Finite Group Databasebeta

← #14325991

Subgroups — #14325991

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×D5×D12C211yesmaximal, characteristic
2C2×#91473C211yesmaximal, characteristic, complemented
3C2×D3×#685C211yesmaximal, characteristic, complemented
4C2×C4×#1203C211yesmaximal, characteristic, complemented
5C2×#91405C211yesmaximal, characteristic, complemented
6#11750766C211yesmaximal, characteristic, complemented
7C5×#4665C211yesmaximal, characteristic, complemented
8C3×#64955C211yesmaximal, characteristic, complemented
9#11748940C211yesmaximal, characteristic, complemented
10#11748940C211yesmaximal, characteristic, complemented
11#11748908C211yesmaximal, characteristic, complemented
12#11748908C211yesmaximal, characteristic, complemented
13#11748904C211yesmaximal, characteristic, complemented
14#11748901C211yesmaximal, characteristic, complemented
15#11748738C211yesmaximal, characteristic, complemented
16#10606609—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C23×D3×D5C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic, complemented
21C22×C5×D12C2211yescharacteristic
22C22×C4×C5×D3C2211yescharacteristic, complemented
23C22×C3×C4×D5C2211yescharacteristic
24C22×#1203C2211yescharacteristic
25C22×#1203C2211yescharacteristic
26C22×#1200C2211yescharacteristic, complemented
27C22×D3×Dic5C2211yescharacteristic, complemented
28C2×D5×D12—24no—
29C2×D5×D12—24no—
30C2×D5×D12C418yescomplemented
31C2×#6714C2211yescharacteristic, complemented
32C2×#6714C2211yescharacteristic, complemented
33C2×#6714C2211yescharacteristic, complemented
34C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
37C2×C3×#685C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×C4×Dic5C2211yescharacteristic, complemented
40C2×C3×C4×Dic5C2211yescharacteristic, complemented
41C2×#6668C2211yescharacteristic, complemented
42C2×#6668C2211yescharacteristic, complemented
43C2×#6667C2211yescharacteristic, complemented
44C2×#6667C2211yescharacteristic, complemented
45C2×#6667C2211yescharacteristic, complemented
46C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
47C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
48C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
49C2×#6665C2211yescharacteristic
50C2×#6665C2211yescharacteristic
51#91473—24no—
52D3×#685—24no—
53C4×#1203—24no—
54#91405—24no—
55C3×C5×#95C2211yescharacteristic, complemented
56#91115C2211yescharacteristic, complemented
57C5×C3⋊#95C2211yescharacteristic, complemented
58C3×#3963C2211yescharacteristic, complemented
59C22⋊C4×D12—51nomaximal, Hall
60C22×D4×D5—31no—
61C2×C4×C22⋊D5—31no—
62C22×#685—31no—
63C2×#4027—31no—
64C2×D5×C22⋊C4—31no—
65C5×#386—31no—
66#65509—31no—
67#65246—31no—
68#65246—31no—
69#65244—31no—
70#65244—31no—
71#64956—31no—
72#64955D311yescharacteristic, complemented
73#64954—31no—
74#64954—31no—
75C23×D15C2311yescharacteristic
76C23×D15C2311yescharacteristic
77C23×C5×D3C2311yescharacteristic
