Finite Group Databasebeta

← #14327149

Subgroups — #14327149

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
2C2×Dic3×C22⋊D5C212yesmaximal
3#11751313C211yesmaximal, characteristic, complemented
4C2×C5×C3⋊#95C211yesmaximal, characteristic, complemented
5#11749511C212yesmaximal, complemented
6#11748900C212yesmaximal, complemented
7D5×C3⋊#95C211yesmaximal, characteristic, complemented
8#11748738C211yesmaximal, characteristic, complemented
9#11748680C212yesmaximal, complemented
10#11748638C211yesmaximal, characteristic, complemented
11#11748580C211yesmaximal, characteristic, complemented
12#10605100—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×C5×Dic3C2212yes—
15C22×C3×C22⋊D5C2211yescharacteristic
16C22×C3×C4×D5C2211yescharacteristic
17C22×D5×Dic3C2212yes—
18C2×#6719C2212yes—
19C2×C4⋊Dic15C2212yes—
20C2×C3×C22⋊Dic5C2211yescharacteristic
21C3×C4×C22⋊D5C418yescomplemented
22C2×C3×#685C2211yescharacteristic
23C2×C3×#683C2211yescharacteristic
24C2×C3×C4×Dic5C2211yescharacteristic
25Dic3×C22⋊D5—28no—
26C2×#6668C2212yes—
27C2×#6668C2212yes—
28C2×#6668C2212yes—
29C2×#6665C2212yes—
30C2×Dic3×Dic5C2212yes—
31#91115C2211yescharacteristic
32#91115C2211yescharacteristic
33C5×C3⋊#95C2211yescharacteristic
34C5×C3⋊#95C2212yes—
35C5×C3⋊#95C2211yescharacteristic
36#90994C2212yes—
37#90994C2212yes—
38#82333—51nomaximal, Hall
39C2×C4×C22⋊D5—32no—
40C2×C4×C22⋊D5D311yescharacteristic
41C2×C5×#95—31no—
42#65501—31no—
43#65499—32no—
44#64957—32no—
45#64956—31no—
46D5×#95—31no—
47#64939—31no—
48#64938—31no—
49#64936—32no—
50C24×C3×C5C2311yescharacteristic
51C23×C3×D5C2311yescharacteristic
52C22×C3×C4×C5—42no—
53C22×C3×C4×C5C2×C414yescomplemented
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15C2312yes—
57C22×Dic15C2312yes—
58C22×C5×Dic3—24no—
59C22×C5×Dic3—24no—
60C22×C5×Dic3—42no—
61C22×C5×Dic3C2312yes—
62C22×C5×Dic3C2312yes—
63C2×C3×C22⋊D5C2×C414yes—
64C2×C3×C22⋊D5D414yes—
65C2×C3×C22⋊D5Q814yes—
66C22×C3×Dic5C2311yescharacteristic
67C22×C3×Dic5C2311yescharacteristic
68C22×C3×Dic5C2311yescharacteristic
69C2×C3×C4×D5—42no—
70C2×C3×C4×D5C2×C414yescomplemented
71C2×D5×Dic3—24no—
72C2×D5×Dic3—24no—
73C2×D5×Dic3—42no—
74#6719—24no—
75C4⋊Dic15—42no—
76C3×C22⋊Dic5C2×C414yescomplemented
77C3×#685C2×C414yescomplemented
78C3×#683C2×C414yescomplemented
79C3×C4×Dic5C2×C414yescomplemented
80#6668—24no—
81#6668—24no—
82#6668—42no—
83#6665—24no—
84Dic3×Dic5—24no—
85C2×C3×C4×D4—51no—
86C2×D4×Dic3—52no—
87#5212—51no—
88#5212—51no—
89C2×C3⋊#95—51no—
90C2×C3⋊#95D511yescharacteristic, complemented
91#4984—52no—
92#4950—52no—
93#4950—52no—
94#4936—51no—
95C4×C4⋊Dic3—51no—
96C23×C4×C5—32no—
97C23×C4×C5C2×D311yescharacteristic
98C22×C22⋊D5C2×D311yescharacteristic
