Finite Group Databasebeta

← C2×#11753941 #14495241

Subgroups — C2×#11753941 #14495241

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×#898C211yesmaximal, characteristic, complemented
3C2×C3×#4040C211yesmaximal, characteristic, complemented
4C2×#91476C211yesmaximal, characteristic, complemented
5C2×#91476C211yesmaximal, characteristic, complemented
6C2×#91474C211yesmaximal, characteristic, complemented
7C2×#91461C211yesmaximal, characteristic, complemented
8C2×#91459C211yesmaximal, characteristic, complemented
9C2×#91458C211yesmaximal, characteristic, complemented
10C2×#91450C211yesmaximal, characteristic, complemented
11C2×#91448C211yesmaximal, characteristic, complemented
12C2×#91420C211yesmaximal, characteristic, complemented
13C2×#91380C211yesmaximal, characteristic, complemented
14C2×#91356C211yesmaximal, characteristic, complemented
15C2×#91354C211yesmaximal, characteristic, complemented
16#11753941C2116yesmaximal, direct product factor
17C2×#66045—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×D60C2211yescharacteristic, complemented
22C22×C4×D15C2211yescharacteristic, complemented
23C22×C3×D20C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic, complemented
25C22×#1203C2211yescharacteristic
26C22×#1203C2211yescharacteristic
27C22×#1202C2211yescharacteristic
28C22×#1202C2211yescharacteristic
29C22×#1202C2211yescharacteristic
30C22×#1202C2211yescharacteristic, complemented
31C22×#1202C2211yescharacteristic, complemented
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
41C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
42C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
43C2×C4×C5×Dic3C2211yescharacteristic, complemented
44C5×#898C2218yescomplemented
45C2×C3×#685C2211yescharacteristic
46C2×C3×#685C2211yescharacteristic
47C2×C3×#685C2211yescharacteristic, complemented
48C2×C3×#683C2211yescharacteristic, complemented
49C3×#4040C2218yescomplemented
50C2×#6669C2211yescharacteristic, complemented
51C2×#6668C2211yescharacteristic, complemented
52C2×#6667C2211yescharacteristic
53C2×#6667C2211yescharacteristic
54C2×#6667C2211yescharacteristic, complemented
55C2×#6665C2211yescharacteristic
56#91476C2218yescomplemented
57#91476C2218yescomplemented
58#91474C2218yescomplemented
59#91461C2218yescomplemented
60#91459C2218yescomplemented
61#91458C2218yescomplemented
62#91450C2218yescomplemented
63#91448C2218yescomplemented
64#91420C2218yescomplemented
65#91380C2218yescomplemented
66#91356C2218yescomplemented
67#91354C2218yescomplemented
68C2×#5666—51nomaximal, Hall
69C2×C5×#126—31no—
70#66045—316no—
71C2×#4041—31no—
72C2×#4041—31no—
73C2×#4041—31no—
74C2×#4040—31no—
75C2×#4040—31no—
76C2×#4040D311yescharacteristic, complemented
77C2×#4030—31no—
78C2×#4030—31no—
79C2×#4030—31no—
80C2×#4028—31no—
81C2×#4028—31no—
82C2×#4028—31no—
83C2×#4022—31no—
84C2×#4020—31no—
85C23×D15C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C23×C3×D5C2311yescharacteristic
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
