Finite Group Databasebeta

← #14438703

Subgroups — #14438703

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66002C211yesmaximal, characteristic
2D5×#870C211yesmaximal, characteristic, complemented
3#11751157C211yesmaximal, characteristic, complemented
4C5×#5056C211yesmaximal, characteristic, complemented
5#11749330C212yesmaximal, complemented
6#11749198C212yesmaximal, complemented
7#11749084C212yesmaximal, complemented
8#11748951C212yesmaximal, complemented
9C4×#6649C211yesmaximal, characteristic, complemented
10#11746896C211yesmaximal, characteristic, complemented
11#11746891C211yesmaximal, characteristic, complemented
12#10613372—31nomaximal, Hall
13C2×C3×#713C2211yescharacteristic
14C2×C3×#711C2211yescharacteristic
15C3×C5×#124C2211yescharacteristic
16#91759C2211yescharacteristic
17C5×#870C2211yescharacteristic
18C3×#4090C2211yescharacteristic
19C3×#4086C2211yescharacteristic
20C3×#4030—22no—
21C3×#4027—22no—
22C3×#4021C2211yescharacteristic
23C3×C42×D5C2211yescharacteristic
24D5×C4⋊Dic3C2212yes—
25D5×Dic3⋊C4—22no—
26#91388C2212yes—
27#91378—22no—
28C2×#6649C2212yes—
29#91119C2212yes—
30#91116C2212yes—
31C4×C3⋊#168C2211yescharacteristic
32C5×#835C2212yes—
33C5×#832C2212yes—
34C4×C5×C3⋊C8C2211yescharacteristic
35#90971C2212yes—
36#90970C2212yes—
37#90965C2212yes—
38#90964C2212yes—
39#90952C2212yes—
40#83284—51nomaximal, Hall
41D5×#125—31no—
42#66002D311yescharacteristic
43C5×#488—31no—
44#65357—31no—
45#65345—31no—
46#65092—32no—
47#65086—32no—
48#65060—32no—
49#65053—32no—
50#64986—31no—
51C4×#676—31no—
52C2×C3×C5×Q8C2311yescharacteristic
53C2×C3×C5×D4C2311yescharacteristic
54C2×C3×C22⋊D5—21no—
55C2×C3×C22⋊D5—22no—
56C22×C3×Dic5—21no—
57C3×#713—24no—
58C3×#711—24no—
59C2×C3×D20—21no—
60C2×C3×D20C2311yescharacteristic
61C2×C3×C4×D5—21no—
62C2×C3×C4×D5D412yes—
63C2×C3×C4×D5C2311yescharacteristic
64C2×C3×Dic10C2311yescharacteristic
65C2×D5×Dic3—22no—
66C3×C5×C22⋊C4—22no—
67C3×C42×C5C2311yescharacteristic
68C4⋊Dic15C2312yes—
69#6712—22no—
70C2×C3⋊#168C2312yes—
71C5×C4⋊Dic3C2312yes—
72C5×Dic3⋊C4—22no—
73C2×C5×C3⋊C8C2312yes—
74C3×#685—22no—
75C3×#683—22no—
76C3×C4×Dic5D412yes—
77C3×C4×Dic5C2311yescharacteristic
78Dic3⋊Dic5—22no—
79#6669—22no—
80#6668—22no—
81#6649—24no—
82C3×#532—51no—
83C2×#870—51no—
84#5232—52no—
85#5232—52no—
86#5082—52no—
87#5071—52no—
88#5056—51no—
89#5056—51no—
90#5056—51no—
91#5056D511yescharacteristic, complemented
92C4×#208—51no—
93C2×#713C2×D311yescharacteristic
94C2×#711C2×D311yescharacteristic
95C5×#125—31no—
96C5×#124C2×D311yescharacteristic
