Finite Group Databasebeta

← #14437830

Subgroups — #14437830

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
1C3×#66050C211yesmaximal, characteristic
2#11752506C211yesmaximal, characteristic, complemented
3#11751171C211yesmaximal, characteristic, complemented
4C5×#5070C211yesmaximal, characteristic, complemented
5#11749085C214yesmaximal, complemented
6#11748961C214yesmaximal, complemented
7C4×D5×C3⋊C8C211yesmaximal, characteristic, complemented
8#11746924C211yesmaximal, characteristic, complemented
9#11746920C211yesmaximal, characteristic, complemented
10#10613293—31nomaximal, Hall
11C2×C3×#711C2212yes—
12C3×C5×#127C2211yescharacteristic
13#91758C2211yescharacteristic
14C5×#869C2211yescharacteristic
15C3×#4084—21no—
16C3×#4084—21no—
17C3×#4082C2212yes—
18C3×D4×Dic5—21no—
19C3×D4×Dic5—21no—
20C3×C42×D5C2211yescharacteristic
21C3×#4015C2211yescharacteristic
22#91388C2212yes—
23#91360—21no—
24#91359—21no—
25#91358C2212yes—
26#91333—21no—
27Dic5×Dic6—21no—
28C2×D5×C3⋊C8C2212yes—
29#91116C2214yes—
30C4×C3⋊#168C2211yescharacteristic
31C5×#832C2214yes—
32C4×C5×C3⋊C8C2211yescharacteristic
33#90971C2214yes—
34#90970C2214yes—
35Dic5×C3⋊C8C2212yes—
36#83281—51nomaximal, Hall
37#66062—31no—
38#66050D311yescharacteristic
39C5×#486—31no—
40#65382—31no—
41#65359—31no—
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×Dic30—21no—
50C2×C5×Dic6—21no—
51C2×C3×C22⋊D5—22no—
52C22×C3×Dic5—22no—
53C3×#711—28no—
54C2×C3×C4×D5D411yescharacteristic
55C2×C3×C4×D5D411yescharacteristic
56C2×C3×C4×D5C2311yescharacteristic
57C2×C3×Dic10C2312yes—
58C3×C42×C5C2311yescharacteristic
59C4⋊Dic15—21no—
60C4⋊Dic15C2312yes—
61C2×C3⋊#168C2312yes—
62C5×C4⋊Dic3—21no—
63C5×C4⋊Dic3C2312yes—
64C2×C5×C3⋊C8C2312yes—
65C3×C22⋊Dic5—22no—
66C3×C22⋊Dic5—22no—
67C3×C4⋊Dic5—21no—
68C3×C4⋊Dic5—21no—
69C3×C4×Dic5D411yescharacteristic
70C3×C4×Dic5D411yescharacteristic
71C3×C4×Dic5C2311yescharacteristic
72Dic3⋊Dic5—22no—
73#6669—22no—
74#6665—22no—
75Dic3×Dic5—22no—
76D5×C3⋊C8—24no—
77C3×#532—51no—
78#5470—51no—
79#5233—54no—
80#5079—51no—
81#5079—51no—
82#5070—51no—
83#5070D511yescharacteristic, complemented
84#5056—54no—
85C2×C4×C3⋊C8—51no—
86C2×#711C2×D312yes—
87C5×C4⋊Q8—31no—
88C5×#127C2×D311yescharacteristic
89#4092—61no—
90Q8×Dic5—61no—
91#4084—21no—
92#4084—21no—
93#4082C2×D312yes—
94D4×Dic5—21no—
95D4×Dic5—21no—
96C2×C8×D5—32no—
97#4043—61no—
98#4038—32no—
99#4036—32no—
100#4033—61no—
101C42×D5C2×D311yescharacteristic
102#4015—31no—
103#4015C2×D311yescharacteristic
104C5×#102—34no—
105C4×C5×C8—31no—
106#3964—34no—
107#3948—34no—
108C8×Dic5—32no—
109#3942—34no—
110C4×#168—31no—
111#3131—151noSylow
112C23×C3×C5—22no—
113C22×C3×D5C2×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
120C2×Dic15—22no—
121Dic30—42no—
122C2×C5×Dic3—22no—
123C5×Dic6—42no—
124C3×C22⋊D5—44no—
125C2×C3×Dic5—22no—
126C2×C3×Dic5—44no—
127C2×C3×Dic5C2×D411yescharacteristic
128C2×C3×Dic5C2×D411yescharacteristic
129C2×C3×Dic5C2×D411yescharacteristic
130C3×C4×D5—22no—
131C3×C4×D5—22no—
132C3×C4×D5#4114yes—
133C3×Dic10—24no—
134C3⋊#168—22no—
135C5×C3⋊C8—22no—
136C2×C3×#41—52no—
137C3×C4⋊Q8—51no—
138C3×#127C2×D511yescharacteristic
139C3×#124—52no—
140C3×#121—101no—
141C3×#121—101no—
142C3×C4×D4—101no—
143C3×C4×D4—101no—
144C2×C3×C42—51no—
