Finite Group Databasebeta

← C2×#11753226 #14482609

Subgroups — C2×#11753226 #14482609

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×#6771C211yesmaximal, characteristic, complemented
3C2×#91773C211yesmaximal, characteristic, complemented
4C2×C5×#883C211yesmaximal, characteristic, complemented
5C2×C3×D5×C22⋊C4C211yesmaximal, characteristic, complemented
6C2×#91564C211yesmaximal, characteristic, complemented
7C2×#91558C211yesmaximal, characteristic, complemented
8C2×#91526C211yesmaximal, characteristic, complemented
9C2×#91476C211yesmaximal, characteristic, complemented
10C2×D3×#685C211yesmaximal, characteristic, complemented
11C2×#91450C211yesmaximal, characteristic, complemented
12C2×#91440C211yesmaximal, characteristic, complemented
13C2×#91430C211yesmaximal, characteristic, complemented
14C2×#91396C211yesmaximal, characteristic, complemented
15C2×#91348C211yesmaximal, characteristic, complemented
16#11753226C2116yesmaximal, direct product factor
17C2×#65988—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic, complemented
22C22×D60C2211yescharacteristic, complemented
23C22×C4×D15C2211yescharacteristic, complemented
24C22×C5×#67C2211yescharacteristic
25C22×C4×C5×D3C2211yescharacteristic, complemented
26C22×C3×C4×D5C2211yescharacteristic, complemented
27C22×C3×C4×D5C2211yescharacteristic, complemented
28C2×D5×#67—28no—
29C2×D5×#67C2218yescomplemented
30C22×#1204C2211yescharacteristic, complemented
31C22×#1203C2211yescharacteristic, complemented
32C22×#1202C2211yescharacteristic
33C22×#1202C2211yescharacteristic
34C22×#1202C2211yescharacteristic, complemented
35C22×#1201C2211yescharacteristic
36C22×D3×Dic5C2211yescharacteristic, complemented
37C22×D5×Dic3C2211yescharacteristic
38C2×#6771—28no—
39C2×#6771C2218yescomplemented
40C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
41C2×#6714C2211yescharacteristic, complemented
42C2×#6712C2211yescharacteristic, complemented
43#91773C2218yescomplemented
44C2×C5×#217C2211yescharacteristic, complemented
45C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
47C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
48C5×#883C2218yescomplemented
49C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
50C2×C3×#685C2211yescharacteristic
51C2×C3×#685C2211yescharacteristic
52C3×D5×C22⋊C4C2218yescomplemented
53#91564C2218yescomplemented
54#91558C2218yescomplemented
55C2×#6669C2211yescharacteristic, complemented
56C2×#6667C2211yescharacteristic, complemented
57C2×#6667C2211yescharacteristic, complemented
58C2×#6667C2211yescharacteristic, complemented
59C2×#6665C2211yescharacteristic
60C2×#6665C2211yescharacteristic, complemented
61C2×Dic3×Dic5C2211yescharacteristic, complemented
62#91526C2218yescomplemented
63#91476C2218yescomplemented
64D3×#685C2218yescomplemented
65#91450C2218yescomplemented
66#91440C2218yescomplemented
67#91430C2218yescomplemented
68#91396C2218yescomplemented
69#91348C2218yescomplemented
70C2×#5490—51nomaximal, Hall
71C22×D4×D5—31no—
72C22×#709—31no—