109C22×C5×Dic3C2311yescharacteristic
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C2×C3×D20—42no—
113C2×C3×D20C2314yes—
114C2×C3×C4×D5—42no—
115C2×C3×C4×D5C2314yescomplemented
116C2×#1203—42no—
117C2×#1203—42no—
118C2×#1203C2314yes—
119C2×#1203C2314yes—
120C2×#1202—42no—
121C2×#1202—42no—
122C2×#1202—42no—
123C2×#1202—42no—
124C2×#1202—42no—
125C2×#1202C2314yes—
126C2×#1202C2314yes—
127C2×#1202C2314yes—
128C2×#1202C2314yescomplemented
129C2×#1202C2314yescomplemented
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)⋊C4C2314yes—
140C5×C4⋊Dic3C2314yescomplemented
141C5×Dic3⋊C4C2314yescomplemented
142C4×C5×Dic3C2314yescomplemented
143C3×#685C2314yes—
144C3×#685C2314yes—
145C3×#685C2314yescomplemented
146C3×#683C2314yescomplemented
147#6669C2314yescomplemented
148#6668C2314yescomplemented
149#6667C2314yes—
150#6667C2314yes—
151#6667C2314yescomplemented
152#6665C2314yes—
153C2×C3×#123—51no—
154C2×#940—51no—
155C2×#937—51no—
156C2×#930—51no—
157C2×#930—51no—
158#5666—516no—
159C2×#898—51no—
160C2×#898D511yescharacteristic, complemented
161C2×#895—51no—
162C2×#895—51no—
163C2×#884—51no—
164C2×#884—51no—
165C2×#883—51no—
166C2×#883—51no—
167C2×#882—51no—
168C2×#882—51no—
169C24×D5—31no—
170C22×C22⋊D5—31no—
171C22×C22⋊D5—31no—
172C22×C22⋊D5—31no—
173C22×D20—31no—
174C22×D20—31no—
175C22×D20—31no—
176C22×D20—31no—
177C22×D20—31no—
178C22×D20—31no—
179C22×D20—31no—
180C22×D20—31no—
181C22×D20C2×D311yescharacteristic
182C22×C4×D5—31no—
183C22×C4×D5—31no—
184C22×C4×D5C2×D311yescharacteristic, complemented
185C5×#126—38no—
186C2×C5×C4⋊C4—31no—
187C2×C5×C4⋊C4—31no—
188C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
189C2×C5×C22⋊C4—31no—
190C2×C5×C22⋊C4—31no—
191C2×C5×C22⋊C4—31no—
192C2×C42×C5—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685—31no—
199C2×#685C2×D311yescharacteristic
200C2×#685C2×D311yescharacteristic
201C2×#685C2×D311yescharacteristic, complemented
202C2×#683—31no—
203C2×#683—31no—
204C2×#683C2×D311yescharacteristic, complemented
205#4041—38no—
206#4041—38no—
207#4041—38no—
208#4040—38no—
209#4040—38no—
210#4040C2×D318yescomplemented
211#4030—38no—
212#4030—38no—
213#4030—38no—
214#4028—38no—
215#4028—38no—
216#4028—38no—
217#4022—38no—
218#4020—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×D3C2412yes—
237C22×C3×D5—22no—
238C22×C3×D5—22no—
239C22×C3×D5—22no—
240C22×C3×D5—22no—
241C22×C3×D5—22no—
242C22×C3×D5—22no—
243C22×C3×D5C2412yes—
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×Dic3—22no—
264C2×C5×Dic3C2412yes—
265C2×C5×Dic3C2412yes—
266C2×C5×Dic3C2412yes—
267C2×C3×Dic5—22no—
268C2×C3×Dic5—22no—
269C2×C3×Dic5C2412yes—
270C2×C3×Dic5C2412yes—
271C3×D20—44no—
272C3×C4×D5—44no—
273#1203—44no—
274#1203—44no—
275#1202—44no—
276#1202—44no—
277#1202—44no—
278#1202—44no—
279#1202—44no—
280#1201—44no—
281#1200—44no—
282C24×D3—51no—
283C22×C3×D4—51no—
284C23×C3×C4—51no—
285C22×#67—51no—
286C22×#67—51no—
287C22×#67—51no—
288C22×#67—51no—
289C22×#67—51no—
290C22×#67—51no—
291C22×D12—51no—
292C22×D12—51no—
293C22×D12—51no—
