Finite Group Databasebeta

← #14301602

Subgroups — #14301602

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
1C2×C3×#4021C211yesmaximal, characteristic
2#11754188C211yesmaximal, characteristic, complemented
3#11748367C211yesmaximal, characteristic
4#11748366C211yesmaximal, characteristic
5C2×#90961C211yesmaximal, characteristic, complemented
6#11746344C211yesmaximal, characteristic, complemented
7C5×#4523C211yesmaximal, characteristic, complemented
8#10599559—31nomaximal, Hall
9C22×C3×D20C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C2×C3×#685—22no—
17C3×#4021—22no—
18C3×#4021C414yescomplemented
19#91528—22no—
20#91331—22no—
21Dic3×Dic10—22no—
22#90965—22no—
23#90964—22no—
24#90961—22no—
25#71724—51nomaximal, Hall
26#65850—31no—
27C2×#4021D311yescharacteristic
28C2×#3956—31no—
29#65420—31no—
30#65290—31no—
31C5×#339—31no—
32#64743—31no—
33C23×C3×D5—21no—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C22×C3×Dic5D412yes—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20C2×C412yes—
43C2×C3×Dic10—21no—
44C2×C3×Dic10—21no—
45C2×C3×Dic10—21no—
46C2×C3×Dic10—21no—
47C2×C3×Dic10C2×C412yes—
48C2×C3×Dic10D412yes—
49C3×C42×C5—21no—
50C3×C42×C5C2×C412yes—
51#6719—21no—
52C4⋊Dic15D412yes—
53C4×Dic15—21no—
54#6710—21no—
55#6710—21no—
56C2×C3⋊#168—21no—
57C5×#217—21no—
58C5×C4⋊Dic3D412yes—
59C4×C5×Dic3—21no—
60C5×#208—21no—
61C5×#208—21no—
62C2×C5×C3⋊C8—21no—
63C3×#685—28no—
64#6668—24no—
65Dic3×Dic5—24no—
66C2×C3×#124—51no—
67#5812—51no—
68C2×#836—51no—
69#5215—51no—
70#5215—51no—
71#4523—51no—
72#4523D511yescharacteristic, complemented
73C22×D20C2×D311yescharacteristic
74C22×Dic10C2×D311yescharacteristic
75C2×C5×M16—31no—
76C5×#117—31no—
77C2×C42×C5C2×D311yescharacteristic
78C2×#685—22no—
79#4072—31no—
80C2×#681—31no—
81#4033—62no—
82#4023—62no—
83#4021—22no—
84#4021Dic314yescomplemented
85C4×Dic10—62no—
86#3956—62no—
87#3953—62no—
88#3941—62no—
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×C5—42no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×Dic15—22no—
104C2×C5×Dic3—22no—
105C2×C3×Dic5—22no—
106C2×C3×Dic5—22no—
107C2×C3×Dic5C22⋊C414yes—
108C3×D20—22no—
109C3×D20—22no—
110C3×D20—41no—
111C3×D20—41no—
112C3×Dic10—22no—
113C3×Dic10—22no—
114C3×Dic10—22no—
115C3×Dic10—22no—
116C3⋊#168—41no—
117C5×C3⋊C8—41no—
118C22×C3×Q8—51no—
119C22×C3×D4—51no—
120C3×#124—54no—
121C3×#124—102no—
122C2×C3×C22⋊C4—102no—
123C2×C3×C42C2×D511yescharacteristic
124Q8×Dic3—102no—
125Q8×Dic3—102no—
126#926—51no—
127#926—102no—
128#926C2×D511yescharacteristic
129C2×#208—51no—
130C2×#208C2×D511yescharacteristic
131#836—102no—
132#832—102no—
133#832—102no—
134C23×D5—21no—
135C22×C4×C5—21no—
136C22×C4×C5C22×D311yescharacteristic
137C22×Dic5#6712yes—
138C2×D20—21no—
139C2×D20—21no—
140C2×D20—21no—
141C2×D20—21no—
142C2×D20—21no—