73C2×C5×#123—31no—
74C2×#4085—31no—
75C22×#685—31no—
76#65988—316no—
77C2×#4042—31no—
78C2×#4041—31no—
79C2×#4040—31no—
80C2×#4039—31no—
81C2×#4031—31no—
82C2×#4030—31no—
83C2×#4028—31no—
84C2×#4028—31no—
85C2×#4027—31no—
86C2×D5×C22⋊C4D311yescharacteristic, complemented
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
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—
101C22×C3×C4×C5C2311yescharacteristic
102C22×C3×C4×C5C2311yescharacteristic
103C2×#1220—24no—
104C2×#1220—42no—
105C2×#1220C2314yes—
106C2×#1220C2314yescomplemented
107C22×Dic15C2311yescharacteristic
108C22×Dic15C2311yescharacteristic
109C2×D60—42no—
110C2×D60C2314yescomplemented
111C2×C4×D15—24no—
112C2×C4×D15C2314yescomplemented
113C2×C5×#67—24no—
114C2×C5×#67C2314yes—
115C22×C5×Dic3C2311yescharacteristic
116C22×C5×Dic3C2311yescharacteristic
117C22×C5×Dic3C2311yescharacteristic
118C2×C4×C5×D3—24no—
119C2×C4×C5×D3C2314yescomplemented
120C22×C3×Dic5C2311yescharacteristic
121C22×C3×Dic5C2311yescharacteristic
122C2×C3×C4×D5—24no—
123C2×C3×C4×D5—42no—
124C2×C3×C4×D5C2314yescomplemented
125C2×C3×C4×D5C2314yescomplemented
126D5×#67—232no—
127C2×#1204—24no—
128C2×#1204C2314yescomplemented
129C2×#1203—24no—
130C2×#1203C2314yescomplemented
131C2×#1202—24no—
132C2×#1202—24no—
133C2×#1202—24no—
134C2×#1202C2314yes—
135C2×#1202C2314yes—
136C2×#1202C2314yescomplemented
137C2×#1201D418yescomplemented
138C2×#1201C2314yes—
139C2×D3×Dic5—42no—
140C2×D3×Dic5C2314yescomplemented
141C2×D5×Dic3—24no—
142C2×D5×Dic3C2314yes—
143#6771—232no—
144C3×C5×C22⋊C4C2314yescomplemented
145#6714C2314yescomplemented
146#6712C2314yescomplemented
147C5×#217C2314yescomplemented
148C5×(C2×D3)⋊C4C2314yescomplemented
149C5×C4⋊Dic3C2314yescomplemented
150C5×Dic3⋊C4C2314yescomplemented
151C3×C22⋊Dic5C2314yescomplemented
152C3×#685C2314yes—
153C3×#685C2314yes—
154#6669C2314yescomplemented
155#6667C2314yescomplemented
156#6667C2314yescomplemented
157#6667C2314yescomplemented
158#6665C2314yes—
159#6665C2314yescomplemented
160Dic3×Dic5C2314yescomplemented
161C23×#67—51no—
162C22×#235—51no—
163C22×C3×C22⋊C4—51no—
164C2×#953—51no—
165C2×#930—51no—
166C2×#929—51no—
167C2×C4×#67—51no—
168C2×#885—51no—
169#5490—516no—
170C2×#884—51no—
171C2×#884—51no—
172C2×#883D511yescharacteristic, complemented
173C2×#882—51no—
174C2×#67⋊C4—51no—
175C2×D3×C22⋊C4—51no—
176C2×#878—51no—
177C24×D5—31no—
178C24×D5C2×D311yescharacteristic
179C22×C5×D4—31no—
180C23×C4×C5—31no—
181C22×C22⋊D5—31no—
182C22×C22⋊D5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C23×Dic5—31no—
186C2×D4×D5—38no—
187C2×D4×D5—68no—
188C2×#709—38no—
189C2×#709—68no—
190C22×D20—31no—
191C22×D20—31no—
192C22×D20—31no—
193C22×D20—31no—
194C22×C4×D5—31no—
195C22×C4×D5—31no—
196C22×C4×D5C2×D311yescharacteristic, complemented
197C22×C4×D5C2×D311yescharacteristic, complemented
198C22×Dic10—31no—
199C5×#123—38no—
200C2×C5×C4⋊C4—31no—
201C2×C5×C4⋊C4—31no—
202C2×C5×C22⋊C4—31no—
203C2×C5×C22⋊C4—31no—
204C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
