Finite Group Databasebeta

← C3×#10600324 #14283260

Subgroups — C3×#10600324 #14283260

Order 1920.

652 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4076C211yesmaximal, characteristic
2C3×C5×#381C211yesmaximal, characteristic, complemented
3C3×#65496C211yesmaximal, characteristic, complemented
4C3×#64671C214yesmaximal, complemented
5#10600324C311yesmaximal, characteristic, direct product factor, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C22×C3×C22⋊D5—21no—
8C22×C3×D20C411yescharacteristic, complemented
9C2×C3×C5×C22⋊C4—21no—
10C3×#4076—21no—
11C3×#4076—21no—
12C3×#4076C412yescomplemented
13C3×#4076C2212yes—
14C2×C3×#685—21no—
15C2×C3×C4⋊Dic5C411yescharacteristic, complemented
16C2×C3×#681—21no—
17C3×C5×#95—21no—
18C3×C5×#95C2212yescomplemented
19C3×C22⋊#168—21no—
20C3×C22⋊#168C2212yescomplemented
21C3×#1510—51nomaximal, Hall
22C2×#4076C2×C311yescharacteristic
23C5×#381C2×C311yescharacteristic, complemented
24#65496C2×C311yescharacteristic, complemented
25#64671C2×C314yescomplemented
26C24×C3×C5D411yescharacteristic
27C23×C3×D5—21no—
28C22×C3×C4×C5—22no—
29C22×C3×C4×C5—42no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5C2×C411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5C2311yescharacteristic
36C2×C3×C22⋊D5—22no—
37C2×C3×C22⋊D5—22no—
38C2×C3×C22⋊D5—44no—
39C22×C3×Dic5—21no—
40C2×C3×D20—21no—
41C2×C3×D20—42no—
42C2×C3×D20C2×C412yes—
43C3×C5×C22⋊C4—42no—
44C3×#685—22no—
45C3×#685—22no—
46C3×C4⋊Dic5—21no—
47C3×C4⋊Dic5C2×C412yes—
48C3×#681—42no—
49C2×C3×#168—22no—
50C2×C3×#121—51no—
51C3×#407—51no—
52C3×#381D511yescharacteristic, complemented
53C3×#327—54no—
54C23×C4×C5C22×C311yescharacteristic
55C22×C22⋊D5—21no—
56C22×D20C3×C411yescharacteristic, complemented
57C2×C5×C22⋊C4—21no—
58#4076—21no—
59#4076—21no—
60#4076C3×C412yescomplemented
61#4076C22×C312yes—
62C2×#685—21no—
63C2×C4⋊Dic5C3×C411yescharacteristic, complemented
64C2×#681—21no—
65C5×#95—21no—
66C5×#95C22×C312yescomplemented
67C22⋊#168—21no—
68C22⋊#168C22×C312yescomplemented
69#1510—51noSylow
70C23×C3×C5—22no—
71C23×C3×C5—22no—
72C23×C3×C5—41no—
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C22⋊C411yescharacteristic
75C23×C3×C5C2×D411yescharacteristic
76C22×C3×D5—22no—
77C22×C3×D5—42no—
78C22×C3×D5—42no—
79C22×C3×D5—42no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—42no—
87C2×C3×C4×C5—42no—
88C2×C3×C4×C5—42no—
89C2×C3×C4×C5C22⋊C411yescharacteristic
90C2×C3×C4×C5C22⋊C411yescharacteristic
91C2×C3×C4×C5C22×C411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C3×C22⋊D5—44no—
94C3×C22⋊D5—44no—
95C2×C3×Dic5—22no—
96C2×C3×Dic5—42no—
97C3×D20—42no—
98C3×D20—42no—
99C3×#168—42no—
100C22×C3×D4—51no—
101C22×C3×D4—101no—
102C23×C3×C4C2×D511yescharacteristic
103C2×C3×M16—101no—
104C3×#121—52no—
105C3×#121—52no—
106C3×#121—101no—
107C3×#121—101no—
108C2×C3×C4⋊C4—51no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—101no—
111C3×C22⋊C8—52no—
112C3×C22⋊C8—101no—
113C3×#95—21no—
114C3×#95C2×D512yescomplemented
115C24×C5C3×D411yescharacteristic
116C23×D5—21no—
117C22×C4×C5—22no—
118C22×C4×C5—42no—
119C22×C4×C5C2×C3×C411yescharacteristic
120C22×C4×C5C2×C3×C411yescharacteristic
121C22×C4×C5C3×D411yescharacteristic
122C22×C4×C5C3×D411yescharacteristic
123C22×C4×C5C3×D411yescharacteristic
124C22×C4×C5C23×C311yescharacteristic
125C2×C22⋊D5—22no—
