Finite Group Databasebeta

← C5×#33662 #11956382

Subgroups — C5×#33662 #11956382

Order 1280.

558 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3168C211yesmaximal, characteristic, complemented
2C4×C5×#135C211yesmaximal, characteristic, complemented
3C5×#2237C211yesmaximal, characteristic, complemented
4C5×#2234C211yesmaximal, characteristic, complemented
5C5×#2229C211yesmaximal, characteristic, complemented
6C5×#2228C211yesmaximal, characteristic, complemented
7C5×#2211C211yesmaximal, characteristic, complemented
8C5×#2210C211yesmaximal, characteristic, complemented
9C5×#2189C211yesmaximal, characteristic, complemented
10C5×#2186C211yesmaximal, characteristic
11C4×C5×Q32C211yesmaximal, characteristic, complemented
12C4×C5×SD32C211yesmaximal, characteristic, complemented
13C4×C5×SD32C211yesmaximal, characteristic, complemented
14C4×C5×D16C211yesmaximal, characteristic, complemented
15C5×#2162C211yesmaximal, characteristic, complemented
16C2×C5×#135C2211yescharacteristic
17C5×#529—21no—
18C4×C5×#41—21no—
19C2×C5×Q32C2211yescharacteristic
20C2×C5×SD32C2211yescharacteristic
21C2×C5×SD32C2211yescharacteristic
22C2×C5×D16C2211yescharacteristic
23C5×#499C2211yescharacteristic
24C5×#495C2211yescharacteristic
25C5×#488—21no—
26C5×#467C2211yescharacteristic
27C5×#466C2211yescharacteristic
28C5×#465—21no—
29C4×C5×Q16C2211yescharacteristic
30C4×C5×Q16C2211yescharacteristic
31C4×C5×Q16C2211yescharacteristic
32C4×C5×SD16—21no—
33C4×C5×SD16—21no—
34C4×C5×SD16—21no—
35C4×C5×D8C2211yescharacteristic
36C4×C5×D8C2211yescharacteristic
37C4×C5×D8C2211yescharacteristic
38C5×#427C2211yescharacteristic
39C5×#416—21no—
40C2×C4×C5×C8C2211yescharacteristic
41C5×#367C2211yescharacteristic
42C5×#367C2211yescharacteristic
43C5×#366C2211yescharacteristic
44C5×#366C2211yescharacteristic
45C5×C4⋊C16C2211yescharacteristic
46C5×C4⋊C16C2211yescharacteristic
47C5×#358C2211yescharacteristic
48C5×#358C2211yescharacteristic
49C5×#358C2211yescharacteristic
50C5×#358C2211yescharacteristic
51C5×#357C2211yescharacteristic
52C5×#357C2211yescharacteristic
53C5×#357C2211yescharacteristic
54C5×#357C2211yescharacteristic
55C5×C22⋊C16C2211yescharacteristic
56C5×C22⋊C16C2211yescharacteristic
57C4×C5×C16C2211yescharacteristic
58C4×C5×C16C2211yescharacteristic
59#33662C511yesmaximal, characteristic, direct product factor, Sylow
60C2×C5×#41—21no—
61C5×#135—22no—
62C5×#135—22no—
63C2×C5×Q16C2311yescharacteristic
64C2×C5×Q16C2311yescharacteristic
65C2×C5×SD16—21no—
66C2×C5×SD16—21no—
67C2×C5×D8C2311yescharacteristic
68C2×C5×D8C2311yescharacteristic
69C22×C5×C8D411yescharacteristic
70C22×C5×C8C2311yescharacteristic
71C5×#126—41no—
72C5×#125—21no—
73C5×#124—21no—
74C5×#123—41no—
75C5×C22⋊Q8—21no—
76C5×#121—21no—
77C4×C5×Q8—21no—
78C4×C5×Q8—21no—
79C4×C5×Q8—21no—
80C4×C5×D4—21no—
81C4×C5×D4—21no—
82C4×C5×D4—21no—
83C4×C5×D4—41no—
84C4×C5×D4—41no—
85C4×C5×D4—41no—
86C5×#117—21no—
87C5×#117—41no—
88C5×#117—41no—
89C2×C42×C5—41no—
90C2×C42×C5D411yescharacteristic
91C5×Q32—22no—
92C5×SD32—22no—
93C5×SD32—22no—
94C5×D16—22no—
95C2×C5×C16C2311yescharacteristic
96C2×C5×C16C2311yescharacteristic
97C2×C5×C16C2311yescharacteristic
98C2×C5×C16C2311yescharacteristic
