Finite Group Databasebeta

← #14320633

Subgroups — #14320633

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1203C211yesmaximal, characteristic
2C2×C4×#1200C211yesmaximal, characteristic, complemented
3C2×#91371C211yesmaximal, characteristic, complemented
4C4×#6714C211yesmaximal, characteristic, complemented
5C4×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C3×#65221C211yesmaximal, characteristic, complemented
7#11748919C212yesmaximal
8#11748895C212yesmaximal, complemented
9C4×#6668C211yesmaximal, characteristic, complemented
10#11748723C212yesmaximal, complemented
11#11748654C212yesmaximal, complemented
12#10605293—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×C4×C5×D3C2211yescharacteristic
15C22×#1203C2211yescharacteristic
16C22×#1200C2212yes—
17C2×C3×C42×C5C2211yescharacteristic
18C2×#6714C2212yes—
19C2×C4×Dic15C2211yescharacteristic
20C2×C5×(C2×D3)⋊C4C2212yes—
21C2×C4×C5×Dic3C2211yescharacteristic
22C2×C3×C4×Dic5C2211yescharacteristic
23C2×C3×C4×Dic5C2211yescharacteristic
24C2×Dic3⋊Dic5C2212yes—
25C2×#6668C2212yes—
26C2×#6668C2211yescharacteristic
27C2×#6667C2211yescharacteristic
28C2×(C2×D3)⋊Dic5C2212yes—
29C2×(C2×D3)⋊Dic5C2211yescharacteristic
30C2×Dic3×Dic5C2212yes—
31C4×#1203C418yescomplemented
32C4×#1200—24no—
33#91371—24no—
34#91115C2212yes—
35C5×C3⋊#95C2212yes—
36C3×#3963C2212yes—
37C3×#3963C2212yes—
38#90994C2212yes—
39#73414—51nomaximal, Hall
40C2×C4×C22⋊D5—31no—
41C2×#4072—31no—
42C2×C42×D5—31no—
43C4×C5×C22⋊C4—31no—
44#65245—32no—
45#65234—32no—
46C4×#685—31no—
47#65221D311yescharacteristic, complemented
48C4×#683—31no—
49#64957—32no—
50#64944—32no—
51C23×D15C2311yescharacteristic
52C23×C5×D3C2311yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2311yescharacteristic
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×C414yescomplemented
65C22×C3×Dic5C2311yescharacteristic
66C22×C3×Dic5C2311yescharacteristic
67C22×C3×Dic5C2312yes—
68C2×#1203—24no—
69C2×#1203C2×C414yes—
70C2×#1200—24no—
71C2×#1200—24no—
72C2×#1200—24no—
73C3×C42×C5—22no—
74#6714—24no—
75C4×Dic15—22no—
76C5×(C2×D3)⋊C4—24no—
77C4×C5×Dic3—22no—
78C3×C4×Dic5C2×C414yescomplemented
79C3×C4×Dic5D414yescomplemented
80Dic3⋊Dic5—24no—
81#6668—24no—
82#6668C2×C414yescomplemented
83#6667C2×C414yes—
84(C2×D3)⋊Dic5—24no—
85(C2×D3)⋊Dic5C2×C414yescomplemented
86Dic3×Dic5—24no—
87C2×C4×D12—51no—
88C2×#872—51no—
89C2×C42×D3—51no—
90C3×#376—51no—
91C4×(C2×D3)⋊C4—51no—
92C4×(C2×D3)⋊C4D511yescharacteristic, complemented
93C4×C4⋊Dic3—51no—
94#4670—52no—
95#4668—52no—
96#4665—52no—
