Finite Group Databasebeta

← C2×#11753259 #14482596

Subgroups — C2×#11753259 #14482596

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×D3×C22⋊D5C211yesmaximal, characteristic, complemented
2C22×#6768C211yesmaximal, characteristic, complemented
3C2×#91772C211yesmaximal, characteristic, complemented
4C2×C5×#882C211yesmaximal, characteristic, complemented
5C2×C3×#4031C211yesmaximal, characteristic, complemented
6C2×#91565C211yesmaximal, characteristic, complemented
7C2×#91557C211yesmaximal, characteristic, complemented
8C2×D3×C22⋊Dic5C211yesmaximal, characteristic, complemented
9C2×#91475C211yesmaximal, characteristic, complemented
10C2×#91473C211yesmaximal, characteristic, complemented
11C2×#91457C211yesmaximal, characteristic, complemented
12C2×#91453C211yesmaximal, characteristic, complemented
13C2×Dic5×D12C211yesmaximal, characteristic, complemented
14C2×#91410C211yesmaximal, characteristic, complemented
15C2×#91405C211yesmaximal, characteristic, complemented
16#11753259C2116yesmaximal, direct product factor
17C2×#65925—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic, complemented
22C22×C5×#67C2211yescharacteristic, complemented
23C22×C5×D12C2211yescharacteristic
24C22×C5×D12C2211yescharacteristic, complemented
25C22×C3×C22⋊D5C2211yescharacteristic
26C22×C3×Dic10C2211yescharacteristic, complemented
27C2×D3×C22⋊D5—28no—
28C2×D3×C22⋊D5C2218yescomplemented
29C22×#1203C2211yescharacteristic
30C22×#1203C2211yescharacteristic, complemented
31C22×#1201C2211yescharacteristic
32C22×#1201C2211yescharacteristic, complemented
33C22×#1200C2211yescharacteristic, complemented
34C22×D3×Dic5C2211yescharacteristic
35C22×D3×Dic5C2211yescharacteristic, complemented
36C22×D3×Dic5C2211yescharacteristic, complemented
37C22×D3×Dic5C2211yescharacteristic, complemented
38C2×#6768—28no—
39C2×#6768C2218yescomplemented
40C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
41C2×#6719C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic, complemented
43C2×C4⋊Dic15C2211yescharacteristic, complemented
44C2×#6712C2211yescharacteristic, complemented
45#91772C2218yescomplemented
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C5×#882C2218yescomplemented
49C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
50C2×C3×#685C2211yescharacteristic, complemented
51C2×C3×#685C2211yescharacteristic, complemented
52C2×C3×C4×Dic5C2211yescharacteristic, complemented
53C3×#4031C2218yescomplemented
54#91565C2218yescomplemented
55#91557C2218yescomplemented
56D3×C22⋊Dic5C2218yescomplemented
57C2×Dic3⋊Dic5C2211yescharacteristic, complemented
58C2×#6668C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic5C2211yescharacteristic
60C2×(C2×D3)⋊Dic5C2211yescharacteristic
61C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
62C2×#6665C2211yescharacteristic, complemented
63#91475C2218yescomplemented
64#91473C2218yescomplemented
65#91457C2218yescomplemented
66#91453C2218yescomplemented
