Finite Group Databasebeta

← #14296866

Subgroups — #14296866

Order 1920.

1224 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#709C211yesmaximal, characteristic
2C2×#91240C212yesmaximal, complemented
3#11752423C212yesmaximal, complemented
4C2×#91228C212yesmaximal, complemented
5#10604891—31nomaximal, Hall
6C23×C3×C4×C5C411yescharacteristic, complemented
7C22×C3×C22⋊D5C411yescharacteristic, complemented
8C22×C3×C22⋊D5C2211yescharacteristic
9C2×C3×#709—24no—
10C2×C3×#709—24no—
11C2×C3×#709—24no—
12C22×C3×D20C2211yescharacteristic
13C22×C3×C4×D5C411yescharacteristic, complemented
14C22×C3×C4×D5C2211yescharacteristic
15C22×C3×Dic10C411yescharacteristic, complemented
16C2×#6763C2214yes—
17#91240—24no—
18#91235—24no—
19#91228—24no—
20#72139—51nomaximal, Hall
21C22×#709D311yescharacteristic
22C2×#4011—32no—
23#65764—32no—
24C2×#3999—32no—
25C24×C3×C5C2×C411yescharacteristic
26C23×C3×D5C2×C411yescharacteristic
27C23×C3×D5C2311yescharacteristic
28C22×ΓL(1,𝔽16)—24no—
29C22×C3×C4×C5—22no—
30C22×C3×C4×C5—22no—
31C22×C3×C4×C5—22no—
32C22×C3×C4×C5C2×C411yescharacteristic
33C22×C3×C4×C5C2×C411yescharacteristic
34C2×C3×C22⋊D5—22no—
35C2×C3×C22⋊D5—22no—
36C2×C3×C22⋊D5—22no—
37C2×C3×C22⋊D5—22no—
38C2×C3×C22⋊D5—22no—
39C2×C3×C22⋊D5D414yes—
40C22×C3×Dic5C2×C411yescharacteristic
41C22×C3×Dic5C2×C411yescharacteristic
42C3×#709—232no—
43C2×C3×D20—22no—
44C2×C3×D20—22no—
45C2×C3×D20D414yes—
46C2×C3×C4×D5—22no—
47C2×C3×C4×D5—22no—
48C2×C3×C4×D5—22no—
49C2×C3×C4×D5—22no—
50C2×C3×C4×D5—22no—
51C2×C3×C4×D5D414yes—
52C2×C3×Dic10—22no—
53C2×C3×Dic10—22no—
54C2×C3×Dic10—22no—
55#6763—24no—
56#6763—24no—
57C22×C3×#41—51no—
58C2×#834—52no—
59C2×#834—52no—
60#5211—52no—
61C23×C4×C5Dic311yescharacteristic, complemented
62C22×C22⋊D5Dic311yescharacteristic, complemented
63C22×C22⋊D5C2×D311yescharacteristic
64C2×#709—24no—
65C2×#709—24no—
66C2×#709—24no—
67C22×D20C2×D311yescharacteristic
68C22×C4×D5Dic311yescharacteristic, complemented
69C22×C4×D5C2×D311yescharacteristic
70C22×Dic10Dic311yescharacteristic, complemented
71C2×C22⋊AGL(1,𝔽5)—34no—
72#4011—64no—
73(C2×AGL(1,𝔽5))⋊C4—64no—
74#3999—64no—
75#1782—151noSylow
76C23×C3×C5—21no—
77C23×C3×C5—21no—
78C23×C3×C5—42no—
79C23×C3×C5C22⋊C412yes—
80C23×C3×C5C22×C411yescharacteristic
81C22×C3×D5—21no—
82C22×C3×D5—21no—
83C22×C3×D5—42no—
84C22×C3×D5—42no—
85C22×C3×D5C22⋊C412yes—
86C22×C3×D5C2×D412yes—
87C22×C3×D5C2×D412yes—
88C22×C3×D5C2×D412yes—
89C2×ΓL(1,𝔽16)—48no—
90C2×ΓL(1,𝔽16)—44no—
91C2×C3×C4×C5—28no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5C22⋊C412yes—
97C2×C3×C4×C5C22⋊C412yes—
98C3×C22⋊D5—28no—
99C3×C22⋊D5—28no—
