Finite Group Databasebeta

← #14325928

Subgroups — #14325928

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×#67C211yesmaximal, characteristic
2C2×C4×#1220C211yesmaximal, characteristic, complemented
3C22×C3×#685C211yesmaximal, characteristic, complemented
4C2×#91552C211yesmaximal, characteristic, complemented
5C2×#91473C211yesmaximal, characteristic, complemented
6C5×#5213C211yesmaximal, characteristic, complemented
7#11749492C211yesmaximal, characteristic, complemented
8#11749488C211yesmaximal, characteristic, complemented
9#11748940C211yesmaximal, characteristic, complemented
10#11748917C211yesmaximal, characteristic, complemented
11#11748916C211yesmaximal, characteristic, complemented
12#11748915C211yesmaximal, characteristic, complemented
13#11748885C211yesmaximal, characteristic, complemented
14#11748884C211yesmaximal, characteristic, complemented
15#11748700C211yesmaximal, characteristic, complemented
16#10606609—31nomaximal, Hall
17C24×C3×D5C2211yescharacteristic
18C23×D3×D5C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic, complemented
20C22×#1220C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic, complemented
22C22×C5×#67C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic, complemented
24C2×D5×#67—24no—
25C2×D5×#67—24no—
26C2×D5×#67C418yescomplemented
27C22×#1202C2211yescharacteristic
28C22×#1201C2211yescharacteristic
29C22×#1200C2211yescharacteristic, complemented
30C22×D5×Dic3C2211yescharacteristic
31C2×#6719C2211yescharacteristic, complemented
32C4×#1220—24no—
33C2×#6714C2211yescharacteristic, complemented
34C2×#6712C2211yescharacteristic, complemented
35C2×C4×Dic15C2211yescharacteristic, complemented
36C2×C5×#217C2211yescharacteristic, complemented
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C2×C3×#685—24no—
40C2×C3×#685C2211yescharacteristic
41C2×C3×#685C2211yescharacteristic
42C2×C3×#685C2211yescharacteristic, complemented
43C2×C3×#685C2211yescharacteristic, complemented
44#91552—24no—
45C2×#6669C2211yescharacteristic, complemented
46C2×#6667C2211yescharacteristic, complemented
47C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
48C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
49C2×#6665C2211yescharacteristic
50C2×#6665C2211yescharacteristic
51C2×#6665C2211yescharacteristic, complemented
52C2×#6665C2211yescharacteristic, complemented
53C2×Dic3×Dic5C2211yescharacteristic, complemented
54#91473—24no—
55C5×C3⋊#95C2211yescharacteristic, complemented
56C5×C3⋊#95C2211yescharacteristic, complemented
57#90994C2211yescharacteristic, complemented
58#90994C2211yescharacteristic, complemented
59C22⋊C4×#67—51nomaximal, Hall
60C22×D4×D5—31no—
61C2×C4×C22⋊D5—31no—
62C22×#685D311yescharacteristic, complemented
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#64954—31no—
75C24×C3×C5C2311yescharacteristic
76C23×D15C2311yescharacteristic
77C23×C5×D3C2311yescharacteristic
78C23×C3×D5—22no—
79C23×C3×D5—22no—
80C23×C3×D5—22no—
81C23×C3×D5—22no—
82C23×C3×D5—41no—
