Subgroups — C₂×C₅×#4818 #14425869

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#944	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#215	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×#204	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#810	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4818	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₅×#461	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₅×D₃	—	2	1	no	—
13	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₅×#944	—	2	2	no	—
17	C₅×#944	C₂²	1	4	yes	complemented
18	C₂×C₅×#215	—	2	4	no	—
19	C₂×C₅×#215	C₂²	1	4	yes	—
20	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
21	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
22	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
23	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×#204	—	2	4	no	—
26	C₂×C₅×#204	C₂²	1	4	yes	—
27	C₅×#893	—	2	2	no	—
28	C₅×#893	C₂²	1	4	yes	—
29	C₃×C₅×#103	C₂²	1	4	yes	complemented
30	C₅×Dic₃⋊C₈	C₂²	1	4	yes	complemented
31	C₅×#810	C₂²	1	4	yes	complemented
32	C₂×#4818	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂²×C₅×SD₁₆	—	3	1	no	—
34	C₂²×C₅×SD₁₆	—	3	1	no	—
35	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
36	C₂×C₄×C₅×D₄	—	3	1	no	—
37	C₅×#461	—	3	8	no	—
38	C₂×C₅×C₄⋊C₈	—	3	1	no	—
39	C₂×C₅×#103	—	3	1	no	—
40	C₂×C₅×#103	D₃	1	1	yes	characteristic, complemented
41	C₂³×C₅×D₃	—	2	1	no	—
42	C₂×C₃×C₅×Q₈	—	2	1	no	—
43	C₂×C₃×C₅×Q₈	—	2	2	no	—
44	C₂×C₃×C₅×Q₈	—	2	2	no	—
45	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	—	2	1	no	—
47	C₂²×C₃×C₄×C₅	—	2	1	no	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₅×Dic₃	—	2	1	no	—
50	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
51	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
52	C₂×C₅×D₁₂	—	2	1	no	—
53	C₂×C₅×D₁₂	—	2	2	no	—
54	C₂×C₅×D₁₂	D₄	1	4	yes	—
55	C₂×C₅×D₁₂	C₂³	1	2	yes	—
56	C₂×C₄×C₅×D₃	—	2	4	no	—
57	C₂×C₄×C₅×D₃	—	4	4	no	—
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	C₂×C₃×C₅×C₈	—	2	2	no	—
63	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	—	2	1	no	—
65	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₅×#215	—	2	8	no	—
67	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
68	C₅×Dic₃⋊C₄	—	2	4	no	—
69	C₅×Dic₃⋊C₄	—	2	4	no	—
70	C₄×C₅×Dic₃	D₄	1	2	yes	—
71	C₄×C₅×Dic₃	C₂³	1	2	yes	—
72	C₂×C₅×C₃⋊C₈	—	2	2	no	—
73	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
74	C₅×#204	—	2	8	no	—
75	C₂×#944	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂²×#215	C₂×C₅	1	1	yes	characteristic
77	C₂²×#204	C₂×C₅	1	1	yes	characteristic
78	C₂×#893	C₂×C₅	1	1	yes	characteristic
79	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂×Dic₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂×#810	C₂×C₅	1	1	yes	characteristic, complemented
82	#4818	C₂×C₅	1	8	yes	direct product factor
83	C₂²×C₅×Q₈	—	3	1	no	—
84	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
85	C₂²×C₅×D₄	—	3	1	no	—
86	C₂³×C₄×C₅	—	6	1	no	—
87	C₂×C₅×SD₁₆	—	3	4	no	—
88	C₂×C₅×SD₁₆	—	3	4	no	—
89	C₂×C₅×SD₁₆	—	6	4	no	—
90	C₂×C₅×SD₁₆	—	6	4	no	—
91	C₂²×C₅×C₈	—	3	1	no	—
92	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
93	C₅×C₄⋊Q₈	—	3	4	no	—
94	C₅×C₄⋊Q₈	—	6	2	no	—
