Finite Group Databasebeta

← C3×#10601123 #14302825

Subgroups — C3×#10601123 #14302825

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66139C211yesmaximal, characteristic
2C3×#66079C211yesmaximal, characteristic, complemented
3C3×C5×#418C211yesmaximal, characteristic, complemented
4C3×#65504C211yesmaximal, characteristic, complemented
5C3×#65295C211yesmaximal, characteristic, complemented
6C3×#64777C211yesmaximal, characteristic, complemented
7C3×#64751C211yesmaximal, characteristic, complemented
8#10601123C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13C3×#4099—22no—
14C3×#4086C412yescomplemented
15C3×#4084—22no—
16C3×#4082C412yescomplemented
17C3×#4072C2211yescharacteristic
18C3×#4072C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C3×#4053—22no—
21C3×D5×M16—22no—
22C3×#4047—22no—
23C3×C5×#102—22no—
24C3×#3964—22no—
25C3×#3938—22no—
26C3×#1910—51nomaximal, Hall
27#66139C2×C311yescharacteristic
28#66079C2×C311yescharacteristic, complemented
29C5×#418C2×C311yescharacteristic, complemented
30#65504C2×C311yescharacteristic, complemented
31#65295C2×C311yescharacteristic, complemented
32#64777C2×C311yescharacteristic, complemented
33#64751C2×C311yescharacteristic, complemented
34C24×C3×C5—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4C2×C412yes—
41C22×C3×C4×C5C2311yescharacteristic
42C2×C3×C22⋊D5—24no—
43C2×C3×C22⋊D5D412yes—
44C3×#709—21no—
45C3×#709—21no—
46C3×#709—21no—
47C3×#709—21no—
48C2×C3×D20C2×C411yescharacteristic
49C2×C3×C4×D5D412yes—
50C2×C3×Dic10C2×C411yescharacteristic
51C3×C5×M16—21no—
52C3×C5×M16—21no—
53C2×C3×C5×C8D412yescomplemented
54C3×C5×C4⋊C4—21no—
55C3×C5×C22⋊C4—21no—
56C3×C42×C5—21no—
57C3×C22⋊Dic5—21no—
58C3×C22⋊Dic5—24no—
59C3×C22⋊Dic5—21no—
60C3×C4⋊Dic5—21no—
61C3×C4⋊Dic5—21no—
62C3×C4×Dic5—21no—
63C3×C4×Dic5C2×C412yes—
64C3×#681—21no—
65C3×#681—21no—
66C2×C3×#168D412yescomplemented
67C3×#676—24no—
68C3×C8×D5—24no—
69C3×#568—51no—
70C3×#535—51no—
71C3×#418—51no—
72C3×#418D511yescharacteristic, complemented
73C3×#410—51no—
74C3×H(3,ℤ/4)—51no—
75C3×H(3,ℤ/4)—51no—
76C22×C5×D4C22×C311yescharacteristic
77C2×#709C22×C311yescharacteristic
78C2×C5×M16C22×C311yescharacteristic
79C5×#117C22×C311yescharacteristic
80#4099—22no—
81#4086C3×C412yescomplemented
82#4084—22no—
83#4082C3×C412yescomplemented
84#4072C22×C311yescharacteristic
85#4072C22×C311yescharacteristic
86C2×#681C22×C311yescharacteristic
87#4053—22no—
88D5×M16—22no—
89#4047—22no—
90C5×#102—22no—
91#3964—22no—
92#3938—22no—
93#1910—51noSylow
94C23×C3×C5—22no—
95C23×C3×C5—41no—
96C23×C3×C5—41no—
97C23×C3×C5—82no—
98C23×C3×C5C2×D411yescharacteristic
99C22×C3×D5C22⋊C412yes—
100C3×C5×D4—22no—
101C3×C5×D4—22no—
102C3×C5×D4—41no—
103C3×C5×D4—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5C22×C411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C3×C22⋊D5—22no—