99C5×#107C2311yescharacteristic
100C5×#107C2311yescharacteristic
101C5×#107C2311yescharacteristic
102C5×#107C2311yescharacteristic
103C5×#106—21no—
104C5×#106—21no—
105C5×#103—21no—
106C5×#103—21no—
107C5×#103—21no—
108C5×#103—21no—
109C5×#102—21no—
110C5×#102—21no—
111C5×#102—21no—
112C5×#102—21no—
113C4×C5×C8D411yescharacteristic
114C4×C5×C8D411yescharacteristic
115C4×C5×C8C2311yescharacteristic
116C4×C5×C8C2311yescharacteristic
117#3168C2×C511yescharacteristic, complemented
118C4×#135C2×C511yescharacteristic, complemented
119#2237C2×C511yescharacteristic, complemented
120#2234C2×C511yescharacteristic, complemented
121#2229C2×C511yescharacteristic, complemented
122#2228C2×C511yescharacteristic, complemented
123#2211C2×C511yescharacteristic, complemented
124#2210C2×C511yescharacteristic, complemented
125#2189C2×C511yescharacteristic, complemented
126#2186C2×C511yescharacteristic
127C4×Q32C2×C511yescharacteristic, complemented
128C4×SD32C2×C511yescharacteristic, complemented
129C4×SD32C2×C511yescharacteristic, complemented
130C4×D16C2×C511yescharacteristic, complemented
131#2162C2×C511yescharacteristic, complemented
132C5×#41—24no—
133C5×#41—42no—
134C2×C5×Q8—21no—
135C2×C5×Q8—21no—
136C2×C5×D4—21no—
137C2×C5×D4—21no—
138C2×C5×D4—41no—
139C2×C5×D4—41no—
140C22×C4×C5—41no—
141C22×C4×C5—41no—
142C22×C4×C5—41no—
143C22×C4×C5—41no—
144C22×C4×C5D811yescharacteristic
145C22×C4×C5D811yescharacteristic
146C22×C4×C5C2×D411yescharacteristic
147C5×Q16—21no—
148C5×Q16—21no—
149C5×Q16—21no—
150C5×Q16#4112yes—
151C5×SD16—24no—
152C5×SD16—42no—
153C5×D8—21no—
154C5×D8—21no—
155C5×D8—21no—
156C5×D8#4112yes—
157C2×C5×C8—21no—
158C2×C5×C8—21no—
159C2×C5×C8—41no—
160C2×C5×C8C2×D411yescharacteristic
161C2×C5×C8C2×D411yescharacteristic
162C2×C5×C8C2×D411yescharacteristic
163C2×C5×C8C2411yescharacteristic
164C5×C4⋊C4—21no—
165C5×C4⋊C4—21no—
166C5×C4⋊C4—21no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—41no—
169C5×C4⋊C4—41no—
170C5×C4⋊C4—41no—
171C5×C4⋊C4—41no—
172C5×C4⋊C4—41no—
173C5×C4⋊C4—41no—
174C5×C22⋊C4—41no—
175C5×C22⋊C4—41no—
176C5×C22⋊C4—41no—
177C5×C22⋊C4—41no—
178C5×C22⋊C4—41no—
179C5×C22⋊C4—41no—
180C5×C22⋊C4—41no—
181C5×C22⋊C4—41no—
182C42×C5—41no—
183C42×C5—41no—
184C42×C5—41no—
185C42×C5—41no—
186C42×C5D811yescharacteristic
187C42×C5D811yescharacteristic
188C42×C5C2×D411yescharacteristic
189C42×C5C2×D411yescharacteristic
190C5×C16—21no—
191C5×C16—21no—
192C5×C16—21no—
193C5×C16—21no—
194C2×#135C22×C511yescharacteristic
195#529—21no—
196C4×#41—21no—
197C2×Q32C22×C511yescharacteristic
198C2×SD32C22×C511yescharacteristic
199C2×SD32C22×C511yescharacteristic
200C2×D16C22×C511yescharacteristic
201#499C22×C511yescharacteristic
202#495C22×C511yescharacteristic
203#488—21no—
204#467C22×C511yescharacteristic
205#466C22×C511yescharacteristic
206#465—21no—
207C4×Q16C22×C511yescharacteristic
208C4×Q16C22×C511yescharacteristic
209C4×Q16C22×C511yescharacteristic
210C4×SD16—21no—
211C4×SD16—21no—
212C4×SD16—21no—
213C4×D8C22×C511yescharacteristic
214C4×D8C22×C511yescharacteristic
215C4×D8C22×C511yescharacteristic
216#427C22×C511yescharacteristic
217#416—21no—
218C2×C4×C8C22×C511yescharacteristic
