Finite Group Databasebeta

← C3×#10601122 #14302316

Subgroups — C3×#10601122 #14302316

Order 1920.

648 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4078C211yesmaximal, characteristic
2C3×#66079C211yesmaximal, characteristic, complemented
3C3×C5×#418C211yesmaximal, characteristic, complemented
4C2×C3×#3965C211yesmaximal, characteristic, complemented
5C3×#65294C211yesmaximal, characteristic, complemented
6C3×#64780C211yesmaximal, characteristic, complemented
7C3×#64753C211yesmaximal, characteristic, complemented
8#10601122C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13C2×C3×#687C412yescomplemented
14C3×#4078—22no—
15C3×#4078—22no—
16C2×C3×#686C412yescomplemented
17C2×C3×#681C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C3×#4053—22no—
21C3×D5×M16—22no—
22C3×#4047—22no—
23C3×C5×#102—22no—
24C3×#3965—22no—
25C3×#3937—22no—
26C3×#1903—51nomaximal, Hall
27C2×#4078C2×C311yescharacteristic
28#66079C2×C311yescharacteristic, complemented
29C5×#418C2×C311yescharacteristic, complemented
30C2×#3965C2×C311yescharacteristic, complemented
31#65294C2×C311yescharacteristic, complemented
32#64780C2×C311yescharacteristic, complemented
33#64753C2×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—21no—
43C3×#709—21no—
44C3×#709—21no—
45C3×#709D412yes—
46C3×#709D412yes—
47C2×C3×D20C2×C411yescharacteristic
48C2×C3×C4×D5—21no—
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×#687—24no—
57C3×#686—24no—
58C3×#681—21no—
59C3×#681—21no—
60C3×#681—21no—
61C3×#681—21no—
62C3×#681—21no—
63C3×#681D412yes—
64C2×C3×#168—21no—
65C2×C3×#168—21no—
66C2×C3×#168C2×C412yes—
67C3×#676—24no—
68C3×C8×D5—24no—
69C2×C3×AGL(1,ℤ/8)—51no—
70C3×#568—51no—
71C3×#421—51no—
72C3×#418D511yescharacteristic, complemented
73C2×C3×#100—51no—
74C3×#344—51no—
75C3×#338—51no—
76C22×C5×D4C22×C311yescharacteristic
77C2×#709C22×C311yescharacteristic
78C2×C5×M16C22×C311yescharacteristic
79C5×#117C22×C311yescharacteristic
80C2×#687C3×C412yescomplemented
81#4078—22no—
82#4078—22no—
83C2×#686C3×C412yescomplemented
84C2×#681C22×C311yescharacteristic
85C2×#681C22×C311yescharacteristic
86C2×#681C22×C311yescharacteristic
87#4053—22no—
88D5×M16—22no—
89#4047—22no—
90C5×#102—22no—
91#3965—22no—
92#3937—22no—
93#1903—51noSylow
94C23×C3×C5—22no—
95C23×C3×C5—41no—
96C23×C3×C5—41no—
97C23×C3×C5—82no—
98C23×C3×C5#4111yescharacteristic
99C22×C3×D5—21no—
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×C5C2×D411yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C3×C22⋊D5—22no—
112C3×C22⋊D5—22no—
113C2×C3×Dic5—21no—
114C3×D20—21no—
115C3×D20C22⋊C412yes—
116C3×C4×D5—22no—
117C3×C4×D5—22no—
118C3×Dic10—21no—
119C3×Dic10C22⋊C412yes—
120C3×C5×C8—22no—
121C3×#168—22no—
122C3×#168—22no—
123C3×#168—41no—
124C2×C3×#41—51no—
125C22×C3×D4C2×D511yescharacteristic
126C3×AGL(1,ℤ/8)—102no—
127C3×AGL(1,ℤ/8)—102no—
128C2×C3×SD16—52no—
129C2×C3×D8—52no—
130C3×#131—102no—
131C3×#131—102no—
132C2×C3×M16—51no—
133C2×C3×M16—51no—
134C2×C3×M16—51no—
135C2×C3×M16—102no—
136C2×C3×M16C2×D511yescharacteristic
137C3×#117C2×D511yescharacteristic
138C3×#104—102no—
139C3×#102—22no—
140C3×#100—102no—
141C24×C5—21no—
142C2×C5×D4—21no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4C2×C3×C412yes—
148C22×C4×C5C23×C311yescharacteristic
149C2×C22⋊D5—21no—
150#709—21no—
151#709—21no—
152#709C3×D412yes—
153#709C3×D412yes—
154C2×D20C2×C3×C411yescharacteristic
155C2×C4×D5—21no—
156C2×Dic10C2×C3×C411yescharacteristic
