Finite Group Databasebeta

← C5×#71670 #14302044

Subgroups — C5×#71670 #14302044

Order 1920.

1196 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#120C211yesmaximal, characteristic
2C22×C5×#217C211yesmaximal, characteristic, complemented
3C5×#5247C211yesmaximal, characteristic, complemented
4C2×C5×#834C212yesmaximal, complemented
5C5×#4526C212yesmaximal, complemented
6C5×#1898—31nomaximal, Hall
7C25×C3×C5C2211yescharacteristic
8C22×C3×C5×D4C412yescomplemented
9C22×C3×C5×D4C2211yescharacteristic
10C23×C5×Dic3—21no—
11C3×C5×#120—21no—
12C3×C5×#120—22no—
13C3×C5×#120—21no—
14C2×C3×C5×C22⋊C4C412yescomplemented
15C2×C3×C5×C22⋊C4C2211yescharacteristic
16C2×C5×#217—21no—
17C2×C5×#217—24no—
18C2×C5×#217—22no—
19C2×C5×#217C2212yes—
20C2×C5×#217C2212yes—
21C5×#834—24no—
22#71670C511yesmaximal, characteristic, direct product factor, Hall
23C2×C5×#120D311yescharacteristic
24C22×C5×C22⋊C4—31no—
25C2×C5×#99—32no—
26C5×#379—31no—
27C5×#342—32no—
28C24×C3×C5—22no—
29C24×C3×C5—22no—
30C24×C3×C5—44no—
31C24×C3×C5C2×C412yes—
32C24×C3×C5C2×C411yescharacteristic, complemented
33C24×C3×C5D411yescharacteristic
34C24×C3×C5D412yes—
35C24×C3×C5D411yescharacteristic
36C24×C3×C5C2311yescharacteristic
37C2×C3×C5×D4—22no—
38C2×C3×C5×D4—22no—
39C2×C3×C5×D4—22no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4—22no—
43C2×C3×C5×D4—44no—
44C22×C3×C4×C5C2×C411yescharacteristic, complemented
45C22×C3×C4×C5C2×C412yescomplemented
46C22×C5×Dic3—24no—
47C22×C5×Dic3—22no—
48C22×C5×Dic3—22no—
49C22×C5×Dic3—44no—
50C3×C5×C22⋊C4—22no—
51C3×C5×C22⋊C4—22no—
52C3×C5×C22⋊C4—21no—
53C3×C5×C22⋊C4—21no—
54C5×#217—24no—
55C5×#217—22no—
56C5×#217—22no—
57C5×#217—22no—
58C5×#217—44no—
59C5×#217D414yescomplemented
60C2×C3×#120C2×C511yescharacteristic
61C22×#217C2×C511yescharacteristic, complemented
62#5247C2×C511yescharacteristic, complemented
63C2×#834C2×C512yescomplemented
64#4526C2×C512yescomplemented
65C25×C5C2×D311yescharacteristic
66C22×C5×D4Dic312yescomplemented
67C22×C5×D4C2×D311yescharacteristic
68C23×C4×C5—61no—
69C5×#120—21no—
70C5×#120—22no—
71C5×#120—21no—
72C2×C5×C22⋊C4—32no—
73C2×C5×C22⋊C4—32no—
74C2×C5×C22⋊C4—64no—
75C2×C5×C22⋊C4—61no—
76C2×C5×C22⋊C4—62no—
77C2×C5×C22⋊C4Dic312yescomplemented
78C2×C5×C22⋊C4C2×D311yescharacteristic
79C5×#99—64no—
80#1898—31noSylow
81C23×C3×C5—24no—
82C23×C3×C5—21no—
83C23×C3×C5—21no—
84C23×C3×C5—24no—
85C23×C3×C5—24no—
86C23×C3×C5—24no—
87C23×C3×C5—21no—
88C23×C3×C5—24no—
89C23×C3×C5—21no—
90C23×C3×C5—21no—
91C23×C3×C5—22no—
92C23×C3×C5—42no—
93C23×C3×C5—42no—
