Finite Group Databasebeta

← C3×#10601515 #14300213

Subgroups — C3×#10601515 #14300213

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×#4053C211yesmaximal, characteristic
2C2×C3×C5×#108C211yesmaximal, characteristic, complemented
3C2×C3×#3957C211yesmaximal, characteristic
4C3×#65408C211yesmaximal, characteristic, complemented
5C3×#65402C211yesmaximal, characteristic
6C3×#64775C211yesmaximal, characteristic, complemented
7C3×#64770C211yesmaximal, characteristic, complemented
8#10601515C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#709C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C22×C3×C5×C8C2211yescharacteristic
13C3×#4072C2211yescharacteristic
14C2×C3×C4×Dic5C2211yescharacteristic
15C22×C3×#168C2211yescharacteristic
16C3×#4053—22no—
17C3×#4053—22no—
18C2×C3×#676—21no—
19C2×C3×C8×D5—21no—
20C3×C5×#108—22no—
21C3×#3957—22no—
22C3×#3953C411yescharacteristic, complemented
23C3×#3953C411yescharacteristic, complemented
24C3×#3948C411yescharacteristic, complemented
25C3×#3948C411yescharacteristic, complemented
26C3×#3946—21no—
27C3×#3946—21no—
28C3×#1866—51nomaximal, Hall
29C2×#4053C2×C311yescharacteristic
30C2×C5×#108C2×C311yescharacteristic, complemented
31C2×#3957C2×C311yescharacteristic
32#65408C2×C311yescharacteristic, complemented
33#65402C2×C311yescharacteristic
34#64775C2×C311yescharacteristic, complemented
35#64770C2×C311yescharacteristic, complemented
36C22×C3×C4×C5C2311yescharacteristic
37C2×C3×C22⋊D5—21no—
38C22×C3×Dic5—21no—
39C3×#709—21no—
40C3×#709—21no—
41C3×#709D412yes—
42C3×#709Q812yes—
43C2×C3×D20C2×C411yescharacteristic
44C2×C3×C4×D5—21no—
45C2×C3×Dic10C2×C411yescharacteristic
46C3×C5×M16—21no—
47C3×C5×M16—21no—
48C3×C5×M16—21no—
49C3×C5×M16D412yes—
50C2×C3×C5×C8—21no—
51C2×C3×C5×C8—21no—
52C2×C3×C5×C8—21no—
53C2×C3×C5×C8—21no—
54C2×C3×C5×C8C2×C411yescharacteristic
55C2×C3×C5×C8C2×C411yescharacteristic
56C3×C22⋊Dic5—21no—
57C3×C4⋊Dic5C2×C411yescharacteristic
58C3×C4⋊Dic5C2×C411yescharacteristic
59C3×C4×Dic5—21no—
60C3×C4×Dic5—21no—
61C3×C4×Dic5—21no—
62C2×C3×#168—21no—
63C2×C3×#168—21no—
64C2×C3×#168D411yescharacteristic
65C2×C3×#168D411yescharacteristic
66C3×#676—24no—
67C3×C8×D5—24no—
68C2×C3×#131—51no—
69C2×C3×#108D511yescharacteristic, complemented
70C3×#424—51no—
71C2×C3×#104—51no—
72C3×#416—51no—
73C3×#339—51no—
74C3×#336—51no—
75C2×#709C22×C311yescharacteristic
76C2×C5×M16C22×C311yescharacteristic
77C2×C5×M16C22×C311yescharacteristic
78C22×C5×C8C22×C311yescharacteristic
79#4072C22×C311yescharacteristic
80C2×C4×Dic5C22×C311yescharacteristic
81C22×#168C22×C311yescharacteristic
82#4053—22no—
83#4053—22no—
84C2×#676—21no—
85C2×C8×D5—21no—
86C5×#108—22no—
87#3957—22no—
88#3953C3×C411yescharacteristic, complemented
89#3953C3×C411yescharacteristic, complemented
90#3948C3×C411yescharacteristic, complemented
91#3948C3×C411yescharacteristic, complemented
