Finite Group Databasebeta

← #14471532

Subgroups — #14471532

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
1Dic6×D20C211yesmaximal, characteristic
2#11752482C211yesmaximal, characteristic, complemented
3#11750952C211yesmaximal, characteristic, complemented
4C5×#4830C211yesmaximal, characteristic, complemented
5C3×#65130C211yesmaximal, characteristic
6#11748028C212yesmaximal, complemented
7#11747861C212yesmaximal, complemented
8Dic3×#677C212yesmaximal
9#11747753C212yesmaximal
10C4×#6657C211yesmaximal, characteristic
11#11746920C211yesmaximal, characteristic, complemented
12#10611656—31nomaximal, Hall
13C2×D5×Dic6—21no—
14#91758C2211yescharacteristic
15C4×Dic30C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C2×C3×#677C2212yes—
18C3×C4×D20C2211yescharacteristic
19C3×#4015C2211yescharacteristic
20#91469C2212yes—
21Dic3×D20C2212yes—
22#91422—22no—
23#91389C2212yes—
24#91384—21no—
25#91360—21no—
26#91346—22no—
27#91344—21no—
28Dic3×Dic10C2212yes—
29C2×#6657C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91101C2212yes—
32#91100C2212yes—
33C5×Dic3⋊C8C2212yes—
34C5×C8×Dic3C2212yes—
35C4×C5×C3⋊C8C2211yescharacteristic
36C3×#3948C2212yes—
37#90987C2211yescharacteristic
38#90974C2211yescharacteristic
39#90971C2212yes—
40#90971C2212yes—
41#90965C2211yescharacteristic
42#80414—51nomaximal, Hall
43Q8×D20—31no—
44#65904—31no—
45C5×C8×Q8—31no—
46#65140—31no—
47#65140—32no—
48#65130—32no—
49#65130D311yescharacteristic
50C4×#677—32no—
51C4×#677—31no—
52#64970—31no—
53#64970—32no—
54C2×Dic30—21no—
55C2×Dic30C2311yescharacteristic
56C2×C5×Dic6D411yescharacteristic
57C2×C3×D20C2311yescharacteristic
58C2×C3×C4×D5—21no—
59C2×C3×Dic10C2312yes—
60C2×#1204—22no—
61C2×D5×Dic3—22no—
62D5×Dic6—44no—
63C2×C3×C5×C8C2312yes—
64C3×C42×C5C2311yescharacteristic
65C4⋊Dic15—21no—
66C4⋊Dic15C2312yes—
67C4⋊Dic15C2311yescharacteristic
68#6712—21no—
69C4×Dic15—21no—
70C5×C4⋊Dic3D411yescharacteristic
71C5×Dic3⋊C4D412yes—
72C4×C5×Dic3C2312yes—
73C2×C5×C3⋊C8C2311yescharacteristic
74C2×C5×C3⋊C8C2311yescharacteristic
75C3×#685—21no—
76C3×C4⋊Dic5—21no—
77C3×C4⋊Dic5—21no—
78C3×C4⋊Dic5C2311yescharacteristic
79C3×#677—24no—
80Dic3⋊Dic5—22no—
81Dic3⋊Dic5—22no—
82Dic3⋊Dic5—22no—
83#6668—22no—
84#6665—22no—
85Dic3×Dic5—22no—
86#6657—22no—
87#5721—51no—
88D4×Dic6—51no—
89C3×#461—51no—
90#5162—52no—
91Dic3×SD16—52no—
92#5079—51no—
93C4×#214—51no—
94#4851—51no—
95#4830D511yescharacteristic, complemented
96#4792—52no—
97#4791—52no—
98C2×Q8×D5—61no—
99C4×C5×Q8—31no—
100Q8×Dic5—61no—
101C2×#677—31no—
102C2×#677C2×D312yes—
103#4043—62no—
104#4043—61no—
105#4036—62no—
106#4036—61no—
107C4×D20—32no—
108C4×D20C2×D311yescharacteristic
109#4015—31no—
110#4015—32no—
111#4015—32no—
112#4015C2×D311yescharacteristic
113C4×Dic10—32no—
114C4×Dic10—31no—
115C5×C4⋊C8—32no—
116C5×C4⋊C8C2×D311yescharacteristic
117C4×C5×C8—32no—
118C4×C5×C8—31no—
119#3953—31no—
120#3949—32no—
121#3949—31no—
122#3948—32no—
123#3948—32no—
124#3948—32no—
125#3948—31no—
126#3948C2×D312yes—
127#3359—151noSylow
128C22×C3×D5—21no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15—21no—
133C2×Dic15—22no—
134C2×Dic15—21no—
135Dic30—21no—
136Dic30—21no—
137Dic30—42no—
138C2×C5×Dic3C2×D412yes—
139C2×C5×Dic3C2×D412yes—
140C5×Dic6SD1614yescomplemented
141C2×C3×Dic5—22no—
142C2×C3×Dic5—21no—
143C3×D20—21no—
144C3×D20#4112yes—
