Finite Group Databasebeta

← C2×#11754791 #14482594

Subgroups — C2×#11754791 #14482594

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×C3×D4×D5C211yesmaximal, characteristic, complemented
2C22×#6780C211yesmaximal, characteristic, complemented
3C2×#91824C211yesmaximal, characteristic, complemented
4C2×C5×#939C211yesmaximal, characteristic, complemented
5C2×#91565C211yesmaximal, characteristic, complemented
6C2×#91563C211yesmaximal, characteristic, complemented
7C2×#91563C211yesmaximal, characteristic, complemented
8C2×Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
9C2×D5×#217C211yesmaximal, characteristic, complemented
10C22×#6665C211yesmaximal, characteristic, complemented
11C2×#91534C211yesmaximal, characteristic, complemented
12#11754791C2116yesmaximal, direct product factor
13C2×#91440C211yesmaximal, characteristic, complemented
14C2×#91408C211yesmaximal, characteristic, complemented
15C2×#91407C211yesmaximal, characteristic, complemented
16C2×#91349C211yesmaximal, characteristic, complemented
17C2×#65944—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C24×C3×D5C2211yescharacteristic
20C22×C3×C5×D4C2211yescharacteristic
21C23×Dic15C2211yescharacteristic, complemented
22C22×C5×#67C2211yescharacteristic, complemented
23C22×C5×#67C2211yescharacteristic, complemented
24C23×C5×Dic3C2211yescharacteristic, complemented
25C22×C3×C22⋊D5C2211yescharacteristic
26C22×C3×C22⋊D5C2211yescharacteristic
27C2×C3×D4×D5—28no—
28C2×C3×D4×D5C2218yescomplemented
29C22×C3×D20C2211yescharacteristic
30C22×C3×C4×D5C2211yescharacteristic
31C22×#1204C2211yescharacteristic, complemented
32C22×#1201C2211yescharacteristic
33C22×#1201C2211yescharacteristic, complemented
34C22×#1201C2211yescharacteristic, complemented
35C22×D3×Dic5C2211yescharacteristic, complemented
36C2×#6780—28no—
37C2×#6780C2218yescomplemented
38C22×D5×Dic3C2211yescharacteristic, complemented
39C22×D5×Dic3C2211yescharacteristic, complemented
40C2×#6719C2211yescharacteristic, complemented
41C2×#6719C2211yescharacteristic, complemented
42C2×#6719C2211yescharacteristic, complemented
43#91824C2218yescomplemented
44C2×#6712C2211yescharacteristic, complemented
45C2×#6712C2211yescharacteristic, complemented
46C2×C5×#217C2211yescharacteristic, complemented
47C5×#939C2218yescomplemented
48C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
50#91565C2218yescomplemented
51#91563C2218yescomplemented
52#91563C2218yescomplemented
53Dic3×C22⋊D5C2218yescomplemented
54D5×#217C2218yescomplemented
55C2×#6668C2211yescharacteristic, complemented
56C2×#6665C2211yescharacteristic
57C2×#6665C2211yescharacteristic
58C2×#6665C2211yescharacteristic
59C2×#6665C2218yescomplemented
60C2×#6665C2211yescharacteristic, complemented
61C2×#6665C2211yescharacteristic, complemented
62C2×#6665C2211yescharacteristic, complemented
63C2×#6665C2211yescharacteristic, complemented
64#91534C2218yescomplemented
65C2×Dic3×Dic5C2211yescharacteristic, complemented
