Subgroups — C₅×#79588 #14417324

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×D₈	C₂	1	1	yes	maximal, characteristic
2	C₅×#5545	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×Dic₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5014	C₂	1	2	yes	maximal, complemented
6	C₅×#4880	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4872	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4785	C₂	1	2	yes	maximal, complemented
9	C₅×#4770	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4689	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2948	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
16	C₅×D₄×Dic₃	C₂²	1	2	yes	complemented
17	C₂×C₅×#213	C₂²	1	2	yes	—
18	C₄×C₅×#67	—	2	2	no	—
19	C₂×C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
20	C₅×D₃×D₈	C₄	1	8	yes	complemented
21	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
22	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
23	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
24	C₅×#893	C₂²	1	2	yes	complemented
25	C₅×#892	C₂²	1	2	yes	—
26	C₅×#67⋊C₄	—	2	2	no	—
27	C₅×D₃×C₂²⋊C₄	—	2	2	no	—
28	C₄×C₅×D₁₂	C₂²	1	2	yes	complemented
29	C₅×#872	C₂²	1	1	yes	characteristic
30	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×#102	C₂²	1	2	yes	complemented
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
33	C₅×#832	C₂²	1	2	yes	complemented
34	C₅×#821	C₂²	1	2	yes	complemented
35	C₅×#818	C₂²	1	1	yes	characteristic, complemented
36	C₅×#815	C₂²	1	1	yes	characteristic, complemented
37	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
38	C₅×#809	C₂²	1	2	yes	complemented
39	C₅×#808	C₂²	1	2	yes	complemented
40	C₅×#803	C₂²	1	1	yes	characteristic, complemented
41	#79588	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
42	C₂²×C₅×D₈	—	3	1	no	—
43	C₅×#518	—	3	2	no	—
44	C₅×#442	—	3	2	no	—
45	C₅×#442	—	3	2	no	—
46	C₄×C₅×D₈	—	3	1	no	—
47	C₄×C₅×D₈	—	3	1	no	—
48	C₄×C₅×D₈	—	3	1	no	—
49	C₄×C₅×D₈	D₃	1	1	yes	characteristic, complemented
50	C₅×#427	—	3	1	no	—
51	C₅×#418	—	3	2	no	—
52	C₅×#405	—	3	1	no	—
53	C₂³×C₅×D₃	—	2	2	no	—
54	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂×C₅×#67	—	2	2	no	—
57	C₂²×C₅×Dic₃	—	2	2	no	—
58	C₅×D₃×D₄	—	2	4	no	—
59	C₅×D₃×D₄	C₂×C₄	1	8	yes	complemented
60	C₂×C₅×D₁₂	C₂³	1	2	yes	—
61	C₂×C₄×C₅×D₃	—	2	2	no	—
62	C₂×C₄×C₅×D₃	—	2	2	no	—
63	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
64	C₃×C₅×D₈	C₂×C₄	1	4	yes	complemented
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₅×#217	—	2	2	no	—
71	C₅×#213	C₂×C₄	1	8	yes	complemented
72	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
73	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
74	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
75	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
76	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
