Finite Group Databasebeta

← C3×#10599670 #14299455

Subgroups — C3×#10599670 #14299455

Order 1920.

632 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4038C211yesmaximal, characteristic
2C2×C3×#3952C211yesmaximal, characteristic
3C2×C3×#3950C211yesmaximal, characteristic, complemented
4C3×#65276C211yesmaximal, characteristic
5C2×C3×#3940C211yesmaximal, characteristic, complemented
6C3×C5×#340C211yesmaximal, characteristic, complemented
7C3×#64749C211yesmaximal, characteristic, complemented
8#10599670C311yesmaximal, 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×#4038—22no—
21C3×#3963—21no—
22C3×#3952C414yescomplemented
23C3×#3950—22no—
24C3×#3940—22no—
25C3×#1854—51nomaximal, Hall
26C2×#4038C2×C311yescharacteristic
27C2×#3952C2×C311yescharacteristic
28C2×#3950C2×C311yescharacteristic, complemented
29#65276C2×C311yescharacteristic
30C2×#3940C2×C311yescharacteristic, complemented
31C5×#340C2×C311yescharacteristic, complemented
32#64749C2×C311yescharacteristic, complemented
33C23×C3×D5D411yescharacteristic
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×C3×Dic5—21no—
38C22×C3×Dic5—21no—
39C22×C3×Dic5D411yescharacteristic
40C2×C3×C4×D5—21no—
41C2×C3×C4×D5—21no—
42C2×C3×C4×D5—21no—
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5C2×C412yes—
45C2×C3×C4×D5Q812yes—
46C2×C3×C5×C8—21no—
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8C2×C412yes—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4D412yes—
53C3×#685—24no—
54C3×#685—42no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5—21no—
57C3×C4⋊Dic5—21no—
58C3×C4⋊Dic5D412yes—
59C3×C4×Dic5—24no—
60C2×C3×#168—21no—
61C2×C3×#168—21no—
62C2×C3×#168C2×C412yes—
63C2×C3×#117—51no—
64C2×C3×#107—51no—
65C2×C3×#106—51no—
66C2×C3×C22⋊C8—51no—
67C3×#380—51no—
68C3×#340—51no—
69C3×#340D511yescharacteristic, complemented
70C22×C4×D5C22×C311yescharacteristic
71C22×C5×C8C22×C311yescharacteristic
72C2×C5×C4⋊C4C22×C311yescharacteristic
73C2×C5×C4⋊C4C22×C311yescharacteristic
74C2×#685—21no—
75C2×#685—21no—
76C2×C4⋊Dic5C22×C311yescharacteristic
77C2×C4⋊Dic5C22×C311yescharacteristic
78C2×C4×Dic5—21no—
79C22×#168C22×C311yescharacteristic
80#4038—22no—
81#4038—22no—
82#3963—21no—
83#3952C3×C414yescomplemented
84#3950—22no—
85#3940—22no—
86#1854—51noSylow
87C23×C3×C5C2×D411yescharacteristic
88C22×C3×D5—21no—
89C22×C3×D5—21no—
90C22×C3×D5—21no—
91C22×C3×D5—21no—
92C22×C3×D5—21no—
93C22×C3×D5—21no—
94C22×C3×D5C4⋊C412yes—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×Q811yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—22no—
110C2×C3×Dic5—41no—
111C2×C3×Dic5—41no—
112C2×C3×Dic5—41no—
113C2×C3×Dic5—41no—
114C2×C3×Dic5—41no—
115C2×C3×Dic5C4⋊C412yes—
116C3×C4×D5—22no—
117C3×C4×D5—22no—
118C3×C4×D5—22no—
119C3×C4×D5—22no—
120C3×C5×C8—22no—
121C3×#168—22no—
122C23×C3×C4—51no—
123C22×C3×C8—51no—
124C22×C3×C8C2×D511yescharacteristic
125C3×#117—102no—
126C3×#117—102no—
127C2×C3×C4⋊C4—51no—
128C2×C3×C4⋊C4—51no—
