Finite Group Databasebeta

← #14327737

Subgroups — #14327737

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic5C211yesmaximal, characteristic
2C2×#91528C212yesmaximal, complemented
3#11751322C211yesmaximal, characteristic
4C5×#5221C211yesmaximal, characteristic
5#11749506C212yesmaximal, complemented
6#11749486C212yesmaximal, complemented
7#11749485C212yesmaximal, complemented
8#11748834C211yesmaximal, characteristic, complemented
9C4×#6668C211yesmaximal, characteristic, complemented
10#11748699C211yesmaximal, characteristic, complemented
11Dic3×C4⋊Dic5C211yesmaximal, characteristic, complemented
12#10608033—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×C3×Dic5C2212yes—
15C2×#6719C2212yes—
16C2×#6719C2212yes—
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C4×Dic15C2211yescharacteristic
19C2×C5×#217C2212yes—
20C2×C5×#217C2212yes—
21C2×C5×C4⋊Dic3C2211yescharacteristic
22C2×C4×C5×Dic3C2211yescharacteristic
23C2×C3×C22⋊Dic5C2212yes—
24C3×D4×Dic5C418yescomplemented
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C2×C3×C4×Dic5C2211yescharacteristic
27C2×#6668C2212yes—
28C2×#6668C2211yescharacteristic
29C2×#6668C2212yes—
30C2×#6668C2211yescharacteristic
31#91528—28no—
32C2×Dic3×Dic5C2212yes—
33C2×Dic3×Dic5C2212yes—
34#90994C2212yes—
35#90994C2212yes—
36#90994C2211yescharacteristic
37#90994C2211yescharacteristic
38#82337—51nomaximal, Hall
39C2×D4×Dic5D311yescharacteristic
40C2×#4023—32no—
41C5×#390—31no—
42#65510—31no—
43#65265—31no—
44C4⋊C4×Dic5—31no—
45#65234—32no—
46#65233—32no—
47#65231—32no—
48C4×C4⋊Dic5—31no—
49C4×#683—31no—
50C24×C3×C5C2312yes—
51C2×C3×C5×D4—22no—
52C2×C3×C5×D4—22no—
53C2×C3×C5×D4C2×C414yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2311yescharacteristic
56C22×Dic15C2312yes—
57C22×Dic15C2311yescharacteristic
58C22×C5×Dic3C2311yescharacteristic
59C22×C5×Dic3C2312yes—
60C22×C5×Dic3C2311yescharacteristic
61C22×C3×Dic5—24no—
62C22×C3×Dic5—24no—
63C22×C3×Dic5C2×C418yes—
64C22×C3×Dic5C2311yescharacteristic
65C22×C3×Dic5C2312yes—
66C22×C3×Dic5C2311yescharacteristic
67#6719—24no—
68#6719—42no—
69C4⋊Dic15—22no—
70C4×Dic15—22no—
71C5×#217—24no—
72C5×#217—42no—
73C5×C4⋊Dic3—22no—
74C4×C5×Dic3—22no—
75C3×C22⋊Dic5C2×C418yes—
76C3×C4⋊Dic5C2×C414yes—
77C3×C4×Dic5C2×C414yes—
78#6668—24no—
79#6668—22no—
80#6668—42no—
81#6668D414yescomplemented
82Dic3×Dic5—24no—
83Dic3×Dic5—24no—
84C2×C3×C4×D4—51no—
85C2×#926—52no—
86#5221—51no—
87#5221D511yescharacteristic
88#5212—52no—
89Dic3×C4⋊C4—51no—
90Dic3×C4⋊C4—51no—
91#4951—52no—
92#4951—52no—
93#4935—51no—
94C4×C4⋊Dic3—51no—
95C22×C5×D4C2×D311yescharacteristic
96C23×Dic5C2×D312yes—
97C2×C5×C4⋊C4—31no—
98C2×C5×C22⋊C4—32no—
