Finite Group Databasebeta

← C2×#11753237 #14482612

Subgroups — C2×#11753237 #14482612

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×#6771C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D15C211yesmaximal, characteristic, complemented
4C2×C5×#884C211yesmaximal, characteristic, complemented
5C2×C3×#4029C211yesmaximal, characteristic, complemented
6C2×#91573C211yesmaximal, characteristic, complemented
7C2×#91549C211yesmaximal, characteristic, complemented
8C2×#91525C211yesmaximal, characteristic, complemented
9C2×#91475C211yesmaximal, characteristic, complemented
10C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#91466C211yesmaximal, characteristic, complemented
12C2×#91446C211yesmaximal, characteristic, complemented
13C2×#91429C211yesmaximal, characteristic, complemented
14C2×#91396C211yesmaximal, characteristic, complemented
15C2×#91355C211yesmaximal, characteristic, complemented
16#11753237C2116yesmaximal, direct product factor
17C2×#65946—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic, complemented
21C22×C4×D15C2211yescharacteristic, complemented
22C22×C5×#67C2211yescharacteristic
23C22×C5×#67C2211yescharacteristic, complemented
24C22×C5×D12C2211yescharacteristic, complemented
25C22×C4×C5×D3C2211yescharacteristic, complemented
26C22×C3×C22⋊D5C2211yescharacteristic
27C22×C3×C4×D5C2211yescharacteristic, complemented
28C2×#6790—28no—
29C2×#6790C2218yescomplemented
30C22×#1204C2211yescharacteristic, complemented
31C22×#1203C2211yescharacteristic
32C22×#1203C2211yescharacteristic
33C22×#1203C2211yescharacteristic, complemented
34C22×#1202C2211yescharacteristic
35C22×#1201C2211yescharacteristic, complemented
36C22×#1200C2211yescharacteristic
37C22×D5×Dic3C2211yescharacteristic, complemented
38C2×#6771—28no—
39C2×#6771C2218yescomplemented
40C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
41C2×#6719C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic
43C2×#6714C2211yescharacteristic
44C22⋊C4×D15C2218yescomplemented
45C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
47C5×#884C2218yescomplemented
48C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
49C2×C3×#685C2211yescharacteristic, complemented
50C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
51C2×C3×#683C2211yescharacteristic, complemented
52C3×#4029C2218yescomplemented
53#91573C2218yescomplemented
54#91549C2218yescomplemented
55C2×Dic3⋊Dic5C2211yescharacteristic, complemented
56C2×#6667C2211yescharacteristic
57C2×#6667C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
61C2×Dic3×Dic5C2211yescharacteristic, complemented
62#91525C2218yescomplemented
63#91475C2218yescomplemented
64D5×(C2×D3)⋊C4C2218yescomplemented
65#91466C2218yescomplemented
66#91446C2218yescomplemented
67#91429C2218yescomplemented
68#91396C2218yescomplemented
