Finite Group Databasebeta

← #14413492

Subgroups — #14413492

Order 1920.

952 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756838C211yesmaximal, characteristic
2#11756836C211yesmaximal, characteristic
3D5×#907C211yesmaximal, characteristic
4#11752386C211yesmaximal, characteristic, complemented
5C3×#65727C211yesmaximal, characteristic, complemented
6#11751726C211yesmaximal, characteristic, complemented
7C2×#91159C211yesmaximal, characteristic, complemented
8#11751658C212yesmaximal, complemented
9#11751654C212yesmaximal, complemented
10#11751653C212yesmaximal, complemented
11D3×#3993C212yesmaximal, complemented
12#10617416—31nomaximal, Hall
13D5×#235C2211yescharacteristic
14#91989C2211yescharacteristic
15C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
16C3×#4130C2211yescharacteristic
17C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
18#67⋊AGL(1,𝔽5)—22no—
19AGL(1,𝔽5)×#67—22no—
20#91921—21no—
21D3×C4⋊AGL(1,𝔽5)C2212yes—
22D3×C4⋊AGL(1,𝔽5)C2212yes—
23AGL(1,𝔽5)×D12—21no—
24ΓL(1,𝔽16)⋊Q8—21no—
25#91907C2212yes—
26#91907C2212yes—
27AGL(1,𝔽5)×Dic6—21no—
28#91796C411yescharacteristic, complemented
29C5×#907C411yescharacteristic, complemented
30C3×D5×M16C2211yescharacteristic
31#91291C411yescharacteristic, complemented
32#91288C411yescharacteristic, complemented
33C2×D5×C3⋊C8C2211yescharacteristic
34#91268C412yescomplemented
35#91267C412yescomplemented
36D5×ΓL(1,𝔽25)C2212yes—
37D3×C8×D5C2212yes—
38#91223C2212yes—
39#91222C2212yes—
40C3×#3994C2212yes—
41C3×#3993C2212yes—
42#91160C2211yescharacteristic
43#91160C2211yescharacteristic
44#91159C2212yes—
45#91159C2212yes—
46#91159C2211yescharacteristic
47#91159C2211yescharacteristic
48#79209—51nomaximal, Hall
49#66266—31no—
50#66266—31no—
51D5×#131—31no—
52#65727—31no—
53#65727—32no—
54#65727—32no—
55#65727D311yescharacteristic, complemented
56#65721—32no—
57#65721—31no—
58C2×#3993—32no—
59C2×#3993—31no—
60C22×ΓL(1,𝔽16)—21no—
61C22×C3×AGL(1,𝔽5)—21no—
62C2×D3×AGL(1,𝔽5)—22no—
63C2×D3×AGL(1,𝔽5)—22no—
64#6817C2×C411yescharacteristic
65C5×#235C2×C411yescharacteristic
66C2×C3×C4×D5C2311yescharacteristic
67D5×#67D412yes—
68#6782Q812yes—
69D5×D12D411yescharacteristic
70C4×D3×D5C2312yes—
71#6773Q811yescharacteristic
72#6772Q811yescharacteristic
73#6771C2×C412yes—
74D5×Dic6D411yescharacteristic
75#6763—21no—
76C4⋊ΓL(1,𝔽16)—21no—
