Finite Group Databasebeta

← #14319726

Subgroups — #14319726

Order 1920.

1560 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91446C212yesmaximal
2C2×C4×#1203C211yesmaximal, characteristic
3#11750767C211yesmaximal, characteristic, complemented
4C5×D3×#95C211yesmaximal, characteristic, complemented
5C3×#64938C211yesmaximal, characteristic, complemented
6#11748888C211yesmaximal, characteristic, complemented
7#11748875C212yesmaximal, complemented
8#11748719C211yesmaximal, characteristic, complemented
9C4×(C2×D3)⋊Dic5C212yesmaximal, complemented
10#11748637C212yesmaximal, complemented
11#11748635C211yesmaximal, characteristic, complemented
12#10605053—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×C4×C5×D3C2211yescharacteristic
15C22×C4×C5×D3C2212yes—
16C22×#1203C2211yescharacteristic
17C22×#1200C2212yes—
18C2×#6714C2212yes—
19C2×C4×Dic15C2212yes—
20C2×C3×#683C2212yes—
21C2×C3×C4×Dic5C2212yes—
22C2×C3×C4×Dic5C2211yescharacteristic
23C2×#6668C2211yescharacteristic
24C2×#6667C2211yescharacteristic
25C2×(C2×D3)⋊Dic5C2211yescharacteristic
26C2×(C2×D3)⋊Dic5C2212yes—
27C2×Dic3×Dic5C2212yes—
28C2×Dic3×Dic5C2212yes—
29#91446C4116yescomplemented
30C4×#1203C418yescomplemented
31C3×C5×#95C2211yescharacteristic
32#91115C2211yescharacteristic
33C5×C3⋊#95C2212yes—
34C5×C3⋊#95C2211yescharacteristic
35C3×#3963C2211yescharacteristic
36#90994C2212yes—
37#90994C2212yes—
38#73751—51nomaximal, Hall
39C2×C4×C22⋊D5—32no—
40C2×C4×C22⋊D5—31no—
41C2×C5×#95—31no—
42C4×C22⋊Dic5—32no—
43C4×C22⋊Dic5—31no—
44#64955—32no—
45#64955—31no—
46D5×#95—31no—
47#64938—32no—
48#64938D311yescharacteristic, complemented
49#64937—31no—
50C23×D15C2311yescharacteristic
51C23×C5×D3C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×Dic15C2311yescharacteristic
55C22×Dic15C2312yes—
56C2×C4×D15—42no—
57C2×C4×D15C2×C414yescomplemented
58C22×C5×Dic3C2312yes—
59C22×C5×Dic3C2311yescharacteristic
60C2×C4×C5×D3—42no—
61C2×C4×C5×D3—42no—
62C2×C4×C5×D3—42no—
63C2×C4×C5×D3C2×C414yescomplemented
64C2×C4×C5×D3C2×C418yescomplemented
65C22×C3×Dic5C2311yescharacteristic
66C22×C3×Dic5C2312yes—
67C22×C3×Dic5C2311yescharacteristic
68C2×#1203C2×C414yes—
69C2×#1203C2×C418yes—
70C2×#1200—42no—
71C2×#1200—42no—
72C2×#1200C2×C418yescomplemented
73#6714C2×C418yescomplemented
74C4×Dic15—42no—
75C3×#683C2×C418yescomplemented
76C3×C4×Dic5—42no—
77C3×C4×Dic5C2×C414yescomplemented
78#6668C2×C414yescomplemented
79#6667C2×C414yescomplemented
80(C2×D3)⋊Dic5C2×C414yescomplemented
81(C2×D3)⋊Dic5C2×C418yescomplemented
82Dic3×Dic5—42no—
83Dic3×Dic5C2×C418yescomplemented
84C2×#893—52no—
85C2×C4×D12—51no—
86C3×C4×C4⋊C4—51no—
87Dic3×C4⋊C4—52no—
88C4×(C2×D3)⋊C4—52no—
