Finite Group Databasebeta

← #14327722

Subgroups — #14327722

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×#4039C211yesmaximal, characteristic
2C2×#91357C212yesmaximal, complemented
3C4⋊C4×Dic15C211yesmaximal, characteristic, complemented
4C5×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
5#11748834C211yesmaximal, characteristic, complemented
6C4×#6668C211yesmaximal, characteristic, complemented
7#11748796C211yesmaximal, characteristic
8#11748791C212yesmaximal, complemented
9#11748785C211yesmaximal, characteristic
10#11748770C212yesmaximal, complemented
11#11748738C212yesmaximal, complemented
12#10605370—31nomaximal, Hall
13C22×C3×D20C2211yescharacteristic
14C22×C3×C4×D5C2212yes—
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C4×Dic15C2212yes—
18C2×C4×Dic15C2211yescharacteristic
19C2×C5×C4⋊Dic3C2211yescharacteristic
20C2×C4×C5×Dic3C2212yes—
21C2×C4×C5×Dic3C2211yescharacteristic
22C2×C3×#685C2212yes—
23C2×C3×C4×Dic5C2211yescharacteristic
24C3×#4039C418yescomplemented
25C2×#6668C2211yescharacteristic
26C2×#6668C2212yes—
27C2×#6668C2212yes—
28C2×#6668C2211yescharacteristic
29C2×#6665C2212yes—
30C2×#6665C2212yes—
31C2×#6665C2212yes—
32C2×#6665C2212yes—
33#91357—28no—
34#91115C2212yes—
35C5×C3⋊#95C2212yes—
36#90994C2211yescharacteristic
37#90994C2211yescharacteristic
38#82337—51nomaximal, Hall
39C2×#4039D311yescharacteristic
40C2×#4018—32no—
41C4×C5×C4⋊C4—31no—
42#65277—31no—
43#65265—31no—
44C4⋊C4×Dic5—31no—
45#65229—32no—
46#65228—31no—
47C4×#683—31no—
48#64958—32no—
49#64956—32no—
50C23×C3×D5C2312yes—
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×Dic5C2311yescharacteristic
61C2×C3×D20—22no—
62C2×C3×D20—22no—
63C2×C3×D20C2×C414yes—
64C2×C3×C4×D5—24no—
65C2×C3×C4×D5—24no—
66C2×C3×C4×D5C2×C418yes—
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×#685C2×C418yes—
75C3×C4×Dic5C2×C414yes—
76#6668—24no—
77#6668—22no—
78#6668—42no—
79#6668D414yescomplemented
80#6665—24no—
81#6665—24no—
82#6665—42no—
83#6665—42no—
84C2×C3×C4×D4—51no—
85C2×#926—52no—
86#5221—51no—
87#5221—51no—
88#5212—52no—
89Dic3×C4⋊C4—51no—
90Dic3×C4⋊C4D511yescharacteristic, complemented
91#4951—52no—
92#4951—52no—
93#4935—51no—
94C4×C4⋊Dic3—51no—
95C22×D20C2×D311yescharacteristic
96C22×C4×D5C2×D312yes—
97C2×C5×C4⋊C4—31no—
98C2×C5×C4⋊C4C2×D311yescharacteristic
99C2×C42×C5—32no—
100C2×C42×C5—31no—
101C2×#685—32no—
102C2×#685—32no—
103C2×#685—32no—
104C2×#685—32no—
105C2×#685C2×D312yes—
106C2×C4⋊Dic5—31no—
107C2×#683—31no—
108C2×#683—32no—
109C2×#683—31no—
110C2×#683—32no—
111C2×C4×Dic5—32no—
112C2×C4×Dic5—31no—
113C2×C4×Dic5C2×D311yescharacteristic
114#4039Dic318yescomplemented
115#4018—68no—
116C5×#95—32no—
117#3963—32no—
118#3963—31no—
119#3963—31no—
120#2354—151noSylow
121C23×C3×C5C2411yescharacteristic
122C22×C3×D5—22no—
123C22×C3×D5—22no—
124C22×C3×D5—22no—
125C22×C3×D5—22no—
126C22×C3×D5—22no—
127C22×C3×D5—22no—
128C22×C3×D5C22×C414yes—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C22×C414yes—
132C2×C3×C4×C5C22×C412yes—
133C2×C3×C4×C5#4112yes—
134C2×C3×C4×C5#4112yes—
135C2×Dic15—21no—
136C2×Dic15—21no—
137C2×Dic15—22no—
138C2×Dic15—21no—
139C2×Dic15—21no—
140C2×Dic15—22no—
141C2×Dic15—21no—
142C2×Dic15—22no—
