Finite Group Databasebeta

← C3×#10601200 #14302395

Subgroups — C3×#10601200 #14302395

Order 1920.

692 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
1C2×C3×#4095C211yesmaximal, characteristic
2C3×#65855C211yesmaximal, characteristic, complemented
3C3×C5×#421C211yesmaximal, characteristic, complemented
4C3×#65529C211yesmaximal, characteristic, complemented
5C3×#65420C211yesmaximal, characteristic, complemented
6C3×#64779C211yesmaximal, characteristic, complemented
7C3×#64751C211yesmaximal, characteristic, complemented
8#10601200C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13C3×#4095—22no—
14C3×#4095—22no—
15C2×C3×#688C412yescomplemented
16C2×C3×#686C412yescomplemented
17C3×#4072C2211yescharacteristic
18C3×#4072C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C3×#4039—22no—
21C3×D5×C22⋊C4—22no—
22C3×C4×D20—22no—
23C3×C5×#104—22no—
24C3×#3966—22no—
25C3×#3953—22no—
26C3×#1904—51nomaximal, Hall
27C2×#4095C2×C311yescharacteristic
28#65855C2×C311yescharacteristic, complemented
29C5×#421C2×C311yescharacteristic, complemented
30#65529C2×C311yescharacteristic, complemented
31#65420C2×C311yescharacteristic, complemented
32#64779C2×C311yescharacteristic, complemented
33#64751C2×C311yescharacteristic, complemented
34C23×C3×D5—21no—
35C3×C5×#41—21no—
36C3×C5×#41—21no—
37C3×C5×#41—21no—
38C3×C5×#41—21no—
39C2×C3×C5×Q8C2×C411yescharacteristic, complemented
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4C2×C411yescharacteristic, complemented
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5C2311yescharacteristic
44C2×C3×D20—21no—
45C2×C3×D20—21no—
46C2×C3×D20—21no—
47C2×C3×D20C2×C412yes—
48C2×C3×D20D412yes—
49C2×C3×D20D412yes—
50C2×C3×C4×D5—24no—
51C3×C5×M16—21no—
52C3×C5×M16—21no—
53C2×C3×C5×C8—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C22⋊C4—21no—
56C3×C42×C5D412yes—
57C3×C22⋊Dic5—21no—
58C3×C22⋊Dic5D412yes—
59C3×#688—24no—
60C3×#686—24no—
61C3×#685—24no—
62C3×C4⋊Dic5—21no—
63C3×C4⋊Dic5—21no—
64C3×C4×Dic5—21no—
65C3×C4×Dic5—21no—
66C3×#681—21no—
67C3×#681—21no—
68C2×C3×#168C2×C412yescomplemented
69C2×C3×AGL(1,ℤ/8)—51no—
70C3×#518—51no—
71C3×#421D511yescharacteristic, complemented
72C3×#418—51no—
73C3×#410—51no—
74C3×#344—51no—
75C3×H(3,ℤ/4)—51no—
76C2×C5×#41C22×C311yescharacteristic
77C22×D20C22×C311yescharacteristic
78C2×C5×M16C22×C311yescharacteristic
79C5×#117C22×C311yescharacteristic
80#4095—22no—
81#4095—22no—
82C2×#688C3×C412yescomplemented
83C2×#686C3×C412yescomplemented
84#4072C22×C311yescharacteristic
85#4072C22×C311yescharacteristic
86C2×#681C22×C311yescharacteristic
87#4039—22no—
88D5×C22⋊C4—22no—
89C4×D20—22no—
90C5×#104—22no—
91#3966—22no—
92#3953—22no—
93#1904—51noSylow
94C23×C3×C5—21no—
95C23×C3×C5C2×D411yescharacteristic
96C22×C3×D5—22no—
97C22×C3×D5—22no—
98C22×C3×D5—22no—
99C22×C3×D5—82no—
100C3×C5×Q8—21no—
101C3×C5×Q8—21no—
102C3×C5×D4—21no—
103C3×C5×D4—21no—
104C3×C5×D4—41no—
105C3×C5×D4—41no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5C22×C411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116C2×C3×Dic5—22no—
117C2×C3×Dic5—41no—
118C3×D20—22no—
119C3×D20—22no—
120C3×D20—22no—
121C3×D20C22⋊C414yes—
122C3×C4×D5—84no—
123C3×C5×C8—41no—
124C3×#168—22no—
125C2×C3×#41C2×D511yescharacteristic
126C22×C3×D4—51no—
127C3×AGL(1,ℤ/8)—102no—
128C3×AGL(1,ℤ/8)—102no—
129C2×C3×SD16—52no—
130C2×C3×D8—52no—
131C2×C3×M16—51no—
132C2×C3×M16C2×D511yescharacteristic
133C3×C4×D4—102no—
134C3×C4×D4—102no—
