Finite Group Databasebeta

← C2×#11755035 #14482603

Subgroups — C2×#11755035 #14482603

Order 1920.

3800 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×#67C211yesmaximal, characteristic, complemented
2C22×#6780C211yesmaximal, characteristic, complemented
3C2×#91828C211yesmaximal, characteristic, complemented
4C2×C5×#938C211yesmaximal, characteristic, complemented
5C2×C3×#4083C211yesmaximal, characteristic, complemented
6C2×#91577C211yesmaximal, characteristic, complemented
7C2×#91559C211yesmaximal, characteristic, complemented
8C2×#91555C211yesmaximal, characteristic, complemented
9C2×#91550C211yesmaximal, characteristic, complemented
10C2×D5×#217C211yesmaximal, characteristic, complemented
11C2×#91526C211yesmaximal, characteristic, complemented
12#11755035C2116yesmaximal, direct product factor
13C2×D3×#685C211yesmaximal, characteristic, complemented
14C2×#91441C211yesmaximal, characteristic, complemented
15C2×#91430C211yesmaximal, characteristic, complemented
16C2×#91413C211yesmaximal, characteristic, complemented
17C2×#65944—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×C3×C5×D4C2211yescharacteristic, complemented
21C22×#1220C2211yescharacteristic
22C22×#1220C2211yescharacteristic, complemented
23C23×Dic15C2211yescharacteristic, complemented
24C22×C5×#67C2211yescharacteristic
25C22×C5×#67C2211yescharacteristic, complemented
26C22×C4×C5×D3C2211yescharacteristic, complemented
27C22×C3×C22⋊D5C2211yescharacteristic
28C22×C3×C22⋊D5C2211yescharacteristic, complemented
29C2×D5×#67—28no—
30C2×D5×#67C2218yescomplemented
31C22×#1204C2211yescharacteristic, complemented
32C22×#1202C2211yescharacteristic
33C22×#1201C2211yescharacteristic
34C22×D3×Dic5C2211yescharacteristic, complemented
35C2×#6780—28no—
36C2×#6780C2218yescomplemented
37C22×D5×Dic3C2211yescharacteristic
38C22×D5×Dic3C2211yescharacteristic, complemented
39C22×D5×Dic3C2211yescharacteristic, complemented
40C2×#6719C2211yescharacteristic, complemented
41#91828C2218yescomplemented
42C2×#6714C2211yescharacteristic, complemented
43C2×#6712C2211yescharacteristic, complemented
44C2×C5×#217C2211yescharacteristic, complemented
45C2×C5×#217C2211yescharacteristic, complemented
46C5×#938C2218yescomplemented
47C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
48C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
49C3×#4083C2218yescomplemented
50C2×C3×#685C2211yescharacteristic
51C2×C3×#685C2211yescharacteristic, complemented
52#91577C2218yescomplemented
53#91559C2218yescomplemented
54#91555C2218yescomplemented
55#91550C2218yescomplemented
56D5×#217C2218yescomplemented
57C2×#6669C2211yescharacteristic, complemented
58C2×#6668C2211yescharacteristic, complemented
59C2×#6667C2211yescharacteristic, complemented
60C2×#6667C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
62C2×#6665C2211yescharacteristic
63C2×#6665C2211yescharacteristic
64C2×Dic3×Dic5C2211yescharacteristic, complemented
65#91526C2218yescomplemented
66D3×#685C2218yescomplemented
67#91441C2218yescomplemented
68#91430C2218yescomplemented
69#91413C2218yescomplemented
70C2×#5591—51nomaximal, Hall
71C22×#711—31no—
72C22×D4×D5—31no—
73C2×C5×#121—31no—
74C2×#4085—31no—
75C2×#4083—31no—
