Finite Group Databasebeta

← C3×#10600760 #14280956

Subgroups — C3×#10600760 #14280956

Order 1920.

880 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#685C211yesmaximal, characteristic
2C3×C5×#407C211yesmaximal, characteristic, complemented
3C3×#65496C211yesmaximal, characteristic, complemented
4C3×#64688C214yesmaximal, complemented
5#10600760C311yesmaximal, characteristic, direct product factor, Hall
6C24×C3×D5C411yescharacteristic
7C23×C3×C4×C5C2211yescharacteristic
8C23×C3×Dic5C411yescharacteristic
9C2×C3×C5×M16—21no—
10C2×C3×#685—21no—
11C2×C3×#685—21no—
12C2×C3×#685—21no—
13C2×C3×#685—21no—
14C2×C3×#685C412yes—
15C2×C3×#685C2212yes—
16C2×C3×#681—21no—
17C3×C5×C22⋊C8—21no—
18C3×C5×C22⋊C8C2212yescomplemented
19C3×C22⋊#168—21no—
20C3×C22⋊#168C2212yescomplemented
21C3×#1462—51nomaximal, Hall
22C22×#685C2×C311yescharacteristic
23C5×#407C2×C311yescharacteristic, complemented
24#65496C2×C311yescharacteristic, complemented
25#64688C2×C314yescomplemented
26C24×C3×C5C2×C411yescharacteristic
27C23×C3×D5—21no—
28C23×C3×D5—21no—
29C23×C3×D5—24no—
30C23×C3×D5—42no—
31C23×C3×D5—42no—
32C23×C3×D5C2×C412yes—
33C22×C3×C4×C5—42no—
34C22×C3×C4×C5C2×C411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5D411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5C2311yescharacteristic
40C22×C3×Dic5—21no—
41C22×C3×Dic5—21no—
42C22×C3×Dic5—42no—
43C22×C3×Dic5C2×C412yes—
44C3×C5×M16—42no—
45C2×C3×C5×C8—22no—
46C3×#685—22no—
47C3×#685—22no—
48C3×#685—22no—
49C3×#685—22no—
50C3×#681—42no—
51C2×C3×#168—22no—
52C22×C3×C22⋊C4—51no—
53C3×#407—51no—
54C3×#407D511yescharacteristic, complemented
55C3×#323—54no—
56C24×D5C3×C411yescharacteristic
57C23×C4×C5C22×C311yescharacteristic
58C23×Dic5C3×C411yescharacteristic
59C2×C5×M16—21no—
60C2×#685—21no—
61C2×#685—21no—
62C2×#685—21no—
63C2×#685—21no—
64C2×#685C3×C412yes—
65C2×#685C22×C312yes—
66C2×#681—21no—
67C5×C22⋊C8—21no—
68C5×C22⋊C8C22×C312yescomplemented
69C22⋊#168—21no—
70C22⋊#168C22×C312yescomplemented
71#1462—51noSylow
72C23×C3×C5—22no—
73C23×C3×C5—22no—
74C23×C3×C5—22no—
75C23×C3×C5C22⋊C411yescharacteristic
76C23×C3×C5C22⋊C411yescharacteristic
77C23×C3×C5C22×C411yescharacteristic
78C22×C3×D5—24no—
79C22×C3×D5—24no—
80C22×C3×D5—22no—
81C22×C3×D5—22no—
82C22×C3×D5—416no—
83C22×C3×D5—42no—
84C22×C3×D5—42no—
85C22×C3×D5—42no—
86C22×C3×D5—42no—
87C22×C3×D5—42no—
88C22×C3×D5—42no—
89C22×C3×D5M1614yescomplemented
90C2×C3×C4×C5—22no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5C22⋊C411yescharacteristic
97C2×C3×C4×C5C22⋊C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×Dic5—22no—
101C2×C3×Dic5—42no—
102C2×C3×Dic5—42no—
