Finite Group Databasebeta

← #14325989

Subgroups — #14325989

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×#6777C211yesmaximal, characteristic
2C2×D3×#685C211yesmaximal, characteristic, complemented
3C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×#91441C211yesmaximal, characteristic, complemented
5C2×#91440C211yesmaximal, characteristic, complemented
6#11750768C211yesmaximal, characteristic, complemented
7C5×#4665C211yesmaximal, characteristic, complemented
8C3×#64954C211yesmaximal, characteristic, complemented
9#11748940C211yesmaximal, characteristic, complemented
10#11748940C211yesmaximal, characteristic, complemented
11#11748916C211yesmaximal, characteristic, complemented
12#11748916C211yesmaximal, characteristic, complemented
13#11748901C211yesmaximal, characteristic, complemented
14#11748896C211yesmaximal, characteristic, complemented
15#11748670C211yesmaximal, characteristic, complemented
16#10606609—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C23×D3×D5C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C5×D12C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic, complemented
22C22×C3×D20C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic, complemented
24C22×#1201C2211yescharacteristic
25C22×#1201C2211yescharacteristic
26C22×D3×Dic5C2211yescharacteristic, complemented
27C22×D5×Dic3C2211yescharacteristic, complemented
28C2×#6777—24no—
29C2×#6777—24no—
30C2×#6777C418yescomplemented
31C2×#6714C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6712C2211yescharacteristic, complemented
34C2×#6712C2211yescharacteristic, complemented
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
38C2×C3×#685C2211yescharacteristic, complemented
39C2×C3×#685C2211yescharacteristic, complemented
40C2×C3×#685C2211yescharacteristic, complemented
41C2×#6667C2211yescharacteristic
42C2×#6667C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
44C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
45C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
46C2×#6665C2211yescharacteristic, complemented
47C2×#6665C2211yescharacteristic, complemented
48C2×#6665C2211yescharacteristic, complemented
49C2×Dic3×Dic5C2211yescharacteristic, complemented
50C2×Dic3×Dic5C2211yescharacteristic, complemented
51D3×#685—24no—
52D5×(C2×D3)⋊C4—24no—
53#91441—24no—
54#91440—24no—
55C3×C5×#95C2211yescharacteristic, complemented
56#91115C2211yescharacteristic, complemented
57C5×C3⋊#95C2211yescharacteristic, complemented
58C3×#3963C2211yescharacteristic, complemented
59#74878—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#64955—31no—
73#64954—31no—
74#64954D311yescharacteristic, complemented
75C23×D15C2311yescharacteristic
76C23×C5×D3C2311yescharacteristic
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
99C22×Dic15C2311yescharacteristic
100C2×C4×D15—22no—
101C2×C4×D15—22no—
102C2×C4×D15C2×C414yescomplemented
103C22×C5×Dic3C2311yescharacteristic
104C22×C5×Dic3C2311yescharacteristic
105C2×C5×D12—22no—
106C2×C5×D12—22no—
107C2×C5×D12C2×C414yescomplemented
108C2×C4×C5×D3—22no—
109C2×C4×C5×D3—22no—
110C2×C4×C5×D3—41no—
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×#1201—22no—
120C2×#1201—22no—
121C2×#1201C2×C414yes—
122C2×#1201C2×C414yescomplemented
123C2×#1201D414yes—
124C2×#1201D414yes—
125C2×D3×Dic5—22no—
126C2×D3×Dic5—22no—
127C2×D3×Dic5—41no—
