Finite Group Databasebeta

← C5×#33879 #11956599

Subgroups — C5×#33879 #11956599

Order 1280.

536 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3336C211yesmaximal, characteristic
2C5×D4×Q16C211yesmaximal, characteristic
3C5×#2245C211yesmaximal, characteristic, complemented
4C5×#2237C211yesmaximal, characteristic, complemented
5C5×#2235C211yesmaximal, characteristic, complemented
6C5×#2229C211yesmaximal, characteristic, complemented
7C5×#2219C211yesmaximal, characteristic, complemented
8C5×#2216C211yesmaximal, characteristic, complemented
9C5×#2209C211yesmaximal, characteristic, complemented
10C5×#2188C211yesmaximal, characteristic, complemented
11C5×#2188C211yesmaximal, characteristic, complemented
12C5×#2176C211yesmaximal, characteristic, complemented
13C5×#2168C211yesmaximal, characteristic
14C5×#2141C211yesmaximal, characteristic, complemented
15C2×C5×#358C211yesmaximal, characteristic, complemented
16C22×C5×Q16C2211yescharacteristic
17C22×C5×Q16C2211yescharacteristic
18C5×#552—21no—
19C5×D4×Q8—21no—
20C2×C5×Q32C2211yescharacteristic
21C2×C5×Q32C2211yescharacteristic
22C2×C5×Q32C2211yescharacteristic
23C2×C5×M32C2211yescharacteristic
24C22×C5×C16C2211yescharacteristic
25C5×#499C2211yescharacteristic
26C5×#494C2211yescharacteristic
27C5×#485—21no—
28C5×#483—21no—
29C5×#479—21no—
30C5×#467C2211yescharacteristic
31C5×#467C2211yescharacteristic
32C5×#467C2211yescharacteristic
33C5×#467C2211yescharacteristic
34C5×#462—21no—
35C5×#451—21no—
36C5×#451—21no—
37C4×C5×Q16C2211yescharacteristic
38C4×C5×Q16C2211yescharacteristic
39C5×C8×D4C2211yescharacteristic
40C5×#427C2211yescharacteristic
41C2×C5×#107C2211yescharacteristic
42C5×#367C2211yescharacteristic
43C5×#367C2211yescharacteristic
44C5×#366C2211yescharacteristic
45C5×C4⋊C16C2211yescharacteristic
46C5×#358C2211yescharacteristic
47C5×#358C2211yescharacteristic
48C5×#358C2211yescharacteristic
49C5×#358C2211yescharacteristic
50C5×#358C2211yescharacteristic
51C5×#358C2211yescharacteristic
52C5×#358C2211yescharacteristic
53C5×#358C2211yescharacteristic
54C5×#358C2211yescharacteristic
55C5×#358C2211yescharacteristic
56C5×C22⋊C16C2211yescharacteristic
57C5×C22⋊C16C2211yescharacteristic
58C5×#346C2211yescharacteristic
59#33879C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8—21no—
61C22×C5×Q8—21no—
62C2×C5×Q16—22no—
63C2×C5×Q16—22no—
64C2×C5×Q16—21no—
65C2×C5×Q16—21no—
66C2×C5×Q16—21no—
67C2×C5×Q16—41no—
68C2×C5×Q16—41no—
69C2×C5×Q16C2311yescharacteristic
70C2×C5×Q16C2311yescharacteristic
71C2×C5×Q16C2311yescharacteristic
72C2×C5×Q16C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C5×C4⋊Q8—21no—
76C5×C4⋊Q8—41no—
77C5×#126—41no—
78C5×#125—21no—
79C5×#125—41no—
80C5×#123—41no—
81C5×C22⋊Q8—21no—
82C5×C22⋊Q8—21no—
83C5×C22⋊Q8—21no—
84C5×C22⋊Q8—21no—
85C5×C22⋊Q8—41no—
86C5×C22⋊Q8—41no—
87C4×C5×Q8—21no—
88C4×C5×Q8—21no—
89C4×C5×D4—41no—
90C4×C5×D4D411yescharacteristic
91C5×#117—21no—
92C5×#117—41no—
93C2×C5×C4⋊C4—21no—
94C5×Q32—22no—
95C5×Q32—41no—
96C5×Q32—41no—
97C5×M32—41no—
98C2×C5×C16—41no—
99C2×C5×C16C2311yescharacteristic
100C2×C5×C16C2311yescharacteristic
101C2×C5×C16C2311yescharacteristic
