Subgroups — C₂×C₅×#5009 #14429928

Order 1920.

896 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#870	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic
5	C₅×#5009	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#808	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#807	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#478	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	—	2	1	no	—
12	C₃×C₄×C₅×D₄	—	2	2	no	—
13	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
20	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
21	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₅×#870	—	2	2	no	—
24	C₅×#870	C₂²	1	4	yes	complemented
25	C₅×#832	C₂²	1	4	yes	—
26	C₅×#832	C₂²	1	4	yes	—
27	C₅×#808	C₂²	1	4	yes	complemented
28	C₅×#807	C₂²	1	4	yes	complemented
29	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
30	C₂×#5009	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#125	—	3	1	no	—
32	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic
33	C₅×#478	—	3	8	no	—
34	C₂×C₅×#107	—	3	1	no	—
35	C₂×C₅×#106	—	3	1	no	—
36	C₂×C₅×C₄⋊C₈	—	3	1	no	—
37	C₂×C₅×#102	—	3	1	no	—
38	C₂×C₅×#102	—	3	1	no	—
39	C₂⁴×C₃×C₅	—	2	1	no	—
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₃×C₅×D₄	—	2	2	no	—
42	C₂×C₃×C₅×D₄	Q₈	1	4	yes	—
43	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	—	2	1	no	—
45	C₂²×C₃×C₄×C₅	—	2	4	no	—
46	C₂²×C₃×C₄×C₅	—	4	4	no	—
47	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₅×Dic₃	—	2	1	no	—
51	C₂²×C₅×Dic₃	—	2	1	no	—
52	C₃×C₅×C₄⋊C₄	—	2	1	no	—
53	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
54	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
55	C₃×C₄²×C₅	D₄	1	2	yes	—
56	C₃×C₄²×C₅	C₂³	1	2	yes	—
57	C₅×C₄⋊Dic₃	—	2	1	no	—
58	C₅×C₄⋊Dic₃	—	2	1	no	—
59	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
60	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
61	C₅×Dic₃⋊C₄	—	2	4	no	—
62	C₅×Dic₃⋊C₄	—	2	4	no	—
63	C₂×C₅×C₃⋊C₈	—	2	2	no	—
64	C₂×C₅×C₃⋊C₈	—	2	2	no	—
65	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
66	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
67	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
68	C₂×#870	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂×#832	C₂×C₅	1	1	yes	characteristic
70	C₂×#832	C₂×C₅	1	1	yes	characteristic
71	#5009	C₂×C₅	1	8	yes	direct product factor
72	C₂×#808	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×#807	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
76	C₂³×C₄×C₅	—	2	1	no	—
77	C₂²×C₅×C₈	—	3	1	no	—
78	C₂²×C₅×C₈	—	3	1	no	—
79	C₅×#125	—	3	4	no	—
80	C₅×#125	—	6	2	no	—
81	C₄×C₅×D₄	—	2	2	no	—
82	C₄×C₅×D₄	C₂×D₃	1	4	yes	—
83	C₂×C₅×C₄⋊C₄	—	3	1	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	—	2	1	no	—
89	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
90	C₅×#107	—	3	4	no	—
91	C₅×#106	—	3	4	no	—
92	C₅×C₄⋊C₈	—	3	4	no	—
93	C₅×#102	—	3	4	no	—
94	C₅×#102	—	3	4	no	—
95	C₂×#478	—	3	1	no	Sylow
96	C₂³×C₃×C₅	—	2	4	no	—
97	C₂³×C₃×C₅	—	2	2	no	—
98	C₂³×C₃×C₅	—	4	2	no	—
99	C₂³×C₃×C₅	—	4	2	no	—
100	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
101	C₃×C₅×D₄	—	2	4	no	—
102	C₃×C₅×D₄	—	2	2	no	—
103	C₃×C₅×D₄	C₂×Q₈	1	4	yes	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	4	8	no	—
108	C₂×C₃×C₄×C₅	—	4	2	no	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
113	C₂×C₃×C₄×C₅	#41	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
115	C₂×C₅×Dic₃	—	2	2	no	—
116	C₂×C₅×Dic₃	—	2	2	no	—
117	C₂×C₅×Dic₃	—	4	2	no	—
