Finite Group Databasebeta

← #14323606

Subgroups — #14323606

Order 1920.

1264 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
1C22×#6712C211yesmaximal, characteristic, complemented
2C2×C4×C5×#67C211yesmaximal, characteristic
3C2×#91543C211yesmaximal, characteristic
4C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
5#11749515C211yesmaximal, characteristic, complemented
6#11749501C211yesmaximal, characteristic
7#11749473C211yesmaximal, characteristic, complemented
8#11748806C212yesmaximal, complemented
9#11748801C212yesmaximal, complemented
10#11748722C212yesmaximal, complemented
11#11748715C212yesmaximal, complemented
12#10614057—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×Dic15C2211yescharacteristic
15C23×Dic15C2211yescharacteristic
16C22×C5×#67C2211yescharacteristic
17C22×C4×C5×D3C2211yescharacteristic
18C2×#6712—24no—
19C2×#6712C2212yes—
20C2×#6712C2212yes—
21C2×C5×#217C2211yescharacteristic
22C4×C5×#67—24no—
23C2×C5×(C2×D3)⋊C4C2211yescharacteristic
24C2×C5×Dic3⋊C4C2211yescharacteristic
25C2×C4×C5×Dic3C2211yescharacteristic
26C2×C3×C22⋊Dic5C2211yescharacteristic
27C2×C3×C22⋊Dic5C2211yescharacteristic
28C2×C3×C4×Dic5C2212yes—
29#91543C418yescomplemented
30C2×#6668C2212yes—
31C2×#6668C2212yes—
32C2×(C2×D3)⋊Dic5C2212yes—
33C2×(C2×D3)⋊Dic5C2212yes—
34C3×#3963C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#73446—51nomaximal, Hall
40C2×C4×C5×D4—31no—
41C2×#4081—31no—
42C22×#683—31no—
43#65509—31no—
44#65499—32no—
45C4×C22⋊Dic5D311yescharacteristic, complemented
46#65261—32no—
47#65235—31no—
48#65234—32no—
49#65232—31no—
50#65222—32no—
51C24×C3×C5C2311yescharacteristic
52C23×C5×D3C2311yescharacteristic
53C22×C3×C4×C5—42no—
54C22×C3×C4×C5D414yes—
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15—22no—
58C22×Dic15—22no—
59C22×Dic15—22no—
60C22×Dic15—42no—
61C22×Dic15C2×C414yescomplemented
62C22×Dic15C2312yes—
63C22×Dic15C2312yes—
64C2×C5×#67—22no—
65C2×C5×#67—22no—
66C2×C5×#67C2×C414yes—
67C22×C5×Dic3C2311yescharacteristic
68C22×C5×Dic3C2311yescharacteristic
69C22×C5×Dic3C2311yescharacteristic
70C2×C4×C5×D3—22no—
71C2×C4×C5×D3—42no—
72C22×C3×Dic5C2312yes—
73C22×C3×Dic5C2312yes—
74#6712—24no—
75#6712—24no—
76C5×#217—22no—
77C5×(C2×D3)⋊C4—22no—
78C5×Dic3⋊C4—22no—
79C4×C5×Dic3—22no—
80C3×C22⋊Dic5—22no—
81C3×C22⋊Dic5C2×C414yescomplemented
82C3×C4×Dic5—42no—
83#6668—42no—
84#6668C2×C418yescomplemented
85(C2×D3)⋊Dic5—42no—
86(C2×D3)⋊Dic5C2×C418yescomplemented
87C2×C4×#67D511yescharacteristic
88C22×Dic3⋊C4—51no—
89C2×#886—51no—
90C3×C4×C22⋊C4—51no—
91#4958—51no—
92#4950—51no—
93#4943—51no—
94#4940—52no—
95#4928—52no—
96#4668—52no—
