Finite Group Databasebeta

← #14326384

Subgroups — #14326384

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic
2C2×#91923C211yesmaximal, characteristic, complemented
3C2×D5×#217C211yesmaximal, characteristic
4#11752459C211yesmaximal, characteristic
5#11752028C211yesmaximal, characteristic, complemented
6#11752027C212yesmaximal, complemented
7Dic3×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
8#11752018C212yesmaximal, complemented
9#11752017C212yesmaximal, complemented
10AGL(1,𝔽5)×#217C212yesmaximal, complemented
11#11751984C211yesmaximal, characteristic, complemented
12#10617072—31nomaximal, Hall
13C24×C3×D5C2211yescharacteristic
14C23×C3×AGL(1,𝔽5)C2212yes—
15C22×D5×Dic3C2211yescharacteristic
16C22×D5×Dic3C2211yescharacteristic
17C2×#6763C2211yescharacteristic
18C2×#6763C2211yescharacteristic
19C2×#6763C2212yes—
20C2×#6763C2212yes—
21C2×C3×C22⋊AGL(1,𝔽5)—24no—
22C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
23C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
24C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
25C2×Dic3⋊AGL(1,𝔽5)C2212yescomplemented
26C2×Dic3⋊AGL(1,𝔽5)C2212yescomplemented
27#91923—24no—
28C2×Dic3×AGL(1,𝔽5)C2212yescomplemented
29C2×Dic3×AGL(1,𝔽5)C2212yescomplemented
30C2×#6719C411yescharacteristic, complemented
31C2×C5×#217C411yescharacteristic, complemented
32D5×#217C411yescharacteristic, complemented
33D5×#217C411yescharacteristic, complemented
34D5×#217C411yescharacteristic, complemented
35D5×#217C411yescharacteristic, complemented
36D5×#217C2211yescharacteristic
37D5×#217C2211yescharacteristic
38D5×#217C2211yescharacteristic
39D5×#217C2211yescharacteristic
40C2×#6665C411yescharacteristic, complemented
41C2×#6665C411yescharacteristic, complemented
42(C2×AGL(1,𝔽5))⋊Dic3C2212yescomplemented
43(C2×AGL(1,𝔽5))⋊Dic3C2212yescomplemented
44(C2×AGL(1,𝔽5))⋊Dic3C2212yescomplemented
45(C2×AGL(1,𝔽5))⋊Dic3C2212yescomplemented
46#82098—51nomaximal, Hall
47C22×C22⋊AGL(1,𝔽5)D311yescharacteristic
48C2×#4130—31no—
49C2×D5×C22⋊C4—31no—
50#65800—31no—
51#65765—31no—
52#65764—31no—
53C4×C22⋊AGL(1,𝔽5)—31no—
54#65700—32no—
55#65700—32no—
56#65699—32no—
57C22⋊C4×AGL(1,𝔽5)—32no—
58C24×C3×C5C2×C411yescharacteristic
59C23×C3×D5—22no—
60C23×C3×D5—22no—
61C23×C3×D5—24no—
62C23×C3×D5—42no—
63C23×C3×D5C2×C411yescharacteristic
64C23×C3×D5C2×C411yescharacteristic
65C23×C3×D5C2×C411yescharacteristic
66C23×C3×D5C2311yescharacteristic
67C23×C3×D5C2311yescharacteristic
68C23×C3×D5C2311yescharacteristic
69C22×ΓL(1,𝔽16)C2312yes—
70C22×ΓL(1,𝔽16)C2312yes—
71C22×C3×AGL(1,𝔽5)—24no—
72C22×C3×AGL(1,𝔽5)—24no—
73C22×C3×AGL(1,𝔽5)—42no—
74C22×C3×AGL(1,𝔽5)C2312yes—
75C22×C3×AGL(1,𝔽5)C2312yes—
76C22×Dic15C2×C411yescharacteristic, complemented
