Finite Group Databasebeta

← C3×#10602466 #14283114

Subgroups — C3×#10602466 #14283114

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#121C211yesmaximal, characteristic
2C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
3C3×#65496C211yesmaximal, characteristic, complemented
4C3×#64757C214yesmaximal, complemented
5#10602466C311yesmaximal, characteristic, direct product factor, Hall
6C22×C3×C5×D4—21no—
7C22×C3×C5×D4C411yescharacteristic, complemented
8C23×C3×C4×C5C2211yescharacteristic
9C3×C5×#121—21no—
10C3×C5×#121—21no—
11C3×C5×#121C412yescomplemented
12C3×C5×#121C2212yes—
13C2×C3×C5×C4⋊C4C411yescharacteristic, complemented
14C2×C3×C5×C22⋊C4—21no—
15C2×C3×C22⋊Dic5—21no—
16C2×C3×C4×Dic5—21no—
17C2×C3×#681—21no—
18C3×#3963C2212yescomplemented
19C3×C22⋊#168—21no—
20C3×C22⋊#168C2212yescomplemented
21C3×#1507—51nomaximal, Hall
22C2×C5×#121C2×C311yescharacteristic
23C4×C22⋊Dic5C2×C311yescharacteristic, complemented
24#65496C2×C311yescharacteristic, complemented
25#64757C2×C314yescomplemented
26C24×C3×C5—21no—
27C24×C3×C5D411yescharacteristic
28C2×C3×C5×D4—22no—
29C2×C3×C5×D4—22no—
30C2×C3×C5×D4—21no—
31C2×C3×C5×D4—42no—
32C2×C3×C5×D4—44no—
33C2×C3×C5×D4C2×C412yes—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5—42no—
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C22×C3×C4×C5D411yescharacteristic
41C22×C3×C4×C5C2311yescharacteristic
42C22×C3×Dic5—22no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4C2×C412yes—
45C3×C5×C22⋊C4—22no—
46C3×C5×C22⋊C4—22no—
47C3×C22⋊Dic5—24no—
48C3×C4×Dic5—42no—
49C3×#681—42no—
50C2×C3×#168—22no—
51C2×C3×#121D511yescharacteristic
52C3×#407—51no—
53C3×C4×C22⋊C4—51no—
54C3×#327—54no—
55C22×C5×D4—21no—
56C22×C5×D4C3×C411yescharacteristic, complemented
57C23×C4×C5C22×C311yescharacteristic
58C5×#121—21no—
59C5×#121—21no—
60C5×#121C3×C412yescomplemented
61C5×#121C22×C312yes—
62C2×C5×C4⋊C4C3×C411yescharacteristic, complemented
63C2×C5×C22⋊C4—21no—
64C2×C22⋊Dic5—21no—
65C2×C4×Dic5—21no—
66C2×#681—21no—
67#3963C22×C312yescomplemented
68C22⋊#168—21no—
69C22⋊#168C22×C312yescomplemented
70#1507—51noSylow
71C23×C3×C5—22no—
72C23×C3×C5—22no—
73C23×C3×C5—22no—
74C23×C3×C5—41no—
75C23×C3×C5—42no—
76C23×C3×C5—42no—
77C23×C3×C5—42no—
78C23×C3×C5C22⋊C411yescharacteristic
79C23×C3×C5C22⋊C411yescharacteristic
80C23×C3×C5C2×D411yescharacteristic
81C3×C5×D4—42no—
82C3×C5×D4—44no—
83C3×C5×D4—44no—
84C3×C5×D4—42no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5—22no—
88C2×C3×C4×C5—22no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5—42no—
93C2×C3×C4×C5C22⋊C411yescharacteristic
94C2×C3×C4×C5C22⋊C411yescharacteristic
95C2×C3×C4×C5C22×C411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×Dic5—24no—
98C2×C3×Dic5—42no—
99C2×C3×Dic5—42no—
100C3×#168—42no—
101C22×C3×D4—21no—
102C22×C3×D4Dic511yescharacteristic, complemented
103C23×C3×C4C2×D511yescharacteristic
104C2×C3×M16—101no—
105C3×#121—21no—
106C3×#121—21no—
107C3×#121Dic512yescomplemented
108C3×#121C2×D512yes—
109C2×C3×C4⋊C4Dic511yescharacteristic, complemented
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—101no—
112C2×C3×C42—101no—
113C3×C22⋊C8—52no—
114C3×C22⋊C8—101no—
115C3×#95—52no—
116C24×C5—21no—
117C24×C5C3×D411yescharacteristic
118C2×C5×D4—22no—
119C2×C5×D4—22no—
120C2×C5×D4—21no—
121C2×C5×D4—42no—
122C2×C5×D4—44no—
123C2×C5×D4C2×C3×C412yes—
124C22×C4×C5—21no—
125C22×C4×C5—42no—
126C22×C4×C5C2×C3×C411yescharacteristic
127C22×C4×C5C2×C3×C411yescharacteristic
128C22×C4×C5C3×D411yescharacteristic