135C3×#117—51no—
136C3×#117—51no—
137C3×#117C2×D511yescharacteristic
138C2×C3×C22⋊C4—102no—
139C3×#104—22no—
140C3×#102—102no—
141C3×#99—102no—
142C23×D5—21no—
143C5×#41—21no—
144C5×#41—21no—
145C5×#41—21no—
146C5×#41—21no—
147C2×C5×Q8C2×C3×C411yescharacteristic, complemented
148C2×C5×D4—21no—
149C2×C5×D4C2×C3×C411yescharacteristic, complemented
150C22×C4×C5—21no—
151C22×C4×C5C23×C311yescharacteristic
152C2×D20—21no—
153C2×D20—21no—
154C2×D20—21no—
155C2×D20C2×C3×C412yes—
156C2×D20C3×D412yes—
157C2×D20C3×D412yes—
158C2×C4×D5—24no—
159C5×M16—21no—
160C5×M16—21no—
161C2×C5×C8—21no—
162C5×C4⋊C4—21no—
163C5×C22⋊C4—21no—
164C42×C5C3×D412yes—
165C22⋊Dic5—21no—
166C22⋊Dic5C3×D412yes—
167#688—24no—
168#686—24no—
169#685—24no—
170C4⋊Dic5—21no—
171C4⋊Dic5—21no—
172C4×Dic5—21no—
173C4×Dic5—21no—
174#681—21no—
175#681—21no—
176C2×#168C2×C3×C412yescomplemented
177C2×AGL(1,ℤ/8)—51no—
178#518—51no—
179#421C3×D511yescharacteristic, complemented
180#418—51no—
181#410—51no—
182#344—51no—
183H(3,ℤ/4)—51no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5—81no—
187C22×C3×C5C4×D411yescharacteristic
188C22×C3×C5#12011yescharacteristic
189C22×C3×C5#12111yescharacteristic
190C2×C3×D5—24no—
191C2×C3×D5—44no—
192C2×C3×D5—82no—
193C2×C3×D5—82no—
194C3×C4×C5—42no—
195C3×C4×C5—41no—
196C3×C4×C5C2×C22⋊C411yescharacteristic
197C3×C4×C5C4×D411yescharacteristic
198C3×C4×C5#12111yescharacteristic
199C3×C4×C5#12311yescharacteristic
200C3×Dic5—42no—
201C3×Dic5—81no—
202C24×C3—101no—
203C3×#41—21no—
204C3×#41—21no—
205C3×#41—21no—
206C3×#41—21no—
207C2×C3×Q8C4×D511yescharacteristic, complemented
208C2×C3×D4—21no—
209C2×C3×D4—52no—
210C2×C3×D4—52no—
211C2×C3×D4—52no—
212C2×C3×D4—101no—
213C2×C3×D4—101no—
214C2×C3×D4—101no—
215C2×C3×D4C4×D511yescharacteristic, complemented
216C22×C3×C4—21no—
217C22×C3×C4—104no—
218C22×C3×C4C22×D511yescharacteristic
219C3×SD16—104no—
220C3×D8—104no—
221C3×M16—21no—
222C3×M16—21no—
223C3×M16—101no—
224C3×M16—101no—
225C2×C3×C8—21no—
226C2×C3×C8—52no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—101no—
229C3×C4⋊C4—101no—
230C3×C22⋊C4—21no—
231C3×C22⋊C4—52no—
232C3×C22⋊C4—104no—
233C3×C22⋊C4—101no—
234C3×C42—101no—
235C3×C42—101no—
236C3×C42C22⋊D512yes—
237C23×C5—21no—
238C23×C5C2×C3×D411yescharacteristic
239C22×D5—22no—
240C22×D5—22no—
241C22×D5—22no—
242C22×D5—82no—
243C5×Q8—21no—
244C5×Q8—21no—
245C5×D4—21no—
246C5×D4—21no—
247C5×D4—41no—
248C5×D4—41no—
249C2×C4×C5—21no—
250C2×C4×C5—22no—
251C2×C4×C5—41no—
252C2×C4×C5—41no—
253C2×C4×C5C22×C3×C411yescharacteristic
254C2×C4×C5C2×C3×D411yescharacteristic
255C2×C4×C5C2×C3×D411yescharacteristic
256C2×C4×C5C2×C3×D411yescharacteristic
257C2×C4×C5C3×#4111yescharacteristic
258C2×C4×C5C3×#4111yescharacteristic
259C2×Dic5—22no—
260C2×Dic5—41no—
261D20—22no—
262D20—22no—
263D20—22no—
264D20C3×C22⋊C414yes—
265C4×D5—84no—
266C5×C8—41no—
267#168—22no—
268C2×#41C2×C3×D511yescharacteristic
269C22×D4—51no—
270AGL(1,ℤ/8)—102no—
271AGL(1,ℤ/8)—102no—
272C2×SD16—52no—
273C2×D8—52no—
274C2×M16—51no—
275C2×M16C2×C3×D511yescharacteristic
276C4×D4—102no—
277C4×D4—102no—
278#117—51no—
279#117—51no—
280#117C2×C3×D511yescharacteristic
281C2×C22⋊C4—102no—
282#104—22no—
283#102—102no—
284#99—102no—
285C2×C3×C5—21no—
286C2×C3×C5—21no—
287C2×C3×C5—21no—
288C2×C3×C5—81no—
289C2×C3×C5#38611yescharacteristic
290C3×D5—44no—
291C23×C3—21no—
292C23×C3—102no—
293C23×C3—102no—
294C23×C3—102no—
295C23×C3—402no—
