Finite Group Databasebeta

← #14411988

Subgroups — #14411988

Order 1920.

1600 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92095C211yesmaximal, characteristic
2#11755413C212yesmaximal, complemented
3C2×C5×#834C211yesmaximal, characteristic, complemented
4C2×C3×#3966C211yesmaximal, characteristic, complemented
5C2×#90997C212yesmaximal, complemented
6#11749174C214yesmaximal, complemented
7#11749171C214yesmaximal, complemented
8#10610419—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×#1220C412yescomplemented
11C22×#1220C2211yescharacteristic
12C22×#1220C2211yescharacteristic
13#92095—24no—
14#92095—24no—
15C2×#6819C412yescomplemented
16C2×#6819C2212yes—
17C2×D4×D15C412yescomplemented
18C2×D4×D15C2212yes—
19C2×#6817C412yescomplemented
20C2×C5×#217C2212yescomplemented
21C2×C3×C22⋊Dic5C2212yescomplemented
22#91561C2214yescomplemented
23#91556—24no—
24#91552—24no—
25#91532C2214yescomplemented
26C5×#834C2214yescomplemented
27C3×#3966C2214yescomplemented
28#90997C2218yescomplemented
29#78688—51nomaximal, Hall
30C2×#4144—31no—
31#65820—32no—
32C2×C5×#99—31no—
33C2×#3966D311yescharacteristic, complemented
34C2×#3938—32no—
35D5×#99—34no—
36#65029—34no—
37C24×C3×C5C2×C411yescharacteristic, complemented
38C24×C3×C5C2311yescharacteristic
39C23×D15C2×C411yescharacteristic, complemented
40C23×D15C2×C412yescomplemented
41C23×D15C2311yescharacteristic
42C2×C3×C5×D4—22no—
43C2×C3×C5×D4—22no—
44C2×C3×C5×D4C2×C412yescomplemented
45C2×C3×C5×D4C2312yes—
46C22×C3×C4×C5C2×C411yescharacteristic, complemented
47C2×#1220—22no—
48C2×#1220—22no—
49C2×#1220—24no—
50C2×#1220—24no—
51C2×#1220C2×C412yes—
52C2×#1220C2×C412yes—
53C2×#1220C2×C412yescomplemented
54C2×#1220C2×C412yescomplemented
55C2×#1220C2×C412yescomplemented
56C2×#1220D414yes—
57C2×#1220D414yes—
58C2×#1220C2312yes—
59C22×Dic15C2×C411yescharacteristic, complemented
60C22×Dic15C2×C412yescomplemented
61C22×Dic15C2311yescharacteristic
62#6819—28no—
63#6819—28no—
64D4×D15—28no—
65D4×D15—28no—
66#6817—24no—
67#6817—24no—
68C2×D60C2×C412yescomplemented
69C2×C4×D15C2×C412yescomplemented
70C2×C4×D15C2×C412yescomplemented
71C2×Dic30C2×C412yescomplemented
72C22×C5×Dic3—22no—
73C22×C3×Dic5—22no—
74C2×#1200—24no—
75C5×#217—22no—
76C5×#217C2314yes—
77C3×C22⋊Dic5—22no—
78C3×C22⋊Dic5C2314yes—
79#6669—24no—
80#6667—24no—
81Dic3×Dic5—24no—
82C2×#1004—51no—
83#5486—52no—
84C2×C3×#99—51no—
85C2×#834D511yescharacteristic, complemented
86C2×#806—52no—
87D3×#99—54no—
88#4740—54no—
89C22×C5×D4C2×D311yescharacteristic
90C22×C22⋊D5—31no—
91C22×C22⋊D5—32no—
92C22×C22⋊D5—31no—
93#4144—64no—
94#4144—64no—
95C2×#711—32no—
96C2×#711—32no—
97C2×D4×D5—32no—
98C2×D4×D5—32no—
99C2×#709—32no—
100C2×C5×C22⋊C4—32no—
101C2×C22⋊Dic5C2×D312yescomplemented
102C4×C22⋊D5—64no—
103#4027—64no—
104D5×C22⋊C4—34no—
105#4023—34no—
106C5×#99—34no—
107#3966C2×D314yescomplemented