66#91440C2218yescomplemented
67#91408C2218yescomplemented
68#91407C2218yescomplemented
69#91349C2218yescomplemented
70C2×#5806—51nomaximal, Hall
71C22×#711—31no—
72C22×D4×D5D311yescharacteristic, complemented
73C2×C5×#121—31no—
74C2×#4085—31no—
75C2×#4083—31no—
76C2×#4083—31no—
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×C5×D3C2311yescharacteristic
90C23×C3×D5—24no—
91C23×C3×D5—24no—
92C23×C3×D5—24no—
93C23×C3×D5—24no—
94C23×C3×D5—42no—
95C23×C3×D5—42no—
96C23×C3×D5C2311yescharacteristic
97C23×C3×D5C2314yes—
98C23×C3×D5C2314yes—
99C23×C3×D5C2311yescharacteristic
100C23×C3×D5C2311yescharacteristic
101C2×C3×C5×D4—24no—
102C2×C3×C5×D4C2314yes—
103C22×C3×C4×C5C2311yescharacteristic
104C22×Dic15—24no—
105C22×Dic15C2311yescharacteristic
106C22×Dic15C2311yescharacteristic
107C22×Dic15C2311yescharacteristic
108C22×Dic15C2311yescharacteristic
109C22×Dic15C2314yescomplemented
110C2×C5×#67—24no—
111C2×C5×#67—42no—
112C2×C5×#67C2314yescomplemented
113C2×C5×#67C2314yescomplemented
114C22×C5×Dic3—42no—
115C22×C5×Dic3C2311yescharacteristic
116C22×C5×Dic3C2311yescharacteristic
117C22×C5×Dic3C2311yescharacteristic
118C22×C5×Dic3C2314yescomplemented
119C2×C3×C22⋊D5—24no—
120C2×C3×C22⋊D5D418yescomplemented
121C2×C3×C22⋊D5C2314yes—
122C2×C3×C22⋊D5C2314yes—
123C22×C3×Dic5C2311yescharacteristic
124C3×D4×D5—232no—
125C2×C3×D20—24no—
126C2×C3×D20C2314yes—
127C2×C3×C4×D5—24no—
128C2×C3×C4×D5C2314yes—
129C2×#1204—24no—
130C2×#1204C2314yescomplemented
131C2×#1201—24no—
132C2×#1201—24no—
133C2×#1201—42no—
134C2×#1201C2314yes—
135C2×#1201C2314yescomplemented
136C2×#1201C2314yescomplemented
137C2×D3×Dic5—24no—
138C2×D3×Dic5C2314yescomplemented
139#6780—232no—
140C2×D5×Dic3—24no—
141C2×D5×Dic3—42no—
142C2×D5×Dic3C2314yescomplemented
143C2×D5×Dic3C2314yescomplemented
144#6719C2314yescomplemented
145#6719C2314yescomplemented
146#6719C2314yescomplemented
147#6712C2314yescomplemented
148#6712C2314yescomplemented
149C5×#217C2314yescomplemented
150C5×(C2×D3)⋊C4C2314yescomplemented
151C5×Dic3⋊C4C2314yescomplemented
152#6668C2314yescomplemented
153#6665C2314yes—
154#6665C2314yes—
155#6665C2314yes—
156#6665C2314yescomplemented
157#6665C2314yescomplemented
158#6665C2314yescomplemented
159#6665C2314yescomplemented
160Dic3×Dic5C2314yescomplemented
161C23×C3×D4—51no—
162C22×#237—51no—
163C2×#953—51no—
164C2×#953—51no—
165C22×#217—51no—
166C22×#217—51no—
167#5806—516no—
168C2×#939—51no—
169C2×#939D511yescharacteristic, complemented
170C2×#938—51no—
171C2×#936—51no—
172C2×#935—51no—
173C2×#935—51no—
174C2×D4×Dic3—51no—
175C2×C4×#67—51no—
176C2×#924—51no—
177C24×D5C2×D311yescharacteristic
178C24×D5C2×D311yescharacteristic
179C22×C5×D4—31no—
180C22×C5×D4—31no—
181C22×C5×D4C2×D311yescharacteristic
182C23×C4×C5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5C2×D311yescharacteristic
187C22×C22⋊D5C2×D311yescharacteristic
188C23×Dic5—31no—
189C23×Dic5—31no—
190C2×#711—38no—
191C2×#711—68no—
192C2×D4×D5—28no—
