Subgroups — C₅×#68881 #14300727

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 584 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×C₅×#821	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#340	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4529	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1875	—	3	1	no	maximal, Hall
9	C₂²×C₅×D₁₂	—	2	1	no	—
10	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₅×D₃	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	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
16	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×Dic₃	—	2	1	no	—
19	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₅×#895	—	2	2	no	—
21	C₅×#895	C₄	1	4	yes	complemented
22	C₅×#892	—	2	2	no	—
23	C₅×#892	—	2	2	no	—
24	C₅×#821	—	2	2	no	—
25	C₅×(C₂×D₃)⋊C₈	—	2	2	no	—
26	C₅×#809	—	2	2	no	—
27	#68881	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₅×#121	—	3	1	no	—
29	C₂×C₅×#117	—	3	1	no	—
30	C₂×C₅×#102	—	3	1	no	—
31	C₂×C₅×#102	—	3	1	no	—
32	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
33	C₅×#340	—	3	1	no	—
34	C₅×#340	D₃	1	1	yes	characteristic, complemented
35	C₂³×C₅×D₃	—	2	1	no	—
36	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	—	2	1	no	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₅×Dic₃	—	2	1	no	—
41	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
42	C₂×C₅×D₁₂	—	2	1	no	—
43	C₂×C₅×D₁₂	—	2	1	no	—
44	C₂×C₅×D₁₂	—	2	1	no	—
45	C₂×C₅×D₁₂	—	2	1	no	—
46	C₂×C₅×D₁₂	—	2	4	no	—
47	C₂×C₅×D₁₂	—	2	1	no	—
48	C₂×C₅×D₁₂	—	4	2	no	—
49	C₂×C₅×D₁₂	—	4	2	no	—
50	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
51	C₂×C₄×C₅×D₃	—	2	1	no	—
52	C₂×C₄×C₅×D₃	—	2	1	no	—
53	C₂×C₄×C₅×D₃	—	2	1	no	—
54	C₂×C₄×C₅×D₃	—	2	1	no	—
55	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
56	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
57	C₂×C₃×C₅×C₈	—	2	1	no	—
58	C₂×C₃×C₅×C₈	—	2	1	no	—
59	C₂×C₃×C₅×C₈	—	2	1	no	—
60	C₃×C₅×C₄⋊C₄	—	2	1	no	—
61	C₃×C₅×C₄⋊C₄	—	2	1	no	—
62	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
63	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	complemented
64	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
65	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
66	C₅×C₄⋊Dic₃	—	2	1	no	—
67	C₅×C₄⋊Dic₃	D₄	1	2	yes	complemented
68	C₄×C₅×Dic₃	—	2	4	no	—
69	C₂×C₅×C₃⋊C₈	—	2	1	no	—
70	C₂×C₅×C₃⋊C₈	—	2	1	no	—
71	C₂×C₅×C₃⋊C₈	—	2	1	no	—
72	C₂×#895	C₂×C₅	1	1	yes	characteristic
73	C₂×#892	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×#821	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×#809	C₂×C₅	1	1	yes	characteristic, complemented
77	C₃×#340	C₂×C₅	1	1	yes	characteristic, complemented
