Finite Group Databasebeta

← C3×#10601169 #14300216

Subgroups — C3×#10601169 #14300216

Order 1920.

540 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
1C2×C3×#4094C211yesmaximal, characteristic
2C2×C3×C5×#104C211yesmaximal, characteristic
3C3×#65522C211yesmaximal, characteristic
4C2×C3×#3954C211yesmaximal, characteristic, complemented
5C3×#65408C211yesmaximal, characteristic, complemented
6C3×#64744C211yesmaximal, characteristic, complemented
7C3×#64743C211yesmaximal, characteristic, complemented
8#10601169C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12C3×#4094—22no—
13C3×#4094—22no—
14C3×#4072C2211yescharacteristic
15C2×C3×#681—21no—
16C2×C3×#681C2211yescharacteristic
17C22×C3×#168—21no—
18C22×C3×#168C2211yescharacteristic
19C22×C3×#168C2211yescharacteristic
20C3×C5×#104—22no—
21C3×#3967C411yescharacteristic, complemented
22C3×#3967C411yescharacteristic, complemented
23C3×#3964C411yescharacteristic, complemented
24C3×#3964C411yescharacteristic, complemented
25C3×#3954—22no—
26C3×#3946—21no—
27C3×#3946—21no—
28C3×#1866—51nomaximal, Hall
29C2×#4094C2×C311yescharacteristic
30C2×C5×#104C2×C311yescharacteristic
31#65522C2×C311yescharacteristic
32C2×#3954C2×C311yescharacteristic, complemented
33#65408C2×C311yescharacteristic, complemented
34#64744C2×C311yescharacteristic, complemented
35#64743C2×C311yescharacteristic, complemented
36C3×C5×#41—21no—
37C3×C5×#41—21no—
38C3×C5×#41D412yes—
39C3×C5×#41Q812yes—
40C2×C3×C5×Q8C2×C411yescharacteristic
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4C2×C411yescharacteristic
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5C2311yescharacteristic
46C3×C5×M16—21no—
47C3×C5×M16—21no—
48C2×C3×C5×C8—21no—
49C3×C42×C5—21no—
50C3×C42×C5—21no—
51C3×C22⋊Dic5—21no—
52C3×C4⋊Dic5C2×C411yescharacteristic
53C3×C4⋊Dic5C2×C411yescharacteristic
54C3×C4×Dic5—21no—
55C3×#681—24no—
56C3×#681—21no—
57C3×#681D412yes—
58C2×C3×#168—24no—
59C2×C3×#168—21no—
60C2×C3×#168—21no—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C2×C3×#168—21no—
64C2×C3×#168C2×C411yescharacteristic
65C2×C3×#168C2×C411yescharacteristic
66C2×C3×#168D411yescharacteristic
67C2×C3×#168D411yescharacteristic
68C2×C3×#131—51no—
69C2×C3×#108—51no—
70C3×#424—51no—
71C2×C3×#104D511yescharacteristic
72C3×#416—51no—
73C3×#339—51no—
74C3×#336—51no—
75C2×C5×#41C22×C311yescharacteristic
76C2×C5×M16C22×C311yescharacteristic
77C2×C42×C5C22×C311yescharacteristic
78#4094—22no—
79#4094—22no—
80#4072C22×C311yescharacteristic
81C2×#681—21no—
82C2×#681C22×C311yescharacteristic
83C22×#168—21no—
84C22×#168C22×C311yescharacteristic
85C22×#168C22×C311yescharacteristic
86C5×#104—22no—
87#3967C3×C411yescharacteristic, complemented
88#3967C3×C411yescharacteristic, complemented
89#3964C3×C411yescharacteristic, complemented
90#3964C3×C411yescharacteristic, complemented
