Finite Group Databasebeta

← #14437831

Subgroups — #14437831

Order 1920.

800 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
1#11756475C211yesmaximal, characteristic
2#11752484C211yesmaximal, characteristic, complemented
3C5×#5070C211yesmaximal, characteristic, complemented
4C3×#65359C211yesmaximal, characteristic, complemented
5#11748969C214yesmaximal, complemented
6#11748944C214yesmaximal, complemented
7C4×#6648C211yesmaximal, characteristic, complemented
8#11746930C211yesmaximal, characteristic, complemented
9#11746921C211yesmaximal, characteristic, complemented
10#10613293—31nomaximal, Hall
11C2×#6819C2212yes—
12C3×C5×#127C2211yescharacteristic
13#91827—21no—
14#91827—21no—
15#91825C2212yes—
16D4×Dic15—21no—
17D4×Dic15—21no—
18C42×D15C2211yescharacteristic
19#91758C2211yescharacteristic
20C5×#869C2211yescharacteristic
21C3×#4015C2211yescharacteristic
22#91390—21no—
23#91384C2212yes—
24#91383—21no—
25#91347C2212yes—
26#91344—21no—
27#91331—21no—
28C2×#6648C2212yes—
29C5×#832C2214yes—
30C4×C5×C3⋊C8C2211yescharacteristic
31C3×#3964C2214yes—
32C3×C4×#168C2211yescharacteristic
33#90975C2214yes—
34#90974C2214yes—
35#90951C2212yes—
36#81562—51nomaximal, Hall
37#66062—31no—
38#66050—31no—
39C5×#486—31no—
40#65382—31no—
41#65359D311yescharacteristic, complemented
42#65061—34no—
43#65057—34no—
44C4×C8×D5—31no—
45#64970—31no—
46C2×C3×C5×D4—21no—
47C2×C3×C5×D4—21no—
48C2×C3×C5×D4C2312yes—
49C2×#1220—22no—
50C22×Dic15—22no—
51#6819—28no—
52C2×C4×D15D411yescharacteristic
53C2×C4×D15D411yescharacteristic
54C2×C4×D15C2311yescharacteristic
55C2×Dic30C2312yes—
56C2×C5×Dic6—21no—
57C2×C3×Dic10—21no—
58C3×C42×C5C2311yescharacteristic
59#6719—22no—
60#6719—22no—
61C4⋊Dic15—21no—
62C4⋊Dic15—21no—
63C4×Dic15D411yescharacteristic
64C4×Dic15D411yescharacteristic
65C4×Dic15C2311yescharacteristic
66C5×C4⋊Dic3—21no—
67C5×C4⋊Dic3C2312yes—
68C2×C5×C3⋊C8C2312yes—
69C3×C4⋊Dic5—21no—
70C3×C4⋊Dic5C2312yes—
71C2×C3×#168C2312yes—
72Dic3⋊Dic5—22no—
73#6668—22no—
74#6667—22no—
75Dic3×Dic5—22no—
76#6648—24no—
77#5728—51no—
78#5716—51no—
79C3×#486—51no—
80#5093—51no—
81#5070D511yescharacteristic, complemented
82#4772—54no—
83#4768—54no—
84C4×D3×C8—51no—
85#4681—51no—
86C2×#711—32no—
87C5×C4⋊Q8—31no—
88C5×#127C2×D311yescharacteristic
89#4092—61no—
90Q8×Dic5—61no—
91#4084—61no—
92#4084—61no—
93#4082—32no—
94D4×Dic5—61no—
95D4×Dic5—61no—
96C2×C8×D5—32no—
97#4043—61no—
98#4038—32no—
99#4036—32no—
100#4033—61no—
101C42×D5—31no—
102#4015—31no—
103#4015C2×D311yescharacteristic
104C5×#102—34no—
105C4×C5×C8—31no—
106#3964C2×D314yes—
107#3948—34no—
108C8×Dic5—32no—
109#3942—34no—
110C4×#168C2×D311yescharacteristic
111#3131—151noSylow
112C23×C3×C5—22no—
113C22×D15C2×D411yescharacteristic
114C3×C5×D4—24no—
115C3×C5×D4—42no—
116C3×C5×D4—42no—
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5C2411yescharacteristic
120#1220—44no—
121C2×Dic15—22no—
122C2×Dic15—44no—
123C2×Dic15C2×D411yescharacteristic
124C2×Dic15C2×D411yescharacteristic
125C2×Dic15C2×D411yescharacteristic
126C4×D15—22no—
127C4×D15—22no—
128C4×D15#4114yes—
129Dic30—24no—
130C2×C5×Dic3—22no—
131C5×Dic6—42no—
132C2×C3×Dic5—22no—
133C3×Dic10—42no—
134C3×#168—22no—
135C5×C3⋊C8—22no—
136C2×#237—52no—
137C3×C4⋊Q8—51no—
