Finite Group Databasebeta

← #14322446

Subgroups — #14322446

Order 1920.

2208 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6790C211yesmaximal, characteristic
2C2×#91403C211yesmaximal, characteristic, complemented
3C2×#91402C211yesmaximal, characteristic, complemented
4#11751056C211yesmaximal, characteristic, complemented
5C5×#4957C211yesmaximal, characteristic, complemented
6C3×#65246C211yesmaximal, characteristic, complemented
7#11749502C211yesmaximal, characteristic, complemented
8#11749489C211yesmaximal, characteristic, complemented
9#11749482C211yesmaximal, characteristic, complemented
10#11748940C211yesmaximal, characteristic, complemented
11#11748940C211yesmaximal, characteristic, complemented
12#11748913C211yesmaximal, characteristic, complemented
13#11748912C211yesmaximal, characteristic, complemented
14#11748909C211yesmaximal, characteristic, complemented
15#11748908C211yesmaximal, characteristic, complemented
16#10608159—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C23×D3×D5C2211yescharacteristic
19C22×C5×#67C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C2×#6790—24no—
22C2×#6790—24no—
23C2×#6790C418yescomplemented
24C22×#1203C2211yescharacteristic
25C22×#1202C2211yescharacteristic
26C22×#1200C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
28C2×#6719C2211yescharacteristic, complemented
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×#6714C2211yescharacteristic, complemented
32C2×#6714C2211yescharacteristic, complemented
33C2×C5×#217C2211yescharacteristic, complemented
34C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
37C2×C4×C5×Dic3C2211yescharacteristic, complemented
38C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
39C2×C3×#685C2211yescharacteristic, complemented
40C2×C3×#685C2211yescharacteristic, complemented
41C2×C3×#683C2211yescharacteristic, complemented
42C2×C3×C4×Dic5C2211yescharacteristic, complemented
43C2×Dic3⋊Dic5C2211yescharacteristic, complemented
44C2×#6668C2211yescharacteristic, complemented
45C2×#6667C2211yescharacteristic
46C2×#6667C2211yescharacteristic
47C2×#6667C2211yescharacteristic, complemented
48C2×#6667C2211yescharacteristic, complemented
49C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
50C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
51C2×#6665C2211yescharacteristic, complemented
52C2×#6665C2211yescharacteristic, complemented
53C2×Dic3×Dic5C2211yescharacteristic, complemented
54C2×Dic3×Dic5C2211yescharacteristic, complemented
55#91403—24no—
56#91402—24no—
57#76428—51nomaximal, Hall
58C22×D4×D5—31no—
59C2×#4038—31no—
60C2×#4018—31no—
61C5×#390—31no—
62#65510—31no—
63#65277—31no—
64#65246—31no—
65#65246—31no—
66#65246—31no—
67#65246D311yescharacteristic, complemented
68#65244—31no—
69#65244—31no—
70#65244—31no—
71#65244—31no—
72#65228—31no—
73C24×C3×C5C2311yescharacteristic
74C23×D15—22no—
75C23×D15—22no—
76C23×D15—41no—
77C23×D15—41no—
78C23×D15—41no—
79C23×D15—41no—
80C23×D15C2×C414yes—
81C23×D15C2311yescharacteristic
82C23×D15C2311yescharacteristic
