Finite Group Databasebeta

← C2×#11753943 #14495239

Subgroups — C2×#11753943 #14495239

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×#91784C211yesmaximal, characteristic, complemented
2C2×C5×#894C211yesmaximal, characteristic, complemented
3C2×C3×#4044C211yesmaximal, characteristic, complemented
4C2×#91476C211yesmaximal, characteristic, complemented
5C2×#91476C211yesmaximal, characteristic, complemented
6C2×#91475C211yesmaximal, characteristic, complemented
7C2×#91461C211yesmaximal, characteristic, complemented
8C2×#91460C211yesmaximal, characteristic, complemented
9C2×#91459C211yesmaximal, characteristic, complemented
10C2×#91454C211yesmaximal, characteristic, complemented
11C2×#91451C211yesmaximal, characteristic, complemented
12C2×#91438C211yesmaximal, characteristic, complemented
13C2×#91420C211yesmaximal, characteristic, complemented
14C2×#91387C211yesmaximal, characteristic, complemented
15C2×#91355C211yesmaximal, characteristic, complemented
16#11753943C2116yesmaximal, direct product factor
17C2×#66000—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×D60C2211yescharacteristic, complemented
22C22×C4×D15C2211yescharacteristic, complemented
23C22×C5×D12C2211yescharacteristic
24C22×C4×C5×D3C2211yescharacteristic, complemented
25C22×#1203C2211yescharacteristic
26C22×#1203C2211yescharacteristic
27C22×#1203C2211yescharacteristic
28C22×#1203C2211yescharacteristic, complemented
29C22×#1203C2211yescharacteristic, complemented
30C22×#1202C2211yescharacteristic
31C22×#1202C2211yescharacteristic
32C22×#1201C2211yescharacteristic
33C22×#1200C2211yescharacteristic, complemented
34C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic, complemented
37#91784C2218yescomplemented
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic
39C2×C5×(C2×D3)⋊C4C2211yescharacteristic
40C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
42C5×#894C2218yescomplemented
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×#6667C2211yescharacteristic
54C2×#6667C2211yescharacteristic, complemented
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56#91476C2218yescomplemented
57#91476C2218yescomplemented
58#91475C2218yescomplemented
59#91461C2218yescomplemented
60#91460C2218yescomplemented
61#91459C2218yescomplemented
62#91454C2218yescomplemented
63#91451C2218yescomplemented
64#91438C2218yescomplemented
65#91420C2218yescomplemented
66#91387C2218yescomplemented
67#91355C2218yescomplemented
68C2×#5711—51nomaximal, Hall
69C2×C5×#123—31no—
70C2×#4086—31no—
71C2×#4083—31no—
72C2×#4076—31no—
73C2×#4076—31no—
74#66000—316no—
75C2×#4044—31no—
76C2×#4044D311yescharacteristic, complemented
77C2×#4041—31no—
78C2×#4041—31no—
79C2×#4030—31no—
80C2×#4030—31no—
81C2×#4029—31no—
82C2×#4029—31no—
83C2×#4028—31no—
84C2×#4028—31no—
85C23×D15C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×D15C2311yescharacteristic
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
99C2×D60—42no—
100C2×D60—42no—
101C2×D60—42no—
102C2×D60C2314yes—
103C2×D60C2314yes—
104C2×D60C2314yescomplemented
105C2×C4×D15—42no—
106C2×C4×D15C2314yescomplemented
107C22×C5×Dic3C2311yescharacteristic
