Finite Group Databasebeta

← #14322419

Subgroups — #14322419

Order 1920.

2320 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6777C211yesmaximal, characteristic
2C2×D3×#685C211yesmaximal, characteristic, complemented
3C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4#11750765C211yesmaximal, characteristic, complemented
5C5×#4665C211yesmaximal, characteristic, complemented
6C3×#64954C211yesmaximal, characteristic, complemented
7#11748940C211yesmaximal, characteristic, complemented
8#11748940C211yesmaximal, characteristic, complemented
9#11748911C211yesmaximal, characteristic, complemented
10#11748910C211yesmaximal, characteristic, complemented
11#11748906C211yesmaximal, characteristic, complemented
12#11748905C211yesmaximal, characteristic, complemented
13#11748901C211yesmaximal, characteristic, complemented
14#11748896C211yesmaximal, characteristic, complemented
15#11748606C211yesmaximal, characteristic, complemented
16#10606605—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C23×D3×D5C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C5×D12C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic, complemented
22C22×C3×D20C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic, complemented
24C22×#1201C2211yescharacteristic
25C22×#1201C2211yescharacteristic
26C22×D3×Dic5C2211yescharacteristic, complemented
27C22×D5×Dic3C2211yescharacteristic, complemented
28C2×#6777—24no—
29C2×#6777—24no—
30C2×#6777C418yescomplemented
31C2×#6714C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
34C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C2×C3×#685C2211yescharacteristic, complemented
37C2×C3×#685C2211yescharacteristic, complemented
38C2×C3×#685C2211yescharacteristic, complemented
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
42C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
43C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
44C2×#6665C2211yescharacteristic, complemented
45C2×#6665C2211yescharacteristic, complemented
46C2×#6665C2211yescharacteristic, complemented
47D3×#685—24no—
48D5×(C2×D3)⋊C4—24no—
49C3×C5×#95C2211yescharacteristic, complemented
50#91115C2211yescharacteristic, complemented
51#91115C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53C5×C3⋊#95C2211yescharacteristic, complemented
54C3×#3963C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57#74874—51nomaximal, Hall
58C22×D4×D5—31no—
59C22×#685—31no—
60C2×D5×C22⋊C4—31no—
61C5×#386—31no—
62#65509—31no—
63#65502—31no—
64#65247—31no—
65#65245—31no—
66#65245—31no—
67#65244—31no—
68#65244—31no—
69#64954—31no—
70#64954D311yescharacteristic, complemented
71#64953—31no—
72#64953—31no—
73C23×D15C2311yescharacteristic
74C23×C5×D3C2311yescharacteristic
75C23×C5×D3C2311yescharacteristic
76C23×C3×D5C2311yescharacteristic
77C23×C3×D5C2311yescharacteristic
78C22×D3×D5—22no—
79C22×D3×D5—22no—
80C22×D3×D5—41no—
81C22×D3×D5—41no—
82C22×D3×D5—41no—
83C22×D3×D5—41no—
84C22×D3×D5—41no—
85C22×D3×D5—41no—
86C22×D3×D5—41no—
87C22×D3×D5—41no—
88C22×D3×D5C2×C414yes—
89C22×D3×D5C2×C414yescomplemented
90C22×D3×D5D414yes—
91C22×D3×D5D414yes—
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2311yescharacteristic