77C22×Dic15C2×C411yescharacteristic, complemented
78C22×C5×Dic3C2×C411yescharacteristic, complemented
79C22×C5×Dic3C2×C411yescharacteristic, complemented
80C2×D5×Dic3—22no—
81C2×D5×Dic3—22no—
82C2×D5×Dic3—42no—
83C2×D5×Dic3C2×C411yescharacteristic, complemented
84C2×D5×Dic3C2×C411yescharacteristic, complemented
85C2×D5×Dic3C2×C411yescharacteristic, complemented
86C2×D5×Dic3C2×C411yescharacteristic, complemented
87C2×D5×Dic3C2311yescharacteristic
88C2×D5×Dic3C2311yescharacteristic
89C2×D5×Dic3C2311yescharacteristic
90C2×D5×Dic3C2311yescharacteristic
91#6763—22no—
92#6763—22no—
93#6763—24no—
94#6763—42no—
95C3×C22⋊AGL(1,𝔽5)—22no—
96C3×C22⋊AGL(1,𝔽5)—24no—
97C3×C22⋊AGL(1,𝔽5)D414yes—
98Dic3⋊AGL(1,𝔽5)—24no—
99Dic3⋊AGL(1,𝔽5)—42no—
100Dic3×AGL(1,𝔽5)—24no—
101Dic3×AGL(1,𝔽5)—42no—
102#6719C2×C411yescharacteristic
103#6719C2×C411yescharacteristic
104#6719C2×C411yescharacteristic, complemented
105#6719C2×C411yescharacteristic, complemented
106C5×#217C2×C411yescharacteristic
107C5×#217C2×C411yescharacteristic
108C5×#217C2×C411yescharacteristic, complemented
109C5×#217C2×C411yescharacteristic, complemented
110#6665C2×C411yescharacteristic
111#6665C2×C411yescharacteristic
112#6665C2×C411yescharacteristic
113#6665C2×C411yescharacteristic
114#6665C2×C411yescharacteristic, complemented
115#6665C2×C411yescharacteristic, complemented
116#6665C2×C411yescharacteristic, complemented
117#6665C2×C411yescharacteristic, complemented
118C22×C3×C22⋊C4—51no—
119C22×#217—51no—
120C2×#877—51no—
121#5247—51no—
122#5210—52no—
123C4×#217—52no—
124#4945—52no—
125#4944—52no—
126#4943—51no—
127#4942—51no—
128Dic3×C22⋊C4—51no—
129C24×D5C2×D311yescharacteristic
130C23×AGL(1,𝔽5)C2×D312yes—
131C22×C4×D5—31no—
132C22×C4×D5—31no—
133C2×C22⋊AGL(1,𝔽5)—24no—
134C2×C22⋊AGL(1,𝔽5)—32no—
135C2×C22⋊AGL(1,𝔽5)—31no—
136C2×C22⋊AGL(1,𝔽5)—31no—
137C2×C22⋊AGL(1,𝔽5)—32no—
138C2×C22⋊AGL(1,𝔽5)C2×D312yes—
139C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
140C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
141#4130—64no—
142C2×C4⋊AGL(1,𝔽5)—32no—
143C2×C4⋊AGL(1,𝔽5)—32no—
144C2×C4×AGL(1,𝔽5)—32no—
145C2×C4×AGL(1,𝔽5)—32no—
146C2×C5×C22⋊C4—31no—
147C2×C22⋊Dic5—31no—
148C2×#685—31no—
149C2×#685—31no—
150D5×C22⋊C4—31no—
151D5×C22⋊C4—31no—
152D5×C22⋊C4—31no—
153D5×C22⋊C4—31no—
154D5×C22⋊C4—31no—
155D5×C22⋊C4—31no—
156D5×C22⋊C4—31no—
157D5×C22⋊C4—31no—
158(C2×AGL(1,𝔽5))⋊C4—32no—
159(C2×AGL(1,𝔽5))⋊C4—32no—
160(C2×AGL(1,𝔽5))⋊C4—32no—
161(C2×AGL(1,𝔽5))⋊C4—32no—
162#2342—151noSylow
163C23×C3×C5—22no—
164C23×C3×C5—22no—
165C23×C3×C5—41no—
166C23×C3×C5C22×C411yescharacteristic
167C23×C3×C5C22×C411yescharacteristic
168C23×C3×C5C22×C411yescharacteristic
169C22×C3×D5—21no—
170C22×C3×D5—22no—
171C22×C3×D5—21no—
172C22×C3×D5—22no—