219#367C22×C511yescharacteristic
220#367C22×C511yescharacteristic
221#366C22×C511yescharacteristic
222#366C22×C511yescharacteristic
223C4⋊C16C22×C511yescharacteristic
224C4⋊C16C22×C511yescharacteristic
225#358C22×C511yescharacteristic
226#358C22×C511yescharacteristic
227#358C22×C511yescharacteristic
228#358C22×C511yescharacteristic
229#357C22×C511yescharacteristic
230#357C22×C511yescharacteristic
231#357C22×C511yescharacteristic
232#357C22×C511yescharacteristic
233C22⋊C16C22×C511yescharacteristic
234C22⋊C16C22×C511yescharacteristic
235C4×C16C22×C511yescharacteristic
236C4×C16C22×C511yescharacteristic
237C23×C5—41no—
238C23×C5—41no—
239C23×C5C2×D811yescharacteristic
240C5×Q8—22no—
241C5×Q8—41no—
242C5×Q8—41no—
243C5×Q8—41no—
244C5×D4—22no—
245C5×D4—44no—
246C5×D4—41no—
247C5×D4—41no—
248C5×D4—41no—
249C5×D4—82no—
250C2×C4×C5—21no—
251C2×C4×C5—21no—
252C2×C4×C5—22no—
253C2×C4×C5—41no—
254C2×C4×C5—44no—
255C2×C4×C5—41no—
256C2×C4×C5—41no—
257C2×C4×C5—41no—
258C2×C4×C5—41no—
259C2×C4×C5—41no—
260C2×C4×C5—41no—
261C2×C4×C5—82no—
262C2×C4×C5—82no—
263C2×C4×C5—82no—
264C2×C4×C5C2×D811yescharacteristic
265C2×C4×C5C2×D811yescharacteristic
266C2×C4×C5C2×D811yescharacteristic
267C2×C4×C5C2×D811yescharacteristic
268C2×C4×C5C2×D811yescharacteristic
269C2×C4×C5C22×D411yescharacteristic
270C5×C8—21no—
271C5×C8—21no—
272C5×C8—21no—
273C5×C8C2×#4111yescharacteristic
274C5×C8C2×#4111yescharacteristic
275C2×#41—21no—
276#135—22no—
277#135—22no—
278C2×Q16C23×C511yescharacteristic
279C2×Q16C23×C511yescharacteristic
280C2×SD16—21no—
281C2×SD16—21no—
282C2×D8C23×C511yescharacteristic
283C2×D8C23×C511yescharacteristic
284C22×C8C5×D411yescharacteristic
285C22×C8C23×C511yescharacteristic
286#126—41no—
287#125—21no—
288#124—21no—
289#123—41no—
290C22⋊Q8—21no—
291#121—21no—
292C4×Q8—21no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×D4—21no—
296C4×D4—21no—
297C4×D4—21no—
298C4×D4—41no—
299C4×D4—41no—
300C4×D4—41no—
301#117—21no—
302#117—41no—
303#117—41no—
304C2×C42—41no—
305C2×C42C5×D411yescharacteristic
306Q32—22no—
307SD32—22no—
308SD32—22no—
309D16—22no—
310C2×C16C23×C511yescharacteristic
311C2×C16C23×C511yescharacteristic
312C2×C16C23×C511yescharacteristic
313C2×C16C23×C511yescharacteristic
314#107C23×C511yescharacteristic
315#107C23×C511yescharacteristic
316#107C23×C511yescharacteristic
317#107C23×C511yescharacteristic
318#106—21no—
319#106—21no—
320#103—21no—
321#103—21no—
322#103—21no—
323#103—21no—
324#102—21no—
325#102—21no—
326#102—21no—
327#102—21no—
328C4×C8C5×D411yescharacteristic
329C4×C8C5×D411yescharacteristic
330C4×C8C23×C511yescharacteristic
331C4×C8C23×C511yescharacteristic
332C22×C5—21no—
333C22×C5—21no—
334C22×C5—21no—
335C22×C5—42no—
336C22×C5—81no—
337C22×C5—81no—
338C22×C5—81no—
339C22×C5—81no—
340C22×C5—81no—
341C22×C5C22×D811yescharacteristic
342C4×C5—21no—
343C4×C5—21no—
344C4×C5—21no—
345C4×C5—21no—
346C4×C5—42no—
347C4×C5—81no—
348C4×C5—81no—
349C4×C5—81no—
350C4×C5—81no—
351C4×C5—81no—
352C4×C5#50812yes—
353C4×C5#52511yescharacteristic
354C4×C5#57511yescharacteristic
355#41—24no—
356#41—42no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4C5×D811yescharacteristic
