Subgroups — C₅×#70154 #14297717

Order 1920.

712 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#102	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4977	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4551	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4529	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1804	—	3	1	no	maximal, Hall
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂³×C₅×Dic₃	—	2	1	no	—
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₅×#217	—	2	1	no	—
14	C₅×D₄×Dic₃	—	2	2	no	—
15	C₅×D₄×Dic₃	C₄	1	4	yes	complemented
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
19	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₃×C₅×#102	—	2	2	no	—
21	C₅×#832	—	2	2	no	—
22	C₅×C₃⋊#95	—	2	1	no	—
23	C₅×C₃⋊#95	—	2	1	no	—
24	C₅×Dic₃⋊C₈	—	2	2	no	—
25	#70154	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₄×C₅×D₄	—	3	1	no	—
27	C₂×C₅×C₄⋊C₈	—	3	1	no	—
28	C₂×C₅×#102	—	3	1	no	—
29	C₂×C₅×#102	D₃	1	1	yes	characteristic
30	C₅×#382	—	3	1	no	—
31	C₅×#340	—	3	1	no	—
32	C₅×#340	—	3	1	no	—
33	C₂⁴×C₃×C₅	—	2	1	no	—
34	C₂×C₃×C₅×D₄	—	2	1	no	—
35	C₂×C₃×C₅×D₄	—	2	1	no	—
36	C₂×C₃×C₅×D₄	—	2	1	no	—
37	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
38	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
39	C₂×C₃×C₅×D₄	Q₈	1	2	yes	—
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₅×Dic₃	—	2	1	no	—
43	C₂²×C₅×Dic₃	—	2	4	no	—
44	C₂²×C₅×Dic₃	—	2	1	no	—
45	C₂²×C₅×Dic₃	—	4	2	no	—
46	C₂²×C₅×Dic₃	—	4	2	no	—
47	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
48	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₂×C₃×C₅×C₈	—	2	1	no	—
51	C₂×C₃×C₅×C₈	—	2	1	no	—
52	C₃×C₅×C₄⋊C₄	—	2	1	no	—
53	C₃×C₅×C₄⋊C₄	—	2	1	no	—
54	C₅×#217	—	2	4	no	—
55	C₅×C₄⋊Dic₃	—	2	1	no	—
56	C₅×C₄⋊Dic₃	—	2	1	no	—
57	C₅×C₄⋊Dic₃	—	2	1	no	—
58	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
59	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
60	C₄×C₅×Dic₃	D₄	1	2	yes	—
61	C₂×C₅×C₃⋊C₈	—	2	1	no	—
62	C₂×C₅×C₃⋊C₈	—	2	1	no	—
63	C₂×C₅×C₃⋊C₈	—	2	1	no	—
64	C₂×D₄×Dic₃	C₂×C₅	1	1	yes	characteristic
65	C₂×C₃×#102	C₂×C₅	1	1	yes	characteristic
66	C₂×#832	C₂×C₅	1	1	yes	characteristic
67	C₂×Dic₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
68	#4977	C₂×C₅	1	1	yes	characteristic, complemented
69	#4551	C₂×C₅	1	1	yes	characteristic, complemented
70	#4529	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
72	C₂³×C₄×C₅	—	6	1	no	—
73	C₂²×C₅×C₈	—	3	1	no	—
74	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
75	C₄×C₅×D₄	—	3	4	no	—
76	C₄×C₅×D₄	—	6	2	no	—
77	C₂×C₅×C₄⋊C₄	—	3	1	no	—
78	C₂×C₅×C₄⋊C₄	—	3	1	no	—