78C23×C5×D3C2311yescharacteristic
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
107C2×C5×D12—22no—
108C2×C5×D12—22no—
109C2×C5×D12C2×C414yescomplemented
110C2×C4×C5×D3—22no—
111C2×C4×C5×D3—22no—
112C2×C4×C5×D3—41no—
113C22×C3×Dic5C2311yescharacteristic
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C2×C3×C4×D5—22no—
117C2×C3×C4×D5—22no—
118C2×C3×C4×D5C2×C414yescomplemented
119C2×#1203—22no—
120C2×#1203—22no—
121C2×#1203C2×C414yes—
122C2×#1203C2×C414yescomplemented
123C2×#1203D414yes—
124C2×#1203D414yes—
125C2×#1200—22no—
126C2×#1200—22no—
127C2×#1200—41no—
128C2×D3×Dic5—22no—
129C2×D3×Dic5—22no—
130C2×D3×Dic5—41no—
131D5×D12—232no—
132#6714—22no—
133#6714—22no—
134#6714—41no—
135C5×(C2×D3)⋊C4—22no—
136C5×(C2×D3)⋊C4—22no—
137C5×(C2×D3)⋊C4—41no—
138C3×#685—22no—
139C3×#685D414yescomplemented
140C3×C4×Dic5—22no—
141C3×C4×Dic5—22no—
142#6668—22no—
143#6668—22no—
144#6667—22no—
145#6667—22no—
146#6667—41no—
147(C2×D3)⋊Dic5—22no—
148(C2×D3)⋊Dic5—22no—
149(C2×D3)⋊Dic5—41no—
150#6665—22no—
151#6665—22no—
152C23×D12—51no—
153C2×D3×C22⋊C4—51no—
154C2×D3×C22⋊C4—51no—
155C2×C4×D12—51no—
156C2×C4×D12—51no—
157C3×C4×C22⋊C4—51no—
158#5212—51no—
159#4955—51no—
160#4955—51no—
161#4939—51no—
162#4939—51no—
163#4665—51no—
164#4665—51no—
165#4665—51no—
166#4665D511yescharacteristic, complemented
167C24×D5—31no—
168C24×D5—31no—
169C22×C5×D4—31no—
170C23×C4×C5—31no—
171C22×C22⋊D5—31no—
172C22×C22⋊D5—31no—
173C23×Dic5—31no—
174C2×D4×D5—38no—
175C2×D4×D5—64no—
176C2×D4×D5—64no—
177C22×D20—31no—
178C22×C4×D5—31no—
179C22×C4×D5—31no—
180C22×C4×D5C2×D311yescharacteristic
181C2×C5×C22⋊C4—31no—
182C2×C5×C22⋊C4—31no—
183C2×C5×C22⋊C4—31no—
184C2×C22⋊Dic5—31no—
185C2×C22⋊Dic5—31no—
186C2×C22⋊Dic5—31no—
187C4×C22⋊D5—64no—
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×#685—64no—
197C2×#685C2×D311yescharacteristic
198C2×#685C2×D311yescharacteristic
199C2×#683—31no—
200C2×#683—31no—
201C2×C4×Dic5C2×D311yescharacteristic, complemented
202C2×C4×Dic5C2×D311yescharacteristic, complemented
203#4027—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×D3—21no—
230C22×C5×D3—21no—
231C22×C5×D3—21no—
232C22×C5×D3—21no—
233C22×C5×D3—21no—
234C22×C5×D3—21no—
235C22×C5×D3C22×C412yes—
236C22×C5×D3C22×C412yes—
237C22×C5×D3C2×D412yes—
238C22×C5×D3C2×D412yes—
239C22×C3×D5—21no—
240C22×C3×D5—21no—
241C22×C3×D5—21no—
242C22×C3×D5—21no—
243C22×C3×D5C22×C412yes—
244C22×C3×D5C2×D412yes—
245C22×C3×D5#4112yes—
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×C5C22×C412yes—
268C2×C3×C4×C5C2×D412yescomplemented
269C2×Dic15—21no—
270C2×Dic15—21no—
271C2×Dic15—21no—
272C2×Dic15—21no—
273C2×Dic15—21no—
274C2×Dic15—21no—
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—
283C5×D12—28no—
284C4×C5×D3—44no—
285C2×C3×Dic5—21no—
286C2×C3×Dic5—21no—
287C2×C3×Dic5—21no—
288C2×C3×Dic5—21no—
289C2×C3×Dic5—21no—
290C2×C3×Dic5C22×C412yes—
291C2×C3×Dic5C2×D412yes—
292C2×C3×Dic5C2×D412yes—
293C2×C3×Dic5C2×D412yescomplemented
