Finite Group Databasebeta

← #14303099

Subgroups — #14303099

Order 1920.

616 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5745C211yesmaximal, characteristic
2#11754271C211yesmaximal, characteristic
3C2×#91108C211yesmaximal, characteristic, complemented
4C2×#90963C211yesmaximal, characteristic, complemented
5#11748355C211yesmaximal, characteristic
6C3×#64779C211yesmaximal, characteristic, complemented
7#11745993C211yesmaximal, characteristic, complemented
8#10602824—31nomaximal, Hall
9C22×Dic30C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C5×#907—22no—
15C5×D3×M16—22no—
16C5×#901—22no—
17C3×#4072C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19#91543C414yes—
20#91376—21no—
21#91373—21no—
22#91365—22no—
23#91108—22no—
24#90963—22no—
25#90962—21no—
26#90959—21no—
27#69041—51nomaximal, Hall
28C5×#568—31no—
29#66159—31no—
30#65526—31no—
31C2×#3956—31no—
32C2×#3956—31no—
33#64779—31no—
34#64779D311yescharacteristic, complemented
35C22×C3×C4×C5C2311yescharacteristic
36C22×Dic15C2×C412yes—
37C2×Dic30—21no—
38C2×Dic30—21no—
39C2×Dic30—21no—
40C2×Dic30—21no—
41C2×Dic30—21no—
42C2×Dic30—21no—
43C2×C5×#67C2×C412yes—
44C5×#235—21no—
45C5×#235—21no—
46C5×#235—21no—
47C5×#235—21no—
48C2×C5×D12D411yescharacteristic
49C2×C4×C5×D3D412yes—
50C2×C5×Dic6D411yescharacteristic
51C3×C5×M16—21no—
52C3×C5×M16D412yes—
53C2×C3×C5×C8—21no—
54#6710—21no—
55#6710—21no—
56C2×C3⋊#168—21no—
57C5×#208—21no—
58C5×#208D412yes—
59C2×C5×C3⋊C8—21no—
60C5×ΓL(1,𝔽25)—24no—
61C5×D3×C8—24no—
62C3×C22⋊Dic5C2×C412yes—
63C3×C4⋊Dic5—21no—
64C3×C4×Dic5—21no—
65C3×#681—21no—
66C3×#681—21no—
67C2×C3×#168—21no—
68#6668—24no—
69(C2×D3)⋊Dic5—24no—
70#5745D511yescharacteristic
71#5526—51no—
72C2×#824—51no—
73C2×#824—51no—
74#5132—51no—
75C3×#344—51no—
76#4533—51no—
77C2×C5×#41—31no—
78C22×Dic10—31no—
79C5×#131—62no—
80C5×#131—62no—
81C2×C5×M16—31no—
82C2×C5×M16—62no—
83C2×C5×M16C2×D311yescharacteristic
84#4090—61no—
85#4082—61no—
86#4081—34no—
87#4072C2×D311yescharacteristic
88#4070—62no—
89C2×#681—31no—
90C2×#681C2×D311yescharacteristic
91#3968—61no—
92#3965—61no—
93#3956—62no—
94#3956—62no—
95#1915—151noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×C5×D3C22⋊C412yes—
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×Dic15—22no—
105C2×Dic15—22no—
106C2×Dic15—22no—
107Dic30—41no—
108Dic30—41no—
109Dic30—41no—
110Dic30—41no—
111C5×#67—22no—
112C5×#67—22no—
113C2×C5×Dic3C22⋊C412yes—
114C5×D12—21no—
115C5×D12—21no—
116C4×C5×D3—22no—
117C4×C5×D3—22no—
118C5×Dic6—21no—
119C5×Dic6—21no—
120C2×C3×Dic5—22no—
121C3×C5×C8—22no—
122C3⋊#168—41no—
123C3×#168—41no—
124C5×C3⋊C8—22no—
125C2×#235C2×D511yescharacteristic
126C22×Dic6—51no—
127C2×C3×M16—51no—
128C2×C3×M16C2×D511yescharacteristic
129C3×#117—51no—
130C2×#208—51no—
131C2×#208C2×D511yescharacteristic
132#907—22no—
133D3×M16—22no—
134#901—22no—
135#897—102no—
136#886—54no—
137#875—101no—
138#869—101no—
139#824—101no—
140#824—102no—
141#824—102no—
142#823—101no—
143C5×#41—61no—
144C5×#41—61no—
145C5×#41—61no—
146C5×#41—61no—
147C2×C5×Q8—31no—
148C2×C5×D4—32no—
149C2×C5×D4—31no—
150C22×C4×C5—32no—
151C22×C4×C5C22×D311yescharacteristic
152C22×Dic5—32no—
