Finite Group Databasebeta

← #14418554

Subgroups — #14418554

Order 1920.

728 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#11753465C211yesmaximal, characteristic
2#11752366C211yesmaximal, characteristic, complemented
3C3×#65703C211yesmaximal, characteristic, complemented
4#11751923C211yesmaximal, characteristic
5#11751902C211yesmaximal, characteristic
6#11751890C211yesmaximal, characteristic
7#11751872C211yesmaximal, characteristic
8#11751872C211yesmaximal, characteristic
9C4×#6738C211yesmaximal, characteristic
10#11751787C211yesmaximal, characteristic, complemented
11#11751771C211yesmaximal, characteristic, complemented
12#11751768C211yesmaximal, characteristic, complemented
13#11751765C211yesmaximal, characteristic, complemented
14#11751758C211yesmaximal, characteristic, complemented
15#11751758C211yesmaximal, characteristic, complemented
16#10617329—31nomaximal, Hall
17C2×#6740C2211yescharacteristic
18C2×#6740C2211yescharacteristic
19C2×#6738C2211yescharacteristic
20C2×#6738C2211yescharacteristic
21#91785C411yescharacteristic
22C5×#889C411yescharacteristic
23C3×#4033C2211yescharacteristic
24#91419C411yescharacteristic
25#91411C411yescharacteristic
26#91402C2211yescharacteristic
27#91402C2211yescharacteristic
28C4×#1200C2211yescharacteristic
29#91379C411yescharacteristic
30#91377C411yescharacteristic
31#91333C2211yescharacteristic
32#91328C411yescharacteristic
33#91327C411yescharacteristic
34#91323C2211yescharacteristic
35#91323C2211yescharacteristic
36#91233C2211yescharacteristic
37#91233C2211yescharacteristic
38#91231C2211yescharacteristic
39#91231C2211yescharacteristic
40C4⋊(C3⋊#170)C2211yescharacteristic
41C4×C3⋊#170C2211yescharacteristic
42C3×#4004C2211yescharacteristic
43C3×#4004C2211yescharacteristic
44C3×C4⋊#170C2211yescharacteristic
45C3×C4×#170C2211yescharacteristic
46C3×C4×#170C2211yescharacteristic
47C3×C4×#170C2211yescharacteristic
48#91177C2211yescharacteristic
49#91177C2211yescharacteristic
50#91177C2211yescharacteristic
51#91177C2211yescharacteristic
52Dic3⋊#170C2211yescharacteristic
53Dic3⋊#170C2211yescharacteristic
54#91169C2211yescharacteristic
55#91169C2211yescharacteristic
56Dic3×#170C2211yescharacteristic
57Dic3×#170C2211yescharacteristic
58Dic3×#170C2211yescharacteristic
59Dic3×#170C2211yescharacteristic
60#79917—51nomaximal, Hall
61#66022—31no—
62#65708—31no—
63#65708—31no—
64#65707—31no—
65#65707—31no—
66#65707—31no—
67#65707—31no—
68#65703—31no—
69#65703—31no—
70#65703—31no—
71#65703D311yescharacteristic, complemented
72#65701—31no—
73#65701—31no—
74#65682—31no—
75C4×D5⋊C8—31no—
76C2×C4×D15C2×C411yescharacteristic
77C2×Dic30C2×C411yescharacteristic
78C2×C3×Dic10C2×C411yescharacteristic
79C2×#1204C2×C411yescharacteristic
80C2×#1204C2×C411yescharacteristic
81C2×#1200C2×C411yescharacteristic
82C2×#1200C2311yescharacteristic
83C2×C3⋊#170C2311yescharacteristic
84C2×C3⋊#170C2311yescharacteristic