97#4653—52no—
98C23×C4×C5—31no—
99C22×C22⋊D5—31no—
100C22×C4×D5—31no—
101C22×C4×D5—32no—
102C2×C5×C22⋊C4—32no—
103C2×C42×C5—31no—
104C2×C42×C5C2×D311yescharacteristic
105C2×C22⋊Dic5—31no—
106C2×C22⋊Dic5—32no—
107C4×C22⋊D5—38no—
108C2×#685—31no—
109C2×#685—32no—
110#4072—64no—
111C2×C4⋊Dic5—32no—
112C2×#683—31no—
113C2×#683—32no—
114C2×C4×Dic5—31no—
115C2×C4×Dic5—32no—
116C2×C4×Dic5C2×D311yescharacteristic
117C2×C4×Dic5C2×D311yescharacteristic
118C42×D5—64no—
119C5×#95—32no—
120#3963—32no—
121#3963—32no—
122#3963C2×D312yes—
123#3963C2×D312yes—
124#2290—151noSylow
125C23×C3×C5C2411yescharacteristic
126C22×D15—21no—
127C22×D15—22no—
128C22×D15—21no—
129C22×D15C22×C412yes—
130C22×D15#4114yes—
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—21no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15C22×C412yes—
148C4×D15—28no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—21no—
153C2×C5×Dic3C22×C412yes—
154C2×C5×Dic3#4114yes—
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×Dic5C2×D414yes—
163#1203—28no—
164#1200—216no—
165C22×D12—51no—
166C22×C4×D3—51no—
167C22×C4×D3—52no—
168C22×C4×D3C2×D511yescharacteristic
169C2×C3×C42—51no—
170C2×C3×C42—51no—
171C2×C3×C42C2×D511yescharacteristic
172C2×(C2×D3)⋊C4—51no—
173C2×(C2×D3)⋊C4—51no—
174C2×(C2×D3)⋊C4—52no—
175C2×(C2×D3)⋊C4—52no—
176C2×(C2×D3)⋊C4C2×D512yes—
177C2×C4⋊Dic3—51no—
178C2×C4⋊Dic3—52no—
179C2×Dic3⋊C4—52no—
180C2×C4×Dic3—51no—
181C2×C4×Dic3—52no—
182C2×C4×Dic3C2×D511yescharacteristic
183C4×D12—58no—
184#872—104no—
185C42×D3—104no—
186C3×#95—52no—
187C3×#95—52no—
188C3⋊#95—52no—
189C3⋊#95—52no—
190C3⋊#95C2×D512yes—
191C24×C5—31no—
192C23×D5—31no—
193C22×C4×C5—32no—
194C22×C4×C5—31no—
195C22×C4×C5—34no—
196C22×C4×C5—62no—
197C22×C4×C5—62no—
198C22×C4×C5C22×D312yes—
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—34no—
201C2×C22⋊D5—64no—
202C22×Dic5—31no—
203C22×Dic5—32no—
204C22×Dic5C22×D311yescharacteristic
205C22×Dic5C22×D311yescharacteristic
206C22×Dic5C22×D312yes—
207C2×C4×D5—34no—
208C2×C4×D5—64no—
209C2×C4×D5—64no—
210C2×C4×D5—62no—
211C2×C4×D5—62no—
212C2×C4×D5—64no—
213C5×C22⋊C4—64no—
214C42×C5—22no—
215C42×C5—62no—
216C22⋊Dic5—34no—
217C22⋊Dic5—64no—
218#685—34no—
219#685—64no—
220C4⋊Dic5—64no—
221#683—34no—
222#683—64no—
223C4×Dic5—62no—
224C4×Dic5—64no—
225C4×Dic5C4×D314yescomplemented
226C4×Dic5D1214yescomplemented
227C2×C4×D4—151no—
228C2×#117—151no—
229C22×C42—151no—
230#388—152no—
231#387—152no—
232#386—152no—
233#385—152no—
234C4×C4⋊C4—151no—
235C4×C22⋊C4—31no—
236C4×C22⋊C4—151no—