153C2×Dic10—61no—
154C2×Dic10—61no—
155C2×Dic10—61no—
156C2×Dic10—61no—
157C2×Dic10—61no—
158C2×Dic10—61no—
159C5×M16—21no—
160C5×M16—32no—
161C5×M16—64no—
162C5×M16—61no—
163C5×M16D1212yes—
164C2×C5×C8—21no—
165C2×C5×C8—64no—
166C2×C5×C8—61no—
167C22⋊Dic5—64no—
168C22⋊Dic5C4×D312yes—
169C4⋊Dic5—21no—
170#683—64no—
171C4×Dic5—21no—
172#681—21no—
173#681—21no—
174#681—61no—
175#681—61no—
176C2×#168—21no—
177C2×#168—61no—
178#568—31no—
179#536—151no—
180#413—151no—
181C2×#101—151no—
182C2×#101—151no—
183#344—51no—
184#344—151no—
185C22×C3×C5—41no—
186C22×C3×C5C2×C22⋊C411yescharacteristic
187C22×C3×C5C4×D411yescharacteristic
188C22×C3×C5C4×D411yescharacteristic
189C2×C5×D3—22no—
190C2×C5×D3—42no—
191C3×C4×C5#12011yescharacteristic
192C3×C4×C5#12111yescharacteristic
193C3×C4×C5#12111yescharacteristic
194C3×C4×C5#12311yescharacteristic
195Dic15—42no—
196C3×Dic5—42no—
197C5×Dic3—22no—
198C22×C3×C4C22×D511yescharacteristic
199C2×#67C4×D512yes—
200C22×Dic3—52no—
201#235—21no—
202#235—21no—
203#235—21no—
204#235—21no—
205C2×D12D2011yescharacteristic
206C2×C4×D3C22⋊D512yes—
207C2×Dic6—101no—
208C2×Dic6—101no—
209C2×Dic6—101no—
210C2×Dic6—101no—
211C2×Dic6—101no—
212C2×Dic6—101no—
213C2×Dic6D2011yescharacteristic
214C3×M16—21no—
215C3×M16—101no—
216C3×M16—101no—
217C3×M16C22⋊D512yes—
218C2×C3×C8—21no—
219C2×C3×C8—101no—
220C3×C4⋊C4—101no—
221C3×C22⋊C4—52no—
222C3×C42—101no—
223(C2×D3)⋊C4—104no—
224C4⋊Dic3—104no—
225#208—21no—
226#208—101no—
227#208—101no—
228#208C22⋊D512yes—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—101no—
231ΓL(1,𝔽25)—24no—
232D3×C8—24no—
233C23×C5—32no—
234C23×C5C2×C4×D311yescharacteristic
235C5×Q8—61no—
236C5×Q8—61no—
237C5×D4—62no—
238C5×D4—62no—
239C5×D4—61no—
240C5×D4—61no—
241C2×C4×C5—32no—
242C2×C4×C5—62no—
243C2×C4×C5—62no—
244C2×C4×C5C2×D1211yescharacteristic
245C2×C4×C5#23511yescharacteristic
246C2×C4×C5D3×D411yescharacteristic
247C2×C4×C5D3×D411yescharacteristic
248C2×C4×C5D3×D411yescharacteristic
249C2×C4×C5#23911yescharacteristic
250C2×Dic5—22no—
251C2×Dic5—62no—
252C2×Dic5—62no—
253C2×Dic5—62no—
254Dic10—121no—
255Dic10—121no—
256Dic10—121no—
257Dic10—121no—
258C5×C8—22no—
259C5×C8—62no—
260#168—41no—
261#168—121no—
262C2×#41—31no—
263C22×Q8—151no—
264#131—62no—
265#131—62no—
266C2×M16—31no—
267C2×M16—51no—
268C2×M16—62no—
269C2×M16—151no—
270C2×M16D3×D511yescharacteristic
271C4⋊Q8—301no—
272#124—301no—
273#123—154no—
274C22⋊Q8—302no—
275#117—51no—
276#101—302no—
277#101—301no—
278#101—302no—
279#100—301no—
280C2×C3×C5—21no—
281C2×C3×C5—21no—
282C2×C3×C5—21no—
283C2×C3×C5#38611yescharacteristic
284C5×D3—42no—
285C23×C3C2×C4×D511yescharacteristic
286C22×D3#68512yes—
287C2×C3×C4—102no—
288C2×C3×C4C2×D2011yescharacteristic
289C2×C3×C4#70911yescharacteristic
290C2×C3×C4#70911yescharacteristic
291C2×C3×C4C2×C22⋊D511yescharacteristic
292C2×C3×C4C2×C22⋊D511yescharacteristic
293C2×C3×C4C2×C22⋊D511yescharacteristic
294#67—22no—
295#67—22no—
296C2×Dic3—102no—
297C2×Dic3—102no—
298C2×Dic3—102no—
299C2×Dic3#68512yes—
300D12—21no—
301D12—21no—
302C4×D3—22no—
303C4×D3—22no—
304Dic6—21no—
305Dic6—21no—
306Dic6—201no—
307Dic6—201no—
308Dic6—201no—
309Dic6—201no—
