Finite Group Databasebeta

← #14326632

Subgroups — #14326632

Order 1920.

1208 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91437C211yesmaximal, characteristic
2C2×#91403C212yesmaximal
3#11751088C211yesmaximal, characteristic
4C5×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
5C3×#65262C211yesmaximal, characteristic, complemented
6#11748889C212yesmaximal
7#11748857C211yesmaximal, characteristic, complemented
8#11748808C212yesmaximal, complemented
9C4×#6667C211yesmaximal, characteristic
10Dic5×C4⋊Dic3C211yesmaximal, characteristic, complemented
11#11748657C212yesmaximal, complemented
12#10605498—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×#1200C2212yes—
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×#6714C2212yes—
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C5×C4⋊Dic3C2211yescharacteristic
19C2×C4×C5×Dic3C2212yes—
20C2×C4×C5×Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic5C2211yescharacteristic
22C2×C3×#683C2212yes—
23C2×C3×C4×Dic5C2211yescharacteristic
24C2×#6669C2212yes—
25C2×#6668C2212yes—
26C2×#6667C2211yescharacteristic
27C2×#6667C2211yescharacteristic
28C2×Dic3×Dic5C2212yes—
29#91437C418yescomplemented
30#91403—28no—
31#91115C2212yes—
32C5×C3⋊#95C2212yes—
33C3×#3963C2212yes—
34#90994C2212yes—
35#90994C2212yes—
36#90994C2211yescharacteristic
37#90994C2211yescharacteristic
38#76200—51nomaximal, Hall
39C2×D5×C4⋊C4—31no—
40C2×#4018—32no—
41C4×C5×C4⋊C4—31no—
42#65276—31no—
43C4⋊C4×Dic5—31no—
44#65262D311yescharacteristic, complemented
45C4×#685—31no—
46#65222—32no—
47#65217—31no—
48#64953—32no—
49#64941—32no—
50C23×D15C2311yescharacteristic
51C22×C3×C4×C5C2312yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15C2312yes—
54C22×Dic15C2311yescharacteristic
55C2×C4×D15—22no—
56C2×C4×D15—22no—
57C2×C4×D15C2×C414yes—
58C22×C5×Dic3C2311yescharacteristic
59C22×C5×Dic3C2312yes—
60C22×C5×Dic3C2311yescharacteristic
61C22×C3×Dic5C2311yescharacteristic
62C22×C3×Dic5C2312yes—
63C22×C3×Dic5C2311yescharacteristic
64C2×#1200—24no—
65C2×#1200—24no—
66C2×#1200C2×C418yes—
67C3×C5×C4⋊C4—22no—
68#6714—24no—
69C4⋊Dic15—22no—
70C5×C4⋊Dic3C2×C414yes—
71C4×C5×Dic3—22no—
72C4×C5×Dic3—24no—
73C3×C4⋊Dic5C2×C414yes—
74C3×#683—24no—
75C3×C4×Dic5—22no—
76#6669C2×C418yes—
77#6668—24no—
78#6667—22no—
79#6667D414yes—
80Dic3×Dic5—24no—
81C2×#892—52no—
82C2×D3×C4⋊C4—51no—
83C3×#389—51no—
84#4987—51no—
85#4984—51no—
86#4978—52no—
87Dic3×C4⋊C4D511yescharacteristic, complemented
88C4×(C2×D3)⋊C4—51no—
89C4×C4⋊Dic3—51no—
90#4664—52no—
91#4655—52no—
92C22×C4×D5—31no—
93C22×C4×D5—32no—
94C2×C5×C4⋊C4—31no—