95	C₄×C₅×D₄	—	3	4	no	—
96	C₄×C₅×D₄	—	6	2	no	—
97	C₂×C₅×C₄⋊C₄	—	6	1	no	—
98	C₂×C₅×C₄⋊C₄	—	6	1	no	—
99	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
100	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
101	C₂×C₄²×C₅	—	3	1	no	—
102	C₅×C₄⋊C₈	—	3	4	no	—
103	C₅×#103	—	3	4	no	—
104	C₅×#103	C₂×D₃	1	4	yes	complemented
105	C₂×#461	—	3	1	no	Sylow
106	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₅×D₃	—	2	4	no	—
108	C₂²×C₅×D₃	—	2	2	no	—
109	C₂²×C₅×D₃	—	4	2	no	—
110	C₂²×C₅×D₃	—	4	2	no	—
111	C₃×C₅×Q₈	—	2	2	no	—
112	C₃×C₅×Q₈	—	2	2	no	—
113	C₃×C₅×Q₈	—	4	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	4	2	no	—
117	C₂×C₃×C₄×C₅	—	4	2	no	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
120	C₂×C₃×C₄×C₅	#41	1	2	yes	—
121	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
122	C₂×C₅×Dic₃	—	2	2	no	—
123	C₂×C₅×Dic₃	—	2	2	no	—
124	C₂×C₅×Dic₃	—	4	2	no	—
125	C₂×C₅×Dic₃	SD₁₆	1	4	yes	complemented
126	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
127	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
128	C₅×D₁₂	—	2	4	no	—
129	C₅×D₁₂	—	2	2	no	—
130	C₅×D₁₂	C₂×D₄	1	4	yes	—
131	C₄×C₅×D₃	—	4	8	no	—
132	C₅×Dic₆	—	2	2	no	—
133	C₅×Dic₆	—	2	2	no	—
134	C₅×Dic₆	—	4	2	no	—
135	C₃×C₅×C₈	—	2	2	no	—
136	C₅×C₃⋊C₈	—	2	2	no	—
137	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
138	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
139	C₂²×C₄×D₃	—	2	1	no	—
140	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
141	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
142	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
143	#944	—	2	2	no	—
144	#944	C₂²×C₅	1	4	yes	complemented
145	C₂×#215	—	2	4	no	—
146	C₂×#215	C₂²×C₅	1	4	yes	—
147	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
148	C₂×Dic₃⋊C₄	—	2	1	no	—
149	C₂×Dic₃⋊C₄	—	2	1	no	—
150	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
151	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
152	C₂×#204	—	2	4	no	—
153	C₂×#204	C₂²×C₅	1	4	yes	—
154	#893	—	2	2	no	—
155	#893	C₂²×C₅	1	4	yes	—
156	C₃×#103	C₂²×C₅	1	4	yes	complemented
157	Dic₃⋊C₈	C₂²×C₅	1	4	yes	complemented
158	#810	C₂²×C₅	1	4	yes	complemented
159	C₂⁴×C₅	—	6	1	no	—
160	C₂×C₅×Q₈	—	2	1	no	—
161	C₂×C₅×Q₈	—	2	2	no	—
162	C₂×C₅×Q₈	—	2	2	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×Q₈	C₂²×D₃	1	2	yes	—
168	C₂×C₅×D₄	—	3	4	no	—
169	C₂×C₅×D₄	—	3	2	no	—
170	C₂×C₅×D₄	—	6	2	no	—
171	C₂×C₅×D₄	—	6	1	no	—
172	C₂²×C₄×C₅	—	2	1	no	—
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	—	3	1	no	—
175	C₂²×C₄×C₅	—	3	1	no	—
176	C₂²×C₄×C₅	—	6	4	no	—
177	C₂²×C₄×C₅	—	6	1	no	—
178	C₂²×C₄×C₅	—	12	4	no	—
179	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
180	C₅×SD₁₆	—	6	8	no	—
181	C₅×SD₁₆	—	6	8	no	—
182	C₂×C₅×C₈	—	2	2	no	—
183	C₂×C₅×C₈	—	3	2	no	—
184	C₂×C₅×C₈	—	6	2	no	—
185	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
186	C₅×C₄⋊C₄	—	2	1	no	—
187	C₅×C₄⋊C₄	—	6	4	no	—
188	C₅×C₄⋊C₄	—	6	4	no	—
189	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
190	C₅×C₂²⋊C₄	—	6	4	no	—
191	C₄²×C₅	—	3	2	no	—
192	C₄²×C₅	—	3	2	no	—
193	C₂²×SD₁₆	—	3	1	no	—
194	C₂²×SD₁₆	—	3	1	no	—
195	C₂×C₄⋊Q₈	—	3	1	no	—
196	C₂×C₄×D₄	—	3	1	no	—
197	#461	—	3	8	no	—
198	C₂×C₄⋊C₈	—	3	1	no	—
199	C₂×#103	—	3	1	no	—