92#3946—21no—
93#3946—21no—
94#1866—51noSylow
95C23×C3×C5#4111yescharacteristic
96C22×C3×D5—21no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×Q811yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C3×C22⋊D5—22no—
104C3×C22⋊D5—22no—
105C2×C3×Dic5—21no—
106C2×C3×Dic5—22no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—41no—
110C2×C3×Dic5—41no—
111C3×D20—21no—
112C3×D20C4⋊C412yes—
113C3×C4×D5—22no—
114C3×C4×D5—22no—
115C3×Dic10—21no—
116C3×Dic10C4⋊C412yes—
117C3×C5×C8—21no—
118C3×C5×C8—21no—
119C3×C5×C8—22no—
120C3×C5×C8—41no—
121C3×#168—21no—
122C3×#168—21no—
123C2×C3×#41—51no—
124C3×#131—102no—
125C3×#131—102no—
126C2×C3×M16—101no—
127C2×C3×M16C2×D511yescharacteristic
128C2×C3×M16C2×D511yescharacteristic
129C22×C3×C8—51no—
130C22×C3×C8—101no—
131C22×C3×C8C2×D511yescharacteristic
132C3×#117—51no—
133C2×C3×C42—51no—
134C3×#108—22no—
135C3×C4⋊C8—101no—
136C3×C4⋊C8—101no—
137C3×#104—102no—
138C3×#103—51no—
139C3×#103—51no—
140C3×#102—51no—
141C3×#102—51no—
142C22×C4×C5C23×C311yescharacteristic
143C2×C22⋊D5—21no—
144C22×Dic5—21no—
145#709—21no—
146#709—21no—
147#709C3×D412yes—
148#709C3×Q812yes—
149C2×D20C2×C3×C411yescharacteristic
150C2×C4×D5—21no—
151C2×Dic10C2×C3×C411yescharacteristic
152C5×M16—21no—
153C5×M16—21no—
154C5×M16—21no—
155C5×M16C3×D412yes—
156C2×C5×C8—21no—
157C2×C5×C8—21no—
158C2×C5×C8—21no—
159C2×C5×C8—21no—
160C2×C5×C8C2×C3×C411yescharacteristic
161C2×C5×C8C2×C3×C411yescharacteristic
162C22⋊Dic5—21no—
163C4⋊Dic5C2×C3×C411yescharacteristic
164C4⋊Dic5C2×C3×C411yescharacteristic
165C4×Dic5—21no—
166C4×Dic5—21no—
167C4×Dic5—21no—
168C2×#168—21no—
169C2×#168—21no—
170C2×#168C3×D411yescharacteristic
171C2×#168C3×D411yescharacteristic
172#676—24no—
173C8×D5—24no—
174C2×#131—51no—
175C2×#108C3×D511yescharacteristic, complemented
176#424—51no—
177C2×#104—51no—
178#416—51no—
179#339—51no—
180#336—51no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5C4×D411yescharacteristic
184C22×C3×C5C22⋊Q811yescharacteristic
185C22×C3×C5#12311yescharacteristic
186C2×C3×D5—22no—
187C2×C3×D5—41no—
188C2×C3×D5—41no—
189C3×C4×C5C2×C4⋊C411yescharacteristic
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5#12011yescharacteristic
192C3×C4×C5C22⋊Q811yescharacteristic
193C3×Dic5—22no—
194C3×Dic5—42no—
195C3×Dic5—41no—
196C3×Dic5—41no—
197C3×#41—52no—
198C3×#41—52no—
199C3×#41—101no—
200C3×#41—101no—
201C2×C3×Q8—51no—
202C2×C3×D4—51no—
203C2×C3×D4—101no—
204C22×C3×C4—101no—
205C22×C3×C4—101no—
206C22×C3×C4C22×D511yescharacteristic
207C3×M16—21no—
208C3×M16—21no—
209C3×M16—21no—
210C3×M16—104no—
211C3×M16C22⋊D512yes—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—51no—
217C2×C3×C8—51no—
218C2×C3×C8—104no—
219C2×C3×C8—101no—
220C2×C3×C8—101no—
221C2×C3×C8C4×D511yescharacteristic
222C2×C3×C8C4×D511yescharacteristic
223C3×C4⋊C4—51no—
224C3×C4⋊C4—51no—
225C3×C22⋊C4—101no—