67Dic5×D12C2218yescomplemented
68#91410C2218yescomplemented
69#91405C2218yescomplemented
70C2×#5676—51nomaximal, Hall
71C23×C22⋊D5—31no—
72C22×#711—31no—
73C2×C5×#120—31no—
74C22×C22⋊Dic5—31no—
75C2×#4085—31no—
76C2×#4085—31no—
77C2×#4084—31no—
78C2×#4083—31no—
79C2×D4×Dic5—31no—
80#65925—316no—
81C2×#4032—31no—
82C2×#4031D311yescharacteristic, complemented
83C2×#4029—31no—
84C2×#4027—31no—
85C2×D5×C22⋊C4—31no—
86C2×#4024—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×C5×D3—24no—
90C23×C5×D3—24no—
91C23×C5×D3—42no—
92C23×C5×D3C2311yescharacteristic
93C23×C5×D3C2314yes—
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
103C2×#1220—24no—
104C2×#1220C2314yes—
105C22×Dic15C2311yescharacteristic
106C22×Dic15C2311yescharacteristic
107C22×Dic15C2311yescharacteristic
108C2×C4×D15—24no—
109C2×C4×D15C2314yescomplemented
110C2×C5×#67—42no—
111C2×C5×#67C2314yescomplemented
112C22×C5×Dic3C2311yescharacteristic
113C2×C5×D12—24no—
114C2×C5×D12—24no—
115C2×C5×D12C2314yes—
116C2×C5×D12C2314yescomplemented
117C2×C3×C22⋊D5—24no—
118C2×C3×C22⋊D5C2314yes—
119C22×C3×Dic5C2311yescharacteristic
120C22×C3×Dic5C2311yescharacteristic
121C22×C3×Dic5C2311yescharacteristic
122C2×C3×Dic10—24no—
123C2×C3×Dic10C2314yescomplemented
124D3×C22⋊D5—232no—
125C2×#1203—24no—
126C2×#1203D418yescomplemented
127C2×#1203C2314yes—
128C2×#1203C2314yescomplemented
129C2×#1201—24no—
130C2×#1201—42no—
131C2×#1201C2314yes—
132C2×#1201C2314yescomplemented
133C2×#1200—42no—
134C2×#1200C2314yescomplemented
135C2×D3×Dic5—24no—
136C2×D3×Dic5—24no—
137C2×D3×Dic5—24no—
138C2×D3×Dic5—42no—
139C2×D3×Dic5C2314yes—
140C2×D3×Dic5C2314yescomplemented
141C2×D3×Dic5C2314yescomplemented
142C2×D3×Dic5C2314yescomplemented
143#6768—232no—
144C3×C5×C22⋊C4C2314yescomplemented
145#6719C2314yescomplemented
146#6714C2314yescomplemented
147C4⋊Dic15C2314yescomplemented
148#6712C2314yescomplemented
149C5×(C2×D3)⋊C4C2314yes—
150C5×(C2×D3)⋊C4C2314yescomplemented
151C3×C22⋊Dic5C2314yescomplemented
152C3×#685C2314yescomplemented
153C3×#685C2314yescomplemented
154C3×C4×Dic5C2314yescomplemented
155Dic3⋊Dic5C2314yescomplemented
156#6668C2314yescomplemented
157(C2×D3)⋊Dic5C2314yes—
158(C2×D3)⋊Dic5C2314yes—
159(C2×D3)⋊Dic5C2314yescomplemented
160#6665C2314yescomplemented
161C22×#239—51no—
162C22×D3×D4—51no—
163C2×C3×#124—51no—
164C2×#946—51no—
165C2×#938—51no—
166#5676—516no—
167C2×#884—51no—
168C2×#884—51no—
169C2×#883—51no—
170C2×#883—51no—
171C2×#882—51no—
172C2×#882D511yescharacteristic, complemented
173C2×D3×C22⋊C4—51no—
174C2×D3×C22⋊C4—51no—
175C2×C4×D12—51no—
176C2×C4×D12—51no—
177C25×C5—31no—
178C24×D5—31no—
179C22×C5×D4—31no—
180C22×C5×D4—31no—
181C22×C5×D4—31no—
182C22×C22⋊D5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C22×C22⋊D5—38no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5—68no—
189C22×C22⋊D5C2×D311yescharacteristic
190C23×Dic5—31no—
191C23×Dic5—31no—
192C23×Dic5—31no—
193C23×Dic5—31no—
