Finite Group Databasebeta

← #14280064

Subgroups — #14280064

Order 1920.

1560 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6763C212yesmaximal
2C22×C4⋊ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
3C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
4C2×#91235C212yesmaximal, complemented
5C2×#91235C211yesmaximal, characteristic, complemented
6#10604254—31nomaximal, Hall
7C24×C3×D5C2211yescharacteristic
8C23×ΓL(1,𝔽16)C2212yes—
9C23×ΓL(1,𝔽16)C2212yes—
10C22×C3×C4×D5C2211yescharacteristic
11C22×C3×C4×D5C2211yescharacteristic
12C2×#6763—24no—
13C2×#6763—24no—
14C2×#6763—24no—
15C2×C4⋊ΓL(1,𝔽16)—24no—
16C2×C4⋊ΓL(1,𝔽16)—22no—
17C2×C3×C5×C22⋊C4C411yescharacteristic, complemented
18C2×C3×C22⋊Dic5C411yescharacteristic, complemented
19C2×C3×#685C411yescharacteristic, complemented
20C2×C3×#685C411yescharacteristic, complemented
21C3×D5×C22⋊C4—22no—
22C3×D5×C22⋊C4—22no—
23#91235—24no—
24#91235—22no—
25#71546—51nomaximal, Hall
26C22×C22⋊AGL(1,𝔽5)—32no—
27C22×C4⋊AGL(1,𝔽5)—31no—
28C2×D5×C22⋊C4D311yescharacteristic
29C2×(C2×AGL(1,𝔽5))⋊C4—32no—
30C2×(C2×AGL(1,𝔽5))⋊C4—31no—
31C24×C3×C5C2×C411yescharacteristic
32C23×C3×D5—22no—
33C23×C3×D5—22no—
34C23×C3×D5—21no—
35C23×C3×D5—21no—
36C23×C3×D5—21no—
37C23×C3×D5—21no—
38C23×C3×D5—22no—
39C23×C3×D5—22no—
40C23×C3×D5C2×C411yescharacteristic
41C23×C3×D5D412yes—
42C23×C3×D5Q812yes—
43C23×C3×D5C2311yescharacteristic
44C22×ΓL(1,𝔽16)—22no—
45C22×ΓL(1,𝔽16)—22no—
46C22×ΓL(1,𝔽16)—22no—
47C22×ΓL(1,𝔽16)—22no—
48C22×ΓL(1,𝔽16)—22no—
49C22×ΓL(1,𝔽16)—22no—
50C22×ΓL(1,𝔽16)—22no—
51C22×ΓL(1,𝔽16)—22no—
52C22×ΓL(1,𝔽16)—22no—
53C22×ΓL(1,𝔽16)—22no—
54C22×ΓL(1,𝔽16)—22no—
55C22×ΓL(1,𝔽16)—22no—
56C22×ΓL(1,𝔽16)D414yes—
57C22×ΓL(1,𝔽16)D414yes—
58C22×C3×C4×C5C2×C411yescharacteristic
59C22×C3×C4×C5C2×C411yescharacteristic
60C22×C3×Dic5C2×C411yescharacteristic
61C22×C3×Dic5C2×C411yescharacteristic
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5—22no—
64C2×C3×C4×D5—22no—
65C2×C3×C4×D5—21no—
66C2×C3×C4×D5—21no—
67C2×C3×C4×D5—22no—
68C2×C3×C4×D5D412yes—
69C2×C3×C4×D5D412yes—
70#6763—216no—
71C4⋊ΓL(1,𝔽16)—28no—
72C3×C5×C22⋊C4—22no—
73C3×C22⋊Dic5—22no—
74C3×#685—22no—
75C3×#685—22no—
76C22×C3×C22⋊C4—51no—
77C22×#217—52no—
78C22×C4⋊Dic3—51no—
79C2×C3⋊#95—52no—
80C2×C3⋊#95—51no—
81C24×D5C2×D311yescharacteristic
82C23×AGL(1,𝔽5)—32no—
83C23×AGL(1,𝔽5)—32no—
84C22×C4×D5C2×D311yescharacteristic
85C22×C4×D5C2×D311yescharacteristic
86C2×C22⋊AGL(1,𝔽5)—64no—
87C2×C22⋊AGL(1,𝔽5)—64no—
88C2×C22⋊AGL(1,𝔽5)—64no—
89C2×C4⋊AGL(1,𝔽5)—64no—
90C2×C4⋊AGL(1,𝔽5)—62no—
