Subgroups — C₅×#21996 #11944716

Order 1280.

930 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₅×#1923	C₂	1	2	yes	maximal, complemented
3	C₅×#1916	C₂	1	2	yes	maximal, complemented
4	C₅×#1869	C₂	1	2	yes	maximal
5	C₅×#1850	C₂	1	2	yes	maximal, complemented
6	C₅×#1839	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1831	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1817	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1797	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#336	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₅×C₈	C₂²	1	2	yes	—
13	C₂×C₄×C₅×D₄	C₄	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	C₄	1	1	yes	characteristic
15	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₅×C₂²⋊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×C₄×C₅×C₈	C₂²	1	2	yes	—
24	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
25	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
26	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₄×C₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
28	C₄×C₅×C₂²⋊C₄	C₄	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	C₄³×C₅	C₂²	1	1	yes	characteristic
34	C₅×#336	C₂²	1	1	yes	characteristic
35	C₅×#336	C₂²	1	1	yes	characteristic
36	C₅×#336	C₂²	1	1	yes	characteristic
37	C₅×#336	C₂²	1	1	yes	characteristic
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	#21996	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₅×C₈	—	2	4	no	—
52	C₂²×C₅×C₈	—	4	2	no	—
53	C₂²×C₅×C₈	—	4	2	no	—
54	C₂²×C₅×C₈	C₂³	1	2	yes	—
55	C₂²×C₅×C₈	C₂³	1	2	yes	—
56	C₂²×C₅×C₈	C₂³	1	2	yes	—
57	C₂²×C₅×C₈	C₂³	1	2	yes	—
58	C₄×C₅×D₄	—	2	4	no	—
59	C₄×C₅×D₄	—	2	4	no	—
60	C₄×C₅×D₄	C₈	1	8	yes	complemented
61	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
67	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₅	—	4	2	no	—
71	C₂×C₄²×C₅	—	4	2	no	—
72	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊C₈	—	4	2	no	—
86	C₅×C₄⋊C₈	—	4	2	no	—
87	C₅×C₂²⋊C₈	—	2	4	no	—
88	C₅×C₂²⋊C₈	—	4	2	no	—
89	C₅×C₂²⋊C₈	—	4	2	no	—
90	C₄×C₅×C₈	—	4	2	no	—
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	C₄²×D₄	C₂×C₅	1	1	yes	characteristic
98	#1923	C₂×C₅	1	2	yes	complemented
99	#1916	C₂×C₅	1	2	yes	complemented
100	#1869	C₂×C₅	1	2	yes	—
101	#1850	C₂×C₅	1	2	yes	complemented
102	#1839	C₂×C₅	1	1	yes	characteristic, complemented
103	#1831	C₂×C₅	1	1	yes	characteristic, complemented
104	#1817	C₂×C₅	1	1	yes	characteristic, complemented
105	#1797	C₂×C₅	1	1	yes	characteristic, complemented
106	C₄×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
107	C₂×#336	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₅×D₄	—	2	2	no	—
111	C₂×C₅×D₄	—	2	2	no	—
112	C₂×C₅×D₄	C₂×C₈	1	4	yes	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	2	1	no	—
115	C₂²×C₄×C₅	—	2	1	no	—
116	C₂²×C₄×C₅	—	2	2	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	4	1	no	—
122	C₂²×C₄×C₅	—	4	1	no	—
123	C₂²×C₄×C₅	—	4	1	no	—
124	C₂²×C₄×C₅	—	4	1	no	—
125	C₂²×C₄×C₅	—	4	1	no	—
126	C₂²×C₄×C₅	—	4	1	no	—
127	C₂²×C₄×C₅	—	4	1	no	—
128	C₂²×C₄×C₅	—	4	1	no	—
129	C₂²×C₄×C₅	C₂×C₈	1	4	yes	—
130	C₂²×C₄×C₅	C₂×C₈	1	4	yes	complemented
131	C₂²×C₄×C₅	M₁₆	1	4	yes	—
132	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	#41	1	4	yes	—
145	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
146	C₂×C₅×C₈	—	2	2	no	—
147	C₂×C₅×C₈	—	2	2	no	—
148	C₂×C₅×C₈	—	2	2	no	—
149	C₂×C₅×C₈	—	2	2	no	—
150	C₂×C₅×C₈	—	2	2	no	—
151	C₂×C₅×C₈	—	2	2	no	—
152	C₂×C₅×C₈	—	2	2	no	—
153	C₂×C₅×C₈	—	2	2	no	—
154	C₂×C₅×C₈	—	2	2	no	—
155	C₂×C₅×C₈	—	2	2	no	—
156	C₂×C₅×C₈	—	2	2	no	—
157	C₂×C₅×C₈	—	2	2	no	—
158	C₂×C₅×C₈	—	4	8	no	—
159	C₅×C₄⋊C₄	—	2	2	no	—
160	C₅×C₄⋊C₄	—	2	2	no	—
161	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	complemented
162	C₅×C₂²⋊C₄	—	2	2	no	—
163	C₅×C₂²⋊C₄	—	2	2	no	—
164	C₅×C₂²⋊C₄	—	2	2	no	—
165	C₅×C₂²⋊C₄	—	2	2	no	—
166	C₅×C₂²⋊C₄	C₂×C₈	1	4	yes	—
