Finite Group Databasebeta

← C5×#68335 #14283150

Subgroups — C5×#68335 #14283150

Order 1920.

588 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
1C5×D3×C22⋊Q8C211yesmaximal, characteristic
2C5×#4726C211yesmaximal, characteristic
3C5×#4666C211yesmaximal, characteristic
4C3×C5×#328C211yesmaximal, characteristic, complemented
5C5×#4538C211yesmaximal, characteristic, complemented
6C5×#4467C211yesmaximal, characteristic, complemented
7C5×#4452C211yesmaximal, characteristic, complemented
8C5×#1508—31nomaximal, Hall
9C2×C5×D3×Q8C411yescharacteristic, complemented
10C22×C4×C5×D3C2211yescharacteristic
11C3×C5×C22⋊Q8C2211yescharacteristic
12C5×#946C411yescharacteristic, complemented
13C2×C5×(C2×D3)⋊C4—21no—
14C5×#924C2211yescharacteristic
15C2×C4×C5×Dic3—21no—
16C2×C5×ΓL(1,𝔽25)—21no—
17C5×#897C411yescharacteristic, complemented
18C5×#896—21no—
19C5×D3×C4⋊C4—21no—
20C5×D3×C4⋊C4C411yescharacteristic, complemented
21C5×D3×C22⋊C4—21no—
22C5×#878—21no—
23C3×C5×C22⋊C8C2211yescharacteristic
24C3×C5×#95C2211yescharacteristic
25C5×C3⋊#95C2211yescharacteristic
26C5×#830C2211yescharacteristic
27C5×(C2×D3)⋊C8—21no—
28#68335C511yesmaximal, characteristic, direct product factor, Hall
29C2×C5×C22⋊Q8—31no—
30C5×#407—31no—
31C4×C5×C22⋊C4—31no—
32C5×#328—31no—
33C5×#328—31no—
34C5×#328—31no—
35C5×#328D311yescharacteristic, complemented
36C23×C5×D3D411yescharacteristic
37C2×C3×C5×Q8C2×C411yescharacteristic
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C22×C5×Dic3—21no—
41C22×C5×Dic3D411yescharacteristic
42C5×D3×Q8—42no—
43C2×C4×C5×D3—21no—
44C2×C4×C5×D3—21no—
45C2×C4×C5×D3—42no—
46C2×C4×C5×D3C2×C411yescharacteristic
47C2×C4×C5×D3C2×C411yescharacteristic
48C2×C4×C5×D3D411yescharacteristic
49C2×C4×C5×D3D411yescharacteristic
50C2×C5×Dic6—21no—
51C2×C5×Dic6C2×C411yescharacteristic
52C2×C3×C5×C8—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4C2×C411yescharacteristic
55C3×C5×C22⋊C4—21no—
56C5×#217—21no—
57C5×(C2×D3)⋊C4—24no—
58C5×(C2×D3)⋊C4—21no—
59C5×(C2×D3)⋊C4—21no—
60C5×C4⋊Dic3—21no—
61C5×C4⋊Dic3C2×C411yescharacteristic
62C5×Dic3⋊C4—21no—
63C5×Dic3⋊C4—21no—
64C5×Dic3⋊C4—21no—
65C4×C5×Dic3—42no—
66C2×C5×C3⋊C8—21no—
67C5×ΓL(1,𝔽25)—42no—
68D3×C22⋊Q8C2×C511yescharacteristic
69#4726C2×C511yescharacteristic
70#4666C2×C511yescharacteristic
71C3×#328C2×C511yescharacteristic, complemented
72#4538C2×C511yescharacteristic, complemented
73#4467C2×C511yescharacteristic, complemented
74#4452C2×C511yescharacteristic, complemented
75C22×C5×Q8—31no—
76C23×C4×C5—31no—
77C2×C5×M16—61no—
78C5×C22⋊Q8—31no—
79C5×C22⋊Q8—31no—
80C5×C22⋊Q8—31no—
81C5×C22⋊Q8—61no—
82C5×C22⋊Q8—61no—
83C5×C22⋊Q8C2×D311yescharacteristic
84C2×C5×C4⋊C4—31no—
85C2×C5×C4⋊C4—61no—
86C2×C5×C22⋊C4—61no—
87C2×C5×C22⋊C4—61no—
88C2×C42×C5—61no—
89C5×C22⋊C8—31no—
90C5×C22⋊C8—61no—
91C5×C22⋊C8C2×D311yescharacteristic
92C5×#95—31no—
93C5×#95C2×D311yescharacteristic
94#1508—31noSylow
95C23×C3×C5C2×D411yescharacteristic
96C22×C5×D3—21no—
97C22×C5×D3—21no—
98C22×C5×D3—22no—
99C22×C5×D3—41no—
100C22×C5×D3C22⋊C411yescharacteristic
101C22×C5×D3C22⋊C411yescharacteristic
