Finite Group Databasebeta

← #14306109

Subgroups — #14306109

Order 1920.

816 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91448C211yesmaximal, characteristic
2C4×#6763C211yesmaximal, characteristic, complemented
3C3×#65765C211yesmaximal, characteristic, complemented
4C2×#91173C212yesmaximal, complemented
5C2×#91172C212yesmaximal, complemented
6#10604222—31nomaximal, Hall
7C22×C3×C4×D5C2211yescharacteristic
8C22×#1203C411yescharacteristic, complemented
9C22×#1202C2211yescharacteristic
10C22×#1201C2211yescharacteristic
11C2×#6763C2212yes—
12C2×C4×ΓL(1,𝔽16)—21no—
13C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
14C2×C3×C4⋊AGL(1,𝔽5)—21no—
15C2×#6714C411yescharacteristic, complemented
16C2×C5×(C2×D3)⋊C4C411yescharacteristic, complemented
17C2×#6668C411yescharacteristic, complemented
18#91448—21no—
19#91448—21no—
20#91448—21no—
21#91448—21no—
22#91235—21no—
23C3×(C2×AGL(1,𝔽5))⋊C4—21no—
24#91173—24no—
25#91172—24no—
26#69528—51nomaximal, Hall
27C2×#4030—31no—
28C2×#4011—32no—
29#65765D311yescharacteristic, complemented
30C4×C22⋊AGL(1,𝔽5)—31no—
31C2×#3999—32no—
32C23×D15C2×C411yescharacteristic
33C23×C5×D3C2×C411yescharacteristic
34C23×C3×D5C2311yescharacteristic
35C22×ΓL(1,𝔽16)—22no—
36C22×C3×AGL(1,𝔽5)—22no—
37C22×C3×C4×C5C2×C411yescharacteristic
38C22×Dic15C2×C411yescharacteristic
39C22×C5×Dic3C2×C411yescharacteristic
40C22×C3×Dic5C2×C411yescharacteristic
41C2×C3×C4×D5—42no—
42C2×C3×C4×D5D411yescharacteristic
43C2×C3×C4×D5D411yescharacteristic
44C2×C3×C4×D5D411yescharacteristic
45C2×C3×C4×D5D411yescharacteristic
46C2×#1203—21no—
47C2×#1203—21no—
48C2×#1203—42no—
49C2×#1202—22no—
50C2×#1202—21no—
51C2×#1202—21no—
52C2×#1202—22no—
53C2×#1201—22no—
54C2×#1201—21no—
55C2×#1201—21no—
56C2×#1201—22no—
57#6763—22no—
58#6763D414yescomplemented
59C4×ΓL(1,𝔽16)—42no—
60C3×C22⋊AGL(1,𝔽5)—22no—
61C3×C22⋊AGL(1,𝔽5)—22no—
62C3×C4⋊AGL(1,𝔽5)—42no—
63#6714—21no—
64#6714—21no—
65C5×(C2×D3)⋊C4—21no—
66C5×(C2×D3)⋊C4—21no—
67#6668—21no—
68#6668—21no—
69C2×#930—51no—
70C3×#380—51no—
71C4×#217—51no—
72C2×#806—52no—
73C2×#806—52no—
74C22×C22⋊D5—31no—
75C22×C22⋊D5—31no—
76C22×D20—31no—
77C22×C4×D5C2×D311yescharacteristic
78C2×C22⋊AGL(1,𝔽5)—32no—
79C2×C22⋊AGL(1,𝔽5)C2×D312yes—
80C2×C4⋊AGL(1,𝔽5)—21no—
81C2×C4×AGL(1,𝔽5)—61no—
82C2×C5×C22⋊C4—31no—
83C2×#685—31no—
84C2×#683—31no—
85#4030—61no—
86#4030—61no—
87#4030—61no—
88#4030—61no—
89#4011—64no—
90(C2×AGL(1,𝔽5))⋊C4—21no—
91(C2×AGL(1,𝔽5))⋊C4—61no—
92#3999—64no—
93#1964—151noSylow
94C23×C3×C5C22×C411yescharacteristic
95C22×D15—21no—
96C22×D15—22no—
