Finite Group Databasebeta

← #14322500

Subgroups — #14322500

Order 1920.

1568 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×Dic6C211yesmaximal, characteristic
2C2×#91923C212yesmaximal
3#11752423C211yesmaximal, characteristic
4C3×#65764C211yesmaximal, characteristic
5#11751984C212yesmaximal
6#11751842C218yesmaximal, complemented
7#10617527—31nomaximal, Hall
8C22×Dic30C411yescharacteristic, complemented
9C22×C5×Dic6C411yescharacteristic, complemented
10C22×C3×C4×D5C2211yescharacteristic
11C22×#1204C411yescharacteristic, complemented
12C22×#1204C411yescharacteristic, complemented
13C22×D5×Dic3C2211yescharacteristic
14C22×D5×Dic3C2211yescharacteristic
15C2×D5×Dic6—28no—
16C2×D5×Dic6C414yescomplemented
17C2×D5×Dic6C2214yes—
18C2×#6763C2212yes—
19C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
20C2×Dic3⋊AGL(1,𝔽5)C2214yes—
21#91923—28no—
22C2×Dic3×AGL(1,𝔽5)C2214yes—
23#91235C2214yes—
24C3×(C2×AGL(1,𝔽5))⋊C4C2214yes—
25(C2×AGL(1,𝔽5))⋊Dic3C2218yes—
26#74053—51nomaximal, Hall
27C22×Q8×D5—31no—
28C2×#4130—32no—
29(C2×AGL(1,𝔽5))⋊Q8—38no—
30#65764—31no—
31#65764—32no—
32#65764D311yescharacteristic
33C23×C3×D5C2311yescharacteristic
34C22×ΓL(1,𝔽16)C2314yes—
35C22×C3×AGL(1,𝔽5)C2314yes—
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×Dic15C2×C411yescharacteristic
38C22×Dic15C2×C411yescharacteristic
39C2×Dic30—24no—
40C2×Dic30C2×C414yes—
41C22×C5×Dic3C2×C411yescharacteristic
42C22×C5×Dic3C2×C411yescharacteristic
43C2×C5×Dic6—24no—
44C2×C5×Dic6C2×C414yes—
45C22×C3×Dic5C2×C411yescharacteristic
46C2×C3×C4×D5—24no—
47C2×C3×C4×D5C2×C412yes—
48C2×C3×C4×D5C2312yes—
49C2×#1204—24no—
50C2×#1204—24no—
51C2×#1204C2×C414yes—
52C2×#1204C2×C414yes—
53C2×D5×Dic3—24no—
54C2×D5×Dic3C2×C412yes—
55C2×D5×Dic3C2×C412yes—
56C2×D5×Dic3D418yes—
57C2×D5×Dic3C2312yes—
58C2×D5×Dic3C2312yes—
59D5×Dic6—216no—
60D5×Dic6—28no—
61D5×Dic6—28no—
62#6763—24no—
63C3×C22⋊AGL(1,𝔽5)—24no—
64Dic3⋊AGL(1,𝔽5)—28no—
65Dic3×AGL(1,𝔽5)—28no—
66C23×Dic6—51no—
67C2×#877—52no—
68C3×#381—51no—
69#5211—51no—
70#4943—52no—
71#4646—58no—
72C22×C5×Q8—31no—
73C2×Q8×D5—34no—
74C2×Q8×D5—34no—
75C2×Q8×D5—68no—
76C22×C4×D5—31no—
77C22×C4×D5—31no—
78C22×C4×D5C2×D311yescharacteristic
79C22×Dic10—31no—
80C22×Dic10—31no—
81C22×Dic10—31no—
82C2×C22⋊AGL(1,𝔽5)—32no—
83C2×C22⋊AGL(1,𝔽5)C2×D312yes—
84#4130—68no—
85C2×C4⋊AGL(1,𝔽5)—34no—
86C2×C4×AGL(1,𝔽5)—34no—
87(C2×AGL(1,𝔽5))⋊C4—38no—
88(C2×AGL(1,𝔽5))⋊C4—34no—
89(C2×AGL(1,𝔽5))⋊C4C2×D314yes—
90#2310—151noSylow
91C23×C3×C5C22×C411yescharacteristic
92C22×C3×D5—24no—
