Finite Group Databasebeta

← #14325987

Subgroups — #14325987

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D20C211yesmaximal, characteristic
2C2×#91473C211yesmaximal, characteristic, complemented
3C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×#91444C211yesmaximal, characteristic, complemented
5C2×#91396C211yesmaximal, characteristic, complemented
6#11750766C211yesmaximal, characteristic, complemented
7C5×#4667C211yesmaximal, characteristic, complemented
8C3×#64954C211yesmaximal, characteristic, complemented
9#11748940C211yesmaximal, characteristic, complemented
10#11748940C211yesmaximal, characteristic, complemented
11#11748913C211yesmaximal, characteristic, complemented
12#11748913C211yesmaximal, characteristic, complemented
13#11748904C211yesmaximal, characteristic, complemented
14#11748896C211yesmaximal, characteristic, complemented
15#11748719C211yesmaximal, characteristic, complemented
16#10605738—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C23×D3×D5C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic, complemented
21C22×C4×C5×D3C2211yescharacteristic
22C22×C3×D20C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic, complemented
24C22×#1202C2211yescharacteristic
25C22×#1202C2211yescharacteristic
26C22×#1200C2211yescharacteristic, complemented
27C22×D5×Dic3C2211yescharacteristic, complemented
28C2×D3×D20—24no—
29C2×D3×D20—24no—
30C2×D3×D20C418yescomplemented
31C2×#6714C2211yescharacteristic, complemented
32C2×#6714C2211yescharacteristic, complemented
33C2×#6714C2211yescharacteristic, complemented
34C2×C5×(C2×D3)⋊C4C2211yescharacteristic
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic
36C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
37C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
38C2×C3×#685C2211yescharacteristic, complemented
39C2×C3×#685C2211yescharacteristic, complemented
40C2×C3×#685C2211yescharacteristic, complemented
41C2×#6667C2211yescharacteristic, complemented
42C2×#6667C2211yescharacteristic, complemented
43C2×#6667C2211yescharacteristic, complemented
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45C2×(C2×D3)⋊Dic5C2211yescharacteristic
46C2×#6665C2211yescharacteristic, complemented
47C2×#6665C2211yescharacteristic, complemented
48C2×#6665C2211yescharacteristic, complemented
49C2×Dic3×Dic5C2211yescharacteristic, complemented
50C2×Dic3×Dic5C2211yescharacteristic, complemented
51#91473—24no—
52D5×(C2×D3)⋊C4—24no—
53#91444—24no—
54#91396—24no—
55C3×C5×#95C2211yescharacteristic, complemented
56#91115C2211yescharacteristic, complemented
57C5×C3⋊#95C2211yescharacteristic, complemented
58C3×#3963C2211yescharacteristic, complemented
59#74878—51nomaximal, Hall
60C23×D20—31no—
61C2×#4039—31no—
62C2×#4039—31no—
63C2×D5×C22⋊C4—31no—
64C2×D5×C22⋊C4—31no—
65C5×#380—31no—
66C4×C22⋊Dic5—31no—
67#65277—31no—
68#65277—31no—
69#65244—31no—
70#65244—31no—
71#64954—31no—
72#64954—31no—
73#64954—31no—
74#64954D311yescharacteristic, complemented
75C23×D15C2311yescharacteristic
76C23×D15C2311yescharacteristic
77C23×C5×D3C2311yescharacteristic
78C23×C3×D5C2311yescharacteristic
79C23×C3×D5C2311yescharacteristic
80C22×D3×D5—22no—
81C22×D3×D5—22no—
82C22×D3×D5—22no—
83C22×D3×D5—22no—
84C22×D3×D5—22no—
85C22×D3×D5—22no—
86C22×D3×D5—22no—
87C22×D3×D5—22no—
88C22×D3×D5—41no—