102C3×C5×Q8—41no—
103C2×C3×C4×C5—22no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C5×Dic3—22no—
112C2×C5×Dic3—22no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3—21no—
115C2×C5×Dic3—41no—
116C2×C5×Dic3—41no—
117C2×C5×Dic3C22⋊C411yescharacteristic
118C2×C5×Dic3C22⋊C411yescharacteristic
119C4×C5×D3—22no—
120C4×C5×D3—22no—
121C4×C5×D3—41no—
122C4×C5×D3—41no—
123C4×C5×D3—42no—
124C4×C5×D3—42no—
125C5×Dic6—42no—
126C5×Dic6—41no—
127C3×C5×C8—41no—
128C5×C3⋊C8—41no—
129C2×D3×Q8C4×C511yescharacteristic, complemented
130C22×C4×D3C22×C511yescharacteristic
131C3×C22⋊Q8C22×C511yescharacteristic
132#946C4×C511yescharacteristic, complemented
133C2×(C2×D3)⋊C4—21no—
134#924C22×C511yescharacteristic
135C2×C4×Dic3—21no—
136C2×ΓL(1,𝔽25)—21no—
137#897C4×C511yescharacteristic, complemented
138#896—21no—
139D3×C4⋊C4—21no—
140D3×C4⋊C4C4×C511yescharacteristic, complemented
141D3×C22⋊C4—21no—
142#878—21no—
143C3×C22⋊C8C22×C511yescharacteristic
144C3×#95C22×C511yescharacteristic
145C3⋊#95C22×C511yescharacteristic
146#830C22×C511yescharacteristic
147(C2×D3)⋊C8—21no—
148C24×C5—31no—
149C2×C5×Q8—31no—
150C2×C5×Q8—61no—
151C2×C5×Q8—122no—
152C2×C5×Q8C4×D311yescharacteristic
153C22×C4×C5—21no—
154C22×C4×C5—31no—
155C22×C4×C5—31no—
156C22×C4×C5—31no—
157C22×C4×C5—31no—
158C22×C4×C5—31no—
159C22×C4×C5—61no—
160C22×C4×C5—61no—
161C22×C4×C5—61no—
162C22×C4×C5—122no—
163C22×C4×C5C22×D311yescharacteristic
164C5×M16—122no—
165C2×C5×C8—21no—
166C2×C5×C8—61no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—31no—
169C5×C4⋊C4—61no—
170C5×C4⋊C4—61no—
171C5×C4⋊C4—61no—
172C5×C4⋊C4—61no—
173C5×C4⋊C4C4×D311yescharacteristic
174C5×C22⋊C4—21no—
175C5×C22⋊C4—61no—
176C5×C22⋊C4—61no—
177C5×C22⋊C4—64no—
178C5×C22⋊C4—61no—
179C42×C5—122no—
180C2×C22⋊Q8—31no—
181#407—31no—
182C4×C22⋊C4—31no—
183#328—31no—
184#328—31no—
185#328—31no—
186#328C5×D311yescharacteristic, complemented
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5C2×C22⋊C411yescharacteristic
190C22×C3×C5#13711yescharacteristic
191C22×C3×C5#13711yescharacteristic
192C2×C5×D3—21no—
193C2×C5×D3—21no—
194C2×C5×D3—21no—
195C2×C5×D3—21no—
196C2×C5×D3—21no—
197C2×C5×D3—42no—
198C2×C5×D3—42no—
199C2×C5×D3#10412yes—
200C3×C4×C5—21no—
201C3×C4×C5—21no—
202C3×C4×C5—42no—
203C3×C4×C5—41no—
204C3×C4×C5—41no—
205C5×Dic3—21no—
206C5×Dic3—42no—
207C5×Dic3—41no—
208C5×Dic3—41no—
209C5×Dic3#9912yes—
210C23×D3C5×D411yescharacteristic
211C2×C3×Q8C2×C4×C511yescharacteristic
212C22×C3×C4—21no—
213C22×C3×C4C23×C511yescharacteristic
214C22×Dic3—21no—
215C22×Dic3C5×D411yescharacteristic
216D3×Q8—42no—
217C2×C4×D3—21no—
218C2×C4×D3—21no—
219C2×C4×D3—42no—
220C2×C4×D3C2×C4×C511yescharacteristic
221C2×C4×D3C2×C4×C511yescharacteristic
222C2×C4×D3C5×D411yescharacteristic
223C2×C4×D3C5×D411yescharacteristic
224C2×Dic6—21no—
225C2×Dic6C2×C4×C511yescharacteristic
226C2×C3×C8—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4C2×C4×C511yescharacteristic
229C3×C22⋊C4—21no—
230#217—21no—
231(C2×D3)⋊C4—24no—
232(C2×D3)⋊C4—21no—
233(C2×D3)⋊C4—21no—
234C4⋊Dic3—21no—
