Finite Group Databasebeta

← #14327154

Subgroups — #14327154

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×C4×#1203C212yesmaximal
2C2×C4×#1203C211yesmaximal, characteristic
3D15×#95C211yesmaximal, characteristic, complemented
4C5×D3×#95C211yesmaximal, characteristic, complemented
5C3×#64938C211yesmaximal, characteristic, complemented
6#11748863C211yesmaximal, characteristic, complemented
7#11748802C212yesmaximal, complemented
8#11748782C211yesmaximal, characteristic, complemented
9#11748729C212yesmaximal, complemented
10#11748716C212yesmaximal, complemented
11#11748580C211yesmaximal, characteristic, complemented
12#10605100—31nomaximal, Hall
13C22×C4×D15C2212yes—
14C22×C4×D15C2211yescharacteristic
15C22×C4×C5×D3C2212yes—
16C22×C4×C5×D3C2211yescharacteristic
17C22×#1203C2211yescharacteristic
18C2×C3×#683C2212yes—
19C2×C3×C4×Dic5C2212yes—
20C2×C3×C4×Dic5C2211yescharacteristic
21C2×Dic3⋊Dic5C2212yes—
22C2×#6669C2212yes—
23C2×#6668C2212yes—
24C2×#6668C2211yescharacteristic
25C2×#6667C2212yes—
26C2×#6667C2211yescharacteristic
27C2×(C2×D3)⋊Dic5C2212yes—
28C2×(C2×D3)⋊Dic5C2211yescharacteristic
29C4×#1203—28no—
30C4×#1203C418yescomplemented
31C3×C5×#95C2211yescharacteristic
32#91115C2212yes—
33#91115C2211yescharacteristic
34C5×C3⋊#95C2212yes—
35C5×C3⋊#95C2211yescharacteristic
36C3×#3963C2211yescharacteristic
37#90994C2212yes—
38#73770—51nomaximal, Hall
39C2×C4×C22⋊D5—31no—
40C2×C4×C22⋊D5—32no—
41C2×C5×#95—31no—
42#65501—31no—
43#65499—32no—
44#64957—32no—
45#64956—31no—
46D5×#95—31no—
47#64939—31no—
48#64938D311yescharacteristic, complemented
49#64936—32no—
50C23×D15C2311yescharacteristic
51C23×C5×D3C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×Dic15C2312yes—
55C22×Dic15C2311yescharacteristic
56C2×C4×D15—24no—
57C2×C4×D15—24no—
58C2×C4×D15—42no—
59C2×C4×D15—42no—
60C2×C4×D15C2×C414yescomplemented
61C22×C5×Dic3C2312yes—
62C22×C5×Dic3C2311yescharacteristic
63C2×C4×C5×D3—24no—
64C2×C4×C5×D3—24no—
65C2×C4×C5×D3—42no—
66C2×C4×C5×D3—42no—
67C2×C4×C5×D3C2×C414yescomplemented
68C22×C3×Dic5C2312yes—
69C22×C3×Dic5C2311yescharacteristic
70C22×C3×Dic5C2311yescharacteristic
71C2×#1203C2×C414yes—
72C2×#1203D414yes—
73C2×#1203Q814yes—
74C3×#683—24no—
75C3×C4×Dic5—24no—
76C3×C4×Dic5C2×C414yescomplemented
77Dic3⋊Dic5—42no—
78#6669—42no—
79#6668—24no—
80#6668C2×C414yescomplemented
81#6667—24no—
82#6667C2×C414yescomplemented
83(C2×D3)⋊Dic5—24no—
84(C2×D3)⋊Dic5C2×C414yescomplemented
85C2×C4×D12—51no—
86C2×C4×D12—52no—
87C3×C4×C4⋊C4—51no—
88#4989—52no—
89#4989—52no—
90#4936—51no—
