Finite Group Databasebeta

← #14320853

Subgroups — #14320853

Order 1920.

1304 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91435C211yesmaximal, characteristic
2C2×#91400C212yesmaximal, complemented
3C4⋊C4×Dic15C211yesmaximal, characteristic, complemented
4C5×#4988C211yesmaximal, characteristic
5C3×#65262C211yesmaximal, characteristic, complemented
6#11748886C212yesmaximal, complemented
7#11748857C211yesmaximal, characteristic, complemented
8#11748764C211yesmaximal, characteristic
9#11748723C212yesmaximal, complemented
10#11748718C212yesmaximal, complemented
11C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
12#10608020—31nomaximal, Hall
13C22×C5×D12C2211yescharacteristic
14C22×D3×Dic5C2212yes—
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C4×Dic15C2212yes—
18C2×C4×Dic15C2211yescharacteristic
19C2×C5×(C2×D3)⋊C4C2212yes—
20C2×C5×(C2×D3)⋊C4C2212yes—
21C2×C4×C5×Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic5C2211yescharacteristic
23C2×C3×#683C2212yes—
24C2×C3×C4×Dic5C2211yescharacteristic
25C2×#6668C2212yes—
26C2×(C2×D3)⋊Dic5C2212yes—
27C2×(C2×D3)⋊Dic5C2212yes—
28C2×(C2×D3)⋊Dic5C2212yes—
29C2×Dic3×Dic5C2211yescharacteristic
30C2×Dic3×Dic5C2211yescharacteristic
31C2×Dic3×Dic5C2211yescharacteristic
32C2×Dic3×Dic5C2211yescharacteristic
33#91435C418yescomplemented
34#91400—28no—
35#91115C2212yes—
36C3×#3963C2212yes—
37#90994C2212yes—
38#75961—51nomaximal, Hall
39C2×D4×Dic5—31no—
40C2×#4023—32no—
41C5×#390—31no—
42#65510—31no—
43C4⋊C4×Dic5—31no—
44#65262D311yescharacteristic, complemented
45#65234—32no—
46#65233—32no—
47C22⋊C4×Dic5—32no—
48C42×Dic5—31no—
49#65217—31no—
50C23×C5×D3C2312yes—
51C22×C3×C4×C5C2312yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15C2312yes—
54C22×Dic15C2311yescharacteristic
55C22×Dic15C2311yescharacteristic
56C22×C5×Dic3C2311yescharacteristic
57C22×C5×Dic3C2311yescharacteristic
58C2×C5×D12—22no—
59C2×C5×D12—22no—
60C2×C5×D12C2×C414yes—
61C22×C3×Dic5C2312yes—
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2311yescharacteristic
64C2×D3×Dic5—24no—
65C2×D3×Dic5—24no—
66C2×D3×Dic5C2×C418yes—
67C3×C5×C4⋊C4—22no—
68C4⋊Dic15—22no—
69C4×Dic15—24no—
70C4×Dic15C2×C414yes—
71C5×(C2×D3)⋊C4—24no—
72C5×(C2×D3)⋊C4—24no—
73C4×C5×Dic3—22no—
74C3×C4⋊Dic5C2×C414yes—
75C3×#683—24no—
76C3×C4×Dic5—22no—
77#6668—24no—
78(C2×D3)⋊Dic5—24no—
79(C2×D3)⋊Dic5—24no—
80(C2×D3)⋊Dic5C2×C418yes—
81Dic3×Dic5—22no—
82Dic3×Dic5—22no—
83Dic3×Dic5—22no—
84Dic3×Dic5D414yescomplemented
85C2×#893—51no—
86C2×#892—52no—
87C3×#389—51no—
88#4990—52no—
89#4988D511yescharacteristic
90#4984—51no—
91Dic3×C4⋊C4—51no—
92#4939—51no—
93C42×Dic3—51no—
94#4670—52no—
95#4666—52no—
96C22×C5×D4—31no—
97C23×Dic5—32no—
