Finite Group Databasebeta

← C3×#10601143 #14302774

Subgroups — C3×#10601143 #14302774

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66150C211yesmaximal, characteristic
2C3×#66079C211yesmaximal, characteristic
3C3×C5×#419C211yesmaximal, characteristic, complemented
4C3×#65514C211yesmaximal, characteristic, complemented
5C3×#65295C211yesmaximal, characteristic
6C3×#64777C211yesmaximal, characteristic, complemented
7C3×#64751C211yesmaximal, characteristic, complemented
8#10601143C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13C3×#4093C412yescomplemented
14C3×#4092—22no—
15C3×#4090C412yescomplemented
16C3×#4075—22no—
17C3×#4072C2211yescharacteristic
18C3×#4072C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C3×#4053—22no—
21C3×D5×M16—22no—
22C3×#4047—22no—
23C3×C5×#103—22no—
24C3×#3967—22no—
25C3×#3938—22no—
26C3×#1909—51nomaximal, Hall
27#66150C2×C311yescharacteristic
28#66079C2×C311yescharacteristic
29C5×#419C2×C311yescharacteristic, complemented
30#65514C2×C311yescharacteristic, complemented
31#65295C2×C311yescharacteristic
32#64777C2×C311yescharacteristic, complemented
33#64751C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8C2×C412yes—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5C2311yescharacteristic
42C2×C3×C22⋊D5D412yes—
43C3×#709—21no—
44C3×#709—21no—
45C3×#709—21no—
46C3×#709—21no—
47C2×C3×D20C2×C411yescharacteristic
48C2×C3×C4×D5D412yes—
49C2×C3×Dic10C2×C411yescharacteristic
50C3×C5×M16—21no—
51C3×C5×M16—21no—
52C2×C3×C5×C8D412yes—
53C3×C5×C4⋊C4—21no—
54C3×C5×C22⋊C4—21no—
55C3×C42×C5—21no—
56C3×C22⋊Dic5—21no—
57C3×C22⋊Dic5—21no—
58C3×#685—24no—
59C3×C4⋊Dic5—21no—
60C3×C4⋊Dic5—21no—
61C3×#683—24no—
62C3×C4×Dic5—21no—
63C3×C4×Dic5C2×C412yes—
64C3×#681—21no—
65C3×#681—21no—
66C2×C3×#168D412yes—
67C3×#676—24no—
68C3×C8×D5—24no—
69C3×#568—51no—
70C3×#536—51no—
71C3×#419—51no—
72C3×#419D511yescharacteristic, complemented
73C3×#410—51no—
74C3×H(3,ℤ/4)—51no—
75C3×H(3,ℤ/4)—51no—
76C22×C5×Q8C22×C311yescharacteristic
77C2×#709C22×C311yescharacteristic
78C2×C5×M16C22×C311yescharacteristic
79C5×#117C22×C311yescharacteristic
80#4093C3×C412yescomplemented
81#4092—22no—
82#4090C3×C412yescomplemented
83#4075—22no—
84#4072C22×C311yescharacteristic
85#4072C22×C311yescharacteristic
86C2×#681C22×C311yescharacteristic
87#4053—22no—
88D5×M16—22no—
89#4047—22no—
90C5×#103—22no—
91#3967—22no—
92#3938—22no—
93#1909—51noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C3×D5C22⋊C412yes—
96C3×C5×Q8—22no—
97C3×C5×Q8—22no—
98C3×C5×Q8—41no—
99C3×C5×Q8—41no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5C22×C411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C3×C22⋊D5—22no—
111C3×C22⋊D5—22no—
112C2×C3×Dic5—22no—
113C2×C3×Dic5—41no—
114C2×C3×Dic5C22⋊C412yes—
115C3×D20—21no—
116C3×D20—21no—
117C3×C4×D5—22no—
118C3×C4×D5—22no—
119C3×Dic10—21no—
120C3×Dic10—21no—
121C3×C5×C8—22no—
122C3×#168—22no—
123C2×C3×#41—51no—
124C22×C3×Q8C2×D511yescharacteristic
125C3×#131—102no—
126C3×#131—102no—
127C2×C3×M16—51no—
128C2×C3×M16—102no—
129C2×C3×M16C2×D511yescharacteristic
130C3×C4⋊Q8—52no—
131C3×#124—52no—
132C3×#123—102no—
133C3×C22⋊Q8—102no—
134C3×#117—51no—
135C3×#117—51no—
136C3×#117C2×D511yescharacteristic
137C3×#103—22no—
138C3×#103—102no—
139C3×#99—102no—
140C2×C5×Q8—21no—
141C2×C5×Q8—21no—
142C2×C5×Q8—21no—
143C2×C5×Q8—21no—
144C2×C5×Q8—21no—
145C2×C5×Q8C2×C3×C412yes—
146C22×C4×C5—21no—
147C22×C4×C5C23×C311yescharacteristic
