Finite Group Databasebeta

← #14320110

Subgroups — #14320110

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D5×Dic3C211yesmaximal, characteristic
2#11751078C211yesmaximal, characteristic, complemented
3C5×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
4C3×#65276C211yesmaximal, characteristic
5Dic3×#685C212yesmaximal
6#11748871C212yesmaximal
7#11748759C211yesmaximal, characteristic
8Dic3×C4⋊Dic5C211yesmaximal, characteristic, complemented
9#11748646C212yesmaximal, complemented
10#11748643C212yesmaximal, complemented
11#11748623C211yesmaximal, characteristic, complemented
12#10605483—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C22×D5×Dic3C2211yescharacteristic
15C22×D5×Dic3C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C4×Dic15C2211yescharacteristic
19C2×C5×C4⋊Dic3C2211yescharacteristic
20C2×C4×C5×Dic3C2212yes—
21C2×C4×C5×Dic3C2211yescharacteristic
22C2×C3×#685C2212yes—
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×#6665C2212yes—
25C2×Dic3×Dic5C2212yes—
26C2×Dic3×Dic5C2211yescharacteristic
27C2×Dic3×Dic5C2211yescharacteristic
28C4×D5×Dic3C418yescomplemented
29#91115C2212yes—
30#91115C2212yes—
31C5×C3⋊#95C2212yes—
32C3×#3963C2212yes—
33#90994C2212yes—
34#90994C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#73863—51nomaximal, Hall
38C2×C42×D5—31no—
39C4×C5×C4⋊C4—31no—
40#65276—31no—
41#65276D311yescharacteristic
42#65266—31no—
43#65266—31no—
44C4×#685—32no—
45C4×C4⋊Dic5—31no—
46#65221—32no—
47#64953—32no—
48#64940—32no—
49C23×C3×D5C2311yescharacteristic
50C22×C3×C4×C5C2312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×Dic15C2312yes—
53C22×Dic15C2311yescharacteristic
54C22×Dic15C2311yescharacteristic
55C22×C5×Dic3C2312yes—
56C22×C5×Dic3C2311yescharacteristic
57C22×C5×Dic3C2311yescharacteristic
58C22×C3×Dic5C2312yes—
59C22×C3×Dic5C2311yescharacteristic
60C2×C3×C4×D5—22no—
61C2×C3×C4×D5—22no—
62C2×C3×C4×D5C2×C414yes—
63C2×D5×Dic3—22no—
64C2×D5×Dic3—22no—
65C2×D5×Dic3—22no—
66C2×D5×Dic3—22no—
67C2×D5×Dic3C2×C414yes—
68C2×D5×Dic3C2×C414yes—
69C3×C5×C4⋊C4—22no—
70C4⋊Dic15—22no—
71C4×Dic15C2×C414yes—
72C5×C4⋊Dic3—22no—
73C4×C5×Dic3—24no—
74C4×C5×Dic3C2×C414yes—
75C3×#685—24no—
76C3×C4⋊Dic5—22no—
77#6665—24no—
78Dic3×Dic5—24no—
79Dic3×Dic5C2×C414yes—
80Dic3×Dic5C2×C414yes—
81C22×C4×Dic3—51no—
82C3×#380—51no—
83#5212—51no—
84#4977—51no—
85#4977—51no—
86Dic3×C4⋊C4—51no—
87Dic3×C4⋊C4D511yescharacteristic, complemented
88#4943—52no—
89Dic3×C22⋊C4—52no—
90#4651—52no—
91#4648—52no—
92C22×C4×D5—31no—
93C22×C4×D5—31no—
94C22×C4×D5C2×D311yescharacteristic
95C2×C5×C4⋊C4—31no—
96C2×C5×C4⋊C4C2×D311yescharacteristic
97C2×C42×C5—31no—
98C2×C42×C5—32no—
99C2×#685—32no—
100C2×#685C2×D312yes—
101C2×C4⋊Dic5—31no—
102C2×C4⋊Dic5C2×D311yescharacteristic
103C2×C4×Dic5—31no—
104C2×C4×Dic5—31no—
105C2×C4×Dic5—31no—
106C2×C4×Dic5—32no—
107C42×D5—38no—
108C5×#95—32no—
109#3963—32no—
110#3963—32no—
111#3963—32no—
112#3963—32no—
113#3963—32no—
114#3963—32no—
115#3963C2×D312yes—
116#2283—151noSylow
117C23×C3×C5C2411yescharacteristic
118C22×C3×D5—21no—
119C22×C3×D5—21no—
120C22×C3×D5—21no—
121C22×C3×D5—21no—
122C22×C3×D5C22×C412yes—
123C22×C3×D5#4112yes—
