Finite Group Databasebeta

← #14320519

Subgroups — #14320519

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×D15C211yesmaximal, characteristic
2C2×#91561C211yesmaximal, characteristic
3C2×#91561C211yesmaximal, characteristic
4C2×#91404C211yesmaximal, characteristic, complemented
5C2×C4×#1200C211yesmaximal, characteristic, complemented
6C5×#4945C211yesmaximal, characteristic, complemented
7C3×#65234C211yesmaximal, characteristic, complemented
8#11749485C211yesmaximal, characteristic, complemented
9#11749478C211yesmaximal, characteristic, complemented
10#11748888C211yesmaximal, characteristic, complemented
11#11748888C211yesmaximal, characteristic, complemented
12#11748728C211yesmaximal, characteristic, complemented
13#11748727C211yesmaximal, characteristic, complemented
14#11748671C211yesmaximal, characteristic, complemented
15#11748668C211yesmaximal, characteristic, complemented
16D5×#388—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×#1200C2211yescharacteristic
21C22×#1200C2211yescharacteristic
22C22×#1200C2211yescharacteristic
23C22×#1200C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C22⋊C4×D15—24no—
29C2×C5×#217C2211yescharacteristic
30C2×C5×#217C2211yescharacteristic
31C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
32C2×C4×C5×Dic3C2211yescharacteristic, complemented
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C2×C3×C22⋊Dic5C2211yescharacteristic
35C2×C3×#683C2211yescharacteristic, complemented
36C2×C3×C4×Dic5C2211yescharacteristic, complemented
37#91561—24no—
38#91561C418yescomplemented
39C2×Dic3⋊Dic5C2211yescharacteristic, complemented
40C2×#6668C2211yescharacteristic, complemented
41C2×#6667C2211yescharacteristic
42C2×#6667C2211yescharacteristic
43C2×#6667C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic, complemented
46C2×Dic3×Dic5C2211yescharacteristic, complemented
47#91404—24no—
48C4×#1200—24no—
49C5×C3⋊#95C2211yescharacteristic, complemented
50C5×C3⋊#95C2211yescharacteristic, complemented
51C3×#3963C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57D3×#388—51nomaximal, Hall
58C2×D5×C4⋊C4—31no—
59C2×D5×C22⋊C4—31no—
60C2×D5×C22⋊C4—31no—
61C2×D5×C22⋊C4—31no—
62C2×C42×D5—31no—
63C5×#388—31no—
64#65279—31no—
65#65240—31no—
66#65234D311yescharacteristic, complemented
67#65233—31no—
68#65229—31no—
69#64959—31no—
70#64958—31no—
71D5×#95—31no—
72D5×#95—31no—
73C24×C3×C5C2311yescharacteristic
74C23×D15—22no—
75C23×D15—22no—
76C23×D15—22no—
77C23×D15—22no—
78C23×D15—22no—
79C23×D15—22no—
80C23×D15C2×C414yes—
81C23×D15C2311yescharacteristic
82C23×D15C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C2×C4×D15—22no—
88C2×C4×D15—22no—
89C2×C4×D15—22no—
90C2×C4×D15—22no—
91C2×C4×D15—22no—
92C2×C4×D15D414yes—
93C22×C5×Dic3C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C22×C5×Dic3C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C2×#1200—22no—
102C2×#1200—22no—
103C2×#1200—22no—
