Finite Group Databasebeta

← #14411434

Subgroups — #14411434

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#704C212yesmaximal
2C2×#91398C211yesmaximal, characteristic
3C4×#6762C211yesmaximal, characteristic, complemented
4C3×C4×#704C211yesmaximal, characteristic, complemented
5Dic3×#704C212yesmaximal, complemented
6#11751870C214yesmaximal, complemented
7#11751868C214yesmaximal, complemented
8#10617050—31nomaximal, Hall
9C22×D3×Dic5C2211yescharacteristic
10C2×#6762C2212yes—
11C2×C3×#704C2212yes—
12C2×#6739C2214yes—
13D3×#704C4116yescomplemented
14C2×D3×#170C2214yes—
15C2×#6712C411yescharacteristic
16C2×C5×(C2×D3)⋊C4C411yescharacteristic
17C2×C3×C4×Dic5C2211yescharacteristic
18C2×#6669C411yescharacteristic
19C2×(C2×D3)⋊Dic5C411yescharacteristic
20C2×Dic3×Dic5C2211yescharacteristic
21#91398C412yes—
22#91398C412yes—
23#91398C2212yes—
24#91398C2212yes—
25#91231C2212yescomplemented
26C4×C3⋊#170C2212yescomplemented
27C3×#4002C2212yescomplemented
28C3×C4×#170C2212yescomplemented
29#91169C2214yescomplemented
30Dic3×#170C2214yescomplemented
31#78514—51nomaximal, Hall
32C22×#704—32no—
33C2×#4023—31no—
34C4×#704—31no—
35C4×#704—32no—
36C4×#704D311yescharacteristic, complemented
37#65691—34no—
38#65691—34no—
39C23×C5×D3C2×C411yescharacteristic
40C22×C3×C4×C5C2×C411yescharacteristic
41C22×Dic15C2×C411yescharacteristic
42C22×Dic15C2×C411yescharacteristic
43C22×C5×Dic3C2×C411yescharacteristic
44C22×C3×Dic5C2×C411yescharacteristic
45C22×C3×Dic5C2311yescharacteristic
46C2×D3×Dic5C2×C412yes—
47C2×D3×Dic5C2×C418yes—
48C2×D3×Dic5C2312yes—
49#6762C2×C418yes—
50C2×C3⋊#170C2314yes—
51C3×#704C2×C418yes—
52C2×C3×#170C2314yes—
53#6739C2×C4116yescomplemented
54D3×#170C2×C4116yescomplemented
55#6712C2×C412yes—
56#6712C2×C412yes—
57C5×(C2×D3)⋊C4C2×C412yes—
58C5×(C2×D3)⋊C4C2×C412yes—
59C3×C4×Dic5C2×C411yescharacteristic
60C3×C4×Dic5C2×C411yescharacteristic
61C3×C4×Dic5C2311yescharacteristic
62C3×C4×Dic5C2311yescharacteristic
63#6669C2×C412yes—
64#6669C2×C412yes—
65(C2×D3)⋊Dic5C2×C412yes—
66(C2×D3)⋊Dic5C2×C412yes—
67Dic3×Dic5C2×C412yes—
68Dic3×Dic5C2312yes—
69C2×D3×M16—52no—
70C2×#872—51no—
71C3×C4×M16—51no—
72Dic3×M16—52no—
73C4×#208—51no—
74#4708—54no—
75#4689—54no—
76C23×Dic5—31no—
77C2×#704—32no—
78C2×#704—316no—
79C2×#704—34no—
80C2×#704C2×D312yes—
81C22×#170—34no—
82C2×C5×C22⋊C4—31no—
83C2×C22⋊Dic5—31no—
84C2×#683—31no—
85C2×#683—31no—
86C2×C4×Dic5—31no—
87C2×C4×Dic5C2×D311yescharacteristic
88#4023—32no—
89#4023—32no—
90#4023—32no—
91#4023—32no—
92#4002—34no—
93#4002—32no—
94#4002C2×D312yescomplemented
95C4×#170—34no—
96C4×#170—32no—
97C4×#170C2×D312yescomplemented
