Finite Group Databasebeta

← #14322418

Subgroups — #14322418

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×D5×D12C211yesmaximal, characteristic
2C2×#91473C211yesmaximal, characteristic, complemented
3C2×D3×#685C211yesmaximal, characteristic, complemented
4#11750766C211yesmaximal, characteristic, complemented
5C5×#4665C211yesmaximal, characteristic, complemented
6C3×#64953C211yesmaximal, characteristic, complemented
7#11748940C211yesmaximal, characteristic, complemented
8#11748940C211yesmaximal, characteristic, complemented
9#11748919C211yesmaximal, characteristic, complemented
10#11748918C211yesmaximal, characteristic, complemented
11#11748914C211yesmaximal, characteristic, complemented
12#11748904C211yesmaximal, characteristic, complemented
13#11748901C211yesmaximal, characteristic, complemented
14#11748883C211yesmaximal, characteristic, complemented
15#11748737C211yesmaximal, characteristic, complemented
16#10606605—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C23×D3×D5C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic, complemented
21C22×C5×D12C2211yescharacteristic
22C22×C4×C5×D3C2211yescharacteristic, complemented
23C22×C3×C4×D5C2211yescharacteristic
24C22×#1203C2211yescharacteristic
25C22×#1203C2211yescharacteristic
26C22×#1200C2211yescharacteristic, complemented
27C22×D3×Dic5C2211yescharacteristic, complemented
28C2×D5×D12—24no—
29C2×D5×D12—24no—
30C2×D5×D12C418yescomplemented
31C2×#6714C2211yescharacteristic, complemented
32C2×#6714C2211yescharacteristic, complemented
33C2×#6714C2211yescharacteristic, complemented
34C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
37C2×C3×#685C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×#6667C2211yescharacteristic, complemented
40C2×#6667C2211yescharacteristic, complemented
41C2×#6667C2211yescharacteristic, complemented
42C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
43C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
44C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
45C2×#6665C2211yescharacteristic
46C2×#6665C2211yescharacteristic
47#91473—24no—
48D3×#685—24no—
49C3×C5×#95C2211yescharacteristic, complemented
50#91115C2211yescharacteristic, complemented
51C5×C3⋊#95C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53C3×#3963C2211yescharacteristic, complemented
54C3×#3963C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57#74119—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#64954—31no—
71#64953—31no—
72#64953D311yescharacteristic, complemented
73C23×D15C2311yescharacteristic
74C23×D15C2311yescharacteristic
75C23×C5×D3C2311yescharacteristic
76C23×C5×D3C2311yescharacteristic
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
97C2×D60—22no—
98C2×D60—22no—
99C2×D60C2×C414yescomplemented
100C2×C4×D15—22no—
101C2×C4×D15—41no—
102C2×C4×D15—41no—
103C22×C5×Dic3C2311yescharacteristic
104C22×C5×Dic3C2311yescharacteristic
105C2×C5×D12—22no—
106C2×C5×D12—22no—
107C2×C5×D12C2×C414yescomplemented
108C2×C4×C5×D3—22no—
109C2×C4×C5×D3—41no—
110C2×C4×C5×D3—41no—
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C2×C3×C4×D5—22no—
115C2×C3×C4×D5—22no—
116C2×C3×C4×D5C2×C414yescomplemented