99C2×C5×C22⋊C4—32no—
100C2×C42×C5—31no—
101C2×C22⋊Dic5—32no—
102C2×C22⋊Dic5—32no—
103C2×C22⋊Dic5C2×D312yes—
104D4×Dic5Dic318yescomplemented
105C2×C4⋊Dic5—31no—
106C2×C4⋊Dic5C2×D311yescharacteristic
107C2×#683—31no—
108C2×#683—32no—
109C2×#683—31no—
110C2×#683—32no—
111C2×C4×Dic5—31no—
112C2×C4×Dic5—32no—
113C2×C4×Dic5—32no—
114C2×C4×Dic5C2×D311yescharacteristic
115#4023—68no—
116#3963—31no—
117#3963—31no—
118#3963—32no—
119#3963—32no—
120#2354—151noSylow
121C23×C3×C5—22no—
122C23×C3×C5—22no—
123C23×C3×C5—22no—
124C23×C3×C5—22no—
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5C22×C414yes—
128C23×C3×C5C2411yescharacteristic
129C3×C5×D4—28no—
130C2×C3×C4×C5C22×C412yes—
131C2×C3×C4×C5#4112yes—
132C2×C3×C4×C5#4112yes—
133C2×Dic15—21no—
134C2×Dic15—21no—
135C2×Dic15—22no—
136C2×Dic15—21no—
137C2×Dic15—21no—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—21no—
141C2×Dic15C2×D412yes—
142C2×C5×Dic3—21no—
143C2×C5×Dic3—21no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—21no—
146C2×C5×Dic3—21no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—21no—
150C2×C5×Dic3C2×D412yes—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5—216no—
156C2×C3×Dic5C22×C412yes—
157C2×C3×Dic5C22×C414yes—
158C2×C3×Dic5C22×C412yes—
159C2×C3×Dic5C2×D412yes—
160C2×C3×Dic5#4112yes—
161C22×C3×D4C2×D511yescharacteristic
162C23×C3×C4—52no—
163C3×C4×D4—58no—
164C2×C3×C4⋊C4—51no—
165C2×C3×C22⋊C4—52no—
166C2×C3×C42—51no—
167C2×#217—52no—
168C2×#217—52no—
169C2×#217C2×D512yes—
170C2×#217C2×D512yes—
171#926—108no—
172C2×C4⋊Dic3—51no—
173C2×C4⋊Dic3—51no—
174C2×C4⋊Dic3—51no—
175C2×C4⋊Dic3—52no—
176C2×C4⋊Dic3—52no—
177C2×C4⋊Dic3C2×D511yescharacteristic
178C2×C4×Dic3—51no—
179C2×C4×Dic3—52no—
180C2×C4×Dic3—52no—
181C2×C4×Dic3C2×D511yescharacteristic
182C3⋊#95—51no—
183C3⋊#95—51no—
184C3⋊#95—52no—
185C3⋊#95—52no—
186C24×C5C22×D312yes—
187C2×C5×D4—22no—
188C2×C5×D4—22no—
189C2×C5×D4C2×Dic314yes—
190C22×C4×C5—31no—
191C22×C4×C5—31no—
192C22×C4×C5—32no—
193C22×C4×C5C22×D311yescharacteristic
194C22×Dic5—24no—
195C22×Dic5—24no—
196C22×Dic5—31no—
197C22×Dic5—31no—
198C22×Dic5—32no—
199C22×Dic5C2×Dic318yes—
200C22×Dic5C22×D311yescharacteristic
201C22×Dic5C22×D312yes—
202C22×Dic5C22×D311yescharacteristic
203C5×C4⋊C4—62no—
204C5×C22⋊C4—64no—
205C5×C22⋊C4—122no—
206C42×C5—62no—
207C22⋊Dic5—64no—
208C22⋊Dic5—122no—
209C22⋊Dic5C2×Dic318yes—
210C4⋊Dic5—62no—
211C4⋊Dic5C2×Dic314yes—
212#683—34no—
213#683—64no—
214#683—62no—
215#683—122no—
216C4×Dic5—64no—
217C4×Dic5—64no—
218C4×Dic5—62no—
219C4×Dic5C2×Dic314yes—
220C2×C4×D4—51no—
221C2×#117—152no—
222#390—31no—
223#390—151no—
224#388—152no—
225#388—152no—
226#384—151no—
227#380—152no—
228C4×C4⋊C4—151no—
