Finite Group Databasebeta

← C3×#10599559 #14301571

Subgroups — C3×#10599559 #14301571

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65850C211yesmaximal, characteristic, complemented
2C2×C3×#4021C211yesmaximal, characteristic
3C2×C3×#3956C211yesmaximal, characteristic, complemented
4C3×#65420C211yesmaximal, characteristic
5C3×#65290C211yesmaximal, characteristic
6C3×C5×#339C211yesmaximal, characteristic, complemented
7C3×#64743C211yesmaximal, characteristic, complemented
8#10599559C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×D20C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13C2×C3×C42×C5C2211yescharacteristic
14C2×C3×#685—22no—
15C3×#4072C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17C3×#4033—22no—
18C3×#4023—22no—
19C3×#4021—22no—
20C3×#4021C414yescomplemented
21C3×C4×Dic10—22no—
22C3×#3956—22no—
23C3×#3953—22no—
24C3×#3941—22no—
25C3×#1888—51nomaximal, Hall
26#65850C2×C311yescharacteristic, complemented
27C2×#4021C2×C311yescharacteristic
28C2×#3956C2×C311yescharacteristic, complemented
29#65420C2×C311yescharacteristic
30#65290C2×C311yescharacteristic
31C5×#339C2×C311yescharacteristic, complemented
32#64743C2×C311yescharacteristic, complemented
33C23×C3×D5—21no—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C22×C3×Dic5D412yes—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20C2×C412yes—
43C2×C3×Dic10—21no—
44C2×C3×Dic10—21no—
45C2×C3×Dic10—21no—
46C2×C3×Dic10—21no—
47C2×C3×Dic10C2×C412yes—
48C2×C3×Dic10D412yes—
49C3×C5×M16—21no—
50C3×C5×M16—21no—
51C2×C3×C5×C8—21no—
52C3×C5×C4⋊C4D412yes—
53C3×C5×C22⋊C4—21no—
54C3×C42×C5—21no—
55C3×C42×C5—21no—
56C3×C42×C5C2×C412yes—
57C3×C22⋊Dic5—21no—
58C3×#685—28no—
59C3×C4⋊Dic5D412yes—
60C3×#683—24no—
61C3×C4×Dic5—24no—
62C3×C4×Dic5—21no—
63C3×#681—21no—
64C3×#681—21no—
65C2×C3×#168—21no—
66C2×C3×#124—51no—
67C3×#519—51no—
68C3×#418—51no—
69C3×#418—51no—
70C2×C3×#101—51no—
71C3×#339—51no—
72C3×#339D511yescharacteristic, complemented
73C22×D20C22×C311yescharacteristic
74C22×Dic10C22×C311yescharacteristic
75C2×C5×M16C22×C311yescharacteristic
76C5×#117C22×C311yescharacteristic
77C2×C42×C5C22×C311yescharacteristic
78C2×#685—22no—
79#4072C22×C311yescharacteristic
80C2×#681C22×C311yescharacteristic
81#4033—22no—
82#4023—22no—
83#4021—22no—
84#4021C3×C414yescomplemented
85C4×Dic10—22no—
86#3956—22no—
87#3953—22no—
88#3941—22no—
89#1888—51noSylow
90C23×C3×C5C2×D411yescharacteristic
91C22×C3×D5—22no—
92C22×C3×D5—44no—
93C22×C3×D5—41no—
94C22×C3×D5—41no—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5—22no—
97C2×C3×C4×C5—42no—
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×C3×Dic5—22no—
105C2×C3×Dic5—22no—
106C2×C3×Dic5—22no—
107C2×C3×Dic5C22⋊C414yes—
108C3×D20—22no—
109C3×D20—22no—
110C3×D20—41no—
111C3×D20—41no—
112C3×Dic10—22no—
113C3×Dic10—22no—
114C3×Dic10—22no—
115C3×Dic10—22no—
116C3×C5×C8—41no—
117C3×#168—41no—
118C22×C3×Q8—51no—
119C22×C3×D4—51no—
120C2×C3×M16—51no—
121C2×C3×M16C2×D511yescharacteristic
122C3×#124—54no—
123C3×#124—102no—
124C3×C4×Q8—102no—
125C3×C4×Q8—102no—
126C3×#117—51no—
127C3×#117—102no—
128C3×#117C2×D511yescharacteristic
129C2×C3×C22⋊C4—102no—
130C2×C3×C42C2×D511yescharacteristic
131C3×#102—102no—
132C3×#102—102no—
133C3×#101—102no—
134C23×D5—21no—
135C22×C4×C5—21no—
136C22×C4×C5C23×C311yescharacteristic
137C22×Dic5C3×D412yes—
138C2×D20—21no—
139C2×D20—21no—
140C2×D20—21no—
141C2×D20—21no—
142C2×D20—21no—
143C2×D20C2×C3×C412yes—
144C2×Dic10—21no—
