Finite Group Databasebeta

← C2×#11753240 #14482600

Subgroups — C2×#11753240 #14482600

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×#6790C211yesmaximal, characteristic, complemented
2C22×#6773C211yesmaximal, characteristic, complemented
3C2×#91771C211yesmaximal, characteristic, complemented
4C2×C5×#885C211yesmaximal, characteristic, complemented
5C2×C3×#4029C211yesmaximal, characteristic, complemented
6C2×#91561C211yesmaximal, characteristic, complemented
7C2×#91557C211yesmaximal, characteristic, complemented
8C2×#91550C211yesmaximal, characteristic, complemented
9C2×#91476C211yesmaximal, characteristic, complemented
10C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#91438C211yesmaximal, characteristic, complemented
12C2×#91428C211yesmaximal, characteristic, complemented
13C2×#91424C211yesmaximal, characteristic, complemented
14C2×#91420C211yesmaximal, characteristic, complemented
15C2×#91395C211yesmaximal, characteristic, complemented
16#11753240C2116yesmaximal, direct product factor
17C2×#66010—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×#1220C2211yescharacteristic, complemented
21C22×D60C2211yescharacteristic
22C22×D60C2211yescharacteristic, complemented
23C22×C5×#67C2211yescharacteristic
24C22×C5×Dic6C2211yescharacteristic, complemented
25C22×C3×C22⋊D5C2211yescharacteristic
26C22×C3×C4×D5C2211yescharacteristic, complemented
27C2×#6790—28no—
28C2×#6790C2218yescomplemented
29C22×#1203C2211yescharacteristic
30C22×#1203C2211yescharacteristic, complemented
31C22×#1202C2211yescharacteristic
32C22×#1202C2211yescharacteristic, complemented
33C22×#1200C2211yescharacteristic
34C22×#1200C2211yescharacteristic, complemented
35C22×#1200C2211yescharacteristic, complemented
36C22×#1200C2211yescharacteristic, complemented
37C22×D5×Dic3C2211yescharacteristic, complemented
38C2×#6773—28no—
39C2×#6773C2218yescomplemented
40C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
41C2×#6714C2211yescharacteristic
42C2×#6714C2211yescharacteristic, complemented
43#91771C2218yescomplemented
44C2×C5×#217C2211yescharacteristic, complemented
45C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×C4×C5×Dic3C2211yescharacteristic, complemented
48C5×#885C2218yescomplemented
49C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
50C2×C3×#685C2211yescharacteristic, complemented
51C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
52C2×C3×#683C2211yescharacteristic, complemented
53C3×#4029C2218yescomplemented
54#91561C2218yescomplemented
55#91557C2218yescomplemented
56#91550C2218yescomplemented
57C2×Dic3⋊Dic5C2211yescharacteristic, complemented
58C2×#6669C2211yescharacteristic, complemented
59C2×#6667C2211yescharacteristic
60C2×#6667C2211yescharacteristic
61C2×#6667C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
63#91476C2218yescomplemented
64D5×(C2×D3)⋊C4C2218yescomplemented
65#91438C2218yescomplemented
66#91428C2218yescomplemented
67#91424C2218yescomplemented
68#91420C2218yescomplemented
69#91395C2218yescomplemented
70C2×#5654—51nomaximal, Hall
71C22×#713—31no—