76C2×#4083D311yescharacteristic, complemented
77C2×#4081—31no—
78C2×C4×C22⋊D5—31no—
79C22×#685—31no—
80#65944—316no—
81C2×#4042—31no—
82C2×#4040—31no—
83C2×#4031—31no—
84C2×#4030—31no—
85C2×#4027—31no—
86C2×D5×C22⋊C4—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C23×C3×D5—24no—
92C23×C3×D5—24no—
93C23×C3×D5—42no—
94C23×C3×D5C2314yes—
95C23×C3×D5C2311yescharacteristic
96C23×C3×D5C2311yescharacteristic
97C22×D3×D5—24no—
98C22×D3×D5—24no—
99C22×D3×D5—42no—
100C22×D3×D5C2314yes—
101C2×C3×C5×D4—42no—
102C2×C3×C5×D4C2314yescomplemented
103C22×C3×C4×C5C2311yescharacteristic
104C2×#1220—24no—
105C2×#1220—42no—
106C2×#1220C2314yes—
107C2×#1220C2314yescomplemented
108C22×Dic15—24no—
109C22×Dic15C2311yescharacteristic
110C22×Dic15C2311yescharacteristic
111C22×Dic15C2311yescharacteristic
112C22×Dic15C2314yescomplemented
113C2×C5×#67—24no—
114C2×C5×#67—24no—
115C2×C5×#67C2314yes—
116C2×C5×#67C2314yescomplemented
117C22×C5×Dic3C2311yescharacteristic
118C22×C5×Dic3C2311yescharacteristic
119C22×C5×Dic3C2311yescharacteristic
120C2×C4×C5×D3—42no—
121C2×C4×C5×D3C2314yescomplemented
122C2×C3×C22⋊D5—24no—
123C2×C3×C22⋊D5—24no—
124C2×C3×C22⋊D5C2314yes—
125C2×C3×C22⋊D5C2314yescomplemented
126C22×C3×Dic5C2311yescharacteristic
127C22×C3×Dic5C2311yescharacteristic
128D5×#67—232no—
129C2×#1204—24no—
130C2×#1204C2314yescomplemented
131C2×#1202—24no—
132C2×#1202C2314yes—
133C2×#1201D418yescomplemented
134C2×#1201C2314yes—
135C2×D3×Dic5—24no—
136C2×D3×Dic5C2314yescomplemented
137#6780—232no—
138C2×D5×Dic3—24no—
139C2×D5×Dic3—24no—
140C2×D5×Dic3—42no—
141C2×D5×Dic3C2314yes—
142C2×D5×Dic3C2314yescomplemented
143C2×D5×Dic3C2314yescomplemented
144#6719C2314yescomplemented
145#6714C2314yescomplemented
146#6712C2314yescomplemented
147C5×#217C2314yescomplemented
148C5×#217C2314yescomplemented
149C5×C4⋊Dic3C2314yescomplemented
150C3×C22⋊Dic5C2314yescomplemented
151C3×#685C2314yes—
152C3×#685C2314yescomplemented
153#6669C2314yescomplemented
154#6668C2314yescomplemented
155#6667C2314yescomplemented
156#6667C2314yescomplemented
157(C2×D3)⋊Dic5C2314yescomplemented
158#6665C2314yes—
159#6665C2314yes—
160Dic3×Dic5C2314yescomplemented
161C23×#67—51no—
162C22×#237—51no—
163C2×C3×#120—51no—
164C22×#217—51no—
165C2×#939—51no—
166C2×#939—51no—
167C2×#938D511yescharacteristic, complemented
168C2×#937—51no—
169C2×D4×Dic3—51no—
170#5591—516no—
171C2×#886—51no—
172C2×#885—51no—
173C2×#883—51no—
174C2×#67⋊C4—51no—
175C2×D3×C22⋊C4—51no—
176C2×#878—51no—
177C24×D5—31no—
178C24×D5C2×D311yescharacteristic
179C22×C5×D4—31no—
180C22×C5×D4—31no—
181C22×C5×D4C2×D311yescharacteristic, complemented
182C23×C4×C5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5C2×D311yescharacteristic
187C22×C22⋊D5C2×D311yescharacteristic, complemented
188C23×Dic5—31no—
189C23×Dic5—31no—
190C2×#711—38no—
191C2×#711—68no—
192C2×D4×D5—38no—
193C2×D4×D5—68no—
194C22×D20—31no—
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5—31no—
198C22×Dic10—31no—
199C5×#121—38no—
200C2×C5×C4⋊C4—31no—
201C2×C5×C22⋊C4—31no—
202C2×C5×C22⋊C4—31no—
203C2×C22⋊Dic5—31no—
204C2×C22⋊Dic5—31no—
205C2×C22⋊Dic5C2×D311yescharacteristic, complemented
206#4085—38no—
207#4083—38no—
208#4083C2×D318yescomplemented