145C2×Dic10—21no—
146C2×Dic10—21no—
147C2×Dic10—21no—
148C2×Dic10C2×C3×C412yes—
149C2×Dic10C3×D412yes—
150C5×M16—21no—
151C5×M16—21no—
152C2×C5×C8—21no—
153C5×C4⋊C4C3×D412yes—
154C5×C22⋊C4—21no—
155C42×C5—21no—
156C42×C5—21no—
157C42×C5C2×C3×C412yes—
158C22⋊Dic5—21no—
159#685—28no—
160C4⋊Dic5C3×D412yes—
161#683—24no—
162C4×Dic5—24no—
163C4×Dic5—21no—
164#681—21no—
165#681—21no—
166C2×#168—21no—
167C2×#124—51no—
168#519—51no—
169#418—51no—
170#418—51no—
171C2×#101—51no—
172#339—51no—
173#339C3×D511yescharacteristic, complemented
174C22×C3×C5—22no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C22×C3×C5#12011yescharacteristic
177C22×C3×C5#12311yescharacteristic
178C2×C3×D5—44no—
179C2×C3×D5—42no—
180C2×C3×D5—82no—
181C2×C3×D5—82no—
182C3×C4×C5—42no—
183C3×C4×C5—42no—
184C3×C4×C5C4×D411yescharacteristic
185C3×C4×C5C4×D411yescharacteristic
186C3×C4×C5#12111yescharacteristic
187C3×C4×C5#12111yescharacteristic
188C3×Dic5—24no—
189C3×Dic5—42no—
190C24×C3—101no—
191C2×C3×Q8—52no—
192C2×C3×Q8—52no—
193C2×C3×Q8—101no—
194C2×C3×Q8—101no—
195C2×C3×Q8—101no—
196C2×C3×Q8—101no—
197C2×C3×D4—52no—
198C2×C3×D4—101no—
199C2×C3×D4—101no—
200C2×C3×D4—101no—
201C2×C3×D4—101no—
202C2×C3×D4—101no—
203C22×C3×C4—21no—
204C22×C3×C4—52no—
205C22×C3×C4C22×D511yescharacteristic
206C3×M16—21no—
207C3×M16—21no—
208C3×M16—101no—
209C3×M16—101no—
210C2×C3×C8—21no—
211C2×C3×C8—101no—
212C3×C4⋊C4—52no—
213C3×C4⋊C4—104no—
214C3×C4⋊C4D2012yes—
215C3×C22⋊C4—21no—
216C3×C22⋊C4—108no—
217C3×C22⋊C4—101no—
218C3×C42—21no—
219C3×C42—21no—
220C3×C42—104no—
221C3×C42—101no—
222C3×C42C4×D512yes—
223C23×C5C2×C3×D411yescharacteristic
224C22×D5—22no—
225C22×D5—44no—
226C22×D5—41no—
227C22×D5—41no—
228C2×C4×C5—22no—
229C2×C4×C5—22no—
230C2×C4×C5—42no—
231C2×C4×C5C22×C3×C411yescharacteristic
232C2×C4×C5C2×C3×D411yescharacteristic
233C2×C4×C5C2×C3×D411yescharacteristic
234C2×C4×C5C2×C3×D411yescharacteristic
235C2×C4×C5C3×#4111yescharacteristic
236C2×C4×C5C3×#4111yescharacteristic
237C2×Dic5—22no—
238C2×Dic5—22no—
239C2×Dic5—22no—
240C2×Dic5C3×C22⋊C414yes—
241D20—22no—
242D20—22no—
243D20—41no—
244D20—41no—
245Dic10—22no—
246Dic10—22no—
247Dic10—22no—
248Dic10—22no—
249C5×C8—41no—
250#168—41no—
251C22×Q8—51no—
252C22×D4—51no—
253C2×M16—51no—
254C2×M16C2×C3×D511yescharacteristic
255#124—54no—
256#124—102no—
257C4×Q8—102no—
258C4×Q8—102no—
259#117—51no—
260#117—102no—
261#117C2×C3×D511yescharacteristic
262C2×C22⋊C4—102no—
263C2×C42C2×C3×D511yescharacteristic
264#102—102no—
265#102—102no—
266#101—102no—
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5#38611yescharacteristic
270C2×C3×C5#45412yes—
271C3×D5—82no—
272C23×C3—102no—
273C23×C3—204no—
274C23×C3—201no—
275C23×C3—201no—
276C23×C3D4×D511yescharacteristic
277C3×Q8—102no—
278C3×Q8—102no—
279C3×Q8—102no—
280C3×Q8—102no—
281C3×D4—102no—
282C3×D4—102no—
283C3×D4—201no—
284C3×D4—201no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—42no—
288C2×C3×C4—54no—
289C2×C3×C4—102no—
290C2×C3×C4—102no—
291C2×C3×C4—102no—
292C2×C3×C4C2×C4×D511yescharacteristic
293C2×C3×C4C2×D2011yescharacteristic
294C2×C3×C4#70911yescharacteristic
295C2×C3×C4D4×D511yescharacteristic
296C2×C3×C4D4×D511yescharacteristic
297C2×C3×C4#71311yescharacteristic
298C3×C8—41no—
299C3×C8—201no—
300C22×C5—22no—
301C22×C5C2×C3×C22⋊C411yescharacteristic
302C22×C5C3×#12011yescharacteristic
303C22×C5C3×#12311yescharacteristic
304C2×D5—44no—
305C2×D5—42no—
306C2×D5—82no—
307C2×D5—82no—
