Finite Group Databasebeta

← #14320172

Subgroups — #14320172

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91402C212yesmaximal
2C2×C4×#1200C211yesmaximal, characteristic
3#11751088C211yesmaximal, characteristic
4C5×#4975C211yesmaximal, characteristic, complemented
5C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
6#11748882C212yesmaximal
7#11748861C211yesmaximal, characteristic, complemented
8#11748799C211yesmaximal, characteristic
9Dic5×C4⋊Dic3C211yesmaximal, characteristic, complemented
10#11748652C212yesmaximal, complemented
11Dic5×Dic3⋊C4C212yesmaximal, complemented
12#10606049—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×#1200C2211yescharacteristic
15C22×#1200C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×#6714C2212yes—
18C2×C4⋊Dic15C2211yescharacteristic
19C2×C5×C4⋊Dic3C2211yescharacteristic
20C2×C5×Dic3⋊C4C2212yes—
21C2×C5×Dic3⋊C4C2212yes—
22C2×C4×C5×Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×C4×Dic5C2212yes—
25C2×C3×C4×Dic5C2211yescharacteristic
26C2×Dic3⋊Dic5C2212yes—
27C2×Dic3⋊Dic5C2212yes—
28C2×#6667C2212yes—
29C2×Dic3×Dic5C2212yes—
30C2×Dic3×Dic5C2211yescharacteristic
31C2×Dic3×Dic5C2211yescharacteristic
32#91402—28no—
33C4×#1200C418yescomplemented
34#91115C2212yes—
35C3×#3963C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#73753—51nomaximal, Hall
39C2×#4038—32no—
40C2×C42×D5—31no—
41C5×#384—31no—
42#65276—31no—
43#65276—32no—
44#65276—31no—
45#65266—32no—
46C4⋊C4×Dic5—32no—
47C4⋊C4×Dic5—31no—
48C4⋊C4×Dic5D311yescharacteristic, complemented
49#65224—31no—
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×Dic3C2312yes—
59C22×C5×Dic3C2311yescharacteristic
60C22×C5×Dic3C2311yescharacteristic
61C22×C3×Dic5C2312yes—
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2311yescharacteristic
64C2×#1200—22no—
65C2×#1200—22no—
66C2×#1200C2×C414yes—
67C2×#1200C2×C414yes—
68C2×#1200D414yes—
69C2×#1200Q814yes—
70C3×C5×C4⋊C4—22no—
71#6714—24no—
72C4⋊Dic15—22no—
73C5×C4⋊Dic3—22no—
74C5×Dic3⋊C4—24no—
75C5×Dic3⋊C4—24no—
76C4×C5×Dic3C2×C414yes—
77C3×C4⋊Dic5—22no—
78C3×C4×Dic5—24no—
79C3×C4×Dic5C2×C414yes—
80Dic3⋊Dic5—24no—
81Dic3⋊Dic5—24no—
82#6667—24no—
83Dic3×Dic5—24no—
84Dic3×Dic5C2×C414yes—
85Dic3×Dic5C2×C414yes—
86C2×#872—52no—
87C2×C42×D3—51no—
88C3×C4×C4⋊C4—51no—
89#4987—51no—
90#4987—51no—
91#4975—51no—
92#4975D511yescharacteristic, complemented
93C4×C4⋊Dic3—51no—
94C4×Dic3⋊C4—52no—
95#4667—52no—
96#4650—52no—
97C22×C4×D5—31no—
98C22×C4×D5—31no—
99C22×C4×D5—31no—
100C2×C5×C4⋊C4—32no—
101C2×C5×C4⋊C4—32no—
102C2×C5×C4⋊C4—31no—
103C2×C5×C4⋊C4C2×D311yescharacteristic
104C2×C42×C5—31no—
105C2×#685—32no—
106C2×#685—32no—
107C2×C4⋊Dic5—31no—
108C2×C4⋊Dic5—32no—
