Finite Group Databasebeta

← #72230059

Subgroups — #72230059

Order 2880.

972 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×#67C211yesmaximal, characteristic
2C2×#10624098C211yesmaximal, characteristic, complemented
3C2×C3×#6763C211yesmaximal, characteristic, complemented
4#13085468C212yesmaximal, complemented
5#13085467C212yesmaximal, complemented
6D5⋊#834—31nomaximal
7D5⋊#806—31nomaximal
8C23×C32×D5C2211yescharacteristic
9C22×C3×D3×D5C411yescharacteristic, complemented
10C22×C3⋊ΓL(1,𝔽16)—21no—
11C22×C3×ΓL(1,𝔽16)—21no—
12C2×C3×#1220C411yescharacteristic, complemented
13C2×C3×C5×#67C411yescharacteristic, complemented
14C3×D5×#67—21no—
15C3×D5×#67—21no—
16C3×D5×#67—21no—
17C3×D5×#67—21no—
18C2×C3×#1202C2211yescharacteristic
19C2×C3×#1201C2211yescharacteristic
20C2×C3×D5×Dic3C411yescharacteristic, complemented
21#10624098—21no—
22#10624098C2212yescomplemented
23C3×#6763—21no—
24C3×#6763C2212yescomplemented
25C2×#63580—51nomaximal, Hall
26C2×C3×D4×D5—31no—
27C2×D5×#67D311yescharacteristic
28C2×#6763—31no—
29C2×#6763—31no—
30C2×#6763—61no—
31C2×#6763D311yescharacteristic, complemented
32C2×C3×C22⋊AGL(1,𝔽5)—31no—
33#91240—32no—
34#91228—32no—
35#91173—32no—
36#91172—32no—
37C23×C32×C5C2×C411yescharacteristic
38C22×C3×D15C2×C411yescharacteristic, complemented
39C22×C3×C5×D3C2×C411yescharacteristic, complemented
40C22×C32×D5—42no—
41C22×C32×D5C2×C411yescharacteristic
42C22×C32×D5D411yescharacteristic
43C22×C32×D5D411yescharacteristic
44C22×C32×D5D411yescharacteristic
45C22×C32×D5D411yescharacteristic
46C22×C32×D5C2311yescharacteristic
47C2×C3×D3×D5—21no—
48C2×C3×D3×D5—21no—
49C2×C3×D3×D5—42no—
50C2×C3⋊ΓL(1,𝔽16)—22no—
51C2×C3⋊ΓL(1,𝔽16)—42no—
52C2×C3×ΓL(1,𝔽16)—22no—
53C2×C3×ΓL(1,𝔽16)—42no—
54C3×#1220—21no—
55C3×#1220—21no—
56C2×C3×Dic15C2×C411yescharacteristic, complemented
57C3×C5×#67—21no—
58C3×C5×#67—21no—
59C2×C3×C5×Dic3C2×C411yescharacteristic, complemented
60C3×#1202—21no—
61C3×#1202—21no—
62C3×#1201—21no—
63C3×#1201—21no—
64C3×D5×Dic3—21no—
65C3×D5×Dic3—21no—
66D5⋊#99—91noHall
67C22×C3×#67—51no—
68C2×#3757—51no—
69C2×C3×#217—51no—
70#63580—52no—
71#63580—52no—
72C23×C3×D5—21no—
73C23×C3×D5—31no—
74C23×C3×D5C2×D311yescharacteristic
75C23×C3×D5C2×D311yescharacteristic
76C22×D3×D5Dic311yescharacteristic, complemented
77C22×ΓL(1,𝔽16)—21no—
78C22×ΓL(1,𝔽16)—61no—
79C22×ΓL(1,𝔽16)—61no—
80C22×ΓL(1,𝔽16)—61no—
81C22×ΓL(1,𝔽16)—61no—
82C22×C3×AGL(1,𝔽5)—61no—
83C2×C3×C5×D4—31no—
84C2×#1220Dic311yescharacteristic, complemented
85C2×C5×#67Dic311yescharacteristic, complemented
86C2×C3×C22⋊D5—31no—
87C2×C3×C22⋊D5—31no—
88C3×D4×D5—61no—
89C3×D4×D5—61no—
90C3×D4×D5—61no—
91C3×D4×D5—61no—
92C2×C3×D20—31no—