193C2×D4×D5C2×D318yescomplemented
194C22×D20C2×D311yescharacteristic
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5C2×D311yescharacteristic
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⋊Dic5—31no—
206#4085—38no—
207#4083—38no—
208#4083—38no—
209#4081—38no—
210C4×C22⋊D5—38no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—31no—
217C2×#685—31no—
218C2×#685—38no—
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×C5C2×D414yes—
236C23×C3×C5C2412yes—
237C23×C3×C5C2412yes—
238C23×C3×C5C2411yescharacteristic
239C22×C5×D3—22no—
240C22×C5×D3—22no—
241C22×C5×D3—22no—
242C22×C5×D3C2412yes—
243C22×C3×D5—22no—
244C22×C3×D5—22no—
245C22×C3×D5—22no—
246C22×C3×D5—22no—
247C22×C3×D5—22no—
248C22×C3×D5—28no—
249C22×C3×D5—22no—
250C22×C3×D5—22no—
251C22×C3×D5—28no—
252C22×C3×D5—28no—
253C22×C3×D5—28no—
254C22×C3×D5—44no—
255C22×C3×D5—44no—
256C22×C3×D5—416no—
257C22×C3×D5—416no—
258C22×C3×D5C2×D414yes—
259C22×C3×D5#4114yescomplemented
260C22×C3×D5C2412yes—
261C22×C3×D5C2412yes—
262C22×C3×D5C2412yes—
263C3×C5×D4—28no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5C2412yes—
266C2×Dic15—22no—
267C2×Dic15—28no—
268C2×Dic15—22no—
269C2×Dic15—22no—
270C2×Dic15—22no—
271C2×Dic15C2412yes—
272C2×Dic15C2412yes—
273C2×Dic15C2412yes—
274C2×Dic15C2412yes—
275C5×#67—28no—
276C5×#67—44no—
277C2×C5×Dic3—22no—
278C2×C5×Dic3—22no—
279C2×C5×Dic3—22no—
280C2×C5×Dic3—44no—
281C2×C5×Dic3C2412yes—
282C2×C5×Dic3C2412yes—
283C2×C5×Dic3C2412yes—
284C3×C22⋊D5—28no—
285C3×C22⋊D5C2×D4116yescomplemented
286C2×C3×Dic5C2×D414yes—
287C2×C3×Dic5C2412yes—
288C3×D20—28no—
289C3×C4×D5—28no—
290#1204—28no—
291#1201—28no—
292#1201—28no—
293#1201—44no—
294D3×Dic5—28no—
295D5×Dic3—28no—
296D5×Dic3—44no—
297C25×C3—51no—
298C25×C3—51no—
299C22×C3×D4—51no—
300C22×C3×D4—51no—
301C22×C3×D4—58no—
302C22×C3×D4—51no—
303C22×C3×D4—108no—
304C22×C3×D4C2×D511yescharacteristic
305C23×C3×C4—51no—
306C22×#67—51no—
307C22×#67—51no—
308C22×#67—51no—
309C22×#67C2×D511yescharacteristic, complemented
310C22×#67C2×D511yescharacteristic, complemented
311C23×Dic3—51no—
312C23×Dic3—51no—
313C23×Dic3—51no—
314C23×Dic3C2×D511yescharacteristic, complemented
315C2×#237—58no—
316C2×#237—108no—
317C22×C4×D3—51no—
318C22×Dic6—51no—
319#953—58no—
320#953—58no—
321C2×#217—51no—
322C2×#217—51no—
323C2×#217—51no—
324C2×#217—51no—
325C2×#217—51no—
326C2×#217—51no—
327C2×#217—51no—
328C2×#217—51no—
329C2×#217—51no—
330C2×#217—51no—
331C2×#217—58no—
332C2×#217—58no—
333C2×#217C2×D511yescharacteristic, complemented
334#939—58no—
335#939C2×D518yescomplemented
336#938—58no—
337#936—58no—
338#935—58no—
339#935—58no—
340D4×Dic3—58no—
341C4×#67—58no—
342C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
343C2×C4⋊Dic3—51no—
344#924—58no—
345C2×Dic3⋊C4—51no—
346C2×Dic3⋊C4—51no—
347C2×Dic3⋊C4C2×D511yescharacteristic, complemented
348C2×C4×Dic3—51no—
349C24×C5—31no—
350C24×C5C22×D311yescharacteristic
351C24×C5C22×D311yescharacteristic
352C23×D5—24no—
