Finite Group Databasebeta

← C5×#72048 #14301089

Subgroups — C5×#72048 #14301089

Order 1920.

748 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×SD16C211yesmaximal, characteristic
2C2×C5×Q8×Dic3C211yesmaximal, characteristic, complemented
3C2×C5×#835C211yesmaximal, characteristic, complemented
4C5×#5221C211yesmaximal, characteristic
5C2×C5×#832C211yesmaximal, characteristic
6C5×#4551C211yesmaximal, characteristic, complemented
7C5×#4550C211yesmaximal, characteristic, complemented
8C5×#1880—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C22×C3×C5×D4C2211yescharacteristic
11C2×C3×C5×SD16—22no—
12C2×C3×C5×SD16—22no—
13C2×C3×C5×SD16C414yescomplemented
14C22×C3×C5×C8C2211yescharacteristic
15C2×C5×#217—21no—
16C2×C5×#217—21no—
17C5×Q8×Dic3—22no—
18C5×Q8×Dic3—22no—
19C2×C5×C4⋊Dic3—21no—
20C2×C5×C4⋊Dic3C2211yescharacteristic
21C2×C5×C4⋊Dic3C2211yescharacteristic
22C2×C4×C5×Dic3—21no—
23C2×C4×C5×Dic3C2211yescharacteristic
24C22×C5×C3⋊C8C2211yescharacteristic
25C5×#835—22no—
26C5×#832—22no—
27#72048C511yesmaximal, characteristic, direct product factor, Hall
28C22×C5×SD16D311yescharacteristic
29C2×C4×C5×Q8—31no—
30C2×C5×#103—31no—
31C2×C5×#102—31no—
32C5×#390—31no—
33C5×#340—31no—
34C5×#336—31no—
35C24×C3×C5—21no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8C2×C412yes—
40C2×C3×C5×Q8D412yes—
41C2×C3×C5×Q8D412yes—
42C2×C3×C5×D4—21no—
43C2×C3×C5×D4—21no—
44C2×C3×C5×D4—21no—
45C2×C3×C5×D4—21no—
46C2×C3×C5×D4—21no—
47C2×C3×C5×D4C2×C412yes—
48C22×C3×C4×C5—21no—
49C22×C3×C4×C5C2311yescharacteristic
50C22×C5×Dic3—21no—
51C22×C5×Dic3—21no—
52C22×C5×Dic3D411yescharacteristic
53C22×C5×Dic3D411yescharacteristic
54C3×C5×SD16—28no—
55C2×C3×C5×C8—21no—
56C2×C3×C5×C8—21no—
57C2×C3×C5×C8C2×C412yes—
58C5×#217—42no—
59C5×#217—42no—
60C5×C4⋊Dic3—24no—
61C5×C4⋊Dic3—21no—
62C5×C4⋊Dic3—21no—
63C5×C4⋊Dic3—21no—
64C5×C4⋊Dic3D412yes—
65C4×C5×Dic3—24no—
66C4×C5×Dic3—21no—
67C4×C5×Dic3—21no—
68C2×C5×C3⋊C8—21no—
69C2×C5×C3⋊C8—21no—
70C2×C5×C3⋊C8—21no—
71C22×C3×SD16C2×C511yescharacteristic
72C2×Q8×Dic3C2×C511yescharacteristic, complemented
73C2×#835C2×C511yescharacteristic, complemented
74#5221C2×C511yescharacteristic
75C2×#832C2×C511yescharacteristic
76#4551C2×C511yescharacteristic, complemented
77#4550C2×C511yescharacteristic, complemented
78C22×C5×Q8C2×D311yescharacteristic
79C22×C5×D4C2×D311yescharacteristic
80C2×C5×SD16—22no—
81C2×C5×SD16—22no—
82C2×C5×SD16Dic314yescomplemented
83C22×C5×C8—31no—
84C22×C5×C8C2×D311yescharacteristic
85C4×C5×Q8—62no—
86C4×C5×Q8—62no—
87C2×C5×C4⋊C4—31no—
88C2×C5×C4⋊C4—31no—
89C2×C5×C4⋊C4—61no—
90C2×C5×C22⋊C4—61no—
91C2×C5×C22⋊C4—61no—
92C2×C42×C5—31no—
93C2×C42×C5—61no—
94C5×#103—62no—
95C5×#102—62no—