83C23×C5×D3C2311yescharacteristic
84C23×C3×D5C2311yescharacteristic
85C22×D3×D5—22no—
86C22×D3×D5—22no—
87C22×D3×D5—41no—
88C22×D3×D5—41no—
89C22×D3×D5—41no—
90C22×D3×D5—41no—
91C22×D3×D5C2×C414yes—
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C22×Dic15C2311yescharacteristic
96C2×C5×#67—22no—
97C2×C5×#67—22no—
98C2×C5×#67C2×C414yes—
99C22×C5×Dic3C2311yescharacteristic
100C22×C5×Dic3C2311yescharacteristic
101C22×C5×Dic3C2311yescharacteristic
102C2×C3×C22⋊D5—22no—
103C2×C3×C22⋊D5—22no—
104C2×C3×C22⋊D5C2×C414yes—
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108#6790—232no—
109C2×#1203—22no—
110C2×#1203—22no—
111C2×#1203C2×C414yes—
112C2×#1202—22no—
113C2×#1202—22no—
114C2×#1202C2×C414yes—
115C2×#1200C2×C414yes—
116C2×#1200D414yes—
117C2×#1200D414yes—
118C3×C5×C22⋊C4—41no—
119#6719—41no—
120#6714—22no—
121#6714—22no—
122#6714—41no—
123#6714—41no—
124C5×#217—41no—
125C5×(C2×D3)⋊C4—41no—
126C5×(C2×D3)⋊C4—41no—
127C5×Dic3⋊C4—22no—
128C4×C5×Dic3—22no—
129C3×C22⋊Dic5—41no—
130C3×#685—41no—
131C3×#685—41no—
132C3×#683—22no—
133C3×C4×Dic5—22no—
134Dic3⋊Dic5—22no—
135#6668—22no—
136#6667—22no—
137#6667—22no—
138#6667—41no—
139#6667—41no—
140(C2×D3)⋊Dic5—41no—
141(C2×D3)⋊Dic5—41no—
142#6665—41no—
143#6665—41no—
144Dic3×Dic5—22no—
145Dic3×Dic5—22no—
146C22×D3×D4—51no—
147C2×#892—51no—
148C2×#872—51no—
149C3×#390—51no—
150#5221—51no—
151#4988—51no—
152#4957—51no—
153#4957—51no—
154#4957—51no—
155#4957D511yescharacteristic, complemented
156#4955—51no—
157#4955—51no—
158#4955—51no—
159#4955—51no—
160#4939—51no—
161C24×D5—31no—
162C24×D5—31no—
163C22×C5×D4—31no—
164C22×C22⋊D5—31no—
165C22×C22⋊D5C2×D311yescharacteristic
166C2×D4×D5—38no—
167C2×D4×D5—64no—
168C2×D4×D5—64no—
169C22×D20—31no—
170C22×C4×D5—31no—
171C2×C5×C4⋊C4—31no—
172C2×C5×C22⋊C4—31no—
173C2×C5×C22⋊C4—31no—
174C2×C5×C22⋊C4—31no—
175C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
176C2×C42×C5—31no—
177C2×C22⋊Dic5—31no—
178C2×C22⋊Dic5—31no—
179C2×C22⋊Dic5—31no—
180C2×C22⋊Dic5C2×D311yescharacteristic, complemented
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—31no—
190C2×#685—31no—
191C2×#685C2×D311yescharacteristic, complemented
192C2×#685C2×D311yescharacteristic, complemented
193C2×C4⋊Dic5—31no—
194C2×#683—31no—
195C2×#683C2×D311yescharacteristic, complemented
196C2×C4×Dic5—31no—
197C2×C4×Dic5—31no—
198C2×C4×Dic5C2×D311yescharacteristic, complemented
199#4038—64no—
200#4018—64no—
201#2309—151noSylow
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—21no—
205C23×C3×C5—21no—
206C23×C3×C5—21no—
207C23×C3×C5—21no—
208C23×C3×C5C22×C412yes—
209C23×C3×C5C2411yescharacteristic
210C22×D15—21no—
211C22×D15—21no—
212C22×D15—21no—
213C22×D15—21no—
214C22×D15—21no—
215C22×D15—21no—
216C22×D15—21no—
217C22×D15—21no—
218C22×D15—21no—
219C22×D15—21no—
220C22×D15—28no—
221C22×D15—44no—
222C22×D15—44no—
223C22×D15—44no—
224C22×D15—44no—
225C22×D15—44no—
226C22×D15—44no—
227C22×D15C22×C412yes—
228C22×D15C22×C412yes—
229C22×D15C2×D412yes—
230C22×D15C2×D412yes—
231C22×C5×D3—21no—
232C22×C5×D3—21no—
233C22×C5×D3—21no—
