Finite Group Databasebeta

← C2×#11753942 #14495244

Subgroups — C2×#11753942 #14495244

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×#91783C211yesmaximal, characteristic, complemented
2C2×C5×#895C211yesmaximal, characteristic, complemented
3C2×C3×#4044C211yesmaximal, characteristic, complemented
4C2×#91476C211yesmaximal, characteristic, complemented
5C2×#91475C211yesmaximal, characteristic, complemented
6C2×#91475C211yesmaximal, characteristic, complemented
7C2×#91466C211yesmaximal, characteristic, complemented
8C2×#91461C211yesmaximal, characteristic, complemented
9C2×#91454C211yesmaximal, characteristic, complemented
10C2×#91453C211yesmaximal, characteristic, complemented
11C2×#91451C211yesmaximal, characteristic, complemented
12C2×#91427C211yesmaximal, characteristic, complemented
13C2×#91416C211yesmaximal, characteristic, complemented
14C2×#91372C211yesmaximal, characteristic, complemented
15C2×#91351C211yesmaximal, characteristic, complemented
16#11753942C2116yesmaximal, direct product factor
17C2×#65954—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic, complemented
21C22×C5×D12C2211yescharacteristic
22C22×C5×D12C2211yescharacteristic
23C22×C5×D12C2211yescharacteristic, complemented
24C22×C4×C5×D3C2211yescharacteristic, complemented
25C22×#1203C2211yescharacteristic
26C22×#1203C2211yescharacteristic
27C22×#1203C2211yescharacteristic
28C22×#1203C2211yescharacteristic, complemented
29C22×#1203C2211yescharacteristic, complemented
30C22×#1202C2211yescharacteristic
31C22×#1201C2211yescharacteristic
32C22×#1201C2211yescharacteristic
33C22×D3×Dic5C2211yescharacteristic, complemented
34C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×#6714C2211yescharacteristic, complemented
38C2×#6712C2211yescharacteristic, complemented
39#91783C2218yescomplemented
40C2×C5×(C2×D3)⋊C4C2211yescharacteristic
41C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C5×#895C2218yescomplemented
43C2×C3×#685C2211yescharacteristic
44C2×C3×#685C2211yescharacteristic
45C2×C3×#685C2211yescharacteristic
46C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
47C2×C3×#683C2211yescharacteristic, complemented
48C2×C3×C4×Dic5C2211yescharacteristic, complemented
49C3×#4044C2218yescomplemented
50C2×Dic3⋊Dic5C2211yescharacteristic, complemented
51C2×#6669C2211yescharacteristic, complemented
52C2×#6667C2211yescharacteristic
53C2×(C2×D3)⋊Dic5C2211yescharacteristic
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
56#91476C2218yescomplemented
57#91475C2218yescomplemented
58#91475C2218yescomplemented
59#91466C2218yescomplemented
60#91461C2218yescomplemented
61#91454C2218yescomplemented
62#91453C2218yescomplemented
63#91451C2218yescomplemented
64#91427C2218yescomplemented
65#91416C2218yescomplemented
