Finite Group Databasebeta

← #14309017

Subgroups — #14309017

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
1C3×C5×#533C211yesmaximal, characteristic, complemented
2#11751107C211yesmaximal, characteristic
3#11751106C211yesmaximal, characteristic
4C2×#91089C211yesmaximal, characteristic
5#11746354C211yesmaximal, characteristic, complemented
6#11746352C211yesmaximal, characteristic, complemented
7#11746344C211yesmaximal, characteristic, complemented
8#10602635—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C3×C5×C4⋊Q8—21no—
11C3×C5×#125—21no—
12C3×C5×C22⋊Q8—22no—
13C3×C4×C5×Q8—22no—
14C3×C5×#117C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16C2×C3×C42×C5C2211yescharacteristic
17#91815C2211yescharacteristic
18C2×#6710C2211yescharacteristic
19C2×#6710C2211yescharacteristic
20#91090—22no—
21#91089—21no—
22#91089—21no—
23#91089—22no—
24#71842—51nomaximal, Hall
25C5×#533D311yescharacteristic, complemented
26#65295—31no—
27#65294—31no—
28C2×#3937—31no—
29#64753—31no—
30#64751—31no—
31#64743—31no—
32C2×C3×C5×Q8—22no—
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5C2311yescharacteristic
35C2×#1220—21no—
36#6817—21no—
37#6817—21no—
38#6817—21no—
39#6817—21no—
40C2×D60Q811yescharacteristic, complemented
41C2×C4×D15—21no—
42C2×Dic30Q811yescharacteristic, complemented
43C3×C5×C4⋊C4—24no—
44C3×C5×C4⋊C4—22no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C22⋊C4—21no—
48C3×C5×C22⋊C4D412yes—
49C3×C42×C5—21no—
50C3×C42×C5—21no—
51C3×C42×C5D411yescharacteristic
52C3×C42×C5D411yescharacteristic
53C3×C42×C5D412yes—
54#6719—21no—
55C4⋊Dic15—21no—
56C4×Dic15—21no—
57#6710—21no—
58#6710—21no—
59#6710—21no—
60#6710—21no—
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63C3×#533D511yescharacteristic, complemented
64#5006—51no—
65#5005—51no—
66C2×#805—51no—
67#4533—51no—
68#4531—51no—
69#4523—51no—
70C2×#709—31no—
71C5×C4⋊Q8—21no—
72C5×#125—21no—
73C5×C22⋊Q8—22no—
74C4×C5×Q8—22no—
75C5×#117C2×D311yescharacteristic
76C5×#117C2×D311yescharacteristic
77C2×C42×C5C2×D311yescharacteristic
78#4072—31no—
79C2×#681—31no—
80C2×#681—31no—
81#3938—62no—
82#3937—62no—
83#3937—61no—
84#3937—61no—
85#2031—151noSylow
86C23×C3×C5C2×D411yescharacteristic
87C22×D15—21no—
88C3×C5×Q8—44no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—42no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×Q811yescharacteristic
97C2×C3×C4×C5#4111yescharacteristic
98C2×C3×C4×C5#4111yescharacteristic
99C2×C3×C4×C5#4111yescharacteristic
100#1220—41no—
101#1220—41no—
102C2×Dic15—21no—
103C2×Dic15—41no—
104D60—21no—
105D60—21no—
106C4×D15—41no—
107C4×D15—41no—
108Dic30—21no—
109Dic30—21no—
110C3⋊#168—41no—
111C3⋊#168—41no—
112C2×#235—51no—
113C3×C4⋊Q8—21no—
114C3×#125—21no—
115C3×C22⋊Q8—22no—
116C3×C4×Q8—22no—
117C3×#117C2×D511yescharacteristic
118C3×#117C2×D511yescharacteristic
119C2×C3×C42C2×D511yescharacteristic
120#926—51no—
121C2×#208—51no—
122C2×#208—51no—
123#806—102no—
124#805—101no—
125#805—101no—
126#805—102no—
127C2×C5×Q8—22no—
128C22×C4×C5—21no—
129C22×C4×C5C22×D311yescharacteristic
130C2×C22⋊D5—61no—
131#709—61no—
132#709—61no—
133#709—61no—
134#709—61no—
135C2×D20—31no—
