Finite Group Databasebeta

← #14425794

Subgroups — #14425794

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
2C5×#5825C211yesmaximal, characteristic, complemented
3#11754251C212yesmaximal, complemented
4#11751341C211yesmaximal, characteristic, complemented
5#11749181C218yesmaximal, complemented
6#11748624C212yesmaximal, complemented
7#10615148—31nomaximal, Hall
8C2×C3×C5×#41C2211yescharacteristic
9C22×C5×Dic6C2211yescharacteristic, 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#91815C2212yescomplemented
19C5×#944—21no—
20C5×#936—21no—
21C5×#935C2214yescomplemented
22C5×#926C2211yescharacteristic, complemented
23C5×#924—22no—
24#91536C2218yescomplemented
25#91385—22no—
26#91368—22no—
27#91359—24no—
28#91118C2214yescomplemented
29#90995C2218yescomplemented
30#84124—51nomaximal, Hall
31#66283D311yescharacteristic
32C5×#536—31no—
33#66150—32no—
34#65529—31no—
35#65342—38no—
36#65295—32no—
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×C5×Dic3C2312yes—
45C2×C5×Dic6—21no—
46C2×C5×Dic6—21no—
47C2×C5×Dic6—22no—
48C2×C5×Dic6—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#6719C2314yes—
71C4⋊Dic15—22no—
72C4×Dic15—22no—
73C5×#217—24no—
74C5×#217C2312yes—
75C5×C4⋊Dic3—21no—
76C5×Dic3⋊C4—24no—
77C4×C5×Dic3—21no—
78#6669—28no—
79#6665—28no—
80C3×#585—51no—
81#5825—52no—
82#5825D511yescharacteristic, complemented
83#5243—58no—
84#5240—51no—
85#5240—52no—
86C2×C5×#41C2×D311yescharacteristic
87C22×C5×Q8—31no—
88#4150—22no—
89#4149—22no—
90D5×#41—24no—
91#4147—21no—
92#4144—21no—
93#4144C2×D314yes—
94C2×#709—22no—
95C2×#709C2×D312yes—
96C5×C4⋊Q8—61no—
97C5×#124—61no—
98C5×#123—34no—
99C5×C22⋊Q8—62no—
100C5×#117—31no—
101#4093—62no—
102#4092—64no—
103#4090—62no—
104#4075—38no—
105#4072—32no—
106#3966—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×D412yes—
120C2×C3×C4×C5C2×D412yes—
121C2×C3×C4×C5C2×D411yescharacteristic
122C2×C3×C4×C5C2×D411yescharacteristic
123C2×Dic15—24no—
124C2×C5×Dic3—24no—
125C2×C5×Dic3—22no—
126C2×C5×Dic3—22no—
127C5×Dic6—41no—
128C5×Dic6—42no—
129C5×Dic6—41no—
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×Dic6C2×D511yescharacteristic, complemented
154#944—21no—
155#944—102no—
156#936—21no—
157#936—102no—
158#935—58no—
159#935C2×D514yescomplemented
160#926—52no—
161#926C2×D511yescharacteristic, complemented
162#924—22no—
163#924—104no—
164#834—54no—
165#834—58no—
166C5×#41—22no—
167C5×#41—22no—
168C2×C5×Q8—61no—
169C2×C5×Q8—61no—
170C2×C5×Q8—62no—
171C2×C5×Q8—62no—
172C2×C5×Q8#6711yescharacteristic
173C2×C5×D4#6711yescharacteristic
174C2×C5×D4C22×D312yes—
175C22×C4×C5—32no—
176C22×C4×C5#6712yes—
177C22×C4×C5C22×D311yescharacteristic
178C2×C22⋊D5—24no—
179C2×C22⋊D5C22×D314yes—
180#713—24no—
181Q8×D5—24no—
182#711—24no—
183#711—28no—
184D4×D5—24no—
185D4×D5—28no—
186#709—24no—
187#709—24no—
188#709—22no—
189#709—24no—
190#709—22no—
191#709—22no—