108C22×C5×Dic3C2311yescharacteristic
109C2×C5×D12—42no—
110C2×C5×D12C2314yes—
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×#1202—42no—
128C2×#1202C2314yes—
129C2×#1202C2314yes—
130C2×#1201—42no—
131C2×#1201C2314yes—
132C2×#1200—42no—
133C2×#1200C2314yescomplemented
134C3×C5×C4⋊C4C2314yescomplemented
135#6714C2314yes—
136#6714C2314yescomplemented
137C5×(C2×D3)⋊C4C2314yes—
138C5×(C2×D3)⋊C4C2314yes—
139C5×(C2×D3)⋊C4C2314yescomplemented
140C5×Dic3⋊C4C2314yescomplemented
141C3×#685C2314yes—
142C3×#685C2314yes—
143C3×#685C2314yes—
144C3×C4⋊Dic5C2314yescomplemented
145C3×#683C2314yescomplemented
146C3×C4×Dic5C2314yescomplemented
147Dic3⋊Dic5C2314yescomplemented
148#6669C2314yescomplemented
149#6667C2314yes—
150#6667C2314yes—
151#6667C2314yescomplemented
152(C2×D3)⋊Dic5C2314yes—
153C2×C3×#126—51no—
154#5711—516no—
155C2×#895—51no—
156C2×#895—51no—
157C2×#895—51no—
158C2×#894—51no—
159C2×#894—51no—
160C2×#894D511yescharacteristic, complemented
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—
171C23×C4×C5—31no—
172C22×C22⋊D5—31no—
173C22×C22⋊D5—31no—
174C22×C22⋊D5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5—31no—
177C22×C22⋊D5—31no—
178C22×D20—31no—
179C22×D20—31no—
180C22×D20—31no—
181C22×D20—31no—
182C22×D20—31no—
183C22×C4×D5—31no—
184C22×C4×D5—31no—
185C5×#123—38no—
186C2×C5×C4⋊C4—31no—
187C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
188C2×C5×C22⋊C4—31no—
189C2×C5×C22⋊C4—31no—
190C2×C5×C22⋊C4—31no—
191C2×C22⋊Dic5—31no—
192#4086—38no—
193#4083—38no—
194#4076—38no—
195#4076—38no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685—31no—
199C2×#685—31no—
200C2×#685—31no—
201C2×#685C2×D311yescharacteristic
202C2×#685C2×D311yescharacteristic
203C2×#685C2×D311yescharacteristic
204C2×C4⋊Dic5—31no—
205C2×C4⋊Dic5C2×D311yescharacteristic, complemented
206C2×#683—31no—
207C2×#683C2×D311yescharacteristic, complemented
208C2×C4×Dic5C2×D311yescharacteristic, complemented
209#4044—38no—
210#4044C2×D318yescomplemented
211#4041—38no—
212#4041—38no—
213#4030—38no—
214#4030—38no—
215#4029—38no—
216#4029—38no—
217#4028—38no—
218#4028—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×D15—22no—
228C22×D15—22no—
229C22×D15—22no—
230C22×D15C2412yes—
231C22×D15C2412yes—
232C22×D15C2412yes—
233C22×C5×D3—22no—
234C22×C5×D3—22no—
235C22×C5×D3—22no—
236C22×C5×D3—22no—
237C22×C5×D3—22no—
238C22×C5×D3—22no—
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×Dic15C2412yes—
257D60—44no—
258D60—44no—
259D60—44no—
260C4×D15—44no—
261C2×C5×Dic3—22no—
262C2×C5×Dic3—22no—
263C2×C5×Dic3C2412yes—
264C2×C5×Dic3C2412yes—
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#1202—44no—
280#1201—44no—
281#1200—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×D12—51no—
293C22×D12—51no—
294C22×D12C2×D511yescharacteristic
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)⋊C4C2×D511yescharacteristic
313C2×(C2×D3)⋊C4C2×D511yescharacteristic
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#894C2×D518yescomplemented
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—
334C23×D5—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—122no—
