Subgroups — C₂×C₅×#5045 #14431599

Order 1920.

832 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×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#835	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#835	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#830	C₂	1	1	yes	maximal, characteristic
6	C₅×#5045	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#808	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#807	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#485	—	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	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
13	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
17	C₂×C₅×#217	—	2	1	no	—
18	C₅×#926	—	2	2	no	—
19	C₅×#926	C₂²	1	4	yes	—
20	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×Dic₃	—	2	1	no	—
23	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₅×#835	C₂²	1	4	yes	complemented
26	C₅×#835	C₂²	1	4	yes	complemented
27	C₅×#830	C₂²	1	4	yes	—
28	C₅×#808	C₂²	1	4	yes	complemented
29	C₅×#807	C₂²	1	4	yes	complemented
30	C₂×#5045	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×C₂²⋊Q₈	D₃	1	1	yes	characteristic
32	C₂×C₅×#117	—	3	1	no	—
33	C₅×#485	—	3	8	no	—
34	C₂×C₅×#107	—	3	1	no	—
35	C₂×C₅×#106	—	3	1	no	—
36	C₂×C₅×#103	—	3	1	no	—
37	C₂×C₅×#103	—	3	1	no	—
38	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
39	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
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	2	no	—
45	C₂²×C₃×C₄×C₅	—	2	2	no	—
46	C₂²×C₃×C₄×C₅	—	2	1	no	—
47	C₂²×C₃×C₄×C₅	—	2	1	no	—
48	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₅×Dic₃	—	2	1	no	—
53	C₂²×C₅×Dic₃	—	2	1	no	—
54	C₃×C₅×C₄⋊C₄	—	2	4	no	—
55	C₃×C₅×C₄⋊C₄	—	2	1	no	—
56	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
57	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
58	C₅×#217	—	2	4	no	—
59	C₅×C₄⋊Dic₃	—	2	1	no	—
60	C₅×C₄⋊Dic₃	—	2	1	no	—
61	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
62	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
63	C₄×C₅×Dic₃	—	2	4	no	—
64	C₂×C₅×C₃⋊C₈	—	2	2	no	—
65	C₂×C₅×C₃⋊C₈	—	2	2	no	—
66	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
67	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
68	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
69	C₂×#926	C₂×C₅	1	1	yes	characteristic
70	C₂×#835	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×#835	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×#830	C₂×C₅	1	1	yes	characteristic
73	#5045	C₂×C₅	1	8	yes	direct product factor
74	C₂×#808	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×#807	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
77	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
78	C₂²×C₅×C₈	—	3	1	no	—
79	C₂²×C₅×C₈	—	3	1	no	—
80	C₅×C₂²⋊Q₈	—	2	2	no	—
81	C₅×C₂²⋊Q₈	C₂×D₃	1	4	yes	—
82	C₅×#117	—	3	4	no	—
83	C₅×#117	—	6	2	no	—
84	C₂×C₅×C₄⋊C₄	—	2	1	no	—
85	C₂×C₅×C₄⋊C₄	—	3	1	no	—
86	C₂×C₅×C₄⋊C₄	—	3	1	no	—
87	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
88	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
90	C₂×C₄²×C₅	—	6	1	no	—
91	C₅×#107	—	3	4	no	—
92	C₅×#106	—	3	4	no	—
93	C₅×#103	—	3	4	no	—
94	C₅×#103	—	3	4	no	—
95	C₅×C₂²⋊C₈	—	3	4	no	—
96	C₂×#485	—	3	1	no	Sylow
97	C₂³×C₃×C₅	—	2	2	no	—
98	C₂³×C₃×C₅	—	2	2	no	—
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
101	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