129C2×C3×C4⋊C4C2×D511yescharacteristic
130C2×C3×C4⋊C4C2×D511yescharacteristic
131C2×C3×C22⋊C4—101no—
132C2×C3×C22⋊C4—101no—
133C2×C3×C42—101no—
134C3×#107—102no—
135C3×#106—102no—
136C3×C22⋊C8—54no—
137C3×#95—101no—
138C23×D5C3×D411yescharacteristic
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5C23×C311yescharacteristic
142C22×Dic5—21no—
143C22×Dic5—21no—
144C22×Dic5C3×D411yescharacteristic
145C2×C4×D5—21no—
146C2×C4×D5—21no—
147C2×C4×D5—21no—
148C2×C4×D5—21no—
149C2×C4×D5C2×C3×C412yes—
150C2×C4×D5C3×Q812yes—
151C2×C5×C8—21no—
152C2×C5×C8—21no—
153C2×C5×C8C2×C3×C412yes—
154C5×C4⋊C4—21no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4—21no—
157C5×C4⋊C4C3×D412yes—
158#685—24no—
159#685—42no—
160C4⋊Dic5—21no—
161C4⋊Dic5—21no—
162C4⋊Dic5—21no—
163C4⋊Dic5C3×D412yes—
164C4×Dic5—24no—
165C2×#168—21no—
166C2×#168—21no—
167C2×#168C2×C3×C412yes—
168C2×#117—51no—
169C2×#107—51no—
170C2×#106—51no—
171C2×C22⋊C8—51no—
172#380—51no—
173#340—51no—
174#340C3×D511yescharacteristic, complemented
175C22×C3×C5C2×C4⋊C411yescharacteristic
176C22×C3×C5#12011yescharacteristic
177C22×C3×C5#12311yescharacteristic
178C22×C3×C5#13511yescharacteristic
179C22×C3×C5#13511yescharacteristic
180C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
181C22×C3×C5#13711yescharacteristic
182C2×C3×D5—22no—
183C2×C3×D5—22no—
184C2×C3×D5—22no—
185C2×C3×D5—41no—
186C2×C3×D5—41no—
187C2×C3×D5—41no—
188C2×C3×D5—41no—
189C3×C4×C5—42no—
190C3×C4×C5—81no—
191C3×C4×C5C4×D411yescharacteristic
192C3×C4×C5C4×D411yescharacteristic
193C3×C4×C5C22⋊Q811yescharacteristic
194C3×C4×C5C22⋊Q811yescharacteristic
195C3×Dic5—22no—
196C3×Dic5—42no—
197C3×Dic5—81no—
198C24×C3—51no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—51no—
202C22×C3×C4—52no—
203C22×C3×C4—52no—
204C22×C3×C4—101no—
205C22×C3×C4—101no—
206C22×C3×C4—101no—
207C22×C3×C4—101no—
208C22×C3×C4—101no—
209C22×C3×C4—101no—
210C22×C3×C4C22×D511yescharacteristic
211C2×C3×C8—21no—
212C2×C3×C8—21no—
213C2×C3×C8—52no—
214C2×C3×C8—101no—
215C2×C3×C8—101no—
216C2×C3×C8C4×D512yes—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—52no—
221C3×C4⋊C4—101no—
222C3×C4⋊C4—101no—
223C3×C4⋊C4—101no—
224C3×C4⋊C4D2012yes—
225C3×C22⋊C4—104no—
226C3×C22⋊C4—202no—
227C3×C42—104no—
228C23×C5C2×C3×D411yescharacteristic
229C22×D5—21no—
230C22×D5—21no—
231C22×D5—21no—
232C22×D5—21no—
233C22×D5—21no—
234C22×D5—21no—
235C22×D5C3×C4⋊C412yes—
236C2×C4×C5—22no—
237C2×C4×C5—41no—
238C2×C4×C5—41no—
239C2×C4×C5—41no—
240C2×C4×C5—41no—
241C2×C4×C5—41no—
242C2×C4×C5C22×C3×C411yescharacteristic
243C2×C4×C5C2×C3×D411yescharacteristic
244C2×C4×C5C2×C3×D411yescharacteristic
245C2×C4×C5C2×C3×Q811yescharacteristic
246C2×C4×C5C3×#4111yescharacteristic
247C2×C4×C5C3×#4111yescharacteristic
248C2×Dic5—21no—
249C2×Dic5—21no—
250C2×Dic5—22no—
251C2×Dic5—41no—
252C2×Dic5—41no—
253C2×Dic5—41no—
254C2×Dic5—41no—
255C2×Dic5—41no—
256C2×Dic5C3×C4⋊C412yes—
257C4×D5—22no—
258C4×D5—22no—
