Finite Group Databasebeta

← #14323347

Subgroups — #14323347

Order 1920.

1616 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91782C211yesmaximal, characteristic, complemented
2C2×#91771C211yesmaximal, characteristic
3C2×C22⋊C4×D15C211yesmaximal, characteristic, complemented
4C3×C5×#388C211yesmaximal, characteristic, complemented
5#11751091C211yesmaximal, characteristic, complemented
6#11751058C211yesmaximal, characteristic, complemented
7#11751057C211yesmaximal, characteristic, complemented
8#11751056C211yesmaximal, characteristic, complemented
9#11751052C211yesmaximal, characteristic, complemented
10#11751040C211yesmaximal, characteristic, complemented
11C4×#6714C211yesmaximal, characteristic, complemented
12#11750770C211yesmaximal, characteristic, complemented
13#11750769C211yesmaximal, characteristic, complemented
14#11750766C211yesmaximal, characteristic, complemented
15#11750766C211yesmaximal, characteristic, complemented
16#10607557—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic
22C22×C4×D15C2211yescharacteristic
23C22×C4×D15C2211yescharacteristic, complemented
24C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C42×C5C2211yescharacteristic, complemented
29C2×#6719C2211yescharacteristic
30C2×#6719C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×#6714C2211yescharacteristic
38C2×#6714C2211yescharacteristic
39C2×#6714C2211yescharacteristic, complemented
40C2×#6714C2211yescharacteristic, complemented
41C2×#6714C2211yescharacteristic, complemented
42C2×C4⋊Dic15C2211yescharacteristic, complemented
43C2×#6712C2211yescharacteristic, complemented
44C2×C4×Dic15C2211yescharacteristic, complemented
45C2×C4×Dic15C2211yescharacteristic, complemented
46#91782—24no—
47#91771C418yescomplemented
48C22⋊C4×D15—24no—
49C3×C5×#95C2211yescharacteristic, complemented
50C3×C5×#95C2211yescharacteristic, complemented
51#91115C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53#91115C2211yescharacteristic, complemented
54#91115C2211yescharacteristic, complemented
55#75826—51nomaximal, Hall
56C2×#4039—31no—
57C2×#4028—31no—
58C2×D5×C22⋊C4—31no—
59C5×#388D311yescharacteristic, complemented
60#65279—31no—
61#65246—31no—
62#65245—31no—
63#65244—31no—
64#65240—31no—
65#65228—31no—
66C4×#685—31no—
67#64958—31no—
68#64957—31no—
69#64954—31no—
70#64954—31no—
71C24×C3×C5C2311yescharacteristic
72C23×D15—22no—
73C23×D15—22no—
74C23×D15—41no—
75C23×D15—41no—
76C23×D15—41no—
77C23×D15—41no—
78C23×D15C2×C414yescomplemented
79C23×D15C2311yescharacteristic
80C23×D15C2311yescharacteristic
81C23×D15C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C2×#1220—41no—
89C2×#1220—41no—
90C2×#1220C2×C414yescomplemented
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C22×Dic15C2311yescharacteristic
96C2×D60—22no—
97C2×D60—22no—
98C2×D60—41no—
99C2×D60—41no—
100C2×D60C2×C414yes—
101C2×D60C2×C414yescomplemented
102C2×C4×D15—22no—
103C2×C4×D15—22no—
104C2×C4×D15—41no—
105C2×C4×D15—41no—
106C2×C4×D15—41no—
107C2×C4×D15—41no—
108C2×C4×D15—41no—
109C2×C4×D15—41no—
110C2×C4×D15D414yescomplemented
111C3×C5×C4⋊C4—22no—
112C3×C5×C22⋊C4—22no—
113C3×C5×C22⋊C4—41no—
114C3×C5×C22⋊C4C2×C414yescomplemented
115C3×C42×C5—41no—
