Finite Group Databasebeta

← #14471533

Subgroups — #14471533

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#11752551C211yesmaximal, characteristic
2#11752490C211yesmaximal, characteristic, complemented
3#11750942C211yesmaximal, characteristic
4C5×#4830C211yesmaximal, characteristic, complemented
5C3×#65140C211yesmaximal, characteristic, complemented
6#11748028C212yesmaximal, complemented
7#11747867C212yesmaximal, complemented
8#11747791C212yesmaximal
9#11747789C212yesmaximal
10C4×#6658C211yesmaximal, characteristic
11#11746921C211yesmaximal, characteristic, complemented
12#10611656—31nomaximal, Hall
13C2×D15⋊Q8—21no—
14C2×#6706C2212yes—
15C4×D60C2211yescharacteristic
16#91758C2211yescharacteristic
17C4×C5×Dic6C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19C3×C4×Dic10C2211yescharacteristic
20#91469C2212yes—
21#91429—22no—
22#91428C2212yes—
23#91390—21no—
24#91389C2212yes—
25#91388—21no—
26#91343—22no—
27#91340C2212yes—
28Dic5×Dic6—21no—
29C2×#6658C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91100C2212yes—
32C5×Dic3⋊C8C2212yes—
33C5×C8×Dic3C2212yes—
34C4×C5×C3⋊C8C2211yescharacteristic
35C3×#3949C2212yes—
36C3×#3948C2212yes—
37#90987C2211yescharacteristic
38#90974C2212yes—
39#90974C2212yes—
40#90971C2211yescharacteristic
41#90968C2211yescharacteristic
42#81037—51nomaximal, Hall
43Q8×D20—31no—
44#65904—31no—
45C5×C8×Q8—31no—
46#65140—32no—
47#65140D311yescharacteristic, complemented
48#65130—31no—
49#65130—32no—
50C4×#677—31no—
51C4×#677—32no—
52#64970—31no—
53#64970—32no—
54C2×D60C2311yescharacteristic
55C2×C4×D15—21no—
56C2×Dic30C2312yes—
57C2×C5×Dic6D411yescharacteristic
58C2×C3×Dic10—21no—
59C2×C3×Dic10C2311yescharacteristic
60C2×#1204—22no—
61C2×#1200—22no—
62D15⋊Q8—44no—
63C2×C3×C5×C8C2312yes—
64C3×C42×C5C2311yescharacteristic
65#6714—21no—
66C4⋊Dic15—21no—
67C4⋊Dic15—21no—
68C4⋊Dic15C2311yescharacteristic
69#6706—24no—
70C5×C4⋊Dic3D411yescharacteristic
71C5×Dic3⋊C4D412yes—
72C4×C5×Dic3C2312yes—
73C2×C5×C3⋊C8C2311yescharacteristic
74C2×C5×C3⋊C8C2311yescharacteristic
75C3×C4⋊Dic5—21no—
76C3×C4⋊Dic5C2312yes—
77C3×C4⋊Dic5C2311yescharacteristic
78C3×#683—21no—
79C3×C4×Dic5—21no—
80Dic3⋊Dic5—22no—
81Dic3⋊Dic5—22no—
82Dic3⋊Dic5—22no—
83#6669—22no—
84#6667—22no—
85Dic3×Dic5—22no—
86#6658—22no—
87#5727—51no—
88#5567—51no—
89C3×#475—51no—
90#5093—51no—
91C4×#215—51no—
92#4854—52no—
93#4852—52no—
94#4841—51no—
95#4830D511yescharacteristic, complemented
96#4818—52no—
97#4792—52no—
98C2×Q8×D5—61no—
99C4×C5×Q8—31no—
100Q8×Dic5—61no—
101C2×#677—31no—
102C2×#677—32no—
103#4043—62no—
104#4043—61no—
105#4036—61no—
106#4036—62no—