93C2×C3×C4×D5—31no—
94D5×#67—21no—
95D5×#67—21no—
96D5×#67—21no—
97D5×#67—21no—
98C2×#1202C2×D311yescharacteristic
99C2×#1201C2×D311yescharacteristic
100C2×D5×Dic3Dic311yescharacteristic, complemented
101#6763—21no—
102#6763—32no—
103#6763—32no—
104#6763—62no—
105#6763—61no—
106#6763—61no—
107#6763—61no—
108#6763—61no—
109#6763C2×D312yescomplemented
110C3×C22⋊AGL(1,𝔽5)—32no—
111C3×C22⋊AGL(1,𝔽5)—61no—
112C2×#834—151no—
113C2×#806—151no—
114C22×C32×C5—41no—
115C22×C32×C5C22⋊C411yescharacteristic
116C22×C32×C5C22⋊C411yescharacteristic
117C22×C32×C5C22×C411yescharacteristic
118C2×C3×D15—21no—
119C2×C3×D15—41no—
120C2×C3×C5×D3—21no—
121C2×C3×C5×D3—41no—
122C2×C32×D5—22no—
123C2×C32×D5—22no—
124C2×C32×D5—22no—
125C2×C32×D5—41no—
126C2×C32×D5—41no—
127C2×C32×D5—41no—
128C2×C32×D5C22⋊C411yescharacteristic
129C2×C32×D5C22⋊C411yescharacteristic
130C2×C32×D5C2×D411yescharacteristic
131C2×C32×D5C2×D411yescharacteristic
132C3×D3×D5—42no—
133C3×D3×D5—42no—
134C3⋊ΓL(1,𝔽16)—42no—
135C3×ΓL(1,𝔽16)—42no—
136C3×Dic15—21no—
137C3×C5×Dic3—21no—
138C2×D4×D5—31no—
139C2×C22⋊AGL(1,𝔽5)—31no—
140C2×C22⋊AGL(1,𝔽5)—91no—
141#4011—92no—
142#3999—92no—
143C24×C32—51no—
144C23×C3×D3—51no—
145C22×C3⋊Dic3—101no—
146C2×C3×#67—51no—
147C2×C3×#67—51no—
148C2×C3×#67—51no—
149C2×C3×#67—101no—
150C2×C3×#67—101no—
151C2×C3×#67—101no—
152C2×C3×#67—101no—
153C2×C3×#67AGL(1,𝔽5)11yescharacteristic, complemented
154C22×C3×Dic3—51no—
155C22×C3×Dic3—101no—
156#3757—52no—
157#3757—101no—
158C3×#217—52no—
159C3×#217—101no—
160C23×C3×C5—21no—
161C23×C3×C5—31no—
162C23×C3×C5C4×D311yescharacteristic
163C23×C3×C5C2×Dic311yescharacteristic
164C22×D15C2×Dic311yescharacteristic, complemented
165C22×C5×D3C2×Dic311yescharacteristic, complemented
166C22×C3×D5—21no—
167C22×C3×D5—21no—
168C22×C3×D5—21no—
169C22×C3×D5—21no—
170C22×C3×D5—21no—
171C22×C3×D5—21no—
172C22×C3×D5—31no—
173C22×C3×D5—42no—
174C22×C3×D5—42no—
175C22×C3×D5—42no—
176C22×C3×D5—42no—
177C22×C3×D5—61no—
178C22×C3×D5—61no—
179C22×C3×D5—122no—
180C22×C3×D5C4×D311yescharacteristic
181C22×C3×D5D1211yescharacteristic
182C22×C3×D5D1211yescharacteristic
183C22×C3×D5C2×Dic311yescharacteristic
184C22×C3×D5#6711yescharacteristic
185C22×C3×D5#6711yescharacteristic
186C22×C3×D5#6711yescharacteristic
187C22×C3×D5#6711yescharacteristic
188C22×C3×D5#6711yescharacteristic
189C22×C3×D5#6711yescharacteristic
190C22×C3×D5C22×D311yescharacteristic
191C22×C3×D5C22×D311yescharacteristic
192C2×D3×D5—21no—
193C2×D3×D5—21no—
194C2×D3×D5—42no—
195C2×ΓL(1,𝔽16)—22no—
196C2×ΓL(1,𝔽16)—42no—
197C2×ΓL(1,𝔽16)—62no—
198C2×ΓL(1,𝔽16)—62no—
199C2×ΓL(1,𝔽16)—62no—
200C2×ΓL(1,𝔽16)—62no—
201C2×ΓL(1,𝔽16)—122no—
202C2×ΓL(1,𝔽16)—122no—
