Subgroups — C₂×C₅×#5040 #14423292

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×#214	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#830	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5040	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#810	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#448	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×D₄	—	2	1	no	—
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₅×Dic₃	—	2	1	no	—
12	C₂²×C₅×Dic₆	—	2	2	no	—
13	C₂²×C₅×Dic₆	—	2	1	no	—
14	C₂²×C₅×Dic₆	—	2	8	no	—
15	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
16	C₂²×C₅×Dic₆	C₂²	1	4	yes	complemented
17	C₃×C₅×#121	—	2	2	no	—
18	C₃×C₅×#121	C₂²	1	4	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
21	C₂×C₅×#214	—	2	8	no	—
22	C₂×C₅×#214	C₂²	1	8	yes	complemented
23	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
24	C₅×#830	C₂²	1	4	yes	complemented
25	C₅×#810	C₂²	1	8	yes	complemented
26	C₂×#5040	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂³×C₅×Q₈	—	3	1	no	—
28	C₂²×C₅×SD₁₆	—	3	2	no	—
29	C₂×C₅×#121	D₃	1	1	yes	characteristic
30	C₅×#448	—	3	8	no	—
31	C₂×C₅×#103	—	3	2	no	—
32	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
33	C₂⁴×C₃×C₅	—	2	1	no	—
34	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
35	C₂×C₃×C₅×D₄	—	2	4	no	—
36	C₂×C₃×C₅×D₄	—	2	4	no	—
37	C₂×C₃×C₅×D₄	—	2	1	no	—
38	C₂×C₃×C₅×D₄	—	4	4	no	—
39	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	—	2	4	no	—
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₅×Dic₃	—	2	8	no	—
47	C₂²×C₅×Dic₃	—	2	2	no	—
48	C₂²×C₅×Dic₃	—	2	4	no	—
49	C₂×C₅×Dic₆	—	2	8	no	—
50	C₂×C₅×Dic₆	—	2	16	no	—
51	C₂×C₅×Dic₆	—	2	2	no	—
52	C₂×C₅×Dic₆	—	2	4	no	—
53	C₂×C₅×Dic₆	—	2	4	no	—
54	C₂×C₅×Dic₆	—	2	16	no	—
55	C₂×C₅×Dic₆	D₄	1	8	yes	complemented
56	C₂×C₅×Dic₆	C₂³	1	4	yes	—
57	C₃×C₅×C₄⋊C₄	—	2	1	no	—
58	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
60	C₅×#214	—	2	16	no	—
61	C₂×C₅×C₃⋊C₈	—	2	4	no	—
62	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
63	C₂³×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
64	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic
65	C₂²×#214	C₂×C₅	1	2	yes	complemented
66	C₂×#830	C₂×C₅	1	1	yes	characteristic, complemented
67	#5040	C₂×C₅	1	8	yes	direct product factor
68	C₂×#810	C₂×C₅	1	2	yes	complemented
69	C₂²×C₅×Q₈	—	3	2	no	—
70	C₂²×C₅×Q₈	—	3	4	no	—
71	C₂²×C₅×Q₈	—	6	8	no	—
72	C₂²×C₅×Q₈	—	6	2	no	—
73	C₂²×C₅×Q₈	—	6	1	no	—
74	C₂²×C₅×D₄	—	2	1	no	—
75	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
76	C₂³×C₄×C₅	—	6	1	no	—
77	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
78	C₂×C₅×SD₁₆	—	3	8	no	—
79	C₂×C₅×SD₁₆	—	6	8	no	—
80	C₂²×C₅×C₈	—	3	2	no	—
81	C₅×#121	—	2	2	no	—
82	C₅×#121	C₂×D₃	1	4	yes	—
83	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
84	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
85	C₅×#103	—	3	8	no	—
86	C₅×C₂²⋊C₈	—	3	4	no	—
87	C₂×#448	—	3	1	no	Sylow
88	C₂³×C₃×C₅	—	2	2	no	—
89	C₂³×C₃×C₅	—	2	2	no	—