237#376—51no—
238C22×C3×C5C23×C411yescharacteristic
239C22×C3×C5C22×D411yescharacteristic
240C22×C3×C5C2×#4112yes—
241C22×C3×C5C2×#4111yescharacteristic
242C22×C3×C5C2×#4112yes—
243C2×D15—22no—
244C2×D15—22no—
245C2×D15—24no—
246C2×D15—24no—
247C2×D15#11714yescomplemented
248C2×C5×D3—22no—
249C2×C5×D3—22no—
250C2×C5×D3—22no—
251C2×C5×D3—42no—
252C2×C5×D3—42no—
253C3×C4×C5—42no—
254C3×C4×C5C4×D414yes—
255Dic15—22no—
256Dic15—42no—
257C3×Dic5—22no—
258C3×Dic5—22no—
259C3×Dic5—24no—
260C5×Dic3—22no—
261C5×Dic3—24no—
262C23×D3—51no—
263C23×D3C22×D511yescharacteristic
264C22×C3×C4—51no—
265C22×C3×C4—52no—
266C22×C3×C4—51no—
267C22×C3×C4C22×D512yes—
268C22×C3×C4C22×D511yescharacteristic
269C22×Dic3—51no—
270C22×Dic3—52no—
271C22×Dic3C22×D511yescharacteristic
272C22×Dic3C22×D512yes—
273C2×D12—54no—
274C2×D12—104no—
275C2×C4×D3—22no—
276C2×C4×D3—22no—
277C2×C4×D3—54no—
278C2×C4×D3—104no—
279C2×C4×D3—104no—
280C2×C4×D3—102no—
281C2×C4×D3—102no—
282C2×C4×D3—104no—
283C2×C4×D3C4×D514yescomplemented
284C3×C42—22no—
285C3×C42—54no—
286C3×C42—54no—
287(C2×D3)⋊C4—24no—
288(C2×D3)⋊C4—54no—
289(C2×D3)⋊C4—54no—
290(C2×D3)⋊C4—104no—
291(C2×D3)⋊C4—104no—
292C4⋊Dic3—54no—
293C4⋊Dic3—104no—
294Dic3⋊C4—104no—
295C4×Dic3—22no—
296C4×Dic3—104no—
297C4×Dic3—102no—
298C23×C5—32no—
299C23×C5—61no—
300C23×C5—61no—
301C23×C5—62no—
302C23×C5—62no—
303C23×C5C23×D311yescharacteristic
304C22×D5—32no—
305C22×D5—34no—
306C22×D5—61no—
307C22×D5—61no—
308C22×D5—62no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—32no—
313C2×C4×C5—34no—
314C2×C4×C5—62no—
315C2×C4×C5—61no—
316C2×C4×C5—61no—
317C2×C4×C5—62no—
318C2×C4×C5—68no—
319C2×C4×C5C2×C4×D312yes—
320C2×C4×C5C2×D1212yes—
321C2×C4×C5#23512yes—
322C22⋊D5—68no—
323C2×Dic5—22no—
324C2×Dic5—22no—
325C2×Dic5—22no—
326C2×Dic5—22no—
327C2×Dic5—32no—
328C2×Dic5—61no—
329C2×Dic5—61no—
330C2×Dic5—62no—
331C2×Dic5—62no—
332C2×Dic5—62no—
333C2×Dic5C2×C4×D312yes—
334C2×Dic5C2×C4×D312yes—
335C2×Dic5C2×D1214yes—
336C4×D5—616no—
337C4×D5—68no—
338C22×D4—151no—
339C23×C4—31no—
340C23×C4—152no—
341C23×C4—151no—
342C4×D4—158no—
343#117—304no—
344C2×C4⋊C4—151no—
345C2×C4⋊C4—152no—
346C2×C4⋊C4—152no—
347C2×C22⋊C4—32no—
348C2×C22⋊C4—151no—
349C2×C22⋊C4—151no—
350C2×C22⋊C4—152no—
351C2×C22⋊C4—152no—
352C2×C42—31no—
353C2×C42—51no—
354C2×C42—51no—
355C2×C42—152no—
356C2×C42—151no—
357C2×C42—304no—
358C2×C42D3×D511yescharacteristic
359#95—32no—
360#95—52no—
361#95—52no—
362#95—152no—
363#95—152no—
364C2×C3×C5C2×#11711yescharacteristic
365C2×C3×C5C2×C4×D411yescharacteristic
