Finite Group Databasebeta

← #14412612

Subgroups — #14412612

Order 1920.

1544 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#235C211yesmaximal, characteristic
2C2×#91989C211yesmaximal, characteristic, complemented
3C2×C3×D5⋊M16C211yesmaximal, characteristic, complemented
4#11751712C212yesmaximal, complemented
5#11751708C214yesmaximal, complemented
6#11751707C212yesmaximal, complemented
7#11751704C214yesmaximal, complemented
8#10617533—31nomaximal, Hall
9C2×#6817C411yescharacteristic, complemented
10C2×C5×#235C411yescharacteristic, complemented
11C22×C3×C4×D5C2211yescharacteristic
12C2×D5×#67—21no—
13C2×#6782—21no—
14D5×#235—21no—
15D5×#235—21no—
16D5×#235—21no—
17D5×#235—21no—
18D5×#235C412yescomplemented
19D5×#235C412yescomplemented
20D5×#235C2212yes—
21D5×#235C2212yes—
22C2×D5×D12C2211yescharacteristic
23C2×C4×D3×D5—21no—
24C2×#6773C411yescharacteristic, complemented
25C2×#6772C411yescharacteristic, complemented
26C2×#6771—21no—
27C2×D5×Dic6C2211yescharacteristic
28C2×#6763—21no—
29#91989—21no—
30#91989—21no—
31#91989C2212yes—
32#91989C2212yescomplemented
33C2×C4⋊ΓL(1,𝔽16)C2212yescomplemented
34C2×C4×ΓL(1,𝔽16)—21no—
35C2×C3×#704—21no—
36C3×D5⋊M16—21no—
37C3×D5⋊M16—21no—
38C3×D5⋊M16C2212yes—
39C3×D5⋊M16C2212yescomplemented
40C2×C3×#700—21no—
41C2×C3×D5⋊C8C2212yescomplemented
42#91154C2218yescomplemented
43#91152C2218yescomplemented
44#83768—51nomaximal, Hall
45C2×D5×#41—31no—
46C2×#4130—31no—
47C2×D5⋊M16D311yescharacteristic, complemented
48#65794—34no—
49#65793—34no—
50#65782—32no—
51#65767—32no—
52C23×C3×D5D411yescharacteristic
53C22×D3×D5—21no—
54C22×ΓL(1,𝔽16)—22no—
55C22×C3×C4×C5C2×C411yescharacteristic
56C2×#1220—21no—
57#6817—21no—
58#6817—21no—
59#6817C2×C412yes—
60#6817C2×C412yescomplemented
61C2×D60C2×C411yescharacteristic, complemented
62C2×C4×D15—21no—
63C2×Dic30C2×C411yescharacteristic, complemented
64C2×C5×#67—21no—
65C5×#235—21no—
66C5×#235—21no—
67C5×#235C2×C412yes—
68C5×#235C2×C412yescomplemented
69C2×C5×D12C2×C411yescharacteristic, complemented
70C2×C4×C5×D3—21no—
71C2×C5×Dic6C2×C411yescharacteristic, complemented
72C22×C3×Dic5D411yescharacteristic
73C2×C3×C4×D5C2×C411yescharacteristic
74C2×C3×C4×D5C2×C411yescharacteristic
75C2×C3×C4×D5C2×C411yescharacteristic
76C2×C3×C4×D5D411yescharacteristic
77C2×C3×C4×D5D411yescharacteristic
78C2×C3×C4×D5D411yescharacteristic
79C2×C3×C4×D5D411yescharacteristic
80C2×C3×C4×D5D411yescharacteristic
81C2×C3×C4×D5D411yescharacteristic
82C2×C3×C4×D5C2311yescharacteristic
83C2×C3×C4×D5C2311yescharacteristic
84C2×C3×C4×D5C2311yescharacteristic
85D5×#67—22no—
86D5×#67—22no—
87D5×#67—22no—
88D5×#67—22no—
89C2×#1204—21no—
90C2×#1203—21no—
91C2×#1202—21no—
92C2×#1201—21no—
93C2×#1200—21no—
94#6782—22no—
95#6782—22no—
96#6782—22no—
97#6782—22no—
98C2×D3×Dic5—21no—
99C2×D5×Dic3—21no—
100D5×D12—21no—
101D5×D12—21no—