143C2×D20C2×Dic312yes—
144C2×Dic10—21no—
145C2×Dic10—21no—
146C2×Dic10—21no—
147C2×Dic10—21no—
148C2×Dic10C2×Dic312yes—
149C2×Dic10#6712yes—
150C5×M16—61no—
151C5×M16—61no—
152C2×C5×C8—61no—
153C5×C4⋊C4—32no—
154C5×C22⋊C4—61no—
155C42×C5—21no—
156C42×C5—61no—
157C42×C5C2×Dic312yes—
158C22⋊Dic5—61no—
159#685—28no—
160C4⋊Dic5—32no—
161#683—64no—
162C4×Dic5—64no—
163C4×Dic5—61no—
164#681—61no—
165#681—61no—
166C2×#168—61no—
167C2×#124—51no—
168#519—151no—
169#418—151no—
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—42no—
188C3×Dic5—24no—
189C5×Dic3—42no—
190C24×C3—101no—
191C2×C3×Q8—52no—
192C2×C3×Q8—52no—
193C2×C3×Q8—101no—
194C2×C3×Q8—101no—
195C2×C3×Q8—101no—
196C2×C3×Q8—101no—
197C2×C3×D4—52no—
198C2×C3×D4—101no—
199C2×C3×D4—101no—
200C2×C3×D4—101no—
201C2×C3×D4—101no—
202C2×C3×D4—101no—
203C22×C3×C4—21no—
204C22×C3×C4—52no—
205C22×C3×C4C22×D511yescharacteristic
206C3×C22⋊C4—108no—
207C3×C42—21no—
208C3×C42C4×D512yes—
209#217—21no—
210#217—101no—
211C4⋊Dic3—52no—
212C4⋊Dic3—104no—
213C4⋊Dic3D2012yes—
214C4×Dic3—21no—
215C4×Dic3—104no—
216C4×Dic3—101no—
217#208—21no—
218#208—21no—
219#208—101no—
220#208—101no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—101no—
223C23×C5C2×#6711yescharacteristic
224C22×D5—22no—
225C22×D5—44no—
226C22×D5—41no—
227C22×D5—41no—
228C2×C4×C5—22no—
229C2×C4×C5—42no—
230C2×C4×C5—62no—
231C2×C4×C5D3×D411yescharacteristic
232C2×C4×C5D3×D411yescharacteristic
233C2×C4×C5#23711yescharacteristic
234C2×C4×C5#23711yescharacteristic
235C2×C4×C5C22×Dic311yescharacteristic
236C2×C4×C5C2×#6711yescharacteristic
237C2×Dic5—22no—
238C2×Dic5—22no—
239C2×Dic5—62no—
240C2×Dic5#21714yes—
241D20—22no—
242D20—22no—
243D20—41no—
244D20—41no—
245Dic10—22no—
246Dic10—22no—
247Dic10—22no—
248Dic10—22no—
249C5×C8—121no—
250#168—121no—
251C22×Q8—51no—
252C22×D4—51no—
253C2×M16—31no—
254C2×M16—151no—
255#124—54no—
256#124—102no—
257C4×Q8—302no—
258C4×Q8—302no—
259#117—31no—
260#117—151no—
261#117—302no—
262C2×C22⋊C4—102no—
263C2×C42D3×D511yescharacteristic
264#102—302no—
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×Q8—102no—
278C3×Q8—102no—
279C3×Q8—102no—
280C3×Q8—102no—
281C3×D4—102no—
282C3×D4—102no—
283C3×D4—201no—
284C3×D4—201no—
285C2×C3×C4—22no—
286C2×C3×C4—42no—
287C2×C3×C4—54no—
288C2×C3×C4—102no—
289C2×C3×C4—102no—
290C2×C3×C4C2×C4×D511yescharacteristic
291C2×C3×C4C2×D2011yescharacteristic
292C2×C3×C4#70911yescharacteristic
293C2×C3×C4D4×D511yescharacteristic
294C2×C3×C4D4×D511yescharacteristic
295C2×C3×C4#71311yescharacteristic
296C2×Dic3—22no—
297C2×Dic3—102no—
298C3⋊C8—41no—
299C3⋊C8—201no—
300C22×C5—22no—
301C22×C5#93511yescharacteristic
302C22×C5#93711yescharacteristic
303C22×C5C2×#21711yescharacteristic
304C2×D5—44no—
305C2×D5—42no—
306C2×D5—82no—
307C2×D5—82no—
308C4×C5—42no—
309C4×C5—122no—