118	C₂×C₅×Dic₃	—	4	2	no	—
119	C₅×C₃⋊C₈	—	2	2	no	—
120	C₅×C₃⋊C₈	—	2	2	no	—
121	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
122	C₂³×C₃×C₄	—	2	1	no	—
123	C₃×C₄×D₄	—	2	2	no	—
124	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
125	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
130	C₂×Dic₃⋊C₄	—	2	1	no	—
131	C₂×Dic₃⋊C₄	—	2	1	no	—
132	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
133	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
134	#870	—	2	2	no	—
135	#870	C₂²×C₅	1	4	yes	complemented
136	#832	C₂²×C₅	1	4	yes	—
137	#832	C₂²×C₅	1	4	yes	—
138	#808	C₂²×C₅	1	4	yes	complemented
139	#807	C₂²×C₅	1	4	yes	complemented
140	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	4	yes	complemented
141	C₂⁴×C₅	—	2	1	no	—
142	C₂×C₅×D₄	—	2	2	no	—
143	C₂×C₅×D₄	—	2	1	no	—
144	C₂×C₅×D₄	Dic₆	1	4	yes	—
145	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	—	2	4	no	—
148	C₂²×C₄×C₅	—	4	4	no	—
149	C₂²×C₄×C₅	—	6	1	no	—
150	C₂²×C₄×C₅	—	6	1	no	—
151	C₂²×C₄×C₅	#67	1	1	yes	characteristic
152	C₂²×C₄×C₅	#67	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
154	C₂×C₅×C₈	—	3	2	no	—
155	C₂×C₅×C₈	—	3	2	no	—
156	C₂×C₅×C₈	—	6	2	no	—
157	C₂×C₅×C₈	—	6	2	no	—
158	C₅×C₄⋊C₄	—	2	1	no	—
159	C₅×C₄⋊C₄	—	3	2	no	—
160	C₅×C₄⋊C₄	—	3	2	no	—
161	C₅×C₄⋊C₄	—	6	1	no	—
162	C₅×C₄⋊C₄	—	6	1	no	—
163	C₅×C₄⋊C₄	—	6	4	no	—
164	C₅×C₄⋊C₄	—	6	4	no	—
165	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
166	C₅×C₂²⋊C₄	—	2	4	no	—
167	C₄²×C₅	#67	1	2	yes	—
168	C₄²×C₅	C₂²×D₃	1	2	yes	—
169	C₂×#125	—	3	1	no	—
170	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic
171	#478	—	3	8	no	—
172	C₂×#107	—	3	1	no	—
173	C₂×#106	—	3	1	no	—
174	C₂×C₄⋊C₈	—	3	1	no	—
175	C₂×#102	—	3	1	no	—
176	C₂×#102	—	3	1	no	—
177	C₂²×C₃×C₅	—	2	4	no	—
178	C₂²×C₃×C₅	—	4	2	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	—	4	8	no	—
181	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
182	C₂²×C₃×C₅	#135	1	2	yes	—
183	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
184	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
185	C₃×C₄×C₅	—	2	2	no	—
186	C₃×C₄×C₅	—	2	2	no	—
187	C₃×C₄×C₅	—	4	2	no	—
188	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
189	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
190	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
191	C₅×Dic₃	—	4	2	no	—
192	C₅×Dic₃	—	4	2	no	—
193	C₂⁴×C₃	—	2	1	no	—
194	C₂×C₃×D₄	—	2	1	no	—
195	C₂×C₃×D₄	—	2	2	no	—
196	C₂×C₃×D₄	C₅×Q₈	1	4	yes	—
197	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
198	C₂²×C₃×C₄	—	2	1	no	—
199	C₂²×C₃×C₄	—	2	4	no	—
200	C₂²×C₃×C₄	—	4	4	no	—
201	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
202	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
203	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
204	C₂²×Dic₃	—	2	1	no	—
205	C₂²×Dic₃	—	2	1	no	—
206	C₃×C₄⋊C₄	—	2	1	no	—
207	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
208	C₃×C₂²⋊C₄	—	2	4	no	—
209	C₃×C₄²	C₅×D₄	1	2	yes	—
210	C₃×C₄²	C₂³×C₅	1	2	yes	—
211	C₄⋊Dic₃	—	2	1	no	—
212	C₄⋊Dic₃	—	2	1	no	—
213	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
214	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
215	Dic₃⋊C₄	—	2	4	no	—
216	Dic₃⋊C₄	—	2	4	no	—
217	C₂×C₃⋊C₈	—	2	2	no	—
218	C₂×C₃⋊C₈	—	2	2	no	—
219	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
220	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
221	C₂³×C₅	—	2	4	no	—
222	C₂³×C₅	—	2	2	no	—
223	C₂³×C₅	—	4	2	no	—
224	C₂³×C₅	—	4	2	no	—
225	C₂³×C₅	C₂×#67	1	1	yes	characteristic
