Finite Group Databasebeta

← C2×#11753218 #14480333

Subgroups — C2×#11753218 #14480333

Order 1920.

3968 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6790C211yesmaximal, characteristic, complemented
2C22×D3×D20C211yesmaximal, characteristic, complemented
3C2×#91771C211yesmaximal, characteristic, complemented
4C2×C5×#883C211yesmaximal, characteristic, complemented
5C2×C3×#4030C211yesmaximal, characteristic, complemented
6C2×#91577C211yesmaximal, characteristic, complemented
7C2×#91572C211yesmaximal, characteristic, complemented
8C2×#91550C211yesmaximal, characteristic, complemented
9C2×#91476C211yesmaximal, characteristic, complemented
10C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#91450C211yesmaximal, characteristic, complemented
12C2×#91433C211yesmaximal, characteristic, complemented
13C2×#91409C211yesmaximal, characteristic, complemented
14C2×#91356C211yesmaximal, characteristic, complemented
15C2×#91351C211yesmaximal, characteristic, complemented
16#11753218C2116yesmaximal, direct product factor
17C2×#65987—31nomaximal, Hall
18C24×D15C2211yescharacteristic, complemented
19C23×D3×D5C2211yescharacteristic
20C23×D3×D5C2211yescharacteristic, complemented
21C22×#1220C2211yescharacteristic, complemented
22C22×D60C2211yescharacteristic
23C22×D60C2211yescharacteristic, complemented
24C22×C5×#67C2211yescharacteristic
25C22×C4×C5×D3C2211yescharacteristic, complemented
26C22×C3×C22⋊D5C2211yescharacteristic, complemented
27C22×C3×C22⋊D5C2211yescharacteristic, complemented
28C22×C3×D20C2211yescharacteristic, complemented
29C22×C3×C4×D5C2211yescharacteristic, complemented
30C2×#6790—28no—
31C2×#6790C2218yescomplemented
32C22×#1203C2211yescharacteristic
33C22×#1202C2211yescharacteristic
34C22×#1202C2211yescharacteristic, complemented
35C22×#1202C2211yescharacteristic, complemented
36C22×#1202C2211yescharacteristic, complemented
37C22×#1200C2211yescharacteristic, complemented
38C22×D5×Dic3C2211yescharacteristic, complemented
39C2×D3×D20—28no—
40C2×D3×D20C2218yescomplemented
41C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic, complemented
43C2×#6714C2211yescharacteristic, complemented
44#91771C2218yescomplemented
45C2×C5×#217C2211yescharacteristic, complemented
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
48C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
49C5×#883C2218yescomplemented
50C2×C3×#685C2211yescharacteristic, complemented
51C2×C3×#683C2211yescharacteristic, complemented
52C3×#4030C2218yescomplemented
53#91577C2218yescomplemented
54#91572C2218yescomplemented
55#91550C2218yescomplemented
56C2×#6669C2211yescharacteristic, complemented
57C2×#6667C2211yescharacteristic, complemented
58C2×#6667C2211yescharacteristic, complemented
59C2×#6667C2211yescharacteristic, complemented
60C2×#6667C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
62C2×#6665C2211yescharacteristic, complemented
63#91476C2218yescomplemented
64D5×(C2×D3)⋊C4C2218yescomplemented
65#91450C2218yescomplemented
66#91433C2218yescomplemented
67#91409C2218yescomplemented
68#91356C2218yescomplemented
69#91351C2218yescomplemented
70C2×#5605—51nomaximal, Hall
71C22×D4×D5—31no—
72C23×D20—31no—
73C2×C5×#123—31no—
74C2×#4083—31no—
75C2×#4075—31no—
76#65987—316no—
77C2×#4041—31no—
78C2×#4041—31no—
79C2×#4040—31no—
80C2×#4040—31no—
81C2×#4030—31no—
82C2×#4030D311yescharacteristic, complemented
83C2×#4028—31no—