353C23×D5—24no—
354C23×D5—24no—
355C23×D5—24no—
356C23×D5—42no—
357C23×D5—42no—
358C23×D5C22×D311yescharacteristic
359C23×D5C22×D314yes—
360C23×D5C22×D314yes—
361C23×D5C22×D311yescharacteristic
362C23×D5C22×D311yescharacteristic
363C2×C5×D4—24no—
364C2×C5×D4—34no—
365C2×C5×D4—34no—
366C2×C5×D4—64no—
367C2×C5×D4—122no—
368C2×C5×D4C22×D314yes—
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—34no—
377C2×C22⋊D5—34no—
378C2×C22⋊D5—34no—
379C2×C22⋊D5—64no—
380C2×C22⋊D5—64no—
381C2×C22⋊D5—122no—
382C2×C22⋊D5#6718yescomplemented
383C2×C22⋊D5C22×D314yes—
384C2×C22⋊D5C22×D314yes—
385C22×Dic5—31no—
386C22×Dic5—31no—
387C22×Dic5—31no—
388C22×Dic5—31no—
389C22×Dic5—34no—
390C22×Dic5—34no—
391C22×Dic5—64no—
392C22×Dic5—64no—
393C22×Dic5C22×D311yescharacteristic
394#711—632no—
395D4×D5—232no—
396C2×D20—24no—
397C2×D20C22×D314yes—
398C2×C4×D5—24no—
399C2×C4×D5—34no—
400C2×C4×D5—34no—
401C2×C4×D5—64no—
402C2×C4×D5—122no—
403C2×C4×D5C22×D314yes—
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⋊Dic5—34no—
412#685—34no—
413#685—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685—34no—
418#685—34no—
419#683—34no—
420#683—34no—
421#683—34no—
422C4×Dic5—34no—
423C22×#41—151no—
424C23×D4—51no—
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—151no—
434C2×#120—151no—
435C2×C4×D4—151no—
436C2×C4×D4—151no—
437C22×C22⋊C4—151no—
438C22×C22⋊C4—151no—
439C22×C3×C5—28no—
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×C5C22×D414yes—
447C22×C3×C5C22×D412yes—
448C22×C3×C5C2×#4112yes—
449C22×C3×C5H(5,𝔽2)12yes—
450C22×C3×C5C2511yescharacteristic
451C2×C5×D3—22no—
452C2×C5×D3—22no—
453C2×C5×D3—22no—
454C2×C5×D3—44no—
455C2×C3×D5—28no—
456C2×C3×D5—28no—
457C2×C3×D5—22no—
458C2×C3×D5—22no—
459C2×C3×D5—22no—
460C2×C3×D5—22no—
461C2×C3×D5—22no—
462C2×C3×D5—22no—
463C2×C3×D5—22no—
464C2×C3×D5—416no—
465C2×C3×D5—416no—
466C2×C3×D5—44no—
467C2×C3×D5C22×D414yes—
468C2×C3×D5C2×#4114yescomplemented
469C3×C4×C5—22no—
470Dic15—22no—
471Dic15—22no—
472Dic15—22no—
473Dic15—22no—
474C3×Dic5C22×D414yes—
475C5×Dic3—22no—
476C5×Dic3—22no—
477C5×Dic3—22no—
478C24×C3—51no—
479C24×C3—51no—
480C24×C3—51no—
481C24×C3—54no—
482C24×C3—54no—
483C24×C3—104no—
484C24×C3—104no—
485C24×C3—104no—
486C24×C3—104no—
487C24×C3—202no—
488C24×C3—202no—
489C24×C3C22×D511yescharacteristic
490C24×C3C22×D511yescharacteristic
491C23×D3C22×D511yescharacteristic
492C2×C3×D4—24no—
493C2×C3×D4—58no—
494C2×C3×D4—54no—
495C2×C3×D4—54no—
496C2×C3×D4—54no—
497C2×C3×D4—104no—
498C2×C3×D4—104no—
499C2×C3×D4—1032no—
500C2×C3×D4C22×D514yes—
501C22×C3×C4—51no—
502C22×C3×C4—54no—
503C22×C3×C4—104no—
504C22×C3×C4C22×D511yescharacteristic
505C2×#67—24no—
506C2×#67—42no—
507C2×#67—54no—
508C2×#67—54no—
509C2×#67—54no—
510C2×#67—104no—
511C2×#67—104no—
512C2×#67—202no—
513C2×#67C22×D514yescomplemented
514C2×#67C22×D514yescomplemented
515C22×Dic3—42no—
516C22×Dic3—51no—
517C22×Dic3—51no—
518C22×Dic3—51no—
519C22×Dic3—51no—
520C22×Dic3—54no—
