Finite Group Databasebeta

← #14418591

Subgroups — #14418591

Order 1920.

696 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752500C211yesmaximal, characteristic
2#11750929C211yesmaximal, characteristic, complemented
3C5×#4837C211yesmaximal, characteristic
4C3×#65117C211yesmaximal, characteristic, complemented
5#11748055C211yesmaximal, characteristic
6#11748052C211yesmaximal, characteristic
7#11747826C211yesmaximal, characteristic, complemented
8#11747825C211yesmaximal, characteristic, complemented
9#11747821C211yesmaximal, characteristic, complemented
10#11747820C211yesmaximal, characteristic, complemented
11#11747661C211yesmaximal, characteristic
12#11747661C211yesmaximal, characteristic
13D3×#3935C211yesmaximal, characteristic
14#11746852C211yesmaximal, characteristic, complemented
15#11746848C211yesmaximal, characteristic, complemented
16#10610776—31nomaximal, Hall
17C4×Dic30C2211yescharacteristic
18C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
19C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
20C42×C5×D3C2211yescharacteristic
21C3×C4×Dic10C2211yescharacteristic
22#91469C411yescharacteristic
23C4×#1204C2211yescharacteristic
24C4×#1204C2211yescharacteristic
25#91389C411yescharacteristic
26#91379C411yescharacteristic
27#91379C411yescharacteristic
28#91371C2211yescharacteristic
29#91371C2211yescharacteristic
30#91369C411yescharacteristic
31#91365C411yescharacteristic
32#91352C411yescharacteristic
33#91352C411yescharacteristic
34C2×D3×#168C2211yescharacteristic
35C2×D3×#168C2211yescharacteristic
36C3×C5×C4⋊C8C2211yescharacteristic
37#91099C2211yescharacteristic
38#91098C2211yescharacteristic
39#91098C2211yescharacteristic
40C8×Dic15C2211yescharacteristic
41#91087C2211yescharacteristic
42C5×Dic3⋊C8C2211yescharacteristic
43C5×Dic3⋊C8C2211yescharacteristic
44C5×C4⋊(C3⋊C8)C2211yescharacteristic
45C3×#3947C2211yescharacteristic
46C3×#3946C2211yescharacteristic
47C3×#3946C2211yescharacteristic
48C3×C8×Dic5C2211yescharacteristic
49C3×#3935C2211yescharacteristic
50#90983C2211yescharacteristic
51#90983C2211yescharacteristic
52#90982C2211yescharacteristic
53#90982C2211yescharacteristic
54#90954C2211yescharacteristic
55#90953C2211yescharacteristic
56#90953C2211yescharacteristic
57#90952C2211yescharacteristic
58#90951C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic
60#79959—51nomaximal, Hall
61#65804—31no—
62C5×#423—31no—
63#65411—31no—
64#65411—31no—
65#65408—31no—
66#65408—31no—
67C2×#3935—31no—
68#65117—31no—
69#65117—31no—
70#65117—31no—
71#65117—31no—
72#65117—31no—
73#65117—31no—
74#65117—31no—