98#2873—151noSylow
99C23×C3×C5C22×C411yescharacteristic
100C22×C5×D3—41no—
101C22×C5×D3—41no—
102C22×C5×D3C4214yes—
103C22×C5×D3C22×C412yes—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5C22×C411yescharacteristic
106C2×C3×C4×C5C22×C411yescharacteristic
107C2×Dic15—41no—
108C2×Dic15C4214yes—
109C2×Dic15C22×C412yes—
110C2×Dic15C22×C412yes—
111C2×C5×Dic3—41no—
112C2×C5×Dic3C22×C412yes—
113C2×C3×Dic5—41no—
114C2×C3×Dic5C22×C411yescharacteristic
115C2×C3×Dic5C22×C411yescharacteristic
116C2×C3×Dic5C22×C411yescharacteristic
117C2×C3×Dic5C22×C414yes—
118C2×C3×Dic5C2411yescharacteristic
119D3×Dic5C4218yes—
120D3×Dic5C22×C414yes—
121D3×Dic5C22×C414yes—
122C3⋊#170C22×C418yes—
123C3×#170C22×C418yes—
124C22×C4×D3—51no—
125C2×C3×M16—52no—
126C2×C3×C42—51no—
127C2×(C2×D3)⋊C4—51no—
128C2×(C2×D3)⋊C4AGL(1,𝔽5)11yescharacteristic
129C2×Dic3⋊C4—51no—
130C2×Dic3⋊C4—51no—
131C2×C4×Dic3—51no—
132C2×#208—52no—
133D3×M16—516no—
134C2×ΓL(1,𝔽25)—54no—
135C2×D3×C8—54no—
136#872—52no—
137#872—52no—
138#872—52no—
139#872—52no—
140C3×#97—52no—
141C3×C4×C8—52no—
142#815—54no—
143C8×Dic3—54no—
144#803—52no—
145C4×C3⋊C8—52no—
146C24×C5—31no—
147C22×C4×C5—31no—
148C22×C4×C5C4×D311yescharacteristic
149C22×Dic5—31no—
150C22×Dic5—38no—
151C22×Dic5—32no—
152C22×Dic5—32no—
153C22×Dic5—31no—
154C22×Dic5C4×D311yescharacteristic
155C22×Dic5C22×D311yescharacteristic
156#704—38no—
157#704—316no—
158#704C4×D318yes—
159C2×#170—34no—
160C2×#170—316no—
161C2×#170C22×D314yes—
162C5×C22⋊C4—32no—
163C5×C22⋊C4—32no—
164C22⋊Dic5—32no—
165C22⋊Dic5—32no—
166#683—32no—
167#683—32no—
168#683—32no—
169#683—32no—
170C4×Dic5—32no—
171C4×Dic5—32no—
172C4×Dic5C4×D311yescharacteristic
173C4×Dic5C4×D311yescharacteristic
174C4×Dic5C22×D311yescharacteristic
175C4×Dic5C22×D311yescharacteristic
176C22×M16—152no—
177C2×#117—151no—
178#405—154no—
179#405—154no—
180C4×M16—51no—
181C4×M16—151no—
182C4×M16—152no—
183C22×C3×C5—21no—
184C22×C3×C5—21no—
185C22×C3×C5C2×C4212yes—
186C22×C3×C5C23×C411yescharacteristic
187C2×C5×D3—22no—
188C2×C5×D3—22no—
189C2×C5×D3—44no—
190C2×C5×D3C2×C4214yes—
191C3×C4×C5—21no—
192C3×C4×C5—21no—
193Dic15—22no—
194Dic15C2×C4214yes—
195C3×Dic5—21no—
196C3×Dic5—21no—
197C3×Dic5C2×C4212yes—
198C3×Dic5C23×C412yes—
199C5×Dic3—22no—
200C23×D3C2×AGL(1,𝔽5)11yescharacteristic
201C22×C3×C4—51no—
202C22×C3×C4—51no—
203C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
204C22×Dic3—51no—
205C22×Dic3—51no—
206C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
207C2×C4×D3—58no—
208C2×C4×D3—52no—
209C2×C4×D3—52no—
210C3×M16—58no—
211C2×C3×C8—54no—
212C3×C42—51no—
213C3×C42—51no—
214C3×C42—51no—
215C3×C42—51no—