78	#4529	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂²×C₅×D₄	—	3	1	no	—
80	C₂²×C₅×D₄	—	6	1	no	—
81	C₂³×C₄×C₅	—	3	1	no	—
82	C₂²×C₅×C₈	—	3	1	no	—
83	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
84	C₅×#121	—	3	4	no	—
85	C₅×#121	—	6	2	no	—
86	C₅×#117	—	6	2	no	—
87	C₅×#117	—	6	2	no	—
88	C₂×C₅×C₄⋊C₄	—	3	1	no	—
89	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
90	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
91	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
92	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
93	C₂×C₄²×C₅	—	6	1	no	—
94	C₅×#102	—	6	2	no	—
95	C₅×#102	—	6	2	no	—
96	C₅×C₂²⋊C₈	—	6	2	no	—
97	#1875	—	3	1	no	Sylow
98	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₅×D₃	—	2	1	no	—
100	C₂²×C₅×D₃	—	2	1	no	—
101	C₂²×C₅×D₃	—	2	1	no	—
102	C₂²×C₅×D₃	—	2	1	no	—
103	C₂²×C₅×D₃	—	2	1	no	—
104	C₂²×C₅×D₃	—	2	1	no	—
105	C₂²×C₅×D₃	—	2	2	no	—
106	C₂²×C₅×D₃	—	4	1	no	—
107	C₂²×C₅×D₃	—	4	1	no	—
108	C₂²×C₅×D₃	—	4	1	no	—
109	C₂²×C₅×D₃	—	4	1	no	—
110	C₂²×C₅×D₃	—	4	1	no	—
111	C₂²×C₅×D₃	—	4	1	no	—
112	C₂²×C₅×D₃	C₂²⋊C₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	4	1	no	—
116	C₂×C₃×C₄×C₅	—	4	1	no	—
117	C₂×C₃×C₄×C₅	—	4	1	no	—
118	C₂×C₃×C₄×C₅	—	4	1	no	—
119	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
124	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
125	C₂×C₅×Dic₃	—	2	1	no	—
126	C₂×C₅×Dic₃	—	2	1	no	—
127	C₂×C₅×Dic₃	—	2	2	no	—
128	C₂×C₅×Dic₃	—	4	1	no	—
129	C₂×C₅×Dic₃	—	4	1	no	—
130	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
131	C₅×D₁₂	—	2	2	no	—
132	C₅×D₁₂	—	2	2	no	—
133	C₅×D₁₂	—	4	8	no	—
134	C₅×D₁₂	—	4	1	no	—
135	C₅×D₁₂	—	4	1	no	—
136	C₄×C₅×D₃	—	2	2	no	—
137	C₄×C₅×D₃	—	2	2	no	—
138	C₄×C₅×D₃	—	2	2	no	—
139	C₄×C₅×D₃	—	2	2	no	—
140	C₃×C₅×C₈	—	4	1	no	—
141	C₅×C₃⋊C₈	—	4	1	no	—
142	C₂²×D₁₂	—	2	1	no	—
143	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
144	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
145	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
148	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
149	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
150	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
151	C₂×C₄×Dic₃	—	2	1	no	—
152	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
153	#895	—	2	2	no	—
154	#895	C₄×C₅	1	4	yes	complemented
155	#892	—	2	2	no	—
156	#892	—	2	2	no	—
157	#821	—	2	2	no	—
158	(C₂×D₃)⋊C₈	—	2	2	no	—
159	#809	—	2	2	no	—
160	C₂⁴×C₅	—	3	1	no	—
161	C₂⁴×C₅	—	6	1	no	—
162	C₂×C₅×D₄	—	3	2	no	—
163	C₂×C₅×D₄	—	6	4	no	—
164	C₂×C₅×D₄	—	6	1	no	—
165	C₂×C₅×D₄	—	6	1	no	—
166	C₂×C₅×D₄	—	6	1	no	—
167	C₂×C₅×D₄	—	6	1	no	—
168	C₂×C₅×D₄	—	6	1	no	—