173C22×C3×D5—22no—
174C22×C3×D5—22no—
175C22×C3×D5—22no—
176C22×C3×D5—22no—
177C22×C3×D5—22no—
178C22×C3×D5—22no—
179C22×C3×D5—22no—
180C22×C3×D5—21no—
181C22×C3×D5—22no—
182C22×C3×D5—21no—
183C22×C3×D5—22no—
184C22×C3×D5—41no—
185C22×C3×D5—41no—
186C22×C3×D5—41no—
187C22×C3×D5—48no—
188C22×C3×D5—48no—
189C22×C3×D5C22×C411yescharacteristic
190C22×C3×D5C22×C411yescharacteristic
191C22×C3×D5C22×C411yescharacteristic
192C22×C3×D5C2×D412yes—
193C22×C3×D5#4114yes—
194C22×C3×D5#4112yes—
195C22×C3×D5C2411yescharacteristic
196C2×ΓL(1,𝔽16)—22no—
197C2×ΓL(1,𝔽16)—22no—
198C2×ΓL(1,𝔽16)—22no—
199C2×ΓL(1,𝔽16)—22no—
200C2×ΓL(1,𝔽16)—22no—
201C2×ΓL(1,𝔽16)—22no—
202C2×C3×AGL(1,𝔽5)—22no—
203C2×C3×AGL(1,𝔽5)—22no—
204C2×C3×AGL(1,𝔽5)—22no—
205C2×C3×AGL(1,𝔽5)—22no—
206C2×C3×AGL(1,𝔽5)—22no—
207C2×C3×AGL(1,𝔽5)—48no—
208C2×C3×AGL(1,𝔽5)C2×D414yes—
209C2×Dic15—22no—
210C2×Dic15—41no—
211C2×Dic15C22×C411yescharacteristic
212C2×Dic15C22×C411yescharacteristic
213C2×Dic15C22×C411yescharacteristic
214C2×Dic15C22×C411yescharacteristic
215C2×C5×Dic3—22no—
216C2×C5×Dic3—41no—
217C2×C5×Dic3C22×C411yescharacteristic
218C2×C5×Dic3C22×C411yescharacteristic
219C2×C5×Dic3C22×C411yescharacteristic
220C2×C5×Dic3C22×C411yescharacteristic
221D5×Dic3—22no—
222D5×Dic3—22no—
223D5×Dic3—21no—
224D5×Dic3—21no—
225D5×Dic3—21no—
226D5×Dic3—21no—
227D5×Dic3—22no—
228D5×Dic3—22no—
229D5×Dic3—41no—
230D5×Dic3—41no—
231C25×C3—51no—
232C23×C3×C4—52no—
233C23×Dic3—51no—
234C23×Dic3—51no—
235C2×C3×C22⋊C4—51no—
236C2×C3×C22⋊C4—51no—
237C2×C3×C22⋊C4—52no—
238C2×C3×C22⋊C4—104no—
239C2×#217—51no—
240C2×#217—51no—
241C2×#217—51no—
242C2×#217—51no—
243C2×#217—51no—
244C2×#217—51no—
245C2×#217—51no—
246C2×#217—51no—
247C2×#217—51no—
248C2×#217—51no—
249C2×#217—51no—
250C2×#217—51no—
251C2×#217—51no—
252C2×#217—52no—
253C2×#217—52no—
254C2×#217AGL(1,𝔽5)11yescharacteristic, complemented
255C2×Dic3⋊C4—52no—
256C2×Dic3⋊C4—52no—
257C2×C4×Dic3—52no—
258C2×C4×Dic3—52no—
259#877—104no—
260C3⋊#95—52no—
261C3⋊#95—52no—
262C3⋊#95—52no—
263C3⋊#95—52no—
264C24×C5C4×D311yescharacteristic
265C23×D5—22no—
266C23×D5—24no—
267C23×D5—22no—
268C23×D5—42no—
269C23×D5C4×D311yescharacteristic
270C23×D5C4×D311yescharacteristic
271C23×D5C4×D311yescharacteristic
272C23×D5C22×D311yescharacteristic
273C23×D5C22×D311yescharacteristic
274C23×D5C22×D311yescharacteristic
275C22×AGL(1,𝔽5)—24no—
276C22×AGL(1,𝔽5)—24no—
277C22×AGL(1,𝔽5)—32no—
278C22×AGL(1,𝔽5)—32no—
279C22×AGL(1,𝔽5)—42no—
280C22×AGL(1,𝔽5)C22×D312yes—
281C22×AGL(1,𝔽5)C22×D312yes—
282C22×C4×C5—31no—
283C22×C4×C5—31no—
284C22×Dic5—31no—
285C22×Dic5—31no—
286C2×C4×D5—31no—
287C2×C4×D5—31no—
288C2×C4×D5—31no—
289C2×C4×D5—31no—
290C2×C4×D5—31no—
291C2×C4×D5—31no—
292C2×C4×D5—31no—
293C2×C4×D5—31no—
