Finite Group Databasebeta

← C3×#10599834 #14303080

Subgroups — C3×#10599834 #14303080

Order 1920.

616 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66079C211yesmaximal, characteristic
2C3×#65860C211yesmaximal, characteristic
3C2×C3×#3956C211yesmaximal, characteristic, complemented
4C2×C3×#3956C211yesmaximal, characteristic, complemented
5C3×#65421C211yesmaximal, characteristic
6C3×C5×#344C211yesmaximal, characteristic, complemented
7C3×#64753C211yesmaximal, characteristic, complemented
8#10599834C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#709C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C3×C5×M16C2211yescharacteristic
13C3×C5×#117C2211yescharacteristic
14C2×C3×#681C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16C3×#4053—22no—
17C3×D5×M16—22no—
18C3×#4047—22no—
19C3×#4043—22no—
20C3×#4032C414yes—
21C3×#4021—21no—
22C3×#4015—21no—
23C3×#3956—21no—
24C3×#3956—22no—
25C3×#3956—22no—
26C3×#3955—21no—
27C3×#1915—51nomaximal, Hall
28#66079C2×C311yescharacteristic
29#65860C2×C311yescharacteristic
30C2×#3956C2×C311yescharacteristic, complemented
31C2×#3956C2×C311yescharacteristic, complemented
32#65421C2×C311yescharacteristic
33C5×#344C2×C311yescharacteristic, complemented
34#64753C2×C311yescharacteristic, complemented
35C22×C3×C4×C5C2311yescharacteristic
36C2×C3×C22⋊D5C2×C412yes—
37C22×C3×Dic5C2×C412yes—
38C3×#709—21no—
39C3×#709—21no—
40C3×#709—21no—
41C3×#709—21no—
42C2×C3×D20D411yescharacteristic
43C2×C3×C4×D5D412yes—
44C2×C3×Dic10—21no—
45C2×C3×Dic10—21no—
46C2×C3×Dic10—21no—
47C2×C3×Dic10—21no—
48C2×C3×Dic10—21no—
49C2×C3×Dic10—21no—
50C2×C3×Dic10D411yescharacteristic
51C3×C5×M16—21no—
52C3×C5×M16—21no—
53C3×C5×M16—21no—
54C3×C5×M16D412yes—
55C2×C3×C5×C8—21no—
56C2×C3×C5×C8—21no—
57C3×C5×C4⋊C4—21no—
58C3×C5×C22⋊C4C2×C412yes—
59C3×C42×C5—21no—
60C3×#685—24no—
61C3×C4⋊Dic5—24no—
62C3×#681—21no—
63C3×#681—21no—
64C3×#681—21no—
65C3×#681D412yes—
66C2×C3×#168—21no—
67C2×C3×#168—21no—
68C3×#676—24no—
69C3×C8×D5—24no—
70C3×#568—51no—
71C3×#536—51no—
72C3×#413—51no—
73C2×C3×#101—51no—
74C2×C3×#101—51no—
75C3×#344—51no—
76C3×#344D511yescharacteristic, complemented
77C2×#709C22×C311yescharacteristic
78C22×Dic10C22×C311yescharacteristic
79C2×C5×M16C22×C311yescharacteristic
80C2×C5×M16C22×C311yescharacteristic
81C5×#117C22×C311yescharacteristic
82C2×#681C22×C311yescharacteristic
83C2×#681C22×C311yescharacteristic
84#4053—22no—
85D5×M16—22no—
86#4047—22no—
87#4043—22no—
88#4032C3×C414yes—
89#4021—21no—
90#4015—21no—
91#3956—21no—
92#3956—22no—
93#3956—22no—
94#3955—21no—
95#1915—51noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×C3×D5C22⋊C412yes—
