Finite Group Databasebeta

← #14471565

Subgroups — #14471565

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#11756486C211yesmaximal, characteristic
2#11752481C211yesmaximal, characteristic, complemented
3C5×#5094C211yesmaximal, characteristic, complemented
4C3×#65382C211yesmaximal, characteristic, complemented
5#11747428C212yesmaximal, complemented
6#11747426C212yesmaximal
7#11747304C212yesmaximal, complemented
8#11747272C212yesmaximal
9#11747085C211yesmaximal, characteristic
10C4×#6660C211yesmaximal, characteristic
11#11746851C211yesmaximal, characteristic, complemented
12#10612768—31nomaximal, Hall
13C2×Q8×D15—21no—
14C3×C5×C4⋊Q8C2211yescharacteristic
15#91835—21no—
16#91785—22no—
17#91782C2212yes—
18#91777C2212yes—
19C4×D60C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C4×C5×Dic6C2211yescharacteristic
22C3×#4015C2211yescharacteristic
23#91385C2212yes—
24#91381—21no—
25#91340—21no—
26#91339—22no—
27#91331C2212yes—
28C2×#6660C2211yescharacteristic
29C2×#6658C2212yes—
30C5×#810C2212yes—
31C5×#808C2212yes—
32C5×C4⋊(C3⋊C8)C2211yescharacteristic
33C3×#3942C2212yes—
34C3×#3942C2212yes—
35C3×C4×#168C2211yescharacteristic
36#90985C2211yescharacteristic
37#90983C2212yes—
38#90973C2211yescharacteristic
39#90971C2212yes—
40#90969C2211yescharacteristic
41#90951C2212yes—
42#81620—51nomaximal, Hall
43#66061—31no—
44#65901—31no—
45C5×#475—31no—
46#65382D311yescharacteristic, complemented
47C4×#688—31no—
48#65143—32no—
49#65141—32no—
50#65130—31no—
51#65119—31no—
52#65107—32no—
53#65081—32no—
54C2×C3×C5×Q8—21no—
55Q8×D15—44no—
56C2×D60C2311yescharacteristic
57C2×C4×D15—21no—
58C2×C4×D15—22no—
59C2×Dic30—22no—
60C2×Dic30D411yescharacteristic
61C2×C5×Dic6C2311yescharacteristic
62C2×C3×Dic10C2312yes—
63C3×C5×C4⋊C4—21no—
64C3×C5×C4⋊C4C2312yes—
65C3×C42×C5C2311yescharacteristic
66#6714—21no—
67#6714—22no—
68C4⋊Dic15D411yescharacteristic
69C4⋊Dic15C2311yescharacteristic
70#6712—22no—
71#6712D412yes—
72C4×Dic15C2312yes—
73C5×C4⋊Dic3C2311yescharacteristic
74C5×Dic3⋊C4—21no—
75C4×C5×Dic3—21no—
76C2×C5×C3⋊C8C2312yes—
77C3×C4⋊Dic5—21no—
78C3×C4⋊Dic5—21no—
79C2×C3×#168C2311yescharacteristic
80C2×C3×#168C2311yescharacteristic
81#6669—22no—
82#6669—22no—
83#6668—22no—
84Dic3×Dic5—22no—
85#6660—22no—
86#6658—24no—
87#5727—51no—
88#5721—51no—
89C3×#487—51no—
90#5094D511yescharacteristic, complemented
91#5083—51no—
92#4818—52no—
93#4792—52no—
94#4791—52no—
95#4788—52no—
96C4×#204—51no—
97C8×Dic6—51no—
98C2×Q8×D5—61no—
99C5×C4⋊Q8C2×D311yescharacteristic
100C4×C5×Q8—31no—
101#4092—61no—
102#4090—32no—
103C2×#688—31no—
104C2×#677—32no—
105#4042—62no—
106#4039—32no—
107#4035—62no—
108#4034—32no—
109#4033—32no—
110C4×D20—31no—
111#4016—61no—
112#4015C2×D311yescharacteristic
113C4×Dic10—31no—
114C4×Dic10—61no—
115C5×#106—32no—
116C5×C4⋊C8—31no—
117C5×#103—32no—
118#3967—31no—
119#3948—32no—
120#3946—32no—
121C8×Dic5—32no—
122#3942C2×D312yes—
123#3942C2×D312yes—
124#3941—31no—
125#3940—31no—
126C4×#168C2×D311yescharacteristic
127#3359—151noSylow
128C22×D15—21no—
129C3×C5×Q8—42no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2411yescharacteristic
134C2×Dic15—21no—
135C2×Dic15C2×D412yes—
136C2×Dic15C2×D412yes—
137D60—21no—
138D60#4112yes—
139C4×D15—42no—
140C4×D15—44no—
141Dic30—44no—
142Dic30SD1614yescomplemented
143C2×C5×Dic3—21no—
144C2×C5×Dic3—21no—
145C5×Dic6—21no—
146C5×Dic6—21no—
147C2×C3×Dic5—22no—