294C2×C4×D5—62no—
295C2×C4×D5—62no—
296C2×C4×D5—122no—
297C22⋊AGL(1,𝔽5)—22no—
298C22⋊AGL(1,𝔽5)—24no—
299C22⋊AGL(1,𝔽5)—62no—
300C22⋊AGL(1,𝔽5)—64no—
301C22⋊AGL(1,𝔽5)—62no—
302C22⋊AGL(1,𝔽5)—122no—
303C22⋊AGL(1,𝔽5)#6714yes—
304C4⋊AGL(1,𝔽5)—64no—
305C4⋊AGL(1,𝔽5)—122no—
306C4×AGL(1,𝔽5)—64no—
307C4×AGL(1,𝔽5)—122no—
308C5×C22⋊C4—31no—
309C5×C22⋊C4—31no—
310C5×C22⋊C4—31no—
311C5×C22⋊C4—31no—
312C22⋊Dic5—31no—
313C22⋊Dic5—31no—
314C22⋊Dic5—31no—
315C22⋊Dic5—31no—
316#685—31no—
317#685—31no—
318#685—31no—
319#685—31no—
320#685—31no—
321#685—31no—
322#685—31no—
323#685—31no—
324C2×#117—151no—
325C22×C22⋊C4—51no—
326C22×C22⋊C4—151no—
327#388—152no—
328#388—152no—
329#385—152no—
330#381—151no—
331#380—151no—
332#379—151no—
333C4×C22⋊C4—151no—
334C4×C22⋊C4—152no—
335C22×C3×C5—21no—
336C22×C3×C5—21no—
337C22×C3×C5—21no—
338C22×C3×C5—21no—
339C22×C3×C5—21no—
340C22×C3×C5—21no—
341C22×C3×C5—21no—
342C22×C3×C5—44no—
343C22×C3×C5#11712yescomplemented
344C22×C3×C5C4×D412yes—
345C22×C3×C5C23×C411yescharacteristic
346C2×C3×D5—21no—
347C2×C3×D5—21no—
348C2×C3×D5—21no—
349C2×C3×D5—21no—
350C2×C3×D5—24no—
351C2×C3×D5—24no—
352C2×C3×D5—24no—
353C2×C3×D5—24no—
354C2×C3×D5—21no—
355C2×C3×D5—21no—
356C2×C3×D5—21no—
357C2×C3×D5—44no—
358C2×C3×D5—44no—
359C2×C3×D5—44no—
360C2×C3×D5—42no—
361C2×C3×D5—42no—
362C2×C3×D5#11712yescomplemented
363C2×C3×D5C4×D412yes—
364C2×C3×D5C22×D411yescharacteristic
365C2×C3×D5C2×#4111yescharacteristic
366C2×C3×D5C2×#4112yes—
367C2×C3×D5H(5,𝔽2)12yes—
368ΓL(1,𝔽16)—42no—
369ΓL(1,𝔽16)—42no—
370C3×AGL(1,𝔽5)—24no—
371C3×AGL(1,𝔽5)—42no—
372Dic15—21no—
373Dic15—21no—
374Dic15—21no—
375Dic15—21no—
376C5×Dic3—21no—
377C5×Dic3—21no—
378C5×Dic3—21no—
379C5×Dic3—21no—
380C24×C3—51no—
381C24×C3—51no—
382C24×C3—51no—
383C24×C3—51no—
384C24×C3—51no—
385C24×C3—51no—
386C24×C3—102no—
387C24×C3—104no—
388C24×C3—102no—
389C24×C3—202no—
390C24×C3C2×AGL(1,𝔽5)11yescharacteristic
391C22×C3×C4—52no—
392C22×C3×C4—52no—
393C22×C3×C4—104no—
394C22×C3×C4—104no—
395C22×C3×C4—202no—
396C22×Dic3—51no—
397C22×Dic3—51no—
398C22×Dic3—51no—
399C22×Dic3—51no—
400C22×Dic3—51no—
401C22×Dic3—51no—
402C22×Dic3—51no—
403C22×Dic3—51no—
404C22×Dic3—51no—
405C22×Dic3—51no—
406C22×Dic3—52no—
407C22×Dic3—52no—
408C22×Dic3—102no—
409C22×Dic3—102no—
410C22×Dic3—202no—
411C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
412C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
413C3×C22⋊C4—54no—
414C3×C22⋊C4—104no—
415C3×C22⋊C4—102no—
416#217—51no—
417#217—51no—
418#217—51no—
419#217—51no—
420#217—51no—
421#217—51no—
422#217—51no—
423#217—51no—
424#217—51no—
425#217—51no—
426#217—51no—
427#217—51no—
428#217—102no—
429#217—104no—
430#217—102no—
431#217—202no—
432#217C2×AGL(1,𝔽5)11yescharacteristic