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C2×C4×D15—22no—
99C2×C4×D15—22no—
100C2×C4×D15C2×C414yescomplemented
101C22×C5×Dic3C2311yescharacteristic
102C22×C5×Dic3C2311yescharacteristic
103C2×C5×D12—22no—
104C2×C5×D12—22no—
105C2×C5×D12C2×C414yescomplemented
106C2×C4×C5×D3—22no—
107C2×C4×C5×D3—41no—
108C2×C4×C5×D3—41no—
109C22×C3×Dic5C2311yescharacteristic
110C22×C3×Dic5C2311yescharacteristic
111C2×C3×D20—22no—
112C2×C3×D20—22no—
113C2×C3×D20C2×C414yescomplemented
114C2×C3×C4×D5—22no—
115C2×C3×C4×D5—41no—
116C2×C3×C4×D5—41no—
117C2×#1201—22no—
118C2×#1201—22no—
119C2×#1201—22no—
120C2×#1201—22no—
121C2×#1201C2×C414yescomplemented
122C2×#1201C2×C414yescomplemented
123C2×D3×Dic5—22no—
124C2×D3×Dic5—41no—
125C2×D3×Dic5—41no—
126C2×D5×Dic3—22no—
127C2×D5×Dic3—41no—
128C2×D5×Dic3—41no—
129#6777—232no—
130#6714—22no—
131#6714—22no—
132C5×(C2×D3)⋊C4—22no—
133C5×(C2×D3)⋊C4—41no—
134C5×(C2×D3)⋊C4—41no—
135C3×#685—22no—
136C3×#685—41no—
137C3×#685—41no—
138#6667—22no—
139#6667—22no—
140(C2×D3)⋊Dic5—22no—
141(C2×D3)⋊Dic5—41no—
142(C2×D3)⋊Dic5—41no—
143#6665—22no—
144#6665—41no—
145#6665—41no—
146C22×D3×D4—51no—
147C22×(C2×D3)⋊C4—51no—
148C2×D3×C22⋊C4—51no—
149C3×#386—51no—
150#5220—51no—
151#5213—51no—
152#4958—51no—
153#4956—51no—
154#4956—51no—
155#4955—51no—
156#4955—51no—
157#4665—51no—
158#4665D511yescharacteristic, complemented
159#4664—51no—
160#4664—51no—
161C24×D5—31no—
162C24×D5—31no—
163C22×C5×D4—31no—
164C23×C4×C5—31no—
165C22×C22⋊D5—31no—
166C22×C22⋊D5—31no—
167C23×Dic5—31no—
168C2×D4×D5—38no—
169C2×D4×D5—64no—
170C2×D4×D5—64no—
171C22×D20C2×D311yescharacteristic
172C22×C4×D5—31no—
173C22×C4×D5—31no—
174C22×C4×D5C2×D311yescharacteristic, complemented
175C2×C5×C22⋊C4—31no—
176C2×C5×C22⋊C4—31no—
177C2×C5×C22⋊C4—31no—
178C2×C22⋊Dic5—31no—
179C2×C22⋊Dic5—31no—
180C2×C22⋊Dic5—31no—
181C2×#685—31no—
182C2×#685—31no—
183C2×#685—31no—
184C2×#685—31no—
185C2×#685—31no—
186C2×#685—31no—
187C2×#685—31no—
188C2×#685—64no—
189C2×#685C2×D311yescharacteristic, complemented
190C2×#685C2×D311yescharacteristic, complemented
191C2×#685C2×D311yescharacteristic, complemented
192D5×C22⋊C4—64no—
193C5×#95—31no—
194C5×#95C2×D311yescharacteristic, complemented
195#3963—31no—
196#3963—31no—
197#3963—31no—
198#3963—31no—
199#3963—31no—
200#3963C2×D311yescharacteristic, complemented
201#2308—151noSylow
202C23×C3×C5C2411yescharacteristic
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—21no—
207C22×D15C22×C412yes—
208C22×D15C2×D412yes—
209C22×D15C2×D412yes—
210C22×C5×D3—21no—
211C22×C5×D3—21no—
212C22×C5×D3—21no—
213C22×C5×D3—21no—
214C22×C5×D3—21no—
215C22×C5×D3—21no—
216C22×C5×D3—21no—
217C22×C5×D3—21no—
218C22×C5×D3—21no—
219C22×C5×D3—21no—
220C22×C5×D3C22×C412yes—
221C22×C5×D3C22×C412yes—
222C22×C5×D3C2×D412yes—
223C22×C5×D3C2×D412yes—
224C22×C3×D5—21no—
225C22×C3×D5—21no—
226C22×C3×D5—21no—
227C22×C3×D5—21no—
228C22×C3×D5—21no—
229C22×C3×D5—21no—
230C22×C3×D5—21no—
231C22×C3×D5—21no—
232C22×C3×D5—21no—
233C22×C3×D5—21no—
234C22×C3×D5C22×C412yes—
235C22×C3×D5C22×C412yes—
236C22×C3×D5C2×D412yes—
237C22×C3×D5C2×D412yes—
238C2×D3×D5—28no—
239C2×D3×D5—44no—
240C2×D3×D5—44no—
241C2×D3×D5—44no—
242C2×D3×D5—44no—
243C2×D3×D5—44no—
