Finite Group Databasebeta

← C5×#33875 #11956595

Subgroups — C5×#33875 #11956595

Order 1280.

580 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3334C211yesmaximal, characteristic, complemented
2C5×#3285C211yesmaximal, characteristic, complemented
3C5×#2243C211yesmaximal, characteristic, complemented
4C5×#2236C211yesmaximal, characteristic, complemented
5C5×#2232C211yesmaximal, characteristic, complemented
6C5×#2227C211yesmaximal, characteristic, complemented
7C5×#2220C211yesmaximal, characteristic, complemented
8C5×#2215C211yesmaximal, characteristic, complemented
9C5×#2210C211yesmaximal, characteristic, complemented
10C5×#2186C211yesmaximal, characteristic, complemented
11C5×#2185C211yesmaximal, characteristic, complemented
12C5×#2175C211yesmaximal, characteristic, complemented
13C5×#2168C211yesmaximal, characteristic, complemented
14C5×#2139C211yesmaximal, characteristic, complemented
15C2×C5×#358C211yesmaximal, characteristic, complemented
16C2×C5×#135C2211yescharacteristic
17C22×C5×Q16C2211yescharacteristic
18C5×#548—21no—
19C5×#547—21no—
20C2×C5×SD32C2211yescharacteristic
21C2×C5×SD32C2211yescharacteristic
22C2×C5×D16C2211yescharacteristic
23C2×C5×M32C2211yescharacteristic
24C22×C5×C16C2211yescharacteristic
25C5×#500C2211yescharacteristic
26C5×#495C2211yescharacteristic
27C5×#480—21no—
28C5×#480—21no—
29C5×#474—21no—
30C5×#467C2211yescharacteristic
31C5×#466C2211yescharacteristic
32C5×#466C2211yescharacteristic
33C5×#466C2211yescharacteristic
34C5×#464—21no—
35C5×#452—21no—
36C5×#448—21no—
37C4×C5×Q16C2211yescharacteristic
38C4×C5×D8C2211yescharacteristic
39C5×C8×D4C2211yescharacteristic
40C2×C5×#107C2211yescharacteristic
41C2×C5×#107C2211yescharacteristic
42C5×#366C2211yescharacteristic
43C5×#366C2211yescharacteristic
44C5×#366C2211yescharacteristic
45C5×C4⋊C16C2211yescharacteristic
46C5×#358C2211yescharacteristic
47C5×#358C2211yescharacteristic
48C5×#358C2211yescharacteristic
49C5×#358C2211yescharacteristic
50C5×#358C2211yescharacteristic
51C5×#358C2211yescharacteristic
52C5×#357C2211yescharacteristic
53C5×#357C2211yescharacteristic
54C5×#357C2211yescharacteristic
55C5×#357C2211yescharacteristic
56C5×C22⋊C16C2211yescharacteristic
57C5×C22⋊C16C2211yescharacteristic
58C5×#346C2211yescharacteristic
59#33875C511yesmaximal, characteristic, direct product factor, Sylow
60C2×C5×#41—21no—
61C2×C5×#41—41no—
62C22×C5×Q8—21no—
63C5×#135—22no—
64C5×#135—41no—
65C2×C5×Q16—22no—
66C2×C5×Q16—21no—
67C2×C5×Q16—41no—
68C2×C5×Q16C2311yescharacteristic
69C2×C5×Q16C2311yescharacteristic
70C2×C5×SD16—21no—
71C2×C5×SD16—21no—
72C2×C5×D8C2311yescharacteristic
73C2×C5×D8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C5×C4⋊Q8—21no—
77C5×#124—21no—
78C5×#124—41no—
79C5×#123—41no—
80C5×#123—41no—
81C5×C22⋊Q8—21no—
82C5×C22⋊Q8—41no—
83C5×C22⋊Q8—41no—
84C5×#121—21no—
85C5×#121—21no—
86C5×#121—21no—
87C5×#121—41no—
88C4×C5×Q8—21no—
89C4×C5×D4—21no—
90C4×C5×D4—41no—
91C4×C5×D4D411yescharacteristic
92C2×C5×C4⋊C4—21no—
93C2×C5×C4⋊C4—21no—
94C5×SD32—22no—
95C5×SD32—41no—
96C5×D16—41no—
97C5×M32—41no—
98C2×C5×C16—41no—
99C2×C5×C16C2311yescharacteristic
100C2×C5×C16C2311yescharacteristic
101C2×C5×C16C2311yescharacteristic
102C2×C5×C16C2311yescharacteristic
103C5×#107—21no—
104C5×#107—21no—
105C5×#107—21no—
106C5×#107C2311yescharacteristic