126C2×C22⋊D5—22no—
127C2×C22⋊D5—44no—
128C22×Dic5—21no—
129C2×D20—21no—
130C2×D20—42no—
131C2×D20C2×C3×C412yes—
132C5×C22⋊C4—42no—
133#685—22no—
134#685—22no—
135C4⋊Dic5—21no—
136C4⋊Dic5C2×C3×C412yes—
137#681—42no—
138C2×#168—22no—
139C2×#121—51no—
140#407—51no—
141#381C3×D511yescharacteristic, complemented
142#327—54no—
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—44no—
151C22×C3×C5#9912yes—
152C22×C3×C5C2×C22⋊C411yescharacteristic
153C22×C3×C5AGL(1,ℤ/8)12yes—
154C2×C3×D5—42no—
155C2×C3×D5—42no—
156C2×C3×D5—42no—
157C2×C3×D5—84no—
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5—82no—
163C3×Dic5—42no—
164C24×C3—101no—
165C24×C3C22⋊D511yescharacteristic
166C2×C3×D4—52no—
167C2×C3×D4—102no—
168C2×C3×D4—102no—
169C2×C3×D4—101no—
170C2×C3×D4—202no—
171C2×C3×D4—204no—
172C22×C3×C4—22no—
173C22×C3×C4—42no—
174C22×C3×C4—101no—
175C22×C3×C4C4×D511yescharacteristic
176C22×C3×C4C4×D511yescharacteristic
177C22×C3×C4D2011yescharacteristic
178C22×C3×C4D2011yescharacteristic
179C22×C3×C4C22⋊D511yescharacteristic
180C22×C3×C4C22×D511yescharacteristic
181C3×M16—202no—
182C2×C3×C8—102no—
183C3×C4⋊C4—52no—
184C3×C4⋊C4—101no—
185C3×C22⋊C4—42no—
186C3×C22⋊C4—102no—
187C3×C22⋊C4—102no—
188C23×C5—22no—
189C23×C5—22no—
190C23×C5—41no—
191C23×C5C3×C22⋊C411yescharacteristic
192C23×C5C3×C22⋊C411yescharacteristic
193C23×C5C2×C3×D411yescharacteristic
194C22×D5—22no—
195C22×D5—42no—
196C22×D5—42no—
197C22×D5—42no—
198C2×C4×C5—22no—
199C2×C4×C5—22no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5—41no—
204C2×C4×C5—42no—
205C2×C4×C5—42no—
206C2×C4×C5—42no—
207C2×C4×C5C3×C22⋊C411yescharacteristic
208C2×C4×C5C3×C22⋊C411yescharacteristic
209C2×C4×C5C22×C3×C411yescharacteristic
210C2×C4×C5C2×C3×D411yescharacteristic
211C22⋊D5—44no—
212C22⋊D5—44no—
213C2×Dic5—22no—
214C2×Dic5—42no—
215D20—42no—
216D20—42no—
217#168—42no—
218C22×D4—51no—
219C22×D4—101no—
220C23×C4C2×C3×D511yescharacteristic
221C2×M16—101no—
222#121—52no—
223#121—52no—
224#121—101no—
225#121—101no—
226C2×C4⋊C4—51no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—101no—
229C22⋊C8—52no—
230C22⋊C8—101no—
231#95—21no—
232#95C2×C3×D512yescomplemented
233C2×C3×C5—22no—
234C2×C3×C5—22no—
235C2×C3×C5—41no—
236C2×C3×C5C2×#9911yescharacteristic
237C2×C3×C5#41811yescharacteristic
238C2×C3×C5#42111yescharacteristic
239C3×D5—82no—
240C23×C3—22no—
241C23×C3—22no—
242C23×C3—41no—
243C23×C3—102no—
244C23×C3—202no—
245C23×C3—202no—
246C23×C3—202no—
247C23×C3#68511yescharacteristic
248C23×C3#68511yescharacteristic
249C23×C3C2×C22⋊D511yescharacteristic
250C3×D4—202no—
251C3×D4—202no—
252C3×D4—204no—
253C3×D4—204no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—42no—
261C2×C3×C4—42no—
262C2×C3×C4—42no—
263C2×C3×C4—102no—
264C2×C3×C4—202no—
265C2×C3×C4#68511yescharacteristic
266C2×C3×C4#68511yescharacteristic
267C2×C3×C4C2×C4×D511yescharacteristic
268C2×C3×C4C2×D2011yescharacteristic
269C3×C8—202no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—21no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—44no—
278C22×C5C3×#9912yes—
279C22×C5C2×C3×C22⋊C411yescharacteristic
280C22×C5C3×AGL(1,ℤ/8)12yes—
281C2×D5—42no—
282C2×D5—42no—
283C2×D5—42no—
284C2×D5—84no—
285C4×C5—21no—
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—21no—
289C4×C5—82no—
290Dic5—42no—
291C24—101no—
