Finite Group Databasebeta

← #14326622

Subgroups — #14326622

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×C3×D5×C4⋊C4C211yesmaximal, characteristic
2C2×#91357C212yesmaximal
3C4⋊C4×Dic15C211yesmaximal, characteristic, complemented
4C5×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
5#11748865C211yesmaximal, characteristic, complemented
6#11748857C211yesmaximal, characteristic, complemented
7#11748759C211yesmaximal, characteristic
8#11748737C212yesmaximal
9C4×#6665C211yesmaximal, characteristic
10#11748601C212yesmaximal, complemented
11#11748590C212yesmaximal, complemented
12#10605498—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C22×C3×C4×D5C2212yes—
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C4×Dic15C2211yescharacteristic
18C2×C4×Dic15C2212yes—
19C2×C5×C4⋊Dic3C2211yescharacteristic
20C2×C4×C5×Dic3C2211yescharacteristic
21C2×C4×C5×Dic3C2212yes—
22C2×C3×C4⋊Dic5C2211yescharacteristic
23C2×C3×#683C2212yes—
24C3×D5×C4⋊C4C418yescomplemented
25C2×#6668C2212yes—
26C2×#6668C2212yes—
27C2×#6665C2211yescharacteristic
28C2×#6665C2212yes—
29C2×#6665C2211yescharacteristic
30#91357—28no—
31#91115C2212yes—
32C5×C3⋊#95C2212yes—
33#90994C2212yes—
34#90994C2211yescharacteristic
35#90994C2211yescharacteristic
36#90994C2212yes—
37#90994C2212yes—
38#82159—51nomaximal, Hall
39C2×D5×C4⋊C4D311yescharacteristic
40C2×#4018—32no—
41C4×C5×C4⋊C4—31no—
42#65276—31no—
43C4⋊C4×Dic5—31no—
44#65262—31no—
45C4×#685—31no—
46#65222—32no—
47#65217—31no—
48#64953—32no—
49#64941—32no—
50C23×C3×D5C2311yescharacteristic
51C22×C3×C4×C5C2312yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15C2311yescharacteristic
54C22×Dic15C2312yes—
55C22×Dic15C2311yescharacteristic
56C22×C5×Dic3C2312yes—
57C22×C5×Dic3C2311yescharacteristic
58C22×C5×Dic3C2311yescharacteristic
59C22×C3×Dic5C2311yescharacteristic
60C22×C3×Dic5C2312yes—
61C2×C3×C4×D5—24no—
62C2×C3×C4×D5—24no—
63C2×C3×C4×D5—22no—
64C2×C3×C4×D5—22no—
65C2×C3×C4×D5C2×C418yes—
66C2×C3×C4×D5C2×C414yes—
67C3×C5×C4⋊C4C2×C414yes—
68C4⋊Dic15—22no—
69C4×Dic15—22no—
70C4×Dic15—24no—
71C5×C4⋊Dic3—22no—
72C4×C5×Dic3—22no—
73C4×C5×Dic3—24no—
74C3×C4⋊Dic5C2×C414yes—
75C3×#683C2×C418yes—
76#6668—24no—
77#6668—24no—
78#6665—24no—
79#6665—22no—
80#6665D414yes—
81C22×C3×C4⋊C4—51no—
82C2×#926—52no—
83#5212—51no—
84#5211—52no—
85C4×#217—51no—
86#4984—51no—
87#4984—51no—
88#4980—52no—
89#4980—52no—
90Dic3×C4⋊C4—51no—
91Dic3×C4⋊C4D511yescharacteristic, complemented
92C22×C4×D5C2×D312yes—
93C22×C4×D5C2×D311yescharacteristic
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×Dic5—31no—
108D5×C4⋊C4Dic318yescomplemented
109#4018—68no—
110C5×#95—32no—
111#3963—32no—
112#3963—31no—
113#3963—32no—
114#3963—32no—
115#3963—32no—
116#3963—31no—
117#2344—151noSylow
118C23×C3×C5C2411yescharacteristic
119C22×C3×D5—21no—
120C22×C3×D5—21no—
121C22×C3×D5—21no—
122C22×C3×D5—21no—
123C22×C3×D5C22×C412yes—
124C22×C3×D5C2×D412yes—
125C22×C3×D5#4112yes—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5C22×C414yes—