124C22×C3×D5#4112yes—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5C22×C412yes—
129C2×C3×C4×C5#4112yes—
130C2×C3×C4×C5#4112yes—
131C2×Dic15—21no—
132C2×Dic15—21no—
133C2×Dic15—21no—
134C2×Dic15—21no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C2×Dic15C22×C412yes—
139C2×Dic15C22×C412yes—
140C2×C5×Dic3—21no—
141C2×C5×Dic3—21no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3C22×C412yes—
146C2×C5×Dic3C22×C412yes—
147C2×C5×Dic3#4112yes—
148C2×C5×Dic3#4112yes—
149C2×C3×Dic5—21no—
150C2×C3×Dic5—21no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5C22×C412yes—
155C3×C4×D5—28no—
156D5×Dic3—28no—
157D5×Dic3—28no—
158C23×C3×C4—51no—
159C23×Dic3—51no—
160C23×Dic3—51no—
161C2×C3×C4⋊C4—51no—
162C2×C3×C4⋊C4C2×D511yescharacteristic
163C2×C3×C22⋊C4—52no—
164C2×#217—52no—
165C2×C4⋊Dic3—51no—
166C2×C4⋊Dic3C2×D511yescharacteristic
167C2×C4×Dic3—51no—
168C2×C4×Dic3—51no—
169C2×C4×Dic3—51no—
170C2×C4×Dic3—58no—
171C2×C4×Dic3—52no—
172C2×C4×Dic3C2×D512yes—
173C2×C4×Dic3C2×D511yescharacteristic
174C3×#95—52no—
175C3⋊#95—52no—
176C3⋊#95—52no—
177C3⋊#95—52no—
178C3⋊#95—52no—
179C3⋊#95—52no—
180C3⋊#95—52no—
181C3⋊#95C2×D512yes—
182C23×D5C22×D311yescharacteristic
183C22×C4×C5—31no—
184C22×C4×C5—31no—
185C22×C4×C5—32no—
186C22×C4×C5C22×D312yes—
187C22×C4×C5C22×D311yescharacteristic
188C22×Dic5—31no—
189C22×Dic5—31no—
190C22×Dic5—32no—
191C22×Dic5C22×D312yes—
192C22×Dic5C22×D311yescharacteristic
193C2×C4×D5—22no—
194C2×C4×D5—22no—
195C2×C4×D5—34no—
196C2×C4×D5—34no—
197C2×C4×D5—62no—
198C2×C4×D5—62no—
199C2×C4×D5—62no—
200C2×C4×D5—62no—
201C2×C4×D5C4×D314yes—
202C5×C4⋊C4—22no—
203C5×C4⋊C4—62no—
204C42×C5—34no—
205C42×C5—64no—
206#685—24no—
207#685—64no—
208C4⋊Dic5—22no—
209C4⋊Dic5—62no—
210C4×Dic5—34no—
211C4×Dic5—34no—
212C4×Dic5—34no—
213C4×Dic5—64no—
214C22×C42—151no—
215#383—152no—
216#382—151no—
217#382—151no—
218#381—152no—
219#380—51no—
220#380—151no—
221C4×C4⋊C4—31no—
222C4×C4⋊C4—151no—
223C4×C22⋊C4—152no—
224#376—152no—
225C22×C3×C5C23×C411yescharacteristic
226C22×C3×C5C2×#4111yescharacteristic
227C22×C3×C5C2×#4111yescharacteristic
228C22×C3×C5C2×#4111yescharacteristic
229C22×C3×C5C2×#4111yescharacteristic
230C22×C3×C5C2×#4111yescharacteristic
231C22×C3×C5C2×#4111yescharacteristic
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×D5#11714yes—
239C3×C4×C5—42no—
240C3×C4×C5#11714yes—
241Dic15—22no—
242Dic15—22no—
243Dic15—42no—
244C3×Dic5—22no—
245C3×Dic5—42no—
246C5×Dic3—22no—
247C5×Dic3—42no—
248C5×Dic3#11714yes—
249C24×C3—51no—
250C22×C3×C4—51no—
251C22×C3×C4—54no—
252C22×C3×C4—52no—
253C22×C3×C4—102no—
254C22×C3×C4—102no—
255C22×C3×C4C22×D512yes—
256C22×C3×C4C22×D511yescharacteristic
257C22×Dic3—51no—
258C22×Dic3—51no—
259C22×Dic3—54no—
260C22×Dic3—54no—
261C22×Dic3—52no—
262C22×Dic3—102no—
263C22×Dic3—102no—
264C22×Dic3—102no—
265C22×Dic3—102no—
266C22×Dic3C22×D512yes—
267C22×Dic3C22×D511yescharacteristic
268C22×Dic3C22×D511yescharacteristic
269C3×C4⋊C4—22no—
270C3×C4⋊C4—102no—
271C3×C22⋊C4—104no—
272#217—104no—
273C4⋊Dic3—22no—
274C4⋊Dic3—102no—
275C4×Dic3—24no—
276C4×Dic3—54no—
277C4×Dic3—54no—
278C4×Dic3—54no—
279C4×Dic3—104no—
280C4×Dic3C4×D514yes—
281C23×C5C23×D311yescharacteristic
282C22×D5—21no—