91#3954—22no—
92#3946—21no—
93#3946—21no—
94#1866—51noSylow
95C23×C3×C5—21no—
96C23×C3×C5#4111yescharacteristic
97C3×C5×Q8—21no—
98C3×C5×Q8C4⋊C412yes—
99C3×C5×D4—22no—
100C3×C5×D4—22no—
101C3×C5×D4—21no—
102C3×C5×D4C4⋊C412yes—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—22no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—22no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×Q811yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×C3×Dic5—21no—
116C2×C3×Dic5—21no—
117C3×C5×C8—41no—
118C3×#168—21no—
119C3×#168—21no—
120C3×#168—21no—
121C3×#168—22no—
122C3×#168—21no—
123C2×C3×#41C2×D511yescharacteristic
124C3×#131—102no—
125C3×#131—102no—
126C2×C3×M16—51no—
127C2×C3×M16—101no—
128C2×C3×M16C2×D511yescharacteristic
129C22×C3×C8—51no—
130C22×C3×C8—51no—
131C22×C3×C8—101no—
132C3×#117—51no—
133C2×C3×C42C2×D511yescharacteristic
134C3×#108—102no—
135C3×C4⋊C8—101no—
136C3×C4⋊C8—101no—
137C3×#104—22no—
138C3×#103—51no—
139C3×#103—51no—
140C3×#102—51no—
141C3×#102—51no—
142C5×#41—21no—
143C5×#41—21no—
144C5×#41C3×D412yes—
145C5×#41C3×Q812yes—
146C2×C5×Q8C2×C3×C411yescharacteristic
147C2×C5×D4—21no—
148C2×C5×D4C2×C3×C411yescharacteristic
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5C23×C311yescharacteristic
152C5×M16—21no—
153C5×M16—21no—
154C2×C5×C8—21no—
155C42×C5—21no—
156C42×C5—21no—
157C22⋊Dic5—21no—
158C4⋊Dic5C2×C3×C411yescharacteristic
159C4⋊Dic5C2×C3×C411yescharacteristic
160C4×Dic5—21no—
161#681—24no—
162#681—21no—
163#681C3×D412yes—
164C2×#168—24no—
165C2×#168—21no—
166C2×#168—21no—
167C2×#168—21no—
168C2×#168—21no—
169C2×#168—21no—
170C2×#168C2×C3×C411yescharacteristic
171C2×#168C2×C3×C411yescharacteristic
172C2×#168C3×D411yescharacteristic
173C2×#168C3×D411yescharacteristic
174C2×#131—51no—
175C2×#108—51no—
176#424—51no—
177C2×#104C3×D511yescharacteristic
178#416—51no—
179#339—51no—
180#336—51no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5—22no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5C4×D411yescharacteristic
187C22×C3×C5C22⋊Q811yescharacteristic
188C22×C3×C5#12311yescharacteristic
189C3×C4×C5—22no—
190C3×C4×C5—42no—
191C3×C4×C5C2×C4⋊C411yescharacteristic
192C3×C4×C5C4×D411yescharacteristic
193C3×C4×C5#12011yescharacteristic
194C3×C4×C5C22⋊Q811yescharacteristic
195C3×Dic5—41no—
196C3×Dic5—41no—
197C3×#41—21no—
198C3×#41—21no—
199C3×#41Dic1012yes—
200C3×#41C22⋊D512yes—
201C2×C3×Q8C4×D511yescharacteristic
202C2×C3×D4—21no—
203C2×C3×D4C4×D511yescharacteristic
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4C22×D511yescharacteristic
207C3×M16—21no—
208C3×M16—21no—
209C3×M16—52no—
210C3×M16—104no—
211C3×M16—101no—
212C2×C3×C8—21no—
213C2×C3×C8—51no—
214C2×C3×C8—51no—
215C2×C3×C8—51no—
216C2×C3×C8—51no—
217C2×C3×C8—104no—
218C2×C3×C8—101no—
219C2×C3×C8—101no—
220C2×C3×C8—101no—
