Finite Group Databasebeta

← #14418567

Subgroups — #14418567

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#11756337C211yesmaximal, characteristic
2C3×C5×#446C211yesmaximal, characteristic, complemented
3#11751125C211yesmaximal, characteristic, complemented
4#11750940C211yesmaximal, characteristic
5#11750940C211yesmaximal, characteristic
6#11750938C211yesmaximal, characteristic
7#11750932C211yesmaximal, characteristic, complemented
8#11750929C211yesmaximal, characteristic, complemented
9#11750929C211yesmaximal, characteristic, complemented
10#11750809C211yesmaximal, characteristic
11D15×#97C211yesmaximal, characteristic
12#11750802C211yesmaximal, characteristic, complemented
13#11750802C211yesmaximal, characteristic, complemented
14#11750790C211yesmaximal, characteristic
15#11750780C211yesmaximal, characteristic, complemented
16#10611690—31nomaximal, Hall
17C3×C4×C5×Q8C2211yescharacteristic
18#91835C411yescharacteristic
19#91833C411yescharacteristic
20C2×#6705C2211yescharacteristic
21C2×#6705C2211yescharacteristic
22C2×C8×D15C2211yescharacteristic
23C2×C8×D15C2211yescharacteristic
24#91786C411yescharacteristic
25#91785C411yescharacteristic
26#91785C411yescharacteristic
27#91778C411yescharacteristic
28#91778C411yescharacteristic
29#91777C411yescharacteristic
30#91761C2211yescharacteristic
31#91761C2211yescharacteristic
32C42×D15C2211yescharacteristic
33C4×Dic30C2211yescharacteristic
34C4×Dic30C2211yescharacteristic
35C4×Dic30C2211yescharacteristic
36C3×C5×C4⋊C8C2211yescharacteristic
37C3×C5×C4⋊C8C2211yescharacteristic
38C3×C5×C4⋊C8C2211yescharacteristic
39C3×C5×#97C2211yescharacteristic
40C3×C5×#97C2211yescharacteristic
41C3×C4×C5×C8C2211yescharacteristic
42#91099C2211yescharacteristic
43#91099C2211yescharacteristic
44#91099C2211yescharacteristic
45#91099C2211yescharacteristic
46#91098C2211yescharacteristic
47#91098C2211yescharacteristic
48#91098C2211yescharacteristic
49#91098C2211yescharacteristic
50#91098C2211yescharacteristic
51#91098C2211yescharacteristic
52C8×Dic15C2211yescharacteristic
53C8×Dic15C2211yescharacteristic
54C4⋊(C3⋊#168)C2211yescharacteristic
55C4⋊(C3⋊#168)C2211yescharacteristic
56C4⋊(C3⋊#168)C2211yescharacteristic
57#91087C2211yescharacteristic
58#91087C2211yescharacteristic
59C4×C3⋊#168C2211yescharacteristic
60#79959—51nomaximal, Hall
61#65912—31no—
62C5×#446D311yescharacteristic, complemented
63#65313—31no—
64#65128—31no—
65#65128—31no—
66#65126—31no—
67#65120—31no—
68#65117—31no—
69#65117—31no—
70#64997—31no—
71D5×#97—31no—
72#64990—31no—
73#64990—31no—
74#64978—31no—
75#64968—31no—
76C2×C3×C5×Q8C2×C411yescharacteristic
77C2×C4×D15C2×C411yescharacteristic
78C2×C4×D15C2×C411yescharacteristic
79C2×C4×D15C2311yescharacteristic
80C2×Dic30C2×C411yescharacteristic
81C2×Dic30C2×C411yescharacteristic
82C2×Dic30C2×C411yescharacteristic
83C2×C3×C5×C8C2311yescharacteristic
84C2×C3×C5×C8C2311yescharacteristic
85C2×C3×C5×C8C2311yescharacteristic
86C2×C3×C5×C8C2311yescharacteristic