129C22×C4×C5C3×D411yescharacteristic
130C22×C4×C5C3×D411yescharacteristic
131C22×C4×C5C23×C311yescharacteristic
132C22×Dic5—22no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4C2×C3×C412yes—
135C5×C22⋊C4—22no—
136C5×C22⋊C4—22no—
137C22⋊Dic5—24no—
138C4×Dic5—42no—
139#681—42no—
140C2×#168—22no—
141C2×#121C3×D511yescharacteristic
142#407—51no—
143C4×C22⋊C4—51no—
144#327—54no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—21no—
152C22×C3×C5—44no—
153C22×C3×C5—42no—
154C22×C3×C5—42no—
155C22×C3×C5—42no—
156C22×C3×C5—84no—
157C22×C3×C5#10412yes—
158C22×C3×C5C2×C22⋊C411yescharacteristic
159C22×C3×C5AGL(1,ℤ/8)12yes—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5—21no—
163C3×C4×C5—42no—
164C3×C4×C5#9912yes—
165C3×Dic5—44no—
166C24×C3—21no—
167C24×C3C22⋊D511yescharacteristic
168C2×C3×D4—22no—
169C2×C3×D4—22no—
170C2×C3×D4—21no—
171C2×C3×D4—42no—
172C2×C3×D4—44no—
173C2×C3×D4C2×Dic512yes—
174C22×C3×C4—21no—
175C22×C3×C4—42no—
176C22×C3×C4—102no—
177C22×C3×C4C2×Dic511yescharacteristic
178C22×C3×C4C2×Dic511yescharacteristic
179C22×C3×C4C22⋊D511yescharacteristic
180C22×C3×C4C22⋊D511yescharacteristic
181C22×C3×C4C22⋊D511yescharacteristic
182C22×C3×C4C22×D511yescharacteristic
183C3×M16—202no—
184C2×C3×C8—102no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4C2×Dic512yes—
187C3×C22⋊C4—22no—
188C3×C22⋊C4—22no—
189C3×C22⋊C4—104no—
190C3×C42—202no—
191C23×C5—22no—
192C23×C5—22no—
193C23×C5—22no—
194C23×C5—41no—
195C23×C5—42no—
196C23×C5—42no—
197C23×C5—42no—
198C23×C5C3×C22⋊C411yescharacteristic
199C23×C5C3×C22⋊C411yescharacteristic
200C23×C5C2×C3×D411yescharacteristic
201C5×D4—42no—
202C5×D4—44no—
203C5×D4—44no—
204C5×D4—42no—
205C2×C4×C5—22no—
206C2×C4×C5—22no—
207C2×C4×C5—22no—
208C2×C4×C5—22no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5—41no—
212C2×C4×C5—42no—
213C2×C4×C5C3×C22⋊C411yescharacteristic
214C2×C4×C5C3×C22⋊C411yescharacteristic
215C2×C4×C5C22×C3×C411yescharacteristic
216C2×C4×C5C2×C3×D411yescharacteristic
217C2×Dic5—24no—
218C2×Dic5—42no—
219C2×Dic5—42no—
220#168—42no—
221C22×D4—21no—
222C22×D4C3×Dic511yescharacteristic, complemented
223C23×C4C2×C3×D511yescharacteristic
224C2×M16—101no—
225#121—21no—
226#121—21no—
227#121C3×Dic512yescomplemented
228#121C2×C3×D512yes—
229C2×C4⋊C4C3×Dic511yescharacteristic, complemented
230C2×C22⋊C4—21no—
231C2×C22⋊C4—101no—
232C2×C42—101no—
233C22⋊C8—52no—
234C22⋊C8—101no—
235#95—52no—
236C2×C3×C5—22no—
237C2×C3×C5—22no—
238C2×C3×C5—41no—
239C2×C3×C5—82no—
240C2×C3×C5C2×#9911yescharacteristic
241C2×C3×C5#41811yescharacteristic
242C2×C3×C5C2×#10411yescharacteristic
243C23×C3—22no—
244C23×C3—22no—
245C23×C3—22no—
246C23×C3—41no—
247C23×C3—42no—
248C23×C3—42no—
249C23×C3—42no—
250C23×C3C22⋊Dic511yescharacteristic
251C23×C3C22⋊Dic511yescharacteristic
252C23×C3C2×C22⋊D511yescharacteristic
253C3×D4—42no—
254C3×D4—44no—
255C3×D4—44no—
256C3×D4—42no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—42no—
265C2×C3×C4—104no—
266C2×C3×C4—202no—
267C2×C3×C4—202no—
268C2×C3×C4C22⋊Dic511yescharacteristic
269C2×C3×C4C22⋊Dic511yescharacteristic
270C2×C3×C4C22×Dic511yescharacteristic
271C2×C3×C4C2×C22⋊D511yescharacteristic
272C3×C8—202no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—21no—
278C22×C5—21no—
279C22×C5—21no—
280C22×C5—44no—
281C22×C5—42no—
282C22×C5—42no—
283C22×C5—42no—
284C22×C5—84no—
285C22×C5C3×#10412yes—
286C22×C5C2×C3×C22⋊C411yescharacteristic
287C22×C5C3×AGL(1,ℤ/8)12yes—
288C4×C5—21no—
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—42no—
