Subgroups — C₅×#22322 #11945042

Order 1280.

652 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2396	C₂	1	1	yes	maximal, characteristic
2	C₅×#1985	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#1984	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1924	C₂	1	1	yes	maximal, characteristic
5	C₅×#1924	C₂	1	1	yes	maximal, characteristic
6	C₅×#1923	C₂	1	1	yes	maximal, characteristic
7	C₅×#1923	C₂	1	1	yes	maximal, characteristic
8	C₅×#1917	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1917	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1917	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1916	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1818	C₂	1	1	yes	maximal, characteristic
13	C₅×#1771	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1750	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#117	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×#97	C₂²	1	1	yes	characteristic
27	C₂×C₅×#97	C₂²	1	1	yes	characteristic
28	C₂×C₅×#97	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₅×#400	C₄	1	1	yes	characteristic
33	C₅×#399	C₄	1	1	yes	characteristic
34	C₅×#398	C₄	1	1	yes	characteristic
35	C₅×#398	C₄	1	1	yes	characteristic
36	C₅×#396	C₄	1	1	yes	characteristic
37	C₅×#396	C₄	1	1	yes	characteristic
38	C₅×#395	C₄	1	1	yes	characteristic
39	C₅×#393	C₄	1	1	yes	characteristic
40	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₅×#336	C₂²	1	1	yes	characteristic
46	C₅×#336	C₂²	1	1	yes	characteristic
47	C₅×#336	C₂²	1	1	yes	characteristic
48	C₅×#336	C₂²	1	1	yes	characteristic
49	C₅×#336	C₂²	1	1	yes	characteristic
50	C₅×#336	C₂²	1	1	yes	characteristic
51	C₅×#336	C₂²	1	1	yes	characteristic
52	C₅×#336	C₂²	1	1	yes	characteristic
53	C₅×#336	C₂²	1	1	yes	characteristic
54	C₅×#336	C₂²	1	1	yes	characteristic
55	C₅×#336	C₂²	1	1	yes	characteristic
56	C₅×#336	C₂²	1	1	yes	characteristic
57	C₅×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	#22322	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₄×C₅×Q₈	—	4	1	no	—
71	C₄×C₅×Q₈	—	4	1	no	—
72	C₅×#117	—	4	1	no	—
73	C₅×#117	—	4	1	no	—
74	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
97	C₅×C₄⋊C₈	—	2	2	no	—
98	C₅×C₄⋊C₈	—	2	2	no	—
99	C₅×C₄⋊C₈	—	4	1	no	—
100	C₅×C₄⋊C₈	—	4	1	no	—
101	C₅×C₂²⋊C₈	—	2	2	no	—
102	C₅×C₂²⋊C₈	—	2	2	no	—
103	C₅×C₂²⋊C₈	—	4	1	no	—
104	C₅×C₂²⋊C₈	—	4	1	no	—
105	C₅×#97	—	2	2	no	—
106	C₅×#97	—	4	1	no	—
107	C₅×#97	—	4	1	no	—
108	C₄×C₅×C₈	—	2	2	no	—
109	C₄×C₅×C₈	—	4	1	no	—
110	C₄×C₅×C₈	—	4	1	no	—
111	C₅×#95	C₂×C₄	1	1	yes	characteristic
112	C₅×#95	C₂×C₄	1	1	yes	characteristic
113	C₅×#95	C₂×C₄	1	1	yes	characteristic
114	C₅×#95	C₂×C₄	1	1	yes	characteristic
115	C₅×#95	C₂×C₄	1	1	yes	characteristic
116	C₅×#95	C₂×C₄	1	1	yes	characteristic
117	C₅×#95	C₂×C₄	1	1	yes	characteristic
118	C₅×#95	C₂×C₄	1	1	yes	characteristic
119	C₅×#95	C₂×C₄	1	1	yes	characteristic
120	C₅×#95	C₂×C₄	1	1	yes	characteristic
121	#2396	C₂×C₅	1	1	yes	characteristic
122	#1985	C₂×C₅	1	1	yes	characteristic, complemented
123	#1984	C₂×C₅	1	1	yes	characteristic, complemented
124	#1924	C₂×C₅	1	1	yes	characteristic
125	#1924	C₂×C₅	1	1	yes	characteristic
126	#1923	C₂×C₅	1	1	yes	characteristic
127	#1923	C₂×C₅	1	1	yes	characteristic
128	#1917	C₂×C₅	1	1	yes	characteristic, complemented
129	#1917	C₂×C₅	1	1	yes	characteristic, complemented
130	#1917	C₂×C₅	1	1	yes	characteristic, complemented
131	#1916	C₂×C₅	1	1	yes	characteristic, complemented
132	#1818	C₂×C₅	1	1	yes	characteristic
133	#1771	C₂×C₅	1	1	yes	characteristic, complemented
134	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
