Finite Group Databasebeta

← C5×#9027 #11931747

Subgroups — C5×#9027 #11931747

Order 1280.

660 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#398C211yesmaximal, characteristic
2C5×#2316C211yesmaximal, characteristic
3C5×#1823C212yesmaximal
4C2×C5×#324C211yesmaximal, characteristic
5C5×#1294C212yesmaximal
6C2×C5×#117—21no—
7C22×C5×C4⋊C4—21no—
8C22×C5×C4⋊C4C2211yescharacteristic
9C22×C5×C4⋊C4C2211yescharacteristic
10C2×C5×C22⋊C8C2212yes—
11C5×#398—22no—
12C5×#398C414yescomplemented
13C5×#389—24no—
14C5×#380—21no—
15C5×#380C2212yes—
16C2×C5×#95—21no—
17C2×C5×#95C2211yescharacteristic
18C5×#340—24no—
19C5×#324—22no—
20#9027C511yesmaximal, 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—
27C5×#117—42no—
28C5×#117—42no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—22no—
32C2×C5×C4⋊C4—22no—
33C2×C5×C4⋊C4—22no—
34C2×C5×C4⋊C4—24no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4—22no—
37C2×C5×C4⋊C4—42no—
38C2×C5×C4⋊C4—42no—
39C2×C5×C4⋊C4C2×C412yes—
40C2×C5×C4⋊C4C2×C412yes—
41C2×C5×C4⋊C4D412yes—
42C2×C5×C4⋊C4D414yes—
43C2×C5×C22⋊C4—22no—
44C2×C42×C5—22no—
45C5×C22⋊C8—22no—
46C5×C22⋊C8—22no—
47C5×#95—22no—
48C5×#95—24no—
49C5×#95—21no—
50C5×#95—22no—
51C5×#95C2×C412yes—
52C2×#398C2×C511yescharacteristic
53#2316C2×C511yescharacteristic
54#1823C2×C512yes—
55C2×#324C2×C511yescharacteristic
56#1294C2×C512yes—
57C24×C5C2×D411yescharacteristic
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—24no—
63C22×C4×C5—22no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—22no—
67C22×C4×C5—24no—
68C22×C4×C5—42no—
69C22×C4×C5—42no—
70C22×C4×C5—41no—
71C22×C4×C5—41no—
72C22×C4×C5—42no—
73C22×C4×C5—41no—
74C22×C4×C5—41no—
75C22×C4×C5—41no—
76C22×C4×C5—41no—
77C22×C4×C5—41no—
78C22×C4×C5—41no—
79C22×C4×C5C22⋊C412yes—
80C22×C4×C5C22⋊C412yes—
81C22×C4×C5D812yes—
82C22×C4×C5SD1612yes—
83C22×C4×C5C22×C411yescharacteristic
84C22×C4×C5C2×D412yes—
85C22×C4×C5C2×D411yescharacteristic
86C22×C4×C5#4112yes—
87C2×C5×C8—44no—
88C2×C5×C8—42no—
89C5×C4⋊C4—24no—
90C5×C4⋊C4—24no—
91C5×C4⋊C4—24no—
92C5×C4⋊C4—44no—
93C5×C4⋊C4—44no—
94C5×C4⋊C4—48no—
95C5×C4⋊C4—42no—
96C5×C4⋊C4—82no—
97C5×C22⋊C4—42no—
98C5×C22⋊C4—42no—
99C42×C5—44no—
100C2×#117—21no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4C22×C511yescharacteristic
103C22×C4⋊C4C22×C511yescharacteristic
104C2×C22⋊C8C22×C512yes—
105#398—22no—
106#398C4×C514yescomplemented
107#389—24no—
108#380—21no—
109#380C22×C512yes—
110C2×#95—21no—
111C2×#95C22×C511yescharacteristic
112#340—24no—
113#324—22no—
114C23×C5—22no—
115C23×C5—22no—
116C23×C5C2×C22⋊C411yescharacteristic
117C23×C5#12011yescharacteristic
118C23×C5#12311yescharacteristic
119C23×C5C2×D811yescharacteristic
120C23×C5C2×SD1611yescharacteristic
121C23×C5AGL(1,ℤ/8)11yescharacteristic
122C23×C5#13711yescharacteristic
123C2×C4×C5—22no—
124C2×C4×C5—22no—
125C2×C4×C5—22no—
126C2×C4×C5—22no—
127C2×C4×C5—24no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5—24no—
131C2×C4×C5—22no—
132C2×C4×C5—41no—
133C2×C4×C5—41no—
134C2×C4×C5—42no—
135C2×C4×C5—44no—
136C2×C4×C5—44no—
137C2×C4×C5—42no—
138C2×C4×C5—42no—
139C2×C4×C5—42no—
140C2×C4×C5—42no—
141C2×C4×C5—42no—
142C2×C4×C5—42no—
143C2×C4×C5—42no—
144C2×C4×C5—44no—
145C2×C4×C5—44no—
146C2×C4×C5—44no—
147C2×C4×C5—81no—
148C2×C4×C5—81no—
149C2×C4×C5—81no—
150C2×C4×C5—81no—
151C2×C4×C5—81no—
152C2×C4×C5#10214yes—