89C22×D3×D5—41no—
90C22×D3×D5—41no—
91C22×D3×D5—41no—
92C22×D3×D5C2×C414yescomplemented
93C22×D3×D5C2×C414yescomplemented
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C2×D60—22no—
100C2×D60—22no—
101C2×D60C2×C414yescomplemented
102C2×C4×D15—22no—
103C2×C4×D15—22no—
104C2×C4×D15—41no—
105C22×C5×Dic3C2311yescharacteristic
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2311yescharacteristic
108C2×C4×C5×D3—22no—
109C2×C4×C5×D3—22no—
110C2×C4×C5×D3C2×C414yescomplemented
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2311yescharacteristic
113C2×C3×D20—22no—
114C2×C3×D20—22no—
115C2×C3×D20C2×C414yescomplemented
116C2×C3×C4×D5—22no—
117C2×C3×C4×D5—22no—
118C2×C3×C4×D5—41no—
119C2×#1202—22no—
120C2×#1202—22no—
121C2×#1202C2×C414yes—
122C2×#1202C2×C414yescomplemented
123C2×#1202D414yes—
124C2×#1202D414yes—
125C2×#1200—22no—
126C2×#1200—22no—
127C2×#1200—41no—
128C2×D5×Dic3—22no—
129C2×D5×Dic3—22no—
130C2×D5×Dic3—41no—
131D3×D20—232no—
132#6714—22no—
133#6714—22no—
134#6714—41no—
135C5×(C2×D3)⋊C4—22no—
136C5×(C2×D3)⋊C4—22no—
137C5×Dic3⋊C4—22no—
138C5×Dic3⋊C4—22no—
139C3×#685—22no—
140C3×#685—22no—
141C3×#685—41no—
142#6667—22no—
143#6667—22no—
144#6667—41no—
145(C2×D3)⋊Dic5—22no—
146(C2×D3)⋊Dic5D414yescomplemented
147#6665—22no—
148#6665—22no—
149#6665—41no—
150Dic3×Dic5—22no—
151Dic3×Dic5—22no—
152C22×D3×D4—51no—
153C2×C4×#67—51no—
154C22×(C2×D3)⋊C4—51no—
155C2×#67⋊C4—51no—
156C2×D3×C22⋊C4—51no—
157C3×#386—51no—
158#5220—51no—
159#4957—51no—
160#4957—51no—
161#4955—51no—
162#4955—51no—
163#4667D511yescharacteristic, complemented
164#4666—51no—
165#4665—51no—
166#4665—51no—
167C24×D5—31no—
168C24×D5—31no—
169C23×C4×C5—31no—
170C22×D20—31no—
171C22×D20—31no—
172C22×D20—31no—
173C22×D20—38no—
174C22×D20—64no—
175C22×D20—64no—
176C22×D20C2×D311yescharacteristic
177C22×C4×D5—31no—
178C22×C4×D5—31no—
179C22×C4×D5—31no—
180C22×C4×D5C2×D311yescharacteristic, complemented
181C2×C5×C4⋊C4—31no—
182C2×C5×C4⋊C4—31no—
183C2×C5×C22⋊C4—31no—
184C2×C5×C22⋊C4—31no—
185C2×C22⋊Dic5—31no—
186C2×C22⋊Dic5—31no—
187C2×#685—31no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685—31no—
191C2×#685—31no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685C2×D311yescharacteristic, complemented
197C2×#685C2×D311yescharacteristic, complemented
198C2×#685C2×D311yescharacteristic, complemented
199C2×C4×Dic5—31no—
200C2×C4×Dic5—31no—
201#4039—64no—
202#4039—64no—
203D5×C22⋊C4—64no—
204D5×C22⋊C4—64no—
205C5×#95—31no—
206C5×#95C2×D311yescharacteristic, complemented
207#3963—31no—
208#3963C2×D311yescharacteristic, complemented
209D4×C22⋊C4—151noSylow
210C23×C3×C5C2411yescharacteristic
211C22×D15—21no—
212C22×D15—21no—
213C22×D15—21no—
214C22×D15—21no—
215C22×D15—21no—
216C22×D15—21no—
217C22×D15—21no—
218C22×D15—21no—
219C22×D15—21no—
220C22×D15—21no—
221C22×D15C22×C412yes—
222C22×D15C22×C412yes—
223C22×D15C2×D412yes—
224C22×D15C2×D412yes—
225C22×C5×D3—21no—
226C22×C5×D3—21no—
227C22×C5×D3—21no—
228C22×C5×D3—21no—
229C22×C5×D3C22×C412yes—
230C22×C5×D3C2×D412yes—
231C22×C5×D3#4112yes—
232C22×C3×D5—21no—
233C22×C3×D5—21no—
234C22×C3×D5—21no—
235C22×C3×D5—21no—
236C22×C3×D5—21no—
237C22×C3×D5—21no—
238C22×C3×D5—21no—
239C22×C3×D5—21no—
240C22×C3×D5—21no—
241C22×C3×D5—21no—
242C22×C3×D5C22×C412yes—
243C22×C3×D5C22×C412yes—
244C22×C3×D5C2×D412yes—