135	#1750	C₂×C₅	1	1	yes	characteristic
136	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₅×Q₈	—	2	2	no	—
138	C₂×C₅×Q₈	—	4	1	no	—
139	C₂×C₅×Q₈	—	4	1	no	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	—	2	1	no	—
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	—	2	1	no	—
146	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
160	C₂×C₅×C₈	—	2	1	no	—
161	C₂×C₅×C₈	—	2	1	no	—
162	C₂×C₅×C₈	—	2	1	no	—
163	C₂×C₅×C₈	—	2	1	no	—
164	C₂×C₅×C₈	—	2	1	no	—
165	C₂×C₅×C₈	—	2	1	no	—
166	C₂×C₅×C₈	—	2	1	no	—
167	C₂×C₅×C₈	—	2	1	no	—
168	C₂×C₅×C₈	—	2	1	no	—
169	C₂×C₅×C₈	—	2	1	no	—
170	C₂×C₅×C₈	—	2	1	no	—
171	C₂×C₅×C₈	—	2	1	no	—
172	C₂×C₅×C₈	—	2	1	no	—
173	C₂×C₅×C₈	—	2	1	no	—
174	C₂×C₅×C₈	—	2	1	no	—
175	C₂×C₅×C₈	—	2	1	no	—
176	C₂×C₅×C₈	—	2	1	no	—
177	C₂×C₅×C₈	—	2	1	no	—
178	C₂×C₅×C₈	—	2	1	no	—
179	C₂×C₅×C₈	—	2	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	#41	1	2	yes	—
183	C₂×C₅×C₈	#41	1	2	yes	—
184	C₅×C₄⋊C₄	—	2	2	no	—
185	C₅×C₄⋊C₄	—	2	2	no	—
186	C₅×C₄⋊C₄	—	2	2	no	—
187	C₅×C₄⋊C₄	—	4	1	no	—
188	C₅×C₄⋊C₄	—	4	1	no	—
189	C₅×C₄⋊C₄	—	4	1	no	—
190	C₅×C₄⋊C₄	—	4	1	no	—
191	C₅×C₄⋊C₄	—	4	1	no	—
192	C₅×C₄⋊C₄	—	4	1	no	—
193	C₅×C₄⋊C₄	—	4	1	no	—
194	C₅×C₄⋊C₄	—	4	1	no	—
195	C₅×C₂²⋊C₄	—	2	2	no	—
196	C₅×C₂²⋊C₄	—	2	2	no	—
197	C₅×C₂²⋊C₄	—	4	1	no	—
198	C₅×C₂²⋊C₄	—	4	1	no	—
199	C₅×C₂²⋊C₄	—	4	1	no	—
200	C₅×C₂²⋊C₄	—	4	1	no	—
201	C₄²×C₅	—	2	1	no	—
202	C₄²×C₅	—	2	1	no	—
203	C₄²×C₅	—	2	1	no	—
204	C₄²×C₅	—	2	1	no	—
205	C₄²×C₅	—	2	1	no	—
206	C₄²×C₅	—	2	1	no	—
207	C₄²×C₅	—	2	1	no	—
208	C₄²×C₅	—	2	1	no	—
209	C₄²×C₅	—	2	1	no	—
210	C₄²×C₅	—	2	1	no	—
211	C₄²×C₅	—	2	1	no	—
212	C₄²×C₅	—	2	1	no	—
213	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
214	C₂×#117	C₂²×C₅	1	1	yes	characteristic
215	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
217	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
218	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
219	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
220	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
221	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
222	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
223	C₂×#97	C₂²×C₅	1	1	yes	characteristic
224	C₂×#97	C₂²×C₅	1	1	yes	characteristic
225	C₂×#97	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
227	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
228	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
229	#400	C₄×C₅	1	1	yes	characteristic
230	#399	C₄×C₅	1	1	yes	characteristic
231	#398	C₄×C₅	1	1	yes	characteristic
232	#398	C₄×C₅	1	1	yes	characteristic
233	#396	C₄×C₅	1	1	yes	characteristic
234	#396	C₄×C₅	1	1	yes	characteristic
235	#395	C₄×C₅	1	1	yes	characteristic
236	#393	C₄×C₅	1	1	yes	characteristic
237	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
238	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
239	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
240	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
241	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
242	#336	C₂²×C₅	1	1	yes	characteristic
243	#336	C₂²×C₅	1	1	yes	characteristic
244	#336	C₂²×C₅	1	1	yes	characteristic
245	#336	C₂²×C₅	1	1	yes	characteristic
246	#336	C₂²×C₅	1	1	yes	characteristic
247	#336	C₂²×C₅	1	1	yes	characteristic
248	#336	C₂²×C₅	1	1	yes	characteristic
249	#336	C₂²×C₅	1	1	yes	characteristic
250	#336	C₂²×C₅	1	1	yes	characteristic
251	#336	C₂²×C₅	1	1	yes	characteristic
252	#336	C₂²×C₅	1	1	yes	characteristic
253	#336	C₂²×C₅	1	1	yes	characteristic
254	#336	C₂²×C₅	1	1	yes	characteristic
255	#336	C₂²×C₅	1	1	yes	characteristic
256	C₂³×C₅	—	2	1	no	—