91#4928—52no—
92#4667—51no—
93#4667—51no—
94D3×#95—51no—
95D3×#95D511yescharacteristic, complemented
96C23×C4×C5—31no—
97C23×C4×C5—32no—
98C22×C22⋊D5—31no—
99C22×C4×D5—31no—
100C22×C4×D5—32no—
101C2×C22⋊Dic5—31no—
102C2×C22⋊Dic5—32no—
103C4×C22⋊D5—38no—
104C4×C22⋊D5—68no—
105C2×#685—31no—
106C2×#685—32no—
107C2×C4⋊Dic5—32no—
108C2×#683—31no—
109C2×#683—32no—
110C2×#683—32no—
111C2×#683C2×D312yes—
112C2×C4×Dic5C2×D312yes—
113C2×C4×Dic5C2×D311yescharacteristic
114C5×#95—32no—
115C5×#95—31no—
116C5×#95C2×D311yescharacteristic
117#3963—32no—
118#3963—31no—
119#3963—32no—
120#3963C2×D311yescharacteristic
121#2349—151noSylow
122C23×C3×C5C2411yescharacteristic
123C22×D15—22no—
124C22×D15—22no—
125C22×D15C22×C412yes—
126C22×D15C2×D412yes—
127C22×D15C2×Q812yes—
128C22×C5×D3—22no—
129C22×C5×D3—22no—
130C22×C5×D3C22×C412yes—
131C22×C5×D3C2×D412yes—
132C22×C5×D3C2×Q812yes—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5C22×C412yes—
137C2×C3×C4×C5#4114yes—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15—22no—
142C2×Dic15C22×C412yes—
143C4×D15—44no—
144C4×D15—48no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3C22×C412yes—
150C4×C5×D3—44no—
151C4×C5×D3—48no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5C22×C412yes—
157C2×C3×Dic5C22×C412yes—
158C2×C3×Dic5C2×D412yes—
159C2×C3×Dic5C2×Q812yes—
160#1203C4⋊C4116yescomplemented
161C22×D12—51no—
162C22×C4×D3—51no—
163C22×C4×D3—52no—
164C22×C4×D3C2×D512yes—
165C22×C4×D3C2×D511yescharacteristic
166C2×C3×C4⋊C4—52no—
167C2×C3×C42—51no—
168C2×C3×C42—52no—
169C2×(C2×D3)⋊C4—51no—
170C2×(C2×D3)⋊C4—51no—
171C2×(C2×D3)⋊C4—52no—
172C2×(C2×D3)⋊C4—52no—
173C2×C4⋊Dic3—51no—
174C2×C4⋊Dic3—52no—
175C2×Dic3⋊C4—52no—
176C2×Dic3⋊C4—52no—
177C4×D12—58no—
178C4×D12—108no—
179C3×#95—51no—
180C3×#95C2×D511yescharacteristic
181C3⋊#95—51no—
182C3⋊#95—52no—
183C3⋊#95—52no—
184C3⋊#95C2×D511yescharacteristic
185C3⋊#95C2×D512yes—
186C24×C5—31no—
187C23×D5—31no—
188C22×C4×C5—31no—
189C22×C4×C5—34no—
190C22×C4×C5—32no—
191C22×C4×C5—64no—
192C22×C4×C5—64no—
193C22×C4×C5—122no—
194C22×C4×C5—122no—
195C22×C4×C5C22×D311yescharacteristic
196C22×C4×C5C22×D312yes—
197C2×C22⋊D5—34no—
198C2×C22⋊D5—34no—
199C2×C22⋊D5—34no—
200C22×Dic5—31no—
201C22×Dic5—32no—
202C22×Dic5C22×D312yes—
203C22×Dic5C22×D311yescharacteristic
204C22×Dic5C22×D311yescharacteristic
205C2×C4×D5—34no—
206C2×C4×D5—64no—
207C2×C4×D5—64no—
208C2×C4×D5—122no—
209C2×C4×D5—122no—
210C22⋊Dic5—34no—
211C22⋊Dic5—64no—
212#685—34no—
213#685—64no—
214C4⋊Dic5—122no—
215#683—24no—
216#683—34no—
