Finite Group Databasebeta

← C3×#10599666 #14298491

Subgroups — C3×#10599666 #14298491

Order 1920.

600 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4038C211yesmaximal, characteristic
2C2×C3×#3952C211yesmaximal, characteristic
3C3×#65276C211yesmaximal, characteristic
4C3×C5×#340C211yesmaximal, characteristic, complemented
5C3×#64771C211yesmaximal, characteristic, complemented
6C3×#64749C211yesmaximal, characteristic, complemented
7C3×#64749C211yesmaximal, characteristic, complemented
8#10599666C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3×#685—21no—
14C2×C3×#685—21no—
15C2×C3×C4⋊Dic5C2211yescharacteristic
16C2×C3×C4⋊Dic5C2211yescharacteristic
17C2×C3×C4×Dic5—21no—
18C22×C3×#168C2211yescharacteristic
19C3×#4038—22no—
20C3×#4038C414yescomplemented
21C3×#3963—21no—
22C3×#3952—22no—
23C3×#1825—51nomaximal, Hall
24C2×#4038C2×C311yescharacteristic
25C2×#3952C2×C311yescharacteristic
26#65276C2×C311yescharacteristic
27C5×#340C2×C311yescharacteristic, complemented
28#64771C2×C311yescharacteristic, complemented
29#64749C2×C311yescharacteristic, complemented
30#64749C2×C311yescharacteristic, complemented
31C23×C3×D5D411yescharacteristic
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5C2311yescharacteristic
35C22×C3×Dic5—21no—
36C22×C3×Dic5—21no—
37C22×C3×Dic5D411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5—21no—
40C2×C3×C4×D5—21no—
41C2×C3×C4×D5—21no—
42C2×C3×C4×D5C2×C412yes—
43C2×C3×C4×D5D412yes—
44C2×C3×C5×C8—21no—
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4C2×C412yes—
51C3×#685—24no—
52C3×#685—42no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5C2×C412yes—
57C3×C4×Dic5—24no—
58C2×C3×#168—21no—
59C2×C3×#168—21no—
60C2×C3×#168—21no—
61C2×C3×#117—51no—
62C2×C3×C22⋊C8—51no—
63C3×#380—51no—
64C3×#340—51no—
65C3×#340—51no—
66C3×#340—51no—
67C3×#340D511yescharacteristic, complemented
68C22×C4×D5C22×C311yescharacteristic
69C22×C5×C8C22×C311yescharacteristic
70C2×C5×C4⋊C4C22×C311yescharacteristic
71C2×C5×C4⋊C4C22×C311yescharacteristic
72C2×#685—21no—
73C2×#685—21no—
74C2×C4⋊Dic5C22×C311yescharacteristic
75C2×C4⋊Dic5C22×C311yescharacteristic
76C2×C4×Dic5—21no—
77C22×#168C22×C311yescharacteristic
78#4038—22no—
79#4038C3×C414yescomplemented
80#3963—21no—
81#3952—22no—
82#1825—51noSylow
83C23×C3×C5C2×D411yescharacteristic
84C22×C3×D5—21no—
85C22×C3×D5—21no—
86C22×C3×D5—21no—
87C22×C3×D5—21no—
88C22×C3×D5—21no—
89C22×C3×D5—21no—
90C22×C3×D5C22⋊C412yes—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5#4111yescharacteristic
100C2×C3×C4×C5#4111yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×Dic5—21no—
104C2×C3×Dic5—21no—
105C2×C3×Dic5—22no—
106C2×C3×Dic5—41no—
107C2×C3×Dic5—41no—
108C2×C3×Dic5—41no—
109C2×C3×Dic5—41no—
110C2×C3×Dic5—41no—
111C2×C3×Dic5C22⋊C412yes—
112C3×C4×D5—22no—
113C3×C4×D5—22no—
114C3×C4×D5—22no—
115C3×C4×D5—22no—
116C3×C5×C8—41no—
117C3×#168—41no—
118C23×C3×C4—51no—
119C22×C3×C8—51no—
120C22×C3×C8C2×D511yescharacteristic
121C3×#117—54no—
122C3×#117—102no—