294C22×D12—51no—
295C22×D12—51no—
296C22×C4×D3—51no—
297C22×C4×D3—51no—
298C3×#123—58no—
299C2×C3×C4⋊C4—51no—
300C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
301C2×C3×C22⋊C4—51no—
302C2×C3×C22⋊C4—51no—
303C2×C3×C22⋊C4—51no—
304C2×#217—51no—
305#940—58no—
306#937—58no—
307#930—58no—
308#930—58no—
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
315C2×(C2×D3)⋊C4C2×D511yescharacteristic
316C2×(C2×D3)⋊C4C2×D511yescharacteristic
317C2×C4⋊Dic3—51no—
318C2×C4⋊Dic3C2×D511yescharacteristic, complemented
319C2×Dic3⋊C4—51no—
320C2×Dic3⋊C4C2×D511yescharacteristic, complemented
321C2×C4×Dic3C2×D511yescharacteristic, complemented
322#898—58no—
323#898C2×D518yescomplemented
324#895—58no—
325#895—58no—
326#884—58no—
327#884—58no—
328#883—58no—
329#883—58no—
330#882—58no—
331#882—58no—
332C24×C5—31no—
333C23×D5—31no—
334C23×D5—31no—
335C23×D5—31no—
336C23×D5—34no—
337C23×D5—122no—
338C23×D5—122no—
339C23×D5—122no—
340C23×D5C22×D311yescharacteristic
341C23×D5C22×D311yescharacteristic
342C22×C4×C5—31no—
343C22×C4×C5—31no—
344C22×C4×C5—31no—
345C22×C4×C5C22×D311yescharacteristic
346C22×C4×C5C22×D311yescharacteristic
347C22×C4×C5C22×D311yescharacteristic
348C2×C22⋊D5—34no—
349C2×C22⋊D5—34no—
350C2×C22⋊D5—34no—
351C2×C22⋊D5—122no—
352C2×C22⋊D5—122no—
353C2×C22⋊D5—122no—
354C22×Dic5—31no—
355C22×Dic5C22×D311yescharacteristic
356C22×Dic5C22×D311yescharacteristic
357C2×D20—34no—
358C2×D20—34no—
359C2×D20—34no—
360C2×D20—34no—
361C2×D20—34no—
362C2×D20—34no—
363C2×D20—34no—
364C2×D20—34no—
365C2×D20—42no—
366C2×D20—122no—
367C2×D20—122no—
368C2×D20—122no—
369C2×D20—122no—
370C2×D20—122no—
371C2×D20—122no—
372C2×D20—122no—
373C2×D20—122no—
374C2×D20C22×D314yes—
375C2×C4×D5—34no—
376C2×C4×D5—34no—
377C2×C4×D5—42no—
378C2×C4×D5—122no—
379C2×C4×D5—122no—
380C2×C4×D5C22×D314yescomplemented
381C5×C4⋊C4—34no—
382C5×C4⋊C4—34no—
383C5×C4⋊C4C22×D314yescomplemented
384C5×C22⋊C4—34no—
385C5×C22⋊C4—34no—
386C5×C22⋊C4—34no—
387C42×C5—34no—
388#685—34no—
389#685—34no—
390#685—34no—
391#685—34no—
392#685—34no—
393#685—34no—
394#685C22×D314yes—
395#685C22×D314yes—
396#685C22×D314yescomplemented
397#683—34no—
398#683—34no—
399#683C22×D314yescomplemented
400#560—1516no—
401C2×#127—151no—
402C2×#126—31no—
403C2×#126—151no—
404C2×#123—51no—
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—44no—
436C2×C3×D5—22no—
437C2×C3×D5—22no—
438C2×C3×D5—22no—
439C2×C3×D5—22no—
440C2×C3×D5—22no—
441C2×C3×D5—22no—
442C2×C3×D5—44no—
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—
451C5×Dic3—22no—
452C5×Dic3—22no—
453C5×Dic3—22no—
454C24×C3—51no—
455C24×C3—51no—
456C23×D3—51no—
457C23×D3—51no—
458C23×D3—51no—
459C23×D3—54no—
460C23×D3—202no—
461C23×D3—202no—
462C23×D3—202no—
463C23×D3C22×D511yescharacteristic
464C2×C3×D4—54no—
465C2×C3×D4—202no—
466C22×C3×C4—51no—
467C22×C3×C4—51no—
468C22×C3×C4—54no—
469C22×C3×C4—202no—
470C22×C3×C4C22×D511yescharacteristic
471C22×C3×C4C22×D511yescharacteristic
472C22×C3×C4C22×D511yescharacteristic
473C2×#67—54no—
474C2×#67—54no—
475C2×#67—54no—