84C2×#4028—31no—
85C2×#4028—31no—
86C2×D5×C22⋊C4—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15—24no—
89C23×D15—42no—
90C23×D15—42no—
91C23×D15C2311yescharacteristic
92C23×D15C2311yescharacteristic
93C23×D15C2311yescharacteristic
94C23×D15C2314yescomplemented
95C23×C5×D3C2311yescharacteristic
96C23×C3×D5C2311yescharacteristic
97C23×C3×D5C2311yescharacteristic
98C22×D3×D5—24no—
99C22×D3×D5—42no—
100C22×D3×D5—42no—
101C22×D3×D5—42no—
102C22×D3×D5—42no—
103C22×D3×D5D418yescomplemented
104C22×D3×D5C2314yes—
105C22×D3×D5C2314yescomplemented
106C22×C3×C4×C5C2311yescharacteristic
107C22×C3×C4×C5C2311yescharacteristic
108C2×#1220—42no—
109C2×#1220C2314yescomplemented
110C22×Dic15C2311yescharacteristic
111C2×D60—24no—
112C2×D60—42no—
113C2×D60C2314yes—
114C2×D60C2314yescomplemented
115C2×C5×#67—24no—
116C2×C5×#67C2314yes—
117C22×C5×Dic3C2311yescharacteristic
118C22×C5×Dic3C2311yescharacteristic
119C22×C5×Dic3C2311yescharacteristic
120C2×C4×C5×D3—24no—
121C2×C4×C5×D3C2314yescomplemented
122C2×C3×C22⋊D5—24no—
123C2×C3×C22⋊D5—42no—
124C2×C3×C22⋊D5C2314yescomplemented
125C2×C3×C22⋊D5C2314yescomplemented
126C22×C3×Dic5C2311yescharacteristic
127C22×C3×Dic5C2311yescharacteristic
128C2×C3×D20—24no—
129C2×C3×D20C2314yescomplemented
130C2×C3×C4×D5—42no—
131C2×C3×C4×D5C2314yescomplemented
132#6790—232no—
133C2×#1203—24no—
134C2×#1203C2314yes—
135C2×#1202—24no—
136C2×#1202—24no—
137C2×#1202—24no—
138C2×#1202—42no—
139C2×#1202C2314yes—
140C2×#1202C2314yescomplemented
141C2×#1202C2314yescomplemented
142C2×#1202C2314yescomplemented
143C2×#1200—24no—
144C2×#1200C2314yescomplemented
145C2×D5×Dic3—42no—
146C2×D5×Dic3C2314yescomplemented
147D3×D20—232no—
148C3×C5×C22⋊C4C2314yescomplemented
149#6714C2314yescomplemented
150#6714C2314yescomplemented
151C5×#217C2314yescomplemented
152C5×(C2×D3)⋊C4C2314yescomplemented
153C5×C4⋊Dic3C2314yescomplemented
154C5×Dic3⋊C4C2314yescomplemented
155C3×#685C2314yescomplemented
156C3×#683C2314yescomplemented
157#6669C2314yescomplemented
158#6667C2314yescomplemented
159#6667C2314yescomplemented
160#6667C2314yescomplemented
161#6667C2314yescomplemented
162(C2×D3)⋊Dic5C2314yescomplemented
163#6665C2314yescomplemented
164C22×D3×D4—51no—
165C22×D3×D4—51no—
166C2×C3×#121—51no—
167C2×#939—51no—
168C2×#939—51no—
169C2×#937—51no—
170C2×#937—51no—
171C2×#930—51no—
172C22×(C2×D3)⋊C4—51no—
173#5605—516no—
174C2×#894—51no—
175C2×#894—51no—
176C2×#883—51no—
177C2×#883D511yescharacteristic, complemented
178C2×#882—51no—
179C2×#882—51no—
180C24×D5—31no—
181C24×D5—31no—
182C24×D5—31no—
183C22×C5×D4—31no—
184C23×C4×C5—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5C2×D311yescharacteristic, complemented
188C22×C22⋊D5C2×D311yescharacteristic, complemented
189C2×D4×D5—38no—
190C2×D4×D5—68no—
191C22×D20—31no—
192C22×D20—31no—
193C22×D20—31no—
194C22×D20—31no—
195C22×D20—31no—
196C22×D20—31no—
197C22×D20—38no—
198C22×D20—68no—
199C22×D20C2×D311yescharacteristic, complemented
200C22×C4×D5—31no—
201C22×C4×D5—31no—
202C22×C4×D5C2×D311yescharacteristic, complemented
203C5×#123—38no—
204C2×C5×C4⋊C4—31no—
205C2×C5×C4⋊C4—31no—
206C2×C5×C22⋊C4—31no—
207C2×C5×C22⋊C4—31no—
208C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
209C2×C22⋊Dic5—31no—
210#4083—38no—
211#4075—38no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—31no—
217C2×#685—31no—
218C2×#685—31no—
219C2×#685C2×D311yescharacteristic, complemented