217#683—64no—
218#683—122no—
219C4×Dic5—24no—
220C4×Dic5C4×D314yescomplemented
221C2×C4×D4—151no—
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—51no—
230C2×#95—31no—
231C2×#95—151no—
232C22×C3×C5C23×C411yescharacteristic
233C22×C3×C5C22×D411yescharacteristic
234C22×C3×C5C22×Q811yescharacteristic
235C22×C3×C5C2×#4112yes—
236C22×C3×C5H(5,𝔽2)12yes—
237C2×D15—22no—
238C2×D15—22no—
239C2×D15—24no—
240C2×D15—24no—
241C2×D15C2×C4⋊C414yes—
242C2×C5×D3—22no—
243C2×C5×D3—22no—
244C2×C5×D3—24no—
245C2×C5×D3—24no—
246C2×C5×D3C2×C4⋊C414yes—
247C3×C4×C5—22no—
248C3×C4×C5—24no—
249Dic15—22no—
250Dic15—42no—
251C3×Dic5—22no—
252C3×Dic5—42no—
253C3×Dic5C2×C4⋊C414yes—
254C5×Dic3—22no—
255C5×Dic3—42no—
256C23×D3—51no—
257C23×D3C22×D511yescharacteristic
258C22×C3×C4—51no—
259C22×C3×C4—51no—
260C22×C3×C4—52no—
261C22×C3×C4C22×D511yescharacteristic
262C22×C3×C4C22×D512yes—
263C22×Dic3—51no—
264C22×Dic3—52no—
265C22×Dic3C22×D512yes—
266C22×Dic3C22×D511yescharacteristic
267C2×D12—54no—
268C2×D12—54no—
269C2×D12—54no—
270C2×C4×D3—24no—
271C2×C4×D3—24no—
272C2×C4×D3—42no—
273C2×C4×D3—42no—
274C2×C4×D3—54no—
275C2×C4×D3—104no—
276C2×C4×D3—104no—
277C2×C4×D3—202no—
278C2×C4×D3—202no—
279C2×C4×D3C4×D514yescomplemented
280C3×C4⋊C4—104no—
281C3×C42—54no—
282C3×C42—104no—
283(C2×D3)⋊C4—54no—
284(C2×D3)⋊C4—54no—
285(C2×D3)⋊C4—104no—
286(C2×D3)⋊C4—104no—
287C4⋊Dic3—54no—
288C4⋊Dic3—104no—
289Dic3⋊C4—202no—
290Dic3⋊C4—202no—
291C23×C5—32no—
292C23×C5—32no—
293C23×C5—32no—
294C23×C5—62no—
295C23×C5—62no—
296C23×C5C23×D311yescharacteristic
297C22×D5—32no—
298C22×D5—32no—
299C22×D5—32no—
300C22×D5—62no—
301C22×D5—62no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—32no—
306C2×C4×C5—62no—
307C2×C4×C5—62no—
308C2×C4×C5—62no—
309C2×C4×C5—62no—
310C2×C4×C5—124no—
311C2×C4×C5—128no—
312C2×C4×C5C2×C4×D312yes—
313C2×C4×C5#23514yes—
314C22⋊D5—316no—
315C2×Dic5—22no—
316C2×Dic5—22no—
317C2×Dic5—22no—
318C2×Dic5—22no—
319C2×Dic5—32no—
320C2×Dic5—62no—
321C2×Dic5—62no—
322C2×Dic5—62no—
323C2×Dic5—62no—
324C2×Dic5C2×C4×D312yes—
325C2×Dic5C2×C4×D312yes—
326C2×Dic5D3×D412yes—
327C2×Dic5D3×Q812yes—
328C4×D5—124no—
329C4×D5—128no—
330C22×D4—151no—
331C23×C4—31no—
332C23×C4—32no—
333C23×C4—151no—
334C23×C4—152no—
335C4×D4—158no—
336C4×D4—308no—
337C2×C4⋊C4—52no—
338C2×C4⋊C4—151no—
339C2×C4⋊C4—152no—
340C2×C4⋊C4—152no—
341C2×C4⋊C4—152no—
342C2×C22⋊C4—151no—
343C2×C22⋊C4—151no—
344C2×C22⋊C4—152no—
345C2×C22⋊C4—152no—
346C2×C42—51no—
347C2×C42—52no—
348#95—31no—
349#95—32no—
350#95—51no—
351#95—152no—
