Finite Group Databasebeta

← #14320887

Subgroups — #14320887

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×#91815C211yesmaximal, characteristic, complemented
2C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
3C2×#91357C211yesmaximal, characteristic, complemented
4C4×C5×#217C211yesmaximal, characteristic, complemented
5#11749489C212yesmaximal
6#11749485C212yesmaximal, complemented
7C4×#6668C211yesmaximal, characteristic, complemented
8#11748772C212yesmaximal, complemented
9C4×#6665C211yesmaximal, characteristic, complemented
10#11748680C212yesmaximal, complemented
11C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
12#10605170—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C2×#6719C2212yes—
17#91815—24no—
18C2×C4⋊Dic15C2212yes—
19C2×C4×Dic15C2211yescharacteristic
20C2×C4×Dic15C2211yescharacteristic
21C2×C5×#217C2212yes—
22C2×C4×C5×Dic3C2211yescharacteristic
23C2×C4×C5×Dic3C2211yescharacteristic
24C2×C3×C22⋊Dic5C2211yescharacteristic
25C3×C4×C22⋊D5C418yescomplemented
26C2×C3×#685C2211yescharacteristic
27C2×C3×#683C2211yescharacteristic
28C2×C3×C4×Dic5C2211yescharacteristic
29C2×#6668C2212yes—
30C2×#6668C2212yes—
31C2×#6665C2212yes—
32C2×#6665C2212yes—
33C2×Dic3×Dic5C2212yes—
34C2×Dic3×Dic5C2212yes—
35#91357—24no—
36C5×C3⋊#95C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#82319—51nomaximal, Hall
40C2×C4×C22⋊D5D311yescharacteristic
41C2×#4072—31no—
42C2×#4018—31no—
43C4×C5×C22⋊C4—31no—
44#65246—32no—
45#65233—32no—
46C4×#685—31no—
47C4×#683—31no—
48C42×Dic5—31no—
49#64959—32no—
50#64936—32no—
51C24×C3×C5C2311yescharacteristic
52C23×C3×D5C2311yescharacteristic
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5C2×C414yes—
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C22×Dic15C2312yes—
59C22×Dic15C2312yes—
60C22×C5×Dic3C2312yes—
61C22×C5×Dic3C2312yes—
62C2×C3×C22⋊D5—24no—
63C2×C3×C22⋊D5C2×C414yes—
64C22×C3×Dic5C2311yescharacteristic
65C22×C3×Dic5C2311yescharacteristic
66C22×C3×Dic5C2311yescharacteristic
67C2×C3×C4×D5—22no—
68C2×C3×C4×D5—22no—
69C2×C3×C4×D5C2×C414yes—
70#6719—24no—
71C4⋊Dic15—24no—
72C4×Dic15—22no—
73C4×Dic15D414yescomplemented
74C5×#217—24no—
75C4×C5×Dic3—22no—
76C4×C5×Dic3—22no—
77C3×C22⋊Dic5C2×C414yes—
78C3×#685C2×C414yes—
79C3×#683C2×C414yes—
80C3×C4×Dic5C2×C414yes—
81#6668—24no—
82#6668—24no—
83#6665—24no—
84#6665—24no—
85Dic3×Dic5—24no—
86Dic3×Dic5—24no—
87C2×C3×C4×D4—51no—
88C2×#926—51no—
89C2×#926—51no—
90#5221—52no—
91C4×#217—51no—
92C4×#217D511yescharacteristic, complemented
93#4984—52no—
94#4951—52no—
95#4951—52no—
96C4×C4⋊Dic3—51no—
97C42×Dic3—51no—
98C23×C4×C5C2×D311yescharacteristic