136C2×C4×D5—61no—
137C2×Dic10—31no—
138C5×C4⋊C4—24no—
139C5×C4⋊C4—22no—
140C5×C4⋊C4—21no—
141C5×C4⋊C4—21no—
142C5×C22⋊C4—21no—
143C5×C22⋊C4#6712yes—
144C42×C5—21no—
145C42×C5—21no—
146C42×C5#6711yescharacteristic
147C42×C5#6711yescharacteristic
148C42×C5#6712yes—
149C22⋊Dic5—61no—
150C4⋊Dic5—61no—
151C4×Dic5—61no—
152#681—61no—
153#681—61no—
154#681—61no—
155#681—61no—
156C2×#168—61no—
157C2×#168—61no—
158#533D1511yescharacteristic, complemented
159#421—151no—
160C2×#104—151no—
161#410—151no—
162#344—151no—
163#339—151no—
164H(3,ℤ/4)—151no—
165C22×C3×C5—41no—
166C22×C3×C5#12011yescharacteristic
167C22×C3×C5C22⋊Q811yescharacteristic
168C22×C3×C5#12411yescharacteristic
169C2×D15—41no—
170C2×D15—81no—
171C3×C4×C5—22no—
172C3×C4×C5—41no—
173C3×C4×C5—42no—
174C3×C4×C5—42no—
175C3×C4×C5C22⋊Q811yescharacteristic
176C3×C4×C5C22⋊Q811yescharacteristic
177C3×C4×C5#12411yescharacteristic
178C3×C4×C5#12411yescharacteristic
179Dic15—41no—
180Dic15—81no—
181C2×C3×Q8—22no—
182C22×C3×C4—21no—
183C22×C3×C4C22×D511yescharacteristic
184C2×#67—101no—
185#235—101no—
186#235—101no—
187#235—101no—
188#235—101no—
189C2×D12—51no—
190C2×C4×D3—101no—
191C2×Dic6—51no—
192C3×C4⋊C4—24no—
193C3×C4⋊C4—22no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—21no—
196C3×C22⋊C4—21no—
197C3×C22⋊C4C22⋊D512yes—
198C3×C42—21no—
199C3×C42—21no—
200C3×C42C22⋊D511yescharacteristic
201C3×C42C22⋊D511yescharacteristic
202C3×C42C22⋊D512yes—
203#217—101no—
204C4⋊Dic3—101no—
205C4×Dic3—101no—
206#208—101no—
207#208—101no—
208#208—101no—
209#208—101no—
210C2×C3⋊C8—101no—
211C2×C3⋊C8—101no—
212C23×C5C2×#6711yescharacteristic
213C22×D5—61no—
214C5×Q8—44no—
215C2×C4×C5—21no—
216C2×C4×C5—21no—
217C2×C4×C5—22no—
218C2×C4×C5—22no—
219C2×C4×C5—42no—
220C2×C4×C5D3×Q811yescharacteristic
221C2×C4×C5#23911yescharacteristic
222C2×C4×C5#23911yescharacteristic
223C2×C4×C5#23911yescharacteristic
224C2×C4×C5C2×#6711yescharacteristic
225C2×C4×C5C2×#6711yescharacteristic
226C22⋊D5—121no—
227C22⋊D5—121no—
228C2×Dic5—61no—
229C2×Dic5—121no—
230D20—61no—
231D20—61no—
232C4×D5—121no—
233C4×D5—121no—
234Dic10—61no—
235Dic10—61no—
236#168—121no—
237#168—121no—
238C2×#41—151no—
239C2×M16—151no—
240C2×M16—151no—
241C4⋊Q8—21no—
242#125—21no—
243C22⋊Q8—22no—
244C4×Q8—22no—
245#117—151no—
246#117C2×D1511yescharacteristic
247#117C2×D1511yescharacteristic
248C2×C42C2×D1511yescharacteristic
249#104—301no—
250#104—301no—
251#104—302no—
252#99—302no—
253C2×C3×C5—21no—
254C2×C3×C5—21no—
255C2×C3×C5—21no—
256C2×C3×C5#39311yescharacteristic
257D15—81no—
258C23×C3C2×C22⋊D511yescharacteristic
259C22×D3—101no—
260C3×Q8—44no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—42no—
266C2×C3×C4Q8×D511yescharacteristic
267C2×C3×C4#71311yescharacteristic
268C2×C3×C4#71311yescharacteristic
269C2×C3×C4#71311yescharacteristic
270C2×C3×C4C2×C22⋊D511yescharacteristic
271C2×C3×C4C2×C22⋊D511yescharacteristic
272#67—201no—
273#67—201no—
274C2×Dic3—101no—
275C2×Dic3—201no—
276D12—101no—
277D12—101no—
278C4×D3—201no—
279C4×D3—201no—
280Dic6—101no—
281Dic6—101no—
282C3⋊C8—201no—
283C3⋊C8—201no—
284C22×C5—41no—
285C22×C5#94611yescharacteristic
286C22×C5#94711yescharacteristic
