Finite Group Databasebeta

← C2×#11753186 #14495231

Subgroups — C2×#11753186 #14495231

Order 1920.

2688 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×#91771C211yesmaximal, characteristic, complemented
2C2×C5×#884C211yesmaximal, characteristic, complemented
3C2×C3×#4025C211yesmaximal, characteristic, complemented
4C2×#91573C211yesmaximal, characteristic, complemented
5C2×#91573C211yesmaximal, characteristic, complemented
6C2×#91558C211yesmaximal, characteristic, complemented
7C2×#91557C211yesmaximal, characteristic, complemented
8C2×#91460C211yesmaximal, characteristic, complemented
9C2×#91451C211yesmaximal, characteristic, complemented
10C2×#91433C211yesmaximal, characteristic, complemented
11C2×#91427C211yesmaximal, characteristic, complemented
12C2×#91420C211yesmaximal, characteristic, complemented
13C2×#91416C211yesmaximal, characteristic, complemented
14C2×#91387C211yesmaximal, characteristic, complemented
15C2×#91351C211yesmaximal, characteristic, complemented
16#11753186C2116yesmaximal, direct product factor
17C2×#65954—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×D60C2211yescharacteristic
22C22×C5×#67C2211yescharacteristic
23C22×C5×#67C2211yescharacteristic
24C22×C5×D12C2211yescharacteristic, complemented
25C22×C4×C5×D3C2211yescharacteristic, complemented
26C22×#1203C2211yescharacteristic
27C22×#1203C2211yescharacteristic
28C22×#1203C2211yescharacteristic
29C22×#1203C2211yescharacteristic
30C22×#1203C2211yescharacteristic, complemented
31C22×#1203C2211yescharacteristic, complemented
32C22×#1200C2211yescharacteristic, complemented
33C22×D3×Dic5C2211yescharacteristic, complemented
34C2×C3×C5×C22⋊C4C2211yescharacteristic
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37#91771C2218yescomplemented
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
40C5×#884C2218yescomplemented
41C2×C3×C22⋊Dic5C2211yescharacteristic
42C2×C3×C22⋊Dic5C2211yescharacteristic
43C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
44C2×C3×#683C2211yescharacteristic, complemented
45C2×C3×#683C2211yescharacteristic, complemented
46C2×C3×C4×Dic5C2211yescharacteristic, complemented
47C3×#4025C2218yescomplemented
48#91573C2218yescomplemented
49#91573C2218yescomplemented
50#91558C2218yescomplemented
51#91557C2218yescomplemented
52C2×Dic3⋊Dic5C2211yescharacteristic, complemented
53C2×#6669C2211yescharacteristic, complemented
54C2×#6667C2211yescharacteristic
55C2×#6667C2211yescharacteristic
56C2×#6667C2211yescharacteristic
57C2×#6667C2211yescharacteristic
58C2×#6667C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
60#91460C2218yescomplemented
61#91451C2218yescomplemented
62#91433C2218yescomplemented
63#91427C2218yescomplemented
64#91420C2218yescomplemented
65#91416C2218yescomplemented
66#91387C2218yescomplemented
67#91351C2218yescomplemented
68C2×#5711—51nomaximal, Hall
69C2×C5×#121—31no—
70C2×#4086—31no—
71C2×#4085—31no—