79	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
80	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
81	C₂×C₄²×C₅	—	3	1	no	—
82	C₅×C₄⋊C₈	—	6	2	no	—
83	C₅×#102	—	2	2	no	—
84	C₅×#102	—	6	2	no	—
85	C₅×#95	—	6	1	no	—
86	C₅×#95	—	6	1	no	—
87	#1804	—	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	1	no	—
92	C₂³×C₃×C₅	—	4	1	no	—
93	C₂³×C₃×C₅	—	4	1	no	—
94	C₂³×C₃×C₅	—	4	1	no	—
95	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
96	C₃×C₅×D₄	—	2	2	no	—
97	C₃×C₅×D₄	—	2	2	no	—
98	C₃×C₅×D₄	—	2	2	no	—
99	C₃×C₅×D₄	C₄⋊C₄	1	4	yes	—
100	C₂×C₃×C₄×C₅	—	4	1	no	—
101	C₂×C₃×C₄×C₅	—	4	1	no	—
102	C₂×C₃×C₄×C₅	—	4	1	no	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
109	C₂×C₅×Dic₃	—	2	1	no	—
110	C₂×C₅×Dic₃	—	2	1	no	—
111	C₂×C₅×Dic₃	—	2	1	no	—
112	C₂×C₅×Dic₃	—	2	1	no	—
113	C₂×C₅×Dic₃	—	2	2	no	—
114	C₂×C₅×Dic₃	—	4	8	no	—
115	C₂×C₅×Dic₃	—	4	1	no	—
116	C₂×C₅×Dic₃	—	4	1	no	—
117	C₂×C₅×Dic₃	—	4	1	no	—
118	C₂×C₅×Dic₃	—	4	1	no	—
119	C₂×C₅×Dic₃	—	4	1	no	—
120	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
121	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
122	C₃×C₅×C₈	—	4	1	no	—
123	C₅×C₃⋊C₈	—	4	1	no	—
124	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
125	C₂³×Dic₃	—	2	1	no	—
126	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
128	C₂×#217	—	2	1	no	—
129	D₄×Dic₃	—	2	2	no	—
130	D₄×Dic₃	C₄×C₅	1	4	yes	complemented
131	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
132	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
134	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
135	C₃×#102	—	2	2	no	—
136	#832	—	2	2	no	—
137	C₃⋊#95	—	2	1	no	—
138	C₃⋊#95	—	2	1	no	—
139	Dic₃⋊C₈	—	2	2	no	—
140	C₂⁴×C₅	—	2	1	no	—
141	C₂×C₅×D₄	—	2	1	no	—
142	C₂×C₅×D₄	—	2	1	no	—
143	C₂×C₅×D₄	—	2	1	no	—
144	C₂×C₅×D₄	Dic₆	1	2	yes	—
145	C₂×C₅×D₄	C₄×D₃	1	2	yes	—
146	C₂×C₅×D₄	#67	1	2	yes	—
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	—	3	1	no	—
149	C₂²×C₄×C₅	—	3	1	no	—
150	C₂²×C₄×C₅	—	6	4	no	—
151	C₂²×C₄×C₅	—	6	1	no	—
152	C₂²×C₄×C₅	—	6	1	no	—
153	C₂²×C₄×C₅	—	12	2	no	—
154	C₂²×C₄×C₅	—	12	2	no	—
155	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	6	1	no	—
160	C₂×C₅×C₈	—	6	1	no	—
161	C₂×C₅×C₈	—	6	1	no	—
162	C₅×C₄⋊C₄	—	2	1	no	—
163	C₅×C₄⋊C₄	—	2	1	no	—
164	C₅×C₄⋊C₄	—	3	2	no	—
165	C₅×C₄⋊C₄	—	6	1	no	—
166	C₅×C₄⋊C₄	—	6	1	no	—
167	C₅×C₄⋊C₄	—	6	1	no	—
168	C₅×C₂²⋊C₄	—	6	4	no	—
169	C₄²×C₅	—	3	2	no	—
170	C₄²×C₅	—	3	2	no	—
171	C₂×C₄×D₄	—	3	1	no	—
172	C₂×C₄⋊C₈	—	3	1	no	—
173	C₂×#102	—	3	1	no	—
174	C₂×#102	C₅×D₃	1	1	yes	characteristic
175	#382	—	3	1	no	—
176	#340	—	3	1	no	—
177	#340	—	3	1	no	—