77C4⋊ΓL(1,𝔽16)C2311yescharacteristic
78C4⋊ΓL(1,𝔽16)C2312yes—
79C4⋊ΓL(1,𝔽16)C2311yescharacteristic
80C4×ΓL(1,𝔽16)—21no—
81C3×C22⋊AGL(1,𝔽5)—21no—
82C3×C4⋊AGL(1,𝔽5)—21no—
83C3×C4⋊AGL(1,𝔽5)C2311yescharacteristic
84C3×C4⋊AGL(1,𝔽5)C2312yes—
85C3×C4⋊AGL(1,𝔽5)C2311yescharacteristic
86C3×C4×AGL(1,𝔽5)—21no—
87Dic3⋊AGL(1,𝔽5)—22no—
88Dic3⋊AGL(1,𝔽5)—22no—
89(C2×D3)⋊AGL(1,𝔽5)—22no—
90(C2×D3)⋊AGL(1,𝔽5)—22no—
91Dic3×AGL(1,𝔽5)—22no—
92Dic3×AGL(1,𝔽5)—22no—
93C3×C5×M16C2×C411yescharacteristic, complemented
94C2×C3⋊#168C2×C411yescharacteristic, complemented
95#6705C2×C412yescomplemented
96C8×D15C2×C412yescomplemented
97C2×C5×C3⋊C8C2×C411yescharacteristic, complemented
98C5×ΓL(1,𝔽25)C2×C412yescomplemented
99C5×D3×C8C2×C412yescomplemented
100C3×#681C2×C411yescharacteristic, complemented
101C3×#676C2×C412yescomplemented
102C3×C8×D5C2312yes—
103#6651C2×C412yescomplemented
104#6650C2×C412yescomplemented
105#6648C2×C412yescomplemented
106D3×#168C2×C412yescomplemented
107D5×C3⋊C8C2×C411yescharacteristic, complemented
108D5×C3⋊C8C2×C411yescharacteristic, complemented
109D5×C3⋊C8C2311yescharacteristic
110D5×C3⋊C8C2311yescharacteristic
111C2×#907—51no—
112#5523—51no—
113#5504—51no—
114C3×#428—51no—
115#5121—51no—
116#4998—51no—
117C2×#808—51no—
118#4881—52no—
119#4880—52no—
120#4861—52no—
121D3×#106—52no—
122D5×#41—31no—
123Q8×AGL(1,𝔽5)—61no—
124Q8×AGL(1,𝔽5)—61no—
125D4×AGL(1,𝔽5)—61no—
126D4×AGL(1,𝔽5)—61no—
127D4×AGL(1,𝔽5)—62no—
128D4×AGL(1,𝔽5)—62no—
129#4130—31no—
130#4130—32no—
131#4130—32no—
132#4130C2×D311yescharacteristic
133C2×C4⋊AGL(1,𝔽5)—31no—
134C2×C4⋊AGL(1,𝔽5)—32no—
135C2×C4⋊AGL(1,𝔽5)—32no—
136C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
137C5×#131—31no—
138#4094—31no—
139#4053—31no—
140#4053—32no—
141D5×M16—32no—
142D5×M16C2×D311yescharacteristic
143#4047—31no—
144#4047—32no—
145C2×C8×D5—31no—
146C2×C8×D5—32no—
147#3994—31no—
148#3994—31no—
149#3994—32no—
150#3994C2×D312yes—
151#3993—31no—
152#3993—32no—
153#3993—32no—
154#3993—31no—
155#3993—32no—
156#3993C2×D312yes—
157#2912—151noSylow
158C22×C3×D5C2×D411yescharacteristic
159C2×D3×D5C2×D412yes—
160C2×ΓL(1,𝔽16)—21no—
161C2×ΓL(1,𝔽16)—22no—
162C2×ΓL(1,𝔽16)—21no—
163C2×ΓL(1,𝔽16)—81no—
164C2×C3×AGL(1,𝔽5)—21no—
165C2×C3×AGL(1,𝔽5)—22no—
166C2×C3×AGL(1,𝔽5)—21no—
167C2×C3×AGL(1,𝔽5)—81no—
168D3×AGL(1,𝔽5)—82no—
169D3×AGL(1,𝔽5)—82no—