94C23×C3×C5—42no—
95C23×C3×C5—42no—
96C23×C3×C5—48no—
97C23×C3×C5—48no—
98C23×C3×C5—42no—
99C23×C3×C5C22⋊C412yes—
100C23×C3×C5C22⋊C412yes—
101C23×C3×C5C22×C411yescharacteristic
102C23×C3×C5C2×D411yescharacteristic
103C23×C3×C5C2×D411yescharacteristic
104C23×C3×C5C2×D412yes—
105C23×C3×C5#4112yes—
106C3×C5×D4—44no—
107C3×C5×D4—44no—
108C3×C5×D4—41no—
109C3×C5×D4—42no—
110C3×C5×D4—41no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—22no—
113C2×C3×C4×C5—22no—
114C2×C3×C4×C5—42no—
115C2×C5×Dic3—24no—
116C2×C5×Dic3—48no—
117C2×C5×Dic3—44no—
118C2×C5×Dic3—44no—
119C2×C5×Dic3—42no—
120C25×C3C22×C511yescharacteristic
121C22×C3×D4C4×C512yescomplemented
122C22×C3×D4C22×C511yescharacteristic
123C23×Dic3—21no—
124C3×#120—21no—
125C3×#120—22no—
126C3×#120—21no—
127C2×C3×C22⋊C4C4×C512yescomplemented
128C2×C3×C22⋊C4C22×C511yescharacteristic
129C2×#217—21no—
130C2×#217—24no—
131C2×#217—22no—
132C2×#217C22×C512yes—
133C2×#217C22×C512yes—
134#834—24no—
135C24×C5—22no—
136C24×C5—22no—
137C24×C5—44no—
138C24×C5C2×Dic312yes—
139C24×C5C2×Dic311yescharacteristic, complemented
140C24×C5#6711yescharacteristic
141C24×C5#6712yes—
142C24×C5#6711yescharacteristic
143C24×C5C22×D311yescharacteristic
144C2×C5×D4—22no—
145C2×C5×D4—22no—
146C2×C5×D4—22no—
147C2×C5×D4—22no—
148C2×C5×D4—21no—
149C2×C5×D4—21no—
150C2×C5×D4—44no—
151C22×C4×C5—64no—
152C22×C4×C5—62no—
153C22×C4×C5—62no—
154C22×C4×C5—124no—
155C22×C4×C5C2×Dic311yescharacteristic, complemented
156C22×C4×C5C2×Dic312yescomplemented
157C5×C22⋊C4—22no—
158C5×C22⋊C4—22no—
159C5×C22⋊C4—21no—
160C5×C22⋊C4—21no—
161C5×C22⋊C4—34no—
162C5×C22⋊C4—64no—
163C5×C22⋊C4—62no—
164C5×C22⋊C4—62no—
165C5×C22⋊C4—62no—
166C5×C22⋊C4—124no—
167C2×#120C5×D311yescharacteristic
168C22×C22⋊C4—31no—
169C2×#99—32no—
170#379—31no—
171#342—32no—
172C22×C3×C5—24no—
173C22×C3×C5—24no—
174C22×C3×C5—22no—
175C22×C3×C5—22no—
176C22×C3×C5—22no—
177C22×C3×C5—22no—
178C22×C3×C5—22no—
179C22×C3×C5—22no—
180C22×C3×C5—22no—
181C22×C3×C5—22no—
182C22×C3×C5—42no—
183C22×C3×C5—42no—
184C22×C3×C5—48no—
185C22×C3×C5—48no—
186C22×C3×C5—42no—
187C22×C3×C5—42no—
188C22×C3×C5—41no—
189C22×C3×C5—42no—
190C22×C3×C5—82no—
191C22×C3×C5#9914yescomplemented
192C22×C3×C5C2×C22⋊C411yescharacteristic
193C22×C3×C5C4×D412yes—
194C22×C3×C5#12011yescharacteristic
195C22×C3×C5#12112yes—
196C22×C3×C5#12311yescharacteristic
197C3×C4×C5—41no—
198C3×C4×C5—42no—
199C5×Dic3—44no—
200C5×Dic3—82no—
201C24×C3—22no—
202C24×C3—22no—
203C24×C3—44no—
204C24×C3C2×C4×C512yes—