203C2×ΓL(1,𝔽16)—122no—
204C2×ΓL(1,𝔽16)—122no—
205C2×C3×AGL(1,𝔽5)—62no—
206C2×C3×AGL(1,𝔽5)—122no—
207C3×C5×D4—61no—
208C3×C5×D4—61no—
209C2×C3×C4×C5—31no—
210#1220—21no—
211#1220—21no—
212C2×Dic15C2×Dic311yescharacteristic, complemented
213C5×#67—21no—
214C5×#67—21no—
215C2×C5×Dic3C2×Dic311yescharacteristic, complemented
216C3×C22⋊D5—61no—
217C3×C22⋊D5—61no—
218C3×C22⋊D5—61no—
219C3×C22⋊D5—61no—
220C2×C3×Dic5—31no—
221C3×D20—61no—
222C3×D20—61no—
223C3×C4×D5—61no—
224C3×C4×D5—61no—
225#1202—21no—
226#1202—21no—
227#1201—21no—
228#1201—21no—
229D5×Dic3—21no—
230D5×Dic3—21no—
231C22×C3×D4—151no—
232C22×#67—51no—
233C2×C3×C22⋊C4—151no—
234C2×#217—51no—
235C2×#217—151no—
236C2×#217—151no—
237C2×#217—301no—
238#834—152no—
239#834—152no—
240#806—152no—
241#806—152no—
242C2×C32×C5—21no—
243C2×C32×C5—21no—
244C2×C32×C5—21no—
245C2×C32×C5C2×C22⋊C411yescharacteristic
246C3×D15—41no—
247C3×C5×D3—41no—
248C32×D5—21no—
249C32×D5—21no—
250C32×D5—21no—
251C32×D5#9912yescomplemented
252C23×D5—31no—
253C23×D5D3211yescharacteristic
254C22×AGL(1,𝔽5)—61no—
255C22×AGL(1,𝔽5)—181no—
256C2×C5×D4—31no—
257C2×C22⋊D5—31no—
258C2×C22⋊D5—31no—
259D4×D5—61no—
260D4×D5—61no—
261D4×D5—61no—
262D4×D5—61no—
263C2×D20—31no—
264C2×C4×D5—31no—
265C22⋊AGL(1,𝔽5)—32no—
266C22⋊AGL(1,𝔽5)—61no—
267C22⋊AGL(1,𝔽5)—92no—
268C22⋊AGL(1,𝔽5)—181no—
269C23×C32—51no—
270C23×C32—51no—
271C23×C32—51no—
272C23×C32—51no—
273C23×C32—51no—
274C23×C32—51no—
275C23×C32—202no—
276C23×C32C2×AGL(1,𝔽5)11yescharacteristic
277C22×C3×D3—51no—
278C22×C3×D3—101no—
279C22×C3×D3—101no—
280C22×C3×D3—202no—
281C22×C3×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
282C2×C3⋊Dic3—102no—
283C2×C3⋊Dic3—202no—
284C3×#67—21no—
285C3×#67—21no—
286C3×#67—101no—
287C3×#67—101no—
288C3×#67—101no—
289C3×#67—101no—
290C3×#67—101no—
291C3×#67—101no—
292C2×C3×Dic3—51no—
293C2×C3×Dic3—101no—
294C2×C3×Dic3—101no—
295C2×C3×Dic3—102no—
296C2×C3×Dic3—202no—
297C2×C3×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
298C2×#99—451noSylow
299C22×C3×C5—21no—
300C22×C3×C5—21no—
301C22×C3×C5—21no—
302C22×C3×C5—41no—
303C22×C3×C5—41no—
304C22×C3×C5—41no—
305C22×C3×C5—41no—
306C22×C3×C5—61no—
307C22×C3×C5—121no—
308C22×C3×C5(C2×D3)⋊C411yescharacteristic
309C22×C3×C5(C2×D3)⋊C411yescharacteristic
310C22×C3×C5#21711yescharacteristic
311C22×C3×C5#21711yescharacteristic
312C22×C3×C5C2×C4×D311yescharacteristic
313C22×C3×C5C22×Dic311yescharacteristic
314C2×D15—21no—
315C2×D15—41no—
316C2×C5×D3—21no—
317C2×C5×D3—41no—
318C2×C3×D5—22no—
319C2×C3×D5—22no—
320C2×C3×D5—22no—
321C2×C3×D5—22no—
322C2×C3×D5—22no—
323C2×C3×D5—22no—
324C2×C3×D5—22no—
325C2×C3×D5—22no—
326C2×C3×D5—21no—