107C4×D20—31no—
108C4×D20—32no—
109#4015—32no—
110#4015—32no—
111#4015—31no—
112#4015C2×D311yescharacteristic
113C4×Dic10—32no—
114C4×Dic10C2×D311yescharacteristic
115C5×C4⋊C8—32no—
116C5×C4⋊C8C2×D311yescharacteristic
117C4×C5×C8—32no—
118C4×C5×C8—31no—
119#3953—31no—
120#3949—31no—
121#3949C2×D312yes—
122#3948—31no—
123#3948—32no—
124#3948—32no—
125#3948—32no—
126#3948C2×D312yes—
127#3359—151noSylow
128C22×D15—21no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15—22no—
133C2×Dic15—21no—
134D60—21no—
135D60#4112yes—
136C4×D15—42no—
137Dic30—22no—
138Dic30—22no—
139C2×C5×Dic3C2×D412yes—
140C2×C5×Dic3C2×D412yes—
141C5×Dic6SD1614yescomplemented
142C2×C3×Dic5—21no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—21no—
145C3×Dic10—21no—
146C3×Dic10—21no—
147C3×Dic10—42no—
148#1204—44no—
149#1200—44no—
150C3×C5×C8—22no—
151C5×C3⋊C8—21no—
152C5×C3⋊C8—21no—
153C2×D3×Q8—101no—
154C3×C4⋊Q8—51no—
155C3×C4×Q8—51no—
156#946—101no—
157#944—52no—
158C2×#215—51no—
159C2×#204—52no—
160#896—102no—
161#893—52no—
162#889—102no—
163#888—52no—
164#887—52no—
165C4×D12—51no—
166#870—101no—
167#869—51no—
168C4×Dic6—101no—
169C4×Dic6C2×D511yescharacteristic
170C3×#106—52no—
171C3×C4⋊C8C2×D511yescharacteristic
172C3×#103—52no—
173#835—51no—
174#816—52no—
175Dic3⋊C8C2×D512yes—
176C8×Dic3C2×D512yes—
177#810—52no—
178#810—52no—
179#809—51no—
180#808—51no—
181C4×C3⋊C8C2×D511yescharacteristic
182C2×C5×Q8—31no—
183Q8×D5—124no—
184C2×D20—31no—
185C2×C4×D5—62no—
186C2×C4×D5—61no—
187C2×Dic10—21no—
188C2×Dic10—32no—
189C2×Dic10—62no—
190C2×Dic10C22×D311yescharacteristic
191C2×C5×C8—31no—
192C2×C5×C8—31no—
193C2×C5×C8C22×D312yes—
194C5×C4⋊C4—32no—
195C5×C4⋊C4—31no—
196C42×C5—32no—
197C42×C5C22×D311yescharacteristic
198#685—62no—
199#685—61no—
200C4⋊Dic5—21no—
201C4⋊Dic5—31no—
202C4⋊Dic5—62no—
203C4⋊Dic5—62no—
204C4⋊Dic5—62no—
205C4⋊Dic5—61no—
206C4⋊Dic5—61no—
207C4⋊Dic5C22×D312yes—
208C4⋊Dic5C22×D311yescharacteristic
209#683—21no—
210#683—62no—
211C4×Dic5—21no—
212C4×Dic5—62no—
213#677—64no—
214#677—62no—
215#557—151no—
216D4×Q8—151no—
217#487—152no—
218#487—151no—
219#475—51no—
220#475—152no—
221#461—152no—
222#461—151no—
223C8×Q8—31no—
224C4×SD16—152no—
225C4×SD16—151no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—22no—
228C2×D15—41no—
229C2×D15—41no—
230C3×C4×C5—21no—
231C3×C4×C5C2×SD1612yes—
232C3×C4×C5C2×#4111yescharacteristic
233C3×C4×C52−1+411yescharacteristic
234Dic15—42no—
235Dic15—41no—
236C3×Dic5—41no—
237C3×Dic5—42no—
238C3×Dic5—41no—
239C5×Dic3—22no—
240C5×Dic3C2×SD1614yes—
241C2×C3×Q8—51no—
242C2×C3×Q8—101no—
243D3×Q8—204no—
244C2×D12—51no—
245C2×C4×D3—101no—