102C2×C5×C16C2311yescharacteristic
103C5×#107—21no—
104C5×#107C2311yescharacteristic
105C5×#107C2311yescharacteristic
106C5×#107C2311yescharacteristic
107C5×#107C2311yescharacteristic
108C5×#106—21no—
109C5×#106—21no—
110C5×C4⋊C8D411yescharacteristic
111C5×#103—21no—
112C5×#103—21no—
113C5×#103—21no—
114C5×#103—21no—
115C5×#103—21no—
116C5×#103—21no—
117C5×C22⋊C8D411yescharacteristic
118C5×C22⋊C8D411yescharacteristic
119C4×C5×C8C2311yescharacteristic
120#3336C2×C511yescharacteristic
121D4×Q16C2×C511yescharacteristic
122#2245C2×C511yescharacteristic, complemented
123#2237C2×C511yescharacteristic, complemented
124#2235C2×C511yescharacteristic, complemented
125#2229C2×C511yescharacteristic, complemented
126#2219C2×C511yescharacteristic, complemented
127#2216C2×C511yescharacteristic, complemented
128#2209C2×C511yescharacteristic, complemented
129#2188C2×C511yescharacteristic, complemented
130#2188C2×C511yescharacteristic, complemented
131#2176C2×C511yescharacteristic, complemented
132#2168C2×C511yescharacteristic
133#2141C2×C511yescharacteristic, complemented
134C2×#358C2×C511yescharacteristic, complemented
135C2×C5×Q8—21no—
136C2×C5×Q8—21no—
137C2×C5×Q8—21no—
138C2×C5×Q8—21no—
139C2×C5×Q8—42no—
140C2×C5×Q8—42no—
141C2×C5×Q8—41no—
142C2×C5×Q8—41no—
143C2×C5×Q8—81no—
144C2×C5×Q8—81no—
145C2×C5×D4D811yescharacteristic
146C22×C4×C5—41no—
147C22×C4×C5—41no—
148C22×C4×C5—41no—
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2×D411yescharacteristic
151C5×Q16—21no—
152C5×Q16—21no—
153C5×Q16—21no—
154C5×Q16—21no—
155C5×Q16—21no—
156C5×Q16—21no—
157C5×Q16—21no—
158C5×Q16—42no—
159C5×Q16—42no—
160C5×Q16—81no—
161C5×Q16#4112yes—
162C2×C5×C8—21no—
163C2×C5×C8—21no—
164C2×C5×C8—21no—
165C2×C5×C8—21no—
166C2×C5×C8C2×D411yescharacteristic
167C2×C5×C8C2×D411yescharacteristic
168C2×C5×C8C2×D411yescharacteristic
169C2×C5×C8C2411yescharacteristic
170C5×C4⋊C4—21no—
171C5×C4⋊C4—21no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—41no—
175C5×C4⋊C4—41no—
176C5×C4⋊C4—41no—
177C5×C4⋊C4—41no—
178C5×C4⋊C4—41no—
179C5×C4⋊C4—41no—
180C5×C4⋊C4—41no—
181C5×C4⋊C4—41no—
182C5×C4⋊C4—41no—
183C5×C4⋊C4—41no—
184C5×C4⋊C4—41no—
185C5×C4⋊C4D811yescharacteristic
186C5×C22⋊C4—41no—
187C5×C22⋊C4—41no—
188C5×C22⋊C4—41no—
189C5×C22⋊C4—41no—
190C5×C22⋊C4—41no—
191C5×C22⋊C4D811yescharacteristic
192C5×C22⋊C4D811yescharacteristic
193C42×C5—41no—
194C42×C5—41no—
195C42×C5—41no—
196C42×C5C2×D411yescharacteristic
197C5×C16—21no—
198C5×C16—21no—
199C5×C16—21no—
200C5×C16—21no—
201C22×Q16C22×C511yescharacteristic
202C22×Q16C22×C511yescharacteristic
203#552—21no—
204D4×Q8—21no—
205C2×Q32C22×C511yescharacteristic
206C2×Q32C22×C511yescharacteristic
207C2×Q32C22×C511yescharacteristic
208C2×M32C22×C511yescharacteristic
209C22×C16C22×C511yescharacteristic
210#499C22×C511yescharacteristic
211#494C22×C511yescharacteristic
212#485—21no—
213#483—21no—
214#479—21no—
215#467C22×C511yescharacteristic
216#467C22×C511yescharacteristic
217#467C22×C511yescharacteristic
218#467C22×C511yescharacteristic
219#462—21no—
220#451—21no—
221#451—21no—
222C4×Q16C22×C511yescharacteristic
223C4×Q16C22×C511yescharacteristic
224C8×D4C22×C511yescharacteristic
