Finite Group Databasebeta

← #14323784

Subgroups — #14323784

Order 1920.

1112 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#872C211yesmaximal, characteristic
2C2×#91365C211yesmaximal, characteristic
3C2×#91340C211yesmaximal, characteristic, complemented
4#11751030C211yesmaximal, characteristic, complemented
5C3×#65217C211yesmaximal, characteristic, complemented
6#11748786C211yesmaximal, characteristic
7#11748721C212yesmaximal
8#11748718C212yesmaximal
9Dic3×C4⋊Dic5C211yesmaximal, characteristic, complemented
10#11748655C212yesmaximal, complemented
11#11748629C212yesmaximal, complemented
12#10613966—31nomaximal, Hall
13C22×Dic30C2211yescharacteristic
14C22×C4×C5×D3C2211yescharacteristic
15C2×C3×C42×C5C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C5×(C2×D3)⋊C4C2211yescharacteristic
18C2×C5×(C2×D3)⋊C4C2211yescharacteristic
19C2×C5×Dic3⋊C4C2211yescharacteristic
20C2×C5×Dic3⋊C4C2211yescharacteristic
21C2×C4×C5×Dic3C2211yescharacteristic
22C5×#872—24no—
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C2×C3×#683C2212yes—
26C2×#6669C2212yes—
27C2×#6668C2212yes—
28C2×(C2×D3)⋊Dic5C2212yes—
29C2×(C2×D3)⋊Dic5C2212yes—
30C2×Dic3×Dic5C2212yes—
31C2×Dic3×Dic5C2212yes—
32#91365C418yescomplemented
33#91340—24no—
34#91115C2212yes—
35#91115C2212yes—
36C3×#3963C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#76197—51nomaximal, Hall
40C2×C5×#117—31no—
41C2×#4070—31no—
42C2×C4×Dic10—31no—
43#65501—31no—
44#65267—32no—
45#65261—32no—
46#65234—32no—
47#65233—32no—
48C4×C4⋊Dic5—31no—
49#65218—31no—
50#65217D311yescharacteristic, complemented
51C23×C5×D3C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2312yes—
57C2×Dic30—22no—
58C2×Dic30—22no—
59C2×Dic30C2×C414yes—
60C22×C5×Dic3C2311yescharacteristic
61C22×C5×Dic3C2311yescharacteristic
62C22×C5×Dic3C2311yescharacteristic
63C2×C4×C5×D3—22no—
64C2×C4×C5×D3—22no—
65C2×C4×C5×D3C2×C414yes—
66C22×C3×Dic5C2312yes—
67C22×C3×Dic5C2312yes—
68C3×C42×C5—22no—
69C4⋊Dic15—22no—
70C5×(C2×D3)⋊C4—22no—
71C5×(C2×D3)⋊C4—22no—
72C5×Dic3⋊C4—22no—
73C5×Dic3⋊C4—22no—
74C4×C5×Dic3D414yes—
75C3×C4⋊Dic5—22no—
76C3×C4⋊Dic5C2×C414yes—
77C3×#683—42no—
78#6669—24no—
79#6668C2×C418yes—
80(C2×D3)⋊Dic5—42no—
81(C2×D3)⋊Dic5C2×C418yes—
82Dic3×Dic5—24no—
83Dic3×Dic5—42no—
84C2×#897—51no—
85C2×#887—51no—
86C2×#872D511yescharacteristic
87C3×#389—51no—
88#4990—52no—
89#4987—51no—
90Dic3×C4⋊C4—51no—
91#4972—52no—
92#4929—51no—
93#4669—52no—
94#4654—52no—
95C23×C4×C5—31no—
96C22×Dic10—31no—
97C5×#117—64no—
98C2×C5×C4⋊C4—31no—
99C2×C5×C4⋊C4—31no—
100C2×C5×C22⋊C4—31no—
101C2×C5×C22⋊C4—31no—