226C3×C42—101no—
227C3×C42—101no—
228C3×C42—101no—
229C23×C5C3×#4111yescharacteristic
230C22×D5—21no—
231C2×C4×C5C22×C3×C411yescharacteristic
232C2×C4×C5C2×C3×D411yescharacteristic
233C2×C4×C5C2×C3×D411yescharacteristic
234C2×C4×C5C2×C3×D411yescharacteristic
235C2×C4×C5C2×C3×Q811yescharacteristic
236C2×C4×C5C3×#4111yescharacteristic
237C22⋊D5—22no—
238C22⋊D5—22no—
239C2×Dic5—21no—
240C2×Dic5—22no—
241C2×Dic5—21no—
242C2×Dic5—21no—
243C2×Dic5—41no—
244C2×Dic5—41no—
245D20—21no—
246D20C3×C4⋊C412yes—
247C4×D5—22no—
248C4×D5—22no—
249Dic10—21no—
250Dic10C3×C4⋊C412yes—
251C5×C8—21no—
252C5×C8—21no—
253C5×C8—22no—
254C5×C8—41no—
255#168—21no—
256#168—21no—
257C2×#41—51no—
258#131—102no—
259#131—102no—
260C2×M16—101no—
261C2×M16C2×C3×D511yescharacteristic
262C2×M16C2×C3×D511yescharacteristic
263C22×C8—51no—
264C22×C8—101no—
265C22×C8C2×C3×D511yescharacteristic
266#117—51no—
267C2×C42—51no—
268#108—22no—
269C4⋊C8—101no—
270C4⋊C8—101no—
271#104—102no—
272#103—51no—
273#103—51no—
274#102—51no—
275#102—51no—
276C2×C3×C5—21no—
277C2×C3×C5—21no—
278C2×C3×C5#38511yescharacteristic
279C2×C3×C5#44311yescharacteristic
280C2×C3×C5#44411yescharacteristic
281C3×D5—42no—
282C23×C3—101no—
283C23×C3#71311yescharacteristic
284C3×Q8—52no—
285C3×Q8—101no—
286C3×D4—52no—
287C3×D4—102no—
288C3×D4—102no—
289C3×D4—101no—
290C2×C3×C4—101no—
291C2×C3×C4—102no—
292C2×C3×C4—102no—
293C2×C3×C4—102no—
294C2×C3×C4—101no—
295C2×C3×C4—101no—
296C2×C3×C4—201no—
297C2×C3×C4—201no—
298C2×C3×C4C2×C4×D511yescharacteristic
299C2×C3×C4#70911yescharacteristic
300C2×C3×C4D4×D511yescharacteristic
301C2×C3×C4D4×D511yescharacteristic
302C2×C3×C4Q8×D511yescharacteristic
303C2×C3×C4C2×C22⋊D511yescharacteristic
304C3×C8—21no—
305C3×C8—21no—
306C3×C8—22no—
307C3×C8—41no—
308C3×C8—101no—
309C3×C8—101no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5C3×C4×D411yescharacteristic
313C22×C5C3×C22⋊Q811yescharacteristic
314C22×C5C3×#12311yescharacteristic
315C2×D5—22no—
316C2×D5—41no—
317C2×D5—41no—
318C4×C5C2×C3×C4⋊C411yescharacteristic
319C4×C5C3×C4×D411yescharacteristic
320C4×C5C3×#12011yescharacteristic
321C4×C5C3×C22⋊Q811yescharacteristic
322Dic5—22no—
323Dic5—42no—
324Dic5—41no—
325Dic5—41no—
326#41—52no—
327#41—52no—
328#41—101no—
329#41—101no—
330C2×Q8—51no—
331C2×D4—51no—
332C2×D4—101no—
333C22×C4—101no—
334C22×C4—101no—
335C22×C4C22×C3×D511yescharacteristic
336M16—21no—
337M16—21no—
338M16—21no—
339M16—104no—
340M16C3×C22⋊D512yes—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—51no—
346C2×C8—51no—
347C2×C8—104no—
348C2×C8—101no—
349C2×C8—101no—
350C2×C8C3×C4×D511yescharacteristic
351C2×C8C3×C4×D511yescharacteristic
352C4⋊C4—51no—
353C4⋊C4—51no—
354C22⋊C4—101no—
355C42—101no—
356C42—101no—
357C42—101no—
358C3×C5#186611yescharacteristic, complemented, Hall
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—102no—
362C22×C3—201no—