123C2×C3×C4⋊C4—51no—
124C2×C3×C4⋊C4—51no—
125C2×C3×C4⋊C4C2×D511yescharacteristic
126C2×C3×C4⋊C4C2×D511yescharacteristic
127C2×C3×C22⋊C4—101no—
128C2×C3×C22⋊C4—101no—
129C2×C3×C42—101no—
130C3×C22⋊C8—102no—
131C3×#95—101no—
132C23×D5C3×D411yescharacteristic
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5C23×C311yescharacteristic
136C22×Dic5—21no—
137C22×Dic5—21no—
138C22×Dic5C3×D411yescharacteristic
139C2×C4×D5—21no—
140C2×C4×D5—21no—
141C2×C4×D5—21no—
142C2×C4×D5—21no—
143C2×C4×D5C2×C3×C412yes—
144C2×C4×D5C3×D412yes—
145C2×C5×C8—21no—
146C2×C5×C8—21no—
147C2×C5×C8—21no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4—21no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4C2×C3×C412yes—
152#685—24no—
153#685—42no—
154C4⋊Dic5—21no—
155C4⋊Dic5—21no—
156C4⋊Dic5—21no—
157C4⋊Dic5C2×C3×C412yes—
158C4×Dic5—24no—
159C2×#168—21no—
160C2×#168—21no—
161C2×#168—21no—
162C2×#117—51no—
163C2×C22⋊C8—51no—
164#380—51no—
165#340—51no—
166#340—51no—
167#340—51no—
168#340C3×D511yescharacteristic, complemented
169C22×C3×C5C2×C22⋊C411yescharacteristic
170C22×C3×C5#12311yescharacteristic
171C22×C3×C5#12311yescharacteristic
172C22×C3×C5#13511yescharacteristic
173C22×C3×C5#13511yescharacteristic
174C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
175C22×C3×C5#13711yescharacteristic
176C2×C3×D5—22no—
177C2×C3×D5—22no—
178C2×C3×D5—22no—
179C2×C3×D5—41no—
180C2×C3×D5—41no—
181C2×C3×D5—41no—
182C2×C3×D5—41no—
183C3×C4×C5—42no—
184C3×C4×C5—81no—
185C3×C4×C5#11711yescharacteristic
186C3×C4×C5#11711yescharacteristic
187C3×C4×C5#12311yescharacteristic
188C3×C4×C5#12311yescharacteristic
189C3×Dic5—22no—
190C3×Dic5—42no—
191C3×Dic5—81no—
192C24×C3—51no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—51no—
196C22×C3×C4—52no—
197C22×C3×C4—52no—
198C22×C3×C4—101no—
199C22×C3×C4—101no—
200C22×C3×C4—101no—
201C22×C3×C4—101no—
202C22×C3×C4—101no—
203C22×C3×C4—101no—
204C22×C3×C4C22×D511yescharacteristic
205C2×C3×C8—21no—
206C2×C3×C8—21no—
207C2×C3×C8—21no—
208C2×C3×C8—101no—
209C2×C3×C8—101no—
210C2×C3×C8—101no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—52no—
215C3×C4⋊C4—101no—
216C3×C4⋊C4—101no—
217C3×C4⋊C4—101no—
218C3×C4⋊C4C4×D512yes—
219C3×C22⋊C4—104no—
220C3×C22⋊C4—202no—
221C3×C42—104no—
222C23×C5C2×C3×D411yescharacteristic
223C22×D5—21no—
224C22×D5—21no—
225C22×D5—21no—
226C22×D5—21no—
227C22×D5—21no—
228C22×D5—21no—
229C22×D5C3×C22⋊C412yes—
230C2×C4×C5—22no—
231C2×C4×C5—41no—
232C2×C4×C5—41no—
233C2×C4×C5—41no—
234C2×C4×C5—41no—
235C2×C4×C5—41no—
236C2×C4×C5C22×C3×C411yescharacteristic
237C2×C4×C5C2×C3×D411yescharacteristic
238C2×C4×C5C3×#4111yescharacteristic
239C2×C4×C5C3×#4111yescharacteristic
240C2×C4×C5C3×#4111yescharacteristic
241C2×C4×C5C3×#4111yescharacteristic
242C2×Dic5—21no—
243C2×Dic5—21no—
244C2×Dic5—22no—
245C2×Dic5—41no—
246C2×Dic5—41no—
247C2×Dic5—41no—
248C2×Dic5—41no—
249C2×Dic5—41no—
250C2×Dic5C3×C22⋊C412yes—
251C4×D5—22no—
252C4×D5—22no—
253C4×D5—22no—
254C4×D5—22no—
255C5×C8—41no—