97#4090C2×D311yescharacteristic
98#4086C2×D311yescharacteristic
99C2×#676—32no—
100D5×C4⋊C4—32no—
101D5×C4⋊C4—62no—
102#4036—32no—
103#4035—62no—
104#4030—22no—
105#4027—22no—
106#4021C2×D311yescharacteristic
107C42×D5C2×D311yescharacteristic
108#4016—31no—
109C5×#103—32no—
110C5×#102—32no—
111C4×C5×C8—31no—
112#3967—32no—
113#3964—32no—
114#3953—32no—
115#3948—32no—
116#3947—32no—
117#3942—32no—
118#3941—32no—
119C4×#168—31no—
120#3142—151noSylow
121C23×C3×C5—21no—
122C22×C3×D5—21no—
123C22×C3×D5C2×D411yescharacteristic
124C3×C5×Q8—22no—
125C3×C5×D4—22no—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5C2×D412yes—
128C2×C3×C4×C5C2411yescharacteristic
129C2×Dic15—22no—
130C2×C5×Dic3—22no—
131C3×C22⋊D5—44no—
132C3×C22⋊D5—42no—
133C2×C3×Dic5—21no—
134C2×C3×Dic5—42no—
135C2×C3×Dic5C2×D412yes—
136C2×C3×Dic5C2×D411yescharacteristic
137C3×D20—22no—
138C3×D20—42no—
139C3×C4×D5—42no—
140C3×C4×D5—42no—
141C3×C4×D5#4114yes—
142C3×Dic10—22no—
143D5×Dic3—44no—
144C3⋊#168—22no—
145C5×C3⋊C8—22no—
146C2×C3×#41—51no—
147C2×C3×#41—51no—
148C3×C4⋊Q8—51no—
149C3×#127—51no—
150C3×#124—51no—
151C3×#124C2×D511yescharacteristic
152C3×#121—102no—
153C3×C4×D4—102no—
154C2×C3×C42—51no—
155C2×C4⋊Dic3—52no—
156C2×Dic3⋊C4—102no—
157C2×#208—52no—
158#870—51no—
159#870—52no—
160#870—102no—
161#870C2×D511yescharacteristic
162#835—52no—
163#835—52no—
164#835—52no—
165#835C2×D512yes—
166#832—52no—
167#832—52no—
168#832—52no—
169#832C2×D512yes—
170#803—52no—
171C4×C3⋊C8—51no—
172C4×C3⋊C8C2×D511yescharacteristic
173C2×C5×Q8C22×D311yescharacteristic
174C2×C5×D4C22×D311yescharacteristic
175C2×C22⋊D5—21no—
176C2×C22⋊D5—22no—
177C22×Dic5—21no—
178#713—24no—
179#711—24no—
180C2×D20—21no—
181C2×D20C22×D311yescharacteristic
182C2×C4×D5—21no—
183C2×C4×D5—62no—
184C2×C4×D5#6712yes—
185C2×C4×D5C22×D311yescharacteristic
186C2×Dic10C22×D311yescharacteristic
187C2×C5×C8—32no—
188C5×C4⋊C4—32no—
189C5×C4⋊C4—62no—
190C5×C22⋊C4—22no—
191C42×C5C22×D311yescharacteristic
192#685—22no—
193C4⋊Dic5—32no—
194C4⋊Dic5—62no—
195#683—22no—
196#683—62no—
197#683—62no—
198#683—62no—
199C4×Dic5#6712yes—
200C4×Dic5C22×D311yescharacteristic
201C2×#168—32no—
202#676—64no—
203#532—51no—
204C2×#125—151no—
205#491—152no—
206#490—152no—
207#488—31no—
208#488—151no—
209#488—151no—
210#488—151no—
211#417—152no—
212#417—152no—
213C4×M16—151no—
214C22×C3×C5—41no—
215C22×C3×C5—42no—
216C22×C3×C5C22×D411yescharacteristic
217C2×C3×D5—22no—
218C2×C3×D5—41no—
219C2×C3×D5—42no—
220C2×C3×D5#12412yes—
221C3×C4×C5—22no—
222C3×C4×C5—41no—
