Finite Group Databasebeta

← #72230447

Subgroups — #72230447

Order 2880.

996 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C3×#91989C211yesmaximal, characteristic, complemented
3C3×D5⋊#208C211yesmaximal, characteristic, complemented
4#13085475C214yesmaximal, complemented
5#11751707—31nomaximal
6#11751706—31nomaximal
7C22×D5×C3⋊D3—21no—
8C2×C4⋊(C3⋊D15)C411yescharacteristic, complemented
9C2×C5×C4⋊(C3⋊D3)C411yescharacteristic, complemented
10C2×C32×C4×D5C2211yescharacteristic
11C2×#67140—21no—
12D5×C4⋊(C3⋊D3)—21no—
13D5×C4⋊(C3⋊D3)—21no—
14D5×C4⋊(C3⋊D3)C412yescomplemented
15D5×C4⋊(C3⋊D3)C2212yes—
16C3×#6763—21no—
17C3×#6762—21no—
18C3×C4⋊ΓL(1,𝔽16)C2212yescomplemented
19C3×C4×ΓL(1,𝔽16)—21no—
20C3×#6758—21no—
21C3×D5⋊(C3⋊C8)C2212yescomplemented
22#10591096—51nomaximal, Hall
23C2×D5×D12—31no—
24C2×D5×D12—31no—
25C2×D5×D12—61no—
26#91989D311yescharacteristic, complemented
27D5⋊#208D311yescharacteristic, complemented
28C3×#4130—31no—
29C3×D5⋊M16—31no—
30#91152—34no—
31#91151—34no—
32C22×C3⋊D15—21no—
33C22×C5×C3⋊D3—21no—
34C22×C32×D5D411yescharacteristic
35C2×D5×C3⋊D3—22no—
36C2×D5×C3⋊D3—22no—
37C2×D5×C3⋊D3—44no—
38C2×C3×ΓL(1,𝔽16)—22no—
39C2×C32×C4×C5C2×C411yescharacteristic
40C4⋊(C3⋊D15)—21no—
41C4⋊(C3⋊D15)C2×C412yes—
42C5×C4⋊(C3⋊D3)—21no—
43C5×C4⋊(C3⋊D3)C2×C412yes—
44C2×C32×Dic5D411yescharacteristic
45C32×C4×D5C2×C411yescharacteristic
46C32×C4×D5D411yescharacteristic
47C32×C4×D5D411yescharacteristic
48C32×C4×D5C2311yescharacteristic
49#67140—22no—
50#67140—22no—
51C3×C3⋊#170—22no—
52#65767—91noHall
53C22×C4⋊(C3⋊D3)—51no—
54C3×#926—51no—
55C2×C3×#208—51no—
56#63564—54no—
57C22×D3×D5—61no—
58C22×D3×D5—61no—
59C22×D3×D5—61no—
60C22×D3×D5—61no—
61C2×D60—31no—
62C2×D60—31no—
63C2×D60—61no—
64C2×C5×D12—31no—
65C2×C5×D12—31no—
66C2×C5×D12—61no—
67C2×C3×C4×D5—21no—
68C2×C3×C4×D5C2×D311yescharacteristic
69C2×C3×C4×D5C2×D311yescharacteristic
70C2×#1203—61no—
71C2×#1203—61no—
72C2×#1203—61no—
73C2×#1203—61no—
74D5×D12—32no—
75D5×D12—32no—
76D5×D12—32no—
77D5×D12—32no—
78D5×D12—61no—
79D5×D12—61no—
80D5×D12—61no—
81D5×D12—61no—
82D5×D12—61no—
83D5×D12—61no—
84D5×D12—61no—
85D5×D12—61no—
86D5×D12—62no—
87D5×D12—62no—
88#6763—21no—
89#6762—21no—
90C4⋊ΓL(1,𝔽16)C2×D312yescomplemented
91C4×ΓL(1,𝔽16)—21no—
92#6758—21no—
93D5⋊(C3⋊C8)C2×D312yescomplemented
94C3×C22⋊AGL(1,𝔽5)—61no—
95C3×#704—61no—
96C3×C4⋊AGL(1,𝔽5)—32no—
97C3×C4×AGL(1,𝔽5)—61no—
98C3×#700—61no—
99C3×D5⋊C8—32no—