90	C₂³×C₃×C₅	—	2	2	no	—
91	C₂³×C₃×C₅	—	4	2	no	—
92	C₂³×C₃×C₅	—	4	2	no	—
93	C₂³×C₃×C₅	—	4	2	no	—
94	C₂³×C₃×C₅	SD₁₆	1	4	yes	complemented
95	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
96	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
97	C₃×C₅×D₄	—	2	4	no	—
98	C₃×C₅×D₄	—	4	8	no	—
99	C₃×C₅×D₄	—	4	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	4	no	—
102	C₂×C₃×C₄×C₅	—	2	4	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	4	2	no	—
105	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
108	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
109	C₂×C₅×Dic₃	—	2	16	no	—
110	C₂×C₅×Dic₃	—	2	8	no	—
111	C₂×C₅×Dic₃	—	2	4	no	—
112	C₅×Dic₆	—	2	16	no	—
113	C₅×Dic₆	—	2	8	no	—
114	C₅×Dic₆	—	2	4	no	—
115	C₅×Dic₆	C₂×D₄	1	8	yes	complemented
116	C₅×C₃⋊C₈	—	2	4	no	—
117	C₂²×C₃×D₄	—	2	1	no	—
118	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
119	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
120	C₂³×Dic₃	—	2	1	no	—
121	C₂²×Dic₆	—	2	2	no	—
122	C₂²×Dic₆	—	2	1	no	—
123	C₂²×Dic₆	—	2	8	no	—
124	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
125	C₂²×Dic₆	C₂²×C₅	1	4	yes	complemented
126	C₃×#121	—	2	2	no	—
127	C₃×#121	C₂²×C₅	1	4	yes	—
128	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
130	C₂×#214	—	2	8	no	—
131	C₂×#214	C₂²×C₅	1	8	yes	complemented
132	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
133	#830	C₂²×C₅	1	4	yes	complemented
134	#810	C₂²×C₅	1	8	yes	complemented
135	C₂⁴×C₅	—	2	1	no	—
136	C₂⁴×C₅	#67	1	1	yes	characteristic
137	C₂×C₅×Q₈	—	3	8	no	—
138	C₂×C₅×Q₈	—	3	4	no	—
139	C₂×C₅×Q₈	—	6	16	no	—
140	C₂×C₅×Q₈	—	6	8	no	—
141	C₂×C₅×Q₈	—	6	16	no	—
142	C₂×C₅×Q₈	—	6	4	no	—
143	C₂×C₅×Q₈	—	6	4	no	—
144	C₂×C₅×Q₈	—	6	2	no	—
145	C₂×C₅×D₄	—	2	4	no	—
146	C₂×C₅×D₄	—	2	4	no	—
147	C₂×C₅×D₄	—	2	1	no	—
148	C₂×C₅×D₄	—	4	4	no	—
149	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
150	C₂²×C₄×C₅	—	2	4	no	—
151	C₂²×C₄×C₅	—	2	1	no	—
152	C₂²×C₄×C₅	—	6	8	no	—
153	C₂²×C₄×C₅	—	6	4	no	—
154	C₂²×C₄×C₅	—	6	2	no	—
155	C₂²×C₄×C₅	#67	1	2	yes	—
156	C₂²×C₄×C₅	#67	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
158	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
159	C₅×SD₁₆	—	6	16	no	—
160	C₂×C₅×C₈	—	3	4	no	—
161	C₂×C₅×C₈	—	6	4	no	—
162	C₅×C₄⋊C₄	—	2	1	no	—
163	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
164	C₅×C₂²⋊C₄	—	2	4	no	—
165	C₂³×Q₈	—	3	1	no	—
166	C₂²×SD₁₆	—	3	2	no	—
167	C₂×#121	C₅×D₃	1	1	yes	characteristic
168	#448	—	3	8	no	—
169	C₂×#103	—	3	2	no	—
170	C₂×C₂²⋊C₈	—	3	1	no	—
171	C₂²×C₃×C₅	—	2	2	no	—
172	C₂²×C₃×C₅	—	2	2	no	—
173	C₂²×C₃×C₅	—	2	8	no	—
174	C₂²×C₃×C₅	—	4	2	no	—
175	C₂²×C₃×C₅	—	4	2	no	—
176	C₂²×C₃×C₅	—	4	2	no	—
177	C₂²×C₃×C₅	—	8	4	no	—
178	C₂²×C₃×C₅	#120	1	2	yes	—
179	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
180	C₂²×C₃×C₅	C₂×SD₁₆	1	4	yes	complemented
181	C₂²×C₃×C₅	#137	1	2	yes	—
182	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
183	C₃×C₄×C₅	—	2	2	no	—
184	C₃×C₄×C₅	—	4	2	no	—
185	C₃×C₄×C₅	#120	1	2	yes	—