97C22×D15—41no—
98C22×D15—41no—
99C22×C5×D3—21no—
100C22×C5×D3—22no—
101C22×C5×D3—41no—
102C22×C5×D3—41no—
103C22×C3×D5—41no—
104C22×C3×D5—41no—
105C22×C3×D5C2×D411yescharacteristic
106C22×C3×D5C2×D411yescharacteristic
107C22×C3×D5C2×D412yes—
108C22×C3×D5#4112yes—
109C2×ΓL(1,𝔽16)—24no—
110C2×ΓL(1,𝔽16)—42no—
111C2×ΓL(1,𝔽16)—42no—
112C2×C3×AGL(1,𝔽5)—42no—
113C2×C3×AGL(1,𝔽5)—42no—
114C2×C3×AGL(1,𝔽5)—42no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5C22⋊C411yescharacteristic
117C2×C3×C4×C5C22⋊C411yescharacteristic
118C2×Dic15—21no—
119C2×Dic15—22no—
120C2×C5×Dic3—21no—
121C2×C5×Dic3—22no—
122C2×C3×Dic5—22no—
123C2×C3×Dic5C22⋊C411yescharacteristic
124C2×C3×Dic5C22⋊C411yescharacteristic
125C3×C4×D5—22no—
126C3×C4×D5—22no—
127C3×C4×D5—41no—
128C3×C4×D5—41no—
129#1203—42no—
130#1203—42no—
131#1202—42no—
132#1202—41no—
133#1202—41no—
134#1201—42no—
135#1201—41no—
136#1201—41no—
137C23×C3×C4—51no—
138C22×#67—51no—
139C22×#67—51no—
140C22×D12—51no—
141C2×C3×C4⋊C4—101no—
142C2×C3×C22⋊C4—52no—
143C2×#217—52no—
144#930—101no—
145#930—101no—
146#930—101no—
147#930—101no—
148C2×(C2×D3)⋊C4—51no—
149C2×(C2×D3)⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
150C2×C4⋊Dic3—51no—
151C2×C4×Dic3—101no—
152C3×#95—101no—
153C3⋊#95—101no—
154#806—104no—
155#806—104no—
156C24×C5—31no—
157C23×D5—31no—
158C23×D5C22×D311yescharacteristic
159C22×AGL(1,𝔽5)—22no—
160C22×AGL(1,𝔽5)—62no—
161C22×C4×C5—31no—
162C22×C4×C5C4×D311yescharacteristic
163C2×C22⋊D5—61no—
164C2×C22⋊D5—62no—
165C2×C22⋊D5—62no—
166C2×C22⋊D5—61no—
167C2×C22⋊D5—61no—
168C2×C22⋊D5—61no—
169C2×C22⋊D5—122no—
170C22×Dic5—31no—
171C22×Dic5C4×D311yescharacteristic
172C2×D20—61no—
173C2×D20—62no—
174C2×D20—62no—
175C2×D20—61no—
176C2×C4×D5—42no—
177C2×C4×D5D1211yescharacteristic
178C2×C4×D5D1211yescharacteristic
179C2×C4×D5#6711yescharacteristic
180C2×C4×D5#6711yescharacteristic
181C22⋊AGL(1,𝔽5)—22no—
182C22⋊AGL(1,𝔽5)—22no—
183C22⋊AGL(1,𝔽5)—34no—
184C22⋊AGL(1,𝔽5)—62no—
185C4⋊AGL(1,𝔽5)—42no—
186C4×AGL(1,𝔽5)—122no—
187C5×C22⋊C4—61no—
188C5×C22⋊C4—61no—
189#685—61no—
190#685—61no—
191#683—61no—
192#683—61no—
193C2×#121—151no—
194C2×#99—152no—
195C2×#99—152no—
196#380—51no—
197C4×C22⋊C4—151no—
198C22×C3×C5—21no—
199C22×C3×C5—21no—
200C22×C3×C5C2×C22⋊C411yescharacteristic
201C22×C3×C5C4×D412yes—
202C2×D15—41no—
203C2×D15—41no—
204C2×D15—41no—
205C2×D15—82no—
206C2×C5×D3—41no—
207C2×C5×D3—41no—
208C2×C5×D3—41no—
209C2×C5×D3—82no—
210C2×C3×D5—21no—
211C2×C3×D5—21no—
212C2×C3×D5—21no—
213C2×C3×D5—21no—
214C2×C3×D5—42no—
215C2×C3×D5—42no—
216C2×C3×D5#12112yes—