100#5131—151no—
101#5001—151no—
102C22×C32×C5C22⋊C411yescharacteristic
103C2×C3⋊D15—22no—
104C2×C3⋊D15—42no—
105C2×C5×C3⋊D3—22no—
106C2×C5×C3⋊D3—42no—
107C2×C32×D5—22no—
108C2×C32×D5C22⋊C411yescharacteristic
109C2×C32×D5C2×D411yescharacteristic
110D5×C3⋊D3—44no—
111D5×C3⋊D3—44no—
112C3×ΓL(1,𝔽16)—42no—
113C32×C4×C5C22⋊C411yescharacteristic
114C32×C4×C5C22×C411yescharacteristic
115C32×Dic5C22⋊C411yescharacteristic
116C32×Dic5C2×D411yescharacteristic
117C2×D4×D5—91no—
118#4130—31no—
119D5⋊M16—31no—
120#4007—94no—
121C23×C3⋊D3—101no—
122C22×C32×C4—51no—
123C2×C4⋊(C3⋊D3)—51no—
124C2×C4⋊(C3⋊D3)—52no—
125C2×C4⋊(C3⋊D3)—52no—
126C2×C4⋊(C3⋊D3)—101no—
127C2×C4⋊(C3⋊D3)—101no—
128C2×C4⋊(C3⋊D3)—101no—
129C2×C4⋊(C3⋊D3)AGL(1,𝔽5)11yescharacteristic, complemented
130C3×#217—101no—
131C3×C4⋊Dic3—52no—
132C3×C4×Dic3—101no—
133C3×#208—101no—
134C3×#208—101no—
135C2×C3×C3⋊C8—52no—
136C22×D15—61no—
137C22×D15—61no—
138C22×D15—61no—
139C22×D15—61no—
140C22×C5×D3—61no—
141C22×C5×D3—61no—
142C22×C5×D3—61no—
143C22×C5×D3—61no—
144C22×C3×D5—21no—
145C22×C3×D5D1211yescharacteristic
146C22×C3×D5#6711yescharacteristic
147C2×D3×D5—62no—
148C2×D3×D5—62no—
149C2×D3×D5—62no—
150C2×D3×D5—62no—
151C2×D3×D5—62no—
152C2×D3×D5—62no—
153C2×D3×D5—62no—
154C2×D3×D5—62no—
155C2×D3×D5—124no—
156C2×D3×D5—124no—
157C2×D3×D5—124no—
158C2×D3×D5—124no—
159C2×ΓL(1,𝔽16)—22no—
160C2×C3×AGL(1,𝔽5)—62no—
161C2×C3×C4×C5—21no—
162C2×C3×C4×C5C4×D311yescharacteristic
163C2×C3×C4×C5C4×D311yescharacteristic
164D60—32no—
165D60—32no—
166D60—61no—
167D60—61no—
168D60—62no—
169D60—61no—
170D60—61no—
171C5×D12—32no—
172C5×D12—32no—
173C5×D12—61no—
174C5×D12—61no—
175C5×D12—62no—
176C5×D12—61no—
177C5×D12—61no—
178C2×C3×Dic5—21no—
179C2×C3×Dic5D1211yescharacteristic
180C2×C3×Dic5#6711yescharacteristic
181C3×C4×D5—21no—
182C3×C4×D5—21no—
183C3×C4×D5—21no—
184C3×C4×D5—21no—
185C3×C4×D5C4×D311yescharacteristic
186C3×C4×D5C4×D311yescharacteristic
187C3×C4×D5D1211yescharacteristic
188C3×C4×D5D1211yescharacteristic
189C3×C4×D5#6711yescharacteristic
190C3×C4×D5#6711yescharacteristic
191C3×C4×D5C22×D311yescharacteristic
192C3×C4×D5C22×D311yescharacteristic
193#1203—62no—
194#1203—62no—
195#1203—62no—
196#1203—62no—
197#1203—62no—
198#1203—62no—
199#1203—62no—
200#1203—62no—
201C3⋊#170—22no—
202C3×#170—62no—
203C22×D12—151no—
204C22×D12—151no—
205C22×D12—301no—
206C2×C3×M16—151no—
207C3×#117—151no—
208#926—51no—
