Finite Group Databasebeta

← C3×#10606415 #14331125

Subgroups — C3×#10606415 #14331125

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4082C211yesmaximal, characteristic
2C3×C5×#386C211yesmaximal, characteristic
3C3×#65509C211yesmaximal, characteristic
4C3×#65499C212yesmaximal, complemented
5C3×#65235C212yesmaximal, complemented
6C3×#65234C212yesmaximal, complemented
7C3×#65233C212yesmaximal, complemented
8C3×#64939C212yesmaximal, complemented
9C3×#64935C212yesmaximal, complemented
10#10606415C311yesmaximal, characteristic, direct product factor, Hall
11C22×C3×C5×D4C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×C3×Dic5C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15C2×C3×C5×C22⋊C4C2211yescharacteristic
16C2×C3×C5×C22⋊C4C2212yes—
17C2×C3×C22⋊Dic5C2212yes—
18C2×C3×C22⋊Dic5C2211yescharacteristic
19C2×C3×C22⋊Dic5C2212yes—
20C2×C3×C22⋊Dic5C2212yes—
21C3×#4082C418yescomplemented
22C2×C3×#683C2212yes—
23C2×C3×#683C2212yes—
24C2×C3×#683C2212yes—
25C2×C3×C4×Dic5C2212yes—
26C2×C3×C4×Dic5C2211yescharacteristic
27C3×C5×#95C2212yes—
28C3×#3963C2212yes—
29C3×#3963C2212yes—
30C3×#3963C2212yes—
31C3×#3963C2212yes—
32C3×#3963C2212yes—
33C3×#2379—51nomaximal, Hall
34C2×#4082C2×C311yescharacteristic
35C5×#386C2×C311yescharacteristic
36#65509C2×C311yescharacteristic
37#65499C2×C312yescomplemented
38#65235C2×C312yescomplemented
39#65234C2×C312yescomplemented
40#65233C2×C312yescomplemented
41#64939C2×C312yescomplemented
42#64935C2×C312yescomplemented
43C24×C3×C5C2311yescharacteristic
44C24×C3×C5C2311yescharacteristic
45C2×C3×C5×D4—41no—
46C2×C3×C5×D4—41no—
47C2×C3×C5×D4C2×C414yes—
48C22×C3×C4×C5—41no—
49C22×C3×C4×C5—42no—
50C22×C3×C4×C5C2312yes—
51C22×C3×C4×C5C2312yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×Dic5—41no—
54C22×C3×Dic5—42no—
55C22×C3×Dic5C2312yes—
56C22×C3×Dic5C2312yes—
57C22×C3×Dic5C2312yes—
58C22×C3×Dic5C2312yes—
59C2×C3×Dic10—41no—
60C2×C3×Dic10—41no—
61C2×C3×Dic10C2×C414yescomplemented
62C3×C5×C22⋊C4—41no—
63C3×C5×C22⋊C4—42no—
64C3×C22⋊Dic5—41no—
65C3×C22⋊Dic5—42no—
66C3×C22⋊Dic5C2×C418yescomplemented
67C3×C22⋊Dic5C2×C418yescomplemented
68C3×#683—42no—
69C3×#683—42no—
70C3×#683—42no—
71C3×C4×Dic5—42no—
72C3×C4×Dic5C2×C414yescomplemented
73C2×C3×#124—51no—
74C3×#391—52no—
75C3×#388—52no—
76C3×#388—52no—
77C3×#386—51no—
78C3×#386D511yescharacteristic
79C3×#385—52no—
80C3×#385—52no—
81C3×#382—52no—
82C22×C5×D4C22×C311yescharacteristic
83C23×C4×C5C22×C311yescharacteristic
84C23×Dic5C22×C311yescharacteristic
85C22×Dic10C22×C311yescharacteristic
86C2×C5×C22⋊C4C22×C311yescharacteristic
87C2×C5×C22⋊C4C22×C312yes—
88C2×C22⋊Dic5C22×C312yes—
89C2×C22⋊Dic5C22×C311yescharacteristic
90C2×C22⋊Dic5C22×C312yes—
91C2×C22⋊Dic5C22×C312yes—
92#4082C3×C418yescomplemented
93C2×#683C22×C312yes—
94C2×#683C22×C312yes—
95C2×#683C22×C312yes—
96C2×C4×Dic5C22×C312yes—
97C2×C4×Dic5C22×C311yescharacteristic
98C5×#95C22×C312yes—
99#3963C22×C312yes—
100#3963C22×C312yes—
101#3963C22×C312yes—
102#3963C22×C312yes—
103#3963C22×C312yes—
104#2379—51noSylow
