Finite Group Databasebeta

← C5×#33807 #11956527

Subgroups — C5×#33807 #11956527

Order 1280.

466 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3176C211yesmaximal, characteristic
2C5×#3164C211yesmaximal, characteristic, complemented
3C5×#2255C211yesmaximal, characteristic, complemented
4C5×#2253C211yesmaximal, characteristic, complemented
5C5×#2244C211yesmaximal, characteristic, complemented
6C5×#2240C211yesmaximal, characteristic, complemented
7C5×#2234C211yesmaximal, characteristic, complemented
8C5×#2234C211yesmaximal, characteristic, complemented
9C5×#2233C211yesmaximal, characteristic, complemented
10C5×#2232C211yesmaximal, characteristic, complemented
11C5×#2228C211yesmaximal, characteristic, complemented
12C5×#2228C211yesmaximal, characteristic, complemented
13C5×#2226C211yesmaximal, characteristic, complemented
14C5×#2224C211yesmaximal, characteristic, complemented
15C5×#2164C211yesmaximal, characteristic, complemented
16C5×#544—21no—
17C5×#540—21no—
18C5×#501—21no—
19C5×#501—21no—
20C5×#500C2211yescharacteristic
21C5×#500C2211yescharacteristic
22C5×#499C2211yescharacteristic
23C5×#499C2211yescharacteristic
24C5×#499C2211yescharacteristic
25C5×#493C2211yescharacteristic
26C5×#490—21no—
27C5×#469—21no—
28C5×#466C2211yescharacteristic
29C5×#466C2211yescharacteristic
30C5×#442—21no—
31C4×C5×D8C2211yescharacteristic
32C4×C5×D8C2211yescharacteristic
33C5×#428—21no—
34C5×#427C2211yescharacteristic
35C2×C5×#107C2211yescharacteristic
36C5×#405C2211yescharacteristic
37C5×#367C2211yescharacteristic
38C5×#367C2211yescharacteristic
39C5×#367C2211yescharacteristic
40C5×#367C2211yescharacteristic
41C5×#366C2211yescharacteristic
42C5×#366C2211yescharacteristic
43C5×#366C2211yescharacteristic
44C5×#366C2211yescharacteristic
45C5×C4⋊C16C2211yescharacteristic
46C5×C4⋊C16C2211yescharacteristic
47C5×#357C2211yescharacteristic
48C5×#357C2211yescharacteristic
49C5×#357C2211yescharacteristic
50C5×#357C2211yescharacteristic
51C5×#357C2211yescharacteristic
52C5×#357C2211yescharacteristic
53C5×#357C2211yescharacteristic
54C5×#357C2211yescharacteristic
55C5×C22⋊C16C2211yescharacteristic
56C5×C22⋊C16C2211yescharacteristic
57C5×#346C2211yescharacteristic
58C4×C5×C16C2211yescharacteristic
59#33807C511yesmaximal, characteristic, direct product factor, Sylow
60C2×C5×D8—21no—
61C2×C5×D8C2311yescharacteristic
62C2×C5×D8C2311yescharacteristic
63C2×C5×M16D411yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C5×C4⋊Q8—21no—
66C5×C4⋊Q8—21no—
67C5×C4⋊Q8—41no—
68C5×#127—21no—
69C5×#125—21no—
70C5×#125—21no—
71C5×#125—21no—
72C5×#125—41no—
73C5×#123—41no—
74C5×#123—41no—
75C5×C22⋊Q8—41no—
76C5×C22⋊Q8—41no—
77C5×#121—21no—
78C5×#121—21no—
79C5×#121—41no—
80C5×#121—41no—
81C4×C5×D4—21no—
82C4×C5×D4—21no—
83C5×#117—21no—
84C5×#117D411yescharacteristic
85C2×C5×C4⋊C4—21no—
86C2×C5×C16C2311yescharacteristic
87C2×C5×C16C2311yescharacteristic
88C2×C5×C16C2311yescharacteristic
89C2×C5×C16C2311yescharacteristic
90C5×#107—21no—
91C5×#107—21no—