220C2×#683—31no—
221C2×#683C2×D311yescharacteristic, complemented
222#4041—38no—
223#4041—38no—
224#4040—38no—
225#4040—38no—
226#4030—38no—
227#4030C2×D318yescomplemented
228#4028—38no—
229#4028—38no—
230#4028—38no—
231D5×C22⋊C4—38no—
232C2×#534—151noSylow
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5—22no—
236C23×C3×C5C2412yes—
237C23×C3×C5C2411yescharacteristic
238C22×D15—22no—
239C22×D15—22no—
240C22×D15—22no—
241C22×D15—22no—
242C22×D15—22no—
243C22×D15—22no—
244C22×D15—22no—
245C22×D15—22no—
246C22×D15—28no—
247C22×D15—44no—
248C22×D15—44no—
249C22×D15—416no—
250C22×D15C2×D414yes—
251C22×D15C2412yes—
252C22×D15C2412yes—
253C22×D15C2412yes—
254C22×C5×D3—22no—
255C22×C5×D3—22no—
256C22×C5×D3C2×D414yes—
257C22×C5×D3C2412yes—
258C22×C3×D5—22no—
259C22×C3×D5—22no—
260C22×C3×D5—22no—
261C22×C3×D5—22no—
262C22×C3×D5—22no—
263C22×C3×D5C2×D414yes—
264C22×C3×D5C2412yes—
265C22×C3×D5C2412yes—
266C2×D3×D5—28no—
267C2×D3×D5—416no—
268C2×D3×D5—44no—
269C2×D3×D5—44no—
270C2×D3×D5—44no—
271C2×D3×D5—44no—
272C2×D3×D5—416no—
273C2×D3×D5C2×D4116yescomplemented
274C2×C3×C4×C5—22no—
275C2×C3×C4×C5—22no—
276C2×C3×C4×C5C2412yes—
277C2×C3×C4×C5C2412yes—
278#1220—44no—
279C2×Dic15—22no—
280C2×Dic15C2412yes—
281D60—28no—
282D60—44no—
283C5×#67—28no—
284C2×C5×Dic3—22no—
285C2×C5×Dic3—22no—
286C2×C5×Dic3—22no—
287C2×C5×Dic3C2412yes—
288C2×C5×Dic3C2412yes—
289C2×C5×Dic3C2412yes—
290C4×C5×D3—28no—
291C3×C22⋊D5—28no—
292C3×C22⋊D5—44no—
293C2×C3×Dic5—22no—
294C2×C3×Dic5—22no—
295C2×C3×Dic5C2412yes—
296C2×C3×Dic5C2412yes—
297C3×D20—28no—
298C3×C4×D5—44no—
299#1203—28no—
300#1202—28no—
301#1202—28no—
302#1202—28no—
303#1202—44no—
304#1200—28no—
305D5×Dic3—44no—
306C24×D3—51no—
307C24×D3—51no—
308C24×D3—51no—
309C22×C3×D4—51no—
310C22×C3×D4—51no—
311C22×C3×D4—51no—
312C23×C3×C4—51no—
313C22×#67—51no—
314C22×#67—51no—
315C22×#67—51no—
316C22×#67—51no—
317C22×#67—51no—
318C22×#67C2×D511yescharacteristic
319C23×Dic3—51no—
320C2×D3×D4—58no—
321C2×D3×D4—58no—
322C2×D3×D4—108no—
323C2×D3×D4—108no—
324C22×D12—51no—
325C22×D12—51no—
326C22×D12—51no—
327C22×C4×D3—51no—
328C22×C4×D3C2×D511yescharacteristic, complemented
329C3×#121—58no—
330C2×C3×C4⋊C4—51no—
331C2×C3×C22⋊C4—51no—
332C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
333C2×#217—51no—
334C2×#217C2×D511yescharacteristic, complemented
335#939—58no—
336#939—58no—
337#937—58no—
338#937—58no—
339#930—58no—
340C2×(C2×D3)⋊C4—51no—
341C2×(C2×D3)⋊C4—51no—
342C2×(C2×D3)⋊C4—51no—
343C2×(C2×D3)⋊C4—51no—
344C2×(C2×D3)⋊C4—51no—
345C2×(C2×D3)⋊C4—51no—
346C2×(C2×D3)⋊C4—51no—
347C2×(C2×D3)⋊C4—58no—
348C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
349C2×C4⋊Dic3C2×D511yescharacteristic, complemented
350C2×Dic3⋊C4—51no—
351C2×Dic3⋊C4C2×D511yescharacteristic, complemented
352#894—58no—
353#894—58no—
354#883—58no—
355#883C2×D518yescomplemented
356#882—58no—
357#882—58no—
358C24×C5—31no—
359C24×C5C22×D311yescharacteristic
360C23×D5—31no—
361C23×D5—38no—
362C23×D5—34no—
363C23×D5—31no—
364C23×D5—31no—
365C23×D5—34no—
366C23×D5—34no—
367C23×D5—64no—
368C23×D5—64no—
369C23×D5—122no—
370C23×D5—122no—
371C23×D5—122no—
372C23×D5—122no—
373C23×D5—122no—
374C23×D5—122no—
375C23×D5C22×D311yescharacteristic
376C23×D5C22×D311yescharacteristic
377C2×C5×D4—34no—
378C2×C5×D4—64no—
379C22×C4×C5—31no—
380C22×C4×C5—31no—
381C22×C4×C5—31no—
382C22×C4×C5—34no—
383C22×C4×C5—64no—