98C2×C5×C4⋊C4C2×D311yescharacteristic
99C2×C5×C22⋊C4—32no—
100C2×C5×C22⋊C4—32no—
101C2×C42×C5—31no—
102C2×C22⋊Dic5—32no—
103C2×C22⋊Dic5—32no—
104C2×C22⋊Dic5—32no—
105D4×Dic5—38no—
106C2×C4⋊Dic5—31no—
107C2×C4⋊Dic5C2×D311yescharacteristic
108C2×#683—32no—
109C2×#683C2×D312yes—
110C2×C4×Dic5—31no—
111C2×C4×Dic5—31no—
112C2×C4×Dic5—32no—
113C2×C4×Dic5—31no—
114C2×C4×Dic5—31no—
115C2×C4×Dic5—31no—
116C2×C4×Dic5C2×D311yescharacteristic
117#4023—68no—
118#3963—32no—
119#3963—32no—
120#3963C2×D312yes—
121#2293—151noSylow
122C23×C3×C5C2411yescharacteristic
123C22×C5×D3—22no—
124C22×C5×D3—22no—
125C22×C5×D3—22no—
126C22×C5×D3—22no—
127C22×C5×D3—22no—
128C22×C5×D3—22no—
129C22×C5×D3C22×C414yes—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5C22×C412yes—
134C2×C3×C4×C5#4112yes—
135C2×C3×C4×C5#4112yes—
136C2×Dic15—21no—
137C2×Dic15—21no—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15C22×C412yes—
142C2×Dic15C22×C412yes—
143C2×Dic15C2×D412yes—
144C2×Dic15#4112yes—
145C2×C5×Dic3—21no—
146C2×C5×Dic3—21no—
147C2×C5×Dic3—21no—
148C2×C5×Dic3—21no—
149C2×C5×Dic3C2×D412yes—
150C2×C5×Dic3#4112yes—
151C5×D12—28no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5C22×C414yes—
159C2×C3×Dic5C2×D412yes—
160C2×C3×Dic5#4112yes—
161D3×Dic5—216no—
162C22×D12C2×D511yescharacteristic
163C22×C4×D3—52no—
164C2×C3×C4⋊C4—51no—
165C2×C3×C4⋊C4—52no—
166C2×C3×C4⋊C4C2×D511yescharacteristic
167C2×C3×C42—51no—
168C2×(C2×D3)⋊C4—52no—
169C2×(C2×D3)⋊C4—52no—
170C2×(C2×D3)⋊C4—52no—
171C2×(C2×D3)⋊C4C2×D512yes—
172C2×(C2×D3)⋊C4C2×D512yes—
173C2×C4⋊Dic3—51no—
174C2×C4⋊Dic3—52no—
175C2×C4×Dic3—51no—
176C2×C4×Dic3—51no—
177C2×C4×Dic3—52no—
178C2×C4×Dic3—51no—
179C2×C4×Dic3—51no—
180C2×C4×Dic3—51no—
181C2×C4×Dic3C2×D511yescharacteristic
182#893—58no—
183#892—108no—
184C3×#95—52no—
185C3⋊#95—52no—
186C3⋊#95—52no—
187C24×C5—32no—
188C2×C5×D4—34no—
189C2×C5×D4—62no—
190C2×C5×D4—62no—
191C22×C4×C5—31no—
192C22×C4×C5—31no—
193C22×C4×C5C22×D312yes—
194C22×C4×C5C22×D311yescharacteristic
195C22×Dic5—31no—
196C22×Dic5—31no—
197C22×Dic5—38no—
198C22×Dic5—32no—
199C22×Dic5—64no—
200C22×Dic5—64no—
201C22×Dic5C22×D312yes—
202C22×Dic5C22×D311yescharacteristic
203C22×Dic5C22×D311yescharacteristic
204C5×C4⋊C4—22no—
205C5×C22⋊C4—64no—
206C5×C22⋊C4—64no—
207C42×C5—62no—
208C22⋊Dic5—38no—
209C22⋊Dic5—64no—
210C22⋊Dic5—64no—
211C4⋊Dic5—62no—
212C4⋊Dic5C4×D314yes—
213#683—24no—
214#683—64no—
215C4×Dic5—22no—
216C4×Dic5—34no—
217C4×Dic5—34no—
218C4×Dic5—62no—
219C4×Dic5—62no—
220C4×Dic5—64no—
221C4×Dic5—62no—
222C2×C4×D4—151no—
223C2×#117—152no—
224#390—31no—
225#390—151no—
226#389—51no—
227#389—151no—
228#388—152no—
229#388—152no—
230C4×C4⋊C4—151no—
231C4×C22⋊C4—152no—