83C23×C3×D5—41no—
84C23×C3×D5C2×C414yescomplemented
85C23×C3×D5C2311yescharacteristic
86C23×C3×D5C2311yescharacteristic
87C22×D3×D5—22no—
88C22×D3×D5—22no—
89C22×D3×D5—22no—
90C22×D3×D5—22no—
91C22×D3×D5—41no—
92C22×D3×D5—41no—
93C22×D3×D5C2×C414yescomplemented
94C22×C3×C4×C5—22no—
95C22×C3×C4×C5—22no—
96C22×C3×C4×C5—41no—
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2311yescharacteristic
99C2×#1220C2×C414yes—
100C2×#1220D414yes—
101C2×#1220D414yes—
102C22×Dic15C2311yescharacteristic
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C2×C4×D15—22no—
106C2×C4×D15—22no—
107C2×C4×D15—41no—
108C2×C5×#67—22no—
109C2×C5×#67—22no—
110C2×C5×#67C2×C414yescomplemented
111C22×C5×Dic3C2311yescharacteristic
112C22×C5×Dic3C2311yescharacteristic
113C22×C5×Dic3C2311yescharacteristic
114C22×C3×Dic5—22no—
115C22×C3×Dic5—22no—
116C22×C3×Dic5—41no—
117C22×C3×Dic5C2311yescharacteristic
118C22×C3×Dic5C2311yescharacteristic
119D5×#67—232no—
120C2×#1202—22no—
121C2×#1202—22no—
122C2×#1202C2×C414yescomplemented
123C2×#1201—22no—
124C2×#1201—22no—
125C2×#1201C2×C414yescomplemented
126C2×#1200—22no—
127C2×#1200—22no—
128C2×#1200—41no—
129C2×D5×Dic3—22no—
130C2×D5×Dic3—22no—
131C2×D5×Dic3C2×C414yescomplemented
132#6719—22no—
133#6714—22no—
134#6712—22no—
135C4×Dic15—22no—
136C5×#217—22no—
137C5×(C2×D3)⋊C4—22no—
138C5×(C2×D3)⋊C4—41no—
139C3×#685—22no—
140C3×#685—22no—
141C3×#685—22no—
142C3×#685D414yescomplemented
143#6669—22no—
144#6667—22no—
145(C2×D3)⋊Dic5—22no—
146(C2×D3)⋊Dic5—41no—
147#6665—22no—
148#6665—22no—
149#6665—41no—
150#6665—41no—
151Dic3×Dic5—22no—
152C23×#67—51no—
153C22×C3×C22⋊C4—51no—
154C2×C4×#67—51no—
155C2×C4×#67—51no—
156C2×D3×C22⋊C4—51no—
157#5247—51no—
158#5213—51no—
159#5213D511yescharacteristic, complemented
160#4957—51no—
161#4957—51no—
162#4956—51no—
163#4956—51no—
164#4955—51no—
165#4942—51no—
166Dic3×C22⋊C4—51no—
167C24×D5—31no—
168C24×D5C2×D311yescharacteristic
169C22×C5×D4—31no—
170C23×C4×C5C2×D311yescharacteristic, complemented
171C22×C22⋊D5—31no—
172C22×C22⋊D5—31no—
173C23×Dic5C2×D311yescharacteristic, complemented
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×D5—31no—
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—24no—
189C2×#685—31no—
190C2×#685—31no—
191C2×#685—31no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685C2×D311yescharacteristic
196C2×#685C2×D311yescharacteristic
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×#95—31no—
207#3963—31no—
208#3963—31no—
209D4×C22⋊C4—151noSylow
210C23×C3×C5—21no—
211C23×C3×C5—21no—
212C23×C3×C5—21no—
213C23×C3×C5—21no—
214C23×C3×C5C22×C412yes—
215C23×C3×C5C2×D412yes—
216C23×C3×C5C2×D412yes—
217C23×C3×C5C2411yescharacteristic
218C22×D15—21no—
219C22×D15—21no—
220C22×D15—21no—
221C22×D15—21no—
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×D3C22×C412yes—
232C22×C3×D5—21no—
233C22×C3×D5—21no—
234C22×C3×D5—21no—
235C22×C3×D5—21no—
236C22×C3×D5—28no—
237C22×C3×D5—21no—
238C22×C3×D5—21no—
239C22×C3×D5—21no—
240C22×C3×D5—21no—
241C22×C3×D5—21no—