259C4×D5—22no—
260C4×D5—22no—
261C5×C8—22no—
262#168—22no—
263C23×C4—51no—
264C22×C8—51no—
265C22×C8C2×C3×D511yescharacteristic
266#117—102no—
267#117—102no—
268C2×C4⋊C4—51no—
269C2×C4⋊C4—51no—
270C2×C4⋊C4C2×C3×D511yescharacteristic
271C2×C4⋊C4C2×C3×D511yescharacteristic
272C2×C22⋊C4—101no—
273C2×C22⋊C4—101no—
274C2×C42—101no—
275#107—102no—
276#106—102no—
277C22⋊C8—54no—
278#95—101no—
279C2×C3×C5#38511yescharacteristic
280C2×C3×C5#42711yescharacteristic
281C2×C3×C5#42811yescharacteristic
282C2×C3×C5#44911yescharacteristic
283C2×C3×C5#45211yescharacteristic
284C2×C3×C5#48211yescharacteristic
285C2×C3×C5#48511yescharacteristic
286C3×D5—42no—
287C23×C3—52no—
288C23×C3—101no—
289C23×C3—101no—
290C23×C3—101no—
291C23×C3—101no—
292C23×C3—101no—
293C23×C3—101no—
294C23×C3D4×D511yescharacteristic
295C2×C3×C4—22no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—52no—
302C2×C3×C4—101no—
303C2×C3×C4—101no—
304C2×C3×C4—102no—
305C2×C3×C4—102no—
306C2×C3×C4—102no—
307C2×C3×C4—102no—
308C2×C3×C4—102no—
309C2×C3×C4—201no—
310C2×C3×C4—201no—
311C2×C3×C4—201no—
312C2×C3×C4—201no—
313C2×C3×C4—201no—
314C2×C3×C4C2×C4×D511yescharacteristic
315C2×C3×C4C2×D2011yescharacteristic
316C2×C3×C4#70911yescharacteristic
317C2×C3×C4D4×D511yescharacteristic
318C2×C3×C4#71111yescharacteristic
319C2×C3×C4Q8×D511yescharacteristic
320C3×C8—22no—
321C3×C8—102no—
322C22×C5C2×C3×C4⋊C411yescharacteristic
323C22×C5C3×#12011yescharacteristic
324C22×C5C3×#12311yescharacteristic
325C22×C5C3×#13511yescharacteristic
326C22×C5C3×#13511yescharacteristic
327C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
328C22×C5C3×#13711yescharacteristic
329C2×D5—22no—
330C2×D5—22no—
331C2×D5—22no—
332C2×D5—41no—
333C2×D5—41no—
334C2×D5—41no—
335C2×D5—41no—
336C4×C5—42no—
337C4×C5—81no—
338C4×C5C3×C4×D411yescharacteristic
339C4×C5C3×C4×D411yescharacteristic
340C4×C5C3×C22⋊Q811yescharacteristic
341C4×C5C3×C22⋊Q811yescharacteristic
342Dic5—22no—
343Dic5—42no—
344Dic5—81no—
345C24—51no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—51no—
349C22×C4—52no—
350C22×C4—52no—
351C22×C4—101no—
352C22×C4—101no—
353C22×C4—101no—
354C22×C4—101no—
355C22×C4—101no—
356C22×C4—101no—
357C22×C4C22×C3×D511yescharacteristic
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—52no—
361C2×C8—101no—
362C2×C8—101no—
363C2×C8C3×C4×D512yes—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—52no—
368C4⋊C4—101no—
369C4⋊C4—101no—
370C4⋊C4—101no—
371C4⋊C4C3×D2012yes—
372C22⋊C4—104no—
373C22⋊C4—202no—
374C42—104no—
375C3×C5#185411yescharacteristic, complemented, Hall
376C22×C3—102no—
377C22×C3—102no—
378C22×C3—102no—
379C22×C3—201no—
380C22×C3—201no—
381C22×C3—201no—
382C22×C3—201no—
383C22×C3#402811yescharacteristic
384C22×C3#402911yescharacteristic
385C22×C3D5×C4⋊C411yescharacteristic
386C22×C3#405811yescharacteristic
387C22×C3#406011yescharacteristic
388C22×C3#406111yescharacteristic
389C22×C3#406511yescharacteristic
390C3×C4—42no—