72C22×D4×D5—31no—
73C2×C5×#124—31no—
74C2×#4092—31no—
75C2×#4084—31no—
76#66010—316no—
77C2×#4030—31no—
78C2×#4030—31no—
79C2×#4029—31no—
80C2×#4029D311yescharacteristic, complemented
81C2×#4028—31no—
82C2×#4028—31no—
83C2×D5×C22⋊C4—31no—
84C2×D5×C22⋊C4—31no—
85C2×C4×D20—31no—
86C2×C4×D20—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15—24no—
89C23×D15—24no—
90C23×D15—42no—
91C23×D15C2311yescharacteristic
92C23×D15C2314yes—
93C23×D15C2311yescharacteristic
94C23×D15C2311yescharacteristic
95C23×C5×D3C2311yescharacteristic
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—42no—
104C2×#1220C2314yescomplemented
105C22×Dic15C2311yescharacteristic
106C2×D60—24no—
107C2×D60—24no—
108C2×D60C2314yes—
109C2×D60C2314yescomplemented
110C2×C5×#67—24no—
111C2×C5×#67C2314yes—
112C22×C5×Dic3C2311yescharacteristic
113C22×C5×Dic3C2311yescharacteristic
114C22×C5×Dic3C2311yescharacteristic
115C2×C5×Dic6—24no—
116C2×C5×Dic6C2314yescomplemented
117C2×C3×C22⋊D5—24no—
118C2×C3×C22⋊D5C2314yes—
119C22×C3×Dic5C2311yescharacteristic
120C22×C3×Dic5C2311yescharacteristic
121C22×C3×Dic5C2311yescharacteristic
122C2×C3×C4×D5—24no—
123C2×C3×C4×D5C2314yescomplemented
124#6790—232no—
125C2×#1203—24no—
126C2×#1203—42no—
127C2×#1203C2314yes—
128C2×#1203C2314yescomplemented
129C2×#1202—24no—
130C2×#1202D418yescomplemented
131C2×#1202C2314yes—
132C2×#1202C2314yescomplemented
133C2×#1200—24no—
134C2×#1200—24no—
135C2×#1200—24no—
136C2×#1200—42no—
137C2×#1200C2314yes—
138C2×#1200C2314yescomplemented
139C2×#1200C2314yescomplemented
140C2×#1200C2314yescomplemented
141C2×D5×Dic3—42no—
142C2×D5×Dic3C2314yescomplemented
143#6773—232no—
144C3×C5×C22⋊C4C2314yescomplemented
145#6714C2314yes—
146#6714C2314yescomplemented
147C5×#217C2314yescomplemented
148C5×(C2×D3)⋊C4C2314yescomplemented
149C5×(C2×D3)⋊C4C2314yescomplemented
150C4×C5×Dic3C2314yescomplemented
151C3×C22⋊Dic5C2314yescomplemented
152C3×#685C2314yescomplemented
153C3×C4⋊Dic5C2314yescomplemented
154C3×#683C2314yescomplemented
155Dic3⋊Dic5C2314yescomplemented
156#6669C2314yescomplemented
157#6667C2314yes—
158#6667C2314yes—
159#6667C2314yescomplemented
160(C2×D3)⋊Dic5C2314yescomplemented
161C22×D3×D4—51no—
162C22×#235—51no—
163C2×C3×#123—51no—
164C2×#939—51no—
165C22×(C2×D3)⋊C4—51no—
166#5654—516no—
167C2×#896—51no—
168C2×#895—51no—
169C2×#894—51no—
170C2×#893—51no—
171C2×#885D511yescharacteristic, complemented
172C2×#884—51no—
173C2×#882—51no—
174C2×#882—51no—
175C2×#67⋊C4—51no—
176C2×D3×C22⋊C4—51no—
177C24×D5—31no—
178C24×D5—31no—
179C22×C5×Q8—31no—
180C22×C5×D4—31no—
181C22×C22⋊D5—31no—
182C22×C22⋊D5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5C2×D311yescharacteristic
185C2×#713—38no—
186C2×#713—68no—
187C2×D4×D5—38no—
188C2×D4×D5—68no—
189C22×D20—31no—
190C22×D20—31no—
191C22×D20—31no—
192C22×D20—31no—
193C22×C4×D5—31no—
194C22×C4×D5—31no—
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5—31no—
198C22×C4×D5C2×D311yescharacteristic, complemented
199C5×#124—38no—
200C2×C5×C22⋊C4—31no—
201C2×C5×C22⋊C4—31no—
202C2×C5×C22⋊C4—31no—