66#91372C2218yescomplemented
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×#4044D311yescharacteristic, complemented
80C2×#4040—31no—
81C2×#4032—31no—
82C2×#4030—31no—
83C2×#4028—31no—
84C2×#4025—31no—
85C23×D15C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C23×C3×D5C2311yescharacteristic
91C22×D3×D5—42no—
92C22×D3×D5—42no—
93C22×D3×D5—42no—
94C22×D3×D5C2314yes—
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C2×D60—42no—
101C2×D60C2314yes—
102C2×C4×D15—42no—
103C2×C4×D15C2314yescomplemented
104C22×C5×Dic3C2311yescharacteristic
105C2×C5×D12—42no—
106C2×C5×D12—42no—
107C2×C5×D12—42no—
108C2×C5×D12C2314yes—
109C2×C5×D12C2314yes—
110C2×C5×D12C2314yescomplemented
111C2×C4×C5×D3—42no—
112C2×C4×C5×D3C2314yescomplemented
113C22×C3×Dic5C2311yescharacteristic
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C2×#1203—42no—
117C2×#1203—42no—
118C2×#1203—42no—
119C2×#1203—42no—
120C2×#1203—42no—
121C2×#1203C2314yes—
122C2×#1203C2314yes—
123C2×#1203C2314yes—
124C2×#1203C2314yescomplemented
125C2×#1203C2314yescomplemented
126C2×#1202—42no—
127C2×#1202C2314yes—
128C2×#1201—42no—
129C2×#1201—42no—
130C2×#1201C2314yes—
131C2×#1201C2314yes—
132C2×D3×Dic5—42no—
133C2×D3×Dic5C2314yescomplemented
134C3×C5×C4⋊C4C2314yescomplemented
135#6714C2314yes—
136#6714C2314yes—
137#6714C2314yescomplemented
138#6712C2314yescomplemented
139C5×(C2×D3)⋊C4C2314yes—
140C5×(C2×D3)⋊C4C2314yescomplemented
141C3×#685C2314yes—
142C3×#685C2314yes—
143C3×#685C2314yes—
144C3×C4⋊Dic5C2314yescomplemented
145C3×#683C2314yescomplemented
146C3×C4×Dic5C2314yescomplemented
147Dic3⋊Dic5C2314yescomplemented
148#6669C2314yescomplemented
149#6667C2314yes—
150(C2×D3)⋊Dic5C2314yes—
151(C2×D3)⋊Dic5C2314yes—
152(C2×D3)⋊Dic5C2314yescomplemented
153C2×C3×#126—51no—
154#5711—516no—
155C2×#895—51no—
156C2×#895—51no—
157C2×#895D511yescharacteristic, complemented
158C2×#894—51no—
159C2×#894—51no—
160C2×#894—51no—
161C2×#884—51no—
162C2×#884—51no—
163C2×#884—51no—
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⋊C4C2×D311yescharacteristic, complemented
187C2×C5×C22⋊C4—31no—
188C2×C5×C22⋊C4—31no—
189C2×C22⋊Dic5—31no—
190C2×C22⋊Dic5—31no—
191C2×C22⋊Dic5—31no—
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×#685C2×D311yescharacteristic
205C2×#685C2×D311yescharacteristic
206C2×#685C2×D311yescharacteristic
207C2×C4⋊Dic5—31no—
208C2×C4⋊Dic5C2×D311yescharacteristic, complemented
209C2×#683—31no—
210C2×#683—31no—
211C2×#683C2×D311yescharacteristic, complemented
212C2×C4×Dic5C2×D311yescharacteristic, complemented
213#4044C2×D318yescomplemented
214#4040—38no—
215#4032—38no—
216#4030—38no—
217#4028—38no—
218#4025—38no—
219C2×#560—151noSylow
220C23×C3×C5C2411yescharacteristic
221C22×D15—22no—
222C22×D15—22no—
223C22×D15—22no—
224C22×D15—22no—
