Finite Group Databasebeta

← C5×#9386 #11932106

Subgroups — C5×#9386 #11932106

Order 1280.

618 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2973C211yesmaximal, characteristic, complemented
2C5×#2543C211yesmaximal, characteristic
3C5×#1799C211yesmaximal, characteristic, complemented
4C5×#1519C212yesmaximal, complemented
5C5×#1294C212yesmaximal, complemented
6C2×C5×#121—21no—
7C2×C5×#121C2211yescharacteristic
8C2×C4×C5×D4C2211yescharacteristic
9C5×#435—24no—
10C5×#432—21no—
11C2×C5×#99—21no—
12C5×#407—21no—
13C2×C5×C22⋊C8C2212yes—
14C5×#398C411yescharacteristic, complemented
15C5×#397C411yescharacteristic, complemented
16C5×#394C411yescharacteristic, complemented
17C5×#392C411yescharacteristic, complemented
18C5×#388—21no—
19C5×#386—21no—
20C5×#386—21no—
21C5×#380C2212yes—
22C2×C5×#95C2211yescharacteristic
23C5×#342—21no—
24C5×#327—24no—
25#9386C511yesmaximal, characteristic, direct product factor, Sylow
26C22×C5×D4—21no—
27C22×C5×D4—21no—
28C22×C5×D4C2×C411yescharacteristic
29C22×C5×D4D411yescharacteristic
30C23×C4×C5—21no—
31C23×C4×C5D411yescharacteristic
32C23×C4×C5C2311yescharacteristic
33C2×C5×M16—22no—
34C22×C5×C8—22no—
35C5×#121—22no—
36C5×#121—22no—
37C5×#121—44no—
38C4×C5×D4—22no—
39C4×C5×D4—22no—
40C2×C5×C4⋊C4—21no—
41C2×C5×C4⋊C4—22no—
42C2×C5×C4⋊C4C2×C411yescharacteristic
43C2×C5×C4⋊C4C2×C411yescharacteristic
44C2×C5×C22⋊C4—21no—
45C2×C5×C22⋊C4—21no—
46C2×C5×C22⋊C4—21no—
47C2×C5×C22⋊C4—21no—
48C2×C5×C22⋊C4—22no—
49C2×C5×C22⋊C4—21no—
50C2×C5×C22⋊C4C2×C411yescharacteristic
51C2×C5×C22⋊C4D411yescharacteristic
52C2×C42×C5D411yescharacteristic
53C5×C4⋊C8—22no—
54C5×#99—42no—
55C5×C22⋊C8—22no—
56C5×C22⋊C8—22no—
57C5×C22⋊C8D414yescomplemented
58C5×#97—22no—
59C5×#95—21no—
60C5×#95—21no—
61C5×#95—21no—
62C5×#95—22no—
63C5×#95C2×C411yescharacteristic
64C5×#95C2×C411yescharacteristic
65#2973C2×C511yescharacteristic, complemented
66#2543C2×C511yescharacteristic
67#1799C2×C511yescharacteristic, complemented
68#1519C2×C512yescomplemented
69#1294C2×C512yescomplemented
70C24×C5—21no—
71C24×C5C22⋊C411yescharacteristic
72C24×C5C2×D411yescharacteristic
73C2×C5×D4—22no—
74C2×C5×D4—22no—
75C2×C5×D4—21no—
76C2×C5×D4—21no—
77C2×C5×D4—22no—
78C2×C5×D4—42no—
79C2×C5×D4—42no—
80C2×C5×D4—42no—
81C2×C5×D4—42no—
82C2×C5×D4—41no—
83C2×C5×D4—41no—
84C2×C5×D4—81no—
85C2×C5×D4—81no—
86C22×C4×C5—21no—
87C22×C4×C5—21no—
88C22×C4×C5—21no—
89C22×C4×C5—21no—
90C22×C4×C5—21no—
91C22×C4×C5—42no—
92C22×C4×C5—42no—
93C22×C4×C5—42no—
94C22×C4×C5—81no—
95C22×C4×C5—81no—
96C22×C4×C5—81no—
97C22×C4×C5C22⋊C411yescharacteristic
98C22×C4×C5C22⋊C411yescharacteristic
99C22×C4×C5C22⋊C411yescharacteristic
100C22×C4×C5C22×C411yescharacteristic
101C22×C4×C5C2×D412yes—
102C22×C4×C5C2×D411yescharacteristic
103C22×C4×C5#4112yes—
104C5×M16—82no—
105C2×C5×C8—24no—
106C2×C5×C8—82no—
107C5×C4⋊C4—22no—
108C5×C4⋊C4—22no—
109C5×C4⋊C4—42no—
110C5×C4⋊C4—82no—
111C5×C22⋊C4—22no—
112C5×C22⋊C4—22no—
113C5×C22⋊C4—42no—
114C5×C22⋊C4—42no—