194C2×#711—38no—
195C2×#711—68no—
196C22×C4×D5—31no—
197C22×C4×D5—31no—
198C22×Dic10C2×D311yescharacteristic, complemented
199C5×#120—38no—
200C2×C5×C22⋊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⋊Dic5—38no—
208C2×C22⋊Dic5C2×D311yescharacteristic, complemented
209#4085—38no—
210#4085—38no—
211#4084—38no—
212#4083—38no—
213D4×Dic5—38no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685C2×D311yescharacteristic, complemented
217C2×#685C2×D311yescharacteristic, complemented
218C2×C4⋊Dic5—31no—
219C2×C4⋊Dic5—31no—
220C2×#683—31no—
221C2×#683—31no—
222C2×C4×Dic5C2×D311yescharacteristic, complemented
223#4032—38no—
224#4031C2×D318yescomplemented
225#4029—38no—
226#4027—38no—
227D5×C22⋊C4—38no—
228#4024—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×D15C2×D414yes—
238C22×D15C2412yes—
239C22×C5×D3—22no—
240C22×C5×D3—22no—
241C22×C5×D3—22no—
242C22×C5×D3—22no—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3—22no—
246C22×C5×D3—28no—
247C22×C5×D3—28no—
248C22×C5×D3—44no—
249C22×C5×D3—416no—
250C22×C5×D3C2×D414yes—
251C22×C5×D3#4114yescomplemented
252C22×C5×D3C2412yes—
253C22×C5×D3C2412yes—
254C22×C5×D3C2412yes—
255C22×C3×D5—22no—
256C22×C3×D5—22no—
257C22×C3×D5—22no—
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—
268C2×Dic15—22no—
269C2×Dic15—22no—
270C2×Dic15—22no—
271C2×Dic15C2412yes—
272C2×Dic15C2412yes—
273C2×Dic15C2412yes—
274C4×D15—28no—
275C5×#67—44no—
276C2×C5×Dic3—22no—
277C2×C5×Dic3C2412yes—
278C5×D12—28no—
279C5×D12—28no—
280C3×C22⋊D5—28no—
281C2×C3×Dic5—22no—
282C2×C3×Dic5—22no—
283C2×C3×Dic5C2×D414yes—
284C2×C3×Dic5C2412yes—
285C2×C3×Dic5C2412yes—
286C2×C3×Dic5C2412yes—
287C3×Dic10—28no—
288#1203—28no—
289#1203C2×D4116yescomplemented
290#1201—28no—
291#1201—44no—
292#1200—44no—
293D3×Dic5—28no—
294D3×Dic5—28no—
295D3×Dic5—28no—
296D3×Dic5—44no—
297C24×D3—51no—
298C24×D3C2×D511yescharacteristic
299C22×C3×Q8—51no—
300C22×C3×D4—51no—
301C22×#67—51no—
302C22×#67—51no—
303C22×#67—51no—
304C22×#67C2×D511yescharacteristic, complemented
305C2×#239—58no—
306C2×#239—108no—
307C2×D3×D4—58no—
308C2×D3×D4—108no—
309C22×D12—51no—
310C22×D12—51no—
311C22×D12C2×D511yescharacteristic
312C22×D12C2×D511yescharacteristic, complemented
313C22×C4×D3—51no—
314C22×C4×D3—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3—51no—
318C22×C4×D3—51no—
319C3×#124—58no—
320C2×C3×C22⋊C4—51no—
321C2×C3×C22⋊C4—51no—
322C2×C3×C22⋊C4—51no—
323C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
324C2×C3×C42—51no—
325C2×#217—51no—
326C2×#217—51no—
327#946—58no—
328#938—58no—
329C2×(C2×D3)⋊C4—51no—
330C2×(C2×D3)⋊C4—51no—
331C2×(C2×D3)⋊C4—51no—
332C2×(C2×D3)⋊C4—51no—
333C2×(C2×D3)⋊C4C2×D511yescharacteristic
334C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
335C2×C4⋊Dic3—51no—
336C2×C4⋊Dic3—51no—
337C2×Dic3⋊C4—51no—
338C2×Dic3⋊C4—51no—
339#884—58no—
340#884—58no—
341#883—58no—
342#883—58no—
343#882—58no—
344#882C2×D518yescomplemented