384C22×C4×C5C22×D311yescharacteristic
385C22×C4×C5C22×D311yescharacteristic
386C2×C22⋊D5—24no—
387C2×C22⋊D5—34no—
388C2×C22⋊D5—34no—
389C2×C22⋊D5—42no—
390C2×C22⋊D5—64no—
391C2×C22⋊D5—122no—
392C2×C22⋊D5C22×D314yescomplemented
393C2×C22⋊D5C22×D314yescomplemented
394C22×Dic5—31no—
395C22×Dic5C22×D311yescharacteristic
396C22×Dic5C22×D311yescharacteristic
397D4×D5—632no—
398C2×D20—24no—
399C2×D20—34no—
400C2×D20—34no—
401C2×D20—34no—
402C2×D20—34no—
403C2×D20—34no—
404C2×D20—34no—
405C2×D20—632no—
406C2×D20—64no—
407C2×D20—64no—
408C2×D20—64no—
409C2×D20—64no—
410C2×D20—122no—
411C2×D20—122no—
412C2×D20C22×D314yescomplemented
413C2×C4×D5—34no—
414C2×C4×D5—34no—
415C2×C4×D5—42no—
416C2×C4×D5—64no—
417C2×C4×D5—122no—
418C2×C4×D5C22×D314yescomplemented
419C5×C4⋊C4—34no—
420C5×C4⋊C4—34no—
421C5×C22⋊C4—34no—
422C5×C22⋊C4—34no—
423C5×C22⋊C4C22×D314yescomplemented
424C22⋊Dic5—34no—
425#685—34no—
426#685—34no—
427#685—34no—
428#685—34no—
429#685—34no—
430#685—34no—
431#685—34no—
432#685C22×D314yescomplemented
433#683—34no—
434#683C22×D314yescomplemented
435C23×D4—151no—
436C23×D4—151no—
437#534—1516no—
438C2×#123—31no—
439C2×#123—151no—
440C2×#123—151no—
441C2×#123—151no—
442C2×#121—51no—
443C2×#121—151no—
444C2×#121—151no—
445C2×#121—151no—
446C2×#120—151no—
447C2×#120—151no—
448C2×#120—151no—
449C2×#120—151no—
450C22×C22⋊C4—151no—
451C22×C3×C5—22no—
452C22×C3×C5—22no—
453C22×C3×C5—22no—
454C22×C3×C5—44no—
455C22×C3×C5C22×D412yes—
456C22×C3×C5H(5,𝔽2)12yes—
457C22×C3×C5H(5,𝔽2)12yes—
458C22×C3×C5C2511yescharacteristic
459C2×D15—28no—
460C2×D15—22no—
461C2×D15—22no—
462C2×D15—22no—
463C2×D15—22no—
464C2×D15—22no—
465C2×D15—22no—
466C2×D15—22no—
467C2×D15—22no—
468C2×D15—416no—
469C2×D15—44no—
470C2×D15—44no—
471C2×D15C22×D414yes—
472C2×C5×D3—28no—
473C2×C5×D3—22no—
474C2×C5×D3—22no—
475C2×C5×D3C22×D414yes—
476C2×C3×D5—28no—
477C2×C3×D5—22no—
478C2×C3×D5—22no—
479C2×C3×D5—22no—
480C2×C3×D5—22no—
481C2×C3×D5—22no—
482C2×C3×D5—44no—
483C2×C3×D5C22×D414yes—
484D3×D5—416no—
485D3×D5—416no—
486C3×C4×C5—22no—
487C3×C4×C5—22no—
488Dic15—22no—
489C3×Dic5—22no—
490C3×Dic5—22no—
491C5×Dic3—22no—
492C5×Dic3—22no—
493C5×Dic3—22no—
494C24×C3—51no—
495C24×C3—51no—
496C24×C3C22×D511yescharacteristic
497C23×D3—51no—
498C23×D3—58no—
499C23×D3—54no—
500C23×D3—51no—
501C23×D3—51no—
502C23×D3—54no—
503C23×D3—54no—
504C23×D3—104no—
505C23×D3—104no—
506C23×D3—202no—
507C23×D3—202no—
508C23×D3—202no—
509C23×D3—202no—
510C23×D3—202no—
511C23×D3—202no—
512C23×D3C22×D511yescharacteristic
513C2×C3×D4—54no—
514C2×C3×D4—54no—
515C2×C3×D4—54no—
516C2×C3×D4—104no—
517C2×C3×D4—104no—
518C2×C3×D4—202no—
519C22×C3×C4—51no—
520C22×C3×C4—51no—
521C22×C3×C4—54no—
522C22×C3×C4—202no—
523C22×C3×C4C22×D511yescharacteristic
524C22×C3×C4C22×D511yescharacteristic
525C2×#67—24no—
526C2×#67—54no—
527C2×#67—54no—
528C2×#67—54no—
529C2×#67—54no—
530C2×#67—54no—
531C2×#67—104no—
532C2×#67—104no—
533C2×#67—104no—
534C2×#67—202no—
535C2×#67—202no—
536C2×#67C22×D514yes—
537C22×Dic3—51no—
538C22×Dic3—54no—
539C22×Dic3—202no—
540C22×Dic3C22×D511yescharacteristic
541C22×Dic3C22×D511yescharacteristic
542C22×Dic3C22×D511yescharacteristic
543D3×D4—1032no—
544D3×D4—1032no—
545C2×D12—54no—
546C2×D12—54no—
547C2×D12—54no—
548C2×D12—104no—
549C2×D12—104no—
550C2×D12—202no—
551C2×C4×D3—24no—
552C2×C4×D3—54no—
553C2×C4×D3—104no—
554C2×C4×D3C22×D514yescomplemented
555C3×C4⋊C4—54no—
556C3×C22⋊C4—54no—