89C4×(C2×D3)⋊C4—52no—
90#4932—51no—
91#4666—51no—
92#4666—51no—
93D3×#95—51no—
94D3×#95D511yescharacteristic, complemented
95C23×C4×C5—32no—
96C23×C4×C5—31no—
97C22×C22⋊D5—31no—
98C22×C4×D5—31no—
99C22×C4×D5—32no—
100C2×C22⋊Dic5—31no—
101C2×C22⋊Dic5—32no—
102C4×C22⋊D5—316no—
103C4×C22⋊D5—38no—
104C2×#685—32no—
105C2×#685—31no—
106C2×#683—31no—
107C2×#683C2×D312yes—
108C2×C4×Dic5—32no—
109C2×C4×Dic5—32no—
110C2×C4×Dic5—32no—
111C2×C4×Dic5C2×D312yes—
112C2×C4×Dic5C2×D311yescharacteristic
113C5×#95—31no—
114C5×#95—32no—
115C5×#95C2×D311yescharacteristic
116#3963—31no—
117#3963—32no—
118#3963—32no—
119#3963C2×D311yescharacteristic
120#2275—151noSylow
121C23×C3×C5C2411yescharacteristic
122C22×D15—21no—
123C22×D15—22no—
124C22×D15—21no—
125C22×D15C22×C412yes—
126C22×D15C22×C414yes—
127C22×C5×D3—21no—
128C22×C5×D3—22no—
129C22×C5×D3—21no—
130C22×C5×D3C22×C412yes—
131C22×C5×D3C22×C414yes—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5C22×C412yes—
136C2×C3×C4×C5C22×C414yes—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15C22×C414yes—
141C2×Dic15C22×C412yes—
142C4×D15—44no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3C22×C414yes—
147C2×C5×Dic3C22×C412yes—
148C4×C5×D3—48no—
149C4×C5×D3—44no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5C22×C412yes—
155C2×C3×Dic5C22×C414yes—
156C2×C3×Dic5C22×C414yes—
157C2×C3×Dic5C22×C412yes—
158#1203C42116yescomplemented
159#1200—48no—
160C22×D12—51no—
161C22×C4×D3—51no—
162C22×C4×D3—52no—
163C22×C4×D3C2×D511yescharacteristic
164C22×C4×D3C2×D512yes—
165C2×C3×C4⋊C4—52no—
166C2×C3×C42—51no—
167C2×C3×C42—52no—
168C2×(C2×D3)⋊C4—52no—
169C2×(C2×D3)⋊C4—51no—
170C2×(C2×D3)⋊C4—52no—
171C2×(C2×D3)⋊C4—51no—
172C2×C4⋊Dic3—51no—
173C2×C4×Dic3—52no—
174C2×C4×Dic3—52no—
175C2×C4×Dic3—52no—
176#893—516no—
177C4×D12—58no—
178C3×#95—51no—
179C3×#95C2×D511yescharacteristic
180C3⋊#95—51no—
181C3⋊#95—52no—
182C3⋊#95—52no—
183C3⋊#95C2×D511yescharacteristic
184C3⋊#95C2×D512yes—
185C24×C5—31no—
186C23×D5—31no—
187C22×C4×C5—32no—
188C22×C4×C5—31no—
189C22×C4×C5—38no—
190C22×C4×C5—34no—
191C22×C4×C5—122no—
192C22×C4×C5—122no—
193C22×C4×C5—122no—
194C22×C4×C5C22×D311yescharacteristic
195C22×C4×C5C22×D312yes—
196C2×C22⋊D5—38no—
197C2×C22⋊D5—34no—
198C22×Dic5—31no—
199C22×Dic5—32no—
200C22×Dic5C22×D312yes—
201C22×Dic5C22×D311yescharacteristic
202C22×Dic5C22×D311yescharacteristic
203C2×C4×D5—34no—
204C2×C4×D5—38no—
205C2×C4×D5—122no—
206C2×C4×D5—122no—
207C2×C4×D5—122no—
208C22⋊Dic5—38no—
209C22⋊Dic5—34no—
210#685—38no—
211#685—34no—
212#683—34no—
213#683C4×D318yescomplemented
214C4×Dic5—38no—
215C4×Dic5—42no—
216C4×Dic5—122no—
217C4×Dic5—122no—
218C4×Dic5C4×D314yescomplemented