245C22×C3×D5C2×D412yes—
246C2×D3×D5—28no—
247C2×D3×D5—28no—
248C2×D3×D5—28no—
249C2×D3×D5—28no—
250C2×D3×D5—44no—
251C2×D3×D5—44no—
252C2×D3×D5—44no—
253C2×D3×D5—44no—
254C2×D3×D5—44no—
255C2×D3×D5—44no—
256C2×D3×D5—44no—
257C2×D3×D5—44no—
258C2×D3×D5—44no—
259C2×D3×D5—44no—
260C2×C3×C4×C5—21no—
261C2×C3×C4×C5—21no—
262C2×C3×C4×C5—21no—
263C2×C3×C4×C5—21no—
264C2×C3×C4×C5—21no—
265C2×C3×C4×C5—21no—
266C2×C3×C4×C5—21no—
267C2×C3×C4×C5—21no—
268C2×C3×C4×C5C22×C412yes—
269C2×Dic15—21no—
270C2×Dic15—21no—
271C2×Dic15—21no—
272C2×Dic15—21no—
273C2×Dic15—21no—
274C2×Dic15C2×D412yescomplemented
275D60—28no—
276C4×D15—44no—
277C2×C5×Dic3—21no—
278C2×C5×Dic3—21no—
279C2×C5×Dic3—21no—
280C2×C5×Dic3—21no—
281C2×C5×Dic3—21no—
282C2×C5×Dic3—21no—
283C2×C5×Dic3C22×C412yes—
284C2×C5×Dic3C2×D412yes—
285C2×C5×Dic3C2×D412yes—
286C4×C5×D3—28no—
287C2×C3×Dic5—21no—
288C2×C3×Dic5—21no—
289C2×C3×Dic5—21no—
290C2×C3×Dic5—21no—
291C2×C3×Dic5—21no—
292C2×C3×Dic5C2×D412yescomplemented
293C3×D20—28no—
294C3×C4×D5—44no—
295#1202—28no—
296#1202C22⋊C4116yescomplemented
297#1200—44no—
298D5×Dic3—44no—
299C24×D3—51no—
300C24×D3—51no—
301C22×C3×D4—51no—
302C23×C3×C4—51no—
303C22×#67—51no—
304C22×#67—51no—
305C23×Dic3—51no—
306C2×D3×D4—58no—
307C2×D3×D4—104no—
308C2×D3×D4—104no—
309C22×D12—51no—
310C22×C4×D3—51no—
311C22×C4×D3—51no—
312C22×C4×D3C2×D511yescharacteristic
313C2×C3×C22⋊C4—51no—
314C2×C3×C22⋊C4—51no—
315C2×C3×C22⋊C4—51no—
316C2×#217—51no—
317C2×#217—51no—
318C2×#217—51no—
319C4×#67—104no—
320C2×(C2×D3)⋊C4—51no—
321C2×(C2×D3)⋊C4—51no—
322C2×(C2×D3)⋊C4—51no—
323C2×(C2×D3)⋊C4—51no—
324C2×(C2×D3)⋊C4—51no—
325C2×(C2×D3)⋊C4—51no—
326C2×(C2×D3)⋊C4—51no—
327C2×(C2×D3)⋊C4—51no—
328C2×(C2×D3)⋊C4—104no—
329C2×(C2×D3)⋊C4C2×D511yescharacteristic
330C2×(C2×D3)⋊C4C2×D511yescharacteristic
331C2×Dic3⋊C4C2×D511yescharacteristic, complemented
332C2×Dic3⋊C4C2×D511yescharacteristic, complemented
333C2×C4×Dic3—51no—
334C2×C4×Dic3—51no—
335#67⋊C4—104no—
336D3×C22⋊C4—104no—
337C3×#95—51no—
338C3×#95C2×D511yescharacteristic, complemented
339C3⋊#95—51no—
340C3⋊#95C2×D511yescharacteristic, complemented
341C24×C5—31no—
342C23×D5—31no—
343C23×D5—31no—
344C23×D5—34no—
345C23×D5—34no—
346C23×D5—62no—
347C23×D5—62no—
348C23×D5—62no—
349C23×D5—62no—
350C23×D5—62no—
351C23×D5—62no—
352C23×D5—62no—
353C23×D5—62no—
354C23×D5—121no—
355C23×D5—121no—
356C23×D5—121no—
357C23×D5—121no—
358C23×D5C22×D311yescharacteristic
359C23×D5C22×D311yescharacteristic
360C22×C4×C5—31no—
361C22×C4×C5—34no—
362C22×C4×C5—31no—
363C22×C4×C5—31no—
364C22×C4×C5—62no—
365C22×C4×C5—62no—
366C22×C4×C5C22×D311yescharacteristic
367C22×C4×C5C22×D311yescharacteristic
368C22×C4×C5C22×D311yescharacteristic
369C22×Dic5—31no—
370C22×Dic5—31no—
371C22×Dic5C22×D311yescharacteristic
372C22×Dic5C22×D311yescharacteristic
373C2×D20—22no—
374C2×D20—22no—
375C2×D20—34no—
376C2×D20—34no—
377C2×D20—34no—
378C2×D20—34no—
379C2×D20—34no—
380C2×D20—632no—
381C2×D20—62no—
382C2×D20—62no—
383C2×D20—62no—
384C2×D20—62no—
385C2×D20C4×D314yescomplemented
386C2×C4×D5—22no—
387C2×C4×D5—22no—
388C2×C4×D5—41no—
389C2×C4×D5—62no—
390C2×C4×D5—62no—
391C2×C4×D5—62no—
392C2×C4×D5—62no—
393C2×C4×D5—62no—
394C2×C4×D5—62no—
395C2×C4×D5—121no—
396C2×C4×D5—121no—
397C2×C4×D5—121no—
398C5×C4⋊C4—62no—
399C5×C4⋊C4—62no—
400C5×C22⋊C4—62no—
