Finite Group Databasebeta

← C5×#11008 #11933728

Subgroups — C5×#11008 #11933728

Order 1280.

2118 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#127C211yesmaximal, characteristic
2C22×C5×#102C214yesmaximal, complemented
3C2×C5×#336C211yesmaximal, characteristic, complemented
4C5×C4⋊#95C211yesmaximal, characteristic, complemented
5C23×C5×D4—22no—
6C23×C5×D4C2212yes—
7C23×C5×C8C2212yes—
8C2×C5×#127—28no—
9C2×C5×#127—22no—
10C2×C5×#127C414yescomplemented
11C22×C5×C4⋊C4C2212yes—
12C22×C42×C5C2211yescharacteristic
13C2×C5×#102—28no—
14C2×C5×#102—28no—
15C2×C5×#102—28no—
16C2×C5×#95—22no—
17C5×#336—22no—
18#11008C511yesmaximal, characteristic, direct product factor, Sylow
19C25×C5—22no—
20C22×C5×D4—216no—
21C22×C5×D4—28no—
22C22×C5×D4—24no—
23C22×C5×D4—24no—
24C22×C5×D4—24no—
25C22×C5×D4—22no—
26C22×C5×D4—24no—
27C22×C5×D4—24no—
28C22×C5×D4—48no—
29C22×C5×D4—44no—
30C22×C5×D4—44no—
31C22×C5×D4C2×C414yes—
32C22×C5×D4D418yes—
33C23×C4×C5—22no—
34C23×C4×C5D412yes—
35C23×C4×C5C2311yescharacteristic
36C22×C5×C8—22no—
37C22×C5×C8—24no—
38C22×C5×C8—24no—
39C22×C5×C8—22no—
40C22×C5×C8D414yescomplemented
41C5×#127—216no—
42C5×#127—216no—
43C2×C5×C4⋊C4—24no—
44C2×C5×C4⋊C4—24no—
45C2×C5×C4⋊C4—22no—
46C2×C5×C4⋊C4D414yescomplemented
47C2×C42×C5—24no—
48C2×C42×C5C2×C412yes—
49C2×C42×C5D412yes—
50C5×#102—232no—
51C5×#95—44no—
52C22×#127C2×C511yescharacteristic
53C22×#102C2×C514yescomplemented
54C2×#336C2×C511yescharacteristic, complemented
55C4⋊#95C2×C511yescharacteristic, complemented
56C24×C5—24no—
57C24×C5—28no—
58C24×C5—44no—
59C24×C5—42no—
60C24×C5—42no—
61C24×C5—44no—
62C24×C5—44no—
63C24×C5—48no—
64C24×C5C2×D411yescharacteristic
65C2×C5×D4—232no—
66C2×C5×D4—24no—
67C2×C5×D4—28no—
68C2×C5×D4—28no—
69C2×C5×D4—28no—
70C2×C5×D4—28no—
71C2×C5×D4—28no—
72C2×C5×D4—28no—
73C2×C5×D4—28no—
74C2×C5×D4—416no—
75C2×C5×D4—432no—
76C2×C5×D4—432no—
77C2×C5×D4—416no—
78C2×C5×D4—44no—
79C2×C5×D4—44no—
80C2×C5×D4—44no—
81C2×C5×D4—44no—
82C2×C5×D4—44no—
83C2×C5×D4—42no—
84C2×C5×D4—42no—
85C2×C5×D4C22⋊C418yes—
86C22×C4×C5—24no—
87C22×C4×C5—24no—
88C22×C4×C5—24no—
89C22×C4×C5—42no—
90C22×C4×C5—42no—
91C22×C4×C5—44no—
92C22×C4×C5—44no—
93C22×C4×C5C22⋊C414yes—
94C22×C4×C5D814yes—
95C22×C4×C5SD1614yes—
96C22×C4×C5C22×C411yescharacteristic
97C22×C4×C5C2×D414yes—
98C22×C4×C5C2×D412yes—
99C22×C4×C5C2×D412yes—
100C22×C4×C5C2×D411yescharacteristic
101C22×C4×C5#4112yes—
102C22×C4×C5#4112yes—
103C2×C5×C8—28no—
104C2×C5×C8—24no—
105C2×C5×C8—42no—
106C2×C5×C8—44no—
107C2×C5×C8—42no—
108C5×C4⋊C4—28no—
109C5×C4⋊C4—44no—
110C42×C5—24no—
111C42×C5—24no—
112C23×D4—22no—
113C23×D4C22×C512yes—
114C23×C8C22×C512yes—
115C2×#127—28no—
116C2×#127—22no—
117C2×#127C4×C514yescomplemented
118C22×C4⋊C4C22×C512yes—
119C22×C42C22×C511yescharacteristic
120C2×#102—28no—
121C2×#102—28no—
122C2×#102—28no—
123C2×#95—22no—
124#336—22no—
125C23×C5—28no—
126C23×C5—44no—
127C23×C5—44no—
128C23×C5—48no—
129C23×C5—48no—
130C23×C5—48no—
131C23×C5—48no—
