Subgroups — C₅×#22647 #11945367

Order 1280.

1028 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#435	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2290	C₂	1	1	yes	maximal, characteristic
6	C₅×#1940	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1851	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1850	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1850	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1850	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1843	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1798	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1797	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1768	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
19	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₅×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₅×#435	—	2	4	no	—
24	C₅×C₈×D₄	—	2	4	no	—
25	C₅×#424	—	2	4	no	—
26	C₂×C₅×C₄⋊C₈	—	2	4	no	—
27	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₅×#97	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
45	C₅×#388	C₄	1	1	yes	characteristic
46	C₅×#388	C₄	1	1	yes	characteristic
47	C₅×#387	C₄	1	1	yes	characteristic
48	C₅×#387	C₄	1	1	yes	characteristic
49	C₅×#386	C₄	1	1	yes	characteristic
50	C₅×#386	C₄	1	1	yes	characteristic
51	C₅×#385	C₄	1	1	yes	characteristic
52	C₅×#385	C₄	1	1	yes	characteristic
53	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
55	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
56	C₅×#376	C₂²	1	1	yes	characteristic
57	C₅×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	C₅×#336	C₂²	1	1	yes	characteristic
60	C₅×#336	C₂²	1	1	yes	characteristic
61	C₅×#336	C₂²	1	1	yes	characteristic
62	C₅×#336	C₂²	1	1	yes	characteristic
63	#22647	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
67	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₅×M₁₆	—	2	2	no	—
70	C₂×C₅×M₁₆	—	2	2	no	—
71	C₂×C₅×M₁₆	—	4	1	no	—
72	C₂²×C₅×C₈	—	2	2	no	—
73	C₂²×C₅×C₈	—	2	2	no	—
74	C₂²×C₅×C₈	—	2	2	no	—
75	C₂²×C₅×C₈	—	2	2	no	—
76	C₂²×C₅×C₈	—	2	2	no	—
77	C₂²×C₅×C₈	—	2	2	no	—
78	C₂²×C₅×C₈	—	4	1	no	—
79	C₂²×C₅×C₈	—	4	1	no	—
80	C₂²×C₅×C₈	—	4	1	no	—
81	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
87	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
88	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₄×C₅×D₄	D₄	1	4	yes	—
90	C₄×C₅×D₄	Q₈	1	4	yes	—
91	C₅×#117	—	2	2	no	—
92	C₅×#117	—	2	2	no	—
93	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₅	—	2	2	no	—
107	C₂×C₄²×C₅	—	2	2	no	—
108	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
115	C₅×C₄⋊C₈	—	2	2	no	—
116	C₅×C₄⋊C₈	—	2	2	no	—
117	C₅×C₄⋊C₈	—	2	2	no	—
118	C₅×C₄⋊C₈	—	2	2	no	—
119	C₅×C₄⋊C₈	—	2	2	no	—
120	C₅×C₄⋊C₈	—	2	2	no	—
121	C₅×C₄⋊C₈	—	2	2	no	—
122	C₅×C₄⋊C₈	—	2	2	no	—
123	C₅×C₄⋊C₈	—	2	2	no	—
124	C₅×C₄⋊C₈	—	4	1	no	—
125	C₅×C₄⋊C₈	—	4	1	no	—
126	C₅×C₄⋊C₈	D₄	1	4	yes	complemented
127	C₅×C₂²⋊C₈	—	2	2	no	—
128	C₅×C₂²⋊C₈	—	2	2	no	—
129	C₅×C₂²⋊C₈	—	2	2	no	—
130	C₅×C₂²⋊C₈	—	2	2	no	—
131	C₅×#97	—	2	2	no	—
132	C₄×C₅×C₈	—	2	2	no	—
133	C₅×#95	C₂×C₄	1	1	yes	characteristic
134	C₅×#95	C₂×C₄	1	1	yes	characteristic
135	C₅×#95	C₂×C₄	1	1	yes	characteristic
136	C₅×#95	C₂×C₄	1	1	yes	characteristic
137	C₅×#95	C₂×C₄	1	1	yes	characteristic
138	C₅×#95	C₂×C₄	1	1	yes	characteristic
