Subgroups — C₂×C₅×#4885 #14431530

Order 1920.

936 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#895	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#821	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#808	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4885	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₅×#482	—	3	1	no	maximal, Hall
10	C₂²×C₅×D₁₂	—	2	1	no	—
11	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
17	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×Dic₃	—	2	1	no	—
20	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₅×#895	—	2	2	no	—
22	C₅×#895	C₂²	1	4	yes	—
23	C₅×#892	—	2	2	no	—
24	C₅×#892	C₂²	1	4	yes	complemented
25	C₃×C₅×#107	C₂²	1	4	yes	complemented
26	C₅×#821	C₂²	1	4	yes	complemented
27	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	complemented
28	C₅×#809	C₂²	1	4	yes	complemented
29	C₅×#808	C₂²	1	4	yes	complemented
30	C₂×#4885	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#121	—	3	1	no	—
32	C₂×C₅×#117	—	3	1	no	—
33	C₅×#482	—	3	8	no	—
34	C₂×C₅×#107	D₃	1	1	yes	characteristic, complemented
35	C₂×C₅×#106	—	3	1	no	—
36	C₂×C₅×#102	—	3	1	no	—
37	C₂×C₅×#102	—	3	1	no	—
38	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
39	C₂³×C₅×D₃	—	2	1	no	—
40	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₅×Dic₃	—	2	1	no	—
45	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
46	C₂×C₅×D₁₂	—	2	2	no	—
47	C₂×C₅×D₁₂	—	2	2	no	—
48	C₂×C₅×D₁₂	—	2	4	no	—
49	C₂×C₅×D₁₂	—	2	1	no	—
50	C₂×C₅×D₁₂	—	4	4	no	—
51	C₂×C₅×D₁₂	C₂³	1	2	yes	—
52	C₂×C₄×C₅×D₃	—	2	2	no	—
53	C₂×C₄×C₅×D₃	—	2	2	no	—
54	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
55	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
56	C₂×C₃×C₅×C₈	—	2	2	no	—
57	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	—	2	1	no	—
59	C₃×C₅×C₄⋊C₄	—	2	1	no	—
60	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
62	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
63	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
64	C₅×C₄⋊Dic₃	—	2	1	no	—
65	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
66	C₄×C₅×Dic₃	—	2	4	no	—
67	C₂×C₅×C₃⋊C₈	—	2	2	no	—
68	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
69	C₂×#895	C₂×C₅	1	1	yes	characteristic
70	C₂×#892	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×#821	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×#809	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×#808	C₂×C₅	1	1	yes	characteristic, complemented
76	#4885	C₂×C₅	1	8	yes	direct product factor
77	C₂²×C₅×D₄	—	3	1	no	—
78	C₂²×C₅×D₄	—	6	1	no	—
79	C₂³×C₄×C₅	—	3	1	no	—
80	C₂²×C₅×C₈	—	3	1	no	—
81	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
82	C₅×#121	—	3	4	no	—
83	C₅×#121	—	6	2	no	—
84	C₅×#117	—	3	4	no	—
85	C₅×#117	—	6	2	no	—
86	C₂×C₅×C₄⋊C₄	—	3	1	no	—
87	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
89	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
90	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
91	C₂×C₄²×C₅	—	6	1	no	—
92	C₅×#107	C₂×D₃	1	4	yes	complemented
93	C₅×#106	—	3	4	no	—
94	C₅×#102	—	3	4	no	—