132C23×C5—416no—
133C23×C5—416no—
134C23×C5—88no—
135C23×C5—88no—
136C23×C5—84no—
137C23×C5—84no—
138C23×C5—82no—
139C23×C5—82no—
140C23×C5—84no—
141C23×C5C2×C22⋊C411yescharacteristic
142C23×C5#12012yes—
143C23×C5#12112yes—
144C23×C5#12411yescharacteristic
145C23×C5#12711yescharacteristic
146C23×C5C2×D812yes—
147C23×C5C2×SD1612yes—
148C23×C5AGL(1,ℤ/8)14yes—
149C5×D4—216no—
150C5×D4—464no—
151C5×D4—48no—
152C5×D4—48no—
153C5×D4—48no—
154C2×C4×C5—24no—
155C2×C4×C5—24no—
156C2×C4×C5—28no—
157C2×C4×C5—28no—
158C2×C4×C5—44no—
159C2×C4×C5—48no—
160C2×C4×C5—84no—
161C2×C4×C5—82no—
162C2×C4×C5—82no—
163C2×C4×C5#10218yescomplemented
164C2×C4×C5C2×C22⋊C412yes—
165C2×C4×C5C4×D412yes—
166C2×C4×C5C4×D412yes—
167C2×C4×C5#12014yes—
168C2×C4×C5#12012yes—
169C2×C4×C5#12114yes—
170C2×C4×C5#12114yes—
171C2×C4×C5#12112yes—
172C2×C4×C5#12314yes—
173C2×C4×C5#12411yescharacteristic
174C2×C4×C5#12711yescharacteristic
175C5×C8—44no—
176C25—22no—
177C22×D4—216no—
178C22×D4—28no—
179C22×D4—24no—
180C22×D4—24no—
181C22×D4—24no—
182C22×D4—22no—
183C22×D4—24no—
184C22×D4—24no—
185C22×D4—48no—
186C22×D4—44no—
187C22×D4—44no—
188C22×D4C2×C4×C514yes—
189C22×D4C5×D418yes—
190C23×C4—22no—
191C23×C4C5×D412yes—
192C23×C4C23×C511yescharacteristic
193C22×C8—22no—
194C22×C8—24no—
195C22×C8—24no—
196C22×C8—22no—
197C22×C8C5×D414yescomplemented
198#127—216no—
199#127—216no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4—24no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4C5×D414yescomplemented
204C2×C42—24no—
205C2×C42C2×C4×C512yes—
206C2×C42C5×D412yes—
207#102—232no—
208#95—44no—
209C22×C5—48no—
210C22×C5—416no—
211C22×C5—84no—
212C22×C5—84no—
213C22×C5—88no—
214C22×C5—88no—
215C22×C5—88no—
216C22×C5—816no—
217C22×C5#37911yescharacteristic
218C22×C5#39011yescharacteristic
219C22×C5#39011yescharacteristic
220C22×C5#39212yes—
221C22×C5#39412yes—
222C22×C5C2×#10212yes—
223C22×C5#41812yes—
224C22×C5#44714yes—
225C22×C5#45014yes—
226C22×C5#45914yes—
227C22×C5#46014yes—
228C22×C5#48612yes—
229C22×C5#49012yes—
230C22×C5#49211yescharacteristic
231C22×C5#49311yescharacteristic
232C22×C5#49612yes—
233C4×C5—28no—
234C4×C5—84no—
235C4×C5#38614yes—
236C4×C5#39212yes—
237C4×C5#39412yes—
238C24—24no—
239C24—28no—
240C24—44no—
241C24—42no—
242C24—42no—
243C24—44no—
244C24—44no—
245C24—48no—
246C24C2×C5×D411yescharacteristic
247C2×D4—232no—
248C2×D4—24no—
249C2×D4—28no—
250C2×D4—28no—
251C2×D4—28no—
252C2×D4—28no—
253C2×D4—28no—
254C2×D4—28no—
255C2×D4—28no—
256C2×D4—416no—
257C2×D4—432no—
258C2×D4—432no—
259C2×D4—44no—
260C2×D4—44no—
261C2×D4—44no—
262C2×D4—44no—
263C2×D4—44no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—416no—
267C2×D4C5×C22⋊C418yes—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—44no—
274C22×C4—44no—
275C22×C4C5×C22⋊C414yes—
276C22×C4C5×D814yes—
277C22×C4C5×SD1614yes—
278C22×C4C22×C4×C511yescharacteristic
279C22×C4C2×C5×D414yes—
280C22×C4C2×C5×D412yes—
281C22×C4C2×C5×D412yes—
282C22×C4C2×C5×D411yescharacteristic
