Finite Group Databasebeta

← #14327188

Subgroups — #14327188

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×D12C211yesmaximal, characteristic
2C2×Dic5×D12C211yesmaximal, characteristic
3C2×Dic5×D12C211yesmaximal, characteristic
4#11751029C211yesmaximal, characteristic, complemented
5C3×C4×#683C211yesmaximal, characteristic, complemented
6#11748892C212yesmaximal, complemented
7#11748887C212yesmaximal, complemented
8D3×#3963C212yesmaximal, complemented
9#11748841C211yesmaximal, characteristic, complemented
10#11748716C212yesmaximal, complemented
11#11748613C211yesmaximal, characteristic, complemented
12#10614065—31nomaximal, Hall
13C22×C5×D12C2211yescharacteristic
14C22×C4×C5×D3C2212yes—
15C22×D3×Dic5C2212yes—
16C22×D3×Dic5C2212yes—
17C2×C3×C42×C5C2211yescharacteristic
18C2×C4⋊Dic15C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20C2×#6712C2212yes—
21C2×C5×(C2×D3)⋊C4C2212yes—
22C2×C5×C4⋊Dic3C2211yescharacteristic
23C4×C5×D12—24no—
24C2×C3×#683C2211yescharacteristic
25C2×C3×#683C2211yescharacteristic
26C2×C3×C4×Dic5C2211yescharacteristic
27C2×C3×C4×Dic5C2211yescharacteristic
28C2×#6669C2212yes—
29C2×(C2×D3)⋊Dic5C2212yes—
30C2×(C2×D3)⋊Dic5C2212yes—
31Dic5×D12—24no—
32Dic5×D12C418yescomplemented
33#91115C2212yes—
34C3×#3963C2211yescharacteristic
35C3×#3963C2211yescharacteristic
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#73770—51nomaximal, Hall
40C2×C4×C5×D4—31no—
41C2×D4×Dic5—31no—
42C2×D4×Dic5—31no—
43#65499—32no—
44C2×#3963—32no—
45#65266—31no—
46#65262—31no—
47#65235—32no—
48#65231—32no—
49C4×#683D311yescharacteristic, complemented
50#65217—31no—
51C23×C5×D3C2312yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2312yes—
57C22×C5×Dic3C2312yes—
58C2×C5×D12C2×C414yes—
59C2×C5×D12D414yes—
60C2×C5×D12Q814yes—
61C2×C4×C5×D3—24no—
62C2×C4×C5×D3—24no—
63C2×C4×C5×D3—42no—
64C22×C3×Dic5C2311yescharacteristic
65C22×C3×Dic5C2311yescharacteristic
66C22×C3×Dic5C2311yescharacteristic
67C22×C3×Dic5C2311yescharacteristic
68C2×D3×Dic5—24no—
69C2×D3×Dic5—24no—
70C2×D3×Dic5—42no—
71C2×D3×Dic5—42no—
72C2×D3×Dic5—42no—
73C2×D3×Dic5C2×C418yescomplemented
74C3×C42×C5—22no—
75C4⋊Dic15—22no—
76C4⋊Dic15C2×C414yescomplemented
77#6712—42no—
78C5×(C2×D3)⋊C4—24no—
79C5×C4⋊Dic3—22no—
80C3×#683—22no—
81C3×#683—22no—
82C3×C4×Dic5—22no—
83C3×C4×Dic5C2×C414yescomplemented
84#6669—42no—
85(C2×D3)⋊Dic5—24no—
86(C2×D3)⋊Dic5C2×C418yescomplemented
87C2×C4×D12—51no—
88C2×C4×D12—51no—
89C2×C4×D12D511yescharacteristic
90C3×C4×C4⋊C4—51no—
91#4989—52no—
92#4989—52no—
93#4936—51no—
94#4928—51no—
95#4928—51no—
96#4667—52no—
97D3×#95—52no—
98C22×C5×D4—31no—
99C23×C4×C5—32no—
100C23×Dic5—32no—
101C23×Dic5—32no—
102C4×C5×D4—64no—
103C2×C5×C4⋊C4—31no—
104C2×C5×C22⋊C4—32no—
105C2×C42×C5C2×D311yescharacteristic