203C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
204C2×C42×C5—31no—
205C2×C22⋊Dic5—31no—
206C2×C22⋊Dic5C2×D311yescharacteristic, complemented
207#4092—38no—
208#4084—38no—
209C2×#685—31no—
210C2×#685—31no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685C2×D311yescharacteristic, complemented
215C2×C4⋊Dic5—31no—
216C2×C4⋊Dic5C2×D311yescharacteristic, complemented
217C2×#683—31no—
218C2×#683C2×D311yescharacteristic, complemented
219#4030—38no—
220#4030—38no—
221#4029—38no—
222#4029C2×D318yescomplemented
223#4028—38no—
224#4028—38no—
225D5×C22⋊C4—38no—
226D5×C22⋊C4—38no—
227C4×D20—38no—
228C4×D20—38no—
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×D15—22no—
242C22×D15—28no—
243C22×D15—28no—
244C22×D15—44no—
245C22×D15—416no—
246C22×D15C2×D414yes—
247C22×D15#4114yescomplemented
248C22×D15C2412yes—
249C22×D15C2412yes—
250C22×D15C2412yes—
251C22×C5×D3—22no—
252C22×C5×D3—22no—
253C22×C5×D3—22no—
254C22×C5×D3C2412yes—
255C22×C3×D5—22no—
256C22×C3×D5—22no—
257C22×C3×D5C2×D414yes—
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—44no—
268C2×Dic15—22no—
269C2×Dic15C2412yes—
270D60—28no—
271D60—28no—
272C5×#67—28no—
273C2×C5×Dic3—22no—
274C2×C5×Dic3—22no—
275C2×C5×Dic3C2×D414yes—
276C2×C5×Dic3C2412yes—
277C2×C5×Dic3C2412yes—
278C2×C5×Dic3C2412yes—
279C5×Dic6—28no—
280C3×C22⋊D5—28no—
281C2×C3×Dic5—22no—
282C2×C3×Dic5—22no—
283C2×C3×Dic5—22no—
284C2×C3×Dic5C2412yes—
285C2×C3×Dic5C2412yes—
286C2×C3×Dic5C2412yes—
287C3×C4×D5—28no—
288#1203—28no—
289#1203—44no—
290#1202—28no—
291#1202C2×D4116yescomplemented
292#1200—28no—
293#1200—28no—
294#1200—28no—
295#1200—44no—
296D5×Dic3—44no—
297C24×D3—51no—
298C24×D3—51no—
299C22×C3×D4—51no—
300C23×C3×C4—51no—
301C22×#67—51no—
302C22×#67—51no—
303C22×#67—51no—
304C22×#67C2×D511yescharacteristic
305C23×Dic3—51no—
306C2×D3×D4—58no—
307C2×D3×D4—108no—
308C2×#235—58no—
309C2×#235—108no—
310C22×D12—51no—
311C22×D12—51no—
312C22×D12—51no—
313C22×D12—51no—
314C22×C4×D3—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3—51no—
318C22×Dic6C2×D511yescharacteristic, complemented
319C3×#123—58no—
320C2×C3×C4⋊C4—51no—
321C2×C3×C4⋊C4—51no—
322C2×C3×C22⋊C4—51no—
323C2×C3×C22⋊C4—51no—
324C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
325C2×#217C2×D511yescharacteristic, complemented
326#939—58no—
327C2×(C2×D3)⋊C4—51no—
328C2×(C2×D3)⋊C4—51no—
329C2×(C2×D3)⋊C4—51no—
330C2×(C2×D3)⋊C4—51no—
331C2×(C2×D3)⋊C4—51no—
332C2×(C2×D3)⋊C4—51no—
333C2×(C2×D3)⋊C4—58no—
334C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
335C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
336C2×Dic3⋊C4—51no—
337C2×Dic3⋊C4—51no—
338C2×C4×Dic3C2×D511yescharacteristic, complemented
339#896—58no—
340#895—58no—
341#894—58no—
342#893—58no—
343#885C2×D518yescomplemented
344#884—58no—
345#882—58no—
346#882—58no—
347#67⋊C4—58no—
348D3×C22⋊C4—58no—
349C24×C5—31no—
350C24×C5C22×D311yescharacteristic
351C23×D5—31no—
352C23×D5—31no—
353C23×D5—31no—
354C23×D5—34no—
355C23×D5—34no—
356C23×D5—64no—
357C23×D5—64no—
358C23×D5—64no—
359C23×D5—64no—
360C23×D5—122no—
361C23×D5—122no—