310C3×C8—22no—
311C3×C8—201no—
312C3⋊C8—22no—
313C3⋊C8—201no—
314C22×C5—41no—
315C22×C5—62no—
316C22×C5—122no—
317C22×C5C4×D1211yescharacteristic
318C22×C5D3×C22⋊C411yescharacteristic
319C22×C5#89311yescharacteristic
320C4×C5—62no—
321C4×C5#88211yescharacteristic
322C4×C5#88411yescharacteristic
323C4×C5#89411yescharacteristic
324C4×C5#89511yescharacteristic
325Dic5—42no—
326Dic5—122no—
327#41—61no—
328#41—61no—
329#41—61no—
330#41—61no—
331C2×Q8—31no—
332C2×Q8—301no—
333C2×Q8—301no—
334C2×Q8—301no—
335C2×Q8—301no—
336C2×Q8—301no—
337C2×Q8—301no—
338C2×D4—32no—
339C2×D4—31no—
340C22×C4—32no—
341C22×C4—152no—
342C22×C4C2×D3×D511yescharacteristic
343M16—21no—
344M16—32no—
345M16—64no—
346M16—61no—
347M16—101no—
348M16—101no—
349M16—301no—
350M16—301no—
351M16#120312yes—
352C2×C8—21no—
353C2×C8—64no—
354C2×C8—61no—
355C2×C8—101no—
356C2×C8—301no—
357C4⋊C4—101no—
358C4⋊C4—304no—
359C22⋊C4—52no—
360C22⋊C4—304no—
361C42—101no—
362C3×C5#191511yescharacteristic, complemented, Hall
363C22×C3—41no—
364C22×C3C2×#68511yescharacteristic
365C22×C3C4×C22⋊D511yescharacteristic
366C22×C3C4×C22⋊D511yescharacteristic
367C2×D3—22no—
368C2×D3—42no—
369C3×C4—202no—
370C3×C4#407511yescharacteristic
371C3×C4#407611yescharacteristic
372C3×C4#407611yescharacteristic
373C3×C4#409911yescharacteristic
374Dic3—22no—
375Dic3—202no—
376C2×C5—21no—
377C2×C5—21no—
378C2×C5—21no—
379C2×C5—122no—
380C2×C5#466511yescharacteristic
381C23—32no—
382C23C4×D3×D511yescharacteristic
383Q8—61no—
384Q8—61no—
385Q8—601no—
386Q8—601no—
387Q8—601no—
388Q8—601no—
389D4—62no—
390D4—62no—
391D4—61no—
392D4—61no—
393C2×C4—32no—
394C2×C4—62no—
395C2×C4—62no—
396C2×C4—102no—
397C2×C4—302no—
398C2×C4—302no—
399C2×C4—302no—
400C2×C4#676911yescharacteristic
401C2×C4#677111yescharacteristic
402C2×C4D3×D2011yescharacteristic
403C2×C4C2×#120311yescharacteristic
404C2×C4D3×C22⋊D511yescharacteristic
405C2×C4D3×C22⋊D511yescharacteristic
406C8—22no—
407C8—62no—
408C8—201no—
409C8—601no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3#6550211yescharacteristic
414D3—42no—
415C5#6904111yescharacteristic, complemented, Sylow
416C22—41no—
417C22—62no—
418C22—122no—
419C22C4×#120311yescharacteristic
420C22#9144611yescharacteristic
421C22D3×#68511yescharacteristic
422C4—62no—
423C4—202no—
424C4—602no—
425C4#9135111yescharacteristic
426C4#9145411yescharacteristic
427C4#9146011yescharacteristic
428C4#9157011yescharacteristic
429C3#1060282411yescharacteristic, complemented, Sylow
430C2—21no—
431C2—21no—
432C2—21no—
433C2—122no—
434C2#1174891411yescharacteristic
subgroupG/H
centerC2#11748914
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radicalC2×C5×#235C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1915
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C2×#91108C2semidirect
4. C2×#90963C2semidirect
6. C3×#64779C2semidirect
7. #11745993C2semidirect
34. #64779D3semidirect
362. C3×C5#1915semidirect
415. C5#69041semidirect
429. C3#10602824semidirect

Maximal subgroups

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

subgroupindex
C5×#57452
#117542712
C2×#911082
C2×#909632
#117483552
C3×#647792
#117459932
#106028243
#690415