Finite Group Databasebeta

← C2×#11753179 #14495234

Subgroups — C2×#11753179 #14495234

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×#879C211yesmaximal, characteristic, complemented
3C2×C3×#4030C211yesmaximal, characteristic, complemented
4C2×#91572C211yesmaximal, characteristic, complemented
5C2×#91572C211yesmaximal, characteristic, complemented
6C2×#91550C211yesmaximal, characteristic, complemented
7C2×#91533C211yesmaximal, characteristic, complemented
8C2×#91459C211yesmaximal, characteristic, complemented
9C2×#91458C211yesmaximal, characteristic, complemented
10C2×#91450C211yesmaximal, characteristic, complemented
11C2×#91433C211yesmaximal, characteristic, complemented
12C2×#91413C211yesmaximal, characteristic, complemented
13C2×#91409C211yesmaximal, characteristic, complemented
14C2×#91380C211yesmaximal, characteristic, complemented
15C2×#91348C211yesmaximal, characteristic, complemented
16#11753179C2116yesmaximal, direct product factor
17C2×#66045—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×D60C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C22×C3×C22⋊D5C2211yescharacteristic
24C22×C3×D20C2211yescharacteristic, complemented
25C22×C3×C4×D5C2211yescharacteristic, complemented
26C22×#1202C2211yescharacteristic
27C22×#1202C2211yescharacteristic
28C22×#1202C2211yescharacteristic
29C22×#1202C2211yescharacteristic
30C22×#1202C2211yescharacteristic, complemented
31C22×#1202C2211yescharacteristic, complemented
32C22×#1200C2211yescharacteristic, complemented
33C22×D5×Dic3C2211yescharacteristic, complemented
34C2×C3×C5×C22⋊C4C2211yescharacteristic
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37#91771C2218yescomplemented
38C2×C5×#217C2211yescharacteristic
39C2×C5×#217C2211yescharacteristic
40C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
41C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
42C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
43C2×C4×C5×Dic3C2211yescharacteristic, complemented
44C5×#879C2218yescomplemented
45C2×C3×#685C2211yescharacteristic, complemented
46C2×C3×#683C2211yescharacteristic, complemented
47C3×#4030C2218yescomplemented
48#91572C2218yescomplemented
49#91572C2218yescomplemented
50#91550C2218yescomplemented
51C2×#6669C2211yescharacteristic, complemented
52C2×#6668C2211yescharacteristic, complemented
53C2×#6667C2211yescharacteristic
54C2×#6667C2211yescharacteristic
55C2×#6667C2211yescharacteristic
56C2×#6667C2211yescharacteristic
57C2×#6667C2211yescharacteristic, complemented
58C2×#6665C2211yescharacteristic, complemented
59#91533C2218yescomplemented
60#91459C2218yescomplemented
61#91458C2218yescomplemented
62#91450C2218yescomplemented
63#91433C2218yescomplemented
64#91413C2218yescomplemented
65#91409C2218yescomplemented
66#91380C2218yescomplemented
67#91348C2218yescomplemented
68C2×#5620—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×#4040—31no—
77C2×#4030—31no—
78C2×#4030—31no—
79C2×#4030D311yescharacteristic, complemented
80C2×#4028—31no—
81C2×#4028—31no—
82C2×#4028—31no—
83C2×#4022—31no—
84C2×#4020—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15—42no—
87C23×D15—42no—
88C23×D15—42no—
89C23×D15C2311yescharacteristic
90C23×D15C2311yescharacteristic
91C23×D15C2311yescharacteristic
92C23×D15C2314yes—
93C23×C3×D5C2311yescharacteristic
94C23×C3×D5C2311yescharacteristic
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—
104C22×C5×Dic3C2311yescharacteristic
105C22×C5×Dic3C2311yescharacteristic