167	C₅×C₂²⋊C₄	C₂×C₈	1	4	yes	complemented
168	C₄²×C₅	—	2	2	no	—
169	C₄²×C₅	—	2	2	no	—
170	C₄²×C₅	—	2	2	no	—
171	C₄²×C₅	—	2	2	no	—
172	C₄²×C₅	—	2	2	no	—
173	C₄²×C₅	—	2	1	no	—
174	C₄²×C₅	—	2	1	no	—
175	C₄²×C₅	—	4	1	no	—
176	C₄²×C₅	—	4	1	no	—
177	C₄²×C₅	—	4	1	no	—
178	C₄²×C₅	—	4	1	no	—
179	C₄²×C₅	—	4	1	no	—
180	C₄²×C₅	—	4	1	no	—
181	C₄²×C₅	C₂×C₈	1	4	yes	complemented
182	C₂³×C₈	C₂²×C₅	1	2	yes	—
183	C₂×C₄×D₄	C₄×C₅	1	1	yes	characteristic
184	C₂×C₄×D₄	C₄×C₅	1	1	yes	characteristic
185	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
186	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
187	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
188	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
189	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
190	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
191	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
192	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
193	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
194	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
195	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
196	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
197	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
198	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
199	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
200	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
201	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
202	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
203	C₄³	C₂²×C₅	1	1	yes	characteristic
204	#336	C₂²×C₅	1	1	yes	characteristic
205	#336	C₂²×C₅	1	1	yes	characteristic
206	#336	C₂²×C₅	1	1	yes	characteristic
207	#336	C₂²×C₅	1	1	yes	characteristic
208	#336	C₂²×C₅	1	2	yes	—
209	#336	C₂²×C₅	1	2	yes	—
210	#336	C₂²×C₅	1	2	yes	—
211	#336	C₂²×C₅	1	2	yes	—
212	#336	C₂²×C₅	1	2	yes	—
213	C₂³×C₅	—	2	1	no	—
214	C₂³×C₅	—	2	1	no	—
215	C₂³×C₅	—	2	1	no	—
216	C₂³×C₅	—	2	1	no	—
217	C₂³×C₅	—	2	1	no	—
218	C₂³×C₅	—	2	1	no	—
219	C₂³×C₅	—	2	1	no	—
220	C₂³×C₅	—	2	1	no	—
221	C₂³×C₅	—	2	1	no	—
222	C₂³×C₅	—	2	1	no	—
223	C₂³×C₅	#117	1	2	yes	—
224	C₂³×C₅	C₂²×C₈	1	2	yes	—
225	C₂³×C₅	C₂²×C₈	1	2	yes	—
226	C₂³×C₅	C₂×M₁₆	1	2	yes	—
227	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
228	C₅×D₄	—	2	8	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	4	no	—
246	C₂×C₄×C₅	—	2	4	no	—
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	2	1	no	—
249	C₂×C₄×C₅	—	2	1	no	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	2	1	no	—
252	C₂×C₄×C₅	—	2	1	no	—
253	C₂×C₄×C₅	—	2	1	no	—
254	C₂×C₄×C₅	—	2	1	no	—
255	C₂×C₄×C₅	—	2	1	no	—
256	C₂×C₄×C₅	—	2	1	no	—
257	C₂×C₄×C₅	—	2	1	no	—
258	C₂×C₄×C₅	—	2	1	no	—
259	C₂×C₄×C₅	—	4	4	no	—
260	C₂×C₄×C₅	—	4	4	no	—
261	C₂×C₄×C₅	—	4	4	no	—
262	C₂×C₄×C₅	—	4	4	no	—
263	C₂×C₄×C₅	—	4	2	no	—
264	C₂×C₄×C₅	—	4	2	no	—
265	C₂×C₄×C₅	#117	1	2	yes	—
266	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
267	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
268	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
269	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
270	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
271	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
272	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
273	C₂×C₄×C₅	C₂×#41	1	2	yes	—
274	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
275	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
276	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
277	C₅×C₈	—	4	2	no	—
278	C₅×C₈	—	4	2	no	—
279	C₅×C₈	—	4	2	no	—
280	C₅×C₈	—	4	2	no	—
281	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
282	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
283	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
284	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