225#427C22×C511yescharacteristic
226C2×#107C22×C511yescharacteristic
227#367C22×C511yescharacteristic
228#367C22×C511yescharacteristic
229#366C22×C511yescharacteristic
230C4⋊C16C22×C511yescharacteristic
231#358C22×C511yescharacteristic
232#358C22×C511yescharacteristic
233#358C22×C511yescharacteristic
234#358C22×C511yescharacteristic
235#358C22×C511yescharacteristic
236#358C22×C511yescharacteristic
237#358C22×C511yescharacteristic
238#358C22×C511yescharacteristic
239#358C22×C511yescharacteristic
240#358C22×C511yescharacteristic
241C22⋊C16C22×C511yescharacteristic
242C22⋊C16C22×C511yescharacteristic
243#346C22×C511yescharacteristic
244C23×C5C2×D811yescharacteristic
245C23×C5C2×D811yescharacteristic
246C5×Q8—22no—
247C5×Q8—41no—
248C5×Q8—41no—
249C5×Q8—41no—
250C5×Q8—41no—
251C5×Q8—41no—
252C5×Q8—41no—
253C5×Q8—41no—
254C5×Q8—82no—
255C5×Q8—82no—
256C5×D4—22no—
257C2×C4×C5—21no—
258C2×C4×C5—21no—
259C2×C4×C5—21no—
260C2×C4×C5—21no—
261C2×C4×C5—41no—
262C2×C4×C5—41no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—41no—
266C2×C4×C5—41no—
267C2×C4×C5—41no—
268C2×C4×C5—41no—
269C2×C4×C5—82no—
270C2×C4×C5—82no—
271C2×C4×C5—82no—
272C2×C4×C5C2×D811yescharacteristic
273C2×C4×C5C2×D811yescharacteristic
274C2×C4×C5C2×D811yescharacteristic
275C2×C4×C5C2×D811yescharacteristic
276C2×C4×C5C22×D411yescharacteristic
277C5×C8—21no—
278C5×C8—21no—
279C5×C8—21no—
280C5×C8C2×#4111yescharacteristic
281C5×C8H(5,𝔽2)11yescharacteristic
282C22×Q8—21no—
283C22×Q8—21no—
284C2×Q16—22no—
285C2×Q16—22no—
286C2×Q16—21no—
287C2×Q16—21no—
288C2×Q16—21no—
289C2×Q16—41no—
290C2×Q16—41no—
291C2×Q16C23×C511yescharacteristic
292C2×Q16C23×C511yescharacteristic
293C2×Q16C23×C511yescharacteristic
294C2×Q16C23×C511yescharacteristic
295C22×C8C23×C511yescharacteristic
296C22×C8C23×C511yescharacteristic
297C4⋊Q8—21no—
298C4⋊Q8—41no—
299#126—41no—
300#125—21no—
301#125—41no—
302#123—41no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C22⋊Q8—41no—
308C22⋊Q8—41no—
309C4×Q8—21no—
310C4×Q8—21no—
311C4×D4—41no—
312C4×D4C5×D411yescharacteristic
313#117—21no—
314#117—41no—
315C2×C4⋊C4—21no—
316Q32—22no—
317Q32—41no—
318Q32—41no—
319M32—41no—
320C2×C16—41no—
321C2×C16C23×C511yescharacteristic
322C2×C16C23×C511yescharacteristic
323C2×C16C23×C511yescharacteristic
324C2×C16C23×C511yescharacteristic
325#107—21no—
326#107C23×C511yescharacteristic
327#107C23×C511yescharacteristic
328#107C23×C511yescharacteristic
329#107C23×C511yescharacteristic
330#106—21no—
331#106—21no—
332C4⋊C8C5×D411yescharacteristic
333#103—21no—
334#103—21no—
335#103—21no—
336#103—21no—
337#103—21no—
338#103—21no—
339C22⋊C8C5×D411yescharacteristic
340C22⋊C8C5×D411yescharacteristic
341C4×C8C23×C511yescharacteristic
342C22×C5—21no—
343C22×C5—21no—
344C22×C5—21no—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5#51012yes—
348C22×C5C22×D811yescharacteristic
349C4×C5—21no—
350C4×C5—21no—
351C4×C5—21no—
352C4×C5—21no—
353C4×C5—42no—
354C4×C5—81no—
355C4×C5—81no—
356C4×C5—81no—
357C4×C5—81no—
358C4×C5—81no—
359C4×C5—81no—
360C4×C5—81no—
361C4×C5#54611yescharacteristic
362C4×C5#57711yescharacteristic
