Finite Group Databasebeta

← #14415643

Subgroups — #14415643

Order 1920.

1004 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5⋊#208C211yesmaximal, characteristic, complemented
2C2×#91911C211yesmaximal, characteristic, complemented
3#11754526C211yesmaximal, characteristic
4C3×D5⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
5#11752039C212yesmaximal, complemented
6#11751992C212yesmaximal, complemented
7#11751924C212yesmaximal, complemented
8#11751879C212yesmaximal, complemented
9#11751822C211yesmaximal, characteristic, complemented
10#11751801C211yesmaximal, characteristic, complemented
11#11751767C211yesmaximal, characteristic, complemented
12#10617230—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C2×#6772C2211yescharacteristic
15C2×#6762C2212yes—
16D5⋊#208—24no—
17C2×#6758C2211yescharacteristic
18C2×#6758C2211yescharacteristic
19C2×D5⋊(C3⋊C8)C2212yes—
20C2×C3×D5⋊C8C2211yescharacteristic
21C2×C3×D5⋊C8C2211yescharacteristic
22C2×#6739C2212yescomplemented
23C2×D3×#170C2212yescomplemented
24#91911—24no—
25#91813C411yescharacteristic
26C5×#930C411yescharacteristic
27#91563C412yes—
28Dic5×#67C2212yes—
29#91449C411yescharacteristic
30#91447C412yes—
31#91440C2212yes—
32#91360C411yescharacteristic
33#91358C2211yescharacteristic
34C3×C22⋊#170C2211yescharacteristic
35C3×C22⋊#170C2211yescharacteristic
36C3×#4003C2211yescharacteristic
37C3×#4003C2211yescharacteristic
38#91177C2212yescomplemented
39Dic3⋊#170C2212yescomplemented
40(C2×D3)⋊#170C2212yescomplemented
41(C2×D3)⋊#170C2212yescomplemented
42#91169C2212yescomplemented
43Dic3×#170C2212yescomplemented
44#78596—51nomaximal, Hall
45C2×#4131—31no—
46C2×D5⋊M16—31no—
47#65940—31no—
48#65776—31no—
49#65774—32no—
50#65773—32no—
51D5⋊(C22⋊C8)D311yescharacteristic, complemented
52#65708—31no—
53#65701—31no—
54#65694—32no—
55#65692—32no—
56C23×C3×D5C2×C411yescharacteristic
57C22×C3×C4×C5C2×C411yescharacteristic
58C2×Dic30C2×C411yescharacteristic
59C2×C5×#67C2×C412yes—
60C2×C5×D12C2×C411yescharacteristic
61C22×C3×Dic5C2311yescharacteristic
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5—22no—
64C2×C3×C4×D5C2×C411yescharacteristic
65C2×C3×C4×D5C2×C411yescharacteristic
66C2×C3×C4×D5C2311yescharacteristic
67C2×C3×C4×D5C2311yescharacteristic
68C2×#1201C2×C412yes—
69C2×#1201C2×C412yes—
70C2×D3×Dic5C2312yes—
71#6772—22no—
72#6772—22no—
73#6762—24no—
74C2×C3⋊#170C2312yes—
75C2×C3⋊#170C2312yes—
76#6758—22no—
77#6758D414yescomplemented
78D5⋊(C3⋊C8)—24no—
79C2×C3×#170C2311yescharacteristic
80C2×C3×#170C2311yescharacteristic
81C2×C3×#170C2311yescharacteristic
82C2×C3×#170C2311yescharacteristic
83C3×D5⋊C8—22no—
84C3×D5⋊C8—22no—
85#6739—24no—
86D3×#170—24no—
87#6719C2×C412yes—
88C4⋊Dic15C2×C411yescharacteristic
89#6712C2×C412yes—
90C5×(C2×D3)⋊C4C2×C412yes—