97#4653—52no—
98C22×C5×D4—31no—
99C23×C4×C5—31no—
100C23×C4×C5C2×D311yescharacteristic
101C23×Dic5—31no—
102C23×Dic5—31no—
103C4×C5×D4—64no—
104C2×C5×C4⋊C4—31no—
105C2×C5×C22⋊C4—31no—
106C2×C5×C22⋊C4—31no—
107C2×C42×C5—31no—
108C2×C22⋊Dic5—32no—
109C2×C22⋊Dic5—32no—
110C2×C22⋊Dic5C2×D311yescharacteristic
111C2×C22⋊Dic5C2×D311yescharacteristic
112#4081—38no—
113C2×#683—32no—
114C2×#683—32no—
115C2×#683—32no—
116C2×#683—32no—
117C2×#683—64no—
118C2×C4×Dic5C2×D312yes—
119#3963—32no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#3963C2×D312yes—
124#2322—151noSylow
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5C22×C412yes—
128C23×C3×C5C2×D412yes—
129C23×C3×C5#4112yes—
130C23×C3×C5C2411yescharacteristic
131C22×C5×D3—21no—
132C22×C5×D3—21no—
133C22×C5×D3—22no—
134C22×C5×D3—22no—
135C22×C5×D3C22×C412yes—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—44no—
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2×D412yes—
141C2×Dic15—28no—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15—44no—
148C2×Dic15C22×C414yes—
149C5×#67—28no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—21no—
152C2×C5×Dic3—21no—
153C2×C5×Dic3—21no—
154C2×C5×Dic3—22no—
155C2×C5×Dic3—22no—
156C2×C5×Dic3C22×C412yes—
157C4×C5×D3—44no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—22no—
163C2×C3×Dic5C22×C414yes—
164C23×C3×C4C2×D511yescharacteristic
165C22×#67C2×D511yescharacteristic
166C23×Dic3—51no—
167C23×Dic3—51no—
168C22×C4×D3C2×D511yescharacteristic
169C2×C3×C22⋊C4—51no—
170C2×C3×C22⋊C4—51no—
171C2×C3×C42—52no—
172C2×#217C2×D511yescharacteristic
173C4×#67—24no—
174C2×(C2×D3)⋊C4—52no—
175C2×(C2×D3)⋊C4—52no—
176C2×(C2×D3)⋊C4C2×D511yescharacteristic
177C2×C4⋊Dic3—52no—
178C2×C4⋊Dic3—52no—
179C2×Dic3⋊C4—52no—
180C2×Dic3⋊C4—52no—
181C2×Dic3⋊C4—104no—
182C2×Dic3⋊C4C2×D511yescharacteristic
183C2×C4×Dic3C2×D511yescharacteristic
184#886—58no—
185C3×#95—52no—
186C3⋊#95—52no—
187C3⋊#95—52no—
188C3⋊#95—52no—
189C3⋊#95—52no—
190C24×C5—31no—
191C24×C5C22×D311yescharacteristic
192C2×C5×D4—34no—
193C2×C5×D4—62no—
194C2×C5×D4—62no—
195C22×C4×C5—31no—
196C22×C4×C5—31no—
197C22×C4×C5—31no—
198C22×C4×C5—42no—
199C22×C4×C5—62no—
200C22×C4×C5—122no—
201C22×C4×C5D1214yes—
202C22×C4×C5C22×D311yescharacteristic
203C22×C4×C5C22×D311yescharacteristic
204C22×Dic5—34no—
205C22×Dic5—32no—
206C22×Dic5—32no—
207C22×Dic5—62no—
208C22×Dic5—62no—
209C22×Dic5—62no—
210C22×Dic5—122no—
211C22×Dic5C22×D312yes—
212C22×Dic5C22×D312yes—
213C5×C4⋊C4—62no—
214C5×C22⋊C4—62no—
215C5×C22⋊C4—62no—
216C42×C5—62no—
217C22⋊Dic5—22no—
218C22⋊Dic5—38no—
219C22⋊Dic5—122no—
220C22⋊Dic5C4×D314yescomplemented