521C22×Dic3—54no—
522C22×Dic3—54no—
523C22×Dic3—104no—
524C22×Dic3—104no—
525C22×Dic3—202no—
526C22×Dic3C22×D511yescharacteristic
527C22×Dic3C22×D511yescharacteristic
528C22×Dic3C22×D511yescharacteristic
529C22×Dic3C22×D514yescomplemented
530#237—1032no—
531C2×C4×D3—54no—
532C2×C4×D3—104no—
533C2×Dic6—54no—
534C2×Dic6—104no—
535#217—54no—
536#217—54no—
537#217—54no—
538#217—54no—
539#217—54no—
540#217—54no—
541#217—54no—
542#217—54no—
543#217—54no—
544#217—54no—
545#217C22×D514yescomplemented
546(C2×D3)⋊C4C22×D514yescomplemented
547C4⋊Dic3—54no—
548Dic3⋊C4—54no—
549Dic3⋊C4—54no—
550Dic3⋊C4C22×D514yescomplemented
551C4×Dic3—54no—
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—22no—
556C23×C5—22no—
557C23×C5—32no—
558C23×C5—62no—
559C23×C5—62no—
560C23×C5—62no—
561C23×C5C2×#6714yes—
562C23×C5C23×D312yes—
563C23×C5C23×D312yes—
564C23×C5C23×D311yescharacteristic
565C22×D5—22no—
566C22×D5—22no—
567C22×D5—22no—
568C22×D5—22no—
569C22×D5—22no—
570C22×D5—22no—
571C22×D5—22no—
572C22×D5—28no—
573C22×D5—28no—
574C22×D5—28no—
575C22×D5—28no—
576C22×D5—44no—
577C22×D5—44no—
578C22×D5—416no—
579C22×D5—416no—
580C22×D5#23714yescomplemented
581C22×D5C2×#6714yes—
582C22×D5C23×D312yes—
583C22×D5C23×D312yes—
584C22×D5C23×D312yes—
585C5×D4—28no—
586C5×D4—68no—
587C5×D4—124no—
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—68no—
599C22⋊D5—68no—
600C22⋊D5—124no—
601C22⋊D5C2×#67116yescomplemented
602C2×Dic5—32no—
603C2×Dic5—32no—
604C2×Dic5—32no—
605C2×Dic5—32no—
606C2×Dic5—62no—
607C2×Dic5—62no—
608C2×Dic5—62no—
609C2×Dic5—62no—
610C2×Dic5—68no—
611C2×Dic5—68no—
612C2×Dic5C2×#6714yes—
613C2×Dic5C23×D312yes—
614D20—28no—
615C4×D5—28no—
616C4×D5—68no—
617C4×D5—124no—
618Dic10—68no—
619C25—51no—
620C25—51no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—151no—
624C22×D4—31no—
625C22×D4—31no—
626C22×D4—51no—
627C22×D4—51no—
628C22×D4—58no—
629C22×D4—51no—
630C22×D4—108no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—151no—
634C22×D4D3×D511yescharacteristic
635C23×C4—31no—
636C23×C4—51no—
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—158no—
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—158no—
659C2×C22⋊C4—151no—
660C2×C22⋊C4—151no—
661C2×C22⋊C4—151no—
662C2×C22⋊C4—151no—
663C2×C22⋊C4—151no—
664C2×C22⋊C4—158no—
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—24no—
672C2×C3×C5—42no—
673C2×C3×C5#54614yescomplemented
674C2×C3×C5C23×D411yescharacteristic
675C2×C3×C5C22×#4111yescharacteristic
676C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
677C3×D5—24no—
678C3×D5—24no—
679C3×D5—42no—
680C5×D3—42no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—22no—
685C23×C3—22no—
686C23×C3—54no—
687C23×C3—54no—
688C23×C3—52no—
689C23×C3—52no—
690C23×C3—52no—
691C23×C3—108no—
692C23×C3—108no—
693C23×C3—108no—
694C23×C3—102no—
695C23×C3—102no—
696C23×C3—102no—
697C23×C3—102no—
698C23×C3—108no—
699C23×C3—102no—
700C23×C3—102no—
701C23×C3—102no—
702C23×C3—204no—