366C2×C3×C5C4×#4111yescharacteristic
367C2×C3×C5#52512yes—
368C2×C3×C5#52912yes—
369D15—24no—
370C5×D3—42no—
371C23×C3C23×D511yescharacteristic
372C22×D3—22no—
373C22×D3—21no—
374C22×D3—21no—
375C22×D3—22no—
376C22×D3—52no—
377C22×D3—54no—
378C22×D3—102no—
379C22×D3—101no—
380C22×D3—101no—
381C22×D3C2×C4×D512yes—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—52no—
386C2×C3×C4—52no—
387C2×C3×C4—54no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4—102no—
391C2×C3×C4—102no—
392C2×C3×C4C2×C4×D512yes—
393C2×C3×C4D4×D512yes—
394C2×C3×C4#71112yes—
395C2×Dic3—22no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—22no—
399C2×Dic3—52no—
400C2×Dic3—101no—
401C2×Dic3—101no—
402C2×Dic3—102no—
403C2×Dic3—102no—
404C2×Dic3—102no—
405C2×Dic3C2×C4×D512yes—
406C2×Dic3#70914yes—
407D12—108no—
408C4×D3—28no—
409C4×D3—1016no—
410C4×D3—108no—
411C22×C5—62no—
412C22×C5—62no—
413C22×C5—62no—
414C22×C5—122no—
415C22×C5—122no—
416C22×C5C22×C4×D311yescharacteristic
417C22×C5C22×D1211yescharacteristic
418C22×C5C2×#23511yescharacteristic
419C22×C5D3×#4112yes—
420C22×C5D3×#4112yes—
421C2×D5—34no—
422C2×D5—62no—
423C2×D5—62no—
424C2×D5—64no—
425C2×D5—64no—
426C4×C5—42no—
427C4×C5—62no—
428C4×C5—64no—
429C4×C5C4×D1214yes—
430Dic5—22no—
431Dic5—22no—
432Dic5—24no—
433Dic5—62no—
434Dic5—122no—
435C24—31no—
436C24—151no—
437C2×D4—154no—
438C2×D4—304no—
439C22×C4—31no—
440C22×C4—32no—
441C22×C4—34no—
442C22×C4—51no—
443C22×C4—52no—
444C22×C4—51no—
445C22×C4—62no—
446C22×C4—62no—
447C22×C4—151no—
448C22×C4—154no—
449C22×C4—152no—
450C22×C4—304no—
451C22×C4—304no—
452C22×C4—304no—
453C22×C4—302no—
454C22×C4—302no—
455C22×C4C2×D3×D512yes—
456C22×C4C2×D3×D511yescharacteristic
457C4⋊C4—154no—
458C4⋊C4—304no—
459C4⋊C4—304no—
460C22⋊C4—64no—
461C22⋊C4—154no—
462C22⋊C4—154no—
463C22⋊C4—304no—
464C22⋊C4—304no—
465C42—22no—
466C42—54no—
467C42—54no—
468C42—62no—
469C42—304no—
470C42—302no—
471C3×C5#229011yescharacteristic, complemented, Hall
472C22×C3C22×C4×D511yescharacteristic
473C22×C3C2×#70912yes—
474C22×C3C2×D4×D511yescharacteristic
475C22×C3C2×#71111yescharacteristic
476C22×C3D5×#4112yes—
477C2×D3—22no—
478C2×D3—22no—
479C2×D3—22no—
480C2×D3—42no—
481C2×D3—42no—
482C2×D3—54no—
483C2×D3—102no—
484C2×D3—102no—
485C2×D3—104no—
486C2×D3—104no—
487C3×C4—42no—
488C3×C4—102no—
489C3×C4—102no—
490C3×C4—104no—
491C3×C4#402714yes—
492Dic3—22no—
493Dic3—24no—
494Dic3—102no—
495Dic3—202no—
496C2×C5—122no—
497C2×C5C2×C4×D1211yescharacteristic
498C2×C5D3×#11711yescharacteristic
