Finite Group Databasebeta

← #14298486

Subgroups — #14298486

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×D5×C4⋊C4C211yesmaximal, characteristic
2#11751855C211yesmaximal, characteristic
3D5⋊((C2×D3)⋊C8)C211yesmaximal, characteristic
4#11746745C211yesmaximal, characteristic, complemented
5C3×#64874C211yesmaximal, characteristic, complemented
6#11746530C211yesmaximal, characteristic, complemented
7#11746528C211yesmaximal, characteristic, complemented
8#10604283—31nomaximal, Hall
9C2×C4×D3×D5—21no—
10C2×C4×D3×D5C2211yescharacteristic
11C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
12C2×D5⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
14C2×C3×D5⋊C8C2211yescharacteristic
15C2×(C2×D3)⋊AGL(1,𝔽5)—21no—
16C4⋊C4×D15C411yescharacteristic, complemented
17C5×D3×C4⋊C4C411yescharacteristic, complemented
18C3×D5×C4⋊C4C2211yescharacteristic
19#91437C411yescharacteristic, complemented
20D3×C4⋊Dic5C411yescharacteristic, complemented
21D5×C4⋊Dic3C2211yescharacteristic
22#91404—21no—
23D3×#683—21no—
24D5×Dic3⋊C4—21no—
25#91171—21no—
26(C2×D3)⋊#170—21no—
27(C2×AGL(1,𝔽5))⋊Dic3—21no—
28#68872—51nomaximal, Hall
29C2×D5×C4⋊C4—31no—
30#65765—31no—
31D5⋊(C22⋊C8)—31no—
32#64874—31no—
33#64874—31no—
34#64874—31no—
35#64874D311yescharacteristic, complemented
36C22×D3×D5D411yescharacteristic
37C22×ΓL(1,𝔽16)—21no—
38C22×C3×AGL(1,𝔽5)—21no—
39C2×C4×D15—21no—
40C2×C4×D15C2×C411yescharacteristic
41C2×C4×C5×D3—21no—
42C2×C4×C5×D3C2×C411yescharacteristic
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5C2311yescharacteristic
45C2×#1200—21no—
46C2×#1200D411yescharacteristic
47C2×D3×Dic5—21no—
48C2×D3×Dic5D411yescharacteristic
49C2×D5×Dic3—21no—
50C2×D5×Dic3D411yescharacteristic
51C4×D3×D5—21no—
52C4×D3×D5—21no—
53C4×D3×D5—21no—
54C4×D3×D5—21no—
55C4×D3×D5—42no—
56C4×D3×D5—42no—
57C2×C3⋊#170—21no—
58C4⋊ΓL(1,𝔽16)—21no—
59C4⋊ΓL(1,𝔽16)—21no—
60D5⋊(C3⋊C8)—21no—
61D5⋊(C3⋊C8)—21no—
62C2×C3×#170—21no—
63C3×C4⋊AGL(1,𝔽5)—21no—
64C3×C4⋊AGL(1,𝔽5)—21no—
65C3×D5⋊C8—21no—
66C3×D5⋊C8—21no—
67(C2×D3)⋊AGL(1,𝔽5)—42no—
68C3×C5×C4⋊C4C2×C411yescharacteristic
69C4⋊Dic15C2×C411yescharacteristic
70#6712—21no—
71C5×C4⋊Dic3C2×C411yescharacteristic
72C5×Dic3⋊C4—21no—
73C3×C4⋊Dic5C2×C411yescharacteristic
74C3×#683—21no—
75Dic3⋊Dic5—21no—
76#6669—21no—
77#6668—21no—
78C2×D3×C4⋊C4—51no—
79C2×(C2×D3)⋊C8—51no—
80#4987—51no—
81C3×#340—51no—
82#4551—51no—
83#4529—51no—
84#4529—51no—
85C22×C4×D5—31no—
86C22×C4×D5—61no—
87C2×C22⋊AGL(1,𝔽5)—61no—
88C2×C4⋊AGL(1,𝔽5)—31no—
89C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
90C2×D5⋊C8—31no—
91C2×D5⋊C8C2×D311yescharacteristic
92C2×C5×C4⋊C4—31no—
93C2×C4⋊Dic5—31no—
94C2×#683—61no—
95D5×C4⋊C4—31no—
96D5×C4⋊C4—31no—
97D5×C4⋊C4—31no—
98D5×C4⋊C4—61no—
99D5×C4⋊C4—61no—
100D5×C4⋊C4C2×D311yescharacteristic
101C22⋊#170—61no—
102(C2×AGL(1,𝔽5))⋊C4—61no—