69#91355C2218yescomplemented
70C2×#5654—51nomaximal, Hall
71C22×D4×D5—31no—
72C22×#709—31no—
73C2×C5×#121—31no—
74C2×#4084—31no—
75C2×#4084—31no—
76C2×#4083—31no—
77C2×#4083—31no—
78C2×#4082—31no—
79C2×C4×C22⋊D5—31no—
80#65946—316no—
81C2×#4043—31no—
82C2×#4039—31no—
83C2×#4029—31no—
84C2×#4029D311yescharacteristic, complemented
85C2×D5×C22⋊C4—31no—
86C2×D5×C22⋊C4—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15—24no—
89C23×D15—24no—
90C23×D15—42no—
91C23×D15C2314yes—
92C23×D15C2311yescharacteristic
93C23×D15C2311yescharacteristic
94C23×C5×D3C2311yescharacteristic
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
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C2×C4×D15—24no—
106C2×C4×D15—42no—
107C2×C4×D15C2314yescomplemented
108C2×C4×D15C2314yescomplemented
109C2×C5×#67—24no—
110C2×C5×#67—42no—
111C2×C5×#67C2314yes—
112C2×C5×#67C2314yescomplemented
113C22×C5×Dic3C2311yescharacteristic
114C22×C5×Dic3C2311yescharacteristic
115C2×C5×D12—42no—
116C2×C5×D12C2314yescomplemented
117C2×C4×C5×D3—24no—
118C2×C4×C5×D3C2314yescomplemented
119C2×C3×C22⋊D5—24no—
120C2×C3×C22⋊D5C2314yes—
121C22×C3×Dic5C2311yescharacteristic
122C22×C3×Dic5C2311yescharacteristic
123C22×C3×Dic5C2311yescharacteristic
124C2×C3×C4×D5—24no—
125C2×C3×C4×D5C2314yescomplemented
126#6790—232no—
127C2×#1204—24no—
128C2×#1204C2314yescomplemented
129C2×#1203—24no—
130C2×#1203—24no—
131C2×#1203—24no—
132C2×#1203C2314yes—
133C2×#1203C2314yes—
134C2×#1203C2314yescomplemented
135C2×#1202D418yescomplemented
136C2×#1202C2314yes—
137C2×#1201—24no—
138C2×#1201C2314yescomplemented
139C2×#1200—24no—
140C2×#1200C2314yes—
141C2×D5×Dic3—42no—
142C2×D5×Dic3C2314yescomplemented
143#6771—232no—
144C3×C5×C22⋊C4C2314yescomplemented
145#6719C2314yescomplemented
146#6714C2314yes—
147#6714C2314yes—
148C5×(C2×D3)⋊C4C2314yescomplemented
149C5×Dic3⋊C4C2314yescomplemented
150C3×C22⋊Dic5C2314yescomplemented
151C3×#685C2314yescomplemented
152C3×C4⋊Dic5C2314yescomplemented
153C3×#683C2314yescomplemented
154Dic3⋊Dic5C2314yescomplemented
155#6667C2314yes—
156#6667C2314yescomplemented
157(C2×D3)⋊Dic5C2314yescomplemented
158(C2×D3)⋊Dic5C2314yescomplemented
159(C2×D3)⋊Dic5C2314yescomplemented
160Dic3×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×#885—51no—
172C2×#884D511yescharacteristic, complemented
173C2×#882—51no—
174C2×#882—51no—
175C2×#67⋊C4—51no—
176C2×D3×C22⋊C4—51no—
177C24×D5—31no—
178C24×D5—31no—
179C22×C5×D4—31no—
180C22×C5×D4—31no—
181C22×C5×D4—31no—
182C23×C4×C5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5C2×D311yescharacteristic
188C2×D4×D5—38no—
189C2×D4×D5—68no—
190C2×#709—38no—
191C2×#709—68no—
192C22×D20—31no—
193C22×C4×D5—31no—
194C22×C4×D5—31no—
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5C2×D311yescharacteristic, complemented