401C5×C22⋊C4—62no—
402C22⋊Dic5—34no—
403C22⋊Dic5—62no—
404#685—22no—
405#685—22no—
406#685—41no—
407#685—62no—
408#685—62no—
409#685—62no—
410#685—62no—
411#685—62no—
412#685—62no—
413#685—121no—
414#685—121no—
415#685—121no—
416C4×Dic5—62no—
417C4×Dic5—62no—
418C23×D4—151no—
419C2×C4×D4—151no—
420C2×C4×D4—151no—
421C22×C22⋊C4—151no—
422C22×C22⋊C4—151no—
423#390—151no—
424#390—151no—
425#386—51no—
426#386—151no—
427#386—151no—
428#386—151no—
429#380—31no—
430#379—151no—
431#379—151no—
432C4×C22⋊C4—151no—
433C22×C3×C5C23×C411yescharacteristic
434C22×C3×C5C22×D411yescharacteristic
435C22×C3×C5C22×D411yescharacteristic
436C22×C3×C5C22×D411yescharacteristic
437C22×C3×C5C2×#4111yescharacteristic
438C22×C3×C5H(5,𝔽2)11yescharacteristic
439C22×C3×C5H(5,𝔽2)11yescharacteristic
440C2×D15—22no—
441C2×D15—22no—
442C2×D15—22no—
443C2×D15—22no—
444C2×D15—22no—
445C2×D15—22no—
446C2×D15—22no—
447C2×D15—22no—
448C2×D15—22no—
449C2×D15—41no—
450C2×D15—41no—
451C2×D15—41no—
452C2×D15—41no—
453C2×D15C2×C22⋊C414yescomplemented
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×D3C4×D414yescomplemented
461C2×C3×D5—22no—
462C2×C3×D5—22no—
463C2×C3×D5—22no—
464C2×C3×D5—22no—
465C2×C3×D5—22no—
466C2×C3×D5—22no—
467C2×C3×D5—22no—
468C2×C3×D5—22no—
469C2×C3×D5—22no—
470C2×C3×D5—41no—
471C2×C3×D5—41no—
472C2×C3×D5—41no—
473C2×C3×D5—41no—
474C2×C3×D5C2×C22⋊C414yescomplemented
475D3×D5—416no—
476D3×D5—416no—
477C3×C4×C5—22no—
478C3×C4×C5—41no—
479C3×C4×C5—41no—
480Dic15—22no—
481Dic15—41no—
482C3×Dic5—22no—
483C3×Dic5—41no—
484C5×Dic3—41no—
485C5×Dic3—41no—
486C5×Dic3C2×C22⋊C414yescomplemented
487C24×C3—51no—
488C24×C3—51no—
489C23×D3—51no—
490C23×D3—51no—
491C23×D3—54no—
492C23×D3—54no—
493C23×D3—102no—
494C23×D3—102no—
495C23×D3—102no—
496C23×D3—102no—
497C23×D3—102no—
498C23×D3—102no—
499C23×D3—102no—
500C23×D3—102no—
501C23×D3—201no—
502C23×D3—201no—
503C23×D3—201no—
504C23×D3—201no—
505C23×D3C22×D511yescharacteristic
506C2×C3×D4—54no—
507C2×C3×D4—102no—
508C2×C3×D4—102no—
509C22×C3×C4—51no—
510C22×C3×C4—51no—
511C22×C3×C4—102no—
512C22×C3×C4—102no—
513C22×C3×C4—201no—
514C22×C3×C4C22×D511yescharacteristic
515C22×C3×C4C22×D511yescharacteristic
516C22×C3×C4C22×D511yescharacteristic
517C2×#67—54no—
518C2×#67—54no—
519C2×#67—54no—
520C2×#67—54no—
521C2×#67—102no—
522C2×#67—102no—
523C22×Dic3—51no—
524C22×Dic3—51no—
525C22×Dic3—102no—
526C22×Dic3—102no—
527C22×Dic3—201no—
528C22×Dic3C22×D511yescharacteristic
529C22×Dic3C22×D511yescharacteristic
530C22×Dic3C22×D511yescharacteristic
531D3×D4—1032no—
532C2×D12—54no—
533C2×D12—102no—
534C2×D12—102no—
535C2×C4×D3—22no—
536C2×C4×D3—22no—
537C2×C4×D3—102no—
538C2×C4×D3—102no—
539C2×C4×D3—102no—
540C2×C4×D3—102no—
541C2×C4×D3—201no—
542C2×C4×D3—201no—
543C2×C4×D3C4×D514yescomplemented
544C3×C22⋊C4—102no—
545C3×C22⋊C4—102no—
546C3×C22⋊C4—201no—
547#217—102no—
548#217—102no—
549#217—201no—
550(C2×D3)⋊C4—22no—
551(C2×D3)⋊C4—22no—
552(C2×D3)⋊C4—54no—
553(C2×D3)⋊C4—102no—
554(C2×D3)⋊C4—102no—
555(C2×D3)⋊C4—102no—
556(C2×D3)⋊C4—102no—
557(C2×D3)⋊C4—102no—
558(C2×D3)⋊C4—201no—
559(C2×D3)⋊C4—201no—
560Dic3⋊C4—22no—
561Dic3⋊C4—22no—
562C4×Dic3—102no—
563C4×Dic3—102no—
564C23×C5—32no—
565C23×C5—32no—
566C23×C5—32no—
567C23×C5—61no—
568C23×C5—61no—
569C23×C5—61no—
570C23×C5—61no—
571C23×C5C23×D311yescharacteristic