226	C₅×D₄	—	2	4	no	—
227	C₅×D₄	—	2	2	no	—
228	C₅×D₄	C₂×Dic₆	1	4	yes	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	4	8	no	—
233	C₂×C₄×C₅	—	4	2	no	—
234	C₂×C₄×C₅	—	6	2	no	—
235	C₂×C₄×C₅	—	6	2	no	—
236	C₂×C₄×C₅	—	12	2	no	—
237	C₂×C₄×C₅	—	12	2	no	—
238	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
239	C₂×C₄×C₅	#235	1	2	yes	—
240	C₂×C₄×C₅	C₂×#67	1	2	yes	—
241	C₂×C₄×C₅	C₂×#67	1	2	yes	—
242	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
244	C₅×C₈	—	6	2	no	—
245	C₅×C₈	—	6	2	no	—
246	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
247	C₂³×C₄	—	2	1	no	—
248	C₂²×C₈	—	3	1	no	—
249	C₂²×C₈	—	3	1	no	—
250	#125	—	3	4	no	—
251	#125	—	6	2	no	—
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	C₂×C₅×D₃	1	4	yes	—
254	C₂×C₄⋊C₄	—	3	1	no	—
255	C₂×C₄⋊C₄	—	3	1	no	—
256	C₂×C₄⋊C₄	—	6	1	no	—
257	C₂×C₄⋊C₄	—	6	1	no	—
258	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
261	#107	—	3	4	no	—
262	#106	—	3	4	no	—
263	C₄⋊C₈	—	3	4	no	—
264	#102	—	3	4	no	—
265	#102	—	3	4	no	—
266	C₂×C₃×C₅	—	4	4	no	—
267	C₂×C₃×C₅	#478	1	4	yes	complemented
268	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
269	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
270	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
271	C₂³×C₃	—	2	4	no	—
272	C₂³×C₃	—	2	2	no	—
273	C₂³×C₃	—	4	2	no	—
274	C₂³×C₃	—	4	2	no	—
275	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
276	C₃×D₄	—	2	4	no	—
277	C₃×D₄	—	2	2	no	—
278	C₃×D₄	C₂×C₅×Q₈	1	4	yes	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	—	4	8	no	—
283	C₂×C₃×C₄	—	4	2	no	—
284	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
285	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
286	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
288	C₂×C₃×C₄	C₅×#41	1	2	yes	—
289	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
290	C₂×Dic₃	—	2	2	no	—
291	C₂×Dic₃	—	2	2	no	—
292	C₂×Dic₃	—	4	2	no	—
293	C₂×Dic₃	—	4	2	no	—
294	C₃⋊C₈	—	2	2	no	—
295	C₃⋊C₈	—	2	2	no	—
296	C₂²×C₅	—	2	4	no	—
297	C₂²×C₅	—	4	8	no	—
298	C₂²×C₅	—	4	2	no	—
299	C₂²×C₅	—	4	2	no	—
300	C₂²×C₅	#924	1	2	yes	—
301	C₂²×C₅	#932	1	2	yes	—
302	C₂²×C₅	#950	1	2	yes	—
303	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
304	C₄×C₅	—	2	2	no	—
305	C₄×C₅	—	2	2	no	—
306	C₄×C₅	—	4	2	no	—
307	C₄×C₅	—	12	2	no	—
308	C₄×C₅	—	12	2	no	—
309	C₄×C₅	#924	1	2	yes	—
310	C₄×C₅	C₂²×Dic₆	1	1	yes	characteristic
311	C₄×C₅	C₂×#235	1	1	yes	characteristic
312	C₂⁴	—	2	1	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	C₅×Dic₆	1	4	yes	—
316	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	—	6	1	no	—
321	C₂²×C₄	—	6	1	no	—
322	C₂²×C₄	C₅×#67	1	1	yes	characteristic
323	C₂²×C₄	C₅×#67	1	1	yes	characteristic
324	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
325	C₂×C₈	—	3	2	no	—
326	C₂×C₈	—	3	2	no	—
327	C₂×C₈	—	6	2	no	—
328	C₂×C₈	—	6	2	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	3	2	no	—
331	C₄⋊C₄	—	3	2	no	—
332	C₄⋊C₄	—	6	1	no	—
333	C₄⋊C₄	—	6	1	no	—
334	C₄⋊C₄	—	6	4	no	—
335	C₄⋊C₄	—	6	4	no	—
336	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₄²	C₅×#67	1	2	yes	—
339	C₄²	C₂²×C₅×D₃	1	2	yes	—
340	C₃×C₅	C₂×#478	1	1	yes	characteristic, complemented, Hall
341	C₂²×C₃	—	2	4	no	—
342	C₂²×C₃	—	4	8	no	—
343	C₂²×C₃	—	4	2	no	—
344	C₂²×C₃	—	4	2	no	—
345	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
346	C₂²×C₃	C₅×#135	1	2	yes	—
347	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
348	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