91C5×C4⋊Dic3C2×C411yescharacteristic
92Dic3⋊Dic5C2×C412yes—
93(C2×D3)⋊Dic5C2×C412yes—
94#6665C2×C412yes—
95#6665C2×C412yes—
96Dic3×Dic5C2312yes—
97#5791—51no—
98C22×#208—51no—
99C2×#901—51no—
100C2×C3×C22⋊C8—51no—
101#5110—51no—
102#5102—51no—
103#5101—51no—
104#4730—52no—
105#4729—52no—
106#4728—52no—
107#67⋊C8—52no—
108C2×#711—31no—
109C22×C4×D5C2×D311yescharacteristic
110C2×#704—32no—
111C2×#704—32no—
112C22×#170—32no—
113#4131—64no—
114D5⋊M16—64no—
115C2×#700—31no—
116C2×#700—31no—
117C2×D5⋊C8—32no—
118C2×D5⋊C8C2×D311yescharacteristic
119C2×D5⋊C8C2×D311yescharacteristic
120C5×#121—31no—
121#4084—31no—
122#4083—32no—
123D4×Dic5—32no—
124#4070—31no—
125#4043—31no—
126#4038—31no—
127#4029—32no—
128#4027—32no—
129C22⋊#170—32no—
130C22⋊#170—32no—
131C22⋊#170C2×D311yescharacteristic
132C22⋊#170C2×D311yescharacteristic
133#4004—32no—
134#4003C2×D311yescharacteristic
135#4003C2×D311yescharacteristic
136#4002—32no—
137C4⋊#170—32no—
138C4×#170—32no—
139#2933—151noSylow
140C23×C3×C5C22×C411yescharacteristic
141C22×C5×D3C22×C412yes—
142C22×C3×D5—22no—
143C22×C3×D5—22no—
144C22×C3×D5—41no—
145C22×C3×D5C22×C411yescharacteristic
146C22×C3×D5C22×C411yescharacteristic
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5C22×C411yescharacteristic
149C2×C3×C4×C5C22×C411yescharacteristic
150C2×Dic15C22×C412yes—
151C2×Dic15C22×C412yes—
152Dic30—22no—
153C5×#67—42no—
154C2×C5×Dic3C22×C412yes—
155C5×D12—22no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—21no—
158C2×C3×Dic5C22×C411yescharacteristic
159C2×C3×Dic5C2411yescharacteristic
160C3×C4×D5—22no—
161C3×C4×D5—22no—
162C3×C4×D5—21no—
163C3×C4×D5—21no—
164C3×C4×D5C2×D412yes—
165C3×C4×D5#4112yes—
166#1201—24no—
167#1201—24no—
168D3×Dic5—22no—
169D3×Dic5—22no—
170C3⋊#170—22no—
171C3⋊#170C2×D414yes—
172C3×#170—21no—
173C3×#170—21no—
174C3×#170—21no—
175C3×#170—21no—
176C23×C3×C4—51no—
177C2×#235—51no—
178C22×C3×C8—51no—
179C22×C3×C8—51no—
180#953—52no—
181#930—51no—
182#930AGL(1,𝔽5)11yescharacteristic
183#929—52no—
184C4×#67—52no—
185C4×#67—52no—
186#926—51no—
187#924—51no—
188#924—51no—
189C2×#208—51no—
190C2×#208—51no—
191C2×#208—52no—
192C2×#208—104no—
193C22×C3⋊C8—52no—
194#901—104no—
195C2×ΓL(1,𝔽25)—52no—
196C2×D3×C8—52no—
197C3×C22⋊C8—51no—
198C3×C22⋊C8—51no—
199C3×C22⋊C8—51no—
200C3×C22⋊C8—51no—
201(C2×D3)⋊C8—52no—
202(C2×D3)⋊C8—52no—
203#815—52no—
204Dic3⋊C8—52no—
205Dic3⋊C8—52no—
206C8×Dic3—52no—
207C23×D5C4×D311yescharacteristic
208C2×C5×D4—32no—
209C2×C5×D4—31no—
210C22×C4×C5C4×D311yescharacteristic
211C2×C22⋊D5—32no—
212C2×C22⋊D5—32no—
213C22×Dic5—32no—
214C22×Dic5C22×D311yescharacteristic
215#711—62no—
216#711—62no—
217C2×C4×D5—22no—
218C2×C4×D5—22no—
219C2×C4×D5C4×D311yescharacteristic
220C2×C4×D5C4×D311yescharacteristic
221C2×C4×D5C22×D311yescharacteristic