139	C₅×#95	C₂×C₄	1	1	yes	characteristic
140	C₅×#95	C₂×C₄	1	1	yes	characteristic
141	C₅×#95	C₂×C₄	1	1	yes	characteristic
142	C₅×#95	C₂×C₄	1	1	yes	characteristic
143	C₂×#435	C₂×C₅	1	1	yes	characteristic
144	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic
145	C₂×#424	C₂×C₅	1	1	yes	characteristic, complemented
146	C₂²×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
147	#2290	C₂×C₅	1	1	yes	characteristic
148	#1940	C₂×C₅	1	1	yes	characteristic, complemented
149	#1939	C₂×C₅	1	1	yes	characteristic, complemented
150	#1851	C₂×C₅	1	1	yes	characteristic, complemented
151	#1850	C₂×C₅	1	1	yes	characteristic, complemented
152	#1850	C₂×C₅	1	1	yes	characteristic, complemented
153	#1850	C₂×C₅	1	1	yes	characteristic, complemented
154	#1843	C₂×C₅	1	1	yes	characteristic, complemented
155	#1798	C₂×C₅	1	1	yes	characteristic, complemented
156	#1797	C₂×C₅	1	1	yes	characteristic, complemented
157	#1768	C₂×C₅	1	1	yes	characteristic, complemented
158	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
159	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₅×D₄	—	2	2	no	—
161	C₂×C₅×D₄	—	2	2	no	—
162	C₂×C₅×D₄	C₄⋊C₄	1	4	yes	—
163	C₂²×C₄×C₅	—	2	2	no	—
164	C₂²×C₄×C₅	—	2	2	no	—
165	C₂²×C₄×C₅	—	2	2	no	—
166	C₂²×C₄×C₅	—	2	1	no	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	—	2	1	no	—
169	C₂²×C₄×C₅	—	2	1	no	—
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	—	2	1	no	—
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	—	2	2	no	—
175	C₂²×C₄×C₅	—	2	2	no	—
176	C₂²×C₄×C₅	—	4	1	no	—
177	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
190	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
192	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
193	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
194	C₅×M₁₆	—	4	4	no	—
195	C₂×C₅×C₈	—	2	1	no	—
196	C₂×C₅×C₈	—	2	1	no	—
197	C₂×C₅×C₈	—	2	1	no	—
198	C₂×C₅×C₈	—	2	1	no	—
199	C₂×C₅×C₈	—	2	1	no	—
200	C₂×C₅×C₈	—	2	1	no	—
201	C₂×C₅×C₈	—	2	1	no	—
202	C₂×C₅×C₈	—	2	1	no	—
203	C₂×C₅×C₈	—	2	1	no	—
204	C₂×C₅×C₈	—	2	1	no	—
205	C₂×C₅×C₈	—	2	1	no	—
206	C₂×C₅×C₈	—	2	1	no	—
207	C₂×C₅×C₈	—	2	1	no	—
208	C₂×C₅×C₈	—	2	1	no	—
209	C₂×C₅×C₈	—	2	1	no	—
210	C₂×C₅×C₈	—	2	1	no	—
211	C₂×C₅×C₈	—	2	1	no	—
212	C₂×C₅×C₈	—	2	1	no	—
213	C₂×C₅×C₈	—	2	1	no	—
214	C₂×C₅×C₈	—	2	1	no	—
215	C₂×C₅×C₈	—	2	1	no	—
216	C₂×C₅×C₈	—	2	1	no	—
217	C₂×C₅×C₈	—	4	4	no	—
218	C₂×C₅×C₈	—	4	4	no	—
219	C₂×C₅×C₈	—	4	4	no	—
220	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
221	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
222	C₅×C₄⋊C₄	—	2	2	no	—
223	C₅×C₄⋊C₄	—	2	2	no	—
224	C₅×C₄⋊C₄	—	2	2	no	—
225	C₅×C₄⋊C₄	—	4	1	no	—
226	C₅×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
227	C₅×C₂²⋊C₄	—	2	2	no	—
228	C₅×C₂²⋊C₄	—	2	2	no	—
229	C₅×C₂²⋊C₄	—	2	2	no	—
230	C₅×C₂²⋊C₄	—	2	2	no	—
231	C₅×C₂²⋊C₄	—	2	2	no	—
232	C₅×C₂²⋊C₄	—	4	1	no	—
233	C₅×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
234	C₅×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
235	C₄²×C₅	—	2	2	no	—
236	C₄²×C₅	—	2	2	no	—
237	C₄²×C₅	—	2	1	no	—
238	C₄²×C₅	—	2	1	no	—
239	C₄²×C₅	—	2	1	no	—
240	C₄²×C₅	—	2	1	no	—
241	C₄²×C₅	—	2	1	no	—
242	C₄²×C₅	—	2	1	no	—
243	C₄²×C₅	C₂×D₄	1	2	yes	—
244	C₄²×C₅	C₂×D₄	1	2	yes	—
245	C₄²×C₅	C₂×Q₈	1	2	yes	—
246	C₄²×C₅	#41	1	2	yes	—
247	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