221C2×C3×C8—101no—
222C2×C3×C8—101no—
223C3×C4⋊C4—51no—
224C3×C4⋊C4—51no—
225C3×C22⋊C4—101no—
226C3×C42—21no—
227C3×C42—21no—
228C3×C42—101no—
229C23×C5—21no—
230C23×C5C3×#4111yescharacteristic
231C5×Q8—21no—
232C5×Q8C3×C4⋊C412yes—
233C5×D4—22no—
234C5×D4—22no—
235C5×D4—21no—
236C5×D4C3×C4⋊C412yes—
237C2×C4×C5—21no—
238C2×C4×C5—22no—
239C2×C4×C5—22no—
240C2×C4×C5—22no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5C22×C3×C411yescharacteristic
244C2×C4×C5C2×C3×D411yescharacteristic
245C2×C4×C5C2×C3×D411yescharacteristic
246C2×C4×C5C2×C3×D411yescharacteristic
247C2×C4×C5C2×C3×Q811yescharacteristic
248C2×C4×C5C3×#4111yescharacteristic
249C2×Dic5—21no—
250C2×Dic5—21no—
251C5×C8—41no—
252#168—21no—
253#168—21no—
254#168—21no—
255#168—22no—
256#168—21no—
257C2×#41C2×C3×D511yescharacteristic
258#131—102no—
259#131—102no—
260C2×M16—51no—
261C2×M16—101no—
262C2×M16C2×C3×D511yescharacteristic
263C22×C8—51no—
264C22×C8—51no—
265C22×C8—101no—
266#117—51no—
267C2×C42C2×C3×D511yescharacteristic
268#108—102no—
269C4⋊C8—101no—
270C4⋊C8—101no—
271#104—22no—
272#103—51no—
273#103—51no—
274#102—51no—
275#102—51no—
276C2×C3×C5—21no—
277C2×C3×C5—21no—
278C2×C3×C5—42no—
279C2×C3×C5#38511yescharacteristic
280C2×C3×C5#44311yescharacteristic
281C2×C3×C5#44411yescharacteristic
282C23×C3—21no—
283C23×C3#71111yescharacteristic
284C3×Q8—21no—
285C3×Q8#68312yes—
286C3×D4—22no—
287C3×D4—22no—
288C3×D4—21no—
289C3×D4#68312yes—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—101no—
297C2×C3×C4—101no—
298C2×C3×C4C2×Dic1011yescharacteristic
299C2×C3×C4C2×C4×D511yescharacteristic
300C2×C3×C4D4×D511yescharacteristic
301C2×C3×C4D4×D511yescharacteristic
302C2×C3×C4#71111yescharacteristic
303C2×C3×C4C2×C22⋊D511yescharacteristic
304C3×C8—41no—
305C3×C8—101no—
306C3×C8—101no—
307C3×C8—101no—
308C3×C8—101no—
309C3×C8—102no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—22no—
313C22×C5—41no—
314C22×C5—41no—
315C22×C5C3×C4×D411yescharacteristic
316C22×C5C3×C22⋊Q811yescharacteristic
317C22×C5C3×#12311yescharacteristic
318C4×C5—22no—
319C4×C5—42no—
320C4×C5C2×C3×C4⋊C411yescharacteristic
321C4×C5C3×C4×D411yescharacteristic
322C4×C5C3×#12011yescharacteristic
323C4×C5C3×C22⋊Q811yescharacteristic
324Dic5—41no—
325Dic5—41no—
326#41—21no—
327#41—21no—
328#41C3×Dic1012yes—
329#41C3×C22⋊D512yes—
330C2×Q8C3×C4×D511yescharacteristic
331C2×D4—21no—
332C2×D4C3×C4×D511yescharacteristic
333C22×C4—21no—
334C22×C4—21no—
335C22×C4C22×C3×D511yescharacteristic
336M16—21no—
337M16—21no—
338M16—52no—
339M16—104no—
340M16—101no—
341C2×C8—21no—
342C2×C8—51no—
343C2×C8—51no—
344C2×C8—51no—
345C2×C8—51no—
346C2×C8—104no—
347C2×C8—101no—
348C2×C8—101no—
349C2×C8—101no—
350C2×C8—101no—
351C2×C8—101no—
352C4⋊C4—51no—
353C4⋊C4—51no—
354C22⋊C4—101no—
355C42—21no—
356C42—21no—
357C42—101no—