294C3×C4×D5—28no—
295#1203—28no—
296#1203C22⋊C4116yescomplemented
297#1200—44no—
298D3×Dic5—44no—
299C24×D3—51no—
300C24×D3—51no—
301C23×C3×C4—51no—
302C22×D12—51no—
303C22×D12—51no—
304C22×D12—51no—
305C22×D12—58no—
306C22×D12—104no—
307C22×D12—104no—
308C22×D12C2×D511yescharacteristic
309C22×C4×D3—51no—
310C22×C4×D3—51no—
311C22×C4×D3—51no—
312C22×C4×D3C2×D511yescharacteristic, complemented
313C2×C3×C22⋊C4—51no—
314C2×C3×C22⋊C4—51no—
315C2×C3×C42—51no—
316C2×C3×C42—51no—
317C2×#217—51no—
318C2×#217—51no—
319C2×(C2×D3)⋊C4—51no—
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)⋊C4C2×D511yescharacteristic, complemented
329C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
330C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
331C2×C4⋊Dic3—51no—
332C2×C4⋊Dic3—51no—
333D3×C22⋊C4—104no—
334D3×C22⋊C4—104no—
335C4×D12—104no—
336C4×D12—104no—
337C3×#95—51no—
338C3×#95C2×D511yescharacteristic, complemented
339C3⋊#95—51no—
340C3⋊#95C2×D511yescharacteristic, complemented
341C24×C5—31no—
342C24×C5—31no—
343C23×D5—31no—
344C23×D5—31no—
345C23×D5—34no—
346C23×D5—34no—
347C23×D5—62no—
348C23×D5—62no—
349C23×D5—62no—
350C23×D5—62no—
351C23×D5—62no—
352C23×D5—62no—
353C23×D5—62no—
354C23×D5—62no—
355C23×D5—121no—
356C23×D5—121no—
357C23×D5—121no—
358C23×D5—121no—
359C23×D5C22×D311yescharacteristic
360C2×C5×D4—34no—
361C2×C5×D4—62no—
362C2×C5×D4—62no—
363C22×C4×C5—31no—
364C22×C4×C5—31no—
365C22×C4×C5—62no—
366C22×C4×C5—62no—
367C22×C4×C5—121no—
368C22×C4×C5C22×D311yescharacteristic
369C22×C4×C5C22×D311yescharacteristic
370C22×C4×C5C22×D311yescharacteristic
371C2×C22⋊D5—34no—
372C2×C22⋊D5—34no—
373C2×C22⋊D5—34no—
374C2×C22⋊D5—34no—
375C2×C22⋊D5—62no—
376C2×C22⋊D5—62no—
377C22×Dic5—31no—
378C22×Dic5—31no—
379C22×Dic5—62no—
380C22×Dic5—62no—
381C22×Dic5—121no—
382C22×Dic5C22×D311yescharacteristic
383C22×Dic5C22×D311yescharacteristic
384C22×Dic5C22×D311yescharacteristic
385D4×D5—632no—
386C2×D20—34no—
387C2×D20—62no—
388C2×D20—62no—
389C2×C4×D5—22no—
390C2×C4×D5—22no—
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×D5C4×D314yescomplemented
398C5×C22⋊C4—62no—
399C5×C22⋊C4—62no—
400C5×C22⋊C4—121no—
401C22⋊Dic5—62no—
402C22⋊Dic5—62no—
403C22⋊Dic5—121no—
404#685—22no—
405#685—62no—
406#685—62no—
407#685—62no—
408#685—62no—
409#685—62no—
410#685—62no—
411#685—121no—
412#685—121no—
413#685D1214yescomplemented
414#683—62no—
415#683—62no—
416C4×Dic5—22no—
417C4×Dic5—22no—
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—31no—
426#386—151no—
427#386—151no—
428#386—151no—
429#380—151no—
430#379—151no—
431#379—151no—
432C4×C22⋊C4—51no—
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×D3—22no—
461C2×C5×D3—22no—
462C2×C5×D3—22no—
463C2×C5×D3—41no—
464C2×C5×D3—41no—
465C2×C5×D3—41no—
466C2×C5×D3—41no—
467C2×C5×D3C2×C22⋊C414yescomplemented
468C2×C3×D5—22no—
469C2×C3×D5—22no—
470C2×C3×D5—22no—
471C2×C3×D5—22no—
472C2×C3×D5—22no—
473C2×C3×D5—22no—