169	C₂×C₅×D₄	—	12	2	no	—
170	C₂×C₅×D₄	—	12	2	no	—
171	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	—	2	1	no	—
173	C₂²×C₄×C₅	—	3	1	no	—
174	C₂²×C₄×C₅	—	3	2	no	—
175	C₂²×C₄×C₅	—	3	2	no	—
176	C₂²×C₄×C₅	—	6	1	no	—
177	C₂²×C₄×C₅	—	6	1	no	—
178	C₂²×C₄×C₅	—	6	1	no	—
179	C₂²×C₄×C₅	—	6	1	no	—
180	C₂²×C₄×C₅	—	6	1	no	—
181	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	1	no	—
185	C₂×C₅×C₈	—	6	1	no	—
186	C₂×C₅×C₈	—	6	1	no	—
187	C₂×C₅×C₈	—	6	1	no	—
188	C₅×C₄⋊C₄	—	2	1	no	—
189	C₅×C₄⋊C₄	—	2	1	no	—
190	C₅×C₄⋊C₄	—	3	2	no	—
191	C₅×C₄⋊C₄	—	6	1	no	—
192	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
193	C₅×C₄⋊C₄	D₁₂	1	2	yes	complemented
194	C₅×C₂²⋊C₄	—	6	4	no	—
195	C₅×C₂²⋊C₄	—	6	4	no	—
196	C₄²×C₅	—	6	4	no	—
197	C₂×#121	—	3	1	no	—
198	C₂×#117	—	3	1	no	—
199	C₂×#102	—	3	1	no	—
200	C₂×#102	—	3	1	no	—
201	C₂×C₂²⋊C₈	—	3	1	no	—
202	#340	—	3	1	no	—
203	#340	C₅×D₃	1	1	yes	characteristic, complemented
204	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂²×C₃×C₅	#120	1	1	yes	characteristic
206	C₂²×C₃×C₅	#123	1	1	yes	characteristic
207	C₂²×C₃×C₅	#135	1	1	yes	characteristic
208	C₂²×C₃×C₅	#135	1	1	yes	characteristic
209	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
210	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
211	C₂×C₅×D₃	—	2	2	no	—
212	C₂×C₅×D₃	—	2	2	no	—
213	C₂×C₅×D₃	—	2	2	no	—
214	C₂×C₅×D₃	—	4	1	no	—
215	C₂×C₅×D₃	—	4	1	no	—
216	C₂×C₅×D₃	—	4	1	no	—
217	C₂×C₅×D₃	—	4	1	no	—
218	C₂×C₅×D₃	—	4	2	no	—
219	C₂×C₅×D₃	—	4	2	no	—
220	C₂×C₅×D₃	—	4	2	no	—
221	C₂×C₅×D₃	—	8	1	no	—
222	C₂×C₅×D₃	—	8	1	no	—
223	C₂×C₅×D₃	—	8	1	no	—
224	C₂×C₅×D₃	—	8	1	no	—
225	C₃×C₄×C₅	—	4	2	no	—
226	C₃×C₄×C₅	—	4	2	no	—
227	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
228	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
229	C₃×C₄×C₅	#121	1	1	yes	characteristic
230	C₃×C₄×C₅	#121	1	1	yes	characteristic
231	C₅×Dic₃	—	2	2	no	—
232	C₅×Dic₃	—	4	2	no	—
233	C₂³×D₃	—	2	1	no	—
234	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
235	C₂²×C₃×C₄	—	2	1	no	—
236	C₂²×C₃×C₄	—	2	1	no	—
237	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
238	C₂²×Dic₃	—	2	1	no	—
239	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
240	C₂×D₁₂	—	2	1	no	—
241	C₂×D₁₂	—	2	1	no	—
242	C₂×D₁₂	—	2	1	no	—
243	C₂×D₁₂	—	2	1	no	—
244	C₂×D₁₂	—	2	4	no	—
245	C₂×D₁₂	—	2	1	no	—
246	C₂×D₁₂	—	4	2	no	—
247	C₂×D₁₂	—	4	2	no	—
248	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
249	C₂×C₄×D₃	—	2	1	no	—
250	C₂×C₄×D₃	—	2	1	no	—
251	C₂×C₄×D₃	—	2	1	no	—
252	C₂×C₄×D₃	—	2	1	no	—
253	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
254	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
255	C₂×C₃×C₈	—	2	1	no	—