433#217C2×AGL(1,𝔽5)11yescharacteristic
434#217C2×AGL(1,𝔽5)11yescharacteristic, complemented
435#217C2×AGL(1,𝔽5)11yescharacteristic, complemented
436Dic3⋊C4—104no—
437Dic3⋊C4—202no—
438C4×Dic3—104no—
439C4×Dic3—202no—
440C23×C5—22no—
441C23×C5—22no—
442C23×C5—41no—
443C23×C5C2×C4×D311yescharacteristic
444C23×C5C2×C4×D311yescharacteristic
445C23×C5C2×C4×D311yescharacteristic
446C22×D5—21no—
447C22×D5—22no—
448C22×D5—22no—
449C22×D5—22no—
450C22×D5—21no—
451C22×D5—22no—
452C22×D5—22no—
453C22×D5—22no—
454C22×D5—22no—
455C22×D5—22no—
456C22×D5—22no—
457C22×D5—21no—
458C22×D5—22no—
459C22×D5—22no—
460C22×D5—21no—
461C22×D5—41no—
462C22×D5—41no—
463C22×D5—41no—
464C22×D5—48no—
465C22×D5—48no—
466C22×D5C2×C4×D311yescharacteristic
467C22×D5C2×C4×D311yescharacteristic
468C22×D5C2×C4×D311yescharacteristic
469C22×D5#23512yes—
470C22×D5#23714yes—
471C22×D5C2×#6712yes—
472C22×D5C23×D311yescharacteristic
473C2×AGL(1,𝔽5)—22no—
474C2×AGL(1,𝔽5)—22no—
475C2×AGL(1,𝔽5)—22no—
476C2×AGL(1,𝔽5)—22no—
477C2×AGL(1,𝔽5)—22no—
478C2×AGL(1,𝔽5)—48no—
479C2×AGL(1,𝔽5)—62no—
480C2×AGL(1,𝔽5)—62no—
481C2×AGL(1,𝔽5)—62no—
482C2×AGL(1,𝔽5)—62no—
483C2×AGL(1,𝔽5)—62no—
484C2×AGL(1,𝔽5)—62no—
485C2×AGL(1,𝔽5)C2×#6714yes—
486C2×C4×C5—31no—
487C2×C4×C5—31no—
488C2×C4×C5—31no—
489C2×C4×C5—31no—
490C2×C4×C5—62no—
491C2×C4×C5—121no—
492C2×Dic5—31no—
493C2×Dic5—31no—
494C2×Dic5—31no—
495C2×Dic5—31no—
496C2×Dic5—62no—
497C2×Dic5—121no—
498C4×D5—62no—
499C4×D5—62no—
500C4×D5—61no—
501C4×D5—61no—
502C4×D5—62no—
503C4×D5—62no—
504C4×D5—61no—
505C4×D5—61no—
506C4×D5—121no—
507C4×D5—121no—
508C25—51no—
509C23×C4—52no—
510C23×C4—151no—
511C23×C4—151no—
512#117—304no—
513C2×C4⋊C4—152no—
514C2×C4⋊C4—152no—
515C2×C22⋊C4—31no—
516C2×C22⋊C4—51no—
517C2×C22⋊C4—51no—
518C2×C22⋊C4—52no—
519C2×C22⋊C4—104no—
520C2×C22⋊C4—151no—
521C2×C22⋊C4—151no—
522C2×C22⋊C4—151no—
523C2×C22⋊C4—151no—
524C2×C22⋊C4—151no—
525C2×C22⋊C4—151no—
526C2×C22⋊C4—151no—
527C2×C22⋊C4—151no—
528C2×C22⋊C4—151no—
529C2×C22⋊C4—151no—
530C2×C22⋊C4—151no—
531C2×C22⋊C4—151no—
532C2×C22⋊C4—151no—
533C2×C22⋊C4—152no—
534C2×C22⋊C4—152no—
535C2×C42—152no—
536C2×C42—152no—
537#95—152no—
538#95—152no—
539#95—152no—
540#95—152no—
541C2×C3×C5—22no—
542C2×C3×C5—22no—
543C2×C3×C5—41no—
544C2×C3×C5C2×#11711yescharacteristic
545C2×C3×C5C2×C4×D411yescharacteristic
546C2×C3×C5#51811yescharacteristic
547C3×D5—22no—
548C3×D5—22no—
549C3×D5—41no—
550C3×D5#54612yes—
551C3×D5#55112yes—
552C23×C3—22no—
553C23×C3—22no—
554C23×C3—41no—
555C23×C3—51no—
556C23×C3—54no—
557C23×C3—52no—
558C23×C3—52no—
559C23×C3—51no—
560C23×C3—51no—
561C23×C3—51no—
562C23×C3—102no—
563C23×C3—101no—
564C23×C3—102no—
565C23×C3—102no—
566C23×C3—101no—
567C23×C3—102no—
568C23×C3—101no—
569C23×C3—102no—
570C23×C3—102no—