221#683—38no—
222#683—64no—
223#683—64no—
224#683—122no—
225C4×Dic5—42no—
226C2×#123—151no—
227C2×C4×D4—31no—
228C22×C4⋊C4—151no—
229#389—152no—
230#388—152no—
231#387—152no—
232#386—151no—
233#385—152no—
234#385—151no—
235#381—151no—
236C4×C22⋊C4—51no—
237C22×C3×C5—24no—
238C22×C3×C5—22no—
239C22×C3×C5—22no—
240C22×C3×C5—24no—
241C22×C3×C5C4×D414yes—
242C22×C3×C5C23×C411yescharacteristic
243C22×C3×C5C22×D411yescharacteristic
244C22×C3×C5C2×#4111yescharacteristic
245C22×C3×C5H(5,𝔽2)12yes—
246C22×C3×C52−1+412yes—
247C2×C5×D3—22no—
248C2×C5×D3—24no—
249C2×C5×D3—41no—
250C2×C5×D3—41no—
251C2×C5×D3—42no—
252C3×C4×C5—22no—
253C3×C4×C5—22no—
254Dic15—24no—
255Dic15—42no—
256C3×Dic5—24no—
257C3×Dic5—42no—
258C5×Dic3—22no—
259C5×Dic3—41no—
260C5×Dic3—41no—
261C24×C3C22×D511yescharacteristic
262C23×D3C22×D511yescharacteristic
263C22×C3×C4—42no—
264C22×C3×C4—52no—
265C22×C3×C4—52no—
266C22×C3×C4C22⋊D514yes—
267C22×C3×C4C22×D511yescharacteristic
268C22×C3×C4C22×D511yescharacteristic
269C2×#67—22no—
270C2×#67—22no—
271C2×#67C4×D514yes—
272C22×Dic3—54no—
273C22×Dic3—52no—
274C22×Dic3—52no—
275C22×Dic3—102no—
276C22×Dic3—102no—
277C22×Dic3—102no—
278C22×Dic3—202no—
279C22×Dic3C22×D511yescharacteristic
280C22×Dic3C22×D511yescharacteristic
281C22×Dic3C22×D511yescharacteristic
282C2×C4×D3—22no—
283C2×C4×D3—42no—
284C3×C22⋊C4—54no—
285C3×C22⋊C4—102no—
286C3×C42—202no—
287#217—22no—
288(C2×D3)⋊C4—22no—
289(C2×D3)⋊C4—58no—
290(C2×D3)⋊C4—202no—
291C4⋊Dic3—58no—
292C4⋊Dic3—202no—
293Dic3⋊C4—22no—
294Dic3⋊C4—104no—
295Dic3⋊C4—104no—
296C4×Dic3—22no—
297C23×C5—22no—
298C23×C5—22no—
299C23×C5—32no—
300C23×C5—61no—
301C23×C5—61no—
302C23×C5—62no—
303C23×C5—62no—
304C23×C5C2×C4×D312yes—
305C23×C5C2×D1212yes—
306C23×C5#23512yes—
307C23×C5C23×D311yescharacteristic
308C5×D4—68no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—32no—
312C2×C4×C5—44no—
313C2×C4×C5—61no—
314C2×C4×C5—61no—
315C2×C4×C5—61no—
316C2×C4×C5—61no—
317C2×C4×C5—62no—
318C2×C4×C5—62no—
319C2×C4×C5—124no—
320C2×C4×C5C2×D1212yes—
321C2×C4×C5C2×D1212yes—
322C2×Dic5—22no—
323C2×Dic5—22no—
324C2×Dic5—22no—
325C2×Dic5—22no—
326C2×Dic5—22no—
327C2×Dic5—34no—
328C2×Dic5—68no—
329C2×Dic5—62no—
330C2×Dic5—62no—
331C2×Dic5—62no—
332C2×Dic5—62no—
333C2×Dic5—62no—
334C2×Dic5—124no—
335C2×Dic5C2×C4×D314yes—
336C22×D4—31no—
337C23×C4—31no—
338C23×C4—151no—
339C23×C4—151no—
340C23×C4D3×D511yescharacteristic
341#123—158no—
342C4×D4—64no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—152no—
345C2×C4⋊C4—152no—
346C2×C4⋊C4—152no—
347C2×C4⋊C4—152no—
348C2×C4⋊C4—304no—
349C2×C22⋊C4—31no—
350C2×C22⋊C4—31no—
351C2×C22⋊C4—51no—