198C22×Dic10—31no—
199C5×#121—38no—
200C2×C5×C4⋊C4—31no—
201C2×C5×C22⋊C4—31no—
202C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
203C2×C22⋊Dic5—31no—
204C2×C22⋊Dic5—31no—
205C2×C22⋊Dic5—31no—
206C2×C22⋊Dic5—31no—
207C2×C22⋊Dic5C2×D311yescharacteristic, complemented
208#4084—38no—
209#4084—38no—
210#4083—38no—
211#4083—38no—
212#4082—38no—
213C4×C22⋊D5—38no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—31no—
217C2×#685—31no—
218C2×#685C2×D311yescharacteristic, complemented
219C2×C4⋊Dic5—31no—
220C2×C4⋊Dic5C2×D311yescharacteristic, complemented
221C2×#683C2×D311yescharacteristic, complemented
222C2×C4×Dic5—31no—
223#4043—38no—
224#4039—38no—
225#4029—38no—
226#4029C2×D318yescomplemented
227D5×C22⋊C4—38no—
228D5×C22⋊C4—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—28no—
240C22×D15—28no—
241C22×D15—44no—
242C22×D15—416no—
243C22×D15C2×D414yes—
244C22×D15#4114yescomplemented
245C22×D15C2412yes—
246C22×D15C2412yes—
247C22×C5×D3—22no—
248C22×C5×D3—22no—
249C22×C5×D3—22no—
250C22×C5×D3—22no—
251C22×C5×D3—22no—
252C22×C5×D3—22no—
253C22×C5×D3C2412yes—
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—
267C2×Dic15—22no—
268C2×Dic15—22no—
269C2×Dic15C2412yes—
270C2×Dic15C2412yes—
271C4×D15—28no—
272C4×D15—44no—
273C5×#67—28no—
274C5×#67—44no—
275C2×C5×Dic3—22no—
276C2×C5×Dic3C2×D414yes—
277C2×C5×Dic3C2412yes—
278C2×C5×Dic3C2412yes—
279C5×D12—44no—
280C4×C5×D3—28no—
281C3×C22⋊D5—28no—
282C2×C3×Dic5—22no—
283C2×C3×Dic5—22no—
284C2×C3×Dic5—22no—
285C2×C3×Dic5C2412yes—
286C2×C3×Dic5C2412yes—
287C2×C3×Dic5C2412yes—
288C3×C4×D5—28no—
289#1204—28no—
290#1203—28no—
291#1203—28no—
292#1203—28no—
293#1202C2×D4116yescomplemented
294#1201—28no—
295#1200—28no—
296D5×Dic3—44no—
297C24×D3—51no—
298C24×D3—51no—
299C22×C3×D4—51no—
300C23×C3×C4—51no—
301C22×#67—51no—
302C22×#67—51no—
303C22×#67C2×D511yescharacteristic
304C22×#67C2×D511yescharacteristic, complemented
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×D12C2×D511yescharacteristic, complemented
314C22×C4×D3—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3C2×D511yescharacteristic, complemented
318C22×Dic6—51no—
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×#217—51no—
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—51no—
334C2×(C2×D3)⋊C4—58no—
335C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
336C2×Dic3⋊C4—51no—
337C2×Dic3⋊C4C2×D511yescharacteristic, complemented
338C2×C4×Dic3—51no—
339#896—58no—
340#895—58no—
341#894—58no—
342#893—58no—
343#885—58no—
344#884C2×D518yescomplemented
345#882—58no—
346#882—58no—
347#67⋊C4—58no—
348D3×C22⋊C4—58no—
349C24×C5—31no—
350C24×C5—31no—
351C24×C5C22×D311yescharacteristic
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×D4—34no—
364C2×C5×D4—34no—
365C2×C5×D4—34no—
366C2×C5×D4—64no—
