Finite Group Databasebeta

← #14327720

Subgroups — #14327720

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×#91435C211yesmaximal, characteristic
2C2×#91398C212yesmaximal, complemented
3C4×#6712C211yesmaximal, characteristic, complemented
4C5×#4939C211yesmaximal, characteristic
5C3×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
6#11748887C212yesmaximal, complemented
7#11748866C211yesmaximal, characteristic, complemented
8#11748797C211yesmaximal, characteristic
9#11748721C212yesmaximal, complemented
10#11748714C212yesmaximal, complemented
11#11748699C211yesmaximal, characteristic, complemented
12#10608033—31nomaximal, Hall
13C22×C5×D12C2211yescharacteristic
14C22×D3×Dic5C2212yes—
15C2×C3×C42×C5C2211yescharacteristic
16C2×#6712C2211yescharacteristic
17C2×#6712C2211yescharacteristic
18C2×C4×Dic15C2211yescharacteristic
19C2×C4×Dic15C2211yescharacteristic
20C2×C5×(C2×D3)⋊C4C2212yes—
21C2×C5×(C2×D3)⋊C4C2212yes—
22C2×C5×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C2×C3×C4×Dic5C2212yes—
26C2×#6669C2212yes—
27C2×#6669C2212yes—
28C2×(C2×D3)⋊Dic5C2212yes—
29C2×(C2×D3)⋊Dic5C2212yes—
30C2×(C2×D3)⋊Dic5C2212yes—
31C2×Dic3×Dic5C2212yes—
32#91435C418yescomplemented
33#91398—28no—
34#91115C2211yescharacteristic
35#91115C2211yescharacteristic
36C3×#3963C2212yes—
37#90994C2212yes—
38#73639—51nomaximal, Hall
39C2×D4×Dic5—31no—
40C2×#4023—32no—
41C5×#390—31no—
42#65510—31no—
43#65265—31no—
44C4⋊C4×Dic5—31no—
45#65234—32no—
46#65233—32no—
47#65231—32no—
48C4×C4⋊Dic5D311yescharacteristic, complemented
49C4×#683—31no—
50C23×C5×D3C2312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15C2311yescharacteristic
55C22×Dic15C2311yescharacteristic
56C22×Dic15C2311yescharacteristic
57C22×Dic15C2311yescharacteristic
58C22×C5×Dic3C2312yes—
59C2×C5×D12—22no—
60C2×C5×D12—22no—
61C2×C5×D12C2×C414yes—
62C22×C3×Dic5C2312yes—
63C22×C3×Dic5C2312yes—
64C2×D3×Dic5—24no—
65C2×D3×Dic5—24no—
66C2×D3×Dic5C2×C418yes—
67C3×C42×C5—22no—
68#6712—22no—
69#6712D414yescomplemented
70C4×Dic15—22no—
71C4×Dic15C2×C414yes—
72C5×(C2×D3)⋊C4—24no—
73C5×(C2×D3)⋊C4—42no—
74C5×C4⋊Dic3—22no—
75C3×C4⋊Dic5—22no—
76C3×C4⋊Dic5C2×C414yes—
77C3×C4×Dic5—24no—
78#6669—24no—
79#6669—42no—
80(C2×D3)⋊Dic5—24no—
81(C2×D3)⋊Dic5—42no—
82(C2×D3)⋊Dic5C2×C418yes—
83Dic3×Dic5—24no—
84C2×#893—51no—
85C2×#872—52no—
86C3×C4×C4⋊C4—51no—
87#4988—51no—
88#4975—51no—
89Dic3×C4⋊C4—51no—
90#4940—52no—
91#4939D511yescharacteristic
92C4×Dic3⋊C4—51no—
93#4669—52no—
94#4667—52no—
95C22×C5×D4—31no—
96C23×Dic5—32no—
97C2×C5×C4⋊C4—31no—
98C2×C5×C22⋊C4—32no—
99C2×C5×C22⋊C4—32no—
100C2×C42×C5C2×D311yescharacteristic
101C2×C22⋊Dic5—32no—
102C2×C22⋊Dic5—32no—
103C2×C22⋊Dic5—32no—
104D4×Dic5—38no—
105C2×C4⋊Dic5C2×D311yescharacteristic
106C2×C4⋊Dic5C2×D311yescharacteristic
107C2×#683—31no—
108C2×#683—31no—
109C2×#683—32no—
110C2×#683—32no—
111C2×C4×Dic5—31no—
112C2×C4×Dic5—31no—
113C2×C4×Dic5—32no—
114C2×C4×Dic5C2×D312yes—
115#4023—68no—
116#3963—31no—
117#3963—31no—
118#3963—32no—
119#3963C2×D312yes—
120#2354—151noSylow
121C23×C3×C5C2411yescharacteristic
122C22×C5×D3—22no—
123C22×C5×D3—22no—
124C22×C5×D3—22no—
125C22×C5×D3—22no—
126C22×C5×D3—22no—