222C2×C4×D5C22×D311yescharacteristic
223C2×Dic10—31no—
224#704—64no—
225#704—64no—
226C2×#170—32no—
227C2×#170—32no—
228C2×#170—64no—
229C2×#170C22×D311yescharacteristic
230C2×#170C22×D311yescharacteristic
231C2×#170C22×D311yescharacteristic
232C2×#170C22×D311yescharacteristic
233#700—34no—
234#700—62no—
235D5⋊C8—22no—
236D5⋊C8—22no—
237D5⋊C8—64no—
238C5×C4⋊C4—31no—
239C5×C22⋊C4—32no—
240C22⋊Dic5—32no—
241C22⋊Dic5—32no—
242#685—32no—
243#685—32no—
244C4⋊Dic5—31no—
245C4⋊Dic5—32no—
246#683—32no—
247C4×Dic5—32no—
248C2×#131—151no—
249C22×M16—151no—
250#525—151no—
251#436—152no—
252#435—152no—
253#435—152no—
254C8×D4—152no—
255#424—151no—
256#408—151no—
257C2×C22⋊C8—51no—
258#405—151no—
259C22×C3×C5—21no—
260C22×C3×C5—21no—
261C22×C3×C5—21no—
262C22×C3×C5C23×C411yescharacteristic
263C2×C5×D3—22no—
264C2×C5×D3—22no—
265C2×C5×D3—22no—
266C2×C3×D5—21no—
267C2×C3×D5—21no—
268C2×C3×D5—21no—
269C2×C3×D5—21no—
270C2×C3×D5—44no—
271C2×C3×D5C4×D412yes—
272C2×C3×D5#13112yescomplemented
273C3×C4×C5—21no—
274C3×C4×C5C4×D412yes—
275Dic15—22no—
276Dic15—22no—
277C3×Dic5—21no—
278C3×Dic5C22×D411yescharacteristic
279C3×Dic5C2×#4111yescharacteristic
280C5×Dic3—22no—
281C24×C3—51no—
282C22×C3×C4—51no—
283C22×C3×C4—51no—
284C22×C3×C4—51no—
285C22×C3×C4—51no—
286C22×C3×C4—51no—
287C22×C3×C4—102no—
288C22×C3×C4—102no—
289C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
290C2×#67—52no—
291C2×#67—52no—
292C2×#67C2×AGL(1,𝔽5)12yes—
293#235—102no—
294#235—102no—
295C2×D12C2×AGL(1,𝔽5)11yescharacteristic
296C2×C4×D3—52no—
297C2×Dic6—51no—
298C2×C3×C8—51no—
299C2×C3×C8—51no—
300C2×C3×C8—51no—
301C2×C3×C8—51no—
302C2×C3×C8—102no—
303C2×C3×C8—102no—
304#217—52no—
305#217—52no—
306#217—52no—
307(C2×D3)⋊C4—52no—
308(C2×D3)⋊C4C2×AGL(1,𝔽5)12yes—
309C4⋊Dic3—51no—
310C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
311Dic3⋊C4—52no—
312Dic3⋊C4—52no—
313C4×Dic3—52no—
314#208—54no—
315#208—104no—
316#208—102no—
317C2×C3⋊C8—52no—
318C2×C3⋊C8—52no—
319C2×C3⋊C8—104no—
320ΓL(1,𝔽25)—104no—
321D3×C8—104no—
322C23×C5—32no—
323C23×C5C2×C4×D311yescharacteristic
324C22×D5—22no—
325C22×D5—22no—
326C22×D5—41no—
327C22×D5C2×C4×D311yescharacteristic
328C22×D5C2×C4×D311yescharacteristic
329C5×D4—62no—
330C5×D4—122no—
331C2×C4×C5—22no—
332C2×C4×C5—32no—
333C2×C4×C5C2×C4×D311yescharacteristic
334C2×C4×C5C2×C4×D311yescharacteristic
335C22⋊D5—64no—
336C22⋊D5—64no—
337C2×Dic5—21no—
338C2×Dic5—21no—
339C2×Dic5—32no—
340C2×Dic5—32no—
341C2×Dic5—62no—
342C2×Dic5—62no—
343C2×Dic5C2×C4×D311yescharacteristic
344C2×Dic5C23×D311yescharacteristic
345C4×D5—22no—
346C4×D5—22no—
347C4×D5—21no—
348C4×D5—21no—
349C4×D5D3×D412yes—
350C4×D5#23712yes—
351Dic10—62no—
352#170—21no—
353#170—21no—
354#170—21no—
355#170—21no—
356#170—34no—
357#170—62no—
358C2×#41—151no—
359C23×C4—51no—