102C2×C42×C5—31no—
103C2×C42×C5C2×D311yescharacteristic
104C2×C22⋊Dic5—32no—
105C2×C22⋊Dic5—32no—
106C2×C4⋊Dic5—31no—
107C2×C4⋊Dic5C2×D311yescharacteristic
108C2×C4⋊Dic5C2×D311yescharacteristic
109#4070—38no—
110C2×#683—32no—
111C2×#683—32no—
112C2×#683C2×D312yes—
113C2×C4×Dic5—32no—
114C2×C4×Dic5—32no—
115C4×Dic10—64no—
116#3963—32no—
117#3963—32no—
118#3963—32no—
119#3963—32no—
120#3963C2×D312yes—
121#2323—151noSylow
122C23×C3×C5C2411yescharacteristic
123C22×C5×D3—21no—
124C22×C5×D3—21no—
125C22×C5×D3—21no—
126C22×C5×D3—21no—
127C22×C5×D3—21no—
128C22×C5×D3—21no—
129C22×C5×D3C22×C412yes—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5C22×C412yes—
137C2×C3×C4×C5C2×D412yes—
138C2×C3×C4×C5#4112yes—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15—22no—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15C22×C414yes—
145Dic30—28no—
146C2×C5×Dic3—21no—
147C2×C5×Dic3—21no—
148C2×C5×Dic3—21no—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—21no—
152C2×C5×Dic3C22×C412yes—
153C2×C5×Dic3C2×D412yes—
154C2×C5×Dic3C2×D412yes—
155C4×C5×D3—28no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5C22×C414yes—
162C22×C4×D3C2×D511yescharacteristic
163C22×Dic6—51no—
164C2×C3×C4⋊C4—51no—
165C2×C3×C4⋊C4—51no—
166C2×C3×C4⋊C4—52no—
167C2×C3×C42C2×D511yescharacteristic
168C2×(C2×D3)⋊C4—52no—
169C2×(C2×D3)⋊C4—52no—
170C2×(C2×D3)⋊C4C2×D511yescharacteristic
171C2×(C2×D3)⋊C4C2×D511yescharacteristic
172C2×C4⋊Dic3—52no—
173C2×C4⋊Dic3—51no—
174C2×Dic3⋊C4—52no—
175C2×Dic3⋊C4C2×D511yescharacteristic
176C2×Dic3⋊C4C2×D511yescharacteristic
177C2×C4×Dic3—52no—
178C2×C4×Dic3—52no—
179C2×C4×Dic3C2×D511yescharacteristic
180#897—58no—
181#887—104no—
182#872—24no—
183C3×#95—52no—
184C3⋊#95—52no—
185C3⋊#95—52no—
186C3⋊#95—52no—
187C3⋊#95—52no—
188C24×C5—31no—
189C22×C4×C5—31no—
190C22×C4×C5—31no—
191C22×C4×C5—31no—
192C22×C4×C5—34no—
193C22×C4×C5—62no—
194C22×C4×C5—62no—
195C22×C4×C5C22×D311yescharacteristic
196C22×C4×C5C22×D311yescharacteristic
197C22×C4×C5C22×D311yescharacteristic
198C22×Dic5—32no—
199C22×Dic5—32no—
200C22×Dic5C22×D312yes—
201C22×Dic5C22×D312yes—
202C2×Dic10—34no—
203C2×Dic10—62no—
204C2×Dic10—62no—
205C5×C4⋊C4—62no—
206C5×C4⋊C4—62no—
207C5×C22⋊C4—62no—
208C5×C22⋊C4—62no—
209C42×C5—22no—
210C42×C5—34no—
211C22⋊Dic5—38no—
212C22⋊Dic5—122no—
213C4⋊Dic5—22no—
214C4⋊Dic5—62no—
215C4⋊Dic5C4×D314yes—
216#683—38no—
217#683—42no—
218#683—64no—
219C4×Dic5—64no—
220C4×Dic5—122no—
221C2×C22⋊Q8—151no—
222C2×C4×Q8—151no—
223C2×#117—31no—
224#391—151no—
225#389—51no—
226#389—152no—
227#388—152no—
228#388—152no—