85C2×C3⋊#170C2311yescharacteristic
86C2×C3⋊#170C2311yescharacteristic
87C2×C3×#170C2311yescharacteristic
88C2×C3×#170C2311yescharacteristic
89C2×C3×#170C2311yescharacteristic
90C2×C3×#170C2311yescharacteristic
91#6740—22no—
92#6740—22no—
93#6738—22no—
94#6738Q814yescomplemented
95C3×C5×C4⋊C4C2×C411yescharacteristic
96#6714C2×C411yescharacteristic
97#6714C2×C411yescharacteristic
98#6712C2×C411yescharacteristic
99#6712C2×C411yescharacteristic
100C5×C4⋊Dic3C2×C411yescharacteristic
101C5×Dic3⋊C4C2×C411yescharacteristic
102C5×Dic3⋊C4C2×C411yescharacteristic
103C5×Dic3⋊C4C2×C411yescharacteristic
104C5×Dic3⋊C4C2×C411yescharacteristic
105C4×C5×Dic3C2×C411yescharacteristic
106C3×#683C2×C411yescharacteristic
107C3×#683C2×C411yescharacteristic
108C3×C4×Dic5C2311yescharacteristic
109C3×C4×Dic5C2311yescharacteristic
110C3×C4×Dic5C2311yescharacteristic
111Dic3⋊Dic5C2×C411yescharacteristic
112Dic3⋊Dic5C2×C411yescharacteristic
113#6669C2×C411yescharacteristic
114#6669C2×C411yescharacteristic
115#6668C2×C411yescharacteristic
116#6668C2×C411yescharacteristic
117#6667C2×C411yescharacteristic
118#6667C2×C411yescharacteristic
119Dic3×Dic5C2×C411yescharacteristic
120Dic3×Dic5C2311yescharacteristic
121Dic3×Dic5C2311yescharacteristic
122Dic3×Dic5C2311yescharacteristic
123#5578—51no—
124C3×C8×Q8—51no—
125#5024—51no—
126#4839—51no—
127#4839—51no—
128#4837—51no—
129#4831—51no—
130#4828—51no—
131#4828—51no—
132#4689—51no—
133#4689—51no—
134C4×D3×C8—51no—
135C8×Dic6—51no—
136C8×Dic6—51no—
137C8×Dic6—51no—
138C2×#700—31no—
139C2×#700—31no—
140C2×D5⋊C8—31no—
141C2×D5⋊C8—31no—
142C5×#125—31no—
143#4042—31no—
144#4042—31no—
145#4042—31no—
146#4042—31no—
147#4038—31no—
148#4038—31no—
149#4034—31no—
150#4034—31no—
151#4033—31no—
152#4033—31no—
153#4033—31no—
154#4033C2×D311yescharacteristic
155C42×D5—31no—
156#4016—31no—
157#4004—31no—
158#4004—31no—
159#4004—31no—
160#4004—31no—
161#4004—31no—
162#4004—31no—
163#4004C2×D311yescharacteristic
164#4004C2×D311yescharacteristic
165#4002—31no—
166#4002—31no—
167#4002—31no—
168#4002—31no—
169C4⋊#170—31no—
170C4⋊#170—31no—
171C4⋊#170—31no—
172C4⋊#170C2×D311yescharacteristic
173C4×#170—31no—
174C4×#170—31no—
175C4×#170—31no—
176C4×#170—31no—
177C4×#170—31no—
178C4×#170C2×D311yescharacteristic
179C4×#170C2×D311yescharacteristic
180C4×#170C2×D311yescharacteristic
181#2960—151noSylow
182C22×D15C22×C411yescharacteristic
183C2×C3×C4×C5C22×C411yescharacteristic
184C2×C3×C4×C5C22×C411yescharacteristic
185C2×C3×C4×C5C22×C411yescharacteristic
186C2×Dic15C22×C411yescharacteristic
187C2×Dic15C22×C411yescharacteristic
188C2×Dic15C22×C411yescharacteristic
189C4×D15—22no—
190Dic30—22no—
191C2×C5×Dic3C22×C411yescharacteristic
192C2×C5×Dic3C22×C411yescharacteristic
193C2×C5×Dic3C22×C411yescharacteristic
194C2×C5×Dic3C22×C411yescharacteristic
195C2×C3×Dic5C22×C411yescharacteristic
196C2×C3×Dic5C22×C411yescharacteristic
197C2×C3×Dic5C22×C411yescharacteristic
