Finite Group Databasebeta

← C5×#68147 #14281362

Subgroups — C5×#68147 #14281362

Order 1920.

540 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#896C211yesmaximal, characteristic
2C5×#4726C211yesmaximal, characteristic
3C5×D3×C22⋊C8C211yesmaximal, characteristic
4C3×C5×#324C211yesmaximal, characteristic, complemented
5C5×#4528C211yesmaximal, characteristic, complemented
6C5×#4469C211yesmaximal, characteristic, complemented
7C5×#4469C211yesmaximal, characteristic, complemented
8C5×#1472—31nomaximal, Hall
9C22×C4×C5×D3C2211yescharacteristic
10C22×C5×Dic6C411yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C5×(C2×D3)⋊C4C411yescharacteristic
13C2×C5×(C2×D3)⋊C4C411yescharacteristic
14C2×C5×Dic3⋊C4C411yescharacteristic
15C2×C5×Dic3⋊C4C2211yescharacteristic
16C2×C5×ΓL(1,𝔽25)—21no—
17C2×C5×D3×C8—21no—
18C5×#896—21no—
19C5×#896—21no—
20C5×#896—21no—
21C5×#896—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23C3×C5×C22⋊C8C2211yescharacteristic
24C5×#830C2211yescharacteristic
25C5×#830C2211yescharacteristic
26C5×(C2×D3)⋊C8—21no—
27C5×(C2×D3)⋊C8—21no—
28#68147C511yesmaximal, characteristic, direct product factor, Hall
29C2×C5×C22⋊Q8—31no—
30C5×#407—31no—
31C2×C5×C22⋊C8—31no—
32C5×#324—31no—
33C5×#324—31no—
34C5×#324—31no—
35C5×#324D311yescharacteristic, complemented
36C23×C5×D3C2×C411yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C22×C3×C4×C5C2×C411yescharacteristic
39C22×C3×C4×C5C2311yescharacteristic
40C22×C5×Dic3C2×C411yescharacteristic
41C22×C5×Dic3C2×C411yescharacteristic
42C22×C5×Dic3C2×C411yescharacteristic
43C2×C4×C5×D3—42no—
44C2×C4×C5×D3D411yescharacteristic
45C2×C4×C5×D3D411yescharacteristic
46C2×C4×C5×D3D411yescharacteristic
47C2×C4×C5×D3D411yescharacteristic
48C2×C5×Dic6—21no—
49C2×C5×Dic6—21no—
50C2×C5×Dic6—42no—
51C2×C3×C5×C8—21no—
52C2×C3×C5×C8—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4—21no—
55C5×(C2×D3)⋊C4—21no—
56C5×(C2×D3)⋊C4—21no—
57C5×(C2×D3)⋊C4—21no—
58C5×(C2×D3)⋊C4—21no—
59C5×Dic3⋊C4—21no—
60C5×Dic3⋊C4—21no—
61C5×Dic3⋊C4—21no—
62C5×Dic3⋊C4—21no—
63C2×C5×C3⋊C8—21no—
64C2×C5×C3⋊C8—21no—
65C5×ΓL(1,𝔽25)—42no—
66C5×D3×C8—42no—
67C2×#896C2×C511yescharacteristic
68#4726C2×C511yescharacteristic
69D3×C22⋊C8C2×C511yescharacteristic
70C3×#324C2×C511yescharacteristic, complemented
71#4528C2×C511yescharacteristic, complemented
72#4469C2×C511yescharacteristic, complemented
73#4469C2×C511yescharacteristic, complemented
74C22×C5×Q8—31no—
75C23×C4×C5—31no—
76C2×C5×M16—61no—
77C22×C5×C8—61no—
78C5×C22⋊Q8—61no—
79C5×C22⋊Q8—61no—
80C5×C22⋊Q8—61no—
81C5×C22⋊Q8—61no—
82C2×C5×C4⋊C4—31no—
83C2×C5×C4⋊C4—31no—
84C2×C5×C4⋊C4C2×D311yescharacteristic
85C2×C5×C22⋊C4—31no—
86C2×C5×C22⋊C4—31no—
87C5×C22⋊C8—31no—
88C5×C22⋊C8—31no—
89C5×C22⋊C8—61no—
90C5×C22⋊C8—61no—
91C5×C22⋊C8C2×D311yescharacteristic
92C5×C22⋊C8C2×D311yescharacteristic
93#1472—31noSylow
94C23×C3×C5C22×C411yescharacteristic
95C22×C5×D3—21no—
