Finite Group Databasebeta

← C5×#10590393 #72260136

Subgroups — C5×#10590393 #72260136

Order 2880.

788 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#64306C211yesmaximal, characteristic
2C42×C5×C3⋊D3C211yesmaximal, characteristic, complemented
3C5×#63818C211yesmaximal, characteristic, complemented
4C3×C5×#805C212yesmaximal, complemented
5C5×#63568C212yesmaximal, complemented
6C5×D3×#104—32nomaximal
7C2×C4×C5×C3⋊D3—21no—
8C2×C4×C5×C3⋊D3C2211yescharacteristic
9C3×C5×#235C2212yes—
10C5×#3811—21no—
11C5×#3805—21no—
12C5×#3802C411yescharacteristic, complemented
13C4×C5×D32—21no—
14C5×#3798—21no—
15C5×#3797C411yescharacteristic, complemented
16C5×#3796C412yescomplemented
17C32×C42×C5C2211yescharacteristic, complemented
18C4×C5×C3⋊Dic3—21no—
19C4×C5×C3⋊Dic3C2211yescharacteristic, complemented
20C3×C5×#208C2212yescomplemented
21C5×#3712—21no—
22C5×#3710—21no—
23#10590393C511yesmaximal, characteristic, direct product factor, Hall
24C5×D3×#41—32no—
25C5×D3×M16—32no—
26C42×C5×D3—32no—
27C42×C5×D3—61no—
28C3×C5×#104—32no—
29C5×#837—32no—
30C5×#825—32no—
31C5×#805D312yescomplemented
32C22×C5×C3⋊D3D411yescharacteristic
33C2×C5×D32—21no—
34C2×C32×C4×C5—21no—
35C2×C32×C4×C5C2311yescharacteristic
36C2×C5×C3⋊Dic3—21no—
37C2×C5×C3⋊Dic3D411yescharacteristic
38C4×C5×C3⋊D3—24no—
39C4×C5×C3⋊D3C2×C411yescharacteristic
40C4×C5×C3⋊D3C2×C411yescharacteristic
41C4×C5×C3⋊D3D411yescharacteristic
42C4×C5×C3⋊D3D411yescharacteristic
43C3×C5×#67—22no—
44C3×C5×D12C2×C412yescomplemented
45C3×C4×C5×D3—22no—
46C3×C5×Dic6C2×C412yescomplemented
47C5×#627—21no—
48C5×#626—22no—
49C5×#625—21no—
50C5×#624—21no—
51C5×D3×Dic3—22no—
52C3×C5×C3⋊C8—22no—
53C2×C5×#104—91noHall
54#64306C2×C511yescharacteristic
55C42×C3⋊D3C2×C511yescharacteristic, complemented
56#63818C2×C511yescharacteristic, complemented
57C3×#805C2×C512yescomplemented
58#63568C2×C512yescomplemented
59C3×C5×#41—32no—
60C5×#239—32no—
61C5×D3×Q8—32no—
62C5×#237—32no—
63C5×#237—62no—
64C5×D3×D4—32no—
65C5×D3×D4—62no—
66C5×#235—62no—
67C5×#235C2×D312yes—
68C2×C4×C5×D3—32no—
69C2×C4×C5×D3—62no—
70C2×C4×C5×D3—61no—
71C2×C4×C5×D3—62no—
72C2×C4×C5×D3—62no—
73C3×C5×M16—32no—
74C3×C42×C5—21no—
75C3×C42×C5C2×D312yescomplemented
76C4×C5×Dic3—32no—
77C4×C5×Dic3—61no—
78C4×C5×Dic3—62no—
79C4×C5×Dic3—62no—
80C5×#208C2×D312yescomplemented
81C5×ΓL(1,𝔽25)—62no—
82C5×D3×C8—62no—
83D3×#104—32no—
84C22×C32×C5C2×D411yescharacteristic
85C2×C5×C3⋊D3—22no—
86C2×C5×C3⋊D3C22⋊C411yescharacteristic
87C2×C5×C3⋊D3C22⋊C411yescharacteristic
88C2×C3×C5×D3—22no—
89C5×D32—42no—
90C32×C4×C5—22no—
91C32×C4×C5C22×C411yescharacteristic
92C32×C4×C5C2×D411yescharacteristic
93C5×C3⋊Dic3—22no—
94C5×C3⋊Dic3C22⋊C411yescharacteristic
95C5×C3⋊Dic3C22⋊C411yescharacteristic
96C3×C5×Dic3—22no—
97C2×C5×#41—91no—
98C2×C5×M16—91no—
99C2×C42×C5—91no—
100C5×#104—32no—
101C5×#104—92no—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C22×C511yescharacteristic
104C3×#235C22×C512yes—
105#3811—21no—
106#3805—21no—
107#3802C4×C511yescharacteristic, complemented
108C4×D32—21no—
109#3798—21no—
110#3797C4×C511yescharacteristic, complemented
111#3796C4×C512yescomplemented
112C32×C42C22×C511yescharacteristic, complemented
113C4×C3⋊Dic3—21no—
114C4×C3⋊Dic3C22×C511yescharacteristic, complemented
115C3×#208C22×C512yescomplemented
116#3712—21no—
117#3710—21no—
118C22×C5×D3—32no—
119C22×C5×D3—62no—
120C22×C5×D3—61no—
121C3×C5×Q8—32no—
122C3×C5×D4—32no—
