Subgroups — C₂×C₅×#4808 #14423508

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×#239	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#216	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#204	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#897	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4808	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₅×#452	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₅×#239	—	2	4	no	—
12	C₂×C₅×#239	—	2	4	no	—
13	C₂×C₅×#239	—	2	2	no	—
14	C₂×C₅×#239	C₂²	1	4	yes	—
15	C₂²×C₅×D₁₂	—	2	1	no	—
16	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₅×D₃	—	2	1	no	—
18	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₅×#216	—	2	4	no	—
23	C₂×C₅×#216	C₂²	1	4	yes	complemented
24	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
25	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
26	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₅×#204	—	2	4	no	—
28	C₂×C₅×#204	C₂²	1	4	yes	complemented
29	C₅×#897	—	2	2	no	—
30	C₅×#897	C₂²	1	4	yes	complemented
31	C₃×C₅×#103	C₂²	1	4	yes	complemented
32	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	complemented
33	C₅×#809	C₂²	1	4	yes	complemented
34	C₂×#4808	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	—	3	1	no	—
39	C₅×#452	—	3	8	no	—
40	C₂×C₅×#103	D₃	1	1	yes	characteristic, complemented
41	C₂×C₅×#102	—	3	1	no	—
42	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
43	C₂³×C₅×D₃	—	2	1	no	—
44	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
45	C₂×C₃×C₅×Q₈	—	2	2	no	—
46	C₂×C₃×C₅×Q₈	—	2	1	no	—
47	C₂×C₃×C₅×Q₈	D₄	1	4	yes	—
48	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	—	2	1	no	—
50	C₂²×C₃×C₄×C₅	—	2	1	no	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₅×Dic₃	—	2	1	no	—
53	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
54	C₅×#239	—	2	16	no	—
55	C₅×#239	—	2	8	no	—
56	C₅×#239	—	2	8	no	—
57	C₂×C₅×D₁₂	—	2	8	no	—
58	C₂×C₅×D₁₂	—	2	4	no	—
59	C₂×C₅×D₁₂	—	2	1	no	—
60	C₂×C₅×D₁₂	—	2	2	no	—
61	C₂×C₅×D₁₂	D₄	1	4	yes	—
62	C₂×C₅×D₁₂	C₂³	1	2	yes	—
63	C₂×C₄×C₅×D₃	—	2	8	no	—
64	C₂×C₄×C₅×D₃	—	2	2	no	—
65	C₂×C₄×C₅×D₃	—	2	2	no	—
66	C₂×C₄×C₅×D₃	—	2	4	no	—
67	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
68	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
69	C₂×C₅×Dic₆	—	2	2	no	—
70	C₂×C₅×Dic₆	—	2	2	no	—
71	C₂×C₅×Dic₆	—	2	1	no	—
72	C₂×C₅×Dic₆	C₂³	1	2	yes	—
73	C₂×C₃×C₅×C₈	—	2	2	no	—
74	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
75	C₃×C₅×C₄⋊C₄	—	2	1	no	—
76	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
77	C₅×#216	—	2	8	no	—
78	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
79	C₅×C₄⋊Dic₃	—	2	4	no	—
80	C₂×C₅×C₃⋊C₈	—	2	2	no	—
81	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
82	C₅×#204	—	2	8	no	—
83	C₂²×#239	C₂×C₅	1	1	yes	characteristic