703C23×C3—204no—
704C23×C3—2016no—
705C23×C3—2016no—
706C23×C3D4×D514yes—
707C23×C3C23×D512yes—
708C23×C3C23×D512yes—
709C23×C3C23×D511yescharacteristic
710C22×D3—22no—
711C22×D3—22no—
712C22×D3—22no—
713C22×D3C23×D512yes—
714C3×D4—28no—
715C3×D4—516no—
716C3×D4—108no—
717C3×D4—108no—
718C2×C3×C4—22no—
719C2×C3×C4—54no—
720C2×C3×C4—52no—
721C2×C3×C4—108no—
722C2×C3×C4C23×D512yes—
723#67—28no—
724#67—44no—
725#67—108no—
726#67—108no—
727#67—204no—
728C2×Dic3—22no—
729C2×Dic3—22no—
730C2×Dic3—22no—
731C2×Dic3—44no—
732C2×Dic3—52no—
733C2×Dic3—52no—
734C2×Dic3—52no—
735C2×Dic3—52no—
736C2×Dic3—108no—
737C2×Dic3—102no—
738C2×Dic3—102no—
739C2×Dic3—108no—
740C2×Dic3—102no—
741C2×Dic3—102no—
742C2×Dic3—204no—
743C2×Dic3C23×D512yes—
744C2×Dic3C23×D512yes—
745C2×Dic3C23×D512yes—
746C4×D3—108no—
747Dic6—108no—
748C22×C5—22no—
749C22×C5—22no—
750C22×C5—28no—
751C22×C5—22no—
752C22×C5—22no—
753C22×C5—22no—
754C22×C5—44no—
755C22×C5—62no—
756C22×C5—62no—
757C22×C5—62no—
758C22×C5—124no—
759C22×C5C2×#23712yes—
760C22×C5#100412yes—
761C22×C5C22×#6714yes—
762C22×C5C22×#6712yes—
763C22×C5C24×D311yescharacteristic
764C2×D5—22no—
765C2×D5—22no—
766C2×D5—22no—
767C2×D5—22no—
768C2×D5—28no—
769C2×D5—28no—
770C2×D5—22no—
771C2×D5—22no—
772C2×D5—22no—
773C2×D5—416no—
774C2×D5—416no—
775C2×D5—44no—
776C2×D5C2×#23714yescomplemented
777C2×D5C22×#6714yes—
778C4×C5—22no—
779C4×C5—62no—
780C4×C5—62no—
781C4×C5—62no—
782Dic5—62no—
783Dic5—62no—
784Dic5—62no—
785Dic5—62no—
786Dic5C22×#6714yes—
787C24—31no—
788C24—51no—
789C24—51no—
790C24—51no—
791C24—54no—
792C24—54no—
793C24—104no—
794C24—104no—
795C24—104no—
796C24—104no—
797C24—202no—
798C24—202no—
799C24C2×D3×D511yescharacteristic
800C24C2×D3×D511yescharacteristic
801#41—3032no—
802C2×Q8—154no—
803C2×Q8—304no—
804C2×D4—24no—
805C2×D4—34no—
806C2×D4—34no—
807C2×D4—58no—
808C2×D4—54no—
809C2×D4—54no—
810C2×D4—54no—
811C2×D4—64no—
812C2×D4—104no—
813C2×D4—104no—
814C2×D4—1032no—
815C2×D4—122no—
816C2×D4—154no—
817C2×D4—154no—
818C2×D4—154no—
819C2×D4—304no—
820C2×D4—304no—
821C2×D4—602no—
822C2×D4C2×D3×D514yes—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—31no—
826C22×C4—34no—
827C22×C4—51no—
828C22×C4—54no—
829C22×C4—104no—
830C22×C4—122no—
831C22×C4—154no—
832C22×C4—154no—
833C22×C4—154no—
834C22×C4—154no—
835C22×C4—151no—
836C22×C4—151no—
837C22×C4—151no—
838C22×C4—151no—
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—154no—
851C22⋊C4—154no—
852C22⋊C4—154no—
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—28no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—22no—
866C22×C3—22no—
867C22×C3—22no—
868C22×C3—44no—
869C22×C3—54no—
870C22×C3—54no—
871C22×C3—108no—
872C22×C3—108no—
873C22×C3—102no—
874C22×C3—102no—
875C22×C3—102no—
876C22×C3—102no—
877C22×C3—102no—
878C22×C3—102no—
879C22×C3—102no—
880C22×C3—2016no—
881C22×C3—2016no—
882C22×C3—204no—
883C22×C3C2×D4×D514yes—
884C22×C3C2×D4×D512yes—
885C22×C3#414412yes—