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—21no—
136C2×Dic15—21no—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×Dic15—21no—
140C2×Dic15C2×D412yes—
141C2×C5×Dic3—21no—
142C2×C5×Dic3—21no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3—21no—
145C2×C5×Dic3—21no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—21no—
149C2×C5×Dic3C2×D412yes—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5C22×C412yes—
155C2×C3×Dic5C22×C414yes—
156C3×C4×D5—216no—
157C3×C4×D5—28no—
158C23×C3×C4—51no—
159C23×C3×C4—52no—
160C2×C3×C4⋊C4—52no—
161C2×C3×C4⋊C4—51no—
162C2×C3×C4⋊C4—58no—
163C2×C3×C4⋊C4C2×D511yescharacteristic
164C2×#217—51no—
165C2×#217—51no—
166C2×#217—52no—
167#926—108no—
168C2×C4⋊Dic3—51no—
169C2×C4⋊Dic3—52no—
170C2×C4⋊Dic3—52no—
171C2×C4⋊Dic3C2×D511yescharacteristic
172C2×C4×Dic3—51no—
173C2×C4×Dic3—52no—
174C2×C4×Dic3C2×D511yescharacteristic
175C2×C4×Dic3C2×D512yes—
176C3⋊#95—52no—
177C3⋊#95—51no—
178C3⋊#95—51no—
179C3⋊#95—52no—
180C3⋊#95—52no—
181C3⋊#95—52no—
182C3⋊#95C2×D512yes—
183C23×D5C22×D311yescharacteristic
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—31no—
191C22×Dic5—32no—
192C22×Dic5C22×D311yescharacteristic
193C22×Dic5C22×D312yes—
194C2×C4×D5—24no—
195C2×C4×D5—24no—
196C2×C4×D5—22no—
197C2×C4×D5—22no—
198C2×C4×D5C2×Dic318yes—
199C2×C4×D5C2×Dic314yes—
200C5×C4⋊C4—62no—
201C5×C4⋊C4C2×Dic314yes—
202C42×C5—64no—
203C42×C5—62no—
204#685—34no—
205#685—64no—
206#685—62no—
207C4⋊Dic5—62no—
208C4⋊Dic5C2×Dic314yes—
209#683—64no—
210#683—64no—
211#683C2×Dic318yes—
212C4×Dic5—64no—
213C4×Dic5—62no—
214C2×#117—152no—
215C22×C4⋊C4—51no—
216#389—151no—
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×C3×D5—22no—
233C2×C3×D5—22no—
234C2×C3×D5—22no—
235C2×C3×D5—22no—
236C2×C3×D5—22no—
237C2×C3×D5—22no—
238C2×C3×D5C4×D414yes—
239C3×C4×C5—24no—
240C3×C4×C5#11714yescomplemented
241Dic15—22no—
242Dic15—42no—
243Dic15—41no—
244C3×Dic5—22no—
245C3×Dic5—24no—
246C5×Dic3—22no—
247C5×Dic3—42no—
248C5×Dic3—41no—
249C24×C3—51no—
250C22×C3×C4—51no—
251C22×C3×C4—52no—
252C22×C3×C4—58no—
253C22×C3×C4—54no—
254C22×C3×C4—104no—
255C22×C3×C4—104no—
256C22×C3×C4—102no—
257C22×C3×C4—102no—
258C22×C3×C4C22×D512yes—
259C22×C3×C4C22×D511yescharacteristic
260C22×Dic3—51no—
261C22×Dic3—51no—
262C22×Dic3—52no—
263C22×Dic3C22×D511yescharacteristic
264C22×Dic3C22×D512yes—
265C22×Dic3C22×D511yescharacteristic
266C3×C4⋊C4—58no—
267C3×C4⋊C4—54no—
268C3×C4⋊C4C4×D514yes—
269#217—54no—
270#217—104no—
271#217—102no—
272C4⋊Dic3—22no—
273C4⋊Dic3—104no—
274C4⋊Dic3—102no—
275C4⋊Dic3—104no—
276C4×Dic3—22no—
277C4×Dic3—24no—
278C4×Dic3—104no—
279C4×Dic3—102no—
280C23×C5C23×D311yescharacteristic
281C22×D5—21no—
282C22×D5—21no—
283C22×D5—21no—
284C22×D5—21no—
285C22×D5D3×D412yes—
286C22×D5#23712yes—
287C22×D5C22×Dic312yes—
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—32no—
291C2×C4×C5—61no—
292C2×C4×C5—61no—
293C2×C4×C5—61no—
294C2×C4×C5—62no—
295C2×C4×C5—62no—
296C2×C4×C5—61no—
297C2×C4×C5—62no—
298C2×C4×C5—61no—