571C23×C3—102no—
572C23×C3—102no—
573C23×C3—101no—
574C23×C3—102no—
575C23×C3—102no—
576C23×C3—102no—
577C23×C3—201no—
578C23×C3—201no—
579C23×C3—201no—
580C23×C3—208no—
581C23×C3—208no—
582C23×C3C22×AGL(1,𝔽5)11yescharacteristic
583C23×C3C22×AGL(1,𝔽5)11yescharacteristic
584C23×C3C22×AGL(1,𝔽5)11yescharacteristic
585C2×C3×C4—54no—
586C2×C3×C4—102no—
587C2×C3×C4—102no—
588C2×C3×C4—102no—
589C2×C3×C4—102no—
590C2×C3×C4—102no—
591C2×C3×C4—208no—
592C2×Dic3—22no—
593C2×Dic3—41no—
594C2×Dic3—51no—
595C2×Dic3—51no—
596C2×Dic3—51no—
597C2×Dic3—51no—
598C2×Dic3—101no—
599C2×Dic3—102no—
600C2×Dic3—101no—
601C2×Dic3—102no—
602C2×Dic3—101no—
603C2×Dic3—101no—
604C2×Dic3—102no—
605C2×Dic3—102no—
606C2×Dic3—102no—
607C2×Dic3—102no—
608C2×Dic3—102no—
609C2×Dic3—102no—
610C2×Dic3—102no—
611C2×Dic3—102no—
612C2×Dic3—102no—
613C2×Dic3—201no—
614C2×Dic3—201no—
615C2×Dic3—201no—
616C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
617C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
618C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
619C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
620C22×C5—21no—
621C22×C5—21no—
622C22×C5—21no—
623C22×C5—21no—
624C22×C5—21no—
625C22×C5—21no—
626C22×C5—21no—
627C22×C5—44no—
628C22×C5#87712yescomplemented
629C22×C5C4×#6712yes—
630C22×C5C22×C4×D311yescharacteristic
631C2×D5—21no—
632C2×D5—21no—
633C2×D5—21no—
634C2×D5—21no—
635C2×D5—24no—
636C2×D5—24no—
637C2×D5—24no—
638C2×D5—24no—
639C2×D5—21no—
640C2×D5—21no—
641C2×D5—21no—
642C2×D5—44no—
643C2×D5—44no—
644C2×D5—44no—
645C2×D5—42no—
646C2×D5—42no—
647C2×D5#87712yescomplemented
648C2×D5C4×#6712yes—
649C2×D5C2×#23511yescharacteristic
650C2×D5C2×#23712yes—
651C2×D5#100412yes—
652C2×D5C22×#6711yescharacteristic
653AGL(1,𝔽5)—24no—
654AGL(1,𝔽5)—42no—
655AGL(1,𝔽5)—122no—
656AGL(1,𝔽5)—122no—
657C4×C5—61no—
658C4×C5—61no—
659C4×C5—61no—
660C4×C5—61no—
661Dic5—61no—
662Dic5—61no—
663Dic5—61no—
664Dic5—61no—
665C24—51no—
666C24—51no—
667C24—51no—
668C24—51no—
669C24—51no—
670C24—51no—
671C24—102no—
672C24—104no—
673C24—102no—
674C24—202no—
675C24D3×AGL(1,𝔽5)11yescharacteristic
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—52no—
679C22×C4—52no—
680C22×C4—104no—
681C22×C4—104no—
682C22×C4—151no—
683C22×C4—151no—
684C22×C4—151no—
685C22×C4—151no—
686C22×C4—151no—
687C22×C4—151no—
688C22×C4—151no—
689C22×C4—151no—
690C22×C4—151no—
691C22×C4—151no—
692C22×C4—152no—
693C22×C4—152no—
694C22×C4—202no—
695C22×C4—302no—
696C22×C4—302no—
697C22×C4—602no—
698C4⋊C4—304no—
699C4⋊C4—602no—
700C22⋊C4—31no—
701C22⋊C4—31no—
702C22⋊C4—31no—
703C22⋊C4—31no—
704C22⋊C4—54no—
705C22⋊C4—104no—
706C22⋊C4—102no—
707C22⋊C4—151no—
708C22⋊C4—151no—
709C22⋊C4—151no—
710C22⋊C4—151no—
711C22⋊C4—151no—
