Finite Group Databasebeta

← #14436245

Subgroups — #14436245

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5731C211yesmaximal, characteristic, complemented
2#11752518C211yesmaximal, characteristic
3#11751191C211yesmaximal, characteristic, complemented
4C3×#65372C211yesmaximal, characteristic, complemented
5#11749403C211yesmaximal, characteristic
6#11749403C211yesmaximal, characteristic
7#11749260C211yesmaximal, characteristic, complemented
8#11749257C211yesmaximal, characteristic, complemented
9#11749234C211yesmaximal, characteristic, complemented
10Dic3×#688C211yesmaximal, characteristic, complemented
11#11749202C211yesmaximal, characteristic, complemented
12#11749200C211yesmaximal, characteristic, complemented
13#11746967C211yesmaximal, characteristic, complemented
14#11746887C211yesmaximal, characteristic, complemented
15#11746854C211yesmaximal, characteristic, complemented
16#10615177—31nomaximal, Hall
17C2×#6765C2211yescharacteristic
18C3×C5×C4⋊Q8C2211yescharacteristic
19C2×#6718C2211yescharacteristic
20C2×#6718C2211yescharacteristic
21C4×Dic30C2211yescharacteristic
22C5×#946C2211yescharacteristic
23C5×#946C2211yescharacteristic
24C5×Q8×Dic3C2211yescharacteristic
25C5×Q8×Dic3C2211yescharacteristic
26C5×#898—21no—
27C5×#898—21no—
28C5×#889—21no—
29C5×#889—21no—
30C5×#872C2211yescharacteristic
31C5×#870C2211yescharacteristic
32C2×C3×#688C2211yescharacteristic
33C2×C3×#688C2211yescharacteristic
34C3×C4×D20C2211yescharacteristic
35#91442—21no—
36#91440—21no—
37D3×C4⋊Dic5C2211yescharacteristic
38Dic3×D20C2211yescharacteristic
39#91394—21no—
40D5×Dic3⋊C4—21no—
41#91340C2211yescharacteristic
42#91119C2211yescharacteristic
43#91119C2211yescharacteristic
44C4⋊(C3⋊#168)C2211yescharacteristic
45C3×#3967C2211yescharacteristic
46C3×#3967C2211yescharacteristic
47C3×C4⋊#168C2211yescharacteristic
48#90989C2211yescharacteristic
49#90988C2211yescharacteristic
50#90986C2211yescharacteristic
51#90985C2211yescharacteristic
52#90975C2211yescharacteristic
53#90975C2211yescharacteristic
54#90964C2211yescharacteristic
55#90964C2211yescharacteristic
56(C2×D3)⋊#168C2211yescharacteristic
57(C2×D3)⋊#168C2211yescharacteristic
58#90953C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#80412—51nomaximal, Hall
61C5×#541—31no—
62#65857—31no—
63#65379—31no—
64#65372D311yescharacteristic, complemented
65#65355—31no—
66#65352—31no—
67#65336—31no—
68#65336—31no—
69#65333—31no—
70#65332—31no—
71#65319—31no—
72C4×#689—31no—
73#65315—31no—
74C4×#688—31no—
75#65289—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×Q8C2311yescharacteristic
78C2×Dic30C2311yescharacteristic
79C2×C4×C5×D3C2311yescharacteristic
80C2×C3×D20C2311yescharacteristic
81C2×C3×C4×D5—21no—
82C2×#1201—21no—
83C2×D3×Dic5—21no—
84C2×D5×Dic3—21no—
85C2×D5×Dic3—21no—
86#6765—22no—
87#6765—22no—
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4—21no—
90C3×C42×C5C2311yescharacteristic
91#6718—22no—
92#6718—22no—
93C4⋊Dic15C2311yescharacteristic
94#6712—21no—
95C4×Dic15—21no—