72C2×#4085—31no—
73C2×#4084—31no—
74C2×#4083—31no—
75C2×#4083—31no—
76C2×#4076—31no—
77C2×#4075—31no—
78#65954—316no—
79C2×#4044—31no—
80C2×#4040—31no—
81C2×#4032—31no—
82C2×#4030—31no—
83C2×#4028—31no—
84C2×#4025D311yescharacteristic, complemented
85C24×C3×C5C2311yescharacteristic
86C23×D15—42no—
87C23×D15—42no—
88C23×D15—42no—
89C23×D15C2311yescharacteristic
90C23×D15C2311yescharacteristic
91C23×D15C2311yescharacteristic
92C23×D15C2314yes—
93C23×C5×D3C2311yescharacteristic
94C23×C5×D3C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C2×#1220—42no—
98C2×#1220C2314yes—
99C22×Dic15C2311yescharacteristic
100C2×D60—42no—
101C2×D60—42no—
102C2×D60C2314yes—
103C2×D60C2314yes—
104C2×C5×#67—42no—
105C2×C5×#67—42no—
106C2×C5×#67C2314yes—
107C2×C5×#67C2314yes—
108C22×C5×Dic3C2311yescharacteristic
109C22×C5×Dic3C2311yescharacteristic
110C2×C5×D12—42no—
111C2×C5×D12C2314yescomplemented
112C2×C4×C5×D3—42no—
113C2×C4×C5×D3C2314yescomplemented
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C22×C3×Dic5C2311yescharacteristic
117C22×C3×Dic5C2311yescharacteristic
118C2×#1203—42no—
119C2×#1203—42no—
120C2×#1203—42no—
121C2×#1203—42no—
122C2×#1203—42no—
123C2×#1203—42no—
124C2×#1203C2314yes—
125C2×#1203C2314yes—
126C2×#1203C2314yes—
127C2×#1203C2314yes—
128C2×#1203C2314yescomplemented
129C2×#1203C2314yescomplemented
130C2×#1200—42no—
131C2×#1200C2314yescomplemented
132C2×D3×Dic5—42no—
133C2×D3×Dic5C2314yescomplemented
134C3×C5×C22⋊C4C2314yes—
135#6714C2314yes—
136#6714C2314yes—
137C5×(C2×D3)⋊C4C2314yescomplemented
138C5×Dic3⋊C4C2314yescomplemented
139C3×C22⋊Dic5C2314yes—
140C3×C22⋊Dic5C2314yes—
141C3×C4⋊Dic5C2314yescomplemented
142C3×#683C2314yescomplemented
143C3×#683C2314yescomplemented
144C3×C4×Dic5C2314yescomplemented
145Dic3⋊Dic5C2314yescomplemented
146#6669C2314yescomplemented
147#6667C2314yes—
148#6667C2314yes—
149#6667C2314yes—
150#6667C2314yes—
151#6667C2314yescomplemented
152(C2×D3)⋊Dic5C2314yescomplemented
153C2×C3×#126—51no—
154#5711—516no—
155C2×#895—51no—
156C2×#895—51no—
157C2×#895—51no—
158C2×#894—51no—
159C2×#894—51no—
160C2×#894—51no—
161C2×#884—51no—
162C2×#884—51no—
163C2×#884D511yescharacteristic, complemented
164C2×#882—51no—
165C2×#882—51no—
166C2×#882—51no—
167C2×#876—51no—
168C2×#874—51no—
169C24×D5—31no—
170C22×C5×D4—31no—
171C22×C5×D4—31no—
172C22×C5×D4—31no—
173C23×C4×C5—31no—
174C22×C22⋊D5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5—31no—
177C22×C22⋊D5—31no—
178C22×C22⋊D5—31no—
179C22×C22⋊D5—31no—
180C22×C22⋊D5—31no—
181C23×Dic5—31no—
182C22×D20—31no—
183C22×D20—31no—
184C22×C4×D5—31no—
185C5×#121—38no—
186C2×C5×C4⋊C4—31no—
187C2×C5×C22⋊C4—31no—
188C2×C5×C22⋊C4C2×D311yescharacteristic
189C2×C22⋊Dic5—31no—
190C2×C22⋊Dic5C2×D311yescharacteristic
191C2×C22⋊Dic5C2×D311yescharacteristic
192#4086—38no—
193#4085—38no—
194#4085—38no—
195#4084—38no—
196#4083—38no—
197#4083—38no—
198#4076—38no—
199#4075—38no—
