Finite Group Databasebeta

← #14301591

Subgroups — #14301591

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756275C211yesmaximal, characteristic, complemented
2C2×#91364C211yesmaximal, characteristic
3C3×#65290C211yesmaximal, characteristic
4#11748367C211yesmaximal, characteristic
5C2×#90963C211yesmaximal, characteristic, complemented
6C5×#4532C211yesmaximal, characteristic, complemented
7#11745976C211yesmaximal, characteristic, complemented
8#10599559—31nomaximal, Hall
9C22×Dic30C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12#91815C2211yescharacteristic
13#91776—22no—
14#91766—22no—
15C4×Dic30—22no—
16C2×C4×C5×Dic3C2211yescharacteristic
17C2×C5×#208C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19C2×#6665—22no—
20#91364—22no—
21#91364C414yescomplemented
22C3×#3941—22no—
23#90965—22no—
24#90963—22no—
25#70325—51nomaximal, Hall
26#65850—31no—
27C2×#4021—31no—
28C2×#3956—31no—
29#65420—31no—
30#65290D311yescharacteristic
31C5×#339—31no—
32#64743—31no—
33C23×C3×D5—21no—
34C22×C3×C4×C5C2311yescharacteristic
35C22×Dic15D412yes—
36C2×Dic30—21no—
37C2×Dic30—21no—
38C2×Dic30—21no—
39C2×Dic30—21no—
40C2×Dic30C2×C412yes—
41C2×Dic30D412yes—
42C22×C5×Dic3—21no—
43C2×C3×D20—21no—
44C2×C3×D20—21no—
45C2×C3×D20—21no—
46C2×C3×D20—21no—
47C2×C3×D20—21no—
48C2×C3×D20C2×C412yes—
49C3×C5×C4⋊C4D412yes—
50C3×C5×C22⋊C4—21no—
51C3×C42×C5—21no—
52#6719—21no—
53C4⋊Dic15D412yes—
54#6712—24no—
55C4×Dic15—24no—
56C4×Dic15—21no—
57C4×C5×Dic3—21no—
58C4×C5×Dic3C2×C412yes—
59C5×#208—21no—
60C5×#208—21no—
61C2×C5×C3⋊C8—21no—
62C3×#681—21no—
63C3×#681—21no—
64C2×C3×#168—21no—
65#6665—28no—
66C2×#936—51no—
67#5516—51no—
68C3×#418—51no—
69#5215—51no—
70C2×#824—51no—
71#4555—51no—
72#4532D511yescharacteristic, complemented
73C22×D20C2×D311yescharacteristic
74C22×Dic10—31no—
75C2×C5×M16—31no—
76C5×#117C2×D311yescharacteristic
77C2×C42×C5—31no—
78C2×#685—62no—
79#4072—31no—
80C2×#681C2×D311yescharacteristic
81#4033—62no—
82#4023—62no—
83#4021—34no—
84#4021—62no—
85C4×Dic10—62no—
86#3956—62no—
87#3953—62no—
88#3941—22no—
89#1888—151noSylow
90C23×C3×C5C2×D411yescharacteristic
91C22×C3×D5—22no—
92C22×C3×D5—44no—
93C22×C3×D5—41no—
94C22×C3×D5—41no—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5#4111yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×Dic15—22no—
103C2×Dic15—22no—
104C2×Dic15—22no—
105C2×Dic15C22⋊C414yes—
106Dic30—22no—
107Dic30—22no—
108Dic30—22no—
109Dic30—22no—
110C2×C5×Dic3—22no—
111C2×C5×Dic3—42no—
112C3×D20—22no—
113C3×D20—22no—
114C3×D20—41no—
115C3×D20—41no—
116C3×#168—41no—
117C5×C3⋊C8—41no—
118C22×C3×D4—51no—
119C22×Dic6—51no—
120C2×C3×M16—51no—
121C3×#117C2×D511yescharacteristic
122C2×#217—102no—
123#936—54no—
124#936—102no—
125#926—51no—
126C2×C4×Dic3C2×D511yescharacteristic
127C2×#208C2×D511yescharacteristic
128#887—102no—
129#877—102no—
130C4×Dic6—102no—
131C3×#102—102no—
132#832—102no—
133#824—102no—
134C23×D5—21no—
135C22×C4×C5—61no—
136C22×C4×C5C22×D311yescharacteristic
137C22×Dic5—32no—
138C2×D20—21no—
139C2×D20—21no—
140C2×D20—21no—
141C2×D20—21no—
142C2×D20—21no—
143C2×D20C4×D312yes—
144C2×Dic10—32no—
145C2×Dic10—32no—
146C2×Dic10—61no—
147C2×Dic10—61no—