96C2×C3⋊#168C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×(C2×D3)⋊C4—21no—
99C5×(C2×D3)⋊C4—21no—
100C5×(C2×D3)⋊C4D411yescharacteristic
101C5×(C2×D3)⋊C4D411yescharacteristic
102C5×C4⋊Dic3—21no—
103C5×C4⋊Dic3—21no—
104C5×C4⋊Dic3C2311yescharacteristic
105C5×C4⋊Dic3C2311yescharacteristic
106C5×Dic3⋊C4—21no—
107C5×Dic3⋊C4—21no—
108C5×Dic3⋊C4—21no—
109C5×Dic3⋊C4—21no—
110C5×Dic3⋊C4D411yescharacteristic
111C5×Dic3⋊C4D411yescharacteristic
112C4×C5×Dic3—21no—
113C4×C5×Dic3—21no—
114C4×C5×Dic3C2311yescharacteristic
115C3×#688—22no—
116C3×#688—22no—
117C3×#685—21no—
118C3×C4⋊Dic5C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120C2×C3×#168C2311yescharacteristic
121Dic3⋊Dic5—21no—
122#6669—21no—
123#6665—21no—
124Dic3×Dic5—21no—
125#5731D511yescharacteristic, complemented
126#5546—51no—
127C3×#461—51no—
128#5173—51no—
129#5173—51no—
130#5164—51no—
131Dic3×SD16—51no—
132#5090—51no—
133#5009—51no—
134#4840—51no—
135#4829—51no—
136#4811—51no—
137#4805—51no—
138#4790—51no—
139#4789—51no—
140C2×#709—31no—
141C5×C4⋊Q8C2×D311yescharacteristic
142C5×#126—61no—
143C5×#126—61no—
144C5×#125—31no—
145C5×#125—61no—
146C5×#125—61no—
147C5×C22⋊Q8—31no—
148C5×C22⋊Q8—31no—
149C4×C5×Q8—31no—
150C4×C5×Q8—31no—
151C5×#117—31no—
152C2×#689—31no—
153C2×#689—31no—
154C2×#688C2×D311yescharacteristic
155C2×#688C2×D311yescharacteristic
156C2×C4⋊Dic5—31no—
157#4038—61no—
158D5×C4⋊C4—61no—
159#4027—61no—
160#4027—61no—
161C4×D20—31no—
162C4×D20C2×D311yescharacteristic
163C4×Dic10—31no—
164C4×Dic10—31no—
165#3967—31no—
166#3967—31no—
167#3967C2×D311yescharacteristic
168#3967C2×D311yescharacteristic
169C22⋊#168—31no—
170C22⋊#168—31no—
171#3942—31no—
172#3942—31no—
173#3941—31no—
174#3941—31no—
175#3940—31no—
176#3940—31no—
177#3939—31no—
178#3939—31no—
179C4⋊#168—31no—
180C4⋊#168C2×D311yescharacteristic
181#3935—31no—
182C4×#168—31no—
183#3120—151noSylow
184C22×C5×D3C2×D411yescharacteristic
185C22×C3×D5—21no—
186C3×C5×Q8—21no—
187C3×C5×Q8—21no—
188C3×C5×Q8—21no—
189C3×C5×Q8—21no—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5C2×D411yescharacteristic
193C2×C3×C4×C5C2×D411yescharacteristic
194C2×C3×C4×C5C2411yescharacteristic
195C2×Dic15—21no—
196C2×Dic15—21no—
197Dic30—21no—
198Dic30#4112yes—
199C2×C5×Dic3—21no—
200C2×C5×Dic3—21no—
201C2×C5×Dic3C2×D411yescharacteristic
202C2×C5×Dic3C2×D411yescharacteristic
203C2×C5×Dic3C2×D411yescharacteristic
204C4×C5×D3—21no—
205C4×C5×D3—21no—
206C2×C3×Dic5—21no—
207C3×D20—21no—
208C3×D20#4112yes—
209C3×C4×D5—81no—
210#1201—24no—
211D3×Dic5—81no—
212D5×Dic3—24no—
213D5×Dic3—81no—
214C3⋊#168—21no—
215C3⋊#168—21no—
216C3×#168—21no—
217C3×#168—21no—
218C2×#237—51no—
219C2×C3×SD16—51no—
220C2×C3×SD16—51no—
221C3×C4⋊Q8C2×D511yescharacteristic
222C3×C4×D4—51no—
223#946C2×D511yescharacteristic
224#946C2×D511yescharacteristic
225Q8×Dic3C2×D511yescharacteristic
226Q8×Dic3C2×D511yescharacteristic
227C2×#216—51no—
228C2×#216—51no—
229D4×Dic3—51no—
230C4×#67—101no—
231C2×Dic3⋊C4—101no—
232#898—21no—
233#898—21no—
234D3×C4⋊C4—51no—
235#889—21no—
