Finite Group Databasebeta

← #14425799

Subgroups — #14425799

Order 1920.

1432 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66283C211yesmaximal, characteristic
2#11756584C211yesmaximal, characteristic, complemented
3#11754252C212yesmaximal, complemented
4C5×#5240C211yesmaximal, characteristic, complemented
5#11749182C218yesmaximal, complemented
6#11748624C212yesmaximal, complemented
7#10610423—31nomaximal, Hall
8C2×C3×C5×#41C2211yescharacteristic
9C22×Dic30C2211yescharacteristic, complemented
10C3×#4150—22no—
11C3×#4149—22no—
12C3×D5×#41—24no—
13C3×#4147—21no—
14C3×#4144—21no—
15C3×#4144C2214yes—
16C2×C3×#709—22no—
17C2×C3×#709C2212yes—
18#91833—21no—
19#91825—21no—
20#91824C2214yescomplemented
21#91815C2211yescharacteristic, complemented
22#91813—22no—
23C5×#926C2212yescomplemented
24#91537C2218yescomplemented
25#91389—22no—
26#91364—22no—
27#91360—24no—
28C5×#834C2214yescomplemented
29#90995C2218yescomplemented
30#84124—51nomaximal, Hall
31#66283D311yescharacteristic
32#66159—31no—
33#65860—32no—
34C5×#410—31no—
35#65295—32no—
36#65031—38no—
37C3×C5×#41—22no—
38C3×C5×#41—22no—
39C2×C3×C5×Q8D411yescharacteristic
40C2×C3×C5×D4D411yescharacteristic
41C2×C3×C5×D4C2312yes—
42C22×C3×C4×C5D412yes—
43C22×C3×C4×C5C2311yescharacteristic
44C22×Dic15C2312yes—
45C2×Dic30—21no—
46C2×Dic30—21no—
47C2×Dic30—22no—
48C2×Dic30—22no—
49C2×C3×C22⋊D5—24no—
50C2×C3×C22⋊D5C2314yes—
51C3×#713—24no—
52C3×Q8×D5—24no—
53C3×#711—24no—
54C3×#711—28no—
55C3×D4×D5—24no—
56C3×D4×D5—28no—
57C3×#709—24no—
58C3×#709—24no—
59C3×#709—22no—
60C3×#709—24no—
61C3×#709—22no—
62C3×#709—22no—
63C3×#709—22no—
64C2×C3×D20—22no—
65C2×C3×D20D412yes—
66C2×C3×C4×D5—24no—
67C2×C3×C4×D5D414yes—
68C2×C3×Dic10—22no—
69C2×C3×Dic10D412yes—
70#6719—24no—
71#6719C2312yes—
72C4⋊Dic15—21no—
73#6712—24no—
74C4×Dic15—21no—
75C5×#217C2314yes—
76C5×C4⋊Dic3—22no—
77C4×C5×Dic3—22no—
78Dic3⋊Dic5—28no—
79#6665—28no—
80C3×#585—51no—
81#5825—51no—
82#5825—52no—
83#5243—58no—
84#5240—52no—
85#5240D511yescharacteristic, complemented
86C2×C5×#41C2×D311yescharacteristic
87#4150—22no—
88#4149—22no—
89D5×#41—24no—
90#4147—21no—
91#4144—21no—
92#4144C2×D314yes—
93C2×#709—22no—
94C2×#709C2×D312yes—
95C22×Dic10—31no—
96C5×#117—32no—
97#4090—61no—
98#4082—61no—
99#4081—34no—
100#4072—31no—
101#4070—62no—
102#4043—64no—
103#4032—38no—
104#4021—62no—
105#4015—62no—
106C5×#99—34no—
107#3938—38no—
108#3028—151noSylow
109C23×C3×C5C2×D412yes—
110C23×C3×C5C2411yescharacteristic
111C22×C3×D5—24no—
112C22×C3×D5C2×D414yes—
113C3×C5×Q8—22no—
114C3×C5×D4—24no—
115C3×C5×D4—22no—
116C2×C3×C4×C5—22no—
117C2×C3×C4×C5—22no—
118C2×C3×C4×C5C2×D412yes—
119C2×C3×C4×C5C2×D411yescharacteristic
120C2×C3×C4×C5C2×D411yescharacteristic
121C2×C3×C4×C5C2×D412yes—
122C2×C3×C4×C5C2×D412yes—