108#3938—38no—
109#2883—151noSylow
110C23×C3×C5—21no—
111C23×C3×C5—21no—
112C23×C3×C5—81no—
113C23×C3×C5—81no—
114C23×C3×C5C22×C412yes—
115C23×C3×C5C22×C411yescharacteristic
116C23×C3×C5C22×C411yescharacteristic
117C23×C3×C5C2×D412yes—
118C23×C3×C5C2×D412yes—
119C23×C3×C5C2411yescharacteristic
120C22×D15—22no—
121C22×D15—24no—
122C22×D15—81no—
123C22×D15—82no—
124C22×D15—81no—
125C22×D15C22×C412yes—
126C22×D15C22×C412yes—
127C22×D15C2×D414yes—
128C3×C5×D4—24no—
129C3×C5×D4—24no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5C22×C412yes—
133#1220—22no—
134#1220—22no—
135#1220—24no—
136#1220—24no—
137#1220—24no—
138#1220C22⋊C414yes—
139#1220C22⋊C414yes—
140#1220C22⋊C418yes—
141C2×Dic15—22no—
142C2×Dic15—24no—
143C2×Dic15C22×C412yes—
144C2×Dic15C22×C412yes—
145C2×Dic15C2×D414yes—
146D60—24no—
147C4×D15—24no—
148C4×D15—24no—
149Dic30—24no—
150C2×C5×Dic3—24no—
151C2×C5×Dic3—82no—
152C2×C3×Dic5—24no—
153C2×C3×Dic5—82no—
154#1200—84no—
155C22×C3×D4C2×D511yescharacteristic
156C22×#67—51no—
157C22×#67—52no—
158C22×#67—51no—
159#1004—104no—
160#1004—104no—
161C2×#237—52no—
162C2×#237—52no—
163C2×D3×D4—52no—
164C2×D3×D4—52no—
165C2×#235—52no—
166C2×C3×C22⋊C4—52no—
167C2×#217C2×D512yescomplemented
168C4×#67—104no—
169#67⋊C4—104no—
170D3×C22⋊C4—54no—
171#877—54no—
172C3×#99—54no—
173#834C2×D514yescomplemented
174#806—58no—
175C24×C5C4×D311yescharacteristic, complemented
176C24×C5C22×D311yescharacteristic
177C23×D5—31no—
178C23×D5—32no—
179C23×D5—31no—
180C2×C5×D4—22no—
181C2×C5×D4—22no—
182C2×C5×D4C4×D312yescomplemented
183C2×C5×D4C22×D312yes—
184C22×C4×C5—62no—
185C22×C4×C5C4×D311yescharacteristic, complemented
186C2×C22⋊D5—32no—
187C2×C22⋊D5—32no—
188C2×C22⋊D5—34no—
189C2×C22⋊D5—34no—
190C2×C22⋊D5—32no—
191C2×C22⋊D5—32no—
192C2×C22⋊D5—32no—
193C2×C22⋊D5—32no—
194C2×C22⋊D5—64no—
195C2×C22⋊D5—64no—
196C2×C22⋊D5—62no—
197C2×C22⋊D5—62no—
198C22×Dic5—22no—
199C22×Dic5—31no—
200C22×Dic5—32no—
201C22×Dic5—31no—
202#711—68no—
203#711—68no—
204D4×D5—68no—
205D4×D5—68no—
206#709—64no—
207#709—64no—
208C2×D20—32no—
209C2×C4×D5—32no—
210C2×C4×D5—32no—
211C2×C4×D5—64no—
212C2×Dic10—32no—
213C5×C22⋊C4—34no—
214C5×C22⋊C4—62no—
215C22⋊Dic5—22no—
216C22⋊Dic5C22×D314yes—
217#685—64no—
218#683—64no—
219C4×Dic5—64no—
220C2×H(5,𝔽2)—151no—
221#518—152no—
222#410—154no—
223C2×#99—31no—
224C2×#99—51no—
225C2×#99—154no—
226C2×#99—152no—
227C22×C3×C5—22no—
228C22×C3×C5—42no—
229C22×C3×C5—42no—
230C22×C3×C5—41no—
231C22×C3×C5—41no—
232C22×C3×C5—41no—
233C22×C3×C5—42no—
234C22×C3×C5—81no—
235C22×C3×C5—81no—
236C22×C3×C5C2×C22⋊C412yes—
237C22×C3×C5C2×C22⋊C411yescharacteristic
238C22×C3×C5C2×C22⋊C411yescharacteristic
239C22×C3×C5C23×C411yescharacteristic
240C22×C3×C5C22×D412yes—
241C2×D15—22no—
242C2×D15—44no—
243C2×D15—42no—
244C2×D15—42no—
245C2×D15—84no—
246C2×D15—82no—
247C2×D15C2×C22⋊C414yes—
248C3×C4×C5—22no—