95	C₅×#102	—	3	4	no	—
96	C₅×C₂²⋊C₈	—	3	4	no	—
97	C₂×#482	—	3	1	no	Sylow
98	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₅×D₃	—	2	2	no	—
100	C₂²×C₅×D₃	—	2	2	no	—
101	C₂²×C₅×D₃	—	2	2	no	—
102	C₂²×C₅×D₃	—	2	2	no	—
103	C₂²×C₅×D₃	—	4	2	no	—
104	C₂²×C₅×D₃	—	4	2	no	—
105	C₂²×C₅×D₃	—	4	2	no	—
106	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	4	2	no	—
110	C₂×C₃×C₄×C₅	—	4	2	no	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	#41	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	C₂×D₄	1	2	yes	—
119	C₅×D₁₂	—	2	2	no	—
120	C₅×D₁₂	—	2	2	no	—
121	C₅×D₁₂	—	4	8	no	—
122	C₅×D₁₂	—	4	2	no	—
123	C₄×C₅×D₃	—	2	4	no	—
124	C₄×C₅×D₃	—	2	2	no	—
125	C₄×C₅×D₃	—	2	2	no	—
126	C₃×C₅×C₈	—	2	2	no	—
127	C₅×C₃⋊C₈	—	2	2	no	—
128	C₂²×D₁₂	—	2	1	no	—
129	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
130	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
131	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
132	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
134	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
135	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
136	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
137	C₂×C₄×Dic₃	—	2	1	no	—
138	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
139	#895	—	2	2	no	—
140	#895	C₂²×C₅	1	4	yes	—
141	#892	—	2	2	no	—
142	#892	C₂²×C₅	1	4	yes	complemented
143	C₃×#107	C₂²×C₅	1	4	yes	complemented
144	#821	C₂²×C₅	1	4	yes	complemented
145	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	complemented
146	#809	C₂²×C₅	1	4	yes	complemented
147	#808	C₂²×C₅	1	4	yes	complemented
148	C₂⁴×C₅	—	3	1	no	—
149	C₂⁴×C₅	—	6	1	no	—
150	C₂×C₅×D₄	—	3	2	no	—
151	C₂×C₅×D₄	—	6	4	no	—
152	C₂×C₅×D₄	—	6	2	no	—
153	C₂×C₅×D₄	—	6	1	no	—
154	C₂×C₅×D₄	—	6	2	no	—
155	C₂×C₅×D₄	—	12	4	no	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	—	2	1	no	—
158	C₂²×C₄×C₅	—	3	1	no	—
159	C₂²×C₄×C₅	—	3	2	no	—
160	C₂²×C₄×C₅	—	3	2	no	—
161	C₂²×C₄×C₅	—	6	2	no	—
162	C₂²×C₄×C₅	—	6	2	no	—
163	C₂²×C₄×C₅	—	6	1	no	—
164	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
165	C₂×C₅×C₈	—	2	2	no	—
166	C₂×C₅×C₈	—	3	2	no	—
167	C₂×C₅×C₈	—	6	2	no	—
168	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
169	C₅×C₄⋊C₄	—	2	1	no	—
170	C₅×C₄⋊C₄	—	2	1	no	—
171	C₅×C₄⋊C₄	—	3	2	no	—
172	C₅×C₄⋊C₄	—	6	1	no	—
173	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
174	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
175	C₅×C₂²⋊C₄	—	6	4	no	—
176	C₅×C₂²⋊C₄	—	6	4	no	—
177	C₄²×C₅	—	6	4	no	—
178	C₂×#121	—	3	1	no	—
179	C₂×#117	—	3	1	no	—
180	#482	—	3	8	no	—
181	C₂×#107	C₅×D₃	1	1	yes	characteristic, complemented
182	C₂×#106	—	3	1	no	—
183	C₂×#102	—	3	1	no	—
184	C₂×#102	—	3	1	no	—
185	C₂×C₂²⋊C₈	—	3	1	no	—
186	C₂²×C₃×C₅	#123	1	2	yes	—
187	C₂²×C₃×C₅	#135	1	2	yes	—
188	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
189	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₅×D₃	—	2	2	no	—
191	C₂×C₅×D₃	—	2	2	no	—
192	C₂×C₅×D₃	—	2	2	no	—
193	C₂×C₅×D₃	—	4	4	no	—
194	C₂×C₅×D₃	—	4	2	no	—
195	C₂×C₅×D₃	—	4	2	no	—
196	C₂×C₅×D₃	—	4	2	no	—
197	C₂×C₅×D₃	—	8	4	no	—
198	C₃×C₄×C₅	—	4	2	no	—