242C22×C3×D5—21no—
243C22×C3×D5—28no—
244C22×C3×D5—44no—
245C22×C3×D5—44no—
246C22×C3×D5—44no—
247C22×C3×D5—44no—
248C22×C3×D5—44no—
249C22×C3×D5C22×C412yes—
250C22×C3×D5C22×C412yes—
251C22×C3×D5C2×D412yes—
252C22×C3×D5#4112yes—
253C2×D3×D5—28no—
254C2×D3×D5—28no—
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—44no—
266C2×C3×C4×C5C2×D412yescomplemented
267#1220C22⋊C4116yescomplemented
268C2×Dic15—21no—
269C2×Dic15—21no—
270C2×Dic15—21no—
271C2×Dic15—21no—
272C2×Dic15—21no—
273C2×Dic15—21no—
274C2×Dic15C22×C412yes—
275C2×Dic15C2×D412yes—
276C2×Dic15C2×D412yes—
277C4×D15—44no—
278C5×#67—28no—
279C2×C5×Dic3—21no—
280C2×C5×Dic3—21no—
281C2×C5×Dic3—21no—
282C2×C5×Dic3—21no—
283C2×C5×Dic3—21no—
284C2×C5×Dic3—21no—
285C2×C5×Dic3—21no—
286C2×C5×Dic3—21no—
287C2×C5×Dic3C22×C412yes—
288C2×C3×Dic5—21no—
289C2×C3×Dic5—21no—
290C2×C3×Dic5—21no—
291C2×C3×Dic5—21no—
292C2×C3×Dic5—21no—
293C2×C3×Dic5—44no—
294C2×C3×Dic5C2×D412yescomplemented
295#1202—28no—
296#1201—28no—
297#1200—44no—
298D5×Dic3—28no—
299C25×C3—51no—
300C24×D3—51no—
301C23×C3×C4—51no—
302C23×C3×C4C2×D511yescharacteristic, complemented
303C22×#67—51no—
304C22×#67—51no—
305C22×#67—58no—
306C22×#67—51no—
307C22×#67—104no—
308C22×#67—104no—
309C22×#67C2×D511yescharacteristic
310C23×Dic3—51no—
311C22×C4×D3—51no—
312C22×C4×D3—51no—
313C2×C3×C22⋊C4—51no—
314C2×C3×C22⋊C4—51no—
315C2×C3×C22⋊C4—51no—
316C2×C3×C22⋊C4—51no—
317C2×C3×C22⋊C4—104no—
318C2×#217—51no—
319C2×#217—51no—
320C2×#217—51no—
321C2×#217—51no—
322C2×#217—51no—
323C2×#217C2×D511yescharacteristic, complemented
324C4×#67—104no—
325C4×#67—104no—
326C2×(C2×D3)⋊C4—51no—
327C2×(C2×D3)⋊C4—51no—
328C2×(C2×D3)⋊C4—51no—
329C2×(C2×D3)⋊C4—51no—
330C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
331C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
332C2×Dic3⋊C4—51no—
333C2×Dic3⋊C4—51no—
334C2×C4×Dic3—51no—
335C2×C4×Dic3—51no—
336D3×C22⋊C4—104no—
337C3⋊#95—51no—
338C3⋊#95—51no—
339C3⋊#95C2×D511yescharacteristic, complemented
340C3⋊#95C2×D511yescharacteristic, complemented
341C24×C5—31no—
342C24×C5C22×D311yescharacteristic
343C23×D5—22no—
344C23×D5—22no—
345C23×D5—22no—
346C23×D5—22no—
347C23×D5—31no—
348C23×D5—34no—
349C23×D5—41no—
350C23×D5—41no—
351C23×D5—62no—
352C23×D5—62no—
353C23×D5—62no—
354C23×D5—62no—
355C23×D5—121no—
356C23×D5—121no—
357C23×D5C4×D314yescomplemented
358C23×D5C22×D311yescharacteristic
359C23×D5C22×D311yescharacteristic
360C2×C5×D4—34no—
361C2×C5×D4—62no—
362C2×C5×D4—62no—
363C22×C4×C5—22no—
364C22×C4×C5—22no—
365C22×C4×C5—31no—
366C22×C4×C5—31no—
367C22×C4×C5—31no—
368C22×C4×C5—41no—
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—22no—
378C22×Dic5—22no—
379C22×Dic5—31no—
380C22×Dic5—31no—
381C22×Dic5—31no—
382C22×Dic5—41no—
383C22×Dic5C22×D311yescharacteristic
384C22×Dic5C22×D311yescharacteristic
385D4×D5—632no—
386C2×D20—34no—
387C2×D20—62no—
388C2×D20—62no—
389C2×C4×D5—34no—
390C2×C4×D5—62no—
391C2×C4×D5—62no—
392C2×C4×D5—62no—
393C2×C4×D5—62no—
394C2×C4×D5—62no—
