Subgroups — C₅×#21924 #11944644

Order 1280.

770 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic
2	C₅×#1924	C₂	1	2	yes	maximal
3	C₅×#1923	C₂	1	2	yes	maximal
4	C₅×#1917	C₂	1	2	yes	maximal, complemented
5	C₅×#1916	C₂	1	2	yes	maximal, complemented
6	C₅×#1842	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1831	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1797	C₂	1	1	yes	maximal, characteristic
9	C₅×#1797	C₂	1	1	yes	maximal, characteristic
10	C₅×#1767	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#117	C₄	1	1	yes	characteristic
13	C₂×C₅×#117	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₅×#97	C₂²	1	2	yes	—
24	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
25	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
26	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
27	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
30	C₄×C₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
31	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₅×#376	C₄	1	1	yes	characteristic
34	C₅×#376	C₄	1	1	yes	characteristic
35	C₄³×C₅	C₂²	1	1	yes	characteristic
36	C₄³×C₅	C₂²	1	1	yes	characteristic
37	C₅×#336	C₂²	1	2	yes	—
38	C₅×#336	C₂²	1	2	yes	—
39	C₅×#336	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	2	yes	—
42	C₅×#336	C₂²	1	2	yes	—
43	#21924	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₂³	1	2	yes	—
48	C₂²×C₅×C₈	C₂³	1	2	yes	—
49	C₂²×C₅×C₈	C₂³	1	2	yes	—
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₅×#117	—	2	4	no	—
52	C₅×#117	—	2	4	no	—
53	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₅	—	2	2	no	—
62	C₂×C₄²×C₅	—	2	2	no	—
63	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₅×C₄⋊C₈	—	2	2	no	—
80	C₅×C₄⋊C₈	—	2	2	no	—
81	C₅×C₄⋊C₈	—	2	2	no	—
82	C₅×C₄⋊C₈	—	2	2	no	—
83	C₅×C₄⋊C₈	—	4	2	no	—
84	C₅×C₄⋊C₈	—	4	2	no	—
85	C₅×C₂²⋊C₈	—	4	2	no	—
86	C₅×C₂²⋊C₈	—	4	2	no	—
87	C₅×#97	—	4	2	no	—
88	C₄×C₅×C₈	—	4	2	no	—
89	C₅×#95	C₂×C₄	1	1	yes	characteristic
90	C₅×#95	C₂×C₄	1	1	yes	characteristic
91	C₅×#95	C₂×C₄	1	1	yes	characteristic
92	C₅×#95	C₂×C₄	1	1	yes	characteristic
93	C₅×#95	C₂×C₄	1	1	yes	characteristic
94	C₅×#95	C₂×C₄	1	1	yes	characteristic
95	C₅×#95	C₂×C₄	1	1	yes	characteristic
96	C₅×#95	C₂×C₄	1	1	yes	characteristic
97	C₄×#117	C₂×C₅	1	1	yes	characteristic
98	#1924	C₂×C₅	1	2	yes	—
99	#1923	C₂×C₅	1	2	yes	—
100	#1917	C₂×C₅	1	2	yes	complemented
101	#1916	C₂×C₅	1	2	yes	complemented
102	#1842	C₂×C₅	1	1	yes	characteristic, complemented
103	#1831	C₂×C₅	1	1	yes	characteristic, complemented
104	#1797	C₂×C₅	1	1	yes	characteristic
105	#1797	C₂×C₅	1	1	yes	characteristic
106	#1767	C₂×C₅	1	1	yes	characteristic, complemented
107	C₄×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	—	2	2	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	2	2	no	—
115	C₂²×C₄×C₅	—	2	1	no	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	1	no	—
118	C₂²×C₄×C₅	—	2	1	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	2	2	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	—	2	2	no	—
146	C₂×C₅×C₈	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	2	no	—
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	M₁₆	1	4	yes	—
151	C₅×C₂²⋊C₄	—	2	2	no	—
152	C₅×C₂²⋊C₄	—	2	2	no	—
153	C₅×C₂²⋊C₄	—	2	2	no	—
154	C₅×C₂²⋊C₄	M₁₆	1	4	yes	—
155	C₄²×C₅	—	2	2	no	—
156	C₄²×C₅	—	2	2	no	—
157	C₄²×C₅	—	2	2	no	—
158	C₄²×C₅	—	2	2	no	—
159	C₄²×C₅	—	2	2	no	—
160	C₄²×C₅	—	2	2	no	—
161	C₄²×C₅	—	2	2	no	—
162	C₄²×C₅	—	2	2	no	—
163	C₄²×C₅	—	2	2	no	—
164	C₄²×C₅	—	2	2	no	—
165	C₄²×C₅	—	2	1	no	—
166	C₄²×C₅	—	2	1	no	—
167	C₄²×C₅	—	2	1	no	—
168	C₄²×C₅	—	2	1	no	—
169	C₄²×C₅	—	2	1	no	—
170	C₄²×C₅	—	2	1	no	—
171	C₄²×C₅	—	2	1	no	—
172	C₄²×C₅	—	2	1	no	—
173	C₄²×C₅	—	2	1	no	—
174	C₄²×C₅	—	2	1	no	—
175	C₄²×C₅	#41	1	2	yes	—
176	C₄²×C₅	#41	1	2	yes	—
177	C₂×#117	C₄×C₅	1	1	yes	characteristic
178	C₂×#117	C₄×C₅	1	1	yes	characteristic
179	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
180	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
181	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
182	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
184	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
185	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
186	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
187	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
188	C₂×#97	C₂²×C₅	1	2	yes	—