102D5×D12C2×C412yescomplemented
103D5×D12C2312yes—
104C4×D3×D5—22no—
105C4×D3×D5—22no—
106C4×D3×D5—22no—
107C4×D3×D5—22no—
108#6773—21no—
109#6773—21no—
110#6773C2×C412yes—
111#6773C2×C412yescomplemented
112#6772—21no—
113#6772—21no—
114#6772C2×C412yes—
115#6772C2×C412yescomplemented
116#6771—22no—
117#6771—22no—
118#6771—22no—
119#6771—22no—
120D5×Dic6—21no—
121D5×Dic6—21no—
122D5×Dic6C2×C412yescomplemented
123D5×Dic6C2312yes—
124#6763—22no—
125#6763—22no—
126C4⋊ΓL(1,𝔽16)—22no—
127C4⋊ΓL(1,𝔽16)C2314yes—
128C4×ΓL(1,𝔽16)—22no—
129C4×ΓL(1,𝔽16)—22no—
130C3×#704—22no—
131C3×#704—22no—
132C2×C3×#170—22no—
133C3×#700—22no—
134C3×#700—22no—
135C3×D5⋊C8—22no—
136C3×D5⋊C8C2314yes—
137C22×#235—51no—
138C22×C3×M16—51no—
139C2×#926—51no—
140#5133—54no—
141#5131—52no—
142#5120—52no—
143#5113—54no—
144C2×C5×#41—31no—
145D5×#41—32no—
146D5×#41—32no—
147D5×#41—32no—
148D5×#41—32no—
149D5×#41—61no—
150D5×#41—61no—
151D5×#41—61no—
152D5×#41—61no—
153C2×#713—31no—
154C2×Q8×D5—31no—
155C2×#711—31no—
156C2×#711—61no—
157C2×D4×D5—31no—
158C2×D4×D5—61no—
159C2×#709—31no—
160C2×#709—61no—
161C22×C4×D5—61no—
162C22×C4×D5C2×D311yescharacteristic
163C2×C22⋊AGL(1,𝔽5)—61no—
164C2×#704—21no—
165#4130—32no—
166#4130—32no—
167#4130—61no—
168#4130—61no—
169C2×C4⋊AGL(1,𝔽5)—32no—
170C2×C4×AGL(1,𝔽5)—61no—
171D5⋊M16—21no—
172D5⋊M16—21no—
173D5⋊M16C2×D312yes—
174D5⋊M16C2×D312yescomplemented
175C2×#700—21no—
176C2×D5⋊C8C2×D312yescomplemented
177#4009—38no—
178#4007—38no—
179#2896—151noSylow
180C23×C3×C5C22⋊C411yescharacteristic
181C22×D15—21no—
182C22×C5×D3—21no—
183C22×C3×D5—42no—
184C22×C3×D5C22⋊C411yescharacteristic
185C22×C3×D5C22⋊C411yescharacteristic
186C22×C3×D5C22⋊C411yescharacteristic
187C22×C3×D5C2×D411yescharacteristic
188C22×C3×D5C2×D411yescharacteristic
189C22×C3×D5C2×D411yescharacteristic
190C2×D3×D5—22no—
191C2×D3×D5—22no—
192C2×D3×D5—44no—
193C2×ΓL(1,𝔽16)—24no—
194C2×ΓL(1,𝔽16)—44no—
195C2×C3×C4×C5C22⋊C411yescharacteristic
196C2×C3×C4×C5C22⋊C411yescharacteristic
197C2×C3×C4×C5C22⋊C411yescharacteristic
198C2×C3×C4×C5C22×C411yescharacteristic
199C2×C3×C4×C5C22×C411yescharacteristic
200C2×C3×C4×C5C22×C411yescharacteristic
201#1220—22no—
202#1220—22no—
203C2×Dic15—21no—
204D60—21no—
205D60C22×C412yes—
206C4×D15—22no—
207C4×D15—22no—
208Dic30—21no—
209Dic30C22×C412yes—
210C5×#67—22no—
211C5×#67—22no—
212C2×C5×Dic3—21no—
213C5×D12—21no—
214C5×D12C22×C412yes—
215C4×C5×D3—22no—
216C4×C5×D3—22no—
217C5×Dic6—21no—
218C5×Dic6C22×C412yes—
219C2×C3×Dic5C22⋊C411yescharacteristic
220C2×C3×Dic5C22⋊C411yescharacteristic
221C2×C3×Dic5C22⋊C411yescharacteristic
222C2×C3×Dic5C2×D411yescharacteristic
223C2×C3×Dic5C2×D411yescharacteristic
224C2×C3×Dic5C2×D411yescharacteristic
225C3×C4×D5C22⋊C411yescharacteristic
226C3×C4×D5C22⋊C411yescharacteristic
227C3×C4×D5C22⋊C411yescharacteristic
228C3×C4×D5C22⋊C411yescharacteristic