95C2×C5×C4⋊C4C2×D311yescharacteristic
96C2×C42×C5—32no—
97C2×C42×C5—31no—
98C2×#685—31no—
99C2×#685—32no—
100C2×#685—31no—
101C2×C4⋊Dic5—31no—
102C2×C4⋊Dic5C2×D311yescharacteristic
103C2×#683—32no—
104C2×#683—32no—
105C2×#683C2×D312yes—
106C2×C4×Dic5—32no—
107C2×C4×Dic5C2×D311yescharacteristic
108D5×C4⋊C4—38no—
109#4018—68no—
110C5×#95—32no—
111#3963—32no—
112#3963—31no—
113#3963—32no—
114#3963—32no—
115#3963—31no—
116#3963C2×D312yes—
117#2344—151noSylow
118C23×C3×C5C2411yescharacteristic
119C22×D15—21no—
120C22×D15—21no—
121C22×D15—21no—
122C22×D15—21no—
123C22×D15C22×C412yes—
124C22×D15C2×D412yes—
125C22×D15#4112yes—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5C22×C412yes—
130C2×C3×C4×C5#4112yes—
131C2×C3×C4×C5#4112yes—
132C2×Dic15—21no—
133C2×Dic15—21no—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15C22×C412yes—
138C4×D15—28no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—21no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—21no—
143C2×C5×Dic3—21no—
144C2×C5×Dic3—21no—
145C2×C5×Dic3—21no—
146C2×C5×Dic3C22×C414yes—
147C2×C5×Dic3C2×D412yes—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—21no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5C22×C414yes—
156C2×C3×Dic5C2×D412yes—
157#1200—216no—
158C22×C4×D3—51no—
159C22×C4×D3—52no—
160C2×C3×C4⋊C4—51no—
161C2×C3×C4⋊C4—52no—
162C2×C3×C4⋊C4C2×D511yescharacteristic
163C2×C3×C42—51no—
164C2×(C2×D3)⋊C4—51no—
165C2×(C2×D3)⋊C4—52no—
166C2×(C2×D3)⋊C4—51no—
167C2×C4⋊Dic3—51no—
168C2×C4⋊Dic3—52no—
169C2×C4⋊Dic3C2×D511yescharacteristic
170C2×Dic3⋊C4—52no—
171C2×C4×Dic3—52no—
172C2×C4×Dic3C2×D512yes—
173C2×C4×Dic3C2×D511yescharacteristic
174#892—108no—
175D3×C4⋊C4—58no—
176C3×#95—52no—
177C3⋊#95—52no—
178C3⋊#95—51no—
179C3⋊#95—52no—
180C3⋊#95—52no—
181C3⋊#95—51no—
182C3⋊#95C2×D512yes—
183C23×D5—31no—
184C22×C4×C5—31no—
185C22×C4×C5—32no—
186C22×C4×C5—31no—
187C22×C4×C5C22×D312yes—
188C22×C4×C5C22×D311yescharacteristic
189C22×Dic5—31no—
190C22×Dic5—32no—
191C22×Dic5C22×D311yescharacteristic
192C22×Dic5C22×D312yes—
193C22×Dic5C22×D311yescharacteristic
194C2×C4×D5—34no—
195C2×C4×D5—38no—
196C2×C4×D5—64no—
197C2×C4×D5—64no—
198C2×C4×D5—62no—
199C2×C4×D5—62no—
200C5×C4⋊C4—22no—
201C5×C4⋊C4—34no—
202C42×C5—64no—
203C42×C5—62no—
204#685—34no—
205#685—62no—
206#685—64no—
207C4⋊Dic5—62no—
208C4⋊Dic5C4×D314yes—
209#683—24no—
210#683—38no—
211#683—64no—
212C4×Dic5—22no—
213C4×Dic5—64no—
214C2×#117—152no—
215C22×C4⋊C4—151no—
216#389—51no—
217#389—151no—
218#387—152no—
219#387—152no—
220#381—152no—
221#380—151no—
222C4×C4⋊C4—31no—
223C4×C4⋊C4—151no—
224C4×C22⋊C4—151no—
