Finite Group Databasebeta

← C5×#71164 #14288239

Subgroups — C5×#71164 #14288239

Order 1920.

560 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5605C211yesmaximal, characteristic
2C3×C5×#480C211yesmaximal, characteristic, complemented
3C5×#4992C211yesmaximal, characteristic, complemented
4C5×#4967C211yesmaximal, characteristic, complemented
5C5×#4537C211yesmaximal, characteristic, complemented
6C5×#4470C211yesmaximal, characteristic, complemented
7C5×#4468C211yesmaximal, characteristic, complemented
8C5×#1607—31nomaximal, Hall
9C2×C5×D3×D4—21no—
10C3×C5×#121C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
12C5×#939—21no—
13C5×#937—21no—
14C5×#930C2211yescharacteristic
15C2×C5×(C2×D3)⋊C4—21no—
16C2×C5×(C2×D3)⋊C4C2211yescharacteristic
17C5×#894—21no—
18C5×#883—21no—
19C5×#882—21no—
20C3×C5×#107—21no—
21C3×C5×#102—21no—
22C3×C5×C22⋊C8C2211yescharacteristic, complemented
23C5×C3⋊#95—21no—
24C5×C3⋊#95C2211yescharacteristic, complemented
25C5×#830C2211yescharacteristic, complemented
26C5×#809—21no—
27C5×#807—21no—
28#71164C511yesmaximal, characteristic, direct product factor, Hall
29C5×#534—31no—
30C5×#480—31no—
31C5×#480D311yescharacteristic, complemented
32C5×#397—31no—
33C5×#327—31no—
34C5×#327—31no—
35C5×#323—31no—
36C23×C5×D3—21no—
37C23×C5×D3D411yescharacteristic
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4D411yescharacteristic
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5C2311yescharacteristic
42C2×C5×#67—21no—
43C2×C5×#67—21no—
44C2×C5×#67—21no—
45C22×C5×Dic3—21no—
46C22×C5×Dic3D411yescharacteristic
47C5×D3×D4—42no—
48C5×D3×D4—42no—
49C2×C5×D12—21no—
50C2×C5×D12D411yescharacteristic
51C2×C4×C5×D3—21no—
52C2×C3×C5×C8—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4D411yescharacteristic
56C3×C5×C22⋊C4—21no—
57C5×#217—21no—
58C5×(C2×D3)⋊C4—21no—
59C5×(C2×D3)⋊C4—21no—
60C5×(C2×D3)⋊C4—21no—
61C5×(C2×D3)⋊C4—21no—
62C5×(C2×D3)⋊C4—42no—
63C5×C4⋊Dic3D411yescharacteristic
64C5×Dic3⋊C4—21no—
65C2×C5×C3⋊C8—21no—
66#5605C2×C511yescharacteristic
67C3×#480C2×C511yescharacteristic, complemented
68#4992C2×C511yescharacteristic, complemented
69#4967C2×C511yescharacteristic, complemented
70#4537C2×C511yescharacteristic, complemented
71#4470C2×C511yescharacteristic, complemented
72#4468C2×C511yescharacteristic, complemented
73C22×C5×D4—61no—
74C5×#123—61no—
75C5×#123—61no—
76C5×#121—31no—
77C5×#121—61no—
78C5×#121C2×D311yescharacteristic
79C5×#120—61no—
80C5×#120—61no—
81C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
82C2×C5×C22⋊C4—31no—
83C2×C5×C22⋊C4—61no—
84C5×#107—21no—
85C5×#107—61no—
86C5×#102—21no—
87C5×#102—61no—
88C5×C22⋊C8—31no—
89C5×C22⋊C8C2×D311yescharacteristic, complemented
90C5×#95—31no—
91C5×#95—61no—
92#1607—31noSylow
93C23×C3×C5—21no—
94C23×C3×C5C2×D411yescharacteristic
95C22×C5×D3—21no—
96C22×C5×D3—21no—
97C22×C5×D3—21no—
98C22×C5×D3—42no—
99C22×C5×D3—41no—
100C22×C5×D3—41no—
101C22×C5×D3—81no—
102C22×C5×D3—81no—
103C22×C5×D3D812yes—
104C3×C5×D4—41no—
105C3×C5×D4—41no—
106C3×C5×D4—41no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C5×#67—42no—
115C5×#67—41no—
116C5×#67—41no—
117C5×#67—81no—
118C2×C5×Dic3—21no—
119C2×C5×Dic3—21no—
120C2×C5×Dic3—41no—
121C2×C5×Dic3—41no—
122C2×C5×Dic3—41no—
123C2×C5×Dic3—41no—
124C5×D12—41no—
125C5×D12—42no—
126C4×C5×D3—42no—
127C3×C5×C8—41no—
128C5×C3⋊C8—41no—
129C2×D3×D4—21no—
130C3×#121C22×C511yescharacteristic
131C2×C3×C4⋊C4C22×C511yescharacteristic, complemented
132#939—21no—
133#937—21no—
134#930C22×C511yescharacteristic
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4C22×C511yescharacteristic
137#894—21no—
138#883—21no—
139#882—21no—
140C3×#107—21no—