344C22×C4×C5—31no—
345C22×C4×C5—31no—
346C22×C4×C5—34no—
347C22×C4×C5—122no—
348C22×C4×C5C22×D311yescharacteristic
349C22×C4×C5C22×D311yescharacteristic
350C22×C4×C5C22×D311yescharacteristic
351C2×C22⋊D5—34no—
352C2×C22⋊D5—34no—
353C2×C22⋊D5—34no—
354C2×C22⋊D5—34no—
355C2×C22⋊D5—34no—
356C2×C22⋊D5—34no—
357C2×C22⋊D5—122no—
358C2×C22⋊D5—122no—
359C2×C22⋊D5—122no—
360C2×C22⋊D5—122no—
361C2×C22⋊D5—122no—
362C2×C22⋊D5—122no—
363C22×Dic5—31no—
364C22×Dic5C22×D311yescharacteristic
365C22×Dic5C22×D311yescharacteristic
366C22×Dic5C22×D311yescharacteristic
367C2×D20—34no—
368C2×D20—34no—
369C2×D20—34no—
370C2×D20—34no—
371C2×D20—34no—
372C2×D20—122no—
373C2×D20—122no—
374C2×D20—122no—
375C2×D20—122no—
376C2×D20—122no—
377C2×C4×D5—34no—
378C2×C4×D5—34no—
379C2×C4×D5—122no—
380C2×C4×D5—122no—
381C5×C4⋊C4—34no—
382C5×C4⋊C4C22×D314yescomplemented
383C5×C22⋊C4—34no—
384C5×C22⋊C4—34no—
385C5×C22⋊C4—34no—
386C22⋊Dic5—34no—
387#685—34no—
388#685—34no—
389#685—34no—
390#685—34no—
391#685—34no—
392#685C22×D314yes—
393#685C22×D314yes—
394#685C22×D314yes—
395C4⋊Dic5—34no—
396C4⋊Dic5C22×D314yescomplemented
397#683—34no—
398#683C22×D314yescomplemented
399C4×Dic5C22×D314yescomplemented
400#560—1516no—
401C2×#127—151no—
402C2×#126—51no—
403C2×#126—151no—
404C2×#123—31no—
405C2×#123—151no—
406C2×#123—151no—
407C2×#121—151no—
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—22no—
427C2×D15—22no—
428C2×D15—22no—
429C2×D15—44no—
430C2×D15—44no—
431C2×D15—44no—
432C2×C5×D3—22no—
433C2×C5×D3—22no—
434C2×C5×D3—22no—
435C2×C5×D3—22no—
436C2×C5×D3—22no—
437C2×C5×D3—22no—
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—
449C3×Dic5—22no—
450C3×Dic5—22no—
451C3×Dic5—22no—
452C5×Dic3—22no—
453C5×Dic3—22no—
454C24×C3—51no—
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×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×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×D514yes—
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)⋊C4C22×D514yes—
517(C2×D3)⋊C4C22×D514yes—
518(C2×D3)⋊C4C22×D514yescomplemented
519Dic3⋊C4—54no—
520Dic3⋊C4—54no—
521Dic3⋊C4C22×D514yescomplemented
522C23×C5—32no—
523C23×C5—32no—
524C23×C5—62no—
525C23×C5—62no—
526C23×C5—62no—
527C23×C5—62no—
528C23×C5—62no—
529C23×C5—62no—
530C23×C5C23×D311yescharacteristic
531C22×D5—22no—
532C22×D5—22no—
533C22×D5—22no—
534C22×D5—32no—
535C22×D5—32no—
536C22×D5—32no—
537C22×D5—62no—
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—124no—
547C22×D5—124no—
548C22×D5—124no—
549C22×D5—1216no—
550C22×D5C23×D312yes—
551C5×D4—124no—
552C2×C4×C5—22no—
553C2×C4×C5—22no—
554C2×C4×C5—22no—
555C2×C4×C5—32no—
556C2×C4×C5—32no—
557C2×C4×C5—62no—
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—
569C2×Dic5—22no—
570C2×Dic5—22no—
571C2×Dic5—22no—
572C2×Dic5—32no—
573C2×Dic5—62no—
574C2×Dic5C23×D312yes—
575C2×Dic5C23×D312yes—
576C2×Dic5C23×D312yes—
577D20—124no—
578D20—124no—
579D20—124no—
580D20—124no—
581D20—124no—
582C4×D5—124no—
583C4×D5—124no—
584C25—151no—
585C22×D4—31no—
586C22×D4—151no—
587C22×D4—151no—
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—38no—
604#123—158no—
605#123—158no—
606#121—158no—