96C22×C5×D3—21no—
97C22×C5×D3—22no—
98C22×C5×D3—41no—
99C22×C5×D3C22⋊C411yescharacteristic
100C22×C5×D3C22⋊C411yescharacteristic
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C5×Dic3—22no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—21no—
112C2×C5×Dic3—21no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3—41no—
115C2×C5×Dic3C22⋊C411yescharacteristic
116C2×C5×Dic3C22⋊C411yescharacteristic
117C4×C5×D3—22no—
118C4×C5×D3—22no—
119C4×C5×D3—41no—
120C4×C5×D3—41no—
121C5×Dic6—42no—
122C5×Dic6—42no—
123C3×C5×C8—41no—
124C3×C5×C8—41no—
125C5×C3⋊C8—41no—
126C5×C3⋊C8—41no—
127C22×C4×D3C22×C511yescharacteristic
128C22×Dic6C4×C511yescharacteristic
129C2×C3×C4⋊C4C22×C511yescharacteristic
130C2×(C2×D3)⋊C4C4×C511yescharacteristic
131C2×(C2×D3)⋊C4C4×C511yescharacteristic
132C2×Dic3⋊C4C4×C511yescharacteristic
133C2×Dic3⋊C4C22×C511yescharacteristic
134C2×ΓL(1,𝔽25)—21no—
135C2×D3×C8—21no—
136#896—21no—
137#896—21no—
138#896—21no—
139#896—21no—
140C3×C22⋊C8C22×C511yescharacteristic
141C3×C22⋊C8C22×C511yescharacteristic
142#830C22×C511yescharacteristic
143#830C22×C511yescharacteristic
144(C2×D3)⋊C8—21no—
145(C2×D3)⋊C8—21no—
146C24×C5—31no—
147C2×C5×Q8—61no—
148C2×C5×Q8—61no—
149C2×C5×Q8—122no—
150C22×C4×C5—31no—
151C22×C4×C5—31no—
152C22×C4×C5—31no—
153C22×C4×C5—31no—
154C22×C4×C5—31no—
155C22×C4×C5—31no—
156C22×C4×C5—31no—
157C22×C4×C5—122no—
158C22×C4×C5C4×D311yescharacteristic
159C22×C4×C5C4×D311yescharacteristic
160C22×C4×C5C22×D311yescharacteristic
161C5×M16—122no—
162C2×C5×C8—21no—
163C2×C5×C8—21no—
164C2×C5×C8—61no—
165C2×C5×C8—61no—
166C2×C5×C8—122no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—21no—
169C5×C4⋊C4—61no—
170C5×C4⋊C4—61no—
171C5×C4⋊C4—61no—
172C5×C4⋊C4—61no—
173C5×C22⋊C4—61no—
174C5×C22⋊C4—61no—
175C5×C22⋊C4—61no—
176C5×C22⋊C4—61no—
177C2×C22⋊Q8—31no—
178#407—31no—
179C2×C22⋊C8—31no—
180#324—31no—
181#324—31no—
182#324—31no—
183#324C5×D311yescharacteristic, complemented
184C22×C3×C5—21no—
185C22×C3×C5—21no—
186C22×C3×C5C2×C22⋊C411yescharacteristic
187C22×C3×C5#13111yescharacteristic
188C22×C3×C5#13111yescharacteristic
189C2×C5×D3—21no—
190C2×C5×D3—21no—
191C2×C5×D3—21no—
192C2×C5×D3—21no—
193C2×C5×D3—21no—
194C2×C5×D3—42no—
195C2×C5×D3—42no—
196C2×C5×D3#10112yes—
197C3×C4×C5—21no—
198C3×C4×C5—21no—
199C3×C4×C5—41no—
200C3×C4×C5—41no—
201C5×Dic3—21no—
202C5×Dic3—41no—
203C5×Dic3—41no—
204C5×Dic3#9912yes—
205C23×D3C2×C4×C511yescharacteristic
206C22×C3×C4C2×C4×C511yescharacteristic
207C22×C3×C4C2×C4×C511yescharacteristic
208C22×C3×C4C23×C511yescharacteristic
209C22×Dic3C2×C4×C511yescharacteristic
210C22×Dic3C2×C4×C511yescharacteristic
211C22×Dic3C2×C4×C511yescharacteristic
212C2×C4×D3—42no—
213C2×C4×D3C5×D411yescharacteristic
214C2×C4×D3C5×D411yescharacteristic
215C2×C4×D3C5×D411yescharacteristic
216C2×C4×D3C5×D411yescharacteristic
217C2×Dic6—21no—
218C2×Dic6—21no—
