Finite Group Databasebeta

← #14329499

Subgroups — #14329499

Order 1920.

1664 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91829C211yesmaximal, characteristic
2C2×#91556C212yesmaximal, complemented
3C2×#91552C212yesmaximal, complemented
4C5×#5220C211yesmaximal, characteristic, complemented
5C3×#65509C211yesmaximal, characteristic, complemented
6#11749483C212yesmaximal, complemented
7#11749483C212yesmaximal, complemented
8#11748904C212yesmaximal, complemented
9#11748663C212yesmaximal, complemented
10#10606410—31nomaximal, Hall
11C22×C3×C5×D4C2211yescharacteristic
12C22×#1220C2212yes—
13C22×#1220C2212yes—
14C22×D60C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C22×#1200C2212yes—
18#91829C418yescomplemented
19C2×C4×Dic15C2211yescharacteristic
20C2×C5×#217C2212yes—
21C2×C5×#217C2211yescharacteristic
22C2×C3×C22⋊Dic5C2212yes—
23C2×C3×C22⋊Dic5C2211yescharacteristic
24#91556—28no—
25#91552—28no—
26C2×#6669C2212yes—
27C2×#6669C2212yes—
28C2×#6667C2212yes—
29C2×#6667C2212yes—
30C2×#6667C2212yes—
31C2×Dic3×Dic5C2212yes—
32C2×Dic3×Dic5C2212yes—
33C5×C3⋊#95C2212yes—
34C3×#3963C2212yes—
35#74679—51nomaximal, Hall
36C2×#4086—31no—
37C2×C4×C22⋊D5—32no—
38C2×#4027—32no—
39C5×#386—31no—
40#65509D311yescharacteristic, complemented
41#65246—32no—
42#65246—32no—
43#64954—32no—
44#64938—32no—
45C24×C3×C5C2311yescharacteristic
46C24×C3×C5C2311yescharacteristic
47C23×D15C2312yes—
48C2×C3×C5×D4—41no—
49C2×C3×C5×D4—41no—
50C2×C3×C5×D4C2×C414yescomplemented
51C22×C3×C4×C5C2311yescharacteristic
52C2×#1220—24no—
53C2×#1220—24no—
54C2×#1220—24no—
55C2×#1220—24no—
56C2×#1220C2×C418yescomplemented
57C2×#1220C2×C418yescomplemented
58C22×Dic15C2312yes—
59C2×D60—41no—
60C2×D60—41no—
61C2×D60C2×C414yescomplemented
62C22×C5×Dic3—24no—
63C22×C5×Dic3—41no—
64C22×C5×Dic3C2312yes—
65C22×C5×Dic3C2312yes—
66C22×C3×Dic5—24no—
67C22×C3×Dic5—41no—
68C22×C3×Dic5C2312yes—
69C22×C3×Dic5C2312yes—
70C2×#1200—24no—
71C2×#1200—24no—
72C2×#1200—42no—
73C4×Dic15C2×C414yescomplemented
74C5×#217—24no—
75C5×#217—41no—
76C3×C22⋊Dic5—24no—
77C3×C22⋊Dic5—41no—
78#6669—24no—
79#6669D418yescomplemented
80#6667—24no—
81#6667—24no—
82#6667—42no—
83Dic3×Dic5—24no—
84Dic3×Dic5—24no—
85C2×#940—51no—
86C2×C4×#67—52no—
87C2×#67⋊C4—52no—
88C3×#386—51no—
89#5220D511yescharacteristic, complemented
90#4957—52no—
91#4957—52no—
92#4665—52no—
93#4649—52no—
94C22×C5×D4C2×D311yescharacteristic
95C23×C4×C5—31no—
96C22×C22⋊D5—32no—
97C22×C22⋊D5—32no—
98C23×Dic5C2×D311yescharacteristic
99C22×D20—31no—
100C22×C4×D5—32no—
101C2×C5×C22⋊C4—32no—
102C2×C5×C22⋊C4—31no—
103C2×C22⋊Dic5C2×D312yes—
104C2×C22⋊Dic5C2×D311yescharacteristic