178	C₂²×C₃×C₅	—	2	4	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	—	4	2	no	—
181	C₂²×C₃×C₅	—	4	2	no	—
182	C₂²×C₃×C₅	—	4	2	no	—
183	C₂²×C₃×C₅	—	4	2	no	—
184	C₂²×C₃×C₅	—	4	2	no	—
185	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂²×C₃×C₅	#121	1	1	yes	characteristic
187	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
188	C₂²×C₃×C₅	#135	1	1	yes	characteristic
189	C₂²×C₃×C₅	#135	1	1	yes	characteristic
190	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
192	C₃×C₄×C₅	—	8	1	no	—
193	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₃×C₄×C₅	#117	1	1	yes	characteristic
195	C₃×C₄×C₅	#121	1	1	yes	characteristic
196	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
197	C₅×Dic₃	—	2	2	no	—
198	C₅×Dic₃	—	2	2	no	—
199	C₅×Dic₃	—	4	2	no	—
200	C₅×Dic₃	—	8	1	no	—
201	C₂⁴×C₃	—	2	1	no	—
202	C₂×C₃×D₄	—	2	1	no	—
203	C₂×C₃×D₄	—	2	1	no	—
204	C₂×C₃×D₄	—	2	1	no	—
205	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
206	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
207	C₂×C₃×D₄	C₅×Q₈	1	2	yes	—
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	—	2	4	no	—
212	C₂²×Dic₃	—	2	1	no	—
213	C₂²×Dic₃	—	4	2	no	—
214	C₂²×Dic₃	—	4	2	no	—
215	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
216	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
217	C₂×C₃×C₈	—	2	1	no	—
218	C₂×C₃×C₈	—	2	1	no	—
219	C₂×C₃×C₈	—	2	1	no	—
220	C₃×C₄⋊C₄	—	2	1	no	—
221	C₃×C₄⋊C₄	—	2	1	no	—
222	#217	—	2	4	no	—
223	C₄⋊Dic₃	—	2	1	no	—
224	C₄⋊Dic₃	—	2	1	no	—
225	C₄⋊Dic₃	—	2	1	no	—
226	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
227	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
228	C₄×Dic₃	C₅×D₄	1	2	yes	—
229	C₂×C₃⋊C₈	—	2	1	no	—
230	C₂×C₃⋊C₈	—	2	1	no	—
231	C₂×C₃⋊C₈	—	2	1	no	—
232	C₂³×C₅	—	2	2	no	—
233	C₂³×C₅	—	2	2	no	—
234	C₂³×C₅	—	2	2	no	—
235	C₂³×C₅	—	4	1	no	—
236	C₂³×C₅	—	4	1	no	—
237	C₂³×C₅	—	4	1	no	—
238	C₂³×C₅	—	4	1	no	—
239	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
240	C₅×D₄	—	2	2	no	—
241	C₅×D₄	—	2	2	no	—
242	C₅×D₄	—	2	2	no	—
243	C₅×D₄	Dic₃⋊C₄	1	4	yes	—
244	C₂×C₄×C₅	—	3	2	no	—
245	C₂×C₄×C₅	—	3	2	no	—
246	C₂×C₄×C₅	—	4	1	no	—
247	C₂×C₄×C₅	—	4	1	no	—
248	C₂×C₄×C₅	—	4	1	no	—
249	C₂×C₄×C₅	—	6	1	no	—
250	C₂×C₄×C₅	—	6	1	no	—
251	C₂×C₄×C₅	—	6	1	no	—
252	C₂×C₄×C₅	—	6	1	no	—
253	C₂×C₄×C₅	—	6	2	no	—
254	C₂×C₄×C₅	—	12	8	no	—
255	C₂×C₄×C₅	—	12	1	no	—
256	C₂×C₄×C₅	—	12	1	no	—
257	C₂×C₄×C₅	—	12	1	no	—
258	C₂×C₄×C₅	—	12	1	no	—
259	C₂×C₄×C₅	—	12	1	no	—
260	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
262	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