103C2×C3×Dic5—42no—
104C3×C5×C8—42no—
105C3×#168—42no—
106C25×C3—51no—
107C23×C3×C4—51no—
108C23×C3×C4C2×D511yescharacteristic
109C2×C3×M16—21no—
110C2×C3×M16—101no—
111C2×C3×C22⋊C4—52no—
112C2×C3×C22⋊C4—52no—
113C2×C3×C22⋊C4—101no—
114C2×C3×C22⋊C4—101no—
115C2×C3×C22⋊C4—101no—
116C2×C3×C22⋊C4—101no—
117C3×C22⋊C8—21no—
118C3×C22⋊C8—52no—
119C3×C22⋊C8—101no—
120C3×C22⋊C8C2×D512yescomplemented
121C24×C5C2×C3×C411yescharacteristic
122C23×D5—21no—
123C23×D5—21no—
124C23×D5—24no—
125C23×D5—42no—
126C23×D5—42no—
127C23×D5C2×C3×C412yes—
128C22×C4×C5—42no—
129C22×C4×C5C2×C3×C411yescharacteristic
130C22×C4×C5C3×D411yescharacteristic
131C22×C4×C5C3×D411yescharacteristic
132C22×C4×C5C3×D411yescharacteristic
133C22×C4×C5C3×D411yescharacteristic
134C22×C4×C5C23×C311yescharacteristic
135C22×Dic5—21no—
136C22×Dic5—21no—
137C22×Dic5—42no—
138C22×Dic5C2×C3×C412yes—
139C5×M16—42no—
140C2×C5×C8—22no—
141#685—22no—
142#685—22no—
143#685—22no—
144#685—22no—
145#681—42no—
146C2×#168—22no—
147C22×C22⋊C4—51no—
148#407—51no—
149#407C3×D511yescharacteristic, complemented
150#323—54no—
151C22×C3×C5—28no—
152C22×C3×C5—21no—
153C22×C3×C5—21no—
154C22×C3×C5—21no—
155C22×C3×C5—21no—
156C22×C3×C5—21no—
157C22×C3×C5—21no—
158C22×C3×C5#9912yes—
159C22×C3×C5#10012yes—
160C22×C3×C5C2×C22⋊C411yescharacteristic
161C22×C3×C5C2×M1612yes—
162C2×C3×D5—24no—
163C2×C3×D5—48no—
164C2×C3×D5—48no—
165C2×C3×D5—44no—
166C2×C3×D5—42no—
167C2×C3×D5—42no—
168C2×C3×D5—44no—
169C3×C4×C5—21no—
170C3×C4×C5—21no—
171C3×C4×C5—21no—
172C3×C4×C5—21no—
173C3×Dic5—42no—
174C24×C3—52no—
175C24×C3—104no—
176C24×C3—101no—
177C24×C3—101no—
178C24×C3—202no—
179C24×C3—202no—
180C24×C3C4×D511yescharacteristic
181C22×C3×C4—42no—
182C22×C3×C4—52no—
183C22×C3×C4—101no—
184C22×C3×C4—101no—
185C22×C3×C4—202no—
186C22×C3×C4C4×D511yescharacteristic
187C22×C3×C4D2011yescharacteristic
188C22×C3×C4D2011yescharacteristic
189C22×C3×C4C22⋊D511yescharacteristic
190C22×C3×C4C22⋊D511yescharacteristic
191C22×C3×C4C22×D511yescharacteristic
192C3×M16—42no—
193C3×M16—202no—
194C2×C3×C8—22no—
195C2×C3×C8—102no—
196C3×C22⋊C4—102no—
197C3×C22⋊C4—102no—
198C3×C22⋊C4—102no—
199C3×C22⋊C4—102no—
200C23×C5—22no—
201C23×C5—22no—
202C23×C5—22no—
203C23×C5C3×C22⋊C411yescharacteristic
204C23×C5C3×C22⋊C411yescharacteristic
205C23×C5C22×C3×C411yescharacteristic
206C22×D5—24no—
207C22×D5—24no—
208C22×D5—22no—
209C22×D5—22no—
210C22×D5—416no—
211C22×D5—42no—
212C22×D5—42no—
213C22×D5—42no—
214C22×D5—42no—
215C22×D5—42no—
216C22×D5—42no—
217C22×D5C3×M1614yescomplemented
218C2×C4×C5—22no—
219C2×C4×C5—22no—
220C2×C4×C5—41no—
221C2×C4×C5—41no—