96#1880—31noSylow
97C23×C3×C5—22no—
98C23×C3×C5—41no—
99C23×C3×C5—41no—
100C23×C3×C5—41no—
101C23×C3×C5—41no—
102C23×C3×C5—41no—
103C23×C3×C5—41no—
104C23×C3×C5C2×D411yescharacteristic
105C3×C5×Q8—22no—
106C3×C5×Q8—22no—
107C3×C5×Q8—22no—
108C3×C5×Q8C22⋊C414yescomplemented
109C3×C5×D4—22no—
110C3×C5×D4—22no—
111C3×C5×D4—41no—
112C3×C5×D4—41no—
113C2×C3×C4×C5—22no—
114C2×C3×C4×C5—22no—
115C2×C3×C4×C5—22no—
116C2×C3×C4×C5C22×C411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5C2×D411yescharacteristic
120C2×C3×C4×C5#4111yescharacteristic
121C2×C3×C4×C5#4111yescharacteristic
122C2×C5×Dic3—21no—
123C2×C5×Dic3—21no—
124C2×C5×Dic3—21no—
125C2×C5×Dic3—22no—
126C2×C5×Dic3—21no—
127C2×C5×Dic3—21no—
128C2×C5×Dic3—41no—
129C2×C5×Dic3—41no—
130C2×C5×Dic3—41no—
131C2×C5×Dic3—41no—
132C2×C5×Dic3—41no—
133C2×C5×Dic3SD1612yescomplemented
134C3×C5×C8—22no—
135C5×C3⋊C8—41no—
136C22×C3×Q8C22×C511yescharacteristic
137C22×C3×D4C22×C511yescharacteristic
138C2×C3×SD16—22no—
139C2×C3×SD16—22no—
140C2×C3×SD16C4×C514yescomplemented
141C22×C3×C8C22×C511yescharacteristic
142C2×#217—21no—
143C2×#217—21no—
144Q8×Dic3—22no—
145Q8×Dic3—22no—
146C2×C4⋊Dic3—21no—
147C2×C4⋊Dic3C22×C511yescharacteristic
148C2×C4⋊Dic3C22×C511yescharacteristic
149C2×C4×Dic3—21no—
150C2×C4×Dic3C22×C511yescharacteristic
151C22×C3⋊C8C22×C511yescharacteristic
152#835—22no—
153#832—22no—
154C24×C5—21no—
155C2×C5×Q8—21no—
156C2×C5×Q8—21no—
157C2×C5×Q8—21no—
158C2×C5×Q8C2×Dic312yes—
159C2×C5×Q8#6712yes—
160C2×C5×Q8#6712yes—
161C2×C5×D4—21no—
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4C2×Dic312yes—
167C22×C4×C5—21no—
168C22×C4×C5—31no—
169C22×C4×C5—31no—
170C22×C4×C5—61no—
171C22×C4×C5—61no—
172C22×C4×C5C22×D311yescharacteristic
173C5×SD16—28no—
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8—61no—
177C2×C5×C8—61no—
178C2×C5×C8—61no—
179C2×C5×C8C2×Dic312yes—
180C5×C4⋊C4—32no—
181C5×C4⋊C4—64no—
182C5×C4⋊C4—61no—
183C5×C4⋊C4—61no—
184C5×C4⋊C4—61no—
185C5×C22⋊C4—122no—
186C5×C22⋊C4—122no—
187C42×C5—64no—
188C42×C5—61no—
189C42×C5—61no—
190C22×SD16C5×D311yescharacteristic
191C2×C4×Q8—31no—
192C2×#103—31no—
193C2×#102—31no—
194#390—31no—
195#340—31no—
196#336—31no—
197C22×C3×C5—42no—
198C22×C3×C5—42no—
199C22×C3×C5—42no—
200C22×C3×C5—81no—
201C22×C3×C5—81no—
202C22×C3×C5—81no—
203C22×C3×C5—81no—
204C22×C3×C5C4×D411yescharacteristic
205C22×C3×C5#12011yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C22×C3×C5C2×SD1611yescharacteristic
208C22×C3×C5#13511yescharacteristic
209C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
210C22×C3×C5#13711yescharacteristic
211C3×C4×C5—24no—
212C3×C4×C5C2×C22⋊C411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12111yescharacteristic