244C2×D3×D5—44no—
245C2×D3×D5—44no—
246C2×D3×D5—44no—
247C2×D3×D5—44no—
248C2×D3×D5—44no—
249C2×D3×D5—44no—
250C2×D3×D5—44no—
251C2×D3×D5C22⋊C4116yescomplemented
252C2×C3×C4×C5—21no—
253C2×C3×C4×C5—21no—
254C2×C3×C4×C5—21no—
255C2×C3×C4×C5—21no—
256C2×C3×C4×C5—21no—
257C2×C3×C4×C5—21no—
258C2×C3×C4×C5—21no—
259C2×C3×C4×C5—21no—
260C2×C3×C4×C5C22×C412yes—
261C2×Dic15—21no—
262C2×Dic15—21no—
263C2×Dic15—21no—
264C2×Dic15—21no—
265C2×Dic15—21no—
266C2×Dic15—21no—
267C2×Dic15—21no—
268C2×Dic15—21no—
269C2×Dic15C22×C412yes—
270C4×D15—28no—
271C2×C5×Dic3—21no—
272C2×C5×Dic3—21no—
273C2×C5×Dic3—21no—
274C2×C5×Dic3—21no—
275C2×C5×Dic3—21no—
276C2×C5×Dic3—21no—
277C5×D12—28no—
278C4×C5×D3—44no—
279C2×C3×Dic5—21no—
280C2×C3×Dic5—21no—
281C2×C3×Dic5—21no—
282C2×C3×Dic5—21no—
283C2×C3×Dic5—21no—
284C2×C3×Dic5—21no—
285C3×D20—28no—
286C3×C4×D5—44no—
287#1201—28no—
288#1201—28no—
289D3×Dic5—44no—
290D5×Dic3—44no—
291C24×D3—51no—
292C24×D3—51no—
293C22×C3×D4—51no—
294C23×C3×C4—51no—
295C22×#67—51no—
296C22×#67—51no—
297C23×Dic3—51no—
298C2×D3×D4—58no—
299C2×D3×D4—104no—
300C2×D3×D4—104no—
301C22×D12C2×D511yescharacteristic
302C22×C4×D3—51no—
303C22×C4×D3—51no—
304C22×C4×D3C2×D511yescharacteristic, complemented
305C2×C3×C22⋊C4—51no—
306C2×C3×C22⋊C4—51no—
307C2×C3×C22⋊C4—51no—
308C2×#217—51no—
309C2×#217—51no—
310C2×#217—51no—
311C2×(C2×D3)⋊C4—51no—
312C2×(C2×D3)⋊C4—51no—
313C2×(C2×D3)⋊C4—51no—
314C2×(C2×D3)⋊C4—51no—
315C2×(C2×D3)⋊C4—51no—
316C2×(C2×D3)⋊C4—51no—
317C2×(C2×D3)⋊C4—51no—
318C2×(C2×D3)⋊C4—104no—
319C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
320C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
321C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
322D3×C22⋊C4—104no—
323C3×#95—51no—
324C3×#95C2×D511yescharacteristic, complemented
325C3⋊#95—51no—
326C3⋊#95—51no—
327C3⋊#95—51no—
328C3⋊#95—51no—
329C3⋊#95—51no—
330C3⋊#95C2×D511yescharacteristic, complemented
331C24×C5—31no—
332C24×C5—31no—
333C23×D5—31no—
334C23×D5—34no—
335C23×D5—34no—
336C23×D5—34no—
337C23×D5—34no—
338C23×D5—62no—
339C23×D5—62no—
340C23×D5—121no—
341C23×D5—121no—
342C23×D5—121no—
343C23×D5—121no—
344C23×D5—121no—
345C23×D5—121no—
346C23×D5—121no—
347C23×D5—121no—
348C23×D5C22×D311yescharacteristic
349C23×D5C22×D311yescharacteristic
350C2×C5×D4—34no—
351C2×C5×D4—62no—
352C2×C5×D4—62no—
353C22×C4×C5—31no—
354C22×C4×C5—31no—
355C22×C4×C5—62no—
356C22×C4×C5—121no—
357C22×C4×C5—121no—
358C22×C4×C5C22×D311yescharacteristic
359C22×C4×C5C22×D311yescharacteristic
360C22×C4×C5C22×D311yescharacteristic
361C2×C22⋊D5—34no—
362C2×C22⋊D5—34no—
363C2×C22⋊D5—62no—
364C2×C22⋊D5—62no—
365C2×C22⋊D5—62no—
366C2×C22⋊D5—62no—
367C22×Dic5—31no—
368C22×Dic5—31no—
369C22×Dic5—31no—
370C22×Dic5—62no—
371C22×Dic5—121no—
372C22×Dic5—121no—
373C22×Dic5C22×D311yescharacteristic
374C22×Dic5C22×D311yescharacteristic
375D4×D5—632no—
376C2×D20—22no—
377C2×D20—22no—
378C2×D20C4×D314yescomplemented
379C2×C4×D5—22no—
380C2×C4×D5—34no—
381C2×C4×D5—41no—
382C2×C4×D5—41no—
383C2×C4×D5—62no—
384C2×C4×D5—62no—
385C2×C4×D5—62no—
386C2×C4×D5—121no—
387C2×C4×D5—121no—
388C5×C22⋊C4—62no—
389C5×C22⋊C4—121no—
390C5×C22⋊C4—121no—
391C22⋊Dic5—62no—
392C22⋊Dic5—121no—
393C22⋊Dic5—121no—