362C23×D5C22×D311yescharacteristic
363C2×C5×Q8—34no—
364C2×C5×Q8—64no—
365C2×C5×D4—34no—
366C2×C5×D4—64no—
367C22×C4×C5—31no—
368C22×C4×C5—31no—
369C22×C4×C5—31no—
370C22×C4×C5C22×D311yescharacteristic
371C22×C4×C5C22×D311yescharacteristic
372C2×C22⋊D5—24no—
373C2×C22⋊D5—34no—
374C2×C22⋊D5—34no—
375C2×C22⋊D5—34no—
376C2×C22⋊D5—64no—
377C2×C22⋊D5—122no—
378C2×C22⋊D5—122no—
379C2×C22⋊D5C22×D314yes—
380C22×Dic5—31no—
381C22×Dic5C22×D311yescharacteristic
382C22×Dic5C22×D311yescharacteristic
383C22×Dic5C22×D311yescharacteristic
384#713—632no—
385D4×D5—632no—
386C2×D20—38no—
387C2×D20—34no—
388C2×D20—34no—
389C2×D20—34no—
390C2×D20—34no—
391C2×D20—64no—
392C2×D20—64no—
393C2×D20—64no—
394C2×C4×D5—24no—
395C2×C4×D5—34no—
396C2×C4×D5—34no—
397C2×C4×D5—34no—
398C2×C4×D5—34no—
399C2×C4×D5—34no—
400C2×C4×D5—64no—
401C2×C4×D5—64no—
402C2×C4×D5—64no—
403C2×C4×D5—122no—
404C2×C4×D5—122no—
405C2×C4×D5C22×D314yescomplemented
406C5×C22⋊C4—34no—
407C5×C22⋊C4—34no—
408C5×C22⋊C4—34no—
409C5×C22⋊C4C22×D314yescomplemented
410C42×C5—34no—
411C22⋊Dic5—34no—
412C22⋊Dic5C22×D314yescomplemented
413#685—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685—34no—
418#685C22×D314yescomplemented
419C4⋊Dic5—34no—
420C4⋊Dic5C22×D314yescomplemented
421#683—34no—
422#683C22×D314yescomplemented
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—31no—
427C2×#123—51no—
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—151no—
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—28no—
448C2×D15—28no—
449C2×D15—22no—
450C2×D15—22no—
451C2×D15—22no—
452C2×D15—22no—
453C2×D15—22no—
454C2×D15—22no—
455C2×D15—22no—
456C2×D15—416no—
457C2×D15—44no—
458C2×D15C22×D414yes—
459C2×D15C2×#4114yescomplemented
460C2×C5×D3—22no—
461C2×C5×D3—22no—
462C2×C5×D3—22no—
463C2×C5×D3—44no—
464C2×C3×D5—28no—
465C2×C3×D5—22no—
466C2×C3×D5—22no—
467C2×C3×D5C22×D414yes—
468D3×D5—416no—
469C3×C4×C5—22no—
470C3×C4×C5—22no—
471Dic15—22no—
472C3×Dic5—22no—
473C3×Dic5—22no—
474C3×Dic5—22no—
475C5×Dic3—22no—
476C5×Dic3—22no—
477C5×Dic3C22×D414yes—
478C24×C3—51no—
479C24×C3C22×D511yescharacteristic
480C23×D3—51no—
481C23×D3—51no—
482C23×D3—51no—
483C23×D3—54no—
484C23×D3—54no—
485C23×D3—104no—
486C23×D3—104no—
487C23×D3—104no—
488C23×D3—104no—
489C23×D3—202no—
490C23×D3—202no—
491C23×D3C22×D511yescharacteristic
492C2×C3×D4—54no—
493C2×C3×D4—104no—
494C22×C3×C4—51no—
495C22×C3×C4—51no—
496C22×C3×C4—51no—
497C22×C3×C4—54no—
498C22×C3×C4—104no—
499C22×C3×C4C22×D511yescharacteristic
500C22×C3×C4C22×D511yescharacteristic
501C2×#67—24no—
502C2×#67—54no—
503C2×#67—58no—
504C2×#67—54no—
505C2×#67—54no—
506C2×#67—104no—
507C2×#67—202no—
508C2×#67C22×D514yes—
509C22×Dic3—51no—
510C22×Dic3—54no—
511C22×Dic3—202no—
512C22×Dic3C22×D511yescharacteristic
513C22×Dic3C22×D511yescharacteristic
514C22×Dic3C22×D511yescharacteristic
515D3×D4—1032no—
516#235—1032no—
517C2×D12—54no—
518C2×D12—54no—
519C2×D12—54no—
520C2×D12—54no—
521C2×D12—104no—
522C2×D12—104no—
523C2×D12—104no—
524C2×D12—202no—
525C2×C4×D3—54no—
526C2×C4×D3—54no—
527C2×C4×D3—54no—
528C2×C4×D3—54no—