138C3×#127C2×D511yescharacteristic
139#946—101no—
140Q8×Dic3—101no—
141#938—101no—
142#938—101no—
143#936—52no—
144D4×Dic3—101no—
145D4×Dic3—101no—
146C2×D3×C8—52no—
147#897—101no—
148#892—52no—
149#890—52no—
150#887—101no—
151C42×D3—51no—
152#869—51no—
153#869C2×D511yescharacteristic
154C3×#102—54no—
155C3×C4×C8—51no—
156#832C2×D514yes—
157#816—54no—
158C8×Dic3—52no—
159#810—54no—
160C4×C3⋊C8C2×D511yescharacteristic
161C2×C5×Q8—61no—
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4C22×D312yes—
165C2×C22⋊D5—62no—
166C22×Dic5—62no—
167#711—68no—
168C2×C4×D5—31no—
169C2×C4×D5—31no—
170C2×C4×D5—31no—
171C2×Dic10—21no—
172C2×Dic10—32no—
173C2×C5×C8—32no—
174C5×C4⋊C4—32no—
175C5×C4⋊C4—61no—
176C42×C5C22×D311yescharacteristic
177C22⋊Dic5—62no—
178C22⋊Dic5—62no—
179#685—62no—
180C4⋊Dic5—21no—
181C4⋊Dic5—62no—
182C4⋊Dic5—61no—
183C4⋊Dic5—61no—
184C4⋊Dic5C22×D312yes—
185#683—62no—
186C4×Dic5—31no—
187C4×Dic5—31no—
188C4×Dic5—31no—
189C4×Dic5—62no—
190C2×#168C22×D312yes—
191C8×D5—64no—
192#533—151no—
193#532—151no—
194#488—154no—
195#487—151no—
196#487—151no—
197#486—31no—
198#486—51no—
199#416—154no—
200C2×C4×C8—151no—
201C22×C3×C5—42no—
202C22×C3×C5—42no—
203C22×C3×C5—42no—
204C22×C3×C5C22×D411yescharacteristic
205C2×D15—21no—
206C2×D15—21no—
207C2×D15#12412yes—
208C3×C4×C5#13512yes—
209C3×C4×C5#13512yes—
210C3×C4×C5C2×#4112yes—
211Dic15—21no—
212Dic15—21no—
213Dic15—42no—
214Dic15#12412yes—
215C3×Dic5—42no—
216C5×Dic3—42no—
217C2×C3×Q8—101no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4C22×D512yes—
221C2×#67—102no—
222C22×Dic3—102no—
223#237—108no—
224C2×C4×D3—51no—
225C2×C4×D3—51no—
226C2×C4×D3—51no—
227C2×Dic6—21no—
228C2×Dic6—52no—
229C2×C3×C8—52no—
230C3×C4⋊C4—52no—
231C3×C4⋊C4—101no—
232C3×C42C22×D511yescharacteristic
233#217—102no—
234#217—102no—
235(C2×D3)⋊C4—102no—
236C4⋊Dic3—21no—
237C4⋊Dic3—102no—
238C4⋊Dic3—101no—
239C4⋊Dic3—101no—
240C4⋊Dic3C22×D512yes—
241Dic3⋊C4—102no—
242C4×Dic3—51no—
243C4×Dic3—51no—
244C4×Dic3—51no—
245C4×Dic3—102no—
246C2×C3⋊C8C22×D512yes—
247D3×C8—104no—
248C23×C5—22no—
249C22×D5—31no—
250C5×Q8—122no—
251C5×D4—24no—
252C5×D4—42no—
253C5×D4—42no—
254C2×C4×C5—62no—
255C2×C4×C5D3×D411yescharacteristic
256C2×C4×C5D3×D411yescharacteristic
257C2×C4×C5C23×D311yescharacteristic
258C22⋊D5—124no—
259C2×Dic5—22no—
260C2×Dic5—31no—
261C2×Dic5—31no—
262C2×Dic5—31no—
263C2×Dic5—62no—
264C2×Dic5—124no—
265C4×D5—34no—
266C4×D5—62no—
267C4×D5—62no—
268Dic10—42no—
269Dic10—64no—
270C5×C8—62no—
271#168—22no—
272C2×#41—152no—
273C22×C8—152no—
274C4⋊Q8—31no—
275C4⋊Q8—51no—
276C4⋊Q8—151no—
277#127D3×D511yescharacteristic
278#125—152no—
279#124—152no—
280C22⋊Q8—301no—
281C22⋊Q8—301no—
282#121—301no—
283#121—301no—
284C4×Q8—301no—
285C4×Q8—301no—
286C4×D4—301no—
287C4×D4—301no—
288#117—152no—
289C2×C42—151no—
290#103—154no—
291#103—154no—
292#102—34no—
293#102—54no—
294C4×C8—31no—
295C4×C8—51no—
296C4×C8—152no—
297C2×C3×C5—82no—
298C2×C3×C5C2×#12411yescharacteristic
299C2×C3×C5C2×#13511yescharacteristic
300C2×C3×C5C2×#13511yescharacteristic
301D15—22no—
302C23×C3—22no—
303C22×D3—51no—
304C3×Q8—202no—
305C3×D4—24no—
306C3×D4—42no—
307C3×D4—42no—
308C2×C3×C4—102no—
309C2×C3×C4D4×D511yescharacteristic
310C2×C3×C4D4×D511yescharacteristic