246C2×C4×D3—102no—
247C2×Dic6—52no—
248C2×Dic6—102no—
249C2×Dic6D2011yescharacteristic
250C2×C3×C8C22×D512yes—
251C3×C4⋊C4—51no—
252C3×C4⋊C4—52no—
253C3×C4⋊C4—101no—
254C3×C4⋊C4—101no—
255C3×C42—101no—
256C3×C42C22×D511yescharacteristic
257#215—102no—
258(C2×D3)⋊C4—101no—
259(C2×D3)⋊C4—102no—
260C4⋊Dic3—51no—
261C4⋊Dic3—101no—
262C4⋊Dic3—101no—
263C4⋊Dic3D2011yescharacteristic
264Dic3⋊C4—102no—
265Dic3⋊C4—102no—
266Dic3⋊C4—102no—
267Dic3⋊C4—102no—
268Dic3⋊C4D2012yes—
269C4×Dic3—102no—
270C4×Dic3C22×D512yes—
271C2×C3⋊C8C22×D511yescharacteristic
272C2×C3⋊C8C22×D511yescharacteristic
273#204—104no—
274C22×D5—61no—
275C5×Q8—34no—
276C2×C4×C5—32no—
277C2×C4×C5—32no—
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5D3×D411yescharacteristic
280C2×C4×C5C23×D311yescharacteristic
281C2×Dic5—21no—
282C2×Dic5—21no—
283C2×Dic5—22no—
284C2×Dic5—62no—
285C2×Dic5—61no—
286D20—32no—
287D20—61no—
288C4×D5—124no—
289C4×D5—122no—
290Dic10—21no—
291Dic10—21no—
292Dic10—42no—
293Dic10—62no—
294Dic10—62no—
295Dic10—124no—
296C5×C8—22no—
297C5×C8—61no—
298C5×C8—61no—
299C22×Q8—301no—
300C2×SD16—151no—
301C2×SD16—152no—
302C4⋊Q8—51no—
303C4⋊Q8—152no—
304C4⋊Q8—152no—
305C4⋊Q8—151no—
306#125—301no—
307#125—302no—
308C22⋊Q8—302no—
309C22⋊Q8—301no—
310C4×Q8—31no—
311C4×Q8—51no—
312C4×Q8—152no—
313C4×Q8—301no—
314C4×D4—152no—
315C4×D4—151no—
316#106—52no—
317#106—151no—
318C4⋊C8—32no—
319C4⋊C8D3×D511yescharacteristic
320#103—52no—
321#103—152no—
322#103—152no—
323#103—151no—
324#103—152no—
325#102—151no—
326C4×C8—32no—
327C4×C8—31no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C22×SD1611yescharacteristic
330C2×C3×C5#57811yescharacteristic
331D15—42no—
332C22×D3—101no—
333C3×Q8—101no—
334C3×Q8—101no—
335C3×Q8—202no—
336C2×C3×C4—101no—
337C2×C3×C4—101no—
338C2×C3×C4—102no—
339C2×C3×C4C2×D2011yescharacteristic
340C2×C3×C4C2×D2011yescharacteristic
341C2×C3×C4C23×D511yescharacteristic
342C2×Dic3—102no—
343C2×Dic3—101no—
344C2×Dic3C2×D2012yes—
345C2×Dic3C2×D2012yes—
346D12—52no—
347D12—101no—
348C4×D3—202no—
349C4×D3—204no—
350Dic6—102no—
351Dic6—102no—
352Dic6—204no—
353Dic6#67714yescomplemented
354C3×C8—22no—
355C3⋊C8—21no—
356C3⋊C8—21no—
357C22×C5C2×D3×D411yescharacteristic
358C2×D5—62no—
359C2×D5—121no—
360C2×D5—121no—
361C4×C5—21no—
362C4×C5—34no—
363C4×C5—62no—
364C4×C5D3×SD1612yes—
365C4×C5#100711yescharacteristic
366C4×C5D3×#4111yescharacteristic
367Dic5—41no—
368Dic5—42no—
369Dic5—41no—
370Dic5—122no—
371Dic5—121no—
372C2×Q8—31no—
373C2×Q8—51no—
374C2×Q8—101no—
375C2×Q8—152no—
376C2×Q8—302no—
377C2×Q8—604no—
378C2×D4—151no—
379C22×C4—302no—
380C22×C4—301no—