199	C₃×C₄×C₅	—	4	2	no	—
200	C₃×C₄×C₅	#123	1	2	yes	—
201	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
202	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
203	C₅×Dic₃	—	2	2	no	—
204	C₅×Dic₃	—	4	2	no	—
205	C₂³×D₃	—	2	1	no	—
206	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
207	C₂²×C₃×C₄	—	2	1	no	—
208	C₂²×C₃×C₄	—	2	1	no	—
209	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
210	C₂²×Dic₃	—	2	1	no	—
211	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
212	C₂×D₁₂	—	2	2	no	—
213	C₂×D₁₂	—	2	2	no	—
214	C₂×D₁₂	—	2	4	no	—
215	C₂×D₁₂	—	2	1	no	—
216	C₂×D₁₂	—	4	4	no	—
217	C₂×D₁₂	C₂³×C₅	1	2	yes	—
218	C₂×C₄×D₃	—	2	2	no	—
219	C₂×C₄×D₃	—	2	2	no	—
220	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
221	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
222	C₂×C₃×C₈	—	2	2	no	—
223	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
224	C₃×C₄⋊C₄	—	2	1	no	—
225	C₃×C₄⋊C₄	—	2	1	no	—
226	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
227	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
228	(C₂×D₃)⋊C₄	—	2	4	no	—
229	(C₂×D₃)⋊C₄	—	2	4	no	—
230	C₄⋊Dic₃	—	2	1	no	—
231	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
232	C₄×Dic₃	—	2	4	no	—
233	C₂×C₃⋊C₈	—	2	2	no	—
234	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
235	C₂³×C₅	—	3	2	no	—
236	C₂³×C₅	—	6	2	no	—
237	C₂³×C₅	—	6	2	no	—
238	C₂³×C₅	—	6	2	no	—
239	C₂³×C₅	—	6	2	no	—
240	C₂³×C₅	—	12	2	no	—
241	C₂³×C₅	—	12	2	no	—
242	C₂³×C₅	—	12	2	no	—
243	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
244	C₅×D₄	—	6	2	no	—
245	C₅×D₄	—	6	2	no	—
246	C₅×D₄	—	12	8	no	—
247	C₅×D₄	—	12	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	3	2	no	—
251	C₂×C₄×C₅	—	4	2	no	—
252	C₂×C₄×C₅	—	4	2	no	—
253	C₂×C₄×C₅	—	6	2	no	—
254	C₂×C₄×C₅	—	6	4	no	—
255	C₂×C₄×C₅	—	6	2	no	—
256	C₂×C₄×C₅	—	6	2	no	—
257	C₂×C₄×C₅	—	6	2	no	—
258	C₂×C₄×C₅	—	12	2	no	—
259	C₂×C₄×C₅	#235	1	2	yes	—
260	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
261	C₂×C₄×C₅	#239	1	2	yes	—
262	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
263	C₅×C₈	—	2	2	no	—
264	C₅×C₈	—	6	2	no	—
265	C₂²×D₄	—	3	1	no	—
266	C₂²×D₄	—	6	1	no	—
267	C₂³×C₄	—	3	1	no	—
268	C₂²×C₈	—	3	1	no	—
269	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
270	#121	—	3	4	no	—
271	#121	—	6	2	no	—
272	#117	—	3	4	no	—
273	#117	—	6	2	no	—
274	C₂×C₄⋊C₄	—	3	1	no	—
275	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	—	6	1	no	—
278	C₂×C₂²⋊C₄	—	6	1	no	—
279	C₂×C₄²	—	6	1	no	—
280	#107	C₂×C₅×D₃	1	4	yes	complemented
281	#106	—	3	4	no	—
282	#102	—	3	4	no	—
283	#102	—	3	4	no	—
284	C₂²⋊C₈	—	3	4	no	—
285	C₂×C₃×C₅	#482	1	4	yes	complemented
286	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
287	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
288	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
289	C₅×D₃	—	4	2	no	—
290	C₅×D₃	—	8	2	no	—
291	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
292	C₂²×D₃	—	2	2	no	—
293	C₂²×D₃	—	2	2	no	—
294	C₂²×D₃	—	2	2	no	—
295	C₂²×D₃	—	2	2	no	—
296	C₂²×D₃	—	4	2	no	—
297	C₂²×D₃	—	4	2	no	—
298	C₂²×D₃	—	4	2	no	—