209#4081—38no—
210C4×C22⋊D5—38no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—38no—
217C2×#685C2×D311yescharacteristic
218C2×#685C2×D311yescharacteristic, complemented
219C2×#683—31no—
220C2×#683—31no—
221C2×#683—31no—
222C2×C4×Dic5—31no—
223#4042—38no—
224#4040—38no—
225#4031—38no—
226#4030—38no—
227#4027—38no—
228D5×C22⋊C4—38no—
229C2×#546—151noSylow
230C23×C3×C5—22no—
231C23×C3×C5—22no—
232C23×C3×C5—22no—
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5—22no—
236C23×C3×C5C2412yes—
237C23×C3×C5C2412yes—
238C23×C3×C5C2411yescharacteristic
239C22×D15—22no—
240C22×D15—22no—
241C22×D15—22no—
242C22×D15C2412yes—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3C2×D414yes—
246C22×C5×D3C2412yes—
247C22×C3×D5—22no—
248C22×C3×D5—22no—
249C22×C3×D5—22no—
250C22×C3×D5—22no—
251C22×C3×D5—28no—
252C22×C3×D5—28no—
253C22×C3×D5—44no—
254C22×C3×D5—416no—
255C22×C3×D5C2×D414yes—
256C22×C3×D5#4114yescomplemented
257C22×C3×D5C2412yes—
258C22×C3×D5C2412yes—
259C2×D3×D5—28no—
260C2×D3×D5—28no—
261C2×D3×D5—44no—
262C2×D3×D5—416no—
263C3×C5×D4—44no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5C2412yes—
266#1220—28no—
267#1220—44no—
268C2×Dic15—22no—
269C2×Dic15—22no—
270C2×Dic15—28no—
271C2×Dic15C2×D414yes—
272C2×Dic15C2412yes—
273C2×Dic15C2412yes—
274C2×Dic15C2412yes—
275C5×#67—28no—
276C5×#67—28no—
277C2×C5×Dic3—22no—
278C2×C5×Dic3—22no—
279C2×C5×Dic3—22no—
280C2×C5×Dic3C2412yes—
281C2×C5×Dic3C2412yes—
282C2×C5×Dic3C2412yes—
283C4×C5×D3—44no—
284C3×C22⋊D5—28no—
285C3×C22⋊D5—28no—
286C2×C3×Dic5—22no—
287C2×C3×Dic5—22no—
288C2×C3×Dic5C2412yes—
289C2×C3×Dic5C2412yes—
290#1204—28no—
291#1202—28no—
292#1201C2×D4116yescomplemented
293D3×Dic5—28no—
294D5×Dic3—28no—
295D5×Dic3—28no—
296D5×Dic3—44no—
297C25×C3—51no—
298C24×D3—51no—
299C22×C3×D4—51no—
300C22×C3×D4—51no—
301C22×C3×D4C2×D511yescharacteristic, complemented
302C22×#67—51no—
303C22×#67—51no—
304C22×#67—51no—
305C22×#67—58no—
306C22×#67—51no—
307C22×#67—108no—
308C22×#67C2×D511yescharacteristic
309C22×#67C2×D511yescharacteristic, complemented
310C23×Dic3—51no—
311C23×Dic3—51no—
312C23×Dic3—51no—
313C23×Dic3—51no—
314C2×#237—58no—
315C2×#237—108no—
316C22×C4×D3—51no—
317C22×C4×D3C2×D511yescharacteristic, complemented
318C22×Dic6—51no—
319C3×#120—58no—
320C2×C3×C22⋊C4—51no—
321C2×C3×C22⋊C4—51no—
322C2×C3×C22⋊C4—51no—
323C2×#217—51no—
324C2×#217—51no—
325C2×#217—51no—
326C2×#217—58no—
327C2×#217C2×D511yescharacteristic, complemented
328C2×#217C2×D511yescharacteristic, complemented
329#939—58no—
330#939—58no—
331#938C2×D518yescomplemented
332#937—58no—
333D4×Dic3—58no—
334C2×(C2×D3)⋊C4—51no—
335C2×(C2×D3)⋊C4—51no—
336C2×(C2×D3)⋊C4—51no—
337C2×(C2×D3)⋊C4—51no—
338C2×C4⋊Dic3—51no—
339C2×C4⋊Dic3C2×D511yescharacteristic, complemented
340C2×Dic3⋊C4—51no—
341C2×Dic3⋊C4—51no—
342C2×C4×Dic3—51no—
343#886—58no—
344#885—58no—
345#883—58no—
346#67⋊C4—58no—
347D3×C22⋊C4—58no—
348#878—58no—
349C24×C5—31no—
350C24×C5C22×D311yescharacteristic
351C24×C5C22×D311yescharacteristic
352C23×D5—24no—
353C23×D5—24no—
354C23×D5—31no—
355C23×D5—34no—
356C23×D5—42no—
357C23×D5—64no—
358C23×D5—64no—
359C23×D5—122no—
360C23×D5C22×D314yes—
361C23×D5C22×D311yescharacteristic
