Finite Group Databasebeta

← C3×#10600713 #14281174

Subgroups — C3×#10600713 #14281174

Order 1920.

560 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4075C211yesmaximal, characteristic
2C2×C3×C5×C22⋊C8C211yesmaximal, characteristic, complemented
3C3×#65496C211yesmaximal, characteristic, complemented
4C3×#64689C212yesmaximal, complemented
5C3×#64688C212yesmaximal, complemented
6#10600713C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C22×C3×C22⋊D5C411yescharacteristic
9C22×C3×C5×C8—21no—
10C2×C3×C22⋊Dic5C411yescharacteristic
11C3×#4075—21no—
12C3×#4075—21no—
13C3×#4075—21no—
14C3×#4075—21no—
15C2×C3×#685C411yescharacteristic
16C2×C3×#685C2211yescharacteristic
17C2×C3×#683C411yescharacteristic
18C2×C3×#683C2211yescharacteristic
19C2×C3×#681—21no—
20C3×C5×C22⋊C8—21no—
21C3×C5×C22⋊C8C2212yes—
22C3×C22⋊#168—21no—
23C3×C22⋊#168C2212yes—
24C3×#1468—51nomaximal, Hall
25C2×#4075C2×C311yescharacteristic
26C2×C5×C22⋊C8C2×C311yescharacteristic, complemented
27#65496C2×C311yescharacteristic, complemented
28#64689C2×C312yescomplemented
29#64688C2×C312yescomplemented
30C24×C3×C5C2×C411yescharacteristic
31C23×C3×D5C2×C411yescharacteristic
32C22×C3×C4×C5—42no—
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5D411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C2×C3×C22⋊D5—21no—
40C2×C3×C22⋊D5—21no—
41C2×C3×C22⋊D5—42no—
42C22×C3×Dic5C2×C411yescharacteristic
43C22×C3×Dic5C2×C411yescharacteristic
44C22×C3×Dic5C2×C411yescharacteristic
45C2×C3×C5×C8—22no—
46C2×C3×C5×C8—42no—
47C3×C22⋊Dic5—21no—
48C3×C22⋊Dic5—21no—
49C3×#685—21no—
50C3×#685—21no—
51C3×#685—21no—
52C3×#685—21no—
53C3×#683—21no—
54C3×#683—21no—
55C3×#683—21no—
56C3×#683—21no—
57C3×#681—42no—
58C2×C3×#168—22no—
59C2×C3×#123—51no—
60C3×#407—51no—
61C2×C3×C22⋊C8D511yescharacteristic, complemented
62C3×#324—52no—
63C3×#323—52no—
64C23×C4×C5C22×C311yescharacteristic
65C22×C22⋊D5C3×C411yescharacteristic
66C22×C5×C8—21no—
67C2×C22⋊Dic5C3×C411yescharacteristic
68#4075—21no—
69#4075—21no—
70#4075—21no—
71#4075—21no—
72C2×#685C3×C411yescharacteristic
73C2×#685C22×C311yescharacteristic
74C2×#683C3×C411yescharacteristic
75C2×#683C22×C311yescharacteristic
76C2×#681—21no—
77C5×C22⋊C8—21no—
78C5×C22⋊C8C22×C312yes—
79C22⋊#168—21no—
80C22⋊#168C22×C312yes—
81#1468—51noSylow
82C23×C3×C5—22no—
83C23×C3×C5—22no—
84C23×C3×C5—41no—
85C23×C3×C5C22⋊C411yescharacteristic
86C23×C3×C5C22⋊C411yescharacteristic
87C23×C3×C5C22×C411yescharacteristic
88C22×C3×D5—21no—
89C22×C3×D5—22no—
90C22×C3×D5—41no—
91C22×C3×D5—41no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C22⋊C411yescharacteristic
