Finite Group Databasebeta

← C3×#10599686 #14297721

Subgroups — C3×#10599686 #14297721

Order 1920.

712 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4039C211yesmaximal, characteristic
2C2×C3×#3953C211yesmaximal, characteristic
3C2×C3×#3946C211yesmaximal, characteristic, complemented
4C3×#65266C211yesmaximal, characteristic, complemented
5C2×C3×#3941C211yesmaximal, characteristic
6C3×C5×#340C211yesmaximal, characteristic, complemented
7C3×#64749C211yesmaximal, characteristic, complemented
8#10599686C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×D20C2211yescharacteristic
10C22×C3×C4×D5—21no—
11C22×C3×C5×C8C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×C3×#685—21no—
15C2×C3×C4⋊Dic5C2211yescharacteristic
16C2×C3×C4×Dic5C2211yescharacteristic
17C22×C3×#168C2211yescharacteristic
18C3×#4039—22no—
19C3×#4039C414yescomplemented
20C3×#3963—21no—
21C3×#3963—21no—
22C3×#3953—22no—
23C3×#3946—22no—
24C3×#3941—22no—
25C3×#1804—51nomaximal, Hall
26C2×#4039C2×C311yescharacteristic
27C2×#3953C2×C311yescharacteristic
28C2×#3946C2×C311yescharacteristic, complemented
29#65266C2×C311yescharacteristic, complemented
30C2×#3941C2×C311yescharacteristic
31C5×#340C2×C311yescharacteristic, complemented
32#64749C2×C311yescharacteristic, complemented
33C23×C3×D5—21no—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×C3×Dic5—21no—
38C22×C3×Dic5D411yescharacteristic
39C22×C3×Dic5D411yescharacteristic
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20C2×C412yes—
44C2×C3×D20D412yes—
45C2×C3×D20Q812yes—
46C2×C3×C4×D5—24no—
47C2×C3×C4×D5—42no—
48C2×C3×C4×D5—42no—
49C2×C3×C5×C8—21no—
50C2×C3×C5×C8—21no—
51C2×C3×C5×C8—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4C2×C412yes—
56C3×#685—24no—
57C3×C4⋊Dic5—21no—
58C3×C4⋊Dic5—21no—
59C3×C4×Dic5C2×C412yes—
60C3×C4×Dic5D412yes—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C2×C3×#168—21no—
64C2×C3×C4×D4—51no—
65C2×C3×C4⋊C8—51no—
66C2×C3×#102—51no—
67C2×C3×#102—51no—
68C3×#382—51no—
69C3×#340—51no—
70C3×#340D511yescharacteristic, complemented
71C22×D20C22×C311yescharacteristic
72C22×C4×D5—21no—
73C22×C5×C8C22×C311yescharacteristic
74C2×C5×C4⋊C4C22×C311yescharacteristic
75C2×C5×C4⋊C4C22×C311yescharacteristic
76C2×#685—21no—
77C2×C4⋊Dic5C22×C311yescharacteristic
78C2×C4×Dic5C22×C311yescharacteristic
79C22×#168C22×C311yescharacteristic
80#4039—22no—
81#4039C3×C414yescomplemented
82#3963—21no—
83#3963—21no—
84#3953—22no—
85#3946—22no—
86#3941—22no—
87#1804—51noSylow
88C23×C3×C5C2×D411yescharacteristic
89C22×C3×D5—22no—
90C22×C3×D5—22no—
91C22×C3×D5—22no—
92C22×C3×D5—41no—
93C22×C3×D5—41no—
94C22×C3×D5—41no—
95C22×C3×D5—41no—
96C2×C3×C4×C5—22no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5C22×C411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×Q811yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×Dic5—21no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—41no—
113C2×C3×Dic5—41no—
114C2×C3×Dic5—41no—
115C2×C3×Dic5C22⋊C412yes—
116C2×C3×Dic5C22⋊C412yes—
117C3×D20—22no—
118C3×D20—22no—
119C3×D20—22no—
120C3×D20C4⋊C414yes—
