Finite Group Databasebeta

← #14471540

Subgroups — #14471540

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756326C211yesmaximal, characteristic, complemented
2#11752552C211yesmaximal, characteristic
3C5×#5020C211yesmaximal, characteristic, complemented
4C3×C4×#688C211yesmaximal, characteristic
5#11749229C212yesmaximal
6#11749189C212yesmaximal, complemented
7#11747227C212yesmaximal
8#11747181C212yesmaximal, complemented
9#11747062C211yesmaximal, characteristic
10#11746930C211yesmaximal, characteristic, complemented
11#11746851C211yesmaximal, characteristic, complemented
12#10612768—31nomaximal, Hall
13C2×D5×Dic6—21no—
14C3×C4×C5×Q8C2211yescharacteristic
15#91833C2212yes—
16#91778—22no—
17#91776C2212yes—
18#91759—21no—
19#91758C2211yescharacteristic
20C4×Dic30—21no—
21C4×Dic30C2211yescharacteristic
22C5×#869C2211yescharacteristic
23C2×C3×#688C2211yescharacteristic
24C3×C4×D20C2211yescharacteristic
25#91470C2212yes—
26#91434C2212yes—
27#91430—22no—
28#91359—21no—
29C2×#6657C2212yes—
30C5×#835C2212yes—
31C5×#808C2212yes—
32C5×C4⋊(C3⋊C8)C2211yescharacteristic
33C3×#3967C2211yescharacteristic
34C3×#3941C2211yescharacteristic
35C3×#3940C2211yescharacteristic
36C3×C4×#168C2211yescharacteristic
37#90983C2212yes—
38#90975C2212yes—
39#90975C2212yes—
40#90974C2212yes—
41#90951C2212yes—
42#79619—51nomaximal, Hall
43#66061—31no—
44#65901—31no—
45C5×#475—31no—
46#65382—31no—
47C4×#688D311yescharacteristic
48#65143—32no—
49#65141—32no—
50#65130—31no—
51#65119—31no—
52#65107—32no—
53#65081—32no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×Dic30D411yescharacteristic
56C2×Dic30C2312yes—
57C2×C5×Dic6—21no—
58C2×C3×D20C2311yescharacteristic
59C2×C3×C4×D5—21no—
60C2×#1204—22no—
61C2×D5×Dic3—22no—
62D5×Dic6—44no—
63C3×C5×C4⋊C4—21no—
64C3×C5×C4⋊C4C2311yescharacteristic
65C3×C42×C5—21no—
66C3×C42×C5C2311yescharacteristic
67C4⋊Dic15—21no—
68C4⋊Dic15—21no—
69C4⋊Dic15D411yescharacteristic
70#6712—22no—
71#6712—22no—
72#6712—22no—
73#6712D412yes—
74C4×Dic15—22no—
75C4×Dic15C2312yes—
76C5×C4⋊Dic3—21no—
77C5×C4⋊Dic3C2312yes—
78C2×C5×C3⋊C8C2312yes—
79C3×#688—22no—
80C3×#685—21no—
81C3×C4⋊Dic5C2311yescharacteristic
82C2×C3×#168C2311yescharacteristic
83C2×C3×#168C2311yescharacteristic
84#6669—22no—
85#6665—22no—
86#6657—24no—
87#5567—51no—
88D4×Dic6—51no—
89C3×C4×SD16—51no—
90#5162—52no—
91#5020D511yescharacteristic, complemented
92#5019—51no—
93#4854—52no—
94#4792—52no—
95#4758—52no—
96#4681—51no—
97C8×Dic6—51no—
98C2×Q8×D5—61no—
99C5×C4⋊Q8—31no—
100C4×C5×Q8C2×D311yescharacteristic
101#4092—61no—
102#4090—32no—
103C2×#688C2×D311yescharacteristic
104C2×#677—32no—
105#4042—62no—