106C2×C22⋊Dic5—32no—
107C2×C22⋊Dic5—32no—
108D4×Dic5—38no—
109D4×Dic5—64no—
110C2×C4⋊Dic5—31no—
111C2×C4⋊Dic5—31no—
112C2×#683—32no—
113C2×#683—32no—
114C2×#683C2×D311yescharacteristic
115C2×#683C2×D311yescharacteristic
116C2×C4×Dic5C2×D311yescharacteristic
117C2×C4×Dic5C2×D311yescharacteristic
118#3963—32no—
119#3963—32no—
120#3963—32no—
121#3963—32no—
122#3963C2×D311yescharacteristic
123#3963C2×D311yescharacteristic
124#2349—151noSylow
125C23×C3×C5C2411yescharacteristic
126C22×C5×D3—22no—
127C22×C5×D3—22no—
128C22×C5×D3—22no—
129C22×C5×D3—22no—
130C22×C5×D3C22×C414yes—
131C22×C5×D3C2×D414yes—
132C22×C5×D3C2×Q814yes—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5C22×C412yes—
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2×Q812yes—
141C2×C3×C4×C5#4112yes—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15C22×C414yes—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—22no—
151C5×D12C4⋊C4116yescomplemented
152C4×C5×D3—48no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—21no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—21no—
160C2×C3×Dic5—21no—
161C2×C3×Dic5—21no—
162C2×C3×Dic5C22×C412yes—
163C2×C3×Dic5C22×C412yes—
164C2×C3×Dic5#4112yes—
165D3×Dic5—48no—
166D3×Dic5—48no—
167C22×D12C2×D511yescharacteristic
168C22×C4×D3—52no—
169C22×C4×D3—52no—
170C22×C4×D3C2×D512yes—
171C2×C3×C4⋊C4—51no—
172C2×C3×C4⋊C4—51no—
173C2×C3×C42—51no—
174C2×C3×C42—51no—
175C2×C3×C42C2×D511yescharacteristic
176C2×(C2×D3)⋊C4—52no—
177C2×(C2×D3)⋊C4—52no—
178C2×(C2×D3)⋊C4C2×D512yes—
179C2×C4⋊Dic3—51no—
180C2×C4⋊Dic3—51no—
181C2×C4⋊Dic3C2×D511yescharacteristic
182C2×Dic3⋊C4—52no—
183C2×Dic3⋊C4—52no—
184C4×D12—24no—
185C4×D12—58no—
186C4×D12—104no—
187C3×#95—51no—
188C3×#95—51no—
189C3⋊#95—52no—
190C3⋊#95—52no—
191C3⋊#95—52no—
192C3⋊#95—52no—
193C24×C5—32no—
194C2×C5×D4—34no—
195C2×C5×D4—34no—
196C2×C5×D4—34no—
197C22×C4×C5—32no—
198C22×C4×C5—64no—
199C22×C4×C5—64no—
200C22×C4×C5—122no—
201C22×C4×C5C22×D311yescharacteristic
202C22×C4×C5C22×D311yescharacteristic
203C22×C4×C5C22×D311yescharacteristic
204C22×Dic5—32no—
205C22×Dic5—38no—
206C22×Dic5—32no—
207C22×Dic5—64no—
208C22×Dic5—64no—
209C22×Dic5—122no—
210C22×Dic5—122no—
211C22×Dic5—122no—
212C22×Dic5C22×D311yescharacteristic
213C22×Dic5C22×D311yescharacteristic
214C22×Dic5C22×D311yescharacteristic
215C22×Dic5C22×D311yescharacteristic
216C5×C4⋊C4—62no—
217C5×C22⋊C4—64no—
218C42×C5—22no—
219C22⋊Dic5—38no—
220C22⋊Dic5—64no—
221C4⋊Dic5—34no—
222C4⋊Dic5—62no—
223#683—22no—
224#683—22no—
225#683—122no—
226#683—122no—
227C4×Dic5—22no—
228C4×Dic5C4×D314yescomplemented
229C2×C4×D4—31no—
230C2×C4×D4—151no—
231C2×C4×D4—151no—
232#389—151no—
233#389—151no—
234#385—152no—
235#385—152no—
236#382—151no—
237#380—152no—