209C2×#208—51no—
210#821—154no—
211#809—154no—
212C2×C32×C5—21no—
213C2×C32×C5C2×C22⋊C411yescharacteristic
214C3⋊D15—42no—
215C5×C3⋊D3—42no—
216C32×D5—21no—
217C32×D5AGL(1,ℤ/8)12yes—
218C23×D5—181no—
219C2×C5×D4—91no—
220C2×C22⋊D5—181no—
221D4×D5—92no—
222D4×D5—92no—
223D4×D5—181no—
224D4×D5—181no—
225C2×D20—91no—
226C2×C4×D5D3211yescharacteristic
227C22⋊AGL(1,𝔽5)—61no—
228#704—61no—
229C4⋊AGL(1,𝔽5)—32no—
230C4×AGL(1,𝔽5)—61no—
231#700—61no—
232D5⋊C8—32no—
233C23×C32—51no—
234C22×C3⋊D3—21no—
235C22×C3⋊D3—102no—
236C22×C3⋊D3—102no—
237C22×C3⋊D3—101no—
238C22×C3⋊D3—204no—
239C2×C32×C4—51no—
240C2×C32×C4—51no—
241C2×C32×C4—51no—
242C2×C32×C4—51no—
243C2×C32×C4—51no—
244C2×C32×C4C2×AGL(1,𝔽5)11yescharacteristic
245C4⋊(C3⋊D3)—21no—
246C4⋊(C3⋊D3)—52no—
247C4⋊(C3⋊D3)—102no—
248C4⋊(C3⋊D3)—102no—
249C4⋊(C3⋊D3)—101no—
250C4⋊(C3⋊D3)C2×AGL(1,𝔽5)12yes—
251C2×C3×Dic3—102no—
252C3×C3⋊C8—102no—
253#418—451noSylow
254C22×C3×C5—21no—
255C22×C3×C5(C2×D3)⋊C411yescharacteristic
256C22×C3×C5(C2×D3)⋊C411yescharacteristic
257C2×D15—62no—
258C2×D15—62no—
259C2×D15—62no—
260C2×D15—62no—
261C2×D15—122no—
262C2×D15—122no—
263C2×D15—122no—
264C2×D15—122no—
265C2×C5×D3—62no—
266C2×C5×D3—62no—
267C2×C5×D3—62no—
268C2×C5×D3—62no—
269C2×C5×D3—122no—
270C2×C5×D3—122no—
271C2×C5×D3—122no—
272C2×C5×D3—122no—
273C2×C3×D5—22no—
274C2×C3×D5—22no—
275C2×C3×D5—22no—
276C2×C3×D5—22no—
277C2×C3×D5—21no—
278C2×C3×D5—21no—
279C2×C3×D5(C2×D3)⋊C411yescharacteristic
280C2×C3×D5(C2×D3)⋊C411yescharacteristic
281C2×C3×D5C2×D1211yescharacteristic
282C2×C3×D5C2×#6711yescharacteristic
283D3×D5—124no—
284D3×D5—124no—
285D3×D5—124no—
286D3×D5—124no—
287D3×D5—124no—
288D3×D5—124no—
289D3×D5—124no—
290D3×D5—124no—
291ΓL(1,𝔽16)—42no—
292C3×AGL(1,𝔽5)—122no—
293C3×C4×C5—21no—
294C3×C4×C5—21no—
295C3×C4×C5(C2×D3)⋊C411yescharacteristic
296C3×C4×C5(C2×D3)⋊C411yescharacteristic
297C3×C4×C5C2×C4×D311yescharacteristic
298C3×C4×C5C2×C4×D311yescharacteristic
299C3×Dic5—21no—
300C3×Dic5—21no—
301C3×Dic5(C2×D3)⋊C411yescharacteristic
302C3×Dic5(C2×D3)⋊C411yescharacteristic
303C3×Dic5C2×D1211yescharacteristic
304C3×Dic5C2×#6711yescharacteristic
305C23×D3—301no—
306C23×D3—301no—
307C23×D3—301no—
308C23×D3—301no—
309C22×C3×C4—51no—
310C22×C3×C4—51no—
311C22×C3×C4—101no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—61no—
315C2×D12—152no—
316C2×D12—152no—
317C2×D12—152no—
318C2×D12—152no—
319C2×D12—151no—
320C2×D12—151no—