106#4039—32no—
107#4035—62no—
108#4034—32no—
109#4033—32no—
110C4×D20C2×D311yescharacteristic
111#4016—61no—
112#4015—31no—
113C4×Dic10—31no—
114C4×Dic10—61no—
115C5×#106—32no—
116C5×C4⋊C8—31no—
117C5×#103—32no—
118#3967C2×D311yescharacteristic
119#3948—32no—
120#3946—32no—
121C8×Dic5—32no—
122#3942—32no—
123#3942—32no—
124#3941C2×D311yescharacteristic
125#3940C2×D311yescharacteristic
126C4×#168C2×D311yescharacteristic
127#3359—151noSylow
128C22×C3×D5—21no—
129C3×C5×Q8—21no—
130C3×C5×Q8—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—22no—
137C2×Dic15C2×D412yes—
138C2×Dic15C2×D412yes—
139Dic30—22no—
140Dic30—22no—
141Dic30SD1614yescomplemented
142C2×C5×Dic3—22no—
143C5×Dic6—42no—
144C2×C3×Dic5—21no—
145C3×D20—21no—
146C3×D20#4112yes—
147C3×C4×D5—42no—
148#1204—44no—
149D5×Dic3—44no—
150C3×#168—21no—
151C3×#168—21no—
152C5×C3⋊C8—22no—
153C22×Dic6—101no—
154C2×C3×SD16—51no—
155C3×C4×Q8C2×D511yescharacteristic
156C3×C4×D4—51no—
157#944—52no—
158D4×Dic3—52no—
159C2×#214—52no—
160#924—101no—
161#889—102no—
162#888—52no—
163#887—52no—
164#878—102no—
165#870—101no—
166#869—51no—
167#869C2×D511yescharacteristic
168C4×Dic6—51no—
169C4×Dic6—101no—
170C3×#106—51no—
171C3×#103—51no—
172C3×#102—51no—
173C3×C4×C8—51no—
174#835C2×D512yes—
175#816—52no—
176#816—52no—
177Dic3⋊C8—52no—
178C8×Dic3—52no—
179#810—52no—
180#808C2×D512yes—
181C4⋊(C3⋊C8)C2×D511yescharacteristic
182C2×C5×Q8—61no—
183C2×C5×Q8C22×D311yescharacteristic
184Q8×D5—124no—
185C2×D20C22×D311yescharacteristic
186C2×C4×D5—21no—
187C2×C4×D5—62no—
188C2×Dic10—31no—
189C2×Dic10—32no—
190C2×Dic10—62no—
191C2×C5×C8—32no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4—32no—
194C5×C4⋊C4—61no—
195C5×C4⋊C4C22×D311yescharacteristic
196C42×C5—21no—
197C42×C5C22×D311yescharacteristic
198#688—22no—
199#685—21no—
200#685—62no—
201C4⋊Dic5—31no—
202C4⋊Dic5—61no—
203C4⋊Dic5—61no—
204C4⋊Dic5C22×D311yescharacteristic
205#683—32no—
206#683—62no—
207#683—62no—
208#683—62no—
209#683—62no—
210C4×Dic5—32no—
211C4×Dic5—62no—
212C2×#168C22×D311yescharacteristic
213C2×#168C22×D311yescharacteristic
214#677—64no—
215#557—151no—
216D4×Q8—151no—
217#487—151no—
218#487—152no—
219#475—31no—
220#475—152no—
221#461—152no—
222#461—151no—
223C8×Q8—151no—
224C4×SD16—51no—
225C4×SD16—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×C3×D5—22no—
228C2×C3×D5—41no—
229C2×C3×D5—41no—
230C3×C4×C5—21no—
231C3×C4×C5—41no—
232C3×C4×C5—41no—
233C3×C4×C5C2×SD1612yes—
234C3×C4×C5C2×#4111yescharacteristic
235C3×C4×C52−1+411yescharacteristic
236Dic15—22no—
237Dic15—42no—
238Dic15C2×SD1614yes—
239C3×Dic5—41no—
240C5×Dic3—42no—