107C5×#107C2311yescharacteristic
108C5×#107C2311yescharacteristic
109C5×#107C2311yescharacteristic
110C5×C4⋊C8D411yescharacteristic
111C5×#103—21no—
112C5×#103—21no—
113C5×#102—21no—
114C5×#102—21no—
115C5×#102—21no—
116C5×#102—21no—
117C5×C22⋊C8D411yescharacteristic
118C5×C22⋊C8D411yescharacteristic
119C4×C5×C8C2311yescharacteristic
120#3334C2×C511yescharacteristic, complemented
121#3285C2×C511yescharacteristic, complemented
122#2243C2×C511yescharacteristic, complemented
123#2236C2×C511yescharacteristic, complemented
124#2232C2×C511yescharacteristic, complemented
125#2227C2×C511yescharacteristic, complemented
126#2220C2×C511yescharacteristic, complemented
127#2215C2×C511yescharacteristic, complemented
128#2210C2×C511yescharacteristic, complemented
129#2186C2×C511yescharacteristic, complemented
130#2185C2×C511yescharacteristic, complemented
131#2175C2×C511yescharacteristic, complemented
132#2168C2×C511yescharacteristic, complemented
133#2139C2×C511yescharacteristic, complemented
134C2×#358C2×C511yescharacteristic, complemented
135C5×#41—42no—
136C5×#41—81no—
137C5×#41—84no—
138C2×C5×Q8—21no—
139C2×C5×Q8—21no—
140C2×C5×Q8—42no—
141C2×C5×Q8—41no—
142C2×C5×Q8—41no—
143C2×C5×Q8—81no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—41no—
147C2×C5×D4—41no—
148C2×C5×D4—41no—
149C2×C5×D4—41no—
150C2×C5×D4D811yescharacteristic
151C22×C4×C5—41no—
152C22×C4×C5—41no—
153C22×C4×C5—41no—
154C22×C4×C5—41no—
155C22×C4×C5—41no—
156C22×C4×C5C2×D411yescharacteristic
157C22×C4×C5C2×D411yescharacteristic
158C5×Q16—21no—
159C5×Q16—21no—
160C5×Q16—21no—
161C5×Q16—42no—
162C5×Q16#4112yescomplemented
163C5×SD16—42no—
164C5×SD16—81no—
165C5×D8—21no—
166C5×D8—21no—
167C5×D8—21no—
168C5×D8—21no—
169C2×C5×C8—21no—
170C2×C5×C8—21no—
171C2×C5×C8—21no—
172C2×C5×C8—21no—
173C2×C5×C8C2×D411yescharacteristic
174C2×C5×C8C2×D411yescharacteristic
175C2×C5×C8C2×D411yescharacteristic
176C2×C5×C8C2411yescharacteristic
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—41no—
182C5×C4⋊C4—41no—
183C5×C4⋊C4—41no—
184C5×C4⋊C4—41no—
185C5×C4⋊C4—41no—
186C5×C4⋊C4D811yescharacteristic
187C5×C22⋊C4—41no—
188C5×C22⋊C4—41no—
189C5×C22⋊C4—41no—
190C5×C22⋊C4—41no—
191C5×C22⋊C4—41no—
192C5×C22⋊C4—41no—
193C5×C22⋊C4—41no—
194C5×C22⋊C4D811yescharacteristic
195C5×C22⋊C4D811yescharacteristic
196C42×C5—41no—
197C42×C5C2×D411yescharacteristic
198C5×C16—21no—
199C5×C16—21no—
200C5×C16—21no—
201C5×C16—21no—
202C2×#135C22×C511yescharacteristic
203C22×Q16C22×C511yescharacteristic
204#548—21no—
205#547—21no—
206C2×SD32C22×C511yescharacteristic
207C2×SD32C22×C511yescharacteristic
208C2×D16C22×C511yescharacteristic
209C2×M32C22×C511yescharacteristic
210C22×C16C22×C511yescharacteristic
211#500C22×C511yescharacteristic
212#495C22×C511yescharacteristic
213#480—21no—
214#480—21no—
215#474—21no—
216#467C22×C511yescharacteristic
217#466C22×C511yescharacteristic
218#466C22×C511yescharacteristic
219#466C22×C511yescharacteristic
220#464—21no—
221#452—21no—
222#448—21no—
223C4×Q16C22×C511yescharacteristic
224C4×D8C22×C511yescharacteristic
225C8×D4C22×C511yescharacteristic
226C2×#107C22×C511yescharacteristic
227C2×#107C22×C511yescharacteristic
228#366C22×C511yescharacteristic
229#366C22×C511yescharacteristic
230#366C22×C511yescharacteristic
231C4⋊C16C22×C511yescharacteristic