474C2×C3×D5C4×D414yescomplemented
475D3×D5—416no—
476D3×D5—416no—
477C3×C4×C5—22no—
478C3×C4×C5—22no—
479C3×C4×C5—41no—
480Dic15—41no—
481Dic15—41no—
482C3×Dic5—22no—
483C3×Dic5—41no—
484C3×Dic5C2×C22⋊C414yescomplemented
485C5×Dic3—41no—
486C5×Dic3—41no—
487C24×C3—51no—
488C23×D3—51no—
489C23×D3—51no—
490C23×D3—54no—
491C23×D3—54no—
492C23×D3—102no—
493C23×D3—102no—
494C23×D3—102no—
495C23×D3—102no—
496C23×D3—102no—
497C23×D3—102no—
498C23×D3—102no—
499C23×D3—102no—
500C23×D3—201no—
501C23×D3—201no—
502C23×D3—201no—
503C23×D3—201no—
504C23×D3C22×D511yescharacteristic
505C23×D3C22×D511yescharacteristic
506C22×C3×C4—51no—
507C22×C3×C4—51no—
508C22×C3×C4—54no—
509C22×C3×C4—51no—
510C22×C3×C4—102no—
511C22×C3×C4—102no—
512C22×C3×C4C22×D511yescharacteristic
513C22×C3×C4C22×D511yescharacteristic
514C22×C3×C4C22×D511yescharacteristic
515C22×Dic3—51no—
516C22×Dic3—51no—
517C22×Dic3C22×D511yescharacteristic
518C22×Dic3C22×D511yescharacteristic
519C2×D12—22no—
520C2×D12—22no—
521C2×D12—54no—
522C2×D12—54no—
523C2×D12—54no—
524C2×D12—54no—
525C2×D12—54no—
526C2×D12—1032no—
527C2×D12—102no—
528C2×D12—102no—
529C2×D12—102no—
530C2×D12—102no—
531C2×D12C4×D514yescomplemented
532C2×C4×D3—22no—
533C2×C4×D3—22no—
534C2×C4×D3—41no—
535C2×C4×D3—102no—
536C2×C4×D3—102no—
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×D3—201no—
544C3×C22⋊C4—54no—
545C3×C22⋊C4—102no—
546C3×C42—102no—
547C3×C42—102no—
548#217—102no—
549#217—102no—
550(C2×D3)⋊C4—22no—
551(C2×D3)⋊C4—22no—
552(C2×D3)⋊C4—41no—
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—102no—
559(C2×D3)⋊C4—201no—
560(C2×D3)⋊C4—201no—
561(C2×D3)⋊C4—201no—
562C4⋊Dic3—102no—
563C4⋊Dic3—102no—
564C23×C5—32no—
565C23×C5—32no—
566C23×C5—32no—
567C23×C5—32no—
568C23×C5—61no—
569C23×C5—61no—
570C23×C5—61no—
571C23×C5—61no—
572C23×C5—61no—
573C23×C5—61no—
574C23×C5—61no—
575C23×C5—61no—
576C23×C5—61no—
577C23×C5—61no—
578C23×C5C23×D311yescharacteristic
579C22×D5—21no—
580C22×D5—21no—
581C22×D5—21no—
582C22×D5—21no—
583C22×D5—32no—
584C22×D5—32no—
585C22×D5—32no—
586C22×D5—32no—
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—68no—
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×D5—124no—
611C22×D5C2×C4×D312yes—
612C22×D5C2×D1212yes—
613C22×D5#23512yes—
614C5×D4—68no—
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—61no—
623C2×C4×C5—61no—
624C2×C4×C5—61no—
625C2×C4×C5—61no—
626C2×C4×C5—61no—
627C2×C4×C5—61no—
628C2×C4×C5—124no—
629C2×C4×C5C2×C4×D312yes—
630C2×C4×C5C2×D1212yescomplemented
631C22⋊D5—316no—
632C22⋊D5—68no—
633C2×Dic5—21no—
634C2×Dic5—21no—
635C2×Dic5—21no—
636C2×Dic5—21no—
637C2×Dic5—21no—
638C2×Dic5—61no—
639C2×Dic5—61no—
640C2×Dic5—61no—
641C2×Dic5—61no—
642C2×Dic5—61no—
643C2×Dic5—61no—
644C2×Dic5—124no—
645C2×Dic5C2×C4×D312yes—
646C2×Dic5C2×D1212yescomplemented
647C2×Dic5D3×D412yes—
648C2×Dic5D3×D412yes—
649D20—68no—
650C4×D5—28no—
651C4×D5—124no—
652C4×D5—124no—
653C25—151no—
654C25—151no—
655C22×D4—31no—