249Dic15—22no—
250Dic15C2×C22⋊C414yes—
251C3×Dic5—44no—
252C5×Dic3—44no—
253C24×C3C4×D511yescharacteristic, complemented
254C24×C3C22×D511yescharacteristic
255C23×D3—51no—
256C23×D3—52no—
257C23×D3—51no—
258C2×C3×D4—22no—
259C2×C3×D4—22no—
260C2×C3×D4C4×D512yescomplemented
261C2×C3×D4C22×D512yes—
262C22×C3×C4—102no—
263C22×C3×C4C4×D511yescharacteristic, complemented
264C2×#67—52no—
265C2×#67—52no—
266C2×#67—54no—
267C2×#67—54no—
268C2×#67—52no—
269C2×#67—52no—
270C2×#67—52no—
271C2×#67—52no—
272C2×#67—104no—
273C2×#67—104no—
274C2×#67—102no—
275C2×#67—102no—
276C22×Dic3—22no—
277C22×Dic3—51no—
278C22×Dic3—52no—
279C22×Dic3—51no—
280#237—108no—
281#237—108no—
282D3×D4—108no—
283D3×D4—108no—
284#235—104no—
285#235—104no—
286C2×D12—52no—
287C2×C4×D3—52no—
288C2×C4×D3—52no—
289C2×C4×D3—104no—
290C2×Dic6—52no—
291C3×C22⋊C4—54no—
292C3×C22⋊C4—102no—
293#217—22no—
294#217C22×D514yes—
295(C2×D3)⋊C4—104no—
296Dic3⋊C4—104no—
297C4×Dic3—104no—
298C23×C5—21no—
299C23×C5—21no—
300C23×C5—81no—
301C23×C5—81no—
302C23×C5C2×C4×D312yes—
303C23×C5C2×C4×D311yescharacteristic
304C23×C5C2×C4×D311yescharacteristic
305C23×C5D3×D412yes—
306C23×C5D3×D412yes—
307C23×C5C23×D311yescharacteristic
308C22×D5—32no—
309C22×D5—34no—
310C22×D5—32no—
311C22×D5—64no—
312C22×D5—62no—
313C22×D5—241no—
314C22×D5—242no—
315C22×D5—241no—
316C5×D4—24no—
317C5×D4—24no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—64no—
321C2×C4×C5—242no—
322C2×C4×C5C2×C4×D312yes—
323C22⋊D5—34no—
324C22⋊D5—34no—
325C22⋊D5—38no—
326C22⋊D5—64no—
327C22⋊D5—64no—
328C22⋊D5—62no—
329C22⋊D5—62no—
330C22⋊D5—64no—
331C2×Dic5—24no—
332C2×Dic5—32no—
333C2×Dic5—34no—
334C2×Dic5—32no—
335C2×Dic5—64no—
336C2×Dic5—62no—
337C2×Dic5—82no—
338D20—64no—
339C4×D5—64no—
340C4×D5—64no—
341C4×D5—244no—
342Dic10—64no—
343H(5,𝔽2)—304no—
344H(5,𝔽2)—304no—
345C2×#41—152no—
346C2×#41—152no—
347C2×#41—152no—
348C22×D4—151no—
349C22×D4—152no—
350C22×D4—151no—
351C22×D4—152no—
352C22×D4—152no—
353C22×D4D3×D511yescharacteristic
354C4×D4—304no—
355C4×D4—304no—
356#117—154no—
357C2×C22⋊C4—32no—
358C2×C22⋊C4—52no—
359C2×C22⋊C4—154no—
360#99—34no—
361#99—54no—
362#99—158no—
363C2×C3×C5—22no—
364C2×C3×C5—21no—
365C2×C3×C5—22no—
366C2×C3×C5—21no—
367C2×C3×C5—21no—
368C2×C3×C5—42no—
369C2×C3×C5C22×C22⋊C411yescharacteristic
370D15—24no—
371D15—42no—
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—81no—
375C23×C3—81no—
376C23×C3C2×C4×D512yes—
377C23×C3C2×C4×D511yescharacteristic
378C23×C3C2×C4×D511yescharacteristic
379C23×C3D4×D512yes—
380C23×C3D4×D512yes—
381C23×C3C23×D511yescharacteristic
382C22×D3—52no—
383C22×D3—54no—
384C22×D3—52no—
385C22×D3—104no—
386C22×D3—102no—
387C22×D3—401no—
388C22×D3—402no—
389C22×D3—401no—
390C3×D4—24no—
391C3×D4—24no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—104no—
395C2×C3×C4—402no—
396C2×C3×C4C2×C4×D512yes—
397#67—54no—
398#67—54no—