557C3×C22⋊C4C22×D514yescomplemented
558#217—54no—
559#217C22×D514yescomplemented
560(C2×D3)⋊C4—54no—
561(C2×D3)⋊C4—54no—
562(C2×D3)⋊C4—54no—
563(C2×D3)⋊C4—54no—
564(C2×D3)⋊C4—54no—
565(C2×D3)⋊C4—54no—
566(C2×D3)⋊C4—54no—
567(C2×D3)⋊C4C22×D514yescomplemented
568C4⋊Dic3C22×D514yescomplemented
569Dic3⋊C4—54no—
570Dic3⋊C4C22×D514yescomplemented
571C23×C5—22no—
572C23×C5—22no—
573C23×C5—22no—
574C23×C5—34no—
575C23×C5—32no—
576C23×C5—62no—
577C23×C5—62no—
578C23×C5C23×D312yes—
579C23×C5C23×D311yescharacteristic
580C22×D5—22no—
581C22×D5—22no—
582C22×D5—22no—
583C22×D5—22no—
584C22×D5—22no—
585C22×D5—34no—
586C22×D5—32no—
587C22×D5—316no—
588C22×D5—32no—
589C22×D5—32no—
590C22×D5—68no—
591C22×D5—68no—
592C22×D5—62no—
593C22×D5—62no—
594C22×D5—62no—
595C22×D5—62no—
596C22×D5—62no—
597C22×D5—62no—
598C22×D5—62no—
599C22×D5—62no—
600C22×D5—124no—
601C22×D5—124no—
602C22×D5—1216no—
603C22×D5—124no—
604C22×D5—124no—
605C22×D5—1216no—
606C22×D5—124no—
607C22×D5—124no—
608C22×D5—1216no—
609C22×D5D3×D414yes—
610C22×D5C23×D312yes—
611C22×D5C23×D312yes—
612C5×D4—68no—
613C2×C4×C5—22no—
614C2×C4×C5—22no—
615C2×C4×C5—32no—
616C2×C4×C5—32no—
617C2×C4×C5—32no—
618C2×C4×C5—68no—
619C2×C4×C5—62no—
620C2×C4×C5—62no—
621C2×C4×C5—62no—
622C2×C4×C5C23×D312yes—
623C2×C4×C5C23×D312yes—
624C22⋊D5—28no—
625C22⋊D5—44no—
626C22⋊D5—68no—
627C22⋊D5—124no—
628C2×Dic5—22no—
629C2×Dic5—22no—
630C2×Dic5—32no—
631C2×Dic5—62no—
632C2×Dic5C23×D312yes—
633C2×Dic5C23×D312yes—
634D20—28no—
635D20—68no—
636D20—68no—
637D20—68no—
638D20—68no—
639D20—124no—
640D20—124no—
641C4×D5—44no—
642C4×D5—68no—
643C4×D5—124no—
644C25—151no—
645C25—151no—
646C25—151no—
647C22×D4—31no—
648C22×D4—51no—
649C22×D4—51no—
650C22×D4—51no—
651C22×D4—158no—
652C22×D4—151no—
653C22×D4—151no—
654C22×D4—151no—
655C22×D4—151no—
656C22×D4—151no—
657C22×D4—158no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—151no—
661C22×D4—308no—
662C22×D4—308no—
663C23×C4—31no—
664C23×C4—51no—
665C23×C4—151no—
666C23×C4—151no—
667#123—38no—
668#123—158no—
669#123—158no—
670#123—158no—
671#121—58no—
672#121—158no—
673#121—158no—
674#121—158no—
675#120—158no—
676#120—158no—
677#120—158no—
678#120—158no—
679C2×C4⋊C4—31no—
680C2×C4⋊C4—31no—
681C2×C4⋊C4—51no—
682C2×C4⋊C4—151no—
683C2×C22⋊C4—31no—
684C2×C22⋊C4—31no—
685C2×C22⋊C4—51no—
686C2×C22⋊C4—158no—
687C2×C22⋊C4—151no—
688C2×C22⋊C4—151no—
689C2×C22⋊C4—151no—
690C2×C22⋊C4—151no—
691C2×C22⋊C4—151no—
692C2×C22⋊C4—151no—
693C2×C22⋊C4—151no—
694C2×C22⋊C4—151no—
695C2×C22⋊C4D3×D511yescharacteristic, complemented
696C2×C3×C5—42no—
697C2×C3×C5#53414yescomplemented
698C2×C3×C5C23×D411yescharacteristic
699C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
700C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
701D15—24no—
702D15—42no—
703D15—42no—
704C3×D5—24no—
705C3×D5—42no—
706C5×D3—24no—
707C23×C3—22no—
708C23×C3—22no—
709C23×C3—22no—
710C23×C3—54no—
711C23×C3—52no—
712C23×C3—52no—
713C23×C3—102no—
714C23×C3—102no—
715C23×C3—102no—
716C23×C3—102no—
717C23×C3—102no—
718C23×C3C23×D512yes—
719C23×C3C23×D511yescharacteristic
720C22×D3—22no—
721C22×D3—22no—
722C22×D3—54no—
723C22×D3—52no—
724C22×D3—516no—
725C22×D3—52no—
726C22×D3—52no—
727C22×D3—108no—
728C22×D3—102no—
729C22×D3—102no—
730C22×D3—102no—
731C22×D3—102no—
732C22×D3—102no—
733C22×D3—102no—
734C22×D3—102no—
735C22×D3—102no—
736C22×D3—108no—
737C22×D3—2016no—