99C22×C22⋊D5C2×D311yescharacteristic
100C22×C4×D5C2×D311yescharacteristic
101C2×C5×C22⋊C4—32no—
102C2×C42×C5—31no—
103C2×C42×C5—31no—
104C2×C22⋊Dic5—32no—
105C2×C22⋊Dic5C2×D311yescharacteristic
106C4×C22⋊D5Dic318yescomplemented
107C2×#685—32no—
108C2×#685—32no—
109C2×#685C2×D311yescharacteristic
110#4072—64no—
111C2×C4⋊Dic5—32no—
112C2×#683—32no—
113C2×#683—32no—
114C2×#683C2×D311yescharacteristic
115C2×C4×Dic5—31no—
116C2×C4×Dic5—31no—
117C2×C4×Dic5—32no—
118C2×C4×Dic5—32no—
119C2×C4×Dic5C2×D311yescharacteristic
120#4018—64no—
121C5×#95—32no—
122#3963—32no—
123#3963—32no—
124#2293—151noSylow
125C23×C3×C5—21no—
126C23×C3×C5—22no—
127C23×C3×C5—22no—
128C23×C3×C5—21no—
129C23×C3×C5C22×C412yes—
130C23×C3×C5C2411yescharacteristic
131C22×C3×D5—21no—
132C22×C3×D5—22no—
133C22×C3×D5—21no—
134C22×C3×D5—22no—
135C22×C3×D5C22×C412yes—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—28no—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C22×C412yes—
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5#4112yes—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15—22no—
148C2×Dic15C2×D414yes—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—22no—
153C2×C5×Dic3—22no—
154C2×C5×Dic3#4114yes—
155C3×C22⋊D5—28no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5C22×C412yes—
160C2×C3×Dic5C22×C412yes—
161C2×C3×Dic5C22×C412yes—
162C2×C3×Dic5#4114yes—
163C3×C4×D5—28no—
164C22×C3×D4—51no—
165C23×C3×C4—51no—
166C23×C3×C4C2×D511yescharacteristic
167C3×C4×D4—58no—
168C2×C3×C4⋊C4—51no—
169C2×C3×C22⋊C4—51no—
170C2×C3×C22⋊C4—51no—
171C2×C3×C42—51no—
172C2×#217—52no—
173C2×#217—52no—
174C2×#217—52no—
175C2×#217C2×D512yes—
176#926—104no—
177#926—104no—
178C2×C4⋊Dic3—52no—
179C2×C4⋊Dic3—52no—
180C2×C4⋊Dic3—52no—
181C2×C4×Dic3—51no—
182C2×C4×Dic3—51no—
183C2×C4×Dic3—52no—
184C2×C4×Dic3—52no—
185C2×C4×Dic3C2×D511yescharacteristic
186C2×C4×Dic3C2×D511yescharacteristic
187C3⋊#95—52no—
188C3⋊#95—52no—
189C3⋊#95C2×D512yes—
190C24×C5C22×D311yescharacteristic
191C23×D5C22×D311yescharacteristic
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—32no—
195C22×C4×C5—32no—
196C22×C4×C5C2×Dic314yes—
197C22×C4×C5C22×D311yescharacteristic
198C22×C4×C5C22×D311yescharacteristic
199C2×C22⋊D5—24no—
200C2×C22⋊D5C2×Dic314yes—
201C22×Dic5—32no—
202C22×Dic5—32no—
203C22×Dic5C22×D311yescharacteristic
204C22×Dic5C22×D311yescharacteristic
205C22×Dic5C22×D311yescharacteristic
206C2×C4×D5—22no—
207C2×C4×D5—22no—
208C2×C4×D5C2×Dic314yes—
209C5×C22⋊C4—64no—
210C42×C5—62no—
211C42×C5—62no—
212C22⋊Dic5—64no—
213C22⋊Dic5C2×Dic314yes—
214#685—64no—
215#685—64no—