84	C₂²×#216	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂²×#204	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂×#897	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂×#809	C₂×C₅	1	1	yes	characteristic, complemented
90	#4808	C₂×C₅	1	8	yes	direct product factor
91	C₂×C₅×#41	—	3	4	no	—
92	C₂×C₅×#41	—	6	2	no	—
93	C₂×C₅×#41	—	6	4	no	—
94	C₂×C₅×#41	—	6	4	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	—	3	1	no	—
100	C₂³×C₄×C₅	—	6	1	no	—
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	C₂×D₃	1	1	yes	characteristic
107	C₅×C₂²⋊Q₈	—	3	4	no	—
108	C₅×C₂²⋊Q₈	—	6	2	no	—
109	C₂×C₅×C₄⋊C₄	—	6	1	no	—
110	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
111	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
112	C₅×#103	C₂×D₃	1	4	yes	complemented
113	C₅×#102	—	3	4	no	—
114	C₅×C₂²⋊C₈	—	3	4	no	—
115	C₂×#452	—	3	1	no	Sylow
116	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₅×D₃	—	2	2	no	—
118	C₂²×C₅×D₃	—	2	4	no	—
119	C₂²×C₅×D₃	—	2	2	no	—
120	C₂²×C₅×D₃	—	2	2	no	—
121	C₂²×C₅×D₃	—	2	2	no	—
122	C₂²×C₅×D₃	—	4	2	no	—
123	C₂²×C₅×D₃	—	4	2	no	—
124	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
125	C₃×C₅×Q₈	—	2	4	no	—
126	C₃×C₅×Q₈	—	2	2	no	—
127	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
128	C₂×C₃×C₄×C₅	—	2	4	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	4	2	no	—
132	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
134	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₂×C₅×Dic₃	—	2	2	no	—
137	C₂×C₅×Dic₃	—	2	2	no	—
138	C₂×C₅×Dic₃	—	4	2	no	—
139	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
140	C₅×D₁₂	—	2	16	no	—
141	C₅×D₁₂	—	2	4	no	—
142	C₅×D₁₂	—	2	2	no	—
143	C₅×D₁₂	C₂×D₄	1	4	yes	—
144	C₄×C₅×D₃	—	2	16	no	—
145	C₄×C₅×D₃	—	2	4	no	—
146	C₄×C₅×D₃	—	2	2	no	—
147	C₄×C₅×D₃	—	2	2	no	—
148	C₅×Dic₆	—	2	2	no	—
149	C₅×Dic₆	—	2	2	no	—
150	C₅×Dic₆	—	4	2	no	—
151	C₃×C₅×C₈	—	2	2	no	—
152	C₅×C₃⋊C₈	—	2	2	no	—
153	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
154	C₂×#239	—	2	4	no	—
155	C₂×#239	—	2	4	no	—
156	C₂×#239	—	2	2	no	—
157	C₂×#239	C₂²×C₅	1	4	yes	—
158	C₂²×D₁₂	—	2	1	no	—
159	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
160	C₂²×C₄×D₃	—	2	1	no	—
161	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
162	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
163	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
165	C₂×#216	—	2	4	no	—
166	C₂×#216	C₂²×C₅	1	4	yes	complemented
167	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
168	C₂×C₄⋊Dic₃	—	2	1	no	—
169	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
170	C₂×#204	—	2	4	no	—
171	C₂×#204	C₂²×C₅	1	4	yes	complemented
172	#897	—	2	2	no	—
173	#897	C₂²×C₅	1	4	yes	complemented
174	C₃×#103	C₂²×C₅	1	4	yes	complemented
175	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	complemented
176	#809	C₂²×C₅	1	4	yes	complemented
177	C₂⁴×C₅	—	3	1	no	—
178	C₂⁴×C₅	—	6	1	no	—
179	C₅×#41	—	6	8	no	—
180	C₅×#41	—	6	16	no	—
181	C₅×#41	—	6	8	no	—
182	C₂×C₅×Q₈	—	2	2	no	—
183	C₂×C₅×Q₈	—	2	1	no	—
184	C₂×C₅×Q₈	—	3	2	no	—