232C43—151no—
233C22×C3×C5C23×C411yescharacteristic
234C22×C3×C5C22×D411yescharacteristic
235C22×C3×C5C2×#4111yescharacteristic
236C22×C3×C5C2×#4111yescharacteristic
237C22×C3×C5C2×#4111yescharacteristic
238C22×C3×C5C2×#4111yescharacteristic
239C22×C3×C5C2×#4111yescharacteristic
240C2×C5×D3—24no—
241C2×C5×D3—24no—
242C2×C5×D3—24no—
243C2×C5×D3—42no—
244C2×C5×D3—42no—
245C2×C5×D3—42no—
246C2×C5×D3—42no—
247C3×C4×C5—42no—
248C3×C4×C5#11714yescomplemented
249Dic15—22no—
250Dic15—42no—
251Dic15C4×D414yes—
252C3×Dic5—24no—
253C3×Dic5—22no—
254C3×Dic5—22no—
255C5×Dic3—22no—
256C5×Dic3—22no—
257C23×D3C22×D512yes—
258C22×C3×C4—52no—
259C22×C3×C4—51no—
260C22×C3×C4—51no—
261C22×C3×C4C22×D512yes—
262C22×C3×C4C22×D511yescharacteristic
263C22×Dic3—51no—
264C22×Dic3—51no—
265C22×Dic3—52no—
266C22×Dic3C22×D511yescharacteristic
267C22×Dic3C22×D511yescharacteristic
268C2×D12—22no—
269C2×D12—22no—
270C2×D12C4×D514yes—
271C2×C4×D3—58no—
272C2×C4×D3—104no—
273C2×C4×D3—104no—
274C3×C4⋊C4—22no—
275C3×C4⋊C4—54no—
276C3×C4⋊C4—104no—
277C3×C42—102no—
278(C2×D3)⋊C4—24no—
279(C2×D3)⋊C4—24no—
280(C2×D3)⋊C4—58no—
281(C2×D3)⋊C4—104no—
282(C2×D3)⋊C4—104no—
283C4⋊Dic3—102no—
284C4⋊Dic3—104no—
285C4×Dic3—22no—
286C4×Dic3—54no—
287C4×Dic3—54no—
288C4×Dic3—102no—
289C4×Dic3—102no—
290C4×Dic3—104no—
291C4×Dic3—102no—
292C23×C5—34no—
293C23×C5—62no—
294C23×C5—62no—
295C23×C5—62no—
296C23×C5—62no—
297C23×C5—62no—
298C23×C5—62no—
299C23×C5C23×D311yescharacteristic
300C5×D4—68no—
301C2×C4×C5—22no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—32no—
305C2×C4×C5—32no—
306C2×C4×C5—61no—
307C2×C4×C5—61no—
308C2×C4×C5—61no—
309C2×C4×C5—61no—
310C2×C4×C5C2×C4×D312yes—
311C2×C4×C5#23712yes—
312C2×C4×C5#23912yes—
313C2×Dic5—22no—
314C2×Dic5—21no—
315C2×Dic5—21no—
316C2×Dic5—21no—
317C2×Dic5—21no—
318C2×Dic5—22no—
319C2×Dic5—32no—
320C2×Dic5—32no—
321C2×Dic5—32no—
322C2×Dic5—32no—
323C2×Dic5—616no—
324C2×Dic5—61no—
325C2×Dic5—61no—
326C2×Dic5—62no—
327C2×Dic5—62no—
328C2×Dic5—62no—
329C2×Dic5C2×C4×D314yes—
330C2×Dic5D3×D412yes—
331C2×Dic5#23912yes—
332C22×D4—31no—
333C23×C4—152no—
334C4×D4—158no—
335#117—308no—
336C2×C4⋊C4—51no—
337C2×C4⋊C4—52no—
338C2×C4⋊C4—152no—
339C2×C4⋊C4—151no—
340C2×C4⋊C4D3×D511yescharacteristic
341C2×C22⋊C4—32no—
342C2×C22⋊C4—32no—
343C2×C22⋊C4—152no—
344C2×C22⋊C4—152no—
345C2×C22⋊C4—152no—
346C2×C42—31no—
347C2×C42—51no—
348C2×C42—151no—
349C2×C42—151no—
350C2×C42—151no—
351C2×C42—151no—
352C2×C42—151no—
353C2×C42—152no—
354#95—52no—
355#95—152no—
356#95—152no—
357C2×C3×C5C2×#11711yescharacteristic
358C2×C3×C5C2×C4×D411yescharacteristic
359C2×C3×C5C4×#4111yescharacteristic
360C2×C3×C5#52911yescharacteristic
361C2×C3×C5#52911yescharacteristic
