Subgroups — C₂×C₅×#4800 #14437728

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#947	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#890	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#835	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#821	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic
8	C₅×#4800	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₅×#488	—	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×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₅×#947	—	2	2	no	—
15	C₅×#947	C₂²	1	4	yes	—
16	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
17	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
18	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
21	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
22	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₅×#890	—	2	2	no	—
24	C₅×#890	C₂²	1	4	yes	complemented
25	C₃×C₅×#103	C₂²	1	4	yes	complemented
26	C₅×#835	C₂²	1	4	yes	complemented
27	C₅×#821	C₂²	1	4	yes	—
28	C₅×C₈×Dic₃	C₂²	1	4	yes	complemented
29	C₅×#809	C₂²	1	4	yes	—
30	C₂×#4800	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#125	—	3	1	no	—
32	C₂×C₅×#124	—	3	1	no	—
33	C₅×#488	—	3	8	no	—
34	C₂×C₅×#103	—	3	1	no	—
35	C₂×C₅×#103	D₃	1	1	yes	characteristic, complemented
36	C₂×C₅×#102	—	3	1	no	—
37	C₂×C₅×#102	—	3	1	no	—
38	C₂×C₄×C₅×C₈	—	3	1	no	—
39	C₂³×C₅×D₃	—	2	1	no	—
40	C₂×C₃×C₅×Q₈	—	2	1	no	—
41	C₂×C₃×C₅×Q₈	—	2	2	no	—
42	C₂×C₃×C₅×Q₈	—	2	2	no	—
43	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	—	2	1	no	—
45	C₂²×C₃×C₄×C₅	—	2	1	no	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₅×Dic₃	—	2	1	no	—
48	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
49	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
50	C₂×C₅×D₁₂	—	2	2	no	—
51	C₂×C₅×D₁₂	—	2	2	no	—
52	C₂×C₅×D₁₂	—	2	1	no	—
53	C₂×C₅×D₁₂	C₂³	1	2	yes	—
54	C₂×C₃×C₅×C₈	—	2	2	no	—
55	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
56	C₃×C₅×C₄⋊C₄	—	2	1	no	—
57	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
58	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
59	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
60	C₅×C₄⋊Dic₃	—	2	1	no	—
61	C₅×C₄⋊Dic₃	—	2	4	no	—
62	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
63	C₅×Dic₃⋊C₄	—	2	4	no	—
64	C₄×C₅×Dic₃	D₄	1	2	yes	—
65	C₄×C₅×Dic₃	C₂³	1	2	yes	—
66	C₂×C₅×C₃⋊C₈	—	2	2	no	—
67	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
68	C₂×#947	C₂×C₅	1	1	yes	characteristic
69	C₂×#890	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×#835	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×#821	C₂×C₅	1	1	yes	characteristic
73	C₂×C₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×#809	C₂×C₅	1	1	yes	characteristic
75	#4800	C₂×C₅	1	8	yes	direct product factor
76	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
77	C₂²×C₅×D₄	—	3	1	no	—
78	C₂²×C₅×C₈	—	3	1	no	—
79	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
