Finite Group Databasebeta

← C5×#9026 #11931746

Subgroups — C5×#9026 #11931746

Order 1280.

616 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#398C211yesmaximal, characteristic
2C5×#2313C211yesmaximal, characteristic
3C5×#1823C212yesmaximal
4C2×C5×#324C211yesmaximal, characteristic
5C5×#1294C212yesmaximal
6C22×C5×C4⋊C4—21no—
7C22×C5×C4⋊C4C2211yescharacteristic
8C22×C5×C4⋊C4C2211yescharacteristic
9C2×C5×C22⋊C8C2212yes—
10C5×#398—22no—
11C5×#398C414yescomplemented
12C5×#387—24no—
13C5×#381—21no—
14C5×#380C2212yes—
15C4×C5×C22⋊C4—21no—
16C2×C5×#95—21no—
17C2×C5×#95C2211yescharacteristic
18C5×#340—24no—
19C5×#324—22no—
20#9026C511yesmaximal, characteristic, direct product factor, Sylow
21C23×C4×C5—21no—
22C23×C4×C5—21no—
23C23×C4×C5D411yescharacteristic
24C23×C4×C5D411yescharacteristic
25C23×C4×C5C2311yescharacteristic
26C22×C5×C8—22no—
27C2×C5×C4⋊C4—22no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—24no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—44no—
34C2×C5×C4⋊C4C2×C412yes—
35C2×C5×C4⋊C4C2×C412yes—
36C2×C5×C4⋊C4D412yes—
37C2×C5×C4⋊C4D414yes—
38C2×C5×C22⋊C4—22no—
39C2×C42×C5—22no—
40C5×C22⋊C8—22no—
41C5×C22⋊C8—22no—
42C5×#95—22no—
43C5×#95—24no—
44C5×#95—24no—
45C5×#95—21no—
46C5×#95—22no—
47C5×#95C2×C412yes—
48C2×#398C2×C511yescharacteristic
49#2313C2×C511yescharacteristic
50#1823C2×C512yes—
51C2×#324C2×C511yescharacteristic
52#1294C2×C512yes—
53C24×C5C2×D411yescharacteristic
54C22×C4×C5—24no—
55C22×C4×C5—22no—
56C22×C4×C5—21no—
57C22×C4×C5—21no—
58C22×C4×C5—21no—
59C22×C4×C5—22no—
60C22×C4×C5—22no—
61C22×C4×C5—21no—
62C22×C4×C5—22no—
63C22×C4×C5—24no—
64C22×C4×C5—42no—
65C22×C4×C5—42no—
66C22×C4×C5—42no—
67C22×C4×C5—42no—
68C22×C4×C5—41no—
69C22×C4×C5—41no—
70C22×C4×C5—42no—
71C22×C4×C5—42no—
72C22×C4×C5C22⋊C412yes—
73C22×C4×C5C22⋊C412yes—
74C22×C4×C5C22×C411yescharacteristic
75C22×C4×C5C2×D412yes—
76C22×C4×C5C2×D411yescharacteristic
77C22×C4×C5#4112yes—
78C2×C5×C8—44no—
79C2×C5×C8—42no—
80C5×C4⋊C4—24no—
81C5×C4⋊C4—24no—
82C5×C4⋊C4—24no—
83C5×C4⋊C4—44no—
84C5×C4⋊C4—48no—
85C5×C4⋊C4—42no—
86C5×C22⋊C4—42no—
87C5×C22⋊C4—42no—
88C42×C5—82no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4C22×C511yescharacteristic
91C22×C4⋊C4C22×C511yescharacteristic
92C2×C22⋊C8C22×C512yes—
93#398—22no—
94#398C4×C514yescomplemented
95#387—24no—
96#381—21no—
97#380C22×C512yes—
98C4×C22⋊C4—21no—
99C2×#95—21no—
100C2×#95C22×C511yescharacteristic
101#340—24no—
102#324—22no—
103C23×C5—22no—
104C23×C5—22no—
105C23×C5C2×C22⋊C411yescharacteristic
106C23×C5#12011yescharacteristic
107C23×C5#12311yescharacteristic
108C23×C5#13512yes—
109C23×C5AGL(1,ℤ/8)12yes—
110C2×C4×C5—24no—
111C2×C4×C5—24no—
112C2×C4×C5—22no—
113C2×C4×C5—22no—
114C2×C4×C5—22no—
115C2×C4×C5—22no—
116C2×C4×C5—41no—
117C2×C4×C5—41no—
118C2×C4×C5—42no—
119C2×C4×C5—48no—
120C2×C4×C5—42no—
121C2×C4×C5—42no—
122C2×C4×C5—42no—
123C2×C4×C5—42no—
124C2×C4×C5—42no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5—42no—
128C2×C4×C5—42no—
129C2×C4×C5—44no—
130C2×C4×C5—44no—
131C2×C4×C5—44no—
132C2×C4×C5—81no—