394#685—22no—
395#685—41no—
396#685—41no—
397#685—62no—
398#685—62no—
399#685—62no—
400#685—62no—
401#685—62no—
402#685—121no—
403#685—121no—
404C23×D4—151no—
405C22×C22⋊C4—151no—
406C22×C22⋊C4—151no—
407#386—31no—
408#386—51no—
409#386—151no—
410#386—151no—
411#386—151no—
412#386—151no—
413#386—151no—
414#386—151no—
415#381—151no—
416#381—151no—
417#379—151no—
418#379—151no—
419C22×C3×C5C23×C411yescharacteristic
420C22×C3×C5C22×D411yescharacteristic
421C22×C3×C5C22×D411yescharacteristic
422C22×C3×C5H(5,𝔽2)11yescharacteristic
423C22×C3×C5H(5,𝔽2)11yescharacteristic
424C22×C3×C5H(5,𝔽2)11yescharacteristic
425C22×C3×C5H(5,𝔽2)11yescharacteristic
426C2×D15—22no—
427C2×D15—22no—
428C2×D15—22no—
429C2×D15—22no—
430C2×D15—22no—
431C2×D15—22no—
432C2×D15C2×C22⋊C414yes—
433C2×C5×D3—22no—
434C2×C5×D3—22no—
435C2×C5×D3—22no—
436C2×C5×D3—22no—
437C2×C5×D3—22no—
438C2×C5×D3—22no—
439C2×C5×D3—22no—
440C2×C5×D3—22no—
441C2×C5×D3—22no—
442C2×C5×D3—41no—
443C2×C5×D3—41no—
444C2×C5×D3—41no—
445C2×C5×D3—41no—
446C2×C5×D3C2×C22⋊C414yes—
447C2×C3×D5—22no—
448C2×C3×D5—22no—
449C2×C3×D5—22no—
450C2×C3×D5—22no—
451C2×C3×D5—22no—
452C2×C3×D5—22no—
453C2×C3×D5—22no—
454C2×C3×D5—22no—
455C2×C3×D5—22no—
456C2×C3×D5—41no—
457C2×C3×D5—41no—
458C2×C3×D5—41no—
459C2×C3×D5—41no—
460C2×C3×D5C2×C22⋊C414yes—
461D3×D5—416no—
462D3×D5—416no—
463C3×C4×C5—22no—
464C3×C4×C5—41no—
465C3×C4×C5—41no—
466Dic15—22no—
467Dic15—41no—
468Dic15—41no—
469C3×Dic5—41no—
470C3×Dic5—41no—
471C5×Dic3—41no—
472C5×Dic3—41no—
473C24×C3—51no—
474C24×C3—51no—
475C23×D3—51no—
476C23×D3—54no—
477C23×D3—54no—
478C23×D3—54no—
479C23×D3—54no—
480C23×D3—102no—
481C23×D3—102no—
482C23×D3—201no—
483C23×D3—201no—
484C23×D3—201no—
485C23×D3—201no—
486C23×D3—201no—
487C23×D3—201no—
488C23×D3—201no—
489C23×D3—201no—
490C23×D3C22×D511yescharacteristic
491C23×D3C22×D511yescharacteristic
492C2×C3×D4—54no—
493C2×C3×D4—102no—
494C2×C3×D4—102no—
495C22×C3×C4—51no—
496C22×C3×C4—51no—
497C22×C3×C4—102no—
498C22×C3×C4—201no—
499C22×C3×C4—201no—
500C22×C3×C4C22×D511yescharacteristic
501C22×C3×C4C22×D511yescharacteristic
502C22×C3×C4C22×D511yescharacteristic
503C2×#67—54no—
504C2×#67—54no—
505C2×#67—102no—
506C2×#67—102no—
507C2×#67—102no—
508C2×#67—102no—
509C22×Dic3—51no—
510C22×Dic3—51no—
511C22×Dic3—51no—
512C22×Dic3—102no—
513C22×Dic3—201no—
514C22×Dic3—201no—
515C22×Dic3C22×D511yescharacteristic
516C22×Dic3C22×D511yescharacteristic
517D3×D4—1032no—
518C2×D12—22no—
519C2×D12—22no—
520C2×D12C4×D514yescomplemented
521C2×C4×D3—22no—
522C2×C4×D3—41no—
523C2×C4×D3—41no—
524C2×C4×D3—54no—
525C2×C4×D3—102no—
526C2×C4×D3—102no—
527C2×C4×D3—102no—
528C2×C4×D3—201no—
529C2×C4×D3—201no—
530C3×C22⋊C4—102no—
531C3×C22⋊C4—201no—
532C3×C22⋊C4—201no—
533#217—102no—
534#217—201no—
535#217—201no—
536(C2×D3)⋊C4—22no—
537(C2×D3)⋊C4—41no—
538(C2×D3)⋊C4—41no—
539(C2×D3)⋊C4—102no—
540(C2×D3)⋊C4—102no—
541(C2×D3)⋊C4—102no—
542(C2×D3)⋊C4—102no—
543(C2×D3)⋊C4—102no—
544(C2×D3)⋊C4—201no—
545(C2×D3)⋊C4—201no—
546C23×C5—32no—
547C23×C5—32no—
548C23×C5—32no—
549C23×C5—32no—
550C23×C5—61no—
551C23×C5—61no—
552C23×C5—61no—
553C23×C5—61no—
554C23×C5—61no—
555C23×C5—61no—
556C23×C5—61no—
557C23×C5—61no—
558C23×C5—61no—