229C3×C4×D5C22⋊C411yescharacteristic
230C3×C4×D5C22⋊C411yescharacteristic
231C3×C4×D5C22×C411yescharacteristic
232C3×C4×D5C22×C411yescharacteristic
233C3×C4×D5C22×C411yescharacteristic
234C3×C4×D5C2×D411yescharacteristic
235C3×C4×D5C2×D411yescharacteristic
236C3×C4×D5C2×D411yescharacteristic
237C3×C4×D5C2×D411yescharacteristic
238C3×C4×D5C2×D411yescharacteristic
239C3×C4×D5C2×D411yescharacteristic
240C3×C4×D5C2411yescharacteristic
241#1204—22no—
242#1204—22no—
243#1203—22no—
244#1203—22no—
245#1202—22no—
246#1202—22no—
247#1201—22no—
248#1201—22no—
249#1200—22no—
250#1200—22no—
251D3×Dic5—22no—
252D3×Dic5—22no—
253D5×Dic3—22no—
254D5×Dic3—22no—
255C3×#170—24no—
256C23×C3×C4—51no—
257C22×#67—101no—
258C2×#235—51no—
259C2×#235—52no—
260C2×#235—52no—
261C2×#235—52no—
262C2×#235—52no—
263C2×#235—51no—
264C2×#235—51no—
265C2×#235—101no—
266C2×#235—101no—
267C2×#235—101no—
268C2×#235—101no—
269C2×#235—101no—
270C2×#235—101no—
271C2×#235AGL(1,𝔽5)11yescharacteristic, complemented
272C22×D12—51no—
273C22×C4×D3—101no—
274C22×Dic6—51no—
275C2×C3×M16—52no—
276C2×C3×M16—52no—
277C2×C3×M16—101no—
278C2×C3×M16—101no—
279C2×C3×M16—101no—
280C2×C3×M16—101no—
281C22×C3×C8—52no—
282C2×#217—101no—
283#926—52no—
284#926—52no—
285#926—101no—
286#926—101no—
287C2×C4⋊Dic3—52no—
288C2×C4×Dic3—101no—
289#821—58no—
290#816—58no—
291C23×D5—61no—
292C23×D5D1211yescharacteristic
293C22×AGL(1,𝔽5)—62no—
294C5×#41—32no—
295C5×#41—32no—
296C5×#41—61no—
297C5×#41—61no—
298C2×C5×Q8—31no—
299C2×C5×D4—31no—
300C2×C5×D4—61no—
301C22×C4×C5—61no—
302C22×C4×C5C4×D311yescharacteristic
303C2×C22⋊D5—61no—
304C2×C22⋊D5—61no—
305C2×C22⋊D5—61no—
306C22×Dic5—61no—
307C22×Dic5#6711yescharacteristic
308#713—32no—
309#713—32no—
310#713—61no—
311#713—61no—
312Q8×D5—32no—
313Q8×D5—32no—
314Q8×D5—61no—
315Q8×D5—61no—
316#711—32no—
317#711—32no—
318#711—62no—
319#711—62no—
320#711—62no—
321#711—62no—
322#711—61no—
323#711—61no—
324D4×D5—32no—
325D4×D5—32no—
326D4×D5—62no—
327D4×D5—62no—
328D4×D5—62no—
329D4×D5—62no—
330D4×D5—61no—
331D4×D5—61no—
332#709—32no—
333#709—32no—
334#709—61no—
335#709—61no—
336#709—62no—
337#709—62no—
338#709—62no—
339#709—62no—
340C2×D20—31no—
341C2×D20—61no—
342C2×C4×D5—61no—
343C2×C4×D5—61no—
344C2×C4×D5—61no—
345C2×C4×D5—62no—
346C2×C4×D5—62no—
347C2×C4×D5—62no—
348C2×C4×D5—62no—
349C2×C4×D5C4×D311yescharacteristic
350C2×C4×D5C4×D311yescharacteristic
351C2×C4×D5C4×D311yescharacteristic
352C2×C4×D5D1211yescharacteristic
353C2×C4×D5D1211yescharacteristic
354C2×C4×D5D1211yescharacteristic
355C2×C4×D5#6711yescharacteristic
356C2×C4×D5#6711yescharacteristic
357C2×C4×D5#6711yescharacteristic
358C2×C4×D5C22×D311yescharacteristic
359C2×C4×D5C22×D311yescharacteristic
360C2×C4×D5C22×D311yescharacteristic
361C2×Dic10—31no—
362C2×Dic10—61no—
363C22⋊AGL(1,𝔽5)—62no—
364C22⋊AGL(1,𝔽5)—62no—
365#704—22no—
366#704—22no—