225C22×C3×C5C23×C411yescharacteristic
226C22×C3×C5C22×D411yescharacteristic
227C22×C3×C5C2×#4111yescharacteristic
228C22×C3×C5C2×#4111yescharacteristic
229C22×C3×C5C2×#4111yescharacteristic
230C22×C3×C52−1+411yescharacteristic
231C22×C3×C52−1+411yescharacteristic
232C2×D15—22no—
233C2×D15—22no—
234C2×D15—22no—
235C2×D15—22no—
236C2×D15—22no—
237C2×D15—22no—
238C2×D15C4×D414yes—
239C3×C4×C5—42no—
240C3×C4×C5#11714yescomplemented
241Dic15—22no—
242Dic15—42no—
243C3×Dic5—24no—
244C3×Dic5—22no—
245C3×Dic5—41no—
246C5×Dic3—24no—
247C5×Dic3—22no—
248C5×Dic3—41no—
249C23×D3—51no—
250C22×C3×C4—52no—
251C22×C3×C4—51no—
252C22×C3×C4—51no—
253C22×C3×C4C22×D512yes—
254C22×C3×C4C22×D511yescharacteristic
255C22×Dic3—51no—
256C22×Dic3—52no—
257C22×Dic3C22×D511yescharacteristic
258C22×Dic3C22×D512yes—
259C22×Dic3C22×D511yescharacteristic
260C2×C4×D3—54no—
261C2×C4×D3—58no—
262C2×C4×D3—104no—
263C2×C4×D3—104no—
264C2×C4×D3—102no—
265C2×C4×D3—102no—
266C3×C4⋊C4—22no—
267C3×C4⋊C4—54no—
268C3×C4⋊C4—104no—
269C3×C42—102no—
270(C2×D3)⋊C4—54no—
271(C2×D3)⋊C4—102no—
272(C2×D3)⋊C4—104no—
273C4⋊Dic3—102no—
274C4⋊Dic3—104no—
275C4⋊Dic3C4×D514yes—
276Dic3⋊C4—58no—
277C4×Dic3—22no—
278C4×Dic3—24no—
279C4×Dic3—104no—
280C23×C5C23×D311yescharacteristic
281C22×D5—32no—
282C22×D5—32no—
283C22×D5—32no—
284C22×D5—61no—
285C22×D5—61no—
286C22×D5—61no—
287C22×D5—61no—
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—34no—
292C2×C4×C5—32no—
293C2×C4×C5—62no—
294C2×C4×C5—61no—
295C2×C4×C5—61no—
296C2×C4×C5—62no—
297C2×C4×C5—61no—
298C2×C4×C5—61no—
299C2×C4×C5—61no—
300C2×C4×C5C2×C4×D312yes—
301C2×C4×C5#23712yes—
302C2×C4×C5#23912yes—
303C2×Dic5—22no—
304C2×Dic5—21no—
305C2×Dic5—22no—
306C2×Dic5—21no—
307C2×Dic5—21no—
308C2×Dic5—21no—
309C2×Dic5—21no—
310C2×Dic5—32no—
311C2×Dic5—61no—
312C2×Dic5—61no—
313C2×Dic5—62no—
314C2×Dic5—62no—
315C2×Dic5—62no—
316C2×Dic5C2×C4×D314yes—
317C2×Dic5D3×D412yes—
318C4×D5—616no—
319C4×D5—68no—
320C23×C4—152no—
321C23×C4—151no—
322#117—308no—
323C2×C4⋊C4—31no—
324C2×C4⋊C4—51no—
325C2×C4⋊C4—52no—
326C2×C4⋊C4—158no—
327C2×C4⋊C4—152no—
328C2×C4⋊C4—152no—
329C2×C4⋊C4—151no—
330C2×C4⋊C4D3×D511yescharacteristic
331C2×C22⋊C4—151no—
332C2×C22⋊C4—151no—
333C2×C22⋊C4—152no—
334C2×C42—32no—
335C2×C42—31no—
336C2×C42—51no—
337C2×C42—152no—
338#95—32no—
339#95—52no—
340#95—151no—
341#95—151no—
342#95—152no—
343#95—152no—
344#95—152no—
345C2×C3×C5C2×#11711yescharacteristic
346C2×C3×C5C2×C4×D411yescharacteristic
347C2×C3×C5#51911yescharacteristic
348C2×C3×C5#54711yescharacteristic
349C2×C3×C5#54711yescharacteristic
350C2×C3×C5#55211yescharacteristic