327C2×C3×D5—21no—
328C2×C3×D5—21no—
329C2×C3×D5—21no—
330C2×C3×D5—42no—
331C2×C3×D5—42no—
332C2×C3×D5—41no—
333C2×C3×D5—41no—
334C2×C3×D5—41no—
335C2×C3×D5—41no—
336C2×C3×D5—41no—
337C2×C3×D5—41no—
338C2×C3×D5—41no—
339C2×C3×D5—41no—
340C2×C3×D5—41no—
341C2×C3×D5—41no—
342C2×C3×D5—41no—
343C2×C3×D5—41no—
344C2×C3×D5—61no—
345C2×C3×D5—122no—
346C2×C3×D5—122no—
347C2×C3×D5—121no—
348C2×C3×D5(C2×D3)⋊C411yescharacteristic
349C2×C3×D5(C2×D3)⋊C411yescharacteristic
350C2×C3×D5#21711yescharacteristic
351C2×C3×D5#21711yescharacteristic
352C2×C3×D5C2×D1211yescharacteristic
353C2×C3×D5C2×#6711yescharacteristic
354C2×C3×D5C2×#6711yescharacteristic
355C2×C3×D5C2×#6711yescharacteristic
356D3×D5—42no—
357D3×D5—42no—
358ΓL(1,𝔽16)—42no—
359ΓL(1,𝔽16)—122no—
360ΓL(1,𝔽16)—122no—
361ΓL(1,𝔽16)—122no—
362ΓL(1,𝔽16)—122no—
363C3×AGL(1,𝔽5)—122no—
364C3×C4×C5—61no—
365Dic15—21no—
366C3×Dic5—61no—
367C5×Dic3—21no—
368C24×C3—51no—
369C24×C3—51no—
370C24×C3—101no—
371C24×C3—151no—
372C23×D3—51no—
373C2×C3×D4—31no—
374C2×C3×D4—151no—
375C2×C3×D4—151no—
376C2×C3×D4—151no—
377C2×C3×D4—301no—
378C2×C3×D4—301no—
379C2×C3×D4—301no—
380C2×C3×D4—301no—
381C22×C3×C4—151no—
382C22×C3×C4—301no—
383C2×#67—51no—
384C2×#67—51no—
385C2×#67—51no—
386C2×#67—101no—
387C2×#67—101no—
388C2×#67—101no—
389C2×#67—101no—
390C2×#67ΓL(1,𝔽16)11yescharacteristic, complemented
391C22×Dic3—51no—
392C22×Dic3—101no—
393C22×Dic3—301no—
394C22×Dic3—301no—
395C22×Dic3—301no—
396C22×Dic3—301no—
397C3×C22⋊C4—152no—
398C3×C22⋊C4—301no—
399#217—52no—
400#217—101no—
401#217—152no—
402#217—152no—
403#217—302no—
404#217—301no—
405#217—301no—
406#217—301no—
407#217—301no—
408C32×C5C2×#9911yescharacteristic, complemented, Hall
409C23×C5—31no—
410C23×C5D3×Dic311yescharacteristic
411C22×D5—31no—
412C22×D5—42no—
413C22×D5—61no—
414C22×D5—61no—
415C22×D5—122no—
416C22×D5D3×Dic311yescharacteristic
417C22×D5#62511yescharacteristic
418C22×D5#62511yescharacteristic
419C22×D5#62611yescharacteristic
420C22×D5#62611yescharacteristic
421C22×D5C2×D3211yescharacteristic
422C2×AGL(1,𝔽5)—62no—
423C2×AGL(1,𝔽5)—122no—
424C2×AGL(1,𝔽5)—182no—
425C2×AGL(1,𝔽5)—362no—
426C5×D4—61no—
427C5×D4—61no—
428C2×C4×C5—31no—
429C22⋊D5—61no—
430C22⋊D5—61no—
431C22⋊D5—61no—
432C22⋊D5—61no—
433C2×Dic5—31no—
434D20—61no—
435D20—61no—
436C4×D5—61no—
437C4×D5—61no—
438C22×C32—41no—
439C22×C32—51no—
440C22×C32—51no—
441C22×C32—51no—
442C22×C32—51no—
443C22×C32—102no—
444C22×C32—102no—
445C22×C32—102no—
446C22×C32—201no—
447C22×C32—201no—
448C22×C32—201no—
449C22×C32C22⋊AGL(1,𝔽5)11yescharacteristic
450C22×C32C22⋊AGL(1,𝔽5)11yescharacteristic
451C22×C32C22×AGL(1,𝔽5)11yescharacteristic
452C2×C3×D3—21no—
453C2×C3×D3—41no—