367C2×#170—22no—
368C4⋊AGL(1,𝔽5)—34no—
369C4⋊AGL(1,𝔽5)—62no—
370C4×AGL(1,𝔽5)—62no—
371C4×AGL(1,𝔽5)—62no—
372#700—22no—
373#700—22no—
374D5⋊C8—22no—
375D5⋊C8C22×D314yes—
376C22×#41—151no—
377C22×M16—51no—
378C2×#117—151no—
379#419—152no—
380#418—152no—
381#417—154no—
382#416—154no—
383C22×C3×C5—41no—
384C22×C3×C5C2×C22⋊C411yescharacteristic
385C22×C3×C5C2×C22⋊C411yescharacteristic
386C22×C3×C5C2×C22⋊C411yescharacteristic
387C2×D15—22no—
388C2×D15—42no—
389C2×C5×D3—22no—
390C2×C5×D3—42no—
391C2×C3×D5—22no—
392C2×C3×D5—22no—
393C2×C3×D5—22no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C2×C3×D5C2×C22⋊C411yescharacteristic
398C2×C3×D5C2×C22⋊C411yescharacteristic
399C2×C3×D5C2×C22⋊C411yescharacteristic
400C2×C3×D5C22×D411yescharacteristic
401D3×D5—44no—
402D3×D5—44no—
403ΓL(1,𝔽16)—44no—
404C3×C4×C5C2×C22⋊C411yescharacteristic
405C3×C4×C5C2×C22⋊C411yescharacteristic
406C3×C4×C5C2×C22⋊C411yescharacteristic
407C3×C4×C5C23×C411yescharacteristic
408Dic15—22no—
409C3×Dic5C2×C22⋊C411yescharacteristic
410C3×Dic5C2×C22⋊C411yescharacteristic
411C3×Dic5C2×C22⋊C411yescharacteristic
412C3×Dic5C22×D411yescharacteristic
413C5×Dic3—22no—
414C24×C3—51no—
415C23×D3—101no—
416C22×C3×C4—51no—
417C22×C3×C4—51no—
418C22×C3×C4—51no—
419C22×C3×C4—51no—
420C22×C3×C4—51no—
421C22×C3×C4—51no—
422C22×C3×C4—51no—
423C22×C3×C4—51no—
424C22×C3×C4—51no—
425C22×C3×C4—51no—
426C22×C3×C4—51no—
427C22×C3×C4—51no—
428C22×C3×C4—51no—
429C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
430C2×#67—21no—
431C2×#67—101no—
432C2×#67—102no—
433C2×#67—102no—
434C2×#67—102no—
435C2×#67—102no—
436C2×#67—101no—
437C2×#67—101no—
438C22×Dic3—101no—
439C22×Dic3—102no—
440#235—21no—
441#235—21no—
442#235—52no—
443#235—52no—
444#235—52no—
445#235—52no—
446#235—52no—
447#235—52no—
448#235—101no—
449#235—101no—
450#235—102no—
451#235—102no—
452#235—102no—
453#235—102no—
454#235—101no—
455#235—101no—
456#235—102no—
457#235—102no—
458#235—102no—
459#235—102no—
460#235—101no—
461#235—101no—
462#235C2×AGL(1,𝔽5)12yes—
463#235C2×AGL(1,𝔽5)12yescomplemented
464C2×D12—51no—
465C2×D12—52no—
466C2×D12—52no—
467C2×D12—101no—
468C2×D12—101no—
469C2×D12—101no—
470C2×D12C2×AGL(1,𝔽5)11yescharacteristic, complemented
471C2×C4×D3—21no—
472C2×C4×D3—102no—
473C2×C4×D3—102no—
474C2×C4×D3—102no—
475C2×C4×D3—102no—
476C2×C4×D3—101no—
477C2×C4×D3—101no—
478C2×C4×D3—101no—
479C2×Dic6—51no—
480C2×Dic6—52no—
481C2×Dic6—52no—
482C2×Dic6—101no—
483C2×Dic6—101no—
484C2×Dic6—101no—
485C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic, complemented
486C3×M16—102no—
487C3×M16—102no—
488C3×M16—102no—
489C3×M16—102no—
490C2×C3×C8—54no—
491C2×C3×C8—102no—
492C2×C3×C8—102no—
493#217—102no—
494#217—102no—
495C4⋊Dic3—54no—
496C4⋊Dic3—102no—
497C4×Dic3—102no—
498C4×Dic3—102no—
499C23×C5—61no—
500C23×C5(C2×D3)⋊C411yescharacteristic
501C22×D5—42no—
