Finite Group Databasebeta

← C5×#9364 #11932084

Subgroups — C5×#9364 #11932084

Order 1280.

732 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3007C211yesmaximal, characteristic
2C5×#2341C211yesmaximal, characteristic
3C5×#1996C211yesmaximal, characteristic, complemented
4C5×#1789C211yesmaximal, characteristic
5C5×#1508C211yesmaximal, characteristic, complemented
6C5×#1305C211yesmaximal, characteristic, complemented
7C5×#1297C211yesmaximal, characteristic, complemented
8C22×C5×#41C2211yescharacteristic
9C2×C5×#137C412yescomplemented
10C2×C5×C22⋊Q8C2211yescharacteristic
11C2×C4×C5×Q8—21no—
12C5×#452—22no—
13C5×#451—21no—
14C5×#450—21no—
15C2×C5×#104—22no—
16C5×#417C412yescomplemented
17C5×#407C2211yescharacteristic
18C5×#407C2211yescharacteristic
19C5×#390—21no—
20C5×#390—22no—
21C5×#380—21no—
22C5×#380C2211yescharacteristic
23C4×C5×C22⋊C4—21no—
24C4×C5×C22⋊C4C2211yescharacteristic
25C4×C5×C22⋊C4C2211yescharacteristic
26C5×#342—22no—
27C5×#328—21no—
28C5×#328—21no—
29#9364C511yesmaximal, characteristic, direct product factor, Sylow
30C2×C5×#41—21no—
31C2×C5×#41—21no—
32C2×C5×#41—44no—
33C2×C5×#41C2×C412yes—
34C2×C5×#41D412yes—
35C22×C5×Q8C2×C411yescharacteristic
36C22×C5×Q8D411yescharacteristic
37C22×C5×D4—21no—
38C22×C5×D4D411yescharacteristic
39C23×C4×C5—21no—
40C23×C4×C5C2311yescharacteristic
41C5×#137—44no—
42C2×C5×Q16—22no—
43C2×C5×SD16—22no—
44C2×C5×M16—21no—
45C2×C5×M16C2×C412yes—
46C5×C22⋊Q8—21no—
47C5×C22⋊Q8—21no—
48C5×C22⋊Q8—21no—
49C5×C22⋊Q8—21no—
50C4×C5×Q8—44no—
51C2×C5×C4⋊C4—22no—
52C2×C5×C4⋊C4—21no—
53C2×C5×C4⋊C4—21no—
54C2×C5×C4⋊C4C2×C411yescharacteristic
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4—22no—
57C2×C5×C22⋊C4—21no—
58C2×C5×C22⋊C4—21no—
59C2×C5×C22⋊C4—22no—
60C2×C5×C22⋊C4D412yes—
61C2×C42×C5—22no—
62C2×C42×C5—21no—
63C2×C42×C5—21no—
64C5×#104—44no—
65C5×#103—22no—
66C5×#102—22no—
67C5×C22⋊C8—21no—
68C5×C22⋊C8—21no—
69C5×C22⋊C8—21no—
70C5×C22⋊C8—21no—
71C5×#95—21no—
72C5×#95—21no—
73C5×#95D411yescharacteristic
74C5×#95D411yescharacteristic
75#3007C2×C511yescharacteristic
76#2341C2×C511yescharacteristic
77#1996C2×C511yescharacteristic, complemented
78#1789C2×C511yescharacteristic
79#1508C2×C511yescharacteristic, complemented
80#1305C2×C511yescharacteristic, complemented
81#1297C2×C511yescharacteristic, complemented
82C24×C5—21no—
83C24×C5C2×D411yescharacteristic
84C5×#41—24no—
85C5×#41—24no—
86C5×#41—42no—
87C5×#41—42no—
88C5×#41—44no—
89C5×#41—44no—
90C2×C5×Q8—24no—
91C2×C5×Q8—21no—
92C2×C5×Q8—21no—
93C2×C5×Q8—21no—
94C2×C5×Q8—42no—
95C2×C5×Q8C22⋊C412yes—
96C2×C5×D4—22no—
97C2×C5×D4—22no—
98C2×C5×D4—21no—
99C2×C5×D4—42no—
100C2×C5×D4—44no—
101C2×C5×D4C22⋊C412yes—
102C22×C4×C5—21no—
103C22×C4×C5—21no—
104C22×C4×C5—22no—
105C22×C4×C5—22no—
106C22×C4×C5—21no—
107C22×C4×C5—22no—
108C22×C4×C5—21no—
109C22×C4×C5—21no—
110C22×C4×C5—42no—
111C22×C4×C5—44no—
112C22×C4×C5—41no—
113C22×C4×C5C22×C411yescharacteristic
114C22×C4×C5C2×D411yescharacteristic
115C22×C4×C5C2×D411yescharacteristic
116C22×C4×C5C2×D411yescharacteristic
117C22×C4×C5#4111yescharacteristic
118C22×C4×C5#4111yescharacteristic