217C2×C3×D5#12411yescharacteristic
218C2×C3×D5#12711yescharacteristic
219ΓL(1,𝔽16)—44no—
220C3×AGL(1,𝔽5)—82no—
221C3×C4×C5—21no—
222C3×C4×C5—21no—
223Dic15—41no—
224C3×Dic5—21no—
225C3×Dic5#9912yescomplemented
226C5×Dic3—41no—
227C24×C3—51no—
228C23×D3—51no—
229C23×D3C2×AGL(1,𝔽5)11yescharacteristic
230C22×C3×C4—51no—
231C22×C3×C4—51no—
232C22×C3×C4—51no—
233C22×C3×C4—51no—
234C22×C3×C4—51no—
235C22×C3×C4—102no—
236C22×C3×C4—202no—
237C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
238C2×#67—102no—
239C2×#67—101no—
240C2×#67—101no—
241C2×#67—102no—
242C2×#67—102no—
243C2×#67—101no—
244C2×#67—101no—
245C2×#67—102no—
246C22×Dic3—51no—
247C22×Dic3—102no—
248C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
249C2×D12—101no—
250C2×D12—101no—
251C2×D12—202no—
252C3×C4⋊C4—202no—
253C3×C22⋊C4—102no—
254C3×C22⋊C4—102no—
255#217—54no—
256#217—102no—
257(C2×D3)⋊C4—21no—
258(C2×D3)⋊C4—21no—
259(C2×D3)⋊C4—101no—
260(C2×D3)⋊C4—101no—
261C4⋊Dic3—101no—
262C4⋊Dic3—101no—
263C4×Dic3—202no—
264C23×C5—61no—
265C23×C5—62no—
266C23×C5—121no—
267C23×C5—121no—
268C23×C5C2×C4×D311yescharacteristic
269C22×D5—41no—
270C22×D5—41no—
271C22×D5—61no—
272C22×D5—62no—
273C22×D5—121no—
274C22×D5—121no—
275C22×D5C2×D1211yescharacteristic
276C22×D5D3×D412yes—
277C22×D5#23912yes—
278C22×D5C2×#6711yescharacteristic
279C2×AGL(1,𝔽5)—42no—
280C2×AGL(1,𝔽5)—42no—
281C2×AGL(1,𝔽5)—42no—
282C2×AGL(1,𝔽5)—64no—
283C2×AGL(1,𝔽5)—122no—
284C2×AGL(1,𝔽5)—122no—
285C2×C4×C5—41no—
286C2×C4×C5—62no—
287C2×C4×C5—61no—
288C2×C4×C5(C2×D3)⋊C411yescharacteristic
289C2×C4×C5(C2×D3)⋊C411yescharacteristic
290C22⋊D5—122no—
291C22⋊D5—122no—
292C22⋊D5—121no—
293C22⋊D5—121no—
294C22⋊D5—122no—
295C2×Dic5—22no—
296C2×Dic5—62no—
297C2×Dic5—61no—
298C2×Dic5(C2×D3)⋊C411yescharacteristic
299C2×Dic5(C2×D3)⋊C411yescharacteristic
300D20—122no—
301D20—121no—
302D20—121no—
303C4×D5—22no—
304C4×D5—22no—
305C4×D5—41no—
306C4×D5—41no—
307C22×D4—151no—
308C22×D4—151no—
309C22×D4—151no—
310C23×C4—51no—
311#121—301no—
312#121—301no—
313#121—301no—
314#121—301no—
315C2×C4⋊C4—101no—
316C2×C4⋊C4—151no—
317C2×C22⋊C4—31no—
318C2×C22⋊C4—52no—
319C2×C22⋊C4—152no—
320C2×C22⋊C4—151no—
321C2×C42—301no—
322#99—304no—
323#99—304no—
324#95—101no—
325#95—301no—
326C2×C3×C5—22no—
327C2×C3×C5#39011yescharacteristic
328C2×C3×C5C2×#9911yescharacteristic
329C2×C3×C5#41011yescharacteristic
330D15—81no—
331C3×D5—21no—
332C3×D5—22no—
333C3×D5—21no—
334C5×D3—81no—
335C23×C3—51no—
336C23×C3—51no—
337C23×C3—52no—
338C23×C3—52no—
339C23×C3—201no—
340C23×C3—201no—