345D3×C22⋊C4—58no—
346D3×C22⋊C4—58no—
347C4×D12—58no—
348C4×D12—58no—
349C24×C5—31no—
350C24×C5—31no—
351C24×C5—31no—
352C24×C5—34no—
353C24×C5—64no—
354C24×C5—64no—
355C24×C5—122no—
356C24×C5C22×D311yescharacteristic
357C23×D5—31no—
358C23×D5—34no—
359C23×D5—64no—
360C23×D5—64no—
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—64no—
368C2×C5×D4—122no—
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—38no—
377C2×C22⋊D5—34no—
378C2×C22⋊D5—34no—
379C2×C22⋊D5—64no—
380C2×C22⋊D5—632no—
381C2×C22⋊D5—64no—
382C2×C22⋊D5—64no—
383C2×C22⋊D5—122no—
384C2×C22⋊D5C22×D314yes—
385C22×Dic5—31no—
386C22×Dic5—31no—
387C22×Dic5—31no—
388C22×Dic5—34no—
389C22×Dic5—34no—
390C22×Dic5—34no—
391C22×Dic5—34no—
392C22×Dic5—64no—
393C22×Dic5—64no—
394C22×Dic5—64no—
395C22×Dic5—122no—
396C22×Dic5C22×D311yescharacteristic
397C22×Dic5C22×D311yescharacteristic
398C22×Dic5C22×D311yescharacteristic
399#711—632no—
400C2×C4×D5—34no—
401C2×C4×D5—34no—
402C2×C4×D5—64no—
403C2×C4×D5—122no—
404C2×Dic10—24no—
405C2×Dic10C22×D314yescomplemented
406C5×C22⋊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#685C22×D314yescomplemented
417#685C22×D314yescomplemented
418C4⋊Dic5—34no—
419C4⋊Dic5—34no—
420#683—34no—
421#683—34no—
422C4×Dic5C22×D314yescomplemented
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—51no—
427C2×#123—151no—
428C2×#123—151no—
429C2×C22⋊Q8—151no—
430C2×#121—151no—
431C2×#121—151no—
432C2×#121—151no—
433C2×#120—31no—
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—22no—
449C2×D15—22no—
450C2×D15C22×D414yes—
451C2×C5×D3—28no—
452C2×C5×D3—28no—
453C2×C5×D3—22no—
454C2×C5×D3—22no—
455C2×C5×D3—22no—
456C2×C5×D3—22no—
457C2×C5×D3—22no—
458C2×C5×D3—22no—
459C2×C5×D3—22no—
460C2×C5×D3—416no—
461C2×C5×D3—44no—
462C2×C5×D3C22×D414yes—
463C2×C5×D3C2×#4114yescomplemented
464C2×C3×D5—22no—
465C2×C3×D5—22no—
466C2×C3×D5—22no—
467C2×C3×D5—44no—
468D3×D5—416no—
469C3×C4×C5—22no—
470C3×C4×C5—22no—
471Dic15—22no—
472Dic15—22no—
473Dic15—22no—
474C3×Dic5—22no—
475C3×Dic5—22no—
476C3×Dic5C22×D414yes—
477C5×Dic3—22no—
478C24×C3—51no—
479C24×C3C22×D511yescharacteristic
480C23×D3—24no—
481C23×D3—24no—
482C23×D3—42no—
483C23×D3—51no—
484C23×D3—54no—
485C23×D3—104no—
486C23×D3—104no—
487C23×D3—202no—
488C23×D3C22×D511yescharacteristic
489C23×D3C22×D514yes—
490C23×D3C22×D511yescharacteristic
491C23×D3C22×D511yescharacteristic
492C2×C3×Q8—54no—
493C2×C3×Q8—104no—
494C2×C3×D4—54no—
495C2×C3×D4—104no—
496C22×C3×C4—51no—
497C22×C3×C4—51no—
498C22×C3×C4—51no—
499C22×C3×C4C22×D511yescharacteristic
500C22×C3×C4C22×D511yescharacteristic
501C2×#67—42no—
502C2×#67—54no—
503C2×#67—54no—
504C2×#67—54no—
505C2×#67—104no—
506C2×#67—104no—
507C2×#67—202no—
508C2×#67C22×D514yescomplemented
509C22×Dic3—51no—
510C22×Dic3—51no—
511C22×Dic3—51no—
512C22×Dic3C22×D511yescharacteristic
513#239—1032no—
514D3×D4—1032no—
515C2×D12—24no—
516C2×D12—24no—
517C2×D12—58no—
518C2×D12—54no—
519C2×D12—54no—