105C23×C3×C5—22no—
106C23×C3×C5—21no—
107C23×C3×C5—22no—
108C23×C3×C5—21no—
109C23×C3×C5—21no—
110C23×C3×C5—21no—
111C23×C3×C5—22no—
112C23×C3×C5—22no—
113C23×C3×C5C22×C412yes—
114C23×C3×C5C22×C412yes—
115C23×C3×C5C2411yescharacteristic
116C3×C5×D4—44no—
117C2×C3×C4×C5—21no—
118C2×C3×C4×C5—21no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—44no—
126C2×C3×C4×C5C22×C412yes—
127C2×C3×Dic5—22no—
128C2×C3×Dic5—22no—
129C2×C3×Dic5—22no—
130C2×C3×Dic5—22no—
131C2×C3×Dic5—22no—
132C2×C3×Dic5—22no—
133C2×C3×Dic5—22no—
134C2×C3×Dic5—22no—
135C2×C3×Dic5—22no—
136C2×C3×Dic5—22no—
137C2×C3×Dic5—44no—
138C2×C3×Dic5C22×C414yes—
139C2×C3×Dic5C22×C414yes—
140C3×Dic10—44no—
141C22×C3×Q8—51no—
142C22×C3×D4C2×D511yescharacteristic
143C23×C3×C4—51no—
144C23×C3×C4C2×D511yescharacteristic
145C3×#124—58no—
146C2×C3×C4⋊C4—52no—
147C2×C3×C4⋊C4—52no—
148C2×C3×C4⋊C4—52no—
149C2×C3×C22⋊C4—52no—
150C2×C3×C22⋊C4—52no—
151C2×C3×C22⋊C4—52no—
152C2×C3×C22⋊C4—51no—
153C2×C3×C22⋊C4C2×D512yes—
154C2×C3×C22⋊C4C2×D511yescharacteristic
155C2×C3×C42—51no—
156C2×C3×C42—52no—
157C3×#95—52no—
158C3×#95—52no—
159C3×#95—52no—
160C3×#95—52no—
161C3×#95—52no—
162C3×#95C2×D512yes—
163C24×C5C23×C311yescharacteristic
164C24×C5C23×C311yescharacteristic
165C2×C5×D4—41no—
166C2×C5×D4—41no—
167C2×C5×D4C2×C3×C414yes—
168C22×C4×C5—41no—
169C22×C4×C5—42no—
170C22×C4×C5C23×C312yes—
171C22×C4×C5C23×C312yes—
172C22×C4×C5C23×C311yescharacteristic
173C22×Dic5—41no—
174C22×Dic5—42no—
175C22×Dic5C23×C312yes—
176C22×Dic5C23×C312yes—
177C22×Dic5C23×C312yes—
178C22×Dic5C23×C312yes—
179C2×Dic10—41no—
180C2×Dic10—41no—
181C2×Dic10C2×C3×C414yescomplemented
182C5×C22⋊C4—41no—
183C5×C22⋊C4—42no—
184C22⋊Dic5—41no—
185C22⋊Dic5—42no—
186C22⋊Dic5C2×C3×C418yescomplemented
187C22⋊Dic5C2×C3×C418yescomplemented
188#683—42no—
189#683—42no—
190#683—42no—
191C4×Dic5—42no—
192C4×Dic5C2×C3×C414yescomplemented
193C2×#124—51no—
194#391—52no—
195#388—52no—
196#388—52no—
197#386—51no—
198#386C3×D511yescharacteristic
199#385—52no—
200#385—52no—
201#382—52no—
202C22×C3×C5—22no—
203C22×C3×C5—22no—
204C22×C3×C5—24no—
205C22×C3×C5—24no—
206C22×C3×C5—41no—
207C22×C3×C5—41no—
208C22×C3×C5—42no—
209C22×C3×C5—42no—
210C22×C3×C5—41no—
211C22×C3×C5—41no—
212C22×C3×C5C23×C411yescharacteristic
213C22×C3×C5H(5,𝔽2)11yescharacteristic
214C22×C3×C5H(5,𝔽2)11yescharacteristic
215C22×C3×C5H(5,𝔽2)12yes—
216C22×C3×C52−1+412yes—
217C3×C4×C5—22no—
218C3×C4×C5—42no—
219C3×C4×C5—42no—
220C3×Dic5—24no—
221C3×Dic5—24no—
222C3×Dic5—42no—
223C3×Dic5—42no—
224C24×C3C22×D511yescharacteristic
225C24×C3C22×D511yescharacteristic
226C2×C3×Q8—54no—
227C2×C3×Q8—201no—
228C2×C3×Q8—201no—
229C2×C3×D4—41no—
230C2×C3×D4—41no—
231C2×C3×D4C4×D514yes—
232C22×C3×C4—42no—
233C22×C3×C4—41no—
234C22×C3×C4—52no—
235C22×C3×C4—52no—
236C22×C3×C4—52no—
237C22×C3×C4—52no—
238C22×C3×C4—202no—
239C22×C3×C4—201no—
240C22×C3×C4C22×D512yes—
241C22×C3×C4C22×D512yes—
242C22×C3×C4C22×D511yescharacteristic
243C3×C4⋊C4—202no—
244C3×C4⋊C4—202no—
245C3×C4⋊C4—202no—
246C3×C22⋊C4—41no—