109C2×C4⋊Dic5—32no—
110C2×C4⋊Dic5C2×D311yescharacteristic
111C2×C4×Dic5—31no—
112C2×C4×Dic5—31no—
113C2×C4×Dic5—32no—
114C2×C4×Dic5C2×D312yes—
115C2×C4×Dic5C2×D311yescharacteristic
116#4038—68no—
117C42×D5—38no—
118#3963—32no—
119#3963—32no—
120#3963—32no—
121#3963C2×D312yes—
122#2285—151noSylow
123C23×C3×C5C2411yescharacteristic
124C22×D15—21no—
125C22×D15—21no—
126C22×D15—21no—
127C22×D15—21no—
128C22×D15C22×C412yes—
129C22×D15C2×D412yes—
130C22×D15C2×Q812yes—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5C22×C412yes—
135C2×C3×C4×C5#4112yes—
136C2×C3×C4×C5#4112yes—
137C2×Dic15—21no—
138C2×Dic15—21no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15—22no—
142C2×Dic15C22×C412yes—
143C4×D15—28no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3C22×C412yes—
148C2×C5×Dic3C22×C412yes—
149C2×C5×Dic3C2×D412yes—
150C2×C5×Dic3C2×Q812yes—
151C2×C5×Dic3#4112yes—
152C2×C5×Dic3#4112yes—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5C22×C412yes—
159C2×C3×Dic5C22×C412yes—
160C2×C3×Dic5C2×D412yes—
161C2×C3×Dic5C2×Q812yes—
162#1200—28no—
163#1200C4⋊C4116yescomplemented
164C22×C4×D3—51no—
165C22×C4×D3—51no—
166C22×C4×D3—51no—
167C2×C3×C4⋊C4—51no—
168C2×C3×C4⋊C4C2×D511yescharacteristic
169C2×C3×C42—51no—
170C2×C3×C42—52no—
171C2×(C2×D3)⋊C4—52no—
172C2×(C2×D3)⋊C4—52no—
173C2×C4⋊Dic3—51no—
174C2×C4⋊Dic3C2×D511yescharacteristic
175C2×Dic3⋊C4—52no—
176C2×Dic3⋊C4—52no—
177C2×Dic3⋊C4C2×D512yes—
178C2×Dic3⋊C4C2×D512yes—
179C2×C4×Dic3—51no—
180C2×C4×Dic3—51no—
181C2×C4×Dic3—52no—
182C2×C4×Dic3C2×D511yescharacteristic
183#872—108no—
184C42×D3—58no—
185C3×#95—52no—
186C3⋊#95—52no—
187C3⋊#95—52no—
188C3⋊#95—52no—
189C23×D5—31no—
190C22×C4×C5—31no—
191C22×C4×C5—31no—
192C22×C4×C5—32no—
193C22×C4×C5C22×D312yes—
194C22×C4×C5C22×D311yescharacteristic
195C22×Dic5—31no—
196C22×Dic5—32no—
197C22×Dic5C22×D312yes—
198C22×Dic5C22×D311yescharacteristic
199C22×Dic5C22×D311yescharacteristic
200C2×C4×D5—34no—
201C2×C4×D5—34no—
202C2×C4×D5—34no—
203C2×C4×D5—34no—
204C2×C4×D5—34no—
205C2×C4×D5—62no—
206C2×C4×D5—62no—
207C2×C4×D5—62no—
208C2×C4×D5—62no—
209C5×C4⋊C4—22no—
210C5×C4⋊C4—64no—
211C5×C4⋊C4—64no—
212C5×C4⋊C4—62no—
213C42×C5—34no—
214#685—64no—
215#685—64no—
216C4⋊Dic5—22no—
217C4⋊Dic5—64no—
218C4⋊Dic5—64no—
219C4⋊Dic5—62no—
220C4×Dic5—24no—
221C4×Dic5—34no—
222C4×Dic5—34no—
223C4×Dic5—64no—
224C4×Dic5C4×D314yes—
225C2×#117—152no—
226C22×C42—151no—
227#384—31no—
228#384—151no—
229#382—152no—
230#380—152no—
231#380—151no—
232#380—151no—
233C4×C4⋊C4—51no—
234C4×C4⋊C4—152no—
235C4×C4⋊C4—151no—
236C22×C3×C5C23×C411yescharacteristic
237C22×C3×C5C22×D411yescharacteristic
238C22×C3×C5C22×Q811yescharacteristic
239C22×C3×C5C2×#4111yescharacteristic