712C22⋊C4—151no—
713C22⋊C4—151no—
714C22⋊C4—151no—
715C22⋊C4—151no—
716C22⋊C4—151no—
717C22⋊C4—151no—
718C22⋊C4—151no—
719C22⋊C4—302no—
720C22⋊C4—304no—
721C22⋊C4—302no—
722C22⋊C4—602no—
723C42—304no—
724C42—602no—
725C3×C5#234211yescharacteristic, complemented, Hall
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—44no—
734C22×C3—52no—
735C22×C3—51no—
736C22×C3—51no—
737C22×C3—52no—
738C22×C3—52no—
739C22×C3—52no—
740C22×C3—104no—
741C22×C3—104no—
742C22×C3—104no—
743C22×C3—104no—
744C22×C3—101no—
745C22×C3—101no—
746C22×C3—101no—
747C22×C3—101no—
748C22×C3—101no—
749C22×C3—101no—
750C22×C3—101no—
751C22×C3—204no—
752C22×C3—204no—
753C22×C3—202no—
754C22×C3—202no—
755C22×C3—204no—
756C22×C3#413012yescomplemented
757C22×C3D4×AGL(1,𝔽5)12yes—
758C22×C3C23×AGL(1,𝔽5)11yescharacteristic
759C3×C4—104no—
760C3×C4—202no—
761Dic3—21no—
762Dic3—21no—
763Dic3—21no—
764Dic3—21no—
765Dic3—101no—
766Dic3—101no—
767Dic3—101no—
768Dic3—101no—
769Dic3—202no—
770Dic3—202no—
771C2×C5—22no—
772C2×C5—22no—
773C2×C5—41no—
774C2×C5C2×#87711yescharacteristic
775C2×C5#548611yescharacteristic
776C2×C5C2×C4×#6711yescharacteristic
777D5—22no—
778D5—22no—
779D5—41no—
780D5#549512yes—
781D5#580612yes—
782C23—22no—
783C23—22no—
784C23—41no—
785C23—51no—
786C23—54no—
787C23—52no—
788C23—52no—
789C23—51no—
790C23—51no—
791C23—51no—
792C23—101no—
793C23—102no—
794C23—102no—
795C23—102no—
796C23—101no—
797C23—101no—
798C23—102no—
799C23—102no—
800C23—102no—
801C23—102no—
802C23—102no—
803C23—101no—
804C23—102no—
805C23—102no—
806C23—102no—
807C23—201no—
808C23—201no—
809C23—201no—
810C23—208no—
811C23—208no—
812C23C2×D3×AGL(1,𝔽5)11yescharacteristic
813C23C2×D3×AGL(1,𝔽5)11yescharacteristic
814C23C2×D3×AGL(1,𝔽5)11yescharacteristic
815C2×C4—31no—
816C2×C4—31no—
817C2×C4—31no—
818C2×C4—31no—
819C2×C4—54no—
820C2×C4—62no—
821C2×C4—102no—
822C2×C4—102no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—121no—
827C2×C4—151no—
828C2×C4—151no—
829C2×C4—151no—
830C2×C4—151no—
831C2×C4—208no—
832C2×C4—301no—
833C2×C4—302no—
834C2×C4—301no—
835C2×C4—302no—
836C2×C4—301no—
837C2×C4—301no—
838C2×C4—302no—
839C2×C4—302no—
840C2×C4—302no—
841C2×C4—302no—
842C2×C4—302no—
843C2×C4—302no—
844C2×C4—302no—
845C2×C4—302no—
846C2×C4—302no—
847C2×C4—601no—
848C2×C4—601no—
849C2×C4—601no—
850C2×C3—22no—
851C2×C3—22no—
852C2×C3—41no—
853C2×C3—52no—
854C2×C3—52no—
855C2×C3—102no—
856C2×C3—102no—
857C2×C3—201no—
858C2×C3C2×#413011yescharacteristic
859C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
860C2×C3#6625811yescharacteristic
861C5#8209811yescharacteristic, complemented, Sylow
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—44no—
870C22—52no—
871C22—51no—
872C22—51no—
873C22—52no—
874C22—52no—