256	C₂×C₃×C₈	—	2	1	no	—
257	C₂×C₃×C₈	—	2	1	no	—
258	C₃×C₄⋊C₄	—	2	1	no	—
259	C₃×C₄⋊C₄	—	2	1	no	—
260	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
261	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	complemented
262	(C₂×D₃)⋊C₄	—	2	4	no	—
263	(C₂×D₃)⋊C₄	—	2	4	no	—
264	C₄⋊Dic₃	—	2	1	no	—
265	C₄⋊Dic₃	C₅×D₄	1	2	yes	complemented
266	C₄×Dic₃	—	2	4	no	—
267	C₂×C₃⋊C₈	—	2	1	no	—
268	C₂×C₃⋊C₈	—	2	1	no	—
269	C₂×C₃⋊C₈	—	2	1	no	—
270	C₂³×C₅	—	3	2	no	—
271	C₂³×C₅	—	6	1	no	—
272	C₂³×C₅	—	6	1	no	—
273	C₂³×C₅	—	6	1	no	—
274	C₂³×C₅	—	6	1	no	—
275	C₂³×C₅	—	6	1	no	—
276	C₂³×C₅	—	6	1	no	—
277	C₂³×C₅	—	6	2	no	—
278	C₂³×C₅	—	12	1	no	—
279	C₂³×C₅	—	12	1	no	—
280	C₂³×C₅	—	12	1	no	—
281	C₂³×C₅	—	12	1	no	—
282	C₂³×C₅	—	12	1	no	—
283	C₂³×C₅	—	12	1	no	—
284	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
285	C₅×D₄	—	6	2	no	—
286	C₅×D₄	—	6	2	no	—
287	C₅×D₄	—	12	8	no	—
288	C₅×D₄	—	12	1	no	—
289	C₅×D₄	—	12	1	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	3	2	no	—
293	C₂×C₄×C₅	—	4	1	no	—
294	C₂×C₄×C₅	—	4	1	no	—
295	C₂×C₄×C₅	—	4	1	no	—
296	C₂×C₄×C₅	—	4	1	no	—
297	C₂×C₄×C₅	—	6	1	no	—
298	C₂×C₄×C₅	—	6	1	no	—
299	C₂×C₄×C₅	—	6	2	no	—
300	C₂×C₄×C₅	—	6	2	no	—
301	C₂×C₄×C₅	—	6	2	no	—
302	C₂×C₄×C₅	—	6	2	no	—
303	C₂×C₄×C₅	—	6	2	no	—
304	C₂×C₄×C₅	—	12	1	no	—
305	C₂×C₄×C₅	—	12	1	no	—
306	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
308	C₂×C₄×C₅	#235	1	1	yes	characteristic
309	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
310	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
311	C₂×C₄×C₅	#239	1	1	yes	characteristic
312	C₅×C₈	—	4	1	no	—
313	C₅×C₈	—	12	1	no	—
314	C₂²×D₄	—	3	1	no	—
315	C₂²×D₄	—	6	1	no	—
316	C₂³×C₄	—	3	1	no	—
317	C₂²×C₈	—	3	1	no	—
318	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
319	#121	—	3	4	no	—
320	#121	—	6	2	no	—
321	#117	—	6	2	no	—
322	#117	—	6	2	no	—
323	C₂×C₄⋊C₄	—	3	1	no	—
324	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	—	6	1	no	—
327	C₂×C₂²⋊C₄	—	6	1	no	—
328	C₂×C₄²	—	6	1	no	—
329	#102	—	6	2	no	—
330	#102	—	6	2	no	—
331	C₂²⋊C₈	—	6	2	no	—
332	C₂×C₃×C₅	#386	1	1	yes	characteristic
333	C₂×C₃×C₅	#416	1	1	yes	characteristic
334	C₂×C₃×C₅	#418	1	1	yes	characteristic
335	C₂×C₃×C₅	#449	1	1	yes	characteristic
336	C₂×C₃×C₅	#449	1	1	yes	characteristic
337	C₂×C₃×C₅	#482	1	1	yes	characteristic
338	C₂×C₃×C₅	#482	1	1	yes	characteristic
339	C₅×D₃	—	4	2	no	—
340	C₅×D₃	—	8	2	no	—
341	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
342	C₂²×D₃	—	2	1	no	—
343	C₂²×D₃	—	2	1	no	—
344	C₂²×D₃	—	2	1	no	—
345	C₂²×D₃	—	2	1	no	—
346	C₂²×D₃	—	2	1	no	—
347	C₂²×D₃	—	2	1	no	—
348	C₂²×D₃	—	2	2	no	—
349	C₂²×D₃	—	4	1	no	—
350	C₂²×D₃	—	4	1	no	—
351	C₂²×D₃	—	4	1	no	—