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—151no—
619C2×C4⋊C4—151no—
620C2×C4⋊C4D3×D511yescharacteristic, complemented
621C2×C22⋊C4—31no—
622C2×C22⋊C4—31no—
623C2×C22⋊C4—31no—
624C2×C22⋊C4—51no—
625C2×C22⋊C4—51no—
626C2×C22⋊C4—51no—
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—
640D15—42no—
641C3×D5—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—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—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—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—62no—
707C22×C5—62no—
708C22×C5—62no—
709C22×C5—62no—
710C22×C5—62no—
711C22×C5—62no—
712C22×C5—124no—
713C22×C5—124no—
714C22×C5#100912yes—
715C22×C5#100912yes—
716C22×C5#100912yes—
717C22×C5C24×D311yescharacteristic
718C2×D5—22no—
719C2×D5—22no—
720C2×D5—22no—
721C2×D5—44no—
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—22no—
738C4×C5—62no—
739C4×C5—62no—
740Dic5—22no—
741Dic5—22no—
742Dic5—22no—
743Dic5—62no—
744C24—31no—
745C24—31no—
746C24—51no—
747C24—154no—
748C24—151no—
749C24—151no—
750C24—151no—
751C24—602no—
752C24—602no—
753C24—602no—
754C2×D4—34no—
755C2×D4—122no—
756C2×D4—154no—
757C2×D4—154no—
758C2×D4—154no—
759C2×D4—154no—
760C2×D4—154no—
761C2×D4—154no—
762C2×D4—154no—
763C2×D4—154no—
764C2×D4—154no—
765C2×D4—154no—
766C2×D4—154no—
767C2×D4—602no—
768C2×D4—602no—
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—122no—
785C22×C4—154no—
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—34no—
794C4⋊C4—54no—
795C4⋊C4—54no—
796C4⋊C4—154no—
797C4⋊C4—154no—
798C4⋊C4C2×D3×D514yescomplemented
799C22⋊C4—34no—
800C22⋊C4—34no—
801C22⋊C4—34no—
802C22⋊C4—54no—
803C22⋊C4—54no—
804C22⋊C4—54no—
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#414912yes—
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—22no—
845C3×C4—102no—
846C3×C4—102no—
847C3×C4—102no—
848Dic3—22no—
849Dic3—22no—
850Dic3—102no—
851C2×C5—122no—
852C2×C5—122no—
853C2×C5#571114yescomplemented
854C2×C5C2×#100911yescharacteristic
855C2×C5C2×#100911yescharacteristic
856C2×C5C2×#100911yescharacteristic
857D5—42no—
858D5—122no—
859D5—122no—
860D5—122no—
861C23—32no—
862C23—32no—
863C23—52no—
864C23—62no—
865C23—62no—
866C23—62no—
867C23—62no—
868C23—62no—
869C23—62no—
870C23—102no—
871C23—102no—
872C23—102no—
873C23—152no—
874C23—152no—
875C23—152no—
876C23—302no—
877C23—302no—
878C23—302no—
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—604no—
892D4—604no—
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—32no—
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—124no—
916C2×C4—152no—
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#6600014yescomplemented
925C2×C3C2×#414411yescharacteristic
926C2×C3C2×#414911yescharacteristic
927C2×C3C2×#414911yescharacteristic
928D3—42no—
929D3—42no—
930D3—202no—
931D3—202no—
932D3—202no—
933C5C2×#571111yescharacteristic, complemented, Sylow
934C22—62no—
935C22—62no—
936C22—62no—
937C22—62no—
938C22—62no—
939C22—62no—
940C22—102no—
941C22—102no—
942C22—102no—
943C22—124no—
944C22—124no—
945C22—204no—
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#9203512yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—22no—
