Finite Group Databasebeta

← #14309047

Subgroups — #14309047

Order 1920.

488 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756229C211yesmaximal, characteristic, complemented
2C2×C3×#3937C211yesmaximal, characteristic
3#11748624C211yesmaximal, characteristic
4#11748420C211yesmaximal, characteristic
5C5×#4523C211yesmaximal, characteristic, complemented
6#11745990C211yesmaximal, characteristic, complemented
7#11745971C211yesmaximal, characteristic, complemented
8#10599572—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11#91815C2211yescharacteristic
12#91815C2211yescharacteristic
13#91813—22no—
14#91759—21no—
15#91758—21no—
16C4×Dic30—22no—
17C5×#926C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C3×#3937—21no—
21C3×#3937—21no—
22#90995—22no—
23#90976—22no—
24#70368—51nomaximal, Hall
25#65804—31no—
26#65428—31no—
27#65295—31no—
28C2×#3937D311yescharacteristic
29C5×#339—31no—
30#64776—31no—
31#64751—31no—
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5C2311yescharacteristic
34C2×Dic30—22no—
35C2×C3×C22⋊D5—21no—
36C3×#709—21no—
37C3×#709—21no—
38C3×#709—21no—
39C3×#709—21no—
40C2×C3×D20Q811yescharacteristic, complemented
41C2×C3×C4×D5—21no—
42C2×C3×Dic10Q811yescharacteristic, complemented
43C3×C42×C5—21no—
44C3×C42×C5D411yescharacteristic
45C3×C42×C5D411yescharacteristic
46#6719—21no—
47#6719D412yes—
48C4⋊Dic15—22no—
49C4⋊Dic15—21no—
50C4⋊Dic15—21no—
51#6712—24no—
52C4×Dic15—21no—
53C4×Dic15D412yes—
54C5×#217—21no—
55C5×C4⋊Dic3—21no—
56C4×C5×Dic3—21no—
57C5×#208—21no—
58C5×#208—21no—
59C2×C5×C3⋊C8—21no—
60C3×#681—21no—
61C3×#681—21no—
62C2×C3×#168—21no—
63#5470—51no—
64C2×C3×#104—51no—
65#5240—51no—
66#5236—51no—
67#4559—51no—
68#4557—51no—
69#4523D511yescharacteristic, complemented
70C2×#709C2×D311yescharacteristic
71C2×C5×M16—31no—
72C5×#117—31no—
73C2×C42×C5C2×D311yescharacteristic
74#4072—31no—
75#4072—31no—
76#4070—62no—
77C2×#681C2×D311yescharacteristic
78#4016—61no—
79#4015—61no—
80C4×Dic10—62no—
81#3957—62no—
82#3938—62no—
83#3937—21no—
84#3937—21no—
85#2031—151noSylow
86C23×C3×C5C2×D411yescharacteristic
87C22×C3×D5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—42no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×Q811yescharacteristic
94C2×C3×C4×C5#4111yescharacteristic
95C2×C3×C4×C5#4111yescharacteristic
96C2×C3×C4×C5#4111yescharacteristic
97C2×Dic15—22no—
98C2×Dic15—22no—
99Dic30—44no—
100C2×C5×Dic3—41no—
101C3×C22⋊D5—41no—
102C3×C22⋊D5—41no—
103C2×C3×Dic5—21no—
104C3×D20—21no—
105C3×D20—21no—
106C3×C4×D5—41no—
107C3×C4×D5—41no—
108C3×Dic10—21no—
109C3×Dic10—21no—
110C3×#168—41no—
111C5×C3⋊C8—41no—
112C2×C3×#41—51no—
113C2×C3×M16—51no—
114C2×C3×C42C2×D511yescharacteristic
115#926—51no—
116#926—51no—
117#926C2×D511yescharacteristic
118#924—102no—
119C2×#208C2×D511yescharacteristic
120#870—101no—
121#869—101no—
122C4×Dic6—102no—
123C3×#104—101no—
124C3×#104—101no—
125#837—102no—
126#834—102no—
127C22×C4×C5—21no—
128C22×C4×C5C22×D311yescharacteristic
129C2×C22⋊D5—21no—
130#709—21no—
131#709—21no—
132#709—21no—
133#709—21no—
134C2×D20Dic611yescharacteristic, complemented
135C2×C4×D5—21no—
136C2×Dic10—62no—