234C22×C5×D3—21no—
235C22×C5×D3—21no—
236C22×C5×D3—21no—
237C22×C5×D3C22×C412yes—
238C22×C3×D5—21no—
239C22×C3×D5—21no—
240C22×C3×D5—21no—
241C22×C3×D5—21no—
242C22×C3×D5—21no—
243C22×C3×D5—21no—
244C22×C3×D5C22×C412yes—
245C2×D3×D5—28no—
246C2×D3×D5—44no—
247C2×D3×D5—44no—
248C2×D3×D5—44no—
249C2×D3×D5—44no—
250C2×D3×D5—44no—
251C2×D3×D5—44no—
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×Dic15—21no—
259C2×Dic15—21no—
260C2×Dic15—21no—
261C2×Dic15—21no—
262C2×Dic15—21no—
263C2×Dic15—21no—
264C5×#67—28no—
265C2×C5×Dic3—21no—
266C2×C5×Dic3—21no—
267C2×C5×Dic3—21no—
268C2×C5×Dic3—21no—
269C2×C5×Dic3—21no—
270C2×C5×Dic3—21no—
271C2×C5×Dic3C22×C412yes—
272C2×C5×Dic3C2×D412yes—
273C2×C5×Dic3C2×D412yes—
274C3×C22⋊D5—28no—
275C2×C3×Dic5—21no—
276C2×C3×Dic5—21no—
277C2×C3×Dic5—21no—
278C2×C3×Dic5—21no—
279C2×C3×Dic5—21no—
280C2×C3×Dic5—21no—
281C2×C3×Dic5C22×C412yes—
282C2×C3×Dic5C2×D412yes—
283C2×C3×Dic5C2×D412yes—
284#1203—28no—
285#1202—28no—
286#1200C22⋊C4116yescomplemented
287C24×D3—51no—
288C24×D3—51no—
289C22×C3×D4—51no—
290C22×#67—51no—
291C22×#67C2×D511yescharacteristic
292C2×D3×D4—58no—
293C2×D3×D4—104no—
294C2×D3×D4—104no—
295C22×D12—51no—
296C22×C4×D3—51no—
297C2×C3×C4⋊C4—51no—
298C2×C3×C22⋊C4—51no—
299C2×C3×C22⋊C4—51no—
300C2×C3×C22⋊C4—51no—
301C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
302C2×C3×C42—51no—
303C2×#217—51no—
304C2×#217—51no—
305C2×#217—51no—
306C2×#217C2×D511yescharacteristic, complemented
307C2×(C2×D3)⋊C4—51no—
308C2×(C2×D3)⋊C4—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)⋊C4C2×D511yescharacteristic, complemented
318C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
319C2×C4⋊Dic3—51no—
320C2×Dic3⋊C4—51no—
321C2×Dic3⋊C4C2×D511yescharacteristic, complemented
322C2×C4×Dic3—51no—
323C2×C4×Dic3—51no—
324C2×C4×Dic3C2×D511yescharacteristic, complemented
325#892—104no—
326#872—104no—
327C24×C5—31no—
328C24×C5C22×D311yescharacteristic
329C23×D5—31no—
330C23×D5—31no—
331C23×D5—34no—
332C23×D5—34no—
333C23×D5—62no—
334C23×D5—62no—
335C23×D5—62no—
336C23×D5—62no—
337C23×D5—121no—
338C23×D5—121no—
339C23×D5—121no—
340C23×D5—121no—
341C23×D5—121no—
342C23×D5—121no—
343C23×D5—121no—
344C23×D5—121no—
345C23×D5C22×D311yescharacteristic
346C2×C5×D4—34no—
347C2×C5×D4—62no—
348C2×C5×D4—62no—
349C22×C4×C5—31no—
350C22×C4×C5—31no—
351C22×C4×C5—31no—
352C22×C4×C5C22×D311yescharacteristic
353C22×C4×C5C22×D311yescharacteristic
354C2×C22⋊D5—22no—
355C2×C22⋊D5—22no—
356C2×C22⋊D5—34no—
357C2×C22⋊D5—62no—
358C2×C22⋊D5—62no—
359C2×C22⋊D5C4×D314yes—
360C22×Dic5—31no—
361C22×Dic5—31no—
362C22×Dic5C22×D311yescharacteristic
363C22×Dic5C22×D311yescharacteristic
364C22×Dic5C22×D311yescharacteristic
365D4×D5—632no—
366C2×D20—34no—
367C2×D20—62no—
368C2×D20—62no—
369C2×C4×D5—34no—
370C2×C4×D5—34no—
371C2×C4×D5—34no—
372C5×C4⋊C4—62no—
373C5×C22⋊C4—41no—
374C5×C22⋊C4—121no—
375C5×C22⋊C4—121no—
376C5×C22⋊C4—121no—
377C42×C5—62no—
378C22⋊Dic5—41no—
379C22⋊Dic5—121no—
380C22⋊Dic5—121no—
381C22⋊Dic5—121no—
382#685—41no—
383#685—41no—
384#685—62no—