123C2×Dic15—24no—
124C2×Dic15—22no—
125C2×Dic15—22no—
126Dic30—41no—
127Dic30—42no—
128Dic30—41no—
129C2×C5×Dic3—24no—
130C3×C22⋊D5—28no—
131C3×C22⋊D5—24no—
132C3×C22⋊D5—24no—
133C2×C3×Dic5—24no—
134C2×C3×Dic5C2×D414yes—
135C3×D20—24no—
136C3×D20—22no—
137C3×D20—22no—
138C3×C4×D5—28no—
139C3×C4×D5—24no—
140C3×C4×D5—24no—
141C3×Dic10—24no—
142C3×Dic10—22no—
143C3×Dic10—22no—
144C3×2−1+4—102no—
145C3×2−1+4—101no—
146C3×H(5,𝔽2)—54no—
147C3×H(5,𝔽2)—102no—
148C3×H(5,𝔽2)—101no—
149C2×C3×#41—52no—
150C2×C3×#41—104no—
151C2×C3×#41—102no—
152C2×C3×#41C2×D511yescharacteristic
153C22×Dic6—51no—
154#944—102no—
155#944—101no—
156#936—102no—
157#936—101no—
158#935—54no—
159#935—58no—
160#926—51no—
161#926C2×D512yescomplemented
162#924—104no—
163#924—102no—
164#834—58no—
165#834C2×D514yescomplemented
166C5×#41—22no—
167C5×#41—22no—
168C2×C5×Q8#6711yescharacteristic
169C2×C5×D4#6711yescharacteristic
170C2×C5×D4C22×D312yes—
171C22×C4×C5#6712yes—
172C22×C4×C5C22×D311yescharacteristic
173C2×C22⋊D5—24no—
174C2×C22⋊D5C22×D314yes—
175C22×Dic5—32no—
176#713—24no—
177Q8×D5—24no—
178#711—24no—
179#711—28no—
180D4×D5—24no—
181D4×D5—28no—
182#709—24no—
183#709—24no—
184#709—22no—
185#709—24no—
186#709—22no—
187#709—22no—
188#709—22no—
189C2×D20—22no—
190C2×D20#6712yes—
191C2×C4×D5—24no—
192C2×C4×D5#6714yes—
193C2×Dic10—22no—
194C2×Dic10—62no—
195C2×Dic10—62no—
196C2×Dic10—61no—
197C2×Dic10—61no—
198C2×Dic10#6712yes—
199C5×C4⋊C4—62no—
200C5×C22⋊C4—34no—
201C42×C5—62no—
202C22⋊Dic5—32no—
203C22⋊Dic5—64no—
204#685—68no—
205C4⋊Dic5—61no—
206C4⋊Dic5—68no—
207#683—64no—
208C4×Dic5—61no—
209#585—51no—
210#536—152no—
211#536—151no—
212#458—158no—
213#410—31no—
214#410—152no—
215C22×C3×C5—22no—
216C22×C3×C5—41no—
217C22×C3×C5—42no—
218C22×C3×C5C22×D411yescharacteristic
219C22×C3×C5C22×D412yes—
220C2×C3×D5—24no—
221C2×C3×D5—44no—
222C2×C3×D5—84no—
223C3×C4×C5—22no—
224C3×C4×C5#12011yescharacteristic
225C3×C4×C5#12012yes—
226C3×C4×C5#12011yescharacteristic
227Dic15—42no—
228Dic15—42no—
229C3×Dic5—24no—
230C5×Dic3—44no—
231C3×#41—22no—
232C3×#41—22no—
233C3×#41—104no—
234C3×#41—104no—
235C3×#41—108no—
236C3×#41—104no—
237C3×#41—104no—
238C3×#41—102no—
239C3×#41—102no—
240C3×#41—104no—
241C3×#41—102no—
242C3×#41—102no—
243C2×C3×Q8—52no—
244C2×C3×Q8—102no—
245C2×C3×Q8—104no—
246C2×C3×Q8D2011yescharacteristic
247C2×C3×D4—54no—
248C2×C3×D4—52no—
249C2×C3×D4—102no—
250C2×C3×D4—108no—
251C2×C3×D4—104no—
252C2×C3×D4—104no—
253C2×C3×D4D2011yescharacteristic
254C2×C3×D4C22×D512yes—
255C22×C3×C4—54no—
256C22×C3×C4—104no—
257C22×C3×C4D2012yes—
258C22×C3×C4C22×D511yescharacteristic
259C22×Dic3—52no—
260C2×Dic6—101no—
261C2×Dic6—101no—
262C2×Dic6—102no—
263C2×Dic6—102no—
264#217—52no—
265#217—108no—
266#217—104no—
267#217C22×D514yes—