529C2×C4×D3—104no—
530C2×C4×D3—104no—
531C2×C4×D3—104no—
532C2×C4×D3—202no—
533C2×Dic6—24no—
534C2×Dic6C22×D514yescomplemented
535C3×C4⋊C4—54no—
536C3×C4⋊C4—54no—
537C3×C22⋊C4—54no—
538C3×C22⋊C4—54no—
539C3×C22⋊C4C22×D514yescomplemented
540#217C22×D514yescomplemented
541(C2×D3)⋊C4—54no—
542(C2×D3)⋊C4—54no—
543(C2×D3)⋊C4—54no—
544(C2×D3)⋊C4—54no—
545(C2×D3)⋊C4—54no—
546(C2×D3)⋊C4—54no—
547(C2×D3)⋊C4C22×D514yescomplemented
548(C2×D3)⋊C4C22×D514yescomplemented
549Dic3⋊C4—54no—
550Dic3⋊C4—54no—
551C4×Dic3C22×D514yescomplemented
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—32no—
556C23×C5—62no—
557C23×C5—62no—
558C23×C5—62no—
559C23×C5C23×D312yes—
560C23×C5C23×D311yescharacteristic
561C22×D5—22no—
562C22×D5—22no—
563C22×D5—34no—
564C22×D5—34no—
565C22×D5—32no—
566C22×D5—32no—
567C22×D5—32no—
568C22×D5—68no—
569C22×D5—68no—
570C22×D5—68no—
571C22×D5—62no—
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—124no—
582C22×D5—1216no—
583C22×D5D3×D414yes—
584C22×D5C23×D312yes—
585C5×Q8—68no—
586C5×D4—68no—
587C2×C4×C5—22no—
588C2×C4×C5—22no—
589C2×C4×C5—34no—
590C2×C4×C5—32no—
591C2×C4×C5—32no—
592C2×C4×C5—32no—
593C2×C4×C5—62no—
594C2×C4×C5—62no—
595C2×C4×C5C23×D312yes—
596C2×C4×C5C23×D312yes—
597C22⋊D5—28no—
598C22⋊D5—68no—
599C22⋊D5—124no—
600C22⋊D5—124no—
601C2×Dic5—22no—
602C2×Dic5—22no—
603C2×Dic5—22no—
604C2×Dic5—32no—
605C2×Dic5—62no—
606C2×Dic5C23×D312yes—
607C2×Dic5C23×D312yes—
608C2×Dic5C23×D312yes—
609D20—316no—
610D20—68no—
611D20—68no—
612D20—68no—
613C4×D5—28no—
614C4×D5—68no—
615C4×D5—68no—
616C4×D5—68no—
617C4×D5—124no—
618C4×D5—124no—
619C25—151no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—31no—
624C22×D4—31no—
625C22×D4—51no—
626C22×D4—151no—
627C22×D4—151no—
628C22×D4—151no—
629C22×D4—151no—
630C22×D4—158no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—151no—
634C22×D4—308no—
635C23×C4—51no—
636C23×C4—151no—
637C23×C4—151no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4—151no—
641#124—38no—
642#123—58no—
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—51no—
653C2×C4⋊C4—51no—
654C2×C4⋊C4—151no—
655C2×C4⋊C4—151no—
656C2×C22⋊C4—31no—
657C2×C22⋊C4—31no—
658C2×C22⋊C4—31no—
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⋊C4D3×D511yescharacteristic, complemented
670C2×C42—31no—
671C2×C3×C5—42no—
672C2×C3×C5#54614yescomplemented
673C2×C3×C5C23×D411yescharacteristic
674C2×C3×C5C22×#4111yescharacteristic
675C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
676D15—24no—
677D15—24no—
678D15—42no—
679C3×D5—24no—
680C5×D3—42no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—54no—
685C23×C3—52no—
686C23×C3—102no—
687C23×C3—102no—
688C23×C3C23×D512yes—
689C23×C3C23×D511yescharacteristic
690C22×D3—22no—
691C22×D3—22no—
692C22×D3—22no—
693C22×D3—54no—
694C22×D3—54no—
695C22×D3—52no—
696C22×D3—52no—
697C22×D3—52no—
698C22×D3—108no—
699C22×D3—108no—
700C22×D3—108no—
701C22×D3—108no—
702C22×D3—102no—
703C22×D3—102no—
704C22×D3—102no—
705C22×D3—102no—
706C22×D3—102no—
707C22×D3—102no—
708C22×D3—102no—
709C22×D3—204no—
710C22×D3—2016no—