572C22×D5—21no—
573C22×D5—21no—
574C22×D5—21no—
575C22×D5—21no—
576C22×D5—21no—
577C22×D5—21no—
578C22×D5—21no—
579C22×D5—21no—
580C22×D5—21no—
581C22×D5—21no—
582C22×D5—32no—
583C22×D5—32no—
584C22×D5—32no—
585C22×D5—32no—
586C22×D5—68no—
587C22×D5—68no—
588C22×D5—68no—
589C22×D5—61no—
590C22×D5—61no—
591C22×D5—61no—
592C22×D5—61no—
593C22×D5—61no—
594C22×D5—61no—
595C22×D5—61no—
596C22×D5—61no—
597C22×D5—61no—
598C22×D5—61no—
599C22×D5—68no—
600C22×D5—124no—
601C22×D5—124no—
602C22×D5—124no—
603C22×D5—124no—
604C22×D5—124no—
605C22×D5—124no—
606C22×D5—124no—
607C22×D5—124no—
608C22×D5—124no—
609C22×D5—124no—
610C22×D5C2×C4×D312yes—
611C22×D5C2×C4×D312yes—
612C22×D5D3×D412yes—
613C22×D5D3×D412yes—
614C2×C4×C5—21no—
615C2×C4×C5—21no—
616C2×C4×C5—21no—
617C2×C4×C5—21no—
618C2×C4×C5—21no—
619C2×C4×C5—21no—
620C2×C4×C5—21no—
621C2×C4×C5—21no—
622C2×C4×C5—32no—
623C2×C4×C5—32no—
624C2×C4×C5—32no—
625C2×C4×C5—68no—
626C2×C4×C5—61no—
627C2×C4×C5—61no—
628C2×C4×C5—61no—
629C2×C4×C5—61no—
630C2×C4×C5—61no—
631C2×C4×C5—61no—
632C2×C4×C5C2×C4×D312yes—
633C2×Dic5—21no—
634C2×Dic5—21no—
635C2×Dic5—21no—
636C2×Dic5—21no—
637C2×Dic5—21no—
638C2×Dic5—32no—
639C2×Dic5—61no—
640C2×Dic5—61no—
641C2×Dic5—61no—
642C2×Dic5—61no—
643C2×Dic5—61no—
644C2×Dic5D3×D412yescomplemented
645D20—28no—
646D20—316no—
647D20—68no—
648D20—68no—
649C4×D5—44no—
650C4×D5—124no—
651C4×D5—124no—
652C4×D5—124no—
653C25—151no—
654C25—151no—
655C22×D4—51no—
656C22×D4—158no—
657C22×D4—151no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—304no—
661C22×D4—304no—
662C23×C4—31no—
663C23×C4—51no—
664C23×C4—151no—
665C23×C4—151no—
666C23×C4—151no—
667C4×D4—304no—
668C4×D4—304no—
669C2×C4⋊C4—31no—
670C2×C4⋊C4—31no—
671C2×C22⋊C4—31no—
672C2×C22⋊C4—31no—
673C2×C22⋊C4—51no—
674C2×C22⋊C4—51no—
675C2×C22⋊C4—51no—
676C2×C22⋊C4—151no—
677C2×C22⋊C4—151no—
678C2×C22⋊C4—151no—
679C2×C22⋊C4—151no—
680C2×C22⋊C4—151no—
681C2×C22⋊C4—151no—
682C2×C22⋊C4—151no—
683C2×C22⋊C4—151no—
684C2×C22⋊C4—151no—
685C2×C22⋊C4—151no—
686C2×C22⋊C4—151no—
687C2×C22⋊C4—304no—
688C2×C22⋊C4—304no—
689C2×C42—151no—
690C2×C42—151no—
691#95—31no—
692#95—51no—
693#95—151no—
694#95D3×D511yescharacteristic, complemented
695C2×C3×C5C22×C22⋊C411yescharacteristic
696C2×C3×C5C2×C4×D411yescharacteristic
697C2×C3×C5#51811yescharacteristic
698C2×C3×C5D4211yescharacteristic
699C2×C3×C5D4211yescharacteristic
700C2×C3×C5#54611yescharacteristic
701C2×C3×C5#54611yescharacteristic
702D15—24no—
703D15—42no—
704C3×D5—24no—
705C3×D5—42no—
706C5×D3—24no—
707C23×C3—52no—
708C23×C3—52no—
709C23×C3—52no—
710C23×C3—52no—
711C23×C3—101no—
712C23×C3—101no—
713C23×C3—101no—
714C23×C3—101no—
715C23×C3—101no—
716C23×C3—101no—
717C23×C3—101no—
718C23×C3—101no—
719C23×C3—101no—
720C23×C3—101no—
721C23×C3C23×D511yescharacteristic
722C22×D3—21no—
723C22×D3—21no—
724C22×D3—21no—
725C22×D3—21no—
726C22×D3—52no—
727C22×D3—52no—
728C22×D3—52no—
729C22×D3—52no—
730C22×D3—108no—
731C22×D3—108no—
732C22×D3—101no—
733C22×D3—101no—
734C22×D3—101no—
735C22×D3—101no—
736C22×D3—101no—
737C22×D3—101no—
738C22×D3—101no—
739C22×D3—101no—
740C22×D3—101no—
741C22×D3—101no—
742C22×D3—108no—
743C22×D3—108no—
744C22×D3—204no—
745C22×D3—204no—
746C22×D3—204no—
747C22×D3—204no—
748C22×D3—204no—
749C22×D3—204no—
750C22×D3—204no—
751C22×D3—204no—
752C22×D3—204no—