476C2×#67—54no—
477C2×#67—54no—
478C2×#67—54no—
479C2×#67—202no—
480C2×#67—202no—
481C2×#67—202no—
482C2×#67—202no—
483C2×#67—202no—
484C2×#67—202no—
485C22×Dic3—51no—
486C22×Dic3C22×D511yescharacteristic
487C22×Dic3C22×D511yescharacteristic
488C22×Dic3C22×D511yescharacteristic
489C2×D12—54no—
490C2×D12—54no—
491C2×D12—54no—
492C2×D12—54no—
493C2×D12—54no—
494C2×D12—202no—
495C2×D12—202no—
496C2×D12—202no—
497C2×D12—202no—
498C2×D12—202no—
499C2×C4×D3—54no—
500C2×C4×D3—54no—
501C2×C4×D3—202no—
502C2×C4×D3—202no—
503C3×C4⋊C4—54no—
504C3×C4⋊C4C22×D514yescomplemented
505C3×C22⋊C4—54no—
506C3×C22⋊C4—54no—
507C3×C22⋊C4—54no—
508#217—54no—
509(C2×D3)⋊C4—54no—
510(C2×D3)⋊C4—54no—
511(C2×D3)⋊C4—54no—
512(C2×D3)⋊C4—54no—
513(C2×D3)⋊C4—54no—
514(C2×D3)⋊C4C22×D514yes—
515(C2×D3)⋊C4C22×D514yes—
516(C2×D3)⋊C4C22×D514yes—
517C4⋊Dic3—54no—
518C4⋊Dic3C22×D514yescomplemented
519Dic3⋊C4—54no—
520Dic3⋊C4C22×D514yescomplemented
521C4×Dic3C22×D514yescomplemented
522C23×C5—32no—
523C23×C5—62no—
524C23×C5—62no—
525C23×C5—62no—
526C23×C5C23×D311yescharacteristic
527C22×D5—22no—
528C22×D5—22no—
529C22×D5—22no—
530C22×D5—22no—
531C22×D5—22no—
532C22×D5—22no—
533C22×D5—32no—
534C22×D5—32no—
535C22×D5—32no—
536C22×D5—62no—
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—124no—
546C22×D5—124no—
547C22×D5—124no—
548C22×D5—1216no—
549C22×D5C23×D312yes—
550C22×D5C23×D312yes—
551C2×C4×C5—22no—
552C2×C4×C5—22no—
553C2×C4×C5—22no—
554C2×C4×C5—32no—
555C2×C4×C5—32no—
556C2×C4×C5—32no—
557C2×C4×C5—62no—
558C2×C4×C5—62no—
559C2×C4×C5—62no—
560C2×C4×C5C23×D312yes—
561C2×C4×C5C23×D312yes—
562C2×C4×C5C23×D312yes—
563C22⋊D5—124no—
564C22⋊D5—124no—
565C22⋊D5—124no—
566C2×Dic5—22no—
567C2×Dic5—22no—
568C2×Dic5—32no—
569C2×Dic5—62no—
570C2×Dic5C23×D312yes—
571C2×Dic5C23×D312yes—
572D20—44no—
573D20—124no—
574D20—124no—
575D20—124no—
576D20—124no—
577D20—124no—
578D20—124no—
579D20—124no—
580D20—124no—
581C4×D5—44no—
582C4×D5—124no—
583C4×D5—124no—
584C25—151no—
585C22×D4—51no—
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—51no—
598C23×C4—151no—
599C23×C4—151no—
600#127—158no—
601#126—38no—
602#126—158no—
603#123—58no—
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—31no—
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—31no—
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—
642C3×D5—42no—
643C5×D3—42no—
644C23×C3—52no—
645C23×C3—52no—
646C23×C3—102no—
647C23×C3—102no—
648C23×C3—102no—
649C23×C3—102no—
650C23×C3—102no—
651C23×C3—102no—
652C23×C3C23×D511yescharacteristic
653C22×D3—22no—
654C22×D3—22no—
655C22×D3—22no—
656C22×D3—52no—
657C22×D3—52no—
658C22×D3—52no—
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—102no—
668C22×D3—204no—
669C22×D3—204no—
670C22×D3—204no—
671C22×D3—2016no—
672C22×D3C23×D512yes—
673C3×D4—204no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—52no—
678C2×C3×C4—52no—
679C2×C3×C4—102no—
680C2×C3×C4—102no—
681C2×C3×C4—204no—
682C2×C3×C4C23×D512yes—
683C2×C3×C4C23×D512yes—
684C2×C3×C4C23×D512yes—
685#67—204no—
686#67—204no—
687#67—204no—