502C22×D5—61no—
503C22×D5—62no—
504C22×D5—62no—
505C22×D5—124no—
506C22×D5(C2×D3)⋊C411yescharacteristic
507C22×D5(C2×D3)⋊C411yescharacteristic
508C22×D5(C2×D3)⋊C411yescharacteristic
509C22×D5C2×D1211yescharacteristic
510C22×D5C2×D1211yescharacteristic
511C22×D5C2×D1211yescharacteristic
512C2×AGL(1,𝔽5)—64no—
513C2×AGL(1,𝔽5)—124no—
514C5×Q8—32no—
515C5×Q8—61no—
516C5×D4—32no—
517C5×D4—62no—
518C5×D4—62no—
519C5×D4—61no—
520C2×C4×C5—61no—
521C2×C4×C5—62no—
522C2×C4×C5—62no—
523C2×C4×C5(C2×D3)⋊C411yescharacteristic
524C2×C4×C5(C2×D3)⋊C411yescharacteristic
525C2×C4×C5(C2×D3)⋊C411yescharacteristic
526C2×C4×C5C2×C4×D311yescharacteristic
527C2×C4×C5C2×C4×D311yescharacteristic
528C2×C4×C5C2×C4×D311yescharacteristic
529C22⋊D5—62no—
530C22⋊D5—62no—
531C22⋊D5—62no—
532C22⋊D5—62no—
533C22⋊D5—62no—
534C22⋊D5—62no—
535C2×Dic5—61no—
536C2×Dic5—62no—
537C2×Dic5—62no—
538C2×Dic5(C2×D3)⋊C411yescharacteristic
539C2×Dic5(C2×D3)⋊C411yescharacteristic
540C2×Dic5(C2×D3)⋊C411yescharacteristic
541C2×Dic5C2×#6711yescharacteristic
542C2×Dic5C2×#6711yescharacteristic
543C2×Dic5C2×#6711yescharacteristic
544D20—32no—
545D20—62no—
546D20—62no—
547D20—61no—
548C4×D5—62no—
549C4×D5—62no—
550C4×D5—62no—
551C4×D5—62no—
552C4×D5—62no—
553C4×D5—62no—
554C4×D5(C2×D3)⋊C411yescharacteristic
555C4×D5(C2×D3)⋊C411yescharacteristic
556C4×D5(C2×D3)⋊C411yescharacteristic
557C4×D5(C2×D3)⋊C411yescharacteristic
558C4×D5(C2×D3)⋊C411yescharacteristic
559C4×D5(C2×D3)⋊C411yescharacteristic
560C4×D5C2×C4×D311yescharacteristic
561C4×D5C2×C4×D311yescharacteristic
562C4×D5C2×C4×D311yescharacteristic
563C4×D5C2×D1211yescharacteristic
564C4×D5C2×D1211yescharacteristic
565C4×D5C2×D1211yescharacteristic
566C4×D5C2×#6711yescharacteristic
567C4×D5C2×#6711yescharacteristic
568C4×D5C2×#6711yescharacteristic
569C4×D5C23×D311yescharacteristic
570Dic10—32no—
571Dic10—61no—
572Dic10—62no—
573Dic10—62no—
574#170—24no—
575C2×#41—31no—
576C2×#41—151no—
577C2×#41—151no—
578C2×#41—152no—
579C2×#41—152no—
580C2×#41—152no—
581C2×#41—152no—
582C2×#41—151no—
583C2×#41—301no—
584C2×#41—301no—
585C2×#41—301no—
586C2×#41—301no—
587C2×#41—301no—
588C2×#41—301no—
589C22×Q8—151no—
590C22×D4—151no—
591C22×D4—301no—
592C23×C4—51no—
593C23×C4—301no—
594C2×M16—52no—
595C2×M16—52no—
596C2×M16—101no—
597C2×M16—101no—
598C2×M16—101no—
599C2×M16—101no—
600C22×C8—52no—
601#117—152no—
602#117—152no—
603#117—301no—
604#117—301no—
605C2×C4⋊C4—152no—
606C2×C22⋊C4—301no—
607C2×C42—301no—
608#103—158no—
609#102—158no—
610C2×C3×C5—21no—
611C2×C3×C5—21no—
612C2×C3×C5—21no—
613C2×C3×C5C22×C22⋊C411yescharacteristic
614D15—42no—
615C3×D5—21no—
616C3×D5—21no—
617C3×D5—21no—
618C3×D5#57512yes—
619C5×D3—42no—
620C23×C3—51no—
621C23×C3—51no—
622C23×C3—51no—
623C23×C3—51no—
624C23×C3—51no—
625C23×C3—51no—
626C23×C3—202no—
627C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