241C2×C3×Q8C22×D511yescharacteristic
242C2×C3×D4—51no—
243C22×C3×C4—101no—
244C22×Dic3—102no—
245C2×Dic6—21no—
246C2×Dic6—51no—
247C2×Dic6—52no—
248C2×Dic6—102no—
249C2×Dic6—204no—
250C3×SD16—102no—
251C2×C3×C8—51no—
252C2×C3×C8—51no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—51no—
255C3×C4⋊C4C22×D511yescharacteristic
256C3×C22⋊C4—101no—
257C3×C42—21no—
258C3×C42C22×D511yescharacteristic
259#217—102no—
260#214—104no—
261C4⋊Dic3—21no—
262C4⋊Dic3—51no—
263C4⋊Dic3—101no—
264C4⋊Dic3—101no—
265C4⋊Dic3C22×D512yes—
266Dic3⋊C4—52no—
267Dic3⋊C4—102no—
268Dic3⋊C4—102no—
269Dic3⋊C4—102no—
270Dic3⋊C4—102no—
271C4×Dic3—52no—
272C4×Dic3—102no—
273C2×C3⋊C8C22×D512yes—
274C22×D5—21no—
275C5×Q8—21no—
276C5×Q8—21no—
277C5×Q8—122no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—62no—
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5D3×D411yescharacteristic
283C2×C4×C5C23×D311yescharacteristic
284C2×Dic5—21no—
285C2×Dic5—32no—
286C2×Dic5—32no—
287C2×Dic5—62no—
288D20—21no—
289D20#23512yes—
290C4×D5—42no—
291C4×D5—124no—
292Dic10—34no—
293Dic10—62no—
294Dic10—62no—
295Dic10—124no—
296C5×C8—62no—
297#168—21no—
298#168—21no—
299C22×Q8—301no—
300C2×SD16—51no—
301C2×SD16—152no—
302C4⋊Q8—31no—
303C4⋊Q8—152no—
304C4⋊Q8—152no—
305C4⋊Q8—151no—
306#125—301no—
307#125—302no—
308C22⋊Q8—302no—
309C22⋊Q8—301no—
310C4×Q8—151no—
311C4×Q8—152no—
312C4×Q8—301no—
313C4×Q8D3×D511yescharacteristic
314C4×D4—51no—
315C4×D4—152no—
316#106—32no—
317#106—51no—
318C4⋊C8—31no—
319C4⋊C8—152no—
320#103—32no—
321#103—51no—
322#103—152no—
323#103—152no—
324#103—152no—
325#102—51no—
326C4×C8—51no—
327C4×C8—152no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C22×SD1611yescharacteristic
330C2×C3×C5#57811yescharacteristic
331C3×D5—42no—
332C23×C3—101no—
333C3×Q8—21no—
334C3×Q8—21no—
335C3×D4—52no—
336C3×D4—101no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—101no—
340C2×C3×C4—202no—
341C2×C3×C4D4×D511yescharacteristic
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4C23×D511yescharacteristic
344C2×Dic3—22no—
345C2×Dic3—52no—
346C2×Dic3—52no—
347C2×Dic3—102no—
348C2×Dic3—204no—
349Dic6—42no—
350Dic6—54no—
351Dic6—102no—
352Dic6—102no—
353Dic6—204no—
354C3×C8—101no—
355C3×C8—101no—
356C3⋊C8—22no—
357C22×C5C2×D3×D411yescharacteristic
358C2×D5—22no—
359C2×D5—41no—
360C2×D5—41no—
361C4×C5—21no—
362C4×C5—41no—
363C4×C5—41no—
364C4×C5—122no—
365C4×C5D3×SD1612yes—
366C4×C5C2×#23511yescharacteristic
367C4×C5#101011yescharacteristic
368Dic5—34no—
369Dic5—41no—
370Dic5—62no—
371Dic5—122no—
372C2×Q8—61no—
373C2×Q8—151no—
374C2×Q8—152no—
375C2×Q8—302no—
376C2×Q8—604no—
377C2×Q8C2×D3×D511yescharacteristic
