Finite Group Databasebeta

← #14436183

Subgroups — #14436183

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×#5518C211yesmaximal, characteristic, complemented
2C3×#65857C211yesmaximal, characteristic
3#11751101C211yesmaximal, characteristic, complemented
4#11748528C211yesmaximal, characteristic
5#11748528C211yesmaximal, characteristic
6#11748471C211yesmaximal, characteristic, complemented
7#11748406C211yesmaximal, characteristic, complemented
8#11747094C211yesmaximal, characteristic, complemented
9#11747089C211yesmaximal, characteristic, complemented
10C4×#6661C211yesmaximal, characteristic, complemented
11#11747059C211yesmaximal, characteristic, complemented
12#11747048C211yesmaximal, characteristic, complemented
13C4×#6655C211yesmaximal, characteristic, complemented
14#11746919C211yesmaximal, characteristic, complemented
15#11746887C211yesmaximal, characteristic, complemented
16#10615177—31nomaximal, Hall
17C2×C3×#709C2211yescharacteristic
18C3×C5×#117C2211yescharacteristic
19C5×#924C2211yescharacteristic
20C5×#924C2211yescharacteristic
21C5×#889—21no—
22C5×#889—21no—
23C5×#879—21no—
24C5×#879—21no—
25C5×#870C2211yescharacteristic
26C5×#869C2211yescharacteristic
27C4×C5×Dic6C2211yescharacteristic
28C4×C5×Dic6C2211yescharacteristic
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C3×#4038—21no—
31C3×D5×C4⋊C4—21no—
32C3×#4027—21no—
33C3×#4027—21no—
34C3×C4×D20C2211yescharacteristic
35C3×C4×D20C2211yescharacteristic
36C3×C4×Dic10C2211yescharacteristic
37C3×C4×Dic10C2211yescharacteristic
38C2×#6661C2211yescharacteristic
39C2×#6661C2211yescharacteristic
40C2×#6655C2211yescharacteristic
41C2×#6655C2211yescharacteristic
42#91114C2211yescharacteristic
43#91114C2211yescharacteristic
44C4⋊(C3⋊#168)C2211yescharacteristic
45C4⋊(C3⋊#168)C2211yescharacteristic
46#91087C2211yescharacteristic
47C4×C3⋊#168C2211yescharacteristic
48#90989C2211yescharacteristic
49#90989C2211yescharacteristic
50#90986C2211yescharacteristic
51#90986C2211yescharacteristic
52#90972C2211yescharacteristic
53#90972C2211yescharacteristic
54#90972C2211yescharacteristic
55#90972C2211yescharacteristic
56#90970C2211yescharacteristic
57#90970C2211yescharacteristic
58#90964C2211yescharacteristic
59#90964C2211yescharacteristic
60#82575—51nomaximal, Hall
61C5×#541—31no—
62#65857D311yescharacteristic
63#65379—31no—
64#65372—31no—
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—
76C22×C3×C4×C5C2311yescharacteristic
77C2×C5×Dic6C2311yescharacteristic
78C2×C5×Dic6C2311yescharacteristic
79C2×C3×C22⋊D5—21no—
80C22×C3×Dic5—21no—
81C3×#709—22no—
82C3×#709—22no—
83C2×C3×D20C2311yescharacteristic
84C2×C3×C4×D5—21no—
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5—21no—
87C2×C3×Dic10C2311yescharacteristic
88C3×C5×C4⋊C4D411yescharacteristic
89C3×C5×C4⋊C4D411yescharacteristic
90C3×C5×C22⋊C4D411yescharacteristic
91C3×C5×C22⋊C4D411yescharacteristic
92C3×C42×C5C2311yescharacteristic