367C2×C5×D4—122no—
368C2×C5×D4—122no—
369C22×C4×C5—31no—
370C22×C4×C5—31no—
371C22×C4×C5—34no—
372C22×C4×C5—64no—
373C22×C4×C5C22×D311yescharacteristic
374C22×C4×C5C22×D311yescharacteristic
375C2×C22⋊D5—24no—
376C2×C22⋊D5—34no—
377C2×C22⋊D5—34no—
378C2×C22⋊D5—34no—
379C2×C22⋊D5—34no—
380C2×C22⋊D5—64no—
381C2×C22⋊D5—64no—
382C2×C22⋊D5—64no—
383C2×C22⋊D5—64no—
384C2×C22⋊D5C22×D314yes—
385C22×Dic5—31no—
386C22×Dic5—31no—
387C22×Dic5C22×D311yescharacteristic
388C22×Dic5C22×D311yescharacteristic
389C22×Dic5C22×D311yescharacteristic
390D4×D5—632no—
391#709—632no—
392C2×D20—38no—
393C2×D20—34no—
394C2×C4×D5—24no—
395C2×C4×D5—34no—
396C2×C4×D5—34no—
397C2×C4×D5—34no—
398C2×C4×D5—34no—
399C2×C4×D5—64no—
400C2×C4×D5—64no—
401C2×C4×D5—122no—
402C2×C4×D5—122no—
403C2×C4×D5C22×D314yescomplemented
404C2×Dic10—34no—
405C2×Dic10—64no—
406C5×C4⋊C4—34no—
407C5×C22⋊C4—34no—
408C5×C22⋊C4C22×D314yescomplemented
409C22⋊Dic5—34no—
410C22⋊Dic5—34no—
411C22⋊Dic5—34no—
412C22⋊Dic5—34no—
413C22⋊Dic5C22×D314yescomplemented
414#685—34no—
415#685—34no—
416#685—34no—
417#685—34no—
418#685C22×D314yescomplemented
419C4⋊Dic5—34no—
420C4⋊Dic5C22×D314yescomplemented
421#683C22×D314yescomplemented
422C4×Dic5—34no—
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—151no—
427C2×#123—51no—
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—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—416no—
454C2×D15C22×D414yes—
455C2×D15C2×#4114yescomplemented
456C2×C5×D3—22no—
457C2×C5×D3—22no—
458C2×C5×D3—22no—
459C2×C5×D3—22no—
460C2×C5×D3—22no—
461C2×C5×D3—22no—
462C2×C5×D3—44no—
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—
472Dic15—22no—
473C3×Dic5—22no—
474C3×Dic5—22no—
475C3×Dic5—22no—
476C5×Dic3—22no—
477C5×Dic3C22×D414yes—
478C24×C3—51no—
479C24×C3C22×D511yescharacteristic
480C23×D3—51no—
481C23×D3—51no—
482C23×D3—54no—
483C23×D3—54no—
484C23×D3—104no—
485C23×D3—104no—
486C23×D3—104no—
487C23×D3—104no—
488C23×D3—202no—
489C23×D3—202no—
490C23×D3C22×D511yescharacteristic
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—42no—
503C2×#67—54no—
504C2×#67—58no—
505C2×#67—54no—
506C2×#67—104no—
507C2×#67C22×D514yes—
508C2×#67C22×D514yescomplemented
509C22×Dic3—51no—
510C22×Dic3—51no—
511C22×Dic3—54no—
512C22×Dic3—202no—
513C22×Dic3C22×D511yescharacteristic
514C22×Dic3C22×D511yescharacteristic
515D3×D4—1032no—
516#235—1032no—
517C2×D12—42no—
518C2×D12—54no—
519C2×D12—54no—
520C2×D12—54no—
521C2×D12—104no—
522C2×D12—104no—
523C2×D12—104no—
524C2×D12C22×D514yescomplemented
525C2×C4×D3—24no—
526C2×C4×D3—54no—
527C2×C4×D3—54no—
528C2×C4×D3—54no—
529C2×C4×D3—104no—
530C2×C4×D3—104no—
531C2×C4×D3—202no—
532C2×C4×D3C22×D514yescomplemented
533C2×Dic6—54no—
534C2×Dic6—104no—
535C3×C4⋊C4—54no—
536C3×C4⋊C4—54no—
537C3×C22⋊C4—54no—
538C3×C22⋊C4—54no—