235C4⋊Dic3C2×C4×C511yescharacteristic
236Dic3⋊C4—21no—
237Dic3⋊C4—21no—
238Dic3⋊C4—21no—
239C4×Dic3—42no—
240C2×C3⋊C8—21no—
241ΓL(1,𝔽25)—42no—
242C23×C5—31no—
243C23×C5—31no—
244C23×C5—62no—
245C23×C5—61no—
246C23×C5—61no—
247C23×C5—121no—
248C23×C5D3×D411yescharacteristic
249C5×Q8—41no—
250C5×Q8—121no—
251C5×Q8—122no—
252C2×C4×C5—22no—
253C2×C4×C5—21no—
254C2×C4×C5—21no—
255C2×C4×C5—31no—
256C2×C4×C5—31no—
257C2×C4×C5—41no—
258C2×C4×C5—41no—
259C2×C4×C5—41no—
260C2×C4×C5—62no—
261C2×C4×C5—62no—
262C2×C4×C5—62no—
263C2×C4×C5—62no—
264C2×C4×C5—61no—
265C2×C4×C5—61no—
266C2×C4×C5—121no—
267C2×C4×C5—121no—
268C2×C4×C5—122no—
269C2×C4×C5—122no—
270C2×C4×C5—121no—
271C2×C4×C5—121no—
272C2×C4×C5C2×C4×D311yescharacteristic
273C2×C4×C5D3×D411yescharacteristic
274C5×C8—41no—
275C5×C8—121no—
276C22×Q8—31no—
277C23×C4—31no—
278C2×M16—61no—
279C22⋊Q8—31no—
280C22⋊Q8—31no—
281C22⋊Q8—31no—
282C22⋊Q8—61no—
283C22⋊Q8—61no—
284C22⋊Q8C2×C5×D311yescharacteristic
285C2×C4⋊C4—31no—
286C2×C4⋊C4—61no—
287C2×C22⋊C4—61no—
288C2×C22⋊C4—61no—
289C2×C42—61no—
290C22⋊C8—31no—
291C22⋊C8—61no—
292C22⋊C8C2×C5×D311yescharacteristic
293#95—31no—
294#95C2×C5×D311yescharacteristic
295C2×C3×C5—21no—
296C2×C3×C5—21no—
297C2×C3×C5C2×#9911yescharacteristic
298C2×C3×C5#41911yescharacteristic
299C2×C3×C5C2×#10411yescharacteristic
300C5×D3—22no—
301C5×D3—41no—
302C23×C3C2×C5×D411yescharacteristic
303C22×D3—21no—
304C22×D3—21no—
305C22×D3—22no—
306C22×D3—41no—
307C22×D3C5×C22⋊C411yescharacteristic
308C22×D3C5×C22⋊C411yescharacteristic
309C3×Q8—41no—
310C2×C3×C4—22no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4C22×C4×C511yescharacteristic
317C2×C3×C4C2×C5×D411yescharacteristic
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—21no—
321C2×Dic3—21no—
322C2×Dic3—41no—
323C2×Dic3—41no—
324C2×Dic3C5×C22⋊C411yescharacteristic
325C2×Dic3C5×C22⋊C411yescharacteristic
326C4×D3—22no—
327C4×D3—22no—
328C4×D3—41no—
329C4×D3—41no—
330C4×D3—42no—
331C4×D3—42no—
332Dic6—42no—
333Dic6—41no—
334C3×C8—41no—
335C3⋊C8—41no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5—32no—
339C22×C5—61no—
340C22×C5—61no—
341C22×C5—61no—
342C22×C5—61no—
343C22×C5—61no—
344C22×C5—122no—
345C22×C5—122no—
346C22×C5D3×C22⋊C411yescharacteristic
347C22×C5#91511yescharacteristic
348C22×C5#91811yescharacteristic
349C4×C5—21no—
350C4×C5—21no—
351C4×C5—32no—
352C4×C5—42no—
353C4×C5—41no—
354C4×C5—41no—
355C4×C5—61no—
356C4×C5—122no—
357C4×C5—121no—
358C4×C5—121no—
359C24—31no—
360C2×Q8—31no—
361C2×Q8—61no—
362C2×Q8—122no—
363C2×Q8C4×C5×D311yescharacteristic
364C22×C4—21no—
365C22×C4—31no—
366C22×C4—31no—
367C22×C4—31no—
368C22×C4—31no—
369C22×C4—31no—
370C22×C4—61no—
371C22×C4—61no—
372C22×C4—61no—
373C22×C4—122no—
374C22×C4C22×C5×D311yescharacteristic
375M16—122no—
376C2×C8—21no—
377C2×C8—61no—
378C4⋊C4—21no—
379C4⋊C4—31no—
380C4⋊C4—61no—
381C4⋊C4—61no—
382C4⋊C4—61no—
383C4⋊C4—61no—
384C4⋊C4C4×C5×D311yescharacteristic
385C22⋊C4—21no—
386C22⋊C4—61no—
387C22⋊C4—61no—
388C22⋊C4—64no—
389C22⋊C4—61no—
390C42—122no—
391C3×C5#150811yescharacteristic, complemented, Hall