268C4⋊Dic3—22no—
269C4⋊Dic3—101no—
270Dic3⋊C4—108no—
271Dic3⋊C4—104no—
272C4×Dic3—22no—
273C4×Dic3—101no—
274C23×C5C2×#6712yes—
275C23×C5C23×D311yescharacteristic
276C22×D5—24no—
277C22×D5C2×#6714yes—
278C5×Q8—22no—
279C5×D4—24no—
280C5×D4—22no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—64no—
284C2×C4×C5C2×#6712yes—
285C2×C4×C5C2×#6711yescharacteristic
286C2×C4×C5C2×#6711yescharacteristic
287C2×C4×C5C2×#6712yes—
288C2×C4×C5C2×#6712yes—
289C22⋊D5—28no—
290C22⋊D5—24no—
291C22⋊D5—24no—
292C2×Dic5—24no—
293C2×Dic5—62no—
294C2×Dic5—62no—
295C2×Dic5—64no—
296C2×Dic5C2×#6714yes—
297D20—24no—
298D20—22no—
299D20—22no—
300C4×D5—28no—
301C4×D5—24no—
302C4×D5—24no—
303Dic10—24no—
304Dic10—22no—
305Dic10—22no—
306Dic10—121no—
307Dic10—122no—
308Dic10—121no—
3092−1+4—102no—
3102−1+4—101no—
311H(5,𝔽2)—54no—
312H(5,𝔽2)—102no—
313H(5,𝔽2)—101no—
314C2×#41—52no—
315C2×#41—104no—
316C2×#41—102no—
317C2×#41D3×D511yescharacteristic
318C22×Q8—151no—
319C4⋊Q8—302no—
320C4⋊Q8—301no—
321#124—302no—
322#124—301no—
323#123—158no—
324#123—154no—
325C22⋊Q8—304no—
326C22⋊Q8—302no—
327#117—32no—
328#117—151no—
329#99—34no—
330#99—158no—
331C2×C3×C5—22no—
332C2×C3×C5—21no—
333C2×C3×C5—42no—
334C2×C3×C5C2×#12011yescharacteristic
335C3×D5—44no—
336C23×C3—54no—
337C23×C3—104no—
338C23×C3C2×D2012yes—
339C23×C3C23×D511yescharacteristic
340C3×Q8—22no—
341C3×Q8—104no—
342C3×Q8—102no—
343C3×Q8—102no—
344C3×D4—24no—
345C3×D4—22no—
346C3×D4—104no—
347C3×D4—108no—
348C3×D4—104no—
349C3×D4—104no—
350C3×D4—102no—
351C3×D4—102no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—54no—
355C2×C3×C4—108no—
356C2×C3×C4—104no—
357C2×C3×C4—104no—
358C2×C3×C4—104no—
359C2×C3×C4C2×D2012yes—
360C2×C3×C4C2×D2011yescharacteristic
361C2×C3×C4C2×D2011yescharacteristic
362C2×C3×C4D4×D512yes—
363C2×C3×C4D4×D512yes—
364C2×Dic3—24no—
365C2×Dic3—102no—
366C2×Dic3—102no—
367C2×Dic3—104no—
368Dic6—201no—
369Dic6—201no—
370Dic6—202no—
371C22×C5—22no—
372C22×C5—41no—
373C22×C5—42no—
374C22×C5C22×#6711yescharacteristic
375C22×C5C22×#6712yes—
376C2×D5—24no—
377C2×D5—44no—
378C2×D5—84no—
379C4×C5—22no—
380C4×C5—124no—
381C4×C5#95311yescharacteristic
382C4×C5#95312yes—
383C4×C5#95311yescharacteristic
384Dic5—24no—
385Dic5—122no—
386Dic5—122no—
387#41—22no—
388#41—22no—
389#41—104no—
390#41—104no—
391#41—108no—
392#41—104no—
393#41—104no—
394#41—102no—
395#41—102no—
396#41—104no—
397#41—102no—
398#41—102no—
399C2×Q8—52no—
400C2×Q8—102no—
401C2×Q8—104no—
402C2×Q8—301no—
403C2×Q8—301no—
404C2×Q8—302no—
405C2×Q8—302no—
406C2×Q8#120211yescharacteristic
407C2×D4—54no—
408C2×D4—52no—
409C2×D4—102no—
410C2×D4—108no—
411C2×D4—104no—
412C2×D4—104no—
413C2×D4#120211yescharacteristic
414C2×D4C2×D3×D512yes—
415C22×C4—54no—
416C22×C4—104no—
417C22×C4—152no—