287C22×C5#95311yescharacteristic
288C2×D5—121no—
289C2×D5—241no—
290C4×C5—22no—
291C4×C5—41no—
292C4×C5—42no—
293C4×C5—42no—
294C4×C5#94611yescharacteristic
295C4×C5#94611yescharacteristic
296C4×C5#94711yescharacteristic
297C4×C5#94711yescharacteristic
298Dic5—121no—
299Dic5—241no—
300#41—301no—
301#41—301no—
302#41—301no—
303#41—301no—
304C2×Q8—22no—
305C2×Q8—151no—
306C2×D4—151no—
307C2×D4—301no—
308C22×C4—21no—
309C22×C4—301no—
310C22×C4C22×D1511yescharacteristic
311M16—301no—
312M16—301no—
313M16—301no—
314M16—301no—
315C2×C8—301no—
316C2×C8—301no—
317C4⋊C4—24no—
318C4⋊C4—22no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—301no—
322C22⋊C4—21no—
323C22⋊C4—301no—
324C22⋊C4#122012yes—
325C42—21no—
326C42—21no—
327C42—301no—
328C42#122011yescharacteristic
329C42#122011yescharacteristic
330C42#122012yes—
331C3×C5#203111yescharacteristic, complemented, Hall
332C22×C3—41no—
333C22×C3#409211yescharacteristic
334C22×C3#409311yescharacteristic
335C22×C3#409911yescharacteristic
336C2×D3—201no—
337C2×D3—401no—
338C3×C4—22no—
339C3×C4—41no—
340C3×C4—42no—
341C3×C4—42no—
342C3×C4#409211yescharacteristic
343C3×C4#409211yescharacteristic
344C3×C4#409311yescharacteristic
345C3×C4#409311yescharacteristic
346Dic3—201no—
347Dic3—401no—
348C2×C5—21no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5#523111yescharacteristic
352D5—241no—
353C23—301no—
354C23C2×#122011yescharacteristic
355Q8—44no—
356Q8—301no—
357Q8—301no—
358D4—301no—
359D4—301no—
360D4—601no—
361D4—601no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—42no—
367C2×C4—301no—
368C2×C4—601no—
369C2×C4—601no—
370C2×C4—601no—
371C2×C4Q8×D1511yescharacteristic
372C2×C4#682111yescharacteristic
373C2×C4#682111yescharacteristic
374C2×C4#682111yescharacteristic
375C2×C4C2×#122011yescharacteristic
376C2×C4C2×#122011yescharacteristic
377C8—601no—
378C8—601no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3#6552011yescharacteristic
383D3—401no—
384C5#7184211yescharacteristic, complemented, Sylow
385C22—41no—
386C22—601no—
387C22—1201no—
388C22#9183511yescharacteristic
389C22#9183611yescharacteristic
390C22#9184211yescharacteristic
391C4—22no—
392C4—41no—
393C4—42no—
394C4—42no—
395C4—601no—
396C4—1201no—
397C4#9183511yescharacteristic
398C4#9183511yescharacteristic
399C4#9183611yescharacteristic
400C4#9183611yescharacteristic
401C3#1060263511yescharacteristic, complemented, Sylow
402C2—21no—
403C2—21no—
404C2—21no—
405C2—1201no—
406C2#1175133211yescharacteristic
subgroupG/H
centerC4#91836
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#533C2
socleC2×C3×C5#393
prime radicalC2×#6817C22
hypercenter#533D15
hypocenterC3×C5#2031
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C3×C5×#533C2semidirect
5. #11746354C2semidirect
6. #11746352C2semidirect
7. #11746344C2semidirect
25. C5×#533D3semidirect
40. C2×D60Q8semidirect
42. C2×Dic30Q8semidirect
63. C3×#533D5semidirect
158. #533D15semidirect
331. C3×C5#2031semidirect
384. C5#71842semidirect
401. C3#10602635semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5332
#117511072
#117511062
C2×#910892
#117463542
#117463522
#117463442
#106026353
#718425