311C2×C3×C4C23×D511yescharacteristic
312#67—204no—
313C2×Dic3—22no—
314C2×Dic3—51no—
315C2×Dic3—51no—
316C2×Dic3—51no—
317C2×Dic3—102no—
318C2×Dic3—204no—
319C4×D3—54no—
320C4×D3—102no—
321C4×D3—102no—
322Dic6—42no—
323Dic6—104no—
324C3×C8—102no—
325C3⋊C8—22no—
326C22×C5—42no—
327C22×C5—42no—
328C22×C5—42no—
329C22×C5C2×D3×D411yescharacteristic
330C2×D5—32no—
331C2×D5—61no—
332C2×D5—61no—
333C4×C5—122no—
334C4×C5#91212yes—
335C4×C5#91612yes—
336C4×C5D3×#4112yes—
337Dic5—32no—
338Dic5—42no—
339Dic5—61no—
340Dic5—61no—
341Dic5—122no—
342#41—308no—
343C2×Q8—61no—
344C2×Q8—101no—
345C2×Q8—152no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—302no—
349C2×D4C2×D3×D512yes—
350C22×C4—151no—
351C22×C4—151no—
352C22×C4—151no—
353C22×C4—302no—
354C2×C8—32no—
355C2×C8—52no—
356C2×C8—304no—
357C4⋊C4—32no—
358C4⋊C4—52no—
359C4⋊C4—61no—
360C4⋊C4—101no—
361C4⋊C4—302no—
362C4⋊C4—302no—
363C4⋊C4—301no—
364C4⋊C4—301no—
365C22⋊C4—302no—
366C22⋊C4—302no—
367C22⋊C4—302no—
368C42—151no—
369C42—151no—
370C42—151no—
371C42—302no—
372C42C2×D3×D511yescharacteristic
373C3×C5#313111yescharacteristic, complemented, Hall
374C22×C3—42no—
375C22×C3—42no—
376C22×C3—42no—
377C22×C3C2×D4×D511yescharacteristic
378C2×D3—52no—
379C2×D3—101no—
380C2×D3—101no—
381C3×C4—202no—
382C3×C4#405812yes—
383C3×C4#406212yes—
384C3×C4D5×#4112yes—
385Dic3—42no—
386Dic3—52no—
387Dic3—101no—
388Dic3—101no—
389Dic3—202no—
390C2×C5—82no—
391C2×C5D3×#12411yescharacteristic
392C2×C5C2×#91211yescharacteristic
393C2×C5C2×#91611yescharacteristic
394D5—62no—
395C23—22no—
396C23—151no—
397Q8—122no—
398Q8—202no—
399Q8—304no—
400D4—24no—
401D4—42no—
402D4—42no—
403D4—604no—
404C2×C4—62no—
405C2×C4—102no—
406C2×C4—151no—
407C2×C4—154no—
408C2×C4—151no—
409C2×C4—151no—
410C2×C4—302no—
411C2×C4—302no—
412C2×C4—302no—
413C2×C4—604no—
414C2×C4#679011yescharacteristic
415C2×C4#679011yescharacteristic
416C2×C4C22×D3×D511yescharacteristic
417C8—62no—
418C8—102no—
419C2×C3—82no—
420C2×C3D5×#12411yescharacteristic
421C2×C3C2×#405811yescharacteristic
422C2×C3C2×#406211yescharacteristic
423D3—102no—
424C5#8156211yescharacteristic, complemented, Sylow
425C22—42no—
426C22—42no—
427C22—42no—
428C22—152no—
429C22—301no—
430C22—301no—
431C22C2×#679011yescharacteristic
432C4—122no—
433C4—152no—
434C4—202no—
435C4—301no—
436C4—301no—
437C4—602no—
438C4#9149712yes—
439C4#9149912yes—
440C4#9202412yes—
441C3#1061329311yescharacteristic, complemented, Sylow
442C2—82no—
443C2—302no—
444C2C2×#9149711yescharacteristic
445C2C2×#9149911yescharacteristic
446C2#1175483111yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C22×D4
prime radical#11756475C2
hypercenter#127D3×D5
hypocenterC3×C5#3131
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #11752484C2semidirect
3. C5×#5070C2semidirect
4. C3×#65359C2semidirect
5. #11748969C2semidirect
6. #11748944C2semidirect
7. C4×#6648C2semidirect
8. #11746930C2semidirect
9. #11746921C2semidirect
41. #65359D3semidirect
81. #5070D5semidirect
373. C3×C5#3131semidirect
424. C5#81562semidirect
441. C3#10613293semidirect

Maximal subgroups

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

subgroupindex
#117564752
#117524842
C5×#50702
C3×#653592
#117489692
#117489442
C4×#66482
#117469302
#117469212
#106132933
#815625