418C22×C4#120212yes—
419C22×C4C2×D3×D511yescharacteristic
420C4⋊C4—62no—
421C4⋊C4—308no—
422C4⋊C4—301no—
423C4⋊C4—304no—
424C22⋊C4—34no—
425C22⋊C4—152no—
426C22⋊C4—308no—
427C22⋊C4—304no—
428C42—62no—
429C42—301no—
430C3×C5#302811yescharacteristic, complemented, Hall
431C22×C3—22no—
432C22×C3—41no—
433C22×C3—42no—
434C22×C3—104no—
435C22×C3—204no—
436C22×C3—404no—
437C22×C3C22×D2011yescharacteristic
438C22×C3C2×D4×D512yes—
439C3×C4—22no—
440C3×C4—104no—
441C3×C4#402811yescharacteristic
442C3×C4#402811yescharacteristic
443C3×C4#402812yes—
444Dic3—44no—
445Dic3—202no—
446Dic3—202no—
447C2×C5—21no—
448C2×C5—22no—
449C2×C5—42no—
450C2×C5C2×#95311yescharacteristic
451D5—44no—
452C23—54no—
453C23—104no—
454C23C2×#120212yes—
455C23C22×D3×D511yescharacteristic
456Q8—22no—
457Q8—104no—
458Q8—102no—
459Q8—102no—
460Q8—601no—
461Q8—601no—
462Q8—602no—
463D4—24no—
464D4—22no—
465D4—104no—
466D4—108no—
467D4—104no—
468D4—104no—
469D4—102no—
470D4—102no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—54no—
474C2×C4—64no—
475C2×C4—108no—
476C2×C4—104no—
477C2×C4—104no—
478C2×C4—104no—
479C2×C4—302no—
480C2×C4—302no—
481C2×C4—304no—
482C2×C4C2×#120212yes—
483C2×C4C2×#120211yescharacteristic
484C2×C4C2×#120211yescharacteristic
485C2×C4D5×#6712yes—
486C2×C4D5×#6712yes—
487C2×C3—22no—
488C2×C3—21no—
489C2×C3—42no—
490C2×C3—204no—
491C2×C3C2×#402811yescharacteristic
492C5#8412411yescharacteristic, complemented, Sylow
493C22—22no—
494C22—41no—
495C22—42no—
496C22—104no—
497C22—204no—
498C22—404no—
499C22C22×#120211yescharacteristic
500C22C2×D5×#6712yes—
501C4—22no—
502C4—104no—
503C4—124no—
504C4—602no—
505C4—602no—
506C4#9156411yescharacteristic
507C4#9156411yescharacteristic
508C4#9156412yes—
509C3#1061042311yescharacteristic, complemented, Sylow
510C2—22no—
511C2—21no—
512C2—42no—
513C2—204no—
514C2C2×#9156411yescharacteristic
subgroupG/H
centerC2C2×#91564
commutator, cosocleC23×C3×C5C24
FrattiniC23C22×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×#120
prime radicalC3×#66283C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3028
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11756584C2semidirect
3. #11754252C2semidirect
4. C5×#5240C2semidirect
5. #11749182C2semidirect
6. #11748624C2semidirect
9. C22×Dic30C22semidirect
20. #91824C22semidirect
21. #91815C22semidirect
23. C5×#926C22semidirect
24. #91537C22semidirect
28. C5×#834C22semidirect
29. #90995C22semidirect
85. #5240D5semidirect
161. #926C2×D5semidirect
165. #834C2×D5semidirect
430. C3×C5#3028semidirect
492. C5#84124semidirect
509. C3#10610423semidirect

Maximal subgroups

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

subgroupindex
C3×#662832
#117565842
#117542522
C5×#52402
#117491822
#117486242
#106104233
#841245