Finite Group Databasebeta

← #14320866

Subgroups — #14320866

Order 1920.

1304 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D4×Dic3C211yesmaximal, characteristic
2C2×#91529C212yesmaximal, complemented
3#11751322C211yesmaximal, characteristic
4C3×#65510C211yesmaximal, characteristic
5Dic3×C22⋊Dic5C212yesmaximal, complemented
6#11749479C212yesmaximal, complemented
7#11749478C212yesmaximal, complemented
8#11748868C211yesmaximal, characteristic, complemented
9#11748842C211yesmaximal, characteristic, complemented
10Dic3×C4⋊Dic5C211yesmaximal, characteristic, complemented
11C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
12#10614050—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×C5×Dic3C2212yes—
15C2×#6719C2212yes—
16C2×#6719C2212yes—
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C4×Dic15C2211yescharacteristic
19C2×C5×#217C2212yes—
20C5×D4×Dic3C418yescomplemented
21C2×C5×C4⋊Dic3C2211yescharacteristic
22C2×C4×C5×Dic3C2211yescharacteristic
23C2×C3×C22⋊Dic5C2212yes—
24C2×C3×C22⋊Dic5C2212yes—
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C2×C3×C4×Dic5C2211yescharacteristic
27C2×Dic3⋊Dic5C2212yes—
28C2×Dic3⋊Dic5C2212yes—
29#91529—28no—
30C2×Dic3×Dic5C2211yescharacteristic
31C2×Dic3×Dic5C2211yescharacteristic
32C2×Dic3×Dic5C2211yescharacteristic
33C2×Dic3×Dic5C2212yes—
34C2×Dic3×Dic5C2211yescharacteristic
35#90994C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#76289—51nomaximal, Hall
39C2×C4×C5×D4—31no—
40C2×#4072—32no—
41#65510—31no—
42#65510D311yescharacteristic
43C4×C22⋊Dic5—32no—
44#65274—31no—
45#65274—31no—
46#65240—32no—
47#65240—32no—
48C4×C4⋊Dic5—31no—
49C42×Dic5—31no—
50C24×C3×C5C2312yes—
51C2×C3×C5×D4—22no—
52C2×C3×C5×D4—22no—
53C2×C3×C5×D4C2×C414yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2311yescharacteristic
57C22×Dic15C2311yescharacteristic
58C22×C5×Dic3—24no—
59C22×C5×Dic3—24no—
60C22×C5×Dic3C2×C418yes—
61C22×C5×Dic3C2311yescharacteristic
62C22×C5×Dic3C2312yes—
63C22×C5×Dic3C2311yescharacteristic
64C22×C3×Dic5C2312yes—
65C22×C3×Dic5C2311yescharacteristic
66C22×C3×Dic5C2311yescharacteristic
67#6719—24no—
68#6719—24no—
69C4⋊Dic15—22no—
70C4×Dic15—22no—
71C5×#217C2×C418yes—
72C5×C4⋊Dic3C2×C414yes—
73C4×C5×Dic3C2×C414yes—
74C3×C22⋊Dic5—24no—
75C3×C22⋊Dic5—24no—
76C3×C4⋊Dic5—22no—
77C3×C4×Dic5—22no—
78Dic3⋊Dic5—24no—
79Dic3⋊Dic5—24no—
80Dic3×Dic5—22no—
81Dic3×Dic5—24no—
82Dic3×Dic5—22no—
83Dic3×Dic5—22no—
84Dic3×Dic5D414yescomplemented
85C2×D4×Dic3D511yescharacteristic
86C2×#877—52no—
87C3×#390—51no—
88#5221—51no—
89Dic3×C4⋊C4—51no—
90#4972—51no—
91#4945—52no—
92#4944—52no—
93Dic3×C22⋊C4—52no—
94C42×Dic3—51no—
95#4928—51no—
96C22×C5×D4C2×D311yescharacteristic