216(C2×D3)⋊C4—52no—
217(C2×D3)⋊C4—52no—
218(C2×D3)⋊C4C2×AGL(1,𝔽5)12yes—
219(C2×D3)⋊C4C2×AGL(1,𝔽5)12yes—
220Dic3⋊C4—52no—
221Dic3⋊C4—52no—
222Dic3⋊C4—52no—
223Dic3⋊C4—52no—
224C4×Dic3—52no—
225C4×Dic3—52no—
226#208—58no—
227C2×C3⋊C8—54no—
228ΓL(1,𝔽25)—516no—
229D3×C8—516no—
230C23×C5—32no—
231C23×C5—34no—
232C23×C5—121no—
233C23×C5—121no—
234C23×C5C2×C4×D311yescharacteristic
235C2×C4×C5—32no—
236C2×C4×C5—41no—
237C2×C4×C5—121no—
238C2×C4×C5C2×C4×D311yescharacteristic
239C2×C4×C5C2×C4×D311yescharacteristic
240C2×Dic5—34no—
241C2×Dic5—32no—
242C2×Dic5—38no—
243C2×Dic5—34no—
244C2×Dic5—34no—
245C2×Dic5—32no—
246C2×Dic5—41no—
247C2×Dic5—121no—
248C2×Dic5C2×C4×D311yescharacteristic
249C2×Dic5C2×C4×D311yescharacteristic
250C2×Dic5C2×C4×D311yescharacteristic
251C2×Dic5C2×C4×D314yes—
252C2×Dic5C23×D311yescharacteristic
253#170—38no—
254#170C2×C4×D318yes—
255C23×C4—151no—
256C2×M16—52no—
257C2×M16—154no—
258C2×M16—1516no—
259C2×M16—152no—
260C22×C8—154no—
261#117—152no—
262#117—152no—
263#117—152no—
264#117—152no—
265C2×C4⋊C4—151no—
266C2×C4⋊C4—151no—
267C2×C22⋊C4—31no—
268C2×C22⋊C4—151no—
269C2×C42—51no—
270C2×C42—151no—
271#97—52no—
272#97—152no—
273#97—154no—
274C4×C8—52no—
275C4×C8—152no—
276C4×C8—154no—
277C2×C3×C5—22no—
278C2×C3×C5C22×C4211yescharacteristic
279C2×C3×C5#56811yescharacteristic
280C2×C3×C5#56811yescharacteristic
281C5×D3—24no—
282C23×C3C22×AGL(1,𝔽5)11yescharacteristic
283C22×D3—41no—
284C22×D3—41no—
285C22×D3C4×AGL(1,𝔽5)14yes—
286C22×D3C22×AGL(1,𝔽5)12yes—
287C2×C3×C4—41no—
288C2×C3×C4—54no—
289C2×C3×C4—51no—
290C2×C3×C4—51no—
291C2×C3×C4—51no—
292C2×C3×C4—51no—
293C2×C3×C4—201no—
294C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
295C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
296C2×Dic3—41no—
297C2×Dic3—54no—
298C2×Dic3—52no—
299C2×Dic3—52no—
300C2×Dic3—201no—
301C2×Dic3C22×AGL(1,𝔽5)12yes—
302C4×D3—58no—
303C4×D3—54no—
304C4×D3—54no—
305C3×C8—58no—
306C3⋊C8—58no—
307C22×C5—21no—
308C22×C5—21no—
309C22×C5—34no—
310C22×C5—62no—
311C22×C5—62no—
312C22×C5—124no—
313C22×C5C42×D312yes—
314C22×C5C22×C4×D311yescharacteristic
315C4×C5—21no—
316C4×C5—21no—
317C4×C5—62no—
318Dic5—21no—
319Dic5—21no—
320Dic5—34no—
321Dic5—62no—
322Dic5C42×D312yes—
323Dic5C22×C4×D312yes—
324C24—31no—
325C22×C4—31no—
326C22×C4—51no—
327C22×C4—51no—
328C22×C4—152no—
329C22×C4—152no—
330C22×C4—158no—
331C22×C4—151no—
332C22×C4—151no—
333C22×C4D3×AGL(1,𝔽5)11yescharacteristic
334M16—58no—
335M16—1516no—
336M16—158no—
337C2×C8—54no—
338C2×C8—1516no—
339C2×C8—154no—
340C4⋊C4—152no—
341C4⋊C4—152no—
342C4⋊C4—152no—
343C4⋊C4—152no—
344C22⋊C4—32no—
345C22⋊C4—32no—
