Finite Group Databasebeta

← #14320114

Subgroups — #14320114

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D5×Dic3C211yesmaximal, characteristic
2#11752423C211yesmaximal, characteristic
3C3×#65764C211yesmaximal, characteristic
4#11752028C212yesmaximal
5Dic3×C22⋊AGL(1,𝔽5)C212yesmaximal
6#11751834C212yesmaximal, complemented
7#11751832C212yesmaximal, complemented
8#11751750C212yesmaximal, complemented
9#11751746C212yesmaximal, complemented
10#10617046—31nomaximal, Hall
11C22×C3×C4×D5C2211yescharacteristic
12C22×D5×Dic3C2211yescharacteristic
13C22×D5×Dic3C2211yescharacteristic
14C2×#6763C2212yes—
15C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
16C2×Dic3⋊AGL(1,𝔽5)C2214yes—
17C2×Dic3×AGL(1,𝔽5)C2214yes—
18C2×C4×Dic15C411yescharacteristic, complemented
19C2×C4×C5×Dic3C411yescharacteristic, complemented
20C2×Dic3×Dic5C411yescharacteristic, complemented
21C2×Dic3×Dic5C411yescharacteristic, complemented
22C4×D5×Dic3C411yescharacteristic, complemented
23C4×D5×Dic3C411yescharacteristic, complemented
24C4×D5×Dic3C411yescharacteristic, complemented
25C4×D5×Dic3C411yescharacteristic, complemented
26C4×D5×Dic3C2211yescharacteristic
27C4×D5×Dic3C2211yescharacteristic
28C4×D5×Dic3C2211yescharacteristic
29C4×D5×Dic3C2211yescharacteristic
30#91235C2212yes—
31#91235C2212yes—
32C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
33C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
34(C2×AGL(1,𝔽5))⋊Dic3C2214yes—
35(C2×AGL(1,𝔽5))⋊Dic3C2214yes—
36#74051—51nomaximal, Hall
37C2×C42×D5—31no—
38#65765—32no—
39#65764—31no—
40#65764D311yescharacteristic
41C4×C22⋊AGL(1,𝔽5)—32no—
42#65690—32no—
43#65689—32no—
44C4×C4⋊AGL(1,𝔽5)—32no—
45#65686—32no—
46C23×C3×D5C2311yescharacteristic
47C22×ΓL(1,𝔽16)C2314yes—
48C22×C3×AGL(1,𝔽5)C2314yes—
49C22×C3×C4×C5C2×C411yescharacteristic
50C22×Dic15C2×C411yescharacteristic
51C22×Dic15C2×C411yescharacteristic
52C22×C5×Dic3C2×C411yescharacteristic
53C22×C5×Dic3C2×C411yescharacteristic
54C22×C3×Dic5C2×C411yescharacteristic
55C2×C3×C4×D5—24no—
56C2×C3×C4×D5C2×C411yescharacteristic
57C2×C3×C4×D5C2×C411yescharacteristic
58C2×C3×C4×D5C2311yescharacteristic
59C2×C3×C4×D5C2311yescharacteristic
60C2×D5×Dic3—24no—
61C2×D5×Dic3—24no—
62C2×D5×Dic3C2×C411yescharacteristic
63C2×D5×Dic3C2×C411yescharacteristic
64C2×D5×Dic3C2×C411yescharacteristic
65C2×D5×Dic3C2×C411yescharacteristic
66C2×D5×Dic3C2311yescharacteristic
67C2×D5×Dic3C2311yescharacteristic
68C2×D5×Dic3C2311yescharacteristic
69C2×D5×Dic3C2311yescharacteristic
70#6763—24no—
71C3×C22⋊AGL(1,𝔽5)—24no—
72Dic3⋊AGL(1,𝔽5)—28no—
73Dic3×AGL(1,𝔽5)—28no—
74C4×Dic15C2×C411yescharacteristic
75C4×Dic15C2×C411yescharacteristic
76C4×Dic15C2×C411yescharacteristic
77C4×Dic15C2×C411yescharacteristic
78C4×C5×Dic3C2×C411yescharacteristic
79C4×C5×Dic3C2×C411yescharacteristic
80C4×C5×Dic3C2×C411yescharacteristic
81C4×C5×Dic3C2×C411yescharacteristic
82Dic3×Dic5C2×C411yescharacteristic
83Dic3×Dic5C2×C411yescharacteristic