103#4003—61no—
104#1824—151noSylow
105C22×D15C22⋊C411yescharacteristic
106C22×C5×D3C22⋊C411yescharacteristic
107C22×C3×D5C2×D411yescharacteristic
108C2×D3×D5—21no—
109C2×D3×D5—21no—
110C2×D3×D5—21no—
111C2×D3×D5—21no—
112C2×D3×D5SD1612yes—
113C2×D3×D5Q1612yes—
114C2×ΓL(1,𝔽16)—41no—
115C2×ΓL(1,𝔽16)—41no—
116C2×ΓL(1,𝔽16)—41no—
117C2×C3×AGL(1,𝔽5)—41no—
118C2×C3×AGL(1,𝔽5)—41no—
119C2×C3×AGL(1,𝔽5)—41no—
120C2×C3×C4×C5—21no—
121C2×C3×C4×C5C22×C411yescharacteristic
122C2×Dic15—21no—
123C2×Dic15C22⋊C411yescharacteristic
124C4×D15—21no—
125C4×D15—21no—
126C4×D15—42no—
127C2×C5×Dic3—21no—
128C2×C5×Dic3C22⋊C411yescharacteristic
129C4×C5×D3—21no—
130C4×C5×D3—21no—
131C4×C5×D3—42no—
132C2×C3×Dic5—21no—
133C2×C3×Dic5C2×D411yescharacteristic
134C3×C4×D5—41no—
135C3×C4×D5—41no—
136C3×C4×D5#4111yescharacteristic
137C3×C4×D5#4111yescharacteristic
138C3×C4×D5#4111yescharacteristic
139C3×C4×D5#4111yescharacteristic
140#1200—21no—
141#1200—21no—
142#1200—42no—
143D3×Dic5—21no—
144D3×Dic5—21no—
145D3×Dic5—42no—
146D5×Dic3—21no—
147D5×Dic3—21no—
148D5×Dic3—41no—
149D5×Dic3—41no—
150C3⋊#170—41no—
151C3×#170—41no—
152C22×C4×D3—51no—
153C22×C4×D3—101no—
154C22×C3×C8—51no—
155C2×C3×C4⋊C4—51no—
156C2×C3×C4⋊C4—51no—
157C2×(C2×D3)⋊C4—101no—
158C2×C4⋊Dic3—51no—
159C2×C4⋊Dic3—51no—
160C2×Dic3⋊C4—101no—
161C22×C3⋊C8—51no—
162D3×C4⋊C4—51no—
163D3×C4⋊C4—51no—
164D3×C4⋊C4—51no—
165D3×C4⋊C4—101no—
166D3×C4⋊C4—101no—
167D3×C4⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
168C3⋊#95—101no—
169(C2×D3)⋊C8—101no—
170(C2×D3)⋊C8—101no—
171C23×D5—31no—
172C22×AGL(1,𝔽5)—21no—
173C22×AGL(1,𝔽5)—61no—
174C22×C4×C5—31no—
175C22×C4×C5—61no—
176C22×Dic5—31no—
177C22×Dic5—61no—
178C2×C4×D5—21no—
179C2×C4×D5—31no—
180C2×C4×D5—31no—
181C2×C4×D5—31no—
182C2×C4×D5—61no—
183C2×C4×D5—61no—
184C2×C4×D5—61no—
185C2×C4×D5—61no—
186C2×C4×D5—61no—
187C2×C4×D5—61no—
188C2×C4×D5—61no—
189C2×C4×D5—122no—
190C2×C4×D5—122no—
191C2×C4×D5C22×D311yescharacteristic
192C22⋊AGL(1,𝔽5)—122no—
193C2×#170—21no—
194C2×#170—61no—
195C4⋊AGL(1,𝔽5)—21no—
196C4⋊AGL(1,𝔽5)—21no—
197C4⋊AGL(1,𝔽5)—61no—
198C4⋊AGL(1,𝔽5)—61no—
199D5⋊C8—21no—
200D5⋊C8—21no—
201D5⋊C8—61no—
202D5⋊C8—61no—
203C5×C4⋊C4—31no—
204C5×C4⋊C4—61no—
205C5×C4⋊C4C4×D311yescharacteristic
206C4⋊Dic5—31no—
207C4⋊Dic5—61no—
208C4⋊Dic5C4×D311yescharacteristic
209#683—21no—
210#683—61no—
211#683—61no—
212#683—61no—
213C22×C4⋊C4—151no—
214C2×C22⋊C8—151no—
215#380—151no—
216#340—51no—
217#340—151no—
218#340—151no—
219#340—151no—
220C22×C3×C5C2×C22⋊C411yescharacteristic
221C2×D15—21no—
222C2×D15—21no—
223C2×D15#10312yes—
224C2×C5×D3—21no—
225C2×C5×D3—21no—
226C2×C5×D3#10312yes—
227C2×C3×D5#12311yescharacteristic
228C2×C3×D5#12311yescharacteristic
229C2×C3×D5C2×SD1611yescharacteristic
230C2×C3×D5C2×Q1611yescharacteristic
231C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