232#358C22×C511yescharacteristic
233#358C22×C511yescharacteristic
234#358C22×C511yescharacteristic
235#358C22×C511yescharacteristic
236#358C22×C511yescharacteristic
237#358C22×C511yescharacteristic
238#357C22×C511yescharacteristic
239#357C22×C511yescharacteristic
240#357C22×C511yescharacteristic
241#357C22×C511yescharacteristic
242C22⋊C16C22×C511yescharacteristic
243C22⋊C16C22×C511yescharacteristic
244#346C22×C511yescharacteristic
245C23×C5—41no—
246C23×C5—41no—
247C23×C5C2×D811yescharacteristic
248C23×C5C2×D811yescharacteristic
249C5×Q8—22no—
250C5×Q8—41no—
251C5×Q8—41no—
252C5×Q8—41no—
253C5×Q8—82no—
254C5×Q8—82no—
255C5×D4—22no—
256C5×D4—41no—
257C5×D4—41no—
258C5×D4—41no—
259C5×D4—41no—
260C5×D4—82no—
261C5×D4—82no—
262C5×D4—82no—
263C5×D4—82no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
268C2×C4×C5—41no—
269C2×C4×C5—41no—
270C2×C4×C5—41no—
271C2×C4×C5—41no—
272C2×C4×C5—41no—
273C2×C4×C5—41no—
274C2×C4×C5—82no—
275C2×C4×C5—82no—
276C2×C4×C5—82no—
277C2×C4×C5—82no—
278C2×C4×C5—82no—
279C2×C4×C5C2×D811yescharacteristic
280C2×C4×C5C2×D811yescharacteristic
281C2×C4×C5C2×D811yescharacteristic
282C2×C4×C5C2×D811yescharacteristic
283C2×C4×C5C22×D411yescharacteristic
284C5×C8—21no—
285C5×C8—21no—
286C5×C8—21no—
287C5×C8C2×#4111yescharacteristic
288C5×C8H(5,𝔽2)11yescharacteristic
289C2×#41—21no—
290C2×#41—41no—
291C22×Q8—21no—
292#135—22no—
293#135—41no—
294C2×Q16—22no—
295C2×Q16—21no—
296C2×Q16—41no—
297C2×Q16C23×C511yescharacteristic
298C2×Q16C23×C511yescharacteristic
299C2×SD16—21no—
300C2×SD16—21no—
301C2×D8C23×C511yescharacteristic
302C2×D8C23×C511yescharacteristic
303C22×C8C23×C511yescharacteristic
304C22×C8C23×C511yescharacteristic
305C4⋊Q8—21no—
306#124—21no—
307#124—41no—
308#123—41no—
309#123—41no—
310C22⋊Q8—21no—
311C22⋊Q8—41no—
312C22⋊Q8—41no—
313#121—21no—
314#121—21no—
315#121—21no—
316#121—41no—
317C4×Q8—21no—
318C4×D4—21no—
319C4×D4—41no—
320C4×D4C5×D411yescharacteristic
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323SD32—22no—
324SD32—41no—
325D16—41no—
326M32—41no—
327C2×C16—41no—
328C2×C16C23×C511yescharacteristic
329C2×C16C23×C511yescharacteristic
330C2×C16C23×C511yescharacteristic
331C2×C16C23×C511yescharacteristic
332#107—21no—
333#107—21no—
334#107—21no—
335#107C23×C511yescharacteristic
336#107C23×C511yescharacteristic
337#107C23×C511yescharacteristic
338#107C23×C511yescharacteristic
339C4⋊C8C5×D411yescharacteristic
340#103—21no—
341#103—21no—
342#102—21no—
343#102—21no—
344#102—21no—
345#102—21no—
346C22⋊C8C5×D411yescharacteristic
347C22⋊C8C5×D411yescharacteristic
348C4×C8C23×C511yescharacteristic
349C22×C5—21no—
350C22×C5—21no—
351C22×C5—21no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5—81no—
355C22×C5—81no—
356C22×C5—81no—
357C22×C5—81no—
358C22×C5—81no—
359C22×C5—81no—
360C22×C5#50912yes—
361C22×C5C22×D811yescharacteristic
362C4×C5—21no—
363C4×C5—21no—
364C4×C5—21no—
365C4×C5—21no—
366C4×C5—42no—
367C4×C5—81no—
368C4×C5—81no—
369C4×C5—81no—
370C4×C5—81no—
371C4×C5—81no—
372C4×C5#54611yescharacteristic
373C4×C5#57711yescharacteristic
374#41—42no—
375#41—81no—
376#41—84no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—42no—
380C2×Q8—41no—
381C2×Q8—41no—
382C2×Q8—81no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4C5×D811yescharacteristic
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4C2×C5×D411yescharacteristic
