Finite Group Databasebeta

← C5×#71888 #14287762

Subgroups — C5×#71888 #14287762

Order 1920.

544 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#539C211yesmaximal, characteristic, complemented
2C5×#5046C211yesmaximal, characteristic, complemented
3C5×#5036C211yesmaximal, characteristic
4C5×#4991C211yesmaximal, characteristic, complemented
5C5×#4538C211yesmaximal, characteristic, complemented
6C5×#4537C211yesmaximal, characteristic, complemented
7C5×#4528C211yesmaximal, characteristic, complemented
8C5×#1597—31nomaximal, Hall
9C22×C5×D12C2211yescharacteristic
10C3×C5×#126—21no—
11C3×C5×#125—21no—
12C3×C5×#123—21no—
13C3×C5×#123—21no—
14C3×C5×C22⋊Q8—21no—
15C3×C5×C22⋊Q8C2211yescharacteristic
16C3×C5×#121C2211yescharacteristic
17C3×C4×C5×D4—21no—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C5×#215—21no—
20C2×C5×#213—21no—
21C2×C5×(C2×D3)⋊C4—21no—
22C2×C5×(C2×D3)⋊C4—21no—
23C5×C3⋊#95C2211yescharacteristic
24C5×#830C2211yescharacteristic
25C5×#830C2211yescharacteristic
26C5×#809—21no—
27C5×#809—21no—
28#71888C511yesmaximal, characteristic, direct product factor, Hall
29C5×#539D311yescharacteristic, complemented
30C5×#450—31no—
31C5×#447—31no—
32C5×#394—31no—
33C5×#328—31no—
34C5×#327—31no—
35C5×#324—31no—
36C23×C5×D3—21no—
37C2×C3×C5×Q8D411yescharacteristic
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4D411yescharacteristic
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5D411yescharacteristic
42C22×C3×C4×C5D411yescharacteristic
43C22×C3×C4×C5C2311yescharacteristic
44C22×C5×Dic3—21no—
45C2×C5×D12—21no—
46C2×C5×D12—21no—
47C2×C5×D12—42no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4D411yescharacteristic
55C3×C5×C4⋊C4D411yescharacteristic
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C5×C22⋊C4—21no—
59C3×C5×C22⋊C4—21no—
60C3×C5×C22⋊C4—21no—
61C3×C42×C5—21no—
62C5×#215—42no—
63C5×#213—42no—
64C5×(C2×D3)⋊C4—42no—
65C5×(C2×D3)⋊C4—42no—
66C2×C5×C3⋊C8—21no—
67C2×C5×C3⋊C8—21no—
68C3×#539C2×C511yescharacteristic, complemented
69#5046C2×C511yescharacteristic, complemented
70#5036C2×C511yescharacteristic
71#4991C2×C511yescharacteristic, complemented
72#4538C2×C511yescharacteristic, complemented
73#4537C2×C511yescharacteristic, complemented
74#4528C2×C511yescharacteristic, complemented
75C22×C5×D4—31no—
76C2×C5×SD16—61no—
77C2×C5×D8—61no—
78C5×#126—21no—
79C5×#125—21no—
80C5×#123—21no—
81C5×#123—21no—
82C5×C22⋊Q8—21no—
83C5×C22⋊Q8C2×D311yescharacteristic
84C5×#121C2×D311yescharacteristic
85C4×C5×D4—21no—
86C2×C5×C4⋊C4C2×D311yescharacteristic
87C2×C5×C22⋊C4—61no—
88C2×C5×C22⋊C4—61no—
89C5×#102—61no—
90C5×#102—61no—
91C5×C22⋊C8—31no—
92C5×C22⋊C8—31no—
93C5×#95—31no—
94#1597—31noSylow
95C23×C3×C5—21no—
96C23×C3×C5C2×D411yescharacteristic
97C22×C5×D3—22no—
98C22×C5×D3—41no—
99C22×C5×D3—41no—
100C22×C5×D3—41no—
101C22×C5×D3—41no—