738C22×D3—204no—
739C22×D3—204no—
740C22×D3—204no—
741C22×D3—204no—
742C22×D3—2016no—
743C22×D3—204no—
744C22×D3—204no—
745C22×D3—2016no—
746C22×D3D4×D514yes—
747C22×D3C23×D512yes—
748C3×D4—108no—
749C3×D4—108no—
750C3×D4—204no—
751C2×C3×C4—22no—
752C2×C3×C4—22no—
753C2×C3×C4—52no—
754C2×C3×C4—52no—
755C2×C3×C4—102no—
756C2×C3×C4—102no—
757C2×C3×C4—204no—
758C2×C3×C4C23×D512yes—
759C2×C3×C4C23×D512yes—
760#67—28no—
761#67—108no—
762#67—108no—
763#67—108no—
764#67—204no—
765#67—204no—
766C2×Dic3—22no—
767C2×Dic3—22no—
768C2×Dic3—22no—
769C2×Dic3—52no—
770C2×Dic3—102no—
771C2×Dic3—204no—
772C2×Dic3C23×D512yes—
773C2×Dic3C23×D512yes—
774C2×Dic3C23×D512yes—
775D12—108no—
776D12—108no—
777D12—204no—
778C4×D3—28no—
779C4×D3—108no—
780C22×C5—22no—
781C22×C5—22no—
782C22×C5—22no—
783C22×C5—34no—
784C22×C5—44no—
785C22×C5—62no—
786C22×C5—62no—
787C22×C5—68no—
788C22×C5C2×D3×D412yes—
789C22×C5#100412yes—
790C22×C5#100912yes—
791C22×C5C24×D311yescharacteristic
792C2×D5—22no—
793C2×D5—22no—
794C2×D5—28no—
795C2×D5—22no—
796C2×D5—22no—
797C2×D5—22no—
798C2×D5—34no—
799C2×D5—44no—
800C2×D5—62no—
801C2×D5—62no—
802C2×D5—68no—
803C2×D5—62no—
804C2×D5—62no—
805C2×D5—62no—
806C2×D5—62no—
807C2×D5—62no—
808C2×D5—62no—
809C2×D5—1216no—
810C2×D5—1216no—
811C2×D5—1216no—
812C2×D5—124no—
813C2×D5—124no—
814C2×D5C2×D3×D414yes—
815C4×C5—22no—
816C4×C5—22no—
817C4×C5—62no—
818C4×C5—62no—
819C4×C5—62no—
820Dic5—22no—
821Dic5—22no—
822Dic5—62no—
823C24—31no—
824C24—51no—
825C24—51no—
826C24—154no—
827C24—158no—
828C24—154no—
829C24—151no—
830C24—151no—
831C24—151no—
832C24—154no—
833C24—304no—
834C24—304no—
835C24—602no—
836C24—602no—
837C24—602no—
838C24—602no—
839C24—602no—
840C24—602no—
841C24C2×D3×D511yescharacteristic
842C2×D4—34no—
843C2×D4—54no—
844C2×D4—54no—
845C2×D4—54no—
846C2×D4—64no—
847C2×D4—104no—
848C2×D4—104no—
849C2×D4—154no—
850C2×D4—154no—
851C2×D4—154no—
852C2×D4—154no—
853C2×D4—154no—
854C2×D4—154no—
855C2×D4—154no—
856C2×D4—154no—
857C2×D4—202no—
858C2×D4—304no—
859C2×D4—3032no—
860C2×D4—304no—
861C2×D4—304no—
862C2×D4—304no—
863C2×D4—304no—
864C2×D4—3032no—
865C2×D4—602no—
866C2×D4—602no—
867C2×D4—602no—
868C22×C4—31no—
869C22×C4—31no—
870C22×C4—31no—
871C22×C4—34no—
872C22×C4—51no—
873C22×C4—51no—
874C22×C4—54no—
875C22×C4—64no—
876C22×C4—154no—
877C22×C4—154no—
878C22×C4—151no—
879C22×C4—202no—
880C22×C4—304no—
881C22×C4—602no—
882C22×C4C2×D3×D511yescharacteristic
883C22×C4C2×D3×D511yescharacteristic
884C4⋊C4—34no—
885C4⋊C4—34no—
886C4⋊C4—54no—
887C4⋊C4—154no—
888C22⋊C4—34no—
889C22⋊C4—34no—
890C22⋊C4—54no—
891C22⋊C4—154no—
892C22⋊C4—154no—
893C22⋊C4—154no—
894C22⋊C4—154no—
895C22⋊C4—154no—
896C22⋊C4—154no—
897C22⋊C4—154no—
898C22⋊C4—154no—
899C22⋊C4C2×D3×D514yescomplemented
900C3×C5C2×#53411yescharacteristic, complemented, Hall
901C22×C3—22no—
902C22×C3—22no—
903C22×C3—22no—
904C22×C3—44no—
905C22×C3—54no—
906C22×C3—108no—
907C22×C3—102no—
908C22×C3—102no—
909C22×C3—102no—
910C22×C3—102no—
911C22×C3—102no—
912C22×C3—204no—
913C22×C3C2×D4×D512yes—
914C22×C3#414912yes—
915C22×C3#414912yes—
916C22×C3C24×D511yescharacteristic
917C2×D3—28no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—54no—
921C2×D3—108no—
922C2×D3—102no—
923C2×D3—102no—
924C2×D3—102no—
925C2×D3—102no—
926C2×D3—102no—
927C2×D3—102no—
928C2×D3—102no—
929C2×D3—102no—
930C2×D3—2016no—
931C2×D3—2016no—
932C2×D3—2016no—
933C2×D3—204no—
934C2×D3—204no—