189	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
190	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
191	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
192	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
193	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
194	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
195	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
196	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
197	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
198	#376	C₄×C₅	1	1	yes	characteristic
199	#376	C₄×C₅	1	1	yes	characteristic
200	C₄³	C₂²×C₅	1	1	yes	characteristic
201	C₄³	C₂²×C₅	1	1	yes	characteristic
202	#336	C₂²×C₅	1	2	yes	—
203	#336	C₂²×C₅	1	2	yes	—
204	#336	C₂²×C₅	1	2	yes	—
205	#336	C₂²×C₅	1	2	yes	—
206	#336	C₂²×C₅	1	2	yes	—
207	#336	C₂²×C₅	1	2	yes	—
208	C₂³×C₅	—	2	1	no	—
209	C₂³×C₅	—	2	1	no	—
210	C₂³×C₅	—	2	1	no	—
211	C₂³×C₅	—	2	1	no	—
212	C₂³×C₅	—	2	1	no	—
213	C₂³×C₅	—	2	1	no	—
214	C₂³×C₅	C₂×M₁₆	1	2	yes	—
215	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₅	—	2	8	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	2	1	no	—
241	C₂×C₄×C₅	—	2	1	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	2	1	no	—
244	C₂×C₄×C₅	—	2	1	no	—
245	C₂×C₄×C₅	—	2	1	no	—
246	C₂×C₄×C₅	—	2	1	no	—
247	C₂×C₄×C₅	—	4	1	no	—
248	C₂×C₄×C₅	—	4	1	no	—
249	C₂×C₄×C₅	—	4	1	no	—
250	C₂×C₄×C₅	—	4	1	no	—
251	C₂×C₄×C₅	—	4	4	no	—
252	C₂×C₄×C₅	#117	1	2	yes	—
253	C₂×C₄×C₅	#117	1	2	yes	—
254	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
255	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
256	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
257	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
258	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
259	C₂×C₄×C₅	#131	1	2	yes	—
260	C₂×C₄×C₅	#131	1	2	yes	—
261	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
264	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
265	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
266	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
267	C₅×C₈	—	4	2	no	—
268	C₅×C₈	—	4	2	no	—
269	C₅×C₈	—	4	2	no	—
270	C₅×C₈	—	4	2	no	—
271	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
272	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
273	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₅	1	2	yes	—
275	C₂²×C₈	C₂³×C₅	1	2	yes	—
276	C₂²×C₈	C₂³×C₅	1	2	yes	—
277	C₂²×C₈	C₂³×C₅	1	2	yes	—
278	#117	—	2	4	no	—
279	#117	—	2	4	no	—
280	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
287	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
291	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
292	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
293	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
294	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
295	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
296	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
297	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
298	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
299	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	2	2	no	—
308	C₄⋊C₈	—	2	2	no	—
309	C₄⋊C₈	—	2	2	no	—
310	C₄⋊C₈	—	4	2	no	—
311	C₄⋊C₈	—	4	2	no	—
312	C₂²⋊C₈	—	4	2	no	—
313	C₂²⋊C₈	—	4	2	no	—
314	#97	—	4	2	no	—
315	C₄×C₈	—	4	2	no	—
316	#95	C₂×C₄×C₅	1	1	yes	characteristic
317	#95	C₂×C₄×C₅	1	1	yes	characteristic
318	#95	C₂×C₄×C₅	1	1	yes	characteristic
319	#95	C₂×C₄×C₅	1	1	yes	characteristic
320	#95	C₂×C₄×C₅	1	1	yes	characteristic
321	#95	C₂×C₄×C₅	1	1	yes	characteristic
322	#95	C₂×C₄×C₅	1	1	yes	characteristic
323	#95	C₂×C₄×C₅	1	1	yes	characteristic
324	C₂²×C₅	—	2	2	no	—
325	C₂²×C₅	—	2	2	no	—
326	C₂²×C₅	—	2	2	no	—
327	C₂²×C₅	—	4	1	no	—
328	C₂²×C₅	—	4	1	no	—
329	C₂²×C₅	—	4	1	no	—
330	C₂²×C₅	—	4	1	no	—
331	C₂²×C₅	C₂×#117	1	1	yes	characteristic
332	C₂²×C₅	#520	1	1	yes	characteristic
333	C₂²×C₅	#520	1	1	yes	characteristic
334	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
335	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
336	C₂²×C₅	C₂×#131	1	1	yes	characteristic
337	C₂²×C₅	C₂×#131	1	1	yes	characteristic
338	C₄×C₅	—	2	2	no	—
339	C₄×C₅	—	2	2	no	—
340	C₄×C₅	—	2	2	no	—
341	C₄×C₅	—	2	2	no	—
342	C₄×C₅	—	2	2	no	—
343	C₄×C₅	—	2	2	no	—
344	C₄×C₅	—	4	1	no	—
345	C₄×C₅	—	4	1	no	—
346	C₄×C₅	—	4	1	no	—
347	C₄×C₅	—	4	1	no	—