362C23×D5C22×D311yescharacteristic
363C2×C5×D4—34no—
364C2×C5×D4—34no—
365C2×C5×D4—42no—
366C2×C5×D4—64no—
367C2×C5×D4—64no—
368C2×C5×D4C22×D314yescomplemented
369C22×C4×C5—31no—
370C22×C4×C5—31no—
371C22×C4×C5—31no—
372C22×C4×C5—34no—
373C22×C4×C5—122no—
374C22×C4×C5C22×D311yescharacteristic
375C2×C22⋊D5—24no—
376C2×C22⋊D5—24no—
377C2×C22⋊D5—38no—
378C2×C22⋊D5—34no—
379C2×C22⋊D5—34no—
380C2×C22⋊D5—34no—
381C2×C22⋊D5—64no—
382C2×C22⋊D5—122no—
383C2×C22⋊D5C22×D314yes—
384C2×C22⋊D5C22×D314yescomplemented
385C22×Dic5—31no—
386C22×Dic5—31no—
387C22×Dic5—31no—
388C22×Dic5—34no—
389C22×Dic5—34no—
390C22×Dic5—64no—
391C22×Dic5—64no—
392C22×Dic5C22×D311yescharacteristic
393C22×Dic5C22×D311yescharacteristic
394#711—632no—
395D4×D5—632no—
396C2×D20—34no—
397C2×D20—64no—
398C2×C4×D5—34no—
399C2×C4×D5—34no—
400C2×C4×D5—34no—
401C2×C4×D5—64no—
402C2×C4×D5—64no—
403C2×C4×D5—122no—
404C2×Dic10—34no—
405C2×Dic10—64no—
406C5×C4⋊C4—34no—
407C5×C22⋊C4—34no—
408C5×C22⋊C4—34no—
409C22⋊Dic5—34no—
410C22⋊Dic5—34no—
411C22⋊Dic5C22×D314yescomplemented
412#685—34no—
413#685—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685C22×D314yes—
418#685C22×D314yescomplemented
419#683—34no—
420#683—34no—
421#683—34no—
422C4×Dic5—34no—
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—151no—
427C2×#123—151no—
428C2×#123—151no—
429C2×C22⋊Q8—151no—
430C2×#121—31no—
431C2×#121—151no—
432C2×#121—151no—
433C2×#120—51no—
434C2×#120—151no—
435C2×C4×D4—151no—
436C2×C4×D4—151no—
437C22×C22⋊C4—151no—
438C22×C22⋊C4—151no—
439C22×C3×C5—22no—
440C22×C3×C5—22no—
441C22×C3×C5—22no—
442C22×C3×C5—22no—
443C22×C3×C5—22no—
444C22×C3×C5—22no—
445C22×C3×C5—44no—
446C22×C3×C5—44no—
447C22×C3×C5C22×D412yes—
448C22×C3×C5C2×#4112yes—
449C22×C3×C5H(5,𝔽2)12yes—
450C22×C3×C5C2511yescharacteristic
451C2×D15—22no—
452C2×D15—22no—
453C2×D15—22no—
454C2×D15—44no—
455C2×C5×D3—28no—
456C2×C5×D3—22no—
457C2×C5×D3—22no—
458C2×C5×D3C22×D414yes—
459C2×C3×D5—28no—
460C2×C3×D5—28no—
461C2×C3×D5—22no—
462C2×C3×D5—22no—
463C2×C3×D5—22no—
464C2×C3×D5—22no—
465C2×C3×D5—416no—
466C2×C3×D5C22×D414yes—
467C2×C3×D5C2×#4114yescomplemented
468D3×D5—416no—
469C3×C4×C5—22no—
470Dic15—22no—
471Dic15—22no—
472Dic15C22×D414yes—
473C3×Dic5—22no—
474C3×Dic5—22no—
475C5×Dic3—22no—
476C5×Dic3—22no—
477C5×Dic3—22no—
478C24×C3—51no—
479C24×C3—51no—
480C24×C3—54no—
481C24×C3—104no—
482C24×C3—104no—
483C24×C3—202no—
484C24×C3C22×D511yescharacteristic
485C24×C3C22×D511yescharacteristic
486C23×D3—51no—
487C23×D3—54no—
488C23×D3—104no—
489C23×D3—104no—
490C23×D3—202no—
491C23×D3C22×D511yescharacteristic
492C2×C3×D4—42no—
493C2×C3×D4—54no—
494C2×C3×D4—54no—
495C2×C3×D4—104no—
496C2×C3×D4—104no—
497C2×C3×D4C22×D514yescomplemented
498C22×C3×C4—51no—
499C22×C3×C4—51no—
500C22×C3×C4C22×D511yescharacteristic
501C2×#67—24no—
502C2×#67—24no—
503C2×#67—58no—
504C2×#67—54no—
505C2×#67—54no—
506C2×#67—54no—
507C2×#67—54no—
508C2×#67—104no—
509C2×#67—104no—
510C2×#67—1032no—
511C2×#67—202no—
512C2×#67C22×D514yes—
513C2×#67C22×D514yescomplemented
514C22×Dic3—51no—
515C22×Dic3—51no—
516C22×Dic3—51no—
517C22×Dic3—54no—
518C22×Dic3—54no—
519C22×Dic3—54no—
520C22×Dic3—54no—
521C22×Dic3—104no—
522C22×Dic3—104no—
523C22×Dic3—104no—