75#65117D311yescharacteristic, complemented
76C2×Dic30C2×C411yescharacteristic
77C2×C4×C5×D3C2×C411yescharacteristic
78C2×C4×C5×D3C2×C411yescharacteristic
79C2×C4×C5×D3C2311yescharacteristic
80C2×C3×Dic10C2×C411yescharacteristic
81C2×#1204C2×C411yescharacteristic
82C2×#1204C2×C411yescharacteristic
83C2×C3×C5×C8C2311yescharacteristic
84C2×C3×C5×C8C2311yescharacteristic
85C3×C42×C5C2311yescharacteristic
86C4⋊Dic15C2×C411yescharacteristic
87#6712C2×C411yescharacteristic
88#6712C2×C411yescharacteristic
89C4×Dic15C2311yescharacteristic
90C4×Dic15C2311yescharacteristic
91C2×C3⋊#168C2311yescharacteristic
92C2×C3⋊#168C2311yescharacteristic
93C4×C5×Dic3C2×C411yescharacteristic
94C4×C5×Dic3C2×C411yescharacteristic
95C4×C5×Dic3C2311yescharacteristic
96C2×C5×C3⋊C8C2311yescharacteristic
97C2×C5×C3⋊C8C2311yescharacteristic
98C5×ΓL(1,𝔽25)—22no—
99C5×ΓL(1,𝔽25)—22no—
100C3×C4⋊Dic5C2×C411yescharacteristic
101C3×#683C2×C411yescharacteristic
102C3×#683C2×C411yescharacteristic
103C3×C4×Dic5C2311yescharacteristic
104C3×C4×Dic5C2311yescharacteristic
105C2×C3×#168C2311yescharacteristic
106C2×C3×#168C2311yescharacteristic
107Dic3⋊Dic5C2×C411yescharacteristic
108Dic3⋊Dic5C2×C411yescharacteristic
109Dic3⋊Dic5C2×C411yescharacteristic
110Dic3⋊Dic5C2×C411yescharacteristic
111Dic3⋊Dic5C2×C411yescharacteristic
112Dic3⋊Dic5C2×C411yescharacteristic
113#6669C2×C411yescharacteristic
114#6669C2×C411yescharacteristic
115#6668C2×C411yescharacteristic
116#6668C2×C411yescharacteristic
117(C2×D3)⋊Dic5C2×C411yescharacteristic
118(C2×D3)⋊Dic5C2×C411yescharacteristic
119(C2×D3)⋊Dic5C2×C411yescharacteristic
120(C2×D3)⋊Dic5C2×C411yescharacteristic
121D3×#168—22no—
122D3×#168Q814yescomplemented
123#5578—51no—
124C3×#446—51no—
125#5024—51no—
126#4839—51no—
127#4839—51no—
128#4837D511yescharacteristic
129#4831—51no—
130#4828—51no—
131#4828—51no—
132#4708—51no—
133D3×#97—51no—
134#4701—51no—
135#4701—51no—
136#4689—51no—
137#4679—51no—
138C2×C5×M16—31no—
139C2×C5×M16—31no—
140C2×C42×C5—31no—
141#4072—31no—
142#4072—31no—
143#4070—31no—
144#4070—31no—
145#4070—31no—
146#4070—31no—
147C22×#168—31no—
148C22×#168—31no—
149#4016—31no—
150#4016—31no—
151#4015—31no—
152#4015—31no—
153C4×Dic10—31no—
154C4×Dic10—31no—
155C4×Dic10—31no—
156C4×Dic10C2×D311yescharacteristic
157C5×C4⋊C8—31no—
158C5×C4⋊C8—31no—
159C5×C4⋊C8—31no—
160C5×C4⋊C8C2×D311yescharacteristic
161#3947—31no—
162#3947—31no—
163#3947—31no—
164#3947C2×D311yescharacteristic
165#3946—31no—
166#3946—31no—
167#3946—31no—
168#3946—31no—
169#3946—31no—
170#3946—31no—
171#3946C2×D311yescharacteristic
172#3946C2×D311yescharacteristic