753C22×D3—204no—
754C22×D3C2×C4×D512yes—
755C22×D3D4×D512yes—
756C22×D3#71312yes—
757C3×D4—108no—
758C2×C3×C4—21no—
759C2×C3×C4—21no—
760C2×C3×C4—21no—
761C2×C3×C4—21no—
762C2×C3×C4—21no—
763C2×C3×C4—21no—
764C2×C3×C4—21no—
765C2×C3×C4—21no—
766C2×C3×C4—52no—
767C2×C3×C4—101no—
768C2×C3×C4—101no—
769C2×C3×C4—101no—
770C2×C3×C4—101no—
771C2×C3×C4—101no—
772C2×C3×C4—204no—
773C2×C3×C4C2×C4×D512yes—
774#67—516no—
775#67—108no—
776C2×Dic3—21no—
777C2×Dic3—21no—
778C2×Dic3—21no—
779C2×Dic3—21no—
780C2×Dic3—21no—
781C2×Dic3—21no—
782C2×Dic3—52no—
783C2×Dic3—101no—
784C2×Dic3—101no—
785C2×Dic3—101no—
786C2×Dic3—101no—
787C2×Dic3—101no—
788C2×Dic3—204no—
789C2×Dic3C2×C4×D512yes—
790C2×Dic3D4×D512yes—
791C2×Dic3D4×D512yes—
792D12—108no—
793C4×D3—28no—
794C4×D3—204no—
795C4×D3—204no—
796C22×C5—34no—
797C22×C5—62no—
798C22×C5—62no—
799C22×C5—62no—
800C22×C5—62no—
801C22×C5—62no—
802C22×C5—62no—
803C22×C5C22×C4×D311yescharacteristic
804C22×C5C2×D3×D411yescharacteristic
805C22×C5C2×D3×D411yescharacteristic
806C22×C5C2×D3×D411yescharacteristic
807C22×C5#100411yescharacteristic
808C22×C5D3×#4111yescharacteristic
809C22×C5#100911yescharacteristic
810C2×D5—22no—
811C2×D5—22no—
812C2×D5—22no—
813C2×D5—22no—
814C2×D5—22no—
815C2×D5—22no—
816C2×D5—22no—
817C2×D5—22no—
818C2×D5—22no—
819C2×D5—34no—
820C2×D5—41no—
821C2×D5—41no—
822C2×D5—41no—
823C2×D5—41no—
824C2×D5—62no—
825C2×D5—62no—
826C2×D5—62no—
827C2×D5—62no—
828C2×D5—62no—
829C2×D5—62no—
830C2×D5—62no—
831C2×D5—62no—
832C2×D5—62no—
833C2×D5—1216no—
834C2×D5—1216no—
835C2×D5—121no—
836C2×D5—121no—
837C2×D5—121no—
838C2×D5—121no—
839C2×D5D3×C22⋊C414yescomplemented
840C4×C5—22no—
841C4×C5—34no—
842C4×C5—41no—
843C4×C5—41no—
844C4×C5—121no—
845C4×C5—121no—
846Dic5—22no—
847Dic5—41no—
848Dic5—62no—
849Dic5—121no—
850C24—31no—
851C24—51no—
852C24—51no—
853C24—154no—
854C24—154no—
855C24—151no—
856C24—151no—
857C24—302no—
858C24—302no—
859C24—302no—
860C24—302no—
861C24—302no—
862C24—302no—
863C24—302no—
864C24—302no—
865C24—601no—
866C24—601no—
867C24—601no—
868C24—601no—
869C2×D4—54no—
870C2×D4—102no—
871C2×D4—102no—
872C2×D4—154no—
873C2×D4—154no—
874C2×D4—154no—
875C2×D4—154no—
876C2×D4—154no—
877C2×D4—302no—
878C2×D4—302no—
879C2×D4—302no—
880C2×D4—302no—
881C2×D4—3032no—
882C22×C4—31no—
883C22×C4—34no—
884C22×C4—31no—
885C22×C4—31no—
886C22×C4—51no—
887C22×C4—51no—
888C22×C4—62no—
889C22×C4—62no—
890C22×C4—102no—
891C22×C4—102no—
892C22×C4—151no—
893C22×C4—151no—
894C22×C4—201no—
895C22×C4—302no—
896C22×C4—302no—
897C22×C4—302no—
898C22×C4—302no—
899C22×C4—302no—
900C22×C4—302no—
901C22×C4—601no—
902C22×C4—601no—
903C22×C4—601no—
904C22×C4C2×D3×D511yescharacteristic
905C22×C4C2×D3×D511yescharacteristic
906C22×C4C2×D3×D511yescharacteristic
907C4⋊C4—62no—
908C4⋊C4—62no—
909C22⋊C4—62no—
910C22⋊C4—62no—
911C22⋊C4—102no—
912C22⋊C4—102no—
913C22⋊C4—154no—
914C22⋊C4—201no—
915C22⋊C4—302no—
916C22⋊C4—302no—
917C22⋊C4—302no—
918C22⋊C4—302no—
919C22⋊C4—302no—
920C22⋊C4—302no—
921C22⋊C4—302no—
922C22⋊C4—601no—
923C22⋊C4—601no—
924C22⋊C4—601no—
925C42—302no—
926C42—302no—
927C3×C5D4×C22⋊C411yescharacteristic, complemented, Hall
928C22×C3—54no—
929C22×C3—102no—
930C22×C3—102no—
931C22×C3—102no—
932C22×C3—102no—
933C22×C3—102no—
934C22×C3—102no—
935C22×C3—102no—
936C22×C3—102no—
937C22×C3—102no—