128C2×D5×Dic3—22no—
129C2×D5×Dic3—22no—
130C2×D5×Dic3—41no—
131#6777—232no—
132#6714—22no—
133#6714—22no—
134#6712—22no—
135#6712—22no—
136C5×(C2×D3)⋊C4—22no—
137C5×(C2×D3)⋊C4—22no—
138C5×(C2×D3)⋊C4—41no—
139C3×#685—22no—
140C3×#685—22no—
141C3×#685—41no—
142#6667—22no—
143#6667D414yescomplemented
144(C2×D3)⋊Dic5—22no—
145(C2×D3)⋊Dic5—22no—
146(C2×D3)⋊Dic5—41no—
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#4667—51no—
164#4666—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×D20C2×D311yescharacteristic
178C22×C4×D5—31no—
179C22×C4×D5—31no—
180C22×C4×D5C2×D311yescharacteristic, complemented
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—64no—
196C2×#685C2×D311yescharacteristic, complemented
197C2×#685C2×D311yescharacteristic, complemented
198C2×#685C2×D311yescharacteristic, complemented
199C2×#683—31no—
200C2×#683—31no—
201C2×C4×Dic5—31no—
202C2×C4×Dic5—31no—
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×D15C22×C412yes—
216C22×D15C2×D412yes—
217C22×D15#4112yes—
218C22×C5×D3—21no—
219C22×C5×D3—21no—
220C22×C5×D3—21no—
221C22×C5×D3—21no—
222C22×C5×D3—21no—
223C22×C5×D3—21no—
224C22×C5×D3—21no—
225C22×C5×D3—21no—
226C22×C5×D3—21no—
227C22×C5×D3—21no—
228C22×C5×D3C22×C412yes—
229C22×C5×D3C22×C412yes—
230C22×C5×D3C2×D412yes—
231C22×C5×D3C2×D412yes—
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×Dic15—21no—
275C2×Dic15C22×C412yes—
276C2×Dic15C2×D412yes—
277C2×Dic15C2×D412yes—
278C4×D15—28no—
279C2×C5×Dic3—21no—
280C2×C5×Dic3—21no—
281C2×C5×Dic3—21no—
282C2×C5×Dic3—21no—
283C2×C5×Dic3—21no—
284C2×C5×Dic3C2×D412yescomplemented
285C5×D12—28no—
286C4×C5×D3—44no—
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#1201—28no—
296#1201C22⋊C4116yescomplemented
297D3×Dic5—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×D12C2×D511yescharacteristic
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×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—104no—
328C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
329C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
330C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
331C2×Dic3⋊C4—51no—
332C2×Dic3⋊C4—51no—
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—
342C24×C5—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
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—31no—
380C22×Dic5—62no—
381C22×Dic5—62no—
382C22×Dic5—121no—
383C22×Dic5C22×D311yescharacteristic
384C22×Dic5C22×D311yescharacteristic
385D4×D5—632no—
386C2×D20—22no—
387C2×D20—22no—
388C2×D20C4×D314yescomplemented
389C2×C4×D5—22no—
390C2×C4×D5—22no—
391C2×C4×D5—34no—
392C2×C4×D5—41no—
393C2×C4×D5—62no—
394C2×C4×D5—62no—
395C2×C4×D5—62no—
396C2×C4×D5—62no—
397C2×C4×D5—121no—
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—22no—
406#685—34no—
407#685—41no—
408#685—62no—
409#685—62no—
410#685—62no—
411#685—62no—
412#685—62no—
413#685—121no—
414#683—62no—
415#683—62no—
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—31no—
426#386—51no—
427#386—151no—
428#386—151no—
429#380—151no—
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×D15C4×D414yescomplemented
447C2×C5×D3—22no—
448C2×C5×D3—22no—
449C2×C5×D3—22no—
450C2×C5×D3—22no—
451C2×C5×D3—22no—
452C2×C5×D3—22no—
453C2×C5×D3—22no—
454C2×C5×D3—22no—
455C2×C5×D3—22no—
456C2×C5×D3—41no—
457C2×C5×D3—41no—
458C2×C5×D3—41no—
459C2×C5×D3—41no—