524C22×Dic3—202no—
525C22×Dic3C22×D511yescharacteristic
526C22×Dic3C22×D511yescharacteristic
527C22×Dic3C22×D511yescharacteristic
528#237—1032no—
529C2×C4×D3—42no—
530C2×C4×D3—54no—
531C2×C4×D3—104no—
532C2×C4×D3C22×D514yescomplemented
533C2×Dic6—54no—
534C2×Dic6—104no—
535C3×C22⋊C4—54no—
536C3×C22⋊C4—54no—
537C3×C22⋊C4—54no—
538#217—54no—
539#217—54no—
540#217—54no—
541#217C22×D514yescomplemented
542#217C22×D514yescomplemented
543(C2×D3)⋊C4—54no—
544(C2×D3)⋊C4—54no—
545(C2×D3)⋊C4—54no—
546(C2×D3)⋊C4—54no—
547C4⋊Dic3—54no—
548C4⋊Dic3C22×D514yescomplemented
549Dic3⋊C4—54no—
550Dic3⋊C4—54no—
551C4×Dic3—54no—
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—22no—
556C23×C5—22no—
557C23×C5—22no—
558C23×C5—34no—
559C23×C5—32no—
560C23×C5—62no—
561C23×C5—62no—
562C23×C5C23×D312yes—
563C23×C5C23×D312yes—
564C23×C5C23×D311yescharacteristic
565C22×D5—22no—
566C22×D5—22no—
567C22×D5—22no—
568C22×D5—22no—
569C22×D5—28no—
570C22×D5—28no—
571C22×D5—32no—
572C22×D5—44no—
573C22×D5—416no—
574C22×D5—68no—
575C22×D5—62no—
576C22×D5—62no—
577C22×D5—62no—
578C22×D5—68no—
579C22×D5—124no—
580C22×D5—1216no—
581C22×D5D3×D414yes—
582C22×D5#23714yescomplemented
583C22×D5C23×D312yes—
584C22×D5C23×D312yes—
585C5×D4—44no—
586C5×D4—68no—
587C5×D4—68no—
588C2×C4×C5—22no—
589C2×C4×C5—32no—
590C2×C4×C5—32no—
591C2×C4×C5—32no—
592C2×C4×C5—62no—
593C2×C4×C5—62no—
594C2×C4×C5—62no—
595C2×C4×C5—124no—
596C2×C4×C5C23×D312yes—
597C22⋊D5—28no—
598C22⋊D5—28no—
599C22⋊D5—316no—
600C22⋊D5—68no—
601C22⋊D5—124no—
602C2×Dic5—22no—
603C2×Dic5—22no—
604C2×Dic5—34no—
605C2×Dic5—32no—
606C2×Dic5—32no—
607C2×Dic5—32no—
608C2×Dic5—68no—
609C2×Dic5—68no—
610C2×Dic5—62no—
611C2×Dic5—62no—
612C2×Dic5C23×D312yes—
613C2×Dic5C23×D312yes—
614D20—68no—
615C4×D5—68no—
616C4×D5—68no—
617C4×D5—124no—
618Dic10—68no—
619C25—51no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—151no—
624C22×D4—31no—
625C22×D4—31no—
626C22×D4—51no—
627C22×D4—51no—
628C22×D4—151no—
629C22×D4—158no—
630C22×D4—151no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—308no—
634C22×D4D3×D511yescharacteristic, complemented
635C23×C4—31no—
636C23×C4—151no—
637C23×C4—151no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4—151no—
641#124—158no—
642#123—158no—
643#123—158no—
644C22⋊Q8—158no—
645#121—38no—
646#121—158no—
647#121—158no—
648#120—58no—
649#120—158no—
650C4×D4—158no—
651C4×D4—158no—
652C2×C4⋊C4—31no—
653C2×C4⋊C4—151no—
654C2×C4⋊C4—151no—
655C2×C4⋊C4—151no—
656C2×C22⋊C4—31no—
657C2×C22⋊C4—31no—
658C2×C22⋊C4—51no—
659C2×C22⋊C4—51no—
660C2×C22⋊C4—51no—
661C2×C22⋊C4—158no—
662C2×C22⋊C4—158no—
663C2×C22⋊C4—151no—
664C2×C22⋊C4—151no—
665C2×C22⋊C4—151no—
666C2×C22⋊C4—151no—
667C2×C22⋊C4—151no—
668C2×C22⋊C4—151no—
669C2×C22⋊C4—151no—
670C2×C42—151no—
671C2×C3×C5—42no—
672C2×C3×C5—42no—
673C2×C3×C5#54614yescomplemented
674C2×C3×C5C23×D411yescharacteristic
675C2×C3×C5C22×#4111yescharacteristic
676C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
677D15—42no—
678C3×D5—24no—
679C3×D5—24no—
680C5×D3—24no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—22no—
685C23×C3—22no—
686C23×C3—22no—
687C23×C3—54no—
688C23×C3—54no—
689C23×C3—52no—
690C23×C3—52no—
691C23×C3—108no—