385#685—62no—
386#685—62no—
387#685—62no—
388#685—121no—
389#685—121no—
390#685—121no—
391#685—121no—
392#685—121no—
393#685—121no—
394C4⋊Dic5—62no—
395#683—22no—
396#683—62no—
397C4×Dic5—22no—
398C4×Dic5—62no—
399C4×Dic5—62no—
400C23×D4—151no—
401C2×#117—151no—
402C2×#117—151no—
403#390—31no—
404#390—51no—
405#390—151no—
406#390—151no—
407#390—151no—
408#390—151no—
409#390—151no—
410#390—151no—
411#379—151no—
412#379—151no—
413#379—151no—
414#379—151no—
415C22×C3×C5—22no—
416C22×C3×C5—22no—
417C22×C3×C5—22no—
418C22×C3×C5—41no—
419C22×C3×C5—41no—
420C22×C3×C5—41no—
421C22×C3×C5—41no—
422C22×C3×C5C23×C411yescharacteristic
423C22×C3×C5C22×D411yescharacteristic
424C22×C3×C5C22×D411yescharacteristic
425C22×C3×C5H(5,𝔽2)11yescharacteristic
426C22×C3×C5H(5,𝔽2)11yescharacteristic
427C22×C3×C5H(5,𝔽2)11yescharacteristic
428C22×C3×C5H(5,𝔽2)11yescharacteristic
429C2×D15—22no—
430C2×D15—22no—
431C2×D15—22no—
432C2×D15—22no—
433C2×D15—22no—
434C2×D15—22no—
435C2×D15—22no—
436C2×D15—22no—
437C2×D15—22no—
438C2×D15—416no—
439C2×D15—41no—
440C2×D15—41no—
441C2×D15—41no—
442C2×D15—41no—
443C2×D15C2×C22⋊C414yes—
444C2×C5×D3—22no—
445C2×C5×D3—22no—
446C2×C5×D3—22no—
447C2×C5×D3—41no—
448C2×C5×D3—41no—
449C2×C5×D3—41no—
450C2×C5×D3—41no—
451C2×C3×D5—22no—
452C2×C3×D5—22no—
453C2×C3×D5—22no—
454C2×C3×D5—41no—
455C2×C3×D5—41no—
456C2×C3×D5—41no—
457C2×C3×D5—41no—
458D3×D5—416no—
459C3×C4×C5—41no—
460C3×C4×C5—41no—
461Dic15—41no—
462Dic15—41no—
463C3×Dic5—41no—
464C3×Dic5—41no—
465C3×Dic5C2×C22⋊C414yes—
466C5×Dic3—41no—
467C5×Dic3—41no—
468C5×Dic3C2×C22⋊C414yes—
469C24×C3—51no—
470C24×C3C22×D511yescharacteristic
471C23×D3—51no—
472C23×D3—51no—
473C23×D3—54no—
474C23×D3—54no—
475C23×D3—102no—
476C23×D3—102no—
477C23×D3—102no—
478C23×D3—102no—
479C23×D3—201no—
480C23×D3—201no—
481C23×D3—201no—
482C23×D3—201no—
483C23×D3—201no—
484C23×D3—201no—
485C23×D3—201no—
486C23×D3—201no—
487C23×D3C22×D511yescharacteristic
488C2×C3×D4—54no—
489C2×C3×D4—102no—
490C2×C3×D4—102no—
491C22×C3×C4—51no—
492C22×C3×C4—51no—
493C22×C3×C4—51no—
494C22×C3×C4C22×D511yescharacteristic
495C22×C3×C4C22×D511yescharacteristic
496C2×#67—22no—
497C2×#67—22no—
498C2×#67—54no—
499C2×#67—102no—
500C2×#67—102no—
501C2×#67C4×D514yes—
502C22×Dic3—51no—
503C22×Dic3—51no—
504C22×Dic3C22×D511yescharacteristic
505C22×Dic3C22×D511yescharacteristic
506C22×Dic3C22×D511yescharacteristic
507D3×D4—1032no—
508C2×D12—54no—
509C2×D12—102no—
510C2×D12—102no—
511C2×C4×D3—54no—
512C2×C4×D3—54no—
513C2×C4×D3—54no—
514C3×C4⋊C4—102no—
515C3×C22⋊C4—41no—
516C3×C22⋊C4—201no—
517C3×C22⋊C4—201no—
518C3×C22⋊C4—201no—
519C3×C42—102no—
520#217—41no—
521#217—201no—
522#217—201no—
523#217—201no—
524(C2×D3)⋊C4—41no—
525(C2×D3)⋊C4—41no—
526(C2×D3)⋊C4—102no—
527(C2×D3)⋊C4—102no—
528(C2×D3)⋊C4—102no—
529(C2×D3)⋊C4—102no—
530(C2×D3)⋊C4—201no—
531(C2×D3)⋊C4—201no—
532(C2×D3)⋊C4—201no—
533(C2×D3)⋊C4—201no—
534(C2×D3)⋊C4—201no—
535(C2×D3)⋊C4—201no—
536C4⋊Dic3—102no—
537Dic3⋊C4—22no—
538Dic3⋊C4—102no—
539C4×Dic3—22no—
540C4×Dic3—102no—
541C4×Dic3—102no—
542C23×C5—21no—