395C2×C4×D5—62no—
396C2×C4×D5—121no—
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—22no—
407#685—62no—
408#685—62no—
409#685—62no—
410#685—62no—
411#685—121no—
412#685—121no—
413#685#6714yescomplemented
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—51no—
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—151no—
433C22×C3×C5—22no—
434C22×C3×C5—22no—
435C22×C3×C5—22no—
436C22×C3×C5—22no—
437C22×C3×C5—22no—
438C22×C3×C5—22no—
439C22×C3×C5C2×C22⋊C414yescomplemented
440C22×C3×C5C23×C411yescharacteristic
441C22×C3×C5C22×D411yescharacteristic
442C22×C3×C5C22×D411yescharacteristic
443C22×C3×C5C22×D411yescharacteristic
444C22×C3×C5C2×#4111yescharacteristic
445C22×C3×C5H(5,𝔽2)11yescharacteristic
446C22×C3×C5H(5,𝔽2)11yescharacteristic
447C2×D15—22no—
448C2×D15—22no—
449C2×D15—22no—
450C2×D15—22no—
451C2×D15—22no—
452C2×D15—22no—
453C2×D15C2×C22⋊C414yescomplemented
454C2×C5×D3—22no—
455C2×C5×D3—22no—
456C2×C5×D3—22no—
457C2×C5×D3—41no—
458C2×C5×D3—41no—
459C2×C5×D3—41no—
460C2×C5×D3—41no—
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—416no—
471C2×C3×D5—41no—
472C2×C3×D5—41no—
473C2×C3×D5—41no—
474C2×C3×D5—41no—
475C2×C3×D5C4×D414yescomplemented
476D3×D5—416no—
477C3×C4×C5—22no—
478C3×C4×C5—41no—
479Dic15—41no—
480Dic15—41no—
481Dic15C2×C22⋊C414yescomplemented
482C3×Dic5—22no—
483C3×Dic5—41no—
484C5×Dic3—22no—
485C5×Dic3—41no—
486C5×Dic3—41no—
487C24×C3—51no—
488C24×C3—51no—
489C24×C3—54no—
490C24×C3—102no—
491C24×C3—102no—
492C24×C3—102no—
493C24×C3—102no—
494C24×C3—201no—
495C24×C3—201no—
496C24×C3C22×D511yescharacteristic
497C23×D3—51no—
498C23×D3—54no—
499C23×D3—102no—
500C23×D3—102no—
501C23×D3—102no—
502C23×D3—102no—
503C23×D3—201no—
504C23×D3—201no—
505C23×D3C22×D511yescharacteristic
506C22×C3×C4—22no—
507C22×C3×C4—22no—
508C22×C3×C4—41no—
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
516C2×#67—22no—
517C2×#67—22no—
518C2×#67—54no—
519C2×#67—54no—
520C2×#67—54no—
521C2×#67—54no—
522C2×#67—54no—
523C2×#67—102no—
524C2×#67—102no—
525C2×#67—102no—
526C2×#67—102no—
527C2×#67—1032no—
528C2×#67C4×D514yescomplemented
529C22×Dic3—51no—
530C22×Dic3—54no—
531C22×Dic3—51no—
532C22×Dic3—51no—
533C22×Dic3—102no—
534C22×Dic3—102no—
535C22×Dic3C22×D511yescharacteristic
536C22×Dic3C22×D511yescharacteristic
537C22×Dic3C22×D511yescharacteristic
538C2×C4×D3—102no—
539C2×C4×D3—102no—
540C2×C4×D3—102no—
541C2×C4×D3—102no—
542C2×C4×D3—201no—
543C2×C4×D3—201no—
544C3×C22⋊C4—54no—
545C3×C22⋊C4—102no—
546C3×C22⋊C4—102no—
547C3×C22⋊C4—102no—
548#217—22no—
549#217—102no—
550#217—102no—
551#217—102no—
552#217—201no—
553#217—201no—
554(C2×D3)⋊C4—22no—
555(C2×D3)⋊C4—41no—
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—21no—
565C23×C5—21no—
566C23×C5—21no—
567C23×C5—21no—
568C23×C5—32no—
569C23×C5—61no—
570C23×C5—61no—
571C23×C5—61no—
572C23×C5—61no—
573C23×C5—61no—
574C23×C5—61no—
575C23×C5C2×C4×D312yes—
576C23×C5D3×D412yes—
577C23×C5D3×D412yes—
578C23×C5C23×D311yescharacteristic
579C22×D5—21no—
580C22×D5—21no—