935C2×D3C2×D4×D514yes—
936C3×C4—22no—
937C3×C4—22no—
938C3×C4—102no—
939C3×C4—102no—
940Dic3—22no—
941Dic3—22no—
942Dic3—22no—
943Dic3—102no—
944C2×C5—42no—
945C2×C5—64no—
946C2×C5#560514yescomplemented
947C2×C5C22×D3×D411yescharacteristic
948C2×C5C2×#100411yescharacteristic
949C2×C5C2×#100911yescharacteristic
950D5—24no—
951D5—42no—
952D5—64no—
953D5—122no—
954D5—122no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—34no—
959C23—32no—
960C23—54no—
961C23—52no—
962C23—52no—
963C23—62no—
964C23—62no—
965C23—102no—
966C23—102no—
967C23—102no—
968C23—102no—
969C23—102no—
970C23—1516no—
971C23—154no—
972C23—152no—
973C23—152no—
974C23—152no—
975C23—308no—
976C23—308no—
977C23—302no—
978C23—302no—
979C23—302no—
980C23—302no—
981C23—302no—
982C23—302no—
983C23—302no—
984C23—302no—
985C23—604no—
986C23—604no—
987C23—6016no—
988C23—6016no—
989C23—604no—
990C23—604no—
991C23—604no—
992C23—604no—
993C23—6016no—
994C23C22×D3×D512yes—
995C23C22×D3×D511yescharacteristic
996D4—68no—
997D4—108no—
998D4—108no—
999D4—204no—
1000D4—308no—
1001D4—308no—
1002D4—308no—
1003D4—308no—
1004D4—308no—
1005D4—604no—
1006D4—604no—
1007D4—604no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—32no—
1011C2×C4—32no—
1012C2×C4—32no—
1013C2×C4—52no—
1014C2×C4—52no—
1015C2×C4—68no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—62no—
1019C2×C4—102no—
1020C2×C4—102no—
1021C2×C4—152no—
1022C2×C4—204no—
1023C2×C4—308no—
1024C2×C4—302no—
1025C2×C4—604no—
1026C2×C4C22×D3×D512yes—
1027C2×C4C22×D3×D512yes—
1028C2×C3—42no—
1029C2×C3—104no—
1030C2×C3—202no—
1031C2×C3#6598714yescomplemented
1032C2×C3C22×D4×D511yescharacteristic
1033C2×C3C2×#414911yescharacteristic
1034C2×C3C2×#414911yescharacteristic
1035D3—24no—
1036D3—104no—
1037D3—202no—
1038D3—202no—
1039C5C2×#560511yescharacteristic, complemented, Sylow
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—34no—
1044C22—44no—
1045C22—54no—
1046C22—68no—
1047C22—62no—
1048C22—62no—
1049C22—108no—
1050C22—102no—
1051C22—102no—
1052C22—102no—
1053C22—102no—
1054C22—102no—
1055C22—154no—
1056C22—204no—
1057C22—308no—
1058C22—302no—
1059C22—302no—
1060C22—302no—
1061C22—302no—
1062C22—302no—
1063C22—302no—
1064C22—302no—
1065C22—302no—
1066C22—6016no—
1067C22—6016no—
1068C22—6016no—
1069C22—604no—
1070C22—604no—
1071C22#9201912yes—
1072C22D3×D4×D512yes—
1073C22#9202612yes—
1074C22C23×D3×D511yescharacteristic
1075C4—22no—
1076C4—22no—
1077C4—62no—
1078C4—62no—
1079C4—62no—
1080C4—102no—
1081C4—102no—
1082C4—302no—
1083C3C2×#6598711yescharacteristic, complemented, Sylow
1084C2—42no—
1085C2—64no—
1086C2—104no—
1087C2—202no—
1088C2—304no—
1089C2—602no—
1090C2—602no—
1091C2#1175321814yesdirect product factor
1092C2C2×#9201911yescharacteristic
1093C2C2×D3×D4×D511yescharacteristic
1094C2C2×#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×#534
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×D3×D20C2semidirect
3. C2×#91771C2semidirect
4. C2×C5×#883C2semidirect
5. C2×C3×#4030C2semidirect
6. C2×#91577C2semidirect
7. C2×#91572C2semidirect
8. C2×#91550C2semidirect
9. C2×#91476C2semidirect
10. C2×D5×(C2×D3)⋊C4C2semidirect
11. C2×#91450C2semidirect
12. C2×#91433C2semidirect
13. C2×#91409C2semidirect
14. C2×#91356C2semidirect
15. C2×#91351C2semidirect
16. #11753218C2direct (N × H)
18. C24×D15C22semidirect
20. C23×D3×D5C22semidirect
21. C22×#1220C22semidirect
23. C22×D60C22semidirect
