Finite Group Databasebeta

← C5×#69508 #14283408

Subgroups — C5×#69508 #14283408

Order 1920.

572 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5791C211yesmaximal, characteristic
2C3×C5×#380C211yesmaximal, characteristic, complemented
3C5×#5207C211yesmaximal, characteristic, complemented
4C5×#4452C212yesmaximal, complemented
5C5×#4451C212yesmaximal, complemented
6C5×#1513—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×C5×#235C411yescharacteristic, complemented
9C2×C3×C5×C4⋊C4—21no—
10C2×C3×C5×C22⋊C4—21no—
11C5×#953—21no—
12C5×#930C411yescharacteristic, complemented
13C5×#930C2211yescharacteristic
14C5×#929—21no—
15C4×C5×#67—21no—
16C4×C5×#67—21no—
17C5×#926C411yescharacteristic, complemented
18C5×#924C411yescharacteristic, complemented
19C5×#924C2211yescharacteristic
20C2×C5×#208—21no—
21C3×C5×#95C2212yes—
22C5×#830—21no—
23C5×#830C2212yes—
24#69508C511yesmaximal, characteristic, direct product factor, Hall
25C5×#525—31no—
26C5×#407—31no—
27C5×#380D311yescharacteristic, complemented
28C5×#328—32no—
29C5×#327—32no—
30C24×C3×C5D411yescharacteristic
31C22×C3×C4×C5—22no—
32C22×C3×C4×C5—42no—
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×C4×C5C2×C411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5D411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C2×C5×#67—21no—
40C2×C5×#67—21no—
41C2×C5×#67—21no—
42C5×#235—42no—
43C2×C5×D12C2×C411yescharacteristic
44C2×C4×C5×D3—21no—
45C2×C5×Dic6C2×C411yescharacteristic
46C3×C5×C4⋊C4—42no—
47C3×C5×C22⋊C4—42no—
48C5×#217—21no—
49C5×#217—21no—
50C5×#217—21no—
51C5×(C2×D3)⋊C4—21no—
52C5×(C2×D3)⋊C4—21no—
53C5×C4⋊Dic3C2×C411yescharacteristic
54C5×C4⋊Dic3C2×C411yescharacteristic
55C5×Dic3⋊C4—21no—
56C5×Dic3⋊C4—21no—
57C4×C5×Dic3—21no—
58C5×#208—42no—
59C2×C5×C3⋊C8—22no—
60#5791C2×C511yescharacteristic
61C3×#380C2×C511yescharacteristic, complemented
62#5207C2×C511yescharacteristic, complemented
63#4452C2×C512yescomplemented
64#4451C2×C512yescomplemented
65C2×C5×#41—31no—
66C23×C4×C5C2×D311yescharacteristic
67C2×C5×M16—61no—
68C5×#123—61no—
69C5×C22⋊Q8—31no—
70C5×C22⋊Q8—31no—
71C5×#121—31no—
72C5×#121—31no—
73C5×#120—61no—
74C4×C5×D4—61no—
75C4×C5×D4—61no—
76C5×#117—31no—
77C2×C5×C4⋊C4—21no—
78C2×C5×C22⋊C4—21no—
79C5×C22⋊C8—32no—
80C5×C22⋊C8—61no—
81C5×#95C2×D312yes—
82#1513—31noSylow
83C23×C3×C5—21no—
84C23×C3×C5—21no—
85C23×C3×C5—41no—
86C23×C3×C5—41no—
87C23×C3×C5C22⋊C411yescharacteristic
88C23×C3×C5C22⋊C411yescharacteristic
89C23×C3×C5C2×D411yescharacteristic
90C22×C5×D3—21no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—42no—
98C2×C3×C4×C5—42no—
99C2×C3×C4×C5—42no—
100C2×C3×C4×C5C22⋊C411yescharacteristic
101C2×C3×C4×C5C22⋊C411yescharacteristic
102C2×C3×C4×C5C22×C411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C5×#67—42no—
105C5×#67—42no—
106C5×#67—41no—
107C5×#67—41no—
