171	C₂×#215	C₂²×C₅	1	4	yes	complemented
172	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
173	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
174	#830	C₂²×C₅	1	4	yes	complemented
175	#810	C₂²×C₅	1	4	yes	complemented
176	#809	C₂²×C₅	1	4	yes	complemented
177	C₂⁴×C₅	—	6	1	no	—
178	C₂⁴×C₅	#67	1	1	yes	characteristic
179	C₅×#41	—	6	8	no	—
180	C₅×#41	—	6	8	no	—
181	C₅×#41	—	6	16	no	—
182	C₂×C₅×Q₈	—	2	1	no	—
183	C₂×C₅×Q₈	—	2	2	no	—
184	C₂×C₅×Q₈	—	2	2	no	—
185	C₂×C₅×Q₈	—	3	4	no	—
186	C₂×C₅×Q₈	—	3	2	no	—
187	C₂×C₅×Q₈	—	6	2	no	—
188	C₂×C₅×Q₈	—	6	1	no	—
189	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
190	C₂×C₅×D₄	—	3	4	no	—
191	C₂×C₅×D₄	—	3	2	no	—
192	C₂×C₅×D₄	—	6	8	no	—
193	C₂×C₅×D₄	—	6	4	no	—
194	C₂×C₅×D₄	—	6	2	no	—
195	C₂×C₅×D₄	—	6	1	no	—
196	C₂²×C₄×C₅	—	2	2	no	—
197	C₂²×C₄×C₅	—	2	2	no	—
198	C₂²×C₄×C₅	—	2	1	no	—
199	C₂²×C₄×C₅	—	2	1	no	—
200	C₂²×C₄×C₅	—	6	8	no	—
201	C₂²×C₄×C₅	—	6	1	no	—
202	C₂²×C₄×C₅	—	6	4	no	—
203	C₂²×C₄×C₅	#67	1	2	yes	—
204	C₂²×C₄×C₅	#67	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
206	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
207	C₅×Q₁₆	—	6	8	no	—
208	C₅×SD₁₆	—	6	8	no	—
209	C₂×C₅×C₈	—	3	2	no	—
210	C₂×C₅×C₈	—	3	2	no	—
211	C₂×C₅×C₈	—	6	2	no	—
212	C₂×C₅×C₈	—	6	2	no	—
213	C₅×C₄⋊C₄	—	2	4	no	—
214	C₅×C₄⋊C₄	—	2	1	no	—
215	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
216	C₅×C₂²⋊C₄	—	2	4	no	—
217	C₂²×#41	—	3	1	no	—
218	C₂²×Q₁₆	—	3	1	no	—
219	C₂²×SD₁₆	—	3	1	no	—
220	C₂×C₂²⋊Q₈	C₅×D₃	1	1	yes	characteristic, complemented
221	#452	—	3	8	no	—
222	C₂×#103	—	3	1	no	—
223	C₂×#102	—	3	1	no	—
224	C₂×C₂²⋊C₈	—	3	1	no	—
225	C₂²×C₃×C₅	—	2	2	no	—
226	C₂²×C₃×C₅	—	2	2	no	—
227	C₂²×C₃×C₅	—	2	2	no	—
228	C₂²×C₃×C₅	—	4	4	no	—
229	C₂²×C₃×C₅	#120	1	2	yes	—
230	C₂²×C₃×C₅	#135	1	2	yes	—
231	C₂²×C₃×C₅	#137	1	2	yes	—
232	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₅×D₃	—	2	4	no	—
234	C₂×C₅×D₃	—	4	2	no	—
235	C₂×C₅×D₃	—	4	2	no	—
236	C₂×C₅×D₃	—	4	8	no	—
237	C₃×C₄×C₅	—	2	2	no	—
238	C₃×C₄×C₅	—	4	2	no	—
239	C₃×C₄×C₅	—	4	2	no	—
240	C₃×C₄×C₅	#120	1	2	yes	—
241	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
242	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
243	C₅×Dic₃	—	2	4	no	—
244	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
245	C₂³×D₃	—	2	1	no	—
246	C₂×C₃×Q₈	—	2	1	no	—
247	C₂×C₃×Q₈	—	2	2	no	—
248	C₂×C₃×Q₈	—	2	2	no	—
249	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
250	C₂²×C₃×C₄	—	2	2	no	—
251	C₂²×C₃×C₄	—	2	2	no	—
252	C₂²×C₃×C₄	—	2	1	no	—
253	C₂²×C₃×C₄	—	2	1	no	—
254	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
255	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
256	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
257	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
258	C₂×#67	—	2	8	no	—
259	C₂×#67	—	2	4	no	—
260	C₂²×Dic₃	—	2	1	no	—
261	#235	—	2	16	no	—
262	#235	—	2	8	no	—
263	#235	—	2	8	no	—
264	C₂×D₁₂	—	2	2	no	—
265	C₂×D₁₂	—	2	1	no	—
266	C₂×D₁₂	C₅×D₄	1	4	yes	—
267	C₂×D₁₂	C₂³×C₅	1	2	yes	—
268	C₂×C₄×D₃	—	2	8	no	—
269	C₂×C₄×D₃	—	2	4	no	—
270	C₂×Dic₆	—	2	2	no	—
271	C₂×Dic₆	—	2	1	no	—