173C8×Dic5—31no—
174C8×Dic5—31no—
175C8×Dic5—31no—
176C8×Dic5C2×D311yescharacteristic
177#3935—31no—
178#3935—31no—
179#3935—31no—
180#3935C2×D311yescharacteristic
181#2961—151noSylow
182C22×C5×D3C22×C411yescharacteristic
183C2×C3×C4×C5C22×C411yescharacteristic
184C2×C3×C4×C5C22×C411yescharacteristic
185C2×C3×C4×C5C2411yescharacteristic
186C2×Dic15C22×C411yescharacteristic
187C2×Dic15C22×C411yescharacteristic
188C2×Dic15C22×C411yescharacteristic
189C2×Dic15C22×C411yescharacteristic
190Dic30—41no—
191C2×C5×Dic3C22×C411yescharacteristic
192C2×C5×Dic3C22×C411yescharacteristic
193C2×C5×Dic3C22×C411yescharacteristic
194C4×C5×D3—41no—
195C4×C5×D3—41no—
196C4×C5×D3C2×Q812yes—
197C4×C5×D3#4112yes—
198C2×C3×Dic5C22×C411yescharacteristic
199C2×C3×Dic5C22×C411yescharacteristic
200C2×C3×Dic5C22×C411yescharacteristic
201C2×C3×Dic5C22×C411yescharacteristic
202C3×Dic10—41no—
203#1204—41no—
204#1204—41no—
205C3×C5×C8—21no—
206C3×C5×C8—21no—
207C3⋊#168—21no—
208C3⋊#168C2×Q812yes—
209C3×#168—21no—
210C3×#168C2×Q812yes—
211C5×C3⋊C8—21no—
212C5×C3⋊C8—21no—
213C3×C4×Q8—51no—
214#946—51no—
215#944—51no—
216C2×ΓL(1,𝔽25)C2×D511yescharacteristic
217C2×ΓL(1,𝔽25)C2×D511yescharacteristic
218C2×D3×C8—51no—
219C2×D3×C8—51no—
220#897—51no—
221#896—51no—
222#896—51no—
223#889—51no—
224#889—51no—
225#888—51no—
226#872—51no—
227#872—51no—
228C42×D3C2×D511yescharacteristic
229C4×Dic6—51no—
230C4×Dic6—51no—
231C4×Dic6—51no—
232C3×C4⋊C8—51no—
233C3×C4⋊C8—51no—
234C3×C4⋊C8C2×D511yescharacteristic
235C3×#97—51no—
236C3×#97—51no—
237C3×C4×C8—51no—
238#815—51no—
239#815—51no—
240#815—51no—
241#815—51no—
242Dic3⋊C8—51no—
243Dic3⋊C8—51no—
244Dic3⋊C8—51no—
245Dic3⋊C8—51no—
246Dic3⋊C8C2×D511yescharacteristic
247Dic3⋊C8C2×D511yescharacteristic
248C8×Dic3—51no—
249C8×Dic3—51no—
250C4⋊(C3⋊C8)—51no—
251C4⋊(C3⋊C8)—51no—
252C4⋊(C3⋊C8)C2×D511yescharacteristic
253#803—51no—
254#803—51no—
255C4×C3⋊C8—51no—
256C22×C4×C5—31no—
257C22×C4×C5—31no—
258C22×C4×C5—31no—
259C2×Dic10—31no—
260C2×Dic10—31no—
261C2×Dic10—31no—
262C2×Dic10C4×D311yescharacteristic
263C5×M16—62no—
264C5×M16—62no—
265C2×C5×C8—31no—
266C2×C5×C8—31no—
267C2×C5×C8C22×D311yescharacteristic
268C2×C5×C8C22×D311yescharacteristic
269C42×C5—31no—
270C42×C5—31no—
271C42×C5—31no—
272C42×C5C22×D311yescharacteristic
273C22⋊Dic5—31no—
274C22⋊Dic5—31no—
275C22⋊Dic5—31no—
276C22⋊Dic5—31no—
277C4⋊Dic5—31no—
278C4⋊Dic5—31no—
279C4⋊Dic5—31no—
280C4⋊Dic5—31no—
281C4⋊Dic5—31no—
282C4⋊Dic5—31no—
283C4⋊Dic5—31no—
284C4⋊Dic5C4×D311yescharacteristic
285#683—31no—
286#683—31no—
287#683—31no—
288#683—31no—
289#683—31no—