77	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
78	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
79	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
80	C₄×C₅×Dic₃	—	2	2	no	—
81	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
82	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
83	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
84	C₅×D₂₄	C₂×C₄	1	4	yes	complemented
85	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
86	C₅×D₃×C₈	C₂×C₄	1	4	yes	complemented
87	C₂×D₃×D₈	C₂×C₅	1	1	yes	characteristic
88	#5545	C₂×C₅	1	2	yes	complemented
89	C₃×C₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
90	Dic₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
91	#5014	C₂×C₅	1	2	yes	complemented
92	#4880	C₂×C₅	1	1	yes	characteristic, complemented
93	#4872	C₂×C₅	1	1	yes	characteristic, complemented
94	#4785	C₂×C₅	1	2	yes	complemented
95	#4770	C₂×C₅	1	2	yes	complemented
96	C₄×D₂₄	C₂×C₅	1	1	yes	characteristic, complemented
97	#4689	C₂×C₅	1	1	yes	characteristic, complemented
98	C₂²×C₅×D₄	—	3	2	no	—
99	C₂×C₅×D₈	—	3	2	no	—
100	C₂×C₅×D₈	—	3	8	no	—
101	C₂×C₅×D₈	—	3	1	no	—
102	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
103	C₂×C₅×M₁₆	—	3	1	no	—
104	C₂²×C₅×C₈	—	3	1	no	—
105	C₄×C₅×D₄	—	3	2	no	—
106	C₄×C₅×D₄	—	3	2	no	—
107	C₄×C₅×D₄	—	3	2	no	—
108	C₄×C₅×D₄	—	6	2	no	—
109	C₄×C₅×D₄	—	6	2	no	—
110	C₄×C₅×D₄	C₂×D₃	1	2	yes	complemented
111	C₅×#117	—	3	1	no	—
112	C₅×#117	—	3	2	no	—
113	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
114	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
115	C₅×#107	—	3	1	no	—
116	C₅×#107	C₂×D₃	1	1	yes	characteristic, complemented
117	C₅×#106	—	3	2	no	—
118	C₅×#102	—	3	2	no	—
119	C₅×#102	—	3	2	no	—
120	C₅×#102	—	3	2	no	—
121	C₅×#102	C₂×D₃	1	2	yes	complemented
122	C₅×#97	—	3	1	no	—
123	C₅×#97	—	3	1	no	—
124	C₄×C₅×C₈	—	3	1	no	—
125	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
126	#2948	—	3	1	no	Sylow
127	C₂³×C₃×C₅	—	2	2	no	—
128	C₂²×C₅×D₃	—	2	2	no	—
129	C₂²×C₅×D₃	—	2	8	no	—
130	C₂²×C₅×D₃	—	8	2	no	—
131	C₂²×C₅×D₃	—	8	2	no	—
132	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
133	C₃×C₅×D₄	—	2	2	no	—
134	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	8	2	no	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₅×#67	—	2	8	no	—
141	C₂×C₅×Dic₃	—	2	2	no	—
142	C₂×C₅×Dic₃	—	8	2	no	—
143	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
146	C₅×D₁₂	—	2	2	no	—
147	C₅×D₁₂	C₂²×C₄	1	4	yes	—
148	C₄×C₅×D₃	—	8	2	no	—
149	C₄×C₅×D₃	—	8	2	no	—
150	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
151	C₄×C₅×D₃	#41	1	2	yes	—
152	C₃×C₅×C₈	—	2	1	no	—
153	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
154	C₅×C₃⋊C₈	—	2	1	no	—
155	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
156	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