520C2×D12—104no—
521C2×D12C22×D514yes—
522C2×D12C22×D514yescomplemented
523C2×C4×D3—54no—
524C2×C4×D3—54no—
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—104no—
533C2×C4×D3—202no—
534C2×C4×D3—202no—
535C3×C22⋊C4—54no—
536C3×C22⋊C4—54no—
537C3×C22⋊C4—54no—
538C3×C22⋊C4C22×D514yescomplemented
539C3×C42—54no—
540#217—54no—
541#217—54no—
542(C2×D3)⋊C4—54no—
543(C2×D3)⋊C4—54no—
544(C2×D3)⋊C4—54no—
545(C2×D3)⋊C4—54no—
546(C2×D3)⋊C4C22×D514yes—
547(C2×D3)⋊C4C22×D514yescomplemented
548C4⋊Dic3—54no—
549C4⋊Dic3—54no—
550Dic3⋊C4—54no—
551Dic3⋊C4—54no—
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—34no—
556C23×C5—34no—
557C23×C5—32no—
558C23×C5—32no—
559C23×C5—32no—
560C23×C5—68no—
561C23×C5—68no—
562C23×C5—62no—
563C23×C5—62no—
564C23×C5—62no—
565C23×C5—62no—
566C23×C5—62no—
567C23×C5—62no—
568C23×C5—62no—
569C23×C5—124no—
570C23×C5—1216no—
571C23×C5C23×D312yes—
572C23×C5C23×D311yescharacteristic
573C22×D5—22no—
574C22×D5—22no—
575C22×D5—22no—
576C22×D5—34no—
577C22×D5—32no—
578C22×D5—68no—
579C22×D5—68no—
580C22×D5—62no—
581C22×D5—62no—
582C22×D5—124no—
583C22×D5—1216no—
584C22×D5C23×D312yes—
585C5×D4—68no—
586C5×D4—68no—
587C5×D4—124no—
588C2×C4×C5—22no—
589C2×C4×C5—22no—
590C2×C4×C5—32no—
591C2×C4×C5—62no—
592C2×C4×C5C23×D312yes—
593C2×C4×C5C23×D312yes—
594C22⋊D5—28no—
595C22⋊D5—316no—
596C22⋊D5—68no—
597C22⋊D5—68no—
598C22⋊D5—68no—
599C22⋊D5—124no—
600C2×Dic5—22no—
601C2×Dic5—22no—
602C2×Dic5—32no—
603C2×Dic5—32no—
604C2×Dic5—32no—
605C2×Dic5—68no—
606C2×Dic5—62no—
607C2×Dic5—62no—
608C2×Dic5—62no—
609C2×Dic5—68no—
610C2×Dic5—68no—
611C2×Dic5—124no—
612C2×Dic5D3×D414yes—
613C2×Dic5C23×D312yes—
614C2×Dic5C23×D312yes—
615C2×Dic5C23×D312yes—
616C4×D5—68no—
617C4×D5—124no—
618Dic10—28no—
619C25—31no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—51no—
624C22×D4—31no—
625C22×D4—31no—
626C22×D4—31no—
627C22×D4—51no—
628C22×D4—151no—
629C22×D4—151no—
630C22×D4—158no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—151no—
634C22×D4—308no—
635C23×C4—151no—
636C23×C4—151no—
637C23×C4—151no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4—151no—
641#124—58no—
642#123—158no—
643#123—158no—
644C22⋊Q8—158no—
645#121—158no—
646#121—158no—
647#121—158no—
648#120—38no—
649#120—158no—
650C4×D4—158no—
651C4×D4—158no—
652C2×C4⋊C4—151no—
653C2×C4⋊C4—151no—
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—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—51no—
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—
677C3×D5—42no—
678C5×D3—24no—
679C5×D3—24no—
680C5×D3—42no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—52no—
685C23×C3—102no—
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—22no—
697C22×D3—28no—
698C22×D3—28no—
699C22×D3—44no—
700C22×D3—416no—
701C22×D3—54no—
702C22×D3—52no—
703C22×D3—108no—
704C22×D3—102no—
705C22×D3—102no—
706C22×D3—108no—
707C22×D3—204no—
708C22×D3—2016no—
709C22×D3D4×D514yes—
710C22×D3#71114yescomplemented