186	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
187	C₅×Dic₃	—	2	8	no	—
188	C₂⁴×C₃	—	2	1	no	—
189	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
190	C₂×C₃×D₄	—	2	4	no	—
191	C₂×C₃×D₄	—	2	4	no	—
192	C₂×C₃×D₄	—	2	1	no	—
193	C₂×C₃×D₄	—	4	4	no	—
194	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
195	C₂²×C₃×C₄	—	2	4	no	—
196	C₂²×C₃×C₄	—	2	1	no	—
197	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
198	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
199	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
200	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
201	C₂²×Dic₃	—	2	8	no	—
202	C₂²×Dic₃	—	2	2	no	—
203	C₂²×Dic₃	—	2	4	no	—
204	C₂×Dic₆	—	2	8	no	—
205	C₂×Dic₆	—	2	16	no	—
206	C₂×Dic₆	—	2	4	no	—
207	C₂×Dic₆	—	2	2	no	—
208	C₂×Dic₆	—	2	4	no	—
209	C₂×Dic₆	—	2	16	no	—
210	C₂×Dic₆	C₅×D₄	1	8	yes	complemented
211	C₂×Dic₆	C₂³×C₅	1	4	yes	—
212	C₃×C₄⋊C₄	—	2	1	no	—
213	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
214	C₃×C₂²⋊C₄	—	2	4	no	—
215	#214	—	2	16	no	—
216	C₂×C₃⋊C₈	—	2	4	no	—
217	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
218	C₂³×C₅	—	2	2	no	—
219	C₂³×C₅	—	2	2	no	—
220	C₂³×C₅	—	2	2	no	—
221	C₂³×C₅	—	4	2	no	—
222	C₂³×C₅	—	4	2	no	—
223	C₂³×C₅	—	4	2	no	—
224	C₂³×C₅	#214	1	4	yes	complemented
225	C₂³×C₅	C₂×#67	1	2	yes	—
226	C₂³×C₅	C₂×#67	1	1	yes	characteristic
227	C₅×Q₈	—	3	8	no	—
228	C₅×Q₈	—	6	16	no	—
229	C₅×Q₈	—	6	8	no	—
230	C₅×Q₈	—	6	4	no	—
231	C₅×D₄	—	2	4	no	—
232	C₅×D₄	—	4	8	no	—
233	C₅×D₄	—	4	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	4	no	—
236	C₂×C₄×C₅	—	2	4	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	4	2	no	—
239	C₂×C₄×C₅	—	6	16	no	—
240	C₂×C₄×C₅	—	6	8	no	—
241	C₂×C₄×C₅	—	6	4	no	—
242	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
243	C₂×C₄×C₅	C₂×#67	1	2	yes	—
244	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
246	C₅×C₈	—	6	4	no	—
247	C₂²×Q₈	—	3	2	no	—
248	C₂²×Q₈	—	3	4	no	—
249	C₂²×Q₈	—	6	8	no	—
250	C₂²×Q₈	—	6	1	no	—
251	C₂²×Q₈	—	6	2	no	—
252	C₂²×D₄	—	2	1	no	—
253	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
254	C₂³×C₄	—	6	1	no	—
255	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
256	C₂×SD₁₆	—	3	8	no	—
257	C₂×SD₁₆	—	6	8	no	—
258	C₂²×C₈	—	3	2	no	—
259	#121	—	2	2	no	—
260	#121	C₂×C₅×D₃	1	4	yes	—
261	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	#103	—	3	8	no	—
264	C₂²⋊C₈	—	3	4	no	—
265	C₂×C₃×C₅	—	2	4	no	—
266	C₂×C₃×C₅	—	8	2	no	—
267	C₂×C₃×C₅	#448	1	4	yes	complemented
268	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
269	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
270	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
271	C₂³×C₃	—	2	2	no	—
272	C₂³×C₃	—	2	2	no	—
273	C₂³×C₃	—	2	2	no	—
274	C₂³×C₃	—	4	2	no	—
275	C₂³×C₃	—	4	2	no	—
276	C₂³×C₃	—	4	2	no	—
277	C₂³×C₃	C₅×SD₁₆	1	4	yes	complemented
278	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
279	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
280	C₃×D₄	—	2	4	no	—
281	C₃×D₄	—	4	8	no	—