200C2×#685—31no—
201C2×#685—31no—
202C2×#685—31no—
203C2×#685—31no—
204C2×#685—31no—
205C2×#685—31no—
206C2×#685—31no—
207C2×C4⋊Dic5—31no—
208C2×C4⋊Dic5C2×D311yescharacteristic, complemented
209C2×#683—31no—
210C2×#683C2×D311yescharacteristic, complemented
211C2×#683C2×D311yescharacteristic, complemented
212C2×C4×Dic5C2×D311yescharacteristic, complemented
213#4044—38no—
214#4040—38no—
215#4032—38no—
216#4030—38no—
217#4028—38no—
218#4025C2×D318yescomplemented
219C2×#560—151noSylow
220C23×C3×C5—22no—
221C23×C3×C5—22no—
222C23×C3×C5—22no—
223C23×C3×C5C2412yes—
224C23×C3×C5C2411yescharacteristic
225C22×D15—22no—
226C22×D15—22no—
227C22×D15—22no—
228C22×D15—22no—
229C22×D15—22no—
230C22×D15—22no—
231C22×D15—22no—
232C22×D15—22no—
233C22×D15—22no—
234C22×D15—44no—
235C22×D15—44no—
236C22×D15—44no—
237C22×D15—416no—
238C22×D15C2412yes—
239C22×D15C2412yes—
240C22×D15C2412yes—
241C22×C5×D3—22no—
242C22×C5×D3—22no—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3—22no—
246C22×C5×D3—22no—
247C22×C5×D3C2412yes—
248C22×C5×D3C2412yes—
249C2×C3×C4×C5—22no—
250C2×C3×C4×C5—22no—
251C2×C3×C4×C5C2412yes—
252C2×C3×C4×C5C2412yes—
253#1220—44no—
254C2×Dic15—22no—
255C2×Dic15C2412yes—
256D60—44no—
257D60—44no—
258C5×#67—44no—
259C5×#67—44no—
260C2×C5×Dic3—22no—
261C2×C5×Dic3—22no—
262C2×C5×Dic3C2412yes—
263C2×C5×Dic3C2412yes—
264C5×D12—44no—
265C4×C5×D3—44no—
266C2×C3×Dic5—22no—
267C2×C3×Dic5—22no—
268C2×C3×Dic5—22no—
269C2×C3×Dic5—22no—
270C2×C3×Dic5C2412yes—
271C2×C3×Dic5C2412yes—
272C2×C3×Dic5C2412yes—
273C2×C3×Dic5C2412yes—
274#1203—44no—
275#1203—44no—
276#1203—44no—
277#1203—44no—
278#1203—44no—
279#1203—44no—
280#1200—44no—
281D3×Dic5—44no—
282C24×D3—51no—
283C22×#67—51no—
284C22×#67C2×D511yescharacteristic
285C22×#67C2×D511yescharacteristic
286C22×D12—51no—
287C22×D12—51no—
288C22×D12—51no—
289C22×D12—51no—
290C22×D12—51no—
291C22×D12—51no—
292C22×D12—51no—
293C22×D12—51no—
294C22×D12C2×D511yescharacteristic, complemented
295C22×C4×D3—51no—
296C22×C4×D3—51no—
297C22×C4×D3C2×D511yescharacteristic, complemented
298C3×#126—58no—
299C2×C3×C4⋊C4—51no—
300C2×C3×C4⋊C4—51no—
301C2×C3×C4⋊C4—51no—
302C2×C3×C22⋊C4—51no—
303C2×C3×C22⋊C4—51no—
304C2×C3×C22⋊C4C2×D511yescharacteristic
305C2×C3×C42—51no—
306C2×(C2×D3)⋊C4—51no—
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)⋊C4C2×D511yescharacteristic, complemented
315C2×Dic3⋊C4—51no—
316C2×Dic3⋊C4—51no—
317C2×Dic3⋊C4C2×D511yescharacteristic, complemented
318#895—58no—
319#895—58no—
320#895—58no—
321#894—58no—
322#894—58no—
323#894—58no—
324#884—58no—
325#884—58no—
326#884C2×D518yescomplemented
327#882—58no—
328#882—58no—
329#882—58no—
330#876—58no—
331#874—58no—
332C24×C5—31no—
333C24×C5—31no—
334C24×C5C22×D311yescharacteristic
335C23×D5—31no—
336C23×D5—31no—
337C23×D5—31no—
338C23×D5—34no—
339C23×D5—122no—
340C23×D5—122no—
341C23×D5—122no—
342C2×C5×D4—34no—
343C2×C5×D4—34no—
344C2×C5×D4—34no—