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	4	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	4	2	no	—
112	C₂×C₃×C₄×C₅	—	4	2	no	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	#41	1	2	yes	—
116	C₂×C₃×C₄×C₅	#41	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₂×C₅×Dic₃	—	2	2	no	—
119	C₂×C₅×Dic₃	—	2	2	no	—
120	C₂×C₅×Dic₃	—	4	2	no	—
121	C₂×C₅×Dic₃	—	4	2	no	—
122	C₅×C₃⋊C₈	—	2	2	no	—
123	C₅×C₃⋊C₈	—	2	2	no	—
124	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
125	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
126	C₃×C₂²⋊Q₈	—	2	2	no	—
127	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
128	C₂×C₃×C₄⋊C₄	—	2	1	no	—
129	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
131	C₂×#217	—	2	1	no	—
132	#926	—	2	2	no	—
133	#926	C₂²×C₅	1	4	yes	—
134	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
136	C₂×C₄×Dic₃	—	2	1	no	—
137	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
138	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
139	#835	C₂²×C₅	1	4	yes	complemented
140	#835	C₂²×C₅	1	4	yes	complemented
141	#830	C₂²×C₅	1	4	yes	—
142	#808	C₂²×C₅	1	4	yes	complemented
143	#807	C₂²×C₅	1	4	yes	complemented
144	C₂⁴×C₅	#67	1	1	yes	characteristic
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	C₂²×C₄×C₅	—	2	2	no	—
150	C₂²×C₄×C₅	—	2	2	no	—
151	C₂²×C₄×C₅	—	2	1	no	—
152	C₂²×C₄×C₅	—	2	1	no	—
153	C₂²×C₄×C₅	—	6	1	no	—
154	C₂²×C₄×C₅	—	6	1	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	C₂×C₅×C₈	—	3	2	no	—
160	C₂×C₅×C₈	—	3	2	no	—
161	C₂×C₅×C₈	—	6	2	no	—
162	C₂×C₅×C₈	—	6	2	no	—
163	C₅×C₄⋊C₄	—	2	4	no	—
164	C₅×C₄⋊C₄	—	2	1	no	—
165	C₅×C₄⋊C₄	—	3	2	no	—
166	C₅×C₄⋊C₄	—	3	2	no	—
167	C₅×C₄⋊C₄	—	6	1	no	—
168	C₅×C₄⋊C₄	—	6	1	no	—
169	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
170	C₅×C₂²⋊C₄	—	2	4	no	—
171	C₅×C₂²⋊C₄	—	6	4	no	—
172	C₄²×C₅	—	6	4	no	—
173	C₂×C₂²⋊Q₈	C₅×D₃	1	1	yes	characteristic
174	C₂×#117	—	3	1	no	—
175	#485	—	3	8	no	—
176	C₂×#107	—	3	1	no	—
177	C₂×#106	—	3	1	no	—
178	C₂×#103	—	3	1	no	—
179	C₂×#103	—	3	1	no	—
180	C₂×C₂²⋊C₈	—	3	1	no	—
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	—	2	2	no	—
183	C₂²×C₃×C₅	—	2	2	no	—
184	C₂²×C₃×C₅	—	4	4	no	—
185	C₂²×C₃×C₅	#123	1	2	yes	—
186	C₂²×C₃×C₅	#135	1	2	yes	—
187	C₂²×C₃×C₅	#137	1	2	yes	—
188	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
189	C₃×C₄×C₅	—	2	2	no	—
190	C₃×C₄×C₅	—	4	2	no	—
191	C₃×C₄×C₅	—	4	2	no	—
192	C₃×C₄×C₅	#123	1	2	yes	—
193	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
194	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
195	C₅×Dic₃	—	4	2	no	—
196	C₅×Dic₃	—	4	2	no	—
197	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
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	2	no	—
203	C₂²×C₃×C₄	—	2	2	no	—
204	C₂²×C₃×C₄	—	2	1	no	—
205	C₂²×C₃×C₄	—	2	1	no	—
206	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
208	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
209	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
210	C₂²×Dic₃	—	2	1	no	—
211	C₂²×Dic₃	—	2	1	no	—
212	C₃×C₄⋊C₄	—	2	4	no	—
213	C₃×C₄⋊C₄	—	2	1	no	—
214	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
215	C₃×C₂²⋊C₄	—	2	4	no	—
216	#217	—	2	4	no	—
217	C₄⋊Dic₃	—	2	1	no	—
218	C₄⋊Dic₃	—	2	1	no	—
219	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
220	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
221	C₄×Dic₃	—	2	4	no	—