349	C₃×C₄	—	2	2	no	—
350	C₃×C₄	—	2	2	no	—
351	C₃×C₄	—	4	2	no	—
352	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
353	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
354	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
355	Dic₃	—	4	2	no	—
356	Dic₃	—	4	2	no	—
357	C₂×C₅	—	4	4	no	—
358	C₂×C₅	#5009	1	4	yes	direct product factor
359	C₂×C₅	C₂×#924	1	1	yes	characteristic
360	C₂×C₅	C₂×#932	1	1	yes	characteristic
361	C₂×C₅	C₂×#950	1	1	yes	characteristic
362	C₂³	—	2	4	no	—
363	C₂³	—	2	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	C₂×C₅×#67	1	1	yes	characteristic
367	D₄	—	2	4	no	—
368	D₄	—	2	2	no	—
369	D₄	C₂×C₅×Dic₆	1	4	yes	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	8	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	6	2	no	—
376	C₂×C₄	—	6	2	no	—
377	C₂×C₄	—	12	2	no	—
378	C₂×C₄	—	12	2	no	—
379	C₂×C₄	C₂×C₅×Dic₆	1	2	yes	—
380	C₂×C₄	C₅×#235	1	2	yes	—
381	C₂×C₄	C₂×C₅×#67	1	2	yes	—
382	C₂×C₄	C₂×C₅×#67	1	2	yes	—
383	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
384	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
385	C₈	—	6	2	no	—
386	C₈	—	6	2	no	—
387	C₂×C₃	—	4	4	no	—
388	C₂×C₃	C₅×#478	1	4	yes	complemented
389	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
390	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
391	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
392	C₅	C₂×#5009	1	1	yes	characteristic, direct product factor, Sylow
393	C₂²	—	2	4	no	—
394	C₂²	—	4	8	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	2	no	—
397	C₂²	C₅×#924	1	2	yes	—
398	C₂²	C₅×#932	1	2	yes	—
399	C₂²	C₅×#950	1	2	yes	—
400	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
401	C₄	—	2	2	no	—
402	C₄	—	2	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	12	2	no	—
405	C₄	—	12	2	no	—
406	C₄	C₅×#924	1	2	yes	—
407	C₄	C₂²×C₅×Dic₆	1	1	yes	characteristic
408	C₄	C₂×C₅×#235	1	1	yes	characteristic
409	C₃	C₂×C₅×#478	1	1	yes	characteristic, complemented, Sylow
410	C₂	—	4	4	no	—
411	C₂	C₅×#5009	1	4	yes	direct product factor
412	C₂	C₂×C₅×#924	1	1	yes	characteristic
413	C₂	C₂×C₅×#932	1	1	yes	characteristic
414	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×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₂×C₅×#478
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#870	C₂	semidirect
5. C₅×#5009	C₂	direct (N × H)
6. C₂×C₅×#808	C₂	semidirect
7. C₂×C₅×#807	C₂	semidirect
8. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
24. C₅×#870	C₂²	semidirect
27. C₅×#808	C₂²	semidirect
28. C₅×#807	C₂²	semidirect
29. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
30. C₂×#5009	C₅	direct (N × H)
68. C₂×#870	C₂×C₅	semidirect
71. #5009	C₂×C₅	direct (N × H)
72. C₂×#808	C₂×C₅	semidirect
73. C₂×#807	C₂×C₅	semidirect
74. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
135. #870	C₂²×C₅	semidirect
138. #808	C₂²×C₅	semidirect
139. #807	C₂²×C₅	semidirect
140. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
267. C₂×C₃×C₅	#478	semidirect
340. C₃×C₅	C₂×#478	semidirect
358. C₂×C₅	#5009	direct (N × H)
388. C₂×C₃	C₅×#478	semidirect
392. C₅	C₂×#5009	direct (N × H)
409. C₃	C₂×C₅×#478	semidirect
411. C₂	C₅×#5009	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×C₄×C₅×D₄	2
C₂×C₅×#870	2
C₂×C₅×#832	2
C₅×#5009	2
C₂×C₅×#808	2
C₂×C₅×#807	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₂×C₅×#478	3
C₂×#5009	5

Subgroups — C2×C5×#5009 #14429928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5009 #14429928