352	C₂²×D₃	—	4	1	no	—
353	C₂²×D₃	—	4	1	no	—
354	C₂²×D₃	—	4	1	no	—
355	C₂²×D₃	C₅×C₂²⋊C₄	1	2	yes	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	4	1	no	—
359	C₂×C₃×C₄	—	4	1	no	—
360	C₂×C₃×C₄	—	4	1	no	—
361	C₂×C₃×C₄	—	4	1	no	—
362	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
363	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
364	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
365	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
366	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
367	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
368	C₂×Dic₃	—	2	1	no	—
369	C₂×Dic₃	—	2	1	no	—
370	C₂×Dic₃	—	2	2	no	—
371	C₂×Dic₃	—	4	1	no	—
372	C₂×Dic₃	—	4	1	no	—
373	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
374	D₁₂	—	2	2	no	—
375	D₁₂	—	2	2	no	—
376	D₁₂	—	4	8	no	—
377	D₁₂	—	4	1	no	—
378	D₁₂	—	4	1	no	—
379	C₄×D₃	—	2	2	no	—
380	C₄×D₃	—	2	2	no	—
381	C₄×D₃	—	2	2	no	—
382	C₄×D₃	—	2	2	no	—
383	C₃×C₈	—	4	1	no	—
384	C₃⋊C₈	—	4	1	no	—
385	C₂²×C₅	—	6	2	no	—
386	C₂²×C₅	—	6	2	no	—
387	C₂²×C₅	—	6	2	no	—
388	C₂²×C₅	—	12	1	no	—
389	C₂²×C₅	—	12	1	no	—
390	C₂²×C₅	—	12	1	no	—
391	C₂²×C₅	—	12	1	no	—
392	C₂²×C₅	—	12	2	no	—
393	C₂²×C₅	—	12	2	no	—
394	C₂²×C₅	—	12	2	no	—
395	C₂²×C₅	—	24	1	no	—
396	C₂²×C₅	—	24	1	no	—
397	C₂²×C₅	—	24	1	no	—
398	C₂²×C₅	—	24	1	no	—
399	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
400	C₂²×C₅	#882	1	1	yes	characteristic
401	C₂²×C₅	#894	1	1	yes	characteristic
402	C₂²×C₅	#911	1	1	yes	characteristic
403	C₂²×C₅	#914	1	1	yes	characteristic
404	C₂²×C₅	#916	1	1	yes	characteristic
405	C₂²×C₅	#919	1	1	yes	characteristic
406	C₄×C₅	—	4	2	no	—
407	C₄×C₅	—	4	2	no	—
408	C₄×C₅	—	6	2	no	—
409	C₄×C₅	—	12	2	no	—
410	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
411	C₄×C₅	#884	1	1	yes	characteristic
412	C₄×C₅	#893	1	1	yes	characteristic
413	C₄×C₅	#895	1	1	yes	characteristic
414	C₂⁴	—	3	1	no	—
415	C₂⁴	—	6	1	no	—
416	C₂×D₄	—	3	2	no	—
417	C₂×D₄	—	6	4	no	—
418	C₂×D₄	—	6	1	no	—
419	C₂×D₄	—	6	1	no	—
420	C₂×D₄	—	6	1	no	—
421	C₂×D₄	—	6	1	no	—
422	C₂×D₄	—	6	1	no	—
423	C₂×D₄	—	12	2	no	—
424	C₂×D₄	—	12	2	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	3	1	no	—
428	C₂²×C₄	—	3	2	no	—
429	C₂²×C₄	—	3	2	no	—
430	C₂²×C₄	—	6	1	no	—
431	C₂²×C₄	—	6	1	no	—
432	C₂²×C₄	—	6	1	no	—
433	C₂²×C₄	—	6	1	no	—
434	C₂²×C₄	—	6	1	no	—
435	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	6	1	no	—
440	C₂×C₈	—	6	1	no	—
441	C₂×C₈	—	6	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	3	2	no	—
445	C₄⋊C₄	—	6	1	no	—
446	C₄⋊C₄	C₄×C₅×D₃	1	2	yes	—
447	C₄⋊C₄	C₅×D₁₂	1	2	yes	complemented
448	C₂²⋊C₄	—	6	4	no	—
449	C₂²⋊C₄	—	6	4	no	—
450	C₄²	—	6	4	no	—