148C2×C22⋊D5C3×D412yes—
149#709—21no—
150#709—21no—
151#709—21no—
152#709—21no—
153C2×D20C2×C3×C411yescharacteristic
154C2×C4×D5C3×D412yes—
155C2×Dic10C2×C3×C411yescharacteristic
156C5×M16—21no—
157C5×M16—21no—
158C2×C5×C8C3×D412yes—
159C5×C4⋊C4—21no—
160C5×C22⋊C4—21no—
161C42×C5—21no—
162C22⋊Dic5—21no—
163C22⋊Dic5—21no—
164#685—24no—
165C4⋊Dic5—21no—
166C4⋊Dic5—21no—
167#683—24no—
168C4×Dic5—21no—
169C4×Dic5C2×C3×C412yes—
170#681—21no—
171#681—21no—
172C2×#168C3×D412yes—
173#676—24no—
174C8×D5—24no—
175#568—51no—
176#536—51no—
177#419—51no—
178#419C3×D511yescharacteristic, complemented
179#410—51no—
180H(3,ℤ/4)—51no—
181H(3,ℤ/4)—51no—
182C22×C3×C5—41no—
183C22×C3×C5C2×C22⋊C411yescharacteristic
184C22×C3×C5#12111yescharacteristic
185C22×C3×C5#12111yescharacteristic
186C2×C3×D5—22no—
187C2×C3×D5—42no—
188C3×C4×C5—42no—
189C3×C4×C5—81no—
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5C4×D411yescharacteristic
192C3×C4×C5#12011yescharacteristic
193C3×C4×C5#12311yescharacteristic
194C3×Dic5—22no—
195C3×Dic5—42no—
196C3×Dic5—81no—
197C3×#41—101no—
198C3×#41—101no—
199C3×#41—101no—
200C3×#41—101no—
201C2×C3×Q8—21no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—51no—
207C2×C3×Q8C4×D512yes—
208C2×C3×D4—52no—
209C2×C3×D4—51no—
210C22×C3×C4—21no—
211C22×C3×C4—52no—
212C22×C3×C4C22×D511yescharacteristic
213C3×M16—21no—
214C3×M16—21no—
215C3×M16—104no—
216C3×M16—101no—
217C3×M16—101no—
218C2×C3×C8—52no—
219C2×C3×C8—104no—
220C2×C3×C8C22⋊D512yes—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—104no—
223C3×C4⋊C4—101no—
224C3×C4⋊C4—101no—
225C3×C22⋊C4—21no—
226C3×C22⋊C4—104no—
227C3×C22⋊C4—101no—
228C3×C22⋊C4—101no—
229C3×C42—21no—
230C3×C42—52no—
231C3×C42—101no—
232C23×C5C2×C3×D411yescharacteristic
233C22×D5C3×C22⋊C412yes—
234C5×Q8—22no—
235C5×Q8—22no—
236C5×Q8—41no—
237C5×Q8—41no—
238C2×C4×C5—22no—
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×D411yescharacteristic
246C2×C4×C5C3×#4111yescharacteristic
247C2×C4×C5C3×#4111yescharacteristic
248C22⋊D5—22no—
249C22⋊D5—22no—
250C2×Dic5—22no—
251C2×Dic5—41no—
252C2×Dic5C3×C22⋊C412yes—
253D20—21no—
254D20—21no—
255C4×D5—22no—
256C4×D5—22no—
257Dic10—21no—
258Dic10—21no—
259C5×C8—22no—
260#168—22no—
261C2×#41—51no—
262C22×Q8C2×C3×D511yescharacteristic
263#131—102no—
264#131—102no—
265C2×M16—51no—
266C2×M16—102no—
267C2×M16C2×C3×D511yescharacteristic
268C4⋊Q8—52no—
269#124—52no—
270#123—102no—
271C22⋊Q8—102no—
272#117—51no—
273#117—51no—
274#117C2×C3×D511yescharacteristic
275#103—22no—
276#103—102no—
277#99—102no—
278C2×C3×C5—21no—
279C2×C3×C5—21no—
280C2×C3×C5—21no—
281C2×C3×C5#38611yescharacteristic
282C3×D5—42no—
283C23×C3—52no—
284C23×C3D4×D511yescharacteristic
285C3×Q8—22no—
286C3×Q8—22no—
287C3×Q8—41no—
288C3×Q8—41no—
289C3×Q8—101no—
290C3×Q8—101no—
291C3×D4—102no—
292C3×D4—102no—
293C3×D4—101no—
294C3×D4—101no—
295C2×C3×C4—22no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—52no—
300C2×C3×C4—102no—
301C2×C3×C4—102no—
302C2×C3×C4—102no—
303C2×C3×C4—201no—
304C2×C3×C4C2×C4×D511yescharacteristic
305C2×C3×C4#70911yescharacteristic
306C2×C3×C4D4×D511yescharacteristic
307C2×C3×C4D4×D511yescharacteristic
308C2×C3×C4#71111yescharacteristic
309C2×C3×C4C2×C22⋊D511yescharacteristic
310C3×C8—22no—
311C3×C8—102no—
312C22×C5—41no—
313C22×C5C2×C3×C22⋊C411yescharacteristic
314C22×C5C3×#12111yescharacteristic
315C22×C5C3×#12111yescharacteristic
316C2×D5—22no—
317C2×D5—42no—
318C4×C5—42no—