100C2×C3×Dic5—21no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—21no—
103C2×C3×Dic5—21no—
104C2×C3×Dic5C22⋊C412yes—
105C2×C3×Dic5C22⋊C412yes—
106C3×D20—28no—
107C3×C4×D5—28no—
108C3×C4×D5—28no—
109C3×Dic10—28no—
110C2×C3×#41—104no—
111C2×C3×#41—104no—
112C2×C3×#41—104no—
113C22×C3×Q8—51no—
114C22×C3×D4—51no—
115C22×C3×D4—51no—
116C22×C3×D4—51no—
117C23×C3×C4—51no—
118C23×C3×C4—51no—
119C23×C3×C4AGL(1,𝔽5)11yescharacteristic, complemented
120C2×#217—54no—
121#834—104no—
122#834—104no—
123C3⋊#95—104no—
124C24×C5C2×Dic311yescharacteristic
125C23×D5C2×Dic311yescharacteristic
126C23×D5C22×D311yescharacteristic
127C22×AGL(1,𝔽5)—64no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5C2×Dic311yescharacteristic
132C22×C4×C5C2×Dic311yescharacteristic
133C2×C22⋊D5—22no—
134C2×C22⋊D5—22no—
135C2×C22⋊D5—22no—
136C2×C22⋊D5—22no—
137C2×C22⋊D5—22no—
138C2×C22⋊D5#6714yes—
139C22×Dic5C2×Dic311yescharacteristic
140C22×Dic5C2×Dic311yescharacteristic
141#709—232no—
142C2×D20—22no—
143C2×D20—22no—
144C2×D20#6714yes—
145C2×C4×D5—22no—
146C2×C4×D5—22no—
147C2×C4×D5—22no—
148C2×C4×D5—22no—
149C2×C4×D5—22no—
150C2×C4×D5#6714yes—
151C2×Dic10—22no—
152C2×Dic10—22no—
153C2×Dic10—22no—
154C22⋊AGL(1,𝔽5)—64no—
155C22⋊AGL(1,𝔽5)—64no—
156C22×#41—51no—
157C2×#99—152no—
158C2×#99—152no—
159#381—152no—
160C22×C3×C5—22no—
161C22×C3×C5—22no—
162C22×C3×C5—42no—
163C22×C3×C5—42no—
164C22×C3×C5—42no—
165C22×C3×C5C2×C22⋊C411yescharacteristic
166C22×C3×C5C2×C22⋊C411yescharacteristic
167C22×C3×C5C2×C22⋊C411yescharacteristic
168C2×C3×D5—24no—
169C2×C3×D5—22no—
170C2×C3×D5—42no—
171C2×C3×D5—42no—
172C2×C3×D5—42no—
173C2×C3×D5—42no—
174C2×C3×D5—42no—
175C2×C3×D5#12014yes—
176ΓL(1,𝔽16)—84no—
177C3×C4×C5—22no—
178C3×C4×C5—22no—
179C3×Dic5—22no—
180C3×Dic5—22no—
181C24×C3—51no—
182C24×C3—51no—
183C24×C3C2×AGL(1,𝔽5)11yescharacteristic
184C3×#41—1032no—
185C2×C3×Q8—102no—
186C2×C3×Q8—102no—
187C2×C3×Q8—102no—
188C2×C3×D4—54no—
189C2×C3×D4—54no—
190C2×C3×D4—102no—
191C2×C3×D4—102no—
192C2×C3×D4—102no—
193C2×C3×D4—102no—
194C2×C3×D4—102no—
195C2×C3×D4—102no—
196C2×C3×D4—102no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—51no—
201C22×C3×C4—51no—
202C22×C3×C4—54no—
203C22×C3×C4—102no—
204C22×C3×C4—102no—
205C22×C3×C4—102no—
206C22×C3×C4—102no—
207C22×C3×C4—102no—
208C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
209C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
210C22×Dic3—104no—
211#217—104no—
212#217—104no—
213C23×C5—21no—
214C23×C5—21no—
215C23×C5—42no—
216C23×C5#21712yes—
217C23×C5C22×Dic311yescharacteristic
218C22×D5—21no—
219C22×D5—21no—
220C22×D5—42no—
221C22×D5—42no—
222C22×D5#21712yes—