229#387—152no—
230#380—151no—
231C4×C4⋊C4—151no—
232C22×C3×C5C23×C411yescharacteristic
233C22×C3×C5C22×D411yescharacteristic
234C22×C3×C5C2×#4111yescharacteristic
235C22×C3×C5H(5,𝔽2)11yescharacteristic
236C22×C3×C52−1+411yescharacteristic
237C22×C3×C52−1+411yescharacteristic
238C22×C3×C52−1+411yescharacteristic
239C2×C5×D3—22no—
240C2×C5×D3—22no—
241C2×C5×D3—22no—
242C2×C5×D3—41no—
243C2×C5×D3—41no—
244C2×C5×D3—41no—
245C2×C5×D3—41no—
246C3×C4×C5—41no—
247C3×C4×C5—41no—
248C3×C4×C5C4×D414yes—
249Dic15—24no—
250Dic15—42no—
251C3×Dic5—24no—
252C3×Dic5—42no—
253C5×Dic3—22no—
254C5×Dic3—22no—
255C5×Dic3—22no—
256C23×D3C22×D511yescharacteristic
257C22×C3×C4—52no—
258C22×C3×C4—52no—
259C22×C3×C4C22×D511yescharacteristic
260C22×C3×C4C22×D511yescharacteristic
261C22×C3×C4C22×D511yescharacteristic
262C22×Dic3—52no—
263C22×Dic3—52no—
264C22×Dic3C22×D511yescharacteristic
265C22×Dic3C22×D511yescharacteristic
266C22×Dic3C22×D511yescharacteristic
267C2×C4×D3—22no—
268C2×C4×D3—22no—
269C2×C4×D3C4×D514yes—
270C2×Dic6—54no—
271C2×Dic6—102no—
272C2×Dic6—102no—
273C3×C4⋊C4—54no—
274C3×C4⋊C4—102no—
275C3×C4⋊C4—202no—
276C3×C42—22no—
277(C2×D3)⋊C4—22no—
278(C2×D3)⋊C4—22no—
279(C2×D3)⋊C4—58no—
280(C2×D3)⋊C4—202no—
281C4⋊Dic3—58no—
282C4⋊Dic3—102no—
283Dic3⋊C4—22no—
284Dic3⋊C4—22no—
285Dic3⋊C4—104no—
286C4×Dic3—104no—
287C4×Dic3—202no—
288C4×Dic3C22⋊D514yes—
289C23×C5—32no—
290C23×C5—61no—
291C23×C5—61no—
292C23×C5—61no—
293C23×C5—61no—
294C23×C5—61no—
295C23×C5—61no—
296C23×C5C23×D311yescharacteristic
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—21no—
303C2×C4×C5—32no—
304C2×C4×C5—32no—
305C2×C4×C5—32no—
306C2×C4×C5—61no—
307C2×C4×C5—61no—
308C2×C4×C5—61no—
309C2×C4×C5—61no—
310C2×C4×C5—61no—
311C2×C4×C5—61no—
312C2×C4×C5—68no—
313C2×C4×C5C2×C4×D312yes—
314C2×C4×C5D3×D412yes—
315C2×C4×C5#23912yes—
316C2×Dic5—22no—
317C2×Dic5—22no—
318C2×Dic5—22no—
319C2×Dic5—22no—
320C2×Dic5—22no—
321C2×Dic5—34no—
322C2×Dic5—62no—
323C2×Dic5—62no—
324C2×Dic5—62no—
325C2×Dic5—62no—
326C2×Dic5—62no—
327C2×Dic5C2×C4×D314yes—
328Dic10—68no—
329C22×Q8—151no—
330C23×C4—31no—
331C22⋊Q8—158no—
332C4×Q8—304no—
333#117—64no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—31no—
336C2×C4⋊C4—51no—
337C2×C4⋊C4—51no—
338C2×C4⋊C4—52no—
339C2×C4⋊C4—152no—
340C2×C4⋊C4—152no—
341C2×C4⋊C4—151no—
342C2×C22⋊C4—31no—
343C2×C22⋊C4—31no—
344C2×C22⋊C4—152no—
345C2×C22⋊C4—152no—
346C2×C42—31no—
347C2×C42—152no—
348C2×C42—152no—
349C2×C42D3×D511yescharacteristic
350#95—52no—
351#95—152no—
352#95—152no—
353#95—152no—
354#95—152no—