91C2×C5×C22⋊C4Dic311yescharacteristic, complemented
92C2×C22⋊Dic5Dic311yescharacteristic, complemented
93C2×#685Dic311yescharacteristic, complemented
94C2×#685Dic311yescharacteristic, complemented
95D5×C22⋊C4—22no—
96D5×C22⋊C4—22no—
97(C2×AGL(1,𝔽5))⋊C4—64no—
98(C2×AGL(1,𝔽5))⋊C4—62no—
99#1439—151noSylow
100C23×C3×C5—21no—
101C23×C3×C5—21no—
102C23×C3×C5—22no—
103C23×C3×C5—22no—
104C23×C3×C5C4⋊C412yescomplemented
105C23×C3×C5C22×C411yescharacteristic
106C22×C3×D5—21no—
107C22×C3×D5—21no—
108C22×C3×D5—22no—
109C22×C3×D5—22no—
110C22×C3×D5—24no—
111C22×C3×D5—22no—
112C22×C3×D5—22no—
113C22×C3×D5—22no—
114C22×C3×D5—22no—
115C22×C3×D5—24no—
116C22×C3×D5—24no—
117C22×C3×D5—24no—
118C22×C3×D5—41no—
119C22×C3×D5—42no—
120C22×C3×D5—42no—
121C22×C3×D5—42no—
122C22×C3×D5—41no—
123C22×C3×D5—42no—
124C22×C3×D5—42no—
125C22×C3×D5—41no—
126C22×C3×D5—42no—
127C22×C3×D5—41no—
128C22×C3×D5C4⋊C412yescomplemented
129C22×C3×D5C2×D412yes—
130C22×C3×D5C2×D411yescharacteristic
131C22×C3×D5C2×D412yes—
132C22×C3×D5C2×D411yescharacteristic
133C22×C3×D5C2×D411yescharacteristic
134C22×C3×D5C2×Q811yescharacteristic
135C22×C3×D5#4111yescharacteristic
136C22×C3×D5#4112yes—
137C22×C3×D5#4111yescharacteristic
138C22×C3×D5#4112yes—
139C2×ΓL(1,𝔽16)—24no—
140C2×ΓL(1,𝔽16)—24no—
141C2×ΓL(1,𝔽16)—24no—
142C2×ΓL(1,𝔽16)—24no—
143C2×ΓL(1,𝔽16)—24no—
144C2×ΓL(1,𝔽16)—24no—
145C2×ΓL(1,𝔽16)—42no—
146C2×ΓL(1,𝔽16)—42no—
147C2×ΓL(1,𝔽16)—42no—
148C2×ΓL(1,𝔽16)—42no—
149C2×ΓL(1,𝔽16)—42no—
150C2×ΓL(1,𝔽16)—42no—
151C2×ΓL(1,𝔽16)—42no—
152C2×ΓL(1,𝔽16)—42no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5C22⋊C412yescomplemented
157C2×C3×Dic5—22no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5C22⋊C412yescomplemented
161C3×C4×D5—22no—
162C3×C4×D5—24no—
163C3×C4×D5—22no—
164C3×C4×D5—42no—
165C3×C4×D5—41no—
166C3×C4×D5—41no—
167C25×C3—51no—
168C23×C3×C4—51no—
169C23×C3×C4—51no—
170C23×Dic3—52no—
171C23×Dic3—52no—
172C2×C3×C22⋊C4—51no—
173C2×C3×C22⋊C4—51no—
174C2×C3×C22⋊C4—51no—
175C2×C3×C22⋊C4—102no—
176C2×C3×C22⋊C4—102no—
177C2×C3×C22⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
178C2×#217—104no—
179C2×#217—104no—
180C2×#217—104no—
181C2×C4⋊Dic3—104no—
182C2×C4⋊Dic3—102no—
183C3⋊#95—104no—
184C3⋊#95—102no—
185C24×C5C2×Dic311yescharacteristic
186C23×D5—21no—
187C23×D5—21no—
188C23×D5—22no—
189C23×D5—22no—
190C23×D5—22no—
191C23×D5—22no—
192C23×D5—21no—
193C23×D5—21no—
194C23×D5Dic612yes—
195C23×D5D1212yes—
196C23×D5C2×Dic311yescharacteristic
197C23×D5C22×D311yescharacteristic
198C22×AGL(1,𝔽5)—34no—
199C22×AGL(1,𝔽5)—34no—
200C22×AGL(1,𝔽5)—62no—