692C23×C3—108no—
693C23×C3—102no—
694C23×C3—102no—
695C23×C3—102no—
696C23×C3—102no—
697C23×C3—204no—
698C23×C3—2016no—
699C23×C3C23×D512yes—
700C23×C3C23×D512yes—
701C23×C3C23×D511yescharacteristic
702C22×D3—22no—
703C22×D3—22no—
704C22×D3—52no—
705C22×D3—108no—
706C22×D3—102no—
707C22×D3—102no—
708C22×D3—102no—
709C22×D3—108no—
710C22×D3—204no—
711C22×D3—2016no—
712C22×D3D4×D514yes—
713C22×D3C23×D512yes—
714C3×D4—44no—
715C3×D4—108no—
716C3×D4—108no—
717C2×C3×C4—22no—
718C2×C3×C4—52no—
719C2×C3×C4—52no—
720C2×C3×C4—102no—
721C2×C3×C4—102no—
722C2×C3×C4C23×D512yes—
723#67—28no—
724#67—28no—
725#67—516no—
726#67—108no—
727#67—108no—
728#67—204no—
729C2×Dic3—22no—
730C2×Dic3—22no—
731C2×Dic3—22no—
732C2×Dic3—54no—
733C2×Dic3—52no—
734C2×Dic3—52no—
735C2×Dic3—52no—
736C2×Dic3—108no—
737C2×Dic3—108no—
738C2×Dic3—108no—
739C2×Dic3—102no—
740C2×Dic3—102no—
741C2×Dic3—204no—
742C2×Dic3C23×D512yes—
743C2×Dic3C23×D512yes—
744C2×Dic3C23×D512yes—
745C4×D3—44no—
746C4×D3—108no—
747Dic6—108no—
748C22×C5—22no—
749C22×C5—22no—
750C22×C5—22no—
751C22×C5—22no—
752C22×C5—22no—
753C22×C5—22no—
754C22×C5—34no—
755C22×C5—44no—
756C22×C5—44no—
757C22×C5—62no—
758C22×C5—62no—
759C22×C5—68no—
760C22×C5C2×D3×D412yes—
761C22×C5C2×#23712yes—
762C22×C5#100412yes—
763C22×C5C24×D311yescharacteristic
764C2×D5—22no—
765C2×D5—22no—
766C2×D5—22no—
767C2×D5—22no—
768C2×D5—28no—
769C2×D5—28no—
770C2×D5—416no—
771C2×D5—62no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—1216no—
775C2×D5—124no—
776C2×D5C2×D3×D414yes—
777C2×D5C2×#23714yescomplemented
778C4×C5—22no—
779C4×C5—62no—
780C4×C5—62no—
781C4×C5—62no—
782Dic5—22no—
783Dic5—22no—
784Dic5—34no—
785Dic5—62no—
786Dic5—62no—
787C24—31no—
788C24—51no—
789C24—51no—
790C24—54no—
791C24—104no—
792C24—104no—
793C24—154no—
794C24—151no—
795C24—202no—
796C24—304no—
797C24—304no—
798C24—602no—
799C24C2×D3×D511yescharacteristic
800C24C2×D3×D511yescharacteristic
801#41—3032no—
802C2×Q8—154no—
803C2×Q8—304no—
804C2×D4—34no—
805C2×D4—34no—
806C2×D4—42no—
807C2×D4—54no—
808C2×D4—54no—
809C2×D4—64no—
810C2×D4—64no—
811C2×D4—104no—
812C2×D4—104no—
813C2×D4—154no—
814C2×D4—154no—
815C2×D4—158no—
816C2×D4—154no—
817C2×D4—154no—
818C2×D4—304no—
819C2×D4—304no—
820C2×D4—3032no—
821C2×D4—602no—
822C2×D4C2×D3×D514yescomplemented
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—31no—
826C22×C4—34no—
827C22×C4—51no—
828C22×C4—51no—
829C22×C4—122no—
830C22×C4—154no—
831C22×C4—154no—
832C22×C4—154no—
833C22×C4—154no—
834C22×C4—151no—
835C22×C4—154no—
836C22×C4—151no—
837C22×C4—151no—
838C22×C4—304no—
839C22×C4—304no—
840C22×C4—304no—
841C22×C4—304no—
842C22×C4—602no—
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—34no—
845C4⋊C4—154no—
846C4⋊C4—154no—
847C4⋊C4—154no—
848C22⋊C4—34no—
849C22⋊C4—34no—
850C22⋊C4—54no—
851C22⋊C4—54no—
852C22⋊C4—54no—
853C22⋊C4—154no—
854C22⋊C4—154no—
855C22⋊C4—154no—
856C22⋊C4—154no—
857C22⋊C4—154no—
858C22⋊C4—154no—
859C22⋊C4—154no—
860C42—154no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—22no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—22no—
866C22×C3—22no—
867C22×C3—22no—
868C22×C3—44no—
869C22×C3—44no—
870C22×C3—54no—
871C22×C3—54no—
872C22×C3—108no—
873C22×C3—108no—