119C5×Q16—44no—
120C5×SD16—44no—
121C5×M16—42no—
122C5×M16—42no—
123C2×C5×C8—22no—
124C2×C5×C8—41no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—44no—
128C5×C4⋊C4—42no—
129C5×C4⋊C4—41no—
130C5×C4⋊C4—41no—
131C5×C22⋊C4—22no—
132C5×C22⋊C4—42no—
133C5×C22⋊C4—44no—
134C5×C22⋊C4—41no—
135C5×C22⋊C4—41no—
136C5×C22⋊C4—41no—
137C5×C22⋊C4—42no—
138C5×C22⋊C4—82no—
139C42×C5—44no—
140C42×C5—42no—
141C42×C5—42no—
142C22×#41C22×C511yescharacteristic
143C2×#137C4×C512yescomplemented
144C2×C22⋊Q8C22×C511yescharacteristic
145C2×C4×Q8—21no—
146#452—22no—
147#451—21no—
148#450—21no—
149C2×#104—22no—
150#417C4×C512yescomplemented
151#407C22×C511yescharacteristic
152#407C22×C511yescharacteristic
153#390—21no—
154#390—22no—
155#380—21no—
156#380C22×C511yescharacteristic
157C4×C22⋊C4—21no—
158C4×C22⋊C4C22×C511yescharacteristic
159C4×C22⋊C4C22×C511yescharacteristic
160#342—22no—
161#328—21no—
162#328—21no—
163C23×C5—21no—
164C23×C5—21no—
165C23×C5—22no—
166C23×C5—41no—
167C23×C5—41no—
168C23×C5—42no—
169C23×C5—42no—
170C23×C5—41no—
171C23×C5—41no—
172C23×C5C4×D411yescharacteristic
173C23×C5#12011yescharacteristic
174C23×C5#12111yescharacteristic
175C5×Q8—24no—
176C5×Q8—22no—
177C5×Q8—42no—
178C5×Q8—81no—
179C5×Q8#9914yes—
180C5×D4—22no—
181C5×D4—22no—
182C5×D4—44no—
183C5×D4—44no—
184C5×D4—42no—
185C2×C4×C5—24no—
186C2×C4×C5—22no—
187C2×C4×C5—22no—
188C2×C4×C5—22no—
189C2×C4×C5—22no—
190C2×C4×C5—22no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—44no—
195C2×C4×C5—44no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5—42no—
200C2×C4×C5—42no—
201C2×C4×C5—41no—
202C2×C4×C5—42no—
203C2×C4×C5—41no—
204C2×C4×C5—41no—
205C2×C4×C5—42no—
206C2×C4×C5—41no—
207C2×C4×C5—81no—
208C2×C4×C5—81no—
209C2×C4×C5—81no—
210C2×C4×C5—81no—
211C2×C4×C5C2×C22⋊C411yescharacteristic
212C2×C4×C5C4×D411yescharacteristic
213C2×C4×C5#12111yescharacteristic
214C2×C4×C5#12311yescharacteristic
215C5×C8—42no—
216C5×C8—81no—
217C2×#41—21no—
218C2×#41—21no—
219C2×#41—44no—
220C2×#41C2×C4×C512yes—
221C2×#41C5×D412yes—
222C22×Q8C2×C4×C511yescharacteristic
223C22×Q8C5×D411yescharacteristic
224C22×D4—21no—
225C22×D4C5×D411yescharacteristic
226C23×C4—21no—
227C23×C4C23×C511yescharacteristic
228#137—44no—
229C2×Q16—22no—
230C2×SD16—22no—
231C2×M16—21no—
232C2×M16C2×C4×C512yes—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C4×Q8—44no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4C2×C4×C511yescharacteristic
242C2×C22⋊C4—21no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4C5×D412yes—
248C2×C42—22no—
249C2×C42—21no—
250C2×C42—21no—
251#104—44no—
252#103—22no—
253#102—22no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258#95—21no—
259#95—21no—
260#95C5×D411yescharacteristic
261#95C5×D411yescharacteristic
262C22×C5—21no—
263C22×C5—21no—
264C22×C5—21no—
265C22×C5—21no—
266C22×C5—21no—
267C22×C5—21no—
268C22×C5—21no—
269C22×C5—21no—
270C22×C5—42no—
271C22×C5—42no—
272C22×C5—42no—
273C22×C5—81no—
274C22×C5—81no—
275C22×C5—82no—
276C22×C5—82no—
277C22×C5#38611yescharacteristic
278C22×C5#45511yescharacteristic