285	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
287	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
288	C₂²×C₈	—	2	4	no	—
289	C₂²×C₈	—	4	2	no	—
290	C₂²×C₈	—	4	2	no	—
291	C₂²×C₈	C₂³×C₅	1	2	yes	—
292	C₂²×C₈	C₂³×C₅	1	2	yes	—
293	C₂²×C₈	C₂³×C₅	1	2	yes	—
294	C₂²×C₈	C₂³×C₅	1	2	yes	—
295	C₄×D₄	—	2	4	no	—
296	C₄×D₄	—	2	4	no	—
297	C₄×D₄	C₅×C₈	1	8	yes	complemented
298	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
307	C₂×C₄²	—	4	2	no	—
308	C₂×C₄²	—	4	2	no	—
309	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
310	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
311	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
312	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
313	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
314	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
315	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
316	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
318	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
322	C₄⋊C₈	—	4	2	no	—
323	C₄⋊C₈	—	4	2	no	—
324	C₂²⋊C₈	—	2	4	no	—
325	C₂²⋊C₈	—	4	2	no	—
326	C₂²⋊C₈	—	4	2	no	—
327	C₄×C₈	—	4	2	no	—
328	#95	C₂×C₄×C₅	1	1	yes	characteristic
329	#95	C₂×C₄×C₅	1	1	yes	characteristic
330	#95	C₂×C₄×C₅	1	1	yes	characteristic
331	#95	C₂×C₄×C₅	1	1	yes	characteristic
332	#95	C₂×C₄×C₅	1	1	yes	characteristic
333	#95	C₂×C₄×C₅	1	1	yes	characteristic
334	C₂²×C₅	—	2	2	no	—
335	C₂²×C₅	—	2	2	no	—
336	C₂²×C₅	—	2	2	no	—
337	C₂²×C₅	—	2	2	no	—
338	C₂²×C₅	—	2	2	no	—
339	C₂²×C₅	—	2	2	no	—
340	C₂²×C₅	—	2	2	no	—
341	C₂²×C₅	—	2	2	no	—
342	C₂²×C₅	—	2	2	no	—
343	C₂²×C₅	—	4	1	no	—
344	C₂²×C₅	—	4	1	no	—
345	C₂²×C₅	—	4	1	no	—
346	C₂²×C₅	—	4	1	no	—
347	C₂²×C₅	#431	1	4	yes	—
348	C₂²×C₅	C₂×#117	1	1	yes	characteristic
349	C₂²×C₅	#518	1	1	yes	characteristic
350	C₂²×C₅	#520	1	1	yes	characteristic
351	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
352	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
353	C₂²×C₅	#568	1	1	yes	characteristic
354	C₂²×C₅	#568	1	1	yes	characteristic
355	C₄×C₅	—	2	2	no	—
356	C₄×C₅	—	2	2	no	—
357	C₄×C₅	—	2	2	no	—
358	C₄×C₅	—	2	2	no	—
359	C₄×C₅	—	2	2	no	—
360	C₄×C₅	—	2	2	no	—
361	C₄×C₅	—	2	2	no	—
362	C₄×C₅	—	2	2	no	—
363	C₄×C₅	—	4	1	no	—
364	C₄×C₅	—	4	1	no	—
365	C₄×C₅	—	4	1	no	—
366	C₄×C₅	—	4	1	no	—
367	C₄×C₅	#538	1	2	yes	—
368	C₄×C₅	#539	1	2	yes	—
369	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
370	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	C₂×C₅×C₈	1	4	yes	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	—	4	1	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	—	4	1	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	C₂×C₅×C₈	1	4	yes	—
391	C₂²×C₄	C₂×C₅×C₈	1	4	yes	complemented
392	C₂²×C₄	C₅×M₁₆	1	4	yes	—
393	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
394	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
395	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
396	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
397	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
398	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
399	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
400	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
401	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
402	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
403	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
404	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
405	C₂²×C₄	C₅×#41	1	4	yes	—
406	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	4	8	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	complemented
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	C₂×C₅×C₈	1	4	yes	—
428	C₂²⋊C₄	C₂×C₅×C₈	1	4	yes	complemented
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	2	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	4	1	no	—