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2311yescharacteristic
108C2×C3×C22⋊D5—42no—
109C2×C3×C22⋊D5—42no—
110C2×C3×C22⋊D5C2314yes—
111C2×C3×C22⋊D5C2314yes—
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C2×C3×D20—42no—
115C2×C3×D20C2314yescomplemented
116C2×C3×C4×D5—42no—
117C2×C3×C4×D5C2314yescomplemented
118C2×#1202—42no—
119C2×#1202—42no—
120C2×#1202—42no—
121C2×#1202—42no—
122C2×#1202—42no—
123C2×#1202—42no—
124C2×#1202C2314yes—
125C2×#1202C2314yes—
126C2×#1202C2314yes—
127C2×#1202C2314yes—
128C2×#1202C2314yescomplemented
129C2×#1202C2314yescomplemented
130C2×#1200—42no—
131C2×#1200C2314yescomplemented
132C2×D5×Dic3—42no—
133C2×D5×Dic3C2314yescomplemented
134C3×C5×C22⋊C4C2314yes—
135#6714C2314yes—
136#6714C2314yes—
137C5×#217C2314yes—
138C5×#217C2314yes—
139C5×C4⋊Dic3C2314yescomplemented
140C5×Dic3⋊C4C2314yescomplemented
141C5×Dic3⋊C4C2314yescomplemented
142C4×C5×Dic3C2314yescomplemented
143C3×#685C2314yescomplemented
144C3×#683C2314yescomplemented
145#6669C2314yescomplemented
146#6668C2314yescomplemented
147#6667C2314yes—
148#6667C2314yes—
149#6667C2314yes—
150#6667C2314yes—
151#6667C2314yescomplemented
152#6665C2314yescomplemented
153C2×C3×#121—51no—
154C2×#940—51no—
155C2×#939—51no—
156C2×#939—51no—
157C2×#938—51no—
158C2×#937—51no—
159C2×#937—51no—
160C2×#930—51no—
161C2×#929—51no—
162#5620—516no—
163C2×#898—51no—
164C2×#894—51no—
165C2×#886—51no—
166C2×#884—51no—
167C2×#882—51no—
168C2×#879D511yescharacteristic, complemented
169C24×D5—31no—
170C22×C22⋊D5—31no—
171C22×C22⋊D5C2×D311yescharacteristic
172C22×C22⋊D5C2×D311yescharacteristic
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, complemented
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⋊C4—31no—
189C2×C5×C22⋊C4—31no—
190C2×C5×C22⋊C4—31no—
191C2×C5×C22⋊C4C2×D311yescharacteristic
192C2×C42×C5—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685—31no—
199C2×#685—31no—
200C2×#685—31no—
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#4040—38no—
211#4030—38no—
212#4030—38no—
213#4030C2×D318yescomplemented
214#4028—38no—
215#4028—38no—
216#4028—38no—
217#4022—38no—
218#4020—38no—
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×C3×D5—22no—
242C22×C3×D5—22no—
243C22×C3×D5—22no—
244C22×C3×D5—22no—
245C22×C3×D5—22no—
246C22×C3×D5—22no—
247C22×C3×D5C2412yes—
248C22×C3×D5C2412yes—
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—
258C2×C5×Dic3—22no—
259C2×C5×Dic3—22no—
260C2×C5×Dic3—22no—
261C2×C5×Dic3—22no—
262C2×C5×Dic3C2412yes—
263C2×C5×Dic3C2412yes—
264C2×C5×Dic3C2412yes—
265C2×C5×Dic3C2412yes—
266C3×C22⋊D5—44no—
267C3×C22⋊D5—44no—
268C2×C3×Dic5—22no—
269C2×C3×Dic5—22no—
270C2×C3×Dic5C2412yes—
271C2×C3×Dic5C2412yes—
272C3×D20—44no—
273C3×C4×D5—44no—
274#1202—44no—
275#1202—44no—
276#1202—44no—
277#1202—44no—
278#1202—44no—
279#1202—44no—
280#1200—44no—
281D5×Dic3—44no—
282C24×D3—51no—
283C22×C3×D4—51no—
284C22×C3×D4—51no—
285C22×C3×D4—51no—
286C23×C3×C4—51no—
287C22×#67—51no—
288C22×#67—51no—
289C22×#67—51no—
290C22×#67—51no—
291C22×#67—51no—
292C22×#67—51no—
293C22×#67—51no—
294C23×Dic3—51no—
295C22×D12—51no—
296C22×D12—51no—
297C22×C4×D3—51no—
298C3×#121—58no—
299C2×C3×C4⋊C4—51no—
300C2×C3×C22⋊C4—51no—
301C2×C3×C22⋊C4C2×D511yescharacteristic
302C2×#217—51no—
303C2×#217C2×D511yescharacteristic
304C2×#217C2×D511yescharacteristic
305#940—58no—
306#939—58no—
307#939—58no—
308#938—58no—
309#937—58no—
310#937—58no—
311#930—58no—
312#929—58no—
313C2×(C2×D3)⋊C4—51no—
314C2×(C2×D3)⋊C4—51no—
315C2×(C2×D3)⋊C4—51no—