219C2×Dic6—42no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224(C2×D3)⋊C4—21no—
225(C2×D3)⋊C4—21no—
226(C2×D3)⋊C4—21no—
227(C2×D3)⋊C4—21no—
228Dic3⋊C4—21no—
229Dic3⋊C4—21no—
230Dic3⋊C4—21no—
231Dic3⋊C4—21no—
232C2×C3⋊C8—21no—
233C2×C3⋊C8—21no—
234ΓL(1,𝔽25)—42no—
235D3×C8—42no—
236C23×C5—31no—
237C23×C5—31no—
238C23×C5—62no—
239C23×C5—61no—
240C23×C5—61no—
241C23×C5—121no—
242C23×C5C2×C4×D311yescharacteristic
243C5×Q8—122no—
244C5×Q8—122no—
245C2×C4×C5—21no—
246C2×C4×C5—21no—
247C2×C4×C5—21no—
248C2×C4×C5—21no—
249C2×C4×C5—31no—
250C2×C4×C5—31no—
251C2×C4×C5—41no—
252C2×C4×C5—41no—
253C2×C4×C5—62no—
254C2×C4×C5—62no—
255C2×C4×C5—62no—
256C2×C4×C5—61no—
257C2×C4×C5—61no—
258C2×C4×C5—61no—
259C2×C4×C5—61no—
260C2×C4×C5—121no—
261C2×C4×C5—121no—
262C2×C4×C5—121no—
263C2×C4×C5D3×D411yescharacteristic
264C2×C4×C5D3×D411yescharacteristic
265C5×C8—41no—
266C5×C8—41no—
267C5×C8—121no—
268C5×C8—121no—
269C22×Q8—31no—
270C23×C4—31no—
271C2×M16—61no—
272C22×C8—61no—
273C22⋊Q8—61no—
274C22⋊Q8—61no—
275C22⋊Q8—61no—
276C22⋊Q8—61no—
277C2×C4⋊C4—31no—
278C2×C4⋊C4—31no—
279C2×C4⋊C4C2×C5×D311yescharacteristic
280C2×C22⋊C4—31no—
281C2×C22⋊C4—31no—
282C22⋊C8—31no—
283C22⋊C8—31no—
284C22⋊C8—61no—
285C22⋊C8—61no—
286C22⋊C8C2×C5×D311yescharacteristic
287C22⋊C8C2×C5×D311yescharacteristic
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5#40811yescharacteristic
291C2×C3×C5C2×#9911yescharacteristic
292C2×C3×C5C2×#10111yescharacteristic
293C5×D3—22no—
294C5×D3—41no—
295C23×C3C22×C4×C511yescharacteristic
296C22×D3—21no—
297C22×D3—21no—
298C22×D3—22no—
299C22×D3—41no—
300C22×D3C5×C22⋊C411yescharacteristic
301C22×D3C5×C22⋊C411yescharacteristic
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4C2×C5×D411yescharacteristic
309C2×C3×C4C2×C5×D411yescharacteristic
310C2×Dic3—22no—
311C2×Dic3—21no—
312C2×Dic3—21no—
313C2×Dic3—21no—
314C2×Dic3—21no—
315C2×Dic3—41no—
316C2×Dic3C5×C22⋊C411yescharacteristic
317C2×Dic3C5×C22⋊C411yescharacteristic
318C4×D3—22no—
319C4×D3—22no—
320C4×D3—41no—
321C4×D3—41no—
322Dic6—42no—
323Dic6—42no—
324C3×C8—41no—
325C3×C8—41no—
326C3⋊C8—41no—
327C3⋊C8—41no—
328C22×C5—21no—
329C22×C5—21no—
330C22×C5—32no—
331C22×C5—61no—
332C22×C5—61no—
333C22×C5—61no—
334C22×C5—61no—
335C22×C5—61no—
336C22×C5—122no—
337C22×C5—122no—
338C22×C5D3×C22⋊C411yescharacteristic
339C22×C5#90111yescharacteristic
340C22×C5#90711yescharacteristic
341C4×C5—21no—
342C4×C5—21no—
343C4×C5—32no—
344C4×C5—41no—
345C4×C5—41no—
346C4×C5—61no—
347C4×C5—121no—
348C4×C5—121no—
349C24—31no—
350C2×Q8—61no—
351C2×Q8—61no—
352C2×Q8—122no—
353C22×C4—31no—
354C22×C4—31no—
355C22×C4—31no—
356C22×C4—31no—
357C22×C4—31no—
358C22×C4—31no—
359C22×C4—31no—
360C22×C4—122no—
361C22×C4C4×C5×D311yescharacteristic
362C22×C4C4×C5×D311yescharacteristic
363C22×C4C22×C5×D311yescharacteristic
364M16—122no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—61no—
368C2×C8—61no—