105#4086—38no—
106C4×C22⋊D5—68no—
107C2×#685—32no—
108C2×#685—32no—
109C2×#685—32no—
110C2×#683—32no—
111C2×#683—32no—
112C2×C4×Dic5—31no—
113C2×C4×Dic5—32no—
114C2×C4×Dic5—32no—
115#4027—68no—
116C5×#95—32no—
117#3963C2×D312yes—
118#2366—151noSylow
119C23×C3×C5—22no—
120C23×C3×C5—22no—
121C23×C3×C5—22no—
122C23×C3×C5—22no—
123C23×C3×C5—21no—
124C23×C3×C5—21no—
125C23×C3×C5—21no—
126C23×C3×C5—21no—
127C23×C3×C5C22×C412yes—
128C23×C3×C5C22×C412yes—
129C23×C3×C5C2411yescharacteristic
130C22×D15—22no—
131C22×D15—22no—
132C22×D15—22no—
133C22×D15—22no—
134C22×D15—22no—
135C22×D15—22no—
136C22×D15C22×C414yes—
137C3×C5×D4—44no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5C22×C412yes—
141#1220—216no—
142#1220—216no—
143C2×Dic15C22×C414yes—
144C2×Dic15C2×D414yes—
145C2×Dic15#4114yes—
146D60—44no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—44no—
153C2×C5×Dic3C2×D414yes—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5—44no—
160C2×C3×Dic5C2×D414yes—
161#1200—48no—
162C22×C3×D4C2×D511yescharacteristic
163C23×C3×C4—51no—
164C22×#67—52no—
165C22×#67—52no—
166C23×Dic3C2×D511yescharacteristic
167C22×D12—51no—
168C22×C4×D3—52no—
169C2×C3×C22⋊C4—52no—
170C2×C3×C22⋊C4—51no—
171C2×#217C2×D512yes—
172C2×#217C2×D511yescharacteristic
173#940—58no—
174C4×#67—108no—
175C2×(C2×D3)⋊C4—52no—
176C2×(C2×D3)⋊C4—52no—
177C2×(C2×D3)⋊C4—52no—
178C2×Dic3⋊C4—52no—
179C2×Dic3⋊C4—52no—
180C2×C4×Dic3—51no—
181C2×C4×Dic3—52no—
182C2×C4×Dic3—52no—
183#67⋊C4—108no—
184C3×#95—52no—
185C3⋊#95C2×D512yes—
186C24×C5C22×D311yescharacteristic
187C24×C5C22×D311yescharacteristic
188C23×D5—32no—
189C2×C5×D4—41no—
190C2×C5×D4—41no—
191C2×C5×D4C4×D314yescomplemented
192C22×C4×C5—32no—
193C22×C4×C5—32no—
194C22×C4×C5—64no—
195C22×C4×C5—121no—
196C22×C4×C5C22×D311yescharacteristic
197C2×C22⋊D5—38no—
198C2×C22⋊D5—38no—
199C2×C22⋊D5—64no—
200C2×C22⋊D5—64no—
201C2×C22⋊D5—64no—
202C2×C22⋊D5—64no—
203C22×Dic5—24no—
204C22×Dic5—32no—
205C22×Dic5—41no—
206C22×Dic5C22×D312yes—
207C22×Dic5C22×D312yes—
208C2×D20—34no—
209C2×D20—121no—
210C2×D20—121no—
211C2×C4×D5—64no—
212C2×C4×D5—64no—
213C2×C4×D5—122no—
214C5×C22⋊C4—64no—
215C5×C22⋊C4—121no—
216C22⋊Dic5—24no—
217C22⋊Dic5—41no—
218#685—64no—
219#685—64no—
220#685—122no—
221#683—38no—
222#683—64no—
223C4×Dic5—34no—
224C4×Dic5—64no—
225C4×Dic5—64no—
226C2×#127—151no—
227C2×C4×D4—152no—
228C2×C4×D4—152no—
229#390—152no—
230#390—152no—
231#386—31no—
232#386—51no—
233#386—152no—
234C4×C4⋊C4—152no—
235C22×C3×C5—24no—
236C22×C3×C5—24no—
237C22×C3×C5—22no—
238C22×C3×C5—22no—
239C22×C3×C5—41no—
240C22×C3×C5—41no—
241C22×C3×C5—42no—