225C22×D15—22no—
226C22×D15—22no—
227C22×D15C2412yes—
228C22×D15C2412yes—
229C22×C5×D3—22no—
230C22×C5×D3—22no—
231C22×C5×D3—22no—
232C22×C5×D3—22no—
233C22×C5×D3—22no—
234C22×C5×D3—22no—
235C22×C5×D3—22no—
236C22×C5×D3—22no—
237C22×C5×D3—22no—
238C22×C5×D3C2412yes—
239C22×C5×D3C2412yes—
240C22×C5×D3C2412yes—
241C22×C3×D5—22no—
242C22×C3×D5—22no—
243C22×C3×D5—22no—
244C22×C3×D5C2412yes—
245C2×D3×D5—44no—
246C2×D3×D5—44no—
247C2×D3×D5—44no—
248C2×D3×D5—416no—
249C2×C3×C4×C5—22no—
250C2×C3×C4×C5—22no—
251C2×C3×C4×C5—22no—
252C2×C3×C4×C5C2412yes—
253C2×C3×C4×C5C2412yes—
254C2×C3×C4×C5C2412yes—
255C2×Dic15—22no—
256C2×Dic15—22no—
257C2×Dic15C2412yes—
258C2×Dic15C2412yes—
259D60—44no—
260C4×D15—44no—
261C2×C5×Dic3—22no—
262C2×C5×Dic3C2412yes—
263C5×D12—44no—
264C5×D12—44no—
265C5×D12—44no—
266C4×C5×D3—44no—
267C2×C3×Dic5—22no—
268C2×C3×Dic5—22no—
269C2×C3×Dic5—22no—
270C2×C3×Dic5C2412yes—
271C2×C3×Dic5C2412yes—
272C2×C3×Dic5C2412yes—
273#1203—44no—
274#1203—44no—
275#1203—44no—
276#1203—44no—
277#1203—44no—
278#1202—44no—
279#1201—44no—
280#1201—44no—
281D3×Dic5—44no—
282C24×D3—51no—
283C22×#67—51no—
284C22×#67—51no—
285C22×#67—51no—
286C22×D12—51no—
287C22×D12—51no—
288C22×D12—51no—
289C22×D12—51no—
290C22×D12—51no—
291C22×D12—51no—
292C22×D12C2×D511yescharacteristic
293C22×D12C2×D511yescharacteristic
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⋊C4C2×D511yescharacteristic, complemented
302C2×C3×C22⋊C4—51no—
303C2×C3×C22⋊C4—51no—
304C2×C3×C22⋊C4—51no—
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)⋊C4C2×D511yescharacteristic
314C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
315C2×Dic3⋊C4—51no—
316C2×Dic3⋊C4—51no—
317C2×Dic3⋊C4—51no—
318#895—58no—
319#895—58no—
320#895C2×D518yescomplemented
321#894—58no—
322#894—58no—
323#894—58no—
324#884—58no—
325#884—58no—
326#884—58no—
327#882—58no—
328#882—58no—
329#882—58no—
330#876—58no—
331#874—58no—
332C24×C5—31no—
333C24×C5—31no—
334C24×C5—31no—
335C23×D5—31no—
336C23×D5—31no—
337C23×D5—34no—
338C23×D5—122no—
339C23×D5—122no—
340C23×D5—122no—
341C23×D5C22×D311yescharacteristic
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—34no—
350C22×C4×C5—122no—
351C22×C4×C5C22×D311yescharacteristic
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—31no—
370C22×Dic5—34no—
371C22×Dic5—122no—
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⋊C4C22×D314yescomplemented
382C5×C22⋊C4—34no—
383C5×C22⋊C4—34no—
384C22⋊Dic5—34no—
385C22⋊Dic5—34no—
386C22⋊Dic5—34no—
387#685—34no—
388#685—34no—
389#685—34no—
390#685—34no—
391#685C22×D314yes—
392#685C22×D314yes—
393#685C22×D314yes—
394C4⋊Dic5—34no—
395C4⋊Dic5C22×D314yescomplemented
396#683—34no—
397#683—34no—
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×C5H(5,𝔽2)12yes—
417C22×C3×C5H(5,𝔽2)12yes—