316C2×(C2×D3)⋊C4—51no—
317C2×(C2×D3)⋊C4—51no—
318C2×(C2×D3)⋊C4—51no—
319C2×(C2×D3)⋊C4—51no—
320C2×C4⋊Dic3—51no—
321C2×C4⋊Dic3C2×D511yescharacteristic, complemented
322C2×Dic3⋊C4—51no—
323C2×Dic3⋊C4C2×D511yescharacteristic, complemented
324C2×Dic3⋊C4C2×D511yescharacteristic, complemented
325C2×C4×Dic3C2×D511yescharacteristic, complemented
326#898—58no—
327#894—58no—
328#886—58no—
329#884—58no—
330#882—58no—
331#879C2×D518yescomplemented
332C24×C5C22×D311yescharacteristic
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×C5—31no—
346C22×C4×C5C22×D311yescharacteristic
347C22×C4×C5C22×D311yescharacteristic
348C2×C22⋊D5—34no—
349C2×C22⋊D5—42no—
350C2×C22⋊D5—42no—
351C2×C22⋊D5—122no—
352C2×C22⋊D5C22×D314yes—
353C2×C22⋊D5C22×D314yes—
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×D314yescomplemented
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⋊C4—34no—
384C5×C22⋊C4—34no—
385C5×C22⋊C4—34no—
386C5×C22⋊C4C22×D314yes—
387C42×C5—34no—
388#685—34no—
389#685—34no—
390#685—34no—
391#685—34no—
392#685—34no—
393#685—34no—
394#685—34no—
395#685—34no—
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—151no—
405C2×#123—151no—
406C2×#123—151no—
407C2×#121—51no—
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×C3×D5—22no—
438C2×C3×D5—22no—
439C2×C3×D5—22no—
440C2×C3×D5—22no—
441C2×C3×D5—22no—
442C2×C3×D5—22no—
443C2×C3×D5—44no—
444C2×C3×D5—44no—
445C3×C4×C5—22no—
446C3×C4×C5—22no—
447Dic15—22no—
448C3×Dic5—22no—
449C3×Dic5—22no—
450C5×Dic3—22no—
451C5×Dic3—22no—
452C5×Dic3—22no—
453C5×Dic3—22no—
454C24×C3—51no—
455C24×C3—51no—
456C24×C3C22×D511yescharacteristic
457C23×D3—51no—
458C23×D3—51no—
459C23×D3—51no—
460C23×D3—54no—
461C23×D3—202no—
462C23×D3—202no—
463C23×D3—202no—
464C2×C3×D4—54no—
465C2×C3×D4—54no—
466C2×C3×D4—54no—
467C2×C3×D4—202no—
468C2×C3×D4—202no—
469C2×C3×D4—202no—
470C22×C3×C4—51no—
471C22×C3×C4—51no—
472C22×C3×C4—54no—
473C22×C3×C4—202no—
474C22×C3×C4C22×D511yescharacteristic
475C22×C3×C4C22×D511yescharacteristic
476C2×#67—54no—
477C2×#67—54no—
478C2×#67—54no—
479C2×#67—54no—
480C2×#67—54no—
481C2×#67—54no—
482C2×#67—54no—
483C2×#67—202no—
484C2×#67—202no—
485C2×#67—202no—
486C2×#67—202no—
487C2×#67—202no—
488C2×#67—202no—
489C2×#67—202no—
490C22×Dic3—51no—
491C22×Dic3—54no—
492C22×Dic3—202no—
493C22×Dic3C22×D511yescharacteristic
494C22×Dic3C22×D511yescharacteristic
495C22×Dic3C22×D511yescharacteristic
496C22×Dic3C22×D511yescharacteristic
497C2×D12—54no—
498C2×D12—54no—
499C2×D12—202no—
500C2×D12—202no—
501C2×C4×D3—54no—
502C2×C4×D3—202no—
503C3×C4⋊C4—54no—
504C3×C22⋊C4—54no—
505C3×C22⋊C4C22×D514yes—
506#217—54no—
507#217C22×D514yes—
508#217C22×D514yes—
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)⋊C4—54no—
515(C2×D3)⋊C4—54no—
516C4⋊Dic3—54no—
517C4⋊Dic3C22×D514yescomplemented
518Dic3⋊C4—54no—
519Dic3⋊C4C22×D514yescomplemented
520Dic3⋊C4C22×D514yescomplemented
521C4×Dic3C22×D514yescomplemented
522C23×C5—22no—
523C23×C5—22no—
524C23×C5—22no—
525C23×C5C23×D312yes—
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—32no—
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×C5—62no—
561C2×C4×C5C23×D312yes—
562C2×C4×C5C23×D312yes—
563C22⋊D5—44no—
564C22⋊D5—44no—
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—51no—
587C22×D4—51no—
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—158no—
604#123—158no—
605#123—158no—
606#121—58no—
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—31no—
618C2×C4⋊C4—51no—
619C2×C4⋊C4—151no—
