Finite Group Databasebeta

← #14330987

Subgroups — #14330987

Order 1920.

928 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
1C2×#91813C211yesmaximal, characteristic
2C3×C5×#380C211yesmaximal, characteristic
3#11751312C211yesmaximal, characteristic
4#11751079C212yesmaximal, complemented
5#11751077C212yesmaximal, complemented
6#11751046C212yesmaximal
7#11751045C212yesmaximal
8#11750755C212yesmaximal, complemented
9#11750747C212yesmaximal, complemented
10#10605617—31nomaximal, Hall
11C23×C3×C4×C5C2211yescharacteristic
12C22×Dic30C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2212yes—
14C2×C3×C5×C22⋊C4C2211yescharacteristic
15C2×C3×C5×C22⋊C4C2211yescharacteristic
16C2×#6719C2212yes—
17C2×#6719C2212yes—
18C2×C4⋊Dic15C2211yescharacteristic
19#91813C418yescomplemented
20C2×#6712C2212yes—
21C2×#6712C2212yes—
22C2×#6712C2212yes—
23C2×C4×Dic15C2212yes—
24C2×C4×Dic15C2212yes—
25C3×C5×#95C2212yes—
26#91115C2212yes—
27#91115C2212yes—
28#91115C2212yes—
29#91115C2212yes—
30#91115C2212yes—
31#91115C2211yescharacteristic
32#91115C2211yescharacteristic
33#73886—51nomaximal, Hall
34C2×#4070—31no—
35C5×#380D311yescharacteristic
36#65500—31no—
37#65267—32no—
38#65261—32no—
39#65234—32no—
40#65233—32no—
41#64943—32no—
42#64935—32no—
43C24×C3×C5C2311yescharacteristic
44C22×C3×C4×C5—42no—
45C22×C3×C4×C5C2×C414yes—
46C22×C3×C4×C5C2312yes—
47C22×C3×C4×C5C2312yes—
48C22×C3×C4×C5C2311yescharacteristic
49C22×C3×C4×C5C2311yescharacteristic
50C22×Dic15C2312yes—
51C22×Dic15C2312yes—
52C22×Dic15C2312yes—
53C22×Dic15C2312yes—
54C2×Dic30—42no—
55C2×Dic30C2×C414yes—
56C3×C5×C4⋊C4—42no—
57C3×C5×C22⋊C4—41no—
58C3×C5×C22⋊C4—41no—
59#6719—42no—
60#6719C2×C418yes—
61C4⋊Dic15C2×C414yes—
62#6712—42no—
63#6712—42no—
64#6712C2×C418yes—
65C4×Dic15—42no—
66C4×Dic15—42no—
67C2×#924—51no—
68C3×#380D511yescharacteristic
69#5211—51no—
70#4978—52no—
71#4976—52no—
72#4945—52no—
73#4944—52no—
74#4654—52no—
75#4646—52no—
76C23×C4×C5C2×D311yescharacteristic
77C22×Dic10—31no—
78C2×C5×C4⋊C4C2×D312yes—
79C2×C5×C22⋊C4C2×D311yescharacteristic
80C2×C5×C22⋊C4C2×D311yescharacteristic
81C2×C22⋊Dic5—32no—
82C2×C22⋊Dic5—32no—
83C2×C4⋊Dic5—31no—
84#4070—38no—
85C2×#683—32no—
86C2×#683—32no—
87C2×#683—32no—
88C2×C4×Dic5—32no—
89C2×C4×Dic5—32no—
90C5×#95C2×D312yes—
91#3963—32no—
92#3963—32no—
93#3963—32no—
94#3963—32no—
95#3963—32no—
96#3963—31no—
97#3963—31no—
98#2378—151noSylow
99C23×C3×C5—22no—
100C23×C3×C5—21no—
101C23×C3×C5—22no—
102C23×C3×C5—21no—
103C23×C3×C5C22×C412yes—
104C23×C3×C5C2411yescharacteristic
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—22no—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—22no—
109C2×C3×C4×C5—22no—
110C2×C3×C4×C5—22no—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5—22no—
113C2×C3×C4×C5—44no—
114C2×C3×C4×C5C22×C412yes—
115C2×C3×C4×C5C22×C412yes—
116C2×Dic15—22no—
117C2×Dic15—22no—
118C2×Dic15—22no—
119C2×Dic15—22no—
120C2×Dic15—22no—
121C2×Dic15—22no—
122C2×Dic15—22no—
123C2×Dic15—22no—
124C2×Dic15—22no—
125C2×Dic15—22no—
126C2×Dic15C22×C414yes—
127C2×Dic15C22×C414yes—
128Dic30—44no—
129C23×C3×C4C2×D511yescharacteristic
130C22×Dic6—51no—
131C2×C3×C4⋊C4C2×D512yes—
132C2×C3×C22⋊C4C2×D511yescharacteristic
133C2×C3×C22⋊C4C2×D511yescharacteristic
134C2×#217—52no—
135C2×#217—52no—
136C2×C4⋊Dic3—51no—
137#924—58no—