346C22⋊C4—152no—
347C22⋊C4—152no—
348C42—51no—
349C42—51no—
350C42—51no—
351C42—51no—
352C42—152no—
353C42—152no—
354C3×C5#287311yescharacteristic, complemented, Hall
355C22×C3—21no—
356C22×C3—21no—
357C22×C3C2×C4×AGL(1,𝔽5)12yes—
358C22×C3C23×AGL(1,𝔽5)11yescharacteristic
359C2×D3—22no—
360C2×D3—22no—
361C2×D3—44no—
362C2×D3C2×C4×AGL(1,𝔽5)14yes—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—52no—
366C3×C4—52no—
367C3×C4—101no—
368C3×C4—101no—
369Dic3—22no—
370Dic3—54no—
371Dic3—102no—
372C2×C5—22no—
373C2×C5—64no—
374C2×C5C2×C42×D311yescharacteristic
375C2×C5#574511yescharacteristic
376C2×C5#574511yescharacteristic
377C23—32no—
378C23—34no—
379C23—121no—
380C23—121no—
381C23C2×D3×AGL(1,𝔽5)11yescharacteristic
382C2×C4—32no—
383C2×C4—41no—
384C2×C4—54no—
385C2×C4—51no—
386C2×C4—51no—
387C2×C4—51no—
388C2×C4—51no—
389C2×C4—121no—
390C2×C4—154no—
391C2×C4—154no—
392C2×C4—158no—
393C2×C4—154no—
394C2×C4—152no—
395C2×C4—152no—
396C2×C4—201no—
397C2×C4—601no—
398C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
399C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
400C8—58no—
401C8—158no—
402C2×C3—22no—
403C2×C3C22×C4×AGL(1,𝔽5)11yescharacteristic
404C2×C3#6625611yescharacteristic
405C2×C3#6625611yescharacteristic
406D3—24no—
407C5#7851411yescharacteristic, complemented, Sylow
408C22—21no—
409C22—21no—
410C22—34no—
411C22—62no—
412C22—62no—
413C22—124no—
414C22C4×D3×AGL(1,𝔽5)12yes—
415C22C22×D3×AGL(1,𝔽5)11yescharacteristic
416C4—21no—
417C4—21no—
418C4—52no—
419C4—52no—
420C4—62no—
421C4—101no—
422C4—101no—
423C4—154no—
424C4—302no—
425C3#1061705011yescharacteristic, complemented, Sylow
426C2—22no—
427C2—64no—
428C2#1175682211yescharacteristic
429C2C2×C4×D3×AGL(1,𝔽5)11yescharacteristic
430C2#1175686311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C23×C4
prime radicalC23×C5×D3C2×C4
cosocleC2×C3×Dic5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2873
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C4×#6762C2semidirect
4. C3×C4×#704C2semidirect
5. Dic3×#704C2semidirect
6. #11751870C2semidirect
7. #11751868C2semidirect
13. D3×#704C4semidirect
25. #91231C22semidirect
26. C4×C3⋊#170C22semidirect
27. C3×#4002C22semidirect
28. C3×C4×#170C22semidirect
29. #91169C22semidirect
30. Dic3×#170C22semidirect
36. C4×#704D3semidirect
53. #6739C2×C4semidirect
54. D3×#170C2×C4semidirect
94. #4002C2×D3semidirect
97. C4×#170C2×D3semidirect
354. C3×C5#2873semidirect
407. C5#78514semidirect
425. C3#10617050semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#7042
C2×#913982
C4×#67622
C3×C4×#7042
Dic3×#7042
#117518702
#117518682
#106170503
#785145