216#685C2×Dic314yes—
217C4⋊Dic5—64no—
218#683—64no—
219#683—64no—
220#683C2×Dic314yes—
221C4×Dic5—34no—
222C4×Dic5—64no—
223C4×Dic5—62no—
224C4×Dic5—64no—
225C4×Dic5C2×Dic314yes—
226C2×C4×D4—51no—
227C2×#117—151no—
228C2×#117—151no—
229#390—152no—
230#389—152no—
231#388—152no—
232#388—152no—
233C4×C4⋊C4—151no—
234C4×C22⋊C4—31no—
235C4×C22⋊C4—151no—
236C43—151no—
237C22×C3×C5—22no—
238C22×C3×C5—22no—
239C22×C3×C5—22no—
240C22×C3×C5—42no—
241C22×C3×C5—42no—
242C22×C3×C5C23×C411yescharacteristic
243C22×C3×C5C22×D411yescharacteristic
244C22×C3×C5C2×#4112yes—
245C22×C3×C5C2×#4111yescharacteristic
246C22×C3×C5C2×#4112yes—
247C2×C3×D5—22no—
248C2×C3×D5—22no—
249C2×C3×D5—22no—
250C2×C3×D5—42no—
251C2×C3×D5—42no—
252C3×C4×C5—22no—
253C3×C4×C5C4×D414yes—
254Dic15—24no—
255Dic15—42no—
256C3×Dic5—22no—
257C3×Dic5—22no—
258C3×Dic5#11714yescomplemented
259C5×Dic3—24no—
260C5×Dic3—42no—
261C24×C3—51no—
262C24×C3C22×D511yescharacteristic
263C2×C3×D4—54no—
264C2×C3×D4—104no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—51no—
268C22×C3×C4—51no—
269C22×C3×C4—51no—
270C22×C3×C4—54no—
271C22×C3×C4—102no—
272C22×C3×C4—102no—
273C22×C3×C4C4×D514yes—
274C22×C3×C4C22×D511yescharacteristic
275C22×C3×C4C22×D511yescharacteristic
276C22×Dic3—52no—
277C22×Dic3—52no—
278C22×Dic3C22×D512yes—
279C22×Dic3C22×D512yes—
280C3×C4⋊C4—54no—
281C3×C22⋊C4—54no—
282C3×C22⋊C4—54no—
283C3×C42—54no—
284#217—24no—
285#217—104no—
286#217—104no—
287#217—104no—
288C4⋊Dic3—104no—
289C4⋊Dic3—104no—
290C4⋊Dic3—104no—
291C4×Dic3—22no—
292C4×Dic3—22no—
293C4×Dic3—54no—
294C4×Dic3—104no—
295C4×Dic3—102no—
296C4×Dic3—104no—
297C23×C5—22no—
298C23×C5—21no—
299C23×C5—21no—
300C23×C5—22no—
301C23×C5C22×Dic312yes—
302C23×C5C23×D311yescharacteristic
303C22×D5—22no—
304C22×D5—21no—
305C22×D5—21no—
306C22×D5—22no—
307C22×D5C22×Dic312yes—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—28no—
311C2×C4×C5—34no—
312C2×C4×C5—62no—
313C2×C4×C5—62no—
314C2×C4×C5—62no—
315C2×C4×C5—62no—
316C2×C4×C5—62no—
317C2×C4×C5D3×D412yes—
318C2×C4×C5#23712yes—
319C2×C4×C5C22×Dic312yes—
320C2×C4×C5C22×Dic312yes—
321C22⋊D5—28no—
322C2×Dic5—21no—
323C2×Dic5—21no—
324C2×Dic5—22no—
325C2×Dic5—34no—
326C2×Dic5—62no—
327C2×Dic5—62no—
328C2×Dic5—62no—
329C2×Dic5—62no—
330C2×Dic5—62no—
331C2×Dic5#23514yes—
332C2×Dic5C22×Dic312yes—
333C2×Dic5C22×Dic312yes—
334C2×Dic5C22×Dic312yes—
335C4×D5—28no—
336C22×D4—51no—
337C23×C4—51no—
338C23×C4D3×D511yescharacteristic
339C4×D4—58no—
340#117—304no—
341#117—304no—
342C2×C4⋊C4—51no—
343C2×C4⋊C4—152no—
344C2×C4⋊C4—152no—
345C2×C4⋊C4—152no—
346C2×C22⋊C4—32no—
347C2×C22⋊C4—51no—
348C2×C22⋊C4—51no—