362C2×C3×C5#53211yescharacteristic
363C2×C3×C5#53211yescharacteristic
364C5×D3—44no—
365C23×C3C23×D511yescharacteristic
366C22×D3—22no—
367C22×D3—22no—
368C22×D3—22no—
369C22×D3—22no—
370C22×D3—22no—
371C22×D3—22no—
372C22×D3C2×C4×D514yes—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—54no—
377C2×C3×C4—52no—
378C2×C3×C4—52no—
379C2×C3×C4—102no—
380C2×C3×C4—101no—
381C2×C3×C4—101no—
382C2×C3×C4—101no—
383C2×C3×C4—101no—
384C2×C3×C4—102no—
385C2×C3×C4C2×C4×D512yes—
386C2×C3×C4#71112yes—
387C2×C3×C4#71112yes—
388C2×Dic3—21no—
389C2×Dic3—21no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—52no—
393C2×Dic3—52no—
394C2×Dic3—52no—
395C2×Dic3—52no—
396C2×Dic3—101no—
397C2×Dic3—101no—
398C2×Dic3—102no—
399C2×Dic3—102no—
400C2×Dic3—102no—
401C2×Dic3D4×D512yes—
402C2×Dic3#71112yes—
403D12—28no—
404C4×D3—1016no—
405C22×C5—64no—
406C22×C5—64no—
407C22×C5—64no—
408C22×C5—122no—
409C22×C5—122no—
410C22×C5—122no—
411C22×C5—122no—
412C22×C5C22×C4×D311yescharacteristic
413C22×C5C2×D3×D411yescharacteristic
414C22×C5C2×#23711yescharacteristic
415C22×C5C2×#23911yescharacteristic
416C22×C5C2×#23911yescharacteristic
417C22×C5D3×#4111yescharacteristic
418C22×C5D3×#4111yescharacteristic
419C4×C5—42no—
420C4×C5—62no—
421C4×C5—62no—
422C4×C5#89214yescomplemented
423Dic5—24no—
424Dic5—22no—
425Dic5—22no—
426Dic5—34no—
427Dic5—62no—
428Dic5—122no—
429C24—32no—
430C2×D4—34no—
431C2×D4—62no—
432C2×D4—62no—
433C22×C4—31no—
434C22×C4—31no—
435C22×C4—51no—
436C22×C4—52no—
437C22×C4—51no—
438C22×C4—158no—
439C22×C4—151no—
440C22×C4—151no—
441C22×C4—152no—
442C22×C4—304no—
443C22×C4—304no—
444C22×C4C2×D3×D512yes—
445C22×C4C2×D3×D511yescharacteristic
446C4⋊C4—22no—
447C4⋊C4—54no—
448C4⋊C4—104no—
449C4⋊C4—304no—
450C4⋊C4—302no—
451C22⋊C4—64no—
452C22⋊C4—64no—
453C22⋊C4—158no—
454C22⋊C4—304no—
455C22⋊C4—304no—
456C42—62no—
457C42—102no—
458C42—154no—
459C42—154no—
460C42—304no—
461C42—302no—
462C42—302no—
463C42—302no—
464C3×C5#229311yescharacteristic, complemented, Hall
465C22×C3C22×C4×D511yescharacteristic
466C22×C3C2×D4×D511yescharacteristic
467C22×C3C2×#71111yescharacteristic
468C22×C3C2×#71111yescharacteristic
469C22×C3C2×#71111yescharacteristic
470C22×C3D5×#4111yescharacteristic
471C22×C3D5×#4111yescharacteristic
472C2×D3—24no—
473C2×D3—24no—
474C2×D3—24no—
475C2×D3—42no—
476C2×D3—42no—
477C2×D3—42no—
478C2×D3—42no—
479C3×C4—42no—
480C3×C4—102no—
481C3×C4—104no—
482C3×C4—102no—
483C3×C4#402314yescomplemented
484Dic3—22no—
485Dic3—22no—
486Dic3—54no—
487Dic3—102no—
488Dic3—202no—
489C2×C5—124no—
490C2×C5C2×#89211yescharacteristic
491C2×C5C4×D3×D411yescharacteristic
492C2×C5C4×#23911yescharacteristic
493C2×C5#559611yescharacteristic