543C23×C5—21no—
544C23×C5—21no—
545C23×C5—21no—
546C23×C5—21no—
547C23×C5—21no—
548C23×C5—32no—
549C23×C5—61no—
550C23×C5—61no—
551C23×C5—61no—
552C23×C5—61no—
553C23×C5—61no—
554C23×C5—61no—
555C23×C5C2×C4×D312yes—
556C23×C5C23×D311yescharacteristic
557C22×D5—21no—
558C22×D5—21no—
559C22×D5—21no—
560C22×D5—21no—
561C22×D5—21no—
562C22×D5—21no—
563C22×D5—32no—
564C22×D5—32no—
565C22×D5—32no—
566C22×D5—32no—
567C22×D5—68no—
568C22×D5—68no—
569C22×D5—61no—
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—124no—
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×D5C2×C4×D312yes—
592C5×D4—68no—
593C2×C4×C5—21no—
594C2×C4×C5—21no—
595C2×C4×C5—21no—
596C2×C4×C5—21no—
597C2×C4×C5—21no—
598C2×C4×C5—21no—
599C2×C4×C5—32no—
600C2×C4×C5—32no—
601C2×C4×C5—32no—
602C2×C4×C5—61no—
603C2×C4×C5—61no—
604C2×C4×C5—61no—
605C2×C4×C5—61no—
606C2×C4×C5—61no—
607C2×C4×C5—61no—
608C22⋊D5—28no—
609C22⋊D5—68no—
610C2×Dic5—21no—
611C2×Dic5—21no—
612C2×Dic5—21no—
613C2×Dic5—21no—
614C2×Dic5—21no—
615C2×Dic5—21no—
616C2×Dic5—61no—
617C2×Dic5—61no—
618C2×Dic5—61no—
619C2×Dic5—61no—
620C2×Dic5—61no—
621C2×Dic5—61no—
622C2×Dic5C2×C4×D312yes—
623C2×Dic5D3×D412yes—
624C2×Dic5D3×D412yes—
625D20—68no—
626C4×D5—316no—
627C25—151no—
628C25—151no—
629C22×D4—31no—
630C22×D4—51no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—158no—
634C22×D4—304no—
635C22×D4—304no—
636C23×C4—151no—
637#117—304no—
638#117—304no—
639C2×C4⋊C4—31no—
640C2×C4⋊C4—51no—
641C2×C4⋊C4—151no—
642C2×C4⋊C4—151no—
643C2×C22⋊C4—31no—
644C2×C22⋊C4—31no—
645C2×C22⋊C4—31no—
646C2×C22⋊C4—51no—
647C2×C22⋊C4—51no—
648C2×C22⋊C4—51no—
649C2×C22⋊C4—151no—
650C2×C22⋊C4—151no—
651C2×C22⋊C4—151no—
652C2×C22⋊C4—151no—
653C2×C22⋊C4—151no—
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⋊C4D3×D511yescharacteristic, complemented
663C2×C42—31no—
664C2×C42—51no—
665C2×C42—151no—
666C2×C42—151no—
667C2×C3×C5—42no—
668C2×C3×C5C22×C22⋊C411yescharacteristic
669C2×C3×C5#51811yescharacteristic
670C2×C3×C5#51811yescharacteristic
671C2×C3×C5#53511yescharacteristic
672C2×C3×C5#53511yescharacteristic
673C2×C3×C5#53511yescharacteristic
674C2×C3×C5#53511yescharacteristic
675D15—24no—
676D15—42no—
677C3×D5—42no—
678C5×D3—42no—
679C23×C3—21no—
680C23×C3—21no—
681C23×C3—21no—
682C23×C3—21no—
683C23×C3—21no—
684C23×C3—21no—
685C23×C3—52no—
686C23×C3—101no—
687C23×C3—101no—
688C23×C3—101no—
689C23×C3—101no—
690C23×C3—101no—
691C23×C3—101no—
692C23×C3C2×C4×D512yes—
693C23×C3C23×D511yescharacteristic
694C22×D3—21no—
695C22×D3—21no—
696C22×D3—21no—
697C22×D3—21no—
698C22×D3—21no—
699C22×D3—21no—
700C22×D3—52no—
701C22×D3—52no—
702C22×D3—52no—
703C22×D3—52no—
704C22×D3—108no—
705C22×D3—108no—
706C22×D3—101no—
707C22×D3—101no—
708C22×D3—101no—
709C22×D3—101no—
710C22×D3—101no—
711C22×D3—101no—
712C22×D3—101no—
713C22×D3—101no—
714C22×D3—101no—
715C22×D3—101no—
716C22×D3—204no—
717C22×D3—204no—
718C22×D3—204no—
719C22×D3—204no—
720C22×D3—204no—
721C22×D3—204no—
722C22×D3—204no—
723C22×D3—204no—
724C22×D3—204no—
725C22×D3—204no—
726C22×D3—204no—