117C2×#1203—22no—
118C2×#1203—22no—
119C2×#1203—22no—
120C2×#1203—22no—
121C2×#1203C2×C414yescomplemented
122C2×#1203C2×C414yescomplemented
123C2×#1200—22no—
124C2×#1200—41no—
125C2×#1200—41no—
126C2×D3×Dic5—22no—
127C2×D3×Dic5—41no—
128C2×D3×Dic5—41no—
129D5×D12—232no—
130#6714—22no—
131#6714—41no—
132#6714—41no—
133C5×(C2×D3)⋊C4—22no—
134C5×(C2×D3)⋊C4—41no—
135C5×(C2×D3)⋊C4—41no—
136C3×#685—22no—
137C3×#685—22no—
138#6667—22no—
139#6667—41no—
140#6667—41no—
141(C2×D3)⋊Dic5—22no—
142(C2×D3)⋊Dic5—41no—
143(C2×D3)⋊Dic5—41no—
144#6665—22no—
145#6665—22no—
146C23×D12—51no—
147C2×D3×C22⋊C4—51no—
148C2×D3×C22⋊C4—51no—
149C3×#381—51no—
150#5211—51no—
151#4955—51no—
152#4955—51no—
153#4665—51no—
154#4665—51no—
155#4665—51no—
156#4665—51no—
157#4665—51no—
158#4665—51no—
159#4665—51no—
160#4665D511yescharacteristic, complemented
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×D20—31no—
172C22×C4×D5—31no—
173C22×C4×D5—31no—
174C22×C4×D5C2×D311yescharacteristic
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—31no—
189C2×#685—64no—
190C2×#685C2×D311yescharacteristic
191C2×#685C2×D311yescharacteristic
192D5×C22⋊C4—64no—
193C5×#95—31no—
194C5×#95C2×D311yescharacteristic, complemented
195#3963—31no—
196#3963—31no—
197#3963—31no—
198#3963C2×D311yescharacteristic, complemented
199#3963C2×D311yescharacteristic, complemented
200#3963C2×D311yescharacteristic, complemented
201#2308—151noSylow
202C23×C3×C5C2411yescharacteristic
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—21no—
207C22×D15—21no—
208C22×D15—21no—
209C22×D15—21no—
210C22×D15—21no—
211C22×D15—21no—
212C22×D15—21no—
213C22×D15C22×C412yes—
214C22×D15C22×C412yes—
215C22×D15C2×D412yes—
216C22×D15C2×D412yes—
217C22×C5×D3—21no—
218C22×C5×D3—21no—
219C22×C5×D3—21no—
220C22×C5×D3—21no—
221C22×C5×D3—21no—
222C22×C5×D3—21no—
223C22×C5×D3—21no—
224C22×C5×D3—21no—
225C22×C5×D3—21no—
226C22×C5×D3—21no—
227C22×C5×D3C22×C412yes—
228C22×C5×D3C22×C412yes—
229C22×C5×D3C2×D412yes—
230C22×C5×D3C2×D412yes—
231C22×C3×D5—21no—
232C22×C3×D5—21no—
233C22×C3×D5—21no—
234C22×C3×D5—21no—
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—
267D60—28no—
268C4×D15—44no—
269C2×C5×Dic3—21no—
270C2×C5×Dic3—21no—
271C2×C5×Dic3—21no—
272C2×C5×Dic3—21no—
273C2×C5×Dic3—21no—
274C2×C5×Dic3—21no—
275C5×D12—28no—
276C4×C5×D3—44no—
277C2×C3×Dic5—21no—
278C2×C3×Dic5—21no—
279C2×C3×Dic5—21no—
280C2×C3×Dic5—21no—
281C2×C3×Dic5—21no—
282C2×C3×Dic5—21no—
283C2×C3×Dic5—21no—
284C2×C3×Dic5—21no—
285C2×C3×Dic5C22×C412yes—
286C3×C4×D5—28no—
287#1203—28no—
288#1203—28no—
289#1200—44no—
290D3×Dic5—44no—
291C24×D3—51no—
292C24×D3—51no—
293C23×C3×C4—51no—
294C22×D12—51no—
295C22×D12—51no—
296C22×D12—51no—
297C22×D12—58no—
298C22×D12—104no—
299C22×D12—104no—
300C22×D12C2×D511yescharacteristic
301C22×C4×D3—51no—
302C22×C4×D3—51no—
303C22×C4×D3—51no—
304C22×C4×D3C2×D511yescharacteristic, complemented
305C2×C3×C22⋊C4—51no—
306C2×C3×C22⋊C4—51no—
307C2×#217—51no—
308C2×#217—51no—
309C2×(C2×D3)⋊C4—51no—
310C2×(C2×D3)⋊C4—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)⋊C4C2×D511yescharacteristic, complemented
319C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