711C22×D3C23×D512yes—
712C22×D3C23×D512yes—
713C22×D3C23×D512yes—
714C3×Q8—108no—
715C3×D4—108no—
716C2×C3×C4—22no—
717C2×C3×C4—22no—
718C2×C3×C4—54no—
719C2×C3×C4—52no—
720C2×C3×C4—52no—
721C2×C3×C4—52no—
722C2×C3×C4—102no—
723C2×C3×C4—102no—
724C2×C3×C4C23×D512yes—
725C2×C3×C4C23×D512yes—
726#67—44no—
727#67—108no—
728#67—108no—
729#67—204no—
730C2×Dic3—22no—
731C2×Dic3—52no—
732C2×Dic3—52no—
733C2×Dic3—52no—
734C2×Dic3—102no—
735C2×Dic3—102no—
736C2×Dic3—102no—
737C2×Dic3C23×D512yes—
738D12—28no—
739D12—28no—
740D12—516no—
741D12—108no—
742C4×D3—108no—
743C4×D3—108no—
744C4×D3—108no—
745C4×D3—108no—
746C4×D3—204no—
747C4×D3—204no—
748C22×C5—22no—
749C22×C5—22no—
750C22×C5—22no—
751C22×C5—34no—
752C22×C5—34no—
753C22×C5—44no—
754C22×C5—68no—
755C22×C5—68no—
756C22×C5—62no—
757C22×C5—62no—
758C22×C5—62no—
759C22×C5—62no—
760C22×C5—62no—
761C22×C5—62no—
762C22×C5—62no—
763C22×C5—1216no—
764C22×C5—124no—
765C22×C5C2×D3×D412yes—
766C22×C5D3×#4112yes—
767C22×C5#100912yes—
768C22×C5C24×D311yescharacteristic
769C2×D5—22no—
770C2×D5—22no—
771C2×D5—22no—
772C2×D5—34no—
773C2×D5—44no—
774C2×D5—68no—
775C2×D5—62no—
776C2×D5—62no—
777C2×D5—1216no—
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—62no—
781Dic5—22no—
782Dic5—22no—
783Dic5—62no—
784Dic5—62no—
785Dic5—62no—
786Dic5C2×D3×D414yes—
787C24—31no—
788C24—31no—
789C24—31no—
790C24—34no—
791C24—51no—
792C24—64no—
793C24—64no—
794C24—122no—
795C24—154no—
796C24—151no—
797C24—304no—
798C24—304no—
799C24—602no—
800C24C2×D3×D511yescharacteristic
801#41—3032no—
802C2×Q8—54no—
803C2×Q8—104no—
804C2×D4—34no—
805C2×D4—34no—
806C2×D4—34no—
807C2×D4—54no—
808C2×D4—64no—
809C2×D4—64no—
810C2×D4—104no—
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—3032no—
820C2×D4—304no—
821C2×D4—304no—
822C2×D4—602no—
823C22×C4—31no—
824C22×C4—51no—
825C22×C4—51no—
826C22×C4—51no—
827C22×C4—154no—
828C22×C4—154no—
829C22×C4—154no—
830C22×C4—154no—
831C22×C4—154no—
832C22×C4—151no—
833C22×C4—151no—
834C22×C4—151no—
835C22×C4—154no—
836C22×C4—304no—
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—154no—
845C4⋊C4—154no—
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—54no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—22no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—44no—
866C22×C3—102no—
867C22×C3—102no—
868C22×C3—102no—
869C22×C3—204no—
870C22×C3C2×D4×D512yes—
871C22×C3C2×#71112yes—
872C22×C3#414412yes—
873C22×C3C24×D511yescharacteristic
874C2×D3—28no—
875C2×D3—28no—
876C2×D3—22no—
877C2×D3—22no—
878C2×D3—22no—
879C2×D3—22no—
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—416no—
884C2×D3—44no—
885C2×D3—54no—
886C2×D3—108no—
887C2×D3—102no—
888C2×D3—102no—
889C2×D3—2016no—
890C2×D3C2×D4×D514yes—
891C2×D3C2×#71114yescomplemented
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—54no—
895C3×C4—102no—
896C3×C4—102no—
897Dic3—22no—
898Dic3—102no—
899Dic3—102no—
900Dic3—102no—