185	C₂×C₅×Q₈	—	6	1	no	—
186	C₂×C₅×Q₈	—	6	2	no	—
187	C₂×C₅×Q₈	—	6	2	no	—
188	C₂×C₅×Q₈	D₁₂	1	4	yes	—
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	4	no	—
193	C₂×C₅×D₄	—	6	8	no	—
194	C₂×C₅×D₄	—	6	2	no	—
195	C₂×C₅×D₄	—	6	1	no	—
196	C₂²×C₄×C₅	—	2	1	no	—
197	C₂²×C₄×C₅	—	2	1	no	—
198	C₂²×C₄×C₅	—	3	1	no	—
199	C₂²×C₄×C₅	—	3	2	no	—
200	C₂²×C₄×C₅	—	3	2	no	—
201	C₂²×C₄×C₅	—	6	4	no	—
202	C₂²×C₄×C₅	—	6	8	no	—
203	C₂²×C₄×C₅	—	6	2	no	—
204	C₂²×C₄×C₅	—	6	2	no	—
205	C₂²×C₄×C₅	—	6	1	no	—
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	—	2	2	no	—
210	C₂×C₅×C₈	—	3	2	no	—
211	C₂×C₅×C₈	—	6	2	no	—
212	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
213	C₅×C₄⋊C₄	—	2	1	no	—
214	C₅×C₄⋊C₄	—	6	4	no	—
215	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
216	C₅×C₂²⋊C₄	—	6	4	no	—
217	C₂²×#41	—	3	1	no	—
218	C₂²×Q₁₆	—	3	1	no	—
219	C₂²×SD₁₆	—	3	1	no	—
220	C₂×C₂²⋊Q₈	—	3	1	no	—
221	#452	—	3	8	no	—
222	C₂×#103	C₅×D₃	1	1	yes	characteristic, complemented
223	C₂×#102	—	3	1	no	—
224	C₂×C₂²⋊C₈	—	3	1	no	—
225	C₂²×C₃×C₅	#120	1	2	yes	—
226	C₂²×C₃×C₅	#135	1	2	yes	—
227	C₂²×C₃×C₅	#137	1	2	yes	—
228	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₅×D₃	—	2	2	no	—
230	C₂×C₅×D₃	—	2	4	no	—
231	C₂×C₅×D₃	—	2	2	no	—
232	C₂×C₅×D₃	—	2	2	no	—
233	C₂×C₅×D₃	—	4	2	no	—
234	C₂×C₅×D₃	—	4	2	no	—
235	C₂×C₅×D₃	—	4	4	no	—
236	C₂×C₅×D₃	—	4	8	no	—
237	C₃×C₄×C₅	—	2	4	no	—
238	C₃×C₄×C₅	—	4	2	no	—
239	C₃×C₄×C₅	#120	1	2	yes	—
240	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
241	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
242	C₅×Dic₃	—	2	2	no	—
243	C₅×Dic₃	—	4	2	no	—
244	C₂³×D₃	—	2	1	no	—
245	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
246	C₂×C₃×Q₈	—	2	2	no	—
247	C₂×C₃×Q₈	—	2	1	no	—
248	C₂×C₃×Q₈	C₅×D₄	1	4	yes	—
249	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
250	C₂²×C₃×C₄	—	2	1	no	—
251	C₂²×C₃×C₄	—	2	1	no	—
252	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
253	C₂²×Dic₃	—	2	1	no	—
254	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
255	#239	—	2	16	no	—
256	#239	—	2	8	no	—
257	#239	—	2	8	no	—
258	C₂×D₁₂	—	2	8	no	—
259	C₂×D₁₂	—	2	4	no	—
260	C₂×D₁₂	—	2	2	no	—
261	C₂×D₁₂	—	2	1	no	—
262	C₂×D₁₂	C₅×D₄	1	4	yes	—
263	C₂×D₁₂	C₂³×C₅	1	2	yes	—
264	C₂×C₄×D₃	—	2	8	no	—
265	C₂×C₄×D₃	—	2	2	no	—
266	C₂×C₄×D₃	—	2	2	no	—
267	C₂×C₄×D₃	—	2	4	no	—
268	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
269	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
270	C₂×Dic₆	—	2	2	no	—
271	C₂×Dic₆	—	2	2	no	—
272	C₂×Dic₆	—	2	1	no	—
273	C₂×Dic₆	C₂³×C₅	1	2	yes	—
274	C₂×C₃×C₈	—	2	2	no	—
275	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
276	C₃×C₄⋊C₄	—	2	1	no	—
277	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
278	#216	—	2	8	no	—
279	(C₂×D₃)⋊C₄	—	2	4	no	—
280	C₄⋊Dic₃	—	2	4	no	—
281	C₂×C₃⋊C₈	—	2	2	no	—
282	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
283	#204	—	2	8	no	—
284	C₂³×C₅	—	3	2	no	—
285	C₂³×C₅	—	6	4	no	—
