Finite Group Databasebeta

← #14472151

Subgroups — #14472151

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5732C211yesmaximal, characteristic
2#11752476C211yesmaximal, characteristic, complemented
3#11751180C211yesmaximal, characteristic, complemented
4C3×#65379C211yesmaximal, characteristic, complemented
5#11749334C212yesmaximal, complemented
6Dic3×#689C212yesmaximal, complemented
7#11749252C212yesmaximal
8#11749188C212yesmaximal
9C4×#6656C211yesmaximal, characteristic
10#11746964C211yesmaximal, characteristic
11#11746857C211yesmaximal, characteristic, complemented
12#10615407—31nomaximal, Hall
13C3×C5×C4⋊Q8C2211yescharacteristic
14#91758C2211yescharacteristic
15C5×#947C2212yes—
16C5×Q8×Dic3C2212yes—
17C5×#898—22no—
18C5×#897—21no—
19C5×#892—21no—
20C4×C5×D12C2211yescharacteristic
21C4×C5×Dic6C2211yescharacteristic
22C2×C3×#689C2212yes—
23C3×C4×Dic10C2211yescharacteristic
24#91381C2212yes—
25#91376—21no—
26#91334—22no—
27#91333—21no—
28Dic3×Dic10C2212yes—
29C2×#6656C2211yescharacteristic
30#91119C2212yes—
31#91119C2212yes—
32C4×C3⋊#168C2211yescharacteristic
33C3×#3967C2212yes—
34C3×C4⋊#168C2211yescharacteristic
35#90988C2212yes—
36#90986C2211yescharacteristic
37Dic3⋊#168C2212yes—
38#90970C2211yescharacteristic
39#90967C2212yes—
40#90966C2211yescharacteristic
41Dic3×#168C2212yes—
42#80463—51nomaximal, Hall
43C5×#556—31no—
44#65901—31no—
45#65379D311yescharacteristic, complemented
46#65370—31no—
47#65345—32no—
48#65343—32no—
49C4×#689—32no—
50Q8×#168—31no—
51#65311—32no—
52C4×#687—31no—
53#65296—31no—
54C2×C3×C5×Q8C2312yes—
55C2×Dic30—21no—
56C2×C5×D12C2311yescharacteristic
57C2×C4×C5×D3—21no—
58C2×C5×Dic6D411yescharacteristic
59C2×C3×Dic10C2311yescharacteristic
60C3×C5×C4⋊C4—21no—
61C3×C5×C4⋊C4—21no—
62C3×C42×C5C2311yescharacteristic
63C4⋊Dic15—21no—
64C4⋊Dic15C2312yes—
65C2×C3⋊#168C2311yescharacteristic
66C2×C3⋊#168C2311yescharacteristic
67C5×(C2×D3)⋊C4—21no—
68C5×(C2×D3)⋊C4—22no—
69C5×(C2×D3)⋊C4—22no—
70C5×C4⋊Dic3—22no—
71C5×C4⋊Dic3D411yescharacteristic
72C5×C4⋊Dic3C2311yescharacteristic
73C5×Dic3⋊C4D412yes—
74C4×C5×Dic3—22no—
75C4×C5×Dic3C2312yes—
76C3×#689—24no—
77C3×C4⋊Dic5C2311yescharacteristic
78C3×#683—21no—
79C3×C4×Dic5—21no—
80C2×C3×#168C2312yes—
81#6669—22no—
82#6668—22no—
83#6668—22no—
84Dic3×Dic5—22no—
85#6656—22no—
86#5732D511yescharacteristic
87#5570—51no—
88C3×#462—51no—
89#5185—52no—
90Dic3×Q16—52no—
91#5079—51no—
92C4×#215—51no—
93#4846—51no—
94#4830—51no—
95#4800—52no—
96#4796—52no—
97C5×C4⋊Q8C2×D311yescharacteristic
98C5×#126—62no—