711C22×D3—204no—
712C22×D3—2016no—
713C22×D3C23×D512yes—
714C3×D4—108no—
715C2×C3×C4—22no—
716C2×C3×C4—22no—
717C2×C3×C4—52no—
718C2×C3×C4—52no—
719C2×C3×C4—52no—
720C2×C3×C4—108no—
721C2×C3×C4—102no—
722C2×C3×C4—102no—
723C2×C3×C4—102no—
724C2×C3×C4C23×D512yes—
725C2×C3×C4C23×D512yes—
726#67—28no—
727#67—516no—
728#67—108no—
729#67—204no—
730C2×Dic3—22no—
731C2×Dic3—22no—
732C2×Dic3—52no—
733C2×Dic3—102no—
734C2×Dic3—204no—
735C2×Dic3D4×D514yes—
736C2×Dic3C23×D512yes—
737C2×Dic3C23×D512yes—
738C2×Dic3C23×D512yes—
739D12—108no—
740D12—108no—
741D12—108no—
742D12—204no—
743C4×D3—108no—
744C4×D3—108no—
745C4×D3—108no—
746C4×D3—204no—
747Dic6—28no—
748C22×C5—22no—
749C22×C5—22no—
750C22×C5—22no—
751C22×C5—44no—
752C22×C5—62no—
753C22×C5—62no—
754C22×C5—62no—
755C22×C5—124no—
756C22×C5C2×D3×D412yes—
757C22×C5D3×#4112yes—
758C22×C5#100912yes—
759C22×C5C24×D311yescharacteristic
760C2×D5—28no—
761C2×D5—22no—
762C2×D5—22no—
763C2×D5—34no—
764C2×D5—34no—
765C2×D5—68no—
766C2×D5—68no—
767C2×D5—62no—
768C2×D5—62no—
769C2×D5—62no—
770C2×D5—62no—
771C2×D5—62no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—1216no—
775C2×D5—1216no—
776C2×D5—124no—
777C2×D5C2×D3×D414yes—
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—34no—
781C4×C5—62no—
782C4×C5—62no—
783Dic5—22no—
784Dic5—22no—
785Dic5—22no—
786Dic5—62no—
787C24—31no—
788C24—51no—
789C24—154no—
790C24—151no—
791C24—151no—
792C24—151no—
793C24—154no—
794C24—304no—
795C24—304no—
796C24—304no—
797C24—304no—
798C24—602no—
799C24—602no—
800C24C2×D3×D511yescharacteristic
801#41—3032no—
802C2×Q8—34no—
803C2×Q8—64no—
804C2×D4—34no—
805C2×D4—54no—
806C2×D4—64no—
807C2×D4—104no—
808C2×D4—154no—
809C2×D4—158no—
810C2×D4—154no—
811C2×D4—154no—
812C2×D4—154no—
813C2×D4—154no—
814C2×D4—154no—
815C2×D4—154no—
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—51no—
827C22×C4—51no—
828C22×C4—51no—
829C22×C4—54no—
830C22×C4—104no—
831C22×C4—154no—
832C22×C4—154no—
833C22×C4—154no—
834C22×C4—154no—
835C22×C4—154no—
836C22×C4—151no—
837C22×C4—304no—
838C22×C4—304no—
839C22×C4—304no—
840C22×C4—602no—
841C22×C4—602no—
842C22×C4C2×D3×D511yescharacteristic
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—54no—
845C4⋊C4—54no—
846C4⋊C4—154no—
847C4⋊C4—154no—
848C22⋊C4—34no—
849C22⋊C4—34no—
850C22⋊C4—34no—
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—34no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—22no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—44no—
866C22×C3—54no—
867C22×C3—108no—
868C22×C3—102no—
869C22×C3—102no—
870C22×C3C2×D4×D512yes—
871C22×C3D5×#4112yes—
872C22×C3#414912yes—
873C22×C3C24×D511yescharacteristic
874C2×D3—22no—
875C2×D3—22no—
876C2×D3—22no—
877C2×D3—44no—
878C2×D3—54no—
879C2×D3—54no—
880C2×D3—108no—
881C2×D3—108no—
882C2×D3—102no—
883C2×D3—102no—
884C2×D3—102no—
885C2×D3—102no—
886C2×D3—102no—
887C2×D3—102no—
888C2×D3—102no—
889C2×D3—2016no—
890C2×D3—2016no—
891C2×D3—204no—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—102no—
895C3×C4—102no—
896C3×C4—102no—
897Dic3—22no—
898Dic3—22no—