192#709—22no—
193C2×D20—22no—
194C2×D20#6712yes—
195C2×C4×D5—24no—
196C2×C4×D5#6714yes—
197C2×Dic10—22no—
198C2×Dic10#6712yes—
199C5×C4⋊C4—61no—
200C5×C4⋊C4—64no—
201C5×C22⋊C4—32no—
202C5×C22⋊C4—64no—
203C42×C5—61no—
204C22⋊Dic5—34no—
205#685—68no—
206C4⋊Dic5—62no—
207#683—68no—
208C4×Dic5—62no—
209#585—51no—
210#536—31no—
211#536—152no—
212#458—158no—
213#410—152no—
214#410—151no—
215C22×C3×C5—22no—
216C22×C3×C5—41no—
217C22×C3×C5—42no—
218C22×C3×C5C22×D412yes—
219C22×C3×C5C22×D411yescharacteristic
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—44no—
228C3×Dic5—24no—
229C5×Dic3—42no—
230C5×Dic3—42no—
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—102no—
241C3×#41—102no—
242C3×#41—104no—
243C2×C3×Q8—52no—
244C2×C3×Q8—102no—
245C2×C3×Q8—104no—
246C2×C3×Q8C22⋊D511yescharacteristic
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×D4C22⋊D511yescharacteristic
254C2×C3×D4C22×D512yes—
255C22×C3×C4—54no—
256C22×C3×C4—104no—
257C22×C3×C4C22⋊D512yes—
258C22×C3×C4C22×D511yescharacteristic
259C22×Dic3C22×D512yes—
260C2×Dic6—22no—
261C2×Dic6—22no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264#217—24no—
265#217—54no—
266#217—108no—
267#217C22×D512yes—
268C4⋊Dic3—21no—
269C4⋊Dic3—102no—
270Dic3⋊C4—24no—
271Dic3⋊C4—108no—
272C4×Dic3—21no—
273C4×Dic3—102no—
274C23×C5C2×#6712yes—
275C23×C5C23×D311yescharacteristic
276C22×D5—24no—
277C22×D5C2×#6714yes—
278C5×Q8—22no—
279C5×Q8—121no—
280C5×Q8—122no—
281C5×Q8—121no—
282C5×D4—24no—
283C5×D4—22no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—64no—
287C2×C4×C5—62no—
288C2×C4×C5—62no—
289C2×C4×C5C2×#6712yes—
290C2×C4×C5C2×#6711yescharacteristic
291C2×C4×C5C2×#6711yescharacteristic
292C2×C4×C5C2×#6712yes—
293C2×C4×C5C2×#6712yes—
294C22⋊D5—28no—
295C22⋊D5—24no—
296C22⋊D5—24no—
297C2×Dic5—24no—
298C2×Dic5—64no—
299C2×Dic5C2×#6714yes—
300D20—24no—
301D20—22no—
302D20—22no—
303C4×D5—28no—
304C4×D5—24no—
305C4×D5—24no—
306Dic10—24no—
307Dic10—22no—
308Dic10—22no—
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—31no—
319C4⋊Q8—61no—
320C4⋊Q8—302no—
321#124—61no—
322#124—302no—
323#123—34no—
324#123—158no—
325C22⋊Q8—62no—
326C22⋊Q8—304no—
327#117—31no—
328#117—152no—
329#99—158no—
330#99—154no—
331C2×C3×C5—21no—
332C2×C3×C5—22no—
333C2×C3×C5—42no—
334C2×C3×C5C2×#12011yescharacteristic
335C3×D5—44no—
336C23×C3—54no—
337C23×C3—104no—
338C23×C3C2×C22⋊D512yes—
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×C4D4×D512yes—
360C2×C3×C4D4×D512yes—
361C2×C3×C4C2×C22⋊D512yes—
362C2×C3×C4C2×C22⋊D511yescharacteristic
363C2×C3×C4C2×C22⋊D511yescharacteristic
364C2×Dic3—24no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—104no—
368Dic6—41no—
369Dic6—41no—
370Dic6—42no—
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—122no—
381C4×C5—122no—
382C4×C5#95311yescharacteristic
383C4×C5#95312yes—
384C4×C5#95311yescharacteristic
385Dic5—24no—