25. C22×C4×C5×D3C22semidirect
26. C22×C3×C22⋊D5C22semidirect
27. C22×C3×C22⋊D5C22semidirect
28. C22×C3×D20C22semidirect
29. C22×C3×C4×D5C22semidirect
31. C2×#6790C22semidirect
34. C22×#1202C22semidirect
35. C22×#1202C22semidirect
36. C22×#1202C22semidirect
37. C22×#1200C22semidirect
38. C22×D5×Dic3C22semidirect
40. C2×D3×D20C22semidirect
41. C2×C3×C5×C22⋊C4C22semidirect
42. C2×#6714C22semidirect
43. C2×#6714C22semidirect
44. #91771C22semidirect
45. C2×C5×#217C22semidirect
46. C2×C5×(C2×D3)⋊C4C22semidirect
47. C2×C5×C4⋊Dic3C22semidirect
48. C2×C5×Dic3⋊C4C22semidirect
49. C5×#883C22semidirect
50. C2×C3×#685C22semidirect
51. C2×C3×#683C22semidirect
52. C3×#4030C22semidirect
53. #91577C22semidirect
54. #91572C22semidirect
55. #91550C22semidirect
56. C2×#6669C22semidirect
57. C2×#6667C22semidirect
58. C2×#6667C22semidirect
59. C2×#6667C22semidirect
60. C2×#6667C22semidirect
61. C2×(C2×D3)⋊Dic5C22semidirect
62. C2×#6665C22semidirect
63. #91476C22semidirect
64. D5×(C2×D3)⋊C4C22semidirect
65. #91450C22semidirect
66. #91433C22semidirect
67. #91409C22semidirect
68. #91356C22semidirect
69. #91351C22semidirect
82. C2×#4030D3semidirect
94. C23×D15C23semidirect
103. C22×D3×D5D4semidirect
105. C22×D3×D5C23semidirect
109. C2×#1220C23semidirect
114. C2×D60C23semidirect
121. C2×C4×C5×D3C23semidirect
124. C2×C3×C22⋊D5C23semidirect
125. C2×C3×C22⋊D5C23semidirect
129. C2×C3×D20C23semidirect
131. C2×C3×C4×D5C23semidirect
140. C2×#1202C23semidirect
141. C2×#1202C23semidirect
142. C2×#1202C23semidirect
144. C2×#1200C23semidirect
146. C2×D5×Dic3C23semidirect
148. C3×C5×C22⋊C4C23semidirect
149. #6714C23semidirect
150. #6714C23semidirect
151. C5×#217C23semidirect
152. C5×(C2×D3)⋊C4C23semidirect
153. C5×C4⋊Dic3C23semidirect
154. C5×Dic3⋊C4C23semidirect
155. C3×#685C23semidirect
156. C3×#683C23semidirect
157. #6669C23semidirect
158. #6667C23semidirect
159. #6667C23semidirect
160. #6667C23semidirect
161. #6667C23semidirect
162. (C2×D3)⋊Dic5C23semidirect
163. #6665C23semidirect
177. C2×#883D5semidirect
187. C22×C22⋊D5C2×D3semidirect
188. C22×C22⋊D5C2×D3semidirect
199. C22×D20C2×D3semidirect
202. C22×C4×D5C2×D3semidirect
208. C2×C5×C22⋊C4C2×D3semidirect
219. C2×#685C2×D3semidirect
221. C2×#683C2×D3semidirect
227. #4030C2×D3semidirect
273. C2×D3×D5C2×D4semidirect
328. C22×C4×D3C2×D5semidirect
332. C2×C3×C22⋊C4C2×D5semidirect
334. C2×#217C2×D5semidirect
348. C2×(C2×D3)⋊C4C2×D5semidirect
349. C2×C4⋊Dic3C2×D5semidirect
351. C2×Dic3⋊C4C2×D5semidirect
355. #883C2×D5semidirect
392. C2×C22⋊D5C22×D3semidirect
393. C2×C22⋊D5C22×D3semidirect
412. C2×D20C22×D3semidirect
418. C2×C4×D5C22×D3semidirect
423. C5×C22⋊C4C22×D3semidirect
432. #685C22×D3semidirect
434. #683C22×D3semidirect
554. C2×C4×D3C22×D5semidirect
557. C3×C22⋊C4C22×D5semidirect
559. #217C22×D5semidirect
567. (C2×D3)⋊C4C22×D5semidirect
568. C4⋊Dic3C22×D5semidirect
570. Dic3⋊C4C22×D5semidirect
695. C2×C22⋊C4D3×D5semidirect
697. C2×C3×C5#534semidirect
899. C22⋊C4C2×D3×D5semidirect
900. C3×C5C2×#534semidirect
946. C2×C5#5605semidirect
1031. C2×C3#65987semidirect
1039. C5C2×#5605semidirect
1083. C3C2×#65987semidirect
1091. C2#11753218direct (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×D3×D202
C2×#917712
C2×C5×#8832
C2×C3×#40302
C2×#915772
C2×#915722
C2×#915502
C2×#914762
C2×D5×(C2×D3)⋊C42
C2×#914502
C2×#914332
C2×#914092
C2×#913562
C2×#913512
#117532182
C2×#659873
C2×#56055