205C2×C22⋊Dic5C2×D311yescharacteristic, complemented
206#4085—38no—
207C2×#685—31no—
208C2×#685—31no—
209C2×#685—31no—
210C2×#685—31no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—38no—
214C2×#685C2×D311yescharacteristic
215C2×#685C2×D311yescharacteristic
216C2×#683—31no—
217C2×#683—31no—
218C2×C4×Dic5—31no—
219#4042—38no—
220#4041—38no—
221#4040—38no—
222#4039—38no—
223#4031—38no—
224#4030—38no—
225#4028—38no—
226#4028—38no—
227#4027—38no—
228D5×C22⋊C4C2×D318yescomplemented
229C2×#546—151noSylow
230C23×C3×C5—22no—
231C23×C3×C5—22no—
232C23×C3×C5—22no—
233C23×C3×C5C2412yes—
234C23×C3×C5C2411yescharacteristic
235C22×D15—22no—
236C22×D15—22no—
237C22×D15—22no—
238C22×D15—22no—
239C22×D15—22no—
240C22×D15—22no—
241C22×D15C2412yes—
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—
263C2×C3×C4×C5—22no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5C2412yes—
266C2×C3×C4×C5C2412yes—
267#1220—28no—
268#1220—44no—
269C2×Dic15—22no—
270C2×Dic15C2×D414yes—
271C2×Dic15C2412yes—
272C2×Dic15C2412yes—
273D60—44no—
274C4×D15—28no—
275C5×#67—28no—
276C2×C5×Dic3—22no—
277C2×C5×Dic3—22no—
278C2×C5×Dic3—22no—
279C2×C5×Dic3C2412yes—
280C2×C5×Dic3C2412yes—
281C2×C5×Dic3C2412yes—
282C4×C5×D3—28no—
283C2×C3×Dic5—22no—
284C2×C3×Dic5—22no—
285C2×C3×Dic5C2412yes—
286C2×C3×Dic5C2412yes—
287C3×C4×D5—28no—
288C3×C4×D5—44no—
289#1204—28no—
290#1203—28no—
291#1202—28no—
292#1202—28no—
293#1202—28no—
294#1201C2×D4116yescomplemented
295D3×Dic5—44no—
296D5×Dic3—28no—
297C25×C3—51no—
298C24×D3—51no—
299C23×C3×C4—51no—
300C23×C3×C4—51no—
301C22×#67—51no—
302C22×#67—51no—
303C22×#67—51no—
304C22×#67—58no—
305C22×#67—51no—
306C22×#67—51no—
307C22×#67—51no—
308C22×#67—108no—
309C22×#67C2×D511yescharacteristic
310C23×Dic3—51no—
311C2×#235—58no—
312C2×#235—108no—
313C22×D12—51no—
314C22×D12—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3C2×D511yescharacteristic, complemented
318C22×Dic6—51no—
319C2×C3×C22⋊C4—51no—
320C2×C3×C22⋊C4—51no—
321C2×C3×C22⋊C4—51no—
322C2×C3×C22⋊C4—58no—
323C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
324#953—58no—
325C2×#217—51no—
326C2×#217—51no—
327C2×#217C2×D511yescharacteristic, complemented
328#930—58no—
329#929—58no—
330C4×#67—58no—
331C2×(C2×D3)⋊C4—51no—
332C2×(C2×D3)⋊C4—51no—
333C2×(C2×D3)⋊C4—51no—
334C2×(C2×D3)⋊C4—51no—
335C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
336C2×C4⋊Dic3C2×D511yescharacteristic, complemented
337C2×Dic3⋊C4—51no—
338C2×Dic3⋊C4—51no—
339C2×Dic3⋊C4C2×D511yescharacteristic, complemented
340C2×C4×Dic3—51no—
341#885—58no—
342#884—58no—
343#884—58no—
344#883C2×D518yescomplemented
345#882—58no—
346#67⋊C4—58no—
347D3×C22⋊C4—58no—
348#878—58no—
349C24×C5—31no—
350C24×C5C22×D311yescharacteristic
351C23×D5—24no—
352C23×D5—24no—
353C23×D5—31no—
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—64no—
365C22×C4×C5—31no—
366C22×C4×C5—31no—
367C22×C4×C5—31no—
368C22×C4×C5—34no—
369C22×C4×C5—64no—
370C22×C4×C5C22×D311yescharacteristic
371C22×C4×C5C22×D311yescharacteristic
