Finite Group Databasebeta

← #14307506

Subgroups — #14307506

Order 1920.

648 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#878C211yesmaximal, characteristic
2#11749513C211yesmaximal, characteristic
3Dic3×C22⋊Dic5C211yesmaximal, characteristic
4#11746347C211yesmaximal, characteristic
5C3×#64746C211yesmaximal, characteristic
6#11746018C211yesmaximal, characteristic
7#11746018C211yesmaximal, characteristic
8#10602494—31nomaximal, Hall
9C23×C5×Dic3C2211yescharacteristic
10C22×C5×Dic6C411yescharacteristic, complemented
11C2×C3×C5×C22⋊C4C2211yescharacteristic
12C2×#6719C2211yescharacteristic
13C2×#6719C2211yescharacteristic
14C2×C5×#217C2211yescharacteristic
15C2×C5×C4⋊Dic3C411yescharacteristic, complemented
16C2×C5×Dic3⋊C4C411yescharacteristic, complemented
17C2×C5×Dic3⋊C4C411yescharacteristic, complemented
18C5×#878—21no—
19C5×#878—21no—
20C5×#878—21no—
21C5×#878—21no—
22C2×C3×C22⋊Dic5C2211yescharacteristic
23C2×C3×C22⋊Dic5C2211yescharacteristic
24C2×Dic3⋊Dic5—21no—
25C2×Dic3×Dic5—21no—
26#90994—21no—
27#90994—21no—
28#68955—51nomaximal, Hall
29C2×C5×C22⋊Q8—31no—
30#65501—31no—
31C4×C22⋊Dic5—31no—
32#64746—31no—
33#64746—31no—
34#64746—31no—
35#64746D311yescharacteristic
36C24×C3×C5C2311yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C22×C3×C4×C5C2×C411yescharacteristic
39C22×Dic15—21no—
40C22×Dic15—21no—
41C22×C5×Dic3—42no—
42C22×C5×Dic3C2×C411yescharacteristic
43C22×C5×Dic3C2×C411yescharacteristic
44C22×C5×Dic3C2×C411yescharacteristic
45C22×C5×Dic3C2×C411yescharacteristic
46C22×C5×Dic3D411yescharacteristic
47C22×C5×Dic3D411yescharacteristic
48C22×C5×Dic3D411yescharacteristic
49C22×C5×Dic3D411yescharacteristic
50C2×C5×Dic6—21no—
51C2×C5×Dic6—21no—
52C2×C5×Dic6—42no—
53C22×C3×Dic5—21no—
54C22×C3×Dic5—21no—
55C3×C5×C22⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57#6719—21no—
58#6719—21no—
59#6719—21no—
60#6719Q812yescomplemented
61C5×#217—21no—
62C5×#217—21no—
63C5×C4⋊Dic3—21no—
64C5×C4⋊Dic3—21no—
65C5×Dic3⋊C4—21no—
66C5×Dic3⋊C4—21no—
67C5×Dic3⋊C4—21no—
68C5×Dic3⋊C4—21no—
69C3×C22⋊Dic5—21no—
70C3×C22⋊Dic5—21no—
71C3×C22⋊Dic5—21no—
72C3×C22⋊Dic5Q812yescomplemented
73Dic3⋊Dic5—42no—
74Dic3×Dic5—42no—
75C2×#878D511yescharacteristic
76#4942—51no—
77Dic3×C22⋊C4—51no—
78C3×#342—51no—
79#4527—51no—
80#4527—51no—
81#4526—51no—
82C22×C5×Q8—31no—
83C23×C4×C5—31no—
84C5×C22⋊Q8—61no—
85C5×C22⋊Q8—61no—
86C5×C22⋊Q8—61no—
87C5×C22⋊Q8—61no—
88C2×C5×C4⋊C4—31no—
89C2×C5×C4⋊C4—31no—
90C2×C5×C4⋊C4—31no—
91C2×C5×C22⋊C4—31no—
92C2×C5×C22⋊C4C2×D311yescharacteristic
93C2×C22⋊Dic5—31no—
94C2×C22⋊Dic5—31no—
95C2×C22⋊Dic5C2×D311yescharacteristic
96C2×C22⋊Dic5C2×D311yescharacteristic
97C2×C4⋊Dic5—61no—
98C2×C4×Dic5—61no—