84Dic3×Dic5C2×C411yescharacteristic
85Dic3×Dic5C2×C411yescharacteristic
86Dic3×Dic5C2×C411yescharacteristic
87Dic3×Dic5C2×C411yescharacteristic
88Dic3×Dic5C2×C411yescharacteristic
89Dic3×Dic5C2×C411yescharacteristic
90C22×C4×Dic3—51no—
91C3×#381—51no—
92#5211—51no—
93#4942—52no—
94Dic3×C22⋊C4—52no—
95#4651—52no—
96#4650—52no—
97#4649—52no—
98#4648—52no—
99C22×C4×D5—31no—
100C22×C4×D5—31no—
101C22×C4×D5C2×D311yescharacteristic
102C2×C22⋊AGL(1,𝔽5)—32no—
103C2×C22⋊AGL(1,𝔽5)C2×D312yes—
104C2×C4⋊AGL(1,𝔽5)—34no—
105C2×C4×AGL(1,𝔽5)—34no—
106C2×C42×C5—31no—
107C2×C4×Dic5—31no—
108C2×C4×Dic5—31no—
109C2×C4×Dic5—31no—
110C42×D5—31no—
111C42×D5—31no—
112C42×D5—31no—
113C42×D5—31no—
114C42×D5—31no—
115C42×D5—31no—
116C42×D5—31no—
117C42×D5—31no—
118(C2×AGL(1,𝔽5))⋊C4—34no—
119(C2×AGL(1,𝔽5))⋊C4—34no—
120(C2×AGL(1,𝔽5))⋊C4—32no—
121(C2×AGL(1,𝔽5))⋊C4—32no—
122(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
123(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
124#2283—151noSylow
125C23×C3×C5C22×C411yescharacteristic
126C22×C3×D5—22no—
127C22×C3×D5—22no—
128C22×C3×D5C22×C411yescharacteristic
129C22×C3×D5#4114yes—
130C22×C3×D5C2411yescharacteristic
131C2×ΓL(1,𝔽16)—24no—
132C2×ΓL(1,𝔽16)—24no—
133C2×ΓL(1,𝔽16)—24no—
134C2×C3×AGL(1,𝔽5)—24no—
135C2×C3×AGL(1,𝔽5)—24no—
136C2×C3×AGL(1,𝔽5)—24no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C22×C411yescharacteristic
139C2×C3×C4×C5C22×C411yescharacteristic
140C2×Dic15—22no—
141C2×Dic15—22no—
142C2×Dic15C22×C411yescharacteristic
143C2×Dic15C22×C411yescharacteristic
144C2×Dic15C22×C411yescharacteristic
145C2×Dic15C22×C411yescharacteristic
146C2×C5×Dic3—22no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3C22×C411yescharacteristic
149C2×C5×Dic3C22×C411yescharacteristic
150C2×C5×Dic3C22×C411yescharacteristic
151C2×C5×Dic3C22×C411yescharacteristic
152C2×C3×Dic5—22no—
153C2×C3×Dic5C22×C411yescharacteristic
154C2×C3×Dic5C22×C411yescharacteristic
155C3×C4×D5—22no—
156C3×C4×D5—22no—
157C3×C4×D5—22no—
158C3×C4×D5—22no—
159D5×Dic3—22no—
160D5×Dic3—22no—
161D5×Dic3—22no—
162D5×Dic3—22no—
163D5×Dic3—22no—
164D5×Dic3—22no—
165D5×Dic3#4114yes—
166D5×Dic3#4114yes—
167C23×C3×C4—51no—
168C23×Dic3—51no—
169C23×Dic3—51no—
170C2×C3×C22⋊C4—52no—
171C2×#217—52no—
172C2×Dic3⋊C4—54no—
173C2×C4×Dic3—51no—
174C2×C4×Dic3—51no—
175C2×C4×Dic3—51no—
176C2×C4×Dic3—51no—
177C2×C4×Dic3—51no—
178C2×C4×Dic3—51no—
179C2×C4×Dic3—51no—
180C2×C4×Dic3—51no—
181C2×C4×Dic3—51no—
182C2×C4×Dic3—51no—
183C2×C4×Dic3—51no—
184C2×C4×Dic3—54no—
185C2×C4×Dic3AGL(1,𝔽5)11yescharacteristic, complemented
186C3×#95—52no—
187C3×#95—52no—
188C3⋊#95—54no—
189C3⋊#95—54no—
190C3⋊#95—52no—
191C3⋊#95—52no—
192C23×D5C22×D311yescharacteristic
193C22×AGL(1,𝔽5)—34no—
194C22×AGL(1,𝔽5)C22×D314yes—
195C22×C4×C5—31no—
196C22×C4×C5—31no—
197C22×C4×C5C4×D311yescharacteristic
198C22×Dic5—31no—
199C22×Dic5—31no—
200C22×Dic5C4×D311yescharacteristic
201C2×C4×D5—24no—
202C2×C4×D5—31no—
203C2×C4×D5—31no—
204C2×C4×D5—31no—