875C22—52no—
876C22—104no—
877C22—104no—
878C22—104no—
879C22—104no—
880C22—101no—
881C22—101no—
882C22—101no—
883C22—101no—
884C22—101no—
885C22—101no—
886C22—101no—
887C22—204no—
888C22—204no—
889C22—202no—
890C22—202no—
891C22—204no—
892C22#9192312yescomplemented
893C22AGL(1,𝔽5)×#6712yes—
894C22C22×D3×AGL(1,𝔽5)11yescharacteristic
895C4—61no—
896C4—61no—
897C4—61no—
898C4—61no—
899C4—104no—
900C4—202no—
901C4—301no—
902C4—301no—
903C4—301no—
904C4—301no—
905C4—602no—
906C4—602no—
907C3#1061707211yescharacteristic, complemented, Sylow
908C2—22no—
909C2—22no—
910C2—41no—
911C2—52no—
912C2—52no—
913C2—102no—
914C2—102no—
915C2—201no—
916C2C2×#9192311yescharacteristic
917C2C2×AGL(1,𝔽5)×#6711yescharacteristic
918C2#1175687111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC24×C3×C5C2×C4
prime radicalC24×C3×D5C22
cosocleC22×C3×D5C24
hypercenterC24D3×AGL(1,𝔽5)
hypocenterC3×C5#2342
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C2×#91923C2semidirect
5. #11752028C2semidirect
6. #11752027C2semidirect
7. Dic3×C22⋊AGL(1,𝔽5)C2semidirect
8. #11752018C2semidirect
9. #11752017C2semidirect
10. AGL(1,𝔽5)×#217C2semidirect
11. #11751984C2semidirect
25. C2×Dic3⋊AGL(1,𝔽5)C22semidirect
26. C2×Dic3⋊AGL(1,𝔽5)C22semidirect
28. C2×Dic3×AGL(1,𝔽5)C22semidirect
29. C2×Dic3×AGL(1,𝔽5)C22semidirect
30. C2×#6719C4semidirect
31. C2×C5×#217C4semidirect
32. D5×#217C4semidirect
33. D5×#217C4semidirect
34. D5×#217C4semidirect
35. D5×#217C4semidirect
40. C2×#6665C4semidirect
41. C2×#6665C4semidirect
42. (C2×AGL(1,𝔽5))⋊Dic3C22semidirect
43. (C2×AGL(1,𝔽5))⋊Dic3C22semidirect
44. (C2×AGL(1,𝔽5))⋊Dic3C22semidirect
45. (C2×AGL(1,𝔽5))⋊Dic3C22semidirect
76. C22×Dic15C2×C4semidirect
77. C22×Dic15C2×C4semidirect
78. C22×C5×Dic3C2×C4semidirect
79. C22×C5×Dic3C2×C4semidirect
83. C2×D5×Dic3C2×C4semidirect
84. C2×D5×Dic3C2×C4semidirect
85. C2×D5×Dic3C2×C4semidirect
86. C2×D5×Dic3C2×C4semidirect
104. #6719C2×C4semidirect
105. #6719C2×C4semidirect
108. C5×#217C2×C4semidirect
109. C5×#217C2×C4semidirect
114. #6665C2×C4semidirect
115. #6665C2×C4semidirect
116. #6665C2×C4semidirect
117. #6665C2×C4semidirect
254. C2×#217AGL(1,𝔽5)semidirect
343. C22×C3×C5#117semidirect
362. C2×C3×D5#117semidirect
411. C22×Dic3C2×AGL(1,𝔽5)semidirect
412. C22×Dic3C2×AGL(1,𝔽5)semidirect
434. #217C2×AGL(1,𝔽5)semidirect
435. #217C2×AGL(1,𝔽5)semidirect
628. C22×C5#877semidirect
647. C2×D5#877semidirect
725. C3×C5#2342semidirect
756. C22×C3#4130semidirect
861. C5#82098semidirect
892. C22#91923semidirect
907. C3#10617072semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊AGL(1,𝔽5)2
C2×#919232
C2×D5×#2172
#117524592
#117520282
#117520272
Dic3×C22⋊AGL(1,𝔽5)2
#117520182
#117520172
AGL(1,𝔽5)×#2172
#117519842
#106170723
#820985