87C3×C5×C4⋊C4C2×C411yescharacteristic
88C3×C5×C4⋊C4C2×C411yescharacteristic
89C3×C5×C4⋊C4C2×C411yescharacteristic
90C3×C42×C5C2311yescharacteristic
91C3×C42×C5C2311yescharacteristic
92C3×C42×C5C2311yescharacteristic
93#6714C2×C411yescharacteristic
94#6714C2×C411yescharacteristic
95#6714C2×C411yescharacteristic
96#6714C2×C411yescharacteristic
97C4⋊Dic15C2×C411yescharacteristic
98C4⋊Dic15C2×C411yescharacteristic
99C4⋊Dic15C2×C411yescharacteristic
100#6712C2×C411yescharacteristic
101#6712C2×C411yescharacteristic
102#6712C2×C411yescharacteristic
103#6712C2×C411yescharacteristic
104#6712C2×C411yescharacteristic
105#6712C2×C411yescharacteristic
106#6712C2×C411yescharacteristic
107#6712C2×C411yescharacteristic
108#6712C2×C411yescharacteristic
109#6712C2×C411yescharacteristic
110C4×Dic15C2×C411yescharacteristic
111C4×Dic15C2×C411yescharacteristic
112C4×Dic15C2311yescharacteristic
113C4×Dic15C2311yescharacteristic
114C4×Dic15C2311yescharacteristic
115C2×C3⋊#168C2311yescharacteristic
116C2×C3⋊#168C2311yescharacteristic
117C2×C3⋊#168C2311yescharacteristic
118C2×C3⋊#168C2311yescharacteristic
119#6705—22no—
120#6705—22no—
121C8×D15—22no—
122C8×D15Q814yescomplemented
123#5578—51no—
124C3×#446D511yescharacteristic, complemented
125#5024—51no—
126#4839—51no—
127#4839—51no—
128#4837—51no—
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—
138C4×C5×Q8C2×D311yescharacteristic
139#4092—31no—
140#4090—31no—
141C2×#676—31no—
142C2×#676—31no—
143C2×C8×D5—31no—
144C2×C8×D5—31no—
145#4043—31no—
146#4042—31no—
147#4042—31no—
148#4035—31no—
149#4035—31no—
150#4034—31no—
151#4018—31no—
152#4018—31no—
153C42×D5—31no—
154C4×Dic10—31no—
155C4×Dic10—31no—
156C4×Dic10—31no—
157C5×C4⋊C8C2×D311yescharacteristic
158C5×C4⋊C8C2×D311yescharacteristic
159C5×C4⋊C8C2×D311yescharacteristic
160C5×#97C2×D311yescharacteristic
161C5×#97C2×D311yescharacteristic
162C4×C5×C8C2×D311yescharacteristic
163#3947—31no—
164#3947—31no—
165#3947—31no—
166#3947—31no—
167#3946—31no—
168#3946—31no—
169#3946—31no—
170#3946—31no—
171#3946—31no—
172#3946—31no—
173C8×Dic5—31no—
174C8×Dic5—31no—
175C4⋊#168—31no—
176C4⋊#168—31no—
177C4⋊#168—31no—
178#3935—31no—
179#3935—31no—
180C4×#168—31no—
181#2961—151noSylow
182C22×D15C22×C411yescharacteristic
183C3×C5×Q8—41no—
184C2×C3×C4×C5C22×C411yescharacteristic
185C2×C3×C4×C5C22×C411yescharacteristic
186C2×C3×C4×C5C22×C411yescharacteristic
187C2×C3×C4×C5C22×C411yescharacteristic
188C2×C3×C4×C5C22×C411yescharacteristic
189C2×C3×C4×C5C22×C411yescharacteristic
190C2×C3×C4×C5C2411yescharacteristic
191C2×Dic15C22×C411yescharacteristic
192C2×Dic15C22×C411yescharacteristic
193C2×Dic15C22×C411yescharacteristic
194C2×Dic15C22×C411yescharacteristic
195C2×Dic15C22×C411yescharacteristic
196C2×Dic15C22×C411yescharacteristic
197C2×Dic15C22×C411yescharacteristic
198C4×D15—41no—
199C4×D15—41no—
200C4×D15C2×Q812yes—
201C4×D15#4112yes—
202Dic30—41no—
203Dic30—41no—
204Dic30—41no—
205C3×C5×C8—21no—
206C3×C5×C8—21no—
207C3×C5×C8—21no—
208C3×C5×C8C2×Q812yes—
209C3⋊#168—21no—