93C22×C3×D5C22×C411yescharacteristic
94C22×C3×D5C2×D414yes—
95C22×C3×D5C2411yescharacteristic
96C2×ΓL(1,𝔽16)—24no—
97C2×ΓL(1,𝔽16)—28no—
98C2×C3×AGL(1,𝔽5)—24no—
99C2×C3×AGL(1,𝔽5)—28no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5C22×C412yes—
102C2×Dic15—22no—
103C2×Dic15C22⋊C414yes—
104C2×Dic15C22×C412yes—
105C2×Dic15C22×C412yes—
106Dic30—28no—
107C2×C5×Dic3—22no—
108C2×C5×Dic3C22⋊C414yes—
109C2×C5×Dic3C22×C412yes—
110C2×C5×Dic3C22×C412yes—
111C5×Dic6—28no—
112C2×C3×Dic5—22no—
113C2×C3×Dic5C22×C412yes—
114C3×C4×D5—24no—
115C3×C4×D5—24no—
116#1204—28no—
117#1204—28no—
118D5×Dic3—24no—
119D5×Dic3—24no—
120D5×Dic3C22⋊C418yes—
121D5×Dic3C2×D414yes—
122D5×Dic3C2×D414yes—
123C23×C3×C4—51no—
124C23×Dic3—51no—
125C23×Dic3—51no—
126C22×Dic6—51no—
127C22×Dic6—51no—
128C22×Dic6—51no—
129C22×Dic6—54no—
130C22×Dic6—54no—
131C22×Dic6—108no—
132C22×Dic6AGL(1,𝔽5)11yescharacteristic, complemented
133C2×C3×C22⋊C4—52no—
134C2×#217—52no—
135C2×Dic3⋊C4—54no—
136C2×C4×Dic3—54no—
137#877—108no—
138C3×#95—54no—
139C3⋊#95—58no—
140C3⋊#95—54no—
141C23×D5C22×D311yescharacteristic
142C22×AGL(1,𝔽5)—34no—
143C22×AGL(1,𝔽5)C22×D314yes—
144C2×C5×Q8—34no—
145C2×C5×Q8—64no—
146C22×C4×C5—31no—
147C22×C4×C5—31no—
148C22×C4×C5C4×D311yescharacteristic
149C22×Dic5—31no—
150C22×Dic5—31no—
151C22×Dic5C4×D311yescharacteristic
152Q8×D5—616no—
153Q8×D5—68no—
154Q8×D5—68no—
155C2×C4×D5—24no—
156C2×C4×D5—32no—
157C2×C4×D5—38no—
158C2×C4×D5—32no—
159C2×C4×D5—32no—
160C2×C4×D5—32no—
161C2×C4×D5—64no—
162C2×C4×D5C4×D312yes—
163C2×C4×D5C22×D312yes—
164C2×Dic10—34no—
165C2×Dic10—34no—
166C2×Dic10—34no—
167C2×Dic10—64no—
168C2×Dic10—64no—
169C2×Dic10—64no—
170C22⋊AGL(1,𝔽5)—24no—
171C22⋊AGL(1,𝔽5)—64no—
172C4⋊AGL(1,𝔽5)—68no—
173C4×AGL(1,𝔽5)—68no—
174C23×Q8—151no—
175C2×#117—152no—
176#391—158no—
177#381—51no—
178#381—152no—
179#381—151no—
180C22×C3×C5—22no—
181C22×C3×C5C2×C22⋊C412yes—
182C22×C3×C5C23×C411yescharacteristic
183C2×C3×D5—22no—
184C2×C3×D5—28no—
185C2×C3×D5C2×C22⋊C412yes—
186C2×C3×D5C22×D412yes—
187C2×C3×D52−1+414yes—
188ΓL(1,𝔽16)—44no—
189C3×AGL(1,𝔽5)—44no—
190C3×C4×C5—22no—
191Dic15—22no—
192Dic15C2×C22⋊C414yes—
193C3×Dic5—22no—
194C5×Dic3—22no—
195C5×Dic3C2×C22⋊C414yes—
196C24×C3—51no—
197C22×C3×C4—51no—
198C22×C3×C4—52no—
199C22×C3×C4—52no—
200C22×C3×C4—54no—
201C22×C3×C4—104no—
202C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
203C22×Dic3—51no—
204C22×Dic3—58no—
205C22×Dic3—52no—
206C22×Dic3—52no—
207C22×Dic3—51no—
208C22×Dic3—52no—
209C22×Dic3—52no—
210C22×Dic3—54no—
211C22×Dic3—104no—