141C3×#102—21no—
142C3×C22⋊C8C22×C511yescharacteristic, complemented
143C3⋊#95—21no—
144C3⋊#95C22×C511yescharacteristic, complemented
145#830C22×C511yescharacteristic, complemented
146#809—21no—
147#807—21no—
148C24×C5—31no—
149C24×C5—61no—
150C2×C5×D4—21no—
151C2×C5×D4—31no—
152C2×C5×D4—61no—
153C2×C5×D4—61no—
154C2×C5×D4—61no—
155C2×C5×D4—61no—
156C2×C5×D4—122no—
157C2×C5×D4—122no—
158C2×C5×D4#6711yescharacteristic
159C22×C4×C5—21no—
160C22×C4×C5—31no—
161C22×C4×C5—61no—
162C22×C4×C5—61no—
163C22×C4×C5C22×D311yescharacteristic
164C2×C5×C8—21no—
165C2×C5×C8—61no—
166C5×C4⋊C4—21no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—31no—
169C5×C4⋊C4—61no—
170C5×C4⋊C4#6711yescharacteristic
171C5×C22⋊C4—21no—
172C5×C22⋊C4—61no—
173C5×C22⋊C4—61no—
174C5×C22⋊C4—61no—
175C5×C22⋊C4—61no—
176C5×C22⋊C4—61no—
177C5×C22⋊C4—122no—
178#534—31no—
179#480—31no—
180#480C5×D311yescharacteristic, complemented
181#397—31no—
182#327—31no—
183#327—31no—
184#323—31no—
185C22×C3×C5—21no—
186C22×C3×C5—21no—
187C22×C3×C5—41no—
188C22×C3×C5—41no—
189C22×C3×C5—41no—
190C22×C3×C5#12011yescharacteristic
191C22×C3×C5C2×D811yescharacteristic
192C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
193C2×C5×D3—22no—
194C2×C5×D3—41no—
195C2×C5×D3—41no—
196C2×C5×D3—42no—
197C2×C5×D3—41no—
198C2×C5×D3—41no—
199C2×C5×D3—41no—
200C2×C5×D3—81no—
201C2×C5×D3—84no—
202C3×C4×C5—21no—
203C3×C4×C5—21no—
204C3×C4×C5—41no—
205C3×C4×C5—81no—
206C5×Dic3—41no—
207C5×Dic3—41no—
208C5×Dic3—81no—
209C23×D3—21no—
210C23×D3C5×D411yescharacteristic
211C2×C3×D4—21no—
212C2×C3×D4C5×D411yescharacteristic
213C22×C3×C4—21no—
214C22×C3×C4C23×C511yescharacteristic
215C2×#67—21no—
216C2×#67—21no—
217C2×#67—21no—
218C22×Dic3—21no—
219C22×Dic3C5×D411yescharacteristic
220D3×D4—42no—
221D3×D4—42no—
222C2×D12—21no—
223C2×D12C5×D411yescharacteristic
224C2×C4×D3—21no—
225C2×C3×C8—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4C5×D411yescharacteristic
229C3×C22⋊C4—21no—
230#217—21no—
231(C2×D3)⋊C4—21no—
232(C2×D3)⋊C4—21no—
233(C2×D3)⋊C4—21no—
234(C2×D3)⋊C4—21no—
235(C2×D3)⋊C4—42no—
236C4⋊Dic3C5×D411yescharacteristic
237Dic3⋊C4—21no—
238C2×C3⋊C8—21no—
239C23×C5—21no—
240C23×C5—32no—
241C23×C5—61no—
242C23×C5—61no—
243C23×C5—61no—
244C23×C5—121no—
245C23×C5—121no—
246C23×C5—122no—
247C23×C5—241no—
248C23×C5—241no—
249C23×C5D3×D411yescharacteristic
250C5×D4—41no—
251C5×D4—41no—
252C5×D4—41no—
253C5×D4—121no—
254C5×D4—122no—
255C5×D4—122no—
256C5×D4—121no—
257C5×D4—121no—
258C5×D4—241no—
259C2×C4×C5—21no—
260C2×C4×C5—41no—
261C2×C4×C5—41no—
262C2×C4×C5—41no—
263C2×C4×C5—41no—
264C2×C4×C5—61no—
265C2×C4×C5—61no—
266C2×C4×C5—122no—
267C2×C4×C5—121no—
268C2×C4×C5—121no—
269C2×C4×C5—121no—
270C2×C4×C5—121no—
271C2×C4×C5D3×D411yescharacteristic
272C2×C4×C5C2×#6711yescharacteristic
273C5×C8—41no—
274C5×C8—121no—
275C22×D4—61no—
276#123—61no—
277#123—61no—
278#121—31no—
279#121—61no—
280#121C2×C5×D311yescharacteristic
281#120—61no—
282#120—61no—
283C2×C4⋊C4C2×C5×D311yescharacteristic, complemented
284C2×C22⋊C4—31no—
285C2×C22⋊C4—61no—
286#107—21no—
287#107—61no—
288#102—21no—
289#102—61no—
290C22⋊C8—31no—
291C22⋊C8C2×C5×D311yescharacteristic, complemented
292#95—31no—
293#95—61no—
294C2×C3×C5—21no—
295C2×C3×C5—21no—
296C2×C3×C5—81no—
297C2×C3×C5#44711yescharacteristic
298C2×C3×C5#45511yescharacteristic
299C2×C3×C5#45811yescharacteristic
300C5×D3—42no—
301C5×D3—81no—
302C23×C3—21no—
303C23×C3C2×C5×D411yescharacteristic
304C22×D3—21no—
305C22×D3—21no—
306C22×D3—21no—
307C22×D3—42no—
308C22×D3—41no—
309C22×D3—41no—
310C22×D3—81no—
311C22×D3—81no—
312C22×D3C5×D812yes—
313C3×D4—41no—
314C3×D4—41no—
315C3×D4—41no—
