Finite Group Databasebeta

← C3×#10601085 #14300228

Subgroups — C3×#10601085 #14300228

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
2C3×C5×#416C211yesmaximal, characteristic
3C2×C3×#3969C211yesmaximal, characteristic
4C2×C3×#3951C211yesmaximal, characteristic, complemented
5C3×#65288C211yesmaximal, characteristic, complemented
6C3×#64770C211yesmaximal, characteristic, complemented
7C3×#64752C211yesmaximal, characteristic, complemented
8#10601085C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C3×#4094—22no—
13C3×#4094—22no—
14C2×C3×C4×Dic5C2211yescharacteristic
15C2×C3×#681—21no—
16C2×C3×#681C2211yescharacteristic
17C2×C3×#681C2211yescharacteristic
18C22×C3×#168—21no—
19C22×C3×#168C2211yescharacteristic
20C3×C5×#103C411yescharacteristic, complemented
21C3×C5×#103C411yescharacteristic, complemented
22C3×C5×#102C411yescharacteristic, complemented
23C3×C5×#102C411yescharacteristic, complemented
24C3×#3969—22no—
25C3×#3951—22no—
26C3×C4⋊#168—21no—
27C3×C4⋊#168—21no—
28C3×#1866—51nomaximal, Hall
29C2×#4094C2×C311yescharacteristic
30C5×#416C2×C311yescharacteristic
31C2×#3969C2×C311yescharacteristic
32C2×#3951C2×C311yescharacteristic, complemented
33#65288C2×C311yescharacteristic, complemented
34#64770C2×C311yescharacteristic, complemented
35#64752C2×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×C5C2311yescharacteristic
45C22×C3×Dic5—21no—
46C2×C3×C5×C8—21no—
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8C2×C411yescharacteristic
49C2×C3×C5×C8C2×C411yescharacteristic
50C3×C5×C4⋊C4C2×C411yescharacteristic
51C3×C5×C4⋊C4C2×C411yescharacteristic
52C3×C5×C22⋊C4—21no—
53C3×C42×C5—21no—
54C3×C4×Dic5—21no—
55C3×C4×Dic5—21no—
56C3×#681—24no—
57C3×#681—21no—
58C3×#681—21no—
59C3×#681—21no—
60C3×#681D412yes—
61C2×C3×#168—24no—
62C2×C3×#168—21no—
63C2×C3×#168—21no—
64C2×C3×#168—21no—
65C2×C3×#168—21no—
66C2×C3×#168D411yescharacteristic
67C2×C3×#168D411yescharacteristic
68C2×C3×#131—51no—
69C2×C3×#108—51no—
70C3×#424—51no—
71C2×C3×#104—51no—
72C3×#416D511yescharacteristic
73C3×#339—51no—
74C3×#336—51no—
75C2×C5×#41C22×C311yescharacteristic
76C22×C5×C8C22×C311yescharacteristic
77C5×#117C22×C311yescharacteristic
78#4094—22no—
79#4094—22no—
80C2×C4×Dic5C22×C311yescharacteristic
81C2×#681—21no—
82C2×#681C22×C311yescharacteristic
83C2×#681C22×C311yescharacteristic
84C22×#168—21no—
85C22×#168C22×C311yescharacteristic
86C5×#103C3×C411yescharacteristic, complemented
87C5×#103C3×C411yescharacteristic, complemented
88C5×#102C3×C411yescharacteristic, complemented
89C5×#102C3×C411yescharacteristic, complemented
90#3969—22no—
91#3951—22no—
92C4⋊#168—21no—
93C4⋊#168—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—21no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×Q811yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×Dic5—22no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5—41no—
117C3×C5×C8—21no—
118C3×C5×C8—21no—
119C3×#168—21no—
120C3×#168—22no—
121C3×#168—21no—
122C3×#168—41no—
123C2×C3×#41C2×D511yescharacteristic
124C3×#131—102no—
125C3×#131—102no—
126C2×C3×M16—51no—
127C2×C3×M16—51no—
128C2×C3×M16—101no—
129C22×C3×C8—51no—
130C22×C3×C8—101no—
131C22×C3×C8C2×D511yescharacteristic
132C3×#117C2×D511yescharacteristic
133C2×C3×C42—51no—
134C3×#108—102no—
135C3×C4⋊C8—101no—
136C3×C4⋊C8—101no—
137C3×#104—102no—
138C3×#103Dic511yescharacteristic, complemented
139C3×#103Dic511yescharacteristic, complemented
140C3×#102Dic511yescharacteristic, complemented
141C3×#102Dic511yescharacteristic, complemented
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×C5C23×C311yescharacteristic
151C22×Dic5—21no—
152C2×C5×C8—21no—
153C2×C5×C8—21no—
154C2×C5×C8C2×C3×C411yescharacteristic
155C2×C5×C8C2×C3×C411yescharacteristic
156C5×C4⋊C4C2×C3×C411yescharacteristic
157C5×C4⋊C4C2×C3×C411yescharacteristic
158C5×C22⋊C4—21no—
159C42×C5—21no—
160C4×Dic5—21no—
161C4×Dic5—21no—
162#681—24no—
163#681—21no—
164#681—21no—
165#681—21no—
166#681C3×D412yes—
167C2×#168—24no—
168C2×#168—21no—
169C2×#168—21no—
170C2×#168—21no—
171C2×#168—21no—
172C2×#168C3×D411yescharacteristic
173C2×#168C3×D411yescharacteristic
174C2×#131—51no—
175C2×#108—51no—
176#424—51no—
177C2×#104—51no—
178#416C3×D511yescharacteristic
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—41no—
191C3×C4×C5—41no—
192C3×C4×C5C2×C4⋊C411yescharacteristic
193C3×C4×C5C4×D411yescharacteristic
194C3×C4×C5#12011yescharacteristic
195C3×C4×C5C22⋊Q811yescharacteristic
196C3×Dic5—42no—
197C3×#41—21no—
198C3×#41—21no—
199C3×#41Dic1012yes—
200C3×#41D2012yes—
201C2×C3×Q8C2×Dic511yescharacteristic
202C2×C3×D4—21no—
203C2×C3×D4C2×Dic511yescharacteristic
204C22×C3×C4—21no—
205C22×C3×C4—101no—
206C22×C3×C4C22×D511yescharacteristic
207C3×M16—52no—
208C3×M16—104no—