104C2×#1200—22no—
105C2×#1200—22no—
106C2×#1200—22no—
107C2×#1200—22no—
108C2×#1200—22no—
109C2×#1200—22no—
110C2×#1200C2×C414yes—
111C2×#1200C2×C414yes—
112C2×#1200D414yes—
113C3×C5×C22⋊C4—22no—
114#6719—22no—
115#6714—22no—
116#6714—22no—
117C5×#217—22no—
118C5×#217C2×C414yescomplemented
119C5×Dic3⋊C4—22no—
120C4×C5×Dic3—22no—
121C3×C22⋊Dic5—22no—
122C3×C22⋊Dic5C2×C414yescomplemented
123C3×#683—22no—
124C3×C4×Dic5—22no—
125Dic3⋊Dic5—22no—
126#6668—22no—
127#6667—22no—
128#6667—22no—
129#6667C2×C414yescomplemented
130#6667C2×C414yescomplemented
131Dic3×Dic5—22no—
132Dic3×Dic5—22no—
133C2×D3×C4⋊C4—51no—
134C2×D3×C22⋊C4—51no—
135C2×D3×C22⋊C4—51no—
136C2×D3×C22⋊C4—51no—
137C2×C42×D3—51no—
138C3×#388—51no—
139#4990—51no—
140#4951—51no—
141#4945D511yescharacteristic, complemented
142#4944—51no—
143#4940—51no—
144#4670—51no—
145#4669—51no—
146D3×#95—51no—
147D3×#95—51no—
148C24×D5—31no—
149C22×C4×D5—31no—
150C22×C4×D5—31no—
151C22×C4×D5—31no—
152C22×C4×D5—31no—
153C22×C4×D5—31no—
154C22×C4×D5—31no—
155C2×C5×C4⋊C4—31no—
156C2×C5×C22⋊C4—31no—
157C2×C5×C22⋊C4—31no—
158C2×C5×C22⋊C4C2×D311yescharacteristic
159C2×C42×C5—31no—
160C2×C22⋊Dic5—31no—
161C2×C22⋊Dic5C2×D311yescharacteristic
162C2×C22⋊Dic5C2×D311yescharacteristic
163C2×#685—31no—
164C2×#685—31no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×C4⋊Dic5—31no—
170C2×#683—31no—
171C2×#683C2×D311yescharacteristic, complemented
172C2×C4×Dic5—31no—
173C2×C4×Dic5—31no—
174C2×C4×Dic5C2×D311yescharacteristic, complemented
175D5×C4⋊C4—64no—
176D5×C22⋊C4—38no—
177D5×C22⋊C4—64no—
178D5×C22⋊C4—64no—
179C42×D5—64no—
180C5×#95—31no—
181C5×#95—31no—
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#3963C2×D311yescharacteristic, complemented
187#3963C2×D311yescharacteristic, complemented
188C2×#388—151noSylow
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5—21no—
194C23×C3×C5—21no—
195C23×C3×C5C22×C412yes—
196C23×C3×C5C2411yescharacteristic
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—21no—
200C22×D15—21no—
201C22×D15—21no—
202C22×D15—21no—
203C22×D15—28no—
204C22×D15—28no—
205C22×D15—28no—
206C22×D15—44no—
207C22×D15—44no—
208C22×D15—44no—
209C22×D15—44no—
210C22×D15C22×C412yes—
211C22×D15C22×C412yes—
212C22×D15C2×D412yes—
213C22×D15C2×D412yes—
214C22×D15#4112yes—
215C22×D15#4112yes—
216C22×D15#4112yes—
217C22×D15#4112yes—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5C2×D412yes—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15C2×D412yes—
230C4×D15—28no—
231C4×D15—44no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—21no—
239C2×C5×Dic3—21no—
240C2×C5×Dic3—21no—
241C2×C5×Dic3C22×C412yes—
242C2×C5×Dic3C22×C412yes—
243C2×C5×Dic3C2×D412yes—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5—21no—
251C2×C3×Dic5—21no—
252C2×C3×Dic5—21no—
253C2×C3×Dic5C22×C412yes—
254C2×C3×Dic5C22×C412yes—
255C2×C3×Dic5C2×D412yes—
256#1200—28no—
257#1200—28no—
258#1200—28no—
259#1200—44no—