272	C₂×Dic₆	C₅×D₄	1	4	yes	—
273	C₂×Dic₆	C₂³×C₅	1	2	yes	—
274	C₃×C₄⋊C₄	—	2	4	no	—
275	C₃×C₄⋊C₄	—	2	1	no	—
276	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
277	C₃×C₂²⋊C₄	—	2	4	no	—
278	#216	—	2	8	no	—
279	#215	—	2	8	no	—
280	C₂×C₃⋊C₈	—	2	2	no	—
281	C₂×C₃⋊C₈	—	2	2	no	—
282	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
283	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
284	C₂³×C₅	—	2	2	no	—
285	C₂³×C₅	—	2	2	no	—
286	C₂³×C₅	—	2	2	no	—
287	C₂³×C₅	—	6	4	no	—
288	C₂³×C₅	—	6	2	no	—
289	C₂³×C₅	—	12	2	no	—
290	C₂³×C₅	—	12	2	no	—
291	C₂³×C₅	C₂×#67	1	2	yes	—
292	C₂³×C₅	C₂×#67	1	1	yes	characteristic
293	C₅×Q₈	—	2	2	no	—
294	C₅×Q₈	—	2	2	no	—
295	C₅×Q₈	—	3	4	no	—
296	C₅×Q₈	—	4	2	no	—
297	C₅×Q₈	—	6	4	no	—
298	C₅×Q₈	—	6	2	no	—
299	C₅×D₄	—	3	4	no	—
300	C₅×D₄	—	6	16	no	—
301	C₅×D₄	—	6	4	no	—
302	C₅×D₄	—	6	2	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	4	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	—	4	2	no	—
310	C₂×C₄×C₅	—	4	2	no	—
311	C₂×C₄×C₅	—	6	16	no	—
312	C₂×C₄×C₅	—	6	4	no	—
313	C₂×C₄×C₅	—	6	2	no	—
314	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
315	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
316	C₂×C₄×C₅	C₂×#67	1	2	yes	—
317	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
318	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
319	C₅×C₈	—	6	2	no	—
320	C₅×C₈	—	6	2	no	—
321	C₂×#41	—	3	4	no	—
322	C₂×#41	—	6	4	no	—
323	C₂×#41	—	6	4	no	—
324	C₂×#41	—	6	2	no	—
325	C₂²×Q₈	—	3	1	no	—
326	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
327	C₂²×D₄	—	3	1	no	—
328	C₂²×D₄	—	6	1	no	—
329	C₂³×C₄	—	6	1	no	—
330	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
331	C₂×Q₁₆	—	3	4	no	—
332	C₂×Q₁₆	—	6	4	no	—
333	C₂×SD₁₆	—	3	4	no	—
334	C₂×SD₁₆	—	6	4	no	—
335	C₂²×C₈	—	3	1	no	—
336	C₂²×C₈	—	3	1	no	—
337	C₂²⋊Q₈	—	2	2	no	—
338	C₂²⋊Q₈	C₂×C₅×D₃	1	4	yes	complemented
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	#103	—	3	4	no	—
343	#102	—	3	4	no	—
344	C₂²⋊C₈	—	3	4	no	—
345	C₂×C₃×C₅	—	4	2	no	—
346	C₂×C₃×C₅	#452	1	4	yes	complemented
347	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
348	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
349	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
350	C₅×D₃	—	4	4	no	—
351	C₂³×C₃	—	2	2	no	—
352	C₂³×C₃	—	2	2	no	—
353	C₂³×C₃	—	2	2	no	—
354	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
355	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
356	C₂²×D₃	—	2	4	no	—
357	C₂²×D₃	—	2	2	no	—
358	C₂²×D₃	—	4	2	no	—
359	C₂²×D₃	—	4	2	no	—
360	C₃×Q₈	—	2	2	no	—
361	C₃×Q₈	—	2	2	no	—
362	C₃×Q₈	—	4	2	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	2	4	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	2	2	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	4	2	no	—
370	C₂×C₃×C₄	—	4	2	no	—
371	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
372	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
373	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
374	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
376	#67	—	2	16	no	—
377	C₂×Dic₃	—	2	4	no	—
378	C₂×Dic₃	—	2	2	no	—