282	C₃×D₄	—	4	2	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	4	no	—
285	C₂×C₃×C₄	—	2	4	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	4	2	no	—
288	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
289	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
290	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
291	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
292	C₂×Dic₃	—	2	16	no	—
293	C₂×Dic₃	—	2	8	no	—
294	C₂×Dic₃	—	2	4	no	—
295	Dic₆	—	2	16	no	—
296	Dic₆	—	2	8	no	—
297	Dic₆	—	2	4	no	—
298	Dic₆	C₂×C₅×D₄	1	8	yes	complemented
299	C₃⋊C₈	—	2	4	no	—
300	C₂²×C₅	—	2	2	no	—
301	C₂²×C₅	—	2	8	no	—
302	C₂²×C₅	—	2	2	no	—
303	C₂²×C₅	—	4	2	no	—
304	C₂²×C₅	—	4	2	no	—
305	C₂²×C₅	—	4	2	no	—
306	C₂²×C₅	—	8	4	no	—
307	C₂²×C₅	C₂×#214	1	2	yes	—
308	C₂²×C₅	C₂×#214	1	4	yes	complemented
309	C₂²×C₅	#937	1	2	yes	—
310	C₂²×C₅	#951	1	2	yes	—
311	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
312	C₄×C₅	—	2	2	no	—
313	C₄×C₅	—	4	2	no	—
314	C₄×C₅	—	6	8	no	—
315	C₄×C₅	#937	1	2	yes	—
316	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
317	C₂⁴	—	2	1	no	—
318	C₂⁴	C₅×#67	1	1	yes	characteristic
319	C₂×Q₈	—	3	8	no	—
320	C₂×Q₈	—	3	4	no	—
321	C₂×Q₈	—	6	16	no	—
322	C₂×Q₈	—	6	8	no	—
323	C₂×Q₈	—	6	16	no	—
324	C₂×Q₈	—	6	4	no	—
325	C₂×Q₈	—	6	4	no	—
326	C₂×Q₈	—	6	2	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	4	4	no	—
331	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	6	8	no	—
335	C₂²×C₄	—	6	4	no	—
336	C₂²×C₄	—	6	2	no	—
337	C₂²×C₄	C₅×#67	1	1	yes	characteristic
338	C₂²×C₄	C₅×#67	1	2	yes	—
339	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
340	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
341	SD₁₆	—	6	16	no	—
342	C₂×C₈	—	3	4	no	—
343	C₂×C₈	—	6	4	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
346	C₂²⋊C₄	—	2	4	no	—
347	C₃×C₅	C₂×#448	1	1	yes	characteristic, complemented, Hall
348	C₂²×C₃	—	2	8	no	—
349	C₂²×C₃	—	2	2	no	—
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	—	4	2	no	—
352	C₂²×C₃	—	4	2	no	—
353	C₂²×C₃	—	4	2	no	—
354	C₂²×C₃	—	8	4	no	—
355	C₂²×C₃	C₅×#120	1	2	yes	—
356	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
357	C₂²×C₃	C₂×C₅×SD₁₆	1	4	yes	complemented
358	C₂²×C₃	C₅×#137	1	2	yes	—
359	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	4	2	no	—
362	C₃×C₄	C₅×#120	1	2	yes	—
363	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
364	Dic₃	—	2	8	no	—
365	C₂×C₅	—	2	4	no	—
366	C₂×C₅	—	8	2	no	—
367	C₂×C₅	#5040	1	4	yes	direct product factor
368	C₂×C₅	C₂²×#214	1	1	yes	characteristic
369	C₂×C₅	C₂×#937	1	1	yes	characteristic
370	C₂×C₅	C₂×#951	1	1	yes	characteristic
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	C₅×#214	1	4	yes	complemented
378	C₂³	C₂×C₅×#67	1	2	yes	—
379	C₂³	C₂×C₅×#67	1	1	yes	characteristic
380	Q₈	—	3	8	no	—
381	Q₈	—	6	16	no	—
382	Q₈	—	6	8	no	—
383	Q₈	—	6	4	no	—
384	D₄	—	2	4	no	—
385	D₄	—	4	8	no	—
386	D₄	—	4	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	6	16	no	—
393	C₂×C₄	—	6	8	no	—