133C2×C4×C5—82no—
134C2×C4×C5—82no—
135C2×C4×C5C4×D412yes—
136C2×C4×C5#12112yes—
137C5×C8—82no—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4C5×D411yescharacteristic
141C23×C4C5×D411yescharacteristic
142C23×C4C23×C511yescharacteristic
143C22×C8—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—24no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—44no—
151C2×C4⋊C4C2×C4×C512yes—
152C2×C4⋊C4C2×C4×C512yes—
153C2×C4⋊C4C5×D412yes—
154C2×C4⋊C4C5×D414yes—
155C2×C22⋊C4—22no—
156C2×C42—22no—
157C22⋊C8—22no—
158C22⋊C8—22no—
159#95—22no—
160#95—24no—
161#95—24no—
162#95—21no—
163#95—22no—
164#95C2×C4×C512yes—
165C22×C5—24no—
166C22×C5—24no—
167C22×C5—21no—
168C22×C5—21no—
169C22×C5—21no—
170C22×C5—21no—
171C22×C5#38611yescharacteristic
172C22×C5#41611yescharacteristic
173C22×C5#41811yescharacteristic
174C22×C5#44912yes—
175C22×C5#45612yes—
176C22×C5#45812yes—
177C22×C5#48212yes—
178C4×C5—22no—
179C4×C5—22no—
180C4×C5—44no—
181C4×C5—42no—
182C4×C5—42no—
183C4×C5—84no—
184C4×C5—82no—
185C24C2×C5×D411yescharacteristic
186C22×C4—24no—
187C22×C4—22no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—21no—
194C22×C4—22no—
195C22×C4—24no—
196C22×C4—42no—
197C22×C4—42no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4C5×C22⋊C412yes—
205C22×C4C5×C22⋊C412yes—
206C22×C4C22×C4×C511yescharacteristic
207C22×C4C2×C5×D412yes—
208C22×C4C2×C5×D411yescharacteristic
209C22×C4C5×#4112yes—
210C2×C8—44no—
211C2×C8—42no—
212C4⋊C4—24no—
213C4⋊C4—24no—
214C4⋊C4—24no—
215C4⋊C4—44no—
216C4⋊C4—48no—
217C4⋊C4—42no—
218C22⋊C4—42no—
219C22⋊C4—42no—
220C42—82no—
221C2×C5—21no—
222C2×C5—21no—
223C2×C5—22no—
224C2×C5#160914yes—
225C2×C5#187511yescharacteristic
226C2×C5#188611yescharacteristic
227C2×C5#189011yescharacteristic
228C23—22no—
229C23—22no—
230C23C2×C5×C22⋊C411yescharacteristic
231C23C5×#12011yescharacteristic
232C23C5×#12311yescharacteristic
233C23C5×#13512yes—
234C23C5×AGL(1,ℤ/8)12yes—
235C2×C4—24no—
236C2×C4—24no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—48no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—44no—
255C2×C4—44no—
256C2×C4—44no—
257C2×C4—81no—
258C2×C4—82no—
259C2×C4—82no—
260C2×C4C4×C5×D412yes—
261C2×C4C5×#12112yes—
262C8—82no—
263C5#902611yescharacteristic, direct product factor, Sylow
264C22—24no—
265C22—24no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22C5×#38611yescharacteristic
271C22C5×#41611yescharacteristic
272C22C5×#41811yescharacteristic
273C22C5×#44912yes—
274C22C5×#45612yes—
275C22C5×#45812yes—
276C22C5×#48212yes—
277C4—22no—
278C4—22no—
279C4—44no—
280C4—42no—
281C4—42no—
282C4—84no—
283C4—82no—
284C2—21no—
285C2—21no—
286C2—22no—
287C2C5×#160914yes—
288C2C5×#187511yescharacteristic
289C2C5×#188611yescharacteristic
290C2C5×#189011yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC24×C5C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
11. C5×#398C4semidirect
20. #9026C5direct (N × H)
94. #398C4×C5semidirect
263. C5#9026direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3982
C5×#23132
C5×#18232
C2×C5×#3242
C5×#12942
#90265