345C2×C5×D4—122no—
346C2×C5×D4—122no—
347C2×C5×D4—122no—
348C22×C4×C5—31no—
349C22×C4×C5—31no—
350C22×C4×C5—34no—
351C22×C4×C5—122no—
352C22×C4×C5C22×D311yescharacteristic
353C22×C4×C5C22×D311yescharacteristic
354C2×C22⋊D5—34no—
355C2×C22⋊D5—34no—
356C2×C22⋊D5—34no—
357C2×C22⋊D5—34no—
358C2×C22⋊D5—34no—
359C2×C22⋊D5—34no—
360C2×C22⋊D5—34no—
361C2×C22⋊D5—122no—
362C2×C22⋊D5—122no—
363C2×C22⋊D5—122no—
364C2×C22⋊D5—122no—
365C2×C22⋊D5—122no—
366C2×C22⋊D5—122no—
367C2×C22⋊D5—122no—
368C22×Dic5—31no—
369C22×Dic5—34no—
370C22×Dic5—122no—
371C22×Dic5C22×D311yescharacteristic
372C22×Dic5C22×D311yescharacteristic
373C22×Dic5C22×D311yescharacteristic
374C22×Dic5C22×D311yescharacteristic
375C2×D20—34no—
376C2×D20—34no—
377C2×D20—122no—
378C2×D20—122no—
379C2×C4×D5—34no—
380C2×C4×D5—122no—
381C5×C4⋊C4—34no—
382C5×C22⋊C4—34no—
383C5×C22⋊C4C22×D314yes—
384C22⋊Dic5—34no—
385C22⋊Dic5C22×D314yes—
386C22⋊Dic5C22×D314yes—
387#685—34no—
388#685—34no—
389#685—34no—
390#685—34no—
391#685—34no—
392#685—34no—
393#685—34no—
394C4⋊Dic5—34no—
395C4⋊Dic5C22×D314yescomplemented
396#683—34no—
397#683C22×D314yescomplemented
398#683C22×D314yescomplemented
399C4×Dic5C22×D314yescomplemented
400#560—1516no—
401C2×#127—151no—
402C2×#126—51no—
403C2×#126—151no—
404C2×#123—151no—
405C2×#123—151no—
406C2×#123—151no—
407C2×#121—31no—
408C2×#121—151no—
409C2×#121—151no—
410C2×#121—151no—
411C2×#121—151no—
412C2×#121—151no—
413C2×#120—151no—
414C2×#120—151no—
415C2×#120—151no—
416C22×C3×C5—22no—
417C22×C3×C5—22no—
418C22×C3×C5—22no—
419C22×C3×C5—44no—
420C22×C3×C5H(5,𝔽2)12yes—
421C22×C3×C5H(5,𝔽2)12yes—
422C22×C3×C5H(5,𝔽2)12yes—
423C22×C3×C5C2511yescharacteristic
424C2×D15—22no—
425C2×D15—22no—
426C2×D15—22no—
427C2×D15—22no—
428C2×D15—22no—
429C2×D15—22no—
430C2×D15—22no—
431C2×D15—22no—
432C2×D15—22no—
433C2×D15—416no—
434C2×D15—44no—
435C2×D15—44no—
436C2×D15—44no—
437C2×C5×D3—22no—
438C2×C5×D3—22no—
439C2×C5×D3—22no—
440C2×C5×D3—22no—
441C2×C5×D3—22no—
442C2×C5×D3—22no—
443C2×C5×D3—44no—
444C2×C5×D3—44no—
445C3×C4×C5—22no—
446C3×C4×C5—22no—
447Dic15—22no—
448C3×Dic5—22no—
449C3×Dic5—22no—
450C3×Dic5—22no—
451C3×Dic5—22no—
452C5×Dic3—22no—
453C5×Dic3—22no—
454C24×C3C22×D511yescharacteristic
455C23×D3—51no—
456C23×D3—51no—
457C23×D3—51no—
458C23×D3—54no—
459C23×D3—202no—
460C23×D3—202no—
461C23×D3—202no—
462C23×D3C22×D511yescharacteristic
463C23×D3C22×D511yescharacteristic
464C22×C3×C4—51no—
465C22×C3×C4—51no—
466C22×C3×C4—51no—
467C22×C3×C4—51no—
468C22×C3×C4C22×D511yescharacteristic
469C22×C3×C4C22×D511yescharacteristic
470C2×#67—42no—
471C2×#67—42no—
472C2×#67—54no—
473C2×#67—202no—
474C2×#67C22×D514yes—
475C2×#67C22×D514yes—
476C22×Dic3—51no—
477C22×Dic3C22×D511yescharacteristic
478C22×Dic3C22×D511yescharacteristic
479C2×D12—42no—
480C2×D12—54no—
481C2×D12—54no—
482C2×D12—54no—
483C2×D12—54no—
484C2×D12—54no—
485C2×D12—54no—
486C2×D12—54no—
487C2×D12—54no—