628C22×D3—21no—
629C22×D3—102no—
630C22×D3—102no—
631C22×D3—101no—
632C22×D3—204no—
633C2×C3×C4—51no—
634C2×C3×C4—51no—
635C2×C3×C4—51no—
636C2×C3×C4—51no—
637C2×C3×C4—51no—
638C2×C3×C4—51no—
639C2×C3×C4—51no—
640C2×C3×C4—51no—
641C2×C3×C4—51no—
642C2×C3×C4—51no—
643C2×C3×C4—51no—
644C2×C3×C4—51no—
645C2×C3×C4—51no—
646C2×C3×C4—51no—
647C2×C3×C4—51no—
648C2×C3×C4—51no—
649C2×C3×C4—51no—
650C2×C3×C4—51no—
651C2×C3×C4—51no—
652C2×C3×C4—51no—
653C2×C3×C4—51no—
654C2×C3×C4—51no—
655C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
656C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
657C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
658C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
659C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
660C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
661#67—22no—
662#67—22no—
663#67—102no—
664#67—102no—
665#67—102no—
666#67—102no—
667#67—102no—
668#67—102no—
669C2×Dic3—21no—
670C2×Dic3—102no—
671C2×Dic3—102no—
672C2×Dic3—101no—
673C2×Dic3—104no—
674C2×Dic3—204no—
675D12—21no—
676D12—52no—
677D12—102no—
678D12—102no—
679D12—101no—
680D12C22×AGL(1,𝔽5)12yes—
681C4×D3—22no—
682C4×D3—22no—
683C4×D3—102no—
684C4×D3—102no—
685C4×D3—102no—
686C4×D3—102no—
687C4×D3—102no—
688C4×D3—102no—
689Dic6—21no—
690Dic6—52no—
691Dic6—102no—
692Dic6—102no—
693Dic6—101no—
694Dic6C22×AGL(1,𝔽5)12yes—
695C3×C8—104no—
696C22×C5—41no—
697C22×C5—62no—
698C22×C5—122no—
699C22×C5C2×(C2×D3)⋊C411yescharacteristic
700C22×C5C2×(C2×D3)⋊C411yescharacteristic
701C22×C5C2×(C2×D3)⋊C411yescharacteristic
702C2×D5—22no—
703C2×D5—22no—
704C2×D5—22no—
705C2×D5—41no—
706C2×D5—41no—
707C2×D5—41no—
708C2×D5—62no—
709C2×D5—124no—
710C2×D5—122no—
711C2×D5—124no—
712C2×D5C2×(C2×D3)⋊C411yescharacteristic
713C2×D5C2×(C2×D3)⋊C411yescharacteristic
714C2×D5C2×(C2×D3)⋊C411yescharacteristic
715C2×D5C22×D1211yescharacteristic
716AGL(1,𝔽5)—124no—
717C4×C5—62no—
718C4×C5C2×(C2×D3)⋊C411yescharacteristic
719C4×C5C2×(C2×D3)⋊C411yescharacteristic
720C4×C5C2×(C2×D3)⋊C411yescharacteristic
721C4×C5C22×C4×D311yescharacteristic
722Dic5—62no—
723Dic5C2×(C2×D3)⋊C411yescharacteristic
724Dic5C2×(C2×D3)⋊C411yescharacteristic
725Dic5C2×(C2×D3)⋊C411yescharacteristic
726Dic5C22×#6711yescharacteristic
727C24—51no—
728C24—301no—
729#41—32no—
730#41—32no—
731#41—61no—
732#41—61no—
733#41—152no—
734#41—152no—
735#41—152no—
736#41—152no—
737#41—152no—
738#41—152no—
739#41—302no—
740#41—302no—
741#41—302no—
742#41—302no—
743#41—302no—
744#41—302no—
745#41—302no—
746#41—302no—
747#41—301no—
748#41—301no—
749#41—301no—
750#41—301no—
751#41—301no—
752#41—301no—
753C2×Q8—31no—
754C2×Q8—152no—
755C2×Q8—152no—
756C2×Q8—151no—
757C2×Q8—301no—
758C2×Q8—301no—
759C2×Q8—301no—
760C2×D4—31no—
761C2×D4—61no—
762C2×D4—152no—
763C2×D4—152no—
764C2×D4—151no—
765C2×D4—301no—
766C2×D4—301no—
767C2×D4—301no—