157C5×M16—21no—
158C5×M16—21no—
159C2×C5×C8C3×D412yes—
160C5×C4⋊C4—21no—
161C5×C22⋊C4—21no—
162C42×C5—21no—
163#687—24no—
164#686—24no—
165#681—21no—
166#681—21no—
167#681—21no—
168#681—21no—
169#681—21no—
170#681C3×D412yes—
171C2×#168—21no—
172C2×#168—21no—
173C2×#168C2×C3×C412yes—
174#676—24no—
175C8×D5—24no—
176C2×AGL(1,ℤ/8)—51no—
177#568—51no—
178#421—51no—
179#418C3×D511yescharacteristic, complemented
180C2×#100—51no—
181#344—51no—
182#338—51no—
183C22×C3×C5—41no—
184C22×C3×C5—42no—
185C22×C3×C5—82no—
186C22×C3×C5—82no—
187C22×C3×C5—82no—
188C22×C3×C5C4×D411yescharacteristic
189C22×C3×C5#12111yescharacteristic
190C22×C3×C5#12311yescharacteristic
191C2×C3×D5—22no—
192C2×C3×D5—81no—
193C3×C4×C5—81no—
194C3×C4×C5C2×C22⋊C411yescharacteristic
195C3×C4×C5C4×D411yescharacteristic
196C3×C4×C5#12011yescharacteristic
197C3×C4×C5#12111yescharacteristic
198C3×Dic5—22no—
199C24×C3—21no—
200C3×#41—52no—
201C3×#41—52no—
202C3×#41—101no—
203C3×#41—101no—
204C2×C3×Q8—51no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—51no—
211C2×C3×D4—101no—
212C2×C3×D4C4×D512yes—
213C22×C3×C4—101no—
214C22×C3×C4C22×D511yescharacteristic
215C3×SD16—104no—
216C3×D8—104no—
217C3×M16—21no—
218C3×M16—21no—
219C3×M16—52no—
220C3×M16—104no—
221C3×M16—101no—
222C3×M16—101no—
223C3×M16—101no—
224C3×M16—101no—
225C3×M16—101no—
226C2×C3×C8—52no—
227C2×C3×C8—104no—
228C2×C3×C8—101no—
229C2×C3×C8—101no—
230C2×C3×C8C22⋊D512yes—
231C3×C4⋊C4—21no—
232C3×C22⋊C4—21no—
233C3×C42—21no—
234C23×C5—22no—
235C23×C5—41no—
236C23×C5—41no—
237C23×C5—82no—
238C23×C5C3×#4111yescharacteristic
239C22×D5—21no—
240C5×D4—22no—
241C5×D4—22no—
242C5×D4—41no—
243C5×D4—41no—
244C2×C4×C5—41no—
245C2×C4×C5C22×C3×C411yescharacteristic
246C2×C4×C5C2×C3×D411yescharacteristic
247C2×C4×C5C2×C3×D411yescharacteristic
248C2×C4×C5C2×C3×D411yescharacteristic
249C2×C4×C5C2×C3×D411yescharacteristic
250C2×C4×C5C3×#4111yescharacteristic
251C22⋊D5—22no—
252C22⋊D5—22no—
253C2×Dic5—21no—
254D20—21no—
255D20C3×C22⋊C412yes—
256C4×D5—22no—
257C4×D5—22no—
258Dic10—21no—
259Dic10C3×C22⋊C412yes—
260C5×C8—22no—
261#168—22no—
262#168—22no—
263#168—41no—
264C2×#41—51no—
265C22×D4C2×C3×D511yescharacteristic
266AGL(1,ℤ/8)—102no—
267AGL(1,ℤ/8)—102no—
268C2×SD16—52no—
269C2×D8—52no—
270#131—102no—
271#131—102no—
272C2×M16—51no—
273C2×M16—51no—
274C2×M16—51no—
275C2×M16—102no—
276C2×M16C2×C3×D511yescharacteristic
277#117C2×C3×D511yescharacteristic
278#104—102no—
279#102—22no—
280#100—102no—
281C2×C3×C5—21no—
282C2×C3×C5—21no—
283C2×C3×C5—21no—
284C2×C3×C5—82no—
285C2×C3×C5#38611yescharacteristic
286C3×D5—42no—
287C23×C3—22no—
288C23×C3—41no—
289C23×C3—41no—
290C23×C3—82no—
291C23×C3—101no—
292C23×C3#71111yescharacteristic
293C3×Q8—52no—
294C3×Q8—101no—
295C3×D4—22no—
296C3×D4—22no—
297C3×D4—41no—
298C3×D4—41no—
299C3×D4—52no—
300C3×D4—102no—
301C3×D4—102no—
302C3×D4—101no—
303C2×C3×C4—41no—
304C2×C3×C4—101no—
305C2×C3×C4—102no—
306C2×C3×C4—102no—
307C2×C3×C4C2×C4×D511yescharacteristic
308C2×C3×C4#70911yescharacteristic
309C2×C3×C4D4×D511yescharacteristic
310C2×C3×C4D4×D511yescharacteristic
311C2×C3×C4D4×D511yescharacteristic
312C2×C3×C4C2×C22⋊D511yescharacteristic
313C3×C8—22no—
314C3×C8—102no—
315C3×C8—102no—
316C3×C8—201no—
317C22×C5—41no—
318C22×C5—42no—
319C22×C5—82no—
320C22×C5—82no—
321C22×C5—82no—
322C22×C5C3×C4×D411yescharacteristic
323C22×C5C3×#12111yescharacteristic
324C22×C5C3×#12311yescharacteristic
325C2×D5—22no—
326C2×D5—81no—