418C22×C3×C5H(5,𝔽2)12yes—
419C22×C3×C5C2511yescharacteristic
420C2×D15—22no—
421C2×D15—22no—
422C2×D15—22no—
423C2×D15—22no—
424C2×D15—22no—
425C2×D15—22no—
426C2×D15—44no—
427C2×D15—44no—
428C2×C5×D3—22no—
429C2×C5×D3—22no—
430C2×C5×D3—22no—
431C2×C5×D3—22no—
432C2×C5×D3—22no—
433C2×C5×D3—22no—
434C2×C5×D3—22no—
435C2×C5×D3—22no—
436C2×C5×D3—22no—
437C2×C5×D3—44no—
438C2×C5×D3—44no—
439C2×C5×D3—44no—
440C2×C3×D5—22no—
441C2×C3×D5—22no—
442C2×C3×D5—22no—
443C2×C3×D5—44no—
444D3×D5—416no—
445C3×C4×C5—22no—
446C3×C4×C5—22no—
447C3×C4×C5—22no—
448Dic15—22no—
449Dic15—22no—
450C3×Dic5—22no—
451C3×Dic5—22no—
452C3×Dic5—22no—
453C5×Dic3—22no—
454C24×C3—51no—
455C23×D3—51no—
456C23×D3—51no—
457C23×D3—54no—
458C23×D3—202no—
459C23×D3—202no—
460C23×D3—202no—
461C23×D3C22×D511yescharacteristic
462C23×D3C22×D511yescharacteristic
463C23×D3C22×D511yescharacteristic
464C22×C3×C4—51no—
465C22×C3×C4—51no—
466C22×C3×C4—51no—
467C22×C3×C4C22×D511yescharacteristic
468C22×C3×C4C22×D511yescharacteristic
469C22×C3×C4C22×D511yescharacteristic
470C2×#67—54no—
471C2×#67—54no—
472C2×#67—54no—
473C2×#67—202no—
474C2×#67—202no—
475C2×#67—202no—
476C22×Dic3—51no—
477C22×Dic3—51no—
478C22×Dic3C22×D511yescharacteristic
479C2×D12—42no—
480C2×D12—42no—
481C2×D12—42no—
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×D12C22×D514yes—
495C2×D12C22×D514yes—
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⋊C4C22×D514yescomplemented
506C3×C22⋊C4—54no—
507C3×C22⋊C4—54no—
508C3×C22⋊C4—54no—
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)⋊C4C22×D514yes—
518(C2×D3)⋊C4C22×D514yescomplemented
519Dic3⋊C4—54no—
520Dic3⋊C4—54no—
521Dic3⋊C4—54no—
522C23×C5—32no—
523C23×C5—32no—
524C23×C5—32no—
525C23×C5—62no—
526C23×C5—62no—
527C23×C5—62no—
528C23×C5—62no—
529C23×C5—62no—
530C23×C5—62no—
531C23×C5—62no—
532C23×C5—62no—
533C23×C5—62no—
534C23×C5C23×D311yescharacteristic
535C22×D5—22no—
536C22×D5—22no—
537C22×D5—22no—
538C22×D5—32no—
539C22×D5—32no—
540C22×D5—62no—
541C22×D5—62no—
542C22×D5—62no—
543C22×D5—62no—
544C22×D5—62no—
545C22×D5—62no—
546C22×D5—124no—
547C22×D5—124no—
548C22×D5—124no—
549C22×D5—1216no—
550C22×D5C23×D312yes—
551C5×D4—124no—
552C5×D4—124no—
553C5×D4—124no—
554C2×C4×C5—22no—
555C2×C4×C5—22no—
556C2×C4×C5—22no—
557C2×C4×C5—32no—
558C2×C4×C5—62no—
559C2×C4×C5—124no—
560C2×C4×C5C23×D312yes—
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—32no—
574C2×Dic5—32no—
575C2×Dic5—62no—
576C2×Dic5—62no—
577C2×Dic5—124no—
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—51no—
616C2×C4⋊C4—51no—
617C2×C4⋊C4—151no—
618C2×C4⋊C4—151no—
619C2×C4⋊C4—151no—
620C2×C4⋊C4D3×D511yescharacteristic, complemented
621C2×C22⋊C4—31no—
622C2×C22⋊C4—31no—
623C2×C22⋊C4—51no—
624C2×C22⋊C4—51no—
625C2×C22⋊C4—51no—
