Finite Group Databasebeta

← C5×#68305 #14283405

Subgroups — C5×#68305 #14283405

Order 1920.

572 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5606C211yesmaximal, characteristic
2C5×#4726C211yesmaximal, characteristic, complemented
3C5×#4667C211yesmaximal, characteristic, complemented
4C3×C5×#327C211yesmaximal, characteristic, complemented
5C5×#4537C211yesmaximal, characteristic, complemented
6C5×#4467C211yesmaximal, characteristic, complemented
7C5×#4452C211yesmaximal, characteristic, complemented
8C5×#1513—31nomaximal, Hall
9C2×C5×#237C411yescharacteristic, complemented
10C22×C4×C5×D3C2211yescharacteristic
11C3×C5×#121C2211yescharacteristic
12C5×#938C411yescharacteristic, complemented
13C5×#937—21no—
14C5×D4×Dic3—21no—
15C2×C5×(C2×D3)⋊C4—21no—
16C5×#924C2211yescharacteristic
17C2×C5×Dic3⋊C4—21no—
18C2×C5×ΓL(1,𝔽25)—21no—
19C5×#897C411yescharacteristic, complemented
20C5×#892C411yescharacteristic, complemented
21C5×#883—21no—
22C5×#67⋊C4—21no—
23C3×C5×C22⋊C8C2211yescharacteristic
24C3×C5×#95C2211yescharacteristic
25C5×C3⋊#95C2211yescharacteristic
26C5×#830C2211yescharacteristic
27C5×(C2×D3)⋊C8—21no—
28#68305C511yesmaximal, characteristic, direct product factor, Hall
29C5×#525—31no—
30C5×#407—31no—
31C5×#380—31no—
32C5×#328—31no—
33C5×#328—31no—
34C5×#327—31no—
35C5×#327D311yescharacteristic, complemented
36C23×C5×D3D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4C2×C411yescharacteristic
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5C2311yescharacteristic
41C2×C5×#67—21no—
42C2×C5×#67—21no—
43C22×C5×Dic3—21no—
44C22×C5×Dic3—21no—
45C22×C5×Dic3D411yescharacteristic
46C5×#237—42no—
47C2×C4×C5×D3—42no—
48C2×C4×C5×D3C2×C411yescharacteristic
49C2×C4×C5×D3C2×C411yescharacteristic
50C2×C4×C5×D3D411yescharacteristic
51C2×C4×C5×D3D411yescharacteristic
52C2×C5×Dic6C2×C411yescharacteristic
53C2×C3×C5×C8—21no—
54C3×C5×C4⋊C4C2×C411yescharacteristic
55C3×C5×C22⋊C4—21no—
56C5×#217—21no—
57C5×#217—21no—
58C5×(C2×D3)⋊C4—21no—
59C5×(C2×D3)⋊C4—21no—
60C5×(C2×D3)⋊C4—42no—
61C5×C4⋊Dic3—21no—
62C5×C4⋊Dic3C2×C411yescharacteristic
63C5×Dic3⋊C4—21no—
64C5×Dic3⋊C4—42no—
65C4×C5×Dic3—21no—
66C2×C5×C3⋊C8—21no—
67C5×ΓL(1,𝔽25)—42no—
68#5606C2×C511yescharacteristic
69#4726C2×C511yescharacteristic, complemented
70#4667C2×C511yescharacteristic, complemented
71C3×#327C2×C511yescharacteristic, complemented
72#4537C2×C511yescharacteristic, complemented
73#4467C2×C511yescharacteristic, complemented
74#4452C2×C511yescharacteristic, complemented
75C2×C5×#41—31no—
76C23×C4×C5—31no—
77C2×C5×M16—61no—
78C5×#123—61no—
79C5×C22⋊Q8—31no—
80C5×C22⋊Q8—31no—
81C5×#121—31no—
82C5×#121C2×D311yescharacteristic
83C5×#120—61no—
84C4×C5×D4—61no—
85C4×C5×D4—61no—
86C5×#117—31no—
87C2×C5×C4⋊C4—61no—
88C2×C5×C22⋊C4—61no—
89C5×C22⋊C8—31no—
90C5×C22⋊C8—61no—
91C5×C22⋊C8C2×D311yescharacteristic
92C5×#95—31no—
93C5×#95C2×D311yescharacteristic
94#1513—31noSylow
95C23×C3×C5—21no—
96C23×C3×C5C2×D411yescharacteristic
97C22×C5×D3—21no—
98C22×C5×D3—21no—
99C22×C5×D3—41no—
100C22×C5×D3—41no—
101C22×C5×D3C22⋊C411yescharacteristic
102C22×C5×D3C22⋊C411yescharacteristic
103C3×C5×D4—41no—
104C3×C5×D4—41no—