901C2×C5—42no—
902C2×C5—64no—
903C2×C5—64no—
904C2×C5—122no—
905C2×C5#567614yescomplemented
906C2×C5C22×D3×D411yescharacteristic
907C2×C5C2×D3×#4111yescharacteristic
908C2×C5C2×#100911yescharacteristic
909D5—42no—
910D5—64no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—34no—
915C23—34no—
916C23—32no—
917C23—32no—
918C23—32no—
919C23—52no—
920C23—68no—
921C23—68no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—102no—
930C23—102no—
931C23—102no—
932C23—124no—
933C23—1216no—
934C23—154no—
935C23—152no—
936C23—308no—
937C23—308no—
938C23—302no—
939C23—302no—
940C23—604no—
941C23—6016no—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—108no—
945D4—68no—
946D4—68no—
947D4—108no—
948D4—124no—
949D4—1516no—
950D4—308no—
951D4—308no—
952D4—308no—
953D4—604no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—32no—
957C2×C4—54no—
958C2×C4—52no—
959C2×C4—52no—
960C2×C4—52no—
961C2×C4—62no—
962C2×C4—102no—
963C2×C4—102no—
964C2×C4—152no—
965C2×C4—152no—
966C2×C4—152no—
967C2×C4—308no—
968C2×C4—308no—
969C2×C4—308no—
970C2×C4—308no—
971C2×C4—302no—
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—202no—
980C2×C3#6592514yescomplemented
981C2×C3C22×D4×D511yescharacteristic
982C2×C3C22×#71111yescharacteristic
983C2×C3C2×#414411yescharacteristic
984D3—24no—
985D3—24no—
986D3—42no—
987D3—104no—
988C5C2×#567611yescharacteristic, complemented, Sylow
989C22—22no—
990C22—22no—
991C22—22no—
992C22—34no—
993C22—34no—
994C22—44no—
995C22—68no—
996C22—68no—
997C22—62no—
998C22—62no—
999C22—62no—
1000C22—62no—
1001C22—62no—
1002C22—62no—
1003C22—62no—
1004C22—102no—
1005C22—102no—
1006C22—102no—
1007C22—1216no—
1008C22—124no—
1009C22—154no—
1010C22—204no—
1011C22—308no—
1012C22—302no—
1013C22—302no—
1014C22—6016no—
1015C22#9201812yes—
1016C22D3×D4×D512yes—
1017C22D3×#71112yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—54no—
1022C4—62no—
1023C4—102no—
1024C4—102no—
1025C4—302no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6592511yescharacteristic, complemented, Sylow
1029C2—42no—
1030C2—64no—
1031C2—64no—
1032C2—122no—
1033C2—202no—
1034C2—304no—
1035C2#1175325914yesdirect product factor
1036C2C2×#9201811yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×D3×#71111yescharacteristic
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×D3×C22⋊D5C2semidirect
2. C22×#6768C2semidirect
3. C2×#91772C2semidirect
4. C2×C5×#882C2semidirect
5. C2×C3×#4031C2semidirect
6. C2×#91565C2semidirect
7. C2×#91557C2semidirect
8. C2×D3×C22⋊Dic5C2semidirect
9. C2×#91475C2semidirect
10. C2×#91473C2semidirect
11. C2×#91457C2semidirect
12. C2×#91453C2semidirect
13. C2×Dic5×D12C2semidirect
14. C2×#91410C2semidirect
15. C2×#91405C2semidirect
16. #11753259C2direct (N × H)
21. C22×C4×D15C22semidirect
22. C22×C5×#67C22semidirect
24. C22×C5×D12C22semidirect
26. C22×C3×Dic10C22semidirect
28. C2×D3×C22⋊D5C22semidirect
30. C22×#1203C22semidirect
32. C22×#1201C22semidirect
