Finite Group Databasebeta

← #14320867

Subgroups — #14320867

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×C5×#872C211yesmaximal, characteristic, complemented
2C2×C4×#1203C211yesmaximal, characteristic
3C2×#91386C211yesmaximal, characteristic, complemented
4C4×#6714C211yesmaximal, characteristic, complemented
5C3×C4×#683C211yesmaximal, characteristic, complemented
6#11748909C212yesmaximal
7#11748721C212yesmaximal, complemented
8C4×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
9#11748669C212yesmaximal, complemented
10C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
11#11748629C212yesmaximal, complemented
12#10613956—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×C4×C5×D3C2211yescharacteristic
15C22×#1203C2211yescharacteristic
16C2×C3×C42×C5C2211yescharacteristic
17C2×#6714C2212yes—
18C2×C4×Dic15C2211yescharacteristic
19C2×C5×(C2×D3)⋊C4C2212yes—
20C2×C5×Dic3⋊C4C2212yes—
21C2×C4×C5×Dic3C2211yescharacteristic
22C5×#872—24no—
23C2×C3×#683C2212yes—
24C2×C3×C4×Dic5C2211yescharacteristic
25C2×C3×C4×Dic5C2211yescharacteristic
26C2×#6669C2212yes—
27C2×#6668C2211yescharacteristic
28C2×#6667C2212yes—
29C2×#6667C2211yescharacteristic
30C2×(C2×D3)⋊Dic5C2212yes—
31C2×(C2×D3)⋊Dic5C2211yescharacteristic
32C2×Dic3×Dic5C2212yes—
33C2×Dic3×Dic5C2212yes—
34C4×#1203C418yescomplemented
35#91386—24no—
36#91115C2212yes—
37C3×#3963C2212yes—
38#90994C2212yes—
39#73617—51nomaximal, Hall
40C2×C5×#117—31no—
41C2×C4×C22⋊D5—31no—
42C2×#4018—31no—
43C4×C22⋊Dic5—31no—
44#65279—32no—
45#65261—32no—
46#65246—32no—
47#65234—32no—
48C4×#685—31no—
49C4×#683D311yescharacteristic, complemented
50C42×Dic5—31no—
51C23×D15C2311yescharacteristic
52C23×C5×D3C2311yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2311yescharacteristic
56C22×Dic15C2312yes—
57C2×C4×D15—22no—
58C2×C4×D15—22no—
59C2×C4×D15C2×C414yes—
60C22×C5×Dic3C2311yescharacteristic
61C22×C5×Dic3C2312yes—
62C2×C4×C5×D3—22no—
63C2×C4×C5×D3—22no—
64C2×C4×C5×D3C2×C414yes—
65C22×C3×Dic5C2312yes—
66C22×C3×Dic5C2311yescharacteristic
67C22×C3×Dic5C2311yescharacteristic
68C2×#1203—24no—
69C2×#1203C2×C414yes—
70C3×C42×C5—22no—
71#6714—24no—
72C4×Dic15—22no—
73C5×(C2×D3)⋊C4—24no—
74C5×Dic3⋊C4—24no—
75C4×C5×Dic3D414yescomplemented
76C3×#683—24no—
77C3×C4×Dic5—22no—
78C3×C4×Dic5C2×C414yes—
79#6669—24no—
80#6668C2×C414yes—
81#6667—24no—
82#6667C2×C414yes—
83(C2×D3)⋊Dic5—24no—
84(C2×D3)⋊Dic5C2×C414yes—
85Dic3×Dic5—24no—
86Dic3×Dic5—24no—
87C2×C4×D12—51no—
88C2×#872—51no—
89C2×#872D511yescharacteristic, complemented
90C3×C4×C4⋊C4—51no—
91#4988—52no—
92#4972—52no—