99C2×C3×C4×C5C22⋊C411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C3×C22⋊D5—42no—
103C3×C22⋊D5—42no—
104C2×C3×Dic5—21no—
105C2×C3×Dic5—21no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—22no—
108C2×C3×Dic5—41no—
109C2×C3×Dic5—41no—
110C3×C5×C8—42no—
111C3×#168—42no—
112C22×C3×D4—51no—
113C23×C3×C4C2×D511yescharacteristic
114C2×C3×M16—101no—
115C22×C3×C8—21no—
116C3×#123—101no—
117C3×#123—101no—
118C3×#123—101no—
119C3×#123—101no—
120C2×C3×C4⋊C4—51no—
121C2×C3×C4⋊C4—51no—
122C2×C3×C22⋊C4—51no—
123C2×C3×C22⋊C4—51no—
124C2×C3×C22⋊C4—51no—
125C3×C22⋊C8—21no—
126C3×C22⋊C8—52no—
127C3×C22⋊C8—101no—
128C3×C22⋊C8C2×D512yes—
129C24×C5C2×C3×C411yescharacteristic
130C23×D5C2×C3×C411yescharacteristic
131C22×C4×C5—42no—
132C22×C4×C5C2×C3×C411yescharacteristic
133C22×C4×C5C3×D411yescharacteristic
134C22×C4×C5C3×D411yescharacteristic
135C22×C4×C5C3×D411yescharacteristic
136C22×C4×C5C3×D411yescharacteristic
137C22×C4×C5C23×C311yescharacteristic
138C2×C22⋊D5—21no—
139C2×C22⋊D5—21no—
140C2×C22⋊D5—42no—
141C22×Dic5C2×C3×C411yescharacteristic
142C22×Dic5C2×C3×C411yescharacteristic
143C22×Dic5C2×C3×C411yescharacteristic
144C2×C5×C8—22no—
145C2×C5×C8—42no—
146C22⋊Dic5—21no—
147C22⋊Dic5—21no—
148#685—21no—
149#685—21no—
150#685—21no—
151#685—21no—
152#683—21no—
153#683—21no—
154#683—21no—
155#683—21no—
156#681—42no—
157C2×#168—22no—
158C2×#123—51no—
159#407—51no—
160C2×C22⋊C8C3×D511yescharacteristic, complemented
161#324—52no—
162#323—52no—
163C22×C3×C5—21no—
164C22×C3×C5—21no—
165C22×C3×C5—21no—
166C22×C3×C5—21no—
167C22×C3×C5—21no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5—44no—
171C22×C3×C5#9912yes—
172C22×C3×C5C2×C22⋊C411yescharacteristic
173C22×C3×C5#13112yes—
174C2×C3×D5—41no—
175C2×C3×D5—41no—
176C2×C3×D5—41no—
177C2×C3×D5—82no—
178C3×C4×C5—21no—
179C3×C4×C5—21no—
180C3×C4×C5—21no—
181C3×C4×C5—21no—
182C3×Dic5—41no—
183C3×Dic5—41no—
184C3×Dic5—41no—
185C24×C3—51no—
186C24×C3C4×D511yescharacteristic
187C2×C3×D4—101no—
188C2×C3×D4—101no—
189C2×C3×D4—202no—
190C22×C3×C4—42no—
191C22×C3×C4—51no—
192C22×C3×C4—51no—
193C22×C3×C4—51no—
194C22×C3×C4C4×D511yescharacteristic
195C22×C3×C4D2011yescharacteristic
196C22×C3×C4D2011yescharacteristic
197C22×C3×C4C22⋊D511yescharacteristic
198C22×C3×C4C22⋊D511yescharacteristic
199C22×C3×C4C22×D511yescharacteristic
200C3×M16—202no—
201C2×C3×C8—22no—
202C2×C3×C8—42no—
203C2×C3×C8—102no—
204C3×C4⋊C4—101no—
205C3×C4⋊C4—101no—
206C3×C4⋊C4—101no—
207C3×C4⋊C4—101no—
208C3×C22⋊C4—101no—
209C3×C22⋊C4—101no—
210C3×C22⋊C4—101no—
211C3×C22⋊C4—101no—
212C3×C22⋊C4—101no—
213C3×C22⋊C4—101no—
214C23×C5—22no—
215C23×C5—22no—
216C23×C5—41no—
217C23×C5C3×C22⋊C411yescharacteristic