290#683—31no—
291#683C4×D311yescharacteristic
292#683C4×D311yescharacteristic
293C4×Dic5—31no—
294C4×Dic5—31no—
295C4×Dic5C22×D311yescharacteristic
296C4×Dic5C22×D311yescharacteristic
297C2×#168—31no—
298C2×#168—34no—
299C2×#168—31no—
300C2×#168—62no—
301C2×#168C22×D311yescharacteristic
302C2×#168C22×D311yescharacteristic
303#533—151no—
304#446—51no—
305#446—151no—
306#446—151no—
307#446—151no—
308#446—151no—
309#446—151no—
310#446—151no—
311#446—151no—
312#424—151no—
313#424—151no—
314#423—31no—
315#405—151no—
316#405—151no—
317C2×#97—151no—
318C22×C3×C5C23×C411yescharacteristic
319C2×C5×D3—21no—
320C2×C5×D3—21no—
321C2×C5×D3C4×Q812yes—
322C3×C4×C5—21no—
323C3×C4×C5—21no—
324C3×C4×C5C22×Q811yescharacteristic
325C3×C4×C5C2×#4111yescharacteristic
326Dic15—21no—
327Dic15—21no—
328Dic15—21no—
329Dic15—21no—
330C3×Dic5—21no—
331C3×Dic5—21no—
332C3×Dic5—21no—
333C3×Dic5—21no—
334C5×Dic3—21no—
335C5×Dic3—21no—
336C5×Dic3C4×Q812yes—
337C2×C3×Q8—51no—
338C2×C4×D3C4×D511yescharacteristic
339C2×C4×D3C4×D511yescharacteristic
340C2×C4×D3C22×D511yescharacteristic
341C2×Dic6—51no—
342C2×Dic6—51no—
343C2×Dic6—51no—
344C2×C3×C8—51no—
345C2×C3×C8—51no—
346C2×C3×C8C22×D511yescharacteristic
347C2×C3×C8C22×D511yescharacteristic
348C3×C4⋊C4—51no—
349C3×C4⋊C4—51no—
350C3×C4⋊C4—51no—
351C3×C42—51no—
352C3×C42—51no—
353C3×C42C22×D511yescharacteristic
354(C2×D3)⋊C4—51no—
355(C2×D3)⋊C4—51no—
356(C2×D3)⋊C4—51no—
357(C2×D3)⋊C4—51no—
358C4⋊Dic3—51no—
359C4⋊Dic3—51no—
360C4⋊Dic3—51no—
361Dic3⋊C4—51no—
362Dic3⋊C4—51no—
363Dic3⋊C4—51no—
364Dic3⋊C4—51no—
365Dic3⋊C4—51no—
366Dic3⋊C4—51no—
367Dic3⋊C4—51no—
368Dic3⋊C4—51no—
369Dic3⋊C4—51no—
370Dic3⋊C4—51no—
371C4×Dic3—51no—
372C4×Dic3—51no—
373C4×Dic3C4×D511yescharacteristic
374C4×Dic3C4×D511yescharacteristic
375C4×Dic3C22×D511yescharacteristic
376C2×C3⋊C8—51no—
377C2×C3⋊C8—51no—
378C2×C3⋊C8C22×D511yescharacteristic
379C2×C3⋊C8C22×D511yescharacteristic
380ΓL(1,𝔽25)—22no—
381ΓL(1,𝔽25)—22no—
382D3×C8—54no—
383D3×C8—102no—
384C23×C5—31no—
385C2×C4×C5—31no—
386C2×C4×C5—32no—
387C2×C4×C5—32no—
388C2×C4×C5—31no—
389C2×C4×C5—31no—
390C2×C4×C5—121no—
391C2×C4×C5—121no—
392C2×C4×C5C2×C4×D311yescharacteristic
393C2×C4×C5C2×C4×D311yescharacteristic
394C2×C4×C5C23×D311yescharacteristic
395C2×Dic5—31no—
396C2×Dic5—31no—
397C2×Dic5—31no—
398C2×Dic5—31no—
399C2×Dic5C2×C4×D311yescharacteristic
400C2×Dic5C2×C4×D311yescharacteristic
401C2×Dic5C2×C4×D311yescharacteristic
402C2×Dic5C2×C4×D311yescharacteristic
403Dic10—41no—
404Dic10—121no—
405Dic10—121no—
406Dic10—121no—
407C5×C8—21no—
408C5×C8—21no—
409C5×C8—61no—
410C5×C8—61no—