559C23×C5—61no—
560C23×C5C23×D311yescharacteristic
561C22×D5—21no—
562C22×D5—21no—
563C22×D5—21no—
564C22×D5—21no—
565C22×D5—21no—
566C22×D5—21no—
567C22×D5—21no—
568C22×D5—21no—
569C22×D5—21no—
570C22×D5—21no—
571C22×D5—32no—
572C22×D5—32no—
573C22×D5—32no—
574C22×D5—316no—
575C22×D5—68no—
576C22×D5—61no—
577C22×D5—61no—
578C22×D5—61no—
579C22×D5—61no—
580C22×D5—124no—
581C22×D5—124no—
582C22×D5—124no—
583C22×D5—124no—
584C22×D5—124no—
585C22×D5—124no—
586C22×D5—124no—
587C22×D5—124no—
588C22×D5—124no—
589C22×D5—124no—
590C22×D5—124no—
591C22×D5—124no—
592C22×D5C2×C4×D312yes—
593C22×D5C2×C4×D312yes—
594C22×D5D3×D412yes—
595C22×D5D3×D412yes—
596C5×D4—68no—
597C2×C4×C5—21no—
598C2×C4×C5—21no—
599C2×C4×C5—21no—
600C2×C4×C5—21no—
601C2×C4×C5—21no—
602C2×C4×C5—21no—
603C2×C4×C5—21no—
604C2×C4×C5—21no—
605C2×C4×C5—61no—
606C2×C4×C5—61no—
607C2×C4×C5—61no—
608C2×C4×C5—61no—
609C2×C4×C5—61no—
610C2×C4×C5—61no—
611C2×C4×C5—124no—
612C2×C4×C5C2×C4×D312yes—
613C22⋊D5—68no—
614C22⋊D5—68no—
615C2×Dic5—21no—
616C2×Dic5—21no—
617C2×Dic5—21no—
618C2×Dic5—21no—
619C2×Dic5—21no—
620C2×Dic5—21no—
621C2×Dic5—32no—
622C2×Dic5—61no—
623C2×Dic5—61no—
624C2×Dic5—61no—
625C2×Dic5—61no—
626C2×Dic5—61no—
627C2×Dic5—61no—
628C2×Dic5—61no—
629C2×Dic5—61no—
630C2×Dic5—124no—
631D20—28no—
632C4×D5—44no—
633C4×D5—68no—
634C4×D5—124no—
635C25—151no—
636C25—151no—
637C22×D4—31no—
638C22×D4—51no—
639C22×D4—158no—
640C22×D4—151no—
641C22×D4—151no—
642C22×D4—304no—
643C22×D4—304no—
644C23×C4—31no—
645C23×C4—51no—
646C23×C4—151no—
647C23×C4—151no—
648C23×C4—151no—
649C2×C22⋊C4—31no—
650C2×C22⋊C4—31no—
651C2×C22⋊C4—31no—
652C2×C22⋊C4—51no—
653C2×C22⋊C4—51no—
654C2×C22⋊C4—51no—
655C2×C22⋊C4—151no—
656C2×C22⋊C4—151no—
657C2×C22⋊C4—151no—
658C2×C22⋊C4—151no—
659C2×C22⋊C4—151no—
660C2×C22⋊C4—151no—
661C2×C22⋊C4—151no—
662C2×C22⋊C4—151no—
663C2×C22⋊C4—151no—
664C2×C22⋊C4—151no—
665C2×C22⋊C4—304no—
666C2×C22⋊C4—304no—
667#95—31no—
668#95—51no—
669#95—151no—
670#95—151no—
671#95—151no—
672#95—151no—
673#95—151no—
674#95D3×D511yescharacteristic, complemented
675C2×C3×C5C22×C22⋊C411yescharacteristic
676C2×C3×C5#51811yescharacteristic
677C2×C3×C5#51811yescharacteristic
678C2×C3×C5#53411yescharacteristic
679C2×C3×C5#53411yescharacteristic
680C2×C3×C5#53411yescharacteristic
681C2×C3×C5#53411yescharacteristic
682D15—24no—
683C3×D5—24no—
684C3×D5—42no—
685C5×D3—24no—
686C5×D3—42no—
687C23×C3—52no—
688C23×C3—52no—
689C23×C3—52no—
690C23×C3—52no—
691C23×C3—101no—
692C23×C3—101no—
693C23×C3—101no—
694C23×C3—101no—
695C23×C3—101no—
696C23×C3—101no—
697C23×C3—101no—
698C23×C3—101no—
699C23×C3—101no—
700C23×C3—101no—
701C23×C3C23×D511yescharacteristic
702C22×D3—21no—
703C22×D3—21no—
704C22×D3—21no—
705C22×D3—21no—
706C22×D3—21no—
707C22×D3—21no—
708C22×D3—21no—
709C22×D3—21no—
710C22×D3—21no—
711C22×D3—21no—
712C22×D3—52no—
713C22×D3—52no—
714C22×D3—52no—
715C22×D3—516no—
716C22×D3—108no—
717C22×D3—101no—
718C22×D3—101no—
719C22×D3—101no—
720C22×D3—101no—
721C22×D3—204no—
722C22×D3—204no—
723C22×D3—204no—
724C22×D3—204no—
725C22×D3—204no—
726C22×D3—204no—
727C22×D3—204no—
728C22×D3—204no—
729C22×D3—204no—
730C22×D3—204no—
731C22×D3—204no—
732C22×D3—204no—
733C22×D3C2×C4×D512yes—