148C3×Dic10—22no—
149C3×Dic10—22no—
150C3×#168—21no—
151C3×#168—21no—
152C5×C3⋊C8—22no—
153C2×D3×Q8—101no—
154C3×C4⋊Q8—51no—
155C3×C4⋊Q8C2×D511yescharacteristic
156#946—101no—
157Q8×Dic3—52no—
158#944—52no—
159C2×#215—52no—
160C2×#204—51no—
161#896—102no—
162#893—52no—
163#890—101no—
164#889—102no—
165#888—52no—
166#887—101no—
167C4×D12—51no—
168C4×Dic6—51no—
169C4×Dic6C2×D511yescharacteristic
170C3×#103—52no—
171C3×#103—52no—
172C3×C4×C8—51no—
173#835—52no—
174#821—51no—
175#817—51no—
176#816—51no—
177Dic3⋊C8—52no—
178C8×Dic3—52no—
179#810C2×D512yes—
180#808C2×D512yes—
181C4⋊(C3⋊C8)C2×D511yescharacteristic
182C2×C5×Q8—21no—
183C2×C5×Q8—31no—
184Q8×D5—124no—
185C2×D20—31no—
186C2×C4×D5—62no—
187C2×C4×D5—61no—
188C2×Dic10—31no—
189C2×Dic10—62no—
190C2×Dic10C22×D312yes—
191C2×C5×C8—32no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4—31no—
194C5×C4⋊C4—61no—
195C5×C4⋊C4C22×D312yes—
196C42×C5—61no—
197C42×C5C22×D311yescharacteristic
198#688—62no—
199#685—62no—
200#685—61no—
201C4⋊Dic5—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5—31no—
204C4⋊Dic5—31no—
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—51no—
218#487—152no—
219#475—31no—
220#475—152no—
221#461—152no—
222#461—151no—
223C8×Q8—151no—
224C4×SD16—151no—
225C4×SD16—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—22no—
228C2×D15—41no—
229C2×D15—41no—
230C3×C4×C5—21no—
231C3×C4×C5—42no—
232C3×C4×C5C2×SD1612yes—
233C3×C4×C5C2×#4111yescharacteristic
234C3×C4×C52−1+411yescharacteristic
235Dic15—22no—
236Dic15—41no—
237Dic15C2×SD1614yes—
238C3×Dic5—42no—
239C5×Dic3—41no—
240C5×Dic3—41no—
241C2×C3×Q8—21no—
242C2×C3×Q8—52no—
243D3×Q8—204no—
244C2×D12—51no—
245C2×C4×D3—102no—
246C2×C4×D3—101no—
247C2×Dic6—51no—
248C2×Dic6—102no—
249C2×Dic6C22×D511yescharacteristic
250C2×C3×C8—51no—
251C2×C3×C8—51no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—101no—
254C3×C4⋊C4—101no—
255C3×C4⋊C4C22×D512yes—
256C3×C42C22×D511yescharacteristic
257#215—104no—
258(C2×D3)⋊C4—102no—
259(C2×D3)⋊C4—101no—
260C4⋊Dic3—51no—
261C4⋊Dic3—51no—
262C4⋊Dic3—102no—
263C4⋊Dic3C22×D511yescharacteristic
264Dic3⋊C4—21no—
265Dic3⋊C4—52no—
266Dic3⋊C4—102no—
267Dic3⋊C4—102no—
268Dic3⋊C4—102no—
269C4×Dic3—21no—
270C4×Dic3—52no—
271C4×Dic3—102no—
272C2×C3⋊C8C22×D512yes—
273#204—102no—
274C22×D5—61no—
275C5×Q8—42no—
276C5×Q8—61no—
277C5×Q8—61no—
278C2×C4×C5—22no—
279C2×C4×C5—61no—
280C2×C4×C5—61no—
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5D3×D411yescharacteristic
283C2×C4×C5C23×D311yescharacteristic
284C2×Dic5—22no—
285C2×Dic5—32no—
286C2×Dic5—32no—
287C2×Dic5—61no—
288D20—32no—
289D20—61no—
290C4×D5—124no—
291C4×D5—122no—
292Dic10—22no—
293Dic10—22no—
294Dic10—34no—
295Dic10—124no—
296C5×C8—62no—
297#168—21no—
298#168—21no—
299C22×Q8—301no—
300C2×SD16—152no—
301C2×SD16—151no—
302C4⋊Q8—51no—
303C4⋊Q8—152no—
304C4⋊Q8—152no—
305C4⋊Q8D3×D511yescharacteristic
306#125—301no—
307#125—302no—
308C22⋊Q8—302no—
309C22⋊Q8—301no—
310C4×Q8—31no—
311C4×Q8—151no—
312C4×Q8—152no—
313C4×Q8—301no—
314C4×D4—152no—
315C4×D4—151no—
316#106—32no—
317#106—151no—
318C4⋊C8—31no—
319C4⋊C8—152no—
320#103—32no—
321#103—52no—
322#103—52no—
323#103—152no—
324#103—151no—
325#102—151no—
326C4×C8—51no—
327C4×C8—152no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C22×SD1611yescharacteristic
330C2×C3×C5#57811yescharacteristic
331D15—42no—
332C22×D3—101no—
333C3×Q8—42no—
334C3×Q8—102no—