212C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
213C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
214C2×Dic6—24no—
215C2×Dic6—54no—
216C2×Dic6—54no—
217C2×Dic6—54no—
218C2×Dic6—1016no—
219C2×Dic6—108no—
220C2×Dic6—108no—
221C2×Dic6—104no—
222C2×Dic6—104no—
223C2×Dic6—104no—
224C2×Dic6C2×AGL(1,𝔽5)14yes—
225C3×C22⋊C4—104no—
226#217—104no—
227Dic3⋊C4—108no—
228C4×Dic3—108no—
229C23×C5C2×C4×D311yescharacteristic
230C22×D5—24no—
231C22×D5C2×C4×D311yescharacteristic
232C22×D5D3×D414yes—
233C22×D5C23×D311yescharacteristic
234C2×AGL(1,𝔽5)—24no—
235C2×AGL(1,𝔽5)—28no—
236C2×AGL(1,𝔽5)—64no—
237C2×AGL(1,𝔽5)—68no—
238C5×Q8—68no—
239C2×C4×C5—22no—
240C2×C4×C5—34no—
241C2×C4×C5—32no—
242C2×C4×C5—32no—
243C2×C4×C5—62no—
244C2×C4×C5C2×C4×D312yes—
245C2×Dic5—22no—
246C2×Dic5—34no—
247C2×Dic5—32no—
248C2×Dic5—32no—
249C2×Dic5—62no—
250C2×Dic5C2×C4×D312yes—
251C4×D5—24no—
252C4×D5—24no—
253C4×D5—38no—
254C4×D5—34no—
255C4×D5—34no—
256C4×D5—64no—
257C4×D5—64no—
258Dic10—68no—
259Dic10—68no—
260Dic10—68no—
261C22×Q8—31no—
262C22×Q8—151no—
263C22×Q8—151no—
264C22×Q8—154no—
265C22×Q8—154no—
266C22×Q8—151no—
267C22×Q8—308no—
268C23×C4—51no—
269C23×C4—151no—
270C23×C4—151no—
271#117—308no—
272C2×C4⋊C4—154no—
273C2×C22⋊C4—52no—
274C2×C22⋊C4—152no—
275C2×C42—154no—
276#95—54no—
277#95—154no—
278#95—158no—
279C2×C3×C5—22no—
280C2×C3×C5C22×C22⋊C411yescharacteristic
281C2×C3×C5#51912yes—
282C3×D5—22no—
283C3×D5#53614yes—
284C23×C3—51no—
285C23×C3—54no—
286C23×C3—51no—
287C23×C3—104no—
288C23×C3C22×AGL(1,𝔽5)11yescharacteristic
289C2×C3×C4—22no—
290C2×C3×C4—52no—
291C2×C3×C4—104no—
292C2×C3×C4—104no—
293C2×C3×C4—102no—
294C2×C3×C4—104no—
295C2×C3×C4—108no—
296C2×C3×C4C22×AGL(1,𝔽5)12yes—
297C2×Dic3—22no—
298C2×Dic3—54no—
299C2×Dic3—52no—
300C2×Dic3—58no—
301C2×Dic3—54no—
302C2×Dic3—54no—
303C2×Dic3—52no—
304C2×Dic3—104no—
305C2×Dic3—104no—
306C2×Dic3—102no—
307C2×Dic3—104no—
308C2×Dic3—108no—
309C2×Dic3C22⋊AGL(1,𝔽5)14yes—
310C2×Dic3C22×AGL(1,𝔽5)12yes—
311C2×Dic3C22×AGL(1,𝔽5)12yes—
312Dic6—28no—
313Dic6—108no—
314Dic6—108no—
315Dic6—108no—
316C22×C5—22no—
317C22×C5D3×C22⋊C412yes—
318C22×C5C22×C4×D311yescharacteristic
319C2×D5—22no—
320C2×D5—28no—
321C2×D5D3×C22⋊C412yes—
322C2×D5C2×D3×D412yes—
323C2×D5#101014yes—
324AGL(1,𝔽5)—44no—
325AGL(1,𝔽5)—124no—
326C4×C5—22no—
327C4×C5—34no—
328C4×C5—62no—
329Dic5—22no—
330Dic5—34no—
331Dic5—62no—
332C24—51no—
333C2×Q8—34no—
334C2×Q8—64no—
335C2×Q8—154no—
336C2×Q8—154no—
337C2×Q8—154no—
338C2×Q8—304no—
339C2×Q8—304no—
340C2×Q8—304no—