257	C₂³×C₅	—	2	1	no	—
258	C₂³×C₅	—	2	1	no	—
259	C₂³×C₅	—	2	1	no	—
260	C₂³×C₅	—	2	1	no	—
261	C₂³×C₅	—	2	1	no	—
262	C₂³×C₅	—	2	1	no	—
263	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
264	C₅×Q₈	—	4	4	no	—
265	C₂×C₄×C₅	—	2	1	no	—
266	C₂×C₄×C₅	—	2	1	no	—
267	C₂×C₄×C₅	—	2	1	no	—
268	C₂×C₄×C₅	—	2	1	no	—
269	C₂×C₄×C₅	—	2	1	no	—
270	C₂×C₄×C₅	—	2	1	no	—
271	C₂×C₄×C₅	—	2	1	no	—
272	C₂×C₄×C₅	—	2	1	no	—
273	C₂×C₄×C₅	—	2	1	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	2	1	no	—
277	C₂×C₄×C₅	—	2	1	no	—
278	C₂×C₄×C₅	—	2	1	no	—
279	C₂×C₄×C₅	—	2	1	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	4	1	no	—
303	C₂×C₄×C₅	—	4	1	no	—
304	C₂×C₄×C₅	—	4	1	no	—
305	C₂×C₄×C₅	—	4	1	no	—
306	C₂×C₄×C₅	#131	1	2	yes	—
307	C₂×C₄×C₅	#131	1	2	yes	—
308	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
310	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
311	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
312	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
313	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
314	C₅×C₈	—	2	2	no	—
315	C₅×C₈	—	2	2	no	—
316	C₅×C₈	—	4	1	no	—
317	C₅×C₈	—	4	1	no	—
318	C₅×C₈	—	4	1	no	—
319	C₅×C₈	—	4	1	no	—
320	C₅×C₈	—	4	1	no	—
321	C₅×C₈	—	4	1	no	—
322	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
323	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
325	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
329	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
332	C₄×Q₈	—	4	1	no	—
333	C₄×Q₈	—	4	1	no	—
334	#117	—	4	1	no	—
335	#117	—	4	1	no	—
336	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
347	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
349	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
351	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
359	C₄⋊C₈	—	2	2	no	—
360	C₄⋊C₈	—	2	2	no	—
361	C₄⋊C₈	—	4	1	no	—
362	C₄⋊C₈	—	4	1	no	—
363	C₂²⋊C₈	—	2	2	no	—
364	C₂²⋊C₈	—	2	2	no	—
365	C₂²⋊C₈	—	4	1	no	—
366	C₂²⋊C₈	—	4	1	no	—
367	#97	—	2	2	no	—
368	#97	—	4	1	no	—
369	#97	—	4	1	no	—
370	C₄×C₈	—	2	2	no	—
371	C₄×C₈	—	4	1	no	—
372	C₄×C₈	—	4	1	no	—
373	#95	C₂×C₄×C₅	1	1	yes	characteristic
374	#95	C₂×C₄×C₅	1	1	yes	characteristic
375	#95	C₂×C₄×C₅	1	1	yes	characteristic
376	#95	C₂×C₄×C₅	1	1	yes	characteristic
377	#95	C₂×C₄×C₅	1	1	yes	characteristic
378	#95	C₂×C₄×C₅	1	1	yes	characteristic
379	#95	C₂×C₄×C₅	1	1	yes	characteristic
380	#95	C₂×C₄×C₅	1	1	yes	characteristic
381	#95	C₂×C₄×C₅	1	1	yes	characteristic
382	#95	C₂×C₄×C₅	1	1	yes	characteristic
383	C₂²×C₅	—	4	1	no	—
384	C₂²×C₅	—	4	1	no	—
385	C₂²×C₅	—	4	1	no	—
386	C₂²×C₅	—	4	1	no	—
387	C₂²×C₅	—	4	1	no	—
388	C₂²×C₅	—	4	1	no	—
389	C₂²×C₅	—	4	1	no	—
390	C₂²×C₅	C₄×#41	1	1	yes	characteristic
391	C₂²×C₅	#518	1	1	yes	characteristic
392	C₂²×C₅	#519	1	1	yes	characteristic
393	C₂²×C₅	C₂×#131	1	1	yes	characteristic
394	C₂²×C₅	C₂×#131	1	1	yes	characteristic
395	C₂²×C₅	#568	1	1	yes	characteristic
396	C₂²×C₅	#568	1	1	yes	characteristic
397	C₄×C₅	—	2	2	no	—
398	C₄×C₅	—	2	2	no	—
399	C₄×C₅	—	4	1	no	—
400	C₄×C₅	—	4	1	no	—
401	C₄×C₅	—	4	1	no	—
402	C₄×C₅	—	4	1	no	—
403	C₄×C₅	—	4	1	no	—
404	C₄×C₅	—	4	1	no	—
405	C₄×C₅	—	4	1	no	—
406	C₄×C₅	—	4	1	no	—
407	C₄×C₅	—	4	1	no	—
408	C₄×C₅	—	4	1	no	—
409	C₄×C₅	—	4	1	no	—
410	C₄×C₅	#539	1	1	yes	characteristic
411	C₄×C₅	#539	1	1	yes	characteristic
412	C₄×C₅	#542	1	1	yes	characteristic
413	C₄×C₅	#542	1	1	yes	characteristic
414	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	4	1	no	—
417	C₂×Q₈	—	4	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
425	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