248	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
249	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
250	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
251	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
252	C₂×#117	C₂²×C₅	1	1	yes	characteristic
253	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
254	#435	—	2	4	no	—
255	C₈×D₄	—	2	4	no	—
256	#424	—	2	4	no	—
257	C₂×C₄⋊C₈	—	2	4	no	—
258	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
266	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
270	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
271	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
272	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
273	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
274	C₂×#97	C₂²×C₅	1	1	yes	characteristic
275	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
276	#388	C₄×C₅	1	1	yes	characteristic
277	#388	C₄×C₅	1	1	yes	characteristic
278	#387	C₄×C₅	1	1	yes	characteristic
279	#387	C₄×C₅	1	1	yes	characteristic
280	#386	C₄×C₅	1	1	yes	characteristic
281	#386	C₄×C₅	1	1	yes	characteristic
282	#385	C₄×C₅	1	1	yes	characteristic
283	#385	C₄×C₅	1	1	yes	characteristic
284	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
285	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
286	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
287	#376	C₂²×C₅	1	1	yes	characteristic
288	#336	C₂²×C₅	1	1	yes	characteristic
289	#336	C₂²×C₅	1	1	yes	characteristic
290	#336	C₂²×C₅	1	1	yes	characteristic
291	#336	C₂²×C₅	1	1	yes	characteristic
292	#336	C₂²×C₅	1	1	yes	characteristic
293	#336	C₂²×C₅	1	1	yes	characteristic
294	C₂³×C₅	—	2	1	no	—
295	C₂³×C₅	—	2	1	no	—
296	C₂³×C₅	—	2	1	no	—
297	C₂³×C₅	—	2	1	no	—
298	C₂³×C₅	—	2	1	no	—
299	C₂³×C₅	—	2	1	no	—
300	C₂³×C₅	—	2	1	no	—
301	C₂³×C₅	—	2	1	no	—
302	C₂³×C₅	—	2	1	no	—
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
305	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
306	C₂³×C₅	#131	1	2	yes	—
307	C₂³×C₅	#131	1	2	yes	—
308	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
309	C₅×D₄	—	2	8	no	—
310	C₂×C₄×C₅	—	2	8	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	1	no	—
325	C₂×C₄×C₅	—	2	2	no	—
326	C₂×C₄×C₅	—	2	2	no	—
327	C₂×C₄×C₅	—	2	2	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	—	2	2	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	2	2	no	—
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	2	1	no	—
336	C₂×C₄×C₅	—	2	1	no	—
337	C₂×C₄×C₅	—	2	1	no	—
338	C₂×C₄×C₅	—	2	1	no	—
339	C₂×C₄×C₅	—	2	1	no	—
340	C₂×C₄×C₅	—	2	1	no	—
341	C₂×C₄×C₅	—	2	1	no	—
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	2	1	no	—
344	C₂×C₄×C₅	—	2	1	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	1	no	—
347	C₂×C₄×C₅	—	2	1	no	—
348	C₂×C₄×C₅	—	4	4	no	—
349	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
350	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
351	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
352	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
353	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
354	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
355	C₂×C₄×C₅	#131	1	2	yes	—
356	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