321C2×D12—302no—
322C2×D12—302no—
323C2×D12—301no—
324C2×D12—301no—
325C2×D12—301no—
326C2×D12—301no—
327C2×D12—301no—
328C2×D12—301no—
329C2×D12—301no—
330C2×D12—301no—
331C2×D12—301no—
332C2×D12—301no—
333C2×D12—301no—
334C2×D12—301no—
335C2×D12—301no—
336C3×M16—301no—
337C3×M16—301no—
338C2×C3×C8—152no—
339C3×C4⋊C4—152no—
340C3×C22⋊C4—301no—
341C3×C42—301no—
342#217—101no—
343C4⋊Dic3—52no—
344C4×Dic3—101no—
345#208—101no—
346#208—101no—
347C2×C3⋊C8—52no—
348C32×C5#41811yescharacteristic, complemented, Hall
349C23×C5—181no—
350C22×D5—181no—
351C22×D5—182no—
352C22×D5—182no—
353C22×D5—364no—
354C22×D5#62611yescharacteristic
355C2×AGL(1,𝔽5)—62no—
356C5×D4—92no—
357C5×D4—181no—
358C2×C4×C5#62411yescharacteristic
359C22⋊D5—182no—
360C22⋊D5—182no—
361C2×Dic5#62611yescharacteristic
362D20—92no—
363D20—181no—
364C4×D5#62411yescharacteristic
365C4×D5#62611yescharacteristic
366C4×D5#62611yescharacteristic
367C4×D5C2×D3211yescharacteristic
368#170—62no—
369C22×C32—51no—
370C22×C32—51no—
371C22×C32—102no—
372C22×C32C22⋊AGL(1,𝔽5)11yescharacteristic
373C2×C3⋊D3—22no—
374C2×C3⋊D3—42no—
375C2×C3⋊D3—102no—
376C2×C3⋊D3—204no—
377C2×C3⋊D3—204no—
378C2×C3⋊D3—202no—
379C32×C4—51no—
380C32×C4—51no—
381C32×C4C22⋊AGL(1,𝔽5)11yescharacteristic
382C32×C4C22×AGL(1,𝔽5)11yescharacteristic
383C3×Dic3—202no—
384C22×D4—451no—
385C2×M16—151no—
386#117—151no—
387#102—454no—
388C2×C3×C5—21no—
389C2×C3×C5—21no—
390C2×C3×C5—21no—
391C2×C3×C5—21no—
392C2×C3×C5—21no—
393C2×C3×C5C2×(C2×D3)⋊C411yescharacteristic
394C2×C3×C5C2×(C2×D3)⋊C411yescharacteristic
395D15—122no—
396D15—122no—
397D15—122no—
398D15—122no—
399C3×D5—21no—
400C3×D5—21no—
401C3×D5—21no—
402C3×D5—21no—
403C3×D5—22no—
404C3×D5#90812yes—
405C3×D5#94912yes—
406C5×D3—122no—
407C5×D3—122no—
408C5×D3—122no—
409C5×D3—122no—
410C23×C3—51no—
411C23×C3—51no—
412C23×C3—101no—
413C22×D3—61no—
414C22×D3—61no—
415C22×D3—61no—
416C22×D3—61no—
417C22×D3—302no—
418C22×D3—302no—
419C22×D3—302no—
420C22×D3—302no—
421C22×D3—302no—
422C22×D3—302no—
423C22×D3—302no—
424C22×D3—302no—
425C22×D3—301no—
426C22×D3—301no—
427C22×D3—301no—
428C22×D3—301no—
429C22×D3—604no—
430C22×D3—604no—
431C22×D3—604no—
432C22×D3—604no—
433C2×C3×C4—21no—
434C2×C3×C4—51no—
435C2×C3×C4—51no—
436C2×C3×C4—51no—
437C2×C3×C4—51no—
438C2×C3×C4—51no—
439C2×C3×C4—51no—
440C2×C3×C4—51no—
441C2×C3×C4—51no—
442C2×C3×C4—51no—
443C2×C3×C4—51no—
444C2×C3×C4—101no—
445C2×C3×C4—101no—