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C3×C22⋊D5—22no—
106C3×C22⋊D5—22no—
107C2×C3×Dic5—22no—
108C2×C3×Dic5—22no—
109C2×C3×Dic5—22no—
110C2×C3×Dic5C22⋊C412yes—
111C3×D20—21no—
112C3×D20—21no—
113C3×C4×D5—22no—
114C3×C4×D5—22no—
115C3×Dic10—21no—
116C3×Dic10—21no—
117C3×Dic10—41no—
118C3×Dic10—41no—
119C3×Dic10—41no—
120C3×Dic10—41no—
121C3×C5×C8—22no—
122C3×C5×C8—41no—
123C3×#168—22no—
124C3×#168—41no—
125C2×C3×#41—51no—
126C22×C3×Q8—51no—
127C3×#131—102no—
128C3×#131—102no—
129C2×C3×M16—51no—
130C2×C3×M16—51no—
131C2×C3×M16—102no—
132C2×C3×M16C2×D511yescharacteristic
133C2×C3×M16C2×D511yescharacteristic
134C3×C4⋊Q8—101no—
135C3×#124—101no—
136C3×#123—54no—
137C3×C22⋊Q8—102no—
138C3×#117C2×D511yescharacteristic
139C3×#101—102no—
140C3×#101—101no—
141C3×#101—102no—
142C3×#100—101no—
143C22×C4×C5C23×C311yescharacteristic
144C2×C22⋊D5C2×C3×C412yes—
145C22×Dic5C2×C3×C412yes—
146#709—21no—
147#709—21no—
148#709—21no—
149#709—21no—
150C2×D20C3×D411yescharacteristic
151C2×C4×D5C3×D412yes—
152C2×Dic10—21no—
153C2×Dic10—21no—
154C2×Dic10—21no—
155C2×Dic10—21no—
156C2×Dic10—21no—
157C2×Dic10—21no—
158C2×Dic10C3×D411yescharacteristic
159C5×M16—21no—
160C5×M16—21no—
161C5×M16—21no—
162C5×M16C3×D412yes—
163C2×C5×C8—21no—
164C2×C5×C8—21no—
165C5×C4⋊C4—21no—
166C5×C22⋊C4C2×C3×C412yes—
167C42×C5—21no—
168#685—24no—
169C4⋊Dic5—24no—
170#681—21no—
171#681—21no—
172#681—21no—
173#681C3×D412yes—
174C2×#168—21no—
175C2×#168—21no—
176#676—24no—
177C8×D5—24no—
178#568—51no—
179#536—51no—
180#413—51no—
181C2×#101—51no—
182C2×#101—51no—
183#344—51no—
184#344C3×D511yescharacteristic, complemented
185C22×C3×C5—41no—
186C22×C3×C5C2×C22⋊C411yescharacteristic
187C22×C3×C5C4×D411yescharacteristic
188C22×C3×C5C4×D411yescharacteristic
189C2×C3×D5—22no—
190C2×C3×D5—42no—
191C3×C4×C5—42no—
192C3×C4×C5#12011yescharacteristic
193C3×C4×C5#12111yescharacteristic
194C3×C4×C5#12111yescharacteristic
195C3×C4×C5#12311yescharacteristic
196C3×Dic5—22no—
197C3×Dic5—42no—
198C3×#41—101no—
199C3×#41—101no—
200C3×#41—101no—
201C3×#41—101no—
202C2×C3×Q8—51no—
203C2×C3×Q8—101no—
204C2×C3×Q8—101no—
205C2×C3×Q8—101no—
206C2×C3×Q8—101no—
207C2×C3×Q8—101no—
208C2×C3×Q8—101no—
209C2×C3×D4—52no—
210C2×C3×D4—51no—
211C22×C3×C4—52no—
212C22×C3×C4—52no—
213C22×C3×C4C22×D511yescharacteristic
214C3×M16—21no—
215C3×M16—21no—
216C3×M16—21no—
217C3×M16—52no—
218C3×M16—104no—
219C3×M16—101no—
220C3×M16—101no—
221C3×M16—101no—
222C3×M16D2012yes—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—104no—
226C2×C3×C8—101no—
227C2×C3×C8—101no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—104no—