215C3×C4×C5#12311yescharacteristic
216C5×Dic3—22no—
217C5×Dic3—41no—
218C5×Dic3—42no—
219C5×Dic3—81no—
220C24×C3—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8C2×C4×C512yes—
225C2×C3×Q8C5×D412yes—
226C2×C3×Q8C5×D412yes—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4C2×C4×C512yes—
233C22×C3×C4—21no—
234C22×C3×C4C23×C511yescharacteristic
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3C5×D411yescharacteristic
238C22×Dic3C5×D411yescharacteristic
239C3×SD16—28no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8C2×C4×C512yes—
243#217—42no—
244#217—42no—
245C4⋊Dic3—24no—
246C4⋊Dic3—21no—
247C4⋊Dic3—21no—
248C4⋊Dic3—21no—
249C4⋊Dic3C5×D412yes—
250C4×Dic3—24no—
251C4×Dic3—21no—
252C4×Dic3—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256C23×C5—22no—
257C23×C5—41no—
258C23×C5—41no—
259C23×C5—41no—
260C23×C5—41no—
261C23×C5—41no—
262C23×C5—41no—
263C23×C5D3×D411yescharacteristic
264C5×Q8—22no—
265C5×Q8—22no—
266C5×Q8—22no—
267C5×Q8#21714yescomplemented
268C5×D4—22no—
269C5×D4—22no—
270C5×D4—41no—
271C5×D4—41no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5—32no—
276C2×C4×C5—61no—
277C2×C4×C5—61no—
278C2×C4×C5—61no—
279C2×C4×C5—61no—
280C2×C4×C5—62no—
281C2×C4×C5—61no—
282C2×C4×C5—121no—
283C2×C4×C5—121no—
284C2×C4×C5—121no—
285C2×C4×C5—121no—
286C2×C4×C5—121no—
287C2×C4×C5D3×D411yescharacteristic
288C2×C4×C5#23711yescharacteristic
289C2×C4×C5#23711yescharacteristic
290C2×C4×C5C22×Dic311yescharacteristic
291C2×C4×C5C2×#6711yescharacteristic
292C2×C4×C5C2×#6711yescharacteristic
293C5×C8—22no—
294C5×C8—121no—
295C22×Q8C2×C5×D311yescharacteristic
296C22×D4C2×C5×D311yescharacteristic
297C2×SD16—22no—
298C2×SD16—22no—
299C2×SD16C5×Dic314yescomplemented
300C22×C8—31no—
301C22×C8C2×C5×D311yescharacteristic
302C4×Q8—62no—
303C4×Q8—62no—
304C2×C4⋊C4—31no—
305C2×C4⋊C4—31no—
306C2×C4⋊C4—61no—
307C2×C22⋊C4—61no—
308C2×C22⋊C4—61no—
309C2×C42—31no—
310C2×C42—61no—
311#103—62no—
312#102—62no—
313C2×C3×C5—82no—
314C2×C3×C5#38611yescharacteristic
315C2×C3×C5C4×SD1611yescharacteristic
316C2×C3×C5#44011yescharacteristic
317C2×C3×C5#44811yescharacteristic
318C2×C3×C5#44911yescharacteristic
319C2×C3×C5#46011yescharacteristic
320C2×C3×C5#46411yescharacteristic
321C23×C3—22no—
322C23×C3—41no—
323C23×C3—41no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3C2×C5×D411yescharacteristic
329C3×Q8—22no—
330C3×Q8—22no—
331C3×Q8—22no—
332C3×Q8C5×C22⋊C414yescomplemented
333C3×D4—22no—
334C3×D4—22no—
335C3×D4—41no—
336C3×D4—41no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4C22×C4×C511yescharacteristic
341C2×C3×C4C2×C5×D411yescharacteristic
342C2×C3×C4C2×C5×D411yescharacteristic
343C2×C3×C4C2×C5×D411yescharacteristic