205C2×C4×D5—31no—
206C2×C4×D5—31no—
207C2×C4×D5—31no—
208C2×C4×D5—31no—
209C2×C4×D5—31no—
210C2×C4×D5—64no—
211C2×C4×D5—64no—
212C2×C4×D5C4×D311yescharacteristic
213C2×C4×D5C4×D311yescharacteristic
214C2×C4×D5C22×D311yescharacteristic
215C2×C4×D5C22×D311yescharacteristic
216C22⋊AGL(1,𝔽5)—24no—
217C22⋊AGL(1,𝔽5)—64no—
218C4⋊AGL(1,𝔽5)—68no—
219C4×AGL(1,𝔽5)—68no—
220C42×C5—31no—
221C42×C5—31no—
222C42×C5—31no—
223C42×C5—31no—
224C4×Dic5—31no—
225C4×Dic5—31no—
226C4×Dic5—31no—
227C4×Dic5—31no—
228C4×Dic5—31no—
229C4×Dic5—31no—
230C4×Dic5—31no—
231C4×Dic5—31no—
232C4×Dic5—31no—
233C4×Dic5—31no—
234C4×Dic5—31no—
235C4×Dic5—31no—
236C22×C42—151no—
237#383—152no—
238#382—152no—
239#381—51no—
240#381—151no—
241#380—152no—
242C4×C4⋊C4—152no—
243C4×C22⋊C4—152no—
244#376—152no—
245C22×C3×C5—21no—
246C22×C3×C5—21no—
247C22×C3×C5#11712yes—
248C22×C3×C5C23×C411yescharacteristic
249C2×C3×D5—21no—
250C2×C3×D5—21no—
251C2×C3×D5—28no—
252C2×C3×D5#11712yes—
253C2×C3×D5C2×#4112yes—
254C2×C3×D5C2×#4112yes—
255C2×C3×D5C2×#4112yes—
256ΓL(1,𝔽16)—44no—
257C3×AGL(1,𝔽5)—44no—
258C3×C4×C5—21no—
259C3×C4×C5—21no—
260Dic15—21no—
261Dic15—21no—
262Dic15#11712yes—
263Dic15#11712yes—
264C3×Dic5—21no—
265C3×Dic5—21no—
266C5×Dic3—21no—
267C5×Dic3—21no—
268C5×Dic3#11712yes—
269C5×Dic3#11712yes—
270C24×C3—51no—
271C22×C3×C4—51no—
272C22×C3×C4—51no—
273C22×C3×C4—51no—
274C22×C3×C4—51no—
275C22×C3×C4—51no—
276C22×C3×C4—54no—
277C22×C3×C4—104no—
278C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
279C22×Dic3—51no—
280C22×Dic3—51no—
281C22×Dic3—51no—
282C22×Dic3—51no—
283C22×Dic3—51no—
284C22×Dic3—51no—
285C22×Dic3—51no—
286C22×Dic3—51no—
287C22×Dic3—51no—
288C22×Dic3—51no—
289C22×Dic3—54no—
290C22×Dic3—104no—
291C22×Dic3—104no—
292C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
293C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
294C3×C22⋊C4—104no—
295#217—104no—
296Dic3⋊C4—108no—
297C4×Dic3—51no—
298C4×Dic3—51no—
299C4×Dic3—51no—
300C4×Dic3—51no—
301C4×Dic3—51no—
302C4×Dic3—51no—
303C4×Dic3—51no—
304C4×Dic3—51no—
305C4×Dic3—51no—
306C4×Dic3—51no—
307C4×Dic3—51no—
308C4×Dic3—51no—
309C4×Dic3—108no—
310C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
311C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
312C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
313C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
314C23×C5C2×C4×D311yescharacteristic
315C22×D5—22no—
316C22×D5—22no—
317C22×D5C2×C4×D311yescharacteristic
318C22×D5#23714yes—
319C22×D5C23×D311yescharacteristic
320C2×AGL(1,𝔽5)—24no—
321C2×AGL(1,𝔽5)—24no—
322C2×AGL(1,𝔽5)—24no—
323C2×AGL(1,𝔽5)—64no—
324C2×AGL(1,𝔽5)—64no—
325C2×AGL(1,𝔽5)—64no—
326C2×C4×C5—22no—
327C2×C4×C5—31no—
328C2×C4×C5—31no—
329C2×C4×C5—31no—
330C2×C4×C5—31no—
331C2×C4×C5—62no—
332C2×C4×C5—62no—
333C2×C4×C5C2×C4×D311yescharacteristic
334C2×C4×C5C2×C4×D311yescharacteristic
335C2×Dic5—22no—
336C2×Dic5—31no—
337C2×Dic5—31no—
338C2×Dic5—31no—
339C2×Dic5—31no—