355C2×C3×C5C2×C4×D411yescharacteristic
356C2×C3×C5#51911yescharacteristic
357C2×C3×C5#52011yescharacteristic
358C2×C3×C5#53611yescharacteristic
359C2×C3×C5#53711yescharacteristic
360C2×C3×C5#54111yescharacteristic
361C2×C3×C5#54211yescharacteristic
362C5×D3—42no—
363C23×C3C23×D511yescharacteristic
364C22×D3—21no—
365C22×D3—21no—
366C22×D3—21no—
367C22×D3—21no—
368C22×D3—21no—
369C22×D3—21no—
370C22×D3C2×C4×D512yes—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—54no—
378C2×C3×C4—102no—
379C2×C3×C4—102no—
380C2×C3×C4—102no—
381C2×C3×C4—102no—
382C2×C3×C4—102no—
383C2×C3×C4C2×C4×D512yes—
384C2×C3×C4#70912yes—
385C2×C3×C4C2×C22⋊D512yes—
386C2×Dic3—21no—
387C2×Dic3—21no—
388C2×Dic3—21no—
389C2×Dic3—21no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—54no—
393C2×Dic3—102no—
394C2×Dic3—102no—
395C2×Dic3—102no—
396C2×Dic3—102no—
397C2×Dic3—102no—
398C2×Dic3C2×C4×D512yes—
399C2×Dic3C2×C22⋊D512yes—
400C2×Dic3C2×C22⋊D512yes—
401C4×D3—28no—
402Dic6—108no—
403C22×C5—62no—
404C22×C5—62no—
405C22×C5—62no—
406C22×C5—121no—
407C22×C5—121no—
408C22×C5—121no—
409C22×C5—121no—
410C22×C5C22×C4×D311yescharacteristic
411C22×C5C2×D3×D411yescharacteristic
412C22×C5#100411yescharacteristic
413C22×C5C2×#23911yescharacteristic
414C22×C5#100711yescharacteristic
415C22×C5#101011yescharacteristic
416C22×C5#101011yescharacteristic
417C4×C5—41no—
418C4×C5—41no—
419C4×C5—62no—
420C4×C5—62no—
421C4×C5—62no—
422C4×C5#89314yes—
423Dic5—24no—
424Dic5—42no—
425Dic5—64no—
426Dic5—122no—
427C24—31no—
428C2×Q8—154no—
429C2×Q8—302no—
430C2×Q8—302no—
431C22×C4—31no—
432C22×C4—31no—
433C22×C4—31no—
434C22×C4—34no—
435C22×C4—52no—
436C22×C4—52no—
437C22×C4—62no—
438C22×C4—62no—
439C22×C4—152no—
440C22×C4—152no—
441C22×C4C2×D3×D511yescharacteristic
442C22×C4C2×D3×D511yescharacteristic
443C22×C4C2×D3×D511yescharacteristic
444C4⋊C4—54no—
445C4⋊C4—62no—
446C4⋊C4—62no—
447C4⋊C4—102no—
448C4⋊C4—158no—
449C4⋊C4—202no—
450C4⋊C4—304no—
451C4⋊C4—302no—
452C22⋊C4—62no—
453C22⋊C4—62no—
454C22⋊C4—158no—
455C22⋊C4—602no—
456C42—22no—
457C42—34no—
458C42—304no—
459C42—602no—
460C3×C5#232311yescharacteristic, complemented, Hall
461C22×C3C22×C4×D511yescharacteristic
462C22×C3C2×#70911yescharacteristic
463C22×C3#414911yescharacteristic
464C22×C3#415011yescharacteristic
465C22×C3#415011yescharacteristic
466C22×C3#415011yescharacteristic
467C22×C3C22×C22⋊D511yescharacteristic
468C2×D3—22no—
469C2×D3—22no—
470C2×D3—22no—
471C2×D3—41no—
472C2×D3—41no—
473C2×D3—41no—
474C2×D3—41no—
475C3×C4—41no—
476C3×C4—41no—
477C3×C4—104no—
478C3×C4—202no—
479C3×C4C4×C22⋊D514yes—