734C22×D3C2×C4×D512yes—
735C22×D3D4×D512yes—
736C22×D3D4×D512yes—
737C3×D4—108no—
738C2×C3×C4—21no—
739C2×C3×C4—21no—
740C2×C3×C4—21no—
741C2×C3×C4—21no—
742C2×C3×C4—21no—
743C2×C3×C4—21no—
744C2×C3×C4—21no—
745C2×C3×C4—21no—
746C2×C3×C4—101no—
747C2×C3×C4—101no—
748C2×C3×C4—101no—
749C2×C3×C4—101no—
750C2×C3×C4—101no—
751C2×C3×C4—101no—
752C2×C3×C4—204no—
753C2×C3×C4C2×C4×D512yes—
754#67—108no—
755#67—108no—
756C2×Dic3—21no—
757C2×Dic3—21no—
758C2×Dic3—21no—
759C2×Dic3—21no—
760C2×Dic3—21no—
761C2×Dic3—21no—
762C2×Dic3—52no—
763C2×Dic3—101no—
764C2×Dic3—101no—
765C2×Dic3—101no—
766C2×Dic3—101no—
767C2×Dic3—101no—
768C2×Dic3—101no—
769C2×Dic3—101no—
770C2×Dic3—101no—
771C2×Dic3—204no—
772D12—28no—
773C4×D3—44no—
774C4×D3—108no—
775C4×D3—204no—
776C22×C5—34no—
777C22×C5—62no—
778C22×C5—62no—
779C22×C5—62no—
780C22×C5—62no—
781C22×C5—62no—
782C22×C5—62no—
783C22×C5—62no—
784C22×C5—62no—
785C22×C5—62no—
786C22×C5—121no—
787C22×C5—121no—
788C22×C5—121no—
789C22×C5—121no—
790C22×C5C22×C4×D311yescharacteristic
791C22×C5C2×D3×D411yescharacteristic
792C22×C5C2×D3×D411yescharacteristic
793C22×C5#100411yescharacteristic
794C22×C5#100411yescharacteristic
795C22×C5#100911yescharacteristic
796C22×C5#100911yescharacteristic
797C2×D5—22no—
798C2×D5—22no—
799C2×D5—22no—
800C2×D5—22no—
801C2×D5—22no—
802C2×D5—22no—
803C2×D5—22no—
804C2×D5—22no—
805C2×D5—22no—
806C2×D5—34no—
807C2×D5—41no—
808C2×D5—41no—
809C2×D5—41no—
810C2×D5—41no—
811C2×D5—62no—
812C2×D5—62no—
813C2×D5—62no—
814C2×D5—62no—
815C2×D5—62no—
816C2×D5—62no—
817C2×D5—1216no—
818C2×D5—1216no—
819C2×D5D3×C22⋊C414yes—
820C4×C5—22no—
821C4×C5—41no—
822C4×C5—41no—
823C4×C5—121no—
824C4×C5—121no—
825Dic5—41no—
826Dic5—41no—
827Dic5—62no—
828Dic5—121no—
829Dic5—121no—
830C24—31no—
831C24—31no—
832C24—51no—
833C24—51no—
834C24—154no—
835C24—154no—
836C24—154no—
837C24—154no—
838C24—151no—
839C24—302no—
840C24—302no—
841C24—601no—
842C24—601no—
843C24—601no—
844C24—601no—
845C24—601no—
846C24—601no—
847C24—601no—
848C24—601no—
849C2×D4—34no—
850C2×D4—54no—
851C2×D4—62no—
852C2×D4—62no—
853C2×D4—102no—
854C2×D4—102no—
855C2×D4—154no—
856C2×D4—154no—
857C2×D4—3032no—
858C2×D4—302no—
859C2×D4—302no—
860C2×D4—302no—
861C2×D4—302no—
862C22×C4—31no—
863C22×C4—31no—
864C22×C4—51no—
865C22×C4—51no—
866C22×C4—62no—
867C22×C4—102no—
868C22×C4—121no—
869C22×C4—121no—
870C22×C4—151no—
871C22×C4—154no—
872C22×C4—151no—
873C22×C4—151no—
874C22×C4—201no—
875C22×C4—201no—
876C22×C4—302no—
877C22×C4—302no—
878C22×C4—302no—
879C22×C4—302no—
880C22×C4—601no—
881C22×C4—601no—
882C22×C4—601no—
883C22×C4—601no—
884C22×C4C2×D3×D511yescharacteristic
885C22×C4C2×D3×D511yescharacteristic
886C22×C4C2×D3×D511yescharacteristic
887C22⋊C4—62no—
888C22⋊C4—102no—
889C22⋊C4—121no—
890C22⋊C4—121no—
891C22⋊C4—201no—
892C22⋊C4—201no—
893C22⋊C4—302no—
894C22⋊C4—302no—
895C22⋊C4—302no—
896C22⋊C4—302no—
897C22⋊C4—302no—
898C22⋊C4—302no—
899C22⋊C4—601no—
900C22⋊C4—601no—
901C22⋊C4—601no—
902C22⋊C4—601no—
903C3×C5#230811yescharacteristic, complemented, Hall
904C22×C3—54no—
905C22×C3—102no—
906C22×C3—102no—
907C22×C3—102no—
908C22×C3—102no—
909C22×C3—102no—
910C22×C3—102no—
911C22×C3—102no—
912C22×C3—102no—