256#168—41no—
257C23×C4—51no—
258C22×C8—51no—
259C22×C8C2×C3×D511yescharacteristic
260#117—54no—
261#117—102no—
262C2×C4⋊C4—51no—
263C2×C4⋊C4—51no—
264C2×C4⋊C4C2×C3×D511yescharacteristic
265C2×C4⋊C4C2×C3×D511yescharacteristic
266C2×C22⋊C4—101no—
267C2×C22⋊C4—101no—
268C2×C42—101no—
269C22⋊C8—102no—
270#95—101no—
271C2×C3×C5#38111yescharacteristic
272C2×C3×C5#41611yescharacteristic
273C2×C3×C5#41711yescharacteristic
274C2×C3×C5#48211yescharacteristic
275C2×C3×C5#48211yescharacteristic
276C2×C3×C5#48511yescharacteristic
277C2×C3×C5#48511yescharacteristic
278C3×D5—42no—
279C23×C3—52no—
280C23×C3—101no—
281C23×C3—101no—
282C23×C3—101no—
283C23×C3—101no—
284C23×C3—101no—
285C23×C3—101no—
286C23×C3D4×D511yescharacteristic
287C2×C3×C4—22no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—52no—
294C2×C3×C4—101no—
295C2×C3×C4—101no—
296C2×C3×C4—102no—
297C2×C3×C4—102no—
298C2×C3×C4—102no—
299C2×C3×C4—102no—
300C2×C3×C4—102no—
301C2×C3×C4—201no—
302C2×C3×C4—201no—
303C2×C3×C4—201no—
304C2×C3×C4—201no—
305C2×C3×C4—201no—
306C2×C3×C4C2×C4×D511yescharacteristic
307C2×C3×C4#70911yescharacteristic
308C2×C3×C4#70911yescharacteristic
309C2×C3×C4D4×D511yescharacteristic
310C2×C3×C4#71111yescharacteristic
311C2×C3×C4#71311yescharacteristic
312C3×C8—41no—
313C3×C8—201no—
314C22×C5C2×C3×C22⋊C411yescharacteristic
315C22×C5C3×#12311yescharacteristic
316C22×C5C3×#12311yescharacteristic
317C22×C5C3×#13511yescharacteristic
318C22×C5C3×#13511yescharacteristic
319C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
320C22×C5C3×#13711yescharacteristic
321C2×D5—22no—
322C2×D5—22no—
323C2×D5—22no—
324C2×D5—41no—
325C2×D5—41no—
326C2×D5—41no—
327C2×D5—41no—
328C4×C5—42no—
329C4×C5—81no—
330C4×C5C3×#11711yescharacteristic
331C4×C5C3×#11711yescharacteristic
332C4×C5C3×#12311yescharacteristic
333C4×C5C3×#12311yescharacteristic
334Dic5—22no—
335Dic5—42no—
336Dic5—81no—
337C24—51no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—51no—
341C22×C4—52no—
342C22×C4—52no—
343C22×C4—101no—
344C22×C4—101no—
345C22×C4—101no—
346C22×C4—101no—
347C22×C4—101no—
348C22×C4—101no—
349C22×C4C22×C3×D511yescharacteristic
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—101no—
354C2×C8—101no—
355C2×C8—101no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—52no—
360C4⋊C4—101no—
361C4⋊C4—101no—
362C4⋊C4—101no—
363C4⋊C4C3×C4×D512yes—
364C22⋊C4—104no—
365C22⋊C4—202no—
366C42—104no—
367C3×C5#182511yescharacteristic, complemented, Hall
368C22×C3—102no—
369C22×C3—102no—
370C22×C3—102no—
371C22×C3—201no—
372C22×C3—201no—
373C22×C3—201no—
374C22×C3—201no—
375C22×C3D5×C22⋊C411yescharacteristic
376C22×C3#402911yescharacteristic
377C22×C3#404011yescharacteristic
378C22×C3#405811yescharacteristic
379C22×C3#406011yescharacteristic
380C22×C3#406211yescharacteristic
381C22×C3#406411yescharacteristic
382C3×C4—42no—
383C3×C4—81no—
384C3×C4—102no—
385C3×C4—202no—
386C3×C4—401no—
387C3×C4#401811yescharacteristic
388C3×C4#402911yescharacteristic
389C3×C4#403811yescharacteristic