359	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
360	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
362	C₅×C₈	—	2	2	no	—
363	C₅×C₈	—	2	2	no	—
364	C₅×C₈	—	4	1	no	—
365	C₅×C₈	—	4	1	no	—
366	C₅×C₈	—	4	1	no	—
367	C₅×C₈	—	4	1	no	—
368	C₅×C₈	—	4	1	no	—
369	C₅×C₈	—	4	1	no	—
370	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
371	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
372	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
373	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
374	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
375	C₂×M₁₆	—	2	2	no	—
376	C₂×M₁₆	—	2	2	no	—
377	C₂×M₁₆	—	4	1	no	—
378	C₂²×C₈	—	2	2	no	—
379	C₂²×C₈	—	2	2	no	—
380	C₂²×C₈	—	2	2	no	—
381	C₂²×C₈	—	2	2	no	—
382	C₂²×C₈	—	2	2	no	—
383	C₂²×C₈	—	2	2	no	—
384	C₂²×C₈	—	4	1	no	—
385	C₂²×C₈	—	4	1	no	—
386	C₂²×C₈	—	4	1	no	—
387	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
390	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
391	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
392	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
395	C₄×D₄	C₅×D₄	1	4	yes	—
396	C₄×D₄	C₅×Q₈	1	4	yes	—
397	#117	—	2	2	no	—
398	#117	—	2	2	no	—
399	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
404	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
405	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
406	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
407	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
410	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
411	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
412	C₂×C₄²	—	2	2	no	—
413	C₂×C₄²	—	2	2	no	—
414	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
415	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
419	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
420	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
421	C₄⋊C₈	—	2	2	no	—
422	C₄⋊C₈	—	2	2	no	—
423	C₄⋊C₈	—	2	2	no	—
424	C₄⋊C₈	—	2	2	no	—
425	C₄⋊C₈	—	2	2	no	—
426	C₄⋊C₈	—	2	2	no	—
427	C₄⋊C₈	—	2	2	no	—
428	C₄⋊C₈	—	2	2	no	—
429	C₄⋊C₈	—	2	2	no	—
430	C₄⋊C₈	—	4	1	no	—
431	C₄⋊C₈	—	4	1	no	—
432	C₄⋊C₈	C₅×D₄	1	4	yes	complemented
433	C₂²⋊C₈	—	2	2	no	—
434	C₂²⋊C₈	—	2	2	no	—
435	C₂²⋊C₈	—	2	2	no	—
436	C₂²⋊C₈	—	2	2	no	—
437	#97	—	2	2	no	—
438	C₄×C₈	—	2	2	no	—
439	#95	C₂×C₄×C₅	1	1	yes	characteristic
440	#95	C₂×C₄×C₅	1	1	yes	characteristic
441	#95	C₂×C₄×C₅	1	1	yes	characteristic
442	#95	C₂×C₄×C₅	1	1	yes	characteristic
443	#95	C₂×C₄×C₅	1	1	yes	characteristic
444	#95	C₂×C₄×C₅	1	1	yes	characteristic
445	#95	C₂×C₄×C₅	1	1	yes	characteristic
446	#95	C₂×C₄×C₅	1	1	yes	characteristic
447	#95	C₂×C₄×C₅	1	1	yes	characteristic
448	#95	C₂×C₄×C₅	1	1	yes	characteristic
449	C₂²×C₅	—	2	2	no	—
450	C₂²×C₅	—	2	2	no	—
451	C₂²×C₅	—	2	2	no	—
452	C₂²×C₅	—	2	2	no	—
453	C₂²×C₅	—	2	2	no	—
454	C₂²×C₅	—	2	2	no	—
455	C₂²×C₅	—	2	2	no	—
456	C₂²×C₅	—	2	2	no	—
457	C₂²×C₅	—	2	2	no	—
458	C₂²×C₅	—	4	1	no	—
459	C₂²×C₅	—	4	1	no	—
460	C₂²×C₅	—	4	1	no	—
461	C₂²×C₅	—	4	1	no	—
462	C₂²×C₅	#424	1	4	yes	complemented
463	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
464	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
465	C₂²×C₅	#520	1	1	yes	characteristic
466	C₂²×C₅	C₂×#131	1	1	yes	characteristic
467	C₂²×C₅	C₂×#131	1	1	yes	characteristic
468	C₂²×C₅	C₂×#131	1	1	yes	characteristic