386Dic5—124no—
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—61no—
401C2×Q8—61no—
402C2×Q8—62no—
403C2×Q8—62no—
404C2×Q8—102no—
405C2×Q8—104no—
406C2×Q8#120111yescharacteristic
407C2×D4—54no—
408C2×D4—52no—
409C2×D4—102no—
410C2×D4—108no—
411C2×D4—104no—
412C2×D4—104no—
413C2×D4#120111yescharacteristic
414C2×D4C2×D3×D512yes—
415C22×C4—32no—
416C22×C4—54no—
417C22×C4—104no—
418C22×C4#120112yes—
419C22×C4C2×D3×D511yescharacteristic
420C4⋊C4—61no—
421C4⋊C4—64no—
422C4⋊C4—308no—
423C4⋊C4—302no—
424C22⋊C4—32no—
425C22⋊C4—64no—
426C22⋊C4—154no—
427C22⋊C4—308no—
428C42—61no—
429C42—302no—
430C3×C5#302811yescharacteristic, complemented, Hall
431C22×C3—22no—
432C22×C3—41no—
433C22×C3—42no—
434C22×C3—104no—
435C22×C3—204no—
436C22×C3—404no—
437C22×C3C2×D4×D512yes—
438C22×C3C22×C22⋊D511yescharacteristic
439C3×C4—22no—
440C3×C4—104no—
441C3×C4#408311yescharacteristic
442C3×C4#408311yescharacteristic
443C3×C4#408312yes—
444Dic3—42no—
445Dic3—42no—
446Dic3—204no—
447C2×C5—22no—
448C2×C5—21no—
449C2×C5—42no—
450C2×C5C2×#95311yescharacteristic
451D5—44no—
452C23—54no—
453C23—104no—
454C23C2×#120112yes—
455C23C22×D3×D511yescharacteristic
456Q8—22no—
457Q8—104no—
458Q8—102no—
459Q8—102no—
460Q8—121no—
461Q8—121no—
462Q8—122no—
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—62no—
475C2×C4—62no—
476C2×C4—64no—
477C2×C4—108no—
478C2×C4—104no—
479C2×C4—104no—
480C2×C4—104no—
481C2×C4—304no—
482C2×C4C2×#120112yes—
483C2×C4C2×#120111yescharacteristic
484C2×C4C2×#120111yescharacteristic
485C2×C4D5×#6712yes—
486C2×C4D5×#6712yes—
487C2×C3—21no—
488C2×C3—22no—
489C2×C3—42no—
490C2×C3—204no—
491C2×C3C2×#408311yescharacteristic
492C5#8412411yescharacteristic, complemented, Sylow
493C22—22no—
494C22—41no—
495C22—42no—
496C22—104no—
497C22—204no—
498C22—404no—
499C22C22×#120111yescharacteristic
500C22C2×D5×#6712yes—
501C4—22no—
502C4—104no—
503C4—122no—
504C4—122no—
505C4—604no—
506C4#9156311yescharacteristic
507C4#9156311yescharacteristic
508C4#9156312yes—
509C3#1061514811yescharacteristic, complemented, Sylow
510C2—21no—
511C2—22no—
512C2—42no—
513C2—204no—
514C2C2×#9156311yescharacteristic
subgroupG/H
centerC2C2×#91563
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. C5×#5825C2semidirect
3. #11754251C2semidirect
4. #11751341C2semidirect
5. #11749181C2semidirect
6. #11748624C2semidirect
9. C22×C5×Dic6C22semidirect
18. #91815C22semidirect
21. C5×#935C22semidirect
22. C5×#926C22semidirect
24. #91536C22semidirect
28. #91118C22semidirect
29. #90995C22semidirect
82. #5825D5semidirect
153. C22×Dic6C2×D5semidirect
159. #935C2×D5semidirect
161. #926C2×D5semidirect
430. C3×C5#3028semidirect
492. C5#84124semidirect
509. C3#10615148semidirect

Maximal subgroups

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

subgroupindex
C3×#662832
C5×#58252
#117542512
#117513412
#117491812
#117486242
#106151483
#841245