494C2×C5#562411yescharacteristic
495C2×C5#569111yescharacteristic
496C2×C5#572511yescharacteristic
497C23—34no—
498C23—62no—
499C23—62no—
500C23—62no—
501C23—62no—
502C23—62no—
503C23—62no—
504C23C22×D3×D511yescharacteristic
505D4—68no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—32no—
510C2×C4—32no—
511C2×C4—54no—
512C2×C4—52no—
513C2×C4—52no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—61no—
517C2×C4—61no—
518C2×C4—102no—
519C2×C4—101no—
520C2×C4—101no—
521C2×C4—102no—
522C2×C4—101no—
523C2×C4—101no—
524C2×C4—152no—
525C2×C4—152no—
526C2×C4—152no—
527C2×C4—152no—
528C2×C4—3016no—
529C2×C4—301no—
530C2×C4—301no—
531C2×C4—302no—
532C2×C4—302no—
533C2×C4—302no—
534C2×C4#676812yes—
535C2×C4C4×D3×D512yes—
536C2×C4#678012yes—
537C2×C3C2×#402311yescharacteristic
538C2×C3C4×#71111yescharacteristic
539C2×C3C4×D4×D511yescharacteristic
540C2×C3#6593011yescharacteristic
541C2×C3#6593411yescharacteristic
542C2×C3#6601411yescharacteristic
543C2×C3#6605011yescharacteristic
544D3—44no—
545C5#7596111yescharacteristic, complemented, Sylow
546C22—64no—
547C22—64no—
548C22—64no—
549C22—122no—
550C22—122no—
551C22—122no—
552C22—122no—
553C22C2×#676811yescharacteristic
554C22C2×C4×D3×D511yescharacteristic
555C22D3×D4×D511yescharacteristic
556C22D3×#71111yescharacteristic
557C22D5×#23911yescharacteristic
558C22#9203411yescharacteristic
559C22C2×#678011yescharacteristic
560C4—42no—
561C4—62no—
562C4—62no—
563C4—102no—
564C4—104no—
565C4—102no—
566C4—154no—
567C4—302no—
568C4—602no—
569C4#9140014yescomplemented
570C3#1060802011yescharacteristic, complemented, Sylow
571C2—124no—
572C2#1175340611yescharacteristic
573C2#1175342311yescharacteristic
574C2#1175357811yescharacteristic
575C2#1175384011yescharacteristic
576C2C2×#9140011yescharacteristic
577C2#1175476211yescharacteristic
578C2#1175519011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×D12C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2293
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×#91400C2semidirect
3. C4⋊C4×Dic15C2semidirect
5. C3×#65262C2semidirect
6. #11748886C2semidirect
7. #11748857C2semidirect
9. #11748723C2semidirect
10. #11748718C2semidirect
11. C4×Dic3×Dic5C2semidirect
33. #91435C4semidirect
44. #65262D3semidirect
84. Dic3×Dic5D4semidirect
248. C3×C4×C5#117semidirect
422. C4×C5#892semidirect
464. C3×C5#2293semidirect
483. C3×C4#4023semidirect
545. C5#75961semidirect
569. C4#91400semidirect
570. C3#10608020semidirect

Maximal subgroups

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

subgroupindex
C2×#914352
C2×#914002
C4⋊C4×Dic152
C5×#49882
C3×#652622
#117488862
#117488572
#117487642
#117487232
#117487182
C4×Dic3×Dic52
#106080203
#759615