283C22×C4C5×#4112yes—
284C22×C4C5×#4112yes—
285C2×C8—28no—
286C2×C8—24no—
287C2×C8—42no—
288C2×C8—44no—
289C2×C8—42no—
290C4⋊C4—28no—
291C4⋊C4—44no—
292C42—24no—
293C42—24no—
294C2×C5—88no—
295C2×C5#143811yescharacteristic
296C2×C5#178612yes—
297C2×C5#195711yescharacteristic
298C2×C5#196111yescharacteristic
299C2×C5#198212yes—
300C2×C5#201112yes—
301C2×C5#201412yes—
302C2×C5#204114yes—
303C23—28no—
304C23—44no—
305C23—44no—
306C23—48no—
307C23—48no—
308C23—48no—
309C23—48no—
310C23—416no—
311C23—416no—
312C23—88no—
313C23—88no—
314C23—84no—
315C23—84no—
316C23—82no—
317C23—82no—
318C23—84no—
319C23C2×C5×C22⋊C411yescharacteristic
320C23C5×#12012yes—
321C23C5×#12112yes—
322C23C5×#12411yescharacteristic
323C23C5×#12711yescharacteristic
324C23C2×C5×D812yes—
325C23C2×C5×SD1612yes—
326C23C5×AGL(1,ℤ/8)14yes—
327D4—216no—
328D4—464no—
329D4—48no—
330D4—48no—
331D4—48no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—28no—
335C2×C4—28no—
336C2×C4—44no—
337C2×C4—48no—
338C2×C4—84no—
339C2×C4—82no—
340C2×C4—82no—
341C2×C4C5×#10218yescomplemented
342C2×C4C2×C5×C22⋊C412yes—
343C2×C4C4×C5×D412yes—
344C2×C4C4×C5×D412yes—
345C2×C4C5×#12014yes—
346C2×C4C5×#12012yes—
347C2×C4C5×#12114yes—
348C2×C4C5×#12114yes—
349C2×C4C5×#12112yes—
350C2×C4C5×#12314yes—
351C2×C4C5×#12411yescharacteristic
352C2×C4C5×#12711yescharacteristic
353C8—44no—
354C5#1100811yescharacteristic, direct product factor, Sylow
355C22—416no—
356C22—48no—
357C22—88no—
358C22—816no—
359C22—84no—
360C22—84no—
361C22—88no—
362C22—88no—
363C22C5×#37911yescharacteristic
364C22C5×#39011yescharacteristic
365C22C5×#39011yescharacteristic
366C22C5×#39212yes—
367C22C5×#39412yes—
368C22C2×C5×#10212yes—
369C22C5×#41812yes—
370C22C5×#44714yes—
371C22C5×#45014yes—
372C22C5×#45914yes—
373C22C5×#46014yes—
374C22C5×#48612yes—
375C22C5×#49012yes—
376C22C5×#49211yescharacteristic
377C22C5×#49311yescharacteristic
378C22C5×#49612yes—
379C4—28no—
380C4—84no—
381C4C5×#38614yes—
382C4C5×#39212yes—
383C4C5×#39412yes—
384C2—88no—
385C2C5×#143811yescharacteristic
386C2C5×#178612yes—
387C2C5×#195711yescharacteristic
388C2C5×#196111yescharacteristic
389C2C5×#198212yes—
390C2C5×#201112yes—
391C2C5×#201412yes—
392C2C5×#204114yes—
subgroupG/H
center, socleC24×C5C2×D4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC22×C5×#127C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C5 ◁ C22×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C5×#102C2semidirect
3. C2×C5×#336C2semidirect
4. C5×C4⋊#95C2semidirect
10. C2×C5×#127C4semidirect
18. #11008C5direct (N × H)
40. C22×C5×C8D4semidirect
46. C2×C5×C4⋊C4D4semidirect
53. C22×#102C2×C5semidirect
54. C2×#336C2×C5semidirect
55. C4⋊#95C2×C5semidirect
117. C2×#127C4×C5semidirect
163. C2×C4×C5#102semidirect
197. C22×C8C5×D4semidirect
203. C2×C4⋊C4C5×D4semidirect
341. C2×C4C5×#102semidirect
354. C5#11008direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1272
C22×C5×#1022
C2×C5×#3362
C5×C4⋊#952
#110085