222C2×C4×C5—41no—
223C2×C4×C5—41no—
224C2×C4×C5C3×C22⋊C411yescharacteristic
225C2×C4×C5C3×C22⋊C411yescharacteristic
226C2×C4×C5C2×C3×D411yescharacteristic
227C2×C4×C5C2×C3×D411yescharacteristic
228C2×Dic5—22no—
229C2×Dic5—42no—
230C2×Dic5—42no—
231C2×Dic5—42no—
232C5×C8—42no—
233#168—42no—
234C25—51no—
235C23×C4—51no—
236C23×C4C2×C3×D511yescharacteristic
237C2×M16—21no—
238C2×M16—101no—
239C2×C22⋊C4—52no—
240C2×C22⋊C4—52no—
241C2×C22⋊C4—101no—
242C2×C22⋊C4—101no—
243C2×C22⋊C4—101no—
244C2×C22⋊C4—101no—
245C22⋊C8—21no—
246C22⋊C8—52no—
247C22⋊C8—101no—
248C22⋊C8C2×C3×D512yescomplemented
249C2×C3×C5—22no—
250C2×C3×C5—22no—
251C2×C3×C5—22no—
252C2×C3×C5#40711yescharacteristic
253C2×C3×C5C2×#9911yescharacteristic
254C2×C3×C5C2×#10011yescharacteristic
255C3×D5—44no—
256C23×C3—22no—
257C23×C3—22no—
258C23×C3—22no—
259C23×C3—54no—
260C23×C3—104no—
261C23×C3—104no—
262C23×C3—102no—
263C23×C3—102no—
264C23×C3—202no—
265C23×C3—202no—
266C23×C3—2016no—
267C23×C3—202no—
268C23×C3—202no—
269C23×C3—202no—
270C23×C3—202no—
271C23×C3#68511yescharacteristic
272C23×C3#68511yescharacteristic
273C23×C3C2×C4×D511yescharacteristic
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—102no—
281C2×C3×C4—202no—
282C2×C3×C4—202no—
283C2×C3×C4—202no—
284C2×C3×C4#68511yescharacteristic
285C2×C3×C4#68511yescharacteristic
286C2×C3×C4C2×D2011yescharacteristic
287C2×C3×C4C2×C22⋊D511yescharacteristic
288C3×C8—42no—
289C3×C8—202no—
290C22×C5—28no—
291C22×C5—21no—
292C22×C5—21no—
293C22×C5—21no—
294C22×C5—21no—
295C22×C5—21no—
296C22×C5—21no—
297C22×C5C3×#9912yes—
298C22×C5C3×#10012yes—
299C22×C5C2×C3×C22⋊C411yescharacteristic
300C22×C5C2×C3×M1612yes—
301C2×D5—24no—
302C2×D5—48no—
303C2×D5—48no—
304C2×D5—44no—
305C2×D5—42no—
306C2×D5—42no—
307C2×D5—44no—
308C4×C5—21no—
309C4×C5—21no—
310C4×C5—21no—
311C4×C5—21no—
312Dic5—42no—
313C24—52no—
314C24—104no—
315C24—101no—
316C24—101no—
317C24—202no—
318C24—202no—
319C24C3×C4×D511yescharacteristic
320C22×C4—42no—
321C22×C4—52no—
322C22×C4—101no—
323C22×C4—101no—
324C22×C4—202no—
325C22×C4C3×C4×D511yescharacteristic
326C22×C4C3×D2011yescharacteristic
327C22×C4C3×D2011yescharacteristic
328C22×C4C3×C22⋊D511yescharacteristic
329C22×C4C3×C22⋊D511yescharacteristic
330C22×C4C22×C3×D511yescharacteristic
331M16—42no—
332M16—202no—
333C2×C8—22no—
334C2×C8—102no—
335C22⋊C4—102no—
336C22⋊C4—102no—
337C22⋊C4—102no—
338C22⋊C4—102no—
339C3×C5#146211yescharacteristic, complemented, Hall
340C22×C3—28no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—104no—
348C22×C3—204no—
349C22×C3—208no—
350C22×C3—208no—
351C22×C3—204no—
352C22×C3—202no—
353C22×C3—202no—