123C3×C5×D4—62no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—21no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—62no—
128C2×C3×C4×C5C22×D312yes—
129C5×#67—22no—
130C5×#67—62no—
131C5×#67—62no—
132C2×C5×Dic3—32no—
133C2×C5×Dic3—62no—
134C2×C5×Dic3—61no—
135C2×C5×Dic3—62no—
136C2×C5×Dic3—62no—
137C5×D12—62no—
138C5×D12C4×D312yescomplemented
139C4×C5×D3—22no—
140C4×C5×D3—32no—
141C4×C5×D3—32no—
142C4×C5×D3—32no—
143C4×C5×D3—32no—
144C4×C5×D3—62no—
145C4×C5×D3—62no—
146C4×C5×D3—61no—
147C4×C5×D3—61no—
148C4×C5×D3—61no—
149C4×C5×D3—61no—
150C4×C5×D3—68no—
151C4×C5×D3—68no—
152C5×Dic6—62no—
153C5×Dic6C4×D312yescomplemented
154C3×C5×C8—62no—
155C5×C3⋊C8—22no—
156D3×#41—32no—
157D3×M16—32no—
158C42×D3—32no—
159C42×D3—61no—
160C3×#104—32no—
161#837—32no—
162#825—32no—
163#805C5×D312yescomplemented
164C2×C32×C5—21no—
165C2×C32×C5C2×C22⋊C411yescharacteristic
166C5×C3⋊D3—21no—
167C5×C3⋊D3#10412yescomplemented
168C3×C5×D3—42no—
169C5×#41—32no—
170C5×#41—92no—
171C5×#41—181no—
172C5×#41—181no—
173C2×C5×Q8—91no—
174C2×C5×D4—91no—
175C2×C5×D4—181no—
176C22×C4×C5—91no—
177C22×C4×C5—181no—
178C22×C4×C5—181no—
179C5×M16—32no—
180C5×M16—181no—
181C2×C5×C8—181no—
182C42×C5—91no—
183C42×C5—181no—
184C42×C5D3211yescharacteristic, complemented
185C22×C3⋊D3C5×D411yescharacteristic
186C2×D32—21no—
187C2×C32×C4—21no—
188C2×C32×C4C23×C511yescharacteristic
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3C5×D411yescharacteristic
191C4×C3⋊D3—24no—
192C4×C3⋊D3C2×C4×C511yescharacteristic
193C4×C3⋊D3C2×C4×C511yescharacteristic
194C4×C3⋊D3C5×D411yescharacteristic
195C4×C3⋊D3C5×D411yescharacteristic
196C3×#67—22no—
197C3×D12C2×C4×C512yescomplemented
198C3×C4×D3—22no—
199C3×Dic6C2×C4×C512yescomplemented
200#627—21no—
201#626—22no—
202#625—21no—
203#624—21no—
204D3×Dic3—22no—
205C3×C3⋊C8—22no—
206C2×#104—91noSylow
207C22×C3×C5—21no—
208C22×C3×C5—62no—
209C22×C3×C5D3×D412yes—
210C2×C5×D3—22no—
211C2×C5×D3—32no—
212C2×C5×D3—32no—
213C2×C5×D3—61no—
214C2×C5×D3—61no—
215C2×C5×D3—64no—
216C2×C5×D3—64no—
217C2×C5×D3—124no—
218C3×C4×C5—24no—
219C3×C4×C5—24no—
220C3×C4×C5—21no—
221C3×C4×C5—21no—
222C3×C4×C5—62no—
223C3×C4×C5C2×C4×D312yes—
224C3×C4×C5D3×D412yes—
225C5×Dic3—22no—
226C5×Dic3—32no—
227C5×Dic3—32no—
228C5×Dic3—61no—
229C5×Dic3—61no—
230C5×Dic3—64no—
231C5×Dic3—64no—
232C3×#41—32no—
233#239—32no—
234D3×Q8—32no—
235#237—32no—
236#237—62no—
237D3×D4—32no—
238D3×D4—62no—
239#235—62no—
240#235C2×C5×D312yes—
241C2×C4×D3—32no—
242C2×C4×D3—61no—
243C2×C4×D3—62no—
244C2×C4×D3—62no—
245C2×C4×D3—62no—
246C3×M16—32no—
247C3×C42—21no—
248C3×C42C2×C5×D312yescomplemented
249C4×Dic3—32no—
250C4×Dic3—61no—
251C4×Dic3—62no—
252C4×Dic3—62no—
253#208C2×C5×D312yescomplemented
254ΓL(1,𝔽25)—62no—
255D3×C8—62no—
256C32×C5C2×#10411yescharacteristic, complemented, Hall
257C23×C5—91no—
258C23×C5—181no—
259C5×Q8—32no—
260C5×Q8—181no—
261C5×D4—32no—
262C5×D4—62no—
263C5×D4—182no—
264C5×D4—181no—
265C2×C4×C5—21no—
266C2×C4×C5—62no—
267C2×C4×C5—91no—
268C2×C4×C5—91no—
269C2×C4×C5—91no—
270C2×C4×C5—91no—
271C2×C4×C5—91no—
272C2×C4×C5—184no—
273C2×C4×C5—181no—
274C2×C4×C5—182no—
275C2×C4×C5—181no—
276C2×C4×C5C2×D3211yescharacteristic
277C5×C8—62no—
278C22×C32C2×C5×D411yescharacteristic
279C2×C3⋊D3—22no—
280C2×C3⋊D3C5×C22⋊C411yescharacteristic
281C2×C3⋊D3C5×C22⋊C411yescharacteristic
282C2×C3×D3—22no—
283D32—42no—
284C32×C4—22no—
285C32×C4C22×C4×C511yescharacteristic
286C32×C4C2×C5×D411yescharacteristic
287C3⋊Dic3—22no—