296C23×C3D4×D511yescharacteristic
297C3×Q8—21no—
298C3×Q8—21no—
299C3×D4—21no—
300C3×D4—21no—
301C3×D4—41no—
302C3×D4—41no—
303C3×D4—54no—
304C3×D4—102no—
305C3×D4—102no—
306C3×D4—102no—
307C2×C3×C4—21no—
308C2×C3×C4—22no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—102no—
312C2×C3×C4—201no—
313C2×C3×C4—404no—
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—41no—
321C3×C8—102no—
322C22×C5—41no—
323C22×C5—41no—
324C22×C5—81no—
325C22×C5C3×C4×D411yescharacteristic
326C22×C5C3×#12011yescharacteristic
327C22×C5C3×#12111yescharacteristic
328C2×D5—24no—
329C2×D5—44no—
330C2×D5—82no—
331C2×D5—82no—
332C4×C5—42no—
333C4×C5—41no—
334C4×C5C2×C3×C22⋊C411yescharacteristic
335C4×C5C3×C4×D411yescharacteristic
336C4×C5C3×#12111yescharacteristic
337C4×C5C3×#12311yescharacteristic
338Dic5—42no—
339Dic5—81no—
340C24—101no—
341#41—21no—
342#41—21no—
343#41—21no—
344#41—21no—
345C2×Q8C3×C4×D511yescharacteristic, complemented
346C2×D4—21no—
347C2×D4—52no—
348C2×D4—52no—
349C2×D4—52no—
350C2×D4—101no—
351C2×D4—101no—
352C2×D4—101no—
353C2×D4C3×C4×D511yescharacteristic, complemented
354C22×C4—21no—
355C22×C4—104no—
356C22×C4C22×C3×D511yescharacteristic
357SD16—104no—
358D8—104no—
359M16—21no—
360M16—21no—
361M16—101no—
362M16—101no—
363C2×C8—21no—
364C2×C8—52no—
365C4⋊C4—21no—
366C4⋊C4—101no—
367C4⋊C4—101no—
368C22⋊C4—21no—
369C22⋊C4—52no—
370C22⋊C4—104no—
371C22⋊C4—101no—
372C42—101no—
373C42—101no—
374C42C3×C22⋊D512yes—
375C3×C5#190411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—81no—
379C22×C3—104no—
380C22×C3—204no—
381C22×C3—402no—
382C22×C3—402no—
383C22×C3#402711yescharacteristic
384C22×C3#403011yescharacteristic
385C22×C3#408311yescharacteristic
386C3×C4—42no—
387C3×C4—41no—
388C3×C4—202no—
389C3×C4—401no—
390C3×C4D5×C22⋊C411yescharacteristic
391C3×C4#402911yescharacteristic
392C3×C4C4×C22⋊D511yescharacteristic
393C3×C4#408411yescharacteristic
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—21no—
397C2×C5—81no—
398C2×C5C3×#38611yescharacteristic
399D5—44no—
400C23—21no—
401C23—102no—
402C23—102no—
403C23—102no—
404C23—402no—
405C23C3×D4×D511yescharacteristic
406Q8—21no—
407Q8—21no—
408D4—21no—
409D4—21no—
410D4—41no—
411D4—41no—
412D4—54no—
413D4—102no—
414D4—102no—
415D4—102no—
416C2×C4—22no—
417C2×C4—21no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—102no—
421C2×C4—201no—
422C2×C4—404no—
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—41no—
430C8—102no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—81no—
435C2×C3—204no—
436C2×C3#6524511yescharacteristic
437C5C3×#190411yescharacteristic, complemented, Sylow
438C22—41no—
439C22—41no—
440C22—81no—
441C22—104no—
442C22—204no—
443C22—402no—
444C22—402no—
445C22C3×#402711yescharacteristic
446C22C3×#403011yescharacteristic
447C22C3×#408311yescharacteristic
448C4—42no—
449C4—41no—
450C4—202no—
451C4—401no—
452C4C3×D5×C22⋊C411yescharacteristic
453C4C3×#402911yescharacteristic
454C4C3×C4×C22⋊D511yescharacteristic
455C4C3×#408411yescharacteristic
456C3#1060120011yescharacteristic, direct product factor, Sylow
457C2—21no—
458C2—21no—
459C2—21no—
460C2—81no—
461C2—204no—
462C2C3×#6524511yescharacteristic
subgroupG/H
centerC2×C3#65245
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#421C2
socleC2×C3×C5#386
prime radicalC2×C3×#4095C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#421D5
hypocenterC5C3×#1904
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#421