379	D₁₂	—	2	4	no	—
380	D₁₂	—	2	2	no	—
381	D₁₂	C₂×C₅×D₄	1	4	yes	—
382	C₄×D₃	—	2	16	no	—
383	Dic₆	—	2	4	no	—
384	Dic₆	—	2	2	no	—
385	Dic₆	C₂×C₅×D₄	1	4	yes	—
386	C₃⋊C₈	—	2	2	no	—
387	C₃⋊C₈	—	2	2	no	—
388	C₂²×C₅	—	2	2	no	—
389	C₂²×C₅	—	2	2	no	—
390	C₂²×C₅	—	2	2	no	—
391	C₂²×C₅	—	4	4	no	—
392	C₂²×C₅	—	6	4	no	—
393	C₂²×C₅	—	12	2	no	—
394	C₂²×C₅	—	12	8	no	—
395	C₂²×C₅	—	12	2	no	—
396	C₂²×C₅	#937	1	2	yes	—
397	C₂²×C₅	#942	1	2	yes	—
398	C₂²×C₅	#950	1	2	yes	—
399	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
400	C₄×C₅	—	2	2	no	—
401	C₄×C₅	—	4	2	no	—
402	C₄×C₅	—	4	2	no	—
403	C₄×C₅	—	6	4	no	—
404	C₄×C₅	#937	1	2	yes	—
405	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
406	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
407	C₂⁴	—	6	1	no	—
408	C₂⁴	C₅×#67	1	1	yes	characteristic
409	#41	—	6	8	no	—
410	#41	—	6	8	no	—
411	#41	—	6	16	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	3	4	no	—
416	C₂×Q₈	—	3	2	no	—
417	C₂×Q₈	—	6	2	no	—
418	C₂×Q₈	—	6	1	no	—
419	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
420	C₂×D₄	—	3	4	no	—
421	C₂×D₄	—	3	2	no	—
422	C₂×D₄	—	6	8	no	—
423	C₂×D₄	—	6	4	no	—
424	C₂×D₄	—	6	2	no	—
425	C₂×D₄	—	6	1	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	6	8	no	—
431	C₂²×C₄	—	6	1	no	—
432	C₂²×C₄	—	6	4	no	—
433	C₂²×C₄	C₅×#67	1	1	yes	characteristic
434	C₂²×C₄	C₅×#67	1	2	yes	—
435	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
436	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
437	Q₁₆	—	6	8	no	—
438	SD₁₆	—	6	8	no	—
439	C₂×C₈	—	3	2	no	—
440	C₂×C₈	—	3	2	no	—
441	C₂×C₈	—	6	2	no	—
442	C₂×C₈	—	6	2	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₃×C₅	C₂×#452	1	1	yes	characteristic, complemented, Hall
448	C₂²×C₃	—	2	2	no	—
449	C₂²×C₃	—	2	2	no	—
450	C₂²×C₃	—	2	2	no	—
451	C₂²×C₃	—	4	4	no	—
452	C₂²×C₃	C₅×#120	1	2	yes	—
453	C₂²×C₃	C₅×#135	1	2	yes	—
454	C₂²×C₃	C₅×#137	1	2	yes	—
455	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
456	C₂×D₃	—	2	4	no	—
457	C₂×D₃	—	4	8	no	—
458	C₂×D₃	—	4	2	no	—
459	C₂×D₃	—	4	2	no	—
460	C₃×C₄	—	2	2	no	—
461	C₃×C₄	—	4	2	no	—
462	C₃×C₄	—	4	2	no	—
463	C₃×C₄	C₅×#120	1	2	yes	—
464	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
465	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
466	Dic₃	—	2	4	no	—
467	C₂×C₅	—	4	2	no	—
468	C₂×C₅	—	12	4	no	—
469	C₂×C₅	#5047	1	4	yes	direct product factor
470	C₂×C₅	C₂×#937	1	1	yes	characteristic
471	C₂×C₅	C₂×#942	1	1	yes	characteristic
472	C₂×C₅	C₂×#950	1	1	yes	characteristic
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	6	4	no	—
477	C₂³	—	6	2	no	—
478	C₂³	—	12	2	no	—
479	C₂³	—	12	2	no	—
480	C₂³	C₂×C₅×#67	1	2	yes	—
481	C₂³	C₂×C₅×#67	1	1	yes	characteristic
482	Q₈	—	2	2	no	—
483	Q₈	—	2	2	no	—
484	Q₈	—	3	4	no	—
485	Q₈	—	4	2	no	—
486	Q₈	—	6	4	no	—
487	Q₈	—	6	2	no	—
488	D₄	—	3	4	no	—
489	D₄	—	6	16	no	—
490	D₄	—	6	4	no	—
491	D₄	—	6	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	6	16	no	—
501	C₂×C₄	—	6	4	no	—
502	C₂×C₄	—	6	2	no	—
503	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
504	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