886C22×C3D5×#4112yes—
887C22×C3C24×D511yescharacteristic
888C2×D3—22no—
889C2×D3—22no—
890C2×D3—22no—
891C2×D3—44no—
892C3×C4—22no—
893C3×C4—54no—
894Dic3—22no—
895Dic3—22no—
896Dic3—22no—
897Dic3—102no—
898Dic3—102no—
899Dic3—102no—
900Dic3—102no—
901C2×C5—24no—
902C2×C5—42no—
903C2×C5—122no—
904C2×C5#580614yescomplemented
905C2×C5C22×#23711yescharacteristic
906C2×C5C2×#100411yescharacteristic
907C2×C5C23×#6711yescharacteristic
908D5—24no—
909D5—24no—
910D5—42no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—32no—
917C23—54no—
918C23—54no—
919C23—52no—
920C23—52no—
921C23—52no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—108no—
926C23—108no—
927C23—108no—
928C23—102no—
929C23—102no—
930C23—102no—
931C23—102no—
932C23—102no—
933C23—102no—
934C23—108no—
935C23—102no—
936C23—204no—
937C23—204no—
938C23—2016no—
939C23—2016no—
940C23D5×#6714yes—
941C23C22×D3×D512yes—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—308no—
945D4—28no—
946D4—516no—
947D4—68no—
948D4—108no—
949D4—108no—
950D4—124no—
951D4—308no—
952D4—308no—
953D4—604no—
954C2×C4—22no—
955C2×C4—32no—
956C2×C4—32no—
957C2×C4—32no—
958C2×C4—54no—
959C2×C4—52no—
960C2×C4—62no—
961C2×C4—62no—
962C2×C4—62no—
963C2×C4—108no—
964C2×C4—124no—
965C2×C4—152no—
966C2×C4—152no—
967C2×C4—152no—
968C2×C4—152no—
969C2×C4—308no—
970C2×C4—308no—
971C2×C4—302no—
972C2×C4—302no—
973C2×C4—302no—
974C2×C4—302no—
975C2×C4—308no—
976C2×C4—604no—
977C2×C4C22×D3×D512yes—
978C2×C3—24no—
979C2×C3—42no—
980C2×C3—104no—
981C2×C3—104no—
982C2×C3—202no—
983C2×C3#6594414yescomplemented
984C2×C3C22×D4×D511yescharacteristic
985C2×C3C2×#414411yescharacteristic
986C2×C3C2×D5×#4111yescharacteristic
987D3—42no—
988C5C2×#580611yescharacteristic, complemented, Sylow
989C22—28no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—44no—
996C22—54no—
997C22—54no—
998C22—62no—
999C22—62no—
1000C22—62no—
1001C22—102no—
1002C22—108no—
1003C22—108no—
1004C22—102no—
1005C22—102no—
1006C22—102no—
1007C22—102no—
1008C22—102no—
1009C22—102no—
1010C22—124no—
1011C22—2016no—
1012C22—2016no—
1013C22—204no—
1014C22D5×#23712yes—
1015C22#9202512yes—
1016C22C2×D5×#6714yes—
1017C22C2×D5×#6712yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—54no—
1021C4—62no—
1022C4—62no—
1023C4—62no—
1024C4—302no—
1025C4—302no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6594411yescharacteristic, complemented, Sylow
1029C2—24no—
1030C2—42no—
1031C2—104no—
1032C2—104no—
1033C2—122no—
1034C2—202no—
1035C2#1175479114yesdirect product factor
1036C2C2×D5×#23711yescharacteristic
1037C2C2×#9202511yescharacteristic
1038C2C22×D5×#6711yescharacteristic
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×C3×D4×D5C2semidirect
2. C22×#6780C2semidirect
3. C2×#91824C2semidirect
4. C2×C5×#939C2semidirect
5. C2×#91565C2semidirect
6. C2×#91563C2semidirect
7. C2×#91563C2semidirect
8. C2×Dic3×C22⋊D5C2semidirect
9. C2×D5×#217C2semidirect
10. C22×#6665C2semidirect
11. C2×#91534C2semidirect