320C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
321D3×C22⋊C4—104no—
322D3×C22⋊C4—104no—
323C3×#95—51no—
324C3×#95—51no—
325C3×#95—51no—
326C3×#95C2×D511yescharacteristic, complemented
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—31no—
338C23×D5—34no—
339C23×D5—62no—
340C23×D5—62no—
341C23×D5—121no—
342C23×D5—121no—
343C23×D5—121no—
344C23×D5—121no—
345C23×D5—121no—
346C23×D5—121no—
347C23×D5—121no—
348C23×D5—121no—
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—62no—
370C22×Dic5—121no—
371C22×Dic5—121no—
372C22×Dic5C22×D311yescharacteristic
373C22×Dic5C22×D311yescharacteristic
374C22×Dic5C22×D311yescharacteristic
375D4×D5—632no—
376C2×D20—34no—
377C2×D20—62no—
378C2×D20—62no—
379C2×C4×D5—22no—
380C2×C4×D5—22no—
381C2×C4×D5—62no—
382C2×C4×D5—62no—
383C2×C4×D5—121no—
384C2×C4×D5—121no—
385C2×C4×D5—121no—
386C2×C4×D5—121no—
387C2×C4×D5C4×D314yescomplemented
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—22no—
396#685—62no—
397#685—62no—
398#685—62no—
399#685—62no—
400#685—121no—
401#685—121no—
402#685—121no—
403#685—121no—
404C23×D4—151no—
405C22×C22⋊C4—151no—
406C22×C22⋊C4—151no—
407#386—31no—
408#386—151no—
409#386—151no—
410#386—151no—
411#386—151no—
412#386—151no—
413#386—151no—
414#386—151no—
415#381—51no—
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×D15—22no—
433C2×D15—22no—
434C2×D15—22no—
435C2×D15—41no—
436C2×D15—41no—
437C2×D15—41no—
438C2×D15—41no—
439C2×D15C2×C22⋊C414yes—
440C2×C5×D3—22no—
441C2×C5×D3—22no—
442C2×C5×D3—22no—
443C2×C5×D3—22no—
444C2×C5×D3—22no—
445C2×C5×D3—22no—
446C2×C5×D3—22no—
447C2×C5×D3—22no—
448C2×C5×D3—22no—
449C2×C5×D3—41no—
450C2×C5×D3—41no—
451C2×C5×D3—41no—
452C2×C5×D3—41no—
453C2×C5×D3C2×C22⋊C414yes—
454C2×C3×D5—22no—
455C2×C3×D5—22no—
456C2×C3×D5—22no—
457C2×C3×D5—22no—
458C2×C3×D5—22no—
459C2×C3×D5—22no—
460C2×C3×D5C2×C22⋊C414yes—
461D3×D5—416no—
462D3×D5—416no—
463C3×C4×C5—22no—
464C3×C4×C5—41no—
465C3×C4×C5—41no—
466Dic15—41no—
467Dic15—41no—
468C3×Dic5—22no—
469C3×Dic5—41no—
470C3×Dic5—41no—
471C5×Dic3—41no—
472C5×Dic3—41no—
473C24×C3—51no—
474C23×D3—51no—
475C23×D3—54no—
476C23×D3—54no—
477C23×D3—54no—
478C23×D3—51no—
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
492C22×C3×C4—51no—
493C22×C3×C4—54no—
494C22×C3×C4—51no—
495C22×C3×C4—51no—
496C22×C3×C4—102no—
497C22×C3×C4—102no—
498C22×C3×C4C22×D511yescharacteristic
499C22×C3×C4C22×D511yescharacteristic
500C22×C3×C4C22×D511yescharacteristic
501C22×Dic3—51no—
502C22×Dic3—51no—
503C22×Dic3C22×D511yescharacteristic
504C22×Dic3C22×D511yescharacteristic
505C2×D12—22no—
506C2×D12—22no—
507C2×D12—54no—
508C2×D12—54no—
509C2×D12—54no—
510C2×D12—1032no—
511C2×D12—102no—
512C2×D12—102no—
513C2×D12—102no—
514C2×D12—102no—
515C2×D12—102no—
516C2×D12—102no—
517C2×D12C4×D514yescomplemented
518C2×C4×D3—22no—
519C2×C4×D3—41no—
520C2×C4×D3—41no—
521C2×C4×D3—102no—
522C2×C4×D3—102no—
523C2×C4×D3—102no—
524C2×C4×D3—201no—
525C2×C4×D3—201no—
526C2×C4×D3—201no—
527C2×C4×D3—201no—
528C2×C4×D3—201no—
529C2×C4×D3—201no—
530C3×C22⋊C4—102no—
531C3×C22⋊C4—102no—
532#217—102no—
533#217—102no—
534(C2×D3)⋊C4—22no—
535(C2×D3)⋊C4—41no—
536(C2×D3)⋊C4—41no—