93C3×C42×C5C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C2×C3⋊#168C2311yescharacteristic
96C2×C3⋊#168C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×#217—21no—
99C5×#217—21no—
100C5×C4⋊Dic3—21no—
101C5×C4⋊Dic3—21no—
102C5×C4⋊Dic3C2311yescharacteristic
103C5×C4⋊Dic3C2311yescharacteristic
104C5×Dic3⋊C4—21no—
105C5×Dic3⋊C4—21no—
106C5×Dic3⋊C4—21no—
107C5×Dic3⋊C4—21no—
108C5×Dic3⋊C4—21no—
109C5×Dic3⋊C4—21no—
110C4×C5×Dic3—21no—
111C4×C5×Dic3—21no—
112C3×#685—21no—
113C3×#685—21no—
114C3×C4⋊Dic5—21no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×C4⋊Dic5C2311yescharacteristic
117C3×#683—21no—
118C3×#683—21no—
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121#6661—22no—
122#6661—22no—
123#6655—22no—
124#6655—22no—
125C3×#520—51no—
126#5518D511yescharacteristic, complemented
127#5239—51no—
128#5239—51no—
129#5031—51no—
130#5030—51no—
131C4×#216—51no—
132#5022—51no—
133#5019—51no—
134#5018—51no—
135C4×#214—51no—
136#5009—51no—
137#5000—51no—
138#4971—51no—
139#4970—51no—
140C2×#709C2×D311yescharacteristic
141C5×C4⋊Q8—31no—
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×#117C2×D311yescharacteristic
152C2×#689—31no—
153C2×#689—31no—
154C2×#688—31no—
155C2×#688—31no—
156C2×C4⋊Dic5C2×D311yescharacteristic
157#4038—21no—
158D5×C4⋊C4—21no—
159#4027—21no—
160#4027—21no—
161C4×D20C2×D311yescharacteristic
162C4×D20C2×D311yescharacteristic
163C4×Dic10C2×D311yescharacteristic
164C4×Dic10C2×D311yescharacteristic
165#3967—31no—
166#3967—31no—
167#3967—31no—
168#3967—31no—
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⋊#168—31no—
181#3935—31no—
182C4×#168—31no—
183#3120—151noSylow
184C23×C3×C5C2×D411yescharacteristic
185C22×C3×D5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5C2×D411yescharacteristic
189C2×C3×C4×C5C2×D411yescharacteristic
190C2×C3×C4×C5C2×D411yescharacteristic
191C2×C3×C4×C5C2×D411yescharacteristic
192C2×C3×C4×C5C2×D411yescharacteristic
193C2×C3×C4×C5C2411yescharacteristic
194C2×C5×Dic3—21no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3—21no—
198C5×Dic6—21no—
199C5×Dic6—21no—
200C5×Dic6—21no—
201C5×Dic6—21no—
202C3×C22⋊D5—24no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—81no—
207C3×D20—21no—
208C3×D20#4112yes—
209C3×C4×D5—24no—
210C3×C4×D5—81no—
211C3×C4×D5—81no—
212C3×Dic10—21no—
213C3×Dic10#4112yes—
214C3⋊#168—21no—
215C3⋊#168—21no—
216C3⋊#168—21no—
217C3⋊#168—21no—
218C2×C3×#41—51no—
219C3×C4×Q8—51no—
220C3×C4×Q8—51no—
221C3×C4×D4—51no—
222C3×C4×D4—51no—
223C3×C4×D4—101no—
224C3×C4×D4—101no—
225C3×#117—101no—
226C3×#117C2×D511yescharacteristic
227C2×C3×C4⋊C4—51no—
228C2×C3×C4⋊C4—101no—
229C2×#216—51no—
230C2×#216—51no—
231C2×#214—51no—
232C2×#214—51no—
233#924C2×D511yescharacteristic
234#924C2×D511yescharacteristic
235#889—21no—
236#889—21no—
237#879—21no—
238#879—21no—
239#870C2×D511yescharacteristic
240#869C2×D511yescharacteristic
241C4×Dic6C2×D511yescharacteristic
242C4×Dic6C2×D511yescharacteristic
243#835—51no—
244#835—51no—