Complements

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

NH ≅ G/Ntype
2. C3×#65855C2semidirect
3. C3×C5×#421C2semidirect
4. C3×#65529C2semidirect
5. C3×#65420C2semidirect
6. C3×#64779C2semidirect
7. C3×#64751C2semidirect
8. #10601200C3direct (N × H)
15. C2×C3×#688C4semidirect
16. C2×C3×#686C4semidirect
28. #65855C2×C3semidirect
29. C5×#421C2×C3semidirect
30. #65529C2×C3semidirect
31. #65420C2×C3semidirect
32. #64779C2×C3semidirect
33. #64751C2×C3semidirect
39. C2×C3×C5×Q8C2×C4semidirect
41. C2×C3×C5×D4C2×C4semidirect
68. C2×C3×#168C2×C4semidirect
71. C3×#421D5semidirect
82. C2×#688C3×C4semidirect
83. C2×#686C3×C4semidirect
147. C2×C5×Q8C2×C3×C4semidirect
149. C2×C5×D4C2×C3×C4semidirect
176. C2×#168C2×C3×C4semidirect
179. #421C3×D5semidirect
207. C2×C3×Q8C4×D5semidirect
215. C2×C3×D4C4×D5semidirect
345. C2×Q8C3×C4×D5semidirect
353. C2×D4C3×C4×D5semidirect
375. C3×C5#1904semidirect
437. C5C3×#1904semidirect
456. C3#10601200direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40952
C3×#658552
C3×C5×#4212
C3×#655292
C3×#654202
C3×#647792
C3×#647512
#106012003
C3×#19045