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—151no—
670C2×C4⋊C4—151no—
671C2×C22⋊C4—31no—
672C2×C22⋊C4—31no—
673C2×C22⋊C4—31no—
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—51no—
690C2×C42—51no—
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—
705C5×D3—24no—
706C5×D3—42no—
707C23×C3—52no—
708C23×C3—52no—
709C23×C3—52no—
710C23×C3—101no—
711C23×C3—101no—
712C23×C3—101no—
713C23×C3—101no—
714C23×C3C23×D511yescharacteristic
715C22×D3—21no—
716C22×D3—21no—
717C22×D3—21no—
718C22×D3—21no—
719C22×D3—21no—
720C22×D3—21no—
721C22×D3—21no—
722C22×D3—21no—
723C22×D3—21no—
724C22×D3—21no—
725C22×D3—52no—
726C22×D3—52no—
727C22×D3—52no—
728C22×D3—52no—
729C22×D3—108no—
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—204no—
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×D3C2×C4×D512yes—
754C22×D3C2×C4×D512yes—
755C22×D3D4×D512yes—
756C22×D3D4×D512yes—
757C2×C3×C4—21no—
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—52no—
765C2×C3×C4—52no—
766C2×C3×C4—52no—
767C2×C3×C4—52no—
768C2×C3×C4—108no—
769C2×C3×C4—101no—
770C2×C3×C4—101no—
771C2×C3×C4—101no—
772C2×C3×C4—101no—
773C2×C3×C4—101no—
774C2×C3×C4C2×C4×D512yes—
775C2×C3×C4D4×D512yescomplemented
776C2×Dic3—21no—
777C2×Dic3—21no—
778C2×Dic3—21no—
779C2×Dic3—21no—
780C2×Dic3—21no—
781C2×Dic3—21no—
782C2×Dic3—101no—
783C2×Dic3—101no—
784C2×Dic3—101no—
785C2×Dic3—101no—
786C2×Dic3—101no—
787C2×Dic3—101no—
788D12—28no—
789D12—516no—
790D12—108no—
791D12—108no—
792C4×D3—44no—
793C4×D3—204no—
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×C5—62no—
804C22×C5—62no—
805C22×C5—62no—
806C22×C5—121no—
807C22×C5—121no—
808C22×C5—121no—
809C22×C5—121no—
810C22×C5C22×C4×D311yescharacteristic
811C22×C5C22×D1211yescharacteristic
812C22×C5C2×#23511yescharacteristic
813C22×C5C2×D3×D411yescharacteristic
814C22×C5C2×D3×D411yescharacteristic
815C22×C5#100911yescharacteristic
816C22×C5#100911yescharacteristic
817C2×D5—22no—
818C2×D5—22no—
819C2×D5—22no—
820C2×D5—22no—
821C2×D5—22no—
822C2×D5—22no—
823C2×D5—34no—
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×D5C4×D1214yescomplemented
840C4×C5—22no—
841C4×C5—22no—
842C4×C5—41no—
843C4×C5—121no—
844C4×C5—121no—
845Dic5—22no—
846Dic5—41no—
847Dic5—121no—
848Dic5—121no—
849Dic5D3×C22⋊C414yescomplemented
850C24—31no—
851C24—31no—
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—34no—
870C2×D4—62no—
871C2×D4—62no—
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—31no—
884C22×C4—51no—
885C22×C4—51no—
886C22×C4—54no—
887C22×C4—51no—
888C22×C4—62no—
889C22×C4—62no—
890C22×C4—102no—
891C22×C4—102no—
892C22×C4—121no—
893C22×C4—151no—
894C22×C4—151no—
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—302no—
908C4⋊C4—302no—
909C22⋊C4—54no—
910C22⋊C4—62no—
911C22⋊C4—62no—
912C22⋊C4—102no—
913C22⋊C4—121no—
914C22⋊C4—302no—
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—102no—
926C42—102no—
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×C3C22×C4×D511yescharacteristic