537(C2×D3)⋊C4—102no—
538(C2×D3)⋊C4—102no—
539(C2×D3)⋊C4—102no—
540(C2×D3)⋊C4—201no—
541(C2×D3)⋊C4—201no—
542(C2×D3)⋊C4—201no—
543(C2×D3)⋊C4—201no—
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—32no—
566C22×D5—32no—
567C22×D5—32no—
568C22×D5—316no—
569C22×D5—32no—
570C22×D5—61no—
571C22×D5—61no—
572C22×D5—61no—
573C22×D5—61no—
574C22×D5—61no—
575C22×D5—61no—
576C22×D5—61no—
577C22×D5—61no—
578C22×D5—61no—
579C22×D5—61no—
580C22×D5—68no—
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×D5—124no—
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—21no—
622C2×Dic5—21no—
623C2×Dic5—61no—
624C2×Dic5—61no—
625C2×Dic5—61no—
626C2×Dic5—61no—
627C2×Dic5—61no—
628C2×Dic5—61no—
629C2×Dic5—124no—
630C2×Dic5C2×C4×D312yes—
631D20—68no—
632C4×D5—28no—
633C4×D5—124no—
634C4×D5—124no—
635C25—151no—
636C25—151no—
637C22×D4—31no—
638C22×D4—158no—
639C22×D4—151no—
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—151no—
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—51no—
670#95—51no—
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—
683D15—42no—
684C3×D5—24no—
685C5×D3—24no—
686C5×D3—42no—
687C23×C3—52no—
688C23×C3—52no—
689C23×C3—52no—
690C23×C3—101no—
691C23×C3—101no—
692C23×C3—101no—
693C23×C3—101no—
694C23×C3C23×D511yescharacteristic
695C22×D3—21no—
696C22×D3—21no—
697C22×D3—21no—
698C22×D3—21no—
699C22×D3—21no—
700C22×D3—21no—
701C22×D3—21no—
702C22×D3—21no—
703C22×D3—21no—
704C22×D3—21no—
705C22×D3—52no—
706C22×D3—52no—
707C22×D3—52no—
708C22×D3—516no—
709C22×D3—52no—
710C22×D3—108no—
711C22×D3—101no—
712C22×D3—101no—
713C22×D3—101no—
714C22×D3—101no—
715C22×D3—101no—
716C22×D3—101no—
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—
737C2×C3×C4—21no—
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—52no—
746C2×C3×C4—108no—
747C2×C3×C4—101no—
748C2×C3×C4—101no—
749C2×C3×C4—101no—
750C2×C3×C4—101no—
751C2×C3×C4—101no—
752C2×C3×C4—101no—
753C2×C3×C4—101no—
754C2×C3×C4—101no—
755C2×C3×C4C2×C4×D512yes—
756C2×Dic3—21no—
757C2×Dic3—21no—
758C2×Dic3—21no—
759C2×Dic3—21no—
760C2×Dic3—21no—
761C2×Dic3—21no—
762C2×Dic3—101no—
763C2×Dic3—101no—
764C2×Dic3—101no—
765C2×Dic3—101no—
766C2×Dic3—101no—
767C2×Dic3—101no—
768D12—28no—
769D12—108no—
770D12—108no—
771D12—108no—
772C4×D3—44no—
773C4×D3—204no—
774C4×D3—204no—
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#100911yescharacteristic
794C22×C5#100911yescharacteristic
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—34no—
804C2×D5—62no—
805C2×D5—62no—
806C2×D5—62no—
807C2×D5—62no—
808C2×D5—62no—
809C2×D5—62no—
810C2×D5—62no—
811C2×D5—62no—
812C2×D5—62no—
813C2×D5—1216no—
814C2×D5—1216no—
815C2×D5—121no—
816C2×D5—121no—
817C2×D5—121no—
818C2×D5—121no—
819C2×D5D3×C22⋊C414yes—
820C4×C5—22no—
821C4×C5—41no—
822C4×C5—41no—
823C4×C5—121no—
824C4×C5—121no—
825Dic5—22no—
826Dic5—41no—
827Dic5—41no—
828Dic5—121no—
829Dic5—121no—
830C24—31no—
831C24—31no—
832C24—51no—
833C24—154no—
834C24—154no—
835C24—154no—
836C24—154no—
837C24—151no—
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—62no—
851C2×D4—62no—
852C2×D4—154no—
853C2×D4—154no—
854C2×D4—154no—
855C2×D4—302no—
856C2×D4—302no—