394	C₂×C₄	—	6	4	no	—
395	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
396	C₂×C₄	C₂×C₅×#67	1	2	yes	—
397	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
398	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
399	C₈	—	6	4	no	—
400	C₂×C₃	—	2	4	no	—
401	C₂×C₃	—	8	2	no	—
402	C₂×C₃	C₅×#448	1	4	yes	complemented
403	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
404	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
405	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
406	C₅	C₂×#5040	1	1	yes	characteristic, direct product factor, Sylow
407	C₂²	—	2	8	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	8	4	no	—
414	C₂²	C₂×C₅×#214	1	2	yes	—
415	C₂²	C₂×C₅×#214	1	4	yes	complemented
416	C₂²	C₅×#937	1	2	yes	—
417	C₂²	C₅×#951	1	2	yes	—
418	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
419	C₄	—	2	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	6	8	no	—
422	C₄	C₅×#937	1	2	yes	—
423	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
424	C₃	C₂×C₅×#448	1	1	yes	characteristic, complemented, Sylow
425	C₂	—	2	4	no	—
426	C₂	—	8	2	no	—
427	C₂	C₅×#5040	1	4	yes	direct product factor
428	C₂	C₂²×C₅×#214	1	1	yes	characteristic
429	C₂	C₂×C₅×#937	1	1	yes	characteristic
430	C₂	C₂×C₅×#951	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, prime radical	C₂×C₃×C₅×#121	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₅×#121	D₃
hypocenter	C₃	C₂×C₅×#448
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂×C₅×#121

Complements

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

N	H ≅ G/N	type
1. C₂³×C₅×Dic₆	C₂	semidirect
3. C₂²×C₅×#214	C₂	semidirect
4. C₂×C₅×#830	C₂	semidirect
5. C₅×#5040	C₂	direct (N × H)
6. C₂×C₅×#810	C₂	semidirect
16. C₂²×C₅×Dic₆	C₂²	semidirect
22. C₂×C₅×#214	C₂²	semidirect
24. C₅×#830	C₂²	semidirect
25. C₅×#810	C₂²	semidirect
26. C₂×#5040	C₅	direct (N × H)
55. C₂×C₅×Dic₆	D₄	semidirect
63. C₂³×Dic₆	C₂×C₅	semidirect
65. C₂²×#214	C₂×C₅	semidirect
66. C₂×#830	C₂×C₅	semidirect
67. #5040	C₂×C₅	direct (N × H)
68. C₂×#810	C₂×C₅	semidirect
94. C₂³×C₃×C₅	SD₁₆	semidirect
115. C₅×Dic₆	C₂×D₄	semidirect
125. C₂²×Dic₆	C₂²×C₅	semidirect
131. C₂×#214	C₂²×C₅	semidirect
133. #830	C₂²×C₅	semidirect
134. #810	C₂²×C₅	semidirect
180. C₂²×C₃×C₅	C₂×SD₁₆	semidirect
210. C₂×Dic₆	C₅×D₄	semidirect
224. C₂³×C₅	#214	semidirect
267. C₂×C₃×C₅	#448	semidirect
277. C₂³×C₃	C₅×SD₁₆	semidirect
298. Dic₆	C₂×C₅×D₄	semidirect
308. C₂²×C₅	C₂×#214	semidirect
347. C₃×C₅	C₂×#448	semidirect
357. C₂²×C₃	C₂×C₅×SD₁₆	semidirect
367. C₂×C₅	#5040	direct (N × H)
377. C₂³	C₅×#214	semidirect
402. C₂×C₃	C₅×#448	semidirect
406. C₅	C₂×#5040	direct (N × H)
415. C₂²	C₂×C₅×#214	semidirect
424. C₃	C₂×C₅×#448	semidirect
427. C₂	C₅×#5040	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₅×Dic₆	2
C₂×C₃×C₅×#121	2
C₂²×C₅×#214	2
C₂×C₅×#830	2
C₅×#5040	2
C₂×C₅×#810	2
C₂×C₅×#448	3
C₂×#5040	5

Subgroups — C2×C5×#5040 #14423292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5040 #14423292