240C22×C3×C5C2×#4111yescharacteristic
241C22×C3×C5C2×#4111yescharacteristic
242C22×C3×C5C2×#4111yescharacteristic
243C2×D15—22no—
244C2×D15—22no—
245C2×D15—22no—
246C2×D15—22no—
247C2×D15—22no—
248C2×D15—22no—
249C2×D15C2×C4⋊C414yes—
250C3×C4×C5—42no—
251C3×C4×C5#11714yescomplemented
252Dic15—22no—
253Dic15—42no—
254C3×Dic5—22no—
255C3×Dic5—42no—
256C3×Dic5C2×C4⋊C414yes—
257C5×Dic3—42no—
258C5×Dic3C2×C4⋊C414yes—
259C5×Dic3#11714yescomplemented
260C23×D3—51no—
261C22×C3×C4—51no—
262C22×C3×C4—51no—
263C22×C3×C4—52no—
264C22×C3×C4C22×D512yes—
265C22×C3×C4C22×D511yescharacteristic
266C22×Dic3—51no—
267C22×Dic3—52no—
268C22×Dic3C22×D512yes—
269C22×Dic3C22×D511yescharacteristic
270C22×Dic3C22×D511yescharacteristic
271C2×C4×D3—54no—
272C2×C4×D3—54no—
273C2×C4×D3—54no—
274C2×C4×D3—54no—
275C2×C4×D3—54no—
276C2×C4×D3—102no—
277C2×C4×D3—102no—
278C2×C4×D3—102no—
279C2×C4×D3—102no—
280C3×C4⋊C4—22no—
281C3×C4⋊C4—102no—
282C3×C42—54no—
283C3×C42—104no—
284(C2×D3)⋊C4—104no—
285(C2×D3)⋊C4—104no—
286C4⋊Dic3—22no—
287C4⋊Dic3—102no—
288Dic3⋊C4—24no—
289Dic3⋊C4—24no—
290Dic3⋊C4—104no—
291Dic3⋊C4—104no—
292C4×Dic3—54no—
293C4×Dic3—54no—
294C4×Dic3—104no—
295C4×Dic3C4×D514yes—
296C23×C5C23×D311yescharacteristic
297C22×D5—32no—
298C22×D5—32no—
299C22×D5—32no—
300C22×D5—61no—
301C22×D5—61no—
302C22×D5—61no—
303C22×D5—61no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—32no—
308C2×C4×C5—32no—
309C2×C4×C5—32no—
310C2×C4×C5—32no—
311C2×C4×C5—32no—
312C2×C4×C5—32no—
313C2×C4×C5—62no—
314C2×C4×C5—62no—
315C2×C4×C5—62no—
316C2×C4×C5C2×C4×D312yes—
317C2×C4×C5#23512yes—
318C2×C4×C5#23512yes—
319C2×Dic5—21no—
320C2×Dic5—21no—
321C2×Dic5—22no—
322C2×Dic5—22no—
323C2×Dic5—22no—
324C2×Dic5—32no—
325C2×Dic5—61no—
326C2×Dic5—61no—
327C2×Dic5—62no—
328C2×Dic5—62no—
329C2×Dic5—62no—
330C2×Dic5C2×C4×D312yes—
331C2×Dic5C2×C4×D312yes—
332C2×Dic5D3×D412yes—
333C2×Dic5D3×Q812yes—
334C4×D5—316no—
335C4×D5—68no—
336C4×D5—68no—
337C23×C4—151no—
338C23×C4—151no—
339C23×C4—151no—
340#117—308no—
341C2×C4⋊C4—32no—
342C2×C4⋊C4—32no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—152no—
346C2×C4⋊C4—152no—
347C2×C4⋊C4—151no—
348C2×C4⋊C4D3×D511yescharacteristic
349C2×C22⋊C4—152no—
350C2×C22⋊C4—152no—
351C2×C42—31no—
352C2×C42—51no—
353C2×C42—52no—
354C2×C42—158no—
355C2×C42—151no—
356C2×C42—151no—
357C2×C42—152no—
358#95—52no—
359#95—152no—
360#95—152no—
361#95—152no—
362C2×C3×C5C22×C4⋊C411yescharacteristic
363C2×C3×C5C2×#11711yescharacteristic
364C2×C3×C5C2×#11711yescharacteristic
365C2×C3×C5#53211yescharacteristic
366C2×C3×C5#53211yescharacteristic
367C2×C3×C5#53311yescharacteristic
368C2×C3×C5#53311yescharacteristic
369D15—24no—
370C23×C3C23×D511yescharacteristic