286	C₂³×C₅	—	6	2	no	—
287	C₂³×C₅	—	6	2	no	—
288	C₂³×C₅	—	6	2	no	—
289	C₂³×C₅	—	6	2	no	—
290	C₂³×C₅	—	12	2	no	—
291	C₂³×C₅	—	12	2	no	—
292	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
293	C₅×Q₈	—	2	4	no	—
294	C₅×Q₈	—	2	2	no	—
295	C₅×Q₈	—	6	2	no	—
296	C₅×Q₈	—	6	2	no	—
297	C₅×Q₈	—	12	2	no	—
298	C₅×Q₈	C₂×D₁₂	1	4	yes	—
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	4	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	3	2	no	—
307	C₂×C₄×C₅	—	4	2	no	—
308	C₂×C₄×C₅	—	6	16	no	—
309	C₂×C₄×C₅	—	6	2	no	—
310	C₂×C₄×C₅	—	6	4	no	—
311	C₂×C₄×C₅	—	6	2	no	—
312	C₂×C₄×C₅	—	6	2	no	—
313	C₂×C₄×C₅	—	6	2	no	—
314	C₂×C₄×C₅	—	12	2	no	—
315	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
316	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
317	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
318	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
319	C₅×C₈	—	2	2	no	—
320	C₅×C₈	—	6	2	no	—
321	C₂×#41	—	3	4	no	—
322	C₂×#41	—	6	2	no	—
323	C₂×#41	—	6	4	no	—
324	C₂×#41	—	6	4	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	—	3	1	no	—
330	C₂³×C₄	—	6	1	no	—
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	C₂×C₅×D₃	1	1	yes	characteristic
337	C₂²⋊Q₈	—	3	4	no	—
338	C₂²⋊Q₈	—	6	2	no	—
339	C₂×C₄⋊C₄	—	6	1	no	—
340	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	—	6	1	no	—
342	#103	C₂×C₅×D₃	1	4	yes	complemented
343	#102	—	3	4	no	—
344	C₂²⋊C₈	—	3	4	no	—
345	C₂×C₃×C₅	#452	1	4	yes	complemented
346	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
347	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
348	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
349	C₅×D₃	—	4	2	no	—
350	C₅×D₃	—	4	4	no	—
351	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
352	C₂²×D₃	—	2	2	no	—
353	C₂²×D₃	—	2	4	no	—
354	C₂²×D₃	—	2	2	no	—
355	C₂²×D₃	—	2	2	no	—
356	C₂²×D₃	—	2	2	no	—
357	C₂²×D₃	—	4	2	no	—
358	C₂²×D₃	—	4	2	no	—
359	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
360	C₃×Q₈	—	2	4	no	—
361	C₃×Q₈	—	2	2	no	—
362	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
363	C₂×C₃×C₄	—	2	4	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	4	2	no	—
367	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
368	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
370	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
371	C₂×Dic₃	—	2	2	no	—
372	C₂×Dic₃	—	2	2	no	—
373	C₂×Dic₃	—	4	2	no	—
374	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
375	D₁₂	—	2	16	no	—
376	D₁₂	—	2	4	no	—
377	D₁₂	—	2	2	no	—
378	D₁₂	C₂×C₅×D₄	1	4	yes	—
379	C₄×D₃	—	2	16	no	—
380	C₄×D₃	—	2	4	no	—
381	C₄×D₃	—	2	2	no	—
382	C₄×D₃	—	2	2	no	—
383	Dic₆	—	2	2	no	—
384	Dic₆	—	2	2	no	—
385	Dic₆	—	4	2	no	—
386	C₃×C₈	—	2	2	no	—
387	C₃⋊C₈	—	2	2	no	—
388	C₂²×C₅	—	6	4	no	—
389	C₂²×C₅	—	6	2	no	—
390	C₂²×C₅	—	6	2	no	—
391	C₂²×C₅	—	6	2	no	—
392	C₂²×C₅	—	12	2	no	—
393	C₂²×C₅	—	12	2	no	—
394	C₂²×C₅	—	12	4	no	—
395	C₂²×C₅	—	12	8	no	—