341C23×C3C22×AGL(1,𝔽5)11yescharacteristic
342C22×D3—21no—
343C22×D3—22no—
344C22×D3—41no—
345C22×D3—41no—
346C22×D3—101no—
347C22×D3—102no—
348C22×D3—201no—
349C22×D3—201no—
350C2×C3×C4—41no—
351C2×C3×C4—51no—
352C2×C3×C4—51no—
353C2×C3×C4—102no—
354C2×C3×C4—102no—
355C2×C3×C4—102no—
356C2×C3×C4—201no—
357C2×C3×C4—201no—
358C2×C3×C4—202no—
359C2×C3×C4—202no—
360C2×C3×C4—202no—
361C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
362C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
363#67—202no—
364#67—201no—
365#67—201no—
366#67—202no—
367#67—201no—
368#67—201no—
369C2×Dic3—22no—
370C2×Dic3—21no—
371C2×Dic3—104no—
372C2×Dic3—102no—
373C2×Dic3—101no—
374C2×Dic3—202no—
375C2×Dic3—202no—
376D12—202no—
377D12—202no—
378C22×C5—21no—
379C22×C5—21no—
380C22×C5—121no—
381C22×C5—121no—
382C22×C5—121no—
383C22×C5—242no—
384C22×C5#89312yes—
385C22×C5C2×(C2×D3)⋊C411yescharacteristic
386C2×D5—21no—
387C2×D5—21no—
388C2×D5—21no—
389C2×D5—21no—
390C2×D5—42no—
391C2×D5—42no—
392C2×D5—121no—
393C2×D5—121no—
394C2×D5—121no—
395C2×D5—242no—
396C2×D5#89512yes—
397C2×D5#94011yescharacteristic
398C2×D5#94711yescharacteristic
399AGL(1,𝔽5)—82no—
400AGL(1,𝔽5)—124no—
401C4×C5—21no—
402C4×C5—21no—
403C4×C5—121no—
404Dic5—21no—
405Dic5—121no—
406Dic5#80612yescomplemented
407C24—31no—
408C24—51no—
409C24—151no—
410C2×D4—301no—
411C2×D4—301no—
412C2×D4—302no—
413C2×D4—301no—
414C2×D4—301no—
415C2×D4—302no—
416C2×D4—302no—
417C2×D4—301no—
418C2×D4—301no—
419C2×D4—302no—
420C2×D4—602no—
421C22×C4—31no—
422C22×C4—51no—
423C22×C4—51no—
424C22×C4—51no—
425C22×C4—51no—
426C22×C4—51no—
427C22×C4—102no—
428C22×C4—151no—
429C22×C4—202no—
430C22×C4—302no—
431C22×C4D3×AGL(1,𝔽5)11yescharacteristic
432C4⋊C4—202no—
433C4⋊C4—301no—
434C4⋊C4—301no—
435C22⋊C4—61no—
436C22⋊C4—61no—
437C22⋊C4—102no—
438C22⋊C4—102no—
439C22⋊C4—154no—
440C22⋊C4—302no—
441C22⋊C4—301no—
442C22⋊C4—301no—
443C42—602no—
444C3×C5#196411yescharacteristic, complemented, Hall
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—52no—
448C22×C3—51no—
449C22×C3—51no—
450C22×C3—101no—
451C22×C3—101no—
452C22×C3—101no—
453C22×C3—101no—
454C22×C3—202no—
455C22×C3—202no—
456C22×C3D4×AGL(1,𝔽5)12yes—
457C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
458C2×D3—41no—
459C2×D3—41no—
460C2×D3—41no—
461C2×D3—82no—
462C2×D3—201no—
463C2×D3—201no—
464C2×D3—201no—
465C2×D3—402no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—52no—
469C3×C4—101no—
470C3×C4—402no—
471Dic3—41no—
472Dic3—204no—
473Dic3—201no—
474C2×C5—22no—
475C2×C5—241no—
476C2×C5C2×#80611yescharacteristic