80	C₅×#125	—	3	4	no	—
81	C₅×#125	—	6	2	no	—
82	C₅×#124	—	3	4	no	—
83	C₅×#124	—	6	2	no	—
84	C₂×C₅×C₄⋊C₄	—	3	1	no	—
85	C₂×C₅×C₄⋊C₄	—	6	1	no	—
86	C₂×C₅×C₄⋊C₄	—	6	1	no	—
87	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
88	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
89	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
90	C₂×C₄²×C₅	—	3	1	no	—
91	C₅×#103	—	3	4	no	—
92	C₅×#103	C₂×D₃	1	4	yes	complemented
93	C₅×#102	—	3	4	no	—
94	C₅×#102	—	3	4	no	—
95	C₄×C₅×C₈	—	3	4	no	—
96	C₂×#488	—	3	1	no	Sylow
97	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₅×D₃	—	2	2	no	—
99	C₂²×C₅×D₃	—	4	2	no	—
100	C₂²×C₅×D₃	—	4	2	no	—
101	C₂²×C₅×D₃	—	4	2	no	—
102	C₃×C₅×Q₈	—	2	2	no	—
103	C₃×C₅×Q₈	—	2	2	no	—
104	C₃×C₅×Q₈	—	4	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	4	2	no	—
108	C₂×C₃×C₄×C₅	—	4	2	no	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	#41	1	2	yes	—
111	C₂×C₃×C₄×C₅	#41	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
113	C₂×C₅×Dic₃	—	2	2	no	—
114	C₂×C₅×Dic₃	—	2	2	no	—
115	C₂×C₅×Dic₃	—	2	2	no	—
116	C₂×C₅×Dic₃	—	4	2	no	—
117	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
118	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
119	C₅×D₁₂	—	2	2	no	—
120	C₅×D₁₂	—	2	2	no	—
121	C₅×D₁₂	—	4	2	no	—
122	C₃×C₅×C₈	—	2	2	no	—
123	C₅×C₃⋊C₈	—	2	2	no	—
124	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
125	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
126	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
128	#947	—	2	2	no	—
129	#947	C₂²×C₅	1	4	yes	—
130	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
131	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
132	C₂×C₄⋊Dic₃	—	2	1	no	—
133	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
134	C₂×Dic₃⋊C₄	—	2	1	no	—
135	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
136	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
137	#890	—	2	2	no	—
138	#890	C₂²×C₅	1	4	yes	complemented
139	C₃×#103	C₂²×C₅	1	4	yes	complemented
140	#835	C₂²×C₅	1	4	yes	complemented
141	#821	C₂²×C₅	1	4	yes	—
142	C₈×Dic₃	C₂²×C₅	1	4	yes	complemented
143	#809	C₂²×C₅	1	4	yes	—
144	C₂⁴×C₅	—	6	1	no	—
145	C₂×C₅×Q₈	—	2	1	no	—
146	C₂×C₅×Q₈	—	2	2	no	—
147	C₂×C₅×Q₈	—	2	2	no	—
148	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
149	C₂×C₅×D₄	—	3	2	no	—
150	C₂×C₅×D₄	—	6	2	no	—
151	C₂×C₅×D₄	—	6	1	no	—
152	C₂×C₅×D₄	—	6	2	no	—
153	C₂²×C₄×C₅	—	2	1	no	—
154	C₂²×C₄×C₅	—	2	1	no	—
155	C₂²×C₄×C₅	—	3	1	no	—
156	C₂²×C₄×C₅	—	3	1	no	—
157	C₂²×C₄×C₅	—	6	1	no	—
158	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
159	C₂×C₅×C₈	—	2	2	no	—
160	C₂×C₅×C₈	—	3	2	no	—
161	C₂×C₅×C₈	—	6	2	no	—
162	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
163	C₅×C₄⋊C₄	—	2	1	no	—
164	C₅×C₄⋊C₄	—	3	2	no	—
165	C₅×C₄⋊C₄	—	6	4	no	—
166	C₅×C₄⋊C₄	—	6	4	no	—
167	C₅×C₄⋊C₄	—	6	1	no	—
168	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
169	C₅×C₂²⋊C₄	—	6	4	no	—