209C3×M16—101no—
210C3×M16—101no—
211C3×M16—101no—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8—51no—
215C2×C3×C8—51no—
216C2×C3×C8—104no—
217C2×C3×C8—101no—
218C2×C3×C8—101no—
219C2×C3×C8—101no—
220C2×C3×C8—101no—
221C2×C3×C8C2×Dic511yescharacteristic
222C2×C3×C8C2×Dic511yescharacteristic
223C3×C4⋊C4C2×Dic511yescharacteristic
224C3×C4⋊C4C2×Dic511yescharacteristic
225C3×C22⋊C4—21no—
226C3×C42—21no—
227C3×C42—101no—
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—21no—
241C2×C4×C5—21no—
242C2×C4×C5C22×C3×C411yescharacteristic
243C2×C4×C5C2×C3×D411yescharacteristic
244C2×C4×C5C2×C3×D411yescharacteristic
245C2×C4×C5C2×C3×D411yescharacteristic
246C2×C4×C5C2×C3×Q811yescharacteristic
247C2×C4×C5C3×#4111yescharacteristic
248C2×Dic5—22no—
249C2×Dic5—41no—
250C2×Dic5—41no—
251C5×C8—21no—
252C5×C8—21no—
253#168—21no—
254#168—22no—
255#168—21no—
256#168—41no—
257C2×#41C2×C3×D511yescharacteristic
258#131—102no—
259#131—102no—
260C2×M16—51no—
261C2×M16—51no—
262C2×M16—101no—
263C22×C8—51no—
264C22×C8—101no—
265C22×C8C2×C3×D511yescharacteristic
266#117C2×C3×D511yescharacteristic
267C2×C42—51no—
268#108—102no—
269C4⋊C8—101no—
270C4⋊C8—101no—
271#104—102no—
272#103C3×Dic511yescharacteristic, complemented
273#103C3×Dic511yescharacteristic, complemented
274#102C3×Dic511yescharacteristic, complemented
275#102C3×Dic511yescharacteristic, complemented
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×Q8C4⋊Dic512yes—
286C3×D4—22no—
287C3×D4—22no—
288C3×D4—21no—
289C3×D4C4⋊Dic512yes—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—102no—
296C2×C3×C4—201no—
297C2×C3×C4—201no—
298C2×C3×C4C2×Dic1011yescharacteristic
299C2×C3×C4C2×D2011yescharacteristic
300C2×C3×C4D4×D511yescharacteristic
301C2×C3×C4D4×D511yescharacteristic
302C2×C3×C4#71111yescharacteristic
303C2×C3×C4C22×Dic511yescharacteristic
304C3×C8—21no—
305C3×C8—21no—
306C3×C8—101no—
307C3×C8—101no—
308C3×C8—102no—
309C3×C8—201no—
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—41no—
320C4×C5—41no—
321C4×C5C2×C3×C4⋊C411yescharacteristic
322C4×C5C3×C4×D411yescharacteristic
323C4×C5C3×#12011yescharacteristic
324C4×C5C3×C22⋊Q811yescharacteristic
325Dic5—42no—
326#41—21no—
327#41—21no—
328#41C3×Dic1012yes—
329#41C3×D2012yes—
330C2×Q8C2×C3×Dic511yescharacteristic
331C2×D4—21no—
332C2×D4C2×C3×Dic511yescharacteristic
333C22×C4—21no—
334C22×C4—101no—
335C22×C4C22×C3×D511yescharacteristic
336M16—52no—
337M16—104no—
338M16—101no—
339M16—101no—
340M16—101no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—51no—
344C2×C8—51no—
345C2×C8—104no—
346C2×C8—101no—
347C2×C8—101no—
348C2×C8—101no—
349C2×C8—101no—
350C2×C8C2×C3×Dic511yescharacteristic
351C2×C8C2×C3×Dic511yescharacteristic
352C4⋊C4C2×C3×Dic511yescharacteristic
353C4⋊C4C2×C3×Dic511yescharacteristic
354C22⋊C4—21no—
355C42—21no—
356C42—101no—
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#403211yescharacteristic
366C22×C3D4×Dic511yescharacteristic
367C3×C4—22no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—202no—
371C3×C4#402411yescharacteristic
372C3×C4#402811yescharacteristic
373C3×C4C2×C4⋊Dic511yescharacteristic
374C3×C4D4×Dic511yescharacteristic
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×C4⋊Dic512yes—
385D4—22no—
386D4—22no—
387D4—21no—
388D4C3×C4⋊Dic512yes—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—102no—
395C2×C4—201no—
396C2×C4—201no—
397C2×C4C2×C3×Dic1011yescharacteristic
398C2×C4C2×C3×D2011yescharacteristic
399C2×C4C3×D4×D511yescharacteristic
400C2×C4C3×D4×D511yescharacteristic
401C2×C4C3×#71111yescharacteristic
402C2×C4C22×C3×Dic511yescharacteristic
403C8—21no—
404C8—21no—
405C8—101no—
406C8—101no—
407C8—102no—
408C8—201no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—42no—
412C2×C3#6523911yescharacteristic
413C2×C3#6548511yescharacteristic
414C2×C3#6548611yescharacteristic
415C5C3×#186611yescharacteristic, complemented, Sylow
416C22—21no—
417C22—21no—
418C22—22no—
419C22—41no—
420C22—41no—
421C22C3×#402411yescharacteristic
422C22C3×#403211yescharacteristic
423C22C3×D4×Dic511yescharacteristic
424C4—22no—
425C4—41no—
426C4—41no—
427C4—202no—
428C4C3×#402411yescharacteristic
429C4C3×#402811yescharacteristic
430C4C2×C3×C4⋊Dic511yescharacteristic
431C4C3×D4×Dic511yescharacteristic
432C3#1060108511yescharacteristic, direct product factor, Sylow
433C2—21no—
434C2—21no—
435C2—42no—
436C2C3×#6523911yescharacteristic
437C2C3×#6548511yescharacteristic
438C2C3×#6548611yescharacteristic
subgroupG/H
centerC2×C3×C4D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#416C2
socleC22×C3×C5C4×D4
prime radicalC2×C3×C5×#41C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#416D5
hypocenterC5C3×#1866
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C3×#416