727C22×D3—204no—
728C22×D3C2×C4×D512yes—
729C3×D4—108no—
730C2×C3×C4—21no—
731C2×C3×C4—21no—
732C2×C3×C4—21no—
733C2×C3×C4—21no—
734C2×C3×C4—21no—
735C2×C3×C4—21no—
736C2×C3×C4—52no—
737C2×C3×C4—52no—
738C2×C3×C4—52no—
739C2×C3×C4—101no—
740C2×C3×C4—101no—
741C2×C3×C4—101no—
742C2×C3×C4—101no—
743C2×C3×C4—101no—
744C2×C3×C4—101no—
745#67—28no—
746#67—108no—
747C2×Dic3—21no—
748C2×Dic3—21no—
749C2×Dic3—21no—
750C2×Dic3—21no—
751C2×Dic3—21no—
752C2×Dic3—21no—
753C2×Dic3—101no—
754C2×Dic3—101no—
755C2×Dic3—101no—
756C2×Dic3—101no—
757C2×Dic3—101no—
758C2×Dic3—101no—
759C2×Dic3C2×C4×D512yes—
760C2×Dic3D4×D512yes—
761C2×Dic3D4×D512yes—
762D12—108no—
763C4×D3—516no—
764C22×C5—22no—
765C22×C5—22no—
766C22×C5—22no—
767C22×C5—41no—
768C22×C5—41no—
769C22×C5—41no—
770C22×C5—41no—
771C22×C5—62no—
772C22×C5—62no—
773C22×C5—62no—
774C22×C5—121no—
775C22×C5—121no—
776C22×C5—121no—
777C22×C5—121no—
778C22×C5C22×C4×D311yescharacteristic
779C22×C5C2×D3×D411yescharacteristic
780C22×C5C2×D3×D411yescharacteristic
781C22×C5#100411yescharacteristic
782C22×C5#100411yescharacteristic
783C22×C5#100911yescharacteristic
784C22×C5#100911yescharacteristic
785C2×D5—22no—
786C2×D5—22no—
787C2×D5—22no—
788C2×D5—34no—
789C2×D5—41no—
790C2×D5—41no—
791C2×D5—41no—
792C2×D5—41no—
793C2×D5—62no—
794C2×D5—62no—
795C2×D5—62no—
796C2×D5—62no—
797C2×D5—62no—
798C2×D5—62no—
799C2×D5—62no—
800C2×D5—62no—
801C2×D5—62no—
802C2×D5—1216no—
803C2×D5—1216no—
804C2×D5—121no—
805C2×D5—121no—
806C2×D5—121no—
807C2×D5—121no—
808C4×C5—34no—
809C4×C5—41no—
810C4×C5—41no—
811C4×C5—121no—
812C4×C5—121no—
813Dic5—41no—
814Dic5—41no—
815Dic5—121no—
816Dic5—121no—
817Dic5D3×C22⋊C414yes—
818C24—31no—
819C24—51no—
820C24—154no—
821C24—151no—
822C24—151no—
823C24—154no—
824C24—302no—
825C24—302no—
826C24—302no—
827C24—302no—
828C24—601no—
829C24—601no—
830C24—601no—
831C24—601no—
832C24—601no—
833C24—601no—
834C24—601no—
835C24—601no—
836C24C2×D3×D511yescharacteristic
837C2×D4—34no—
838C2×D4—54no—
839C2×D4—62no—
840C2×D4—62no—
841C2×D4—102no—
842C2×D4—102no—
843C2×D4—154no—
844C2×D4—154no—
845C2×D4—302no—
846C2×D4—302no—
847C2×D4—302no—
848C2×D4—302no—
849C2×D4—3032no—
850C22×C4—31no—
851C22×C4—31no—
852C22×C4—31no—
853C22×C4—51no—
854C22×C4—51no—
855C22×C4—51no—
856C22×C4—154no—
857C22×C4—154no—
858C22×C4—154no—
859C22×C4—151no—
860C22×C4—151no—
861C22×C4C2×D3×D511yescharacteristic
862C22×C4C2×D3×D511yescharacteristic
863C4⋊C4—62no—
864C4⋊C4—102no—
865C4⋊C4—302no—
866C4⋊C4—302no—
867C22⋊C4—41no—
868C22⋊C4—121no—
869C22⋊C4—121no—
870C22⋊C4—121no—
871C22⋊C4—201no—
872C22⋊C4—201no—
873C22⋊C4—201no—
874C22⋊C4—302no—
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⋊C4—601no—
885C22⋊C4—601no—
886C22⋊C4—601no—
887C42—62no—
888C42—102no—
889C42—302no—
890C42—302no—
891C3×C5#230911yescharacteristic, complemented, Hall
892C22×C3—22no—
893C22×C3—22no—
894C22×C3—22no—
895C22×C3—41no—
896C22×C3—41no—
897C22×C3—41no—
898C22×C3—41no—
899C22×C3—102no—
900C22×C3—102no—
901C22×C3—102no—
902C22×C3—201no—
903C22×C3—201no—
904C22×C3—201no—