99C22×C4×D5—32no—
100C22×C4×D5C2×D311yescharacteristic
101C2×C22⋊Dic5—32no—
102C2×C22⋊Dic5C2×D311yescharacteristic
103C4×C22⋊D5—68no—
104C4×C22⋊D5Dic318yescomplemented
105C2×#685—32no—
106C2×#685C2×D311yescharacteristic
107C2×C4⋊Dic5—32no—
108C2×#683—32no—
109C2×#683—32no—
110C2×#683—32no—
111C2×#683C2×D311yescharacteristic
112C2×C4×Dic5—32no—
113C2×C4×Dic5C2×D311yescharacteristic
114C5×#95—32no—
115C5×#95—31no—
116C5×#95—31no—
117#3963—31no—
118#3963—31no—
119#3963—32no—
120#3963—32no—
121#2349—151noSylow
122C23×C3×C5—22no—
123C23×C3×C5—22no—
124C23×C3×C5C22×C412yes—
125C23×C3×C5C2×D412yes—
126C23×C3×C5C2×Q812yes—
127C23×C3×C5C2411yescharacteristic
128C22×C3×D5—22no—
129C22×C3×D5—22no—
130C22×C3×D5C22×C412yes—
131C22×C3×D5C2×D412yes—
132C22×C3×D5C2×Q812yes—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—44no—
136C2×C3×C4×C5C22×C412yes—
137C2×C3×C4×C5C22×C412yes—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15—22no—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—48no—
150C2×C5×Dic3#4114yes—
151C3×C22⋊D5C4⋊C4116yescomplemented
152C2×C3×Dic5—22no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5C22×C412yes—
155C2×C3×Dic5C22×C412yes—
156C2×C3×Dic5C22×C412yes—
157C2×C3×Dic5C2×D412yes—
158C2×C3×Dic5C2×Q812yes—
159C3×C4×D5—44no—
160D5×Dic3—48no—
161C22×C3×D4—51no—
162C23×C3×C4—51no—
163C23×C3×C4C2×D511yescharacteristic
164C23×Dic3—52no—
165C23×Dic3C2×D512yes—
166C3×C4×D4—58no—
167C2×C3×C4⋊C4—51no—
168C2×C3×C22⋊C4—51no—
169C2×C3×C22⋊C4—51no—
170C2×C3×C42—51no—
171C2×#217—52no—
172C2×#217—52no—
173D4×Dic3—108no—
174C2×C4⋊Dic3—52no—
175C2×C4⋊Dic3—52no—
176C2×C4⋊Dic3—52no—
177C2×C4⋊Dic3—52no—
178C2×C4×Dic3—52no—
179C3⋊#95—51no—
180C3⋊#95—51no—
181C3⋊#95—52no—
182C3⋊#95—52no—
183C3⋊#95C2×D511yescharacteristic
184C3⋊#95C2×D511yescharacteristic
185C3⋊#95C2×D512yes—
186C24×C5C22×D311yescharacteristic
187C23×D5C22×D311yescharacteristic
188C22×C4×C5—32no—
189C22×C4×C5—32no—
190C22×C4×C5—42no—
191C22×C4×C5—64no—
192C22×C4×C5—64no—
193C22×C4×C5—122no—
194C22×C4×C5C2×Dic314yescomplemented
195C22×C4×C5C22×D311yescharacteristic
196C22×C4×C5C22×D311yescharacteristic
197C2×C22⋊D5Dic614yes—
198C2×C22⋊D5D1214yes—
199C2×C22⋊D5C2×Dic314yes—
200C22×Dic5—32no—
201C22×Dic5—32no—
202C22×Dic5C22×D311yescharacteristic
203C22×Dic5C22×D311yescharacteristic
204C22×Dic5C22×D311yescharacteristic
205C2×C4×D5—42no—
206C2×C4×D5—64no—
207C2×C4×D5—64no—
208C2×C4×D5—122no—
209C2×C4×D5C2×Dic314yescomplemented
210C22⋊Dic5—64no—
211C22⋊Dic5C2×Dic314yescomplemented
212#685—64no—
213#685C2×Dic314yescomplemented
214C4⋊Dic5—122no—
215#683—64no—
216#683—64no—
217#683—122no—
218#683C2×Dic314yescomplemented
219C4×Dic5—64no—