201C22×AGL(1,𝔽5)—62no—
202C22×AGL(1,𝔽5)—62no—
203C22×AGL(1,𝔽5)—62no—
204C22×AGL(1,𝔽5)—62no—
205C22×AGL(1,𝔽5)—62no—
206C22×AGL(1,𝔽5)—62no—
207C22×AGL(1,𝔽5)—62no—
208C22×AGL(1,𝔽5)—62no—
209C22×AGL(1,𝔽5)—62no—
210C22×AGL(1,𝔽5)—62no—
211C22×AGL(1,𝔽5)—62no—
212C22×C4×C5C2×Dic311yescharacteristic
213C22×C4×C5C2×Dic311yescharacteristic
214C22×Dic5C2×Dic311yescharacteristic
215C22×Dic5C2×Dic311yescharacteristic
216C2×C4×D5—22no—
217C2×C4×D5—22no—
218C2×C4×D5—22no—
219C2×C4×D5—22no—
220C2×C4×D5—21no—
221C2×C4×D5—21no—
222C2×C4×D5#6712yes—
223C2×C4×D5#6712yes—
224C22⋊AGL(1,𝔽5)—616no—
225C4⋊AGL(1,𝔽5)—68no—
226C5×C22⋊C4—22no—
227C22⋊Dic5—22no—
228#685—22no—
229#685—22no—
230C22×C4⋊C4—151no—
231C22×C22⋊C4—51no—
232C22×C22⋊C4—152no—
233C2×#95—151no—
234C2×#95—152no—
235C22×C3×C5—22no—
236C22×C3×C5—24no—
237C22×C3×C5—41no—
238C22×C3×C5—42no—
239C22×C3×C5—41no—
240C22×C3×C5C2×C22⋊C411yescharacteristic
241C22×C3×C5C2×C4⋊C411yescharacteristic
242C22×C3×C5#11711yescharacteristic
243C22×C3×C5C4×D412yes—
244C22×C3×C5C4×D412yes—
245C2×C3×D5—22no—
246C2×C3×D5—24no—
247C2×C3×D5—41no—
248C2×C3×D5—42no—
249C2×C3×D5—41no—
250C2×C3×D5—42no—
251C2×C3×D5—42no—
252C2×C3×D5—44no—
253C2×C3×D5—44no—
254C2×C3×D5—42no—
255C2×C3×D5—42no—
256C2×C3×D5#12012yes—
257C2×C3×D5#12011yescharacteristic
258C2×C3×D5#12112yes—
259C2×C3×D5#12111yescharacteristic
260C2×C3×D5#12111yescharacteristic
261C2×C3×D5#12112yes—
262C2×C3×D5#12112yes—
263C2×C3×D5C22⋊Q812yes—
264C2×C3×D5C22⋊Q812yes—
265C2×C3×D5C22⋊Q811yescharacteristic
266C2×C3×D5C22⋊Q811yescharacteristic
267C2×C3×D5#12312yes—
268C2×C3×D5#12312yes—
269C2×C3×D5#12311yescharacteristic
270C2×C3×D5#12412yes—
271C2×C3×D5#12411yescharacteristic
272C2×C3×D5#12612yes—
273C2×C3×D5#12711yescharacteristic
274ΓL(1,𝔽16)—44no—
275ΓL(1,𝔽16)—44no—
276C3×C4×C5—22no—
277C3×C4×C5—41no—
278C3×Dic5—22no—
279C3×Dic5—41no—
280C24×C3—51no—
281C24×C3—52no—
282C24×C3—52no—
283C24×C3—51no—
284C24×C3—102no—
285C24×C3—102no—
286C24×C3—101no—
287C24×C3—101no—
288C24×C3—101no—
289C24×C3—101no—
290C24×C3—102no—
291C24×C3—102no—
292C24×C3C2×AGL(1,𝔽5)11yescharacteristic
293C22×C3×C4—51no—
294C22×C3×C4—52no—
295C22×C3×C4—52no—
296C22×C3×C4—51no—
297C22×C3×C4—102no—
298C22×C3×C4—102no—
299C22×C3×C4—102no—
300C22×C3×C4—101no—
301C22×C3×C4—101no—
302C22×C3×C4—102no—
303C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
304C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
305C22×Dic3—54no—
306C22×Dic3—54no—
307C22×Dic3—102no—
308C22×Dic3—102no—
309C22×Dic3—102no—
310C22×Dic3—102no—
311C22×Dic3—102no—
312C22×Dic3—102no—