539C3×C22⋊C4C22×D514yescomplemented
540#217—54no—
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)⋊C4—54no—
548(C2×D3)⋊C4C22×D514yescomplemented
549Dic3⋊C4—54no—
550Dic3⋊C4C22×D514yescomplemented
551C4×Dic3—54no—
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—32no—
556C23×C5—32no—
557C23×C5—62no—
558C23×C5—62no—
559C23×C5—62no—
560C23×C5—62no—
561C23×C5—62no—
562C23×C5—62no—
563C23×C5C23×D312yes—
564C23×C5C23×D311yescharacteristic
565C22×D5—22no—
566C22×D5—22no—
567C22×D5—34no—
568C22×D5—34no—
569C22×D5—32no—
570C22×D5—32no—
571C22×D5—68no—
572C22×D5—68no—
573C22×D5—68no—
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×D4—68no—
586C5×D4—124no—
587C5×D4—124no—
588C2×C4×C5—22no—
589C2×C4×C5—22no—
590C2×C4×C5—34no—
591C2×C4×C5—32no—
592C2×C4×C5—32no—
593C2×C4×C5—68no—
594C2×C4×C5—62no—
595C2×C4×C5C23×D312yes—
596C2×C4×C5C23×D312yes—
597C22⋊D5—28no—
598C22⋊D5—68no—
599C22⋊D5—68no—
600C22⋊D5—68no—
601C22⋊D5—68no—
602C2×Dic5—22no—
603C2×Dic5—22no—
604C2×Dic5—22no—
605C2×Dic5—32no—
606C2×Dic5—32no—
607C2×Dic5—62no—
608C2×Dic5—62no—
609C2×Dic5C23×D312yes—
610C2×Dic5C23×D312yes—
611C2×Dic5C23×D312yes—
612D20—316no—
613C4×D5—28no—
614C4×D5—68no—
615C4×D5—68no—
616C4×D5—124no—
617C4×D5—124no—
618Dic10—68no—
619C25—151no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—151no—
624C22×D4—31no—
625C22×D4—31no—
626C22×D4—31no—
627C22×D4—51no—
628C22×D4—151no—
629C22×D4—151no—
630C22×D4—151no—
631C22×D4—151no—
632C22×D4—158no—
633C22×D4—151no—
634C22×D4—308no—
635C23×C4—31no—
636C23×C4—51no—
637C23×C4—151no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4—151no—
641#124—158no—
642#123—58no—
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—51no—
654C2×C4⋊C4—51no—
655C2×C4⋊C4—151no—
656C2×C22⋊C4—31no—
657C2×C22⋊C4—51no—
658C2×C22⋊C4—51no—
659C2×C22⋊C4—158no—
660C2×C22⋊C4—151no—
661C2×C22⋊C4—151no—
662C2×C22⋊C4—151no—
663C2×C22⋊C4—151no—
664C2×C22⋊C4—151no—
665C2×C22⋊C4—151no—
666C2×C22⋊C4—151no—
667C2×C22⋊C4—151no—
668C2×C22⋊C4—158no—
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—24no—
677D15—24no—
678C3×D5—24no—
679C5×D3—42no—
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—22no—
694C22×D3—22no—
695C22×D3—22no—
696C22×D3—54no—
697C22×D3—54no—
698C22×D3—52no—
699C22×D3—52no—
700C22×D3—108no—
701C22×D3—108no—
702C22×D3—108no—
703C22×D3—108no—
704C22×D3—102no—
705C22×D3—102no—
706C22×D3—102no—
707C22×D3—102no—
708C22×D3—204no—
709C22×D3—2016no—
710C22×D3—204no—
711C22×D3—2016no—
712C22×D3C23×D512yes—
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—44no—
728#67—516no—
729#67—108no—
730C2×Dic3—22no—
731C2×Dic3—52no—
732C2×Dic3—52no—
733C2×Dic3—102no—
734C2×Dic3—102no—
735C2×Dic3—204no—
736C2×Dic3D4×D514yes—
737C2×Dic3C23×D512yes—
738C2×Dic3C23×D512yes—
739D12—44no—
740D12—108no—
741D12—108no—