170C2×C3×C4×C5C22×C411yescharacteristic
171#1220C4⋊C412yes—
172D60C4⋊C411yescharacteristic
173C4×D15C22×C412yes—
174Dic30C4⋊C411yescharacteristic
175C5×#67C4⋊C412yes—
176C5×D12C4⋊C411yescharacteristic
177C4×C5×D3C22×C412yes—
178C5×Dic6C4⋊C411yescharacteristic
179C2×C3×Dic5C2×Q811yescharacteristic
180C3×C4×D5C22×C411yescharacteristic
181C3×C4×D5C2×D411yescharacteristic
182C3×C4×D5C2×Q811yescharacteristic
183C3×C4×D5C2411yescharacteristic
184#1204C4⋊C412yes—
185#1203C4⋊C412yes—
186#1202C4⋊C412yes—
187#1201C4⋊C412yes—
188#1200C2×Q812yes—
189D3×Dic5C2×Q812yes—
190D5×Dic3C2×D412yes—
191C3×C5×C8C22×C412yes—
192C3⋊#168C22×C411yescharacteristic
193C3⋊#168C22×C411yescharacteristic
194C3×#168C22×C412yes—
195C5×C3⋊C8C22×C411yescharacteristic
196C5×C3⋊C8C22×C411yescharacteristic
197C2×#235—51no—
198C2×C3×M16—51no—
199C3×#117—51no—
200C2×C3×C4⋊C4—51no—
201C4×#67—102no—
202#926—51no—
203C2×C4⋊Dic3—51no—
204C22×C3⋊C8—51no—
205#907—51no—
206#907—51no—
207#907—51no—
208#907—52no—
209#907—52no—
210#907AGL(1,𝔽5)11yescharacteristic, complemented
211C2×ΓL(1,𝔽25)—52no—
212C2×D3×C8—52no—
213#893—101no—
214#892—52no—
215#892—52no—
216D3×C4⋊C4—52no—
217D3×C4⋊C4—52no—
218#887—101no—
219#67⋊C4—102no—
220C4×D12—101no—
221C4×Dic6—101no—
222C3×#107—52no—
223C3×#106—52no—
224#818—52no—
225#817—52no—
226#808—51no—
227#808—52no—
228#808—52no—
229#808—51no—
230#807—51no—
231#807—51no—
232C22×AGL(1,𝔽5)—21no—
233C22×AGL(1,𝔽5)—62no—
234C22×AGL(1,𝔽5)—62no—
235C22×AGL(1,𝔽5)—61no—
236C5×#41—31no—
237#713—31no—
238Q8×D5—31no—
239#711—32no—
240#711—31no—
241D4×D5—32no—
242D4×D5—31no—
243#709—31no—
244#709—32no—
245C2×C4×D5—32no—
246C2×C4×D5C22×D311yescharacteristic
247C22⋊AGL(1,𝔽5)—21no—
248C22⋊AGL(1,𝔽5)—62no—
249C22⋊AGL(1,𝔽5)—62no—
250C22⋊AGL(1,𝔽5)—61no—
251C4⋊AGL(1,𝔽5)—21no—
252C4⋊AGL(1,𝔽5)—32no—
253C4⋊AGL(1,𝔽5)—31no—
254C4⋊AGL(1,𝔽5)—31no—
255C4⋊AGL(1,𝔽5)—62no—
256C4⋊AGL(1,𝔽5)—62no—
257C4⋊AGL(1,𝔽5)—61no—
258C4⋊AGL(1,𝔽5)C22×D311yescharacteristic
259C4⋊AGL(1,𝔽5)C22×D312yes—
260C4⋊AGL(1,𝔽5)C22×D311yescharacteristic
261C4×AGL(1,𝔽5)—21no—
262C4×AGL(1,𝔽5)—62no—
263C4×AGL(1,𝔽5)—62no—
264C4×AGL(1,𝔽5)—61no—
265C5×M16—32no—
266C5×M16C4×D311yescharacteristic, complemented
267C2×C5×C8—31no—
268C2×C5×C8—32no—
269#681—32no—
270#681C4×D311yescharacteristic, complemented
271C2×#168—31no—
272C2×#168—32no—
273#676—32no—
274#676—32no—