292C24C3×C22⋊D511yescharacteristic
293C2×D4—52no—
294C2×D4—102no—
295C2×D4—102no—
296C2×D4—101no—
297C2×D4—202no—
298C2×D4—204no—
299C22×C4—22no—
300C22×C4—42no—
301C22×C4—101no—
302C22×C4C3×C4×D511yescharacteristic
303C22×C4C3×C4×D511yescharacteristic
304C22×C4C3×D2011yescharacteristic
305C22×C4C3×D2011yescharacteristic
306C22×C4C3×C22⋊D511yescharacteristic
307C22×C4C22×C3×D511yescharacteristic
308M16—202no—
309C2×C8—102no—
310C4⋊C4—52no—
311C4⋊C4—101no—
312C22⋊C4—42no—
313C22⋊C4—102no—
314C22⋊C4—102no—
315C3×C5#151011yescharacteristic, complemented, Hall
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—44no—
324C22×C3—202no—
325C22×C3—202no—
326C22×C3—202no—
327C22×C3—404no—
328C22×C3#393812yes—
329C22×C3C2×#68511yescharacteristic
330C22×C3#409512yes—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—82no—
336C3×C4—202no—
337C2×C5—22no—
338C2×C5—22no—
339C2×C5—41no—
340C2×C5C2×C3×#9911yescharacteristic
341C2×C5C3×#41811yescharacteristic
342C2×C5C3×#42111yescharacteristic
343D5—82no—
344C23—22no—
345C23—22no—
346C23—41no—
347C23—102no—
348C23—202no—
349C23—202no—
350C23—202no—
351C23C3×#68511yescharacteristic
352C23C3×#68511yescharacteristic
353C23C2×C3×C22⋊D511yescharacteristic
354D4—202no—
355D4—202no—
356D4—204no—
357D4—204no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—102no—
368C2×C4—202no—
369C2×C4C3×#68511yescharacteristic
370C2×C4C3×#68511yescharacteristic
371C2×C4C2×C3×C4×D511yescharacteristic
372C2×C4C2×C3×D2011yescharacteristic
373C8—202no—
374C2×C3—22no—
375C2×C3—22no—
376C2×C3—41no—
377C2×C3—402no—
378C2×C3C2×#393811yescharacteristic
379C2×C3#6529011yescharacteristic
380C2×C3#6529411yescharacteristic
381C5C3×#151011yescharacteristic, complemented, Sylow
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—44no—
390C22—202no—
391C22—202no—
392C22—202no—
393C22—404no—
394C22C3×#393812yes—
395C22C2×C3×#68511yescharacteristic
396C22C3×#409512yes—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—82no—
402C4—202no—
403C3#1060032411yescharacteristic, direct product factor, Sylow
404C2—22no—
405C2—22no—
406C2—41no—
407C2—402no—
408C2C2×C3×#393811yescharacteristic
409C2C3×#6529011yescharacteristic
410C2C3×#6529411yescharacteristic
subgroupG/H
centerC22×C3C2×#685
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#381C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#4076C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#381D5
hypocenterC5C3×#1510
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#381

Complements

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

NH ≅ G/Ntype
2. C3×C5×#381C2semidirect
3. C3×#65496C2semidirect
4. C3×#64671C2semidirect
5. #10600324C3direct (N × H)
8. C22×C3×D20C4semidirect
12. C3×#4076C4semidirect
15. C2×C3×C4⋊Dic5C4semidirect
18. C3×C5×#95C22semidirect
20. C3×C22⋊#168C22semidirect
23. C5×#381C2×C3semidirect
24. #65496C2×C3semidirect
25. #64671C2×C3semidirect
52. C3×#381D5semidirect
56. C22×D20C3×C4semidirect
60. #4076C3×C4semidirect
63. C2×C4⋊Dic5C3×C4semidirect
66. C5×#95C22×C3semidirect
68. C22⋊#168C22×C3semidirect
114. C3×#95C2×D5semidirect
141. #381C3×D5semidirect
232. #95C2×C3×D5semidirect
315. C3×C5#1510semidirect
381. C5C3×#1510semidirect
403. C3#10600324direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40762
C3×C5×#3812
C3×#654962
C3×#646712
#106003243
C3×#15105