688#67—204no—
689#67—204no—
690#67—204no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—52no—
695C2×Dic3—102no—
696C2×Dic3C23×D512yes—
697C2×Dic3C23×D512yes—
698C2×Dic3C23×D512yes—
699D12—204no—
700D12—204no—
701D12—204no—
702D12—204no—
703D12—204no—
704C4×D3—204no—
705C4×D3—204no—
706C22×C5—62no—
707C22×C5—62no—
708C22×C5—62no—
709C22×C5—124no—
710C22×C5#100412yes—
711C22×C5#100912yes—
712C22×C5#100912yes—
713C22×C5C24×D311yescharacteristic
714C2×D5—22no—
715C2×D5—22no—
716C2×D5—22no—
717C2×D5—22no—
718C2×D5—22no—
719C2×D5—22no—
720C2×D5—44no—
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—
740C4×C5—62no—
741Dic5—22no—
742Dic5—22no—
743Dic5—62no—
744C24—31no—
745C24—51no—
746C24—51no—
747C24—154no—
748C24—151no—
749C24—151no—
750C24—151no—
751C24—602no—
752C24—602no—
753C24—602no—
754C2×D4—54no—
755C2×D4—154no—
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—202no—
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—31no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—54no—
784C22×C4—154no—
785C22×C4—151no—
786C22×C4—154no—
787C22×C4—202no—
788C22×C4—602no—
789C22×C4—602no—
790C22×C4C2×D3×D511yescharacteristic
791C22×C4C2×D3×D511yescharacteristic
792C22×C4C2×D3×D511yescharacteristic
793C4⋊C4—34no—
794C4⋊C4—34no—
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—34no—
812C3×C5C2×#56011yescharacteristic, complemented, Hall
813C22×C3—102no—
814C22×C3—102no—
815C22×C3—102no—
816C22×C3—102no—
817C22×C3—102no—
818C22×C3—102no—
819C22×C3—204no—
820C22×C3—204no—
821C22×C3#414912yes—
822C22×C3#414912yes—
823C22×C3#414912yes—
824C22×C3C24×D511yescharacteristic
825C2×D3—22no—
826C2×D3—22no—
827C2×D3—22no—
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—
847Dic3—22no—
848Dic3—22no—
849Dic3—22no—
850Dic3—102no—
851C2×C5—122no—
852C2×C5#566614yescomplemented
853C2×C5C2×#100411yescharacteristic
854C2×C5C2×#100911yescharacteristic
855C2×C5C2×#100911yescharacteristic
856D5—42no—
857D5—42no—
858D5—122no—
859D5—122no—
860D5—122no—
861C23—32no—
862C23—52no—
863C23—52no—
864C23—62no—
865C23—62no—
866C23—62no—
867C23—102no—
868C23—102no—
869C23—102no—
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—204no—
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—32no—
908C2×C4—52no—
909C2×C4—52no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—102no—
914C2×C4—102no—
915C2×C4—152no—
916C2×C4—204no—
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—202no—
925C2×C3#6604514yescomplemented
926C2×C3C2×#414911yescharacteristic
927C2×C3C2×#414911yescharacteristic
928C2×C3C2×#414911yescharacteristic
929D3—42no—
930D3—202no—
931D3—202no—
932D3—202no—
933C5C2×#566611yescharacteristic, complemented, Sylow
934C22—62no—
935C22—62no—
936C22—62no—
937C22—102no—
938C22—102no—
939C22—102no—
940C22—102no—
941C22—102no—
942C22—102no—
943C22—124no—
944C22—204no—
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#9202612yes—
961C22#9203512yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—22no—
966C4—62no—
967C4—62no—
968C4—62no—