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—54no—
866C22×C4—51no—
867C22×C4—51no—
868C22×C4—62no—
869C22×C4—102no—
870C22×C4—102no—
871C22×C4—121no—
872C22×C4—121no—
873C22×C4—151no—
874C22×C4—151no—
875C22×C4—302no—
876C22×C4—302no—
877C22×C4—302no—
878C22×C4—601no—
879C22×C4—601no—
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—102no—
890C22⋊C4—121no—
891C22⋊C4—121no—
892C22⋊C4—302no—
893C22⋊C4—302no—
894C22⋊C4—302no—
895C22⋊C4—302no—
896C22⋊C4—302no—
897C22⋊C4—601no—
898C22⋊C4—601no—
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×C3C22×C4×D511yescharacteristic
912C22×C3C2×D4×D511yescharacteristic
913C22×C3C2×D4×D511yescharacteristic
914C22×C3#414411yescharacteristic
915C22×C3#414411yescharacteristic
916C22×C3#414911yescharacteristic
917C22×C3#414911yescharacteristic
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—22no—
923C2×D3—22no—
924C2×D3—22no—
925C2×D3—22no—
926C2×D3—22no—
927C2×D3—41no—
928C2×D3—41no—
929C2×D3—41no—
930C2×D3—41no—
931C2×D3—54no—
932C2×D3—102no—
933C2×D3—102no—
934C2×D3—102no—
935C2×D3—102no—
936C2×D3—102no—
937C2×D3—102no—
938C2×D3—102no—
939C2×D3—102no—
940C2×D3—102no—
941C2×D3—2016no—
942C2×D3—2016no—
943C2×D3—201no—
944C2×D3—201no—
945C2×D3—201no—
946C2×D3—201no—
947C2×D3D5×C22⋊C414yes—
948C3×C4—22no—
949C3×C4—41no—
950C3×C4—41no—
951C3×C4—102no—
952C3×C4—201no—
953C3×C4—201no—
954Dic3—41no—
955Dic3—41no—
956Dic3—201no—
957Dic3—201no—
958C2×C5—64no—
959C2×C5—122no—
960C2×C5C2×D3×C22⋊C411yescharacteristic
961C2×C5#552111yescharacteristic
962C2×C5#552111yescharacteristic
963C2×C5#565311yescharacteristic
964C2×C5#565311yescharacteristic
965C2×C5#565311yescharacteristic
966C2×C5#565311yescharacteristic
967D5—24no—
968D5—64no—
969D5—122no—
970C23—32no—
971C23—32no—
972C23—32no—
973C23—32no—
974C23—52no—
975C23—52no—
976C23—52no—
977C23—61no—
978C23—61no—
979C23—61no—
980C23—61no—
981C23—61no—
982C23—61no—
983C23—61no—
984C23—61no—
985C23—61no—
986C23—61no—
987C23—101no—
988C23—101no—
989C23—101no—
990C23—101no—
991C23—1516no—
992C23—152no—
993C23—152no—
994C23—152no—
995C23—152no—
996C23—308no—
997C23—301no—
998C23—301no—
999C23—301no—
1000C23—301no—
1001C23—301no—
1002C23—301no—
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—308no—
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—52no—
1033C2×C4—61no—
1034C2×C4—61no—
1035C2×C4—61no—
1036C2×C4—61no—
1037C2×C4—61no—
1038C2×C4—61no—
1039C2×C4—108no—
1040C2×C4—101no—
1041C2×C4—101no—
1042C2×C4—101no—
1043C2×C4—101no—
1044C2×C4—101no—
1045C2×C4—101no—
1046C2×C4—101no—
1047C2×C4—101no—
1048C2×C4—124no—
1049C2×C4—301no—
1050C2×C4—301no—
1051C2×C4—301no—
1052C2×C4—301no—
1053C2×C4—301no—
1054C2×C4—301no—
1055C2×C4—604no—
1056C2×C4—604no—
1057C2×C4—604no—
1058C2×C4C4×D3×D512yes—
1059C2×C3—104no—
1060C2×C3C2×D5×C22⋊C411yescharacteristic
1061C2×C3#6587911yescharacteristic
1062C2×C3#6587911yescharacteristic
1063C2×C3#6592311yescharacteristic
1064C2×C3#6593911yescharacteristic
1065C2×C3#6593911yescharacteristic
1066C2×C3#6598711yescharacteristic
1067D3—24no—
1068D3—42no—
1069D3—104no—
1070D3—202no—
1071C5#7411911yescharacteristic, 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—121no—
1090C22—121no—