469	C₂²×C₅	#568	1	1	yes	characteristic
470	C₄×C₅	—	2	2	no	—
471	C₄×C₅	—	2	2	no	—
472	C₄×C₅	—	2	2	no	—
473	C₄×C₅	—	2	2	no	—
474	C₄×C₅	—	2	2	no	—
475	C₄×C₅	—	2	2	no	—
476	C₄×C₅	—	2	2	no	—
477	C₄×C₅	—	4	1	no	—
478	C₄×C₅	—	4	1	no	—
479	C₄×C₅	—	4	1	no	—
480	C₄×C₅	—	4	1	no	—
481	C₄×C₅	—	4	1	no	—
482	C₄×C₅	D₄²	1	1	yes	characteristic
483	C₄×C₅	#547	1	1	yes	characteristic
484	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
485	C₄×C₅	#554	1	1	yes	characteristic
486	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
487	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	C₅×C₄⋊C₄	1	4	yes	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	4	1	no	—
505	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
506	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
507	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
508	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
509	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
510	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
511	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
512	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
513	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
514	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
515	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
516	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
517	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
518	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
519	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
520	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
522	M₁₆	—	4	4	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	4	4	no	—
546	C₂×C₈	—	4	4	no	—
547	C₂×C₈	—	4	4	no	—
548	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
549	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
550	C₄⋊C₄	—	2	2	no	—
551	C₄⋊C₄	—	2	2	no	—
552	C₄⋊C₄	—	2	2	no	—
553	C₄⋊C₄	—	4	1	no	—
554	C₄⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
555	C₂²⋊C₄	—	2	2	no	—
556	C₂²⋊C₄	—	2	2	no	—
557	C₂²⋊C₄	—	2	2	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	4	1	no	—
561	C₂²⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
562	C₂²⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
563	C₄²	—	2	2	no	—
564	C₄²	—	2	2	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	2	1	no	—
570	C₄²	—	2	1	no	—
571	C₄²	C₂×C₅×D₄	1	2	yes	—
572	C₄²	C₂×C₅×D₄	1	2	yes	—
573	C₄²	C₂×C₅×Q₈	1	2	yes	—
574	C₄²	C₅×#41	1	2	yes	—
575	C₂×C₅	—	2	4	no	—
576	C₂×C₅	—	4	2	no	—
577	C₂×C₅	D₄×C₄⋊C₄	1	1	yes	characteristic
578	C₂×C₅	C₂×#424	1	1	yes	characteristic
579	C₂×C₅	#2906	1	1	yes	characteristic
580	C₂×C₅	#2929	1	1	yes	characteristic
581	C₂×C₅	#2933	1	1	yes	characteristic
582	C₂×C₅	#2992	1	1	yes	characteristic
583	C₂×C₅	#2994	1	1	yes	characteristic
584	C₂³	—	2	1	no	—
585	C₂³	—	2	1	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
595	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
596	C₂³	C₅×#131	1	2	yes	—
597	C₂³	C₅×#131	1	2	yes	—
598	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
599	D₄	—	2	8	no	—
600	C₂×C₄	—	2	8	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	4	4	no	—
639	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
640	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