Complements

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

NH ≅ G/Ntype
4. C2×C3×#3951C2semidirect
5. C3×#65288C2semidirect
6. C3×#64770C2semidirect
7. C3×#64752C2semidirect
8. #10601085C3direct (N × H)
20. C3×C5×#103C4semidirect
21. C3×C5×#103C4semidirect
22. C3×C5×#102C4semidirect
23. C3×C5×#102C4semidirect
32. C2×#3951C2×C3semidirect
33. #65288C2×C3semidirect
34. #64770C2×C3semidirect
35. #64752C2×C3semidirect
86. C5×#103C3×C4semidirect
87. C5×#103C3×C4semidirect
88. C5×#102C3×C4semidirect
89. C5×#102C3×C4semidirect
138. C3×#103Dic5semidirect
139. C3×#103Dic5semidirect
140. C3×#102Dic5semidirect
141. C3×#102Dic5semidirect
272. #103C3×Dic5semidirect
273. #103C3×Dic5semidirect
274. #102C3×Dic5semidirect
275. #102C3×Dic5semidirect
358. C3×C5#1866semidirect
415. C5C3×#1866semidirect
432. C3#10601085direct (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
C3×C5×#4162
C2×C3×#39692
C2×C3×#39512
C3×#652882
C3×#647702
C3×#647522
#106010853
C3×#18665