899Dic3—102no—
900Dic3C2×D4×D514yes—
901C2×C5—42no—
902C2×C5—122no—
903C2×C5#565414yescomplemented
904C2×C5C22×D3×D411yescharacteristic
905C2×C5C2×D3×#4111yescharacteristic
906C2×C5C2×#100911yescharacteristic
907D5—24no—
908D5—64no—
909D5—64no—
910D5—122no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—32no—
915C23—54no—
916C23—52no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—102no—
921C23—102no—
922C23—154no—
923C23—154no—
924C23—152no—
925C23—152no—
926C23—152no—
927C23—308no—
928C23—308no—
929C23—308no—
930C23—308no—
931C23—302no—
932C23—302no—
933C23—302no—
934C23—302no—
935C23—302no—
936C23—302no—
937C23—302no—
938C23—604no—
939C23—6016no—
940C23—604no—
941C23—6016no—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—68no—
945D4—68no—
946D4—108no—
947D4—1516no—
948D4—308no—
949D4—308no—
950D4—308no—
951D4—308no—
952D4—604no—
953D4—604no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—34no—
957C2×C4—32no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—52no—
961C2×C4—52no—
962C2×C4—52no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—108no—
966C2×C4—102no—
967C2×C4—102no—
968C2×C4—102no—
969C2×C4—152no—
970C2×C4—308no—
971C2×C4—308no—
972C2×C4—308no—
973C2×C4—302no—
974C2×C4—604no—
975C2×C4—604no—
976C2×C4C22×D3×D512yes—
977C2×C4C22×D3×D512yes—
978C2×C3—42no—
979C2×C3—104no—
980C2×C3#6601014yescomplemented
981C2×C3C22×D4×D511yescharacteristic
982C2×C3C2×D5×#4111yescharacteristic
983C2×C3C2×#414911yescharacteristic
984D3—42no—
985D3—104no—
986D3—104no—
987D3—202no—
988C5C2×#565411yescharacteristic, complemented, Sylow
989C22—22no—
990C22—22no—
991C22—22no—
992C22—44no—
993C22—54no—
994C22—62no—
995C22—62no—
996C22—62no—
997C22—108no—
998C22—102no—
999C22—102no—
1000C22—124no—
1001C22—154no—
1002C22—154no—
1003C22—308no—
1004C22—308no—
1005C22—302no—
1006C22—302no—
1007C22—302no—
1008C22—302no—
1009C22—302no—
1010C22—302no—
1011C22—302no—
1012C22—6016no—
1013C22—6016no—
1014C22—604no—
1015C22#9201912yes—
1016C22D3×D4×D512yes—
1017C22#9202412yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—34no—
1022C4—62no—
1023C4—62no—
1024C4—102no—
1025C4—102no—
1026C4—102no—
1027C4—302no—
1028C3C2×#6601011yescharacteristic, complemented, Sylow
1029C2—42no—
1030C2—104no—
1031C2—122no—
1032C2—304no—
1033C2—304no—
1034C2—602no—
1035C2#1175324014yesdirect product factor
1036C2C2×#9201911yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×#9202411yescharacteristic
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×#6790C2semidirect
2. C22×#6773C2semidirect
3. C2×#91771C2semidirect
4. C2×C5×#885C2semidirect
5. C2×C3×#4029C2semidirect
6. C2×#91561C2semidirect
7. C2×#91557C2semidirect
8. C2×#91550C2semidirect
9. C2×#91476C2semidirect
10. C2×D5×(C2×D3)⋊C4C2semidirect
11. C2×#91438C2semidirect
12. C2×#91428C2semidirect
13. C2×#91424C2semidirect
14. C2×#91420C2semidirect
15. C2×#91395C2semidirect
16. #11753240C2direct (N × H)
20. C22×#1220C22semidirect
22. C22×D60C22semidirect
24. C22×C5×Dic6C22semidirect
26. C22×C3×C4×D5C22semidirect
28. C2×#6790C22semidirect