116#6719—22no—
117#6719—41no—
118#6714—22no—
119#6714—22no—
120#6714—22no—
121#6714—22no—
122#6714—22no—
123#6714—41no—
124#6714—41no—
125#6714—41no—
126#6714—41no—
127#6714C2×C414yescomplemented
128#6714C2×C414yescomplemented
129C4⋊Dic15—41no—
130#6712—41no—
131C4×Dic15—22no—
132C4×Dic15—41no—
133C2×#893—51no—
134C2×#882—51no—
135C2×D3×C22⋊C4—51no—
136C3×#388D511yescharacteristic, complemented
137#4990—51no—
138#4957—51no—
139#4956—51no—
140#4955—51no—
141#4951—51no—
142#4939—51no—
143C4×(C2×D3)⋊C4—51no—
144#4669—51no—
145#4668—51no—
146#4665—51no—
147#4665—51no—
148C24×D5—31no—
149C22×C22⋊D5—31no—
150C22×D20—31no—
151C22×D20—31no—
152C22×C4×D5—31no—
153C22×C4×D5—31no—
154C22×C4×D5—31no—
155C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
156C2×C5×C22⋊C4C2×D311yescharacteristic
157C2×C5×C22⋊C4C2×D311yescharacteristic
158C2×C5×C22⋊C4C2×D311yescharacteristic
159C2×C42×C5C2×D311yescharacteristic, complemented
160C2×C22⋊Dic5—31no—
161C2×C22⋊Dic5—31no—
162C2×#685—31no—
163C2×#685—31no—
164C2×#685—31no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685—31no—
170C2×#685—31no—
171C2×#685—31no—
172C2×#685—31no—
173C2×C4⋊Dic5—31no—
174C2×#683—31no—
175C2×C4×Dic5—31no—
176C2×C4×Dic5—31no—
177#4039—64no—
178#4028—38no—
179D5×C22⋊C4—64no—
180C5×#95C2×D311yescharacteristic, complemented
181C5×#95C2×D311yescharacteristic, complemented
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#2321—151noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5C22×C412yes—
194C23×C3×C5C2411yescharacteristic
195C22×D15—21no—
196C22×D15—21no—
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—21no—
200C22×D15—21no—
201C22×D15—21no—
202C22×D15—21no—
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—21no—
207C22×D15—21no—
208C22×D15—21no—
209C22×D15—21no—
210C22×D15—21no—
211C22×D15—28no—
212C22×D15—44no—
213C22×D15—44no—
214C22×D15—44no—
215C22×D15—44no—
216C22×D15—44no—
217C22×D15—44no—
218C22×D15C22×C412yes—
219C22×D15C22×C412yes—
220C22×D15C22×C412yes—
221C22×D15C2×D412yes—
222C22×D15#4112yes—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5—21no—
236C2×C3×C4×C5—21no—
237C2×C3×C4×C5—21no—
238C2×C3×C4×C5C22×C412yes—
239C2×C3×C4×C5C22×C412yes—
240C2×C3×C4×C5C2×D412yes—
241#1220—44no—
242C2×Dic15—21no—
243C2×Dic15—21no—
244C2×Dic15—21no—
245C2×Dic15—21no—
246C2×Dic15—21no—
247C2×Dic15—21no—
248C2×Dic15—21no—
249C2×Dic15—21no—
250C2×Dic15—21no—
251C2×Dic15—21no—
252C2×Dic15—21no—
253C2×Dic15—21no—
254C2×Dic15—21no—
255C2×Dic15C22×C412yes—
256C2×Dic15C2×D412yes—
257D60—28no—
258D60—44no—
259C4×D15—44no—
260C4×D15—44no—
261C4×D15—44no—
262C24×D3—51no—
263C22×#67—51no—
264C22×D12—51no—
265C22×D12—51no—
266C22×C4×D3—51no—
267C22×C4×D3—51no—
268C22×C4×D3—51no—
269C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
270C2×C3×C22⋊C4C2×D511yescharacteristic
271C2×C3×C22⋊C4C2×D511yescharacteristic
272C2×C3×C22⋊C4C2×D511yescharacteristic
273C2×C3×C42C2×D511yescharacteristic, complemented
274C2×#217—51no—
275C2×#217—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×(C2×D3)⋊C4—51no—
282C2×(C2×D3)⋊C4—51no—
283C2×(C2×D3)⋊C4—51no—
284C2×(C2×D3)⋊C4—51no—
285C2×(C2×D3)⋊C4—51no—
286C2×(C2×D3)⋊C4—51no—