396	C₂²×C₅	#882	1	2	yes	—
397	C₂²×C₅	#916	1	2	yes	—
398	C₂²×C₅	#918	1	2	yes	—
399	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
400	C₄×C₅	—	2	4	no	—
401	C₄×C₅	—	4	2	no	—
402	C₄×C₅	—	6	2	no	—
403	C₄×C₅	—	12	2	no	—
404	C₄×C₅	#882	1	2	yes	—
405	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
406	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
407	C₂⁴	—	3	1	no	—
408	C₂⁴	—	6	1	no	—
409	#41	—	6	8	no	—
410	#41	—	6	16	no	—
411	#41	—	6	8	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	3	2	no	—
415	C₂×Q₈	—	6	1	no	—
416	C₂×Q₈	—	6	2	no	—
417	C₂×Q₈	—	6	2	no	—
418	C₂×Q₈	C₅×D₁₂	1	4	yes	—
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	4	no	—
423	C₂×D₄	—	6	8	no	—
424	C₂×D₄	—	6	2	no	—
425	C₂×D₄	—	6	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	3	1	no	—
429	C₂²×C₄	—	3	2	no	—
430	C₂²×C₄	—	3	2	no	—
431	C₂²×C₄	—	6	4	no	—
432	C₂²×C₄	—	6	8	no	—
433	C₂²×C₄	—	6	2	no	—
434	C₂²×C₄	—	6	2	no	—
435	C₂²×C₄	—	6	1	no	—
436	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
437	Q₁₆	—	6	8	no	—
438	SD₁₆	—	6	8	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	3	2	no	—
441	C₂×C₈	—	6	2	no	—
442	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	6	4	no	—
445	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
446	C₂²⋊C₄	—	6	4	no	—
447	C₃×C₅	C₂×#452	1	1	yes	characteristic, complemented, Hall
448	C₂²×C₃	C₅×#120	1	2	yes	—
449	C₂²×C₃	C₅×#135	1	2	yes	—
450	C₂²×C₃	C₅×#137	1	2	yes	—
451	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
452	C₂×D₃	—	2	2	no	—
453	C₂×D₃	—	2	4	no	—
454	C₂×D₃	—	2	2	no	—
455	C₂×D₃	—	2	2	no	—
456	C₂×D₃	—	4	4	no	—
457	C₂×D₃	—	4	8	no	—
458	C₂×D₃	—	4	2	no	—
459	C₂×D₃	—	4	2	no	—
460	C₃×C₄	—	2	4	no	—
461	C₃×C₄	—	4	2	no	—
462	C₃×C₄	C₅×#120	1	2	yes	—
463	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
464	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
465	Dic₃	—	2	2	no	—
466	Dic₃	—	4	2	no	—
467	C₂×C₅	—	12	2	no	—
468	C₂×C₅	—	12	4	no	—
469	C₂×C₅	#4808	1	4	yes	direct product factor
470	C₂×C₅	C₂×#882	1	1	yes	characteristic
471	C₂×C₅	C₂×#916	1	1	yes	characteristic
472	C₂×C₅	C₂×#918	1	1	yes	characteristic
473	C₂³	—	3	2	no	—
474	C₂³	—	6	4	no	—
475	C₂³	—	6	2	no	—
476	C₂³	—	6	2	no	—
477	C₂³	—	6	2	no	—
478	C₂³	—	6	2	no	—
479	C₂³	—	12	2	no	—
480	C₂³	—	12	2	no	—
481	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
482	Q₈	—	2	4	no	—
483	Q₈	—	2	2	no	—
484	Q₈	—	6	2	no	—
485	Q₈	—	6	2	no	—
486	Q₈	—	12	2	no	—
487	Q₈	C₂×C₅×D₁₂	1	4	yes	—
488	D₄	—	3	4	no	—
489	D₄	—	6	16	no	—
490	D₄	—	6	4	no	—
491	D₄	—	6	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	3	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	6	16	no	—
498	C₂×C₄	—	6	2	no	—
499	C₂×C₄	—	6	4	no	—
500	C₂×C₄	—	6	2	no	—
501	C₂×C₄	—	6	2	no	—
502	C₂×C₄	—	6	2	no	—
503	C₂×C₄	—	12	2	no	—
504	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
505	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