97C23×C4×C5—32no—
98C4×C5×D4—38no—
99C2×C5×C4⋊C4—31no—
100C2×C5×C22⋊C4—32no—
101C2×C42×C5—31no—
102C2×C22⋊Dic5—32no—
103C2×C22⋊Dic5—32no—
104C2×C22⋊Dic5C2×D312yes—
105C2×C22⋊Dic5C2×D312yes—
106#4072—68no—
107C2×C4⋊Dic5—31no—
108C2×C4⋊Dic5—32no—
109C2×C4⋊Dic5—32no—
110C2×C4⋊Dic5C2×D311yescharacteristic
111C2×C4×Dic5—31no—
112C2×C4×Dic5—31no—
113C2×C4×Dic5—32no—
114C2×C4×Dic5—31no—
115C2×C4×Dic5—31no—
116C2×C4×Dic5—31no—
117C2×C4×Dic5C2×D311yescharacteristic
118#3963—32no—
119#3963—32no—
120#3963—32no—
121#2293—151noSylow
122C23×C3×C5—22no—
123C23×C3×C5—22no—
124C23×C3×C5—22no—
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5—22no—
128C23×C3×C5C22×C414yes—
129C23×C3×C5C2411yescharacteristic
130C3×C5×D4—28no—
131C2×C3×C4×C5C22×C412yes—
132C2×C3×C4×C5#4112yes—
133C2×C3×C4×C5#4112yes—
134C2×Dic15—21no—
135C2×Dic15—21no—
136C2×Dic15—21no—
137C2×Dic15—21no—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15C2×D412yes—
142C2×Dic15#4112yes—
143C2×C5×Dic3—22no—
144C2×C5×Dic3—21no—
145C2×C5×Dic3—21no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—216no—
148C2×C5×Dic3C22×C412yes—
149C2×C5×Dic3C22×C414yes—
150C2×C5×Dic3C22×C412yes—
151C2×C5×Dic3C2×D412yes—
152C2×C5×Dic3#4112yes—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5C2×D412yes—
161C2×C3×Dic5#4112yes—
162C22×C3×D4C2×D511yescharacteristic
163C23×Dic3C2×D512yes—
164C2×C3×C4⋊C4—51no—
165C2×C3×C22⋊C4—52no—
166C2×C3×C22⋊C4—52no—
167C2×C3×C42—51no—
168C2×#217—52no—
169C2×#217—52no—
170C2×#217C2×D512yes—
171D4×Dic3Dic518yescomplemented
172C2×C4⋊Dic3—51no—
173C2×C4⋊Dic3C2×D511yescharacteristic
174C2×Dic3⋊C4—52no—
175C2×Dic3⋊C4—52no—
176C2×C4×Dic3—51no—
177C2×C4×Dic3—51no—
178C2×C4×Dic3—51no—
179C2×C4×Dic3—51no—
180C2×C4×Dic3—51no—
181C2×C4×Dic3—52no—
182C2×C4×Dic3C2×D511yescharacteristic
183#877—108no—
184C3⋊#95—52no—
185C3⋊#95—52no—
186C3⋊#95—52no—
187C24×C5C22×D312yes—
188C2×C5×D4—22no—
189C2×C5×D4—22no—
190C2×C5×D4C4×D314yes—
191C22×C4×C5—31no—
192C22×C4×C5—38no—
193C22×C4×C5—31no—
194C22×C4×C5—32no—
195C22×C4×C5—64no—
196C22×C4×C5—64no—
197C22×C4×C5C22×D311yescharacteristic
198C22×Dic5—31no—
199C22×Dic5—31no—
200C22×Dic5—32no—
201C22×Dic5C22×D312yes—
202C22×Dic5C22×D311yescharacteristic
203C22×Dic5C22×D311yescharacteristic
204C5×C4⋊C4—34no—
205C5×C22⋊C4—38no—
206C42×C5—34no—
207C22⋊Dic5—24no—
208C22⋊Dic5—24no—
209C22⋊Dic5—64no—
210C22⋊Dic5—64no—
211C4⋊Dic5—22no—
212C4⋊Dic5—64no—
213C4⋊Dic5—62no—
214C4⋊Dic5—64no—
215C4×Dic5—22no—
216C4×Dic5—34no—
217C4×Dic5—62no—
218C4×Dic5—62no—
219C4×Dic5—64no—
220C4×Dic5—62no—
221C4×Dic5—62no—
222C2×C4×D4—31no—
223C2×#117—152no—
224#390—51no—
225#390—151no—
226#389—151no—
227#389—151no—
228#388—152no—
229#388—152no—
230C4×C4⋊C4—151no—