279C22×C5#45611yescharacteristic
280C4×C5—21no—
281C4×C5—24no—
282C4×C5—21no—
283C4×C5—21no—
284C4×C5—42no—
285C4×C5—82no—
286C4×C5—81no—
287C4×C5—82no—
288C4×C5—81no—
289C4×C5—81no—
290C4×C5C2×#9912yes—
291C24—21no—
292C24C2×C5×D411yescharacteristic
293#41—24no—
294#41—24no—
295#41—42no—
296#41—42no—
297#41—44no—
298#41—44no—
299C2×Q8—24no—
300C2×Q8—21no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—42no—
304C2×Q8C5×C22⋊C412yes—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—21no—
308C2×D4—42no—
309C2×D4—44no—
310C2×D4C5×C22⋊C412yes—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—42no—
320C22×C4—44no—
321C22×C4—41no—
322C22×C4C22×C4×C511yescharacteristic
323C22×C4C2×C5×D411yescharacteristic
324C22×C4C2×C5×D411yescharacteristic
325C22×C4C2×C5×D411yescharacteristic
326C22×C4C5×#4111yescharacteristic
327C22×C4C5×#4111yescharacteristic
328Q16—44no—
329SD16—44no—
330M16—42no—
331M16—42no—
332C2×C8—22no—
333C2×C8—41no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—44no—
337C4⋊C4—42no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C22⋊C4—22no—
341C22⋊C4—42no—
342C22⋊C4—44no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—42no—
347C22⋊C4—82no—
348C42—44no—
349C42—42no—
350C42—42no—
351C2×C5—21no—
352C2×C5—21no—
353C2×C5—41no—
354C2×C5—41no—
355C2×C5—82no—
356C2×C5#188211yescharacteristic
357C2×C5#189811yescharacteristic
358C2×C5#190611yescharacteristic
359C23—21no—
360C23—21no—
361C23—22no—
362C23—41no—
363C23—41no—
364C23—42no—
365C23—42no—
366C23—41no—
367C23—41no—
368C23C4×C5×D411yescharacteristic
369C23C5×#12011yescharacteristic
370C23C5×#12111yescharacteristic
371Q8—24no—
372Q8—22no—
373Q8—42no—
374Q8—81no—
375Q8C5×#9914yes—
376D4—22no—
377D4—22no—
378D4—44no—
379D4—44no—
380D4—42no—
381C2×C4—24no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4C2×C5×C22⋊C411yescharacteristic
408C2×C4C4×C5×D411yescharacteristic
409C2×C4C5×#12111yescharacteristic
410C2×C4C5×#12311yescharacteristic
411C8—42no—
412C8—81no—
413C5#936411yescharacteristic, direct product factor, Sylow
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—82no—
428C22—82no—
429C22C5×#38611yescharacteristic
430C22C5×#45511yescharacteristic
431C22C5×#45611yescharacteristic
432C4—21no—
433C4—24no—
434C4—21no—
435C4—21no—
436C4—42no—
437C4—82no—
438C4—81no—
439C4—82no—
440C4—81no—
441C4—81no—
442C4C2×C5×#9912yes—
443C2—21no—
444C2—21no—
445C2—41no—
446C2—41no—
447C2—82no—
448C2C5×#188211yescharacteristic
449C2C5×#189811yescharacteristic
450C2C5×#190611yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC22×C5×#41C22
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
3. C5×#1996C2semidirect
5. C5×#1508C2semidirect
6. C5×#1305C2semidirect
7. C5×#1297C2semidirect
9. C2×C5×#137C4semidirect
16. C5×#417C4semidirect
29. #9364C5direct (N × H)
77. #1996C2×C5semidirect
79. #1508C2×C5semidirect
80. #1305C2×C5semidirect
81. #1297C2×C5semidirect
143. C2×#137C4×C5semidirect
150. #417C4×C5semidirect
413. C5#9364direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30072
C5×#23412
C5×#19962
C5×#17892
C5×#15082
C5×#13052
C5×#12972
#93645