245#832—51no—
246#832—51no—
247#830—51no—
248#830—51no—
249#810—51no—
250#810—51no—
251#810—51no—
252#810—51no—
253#808—51no—
254#808—51no—
255#807—51no—
256#807—51no—
257C4⋊(C3⋊C8)—51no—
258C4⋊(C3⋊C8)—51no—
259#803—51no—
260C4×C3⋊C8—51no—
261C2×C5×Q8—31no—
262C2×C5×Q8—31no—
263C22×C4×C5C22×D311yescharacteristic
264C2×C22⋊D5—21no—
265C22×Dic5—21no—
266#709—22no—
267#709—22no—
268C2×D20C22×D311yescharacteristic
269C2×C4×D5—21no—
270C2×C4×D5—21no—
271C2×C4×D5—21no—
272C2×Dic10C22×D311yescharacteristic
273C5×C4⋊C4—31no—
274C5×C4⋊C4—31no—
275C5×C4⋊C4—61no—
276C5×C4⋊C4—61no—
277C5×C4⋊C4—61no—
278C5×C4⋊C4—61no—
279C5×C4⋊C4—61no—
280C5×C4⋊C4—61no—
281C5×C4⋊C4—61no—
282C5×C4⋊C4—61no—
283C5×C4⋊C4#6711yescharacteristic
284C5×C4⋊C4#6711yescharacteristic
285C5×C22⋊C4—61no—
286C5×C22⋊C4—61no—
287C5×C22⋊C4#6711yescharacteristic
288C5×C22⋊C4#6711yescharacteristic
289C42×C5—61no—
290C42×C5—61no—
291C42×C5C22×D311yescharacteristic
292C42×C5C22×D311yescharacteristic
293#689—62no—
294#689—62no—
295#688—62no—
296#688—62no—
297#685—21no—
298#685—21no—
299C4⋊Dic5—21no—
300C4⋊Dic5C22×D311yescharacteristic
301C4⋊Dic5C22×D311yescharacteristic
302#683—21no—
303#683—21no—
304C4×Dic5—21no—
305C4×Dic5—21no—
306C2×#168—31no—
307C2×#168—31no—
308C2×#168—31no—
309C2×#168—31no—
310#541—31no—
311#520—51no—
312#484—151no—
313#483—151no—
314#479—151no—
315#478—151no—
316#462—151no—
317#461—151no—
318#452—151no—
319#452—151no—
320#441—151no—
321#440—151no—
322C4×Q16—151no—
323C4×SD16—151no—
324#433—151no—
325C22×C3×C5—21no—
326C22×C3×C5—21no—
327C22×C3×C5—21no—
328C22×C3×C5C22×D411yescharacteristic
329C2×C3×D5—22no—
330C2×C3×D5—41no—
331C2×C3×D5—41no—
332C3×C4×C5—21no—
333C3×C4×C5—21no—
334C3×C4×C5—21no—
335C3×C4×C5—21no—
336C3×C4×C5—21no—
337C3×C4×C5C2×#4111yescharacteristic
338C3×C4×C5C2×#4111yescharacteristic
339C3×Dic5—22no—
340C3×Dic5—41no—
341C3×Dic5—41no—
342C5×Dic3—41no—
343C5×Dic3—41no—
344C5×Dic3—41no—
345C5×Dic3—41no—
346C3×#41—102no—
347C3×#41—102no—
348C2×C3×Q8—51no—
349C2×C3×D4—51no—
350C2×C3×D4—101no—
351C22×C3×C4—101no—
352C22×C3×C4—101no—
353C22×C3×C4—101no—
354C22×C3×C4—101no—
355C22×C3×C4C22×D511yescharacteristic
356C2×Dic6C22×D511yescharacteristic
357C2×Dic6C22×D511yescharacteristic
358C3×C4⋊C4—51no—
359C3×C4⋊C4—51no—
360C3×C4⋊C4—101no—
361C3×C4⋊C4—101no—
362C3×C4⋊C4—101no—
363C3×C4⋊C4C22⋊D511yescharacteristic
364C3×C4⋊C4C22⋊D511yescharacteristic
365C3×C22⋊C4—101no—
366C3×C22⋊C4—101no—
367C3×C22⋊C4C22⋊D511yescharacteristic
368C3×C22⋊C4C22⋊D511yescharacteristic
369C3×C42—101no—
370C3×C42—101no—
371C3×C42C22×D511yescharacteristic
372C3×C42C22×D511yescharacteristic
373#217—21no—
374#217—21no—
375#216—102no—
376#216—102no—
377#214—102no—
378#214—102no—
379C4⋊Dic3—21no—
380C4⋊Dic3—21no—
381C4⋊Dic3C22×D511yescharacteristic
382C4⋊Dic3C22×D511yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391C2×C3⋊C8—51no—
392C2×C3⋊C8—51no—
393C2×C3⋊C8—51no—
394C2×C3⋊C8—51no—
395C23×C5C2×#6711yescharacteristic