913C22×C3—102no—
914C22×C3—201no—
915C22×C3—201no—
916C22×C3—201no—
917C22×C3—201no—
918C22×C3C22×C4×D511yescharacteristic
919C22×C3C2×D4×D511yescharacteristic
920C22×C3C2×D4×D511yescharacteristic
921C22×C3#414411yescharacteristic
922C22×C3#414411yescharacteristic
923C22×C3#414911yescharacteristic
924C22×C3#414911yescharacteristic
925C2×D3—22no—
926C2×D3—22no—
927C2×D3—22no—
928C2×D3—22no—
929C2×D3—22no—
930C2×D3—22no—
931C2×D3—22no—
932C2×D3—22no—
933C2×D3—22no—
934C2×D3—41no—
935C2×D3—41no—
936C2×D3—41no—
937C2×D3—41no—
938C2×D3—54no—
939C2×D3—102no—
940C2×D3—102no—
941C2×D3—102no—
942C2×D3—102no—
943C2×D3—102no—
944C2×D3—102no—
945C2×D3—2016no—
946C2×D3—2016no—
947C2×D3D5×C22⋊C414yes—
948C3×C4—22no—
949C3×C4—41no—
950C3×C4—41no—
951C3×C4—201no—
952C3×C4—201no—
953Dic3—41no—
954Dic3—41no—
955Dic3—102no—
956Dic3—201no—
957Dic3—201no—
958C2×C5—64no—
959C2×C5—122no—
960C2×C5C2×D3×C22⋊C411yescharacteristic
961C2×C5#554511yescharacteristic
962C2×C5#554511yescharacteristic
963C2×C5#558911yescharacteristic
964C2×C5#560511yescharacteristic
965C2×C5#560511yescharacteristic
966C2×C5#565311yescharacteristic
967D5—24no—
968D5—42no—
969D5—64no—
970C23—32no—
971C23—32no—
972C23—32no—
973C23—32no—
974C23—52no—
975C23—52no—
976C23—52no—
977C23—52no—
978C23—61no—
979C23—61no—
980C23—61no—
981C23—61no—
982C23—61no—
983C23—61no—
984C23—61no—
985C23—61no—
986C23—61no—
987C23—61no—
988C23—101no—
989C23—101no—
990C23—101no—
991C23—101no—
992C23—101no—
993C23—101no—
994C23—101no—
995C23—101no—
996C23—101no—
997C23—101no—
998C23—1516no—
999C23—152no—
1000C23—152no—
1001C23—152no—
1002C23—308no—
1003C23—301no—
1004C23—301no—
1005C23—301no—
1006C23—301no—
1007C23—604no—
1008C23—604no—
1009C23—604no—
1010C23—604no—
1011C23—604no—
1012C23—604no—
1013C23—604no—
1014C23—604no—
1015C23—604no—
1016C23—604no—
1017C23—604no—
1018C23—604no—
1019C23C22×D3×D511yescharacteristic
1020D4—68no—
1021D4—108no—
1022D4—308no—
1023D4—308no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—61no—
1033C2×C4—61no—
1034C2×C4—61no—
1035C2×C4—61no—
1036C2×C4—61no—
1037C2×C4—61no—
1038C2×C4—101no—
1039C2×C4—101no—
1040C2×C4—101no—
1041C2×C4—101no—
1042C2×C4—101no—
1043C2×C4—101no—
1044C2×C4—124no—
1045C2×C4—152no—
1046C2×C4—204no—
1047C2×C4—308no—
1048C2×C4—301no—
1049C2×C4—301no—
1050C2×C4—301no—
1051C2×C4—301no—
1052C2×C4—301no—
1053C2×C4—301no—
1054C2×C4—301no—
1055C2×C4—301no—
1056C2×C4—604no—
1057C2×C4—604no—
1058C2×C4C4×D3×D512yes—
1059C2×C3—104no—
1060C2×C3—202no—
1061C2×C3C2×D5×C22⋊C411yescharacteristic
1062C2×C3#6587911yescharacteristic
1063C2×C3#6587911yescharacteristic
1064C2×C3#6592311yescharacteristic
1065C2×C3#6593911yescharacteristic
1066C2×C3#6593911yescharacteristic
1067C2×C3#6598711yescharacteristic
1068D3—24no—
1069D3—42no—
1070D3—104no—
1071C5#7487411yescharacteristic, complemented, Sylow
1072C22—34no—
1073C22—54no—
1074C22—62no—
1075C22—62no—
1076C22—62no—
1077C22—62no—
1078C22—62no—
1079C22—62no—
1080C22—62no—
1081C22—62no—
1082C22—62no—
1083C22—102no—
1084C22—102no—
1085C22—102no—
1086C22—102no—
1087C22—102no—
1088C22—102no—
1089C22—102no—
1090C22—102no—
1091C22—102no—
1092C22—121no—
1093C22—121no—
1094C22—121no—
1095C22—121no—