198C2×C3×Dic5C2411yescharacteristic
199C3×Dic10—22no—
200#1204—22no—
201#1204—22no—
202#1200—22no—
203#1200C2×Q812yes—
204#1200#4112yes—
205C3⋊#170—21no—
206C3⋊#170—21no—
207C3⋊#170—21no—
208C3⋊#170C2×Q812yes—
209C3×#170—21no—
210C3×#170—21no—
211C3×#170—21no—
212C3×#170C2×Q812yes—
213C3×C4×Q8—51no—
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#889AGL(1,𝔽5)11yescharacteristic
225#888—51no—
226#872—51no—
227#872—51no—
228C42×D3—51no—
229C4×Dic6—51no—
230C4×Dic6—51no—
231C4×Dic6—51no—
232C3×C4⋊C8—51no—
233C3×C4⋊C8—51no—
234C3×C4⋊C8—51no—
235C3×C4×C8—51no—
236C3×C4×C8—51no—
237C3×C4×C8—51no—
238#815—51no—
239#815—51no—
240Dic3⋊C8—51no—
241Dic3⋊C8—51no—
242Dic3⋊C8—51no—
243Dic3⋊C8—51no—
244Dic3⋊C8—51no—
245Dic3⋊C8—51no—
246C8×Dic3—51no—
247C8×Dic3—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×C4×D5—31no—
257C2×C4×D5—31no—
258C2×C4×D5—31no—
259C2×Dic10—31no—
260C2×Dic10—31no—
261C2×Dic10—31no—
262C2×Dic10C4×D311yescharacteristic
263C2×#170—31no—
264C2×#170—31no—
265C2×#170—31no—
266C2×#170—31no—
267C2×#170C22×D311yescharacteristic
268C2×#170C22×D311yescharacteristic
269C2×#170C22×D311yescharacteristic
270C2×#170C22×D311yescharacteristic
271#700—62no—
272#700—62no—
273D5⋊C8—34no—
274D5⋊C8—62no—
275C5×C4⋊C4—31no—
276C5×C4⋊C4—31no—
277C5×C4⋊C4—31no—
278C5×C4⋊C4—31no—
279C5×C4⋊C4—31no—
280C5×C4⋊C4C4×D311yescharacteristic
281C42×C5—31no—
282#685—31no—
283#685—31no—
284#685—31no—
285#685—31no—
286C4⋊Dic5—31no—
287C4⋊Dic5—31no—
288#683—31no—
289#683—31no—
290#683—31no—
291#683—31no—
292#683—31no—
293#683—31no—
294#683C4×D311yescharacteristic
295#683C4×D311yescharacteristic
296C4×Dic5—31no—
297C4×Dic5—31no—
298C4×Dic5—31no—
299C4×Dic5—31no—
300C4×Dic5C22×D311yescharacteristic
301C4×Dic5C22×D311yescharacteristic
302C4×Dic5C22×D311yescharacteristic
303#533—151no—
304#446—151no—
305#446—151no—
306#446—151no—
307#446—151no—
308C8×Q8—51no—
309C8×Q8—151no—
310C8×Q8—151no—
311C8×Q8—151no—
312#424—151no—
313#424—151no—
314#423—151no—
315#405—151no—
316#405—151no—
317C2×C4×C8—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—
325Dic15—21no—
326Dic15—21no—
327Dic15#13112yes—
328C3×Dic5—21no—
329C3×Dic5—21no—
330C3×Dic5#13112yes—
331C3×Dic5C22×Q811yescharacteristic
332C3×Dic5C2×#4111yescharacteristic
333C5×Dic3—21no—
334C5×Dic3—21no—
335C5×Dic3—21no—
336C5×Dic3C4×Q812yes—
337C2×C3×Q8—51no—
338C2×C4×D3—51no—
339C2×C4×D3—51no—
340C2×C4×D3—51no—
341C2×Dic6—51no—
342C2×Dic6—51no—
343C2×Dic6—51no—
344C2×C3×C8—51no—
345C2×C3×C8—51no—
346C2×C3×C8—51no—
347C2×C3×C8—51no—
348C3×C4⋊C4—51no—
349C3×C4⋊C4—51no—
350C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
351C3×C42—51no—
352C3×C42—51no—
353C3×C42—51no—
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⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
361Dic3⋊C4—51no—
362Dic3⋊C4—51no—
363Dic3⋊C4—51no—
364Dic3⋊C4—51no—
365Dic3⋊C4—51no—
366Dic3⋊C4—51no—
367Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
368Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
369Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
370Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
371C4×Dic3—51no—
372C4×Dic3—51no—
373C4×Dic3—51no—
374C4×Dic3—51no—
375C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
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—
385C2×C4×C5—31no—
386C2×C4×C5—31no—
387C2×C4×C5—31no—
388C2×C4×C5—31no—
389C2×C4×C5C2×C4×D311yescharacteristic
390C2×C4×C5C2×C4×D311yescharacteristic
391C2×C4×C5C2×C4×D311yescharacteristic
392C2×Dic5—31no—
393C2×Dic5—31no—
394C2×Dic5—31no—
395C2×Dic5C2×C4×D311yescharacteristic
396C2×Dic5C2×C4×D311yescharacteristic
397C2×Dic5C2×C4×D311yescharacteristic
398C2×Dic5C23×D311yescharacteristic
399C4×D5—32no—
400C4×D5—32no—
401C4×D5—62no—
402C4×D5—62no—
403Dic10—22no—
404Dic10—62no—
405Dic10—62no—
406Dic10—62no—
407#170—21no—
408#170—21no—
409#170—21no—
410#170—32no—
411#170—61no—
412#170—61no—
413#170—61no—
414#170D3×Q812yes—
415C2×M16—151no—
416C2×M16—151no—
417C22×C8—151no—
418C22×C8—151no—
419C4⋊Q8—151no—
420C4⋊Q8—151no—
421#125—31no—
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—151no—
434C4⋊C8—51no—
435C4⋊C8—51no—
436C4⋊C8—51no—
437C4⋊C8—151no—
438C4⋊C8—151no—
439C4⋊C8—151no—
440C4⋊C8—151no—
441C4⋊C8—151no—
442C4⋊C8—151no—
443C4⋊C8—151no—
444C4⋊C8—151no—
445C4⋊C8—151no—
446#97—151no—
447#97—151no—
448#97—151no—
449#97—151no—
450C4×C8—51no—
451C4×C8—51no—
452C4×C8—51no—
453C4×C8—151no—
454C4×C8—151no—
455C4×C8—151no—
456C4×C8—151no—
457C4×C8—151no—
458C2×C3×C5C2×C4×Q811yescharacteristic
459C2×C3×C5C2×#13111yescharacteristic
460C2×C3×C5C2×#13111yescharacteristic
461D15—22no—
462C22×D3—51no—
463C3×Q8—102no—
464C2×C3×C4—51no—
465C2×C3×C4—51no—
466C2×C3×C4—51no—
467C2×C3×C4—51no—
468C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
469C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
470C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
471C2×Dic3—51no—
472C2×Dic3—51no—
473C2×Dic3—51no—
474C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
475C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
476C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
477C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
478C4×D3—52no—
479C4×D3—52no—
480C4×D3—102no—
481C4×D3—102no—
482Dic6—102no—
483Dic6—102no—
484Dic6—102no—
485C3×C8—52no—
486C3×C8—101no—
487C3×C8—101no—
488C3×C8—101no—
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—32no—
501C4×C5—61no—
502C4×C5—61no—
503C4×C5—61no—
504Dic5—21no—
505Dic5—21no—
506Dic5—32no—
507Dic5—61no—
508Dic5—61no—
509Dic5#90112yes—
510Dic5C2×D3×Q811yescharacteristic
511Dic5D3×#4111yescharacteristic
512C2×Q8—51no—
513C2×Q8—151no—
514C2×Q8—151no—
515C2×Q8—151no—
516C22×C4—151no—
517C22×C4—151no—
518C22×C4—151no—
519M16—302no—
520M16—302no—
521C2×C8—51no—
522C2×C8—51no—
523C2×C8—51no—
524C2×C8—51no—
525C2×C8—154no—
526C2×C8—151no—