210C3⋊#168—21no—
211C3⋊#168—21no—
212C3⋊#168C2×Q812yes—
213C3×C4×Q8C2×D511yescharacteristic
214#946—51no—
215#944—51no—
216C2×ΓL(1,𝔽25)—51no—
217C2×ΓL(1,𝔽25)—51no—
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×D3—51no—
229C4×Dic6—51no—
230C4×Dic6—51no—
231C4×Dic6—51no—
232C3×C4⋊C8C2×D511yescharacteristic
233C3×C4⋊C8C2×D511yescharacteristic
234C3×C4⋊C8C2×D511yescharacteristic
235C3×#97C2×D511yescharacteristic
236C3×#97C2×D511yescharacteristic
237C3×C4×C8C2×D511yescharacteristic
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⋊C8—51no—
247Dic3⋊C8—51no—
248C8×Dic3—51no—
249C8×Dic3—51no—
250C4⋊(C3⋊C8)—51no—
251C4⋊(C3⋊C8)—51no—
252C4⋊(C3⋊C8)—51no—
253#803—51no—
254#803—51no—
255C4×C3⋊C8—51no—
256C2×C5×Q8C4×D311yescharacteristic
257C2×C4×D5—31no—
258C2×C4×D5—31no—
259C2×C4×D5—31no—
260C2×Dic10—31no—
261C2×Dic10—31no—
262C2×Dic10—31no—
263C2×C5×C8C22×D311yescharacteristic
264C2×C5×C8C22×D311yescharacteristic
265C2×C5×C8C22×D311yescharacteristic
266C2×C5×C8C22×D311yescharacteristic
267C5×C4⋊C4C4×D311yescharacteristic
268C5×C4⋊C4C4×D311yescharacteristic
269C5×C4⋊C4C4×D311yescharacteristic
270C42×C5C22×D311yescharacteristic
271C42×C5C22×D311yescharacteristic
272C42×C5C22×D311yescharacteristic
273#685—31no—
274#685—31no—
275#685—31no—
276#685—31no—
277C4⋊Dic5—31no—
278C4⋊Dic5—31no—
279C4⋊Dic5—31no—
280#683—31no—
281#683—31no—
282#683—31no—
283#683—31no—
284#683—31no—
285#683—31no—
286#683—31no—
287#683—31no—
288#683—31no—
289#683—31no—
290C4×Dic5—31no—
291C4×Dic5—31no—
292C4×Dic5—31no—
293C4×Dic5—31no—
294C4×Dic5—31no—
295C2×#168—31no—
296C2×#168—31no—
297C2×#168—31no—
298C2×#168—31no—
299#676—62no—
300#676—62no—
301C8×D5—34no—
302C8×D5—62no—
303#533—151no—
304#446—151no—
305#446—151no—
306#446—151no—
307#446—151no—
308#446—151no—
309#446—151no—
310#446—151no—
311#446D1511yescharacteristic, complemented
312#424—151no—
313#424—151no—
314#423—151no—
315#405—151no—
316#405—151no—
317C2×#97—151no—
318C22×C3×C5C23×C411yescharacteristic
319C2×D15—21no—
320C2×D15—21no—
321C2×D15C4×Q812yes—
322C3×C4×C5—21no—
323C3×C4×C5—21no—
324C3×C4×C5—21no—
325C3×C4×C5—21no—
326C3×C4×C5—21no—
327C3×C4×C5—21no—
328C3×C4×C5C22×Q811yescharacteristic
329C3×C4×C5C2×#4111yescharacteristic
330Dic15—21no—
331Dic15—21no—
332Dic15—21no—
333Dic15—21no—
334Dic15—21no—
335Dic15—21no—
336Dic15C4×Q812yes—
337C2×C3×Q8C4×D511yescharacteristic
338C2×C4×D3—51no—
339C2×C4×D3—51no—
340C2×C4×D3—51no—
341C2×Dic6—51no—
342C2×Dic6—51no—
343C2×Dic6—51no—
344C2×C3×C8C22×D511yescharacteristic
345C2×C3×C8C22×D511yescharacteristic
346C2×C3×C8C22×D511yescharacteristic
347C2×C3×C8C22×D511yescharacteristic
348C3×C4⋊C4C4×D511yescharacteristic
349C3×C4⋊C4C4×D511yescharacteristic
350C3×C4⋊C4C4×D511yescharacteristic
351C3×C42C22×D511yescharacteristic
352C3×C42C22×D511yescharacteristic
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×Dic3—51no—
374C4×Dic3—51no—
375C4×Dic3—51no—
376C2×C3⋊C8—51no—
377C2×C3⋊C8—51no—
378C2×C3⋊C8—51no—
379C2×C3⋊C8—51no—
380ΓL(1,𝔽25)—102no—