874C22×C3—102no—
875C22×C3—102no—
876C22×C3—102no—
877C22×C3—102no—
878C22×C3—2016no—
879C22×C3C2×D4×D512yes—
880C22×C3#414412yes—
881C22×C3D5×#4112yes—
882C22×C3C24×D511yescharacteristic
883C2×D3—28no—
884C2×D3—22no—
885C2×D3—22no—
886C2×D3—102no—
887C2×D3—102no—
888C2×D3—102no—
889C2×D3—2016no—
890C2×D3—204no—
891C2×D3C2×D4×D514yes—
892C3×C4—22no—
893C3×C4—102no—
894C3×C4—102no—
895Dic3—22no—
896Dic3—22no—
897Dic3—22no—
898Dic3—54no—
899Dic3—102no—
900Dic3—102no—
901C2×C5—42no—
902C2×C5—42no—
903C2×C5—64no—
904C2×C5#559114yescomplemented
905C2×C5C22×D3×D411yescharacteristic
906C2×C5C22×#23711yescharacteristic
907C2×C5C2×#100411yescharacteristic
908D5—24no—
909D5—24no—
910D5—122no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—34no—
918C23—32no—
919C23—54no—
920C23—54no—
921C23—52no—
922C23—52no—
923C23—62no—
924C23—62no—
925C23—108no—
926C23—108no—
927C23—102no—
928C23—102no—
929C23—102no—
930C23—102no—
931C23—152no—
932C23—204no—
933C23—2016no—
934C23—308no—
935C23—308no—
936C23—302no—
937C23—302no—
938C23—302no—
939C23—604no—
940C23—6016no—
941C23C22×D3×D512yes—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—308no—
945D4—44no—
946D4—68no—
947D4—68no—
948D4—108no—
949D4—108no—
950D4—1516no—
951D4—308no—
952D4—308no—
953D4—604no—
954C2×C4—22no—
955C2×C4—32no—
956C2×C4—32no—
957C2×C4—32no—
958C2×C4—52no—
959C2×C4—52no—
960C2×C4—62no—
961C2×C4—62no—
962C2×C4—62no—
963C2×C4—102no—
964C2×C4—102no—
965C2×C4—124no—
966C2×C4—154no—
967C2×C4—152no—
968C2×C4—152no—
969C2×C4—152no—
970C2×C4—308no—
971C2×C4—308no—
972C2×C4—308no—
973C2×C4—308no—
974C2×C4—302no—
975C2×C4—302no—
976C2×C4—604no—
977C2×C4C22×D3×D512yes—
978C2×C3—42no—
979C2×C3—42no—
980C2×C3—104no—
981C2×C3—104no—
982C2×C3#6594414yescomplemented
983C2×C3C22×D4×D511yescharacteristic
984C2×C3C2×#414411yescharacteristic
985C2×C3C2×D5×#4111yescharacteristic
986D3—24no—
987D3—202no—
988C5C2×#559111yescharacteristic, complemented, Sylow
989C22—22no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—34no—
996C22—44no—
997C22—44no—
998C22—54no—
999C22—54no—
1000C22—62no—
1001C22—68no—
1002C22—62no—
1003C22—102no—
1004C22—102no—
1005C22—108no—
1006C22—108no—
1007C22—102no—
1008C22—102no—
1009C22—2016no—
1010C22—302no—
1011C22—302no—
1012C22—302no—
1013C22—6016no—
1014C22—604no—
1015C22D3×D4×D512yes—
1016C22D5×#23712yes—
1017C22#9204912yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—62no—
1021C4—62no—
1022C4—62no—
1023C4—102no—
1024C4—102no—
1025C4—154no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6594411yescharacteristic, complemented, Sylow
1029C2—42no—
1030C2—42no—
1031C2—64no—
1032C2—104no—
1033C2—104no—
1034C2—602no—
1035C2#1175503514yesdirect product factor
1036C2C2×D3×D4×D511yescharacteristic
1037C2C2×D5×#23711yescharacteristic
1038C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#546
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×D5×#67C2semidirect
2. C22×#6780C2semidirect
3. C2×#91828C2semidirect
4. C2×C5×#938C2semidirect
5. C2×C3×#4083C2semidirect
6. C2×#91577C2semidirect
7. C2×#91559C2semidirect
8. C2×#91555C2semidirect
9. C2×#91550C2semidirect
10. C2×D5×#217C2semidirect
11. C2×#91526C2semidirect