351C2×C3×C5#55211yescharacteristic
352D15—24no—
353C23×C3C23×D511yescharacteristic
354C22×D3—52no—
355C22×D3—52no—
356C22×D3—52no—
357C22×D3—101no—
358C22×D3—101no—
359C22×D3—101no—
360C22×D3—101no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—54no—
365C2×C3×C4—52no—
366C2×C3×C4—101no—
367C2×C3×C4—102no—
368C2×C3×C4—102no—
369C2×C3×C4—101no—
370C2×C3×C4—101no—
371C2×C3×C4—101no—
372C2×C3×C4—101no—
373C2×C3×C4C2×C4×D512yes—
374C2×C3×C4#70912yes—
375C2×C3×C4#70912yes—
376C2×Dic3—21no—
377C2×Dic3—22no—
378C2×Dic3—21no—
379C2×Dic3—22no—
380C2×Dic3—21no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—52no—
384C2×Dic3—101no—
385C2×Dic3—101no—
386C2×Dic3—102no—
387C2×Dic3—102no—
388C2×Dic3—102no—
389C2×Dic3C2×C4×D514yes—
390C2×Dic3D4×D512yes—
391C4×D3—1016no—
392C4×D3—108no—
393C22×C5C22×C4×D311yescharacteristic
394C22×C5C2×D3×D411yescharacteristic
395C22×C5C2×#23711yescharacteristic
396C22×C5C2×#23911yescharacteristic
397C22×C5#100711yescharacteristic
398C22×C5D3×#4111yescharacteristic
399C22×C5#101011yescharacteristic
400C2×D5—34no—
401C2×D5—62no—
402C2×D5—62no—
403C2×D5—62no—
404C2×D5—62no—
405C2×D5—62no—
406C2×D5—62no—
407C4×C5—42no—
408C4×C5—62no—
409C4×C5—64no—
410C4×C5—121no—
411C4×C5#89214yescomplemented
412Dic5—24no—
413Dic5—22no—
414Dic5—41no—
415Dic5—62no—
416Dic5—122no—
417C24—151no—
418C22×C4—32no—
419C22×C4—31no—
420C22×C4—31no—
421C22×C4—52no—
422C22×C4—51no—
423C22×C4—51no—
424C22×C4—158no—
425C22×C4—151no—
426C22×C4—154no—
427C22×C4—152no—
428C22×C4—304no—
429C22×C4—304no—
430C22×C4—302no—
431C22×C4—302no—
432C22×C4C2×D3×D512yes—
433C22×C4C2×D3×D511yescharacteristic
434C4⋊C4—22no—
435C4⋊C4—34no—
436C4⋊C4—54no—
437C4⋊C4—104no—
438C4⋊C4—158no—
439C4⋊C4—304no—
440C4⋊C4—302no—
441C22⋊C4—154no—
442C22⋊C4—304no—
443C22⋊C4—302no—
444C42—64no—
445C42—62no—
446C42—102no—
447C42—304no—
448C3×C5#234411yescharacteristic, complemented, Hall
449C22×C3C22×C4×D511yescharacteristic
450C22×C3C2×#70911yescharacteristic
451C22×C3C2×#70911yescharacteristic
452C22×C3C2×D4×D511yescharacteristic
453C22×C3#414711yescharacteristic
454C22×C3D5×#4111yescharacteristic
455C22×C3#415011yescharacteristic
456C2×D3—54no—
457C2×D3—102no—
458C2×D3—102no—
459C2×D3—102no—
460C2×D3—102no—
461C2×D3—102no—
462C2×D3—102no—
463C3×C4—42no—
464C3×C4—104no—
465C3×C4—102no—
466C3×C4—201no—
467C3×C4#401814yescomplemented
468Dic3—22no—
469Dic3—24no—
470Dic3—41no—
471Dic3—102no—
472Dic3—202no—
473C2×C5C2×#89211yescharacteristic
474C2×C5C4×D3×D411yescharacteristic
475C2×C5#557211yescharacteristic
476C2×C5#561111yescharacteristic