488C2×D12—202no—
489C2×D12—202no—
490C2×D12—202no—
491C2×D12—202no—
492C2×D12—202no—
493C2×D12—202no—
494C2×D12—202no—
495C2×D12—202no—
496C2×D12C22×D514yescomplemented
497C2×C4×D3—42no—
498C2×C4×D3—54no—
499C2×C4×D3—54no—
500C2×C4×D3—202no—
501C2×C4×D3—202no—
502C2×C4×D3C22×D514yescomplemented
503C3×C4⋊C4—54no—
504C3×C4⋊C4—54no—
505C3×C4⋊C4—54no—
506C3×C22⋊C4—54no—
507C3×C22⋊C4—54no—
508C3×C22⋊C4C22×D514yes—
509C3×C42—54no—
510(C2×D3)⋊C4—54no—
511(C2×D3)⋊C4—54no—
512(C2×D3)⋊C4—54no—
513(C2×D3)⋊C4—54no—
514(C2×D3)⋊C4—54no—
515(C2×D3)⋊C4—54no—
516(C2×D3)⋊C4—54no—
517(C2×D3)⋊C4—54no—
518(C2×D3)⋊C4C22×D514yescomplemented
519Dic3⋊C4—54no—
520Dic3⋊C4—54no—
521Dic3⋊C4C22×D514yescomplemented
522C23×C5—22no—
523C23×C5—22no—
524C23×C5—22no—
525C23×C5—32no—
526C23×C5—32no—
527C23×C5—62no—
528C23×C5—62no—
529C23×C5—62no—
530C23×C5—62no—
531C23×C5—62no—
532C23×C5—62no—
533C23×C5C23×D312yes—
534C23×C5C23×D311yescharacteristic
535C22×D5—32no—
536C22×D5—32no—
537C22×D5—32no—
538C22×D5—62no—
539C22×D5—62no—
540C22×D5—62no—
541C22×D5—62no—
542C22×D5—62no—
543C22×D5—62no—
544C22×D5—62no—
545C22×D5—62no—
546C22×D5—62no—
547C22×D5—124no—
548C22×D5—124no—
549C22×D5—124no—
550C22×D5—1216no—
551C5×D4—124no—
552C5×D4—124no—
553C5×D4—124no—
554C2×C4×C5—22no—
555C2×C4×C5—22no—
556C2×C4×C5—32no—
557C2×C4×C5—32no—
558C2×C4×C5—62no—
559C2×C4×C5—62no—
560C2×C4×C5—124no—
561C2×C4×C5C23×D312yes—
562C2×C4×C5C23×D312yes—
563C22⋊D5—124no—
564C22⋊D5—124no—
565C22⋊D5—124no—
566C22⋊D5—124no—
567C22⋊D5—124no—
568C22⋊D5—124no—
569C22⋊D5—124no—
570C2×Dic5—22no—
571C2×Dic5—22no—
572C2×Dic5—22no—
573C2×Dic5—22no—
574C2×Dic5—32no—
575C2×Dic5—62no—
576C2×Dic5—124no—
577C2×Dic5C23×D312yes—
578C2×Dic5C23×D312yes—
579C2×Dic5C23×D312yes—
580C2×Dic5C23×D312yes—
581D20—124no—
582D20—124no—
583C4×D5—124no—
584C25—151no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—151no—
589C22×D4—151no—
590C22×D4—151no—
591C22×D4—151no—
592C22×D4—151no—
593C22×D4—151no—
594C22×D4—151no—
595C22×D4—151no—
596C22×D4—151no—
597C23×C4—31no—
598C23×C4—151no—
599C23×C4—151no—
600#127—158no—
601#126—58no—
602#126—158no—
603#123—158no—
604#123—158no—
605#123—158no—
606#121—38no—
607#121—158no—
608#121—158no—
609#121—158no—
610#121—158no—
611#121—158no—
612#120—158no—
613#120—158no—
614#120—158no—
615C2×C4⋊C4—31no—
616C2×C4⋊C4—51no—
617C2×C4⋊C4—51no—
618C2×C4⋊C4—51no—
619C2×C4⋊C4—151no—
620C2×C4⋊C4—151no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—51no—
623C2×C22⋊C4—51no—
624C2×C22⋊C4—151no—
625C2×C22⋊C4—151no—
626C2×C22⋊C4—151no—
627C2×C22⋊C4—151no—
628C2×C22⋊C4—151no—
629C2×C22⋊C4—151no—
630C2×C22⋊C4—151no—
631C2×C22⋊C4—151no—
632C2×C22⋊C4D3×D511yescharacteristic
633C2×C42—51no—
634C2×C3×C5—42no—
635C2×C3×C5#56014yescomplemented
636C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
637C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
638C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