242C22×C3×C5—42no—
243C22×C3×C5—41no—
244C22×C3×C5—41no—
245C22×C3×C5C23×C411yescharacteristic
246C22×C3×C5C22×D412yes—
247C22×C3×C5C2×#4112yes—
248C22×C3×C5H(5,𝔽2)11yescharacteristic
249C22×C3×C5H(5,𝔽2)11yescharacteristic
250C2×D15—24no—
251C2×D15—24no—
252C2×D15—24no—
253C2×D15—42no—
254C2×D15—42no—
255C2×D15—42no—
256C2×D15—42no—
257C3×C4×C5—22no—
258Dic15C4×D418yescomplemented
259C3×Dic5—24no—
260C3×Dic5—42no—
261C5×Dic3—24no—
262C5×Dic3—42no—
263C24×C3C22×D511yescharacteristic
264C24×C3C22×D511yescharacteristic
265C23×D3—52no—
266C2×C3×D4—41no—
267C2×C3×D4—41no—
268C2×C3×D4C4×D514yescomplemented
269C22×C3×C4—52no—
270C22×C3×C4—52no—
271C22×C3×C4—104no—
272C22×C3×C4—201no—
273C22×C3×C4C22×D511yescharacteristic
274C2×#67—58no—
275C2×#67—58no—
276C2×#67—104no—
277C2×#67—104no—
278C2×#67—104no—
279C2×#67—104no—
280C22×Dic3—24no—
281C22×Dic3—41no—
282C22×Dic3—52no—
283C22×Dic3C22×D512yes—
284C22×Dic3C22×D512yes—
285C2×D12—54no—
286C2×D12—201no—
287C2×D12—201no—
288C2×C4×D3—104no—
289C2×C4×D3—104no—
290C2×C4×D3—202no—
291C3×C22⋊C4—104no—
292C3×C22⋊C4—201no—
293#217—24no—
294#217—41no—
295(C2×D3)⋊C4—104no—
296(C2×D3)⋊C4—104no—
297(C2×D3)⋊C4—202no—
298Dic3⋊C4—58no—
299Dic3⋊C4—104no—
300C4×Dic3—54no—
301C4×Dic3—104no—
302C4×Dic3—104no—
303C23×C5—22no—
304C23×C5—22no—
305C23×C5—21no—
306C23×C5—21no—
307C23×C5—21no—
308C23×C5—21no—
309C23×C5—22no—
310C23×C5—22no—
311C23×C5C2×C4×D312yes—
312C23×C5C2×C4×D312yes—
313C23×C5C23×D311yescharacteristic
314C22×D5—34no—
315C22×D5—62no—
316C22×D5—62no—
317C22×D5—62no—
318C22×D5—62no—
319C22×D5—62no—
320C22×D5—62no—
321C5×D4—44no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—34no—
325C2×C4×C5—62no—
326C2×C4×C5—62no—
327C2×C4×C5—62no—
328C2×C4×C5—62no—
329C2×C4×C5—62no—
330C2×C4×C5—124no—
331C2×C4×C5C2×C4×D312yes—
332C22⋊D5—616no—
333C22⋊D5—616no—
334C2×Dic5—22no—
335C2×Dic5—22no—
336C2×Dic5—22no—
337C2×Dic5—22no—
338C2×Dic5—22no—
339C2×Dic5—34no—
340C2×Dic5—34no—
341C2×Dic5—34no—
342C2×Dic5—44no—
343C2×Dic5D3×D414yes—
344D20—124no—
345C4×D5—128no—
346C22×D4—152no—
347C22×D4—152no—
348C22×D4—151no—
349C22×D4D3×D511yescharacteristic
350C23×C4—31no—
351C23×C4—51no—
352C23×C4—152no—
353#127—158no—
354C4×D4—308no—
355C4×D4—308no—
356C2×C4⋊C4—152no—
357C2×C4⋊C4—152no—
358C2×C22⋊C4—32no—
359C2×C22⋊C4—31no—
360C2×C22⋊C4—52no—
361C2×C22⋊C4—51no—
362C2×C22⋊C4—152no—
363C2×C22⋊C4—152no—
364C2×C22⋊C4—152no—
365C2×C42—151no—
366C2×C42—152no—
367C2×C42—152no—
368#95—32no—
369#95—52no—
370C2×C3×C5—42no—
371C2×C3×C5—42no—
372C2×C3×C5C2×C4×D412yes—
373C2×C3×C5#51811yescharacteristic
374C2×C3×C5D4211yescharacteristic