477C2×C5#563911yescharacteristic
478C2×C5#569411yescharacteristic
479C2×C5#572611yescharacteristic
480D5—64no—
481C23—152no—
482C23—152no—
483C23—152no—
484C23—301no—
485C23—301no—
486C23—301no—
487C23—301no—
488C23C22×D3×D511yescharacteristic
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—34no—
493C2×C4—32no—
494C2×C4—54no—
495C2×C4—52no—
496C2×C4—61no—
497C2×C4—62no—
498C2×C4—61no—
499C2×C4—62no—
500C2×C4—61no—
501C2×C4—61no—
502C2×C4—61no—
503C2×C4—101no—
504C2×C4—102no—
505C2×C4—102no—
506C2×C4—101no—
507C2×C4—101no—
508C2×C4—101no—
509C2×C4—101no—
510C2×C4—152no—
511C2×C4—3016no—
512C2×C4—301no—
513C2×C4—301no—
514C2×C4—308no—
515C2×C4—302no—
516C2×C4—302no—
517C2×C4—302no—
518C2×C4#676912yes—
519C2×C4C4×D3×D512yes—
520C2×C4#677912yes—
521C2×C3C2×#401811yescharacteristic
522C2×C3#6584111yescharacteristic
523C2×C3#6586311yescharacteristic
524C2×C3C4×D4×D511yescharacteristic
525C2×C3#6588511yescharacteristic
526C2×C3#6590611yescharacteristic
527C2×C3#6591511yescharacteristic
528D3—104no—
529C5#7620011yescharacteristic, complemented, Sylow
530C22—154no—
531C22—302no—
532C22—302no—
533C22—302no—
534C22—302no—
535C22—302no—
536C22—302no—
537C22C2×#676911yescharacteristic
538C22C2×C4×D3×D511yescharacteristic
539C22#9202011yescharacteristic
540C22D3×D4×D511yescharacteristic
541C22#9202911yescharacteristic
542C22#9203411yescharacteristic
543C22C2×#677911yescharacteristic
544C4—42no—
545C4—64no—
546C4—62no—
547C4—102no—
548C4—104no—
549C4—121no—
550C4—201no—
551C4—302no—
552C4—602no—
553C4#9140314yescomplemented
554C3#1060549811yescharacteristic, complemented, Sylow
555C2—304no—
556C2#1175332911yescharacteristic
557C2#1175334011yescharacteristic
558C2#1175338111yescharacteristic
559C2#1175384011yescharacteristic
560C2C2×#9140311yescharacteristic
561C2#1175476511yescharacteristic
562C2#1175513211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2344
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C5×Dic3×C4⋊C4C2semidirect
5. C3×#65262C2semidirect
7. #11748857C2semidirect
8. #11748808C2semidirect
10. Dic5×C4⋊Dic3C2semidirect
11. #11748657C2semidirect
29. #91437C4semidirect
44. #65262D3semidirect
87. Dic3×C4⋊C4D5semidirect
240. C3×C4×C5#117semidirect
411. C4×C5#892semidirect
448. C3×C5#2344semidirect
467. C3×C4#4018semidirect
529. C5#76200semidirect
553. C4#91403semidirect
554. C3#10605498semidirect

Maximal subgroups

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

subgroupindex
C2×#914372
C2×#914032
#117510882
C5×Dic3×C4⋊C42
C3×#652622
#117488892
#117488572
#117488082
C4×#66672
Dic5×C4⋊Dic32
#117486572
#106054983
#762005