292C4×C5C3×#9912yes—
293Dic5—44no—
294C24—21no—
295C24C3×C22⋊D511yescharacteristic
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—21no—
299C2×D4—42no—
300C2×D4—44no—
301C2×D4C2×C3×Dic512yes—
302C22×C4—21no—
303C22×C4—42no—
304C22×C4—102no—
305C22×C4C2×C3×Dic511yescharacteristic
306C22×C4C2×C3×Dic511yescharacteristic
307C22×C4C3×C22⋊D511yescharacteristic
308C22×C4C3×C22⋊D511yescharacteristic
309C22×C4C3×C22⋊D511yescharacteristic
310C22×C4C22×C3×D511yescharacteristic
311M16—202no—
312C2×C8—102no—
313C4⋊C4—21no—
314C4⋊C4C2×C3×Dic512yes—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C22⋊C4—104no—
318C42—202no—
319C3×C5#150711yescharacteristic, complemented, Hall
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—44no—
328C22×C3—42no—
329C22×C3—42no—
330C22×C3—42no—
331C22×C3—84no—
332C22×C3#396912yes—
333C22×C3#407812yes—
334C22×C3C2×C22⋊Dic511yescharacteristic
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—42no—
339C3×C4—204no—
340C3×C4#396612yes—
341C2×C5—22no—
342C2×C5—22no—
343C2×C5—41no—
344C2×C5—82no—
345C2×C5C2×C3×#9911yescharacteristic
346C2×C5C3×#41811yescharacteristic
347C2×C5C2×C3×#10411yescharacteristic
348C23—22no—
349C23—22no—
350C23—22no—
351C23—41no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23C3×C22⋊Dic511yescharacteristic
356C23C3×C22⋊Dic511yescharacteristic
357C23C2×C3×C22⋊D511yescharacteristic
358D4—42no—
359D4—44no—
360D4—44no—
361D4—42no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—104no—
371C2×C4—202no—
372C2×C4—202no—
373C2×C4C3×C22⋊Dic511yescharacteristic
374C2×C4C3×C22⋊Dic511yescharacteristic
375C2×C4C22×C3×Dic511yescharacteristic
376C2×C4C2×C3×C22⋊D511yescharacteristic
377C8—202no—
378C2×C3—22no—
379C2×C3—22no—
380C2×C3—41no—
381C2×C3—82no—
382C2×C3#6550411yescharacteristic
383C2×C3C2×#396611yescharacteristic
384C2×C3C2×#396911yescharacteristic
385C5C3×#150711yescharacteristic, complemented, Sylow
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—42no—
395C22—42no—
396C22—42no—
397C22—84no—
398C22C3×#396912yes—
399C22C3×#407812yes—
400C22C2×C3×C22⋊Dic511yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—42no—
405C4—204no—
406C4C3×#396612yes—
407C3#1060246611yescharacteristic, direct product factor, Sylow
408C2—22no—
409C2—22no—
410C2—41no—
411C2—82no—
412C2C3×#6550411yescharacteristic
413C2C2×C3×#396611yescharacteristic
414C2C2×C3×#396911yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊Dic5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
Fitting, prime radicalC2×C3×C5×#121C2
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#121D5
hypocenterC5C3×#1507
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
2. C3×C4×C22⋊Dic5C2semidirect
3. C3×#65496C2semidirect
4. C3×#64757C2semidirect
5. #10602466C3direct (N × H)
7. C22×C3×C5×D4C4semidirect
11. C3×C5×#121C4semidirect
13. C2×C3×C5×C4⋊C4C4semidirect
18. C3×#3963C22semidirect
20. C3×C22⋊#168C22semidirect
23. C4×C22⋊Dic5C2×C3semidirect
24. #65496C2×C3semidirect
25. #64757C2×C3semidirect
56. C22×C5×D4C3×C4semidirect
60. C5×#121C3×C4semidirect
62. C2×C5×C4⋊C4C3×C4semidirect
67. #3963C22×C3semidirect
69. C22⋊#168C22×C3semidirect
102. C22×C3×D4Dic5semidirect
107. C3×#121Dic5semidirect
109. C2×C3×C4⋊C4Dic5semidirect
222. C22×D4C3×Dic5semidirect
227. #121C3×Dic5semidirect
229. C2×C4⋊C4C3×Dic5semidirect
319. C3×C5#1507semidirect
385. C5C3×#1507semidirect
407. C3#10602466direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1212
C3×C4×C22⋊Dic52
C3×#654962
C3×#647572
#106024663
C3×#15075