260C24×D3—51no—
261C22×C4×D3—51no—
262C22×C4×D3—51no—
263C22×C4×D3—51no—
264C22×C4×D3—51no—
265C22×C4×D3—51no—
266C22×C4×D3—51no—
267C2×C3×C4⋊C4—51no—
268C2×C3×C22⋊C4—51no—
269C2×C3×C22⋊C4—51no—
270C2×C3×C22⋊C4C2×D511yescharacteristic
271C2×C3×C42—51no—
272C2×#217—51no—
273C2×#217C2×D511yescharacteristic
274C2×#217C2×D511yescharacteristic
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4—51no—
281C2×C4⋊Dic3—51no—
282C2×Dic3⋊C4—51no—
283C2×Dic3⋊C4C2×D511yescharacteristic, complemented
284C2×C4×Dic3—51no—
285C2×C4×Dic3—51no—
286C2×C4×Dic3C2×D511yescharacteristic, complemented
287D3×C4⋊C4—104no—
288D3×C22⋊C4—58no—
289D3×C22⋊C4—104no—
290D3×C22⋊C4—104no—
291C42×D3—104no—
292C3×#95—51no—
293C3×#95—51no—
294C3⋊#95—51no—
295C3⋊#95—51no—
296C3⋊#95—51no—
297C3⋊#95—51no—
298C3⋊#95C2×D511yescharacteristic, complemented
299C3⋊#95C2×D511yescharacteristic, complemented
300C24×C5C22×D311yescharacteristic
301C23×D5—31no—
302C23×D5—34no—
303C23×D5—31no—
304C23×D5—62no—
305C23×D5—62no—
306C23×D5—62no—
307C23×D5—62no—
308C23×D5—62no—
309C23×D5—62no—
310C22×C4×C5—31no—
311C22×C4×C5—31no—
312C22×C4×C5—31no—
313C22×C4×C5—31no—
314C22×C4×C5C22×D311yescharacteristic
315C22×C4×C5C22×D311yescharacteristic
316C22×Dic5—31no—
317C22×Dic5—31no—
318C22×Dic5C22×D311yescharacteristic
319C22×Dic5C22×D311yescharacteristic
320C22×Dic5C22×D311yescharacteristic
321C22×Dic5C22×D311yescharacteristic
322C2×C4×D5—34no—
323C2×C4×D5—34no—
324C2×C4×D5—34no—
325C2×C4×D5—34no—
326C2×C4×D5—62no—
327C2×C4×D5—62no—
328C2×C4×D5—62no—
329C2×C4×D5—62no—
330C2×C4×D5—62no—
331C2×C4×D5—62no—
332C2×C4×D5—62no—
333C2×C4×D5—62no—
334C2×C4×D5—62no—
335C2×C4×D5—62no—
336C2×C4×D5—62no—
337C2×C4×D5—62no—
338C2×C4×D5—62no—
339C2×C4×D5—62no—
340C5×C4⋊C4—62no—
341C5×C22⋊C4—22no—
342C5×C22⋊C4—34no—
343C5×C22⋊C4—62no—
344C42×C5—62no—
345C22⋊Dic5—22no—
346C22⋊Dic5—62no—
347C22⋊Dic5C4×D314yescomplemented
348#685—34no—
349#685—34no—
350#685—62no—
351#685—62no—
352#685—62no—
353#685—62no—
354C4⋊Dic5—62no—
355#683—22no—
356#683—62no—
357C4×Dic5—22no—
358C4×Dic5—62no—
359C4×Dic5—62no—
360C22×C4⋊C4—151no—
361C22×C22⋊C4—151no—
362C22×C22⋊C4—151no—
363C22×C22⋊C4—151no—
364C22×C42—151no—
365#388—31no—
366#388—51no—
367#388—151no—
368#388—151no—
369#388—151no—
370#388—151no—
371#388—151no—
372#388—151no—
373C2×#95—151no—
374C2×#95—151no—
375C22×C3×C5—22no—
376C22×C3×C5—22no—
377C22×C3×C5—22no—
378C22×C3×C5—41no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5—41no—
382C22×C3×C5C23×C411yescharacteristic
383C22×C3×C5C22×D411yescharacteristic
384C22×C3×C5C22×D411yescharacteristic
385C22×C3×C5C2×#4111yescharacteristic
386C22×C3×C5C2×#4111yescharacteristic
387C22×C3×C5C2×#4111yescharacteristic
388C22×C3×C5C2×#4111yescharacteristic
389C2×D15—22no—
390C2×D15—22no—
391C2×D15—22no—
392C2×D15—41no—
393C2×D15—41no—
394C2×D15—41no—
395C2×D15—41no—
396C2×D15—416no—
397C2×D15#11714yes—
398C2×D15C4×D414yes—
399C2×D15C4×D414yes—