145C3×C4×D5—42no—
146C3×Dic10—22no—
147C3×Dic10—22no—
148#1204—44no—
149D5×Dic3—44no—
150C3×C5×C8—22no—
151C5×C3⋊C8—21no—
152C5×C3⋊C8—21no—
153C22×Dic6—101no—
154C2×C3×SD16—52no—
155C3×C4⋊Q8—51no—
156C3×C4×D4—51no—
157Q8×Dic3—52no—
158#944—52no—
159D4×Dic3—52no—
160C2×#214—51no—
161#924—101no—
162#890—101no—
163#889—102no—
164#888—52no—
165#887—101no—
166#878—102no—
167#869—51no—
168C4×Dic6—51no—
169C4×Dic6C2×D511yescharacteristic
170C3×C4⋊C8C2×D511yescharacteristic
171C3×#103—52no—
172#835—52no—
173#835—52no—
174#832—51no—
175#817—52no—
176#816—52no—
177Dic3⋊C8C2×D512yes—
178C8×Dic3C2×D512yes—
179#810—51no—
180#808—51no—
181C4×C3⋊C8C2×D511yescharacteristic
182C2×C5×Q8—31no—
183Q8×D5—124no—
184C2×D20C22×D311yescharacteristic
185C2×C4×D5—21no—
186C2×C4×D5—62no—
187C2×Dic10—31no—
188C2×Dic10—62no—
189C2×Dic10—61no—
190C2×Dic10C22×D312yes—
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—21no—
199#685—62no—
200C4⋊Dic5—21no—
201C4⋊Dic5—21no—
202C4⋊Dic5—32no—
203C4⋊Dic5—31no—
204C4⋊Dic5—62no—
205C4⋊Dic5—62no—
206C4⋊Dic5—62no—
207C4⋊Dic5—61no—
208C4⋊Dic5C22×D311yescharacteristic
209#683—62no—
210#683—61no—
211C4×Dic5—62no—
212C4×Dic5—61no—
213#677—24no—
214#677—62no—
215#557—151no—
216D4×Q8—151no—
217#487—152no—
218#487—151no—
219#475—152no—
220#475—151no—
221#461—51no—
222#461—152no—
223C8×Q8—31no—
224C4×SD16—151no—
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×C5C2×SD1612yes—
232C3×C4×C5C2×#4111yescharacteristic
233C3×C4×C52−1+411yescharacteristic
234Dic15—41no—
235Dic15—42no—
236Dic15—41no—
237C3×Dic5—42no—
238C3×Dic5—41no—
239C5×Dic3—22no—
240C5×Dic3C2×SD1614yes—
241C2×C3×Q8—52no—
242C2×C3×D4—51no—
243C22×C3×C4—101no—
244C22×Dic3—102no—
245C2×Dic6—51no—
246C2×Dic6—101no—
247C2×Dic6—102no—
248C2×Dic6—204no—
249C2×Dic6D2011yescharacteristic
250C3×SD16—104no—
251C2×C3×C8C22×D512yes—
252C3×C4⋊C4—51no—
253C3×C4⋊C4—101no—
254C3×C4⋊C4—101no—
255C3×C22⋊C4—101no—
256C3×C42C22×D511yescharacteristic
257#217—102no—
258#214—102no—
259C4⋊Dic3—51no—
260C4⋊Dic3—52no—
261C4⋊Dic3—101no—
262C4⋊Dic3—102no—
263C4⋊Dic3D2011yescharacteristic
264Dic3⋊C4—101no—
265Dic3⋊C4—102no—
266Dic3⋊C4—102no—
267Dic3⋊C4—102no—
268Dic3⋊C4D2012yes—
269C4×Dic3—101no—
270C4×Dic3—102no—
271C4×Dic3C22×D512yes—
272C2×C3⋊C8C22×D511yescharacteristic
273C2×C3⋊C8C22×D511yescharacteristic
274C22×D5—21no—
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—22no—
282C2×Dic5—21no—
283C2×Dic5—61no—
284C2×Dic5—61no—
285C2×Dic5—62no—
286D20—21no—
287D20#23712yes—
288C4×D5—42no—
289C4×D5—124no—
290Dic10—22no—
291Dic10—22no—
292Dic10—61no—
293Dic10—61no—
294Dic10—124no—
295Dic10—122no—
296C5×C8—22no—
297C5×C8—61no—
298C5×C8—61no—
299C22×Q8—301no—
300C2×SD16—52no—
301C2×SD16—151no—
302C4⋊Q8—51no—
303C4⋊Q8—152no—
304C4⋊Q8—152no—
305C4⋊Q8—151no—
306#125—302no—
307#125—301no—
308C22⋊Q8—302no—
309C22⋊Q8—301no—
310C4×Q8—31no—
311C4×Q8—152no—
312C4×Q8—151no—
313C4×Q8—301no—
314C4×D4—51no—
315C4×D4—152no—
316#106—151no—
317#106—152no—
318C4⋊C8—32no—
319C4⋊C8D3×D511yescharacteristic
320#103—52no—
321#103—151no—
322#103—152no—
323#103—152no—
324#103—152no—
325#102—151no—
326C4×C8—32no—
327C4×C8—31no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C22×SD1611yescharacteristic
330C2×C3×C5#57811yescharacteristic
331C3×D5—42no—
332C23×C3—101no—
333C3×Q8—102no—
334C3×Q8—102no—
335C3×D4—52no—
336C3×D4—101no—