938C22×C3—201no—
939C22×C3—201no—
940C22×C3—201no—
941C22×C3—201no—
942C22×C3C22×C4×D511yescharacteristic
943C22×C3C2×D4×D511yescharacteristic
944C22×C3C2×D4×D511yescharacteristic
945C22×C3C2×D4×D511yescharacteristic
946C22×C3C2×#71311yescharacteristic
947C22×C3#414911yescharacteristic
948C22×C3#414911yescharacteristic
949C2×D3—22no—
950C2×D3—22no—
951C2×D3—22no—
952C2×D3—22no—
953C2×D3—22no—
954C2×D3—22no—
955C2×D3—54no—
956C2×D3—102no—
957C2×D3—102no—
958C2×D3—102no—
959C2×D3—102no—
960C2×D3—102no—
961C2×D3—102no—
962C2×D3—102no—
963C2×D3—102no—
964C2×D3—102no—
965C2×D3—2016no—
966C2×D3—2016no—
967C2×D3—201no—
968C2×D3—201no—
969C2×D3—201no—
970C2×D3—201no—
971C2×D3#403914yescomplemented
972C3×C4—22no—
973C3×C4—41no—
974C3×C4—41no—
975C3×C4—102no—
976C3×C4—201no—
977Dic3—41no—
978Dic3—41no—
979Dic3—102no—
980Dic3—201no—
981Dic3D5×C22⋊C414yescomplemented
982C2×C5—64no—
983C2×C5C2×D3×C22⋊C411yescharacteristic
984C2×C5C4×D3×D411yescharacteristic
985C2×C5#554511yescharacteristic
986C2×C5#559011yescharacteristic
987C2×C5#560911yescharacteristic
988C2×C5#561011yescharacteristic
989C2×C5#565411yescharacteristic
990D5—24no—
991D5—42no—
992D5—64no—
993D5—122no—
994C23—32no—
995C23—32no—
996C23—32no—
997C23—52no—
998C23—52no—
999C23—52no—
1000C23—52no—
1001C23—61no—
1002C23—61no—
1003C23—61no—
1004C23—61no—
1005C23—101no—
1006C23—101no—
1007C23—101no—
1008C23—101no—
1009C23—101no—
1010C23—101no—
1011C23—101no—
1012C23—101no—
1013C23—101no—
1014C23—101no—
1015C23—152no—
1016C23—152no—
1017C23—152no—
1018C23—152no—
1019C23—308no—
1020C23—308no—
1021C23—308no—
1022C23—308no—
1023C23—301no—
1024C23—301no—
1025C23—301no—
1026C23—301no—
1027C23—301no—
1028C23—301no—
1029C23—301no—
1030C23—301no—
1031C23—301no—
1032C23—301no—
1033C23—604no—
1034C23—604no—
1035C23—604no—
1036C23—604no—
1037C23—604no—
1038C23—604no—
1039C23—604no—
1040C23—604no—
1041C23—604no—
1042C23—604no—
1043C23C22×D3×D511yescharacteristic
1044D4—108no—
1045D4—1516no—
1046D4—308no—
1047D4—308no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—32no—
1057C2×C4—32no—
1058C2×C4—32no—
1059C2×C4—52no—
1060C2×C4—68no—
1061C2×C4—61no—
1062C2×C4—61no—
1063C2×C4—61no—
1064C2×C4—61no—
1065C2×C4—61no—
1066C2×C4—61no—
1067C2×C4—101no—
1068C2×C4—101no—
1069C2×C4—101no—
1070C2×C4—101no—
1071C2×C4—101no—
1072C2×C4—152no—
1073C2×C4—204no—
1074C2×C4—301no—
1075C2×C4—301no—
1076C2×C4—301no—
1077C2×C4—301no—
1078C2×C4—301no—
1079C2×C4—604no—
1080C2×C4—604no—
1081C2×C4—604no—
1082C2×C4C4×D3×D512yes—
1083C2×C3—104no—
1084C2×C3—202no—
1085C2×C3C2×D5×C22⋊C411yescharacteristic
1086C2×C3C2×#403911yescharacteristic
1087C2×C3#6585511yescharacteristic
1088C2×C3#6594311yescharacteristic
1089C2×C3#6594311yescharacteristic
1090C2×C3#6596411yescharacteristic
1091C2×C3#6596411yescharacteristic
1092D3—24no—
1093D3—104no—
1094D3—202no—
1095C5#7487811yescharacteristic, complemented, Sylow
1096C22—34no—
1097C22—54no—
1098C22—62no—
1099C22—62no—
1100C22—62no—
1101C22—62no—
1102C22—62no—
1103C22—62no—
1104C22—102no—
1105C22—102no—
1106C22—102no—
1107C22—102no—
1108C22—102no—
1109C22—102no—
1110C22—102no—
1111C22—102no—
1112C22—102no—
1113C22—154no—
1114C22—201no—
1115C22—201no—
1116C22—201no—
1117C22—201no—
1118C22—302no—
1119C22—302no—
1120C22—302no—
1121C22—302no—
1122C22—302no—
1123C22—302no—
1124C22—302no—