352C2×C22⋊C4—51no—
353C2×C22⋊C4—152no—
354C2×C22⋊C4—152no—
355C2×C42—31no—
356C2×C42—52no—
357#95—52no—
358#95—152no—
359#95—152no—
360#95—152no—
361#95—152no—
362C2×C3×C5—24no—
363C2×C3×C5C2×C4×D411yescharacteristic
364C2×C3×C5#52012yes—
365C2×C3×C5#53411yescharacteristic
366C2×C3×C5#53611yescharacteristic
367C2×C3×C5#53912yes—
368C5×D3—42no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3C2×C4×D512yes—
372C23×C3#70912yes—
373C23×C3C2×C22⋊D512yes—
374C23×C3C23×D511yescharacteristic
375C22×D3—21no—
376C22×D3—22no—
377C22×D3—22no—
378C22×D3—21no—
379C22×D3C2×C4×D512yes—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—44no—
383C2×C3×C4—54no—
384C2×C3×C4—102no—
385C2×C3×C4—102no—
386C2×C3×C4—102no—
387C2×C3×C4—102no—
388C2×C3×C4—102no—
389C2×C3×C4C2×C22⋊D512yes—
390C2×C3×C4C2×C22⋊D512yes—
391#67—28no—
392C2×Dic3—21no—
393C2×Dic3—21no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—54no—
399C2×Dic3—102no—
400C2×Dic3—102no—
401C2×Dic3—108no—
402C2×Dic3—102no—
403C2×Dic3—102no—
404C2×Dic3—102no—
405C2×Dic3—204no—
406C2×Dic3C2×C4×D512yes—
407C4×D3—44no—
408C22×C5—22no—
409C22×C5—22no—
410C22×C5—24no—
411C22×C5—24no—
412C22×C5—62no—
413C22×C5—64no—
414C22×C5—121no—
415C22×C5—121no—
416C22×C5—122no—
417C22×C5C4×D1214yes—
418C22×C5C22×C4×D311yescharacteristic
419C22×C5C22×D1211yescharacteristic
420C22×C5C2×#23511yescharacteristic
421C22×C5#100412yes—
422C22×C5#101012yes—
423C4×C5—22no—
424C4×C5—22no—
425C4×C5—62no—
426C4×C5—121no—
427C4×C5—121no—
428Dic5—24no—
429Dic5—42no—
430Dic5—64no—
431Dic5—122no—
432C24—31no—
433C24C2×D3×D511yescharacteristic
434C2×D4—34no—
435C2×D4—62no—
436C2×D4—62no—
437C22×C4—31no—
438C22×C4—31no—
439C22×C4—31no—
440C22×C4—42no—
441C22×C4—52no—
442C22×C4—52no—
443C22×C4—62no—
444C22×C4—122no—
445C22×C4—154no—
446C22×C4—152no—
447C22×C4—152no—
448C22×C4—302no—
449C22×C4—302no—
450C22×C4—302no—
451C22×C4—602no—
452C22×C4#120314yes—
453C22×C4C2×D3×D511yescharacteristic
454C22×C4C2×D3×D511yescharacteristic
455C4⋊C4—62no—
456C4⋊C4—158no—
457C4⋊C4—304no—
458C4⋊C4—304no—
459C4⋊C4—602no—
460C22⋊C4—54no—
461C22⋊C4—62no—
462C22⋊C4—62no—
463C22⋊C4—102no—
464C22⋊C4—158no—
465C22⋊C4—602no—
466C42—62no—
467C42—202no—
468C3×C5#232211yescharacteristic, complemented, Hall
469C22×C3—24no—
470C22×C3—22no—
471C22×C3—24no—
472C22×C3—22no—
473C22×C3C4×C22⋊D514yes—
474C22×C3C22×C4×D511yescharacteristic
475C22×C3C2×#70911yescharacteristic
476C22×C3#414412yes—
477C22×C3#415012yes—
478C22×C3C22×C22⋊D511yescharacteristic
479C2×D3—22no—
480C2×D3—24no—
481C2×D3—41no—
482C2×D3—42no—
483C2×D3—41no—
484C3×C4—22no—
485C3×C4—22no—
486C3×C4—104no—
487C3×C4—202no—