768C2×D4—301no—
769C2×D4—302no—
770C2×D4—302no—
771C2×D4—302no—
772C2×D4—302no—
773C2×D4—301no—
774C2×D4—301no—
775C22×C4—51no—
776C22×C4—51no—
777C22×C4—51no—
778C22×C4—51no—
779C22×C4—51no—
780C22×C4—51no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—51no—
785C22×C4—51no—
786C22×C4—51no—
787C22×C4—51no—
788C22×C4—61no—
789C22×C4—301no—
790C22×C4—302no—
791C22×C4—302no—
792C22×C4—302no—
793C22×C4—302no—
794C22×C4—301no—
795C22×C4—301no—
796C22×C4—301no—
797C22×C4—302no—
798C22×C4D3×AGL(1,𝔽5)11yescharacteristic
799M16—102no—
800M16—102no—
801M16—102no—
802M16—102no—
803C2×C8—54no—
804C2×C8—102no—
805C2×C8—102no—
806C4⋊C4—154no—
807C4⋊C4—302no—
808C22⋊C4—302no—
809C22⋊C4—302no—
810C42—302no—
811C42—302no—
812C3×C5#289611yescharacteristic, complemented, Hall
813C22×C3—41no—
814C22×C3—51no—
815C22×C3—51no—
816C22×C3—51no—
817C22×C3—51no—
818C22×C3—102no—
819C22×C3—102no—
820C22×C3—102no—
821C22×C3—201no—
822C22×C3—201no—
823C22×C3—201no—
824C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
825C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
826C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
827C2×D3—22no—
828C2×D3—42no—
829C2×D3—102no—
830C2×D3—204no—
831C2×D3—204no—
832C2×D3—202no—
833C3×C4—51no—
834C3×C4—51no—
835C3×C4—51no—
836C3×C4—51no—
837C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
838C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
839C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
840C3×C4C23×AGL(1,𝔽5)11yescharacteristic
841Dic3—22no—
842Dic3—102no—
843Dic3—204no—
844C2×C5—21no—
845C2×C5—21no—
846C2×C5—21no—
847C2×C5—122no—
848C2×C5C22×(C2×D3)⋊C411yescharacteristic
849D5—21no—
850D5—21no—
851D5—21no—
852D5—122no—
853D5#574812yes—
854C23—51no—
855C23—51no—
856C23—51no—
857C23—51no—
858C23—51no—
859C23—51no—
860C23—61no—
861C23—202no—
862C23—302no—
863C23—302no—
864C23—301no—
865C23—604no—
866C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
867Q8—32no—
868Q8—61no—
869Q8—152no—
870Q8—302no—
871Q8—302no—
872Q8—301no—
873D4—32no—
874D4—62no—
875D4—62no—
876D4—61no—
877D4—152no—
878D4—302no—
879D4—302no—
880D4—302no—
881D4—302no—
882D4—302no—
883D4—302no—
884D4—302no—
885D4—302no—
886D4—301no—
887C2×C4—51no—
888C2×C4—51no—
889C2×C4—51no—
890C2×C4—51no—
891C2×C4—51no—
892C2×C4—51no—
893C2×C4—51no—
894C2×C4—51no—
895C2×C4—51no—
896C2×C4—51no—
897C2×C4—51no—
898C2×C4—51no—
899C2×C4—51no—
900C2×C4—51no—
901C2×C4—51no—
902C2×C4—51no—
903C2×C4—51no—
904C2×C4—51no—
905C2×C4—51no—
906C2×C4—51no—
907C2×C4—51no—
908C2×C4—51no—
909C2×C4—61no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—302no—
913C2×C4—302no—
914C2×C4—302no—
915C2×C4—302no—
916C2×C4—302no—
917C2×C4—302no—
918C2×C4—301no—
919C2×C4—302no—
920C2×C4—302no—
921C2×C4—304no—
922C2×C4—604no—
923C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