219C2×C4×D4—151no—
220C2×C4×D4—152no—
221C4×C4⋊C4—51no—
222C4×C4⋊C4—152no—
223C4×C22⋊C4—152no—
224C4×C22⋊C4—151no—
225C4×C22⋊C4—152no—
226C4×C22⋊C4—151no—
227#376—151no—
228C2×#95—31no—
229C2×#95—151no—
230C22×C3×C5C23×C411yescharacteristic
231C22×C3×C5C23×C412yes—
232C22×C3×C5H(5,𝔽2)11yescharacteristic
233C22×C3×C5H(5,𝔽2)12yes—
234C22×C3×C52−1+411yescharacteristic
235C2×D15—24no—
236C2×D15—22no—
237C2×D15—22no—
238C2×D15—24no—
239C2×D15C2×C4214yes—
240C2×C5×D3—22no—
241C2×C5×D3—24no—
242C2×C5×D3—22no—
243C2×C5×D3—24no—
244C2×C5×D3C2×C4214yes—
245C3×C4×C5—22no—
246C3×C4×C5—24no—
247Dic15—22no—
248Dic15—24no—
249C3×Dic5—24no—
250C3×Dic5—22no—
251C3×Dic5C2×C4214yes—
252C5×Dic3—24no—
253C5×Dic3—22no—
254C23×D3—51no—
255C23×D3C22×D511yescharacteristic
256C22×C3×C4—51no—
257C22×C3×C4—51no—
258C22×C3×C4—52no—
259C22×C3×C4C22×D511yescharacteristic
260C22×C3×C4C22×D512yes—
261C22×Dic3—52no—
262C22×Dic3—51no—
263C22×Dic3C22×D512yes—
264C22×Dic3C22×D511yescharacteristic
265C2×D12—54no—
266C2×D12—58no—
267C2×C4×D3—42no—
268C2×C4×D3—42no—
269C2×C4×D3—42no—
270C2×C4×D3—54no—
271C2×C4×D3—58no—
272C2×C4×D3—202no—
273C2×C4×D3—202no—
274C2×C4×D3—202no—
275C2×C4×D3C4×D514yescomplemented
276C2×C4×D3C4×D518yescomplemented
277C3×C4⋊C4—58no—
278C3×C42—54no—
279C3×C42—202no—
280(C2×D3)⋊C4—54no—
281(C2×D3)⋊C4—58no—
282(C2×D3)⋊C4—58no—
283(C2×D3)⋊C4—54no—
284C4⋊Dic3—54no—
285C4×Dic3—58no—
286C4×Dic3—202no—
287C4×Dic3—202no—
288C23×C5—32no—
289C23×C5—34no—
290C23×C5—61no—
291C23×C5—61no—
292C23×C5—62no—
293C23×C5C23×D311yescharacteristic
294C22×D5—32no—
295C22×D5—34no—
296C22×D5—61no—
297C22×D5—61no—
298C22×D5—62no—
299C2×C4×C5—22no—
300C2×C4×C5—22no—
301C2×C4×C5—22no—
302C2×C4×C5—34no—
303C2×C4×C5—32no—
304C2×C4×C5—62no—
305C2×C4×C5—62no—
306C2×C4×C5—62no—
307C2×C4×C5—124no—
308C2×C4×C5—128no—
309C2×C4×C5C2×C4×D312yes—
310C2×C4×C5C2×C4×D314yes—
311C22⋊D5—316no—
312C2×Dic5—21no—
313C2×Dic5—22no—
314C2×Dic5—21no—
315C2×Dic5—22no—
316C2×Dic5—34no—
317C2×Dic5—32no—
318C2×Dic5—62no—
319C2×Dic5—62no—
320C2×Dic5—62no—
321C2×Dic5C2×C4×D312yes—
322C2×Dic5C2×C4×D314yes—
323C2×Dic5C2×C4×D314yes—
324C2×Dic5C2×C4×D312yes—
325C4×D5—128no—
326C4×D5—124no—
327C22×D4—151no—
328C23×C4—32no—
329C23×C4—31no—
330C23×C4—152no—
331C23×C4—151no—
332C4×D4—158no—
333C4×D4—1516no—
334C2×C4⋊C4—52no—
335C2×C4⋊C4—151no—
336C2×C22⋊C4—151no—
337C2×C22⋊C4—152no—
338C2×C22⋊C4—151no—
339C2×C22⋊C4—152no—
340C2×C42—51no—
341C2×C42—52no—
342C2×C42—152no—
343C2×C42—152no—
344C2×C42—152no—
345#95—31no—
346#95—32no—
347#95—51no—
348#95—152no—
349#95—152no—
350#95—151no—
351#95D3×D511yescharacteristic
352C2×C3×C5C22×C4211yescharacteristic
353C2×C3×C5#51811yescharacteristic