223C22×D5C2×#6712yes—
224C22×D5C2×#6712yes—
225C22×D5C2×#6712yes—
226C2×AGL(1,𝔽5)—128no—
227C2×AGL(1,𝔽5)—124no—
228C2×C4×C5—28no—
229C2×C4×C5—21no—
230C2×C4×C5—21no—
231C2×C4×C5—21no—
232C2×C4×C5—21no—
233C2×C4×C5#21712yes—
234C2×C4×C5#21712yes—
235C22⋊D5—28no—
236C22⋊D5—28no—
237C2×Dic5—21no—
238C2×Dic5—21no—
239C2×Dic5—21no—
240C2×Dic5—21no—
241C2×Dic5#21712yes—
242C2×Dic5#21712yes—
243D20—28no—
244C4×D5—28no—
245C4×D5—28no—
246Dic10—28no—
247C2×#41—104no—
248C2×#41—104no—
249C2×#41—104no—
250C22×Q8—51no—
251C22×D4—51no—
252C22×D4—51no—
253C22×D4—51no—
254C23×C4—51no—
255C23×C4—51no—
256C23×C4ΓL(1,𝔽16)11yescharacteristic, complemented
257C2×C22⋊C4—154no—
258#99—304no—
259#99—304no—
260#95—304no—
261C2×C3×C5—21no—
262C2×C3×C5—21no—
263C2×C3×C5—42no—
264C2×C3×C5#37911yescharacteristic
265C2×C3×C5#41012yes—
266C3×D5—24no—
267C3×D5—42no—
268C23×C3—21no—
269C23×C3—21no—
270C23×C3—42no—
271C23×C3—52no—
272C23×C3—52no—
273C23×C3—52no—
274C23×C3—52no—
275C23×C3—101no—
276C23×C3—101no—
277C23×C3—202no—
278C23×C3—202no—
279C23×C3C22⋊AGL(1,𝔽5)12yes—
280C23×C3C22×AGL(1,𝔽5)11yescharacteristic
281C3×Q8—108no—
282C3×D4—108no—
283C3×D4—108no—
284C3×D4—108no—
285C2×C3×C4—28no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—52no—
291C2×C3×C4—52no—
292C2×C3×C4—108no—
293C2×C3×C4—108no—
294C2×C3×C4—101no—
295C2×C3×C4—101no—
296C2×C3×C4—101no—
297C2×C3×C4—101no—
298C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
299C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
300C2×Dic3—204no—
301C2×Dic3—208no—
302C22×C5—22no—
303C22×C5—22no—
304C22×C5—42no—
305C22×C5—42no—
306C22×C5—42no—
307C22×C5C2×#21711yescharacteristic
308C22×C5C2×#21711yescharacteristic
309C22×C5C2×#21711yescharacteristic
310C2×D5—24no—
311C2×D5—22no—
312C2×D5—42no—
313C2×D5—42no—
314C2×D5—42no—
315C2×D5—42no—
316C2×D5—42no—
317C2×D5#95314yes—
318AGL(1,𝔽5)—244no—
319C4×C5—22no—
320C4×C5—22no—
321Dic5—22no—
322Dic5—22no—
323C24—51no—
324C24—51no—
325C24C2×ΓL(1,𝔽16)11yescharacteristic
326#41—1032no—
327C2×Q8—102no—
328C2×Q8—102no—
329C2×Q8—102no—
330C2×D4—54no—
331C2×D4—54no—
332C2×D4—102no—
333C2×D4—102no—
334C2×D4—102no—
335C2×D4—102no—
336C2×D4—102no—
337C2×D4—102no—
338C2×D4—102no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—51no—
343C22×C4—51no—
344C22×C4—54no—
345C22×C4—102no—
346C22×C4—102no—
347C22×C4—102no—
348C22×C4—102no—
349C22×C4—102no—
350C22×C4—304no—
351C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
352C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
353C22⋊C4—304no—
354C22⋊C4—304no—
355C3×C5#178211yescharacteristic, complemented, Hall
356C22×C3—22no—
357C22×C3—22no—