222	C₂×C₃⋊C₈	—	2	2	no	—
223	C₂×C₃⋊C₈	—	2	2	no	—
224	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
225	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
226	C₂³×C₅	—	2	2	no	—
227	C₂³×C₅	—	2	2	no	—
228	C₂³×C₅	—	2	2	no	—
229	C₂³×C₅	C₂×#67	1	2	yes	—
230	C₂³×C₅	C₂×#67	1	1	yes	characteristic
231	C₅×Q₈	—	2	2	no	—
232	C₅×Q₈	—	2	2	no	—
233	C₅×Q₈	—	4	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	4	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	4	2	no	—
241	C₂×C₄×C₅	—	4	2	no	—
242	C₂×C₄×C₅	—	6	2	no	—
243	C₂×C₄×C₅	—	6	2	no	—
244	C₂×C₄×C₅	—	12	2	no	—
245	C₂×C₄×C₅	—	12	2	no	—
246	C₂×C₄×C₅	#237	1	2	yes	—
247	C₂×C₄×C₅	#237	1	2	yes	—
248	C₂×C₄×C₅	C₂×#67	1	2	yes	—
249	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
251	C₅×C₈	—	6	2	no	—
252	C₅×C₈	—	6	2	no	—
253	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
254	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
255	C₂²×C₈	—	3	1	no	—
256	C₂²×C₈	—	3	1	no	—
257	C₂²⋊Q₈	—	2	2	no	—
258	C₂²⋊Q₈	C₂×C₅×D₃	1	4	yes	—
259	#117	—	3	4	no	—
260	#117	—	6	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	3	1	no	—
263	C₂×C₄⋊C₄	—	3	1	no	—
264	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₂²⋊C₄	—	6	1	no	—
267	C₂×C₄²	—	6	1	no	—
268	#107	—	3	4	no	—
269	#106	—	3	4	no	—
270	#103	—	3	4	no	—
271	#103	—	3	4	no	—
272	C₂²⋊C₈	—	3	4	no	—
273	C₂×C₃×C₅	—	4	2	no	—
274	C₂×C₃×C₅	#485	1	4	yes	complemented
275	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
277	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
278	C₂³×C₃	—	2	2	no	—
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	—	2	2	no	—
281	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
282	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
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	4	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	4	2	no	—
293	C₂×C₃×C₄	—	4	2	no	—
294	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
295	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
296	C₂×C₃×C₄	C₅×#41	1	2	yes	—
297	C₂×C₃×C₄	C₅×#41	1	2	yes	—
298	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
299	C₂×Dic₃	—	2	2	no	—
300	C₂×Dic₃	—	2	2	no	—
301	C₂×Dic₃	—	4	2	no	—
302	C₂×Dic₃	—	4	2	no	—
303	C₃⋊C₈	—	2	2	no	—
304	C₃⋊C₈	—	2	2	no	—
305	C₂²×C₅	—	2	2	no	—
306	C₂²×C₅	—	2	2	no	—
307	C₂²×C₅	—	2	2	no	—
308	C₂²×C₅	—	4	4	no	—
309	C₂²×C₅	#935	1	2	yes	—
310	C₂²×C₅	#942	1	2	yes	—
311	C₂²×C₅	#950	1	2	yes	—
312	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
313	C₄×C₅	—	2	2	no	—
314	C₄×C₅	—	4	2	no	—
315	C₄×C₅	—	4	2	no	—
316	C₄×C₅	—	12	2	no	—
317	C₄×C₅	—	12	2	no	—
318	C₄×C₅	#935	1	2	yes	—
319	C₄×C₅	C₂×#237	1	1	yes	characteristic
320	C₄×C₅	C₂×#237	1	1	yes	characteristic
321	C₂⁴	C₅×#67	1	1	yes	characteristic
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	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	6	1	no	—
331	C₂²×C₄	—	6	1	no	—
332	C₂²×C₄	C₅×#67	1	1	yes	characteristic
333	C₂²×C₄	C₅×#67	1	2	yes	—
334	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
335	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
336	C₂×C₈	—	3	2	no	—
337	C₂×C₈	—	3	2	no	—
338	C₂×C₈	—	6	2	no	—
339	C₂×C₈	—	6	2	no	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	3	2	no	—
343	C₄⋊C₄	—	3	2	no	—
344	C₄⋊C₄	—	6	1	no	—
345	C₄⋊C₄	—	6	1	no	—
346	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
347	C₂²⋊C₄	—	2	4	no	—
348	C₂²⋊C₄	—	6	4	no	—