506	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
507	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
508	C₈	—	2	2	no	—
509	C₈	—	6	2	no	—
510	C₂×C₃	C₅×#452	1	4	yes	complemented
511	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
512	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
513	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
514	D₃	—	4	2	no	—
515	D₃	—	4	4	no	—
516	C₅	C₂×#4808	1	1	yes	characteristic, direct product factor, Sylow
517	C₂²	—	6	4	no	—
518	C₂²	—	6	2	no	—
519	C₂²	—	6	2	no	—
520	C₂²	—	6	2	no	—
521	C₂²	—	12	2	no	—
522	C₂²	—	12	2	no	—
523	C₂²	—	12	4	no	—
524	C₂²	—	12	8	no	—
525	C₂²	C₅×#882	1	2	yes	—
526	C₂²	C₅×#916	1	2	yes	—
527	C₂²	C₅×#918	1	2	yes	—
528	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
529	C₄	—	2	4	no	—
530	C₄	—	4	2	no	—
531	C₄	—	6	2	no	—
532	C₄	—	12	2	no	—
533	C₄	C₅×#882	1	2	yes	—
534	C₄	C₂²×C₅×D₁₂	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	—	12	2	no	—
538	C₂	—	12	4	no	—
539	C₂	C₅×#4808	1	4	yes	direct product factor
540	C₂	C₂×C₅×#882	1	1	yes	characteristic
541	C₂	C₂×C₅×#916	1	1	yes	characteristic
542	C₂	C₂×C₅×#918	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#103	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×#239	C₂
hypercenter	C₂×C₅×#103	D₃
hypocenter	C₃	C₂×C₅×#452
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#103

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×#216	C₂	semidirect
3. C₂²×C₅×#204	C₂	semidirect
4. C₂×C₅×#897	C₂	semidirect
5. C₂×C₃×C₅×#103	C₂	semidirect
6. C₂×C₅×(C₂×D₃)⋊C₈	C₂	semidirect
7. C₂×C₅×#809	C₂	semidirect
8. C₅×#4808	C₂	direct (N × H)
23. C₂×C₅×#216	C₂²	semidirect
28. C₂×C₅×#204	C₂²	semidirect
30. C₅×#897	C₂²	semidirect
31. C₃×C₅×#103	C₂²	semidirect
32. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
33. C₅×#809	C₂²	semidirect
34. C₂×#4808	C₅	direct (N × H)
40. C₂×C₅×#103	D₃	semidirect
84. C₂²×#216	C₂×C₅	semidirect
85. C₂²×#204	C₂×C₅	semidirect
86. C₂×#897	C₂×C₅	semidirect
87. C₂×C₃×#103	C₂×C₅	semidirect
88. C₂×(C₂×D₃)⋊C₈	C₂×C₅	semidirect
89. C₂×#809	C₂×C₅	semidirect
90. #4808	C₂×C₅	direct (N × H)
112. C₅×#103	C₂×D₃	semidirect
166. C₂×#216	C₂²×C₅	semidirect
171. C₂×#204	C₂²×C₅	semidirect
173. #897	C₂²×C₅	semidirect
174. C₃×#103	C₂²×C₅	semidirect
175. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
176. #809	C₂²×C₅	semidirect
222. C₂×#103	C₅×D₃	semidirect
342. #103	C₂×C₅×D₃	semidirect
345. C₂×C₃×C₅	#452	semidirect
447. C₃×C₅	C₂×#452	semidirect
469. C₂×C₅	#4808	direct (N × H)
510. C₂×C₃	C₅×#452	semidirect
516. C₅	C₂×#4808	direct (N × H)
536. C₃	C₂×C₅×#452	semidirect
539. C₂	C₅×#4808	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×#239	2
C₂²×C₅×#216	2
C₂²×C₅×#204	2
C₂×C₅×#897	2
C₂×C₃×C₅×#103	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₂×C₅×#809	2
C₅×#4808	2
C₂×C₅×#452	3
C₂×#4808	5

Subgroups — C2×C5×#4808 #14423508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4808 #14423508