143C2×Dic15C2×D412yes—
144C2×C5×Dic3—21no—
145C2×C5×Dic3—21no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—21no—
148C2×C5×Dic3—21no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3C2×D412yes—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5C22×C412yes—
156C2×C3×Dic5C22×C412yes—
157C2×C3×Dic5C2×D412yes—
158C2×C3×Dic5#4112yes—
159C3×D20—28no—
160C3×C4×D5—216no—
161C22×C3×D4—51no—
162C23×C3×C4—52no—
163C3×C4×D4—58no—
164C2×C3×C4⋊C4C2×D511yescharacteristic
165C2×C3×C22⋊C4—52no—
166C2×C3×C42—51no—
167C2×#217—52no—
168C2×#217—52no—
169C2×#217—52no—
170C2×#217—52no—
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×Dic3C2×D511yescharacteristic
181C2×C4×Dic3C2×D512yes—
182C3⋊#95—52no—
183C3⋊#95—51no—
184C3⋊#95—51no—
185C3⋊#95C2×D512yes—
186C23×D5C22×D312yes—
187C22×C4×C5—31no—
188C22×C4×C5—32no—
189C22×C4×C5—31no—
190C22×C4×C5C22×D312yes—
191C22×C4×C5C22×D311yescharacteristic
192C22×Dic5—31no—
193C22×Dic5—31no—
194C22×Dic5—32no—
195C22×Dic5C22×D311yescharacteristic
196C22×Dic5C22×D311yescharacteristic
197C2×D20—22no—
198C2×D20—22no—
199C2×D20C2×Dic314yes—
200C2×C4×D5—24no—
201C2×C4×D5—24no—
202C2×C4×D5C2×Dic318yes—
203C5×C4⋊C4—62no—
204C5×C4⋊C4C2×Dic314yes—
205C42×C5—64no—
206C42×C5—62no—
207#685—64no—
208#685—64no—
209#685—122no—
210#685—122no—
211#685C2×Dic318yes—
212C4⋊Dic5—62no—
213#683—34no—
214#683—64no—
215#683—62no—
216#683—122no—
217C4×Dic5—64no—
218C4×Dic5—62no—
219C4×Dic5C2×Dic314yes—
220C2×C4×D4—51no—
221C2×#117—152no—
222#390—151no—
223#390—151no—
224#388—152no—
225#388—152no—
226#384—151no—
227#380—152no—
228C4×C4⋊C4—31no—
229C4×C4⋊C4—151no—
230C4×C4⋊C4—151no—
231C22×C3×C5C23×C411yescharacteristic
232C22×C3×C5C22×D411yescharacteristic
233C22×C3×C5C2×#4111yescharacteristic
234C22×C3×C5C2×#4111yescharacteristic
235C22×C3×C5C2×#4111yescharacteristic
236C22×C3×C5H(5,𝔽2)11yescharacteristic
237C22×C3×C52−1+411yescharacteristic
238C2×C3×D5—24no—
239C2×C3×D5—24no—
240C2×C3×D5—24no—
241C2×C3×D5—42no—
242C2×C3×D5—42no—
243C2×C3×D5—42no—
244C2×C3×D5—42no—
245C3×C4×C5—24no—
246C3×C4×C5#11714yescomplemented
247Dic15—22no—
248Dic15—42no—
249Dic15—41no—
250C3×Dic5—22no—
251C3×Dic5C4×D414yes—
252C5×Dic3—22no—
253C5×Dic3—42no—
254C5×Dic3—41no—
255C24×C3—52no—
256C2×C3×D4—54no—
257C2×C3×D4—102no—
258C2×C3×D4—102no—
259C22×C3×C4—51no—
260C22×C3×C4—51no—
261C22×C3×C4—58no—
262C22×C3×C4—104no—
263C22×C3×C4—104no—
264C22×C3×C4C22×D512yes—
265C22×C3×C4C22×D511yescharacteristic
266C22×Dic3—51no—
267C22×Dic3—51no—
268C22×Dic3—52no—
269C22×Dic3C22×D511yescharacteristic
270C22×Dic3C22×D512yes—
271C22×Dic3C22×D511yescharacteristic
272C3×C4⋊C4C4×D514yes—
273C3×C22⋊C4—58no—
274C3×C42—54no—
275#217—104no—
276#217—104no—
277#217—202no—
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—24no—
287C4×Dic3—104no—
288C4×Dic3—102no—
289C23×C5C23×D311yescharacteristic
290C22×D5—22no—
291C22×D5—22no—
292C22×D5—22no—
293C22×D5—22no—
294C22×D5—22no—
295C22×D5—22no—
296C22×D5C22×Dic314yes—
297C2×C4×C5—22no—
298C2×C4×C5—22no—
299C2×C4×C5—32no—
300C2×C4×C5—61no—
301C2×C4×C5—61no—
302C2×C4×C5—61no—
303C2×C4×C5—62no—
304C2×C4×C5—62no—
305C2×C4×C5—61no—
306C2×C4×C5—62no—
307C2×C4×C5—61no—
308C2×C4×C5#23512yes—
309C2×C4×C5#23512yes—
310C2×C4×C5C22×Dic314yes—