99C5×#124—32no—
100C5×C22⋊Q8—61no—
101C4×C5×Q8—31no—
102C4×C5×Q8—32no—
103C4×C5×D4—31no—
104C5×#117—61no—
105#4090—61no—
106C2×#689C2×D312yes—
107C2×#687—31no—
108#4035—62no—
109#4033—61no—
110#4016—32no—
111#4015—31no—
112C4×Dic10—32no—
113C4×Dic10C2×D311yescharacteristic
114#3967—32no—
115#3967—32no—
116#3967C2×D312yes—
117#3964—31no—
118#3964—32no—
119#3942—31no—
120#3940—31no—
121#3939—32no—
122C4⋊#168—32no—
123C4⋊#168C2×D311yescharacteristic
124C4×#168—31no—
125C4×#168—32no—
126#3364—151noSylow
127C22×C5×D3—21no—
128C3×C5×Q8—22no—
129C3×C5×Q8—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2411yescharacteristic
134C2×Dic15—22no—
135Dic30—42no—
136C2×C5×Dic3—21no—
137C2×C5×Dic3C2×D412yes—
138C2×C5×Dic3C2×D412yes—
139C5×D12—21no—
140C5×D12—21no—
141C4×C5×D3—42no—
142C5×Dic6—22no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—21no—
145C3×Dic10—21no—
146C3×Dic10#4112yes—
147C3⋊#168—21no—
148C3⋊#168—21no—
149C3×#168—22no—
150C2×C3×Q16—52no—
151C3×C4⋊Q8C2×D511yescharacteristic
152C3×C4×Q8—51no—
153#947C2×D512yes—
154Q8×Dic3—52no—
155Q8×Dic3C2×D512yes—
156C2×#215—51no—
157#898—22no—
158#897—21no—
159#892—21no—
160#890—52no—
161#890—102no—
162C4×D12C2×D511yescharacteristic
163#869—51no—
164#869—101no—
165C4×Dic6—101no—
166C4×Dic6C2×D511yescharacteristic
167C3×C4⋊C8—51no—
168C3×#103—52no—
169#835—52no—
170#835—52no—
171#835—51no—
172#821—52no—
173#818—52no—
174Dic3⋊C8—52no—
175C8×Dic3—52no—
176#809—51no—
177#808—51no—
178C4×C3⋊C8—51no—
179C2×C5×Q8—31no—
180C2×C5×Q8C22×D312yes—
181C2×C5×D4—31no—
182C22×C4×C5—61no—
183C2×Dic10—61no—
184C2×Dic10C22×D311yescharacteristic
185C5×C4⋊C4—21no—
186C5×C4⋊C4—21no—
187C5×C4⋊C4—31no—
188C5×C4⋊C4—32no—
189C5×C4⋊C4—31no—
190C5×C4⋊C4—62no—
191C5×C22⋊C4—62no—
192C5×C22⋊C4—62no—
193C5×C22⋊C4—61no—
194C42×C5—32no—
195C42×C5—62no—
196C42×C5C22×D311yescharacteristic
197#689—24no—
198#687—62no—
199C4⋊Dic5—32no—
200C4⋊Dic5—61no—
201C4⋊Dic5C22×D311yescharacteristic
202#683—21no—
203#683—62no—
204#683—62no—
205#683—62no—
206C4×Dic5—21no—
207C4×Dic5—62no—
208C2×#168—31no—
209C2×#168—31no—
210C2×#168C22×D312yes—
211#557—151no—
212#556—31no—
213#488—152no—
214#487—151no—
215#479—152no—
216#474—151no—
217#464—152no—
218#462—51no—
219C8×Q8—151no—
220C4×Q16—152no—
221C4×SD16—151no—
222C22×C3×C5C22×D411yescharacteristic
223C2×C5×D3—41no—
224C2×C5×D3—41no—
225C2×C5×D3—41no—
226C3×C4×C5—21no—
227C3×C4×C5—42no—
228C3×C4×C5#13512yes—
229C3×C4×C5C2×#4111yescharacteristic
230C3×C4×C52−1+411yescharacteristic
231Dic15—42no—
232C3×Dic5—22no—