310C4×C5D4×Dic311yescharacteristic
311C4×C5D4×Dic311yescharacteristic
312C4×C5#93911yescharacteristic
313C4×C5#93911yescharacteristic
314Dic5—24no—
315Dic5—122no—
316C24—101no—
317C2×Q8—52no—
318C2×Q8—52no—
319C2×Q8—101no—
320C2×Q8—101no—
321C2×Q8—101no—
322C2×Q8—101no—
323C2×D4—52no—
324C2×D4—101no—
325C2×D4—101no—
326C2×D4—101no—
327C2×D4—101no—
328C2×D4—101no—
329C22×C4—21no—
330C22×C4—52no—
331C22×C4C2×D3×D511yescharacteristic
332M16—61no—
333M16—61no—
334M16—301no—
335M16—301no—
336C2×C8—61no—
337C2×C8—301no—
338C4⋊C4—32no—
339C4⋊C4—152no—
340C4⋊C4—304no—
341C22⋊C4—61no—
342C22⋊C4—108no—
343C22⋊C4—301no—
344C42—21no—
345C42—61no—
346C42—304no—
347C42—301no—
348C42D5×Dic312yes—
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×C4—104no—
360C3×C4C4×D2011yescharacteristic
361C3×C4#403011yescharacteristic
362C3×C4#403911yescharacteristic
363C3×C4#404111yescharacteristic
364Dic3—42no—
365Dic3—202no—
366C2×C5—21no—
367C2×C5—21no—
368C2×C5#506212yes—
369C2×C5#522011yescharacteristic
370D5—82no—
371C23—102no—
372C23—204no—
373C23—201no—
374C23—201no—
375C23D5×#6711yescharacteristic
376Q8—102no—
377Q8—102no—
378Q8—102no—
379Q8—102no—
380D4—102no—
381D4—102no—
382D4—201no—
383D4—201no—
384C2×C4—22no—
385C2×C4—42no—
386C2×C4—54no—
387C2×C4—62no—
388C2×C4—102no—
389C2×C4—102no—
390C2×C4—302no—
391C2×C4#676511yescharacteristic
392C2×C4#676611yescharacteristic
393C2×C4D3×D2011yescharacteristic
394C2×C4#677711yescharacteristic
395C2×C4C2×D5×Dic311yescharacteristic
396C2×C4D5×#6711yescharacteristic
397C8—121no—
398C8—601no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—402no—
402C2×C3#6495411yescharacteristic
403C2×C3#6511612yes—
404C5#7172411yescharacteristic, complemented, Sylow
405C22—22no—
406C22—204no—
407C22—202no—
408C22—402no—
409C22—402no—
410C22#9140711yescharacteristic
411C22#9147411yescharacteristic
412C22D5×#21711yescharacteristic
413C4—42no—
414C4—104no—
415C4—122no—
416C4—602no—
417C4#9140811yescharacteristic
418C4#9140911yescharacteristic
419C4Dic3×D2011yescharacteristic
420C4#9143411yescharacteristic
421C3#1059955911yescharacteristic, complemented, Sylow
422C2—21no—
423C2—21no—
424C2—402no—
425C2#1174712112yes—
426C2#1174889611yescharacteristic
subgroupG/H
centerC22#91474
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5#120
prime radicalC22×C3×D20C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1888
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11754188C2semidirect
5. C2×#90961C2semidirect
6. #11746344C2semidirect
7. C5×#4523C2semidirect
18. C3×#4021C4semidirect
72. #4523D5semidirect
84. #4021Dic3semidirect
349. C3×C5#1888semidirect
404. C5#71724semidirect
421. C3#10599559semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40212
#117541882
#117483672
#117483662
C2×#909612
#117463442
C5×#45232
#105995593
#717245