232C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
233D3×D5—22no—
234D3×D5—22no—
235D3×D5—22no—
236D3×D5—22no—
237ΓL(1,𝔽16)—81no—
238C3×AGL(1,𝔽5)—81no—
239C3×C4×C5—41no—
240C3×C4×C5#11711yescharacteristic
241C3×C4×C5#11711yescharacteristic
242Dic15—21no—
243Dic15—41no—
244C3×Dic5—41no—
245C3×Dic5#12311yescharacteristic
246C3×Dic5#12311yescharacteristic
247C5×Dic3—21no—
248C5×Dic3—41no—
249C23×D3—51no—
250C22×C3×C4—51no—
251C22×C3×C4—101no—
252C22×C3×C4—101no—
253C22×Dic3—51no—
254C22×Dic3—101no—
255C22×Dic3—101no—
256C2×C4×D3—21no—
257C2×C4×D3—51no—
258C2×C4×D3—51no—
259C2×C4×D3—51no—
260C2×C4×D3—101no—
261C2×C4×D3—101no—
262C2×C4×D3—101no—
263C2×C4×D3—101no—
264C2×C4×D3—101no—
265C2×C4×D3—101no—
266C2×C4×D3—101no—
267C2×C4×D3—202no—
268C2×C4×D3—202no—
269C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
270C2×C3×C8—101no—
271C2×C3×C8—101no—
272C2×C3×C8—101no—
273C3×C4⋊C4—51no—
274C3×C4⋊C4—101no—
275C3×C4⋊C4—101no—
276C3×C4⋊C4—101no—
277C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
278(C2×D3)⋊C4—202no—
279C4⋊Dic3—51no—
280C4⋊Dic3—101no—
281C4⋊Dic3—101no—
282C4⋊Dic3—101no—
283C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
284Dic3⋊C4—21no—
285Dic3⋊C4—101no—
286Dic3⋊C4—101no—
287Dic3⋊C4—101no—
288C2×C3⋊C8—101no—
289C2×C3⋊C8—101no—
290C2×C3⋊C8—101no—
291C23×C5—31no—
292C22×D5—31no—
293C22×D5—32no—
294C22×D5—32no—
295C22×D5—61no—
296C22×D5—61no—
297C22×D5—61no—
298C22×D5—61no—
299C22×D5D3×D411yescharacteristic
300C2×AGL(1,𝔽5)—41no—
301C2×AGL(1,𝔽5)—41no—
302C2×AGL(1,𝔽5)—41no—
303C2×AGL(1,𝔽5)—121no—
304C2×AGL(1,𝔽5)—121no—
305C2×AGL(1,𝔽5)—121no—
306C2×C4×C5—21no—
307C2×C4×C5—31no—
308C2×C4×C5—61no—
309C2×C4×C5—61no—
310C2×C4×C5—61no—
311C2×C4×C5—122no—
312C2×C4×C5C2×C4×D311yescharacteristic
313C2×Dic5—21no—
314C2×Dic5—31no—
315C2×Dic5—61no—
316C2×Dic5—61no—
317C2×Dic5—61no—
318C2×Dic5—122no—
319C2×Dic5D3×D411yescharacteristic
320C4×D5—41no—
321C4×D5—41no—
322C4×D5—61no—
323C4×D5—61no—
324C4×D5—61no—
325C4×D5—61no—
326C4×D5—61no—
327C4×D5—61no—
328C4×D5—122no—
329C4×D5—122no—
330C4×D5—121no—
331C4×D5—121no—
332C4×D5#23511yescharacteristic
333C4×D5#23511yescharacteristic
334C4×D5#23711yescharacteristic
335C4×D5#23911yescharacteristic
336#170—41no—
337#170—121no—
338C23×C4—151no—
339C23×C4—301no—
340C22×C8—51no—
341C22×C8—151no—
342C2×C4⋊C4—31no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—151no—
346C2×C4⋊C4—151no—
347C2×C4⋊C4—151no—
348C2×C4⋊C4—151no—
349C2×C4⋊C4—151no—
350C2×C4⋊C4—301no—
351C2×C4⋊C4—301no—
352C2×C4⋊C4—301no—
353C2×C22⋊C4—301no—
354C22⋊C8—301no—
355C22⋊C8—301no—
356#95—301no—
357C2×C3×C5#38111yescharacteristic
358C2×C3×C5C2×#10311yescharacteristic
359C2×C3×C5#41811yescharacteristic
360D15—22no—
361C3×D5#48111yescharacteristic
362C3×D5#48111yescharacteristic
363C3×D5#48411yescharacteristic
364C3×D5#48411yescharacteristic