311C2×C4×C5C22×Dic312yes—
312C2×Dic5—21no—
313C2×Dic5—21no—
314C2×Dic5—32no—
315C2×Dic5—61no—
316C2×Dic5—61no—
317C2×Dic5—61no—
318C2×Dic5—62no—
319C2×Dic5—62no—
320C2×Dic5—61no—
321C2×Dic5—62no—
322C2×Dic5—61no—
323C2×Dic5D3×D412yes—
324C2×Dic5#23712yes—
325C2×Dic5C22×Dic312yes—
326C2×Dic5C22×Dic312yes—
327D20—28no—
328C4×D5—216no—
329C22×D4—51no—
330C23×C4—52no—
331C4×D4—58no—
332#117—308no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—151no—
335C2×C4⋊C4—152no—
336C2×C4⋊C4—151no—
337C2×C4⋊C4—151no—
338C2×C4⋊C4—152no—
339C2×C4⋊C4D3×D511yescharacteristic
340C2×C22⋊C4—52no—
341C2×C22⋊C4—152no—
342C2×C22⋊C4—152no—
343C2×C22⋊C4—152no—
344C2×C22⋊C4—152no—
345C2×C42—32no—
346C2×C42—31no—
347C2×C42—51no—
348C2×C42—152no—
349C2×C42—151no—
350#95—32no—
351#95—151no—
352#95—151no—
353#95—152no—
354C2×C3×C5C2×#11711yescharacteristic
355C2×C3×C5C2×C4×D411yescharacteristic
356C2×C3×C5#52011yescharacteristic
357C2×C3×C5#54711yescharacteristic
358C2×C3×C5#55011yescharacteristic
359C2×C3×C5#55511yescharacteristic
360C2×C3×C5#55611yescharacteristic
361C3×D5—44no—
362C23×C3—54no—
363C23×C3—102no—
364C23×C3—102no—
365C23×C3—102no—
366C23×C3—102no—
367C23×C3—102no—
368C23×C3—102no—
369C23×C3C23×D511yescharacteristic
370C3×D4—108no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—52no—
374C2×C3×C4—52no—
375C2×C3×C4—52no—
376C2×C3×C4—52no—
377C2×C3×C4—1016no—
378C2×C3×C4—101no—
379C2×C3×C4—101no—
380C2×C3×C4C2×C4×D514yes—
381C2×C3×C4C2×C4×D512yes—
382C2×C3×C4#70912yes—
383C2×C3×C4#70912yes—
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3—21no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—21no—
390C2×Dic3—22no—
391C2×Dic3—21no—
392C2×Dic3—52no—
393C2×Dic3—101no—
394C2×Dic3—101no—
395C2×Dic3—101no—
396C2×Dic3—102no—
397C2×Dic3—102no—
398C2×Dic3—101no—
399C2×Dic3—102no—
400C2×Dic3—101no—
401C2×Dic3D4×D512yes—
402C22×C5C2×#23511yescharacteristic
403C22×C5C2×#23511yescharacteristic
404C22×C5C2×D3×D411yescharacteristic
405C22×C5C2×#23711yescharacteristic
406C22×C5#100911yescharacteristic
407C22×C5#101011yescharacteristic
408C22×C5C23×Dic311yescharacteristic
409C2×D5—24no—
410C2×D5—24no—
411C2×D5—24no—
412C2×D5—42no—
413C2×D5—42no—
414C2×D5—42no—
415C2×D5—42no—
416C4×C5—24no—
417C4×C5—62no—
418C4×C5—122no—
419C4×C5—121no—
420C4×C5#92614yescomplemented
421Dic5—22no—
422Dic5—62no—
423Dic5—122no—
424Dic5—121no—
425Dic5D4×Dic314yes—
426C24—52no—
427C2×D4—54no—
428C2×D4—102no—
429C2×D4—102no—
430C22×C4—31no—
431C22×C4—31no—
432C22×C4—32no—
433C22×C4—51no—
434C22×C4—51no—
435C22×C4—58no—
436C22×C4—104no—
437C22×C4—104no—
438C22×C4—151no—
439C22×C4—151no—
440C22×C4—152no—
441C22×C4C2×D3×D512yes—
442C22×C4C2×D3×D511yescharacteristic
443C4⋊C4—62no—
444C4⋊C4—154no—
445C4⋊C4—304no—
446C4⋊C4—302no—
447C4⋊C4—302no—
448C4⋊C4—602no—
449C4⋊C4D5×Dic314yes—
450C22⋊C4—58no—
451C22⋊C4—304no—
452C22⋊C4—304no—
453C22⋊C4—602no—
454C22⋊C4—602no—
455C42—54no—
456C42—64no—
457C42—62no—
458C42—304no—
459C42—302no—
460C3×C5#235411yescharacteristic, complemented, Hall
461C22×C3—104no—
462C22×C3—104no—
463C22×C3—104no—
464C22×C3—202no—
465C22×C3—202no—
466C22×C3—202no—
467C22×C3—202no—
468C22×C3C22×C4×D511yescharacteristic
469C22×C3C2×#70911yescharacteristic