477C2×C5#498811yescharacteristic
478C2×C5#500611yescharacteristic
479D5—21no—
480D5—22no—
481D5—21no—
482D5—241no—
483C23—51no—
484C23—51no—
485C23—52no—
486C23—52no—
487C23—61no—
488C23—62no—
489C23—121no—
490C23—121no—
491C23—201no—
492C23—201no—
493C23—301no—
494C23—302no—
495C23—601no—
496C23—601no—
497C23C2×D3×AGL(1,𝔽5)11yescharacteristic
498D4—602no—
499D4—602no—
500D4—601no—
501D4—602no—
502D4—601no—
503D4—601no—
504D4—602no—
505D4—601no—
506C2×C4—41no—
507C2×C4—51no—
508C2×C4—51no—
509C2×C4—62no—
510C2×C4—61no—
511C2×C4—102no—
512C2×C4—102no—
513C2×C4—102no—
514C2×C4—201no—
515C2×C4—201no—
516C2×C4—202no—
517C2×C4—202no—
518C2×C4—202no—
519C2×C4—304no—
520C2×C4—302no—
521C2×C4—301no—
522C2×C4—602no—
523C2×C4—602no—
524C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
525C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
526C2×C3—22no—
527C2×C3—102no—
528C2×C3—101no—
529C2×C3—101no—
530C2×C3#6574511yescharacteristic
531C2×C3D5⋊#9911yescharacteristic
532C2×C3#6578011yescharacteristic
533D3—81no—
534D3—401no—
535C5#6952811yescharacteristic, complemented, Sylow
536C22—21no—
537C22—21no—
538C22—51no—
539C22—52no—
540C22—51no—
541C22—101no—
542C22—101no—
543C22—101no—
544C22—101no—
545C22—121no—
546C22—121no—
547C22—121no—
548C22—202no—
549C22—202no—
550C22—242no—
551C22—601no—
552C22—601no—
553C22—601no—
554C22—1202no—
555C22#9192112yes—
556C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
557C4—21no—
558C4—21no—
559C4—52no—
560C4—101no—
561C4—121no—
562C4—402no—
563C4—604no—
564C4—601no—
565C3#1060422211yescharacteristic, complemented, Sylow
566C2—22no—
567C2—101no—
568C2—102no—
569C2—101no—
570C2—241no—
571C2—1201no—
572C2#1175181511yescharacteristic
573C2#1175185711yescharacteristic
574C2D5⋊#80611yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#91448C2
cosocleC23×C3×D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1964
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C4×#6763C2semidirect
3. C3×#65765C2semidirect
4. C2×#91173C2semidirect
5. C2×#91172C2semidirect
8. C22×#1203C4semidirect
15. C2×#6714C4semidirect
16. C2×C5×(C2×D3)⋊C4C4semidirect
17. C2×#6668C4semidirect
29. #65765D3semidirect
58. #6763D4semidirect
149. C2×(C2×D3)⋊C4AGL(1,𝔽5)semidirect
225. C3×Dic5#99semidirect
406. Dic5#806semidirect
444. C3×C5#1964semidirect
535. C5#69528semidirect
565. C3#10604222semidirect

Maximal subgroups

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

subgroupindex
C2×#914482
C4×#67632
C3×#657652
C2×#911732
C2×#911722
#106042223
#695285