460C2×C5×D3C2×C22⋊C414yescomplemented
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—41no—
481Dic15—41no—
482Dic15C2×C22⋊C414yescomplemented
483C3×Dic5—22no—
484C3×Dic5—41no—
485C5×Dic3—22no—
486C5×Dic3—41no—
487C24×C3—51no—
488C24×C3—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
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—51no—
526C22×Dic3—102no—
527C22×Dic3—102no—
528C22×Dic3—201no—
529C22×Dic3C22×D511yescharacteristic
530C22×Dic3C22×D511yescharacteristic
531D3×D4—1032no—
532C2×D12—22no—
533C2×D12—22no—
534C2×D12C4×D514yescomplemented
535C2×C4×D3—22no—
536C2×C4×D3—22no—
537C2×C4×D3—41no—
538C2×C4×D3—54no—
539C2×C4×D3—102no—
540C2×C4×D3—102no—
541C2×C4×D3—102no—
542C2×C4×D3—102no—
543C2×C4×D3—201no—
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—41no—
553(C2×D3)⋊C4—54no—
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—
560Dic3⋊C4—102no—
561Dic3⋊C4—102no—
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—21no—
584C22×D5—21no—
585C22×D5—21no—
586C22×D5—21no—
587C22×D5—21no—
588C22×D5—21no—
589C22×D5—32no—
590C22×D5—32no—
591C22×D5—32no—
592C22×D5—68no—
593C22×D5—68no—
594C22×D5—68no—
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—
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—21no—
623C2×C4×C5—32no—
624C2×C4×C5—61no—
625C2×C4×C5—61no—
626C2×C4×C5—61no—
627C2×C4×C5—61no—
628C2×C4×C5—61no—
629C2×C4×C5—124no—
630C2×C4×C5C2×C4×D312yes—
631C22⋊D5—316no—
632C22⋊D5—68no—
633C2×Dic5—21no—
634C2×Dic5—21no—
635C2×Dic5—21no—
636C2×Dic5—21no—
637C2×Dic5—21no—
638C2×Dic5—32no—
639C2×Dic5—32no—
640C2×Dic5—32no—
641C2×Dic5—61no—
642C2×Dic5—61no—
643C2×Dic5—61no—
644C2×Dic5—61no—
645C2×Dic5—61no—
646C2×Dic5—61no—
647C2×Dic5—124no—
648C2×Dic5D3×D412yescomplemented
649D20—28no—
650C4×D5—44no—
651C4×D5—68no—
652C4×D5—124no—
653C25—151no—
654C25—151no—
655C22×D4—31no—
656C22×D4—51no—
657C22×D4—158no—
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—51no—
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—
703C3×D5—24no—
704C3×D5—42no—
705C5×D3—24no—
706C5×D3—42no—
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—21no—
727C22×D3—21no—
728C22×D3—21no—
729C22×D3—21no—
730C22×D3—21no—
731C22×D3—21no—
732C22×D3—52no—
733C22×D3—52no—
734C22×D3—52no—
735C22×D3—108no—
736C22×D3—108no—
737C22×D3—108no—
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—
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—52no—
782C2×Dic3—52no—
783C2×Dic3—52no—
784C2×Dic3—101no—
785C2×Dic3—101no—
786C2×Dic3—101no—
787C2×Dic3—101no—
788C2×Dic3—101no—
789C2×Dic3—101no—
790C2×Dic3—204no—
791C2×Dic3D4×D512yescomplemented
792D12—28no—
793C4×D3—44no—
794C4×D3—108no—
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×C5C2×D3×D411yescharacteristic
812C22×C5C2×D3×D411yescharacteristic
813C22×C5C2×D3×D411yescharacteristic
814C22×C5#100411yescharacteristic
815C22×C5D3×#4111yescharacteristic
816C22×C5#100911yescharacteristic
817C2×D5—22no—
818C2×D5—22no—
819C2×D5—22no—
820C2×D5—22no—
821C2×D5—22no—
822C2×D5—22no—
823C2×D5—22no—
824C2×D5—22no—
825C2×D5—22no—
826C2×D5—34no—
827C2×D5—41no—
828C2×D5—41no—
829C2×D5—41no—
830C2×D5—41no—
831C2×D5—62no—
832C2×D5—62no—
833C2×D5—62no—
834C2×D5—62no—
835C2×D5—62no—
836C2×D5—62no—
837C2×D5—1216no—
838C2×D5—1216no—
839C2×D5D3×C22⋊C414yescomplemented
840C4×C5—22no—
841C4×C5—41no—
842C4×C5—41no—