157	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
158	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
159	D₄×Dic₃	C₂²×C₅	1	2	yes	complemented
160	C₂×#213	C₂²×C₅	1	2	yes	—
161	C₄×#67	—	2	2	no	—
162	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
163	D₃×D₈	C₄×C₅	1	8	yes	complemented
164	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
165	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
166	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
167	#893	C₂²×C₅	1	2	yes	complemented
168	#892	C₂²×C₅	1	2	yes	—
169	#67⋊C₄	—	2	2	no	—
170	D₃×C₂²⋊C₄	—	2	2	no	—
171	C₄×D₁₂	C₂²×C₅	1	2	yes	complemented
172	#872	C₂²×C₅	1	1	yes	characteristic
173	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
174	C₃×#102	C₂²×C₅	1	2	yes	complemented
175	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
176	#832	C₂²×C₅	1	2	yes	complemented
177	#821	C₂²×C₅	1	2	yes	complemented
178	#818	C₂²×C₅	1	1	yes	characteristic, complemented
179	#815	C₂²×C₅	1	1	yes	characteristic, complemented
180	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
181	#809	C₂²×C₅	1	2	yes	complemented
182	#808	C₂²×C₅	1	2	yes	complemented
183	#803	C₂²×C₅	1	1	yes	characteristic, complemented
184	C₂⁴×C₅	—	6	2	no	—
185	C₂×C₅×D₄	—	3	8	no	—
186	C₂×C₅×D₄	—	3	2	no	—
187	C₂×C₅×D₄	—	6	4	no	—
188	C₂×C₅×D₄	—	6	2	no	—
189	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
190	C₂²×C₄×C₅	—	2	2	no	—
191	C₂²×C₄×C₅	—	3	1	no	—
192	C₂²×C₄×C₅	—	6	2	no	—
193	C₂²×C₄×C₅	—	6	2	no	—
194	C₂²×C₄×C₅	—	6	2	no	—
195	C₅×D₈	—	3	8	no	—
196	C₅×D₈	—	3	4	no	—
197	C₅×D₈	C₄×D₃	1	4	yes	complemented
198	C₅×M₁₆	—	6	2	no	—
199	C₂×C₅×C₈	—	3	1	no	—
200	C₂×C₅×C₈	—	3	4	no	—
201	C₂×C₅×C₈	—	3	1	no	—
202	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
203	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
204	C₅×C₄⋊C₄	—	3	1	no	—
205	C₅×C₄⋊C₄	—	3	1	no	—
206	C₅×C₄⋊C₄	—	3	2	no	—
207	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
208	C₅×C₂²⋊C₄	—	2	2	no	—
209	C₅×C₂²⋊C₄	—	3	1	no	—
210	C₅×C₂²⋊C₄	—	3	1	no	—
211	C₅×C₂²⋊C₄	—	6	2	no	—
212	C₅×C₂²⋊C₄	—	6	2	no	—
213	C₅×C₂²⋊C₄	—	6	2	no	—
214	C₅×C₂²⋊C₄	—	6	2	no	—
215	C₄²×C₅	—	3	1	no	—
216	C₄²×C₅	—	6	2	no	—
217	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
218	C₂²×D₈	—	3	1	no	—
219	#518	—	3	2	no	—
220	#442	—	3	2	no	—
221	#442	—	3	2	no	—
222	C₄×D₈	—	3	1	no	—
223	C₄×D₈	—	3	1	no	—
224	C₄×D₈	—	3	1	no	—
225	C₄×D₈	C₅×D₃	1	1	yes	characteristic, complemented
226	#427	—	3	1	no	—
227	#418	—	3	2	no	—
228	#405	—	3	1	no	—
229	C₂²×C₃×C₅	—	2	4	no	—
230	C₂²×C₃×C₅	—	4	2	no	—
231	C₂²×C₃×C₅	—	4	2	no	—
232	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₅×D₃	—	2	1	no	—
234	C₂×C₅×D₃	—	2	1	no	—
235	C₂×C₅×D₃	—	2	4	no	—
236	C₂×C₅×D₃	—	4	2	no	—
237	C₂×C₅×D₃	—	4	2	no	—
238	C₂×C₅×D₃	—	8	8	no	—
239	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