218C23×C5C3×C22⋊C411yescharacteristic
219C23×C5C22×C3×C411yescharacteristic
220C22×D5—21no—
221C22×D5—22no—
222C22×D5—41no—
223C22×D5—41no—
224C2×C4×C5—22no—
225C2×C4×C5—22no—
226C2×C4×C5—41no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5C3×C22⋊C411yescharacteristic
231C2×C4×C5C3×C22⋊C411yescharacteristic
232C2×C4×C5C2×C3×D411yescharacteristic
233C2×C4×C5C2×C3×D411yescharacteristic
234C22⋊D5—42no—
235C22⋊D5—42no—
236C2×Dic5—21no—
237C2×Dic5—21no—
238C2×Dic5—21no—
239C2×Dic5—22no—
240C2×Dic5—41no—
241C2×Dic5—41no—
242C5×C8—42no—
243#168—42no—
244C22×D4—51no—
245C23×C4C2×C3×D511yescharacteristic
246C2×M16—101no—
247C22×C8—21no—
248#123—101no—
249#123—101no—
250#123—101no—
251#123—101no—
252C2×C4⋊C4—51no—
253C2×C4⋊C4—51no—
254C2×C22⋊C4—51no—
255C2×C22⋊C4—51no—
256C2×C22⋊C4—51no—
257C22⋊C8—21no—
258C22⋊C8—52no—
259C22⋊C8—101no—
260C22⋊C8C2×C3×D512yes—
261C2×C3×C5—22no—
262C2×C3×C5—22no—
263C2×C3×C5—41no—
264C2×C3×C5#40811yescharacteristic
265C2×C3×C5C2×#9911yescharacteristic
266C2×C3×C5#41311yescharacteristic
267C3×D5—81no—
268C23×C3—22no—
269C23×C3—22no—
270C23×C3—41no—
271C23×C3—101no—
272C23×C3—102no—
273C23×C3—201no—
274C23×C3—201no—
275C23×C3#68511yescharacteristic
276C23×C3#68511yescharacteristic
277C23×C3C2×C4×D511yescharacteristic
278C3×D4—202no—
279C3×D4—202no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—102no—
287C2×C3×C4—101no—
288C2×C3×C4—101no—
289C2×C3×C4—101no—
290C2×C3×C4—201no—
291C2×C3×C4—201no—
292C2×C3×C4#68511yescharacteristic
293C2×C3×C4#68511yescharacteristic
294C2×C3×C4C2×D2011yescharacteristic
295C2×C3×C4C2×C22⋊D511yescharacteristic
296C3×C8—42no—
297C3×C8—202no—
298C22×C5—21no—
299C22×C5—21no—
300C22×C5—21no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5—21no—
304C22×C5—21no—
305C22×C5—44no—
306C22×C5C3×#9912yes—
307C22×C5C2×C3×C22⋊C411yescharacteristic
308C22×C5C3×#13112yes—
309C2×D5—41no—
310C2×D5—41no—
311C2×D5—41no—
312C2×D5—82no—
313C4×C5—21no—
314C4×C5—21no—
315C4×C5—21no—
316C4×C5—21no—
317Dic5—41no—
318Dic5—41no—
319Dic5—41no—
320C24—51no—
321C24C3×C4×D511yescharacteristic
322C2×D4—101no—
323C2×D4—101no—
324C2×D4—202no—
325C22×C4—42no—
326C22×C4—51no—
327C22×C4—51no—
328C22×C4—51no—
329C22×C4C3×C4×D511yescharacteristic
330C22×C4C3×D2011yescharacteristic
331C22×C4C3×D2011yescharacteristic
332C22×C4C3×C22⋊D511yescharacteristic
333C22×C4C3×C22⋊D511yescharacteristic
334C22×C4C22×C3×D511yescharacteristic
335M16—202no—
336C2×C8—22no—
337C2×C8—42no—
338C2×C8—102no—
339C4⋊C4—101no—
340C4⋊C4—101no—
341C4⋊C4—101no—
342C4⋊C4—101no—
343C22⋊C4—101no—
344C22⋊C4—101no—
345C22⋊C4—101no—
346C22⋊C4—101no—
347C22⋊C4—101no—
348C22⋊C4—101no—