205C24×C3C2×C4×C511yescharacteristic, complemented
206C24×C3C5×D411yescharacteristic
207C24×C3C5×D412yes—
208C24×C3C5×D411yescharacteristic
209C24×C3C23×C511yescharacteristic
210C2×C3×D4—22no—
211C2×C3×D4—22no—
212C2×C3×D4—22no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—22no—
216C2×C3×D4—44no—
217C22×C3×C4C2×C4×C511yescharacteristic, complemented
218C22×C3×C4C2×C4×C512yescomplemented
219C22×Dic3—24no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—44no—
223C3×C22⋊C4—22no—
224C3×C22⋊C4—22no—
225C3×C22⋊C4—21no—
226C3×C22⋊C4—21no—
227#217—24no—
228#217—22no—
229#217—22no—
230#217—22no—
231#217—44no—
232#217C5×D414yescomplemented
233C23×C5—24no—
234C23×C5—21no—
235C23×C5—21no—
236C23×C5—24no—
237C23×C5—24no—
238C23×C5—24no—
239C23×C5—21no—
240C23×C5—21no—
241C23×C5—24no—
242C23×C5—21no—
243C23×C5—22no—
244C23×C5—42no—
245C23×C5—42no—
246C23×C5—42no—
247C23×C5—42no—
248C23×C5—48no—
249C23×C5—48no—
250C23×C5—42no—
251C23×C5#21712yes—
252C23×C5#21712yes—
253C23×C5D3×D412yes—
254C23×C5#23712yes—
255C23×C5C22×Dic311yescharacteristic
256C23×C5C2×#6711yescharacteristic
257C23×C5C2×#6711yescharacteristic
258C5×D4—44no—
259C5×D4—44no—
260C5×D4—41no—
261C5×D4—41no—
262C5×D4—42no—
263C2×C4×C5—22no—
264C2×C4×C5—22no—
265C2×C4×C5—21no—
266C2×C4×C5—42no—
267C2×C4×C5—64no—
268C2×C4×C5—128no—
269C2×C4×C5—124no—
270C2×C4×C5—124no—
271C2×C4×C5—122no—
272C25C2×C5×D311yescharacteristic
273C22×D4C5×Dic312yescomplemented
274C22×D4C2×C5×D311yescharacteristic
275C23×C4—61no—
276#120—21no—
277#120—22no—
278#120—21no—
279C2×C22⋊C4—32no—
280C2×C22⋊C4—32no—
281C2×C22⋊C4—64no—
282C2×C22⋊C4—61no—
283C2×C22⋊C4—62no—
284C2×C22⋊C4C5×Dic312yescomplemented
285C2×C22⋊C4C2×C5×D311yescharacteristic
286#99—64no—
287C2×C3×C5—21no—
288C2×C3×C5—22no—
289C2×C3×C5—24no—
290C2×C3×C5—21no—
291C2×C3×C5—22no—
292C2×C3×C5—42no—
293C2×C3×C5—81no—
294C2×C3×C5#38611yescharacteristic
295C2×C3×C5C2×#9912yes—
296C23×C3—21no—
297C23×C3—21no—
298C23×C3—24no—
299C23×C3—24no—
300C23×C3—21no—
301C23×C3—24no—
302C23×C3—21no—
303C23×C3—24no—
304C23×C3—24no—
305C23×C3—21no—
306C23×C3—22no—
307C23×C3—42no—
308C23×C3—42no—
309C23×C3—42no—
310C23×C3—42no—
311C23×C3—48no—
312C23×C3—48no—
313C23×C3—42no—
314C23×C3C5×C22⋊C412yes—
315C23×C3C5×C22⋊C412yes—
316C23×C3C22×C4×C511yescharacteristic
317C23×C3C2×C5×D412yes—
318C23×C3C2×C5×D411yescharacteristic
319C23×C3C2×C5×D411yescharacteristic
320C23×C3C5×#4112yes—
321C3×D4—44no—
322C3×D4—41no—
323C3×D4—42no—
324C3×D4—41no—
325C3×D4—44no—
326C2×C3×C4—21no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—42no—