1096C22—154no—
1097C22—201no—
1098C22—201no—
1099C22—201no—
1100C22—201no—
1101C22—302no—
1102C22—302no—
1103C22—302no—
1104C22—302no—
1105C22—302no—
1106C22—302no—
1107C22—6016no—
1108C22—6016no—
1109C22C2×C4×D3×D511yescharacteristic
1110C22#9201711yescharacteristic
1111C22#9201811yescharacteristic
1112C22D3×D4×D511yescharacteristic
1113C22D3×D4×D511yescharacteristic
1114C22#9202511yescharacteristic
1115C22#9203511yescharacteristic
1116C4—22no—
1117C4—41no—
1118C4—41no—
1119C4—121no—
1120C4—121no—
1121C4—201no—
1122C4—201no—
1123C4—302no—
1124C4—601no—
1125C4—601no—
1126C3#1060660511yescharacteristic, complemented, Sylow
1127C2—64no—
1128C2—104no—
1129C2—122no—
1130C2—202no—
1131C2—304no—
1132C2#1175272911yescharacteristic
1133C2D3×D5×C22⋊C411yescharacteristic
1134C2#1175321311yescharacteristic
1135C2#1175321711yescharacteristic
1136C2#1175384111yescharacteristic
1137C2#1175384711yescharacteristic
1138C2#1175384911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#6777C2
hypercenter#95D3×D5
hypocenterC3×C5#2308
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×D3×#685C2semidirect
3. C2×D5×(C2×D3)⋊C4C2semidirect
4. #11750765C2semidirect
5. C5×#4665C2semidirect
6. C3×#64954C2semidirect
7. #11748940C2semidirect
8. #11748940C2semidirect
9. #11748911C2semidirect
10. #11748910C2semidirect
11. #11748906C2semidirect
12. #11748905C2semidirect
13. #11748901C2semidirect
14. #11748896C2semidirect
15. #11748606C2semidirect
21. C22×C4×C5×D3C22semidirect
23. C22×C3×C4×D5C22semidirect
26. C22×D3×Dic5C22semidirect
27. C22×D5×Dic3C22semidirect
30. C2×#6777C4semidirect
33. C2×C5×(C2×D3)⋊C4C22semidirect
34. C2×C5×(C2×D3)⋊C4C22semidirect
35. C2×C5×(C2×D3)⋊C4C22semidirect
36. C2×C3×#685C22semidirect
37. C2×C3×#685C22semidirect
38. C2×C3×#685C22semidirect
41. C2×(C2×D3)⋊Dic5C22semidirect
42. C2×(C2×D3)⋊Dic5C22semidirect
43. C2×(C2×D3)⋊Dic5C22semidirect
44. C2×#6665C22semidirect
45. C2×#6665C22semidirect
46. C2×#6665C22semidirect
49. C3×C5×#95C22semidirect
50. #91115C22semidirect
51. #91115C22semidirect
52. #91115C22semidirect
53. C5×C3⋊#95C22semidirect
54. C3×#3963C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
70. #64954D3semidirect
89. C22×D3×D5C2×C4semidirect
100. C2×C4×D15C2×C4semidirect
105. C2×C5×D12C2×C4semidirect
113. C2×C3×D20C2×C4semidirect
121. C2×#1201C2×C4semidirect
122. C2×#1201C2×C4semidirect
158. #4665D5semidirect
174. C22×C4×D5C2×D3semidirect
189. C2×#685C2×D3semidirect
190. C2×#685C2×D3semidirect
191. C2×#685C2×D3semidirect
194. C5×#95C2×D3semidirect
200. #3963C2×D3semidirect
251. C2×D3×D5C22⋊C4semidirect
304. C22×C4×D3C2×D5semidirect
319. C2×(C2×D3)⋊C4C2×D5semidirect
320. C2×(C2×D3)⋊C4C2×D5semidirect
321. C2×(C2×D3)⋊C4C2×D5semidirect
324. C3×#95C2×D5semidirect
330. C3⋊#95C2×D5semidirect
378. C2×D20C4×D3semidirect
520. C2×D12C4×D5semidirect
674. #95D3×D5semidirect
903. C3×C5#2308semidirect
1071. C5#74874semidirect
1126. C3#10606605semidirect

Maximal subgroups

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

subgroupindex
C22×#67772
C2×D3×#6852
C2×D5×(C2×D3)⋊C42
#117507652
C5×#46652
C3×#649542
#117489402
#117489112
#117489102
#117489062
#117489052
#117489012
#117488962
#117486062
#106066053
#748745