446C2×C3×C4—101no—
447C2×C3×C4—101no—
448C2×C3×C4—101no—
449C2×C3×C4—302no—
450C2×C3×C4D3×AGL(1,𝔽5)11yescharacteristic
451C2×C3×C4D3×AGL(1,𝔽5)11yescharacteristic
452C2×Dic3—102no—
453D12—32no—
454D12—32no—
455D12—62no—
456D12—61no—
457D12—61no—
458D12—61no—
459D12—61no—
460D12—152no—
461D12—152no—
462D12—302no—
463D12—301no—
464D12—301no—
465D12—302no—
466D12—302no—
467D12—302no—
468D12—302no—
469D12—302no—
470D12—302no—
471D12—302no—
472D12—302no—
473D12—301no—
474D12—301no—
475C3×C8—302no—
476C3⋊C8—102no—
477C22×C5—182no—
478C22×C5—362no—
479C22×C5#372211yescharacteristic
480C2×D5—22no—
481C2×D5—182no—
482C2×D5—364no—
483C2×D5—362no—
484C2×D5—364no—
485C2×D5#372211yescharacteristic
486C2×D5C2×#62611yescharacteristic
487AGL(1,𝔽5)—122no—
488C4×C5#372211yescharacteristic
489C4×C5C2×#62411yescharacteristic
490Dic5#372211yescharacteristic
491Dic5C2×#62611yescharacteristic
492C2×C32—21no—
493C2×C32—52no—
494C2×C32—101no—
495C2×C32C2×C22⋊AGL(1,𝔽5)11yescharacteristic
496C3⋊D3—42no—
497C3⋊D3—202no—
498C24—901no—
499C2×D4—91no—
500C2×D4—452no—
501C2×D4—452no—
502C2×D4—451no—
503C2×D4—901no—
504C2×D4—901no—
505C2×D4—901no—
506C22×C4—51no—
507M16—301no—
508M16—301no—
509C2×C8—152no—
510C4⋊C4—152no—
511C22⋊C4—301no—
512C42—301no—
513C3×C5—21no—
514C3×C5#500111yescharacteristic, complemented
515C3×C5#513111yescharacteristic, complemented
516C22×C3—21no—
517C22×C3—51no—
518C22×C3—51no—
519C22×C3—51no—
520C22×C3—51no—
521C22×C3—101no—
522C22×C3—101no—
523C22×C3—102no—
524C22×C3—102no—
525C22×C3—102no—
526C22×C3—102no—
527C22×C3(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
528C22×C3(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
529C2×D3—62no—
530C2×D3—62no—
531C2×D3—62no—
532C2×D3—62no—
533C2×D3—122no—
534C2×D3—122no—
535C2×D3—122no—
536C2×D3—122no—
537C2×D3—302no—
538C2×D3—302no—
539C2×D3—302no—
540C2×D3—302no—
541C2×D3—604no—
542C2×D3—604no—
543C2×D3—604no—
544C2×D3—604no—
545C2×D3—604no—
546C2×D3—604no—
547C2×D3—604no—
548C2×D3—604no—
549C2×D3—602no—
550C2×D3—602no—
551C2×D3—602no—
552C2×D3—602no—
553C3×C4—21no—
554C3×C4—21no—
555C3×C4—51no—
556C3×C4—51no—
557C3×C4—51no—
558C3×C4—51no—
559C3×C4—101no—
560C3×C4—101no—
561C3×C4—602no—
562C3×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
563C3×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
564C3×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
565C3×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