223C3×C4×C5C2×#4112yes—
224Dic15—42no—
225C3×Dic5—22no—
226C3×Dic5—41no—
227C3×Dic5#12412yes—
228C5×Dic3—42no—
229C3×#41—104no—
230C3×#41—104no—
231C2×C3×Q8—51no—
232C2×C3×Q8C22×D511yescharacteristic
233C2×C3×D4—51no—
234C2×C3×D4—101no—
235C2×C3×D4—102no—
236C2×C3×D4—101no—
237C2×C3×D4C22×D511yescharacteristic
238C22×C3×C4—51no—
239C22×C3×C4—52no—
240C22×C3×C4—101no—
241C22×C3×C4—101no—
242C22×Dic3—102no—
243C3×C4⋊C4—102no—
244C3×C22⋊C4—22no—
245C3×C22⋊C4—102no—
246C3×C42—52no—
247C3×C42—51no—
248C3×C42C22×D511yescharacteristic
249C4⋊Dic3—52no—
250C4⋊Dic3—102no—
251C4⋊Dic3C22×D512yes—
252Dic3⋊C4—22no—
253Dic3⋊C4—102no—
254Dic3⋊C4—102no—
255Dic3⋊C4—102no—
256#208—104no—
257C2×C3⋊C8—52no—
258C2×C3⋊C8C22×D512yes—
259C23×C5—21no—
260C22×D5—21no—
261C22×D5C2×#6711yescharacteristic
262C5×Q8—22no—
263C5×D4—22no—
264C2×C4×C5—21no—
265C2×C4×C5—62no—
266C2×C4×C5C2×#6712yes—
267C2×C4×C5C23×D311yescharacteristic
268C22⋊D5—44no—
269C22⋊D5—42no—
270C2×Dic5—21no—
271C2×Dic5—42no—
272C2×Dic5—62no—
273C2×Dic5C2×#6712yes—
274C2×Dic5C2×#6711yescharacteristic
275D20—22no—
276D20—42no—
277C4×D5—42no—
278C4×D5—42no—
279C4×D5—124no—
280C4×D5#23714yes—
281Dic10—22no—
282C5×C8—62no—
283#168—62no—
284C2×#41—51no—
285C2×#41—51no—
286C2×M16—152no—
287C4⋊Q8—51no—
288#127—51no—
289#125—31no—
290#125—152no—
291#125—151no—
292#125—302no—
293#124—51no—
294#124D3×D511yescharacteristic
295#121—102no—
296C4×D4—102no—
297C2×C4⋊C4—152no—
298C2×C4⋊C4—302no—
299C2×C42—51no—
300#103—32no—
301#103—152no—
302#103—152no—
303#103—152no—
304#102—32no—
305#102—152no—
306#102—152no—
307#102—152no—
308#97—152no—
309C4×C8—31no—
310C4×C8—151no—
311C2×C3×C5—81no—
312C2×C3×C5C2×#12411yescharacteristic
313C2×C3×C5#57512yes—
314C3×D5—22no—
315C3×D5—81no—
316C23×C3—21no—
317C23×C3—51no—
318C23×C3—101no—
319C3×Q8—22no—
320C3×Q8—102no—
321C3×D4—22no—
322C3×D4—102no—
323C3×D4—202no—
324C3×D4—204no—
325C3×D4—202no—
326C2×C3×C4—21no—
327C2×C3×C4—51no—
328C2×C3×C4—54no—
329C2×C3×C4—52no—
330C2×C3×C4—101no—
331C2×C3×C4—202no—
332C2×C3×C4—202no—
333C2×C3×C4—202no—
334C2×C3×C4D4×D512yes—
335C2×C3×C4C23×D511yescharacteristic
336C2×Dic3—22no—
337C2×Dic3—102no—
338C2×Dic3—204no—
339C3⋊C8—22no—
340C3⋊C8—102no—
341C22×C5—41no—
342C22×C5—42no—
343C22×C5C22×#6711yescharacteristic
344C2×D5—22no—
345C2×D5—41no—
346C2×D5—42no—
347C2×D5#93612yes—
348C4×C5—22no—
349C4×C5—41no—
350C4×C5—122no—
351C4×C5C2×#23712yes—
352Dic5—22no—
353Dic5—41no—
354Dic5—122no—
355Dic5#93612yes—
356#41—104no—
357#41—104no—
358C2×Q8—51no—
359C2×Q8C2×D3×D511yescharacteristic