236#889—21no—
237#887—51no—
238#67⋊C4—101no—
239#877—101no—
240#872C2×D511yescharacteristic
241#870C2×D511yescharacteristic
242C4×Dic6—51no—
243C3×C4⋊C8—51no—
244C3×#103—51no—
245C3×#103—51no—
246#835—51no—
247#835—51no—
248#832—51no—
249#832—51no—
250(C2×D3)⋊C8—51no—
251(C2×D3)⋊C8—51no—
252#818—51no—
253#817—51no—
254#816—51no—
255#816—51no—
256#815—51no—
257C8×Dic3—51no—
258#808—51no—
259#807—51no—
260C4⋊(C3⋊C8)—51no—
261C2×C5×Q8C22×D311yescharacteristic
262C2×C5×Q8C22×D311yescharacteristic
263C22×C4×C5—31no—
264C2×C22⋊D5—61no—
265C22×Dic5—61no—
266#709—62no—
267#709—62no—
268C2×D20C22×D311yescharacteristic
269C2×C4×D5—21no—
270C2×C4×D5—61no—
271C2×C4×D5—61no—
272C2×Dic10—31no—
273C5×C4⋊C4—21no—
274C5×C4⋊C4—21no—
275C5×C4⋊C4—31no—
276C5×C4⋊C4—31no—
277C5×C4⋊C4—31no—
278C5×C4⋊C4—31no—
279C5×C4⋊C4—61no—
280C5×C4⋊C4—61no—
281C5×C4⋊C4—61no—
282C5×C4⋊C4—61no—
283C5×C4⋊C4—61no—
284C5×C4⋊C4—61no—
285C5×C22⋊C4—31no—
286C5×C22⋊C4—31no—
287C5×C22⋊C4—61no—
288C5×C22⋊C4—61no—
289C42×C5—31no—
290C42×C5—61no—
291C42×C5—61no—
292C42×C5C22×D311yescharacteristic
293#689—62no—
294#689—62no—
295#688—22no—
296#688—22no—
297#685—21no—
298#685—61no—
299C4⋊Dic5—31no—
300C4⋊Dic5—61no—
301C4⋊Dic5C22×D311yescharacteristic
302#683—61no—
303#683—61no—
304C4×Dic5—61no—
305C4×Dic5—61no—
306C2×#168—31no—
307C2×#168—31no—
308C2×#168C22×D311yescharacteristic
309C2×#168C22×D311yescharacteristic
310#541—31no—
311#520—151no—
312#484—151no—
313#483—151no—
314#479—151no—
315#478—151no—
316#462—151no—
317#461—51no—
318#452—151no—
319#452—151no—
320#441—151no—
321#440—151no—
322C4×Q16—151no—
323C4×SD16—151no—
324#433—151no—
325C22×C3×C5C22×D411yescharacteristic
326C2×C5×D3—21no—
327C2×C5×D3—21no—
328C2×C5×D3—21no—
329C2×C3×D5—22no—
330C2×C3×D5—41no—
331C2×C3×D5—41no—
332C3×C4×C5—21no—
333C3×C4×C5—21no—
334C3×C4×C5—41no—
335C3×C4×C5—41no—
336C3×C4×C5C2×#4111yescharacteristic
337C3×C4×C5C2×#4111yescharacteristic
338Dic15—22no—
339Dic15—41no—
340C3×Dic5—41no—
341C5×Dic3—21no—
342C5×Dic3—21no—
343C5×Dic3—21no—
344C5×Dic3—41no—
345C5×Dic3—41no—
346C2×C3×Q8C22×D511yescharacteristic
347C2×C3×Q8C22×D511yescharacteristic
348C2×C3×D4—51no—
349C22×C3×C4—101no—
350C2×#67—101no—
351C22×Dic3—101no—
352C22×Dic3—101no—
353#237—102no—
354#237—102no—
355C2×C4×D3—101no—
356C2×C4×D3C22×D511yescharacteristic
357C2×Dic6—51no—
358C3×SD16—102no—
359C3×SD16—102no—
360C2×C3×C8—51no—
361C2×C3×C8—51no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—51no—
365C3×C22⋊C4—101no—
366C3×C42C22×D511yescharacteristic
367#217—101no—
368#216—102no—
369#216—102no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4C22⋊D511yescharacteristic
373(C2×D3)⋊C4C22⋊D511yescharacteristic
374C4⋊Dic3—21no—
375C4⋊Dic3—21no—
376C4⋊Dic3—51no—
377C4⋊Dic3C22×D511yescharacteristic
378C4⋊Dic3C22×D511yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385Dic3⋊C4—101no—
386Dic3⋊C4C22⋊D511yescharacteristic
387Dic3⋊C4C22⋊D511yescharacteristic
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3—101no—
391C4×Dic3—101no—