313C22×Dic3—102no—
314C22×Dic3—102no—
315C22×Dic3—102no—
316C22×Dic3—102no—
317C22×Dic3—102no—
318C22×Dic3—102no—
319C3×C22⋊C4—22no—
320C3×C22⋊C4—102no—
321C3×C22⋊C4—102no—
322C3×C22⋊C4—102no—
323#217—1016no—
324C4⋊Dic3—108no—
325C23×C5—21no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—21no—
329C23×C5C4⋊Dic312yescomplemented
330C23×C5C22×Dic311yescharacteristic
331C22×D5—21no—
332C22×D5—22no—
333C22×D5—22no—
334C22×D5—21no—
335C22×D5—24no—
336C22×D5—24no—
337C22×D5—24no—
338C22×D5—24no—
339C22×D5—22no—
340C22×D5—22no—
341C22×D5—22no—
342C22×D5—22no—
343C22×D5—42no—
344C22×D5—42no—
345C22×D5—42no—
346C22×D5—42no—
347C22×D5—41no—
348C22×D5—41no—
349C22×D5—41no—
350C22×D5—42no—
351C22×D5—42no—
352C22×D5—41no—
353C22×D5C4⋊Dic312yescomplemented
354C22×D5C2×Dic611yescharacteristic
355C22×D5C2×D1211yescharacteristic
356C22×D5#23511yescharacteristic
357C22×D5#23511yescharacteristic
358C22×D5D3×D412yes—
359C22×D5D3×D412yes—
360C22×D5#23712yes—
361C22×D5#23712yes—
362C22×D5C2×#6711yescharacteristic
363C22×D5C2×#6711yescharacteristic
364C2×AGL(1,𝔽5)—64no—
365C2×AGL(1,𝔽5)—64no—
366C2×AGL(1,𝔽5)—64no—
367C2×AGL(1,𝔽5)—64no—
368C2×AGL(1,𝔽5)—64no—
369C2×AGL(1,𝔽5)—64no—
370C2×AGL(1,𝔽5)—122no—
371C2×AGL(1,𝔽5)—122no—
372C2×AGL(1,𝔽5)—122no—
373C2×AGL(1,𝔽5)—122no—
374C2×AGL(1,𝔽5)—122no—
375C2×AGL(1,𝔽5)—122no—
376C2×AGL(1,𝔽5)—122no—
377C2×AGL(1,𝔽5)—122no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—21no—
381C2×C4×C5#21712yescomplemented
382C2×Dic5—22no—
383C2×Dic5—22no—
384C2×Dic5—21no—
385C2×Dic5#21712yescomplemented
386C4×D5—22no—
387C4×D5—22no—
388C4×D5—24no—
389C4×D5—41no—
390C4×D5—42no—
391C4×D5—41no—
392C25—51no—
393C23×C4—51no—
394C23×C4—51no—
395C23×C4—152no—
396C23×C4—152no—
397C2×C4⋊C4—302no—
398C2×C4⋊C4—304no—
399C2×C22⋊C4—51no—
400C2×C22⋊C4—51no—
401C2×C22⋊C4—51no—
402C2×C22⋊C4—102no—
403C2×C22⋊C4—102no—
404C2×C22⋊C4—304no—
405C2×C22⋊C4—304no—
406C2×C22⋊C4—304no—
407C2×C22⋊C4ΓL(1,𝔽16)11yescharacteristic, complemented
408#95—302no—
409#95—304no—
410C2×C3×C5—42no—
411C2×C3×C5#38011yescharacteristic
412C2×C3×C5#38512yes—
413C2×C3×C5#38611yescharacteristic
414C2×C3×C5#38812yes—
415C2×C3×C5#39011yescharacteristic
416C3×D5—42no—
417C3×D5#39211yescharacteristic
418C3×D5#39311yescharacteristic
419C3×D5#39412yes—
420C3×D5#39612yes—
421C3×D5#39711yescharacteristic
422C3×D5#39911yescharacteristic
423C23×C3—21no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—21no—
427C23×C3—51no—
428C23×C3—51no—
429C23×C3—51no—
430C23×C3—51no—
431C23×C3—52no—
432C23×C3—52no—
433C23×C3—52no—
434C23×C3—52no—