240	C₃×C₄×C₅	—	2	1	no	—
241	C₃×C₄×C₅	—	2	1	no	—
242	C₃×C₄×C₅	—	4	2	no	—
243	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
244	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
245	C₅×Dic₃	—	2	1	no	—
246	C₅×Dic₃	—	2	1	no	—
247	C₅×Dic₃	—	4	2	no	—
248	C₅×Dic₃	C₄×D₄	1	2	yes	—
249	C₂³×D₃	—	2	2	no	—
250	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
251	C₂²×C₃×C₄	—	2	2	no	—
252	C₂×#67	—	2	2	no	—
253	C₂²×Dic₃	—	2	2	no	—
254	D₃×D₄	—	2	4	no	—
255	D₃×D₄	C₂×C₄×C₅	1	8	yes	complemented
256	C₂×D₁₂	C₂³×C₅	1	2	yes	—
257	C₂×C₄×D₃	—	2	2	no	—
258	C₂×C₄×D₃	—	2	2	no	—
259	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
260	C₃×D₈	C₂×C₄×C₅	1	4	yes	complemented
261	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
262	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
263	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
264	C₃×C₂²⋊C₄	—	2	2	no	—
265	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
266	#217	—	2	2	no	—
267	#213	C₂×C₄×C₅	1	8	yes	complemented
268	(C₂×D₃)⋊C₄	—	2	2	no	—
269	(C₂×D₃)⋊C₄	—	2	2	no	—
270	(C₂×D₃)⋊C₄	—	2	2	no	—
271	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
272	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
273	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
274	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
275	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
276	C₄×Dic₃	—	2	2	no	—
277	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
279	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
280	D₂₄	C₂×C₄×C₅	1	4	yes	complemented
281	ΓL(1,𝔽₂₅)	—	2	2	no	—
282	D₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
283	C₂³×C₅	—	2	2	no	—
284	C₂³×C₅	—	3	1	no	—
285	C₂³×C₅	—	6	8	no	—
286	C₂³×C₅	—	6	2	no	—
287	C₂³×C₅	—	24	2	no	—
288	C₂³×C₅	—	24	2	no	—
289	C₅×D₄	—	2	2	no	—
290	C₅×D₄	—	3	4	no	—
291	C₅×D₄	—	6	8	no	—
292	C₅×D₄	—	6	2	no	—
293	C₅×D₄	C₂×C₄×D₃	1	4	yes	—
294	C₂×C₄×C₅	—	2	2	no	—
295	C₂×C₄×C₅	—	3	1	no	—
296	C₂×C₄×C₅	—	3	2	no	—
297	C₂×C₄×C₅	—	3	2	no	—
298	C₂×C₄×C₅	—	3	1	no	—
299	C₂×C₄×C₅	—	3	1	no	—
300	C₂×C₄×C₅	—	6	2	no	—
301	C₂×C₄×C₅	—	8	2	no	—
302	C₂×C₄×C₅	—	24	2	no	—
303	C₂×C₄×C₅	—	24	2	no	—
304	C₂×C₄×C₅	—	24	2	no	—
305	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
306	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
308	C₅×C₈	—	2	1	no	—
309	C₅×C₈	—	3	2	no	—
310	C₅×C₈	—	6	1	no	—
311	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
312	C₂²×D₄	—	3	2	no	—
313	C₂×D₈	—	3	2	no	—
314	C₂×D₈	—	3	8	no	—
315	C₂×D₈	—	3	1	no	—
316	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
317	C₂×M₁₆	—	3	1	no	—
318	C₂²×C₈	—	3	1	no	—
319	C₄×D₄	—	3	2	no	—
320	C₄×D₄	—	3	2	no	—
321	C₄×D₄	—	3	2	no	—
322	C₄×D₄	—	6	2	no	—
323	C₄×D₄	—	6	2	no	—
324	C₄×D₄	C₂×C₅×D₃	1	2	yes	complemented
325	#117	—	3	1	no	—
326	#117	—	3	2	no	—
327	C₂×C₂²⋊C₄	—	6	2	no	—