437	C₄²	—	4	1	no	—
438	C₄²	—	4	1	no	—
439	C₄²	—	4	1	no	—
440	C₄²	—	4	1	no	—
441	C₄²	—	4	1	no	—
442	C₄²	C₂×C₅×C₈	1	4	yes	complemented
443	C₂×C₅	—	2	4	no	—
444	C₂×C₅	—	4	2	no	—
445	C₂×C₅	#2318	1	1	yes	characteristic
446	C₂×C₅	C₂×#431	1	1	yes	characteristic
447	C₂×C₅	#2923	1	1	yes	characteristic
448	C₂×C₅	#2972	1	1	yes	characteristic
449	C₂×C₅	#2973	1	1	yes	characteristic
450	C₂×C₅	#2988	1	1	yes	characteristic
451	C₂×C₅	#2989	1	1	yes	characteristic
452	C₂³	—	2	1	no	—
453	C₂³	—	2	1	no	—
454	C₂³	—	2	1	no	—
455	C₂³	—	2	1	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	C₅×#117	1	2	yes	—
463	C₂³	C₂²×C₅×C₈	1	2	yes	—
464	C₂³	C₂²×C₅×C₈	1	2	yes	—
465	C₂³	C₂×C₅×M₁₆	1	2	yes	—
466	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
467	D₄	—	2	8	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	4	4	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	—	4	4	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	C₅×#117	1	2	yes	—
505	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
506	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
507	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
508	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
509	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
510	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
511	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
512	C₂×C₄	C₂×C₅×#41	1	2	yes	—
513	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
515	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
516	C₈	—	4	2	no	—
517	C₈	—	4	2	no	—
518	C₈	—	4	2	no	—
519	C₈	—	4	2	no	—
520	C₅	#21996	1	1	yes	characteristic, direct product factor, Sylow
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	C₅×#431	1	4	yes	—
535	C₂²	C₂×C₅×#117	1	1	yes	characteristic
536	C₂²	C₅×#518	1	1	yes	characteristic
537	C₂²	C₅×#520	1	1	yes	characteristic
538	C₂²	C₂³×C₅×C₈	1	1	yes	characteristic
539	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
540	C₂²	C₅×#568	1	1	yes	characteristic
541	C₂²	C₅×#568	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	2	no	—
546	C₄	—	2	2	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	C₅×#538	1	2	yes	—
555	C₄	C₅×#539	1	2	yes	—
556	C₂	—	2	4	no	—
557	C₂	—	4	2	no	—
558	C₂	C₅×#2318	1	1	yes	characteristic
559	C₂	C₂×C₅×#431	1	1	yes	characteristic
560	C₂	C₅×#2923	1	1	yes	characteristic
561	C₂	C₅×#2972	1	1	yes	characteristic
562	C₂	C₅×#2973	1	1	yes	characteristic
563	C₂	C₅×#2988	1	1	yes	characteristic
564	C₂	C₅×#2989	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂²	C₂³×C₅×C₈
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂²×C₅×D₄	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#1923	C₂	semidirect
3. C₅×#1916	C₂	semidirect
5. C₅×#1850	C₂	semidirect
6. C₅×#1839	C₂	semidirect
7. C₅×#1831	C₂	semidirect
8. C₅×#1817	C₂	semidirect
9. C₅×#1797	C₂	semidirect
10. C₄×C₅×C₂²⋊C₈	C₂	semidirect
11. C₂×C₅×#336	C₂	semidirect
43. #21996	C₅	direct (N × H)
60. C₄×C₅×D₄	C₈	semidirect
98. #1923	C₂×C₅	semidirect
99. #1916	C₂×C₅	semidirect
101. #1850	C₂×C₅	semidirect
102. #1839	C₂×C₅	semidirect
103. #1831	C₂×C₅	semidirect
104. #1817	C₂×C₅	semidirect
105. #1797	C₂×C₅	semidirect
106. C₄×C₂²⋊C₈	C₂×C₅	semidirect
107. C₂×#336	C₂×C₅	semidirect
130. C₂²×C₄×C₅	C₂×C₈	semidirect
161. C₅×C₄⋊C₄	C₂×C₈	semidirect
167. C₅×C₂²⋊C₄	C₂×C₈	semidirect
181. C₄²×C₅	C₂×C₈	semidirect
297. C₄×D₄	C₅×C₈	semidirect
391. C₂²×C₄	C₂×C₅×C₈	semidirect
422. C₄⋊C₄	C₂×C₅×C₈	semidirect
428. C₂²⋊C₄	C₂×C₅×C₈	semidirect
442. C₄²	C₂×C₅×C₈	semidirect
520. C₅	#21996	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×C₅×D₄	2
C₅×#1923	2
C₅×#1916	2
C₅×#1869	2
C₅×#1850	2
C₅×#1839	2
C₅×#1831	2
C₅×#1817	2
C₅×#1797	2
C₄×C₅×C₂²⋊C₈	2
C₂×C₅×#336	2
#21996	5

Subgroups — C5×#21996 #11944716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21996 #11944716