451	C₃×C₅	#1875	1	1	yes	characteristic, complemented, Hall
452	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
453	C₂²×C₃	C₅×#120	1	1	yes	characteristic
454	C₂²×C₃	C₅×#123	1	1	yes	characteristic
455	C₂²×C₃	C₅×#135	1	1	yes	characteristic
456	C₂²×C₃	C₅×#135	1	1	yes	characteristic
457	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
458	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
459	C₂×D₃	—	2	2	no	—
460	C₂×D₃	—	2	2	no	—
461	C₂×D₃	—	2	2	no	—
462	C₂×D₃	—	4	1	no	—
463	C₂×D₃	—	4	1	no	—
464	C₂×D₃	—	4	1	no	—
465	C₂×D₃	—	4	1	no	—
466	C₂×D₃	—	4	2	no	—
467	C₂×D₃	—	4	2	no	—
468	C₂×D₃	—	4	2	no	—
469	C₂×D₃	—	8	1	no	—
470	C₂×D₃	—	8	1	no	—
471	C₂×D₃	—	8	1	no	—
472	C₂×D₃	—	8	1	no	—
473	C₃×C₄	—	4	2	no	—
474	C₃×C₄	—	4	2	no	—
475	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
476	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
477	C₃×C₄	C₅×#121	1	1	yes	characteristic
478	C₃×C₄	C₅×#121	1	1	yes	characteristic
479	Dic₃	—	2	2	no	—
480	Dic₃	—	4	2	no	—
481	C₂×C₅	—	12	2	no	—
482	C₂×C₅	—	24	2	no	—
483	C₂×C₅	#4665	1	1	yes	characteristic
484	C₂×C₅	#4770	1	1	yes	characteristic
485	C₂×C₅	#4781	1	1	yes	characteristic
486	C₂×C₅	#4804	1	1	yes	characteristic
487	C₂×C₅	#4810	1	1	yes	characteristic
488	C₂×C₅	#4866	1	1	yes	characteristic
489	C₂×C₅	#4885	1	1	yes	characteristic
490	C₂³	—	3	2	no	—
491	C₂³	—	6	1	no	—
492	C₂³	—	6	1	no	—
493	C₂³	—	6	1	no	—
494	C₂³	—	6	1	no	—
495	C₂³	—	6	1	no	—
496	C₂³	—	6	1	no	—
497	C₂³	—	6	2	no	—
498	C₂³	—	12	1	no	—
499	C₂³	—	12	1	no	—
500	C₂³	—	12	1	no	—
501	C₂³	—	12	1	no	—
502	C₂³	—	12	1	no	—
503	C₂³	—	12	1	no	—
504	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
505	D₄	—	6	2	no	—
506	D₄	—	6	2	no	—
507	D₄	—	12	8	no	—
508	D₄	—	12	1	no	—
509	D₄	—	12	1	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	3	2	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	6	1	no	—
518	C₂×C₄	—	6	1	no	—
519	C₂×C₄	—	6	2	no	—
520	C₂×C₄	—	6	2	no	—
521	C₂×C₄	—	6	2	no	—
522	C₂×C₄	—	6	2	no	—
523	C₂×C₄	—	6	2	no	—
524	C₂×C₄	—	12	1	no	—
525	C₂×C₄	—	12	1	no	—
526	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
527	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
528	C₂×C₄	C₅×#235	1	1	yes	characteristic
529	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
530	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
531	C₂×C₄	C₅×#239	1	1	yes	characteristic
532	C₈	—	4	1	no	—
533	C₈	—	12	1	no	—
534	C₂×C₃	C₅×#386	1	1	yes	characteristic
535	C₂×C₃	C₅×#416	1	1	yes	characteristic
536	C₂×C₃	C₅×#418	1	1	yes	characteristic
537	C₂×C₃	C₅×#449	1	1	yes	characteristic
538	C₂×C₃	C₅×#449	1	1	yes	characteristic
539	C₂×C₃	C₅×#482	1	1	yes	characteristic