360C2×D4—51no—
361C2×D4—101no—
362C2×D4—102no—
363C2×D4—101no—
364C2×D4C2×D3×D511yescharacteristic
365C22×C4—51no—
366C22×C4—52no—
367C22×C4—101no—
368C22×C4—101no—
369C22×C4—302no—
370M16—304no—
371C2×C8—32no—
372C2×C8—152no—
373C4⋊C4—32no—
374C4⋊C4—62no—
375C4⋊C4—102no—
376C4⋊C4—152no—
377C4⋊C4—302no—
378C4⋊C4—302no—
379C4⋊C4—302no—
380C4⋊C4—302no—
381C22⋊C4—22no—
382C22⋊C4—102no—
383C42—52no—
384C42—51no—
385C42C2×D3×D511yescharacteristic
386C3×C5#314211yescharacteristic, complemented, Hall
387C22×C3—42no—
388C22×C3—41no—
389C22×C3—52no—
390C22×C3—102no—
391C22×C3—202no—
392C22×C3—201no—
393C22×C3C2×D4×D511yescharacteristic
394C3×C4—22no—
395C3×C4—41no—
396C3×C4—52no—
397C3×C4—102no—
398C3×C4—201no—
399C3×C4D5×#4112yes—
400Dic3—42no—
401Dic3—202no—
402C2×C5—81no—
403C2×C5C2×#93611yescharacteristic
404C2×C5#582212yes—
405D5—22no—
406D5—81no—
407C23—21no—
408C23—51no—
409C23—101no—
410Q8—22no—
411Q8—102no—
412D4—22no—
413D4—102no—
414D4—202no—
415D4—204no—
416D4—202no—
417C2×C4—21no—
418C2×C4—51no—
419C2×C4—54no—
420C2×C4—52no—
421C2×C4—62no—
422C2×C4—101no—
423C2×C4—202no—
424C2×C4—202no—
425C2×C4—202no—
426C2×C4—302no—
427C2×C4—604no—
428C2×C4D5×#6712yes—
429C2×C4C22×D3×D511yescharacteristic
430C8—62no—
431C8—302no—
432C2×C3—81no—
433C2×C3—102no—
434C2×C3—401no—
435C2×C3D5×#12411yescharacteristic
436C2×C3#6610212yes—
437C5#8328411yescharacteristic, complemented, Sylow
438C22—41no—
439C22—42no—
440C22—52no—
441C22—102no—
442C22—201no—
443C22—202no—
444C22C2×D5×#6711yescharacteristic
445C4—22no—
446C4—41no—
447C4—52no—
448C4—102no—
449C4—122no—
450C4—201no—
451C4—602no—
452C4D5×#23712yes—
453C3#1061337211yescharacteristic, complemented, Sylow
454C2—81no—
455C2—102no—
456C2—401no—
457C2D5×#93611yescharacteristic
458C2#1175531512yes—
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
prime radicalC3×#66002C2
hypercenter#124D3×D5
hypocenterC3×C5#3142
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. D5×#870C2semidirect
3. #11751157C2semidirect
4. C5×#5056C2semidirect
5. #11749330C2semidirect
6. #11749198C2semidirect
7. #11749084C2semidirect
8. #11748951C2semidirect
9. C4×#6649C2semidirect
10. #11746896C2semidirect
11. #11746891C2semidirect
91. #5056D5semidirect
386. C3×C5#3142semidirect
437. C5#83284semidirect
453. C3#10613372semidirect

Maximal subgroups

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

subgroupindex
C3×#660022
D5×#8702
#117511572
C5×#50562
#117493302
#117491982
#117490842
#117489512
C4×#66492
#117468962
#117468912
#106133723
#832845