435C23×C3—51no—
436C23×C3—51no—
437C23×C3—52no—
438C23×C3—104no—
439C23×C3—104no—
440C23×C3—104no—
441C23×C3—104no—
442C23×C3—102no—
443C23×C3—102no—
444C23×C3—102no—
445C23×C3—102no—
446C23×C3—101no—
447C23×C3—102no—
448C23×C3—102no—
449C23×C3—101no—
450C23×C3—202no—
451C23×C3—202no—
452C23×C3—202no—
453C23×C3—202no—
454C23×C3—201no—
455C23×C3—202no—
456C23×C3—201no—
457C23×C3—202no—
458C23×C3—201no—
459C23×C3—201no—
460C23×C3C4⋊AGL(1,𝔽5)12yescomplemented
461C23×C3C22×AGL(1,𝔽5)11yescharacteristic
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—52no—
466C2×C3×C4—102no—
467C2×C3×C4—104no—
468C2×C3×C4—102no—
469C2×C3×C4—102no—
470C2×C3×C4—102no—
471C2×C3×C4—101no—
472C2×C3×C4—202no—
473C2×C3×C4—201no—
474C2×C3×C4—201no—
475C2×C3×C4C22⋊AGL(1,𝔽5)12yescomplemented
476C2×Dic3—104no—
477C2×Dic3—104no—
478C2×Dic3—104no—
479C2×Dic3—104no—
480C2×Dic3—104no—
481C2×Dic3—104no—
482C2×Dic3—202no—
483C2×Dic3—202no—
484C2×Dic3—202no—
485C2×Dic3—202no—
486C2×Dic3—202no—
487C2×Dic3—202no—
488C2×Dic3—202no—
489C2×Dic3—202no—
490C22×C5—24no—
491C22×C5—22no—
492C22×C5—42no—
493C22×C5—41no—
494C22×C5—41no—
495C22×C5C2×C4⋊Dic311yescharacteristic
496C22×C5#92611yescharacteristic
497C22×C5D4×Dic312yes—
498C22×C5D4×Dic312yes—
499C22×C5C2×#21711yescharacteristic
500C2×D5—24no—
501C2×D5—22no—
502C2×D5—42no—
503C2×D5—41no—
504C2×D5—41no—
505C2×D5—42no—
506C2×D5—44no—
507C2×D5—42no—
508C2×D5—42no—
509C2×D5—42no—
510C2×D5—44no—
511C2×D5#87812yes—
512C2×D5#87812yes—
513C2×D5#87912yes—
514C2×D5#88212yes—
515C2×D5#88312yes—
516C2×D5#88412yes—
517C2×D5#88512yes—
518C2×D5#88612yes—
519C2×D5#92411yescharacteristic
520C2×D5#92411yescharacteristic
521C2×D5#93011yescharacteristic
522C2×D5#93011yescharacteristic
523C2×D5#93511yescharacteristic
524C2×D5#93611yescharacteristic
525C2×D5#93711yescharacteristic
526C2×D5#93812yes—
527C2×D5#93912yes—
528C2×D5#94011yescharacteristic
529AGL(1,𝔽5)—124no—
530AGL(1,𝔽5)—124no—
531C4×C5—22no—
532C4×C5—41no—
533Dic5—22no—
534Dic5—41no—
535C24—51no—
536C24—52no—
537C24—52no—
538C24—51no—
539C24—101no—
540C24—101no—
541C24—102no—
542C24—102no—
543C24—101no—
544C24—101no—
545C24—102no—
546C24—102no—
547C24C2×ΓL(1,𝔽16)11yescharacteristic
548C22×C4—51no—
549C22×C4—52no—
550C22×C4—52no—
551C22×C4—51no—
552C22×C4—102no—
553C22×C4—102no—
554C22×C4—102no—
555C22×C4—101no—
556C22×C4—101no—
557C22×C4—102no—
558C22×C4—154no—
559C22×C4—154no—
560C22×C4—302no—
561C22×C4—302no—
562C22×C4—302no—
563C22×C4—302no—
564C22×C4—302no—
565C22×C4—302no—
566C22×C4—302no—
567C22×C4—302no—
568C22×C4—302no—