93C4×(C2×D3)⋊C4—51no—
94C4×(C2×D3)⋊C4—51no—
95C42×Dic3—51no—
96#4669—52no—
97#4669—52no—
98C23×C4×C5—31no—
99C22×C22⋊D5—31no—
100C22×C4×D5—31no—
101C5×#117—64no—
102C2×C5×C4⋊C4—32no—
103C2×C5×C22⋊C4—32no—
104C2×C42×C5—31no—
105C2×C42×C5C2×D311yescharacteristic
106C2×C22⋊Dic5—31no—
107C2×C22⋊Dic5—32no—
108C4×C22⋊D5—38no—
109C2×#685—31no—
110C2×#685—32no—
111C2×#685—32no—
112C2×#683—31no—
113C2×#683—32no—
114C2×#683C2×D312yes—
115C2×C4×Dic5—31no—
116C2×C4×Dic5—32no—
117C2×C4×Dic5—32no—
118C2×C4×Dic5C2×D311yescharacteristic
119C2×C4×Dic5C2×D311yescharacteristic
120#4018—64no—
121#3963—32no—
122#3963—32no—
123#3963C2×D312yes—
124#2293—151noSylow
125C23×C3×C5C2411yescharacteristic
126C22×D15—21no—
127C22×D15—22no—
128C22×D15—22no—
129C22×D15—21no—
130C22×D15C22×C412yes—
131C22×C5×D3—21no—
132C22×C5×D3—22no—
133C22×C5×D3—22no—
134C22×C5×D3—21no—
135C22×C5×D3C22×C412yes—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5#4112yes—
142C2×Dic15—21no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—21no—
146C2×Dic15C22×C412yes—
147C2×Dic15#4114yes—
148C4×D15—28no—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—21no—
153C2×C5×Dic3C22×C412yes—
154C2×C5×Dic3C2×D414yes—
155C4×C5×D3—28no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5C22×C412yes—
161C2×C3×Dic5C22×C412yes—
162C2×C3×Dic5#4114yes—
163#1203—28no—
164C22×D12—51no—
165C22×C4×D3—51no—
166C22×C4×D3C2×D511yescharacteristic
167C2×C3×C4⋊C4—52no—
168C2×C3×C42—51no—
169C2×C3×C42—51no—
170C2×C3×C42C2×D511yescharacteristic
171C2×(C2×D3)⋊C4—51no—
172C2×(C2×D3)⋊C4—51no—
173C2×(C2×D3)⋊C4—52no—
174C2×(C2×D3)⋊C4—52no—
175C2×(C2×D3)⋊C4—52no—
176C2×(C2×D3)⋊C4C2×D512yes—
177C2×C4⋊Dic3—51no—
178C2×Dic3⋊C4—52no—
179C2×Dic3⋊C4C2×D512yes—
180C2×C4×Dic3—51no—
181C2×C4×Dic3—52no—
182C2×C4×Dic3—52no—
183C2×C4×Dic3C2×D511yescharacteristic
184C4×D12—58no—
185#872—24no—
186#872—104no—
187C3×#95—52no—
188C3⋊#95—52no—
189C3⋊#95—52no—
190C24×C5—31no—
191C23×D5—31no—
192C22×C4×C5—32no—
193C22×C4×C5—31no—
194C22×C4×C5—34no—
195C22×C4×C5—62no—
196C22×C4×C5—62no—
197C22×C4×C5C22×D312yes—
198C22×C4×C5C22×D311yescharacteristic
199C2×C22⋊D5—34no—
200C2×C22⋊D5—64no—
201C22×Dic5—31no—
202C22×Dic5—32no—
203C22×Dic5C22×D312yes—
204C22×Dic5C22×D311yescharacteristic
205C22×Dic5C22×D311yescharacteristic
206C2×C4×D5—34no—
207C2×C4×D5—62no—
208C2×C4×D5—62no—
209C5×C4⋊C4—64no—
210C5×C22⋊C4—64no—
211C42×C5—22no—
212C42×C5—34no—
213C22⋊Dic5—34no—
214C22⋊Dic5—64no—
215#685—34no—
216#685—64no—
217#685—64no—
218#683—24no—
219#683—34no—
220#683—64no—
221C4×Dic5—22no—
222C4×Dic5—64no—