363C22×C3—201no—
364C22×C3#403911yescharacteristic
365C22×C3#404011yescharacteristic
366C22×C3#409211yescharacteristic
367C3×C4—102no—
368C3×C4—202no—
369C3×C4—201no—
370C3×C4—201no—
371C3×C4D5×C4⋊C411yescharacteristic
372C3×C4#404211yescharacteristic
373C3×C4C4×C22⋊D511yescharacteristic
374C3×C4#408311yescharacteristic
375C2×C5—21no—
376C2×C5—21no—
377C2×C5C3×#38511yescharacteristic
378C2×C5C3×#44311yescharacteristic
379C2×C5C3×#44411yescharacteristic
380D5—42no—
381C23—101no—
382C23C3×#71311yescharacteristic
383Q8—52no—
384Q8—101no—
385D4—52no—
386D4—102no—
387D4—102no—
388D4—101no—
389C2×C4—101no—
390C2×C4—102no—
391C2×C4—102no—
392C2×C4—102no—
393C2×C4—101no—
394C2×C4—101no—
395C2×C4—201no—
396C2×C4—201no—
397C2×C4C2×C3×C4×D511yescharacteristic
398C2×C4C3×#70911yescharacteristic
399C2×C4C3×D4×D511yescharacteristic
400C2×C4C3×D4×D511yescharacteristic
401C2×C4C3×Q8×D511yescharacteristic
402C2×C4C2×C3×C22⋊D511yescharacteristic
403C8—22no—
404C8—21no—
405C8—21no—
406C8—41no—
407C8—101no—
408C8—101no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—202no—
412C2×C3#6518311yescharacteristic
413C2×C3#6518411yescharacteristic
414C2×C3#6527811yescharacteristic
415C5C3×#186611yescharacteristic, complemented, Sylow
416C22—21no—
417C22—21no—
418C22—102no—
419C22—201no—
420C22—201no—
421C22C3×#403911yescharacteristic
422C22C3×#404011yescharacteristic
423C22C3×#409211yescharacteristic
424C4—102no—
425C4—202no—
426C4—201no—
427C4—201no—
428C4C3×D5×C4⋊C411yescharacteristic
429C4C3×#404211yescharacteristic
430C4C3×C4×C22⋊D511yescharacteristic
431C4C3×#408311yescharacteristic
432C3#1060151511yescharacteristic, direct product factor, Sylow
433C2—21no—
434C2—21no—
435C2—202no—
436C2C3×#6518311yescharacteristic
437C2C3×#6518411yescharacteristic
438C2C3×#6527811yescharacteristic
subgroupG/H
centerC2×C3×C4D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#108C2
socleC22×C3×C5C4×D4
prime radicalC2×C3×#709C22
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#108D5
hypocenterC5C3×#1866
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#108

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#108C2semidirect
4. C3×#65408C2semidirect
6. C3×#64775C2semidirect
7. C3×#64770C2semidirect
8. #10601515C3direct (N × H)
22. C3×#3953C4semidirect
23. C3×#3953C4semidirect
24. C3×#3948C4semidirect
25. C3×#3948C4semidirect
30. C2×C5×#108C2×C3semidirect
32. #65408C2×C3semidirect
34. #64775C2×C3semidirect
35. #64770C2×C3semidirect
69. C2×C3×#108D5semidirect
88. #3953C3×C4semidirect
89. #3953C3×C4semidirect
90. #3948C3×C4semidirect
91. #3948C3×C4semidirect
175. C2×#108C3×D5semidirect
358. C3×C5#1866semidirect
415. C5C3×#1866semidirect
432. C3#10601515direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40532
C2×C3×C5×#1082
C2×C3×#39572
C3×#654082
C3×#654022
C3×#647752
C3×#647702
#106015153
C3×#18665