229C4×C4⋊C4—151no—
230C4×C4⋊C4—151no—
231C22×C3×C5—24no—
232C22×C3×C5—24no—
233C22×C3×C5—24no—
234C22×C3×C5—42no—
235C22×C3×C5—42no—
236C22×C3×C5—42no—
237C22×C3×C5—42no—
238C22×C3×C5C23×C411yescharacteristic
239C22×C3×C5C22×D411yescharacteristic
240C22×C3×C5C2×#4111yescharacteristic
241C22×C3×C5C2×#4111yescharacteristic
242C22×C3×C5C2×#4111yescharacteristic
243C22×C3×C5H(5,𝔽2)11yescharacteristic
244C22×C3×C52−1+411yescharacteristic
245C3×C4×C5#11714yescomplemented
246Dic15—22no—
247Dic15—42no—
248Dic15—41no—
249C3×Dic5—24no—
250C3×Dic5—22no—
251C3×Dic5C4×D414yes—
252C5×Dic3—22no—
253C5×Dic3—42no—
254C5×Dic3—41no—
255C24×C3C22×D512yes—
256C2×C3×D4—22no—
257C2×C3×D4—22no—
258C2×C3×D4C4×D514yes—
259C22×C3×C4—51no—
260C22×C3×C4—58no—
261C22×C3×C4—52no—
262C22×C3×C4—51no—
263C22×C3×C4—104no—
264C22×C3×C4—104no—
265C22×C3×C4C22×D511yescharacteristic
266C22×Dic3—51no—
267C22×Dic3—51no—
268C22×Dic3—52no—
269C22×Dic3C22×D511yescharacteristic
270C22×Dic3C22×D512yes—
271C22×Dic3C22×D511yescharacteristic
272C3×C4⋊C4—54no—
273C3×C22⋊C4—58no—
274C3×C42—54no—
275#217—24no—
276#217—42no—
277#217—104no—
278#217—202no—
279C4⋊Dic3—22no—
280C4⋊Dic3—54no—
281C4⋊Dic3—102no—
282C4⋊Dic3—104no—
283C4⋊Dic3—102no—
284C4⋊Dic3—202no—
285C4×Dic3—22no—
286C4×Dic3—104no—
287C4×Dic3—102no—
288C4×Dic3—104no—
289C23×C5—22no—
290C23×C5—22no—
291C23×C5—22no—
292C23×C5—22no—
293C23×C5—22no—
294C23×C5—22no—
295C23×C5C22×Dic314yes—
296C23×C5C23×D311yescharacteristic
297C5×D4—28no—
298C2×C4×C5—32no—
299C2×C4×C5—61no—
300C2×C4×C5—61no—
301C2×C4×C5—61no—
302C2×C4×C5—62no—
303C2×C4×C5—62no—
304C2×C4×C5—61no—
305C2×C4×C5—62no—
306C2×C4×C5—61no—
307C2×C4×C5#23512yes—
308C2×C4×C5#23512yes—
309C2×C4×C5C22×Dic312yes—
310C2×Dic5—22no—
311C2×Dic5—22no—
312C2×Dic5—21no—
313C2×Dic5—21no—
314C2×Dic5—216no—
315C2×Dic5—32no—
316C2×Dic5—61no—
317C2×Dic5—61no—
318C2×Dic5—61no—
319C2×Dic5—62no—
320C2×Dic5—62no—
321C2×Dic5—61no—
322C2×Dic5—62no—
323C2×Dic5—61no—
324C2×Dic5D3×D412yes—
325C2×Dic5#23712yes—
326C2×Dic5C22×Dic312yes—
327C2×Dic5C22×Dic314yes—
328C2×Dic5C22×Dic312yes—
329C22×D4D3×D511yescharacteristic
330C23×C4—52no—
331C4×D4—58no—
332#117—308no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—51no—
335C2×C4⋊C4—151no—
336C2×C4⋊C4—152no—
337C2×C4⋊C4—151no—
338C2×C4⋊C4—151no—
339C2×C4⋊C4—152no—
340C2×C22⋊C4—32no—
341C2×C22⋊C4—32no—
342C2×C22⋊C4—52no—
343C2×C22⋊C4—152no—
344C2×C22⋊C4—152no—
345C2×C42—31no—
346C2×C42—51no—
347C2×C42—152no—
348C2×C42—152no—
349C2×C42—151no—
350#95—152no—
351#95—152no—
352#95—151no—
353#95—151no—
354C2×C3×C5—44no—
355C2×C3×C5C2×#11711yescharacteristic
356C2×C3×C5C2×C4×D411yescharacteristic
357C2×C3×C5#52011yescharacteristic