480Dic3—22no—
481Dic3—22no—
482Dic3—22no—
483Dic3—104no—
484Dic3—202no—
485C2×C5—122no—
486C2×C5C2×#89311yescharacteristic
487C2×C5#554611yescharacteristic
488C2×C5#557211yescharacteristic
489C2×C5#560811yescharacteristic
490C2×C5#562811yescharacteristic
491C2×C5#569811yescharacteristic
492C2×C5#573311yescharacteristic
493C23—32no—
494C23—61no—
495C23—61no—
496C23—61no—
497C23—61no—
498C23—61no—
499C23—61no—
500C23C22×D3×D511yescharacteristic
501Q8—308no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—32no—
509C2×C4—32no—
510C2×C4—32no—
511C2×C4—54no—
512C2×C4—61no—
513C2×C4—61no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—61no—
517C2×C4—61no—
518C2×C4—68no—
519C2×C4—102no—
520C2×C4—102no—
521C2×C4—102no—
522C2×C4—102no—
523C2×C4—102no—
524C2×C4—154no—
525C2×C4—302no—
526C2×C4—302no—
527C2×C4—302no—
528C2×C4—302no—
529C2×C4—302no—
530C2×C4#676912yes—
531C2×C4C4×D3×D512yes—
532C2×C4D3×C22⋊D512yes—
533C2×C3#6585011yescharacteristic
534C2×C3#6585211yescharacteristic
535C2×C3#6585711yescharacteristic
536C2×C3#6586811yescharacteristic
537C2×C3C2×C4×C22⋊D511yescharacteristic
538C2×C3#6615911yescharacteristic
539C2×C3#6616711yescharacteristic
540D3—42no—
541C5#7619711yescharacteristic, complemented, Sylow
542C22—62no—
543C22—62no—
544C22—62no—
545C22—121no—
546C22—121no—
547C22—121no—
548C22—121no—
549C22#9200111yescharacteristic
550C22#9200111yescharacteristic
551C22#9200411yescharacteristic
552C22C2×#676911yescharacteristic
553C22C2×C4×D3×D511yescharacteristic
554C22#9201711yescharacteristic
555C22C2×D3×C22⋊D511yescharacteristic
556C4—41no—
557C4—41no—
558C4—62no—
559C4—62no—
560C4—62no—
561C4—104no—
562C4—202no—
563C4—304no—
564C4—602no—
565C4#9144614yes—
566C3#1061396611yescharacteristic, complemented, Sylow
567C2—122no—
568C2#1175249211yescharacteristic
569C2#1175251811yescharacteristic
570C2#1175252311yescharacteristic
571C2#1175264311yescharacteristic
572C2#1175434211yescharacteristic
573C2#1175434811yescharacteristic
574C2C2×#9144611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#2323
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C2×#91340C2semidirect
4. #11751030C2semidirect
5. C3×#65217C2semidirect
9. Dic3×C4⋊Dic5C2semidirect
10. #11748655C2semidirect
11. #11748629C2semidirect
32. #91365C4semidirect
50. #65217D3semidirect
460. C3×C5#2323semidirect
541. C5#76197semidirect
566. C3#10613966semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8722
C2×#913652
C2×#913402
#117510302
C3×#652172
#117487862
#117487212
#117487182
Dic3×C4⋊Dic52
#117486552
#117486292
#106139663
#761975