378C2×D4—51no—
379C22×C4—101no—
380C22×C4—302no—
381SD16—102no—
382SD16—304no—
383C2×C8—32no—
384C2×C8—51no—
385C2×C8—51no—
386C4⋊C4—21no—
387C4⋊C4—32no—
388C4⋊C4—51no—
389C4⋊C4—61no—
390C4⋊C4—152no—
391C4⋊C4—151no—
392C4⋊C4—302no—
393C4⋊C4—302no—
394C4⋊C4—302no—
395C4⋊C4—302no—
396C4⋊C4—301no—
397C4⋊C4—301no—
398C4⋊C4C2×D3×D511yescharacteristic
399C22⋊C4—101no—
400C22⋊C4—302no—
401C42—21no—
402C42—152no—
403C42—302no—
404C42C2×D3×D511yescharacteristic
405C3×C5#335911yescharacteristic, complemented, Hall
406C22×C3—102no—
407C22×C3—201no—
408C22×C3—201no—
409C22×C3C2×D4×D511yescharacteristic
410C3×C4—21no—
411C3×C4—41no—
412C3×C4—41no—
413C3×C4—201no—
414C3×C4D5×SD1612yes—
415C3×C4#414711yescharacteristic
416C3×C4D5×#4111yescharacteristic
417Dic3—42no—
418Dic3—54no—
419Dic3—102no—
420Dic3—202no—
421C2×C5#555211yescharacteristic
422C2×C5C2×D3×SD1611yescharacteristic
423C2×C5#577111yescharacteristic
424D5—42no—
425C23—101no—
426Q8—21no—
427Q8—21no—
428Q8—122no—
429Q8—154no—
430Q8—302no—
431Q8—302no—
432Q8—604no—
433D4—52no—
434D4—101no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—62no—
438C2×C4—101no—
439C2×C4—152no—
440C2×C4—152no—
441C2×C4—202no—
442C2×C4—302no—
443C2×C4—604no—
444C2×C4#679011yescharacteristic
445C2×C4#679011yescharacteristic
446C2×C4C22×D3×D511yescharacteristic
447C8—62no—
448C8—101no—
449C8—101no—
450C2×C3—202no—
451C2×C3#6596711yescharacteristic
452C2×C3C2×D5×SD1611yescharacteristic
453C2×C3#6611311yescharacteristic
454C5#7961911yescharacteristic, complemented, Sylow
455C22—102no—
456C22—201no—
457C22—201no—
458C22C2×#679011yescharacteristic
459C4—21no—
460C4—41no—
461C4—41no—
462C4—122no—
463C4—154no—
464C4—201no—
465C4—302no—
466C4—602no—
467C4#9150512yes—
468C4#9200011yescharacteristic
469C4D5×#23511yescharacteristic
470C3#1061276811yescharacteristic, complemented, Sylow
471C2—202no—
472C2#1175436711yescharacteristic
473C2C2×#9150511yescharacteristic
474C2#1175535011yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D20C23
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3359
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #11756326C2semidirect
3. C5×#5020C2semidirect
6. #11749189C2semidirect
8. #11747181C2semidirect
10. #11746930C2semidirect
11. #11746851C2semidirect
91. #5020D5semidirect
141. Dic30SD16semidirect
405. C3×C5#3359semidirect
454. C5#79619semidirect
470. C3#10612768semidirect

Maximal subgroups

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

subgroupindex
#117563262
#117525522
C5×#50202
C3×C4×#6882
#117492292
#117491892
#117472272
#117471812
#117470622
#117469302
#117468512
#106127683
#796195