153C2×C4×C5C4×D412yes—
154C2×C4×C5#12112yes—
155C5×C8—82no—
156C23×C4—21no—
157C23×C4—21no—
158C23×C4C5×D411yescharacteristic
159C23×C4C5×D411yescharacteristic
160C23×C4C23×C511yescharacteristic
161C22×C8—22no—
162#117—42no—
163#117—42no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—24no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—42no—
173C2×C4⋊C4—42no—
174C2×C4⋊C4C2×C4×C512yes—
175C2×C4⋊C4C2×C4×C512yes—
176C2×C4⋊C4C5×D412yes—
177C2×C4⋊C4C5×D414yes—
178C2×C22⋊C4—22no—
179C2×C42—22no—
180C22⋊C8—22no—
181C22⋊C8—22no—
182#95—22no—
183#95—24no—
184#95—21no—
185#95—22no—
186#95C2×C4×C512yes—
187C22×C5—22no—
188C22×C5—22no—
189C22×C5—22no—
190C22×C5—22no—
191C22×C5—21no—
192C22×C5—21no—
193C22×C5—21no—
194C22×C5—21no—
195C22×C5#38611yescharacteristic
196C22×C5C2×#10211yescharacteristic
197C22×C5#41711yescharacteristic
198C22×C5#44711yescharacteristic
199C22×C5#44811yescharacteristic
200C22×C5#45612yes—
201C22×C5#45812yes—
202C22×C5#48011yescharacteristic
203C22×C5#48111yescharacteristic
204C4×C5—24no—
205C4×C5—22no—
206C4×C5—22no—
207C4×C5—44no—
208C4×C5—42no—
209C4×C5—84no—
210C4×C5—82no—
211C24C2×C5×D411yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—24no—
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—24no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—42no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4C5×C22⋊C412yes—
234C22×C4C5×C22⋊C412yes—
235C22×C4C5×D812yes—
236C22×C4C5×SD1612yes—
237C22×C4C22×C4×C511yescharacteristic
238C22×C4C2×C5×D412yes—
239C22×C4C2×C5×D411yescharacteristic
240C22×C4C5×#4112yes—
241C2×C8—44no—
242C2×C8—42no—
243C4⋊C4—24no—
244C4⋊C4—24no—
245C4⋊C4—24no—
246C4⋊C4—44no—
247C4⋊C4—44no—
248C4⋊C4—42no—
249C4⋊C4—48no—
250C4⋊C4—82no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C42—44no—
254C2×C5—21no—
255C2×C5—21no—
256C2×C5—21no—
257C2×C5—21no—
258C2×C5#161012yes—
259C2×C5#161112yes—
260C2×C5#187411yescharacteristic
261C2×C5#188611yescharacteristic
262C2×C5#189011yescharacteristic
263C23—22no—
264C23—22no—
265C23C2×C5×C22⋊C411yescharacteristic
266C23C5×#12011yescharacteristic
267C23C5×#12311yescharacteristic
268C23C2×C5×D811yescharacteristic
269C23C2×C5×SD1611yescharacteristic
270C23C5×AGL(1,ℤ/8)11yescharacteristic
271C23C5×#13711yescharacteristic
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—24no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4C5×#10214yes—
302C2×C4C4×C5×D412yes—
303C2×C4C5×#12112yes—
304C8—82no—
305C5#902711yescharacteristic, direct product factor, Sylow
306C22—22no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22C5×#38611yescharacteristic
315C22C2×C5×#10211yescharacteristic
316C22C5×#41711yescharacteristic
317C22C5×#44711yescharacteristic
318C22C5×#44811yescharacteristic
319C22C5×#45612yes—
320C22C5×#45812yes—
321C22C5×#48011yescharacteristic
322C22C5×#48111yescharacteristic
323C4—24no—
324C4—22no—
325C4—22no—
326C4—44no—
327C4—42no—
328C4—84no—
329C4—82no—
330C2—21no—
331C2—21no—
332C2—21no—
333C2—21no—
334C2C5×#161012yes—
335C2C5×#161112yes—
336C2C5×#187411yescharacteristic
337C2C5×#188611yescharacteristic
338C2C5×#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
12. C5×#398C4semidirect
20. #9027C5direct (N × H)
106. #398C4×C5semidirect
305. C5#9027direct (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×#23162
C5×#18232
C2×C5×#3242
C5×#12942
#90275