392C4×Dic3C22×D511yescharacteristic
393C2×C3⋊C8—51no—
394C2×C3⋊C8—51no—
395C23×C5—31no—
396C22×D5—21no—
397C5×Q8—21no—
398C5×Q8—21no—
399C5×Q8—21no—
400C5×Q8—21no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—31no—
404C2×C4×C5—31no—
405C2×C4×C5—31no—
406C2×C4×C5—61no—
407C2×C4×C5—61no—
408C2×C4×C5—61no—
409C2×C4×C5—61no—
410C2×C4×C5D3×D411yescharacteristic
411C2×C4×C5D3×D411yescharacteristic
412C2×C4×C5C23×D311yescharacteristic
413C22⋊D5—64no—
414C2×Dic5—21no—
415C2×Dic5—61no—
416C2×Dic5—61no—
417C2×Dic5—241no—
418D20—21no—
419D20#23712yes—
420C4×D5—64no—
421C4×D5—81no—
422C4×D5—241no—
423Dic10—32no—
424Dic10—61no—
425#168—21no—
426#168—21no—
427#168—61no—
428#168—61no—
429C2×#41—151no—
430C2×Q16—151no—
431C2×Q16—151no—
432C2×SD16—51no—
433C2×SD16—51no—
434C4⋊Q8D3×D511yescharacteristic
435#126—61no—
436#126—61no—
437#125—31no—
438#125—61no—
439#125—61no—
440C22⋊Q8—31no—
441C22⋊Q8—31no—
442C4×Q8—31no—
443C4×Q8—31no—
444C4×Q8—151no—
445C4×Q8—151no—
446C4×D4—51no—
447C4×D4—151no—
448C4×D4—301no—
449C4×D4—301no—
450#117—31no—
451#117—301no—
452C2×C4⋊C4—151no—
453C2×C4⋊C4—301no—
454#107—151no—
455#107—151no—
456#106—151no—
457#106—151no—
458C4⋊C8—51no—
459C4⋊C8—151no—
460#103—51no—
461#103—51no—
462#103—151no—
463#103—151no—
464#103—151no—
465#103—151no—
466#102—151no—
467#102—151no—
468C22⋊C8—151no—
469C22⋊C8—151no—
470#97—151no—
471C4×C8—151no—
472C2×C3×C5#52511yescharacteristic
473C2×C3×C5#57711yescharacteristic
474C2×C3×C5#57811yescharacteristic
475C3×D5—42no—
476C5×D3—41no—
477C23×C3—101no—
478C22×D3C2×C22⋊D511yescharacteristic
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×D4—52no—
484C3×D4—101no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—101no—
488C2×C3×C4—401no—
489C2×C3×C4C2×C22⋊D511yescharacteristic
490C2×C3×C4C2×C22⋊D511yescharacteristic
491C2×C3×C4C23×D511yescharacteristic
492#67—104no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—104no—
496C2×Dic3—101no—
497C2×Dic3—101no—
498C2×Dic3—401no—
499C2×Dic3C2×C22⋊D511yescharacteristic
500C2×Dic3C2×C22⋊D511yescharacteristic
501C2×Dic3C2×C22⋊D511yescharacteristic
502C4×D3—21no—
503C4×D3—21no—
504C4×D3—401no—
505Dic6—52no—
506Dic6—101no—
507C3×C8—101no—
508C3×C8—101no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—61no—
512C22×C5—61no—
513C22×C5—61no—
514C22×C5C2×D3×D411yescharacteristic
515C2×D5—22no—
516C2×D5—41no—
517C2×D5—41no—
518C4×C5—21no—
519C4×C5—21no—
520C4×C5—41no—
521C4×C5—41no—
522C4×C5—61no—
523C4×C5—61no—
524C4×C5—61no—
525C4×C5—121no—
526C4×C5—121no—
527C4×C5C2×#23711yescharacteristic
528C4×C5D3×#4111yescharacteristic
529Dic5—41no—
530Dic5—62no—
531Dic5—121no—
532#41—302no—
533#41—302no—
534C2×Q8—151no—
535C2×Q8C2×D3×D511yescharacteristic
536C2×Q8C2×D3×D511yescharacteristic
537C2×D4—51no—
538C2×D4—301no—
539C22×C4—31no—
540C22×C4—101no—
541C22×C4—301no—
542C22×C4—301no—
543C22×C4—301no—
544Q16—302no—
545Q16—302no—
546SD16—102no—
547SD16—102no—
548C2×C8—51no—
549C2×C8—51no—
550C2×C8—151no—
551C2×C8—151no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—31no—