247C3×C22⋊C4—42no—
248C3×C22⋊C4—58no—
249C3×C22⋊C4—58no—
250C3×C22⋊C4—201no—
251C3×C22⋊C4—202no—
252C3×C42—54no—
253C3×C42—202no—
254C23×C5—22no—
255C23×C5—21no—
256C23×C5—22no—
257C23×C5—21no—
258C23×C5—21no—
259C23×C5—21no—
260C23×C5—22no—
261C23×C5—22no—
262C23×C5C22×C3×C412yes—
263C23×C5C22×C3×C412yes—
264C23×C5C24×C311yescharacteristic
265C5×D4—44no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—44no—
275C2×C4×C5C22×C3×C412yes—
276C2×Dic5—22no—
277C2×Dic5—22no—
278C2×Dic5—22no—
279C2×Dic5—22no—
280C2×Dic5—22no—
281C2×Dic5—22no—
282C2×Dic5—22no—
283C2×Dic5—22no—
284C2×Dic5—22no—
285C2×Dic5—22no—
286C2×Dic5—44no—
287C2×Dic5C22×C3×C414yes—
288C2×Dic5C22×C3×C414yes—
289Dic10—44no—
290C22×Q8—51no—
291C22×D4C2×C3×D511yescharacteristic
292C23×C4—51no—
293C23×C4C2×C3×D511yescharacteristic
294#124—58no—
295C2×C4⋊C4—52no—
296C2×C4⋊C4—52no—
297C2×C4⋊C4—52no—
298C2×C22⋊C4—52no—
299C2×C22⋊C4—52no—
300C2×C22⋊C4—52no—
301C2×C22⋊C4—51no—
302C2×C22⋊C4C2×C3×D512yes—
303C2×C22⋊C4C2×C3×D511yescharacteristic
304C2×C42—51no—
305C2×C42—52no—
306#95—52no—
307#95—52no—
308#95—52no—
309#95—52no—
310#95—52no—
311#95C2×C3×D512yes—
312C2×C3×C5—42no—
313C2×C3×C5—42no—
314C2×C3×C5#51811yescharacteristic
315C2×C3×C5#52012yes—
316C2×C3×C5H(3,𝔽4)11yescharacteristic
317C2×C3×C5#56212yes—
318C2×C3×C5#56311yescharacteristic
319C23×C3—22no—
320C23×C3—21no—
321C23×C3—22no—
322C23×C3—21no—
323C23×C3—21no—
324C23×C3—21no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3C2×C4×D512yes—
328C23×C3C2×C4×D512yes—
329C23×C3C23×D511yescharacteristic
330C3×Q8—204no—
331C3×D4—44no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—44no—
341C2×C3×C4—54no—
342C2×C3×C4—54no—
343C2×C3×C4—102no—
344C2×C3×C4—102no—
345C2×C3×C4—102no—
346C2×C3×C4—102no—
347C2×C3×C4—102no—
348C2×C3×C4—102no—
349C2×C3×C4—102no—
350C2×C3×C4—102no—
351C2×C3×C4—102no—
352C2×C3×C4—102no—
353C2×C3×C4—204no—
354C2×C3×C4C2×C4×D512yes—
355C22×C5—22no—
356C22×C5—22no—
357C22×C5—24no—
358C22×C5—24no—
359C22×C5—41no—
360C22×C5—41no—
361C22×C5—42no—
362C22×C5—42no—
363C22×C5—41no—
364C22×C5—41no—
365C22×C5C23×C3×C411yescharacteristic
366C22×C5C3×H(5,𝔽2)12yes—
367C22×C5C3×H(5,𝔽2)11yescharacteristic
368C22×C5C3×H(5,𝔽2)11yescharacteristic
369C22×C5C3×2−1+412yes—
370C4×C5—22no—
371C4×C5—42no—
372C4×C5—42no—
373Dic5—24no—
374Dic5—24no—
375Dic5—42no—
376Dic5—42no—
377C24C22×C3×D511yescharacteristic
378C24C22×C3×D511yescharacteristic
379C2×Q8—54no—
380C2×Q8—201no—
381C2×Q8—201no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4C3×C4×D514yes—
385C22×C4—42no—
386C22×C4—41no—
387C22×C4—52no—
388C22×C4—52no—
389C22×C4—52no—
390C22×C4—52no—
391C22×C4—202no—
392C22×C4—201no—
393C22×C4C22×C3×D512yes—
394C22×C4C22×C3×D512yes—
395C22×C4C22×C3×D511yescharacteristic
396C4⋊C4—202no—
397C4⋊C4—202no—
398C4⋊C4—202no—
399C22⋊C4—41no—
400C22⋊C4—42no—
401C22⋊C4—58no—
402C22⋊C4—58no—
403C22⋊C4—201no—
404C22⋊C4—202no—
405C42—54no—
406C42—202no—
407C3×C5#237911yescharacteristic, complemented, Hall