344C2×C3×C4C5×#4111yescharacteristic
345C2×C3×C4C5×#4111yescharacteristic
346C2×Dic3—21no—
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—22no—
350C2×Dic3—21no—
351C2×Dic3—21no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354C2×Dic3—41no—
355C2×Dic3—41no—
356C2×Dic3—41no—
357C2×Dic3C5×SD1612yescomplemented
358C3×C8—22no—
359C3⋊C8—41no—
360C22×C5—42no—
361C22×C5—42no—
362C22×C5—42no—
363C22×C5—81no—
364C22×C5—81no—
365C22×C5—81no—
366C22×C5—81no—
367C22×C5D3×SD1611yescharacteristic
368C22×C5#91411yescharacteristic
369C22×C5#91511yescharacteristic
370C22×C5#91611yescharacteristic
371C22×C5D4×Dic311yescharacteristic
372C22×C5#93711yescharacteristic
373C22×C5#93911yescharacteristic
374C4×C5—24no—
375C4×C5—62no—
376C4×C5—121no—
377C4×C5—122no—
378C4×C5—241no—
379C4×C5D4×Dic311yescharacteristic
380C4×C5#93511yescharacteristic
381C4×C5#93911yescharacteristic
382C4×C5C2×#21711yescharacteristic
383C24—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8C2×C5×Dic312yes—
388C2×Q8C5×#6712yes—
389C2×Q8C5×#6712yes—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4C2×C5×Dic312yes—
396C22×C4—21no—
397C22×C4—31no—
398C22×C4—31no—
399C22×C4—61no—
400C22×C4—61no—
401C22×C4C22×C5×D311yescharacteristic
402SD16—28no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—61no—
406C2×C8—61no—
407C2×C8—61no—
408C2×C8C2×C5×Dic312yes—
409C4⋊C4—32no—
410C4⋊C4—64no—
411C4⋊C4—61no—
412C4⋊C4—61no—
413C4⋊C4—61no—
414C22⋊C4—122no—
415C22⋊C4—122no—
416C42—64no—
417C42—61no—
418C42—61no—
419C3×C5#188011yescharacteristic, complemented, Hall
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—81no—
424C22×C3—81no—
425C22×C3—81no—
426C22×C3—81no—
427C22×C3C4×C5×D411yescharacteristic
428C22×C3C5×#12011yescharacteristic
429C22×C3C5×#12111yescharacteristic
430C22×C3C2×C5×SD1611yescharacteristic
431C22×C3C5×#13511yescharacteristic
432C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
433C22×C3C5×#13711yescharacteristic
434C3×C4—24no—
435C3×C4C2×C5×C22⋊C411yescharacteristic
436C3×C4C4×C5×D411yescharacteristic
437C3×C4C5×#12111yescharacteristic
438C3×C4C5×#12311yescharacteristic
439Dic3—22no—
440Dic3—41no—
441Dic3—42no—
442Dic3—81no—
443C2×C5—82no—
444C2×C5Dic3×SD1611yescharacteristic
445C2×C5#516311yescharacteristic
446C2×C5#516411yescharacteristic
447C2×C5#516611yescharacteristic
448C2×C5#517011yescharacteristic
449C2×C5#517211yescharacteristic
450C2×C5#522011yescharacteristic
451C23—22no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23C5×D3×D411yescharacteristic
459Q8—22no—
460Q8—22no—
461Q8—22no—
462Q8C5×#21714yescomplemented
463D4—22no—
464D4—22no—
465D4—41no—