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⋊C4—151no—
633C2×C42—51no—
634C2×C3×C5#56014yescomplemented
635C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
636C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
637C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
638D15—42no—
639D15—42no—
640C3×D5—42no—
641C5×D3—42no—
642C5×D3—42no—
643C5×D3—42no—
644C23×C3—52no—
645C23×C3—102no—
646C23×C3—102no—
647C23×C3—102no—
648C23×C3C23×D511yescharacteristic
649C22×D3—22no—
650C22×D3—22no—
651C22×D3—22no—
652C22×D3—22no—
653C22×D3—22no—
654C22×D3—22no—
655C22×D3—22no—
656C22×D3—22no—
657C22×D3—22no—
658C22×D3—52no—
659C22×D3—52no—
660C22×D3—102no—
661C22×D3—102no—
662C22×D3—102no—
663C22×D3—102no—
664C22×D3—102no—
665C22×D3—102no—
666C22×D3—204no—
667C22×D3—204no—
668C22×D3—204no—
669C22×D3—2016no—
670C22×D3C23×D512yes—
671C22×D3C23×D512yes—
672C22×D3C23×D512yes—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
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×C4C23×D512yes—
683C2×C3×C4C23×D512yes—
684C2×C3×C4C23×D512yes—
685#67—204no—
686#67—204no—
687#67—204no—
688C2×Dic3—22no—
689C2×Dic3—52no—
690C2×Dic3—52no—
691C2×Dic3—102no—
692C2×Dic3—102no—
693C2×Dic3C23×D512yes—
694D12—44no—
695D12—44no—
696D12—44no—
697D12—204no—
698D12—204no—
699D12—204no—
700D12—204no—
701D12—204no—
702D12—204no—
703C4×D3—44no—
704C4×D3—204no—
705C4×D3—204no—
706C22×C5—62no—
707C22×C5—62no—
708C22×C5—62no—
709C22×C5—62no—
710C22×C5—62no—
711C22×C5—62no—
712C22×C5—62no—
713C22×C5—62no—
714C22×C5—62no—
715C22×C5—124no—
716C22×C5—124no—
717C22×C5—124no—
718C22×C5#100912yes—
719C22×C5#100912yes—
720C22×C5#100912yes—
721C22×C5C24×D311yescharacteristic
722C2×D5—22no—
723C2×D5—22no—
724C2×D5—22no—
725C2×D5—44no—
726C2×D5—62no—
727C2×D5—62no—
728C2×D5—62no—
729C2×D5—62no—
730C2×D5—62no—
731C2×D5—62no—
732C2×D5—1216no—
733C2×D5—124no—
734C2×D5—124no—
735C4×C5—22no—
736C4×C5—22no—
737C4×C5—22no—
738C4×C5—62no—
739Dic5—22no—
740Dic5—22no—
741Dic5—22no—
742Dic5—62no—
743Dic5—62no—
744C24—31no—
745C24—31no—
746C24—31no—
747C24—51no—
748C24—154no—
749C24—151no—
750C24—151no—
751C24—602no—
752C24—602no—
753C24—602no—
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—34no—
780C22×C4—51no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—122no—
784C22×C4—154no—
785C22×C4—151no—
786C22×C4—151no—
787C22×C4—154no—
788C22×C4—602no—
789C22×C4—602no—
790C22×C4C2×D3×D511yescharacteristic
791C22×C4C2×D3×D511yescharacteristic
792C22×C4C2×D3×D511yescharacteristic
793C4⋊C4—54no—
794C4⋊C4—54no—
795C4⋊C4—154no—
796C4⋊C4—154no—
797C4⋊C4—154no—
798C4⋊C4C2×D3×D514yescomplemented
799C22⋊C4—34no—
800C22⋊C4—34no—
801C22⋊C4—54no—
802C22⋊C4—54no—
803C22⋊C4—54no—
804C22⋊C4—154no—
805C22⋊C4—154no—
806C22⋊C4—154no—
807C22⋊C4—154no—