112C3×C22⋊D5—22no—
113C3×C22⋊D5—84no—
114C2×C3×Dic5—22no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5C22⋊C412yes—
117C3×D20—21no—
118C3×D20—21no—
119C3×C4×D5—22no—
120C3×C4×D5—22no—
121C3×Dic10—21no—
122C3×Dic10—21no—
123C3×C5×C8—22no—
124C3×#168—22no—
125C2×C3×#41—51no—
126C22×C3×D4C2×D511yescharacteristic
127C3×#131—102no—
128C3×#131—102no—
129C2×C3×M16—51no—
130C2×C3×M16—102no—
131C2×C3×M16C2×D511yescharacteristic
132C3×#127—52no—
133C3×#124—52no—
134C3×#121—102no—
135C3×#120—102no—
136C3×#117—51no—
137C3×#117—51no—
138C3×#117C2×D511yescharacteristic
139C3×#102—22no—
140C3×#102—102no—
141C3×#99—102no—
142C24×C5—21no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4—21no—
148C2×C5×D4C2×C3×C412yes—
149C22×C4×C5C23×C311yescharacteristic
150C2×C22⋊D5—24no—
151C2×C22⋊D5C3×D412yes—
152#709—21no—
153#709—21no—
154#709—21no—
155#709—21no—
156C2×D20C2×C3×C411yescharacteristic
157C2×C4×D5C3×D412yes—
158C2×Dic10C2×C3×C411yescharacteristic
159C5×M16—21no—
160C5×M16—21no—
161C2×C5×C8C3×D412yescomplemented
162C5×C4⋊C4—21no—
163C5×C22⋊C4—21no—
164C42×C5—21no—
165C22⋊Dic5—21no—
166C22⋊Dic5—24no—
167C22⋊Dic5—21no—
168C4⋊Dic5—21no—
169C4⋊Dic5—21no—
170C4×Dic5—21no—
171C4×Dic5C2×C3×C412yes—
172#681—21no—
173#681—21no—
174C2×#168C3×D412yescomplemented
175#676—24no—
176C8×D5—24no—
177#568—51no—
178#535—51no—
179#418—51no—
180#418C3×D511yescharacteristic, complemented
181#410—51no—
182H(3,ℤ/4)—51no—
183H(3,ℤ/4)—51no—
184C22×C3×C5—41no—
185C22×C3×C5—44no—
186C22×C3×C5—42no—
187C22×C3×C5—82no—
188C22×C3×C5—82no—
189C22×C3×C5C2×C22⋊C411yescharacteristic
190C22×C3×C5#12111yescharacteristic
191C22×C3×C5#12111yescharacteristic
192C2×C3×D5—22no—
193C2×C3×D5—42no—
194C3×C4×C5—81no—
195C3×C4×C5C4×D411yescharacteristic
196C3×C4×C5C4×D411yescharacteristic
197C3×C4×C5#12011yescharacteristic
198C3×C4×C5#12311yescharacteristic
199C3×Dic5—22no—
200C3×Dic5—42no—
201C3×Dic5—81no—
202C24×C3—21no—
203C3×#41—101no—
204C3×#41—101no—
205C3×#41—101no—
206C3×#41—101no—
207C2×C3×Q8—51no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—52no—
214C2×C3×D4—51no—
215C2×C3×D4—104no—
216C2×C3×D4C4×D512yes—
217C22×C3×C4—52no—
218C22×C3×C4C22×D511yescharacteristic
219C3×M16—21no—
220C3×M16—21no—
221C3×M16—104no—
222C3×M16—101no—
223C3×M16—101no—
224C2×C3×C8—52no—
225C2×C3×C8—104no—
226C2×C3×C8C22⋊D512yescomplemented
227C3×C4⋊C4—21no—
228C3×C4⋊C4—101no—
229C3×C4⋊C4—101no—
230C3×C22⋊C4—21no—
231C3×C22⋊C4—104no—
232C3×C22⋊C4—101no—
233C3×C22⋊C4—101no—
234C3×C42—21no—
235C3×C42—52no—
236C3×C42—101no—
237C23×C5—22no—
238C23×C5—41no—
239C23×C5—41no—
240C23×C5—82no—
241C23×C5C2×C3×D411yescharacteristic
242C22×D5C3×C22⋊C412yes—
243C5×D4—22no—
244C5×D4—22no—
245C5×D4—41no—
246C5×D4—41no—
247C2×C4×C5—41no—
248C2×C4×C5C22×C3×C411yescharacteristic