127C22×C5×D3—22no—
128C22×C5×D3C22×C414yes—
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5C22×C412yes—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5#4112yes—
137C2×C3×C4×C5#4112yes—
138C2×Dic15—21no—
139C2×Dic15—21no—
140C2×Dic15—21no—
141C2×Dic15—21no—
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×Dic15—21no—
145C2×Dic15C22×C412yes—
146C2×Dic15C22×C412yes—
147C2×Dic15C2×D412yes—
148C2×Dic15C2×D412yes—
149C2×Dic15#4112yes—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—22no—
153C5×D12—28no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5C22×C414yes—
160D3×Dic5—216no—
161C22×D12C2×D511yescharacteristic
162C22×C4×D3—52no—
163C2×C3×C4⋊C4—51no—
164C2×C3×C4⋊C4—51no—
165C2×C3×C42—52no—
166C2×C3×C42C2×D511yescharacteristic
167C2×(C2×D3)⋊C4—52no—
168C2×(C2×D3)⋊C4—52no—
169C2×(C2×D3)⋊C4—52no—
170C2×(C2×D3)⋊C4C2×D512yes—
171C2×(C2×D3)⋊C4C2×D512yes—
172C2×C4⋊Dic3C2×D511yescharacteristic
173C2×Dic3⋊C4—51no—
174C2×Dic3⋊C4—51no—
175C2×Dic3⋊C4—52no—
176C2×Dic3⋊C4—52no—
177C2×C4×Dic3—51no—
178C2×C4×Dic3—51no—
179C2×C4×Dic3—52no—
180#893—58no—
181#872—108no—
182C3×#95—52no—
183C3⋊#95—51no—
184C3⋊#95—51no—
185C3⋊#95—52no—
186C24×C5—32no—
187C2×C5×D4—34no—
188C2×C5×D4—62no—
189C2×C5×D4—62no—
190C22×C4×C5—32no—
191C22×C4×C5C22×D311yescharacteristic
192C22×C4×C5C22×D311yescharacteristic
193C22×C4×C5C22×D311yescharacteristic
194C22×Dic5—31no—
195C22×Dic5—31no—
196C22×Dic5—31no—
197C22×Dic5—38no—
198C22×Dic5—31no—
199C22×Dic5—64no—
200C22×Dic5—64no—
201C22×Dic5C22×D312yes—
202C22×Dic5C22×D312yes—
203C5×C4⋊C4—62no—
204C5×C22⋊C4—64no—
205C5×C22⋊C4—122no—
206C42×C5—22no—
207C22⋊Dic5—38no—
208C22⋊Dic5—64no—
209C22⋊Dic5—122no—
210C4⋊Dic5—22no—
211C4⋊Dic5C4×D314yes—
212#683—34no—
213#683—64no—
214#683—62no—
215#683—122no—
216C4×Dic5—24no—
217C4×Dic5—34no—
218C4×Dic5—64no—
219C4×Dic5—62no—
220C2×C4×D4—151no—
221C2×#117—152no—
222#390—31no—
223#390—151no—
224#388—152no—
225#388—152no—
226#384—151no—
227#380—152no—
228C4×C4⋊C4—51no—
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×C5×D3—24no—
239C2×C5×D3—24no—
240C2×C5×D3—24no—
241C2×C5×D3—42no—
242C2×C5×D3—42no—
243C2×C5×D3—42no—
244C2×C5×D3—42no—
245C3×C4×C5—22no—
246C3×C4×C5—41no—
247C3×C4×C5#11714yescomplemented
248Dic15—22no—
249Dic15—22no—
250Dic15—41no—
251Dic15C4×D414yes—
252C3×Dic5—24no—
253C3×Dic5—42no—
254C5×Dic3—42no—
255C23×D3C22×D512yes—
256C22×C3×C4—52no—
257C22×C3×C4—52no—
258C22×C3×C4C22×D511yescharacteristic
259C22×C3×C4C22×D511yescharacteristic
260C22×C3×C4C22×D511yescharacteristic
261C22×Dic3—51no—
262C22×Dic3—51no—
263C22×Dic3—51no—
264C22×Dic3—51no—
265C22×Dic3C22×D512yes—
266C2×D12—22no—
267C2×D12—22no—
268C2×D12C4×D514yes—
269C2×C4×D3—58no—
270C2×C4×D3—104no—
271C2×C4×D3—104no—
272C3×C4⋊C4—54no—
273C3×C4⋊C4—102no—
274C3×C42—22no—
275C3×C42—104no—
276(C2×D3)⋊C4—24no—
277(C2×D3)⋊C4—42no—
278(C2×D3)⋊C4—58no—
279(C2×D3)⋊C4—104no—
280(C2×D3)⋊C4—202no—
281C4⋊Dic3—22no—
282Dic3⋊C4—54no—
283Dic3⋊C4—104no—
284Dic3⋊C4—102no—
285Dic3⋊C4—202no—
286C4×Dic3—54no—
287C4×Dic3—104no—
288C4×Dic3—102no—
289C23×C5—34no—
290C23×C5—62no—
291C23×C5—62no—
292C23×C5—62no—
293C23×C5—62no—
294C23×C5—62no—
295C23×C5—62no—