354C22×C3#393812yes—
355C22×C3#395512yes—
356C22×C3D5×M1612yes—
357C22×C3C2×#68511yescharacteristic
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—202no—
363C2×C5—22no—
364C2×C5—22no—
365C2×C5—22no—
366C2×C5C3×#40711yescharacteristic
367C2×C5C2×C3×#9911yescharacteristic
368C2×C5C2×C3×#10011yescharacteristic
369D5—44no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—54no—
374C23—104no—
375C23—104no—
376C23—102no—
377C23—102no—
378C23—202no—
379C23—202no—
380C23—2016no—
381C23—202no—
382C23—202no—
383C23—202no—
384C23—202no—
385C23C3×#68511yescharacteristic
386C23C3×#68511yescharacteristic
387C23C2×C3×C4×D511yescharacteristic
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—102no—
395C2×C4—202no—
396C2×C4—202no—
397C2×C4—202no—
398C2×C4C3×#68511yescharacteristic
399C2×C4C3×#68511yescharacteristic
400C2×C4C2×C3×D2011yescharacteristic
401C2×C4C2×C3×C22⋊D511yescharacteristic
402C8—42no—
403C8—202no—
404C2×C3—22no—
405C2×C3—22no—
406C2×C3—22no—
407C2×C3—204no—
408C2×C3C2×#393811yescharacteristic
409C2×C3#6541511yescharacteristic
410C2×C3C2×#395511yescharacteristic
411C5C3×#146211yescharacteristic, complemented, Sylow
412C22—28no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—104no—
420C22—204no—
421C22—208no—
422C22—208no—
423C22—204no—
424C22—202no—
425C22—202no—
426C22C3×#393812yes—
427C22C3×#395512yes—
428C22C3×D5×M1612yes—
429C22C2×C3×#68511yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—202no—
435C3#1060076011yescharacteristic, direct product factor, Sylow
436C2—22no—
437C2—22no—
438C2—22no—
439C2—204no—
440C2C2×C3×#393811yescharacteristic
441C2C3×#6541511yescharacteristic
442C2C2×C3×#395511yescharacteristic
subgroupG/H
centerC22×C3C2×#685
commutatorC23×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#407C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×D5C4
cosocleC22×C4×C5C23×C3
hypercenterC3×#407D5
hypocenterC5C3×#1462
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
2. C3×C5×#407C2semidirect
3. C3×#65496C2semidirect
4. C3×#64688C2semidirect
5. #10600760C3direct (N × H)
18. C3×C5×C22⋊C8C22semidirect
20. C3×C22⋊#168C22semidirect
23. C5×#407C2×C3semidirect
24. #65496C2×C3semidirect
25. #64688C2×C3semidirect
54. C3×#407D5semidirect
68. C5×C22⋊C8C22×C3semidirect
70. C22⋊#168C22×C3semidirect
89. C22×C3×D5M16semidirect
120. C3×C22⋊C8C2×D5semidirect
149. #407C3×D5semidirect
217. C22×D5C3×M16semidirect
248. C22⋊C8C2×C3×D5semidirect
339. C3×C5#1462semidirect
411. C5C3×#1462semidirect
435. C3#10600760direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#6852
C3×C5×#4072
C3×#654962
C3×#646882
#106007603
C3×#14625