105C3×C5×D4—41no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5C22×C411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C5×#67—42no—
114C5×#67—42no—
115C2×C5×Dic3—22no—
116C2×C5×Dic3—21no—
117C2×C5×Dic3—21no—
118C2×C5×Dic3—42no—
119C2×C5×Dic3—41no—
120C2×C5×Dic3—41no—
121C2×C5×Dic3—41no—
122C2×C5×Dic3C22⋊C411yescharacteristic
123C2×C5×Dic3C22⋊C411yescharacteristic
124C4×C5×D3—22no—
125C4×C5×D3—22no—
126C4×C5×D3—41no—
127C4×C5×D3—41no—
128C5×Dic6—41no—
129C3×C5×C8—41no—
130C5×C3⋊C8—41no—
131C2×#237C4×C511yescharacteristic, complemented
132C22×C4×D3C22×C511yescharacteristic
133C3×#121C22×C511yescharacteristic
134#938C4×C511yescharacteristic, complemented
135#937—21no—
136D4×Dic3—21no—
137C2×(C2×D3)⋊C4—21no—
138#924C22×C511yescharacteristic
139C2×Dic3⋊C4—21no—
140C2×ΓL(1,𝔽25)—21no—
141#897C4×C511yescharacteristic, complemented
142#892C4×C511yescharacteristic, complemented
143#883—21no—
144#67⋊C4—21no—
145C3×C22⋊C8C22×C511yescharacteristic
146C3×#95C22×C511yescharacteristic
147C3⋊#95C22×C511yescharacteristic
148#830C22×C511yescharacteristic
149(C2×D3)⋊C8—21no—
150C24×C5—31no—
151C5×#41—122no—
152C2×C5×Q8—31no—
153C2×C5×D4—21no—
154C2×C5×D4—61no—
155C2×C5×D4—61no—
156C2×C5×D4C4×D311yescharacteristic
157C22×C4×C5—21no—
158C22×C4×C5—31no—
159C22×C4×C5—31no—
160C22×C4×C5—31no—
161C22×C4×C5—31no—
162C22×C4×C5—31no—
163C22×C4×C5—61no—
164C22×C4×C5—61no—
165C22×C4×C5—122no—
166C22×C4×C5C22×D311yescharacteristic
167C5×M16—122no—
168C2×C5×C8—21no—
169C2×C5×C8—61no—
170C5×C4⋊C4—31no—
171C5×C4⋊C4—61no—
172C5×C4⋊C4—61no—
173C5×C4⋊C4—122no—
174C5×C4⋊C4C4×D311yescharacteristic
175C5×C22⋊C4—21no—
176C5×C22⋊C4—61no—
177C5×C22⋊C4—61no—
178C5×C22⋊C4—61no—
179C5×C22⋊C4—61no—
180C5×C22⋊C4—122no—
181C42×C5—61no—
182#525—31no—
183#407—31no—
184#380—31no—
185#328—31no—
186#328—31no—
187#327—31no—
188#327C5×D311yescharacteristic, complemented
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5—41no—
192C22×C3×C5—41no—
193C22×C3×C5—41no—
194C22×C3×C5C2×C22⋊C411yescharacteristic
195C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
196C22×C3×C5#13711yescharacteristic
197C2×C5×D3—21no—
198C2×C5×D3—21no—
199C2×C5×D3—21no—
200C2×C5×D3—21no—
201C2×C5×D3—21no—
202C2×C5×D3—21no—
203C2×C5×D3—42no—
204C2×C5×D3—42no—
205C3×C4×C5—21no—
206C3×C4×C5—21no—
207C3×C4×C5—41no—
208C3×C4×C5—81no—
209C5×Dic3—21no—
210C5×Dic3—41no—
211C5×Dic3—41no—
212C5×Dic3—81no—
213C5×Dic3#9912yes—
214C23×D3C5×D411yescharacteristic
215C2×C3×D4—21no—
216C2×C3×D4C2×C4×C511yescharacteristic
217C22×C3×C4—21no—
218C22×C3×C4C23×C511yescharacteristic
219C2×#67—21no—
220C2×#67—21no—
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3C5×D411yescharacteristic
224#237—42no—
225C2×C4×D3—42no—
226C2×C4×D3C2×C4×C511yescharacteristic
227C2×C4×D3C2×C4×C511yescharacteristic
228C2×C4×D3C5×D411yescharacteristic
229C2×C4×D3C5×D411yescharacteristic
230C2×Dic6C2×C4×C511yescharacteristic
231C2×C3×C8—21no—
232C3×C4⋊C4C2×C4×C511yescharacteristic
233C3×C22⋊C4—21no—
234#217—21no—
235#217—21no—
236(C2×D3)⋊C4—21no—
237(C2×D3)⋊C4—21no—
238(C2×D3)⋊C4—42no—
239C4⋊Dic3—21no—
240C4⋊Dic3C2×C4×C511yescharacteristic
241Dic3⋊C4—21no—
242Dic3⋊C4—42no—