249C2×C4×C5C2×C3×D411yescharacteristic
250C2×C4×C5C2×C3×D411yescharacteristic
251C2×C4×C5C2×C3×D411yescharacteristic
252C2×C4×C5C3×#4111yescharacteristic
253C2×C4×C5C3×#4111yescharacteristic
254C22⋊D5—22no—
255C22⋊D5—22no—
256C22⋊D5—84no—
257C2×Dic5—22no—
258C2×Dic5—41no—
259C2×Dic5C3×C22⋊C412yes—
260D20—21no—
261D20—21no—
262C4×D5—22no—
263C4×D5—22no—
264Dic10—21no—
265Dic10—21no—
266C5×C8—22no—
267#168—22no—
268C2×#41—51no—
269C22×D4C2×C3×D511yescharacteristic
270#131—102no—
271#131—102no—
272C2×M16—51no—
273C2×M16—102no—
274C2×M16C2×C3×D511yescharacteristic
275#127—52no—
276#124—52no—
277#121—102no—
278#120—102no—
279#117—51no—
280#117—51no—
281#117C2×C3×D511yescharacteristic
282#102—22no—
283#102—102no—
284#99—102no—
285C2×C3×C5—21no—
286C2×C3×C5—21no—
287C2×C3×C5—21no—
288C2×C3×C5—82no—
289C2×C3×C5#38611yescharacteristic
290C3×D5—42no—
291C23×C3—22no—
292C23×C3—41no—
293C23×C3—41no—
294C23×C3—52no—
295C23×C3—82no—
296C23×C3D4×D511yescharacteristic
297C3×Q8—101no—
298C3×Q8—101no—
299C3×D4—22no—
300C3×D4—22no—
301C3×D4—41no—
302C3×D4—41no—
303C3×D4—102no—
304C3×D4—102no—
305C3×D4—101no—
306C3×D4—101no—
307C3×D4—404no—
308C2×C3×C4—41no—
309C2×C3×C4—52no—
310C2×C3×C4—102no—
311C2×C3×C4—102no—
312C2×C3×C4—102no—
313C2×C3×C4—201no—
314C2×C3×C4C2×C4×D511yescharacteristic
315C2×C3×C4#70911yescharacteristic
316C2×C3×C4D4×D511yescharacteristic
317C2×C3×C4D4×D511yescharacteristic
318C2×C3×C4#71111yescharacteristic
319C2×C3×C4C2×C22⋊D511yescharacteristic
320C3×C8—22no—
321C3×C8—102no—
322C22×C5—41no—
323C22×C5—44no—
324C22×C5—42no—
325C22×C5—82no—
326C22×C5—82no—
327C22×C5C2×C3×C22⋊C411yescharacteristic
328C22×C5C3×#12111yescharacteristic
329C22×C5C3×#12111yescharacteristic
330C2×D5—22no—
331C2×D5—42no—
332C4×C5—81no—
333C4×C5C3×C4×D411yescharacteristic
334C4×C5C3×C4×D411yescharacteristic
335C4×C5C3×#12011yescharacteristic
336C4×C5C3×#12311yescharacteristic
337Dic5—22no—
338Dic5—42no—
339Dic5—81no—
340C24—21no—
341#41—101no—
342#41—101no—
343#41—101no—
344#41—101no—
345C2×Q8—51no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—52no—
352C2×D4—51no—
353C2×D4—104no—
354C2×D4C3×C4×D512yes—
355C22×C4—52no—
356C22×C4C22×C3×D511yescharacteristic
357M16—21no—
358M16—21no—
359M16—104no—
360M16—101no—
361M16—101no—
362C2×C8—52no—
363C2×C8—104no—
364C2×C8C3×C22⋊D512yescomplemented
365C4⋊C4—21no—
366C4⋊C4—101no—
367C4⋊C4—101no—
368C22⋊C4—21no—
369C22⋊C4—104no—
370C22⋊C4—101no—
371C22⋊C4—101no—
372C42—21no—
373C42—52no—
374C42—101no—
375C3×C5#191011yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3—44no—
378C22×C3—42no—
379C22×C3—82no—
380C22×C3—82no—
381C22×C3—102no—
382C22×C3—202no—
383C22×C3D5×C22⋊C411yescharacteristic
384C22×C3#403011yescharacteristic
385C22×C3#408411yescharacteristic
386C3×C4—81no—
387C3×C4—102no—
388C3×C4—202no—