375C2×C3×C5#55012yes—
376C2×C3×C5#55911yescharacteristic
377D15—44no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3C2×C4×D512yes—
387C23×C3C2×C4×D512yes—
388C23×C3C23×D511yescharacteristic
389C22×D3—54no—
390C22×D3—102no—
391C22×D3—102no—
392C22×D3—102no—
393C22×D3—102no—
394C22×D3—102no—
395C22×D3—102no—
396C3×D4—44no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—54no—
400C2×C3×C4—102no—
401C2×C3×C4—102no—
402C2×C3×C4—102no—
403C2×C3×C4—102no—
404C2×C3×C4—102no—
405C2×C3×C4—204no—
406C2×C3×C4C2×C4×D512yes—
407#67—1016no—
408#67—1016no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—44no—
415C2×Dic3—54no—
416C2×Dic3—54no—
417C2×Dic3—54no—
418C2×Dic3D4×D514yes—
419D12—204no—
420C4×D3—208no—
421C22×C5—22no—
422C22×C5—22no—
423C22×C5—24no—
424C22×C5—24no—
425C22×C5—41no—
426C22×C5—41no—
427C22×C5—41no—
428C22×C5—41no—
429C22×C5—42no—
430C22×C5—42no—
431C22×C5C22×C4×D311yescharacteristic
432C22×C5C2×D3×D412yes—
433C22×C5#100411yescharacteristic
434C22×C5#100411yescharacteristic
435C22×C5D3×#4112yes—
436C2×D5—64no—
437C2×D5—64no—
438C2×D5—64no—
439C2×D5—122no—
440C2×D5—122no—
441C2×D5—122no—
442C2×D5—122no—
443C4×C5—22no—
444C4×C5—64no—
445C4×C5—122no—
446Dic5—24no—
447Dic5—38no—
448Dic5—42no—
449C24—152no—
450C24C2×D3×D511yescharacteristic
451C24C2×D3×D511yescharacteristic
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—158no—
455C2×D4—158no—
456C2×D4—154no—
457C2×D4—304no—
458C2×D4—304no—
459C2×D4—304no—
460C2×D4—304no—
461C2×D4—601no—
462C2×D4—601no—
463C2×D4#120014yescomplemented
464C22×C4—32no—
465C22×C4—32no—
466C22×C4—52no—
467C22×C4—52no—
468C22×C4—64no—
469C22×C4—104no—
470C22×C4—121no—
471C22×C4—152no—
472C22×C4—201no—
473C22×C4—304no—
474C22×C4—304no—
475C22×C4—602no—
476C22×C4C2×D3×D511yescharacteristic
477C4⋊C4—158no—
478C4⋊C4—304no—
479C22⋊C4—64no—
480C22⋊C4—104no—
481C22⋊C4—121no—
482C22⋊C4—201no—
483C22⋊C4—304no—
484C22⋊C4—304no—
485C22⋊C4—602no—
486C42—154no—
487C42—304no—
488C42—304no—
489C3×C5#236611yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—24no—
493C22×C3—24no—
494C22×C3—41no—
495C22×C3—41no—
496C22×C3—42no—
497C22×C3—42no—
498C22×C3—41no—
499C22×C3—41no—
500C22×C3C22×C4×D511yescharacteristic
501C22×C3C2×D4×D512yes—
502C22×C3#414411yescharacteristic
503C22×C3#414411yescharacteristic
504C22×C3D5×#4112yes—
505C2×D3—104no—
506C2×D3—104no—
507C2×D3—104no—
508C2×D3—202no—
509C2×D3—202no—
510C2×D3—202no—
511C2×D3—202no—
512C3×C4—22no—
513C3×C4—104no—
514C3×C4—202no—
515Dic3—24no—
516Dic3—42no—
517Dic3—58no—
518C2×C5—42no—
519C2×C5—42no—
520C2×C5#548611yescharacteristic
521C2×C5C4×D3×D412yes—