231C4×C22⋊C4—152no—
232C43—151no—
233C22×C3×C5—24no—
234C22×C3×C5—24no—
235C22×C3×C5—24no—
236C22×C3×C5—42no—
237C22×C3×C5—42no—
238C22×C3×C5—42no—
239C22×C3×C5—42no—
240C22×C3×C5C23×C411yescharacteristic
241C22×C3×C5C22×D411yescharacteristic
242C22×C3×C5C2×#4111yescharacteristic
243C22×C3×C5C2×#4111yescharacteristic
244C22×C3×C5C2×#4111yescharacteristic
245C22×C3×C5C2×#4111yescharacteristic
246C22×C3×C5C2×#4111yescharacteristic
247C3×C4×C5#11714yescomplemented
248Dic15—22no—
249Dic15—22no—
250Dic15—42no—
251C3×Dic5—22no—
252C3×Dic5—22no—
253C3×Dic5—42no—
254C5×Dic3—24no—
255C5×Dic3—22no—
256C5×Dic3C4×D414yes—
257C24×C3C22×D512yes—
258C2×C3×D4—22no—
259C2×C3×D4—22no—
260C2×C3×D4C2×Dic514yes—
261C22×C3×C4—51no—
262C22×C3×C4—51no—
263C22×C3×C4—52no—
264C22×C3×C4C22×D511yescharacteristic
265C22×Dic3—24no—
266C22×Dic3—24no—
267C22×Dic3—51no—
268C22×Dic3—51no—
269C22×Dic3—52no—
270C22×Dic3C2×Dic518yes—
271C22×Dic3C22×D511yescharacteristic
272C22×Dic3C22×D512yes—
273C22×Dic3C22×D511yescharacteristic
274C3×C4⋊C4—102no—
275C3×C22⋊C4—104no—
276C3×C22⋊C4—104no—
277C3×C42—102no—
278#217—104no—
279#217—104no—
280#217C2×Dic518yes—
281C4⋊Dic3—102no—
282C4⋊Dic3C2×Dic514yes—
283Dic3⋊C4—104no—
284Dic3⋊C4—104no—
285C4×Dic3—54no—
286C4×Dic3—102no—
287C4×Dic3—102no—
288C4×Dic3—102no—
289C4×Dic3—104no—
290C4×Dic3—102no—
291C4×Dic3C2×Dic514yes—
292C23×C5—22no—
293C23×C5—22no—
294C23×C5—22no—
295C23×C5—22no—
296C23×C5—22no—
297C23×C5—22no—
298C23×C5C2×C4×D314yes—
299C23×C5C23×D311yescharacteristic
300C5×D4—28no—
301C2×C4×C5—32no—
302C2×C4×C5—32no—
303C2×C4×C5—32no—
304C2×C4×C5—32no—
305C2×C4×C5—34no—
306C2×C4×C5—616no—
307C2×C4×C5—62no—
308C2×C4×C5—61no—
309C2×C4×C5—61no—
310C2×C4×C5—62no—
311C2×C4×C5C2×C4×D312yes—
312C2×C4×C5#23712yes—
313C2×C4×C5#23712yes—
314C2×Dic5—21no—
315C2×Dic5—21no—
316C2×Dic5—21no—
317C2×Dic5—21no—
318C2×Dic5—22no—
319C2×Dic5—22no—
320C2×Dic5—22no—
321C2×Dic5—32no—
322C2×Dic5—32no—
323C2×Dic5—61no—
324C2×Dic5—61no—
325C2×Dic5—61no—
326C2×Dic5—61no—
327C2×Dic5—62no—
328C2×Dic5—62no—
329C2×Dic5—62no—
330C2×Dic5D3×D412yes—
331C2×Dic5#23712yes—
332C22×D4D3×D511yescharacteristic
333C23×C4—32no—
334C4×D4—38no—
335#117—308no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—51no—
338C2×C4⋊C4—152no—
339C2×C4⋊C4—152no—
340C2×C4⋊C4—151no—
341C2×C22⋊C4—32no—
342C2×C22⋊C4—52no—
343C2×C22⋊C4—52no—
344C2×C22⋊C4—152no—
345C2×C22⋊C4—152no—
346C2×C42—31no—
347C2×C42—51no—
348C2×C42—151no—
349C2×C42—152no—
350C2×C42—151no—
351C2×C42—151no—
352C2×C42—151no—
353C2×C42—151no—
354#95—152no—
355#95—152no—
356#95—152no—
357C2×C3×C5—44no—
358C2×C3×C5C2×#11711yescharacteristic
359C2×C3×C5C2×C4×D411yescharacteristic
360C2×C3×C5C4×#4111yescharacteristic