371C22×D3—52no—
372C22×D3—52no—
373C22×D3—52no—
374C22×D3—101no—
375C22×D3—101no—
376C22×D3—101no—
377C22×D3—101no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—52no—
382C2×C3×C4—52no—
383C2×C3×C4—52no—
384C2×C3×C4—52no—
385C2×C3×C4—101no—
386C2×C3×C4—101no—
387C2×C3×C4—102no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4C2×C4×D512yes—
391C2×C3×C4#71112yes—
392C2×C3×C4#71312yes—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—52no—
397C2×Dic3—101no—
398C2×Dic3—101no—
399C2×Dic3—102no—
400C2×Dic3—102no—
401C2×Dic3—102no—
402C2×Dic3C2×C4×D512yes—
403C2×Dic3C2×C4×D512yes—
404C2×Dic3D4×D512yes—
405C2×Dic3#71112yes—
406C2×Dic3Q8×D512yes—
407C2×Dic3#71312yes—
408C4×D3—516no—
409C4×D3—108no—
410C4×D3—108no—
411C22×C5C22×C4×D311yescharacteristic
412C22×C5C2×#23511yescharacteristic
413C22×C5C2×#23511yescharacteristic
414C22×C5C2×D3×D411yescharacteristic
415C22×C5C2×D3×Q811yescharacteristic
416C22×C5D3×#4111yescharacteristic
417C22×C5D3×#4111yescharacteristic
418C2×D5—34no—
419C2×D5—62no—
420C2×D5—62no—
421C2×D5—62no—
422C2×D5—62no—
423C2×D5—62no—
424C2×D5—62no—
425C4×C5—34no—
426C4×C5—34no—
427C4×C5—42no—
428C4×C5—122no—
429C4×C5#87214yescomplemented
430Dic5—22no—
431Dic5—42no—
432Dic5—62no—
433Dic5—122no—
434Dic5D3×C4⋊C414yes—
435C24—151no—
436C22×C4—31no—
437C22×C4—31no—
438C22×C4—32no—
439C22×C4—51no—
440C22×C4—51no—
441C22×C4—52no—
442C22×C4—154no—
443C22×C4—154no—
444C22×C4—154no—
445C22×C4—154no—
446C22×C4—151no—
447C22×C4—154no—
448C22×C4—152no—
449C22×C4—302no—
450C22×C4—302no—
451C22×C4—302no—
452C22×C4—302no—
453C22×C4C2×D3×D512yes—
454C22×C4C2×D3×D511yescharacteristic
455C4⋊C4—22no—
456C4⋊C4—64no—
457C4⋊C4—64no—
458C4⋊C4—62no—
459C4⋊C4—102no—
460C4⋊C4—304no—
461C4⋊C4—304no—
462C4⋊C4—302no—
463C22⋊C4—304no—
464C22⋊C4—304no—
465C42—34no—
466C42—54no—
467C42—104no—
468C42—154no—
469C42—154no—
470C42—304no—
471C3×C5#228511yescharacteristic, complemented, Hall
472C22×C3C22×C4×D511yescharacteristic
473C22×C3C2×D4×D511yescharacteristic
474C22×C3C2×#71111yescharacteristic
475C22×C3C2×#71111yescharacteristic
476C22×C3C2×Q8×D511yescharacteristic
477C22×C3C2×#71311yescharacteristic
478C22×C3C2×#71311yescharacteristic
479C2×D3—54no—
480C2×D3—102no—
481C2×D3—102no—
482C2×D3—102no—
483C2×D3—102no—
484C2×D3—102no—
485C2×D3—102no—
486C3×C4—42no—
487C3×C4—54no—
488C3×C4—102no—
489C3×C4—202no—
490C3×C4#403814yescomplemented
491Dic3—42no—
492Dic3—102no—
493Dic3—202no—
494Dic3D5×C4⋊C414yes—
495Dic3#403814yescomplemented
496C2×C5C2×#87211yescharacteristic
497C2×C5C2×D3×C4⋊C411yescharacteristic
498C2×C5D3×#11711yescharacteristic
499C2×C5#554811yescharacteristic
500C2×C5#554811yescharacteristic
