Finite Group Databasebeta

← C5×#33823 #11956543

Subgroups — C5×#33823 #11956543

Order 1280.

500 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3176C211yesmaximal, characteristic, complemented
2C5×#3175C211yesmaximal, characteristic, complemented
3C5×#2229C211yesmaximal, characteristic, complemented
4C5×#2228C211yesmaximal, characteristic, complemented
5C5×#2226C211yesmaximal, characteristic, complemented
6C5×#2224C211yesmaximal, characteristic, complemented
7C5×#2220C211yesmaximal, characteristic, complemented
8C5×#2218C211yesmaximal, characteristic, complemented
9C5×#2217C211yesmaximal, characteristic, complemented
10C5×#2215C211yesmaximal, characteristic, complemented
11C5×#2210C211yesmaximal, characteristic, complemented
12C5×#2210C211yesmaximal, characteristic, complemented
13C5×#2207C211yesmaximal, characteristic, complemented
14C5×#2206C211yesmaximal, characteristic, complemented
15C5×#2151C211yesmaximal, characteristic, complemented
16C5×#542—21no—
17C5×#540—21no—
18C2×C5×SD32C2211yescharacteristic
19C2×C5×SD32C2211yescharacteristic
20C2×C5×D16C2211yescharacteristic
21C2×C5×D16C2211yescharacteristic
22C2×C5×M32C2211yescharacteristic
23C22×C5×C16C2211yescharacteristic
24C5×#500C2211yescharacteristic
25C5×#499C2211yescharacteristic
26C5×#495C2211yescharacteristic
27C5×#493C2211yescharacteristic
28C5×#490—21no—
29C5×#489—21no—
30C5×#469—21no—
31C5×#468—21no—
32C5×#467C2211yescharacteristic
33C5×#466C2211yescharacteristic
34C5×#466C2211yescharacteristic
35C5×#466C2211yescharacteristic
36C5×#442—21no—
37C5×#440—21no—
38C4×C5×Q16C2211yescharacteristic
39C4×C5×D8C2211yescharacteristic
40C4×C5×D8C2211yescharacteristic
41C4×C5×D8C2211yescharacteristic
42C5×#405C2211yescharacteristic
43C5×#367C2211yescharacteristic
44C5×#367C2211yescharacteristic
45C5×#366C2211yescharacteristic
46C5×#366C2211yescharacteristic
47C5×C4⋊C16C2211yescharacteristic
48C5×C4⋊C16C2211yescharacteristic
49C5×C4⋊C16C2211yescharacteristic
50C5×C4⋊C16C2211yescharacteristic
51C5×#358C2211yescharacteristic
52C5×#358C2211yescharacteristic
53C5×#357C2211yescharacteristic
54C5×#357C2211yescharacteristic
55C5×#357C2211yescharacteristic
56C5×#357C2211yescharacteristic
57C5×#357C2211yescharacteristic
58C5×#357C2211yescharacteristic
59#33823C511yesmaximal, characteristic, direct product factor, Sylow
60C2×C5×Q16C2311yescharacteristic
61C2×C5×SD16—21no—
62C2×C5×D8—21no—
63C2×C5×D8C2311yescharacteristic
64C2×C5×D8C2311yescharacteristic
65C2×C5×D8C2311yescharacteristic
66C2×C5×M16D411yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C5×C4⋊Q8—21no—
69C5×#127—21no—
70C5×#126—41no—
71C5×#125—21no—
72C5×#124—21no—
73C5×#124—41no—
74C5×#123—41no—
75C5×#123—41no—
76C5×#123—41no—
77C5×C22⋊Q8—21no—
78C5×C22⋊Q8—41no—
79C5×#121—21no—
80C5×#121—21no—
81C5×#121—21no—
82C5×#121—41no—
83C5×#121—41no—
84C4×C5×Q8—21no—
85C4×C5×D4—21no—
86C4×C5×D4—21no—
87C4×C5×D4—21no—
88C5×#117D411yescharacteristic
89C5×SD32—41no—
90C5×SD32—41no—
91C5×D16—41no—
92C5×D16—41no—
93C5×M32—41no—
94C2×C5×C16—41no—
95C2×C5×C16C2311yescharacteristic
96C2×C5×C16C2311yescharacteristic