328	C₂×C₂²⋊C₄	—	6	2	no	—
329	#107	—	3	1	no	—
330	#107	C₂×C₅×D₃	1	1	yes	characteristic, complemented
331	#106	—	3	2	no	—
332	#102	—	3	2	no	—
333	#102	—	3	2	no	—
334	#102	—	3	2	no	—
335	#102	C₂×C₅×D₃	1	2	yes	complemented
336	#97	—	3	1	no	—
337	#97	—	3	1	no	—
338	C₄×C₈	—	3	1	no	—
339	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
340	C₂×C₃×C₅	—	4	4	no	—
341	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
342	C₂×C₃×C₅	#576	1	1	yes	characteristic
343	C₂×C₃×C₅	#576	1	1	yes	characteristic
344	C₅×D₃	—	2	2	no	—
345	C₅×D₃	—	4	4	no	—
346	C₂³×C₃	—	2	2	no	—
347	C₂²×D₃	—	2	2	no	—
348	C₂²×D₃	—	2	8	no	—
349	C₂²×D₃	—	8	2	no	—
350	C₂²×D₃	—	8	2	no	—
351	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
352	C₃×D₄	—	2	2	no	—
353	C₃×D₄	C₂²×C₄×C₅	1	4	yes	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	8	2	no	—
356	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
357	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
358	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
359	#67	—	2	8	no	—
360	C₂×Dic₃	—	2	2	no	—
361	C₂×Dic₃	—	8	2	no	—
362	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
363	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
364	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
365	D₁₂	—	2	2	no	—
366	D₁₂	C₂²×C₄×C₅	1	4	yes	—
367	C₄×D₃	—	8	2	no	—
368	C₄×D₃	—	8	2	no	—
369	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
370	C₄×D₃	C₅×#41	1	2	yes	—
371	C₃×C₈	—	2	1	no	—
372	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
373	C₃⋊C₈	—	2	1	no	—
374	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
375	C₂²×C₅	—	2	4	no	—
376	C₂²×C₅	—	3	2	no	—
377	C₂²×C₅	—	4	2	no	—
378	C₂²×C₅	—	4	2	no	—
379	C₂²×C₅	—	6	1	no	—
380	C₂²×C₅	—	6	1	no	—
381	C₂²×C₅	—	6	4	no	—
382	C₂²×C₅	—	12	2	no	—
383	C₂²×C₅	—	12	2	no	—
384	C₂²×C₅	—	24	8	no	—
385	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
386	C₄×C₅	—	2	1	no	—
387	C₄×C₅	—	2	1	no	—
388	C₄×C₅	—	3	2	no	—
389	C₄×C₅	—	4	2	no	—
390	C₄×C₅	—	6	1	no	—
391	C₄×C₅	—	6	1	no	—
392	C₄×C₅	—	12	2	no	—
393	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
394	C₄×C₅	D₃×#41	1	1	yes	characteristic
395	C₂⁴	—	6	2	no	—
396	C₂×D₄	—	3	8	no	—
397	C₂×D₄	—	3	2	no	—
398	C₂×D₄	—	6	4	no	—
399	C₂×D₄	—	6	2	no	—
400	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	3	1	no	—
403	C₂²×C₄	—	6	2	no	—
404	C₂²×C₄	—	6	2	no	—
405	C₂²×C₄	—	6	2	no	—
406	D₈	—	3	8	no	—
407	D₈	—	3	4	no	—
408	D₈	C₄×C₅×D₃	1	4	yes	complemented
409	M₁₆	—	6	2	no	—
410	C₂×C₈	—	3	1	no	—
411	C₂×C₈	—	3	4	no	—
412	C₂×C₈	—	3	1	no	—
413	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
414	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
415	C₄⋊C₄	—	3	1	no	—
416	C₄⋊C₄	—	3	1	no	—
417	C₄⋊C₄	—	3	2	no	—
418	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	3	1	no	—
421	C₂²⋊C₄	—	3	1	no	—
422	C₂²⋊C₄	—	6	2	no	—