361C2×C3×C5#52911yescharacteristic
362C2×C3×C5#52911yescharacteristic
363C2×C3×C5#53211yescharacteristic
364C2×C3×C5#53211yescharacteristic
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3C22×Dic514yes—
372C23×C3C23×D511yescharacteristic
373C3×D4—28no—
374C2×C3×C4—52no—
375C2×C3×C4—52no—
376C2×C3×C4—101no—
377C2×C3×C4—101no—
378C2×C3×C4—101no—
379C2×C3×C4—101no—
380C2×C3×C4—102no—
381C2×C3×C4—102no—
382C2×C3×C4—102no—
383C2×C3×C4#70912yes—
384C2×C3×C4#70912yes—
385C2×C3×C4C22×Dic512yes—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—21no—
389C2×Dic3—21no—
390C2×Dic3—216no—
391C2×Dic3—52no—
392C2×Dic3—52no—
393C2×Dic3—101no—
394C2×Dic3—101no—
395C2×Dic3—101no—
396C2×Dic3—101no—
397C2×Dic3—102no—
398C2×Dic3—102no—
399C2×Dic3—102no—
400C2×Dic3D4×D512yes—
401C2×Dic3#71112yes—
402C2×Dic3C22×Dic512yes—
403C2×Dic3C22×Dic514yes—
404C2×Dic3C22×Dic512yes—
405C22×C5—24no—
406C22×C5—24no—
407C22×C5—24no—
408C22×C5—42no—
409C22×C5—42no—
410C22×C5—42no—
411C22×C5—42no—
412C22×C5C22×C4×D311yescharacteristic
413C22×C5C2×D3×D411yescharacteristic
414C22×C5C2×#23711yescharacteristic
415C22×C5C2×#23711yescharacteristic
416C22×C5C2×#23711yescharacteristic
417C22×C5D3×#4111yescharacteristic
418C22×C5D3×#4111yescharacteristic
419C4×C5—34no—
420C4×C5—62no—
421C4×C5—64no—
422C4×C5#87714yescomplemented
423Dic5—22no—
424Dic5—22no—
425Dic5—42no—
426Dic5—62no—
427Dic5—62no—
428Dic5—122no—
429C24C2×D3×D512yes—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4D3×Dic514yes—
433C22×C4—31no—
434C22×C4—38no—
435C22×C4—31no—
436C22×C4—32no—
437C22×C4—51no—
438C22×C4—51no—
439C22×C4—52no—
440C22×C4—64no—
441C22×C4—64no—
442C22×C4—151no—
443C22×C4—151no—
444C22×C4—152no—
445C22×C4C2×D3×D511yescharacteristic
446C4⋊C4—34no—
447C4⋊C4—102no—
448C4⋊C4—304no—
449C4⋊C4—304no—
450C4⋊C4—302no—
451C22⋊C4—38no—
452C22⋊C4—104no—
453C22⋊C4—104no—
454C22⋊C4—304no—
455C22⋊C4—304no—
456C42—34no—
457C42—102no—
458C42—154no—
459C42—304no—
460C42—302no—
461C42—302no—
462C42—302no—
463C42—302no—
464C3×C5#229311yescharacteristic, complemented, Hall
465C22×C3—24no—
466C22×C3—24no—
467C22×C3—24no—
468C22×C3—42no—
469C22×C3—42no—
470C22×C3—42no—
471C22×C3—42no—
472C22×C3C2×#70911yescharacteristic
473C22×C3C2×#70911yescharacteristic
474C22×C3C2×D4×D511yescharacteristic
475C22×C3C2×#71111yescharacteristic
476C22×C3D5×#4111yescharacteristic
477C22×C3D5×#4111yescharacteristic
478C22×C3C23×Dic511yescharacteristic
479C3×C4—102no—
480C3×C4—102no—
481C3×C4—202no—
482C3×C4#407214yescomplemented
483Dic3—24no—
484Dic3—22no—
485Dic3—102no—
486Dic3—102no—
487Dic3—202no—
488Dic3D4×Dic514yes—
489C2×C5—44no—
490C2×C5C2×#87711yescharacteristic
491C2×C5C4×#23711yescharacteristic