1125C22—302no—
1126C22—302no—
1127C22—6016no—
1128C22—6016no—
1129C22—601no—
1130C22—601no—
1131C22—601no—
1132C22—601no—
1133C22C2×C4×D3×D511yescharacteristic
1134C22#9201711yescharacteristic
1135C22#9201911yescharacteristic
1136C22D3×D4×D511yescharacteristic
1137C22D3×D4×D511yescharacteristic
1138C22D3×D4×D511yescharacteristic
1139C22D3×#71311yescharacteristic
1140C4—22no—
1141C4—34no—
1142C4—41no—
1143C4—41no—
1144C4—102no—
1145C4—121no—
1146C4—121no—
1147C4—201no—
1148C4—302no—
1149C4—601no—
1150C3#1060573811yescharacteristic, complemented, Sylow
1151C2—64no—
1152C2—104no—
1153C2—202no—
1154C2—304no—
1155C2—602no—
1156C2#1175272711yescharacteristic
1157C2D3×D5×C22⋊C411yescharacteristic
1158C2#1175323011yescharacteristic
1159C2#1175324211yescharacteristic
1160C2D3×#403911yescharacteristic
1161C2#1175385911yescharacteristic
1162C2#1175386111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×D3×D20C2
hypercenter#95D3×D5
hypocenterC3×C5D4×C22⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#91473C2semidirect
3. C2×D5×(C2×D3)⋊C4C2semidirect
4. C2×#91444C2semidirect
5. C2×#91396C2semidirect
6. #11750766C2semidirect
7. C5×#4667C2semidirect
8. C3×#64954C2semidirect
9. #11748940C2semidirect
10. #11748940C2semidirect
11. #11748913C2semidirect
12. #11748913C2semidirect
13. #11748904C2semidirect
14. #11748896C2semidirect
15. #11748719C2semidirect
20. C22×C4×D15C22semidirect
23. C22×C3×C4×D5C22semidirect
26. C22×#1200C22semidirect
27. C22×D5×Dic3C22semidirect
30. C2×D3×D20C4semidirect
31. C2×#6714C22semidirect
32. C2×#6714C22semidirect
33. C2×#6714C22semidirect
36. C2×C5×Dic3⋊C4C22semidirect
37. C2×C5×Dic3⋊C4C22semidirect
38. C2×C3×#685C22semidirect
39. C2×C3×#685C22semidirect
40. C2×C3×#685C22semidirect
41. C2×#6667C22semidirect
42. C2×#6667C22semidirect
43. C2×#6667C22semidirect
46. C2×#6665C22semidirect
47. C2×#6665C22semidirect
48. C2×#6665C22semidirect
49. C2×Dic3×Dic5C22semidirect
50. C2×Dic3×Dic5C22semidirect
55. C3×C5×#95C22semidirect
56. #91115C22semidirect
57. C5×C3⋊#95C22semidirect
58. C3×#3963C22semidirect
74. #64954D3semidirect
92. C22×D3×D5C2×C4semidirect
93. C22×D3×D5C2×C4semidirect
101. C2×D60C2×C4semidirect
110. C2×C4×C5×D3C2×C4semidirect
115. C2×C3×D20C2×C4semidirect
122. C2×#1202C2×C4semidirect
146. (C2×D3)⋊Dic5D4semidirect
163. #4667D5semidirect
180. C22×C4×D5C2×D3semidirect
196. C2×#685C2×D3semidirect
197. C2×#685C2×D3semidirect
198. C2×#685C2×D3semidirect
206. C5×#95C2×D3semidirect
208. #3963C2×D3semidirect
274. C2×Dic15C2×D4semidirect
292. C2×C3×Dic5C2×D4semidirect
296. #1202C22⋊C4semidirect
331. C2×Dic3⋊C4C2×D5semidirect
332. C2×Dic3⋊C4C2×D5semidirect
338. C3×#95C2×D5semidirect
340. C3⋊#95C2×D5semidirect
385. C2×D20C4×D3semidirect
453. C2×D15C2×C22⋊C4semidirect
460. C2×C5×D3C4×D4semidirect
474. C2×C3×D5C2×C22⋊C4semidirect
486. C5×Dic3C2×C22⋊C4semidirect
543. C2×C4×D3C4×D5semidirect
644. C2×Dic5D3×D4semidirect
694. #95D3×D5semidirect
839. C2×D5D3×C22⋊C4semidirect
927. C3×C5D4×C22⋊C4semidirect
971. C2×D3#4039semidirect
981. Dic3D5×C22⋊C4semidirect
1095. C5#74878semidirect
1150. C3#10605738semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D202
C2×#914732
C2×D5×(C2×D3)⋊C42
C2×#914442
C2×#913962
#117507662
C5×#46672
C3×#649542
#117489402
#117489132
#117489042
#117488962
#117487192
#106057383
#748785