340C2×Dic5—62no—
341C2×Dic5—62no—
342C2×Dic5C2×C4×D311yescharacteristic
343C2×Dic5C2×C4×D311yescharacteristic
344C4×D5—22no—
345C4×D5—22no—
346C4×D5—22no—
347C4×D5—22no—
348C4×D5—34no—
349C4×D5—34no—
350C4×D5—62no—
351C4×D5—62no—
352C4×D5—62no—
353C4×D5—62no—
354C4×D5—62no—
355C4×D5—62no—
356C23×C4—51no—
357C23×C4—151no—
358C23×C4—151no—
359C2×C4⋊C4—154no—
360C2×C22⋊C4—52no—
361C2×C22⋊C4—152no—
362C2×C42—31no—
363C2×C42—151no—
364C2×C42—151no—
365C2×C42—151no—
366C2×C42—151no—
367C2×C42—151no—
368C2×C42—151no—
369C2×C42—151no—
370C2×C42—151no—
371C2×C42—151no—
372C2×C42—151no—
373C2×C42—151no—
374C2×C42—154no—
375#95—52no—
376#95—52no—
377#95—154no—
378#95—152no—
379#95—154no—
380#95—152no—
381C2×C3×C5—22no—
382C2×C3×C5C2×#11711yescharacteristic
383C2×C3×C5C2×#11711yescharacteristic
384C2×C3×C5C2×#11711yescharacteristic
385C3×D5—22no—
386C3×D5#52914yes—
387C23×C3—51no—
388C23×C3—54no—
389C23×C3—51no—
390C23×C3—102no—
391C23×C3—102no—
392C23×C3C22×AGL(1,𝔽5)11yescharacteristic
393C2×C3×C4—22no—
394C2×C3×C4—51no—
395C2×C3×C4—51no—
396C2×C3×C4—102no—
397C2×C3×C4—102no—
398C2×C3×C4—102no—
399C2×C3×C4—102no—
400C2×C3×C4—102no—
401C2×C3×C4—104no—
402C2×C3×C4—104no—
403C2×C3×C4—104no—
404C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
405C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—51no—
409C2×Dic3—51no—
410C2×Dic3—54no—
411C2×Dic3—54no—
412C2×Dic3—51no—
413C2×Dic3—51no—
414C2×Dic3—102no—
415C2×Dic3—102no—
416C2×Dic3—102no—
417C2×Dic3—102no—
418C2×Dic3—102no—
419C2×Dic3—102no—
420C2×Dic3—102no—
421C2×Dic3—102no—
422C2×Dic3—104no—
423C2×Dic3—104no—
424C2×Dic3—104no—
425C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
426C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
427C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
428C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
429C22×C5—21no—
430C22×C5—21no—
431C22×C5#87712yes—
432C22×C5C22×C4×D311yescharacteristic
433C2×D5—21no—
434C2×D5—21no—
435C2×D5—28no—
436C2×D5#87712yes—
437C2×D5C2×#23712yes—
438C2×D5D3×#4112yes—
439C2×D5D3×#4112yes—
440AGL(1,𝔽5)—44no—
441AGL(1,𝔽5)—124no—
442C4×C5—21no—
443C4×C5—21no—
444C4×C5—32no—
445C4×C5—32no—
446C4×C5—61no—
447C4×C5—61no—
448Dic5—21no—
449Dic5—21no—
450Dic5—32no—
451Dic5—32no—
452Dic5—61no—
453Dic5—61no—
454C24—51no—
455C22×C4—31no—
456C22×C4—31no—
457C22×C4—51no—
458C22×C4—51no—
459C22×C4—51no—
460C22×C4—51no—
461C22×C4—51no—
462C22×C4—54no—
463C22×C4—104no—
464C22×C4—151no—
465C22×C4—151no—
466C22×C4—151no—
467C22×C4—151no—
468C22×C4—151no—
469C22×C4—151no—
470C22×C4—151no—
471C22×C4—151no—
472C22×C4—151no—
473C22×C4—151no—
474C22×C4—154no—
475C22×C4—304no—
476C22×C4—304no—
477C22×C4D3×AGL(1,𝔽5)11yescharacteristic
478C4⋊C4—308no—
479C22⋊C4—104no—
480C22⋊C4—304no—
481C42—31no—
482C42—31no—
483C42—31no—
484C42—31no—
485C42—151no—
486C42—151no—
487C42—151no—
488C42—151no—
489C42—151no—
490C42—151no—
491C42—151no—
492C42—151no—
493C42—151no—
494C42—151no—