466D4—41no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—32no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—62no—
476C2×C4—61no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4—121no—
481C2×C4—121no—
482C2×C4C5×D3×D411yescharacteristic
483C2×C4C5×#23711yescharacteristic
484C2×C4C5×#23711yescharacteristic
485C2×C4C22×C5×Dic311yescharacteristic
486C2×C4C2×C5×#6711yescharacteristic
487C2×C4C2×C5×#6711yescharacteristic
488C8—22no—
489C8—121no—
490C2×C3—82no—
491C2×C3C5×#38611yescharacteristic
492C2×C3C4×C5×SD1611yescharacteristic
493C2×C3C5×#44011yescharacteristic
494C2×C3C5×#44811yescharacteristic
495C2×C3C5×#44911yescharacteristic
496C2×C3C5×#46011yescharacteristic
497C2×C3C5×#46411yescharacteristic
498C5#7204811yescharacteristic, direct product factor, Sylow
499C22—42no—
500C22—42no—
501C22—42no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22C5×D3×SD1611yescharacteristic
507C22C5×#91411yescharacteristic
508C22C5×#91511yescharacteristic
509C22C5×#91611yescharacteristic
510C22C5×D4×Dic311yescharacteristic
511C22C5×#93711yescharacteristic
512C22C5×#93911yescharacteristic
513C4—24no—
514C4—62no—
515C4—121no—
516C4—122no—
517C4—241no—
518C4C5×D4×Dic311yescharacteristic
519C4C5×#93511yescharacteristic
520C4C5×#93911yescharacteristic
521C4C2×C5×#21711yescharacteristic
522C3C5×#188011yescharacteristic, complemented, Sylow
523C2—82no—
524C2C5×Dic3×SD1611yescharacteristic
525C2C5×#516311yescharacteristic
526C2C5×#516411yescharacteristic
527C2C5×#516611yescharacteristic
528C2C5×#517011yescharacteristic
529C2C5×#517211yescharacteristic
530C2C5×#522011yescharacteristic
subgroupG/H
centerC23×C5D3×D4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC22×C3×C5×SD16C2
socleC23×C3×C5C2×D4
prime radicalC22×C3×C5×D4C22
cosocleC22×C3×C4C23×C5
hypercenterC22×C5×SD16D3
hypocenterC3C5×#1880
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C22×C4×C5 ◁ C22×C5×SD16

Complements

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

NH ≅ G/Ntype
2. C2×C5×Q8×Dic3C2semidirect
3. C2×C5×#835C2semidirect
6. C5×#4551C2semidirect
7. C5×#4550C2semidirect
13. C2×C3×C5×SD16C4semidirect
27. #72048C5direct (N × H)
72. C2×Q8×Dic3C2×C5semidirect
73. C2×#835C2×C5semidirect
76. #4551C2×C5semidirect
77. #4550C2×C5semidirect
82. C2×C5×SD16Dic3semidirect
108. C3×C5×Q8C22⋊C4semidirect
133. C2×C5×Dic3SD16semidirect
140. C2×C3×SD16C4×C5semidirect
267. C5×Q8#217semidirect
299. C2×SD16C5×Dic3semidirect
332. C3×Q8C5×C22⋊C4semidirect
357. C2×Dic3C5×SD16semidirect
419. C3×C5#1880semidirect
462. Q8C5×#217semidirect
498. C5#72048direct (N × H)
522. C3C5×#1880semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C5×SD162
C2×C5×Q8×Dic32
C2×C5×#8352
C5×#52212
C2×C5×#8322
C5×#45512
C5×#45502
C5×#18803
#720485