137C2×Dic10Dic611yescharacteristic, complemented
138C5×M16—61no—
139C5×M16—61no—
140C2×C5×C8—61no—
141C5×C4⋊C4—61no—
142C5×C22⋊C4—61no—
143C42×C5—21no—
144C42×C5—61no—
145C42×C5#6711yescharacteristic
146C42×C5#6711yescharacteristic
147C22⋊Dic5—32no—
148C22⋊Dic5—61no—
149C4⋊Dic5—62no—
150C4⋊Dic5—61no—
151C4⋊Dic5—61no—
152#683—64no—
153C4×Dic5—32no—
154C4×Dic5—61no—
155#681—21no—
156#681—21no—
157C2×#168—21no—
158#533—151no—
159#421—151no—
160C2×#104—51no—
161#410—151no—
162#344—151no—
163#339—31no—
164H(3,ℤ/4)—151no—
165C22×C3×C5—41no—
166C22×C3×C5#12011yescharacteristic
167C22×C3×C5C22⋊Q811yescharacteristic
168C22×C3×C5#12411yescharacteristic
169C2×C3×D5—41no—
170C2×C3×D5—81no—
171C3×C4×C5—22no—
172C3×C4×C5—41no—
173C3×C4×C5C22⋊Q811yescharacteristic
174C3×C4×C5C22⋊Q811yescharacteristic
175C3×C4×C5#12411yescharacteristic
176C3×C4×C5#12411yescharacteristic
177Dic15—42no—
178Dic15—42no—
179C3×Dic5—41no—
180C5×Dic3—81no—
181C3×#41—101no—
182C3×#41—101no—
183C3×#41—101no—
184C3×#41—101no—
185C2×C3×Q8—51no—
186C2×C3×D4—51no—
187C2×C3×D4—101no—
188C22×C3×C4—21no—
189C22×C3×C4—101no—
190C22×C3×C4C22×D511yescharacteristic
191C2×Dic6—102no—
192C3×M16—101no—
193C3×M16—101no—
194C2×C3×C8—101no—
195C3×C42—21no—
196C3×C42D2011yescharacteristic
197C3×C42D2011yescharacteristic
198#217—21no—
199#217—52no—
200#217—101no—
201C4⋊Dic3—21no—
202C4⋊Dic3—102no—
203C4⋊Dic3—101no—
204C4⋊Dic3—101no—
205Dic3⋊C4—104no—
206C4×Dic3—21no—
207C4×Dic3—52no—
208C4×Dic3—101no—
209#208—21no—
210#208—21no—
211C2×C3⋊C8—21no—
212C23×C5D3×D411yescharacteristic
213C22×D5—21no—
214C2×C4×C5—21no—
215C2×C4×C5—21no—
216C2×C4×C5—42no—
217C2×C4×C5—121no—
218C2×C4×C5C2×Dic611yescharacteristic
219C2×C4×C5#23511yescharacteristic
220C2×C4×C5D3×D411yescharacteristic
221C2×C4×C5#23711yescharacteristic
222C2×C4×C5#23711yescharacteristic
223C2×C4×C5C2×#6711yescharacteristic
224C22⋊D5—41no—
225C22⋊D5—41no—
226C2×Dic5—21no—
227C2×Dic5—62no—
228C2×Dic5—62no—
229D20—21no—
230D20—21no—
231C4×D5—41no—
232C4×D5—41no—
233Dic10—21no—
234Dic10—21no—
235Dic10—124no—
236C5×C8—121no—
237#168—41no—
238C2×#41—51no—
239C2×M16—31no—
240C2×M16—51no—
241C4⋊Q8—301no—
242#125—301no—
243C22⋊Q8—302no—
244C4×Q8—302no—
245#117—31no—
246#117—151no—
247#117—151no—
248C2×C42D3×D511yescharacteristic
249#104—101no—
250#104—101no—
251#104—302no—
252#99—302no—
253C2×C3×C5—21no—
254C2×C3×C5—21no—
255C2×C3×C5—21no—
256C2×C3×C5#39311yescharacteristic
257C3×D5—81no—
258C23×C3—101no—
259C23×C3D4×D511yescharacteristic
260C3×Q8—101no—
261C3×Q8—101no—
262C3×D4—101no—
263C3×D4—101no—
264C3×D4—201no—
265C3×D4—201no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—42no—
269C2×C3×C4—101no—
270C2×C3×C4—201no—
271C2×C3×C4—201no—
272C2×C3×C4C2×D2011yescharacteristic
273C2×C3×C4#70911yescharacteristic
274C2×C3×C4#70911yescharacteristic
275C2×C3×C4D4×D511yescharacteristic
276C2×C3×C4#71111yescharacteristic
277C2×C3×C4Q8×D511yescharacteristic
278C2×Dic3—41no—
279C2×Dic3—102no—
280C2×Dic3—102no—
281Dic6—204no—
282C3×C8—201no—
283C3⋊C8—41no—
284C22×C5—41no—
285C22×C5#87811yescharacteristic
286C22×C5#88511yescharacteristic
287C22×C5#93711yescharacteristic
288C2×D5—41no—