102C22×C5×D3—41no—
103C22×C5×D3—41no—
104C3×C5×Q8—41no—
105C3×C5×D4—41no—
106C3×C5×D4—41no—
107C3×C5×D4—41no—
108C2×C3×C4×C5—21no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—21no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5—81no—
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5C2×D411yescharacteristic
120C2×C5×Dic3—41no—
121C2×C5×Dic3—41no—
122C2×C5×Dic3—41no—
123C5×D12—22no—
124C5×D12—22no—
125C5×D12—41no—
126C5×D12—41no—
127C5×C3⋊C8—41no—
128C5×C3⋊C8—41no—
129C22×D12C22×C511yescharacteristic
130C3×#126—21no—
131C3×#125—21no—
132C3×#123—21no—
133C3×#123—21no—
134C3×C22⋊Q8—21no—
135C3×C22⋊Q8C22×C511yescharacteristic
136C3×#121C22×C511yescharacteristic
137C3×C4×D4—21no—
138C2×C3×C4⋊C4C22×C511yescharacteristic
139C2×#215—21no—
140C2×#213—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C3⋊#95C22×C511yescharacteristic
144#830C22×C511yescharacteristic
145#830C22×C511yescharacteristic
146#809—21no—
147#809—21no—
148C24×C5—61no—
149C2×C5×Q8#6711yescharacteristic
150C2×C5×D4—21no—
151C2×C5×D4—61no—
152C2×C5×D4—61no—
153C2×C5×D4—122no—
154C2×C5×D4#6711yescharacteristic
155C22×C4×C5—21no—
156C22×C4×C5—61no—
157C22×C4×C5#6711yescharacteristic
158C22×C4×C5#6711yescharacteristic
159C22×C4×C5C22×D311yescharacteristic
160C5×SD16—122no—
161C5×D8—122no—
162C2×C5×C8—61no—
163C2×C5×C8—61no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—21no—
166C5×C4⋊C4—21no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—21no—
169C5×C4⋊C4—21no—
170C5×C4⋊C4#6711yescharacteristic
171C5×C4⋊C4#6711yescharacteristic
172C5×C22⋊C4—21no—
173C5×C22⋊C4—21no—
174C5×C22⋊C4—21no—
175C5×C22⋊C4—21no—
176C5×C22⋊C4—21no—
177C5×C22⋊C4—122no—
178C5×C22⋊C4—122no—
179C42×C5—21no—
180#539C5×D311yescharacteristic, complemented
181#450—31no—
182#447—31no—
183#394—31no—
184#328—31no—
185#327—31no—
186#324—31no—
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5—41no—
190C22×C3×C5—41no—
191C22×C3×C5—41no—
192C22×C3×C5#12011yescharacteristic
193C22×C3×C5#13511yescharacteristic
194C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
195C2×C5×D3—42no—
196C2×C5×D3—42no—
197C2×C5×D3—42no—
198C2×C5×D3—81no—
199C2×C5×D3—81no—
200C2×C5×D3—81no—
201C2×C5×D3—81no—
202C3×C4×C5—21no—
203C3×C4×C5—21no—
204C3×C4×C5—41no—
205C3×C4×C5—41no—
206C3×C4×C5—41no—
207C3×C4×C5—41no—
208C3×C4×C5—41no—
209C5×Dic3—81no—
210C23×D3—21no—
211C2×C3×Q8C5×D411yescharacteristic
212C2×C3×D4—21no—
213C2×C3×D4C5×D411yescharacteristic
214C22×C3×C4—21no—
215C22×C3×C4C5×D411yescharacteristic
216C22×C3×C4C5×D411yescharacteristic
217C22×C3×C4C23×C511yescharacteristic
218C22×Dic3—21no—
219C2×D12—21no—
220C2×D12—21no—
221C2×D12—42no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4C5×D411yescharacteristic
229C3×C4⋊C4C5×D411yescharacteristic
230C3×C22⋊C4—21no—
231C3×C22⋊C4—21no—
232C3×C22⋊C4—21no—
233C3×C22⋊C4—21no—