330C2×Dic3—24no—
331C2×Dic3—48no—
332C2×Dic3—44no—
333C2×Dic3—44no—
334C2×Dic3—42no—
335C22×C5—24no—
336C22×C5—24no—
337C22×C5—22no—
338C22×C5—22no—
339C22×C5—22no—
340C22×C5—22no—
341C22×C5—22no—
342C22×C5—22no—
343C22×C5—22no—
344C22×C5—22no—
345C22×C5—42no—
346C22×C5—42no—
347C22×C5—48no—
348C22×C5—48no—
349C22×C5—42no—
350C22×C5—42no—
351C22×C5—42no—
352C22×C5—41no—
353C22×C5—82no—
354C22×C5#83414yescomplemented
355C22×C5D4×Dic312yes—
356C22×C5#93511yescharacteristic
357C22×C5#93711yescharacteristic
358C22×C5#93912yes—
359C22×C5C2×#21711yescharacteristic
360C4×C5—42no—
361C4×C5—41no—
362C4×C5—124no—
363C4×C5—242no—
364C24—22no—
365C24—22no—
366C24—44no—
367C24C2×C5×Dic312yes—
368C24C2×C5×Dic311yescharacteristic, complemented
369C24C5×#6711yescharacteristic
370C24C5×#6712yes—
371C24C5×#6711yescharacteristic
372C24C22×C5×D311yescharacteristic
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—44no—
380C22×C4—64no—
381C22×C4—62no—
382C22×C4—62no—
383C22×C4—124no—
384C22×C4C2×C5×Dic311yescharacteristic, complemented
385C22×C4C2×C5×Dic312yescomplemented
386C22⋊C4—22no—
387C22⋊C4—22no—
388C22⋊C4—21no—
389C22⋊C4—21no—
390C22⋊C4—34no—
391C22⋊C4—64no—
392C22⋊C4—62no—
393C22⋊C4—62no—
394C22⋊C4—62no—
395C22⋊C4—124no—
396C3×C5#189811yescharacteristic, complemented, Hall
397C22×C3—24no—
398C22×C3—24no—
399C22×C3—22no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—22no—
403C22×C3—22no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—48no—
410C22×C3—48no—
411C22×C3—42no—
412C22×C3—42no—
413C22×C3—41no—
414C22×C3—42no—
415C22×C3—82no—
416C22×C3C5×#9914yescomplemented
417C22×C3C2×C5×C22⋊C411yescharacteristic
418C22×C3C4×C5×D412yes—
419C22×C3C5×#12011yescharacteristic
420C22×C3C5×#12112yes—
421C22×C3C5×#12311yescharacteristic
422C3×C4—41no—
423C3×C4—42no—
424Dic3—44no—
425Dic3—82no—
426C2×C5—21no—
427C2×C5—22no—
428C2×C5—24no—
429C2×C5—21no—
430C2×C5—22no—
431C2×C5—42no—
432C2×C5—81no—
433C2×C5C2×#83412yes—
434C2×C5#522011yescharacteristic
435C23—21no—
436C23—21no—
437C23—24no—
438C23—24no—
439C23—21no—
440C23—21no—
441C23—24no—
442C23—24no—
443C23—24no—
444C23—21no—
445C23—22no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—48no—
451C23—48no—
452C23—42no—
453C23C5×#21712yes—
454C23C5×#21712yes—
455C23C5×D3×D412yes—
456C23C5×#23712yes—
457C23C22×C5×Dic311yescharacteristic
458C23C2×C5×#6711yescharacteristic
459C23C2×C5×#6711yescharacteristic
460D4—44no—
461D4—41no—
462D4—41no—
463D4—42no—
464D4—44no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—42no—