381ΓL(1,𝔽25)—102no—
382D3×C8—54no—
383D3×C8—102no—
384C22×D5—31no—
385C5×Q8—41no—
386C2×C4×C5C2×C4×D311yescharacteristic
387C2×C4×C5C2×C4×D311yescharacteristic
388C2×C4×C5C2×C4×D311yescharacteristic
389C2×C4×C5C2×C4×D311yescharacteristic
390C2×C4×C5C2×C4×D311yescharacteristic
391C2×C4×C5C2×C4×D311yescharacteristic
392C2×C4×C5C23×D311yescharacteristic
393C2×Dic5—31no—
394C2×Dic5—31no—
395C2×Dic5—31no—
396C2×Dic5—31no—
397C2×Dic5—31no—
398C2×Dic5—31no—
399C2×Dic5—31no—
400C4×D5—32no—
401C4×D5—32no—
402C4×D5—121no—
403C4×D5—121no—
404Dic10—121no—
405Dic10—121no—
406Dic10—121no—
407C5×C8—21no—
408C5×C8—21no—
409C5×C8—21no—
410C5×C8D3×Q812yes—
411#168—32no—
412#168—61no—
413#168—61no—
414#168—61no—
415C2×M16—151no—
416C2×M16—151no—
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—151no—
428C4×Q8—151no—
429C4×Q8—151no—
430C4×Q8C2×D1511yescharacteristic
431#117—151no—
432#117—151no—
433C2×C42—151no—
434C4⋊C8—151no—
435C4⋊C8—151no—
436C4⋊C8—151no—
437C4⋊C8—151no—
438C4⋊C8—151no—
439C4⋊C8—151no—
440C4⋊C8—151no—
441C4⋊C8—151no—
442C4⋊C8—151no—
443C4⋊C8C2×D1511yescharacteristic
444C4⋊C8C2×D1511yescharacteristic
445C4⋊C8C2×D1511yescharacteristic
446#97—151no—
447#97—151no—
448#97—151no—
449#97—151no—
450#97—151no—
451#97—151no—
452#97C2×D1511yescharacteristic
453#97C2×D1511yescharacteristic
454C4×C8—151no—
455C4×C8—151no—
456C4×C8—151no—
457C4×C8C2×D1511yescharacteristic
458C2×C3×C5C2×C4×Q811yescharacteristic
459C2×C3×C5#56811yescharacteristic
460C2×C3×C5#56811yescharacteristic
461D15—22no—
462C22×D3—51no—
463C3×Q8—41no—
464C2×C3×C4C2×C4×D511yescharacteristic
465C2×C3×C4C2×C4×D511yescharacteristic
466C2×C3×C4C2×C4×D511yescharacteristic
467C2×C3×C4C2×C4×D511yescharacteristic
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×Dic3—51no—
476C2×Dic3—51no—
477C2×Dic3—51no—
478C4×D3—52no—
479C4×D3—52no—
480C4×D3—201no—
481C4×D3—201no—
482Dic6—201no—
483Dic6—201no—
484Dic6—201no—
485C3×C8—21no—
486C3×C8—21no—
487C3×C8—21no—
488C3×C8Q8×D512yes—
489C3⋊C8—52no—
490C3⋊C8—101no—
491C3⋊C8—101no—
492C3⋊C8—101no—
493C22×C5C22×C4×D311yescharacteristic
494C2×D5—32no—
495C2×D5—61no—
496C2×D5—61no—
497C4×C5—21no—
498C4×C5—21no—
499C4×C5—21no—
500C4×C5—21no—
501C4×C5—21no—
502C4×C5—21no—
503C4×C5C2×D3×Q811yescharacteristic
504C4×C5D3×#4111yescharacteristic
505Dic5—32no—
506Dic5—61no—
507Dic5—61no—
508Dic5—61no—
509Dic5—61no—
510Dic5—61no—
511Dic5—61no—
512C2×Q8—151no—
513C2×Q8—151no—
514C2×Q8—151no—
515C2×Q8C4×D1511yescharacteristic
516C22×C4—151no—
517C22×C4—151no—
518C22×C4—151no—
519M16—302no—
520M16—302no—
521C2×C8—151no—
522C2×C8—154no—
523C2×C8—151no—
524C2×C8—151no—
525C2×C8—151no—
526C2×C8—302no—
527C2×C8C22×D1511yescharacteristic
528C2×C8C22×D1511yescharacteristic
529C2×C8C22×D1511yescharacteristic
530C2×C8C22×D1511yescharacteristic
531C4⋊C4—151no—
532C4⋊C4—151no—
533C4⋊C4—151no—
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⋊C4C4×D1511yescharacteristic
545C4⋊C4C4×D1511yescharacteristic
546C4⋊C4C4×D1511yescharacteristic