639D15—42no—
640D15—42no—
641D15—42no—
642C5×D3—42no—
643C5×D3—42no—
644C23×C3—22no—
645C23×C3—22no—
646C23×C3—22no—
647C23×C3C23×D512yes—
648C23×C3C23×D511yescharacteristic
649C22×D3—22no—
650C22×D3—22no—
651C22×D3—22no—
652C22×D3—22no—
653C22×D3—22no—
654C22×D3—22no—
655C22×D3—52no—
656C22×D3—52no—
657C22×D3—52no—
658C22×D3—102no—
659C22×D3—102no—
660C22×D3—102no—
661C22×D3—102no—
662C22×D3—102no—
663C22×D3—102no—
664C22×D3—102no—
665C22×D3—102no—
666C22×D3—102no—
667C22×D3—204no—
668C22×D3—204no—
669C22×D3—204no—
670C22×D3—2016no—
671C22×D3C23×D512yes—
672C22×D3C23×D512yes—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—52no—
676C2×C3×C4—52no—
677C2×C3×C4—52no—
678C2×C3×C4—52no—
679C2×C3×C4—102no—
680C2×C3×C4—102no—
681C2×C3×C4—102no—
682C2×C3×C4—102no—
683C2×C3×C4C23×D512yes—
684C2×C3×C4C23×D512yes—
685#67—44no—
686#67—44no—
687#67—204no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—52no—
691C2×Dic3—102no—
692C2×Dic3C23×D512yes—
693C2×Dic3C23×D512yes—
694D12—44no—
695D12—204no—
696D12—204no—
697D12—204no—
698D12—204no—
699D12—204no—
700D12—204no—
701D12—204no—
702D12—204no—
703C4×D3—44no—
704C4×D3—204no—
705C4×D3—204no—
706C22×C5—22no—
707C22×C5—22no—
708C22×C5—22no—
709C22×C5—44no—
710C22×C5—62no—
711C22×C5—62no—
712C22×C5—62no—
713C22×C5—62no—
714C22×C5—62no—
715C22×C5—62no—
716C22×C5—124no—
717C22×C5—124no—
718C22×C5#100912yes—
719C22×C5#100912yes—
720C22×C5#100912yes—
721C22×C5C24×D311yescharacteristic
722C2×D5—62no—
723C2×D5—62no—
724C2×D5—62no—
725C2×D5—62no—
726C2×D5—62no—
727C2×D5—62no—
728C2×D5—62no—
729C2×D5—62no—
730C2×D5—62no—
731C2×D5—1216no—
732C2×D5—124no—
733C2×D5—124no—
734C2×D5—124no—
735C4×C5—22no—
736C4×C5—22no—
737C4×C5—62no—
738C4×C5—62no—
739Dic5—22no—
740Dic5—22no—
741Dic5—22no—
742Dic5—22no—
743Dic5—62no—
744C24—31no—
745C24—31no—
746C24—151no—
747C24—151no—
748C24—151no—
749C24—154no—
750C24—602no—
751C24—602no—
752C24—602no—
753C24C2×D3×D511yescharacteristic
754C2×D4—34no—
755C2×D4—34no—
756C2×D4—34no—
757C2×D4—122no—
758C2×D4—122no—
759C2×D4—122no—
760C2×D4—154no—
761C2×D4—154no—
762C2×D4—154no—
763C2×D4—154no—
764C2×D4—154no—
765C2×D4—154no—
766C2×D4—154no—
767C2×D4—154no—
768C2×D4—154no—
769C2×D4—602no—
770C2×D4—602no—
771C2×D4—602no—
772C2×D4—602no—
773C2×D4—602no—
774C2×D4—602no—
775C2×D4—602no—
776C2×D4—602no—
777C2×D4—602no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—34no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—51no—
785C22×C4—122no—
786C22×C4—154no—
787C22×C4—154no—
788C22×C4—151no—
789C22×C4—602no—
790C22×C4—602no—
791C22×C4C2×D3×D511yescharacteristic
792C22×C4C2×D3×D511yescharacteristic
793C4⋊C4—34no—
794C4⋊C4—54no—
795C4⋊C4—54no—
796C4⋊C4—54no—
797C4⋊C4—154no—
798C4⋊C4—154no—
799C22⋊C4—34no—
800C22⋊C4—54no—
801C22⋊C4—54no—
802C22⋊C4—154no—
803C22⋊C4—154no—
804C22⋊C4—154no—
805C22⋊C4—154no—
806C22⋊C4—154no—
807C22⋊C4—154no—
808C22⋊C4—154no—