522C2×C5#559011yescharacteristic
523C2×C5#559912yes—
524C2×C5#566411yescharacteristic
525D5—124no—
526C23—22no—
527C23—22no—
528C23—22no—
529C23—22no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—154no—
535C23—302no—
536C23—302no—
537C23—302no—
538C23—302no—
539C23—302no—
540C23—302no—
541C23C2×#120012yes—
542C23C2×#120012yes—
543C23C22×D3×D511yescharacteristic
544D4—44no—
545D4—3016no—
546D4—3016no—
547D4—604no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—34no—
551C2×C4—54no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—102no—
558C2×C4—102no—
559C2×C4—102no—
560C2×C4—102no—
561C2×C4—102no—
562C2×C4—124no—
563C2×C4—154no—
564C2×C4—154no—
565C2×C4—154no—
566C2×C4—204no—
567C2×C4—608no—
568C2×C4C2×#120012yes—
569C2×C3—42no—
570C2×C3—42no—
571C2×C3#6582011yescharacteristic
572C2×C3C4×D4×D512yes—
573C2×C3#6592411yescharacteristic
574C2×C3#6593312yes—
575C2×C3#6599811yescharacteristic
576D3—204no—
577C5#7467911yescharacteristic, complemented, Sylow
578C22—24no—
579C22—24no—
580C22—22no—
581C22—22no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—42no—
587C22—42no—
588C22—304no—
589C22—304no—
590C22—304no—
591C22—602no—
592C22—602no—
593C22—602no—
594C22—602no—
595C22D3×D4×D512yes—
596C22#9202412yes—
597C22C22×#120011yescharacteristic
598C22#9204911yescharacteristic
599C22#9204911yescharacteristic
600C4—22no—
601C4—64no—
602C4—104no—
603C4—122no—
604C4—158no—
605C4—202no—
606C3#1060641011yescharacteristic, complemented, Sylow
607C2—42no—
608C2—42no—
609C2—604no—
610C2D4×#120012yes—
611C2#1175490611yescharacteristic
612C2#1175500612yes—
613C2#1175503411yescharacteristic
614C2#1175541311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91829C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#2366
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#91556C2semidirect
3. C2×#91552C2semidirect
4. C5×#5220C2semidirect
5. C3×#65509C2semidirect
6. #11749483C2semidirect
7. #11749483C2semidirect
8. #11748904C2semidirect
9. #11748663C2semidirect
18. #91829C4semidirect
40. #65509D3semidirect
50. C2×C3×C5×D4C2×C4semidirect
56. C2×#1220C2×C4semidirect
57. C2×#1220C2×C4semidirect
61. C2×D60C2×C4semidirect
73. C4×Dic15C2×C4semidirect
79. #6669D4semidirect
89. #5220D5semidirect
191. C2×C5×D4C4×D3semidirect
258. Dic15C4×D4semidirect
268. C2×C3×D4C4×D5semidirect
463. C2×D4#1200semidirect
489. C3×C5#2366semidirect
577. C5#74679semidirect
606. C3#10606410semidirect

Maximal subgroups

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

subgroupindex
C2×#918292
C2×#915562
C2×#915522
C5×#52202
C3×#655092
#117494832
#117489042
#117486632
#106064103
#746795