230C3×C22⋊C4—104no—
231C3×C22⋊C4C4×D512yes—
232C3×C42—21no—
233C23×C5C22×C3×C411yescharacteristic
234C22×D5C3×C22⋊C412yes—
235C2×C4×C5—22no—
236C2×C4×C5C2×C3×D411yescharacteristic
237C2×C4×C5C2×C3×D411yescharacteristic
238C2×C4×C5C2×C3×D411yescharacteristic
239C2×C4×C5C2×C3×D411yescharacteristic
240C2×C4×C5C3×#4111yescharacteristic
241C2×C4×C5C3×#4111yescharacteristic
242C22⋊D5—22no—
243C22⋊D5—22no—
244C2×Dic5—22no—
245C2×Dic5—22no—
246C2×Dic5—22no—
247C2×Dic5C3×C22⋊C412yes—
248D20—21no—
249D20—21no—
250C4×D5—22no—
251C4×D5—22no—
252Dic10—21no—
253Dic10—21no—
254Dic10—41no—
255Dic10—41no—
256Dic10—41no—
257Dic10—41no—
258C5×C8—22no—
259C5×C8—41no—
260#168—22no—
261#168—41no—
262C2×#41—51no—
263C22×Q8—51no—
264#131—102no—
265#131—102no—
266C2×M16—51no—
267C2×M16—51no—
268C2×M16—102no—
269C2×M16C2×C3×D511yescharacteristic
270C2×M16C2×C3×D511yescharacteristic
271C4⋊Q8—101no—
272#124—101no—
273#123—54no—
274C22⋊Q8—102no—
275#117C2×C3×D511yescharacteristic
276#101—102no—
277#101—101no—
278#101—102no—
279#100—101no—
280C2×C3×C5—21no—
281C2×C3×C5—21no—
282C2×C3×C5—21no—
283C2×C3×C5#38611yescharacteristic
284C3×D5—42no—
285C23×C3—52no—
286C23×C3C2×C4×D511yescharacteristic
287C3×Q8—101no—
288C3×Q8—101no—
289C3×Q8—201no—
290C3×Q8—201no—
291C3×Q8—201no—
292C3×Q8—201no—
293C3×D4—102no—
294C3×D4—102no—
295C3×D4—101no—
296C3×D4—101no—
297C2×C3×C4—22no—
298C2×C3×C4—52no—
299C2×C3×C4—102no—
300C2×C3×C4—102no—
301C2×C3×C4—102no—
302C2×C3×C4—102no—
303C2×C3×C4—102no—
304C2×C3×C4C2×D2011yescharacteristic
305C2×C3×C4#70911yescharacteristic
306C2×C3×C4D4×D511yescharacteristic
307C2×C3×C4D4×D511yescharacteristic
308C2×C3×C4D4×D511yescharacteristic
309C2×C3×C4#71311yescharacteristic
310C3×C8—22no—
311C3×C8—41no—
312C3×C8—102no—
313C3×C8—201no—
314C22×C5—41no—
315C22×C5C2×C3×C22⋊C411yescharacteristic
316C22×C5C3×C4×D411yescharacteristic
317C22×C5C3×C4×D411yescharacteristic
318C2×D5—22no—
319C2×D5—42no—
320C4×C5—42no—
321C4×C5C3×#12011yescharacteristic
322C4×C5C3×#12111yescharacteristic
323C4×C5C3×#12111yescharacteristic
324C4×C5C3×#12311yescharacteristic
325Dic5—22no—
326Dic5—42no—
327#41—101no—
328#41—101no—
329#41—101no—
330#41—101no—
331C2×Q8—51no—
332C2×Q8—101no—
333C2×Q8—101no—
334C2×Q8—101no—
335C2×Q8—101no—
336C2×Q8—101no—
337C2×Q8—101no—
338C2×D4—52no—
339C2×D4—51no—
340C22×C4—52no—
341C22×C4—52no—
342C22×C4C22×C3×D511yescharacteristic
343M16—21no—
344M16—21no—
345M16—21no—
346M16—52no—
347M16—104no—
348M16—101no—
349M16—101no—
350M16—101no—
351M16C3×D2012yes—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—104no—
355C2×C8—101no—
356C2×C8—101no—