400C2×D15#12114yes—
401C2×D15#12314yes—
402C2×D15#12414yes—
403C2×D15#12614yes—
404C3×C4×C5—22no—
405C3×C4×C5—41no—
406Dic15—22no—
407Dic15—41no—
408C3×Dic5—22no—
409C3×Dic5—22no—
410C3×Dic5—22no—
411C3×Dic5—41no—
412C5×Dic3—22no—
413C5×Dic3—22no—
414C5×Dic3—22no—
415C5×Dic3—41no—
416C24×C3C22×D511yescharacteristic
417C23×D3—51no—
418C23×D3—54no—
419C23×D3—51no—
420C23×D3—102no—
421C23×D3—102no—
422C23×D3—102no—
423C23×D3—102no—
424C23×D3—102no—
425C23×D3—102no—
426C22×C3×C4—51no—
427C22×C3×C4—51no—
428C22×C3×C4—51no—
429C22×C3×C4—51no—
430C22×C3×C4C22×D511yescharacteristic
431C22×C3×C4C22×D511yescharacteristic
432C22×Dic3—51no—
433C22×Dic3—51no—
434C22×Dic3C22×D511yescharacteristic
435C22×Dic3C22×D511yescharacteristic
436C22×Dic3C22×D511yescharacteristic
437C22×Dic3C22×D511yescharacteristic
438C2×C4×D3—54no—
439C2×C4×D3—54no—
440C2×C4×D3—54no—
441C2×C4×D3—54no—
442C2×C4×D3—102no—
443C2×C4×D3—102no—
444C2×C4×D3—102no—
445C2×C4×D3—102no—
446C2×C4×D3—102no—
447C2×C4×D3—102no—
448C2×C4×D3—102no—
449C2×C4×D3—102no—
450C2×C4×D3—102no—
451C2×C4×D3—102no—
452C2×C4×D3—102no—
453C2×C4×D3—102no—
454C2×C4×D3—102no—
455C2×C4×D3—102no—
456C3×C4⋊C4—102no—
457C3×C22⋊C4—22no—
458C3×C22⋊C4—54no—
459C3×C22⋊C4—102no—
460C3×C42—102no—
461#217—22no—
462#217—102no—
463#217C4×D514yescomplemented
464(C2×D3)⋊C4—54no—
465(C2×D3)⋊C4—54no—
466(C2×D3)⋊C4—102no—
467(C2×D3)⋊C4—102no—
468(C2×D3)⋊C4—102no—
469(C2×D3)⋊C4—102no—
470C4⋊Dic3—102no—
471Dic3⋊C4—22no—
472Dic3⋊C4—102no—
473C4×Dic3—22no—
474C4×Dic3—102no—
475C4×Dic3—102no—
476C23×C5—21no—
477C23×C5—21no—
478C23×C5—21no—
479C23×C5—21no—
480C23×C5—21no—
481C23×C5—21no—
482C23×C5C2×C4×D312yes—
483C23×C5C23×D311yescharacteristic
484C22×D5—32no—
485C22×D5—32no—
486C22×D5—32no—
487C22×D5—32no—
488C22×D5—32no—
489C22×D5—32no—
490C22×D5—32no—
491C22×D5—32no—
492C22×D5—68no—
493C22×D5—68no—
494C22×D5—68no—
495C22×D5—61no—
496C22×D5—61no—
497C22×D5—61no—
498C22×D5—61no—
499C22×D5—61no—
500C22×D5—61no—
501C22×D5—124no—
502C22×D5—124no—
503C22×D5—124no—
504C22×D5—124no—
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—21no—
509C2×C4×C5—21no—
510C2×C4×C5—32no—
511C2×C4×C5—32no—
512C2×C4×C5—32no—
513C2×C4×C5—61no—
514C2×C4×C5—61no—
515C2×C4×C5—61no—
516C2×C4×C5—61no—
517C2×C4×C5—61no—
518C2×C4×C5—61no—
519C2×C4×C5—61no—
520C2×C4×C5—61no—
521C2×C4×C5—61no—
522C2×C4×C5D3×D412yes—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5—21no—
526C2×Dic5—21no—
527C2×Dic5—21no—
528C2×Dic5—21no—
529C2×Dic5—21no—
530C2×Dic5—21no—
531C2×Dic5—21no—
532C2×Dic5—32no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5—61no—
536C2×Dic5—61no—
537C2×Dic5—61no—
538C2×Dic5C2×C4×D312yes—
539C2×Dic5C2×C4×D312yes—
540C2×Dic5D3×D412yes—
541C4×D5—68no—
542C4×D5—68no—
543C4×D5—68no—
544C4×D5—68no—
545C4×D5—124no—
546C4×D5—124no—
547C25—151no—
548C23×C4—151no—
549C23×C4—151no—
550C23×C4—151no—
551C23×C4—151no—
552C23×C4—151no—
553C23×C4—151no—
554C2×C4⋊C4—31no—