263	C₂×C₄×C₅	#237	1	1	yes	characteristic
264	C₂×C₄×C₅	#237	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
266	C₅×C₈	—	4	1	no	—
267	C₅×C₈	—	12	1	no	—
268	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
269	C₂³×C₄	—	6	1	no	—
270	C₂²×C₈	—	3	1	no	—
271	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
272	C₄×D₄	—	3	4	no	—
273	C₄×D₄	—	6	2	no	—
274	C₂×C₄⋊C₄	—	3	1	no	—
275	C₂×C₄⋊C₄	—	3	1	no	—
276	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	—	6	1	no	—
278	C₂×C₄²	—	3	1	no	—
279	C₄⋊C₈	—	6	2	no	—
280	#102	—	2	2	no	—
281	#102	—	6	2	no	—
282	#95	—	6	1	no	—
283	#95	—	6	1	no	—
284	C₂×C₃×C₅	—	4	4	no	—
285	C₂×C₃×C₅	#380	1	1	yes	characteristic
286	C₂×C₃×C₅	#416	1	1	yes	characteristic
287	C₂×C₃×C₅	#418	1	1	yes	characteristic
288	C₂×C₃×C₅	#463	1	1	yes	characteristic
289	C₂×C₃×C₅	#463	1	1	yes	characteristic
290	C₂×C₃×C₅	#478	1	1	yes	characteristic
291	C₂×C₃×C₅	#478	1	1	yes	characteristic
292	C₂³×C₃	—	2	2	no	—
293	C₂³×C₃	—	2	2	no	—
294	C₂³×C₃	—	2	2	no	—
295	C₂³×C₃	—	4	1	no	—
296	C₂³×C₃	—	4	1	no	—
297	C₂³×C₃	—	4	1	no	—
298	C₂³×C₃	—	4	1	no	—
299	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
300	C₃×D₄	—	2	2	no	—
301	C₃×D₄	—	2	2	no	—
302	C₃×D₄	—	2	2	no	—
303	C₃×D₄	C₅×C₄⋊C₄	1	4	yes	—
304	C₂×C₃×C₄	—	4	1	no	—
305	C₂×C₃×C₄	—	4	1	no	—
306	C₂×C₃×C₄	—	4	1	no	—
307	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
308	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
309	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
310	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
311	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
312	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
313	C₂×Dic₃	—	2	1	no	—
314	C₂×Dic₃	—	2	1	no	—
315	C₂×Dic₃	—	2	1	no	—
316	C₂×Dic₃	—	2	1	no	—
317	C₂×Dic₃	—	2	2	no	—
318	C₂×Dic₃	—	4	8	no	—
319	C₂×Dic₃	—	4	1	no	—
320	C₂×Dic₃	—	4	1	no	—
321	C₂×Dic₃	—	4	1	no	—
322	C₂×Dic₃	—	4	1	no	—
323	C₂×Dic₃	—	4	1	no	—
324	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
325	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
326	C₃×C₈	—	4	1	no	—
327	C₃⋊C₈	—	4	1	no	—
328	C₂²×C₅	—	2	4	no	—
329	C₂²×C₅	—	4	2	no	—
330	C₂²×C₅	—	4	2	no	—
331	C₂²×C₅	—	4	2	no	—
332	C₂²×C₅	—	4	2	no	—
333	C₂²×C₅	—	4	2	no	—
334	C₂²×C₅	—	4	2	no	—
335	C₂²×C₅	#878	1	1	yes	characteristic
336	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
337	C₂²×C₅	#911	1	1	yes	characteristic
338	C₂²×C₅	#912	1	1	yes	characteristic
339	C₂²×C₅	#914	1	1	yes	characteristic
340	C₂²×C₅	#916	1	1	yes	characteristic
341	C₂²×C₅	#939	1	1	yes	characteristic
342	C₄×C₅	—	6	2	no	—
343	C₄×C₅	—	6	2	no	—
344	C₄×C₅	—	8	1	no	—