296C23×C5C23×D311yescharacteristic
297C5×D4—68no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—21no—
303C2×C4×C5—62no—
304C2×C4×C5—62no—
305C2×C4×C5—62no—
306C2×C4×C5C2×C4×D312yes—
307C2×C4×C5#23512yes—
308C2×C4×C5#23512yes—
309C2×C4×C5D3×D412yes—
310C2×Dic5—22no—
311C2×Dic5—22no—
312C2×Dic5—22no—
313C2×Dic5—22no—
314C2×Dic5—22no—
315C2×Dic5—32no—
316C2×Dic5—32no—
317C2×Dic5—32no—
318C2×Dic5—32no—
319C2×Dic5—32no—
320C2×Dic5—616no—
321C2×Dic5—61no—
322C2×Dic5—61no—
323C2×Dic5—61no—
324C2×Dic5—61no—
325C2×Dic5—61no—
326C2×Dic5—61no—
327C2×Dic5—61no—
328C2×Dic5C2×C4×D314yes—
329C22×D4—31no—
330C23×C4—152no—
331C4×D4—158no—
332#117—308no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—51no—
335C2×C4⋊C4—51no—
336C2×C4⋊C4—151no—
337C2×C4⋊C4—152no—
338C2×C4⋊C4—151no—
339C2×C4⋊C4—152no—
340C2×C22⋊C4—32no—
341C2×C22⋊C4—32no—
342C2×C22⋊C4—152no—
343C2×C22⋊C4—152no—
344C2×C22⋊C4—152no—
345C2×C42—52no—
346C2×C42—151no—
347C2×C42—152no—
348C2×C42—151no—
349C2×C42D3×D511yescharacteristic
350#95—52no—
351#95—152no—
352#95—151no—
353#95—151no—
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
361C5×D3—44no—
362C23×C3C23×D511yescharacteristic
363C22×D3—22no—
364C22×D3—22no—
365C22×D3—22no—
366C22×D3—22no—
367C22×D3—22no—
368C22×D3—22no—
369C22×D3C2×C4×D514yes—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—54no—
376C2×C3×C4—102no—
377C2×C3×C4—102no—
378C2×C3×C4—102no—
379C2×C3×C4—102no—
380C2×C3×C4—102no—
381C2×C3×C4C2×C4×D512yes—
382C2×C3×C4D4×D512yes—
383C2×C3×C4#71112yes—
384C2×C3×C4#71112yes—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—52no—
389C2×Dic3—52no—
390C2×Dic3—52no—
391C2×Dic3—52no—
392C2×Dic3—52no—
393C2×Dic3—101no—
394C2×Dic3—101no—
395C2×Dic3—101no—
396C2×Dic3—101no—
397C2×Dic3—101no—
398C2×Dic3—101no—
399C2×Dic3—101no—
400D12—28no—
401C4×D3—1016no—
402C22×C5—64no—
403C22×C5—64no—
404C22×C5—64no—
405C22×C5—122no—
406C22×C5—122no—
407C22×C5—122no—
408C22×C5—122no—
409C22×C5C22×C4×D311yescharacteristic
410C22×C5C2×#23511yescharacteristic
411C22×C5C2×#23511yescharacteristic
412C22×C5C2×D3×D411yescharacteristic
413C22×C5#100711yescharacteristic
414C22×C5D3×#4111yescharacteristic
415C22×C5#100911yescharacteristic
416C4×C5—22no—
417C4×C5—41no—
418C4×C5—122no—
419C4×C5#87214yescomplemented
420Dic5—24no—
421Dic5—34no—
422Dic5—42no—
423Dic5—62no—
424Dic5—62no—
425Dic5—121no—
426C24—32no—
427C2×D4—34no—
428C2×D4—62no—
429C2×D4—62no—
430C22×C4—32no—
431C22×C4—52no—
432C22×C4—52no—
433C22×C4—158no—
434C22×C4—151no—
435C22×C4—151no—
436C22×C4—151no—
437C22×C4—151no—
438C22×C4—304no—
439C22×C4—304no—
440C22×C4C2×D3×D511yescharacteristic
441C22×C4C2×D3×D511yescharacteristic
442C22×C4C2×D3×D511yescharacteristic
443C4⋊C4—54no—
444C4⋊C4—62no—
445C4⋊C4—102no—
446C4⋊C4—154no—
447C4⋊C4—302no—
448C4⋊C4—304no—
449C4⋊C4—602no—
450C22⋊C4—64no—
451C22⋊C4—122no—
452C22⋊C4—158no—
453C22⋊C4—304no—
454C22⋊C4—602no—
455C42—22no—
456C42—104no—
457C42—154no—
458C42—304no—
459C42—302no—
460C3×C5#235411yescharacteristic, complemented, Hall
461C22×C3C22×C4×D511yescharacteristic
462C22×C3C2×D4×D511yescharacteristic
463C22×C3C2×#71111yescharacteristic
464C22×C3C2×#71111yescharacteristic