234C3×C22⋊C4—21no—
235C3×C42—21no—
236#215—42no—
237#213—42no—
238(C2×D3)⋊C4—42no—
239(C2×D3)⋊C4—42no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—21no—
242C23×C5—21no—
243C23×C5—62no—
244C23×C5—121no—
245C23×C5—121no—
246C23×C5—121no—
247C23×C5—121no—
248C23×C5—121no—
249C23×C5—121no—
250C23×C5C2×#6711yescharacteristic
251C5×Q8—41no—
252C5×D4—41no—
253C5×D4—41no—
254C5×D4—41no—
255C5×D4—62no—
256C5×D4—62no—
257C5×D4—121no—
258C5×D4—121no—
259C2×C4×C5—21no—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—41no—
267C2×C4×C5—41no—
268C2×C4×C5—81no—
269C2×C4×C5—121no—
270C2×C4×C5—121no—
271C2×C4×C5—121no—
272C2×C4×C5C2×#6711yescharacteristic
273C2×C4×C5C2×#6711yescharacteristic
274C5×C8—121no—
275C5×C8—121no—
276C22×D4—31no—
277C2×SD16—61no—
278C2×D8—61no—
279#126—21no—
280#125—21no—
281#123—21no—
282#123—21no—
283C22⋊Q8—21no—
284C22⋊Q8C2×C5×D311yescharacteristic
285#121C2×C5×D311yescharacteristic
286C4×D4—21no—
287C2×C4⋊C4C2×C5×D311yescharacteristic
288C2×C22⋊C4—61no—
289C2×C22⋊C4—61no—
290#102—61no—
291#102—61no—
292C22⋊C8—31no—
293C22⋊C8—31no—
294#95—31no—
295C2×C3×C5—21no—
296C2×C3×C5—21no—
297C2×C3×C5—81no—
298C2×C3×C5#44911yescharacteristic
299C2×C3×C5#45411yescharacteristic
300C2×C3×C5B(4,𝔽2)11yescharacteristic
301C5×D3—82no—
302C23×C3—21no—
303C23×C3C2×C5×D411yescharacteristic
304C22×D3—22no—
305C22×D3—41no—
306C22×D3—41no—
307C22×D3—41no—
308C22×D3—41no—
309C22×D3—41no—
310C22×D3—41no—
311C3×Q8—41no—
312C3×D4—41no—
313C3×D4—41no—
314C3×D4—41no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—81no—
325C2×C3×C4C2×C5×D411yescharacteristic
326C2×C3×C4C2×C5×D411yescharacteristic
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330D12—22no—
331D12—22no—
332D12—41no—
333D12—41no—
334C3⋊C8—41no—
335C3⋊C8—41no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5—41no—
339C22×C5—41no—
340C22×C5—41no—
341C22×C5—122no—
342C22×C5—122no—
343C22×C5—122no—
344C22×C5—241no—
345C22×C5—241no—
346C22×C5—241no—
347C22×C5—241no—
348C22×C5#94911yescharacteristic
349C22×C5#95011yescharacteristic
350C22×C5#95311yescharacteristic
351C4×C5—21no—
352C4×C5—21no—
353C4×C5—41no—
354C4×C5—41no—
355C4×C5—41no—
356C4×C5—41no—
357C4×C5—41no—
358C4×C5—241no—
359C24—61no—
360C2×Q8C5×#6711yescharacteristic
361C2×D4—21no—
362C2×D4—61no—
363C2×D4—61no—
364C2×D4—122no—
365C2×D4C5×#6711yescharacteristic
366C22×C4—21no—
367C22×C4—61no—
368C22×C4C5×#6711yescharacteristic
369C22×C4C5×#6711yescharacteristic
370C22×C4C22×C5×D311yescharacteristic
371SD16—122no—
372D8—122no—
373C2×C8—61no—
374C2×C8—61no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4C5×#6711yescharacteristic
382C4⋊C4C5×#6711yescharacteristic
383C22⋊C4—21no—
384C22⋊C4—21no—
385C22⋊C4—21no—
386C22⋊C4—21no—
387C22⋊C4—21no—
388C22⋊C4—122no—
389C22⋊C4—122no—
390C42—21no—
391C3×C5#159711yescharacteristic, complemented, Hall