557C4⋊C4—31no—
558C4⋊C4—51no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—151no—
566C4⋊C4—301no—
567C4⋊C4—301no—
568C4⋊C4—301no—
569C22⋊C4—31no—
570C22⋊C4—31no—
571C22⋊C4—61no—
572C22⋊C4—61no—
573C22⋊C4—101no—
574C22⋊C4—301no—
575C42—31no—
576C42—61no—
577C42—61no—
578C42—301no—
579C42—301no—
580C42C2×D3×D511yescharacteristic
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—102no—
583C22×C3—201no—
584C22×C3—201no—
585C22×C3C22×C22⋊D511yescharacteristic
586C2×D3—21no—
587C2×D3—21no—
588C2×D3—21no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—201no—
594C3×C4D5×#4111yescharacteristic
595C3×C4D5×#4111yescharacteristic
596Dic3—21no—
597Dic3—21no—
598Dic3—21no—
599Dic3—41no—
600Dic3—41no—
601Dic3—102no—
602Dic3—201no—
603C2×C5—121no—
604C2×C5#560611yescharacteristic
605C2×C5#576211yescharacteristic
606C2×C5#577911yescharacteristic
607D5—42no—
608C23—31no—
609C23—101no—
610Q8—21no—
611Q8—21no—
612Q8—21no—
613Q8—21no—
614Q8—152no—
615Q8—301no—
616D4—52no—
617D4—101no—
618D4—304no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—31no—
622C2×C4—31no—
623C2×C4—31no—
624C2×C4—61no—
625C2×C4—61no—
626C2×C4—61no—
627C2×C4—61no—
628C2×C4—101no—
629C2×C4—304no—
630C2×C4—301no—
631C2×C4—301no—
632C2×C4—401no—
633C2×C4—1201no—
634C2×C4—1201no—
635C2×C4D3×C22⋊D511yescharacteristic
636C2×C4D3×C22⋊D511yescharacteristic
637C2×C4C22×D3×D511yescharacteristic
638C8—101no—
639C8—101no—
640C8—301no—
641C8—301no—
642C2×C3—202no—
643C2×C3#6616211yescharacteristic
644C2×C3#6617111yescharacteristic
645C2×C3#6617211yescharacteristic
646D3—41no—
647C5#8041211yescharacteristic, complemented, Sylow
648C22—61no—
649C22—61no—
650C22—61no—
651C22—102no—
652C22—201no—
653C22—201no—
654C22C2×D3×C22⋊D511yescharacteristic
655C4—21no—
656C4—21no—
657C4—41no—
658C4—41no—
659C4—61no—
660C4—61no—
661C4—61no—
662C4—121no—
663C4—121no—
664C4—201no—
665C4—302no—
666C4—601no—
667C4D5×#23711yescharacteristic
668C4#9202411yescharacteristic
669C3#1061517711yescharacteristic, complemented, Sylow
670C2—121no—
671C2—202no—
672C2#1175506511yescharacteristic
673C2#1175509111yescharacteristic
674C2#1175511411yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6765C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3120
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5731C2semidirect
3. #11751191C2semidirect
4. C3×#65372C2semidirect
7. #11749260C2semidirect
8. #11749257C2semidirect
9. #11749234C2semidirect
10. Dic3×#688C2semidirect
11. #11749202C2semidirect
12. #11749200C2semidirect
13. #11746967C2semidirect
14. #11746887C2semidirect
15. #11746854C2semidirect
64. #65372D3semidirect
125. #5731D5semidirect
581. C3×C5#3120semidirect
647. C5#80412semidirect
669. C3#10615177semidirect

Maximal subgroups

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

subgroupindex
C5×#57312
#117525182
#117511912
C3×#653722
#117494032
#117492602
#117492572
#117492342
Dic3×#6882
#117492022
#117492002
#117469672
#117468872
#117468542
#106151773
#804125