200	C₂×#103	C₅×D₃	1	1	yes	characteristic, complemented
201	C₂²×C₃×C₅	#121	1	2	yes	—
202	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
203	C₂²×C₃×C₅	#137	1	2	yes	—
204	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₅×D₃	—	2	4	no	—
206	C₂×C₅×D₃	—	4	2	no	—
207	C₂×C₅×D₃	—	4	2	no	—
208	C₂×C₅×D₃	—	4	8	no	—
209	C₃×C₄×C₅	—	4	2	no	—
210	C₃×C₄×C₅	—	4	2	no	—
211	C₃×C₄×C₅	#121	1	2	yes	—
212	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
213	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
214	C₅×Dic₃	—	2	2	no	—
215	C₅×Dic₃	—	4	2	no	—
216	C₅×Dic₃	C₂×SD₁₆	1	4	yes	complemented
217	C₂³×D₃	—	2	1	no	—
218	C₂×C₃×Q₈	—	2	1	no	—
219	C₂×C₃×Q₈	—	2	2	no	—
220	C₂×C₃×Q₈	—	2	2	no	—
221	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
222	C₂²×C₃×C₄	—	2	1	no	—
223	C₂²×C₃×C₄	—	2	1	no	—
224	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
225	C₂²×Dic₃	—	2	1	no	—
226	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
227	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
228	C₂×D₁₂	—	2	1	no	—
229	C₂×D₁₂	—	2	2	no	—
230	C₂×D₁₂	C₅×D₄	1	4	yes	—
231	C₂×D₁₂	C₂³×C₅	1	2	yes	—
232	C₂×C₄×D₃	—	2	4	no	—
233	C₂×C₄×D₃	—	4	4	no	—
234	C₂×Dic₆	—	2	2	no	—
235	C₂×Dic₆	—	2	2	no	—
236	C₂×Dic₆	—	2	1	no	—
237	C₂×Dic₆	C₂³×C₅	1	2	yes	—
238	C₂×C₃×C₈	—	2	2	no	—
239	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
240	C₃×C₄⋊C₄	—	2	1	no	—
241	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
242	#215	—	2	8	no	—
243	(C₂×D₃)⋊C₄	—	2	4	no	—
244	Dic₃⋊C₄	—	2	4	no	—
245	Dic₃⋊C₄	—	2	4	no	—
246	C₄×Dic₃	C₅×D₄	1	2	yes	—
247	C₄×Dic₃	C₂³×C₅	1	2	yes	—
248	C₂×C₃⋊C₈	—	2	2	no	—
249	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
250	#204	—	2	8	no	—
251	C₂³×C₅	—	6	4	no	—
252	C₂³×C₅	—	6	2	no	—
253	C₂³×C₅	—	12	2	no	—
254	C₂³×C₅	—	12	2	no	—
255	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
256	C₅×Q₈	—	2	2	no	—
257	C₅×Q₈	—	2	2	no	—
258	C₅×Q₈	—	4	2	no	—
259	C₅×Q₈	—	6	2	no	—
260	C₅×Q₈	—	6	2	no	—
261	C₅×Q₈	—	12	2	no	—
262	C₅×D₄	—	3	4	no	—
263	C₅×D₄	—	6	4	no	—
264	C₅×D₄	—	6	2	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	3	4	no	—
268	C₂×C₄×C₅	—	3	2	no	—
269	C₂×C₄×C₅	—	3	2	no	—
270	C₂×C₄×C₅	—	4	2	no	—
271	C₂×C₄×C₅	—	4	2	no	—
272	C₂×C₄×C₅	—	6	2	no	—
273	C₂×C₄×C₅	—	6	2	no	—
274	C₂×C₄×C₅	—	12	8	no	—
275	C₂×C₄×C₅	—	12	2	no	—
276	C₂×C₄×C₅	#235	1	2	yes	—
277	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
278	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
279	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
280	C₅×C₈	—	2	2	no	—
281	C₅×C₈	—	6	2	no	—
282	C₂²×Q₈	—	3	1	no	—
283	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
284	C₂²×D₄	—	3	1	no	—
285	C₂³×C₄	—	6	1	no	—
286	C₂×SD₁₆	—	3	4	no	—
287	C₂×SD₁₆	—	3	4	no	—
288	C₂×SD₁₆	—	6	4	no	—
289	C₂×SD₁₆	—	6	4	no	—
290	C₂²×C₈	—	3	1	no	—
291	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
292	C₄⋊Q₈	—	3	4	no	—
293	C₄⋊Q₈	—	6	2	no	—
294	C₄×D₄	—	3	4	no	—
295	C₄×D₄	—	6	2	no	—
296	C₂×C₄⋊C₄	—	6	1	no	—
297	C₂×C₄⋊C₄	—	6	1	no	—
298	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	—	6	1	no	—
300	C₂×C₄²	—	3	1	no	—
301	C₄⋊C₈	—	3	4	no	—
302	#103	—	3	4	no	—
303	#103	C₂×C₅×D₃	1	4	yes	complemented
304	C₂×C₃×C₅	#461	1	4	yes	complemented