92C5×#107—21no—
93C5×#107C2311yescharacteristic
94C5×#107C2311yescharacteristic
95C5×#107C2311yescharacteristic
96C5×#107C2311yescharacteristic
97C5×#107C2311yescharacteristic
98C5×#107C2311yescharacteristic
99C5×#106—21no—
100C5×#106—21no—
101C5×#106—21no—
102C5×#106—21no—
103C5×#102—21no—
104C5×#102—21no—
105C5×#102—21no—
106C5×#102—21no—
107C5×#97D411yescharacteristic
108C5×#97D411yescharacteristic
109C4×C5×C8C2311yescharacteristic
110C4×C5×C8C2311yescharacteristic
111#3176C2×C511yescharacteristic
112#3164C2×C511yescharacteristic, complemented
113#2255C2×C511yescharacteristic, complemented
114#2253C2×C511yescharacteristic, complemented
115#2244C2×C511yescharacteristic, complemented
116#2240C2×C511yescharacteristic, complemented
117#2234C2×C511yescharacteristic, complemented
118#2234C2×C511yescharacteristic, complemented
119#2233C2×C511yescharacteristic, complemented
120#2232C2×C511yescharacteristic, complemented
121#2228C2×C511yescharacteristic, complemented
122#2228C2×C511yescharacteristic, complemented
123#2226C2×C511yescharacteristic, complemented
124#2224C2×C511yescharacteristic, complemented
125#2164C2×C511yescharacteristic, complemented
126C2×C5×Q8—41no—
127C2×C5×Q8—41no—
128C2×C5×D4—21no—
129C2×C5×D4—21no—
130C2×C5×D4—41no—
131C2×C5×D4—41no—
132C2×C5×D4—41no—
133C2×C5×D4—41no—
134C22×C4×C5—41no—
135C22×C4×C5—41no—
136C22×C4×C5—41no—
137C22×C4×C5C2×D411yescharacteristic
138C5×D8—21no—
139C5×D8—21no—
140C5×D8—21no—
141C5×D8—21no—
142C5×D8—42no—
143C5×M16—22no—
144C2×C5×C8—21no—
145C2×C5×C8—21no—
146C2×C5×C8C2×D411yescharacteristic
147C2×C5×C8C2×D411yescharacteristic
148C2×C5×C8C2×D411yescharacteristic
149C2×C5×C8C2411yescharacteristic
150C5×C4⋊C4—21no—
151C5×C4⋊C4—21no—
152C5×C4⋊C4—21no—
153C5×C4⋊C4—21no—
154C5×C4⋊C4—21no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4—41no—
157C5×C4⋊C4—41no—
158C5×C4⋊C4—41no—
159C5×C4⋊C4—41no—
160C5×C4⋊C4—41no—
161C5×C4⋊C4—41no—
162C5×C4⋊C4—41no—
163C5×C4⋊C4—41no—
164C5×C4⋊C4—41no—
165C5×C4⋊C4D811yescharacteristic
166C5×C4⋊C4D811yescharacteristic
167C5×C22⋊C4—41no—
168C5×C22⋊C4—41no—
169C5×C22⋊C4—41no—
170C5×C22⋊C4—41no—
171C5×C22⋊C4—41no—
172C5×C22⋊C4D811yescharacteristic
173C5×C22⋊C4D811yescharacteristic
174C42×C5—41no—
175C42×C5C2×D411yescharacteristic
176C42×C5C2×D411yescharacteristic
177C5×C16—21no—
178C5×C16—21no—
179C5×C16—21no—
180C5×C16—21no—
181#544—21no—
182#540—21no—
183#501—21no—
184#501—21no—
185#500C22×C511yescharacteristic
186#500C22×C511yescharacteristic
187#499C22×C511yescharacteristic
188#499C22×C511yescharacteristic
189#499C22×C511yescharacteristic
190#493C22×C511yescharacteristic
191#490—21no—
192#469—21no—
193#466C22×C511yescharacteristic
194#466C22×C511yescharacteristic
195#442—21no—
196C4×D8C22×C511yescharacteristic
197C4×D8C22×C511yescharacteristic
198#428—21no—
199#427C22×C511yescharacteristic
200C2×#107C22×C511yescharacteristic
201#405C22×C511yescharacteristic
202#367C22×C511yescharacteristic
203#367C22×C511yescharacteristic
204#367C22×C511yescharacteristic