99#3963—61no—
100#3963—61no—
101#1996—151noSylow
102C23×C3×C5—41no—
103C23×C3×C5—41no—
104C23×C3×C5C22×C411yescharacteristic
105C23×C3×C5C2×D411yescharacteristic
106C23×C3×C5C2×D411yescharacteristic
107C23×C3×C5C2×Q811yescharacteristic
108C23×C3×C5C2×Q811yescharacteristic
109C23×C3×C5#4111yescharacteristic
110C23×C3×C5#4111yescharacteristic
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—21no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5—41no—
115C2×Dic15—22no—
116C2×Dic15—41no—
117C2×Dic15—41no—
118C2×Dic15—41no—
119C2×Dic15—41no—
120C2×Dic15—41no—
121C2×C5×Dic3—22no—
122C2×C5×Dic3—22no—
123C2×C5×Dic3—22no—
124C2×C5×Dic3—21no—
125C2×C5×Dic3—21no—
126C2×C5×Dic3—41no—
127C2×C5×Dic3—41no—
128C2×C5×Dic3—41no—
129C2×C5×Dic3—41no—
130C2×C5×Dic3—41no—
131C2×C5×Dic3C22⋊C411yescharacteristic
132C2×C5×Dic3C22⋊C411yescharacteristic
133C2×C5×Dic3C22⋊C411yescharacteristic
134C2×C5×Dic3C22⋊C411yescharacteristic
135C5×Dic6—42no—
136C5×Dic6—42no—
137C2×C3×Dic5—22no—
138C2×C3×Dic5—41no—
139C2×C3×Dic5—41no—
140C2×C3×Dic5—41no—
141C2×C3×Dic5—41no—
142C2×C3×Dic5—41no—
143C23×Dic3C2×D511yescharacteristic
144C22×Dic6Dic511yescharacteristic, complemented
145C2×C3×C22⋊C4—51no—
146C2×C3×C22⋊C4—51no—
147C2×C3×C22⋊C4C2×D511yescharacteristic
148C2×#217—51no—
149C2×#217—51no—
150C2×#217C2×D511yescharacteristic
151C2×C4⋊Dic3Dic511yescharacteristic, complemented
152C2×Dic3⋊C4—101no—
153C2×Dic3⋊C4Dic511yescharacteristic, complemented
154C2×Dic3⋊C4Dic511yescharacteristic, complemented
155C2×C4×Dic3—101no—
156#878—21no—
157#878—21no—
158#878—21no—
159#878—21no—
160C3⋊#95—101no—
161C3⋊#95—101no—
162C24×C5C22×D311yescharacteristic
163C2×C5×Q8—61no—
164C2×C5×Q8—61no—
165C2×C5×Q8—122no—
166C22×C4×C5—31no—
167C22×C4×C5—31no—
168C22×C4×C5—31no—
169C22×C4×C5—31no—
170C22×C4×C5—31no—
171C22×C4×C5—31no—
172C22×C4×C5—31no—
173C22×C4×C5—31no—
174C22×C4×C5—122no—
175C22×C4×C5C4×D311yescharacteristic
176C22×C4×C5C4×D311yescharacteristic
177C22×Dic5—21no—
178C22×Dic5—21no—
179C22×Dic5—61no—
180C22×Dic5—61no—
181C5×C4⋊C4—61no—
182C5×C4⋊C4—61no—
183C5×C4⋊C4—61no—
184C5×C4⋊C4—61no—
185C5×C4⋊C4—61no—
186C5×C4⋊C4—61no—
187C5×C22⋊C4—21no—
188C5×C22⋊C4—21no—
189C5×C22⋊C4—61no—
190C5×C22⋊C4—61no—
191C22⋊Dic5—21no—
192C22⋊Dic5—21no—
193C22⋊Dic5—21no—
194C22⋊Dic5—32no—
195C22⋊Dic5—61no—
196C22⋊Dic5—61no—
197C22⋊Dic5—61no—
198C22⋊Dic5Dic612yescomplemented
199C4⋊Dic5—122no—
200C4×Dic5—122no—
201C2×C22⋊Q8—31no—
202#380—151no—
203C4×C22⋊C4—151no—
204#342—51no—
205#342—151no—
206#342—151no—
207#342—151no—
208C22×C3×C5—21no—
209C22×C3×C5—21no—
210C22×C3×C5—21no—
211C22×C3×C5—21no—
212C22×C3×C5—21no—
213C22×C3×C5—21no—
214C22×C3×C5—41no—
215C22×C3×C5—41no—