581C22×D5—21no—
582C22×D5—21no—
583C22×D5—28no—
584C22×D5—21no—
585C22×D5—21no—
586C22×D5—21no—
587C22×D5—21no—
588C22×D5—21no—
589C22×D5—21no—
590C22×D5—28no—
591C22×D5—32no—
592C22×D5—32no—
593C22×D5—32no—
594C22×D5—44no—
595C22×D5—44no—
596C22×D5—44no—
597C22×D5—44no—
598C22×D5—44no—
599C22×D5—68no—
600C22×D5—61no—
601C22×D5—61no—
602C22×D5—61no—
603C22×D5—61no—
604C22×D5—68no—
605C22×D5—124no—
606C22×D5—124no—
607C22×D5—124no—
608C22×D5—124no—
609C22×D5—124no—
610C22×D5C2×C4×D312yes—
611C22×D5C2×C4×D312yes—
612C22×D5#23512yes—
613C22×D5C2×#6712yes—
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—32no—
621C2×C4×C5—44no—
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—61no—
629C2×C4×C5—61no—
630C2×C4×C5C2×#6712yescomplemented
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—44no—
642C2×Dic5—61no—
643C2×Dic5—61no—
644C2×Dic5—61no—
645C2×Dic5—61no—
646C2×Dic5—61no—
647C2×Dic5—61no—
648C2×Dic5C2×#6712yescomplemented
649D20—68no—
650C4×D5—68no—
651C4×D5—124no—
652C4×D5—124no—
653C25—51no—
654C25—151no—
655C22×D4—31no—
656C22×D4—151no—
657C22×D4—158no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—304no—
661C22×D4—304no—
662C23×C4—51no—
663C23×C4—151no—
664C23×C4—151no—
665C23×C4—151no—
666C23×C4D3×D511yescharacteristic, complemented
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—51no—
678C2×C22⋊C4—104no—
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—151no—
688C2×C22⋊C4—304no—
689C2×C42—151no—
690C2×C42—151no—
691#95—31no—
692#95—31no—
693#95—151no—
694#95—151no—
695C2×C3×C5—24no—
696C2×C3×C5C22×C22⋊C411yescharacteristic
697C2×C3×C5C2×C4×D411yescharacteristic
698C2×C3×C5#51811yescharacteristic
699C2×C3×C5D4211yescharacteristic
700C2×C3×C5D4211yescharacteristic
701C2×C3×C5#54611yescharacteristic
702C2×C3×C5#54611yescharacteristic
703D15—24no—
704C3×D5—24no—
705C3×D5—42no—
706C5×D3—42no—
707C23×C3—21no—
708C23×C3—21no—
709C23×C3—21no—
710C23×C3—21no—
711C23×C3—52no—
712C23×C3—52no—
713C23×C3—52no—
714C23×C3—52no—
715C23×C3—108no—
716C23×C3—101no—
717C23×C3—101no—
718C23×C3—101no—
719C23×C3—101no—
720C23×C3—101no—
721C23×C3—101no—
722C23×C3—101no—
723C23×C3—101no—
724C23×C3—101no—
725C23×C3—101no—
726C23×C3—108no—
727C23×C3—204no—
728C23×C3—204no—
729C23×C3—204no—
730C23×C3—204no—
731C23×C3—204no—
732C23×C3C2×C4×D512yes—
733C23×C3D4×D512yes—
734C23×C3D4×D512yes—
735C23×C3C23×D511yescharacteristic
736C22×D3—21no—
737C22×D3—21no—
738C22×D3—21no—
739C22×D3—21no—
740C22×D3—21no—
741C22×D3—21no—
742C22×D3—52no—
743C22×D3—52no—
744C22×D3—52no—
745C22×D3—108no—
746C22×D3—108no—
747C22×D3—101no—
748C22×D3—101no—
749C22×D3—101no—
750C22×D3—101no—
751C22×D3—204no—
752C22×D3—204no—
753C22×D3—204no—
754C22×D3—204no—
755C22×D3—204no—
756C22×D3C2×C4×D512yes—
757C2×C3×C4—21no—
758C2×C3×C4—21no—
759C2×C3×C4—21no—
760C2×C3×C4—21no—
761C2×C3×C4—21no—
762C2×C3×C4—44no—
763C2×C3×C4—52no—
764C2×C3×C4—101no—
765C2×C3×C4—101no—
766C2×C3×C4—101no—
767C2×C3×C4—101no—
768C2×C3×C4—101no—
769C2×C3×C4—204no—