148C2×Dic10—61no—
149C2×Dic10—61no—
150C5×M16—61no—
151C5×M16—61no—
152C2×C5×C8—61no—
153C5×C4⋊C4#6712yes—
154C5×C22⋊C4—21no—
155C42×C5—21no—
156C42×C5—32no—
157C42×C5—61no—
158C22⋊Dic5—61no—
159#685—68no—
160C4⋊Dic5—32no—
161#683—64no—
162C4×Dic5—64no—
163C4×Dic5—61no—
164#681—21no—
165#681—21no—
166C2×#168—21no—
167C2×#124—151no—
168#519—151no—
169#418—51no—
170#418—151no—
171C2×#101—151no—
172#339—31no—
173#339—151no—
174C22×C3×C5—22no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C22×C3×C5#12011yescharacteristic
177C22×C3×C5#12311yescharacteristic
178C2×C3×D5—44no—
179C2×C3×D5—42no—
180C2×C3×D5—82no—
181C2×C3×D5—82no—
182C3×C4×C5—42no—
183C3×C4×C5C4×D411yescharacteristic
184C3×C4×C5C4×D411yescharacteristic
185C3×C4×C5#12111yescharacteristic
186C3×C4×C5#12111yescharacteristic
187Dic15—24no—
188Dic15—42no—
189C5×Dic3—42no—
190C24×C3—101no—
191C2×C3×D4—52no—
192C2×C3×D4—101no—
193C2×C3×D4—101no—
194C2×C3×D4—101no—
195C2×C3×D4—101no—
196C2×C3×D4—101no—
197C22×C3×C4C22×D511yescharacteristic
198C22×Dic3—21no—
199C22×Dic3—52no—
200C2×Dic6—52no—
201C2×Dic6—52no—
202C2×Dic6—101no—
203C2×Dic6—101no—
204C2×Dic6—101no—
205C2×Dic6—101no—
206C3×M16—101no—
207C3×M16—101no—
208C2×C3×C8—101no—
209C3×C4⋊C4D2012yes—
210C3×C22⋊C4—21no—
211C3×C42—21no—
212#217—108no—
213#217—101no—
214C4⋊Dic3—52no—
215Dic3⋊C4—104no—
216C4×Dic3—21no—
217C4×Dic3—104no—
218C4×Dic3—101no—
219C4×Dic3C4×D512yes—
220#208—21no—
221#208—21no—
222C2×C3⋊C8—21no—
223C23×C5D3×D411yescharacteristic
224C22×D5—22no—
225C22×D5—44no—
226C22×D5—41no—
227C22×D5—41no—
228C2×C4×C5—22no—
229C2×C4×C5—62no—
230C2×C4×C5—122no—
231C2×C4×C5C2×C4×D311yescharacteristic
232C2×C4×C5#23511yescharacteristic
233C2×C4×C5D3×D411yescharacteristic
234C2×C4×C5D3×D411yescharacteristic
235C2×C4×C5#23711yescharacteristic
236C2×C4×C5C2×#6711yescharacteristic
237C2×Dic5—34no—
238C2×Dic5—62no—
239C2×Dic5—62no—
240C2×Dic5—62no—
241D20—22no—
242D20—22no—
243D20—41no—
244D20—41no—
245Dic10—62no—
246Dic10—62no—
247Dic10—62no—
248Dic10—62no—
249C5×C8—121no—
250#168—41no—
251C22×Q8—151no—
252C22×D4—51no—
253C2×M16—31no—
254C2×M16—51no—
255#124—154no—
256#124—302no—
257C4×Q8—302no—
258C4×Q8—302no—
259#117—151no—
260#117—302no—
261#117D3×D511yescharacteristic
262C2×C22⋊C4—302no—
263C2×C42—31no—
264#102—102no—
265#102—302no—
266#101—302no—
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5#38611yescharacteristic
270C2×C3×C5#45412yes—
271C3×D5—82no—
272C23×C3—102no—
273C23×C3—204no—
274C23×C3—201no—
275C23×C3—201no—
276C23×C3D4×D511yescharacteristic
277C3×D4—102no—
278C3×D4—102no—
279C3×D4—201no—
280C3×D4—201no—
281C2×C3×C4—22no—
282C2×C3×C4C2×C4×D511yescharacteristic
283C2×C3×C4C2×D2011yescharacteristic
284C2×C3×C4#70911yescharacteristic
285C2×C3×C4D4×D511yescharacteristic
286C2×C3×C4D4×D511yescharacteristic
287C2×C3×C4#71311yescharacteristic
288C2×Dic3—22no—
289C2×Dic3—42no—
290C2×Dic3—54no—
291C2×Dic3—102no—
292C2×Dic3—102no—
293C2×Dic3—102no—
294Dic6—102no—
295Dic6—102no—
296Dic6—102no—
297Dic6—102no—
298C3×C8—201no—
299C3⋊C8—41no—
300C22×C5—22no—
301C22×C5D3×C22⋊C411yescharacteristic
302C22×C5#88311yescharacteristic
303C22×C5#93711yescharacteristic