220C4×Dic5C2×Dic314yescomplemented
221C2×C4×D4—51no—
222C2×C4×D4—152no—
223#389—152no—
224#385—152no—
225#385—152no—
226#382—151no—
227#380—151no—
228#380—151no—
229C4×C4⋊C4—151no—
230C2×#95—31no—
231C2×#95—151no—
232C22×C3×C5—22no—
233C22×C3×C5—22no—
234C22×C3×C5—24no—
235C22×C3×C5—24no—
236C22×C3×C5C2×C4⋊C414yes—
237C22×C3×C5C23×C411yescharacteristic
238C22×C3×C5C22×D411yescharacteristic
239C22×C3×C5C22×Q811yescharacteristic
240C22×C3×C5C2×#4112yes—
241C22×C3×C5H(5,𝔽2)12yes—
242C2×C3×D5—22no—
243C2×C3×D5—22no—
244C2×C3×D5—24no—
245C2×C3×D5—24no—
246C2×C3×D5C2×C4⋊C414yes—
247C3×C4×C5—22no—
248C3×C4×C5—22no—
249Dic15—42no—
250Dic15—42no—
251C3×Dic5—22no—
252C3×Dic5—22no—
253C3×Dic5C2×C4⋊C414yes—
254C5×Dic3—24no—
255C5×Dic3—42no—
256C24×C3—51no—
257C24×C3C22×D511yescharacteristic
258C2×C3×D4—54no—
259C2×C3×D4—54no—
260C2×C3×D4—54no—
261C22×C3×C4—42no—
262C22×C3×C4—51no—
263C22×C3×C4—51no—
264C22×C3×C4—51no—
265C22×C3×C4—54no—
266C22×C3×C4—202no—
267C22×C3×C4C4×D514yescomplemented
268C22×C3×C4C22×D511yescharacteristic
269C22×C3×C4C22×D511yescharacteristic
270C22×Dic3—24no—
271C22×Dic3—24no—
272C22×Dic3—42no—
273C22×Dic3—52no—
274C22×Dic3—52no—
275C22×Dic3—104no—
276C22×Dic3—104no—
277C22×Dic3—202no—
278C22×Dic3C22×D512yes—
279C22×Dic3C22×D512yes—
280C3×C4⋊C4—54no—
281C3×C22⋊C4—54no—
282C3×C22⋊C4—54no—
283C3×C42—54no—
284#217—104no—
285#217—104no—
286C4⋊Dic3—104no—
287C4⋊Dic3—104no—
288C4⋊Dic3—202no—
289C4⋊Dic3—202no—
290C4×Dic3—104no—
291C23×C5—22no—
292C23×C5—22no—
293C23×C5C2×Dic612yes—
294C23×C5C2×D1212yes—
295C23×C5C22×Dic312yes—
296C23×C5C23×D311yescharacteristic
297C22×D5—22no—
298C22×D5—22no—
299C22×D5C2×Dic612yes—
300C22×D5C2×D1212yes—
301C22×D5C22×Dic312yes—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—34no—
305C2×C4×C5—44no—
306C2×C4×C5—62no—
307C2×C4×C5—62no—
308C2×C4×C5—62no—
309C2×C4×C5—62no—
310C2×C4×C5—62no—
311C2×C4×C5—128no—
312C2×C4×C5C22×Dic312yes—
313C2×C4×C5C22×Dic312yes—
314C22⋊D5C4⋊Dic3116yescomplemented
315C2×Dic5—22no—
316C2×Dic5—22no—
317C2×Dic5—62no—
318C2×Dic5—62no—
319C2×Dic5—62no—
320C2×Dic5—62no—
321C2×Dic5—62no—
322C2×Dic5—62no—
323C2×Dic5C2×Dic612yes—
324C2×Dic5C2×D1212yes—
325C2×Dic5C22×Dic312yes—
326C2×Dic5C22×Dic312yes—
327C2×Dic5C22×Dic312yes—
328C4×D5—44no—
329C4×D5—128no—
330C22×D4—51no—
331C23×C4—32no—
332C23×C4—51no—
333C23×C4—152no—
334C23×C4D3×D511yescharacteristic
335C4×D4—58no—
336C4×D4—308no—
337C2×C4⋊C4—51no—
338C2×C4⋊C4—152no—
339C2×C4⋊C4—152no—
340C2×C4⋊C4—152no—
341C2×C4⋊C4—152no—
342C2×C22⋊C4—51no—
343C2×C22⋊C4—51no—
344C2×C22⋊C4—152no—
345C2×C22⋊C4—152no—
346C2×C42—51no—
347C2×C42—152no—
348#95—31no—
349#95—31no—
350#95—32no—
351#95—152no—
352#95—152no—
353#95—151no—