555C2×C4⋊C4—51no—
556C2×C4⋊C4—151no—
557C2×C4⋊C4—151no—
558C2×C4⋊C4—304no—
559C2×C22⋊C4—31no—
560C2×C22⋊C4—31no—
561C2×C22⋊C4—51no—
562C2×C22⋊C4—51no—
563C2×C22⋊C4—158no—
564C2×C22⋊C4—151no—
565C2×C22⋊C4—151no—
566C2×C22⋊C4—151no—
567C2×C22⋊C4—151no—
568C2×C22⋊C4—151no—
569C2×C22⋊C4—151no—
570C2×C22⋊C4—151no—
571C2×C22⋊C4—304no—
572C2×C22⋊C4—304no—
573C2×C22⋊C4D3×D511yescharacteristic
574C2×C42—31no—
575C2×C42—51no—
576C2×C42—151no—
577C2×C42—151no—
578C2×C42—304no—
579#95—31no—
580#95—31no—
581#95—51no—
582#95—51no—
583#95—151no—
584#95—151no—
585#95—151no—
586#95—151no—
587C2×C3×C5—42no—
588C2×C3×C5C2×#11711yescharacteristic
589C2×C3×C5C2×C4×D411yescharacteristic
590C2×C3×C5C2×C4×D411yescharacteristic
591C2×C3×C5C2×#12111yescharacteristic
592C2×C3×C5C2×#12311yescharacteristic
593C2×C3×C5C2×#12411yescharacteristic
594C2×C3×C5C2×#12611yescharacteristic
595D15—42no—
596D15#38818yescomplemented
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—21no—
603C23×C3C2×C4×D512yes—
604C23×C3C23×D511yescharacteristic
605C22×D3—52no—
606C22×D3—52no—
607C22×D3—52no—
608C22×D3—52no—
609C22×D3—52no—
610C22×D3—52no—
611C22×D3—52no—
612C22×D3—52no—
613C22×D3—108no—
614C22×D3—108no—
615C22×D3—108no—
616C22×D3—101no—
617C22×D3—101no—
618C22×D3—101no—
619C22×D3—101no—
620C22×D3—101no—
621C22×D3—101no—
622C22×D3—204no—
623C22×D3—204no—
624C22×D3—204no—
625C22×D3—204no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—52no—
632C2×C3×C4—52no—
633C2×C3×C4—52no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4—101no—
639C2×C3×C4—101no—
640C2×C3×C4—101no—
641C2×C3×C4—101no—
642C2×C3×C4—101no—
643C2×C3×C4D4×D512yes—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—52no—
654C2×Dic3—101no—
655C2×Dic3—101no—
656C2×Dic3—101no—
657C2×Dic3—101no—
658C2×Dic3—101no—
659C2×Dic3C2×C4×D512yes—
660C2×Dic3C2×C4×D512yes—
661C2×Dic3D4×D512yes—
662C4×D3—108no—
663C4×D3—108no—
664C4×D3—108no—
665C4×D3—108no—
666C4×D3—204no—
667C4×D3—204no—
668C22×C5—22no—
669C22×C5—22no—
670C22×C5—22no—
671C22×C5—41no—
672C22×C5—41no—
673C22×C5—41no—
674C22×C5—41no—
675C22×C5C22×C4×D311yescharacteristic
676C22×C5C2×D3×D411yescharacteristic
677C22×C5C2×D3×D411yescharacteristic
678C22×C5D3×#4111yescharacteristic
679C22×C5D3×#4111yescharacteristic
680C22×C5D3×#4111yescharacteristic
681C22×C5D3×#4111yescharacteristic
682C2×D5—34no—
683C2×D5—34no—
684C2×D5—34no—
685C2×D5—34no—
686C2×D5—34no—
687C2×D5—34no—
688C2×D5—34no—
689C2×D5—62no—
690C2×D5—62no—
691C2×D5—62no—
692C2×D5—1216no—
693C2×D5—121no—
694C2×D5—121no—
695C2×D5—121no—
696C2×D5—121no—
697C4×C5—22no—
698C4×C5—41no—
699C4×C5—62no—
700C4×C5—62no—
701C4×C5—62no—
702C4×C5—121no—
703Dic5—22no—
704Dic5—22no—
705Dic5—22no—
706Dic5—41no—
707Dic5—62no—
708Dic5—121no—
709C24—151no—
710C24—154no—
711C24—151no—
712C24—302no—
713C24—302no—
714C24—302no—
715C24—302no—
716C24—302no—
717C24—302no—
718C24C2×D3×D511yescharacteristic
719C22×C4—31no—