966C4—62no—
967C4—62no—
968C4—102no—
969C4—102no—
970C4—102no—
971C4—302no—
972C3C2×#6600011yescharacteristic, complemented, Sylow
973C2—122no—
974C2—122no—
975C2—202no—
976C2—602no—
977C2—602no—
978C2—602no—
979C2#1175394314yesdirect product factor
980C2C2×#9201911yescharacteristic
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×#91784C2semidirect
2. C2×C5×#894C2semidirect
3. C2×C3×#4044C2semidirect
4. C2×#91476C2semidirect
5. C2×#91476C2semidirect
6. C2×#91475C2semidirect
7. C2×#91461C2semidirect
8. C2×#91460C2semidirect
9. C2×#91459C2semidirect
10. C2×#91454C2semidirect
11. C2×#91451C2semidirect
12. C2×#91438C2semidirect
13. C2×#91420C2semidirect
14. C2×#91387C2semidirect
15. C2×#91355C2semidirect
16. #11753943C2direct (N × H)
21. C22×D60C22semidirect
22. C22×C4×D15C22semidirect
24. C22×C4×C5×D3C22semidirect
28. C22×#1203C22semidirect
29. C22×#1203C22semidirect
33. C22×#1200C22semidirect
34. C2×C3×C5×C4⋊C4C22semidirect
36. C2×#6714C22semidirect
37. #91784C22semidirect
40. C2×C5×(C2×D3)⋊C4C22semidirect
41. C2×C5×Dic3⋊C4C22semidirect
42. C5×#894C22semidirect
46. C2×C3×C4⋊Dic5C22semidirect
47. C2×C3×#683C22semidirect
48. C2×C3×C4×Dic5C22semidirect
49. C3×#4044C22semidirect
50. C2×Dic3⋊Dic5C22semidirect
51. C2×#6669C22semidirect
54. C2×#6667C22semidirect
56. #91476C22semidirect
57. #91476C22semidirect
58. #91475C22semidirect
59. #91461C22semidirect
60. #91460C22semidirect
61. #91459C22semidirect
62. #91454C22semidirect
63. #91451C22semidirect
64. #91438C22semidirect
65. #91420C22semidirect
66. #91387C22semidirect
67. #91355C22semidirect
76. C2×#4044D3semidirect
104. C2×D60C23semidirect
106. C2×C4×D15C23semidirect
112. C2×C4×C5×D3C23semidirect
124. C2×#1203C23semidirect
125. C2×#1203C23semidirect
133. C2×#1200C23semidirect
134. C3×C5×C4⋊C4C23semidirect
136. #6714C23semidirect
139. C5×(C2×D3)⋊C4C23semidirect
140. C5×Dic3⋊C4C23semidirect
144. C3×C4⋊Dic5C23semidirect
145. C3×#683C23semidirect
146. C3×C4×Dic5C23semidirect
147. Dic3⋊Dic5C23semidirect
148. #6669C23semidirect
151. #6667C23semidirect
160. C2×#894D5semidirect
187. C2×C5×C4⋊C4C2×D3semidirect
205. C2×C4⋊Dic5C2×D3semidirect
207. C2×#683C2×D3semidirect
208. C2×C4×Dic5C2×D3semidirect
210. #4044C2×D3semidirect
297. C22×C4×D3C2×D5semidirect
301. C2×C3×C4⋊C4C2×D5semidirect
314. C2×(C2×D3)⋊C4C2×D5semidirect
317. C2×Dic3⋊C4C2×D5semidirect
323. #894C2×D5semidirect
382. C5×C4⋊C4C22×D3semidirect
396. C4⋊Dic5C22×D3semidirect
398. #683C22×D3semidirect
399. C4×Dic5C22×D3semidirect
502. C2×C4×D3C22×D5semidirect
505. C3×C4⋊C4C22×D5semidirect
518. (C2×D3)⋊C4C22×D5semidirect
521. Dic3⋊C4C22×D5semidirect
620. C2×C4⋊C4D3×D5semidirect
634. C2×C3×C5#560semidirect
798. C4⋊C4C2×D3×D5semidirect
812. C3×C5C2×#560semidirect
853. C2×C5#5711semidirect
924. C2×C3#66000semidirect
933. C5C2×#5711semidirect
972. C3C2×#66000semidirect
979. C2#11753943direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917842
C2×C5×#8942
C2×C3×#40442
C2×#914762
C2×#914752
C2×#914612
C2×#914602
C2×#914592
C2×#914542
C2×#914512
C2×#914382
C2×#914202
C2×#913872
C2×#913552
#117539432
C2×#660003
C2×#57115