770C2×C3×C4D4×D512yescomplemented
771#67—28no—
772#67—516no—
773#67—108no—
774#67—108no—
775C2×Dic3—21no—
776C2×Dic3—21no—
777C2×Dic3—21no—
778C2×Dic3—21no—
779C2×Dic3—21no—
780C2×Dic3—21no—
781C2×Dic3—21no—
782C2×Dic3—21no—
783C2×Dic3—52no—
784C2×Dic3—52no—
785C2×Dic3—52no—
786C2×Dic3—108no—
787C2×Dic3—101no—
788C2×Dic3—101no—
789C2×Dic3—101no—
790C2×Dic3—101no—
791C2×Dic3—101no—
792C2×Dic3—101no—
793C2×Dic3C2×C4×D512yes—
794C4×D3—204no—
795C4×D3—204no—
796C22×C5—22no—
797C22×C5—22no—
798C22×C5—22no—
799C22×C5—22no—
800C22×C5—22no—
801C22×C5—22no—
802C22×C5—62no—
803C22×C5—62no—
804C22×C5—62no—
805C22×C5—121no—
806C22×C5—121no—
807C22×C5—121no—
808C22×C5—121no—
809C22×C5D3×C22⋊C414yescomplemented
810C22×C5C22×C4×D311yescharacteristic
811C22×C5C2×#23511yescharacteristic
812C22×C5C2×D3×D411yescharacteristic
813C22×C5C2×D3×D411yescharacteristic
814C22×C5#100411yescharacteristic
815C22×C5#100411yescharacteristic
816C22×C5C22×#6711yescharacteristic
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—416no—
828C2×D5—41no—
829C2×D5—41no—
830C2×D5—41no—
831C2×D5—41no—
832C2×D5—62no—
833C2×D5—62no—
834C2×D5—62no—
835C2×D5—62no—
836C2×D5—62no—
837C2×D5—62no—
838C2×D5—1216no—
839C2×D5C4×#6714yescomplemented
840C4×C5—22no—
841C4×C5—41no—
842C4×C5—62no—
843C4×C5—121no—
844C4×C5—121no—
845Dic5—22no—
846Dic5—34no—
847Dic5—41no—
848Dic5—121no—
849Dic5—121no—
850C24—31no—
851C24—51no—
852C24—51no—
853C24—54no—
854C24—102no—
855C24—102no—
856C24—102no—
857C24—102no—
858C24—154no—
859C24—151no—
860C24—201no—
861C24—201no—
862C24—302no—
863C24—302no—
864C24—302no—
865C24—302no—
866C24—601no—
867C24—601no—
868C24C2×D3×D511yescharacteristic
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—22no—
883C22×C4—22no—
884C22×C4—31no—
885C22×C4—31no—
886C22×C4—31no—
887C22×C4—41no—
888C22×C4—51no—
889C22×C4—51no—
890C22×C4—102no—
891C22×C4—102no—
892C22×C4—154no—
893C22×C4—151no—
894C22×C4—151no—
895C22×C4—151no—
896C22×C4—201no—
897C22×C4—302no—
898C22×C4—302no—
899C22×C4—302no—
900C22×C4—302no—
901C22×C4—302no—
902C22×C4—302no—
903C22×C4—601no—
904C22×C4—601no—
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—102no—
914C22⋊C4—102no—
915C22⋊C4—121no—
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—22no—
929C22×C3—22no—
930C22×C3—22no—
931C22×C3—22no—
932C22×C3—22no—
933C22×C3—22no—
934C22×C3—54no—
935C22×C3—102no—
936C22×C3—102no—
937C22×C3—102no—
938C22×C3—102no—
939C22×C3—102no—
940C22×C3—102no—
941C22×C3—102no—
942C22×C3—102no—
943C22×C3—102no—
944C22×C3—2016no—
945C22×C3—201no—
946C22×C3—201no—
947C22×C3—201no—
948C22×C3—201no—
949C22×C3D5×C22⋊C414yescomplemented
950C22×C3C22×C4×D511yescharacteristic
951C22×C3C2×D4×D511yescharacteristic
952C22×C3C2×D4×D511yescharacteristic
953C22×C3C2×D4×D511yescharacteristic
954C22×C3#414411yescharacteristic
955C22×C3D5×#4111yescharacteristic
956C22×C3#414911yescharacteristic
957C2×D3—22no—
958C2×D3—22no—
959C2×D3—22no—
960C2×D3—41no—
961C2×D3—41no—
962C2×D3—41no—
963C2×D3—41no—
964C2×D3—54no—