121C3×C4×D5—48no—
122C3×C5×C8—41no—
123C3×#168—41no—
124C22×C3×D4—51no—
125C23×C3×C4—101no—
126C22×C3×C8—51no—
127C22×C3×C8C2×D511yescharacteristic
128C3×C4×D4—54no—
129C3×C4×D4—102no—
130C2×C3×C4⋊C4—51no—
131C2×C3×C4⋊C4C2×D511yescharacteristic
132C2×C3×C4⋊C4C2×D511yescharacteristic
133C2×C3×C22⋊C4—101no—
134C2×C3×C42—51no—
135C3×C4⋊C8—102no—
136C3×#102—102no—
137C3×#102—102no—
138C3×#95—101no—
139C3×#95—101no—
140C23×D5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5C23×C311yescharacteristic
144C22×Dic5—21no—
145C22×Dic5C3×D411yescharacteristic
146C22×Dic5C3×D411yescharacteristic
147C2×D20—21no—
148C2×D20—21no—
149C2×D20—21no—
150C2×D20C2×C3×C412yes—
151C2×D20C3×D412yes—
152C2×D20C3×Q812yes—
153C2×C4×D5—24no—
154C2×C4×D5—42no—
155C2×C4×D5—42no—
156C2×C5×C8—21no—
157C2×C5×C8—21no—
158C2×C5×C8—21no—
159C5×C4⋊C4—21no—
160C5×C4⋊C4—21no—
161C5×C4⋊C4—21no—
162C5×C4⋊C4C2×C3×C412yes—
163#685—24no—
164C4⋊Dic5—21no—
165C4⋊Dic5—21no—
166C4×Dic5C2×C3×C412yes—
167C4×Dic5C3×D412yes—
168C2×#168—21no—
169C2×#168—21no—
170C2×#168—21no—
171C2×C4×D4—51no—
172C2×C4⋊C8—51no—
173C2×#102—51no—
174C2×#102—51no—
175#382—51no—
176#340—51no—
177#340C3×D511yescharacteristic, complemented
178C22×C3×C5C2×C22⋊C411yescharacteristic
179C22×C3×C5#12111yescharacteristic
180C22×C3×C5C22⋊Q811yescharacteristic
181C22×C3×C5#13511yescharacteristic
182C22×C3×C5#13511yescharacteristic
183C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
184C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
185C2×C3×D5—24no—
186C2×C3×D5—42no—
187C2×C3×D5—42no—
188C2×C3×D5—42no—
189C2×C3×D5—42no—
190C2×C3×D5—42no—
191C2×C3×D5—42no—
192C3×C4×C5—42no—
193C3×C4×C5—81no—
194C3×C4×C5C2×C4⋊C411yescharacteristic
195C3×C4×C5#11711yescharacteristic
196C3×C4×C5#12111yescharacteristic
197C3×C4×C5C22⋊Q811yescharacteristic
198C3×Dic5—22no—
199C3×Dic5—22no—
200C3×Dic5—81no—
201C24×C3—101no—
202C2×C3×D4—52no—
203C2×C3×D4—52no—
204C2×C3×D4—52no—
205C2×C3×D4—101no—
206C2×C3×D4—101no—
207C2×C3×D4—101no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—51no—
211C22×C3×C4—51no—
212C22×C3×C4—104no—
213C22×C3×C4—101no—
214C22×C3×C4—202no—
215C22×C3×C4—202no—
216C22×C3×C4C22×D511yescharacteristic
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—101no—
221C2×C3×C8—101no—
222C2×C3×C8—101no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—101no—
227C3×C4⋊C4—101no—
228C3×C4⋊C4C4×D512yes—
229C3×C22⋊C4—104no—
230C3×C42—52no—
231C3×C42—52no—
232C23×C5C2×C3×D411yescharacteristic
233C22×D5—22no—
234C22×D5—22no—
235C22×D5—22no—
236C22×D5—41no—
237C22×D5—41no—
238C22×D5—41no—
239C22×D5—41no—
240C2×C4×C5—22no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5—41no—
244C2×C4×C5—41no—
245C2×C4×C5—41no—
246C2×C4×C5C22×C3×C411yescharacteristic
247C2×C4×C5C2×C3×D411yescharacteristic
248C2×C4×C5C2×C3×D411yescharacteristic
249C2×C4×C5C2×C3×Q811yescharacteristic
250C2×C4×C5C3×#4111yescharacteristic
251C2×C4×C5C3×#4111yescharacteristic
252C2×Dic5—21no—
253C2×Dic5—21no—
254C2×Dic5—21no—
255C2×Dic5—21no—
256C2×Dic5—41no—
257C2×Dic5—41no—
258C2×Dic5—41no—
259C2×Dic5C3×C22⋊C412yes—