304C2×D5—44no—
305C2×D5—42no—
306C2×D5—82no—
307C2×D5—82no—
308C4×C5—42no—
309C4×C5—122no—
310C4×C5#67⋊C411yescharacteristic
311C4×C5#88411yescharacteristic
312C4×C5C4×#6711yescharacteristic
313C4×C5#93811yescharacteristic
314Dic5—64no—
315Dic5—122no—
316C24—101no—
317C2×Q8—152no—
318C2×Q8—152no—
319C2×Q8—301no—
320C2×Q8—301no—
321C2×Q8—301no—
322C2×Q8—301no—
323C2×D4—52no—
324C2×D4—101no—
325C2×D4—101no—
326C2×D4—101no—
327C2×D4—101no—
328C2×D4—101no—
329C22×C4—61no—
330C22×C4—152no—
331C22×C4C2×D3×D511yescharacteristic
332M16—61no—
333M16—61no—
334M16—101no—
335M16—101no—
336C2×C8—61no—
337C2×C8—101no—
338C4⋊C4—152no—
339C4⋊C4—304no—
340C4⋊C4#120212yes—
341C22⋊C4—21no—
342C22⋊C4—308no—
343C22⋊C4—301no—
344C42—21no—
345C42—32no—
346C42—61no—
347C42—304no—
348C42—301no—
349C3×C5#188811yescharacteristic, complemented, Hall
350C22×C3—22no—
351C22×C3—204no—
352C22×C3—202no—
353C22×C3—402no—
354C22×C3—402no—
355C22×C3D5×C22⋊C411yescharacteristic
356C22×C3#402811yescharacteristic
357C22×C3#404011yescharacteristic
358C3×C4—42no—
359C3×C4C4×D2011yescharacteristic
360C3×C4#403011yescharacteristic
361C3×C4#403911yescharacteristic
362C3×C4#404111yescharacteristic
363Dic3—42no—
364Dic3—104no—
365Dic3—202no—
366C2×C5—21no—
367C2×C5—21no—
368C2×C5#495611yescharacteristic
369C2×C5#520112yes—
370D5—82no—
371C23—102no—
372C23—204no—
373C23—201no—
374C23—201no—
375C23#679011yescharacteristic
376Q8—302no—
377Q8—302no—
378Q8—302no—
379Q8—302no—
380D4—102no—
381D4—102no—
382D4—201no—
383D4—201no—
384C2×C4—22no—
385C2×C4—62no—
386C2×C4—122no—
387C2×C4—154no—
388C2×C4—302no—
389C2×C4—302no—
390C2×C4—302no—
391C2×C4#676611yescharacteristic
392C2×C4#677111yescharacteristic
393C2×C4C4×D3×D511yescharacteristic
394C2×C4#677711yescharacteristic
395C2×C4C2×#120211yescharacteristic
396C2×C4#679011yescharacteristic
397C8—121no—
398C8—201no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—402no—
402C2×C3#6495411yescharacteristic
403C2×C3#6511612yes—
404C5#7032511yescharacteristic, complemented, Sylow
405C22—22no—
406C22—204no—
407C22—202no—
408C22—402no—
409C22—402no—
410C22#9135411yescharacteristic
411C22#9147311yescharacteristic
412C22#9157211yescharacteristic
413C4—42no—
414C4—122no—
415C4—304no—
416C4—602no—
417C4#9139611yescharacteristic
418C4C4×#120211yescharacteristic
419C4#9146111yescharacteristic
420C4#9146511yescharacteristic
421C3#1059955911yescharacteristic, complemented, Sylow
422C2—21no—
423C2—21no—
424C2—402no—
425C2#1174891711yescharacteristic
426C2#1174946012yes—
subgroupG/H
centerC22#91572
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5#120
prime radicalC22×C3×D20C22
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1888
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11756275C2semidirect
5. C2×#90963C2semidirect
6. C5×#4532C2semidirect
7. #11745976C2semidirect
21. #91364C4semidirect
72. #4532D5semidirect
349. C3×C5#1888semidirect
404. C5#70325semidirect
421. C3#10599559semidirect

Maximal subgroups

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

subgroupindex
#117562752
C2×#913642
C3×#652902
#117483672
C2×#909632
C5×#45322
#117459762
#105995593
#703255