216C22×C3×C5—41no—
217C22×C3×C5—41no—
218C22×C3×C5C2×C22⋊C411yescharacteristic
219C22×C3×C5C4×Q811yescharacteristic
220C22×C3×C5C4×Q811yescharacteristic
221C22×C3×C5C22⋊Q811yescharacteristic
222C22×C3×C5C22⋊Q811yescharacteristic
223C22×C3×C5#12411yescharacteristic
224C22×C3×C5C4⋊Q811yescharacteristic
225C3×C4×C5—41no—
226C3×C4×C5—41no—
227Dic15—42no—
228Dic15—81no—
229C3×Dic5—42no—
230C3×Dic5—81no—
231C5×Dic3—21no—
232C5×Dic3—21no—
233C5×Dic3—21no—
234C5×Dic3—41no—
235C5×Dic3—41no—
236C5×Dic3#9912yes—
237C24×C3C22×D511yescharacteristic
238C22×C3×C4—101no—
239C22×C3×C4—101no—
240C22×C3×C4C2×Dic511yescharacteristic
241C22×C3×C4C2×Dic511yescharacteristic
242C22×Dic3—42no—
243C22×Dic3—101no—
244C22×Dic3—101no—
245C22×Dic3C2×Dic511yescharacteristic
246C22×Dic3C2×Dic511yescharacteristic
247C22×Dic3C2×Dic511yescharacteristic
248C22×Dic3C2×Dic511yescharacteristic
249C22×Dic3C22⋊D511yescharacteristic
250C22×Dic3C22⋊D511yescharacteristic
251C22×Dic3C22⋊D511yescharacteristic
252C22×Dic3C22⋊D511yescharacteristic
253C2×Dic6—21no—
254C2×Dic6—21no—
255C2×Dic6—42no—
256C3×C22⋊C4—21no—
257C3×C22⋊C4—21no—
258C3×C22⋊C4—52no—
259C3×C22⋊C4—101no—
260C3×C22⋊C4—101no—
261C3×C22⋊C4—101no—
262#217—21no—
263#217—21no—
264#217—52no—
265#217—101no—
266#217—101no—
267#217—101no—
268C4⋊Dic3—21no—
269C4⋊Dic3—21no—
270Dic3⋊C4—21no—
271Dic3⋊C4—21no—
272Dic3⋊C4—21no—
273Dic3⋊C4—21no—
274Dic3⋊C4—202no—
275C4×Dic3—202no—
276C23×C5—41no—
277C23×C5—41no—
278C23×C5C2×Dic611yescharacteristic
279C23×C5C2×C4×D311yescharacteristic
280C23×C5#23511yescharacteristic
281C23×C5D3×D411yescharacteristic
282C23×C5D3×D411yescharacteristic
283C23×C5#23711yescharacteristic
284C23×C5D3×Q811yescharacteristic
285C5×Q8—122no—
286C5×Q8—122no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—31no—
290C2×C4×C5—31no—
291C2×C4×C5—31no—
292C2×C4×C5—31no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5—62no—
296C2×C4×C5—62no—
297C2×C4×C5—62no—
298C2×C4×C5—61no—
299C2×C4×C5—61no—
300C2×C4×C5—121no—
301C2×C4×C5—121no—
302C2×C4×C5—121no—
303C2×C4×C5—121no—
304C2×C4×C5—121no—
305C2×Dic5—22no—
306C2×Dic5—41no—
307C2×Dic5—41no—
308C2×Dic5—41no—
309C2×Dic5—41no—
310C2×Dic5—41no—
311C2×Dic5—62no—
312C2×Dic5—121no—
313C2×Dic5—121no—
314C2×Dic5—121no—
315C2×Dic5—121no—
316C2×Dic5—121no—
317C22×Q8—31no—
318C23×C4—31no—
319C22⋊Q8—61no—
320C22⋊Q8—61no—
321C22⋊Q8—61no—
322C22⋊Q8—61no—
323C2×C4⋊C4—31no—
324C2×C4⋊C4—31no—
325C2×C4⋊C4—31no—
326C2×C4⋊C4—301no—
327C2×C22⋊C4—31no—
328C2×C22⋊C4—51no—
329C2×C22⋊C4—51no—
330C2×C22⋊C4—151no—
331C2×C22⋊C4—151no—
332C2×C22⋊C4D3×D511yescharacteristic
333C2×C42—301no—
334#95—301no—
335#95—301no—
336C2×C3×C5—21no—
337C2×C3×C5—21no—
338C2×C3×C5—21no—