260C2×Dic5C3×C22⋊C412yes—
261D20—22no—
262D20—22no—
263D20—22no—
264D20C3×C4⋊C414yes—
265C4×D5—48no—
266C5×C8—41no—
267#168—41no—
268C22×D4—51no—
269C23×C4—101no—
270C22×C8—51no—
271C22×C8C2×C3×D511yescharacteristic
272C4×D4—54no—
273C4×D4—102no—
274C2×C4⋊C4—51no—
275C2×C4⋊C4C2×C3×D511yescharacteristic
276C2×C4⋊C4C2×C3×D511yescharacteristic
277C2×C22⋊C4—101no—
278C2×C42—51no—
279C4⋊C8—102no—
280#102—102no—
281#102—102no—
282#95—101no—
283#95—101no—
284C2×C3×C5#38011yescharacteristic
285C2×C3×C5#41611yescharacteristic
286C2×C3×C5#41811yescharacteristic
287C2×C3×C5#46311yescharacteristic
288C2×C3×C5#46311yescharacteristic
289C2×C3×C5#47811yescharacteristic
290C2×C3×C5#47811yescharacteristic
291C3×D5—44no—
292C23×C3—102no—
293C23×C3—102no—
294C23×C3—102no—
295C23×C3—201no—
296C23×C3—201no—
297C23×C3—201no—
298C23×C3—201no—
299C23×C3D4×D511yescharacteristic
300C3×D4—54no—
301C3×D4—102no—
302C3×D4—102no—
303C3×D4—102no—
304C2×C3×C4—22no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—52no—
311C2×C3×C4—52no—
312C2×C3×C4—101no—
313C2×C3×C4—101no—
314C2×C3×C4—101no—
315C2×C3×C4—101no—
316C2×C3×C4—208no—
317C2×C3×C4—201no—
318C2×C3×C4—201no—
319C2×C3×C4—201no—
320C2×C3×C4C2×C4×D511yescharacteristic
321C2×C3×C4#70911yescharacteristic
322C2×C3×C4#70911yescharacteristic
323C2×C3×C4D4×D511yescharacteristic
324C2×C3×C4D4×D511yescharacteristic
325C2×C3×C4Q8×D511yescharacteristic
326C3×C8—41no—
327C3×C8—201no—
328C22×C5C2×C3×C22⋊C411yescharacteristic
329C22×C5C3×#12111yescharacteristic
330C22×C5C3×C22⋊Q811yescharacteristic
331C22×C5C3×#13511yescharacteristic
332C22×C5C3×#13511yescharacteristic
333C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
334C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
335C2×D5—24no—
336C2×D5—42no—
337C2×D5—42no—
338C2×D5—42no—
339C2×D5—42no—
340C2×D5—42no—
341C2×D5—42no—
342C4×C5—42no—
343C4×C5—81no—
344C4×C5C2×C3×C4⋊C411yescharacteristic
345C4×C5C3×#11711yescharacteristic
346C4×C5C3×#12111yescharacteristic
347C4×C5C3×C22⋊Q811yescharacteristic
348Dic5—22no—
349Dic5—22no—
350Dic5—81no—
351C24—101no—
352C2×D4—52no—
353C2×D4—52no—
354C2×D4—52no—
355C2×D4—101no—
356C2×D4—101no—
357C2×D4—101no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—51no—
361C22×C4—51no—
362C22×C4—104no—
363C22×C4—101no—
364C22×C4—202no—
365C22×C4—202no—
366C22×C4C22×C3×D511yescharacteristic
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—101no—
371C2×C8—101no—
372C2×C8—101no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—101no—
377C4⋊C4—101no—
378C4⋊C4C3×C4×D512yes—
379C22⋊C4—104no—
380C42—52no—
381C42—52no—
382C3×C5#180411yescharacteristic, complemented, Hall
383C22×C3—104no—
384C22×C3—202no—
385C22×C3—202no—
386C22×C3—202no—
387C22×C3—202no—
388C22×C3—202no—
389C22×C3—202no—
390C22×C3D5×C22⋊C411yescharacteristic
391C22×C3#403011yescharacteristic
392C22×C3#404211yescharacteristic
393C22×C3#405711yescharacteristic
394C22×C3#406011yescharacteristic
395C22×C3#406211yescharacteristic
396C22×C3#406511yescharacteristic
397C3×C4—42no—
398C3×C4—81no—
399C3×C4—102no—