742D12—108no—
743C4×D3—28no—
744C4×D3—108no—
745C4×D3—108no—
746C4×D3—204no—
747Dic6—108no—
748C22×C5—22no—
749C22×C5—22no—
750C22×C5—22no—
751C22×C5—44no—
752C22×C5—62no—
753C22×C5—62no—
754C22×C5—62no—
755C22×C5—62no—
756C22×C5—62no—
757C22×C5—62no—
758C22×C5—124no—
759C22×C5—124no—
760C22×C5C2×D3×D412yes—
761C22×C5D3×#4112yes—
762C22×C5#100912yes—
763C22×C5C24×D311yescharacteristic
764C2×D5—28no—
765C2×D5—22no—
766C2×D5—22no—
767C2×D5—34no—
768C2×D5—34no—
769C2×D5—68no—
770C2×D5—68no—
771C2×D5—62no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—62no—
775C2×D5—1216no—
776C2×D5—1216no—
777C2×D5C2×D3×D414yes—
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—34no—
781C4×C5—62no—
782Dic5—22no—
783Dic5—22no—
784Dic5—22no—
785Dic5—62no—
786Dic5—62no—
787C24—31no—
788C24—31no—
789C24—51no—
790C24—154no—
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—154no—
803C2×Q8—304no—
804C2×D4—34no—
805C2×D4—34no—
806C2×D4—34no—
807C2×D4—54no—
808C2×D4—64no—
809C2×D4—104no—
810C2×D4—122no—
811C2×D4—122no—
812C2×D4—154no—
813C2×D4—158no—
814C2×D4—154no—
815C2×D4—154no—
816C2×D4—154no—
817C2×D4—154no—
818C2×D4—304no—
819C2×D4—304no—
820C2×D4—304no—
821C2×D4—3032no—
822C2×D4—304no—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—34no—
826C22×C4—51no—
827C22×C4—51no—
828C22×C4—51no—
829C22×C4—54no—
830C22×C4—64no—
831C22×C4—104no—
832C22×C4—154no—
833C22×C4—154no—
834C22×C4—151no—
835C22×C4—151no—
836C22×C4—154no—
837C22×C4—154no—
838C22×C4—304no—
839C22×C4—304no—
840C22×C4—602no—
841C22×C4—602no—
842C22×C4C2×D3×D511yescharacteristic
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—34no—
845C4⋊C4—54no—
846C4⋊C4—54no—
847C4⋊C4—154no—
848C22⋊C4—34no—
849C22⋊C4—54no—
850C22⋊C4—54no—
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⋊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—108no—
868C22×C3—102no—
869C22×C3—102no—
870C22×C3C2×D4×D512yes—
871C22×C3#414412yes—
872C22×C3D5×#4112yes—
873C22×C3C24×D511yescharacteristic
874C2×D3—22no—
875C2×D3—22no—
876C2×D3—22no—
877C2×D3—22no—
878C2×D3—22no—
879C2×D3—22no—
880C2×D3—44no—
881C2×D3—44no—
882C2×D3—54no—
883C2×D3—54no—
884C2×D3—108no—
885C2×D3—108no—
886C2×D3—102no—
887C2×D3—102no—
888C2×D3—102no—
889C2×D3—102no—
890C2×D3—2016no—
891C2×D3—2016no—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—102no—
895C3×C4—102no—
896C3×C4—102no—
897Dic3—22no—
898Dic3—102no—
899Dic3—102no—
900Dic3C2×D4×D514yes—
901C2×C5—42no—
902C2×C5—122no—
903C2×C5—122no—
904C2×C5#565414yescomplemented
905C2×C5C22×D3×D411yescharacteristic
906C2×C5C2×D3×#4111yescharacteristic
907C2×C5C2×#100911yescharacteristic
908D5—24no—
909D5—64no—
910D5—64no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—32no—
915C23—32no—
916C23—54no—
917C23—52no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—102no—