275#676C4×D312yescomplemented
276C8×D5—31no—
277C8×D5—31no—
278C8×D5—31no—
279C8×D5—31no—
280C8×D5—32no—
281C8×D5—32no—
282C8×D5C22×D312yes—
283C2×#131—151no—
284#520—151no—
285#520—151no—
286#428—51no—
287#428—152no—
288#428—152no—
289#428—151no—
290#427—152no—
291#427—151no—
292C2×#106—152no—
293C2×#106—151no—
294C22×C3×C5C2×C4⋊C411yescharacteristic
295C2×D15C2×C4⋊C412yes—
296C2×C5×D3C2×C4⋊C412yes—
297C2×C3×D5—21no—
298C2×C3×D5—21no—
299C2×C3×D5C2×C4⋊C411yescharacteristic
300C2×C3×D5C22×D411yescharacteristic
301D3×D5—22no—
302D3×D5—22no—
303ΓL(1,𝔽16)—41no—
304ΓL(1,𝔽16)—42no—
305ΓL(1,𝔽16)—41no—
306C3×AGL(1,𝔽5)—41no—
307C3×AGL(1,𝔽5)—42no—
308C3×AGL(1,𝔽5)—41no—
309C3×C4×C5C2×C4⋊C411yescharacteristic
310C3×C4×C5C23×C411yescharacteristic
311Dic15C2×C4⋊C412yes—
312C3×Dic5C2×C4⋊C411yescharacteristic
313C3×Dic5C22×Q811yescharacteristic
314C5×Dic3C2×C4⋊C412yes—
315C22×C3×C4—51no—
316C22×C3×C4—101no—
317C2×#67—52no—
318C22×Dic3—101no—
319#235—51no—
320#235—52no—
321#235—51no—
322#235—52no—
323#235—51no—
324#235C2×AGL(1,𝔽5)11yescharacteristic
325C2×D12—51no—
326C2×C4×D3—52no—
327C2×C4×D3—102no—
328C2×C4×D3—102no—
329C2×Dic6—51no—
330C3×M16—51no—
331C3×M16—52no—
332C3×M16C2×AGL(1,𝔽5)11yescharacteristic, complemented
333C2×C3×C8—52no—
334C3×C4⋊C4—51no—
335C3×C4⋊C4—51no—
336C3×C4⋊C4—52no—
337C3×C4⋊C4—101no—
338C3×C22⋊C4—101no—
339C3×C42—101no—
340#217—101no—
341(C2×D3)⋊C4—102no—
342(C2×D3)⋊C4—102no—
343C4⋊Dic3—51no—
344C4⋊Dic3—51no—
345C4⋊Dic3—52no—
346C4⋊Dic3—101no—
347Dic3⋊C4—102no—
348Dic3⋊C4—102no—
349C4×Dic3—102no—
350C4×Dic3—102no—
351C4×Dic3—101no—
352C2×C3⋊C8—51no—
353C2×C3⋊C8—51no—
354C2×C3⋊C8—51no—
355C2×C3⋊C8—51no—
356C2×C3⋊C8—51no—
357C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic, complemented
358ΓL(1,𝔽25)—52no—
359ΓL(1,𝔽25)—52no—
360ΓL(1,𝔽25)—52no—
361ΓL(1,𝔽25)C2×AGL(1,𝔽5)12yescomplemented
362D3×C8—52no—
363D3×C8—52no—
364D3×C8—52no—
365D3×C8C2×AGL(1,𝔽5)12yescomplemented
366C22×D5—32no—
367C22×D5D3×D411yescharacteristic
368C2×AGL(1,𝔽5)—21no—
369C2×AGL(1,𝔽5)—21no—
370C2×AGL(1,𝔽5)—22no—
371C2×AGL(1,𝔽5)—61no—
372C2×AGL(1,𝔽5)—61no—
373C2×AGL(1,𝔽5)—62no—
374C2×AGL(1,𝔽5)—81no—
375C2×AGL(1,𝔽5)—242no—
376C2×AGL(1,𝔽5)—242no—
377C2×AGL(1,𝔽5)—241no—
378C5×Q8—31no—
379C5×D4—32no—
380C5×D4—31no—
381C2×C4×C5—32no—
382C2×C4×C5C2×C4×D311yescharacteristic
383C22⋊D5—32no—
384C22⋊D5—32no—