305	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
306	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
307	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
308	C₅×D₃	—	4	4	no	—
309	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
310	C₂²×D₃	—	2	4	no	—
311	C₂²×D₃	—	2	2	no	—
312	C₂²×D₃	—	4	2	no	—
313	C₂²×D₃	—	4	2	no	—
314	C₃×Q₈	—	2	2	no	—
315	C₃×Q₈	—	2	2	no	—
316	C₃×Q₈	—	4	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	4	2	no	—
320	C₂×C₃×C₄	—	4	2	no	—
321	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
323	C₂×C₃×C₄	C₅×#41	1	2	yes	—
324	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
325	C₂×Dic₃	—	2	2	no	—
326	C₂×Dic₃	—	2	2	no	—
327	C₂×Dic₃	—	4	2	no	—
328	C₂×Dic₃	C₅×SD₁₆	1	4	yes	complemented
329	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
330	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
331	D₁₂	—	2	4	no	—
332	D₁₂	—	2	2	no	—
333	D₁₂	C₂×C₅×D₄	1	4	yes	—
334	C₄×D₃	—	4	8	no	—
335	Dic₆	—	2	2	no	—
336	Dic₆	—	2	2	no	—
337	Dic₆	—	4	2	no	—
338	C₃×C₈	—	2	2	no	—
339	C₃⋊C₈	—	2	2	no	—
340	C₂²×C₅	—	6	4	no	—
341	C₂²×C₅	—	12	2	no	—
342	C₂²×C₅	—	12	2	no	—
343	C₂²×C₅	—	12	8	no	—
344	C₂²×C₅	#884	1	2	yes	—
345	C₂²×C₅	D₃×SD₁₆	1	2	yes	—
346	C₂²×C₅	#918	1	2	yes	—
347	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
348	C₄×C₅	—	3	4	no	—
349	C₄×C₅	—	4	2	no	—
350	C₄×C₅	—	4	2	no	—
351	C₄×C₅	—	6	2	no	—
352	C₄×C₅	—	12	2	no	—
353	C₄×C₅	#884	1	2	yes	—
354	C₄×C₅	C₂×#235	1	1	yes	characteristic
355	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
356	C₂⁴	—	6	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	3	2	no	—
361	C₂×Q₈	—	6	1	no	—
362	C₂×Q₈	—	6	2	no	—
363	C₂×Q₈	—	6	2	no	—
364	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
365	C₂×D₄	—	3	4	no	—
366	C₂×D₄	—	3	2	no	—
367	C₂×D₄	—	6	2	no	—
368	C₂×D₄	—	6	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	3	1	no	—
372	C₂²×C₄	—	3	1	no	—
373	C₂²×C₄	—	6	4	no	—
374	C₂²×C₄	—	6	1	no	—
375	C₂²×C₄	—	12	4	no	—
376	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
377	SD₁₆	—	6	8	no	—
378	SD₁₆	—	6	8	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	3	2	no	—
381	C₂×C₈	—	6	2	no	—
382	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	6	4	no	—
385	C₄⋊C₄	—	6	4	no	—
386	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
387	C₂²⋊C₄	—	6	4	no	—
388	C₄²	—	3	2	no	—
389	C₄²	—	3	2	no	—
390	C₃×C₅	C₂×#461	1	1	yes	characteristic, complemented, Hall
391	C₂²×C₃	C₅×#121	1	2	yes	—
392	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
393	C₂²×C₃	C₅×#137	1	2	yes	—
394	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
395	C₂×D₃	—	2	4	no	—
396	C₂×D₃	—	4	8	no	—
397	C₂×D₃	—	4	2	no	—
398	C₂×D₃	—	4	2	no	—
399	C₃×C₄	—	4	2	no	—
400	C₃×C₄	—	4	2	no	—
401	C₃×C₄	C₅×#121	1	2	yes	—
402	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
403	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
404	Dic₃	—	2	2	no	—
405	Dic₃	—	4	2	no	—
406	Dic₃	C₂×C₅×SD₁₆	1	4	yes	complemented
407	C₂×C₅	—	12	4	no	—
408	C₂×C₅	#4818	1	4	yes	direct product factor
409	C₂×C₅	C₂×#884	1	1	yes	characteristic
410	C₂×C₅	C₂×D₃×SD₁₆	1	1	yes	characteristic
411	C₂×C₅	C₂×#918	1	1	yes	characteristic
412	C₂³	—	6	4	no	—
413	C₂³	—	6	2	no	—
414	C₂³	—	12	2	no	—
415	C₂³	—	12	2	no	—