308C4×C5—42no—
309C4×C5—42no—
310C4×C5C3×C4×D411yescharacteristic
311C4×C5C3×C4×D411yescharacteristic
312C4×C5C3×#12111yescharacteristic
313C4×C5C3×#12111yescharacteristic
314Dic5—24no—
315Dic5—42no—
316C24—101no—
317C2×Q8—52no—
318C2×Q8—52no—
319C2×Q8—101no—
320C2×Q8—101no—
321C2×Q8—101no—
322C2×Q8—101no—
323C2×D4—52no—
324C2×D4—101no—
325C2×D4—101no—
326C2×D4—101no—
327C2×D4—101no—
328C2×D4—101no—
329C22×C4—21no—
330C22×C4—52no—
331C22×C4C22×C3×D511yescharacteristic
332M16—21no—
333M16—21no—
334M16—101no—
335M16—101no—
336C2×C8—21no—
337C2×C8—101no—
338C4⋊C4—52no—
339C4⋊C4—104no—
340C4⋊C4C3×D2012yes—
341C22⋊C4—21no—
342C22⋊C4—108no—
343C22⋊C4—101no—
344C42—21no—
345C42—21no—
346C42—104no—
347C42—101no—
348C42C3×C4×D512yes—
349C3×C5#188811yescharacteristic, complemented, Hall
350C22×C3—22no—
351C22×C3—204no—
352C22×C3—202no—
353C22×C3—402no—
354C22×C3—402no—
355C22×C3D5×C22⋊C411yescharacteristic
356C22×C3#402811yescharacteristic
357C22×C3#404011yescharacteristic
358C3×C4—42no—
359C3×C4—42no—
360C3×C4—104no—
361C3×C4—202no—
362C3×C4C4×D2011yescharacteristic
363C3×C4#403011yescharacteristic
364C3×C4#403911yescharacteristic
365C3×C4#404111yescharacteristic
366C2×C5—21no—
367C2×C5—21no—
368C2×C5C3×#38611yescharacteristic
369C2×C5C3×#45412yes—
370D5—82no—
371C23—102no—
372C23—204no—
373C23—201no—
374C23—201no—
375C23C3×D4×D511yescharacteristic
376Q8—102no—
377Q8—102no—
378Q8—102no—
379Q8—102no—
380D4—102no—
381D4—102no—
382D4—201no—
383D4—201no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—42no—
387C2×C4—54no—
388C2×C4—102no—
389C2×C4—102no—
390C2×C4—102no—
391C2×C4C2×C3×C4×D511yescharacteristic
392C2×C4C2×C3×D2011yescharacteristic
393C2×C4C3×#70911yescharacteristic
394C2×C4C3×D4×D511yescharacteristic
395C2×C4C3×D4×D511yescharacteristic
396C2×C4C3×#71311yescharacteristic
397C8—41no—
398C8—201no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—402no—
402C2×C3#6495411yescharacteristic
403C2×C3#6511612yes—
404C5C3×#188811yescharacteristic, complemented, Sylow
405C22—22no—
406C22—204no—
407C22—202no—
408C22—402no—
409C22—402no—
410C22C3×D5×C22⋊C411yescharacteristic
411C22C3×#402811yescharacteristic
412C22C3×#404011yescharacteristic
413C4—42no—
414C4—42no—
415C4—104no—
416C4—202no—
417C4C3×C4×D2011yescharacteristic
418C4C3×#403011yescharacteristic
419C4C3×#403911yescharacteristic
420C4C3×#404111yescharacteristic
421C3#1059955911yescharacteristic, direct product factor, Sylow
422C2—21no—
423C2—21no—
424C2—402no—
425C2C3×#6495411yescharacteristic
426C2C3×#6511612yes—
subgroupG/H
centerC22×C3#4028
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#339C2
socleC22×C3×C5#120
prime radicalC22×C3×D20C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#339D5
hypocenterC5C3×#1888
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#339

Complements

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

NH ≅ G/Ntype
1. C3×#65850C2semidirect
3. C2×C3×#3956C2semidirect
6. C3×C5×#339C2semidirect
7. C3×#64743C2semidirect
8. #10599559C3direct (N × H)
20. C3×#4021C4semidirect
26. #65850C2×C3semidirect
28. C2×#3956C2×C3semidirect
31. C5×#339C2×C3semidirect
32. #64743C2×C3semidirect
72. C3×#339D5semidirect
84. #4021C3×C4semidirect
173. #339C3×D5semidirect
349. C3×C5#1888semidirect
404. C5C3×#1888semidirect
421. C3#10599559direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658502
C2×C3×#40212
C2×C3×#39562
C3×#654202
C3×#652902
C3×C5×#3392
C3×#647432
#105995593
C3×#18885