360#131—304no—
361C2×M16—152no—
362C2×M16—151no—
363C2×M16—151no—
364C2×M16—152no—
365C2×M16—304no—
366C22×C8—51no—
367C22×C8—51no—
368C22×C8—152no—
369C22×C8—152no—
370#123—152no—
371C22⋊Q8—151no—
372C22⋊Q8—151no—
373#121—31no—
374#121—151no—
375#120—152no—
376C4×D4—152no—
377C4×D4—152no—
378#117—151no—
379C4⋊C8—152no—
380C4⋊C8—152no—
381C22⋊C8—51no—
382C22⋊C8—51no—
383C22⋊C8—51no—
384C22⋊C8—51no—
385C22⋊C8—152no—
386C22⋊C8—152no—
387#97—152no—
388C4×C8—152no—
389C2×C3×C5—41no—
390C2×C3×C5C2×C4×D411yescharacteristic
391C2×C3×C5C2×#13111yescharacteristic
392C2×C3×C5#56811yescharacteristic
393C3×D5—22no—
394C3×D5—22no—
395C5×D3—42no—
396C23×C3—51no—
397C23×C3—51no—
398C23×C3—102no—
399C23×C3—102no—
400C23×C3—201no—
401C23×C3C22×AGL(1,𝔽5)11yescharacteristic
402C22×D3C22×AGL(1,𝔽5)12yes—
403C2×C3×C4—22no—
404C2×C3×C4—51no—
405C2×C3×C4—52no—
406C2×C3×C4—52no—
407C2×C3×C4—51no—
408C2×C3×C4—101no—
409C2×C3×C4—101no—
410C2×C3×C4—102no—
411C2×C3×C4—101no—
412C2×C3×C4—101no—
413C2×C3×C4—102no—
414C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
415C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
416#67—42no—
417#67—104no—
418#67—104no—
419C2×Dic3—52no—
420C2×Dic3—52no—
421C2×Dic3C22×AGL(1,𝔽5)12yes—
422D12—22no—
423C4×D3—102no—
424C4×D3—102no—
425Dic6—102no—
426C3×C8—101no—
427C3×C8—101no—
428C3×C8—101no—
429C3×C8—101no—
430C3⋊C8—54no—
431C3⋊C8—102no—
432C22×C5—21no—
433C22×C5—21no—
434C22×C5—21no—
435C22×C5—62no—
436C22×C5—62no—
437C22×C5—62no—
438C22×C5C22×C4×D311yescharacteristic
439C2×D5—21no—
440C2×D5—21no—
441C2×D5—21no—
442C2×D5—21no—
443C2×D5—44no—
444C2×D5#67⋊C412yes—
445C2×D5#90112yescomplemented
446C4×C5—21no—
447C4×C5—62no—
448C4×C5#67⋊C412yes—
449Dic5—21no—
450Dic5—62no—
451Dic5—62no—
452Dic5C2×D3×D411yescharacteristic
453Dic5C2×#23711yescharacteristic
454C24—51no—
455#41—302no—
456#41—302no—
457C2×Q8—151no—
458C2×D4—32no—
459C2×D4—31no—
460C2×D4—152no—
461C2×D4—152no—
462C22×C4—51no—
463C22×C4—51no—
464C22×C4—51no—
465C22×C4—51no—
466C22×C4—51no—
467C22×C4—102no—
468C22×C4—102no—
469C22×C4—152no—
470C22×C4D3×AGL(1,𝔽5)11yescharacteristic
471M16—154no—
472M16—304no—
473M16—304no—
474M16—302no—
475C2×C8—51no—
476C2×C8—51no—
477C2×C8—51no—
478C2×C8—51no—
479C2×C8—102no—
480C2×C8—102no—
481C2×C8—152no—
482C2×C8—152no—
483C2×C8—304no—
484C2×C8—304no—
485C4⋊C4—31no—
486C4⋊C4—152no—
487C4⋊C4—151no—
488C4⋊C4—152no—
489C22⋊C4—32no—
490C22⋊C4—152no—
491C22⋊C4—152no—
492C22⋊C4—152no—
493C22⋊C4—152no—
494C42—152no—
495C3×C5#293311yescharacteristic, complemented, Hall
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—52no—
500C22×C3—52no—
501C22×C3—101no—
502C22×C3—101no—
503C22×C3—101no—
504C22×C3—101no—
505C22×C3—204no—
506C22×C3C23×AGL(1,𝔽5)11yescharacteristic
507C2×D3—22no—
508C2×D3—22no—
509C2×D3—22no—