411#168—21no—
412#168—32no—
413#168—61no—
414#168D3×Q812yes—
415C2×M16—31no—
416C2×M16—31no—
417C22×C8—151no—
418C22×C8—151no—
419C4⋊Q8—151no—
420C4⋊Q8—151no—
421#125—151no—
422#125—151no—
423C22⋊Q8—151no—
424C22⋊Q8—151no—
425C22⋊Q8—151no—
426C22⋊Q8—151no—
427C4×Q8—51no—
428C4×Q8—151no—
429C4×Q8—151no—
430C4×Q8—151no—
431#117—151no—
432#117—151no—
433C2×C42—31no—
434C4⋊C8—31no—
435C4⋊C8—31no—
436C4⋊C8—31no—
437C4⋊C8—51no—
438C4⋊C8—51no—
439C4⋊C8—151no—
440C4⋊C8—151no—
441C4⋊C8—151no—
442C4⋊C8—151no—
443C4⋊C8—151no—
444C4⋊C8—151no—
445C4⋊C8D3×D511yescharacteristic
446#97—51no—
447#97—51no—
448#97—151no—
449#97—151no—
450#97—151no—
451#97—151no—
452#97—151no—
453#97—151no—
454C4×C8—51no—
455C4×C8—151no—
456C4×C8—151no—
457C4×C8—151no—
458C2×C3×C5C2×C4×Q811yescharacteristic
459C2×C3×C5#56811yescharacteristic
460C2×C3×C5#56811yescharacteristic
461C5×D3—22no—
462C22×D3C2×C4×D511yescharacteristic
463C3×Q8—201no—
464C2×C3×C4—51no—
465C2×C3×C4—51no—
466C2×C3×C4—51no—
467C2×C3×C4—51no—
468C2×C3×C4C2×C4×D511yescharacteristic
469C2×C3×C4C2×C4×D511yescharacteristic
470C2×C3×C4C23×D511yescharacteristic
471C2×Dic3—51no—
472C2×Dic3—51no—
473C2×Dic3—51no—
474C2×Dic3—51no—
475C2×Dic3C2×C4×D511yescharacteristic
476C2×Dic3C2×C4×D511yescharacteristic
477C2×Dic3C2×C4×D511yescharacteristic
478C4×D3—41no—
479C4×D3—41no—
480C4×D3#71112yes—
481C4×D3Q8×D512yes—
482Dic6—201no—
483Dic6—201no—
484Dic6—201no—
485C3×C8—21no—
486C3×C8—21no—
487C3×C8—52no—
488C3×C8—101no—
489C3⋊C8—21no—
490C3⋊C8—21no—
491C3⋊C8—52no—
492C3⋊C8—101no—
493C22×C5—32no—
494C22×C5—61no—
495C22×C5—61no—
496C22×C5C22×C4×D311yescharacteristic
497C4×C5—21no—
498C4×C5—21no—
499C4×C5—32no—
500C4×C5—61no—
501C4×C5—61no—
502C4×C5C2×D3×Q811yescharacteristic
503C4×C5D3×#4111yescharacteristic
504Dic5—21no—
505Dic5—21no—
506Dic5—21no—
507Dic5—21no—
508Dic5—61no—
509Dic5—61no—
510Dic5—61no—
511Dic5—61no—
512C2×Q8—51no—
513C2×Q8—151no—
514C2×Q8—151no—
515C2×Q8—151no—
516C22×C4—31no—
517C22×C4—31no—
518C22×C4—31no—
519M16—62no—
520M16—62no—
521C2×C8—31no—
522C2×C8—31no—
523C2×C8—51no—
524C2×C8—51no—
525C2×C8—154no—
526C2×C8—151no—
527C2×C8—151no—
528C2×C8—302no—
529C2×C8C2×D3×D511yescharacteristic
530C2×C8C2×D3×D511yescharacteristic
531C4⋊C4—51no—
532C4⋊C4—51no—
533C4⋊C4—51no—
534C4⋊C4—151no—
535C4⋊C4—151no—
536C4⋊C4—151no—
537C4⋊C4—151no—
538C4⋊C4—151no—
539C4⋊C4—151no—
540C4⋊C4—151no—
541C4⋊C4—151no—
542C4⋊C4—151no—
543C4⋊C4—151no—
544C4⋊C4—151no—
545C4⋊C4—151no—
546C4⋊C4—151no—
547C22⋊C4—151no—
548C22⋊C4—151no—
549C22⋊C4—151no—
550C22⋊C4—151no—
551C42—31no—
552C42—31no—
553C42—31no—