287C2×C4⋊Dic3—51no—
288C2×Dic3⋊C4—51no—
289C2×C4×Dic3—51no—
290C2×C4×Dic3—51no—
291#893—104no—
292#882—58no—
293D3×C22⋊C4—104no—
294C3×#95C2×D511yescharacteristic, complemented
295C3×#95C2×D511yescharacteristic, complemented
296C3⋊#95—51no—
297C3⋊#95—51no—
298C3⋊#95—51no—
299C3⋊#95—51no—
300C24×C5C22×D311yescharacteristic
301C23×D5—31no—
302C23×D5—31no—
303C23×D5—31no—
304C23×D5—34no—
305C23×D5—62no—
306C23×D5—62no—
307C23×D5—121no—
308C23×D5—121no—
309C23×D5—121no—
310C23×D5—121no—
311C22×C4×C5C22×D311yescharacteristic
312C22×C4×C5C22×D311yescharacteristic
313C22×C4×C5C22×D311yescharacteristic
314C22×C4×C5C22×D311yescharacteristic
315C22×C4×C5C22×D311yescharacteristic
316C22×C4×C5C22×D311yescharacteristic
317C2×C22⋊D5—34no—
318C2×C22⋊D5—121no—
319C2×C22⋊D5—121no—
320C22×Dic5—31no—
321C22×Dic5—31no—
322C22×Dic5—31no—
323C22×Dic5—31no—
324C22×Dic5—31no—
325C2×D20—34no—
326C2×D20—34no—
327C2×D20—62no—
328C2×D20—62no—
329C2×D20—121no—
330C2×D20—121no—
331C2×C4×D5—34no—
332C2×C4×D5—62no—
333C2×C4×D5—62no—
334C2×C4×D5—121no—
335C2×C4×D5—121no—
336C2×C4×D5—121no—
337C2×C4×D5—121no—
338C2×C4×D5—121no—
339C2×C4×D5—121no—
340C5×C4⋊C4—22no—
341C5×C22⋊C4—22no—
342C5×C22⋊C4—41no—
343C5×C22⋊C4C4×D314yescomplemented
344C42×C5—41no—
345C22⋊Dic5—62no—
346C22⋊Dic5—121no—
347#685—34no—
348#685—34no—
349#685—62no—
350#685—62no—
351#685—62no—
352#685—62no—
353#685—62no—
354#685—121no—
355#685—121no—
356#685—121no—
357#685—121no—
358C4⋊Dic5—121no—
359#683—121no—
360C4×Dic5—62no—
361C4×Dic5—121no—
362C2×#120—151no—
363C2×C4×D4—151no—
364C22×C22⋊C4—151no—
365#390—151no—
366#390—151no—
367#388—151no—
368#388—151no—
369#388—151no—
370#388D1511yescharacteristic, complemented
371#386—151no—
372#386—151no—
373#386—151no—
374#385—151no—
375#379—151no—
376C4×C22⋊C4—151no—
377C22×C3×C5—22no—
378C22×C3×C5—22no—
379C22×C3×C5—22no—
380C22×C3×C5—41no—
381C22×C3×C5—41no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5C23×C411yescharacteristic
385C22×C3×C5C22×D411yescharacteristic
386C22×C3×C5C2×#4111yescharacteristic
387C22×C3×C5H(5,𝔽2)11yescharacteristic
388C22×C3×C5H(5,𝔽2)11yescharacteristic
389C22×C3×C5H(5,𝔽2)11yescharacteristic
390C22×C3×C5H(5,𝔽2)11yescharacteristic
391C2×D15—22no—
392C2×D15—22no—
393C2×D15—22no—
394C2×D15—22no—
395C2×D15—22no—
396C2×D15—22no—
397C2×D15—22no—
398C2×D15—22no—
399C2×D15—22no—
400C2×D15—22no—
401C2×D15—22no—
402C2×D15—22no—
403C2×D15—416no—
404C2×D15—41no—
405C2×D15—41no—
406C2×D15—41no—
407C2×D15—41no—
408C2×D15—41no—
409C2×D15—41no—
410C2×D15—41no—
411C2×D15—41no—
412C2×D15C4×D414yes—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415C3×C4×C5—22no—
416C3×C4×C5—41no—
417C3×C4×C5—41no—
418C3×C4×C5—41no—
419Dic15—22no—
420Dic15—22no—
421Dic15—41no—
422Dic15—41no—
423Dic15—41no—
424C24×C3C22×D511yescharacteristic
425C23×D3—51no—
426C23×D3—51no—
427C23×D3—51no—
428C23×D3—54no—
429C23×D3—102no—
430C23×D3—102no—
431C23×D3—201no—
432C23×D3—201no—
433C23×D3—201no—
434C23×D3—201no—
435C22×C3×C4C22×D511yescharacteristic
436C22×C3×C4C22×D511yescharacteristic
437C22×C3×C4C22×D511yescharacteristic
438C22×C3×C4C22×D511yescharacteristic
439C22×C3×C4C22×D511yescharacteristic
440C22×C3×C4C22×D511yescharacteristic