341C2×Q8—308no—
342C2×Q8—308no—
343C2×Q8—3016no—
344C22×C4—31no—
345C22×C4—31no—
346C22×C4—51no—
347C22×C4—52no—
348C22×C4—52no—
349C22×C4—54no—
350C22×C4—104no—
351C22×C4—152no—
352C22×C4—158no—
353C22×C4—152no—
354C22×C4—152no—
355C22×C4—152no—
356C22×C4—151no—
357C22×C4—151no—
358C22×C4—154no—
359C22×C4—304no—
360C22×C4D3×AGL(1,𝔽5)11yescharacteristic
361C4⋊C4—308no—
362C22⋊C4—104no—
363C22⋊C4—304no—
364C42—308no—
365C3×C5#231011yescharacteristic, complemented, Hall
366C22×C3—22no—
367C22×C3—54no—
368C22×C3—52no—
369C22×C3—52no—
370C22×C3—108no—
371C22×C3—102no—
372C22×C3C2×C22⋊AGL(1,𝔽5)12yes—
373C22×C3C23×AGL(1,𝔽5)11yescharacteristic
374C3×C4—22no—
375C3×C4—102no—
376C3×C4—204no—
377Dic3—22no—
378Dic3—54no—
379Dic3—102no—
380Dic3—204no—
381Dic3C2×C22⋊AGL(1,𝔽5)14yes—
382C2×C5—22no—
383C2×C5C2×D3×C22⋊C411yescharacteristic
384C2×C5#551612yes—
385D5—22no—
386D5#564814yes—
387C23—51no—
388C23—54no—
389C23—51no—
390C23—104no—
391C23C2×D3×AGL(1,𝔽5)11yescharacteristic
392Q8—68no—
393Q8—308no—
394Q8—308no—
395Q8—308no—
396C2×C4—22no—
397C2×C4—34no—
398C2×C4—32no—
399C2×C4—32no—
400C2×C4—52no—
401C2×C4—62no—
402C2×C4—104no—
403C2×C4—104no—
404C2×C4—102no—
405C2×C4—104no—
406C2×C4—108no—
407C2×C4—154no—
408C2×C4—154no—
409C2×C4—158no—
410C2×C4—154no—
411C2×C4—152no—
412C2×C4—152no—
413C2×C4—304no—
414C2×C4—304no—
415C2×C4—302no—
416C2×C4—304no—
417C2×C4—308no—
418C2×C4C2×D3×AGL(1,𝔽5)12yes—
419C2×C3—22no—
420C2×C3—54no—
421C2×C3—102no—
422C2×C3#6626212yes—
423C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
424C5#7405311yescharacteristic, complemented, Sylow
425C22—22no—
426C22—54no—
427C22—52no—
428C22—52no—
429C22—108no—
430C22—102no—
431C22D3×C22⋊AGL(1,𝔽5)12yes—
432C22C22×D3×AGL(1,𝔽5)11yescharacteristic
433C4—22no—
434C4—34no—
435C4—62no—
436C4—102no—
437C4—154no—
438C4—204no—
439C4—302no—
440C4—604no—
441C3#1061752711yescharacteristic, complemented, Sylow
442C2—22no—
443C2—54no—
444C2—102no—
445C2#1175681212yes—
446C2C2×D3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2310
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. #11751842C2semidirect
8. C22×Dic30C4semidirect
9. C22×C5×Dic6C4semidirect
11. C22×#1204C4semidirect
12. C22×#1204C4semidirect
16. C2×D5×Dic6C4semidirect
132. C22×Dic6AGL(1,𝔽5)semidirect
365. C3×C5#2310semidirect
424. C5#74053semidirect
441. C3#10617527semidirect

Maximal subgroups

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

subgroupindex
C22×D5×Dic62
C2×#919232
#117524232
C3×#657642
#117519842
#117518422
#106175273
#740535