138C2×Dic3⋊C4—52no—
139C2×Dic3⋊C4—52no—
140C2×Dic3⋊C4—52no—
141C2×C4×Dic3—52no—
142C2×C4×Dic3—52no—
143C3×#95C2×D512yes—
144C3⋊#95—52no—
145C3⋊#95—52no—
146C3⋊#95—52no—
147C3⋊#95—52no—
148C3⋊#95—52no—
149C3⋊#95—51no—
150C3⋊#95—51no—
151C24×C5C22×D311yescharacteristic
152C22×C4×C5—42no—
153C22×C4×C5C4×D314yes—
154C22×C4×C5C22×D312yes—
155C22×C4×C5C22×D312yes—
156C22×C4×C5C22×D311yescharacteristic
157C22×C4×C5C22×D311yescharacteristic
158C22×Dic5—32no—
159C22×Dic5—32no—
160C22×Dic5—32no—
161C22×Dic5—32no—
162C2×Dic10—34no—
163C2×Dic10—122no—
164C5×C4⋊C4—42no—
165C5×C22⋊C4—41no—
166C5×C22⋊C4—41no—
167C22⋊Dic5—38no—
168C22⋊Dic5—122no—
169C4⋊Dic5—34no—
170#683—38no—
171#683—122no—
172#683—122no—
173C4×Dic5—122no—
174C4×Dic5—122no—
175C2×C22⋊Q8—151no—
176#391—152no—
177#389—152no—
178#388—152no—
179#388—152no—
180#387—152no—
181#387—152no—
182#381—151no—
183#380D1511yescharacteristic
184C22×C3×C5—22no—
185C22×C3×C5—22no—
186C22×C3×C5—22no—
187C22×C3×C5—42no—
188C22×C3×C5—42no—
189C22×C3×C5C23×C411yescharacteristic
190C22×C3×C5H(5,𝔽2)12yes—
191C22×C3×C5H(5,𝔽2)11yescharacteristic
192C22×C3×C52−1+411yescharacteristic
193C22×C3×C52−1+412yes—
194C3×C4×C5—22no—
195C3×C4×C5—22no—
196C3×C4×C5—42no—
197C3×C4×C5—42no—
198Dic15—24no—
199Dic15—24no—
200Dic15—42no—
201Dic15—42no—
202C24×C3C22×D511yescharacteristic
203C22×C3×C4—42no—
204C22×C3×C4C4×D514yes—
205C22×C3×C4C22×D512yes—
206C22×C3×C4C22×D512yes—
207C22×C3×C4C22×D511yescharacteristic
208C22×C3×C4C22×D511yescharacteristic
209C22×Dic3—52no—
210C22×Dic3—52no—
211C22×Dic3—52no—
212C22×Dic3—52no—
213C2×Dic6—54no—
214C2×Dic6—202no—
215C3×C4⋊C4—42no—
216C3×C22⋊C4—41no—
217C3×C22⋊C4—41no—
218#217—58no—
219#217—202no—
220C4⋊Dic3—54no—
221Dic3⋊C4—58no—
222Dic3⋊C4—202no—
223Dic3⋊C4—202no—
224C4×Dic3—202no—
225C4×Dic3—202no—
226C23×C5—22no—
227C23×C5—21no—
228C23×C5—21no—
229C23×C5—22no—
230C23×C5C2×C4×D312yes—
231C23×C5C23×D311yescharacteristic
232C2×C4×C5—22no—
233C2×C4×C5—22no—
234C2×C4×C5—22no—
235C2×C4×C5—22no—
236C2×C4×C5—22no—
237C2×C4×C5—22no—
238C2×C4×C5—22no—
239C2×C4×C5—22no—
240C2×C4×C5—44no—
241C2×C4×C5C2×C4×D312yes—
242C2×C4×C5C2×C4×D312yes—
243C2×Dic5—34no—
244C2×Dic5—34no—
245C2×Dic5—62no—
246C2×Dic5—62no—
247C2×Dic5—62no—
248C2×Dic5—62no—
249C2×Dic5—62no—
250C2×Dic5—62no—
251C2×Dic5—62no—
252C2×Dic5—62no—
253C2×Dic5—62no—
254C2×Dic5—62no—
255Dic10—124no—
256C22×Q8—151no—
257C23×C4C2×D1511yescharacteristic
258C22⋊Q8—158no—
259C2×C4⋊C4—151no—
260C2×C4⋊C4—152no—
261C2×C4⋊C4—152no—
262C2×C4⋊C4—152no—
263C2×C4⋊C4C2×D1512yes—
264C2×C22⋊C4—152no—
265C2×C22⋊C4—152no—
266C2×C22⋊C4C2×D1511yescharacteristic
267C2×C22⋊C4C2×D1511yescharacteristic
268C2×C42—152no—
269C2×C42—152no—
270#95—151no—
271#95—152no—
272#95—151no—
273#95—152no—
274#95—152no—
275#95—152no—
276#95—152no—
277#95C2×D1512yes—
278C2×C3×C5—42no—
279C2×C3×C5#51811yescharacteristic
280C2×C3×C5#51911yescharacteristic
281C2×C3×C5#52011yescharacteristic
282C2×C3×C5#56212yes—
283C2×C3×C5#56312yes—
284C23×C3—22no—
285C23×C3—21no—
286C23×C3—21no—
287C23×C3—22no—
288C23×C3C2×C4×D512yes—
289C23×C3C23×D511yescharacteristic
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—44no—
299C2×C3×C4C2×C4×D512yes—
300C2×C3×C4C2×C4×D512yes—
301C2×Dic3—54no—
302C2×Dic3—54no—
303C2×Dic3—102no—
304C2×Dic3—102no—
305C2×Dic3—102no—