354#95—151no—
355C2×C3×C5—24no—
356C2×C3×C5C22×C4⋊C411yescharacteristic
357C2×C3×C5C4×#4111yescharacteristic
358C2×C3×C5#51811yescharacteristic
359C2×C3×C5#54612yes—
360C2×C3×C5#55412yes—
361C3×D5—24no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—52no—
365C23×C3—52no—
366C23×C3—52no—
367C23×C3—102no—
368C23×C3—102no—
369C23×C3C2×C4×D512yes—
370C23×C3D4×D512yes—
371C23×C3Q8×D512yes—
372C23×C3C23×D511yescharacteristic
373C3×D4—516no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—44no—
377C2×C3×C4—52no—
378C2×C3×C4—52no—
379C2×C3×C4—52no—
380C2×C3×C4—52no—
381C2×C3×C4—52no—
382C2×C3×C4—102no—
383C2×C3×C4—102no—
384C2×C3×C4—204no—
385C2×C3×C4C2×C4×D512yes—
386C2×C3×C4C2×C4×D512yes—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—48no—
393C2×Dic3—102no—
394C2×Dic3—102no—
395C2×Dic3—102no—
396C2×Dic3—102no—
397C2×Dic3—102no—
398C2×Dic3—102no—
399C2×Dic3—208no—
400C2×Dic3#70914yes—
401C22×C5—24no—
402C22×C5—22no—
403C22×C5—24no—
404C22×C5—22no—
405C22×C5C2×C4⋊Dic314yes—
406C22×C5C22×Dic611yescharacteristic
407C22×C5C22×D1211yescharacteristic
408C22×C5#100412yes—
409C22×C5D3×#4112yes—
410C22×C5C23×Dic311yescharacteristic
411C2×D5—24no—
412C2×D5—22no—
413C2×D5—24no—
414C2×D5—22no—
415C2×D5C2×C4⋊Dic314yes—
416C4×C5—22no—
417C4×C5—22no—
418C4×C5—64no—
419C4×C5—122no—
420Dic5—22no—
421Dic5—22no—
422Dic5—122no—
423Dic5—122no—
424Dic5C2×C4⋊Dic314yes—
425C24—51no—
426C24C2×D3×D511yescharacteristic
427C2×D4—54no—
428C2×D4—54no—
429C2×D4—54no—
430C22×C4—32no—
431C22×C4—32no—
432C22×C4—42no—
433C22×C4—51no—
434C22×C4—51no—
435C22×C4—51no—
436C22×C4—54no—
437C22×C4—64no—
438C22×C4—64no—
439C22×C4—122no—
440C22×C4—152no—
441C22×C4—152no—
442C22×C4—202no—
443C22×C4—304no—
444C22×C4—304no—
445C22×C4—602no—
446C22×C4D5×Dic314yescomplemented
447C22×C4C2×D3×D511yescharacteristic
448C22×C4C2×D3×D511yescharacteristic
449C4⋊C4—54no—
450C4⋊C4—304no—
451C4⋊C4—304no—
452C4⋊C4—602no—
453C4⋊C4—602no—
454C22⋊C4—54no—
455C22⋊C4—54no—
456C22⋊C4—304no—
457C22⋊C4—304no—
458C42—54no—
459C42—304no—
460C3×C5#234911yescharacteristic, complemented, Hall
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—24no—
464C22×C3—24no—
465C22×C3—54no—
466C22×C3—102no—
467C22×C3—102no—
468C22×C3—104no—
469C22×C3—104no—
470C22×C3D5×C4⋊C414yes—
471C22×C3C22×C4×D511yescharacteristic
472C22×C3C2×#70912yes—
473C22×C3C2×D4×D511yescharacteristic
474C22×C3#414412yes—
475C22×C3C2×Q8×D511yescharacteristic
476C3×C4—22no—
477C3×C4—22no—
478C3×C4—54no—
479C3×C4—102no—
480C3×C4—102no—
481Dic3—24no—
482Dic3—42no—
483Dic3—202no—
484Dic3—202no—
485C2×C5—24no—
486C2×C5#553912yes—
487C2×C5#555412yes—
488C2×C5C22×C4⋊Dic311yescharacteristic
489C2×C5#579811yescharacteristic