33. C22×#1200C22semidirect
35. C22×D3×Dic5C22semidirect
36. C22×D3×Dic5C22semidirect
37. C22×D3×Dic5C22semidirect
39. C2×#6768C22semidirect
40. C2×C3×C5×C22⋊C4C22semidirect
41. C2×#6719C22semidirect
42. C2×#6714C22semidirect
43. C2×C4⋊Dic15C22semidirect
44. C2×#6712C22semidirect
45. #91772C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C5×#882C22semidirect
49. C2×C3×C22⋊Dic5C22semidirect
50. C2×C3×#685C22semidirect
51. C2×C3×#685C22semidirect
52. C2×C3×C4×Dic5C22semidirect
53. C3×#4031C22semidirect
54. #91565C22semidirect
55. #91557C22semidirect
56. D3×C22⋊Dic5C22semidirect
57. C2×Dic3⋊Dic5C22semidirect
58. C2×#6668C22semidirect
61. C2×(C2×D3)⋊Dic5C22semidirect
62. C2×#6665C22semidirect
63. #91475C22semidirect
64. #91473C22semidirect
65. #91457C22semidirect
66. #91453C22semidirect
67. Dic5×D12C22semidirect
68. #91410C22semidirect
69. #91405C22semidirect
82. C2×#4031D3semidirect
109. C2×C4×D15C23semidirect
111. C2×C5×#67C23semidirect
116. C2×C5×D12C23semidirect
123. C2×C3×Dic10C23semidirect
126. C2×#1203D4semidirect
128. C2×#1203C23semidirect
132. C2×#1201C23semidirect
134. C2×#1200C23semidirect
140. C2×D3×Dic5C23semidirect
141. C2×D3×Dic5C23semidirect
142. C2×D3×Dic5C23semidirect
144. C3×C5×C22⋊C4C23semidirect
145. #6719C23semidirect
146. #6714C23semidirect
147. C4⋊Dic15C23semidirect
148. #6712C23semidirect
150. C5×(C2×D3)⋊C4C23semidirect
151. C3×C22⋊Dic5C23semidirect
152. C3×#685C23semidirect
153. C3×#685C23semidirect
154. C3×C4×Dic5C23semidirect
155. Dic3⋊Dic5C23semidirect
156. #6668C23semidirect
159. (C2×D3)⋊Dic5C23semidirect
160. #6665C23semidirect
172. C2×#882D5semidirect
198. C22×Dic10C2×D3semidirect
202. C2×C5×C22⋊C4C2×D3semidirect
208. C2×C22⋊Dic5C2×D3semidirect
216. C2×#685C2×D3semidirect
217. C2×#685C2×D3semidirect
222. C2×C4×Dic5C2×D3semidirect
224. #4031C2×D3semidirect
251. C22×C5×D3#41semidirect
289. #1203C2×D4semidirect
304. C22×#67C2×D5semidirect
312. C22×D12C2×D5semidirect
323. C2×C3×C22⋊C4C2×D5semidirect
334. C2×(C2×D3)⋊C4C2×D5semidirect
344. #882C2×D5semidirect
405. C2×Dic10C22×D3semidirect
408. C5×C22⋊C4C22×D3semidirect
413. C22⋊Dic5C22×D3semidirect
416. #685C22×D3semidirect
417. #685C22×D3semidirect
422. C4×Dic5C22×D3semidirect
463. C2×C5×D3C2×#41semidirect
508. C2×#67C22×D5semidirect
522. C2×D12C22×D5semidirect
538. C3×C22⋊C4C22×D5semidirect
547. (C2×D3)⋊C4C22×D5semidirect
669. C2×C22⋊C4D3×D5semidirect
672. C2×C3×C5#546semidirect
710. C22×D3#711semidirect
859. C22⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
891. C2×D3C2×#711semidirect
905. C2×C5#5676semidirect
980. C2×C3#65925semidirect
988. C5C2×#5676semidirect
1028. C3C2×#65925semidirect
1035. C2#11753259direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×C22⋊D52
C22×#67682
C2×#917722
C2×C5×#8822
C2×C3×#40312
C2×#915652
C2×#915572
C2×D3×C22⋊Dic52
C2×#914752
C2×#914732
C2×#914572
C2×#914532
C2×Dic5×D122
C2×#914102
C2×#914052
#117532592
C2×#659253
C2×#56765