243C4×Dic3—21no—
244C2×C3⋊C8—21no—
245ΓL(1,𝔽25)—42no—
246C23×C5—21no—
247C23×C5—31no—
248C23×C5—31no—
249C23×C5—61no—
250C23×C5—61no—
251C23×C5—121no—
252C23×C5—121no—
253C23×C5D3×D411yescharacteristic
254C5×Q8—121no—
255C5×D4—41no—
256C5×D4—41no—
257C5×D4—41no—
258C5×D4—122no—
259C5×D4—122no—
260C2×C4×C5—21no—
261C2×C4×C5—31no—
262C2×C4×C5—31no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—41no—
266C2×C4×C5—41no—
267C2×C4×C5—62no—
268C2×C4×C5—62no—
269C2×C4×C5—62no—
270C2×C4×C5—61no—
271C2×C4×C5—61no—
272C2×C4×C5—121no—
273C2×C4×C5—121no—
274C2×C4×C5—122no—
275C2×C4×C5—121no—
276C2×C4×C5—121no—
277C2×C4×C5—121no—
278C2×C4×C5C2×C4×D311yescharacteristic
279C2×C4×C5D3×D411yescharacteristic
280C5×C8—41no—
281C5×C8—121no—
282C2×#41—31no—
283C23×C4—31no—
284C2×M16—61no—
285#123—61no—
286C22⋊Q8—31no—
287C22⋊Q8—31no—
288#121—31no—
289#121C2×C5×D311yescharacteristic
290#120—61no—
291C4×D4—61no—
292C4×D4—61no—
293#117—31no—
294C2×C4⋊C4—61no—
295C2×C22⋊C4—61no—
296C22⋊C8—31no—
297C22⋊C8—61no—
298C22⋊C8C2×C5×D311yescharacteristic
299#95—31no—
300#95C2×C5×D311yescharacteristic
301C2×C3×C5—21no—
302C2×C3×C5—21no—
303C2×C3×C5—81no—
304C2×C3×C5C2×#9911yescharacteristic
305C2×C3×C5#41711yescharacteristic
306C2×C3×C5#42111yescharacteristic
307C5×D3—41no—
308C5×D3—41no—
309C23×C3—21no—
310C23×C3C2×C5×D411yescharacteristic
311C22×D3—21no—
312C22×D3—21no—
313C22×D3—41no—
314C22×D3—41no—
315C22×D3C5×C22⋊C411yescharacteristic
316C22×D3C5×C22⋊C411yescharacteristic
317C3×D4—41no—
318C3×D4—41no—
319C3×D4—41no—
320C2×C3×C4—21no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4C22×C4×C511yescharacteristic
326C2×C3×C4C2×C5×D411yescharacteristic
327#67—42no—
328#67—42no—
329C2×Dic3—22no—
330C2×Dic3—21no—
331C2×Dic3—21no—
332C2×Dic3—42no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3—41no—
336C2×Dic3C5×C22⋊C411yescharacteristic
337C2×Dic3C5×C22⋊C411yescharacteristic
338C4×D3—22no—
339C4×D3—22no—
340C4×D3—41no—
341C4×D3—41no—
342Dic6—41no—
343C3×C8—41no—
344C3⋊C8—41no—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5—41no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5—61no—
351C22×C5—61no—
352C22×C5—61no—
353C22×C5—61no—
354C22×C5—61no—
355C22×C5—61no—
356C22×C5—122no—
357C22×C5—122no—
358C22×C5D3×C22⋊C411yescharacteristic
359C22×C5#91111yescharacteristic
360C22×C5#91511yescharacteristic
361C4×C5—21no—
362C4×C5—21no—
363C4×C5—32no—
364C4×C5—41no—
365C4×C5—61no—
366C4×C5—81no—
367C4×C5—121no—
368C4×C5—121no—
369C4×C5—241no—
370C24—31no—
371#41—122no—
372C2×Q8—31no—
373C2×D4—21no—
374C2×D4—61no—
375C2×D4—61no—
376C2×D4C4×C5×D311yescharacteristic
377C22×C4—21no—
378C22×C4—31no—
379C22×C4—31no—
380C22×C4—31no—
381C22×C4—31no—
382C22×C4—31no—
383C22×C4—61no—
384C22×C4—61no—
385C22×C4—122no—
386C22×C4C22×C5×D311yescharacteristic
387M16—122no—
388C2×C8—21no—
389C2×C8—61no—
390C4⋊C4—31no—
391C4⋊C4—61no—
392C4⋊C4—61no—
393C4⋊C4—122no—
394C4⋊C4C4×C5×D311yescharacteristic
395C22⋊C4—21no—
396C22⋊C4—61no—
397C22⋊C4—61no—
398C22⋊C4—61no—
399C22⋊C4—61no—
400C22⋊C4—122no—
401C42—61no—
402C3×C5#151311yescharacteristic, complemented, Hall