527C2×C8—151no—
528C2×C8—151no—
529C2×C8—151no—
530C2×C8—302no—
531C4⋊C4—31no—
532C4⋊C4—31no—
533C4⋊C4—31no—
534C4⋊C4—31no—
535C4⋊C4—31no—
536C4⋊C4—51no—
537C4⋊C4—51no—
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⋊C4D3×AGL(1,𝔽5)11yescharacteristic
547C22⋊C4—151no—
548C22⋊C4—151no—
549C22⋊C4—151no—
550C22⋊C4—151no—
551C42—31no—
552C42—51no—
553C42—51no—
554C42—51no—
555C42—151no—
556C42—151no—
557C42—151no—
558C42—151no—
559C3×C5#296011yescharacteristic, complemented, Hall
560C22×C3C23×AGL(1,𝔽5)11yescharacteristic
561C2×D3—52no—
562C2×D3—101no—
563C2×D3—101no—
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—21no—
567C3×C4—51no—
568C3×C4—51no—
569C3×C4—52no—
570C3×C4—101no—
571C3×C4—101no—
572Dic3—21no—
573Dic3—21no—
574Dic3—21no—
575Dic3—52no—
576Dic3—101no—
577Dic3—101no—
578Dic3Q8×AGL(1,𝔽5)12yes—
579C2×C5C4×D3×Q811yescharacteristic
580C2×C5C2×#90111yescharacteristic
581C2×C5D3×#13111yescharacteristic
582D5—62no—
583C23—151no—
584Q8—102no—
585Q8—302no—
586Q8—302no—
587Q8—302no—
588C2×C4—31no—
589C2×C4—31no—
590C2×C4—31no—
591C2×C4—31no—
592C2×C4—51no—
593C2×C4—51no—
594C2×C4—51no—
595C2×C4—51no—
596C2×C4—152no—
597C2×C4—152no—
598C2×C4—151no—
599C2×C4—151no—
600C2×C4—151no—
601C2×C4—302no—
602C2×C4—302no—
603C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
604C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
605C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
606C8—52no—
607C8—101no—
608C8—101no—
609C8—101no—
610C8—152no—
611C8—301no—
612C8—301no—
613C8—301no—
614C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
615C2×C3D5⋊#13111yescharacteristic
616C2×C3D5⋊#13111yescharacteristic
617D3—102no—
618C5#7991711yescharacteristic, complemented, Sylow
619C22—152no—
620C22—301no—
621C22—301no—
622C22C22×D3×AGL(1,𝔽5)11yescharacteristic
623C4—21no—
624C4—21no—
625C4—21no—
626C4—32no—
627C4—52no—
628C4—51no—
629C4—51no—
630C4—61no—
631C4—61no—
632C4—61no—
633C4—101no—
634C4—101no—
635C4—152no—
636C4—301no—
637C4—301no—
638C3#1061732911yescharacteristic, complemented, Sylow
639C2—302no—
640C2D5⋊#90111yescharacteristic
641C2#1175684011yescharacteristic
642C2D3×Q8×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radicalC22×D15C22×C4
cosocleC2×C3×Dic5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2960
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11752366C2semidirect
3. C3×#65703C2semidirect
10. #11751787C2semidirect
11. #11751771C2semidirect
12. #11751768C2semidirect
13. #11751765C2semidirect
14. #11751758C2semidirect
15. #11751758C2semidirect
71. #65703D3semidirect
94. #6738Q8semidirect
559. C3×C5#2960semidirect
618. C5#79917semidirect
638. C3#10617329semidirect

Maximal subgroups

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

subgroupindex
#117534652
#117523662
C3×#657032
#117519232
#117519022
#117518902
#117518722
C4×#67382
#117517872
#117517712
#117517682
#117517652
#117517582
#106173293
#799175