369C2×C8—122no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—61no—
373C4⋊C4—61no—
374C4⋊C4—61no—
375C4⋊C4—61no—
376C22⋊C4—61no—
377C22⋊C4—61no—
378C22⋊C4—61no—
379C22⋊C4—61no—
380C3×C5#147211yescharacteristic, complemented, Hall
381C22×C3—21no—
382C22×C3—21no—
383C22×C3C2×C5×C22⋊C411yescharacteristic
384C22×C3C5×#13111yescharacteristic
385C22×C3C5×#13111yescharacteristic
386C2×D3—21no—
387C2×D3—21no—
388C2×D3—21no—
389C2×D3—21no—
390C2×D3—21no—
391C2×D3—42no—
392C2×D3—42no—
393C2×D3C5×#10112yes—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—41no—
397C3×C4—41no—
398Dic3—21no—
399Dic3—41no—
400Dic3—41no—
401Dic3C5×#9912yes—
402C2×C5—21no—
403C2×C5—21no—
404C2×C5—62no—
405C2×C5—121no—
406C2×C5#472711yescharacteristic
407C2×C5D3×#9911yescharacteristic
408C2×C5D3×#10111yescharacteristic
409C23—31no—
410C23—31no—
411C23—62no—
412C23—61no—
413C23—61no—
414C23—121no—
415C23C2×C4×C5×D311yescharacteristic
416Q8—122no—
417Q8—122no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—31no—
423C2×C4—31no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—61no—
433C2×C4—121no—
434C2×C4—121no—
435C2×C4—121no—
436C2×C4C5×D3×D411yescharacteristic
437C2×C4C5×D3×D411yescharacteristic
438C8—41no—
439C8—41no—
440C8—121no—
441C8—121no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3C5×#40811yescharacteristic
445C2×C3C2×C5×#9911yescharacteristic
446C2×C3C2×C5×#10111yescharacteristic
447D3—22no—
448D3—41no—
449C5#6814711yescharacteristic, direct product factor, Sylow
450C22—21no—
451C22—21no—
452C22—32no—
453C22—61no—
454C22—61no—
455C22—61no—
456C22—61no—
457C22—61no—
458C22—122no—
459C22—122no—
460C22C5×D3×C22⋊C411yescharacteristic
461C22C5×#90111yescharacteristic
462C22C5×#90711yescharacteristic
463C4—21no—
464C4—21no—
465C4—32no—
466C4—41no—
467C4—41no—
468C4—61no—
469C4—121no—
470C4—121no—
471C3C5×#147211yescharacteristic, complemented, Sylow
472C2—21no—
473C2—21no—
474C2—62no—
475C2—121no—
476C2C5×#472711yescharacteristic
477C2C5×D3×#9911yescharacteristic
478C2C5×D3×#10111yescharacteristic
subgroupG/H
centerC22×C5D3×C22⋊C4
commutatorC23×C3C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#324C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C5×D3C2×C4
cosocleC22×C3×C4C23×C5
hypercenterC5×#324D3
hypocenterC3C5×#1472
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#324

Complements

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

NH ≅ G/Ntype
4. C3×C5×#324C2semidirect
5. C5×#4528C2semidirect
6. C5×#4469C2semidirect
7. C5×#4469C2semidirect
28. #68147C5direct (N × H)
35. C5×#324D3semidirect
70. C3×#324C2×C5semidirect
71. #4528C2×C5semidirect
72. #4469C2×C5semidirect
73. #4469C2×C5semidirect
183. #324C5×D3semidirect
380. C3×C5#1472semidirect
449. C5#68147direct (N × H)
471. C3C5×#1472semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8962
C5×#47262
C5×D3×C22⋊C82
C3×C5×#3242
C5×#45282
C5×#44692
C5×#14723
#681475