339C2×C3×C5—21no—
340C2×C3×C5—21no—
341C2×C3×C5—21no—
342C2×C3×C5#39111yescharacteristic
343C2×C3×C5C2×#9911yescharacteristic
344C2×C3×C5#41011yescharacteristic
345C23×C3—41no—
346C23×C3—41no—
347C23×C3Q8×D511yescharacteristic
348C23×C3Q8×D511yescharacteristic
349C23×C3#71311yescharacteristic
350C23×C3#71311yescharacteristic
351C23×C3C22×Dic511yescharacteristic
352C23×C3C2×C22⋊D511yescharacteristic
353C23×C3C2×C22⋊D511yescharacteristic
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—41no—
357C2×C3×C4—41no—
358C2×C3×C4—102no—
359C2×C3×C4—201no—
360C2×C3×C4—201no—
361C2×C3×C4—201no—
362C2×C3×C4—201no—
363C2×C3×C4—201no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—41no—
370C2×Dic3—41no—
371C2×Dic3—41no—
372C2×Dic3—41no—
373C2×Dic3—41no—
374C2×Dic3—102no—
375C2×Dic3—201no—
376C2×Dic3—201no—
377C2×Dic3—201no—
378C2×Dic3—201no—
379C2×Dic3—201no—
380C2×Dic3C22⋊Dic511yescharacteristic
381C2×Dic3C22⋊Dic511yescharacteristic
382C2×Dic3C22⋊Dic511yescharacteristic
383C2×Dic3C22⋊Dic511yescharacteristic
384Dic6—42no—
385Dic6—42no—
386C22×C5—21no—
387C22×C5—21no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5—41no—
393C22×C5—41no—
394C22×C5—41no—
395C22×C5—41no—
396C22×C5C4×Dic611yescharacteristic
397C22×C5#87811yescharacteristic
398C22×C5D3×C22⋊C411yescharacteristic
399C22×C5#88511yescharacteristic
400C22×C5#88711yescharacteristic
401C22×C5#88811yescharacteristic
402C22×C5#89611yescharacteristic
403C4×C5—32no—
404C4×C5—41no—
405C4×C5—41no—
406C4×C5—61no—
407C4×C5—61no—
408C4×C5—61no—
409C4×C5—121no—
410C4×C5—121no—
411Dic5—42no—
412Dic5—81no—
413Dic5—122no—
414Dic5—241no—
415C24C2×D3×D511yescharacteristic
416C2×Q8—61no—
417C2×Q8—61no—
418C2×Q8—122no—
419C22×C4—31no—
420C22×C4—31no—
421C22×C4—31no—
422C22×C4—31no—
423C22×C4—31no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—31no—
427C22×C4—101no—
428C22×C4—101no—
429C22×C4—122no—
430C22×C4—301no—
431C22×C4—301no—
432C22×C4D3×Dic511yescharacteristic
433C22×C4D3×Dic511yescharacteristic
434C4⋊C4—61no—
435C4⋊C4—61no—
436C4⋊C4—61no—
437C4⋊C4—61no—
438C4⋊C4—61no—
439C4⋊C4—61no—
440C4⋊C4—602no—
441C22⋊C4—21no—
442C22⋊C4—21no—
443C22⋊C4—52no—
444C22⋊C4—61no—
445C22⋊C4—61no—
446C22⋊C4—101no—
447C22⋊C4—101no—
448C22⋊C4—101no—
449C22⋊C4—152no—
450C22⋊C4—301no—
451C22⋊C4—301no—
452C22⋊C4—301no—
453C42—602no—
454C3×C5#199611yescharacteristic, complemented, Hall
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3#409011yescharacteristic
466C22×C3Q8×Dic511yescharacteristic
467C22×C3Q8×Dic511yescharacteristic
468C22×C3#409211yescharacteristic
469C22×C3#409211yescharacteristic
470C22×C3#409311yescharacteristic
471C22×C3C2×C22⋊Dic511yescharacteristic
472C3×C4—41no—