423	C₂²⋊C₄	—	6	2	no	—
424	C₂²⋊C₄	—	6	2	no	—
425	C₂²⋊C₄	—	6	2	no	—
426	C₄²	—	3	1	no	—
427	C₄²	—	6	2	no	—
428	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
429	C₃×C₅	#2948	1	1	yes	characteristic, complemented, Hall
430	C₂²×C₃	—	2	4	no	—
431	C₂²×C₃	—	4	2	no	—
432	C₂²×C₃	—	4	2	no	—
433	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
434	C₂×D₃	—	2	1	no	—
435	C₂×D₃	—	2	1	no	—
436	C₂×D₃	—	2	4	no	—
437	C₂×D₃	—	4	2	no	—
438	C₂×D₃	—	4	2	no	—
439	C₂×D₃	—	8	8	no	—
440	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
441	C₃×C₄	—	2	1	no	—
442	C₃×C₄	—	2	1	no	—
443	C₃×C₄	—	4	2	no	—
444	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
445	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
446	Dic₃	—	2	1	no	—
447	Dic₃	—	2	1	no	—
448	Dic₃	—	4	2	no	—
449	Dic₃	C₄×C₅×D₄	1	2	yes	—
450	C₂×C₅	—	4	4	no	—
451	C₂×C₅	—	6	2	no	—
452	C₂×C₅	—	12	4	no	—
453	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
454	C₂×C₅	#5757	1	1	yes	characteristic
455	C₂×C₅	#5769	1	1	yes	characteristic
456	C₂³	—	2	2	no	—
457	C₂³	—	3	1	no	—
458	C₂³	—	6	8	no	—
459	C₂³	—	6	2	no	—
460	C₂³	—	24	2	no	—
461	C₂³	—	24	2	no	—
462	D₄	—	2	2	no	—
463	D₄	—	3	4	no	—
464	D₄	—	6	8	no	—
465	D₄	—	6	2	no	—
466	D₄	C₂×C₄×C₅×D₃	1	4	yes	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	3	1	no	—
469	C₂×C₄	—	3	2	no	—
470	C₂×C₄	—	3	2	no	—
471	C₂×C₄	—	3	1	no	—
472	C₂×C₄	—	3	1	no	—
473	C₂×C₄	—	6	2	no	—
474	C₂×C₄	—	8	2	no	—
475	C₂×C₄	—	24	2	no	—
476	C₂×C₄	—	24	2	no	—
477	C₂×C₄	—	24	2	no	—
478	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
479	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
480	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
481	C₈	—	2	1	no	—
482	C₈	—	3	2	no	—
483	C₈	—	6	1	no	—
484	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
485	C₂×C₃	—	4	4	no	—
486	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
487	C₂×C₃	C₅×#576	1	1	yes	characteristic
488	C₂×C₃	C₅×#576	1	1	yes	characteristic
489	D₃	—	2	2	no	—
490	D₃	—	4	4	no	—
491	C₅	#79588	1	1	yes	characteristic, direct product factor, Sylow
492	C₂²	—	2	4	no	—
493	C₂²	—	3	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	6	1	no	—
497	C₂²	—	6	1	no	—
498	C₂²	—	6	4	no	—
499	C₂²	—	12	2	no	—
500	C₂²	—	12	2	no	—
501	C₂²	—	24	8	no	—
502	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	3	2	no	—
506	C₄	—	4	2	no	—
507	C₄	—	6	1	no	—
508	C₄	—	6	1	no	—
509	C₄	—	12	2	no	—
510	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
511	C₄	C₅×D₃×#41	1	1	yes	characteristic
512	C₃	C₅×#2948	1	1	yes	characteristic, complemented, Sylow
513	C₂	—	4	4	no	—
514	C₂	—	6	2	no	—
515	C₂	—	12	4	no	—
516	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
517	C₂	C₅×#5757	1	1	yes	characteristic
518	C₂	C₅×#5769	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×D₈	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×D₃×D₈	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₄×C₅×D₈	D₃