465C22×C3#414411yescharacteristic
466C22×C3D5×#4111yescharacteristic
467C22×C3#415011yescharacteristic
468C2×D3—24no—
469C2×D3—24no—
470C2×D3—24no—
471C2×D3—42no—
472C2×D3—42no—
473C2×D3—42no—
474C2×D3—42no—
475C3×C4—22no—
476C3×C4—41no—
477C3×C4—104no—
478C3×C4—202no—
479C3×C4#402314yescomplemented
480Dic3—42no—
481Dic3—54no—
482Dic3—102no—
483Dic3—102no—
484Dic3—201no—
485C2×C5—124no—
486C2×C5C2×#87211yescharacteristic
487C2×C5#550711yescharacteristic
488C2×C5#553211yescharacteristic
489C2×C5C4×D3×D411yescharacteristic
490C2×C5#555311yescharacteristic
491C2×C5#556811yescharacteristic
492C2×C5#557411yescharacteristic
493C23—34no—
494C23—62no—
495C23—62no—
496C23—62no—
497C23—62no—
498C23—62no—
499C23—62no—
500C23C22×D3×D511yescharacteristic
501D4—68no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—54no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—102no—
512C2×C4—102no—
513C2×C4—102no—
514C2×C4—102no—
515C2×C4—102no—
516C2×C4—152no—
517C2×C4—152no—
518C2×C4—152no—
519C2×C4—152no—
520C2×C4—152no—
521C2×C4—3016no—
522C2×C4—301no—
523C2×C4—301no—
524C2×C4—301no—
525C2×C4—301no—
526C2×C4—301no—
527C2×C4—301no—
528C2×C4—301no—
529C2×C4#677212yes—
530C2×C4C4×D3×D512yes—
531C2×C4#677712yes—
532C2×C4#678212yes—
533C2×C3C2×#402311yescharacteristic
534C2×C3C4×D4×D511yescharacteristic
535C2×C3#6588011yescharacteristic
536C2×C3#6594511yescharacteristic
537C2×C3#6595011yescharacteristic
538C2×C3#6600511yescharacteristic
539C2×C3#6605211yescharacteristic
540D3—44no—
541C5#7363911yescharacteristic, complemented, Sylow
542C22—64no—
543C22—64no—
544C22—64no—
545C22—122no—
546C22—122no—
547C22—122no—
548C22—122no—
549C22#9200411yescharacteristic
550C22C2×#677211yescharacteristic
551C22C2×C4×D3×D511yescharacteristic
552C22C2×#677711yescharacteristic
553C22#9201611yescharacteristic
554C22#9201811yescharacteristic
555C22C2×#678211yescharacteristic
556C4—22no—
557C4—41no—
558C4—104no—
559C4—122no—
560C4—154no—
561C4—202no—
562C4—302no—
563C4—302no—
564C4—601no—
565C4#9139814yescomplemented
566C3#1060803311yescharacteristic, complemented, Sylow
567C2—124no—
568C2#1175252511yescharacteristic
569C2#1175262611yescharacteristic
570C2#1175268011yescharacteristic
571C2C4×#677711yescharacteristic
572C2C2×#9139811yescharacteristic
573C2#1175439011yescharacteristic
574C2#1175445711yescharacteristic
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#2354
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#91398C2semidirect
3. C4×#6712C2semidirect
5. C3×C4×C4⋊Dic5C2semidirect
6. #11748887C2semidirect
7. #11748866C2semidirect
9. #11748721C2semidirect
10. #11748714C2semidirect
11. #11748699C2semidirect
32. #91435C4semidirect
48. C4×C4⋊Dic5D3semidirect
69. #6712D4semidirect
247. C3×C4×C5#117semidirect
419. C4×C5#872semidirect
460. C3×C5#2354semidirect
479. C3×C4#4023semidirect
541. C5#73639semidirect
565. C4#91398semidirect
566. C3#10608033semidirect

Maximal subgroups

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

subgroupindex
C2×#914352
C2×#913982
C4×#67122
C5×#49392
C3×C4×C4⋊Dic52
#117488872
#117488662
#117487972
#117487212
#117487142
#117486992
#106080333
#736395