492C2×C5C4×D3×D411yescharacteristic
493C2×C5#559611yescharacteristic
494C2×C5#560011yescharacteristic
495C2×C5#568011yescharacteristic
496C2×C5#571611yescharacteristic
497C23—22no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23C2×D3×Dic514yes—
504C23C22×D3×D511yescharacteristic
505D4—28no—
506C2×C4—32no—
507C2×C4—32no—
508C2×C4—32no—
509C2×C4—32no—
510C2×C4—34no—
511C2×C4—52no—
512C2×C4—52no—
513C2×C4—616no—
514C2×C4—62no—
515C2×C4—61no—
516C2×C4—62no—
517C2×C4—61no—
518C2×C4—101no—
519C2×C4—101no—
520C2×C4—101no—
521C2×C4—101no—
522C2×C4—102no—
523C2×C4—102no—
524C2×C4—102no—
525C2×C4—152no—
526C2×C4—152no—
527C2×C4—301no—
528C2×C4—301no—
529C2×C4—301no—
530C2×C4—301no—
531C2×C4—302no—
532C2×C4—302no—
533C2×C4—302no—
534C2×C4#677912yes—
535C2×C4#677912yes—
536C2×C4C2×D3×Dic512yes—
537C2×C3—44no—
538C2×C3#6588211yescharacteristic
539C2×C3#6588211yescharacteristic
540C2×C3#6589111yescharacteristic
541C2×C3#6589111yescharacteristic
542C2×C3C2×#407211yescharacteristic
543C2×C3C2×D4×Dic511yescharacteristic
544C2×C3#41×Dic511yescharacteristic
545C5#7628911yescharacteristic, complemented, Sylow
546C22—24no—
547C22—24no—
548C22—24no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22D3×D4×D511yescharacteristic
554C22D5×#23711yescharacteristic
555C22D3×#71111yescharacteristic
556C22#9202411yescharacteristic
557C22C2×#677911yescharacteristic
558C22C2×#677911yescharacteristic
559C22C22×D3×Dic511yescharacteristic
560C4—34no—
561C4—64no—
562C4—62no—
563C4—102no—
564C4—102no—
565C4—202no—
566C4—302no—
567C4—302no—
568C4—602no—
569C4#9152914yescomplemented
570C3#1061405011yescharacteristic, complemented, Sylow
571C2—44no—
572C2#1175476011yescharacteristic
573C2D3×D4×Dic511yescharacteristic
574C2#1175477711yescharacteristic
575C2#1175483311yescharacteristic
576C2Dic5×#23711yescharacteristic
577C2#1175487811yescharacteristic
578C2C2×#9152911yescharacteristic
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#2293
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×#91529C2semidirect
5. Dic3×C22⋊Dic5C2semidirect
6. #11749479C2semidirect
7. #11749478C2semidirect
8. #11748868C2semidirect
9. #11748842C2semidirect
10. Dic3×C4⋊Dic5C2semidirect
11. C4×Dic3×Dic5C2semidirect
20. C5×D4×Dic3C4semidirect
84. Dic3×Dic5D4semidirect
171. D4×Dic3Dic5semidirect
247. C3×C4×C5#117semidirect
422. C4×C5#877semidirect
464. C3×C5#2293semidirect
482. C3×C4#4072semidirect
545. C5#76289semidirect
569. C4#91529semidirect
570. C3#10614050semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D4×Dic32
C2×#915292
#117513222
C3×#655102
Dic3×C22⋊Dic52
#117494792
#117494782
#117488682
#117488422
Dic3×C4⋊Dic52
C4×Dic3×Dic52
#106140503
#762895