30. C22×#1203C22semidirect
32. C22×#1202C22semidirect
34. C22×#1200C22semidirect
35. C22×#1200C22semidirect
36. C22×#1200C22semidirect
37. C22×D5×Dic3C22semidirect
39. C2×#6773C22semidirect
40. C2×C3×C5×C22⋊C4C22semidirect
42. C2×#6714C22semidirect
43. #91771C22semidirect
44. C2×C5×#217C22semidirect
45. C2×C5×(C2×D3)⋊C4C22semidirect
46. C2×C5×(C2×D3)⋊C4C22semidirect
47. C2×C4×C5×Dic3C22semidirect
48. C5×#885C22semidirect
49. C2×C3×C22⋊Dic5C22semidirect
50. C2×C3×#685C22semidirect
51. C2×C3×C4⋊Dic5C22semidirect
52. C2×C3×#683C22semidirect
53. C3×#4029C22semidirect
54. #91561C22semidirect
55. #91557C22semidirect
56. #91550C22semidirect
57. C2×Dic3⋊Dic5C22semidirect
58. C2×#6669C22semidirect
61. C2×#6667C22semidirect
62. C2×(C2×D3)⋊Dic5C22semidirect
63. #91476C22semidirect
64. D5×(C2×D3)⋊C4C22semidirect
65. #91438C22semidirect
66. #91428C22semidirect
67. #91424C22semidirect
68. #91420C22semidirect
69. #91395C22semidirect
80. C2×#4029D3semidirect
104. C2×#1220C23semidirect
109. C2×D60C23semidirect
116. C2×C5×Dic6C23semidirect
123. C2×C3×C4×D5C23semidirect
128. C2×#1203C23semidirect
130. C2×#1202D4semidirect
132. C2×#1202C23semidirect
138. C2×#1200C23semidirect
139. C2×#1200C23semidirect
140. C2×#1200C23semidirect
142. C2×D5×Dic3C23semidirect
144. C3×C5×C22⋊C4C23semidirect
146. #6714C23semidirect
147. C5×#217C23semidirect
148. C5×(C2×D3)⋊C4C23semidirect
149. C5×(C2×D3)⋊C4C23semidirect
150. C4×C5×Dic3C23semidirect
151. C3×C22⋊Dic5C23semidirect
152. C3×#685C23semidirect
153. C3×C4⋊Dic5C23semidirect
154. C3×#683C23semidirect
155. Dic3⋊Dic5C23semidirect
156. #6669C23semidirect
159. #6667C23semidirect
160. (C2×D3)⋊Dic5C23semidirect
171. C2×#885D5semidirect
198. C22×C4×D5C2×D3semidirect
203. C2×C5×C22⋊C4C2×D3semidirect
206. C2×C22⋊Dic5C2×D3semidirect
214. C2×#685C2×D3semidirect
216. C2×C4⋊Dic5C2×D3semidirect
218. C2×#683C2×D3semidirect
222. #4029C2×D3semidirect
247. C22×D15#41semidirect
291. #1202C2×D4semidirect
318. C22×Dic6C2×D5semidirect
324. C2×C3×C22⋊C4C2×D5semidirect
325. C2×#217C2×D5semidirect
334. C2×(C2×D3)⋊C4C2×D5semidirect
335. C2×(C2×D3)⋊C4C2×D5semidirect
338. C2×C4×Dic3C2×D5semidirect
343. #885C2×D5semidirect
405. C2×C4×D5C22×D3semidirect
409. C5×C22⋊C4C22×D3semidirect
412. C22⋊Dic5C22×D3semidirect
418. #685C22×D3semidirect
420. C4⋊Dic5C22×D3semidirect
422. #683C22×D3semidirect
459. C2×D15C2×#41semidirect
534. C2×Dic6C22×D5semidirect
539. C3×C22⋊C4C22×D5semidirect
540. #217C22×D5semidirect
547. (C2×D3)⋊C4C22×D5semidirect
548. (C2×D3)⋊C4C22×D5semidirect
551. C4×Dic3C22×D5semidirect
669. C2×C22⋊C4D3×D5semidirect
672. C2×C3×C5#546semidirect
859. C22⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
903. C2×C5#5654semidirect
980. C2×C3#66010semidirect
988. C5C2×#5654semidirect
1028. C3C2×#66010semidirect
1035. C2#11753240direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67902
C22×#67732
C2×#917712
C2×C5×#8852
C2×C3×#40292
C2×#915612
C2×#915572
C2×#915502
C2×#914762
C2×D5×(C2×D3)⋊C42
C2×#914382
C2×#914282
C2×#914242
C2×#914202
C2×#913952
#117532402
C2×#660103
C2×#56545