205#367C22×C511yescharacteristic
206#366C22×C511yescharacteristic
207#366C22×C511yescharacteristic
208#366C22×C511yescharacteristic
209#366C22×C511yescharacteristic
210C4⋊C16C22×C511yescharacteristic
211C4⋊C16C22×C511yescharacteristic
212#357C22×C511yescharacteristic
213#357C22×C511yescharacteristic
214#357C22×C511yescharacteristic
215#357C22×C511yescharacteristic
216#357C22×C511yescharacteristic
217#357C22×C511yescharacteristic
218#357C22×C511yescharacteristic
219#357C22×C511yescharacteristic
220C22⋊C16C22×C511yescharacteristic
221C22⋊C16C22×C511yescharacteristic
222#346C22×C511yescharacteristic
223C4×C16C22×C511yescharacteristic
224C23×C5—41no—
225C23×C5—41no—
226C23×C5C2×D811yescharacteristic
227C5×Q8—161no—
228C5×Q8—161no—
229C5×D4—41no—
230C5×D4—41no—
231C5×D4—41no—
232C5×D4—41no—
233C5×D4—161no—
234C5×D4—161no—
235C5×D4—161no—
236C5×D4—161no—
237C2×C4×C5—21no—
238C2×C4×C5—21no—
239C2×C4×C5—41no—
240C2×C4×C5—41no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5—41no—
244C2×C4×C5—41no—
245C2×C4×C5—161no—
246C2×C4×C5—161no—
247C2×C4×C5—161no—
248C2×C4×C5C2×D811yescharacteristic
249C2×C4×C5C2×D811yescharacteristic
250C2×C4×C5C2×D811yescharacteristic
251C2×C4×C5C2×D811yescharacteristic
252C2×C4×C5C2×D811yescharacteristic
253C2×C4×C5C22×D411yescharacteristic
254C5×C8—21no—
255C5×C8—21no—
256C5×C8#13712yes—
257C5×C82−1+411yescharacteristic
258C5×C82−1+411yescharacteristic
259C2×D8—21no—
260C2×D8C23×C511yescharacteristic
261C2×D8C23×C511yescharacteristic
262C2×M16C5×D411yescharacteristic
263C22×C8C23×C511yescharacteristic
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8—41no—
267#127—21no—
268#125—21no—
269#125—21no—
270#125—21no—
271#125—41no—
272#123—41no—
273#123—41no—
274C22⋊Q8—41no—
275C22⋊Q8—41no—
276#121—21no—
277#121—21no—
278#121—41no—
279#121—41no—
280C4×D4—21no—
281C4×D4—21no—
282#117—21no—
283#117C5×D411yescharacteristic
284C2×C4⋊C4—21no—
285C2×C16C23×C511yescharacteristic
286C2×C16C23×C511yescharacteristic
287C2×C16C23×C511yescharacteristic
288C2×C16C23×C511yescharacteristic
289#107—21no—
290#107—21no—
291#107—21no—
292#107C23×C511yescharacteristic
293#107C23×C511yescharacteristic
294#107C23×C511yescharacteristic
295#107C23×C511yescharacteristic
296#107C23×C511yescharacteristic
297#107C23×C511yescharacteristic
298#106—21no—
299#106—21no—
300#106—21no—
301#106—21no—
302#102—21no—
303#102—21no—
304#102—21no—
305#102—21no—
306#97C5×D411yescharacteristic
307#97C5×D411yescharacteristic
308C4×C8C23×C511yescharacteristic
309C4×C8C23×C511yescharacteristic
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—81no—
314C22×C5—81no—
315C22×C5—81no—
316C22×C5—81no—
317C22×C5—81no—
318C22×C5—81no—
319C22×C5C22×D811yescharacteristic
320C4×C5—21no—
321C4×C5—21no—
322C4×C5—21no—
323C4×C5—21no—
324C4×C5—21no—
325C4×C5—81no—
326C4×C5—81no—
327C4×C5—81no—
328C4×C5—81no—
329C4×C5—81no—
330C4×C5—81no—
331C4×C5#53611yescharacteristic
332C4×C5C2×#13711yescharacteristic
333C2×Q8—41no—