488Dic3—22no—
489Dic3—41no—
490Dic3—41no—
491Dic3—104no—
492Dic3—202no—
493C2×C5—24no—
494C2×C5—122no—
495C2×C5C2×C4×D1211yescharacteristic
496C2×C5#549311yescharacteristic
497C2×C5#552611yescharacteristic
498C2×C5#554612yes—
499C2×C5#556412yes—
500C23—22no—
501C23—22no—
502C23—32no—
503C23—62no—
504C23—61no—
505C23—61no—
506C23—62no—
507C23#677112yes—
508C23C4×D3×D512yes—
509C23C2×#120312yes—
510C23C22×D3×D511yescharacteristic
511D4—68no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—32no—
515C2×C4—44no—
516C2×C4—54no—
517C2×C4—61no—
518C2×C4—61no—
519C2×C4—62no—
520C2×C4—61no—
521C2×C4—61no—
522C2×C4—62no—
523C2×C4—102no—
524C2×C4—102no—
525C2×C4—102no—
526C2×C4—102no—
527C2×C4—102no—
528C2×C4—124no—
529C2×C4—154no—
530C2×C4—308no—
531C2×C4—302no—
532C2×C4—302no—
533C2×C4—302no—
534C2×C4—302no—
535C2×C4—302no—
536C2×C4—604no—
537C2×C4C2×#120312yes—
538C2×C4C2×#120312yes—
539C2×C3—24no—
540C2×C3#6588012yes—
541C2×C3#6589812yes—
542C2×C3C2×C4×C22⋊D511yescharacteristic
543C2×C3#6613811yescharacteristic
544C2×C3#6615911yescharacteristic
545D3—42no—
546C5#7344611yescharacteristic, complemented, Sylow
547C22—22no—
548C22—24no—
549C22—24no—
550C22—22no—
551C22—62no—
552C22—64no—
553C22—121no—
554C22—122no—
555C22—121no—
556C22C4×#120314yes—
557C22#9200112yes—
558C22C2×#677111yescharacteristic
559C22C2×C4×D3×D511yescharacteristic
560C22C22×#120311yescharacteristic
561C22#9204912yes—
562C4—22no—
563C4—22no—
564C4—62no—
565C4—104no—
566C4—121no—
567C4—121no—
568C4—202no—
569C4—304no—
570C4—602no—
571C3#1061405711yescharacteristic, complemented, Sylow
572C2—24no—
573C2—122no—
574C2#1175427111yescharacteristic
575C2#1175428612yes—
576C2C2×C4×#120311yescharacteristic
577C2#1175459612yes—
578C2#1175542811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×#67C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2322
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#6712C2semidirect
4. C3×C4×C22⋊Dic5C2semidirect
5. #11749515C2semidirect
7. #11749473C2semidirect
8. #11748806C2semidirect
9. #11748801C2semidirect
10. #11748722C2semidirect
11. #11748715C2semidirect
29. #91543C4semidirect
45. C4×C22⋊Dic5D3semidirect
61. C22×Dic15C2×C4semidirect
81. C3×C22⋊Dic5C2×C4semidirect
84. #6668C2×C4semidirect
86. (C2×D3)⋊Dic5C2×C4semidirect
220. C22⋊Dic5C4×D3semidirect
468. C3×C5#2322semidirect
546. C5#73446semidirect
571. C3#10614057semidirect

Maximal subgroups

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

subgroupindex
C22×#67122
C2×C4×C5×#672
C2×#915432
C3×C4×C22⋊Dic52
#117495152
#117495012
#117494732
#117488062
#117488012
#117487222
#117487152
#106140573
#734465