969C4—102no—
970C4—102no—
971C4—302no—
972C3C2×#6604511yescharacteristic, complemented, Sylow
973C2—122no—
974C2—202no—
975C2—202no—
976C2—602no—
977C2—602no—
978C2—602no—
979C2#1175394114yesdirect product factor
980C2C2×#9201911yescharacteristic
981C2C2×#9202611yescharacteristic
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×#898C2semidirect
3. C2×C3×#4040C2semidirect
4. C2×#91476C2semidirect
5. C2×#91476C2semidirect
6. C2×#91474C2semidirect
7. C2×#91461C2semidirect
8. C2×#91459C2semidirect
9. C2×#91458C2semidirect
10. C2×#91450C2semidirect
11. C2×#91448C2semidirect
12. C2×#91420C2semidirect
13. C2×#91380C2semidirect
14. C2×#91356C2semidirect
15. C2×#91354C2semidirect
16. #11753941C2direct (N × H)
21. C22×D60C22semidirect
22. C22×C4×D15C22semidirect
24. C22×C3×C4×D5C22semidirect
30. C22×#1202C22semidirect
31. C22×#1202C22semidirect
33. C22×#1200C22semidirect
34. C2×C3×C5×C4⋊C4C22semidirect
36. C2×#6714C22semidirect
37. #91784C22semidirect
41. C2×C5×C4⋊Dic3C22semidirect
42. C2×C5×Dic3⋊C4C22semidirect
43. C2×C4×C5×Dic3C22semidirect
44. C5×#898C22semidirect
47. C2×C3×#685C22semidirect
48. C2×C3×#683C22semidirect
49. C3×#4040C22semidirect
50. C2×#6669C22semidirect
51. C2×#6668C22semidirect
54. C2×#6667C22semidirect
56. #91476C22semidirect
57. #91476C22semidirect
58. #91474C22semidirect
59. #91461C22semidirect
60. #91459C22semidirect
61. #91458C22semidirect
62. #91450C22semidirect
63. #91448C22semidirect
64. #91420C22semidirect
65. #91380C22semidirect
66. #91356C22semidirect
67. #91354C22semidirect
76. C2×#4040D3semidirect
104. C2×D60C23semidirect
106. C2×C4×D15C23semidirect
115. C2×C3×C4×D5C23semidirect
128. C2×#1202C23semidirect
129. C2×#1202C23semidirect
133. C2×#1200C23semidirect
134. C3×C5×C4⋊C4C23semidirect
136. #6714C23semidirect
140. C5×C4⋊Dic3C23semidirect
141. C5×Dic3⋊C4C23semidirect
142. C4×C5×Dic3C23semidirect
145. C3×#685C23semidirect
146. C3×#683C23semidirect
147. #6669C23semidirect
148. #6668C23semidirect
151. #6667C23semidirect
160. C2×#898D5semidirect
184. C22×C4×D5C2×D3semidirect
188. C2×C5×C4⋊C4C2×D3semidirect
201. C2×#685C2×D3semidirect
204. C2×#683C2×D3semidirect
210. #4040C2×D3semidirect
300. C2×C3×C4⋊C4C2×D5semidirect
318. C2×C4⋊Dic3C2×D5semidirect
320. C2×Dic3⋊C4C2×D5semidirect
321. C2×C4×Dic3C2×D5semidirect
323. #898C2×D5semidirect
380. C2×C4×D5C22×D3semidirect
383. C5×C4⋊C4C22×D3semidirect
396. #685C22×D3semidirect
399. #683C22×D3semidirect
504. C3×C4⋊C4C22×D5semidirect
518. C4⋊Dic3C22×D5semidirect
520. Dic3⋊C4C22×D5semidirect
521. C4×Dic3C22×D5semidirect
620. C2×C4⋊C4D3×D5semidirect
634. C2×C3×C5#560semidirect
798. C4⋊C4C2×D3×D5semidirect
812. C3×C5C2×#560semidirect
852. C2×C5#5666semidirect
925. C2×C3#66045semidirect
933. C5C2×#5666semidirect
972. C3C2×#66045semidirect
979. C2#11753941direct (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×#8982
C2×C3×#40402
C2×#914762
C2×#914742
C2×#914612
C2×#914592
C2×#914582
C2×#914502
C2×#914482
C2×#914202
C2×#913802
C2×#913562
C2×#913542
#117539412
C2×#660453
C2×#56665