925C23—102no—
926C23—154no—
927C23—154no—
928C23—152no—
929C23—152no—
930C23—308no—
931C23—308no—
932C23—308no—
933C23—308no—
934C23—302no—
935C23—302no—
936C23—302no—
937C23—302no—
938C23—604no—
939C23—6016no—
940C23—604no—
941C23—6016no—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—308no—
945D4—68no—
946D4—108no—
947D4—124no—
948D4—124no—
949D4—1516no—
950D4—308no—
951D4—308no—
952D4—308no—
953D4—308no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—34no—
957C2×C4—32no—
958C2×C4—32no—
959C2×C4—52no—
960C2×C4—52no—
961C2×C4—52no—
962C2×C4—68no—
963C2×C4—62no—
964C2×C4—108no—
965C2×C4—102no—
966C2×C4—102no—
967C2×C4—102no—
968C2×C4—152no—
969C2×C4—152no—
970C2×C4—308no—
971C2×C4—308no—
972C2×C4—302no—
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#6594614yescomplemented
981C2×C3C22×D4×D511yescharacteristic
982C2×C3C2×#414411yescharacteristic
983C2×C3C2×D5×#4111yescharacteristic
984D3—42no—
985D3—42no—
986D3—104no—
987D3—104no—
988C5C2×#565411yescharacteristic, complemented, Sylow
989C22—22no—
990C22—22no—
991C22—22no—
992C22—44no—
993C22—54no—
994C22—62no—
995C22—62no—
996C22—62no—
997C22—62no—
998C22—62no—
999C22—62no—
1000C22—108no—
1001C22—102no—
1002C22—102no—
1003C22—124no—
1004C22—124no—
1005C22—154no—
1006C22—154no—
1007C22—308no—
1008C22—308no—
1009C22—302no—
1010C22—302no—
1011C22—302no—
1012C22—302no—
1013C22—6016no—
1014C22—6016no—
1015C22#9201612yes—
1016C22D3×D4×D512yes—
1017C22#9202712yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—34no—
1022C4—62no—
1023C4—102no—
1024C4—102no—
1025C4—102no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6594611yescharacteristic, complemented, Sylow
1029C2—42no—
1030C2—104no—
1031C2—122no—
1032C2—122no—
1033C2—304no—
1034C2—304no—
1035C2#1175323714yesdirect product factor
1036C2C2×#9201611yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×#9202711yescharacteristic
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×#6771C2semidirect
3. C2×C22⋊C4×D15C2semidirect
4. C2×C5×#884C2semidirect
5. C2×C3×#4029C2semidirect
6. C2×#91573C2semidirect
7. C2×#91549C2semidirect
8. C2×#91525C2semidirect
9. C2×#91475C2semidirect
10. C2×D5×(C2×D3)⋊C4C2semidirect
11. C2×#91466C2semidirect
12. C2×#91446C2semidirect
13. C2×#91429C2semidirect
14. C2×#91396C2semidirect
15. C2×#91355C2semidirect
16. #11753237C2direct (N × H)
20. C22×C4×D15C22semidirect
21. C22×C4×D15C22semidirect
23. C22×C5×#67C22semidirect
24. C22×C5×D12C22semidirect
25. C22×C4×C5×D3C22semidirect
27. C22×C3×C4×D5C22semidirect
29. C2×#6790C22semidirect
30. C22×#1204C22semidirect
33. C22×#1203C22semidirect
35. C22×#1201C22semidirect
37. C22×D5×Dic3C22semidirect
39. C2×#6771C22semidirect
40. C2×C3×C5×C22⋊C4C22semidirect
41. C2×#6719C22semidirect
44. C22⋊C4×D15C22semidirect