416	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
417	Q₈	—	2	2	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	4	2	no	—
420	Q₈	—	6	2	no	—
421	Q₈	—	6	2	no	—
422	Q₈	—	12	2	no	—
423	D₄	—	3	4	no	—
424	D₄	—	6	4	no	—
425	D₄	—	6	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	3	4	no	—
429	C₂×C₄	—	3	2	no	—
430	C₂×C₄	—	3	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	6	2	no	—
434	C₂×C₄	—	6	2	no	—
435	C₂×C₄	—	12	8	no	—
436	C₂×C₄	—	12	2	no	—
437	C₂×C₄	C₅×#235	1	2	yes	—
438	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
439	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
440	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
441	C₈	—	2	2	no	—
442	C₈	—	6	2	no	—
443	C₂×C₃	C₅×#461	1	4	yes	complemented
444	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
445	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
446	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
447	D₃	—	4	4	no	—
448	C₅	C₂×#4818	1	1	yes	characteristic, direct product factor, Sylow
449	C₂²	—	6	4	no	—
450	C₂²	—	12	2	no	—
451	C₂²	—	12	2	no	—
452	C₂²	—	12	8	no	—
453	C₂²	C₅×#884	1	2	yes	—
454	C₂²	C₅×D₃×SD₁₆	1	2	yes	—
455	C₂²	C₅×#918	1	2	yes	—
456	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
457	C₄	—	3	4	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	6	2	no	—
461	C₄	—	12	2	no	—
462	C₄	C₅×#884	1	2	yes	—
463	C₄	C₂×C₅×#235	1	1	yes	characteristic
464	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
465	C₃	C₂×C₅×#461	1	1	yes	characteristic, complemented, Sylow
466	C₂	—	12	4	no	—
467	C₂	C₅×#4818	1	4	yes	direct product factor
468	C₂	C₂×C₅×#884	1	1	yes	characteristic
469	C₂	C₂×C₅×D₃×SD₁₆	1	1	yes	characteristic
470	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×D₁₂	C₂²
hypercenter	C₂×C₅×#103	D₃
hypocenter	C₃	C₂×C₅×#461
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
1. C₂×C₅×#944	C₂	semidirect
5. C₂×C₃×C₅×#103	C₂	semidirect
6. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
7. C₂×C₅×#810	C₂	semidirect
8. C₅×#4818	C₂	direct (N × H)
17. C₅×#944	C₂²	semidirect
29. C₃×C₅×#103	C₂²	semidirect
30. C₅×Dic₃⋊C₈	C₂²	semidirect
31. C₅×#810	C₂²	semidirect
32. C₂×#4818	C₅	direct (N × H)
40. C₂×C₅×#103	D₃	semidirect
75. C₂×#944	C₂×C₅	semidirect
79. C₂×C₃×#103	C₂×C₅	semidirect
80. C₂×Dic₃⋊C₈	C₂×C₅	semidirect
81. C₂×#810	C₂×C₅	semidirect
82. #4818	C₂×C₅	direct (N × H)
104. C₅×#103	C₂×D₃	semidirect
125. C₂×C₅×Dic₃	SD₁₆	semidirect
144. #944	C₂²×C₅	semidirect
156. C₃×#103	C₂²×C₅	semidirect
157. Dic₃⋊C₈	C₂²×C₅	semidirect
158. #810	C₂²×C₅	semidirect
200. C₂×#103	C₅×D₃	semidirect
216. C₅×Dic₃	C₂×SD₁₆	semidirect
303. #103	C₂×C₅×D₃	semidirect
304. C₂×C₃×C₅	#461	semidirect
328. C₂×Dic₃	C₅×SD₁₆	semidirect
390. C₃×C₅	C₂×#461	semidirect
406. Dic₃	C₂×C₅×SD₁₆	semidirect
408. C₂×C₅	#4818	direct (N × H)
443. C₂×C₃	C₅×#461	semidirect
448. C₅	C₂×#4818	direct (N × H)
465. C₃	C₂×C₅×#461	semidirect
467. C₂	C₅×#4818	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×C₅×#944	2
C₂²×C₅×#215	2
C₂²×C₅×#204	2
C₂×C₅×#893	2
C₂×C₃×C₅×#103	2
C₂×C₅×Dic₃⋊C₈	2
C₂×C₅×#810	2
C₅×#4818	2
C₂×C₅×#461	3
C₂×#4818	5

Subgroups — C2×C5×#4818 #14425869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4818 #14425869