399#67—58no—
400#67—104no—
401#67—104no—
402#67—104no—
403#67—102no—
404#67—102no—
405C2×Dic3—24no—
406C2×Dic3—52no—
407C2×Dic3—54no—
408C2×Dic3—52no—
409C2×Dic3—82no—
410C2×Dic3—104no—
411C2×Dic3—102no—
412D12—104no—
413C4×D3—104no—
414C4×D3—104no—
415C4×D3—404no—
416Dic6—104no—
417C22×C5—22no—
418C22×C5—42no—
419C22×C5—42no—
420C22×C5—41no—
421C22×C5—41no—
422C22×C5—41no—
423C22×C5—42no—
424C22×C5—81no—
425C22×C5—81no—
426C22×C5D3×C22⋊C412yes—
427C22×C5D3×C22⋊C411yescharacteristic
428C22×C5D3×C22⋊C411yescharacteristic
429C22×C5C22×C4×D311yescharacteristic
430C22×C5C2×D3×D412yes—
431C2×D5—34no—
432C2×D5—62no—
433C2×D5—124no—
434C2×D5—122no—
435C2×D5—122no—
436C2×D5—244no—
437C2×D5—242no—
438C4×C5—22no—
439C4×C5—124no—
440Dic5—34no—
441Dic5—44no—
442Dic5—62no—
443C24—151no—
444C24—152no—
445C24—151no—
446C24#120011yescharacteristic, complemented
447C24C2×D3×D511yescharacteristic
448#41—304no—
449#41—304no—
450#41—308no—
451#41—308no—
452C2×Q8—152no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—152no—
456C2×D4—152no—
457C2×D4—154no—
458C2×D4—154no—
459C2×D4—152no—
460C2×D4—152no—
461C2×D4—152no—
462C2×D4—152no—
463C2×D4—152no—
464C2×D4—308no—
465C2×D4—308no—
466C2×D4—304no—
467C2×D4—304no—
468C2×D4—302no—
469C2×D4—302no—
470C2×D4#120012yescomplemented
471C2×D4C2×D3×D512yes—
472C22×C4—62no—
473C22×C4—102no—
474C22×C4—151no—
475C22×C4—152no—
476C22×C4—151no—
477C22×C4—152no—
478C22×C4—152no—
479C22×C4—304no—
480C22×C4#120011yescharacteristic, complemented
481C4⋊C4—304no—
482C22⋊C4—34no—
483C22⋊C4—54no—
484C22⋊C4—62no—
485C22⋊C4—102no—
486C22⋊C4—304no—
487C42—304no—
488C3×C5#288311yescharacteristic, complemented, Hall
489C22×C3—22no—
490C22×C3—42no—
491C22×C3—42no—
492C22×C3—41no—
493C22×C3—41no—
494C22×C3—41no—
495C22×C3—42no—
496C22×C3—81no—
497C22×C3—81no—
498C22×C3D5×C22⋊C412yes—
499C22×C3D5×C22⋊C411yescharacteristic
500C22×C3D5×C22⋊C411yescharacteristic
501C22×C3C22×C4×D511yescharacteristic
502C22×C3C2×D4×D512yes—
503C2×D3—54no—
504C2×D3—102no—
505C2×D3—204no—
506C2×D3—202no—
507C2×D3—202no—
508C2×D3—404no—
509C2×D3—402no—
510C3×C4—22no—
511C3×C4—204no—
512Dic3—44no—
513Dic3—54no—
514Dic3—102no—
515C2×C5—22no—
516C2×C5—21no—
517C2×C5—22no—
518C2×C5—21no—
519C2×C5—21no—
520C2×C5—42no—
521C2×C5C2×D3×C22⋊C411yescharacteristic
522D5—64no—
523D5—122no—
524C23—21no—
525C23—21no—
526C23—81no—
527C23—81no—
528C23—152no—
529C23—154no—
530C23—152no—
531C23—304no—
532C23—302no—
533C23—1201no—
534C23—1201no—
535C23—1202no—
536C23C2×#120012yes—
537C23C2×#120011yescharacteristic
538C23C2×#120011yescharacteristic
539C23#679012yes—
540C23#679012yes—
541C23C22×D3×D511yescharacteristic
542Q8—304no—
543D4—24no—
544D4—24no—
545D4—154no—
546D4—154no—
547D4—158no—
548D4—304no—
549D4—304no—
550D4—304no—
551D4—304no—
552D4—302no—
553D4—302no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—64no—