808C22⋊C4—154no—
809C22⋊C4—154no—
810C22⋊C4—154no—
811C42—54no—
812C3×C5C2×#56011yescharacteristic, complemented, Hall
813C22×C3—102no—
814C22×C3—102no—
815C22×C3—102no—
816C22×C3—204no—
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—22no—
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—44no—
831C2×D3—44no—
832C2×D3—44no—
833C2×D3—102no—
834C2×D3—102no—
835C2×D3—102no—
836C2×D3—102no—
837C2×D3—102no—
838C2×D3—102no—
839C2×D3—2016no—
840C2×D3—204no—
841C2×D3—204no—
842C3×C4—22no—
843C3×C4—22no—
844C3×C4—22no—
845C3×C4—102no—
846C3×C4—102no—
847C3×C4—102no—
848Dic3—22no—
849Dic3—102no—
850Dic3—102no—
851C2×C5—122no—
852C2×C5—122no—
853C2×C5—122no—
854C2×C5#571114yescomplemented
855C2×C5C2×#100911yescharacteristic
856C2×C5C2×#100911yescharacteristic
857C2×C5C2×#100911yescharacteristic
858D5—42no—
859D5—122no—
860D5—122no—
861C23—32no—
862C23—32no—
863C23—32no—
864C23—52no—
865C23—62no—
866C23—62no—
867C23—62no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23—102no—
875C23—102no—
876C23—102no—
877C23—152no—
878C23—152no—
879C23—302no—
880C23—302no—
881C23—302no—
882C23—302no—
883C23—302no—
884C23—302no—
885C23—604no—
886C23—604no—
887C23—604no—
888C23—6016no—
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—22no—
905C2×C4—32no—
906C2×C4—52no—
907C2×C4—52no—
908C2×C4—52no—
909C2×C4—62no—
910C2×C4—102no—
911C2×C4—102no—
912C2×C4—102no—
913C2×C4—124no—
914C2×C4—152no—
915C2×C4—152no—
916C2×C4—302no—
917C2×C4—302no—
918C2×C4—604no—
919C2×C4—604no—
920C2×C4C22×D3×D512yes—
921C2×C4C22×D3×D512yes—
922C2×C4C22×D3×D512yes—
923C2×C3—202no—
924C2×C3#6595414yescomplemented
925C2×C3C2×#414411yescharacteristic
926C2×C3C2×#414411yescharacteristic
927C2×C3C2×#414911yescharacteristic
928D3—42no—
929D3—42no—
930D3—42no—
931D3—202no—
932D3—202no—
933C5C2×#571111yescharacteristic, complemented, Sylow
934C22—62no—
935C22—62no—
936C22—62no—
937C22—62no—
938C22—62no—
939C22—62no—
940C22—62no—
941C22—62no—
942C22—62no—
943C22—102no—
944C22—102no—
945C22—102no—
946C22—124no—
947C22—124no—
948C22—124no—
949C22—204no—
950C22—302no—
951C22—302no—
952C22—302no—
953C22—302no—
954C22—302no—
955C22—302no—
956C22—6016no—
957C22—604no—
958C22—604no—
959C22#9201812yes—
960C22#9202712yes—
961C22#9203512yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—22no—
966C4—62no—
967C4—102no—
968C4—102no—
969C4—102no—
970C4—302no—
971C4—302no—
972C3C2×#6595411yescharacteristic, complemented, Sylow
973C2—122no—
974C2—122no—
975C2—122no—
976C2—202no—
977C2—602no—
978C2—602no—
979C2#1175394214yesdirect product factor
980C2C2×#9201811yescharacteristic
981C2C2×#9202711yescharacteristic
982C2C2×#9203511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#560
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91783C2semidirect