108C2×C5×Dic3—21no—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—21no—
111C5×D12—41no—
112C4×C5×D3—42no—
113C5×Dic6—41no—
114C5×C3⋊C8—42no—
115C23×C3×C4C22×C511yescharacteristic
116C2×#235C4×C511yescharacteristic, complemented
117C2×C3×C4⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119#953—21no—
120#930C4×C511yescharacteristic, complemented
121#930C22×C511yescharacteristic
122#929—21no—
123C4×#67—21no—
124C4×#67—21no—
125#926C4×C511yescharacteristic, complemented
126#924C4×C511yescharacteristic, complemented
127#924C22×C511yescharacteristic
128C2×#208—21no—
129C3×#95C22×C512yes—
130#830—21no—
131#830C22×C512yes—
132C24×C5#6711yescharacteristic
133C5×#41—122no—
134C2×C5×Q8—31no—
135C2×C5×D4—31no—
136C2×C5×D4—61no—
137C2×C5×D4—61no—
138C2×C5×D4—61no—
139C22×C4×C5—22no—
140C22×C4×C5—42no—
141C22×C4×C5—61no—
142C22×C4×C5C4×D311yescharacteristic
143C22×C4×C5C4×D311yescharacteristic
144C22×C4×C5D1211yescharacteristic
145C22×C4×C5D1211yescharacteristic
146C22×C4×C5#6711yescharacteristic
147C22×C4×C5C22×D311yescharacteristic
148C5×M16—122no—
149C2×C5×C8—62no—
150C5×C4⋊C4—31no—
151C5×C4⋊C4—31no—
152C5×C4⋊C4—42no—
153C5×C4⋊C4—61no—
154C5×C4⋊C4—61no—
155C5×C22⋊C4—42no—
156C5×C22⋊C4—61no—
157C5×C22⋊C4—61no—
158C5×C22⋊C4—61no—
159C5×C22⋊C4—61no—
160C5×C22⋊C4—61no—
161C42×C5—61no—
162#525—31no—
163#407—31no—
164#380C5×D311yescharacteristic, complemented
165#328—32no—
166#327—32no—
167C22×C3×C5—21no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5—21no—
171C22×C3×C5—21no—
172C22×C3×C5—21no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5—42no—
176C22×C3×C5—42no—
177C22×C3×C5C2×C22⋊C411yescharacteristic
178C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
179C22×C3×C5#13711yescharacteristic
180C2×C5×D3—41no—
181C2×C5×D3—41no—
182C2×C5×D3—41no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5—21no—
186C3×C4×C5—82no—
187C3×C4×C5#9912yes—
188C5×Dic3—41no—
189C5×Dic3—41no—
190C5×Dic3—41no—
191C24×C3C5×D411yescharacteristic
192C22×C3×C4—22no—
193C22×C3×C4—42no—
194C22×C3×C4C2×C4×C511yescharacteristic
195C22×C3×C4C2×C4×C511yescharacteristic
196C22×C3×C4C5×D411yescharacteristic
197C22×C3×C4C5×D411yescharacteristic
198C22×C3×C4C5×D411yescharacteristic
199C22×C3×C4C23×C511yescharacteristic
200C2×#67—21no—
201C2×#67—21no—
202C2×#67—21no—
203#235—42no—
204C2×D12C2×C4×C511yescharacteristic
205C2×C4×D3—21no—
206C2×Dic6C2×C4×C511yescharacteristic
207C3×C4⋊C4—42no—
208C3×C22⋊C4—42no—
209#217—21no—
210#217—21no—
211#217—21no—
212(C2×D3)⋊C4—21no—
213(C2×D3)⋊C4—21no—
214C4⋊Dic3C2×C4×C511yescharacteristic
215C4⋊Dic3C2×C4×C511yescharacteristic
216Dic3⋊C4—21no—
217Dic3⋊C4—21no—
218C4×Dic3—21no—
219#208—42no—
220C2×C3⋊C8—22no—
221C23×C5—21no—
222C23×C5—21no—
223C23×C5—41no—
224C23×C5—41no—
225C23×C5—61no—
226C23×C5(C2×D3)⋊C411yescharacteristic
227C23×C5(C2×D3)⋊C411yescharacteristic