936C22×C3C2×D4×D511yescharacteristic
937C22×C3C2×D4×D511yescharacteristic
938C22×C3C2×D4×D511yescharacteristic
939C22×C3#414411yescharacteristic
940C22×C3D5×#4111yescharacteristic
941C22×C3#414911yescharacteristic
942C2×D3—22no—
943C2×D3—22no—
944C2×D3—22no—
945C2×D3—22no—
946C2×D3—22no—
947C2×D3—22no—
948C2×D3—22no—
949C2×D3—22no—
950C2×D3—22no—
951C2×D3—41no—
952C2×D3—41no—
953C2×D3—41no—
954C2×D3—41no—
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×D3D5×C22⋊C414yescomplemented
972C3×C4—22no—
973C3×C4—22no—
974C3×C4—41no—
975C3×C4—54no—
976C3×C4—102no—
977C3×C4—201no—
978Dic3—41no—
979Dic3—41no—
980Dic3—201no—
981Dic3—201no—
982C2×C5—64no—
983C2×C5—122no—
984C2×C5C2×C4×D1211yescharacteristic
985C2×C5C2×D3×C22⋊C411yescharacteristic
986C2×C5#552111yescharacteristic
987C2×C5D4×D1211yescharacteristic
988C2×C5D4×D1211yescharacteristic
989C2×C5#555011yescharacteristic
990C2×C5#555011yescharacteristic
991D5—24no—
992D5—64no—
993D5—122no—
994C23—32no—
995C23—32no—
996C23—32no—
997C23—32no—
998C23—52no—
999C23—52no—
1000C23—52no—
1001C23—61no—
1002C23—61no—
1003C23—61no—
1004C23—61no—
1005C23—61no—
1006C23—61no—
1007C23—61no—
1008C23—61no—
1009C23—61no—
1010C23—61no—
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—68no—
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—52no—
1056C2×C4—52no—
1057C2×C4—52no—
1058C2×C4—52no—
1059C2×C4—61no—
1060C2×C4—61no—
1061C2×C4—61no—
1062C2×C4—61no—
1063C2×C4—61no—
1064C2×C4—61no—
1065C2×C4—108no—
1066C2×C4—101no—
1067C2×C4—101no—
1068C2×C4—101no—
1069C2×C4—101no—
1070C2×C4—101no—
1071C2×C4—124no—
1072C2×C4—301no—
1073C2×C4—301no—
1074C2×C4—301no—
1075C2×C4—301no—
1076C2×C4—301no—
1077C2×C4—301no—
1078C2×C4—604no—
1079C2×C4—604no—
1080C2×C4—604no—
1081C2×C4C4×D3×D512yes—
1082C2×C4D5×D1212yescomplemented
1083C2×C3—104no—
1084C2×C3C2×D5×C22⋊C411yescharacteristic
1085C2×C3C4×D4×D511yescharacteristic
1086C2×C3#6587911yescharacteristic
1087C2×C3#6592411yescharacteristic
1088C2×C3#6594311yescharacteristic
1089C2×C3#6594411yescharacteristic
1090C2×C3#6598811yescharacteristic
1091D3—24no—
1092D3—42no—
1093D3—104no—
1094D3—202no—
1095C5C22⋊C4×D1211yescharacteristic, complemented, Sylow
1096C22—34no—
1097C22—54no—
1098C22—62no—
1099C22—62no—
1100C22—62no—
1101C22—62no—
1102C22—62no—
1103C22—62no—
1104C22—62no—
1105C22—62no—
1106C22—62no—
1107C22—102no—
1108C22—102no—
1109C22—102no—
1110C22—102no—
1111C22—102no—
1112C22—102no—
1113C22—121no—
1114C22—121no—
1115C22—121no—
1116C22—121no—
1117C22—154no—
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
1134C22C2×D5×D1211yescharacteristic
1135C22D5×#23511yescharacteristic
1136C22D3×D4×D511yescharacteristic
1137C22D3×D4×D511yescharacteristic
1138C22#9202711yescharacteristic
1139C22#9203511yescharacteristic
1140C4—22no—
1141C4—22no—
1142C4—41no—
1143C4—54no—
1144C4—102no—
1145C4—121no—
1146C4—121no—
1147C4—201no—
1148C4—601no—
1149C4—601no—