372C2×C22⋊D5—38no—
373C2×C22⋊D5—34no—
374C2×C22⋊D5—34no—
375C2×C22⋊D5—34no—
376C2×C22⋊D5—34no—
377C2×C22⋊D5—64no—
378C2×C22⋊D5—64no—
379C2×C22⋊D5—122no—
380C22×Dic5—31no—
381C22×Dic5—31no—
382C22×Dic5—34no—
383C22×Dic5—122no—
384C22×Dic5C22×D311yescharacteristic
385C22×Dic5C22×D311yescharacteristic
386D4×D5—632no—
387#709—632no—
388C2×D20—34no—
389C2×D20—34no—
390C2×D20—34no—
391C2×D20—34no—
392C2×D20—64no—
393C2×D20—64no—
394C2×D20—64no—
395C2×D20—122no—
396C2×C4×D5—24no—
397C2×C4×D5—34no—
398C2×C4×D5—34no—
399C2×C4×D5—42no—
400C2×C4×D5—64no—
401C2×C4×D5—64no—
402C2×C4×D5C22×D314yescomplemented
403C2×C4×D5C22×D314yescomplemented
404C2×Dic10—34no—
405C2×Dic10—64no—
406C5×C4⋊C4—34no—
407C5×C4⋊C4—34no—
408C5×C22⋊C4—34no—
409C5×C22⋊C4—34no—
410C5×C22⋊C4C22×D314yescomplemented
411C22⋊Dic5C22×D314yescomplemented
412#685—34no—
413#685—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685—34no—
418#685C22×D314yes—
419#685C22×D314yes—
420#683—34no—
421#683—34no—
422C4×Dic5—34no—
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—151no—
427C2×#123—31no—
428C2×#123—151no—
429C2×C22⋊Q8—151no—
430C2×#121—151no—
431C2×#121—151no—
432C2×#121—151no—
433C2×#120—151no—
434C2×#120—151no—
435C2×C4×D4—151no—
436C2×C4×D4—151no—
437C22×C22⋊C4—51no—
438C22×C22⋊C4—151no—
439C22×C3×C5—22no—
440C22×C3×C5—22no—
441C22×C3×C5—22no—
442C22×C3×C5—44no—
443C22×C3×C5C22×D412yes—
444C22×C3×C5C2×#4112yes—
445C22×C3×C5H(5,𝔽2)12yes—
446C22×C3×C5C2511yescharacteristic
447C2×D15—22no—
448C2×D15—22no—
449C2×D15—22no—
450C2×D15—22no—
451C2×D15—22no—
452C2×D15—22no—
453C2×D15—44no—
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—
470C3×C4×C5—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
485C23×D3—51no—
486C23×D3—51no—
487C23×D3—54no—
488C23×D3—104no—
489C23×D3—104no—
490C23×D3—202no—
491C23×D3C22×D511yescharacteristic
492C22×C3×C4—51no—
493C22×C3×C4—51no—
494C22×C3×C4—54no—
495C22×C3×C4—54no—
496C22×C3×C4—104no—
497C22×C3×C4—202no—
498C22×C3×C4C22×D511yescharacteristic
499C22×C3×C4C22×D511yescharacteristic
500C2×#67—24no—
501C2×#67—58no—
502C2×#67—54no—
503C2×#67—54no—
504C2×#67—54no—
505C2×#67—54no—
506C2×#67—54no—
507C2×#67—54no—
508C2×#67—104no—
509C2×#67—104no—
510C2×#67—104no—
511C2×#67—104no—
512C2×#67—1032no—
513C2×#67—202no—
514C2×#67C22×D514yes—
515C22×Dic3—51no—
516C22×Dic3—51no—
517C22×Dic3—54no—
518C22×Dic3—104no—
519C22×Dic3C22×D511yescharacteristic
520C22×Dic3C22×D511yescharacteristic
521C22×Dic3C22×D511yescharacteristic
522#235—1032no—
523C2×D12—54no—
524C2×D12—54no—
525C2×D12—104no—
526C2×D12—202no—
527C2×C4×D3—24no—
528C2×C4×D3—54no—
529C2×C4×D3—54no—
530C2×C4×D3—104no—
531C2×C4×D3—202no—
532C2×C4×D3C22×D514yescomplemented
533C2×Dic6—54no—
534C2×Dic6—104no—
535C3×C22⋊C4—54no—
536C3×C22⋊C4—54no—
537C3×C22⋊C4—54no—
538C3×C22⋊C4C22×D514yescomplemented
539#217—54no—
540#217—54no—
541#217C22×D514yescomplemented
542(C2×D3)⋊C4—54no—
543(C2×D3)⋊C4—54no—
544(C2×D3)⋊C4—54no—
545(C2×D3)⋊C4—54no—
546(C2×D3)⋊C4C22×D514yescomplemented