hypocenter	C₃	C₅×#2948
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×D₈

Complements

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

N	H ≅ G/N	type
2. C₅×#5545	C₂	semidirect
3. C₃×C₄×C₅×D₈	C₂	semidirect
4. C₅×Dic₃×D₈	C₂	semidirect
5. C₅×#5014	C₂	semidirect
6. C₅×#4880	C₂	semidirect
7. C₅×#4872	C₂	semidirect
8. C₅×#4785	C₂	semidirect
9. C₅×#4770	C₂	semidirect
10. C₄×C₅×D₂₄	C₂	semidirect
11. C₅×#4689	C₂	semidirect
15. C₃×C₄×C₅×D₄	C₂²	semidirect
16. C₅×D₄×Dic₃	C₂²	semidirect
20. C₅×D₃×D₈	C₄	semidirect
24. C₅×#893	C₂²	semidirect
28. C₄×C₅×D₁₂	C₂²	semidirect
30. C₃×C₅×#107	C₂²	semidirect
31. C₃×C₅×#102	C₂²	semidirect
32. C₃×C₄×C₅×C₈	C₂²	semidirect
33. C₅×#832	C₂²	semidirect
34. C₅×#821	C₂²	semidirect
35. C₅×#818	C₂²	semidirect
36. C₅×#815	C₂²	semidirect
37. C₅×C₈×Dic₃	C₂²	semidirect
38. C₅×#809	C₂²	semidirect
39. C₅×#808	C₂²	semidirect
40. C₅×#803	C₂²	semidirect
41. #79588	C₅	direct (N × H)
49. C₄×C₅×D₈	D₃	semidirect
59. C₅×D₃×D₄	C₂×C₄	semidirect
64. C₃×C₅×D₈	C₂×C₄	semidirect
71. C₅×#213	C₂×C₄	semidirect
84. C₅×D₂₄	C₂×C₄	semidirect
86. C₅×D₃×C₈	C₂×C₄	semidirect
88. #5545	C₂×C₅	semidirect
89. C₃×C₄×D₈	C₂×C₅	semidirect
90. Dic₃×D₈	C₂×C₅	semidirect
91. #5014	C₂×C₅	semidirect
92. #4880	C₂×C₅	semidirect
93. #4872	C₂×C₅	semidirect
94. #4785	C₂×C₅	semidirect
95. #4770	C₂×C₅	semidirect
96. C₄×D₂₄	C₂×C₅	semidirect
97. #4689	C₂×C₅	semidirect
110. C₄×C₅×D₄	C₂×D₃	semidirect
116. C₅×#107	C₂×D₃	semidirect
121. C₅×#102	C₂×D₃	semidirect
125. C₄×C₅×C₈	C₂×D₃	semidirect
158. C₃×C₄×D₄	C₂²×C₅	semidirect
159. D₄×Dic₃	C₂²×C₅	semidirect
163. D₃×D₈	C₄×C₅	semidirect
167. #893	C₂²×C₅	semidirect
171. C₄×D₁₂	C₂²×C₅	semidirect
173. C₃×#107	C₂²×C₅	semidirect
174. C₃×#102	C₂²×C₅	semidirect
175. C₃×C₄×C₈	C₂²×C₅	semidirect
176. #832	C₂²×C₅	semidirect
177. #821	C₂²×C₅	semidirect
178. #818	C₂²×C₅	semidirect
179. #815	C₂²×C₅	semidirect
180. C₈×Dic₃	C₂²×C₅	semidirect
181. #809	C₂²×C₅	semidirect
182. #808	C₂²×C₅	semidirect
183. #803	C₂²×C₅	semidirect
197. C₅×D₈	C₄×D₃	semidirect
225. C₄×D₈	C₅×D₃	semidirect
255. D₃×D₄	C₂×C₄×C₅	semidirect
260. C₃×D₈	C₂×C₄×C₅	semidirect
267. #213	C₂×C₄×C₅	semidirect
280. D₂₄	C₂×C₄×C₅	semidirect
282. D₃×C₈	C₂×C₄×C₅	semidirect
324. C₄×D₄	C₂×C₅×D₃	semidirect
330. #107	C₂×C₅×D₃	semidirect
335. #102	C₂×C₅×D₃	semidirect
339. C₄×C₈	C₂×C₅×D₃	semidirect
408. D₈	C₄×C₅×D₃	semidirect
429. C₃×C₅	#2948	semidirect
491. C₅	#79588	direct (N × H)
512. C₃	C₅×#2948	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×D₈	2
C₅×#5545	2
C₃×C₄×C₅×D₈	2
C₅×Dic₃×D₈	2
C₅×#5014	2
C₅×#4880	2
C₅×#4872	2
C₅×#4785	2
C₅×#4770	2
C₄×C₅×D₂₄	2
C₅×#4689	2
C₅×#2948	3
#79588	5

Subgroups — C5×#79588 #14417324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79588 #14417324