470C22×C3C2×#70911yescharacteristic
471C22×C3C2×D4×D511yescharacteristic
472C22×C3#414711yescharacteristic
473C22×C3D5×#4111yescharacteristic
474C22×C3#414911yescharacteristic
475C3×C4—24no—
476C3×C4—54no—
477C3×C4—102no—
478C3×C4#401814yescomplemented
479Dic3—22no—
480Dic3—41no—
481Dic3—42no—
482Dic3—102no—
483Dic3—201no—
484Dic3—202no—
485C2×C5#554211yescharacteristic
486C2×C5#555111yescharacteristic
487C2×C5#555311yescharacteristic
488C2×C5#556311yescharacteristic
489C2×C5C2×#92611yescharacteristic
490C2×C5C2×D4×Dic311yescharacteristic
491C2×C5#582711yescharacteristic
492D5—44no—
493C23—54no—
494C23—102no—
495C23—102no—
496C23—102no—
497C23—102no—
498C23—102no—
499C23—102no—
500C23C22×D3×D511yescharacteristic
501D4—108no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—32no—
505C2×C4—52no—
506C2×C4—52no—
507C2×C4—52no—
508C2×C4—52no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—61no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—62no—
517C2×C4—1016no—
518C2×C4—101no—
519C2×C4—101no—
520C2×C4—152no—
521C2×C4—301no—
522C2×C4—301no—
523C2×C4—301no—
524C2×C4—302no—
525C2×C4—302no—
526C2×C4—301no—
527C2×C4—301no—
528C2×C4—302no—
529C2×C4#677112yes—
530C2×C4#677112yes—
531C2×C4C2×D5×Dic314yes—
532C2×C4C2×D5×Dic312yes—
533C2×C3—204no—
534C2×C3C2×#401811yescharacteristic
535C2×C3#6584111yescharacteristic
536C2×C3#6586611yescharacteristic
537C2×C3C4×D4×D511yescharacteristic
538C2×C3#6588711yescharacteristic
539C2×C3#6590211yescharacteristic
540C2×C3#6590811yescharacteristic
541C5#8233711yescharacteristic, complemented, Sylow
542C22—104no—
543C22—104no—
544C22—104no—
545C22—202no—
546C22—202no—
547C22—202no—
548C22—202no—
549C22C2×#677111yescharacteristic
550C22C2×#677111yescharacteristic
551C22D3×D4×D511yescharacteristic
552C22D5×#23711yescharacteristic
553C22#9202811yescharacteristic
554C22#9203511yescharacteristic
555C22C22×D5×Dic311yescharacteristic
556C4—24no—
557C4—54no—
558C4—62no—
559C4—102no—
560C4—121no—
561C4—122no—
562C4—302no—
563C4—601no—
564C4—602no—
565C4#9135714yescomplemented
566C3#1060537011yescharacteristic, complemented, Sylow
567C2—204no—
568C2#1175335011yescharacteristic
569C2#1175368411yescharacteristic
570C2#1175368711yescharacteristic
571C2#1175373611yescharacteristic
572C2C2×#9135711yescharacteristic
573C2D4×D5×Dic311yescharacteristic
574C2#1175521711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×D20C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2354
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
2. C2×#91357C2semidirect
3. C4⋊C4×Dic15C2semidirect
4. C5×Dic3×C4⋊C4C2semidirect
5. #11748834C2semidirect
6. C4×#6668C2semidirect
8. #11748791C2semidirect
10. #11748770C2semidirect
11. #11748738C2semidirect
24. C3×#4039C4semidirect
79. #6668D4semidirect
90. Dic3×C4⋊C4D5semidirect
114. #4039Dic3semidirect
246. C3×C4×C5#117semidirect
420. C4×C5#926semidirect
460. C3×C5#2354semidirect
478. C3×C4#4018semidirect
541. C5#82337semidirect
565. C4#91357semidirect
566. C3#10605370semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40392
C2×#913572
C4⋊C4×Dic152
C5×Dic3×C4⋊C42
#117488342
C4×#66682
#117487962
#117487912
#117487852
#117487702
#117487382
#106053703
#823375