337C2×C3×C4—102no—
338C2×C3×C4—101no—
339C2×C3×C4—202no—
340C2×C3×C4C2×D2011yescharacteristic
341C2×C3×C4C2×D2011yescharacteristic
342C2×C3×C4C23×D511yescharacteristic
343C2×Dic3—101no—
344C2×Dic3—101no—
345C2×Dic3—102no—
346C2×Dic3—204no—
347C2×Dic3C2×D2012yes—
348C2×Dic3C2×D2012yes—
349Dic6—101no—
350Dic6—101no—
351Dic6—202no—
352Dic6—204no—
353Dic6#67714yescomplemented
354C3×C8—22no—
355C3⋊C8—21no—
356C3⋊C8—21no—
357C22×C5C2×D3×D411yescharacteristic
358C2×D5—22no—
359C2×D5—41no—
360C2×D5—41no—
361C4×C5—21no—
362C4×C5—34no—
363C4×C5—62no—
364C4×C5D3×SD1612yes—
365C4×C5C2×#23711yescharacteristic
366C4×C5#101011yescharacteristic
367Dic5—41no—
368Dic5—42no—
369Dic5—122no—
370Dic5—121no—
371Dic5—121no—
372C2×Q8—31no—
373C2×Q8—52no—
374C2×Q8—151no—
375C2×Q8—302no—
376C2×Q8—301no—
377C2×Q8—604no—
378C2×D4—51no—
379C22×C4—101no—
380C22×C4—302no—
381SD16—104no—
382SD16—302no—
383C2×C8—31no—
384C2×C8—31no—
385C2×C8C2×D3×D512yes—
386C4⋊C4—32no—
387C4⋊C4—31no—
388C4⋊C4—51no—
389C4⋊C4—101no—
390C4⋊C4—101no—
391C4⋊C4—151no—
392C4⋊C4—152no—
393C4⋊C4—302no—
394C4⋊C4—302no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4—301no—
398C4⋊C4—301no—
399C22⋊C4—101no—
400C22⋊C4—302no—
401C42—32no—
402C42—302no—
403C42—301no—
404C42C2×D3×D511yescharacteristic
405C3×C5#335911yescharacteristic, complemented, Hall
406C22×C3—102no—
407C22×C3—201no—
408C22×C3—201no—
409C22×C3C22×D2011yescharacteristic
410C3×C4—21no—
411C3×C4—201no—
412C3×C4—202no—
413C3×C4C2×#67712yes—
414C3×C4#414711yescharacteristic
415C3×C4D5×#4111yescharacteristic
416Dic3—22no—
417Dic3—202no—
418Dic3—201no—
419Dic3—201no—
420Dic3C2×#67714yes—
421C2×C5#559811yescharacteristic
422C2×C5C2×D3×SD1611yescharacteristic
423C2×C5#577911yescharacteristic
424D5—42no—
425C23—101no—
426Q8—34no—
427Q8—102no—
428Q8—102no—
429Q8—301no—
430Q8—301no—
431Q8—604no—
432Q8—602no—
433D4—52no—
434D4—101no—
435C2×C4—32no—
436C2×C4—32no—
437C2×C4—102no—
438C2×C4—101no—
439C2×C4—202no—
440C2×C4—301no—
441C2×C4—301no—
442C2×C4—302no—
443C2×C4—604no—
444C2×C4D3×D2011yescharacteristic
445C2×C4D3×D2011yescharacteristic
446C2×C4C22×D3×D511yescharacteristic
447C8—22no—
448C8—61no—
449C8—61no—
450C2×C3—202no—
451C2×C3#6591011yescharacteristic
452C2×C3C22×#67711yescharacteristic
453C2×C3#6608711yescharacteristic
454C5#8041411yescharacteristic, complemented, Sylow
455C22—102no—
456C22—201no—
457C22—201no—
458C22C2×D3×D2011yescharacteristic
459C4—21no—
460C4—34no—
461C4—62no—
462C4—202no—
463C4—201no—
464C4—601no—
465C4—601no—
466C4—602no—
467C4D3×#67712yes—
468C4D5×#23711yescharacteristic
469C4#9202811yescharacteristic
470C3#1061165611yescharacteristic, complemented, Sylow
471C2—202no—
472C2#1175343911yescharacteristic
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×C3×D20C23
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. #11752482C2semidirect
3. #11750952C2semidirect
4. C5×#4830C2semidirect
6. #11748028C2semidirect
7. #11747861C2semidirect
11. #11746920C2semidirect
95. #4830D5semidirect
140. C5×Dic6SD16semidirect
353. Dic6#677semidirect
405. C3×C5#3359semidirect
454. C5#80414semidirect
470. C3#10611656semidirect

Maximal subgroups

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

subgroupindex
Dic6×D202
#117524822
#117509522
C5×#48302
C3×#651302
#117480282
#117478612
Dic3×#6772
#117477532
C4×#66572
#117469202
#106116563
#804145