924C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
925C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
926C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
927C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
928C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
929C8—104no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—52no—
934C2×C3—101no—
935C2×C3—101no—
936C2×C3—101no—
937C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
938D3—42no—
939D3—202no—
940C5#8376811yescharacteristic, complemented, Sylow
941C22—41no—
942C22—51no—
943C22—51no—
944C22—51no—
945C22—51no—
946C22—62no—
947C22—102no—
948C22—102no—
949C22—102no—
950C22—122no—
951C22—201no—
952C22—201no—
953C22—201no—
954C22—302no—
955C22—602no—
956C22—604no—
957C22—604no—
958C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
959C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
960C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
961C4—51no—
962C4—51no—
963C4—51no—
964C4—51no—
965C4—62no—
966C4—302no—
967C4—604no—
968C4C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
969C4C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
970C4C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
971C4C22×D3×AGL(1,𝔽5)11yescharacteristic
972C3#1061753311yescharacteristic, complemented, Sylow
973C2—21no—
974C2—21no—
975C2—21no—
976C2—52no—
977C2—101no—
978C2—101no—
979C2—101no—
980C2—122no—
981C2—602no—
982C2C22×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC4C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×D5×#235C2
cosocleC3×C4×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2896
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#91989C2semidirect
3. C2×C3×D5⋊M16C2semidirect
4. #11751712C2semidirect
5. #11751708C2semidirect
6. #11751707C2semidirect
7. #11751704C2semidirect
9. C2×#6817C4semidirect
10. C2×C5×#235C4semidirect
18. D5×#235C4semidirect
19. D5×#235C4semidirect
24. C2×#6773C4semidirect
25. C2×#6772C4semidirect
32. #91989C22semidirect
33. C2×C4⋊ΓL(1,𝔽16)C22semidirect
39. C3×D5⋊M16C22semidirect
41. C2×C3×D5⋊C8C22semidirect
42. #91154C22semidirect
43. #91152C22semidirect
47. C2×D5⋊M16D3semidirect
60. #6817C2×C4semidirect
61. C2×D60C2×C4semidirect
63. C2×Dic30C2×C4semidirect
68. C5×#235C2×C4semidirect
69. C2×C5×D12C2×C4semidirect
71. C2×C5×Dic6C2×C4semidirect
102. D5×D12C2×C4semidirect
111. #6773C2×C4semidirect
115. #6772C2×C4semidirect
122. D5×Dic6C2×C4semidirect
174. D5⋊M16C2×D3semidirect
176. C2×D5⋊C8C2×D3semidirect
271. C2×#235AGL(1,𝔽5)semidirect
463. #235C2×AGL(1,𝔽5)semidirect
470. C2×D12C2×AGL(1,𝔽5)semidirect
485. C2×Dic6C2×AGL(1,𝔽5)semidirect
812. C3×C5#2896semidirect
940. C5#83768semidirect
972. C3#10617533semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#2352
C2×#919892
C2×C3×D5⋊M162
#117517122
#117517082
#117517072
#117517042
#106175333
#837685