345	C₄×C₅	—	12	2	no	—
346	C₄×C₅	—	24	1	no	—
347	C₄×C₅	#877	1	1	yes	characteristic
348	C₄×C₅	#878	1	1	yes	characteristic
349	C₄×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
350	C₄×C₅	#939	1	1	yes	characteristic
351	C₂⁴	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	C₅×Dic₆	1	2	yes	—
356	C₂×D₄	C₄×C₅×D₃	1	2	yes	—
357	C₂×D₄	C₅×#67	1	2	yes	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	3	1	no	—
360	C₂²×C₄	—	3	1	no	—
361	C₂²×C₄	—	6	4	no	—
362	C₂²×C₄	—	6	1	no	—
363	C₂²×C₄	—	6	1	no	—
364	C₂²×C₄	—	12	2	no	—
365	C₂²×C₄	—	12	2	no	—
366	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	6	1	no	—
371	C₂×C₈	—	6	1	no	—
372	C₂×C₈	—	6	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	3	2	no	—
376	C₄⋊C₄	—	6	1	no	—
377	C₄⋊C₄	—	6	1	no	—
378	C₄⋊C₄	—	6	1	no	—
379	C₂²⋊C₄	—	6	4	no	—
380	C₄²	—	3	2	no	—
381	C₄²	—	3	2	no	—
382	C₃×C₅	#1804	1	1	yes	characteristic, complemented, Hall
383	C₂²×C₃	—	2	4	no	—
384	C₂²×C₃	—	4	2	no	—
385	C₂²×C₃	—	4	2	no	—
386	C₂²×C₃	—	4	2	no	—
387	C₂²×C₃	—	4	2	no	—
388	C₂²×C₃	—	4	2	no	—
389	C₂²×C₃	—	4	2	no	—
390	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
391	C₂²×C₃	C₅×#121	1	1	yes	characteristic
392	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
393	C₂²×C₃	C₅×#135	1	1	yes	characteristic
394	C₂²×C₃	C₅×#135	1	1	yes	characteristic
395	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
396	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
397	C₃×C₄	—	8	1	no	—
398	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
399	C₃×C₄	C₅×#117	1	1	yes	characteristic
400	C₃×C₄	C₅×#121	1	1	yes	characteristic
401	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
402	Dic₃	—	2	2	no	—
403	Dic₃	—	2	2	no	—
404	Dic₃	—	4	2	no	—
405	Dic₃	—	8	1	no	—
406	C₂×C₅	—	4	4	no	—
407	C₂×C₅	#4763	1	1	yes	characteristic
408	C₂×C₅	#4766	1	1	yes	characteristic
409	C₂×C₅	#4770	1	1	yes	characteristic
410	C₂×C₅	#4772	1	1	yes	characteristic
411	C₂×C₅	#4942	1	1	yes	characteristic
412	C₂×C₅	#5153	1	1	yes	characteristic
413	C₂×C₅	#5165	1	1	yes	characteristic
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	1	no	—
421	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	2	2	no	—
425	D₄	C₅×Dic₃⋊C₄	1	4	yes	—
426	C₂×C₄	—	3	2	no	—
427	C₂×C₄	—	3	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	6	1	no	—
432	C₂×C₄	—	6	1	no	—
433	C₂×C₄	—	6	1	no	—
434	C₂×C₄	—	6	1	no	—
435	C₂×C₄	—	6	2	no	—
436	C₂×C₄	—	12	8	no	—
437	C₂×C₄	—	12	1	no	—
438	C₂×C₄	—	12	1	no	—
439	C₂×C₄	—	12	1	no	—
440	C₂×C₄	—	12	1	no	—
441	C₂×C₄	—	12	1	no	—
442	C₂×C₄	C₂×C₅×Dic₆	1	1	yes	characteristic