349C2×C22⋊C4—152no—
350C2×C22⋊C4—152no—
351C2×C22⋊C4—152no—
352C2×C42—31no—
353C2×C42—31no—
354C2×C42—51no—
355C2×C42—151no—
356C2×C42—152no—
357C2×C42—152no—
358C2×C42—151no—
359#95—32no—
360#95—152no—
361#95—152no—
362C2×C3×C5—42no—
363C2×C3×C5C2×#11711yescharacteristic
364C2×C3×C5C2×C4×D411yescharacteristic
365C2×C3×C5C4×#4111yescharacteristic
366C2×C3×C5#52912yes—
367C2×C3×C5#53212yes—
368C3×D5—42no—
369C23×C3—22no—
370C23×C3—21no—
371C23×C3—21no—
372C23×C3—22no—
373C23×C3—52no—
374C23×C3—102no—
375C23×C3—101no—
376C23×C3—101no—
377C23×C3—102no—
378C23×C3C2×C4×D512yes—
379C23×C3C23×D511yescharacteristic
380C3×D4—108no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—28no—
384C2×C3×C4—52no—
385C2×C3×C4—54no—
386C2×C3×C4—52no—
387C2×C3×C4—52no—
388C2×C3×C4—102no—
389C2×C3×C4—101no—
390C2×C3×C4—101no—
391C2×C3×C4—108no—
392C2×C3×C4C2×C4×D512yes—
393C2×C3×C4C2×C4×D512yes—
394C2×C3×C4D4×D512yes—
395C2×C3×C4#71112yes—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—54no—
402C2×Dic3—102no—
403C2×Dic3—102no—
404C2×Dic3—102no—
405C2×Dic3—102no—
406C2×Dic3—102no—
407C2×Dic3#70914yes—
408C22×C5—22no—
409C22×C5—22no—
410C22×C5—22no—
411C22×C5—42no—
412C22×C5—42no—
413C22×C5C2×#23512yes—
414C22×C5C2×D3×D411yescharacteristic
415C22×C5C2×#23711yescharacteristic
416C22×C5D3×#4112yes—
417C22×C5C23×Dic311yescharacteristic
418C2×D5—22no—
419C2×D5—22no—
420C2×D5—22no—
421C2×D5—42no—
422C2×D5—42no—
423C4×C5—22no—
424C4×C5—64no—
425C4×C5—122no—
426C4×C5D4×Dic314yes—
427Dic5—22no—
428Dic5—22no—
429Dic5—64no—
430Dic5—122no—
431Dic5#92614yescomplemented
432C24—51no—
433C24C2×D3×D511yescharacteristic
434C2×D4—54no—
435C2×D4—104no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—32no—
439C22×C4—32no—
440C22×C4—51no—
441C22×C4—51no—
442C22×C4—51no—
443C22×C4—54no—
444C22×C4—102no—
445C22×C4—102no—
446C22×C4—152no—
447C22×C4—152no—
448C22×C4D5×Dic314yes—
449C22×C4C2×D3×D511yescharacteristic
450C22×C4C2×D3×D511yescharacteristic
451C4⋊C4—54no—
452C4⋊C4—304no—
453C4⋊C4—304no—
454C4⋊C4—304no—
455C22⋊C4—54no—
456C22⋊C4—54no—
457C22⋊C4—64no—
458C22⋊C4—304no—
459C22⋊C4—304no—
460C22⋊C4—304no—
461C42—54no—
462C42—62no—
463C42—62no—
464C42—154no—
465C42—304no—
466C42—304no—
467C42—302no—
468C3×C5#229311yescharacteristic, complemented, Hall
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—22no—
472C22×C3—42no—
473C22×C3—42no—
474C22×C3—102no—
475C22×C3—102no—
476C22×C3—102no—
477C22×C3—202no—
478C22×C3—202no—
479C22×C3C22×C4×D511yescharacteristic
480C22×C3C2×#70912yes—
481C22×C3C2×D4×D511yescharacteristic
482C22×C3C2×#71111yescharacteristic