365C5×D3—22no—
366C23×C3—51no—
367C22×D3—51no—
368C22×D3—52no—
369C22×D3—52no—
370C22×D3—101no—
371C22×D3—101no—
372C22×D3—101no—
373C22×D3—101no—
374C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
375C2×C3×C4—21no—
376C2×C3×C4—51no—
377C2×C3×C4—51no—
378C2×C3×C4—51no—
379C2×C3×C4—51no—
380C2×C3×C4—51no—
381C2×C3×C4—101no—
382C2×C3×C4—201no—
383C2×C3×C4—201no—
384C2×C3×C4—201no—
385C2×C3×C4—201no—
386C2×C3×C4—201no—
387C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
388C2×Dic3—21no—
389C2×Dic3—51no—
390C2×Dic3—101no—
391C2×Dic3—101no—
392C2×Dic3—101no—
393C2×Dic3—201no—
394C2×Dic3—201no—
395C2×Dic3—201no—
396C2×Dic3—201no—
397C2×Dic3—201no—
398C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
399C4×D3—21no—
400C4×D3—21no—
401C4×D3—42no—
402C4×D3—101no—
403C4×D3—101no—
404C4×D3—101no—
405C4×D3—101no—
406C4×D3—101no—
407C4×D3—101no—
408C4×D3—202no—
409C4×D3—202no—
410C4×D3—202no—
411C3×C8—201no—
412C3⋊C8—201no—
413C22×C5—32no—
414C22×C5—61no—
415C22×C5—61no—
416C22×C5D3×C22⋊C411yescharacteristic
417C2×D5—32no—
418C2×D5—61no—
419C2×D5—61no—
420C2×D5—62no—
421C2×D5—62no—
422C2×D5—62no—
423C2×D5—62no—
424C2×D5#88311yescharacteristic
425C2×D5#89411yescharacteristic
426C2×D5#91111yescharacteristic
427C2×D5D3×SD1611yescharacteristic
428C2×D5#91411yescharacteristic
429C2×D5D3×Q1611yescharacteristic
430AGL(1,𝔽5)—81no—
431AGL(1,𝔽5)—241no—
432C4×C5—41no—
433C4×C5—61no—
434C4×C5—121no—
435C4×C5#87211yescharacteristic
436C4×C5#89211yescharacteristic
437Dic5—41no—
438Dic5—61no—
439Dic5—121no—
440Dic5#88311yescharacteristic
441Dic5#89411yescharacteristic
442C24—151no—
443C22×C4—31no—
444C22×C4—51no—
445C22×C4—61no—
446C22×C4—101no—
447C22×C4—101no—
448C22×C4—151no—
449C22×C4—151no—
450C22×C4—151no—
451C22×C4—151no—
452C22×C4—301no—
453C22×C4—301no—
454C22×C4—301no—
455C22×C4—301no—
456C22×C4—301no—
457C22×C4—301no—
458C22×C4—301no—
459C22×C4—301no—
460C22×C4—301no—
461C22×C4—602no—
462C22×C4—602no—
463C2×C8—101no—
464C2×C8—101no—
465C2×C8—101no—
466C2×C8—301no—
467C2×C8—301no—
468C2×C8—301no—
469C4⋊C4—31no—
470C4⋊C4—51no—
471C4⋊C4—61no—
472C4⋊C4—101no—
473C4⋊C4—101no—
474C4⋊C4—101no—
475C4⋊C4—151no—
476C4⋊C4—301no—
477C4⋊C4—301no—
478C4⋊C4—301no—
479C4⋊C4—301no—
480C4⋊C4—301no—
481C4⋊C4—301no—
482C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
483C22⋊C4—602no—
484C3×C5#182411yescharacteristic, complemented, Hall
485C22×C3—51no—
486C22×C3—51no—
487C22×C3—51no—
488C22×C3—51no—
489C22×C3—51no—
490C22×C3—51no—
491C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
492C2×D3—21no—
493C2×D3—21no—
494C2×D3—52no—
495C2×D3—102no—
496C2×D3—102no—
497C2×D3—102no—
498C2×D3—102no—
499C2×D3—101no—
500C2×D3—101no—
501C2×D3#400912yes—
502C3×C4—41no—
503C3×C4—51no—
504C3×C4—51no—
505C3×C4—201no—
506C3×C4—401no—
507C3×C4#413011yescharacteristic