97C2×C5×C16C2311yescharacteristic
98C2×C5×C16C2311yescharacteristic
99C5×#107—21no—
100C5×#107C2311yescharacteristic
101C5×#107C2311yescharacteristic
102C5×#107C2311yescharacteristic
103C5×#107C2311yescharacteristic
104C5×#106—21no—
105C5×#103—21no—
106C5×#103—21no—
107C5×#102—21no—
108C5×#102—21no—
109C5×#102—21no—
110C5×#102—21no—
111C5×#102—21no—
112C5×#102—21no—
113C5×#97D411yescharacteristic
114C5×#97D411yescharacteristic
115C4×C5×C8C2311yescharacteristic
116C4×C5×C8C2311yescharacteristic
117#3176C2×C511yescharacteristic, complemented
118#3175C2×C511yescharacteristic, complemented
119#2229C2×C511yescharacteristic, complemented
120#2228C2×C511yescharacteristic, complemented
121#2226C2×C511yescharacteristic, complemented
122#2224C2×C511yescharacteristic, complemented
123#2220C2×C511yescharacteristic, complemented
124#2218C2×C511yescharacteristic, complemented
125#2217C2×C511yescharacteristic, complemented
126#2215C2×C511yescharacteristic, complemented
127#2210C2×C511yescharacteristic, complemented
128#2210C2×C511yescharacteristic, complemented
129#2207C2×C511yescharacteristic, complemented
130#2206C2×C511yescharacteristic, complemented
131#2151C2×C511yescharacteristic, complemented
132C2×C5×Q8—21no—
133C2×C5×Q8—41no—
134C2×C5×D4—21no—
135C2×C5×D4—21no—
136C2×C5×D4—21no—
137C2×C5×D4—41no—
138C2×C5×D4—41no—
139C2×C5×D4—41no—
140C2×C5×D4—41no—
141C2×C5×D4—41no—
142C22×C4×C5—41no—
143C22×C4×C5—41no—
144C22×C4×C5—41no—
145C22×C4×C5C2×D411yescharacteristic
146C5×Q16—21no—
147C5×Q16—21no—
148C5×SD16—42no—
149C5×D8—21no—
150C5×D8—21no—
151C5×D8—21no—
152C5×D8—21no—
153C5×D8—21no—
154C5×D8—21no—
155C5×D8—42no—
156C5×M16—41no—
157C2×C5×C8—21no—
158C2×C5×C8—21no—
159C2×C5×C8C2×D411yescharacteristic
160C2×C5×C8C2×D411yescharacteristic
161C2×C5×C8C2×D411yescharacteristic
162C2×C5×C8C2411yescharacteristic
163C5×C4⋊C4—21no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—21no—
166C5×C4⋊C4—21no—
167C5×C4⋊C4—41no—
168C5×C4⋊C4—41no—
169C5×C4⋊C4—41no—
170C5×C4⋊C4—41no—
171C5×C4⋊C4—41no—
172C5×C4⋊C4D811yescharacteristic
173C5×C4⋊C4D811yescharacteristic
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—
182C5×C22⋊C4—41no—
183C5×C22⋊C4D811yescharacteristic
184C5×C22⋊C4D811yescharacteristic
185C42×C5—41no—
186C42×C5C2×D411yescharacteristic
187C42×C5C2×D411yescharacteristic
188C5×C16—21no—
189C5×C16—21no—
190C5×C16—21no—
191C5×C16—21no—
192#542—21no—
193#540—21no—
194C2×SD32C22×C511yescharacteristic
195C2×SD32C22×C511yescharacteristic
196C2×D16C22×C511yescharacteristic
197C2×D16C22×C511yescharacteristic
198C2×M32C22×C511yescharacteristic
199C22×C16C22×C511yescharacteristic
200#500C22×C511yescharacteristic
201#499C22×C511yescharacteristic
202#495C22×C511yescharacteristic
203#493C22×C511yescharacteristic
204#490—21no—
205#489—21no—
206#469—21no—
207#468—21no—
208#467C22×C511yescharacteristic
209#466C22×C511yescharacteristic
210#466C22×C511yescharacteristic
211#466C22×C511yescharacteristic
212#442—21no—
213#440—21no—
214C4×Q16C22×C511yescharacteristic
215C4×D8C22×C511yescharacteristic
216C4×D8C22×C511yescharacteristic
217C4×D8C22×C511yescharacteristic