358C3×C5#186611yescharacteristic, complemented, Hall
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—22no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3#402411yescharacteristic
365C22×C3#402711yescharacteristic
366C22×C3#408111yescharacteristic
367C3×C4—22no—
368C3×C4—42no—
369C3×C4—201no—
370C3×C4—201no—
371C3×C4#402411yescharacteristic
372C3×C4#402711yescharacteristic
373C3×C4C2×#68311yescharacteristic
374C3×C4#408311yescharacteristic
375C2×C5—21no—
376C2×C5—21no—
377C2×C5—42no—
378C2×C5C3×#38511yescharacteristic
379C2×C5C3×#44311yescharacteristic
380C2×C5C3×#44411yescharacteristic
381C23—21no—
382C23C3×#71111yescharacteristic
383Q8—21no—
384Q8C3×#68312yes—
385D4—22no—
386D4—22no—
387D4—21no—
388D4C3×#68312yes—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—101no—
396C2×C4—101no—
397C2×C4C2×C3×Dic1011yescharacteristic
398C2×C4C2×C3×C4×D511yescharacteristic
399C2×C4C3×D4×D511yescharacteristic
400C2×C4C3×D4×D511yescharacteristic
401C2×C4C3×#71111yescharacteristic
402C2×C4C2×C3×C22⋊D511yescharacteristic
403C8—41no—
404C8—101no—
405C8—101no—
406C8—102no—
407C8—101no—
408C8—101no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—42no—
412C2×C3#6511211yescharacteristic
413C2×C3#6511311yescharacteristic
414C2×C3#6523511yescharacteristic
415C5C3×#186611yescharacteristic, complemented, Sylow
416C22—21no—
417C22—21no—
418C22—22no—
419C22—41no—
420C22—41no—
421C22C3×#402411yescharacteristic
422C22C3×#402711yescharacteristic
423C22C3×#408111yescharacteristic
424C4—22no—
425C4—42no—
426C4—201no—
427C4—201no—
428C4C3×#402411yescharacteristic
429C4C3×#402711yescharacteristic
430C4C2×C3×#68311yescharacteristic
431C4C3×#408311yescharacteristic
432C3#1060116911yescharacteristic, direct product factor, Sylow
433C2—21no—
434C2—21no—
435C2—42no—
436C2C3×#6511211yescharacteristic
437C2C3×#6511311yescharacteristic
438C2C3×#6523511yescharacteristic
subgroupG/H
centerC2×C3×C4D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#104C2
socleC22×C3×C5C4×D4
prime radicalC2×C3×C5×#41C22
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#104D5
hypocenterC5C3×#1866
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
4. C2×C3×#3954C2semidirect
5. C3×#65408C2semidirect
6. C3×#64744C2semidirect
7. C3×#64743C2semidirect
8. #10601169C3direct (N × H)
21. C3×#3967C4semidirect
22. C3×#3967C4semidirect
23. C3×#3964C4semidirect
24. C3×#3964C4semidirect
32. C2×#3954C2×C3semidirect
33. #65408C2×C3semidirect
34. #64744C2×C3semidirect
35. #64743C2×C3semidirect
87. #3967C3×C4semidirect
88. #3967C3×C4semidirect
89. #3964C3×C4semidirect
90. #3964C3×C4semidirect
358. C3×C5#1866semidirect
415. C5C3×#1866semidirect
432. C3#10601169direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40942
C2×C3×C5×#1042
C3×#655222
C2×C3×#39542
C3×#654082
C3×#647442
C3×#647432
#106011693
C3×#18665