392C22×C3—21no—
393C22×C3—21no—
394C22×C3C2×C5×C22⋊C411yescharacteristic
395C22×C3C5×#13711yescharacteristic
396C22×C3C5×#13711yescharacteristic
397C2×D3—21no—
398C2×D3—21no—
399C2×D3—21no—
400C2×D3—21no—
401C2×D3—21no—
402C2×D3—42no—
403C2×D3—42no—
404C2×D3C5×#10412yes—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—42no—
408C3×C4—41no—
409C3×C4—41no—
410Dic3—21no—
411Dic3—42no—
412Dic3—41no—
413Dic3—41no—
414Dic3C5×#9912yes—
415C2×C5—21no—
416C2×C5—21no—
417C2×C5—62no—
418C2×C5—121no—
419C2×C5D3×#9911yescharacteristic
420C2×C5#480211yescharacteristic
421C2×C5D3×#10411yescharacteristic
422C23—31no—
423C23—31no—
424C23—62no—
425C23—61no—
426C23—61no—
427C23—121no—
428C23C5×D3×D411yescharacteristic
429Q8—41no—
430Q8—121no—
431Q8—122no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—31no—
436C2×C4—31no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—62no—
444C2×C4—61no—
445C2×C4—61no—
446C2×C4—121no—
447C2×C4—121no—
448C2×C4—122no—
449C2×C4—122no—
450C2×C4—121no—
451C2×C4—121no—
452C2×C4C2×C4×C5×D311yescharacteristic
453C2×C4C5×D3×D411yescharacteristic
454C8—41no—
455C8—121no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3C2×C5×#9911yescharacteristic
459C2×C3C5×#41911yescharacteristic
460C2×C3C2×C5×#10411yescharacteristic
461D3—22no—
462D3—41no—
463C5#6833511yescharacteristic, direct product factor, Sylow
464C22—21no—
465C22—21no—
466C22—32no—
467C22—61no—
468C22—61no—
469C22—61no—
470C22—61no—
471C22—61no—
472C22—122no—
473C22—122no—
474C22C5×D3×C22⋊C411yescharacteristic
475C22C5×#91511yescharacteristic
476C22C5×#91811yescharacteristic
477C4—21no—
478C4—21no—
479C4—32no—
480C4—42no—
481C4—41no—
482C4—41no—
483C4—61no—
484C4—122no—
485C4—121no—
486C4—121no—
487C3C5×#150811yescharacteristic, complemented, Sylow
488C2—21no—
489C2—21no—
490C2—62no—
491C2—121no—
492C2C5×D3×#9911yescharacteristic
493C2C5×#480211yescharacteristic
494C2C5×D3×#10411yescharacteristic
subgroupG/H
centerC22×C5D3×C22⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#328C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C5×D3D4
cosocleC22×C3×C4C23×C5
hypercenterC5×#328D3
hypocenterC3C5×#1508
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#328

Complements

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

NH ≅ G/Ntype
4. C3×C5×#328C2semidirect
5. C5×#4538C2semidirect
6. C5×#4467C2semidirect
7. C5×#4452C2semidirect
9. C2×C5×D3×Q8C4semidirect
12. C5×#946C4semidirect
17. C5×#897C4semidirect
20. C5×D3×C4⋊C4C4semidirect
28. #68335C5direct (N × H)
35. C5×#328D3semidirect
71. C3×#328C2×C5semidirect
72. #4538C2×C5semidirect
73. #4467C2×C5semidirect
74. #4452C2×C5semidirect
129. C2×D3×Q8C4×C5semidirect
132. #946C4×C5semidirect
137. #897C4×C5semidirect
140. D3×C4⋊C4C4×C5semidirect
186. #328C5×D3semidirect
391. C3×C5#1508semidirect
463. C5#68335direct (N × H)
487. C3C5×#1508semidirect

Maximal subgroups

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

subgroupindex
C5×D3×C22⋊Q82
C5×#47262
C5×#46662
C3×C5×#3282
C5×#45382
C5×#44672
C5×#44522
C5×#15083
#683355