354C2×C3×C5#51812yes—
355C2×C3×C5#52011yescharacteristic
356C2×C3×C5#52012yes—
357D15—24no—
358C5×D3—24no—
359C23×C3C23×D511yescharacteristic
360C22×D3—21no—
361C22×D3—22no—
362C22×D3—21no—
363C22×D3—54no—
364C22×D3—52no—
365C22×D3—101no—
366C22×D3—102no—
367C22×D3—101no—
368C22×D3C2×C4×D512yes—
369C22×D3C2×C4×D514yes—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—54no—
374C2×C3×C4—52no—
375C2×C3×C4—52no—
376C2×C3×C4—54no—
377C2×C3×C4—102no—
378C2×C3×C4—101no—
379C2×C3×C4—102no—
380C2×C3×C4—101no—
381C2×C3×C4C2×C4×D514yes—
382C2×C3×C4C2×C4×D512yes—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—22no—
386C2×Dic3—54no—
387C2×Dic3—52no—
388C2×Dic3—102no—
389C2×Dic3—102no—
390C2×Dic3—102no—
391C2×Dic3C2×C4×D514yes—
392C2×Dic3C2×C4×D512yes—
393D12—516no—
394C4×D3—48no—
395C4×D3—44no—
396C4×D3—208no—
397C4×D3—204no—
398C22×C5—34no—
399C22×C5—62no—
400C22×C5—62no—
401C22×C5—64no—
402C22×C5—64no—
403C22×C5C22×C4×D311yescharacteristic
404C22×C5C22×C4×D312yes—
405C22×C5#100411yescharacteristic
406C22×C5#100711yescharacteristic
407C22×C5#100912yes—
408C2×D5—34no—
409C2×D5—62no—
410C2×D5—62no—
411C2×D5—64no—
412C2×D5—64no—
413C4×C5—22no—
414C4×C5—24no—
415C4×C5—62no—
416C4×C5—64no—
417Dic5—22no—
418Dic5—24no—
419Dic5—62no—
420Dic5—64no—
421Dic5C42×D314yes—
422C24—31no—
423C24—151no—
424C2×D4—154no—
425C2×D4—158no—
426C22×C4—32no—
427C22×C4—31no—
428C22×C4—38no—
429C22×C4—34no—
430C22×C4—51no—
431C22×C4—52no—
432C22×C4—51no—
433C22×C4—122no—
434C22×C4—122no—
435C22×C4—122no—
436C22×C4—158no—
437C22×C4—152no—
438C22×C4—151no—
439C22×C4—154no—
440C22×C4—602no—
441C22×C4—602no—
442C22×C4—602no—
443C22×C4C2×D3×D511yescharacteristic
444C22×C4C2×D3×D512yes—
445C4⋊C4—58no—
446C4⋊C4—154no—
447C22⋊C4—154no—
448C22⋊C4—154no—
449C22⋊C4—158no—
450C22⋊C4—158no—
451C42—54no—
452C42—158no—
453C42—202no—
454C42—602no—
455C42—602no—
456C3×C5#227511yescharacteristic, complemented, Hall
457C22×C3C22×C4×D511yescharacteristic
458C22×C3C22×C4×D512yes—
459C22×C3#414411yescharacteristic
460C22×C3#414412yes—
461C22×C3#414711yescharacteristic
462C2×D3—22no—
463C2×D3—24no—
464C2×D3—24no—
465C2×D3—22no—
466C2×D3—54no—
467C2×D3—102no—
468C2×D3—104no—
469C2×D3—104no—
470C2×D3—102no—
471C2×D3C42×D514yes—
472C3×C4—22no—
473C3×C4—24no—
474C3×C4—54no—
475C3×C4—104no—
476C3×C4—102no—
477Dic3—24no—
478Dic3—22no—
479Dic3—102no—
480Dic3—104no—
481C2×C5—64no—
482C2×C5C2×C42×D311yescharacteristic
483C2×C5#550411yescharacteristic
484C2×C5#552111yescharacteristic
485C2×C5#554512yes—
486C2×C5#557412yes—
487D5—64no—
488C23—32no—
489C23—34no—
490C23—61no—
491C23—62no—
492C23—61no—
493C23—152no—
494C23—154no—
495C23—301no—
496C23—302no—
497C23—301no—