443	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
444	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
445	C₂×C₄	C₅×#237	1	1	yes	characteristic
446	C₂×C₄	C₅×#237	1	1	yes	characteristic
447	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
448	C₈	—	4	1	no	—
449	C₈	—	12	1	no	—
450	C₂×C₃	—	4	4	no	—
451	C₂×C₃	C₅×#380	1	1	yes	characteristic
452	C₂×C₃	C₅×#416	1	1	yes	characteristic
453	C₂×C₃	C₅×#418	1	1	yes	characteristic
454	C₂×C₃	C₅×#463	1	1	yes	characteristic
455	C₂×C₃	C₅×#463	1	1	yes	characteristic
456	C₂×C₃	C₅×#478	1	1	yes	characteristic
457	C₂×C₃	C₅×#478	1	1	yes	characteristic
458	C₅	#70154	1	1	yes	characteristic, direct product factor, Sylow
459	C₂²	—	2	4	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	C₅×#878	1	1	yes	characteristic
467	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
468	C₂²	C₅×#911	1	1	yes	characteristic
469	C₂²	C₅×#912	1	1	yes	characteristic
470	C₂²	C₅×#914	1	1	yes	characteristic
471	C₂²	C₅×#916	1	1	yes	characteristic
472	C₂²	C₅×#939	1	1	yes	characteristic
473	C₄	—	6	2	no	—
474	C₄	—	6	2	no	—
475	C₄	—	8	1	no	—
476	C₄	—	12	2	no	—
477	C₄	—	24	1	no	—
478	C₄	C₅×#877	1	1	yes	characteristic
479	C₄	C₅×#878	1	1	yes	characteristic
480	C₄	C₂×C₅×Dic₃⋊C₄	1	1	yes	characteristic
481	C₄	C₅×#939	1	1	yes	characteristic
482	C₃	C₅×#1804	1	1	yes	characteristic, complemented, Sylow
483	C₂	—	4	4	no	—
484	C₂	C₅×#4763	1	1	yes	characteristic
485	C₂	C₅×#4766	1	1	yes	characteristic
486	C₂	C₅×#4770	1	1	yes	characteristic
487	C₂	C₅×#4772	1	1	yes	characteristic
488	C₂	C₅×#4942	1	1	yes	characteristic
489	C₂	C₅×#5153	1	1	yes	characteristic
490	C₂	C₅×#5165	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	C₂×C₃×C₅×#102	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×#102	D₃
hypocenter	C₃	C₅×#1804
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#102

Complements

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

N	H ≅ G/N	type
4. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
5. C₅×#4977	C₂	semidirect
6. C₅×#4551	C₂	semidirect
7. C₅×#4529	C₂	semidirect
15. C₅×D₄×Dic₃	C₄	semidirect
25. #70154	C₅	direct (N × H)
67. C₂×Dic₃⋊C₈	C₂×C₅	semidirect
68. #4977	C₂×C₅	semidirect
69. #4551	C₂×C₅	semidirect
70. #4529	C₂×C₅	semidirect
130. D₄×Dic₃	C₄×C₅	semidirect
382. C₃×C₅	#1804	semidirect
458. C₅	#70154	direct (N × H)
482. C₃	C₅×#1804	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₄×Dic₃	2
C₂×C₃×C₅×#102	2
C₂×C₅×#832	2
C₂×C₅×Dic₃⋊C₈	2
C₅×#4977	2
C₅×#4551	2
C₅×#4529	2
C₅×#1804	3
#70154	5

Subgroups — C5×#70154 #14297717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70154 #14297717