495C42—151no—
496C42—151no—
497C42—308no—
498C3×C5#228311yescharacteristic, complemented, Hall
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—52no—
502C22×C3—52no—
503C22×C3—52no—
504C22×C3—52no—
505C22×C3—108no—
506C22×C3—101no—
507C22×C3—101no—
508C22×C3#413012yes—
509C22×C3C23×AGL(1,𝔽5)11yescharacteristic
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—101no—
513C3×C4—101no—
514C3×C4—204no—
515Dic3—21no—
516Dic3—21no—
517Dic3—52no—
518Dic3—52no—
519Dic3—101no—
520Dic3—101no—
521Dic3—204no—
522Dic3#413012yes—
523Dic3#413012yes—
524C2×C5—22no—
525C2×C5C2×#87711yescharacteristic
526C2×C5D3×#11711yescharacteristic
527C2×C5D3×#11711yescharacteristic
528D5—22no—
529D5#564914yes—
530C23—51no—
531C23—54no—
532C23—51no—
533C23—102no—
534C23—102no—
535C23C2×D3×AGL(1,𝔽5)11yescharacteristic
536C2×C4—22no—
537C2×C4—31no—
538C2×C4—31no—
539C2×C4—31no—
540C2×C4—31no—
541C2×C4—51no—
542C2×C4—51no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—102no—
546C2×C4—102no—
547C2×C4—102no—
548C2×C4—102no—
549C2×C4—102no—
550C2×C4—104no—
551C2×C4—104no—
552C2×C4—104no—
553C2×C4—154no—
554C2×C4—154no—
555C2×C4—151no—
556C2×C4—151no—
557C2×C4—151no—
558C2×C4—151no—
559C2×C4—302no—
560C2×C4—302no—
561C2×C4—302no—
562C2×C4—302no—
563C2×C4—302no—
564C2×C4—302no—
565C2×C4—302no—
566C2×C4—302no—
567C2×C4—304no—
568C2×C4—304no—
569C2×C4—304no—
570C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
571C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
572C2×C3—22no—
573C2×C3—54no—
574C2×C3—102no—
575C2×C3C2×#413011yescharacteristic
576C2×C3C2×#413011yescharacteristic
577C2×C3C2×#413011yescharacteristic
578C5#7405111yescharacteristic, complemented, Sylow
579C22—21no—
580C22—21no—
581C22—52no—
582C22—52no—
583C22—52no—
584C22—52no—
585C22—108no—
586C22—101no—
587C22—101no—
588C22#9192312yes—
589C22C22×D3×AGL(1,𝔽5)11yescharacteristic
590C4—21no—
591C4—21no—
592C4—32no—
593C4—32no—
594C4—61no—
595C4—61no—
596C4—101no—
597C4—101no—
598C4—152no—
599C4—152no—
600C4—204no—
601C4—301no—
602C4—301no—
603C4—604no—
604C3#1061704611yescharacteristic, complemented, Sylow
605C2—22no—
606C2—54no—
607C2—102no—
608C2D3×#413011yescharacteristic
609C2D3×#413011yescharacteristic
610C2C2×#9192311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2283
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. #11751834C2semidirect
7. #11751832C2semidirect
8. #11751750C2semidirect
9. #11751746C2semidirect
18. C2×C4×Dic15C4semidirect
19. C2×C4×C5×Dic3C4semidirect
20. C2×Dic3×Dic5C4semidirect
21. C2×Dic3×Dic5C4semidirect
22. C4×D5×Dic3C4semidirect
23. C4×D5×Dic3C4semidirect
24. C4×D5×Dic3C4semidirect
25. C4×D5×Dic3C4semidirect
185. C2×C4×Dic3AGL(1,𝔽5)semidirect
498. C3×C5#2283semidirect
578. C5#74051semidirect
604. C3#10617046semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D5×Dic32
#117524232
C3×#657642
#117520282
Dic3×C22⋊AGL(1,𝔽5)2
#117518342
#117518322
#117517502
#117517462
#106170463
#740515