327C4×C5—81no—
328C4×C5C2×C3×C22⋊C411yescharacteristic
329C4×C5C3×C4×D411yescharacteristic
330C4×C5C3×#12011yescharacteristic
331C4×C5C3×#12111yescharacteristic
332Dic5—22no—
333C24—21no—
334#41—52no—
335#41—52no—
336#41—101no—
337#41—101no—
338C2×Q8—51no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—51no—
345C2×D4—101no—
346C2×D4C3×C4×D512yes—
347C22×C4—101no—
348C22×C4C22×C3×D511yescharacteristic
349SD16—104no—
350D8—104no—
351M16—21no—
352M16—21no—
353M16—52no—
354M16—104no—
355M16—101no—
356M16—101no—
357M16—101no—
358M16—101no—
359M16—101no—
360C2×C8—52no—
361C2×C8—104no—
362C2×C8—101no—
363C2×C8—101no—
364C2×C8C3×C22⋊D512yes—
365C4⋊C4—21no—
366C22⋊C4—21no—
367C42—21no—
368C3×C5#190311yescharacteristic, complemented, Hall
369C22×C3—41no—
370C22×C3—42no—
371C22×C3—82no—
372C22×C3—82no—
373C22×C3—82no—
374C22×C3—102no—
375C22×C3—401no—
376C22×C3#402711yescharacteristic
377C22×C3#402911yescharacteristic
378C22×C3#408411yescharacteristic
379C3×C4—81no—
380C3×C4—102no—
381C3×C4D5×C22⋊C411yescharacteristic
382C3×C4#403011yescharacteristic
383C3×C4C4×C22⋊D511yescharacteristic
384C3×C4#408311yescharacteristic
385C2×C5—21no—
386C2×C5—21no—
387C2×C5—21no—
388C2×C5—82no—
389C2×C5C3×#38611yescharacteristic
390D5—42no—
391C23—22no—
392C23—41no—
393C23—41no—
394C23—82no—
395C23—101no—
396C23C3×#71111yescharacteristic
397Q8—52no—
398Q8—101no—
399D4—22no—
400D4—22no—
401D4—41no—
402D4—41no—
403D4—52no—
404D4—102no—
405D4—102no—
406D4—101no—
407C2×C4—41no—
408C2×C4—101no—
409C2×C4—102no—
410C2×C4—102no—
411C2×C4C2×C3×C4×D511yescharacteristic
412C2×C4C3×#70911yescharacteristic
413C2×C4C3×D4×D511yescharacteristic
414C2×C4C3×D4×D511yescharacteristic
415C2×C4C3×D4×D511yescharacteristic
416C2×C4C2×C3×C22⋊D511yescharacteristic
417C8—22no—
418C8—102no—
419C8—102no—
420C8—201no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—82no—
425C2×C3—202no—
426C2×C3#6524511yescharacteristic
427C5C3×#190311yescharacteristic, complemented, Sylow
428C22—41no—
429C22—42no—
430C22—82no—
431C22—82no—
432C22—82no—
433C22—102no—
434C22—401no—
435C22C3×#402711yescharacteristic
436C22C3×#402911yescharacteristic
437C22C3×#408411yescharacteristic
438C4—81no—
439C4—102no—
440C4C3×D5×C22⋊C411yescharacteristic
441C4C3×#403011yescharacteristic
442C4C3×C4×C22⋊D511yescharacteristic
443C4C3×#408311yescharacteristic
444C3#1060112211yescharacteristic, direct product factor, Sylow
445C2—21no—
446C2—21no—
447C2—21no—
448C2—82no—
449C2—202no—
450C2C3×#6524511yescharacteristic
subgroupG/H
centerC2×C3#65245
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#418C2
socleC2×C3×C5#386
prime radicalC2×C3×#4078C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#418D5
hypocenterC5C3×#1903
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. C2×C3×#3965C2semidirect
5. C3×#65294C2semidirect
6. C3×#64780C2semidirect
7. C3×#64753C2semidirect
8. #10601122C3direct (N × H)
13. C2×C3×#687C4semidirect
16. C2×C3×#686C4semidirect
28. #66079C2×C3semidirect
29. C5×#418C2×C3semidirect
30. C2×#3965C2×C3semidirect
31. #65294C2×C3semidirect
32. #64780C2×C3semidirect
33. #64753C2×C3semidirect
72. C3×#418D5semidirect
80. C2×#687C3×C4semidirect
83. C2×#686C3×C4semidirect
179. #418C3×D5semidirect
368. C3×C5#1903semidirect
427. C5C3×#1903semidirect
444. C3#10601122direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40782
C3×#660792
C3×C5×#4182
C2×C3×#39652
C3×#652942
C3×#647802
C3×#647532
#106011223
C3×#19035