299	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	4	2	no	—
303	C₂×C₃×C₄	—	4	2	no	—
304	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
305	C₂×C₃×C₄	C₅×#41	1	2	yes	—
306	C₂×C₃×C₄	C₅×#41	1	2	yes	—
307	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
308	C₂×Dic₃	—	2	2	no	—
309	C₂×Dic₃	—	2	2	no	—
310	C₂×Dic₃	—	4	2	no	—
311	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
312	D₁₂	—	2	2	no	—
313	D₁₂	—	2	2	no	—
314	D₁₂	—	4	8	no	—
315	D₁₂	—	4	2	no	—
316	C₄×D₃	—	2	4	no	—
317	C₄×D₃	—	2	2	no	—
318	C₄×D₃	—	2	2	no	—
319	C₃×C₈	—	2	2	no	—
320	C₃⋊C₈	—	2	2	no	—
321	C₂²×C₅	—	6	2	no	—
322	C₂²×C₅	—	6	2	no	—
323	C₂²×C₅	—	6	2	no	—
324	C₂²×C₅	—	12	4	no	—
325	C₂²×C₅	—	12	2	no	—
326	C₂²×C₅	—	12	2	no	—
327	C₂²×C₅	—	12	2	no	—
328	C₂²×C₅	—	24	4	no	—
329	C₂²×C₅	#894	1	2	yes	—
330	C₂²×C₅	#911	1	2	yes	—
331	C₂²×C₅	#919	1	2	yes	—
332	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
333	C₄×C₅	—	4	2	no	—
334	C₄×C₅	—	4	2	no	—
335	C₄×C₅	—	6	2	no	—
336	C₄×C₅	—	12	2	no	—
337	C₄×C₅	#894	1	2	yes	—
338	C₄×C₅	C₂×#235	1	1	yes	characteristic
339	C₄×C₅	C₂×#239	1	1	yes	characteristic
340	C₂⁴	—	3	1	no	—
341	C₂⁴	—	6	1	no	—
342	C₂×D₄	—	3	2	no	—
343	C₂×D₄	—	6	4	no	—
344	C₂×D₄	—	6	2	no	—
345	C₂×D₄	—	6	1	no	—
346	C₂×D₄	—	6	2	no	—
347	C₂×D₄	—	12	4	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	3	1	no	—
351	C₂²×C₄	—	3	2	no	—
352	C₂²×C₄	—	3	2	no	—
353	C₂²×C₄	—	6	2	no	—
354	C₂²×C₄	—	6	2	no	—
355	C₂²×C₄	—	6	1	no	—
356	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	3	2	no	—
359	C₂×C₈	—	6	2	no	—
360	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	3	2	no	—
364	C₄⋊C₄	—	6	1	no	—
365	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
366	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
367	C₂²⋊C₄	—	6	4	no	—
368	C₂²⋊C₄	—	6	4	no	—
369	C₄²	—	6	4	no	—
370	C₃×C₅	C₂×#482	1	1	yes	characteristic, complemented, Hall
371	C₂²×C₃	C₅×#123	1	2	yes	—
372	C₂²×C₃	C₅×#135	1	2	yes	—
373	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
374	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
375	C₂×D₃	—	2	2	no	—
376	C₂×D₃	—	2	2	no	—
377	C₂×D₃	—	2	2	no	—
378	C₂×D₃	—	4	4	no	—
379	C₂×D₃	—	4	2	no	—
380	C₂×D₃	—	4	2	no	—
381	C₂×D₃	—	4	2	no	—
382	C₂×D₃	—	8	4	no	—
383	C₃×C₄	—	4	2	no	—
384	C₃×C₄	—	4	2	no	—
385	C₃×C₄	C₅×#123	1	2	yes	—
386	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
387	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
388	Dic₃	—	2	2	no	—
389	Dic₃	—	4	2	no	—
390	C₂×C₅	—	12	2	no	—
391	C₂×C₅	—	24	2	no	—
392	C₂×C₅	#4885	1	4	yes	direct product factor
393	C₂×C₅	C₂×#894	1	1	yes	characteristic
394	C₂×C₅	C₂×#911	1	1	yes	characteristic
395	C₂×C₅	C₂×#919	1	1	yes	characteristic
396	C₂³	—	3	2	no	—
397	C₂³	—	6	2	no	—
398	C₂³	—	6	2	no	—
399	C₂³	—	6	2	no	—
400	C₂³	—	6	2	no	—
401	C₂³	—	12	2	no	—
402	C₂³	—	12	2	no	—
403	C₂³	—	12	2	no	—
404	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
405	D₄	—	6	2	no	—
406	D₄	—	6	2	no	—
407	D₄	—	12	8	no	—
408	D₄	—	12	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	3	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	6	2	no	—
415	C₂×C₄	—	6	4	no	—