358C2×C3×C5#54711yescharacteristic
359C2×C3×C5#55011yescharacteristic
360C2×C3×C5#55511yescharacteristic
361C2×C3×C5#55611yescharacteristic
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3C2×C4×D514yes—
369C23×C3C23×D511yescharacteristic
370C3×D4—28no—
371C2×C3×C4—52no—
372C2×C3×C4—52no—
373C2×C3×C4—52no—
374C2×C3×C4—52no—
375C2×C3×C4—54no—
376C2×C3×C4—1016no—
377C2×C3×C4—102no—
378C2×C3×C4—101no—
379C2×C3×C4—102no—
380C2×C3×C4—101no—
381C2×C3×C4C2×C4×D512yes—
382C2×C3×C4#71112yes—
383C2×C3×C4#71112yes—
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3—22no—
387C2×Dic3—21no—
388C2×Dic3—22no—
389C2×Dic3—22no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—52no—
393C2×Dic3—101no—
394C2×Dic3—101no—
395C2×Dic3—102no—
396C2×Dic3—101no—
397C2×Dic3—102no—
398C2×Dic3—102no—
399C2×Dic3—101no—
400C2×Dic3—101no—
401C2×Dic3D4×D512yes—
402C22×C5—24no—
403C22×C5—24no—
404C22×C5—24no—
405C22×C5—42no—
406C22×C5—42no—
407C22×C5—42no—
408C22×C5—42no—
409C22×C5C2×#23511yescharacteristic
410C22×C5C2×#23511yescharacteristic
411C22×C5C2×D3×D411yescharacteristic
412C22×C5C2×#23711yescharacteristic
413C22×C5#100911yescharacteristic
414C22×C5#101011yescharacteristic
415C22×C5C23×Dic311yescharacteristic
416C4×C5—62no—
417C4×C5—122no—
418C4×C5—121no—
419C4×C5#92614yescomplemented
420Dic5—24no—
421Dic5—22no—
422Dic5—62no—
423Dic5—122no—
424Dic5—121no—
425Dic5D4×Dic314yes—
426C24C2×D3×D512yes—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4D5×Dic314yes—
430C22×C4—31no—
431C22×C4—31no—
432C22×C4—32no—
433C22×C4—51no—
434C22×C4—58no—
435C22×C4—51no—
436C22×C4—52no—
437C22×C4—104no—
438C22×C4—104no—
439C22×C4—151no—
440C22×C4—151no—
441C22×C4—152no—
442C22×C4C2×D3×D511yescharacteristic
443C4⋊C4—54no—
444C4⋊C4—62no—
445C4⋊C4—154no—
446C4⋊C4—304no—
447C4⋊C4—302no—
448C4⋊C4—302no—
449C4⋊C4—602no—
450C22⋊C4—58no—
451C22⋊C4—64no—
452C22⋊C4—122no—
453C22⋊C4—304no—
454C22⋊C4—602no—
455C42—54no—
456C42—62no—
457C42—304no—
458C42—304no—
459C42—302no—
460C3×C5#235411yescharacteristic, complemented, Hall
461C22×C3—24no—
462C22×C3—24no—
463C22×C3—24no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3C22×C4×D511yescharacteristic
469C22×C3C2×D4×D511yescharacteristic
470C22×C3C2×#71111yescharacteristic
471C22×C3C2×#71111yescharacteristic
472C22×C3#414411yescharacteristic
473C22×C3D5×#4111yescharacteristic
474C22×C3#415011yescharacteristic
475C3×C4—54no—
476C3×C4—104no—
477C3×C4—102no—
478C3×C4#402314yescomplemented
479Dic3—22no—
480Dic3—42no—
481Dic3—41no—
482Dic3—102no—
483Dic3—202no—
484Dic3—201no—
485C2×C5—44no—
486C2×C5#554211yescharacteristic
487C2×C5#555111yescharacteristic
488C2×C5#555311yescharacteristic