349C3×C5#146811yescharacteristic, complemented, Hall
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—44no—
358C22×C3—201no—
359C22×C3—201no—
360C22×C3—201no—
361C22×C3—402no—
362C22×C3#393812yes—
363C22×C3#404712yes—
364C22×C3C2×#68511yescharacteristic
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—201no—
370C3×C4—201no—
371C3×C4—201no—
372C2×C5—22no—
373C2×C5—22no—
374C2×C5—41no—
375C2×C5C3×#40811yescharacteristic
376C2×C5C2×C3×#9911yescharacteristic
377C2×C5C3×#41311yescharacteristic
378D5—81no—
379C23—22no—
380C23—22no—
381C23—41no—
382C23—101no—
383C23—102no—
384C23—201no—
385C23—201no—
386C23C3×#68511yescharacteristic
387C23C3×#68511yescharacteristic
388C23C2×C3×C4×D511yescharacteristic
389D4—202no—
390D4—202no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—102no—
398C2×C4—101no—
399C2×C4—101no—
400C2×C4—101no—
401C2×C4—201no—
402C2×C4—201no—
403C2×C4C3×#68511yescharacteristic
404C2×C4C3×#68511yescharacteristic
405C2×C4C2×C3×D2011yescharacteristic
406C2×C4C2×C3×C22⋊D511yescharacteristic
407C8—42no—
408C8—202no—
409C2×C3—22no—
410C2×C3—22no—
411C2×C3—41no—
412C2×C3—401no—
413C2×C3C2×#393811yescharacteristic
414C2×C3#6539911yescharacteristic
415C2×C3#6542111yescharacteristic
416C5C3×#146811yescharacteristic, complemented, Sylow
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—44no—
425C22—201no—
426C22—201no—
427C22—201no—
428C22—402no—
429C22C3×#393812yes—
430C22C3×#404712yes—
431C22C2×C3×#68511yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—201no—
437C4—201no—
438C4—201no—
439C3#1060071311yescharacteristic, direct product factor, Sylow
440C2—22no—
441C2—22no—
442C2—41no—
443C2—401no—
444C2C2×C3×#393811yescharacteristic
445C2C3×#6539911yescharacteristic
446C2C3×#6542111yescharacteristic
subgroupG/H
centerC22×C3C2×#685
commutatorC23×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×C22⋊C8C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×C22⋊D5C4
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×C22⋊C8D5
hypocenterC5C3×#1468
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C2×C3×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×C22⋊C8C2semidirect
3. C3×#65496C2semidirect
4. C3×#64689C2semidirect
5. C3×#64688C2semidirect
6. #10600713C3direct (N × H)
26. C2×C5×C22⋊C8C2×C3semidirect
27. #65496C2×C3semidirect
28. #64689C2×C3semidirect
29. #64688C2×C3semidirect
61. C2×C3×C22⋊C8D5semidirect
160. C2×C22⋊C8C3×D5semidirect
349. C3×C5#1468semidirect
416. C5C3×#1468semidirect
439. C3#10600713direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40752
C2×C3×C5×C22⋊C82
C3×#654962
C3×#646892
C3×#646882
#106007133
C3×#14685