473C3×C4—41no—
474C3×C4—202no—
475C3×C4—401no—
476Dic3—21no—
477Dic3—21no—
478Dic3—21no—
479Dic3—41no—
480Dic3—41no—
481Dic3—202no—
482Dic3—401no—
483Dic3#396612yes—
484C2×C5—21no—
485C2×C5—21no—
486C2×C5—21no—
487C2×C5—21no—
488C2×C5—21no—
489C2×C5—21no—
490C2×C5#464611yescharacteristic
491C2×C5#474011yescharacteristic
492C2×C5D3×#9911yescharacteristic
493C23—41no—
494C23—41no—
495C23D5×Dic611yescharacteristic
496C23#676611yescharacteristic
497C23D15⋊Q811yescharacteristic
498C23#677311yescharacteristic
499C23C2×D3×Dic511yescharacteristic
500C23D3×C22⋊D511yescharacteristic
501C23D3×C22⋊D511yescharacteristic
502Q8—122no—
503Q8—122no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—31no—
507C2×C4—31no—
508C2×C4—31no—
509C2×C4—31no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—61no—
516C2×C4—61no—
517C2×C4—102no—
518C2×C4—121no—
519C2×C4—121no—
520C2×C4—121no—
521C2×C4—121no—
522C2×C4—121no—
523C2×C4—201no—
524C2×C4—201no—
525C2×C4—201no—
526C2×C4—201no—
527C2×C4—201no—
528C2×C4—302no—
529C2×C4—601no—
530C2×C4—601no—
531C2×C4—601no—
532C2×C4—601no—
533C2×C4—601no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3C2×#396611yescharacteristic
541C2×C3#6551911yescharacteristic
542C2×C3#6552911yescharacteristic
543C5#6895511yescharacteristic, complemented, Sylow
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22#9132911yescharacteristic
555C22Dic5×Dic611yescharacteristic
556C22#9134411yescharacteristic
557C22#9142111yescharacteristic
558C22#9142411yescharacteristic
559C22#9145511yescharacteristic
560C22D3×C22⋊Dic511yescharacteristic
561C4—32no—
562C4—41no—
563C4—41no—
564C4—61no—
565C4—61no—
566C4—61no—
567C4—121no—
568C4—121no—
569C4—202no—
570C4—401no—
571C4—602no—
572C4—1201no—
573C3#1060249411yescharacteristic, complemented, Sylow
574C2—21no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—21no—
580C2#1174869211yescharacteristic
581C2D3×#396611yescharacteristic
582C2#1174917311yescharacteristic
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5C2×C22⋊C4
prime radical, cosocleC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#1996
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
10. C22×C5×Dic6C4semidirect
15. C2×C5×C4⋊Dic3C4semidirect
16. C2×C5×Dic3⋊C4C4semidirect
17. C2×C5×Dic3⋊C4C4semidirect
60. #6719Q8semidirect
72. C3×C22⋊Dic5Q8semidirect
144. C22×Dic6Dic5semidirect
151. C2×C4⋊Dic3Dic5semidirect
153. C2×Dic3⋊C4Dic5semidirect
154. C2×Dic3⋊C4Dic5semidirect
198. C22⋊Dic5Dic6semidirect
454. C3×C5#1996semidirect
543. C5#68955semidirect
573. C3#10602494semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8782
#117495132
Dic3×C22⋊Dic52
#117463472
C3×#647462
#117460182
#106024943
#689555