349	C₄²	—	6	4	no	—
350	C₃×C₅	C₂×#485	1	1	yes	characteristic, complemented, Hall
351	C₂²×C₃	—	2	2	no	—
352	C₂²×C₃	—	2	2	no	—
353	C₂²×C₃	—	2	2	no	—
354	C₂²×C₃	—	4	4	no	—
355	C₂²×C₃	C₅×#123	1	2	yes	—
356	C₂²×C₃	C₅×#135	1	2	yes	—
357	C₂²×C₃	C₅×#137	1	2	yes	—
358	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
359	C₃×C₄	—	2	2	no	—
360	C₃×C₄	—	4	2	no	—
361	C₃×C₄	—	4	2	no	—
362	C₃×C₄	C₅×#123	1	2	yes	—
363	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
364	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
365	Dic₃	—	4	2	no	—
366	Dic₃	—	4	2	no	—
367	C₂×C₅	—	4	2	no	—
368	C₂×C₅	#5045	1	4	yes	direct product factor
369	C₂×C₅	C₂×#935	1	1	yes	characteristic
370	C₂×C₅	C₂×#942	1	1	yes	characteristic
371	C₂×C₅	C₂×#950	1	1	yes	characteristic
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	C₂×C₅×#67	1	2	yes	—
376	C₂³	C₂×C₅×#67	1	1	yes	characteristic
377	Q₈	—	2	2	no	—
378	Q₈	—	2	2	no	—
379	Q₈	—	4	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	6	2	no	—
389	C₂×C₄	—	6	2	no	—
390	C₂×C₄	—	12	2	no	—
391	C₂×C₄	—	12	2	no	—
392	C₂×C₄	C₅×#237	1	2	yes	—
393	C₂×C₄	C₅×#237	1	2	yes	—
394	C₂×C₄	C₂×C₅×#67	1	2	yes	—
395	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
396	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
397	C₈	—	6	2	no	—
398	C₈	—	6	2	no	—
399	C₂×C₃	—	4	2	no	—
400	C₂×C₃	C₅×#485	1	4	yes	complemented
401	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
402	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
403	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
404	C₅	C₂×#5045	1	1	yes	characteristic, direct product factor, Sylow
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	4	no	—
409	C₂²	C₅×#935	1	2	yes	—
410	C₂²	C₅×#942	1	2	yes	—
411	C₂²	C₅×#950	1	2	yes	—
412	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	12	2	no	—
417	C₄	—	12	2	no	—
418	C₄	C₅×#935	1	2	yes	—
419	C₄	C₂×C₅×#237	1	1	yes	characteristic
420	C₄	C₂×C₅×#237	1	1	yes	characteristic
421	C₃	C₂×C₅×#485	1	1	yes	characteristic, complemented, Sylow
422	C₂	—	4	2	no	—
423	C₂	C₅×#5045	1	4	yes	direct product factor
424	C₂	C₂×C₅×#935	1	1	yes	characteristic
425	C₂	C₂×C₅×#942	1	1	yes	characteristic
426	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	C₂⁴×C₃×C₅	D₄
hypercenter	C₂×C₅×C₂²⋊Q₈	D₃
hypocenter	C₃	C₂×C₅×#485
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
3. C₂×C₅×#835	C₂	semidirect
4. C₂×C₅×#835	C₂	semidirect
6. C₅×#5045	C₂	direct (N × H)
7. C₂×C₅×#808	C₂	semidirect
8. C₂×C₅×#807	C₂	semidirect
25. C₅×#835	C₂²	semidirect
26. C₅×#835	C₂²	semidirect
28. C₅×#808	C₂²	semidirect
29. C₅×#807	C₂²	semidirect
30. C₂×#5045	C₅	direct (N × H)
70. C₂×#835	C₂×C₅	semidirect
71. C₂×#835	C₂×C₅	semidirect
73. #5045	C₂×C₅	direct (N × H)
74. C₂×#808	C₂×C₅	semidirect
75. C₂×#807	C₂×C₅	semidirect
139. #835	C₂²×C₅	semidirect
140. #835	C₂²×C₅	semidirect
142. #808	C₂²×C₅	semidirect
143. #807	C₂²×C₅	semidirect
274. C₂×C₃×C₅	#485	semidirect
350. C₃×C₅	C₂×#485	semidirect
368. C₂×C₅	#5045	direct (N × H)
400. C₂×C₃	C₅×#485	semidirect
404. C₅	C₂×#5045	direct (N × H)
421. C₃	C₂×C₅×#485	semidirect
423. C₂	C₅×#5045	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×C₃×C₅×C₂²⋊Q₈	2
C₂×C₅×#926	2
C₂×C₅×#835	2
C₂×C₅×#830	2
C₅×#5045	2
C₂×C₅×#808	2
C₂×C₅×#807	2
C₂×C₅×#485	3
C₂×#5045	5

Subgroups — C2×C5×#5045 #14431599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5045 #14431599