316C2×C3×C4—21no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4C2×C5×D411yescharacteristic
322C2×C3×C4C2×C5×D411yescharacteristic
323#67—42no—
324#67—41no—
325#67—41no—
326#67—81no—
327C2×Dic3—21no—
328C2×Dic3—21no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333D12—41no—
334D12—42no—
335C4×D3—42no—
336C3×C8—41no—
337C3⋊C8—41no—
338C22×C5—21no—
339C22×C5—21no—
340C22×C5—41no—
341C22×C5—41no—
342C22×C5—41no—
343C22×C5—62no—
344C22×C5—122no—
345C22×C5—121no—
346C22×C5—121no—
347C22×C5—121no—
348C22×C5—121no—
349C22×C5—121no—
350C22×C5—241no—
351C22×C5—244no—
352C22×C5D3×D811yescharacteristic
353C22×C5#91111yescharacteristic
354C22×C5#93711yescharacteristic
355C4×C5—21no—
356C4×C5—21no—
357C4×C5—41no—
358C4×C5—81no—
359C4×C5—121no—
360C4×C5—121no—
361C4×C5—241no—
362C24—31no—
363C24—61no—
364C2×D4—21no—
365C2×D4—31no—
366C2×D4—61no—
367C2×D4—61no—
368C2×D4—61no—
369C2×D4—61no—
370C2×D4—122no—
371C2×D4—122no—
372C2×D4C5×#6711yescharacteristic
373C22×C4—21no—
374C22×C4—31no—
375C22×C4—61no—
376C22×C4—61no—
377C22×C4C22×C5×D311yescharacteristic
378C2×C8—21no—
379C2×C8—61no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—31no—
383C4⋊C4—61no—
384C4⋊C4C5×#6711yescharacteristic
385C22⋊C4—21no—
386C22⋊C4—61no—
387C22⋊C4—61no—
388C22⋊C4—61no—
389C22⋊C4—61no—
390C22⋊C4—61no—
391C22⋊C4—122no—
392C3×C5#160711yescharacteristic, complemented, Hall
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3C5×#12011yescharacteristic
399C22×C3C2×C5×D811yescharacteristic
400C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
401C2×D3—22no—
402C2×D3—41no—
403C2×D3—41no—
404C2×D3—42no—
405C2×D3—41no—
406C2×D3—41no—
407C2×D3—41no—
408C2×D3—81no—
409C2×D3—84no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—41no—
413C3×C4—81no—
414Dic3—41no—
415Dic3—41no—
416Dic3—81no—
417C2×C5—21no—
418C2×C5—21no—
419C2×C5—81no—
420C2×C5—122no—
421C2×C5—241no—
422C2×C5#505311yescharacteristic
423C2×C5#515611yescharacteristic
424C2×C5#520211yescharacteristic
425C23—21no—
426C23—32no—
427C23—61no—
428C23—61no—
429C23—61no—
430C23—121no—
431C23—121no—
432C23—122no—
433C23—241no—
434C23—241no—
435C23C5×D3×D411yescharacteristic
436D4—41no—
437D4—41no—
438D4—41no—
439D4—121no—
440D4—122no—
441D4—122no—
442D4—121no—
443D4—121no—
444D4—241no—
445C2×C4—21no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—122no—
453C2×C4—121no—
454C2×C4—121no—
455C2×C4—121no—
456C2×C4—121no—
457C2×C4C5×D3×D411yescharacteristic
458C2×C4C2×C5×#6711yescharacteristic
459C8—41no—
460C8—121no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—81no—
464C2×C3C5×#44711yescharacteristic
465C2×C3C5×#45511yescharacteristic
466C2×C3C5×#45811yescharacteristic
467D3—42no—
468D3—81no—
469C5#7116411yescharacteristic, direct product factor, Sylow
470C22—21no—
471C22—21no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—62no—
476C22—122no—
477C22—121no—
478C22—121no—
479C22—121no—
480C22—121no—
481C22—121no—
482C22—241no—
483C22—244no—
484C22C5×D3×D811yescharacteristic
485C22C5×#91111yescharacteristic
486C22C5×#93711yescharacteristic
487C4—21no—
488C4—21no—
489C4—41no—
490C4—81no—
491C4—121no—
492C4—121no—
493C4—241no—
494C3C5×#160711yescharacteristic, complemented, Sylow
495C2—21no—
496C2—21no—
497C2—81no—
498C2—122no—
499C2—241no—
500C2C5×#505311yescharacteristic
501C2C5×#515611yescharacteristic
502C2C5×#520211yescharacteristic
subgroupG/H
centerC22×C5#937
commutator, cosocleC22×C3×C4C23×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#480C2
socleC22×C3×C5#120
prime radicalC5×#5605C2
hypercenterC5×#480D3
hypocenterC3C5×#1607
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#480