809C22⋊C4—154no—
810C22⋊C4C2×D3×D514yes—
811C42—54no—
812C3×C5C2×#56011yescharacteristic, complemented, Hall
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—44no—
817C22×C3#414412yes—
818C22×C3#414412yes—
819C22×C3#414912yes—
820C22×C3C24×D511yescharacteristic
821C2×D3—22no—
822C2×D3—22no—
823C2×D3—22no—
824C2×D3—22no—
825C2×D3—22no—
826C2×D3—22no—
827C2×D3—44no—
828C2×D3—44no—
829C2×D3—102no—
830C2×D3—102no—
831C2×D3—102no—
832C2×D3—102no—
833C2×D3—102no—
834C2×D3—102no—
835C2×D3—102no—
836C2×D3—102no—
837C2×D3—102no—
838C2×D3—2016no—
839C2×D3—204no—
840C2×D3—204no—
841C2×D3—204no—
842C3×C4—22no—
843C3×C4—22no—
844C3×C4—102no—
845C3×C4—102no—
846C3×C4—102no—
847C3×C4—102no—
848Dic3—22no—
849Dic3—22no—
850Dic3—102no—
851C2×C5—42no—
852C2×C5—122no—
853C2×C5—122no—
854C2×C5#571114yescomplemented
855C2×C5C2×#100911yescharacteristic
856C2×C5C2×#100911yescharacteristic
857C2×C5C2×#100911yescharacteristic
858D5—122no—
859D5—122no—
860D5—122no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—32no—
865C23—32no—
866C23—62no—
867C23—62no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—152no—
873C23—152no—
874C23—152no—
875C23—302no—
876C23—302no—
877C23—302no—
878C23—302no—
879C23—302no—
880C23—302no—
881C23—302no—
882C23—302no—
883C23—302no—
884C23—604no—
885C23—604no—
886C23—604no—
887C23—6016no—
888C23C22×D3×D512yes—
889C23C22×D3×D511yescharacteristic
890D4—124no—
891D4—124no—
892D4—124no—
893D4—604no—
894D4—604no—
895D4—604no—
896D4—604no—
897D4—604no—
898D4—604no—
899D4—604no—
900D4—604no—
901D4—604no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—32no—
905C2×C4—32no—
906C2×C4—52no—
907C2×C4—52no—
908C2×C4—52no—
909C2×C4—52no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—102no—
913C2×C4—102no—
914C2×C4—102no—
915C2×C4—102no—
916C2×C4—124no—
917C2×C4—152no—
918C2×C4—302no—
919C2×C4—604no—
920C2×C4—604no—
921C2×C4C22×D3×D512yes—
922C2×C4C22×D3×D512yes—
923C2×C3—42no—
924C2×C3#6595414yescomplemented
925C2×C3C2×#414411yescharacteristic
926C2×C3C2×#414411yescharacteristic
927C2×C3C2×#414911yescharacteristic
928D3—42no—
929D3—42no—
930D3—202no—
931D3—202no—
932D3—202no—
933C5C2×#571111yescharacteristic, complemented, Sylow
934C22—22no—
935C22—22no—
936C22—22no—
937C22—44no—
938C22—62no—
939C22—62no—
940C22—62no—
941C22—62no—
942C22—62no—
943C22—62no—
944C22—124no—
945C22—124no—
946C22—302no—
947C22—302no—
948C22—302no—
949C22—302no—
950C22—302no—
951C22—302no—
952C22—302no—
953C22—302no—
954C22—302no—
955C22—6016no—
956C22—604no—
957C22—604no—
958C22—604no—
959C22#9201912yes—
960C22#9202712yes—
961C22#9202712yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—62no—
966C4—62no—
967C4—102no—
968C4—102no—
969C4—102no—
970C4—102no—
971C4—302no—
972C3C2×#6595411yescharacteristic, complemented, Sylow
973C2—42no—
974C2—122no—
975C2—122no—
976C2—602no—
977C2—602no—
978C2—602no—
979C2#1175318614yesdirect product factor