283C22×D5—21no—
284C22×D5—21no—
285C22×D5—21no—
286C22×D5C2×C4×D312yes—
287C22×D5#23712yes—
288C22×D5#23912yes—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—32no—
293C2×C4×C5—32no—
294C2×C4×C5—32no—
295C2×C4×C5—32no—
296C2×C4×C5—61no—
297C2×C4×C5—61no—
298C2×C4×C5—62no—
299C2×C4×C5—62no—
300C2×C4×C5—62no—
301C2×C4×C5C2×C4×D312yes—
302C2×C4×C5#23712yes—
303C2×C4×C5#23712yes—
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—22no—
307C2×Dic5—22no—
308C2×Dic5—22no—
309C2×Dic5—32no—
310C2×Dic5—32no—
311C2×Dic5—61no—
312C2×Dic5—61no—
313C2×Dic5—61no—
314C2×Dic5—61no—
315C2×Dic5—62no—
316C2×Dic5—62no—
317C2×Dic5—62no—
318C2×Dic5C2×C4×D312yes—
319C4×D5—28no—
320C4×D5—68no—
321C4×D5—68no—
322C23×C4—51no—
323C23×C4—151no—
324C23×C4—151no—
325C2×C4⋊C4—31no—
326C2×C4⋊C4—51no—
327C2×C4⋊C4—151no—
328C2×C4⋊C4D3×D511yescharacteristic
329C2×C22⋊C4—52no—
330C2×C22⋊C4—152no—
331C2×C42—31no—
332C2×C42—32no—
333C2×C42—158no—
334C2×C42—151no—
335C2×C42—151no—
336C2×C42—151no—
337C2×C42—152no—
338#95—32no—
339#95—52no—
340#95—152no—
341#95—152no—
342#95—152no—
343#95—152no—
344#95—152no—
345#95—152no—
346C2×C3×C5C2×#11711yescharacteristic
347C2×C3×C5C2×#11711yescharacteristic
348C2×C3×C5C2×#11711yescharacteristic
349C2×C3×C5#52911yescharacteristic
350C2×C3×C5#52911yescharacteristic
351C2×C3×C5#52911yescharacteristic
352C2×C3×C5#52911yescharacteristic
353C3×D5—24no—
354C23×C3—52no—
355C23×C3—52no—
356C23×C3—52no—
357C23×C3—101no—
358C23×C3—101no—
359C23×C3—101no—
360C23×C3—101no—
361C23×C3C23×D511yescharacteristic
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—52no—
366C2×C3×C4—101no—
367C2×C3×C4—101no—
368C2×C3×C4—108no—
369C2×C3×C4—102no—
370C2×C3×C4—102no—
371C2×C3×C4—102no—
372C2×C3×C4C2×C4×D512yes—
373C2×C3×C4#70912yes—
374C2×C3×C4#70912yes—
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—52no—
381C2×Dic3—52no—
382C2×Dic3—108no—
383C2×Dic3—101no—
384C2×Dic3—101no—
385C2×Dic3—101no—
386C2×Dic3—101no—
387C2×Dic3—108no—
388C2×Dic3—102no—
389C2×Dic3—102no—
390C2×Dic3—102no—
391C2×Dic3C2×C4×D512yes—
392C2×Dic3C2×C4×D512yes—
393C2×Dic3#71112yes—
394C2×Dic3#71312yes—
395C22×C5C22×C4×D311yescharacteristic
396C22×C5C2×#23711yescharacteristic
397C22×C5C2×#23711yescharacteristic
398C22×C5C2×#23711yescharacteristic
399C22×C5C2×#23911yescharacteristic
400C22×C5D3×#4111yescharacteristic
401C22×C5D3×#4111yescharacteristic
402C2×D5—22no—
403C2×D5—22no—
404C2×D5—22no—
405C2×D5—22no—
406C2×D5—22no—
407C2×D5—22no—
408C2×D5#89214yes—
409C4×C5—34no—
410C4×C5—42no—
411C4×C5—62no—
412C4×C5—122no—
413C4×C5#87714yes—
414Dic5—22no—
415Dic5—42no—
416Dic5—62no—
417Dic5—62no—
418Dic5—122no—
419C24—51no—
420C22×C4—31no—
421C22×C4—31no—
422C22×C4—32no—
423C22×C4—51no—
424C22×C4—54no—
425C22×C4—52no—
426C22×C4—102no—
427C22×C4—102no—
428C22×C4—154no—
429C22×C4—154no—
430C22×C4—151no—
431C22×C4—151no—
432C22×C4—152no—
433C22×C4—302no—
434C22×C4—302no—
435C22×C4—302no—
436C22×C4—302no—
437C22×C4C2×D3×D512yes—
438C22×C4C2×D3×D511yescharacteristic
439C4⋊C4—22no—
440C4⋊C4—62no—
441C4⋊C4—102no—
442C4⋊C4—302no—
443C22⋊C4—104no—
444C22⋊C4—304no—
445C42—34no—
446C42—64no—
447C42—154no—
448C42—154no—
449C42—154no—
450C42—304no—