508C3×C4#413011yescharacteristic
509Dic3—21no—
510Dic3—41no—
511Dic3—101no—
512Dic3—201no—
513Dic3—401no—
514C2×C5—62no—
515C2×C5#466411yescharacteristic
516C2×C5#477011yescharacteristic
517C2×C5D3×#10311yescharacteristic
518D5—62no—
519D5#477711yescharacteristic
520D5#481111yescharacteristic
521D5#486311yescharacteristic
522D5#488411yescharacteristic
523C23—31no—
524C23—51no—
525C23—152no—
526C23—152no—
527C23—151no—
528C23—301no—
529C23—301no—
530C23—301no—
531C23—301no—
532C2×C4—21no—
533C2×C4—31no—
534C2×C4—51no—
535C2×C4—51no—
536C2×C4—51no—
537C2×C4—51no—
538C2×C4—51no—
539C2×C4—61no—
540C2×C4—61no—
541C2×C4—61no—
542C2×C4—101no—
543C2×C4—122no—
544C2×C4—151no—
545C2×C4—201no—
546C2×C4—201no—
547C2×C4—201no—
548C2×C4—201no—
549C2×C4—201no—
550C2×C4—301no—
551C2×C4—301no—
552C2×C4—301no—
553C2×C4—301no—
554C2×C4—301no—
555C2×C4—301no—
556C2×C4—301no—
557C2×C4—301no—
558C2×C4—301no—
559C2×C4—602no—
560C2×C4—602no—
561C2×C4—601no—
562C2×C4—601no—
563C2×C4—602no—
564C2×C4—601no—
565C2×C4—601no—
566C2×C4—601no—
567C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
568C8—201no—
569C8—601no—
570C2×C3—51no—
571C2×C3—51no—
572C2×C3—51no—
573C2×C3—51no—
574C2×C3#6576411yescharacteristic
575C2×C3#6576711yescharacteristic
576C2×C3C2×#400911yescharacteristic
577D3—22no—
578D3—102no—
579C5#6887211yescharacteristic, complemented, Sylow
580C22—32no—
581C22—51no—
582C22—51no—
583C22—51no—
584C22—51no—
585C22—51no—
586C22—51no—
587C22—61no—
588C22—61no—
589C22—152no—
590C22—302no—
591C22—302no—
592C22—302no—
593C22—302no—
594C22—301no—
595C22—301no—
596C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
597C4—41no—
598C4—51no—
599C4—51no—
600C4—61no—
601C4—121no—
602C4—201no—
603C4—301no—
604C4—401no—
605C4—601no—
606C4—1201no—
607C4#9190711yescharacteristic
608C4#9190911yescharacteristic
609C3#1060428311yescharacteristic, complemented, Sylow
610C2—51no—
611C2—51no—
612C2—51no—
613C2—51no—
614C2—62no—
615C2—302no—
616C2#1175185311yescharacteristic
617C2#1175193811yescharacteristic
618C2D3×#400911yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C5×C4⋊C4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D3×D5D4
cosocleC2×C3×C4×D5C23
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1824
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11746745C2semidirect
5. C3×#64874C2semidirect
6. #11746530C2semidirect
7. #11746528C2semidirect
16. C4⋊C4×D15C4semidirect
17. C5×D3×C4⋊C4C4semidirect
19. #91437C4semidirect
20. D3×C4⋊Dic5C4semidirect
35. #64874D3semidirect
167. D3×C4⋊C4AGL(1,𝔽5)semidirect
484. C3×C5#1824semidirect
579. C5#68872semidirect
609. C3#10604283semidirect

Maximal subgroups

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

subgroupindex
D3×D5×C4⋊C42
#117518552
D5⋊((C2×D3)⋊C8)2
#117467452
C3×#648742
#117465302
#117465282
#106042833
#688725