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3C2×C5×C22⋊C411yescharacteristic
409C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
410C22×C3C5×#13711yescharacteristic
411C2×D3—21no—
412C2×D3—21no—
413C2×D3—21no—
414C2×D3—21no—
415C2×D3—21no—
416C2×D3—21no—
417C2×D3—42no—
418C2×D3—42no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—41no—
422C3×C4—81no—
423Dic3—21no—
424Dic3—41no—
425Dic3—41no—
426Dic3—81no—
427Dic3C5×#9912yes—
428C2×C5—21no—
429C2×C5—21no—
430C2×C5—81no—
431C2×C5—121no—
432C2×C5—121no—
433C2×C5D3×#9911yescharacteristic
434C2×C5#477111yescharacteristic
435C2×C5#482111yescharacteristic
436C23—21no—
437C23—31no—
438C23—31no—
439C23—61no—
440C23—61no—
441C23—121no—
442C23—121no—
443C23C5×D3×D411yescharacteristic
444Q8—121no—
445D4—41no—
446D4—41no—
447D4—41no—
448D4—122no—
449D4—122no—
450C2×C4—21no—
451C2×C4—31no—
452C2×C4—31no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—121no—
463C2×C4—121no—
464C2×C4—122no—
465C2×C4—121no—
466C2×C4—121no—
467C2×C4—121no—
468C2×C4C2×C4×C5×D311yescharacteristic
469C2×C4C5×D3×D411yescharacteristic
470C8—41no—
471C8—121no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—81no—
475C2×C3C2×C5×#9911yescharacteristic
476C2×C3C5×#41711yescharacteristic
477C2×C3C5×#42111yescharacteristic
478D3—41no—
479D3—41no—
480C5#6830511yescharacteristic, direct product factor, Sylow
481C22—21no—
482C22—21no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—61no—
487C22—61no—
488C22—61no—
489C22—61no—
490C22—61no—
491C22—61no—
492C22—122no—
493C22—122no—
494C22C5×D3×C22⋊C411yescharacteristic
495C22C5×#91111yescharacteristic
496C22C5×#91511yescharacteristic
497C4—21no—
498C4—21no—
499C4—32no—
500C4—41no—
501C4—61no—
502C4—81no—
503C4—121no—
504C4—121no—
505C4—241no—
506C3C5×#151311yescharacteristic, complemented, Sylow
507C2—21no—
508C2—21no—
509C2—81no—
510C2—121no—
511C2—121no—
512C2C5×D3×#9911yescharacteristic
513C2C5×#477111yescharacteristic
514C2C5×#482111yescharacteristic
subgroupG/H
centerC22×C5D3×C22⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#327C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5606C2
cosocleC22×C3×C4C23×C5
hypercenterC5×#327D3
hypocenterC3C5×#1513
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#327

Complements

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

NH ≅ G/Ntype
2. C5×#4726C2semidirect
3. C5×#4667C2semidirect
4. C3×C5×#327C2semidirect
5. C5×#4537C2semidirect
6. C5×#4467C2semidirect
7. C5×#4452C2semidirect
9. C2×C5×#237C4semidirect
12. C5×#938C4semidirect
19. C5×#897C4semidirect
20. C5×#892C4semidirect
28. #68305C5direct (N × H)
35. C5×#327D3semidirect
69. #4726C2×C5semidirect
70. #4667C2×C5semidirect
71. C3×#327C2×C5semidirect
72. #4537C2×C5semidirect
73. #4467C2×C5semidirect
74. #4452C2×C5semidirect
131. C2×#237C4×C5semidirect
134. #938C4×C5semidirect
141. #897C4×C5semidirect
142. #892C4×C5semidirect
188. #327C5×D3semidirect
402. C3×C5#1513semidirect
480. C5#68305direct (N × H)
506. C3C5×#1513semidirect

Maximal subgroups

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

subgroupindex
C5×#56062
C5×#47262
C5×#46672
C3×C5×#3272
C5×#45372
C5×#44672
C5×#44522
C5×#15133
#683055