299C2×C4×C5#23512yes—
300C2×C4×C5#23512yes—
301C2×C4×C5C22×Dic314yes—
302C2×C4×C5C22×Dic312yes—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—22no—
306C2×Dic5—22no—
307C2×Dic5—32no—
308C2×Dic5—61no—
309C2×Dic5—61no—
310C2×Dic5—61no—
311C2×Dic5—62no—
312C2×Dic5—62no—
313C2×Dic5—61no—
314C2×Dic5—62no—
315C2×Dic5—61no—
316C2×Dic5C22×Dic312yes—
317C2×Dic5C22×Dic314yes—
318C4×D5—216no—
319C4×D5—28no—
320C23×C4—52no—
321C23×C4—51no—
322#117—308no—
323C2×C4⋊C4—31no—
324C2×C4⋊C4—52no—
325C2×C4⋊C4—51no—
326C2×C4⋊C4—58no—
327C2×C4⋊C4—152no—
328C2×C4⋊C4—152no—
329C2×C4⋊C4—151no—
330C2×C4⋊C4D3×D511yescharacteristic
331C2×C22⋊C4—151no—
332C2×C22⋊C4—152no—
333C2×C22⋊C4—151no—
334C2×C42—32no—
335C2×C42—31no—
336C2×C42—152no—
337C2×C42—151no—
338#95—32no—
339#95—151no—
340#95—151no—
341#95—152no—
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
352C3×D5—24no—
353C23×C3—52no—
354C23×C3—52no—
355C23×C3—52no—
356C23×C3—101no—
357C23×C3—101no—
358C23×C3—101no—
359C23×C3—101no—
360C23×C3C23×D511yescharacteristic
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—52no—
364C2×C3×C4—54no—
365C2×C3×C4—1016no—
366C2×C3×C4—101no—
367C2×C3×C4—101no—
368C2×C3×C4—102no—
369C2×C3×C4—102no—
370C2×C3×C4—108no—
371C2×C3×C4C2×C4×D514yes—
372C2×C3×C4C2×C4×D512yes—
373C2×C3×C4#70912yes—
374C2×C3×C4#70912yes—
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—21no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—21no—
381C2×Dic3—21no—
382C2×Dic3—22no—
383C2×Dic3—52no—
384C2×Dic3—101no—
385C2×Dic3—101no—
386C2×Dic3—101no—
387C2×Dic3—102no—
388C2×Dic3—102no—
389C2×Dic3—102no—
390C2×Dic3—101no—
391C2×Dic3—101no—
392C2×Dic3D4×D512yes—
393C22×C5C2×#23511yescharacteristic
394C22×C5C2×#23511yescharacteristic
395C22×C5C2×D3×D411yescharacteristic
396C22×C5C2×#23711yescharacteristic
397C22×C5#100711yescharacteristic
398C22×C5#100711yescharacteristic
399C22×C5C23×Dic311yescharacteristic
400C2×D5—22no—
401C2×D5—22no—
402C2×D5—22no—
403C2×D5—22no—
404C2×D5—22no—
405C2×D5—22no—
406C2×D5D4×Dic314yes—
407C4×C5—24no—
408C4×C5—62no—
409C4×C5—122no—
410C4×C5—121no—
411C4×C5#92614yescomplemented
412Dic5—22no—
413Dic5—24no—
414Dic5—62no—
415Dic5—122no—
416Dic5—121no—
417C24—51no—
418C22×C4—31no—
419C22×C4—31no—
420C22×C4—32no—
421C22×C4—51no—
422C22×C4—52no—
423C22×C4—58no—
424C22×C4—54no—
425C22×C4—104no—
426C22×C4—104no—
427C22×C4—102no—
428C22×C4—102no—
429C22×C4—151no—
430C22×C4—151no—
431C22×C4—152no—
432C22×C4C2×D3×D512yes—
433C22×C4C2×D3×D511yescharacteristic
434C4⋊C4—58no—
435C4⋊C4—54no—
436C4⋊C4—62no—
437C4⋊C4—304no—
438C4⋊C4—304no—
439C4⋊C4—302no—
440C4⋊C4D5×Dic314yes—
441C22⋊C4—154no—
442C22⋊C4—304no—
443C22⋊C4—302no—
444C42—64no—
445C42—62no—
446C42—304no—
447C42—302no—
448C3×C5#234411yescharacteristic, complemented, Hall
449C22×C3—54no—
450C22×C3—102no—
451C22×C3—102no—
452C22×C3—102no—
453C22×C3—102no—
454C22×C3—102no—
455C22×C3—102no—
456C22×C3C22×C4×D511yescharacteristic
457C22×C3C2×#70911yescharacteristic
458C22×C3C2×#70911yescharacteristic