228C23×C5C2×#6711yescharacteristic
229C5×Q8—121no—
230C5×D4—121no—
231C5×D4—122no—
232C5×D4—122no—
233C5×D4—121no—
234C5×D4—121no—
235C2×C4×C5—22no—
236C2×C4×C5—22no—
237C2×C4×C5—22no—
238C2×C4×C5—41no—
239C2×C4×C5—41no—
240C2×C4×C5—41no—
241C2×C4×C5—42no—
242C2×C4×C5—42no—
243C2×C4×C5—42no—
244C2×C4×C5—61no—
245C2×C4×C5—61no—
246C2×C4×C5—61no—
247C2×C4×C5—122no—
248C2×C4×C5(C2×D3)⋊C411yescharacteristic
249C2×C4×C5(C2×D3)⋊C411yescharacteristic
250C2×C4×C5C2×C4×D311yescharacteristic
251C2×C4×C5C2×D1211yescharacteristic
252C5×C8—122no—
253C2×#41—31no—
254C23×C4C2×C5×D311yescharacteristic
255C2×M16—61no—
256#123—61no—
257C22⋊Q8—31no—
258C22⋊Q8—31no—
259#121—31no—
260#121—31no—
261#120—61no—
262C4×D4—61no—
263C4×D4—61no—
264#117—31no—
265C2×C4⋊C4—21no—
266C2×C22⋊C4—21no—
267C22⋊C8—32no—
268C22⋊C8—61no—
269#95C2×C5×D312yes—
270C2×C3×C5—21no—
271C2×C3×C5—21no—
272C2×C3×C5—41no—
273C2×C3×C5—41no—
274C2×C3×C5C2×#9911yescharacteristic
275C2×C3×C5#41711yescharacteristic
276C2×C3×C5#42111yescharacteristic
277C5×D3—81no—
278C23×C3—21no—
279C23×C3—21no—
280C23×C3—41no—
281C23×C3—41no—
282C23×C3C5×C22⋊C411yescharacteristic
283C23×C3C5×C22⋊C411yescharacteristic
284C23×C3C2×C5×D411yescharacteristic
285C22×D3—21no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—42no—
293C2×C3×C4—42no—
294C2×C3×C4—42no—
295C2×C3×C4C5×C22⋊C411yescharacteristic
296C2×C3×C4C5×C22⋊C411yescharacteristic
297C2×C3×C4C22×C4×C511yescharacteristic
298C2×C3×C4C2×C5×D411yescharacteristic
299#67—42no—
300#67—42no—
301#67—41no—
302#67—41no—
303C2×Dic3—21no—
304C2×Dic3—21no—
305C2×Dic3—21no—
306D12—41no—
307C4×D3—42no—
308Dic6—41no—
309C3⋊C8—42no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—21no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5—21no—
317C22×C5—21no—
318C22×C5—42no—
319C22×C5—42no—
320C22×C5—121no—
321C22×C5—121no—
322C22×C5—121no—
323C22×C5C2×(C2×D3)⋊C411yescharacteristic
324C22×C5#93211yescharacteristic
325C22×C5#94211yescharacteristic
326C4×C5—21no—
327C4×C5—21no—
328C4×C5—21no—
329C4×C5—82no—
330C4×C5—121no—
331C4×C5—121no—
332C4×C5—121no—
333C4×C5#80612yes—
334C24C5×#6711yescharacteristic
335#41—122no—
336C2×Q8—31no—
337C2×D4—31no—
338C2×D4—61no—
339C2×D4—61no—
340C2×D4—61no—
341C22×C4—22no—
342C22×C4—42no—
343C22×C4—61no—
344C22×C4C4×C5×D311yescharacteristic
345C22×C4C4×C5×D311yescharacteristic
346C22×C4C5×D1211yescharacteristic
347C22×C4C5×D1211yescharacteristic
348C22×C4C5×#6711yescharacteristic
349C22×C4C22×C5×D311yescharacteristic
350M16—122no—
351C2×C8—62no—
352C4⋊C4—31no—
353C4⋊C4—31no—
354C4⋊C4—42no—
355C4⋊C4—61no—
356C4⋊C4—61no—
357C22⋊C4—42no—
358C22⋊C4—61no—
359C22⋊C4—61no—
360C22⋊C4—61no—
361C22⋊C4—61no—
362C22⋊C4—61no—
363C42—61no—
364C3×C5#151311yescharacteristic, complemented, Hall
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—42no—
374C22×C3—42no—