357C4⋊C4—21no—
358C4⋊C4—104no—
359C22⋊C4—104no—
360C22⋊C4C3×C4×D512yes—
361C42—21no—
362C3×C5#191511yescharacteristic, complemented, Hall
363C22×C3—41no—
364C22×C3—102no—
365C22×C3—202no—
366C22×C3C4×D2011yescharacteristic
367C22×C3D5×C22⋊C411yescharacteristic
368C22×C3#403911yescharacteristic
369C3×C4—42no—
370C3×C4—102no—
371C3×C4—202no—
372C3×C4#402811yescharacteristic
373C3×C4#403011yescharacteristic
374C3×C4#404011yescharacteristic
375C3×C4#404111yescharacteristic
376C2×C5—21no—
377C2×C5—21no—
378C2×C5—21no—
379C2×C5C3×#38611yescharacteristic
380D5—42no—
381C23—52no—
382C23C2×C3×C4×D511yescharacteristic
383Q8—101no—
384Q8—101no—
385Q8—201no—
386Q8—201no—
387Q8—201no—
388Q8—201no—
389D4—102no—
390D4—102no—
391D4—101no—
392D4—101no—
393C2×C4—22no—
394C2×C4—52no—
395C2×C4—102no—
396C2×C4—102no—
397C2×C4—102no—
398C2×C4—102no—
399C2×C4—102no—
400C2×C4C2×C3×D2011yescharacteristic
401C2×C4C3×#70911yescharacteristic
402C2×C4C3×D4×D511yescharacteristic
403C2×C4C3×D4×D511yescharacteristic
404C2×C4C3×D4×D511yescharacteristic
405C2×C4C3×#71311yescharacteristic
406C8—22no—
407C8—41no—
408C8—102no—
409C8—201no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—202no—
414C2×C3#6495411yescharacteristic
415C5C3×#191511yescharacteristic, complemented, Sylow
416C22—41no—
417C22—102no—
418C22—202no—
419C22C3×C4×D2011yescharacteristic
420C22C3×D5×C22⋊C411yescharacteristic
421C22C3×#403911yescharacteristic
422C4—42no—
423C4—102no—
424C4—202no—
425C4C3×#402811yescharacteristic
426C4C3×#403011yescharacteristic
427C4C3×#404011yescharacteristic
428C4C3×#404111yescharacteristic
429C3#1059983411yescharacteristic, direct product factor, Sylow
430C2—21no—
431C2—21no—
432C2—21no—
433C2—202no—
434C2C3×#6495411yescharacteristic
subgroupG/H
centerC2×C3#64954
commutatorC23×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#344C2
socleC2×C3×C5#386
prime radicalC2×C3×#709C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#344D5
hypocenterC5C3×#1915
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#344

Complements

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

NH ≅ G/Ntype
3. C2×C3×#3956C2semidirect
4. C2×C3×#3956C2semidirect
6. C3×C5×#344C2semidirect
7. C3×#64753C2semidirect
8. #10599834C3direct (N × H)
30. C2×#3956C2×C3semidirect
31. C2×#3956C2×C3semidirect
33. C5×#344C2×C3semidirect
34. #64753C2×C3semidirect
76. C3×#344D5semidirect
184. #344C3×D5semidirect
362. C3×C5#1915semidirect
415. C5C3×#1915semidirect
429. C3#10599834direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660792
C3×#658602
C2×C3×#39562
C3×#654212
C3×C5×#3442
C3×#647532
#105998343
C3×#19155