218#405C22×C511yescharacteristic
219#367C22×C511yescharacteristic
220#367C22×C511yescharacteristic
221#366C22×C511yescharacteristic
222#366C22×C511yescharacteristic
223C4⋊C16C22×C511yescharacteristic
224C4⋊C16C22×C511yescharacteristic
225C4⋊C16C22×C511yescharacteristic
226C4⋊C16C22×C511yescharacteristic
227#358C22×C511yescharacteristic
228#358C22×C511yescharacteristic
229#357C22×C511yescharacteristic
230#357C22×C511yescharacteristic
231#357C22×C511yescharacteristic
232#357C22×C511yescharacteristic
233#357C22×C511yescharacteristic
234#357C22×C511yescharacteristic
235C23×C5—41no—
236C23×C5—41no—
237C23×C5—41no—
238C23×C5C2×D811yescharacteristic
239C5×Q8—41no—
240C5×Q8—41no—
241C5×Q8—161no—
242C5×D4—41no—
243C5×D4—41no—
244C5×D4—41no—
245C5×D4—41no—
246C5×D4—41no—
247C5×D4—41no—
248C5×D4—161no—
249C5×D4—161no—
250C5×D4—161no—
251C5×D4—161no—
252C5×D4—161no—
253C2×C4×C5—21no—
254C2×C4×C5—21no—
255C2×C4×C5—41no—
256C2×C4×C5—41no—
257C2×C4×C5—41no—
258C2×C4×C5—41no—
259C2×C4×C5—41no—
260C2×C4×C5—161no—
261C2×C4×C5—161no—
262C2×C4×C5—161no—
263C2×C4×C5C2×D811yescharacteristic
264C2×C4×C5C2×D811yescharacteristic
265C2×C4×C5C2×D811yescharacteristic
266C2×C4×C5C2×D811yescharacteristic
267C2×C4×C5C2×D811yescharacteristic
268C2×C4×C5C22×D411yescharacteristic
269C5×C8—21no—
270C5×C8—21no—
271C5×C8—21no—
272C5×C8H(5,𝔽2)11yescharacteristic
273C5×C82−1+411yescharacteristic
274C2×Q16C23×C511yescharacteristic
275C2×SD16—21no—
276C2×D8—21no—
277C2×D8C23×C511yescharacteristic
278C2×D8C23×C511yescharacteristic
279C2×D8C23×C511yescharacteristic
280C2×M16C5×D411yescharacteristic
281C22×C8C23×C511yescharacteristic
282C4⋊Q8—21no—
283#127—21no—
284#126—41no—
285#125—21no—
286#124—21no—
287#124—41no—
288#123—41no—
289#123—41no—
290#123—41no—
291C22⋊Q8—21no—
292C22⋊Q8—41no—
293#121—21no—
294#121—21no—
295#121—21no—
296#121—41no—
297#121—41no—
298C4×Q8—21no—
299C4×D4—21no—
300C4×D4—21no—
301C4×D4—21no—
302#117C5×D411yescharacteristic
303SD32—41no—
304SD32—41no—
305D16—41no—
306D16—41no—
307M32—41no—
308C2×C16—41no—
309C2×C16C23×C511yescharacteristic
310C2×C16C23×C511yescharacteristic
311C2×C16C23×C511yescharacteristic
312C2×C16C23×C511yescharacteristic
313#107—21no—
314#107C23×C511yescharacteristic
315#107C23×C511yescharacteristic
316#107C23×C511yescharacteristic
317#107C23×C511yescharacteristic
318#106—21no—
319#103—21no—
320#103—21no—
321#102—21no—
322#102—21no—
323#102—21no—
324#102—21no—
325#102—21no—
326#102—21no—
327#97C5×D411yescharacteristic
328#97C5×D411yescharacteristic
329C4×C8C23×C511yescharacteristic
330C4×C8C23×C511yescharacteristic
331C22×C5—21no—
332C22×C5—21no—
333C22×C5—21no—
334C22×C5—81no—
335C22×C5—81no—
336C22×C5—81no—
337C22×C5—81no—
338C22×C5—81no—
339C22×C5—81no—
340C22×C5—81no—
341C22×C5—81no—
342C22×C5—81no—
343C22×C5C22×D811yescharacteristic
344C4×C5—21no—
345C4×C5—21no—
346C4×C5—21no—
347C4×C5—21no—
348C4×C5—21no—
349C4×C5—81no—
350C4×C5—81no—
351C4×C5—81no—
352C4×C5—81no—
353C4×C5—81no—
354C4×C5#53711yescharacteristic
355C4×C5#57511yescharacteristic
356C2×Q8—21no—