451C3×C5#228311yescharacteristic, complemented, Hall
452C22×C3—54no—
453C22×C3—102no—
454C22×C3—102no—
455C22×C3—102no—
456C22×C3—102no—
457C22×C3—102no—
458C22×C3—102no—
459C22×C3C22×C4×D511yescharacteristic
460C22×C3C2×#70911yescharacteristic
461C22×C3C2×#70911yescharacteristic
462C22×C3C2×#71111yescharacteristic
463C22×C3C2×#71311yescharacteristic
464C22×C3D5×#4111yescharacteristic
465C22×C3D5×#4111yescharacteristic
466C3×C4—42no—
467C3×C4—102no—
468C3×C4—202no—
469C3×C4#401814yes—
470Dic3—22no—
471Dic3—42no—
472Dic3—102no—
473Dic3—102no—
474Dic3—202no—
475Dic3#403814yes—
476C2×C5C2×#87711yescharacteristic
477C2×C5C2×#89211yescharacteristic
478C2×C5D3×#11711yescharacteristic
479C2×C5#560011yescharacteristic
480C2×C5#560011yescharacteristic
481C2×C5#562411yescharacteristic
482C2×C5#562411yescharacteristic
483D5—24no—
484C23—52no—
485C23—52no—
486C23—52no—
487C23—101no—
488C23—101no—
489C23—101no—
490C23—101no—
491C23C22×D3×D511yescharacteristic
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—32no—
496C2×C4—32no—
497C2×C4—32no—
498C2×C4—32no—
499C2×C4—52no—
500C2×C4—61no—
501C2×C4—61no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—101no—
506C2×C4—101no—
507C2×C4—108no—
508C2×C4—102no—
509C2×C4—102no—
510C2×C4—102no—
511C2×C4—152no—
512C2×C4—152no—
513C2×C4—308no—
514C2×C4—308no—
515C2×C4—301no—
516C2×C4—301no—
517C2×C4—301no—
518C2×C4—301no—
519C2×C4—302no—
520C2×C4—302no—
521C2×C4—302no—
522C2×C4#676512yes—
523C2×C4C4×D3×D512yes—
524C2×C4#677912yes—
525C2×C3—104no—
526C2×C3C2×#401811yescharacteristic
527C2×C3C2×#403811yescharacteristic
528C2×C3D5×#11711yescharacteristic
529C2×C3#6589111yescharacteristic
530C2×C3#6589111yescharacteristic
531C2×C3#6591411yescharacteristic
532C2×C3#6591411yescharacteristic
533C5#7386311yescharacteristic, complemented, Sylow
534C22—54no—
535C22—102no—
536C22—102no—
537C22—102no—
538C22—102no—
539C22—102no—
540C22—102no—
541C22C2×#676511yescharacteristic
542C22C2×C4×D3×D511yescharacteristic
543C22D5×#23711yescharacteristic
544C22D3×#71111yescharacteristic
545C22D5×#23911yescharacteristic
546C22D3×#71311yescharacteristic
547C22C2×#677911yescharacteristic
548C4—34no—
549C4—42no—
550C4—62no—
551C4—102no—
552C4—122no—
553C4—202no—
554C4—302no—
555C4—302no—
556C4—602no—
557C4#9139314yes—
558C3#1060548311yescharacteristic, complemented, Sylow
559C2—104no—
560C2#1175349811yescharacteristic
561C2#1175352811yescharacteristic
562C2D5×#89211yescharacteristic
563C2D3×#403811yescharacteristic
564C2C2×#9139311yescharacteristic
565C2#1175483311yescharacteristic
566C2#1175518911yescharacteristic
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#2283
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. #11751078C2semidirect
3. C5×Dic3×C4⋊C4C2semidirect
8. Dic3×C4⋊Dic5C2semidirect
9. #11748646C2semidirect
10. #11748643C2semidirect
11. #11748623C2semidirect
28. C4×D5×Dic3C4semidirect
87. Dic3×C4⋊C4D5semidirect
451. C3×C5#2283semidirect
533. C5#73863semidirect
558. C3#10605483semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D5×Dic32
#117510782
C5×Dic3×C4⋊C42
C3×#652762
Dic3×#6852
#117488712
#117487592
Dic3×C4⋊Dic52
#117486462
#117486432
#117486232
#106054833
#738635