499C2×C5#552211yescharacteristic
500C2×C5#552412yes—
501C2×C5#552812yes—
502D5—64no—
503C23—32no—
504C23—61no—
505C23—62no—
506C23—62no—
507C23—61no—
508C23—152no—
509C23—154no—
510C23—301no—
511C23—302no—
512C23—301no—
513C23C22×D3×D511yescharacteristic
514D4—308no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—32no—
519C2×C4—34no—
520C2×C4—52no—
521C2×C4—52no—
522C2×C4—54no—
523C2×C4—62no—
524C2×C4—61no—
525C2×C4—62no—
526C2×C4—61no—
527C2×C4—68no—
528C2×C4—102no—
529C2×C4—102no—
530C2×C4—102no—
531C2×C4—102no—
532C2×C4—152no—
533C2×C4—3016no—
534C2×C4—301no—
535C2×C4—301no—
536C2×C4—308no—
537C2×C4—302no—
538C2×C4—302no—
539C2×C4—302no—
540C2×C4C4×D3×D512yes—
541C2×C4D5×D1212yes—
542C2×C4#678212yes—
543C2×C3C4×#70911yescharacteristic
544C2×C3C2×#402711yescharacteristic
545C2×C3D5×#11711yescharacteristic
546C2×C3#6588112yes—
547C2×C3#6589112yes—
548D3—42no—
549D3—104no—
550C5#7341411yescharacteristic, complemented, Sylow
551C22—62no—
552C22—62no—
553C22—62no—
554C22—122no—
555C22—122no—
556C22—154no—
557C22—304no—
558C22—302no—
559C22—304no—
560C22—302no—
561C22C2×C4×D3×D511yescharacteristic
562C22C2×D5×D1211yescharacteristic
563C22D3×#70912yes—
564C22#9201612yes—
565C22C2×#678211yescharacteristic
566C4—42no—
567C4—64no—
568C4—62no—
569C4—102no—
570C4—104no—
571C4—102no—
572C4—302no—
573C4—602no—
574C4#9140514yes—
575C3#1060529311yescharacteristic, complemented, Sylow
576C2—122no—
577C2—304no—
578C2#1175266611yescharacteristic
579C2#1175272311yescharacteristic
580C2#1175273012yes—
581C2C2×#9140511yescharacteristic
582C2#1175443712yes—
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#2290
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
2. C2×C4×#1200C2semidirect
3. C2×#91371C2semidirect
4. C4×#6714C2semidirect
5. C4×C5×(C2×D3)⋊C4C2semidirect
6. C3×#65221C2semidirect
8. #11748895C2semidirect
9. C4×#6668C2semidirect
10. #11748723C2semidirect
11. #11748654C2semidirect
31. C4×#1203C4semidirect
47. #65221D3semidirect
64. C2×C4×C5×D3C2×C4semidirect
78. C3×C4×Dic5C2×C4semidirect
79. C3×C4×Dic5D4semidirect
82. #6668C2×C4semidirect
85. (C2×D3)⋊Dic5C2×C4semidirect
92. C4×(C2×D3)⋊C4D5semidirect
225. C4×Dic5C4×D3semidirect
226. C4×Dic5D12semidirect
247. C2×D15#117semidirect
283. C2×C4×D3C4×D5semidirect
471. C3×C5#2290semidirect
550. C5#73414semidirect
575. C3#10605293semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12032
C2×C4×#12002
C2×#913712
C4×#67142
C4×C5×(C2×D3)⋊C42
C3×#652212
#117489192
#117488952
C4×#66682
#117487232
#117486542
#106052933
#734145