905C22×C3—201no—
906C22×C3C22×C4×D511yescharacteristic
907C22×C3C2×D4×D511yescharacteristic
908C22×C3C2×D4×D511yescharacteristic
909C22×C3#414411yescharacteristic
910C22×C3#414411yescharacteristic
911C22×C3#414911yescharacteristic
912C22×C3#414911yescharacteristic
913C2×D3—22no—
914C2×D3—22no—
915C2×D3—22no—
916C2×D3—41no—
917C2×D3—41no—
918C2×D3—41no—
919C2×D3—41no—
920C2×D3—54no—
921C2×D3—102no—
922C2×D3—102no—
923C2×D3—102no—
924C2×D3—102no—
925C2×D3—102no—
926C2×D3—102no—
927C2×D3—102no—
928C2×D3—102no—
929C2×D3—102no—
930C2×D3—2016no—
931C2×D3—2016no—
932C2×D3—201no—
933C2×D3—201no—
934C2×D3—201no—
935C2×D3—201no—
936C3×C4—41no—
937C3×C4—41no—
938C3×C4—54no—
939C3×C4—201no—
940C3×C4—201no—
941Dic3—41no—
942Dic3—41no—
943Dic3—201no—
944Dic3—201no—
945Dic3D5×C22⋊C414yes—
946C2×C5—42no—
947C2×C5—122no—
948C2×C5C2×D3×C22⋊C411yescharacteristic
949C2×C5#554511yescharacteristic
950C2×C5#554511yescharacteristic
951C2×C5#560711yescharacteristic
952C2×C5#560711yescharacteristic
953C2×C5#567411yescharacteristic
954C2×C5#571511yescharacteristic
955D5—42no—
956D5—64no—
957D5—122no—
958C23—21no—
959C23—21no—
960C23—21no—
961C23—21no—
962C23—21no—
963C23—21no—
964C23—32no—
965C23—52no—
966C23—61no—
967C23—61no—
968C23—61no—
969C23—61no—
970C23—61no—
971C23—61no—
972C23—101no—
973C23—101no—
974C23—101no—
975C23—101no—
976C23—101no—
977C23—101no—
978C23—152no—
979C23—152no—
980C23—152no—
981C23—152no—
982C23—308no—
983C23—308no—
984C23—301no—
985C23—301no—
986C23—301no—
987C23—301no—
988C23—301no—
989C23—301no—
990C23—301no—
991C23—301no—
992C23—301no—
993C23—301no—
994C23—604no—
995C23—604no—
996C23—604no—
997C23—604no—
998C23—604no—
999C23—604no—
1000C23—604no—
1001C23—604no—
1002C23—604no—
1003C23—604no—
1004C23—604no—
1005C23—604no—
1006C23C4×D3×D512yes—
1007C23C22×D3×D511yescharacteristic
1008D4—68no—
1009D4—108no—
1010D4—308no—
1011D4—308no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—32no—
1019C2×C4—32no—
1020C2×C4—32no—
1021C2×C4—52no—
1022C2×C4—52no—
1023C2×C4—52no—
1024C2×C4—61no—
1025C2×C4—61no—
1026C2×C4—61no—
1027C2×C4—61no—
1028C2×C4—61no—
1029C2×C4—61no—
1030C2×C4—101no—
1031C2×C4—101no—
1032C2×C4—101no—
1033C2×C4—101no—
1034C2×C4—101no—
1035C2×C4—101no—
1036C2×C4—1516no—
1037C2×C4—301no—
1038C2×C4—301no—
1039C2×C4—301no—
1040C2×C4—301no—
1041C2×C4—301no—
1042C2×C4—301no—
1043C2×C3—42no—
1044C2×C3—202no—
1045C2×C3C2×D5×C22⋊C411yescharacteristic
1046C2×C3#6587911yescharacteristic
1047C2×C3#6587911yescharacteristic
1048C2×C3#6594111yescharacteristic
1049C2×C3#6594111yescharacteristic
1050C2×C3#6600811yescharacteristic
1051C2×C3#6604911yescharacteristic
1052D3—42no—
1053D3—104no—
1054D3—202no—
1055C5#7642811yescharacteristic, complemented, Sylow
1056C22—22no—
1057C22—22no—
1058C22—22no—
1059C22—41no—
1060C22—41no—
1061C22—41no—
1062C22—41no—
1063C22—62no—
1064C22—62no—
1065C22—62no—
1066C22—102no—
1067C22—102no—
1068C22—102no—
1069C22—121no—
1070C22—121no—
1071C22—121no—
1072C22—121no—
1073C22—154no—
1074C22—201no—
1075C22—201no—
1076C22—201no—
1077C22—201no—