498C23C22×D3×D511yescharacteristic
499D4—1516no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—34no—
504C2×C4—32no—
505C2×C4—52no—
506C2×C4—54no—
507C2×C4—52no—
508C2×C4—54no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—101no—
513C2×C4—102no—
514C2×C4—102no—
515C2×C4—101no—
516C2×C4—124no—
517C2×C4—128no—
518C2×C4—154no—
519C2×C4—152no—
520C2×C4—302no—
521C2×C4—302no—
522C2×C4—302no—
523C2×C4—604no—
524C2×C4—608no—
525C2×C4C4×D3×D512yes—
526C2×C4C4×D3×D514yes—
527C2×C3C2×C42×D511yescharacteristic
528C2×C3#6582011yescharacteristic
529C2×C3#6582012yes—
530C2×C3#6583812yes—
531C2×C3#6583811yescharacteristic
532D3—24no—
533D3—104no—
534C5#7375111yescharacteristic, complemented, Sylow
535C22—34no—
536C22—62no—
537C22—64no—
538C22—62no—
539C22—64no—
540C22—154no—
541C22—302no—
542C22—304no—
543C22—302no—
544C22—304no—
545C22C2×C4×D3×D511yescharacteristic
546C22C2×C4×D3×D512yes—
547C22#9202511yescharacteristic
548C22#9202712yes—
549C22#9202911yescharacteristic
550C4—22no—
551C4—24no—
552C4—54no—
553C4—62no—
554C4—64no—
555C4—102no—
556C4—104no—
557C4—302no—
558C4—304no—
559C3#1060505311yescharacteristic, complemented, Sylow
560C2—64no—
561C2—304no—
562C2C42×D3×D511yescharacteristic
563C2#1175306711yescharacteristic
564C2#1175320212yes—
565C2#1175333712yes—
566C2#1175366711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC2×C3×C5C22×C42
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1203C22
hypercenter#95D3×D5
hypocenterC3×C5#2275
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. #11750767C2semidirect
4. C5×D3×#95C2semidirect
5. C3×#64938C2semidirect
6. #11748888C2semidirect
7. #11748875C2semidirect
8. #11748719C2semidirect
9. C4×(C2×D3)⋊Dic5C2semidirect
10. #11748637C2semidirect
11. #11748635C2semidirect
29. #91446C4semidirect
30. C4×#1203C4semidirect
48. #64938D3semidirect
57. C2×C4×D15C2×C4semidirect
63. C2×C4×C5×D3C2×C4semidirect
64. C2×C4×C5×D3C2×C4semidirect
72. C2×#1200C2×C4semidirect
73. #6714C2×C4semidirect
75. C3×#683C2×C4semidirect
77. C3×C4×Dic5C2×C4semidirect
78. #6668C2×C4semidirect
79. #6667C2×C4semidirect
80. (C2×D3)⋊Dic5C2×C4semidirect
81. (C2×D3)⋊Dic5C2×C4semidirect
83. Dic3×Dic5C2×C4semidirect
94. D3×#95D5semidirect
158. #1203C42semidirect
213. #683C4×D3semidirect
218. C4×Dic5C4×D3semidirect
275. C2×C4×D3C4×D5semidirect
276. C2×C4×D3C4×D5semidirect
456. C3×C5#2275semidirect
534. C5#73751semidirect
559. C3#10605053semidirect

Maximal subgroups

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

subgroupindex
C2×#914462
C2×C4×#12032
#117507672
C5×D3×#952
C3×#649382
#117488882
#117488752
#117487192
C4×(C2×D3)⋊Dic52
#117486372
#117486352
#106050533
#737515