843C4×C5—62no—
844C4×C5—121no—
845Dic5—22no—
846Dic5—34no—
847Dic5—41no—
848Dic5—121no—
849Dic5—121no—
850C24—31no—
851C24—31no—
852C24—51no—
853C24—51no—
854C24—154no—
855C24—154no—
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—54no—
871C2×D4—62no—
872C2×D4—62no—
873C2×D4—102no—
874C2×D4—102no—
875C2×D4—154no—
876C2×D4—154no—
877C2×D4—154no—
878C2×D4—154no—
879C2×D4—302no—
880C2×D4—302no—
881C2×D4—3032no—
882C22×C4—31no—
883C22×C4—31no—
884C22×C4—51no—
885C22×C4—51no—
886C22×C4—62no—
887C22×C4—62no—
888C22×C4—102no—
889C22×C4—102no—
890C22×C4—121no—
891C22×C4—151no—
892C22×C4—154no—
893C22×C4—151no—
894C22×C4—151no—
895C22×C4—201no—
896C22×C4—302no—
897C22×C4—302no—
898C22×C4—302no—
899C22×C4—302no—
900C22×C4—302no—
901C22×C4—302no—
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—62no—
910C22⋊C4—62no—
911C22⋊C4—102no—
912C22⋊C4—102no—
913C22⋊C4—121no—
914C22⋊C4—154no—
915C22⋊C4—201no—
916C22⋊C4—302no—
917C22⋊C4—302no—
918C22⋊C4—302no—
919C22⋊C4—302no—
920C22⋊C4—302no—
921C22⋊C4—302no—
922C22⋊C4—302no—
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×C3#414411yescharacteristic
947C22×C3D5×#4111yescharacteristic
948C22×C3#414911yescharacteristic
949C2×D3—22no—
950C2×D3—22no—
951C2×D3—22no—
952C2×D3—22no—
953C2×D3—22no—
954C2×D3—22no—
955C2×D3—22no—
956C2×D3—22no—
957C2×D3—22no—
958C2×D3—41no—
959C2×D3—41no—
960C2×D3—41no—
961C2×D3—41no—
962C2×D3—54no—
963C2×D3—102no—
964C2×D3—102no—
965C2×D3—102no—
966C2×D3—102no—
967C2×D3—102no—
968C2×D3—102no—
969C2×D3—2016no—
970C2×D3—2016no—
971C2×D3D5×C22⋊C414yescomplemented
972C3×C4—22no—
973C3×C4—41no—
974C3×C4—41no—
975C3×C4—102no—
976C3×C4—201no—
977Dic3—22no—
978Dic3—41no—
979Dic3—54no—
980Dic3—201no—
981Dic3—201no—
982C2×C5—64no—
983C2×C5—122no—
984C2×C5C2×D3×C22⋊C411yescharacteristic
985C2×C5C4×D3×D411yescharacteristic
986C2×C5#554511yescharacteristic
987C2×C5#559011yescharacteristic
988C2×C5#560911yescharacteristic
989C2×C5#561011yescharacteristic
990C2×C5#565411yescharacteristic
991D5—24no—
992D5—42no—
993D5—64no—
994C23—32no—
995C23—32no—
996C23—32no—
997C23—32no—
998C23—52no—
999C23—52no—
1000C23—52no—
1001C23—52no—
1002C23—61no—
1003C23—61no—
1004C23—61no—
1005C23—61no—
1006C23—61no—
1007C23—61no—
1008C23—61no—
1009C23—61no—
1010C23—61no—
1011C23—61no—
1012C23—101no—
1013C23—101no—
1014C23—101no—
1015C23—101no—
1016C23—101no—
1017C23—101no—
1018C23—101no—
1019C23—101no—
1020C23—101no—
1021C23—101no—
1022C23—152no—
1023C23—152no—
1024C23—152no—
1025C23—308no—
1026C23—308no—
1027C23—308no—
1028C23—308no—
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—108no—
1046D4—1516no—
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—52no—
1058C2×C4—61no—
1059C2×C4—61no—
1060C2×C4—61no—
1061C2×C4—61no—
1062C2×C4—61no—
1063C2×C4—101no—
1064C2×C4—101no—
1065C2×C4—101no—
1066C2×C4—101no—
1067C2×C4—101no—
1068C2×C4—124no—
1069C2×C4—152no—
1070C2×C4—152no—
1071C2×C4—152no—
1072C2×C4—204no—
1073C2×C4—308no—
1074C2×C4—301no—
1075C2×C4—301no—
1076C2×C4—301no—
1077C2×C4—301no—
1078C2×C4—301no—
1079C2×C4—301no—
1080C2×C4—604no—
1081C2×C4—604no—
1082C2×C4C4×D3×D512yes—
1083C2×C3—104no—
1084C2×C3—202no—
1085C2×C3C2×D5×C22⋊C411yescharacteristic
1086C2×C3C4×D4×D511yescharacteristic
1087C2×C3#6587911yescharacteristic
1088C2×C3#6592411yescharacteristic
1089C2×C3#6594311yescharacteristic
1090C2×C3#6594411yescharacteristic