400C3×C4—102no—
401C3×C4—401no—
402C3×C4#401811yescharacteristic
403C3×C4#403011yescharacteristic
404C3×C4D5×C4⋊C411yescharacteristic
405C3×C4#404211yescharacteristic
406C2×C5C3×#38011yescharacteristic
407C2×C5C3×#41611yescharacteristic
408C2×C5C3×#41811yescharacteristic
409C2×C5C3×#46311yescharacteristic
410C2×C5C3×#46311yescharacteristic
411C2×C5C3×#47811yescharacteristic
412C2×C5C3×#47811yescharacteristic
413D5—44no—
414C23—102no—
415C23—102no—
416C23—102no—
417C23—201no—
418C23—201no—
419C23—201no—
420C23—201no—
421C23C3×D4×D511yescharacteristic
422D4—54no—
423D4—102no—
424D4—102no—
425D4—102no—
426C2×C4—22no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—52no—
433C2×C4—52no—
434C2×C4—101no—
435C2×C4—101no—
436C2×C4—101no—
437C2×C4—101no—
438C2×C4—208no—
439C2×C4—201no—
440C2×C4—201no—
441C2×C4—201no—
442C2×C4C2×C3×C4×D511yescharacteristic
443C2×C4C3×#70911yescharacteristic
444C2×C4C3×#70911yescharacteristic
445C2×C4C3×D4×D511yescharacteristic
446C2×C4C3×D4×D511yescharacteristic
447C2×C4C3×Q8×D511yescharacteristic
448C8—41no—
449C8—201no—
450C2×C3—204no—
451C2×C3#6495611yescharacteristic
452C2×C3#6505911yescharacteristic
453C2×C3#6507611yescharacteristic
454C2×C3#6509311yescharacteristic
455C2×C3#6510811yescharacteristic
456C2×C3#6516011yescharacteristic
457C2×C3#6518011yescharacteristic
458C5C3×#180411yescharacteristic, complemented, Sylow
459C22—104no—
460C22—202no—
461C22—202no—
462C22—202no—
463C22—202no—
464C22—202no—
465C22—202no—
466C22C3×D5×C22⋊C411yescharacteristic
467C22C3×#403011yescharacteristic
468C22C3×#404211yescharacteristic
469C22C3×#405711yescharacteristic
470C22C3×#406011yescharacteristic
471C22C3×#406211yescharacteristic
472C22C3×#406511yescharacteristic
473C4—42no—
474C4—81no—
475C4—102no—
476C4—102no—
477C4—401no—
478C4C3×#401811yescharacteristic
479C4C3×#403011yescharacteristic
480C4C3×D5×C4⋊C411yescharacteristic
481C4C3×#404211yescharacteristic
482C3#1059968611yescharacteristic, direct product factor, Sylow
483C2—204no—
484C2C3×#6495611yescharacteristic
485C2C3×#6505911yescharacteristic
486C2C3×#6507611yescharacteristic
487C2C3×#6509311yescharacteristic
488C2C3×#6510811yescharacteristic
489C2C3×#6516011yescharacteristic
490C2C3×#6518011yescharacteristic
subgroupG/H
centerC23×C3D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#340C2
socleC23×C3×C5C2×D4
prime radicalC22×C3×D20C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#340D5
hypocenterC5C3×#1804
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
3. C2×C3×#3946C2semidirect
4. C3×#65266C2semidirect
6. C3×C5×#340C2semidirect
7. C3×#64749C2semidirect
8. #10599686C3direct (N × H)
19. C3×#4039C4semidirect
28. C2×#3946C2×C3semidirect
29. #65266C2×C3semidirect
31. C5×#340C2×C3semidirect
32. #64749C2×C3semidirect
70. C3×#340D5semidirect
81. #4039C3×C4semidirect
177. #340C3×D5semidirect
382. C3×C5#1804semidirect
458. C5C3×#1804semidirect
482. C3#10599686direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40392
C2×C3×#39532
C2×C3×#39462
C3×#652662
C2×C3×#39412
C3×C5×#3402
C3×#647492
#105996863
C3×#18045