368C22×C4C5×D811yescharacteristic
369C22×C4C2×C5×D411yescharacteristic
370Q16—21no—
371Q16—21no—
372Q16—21no—
373Q16C5×#4112yes—
374SD16—24no—
375SD16—42no—
376D8—21no—
377D8—21no—
378D8—21no—
379D8C5×#4112yes—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—41no—
383C2×C8C2×C5×D411yescharacteristic
384C2×C8C2×C5×D411yescharacteristic
385C2×C8C2×C5×D411yescharacteristic
386C2×C8C24×C511yescharacteristic
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C42—41no—
406C42—41no—
407C42—41no—
408C42—41no—
409C42C5×D811yescharacteristic
410C42C5×D811yescharacteristic
411C42C2×C5×D411yescharacteristic
412C42C2×C5×D411yescharacteristic
413C16—21no—
414C16—21no—
415C16—21no—
416C16—21no—
417C2×C5—41no—
418C2×C5—82no—
419C2×C5—161no—
420C2×C5#310011yescharacteristic
421C2×C5C2×#50811yescharacteristic
422C2×C5#341411yescharacteristic
423C23—41no—
424C23—41no—
425C23C2×C5×D811yescharacteristic
426Q8—22no—
427Q8—41no—
428Q8—41no—
429Q8—41no—
430D4—22no—
431D4—44no—
432D4—41no—
433D4—41no—
434D4—41no—
435D4—82no—
436C2×C4—22no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—41no—
440C2×C4—44no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4C2×C5×D811yescharacteristic
451C2×C4C2×C5×D811yescharacteristic
452C2×C4C2×C5×D811yescharacteristic
453C2×C4C2×C5×D811yescharacteristic
454C2×C4C2×C5×D811yescharacteristic
455C2×C4C22×C5×D411yescharacteristic
456C8—21no—
457C8—21no—
458C8—21no—
459C8C2×C5×#4111yescharacteristic
460C8C2×C5×#4111yescharacteristic
461C5#3366211yescharacteristic, direct product factor, Sylow
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22C22×C5×D811yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—42no—
477C4—81no—
478C4—81no—
479C4—81no—
480C4—81no—
481C4—81no—
482C4C5×#50812yes—
483C4C5×#52511yescharacteristic
484C4C5×#57511yescharacteristic
485C2—41no—
486C2—82no—
487C2—161no—
488C2C5×#310011yescharacteristic
489C2C2×C5×#50811yescharacteristic
490C2C5×#341411yescharacteristic
subgroupG/H
centerC2×C4×C5C2×D8
commutator, Frattini, cosocleC2×C8C24×C5
socleC22×C5C22×D8
prime radicalC5×#2186C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C5 ◁ C2×C42×C5 ◁ C2×C4×C5×C8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3168C2semidirect
2. C4×C5×#135C2semidirect
3. C5×#2237C2semidirect
4. C5×#2234C2semidirect
5. C5×#2229C2semidirect
6. C5×#2228C2semidirect
7. C5×#2211C2semidirect
8. C5×#2210C2semidirect
9. C5×#2189C2semidirect
11. C4×C5×Q32C2semidirect
12. C4×C5×SD32C2semidirect
13. C4×C5×SD32C2semidirect
14. C4×C5×D16C2semidirect
15. C5×#2162C2semidirect
59. #33662C5direct (N × H)
117. #3168C2×C5semidirect
118. C4×#135C2×C5semidirect
119. #2237C2×C5semidirect
120. #2234C2×C5semidirect
121. #2229C2×C5semidirect
122. #2228C2×C5semidirect
123. #2211C2×C5semidirect
124. #2210C2×C5semidirect
125. #2189C2×C5semidirect
127. C4×Q32C2×C5semidirect
128. C4×SD32C2×C5semidirect
129. C4×SD32C2×C5semidirect
130. C4×D16C2×C5semidirect
131. #2162C2×C5semidirect
461. C5#33662direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#31682
C4×C5×#1352
C5×#22372
C5×#22342
C5×#22292
C5×#22282
C5×#22112
C5×#22102
C5×#21892
C5×#21862
C4×C5×Q322
C4×C5×SD322
C4×C5×D162
C5×#21622
#336625