223C4×Dic5—62no—
224C4×Dic5—64no—
225C4×Dic5C4×D314yes—
226C2×C4×D4—151no—
227C2×#117—31no—
228C2×#117—151no—
229#390—152no—
230#389—152no—
231#388—152no—
232#388—152no—
233C4×C4⋊C4—51no—
234C4×C22⋊C4—151no—
235C4×C22⋊C4—151no—
236C43—151no—
237C22×C3×C5C23×C411yescharacteristic
238C22×C3×C5C22×D411yescharacteristic
239C22×C3×C5C2×#4111yescharacteristic
240C22×C3×C5C2×#4112yes—
241C22×C3×C5C2×#4112yes—
242C2×D15—22no—
243C2×D15—22no—
244C2×D15—22no—
245C2×D15—42no—
246C2×D15—42no—
247C2×C5×D3—22no—
248C2×C5×D3—22no—
249C2×C5×D3—22no—
250C2×C5×D3—42no—
251C2×C5×D3—42no—
252C3×C4×C5—42no—
253C3×C4×C5C4×D414yes—
254Dic15—22no—
255Dic15—24no—
256C3×Dic5—22no—
257C3×Dic5—42no—
258C3×Dic5#11714yescomplemented
259C5×Dic3—22no—
260C5×Dic3—24no—
261C23×D3—51no—
262C23×D3C22×D511yescharacteristic
263C22×C3×C4—51no—
264C22×C3×C4—51no—
265C22×C3×C4—52no—
266C22×C3×C4C22×D512yes—
267C22×C3×C4C22×D511yescharacteristic
268C22×Dic3—52no—
269C22×Dic3—51no—
270C22×Dic3C22×D511yescharacteristic
271C22×Dic3C22×D512yes—
272C2×D12—54no—
273C2×D12—104no—
274C2×C4×D3—22no—
275C2×C4×D3—22no—
276C2×C4×D3—54no—
277C2×C4×D3—102no—
278C2×C4×D3—102no—
279C2×C4×D3C4×D514yes—
280C3×C4⋊C4—104no—
281C3×C42—22no—
282C3×C42—54no—
283C3×C42—102no—
284(C2×D3)⋊C4—24no—
285(C2×D3)⋊C4—54no—
286(C2×D3)⋊C4—54no—
287(C2×D3)⋊C4—104no—
288(C2×D3)⋊C4—104no—
289(C2×D3)⋊C4—104no—
290C4⋊Dic3—54no—
291Dic3⋊C4—24no—
292Dic3⋊C4—104no—
293C4×Dic3—104no—
294C4×Dic3—104no—
295C4×Dic3—102no—
296C4×Dic3C22⋊D514yescomplemented
297C23×C5—32no—
298C23×C5—62no—
299C23×C5—61no—
300C23×C5—61no—
301C23×C5—62no—
302C23×C5C23×D311yescharacteristic
303C22×D5—32no—
304C22×D5—62no—
305C22×D5—61no—
306C22×D5—61no—
307C22×D5—62no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—32no—
312C2×C4×C5—34no—
313C2×C4×C5—62no—
314C2×C4×C5—61no—
315C2×C4×C5—61no—
316C2×C4×C5—62no—
317C2×C4×C5—68no—
318C2×C4×C5C2×C4×D312yes—
319C2×C4×C5D3×D412yes—
320C2×C4×C5#23912yes—
321C22⋊D5—68no—
322C2×Dic5—22no—
323C2×Dic5—22no—
324C2×Dic5—22no—
325C2×Dic5—22no—
326C2×Dic5—32no—
327C2×Dic5—34no—
328C2×Dic5—62no—
329C2×Dic5—61no—
330C2×Dic5—62no—
331C2×Dic5—61no—
332C2×Dic5C2×C4×D312yes—
333C2×Dic5C2×C4×D312yes—
334C2×Dic5#23514yes—
335C4×D5—68no—
336C22×D4—151no—
337C23×C4—31no—
338C23×C4—151no—
339C4×D4—158no—
340#117—64no—
341#117—304no—
342C2×C4⋊C4—32no—
343C2×C4⋊C4—52no—
344C2×C4⋊C4—151no—
345C2×C4⋊C4—152no—
346C2×C22⋊C4—32no—
347C2×C22⋊C4—151no—
348C2×C22⋊C4—151no—
349C2×C22⋊C4—152no—
350C2×C22⋊C4—152no—
351C2×C22⋊C4—152no—
352C2×C42—31no—
353C2×C42—51no—
354C2×C42—51no—
355C2×C42—152no—