547C4⋊Dic3C22×D514yescomplemented
548Dic3⋊C4—54no—
549Dic3⋊C4—54no—
550Dic3⋊C4C22×D514yescomplemented
551C4×Dic3—54no—
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—34no—
556C23×C5—32no—
557C23×C5—62no—
558C23×C5—62no—
559C23×C5C23×D312yes—
560C23×C5C23×D311yescharacteristic
561C22×D5—22no—
562C22×D5—22no—
563C22×D5—22no—
564C22×D5—22no—
565C22×D5—28no—
566C22×D5—28no—
567C22×D5—32no—
568C22×D5—32no—
569C22×D5—44no—
570C22×D5—416no—
571C22×D5—68no—
572C22×D5—62no—
573C22×D5—62no—
574C22×D5—62no—
575C22×D5—62no—
576C22×D5—62no—
577C22×D5—62no—
578C22×D5—68no—
579C22×D5—124no—
580C22×D5—1216no—
581C22×D5#23514yescomplemented
582C22×D5D3×D414yes—
583C22×D5C23×D312yes—
584C22×D5C23×D312yes—
585C5×D4—68no—
586C2×C4×C5—22no—
587C2×C4×C5—22no—
588C2×C4×C5—32no—
589C2×C4×C5—32no—
590C2×C4×C5—32no—
591C2×C4×C5—68no—
592C2×C4×C5—62no—
593C2×C4×C5—62no—
594C2×C4×C5—62no—
595C2×C4×C5C23×D312yes—
596C2×C4×C5C23×D312yes—
597C22⋊D5—316no—
598C22⋊D5—68no—
599C22⋊D5—68no—
600C22⋊D5—124no—
601C2×Dic5—22no—
602C2×Dic5—22no—
603C2×Dic5—34no—
604C2×Dic5—32no—
605C2×Dic5—32no—
606C2×Dic5—62no—
607C2×Dic5—124no—
608C2×Dic5C23×D312yes—
609C2×Dic5C23×D312yes—
610D20—68no—
611D20—68no—
612D20—68no—
613D20—124no—
614C4×D5—28no—
615C4×D5—44no—
616C4×D5—68no—
617C4×D5—68no—
618Dic10—68no—
619C25—51no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—151no—
624C22×D4—31no—
625C22×D4—151no—
626C22×D4—151no—
627C22×D4—151no—
628C22×D4—151no—
629C22×D4—158no—
630C22×D4—151no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—151no—
634C22×D4—308no—
635C23×C4—31no—
636C23×C4—51no—
637C23×C4—51no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4—151no—
641#124—158no—
642#123—38no—
643#123—158no—
644C22⋊Q8—158no—
645#121—158no—
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—31no—
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—58no—
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⋊C4D3×D511yescharacteristic, complemented
670C2×C42—151no—
671C2×C3×C5—42no—
672C2×C3×C5#54614yescomplemented
673C2×C3×C5C23×D411yescharacteristic
674C2×C3×C5C22×#4111yescharacteristic
675C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
676D15—42no—
677D15—42no—
678C3×D5—24no—
679C3×D5—24no—
680C5×D3—24no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—54no—
685C23×C3—54no—
686C23×C3—52no—
687C23×C3—52no—
688C23×C3—108no—
689C23×C3—108no—
690C23×C3—102no—
691C23×C3—102no—
692C23×C3—102no—
693C23×C3—102no—
694C23×C3—204no—
695C23×C3—2016no—
696C23×C3C23×D512yes—
697C23×C3C23×D511yescharacteristic
698C22×D3—22no—
699C22×D3—22no—
700C22×D3—52no—
701C22×D3—52no—
702C22×D3—108no—
703C22×D3—102no—
704C22×D3—102no—
705C22×D3—102no—
706C22×D3—102no—
707C22×D3—102no—
708C22×D3—102no—
709C22×D3—108no—
710C22×D3—204no—
711C22×D3—2016no—
712C22×D3D4×D514yes—
713C22×D3C23×D512yes—
714C2×C3×C4—22no—
715C2×C3×C4—22no—
716C2×C3×C4—52no—
717C2×C3×C4—52no—
718C2×C3×C4—108no—
719C2×C3×C4—102no—
720C2×C3×C4—102no—
721C2×C3×C4—204no—