12. #11755035C2direct (N × H)
13. C2×D3×#685C2semidirect
14. C2×#91441C2semidirect
15. C2×#91430C2semidirect
16. C2×#91413C2semidirect
20. C22×C3×C5×D4C22semidirect
22. C22×#1220C22semidirect
23. C23×Dic15C22semidirect
25. C22×C5×#67C22semidirect
26. C22×C4×C5×D3C22semidirect
28. C22×C3×C22⋊D5C22semidirect
30. C2×D5×#67C22semidirect
31. C22×#1204C22semidirect
34. C22×D3×Dic5C22semidirect
36. C2×#6780C22semidirect
38. C22×D5×Dic3C22semidirect
39. C22×D5×Dic3C22semidirect
40. C2×#6719C22semidirect
41. #91828C22semidirect
42. C2×#6714C22semidirect
43. C2×#6712C22semidirect
44. C2×C5×#217C22semidirect
45. C2×C5×#217C22semidirect
46. C5×#938C22semidirect
47. C2×C5×C4⋊Dic3C22semidirect
48. C2×C3×C22⋊Dic5C22semidirect
49. C3×#4083C22semidirect
51. C2×C3×#685C22semidirect
52. #91577C22semidirect
53. #91559C22semidirect
54. #91555C22semidirect
55. #91550C22semidirect
56. D5×#217C22semidirect
57. C2×#6669C22semidirect
58. C2×#6668C22semidirect
59. C2×#6667C22semidirect
60. C2×#6667C22semidirect
61. C2×(C2×D3)⋊Dic5C22semidirect
64. C2×Dic3×Dic5C22semidirect
65. #91526C22semidirect
66. D3×#685C22semidirect
67. #91441C22semidirect
68. #91430C22semidirect
69. #91413C22semidirect
76. C2×#4083D3semidirect
102. C2×C3×C5×D4C23semidirect
107. C2×#1220C23semidirect
112. C22×Dic15C23semidirect
116. C2×C5×#67C23semidirect
121. C2×C4×C5×D3C23semidirect
125. C2×C3×C22⋊D5C23semidirect
130. C2×#1204C23semidirect
133. C2×#1201D4semidirect
136. C2×D3×Dic5C23semidirect
142. C2×D5×Dic3C23semidirect
143. C2×D5×Dic3C23semidirect
144. #6719C23semidirect
145. #6714C23semidirect
146. #6712C23semidirect
147. C5×#217C23semidirect
148. C5×#217C23semidirect
149. C5×C4⋊Dic3C23semidirect
150. C3×C22⋊Dic5C23semidirect
152. C3×#685C23semidirect
153. #6669C23semidirect
154. #6668C23semidirect
155. #6667C23semidirect
156. #6667C23semidirect
157. (C2×D3)⋊Dic5C23semidirect
160. Dic3×Dic5C23semidirect
167. C2×#938D5semidirect
181. C22×C5×D4C2×D3semidirect
187. C22×C22⋊D5C2×D3semidirect
205. C2×C22⋊Dic5C2×D3semidirect
208. #4083C2×D3semidirect
218. C2×#685C2×D3semidirect
256. C22×C3×D5#41semidirect
292. #1201C2×D4semidirect
301. C22×C3×D4C2×D5semidirect
309. C22×#67C2×D5semidirect
317. C22×C4×D3C2×D5semidirect
327. C2×#217C2×D5semidirect
328. C2×#217C2×D5semidirect
331. #938C2×D5semidirect
339. C2×C4⋊Dic3C2×D5semidirect
368. C2×C5×D4C22×D3semidirect
384. C2×C22⋊D5C22×D3semidirect
411. C22⋊Dic5C22×D3semidirect
418. #685C22×D3semidirect
467. C2×C3×D5C2×#41semidirect
497. C2×C3×D4C22×D5semidirect
513. C2×#67C22×D5semidirect
532. C2×C4×D3C22×D5semidirect
541. #217C22×D5semidirect
542. #217C22×D5semidirect
548. C4⋊Dic3C22×D5semidirect
582. C22×D5#237semidirect
634. C22×D4D3×D5semidirect
673. C2×C3×C5#546semidirect
777. C2×D5C2×#237semidirect
822. C2×D4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
904. C2×C5#5591semidirect
982. C2×C3#65944semidirect
988. C5C2×#5591semidirect
1028. C3C2×#65944semidirect
1035. C2#11755035direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×#672
C22×#67802
C2×#918282
C2×C5×#9382
C2×C3×#40832
C2×#915772
C2×#915592
C2×#915552
C2×#915502
C2×D5×#2172
C2×#915262
#117550352
C2×D3×#6852
C2×#914412
C2×#914302
C2×#914132
C2×#659443
C2×#55915