554C42—51no—
555C42—51no—
556C42—151no—
557C42—151no—
558C42C2×D3×D511yescharacteristic
559C3×C5#296111yescharacteristic, complemented, Hall
560C22×C3C22×C4×D511yescharacteristic
561C2×D3—21no—
562C2×D3—21no—
563C2×D3#403312yes—
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—101no—
567C3×C4—101no—
568C3×C4—101no—
569C3×C4—101no—
570C3×C4C2×#71111yescharacteristic
571C3×C4C2×Q8×D511yescharacteristic
572Dic3—21no—
573Dic3—21no—
574Dic3—101no—
575Dic3—101no—
576Dic3—101no—
577Dic3—101no—
578Dic3#403312yes—
579C2×C5—62no—
580C2×C5C4×D3×Q811yescharacteristic
581C2×C5#574511yescharacteristic
582C2×C5#575011yescharacteristic
583C23—31no—
584Q8—201no—
585Q8—601no—
586Q8—601no—
587Q8—601no—
588C2×C4—31no—
589C2×C4—32no—
590C2×C4—32no—
591C2×C4—31no—
592C2×C4—31no—
593C2×C4—51no—
594C2×C4—51no—
595C2×C4—51no—
596C2×C4—51no—
597C2×C4—121no—
598C2×C4—121no—
599C2×C4—151no—
600C2×C4—151no—
601C2×C4—151no—
602C2×C4—151no—
603C2×C4C4×D3×D511yescharacteristic
604C2×C4C4×D3×D511yescharacteristic
605C2×C4C22×D3×D511yescharacteristic
606C8—21no—
607C8—21no—
608C8—52no—
609C8—61no—
610C8—61no—
611C8—101no—
612C8—152no—
613C8—301no—
614C2×C3C2×#403311yescharacteristic
615C2×C3#6607911yescharacteristic
616C2×C3#6607911yescharacteristic
617D3—22no—
618C5#7995911yescharacteristic, complemented, Sylow
619C22—32no—
620C22—61no—
621C22—61no—
622C22C2×C4×D3×D511yescharacteristic
623C4—21no—
624C4—21no—
625C4—32no—
626C4—61no—
627C4—61no—
628C4—101no—
629C4—101no—
630C4—101no—
631C4—101no—
632C4—301no—
633C4—301no—
634C4—301no—
635C4—301no—
636C4D3×#71111yescharacteristic
637C4D3×Q8×D511yescharacteristic
638C3#1061077611yescharacteristic, complemented, Sylow
639C2—62no—
640C2D3×#403311yescharacteristic
641C2#1175395111yescharacteristic
642C2#1175404111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C8C22
prime radicalC22×C5×D3C22×C4
cosocleC2×C3×C4×C5C24
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#2961
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750929C2semidirect
4. C3×#65117C2semidirect
7. #11747826C2semidirect
8. #11747825C2semidirect
9. #11747821C2semidirect
10. #11747820C2semidirect
14. #11746852C2semidirect
15. #11746848C2semidirect
75. #65117D3semidirect
122. D3×#168Q8semidirect
559. C3×C5#2961semidirect
618. C5#79959semidirect
638. C3#10610776semidirect

Maximal subgroups

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

subgroupindex
#117525002
#117509292
C5×#48372
C3×#651172
#117480552
#117480522
#117478262
#117478252
#117478212
#117478202
#117476612
D3×#39352
#117468522
#117468482
#106107763
#799595