385C22⋊D5—32no—
386C2×Dic5—32no—
387C2×Dic5D3×Q811yescharacteristic
388D20—32no—
389D20—31no—
390C4×D5—32no—
391C4×D5—32no—
392C4×D5—32no—
393C4×D5C2×C4×D311yescharacteristic
394C4×D5D3×D411yescharacteristic
395C4×D5D3×Q811yescharacteristic
396C4×D5C23×D311yescharacteristic
397Dic10—31no—
398Dic10—32no—
399C5×C8—31no—
400C5×C8—31no—
401C5×C8C2×C4×D312yes—
402#168—31no—
403#168—31no—
404#168C2×C4×D312yes—
405C2×#41—151no—
406#131—31no—
407#131—151no—
408#131—152no—
409#131—152no—
410#131—151no—
411#131—151no—
412C2×M16—51no—
413C2×M16—152no—
414C22×C8—152no—
415C22×C8—151no—
416C4×Q8—301no—
417C4×Q8—301no—
418C4×D4—301no—
419C4×D4—302no—
420C4×D4—301no—
421C4×D4—302no—
422#117—51no—
423#117—152no—
424#117—152no—
425#117—151no—
426C2×C4⋊C4—51no—
427C2×C4⋊C4—152no—
428C2×C4⋊C4—152no—
429C2×C4⋊C4—151no—
430#107—52no—
431#107—151no—
432#107—151no—
433#107—152no—
434#106—52no—
435#106—151no—
436#106—152no—
437#106—152no—
438#106—151no—
439#106—152no—
440C2×C3×C5—21no—
441C2×C3×C5C22×C4⋊C411yescharacteristic
442D15—22no—
443C3×D5—21no—
444C3×D5#57711yescharacteristic
445C3×D5#57711yescharacteristic
446C5×D3—22no—
447C23×C3—51no—
448C22×D3—52no—
449C2×C3×C4—51no—
450C2×C3×C4—51no—
451C2×C3×C4—51no—
452C2×C3×C4—51no—
453C2×C3×C4—51no—
454C2×C3×C4—101no—
455C2×C3×C4—102no—
456C2×C3×C4—101no—
457C2×C3×C4—401no—
458C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
459#67—52no—
460#67—52no—
461#67—52no—
462#67C4⋊AGL(1,𝔽5)12yes—
463C2×Dic3—52no—
464C2×Dic3—101no—
465C2×Dic3—101no—
466C2×Dic3—102no—
467C2×Dic3—401no—
468D12—52no—
469D12—51no—
470D12C4⋊AGL(1,𝔽5)11yescharacteristic
471C4×D3—52no—
472C4×D3—52no—
473C4×D3—52no—
474C4×D3—402no—
475C4×D3—402no—
476C4×D3C22×AGL(1,𝔽5)12yes—
477Dic6—51no—
478Dic6—52no—
479Dic6C4⋊AGL(1,𝔽5)11yescharacteristic
480C3×C8—52no—
481C3×C8C22×AGL(1,𝔽5)12yes—
482C3⋊C8—51no—
483C3⋊C8—51no—
484C3⋊C8C22×AGL(1,𝔽5)11yescharacteristic
485C3⋊C8C22×AGL(1,𝔽5)11yescharacteristic
486C22×C5—32no—
487C22×C5D3×C4⋊C411yescharacteristic
488C2×D5—21no—
489C2×D5—21no—
490C2×D5—32no—
491C2×D5—62no—
492C2×D5—62no—
493C2×D5D3×C4⋊C411yescharacteristic
494C2×D5C2×D3×D411yescharacteristic
495AGL(1,𝔽5)—41no—
496AGL(1,𝔽5)—42no—
497AGL(1,𝔽5)—41no—
498AGL(1,𝔽5)—121no—
499AGL(1,𝔽5)—121no—
500AGL(1,𝔽5)—122no—
501C4×C5—32no—
502C4×C5D3×C4⋊C411yescharacteristic
503C4×C5C22×C4×D311yescharacteristic