641	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
642	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
643	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
644	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
645	C₂×C₄	C₅×#131	1	2	yes	—
646	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
647	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
648	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
649	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
650	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
651	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
652	C₈	—	2	2	no	—
653	C₈	—	2	2	no	—
654	C₈	—	4	1	no	—
655	C₈	—	4	1	no	—
656	C₈	—	4	1	no	—
657	C₈	—	4	1	no	—
658	C₈	—	4	1	no	—
659	C₈	—	4	1	no	—
660	C₅	#22647	1	1	yes	characteristic, direct product factor, Sylow
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	4	1	no	—
671	C₂²	—	4	1	no	—
672	C₂²	—	4	1	no	—
673	C₂²	—	4	1	no	—
674	C₂²	C₅×#424	1	4	yes	complemented
675	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
676	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
677	C₂²	C₅×#520	1	1	yes	characteristic
678	C₂²	C₂×C₅×#131	1	1	yes	characteristic
679	C₂²	C₂×C₅×#131	1	1	yes	characteristic
680	C₂²	C₂×C₅×#131	1	1	yes	characteristic
681	C₂²	C₅×#568	1	1	yes	characteristic
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	2	no	—
689	C₄	—	4	1	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	1	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	1	no	—
694	C₄	C₅×D₄²	1	1	yes	characteristic
695	C₄	C₅×#547	1	1	yes	characteristic
696	C₄	C₅×D₄×Q₈	1	1	yes	characteristic
697	C₄	C₅×#554	1	1	yes	characteristic
698	C₂	—	2	4	no	—
699	C₂	—	4	2	no	—
700	C₂	C₅×D₄×C₄⋊C₄	1	1	yes	characteristic
701	C₂	C₂×C₅×#424	1	1	yes	characteristic
702	C₂	C₅×#2906	1	1	yes	characteristic
703	C₂	C₅×#2929	1	1	yes	characteristic
704	C₂	C₅×#2933	1	1	yes	characteristic
705	C₂	C₅×#2992	1	1	yes	characteristic
706	C₂	C₅×#2994	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	C₂²×C₅×D₄	C₂×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
3. C₂×C₅×#424	C₂	semidirect
4. C₂²×C₅×C₄⋊C₈	C₂	semidirect
6. C₅×#1940	C₂	semidirect
7. C₅×#1939	C₂	semidirect
8. C₅×#1851	C₂	semidirect
9. C₅×#1850	C₂	semidirect
10. C₅×#1850	C₂	semidirect
11. C₅×#1850	C₂	semidirect
12. C₅×#1843	C₂	semidirect
13. C₅×#1798	C₂	semidirect
14. C₅×#1797	C₂	semidirect
15. C₅×#1768	C₂	semidirect
63. #22647	C₅	direct (N × H)
126. C₅×C₄⋊C₈	D₄	semidirect
145. C₂×#424	C₂×C₅	semidirect
146. C₂²×C₄⋊C₈	C₂×C₅	semidirect
148. #1940	C₂×C₅	semidirect
149. #1939	C₂×C₅	semidirect
150. #1851	C₂×C₅	semidirect
151. #1850	C₂×C₅	semidirect
152. #1850	C₂×C₅	semidirect
153. #1850	C₂×C₅	semidirect
154. #1843	C₂×C₅	semidirect
155. #1798	C₂×C₅	semidirect
156. #1797	C₂×C₅	semidirect
157. #1768	C₂×C₅	semidirect
432. C₄⋊C₈	C₅×D₄	semidirect
462. C₂²×C₅	#424	semidirect
660. C₅	#22647	direct (N × H)
674. C₂²	C₅×#424	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#435	2
C₂×C₅×C₈×D₄	2
C₂×C₅×#424	2
C₂²×C₅×C₄⋊C₈	2
C₅×#2290	2
C₅×#1940	2
C₅×#1939	2
C₅×#1851	2
C₅×#1850	2
C₅×#1843	2
C₅×#1798	2
C₅×#1797	2
C₅×#1768	2
#22647	5

Subgroups — C5×#22647 #11945367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22647 #11945367