115C5×C22⋊C4—42no—
116C5×C22⋊C4—41no—
117C5×C22⋊C4—41no—
118C5×C22⋊C4—42no—
119C5×C22⋊C4—42no—
120C5×C22⋊C4—81no—
121C42×C5—21no—
122C42×C5—21no—
123C2×#121—21no—
124C2×#121C22×C511yescharacteristic
125C2×C4×D4C22×C511yescharacteristic
126#435—24no—
127#432—21no—
128C2×#99—21no—
129#407—21no—
130C2×C22⋊C8C22×C512yes—
131#398C4×C511yescharacteristic, complemented
132#397C4×C511yescharacteristic, complemented
133#394C4×C511yescharacteristic, complemented
134#392C4×C511yescharacteristic, complemented
135#388—21no—
136#386—21no—
137#386—21no—
138#380C22×C512yes—
139C2×#95C22×C511yescharacteristic
140#342—21no—
141#327—24no—
142C23×C5—21no—
143C23×C5—21no—
144C23×C5—21no—
145C23×C5—41no—
146C23×C5—41no—
147C23×C5—41no—
148C23×C5—41no—
149C23×C5—41no—
150C23×C5—41no—
151C23×C5—41no—
152C23×C5—41no—
153C23×C5—41no—
154C23×C5—41no—
155C23×C5—41no—
156C23×C5C2×C22⋊C411yescharacteristic
157C23×C5#12112yes—
158C23×C5AGL(1,ℤ/8)11yescharacteristic
159C23×C5AGL(1,ℤ/8)12yes—
160C23×C5#13711yescharacteristic
161C5×D4—42no—
162C5×D4—42no—
163C5×D4—82no—
164C5×D4—84no—
165C5×D4—82no—
166C5×D4—82no—
167C2×C4×C5—22no—
168C2×C4×C5—21no—
169C2×C4×C5—21no—
170C2×C4×C5—21no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—42no—
174C2×C4×C5—42no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—42no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—81no—
189C2×C4×C5—84no—
190C2×C4×C5—82no—
191C2×C4×C5—82no—
192C2×C4×C5—82no—
193C2×C4×C5C4×D412yes—
194C2×C4×C5#12011yescharacteristic
195C2×C4×C5#12311yescharacteristic
196C5×C8—44no—
197C22×D4—21no—
198C22×D4—21no—
199C22×D4C2×C4×C511yescharacteristic
200C22×D4C5×D411yescharacteristic
201C23×C4—21no—
202C23×C4C5×D411yescharacteristic
203C23×C4C23×C511yescharacteristic
204C2×M16—22no—
205C22×C8—22no—
206#121—22no—
207#121—22no—
208#121—44no—
209C4×D4—22no—
210C4×D4—22no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4C2×C4×C511yescharacteristic
214C2×C4⋊C4C2×C4×C511yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4C2×C4×C511yescharacteristic
222C2×C22⋊C4C5×D411yescharacteristic
223C2×C42C5×D411yescharacteristic
224C4⋊C8—22no—
225#99—42no—
226C22⋊C8—22no—
227C22⋊C8—22no—
228C22⋊C8C5×D414yescomplemented
229#97—22no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—22no—
234#95C2×C4×C511yescharacteristic
235#95C2×C4×C511yescharacteristic
236C22×C5—21no—
237C22×C5—22no—
238C22×C5—21no—
239C22×C5—22no—
240C22×C5—42no—
241C22×C5—41no—
242C22×C5—41no—
243C22×C5—42no—
244C22×C5—41no—
245C22×C5—41no—
246C22×C5—41no—
247C22×C5—81no—
248C22×C5—81no—
249C22×C5—81no—
250C22×C5—81no—
251C22×C5—81no—
252C22×C5—81no—
253C22×C5—81no—
254C22×C5—81no—
255C22×C5#38611yescharacteristic
256C22×C5#41711yescharacteristic
257C22×C5#41811yescharacteristic
258C22×C5#46812yes—
259C22×C5#46912yes—
260C4×C5—21no—
261C4×C5—21no—
262C4×C5—22no—
263C4×C5—42no—
264C4×C5—41no—
265C4×C5—41no—
266C4×C5—41no—
267C4×C5—81no—
268C4×C5—81no—
269C4×C5—162no—
270C24—21no—
271C24C5×C22⋊C411yescharacteristic