375C22×C3C2×C5×C22⋊C411yescharacteristic
376C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
377C22×C3C5×#13711yescharacteristic
378C2×D3—41no—
379C2×D3—41no—
380C2×D3—41no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—82no—
385C3×C4C5×#9912yes—
386Dic3—41no—
387Dic3—41no—
388Dic3—41no—
389C2×C5—21no—
390C2×C5—21no—
391C2×C5—41no—
392C2×C5—41no—
393C2×C5—241no—
394C2×C5C2×#80611yescharacteristic
395C2×C5#496611yescharacteristic
396C2×C5#500511yescharacteristic
397C23—21no—
398C23—21no—
399C23—41no—
400C23—41no—
401C23—61no—
402C23C5×(C2×D3)⋊C411yescharacteristic
403C23C5×(C2×D3)⋊C411yescharacteristic
404C23C2×C5×#6711yescharacteristic
405Q8—121no—
406D4—121no—
407D4—122no—
408D4—122no—
409D4—121no—
410D4—121no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—122no—
424C2×C4C5×(C2×D3)⋊C411yescharacteristic
425C2×C4C5×(C2×D3)⋊C411yescharacteristic
426C2×C4C2×C4×C5×D311yescharacteristic
427C2×C4C2×C5×D1211yescharacteristic
428C8—122no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—41no—
432C2×C3—41no—
433C2×C3C2×C5×#9911yescharacteristic
434C2×C3C5×#41711yescharacteristic
435C2×C3C5×#42111yescharacteristic
436D3—81no—
437C5#6950811yescharacteristic, direct product factor, Sylow
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—42no—
447C22—42no—
448C22—121no—
449C22—121no—
450C22—121no—
451C22C2×C5×(C2×D3)⋊C411yescharacteristic
452C22C5×#93211yescharacteristic
453C22C5×#94211yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—82no—
458C4—121no—
459C4—121no—
460C4—121no—
461C4C5×#80612yes—
462C3C5×#151311yescharacteristic, complemented, Sylow
463C2—21no—
464C2—21no—
465C2—41no—
466C2—41no—
467C2—241no—
468C2C2×C5×#80611yescharacteristic
469C2C5×#496611yescharacteristic
470C2C5×#500511yescharacteristic
subgroupG/H
centerC22×C5C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#380C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5791C2
cosocleC22×C3×C4C23×C5
hypercenterC5×#380D3
hypocenterC3C5×#1513
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ C5×#380

Complements

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

NH ≅ G/Ntype
2. C3×C5×#380C2semidirect
3. C5×#5207C2semidirect
4. C5×#4452C2semidirect
5. C5×#4451C2semidirect
8. C2×C5×#235C4semidirect
12. C5×#930C4semidirect
17. C5×#926C4semidirect
18. C5×#924C4semidirect
24. #69508C5direct (N × H)
27. C5×#380D3semidirect
61. C3×#380C2×C5semidirect
62. #5207C2×C5semidirect
63. #4452C2×C5semidirect
64. #4451C2×C5semidirect
116. C2×#235C4×C5semidirect
120. #930C4×C5semidirect
125. #926C4×C5semidirect
126. #924C4×C5semidirect
164. #380C5×D3semidirect
364. C3×C5#1513semidirect
437. C5#69508direct (N × H)
462. C3C5×#1513semidirect

Maximal subgroups

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

subgroupindex
C5×#57912
C3×C5×#3802
C5×#52072
C5×#44522
C5×#44512
C5×#15133
#695085