620C2×C4⋊C4—151no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—31no—
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—31no—
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—
642C3×D5—42no—
643C3×D5—42no—
644C23×C3—22no—
645C23×C3—22no—
646C23×C3—22no—
647C23×C3—52no—
648C23×C3—52no—
649C23×C3—102no—
650C23×C3—102no—
651C23×C3—102no—
652C23×C3—102no—
653C23×C3—102no—
654C23×C3—102no—
655C23×C3C23×D512yes—
656C23×C3C23×D511yescharacteristic
657C22×D3—52no—
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—102no—
667C22×D3—102no—
668C22×D3—102no—
669C22×D3—204no—
670C22×D3—204no—
671C22×D3—204no—
672C22×D3—2016no—
673C3×D4—204no—
674C3×D4—204no—
675C3×D4—204no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—52no—
679C2×C3×C4—52no—
680C2×C3×C4—102no—
681C2×C3×C4—102no—
682C2×C3×C4—204no—
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—
691#67—204no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—52no—
697C2×Dic3—102no—
698C2×Dic3—204no—
699C2×Dic3C23×D512yes—
700C2×Dic3C23×D512yes—
701C2×Dic3C23×D512yes—
702C2×Dic3C23×D512yes—
703D12—204no—
704D12—204no—
705C4×D3—204no—
706C22×C5—22no—
707C22×C5—22no—
708C22×C5—22no—
709C22×C5—44no—
710C22×C5#100412yes—
711C22×C5#100412yes—
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—62no—
738C4×C5—62no—
739C4×C5—62no—
740C4×C5—62no—
741Dic5—22no—
742Dic5—22no—
743Dic5—62no—
744C24—51no—
745C24—51no—
746C24—151no—
747C24—151no—
748C24—151no—
749C24—154no—
750C24—602no—
751C24—602no—
752C24—602no—
753C24C2×D3×D511yescharacteristic
754C2×D4—54no—
755C2×D4—54no—
756C2×D4—54no—
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—202no—
768C2×D4—202no—
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—31no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—54no—
785C22×C4—154no—
786C22×C4—154no—
787C22×C4—151no—
788C22×C4—202no—
789C22×C4—602no—
790C22×C4—602no—
791C22×C4C2×D3×D511yescharacteristic
792C22×C4C2×D3×D511yescharacteristic
793C4⋊C4—34no—
794C4⋊C4—34no—
795C4⋊C4—34no—
796C4⋊C4—54no—
797C4⋊C4—154no—
798C4⋊C4—154no—
799C22⋊C4—34no—
800C22⋊C4—34no—
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—34no—
812C3×C5C2×#56011yescharacteristic, complemented, Hall
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—44no—
817C22×C3—102no—
818C22×C3—102no—
819C22×C3—102no—
820C22×C3—102no—
821C22×C3—102no—
822C22×C3—102no—
823C22×C3—204no—
824C22×C3—204no—
825C22×C3#414912yes—
826C22×C3#414912yes—
827C22×C3#414912yes—
828C22×C3C24×D511yescharacteristic
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—
846Dic3—22no—
847Dic3—22no—
848Dic3—22no—
849Dic3—22no—
850Dic3—102no—
851C2×C5—42no—
852C2×C5#562014yescomplemented
853C2×C5C2×#100411yescharacteristic
854C2×C5C2×#100411yescharacteristic
855C2×C5C2×#100911yescharacteristic
856D5—42no—
857D5—42no—
858D5—122no—
859D5—122no—
860D5—122no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—52no—
865C23—52no—
866C23—102no—
867C23—102no—
868C23—102no—
869C23—102no—
870C23—102no—
871C23—102no—
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—204no—
891D4—204no—
892D4—204no—
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—32no—
907C2×C4—32no—
908C2×C4—52no—
909C2×C4—52no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—62no—
914C2×C4—102no—
915C2×C4—102no—
916C2×C4—152no—
917C2×C4—204no—
918C2×C4—302no—
919C2×C4—604no—
920C2×C4—604no—
921C2×C4C22×D3×D512yes—
922C2×C4C22×D3×D512yes—
923C2×C3—42no—
924C2×C3—202no—
925C2×C3—202no—
926C2×C3#6604514yescomplemented