505	C₂×C₄	C₂×C₅×#67	1	2	yes	—
506	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
507	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
508	C₈	—	6	2	no	—
509	C₈	—	6	2	no	—
510	C₂×C₃	—	4	2	no	—
511	C₂×C₃	C₅×#452	1	4	yes	complemented
512	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
513	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
514	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
515	D₃	—	4	4	no	—
516	C₅	C₂×#5047	1	1	yes	characteristic, direct product factor, Sylow
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	6	4	no	—
522	C₂²	—	12	8	no	—
523	C₂²	—	12	2	no	—
524	C₂²	—	12	2	no	—
525	C₂²	C₅×#937	1	2	yes	—
526	C₂²	C₅×#942	1	2	yes	—
527	C₂²	C₅×#950	1	2	yes	—
528	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
529	C₄	—	2	2	no	—
530	C₄	—	4	2	no	—
531	C₄	—	4	2	no	—
532	C₄	—	6	4	no	—
533	C₄	C₅×#937	1	2	yes	—
534	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
535	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
536	C₃	C₂×C₅×#452	1	1	yes	characteristic, complemented, Sylow
537	C₂	—	4	2	no	—
538	C₂	—	12	4	no	—
539	C₂	C₅×#5047	1	4	yes	direct product factor
540	C₂	C₂×C₅×#937	1	1	yes	characteristic
541	C₂	C₂×C₅×#942	1	1	yes	characteristic
542	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×C₅×C₂²⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×#235	C₂
hypercenter	C₂×C₅×C₂²⋊Q₈	D₃
hypocenter	C₃	C₂×C₅×#452
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂×C₅×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
3. C₂²×C₅×#216	C₂	semidirect
4. C₂²×C₅×#215	C₂	semidirect
5. C₂×C₅×#830	C₂	semidirect
6. C₅×#5047	C₂	direct (N × H)
7. C₂×C₅×#810	C₂	semidirect
8. C₂×C₅×#809	C₂	semidirect
21. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₅×#216	C₂²	semidirect
28. C₂×C₅×#215	C₂²	semidirect
31. C₅×#830	C₂²	semidirect
32. C₅×#810	C₂²	semidirect
33. C₅×#809	C₂²	semidirect
34. C₂×#5047	C₅	direct (N × H)
38. C₂×C₅×C₂²⋊Q₈	D₃	semidirect
84. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
85. C₂²×#216	C₂×C₅	semidirect
86. C₂²×#215	C₂×C₅	semidirect
87. C₂×#830	C₂×C₅	semidirect
88. #5047	C₂×C₅	direct (N × H)
89. C₂×#810	C₂×C₅	semidirect
90. C₂×#809	C₂×C₅	semidirect
108. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
164. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
169. C₂×#216	C₂²×C₅	semidirect
171. C₂×#215	C₂²×C₅	semidirect
174. #830	C₂²×C₅	semidirect
175. #810	C₂²×C₅	semidirect
176. #809	C₂²×C₅	semidirect
220. C₂×C₂²⋊Q₈	C₅×D₃	semidirect
338. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
346. C₂×C₃×C₅	#452	semidirect
447. C₃×C₅	C₂×#452	semidirect
469. C₂×C₅	#5047	direct (N × H)
511. C₂×C₃	C₅×#452	semidirect
516. C₅	C₂×#5047	direct (N × H)
536. C₃	C₂×C₅×#452	semidirect
539. C₂	C₅×#5047	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#235	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₂²×C₅×#216	2
C₂²×C₅×#215	2
C₂×C₅×#830	2
C₅×#5047	2
C₂×C₅×#810	2
C₂×C₅×#809	2
C₂×C₅×#452	3
C₂×#5047	5

Subgroups — C2×C5×#5047 #14423493

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5047 #14423493