1091C22—121no—
1092C22—121no—
1093C22—154no—
1094C22—302no—
1095C22—302no—
1096C22—302no—
1097C22—302no—
1098C22—302no—
1099C22—302no—
1100C22—302no—
1101C22—302no—
1102C22—302no—
1103C22—6016no—
1104C22—6016no—
1105C22—601no—
1106C22—601no—
1107C22—601no—
1108C22—601no—
1109C22C2×C4×D3×D511yescharacteristic
1110C22#9201811yescharacteristic
1111C22#9201911yescharacteristic
1112C22D3×D4×D511yescharacteristic
1113C22D3×D4×D511yescharacteristic
1114C22#9202711yescharacteristic
1115C22#9203511yescharacteristic
1116C4—22no—
1117C4—41no—
1118C4—41no—
1119C4—102no—
1120C4—121no—
1121C4—121no—
1122C4—201no—
1123C4—201no—
1124C4—601no—
1125C4—601no—
1126C3#1060660511yescharacteristic, complemented, Sylow
1127C2—64no—
1128C2—104no—
1129C2—122no—
1130C2—304no—
1131C2—602no—
1132C2#1175272511yescharacteristic
1133C2D3×D5×C22⋊C411yescharacteristic
1134C2#1175321411yescharacteristic
1135C2#1175321511yescharacteristic
1136C2#1175383711yescharacteristic
1137C2#1175384611yescharacteristic
1138C2#1175384711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×D5×D12C2
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×#91473C2semidirect
3. C2×D3×#685C2semidirect
4. #11750766C2semidirect
5. C5×#4665C2semidirect
6. C3×#64953C2semidirect
7. #11748940C2semidirect
8. #11748940C2semidirect
9. #11748919C2semidirect
10. #11748918C2semidirect
11. #11748914C2semidirect
12. #11748904C2semidirect
13. #11748901C2semidirect
14. #11748883C2semidirect
15. #11748737C2semidirect
20. C22×C4×D15C22semidirect
22. C22×C4×C5×D3C22semidirect
26. C22×#1200C22semidirect
27. C22×D3×Dic5C22semidirect
30. C2×D5×D12C4semidirect
31. C2×#6714C22semidirect
32. C2×#6714C22semidirect
33. C2×#6714C22semidirect
34. C2×C5×(C2×D3)⋊C4C22semidirect
35. C2×C5×(C2×D3)⋊C4C22semidirect
36. C2×C5×(C2×D3)⋊C4C22semidirect
39. C2×#6667C22semidirect
40. C2×#6667C22semidirect
41. C2×#6667C22semidirect
42. C2×(C2×D3)⋊Dic5C22semidirect
43. C2×(C2×D3)⋊Dic5C22semidirect
44. C2×(C2×D3)⋊Dic5C22semidirect
49. C3×C5×#95C22semidirect
50. #91115C22semidirect
51. C5×C3⋊#95C22semidirect
52. C3×#3963C22semidirect
53. C3×#3963C22semidirect
54. C3×#3963C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
72. #64953D3semidirect
89. C22×D3×D5C2×C4semidirect
99. C2×D60C2×C4semidirect
107. C2×C5×D12C2×C4semidirect
116. C2×C3×C4×D5C2×C4semidirect
121. C2×#1203C2×C4semidirect
122. C2×#1203C2×C4semidirect
160. #4665D5semidirect
194. C5×#95C2×D3semidirect
198. #3963C2×D3semidirect
199. #3963C2×D3semidirect
200. #3963C2×D3semidirect
251. C2×D3×D5C22⋊C4semidirect
304. C22×C4×D3C2×D5semidirect
318. C2×(C2×D3)⋊C4C2×D5semidirect
319. C2×(C2×D3)⋊C4C2×D5semidirect
320. C2×(C2×D3)⋊C4C2×D5semidirect
326. C3×#95C2×D5semidirect
330. C3⋊#95C2×D5semidirect
387. C2×C4×D5C4×D3semidirect
517. C2×D12C4×D5semidirect
674. #95D3×D5semidirect
903. C3×C5#2308semidirect
1071. C5#74119semidirect
1126. C3#10606605semidirect

Maximal subgroups

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

subgroupindex
C22×D5×D122
C2×#914732
C2×D3×#6852
#117507662
C5×#46652
C3×#649532
#117489402
#117489192
#117489182
#117489142
#117489042
#117489012
#117488832
#117487372
#106066053
#741195