454C2×C3×D3—101no—
455C2×C3×D3—202no—
456C2×C3×D3—202no—
457C2×C3×D3—201no—
458C3⋊Dic3—202no—
459C3×Dic3—21no—
460C3×Dic3—101no—
461C3×Dic3—202no—
462C22×D4—151no—
463C2×C22⋊C4—151no—
464C2×C22⋊C4—451no—
465#99—452no—
466#99—452no—
467C2×C3×C5—21no—
468C2×C3×C5—21no—
469C2×C3×C5—21no—
470C2×C3×C5—21no—
471C2×C3×C5—21no—
472C2×C3×C5—21no—
473C2×C3×C5—21no—
474C2×C3×C5—21no—
475C2×C3×C5—21no—
476C2×C3×C5—41no—
477C2×C3×C5—41no—
478C2×C3×C5—121no—
479C2×C3×C5C2×(C2×D3)⋊C411yescharacteristic
480C2×C3×C5C2×#21711yescharacteristic
481D15—41no—
482C3×D5—21no—
483C3×D5—21no—
484C3×D5—21no—
485C3×D5—21no—
486C3×D5—21no—
487C3×D5—21no—
488C3×D5—21no—
489C3×D5—21no—
490C3×D5—22no—
491C3×D5—41no—
492C3×D5—41no—
493C3×D5—121no—
494C3×D5#80612yescomplemented
495C3×D5#83412yescomplemented
496C5×D3—41no—
497C23×C3—21no—
498C23×C3—31no—
499C23×C3—51no—
500C23×C3—51no—
501C23×C3—51no—
502C23×C3—51no—
503C23×C3—51no—
504C23×C3—51no—
505C23×C3—51no—
506C23×C3—51no—
507C23×C3—51no—
508C23×C3—51no—
509C23×C3—51no—
510C23×C3—51no—
511C23×C3—101no—
512C23×C3—101no—
513C23×C3—101no—
514C23×C3—101no—
515C23×C3—101no—
516C23×C3—101no—
517C23×C3—151no—
518C23×C3—202no—
519C23×C3—202no—
520C23×C3—202no—
521C23×C3—202no—
522C23×C3—301no—
523C23×C3—301no—
524C23×C3—602no—
525C23×C3D3×AGL(1,𝔽5)11yescharacteristic
526C23×C3C2×ΓL(1,𝔽16)11yescharacteristic
527C22×D3—51no—
528C22×D3—101no—
529C22×D3—101no—
530C22×D3—202no—
531C22×D3C2×ΓL(1,𝔽16)11yescharacteristic, complemented
532C3×D4—61no—
533C3×D4—61no—
534C3×D4—301no—
535C3×D4—301no—
536C3×D4—301no—
537C3×D4—301no—
538C3×D4—301no—
539C3×D4—301no—
540C2×C3×C4—31no—
541C2×C3×C4—151no—
542C2×C3×C4—301no—
543C2×C3×C4—301no—
544C2×C3×C4—302no—
545C2×C3×C4—602no—
546#67—21no—
547#67—21no—
548#67—101no—
549#67—101no—
550#67—101no—
551#67—101no—
552#67—101no—
553#67—101no—
554C2×Dic3—51no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—102no—
558C2×Dic3—202no—
559C2×Dic3—302no—
560C2×Dic3—302no—
561C2×Dic3—302no—
562C2×Dic3—302no—
563C2×Dic3—602no—
564C2×Dic3—602no—
565C2×Dic3—602no—
566C2×Dic3—602no—
567C2×Dic3C2×ΓL(1,𝔽16)11yescharacteristic, complemented
568C22×C5—41no—
569C22×C5—61no—
570C22×C5—121no—
571C22×C5(C2×D3)⋊Dic311yescharacteristic
572C22×C5(C2×D3)⋊Dic311yescharacteristic
573C22×C5C2×D3×Dic311yescharacteristic
574C2×D5—22no—
575C2×D5—22no—
576C2×D5—22no—
577C2×D5—41no—
578C2×D5—41no—
579C2×D5—41no—
580C2×D5—61no—
581C2×D5—122no—
582C2×D5—122no—
583C2×D5—121no—
584C2×D5(C2×D3)⋊Dic311yescharacteristic
585C2×D5(C2×D3)⋊Dic311yescharacteristic
586C2×D5C2×#62511yescharacteristic
587C2×D5C2×#62611yescharacteristic
588AGL(1,𝔽5)—122no—
589AGL(1,𝔽5)—362no—
590C4×C5—61no—