358C22×C3—42no—
359C22×C3—42no—
360C22×C3—42no—
361C22×C3—54no—
362C22×C3—104no—
363C22×C3—102no—
364C22×C3—202no—
365C22×C3—202no—
366C22×C3—202no—
367C22×C3—202no—
368C22×C3—202no—
369C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
370C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
371C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
372C3×C4—22no—
373C3×C4—22no—
374C3×C4—102no—
375C3×C4—102no—
376Dic3—404no—
377C2×C5—21no—
378C2×C5—21no—
379C2×C5—42no—
380C2×C5#524012yes—
381C2×C5#524711yescharacteristic
382D5—24no—
383D5—42no—
384C23—21no—
385C23—21no—
386C23—42no—
387C23—52no—
388C23—52no—
389C23—52no—
390C23—52no—
391C23—101no—
392C23—101no—
393C23—202no—
394C23—202no—
395C23#676312yes—
396C23C22×ΓL(1,𝔽16)11yescharacteristic
397Q8—108no—
398D4—108no—
399D4—108no—
400D4—108no—
401C2×C4—28no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—52no—
407C2×C4—52no—
408C2×C4—108no—
409C2×C4—108no—
410C2×C4—101no—
411C2×C4—101no—
412C2×C4—101no—
413C2×C4—101no—
414C2×C4—604no—
415C2×C4—608no—
416C2×C4#676312yes—
417C2×C4#676312yes—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—42no—
421C2×C3—104no—
422C2×C3—202no—
423C2×C3#6574512yes—
424C2×C3#6580011yescharacteristic
425C5#7213911yescharacteristic, complemented, Sylow
426C22—22no—
427C22—22no—
428C22—42no—
429C22—42no—
430C22—42no—
431C22—54no—
432C22—104no—
433C22—102no—
434C22—202no—
435C22—202no—
436C22—202no—
437C22—202no—
438C22—202no—
439C22C2×#676311yescharacteristic
440C22C2×#676311yescharacteristic
441C22C2×#676311yescharacteristic
442C4—22no—
443C4—22no—
444C4—102no—
445C4—102no—
446C4—1204no—
447C3#1060489111yescharacteristic, complemented, Sylow
448C2—21no—
449C2—21no—
450C2—42no—
451C2—104no—
452C2—202no—
453C2#1175240412yes—
454C2#1175245911yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC23×C3×C5C22×C4
FrattiniC23C22×ΓL(1,𝔽16)
FittingC23×C3×C4×C5C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×#709C2
cosocleC23×C3×D5C23
hypercenterC23×C4ΓL(1,𝔽16)
hypocenterC3×C5#1782
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#91240C2semidirect
3. #11752423C2semidirect
4. C2×#91228C2semidirect
6. C23×C3×C4×C5C4semidirect
7. C22×C3×C22⋊D5C4semidirect
13. C22×C3×C4×D5C4semidirect
15. C22×C3×Dic10C4semidirect
61. C23×C4×C5Dic3semidirect
62. C22×C22⋊D5Dic3semidirect
68. C22×C4×D5Dic3semidirect
70. C22×Dic10Dic3semidirect
119. C23×C3×C4AGL(1,𝔽5)semidirect
256. C23×C4ΓL(1,𝔽16)semidirect
355. C3×C5#1782semidirect
425. C5#72139semidirect
447. C3#10604891semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#7092
C2×#912402
#117524232
C2×#912282
#106048913
#721395