490C2×C5Dic3×#4111yescharacteristic
491D5—24no—
492C23—22no—
493C23—22no—
494C23—52no—
495C23—52no—
496C23—52no—
497C23—102no—
498C23—102no—
499C23D5×Dic612yes—
500C23D5×D1212yes—
501C23C2×D5×Dic312yes—
502C23C22×D3×D511yescharacteristic
503D4—516no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—34no—
507C2×C4—44no—
508C2×C4—52no—
509C2×C4—52no—
510C2×C4—52no—
511C2×C4—52no—
512C2×C4—52no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—102no—
519C2×C4—102no—
520C2×C4—128no—
521C2×C4—204no—
522C2×C4—302no—
523C2×C4—302no—
524C2×C4—302no—
525C2×C4—302no—
526C2×C4—302no—
527C2×C4—302no—
528C2×C4—608no—
529C2×C4C2×D5×Dic312yes—
530C2×C4C2×D5×Dic312yes—
531C2×C3—24no—
532C2×C3—104no—
533C2×C3C4×#70911yescharacteristic
534C2×C3#6582011yescharacteristic
535C2×C3#6582412yes—
536C2×C3C2×D5×C4⋊C411yescharacteristic
537C2×C3#6584512yes—
538C5#8233311yescharacteristic, complemented, Sylow
539C22—22no—
540C22—24no—
541C22—22no—
542C22—24no—
543C22—54no—
544C22—102no—
545C22—104no—
546C22—102no—
547C22—104no—
548C22D5×C4⋊Dic314yes—
549C22C2×D5×Dic611yescharacteristic
550C22C2×D5×D1211yescharacteristic
551C22D3×#70912yes—
552C22C22×D5×Dic311yescharacteristic
553C22#9204912yes—
554C4—22no—
555C4—22no—
556C4—54no—
557C4—64no—
558C4—102no—
559C4—102no—
560C4—122no—
561C4—602no—
562C4—602no—
563C3#1060510011yescharacteristic, complemented, Sylow
564C2—24no—
565C2—104no—
566C2C2×D5×C4⋊Dic311yescharacteristic
567C2Dic3×#70911yescharacteristic
568C2#1175441912yes—
569C2#1175464612yes—
570C2#1175540611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2349
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #11751313C2semidirect
4. C2×C5×C3⋊#95C2semidirect
5. #11749511C2semidirect
6. #11748900C2semidirect
7. D5×C3⋊#95C2semidirect
8. #11748738C2semidirect
9. #11748680C2semidirect
10. #11748638C2semidirect
11. #11748580C2semidirect
21. C3×C4×C22⋊D5C4semidirect
53. C22×C3×C4×C5C2×C4semidirect
70. C2×C3×C4×D5C2×C4semidirect
76. C3×C22⋊Dic5C2×C4semidirect
77. C3×#685C2×C4semidirect
78. C3×#683C2×C4semidirect
79. C3×C4×Dic5C2×C4semidirect
90. C2×C3⋊#95D5semidirect
104. C4×C22⋊D5Dic3semidirect
151. C3×C22⋊D5C4⋊C4semidirect
194. C22×C4×C5C2×Dic3semidirect
209. C2×C4×D5C2×Dic3semidirect
211. C22⋊Dic5C2×Dic3semidirect
213. #685C2×Dic3semidirect
218. #683C2×Dic3semidirect
220. C4×Dic5C2×Dic3semidirect
267. C22×C3×C4C4×D5semidirect
314. C22⋊D5C4⋊Dic3semidirect
446. C22×C4D5×Dic3semidirect
460. C3×C5#2349semidirect
538. C5#82333semidirect
563. C3#10605100semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊D52
C2×Dic3×C22⋊D52
#117513132
C2×C5×C3⋊#952
#117495112
#117489002
D5×C3⋊#952
#117487382
#117486802
#117486382
#117485802
#106051003
#823335