489C2×C5#556311yescharacteristic
490C2×C5C2×#92611yescharacteristic
491C2×C5C2×D4×Dic311yescharacteristic
492C2×C5#582711yescharacteristic
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23C2×D5×Dic314yes—
500C23C22×D3×D511yescharacteristic
501D4—28no—
502C2×C4—32no—
503C2×C4—52no—
504C2×C4—52no—
505C2×C4—52no—
506C2×C4—52no—
507C2×C4—54no—
508C2×C4—61no—
509C2×C4—61no—
510C2×C4—62no—
511C2×C4—61no—
512C2×C4—61no—
513C2×C4—62no—
514C2×C4—61no—
515C2×C4—62no—
516C2×C4—1016no—
517C2×C4—101no—
518C2×C4—102no—
519C2×C4—102no—
520C2×C4—101no—
521C2×C4—152no—
522C2×C4—301no—
523C2×C4—301no—
524C2×C4—302no—
525C2×C4—301no—
526C2×C4—301no—
527C2×C4—302no—
528C2×C4—301no—
529C2×C4—302no—
530C2×C4C2×D5×Dic312yes—
531C2×C4#678212yes—
532C2×C4#678212yes—
533C2×C3—44no—
534C2×C3C2×#402311yescharacteristic
535C2×C3C4×D4×D511yescharacteristic
536C2×C3#6588011yescharacteristic
537C2×C3#6594511yescharacteristic
538C2×C3#6595011yescharacteristic
539C2×C3#6600511yescharacteristic
540C2×C3#6605211yescharacteristic
541C5#8233711yescharacteristic, complemented, Sylow
542C22—24no—
543C22—24no—
544C22—24no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22#9202011yescharacteristic
550C22D3×D4×D511yescharacteristic
551C22D5×#23711yescharacteristic
552C22#9202711yescharacteristic
553C22C22×D5×Dic311yescharacteristic
554C22C2×#678211yescharacteristic
555C22C2×#678211yescharacteristic
556C4—54no—
557C4—62no—
558C4—104no—
559C4—102no—
560C4—122no—
561C4—121no—
562C4—302no—
563C4—602no—
564C4—601no—
565C4#9152814yescomplemented
566C3#1060803311yescharacteristic, complemented, Sylow
567C2—44no—
568C2D4×D5×Dic311yescharacteristic
569C2#1175477911yescharacteristic
570C2#1175478311yescharacteristic
571C2#1175492311yescharacteristic
572C2#1175496611yescharacteristic
573C2#1175501111yescharacteristic
574C2C2×#9152811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
Fitting, prime radicalC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5#2354
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#91528C2semidirect
5. #11749506C2semidirect
6. #11749486C2semidirect
7. #11749485C2semidirect
8. #11748834C2semidirect
9. C4×#6668C2semidirect
10. #11748699C2semidirect
11. Dic3×C4⋊Dic5C2semidirect
24. C3×D4×Dic5C4semidirect
81. #6668D4semidirect
104. D4×Dic5Dic3semidirect
245. C3×C4×C5#117semidirect
419. C4×C5#926semidirect
460. C3×C5#2354semidirect
478. C3×C4#4023semidirect
541. C5#82337semidirect
565. C4#91528semidirect
566. C3#10608033semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic52
C2×#915282
#117513222
C5×#52212
#117495062
#117494862
#117494852
#117488342
C4×#66682
#117486992
Dic3×C4⋊Dic52
#106080333
#823375