233C3×Dic5—41no—
234C5×Dic3—22no—
235C5×Dic3—22no—
236C5×Dic3—41no—
237C2×C3×Q8—51no—
238C2×C3×Q8C22×D512yes—
239C2×D12C22×D511yescharacteristic
240C2×C4×D3—21no—
241C2×Dic6—101no—
242C2×Dic6C22⋊D511yescharacteristic
243C3×Q16—104no—
244C2×C3×C8—52no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—51no—
248C3×C4⋊C4—101no—
249C3×C42—101no—
250C3×C42C22×D511yescharacteristic
251#215—102no—
252(C2×D3)⋊C4—21no—
253(C2×D3)⋊C4—22no—
254(C2×D3)⋊C4—22no—
255C4⋊Dic3—22no—
256C4⋊Dic3—52no—
257C4⋊Dic3—101no—
258C4⋊Dic3—102no—
259C4⋊Dic3—102no—
260C4⋊Dic3C22⋊D511yescharacteristic
261C4⋊Dic3C22×D511yescharacteristic
262Dic3⋊C4—102no—
263Dic3⋊C4C22⋊D512yes—
264C4×Dic3—22no—
265C4×Dic3—102no—
266C4×Dic3C22×D512yes—
267C2×C3⋊C8—51no—
268C2×C3⋊C8—51no—
269C23×C5—61no—
270C5×Q8—22no—
271C5×Q8—22no—
272C5×Q8—62no—
273C5×D4—61no—
274C5×D4—61no—
275C2×C4×C5—22no—
276C2×C4×C5—32no—
277C2×C4×C5—32no—
278C2×C4×C5—61no—
279C2×C4×C5—122no—
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5C23×D311yescharacteristic
283C2×Dic5—21no—
284C2×Dic5—21no—
285C2×Dic5—62no—
286Dic10—21no—
287Dic10—122no—
288Dic10#23712yes—
289#168—22no—
290#168—61no—
291#168—61no—
292C2×Q16—52no—
293C2×SD16—151no—
294C4⋊Q8—151no—
295C4⋊Q8—301no—
296C4⋊Q8D3×D511yescharacteristic
297#126—62no—
298#125—152no—
299#125—302no—
300#124—32no—
301C22⋊Q8—61no—
302C4×Q8—31no—
303C4×Q8—32no—
304C4×Q8—51no—
305C4×Q8—152no—
306C4×Q8—301no—
307C4×D4—31no—
308#117—61no—
309#107—152no—
310#106—151no—
311C4⋊C8—51no—
312C4⋊C8—152no—
313#103—52no—
314#103—151no—
315#103—152no—
316#103—152no—
317#102—151no—
318#102—152no—
319C4×C8—152no—
320C4×C8—151no—
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324C5×D3—81no—
325C22×D3—21no—
326C3×Q8—22no—
327C3×Q8—22no—
328C3×Q8—52no—
329C3×Q8—101no—
330C2×C3×C4—22no—
331C2×C3×C4—101no—
332C2×C3×C4—101no—
333C2×C3×C4C2×C22⋊D511yescharacteristic
334C2×C3×C4C2×C22⋊D511yescharacteristic
335C2×C3×C4C23×D511yescharacteristic
336C2×Dic3—21no—
337C2×Dic3—102no—
338C2×Dic3C2×C22⋊D512yes—
339C2×Dic3C2×C22⋊D512yes—
340D12—21no—
341D12—21no—
342C4×D3—42no—
343Dic6—22no—
344Dic6—202no—
345C3×C8—102no—
346C3⋊C8—101no—
347C3⋊C8—101no—
348C22×C5—121no—
349C22×C5—121no—
350C22×C5—121no—
351C22×C5C2×D3×D411yescharacteristic
352C4×C5—21no—
353C4×C5—42no—
354C4×C5—62no—
355C4×C5—62no—
356C4×C5—121no—
357C4×C5#91912yes—
358C4×C5C2×#23711yescharacteristic
359C4×C5#101011yescharacteristic
360Dic5—22no—
361Dic5—41no—
362Dic5—122no—
363C2×Q8—31no—
364C2×Q8—51no—
365C2×Q8—301no—
366C2×Q8C2×D3×D512yes—