1091C2×C3#6598811yescharacteristic
1092D3—24no—
1093D3—42no—
1094D3—104no—
1095C5#7487811yescharacteristic, 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—102no—
1114C22—102no—
1115C22—102no—
1116C22—121no—
1117C22—121no—
1118C22—121no—
1119C22—121no—
1120C22—154no—
1121C22—201no—
1122C22—201no—
1123C22—201no—
1124C22—201no—
1125C22—302no—
1126C22—302no—
1127C22—302no—
1128C22—302no—
1129C22—302no—
1130C22—302no—
1131C22—6016no—
1132C22—6016no—
1133C22C2×C4×D3×D511yescharacteristic
1134C22#9201711yescharacteristic
1135C22#9201811yescharacteristic
1136C22D3×D4×D511yescharacteristic
1137C22D3×D4×D511yescharacteristic
1138C22D3×D4×D511yescharacteristic
1139C22#9203411yescharacteristic
1140C4—22no—
1141C4—41no—
1142C4—41no—
1143C4—62no—
1144C4—102no—
1145C4—121no—
1146C4—154no—
1147C4—201no—
1148C4—601no—
1149C4—601no—
1150C3#1060660911yescharacteristic, complemented, Sylow
1151C2—64no—
1152C2—104no—
1153C2—122no—
1154C2—202no—
1155C2—304no—
1156C2#1175272911yescharacteristic
1157C2D3×D5×C22⋊C411yescharacteristic
1158C2#1175323011yescharacteristic
1159C2#1175323311yescharacteristic
1160C2#1175384011yescharacteristic
1161C2#1175385511yescharacteristic
1162C2#1175385611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#6777C2
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×D3×#685C2semidirect
3. C2×D5×(C2×D3)⋊C4C2semidirect
4. C2×#91441C2semidirect
5. C2×#91440C2semidirect
6. #11750768C2semidirect
7. C5×#4665C2semidirect
8. C3×#64954C2semidirect
9. #11748940C2semidirect
10. #11748940C2semidirect
11. #11748916C2semidirect
12. #11748916C2semidirect
13. #11748901C2semidirect
14. #11748896C2semidirect
15. #11748670C2semidirect
21. C22×C4×C5×D3C22semidirect
23. C22×C3×C4×D5C22semidirect
26. C22×D3×Dic5C22semidirect
27. C22×D5×Dic3C22semidirect
30. C2×#6777C4semidirect
33. C2×#6712C22semidirect
34. C2×#6712C22semidirect
35. C2×C5×(C2×D3)⋊C4C22semidirect
36. C2×C5×(C2×D3)⋊C4C22semidirect
37. C2×C5×(C2×D3)⋊C4C22semidirect
38. C2×C3×#685C22semidirect
39. C2×C3×#685C22semidirect
40. C2×C3×#685C22semidirect
43. C2×(C2×D3)⋊Dic5C22semidirect
44. C2×(C2×D3)⋊Dic5C22semidirect
45. C2×(C2×D3)⋊Dic5C22semidirect
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
102. C2×C4×D15C2×C4semidirect
107. C2×C5×D12C2×C4semidirect
115. C2×C3×D20C2×C4semidirect
122. C2×#1201C2×C4semidirect
143. #6667D4semidirect
166. #4665D5semidirect
180. C22×C4×D5C2×D3semidirect
196. C2×#685C2×D3semidirect
197. C2×#685C2×D3semidirect
198. C2×#685C2×D3semidirect
206. C5×#95C2×D3semidirect
208. #3963C2×D3semidirect
284. C2×C5×Dic3C2×D4semidirect
292. C2×C3×Dic5C2×D4semidirect
296. #1201C22⋊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
388. C2×D20C4×D3semidirect
446. C2×D15C4×D4semidirect
460. C2×C5×D3C2×C22⋊C4semidirect
474. C2×C3×D5C2×C22⋊C4semidirect
482. Dic15C2×C22⋊C4semidirect
534. C2×D12C4×D5semidirect
648. C2×Dic5D3×D4semidirect
694. #95D3×D5semidirect
791. C2×Dic3D4×D5semidirect
839. C2×D5D3×C22⋊C4semidirect
927. C3×C5D4×C22⋊C4semidirect
971. C2×D3D5×C22⋊C4semidirect
1095. C5#74878semidirect
1150. C3#10606609semidirect

Maximal subgroups

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

subgroupindex
C22×#67772
C2×D3×#6852
C2×D5×(C2×D3)⋊C42
C2×#914412
C2×#914402
#117507682
C5×#46652
C3×#649542
#117489402
#117489162
#117489012
#117488962
#117486702
#106066093
#748785