566Dic3—202no—
567C2×C5—21no—
568C2×C5—362no—
569C2×C5C2×#372211yescharacteristic
570D5—21no—
571D5—362no—
572D5#6382512yes—
573C32#6576711yescharacteristic, complemented, Sylow
574C23—51no—
575C23—181no—
576C23—902no—
577C23—902no—
578C23—901no—
579C23—1804no—
580D4—92no—
581D4—181no—
582D4—452no—
583D4—902no—
584D4—902no—
585D4—901no—
586C2×C4—51no—
587C2×C4—51no—
588C2×C4—51no—
589C2×C4—51no—
590C2×C4—51no—
591C2×C4—302no—
592C2×C4ΓL(1,𝔽16)⋊D311yescharacteristic
593C8—302no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—52no—
600C2×C3—52no—
601C2×C3—102no—
602C2×C3—101no—
603C2×C3—101no—
604C2×C3—101no—
605C2×C3—101no—
606C2×C3C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
607C2×C3C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
608D3—122no—
609D3—122no—
610D3—122no—
611D3—122no—
612D3—602no—
613D3—602no—
614D3—602no—
615D3—602no—
616C5#1059109611yescharacteristic, complemented, Sylow
617C22—51no—
618C22—51no—
619C22—102no—
620C22—182no—
621C22—362no—
622C22—902no—
623C22—1802no—
624C22—1804no—
625C22—1804no—
626C22#1062397811yescharacteristic
627C4—51no—
628C4—51no—
629C4—602no—
630C4#1062397811yescharacteristic
631C4C2×ΓL(1,𝔽16)⋊D311yescharacteristic
632C3—21no—
633C3#1175170611yescharacteristic, complemented
634C3#1175170711yescharacteristic, complemented
635C2—21no—
636C2—52no—
637C2—101no—
638C2—362no—
639C2—1802no—
640C2C2×#1062397811yescharacteristic
subgroupG/H
centerC2C2×#10623978
commutatorC32×C4×C5C22×C4
FrattiniC4C2×ΓL(1,𝔽16)⋊D3
FittingC2×C32×C4×C5C2×C4
socleC2×C32×C5C2×C22⋊C4
prime radicalC2×D5×C4⋊(C3⋊D3)C2
cosocleC32×C4×D5C23
hypercenterC2×C4ΓL(1,𝔽16)⋊D3
hypocenterC32×C5#418
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C3×#91989C2semidirect
3. C3×D5⋊#208C2semidirect
4. #13085475C2semidirect
8. C2×C4⋊(C3⋊D15)C4semidirect
9. C2×C5×C4⋊(C3⋊D3)C4semidirect
14. D5×C4⋊(C3⋊D3)C4semidirect
18. C3×C4⋊ΓL(1,𝔽16)C22semidirect
21. C3×D5⋊(C3⋊C8)C22semidirect
26. #91989D3semidirect
27. D5⋊#208D3semidirect
90. C4⋊ΓL(1,𝔽16)C2×D3semidirect
93. D5⋊(C3⋊C8)C2×D3semidirect
129. C2×C4⋊(C3⋊D3)AGL(1,𝔽5)semidirect
348. C32×C5#418semidirect
514. C3×C5#5001semidirect
515. C3×C5#5131semidirect
573. C32#65767semidirect
616. C5#10591096semidirect
633. C3#11751706semidirect
634. C3#11751707semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊(C3⋊D3)2
C3×#919892
C3×D5⋊#2082
#130854752
#117517073
#117517063
#105910965