348	C₄×C₅	—	4	1	no	—
349	C₄×C₅	—	4	1	no	—
350	C₄×C₅	#433	1	4	yes	—
351	C₄×C₅	#540	1	1	yes	characteristic
352	C₄×C₅	#541	1	1	yes	characteristic
353	C₄×C₅	#542	1	1	yes	characteristic
354	C₄×C₅	#542	1	1	yes	characteristic
355	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
369	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
370	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
371	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
372	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
374	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
375	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
376	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
377	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
378	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
379	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
380	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
381	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	C₅×M₁₆	1	4	yes	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	C₅×M₁₆	1	4	yes	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	1	no	—
413	C₄²	—	2	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	1	no	—
422	C₄²	C₅×#41	1	2	yes	—
423	C₄²	C₅×#41	1	2	yes	—
424	C₂×C₅	—	4	2	no	—
425	C₂×C₅	#2314	1	1	yes	characteristic
426	C₂×C₅	C₂×#433	1	1	yes	characteristic
427	C₂×C₅	#2920	1	1	yes	characteristic
428	C₂×C₅	#2990	1	1	yes	characteristic
429	C₂×C₅	#2990	1	1	yes	characteristic
430	C₂×C₅	#2990	1	1	yes	characteristic
431	C₂×C₅	#2991	1	1	yes	characteristic
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	C₂×C₅×M₁₆	1	2	yes	—
439	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	C₅×#117	1	2	yes	—
477	C₂×C₄	C₅×#117	1	2	yes	—
478	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
479	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
480	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
481	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
482	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
483	C₂×C₄	C₅×#131	1	2	yes	—
484	C₂×C₄	C₅×#131	1	2	yes	—
485	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
486	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
487	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
488	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
489	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
490	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
491	C₈	—	4	2	no	—
492	C₈	—	4	2	no	—
493	C₈	—	4	2	no	—
494	C₈	—	4	2	no	—
495	C₅	#21924	1	1	yes	characteristic, direct product factor, Sylow
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	1	no	—
503	C₂²	C₂×C₅×#117	1	1	yes	characteristic
504	C₂²	C₅×#520	1	1	yes	characteristic
505	C₂²	C₅×#520	1	1	yes	characteristic
506	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
507	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
508	C₂²	C₂×C₅×#131	1	1	yes	characteristic
509	C₂²	C₂×C₅×#131	1	1	yes	characteristic
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	2	2	no	—
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	1	no	—
522	C₄	C₅×#433	1	4	yes	—
523	C₄	C₅×#540	1	1	yes	characteristic
524	C₄	C₅×#541	1	1	yes	characteristic
525	C₄	C₅×#542	1	1	yes	characteristic
526	C₄	C₅×#542	1	1	yes	characteristic
527	C₂	—	4	2	no	—
528	C₂	C₅×#2314	1	1	yes	characteristic
529	C₂	C₂×C₅×#433	1	1	yes	characteristic
530	C₂	C₅×#2920	1	1	yes	characteristic
531	C₂	C₅×#2990	1	1	yes	characteristic
532	C₂	C₅×#2990	1	1	yes	characteristic
533	C₂	C₅×#2990	1	1	yes	characteristic
534	C₂	C₅×#2991	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂⁴×C₅	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1917	C₂	semidirect
5. C₅×#1916	C₂	semidirect
6. C₅×#1842	C₂	semidirect
7. C₅×#1831	C₂	semidirect
10. C₅×#1767	C₂	semidirect
11. C₄×C₅×C₄⋊C₈	C₂	semidirect
43. #21924	C₅	direct (N × H)
100. #1917	C₂×C₅	semidirect
101. #1916	C₂×C₅	semidirect
102. #1842	C₂×C₅	semidirect
103. #1831	C₂×C₅	semidirect
106. #1767	C₂×C₅	semidirect
107. C₄×C₄⋊C₈	C₂×C₅	semidirect
495. C₅	#21924	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×#117	2
C₅×#1924	2
C₅×#1923	2
C₅×#1917	2
C₅×#1916	2
C₅×#1842	2
C₅×#1831	2
C₅×#1797	2
C₅×#1767	2
C₄×C₅×C₄⋊C₈	2
#21924	5

Subgroups — C5×#21924 #11944644

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21924 #11944644