426	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
427	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
428	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
429	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
430	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
431	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
432	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
433	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
434	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
435	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
436	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
437	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	C₅×#41	1	2	yes	—
461	C₂×C₈	C₅×#41	1	2	yes	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₂²⋊C₄	—	4	1	no	—
477	C₂²⋊C₄	—	4	1	no	—
478	C₂²⋊C₄	—	4	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₂×C₅	—	8	1	no	—
492	C₂×C₅	#2332	1	1	yes	characteristic
493	C₂×C₅	#2966	1	1	yes	characteristic
494	C₂×C₅	#2967	1	1	yes	characteristic
495	C₂×C₅	#2976	1	1	yes	characteristic
496	C₂×C₅	#2981	1	1	yes	characteristic
497	C₂×C₅	#2985	1	1	yes	characteristic
498	C₂×C₅	#2985	1	1	yes	characteristic
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	2	1	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
507	Q₈	—	4	4	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	C₅×#131	1	2	yes	—
550	C₂×C₄	C₅×#131	1	2	yes	—
551	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
552	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
553	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
554	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
555	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
556	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
557	C₈	—	2	2	no	—
558	C₈	—	2	2	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₅	#22322	1	1	yes	characteristic, direct product factor, Sylow
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	C₄×C₅×#41	1	1	yes	characteristic
574	C₂²	C₅×#518	1	1	yes	characteristic
575	C₂²	C₅×#519	1	1	yes	characteristic
576	C₂²	C₂×C₅×#131	1	1	yes	characteristic
577	C₂²	C₂×C₅×#131	1	1	yes	characteristic
578	C₂²	C₅×#568	1	1	yes	characteristic
579	C₂²	C₅×#568	1	1	yes	characteristic
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	C₅×#539	1	1	yes	characteristic
594	C₄	C₅×#539	1	1	yes	characteristic
595	C₄	C₅×#542	1	1	yes	characteristic
596	C₄	C₅×#542	1	1	yes	characteristic
597	C₂	—	8	1	no	—
598	C₂	C₅×#2332	1	1	yes	characteristic
599	C₂	C₅×#2966	1	1	yes	characteristic
600	C₂	C₅×#2967	1	1	yes	characteristic
601	C₂	C₅×#2976	1	1	yes	characteristic
602	C₂	C₅×#2981	1	1	yes	characteristic
603	C₂	C₅×#2985	1	1	yes	characteristic
604	C₂	C₅×#2985	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
2. C₅×#1985	C₂	semidirect
3. C₅×#1984	C₂	semidirect
8. C₅×#1917	C₂	semidirect
9. C₅×#1917	C₂	semidirect
10. C₅×#1917	C₂	semidirect
11. C₅×#1916	C₂	semidirect
13. C₅×#1771	C₂	semidirect
14. C₅×C₈×C₄⋊C₄	C₂	semidirect
59. #22322	C₅	direct (N × H)
122. #1985	C₂×C₅	semidirect
123. #1984	C₂×C₅	semidirect
128. #1917	C₂×C₅	semidirect
129. #1917	C₂×C₅	semidirect
130. #1917	C₂×C₅	semidirect
131. #1916	C₂×C₅	semidirect
133. #1771	C₂×C₅	semidirect
134. C₈×C₄⋊C₄	C₂×C₅	semidirect
565. C₅	#22322	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2396	2
C₅×#1985	2
C₅×#1984	2
C₅×#1924	2
C₅×#1923	2
C₅×#1917	2
C₅×#1916	2
C₅×#1818	2
C₅×#1771	2
C₅×C₈×C₄⋊C₄	2
C₅×#1750	2
#22322	5

Subgroups — C5×#22322 #11945042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22322 #11945042