396C22×D5—21no—
397C5×Q8—61no—
398C5×Q8—61no—
399C5×Q8—61no—
400C5×Q8—61no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—61no—
404C2×C4×C5—61no—
405C2×C4×C5—61no—
406C2×C4×C5—61no—
407C2×C4×C5C2×#6711yescharacteristic
408C2×C4×C5C2×#6711yescharacteristic
409C2×C4×C5C2×#6711yescharacteristic
410C2×C4×C5C2×#6711yescharacteristic
411C2×C4×C5C2×#6711yescharacteristic
412C2×C4×C5C23×D311yescharacteristic
413C22⋊D5—24no—
414C2×Dic5—21no—
415C2×Dic5—21no—
416C2×Dic5—21no—
417C2×Dic5—81no—
418D20—21no—
419D20#23512yes—
420C4×D5—24no—
421C4×D5—81no—
422C4×D5—81no—
423Dic10—21no—
424Dic10#23512yes—
425#168—61no—
426#168—61no—
427#168—61no—
428#168—61no—
429C2×#41—51no—
430C2×Q16—151no—
431C2×Q16—151no—
432C2×SD16—151no—
433C2×SD16—151no—
434C4⋊Q8—31no—
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—51no—
445C4×Q8—51no—
446C4×D4—51no—
447C4×D4—51no—
448C4×D4—101no—
449C4×D4—101no—
450#117—101no—
451#117D3×D511yescharacteristic
452C2×C4⋊C4—51no—
453C2×C4⋊C4—101no—
454#107—151no—
455#107—151no—
456#106—151no—
457#106—151no—
458C4⋊C8—151no—
459C4⋊C8—151no—
460#103—151no—
461#103—151no—
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—41no—
473C2×C3×C5#52511yescharacteristic
474C2×C3×C5#57711yescharacteristic
475C2×C3×C5#57811yescharacteristic
476C3×D5—42no—
477C23×C3—101no—
478C23×C3C2×C22⋊D511yescharacteristic
479C3×Q8—52no—
480C3×Q8—101no—
481C3×D4—52no—
482C3×D4—104no—
483C3×D4—101no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—104no—
487C2×C3×C4—101no—
488C2×C3×C4—101no—
489C2×C3×C4—101no—
490C2×C3×C4—401no—
491C2×C3×C4—401no—
492C2×C3×C4—401no—
493C2×C3×C4C2×C22⋊D511yescharacteristic
494C2×C3×C4C2×C22⋊D511yescharacteristic
495C2×C3×C4C2×C22⋊D511yescharacteristic
496C2×C3×C4C2×C22⋊D511yescharacteristic
497C2×C3×C4C2×C22⋊D511yescharacteristic
498C2×C3×C4C23×D511yescharacteristic
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503Dic6—21no—
504Dic6—21no—
505Dic6—21no—
506Dic6—21no—
507C3⋊C8—101no—
508C3⋊C8—101no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—21no—
512C22×C5—21no—
513C22×C5—21no—
514C22×C5C22×#6711yescharacteristic
515C2×D5—22no—
516C2×D5—41no—
517C2×D5—41no—
518C4×C5—21no—
519C4×C5—21no—
520C4×C5—21no—
521C4×C5—21no—
522C4×C5—21no—
523C4×C5—121no—
524C4×C5—121no—
525C4×C5—121no—
526C4×C5—121no—
527C4×C5C2×#23511yescharacteristic
528C4×C5C2×#23511yescharacteristic
529Dic5—22no—
530Dic5—41no—
531Dic5—41no—
532#41—102no—
533#41—102no—
534C2×Q8—31no—
535C2×Q8—31no—
536C2×Q8—51no—
537C2×D4—51no—
538C2×D4—101no—
539C22×C4—101no—
540C22×C4—101no—
541C22×C4—101no—
542C22×C4—101no—
543C22×C4C2×D3×D511yescharacteristic
544Q16—302no—
545Q16—302no—
546SD16—302no—
547SD16—302no—
548C2×C8—151no—
549C2×C8—151no—
550C2×C8—151no—
551C2×C8—151no—
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—51no—
555C4⋊C4—51no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—101no—
565C4⋊C4—101no—
566C4⋊C4—101no—
567C4⋊C4#120111yescharacteristic