396C22×C4C2×C5×D411yescharacteristic
397Q16—21no—
398Q16—21no—
399Q16—21no—
400Q16—42no—
401Q16C5×#4112yescomplemented
402SD16—42no—
403SD16—81no—
404D8—21no—
405D8—21no—
406D8—21no—
407D8—21no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8C2×C5×D411yescharacteristic
413C2×C8C2×C5×D411yescharacteristic
414C2×C8C2×C5×D411yescharacteristic
415C2×C8C24×C511yescharacteristic
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4C5×D811yescharacteristic
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C22⋊C4C5×D811yescharacteristic
434C22⋊C4C5×D811yescharacteristic
435C42—41no—
436C42C2×C5×D411yescharacteristic
437C16—21no—
438C16—21no—
439C16—21no—
440C16—21no—
441C2×C5—22no—
442C2×C5—41no—
443C2×C5—161no—
444C2×C5—161no—
445C2×C5#329411yescharacteristic
446C2×C5C2×#50911yescharacteristic
447C2×C5#341711yescharacteristic
448C23—41no—
449C23—41no—
450C23C2×C5×D811yescharacteristic
451C23C2×C5×D811yescharacteristic
452Q8—22no—
453Q8—41no—
454Q8—41no—
455Q8—41no—
456Q8—82no—
457Q8—82no—
458D4—22no—
459D4—41no—
460D4—41no—
461D4—41no—
462D4—41no—
463D4—82no—
464D4—82no—
465D4—82no—
466D4—82no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—82no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4C2×C5×D811yescharacteristic
483C2×C4C2×C5×D811yescharacteristic
484C2×C4C2×C5×D811yescharacteristic
485C2×C4C2×C5×D811yescharacteristic
486C2×C4C22×C5×D411yescharacteristic
487C8—21no—
488C8—21no—
489C8—21no—
490C8C2×C5×#4111yescharacteristic
491C8C5×H(5,𝔽2)11yescharacteristic
492C5#3387511yescharacteristic, direct product factor, Sylow
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22C5×#50912yes—
505C22C22×C5×D811yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—42no—
511C4—81no—
512C4—81no—
513C4—81no—
514C4—81no—
515C4—81no—
516C4C5×#54611yescharacteristic
517C4C5×#57711yescharacteristic
518C2—22no—
519C2—41no—
520C2—161no—
521C2—161no—
522C2C5×#329411yescharacteristic
523C2C2×C5×#50911yescharacteristic
524C2C5×#341711yescharacteristic
subgroupG/H
center, socleC22×C5C22×D8
commutator, Frattini, cosocleC2×C8C24×C5
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C4×C5×D4 ◁ C5×C8×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3334C2semidirect
2. C5×#3285C2semidirect
3. C5×#2243C2semidirect
4. C5×#2236C2semidirect
5. C5×#2232C2semidirect
6. C5×#2227C2semidirect
7. C5×#2220C2semidirect
8. C5×#2215C2semidirect
9. C5×#2210C2semidirect
10. C5×#2186C2semidirect
11. C5×#2185C2semidirect
12. C5×#2175C2semidirect
13. C5×#2168C2semidirect
14. C5×#2139C2semidirect
15. C2×C5×#358C2semidirect
59. #33875C5direct (N × H)
120. #3334C2×C5semidirect
121. #3285C2×C5semidirect
122. #2243C2×C5semidirect
123. #2236C2×C5semidirect
124. #2232C2×C5semidirect
125. #2227C2×C5semidirect
126. #2220C2×C5semidirect
127. #2215C2×C5semidirect
128. #2210C2×C5semidirect
129. #2186C2×C5semidirect
130. #2185C2×C5semidirect
131. #2175C2×C5semidirect
132. #2168C2×C5semidirect
133. #2139C2×C5semidirect
134. C2×#358C2×C5semidirect
162. C5×Q16#41semidirect
401. Q16C5×#41semidirect
492. C5#33875direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#33342
C5×#32852
C5×#22432
C5×#22362
C5×#22322
C5×#22272
C5×#22202
C5×#22152
C5×#22102
C5×#21862
C5×#21852
C5×#21752
C5×#21682
C5×#21392
C2×C5×#3582
#338755