547C22⋊C4—151no—
548C22⋊C4—151no—
549C22⋊C4—151no—
550C22⋊C4—151no—
551C42—151no—
552C42—151no—
553C42—151no—
554C42—151no—
555C42—151no—
556C42C22×D1511yescharacteristic
557C42C22×D1511yescharacteristic
558C42C22×D1511yescharacteristic
559C3×C5#296111yescharacteristic, complemented, Hall
560C22×C3C22×C4×D511yescharacteristic
561C2×D3—52no—
562C2×D3—101no—
563C2×D3—101no—
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—21no—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4C2×Q8×D511yescharacteristic
571C3×C4D5×#4111yescharacteristic
572Dic3—52no—
573Dic3—101no—
574Dic3—101no—
575Dic3—101no—
576Dic3—101no—
577Dic3—101no—
578Dic3—101no—
579C2×C5C4×D3×Q811yescharacteristic
580C2×C5#574511yescharacteristic
581C2×C5#575011yescharacteristic
582D5—62no—
583C23—151no—
584Q8—41no—
585Q8—601no—
586Q8—601no—
587Q8—601no—
588C2×C4—151no—
589C2×C4—152no—
590C2×C4—152no—
591C2×C4—151no—
592C2×C4—151no—
593C2×C4—151no—
594C2×C4—151no—
595C2×C4—151no—
596C2×C4—151no—
597C2×C4—601no—
598C2×C4—601no—
599C2×C4C2×C4×D1511yescharacteristic
600C2×C4C2×C4×D1511yescharacteristic
601C2×C4C2×C4×D1511yescharacteristic
602C2×C4C2×C4×D1511yescharacteristic
603C2×C4C2×C4×D1511yescharacteristic
604C2×C4C2×C4×D1511yescharacteristic
605C2×C4C23×D1511yescharacteristic
606C8—21no—
607C8—21no—
608C8—21no—
609C8—152no—
610C8—301no—
611C8—301no—
612C8—301no—
613C8Q8×D1512yes—
614C2×C3C4×Q8×D511yescharacteristic
615C2×C3#6607911yescharacteristic
616C2×C3#6608411yescharacteristic
617D3—102no—
618C5#7995911yescharacteristic, complemented, Sylow
619C22—152no—
620C22—301no—
621C22—301no—
622C22C22×C4×D1511yescharacteristic
623C4—21no—
624C4—21no—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—21no—
629C4—152no—
630C4—301no—
631C4—301no—
632C4—301no—
633C4—301no—
634C4—301no—
635C4—301no—
636C4C2×Q8×D1511yescharacteristic
637C4#41×D1511yescharacteristic
638C3#1061169011yescharacteristic, complemented, Sylow
639C2—302no—
640C2C4×Q8×D1511yescharacteristic
641C2#1175650411yescharacteristic
642C2#1175650911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D15
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×#446C2
prime radicalC22×D15C22×C4
cosocleC2×C3×C4×C5C24
hypercenter#446D15
hypocenterC3×C5#2961
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ #446

Complements

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

NH ≅ G/Ntype
2. C3×C5×#446C2semidirect
3. #11751125C2semidirect
7. #11750932C2semidirect
8. #11750929C2semidirect
9. #11750929C2semidirect
12. #11750802C2semidirect
13. #11750802C2semidirect
15. #11750780C2semidirect
62. C5×#446D3semidirect
122. C8×D15Q8semidirect
124. C3×#446D5semidirect
311. #446D15semidirect
559. C3×C5#2961semidirect
618. C5#79959semidirect
638. C3#10611690semidirect

Maximal subgroups

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

subgroupindex
#117563372
C3×C5×#4462
#117511252
#117509402
#117509382
#117509322
#117509292
#117508092
D15×#972
#117508022
#117507902
#117507802
#106116903
#799595