568C4⋊C4#120111yescharacteristic
569C22⋊C4—61no—
570C22⋊C4—61no—
571C22⋊C4—101no—
572C22⋊C4—101no—
573C22⋊C4#120111yescharacteristic
574C22⋊C4#120111yescharacteristic
575C42—61no—
576C42—61no—
577C42—101no—
578C42—101no—
579C42C2×D3×D511yescharacteristic
580C42C2×D3×D511yescharacteristic
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—102no—
586C22×C3—201no—
587C22×C3—201no—
588C22×C3C22×C22⋊D511yescharacteristic
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—102no—
595C3×C4—201no—
596C3×C4—201no—
597C3×C4D5×#4111yescharacteristic
598C3×C4D5×#4111yescharacteristic
599Dic3—41no—
600Dic3—41no—
601Dic3—41no—
602Dic3—41no—
603C2×C5—41no—
604C2×C5#579111yescharacteristic
605C2×C5#583611yescharacteristic
606C2×C5#583811yescharacteristic
607D5—42no—
608C23—101no—
609C23C2×#120111yescharacteristic
610Q8—52no—
611Q8—61no—
612Q8—61no—
613Q8—61no—
614Q8—61no—
615Q8—101no—
616D4—52no—
617D4—104no—
618D4—101no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—61no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—61no—
625C2×C4—104no—
626C2×C4—101no—
627C2×C4—101no—
628C2×C4—101no—
629C2×C4—401no—
630C2×C4—401no—
631C2×C4—401no—
632C2×C4C2×#120111yescharacteristic
633C2×C4C2×#120111yescharacteristic
634C2×C4C2×#120111yescharacteristic
635C2×C4C2×#120111yescharacteristic
636C2×C4C2×#120111yescharacteristic
637C2×C4C22×D3×D511yescharacteristic
638C8—301no—
639C8—301no—
640C8—301no—
641C8—301no—
642C2×C3—41no—
643C2×C3—202no—
644C2×C3#6616211yescharacteristic
645C2×C3#6617111yescharacteristic
646C2×C3#6617211yescharacteristic
647C5#8257511yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—102no—
652C22—201no—
653C22—201no—
654C22C22×#120111yescharacteristic
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—102no—
661C4—121no—
662C4—121no—
663C4—121no—
664C4—121no—
665C4—201no—
666C4—201no—
667C4D5×#23511yescharacteristic
668C4D5×#23511yescharacteristic
669C3#1061517711yescharacteristic, complemented, Sylow
670C2—41no—
671C2—202no—
672C2#1175456311yescharacteristic
673C2#1175530211yescharacteristic
674C2#1175530311yescharacteristic
subgroupG/H
centerC22C22×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
hypercenter#117D3×D5
hypocenterC3×C5#3120
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C5×#5518C2semidirect
3. #11751101C2semidirect
6. #11748471C2semidirect
7. #11748406C2semidirect
8. #11747094C2semidirect
9. #11747089C2semidirect
10. C4×#6661C2semidirect
11. #11747059C2semidirect
12. #11747048C2semidirect
13. C4×#6655C2semidirect
14. #11746919C2semidirect
15. #11746887C2semidirect
126. #5518D5semidirect
581. C3×C5#3120semidirect
647. C5#82575semidirect
669. C3#10615177semidirect

Maximal subgroups

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

subgroupindex
C5×#55182
C3×#658572
#117511012
#117485282
#117484712
#117484062
#117470942
#117470892
C4×#66612
#117470592
#117470482
C4×#66552
#117469192
#117468872
#106151773
#825755