591Dic5—61no—
592C2×C32—21no—
593C2×C32—21no—
594C2×C32—21no—
595C2×C32—52no—
596C2×C32—101no—
597C2×C32—101no—
598C2×C32—101no—
599C2×C32C2×C22⋊AGL(1,𝔽5)11yescharacteristic
600C3×D3—41no—
601C3×D3—201no—
602C24—51no—
603C24—151no—
604C2×D4—31no—
605C2×D4—151no—
606C2×D4—151no—
607C2×D4—151no—
608C2×D4—301no—
609C2×D4—301no—
610C2×D4—301no—
611C2×D4—301no—
612C22×C4—151no—
613C22×C4—301no—
614C22×C4—901no—
615C22⋊C4—152no—
616C22⋊C4—301no—
617C22⋊C4—452no—
618C22⋊C4—901no—
619C3×C5—21no—
620C3×C5C2×#80611yescharacteristic, complemented
621C3×C5C2×#83411yescharacteristic, complemented
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—51no—
630C22×C3—51no—
631C22×C3—51no—
632C22×C3—51no—
633C22×C3—51no—
634C22×C3—51no—
635C22×C3—51no—
636C22×C3—51no—
637C22×C3—61no—
638C22×C3—101no—
639C22×C3—101no—
640C22×C3—101no—
641C22×C3—101no—
642C22×C3—102no—
643C22×C3—102no—
644C22×C3—102no—
645C22×C3—102no—
646C22×C3—102no—
647C22×C3—102no—
648C22×C3—102no—
649C22×C3—102no—
650C22×C3—121no—
651C22×C3—202no—
652C22×C3—202no—
653C22×C3—201no—
654C22×C3—201no—
655C22×C3—201no—
656C22×C3—201no—
657C22×C3—201no—
658C22×C3—201no—
659C22×C3—201no—
660C22×C3—201no—
661C22×C3—201no—
662C22×C3—201no—
663C22×C3—201no—
664C22×C3—201no—
665C22×C3—301no—
666C22×C3—601no—
667C22×C3—602no—
668C22×C3—602no—
669C22×C3(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
670C22×C3(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
671C22×C3#676311yescharacteristic
672C22×C3#676311yescharacteristic
673C22×C3C2×D3×AGL(1,𝔽5)11yescharacteristic
674C22×C3C22×ΓL(1,𝔽16)11yescharacteristic
675C2×D3—21no—
676C2×D3—41no—
677C2×D3—101no—
678C2×D3—202no—
679C2×D3—202no—
680C2×D3—201no—
681C3×C4—61no—
682C3×C4—301no—
683C3×C4—602no—
684Dic3—21no—
685Dic3—101no—
686Dic3—202no—
687Dic3—602no—
688Dic3—602no—
689Dic3—602no—
690Dic3—602no—
691C2×C5—21no—
692C2×C5—21no—
693C2×C5—21no—
694C2×C5—121no—
695C2×C5C2×(C2×D3)⋊Dic311yescharacteristic
696D5—21no—
697D5—21no—
698D5—21no—
699D5—121no—
700D5#6358012yescomplemented
701C32D5⋊#9911yescharacteristic, complemented, Sylow
702C23—31no—
703C23—51no—
704C23—51no—
705C23—51no—
706C23—51no—
707C23—51no—
708C23—51no—
709C23—151no—
710C23—202no—
711C23—301no—
712C23—301no—
713C23—602no—
714C23D3×ΓL(1,𝔽16)11yescharacteristic
715D4—61no—
716D4—61no—
717D4—301no—
718D4—301no—
719D4—301no—
720D4—301no—
721D4—301no—
722D4—301no—
723C2×C4—31no—
724C2×C4—151no—
725C2×C4—301no—
726C2×C4—301no—
727C2×C4—302no—
728C2×C4—602no—
729C2×C4—902no—
730C2×C4—1802no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—41no—
741C2×C3—41no—
742C2×C3—52no—
743C2×C3—52no—
744C2×C3—102no—
745C2×C3—101no—