352#95—151no—
353#95—152no—
354#95D3×D511yescharacteristic
355C2×C3×C5C22×C4⋊C411yescharacteristic
356C2×C3×C5C4×#4111yescharacteristic
357C2×C3×C5#51811yescharacteristic
358C2×C3×C5#54612yes—
359C2×C3×C5#55412yes—
360D15—24no—
361C5×D3—24no—
362C23×C3C23×D511yescharacteristic
363C22×D3—22no—
364C22×D3—22no—
365C22×D3—52no—
366C22×D3—52no—
367C22×D3—52no—
368C22×D3—102no—
369C22×D3—102no—
370C22×D3C2×C4×D512yes—
371C22×D3D4×D512yes—
372C22×D3Q8×D512yes—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—52no—
377C2×C3×C4—52no—
378C2×C3×C4—52no—
379C2×C3×C4—52no—
380C2×C3×C4—102no—
381C2×C3×C4—102no—
382C2×C3×C4—102no—
383C2×C3×C4—102no—
384C2×C3×C4C2×C4×D512yes—
385C2×C3×C4#70914yes—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—22no—
390C2×Dic3—52no—
391C2×Dic3—102no—
392C2×Dic3—102no—
393C2×Dic3—102no—
394C2×Dic3—102no—
395C2×Dic3C2×C4×D512yes—
396D12—516no—
397C4×D3—44no—
398C4×D3—48no—
399C4×D3—204no—
400C4×D3—208no—
401C22×C5—34no—
402C22×C5—62no—
403C22×C5—62no—
404C22×C5—64no—
405C22×C5—64no—
406C22×C5C22×C4×D311yescharacteristic
407C22×C5C2×#23512yes—
408C22×C5C2×D3×D411yescharacteristic
409C22×C5C2×D3×Q811yescharacteristic
410C22×C5#100912yes—
411C2×D5—34no—
412C2×D5—62no—
413C2×D5—62no—
414C2×D5—64no—
415C2×D5—64no—
416C4×C5—22no—
417C4×C5—24no—
418C4×C5—62no—
419C4×C5—122no—
420Dic5—22no—
421Dic5—42no—
422Dic5—62no—
423Dic5—122no—
424Dic5D3×C4⋊C414yes—
425C24—31no—
426C24—151no—
427C2×D4—154no—
428C2×D4—154no—
429C2×D4—154no—
430C22×C4—31no—
431C22×C4—34no—
432C22×C4—32no—
433C22×C4—51no—
434C22×C4—51no—
435C22×C4—52no—
436C22×C4—64no—
437C22×C4—64no—
438C22×C4—122no—
439C22×C4—122no—
440C22×C4—151no—
441C22×C4—154no—
442C22×C4—152no—
443C22×C4—304no—
444C22×C4—304no—
445C22×C4—602no—
446C22×C4—602no—
447C22×C4C2×D3×D512yes—
448C22×C4C2×D3×D511yescharacteristic
449C4⋊C4—104no—
450C4⋊C4—154no—
451C4⋊C4—304no—
452C4⋊C4—602no—
453C4⋊C4—602no—
454C22⋊C4—154no—
455C22⋊C4—154no—
456C22⋊C4—304no—
457C22⋊C4—304no—
458C42—54no—
459C42—104no—
460C3×C5#234911yescharacteristic, complemented, Hall
461C22×C3C22×C4×D511yescharacteristic
462C22×C3C2×#70912yes—
463C22×C3C2×D4×D511yescharacteristic
464C22×C3#414412yes—
465C22×C3C2×Q8×D511yescharacteristic
466C2×D3—22no—
467C2×D3—22no—
468C2×D3—24no—
469C2×D3—24no—
470C2×D3—54no—
471C2×D3—102no—
472C2×D3—102no—
473C2×D3—104no—
474C2×D3—104no—
475C2×D3D5×C4⋊C414yes—
476C3×C4—22no—
477C3×C4—24no—
478C3×C4—54no—
479C3×C4—102no—
480C3×C4—202no—
481Dic3—22no—
482Dic3—42no—
483Dic3—102no—
484Dic3—202no—
485C2×C5—64no—