569C22×C4—302no—
570C22×C4—302no—
571C22×C4—302no—
572C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
573C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
574C4⋊C4—308no—
575C22⋊C4—22no—
576C22⋊C4—102no—
577C22⋊C4—102no—
578C22⋊C4—102no—
579C22⋊C4—3016no—
580C3×C5#143911yescharacteristic, complemented, Hall
581C22×C3—24no—
582C22×C3—22no—
583C22×C3—42no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—52no—
587C22×C3—52no—
588C22×C3—52no—
589C22×C3—52no—
590C22×C3—52no—
591C22×C3—52no—
592C22×C3—52no—
593C22×C3—52no—
594C22×C3—51no—
595C22×C3—51no—
596C22×C3—51no—
597C22×C3—51no—
598C22×C3—51no—
599C22×C3—52no—
600C22×C3—51no—
601C22×C3—52no—
602C22×C3—51no—
603C22×C3—51no—
604C22×C3—104no—
605C22×C3—102no—
606C22×C3—202no—
607C22×C3—204no—
608C22×C3—202no—
609C22×C3—204no—
610C22×C3—202no—
611C22×C3—202no—
612C22×C3—202no—
613C22×C3—201no—
614C22×C3—201no—
615C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
616C22×C3#413011yescharacteristic
617C22×C3D4×AGL(1,𝔽5)12yes—
618C22×C3D4×AGL(1,𝔽5)12yes—
619C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
620C3×C4—22no—
621C3×C4—41no—
622C3×C4—102no—
623C3×C4—201no—
624Dic3—204no—
625Dic3—204no—
626C2×C5—42no—
627C2×C5#495012yes—
628C2×C5#495112yes—
629C2×C5#521211yescharacteristic
630C2×C5#522011yescharacteristic
631C2×C5#522111yescharacteristic
632D5—42no—
633D5#494711yescharacteristic
634D5#494812yes—
635D5#494911yescharacteristic
636D5#495311yescharacteristic
637D5#496011yescharacteristic
638D5#496112yes—
639C23—21no—
640C23—22no—
641C23—22no—
642C23—21no—
643C23—51no—
644C23—51no—
645C23—51no—
646C23—51no—
647C23—52no—
648C23—52no—
649C23—52no—
650C23—52no—
651C23—51no—
652C23—51no—
653C23—52no—
654C23—104no—
655C23—104no—
656C23—104no—
657C23—104no—
658C23—102no—
659C23—102no—
660C23—102no—
661C23—102no—
662C23—101no—
663C23—102no—
664C23—102no—
665C23—101no—
666C23—202no—
667C23—202no—
668C23—202no—
669C23—202no—
670C23—201no—
671C23—202no—
672C23—201no—
673C23—202no—
674C23—201no—
675C23—201no—
676C23C4⋊ΓL(1,𝔽16)12yescomplemented
677C23C22×ΓL(1,𝔽16)11yescharacteristic
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—52no—
682C2×C4—102no—
683C2×C4—104no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—101no—
688C2×C4—202no—
689C2×C4—201no—
690C2×C4—201no—
691C2×C4—304no—
692C2×C4—304no—
693C2×C4—304no—
694C2×C4—304no—
695C2×C4—304no—
696C2×C4—304no—
697C2×C4—602no—
698C2×C4—602no—
699C2×C4—602no—
700C2×C4—602no—
701C2×C4—602no—
702C2×C4—602no—
703C2×C4—602no—
704C2×C4—602no—
705C2×C4#676312yescomplemented