238C4×C4⋊C4—51no—
239C2×#95—152no—
240C22×C3×C5C23×C411yescharacteristic
241C22×C3×C5C22×D411yescharacteristic
242C22×C3×C5C22×Q811yescharacteristic
243C22×C3×C5C2×#4111yescharacteristic
244C22×C3×C5C2×#4111yescharacteristic
245C22×C3×C5H(5,𝔽2)11yescharacteristic
246C22×C3×C5H(5,𝔽2)11yescharacteristic
247C2×C5×D3—24no—
248C2×C5×D3—24no—
249C2×C5×D3—24no—
250C2×C5×D3—24no—
251C2×C5×D3—24no—
252C2×C5×D3—24no—
253C2×C5×D3C2×C4⋊C418yes—
254C3×C4×C5—22no—
255C3×C4×C5—41no—
256C3×C4×C5C2×C4⋊C414yes—
257Dic15—24no—
258Dic15—42no—
259C3×Dic5—22no—
260C3×Dic5—22no—
261C3×Dic5—22no—
262C3×Dic5—41no—
263C5×Dic3—42no—
264C23×D3C22×D512yes—
265C22×C3×C4—51no—
266C22×C3×C4—51no—
267C22×C3×C4—51no—
268C22×C3×C4—51no—
269C22×C3×C4C22×D511yescharacteristic
270C22×C3×C4C22×D511yescharacteristic
271C22×C3×C4C22×D511yescharacteristic
272C22×Dic3—52no—
273C22×Dic3—52no—
274C22×Dic3C22×D512yes—
275C2×D12Dic1014yes—
276C2×D12C4×D514yes—
277C2×D12C22⋊D514yes—
278C2×C4×D3—24no—
279C2×C4×D3—24no—
280C2×C4×D3—42no—
281C2×C4×D3—58no—
282C2×C4×D3—104no—
283C2×C4×D3—104no—
284C2×C4×D3—202no—
285C2×C4×D3—202no—
286C2×C4×D3—202no—
287C3×C4⋊C4—102no—
288C3×C4⋊C4—102no—
289C3×C42—22no—
290C3×C42—54no—
291C3×C42—102no—
292(C2×D3)⋊C4—24no—
293(C2×D3)⋊C4—58no—
294(C2×D3)⋊C4—104no—
295C4⋊Dic3—22no—
296C4⋊Dic3—54no—
297C4⋊Dic3—102no—
298Dic3⋊C4—202no—
299Dic3⋊C4—202no—
300C23×C5—34no—
301C23×C5—34no—
302C23×C5—34no—
303C23×C5—62no—
304C23×C5—62no—
305C23×C5—62no—
306C23×C5—62no—
307C23×C5C23×D311yescharacteristic
308C5×D4—316no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—62no—
315C2×C4×C5—62no—
316C2×C4×C5—62no—
317C2×C4×C5—128no—
318C2×C4×C5C2×C4×D312yes—
319C2×C4×C5#23512yes—
320C2×C4×C5D3×D412yes—
321C2×C4×C5D3×Q812yes—
322C2×Dic5—21no—
323C2×Dic5—21no—
324C2×Dic5—21no—
325C2×Dic5—21no—
326C2×Dic5—21no—
327C2×Dic5—21no—
328C2×Dic5—21no—
329C2×Dic5—21no—
330C2×Dic5—21no—
331C2×Dic5—34no—
332C2×Dic5—62no—
333C2×Dic5—62no—
334C2×Dic5—62no—
335C2×Dic5—62no—
336C2×Dic5—62no—
337C2×Dic5—128no—
338C2×Dic5—128no—
339C2×Dic5C2×C4×D312yes—
340C2×Dic5C2×C4×D312yes—
341C2×Dic5#23512yes—
342C22×D4—31no—
343C23×C4—32no—
344C23×C4—152no—
345C23×C4—152no—
346C4×D4—64no—
347C4×D4—158no—
348C4×D4—304no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—51no—
351C2×C4⋊C4—51no—
352C2×C4⋊C4—151no—
353C2×C4⋊C4—151no—
354C2×C4⋊C4—152no—
355C2×C4⋊C4—152no—
356C2×C22⋊C4—32no—
357C2×C22⋊C4—152no—
358C2×C22⋊C4—152no—
359C2×C42—51no—
360C2×C42—51no—
361C2×C42D3×D511yescharacteristic
362#95—51no—
363#95—51no—
364#95—152no—
365#95—152no—
366#95—152no—
367#95—152no—
368C2×C3×C5C22×C4⋊C411yescharacteristic
369C2×C3×C5C4×#4111yescharacteristic
370C2×C3×C5#51811yescharacteristic
371C2×C3×C5#54611yescharacteristic