45. C2×C5×(C2×D3)⋊C4C22semidirect
46. C2×C5×Dic3⋊C4C22semidirect
47. C5×#884C22semidirect
48. C2×C3×C22⋊Dic5C22semidirect
49. C2×C3×#685C22semidirect
50. C2×C3×C4⋊Dic5C22semidirect
51. C2×C3×#683C22semidirect
52. C3×#4029C22semidirect
53. #91573C22semidirect
54. #91549C22semidirect
55. C2×Dic3⋊Dic5C22semidirect
57. C2×#6667C22semidirect
58. C2×(C2×D3)⋊Dic5C22semidirect
59. C2×(C2×D3)⋊Dic5C22semidirect
60. C2×(C2×D3)⋊Dic5C22semidirect
61. C2×Dic3×Dic5C22semidirect
62. #91525C22semidirect
63. #91475C22semidirect
64. D5×(C2×D3)⋊C4C22semidirect
65. #91466C22semidirect
66. #91446C22semidirect
67. #91429C22semidirect
68. #91396C22semidirect
69. #91355C22semidirect
84. C2×#4029D3semidirect
107. C2×C4×D15C23semidirect
108. C2×C4×D15C23semidirect
112. C2×C5×#67C23semidirect
116. C2×C5×D12C23semidirect
118. C2×C4×C5×D3C23semidirect
125. C2×C3×C4×D5C23semidirect
128. C2×#1204C23semidirect
134. C2×#1203C23semidirect
135. C2×#1202D4semidirect
138. C2×#1201C23semidirect
142. C2×D5×Dic3C23semidirect
144. C3×C5×C22⋊C4C23semidirect
145. #6719C23semidirect
148. C5×(C2×D3)⋊C4C23semidirect
149. C5×Dic3⋊C4C23semidirect
150. C3×C22⋊Dic5C23semidirect
151. C3×#685C23semidirect
152. C3×C4⋊Dic5C23semidirect
153. C3×#683C23semidirect
154. Dic3⋊Dic5C23semidirect
156. #6667C23semidirect
157. (C2×D3)⋊Dic5C23semidirect
158. (C2×D3)⋊Dic5C23semidirect
159. (C2×D3)⋊Dic5C23semidirect
160. Dic3×Dic5C23semidirect
172. C2×#884D5semidirect
197. C22×C4×D5C2×D3semidirect
202. C2×C5×C22⋊C4C2×D3semidirect
207. C2×C22⋊Dic5C2×D3semidirect
218. C2×#685C2×D3semidirect
220. C2×C4⋊Dic5C2×D3semidirect
221. C2×#683C2×D3semidirect
226. #4029C2×D3semidirect
244. C22×D15#41semidirect
293. #1202C2×D4semidirect
304. C22×#67C2×D5semidirect
313. C22×D12C2×D5semidirect
317. C22×C4×D3C2×D5semidirect
324. C2×C3×C22⋊C4C2×D5semidirect
335. C2×(C2×D3)⋊C4C2×D5semidirect
337. C2×Dic3⋊C4C2×D5semidirect
344. #884C2×D5semidirect
403. C2×C4×D5C22×D3semidirect
408. C5×C22⋊C4C22×D3semidirect
413. C22⋊Dic5C22×D3semidirect
418. #685C22×D3semidirect
420. C4⋊Dic5C22×D3semidirect
421. #683C22×D3semidirect
455. C2×D15C2×#41semidirect
508. C2×#67C22×D5semidirect
524. C2×D12C22×D5semidirect
532. C2×C4×D3C22×D5semidirect
539. C3×C22⋊C4C22×D5semidirect
548. (C2×D3)⋊C4C22×D5semidirect
550. Dic3⋊C4C22×D5semidirect
669. C2×C22⋊C4D3×D5semidirect
672. C2×C3×C5#546semidirect
859. C22⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
904. C2×C5#5654semidirect
980. C2×C3#65946semidirect
988. C5C2×#5654semidirect
1028. C3C2×#65946semidirect
1035. C2#11753237direct (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×#67712
C2×C22⋊C4×D152
C2×C5×#8842
C2×C3×#40292
C2×#915732
C2×#915492
C2×#915252
C2×#914752
C2×D5×(C2×D3)⋊C42
C2×#914662
C2×#914462
C2×#914292
C2×#913962
C2×#913552
#117532372
C2×#659463
C2×#56545