720C22×C4—31no—
721C22×C4—31no—
722C22×C4—31no—
723C22×C4—51no—
724C22×C4—51no—
725C22×C4—51no—
726C22×C4—51no—
727C22×C4—154no—
728C22×C4—154no—
729C22×C4—154no—
730C22×C4—151no—
731C22×C4—154no—
732C22×C4—151no—
733C22×C4—302no—
734C22×C4—302no—
735C22×C4—302no—
736C22×C4—302no—
737C22×C4—302no—
738C22×C4—302no—
739C22×C4—302no—
740C22×C4—302no—
741C22×C4—302no—
742C22×C4—302no—
743C22×C4—302no—
744C22×C4—302no—
745C22×C4—302no—
746C22×C4—302no—
747C22×C4C2×D3×D511yescharacteristic
748C22×C4C2×D3×D511yescharacteristic
749C4⋊C4—62no—
750C4⋊C4—102no—
751C4⋊C4—302no—
752C4⋊C4—302no—
753C22⋊C4—22no—
754C22⋊C4—34no—
755C22⋊C4—54no—
756C22⋊C4—62no—
757C22⋊C4—102no—
758C22⋊C4—154no—
759C22⋊C4—154no—
760C22⋊C4—302no—
761C22⋊C4—302no—
762C22⋊C4—302no—
763C22⋊C4—302no—
764C22⋊C4—302no—
765C42—62no—
766C42—102no—
767C42—302no—
768C42—302no—
769C3×C5C2×#38811yescharacteristic, complemented, Hall
770C22×C3—22no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3C22×C4×D511yescharacteristic
778C22×C3C2×D4×D511yescharacteristic
779C22×C3C2×D4×D511yescharacteristic
780C22×C3D5×#4111yescharacteristic
781C22×C3D5×#4111yescharacteristic
782C22×C3D5×#4111yescharacteristic
783C22×C3D5×#4111yescharacteristic
784C2×D3—54no—
785C2×D3—54no—
786C2×D3—54no—
787C2×D3—54no—
788C2×D3—54no—
789C2×D3—54no—
790C2×D3—54no—
791C2×D3—102no—
792C2×D3—102no—
793C2×D3—102no—
794C2×D3—2016no—
795C2×D3—201no—
796C2×D3—201no—
797C2×D3—201no—
798C2×D3—201no—
799C3×C4—22no—
800C3×C4—41no—
801C3×C4—102no—
802C3×C4—102no—
803C3×C4—102no—
804C3×C4—201no—
805Dic3—22no—
806Dic3—22no—
807Dic3—22no—
808Dic3—41no—
809Dic3—102no—
810Dic3—201no—
811C2×C5—42no—
812C2×C5D3×#11711yescharacteristic
813C2×C5C4×D3×D411yescharacteristic
814C2×C5C4×D3×D411yescharacteristic
815C2×C5D3×#12111yescharacteristic
816C2×C5D3×#12311yescharacteristic
817C2×C5D3×#12411yescharacteristic
818C2×C5D3×#12611yescharacteristic
819D5—38no—
820D5—122no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—152no—
828C23—152no—
829C23—152no—
830C23—152no—
831C23—152no—
832C23—152no—
833C23—152no—
834C23—152no—
835C23—308no—
836C23—308no—
837C23—308no—
838C23—301no—
839C23—301no—
840C23—301no—
841C23—301no—
842C23—301no—
843C23—301no—
844C23—604no—
845C23—604no—
846C23—604no—
847C23—604no—
848C23C4×D3×D512yes—
849C23C22×D3×D511yescharacteristic
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—32no—
856C2×C4—32no—
857C2×C4—32no—
858C2×C4—52no—
859C2×C4—52no—
860C2×C4—52no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—101no—
871C2×C4—101no—
872C2×C4—101no—
873C2×C4—101no—
874C2×C4—101no—
875C2×C4—101no—
876C2×C4—101no—
877C2×C4—101no—
878C2×C4—101no—
879C2×C4—152no—
880C2×C4—308no—
881C2×C4—308no—
882C2×C4—308no—
883C2×C4—308no—
884C2×C4—301no—
885C2×C4—301no—
886C2×C4—301no—
887C2×C4—301no—
888C2×C4—301no—
889C2×C4—604no—
890C2×C4—604no—
891C2×C4#679012yes—
892C2×C3—42no—
893C2×C3D5×#11711yescharacteristic