145#926—52no—
146#924—101no—
147#924—101no—
148C22×C3⋊C8—52no—
149#870—52no—
150#869—51no—
151#869C2×D511yescharacteristic
152C4×Dic6—101no—
153C4×Dic6—101no—
154#835—54no—
155#835—54no—
156#832—54no—
157#832C2×D514yes—
158C4×C3⋊C8—51no—
159C4×C3⋊C8—52no—
160C4×C3⋊C8C2×D511yescharacteristic
161C2×C5×Q8—61no—
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4C22×D312yes—
165C2×C22⋊D5—22no—
166C22×Dic5—22no—
167#711—28no—
168C2×C4×D5#6711yescharacteristic
169C2×C4×D5#6711yescharacteristic
170C2×C4×D5C22×D311yescharacteristic
171C2×Dic10—61no—
172C2×Dic10C22×D312yes—
173C2×C5×C8—32no—
174C5×C4⋊C4—32no—
175C5×C4⋊C4—61no—
176C42×C5C22×D311yescharacteristic
177C22⋊Dic5—22no—
178C22⋊Dic5—22no—
179#685—62no—
180C4⋊Dic5—21no—
181C4⋊Dic5—21no—
182C4⋊Dic5—32no—
183C4⋊Dic5—61no—
184C4⋊Dic5—62no—
185#683—62no—
186C4×Dic5—62no—
187C4×Dic5#6711yescharacteristic
188C4×Dic5#6711yescharacteristic
189C4×Dic5C22×D311yescharacteristic
190C2×#168—32no—
191C8×D5—64no—
192#533—151no—
193#532—51no—
194#488—154no—
195#487—151no—
196#487—151no—
197#486—31no—
198#486—151no—
199#416—154no—
200C2×C4×C8—151no—
201C22×C3×C5—42no—
202C22×C3×C5—42no—
203C22×C3×C5—42no—
204C22×C3×C5C22×D411yescharacteristic
205C2×C3×D5—21no—
206C2×C3×D5—21no—
207C2×C3×D5#12412yes—
208C3×C4×C5#13512yes—
209C3×C4×C5#13512yes—
210C3×C4×C5C2×#4112yes—
211Dic15—42no—
212C3×Dic5—21no—
213C3×Dic5—21no—
214C3×Dic5—42no—
215C3×Dic5#12412yes—
216C5×Dic3—42no—
217C3×#41—108no—
218C2×C3×Q8—52no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—102no—
222C2×C3×D4C22×D512yes—
223C22×C3×C4—51no—
224C22×C3×C4—51no—
225C22×C3×C4—51no—
226C22×C3×C4—102no—
227C2×Dic6—21no—
228C2×Dic6—101no—
229C3×C4⋊C4—101no—
230C3×C4⋊C4—101no—
231C3×C22⋊C4—102no—
232C3×C22⋊C4—102no—
233C3×C42—51no—
234C3×C42—51no—
235C3×C42—51no—
236C3×C42C22×D511yescharacteristic
237#217—102no—
238C4⋊Dic3—21no—
239C4⋊Dic3—52no—
240C4⋊Dic3—101no—
241C4⋊Dic3C22×D512yes—
242Dic3⋊C4—102no—
243Dic3⋊C4—102no—
244C4×Dic3—102no—
245C2×C3⋊C8—52no—
246C2×C3⋊C8—104no—
247C2×C3⋊C8C22×D512yes—
248C23×C5—22no—
249C22×D5C2×#6711yescharacteristic
250C5×Q8—122no—
251C5×D4—24no—
252C5×D4—42no—
253C5×D4—42no—
254C2×C4×C5—62no—
255C2×C4×C5C2×#6711yescharacteristic
256C2×C4×C5C2×#6711yescharacteristic
257C2×C4×C5C23×D311yescharacteristic
258C22⋊D5—44no—
259C2×Dic5—22no—
260C2×Dic5—44no—
261C2×Dic5—62no—
262C2×Dic5C2×#6711yescharacteristic
263C2×Dic5C2×#6711yescharacteristic
264C2×Dic5C2×#6711yescharacteristic
265C4×D5—22no—
266C4×D5—22no—
267C4×D5#23714yes—
268Dic10—24no—
269Dic10—122no—
270C5×C8—62no—
271#168—62no—
272C2×#41—52no—
273C22×C8—152no—
274C4⋊Q8—31no—
275C4⋊Q8—51no—
276C4⋊Q8—151no—
277#127D3×D511yescharacteristic
278#125—152no—
279#124—52no—
280C22⋊Q8—301no—
281C22⋊Q8—301no—
282#121—101no—
283#121—101no—
284C4×Q8—301no—
285C4×Q8—301no—
286C4×D4—101no—
287C4×D4—101no—
288#117—152no—
289C2×C42—51no—
290#103—154no—
291#103—154no—
292#102—34no—
293#102—154no—
294C4×C8—31no—
295C4×C8—152no—
296C4×C8—151no—
297C2×C3×C5—82no—
298C2×C3×C5C2×#12411yescharacteristic
299C2×C3×C5C2×#13511yescharacteristic
300C2×C3×C5C2×#13511yescharacteristic
301C3×D5—22no—
302C23×C3—22no—
303C23×C3—51no—
304C3×Q8—104no—
305C3×D4—24no—
306C3×D4—42no—
307C3×D4—42no—
308C3×D4—204no—
309C2×C3×C4—51no—
310C2×C3×C4—54no—