504Dic5—32no—
505Dic5D3×C4⋊C411yescharacteristic
506Dic5C2×D3×Q811yescharacteristic
507#41—31no—
508#41—152no—
509#41—152no—
510#41—151no—
511#41—151no—
512#41—151no—
513C2×Q8—151no—
514C2×D4—151no—
515C2×D4—152no—
516C22×C4—51no—
517C22×C4—101no—
518C22×C4—152no—
519C22×C4—302no—
520C22×C4—302no—
521C22×C4—301no—
522M16—32no—
523M16—51no—
524M16—52no—
525M16—152no—
526M16—152no—
527M16—152no—
528M16D3×AGL(1,𝔽5)11yescharacteristic, complemented
529C2×C8—31no—
530C2×C8—32no—
531C2×C8—52no—
532C2×C8—152no—
533C2×C8—151no—
534C2×C8—151no—
535C2×C8—151no—
536C2×C8—151no—
537C2×C8—152no—
538C2×C8—151no—
539C2×C8—152no—
540C4⋊C4—51no—
541C4⋊C4—52no—
542C4⋊C4—51no—
543C4⋊C4—101no—
544C4⋊C4—152no—
545C4⋊C4—151no—
546C4⋊C4—151no—
547C4⋊C4—301no—
548C4⋊C4—302no—
549C4⋊C4—302no—
550C22⋊C4—101no—
551C22⋊C4—302no—
552C22⋊C4—302no—
553C22⋊C4—301no—
554C42—101no—
555C42—301no—
556C42—302no—
557C42—302no—
558C3×C5#291211yescharacteristic, complemented, Hall
559C22×C3—51no—
560C22×C3—51no—
561C22×C3—101no—
562C22×C3—101no—
563C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
564C2×D3—52no—
565C2×D3—102no—
566C2×D3—102no—
567C2×D3C2×C4⋊AGL(1,𝔽5)12yes—
568C3×C4—51no—
569C3×C4—51no—
570C3×C4—201no—
571C3×C4—202no—
572C3×C4—201no—
573C3×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
574C3×C4C23×AGL(1,𝔽5)11yescharacteristic
575Dic3—52no—
576Dic3—201no—
577Dic3—202no—
578Dic3—201no—
579Dic3C2×C4⋊AGL(1,𝔽5)12yes—
580C2×C5—21no—
581C2×C5—62no—
582C2×C5C2×D3×C4⋊C411yescharacteristic
583D5—21no—
584D5—62no—
585D5#577511yescharacteristic
586D5#577811yescharacteristic
587C23—51no—
588C23—152no—
589Q8—31no—
590Q8—152no—
591Q8—151no—
592D4—32no—
593D4—31no—
594D4—152no—
595D4—152no—
596D4—152no—
597D4—152no—
598D4—151no—
599C2×C4—32no—
600C2×C4—51no—
601C2×C4—51no—
602C2×C4—51no—
603C2×C4—51no—
604C2×C4—51no—
605C2×C4—101no—
606C2×C4—101no—
607C2×C4—102no—
608C2×C4—152no—
609C2×C4—152no—
610C2×C4—152no—
611C2×C4—152no—
612C2×C4—301no—
613C2×C4—301no—
614C2×C4—302no—
615C2×C4—401no—
616C2×C4—1202no—
617C2×C4—1202no—
618C2×C4—1201no—
619C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
620C8—31no—
621C8—31no—
622C8—52no—
623C8—151no—
624C8—151no—
625C8C2×D3×AGL(1,𝔽5)12yes—
626C2×C3—21no—
627C2×C3—51no—
628C2×C3—51no—
629C2×C3—101no—
630C2×C3C22×C4⋊AGL(1,𝔽5)11yescharacteristic
631D3—22no—