746C2×C3—101no—
747C2×C3—101no—
748C2×C3—101no—
749C2×C3—101no—
750C2×C3—101no—
751C2×C3—101no—
752C2×C3—101no—
753C2×C3—121no—
754C2×C3—201no—
755C2×C3—201no—
756C2×C3—601no—
757C2×C3C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
758C2×C3C2×#676311yescharacteristic
759D3—41no—
760D3—201no—
761C5C2×#6358011yescharacteristic, complemented, Sylow
762C22—41no—
763C22—51no—
764C22—51no—
765C22—51no—
766C22—51no—
767C22—61no—
768C22—102no—
769C22—102no—
770C22—102no—
771C22—121no—
772C22—201no—
773C22—201no—
774C22—201no—
775C22—301no—
776C22—601no—
777C22—602no—
778C22—602no—
779C22(C2×D3)⋊ΓL(1,𝔽16)11yescharacteristic
780C22(C2×D3)⋊ΓL(1,𝔽16)11yescharacteristic
781C22C2×D3×ΓL(1,𝔽16)11yescharacteristic
782C4—61no—
783C4—301no—
784C4—602no—
785C4—1802no—
786C3—21no—
787C3D5⋊#80611yescharacteristic, complemented
788C3D5⋊#83411yescharacteristic, complemented
789C2—21no—
790C2—21no—
791C2—21no—
792C2—52no—
793C2—101no—
794C2—101no—
795C2—101no—
796C2—121no—
797C2—601no—
798C2C2×(C2×D3)⋊ΓL(1,𝔽16)11yescharacteristic
subgroupG/H
centerC2C2×(C2×D3)⋊ΓL(1,𝔽16)
commutatorC22×C32×C5C22×C4
FrattiniC22C2×D3×ΓL(1,𝔽16)
FittingC23×C32×C5C2×C4
socleC2×C32×C5C2×C22⋊C4
prime radicalC2×C3×D5×#67C2
cosocleC22×C32×D5C23
hypercenterC23D3×ΓL(1,𝔽16)
hypocenterC32×C5C2×#99
LCSG ▷ C22×C32×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×#10624098C2semidirect
3. C2×C3×#6763C2semidirect
4. #13085468C2semidirect
5. #13085467C2semidirect
9. C22×C3×D3×D5C4semidirect
12. C2×C3×#1220C4semidirect
13. C2×C3×C5×#67C4semidirect
20. C2×C3×D5×Dic3C4semidirect
22. #10624098C22semidirect
24. C3×#6763C22semidirect
31. C2×#6763D3semidirect
38. C22×C3×D15C2×C4semidirect
39. C22×C3×C5×D3C2×C4semidirect
56. C2×C3×Dic15C2×C4semidirect
59. C2×C3×C5×Dic3C2×C4semidirect
76. C22×D3×D5Dic3semidirect
84. C2×#1220Dic3semidirect
85. C2×C5×#67Dic3semidirect
100. C2×D5×Dic3Dic3semidirect
109. #6763C2×D3semidirect
153. C2×C3×#67AGL(1,𝔽5)semidirect
164. C22×D15C2×Dic3semidirect
165. C22×C5×D3C2×Dic3semidirect
212. C2×Dic15C2×Dic3semidirect
215. C2×C5×Dic3C2×Dic3semidirect
251. C32×D5#99semidirect
281. C22×C3×D3C2×AGL(1,𝔽5)semidirect
297. C2×C3×Dic3C2×AGL(1,𝔽5)semidirect
390. C2×#67ΓL(1,𝔽16)semidirect
408. C32×C5C2×#99semidirect
494. C3×D5#806semidirect
495. C3×D5#834semidirect
531. C22×D3C2×ΓL(1,𝔽16)semidirect
567. C2×Dic3C2×ΓL(1,𝔽16)semidirect
620. C3×C5C2×#806semidirect
621. C3×C5C2×#834semidirect
700. D5#63580semidirect
701. C32D5⋊#99semidirect
761. C5C2×#63580semidirect
787. C3D5⋊#806semidirect
788. C3D5⋊#834semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×#672
C2×#106240982
C2×C3×#67632
#130854682
#130854672
D5⋊#8343
D5⋊#8063
C2×#635805