356C2×C42—152no—
357C2×C42—151no—
358C2×C42D3×D511yescharacteristic
359#95—52no—
360#95—152no—
361#95—152no—
362C2×C3×C5C2×#11711yescharacteristic
363C2×C3×C5C2×C4×D411yescharacteristic
364C2×C3×C5C4×#4111yescharacteristic
365C2×C3×C5#52912yes—
366C2×C3×C5#53212yes—
367D15—42no—
368C5×D3—42no—
369C23×C3C23×D511yescharacteristic
370C22×D3—21no—
371C22×D3—22no—
372C22×D3—22no—
373C22×D3—21no—
374C22×D3—52no—
375C22×D3—101no—
376C22×D3—102no—
377C22×D3—102no—
378C22×D3—101no—
379C22×D3C2×C4×D512yes—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—52no—
384C2×C3×C4—54no—
385C2×C3×C4—52no—
386C2×C3×C4—102no—
387C2×C3×C4—102no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4C2×C4×D512yes—
391C2×C3×C4#70912yes—
392C2×C3×C4C2×C22⋊D512yes—
393C2×Dic3—21no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—21no—
397C2×Dic3—52no—
398C2×Dic3—54no—
399C2×Dic3—102no—
400C2×Dic3—101no—
401C2×Dic3—102no—
402C2×Dic3—101no—
403C2×Dic3C2×C4×D512yes—
404C2×Dic3C2×C22⋊D514yes—
405D12—108no—
406C4×D3—28no—
407C4×D3—108no—
408C22×C5—62no—
409C22×C5—62no—
410C22×C5—62no—
411C22×C5—122no—
412C22×C5—122no—
413C22×C5C22×C4×D311yescharacteristic
414C22×C5C2×#23512yes—
415C22×C5C2×D3×D411yescharacteristic
416C22×C5C2×#23911yescharacteristic
417C22×C5D3×#4112yes—
418C2×D5—62no—
419C2×D5—62no—
420C2×D5—62no—
421C2×D5—122no—
422C2×D5—122no—
423C4×C5—42no—
424C4×C5—62no—
425C4×C5—64no—
426C4×C5#89314yes—
427Dic5—22no—
428Dic5—42no—
429Dic5—62no—
430Dic5—64no—
431Dic5#87214yescomplemented
432C24—31no—
433C24—151no—
434C2×D4—154no—
435C2×D4—304no—
436C22×C4—31no—
437C22×C4—32no—
438C22×C4—34no—
439C22×C4—51no—
440C22×C4—51no—
441C22×C4—52no—
442C22×C4—62no—
443C22×C4—62no—
444C22×C4—152no—
445C22×C4—151no—
446C22×C4—154no—
447C22×C4—302no—
448C22×C4—302no—
449C22×C4C2×D3×D512yes—
450C22×C4C2×D3×D511yescharacteristic
451C4⋊C4—64no—
452C4⋊C4—104no—
453C4⋊C4—154no—
454C4⋊C4—304no—
455C22⋊C4—64no—
456C22⋊C4—154no—
457C22⋊C4—154no—
458C22⋊C4—304no—
459C22⋊C4—304no—
460C22⋊C4—304no—
461C42—22no—
462C42—34no—
463C42—54no—
464C42—102no—
465C42—304no—
466C42—304no—
467C42—302no—
468C3×C5#229311yescharacteristic, complemented, Hall
469C22×C3C22×C4×D511yescharacteristic
470C22×C3C2×#70911yescharacteristic
471C22×C3D5×#4112yes—
472C22×C3D5×#4112yes—
473C22×C3C22×C22⋊D511yescharacteristic
474C2×D3—22no—
475C2×D3—22no—
476C2×D3—22no—
477C2×D3—42no—
478C2×D3—42no—
479C2×D3—102no—
480C2×D3—102no—
481C2×D3—102no—
482C2×D3—202no—
483C2×D3—202no—
484C3×C4—42no—
485C3×C4—54no—
486C3×C4—102no—
487C3×C4—202no—
488C3×C4C4×C22⋊D514yes—
489Dic3—22no—