Complements

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

NH ≅ G/Ntype
2. C3×C5×#480C2semidirect
3. C5×#4992C2semidirect
4. C5×#4967C2semidirect
5. C5×#4537C2semidirect
6. C5×#4470C2semidirect
7. C5×#4468C2semidirect
11. C2×C3×C5×C4⋊C4C22semidirect
22. C3×C5×C22⋊C8C22semidirect
24. C5×C3⋊#95C22semidirect
25. C5×#830C22semidirect
28. #71164C5direct (N × H)
31. C5×#480D3semidirect
67. C3×#480C2×C5semidirect
68. #4992C2×C5semidirect
69. #4967C2×C5semidirect
70. #4537C2×C5semidirect
71. #4470C2×C5semidirect
72. #4468C2×C5semidirect
81. C2×C5×C4⋊C4C2×D3semidirect
89. C5×C22⋊C8C2×D3semidirect
131. C2×C3×C4⋊C4C22×C5semidirect
142. C3×C22⋊C8C22×C5semidirect
144. C3⋊#95C22×C5semidirect
145. #830C22×C5semidirect
180. #480C5×D3semidirect
283. C2×C4⋊C4C2×C5×D3semidirect
291. C22⋊C8C2×C5×D3semidirect
392. C3×C5#1607semidirect
469. C5#71164direct (N × H)
494. C3C5×#1607semidirect

Maximal subgroups

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

subgroupindex
C5×#56052
C3×C5×#4802
C5×#49922
C5×#49672
C5×#45372
C5×#44702
C5×#44682
C5×#16073
#711645