311C2×C3×C4—51no—
312C2×C3×C4—51no—
313C2×C3×C4—102no—
314C2×C3×C4—102no—
315C2×C3×C4—102no—
316C2×C3×C4—204no—
317C2×C3×C4D4×D511yescharacteristic
318C2×C3×C4D4×D511yescharacteristic
319C2×C3×C4C23×D511yescharacteristic
320C2×Dic3—22no—
321C2×Dic3—102no—
322Dic6—42no—
323Dic6—202no—
324C3⋊C8—22no—
325C3⋊C8—102no—
326C22×C5—42no—
327C22×C5—42no—
328C22×C5—42no—
329C22×C5C22×#6711yescharacteristic
330C2×D5—21no—
331C2×D5—21no—
332C2×D5#93612yes—
333C4×C5—122no—
334C4×C5#95012yes—
335C4×C5#95012yes—
336C4×C5C2×#23712yes—
337Dic5—21no—
338Dic5—21no—
339Dic5—42no—
340Dic5—122no—
341Dic5#93612yes—
342#41—108no—
343C2×Q8—52no—
344C2×Q8—61no—
345C2×Q8—301no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—102no—
349C2×D4C2×D3×D512yes—
350C22×C4—51no—
351C22×C4—51no—
352C22×C4—51no—
353C22×C4—102no—
354C2×C8—32no—
355C2×C8—152no—
356C2×C8—304no—
357C4⋊C4—32no—
358C4⋊C4—61no—
359C4⋊C4—101no—
360C4⋊C4—101no—
361C4⋊C4—152no—
362C4⋊C4—302no—
363C4⋊C4—302no—
364C4⋊C4—301no—
365C22⋊C4—102no—
366C22⋊C4—102no—
367C22⋊C4—302no—
368C42—51no—
369C42—51no—
370C42—51no—
371C42—302no—
372C42C2×D3×D511yescharacteristic
373C3×C5#313111yescharacteristic, complemented, Hall
374C22×C3—42no—
375C22×C3—42no—
376C22×C3—42no—
377C22×C3—52no—
378C22×C3—101no—
379C22×C3—101no—
380C22×C3C2×D4×D511yescharacteristic
381C3×C4—52no—
382C3×C4—101no—
383C3×C4—101no—
384C3×C4—202no—
385C3×C4#405812yes—
386C3×C4#406212yes—
387C3×C4D5×#4112yes—
388Dic3—42no—
389Dic3—202no—
390C2×C5—82no—
391C2×C5C2×#93611yescharacteristic
392C2×C5C2×#95011yescharacteristic
393C2×C5C2×#95011yescharacteristic
394D5—22no—
395C23—22no—
396C23—51no—
397Q8—104no—
398Q8—122no—
399Q8—602no—
400D4—24no—
401D4—42no—
402D4—42no—
403D4—204no—
404C2×C4—51no—
405C2×C4—54no—
406C2×C4—51no—
407C2×C4—51no—
408C2×C4—62no—
409C2×C4—102no—
410C2×C4—102no—
411C2×C4—102no—
412C2×C4—204no—
413C2×C4—302no—
414C2×C4D5×#6711yescharacteristic
415C2×C4D5×#6711yescharacteristic
416C2×C4C22×D3×D511yescharacteristic
417C8—62no—
418C8—302no—
419C2×C3—82no—
420C2×C3—102no—
421C2×C3D5×#12411yescharacteristic
422C2×C3C2×#405811yescharacteristic
423C2×C3C2×#406211yescharacteristic
424C5#8328111yescharacteristic, complemented, Sylow
425C22—42no—
426C22—42no—
427C22—42no—
428C22—52no—
429C22—101no—
430C22—101no—
431C22C2×D5×#6711yescharacteristic
432C4—52no—
433C4—101no—
434C4—101no—
435C4—122no—
436C4—202no—
437C4—602no—
438C4#9149012yes—
439C4#9149212yes—
440C4D5×#23712yes—
441C3#1061329311yescharacteristic, complemented, Sylow
442C2—82no—
443C2—102no—
444C2C2×#9149011yescharacteristic
445C2C2×#9149211yescharacteristic
446C2D5×#93611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C22×D4
prime radicalC3×#66050C2
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. #11752506C2semidirect
3. #11751171C2semidirect
4. C5×#5070C2semidirect
5. #11749085C2semidirect
6. #11748961C2semidirect
7. C4×D5×C3⋊C8C2semidirect
8. #11746924C2semidirect
9. #11746920C2semidirect
83. #5070D5semidirect
373. C3×C5#3131semidirect
424. C5#83281semidirect
441. C3#10613293semidirect

Maximal subgroups

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

subgroupindex
C3×#660502
#117525062
#117511712
C5×#50702
#117490852
#117489612
C4×D5×C3⋊C82
#117469242
#117469202
#106132933
#832815