2. C2×C5×#895C2semidirect
3. C2×C3×#4044C2semidirect
4. C2×#91476C2semidirect
5. C2×#91475C2semidirect
6. C2×#91475C2semidirect
7. C2×#91466C2semidirect
8. C2×#91461C2semidirect
9. C2×#91454C2semidirect
10. C2×#91453C2semidirect
11. C2×#91451C2semidirect
12. C2×#91427C2semidirect
13. C2×#91416C2semidirect
14. C2×#91372C2semidirect
15. C2×#91351C2semidirect
16. #11753942C2direct (N × H)
20. C22×C4×D15C22semidirect
23. C22×C5×D12C22semidirect
24. C22×C4×C5×D3C22semidirect
28. C22×#1203C22semidirect
29. C22×#1203C22semidirect
33. C22×D3×Dic5C22semidirect
34. C2×C3×C5×C4⋊C4C22semidirect
37. C2×#6714C22semidirect
38. C2×#6712C22semidirect
39. #91783C22semidirect
41. C2×C5×(C2×D3)⋊C4C22semidirect
42. C5×#895C22semidirect
46. C2×C3×C4⋊Dic5C22semidirect
47. C2×C3×#683C22semidirect
48. C2×C3×C4×Dic5C22semidirect
49. C3×#4044C22semidirect
50. C2×Dic3⋊Dic5C22semidirect
51. C2×#6669C22semidirect
55. C2×(C2×D3)⋊Dic5C22semidirect
56. #91476C22semidirect
57. #91475C22semidirect
58. #91475C22semidirect
59. #91466C22semidirect
60. #91461C22semidirect
61. #91454C22semidirect
62. #91453C22semidirect
63. #91451C22semidirect
64. #91427C22semidirect
65. #91416C22semidirect
66. #91372C22semidirect
67. #91351C22semidirect
79. C2×#4044D3semidirect
103. C2×C4×D15C23semidirect
110. C2×C5×D12C23semidirect
112. C2×C4×C5×D3C23semidirect
124. C2×#1203C23semidirect
125. C2×#1203C23semidirect
133. C2×D3×Dic5C23semidirect
134. C3×C5×C4⋊C4C23semidirect
137. #6714C23semidirect
138. #6712C23semidirect
140. C5×(C2×D3)⋊C4C23semidirect
144. C3×C4⋊Dic5C23semidirect
145. C3×#683C23semidirect
146. C3×C4×Dic5C23semidirect
147. Dic3⋊Dic5C23semidirect
148. #6669C23semidirect
152. (C2×D3)⋊Dic5C23semidirect
157. C2×#895D5semidirect
186. C2×C5×C4⋊C4C2×D3semidirect
208. C2×C4⋊Dic5C2×D3semidirect
211. C2×#683C2×D3semidirect
212. C2×C4×Dic5C2×D3semidirect
213. #4044C2×D3semidirect
294. C22×D12C2×D5semidirect
297. C22×C4×D3C2×D5semidirect
301. C2×C3×C4⋊C4C2×D5semidirect
314. C2×(C2×D3)⋊C4C2×D5semidirect
320. #895C2×D5semidirect
381. C5×C4⋊C4C22×D3semidirect
395. C4⋊Dic5C22×D3semidirect
398. #683C22×D3semidirect
399. C4×Dic5C22×D3semidirect
496. C2×D12C22×D5semidirect
502. C2×C4×D3C22×D5semidirect
505. C3×C4⋊C4C22×D5semidirect
518. (C2×D3)⋊C4C22×D5semidirect
620. C2×C4⋊C4D3×D5semidirect
634. C2×C3×C5#560semidirect
798. C4⋊C4C2×D3×D5semidirect
812. C3×C5C2×#560semidirect
854. C2×C5#5711semidirect
924. C2×C3#65954semidirect
933. C5C2×#5711semidirect
972. C3C2×#65954semidirect
979. C2#11753942direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917832
C2×C5×#8952
C2×C3×#40442
C2×#914762
C2×#914752
C2×#914662
C2×#914612
C2×#914542
C2×#914532
C2×#914512
C2×#914272
C2×#914162
C2×#913722
C2×#913512
#117539422
C2×#659543
C2×#57115