288C3⋊Dic3C5×C22⋊C411yescharacteristic
289C3⋊Dic3C5×C22⋊C411yescharacteristic
290C3×Dic3—22no—
291C2×#41—91no—
292C2×M16—91no—
293C2×C42—91no—
294#104—32no—
295#104—92no—
296C2×C3×C5—22no—
297C2×C3×C5—22no—
298C2×C3×C5—21no—
299C2×C3×C5—122no—
300C2×C3×C5D3×C22⋊C412yes—
301C5×D3—34no—
302C5×D3—42no—
303C5×D3—62no—
304C5×D3—62no—
305C5×D3—62no—
306C22×D3—32no—
307C22×D3—61no—
308C22×D3—62no—
309C3×Q8—32no—
310C3×D4—32no—
311C3×D4—62no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—21no—
315C2×C3×C4—62no—
316C2×C3×C4C22×C5×D312yes—
317#67—22no—
318#67—62no—
319#67—62no—
320C2×Dic3—32no—
321C2×Dic3—61no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325D12—62no—
326D12C4×C5×D312yescomplemented
327C4×D3—22no—
328C4×D3—32no—
329C4×D3—32no—
330C4×D3—32no—
331C4×D3—32no—
332C4×D3—61no—
333C4×D3—61no—
334C4×D3—61no—
335C4×D3—61no—
336C4×D3—62no—
337C4×D3—62no—
338C4×D3—68no—
339C4×D3—68no—
340Dic6—62no—
341Dic6C4×C5×D312yescomplemented
342C3×C8—62no—
343C3⋊C8—22no—
344C22×C5—62no—
345C22×C5—91no—
346C22×C5—91no—
347C22×C5—182no—
348C22×C5—362no—
349C22×C5#381111yescharacteristic
350C4×C5—22no—
351C4×C5—62no—
352C4×C5—91no—
353C4×C5—91no—
354C4×C5—182no—
355C4×C5C4×D3211yescharacteristic
356C4×C5#380211yescharacteristic
357C2×C32—21no—
358C2×C32C2×C5×C22⋊C411yescharacteristic
359C3⋊D3—21no—
360C3⋊D3C5×#10412yescomplemented
361C3×D3—42no—
362#41—32no—
363#41—92no—
364#41—181no—
365#41—181no—
366C2×Q8—91no—
367C2×D4—91no—
368C2×D4—181no—
369C22×C4—91no—
370C22×C4—181no—
371C22×C4—181no—
372M16—32no—
373M16—181no—
374C2×C8—181no—
375C42—91no—
376C42—181no—
377C42C5×D3211yescharacteristic, complemented
378C3×C5—21no—
379C3×C5D3×#10412yescomplemented
380C22×C3—21no—
381C22×C3—62no—
382C22×C3C5×D3×D412yes—
383C2×D3—22no—
384C2×D3—32no—
385C2×D3—32no—
386C2×D3—61no—
387C2×D3—61no—
388C2×D3—64no—
389C2×D3—64no—
390C2×D3—124no—
391C3×C4—24no—
392C3×C4—24no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—62no—
396C3×C4C2×C4×C5×D312yes—
397C3×C4C5×D3×D412yes—
398Dic3—22no—
399Dic3—32no—
400Dic3—32no—
401Dic3—61no—
402Dic3—61no—
403Dic3—64no—
404Dic3—64no—
405C2×C5—21no—
406C2×C5—92no—
407C2×C5—122no—
408C2×C5—181no—
409C2×C5#6392111yescharacteristic
410C32C2×C5×#10411yescharacteristic, complemented, Sylow
411C23—91no—
412C23—181no—
413Q8—32no—
414Q8—181no—
415D4—32no—
416D4—62no—
417D4—182no—
418D4—181no—
419C2×C4—21no—
420C2×C4—62no—
421C2×C4—91no—
422C2×C4—91no—
423C2×C4—91no—
424C2×C4—91no—
425C2×C4—91no—
426C2×C4—184no—
427C2×C4—181no—
428C2×C4—182no—
429C2×C4—181no—
430C2×C4C2×C5×D3211yescharacteristic
431C8—62no—
432C2×C3—22no—
433C2×C3—22no—
434C2×C3—21no—
435C2×C3—122no—
436C2×C3C5×D3×C22⋊C412yes—
437D3—34no—
438D3—42no—
439D3—62no—
440D3—62no—
441D3—62no—
442C5#1059039311yescharacteristic, direct product factor, Sylow
443C22—62no—
444C22—91no—
445C22—91no—
446C22—182no—
447C22—362no—
448C22C5×#381111yescharacteristic
449C4—22no—
450C4—62no—
451C4—91no—
452C4—91no—
453C4—182no—
454C4C4×C5×D3211yescharacteristic
455C4C5×#380211yescharacteristic
456C3—21no—
457C3C5×D3×#10412yescomplemented
458C2—21no—
459C2—92no—
460C2—122no—
461C2—181no—
462C2C5×#6392111yescharacteristic
subgroupG/H
centerC4×C5#3802
commutatorC32×C4C22×C4×C5
FrattiniC2×C4C2×C5×D32
FittingC32×C42×C5C22
socleC2×C32×C5C2×C22⋊C4
prime radicalC5×#64306C2
cosocleC2×C32×C4C23×C5
hypercenterC42×C5D32
hypocenterC32C2×C5×#104
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C42×C5