927C2×C3C2×#414911yescharacteristic
928C2×C3C2×#414911yescharacteristic
929C2×C3C2×#414911yescharacteristic
930D3—202no—
931D3—202no—
932D3—202no—
933C5C2×#562011yescharacteristic, complemented, Sylow
934C22—22no—
935C22—22no—
936C22—22no—
937C22—44no—
938C22—102no—
939C22—102no—
940C22—102no—
941C22—102no—
942C22—102no—
943C22—102no—
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#9202612yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—62no—
966C4—62no—
967C4—62no—
968C4—62no—
969C4—102no—
970C4—102no—
971C4—302no—
972C3C2×#6604511yescharacteristic, complemented, Sylow
973C2—42no—
974C2—202no—
975C2—202no—
976C2—602no—
977C2—602no—
978C2—602no—
979C2#1175317914yesdirect product factor
980C2C2×#9201911yescharacteristic
981C2C2×#9202611yescharacteristic
982C2C2×#9202611yescharacteristic
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×#879C2semidirect
3. C2×C3×#4030C2semidirect
4. C2×#91572C2semidirect
5. C2×#91572C2semidirect
6. C2×#91550C2semidirect
7. C2×#91533C2semidirect
8. C2×#91459C2semidirect
9. C2×#91458C2semidirect
10. C2×#91450C2semidirect
11. C2×#91433C2semidirect
12. C2×#91413C2semidirect
13. C2×#91409C2semidirect
14. C2×#91380C2semidirect
15. C2×#91348C2semidirect
16. #11753179C2direct (N × H)
24. C22×C3×D20C22semidirect
25. C22×C3×C4×D5C22semidirect
30. C22×#1202C22semidirect
31. C22×#1202C22semidirect
32. C22×#1200C22semidirect
33. C22×D5×Dic3C22semidirect
37. #91771C22semidirect
40. C2×C5×C4⋊Dic3C22semidirect
41. C2×C5×Dic3⋊C4C22semidirect
42. C2×C5×Dic3⋊C4C22semidirect
43. C2×C4×C5×Dic3C22semidirect
44. C5×#879C22semidirect
45. C2×C3×#685C22semidirect
46. C2×C3×#683C22semidirect
47. C3×#4030C22semidirect
48. #91572C22semidirect
49. #91572C22semidirect
50. #91550C22semidirect
51. C2×#6669C22semidirect
52. C2×#6668C22semidirect
57. C2×#6667C22semidirect
58. C2×#6665C22semidirect
59. #91533C22semidirect
60. #91459C22semidirect
61. #91458C22semidirect
62. #91450C22semidirect
63. #91433C22semidirect
64. #91413C22semidirect
65. #91409C22semidirect
66. #91380C22semidirect
67. #91348C22semidirect
79. C2×#4030D3semidirect
115. C2×C3×D20C23semidirect
117. C2×C3×C4×D5C23semidirect
128. C2×#1202C23semidirect
129. C2×#1202C23semidirect
131. C2×#1200C23semidirect
133. C2×D5×Dic3C23semidirect
139. C5×C4⋊Dic3C23semidirect
140. C5×Dic3⋊C4C23semidirect
141. C5×Dic3⋊C4C23semidirect
142. C4×C5×Dic3C23semidirect
143. C3×#685C23semidirect
144. C3×#683C23semidirect
145. #6669C23semidirect
146. #6668C23semidirect
151. #6667C23semidirect
152. #6665C23semidirect
168. C2×#879D5semidirect
181. C22×D20C2×D3semidirect
184. C22×C4×D5C2×D3semidirect
201. C2×#685C2×D3semidirect
204. C2×#683C2×D3semidirect
213. #4030C2×D3semidirect
321. C2×C4⋊Dic3C2×D5semidirect
323. C2×Dic3⋊C4C2×D5semidirect
324. C2×Dic3⋊C4C2×D5semidirect
325. C2×C4×Dic3C2×D5semidirect
331. #879C2×D5semidirect
374. C2×D20C22×D3semidirect
380. C2×C4×D5C22×D3semidirect
396. #685C22×D3semidirect
399. #683C22×D3semidirect
517. C4⋊Dic3C22×D5semidirect
519. Dic3⋊C4C22×D5semidirect
520. Dic3⋊C4C22×D5semidirect
521. C4×Dic3C22×D5semidirect
635. C2×C3×C5#560semidirect
812. C3×C5C2×#560semidirect
852. C2×C5#5620semidirect
926. C2×C3#66045semidirect
933. C5C2×#5620semidirect
972. C3C2×#66045semidirect
979. C2#11753179direct (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×#8792
C2×C3×#40302
C2×#915722
C2×#915502
C2×#915332
C2×#914592
C2×#914582
C2×#914502
C2×#914332
C2×#914132
C2×#914092
C2×#913802
C2×#913482
#117531792
C2×#660453
C2×#56205