722C2×C3×C4C23×D512yes—
723C2×C3×C4C23×D512yes—
724#67—28no—
725#67—516no—
726#67—108no—
727#67—108no—
728#67—108no—
729#67—108no—
730#67—204no—
731C2×Dic3—22no—
732C2×Dic3—22no—
733C2×Dic3—22no—
734C2×Dic3—54no—
735C2×Dic3—52no—
736C2×Dic3—52no—
737C2×Dic3—108no—
738C2×Dic3—102no—
739C2×Dic3C23×D512yes—
740C2×Dic3C23×D512yes—
741C2×Dic3C23×D512yes—
742D12—108no—
743D12—204no—
744C4×D3—28no—
745C4×D3—108no—
746C4×D3—204no—
747Dic6—108no—
748C22×C5—22no—
749C22×C5—22no—
750C22×C5—22no—
751C22×C5—34no—
752C22×C5—44no—
753C22×C5—62no—
754C22×C5—62no—
755C22×C5—68no—
756C22×C5C2×#23512yes—
757C22×C5C2×D3×D412yes—
758C22×C5#100412yes—
759C22×C5C24×D311yescharacteristic
760C2×D5—22no—
761C2×D5—22no—
762C2×D5—22no—
763C2×D5—22no—
764C2×D5—28no—
765C2×D5—28no—
766C2×D5—416no—
767C2×D5—62no—
768C2×D5—62no—
769C2×D5—62no—
770C2×D5—62no—
771C2×D5—62no—
772C2×D5—62no—
773C2×D5—1216no—
774C2×D5—124no—
775C2×D5—124no—
776C2×D5C2×#23514yescomplemented
777C2×D5C2×D3×D414yes—
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—62no—
781C4×C5—62no—
782C4×C5—62no—
783Dic5—22no—
784Dic5—22no—
785Dic5—34no—
786Dic5—62no—
787C24—31no—
788C24—51no—
789C24—51no—
790C24—54no—
791C24—104no—
792C24—104no—
793C24—154no—
794C24—151no—
795C24—151no—
796C24—202no—
797C24—304no—
798C24—304no—
799C24—602no—
800C24C2×D3×D511yescharacteristic
801#41—3032no—
802C2×Q8—154no—
803C2×Q8—304no—
804C2×D4—34no—
805C2×D4—64no—
806C2×D4—154no—
807C2×D4—154no—
808C2×D4—154no—
809C2×D4—154no—
810C2×D4—154no—
811C2×D4—158no—
812C2×D4—154no—
813C2×D4—154no—
814C2×D4—154no—
815C2×D4—304no—
816C2×D4—304no—
817C2×D4—304no—
818C2×D4—304no—
819C2×D4—304no—
820C2×D4—3032no—
821C2×D4—602no—
822C2×D4—602no—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—31no—
826C22×C4—34no—
827C22×C4—51no—
828C22×C4—51no—
829C22×C4—54no—
830C22×C4—54no—
831C22×C4—64no—
832C22×C4—104no—
833C22×C4—154no—
834C22×C4—154no—
835C22×C4—151no—
836C22×C4—151no—
837C22×C4—154no—
838C22×C4—202no—
839C22×C4—304no—
840C22×C4—304no—
841C22×C4—602no—
842C22×C4C2×D3×D511yescharacteristic
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—34no—
845C4⋊C4—34no—
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⋊C4C2×D3×D514yescomplemented
860C42—154no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—22no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—44no—
866C22×C3—54no—
867C22×C3—54no—
868C22×C3—108no—
869C22×C3—108no—
870C22×C3—102no—
871C22×C3—102no—
872C22×C3—102no—
873C22×C3—102no—
874C22×C3—2016no—
875C22×C3C2×D4×D512yes—
876C22×C3D5×#4112yes—
877C22×C3#414912yes—
878C22×C3C24×D511yescharacteristic
879C2×D3—28no—
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—102no—
883C2×D3—102no—
884C2×D3—102no—
885C2×D3—102no—
886C2×D3—102no—
887C2×D3—102no—
888C2×D3—2016no—
889C2×D3—204no—
890C2×D3—204no—
891C2×D3C2×D4×D514yes—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—102no—
895C3×C4—102no—
896Dic3—22no—
897Dic3—22no—
898Dic3—22no—
899Dic3—54no—
900Dic3—102no—
901C2×C5—42no—