12. #11754791C2direct (N × H)
13. C2×#91440C2semidirect
14. C2×#91408C2semidirect
15. C2×#91407C2semidirect
16. C2×#91349C2semidirect
21. C23×Dic15C22semidirect
22. C22×C5×#67C22semidirect
23. C22×C5×#67C22semidirect
24. C23×C5×Dic3C22semidirect
28. C2×C3×D4×D5C22semidirect
31. C22×#1204C22semidirect
33. C22×#1201C22semidirect
34. C22×#1201C22semidirect
35. C22×D3×Dic5C22semidirect
37. C2×#6780C22semidirect
38. C22×D5×Dic3C22semidirect
39. C22×D5×Dic3C22semidirect
40. C2×#6719C22semidirect
41. C2×#6719C22semidirect
42. C2×#6719C22semidirect
43. #91824C22semidirect
44. C2×#6712C22semidirect
45. C2×#6712C22semidirect
46. C2×C5×#217C22semidirect
47. C5×#939C22semidirect
48. C2×C5×(C2×D3)⋊C4C22semidirect
49. C2×C5×Dic3⋊C4C22semidirect
50. #91565C22semidirect
51. #91563C22semidirect
52. #91563C22semidirect
53. Dic3×C22⋊D5C22semidirect
54. D5×#217C22semidirect
55. C2×#6668C22semidirect
59. C2×#6665C22semidirect
60. C2×#6665C22semidirect
61. C2×#6665C22semidirect
62. C2×#6665C22semidirect
63. C2×#6665C22semidirect
64. #91534C22semidirect
65. C2×Dic3×Dic5C22semidirect
66. #91440C22semidirect
67. #91408C22semidirect
68. #91407C22semidirect
69. #91349C22semidirect
72. C22×D4×D5D3semidirect
109. C22×Dic15C23semidirect
112. C2×C5×#67C23semidirect
113. C2×C5×#67C23semidirect
118. C22×C5×Dic3C23semidirect
120. C2×C3×C22⋊D5D4semidirect
130. C2×#1204C23semidirect
135. C2×#1201C23semidirect
136. C2×#1201C23semidirect
138. C2×D3×Dic5C23semidirect
142. C2×D5×Dic3C23semidirect
143. C2×D5×Dic3C23semidirect
144. #6719C23semidirect
145. #6719C23semidirect
146. #6719C23semidirect
147. #6712C23semidirect
148. #6712C23semidirect
149. C5×#217C23semidirect
150. C5×(C2×D3)⋊C4C23semidirect
151. C5×Dic3⋊C4C23semidirect
152. #6668C23semidirect
156. #6665C23semidirect
157. #6665C23semidirect
158. #6665C23semidirect
159. #6665C23semidirect
160. Dic3×Dic5C23semidirect
169. C2×#939D5semidirect
193. C2×D4×D5C2×D3semidirect
259. C22×C3×D5#41semidirect
285. C3×C22⋊D5C2×D4semidirect
309. C22×#67C2×D5semidirect
310. C22×#67C2×D5semidirect
314. C23×Dic3C2×D5semidirect
333. C2×#217C2×D5semidirect
335. #939C2×D5semidirect
342. C2×(C2×D3)⋊C4C2×D5semidirect
347. C2×Dic3⋊C4C2×D5semidirect
382. C2×C22⋊D5#67semidirect
468. C2×C3×D5C2×#41semidirect
513. C2×#67C22×D5semidirect
514. C2×#67C22×D5semidirect
529. C22×Dic3C22×D5semidirect
545. #217C22×D5semidirect
546. (C2×D3)⋊C4C22×D5semidirect
550. Dic3⋊C4C22×D5semidirect
580. C22×D5#237semidirect
601. C22⋊D5C2×#67semidirect
673. C2×C3×C5#546semidirect
776. C2×D5C2×#237semidirect
861. C3×C5C2×#546semidirect
904. C2×C5#5806semidirect
983. C2×C3#65944semidirect
988. C5C2×#5806semidirect
1028. C3C2×#65944semidirect
1035. C2#11754791direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D4×D52
C22×#67802
C2×#918242
C2×C5×#9392
C2×#915652
C2×#915632
C2×Dic3×C22⋊D52
C2×D5×#2172
C22×#66652
C2×#915342
#117547912
C2×#914402
C2×#914082
C2×#914072
C2×#913492
C2×#659443
C2×#58065