335C3×Q8—102no—
336C2×C3×C4—22no—
337C2×C3×C4—102no—
338C2×C3×C4D4×D511yescharacteristic
339C2×C3×C4D4×D511yescharacteristic
340C2×C3×C4C23×D511yescharacteristic
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—52no—
344C2×Dic3—52no—
345C2×Dic3—101no—
346D12—52no—
347D12—101no—
348C4×D3—204no—
349C4×D3—202no—
350Dic6—21no—
351Dic6—21no—
352Dic6—54no—
353Dic6—204no—
354C3×C8—101no—
355C3×C8—101no—
356C3⋊C8—22no—
357C22×C5C2×D3×D411yescharacteristic
358C2×D5—62no—
359C2×D5—121no—
360C2×D5—121no—
361C4×C5—21no—
362C4×C5—42no—
363C4×C5—121no—
364C4×C5—121no—
365C4×C5D3×SD1612yes—
366C4×C5D3×#4111yescharacteristic
367C4×C5#101011yescharacteristic
368Dic5—34no—
369Dic5—42no—
370Dic5—62no—
371Dic5—121no—
372C2×Q8—21no—
373C2×Q8—31no—
374C2×Q8—52no—
375C2×Q8—151no—
376C2×Q8—302no—
377C2×Q8—604no—
378C2×D4—151no—
379C22×C4—302no—
380C22×C4—301no—
381SD16—304no—
382SD16—302no—
383C2×C8—32no—
384C2×C8—51no—
385C2×C8—51no—
386C4⋊C4—21no—
387C4⋊C4—31no—
388C4⋊C4—61no—
389C4⋊C4—101no—
390C4⋊C4—101no—
391C4⋊C4—152no—
392C4⋊C4—151no—
393C4⋊C4—151no—
394C4⋊C4—302no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4—302no—
398C4⋊C4C2×D3×D512yes—
399C22⋊C4—302no—
400C22⋊C4—301no—
401C42—61no—
402C42—152no—
403C42—302no—
404C42C2×D3×D511yescharacteristic
405C3×C5#335911yescharacteristic, complemented, Hall
406C22×C3C2×D4×D511yescharacteristic
407C2×D3—102no—
408C2×D3—201no—
409C2×D3—201no—
410C3×C4—21no—
411C3×C4—42no—
412C3×C4—202no—
413C3×C4D5×SD1612yes—
414C3×C4#414711yescharacteristic
415C3×C4D5×#4111yescharacteristic
416Dic3—41no—
417Dic3—41no—
418Dic3—54no—
419Dic3—102no—
420Dic3—201no—
421C2×C5#567711yescharacteristic
422C2×C5C2×D3×SD1611yescharacteristic
423C2×C5#576611yescharacteristic
424D5—122no—
425C23—301no—
426Q8—42no—
427Q8—61no—
428Q8—61no—
429Q8—102no—
430Q8—102no—
431Q8—154no—
432Q8—604no—
433D4—152no—
434D4—301no—
435C2×C4—22no—
436C2×C4—61no—
437C2×C4—61no—
438C2×C4—102no—
439C2×C4—152no—
440C2×C4—152no—
441C2×C4—301no—
442C2×C4—604no—
443C2×C4—602no—
444C2×C4#679011yescharacteristic
445C2×C4#679011yescharacteristic
446C2×C4C22×D3×D511yescharacteristic
447C8—62no—
448C8—101no—
449C8—101no—
450C2×C3#6596711yescharacteristic
451C2×C3C2×D5×SD1611yescharacteristic
452C2×C3#6611311yescharacteristic
453D3—202no—
454C5#8162011yescharacteristic, complemented, Sylow
455C22—302no—
456C22—601no—
457C22—601no—
458C22C2×#679011yescharacteristic
459C4—21no—
460C4—42no—
461C4—121no—
462C4—121no—
463C4—154no—
464C4—202no—
465C4—302no—
466C4—601no—
467C4#9148712yes—
468C4#9202811yescharacteristic
469C4#9203411yescharacteristic
470C3#1061276811yescharacteristic, complemented, Sylow
471C2—602no—
472C2C2×#9148711yescharacteristic
473C2#1175512211yescharacteristic
474C2#1175516611yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×D60C23
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
2. #11752481C2semidirect
3. C5×#5094C2semidirect
4. C3×#65382C2semidirect
5. #11747428C2semidirect
7. #11747304C2semidirect
11. #11746851C2semidirect
46. #65382D3semidirect
90. #5094D5semidirect
142. Dic30SD16semidirect
405. C3×C5#3359semidirect
454. C5#81620semidirect
470. C3#10612768semidirect

Maximal subgroups

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

subgroupindex
#117564862
#117524812
C5×#50942
C3×#653822
#117474282
#117474262
#117473042
#117472722
#117470852
C4×#66602
#117468512
#106127683
#816205