902C2×C5—64no—
903C2×C5#549014yescomplemented
904C2×C5C22×#23511yescharacteristic
905C2×C5C22×D3×D411yescharacteristic
906C2×C5C2×#100411yescharacteristic
907D5—24no—
908D5—24no—
909D5—122no—
910D5—122no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—34no—
915C23—32no—
916C23—54no—
917C23—54no—
918C23—52no—
919C23—52no—
920C23—62no—
921C23—62no—
922C23—108no—
923C23—108no—
924C23—102no—
925C23—102no—
926C23—102no—
927C23—102no—
928C23—152no—
929C23—152no—
930C23—204no—
931C23—2016no—
932C23—308no—
933C23—308no—
934C23—302no—
935C23—302no—
936C23—302no—
937C23—302no—
938C23—302no—
939C23—302no—
940C23—604no—
941C23—6016no—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—308no—
945D4—68no—
946D4—1516no—
947D4—308no—
948D4—308no—
949D4—308no—
950D4—308no—
951D4—308no—
952D4—604no—
953D4—604no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—32no—
957C2×C4—32no—
958C2×C4—32no—
959C2×C4—52no—
960C2×C4—52no—
961C2×C4—68no—
962C2×C4—62no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—108no—
966C2×C4—102no—
967C2×C4—102no—
968C2×C4—154no—
969C2×C4—152no—
970C2×C4—152no—
971C2×C4—204no—
972C2×C4—308no—
973C2×C4—308no—
974C2×C4—302no—
975C2×C4—604no—
976C2×C4C22×D3×D512yes—
977C2×C4C22×D3×D512yes—
978C2×C3—42no—
979C2×C3—104no—
980C2×C3—104no—
981C2×C3#6598814yescomplemented
982C2×C3C22×D4×D511yescharacteristic
983C2×C3C2×D5×#4111yescharacteristic
984C2×C3C2×#414911yescharacteristic
985D3—24no—
986D3—202no—
987D3—202no—
988C5C2×#549011yescharacteristic, complemented, Sylow
989C22—22no—
990C22—22no—
991C22—22no—
992C22—34no—
993C22—44no—
994C22—54no—
995C22—54no—
996C22—68no—
997C22—62no—
998C22—62no—
999C22—108no—
1000C22—108no—
1001C22—102no—
1002C22—102no—
1003C22—102no—
1004C22—102no—
1005C22—2016no—
1006C22—302no—
1007C22—302no—
1008C22—302no—
1009C22—302no—
1010C22—302no—
1011C22—302no—
1012C22—6016no—
1013C22—604no—
1014C22—604no—
1015C22D5×#23512yes—
1016C22D3×D4×D512yes—
1017C22#9202612yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—62no—
1022C4—62no—
1023C4—62no—
1024C4—102no—
1025C4—102no—
1026C4—154no—
1027C4—302no—
1028C3C2×#6598811yescharacteristic, complemented, Sylow
1029C2—42no—
1030C2—64no—
1031C2—104no—
1032C2—104no—
1033C2—602no—
1034C2—602no—
1035C2#1175322614yesdirect product factor
1036C2C2×D5×#23511yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×#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×#546
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. C22×D5×#67C2semidirect
2. C22×#6771C2semidirect
3. C2×#91773C2semidirect
4. C2×C5×#883C2semidirect
5. C2×C3×D5×C22⋊C4C2semidirect
6. C2×#91564C2semidirect
7. C2×#91558C2semidirect
8. C2×#91526C2semidirect
9. C2×#91476C2semidirect
10. C2×D3×#685C2semidirect
11. C2×#91450C2semidirect
12. C2×#91440C2semidirect
13. C2×#91430C2semidirect
14. C2×#91396C2semidirect
15. C2×#91348C2semidirect
16. #11753226C2direct (N × H)
21. C22×#1220C22semidirect
22. C22×D60C22semidirect
23. C22×C4×D15C22semidirect
25. C22×C4×C5×D3C22semidirect