1078C22—302no—
1079C22—302no—
1080C22—302no—
1081C22—302no—
1082C22—302no—
1083C22—302no—
1084C22—302no—
1085C22—302no—
1086C22—302no—
1087C22—6016no—
1088C22—6016no—
1089C22—601no—
1090C22—601no—
1091C22—601no—
1092C22—601no—
1093C22C2×C4×D3×D511yescharacteristic
1094C22#9201911yescharacteristic
1095C22D3×D4×D511yescharacteristic
1096C22D3×D4×D511yescharacteristic
1097C22#9202611yescharacteristic
1098C22#9202711yescharacteristic
1099C22#9204911yescharacteristic
1100C4—34no—
1101C4—41no—
1102C4—41no—
1103C4—54no—
1104C4—121no—
1105C4—121no—
1106C4—201no—
1107C4—201no—
1108C4—601no—
1109C4—601no—
1110C3#1060815911yescharacteristic, complemented, Sylow
1111C2—42no—
1112C2—122no—
1113C2—202no—
1114C2—304no—
1115C2—602no—
1116C2D3×D5×C22⋊C411yescharacteristic
1117C2#1175320411yescharacteristic
1118C2#1175325111yescharacteristic
1119C2#1175325211yescharacteristic
1120C2#1175462911yescharacteristic
1121C2#1175505011yescharacteristic
1122C2#1175505111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#6790C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2309
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#91403C2semidirect
3. C2×#91402C2semidirect
4. #11751056C2semidirect
5. C5×#4957C2semidirect
6. C3×#65246C2semidirect
7. #11749502C2semidirect
8. #11749489C2semidirect
9. #11749482C2semidirect
10. #11748940C2semidirect
11. #11748940C2semidirect
12. #11748913C2semidirect
13. #11748912C2semidirect
14. #11748909C2semidirect
15. #11748908C2semidirect
23. C2×#6790C4semidirect
27. C2×C3×C5×C22⋊C4C22semidirect
28. C2×#6719C22semidirect
31. C2×#6714C22semidirect
32. C2×#6714C22semidirect
33. C2×C5×#217C22semidirect
34. C2×C5×(C2×D3)⋊C4C22semidirect
35. C2×C5×(C2×D3)⋊C4C22semidirect
36. C2×C5×Dic3⋊C4C22semidirect
37. C2×C4×C5×Dic3C22semidirect
38. C2×C3×C22⋊Dic5C22semidirect
39. C2×C3×#685C22semidirect
40. C2×C3×#685C22semidirect
41. C2×C3×#683C22semidirect
42. C2×C3×C4×Dic5C22semidirect
43. C2×Dic3⋊Dic5C22semidirect
44. C2×#6668C22semidirect
47. C2×#6667C22semidirect
48. C2×#6667C22semidirect
49. C2×(C2×D3)⋊Dic5C22semidirect
50. C2×(C2×D3)⋊Dic5C22semidirect
51. C2×#6665C22semidirect
52. C2×#6665C22semidirect
53. C2×Dic3×Dic5C22semidirect
54. C2×Dic3×Dic5C22semidirect
67. #65246D3semidirect
155. #4957D5semidirect
175. C2×C5×C22⋊C4C2×D3semidirect
180. C2×C22⋊Dic5C2×D3semidirect
191. C2×#685C2×D3semidirect
192. C2×#685C2×D3semidirect
195. C2×#683C2×D3semidirect
198. C2×C4×Dic5C2×D3semidirect
286. #1200C22⋊C4semidirect
301. C2×C3×C22⋊C4C2×D5semidirect
306. C2×#217C2×D5semidirect
317. C2×(C2×D3)⋊C4C2×D5semidirect
318. C2×(C2×D3)⋊C4C2×D5semidirect
321. C2×Dic3⋊C4C2×D5semidirect
324. C2×C4×Dic3C2×D5semidirect
662. C2×C22⋊C4D3×D5semidirect
891. C3×C5#2309semidirect
1055. C5#76428semidirect
1110. C3#10608159semidirect

Maximal subgroups

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

subgroupindex
C22×#67902
C2×#914032
C2×#914022
#117510562
C5×#49572
C3×#652462
#117495022
#117494892
#117494822
#117489402
#117489132
#117489122
#117489092
#117489082
#106081593
#764285