965C2×D3—102no—
966C2×D3—102no—
967C2×D3—102no—
968C2×D3—102no—
969C2×D3—102no—
970C2×D3—102no—
971C2×D3—2016no—
972C3×C4—22no—
973C3×C4—41no—
974C3×C4—102no—
975C3×C4—201no—
976Dic3—22no—
977Dic3—41no—
978Dic3—41no—
979Dic3—54no—
980Dic3—201no—
981Dic3—201no—
982C2×C5—24no—
983C2×C5—122no—
984C2×C5C2×D3×C22⋊C411yescharacteristic
985C2×C5#548611yescharacteristic
986C2×C5#549011yescharacteristic
987C2×C5#549011yescharacteristic
988C2×C5C2×C4×#6711yescharacteristic
989C2×C5D4×#6711yescharacteristic
990C2×C5D4×#6711yescharacteristic
991D5—24no—
992D5—42no—
993D5—64no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—32no—
999C23—52no—
1000C23—52no—
1001C23—52no—
1002C23—52no—
1003C23—61no—
1004C23—61no—
1005C23—61no—
1006C23—61no—
1007C23—61no—
1008C23—61no—
1009C23—108no—
1010C23—101no—
1011C23—101no—
1012C23—101no—
1013C23—101no—
1014C23—108no—
1015C23—101no—
1016C23—101no—
1017C23—101no—
1018C23—101no—
1019C23—101no—
1020C23—101no—
1021C23—152no—
1022C23—152no—
1023C23—152no—
1024C23—204no—
1025C23—204no—
1026C23—204no—
1027C23—204no—
1028C23—204no—
1029C23—308no—
1030C23—308no—
1031C23—301no—
1032C23—301no—
1033C23—301no—
1034C23—301no—
1035C23—604no—
1036C23—604no—
1037C23—604no—
1038C23—604no—
1039C23—604no—
1040C23C4×D3×D512yes—
1041C23#677712yes—
1042C23#679012yes—
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—32no—
1054C2×C4—44no—
1055C2×C4—52no—
1056C2×C4—61no—
1057C2×C4—61no—
1058C2×C4—61no—
1059C2×C4—61no—
1060C2×C4—61no—
1061C2×C4—61no—
1062C2×C4—61no—
1063C2×C4—61no—
1064C2×C4—101no—
1065C2×C4—101no—
1066C2×C4—101no—
1067C2×C4—101no—
1068C2×C4—101no—
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×C4D5×#6712yescomplemented
1083C2×C3—24no—
1084C2×C3—104no—
1085C2×C3—202no—
1086C2×C3C2×D5×C22⋊C411yescharacteristic
1087C2×C3C4×D4×D511yescharacteristic
1088C2×C3#6587911yescharacteristic
1089C2×C3#6592411yescharacteristic
1090C2×C3#6594311yescharacteristic
1091C2×C3#6594411yescharacteristic
1092C2×C3#6598811yescharacteristic
1093D3—42no—
1094D3—104no—
1095C5C22⋊C4×#6711yescharacteristic, complemented, Sylow
1096C22—22no—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—54no—
1103C22—62no—
1104C22—62no—
1105C22—62no—
1106C22—102no—
1107C22—102no—
1108C22—102no—
1109C22—102no—
1110C22—102no—
1111C22—102no—
1112C22—102no—
1113C22—102no—
1114C22—102no—
1115C22—121no—
1116C22—121no—
1117C22—121no—
1118C22—121no—
1119C22—154no—
1120C22—2016no—
1121C22—201no—
1122C22—201no—
1123C22—201no—
1124C22—201no—
1125C22—302no—
1126C22—302no—
1127C22—302no—
1128C22—302no—
1129C22—302no—
1130C22—302no—
1131C22—6016no—
1132C22#9147314yescomplemented
1133C22C2×C4×D3×D511yescharacteristic
1134C22C2×#677711yescharacteristic
1135C22D5×#23511yescharacteristic
1136C22#9201711yescharacteristic
1137C22C2×D5×#6711yescharacteristic
1138C22C2×#679011yescharacteristic
1139C22#9204911yescharacteristic
1140C4—22no—
1141C4—41no—
1142C4—62no—
1143C4—102no—
1144C4—121no—
1145C4—121no—
1146C4—154no—
1147C4—201no—
1148C4—601no—