372C2×C3×C5#54611yescharacteristic
373C2×C3×C5#55411yescharacteristic
374C2×C3×C5#55411yescharacteristic
375C5×D3—28no—
376C23×C3C23×D511yescharacteristic
377C22×D3—22no—
378C22×D3—22no—
379C22×D3—22no—
380C22×D3—22no—
381C22×D3C2×Dic1014yes—
382C22×D3C2×C4×D514yes—
383C22×D3C2×C22⋊D514yes—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—52no—
390C2×C3×C4—52no—
391C2×C3×C4—52no—
392C2×C3×C4—101no—
393C2×C3×C4—101no—
394C2×C3×C4—101no—
395C2×C3×C4—101no—
396C2×C3×C4—101no—
397C2×C3×C4—101no—
398C2×C3×C4—101no—
399C2×C3×C4—101no—
400C2×C3×C4—101no—
401C2×C3×C4C2×Dic1012yes—
402C2×C3×C4C2×C4×D512yes—
403C2×C3×C4#71112yes—
404C2×C3×C4C2×C22⋊D512yes—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—54no—
409C2×Dic3—102no—
410C2×Dic3—102no—
411C2×Dic3—102no—
412C2×Dic3—102no—
413C2×Dic3—102no—
414D12#683116yescomplemented
415C4×D3—48no—
416C4×D3—208no—
417C4×D3—208no—
418C22×C5—38no—
419C22×C5—64no—
420C22×C5—64no—
421C22×C5—64no—
422C22×C5—64no—
423C22×C5—64no—
424C22×C5—64no—
425C22×C5C22×C4×D311yescharacteristic
426C22×C5C2×#23511yescharacteristic
427C22×C5C2×#23511yescharacteristic
428C22×C5C2×D3×D411yescharacteristic
429C22×C5C2×D3×Q811yescharacteristic
430C22×C5#100911yescharacteristic
431C22×C5#100911yescharacteristic
432C4×C5—22no—
433C4×C5—41no—
434C4×C5—122no—
435C4×C5D3×C4⋊C414yes—
436Dic5—22no—
437Dic5—22no—
438Dic5—22no—
439Dic5—41no—
440Dic5—64no—
441Dic5—122no—
442C24—32no—
443C2×D4—34no—
444C2×D4—34no—
445C2×D4—34no—
446C22×C4—32no—
447C22×C4—51no—
448C22×C4—51no—
449C22×C4—51no—
450C22×C4—51no—
451C22×C4—64no—
452C22×C4—64no—
453C22×C4—122no—
454C22×C4—158no—
455C22×C4—152no—
456C22×C4—152no—
457C22×C4—304no—
458C22×C4—304no—
459C22×C4—602no—
460C22×C4—602no—
461C22×C4—602no—
462C22×C4C2×D3×D511yescharacteristic
463C22×C4C2×D3×D511yescharacteristic
464C22×C4C2×D3×D511yescharacteristic
465C4⋊C4—62no—
466C4⋊C4—102no—
467C4⋊C4—102no—
468C4⋊C4—154no—
469C4⋊C4—302no—
470C4⋊C4—602no—
471C4⋊C4—602no—
472C22⋊C4—64no—
473C22⋊C4—158no—
474C22⋊C4—304no—
475C42—22no—
476C42—54no—
477C42—102no—
478C3×C5#234911yescharacteristic, complemented, Hall
479C22×C3C22×Dic1011yescharacteristic
480C22×C3C22×C4×D511yescharacteristic
481C22×C3C2×#71111yescharacteristic
482C22×C3#414411yescharacteristic
483C22×C3D5×#4111yescharacteristic
484C22×C3#414911yescharacteristic
485C22×C3C22×C22⋊D511yescharacteristic
486C2×D3—24no—
487C2×D3—24no—
488C2×D3—24no—
489C2×D3—24no—
490C2×D3—24no—
491C2×D3—24no—
492C2×D3C2×#68318yes—
493C3×C4—22no—
494C3×C4—41no—
495C3×C4—102no—
496C3×C4—102no—
497C3×C4—102no—
498C3×C4—201no—
499C3×C4C2×#68314yes—
500Dic3—42no—
501Dic3—104no—
502Dic3—202no—
503C2×C5—68no—
504C2×C5C4×#23511yescharacteristic
505C2×C5C2×D3×C4⋊C411yescharacteristic
506C2×C5#552111yescharacteristic