416	C₂×C₄	—	6	2	no	—
417	C₂×C₄	—	6	2	no	—
418	C₂×C₄	—	6	2	no	—
419	C₂×C₄	—	12	2	no	—
420	C₂×C₄	C₅×#235	1	2	yes	—
421	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
422	C₂×C₄	C₅×#239	1	2	yes	—
423	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
424	C₈	—	2	2	no	—
425	C₈	—	6	2	no	—
426	C₂×C₃	C₅×#482	1	4	yes	complemented
427	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
428	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
429	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
430	D₃	—	4	2	no	—
431	D₃	—	8	2	no	—
432	C₅	C₂×#4885	1	1	yes	characteristic, direct product factor, Sylow
433	C₂²	—	6	2	no	—
434	C₂²	—	6	2	no	—
435	C₂²	—	6	2	no	—
436	C₂²	—	12	4	no	—
437	C₂²	—	12	2	no	—
438	C₂²	—	12	2	no	—
439	C₂²	—	12	2	no	—
440	C₂²	—	24	4	no	—
441	C₂²	C₅×#894	1	2	yes	—
442	C₂²	C₅×#911	1	2	yes	—
443	C₂²	C₅×#919	1	2	yes	—
444	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	6	2	no	—
448	C₄	—	12	2	no	—
449	C₄	C₅×#894	1	2	yes	—
450	C₄	C₂×C₅×#235	1	1	yes	characteristic
451	C₄	C₂×C₅×#239	1	1	yes	characteristic
452	C₃	C₂×C₅×#482	1	1	yes	characteristic, complemented, Sylow
453	C₂	—	12	2	no	—
454	C₂	—	24	2	no	—
455	C₂	C₅×#4885	1	4	yes	direct product factor
456	C₂	C₂×C₅×#894	1	1	yes	characteristic
457	C₂	C₂×C₅×#911	1	1	yes	characteristic
458	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×#107	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂×C₅×#895	C₂
hypercenter	C₂×C₅×#107	D₃
hypocenter	C₃	C₂×C₅×#482
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#107

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#892	C₂	semidirect
3. C₂×C₃×C₅×#107	C₂	semidirect
4. C₂×C₅×#821	C₂	semidirect
5. C₂×C₅×(C₂×D₃)⋊C₈	C₂	semidirect
6. C₂×C₅×#809	C₂	semidirect
7. C₂×C₅×#808	C₂	semidirect
8. C₅×#4885	C₂	direct (N × H)
24. C₅×#892	C₂²	semidirect
25. C₃×C₅×#107	C₂²	semidirect
26. C₅×#821	C₂²	semidirect
27. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
28. C₅×#809	C₂²	semidirect
29. C₅×#808	C₂²	semidirect
30. C₂×#4885	C₅	direct (N × H)
34. C₂×C₅×#107	D₃	semidirect
70. C₂×#892	C₂×C₅	semidirect
71. C₂×C₃×#107	C₂×C₅	semidirect
72. C₂×#821	C₂×C₅	semidirect
73. C₂×(C₂×D₃)⋊C₈	C₂×C₅	semidirect
74. C₂×#809	C₂×C₅	semidirect
75. C₂×#808	C₂×C₅	semidirect
76. #4885	C₂×C₅	direct (N × H)
92. C₅×#107	C₂×D₃	semidirect
142. #892	C₂²×C₅	semidirect
143. C₃×#107	C₂²×C₅	semidirect
144. #821	C₂²×C₅	semidirect
145. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
146. #809	C₂²×C₅	semidirect
147. #808	C₂²×C₅	semidirect
181. C₂×#107	C₅×D₃	semidirect
280. #107	C₂×C₅×D₃	semidirect
285. C₂×C₃×C₅	#482	semidirect
370. C₃×C₅	C₂×#482	semidirect
392. C₂×C₅	#4885	direct (N × H)
426. C₂×C₃	C₅×#482	semidirect
432. C₅	C₂×#4885	direct (N × H)
452. C₃	C₂×C₅×#482	semidirect
455. C₂	C₅×#4885	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×#895	2
C₂×C₅×#892	2
C₂×C₃×C₅×#107	2
C₂×C₅×#821	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₂×C₅×#809	2
C₂×C₅×#808	2
C₅×#4885	2
C₂×C₅×#482	3
C₂×#4885	5

Subgroups — C2×C5×#4885 #14431530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4885 #14431530