26. C22×C3×C4×D5C22semidirect
27. C22×C3×C4×D5C22semidirect
29. C2×D5×#67C22semidirect
30. C22×#1204C22semidirect
31. C22×#1203C22semidirect
34. C22×#1202C22semidirect
36. C22×D3×Dic5C22semidirect
39. C2×#6771C22semidirect
40. C2×C3×C5×C22⋊C4C22semidirect
41. C2×#6714C22semidirect
42. C2×#6712C22semidirect
43. #91773C22semidirect
44. C2×C5×#217C22semidirect
45. C2×C5×(C2×D3)⋊C4C22semidirect
46. C2×C5×C4⋊Dic3C22semidirect
47. C2×C5×Dic3⋊C4C22semidirect
48. C5×#883C22semidirect
49. C2×C3×C22⋊Dic5C22semidirect
52. C3×D5×C22⋊C4C22semidirect
53. #91564C22semidirect
54. #91558C22semidirect
55. C2×#6669C22semidirect
56. C2×#6667C22semidirect
57. C2×#6667C22semidirect
58. C2×#6667C22semidirect
60. C2×#6665C22semidirect
61. C2×Dic3×Dic5C22semidirect
62. #91526C22semidirect
63. #91476C22semidirect
64. D3×#685C22semidirect
65. #91450C22semidirect
66. #91440C22semidirect
67. #91430C22semidirect
68. #91396C22semidirect
69. #91348C22semidirect
86. C2×D5×C22⋊C4D3semidirect
106. C2×#1220C23semidirect
110. C2×D60C23semidirect
112. C2×C4×D15C23semidirect
119. C2×C4×C5×D3C23semidirect
124. C2×C3×C4×D5C23semidirect
125. C2×C3×C4×D5C23semidirect
128. C2×#1204C23semidirect
130. C2×#1203C23semidirect
136. C2×#1202C23semidirect
137. C2×#1201D4semidirect
140. C2×D3×Dic5C23semidirect
144. C3×C5×C22⋊C4C23semidirect
145. #6714C23semidirect
146. #6712C23semidirect
147. C5×#217C23semidirect
148. C5×(C2×D3)⋊C4C23semidirect
149. C5×C4⋊Dic3C23semidirect
150. C5×Dic3⋊C4C23semidirect
151. C3×C22⋊Dic5C23semidirect
154. #6669C23semidirect
155. #6667C23semidirect
156. #6667C23semidirect
157. #6667C23semidirect
159. #6665C23semidirect
160. Dic3×Dic5C23semidirect
172. C2×#883D5semidirect
196. C22×C4×D5C2×D3semidirect
197. C22×C4×D5C2×D3semidirect
204. C2×C5×C22⋊C4C2×D3semidirect
205. C2×C22⋊Dic5C2×D3semidirect
228. D5×C22⋊C4C2×D3semidirect
256. C22×C3×D5#41semidirect
294. #1201C2×D4semidirect
317. C22×C4×D3C2×D5semidirect
323. C2×C3×C22⋊C4C2×D5semidirect
327. C2×#217C2×D5semidirect
335. C2×(C2×D3)⋊C4C2×D5semidirect
336. C2×C4⋊Dic3C2×D5semidirect
339. C2×Dic3⋊C4C2×D5semidirect
344. #883C2×D5semidirect
402. C2×C4×D5C22×D3semidirect
403. C2×C4×D5C22×D3semidirect
410. C5×C22⋊C4C22×D3semidirect
411. C22⋊Dic5C22×D3semidirect
467. C2×C3×D5C2×#41semidirect
532. C2×C4×D3C22×D5semidirect
538. C3×C22⋊C4C22×D5semidirect
541. #217C22×D5semidirect
546. (C2×D3)⋊C4C22×D5semidirect
547. C4⋊Dic3C22×D5semidirect
550. Dic3⋊C4C22×D5semidirect
581. C22×D5#235semidirect
669. C2×C22⋊C4D3×D5semidirect
672. C2×C3×C5#546semidirect
776. C2×D5C2×#235semidirect
859. C22⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
903. C2×C5#5490semidirect
981. C2×C3#65988semidirect
988. C5C2×#5490semidirect
1028. C3C2×#65988semidirect
1035. C2#11753226direct (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×#67712
C2×#917732
C2×C5×#8832
C2×C3×D5×C22⋊C42
C2×#915642
C2×#915582
C2×#915262
C2×#914762
C2×D3×#6852
C2×#914502
C2×#914402
C2×#914302
C2×#913962
C2×#913482
#117532262
C2×#659883
C2×#54905