306C2×Dic3—102no—
307C2×Dic3—102no—
308C2×Dic3—102no—
309C2×Dic3—102no—
310C2×Dic3—102no—
311C2×Dic3—102no—
312C2×Dic3—102no—
313Dic6—204no—
314C22×C5—22no—
315C22×C5—22no—
316C22×C5—22no—
317C22×C5—42no—
318C22×C5—42no—
319C22×C5C22×C4×D311yescharacteristic
320C22×C5#100412yes—
321C22×C5#100411yescharacteristic
322C22×C5#100711yescharacteristic
323C22×C5#101012yes—
324C4×C5—22no—
325C4×C5—22no—
326C4×C5—42no—
327C4×C5—42no—
328Dic5—64no—
329Dic5—64no—
330Dic5—122no—
331Dic5—122no—
332C24C22×D1511yescharacteristic
333C2×Q8—154no—
334C2×Q8—602no—
335C22×C4—42no—
336C22×C4—152no—
337C22×C4—152no—
338C22×C4—152no—
339C22×C4—152no—
340C22×C4C4×D1514yes—
341C22×C4C22×D1512yes—
342C22×C4C22×D1512yes—
343C22×C4C22×D1511yescharacteristic
344C22×C4C22×D1511yescharacteristic
345C4⋊C4—42no—
346C4⋊C4—158no—
347C4⋊C4—154no—
348C4⋊C4—602no—
349C4⋊C4—602no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—158no—
353C22⋊C4—602no—
354C42—602no—
355C42—602no—
356C3×C5#237811yescharacteristic, complemented, Hall
357C22×C3—22no—
358C22×C3—22no—
359C22×C3—22no—
360C22×C3—42no—
361C22×C3—42no—
362C22×C3C22×C4×D511yescharacteristic
363C22×C3#414412yes—
364C22×C3#414411yescharacteristic
365C22×C3#414711yescharacteristic
366C22×C3#415012yes—
367C3×C4—22no—
368C3×C4—22no—
369C3×C4—42no—
370C3×C4—42no—
371Dic3—104no—
372Dic3—104no—
373Dic3—202no—
374Dic3—202no—
375C2×C5—42no—
376C2×C5#548611yescharacteristic
377C2×C5#550411yescharacteristic
378C2×C5#551611yescharacteristic
379C2×C5#562112yes—
380C2×C5#564612yes—
381C23—21no—
382C23—22no—
383C23—21no—
384C23—22no—
385C23C2×C4×D1512yes—
386C23C23×D1511yescharacteristic
387Q8—604no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—44no—
397C2×C4—154no—
398C2×C4—154no—
399C2×C4—302no—
400C2×C4—302no—
401C2×C4—302no—
402C2×C4—302no—
403C2×C4—302no—
404C2×C4—302no—
405C2×C4—302no—
406C2×C4—302no—
407C2×C4—302no—
408C2×C4—302no—
409C2×C4C2×C4×D1512yes—
410C2×C4C2×C4×D1512yes—
411C2×C3—42no—
412C2×C3#6582011yescharacteristic
413C2×C3#6583811yescharacteristic
414C2×C3#6585011yescharacteristic
415C2×C3#6595512yes—
416C2×C3#6598012yes—
417C5#7388611yescharacteristic, complemented, Sylow
418C22—22no—
419C22—22no—
420C22—22no—
421C22—42no—
422C22—42no—
423C22C22×C4×D1511yescharacteristic
424C22#9209511yescharacteristic
425C22#9209512yes—
426C22#9209811yescharacteristic
427C22#9210112yes—
428C4—22no—
429C4—22no—
430C4—42no—
431C4—42no—
432C4—304no—
433C4—304no—
434C4—602no—
435C4—602no—
436C3#1060561711yescharacteristic, complemented, Sylow
437C2—42no—
438C2#1175624511yescharacteristic
439C2#1175626311yescharacteristic
440C2#1175627511yescharacteristic
441C2#1175638012yes—
442C2#1175640512yes—
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#380C2
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenter#380D15
hypocenterC3×C5#2378
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
4. #11751079C2semidirect
5. #11751077C2semidirect
8. #11750755C2semidirect
9. #11750747C2semidirect
19. #91813C4semidirect
356. C3×C5#2378semidirect
417. C5#73886semidirect
436. C3#10605617semidirect

Maximal subgroups

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

subgroupindex
C2×#918132
C3×C5×#3802
#117513122
#117510792
#117510772
#117510462
#117510452
#117507552
#117507472
#106056173
#738865