334C2×Q8—41no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4C2×C5×D411yescharacteristic
345D8—21no—
346D8—21no—
347D8—21no—
348D8—21no—
349D8—42no—
350M16—22no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8C2×C5×D411yescharacteristic
354C2×C8C2×C5×D411yescharacteristic
355C2×C8C2×C5×D411yescharacteristic
356C2×C8C24×C511yescharacteristic
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4C5×D811yescharacteristic
373C4⋊C4C5×D811yescharacteristic
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4C5×D811yescharacteristic
380C22⋊C4C5×D811yescharacteristic
381C42—41no—
382C42C2×C5×D411yescharacteristic
383C42C2×C5×D411yescharacteristic
384C16—21no—
385C16—21no—
386C16—21no—
387C16—21no—
388C2×C5—41no—
389C2×C5—161no—
390C2×C5—161no—
391C2×C5#322611yescharacteristic
392C2×C5#341511yescharacteristic
393C2×C5#341611yescharacteristic
394C23—41no—
395C23—41no—
396C23C2×C5×D811yescharacteristic
397Q8—161no—
398Q8—161no—
399D4—41no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—161no—
404D4—161no—
405D4—161no—
406D4—161no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—161no—
416C2×C4—161no—
417C2×C4—161no—
418C2×C4C2×C5×D811yescharacteristic
419C2×C4C2×C5×D811yescharacteristic
420C2×C4C2×C5×D811yescharacteristic
421C2×C4C2×C5×D811yescharacteristic
422C2×C4C2×C5×D811yescharacteristic
423C2×C4C22×C5×D411yescharacteristic
424C8—21no—
425C8—21no—
426C8C5×#13712yes—
427C8C5×2−1+411yescharacteristic
428C8C5×2−1+411yescharacteristic
429C5#3380711yescharacteristic, direct product factor, Sylow
430C22—21no—
431C22—21no—
432C22—21no—
433C22—81no—
434C22—81no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22C22×C5×D811yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4C5×#53611yescharacteristic
452C4C2×C5×#13711yescharacteristic
453C2—41no—
454C2—161no—
455C2—161no—
456C2C5×#322611yescharacteristic
457C2C5×#341511yescharacteristic
458C2C5×#341611yescharacteristic
subgroupG/H
center, socleC22×C5C22×D8
commutator, Frattini, cosocleC2×C8C24×C5
prime radicalC5×#3176C2
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
2. C5×#3164C2semidirect
3. C5×#2255C2semidirect
4. C5×#2253C2semidirect
5. C5×#2244C2semidirect
6. C5×#2240C2semidirect
7. C5×#2234C2semidirect
8. C5×#2234C2semidirect
9. C5×#2233C2semidirect
10. C5×#2232C2semidirect
11. C5×#2228C2semidirect
12. C5×#2228C2semidirect
13. C5×#2226C2semidirect
14. C5×#2224C2semidirect
15. C5×#2164C2semidirect
59. #33807C5direct (N × H)
112. #3164C2×C5semidirect
113. #2255C2×C5semidirect
114. #2253C2×C5semidirect
115. #2244C2×C5semidirect
116. #2240C2×C5semidirect
117. #2234C2×C5semidirect
118. #2234C2×C5semidirect
119. #2233C2×C5semidirect
120. #2232C2×C5semidirect
121. #2228C2×C5semidirect
122. #2228C2×C5semidirect
123. #2226C2×C5semidirect
124. #2224C2×C5semidirect
125. #2164C2×C5semidirect
429. C5#33807direct (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×#31642
C5×#22552
C5×#22532
C5×#22442
C5×#22402
C5×#22342
C5×#22332
C5×#22322
C5×#22282
C5×#22262
C5×#22242
C5×#21642
#338075