Complements

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

NH ≅ G/Ntype
2. C42×C5×C3⋊D3C2semidirect
3. C5×#63818C2semidirect
4. C3×C5×#805C2semidirect
5. C5×#63568C2semidirect
12. C5×#3802C4semidirect
15. C5×#3797C4semidirect
16. C5×#3796C4semidirect
17. C32×C42×C5C22semidirect
19. C4×C5×C3⋊Dic3C22semidirect
20. C3×C5×#208C22semidirect
23. #10590393C5direct (N × H)
31. C5×#805D3semidirect
44. C3×C5×D12C2×C4semidirect
46. C3×C5×Dic6C2×C4semidirect
55. C42×C3⋊D3C2×C5semidirect
56. #63818C2×C5semidirect
57. C3×#805C2×C5semidirect
58. #63568C2×C5semidirect
75. C3×C42×C5C2×D3semidirect
80. C5×#208C2×D3semidirect
107. #3802C4×C5semidirect
110. #3797C4×C5semidirect
111. #3796C4×C5semidirect
112. C32×C42C22×C5semidirect
114. C4×C3⋊Dic3C22×C5semidirect
115. C3×#208C22×C5semidirect
138. C5×D12C4×D3semidirect
153. C5×Dic6C4×D3semidirect
163. #805C5×D3semidirect
167. C5×C3⋊D3#104semidirect
184. C42×C5D32semidirect
197. C3×D12C2×C4×C5semidirect
199. C3×Dic6C2×C4×C5semidirect
248. C3×C42C2×C5×D3semidirect
253. #208C2×C5×D3semidirect
256. C32×C5C2×#104semidirect
326. D12C4×C5×D3semidirect
341. Dic6C4×C5×D3semidirect
360. C3⋊D3C5×#104semidirect
377. C42C5×D32semidirect
379. C3×C5D3×#104semidirect
410. C32C2×C5×#104semidirect
442. C5#10590393direct (N × H)
457. C3C5×D3×#104semidirect

Maximal subgroups

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

subgroupindex
C5×#643062
C42×C5×C3⋊D32
C5×#638182
C3×C5×#8052
C5×#635682
C5×D3×#1043
#105903935