170	C₅×C₂²⋊C₄	—	6	4	no	—
171	C₄²×C₅	—	3	2	no	—
172	C₄²×C₅	—	3	2	no	—
173	C₂×#125	—	3	1	no	—
174	C₂×#124	—	3	1	no	—
175	#488	—	3	8	no	—
176	C₂×#103	—	3	1	no	—
177	C₂×#103	C₅×D₃	1	1	yes	characteristic, complemented
178	C₂×#102	—	3	1	no	—
179	C₂×#102	—	3	1	no	—
180	C₂×C₄×C₈	—	3	1	no	—
181	C₂²×C₃×C₅	#124	1	2	yes	—
182	C₂²×C₃×C₅	#135	1	2	yes	—
183	C₂²×C₃×C₅	#135	1	2	yes	—
184	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₅×D₃	—	4	2	no	—
186	C₂×C₅×D₃	—	4	2	no	—
187	C₂×C₅×D₃	—	4	2	no	—
188	C₂×C₅×D₃	—	8	4	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	—	4	2	no	—
191	C₃×C₄×C₅	#124	1	2	yes	—
192	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
193	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
194	C₅×Dic₃	—	2	2	no	—
195	C₅×Dic₃	—	2	2	no	—
196	C₅×Dic₃	—	4	2	no	—
197	C₂³×D₃	—	2	1	no	—
198	C₂×C₃×Q₈	—	2	1	no	—
199	C₂×C₃×Q₈	—	2	2	no	—
200	C₂×C₃×Q₈	—	2	2	no	—
201	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
202	C₂²×C₃×C₄	—	2	1	no	—
203	C₂²×C₃×C₄	—	2	1	no	—
204	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
205	C₂²×Dic₃	—	2	1	no	—
206	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
207	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
208	C₂×D₁₂	—	2	2	no	—
209	C₂×D₁₂	—	2	2	no	—
210	C₂×D₁₂	—	2	1	no	—
211	C₂×D₁₂	C₂³×C₅	1	2	yes	—
212	C₂×C₃×C₈	—	2	2	no	—
213	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
214	C₃×C₄⋊C₄	—	2	1	no	—
215	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
216	(C₂×D₃)⋊C₄	—	2	4	no	—
217	(C₂×D₃)⋊C₄	—	2	4	no	—
218	C₄⋊Dic₃	—	2	1	no	—
219	C₄⋊Dic₃	—	2	4	no	—
220	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
221	Dic₃⋊C₄	—	2	4	no	—
222	C₄×Dic₃	C₅×D₄	1	2	yes	—
223	C₄×Dic₃	C₂³×C₅	1	2	yes	—
224	C₂×C₃⋊C₈	—	2	2	no	—
225	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
226	C₂³×C₅	—	6	2	no	—
227	C₂³×C₅	—	12	2	no	—
228	C₂³×C₅	—	12	2	no	—
229	C₂³×C₅	—	12	2	no	—
230	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
231	C₅×Q₈	—	2	2	no	—
232	C₅×Q₈	—	2	2	no	—
233	C₅×Q₈	—	4	2	no	—
234	C₅×D₄	—	6	2	no	—
235	C₅×D₄	—	6	2	no	—
236	C₅×D₄	—	12	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	3	2	no	—
240	C₂×C₄×C₅	—	3	2	no	—
241	C₂×C₄×C₅	—	4	2	no	—
242	C₂×C₄×C₅	—	4	2	no	—
243	C₂×C₄×C₅	—	6	2	no	—
244	C₂×C₄×C₅	—	6	2	no	—
245	C₂×C₄×C₅	—	6	2	no	—
246	C₂×C₄×C₅	—	12	2	no	—
247	C₂×C₄×C₅	#235	1	2	yes	—
248	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	#237	1	2	yes	—
250	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
251	C₅×C₈	—	2	2	no	—
252	C₅×C₈	—	6	2	no	—
253	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
254	C₂²×D₄	—	3	1	no	—
255	C₂²×C₈	—	3	1	no	—
256	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
257	#125	—	3	4	no	—
258	#125	—	6	2	no	—
259	#124	—	3	4	no	—
260	#124	—	6	2	no	—
261	C₂×C₄⋊C₄	—	3	1	no	—
262	C₂×C₄⋊C₄	—	6	1	no	—
263	C₂×C₄⋊C₄	—	6	1	no	—
264	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	6	1	no	—