980C2C2×#9201911yescharacteristic
981C2C2×#9202711yescharacteristic
982C2C2×#9202711yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#560
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
1. C2×#91771C2semidirect
2. C2×C5×#884C2semidirect
3. C2×C3×#4025C2semidirect
4. C2×#91573C2semidirect
5. C2×#91573C2semidirect
6. C2×#91558C2semidirect
7. C2×#91557C2semidirect
8. C2×#91460C2semidirect
9. C2×#91451C2semidirect
10. C2×#91433C2semidirect
11. C2×#91427C2semidirect
12. C2×#91420C2semidirect
13. C2×#91416C2semidirect
14. C2×#91387C2semidirect
15. C2×#91351C2semidirect
16. #11753186C2direct (N × H)
24. C22×C5×D12C22semidirect
25. C22×C4×C5×D3C22semidirect
30. C22×#1203C22semidirect
31. C22×#1203C22semidirect
32. C22×#1200C22semidirect
33. C22×D3×Dic5C22semidirect
37. #91771C22semidirect
38. C2×C5×(C2×D3)⋊C4C22semidirect
39. C2×C5×Dic3⋊C4C22semidirect
40. C5×#884C22semidirect
43. C2×C3×C4⋊Dic5C22semidirect
44. C2×C3×#683C22semidirect
45. C2×C3×#683C22semidirect
46. C2×C3×C4×Dic5C22semidirect
47. C3×#4025C22semidirect
48. #91573C22semidirect
49. #91573C22semidirect
50. #91558C22semidirect
51. #91557C22semidirect
52. C2×Dic3⋊Dic5C22semidirect
53. C2×#6669C22semidirect
58. C2×#6667C22semidirect
59. C2×(C2×D3)⋊Dic5C22semidirect
60. #91460C22semidirect
61. #91451C22semidirect
62. #91433C22semidirect
63. #91427C22semidirect
64. #91420C22semidirect
65. #91416C22semidirect
66. #91387C22semidirect
67. #91351C22semidirect
84. C2×#4025D3semidirect
111. C2×C5×D12C23semidirect
113. C2×C4×C5×D3C23semidirect
128. C2×#1203C23semidirect
129. C2×#1203C23semidirect
131. C2×#1200C23semidirect
133. C2×D3×Dic5C23semidirect
137. C5×(C2×D3)⋊C4C23semidirect
138. C5×Dic3⋊C4C23semidirect
141. C3×C4⋊Dic5C23semidirect
142. C3×#683C23semidirect
143. C3×#683C23semidirect
144. C3×C4×Dic5C23semidirect
145. Dic3⋊Dic5C23semidirect
146. #6669C23semidirect
151. #6667C23semidirect
152. (C2×D3)⋊Dic5C23semidirect
163. C2×#884D5semidirect
208. C2×C4⋊Dic5C2×D3semidirect
210. C2×#683C2×D3semidirect
211. C2×#683C2×D3semidirect
212. C2×C4×Dic5C2×D3semidirect
218. #4025C2×D3semidirect
294. C22×D12C2×D5semidirect
297. C22×C4×D3C2×D5semidirect
314. C2×(C2×D3)⋊C4C2×D5semidirect
317. C2×Dic3⋊C4C2×D5semidirect
326. #884C2×D5semidirect
395. C4⋊Dic5C22×D3semidirect
397. #683C22×D3semidirect
398. #683C22×D3semidirect
399. C4×Dic5C22×D3semidirect
496. C2×D12C22×D5semidirect
502. C2×C4×D3C22×D5semidirect
518. (C2×D3)⋊C4C22×D5semidirect
521. Dic3⋊C4C22×D5semidirect
635. C2×C3×C5#560semidirect
812. C3×C5C2×#560semidirect
854. C2×C5#5711semidirect
924. C2×C3#65954semidirect
933. C5C2×#5711semidirect
972. C3C2×#65954semidirect
979. C2#11753186direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917712
C2×C5×#8842
C2×C3×#40252
C2×#915732
C2×#915582
C2×#915572
C2×#914602
C2×#914512
C2×#914332
C2×#914272
C2×#914202
C2×#914162
C2×#913872
C2×#913512
#117531862
C2×#659543
C2×#57115