469C2×C4—64no—
470C2×C4—128no—
471C2×C4—124no—
472C2×C4—124no—
473C2×C4—122no—
474C2×C3—21no—
475C2×C3—22no—
476C2×C3—21no—
477C2×C3—24no—
478C2×C3—22no—
479C2×C3—42no—
480C2×C3—81no—
481C2×C3C5×#38611yescharacteristic
482C2×C3C2×C5×#9912yes—
483C5#7167011yescharacteristic, direct product factor, Sylow
484C22—24no—
485C22—24no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—42no—
495C22—42no—
496C22—48no—
497C22—48no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—41no—
502C22—82no—
503C22C5×#83414yescomplemented
504C22C5×D4×Dic312yes—
505C22C5×#93511yescharacteristic
506C22C5×#93711yescharacteristic
507C22C5×#93912yes—
508C22C2×C5×#21711yescharacteristic
509C4—42no—
510C4—41no—
511C4—124no—
512C4—242no—
513C3C5×#189811yescharacteristic, complemented, Sylow
514C2—21no—
515C2—22no—
516C2—21no—
517C2—24no—
518C2—22no—
519C2—42no—
520C2—81no—
521C2C2×C5×#83412yes—
522C2C5×#522011yescharacteristic
subgroupG/H
centerC22×C5C2×#217
commutatorC23×C3C22×C4×C5
FrattiniC24C22×C5×D3
Fitting, prime radicalC2×C3×C5×#120C2
socleC22×C3×C5C2×C22⋊C4
cosocleC24×C3C23×C5
hypercenterC2×C5×#120D3
hypocenterC3C5×#1898
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C25×C5 ◁ C2×C5×#120

Complements

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

NH ≅ G/Ntype
2. C22×C5×#217C2semidirect
3. C5×#5247C2semidirect
4. C2×C5×#834C2semidirect
5. C5×#4526C2semidirect
8. C22×C3×C5×D4C4semidirect
14. C2×C3×C5×C22⋊C4C4semidirect
22. #71670C5direct (N × H)
32. C24×C3×C5C2×C4semidirect
44. C22×C3×C4×C5C2×C4semidirect
45. C22×C3×C4×C5C2×C4semidirect
59. C5×#217D4semidirect
61. C22×#217C2×C5semidirect
62. #5247C2×C5semidirect
63. C2×#834C2×C5semidirect
64. #4526C2×C5semidirect
66. C22×C5×D4Dic3semidirect
77. C2×C5×C22⋊C4Dic3semidirect
121. C22×C3×D4C4×C5semidirect
127. C2×C3×C22⋊C4C4×C5semidirect
139. C24×C5C2×Dic3semidirect
155. C22×C4×C5C2×Dic3semidirect
156. C22×C4×C5C2×Dic3semidirect
191. C22×C3×C5#99semidirect
205. C24×C3C2×C4×C5semidirect
217. C22×C3×C4C2×C4×C5semidirect
218. C22×C3×C4C2×C4×C5semidirect
232. #217C5×D4semidirect
273. C22×D4C5×Dic3semidirect
284. C2×C22⋊C4C5×Dic3semidirect
354. C22×C5#834semidirect
368. C24C2×C5×Dic3semidirect
384. C22×C4C2×C5×Dic3semidirect
385. C22×C4C2×C5×Dic3semidirect
396. C3×C5#1898semidirect
416. C22×C3C5×#99semidirect
483. C5#71670direct (N × H)
503. C22C5×#834semidirect
513. C3C5×#1898semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1202
C22×C5×#2172
C5×#52472
C2×C5×#8342
C5×#45262
C5×#18983
#716705