501C2×C5#557811yescharacteristic
502C2×C5#557811yescharacteristic
503D5—64no—
504C23—152no—
505C23—152no—
506C23—152no—
507C23—301no—
508C23—301no—
509C23—301no—
510C23—301no—
511C23C22×D3×D511yescharacteristic
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—32no—
516C2×C4—32no—
517C2×C4—32no—
518C2×C4—32no—
519C2×C4—32no—
520C2×C4—32no—
521C2×C4—52no—
522C2×C4—52no—
523C2×C4—52no—
524C2×C4—52no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—101no—
529C2×C4—101no—
530C2×C4—102no—
531C2×C4—102no—
532C2×C4—102no—
533C2×C4—1516no—
534C2×C4—152no—
535C2×C4—308no—
536C2×C4—301no—
537C2×C4—301no—
538C2×C4—308no—
539C2×C4—302no—
540C2×C4—302no—
541C2×C4—302no—
542C2×C4#677312yes—
543C2×C4C4×D3×D512yes—
544C2×C4#678212yes—
545C2×C3C2×D5×C4⋊C411yescharacteristic
546C2×C3C2×#403811yescharacteristic
547C2×C3C2×#403811yescharacteristic
548C2×C3#6605011yescharacteristic
549C2×C3#6605911yescharacteristic
550C2×C3#6606211yescharacteristic
551C2×C3#6606211yescharacteristic
552D3—104no—
553C5#7375311yescharacteristic, complemented, Sylow
554C22—154no—
555C22—302no—
556C22—302no—
557C22—302no—
558C22—302no—
559C22—302no—
560C22—302no—
561C22C2×#677311yescharacteristic
562C22C2×C4×D3×D511yescharacteristic
563C22D3×D4×D511yescharacteristic
564C22D3×#71111yescharacteristic
565C22D3×Q8×D511yescharacteristic
566C22D3×#71311yescharacteristic
567C22C2×#678211yescharacteristic
568C4—34no—
569C4—34no—
570C4—42no—
571C4—54no—
572C4—102no—
573C4—122no—
574C4—202no—
575C4—302no—
576C4—602no—
577C4#9140214yescomplemented
578C3#1060604911yescharacteristic, complemented, Sylow
579C2—304no—
580C2#1175346411yescharacteristic
581C2#1175368211yescharacteristic
582C2D3×D5×C4⋊C411yescharacteristic
583C2D3×#403811yescharacteristic
584C2C2×#9140211yescharacteristic
585C2#1175477511yescharacteristic
586C2#1175518411yescharacteristic
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#2285
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×#4975C2semidirect
5. C3×C4⋊C4×Dic5C2semidirect
7. #11748861C2semidirect
9. Dic5×C4⋊Dic3C2semidirect
10. #11748652C2semidirect
11. Dic5×Dic3⋊C4C2semidirect
33. C4×#1200C4semidirect
48. C4⋊C4×Dic5D3semidirect
92. #4975D5semidirect
163. #1200C4⋊C4semidirect
251. C3×C4×C5#117semidirect
259. C5×Dic3#117semidirect
429. C4×C5#872semidirect
471. C3×C5#2285semidirect
490. C3×C4#4038semidirect
495. Dic3#4038semidirect
553. C5#73753semidirect
577. C4#91402semidirect
578. C3#10606049semidirect

Maximal subgroups

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

subgroupindex
C2×#914022
C2×C4×#12002
#117510882
C5×#49752
C3×C4⋊C4×Dic52
#117488822
#117488612
#117487992
Dic5×C4⋊Dic32
#117486522
Dic5×Dic3⋊C42
#106060493
#737535