1149C4—601no—
1150C3#1060660911yescharacteristic, complemented, Sylow
1151C2—24no—
1152C2—104no—
1153C2—122no—
1154C2—202no—
1155C2—304no—
1156C2C2×#9147311yescharacteristic
1157C2C4×D5×#6711yescharacteristic
1158C2#1175462511yescharacteristic
1159C2#1175464011yescharacteristic
1160C2#1175466411yescharacteristic
1161C2#1175467211yescharacteristic
1162C2#1175543711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×D5×#67C2
hypercenterC23×C4D3×D5
hypocenterC3×C5D4×C22⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#1220C2semidirect
3. C22×C3×#685C2semidirect
4. C2×#91552C2semidirect
5. C2×#91473C2semidirect
6. C5×#5213C2semidirect
7. #11749492C2semidirect
8. #11749488C2semidirect
9. #11748940C2semidirect
10. #11748917C2semidirect
11. #11748916C2semidirect
12. #11748915C2semidirect
13. #11748885C2semidirect
14. #11748884C2semidirect
15. #11748700C2semidirect
19. C23×C3×C4×C5C22semidirect
21. C22×C4×D15C22semidirect
23. C23×C3×Dic5C22semidirect
26. C2×D5×#67C4semidirect
29. C22×#1200C22semidirect
31. C2×#6719C22semidirect
33. C2×#6714C22semidirect
34. C2×#6712C22semidirect
35. C2×C4×Dic15C22semidirect
36. C2×C5×#217C22semidirect
37. C2×C5×(C2×D3)⋊C4C22semidirect
38. C2×C5×(C2×D3)⋊C4C22semidirect
42. C2×C3×#685C22semidirect
43. C2×C3×#685C22semidirect
45. C2×#6669C22semidirect
46. C2×#6667C22semidirect
47. C2×(C2×D3)⋊Dic5C22semidirect
48. C2×(C2×D3)⋊Dic5C22semidirect
51. C2×#6665C22semidirect
52. C2×#6665C22semidirect
53. C2×Dic3×Dic5C22semidirect
55. C5×C3⋊#95C22semidirect
56. C5×C3⋊#95C22semidirect
57. #90994C22semidirect
58. #90994C22semidirect
62. C22×#685D3semidirect
84. C23×C3×D5C2×C4semidirect
93. C22×D3×D5C2×C4semidirect
110. C2×C5×#67C2×C4semidirect
122. C2×#1202C2×C4semidirect
125. C2×#1201C2×C4semidirect
131. C2×D5×Dic3C2×C4semidirect
142. C3×#685D4semidirect
159. #5213D5semidirect
170. C23×C4×C5C2×D3semidirect
173. C23×Dic5C2×D3semidirect
197. C2×#685C2×D3semidirect
198. C2×#685C2×D3semidirect
266. C2×C3×C4×C5C2×D4semidirect
267. #1220C22⋊C4semidirect
294. C2×C3×Dic5C2×D4semidirect
302. C23×C3×C4C2×D5semidirect
323. C2×#217C2×D5semidirect
330. C2×(C2×D3)⋊C4C2×D5semidirect
331. C2×(C2×D3)⋊C4C2×D5semidirect
339. C3⋊#95C2×D5semidirect
340. C3⋊#95C2×D5semidirect
357. C23×D5C4×D3semidirect
413. #685#67semidirect
439. C22×C3×C5C2×C22⋊C4semidirect
453. C2×D15C2×C22⋊C4semidirect
475. C2×C3×D5C4×D4semidirect
481. Dic15C2×C22⋊C4semidirect
528. C2×#67C4×D5semidirect
630. C2×C4×C5C2×#67semidirect
648. C2×Dic5C2×#67semidirect
666. C23×C4D3×D5semidirect
770. C2×C3×C4D4×D5semidirect
809. C22×C5D3×C22⋊C4semidirect
839. C2×D5C4×#67semidirect
927. C3×C5D4×C22⋊C4semidirect
949. C22×C3D5×C22⋊C4semidirect
1082. C2×C4D5×#67semidirect
1095. C5C22⋊C4×#67semidirect
1132. C22#91473semidirect
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×#672
C2×C4×#12202
C22×C3×#6852
C2×#915522
C2×#914732
C5×#52132
#117494922
#117494882
#117489402
#117489172
#117489162
#117489152
#117488852
#117488842
#117487002
#106066093
C22⋊C4×#675