391C3×C4—81no—
392C3×C4—102no—
393C3×C4—202no—
394C3×C4—401no—
395C3×C4C4×D2011yescharacteristic
396C3×C4#402711yescharacteristic
397C3×C4#404211yescharacteristic
398C3×C4#404311yescharacteristic
399C2×C5C3×#38511yescharacteristic
400C2×C5C3×#42711yescharacteristic
401C2×C5C3×#42811yescharacteristic
402C2×C5C3×#44911yescharacteristic
403C2×C5C3×#45211yescharacteristic
404C2×C5C3×#48211yescharacteristic
405C2×C5C3×#48511yescharacteristic
406D5—42no—
407C23—52no—
408C23—101no—
409C23—101no—
410C23—101no—
411C23—101no—
412C23—101no—
413C23—101no—
414C23C3×D4×D511yescharacteristic
415C2×C4—22no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—52no—
422C2×C4—101no—
423C2×C4—101no—
424C2×C4—102no—
425C2×C4—102no—
426C2×C4—102no—
427C2×C4—102no—
428C2×C4—102no—
429C2×C4—201no—
430C2×C4—201no—
431C2×C4—201no—
432C2×C4—201no—
433C2×C4—201no—
434C2×C4C2×C3×C4×D511yescharacteristic
435C2×C4C2×C3×D2011yescharacteristic
436C2×C4C3×#70911yescharacteristic
437C2×C4C3×D4×D511yescharacteristic
438C2×C4C3×#71111yescharacteristic
439C2×C4C3×Q8×D511yescharacteristic
440C8—22no—
441C8—102no—
442C2×C3—202no—
443C2×C3#6495711yescharacteristic
444C2×C3#6507211yescharacteristic
445C2×C3#6507311yescharacteristic
446C2×C3#6510011yescharacteristic
447C2×C3#6510311yescharacteristic
448C2×C3#6515011yescharacteristic
449C2×C3#6516911yescharacteristic
450C5C3×#185411yescharacteristic, complemented, Sylow
451C22—102no—
452C22—102no—
453C22—102no—
454C22—201no—
455C22—201no—
456C22—201no—
457C22—201no—
458C22C3×#402811yescharacteristic
459C22C3×#402911yescharacteristic
460C22C3×D5×C4⋊C411yescharacteristic
461C22C3×#405811yescharacteristic
462C22C3×#406011yescharacteristic
463C22C3×#406111yescharacteristic
464C22C3×#406511yescharacteristic
465C4—42no—
466C4—81no—
467C4—102no—
468C4—202no—
469C4—401no—
470C4C3×C4×D2011yescharacteristic
471C4C3×#402711yescharacteristic
472C4C3×#404211yescharacteristic
473C4C3×#404311yescharacteristic
474C3#1059967011yescharacteristic, direct product factor, Sylow
475C2—202no—
476C2C3×#6495711yescharacteristic
477C2C3×#6507211yescharacteristic
478C2C3×#6507311yescharacteristic
479C2C3×#6510011yescharacteristic
480C2C3×#6510311yescharacteristic
481C2C3×#6515011yescharacteristic
482C2C3×#6516911yescharacteristic
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×#1854
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×#3950C2semidirect
5. C2×C3×#3940C2semidirect
6. C3×C5×#340C2semidirect
7. C3×#64749C2semidirect
8. #10599670C3direct (N × H)
22. C3×#3952C4semidirect
28. C2×#3950C2×C3semidirect
30. C2×#3940C2×C3semidirect
31. C5×#340C2×C3semidirect
32. #64749C2×C3semidirect
69. C3×#340D5semidirect
83. #3952C3×C4semidirect
174. #340C3×D5semidirect
375. C3×C5#1854semidirect
450. C5C3×#1854semidirect
474. C3#10599670direct (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
C2×C3×#39502
C3×#652762
C2×C3×#39402
C3×C5×#3402
C3×#647492
#105996703
C3×#18545