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—42no—
368C2×Q8—42no—
369C2×Q8—41no—
370C2×Q8—41no—
371C2×Q8—81no—
372C2×Q8—81no—
373C2×D4C5×D811yescharacteristic
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4C2×C5×D411yescharacteristic
378C22×C4C2×C5×D411yescharacteristic
379Q16—21no—
380Q16—21no—
381Q16—21no—
382Q16—21no—
383Q16—21no—
384Q16—21no—
385Q16—21no—
386Q16—42no—
387Q16—42no—
388Q16—81no—
389Q16C5×#4112yes—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8C2×C5×D411yescharacteristic
395C2×C8C2×C5×D411yescharacteristic
396C2×C8C2×C5×D411yescharacteristic
397C2×C8C24×C511yescharacteristic
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4C5×D811yescharacteristic
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4C5×D811yescharacteristic
420C22⋊C4C5×D811yescharacteristic
421C42—41no—
422C42—41no—
423C42—41no—
424C42C2×C5×D411yescharacteristic
425C16—21no—
426C16—21no—
427C16—21no—
428C16—21no—
429C2×C5—22no—
430C2×C5—41no—
431C2×C5#329411yescharacteristic
432C2×C5C2×#51011yescharacteristic
433C2×C5#341711yescharacteristic
434C23C2×C5×D811yescharacteristic
435C23C2×C5×D811yescharacteristic
436Q8—22no—
437Q8—41no—
438Q8—41no—
439Q8—41no—
440Q8—41no—
441Q8—41no—
442Q8—41no—
443Q8—41no—
444Q8—82no—
445Q8—82no—
446D4—22no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—82no—
460C2×C4—82no—
461C2×C4—82no—
462C2×C4C2×C5×D811yescharacteristic
463C2×C4C2×C5×D811yescharacteristic
464C2×C4C2×C5×D811yescharacteristic
465C2×C4C2×C5×D811yescharacteristic
466C2×C4C22×C5×D411yescharacteristic
467C8—21no—
468C8—21no—
469C8—21no—
470C8C2×C5×#4111yescharacteristic
471C8C5×H(5,𝔽2)11yescharacteristic
472C5#3387911yescharacteristic, direct product factor, Sylow
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22C5×#51012yes—
479C22C22×C5×D811yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—42no—
485C4—81no—
486C4—81no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—81no—
491C4—81no—
492C4C5×#54611yescharacteristic
493C4C5×#57711yescharacteristic
494C2—22no—
495C2—41no—
496C2C5×#329411yescharacteristic
497C2C2×C5×#51011yescharacteristic
498C2C5×#341711yescharacteristic
subgroupG/H
center, socleC22×C5C22×D8
commutator, Frattini, cosocleC2×C8C24×C5
prime radicalC2×C5×D4D8
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
3. C5×#2245C2semidirect
4. C5×#2237C2semidirect
5. C5×#2235C2semidirect
6. C5×#2229C2semidirect
7. C5×#2219C2semidirect
8. C5×#2216C2semidirect
9. C5×#2209C2semidirect
10. C5×#2188C2semidirect
11. C5×#2188C2semidirect
12. C5×#2176C2semidirect
14. C5×#2141C2semidirect
15. C2×C5×#358C2semidirect
59. #33879C5direct (N × H)
122. #2245C2×C5semidirect
123. #2237C2×C5semidirect
124. #2235C2×C5semidirect
125. #2229C2×C5semidirect
126. #2219C2×C5semidirect
127. #2216C2×C5semidirect
128. #2209C2×C5semidirect
129. #2188C2×C5semidirect
130. #2188C2×C5semidirect
131. #2176C2×C5semidirect
133. #2141C2×C5semidirect
134. C2×#358C2×C5semidirect
472. C5#33879direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#33362
C5×D4×Q162
C5×#22452
C5×#22372
C5×#22352
C5×#22292
C5×#22192
C5×#22162
C5×#22092
C5×#21882
C5×#21762
C5×#21682
C5×#21412
C2×C5×#3582
#338795