507C2×C5#555011yescharacteristic
508C2×C5#555011yescharacteristic
509C2×C5#557911yescharacteristic
510C2×C5#557911yescharacteristic
511C23—34no—
512C23—34no—
513C23—34no—
514C23—62no—
515C23—62no—
516C23—62no—
517C23—62no—
518C23C22×D3×D511yescharacteristic
519D4—316no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—52no—
526C2×C4—52no—
527C2×C4—52no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—101no—
532C2×C4—101no—
533C2×C4—101no—
534C2×C4—101no—
535C2×C4—101no—
536C2×C4—101no—
537C2×C4—101no—
538C2×C4—101no—
539C2×C4—101no—
540C2×C4—128no—
541C2×C4—154no—
542C2×C4—302no—
543C2×C4—302no—
544C2×C4—302no—
545C2×C4—302no—
546C2×C4—302no—
547C2×C4—608no—
548C2×C4—608no—
549C2×C4D3×Dic1012yes—
550C2×C4#677212yes—
551C2×C4C4×D3×D512yes—
552C2×C4D3×C22⋊D512yes—
553C2×C3C4×#71111yescharacteristic
554C2×C3#6587311yescharacteristic
555C2×C3#6587711yescharacteristic
556C2×C3#6587911yescharacteristic
557C2×C3C22×#68311yescharacteristic
558C2×C3#6614011yescharacteristic
559C2×C3#6616311yescharacteristic
560D3—28no—
561C5#7377011yescharacteristic, complemented, Sylow
562C22—38no—
563C22—64no—
564C22—64no—
565C22—64no—
566C22—64no—
567C22—64no—
568C22—64no—
569C22C2×D3×Dic1011yescharacteristic
570C22C2×#677211yescharacteristic
571C22C2×C4×D3×D511yescharacteristic
572C22D5×#23511yescharacteristic
573C22#9201811yescharacteristic
574C22#9201911yescharacteristic
575C22C2×D3×C22⋊D511yescharacteristic
576C4—22no—
577C4—41no—
578C4—102no—
579C4—102no—
580C4—102no—
581C4—122no—
582C4—201no—
583C4—304no—
584C4—602no—
585C4D3×#68314yes—
586C3#1061406511yescharacteristic, complemented, Sylow
587C2—68no—
588C2#1175258311yescharacteristic
589C2#1175266011yescharacteristic
590C2C4×#677211yescharacteristic
591C2#1175272511yescharacteristic
592C2C2×D3×#68311yescharacteristic
593C2#1175454011yescharacteristic
594C2#1175465111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×D12C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2349
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. #11751029C2semidirect
5. C3×C4×#683C2semidirect
6. #11748892C2semidirect
7. #11748887C2semidirect
8. D3×#3963C2semidirect
9. #11748841C2semidirect
10. #11748716C2semidirect
11. #11748613C2semidirect
32. Dic5×D12C4semidirect
49. C4×#683D3semidirect
73. C2×D3×Dic5C2×C4semidirect
76. C4⋊Dic15C2×C4semidirect
83. C3×C4×Dic5C2×C4semidirect
86. (C2×D3)⋊Dic5C2×C4semidirect
151. C5×D12C4⋊C4semidirect
228. C4×Dic5C4×D3semidirect
414. D12#683semidirect
478. C3×C5#2349semidirect
561. C5#73770semidirect
586. C3#10614065semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×D122
C2×Dic5×D122
#117510292
C3×C4×#6832
#117488922
#117488872
D3×#39632
#117488412
#117487162
#117486132
#106140653
#737705