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—24no—
411C22×C3—24no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3—41no—
417C22×C3—41no—
418C22×C3C22×C4×D511yescharacteristic
419C22×C3#414411yescharacteristic
420C22×C3#414411yescharacteristic
421C22×C3#414412yes—
422C22×C3#415012yes—
423C3×C4—22no—
424C3×C4—42no—
425C3×C4—42no—
426C3×C4—104no—
427C3×C4—104no—
428C3×C4—202no—
429C3×C4—202no—
430C2×C5—42no—
431C2×C5—42no—
432C2×C5C3×#51811yescharacteristic
433C2×C5C3×#52012yes—
434C2×C5C3×H(3,𝔽4)11yescharacteristic
435C2×C5C3×#56212yes—
436C2×C5C3×#56311yescharacteristic
437C23—22no—
438C23—21no—
439C23—22no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—22no—
444C23—22no—
445C23C2×C3×C4×D512yes—
446C23C2×C3×C4×D512yes—
447C23C23×C3×D511yescharacteristic
448Q8—204no—
449D4—44no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—44no—
459C2×C4—54no—
460C2×C4—54no—
461C2×C4—102no—
462C2×C4—102no—
463C2×C4—102no—
464C2×C4—102no—
465C2×C4—102no—
466C2×C4—102no—
467C2×C4—102no—
468C2×C4—102no—
469C2×C4—102no—
470C2×C4—102no—
471C2×C4—204no—
472C2×C4C2×C3×C4×D512yes—
473C2×C3—42no—
474C2×C3—42no—
475C2×C3#6582011yescharacteristic
476C2×C3#6588012yes—
477C2×C3#6592811yescharacteristic
478C2×C3#6595512yes—
479C2×C3#6598511yescharacteristic
480C5C3×#237911yescharacteristic, complemented, Sylow
481C22—24no—
482C22—24no—
483C22—22no—
484C22—22no—
485C22—41no—
486C22—41no—
487C22—42no—
488C22—42no—
489C22—41no—
490C22—41no—
491C22C22×C3×C4×D511yescharacteristic
492C22C3×#414412yes—
493C22C3×#414411yescharacteristic
494C22C3×#414411yescharacteristic
495C22C3×#415012yes—
496C4—22no—
497C4—42no—
498C4—42no—
499C4—104no—
500C4—104no—
501C4—202no—
502C4—202no—
503C3#1060641511yescharacteristic, direct product factor, Sylow
504C2—42no—
505C2—42no—
506C2C3×#6582011yescharacteristic
507C2C3×#6588012yes—
508C2C3×#6592811yescharacteristic
509C2C3×#6595512yes—
510C2C3×#6598511yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#386C2
socleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
cosocleC23×C5C24×C3
hypercenterC3×#386D5
hypocenterC5C3×#2379
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
4. C3×#65499C2semidirect
5. C3×#65235C2semidirect
6. C3×#65234C2semidirect
7. C3×#65233C2semidirect
8. C3×#64939C2semidirect
9. C3×#64935C2semidirect
10. #10606415C3direct (N × H)
21. C3×#4082C4semidirect
37. #65499C2×C3semidirect
38. #65235C2×C3semidirect
39. #65234C2×C3semidirect
40. #65233C2×C3semidirect
41. #64939C2×C3semidirect
42. #64935C2×C3semidirect
61. C2×C3×Dic10C2×C4semidirect
66. C3×C22⋊Dic5C2×C4semidirect
67. C3×C22⋊Dic5C2×C4semidirect
72. C3×C4×Dic5C2×C4semidirect
92. #4082C3×C4semidirect
181. C2×Dic10C2×C3×C4semidirect
186. C22⋊Dic5C2×C3×C4semidirect
187. C22⋊Dic5C2×C3×C4semidirect
192. C4×Dic5C2×C3×C4semidirect
407. C3×C5#2379semidirect
480. C5C3×#2379semidirect
503. C3#10606415direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40822
C3×C5×#3862
C3×#655092
C3×#654992
C3×#652352
C3×#652342
C3×#652332
C3×#649392
C3×#649352
#106064153
C3×#23795