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—41no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3C5×#12011yescharacteristic
398C22×C3C5×#13511yescharacteristic
399C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
400C2×D3—42no—
401C2×D3—42no—
402C2×D3—42no—
403C2×D3—81no—
404C2×D3—81no—
405C2×D3—81no—
406C2×D3—81no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—41no—
410C3×C4—41no—
411C3×C4—41no—
412C3×C4—41no—
413C3×C4—41no—
414Dic3—81no—
415C2×C5—21no—
416C2×C5—21no—
417C2×C5—81no—
418C2×C5—242no—
419C2×C5#523811yescharacteristic
420C2×C5#524411yescharacteristic
421C2×C5#524511yescharacteristic
422C23—21no—
423C23—62no—
424C23—121no—
425C23—121no—
426C23—121no—
427C23—121no—
428C23—121no—
429C23—121no—
430C23C2×C5×#6711yescharacteristic
431Q8—41no—
432D4—41no—
433D4—41no—
434D4—41no—
435D4—62no—
436D4—62no—
437D4—121no—
438D4—121no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—81no—
449C2×C4—121no—
450C2×C4—121no—
451C2×C4—121no—
452C2×C4C2×C5×#6711yescharacteristic
453C2×C4C2×C5×#6711yescharacteristic
454C8—121no—
455C8—121no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—81no—
459C2×C3C5×#44911yescharacteristic
460C2×C3C5×#45411yescharacteristic
461C2×C3C5×B(4,𝔽2)11yescharacteristic
462D3—82no—
463C5#7188811yescharacteristic, direct product factor, Sylow
464C22—21no—
465C22—21no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—122no—
470C22—122no—
471C22—122no—
472C22—241no—
473C22—241no—
474C22—241no—
475C22—241no—
476C22C5×#94911yescharacteristic
477C22C5×#95011yescharacteristic
478C22C5×#95311yescharacteristic
479C4—21no—
480C4—21no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—241no—
487C3C5×#159711yescharacteristic, complemented, Sylow
488C2—21no—
489C2—21no—
490C2—81no—
491C2—242no—
492C2C5×#523811yescharacteristic
493C2C5×#524411yescharacteristic
494C2C5×#524511yescharacteristic
subgroupG/H
centerC22×C5#953
commutator, cosocleC22×C3×C4C23×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#539C2
socleC22×C3×C5#120
prime radicalC5×#5036C2
hypercenterC5×#539D3
hypocenterC3C5×#1597
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#539

Complements

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

NH ≅ G/Ntype
1. C3×C5×#539C2semidirect
2. C5×#5046C2semidirect
4. C5×#4991C2semidirect
5. C5×#4538C2semidirect
6. C5×#4537C2semidirect
7. C5×#4528C2semidirect
28. #71888C5direct (N × H)
29. C5×#539D3semidirect
68. C3×#539C2×C5semidirect
69. #5046C2×C5semidirect
71. #4991C2×C5semidirect
72. #4538C2×C5semidirect
73. #4537C2×C5semidirect
74. #4528C2×C5semidirect
180. #539C5×D3semidirect
391. C3×C5#1597semidirect
463. C5#71888direct (N × H)
487. C3C5×#1597semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5392
C5×#50462
C5×#50362
C5×#49912
C5×#45382
C5×#45372
C5×#45282
C5×#15973
#718885