357C2×Q8—41no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4C2×C5×D411yescharacteristic
370Q16—21no—
371Q16—21no—
372SD16—42no—
373D8—21no—
374D8—21no—
375D8—21no—
376D8—21no—
377D8—21no—
378D8—21no—
379D8—42no—
380M16—41no—
381C2×C8—21no—
382C2×C8—21no—
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⋊C4C5×D811yescharacteristic
397C4⋊C4C5×D811yescharacteristic
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4C5×D811yescharacteristic
408C22⋊C4C5×D811yescharacteristic
409C42—41no—
410C42C2×C5×D411yescharacteristic
411C42C2×C5×D411yescharacteristic
412C16—21no—
413C16—21no—
414C16—21no—
415C16—21no—
416C2×C5—41no—
417C2×C5—161no—
418C2×C5—161no—
419C2×C5—161no—
420C2×C5#324511yescharacteristic
421C2×C5#341511yescharacteristic
422C2×C5#341611yescharacteristic
423C23—41no—
424C23—41no—
425C23—41no—
426C23C2×C5×D811yescharacteristic
427Q8—41no—
428Q8—41no—
429Q8—161no—
430D4—41no—
431D4—41no—
432D4—41no—
433D4—41no—
434D4—41no—
435D4—41no—
436D4—161no—
437D4—161no—
438D4—161no—
439D4—161no—
440D4—161no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—161no—
449C2×C4—161no—
450C2×C4—161no—
451C2×C4C2×C5×D811yescharacteristic
452C2×C4C2×C5×D811yescharacteristic
453C2×C4C2×C5×D811yescharacteristic
454C2×C4C2×C5×D811yescharacteristic
455C2×C4C2×C5×D811yescharacteristic
456C2×C4C22×C5×D411yescharacteristic
457C8—21no—
458C8—21no—
459C8—21no—
460C8C5×H(5,𝔽2)11yescharacteristic
461C8C5×2−1+411yescharacteristic
462C5#3382311yescharacteristic, direct product factor, Sylow
463C22—21no—
464C22—21no—
465C22—21no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22C22×C5×D811yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—81no—
482C4—81no—
483C4—81no—
484C4—81no—
485C4—81no—
486C4C5×#53711yescharacteristic
487C4C5×#57511yescharacteristic
488C2—41no—
489C2—161no—
490C2—161no—
491C2—161no—
492C2C5×#324511yescharacteristic
493C2C5×#341511yescharacteristic
494C2C5×#341611yescharacteristic
subgroupG/H
center, socleC22×C5C22×D8
commutator, Frattini, cosocleC2×C8C24×C5
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C5×#117 ◁ C5×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3176C2semidirect
2. C5×#3175C2semidirect
3. C5×#2229C2semidirect
4. C5×#2228C2semidirect
5. C5×#2226C2semidirect
6. C5×#2224C2semidirect
7. C5×#2220C2semidirect
8. C5×#2218C2semidirect
9. C5×#2217C2semidirect
10. C5×#2215C2semidirect
11. C5×#2210C2semidirect
12. C5×#2210C2semidirect
13. C5×#2207C2semidirect
14. C5×#2206C2semidirect
15. C5×#2151C2semidirect
59. #33823C5direct (N × H)
117. #3176C2×C5semidirect
118. #3175C2×C5semidirect
119. #2229C2×C5semidirect
120. #2228C2×C5semidirect
121. #2226C2×C5semidirect
122. #2224C2×C5semidirect
123. #2220C2×C5semidirect
124. #2218C2×C5semidirect
125. #2217C2×C5semidirect
126. #2215C2×C5semidirect
127. #2210C2×C5semidirect
128. #2210C2×C5semidirect
129. #2207C2×C5semidirect
130. #2206C2×C5semidirect
131. #2151C2×C5semidirect
462. C5#33823direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#31762
C5×#31752
C5×#22292
C5×#22282
C5×#22262
C5×#22242
C5×#22202
C5×#22182
C5×#22172
C5×#22152
C5×#22102
C5×#22072
C5×#22062
C5×#21512
#338235