894C2×C3C4×D4×D511yescharacteristic
895C2×C3C4×D4×D511yescharacteristic
896C2×C3D5×#12111yescharacteristic
897C2×C3D5×#12311yescharacteristic
898C2×C3D5×#12411yescharacteristic
899C2×C3D5×#12611yescharacteristic
900D3—58no—
901D3—202no—
902C5D3×#38811yescharacteristic, complemented, Sylow
903C22—22no—
904C22—22no—
905C22—22no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—154no—
911C22—154no—
912C22—154no—
913C22—154no—
914C22—154no—
915C22—154no—
916C22—154no—
917C22—302no—
918C22—302no—
919C22—302no—
920C22—6016no—
921C22—601no—
922C22—601no—
923C22—601no—
924C22—601no—
925C22C2×C4×D3×D511yescharacteristic
926C22#9201611yescharacteristic
927C22D3×D4×D511yescharacteristic
928C22#9202411yescharacteristic
929C22#9202411yescharacteristic
930C22#9202411yescharacteristic
931C22C2×#679011yescharacteristic
932C4—22no—
933C4—41no—
934C4—62no—
935C4—62no—
936C4—62no—
937C4—102no—
938C4—102no—
939C4—102no—
940C4—121no—
941C4—201no—
942C4—302no—
943C4—601no—
944C3D5×#38811yescharacteristic, complemented, Sylow
945C2—42no—
946C2—158no—
947C2—602no—
948C2#1175282511yescharacteristic
949C2#1175301711yescharacteristic
950C2#1175320311yescharacteristic
951C2#1175321011yescharacteristic
952C2C4×#679011yescharacteristic
953C2#1175483111yescharacteristic
954C2#1175504911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×D15C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#388
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#91404C2semidirect
5. C2×C4×#1200C2semidirect
6. C5×#4945C2semidirect
7. C3×#65234C2semidirect
8. #11749485C2semidirect
9. #11749478C2semidirect
10. #11748888C2semidirect
11. #11748888C2semidirect
12. #11748728C2semidirect
13. #11748727C2semidirect
14. #11748671C2semidirect
15. #11748668C2semidirect
31. C2×C5×Dic3⋊C4C22semidirect
32. C2×C4×C5×Dic3C22semidirect
35. C2×C3×#683C22semidirect
36. C2×C3×C4×Dic5C22semidirect
38. #91561C4semidirect
39. C2×Dic3⋊Dic5C22semidirect
40. C2×#6668C22semidirect
45. C2×Dic3×Dic5C22semidirect
46. C2×Dic3×Dic5C22semidirect
49. C5×C3⋊#95C22semidirect
50. C5×C3⋊#95C22semidirect
51. C3×#3963C22semidirect
52. C3×#3963C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
66. #65234D3semidirect
118. C5×#217C2×C4semidirect
122. C3×C22⋊Dic5C2×C4semidirect
129. #6667C2×C4semidirect
130. #6667C2×C4semidirect
141. #4945D5semidirect
171. C2×#683C2×D3semidirect
174. C2×C4×Dic5C2×D3semidirect
186. #3963C2×D3semidirect
187. #3963C2×D3semidirect
283. C2×Dic3⋊C4C2×D5semidirect
286. C2×C4×Dic3C2×D5semidirect
298. C3⋊#95C2×D5semidirect
299. C3⋊#95C2×D5semidirect
347. C22⋊Dic5C4×D3semidirect
463. #217C4×D5semidirect
596. D15#388semidirect
769. C3×C5C2×#388semidirect
902. C5D3×#388semidirect
944. C3D5×#388semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D152
C2×#915612
C2×#914042
C2×C4×#12002
C5×#49452
C3×#652342
#117494852
#117494782
#117488882
#117487282
#117487272
#117486712
#117486682
D5×#3883
D3×#3885