486C2×C5C4×#23511yescharacteristic
487C2×C5C2×D3×C4⋊C411yescharacteristic
488C2×C5#552111yescharacteristic
489C2×C5#555012yes—
490C2×C5#557912yes—
491D5—64no—
492C23—32no—
493C23—32no—
494C23—32no—
495C23—62no—
496C23—62no—
497C23—152no—
498C23—152no—
499C23—152no—
500C23—302no—
501C23—302no—
502C23C22×D3×D511yescharacteristic
503D4—1516no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—32no—
508C2×C4—52no—
509C2×C4—52no—
510C2×C4—52no—
511C2×C4—52no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—102no—
517C2×C4—102no—
518C2×C4—102no—
519C2×C4—102no—
520C2×C4—124no—
521C2×C4—128no—
522C2×C4—152no—
523C2×C4—302no—
524C2×C4—302no—
525C2×C4—302no—
526C2×C4—302no—
527C2×C4—604no—
528C2×C4—608no—
529C2×C4#677114yes—
530C2×C4C4×D3×D512yes—
531C2×C3C4×#70911yescharacteristic
532C2×C3#6582011yescharacteristic
533C2×C3#6582412yes—
534C2×C3C2×D5×C4⋊C411yescharacteristic
535C2×C3#6584512yes—
536D3—24no—
537D3—104no—
538C5#7377011yescharacteristic, complemented, Sylow
539C22—34no—
540C22—62no—
541C22—64no—
542C22—62no—
543C22—64no—
544C22—154no—
545C22—302no—
546C22—304no—
547C22—302no—
548C22—304no—
549C22C2×#677112yes—
550C22C2×C4×D3×D511yescharacteristic
551C22D3×D4×D511yescharacteristic
552C22#9202712yes—
553C22D3×Q8×D511yescharacteristic
554C4—22no—
555C4—24no—
556C4—54no—
557C4—62no—
558C4—102no—
559C4—122no—
560C4—202no—
561C4—302no—
562C4—602no—
563C3#1060510011yescharacteristic, complemented, Sylow
564C2—64no—
565C2—304no—
566C2C4×#677111yescharacteristic
567C2#1175306711yescharacteristic
568C2#1175307612yes—
569C2#1175371512yes—
570C2D3×D5×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1203C22
hypercenter#95D3×D5
hypocenterC3×C5#2349
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. D15×#95C2semidirect
4. C5×D3×#95C2semidirect
5. C3×#64938C2semidirect
6. #11748863C2semidirect
7. #11748802C2semidirect
8. #11748782C2semidirect
9. #11748729C2semidirect
10. #11748716C2semidirect
11. #11748580C2semidirect
30. C4×#1203C4semidirect
48. #64938D3semidirect
60. C2×C4×D15C2×C4semidirect
67. C2×C4×C5×D3C2×C4semidirect
76. C3×C4×Dic5C2×C4semidirect
80. #6668C2×C4semidirect
82. #6667C2×C4semidirect
84. (C2×D3)⋊Dic5C2×C4semidirect
95. D3×#95D5semidirect
160. #1203C4⋊C4semidirect
220. C4×Dic5C4×D3semidirect
279. C2×C4×D3C4×D5semidirect
460. C3×C5#2349semidirect
538. C5#73770semidirect
563. C3#10605100semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12032
D15×#952
C5×D3×#952
C3×#649382
#117488632
#117488022
#117487822
#117487292
#117487162
#117485802
#106051003
#737705