289C2×D5—81no—
290C4×C5—22no—
291C4×C5—41no—
292C4×C5—241no—
293C4×C5#87811yescharacteristic
294C4×C5#88511yescharacteristic
295C4×C5#92411yescharacteristic
296C4×C5#93611yescharacteristic
297Dic5—41no—
298Dic5—122no—
299Dic5—122no—
300#41—101no—
301#41—101no—
302#41—101no—
303#41—101no—
304C2×Q8—51no—
305C2×Q8—302no—
306C2×D4—51no—
307C2×D4—101no—
308C22×C4—21no—
309C22×C4—101no—
310C22×C4C2×D3×D511yescharacteristic
311M16—61no—
312M16—61no—
313M16—101no—
314M16—101no—
315C2×C8—61no—
316C2×C8—101no—
317C4⋊C4—61no—
318C4⋊C4—304no—
319C4⋊C4—302no—
320C4⋊C4—301no—
321C4⋊C4—301no—
322C22⋊C4—61no—
323C22⋊C4—152no—
324C22⋊C4—301no—
325C42—21no—
326C42—61no—
327C42—152no—
328C42—301no—
329C42#120211yescharacteristic
330C42#120211yescharacteristic
331C3×C5#203111yescharacteristic, complemented, Hall
332C22×C3—41no—
333C22×C3—201no—
334C22×C3—401no—
335C22×C3#402811yescharacteristic
336C22×C3#403111yescharacteristic
337C22×C3#404211yescharacteristic
338C3×C4—22no—
339C3×C4—41no—
340C3×C4—201no—
341C3×C4#402111yescharacteristic
342C3×C4#403111yescharacteristic
343C3×C4#404211yescharacteristic
344C3×C4#404311yescharacteristic
345Dic3—81no—
346Dic3—202no—
347Dic3—202no—
348C2×C5—21no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5#494711yescharacteristic
352D5—81no—
353C23—101no—
354C23#679011yescharacteristic
355Q8—101no—
356Q8—101no—
357Q8—604no—
358D4—101no—
359D4—101no—
360D4—201no—
361D4—201no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—101no—
366C2×C4—121no—
367C2×C4—201no—
368C2×C4—201no—
369C2×C4—302no—
370C2×C4—302no—
371C2×C4D5×Dic611yescharacteristic
372C2×C4#676511yescharacteristic
373C2×C4#676511yescharacteristic
374C2×C4#677211yescharacteristic
375C2×C4C2×#120211yescharacteristic
376C2×C4#679011yescharacteristic
377C8—121no—
378C8—201no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—401no—
383C2×C3#6496211yescharacteristic
384C5#7036811yescharacteristic, complemented, Sylow
385C22—41no—
386C22—201no—
387C22—401no—
388C22#9143111yescharacteristic
389C22#9146211yescharacteristic
390C22#9157211yescharacteristic
391C4—22no—
392C4—41no—
393C4—201no—
394C4—241no—
395C4—602no—
396C4—602no—
397C4#9136011yescharacteristic
398C4#9136411yescharacteristic
399C4#9143111yescharacteristic
400C4#9146211yescharacteristic
401C3#1059957211yescharacteristic, complemented, Sylow
402C2—21no—
403C2—21no—
404C2—21no—
405C2—401no—
406C2#1174879311yescharacteristic
subgroupG/H
centerC4#91462
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC2×C3×C5#393
prime radicalC2×C3×#709C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2031
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #11756229C2semidirect
5. C5×#4523C2semidirect
6. #11745990C2semidirect
7. #11745971C2semidirect
40. C2×C3×D20Q8semidirect
42. C2×C3×Dic10Q8semidirect
69. #4523D5semidirect
134. C2×D20Dic6semidirect
137. C2×Dic10Dic6semidirect
331. C3×C5#2031semidirect
384. C5#70368semidirect
401. C3#10599572semidirect

Maximal subgroups

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

subgroupindex
#117562292
C2×C3×#39372
#117486242
#117484202
C5×#45232
#117459902
#117459712
#105995723
#703685