490Dic3—24no—
491Dic3—104no—
492Dic3—102no—
493C2×C5—122no—
494C2×C5C2×#87211yescharacteristic
495C2×C5C2×#89311yescharacteristic
496C2×C5#552211yescharacteristic
497C2×C5#554812yes—
498C2×C5#558012yes—
499D5—122no—
500C23—32no—
501C23—61no—
502C23—62no—
503C23—62no—
504C23—61no—
505C23—152no—
506C23—301no—
507C23—302no—
508C23—302no—
509C23—301no—
510C23C22×D3×D511yescharacteristic
511D4—308no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—32no—
516C2×C4—34no—
517C2×C4—52no—
518C2×C4—54no—
519C2×C4—52no—
520C2×C4—61no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—61no—
524C2×C4—68no—
525C2×C4—102no—
526C2×C4—102no—
527C2×C4—102no—
528C2×C4—102no—
529C2×C4—152no—
530C2×C4—154no—
531C2×C4—302no—
532C2×C4—301no—
533C2×C4—302no—
534C2×C4—301no—
535C2×C4—308no—
536C2×C4#676912yes—
537C2×C4C4×D3×D512yes—
538C2×C4D3×C22⋊D512yes—
539C2×C3D5×#11711yescharacteristic
540C2×C3#6585611yescharacteristic
541C2×C3#6586212yes—
542C2×C3C2×C4×C22⋊D511yescharacteristic
543C2×C3#6616612yes—
544D3—42no—
545D3—202no—
546C5#7361711yescharacteristic, complemented, Sylow
547C22—62no—
548C22—62no—
549C22—62no—
550C22—122no—
551C22—122no—
552C22—302no—
553C22—302no—
554C22—302no—
555C22—602no—
556C22—602no—
557C22C2×#676911yescharacteristic
558C22C2×C4×D3×D511yescharacteristic
559C22D5×#23512yes—
560C22#9201612yes—
561C22C2×D3×C22⋊D511yescharacteristic
562C4—42no—
563C4—54no—
564C4—62no—
565C4—64no—
566C4—102no—
567C4—202no—
568C4—302no—
569C4—304no—
570C4#9144614yes—
571C3#1061395611yescharacteristic, complemented, Sylow
572C2—122no—
573C2—602no—
574C2#1175258712yes—
575C2#1175266711yescharacteristic
576C2D5×#87211yescharacteristic
577C2C2×#9144611yescharacteristic
578C2#1175453912yes—
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1203C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2293
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C5×#872C2semidirect
3. C2×#91386C2semidirect
4. C4×#6714C2semidirect
5. C3×C4×#683C2semidirect
7. #11748721C2semidirect
8. C4×(C2×D3)⋊Dic5C2semidirect
9. #11748669C2semidirect
10. C4×Dic3×Dic5C2semidirect
11. #11748629C2semidirect
34. C4×#1203C4semidirect
49. C4×#683D3semidirect
75. C4×C5×Dic3D4semidirect
89. C2×#872D5semidirect
258. C3×Dic5#117semidirect
296. C4×Dic3C22⋊D5semidirect
431. Dic5#872semidirect
468. C3×C5#2293semidirect
546. C5#73617semidirect
571. C3#10613956semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8722
C2×C4×#12032
C2×#913862
C4×#67142
C3×C4×#6832
#117489092
#117487212
C4×(C2×D3)⋊Dic52
#117486692
C4×Dic3×Dic52
#117486292
#106139563
#736175