390C3×C4#404011yescharacteristic
391C2×C5C3×#38111yescharacteristic
392C2×C5C3×#41611yescharacteristic
393C2×C5C3×#41711yescharacteristic
394C2×C5C3×#48211yescharacteristic
395C2×C5C3×#48211yescharacteristic
396C2×C5C3×#48511yescharacteristic
397C2×C5C3×#48511yescharacteristic
398D5—42no—
399C23—52no—
400C23—101no—
401C23—101no—
402C23—101no—
403C23—101no—
404C23—101no—
405C23—101no—
406C23C3×D4×D511yescharacteristic
407C2×C4—22no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—52no—
414C2×C4—101no—
415C2×C4—101no—
416C2×C4—102no—
417C2×C4—102no—
418C2×C4—102no—
419C2×C4—102no—
420C2×C4—102no—
421C2×C4—201no—
422C2×C4—201no—
423C2×C4—201no—
424C2×C4—201no—
425C2×C4—201no—
426C2×C4C2×C3×C4×D511yescharacteristic
427C2×C4C3×#70911yescharacteristic
428C2×C4C3×#70911yescharacteristic
429C2×C4C3×D4×D511yescharacteristic
430C2×C4C3×#71111yescharacteristic
431C2×C4C3×#71311yescharacteristic
432C8—41no—
433C8—201no—
434C2×C3—202no—
435C2×C3#6495311yescharacteristic
436C2×C3#6506111yescharacteristic
437C2×C3#6507311yescharacteristic
438C2×C3#6509211yescharacteristic
439C2×C3#6510411yescharacteristic
440C2×C3#6515511yescharacteristic
441C2×C3#6517711yescharacteristic
442C5C3×#182511yescharacteristic, complemented, Sylow
443C22—102no—
444C22—102no—
445C22—102no—
446C22—201no—
447C22—201no—
448C22—201no—
449C22—201no—
450C22C3×D5×C22⋊C411yescharacteristic
451C22C3×#402911yescharacteristic
452C22C3×#404011yescharacteristic
453C22C3×#405811yescharacteristic
454C22C3×#406011yescharacteristic
455C22C3×#406211yescharacteristic
456C22C3×#406411yescharacteristic
457C4—42no—
458C4—81no—
459C4—102no—
460C4—202no—
461C4—401no—
462C4C3×#401811yescharacteristic
463C4C3×#402911yescharacteristic
464C4C3×#403811yescharacteristic
465C4C3×#404011yescharacteristic
466C3#1059966611yescharacteristic, direct product factor, Sylow
467C2—202no—
468C2C3×#6495311yescharacteristic
469C2C3×#6506111yescharacteristic
470C2C3×#6507311yescharacteristic
471C2C3×#6509211yescharacteristic
472C2C3×#6510411yescharacteristic
473C2C3×#6515511yescharacteristic
474C2C3×#6517711yescharacteristic
subgroupG/H
centerC23×C3D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#340C2
socleC23×C3×C5C2×D4
prime radicalC23×C3×D5D4
cosocleC22×C4×C5C23×C3
hypercenterC3×#340D5
hypocenterC5C3×#1825
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C3×#340

Complements

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

NH ≅ G/Ntype
4. C3×C5×#340C2semidirect
5. C3×#64771C2semidirect
6. C3×#64749C2semidirect
7. C3×#64749C2semidirect
8. #10599666C3direct (N × H)
20. C3×#4038C4semidirect
27. C5×#340C2×C3semidirect
28. #64771C2×C3semidirect
29. #64749C2×C3semidirect
30. #64749C2×C3semidirect
67. C3×#340D5semidirect
79. #4038C3×C4semidirect
168. #340C3×D5semidirect
367. C3×C5#1825semidirect
442. C5C3×#1825semidirect
466. C3#10599666direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40382
C2×C3×#39522
C3×#652762
C3×C5×#3402
C3×#647712
C3×#647492
#105996663
C3×#18255