381SD16—304no—
382SD16—302no—
383C2×C8—31no—
384C2×C8—31no—
385C2×C8C2×D3×D512yes—
386C4⋊C4—32no—
387C4⋊C4—31no—
388C4⋊C4—51no—
389C4⋊C4—52no—
390C4⋊C4—101no—
391C4⋊C4—101no—
392C4⋊C4—151no—
393C4⋊C4—302no—
394C4⋊C4—302no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4—301no—
398C4⋊C4—301no—
399C22⋊C4—302no—
400C22⋊C4—301no—
401C42—32no—
402C42—101no—
403C42—302no—
404C42C2×D3×D511yescharacteristic
405C3×C5#335911yescharacteristic, complemented, Hall
406C22×C3C22×D2011yescharacteristic
407C2×D3—102no—
408C2×D3—201no—
409C2×D3—201no—
410C3×C4—21no—
411C3×C4—202no—
412C3×C4—201no—
413C3×C4—201no—
414C3×C4C2×#67712yes—
415C3×C4#414711yescharacteristic
416C3×C4D5×#4111yescharacteristic
417Dic3—22no—
418Dic3—201no—
419Dic3—202no—
420Dic3C2×#67714yes—
421C2×C5#563311yescharacteristic
422C2×C5C2×D3×SD1611yescharacteristic
423C2×C5#577911yescharacteristic
424D5—122no—
425C23—301no—
426Q8—34no—
427Q8—101no—
428Q8—101no—
429Q8—202no—
430Q8—302no—
431Q8—302no—
432Q8—604no—
433D4—152no—
434D4—301no—
435C2×C4—32no—
436C2×C4—32no—
437C2×C4—101no—
438C2×C4—101no—
439C2×C4—102no—
440C2×C4—302no—
441C2×C4—301no—
442C2×C4—604no—
443C2×C4—602no—
444C2×C4D3×D2011yescharacteristic
445C2×C4D3×D2011yescharacteristic
446C2×C4C22×D3×D511yescharacteristic
447C8—22no—
448C8—61no—
449C8—61no—
450C2×C3#6591011yescharacteristic
451C2×C3C22×#67711yescharacteristic
452C2×C3#6608711yescharacteristic
453D3—202no—
454C5#8103711yescharacteristic, complemented, Sylow
455C22—302no—
456C22—601no—
457C22—601no—
458C22C2×D3×D2011yescharacteristic
459C4—21no—
460C4—34no—
461C4—62no—
462C4—201no—
463C4—201no—
464C4—202no—
465C4—602no—
466C4—601no—
467C4D3×#67712yes—
468C4#9202411yescharacteristic
469C4#9202911yescharacteristic
470C3#1061165611yescharacteristic, complemented, Sylow
471C2—602no—
472C2#1175334211yescharacteristic
473C2C2×D3×#67711yescharacteristic
474C2#1175404211yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC2×D60C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3359
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11752490C2semidirect
4. C5×#4830C2semidirect
5. C3×#65140C2semidirect
6. #11748028C2semidirect
7. #11747867C2semidirect
11. #11746921C2semidirect
47. #65140D3semidirect
95. #4830D5semidirect
141. C5×Dic6SD16semidirect
353. Dic6#677semidirect
405. C3×C5#3359semidirect
454. C5#81037semidirect
470. C3#10611656semidirect

Maximal subgroups

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

subgroupindex
#117525512
#117524902
#117509422
C5×#48302
C3×#651402
#117480282
#117478672
#117477912
#117477892
C4×#66582
#117469212
#106116563
#810375