557C2×C4—104no—
558C2×C4—152no—
559C2×C4—154no—
560C2×C4—152no—
561C2×C4—242no—
562C2×C4—304no—
563C2×C4—304no—
564C2×C4—304no—
565C2×C4—302no—
566C2×C4—402no—
567C2×C4—1204no—
568C2×C4C2×#120012yes—
569C2×C3—22no—
570C2×C3—21no—
571C2×C3—22no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—42no—
575C2×C3C2×D5×C22⋊C411yescharacteristic
576D3—104no—
577D3—202no—
578C5#7868811yescharacteristic, complemented, Sylow
579C22—22no—
580C22—42no—
581C22—42no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—42no—
586C22—81no—
587C22—81no—
588C22—154no—
589C22—302no—
590C22—604no—
591C22—602no—
592C22—602no—
593C22—1202no—
594C22—1204no—
595C22#9156111yescharacteristic
596C22#9156111yescharacteristic
597C22#9156112yes—
598C22C22×#120011yescharacteristic
599C22C2×#679012yes—
600C4—22no—
601C4—124no—
602C4—154no—
603C4—204no—
604C4—302no—
605C3#1061041911yescharacteristic, complemented, Sylow
606C2—22no—
607C2—21no—
608C2—21no—
609C2—21no—
610C2—22no—
611C2—42no—
612C2—304no—
613C2—602no—
614C2C2×#9156111yescharacteristic
subgroupG/H
centerC2C2×#91561
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC22×C3×C5×D4C22
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×#92095C2
cosocleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5#2883
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11755413C2semidirect
3. C2×C5×#834C2semidirect
4. C2×C3×#3966C2semidirect
5. C2×#90997C2semidirect
6. #11749174C2semidirect
7. #11749171C2semidirect
10. C22×#1220C4semidirect
15. C2×#6819C4semidirect
17. C2×D4×D15C4semidirect
19. C2×#6817C4semidirect
20. C2×C5×#217C22semidirect
21. C2×C3×C22⋊Dic5C22semidirect
22. #91561C22semidirect
25. #91532C22semidirect
26. C5×#834C22semidirect
27. C3×#3966C22semidirect
28. #90997C22semidirect
33. C2×#3966D3semidirect
37. C24×C3×C5C2×C4semidirect
39. C23×D15C2×C4semidirect
40. C23×D15C2×C4semidirect
44. C2×C3×C5×D4C2×C4semidirect
46. C22×C3×C4×C5C2×C4semidirect
53. C2×#1220C2×C4semidirect
54. C2×#1220C2×C4semidirect
55. C2×#1220C2×C4semidirect
59. C22×Dic15C2×C4semidirect
60. C22×Dic15C2×C4semidirect
68. C2×D60C2×C4semidirect
69. C2×C4×D15C2×C4semidirect
70. C2×C4×D15C2×C4semidirect
71. C2×Dic30C2×C4semidirect
85. C2×#834D5semidirect
101. C2×C22⋊Dic5C2×D3semidirect
107. #3966C2×D3semidirect
167. C2×#217C2×D5semidirect
173. #834C2×D5semidirect
175. C24×C5C4×D3semidirect
182. C2×C5×D4C4×D3semidirect
185. C22×C4×C5C4×D3semidirect
253. C24×C3C4×D5semidirect
260. C2×C3×D4C4×D5semidirect
263. C22×C3×C4C4×D5semidirect
446. C24#1200semidirect
470. C2×D4#1200semidirect
480. C22×C4#1200semidirect
488. C3×C5#2883semidirect
578. C5#78688semidirect
605. C3#10610419semidirect

Maximal subgroups

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

subgroupindex
C2×#920952
#117554132
C2×C5×#8342
C2×C3×#39662
C2×#909972
#117491742
#117491712
#106104193
#786885