389C3×C4—401no—
390C3×C4#402711yescharacteristic
391C3×C4#402911yescharacteristic
392C3×C4C4×C22⋊D511yescharacteristic
393C3×C4#408311yescharacteristic
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—21no—
397C2×C5—82no—
398C2×C5C3×#38611yescharacteristic
399D5—42no—
400C23—22no—
401C23—41no—
402C23—41no—
403C23—52no—
404C23—82no—
405C23C3×D4×D511yescharacteristic
406Q8—101no—
407Q8—101no—
408D4—22no—
409D4—22no—
410D4—41no—
411D4—41no—
412D4—102no—
413D4—102no—
414D4—101no—
415D4—101no—
416D4—404no—
417C2×C4—41no—
418C2×C4—52no—
419C2×C4—102no—
420C2×C4—102no—
421C2×C4—102no—
422C2×C4—201no—
423C2×C4C2×C3×C4×D511yescharacteristic
424C2×C4C3×#70911yescharacteristic
425C2×C4C3×D4×D511yescharacteristic
426C2×C4C3×D4×D511yescharacteristic
427C2×C4C3×#71111yescharacteristic
428C2×C4C2×C3×C22⋊D511yescharacteristic
429C8—22no—
430C8—102no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—82no—
435C2×C3—202no—
436C2×C3#6524511yescharacteristic
437C5C3×#191011yescharacteristic, complemented, Sylow
438C22—41no—
439C22—44no—
440C22—42no—
441C22—82no—
442C22—82no—
443C22—102no—
444C22—202no—
445C22C3×D5×C22⋊C411yescharacteristic
446C22C3×#403011yescharacteristic
447C22C3×#408411yescharacteristic
448C4—81no—
449C4—102no—
450C4—202no—
451C4—401no—
452C4C3×#402711yescharacteristic
453C4C3×#402911yescharacteristic
454C4C3×C4×C22⋊D511yescharacteristic
455C4C3×#408311yescharacteristic
456C3#1060112311yescharacteristic, direct product factor, Sylow
457C2—21no—
458C2—21no—
459C2—21no—
460C2—82no—
461C2—202no—
462C2C3×#6524511yescharacteristic
subgroupG/H
centerC2×C3#65245
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#418C2
socleC2×C3×C5#386
prime radicalC3×#66139C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#418D5
hypocenterC5C3×#1910
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#418

Complements

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

NH ≅ G/Ntype
2. C3×#66079C2semidirect
3. C3×C5×#418C2semidirect
4. C3×#65504C2semidirect
5. C3×#65295C2semidirect
6. C3×#64777C2semidirect
7. C3×#64751C2semidirect
8. #10601123C3direct (N × H)
14. C3×#4086C4semidirect
16. C3×#4082C4semidirect
28. #66079C2×C3semidirect
29. C5×#418C2×C3semidirect
30. #65504C2×C3semidirect
31. #65295C2×C3semidirect
32. #64777C2×C3semidirect
33. #64751C2×C3semidirect
53. C2×C3×C5×C8D4semidirect
66. C2×C3×#168D4semidirect
72. C3×#418D5semidirect
81. #4086C3×C4semidirect
83. #4082C3×C4semidirect
161. C2×C5×C8C3×D4semidirect
174. C2×#168C3×D4semidirect
180. #418C3×D5semidirect
226. C2×C3×C8C22⋊D5semidirect
364. C2×C8C3×C22⋊D5semidirect
375. C3×C5#1910semidirect
437. C5C3×#1910semidirect
456. C3#10601123direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661392
C3×#660792
C3×C5×#4182
C3×#655042
C3×#652952
C3×#647772
C3×#647512
#106011233
C3×#19105