459C22×C3C2×D4×D511yescharacteristic
460C22×C3#414711yescharacteristic
461C22×C3D5×#4111yescharacteristic
462C22×C3#415011yescharacteristic
463C3×C4—24no—
464C3×C4—102no—
465C3×C4—104no—
466C3×C4#401814yescomplemented
467Dic3—22no—
468Dic3—41no—
469Dic3—42no—
470Dic3—102no—
471Dic3—202no—
472Dic3—201no—
473C2×C5#550711yescharacteristic
474C2×C5#550711yescharacteristic
475C2×C5#551311yescharacteristic
476C2×C5#551311yescharacteristic
477C2×C5C2×#92611yescharacteristic
478C2×C5C2×D4×Dic311yescharacteristic
479C2×C5#581211yescharacteristic
480D5—24no—
481C23—52no—
482C23—52no—
483C23—52no—
484C23—101no—
485C23—101no—
486C23—101no—
487C23—101no—
488C23C22×D3×D511yescharacteristic
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—32no—
492C2×C4—54no—
493C2×C4—52no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—61no—
500C2×C4—61no—
501C2×C4—62no—
502C2×C4—1016no—
503C2×C4—101no—
504C2×C4—101no—
505C2×C4—102no—
506C2×C4—102no—
507C2×C4—108no—
508C2×C4—152no—
509C2×C4—301no—
510C2×C4—301no—
511C2×C4—301no—
512C2×C4—302no—
513C2×C4—302no—
514C2×C4—301no—
515C2×C4—301no—
516C2×C4—302no—
517C2×C4#677112yes—
518C2×C4#677112yes—
519C2×C4C2×D5×Dic314yes—
520C2×C4C2×D5×Dic312yes—
521C2×C3—104no—
522C2×C3C2×#401811yescharacteristic
523C2×C3#6584111yescharacteristic
524C2×C3#6586311yescharacteristic
525C2×C3C4×D4×D511yescharacteristic
526C2×C3#6588511yescharacteristic
527C2×C3#6590611yescharacteristic
528C2×C3#6591511yescharacteristic
529C5#8215911yescharacteristic, complemented, Sylow
530C22—54no—
531C22—102no—
532C22—102no—
533C22—102no—
534C22—102no—
535C22—102no—
536C22—102no—
537C22C2×#677111yescharacteristic
538C22C2×#677111yescharacteristic
539C22D3×D4×D511yescharacteristic
540C22D5×#23711yescharacteristic
541C22#9202911yescharacteristic
542C22#9203011yescharacteristic
543C22C22×D5×Dic311yescharacteristic
544C4—24no—
545C4—62no—
546C4—104no—
547C4—102no—
548C4—121no—
549C4—122no—
550C4—302no—
551C4—601no—
552C4—602no—
553C4#9135714yescomplemented
554C3#1060549811yescharacteristic, complemented, Sylow
555C2—104no—
556C2#1175334711yescharacteristic
557C2#1175367211yescharacteristic
558C2#1175367711yescharacteristic
559C2#1175373111yescharacteristic
560C2C2×#9135711yescharacteristic
561C2D4×D5×Dic311yescharacteristic
562C2#1175514011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
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
3. C4⋊C4×Dic15C2semidirect
4. C5×Dic3×C4⋊C4C2semidirect
5. #11748865C2semidirect
6. #11748857C2semidirect
10. #11748601C2semidirect
11. #11748590C2semidirect
24. C3×D5×C4⋊C4C4semidirect
91. Dic3×C4⋊C4D5semidirect
108. D5×C4⋊C4Dic3semidirect
240. C3×C4×C5#117semidirect
411. C4×C5#926semidirect
448. C3×C5#2344semidirect
466. C3×C4#4018semidirect
529. C5#82159semidirect
553. C4#91357semidirect
554. C3#10605498semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×C4⋊C42
C2×#913572
C4⋊C4×Dic152
C5×Dic3×C4⋊C42
#117488652
#117488572
#117487592
#117487372
C4×#66652
#117486012
#117485902
#106054983
#821595