1150C3#1060660911yescharacteristic, complemented, Sylow
1151C2—64no—
1152C2—104no—
1153C2—122no—
1154C2—304no—
1155C2—602no—
1156C2C4×D5×D1211yescharacteristic
1157C2D3×D5×C22⋊C411yescharacteristic
1158C2#1175325411yescharacteristic
1159C2#1175325711yescharacteristic
1160C2#1175383711yescharacteristic
1161C2#1175386811yescharacteristic
1162C2#1175386911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×D5×D12C2
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×D3×#685C2semidirect
4. C2×C4×#1203C2semidirect
5. C2×#91405C2semidirect
6. #11750766C2semidirect
7. C5×#4665C2semidirect
8. C3×#64955C2semidirect
9. #11748940C2semidirect
10. #11748940C2semidirect
11. #11748908C2semidirect
12. #11748908C2semidirect
13. #11748904C2semidirect
14. #11748901C2semidirect
15. #11748738C2semidirect
20. C22×C4×D15C22semidirect
22. C22×C4×C5×D3C22semidirect
26. C22×#1200C22semidirect
27. C22×D3×Dic5C22semidirect
30. C2×D5×D12C4semidirect
31. C2×#6714C22semidirect
32. C2×#6714C22semidirect
33. C2×#6714C22semidirect
34. C2×C5×(C2×D3)⋊C4C22semidirect
35. C2×C5×(C2×D3)⋊C4C22semidirect
36. C2×C5×(C2×D3)⋊C4C22semidirect
39. C2×C3×C4×Dic5C22semidirect
40. C2×C3×C4×Dic5C22semidirect
41. C2×#6668C22semidirect
42. C2×#6668C22semidirect
43. C2×#6667C22semidirect
44. C2×#6667C22semidirect
45. C2×#6667C22semidirect
46. C2×(C2×D3)⋊Dic5C22semidirect
47. C2×(C2×D3)⋊Dic5C22semidirect
48. C2×(C2×D3)⋊Dic5C22semidirect
55. C3×C5×#95C22semidirect
56. #91115C22semidirect
57. C5×C3⋊#95C22semidirect
58. C3×#3963C22semidirect
72. #64955D3semidirect
92. C22×D3×D5C2×C4semidirect
93. C22×D3×D5C2×C4semidirect
101. C2×D60C2×C4semidirect
109. C2×C5×D12C2×C4semidirect
118. C2×C3×C4×D5C2×C4semidirect
122. C2×#1203C2×C4semidirect
139. C3×#685D4semidirect
166. #4665D5semidirect
201. C2×C4×Dic5C2×D3semidirect
202. C2×C4×Dic5C2×D3semidirect
206. C5×#95C2×D3semidirect
208. #3963C2×D3semidirect
268. C2×C3×C4×C5C2×D4semidirect
293. C2×C3×Dic5C2×D4semidirect
296. #1203C22⋊C4semidirect
312. C22×C4×D3C2×D5semidirect
328. C2×(C2×D3)⋊C4C2×D5semidirect
329. C2×(C2×D3)⋊C4C2×D5semidirect
330. C2×(C2×D3)⋊C4C2×D5semidirect
338. C3×#95C2×D5semidirect
340. C3⋊#95C2×D5semidirect
397. C2×C4×D5C4×D3semidirect
413. #685D12semidirect
453. C2×D15C2×C22⋊C4semidirect
467. C2×C5×D3C2×C22⋊C4semidirect
474. C2×C3×D5C4×D4semidirect
484. C3×Dic5C2×C22⋊C4semidirect
531. C2×D12C4×D5semidirect
630. C2×C4×C5C2×D12semidirect
646. C2×Dic5C2×D12semidirect
694. #95D3×D5semidirect
775. C2×C3×C4D4×D5semidirect
839. C2×D5C4×D12semidirect
849. Dic5D3×C22⋊C4semidirect
927. C3×C5D4×C22⋊C4semidirect
971. C2×D3D5×C22⋊C4semidirect
1082. C2×C4D5×D12semidirect
1095. C5C22⋊C4×D12semidirect
1150. C3#10606609semidirect

Maximal subgroups

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

subgroupindex
C22×D5×D122
C2×#914732
C2×D3×#6852
C2×C4×#12032
C2×#914052
#117507662
C5×#46652
C3×#649552
#117489402
#117489082
#117489042
#117489012
#117487382
#106066093
C22⋊C4×D125