632D3—102no—
633C5#7920911yescharacteristic, complemented, Sylow
634C22—32no—
635C22—51no—
636C22—51no—
637C22—101no—
638C22—101no—
639C22—152no—
640C22—302no—
641C22—302no—
642C22D3×C4⋊AGL(1,𝔽5)11yescharacteristic
643C4—32no—
644C4—51no—
645C4—51no—
646C4—152no—
647C4—202no—
648C4—201no—
649C4—201no—
650C4—601no—
651C4—602no—
652C4—601no—
653C4D3×C4⋊AGL(1,𝔽5)11yescharacteristic
654C4C22×D3×AGL(1,𝔽5)11yescharacteristic
655C3#1061741611yescharacteristic, complemented, Sylow
656C2—21no—
657C2—51no—
658C2—51no—
659C2—62no—
660C2—101no—
661C2—302no—
662C2C2×D3×C4⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2C2×D3×C4⋊AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC3×C5×M16C2×C4
socleC2×C3×C5C22×C4⋊C4
prime radicalD5×#235C22
cosocleC3×C4×D5C24
hypercenterM16D3×AGL(1,𝔽5)
hypocenterC3×C5#2912
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ M16

Complements

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

NH ≅ G/Ntype
4. #11752386C2semidirect
5. C3×#65727C2semidirect
6. #11751726C2semidirect
7. C2×#91159C2semidirect
8. #11751658C2semidirect
9. #11751654C2semidirect
10. #11751653C2semidirect
11. D3×#3993C2semidirect
28. #91796C4semidirect
29. C5×#907C4semidirect
31. #91291C4semidirect
32. #91288C4semidirect
34. #91268C4semidirect
35. #91267C4semidirect
55. #65727D3semidirect
93. C3×C5×M16C2×C4semidirect
94. C2×C3⋊#168C2×C4semidirect
95. #6705C2×C4semidirect
96. C8×D15C2×C4semidirect
97. C2×C5×C3⋊C8C2×C4semidirect
98. C5×ΓL(1,𝔽25)C2×C4semidirect
99. C5×D3×C8C2×C4semidirect
100. C3×#681C2×C4semidirect
101. C3×#676C2×C4semidirect
103. #6651C2×C4semidirect
104. #6650C2×C4semidirect
105. #6648C2×C4semidirect
106. D3×#168C2×C4semidirect
107. D5×C3⋊C8C2×C4semidirect
108. D5×C3⋊C8C2×C4semidirect
210. #907AGL(1,𝔽5)semidirect
266. C5×M16C4×D3semidirect
270. #681C4×D3semidirect
275. #676C4×D3semidirect
332. C3×M16C2×AGL(1,𝔽5)semidirect
357. C2×C3⋊C8C2×AGL(1,𝔽5)semidirect
361. ΓL(1,𝔽25)C2×AGL(1,𝔽5)semidirect
365. D3×C8C2×AGL(1,𝔽5)semidirect
528. M16D3×AGL(1,𝔽5)semidirect
558. C3×C5#2912semidirect
633. C5#79209semidirect
655. C3#10617416semidirect

Maximal subgroups

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

subgroupindex
#117568382
#117568362
D5×#9072
#117523862
C3×#657272
#117517262
C2×#911592
#117516582
#117516542
#117516532
D3×#39932
#106174163
#792095