319C4×C5—81no—
320C4×C5C3×C4×D411yescharacteristic
321C4×C5C3×C4×D411yescharacteristic
322C4×C5C3×#12011yescharacteristic
323C4×C5C3×#12311yescharacteristic
324Dic5—22no—
325Dic5—42no—
326Dic5—81no—
327#41—101no—
328#41—101no—
329#41—101no—
330#41—101no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—51no—
337C2×Q8C3×C4×D512yes—
338C2×D4—52no—
339C2×D4—51no—
340C22×C4—21no—
341C22×C4—52no—
342C22×C4C22×C3×D511yescharacteristic
343M16—21no—
344M16—21no—
345M16—104no—
346M16—101no—
347M16—101no—
348C2×C8—52no—
349C2×C8—104no—
350C2×C8C3×C22⋊D512yes—
351C4⋊C4—21no—
352C4⋊C4—104no—
353C4⋊C4—101no—
354C4⋊C4—101no—
355C22⋊C4—21no—
356C22⋊C4—104no—
357C22⋊C4—101no—
358C22⋊C4—101no—
359C42—21no—
360C42—52no—
361C42—101no—
362C3×C5#190911yescharacteristic, complemented, Hall
363C22×C3—41no—
364C22×C3—102no—
365C22×C3—202no—
366C22×C3D5×C22⋊C411yescharacteristic
367C22×C3#403011yescharacteristic
368C22×C3#408411yescharacteristic
369C3×C4—42no—
370C3×C4—81no—
371C3×C4—102no—
372C3×C4—202no—
373C3×C4—401no—
374C3×C4#402711yescharacteristic
375C3×C4#402911yescharacteristic
376C3×C4C4×C22⋊D511yescharacteristic
377C3×C4#408311yescharacteristic
378C2×C5—21no—
379C2×C5—21no—
380C2×C5—21no—
381C2×C5C3×#38611yescharacteristic
382D5—42no—
383C23—52no—
384C23C3×D4×D511yescharacteristic
385Q8—22no—
386Q8—22no—
387Q8—41no—
388Q8—41no—
389Q8—101no—
390Q8—101no—
391D4—102no—
392D4—102no—
393D4—101no—
394D4—101no—
395C2×C4—22no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—52no—
400C2×C4—102no—
401C2×C4—102no—
402C2×C4—102no—
403C2×C4—201no—
404C2×C4C2×C3×C4×D511yescharacteristic
405C2×C4C3×#70911yescharacteristic
406C2×C4C3×D4×D511yescharacteristic
407C2×C4C3×D4×D511yescharacteristic
408C2×C4C3×#71111yescharacteristic
409C2×C4C2×C3×C22⋊D511yescharacteristic
410C8—22no—
411C8—102no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—202no—
416C2×C3#6524511yescharacteristic
417C5C3×#190911yescharacteristic, complemented, Sylow
418C22—41no—
419C22—102no—
420C22—202no—
421C22C3×D5×C22⋊C411yescharacteristic
422C22C3×#403011yescharacteristic
423C22C3×#408411yescharacteristic
424C4—42no—
425C4—81no—
426C4—102no—
427C4—202no—
428C4—401no—
429C4C3×#402711yescharacteristic
430C4C3×#402911yescharacteristic
431C4C3×C4×C22⋊D511yescharacteristic
432C4C3×#408311yescharacteristic
433C3#1060114311yescharacteristic, direct product factor, Sylow
434C2—21no—
435C2—21no—
436C2—21no—
437C2—202no—
438C2C3×#6524511yescharacteristic
subgroupG/H
centerC2×C3#65245
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#419C2
socleC2×C3×C5#386
prime radicalC2×C3×#709C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#419D5
hypocenterC5C3×#1909
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#419

Complements

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

NH ≅ G/Ntype
3. C3×C5×#419C2semidirect
4. C3×#65514C2semidirect
6. C3×#64777C2semidirect
7. C3×#64751C2semidirect
8. #10601143C3direct (N × H)
13. C3×#4093C4semidirect
15. C3×#4090C4semidirect
29. C5×#419C2×C3semidirect
30. #65514C2×C3semidirect
32. #64777C2×C3semidirect
33. #64751C2×C3semidirect
72. C3×#419D5semidirect
80. #4093C3×C4semidirect
82. #4090C3×C4semidirect
178. #419C3×D5semidirect
362. C3×C5#1909semidirect
417. C5C3×#1909semidirect
433. C3#10601143direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661502
C3×#660792
C3×C5×#4192
C3×#655142
C3×#652952
C3×#647772
C3×#647512
#106011433
C3×#19095