706C2×C3—42no—
707C2×C3—51no—
708C2×C3—52no—
709C2×C3—51no—
710C2×C3—52no—
711C2×C3—51no—
712C2×C3—51no—
713C2×C3—202no—
714C2×C3#6569912yes—
715C2×C3#6570012yes—
716C2×C3#6576511yescharacteristic
717C2×C3#6577911yescharacteristic
718C2×C3#6578011yescharacteristic
719C5#7154611yescharacteristic, complemented, Sylow
720C22—24no—
721C22—22no—
722C22—42no—
723C22—41no—
724C22—41no—
725C22—52no—
726C22—52no—
727C22—52no—
728C22—52no—
729C22—52no—
730C22—52no—
731C22—52no—
732C22—52no—
733C22—51no—
734C22—51no—
735C22—51no—
736C22—51no—
737C22—51no—
738C22—52no—
739C22—51no—
740C22—52no—
741C22—51no—
742C22—51no—
743C22—104no—
744C22—102no—
745C22—202no—
746C22—204no—
747C22—202no—
748C22—204no—
749C22—202no—
750C22—202no—
751C22—202no—
752C22—201no—
753C22—201no—
754C22C2×C4⋊ΓL(1,𝔽16)11yescharacteristic
755C22#9198911yescharacteristic
756C22D4×ΓL(1,𝔽16)12yes—
757C22D4×ΓL(1,𝔽16)12yes—
758C22C2×#676311yescharacteristic
759C4—22no—
760C4—41no—
761C4—102no—
762C4—201no—
763C4—604no—
764C4—604no—
765C3#1060425411yescharacteristic, complemented, Sylow
766C2—42no—
767C2—51no—
768C2—52no—
769C2—51no—
770C2—52no—
771C2—51no—
772C2—51no—
773C2—202no—
774C2#1175235812yes—
775C2#1175235912yes—
776C2#1175242411yescharacteristic
777C2#1175243811yescharacteristic
778C2#1175243911yescharacteristic
subgroupG/H
center, FrattiniC23C22×ΓL(1,𝔽16)
commutator, socleC23×C3×C5C22×C4
FittingC2×C3×C5×C22⋊C4C4
prime radicalC24×C3×D5C22
cosocleC23×C3×D5C23
hypercenterC2×C22⋊C4ΓL(1,𝔽16)
hypocenterC3×C5#1439
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊ΓL(1,𝔽16)C2semidirect
4. C2×#91235C2semidirect
5. C2×#91235C2semidirect
17. C2×C3×C5×C22⋊C4C4semidirect
18. C2×C3×C22⋊Dic5C4semidirect
19. C2×C3×#685C4semidirect
20. C2×C3×#685C4semidirect
91. C2×C5×C22⋊C4Dic3semidirect
92. C2×C22⋊Dic5Dic3semidirect
93. C2×#685Dic3semidirect
94. C2×#685Dic3semidirect
104. C23×C3×C5C4⋊C4semidirect
128. C22×C3×D5C4⋊C4semidirect
156. C2×C3×C4×C5C22⋊C4semidirect
160. C2×C3×Dic5C22⋊C4semidirect
177. C2×C3×C22⋊C4AGL(1,𝔽5)semidirect
329. C23×C5C4⋊Dic3semidirect
353. C22×D5C4⋊Dic3semidirect
381. C2×C4×C5#217semidirect
385. C2×Dic5#217semidirect
407. C2×C22⋊C4ΓL(1,𝔽16)semidirect
460. C23×C3C4⋊AGL(1,𝔽5)semidirect
475. C2×C3×C4C22⋊AGL(1,𝔽5)semidirect
580. C3×C5#1439semidirect
676. C23C4⋊ΓL(1,𝔽16)semidirect
705. C2×C4#6763semidirect
719. C5#71546semidirect
765. C3#10604254semidirect

Maximal subgroups

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

subgroupindex
C22×#67632
C22×C4⋊ΓL(1,𝔽16)2
C2×C3×D5×C22⋊C42
C2×#912352
#106042543
#715465