266	C₂×C₂²⋊C₄	—	6	1	no	—
267	C₂×C₄²	—	3	1	no	—
268	#103	—	3	4	no	—
269	#103	C₂×C₅×D₃	1	4	yes	complemented
270	#102	—	3	4	no	—
271	#102	—	3	4	no	—
272	C₄×C₈	—	3	4	no	—
273	C₂×C₃×C₅	#488	1	4	yes	complemented
274	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
275	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
277	C₅×D₃	—	8	2	no	—
278	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
279	C₂²×D₃	—	2	2	no	—
280	C₂²×D₃	—	4	2	no	—
281	C₂²×D₃	—	4	2	no	—
282	C₂²×D₃	—	4	2	no	—
283	C₃×Q₈	—	2	2	no	—
284	C₃×Q₈	—	2	2	no	—
285	C₃×Q₈	—	4	2	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	4	2	no	—
289	C₂×C₃×C₄	—	4	2	no	—
290	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
291	C₂×C₃×C₄	C₅×#41	1	2	yes	—
292	C₂×C₃×C₄	C₅×#41	1	2	yes	—
293	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
294	C₂×Dic₃	—	2	2	no	—
295	C₂×Dic₃	—	2	2	no	—
296	C₂×Dic₃	—	2	2	no	—
297	C₂×Dic₃	—	4	2	no	—
298	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
299	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
300	D₁₂	—	2	2	no	—
301	D₁₂	—	2	2	no	—
302	D₁₂	—	4	2	no	—
303	C₃×C₈	—	2	2	no	—
304	C₃⋊C₈	—	2	2	no	—
305	C₂²×C₅	—	12	2	no	—
306	C₂²×C₅	—	12	2	no	—
307	C₂²×C₅	—	12	2	no	—
308	C₂²×C₅	—	24	4	no	—
309	C₂²×C₅	#885	1	2	yes	—
310	C₂²×C₅	#916	1	2	yes	—
311	C₂²×C₅	#919	1	2	yes	—
312	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
313	C₄×C₅	—	4	2	no	—
314	C₄×C₅	—	4	2	no	—
315	C₄×C₅	—	6	2	no	—
316	C₄×C₅	—	6	2	no	—
317	C₄×C₅	—	12	2	no	—
318	C₄×C₅	#885	1	2	yes	—
319	C₄×C₅	C₂×#235	1	1	yes	characteristic
320	C₄×C₅	C₂×#237	1	1	yes	characteristic
321	C₂⁴	—	6	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
326	C₂×D₄	—	3	2	no	—
327	C₂×D₄	—	6	2	no	—
328	C₂×D₄	—	6	1	no	—
329	C₂×D₄	—	6	2	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	3	1	no	—
333	C₂²×C₄	—	3	1	no	—
334	C₂²×C₄	—	6	1	no	—
335	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	3	2	no	—
338	C₂×C₈	—	6	2	no	—
339	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	3	2	no	—
342	C₄⋊C₄	—	6	4	no	—
343	C₄⋊C₄	—	6	4	no	—
344	C₄⋊C₄	—	6	1	no	—
345	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
346	C₂²⋊C₄	—	6	4	no	—
347	C₂²⋊C₄	—	6	4	no	—
348	C₄²	—	3	2	no	—
349	C₄²	—	3	2	no	—
350	C₃×C₅	C₂×#488	1	1	yes	characteristic, complemented, Hall
351	C₂²×C₃	C₅×#124	1	2	yes	—
352	C₂²×C₃	C₅×#135	1	2	yes	—
353	C₂²×C₃	C₅×#135	1	2	yes	—
354	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
355	C₂×D₃	—	4	2	no	—
356	C₂×D₃	—	4	2	no	—
357	C₂×D₃	—	4	2	no	—
358	C₂×D₃	—	8	4	no	—
359	C₃×C₄	—	4	2	no	—
360	C₃×C₄	—	4	2	no	—
361	C₃×C₄	C₅×#124	1	2	yes	—
362	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
363	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
364	Dic₃	—	2	2	no	—
365	Dic₃	—	2	2	no	—
366	Dic₃	—	4	2	no	—
367	C₂×C₅	—	24	2	no	—
368	C₂×C₅	#4800	1	4	yes	direct product factor
369	C₂×C₅	C₂×#885	1	1	yes	characteristic
370	C₂×C₅	C₂×#916	1	1	yes	characteristic