367C2×D4—31no—
368C22×C4—61no—
369Q16—104no—
370SD16—302no—
371C2×C8—52no—
372C2×C8—151no—
373C2×C8—151no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—31no—
377C4⋊C4—32no—
378C4⋊C4—31no—
379C4⋊C4—51no—
380C4⋊C4—62no—
381C4⋊C4—101no—
382C4⋊C4—152no—
383C4⋊C4—302no—
384C4⋊C4—302no—
385C4⋊C4—302no—
386C4⋊C4—301no—
387C22⋊C4—62no—
388C22⋊C4—62no—
389C22⋊C4—61no—
390C42—32no—
391C42—62no—
392C42—101no—
393C42—302no—
394C42C2×D3×D511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3C22×C22⋊D511yescharacteristic
397C2×D3—41no—
398C2×D3—41no—
399C2×D3—41no—
400C3×C4—21no—
401C3×C4—42no—
402C3×C4—102no—
403C3×C4—201no—
404C3×C4#409612yes—
405C3×C4D5×#4111yescharacteristic
406C3×C4#415011yescharacteristic
407Dic3—22no—
408Dic3—22no—
409Dic3—41no—
410Dic3—202no—
411C2×C5—241no—
412C2×C5#559811yescharacteristic
413C2×C5C2×#91911yescharacteristic
414C2×C5#577911yescharacteristic
415C23—61no—
416Q8—22no—
417Q8—22no—
418Q8—52no—
419Q8—62no—
420Q8—101no—
421Q8—602no—
422D4—61no—
423D4—61no—
424C2×C4—22no—
425C2×C4—32no—
426C2×C4—32no—
427C2×C4—61no—
428C2×C4—101no—
429C2×C4—101no—
430C2×C4—122no—
431C2×C4—302no—
432C2×C4D3×C22⋊D511yescharacteristic
433C2×C4D3×C22⋊D511yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—102no—
436C8—301no—
437C8—301no—
438C2×C3C2×#409611yescharacteristic
439C2×C3#6616511yescharacteristic
440C2×C3#6617211yescharacteristic
441D3—81no—
442C5#8046311yescharacteristic, complemented, Sylow
443C22—121no—
444C22—121no—
445C22—121no—
446C22C2×D3×C22⋊D511yescharacteristic
447C4—21no—
448C4—42no—
449C4—62no—
450C4—62no—
451C4—102no—
452C4—121no—
453C4—201no—
454C4—602no—
455C4#9151912yes—
456C4#9202011yescharacteristic
457C4D5×#23711yescharacteristic
458C3#1061540711yescharacteristic, complemented, Sylow
459C2—241no—
460C2#1175480211yescharacteristic
461C2#1175511411yescharacteristic
462C2C2×#9151911yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×D12C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3364
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. #11752476C2semidirect
3. #11751180C2semidirect
4. C3×#65379C2semidirect
5. #11749334C2semidirect
6. Dic3×#689C2semidirect
11. #11746857C2semidirect
45. #65379D3semidirect
395. C3×C5#3364semidirect
442. C5#80463semidirect
458. C3#10615407semidirect

Maximal subgroups

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

subgroupindex
C5×#57322
#117524762
#117511802
C3×#653792
#117493342
Dic3×#6892
#117492522
#117491882
C4×#66562
#117469642
#117468572
#106154073
#804635