540	C₂×C₃	C₅×#482	1	1	yes	characteristic
541	D₃	—	4	2	no	—
542	D₃	—	8	2	no	—
543	C₅	#68881	1	1	yes	characteristic, direct product factor, Sylow
544	C₂²	—	6	2	no	—
545	C₂²	—	6	2	no	—
546	C₂²	—	6	2	no	—
547	C₂²	—	12	1	no	—
548	C₂²	—	12	1	no	—
549	C₂²	—	12	1	no	—
550	C₂²	—	12	1	no	—
551	C₂²	—	12	2	no	—
552	C₂²	—	12	2	no	—
553	C₂²	—	12	2	no	—
554	C₂²	—	24	1	no	—
555	C₂²	—	24	1	no	—
556	C₂²	—	24	1	no	—
557	C₂²	—	24	1	no	—
558	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
559	C₂²	C₅×#882	1	1	yes	characteristic
560	C₂²	C₅×#894	1	1	yes	characteristic
561	C₂²	C₅×#911	1	1	yes	characteristic
562	C₂²	C₅×#914	1	1	yes	characteristic
563	C₂²	C₅×#916	1	1	yes	characteristic
564	C₂²	C₅×#919	1	1	yes	characteristic
565	C₄	—	4	2	no	—
566	C₄	—	4	2	no	—
567	C₄	—	6	2	no	—
568	C₄	—	12	2	no	—
569	C₄	C₄×C₅×D₁₂	1	1	yes	characteristic
570	C₄	C₅×#884	1	1	yes	characteristic
571	C₄	C₅×#893	1	1	yes	characteristic
572	C₄	C₅×#895	1	1	yes	characteristic
573	C₃	C₅×#1875	1	1	yes	characteristic, complemented, Sylow
574	C₂	—	12	2	no	—
575	C₂	—	24	2	no	—
576	C₂	C₅×#4665	1	1	yes	characteristic
577	C₂	C₅×#4770	1	1	yes	characteristic
578	C₂	C₅×#4781	1	1	yes	characteristic
579	C₂	C₅×#4804	1	1	yes	characteristic
580	C₂	C₅×#4810	1	1	yes	characteristic
581	C₂	C₅×#4866	1	1	yes	characteristic
582	C₂	C₅×#4885	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#340	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂×C₅×#895	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#340	D₃
hypocenter	C₃	C₅×#1875
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#340

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#892	C₂	semidirect
3. C₂×C₅×#821	C₂	semidirect
4. C₂×C₅×(C₂×D₃)⋊C₈	C₂	semidirect
5. C₂×C₅×#809	C₂	semidirect
6. C₃×C₅×#340	C₂	semidirect
7. C₅×#4529	C₂	semidirect
21. C₅×#895	C₄	semidirect
27. #68881	C₅	direct (N × H)
34. C₅×#340	D₃	semidirect
63. C₃×C₅×C₄⋊C₄	D₄	semidirect
67. C₅×C₄⋊Dic₃	D₄	semidirect
73. C₂×#892	C₂×C₅	semidirect
74. C₂×#821	C₂×C₅	semidirect
75. C₂×(C₂×D₃)⋊C₈	C₂×C₅	semidirect
76. C₂×#809	C₂×C₅	semidirect
77. C₃×#340	C₂×C₅	semidirect
78. #4529	C₂×C₅	semidirect
154. #895	C₄×C₅	semidirect
193. C₅×C₄⋊C₄	D₁₂	semidirect
203. #340	C₅×D₃	semidirect
261. C₃×C₄⋊C₄	C₅×D₄	semidirect
265. C₄⋊Dic₃	C₅×D₄	semidirect
447. C₄⋊C₄	C₅×D₁₂	semidirect
451. C₃×C₅	#1875	semidirect
543. C₅	#68881	direct (N × H)
573. C₃	C₅×#1875	semidirect

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×C₅×#821	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₂×C₅×#809	2
C₃×C₅×#340	2
C₅×#4529	2
C₅×#1875	3
#68881	5

Subgroups — C5×#68881 #14300727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68881 #14300727