483C22×C3D5×#4112yes—
484C3×C4—22no—
485C3×C4—54no—
486C3×C4—102no—
487C3×C4—102no—
488C3×C4#402714yes—
489Dic3—24no—
490Dic3—42no—
491Dic3—104no—
492Dic3—202no—
493C2×C5—42no—
494C2×C5#554812yes—
495C2×C5#555712yes—
496C2×C5C2×#92611yescharacteristic
497C2×C5C2×D4×Dic311yescharacteristic
498C2×C5Dic3×#4111yescharacteristic
499D5—42no—
500C23—22no—
501C23—22no—
502C23—21no—
503C23—21no—
504C23—52no—
505C23—102no—
506C23—102no—
507C23—101no—
508C23—101no—
509C23C2×D5×Dic312yes—
510C23C22×D3×D511yescharacteristic
511D4—108no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—28no—
515C2×C4—34no—
516C2×C4—54no—
517C2×C4—52no—
518C2×C4—52no—
519C2×C4—52no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—102no—
526C2×C4—101no—
527C2×C4—101no—
528C2×C4—108no—
529C2×C4—154no—
530C2×C4—302no—
531C2×C4—302no—
532C2×C4—302no—
533C2×C4—302no—
534C2×C4—302no—
535C2×C4C2×D5×Dic312yes—
536C2×C4C2×D5×Dic312yes—
537C2×C4#678012yes—
538C2×C4#679012yes—
539C2×C3—42no—
540C2×C3—202no—
541C2×C3C4×#70911yescharacteristic
542C2×C3C2×#402711yescharacteristic
543C2×C3D5×#11711yescharacteristic
544C2×C3#6587212yes—
545C2×C3#6588212yes—
546C5#8231911yescharacteristic, complemented, Sylow
547C22—22no—
548C22—22no—
549C22—22no—
550C22—42no—
551C22—42no—
552C22—102no—
553C22—102no—
554C22—102no—
555C22—202no—
556C22—202no—
557C22D5×#23512yes—
558C22D3×#70912yes—
559C22C22×D5×Dic311yescharacteristic
560C22C2×#678011yescharacteristic
561C22C2×#679011yescharacteristic
562C4—22no—
563C4—54no—
564C4—64no—
565C4—102no—
566C4—102no—
567C4—122no—
568C4—304no—
569C4—602no—
570C4#9155914yes—
571C3#1060517011yescharacteristic, complemented, Sylow
572C2—42no—
573C2—202no—
574C2D5×#92611yescharacteristic
575C2Dic3×#70911yescharacteristic
576C2#1175455512yes—
577C2#1175456512yes—
578C2C2×#9155911yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2293
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#91815C2semidirect
3. C2×#91357C2semidirect
4. C4×C5×#217C2semidirect
6. #11749485C2semidirect
7. C4×#6668C2semidirect
8. #11748772C2semidirect
9. C4×#6665C2semidirect
10. #11748680C2semidirect
11. C4×Dic3×Dic5C2semidirect
25. C3×C4×C22⋊D5C4semidirect
73. C4×Dic15D4semidirect
92. C4×#217D5semidirect
106. C4×C22⋊D5Dic3semidirect
258. C3×Dic5#117semidirect
431. Dic5#926semidirect
468. C3×C5#2293semidirect
546. C5#82319semidirect
571. C3#10605170semidirect

Maximal subgroups

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

subgroupindex
C2×#918152
C2×C3×C4×C22⋊D52
C2×#913572
C4×C5×#2172
#117494892
#117494852
C4×#66682
#117487722
C4×#66652
#117486802
C4×Dic3×Dic52
#106051703
#823195