510C3×C4—21no—
511C3×C4—51no—
512C3×C4—51no—
513C3×C4—101no—
514C3×C4D4×AGL(1,𝔽5)12yes—
515Dic3—22no—
516Dic3—102no—
517Dic3—102no—
518C2×C5—41no—
519C2×C5—122no—
520C2×C5C2×#67⋊C411yescharacteristic
521C2×C5C2×#90111yescharacteristic
522C2×C5#574511yescharacteristic
523D5—22no—
524D5—22no—
525C23—32no—
526C23—51no—
527C23—51no—
528C23—102no—
529C23—102no—
530C23—201no—
531C23C2×D3×AGL(1,𝔽5)11yescharacteristic
532Q8—302no—
533D4—62no—
534D4—122no—
535D4—304no—
536D4—304no—
537C2×C4—22no—
538C2×C4—32no—
539C2×C4—51no—
540C2×C4—52no—
541C2×C4—52no—
542C2×C4—51no—
543C2×C4—101no—
544C2×C4—101no—
545C2×C4—102no—
546C2×C4—101no—
547C2×C4—101no—
548C2×C4—102no—
549C2×C4—152no—
550C2×C4—152no—
551C2×C4—302no—
552C2×C4—302no—
553C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
554C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
555C8—101no—
556C8—101no—
557C8—101no—
558C8—101no—
559C8—154no—
560C8—302no—
561C2×C3—41no—
562C2×C3—102no—
563C2×C3—102no—
564C2×C3#6625611yescharacteristic
565C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
566C2×C3D5⋊#13111yescharacteristic
567D3—42no—
568C5#7859611yescharacteristic, complemented, Sylow
569C22—21no—
570C22—21no—
571C22—21no—
572C22—52no—
573C22—52no—
574C22—62no—
575C22—62no—
576C22—62no—
577C22—101no—
578C22—101no—
579C22—101no—
580C22—101no—
581C22—204no—
582C22C22×D3×AGL(1,𝔽5)11yescharacteristic
583C4—21no—
584C4—51no—
585C4—51no—
586C4—62no—
587C4—101no—
588C4—302no—
589C4—302no—
590C4#67⋊AGL(1,𝔽5)12yes—
591C3#1061723011yescharacteristic, complemented, Sylow
592C2—41no—
593C2—102no—
594C2—102no—
595C2—122no—
596C2D5⋊#90111yescharacteristic
597C2#1175682211yescharacteristic
598C2C2×#67⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radical#11754526C2
cosocleC2×C3×Dic5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2933
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×D5⋊#208C2semidirect
2. C2×#91911C2semidirect
4. C3×D5⋊(C22⋊C8)C2semidirect
5. #11752039C2semidirect
6. #11751992C2semidirect
7. #11751924C2semidirect
8. #11751879C2semidirect
9. #11751822C2semidirect
10. #11751801C2semidirect
11. #11751767C2semidirect
22. C2×#6739C22semidirect
23. C2×D3×#170C22semidirect
38. #91177C22semidirect
39. Dic3⋊#170C22semidirect
40. (C2×D3)⋊#170C22semidirect
41. (C2×D3)⋊#170C22semidirect
42. #91169C22semidirect
43. Dic3×#170C22semidirect
51. D5⋊(C22⋊C8)D3semidirect
77. #6758D4semidirect
272. C2×C3×D5#131semidirect
445. C2×D5#901semidirect
495. C3×C5#2933semidirect
568. C5#78596semidirect
591. C3#10617230semidirect

Maximal subgroups

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

subgroupindex
C2×D5⋊#2082
C2×#919112
#117545262
C3×D5⋊(C22⋊C8)2
#117520392
#117519922
#117519242
#117518792
#117518222
#117518012
#117517672
#106172303
#785965