272C24C2×C5×D411yescharacteristic
273C2×D4—22no—
274C2×D4—21no—
275C2×D4—22no—
276C2×D4—21no—
277C2×D4—22no—
278C2×D4—42no—
279C2×D4—42no—
280C2×D4—42no—
281C2×D4—42no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—81no—
285C2×D4—81no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—81no—
295C22×C4—81no—
296C22×C4—81no—
297C22×C4C5×C22⋊C411yescharacteristic
298C22×C4C5×C22⋊C411yescharacteristic
299C22×C4C5×C22⋊C411yescharacteristic
300C22×C4C22×C4×C511yescharacteristic
301C22×C4C2×C5×D412yes—
302C22×C4C2×C5×D411yescharacteristic
303C22×C4C5×#4112yes—
304M16—82no—
305C2×C8—24no—
306C2×C8—82no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—42no—
310C4⋊C4—82no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—42no—
314C22⋊C4—42no—
315C22⋊C4—42no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—81no—
321C42—21no—
322C42—21no—
323C2×C5—21no—
324C2×C5—22no—
325C2×C5—21no—
326C2×C5—22no—
327C2×C5—81no—
328C2×C5—161no—
329C2×C5#188411yescharacteristic
330C2×C5#189511yescharacteristic
331C2×C5#191311yescharacteristic
332C23—21no—
333C23—21no—
334C23—21no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23C2×C5×C22⋊C411yescharacteristic
347C23C5×#12112yes—
348C23C5×AGL(1,ℤ/8)11yescharacteristic
349C23C5×AGL(1,ℤ/8)12yes—
350C23C5×#13711yescharacteristic
351D4—42no—
352D4—42no—
353D4—82no—
354D4—84no—
355D4—82no—
356D4—82no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—81no—
379C2×C4—84no—
380C2×C4—82no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4C4×C5×D412yes—
384C2×C4C5×#12011yescharacteristic
385C2×C4C5×#12311yescharacteristic
386C8—44no—
387C5#938611yescharacteristic, direct product factor, Sylow
388C22—21no—
389C22—22no—
390C22—21no—
391C22—22no—
392C22—42no—
393C22—41no—
394C22—41no—
395C22—42no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22C5×#38611yescharacteristic
408C22C5×#41711yescharacteristic
409C22C5×#41811yescharacteristic
410C22C5×#46812yes—
411C22C5×#46912yes—
412C4—21no—
413C4—21no—
414C4—22no—
415C4—42no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—81no—
420C4—81no—
421C4—162no—
422C2—21no—
423C2—22no—
424C2—21no—
425C2—22no—
426C2—81no—
427C2—161no—
428C2C5×#188411yescharacteristic
429C2C5×#189511yescharacteristic
430C2C5×#191311yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC5×#2543C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#2973C2semidirect
3. C5×#1799C2semidirect
4. C5×#1519C2semidirect
5. C5×#1294C2semidirect
14. C5×#398C4semidirect
15. C5×#397C4semidirect
16. C5×#394C4semidirect
17. C5×#392C4semidirect
25. #9386C5direct (N × H)
57. C5×C22⋊C8D4semidirect
65. #2973C2×C5semidirect
67. #1799C2×C5semidirect
68. #1519C2×C5semidirect
69. #1294C2×C5semidirect
131. #398C4×C5semidirect
132. #397C4×C5semidirect
133. #394C4×C5semidirect
134. #392C4×C5semidirect
228. C22⋊C8C5×D4semidirect
387. C5#9386direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#29732
C5×#25432
C5×#17992
C5×#15192
C5×#12942
#93865