371	C₂×C₅	C₂×#919	1	1	yes	characteristic
372	C₂³	—	6	2	no	—
373	C₂³	—	12	2	no	—
374	C₂³	—	12	2	no	—
375	C₂³	—	12	2	no	—
376	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
377	Q₈	—	2	2	no	—
378	Q₈	—	2	2	no	—
379	Q₈	—	4	2	no	—
380	D₄	—	6	2	no	—
381	D₄	—	6	2	no	—
382	D₄	—	12	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	3	2	no	—
386	C₂×C₄	—	3	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	6	2	no	—
390	C₂×C₄	—	6	2	no	—
391	C₂×C₄	—	6	2	no	—
392	C₂×C₄	—	12	2	no	—
393	C₂×C₄	C₅×#235	1	2	yes	—
394	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
395	C₂×C₄	C₅×#237	1	2	yes	—
396	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
397	C₈	—	2	2	no	—
398	C₈	—	6	2	no	—
399	C₂×C₃	C₅×#488	1	4	yes	complemented
400	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
401	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
402	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
403	D₃	—	8	2	no	—
404	C₅	C₂×#4800	1	1	yes	characteristic, direct product factor, Sylow
405	C₂²	—	12	2	no	—
406	C₂²	—	12	2	no	—
407	C₂²	—	12	2	no	—
408	C₂²	—	24	4	no	—
409	C₂²	C₅×#885	1	2	yes	—
410	C₂²	C₅×#916	1	2	yes	—
411	C₂²	C₅×#919	1	2	yes	—
412	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	6	2	no	—
416	C₄	—	6	2	no	—
417	C₄	—	12	2	no	—
418	C₄	C₅×#885	1	2	yes	—
419	C₄	C₂×C₅×#235	1	1	yes	characteristic
420	C₄	C₂×C₅×#237	1	1	yes	characteristic
421	C₃	C₂×C₅×#488	1	1	yes	characteristic, complemented, Sylow
422	C₂	—	24	2	no	—
423	C₂	C₅×#4800	1	4	yes	direct product factor
424	C₂	C₂×C₅×#885	1	1	yes	characteristic
425	C₂	C₂×C₅×#916	1	1	yes	characteristic
426	C₂	C₂×C₅×#919	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×#488
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. C₂×C₅×#890	C₂	semidirect
3. C₂×C₃×C₅×#103	C₂	semidirect
4. C₂×C₅×#835	C₂	semidirect
6. C₂×C₅×C₈×Dic₃	C₂	semidirect
8. C₅×#4800	C₂	direct (N × H)
24. C₅×#890	C₂²	semidirect
25. C₃×C₅×#103	C₂²	semidirect
26. C₅×#835	C₂²	semidirect
28. C₅×C₈×Dic₃	C₂²	semidirect
30. C₂×#4800	C₅	direct (N × H)
35. C₂×C₅×#103	D₃	semidirect
69. C₂×#890	C₂×C₅	semidirect
70. C₂×C₃×#103	C₂×C₅	semidirect
71. C₂×#835	C₂×C₅	semidirect
73. C₂×C₈×Dic₃	C₂×C₅	semidirect
75. #4800	C₂×C₅	direct (N × H)
92. C₅×#103	C₂×D₃	semidirect
138. #890	C₂²×C₅	semidirect
139. C₃×#103	C₂²×C₅	semidirect
140. #835	C₂²×C₅	semidirect
142. C₈×Dic₃	C₂²×C₅	semidirect
177. C₂×#103	C₅×D₃	semidirect
269. #103	C₂×C₅×D₃	semidirect
273. C₂×C₃×C₅	#488	semidirect
350. C₃×C₅	C₂×#488	semidirect
368. C₂×C₅	#4800	direct (N × H)
399. C₂×C₃	C₅×#488	semidirect
404. C₅	C₂×#4800	direct (N × H)
421. C₃	C₂×C₅×#488	semidirect
423. C₂	C₅×#4800	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×#947	2
C₂×C₅×#890	2
C₂×C₃×C₅×#103	2
C₂×C₅×#835	2
C₂×C₅×#821	2
C₂×C₅×C₈×Dic₃	2
C₂×C₅×#809	2
C₅×#4800	2
C₂×C₅×#488	3
C₂×#4800	5

Subgroups — C2×C5×#4800 #14437728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4800 #14437728