441C2×#67—54no—
442C2×#67—201no—
443C2×#67—201no—
444C22×Dic3—51no—
445C22×Dic3—51no—
446C22×Dic3—51no—
447C22×Dic3—51no—
448C22×Dic3—51no—
449C2×D12—54no—
450C2×D12—54no—
451C2×D12—102no—
452C2×D12—102no—
453C2×D12—201no—
454C2×D12—201no—
455C2×C4×D3—54no—
456C2×C4×D3—102no—
457C2×C4×D3—102no—
458C2×C4×D3—201no—
459C2×C4×D3—201no—
460C2×C4×D3—201no—
461C2×C4×D3—201no—
462C2×C4×D3—201no—
463C2×C4×D3—201no—
464C3×C4⋊C4—22no—
465C3×C22⋊C4—22no—
466C3×C22⋊C4—41no—
467C3×C22⋊C4C4×D514yescomplemented
468C3×C42—41no—
469#217—102no—
470#217—201no—
471(C2×D3)⋊C4—54no—
472(C2×D3)⋊C4—54no—
473(C2×D3)⋊C4—102no—
474(C2×D3)⋊C4—102no—
475(C2×D3)⋊C4—102no—
476(C2×D3)⋊C4—102no—
477(C2×D3)⋊C4—102no—
478(C2×D3)⋊C4—201no—
479(C2×D3)⋊C4—201no—
480(C2×D3)⋊C4—201no—
481(C2×D3)⋊C4—201no—
482C4⋊Dic3—201no—
483Dic3⋊C4—201no—
484C4×Dic3—102no—
485C4×Dic3—201no—
486C23×C5—21no—
487C23×C5—21no—
488C23×C5—21no—
489C23×C5—21no—
490C23×C5—21no—
491C23×C5—21no—
492C23×C5C2×C4×D312yes—
493C23×C5C23×D311yescharacteristic
494C22×D5—32no—
495C22×D5—32no—
496C22×D5—32no—
497C22×D5—32no—
498C22×D5—32no—
499C22×D5—68no—
500C22×D5—61no—
501C22×D5—61no—
502C22×D5—61no—
503C22×D5—61no—
504C22×D5—61no—
505C22×D5—61no—
506C22×D5—61no—
507C22×D5—61no—
508C22×D5—61no—
509C22×D5—61no—
510C22×D5—61no—
511C22×D5—61no—
512C22×D5—61no—
513C22×D5—61no—
514C22×D5—61no—
515C22×D5—61no—
516C22×D5—124no—
517C22×D5—124no—
518C22×D5—124no—
519C22×D5—124no—
520C22×D5—124no—
521C22×D5—124no—
522C2×C4×C5—21no—
523C2×C4×C5—21no—
524C2×C4×C5—21no—
525C2×C4×C5—21no—
526C2×C4×C5—21no—
527C2×C4×C5—21no—
528C2×C4×C5—21no—
529C2×C4×C5—21no—
530C2×C4×C5—21no—
531C2×C4×C5—21no—
532C2×C4×C5—21no—
533C2×C4×C5—21no—
534C2×C4×C5—21no—
535C2×C4×C5—21no—
536C2×C4×C5—21no—
537C2×C4×C5C2×C4×D312yes—
538C2×C4×C5C2×C4×D312yes—
539C2×C4×C5D3×D412yes—
540C22⋊D5—124no—
541C2×Dic5—32no—
542C2×Dic5—32no—
543C2×Dic5—61no—
544C2×Dic5—61no—
545C2×Dic5—61no—
546C2×Dic5—61no—
547C2×Dic5—61no—
548C2×Dic5—61no—
549C2×Dic5—61no—
550C2×Dic5—61no—
551C2×Dic5—61no—
552C2×Dic5—61no—
553C2×Dic5—61no—
554C2×Dic5—61no—
555C2×Dic5—61no—
556D20—68no—
557D20—124no—
558C4×D5—124no—
559C4×D5—124no—
560C4×D5—124no—
561C25—151no—
562C22×D4—151no—
563C22×D4—151no—
564C22×D4—151no—
565C23×C4—151no—
566C23×C4—151no—
567C23×C4—151no—
568#120—158no—
569C4×D4—304no—
570C2×C4⋊C4—151no—
571C2×C4⋊C4—151no—
572C2×C4⋊C4C2×D1511yescharacteristic, complemented
573C2×C22⋊C4—151no—
574C2×C22⋊C4—151no—
575C2×C22⋊C4—151no—
576C2×C22⋊C4—151no—
577C2×C22⋊C4—151no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—151no—
584C2×C22⋊C4—151no—
585C2×C22⋊C4—151no—
586C2×C22⋊C4—304no—
587C2×C22⋊C4C2×D1511yescharacteristic
588C2×C22⋊C4C2×D1511yescharacteristic
589C2×C22⋊C4C2×D1511yescharacteristic
590C2×C42—151no—
591C2×C42—151no—
592C2×C42C2×D1511yescharacteristic, complemented
593#95—151no—
594#95—151no—
595#95—151no—
596#95—151no—
597#95C2×D1511yescharacteristic, complemented
598#95C2×D1511yescharacteristic, complemented
599C2×C3×C5—42no—
600C2×C3×C5C2×C4×D411yescharacteristic
601C2×C3×C5#51811yescharacteristic
602C2×C3×C5#51811yescharacteristic
603C2×C3×C5#53411yescharacteristic
604C2×C3×C5#53511yescharacteristic
605C2×C3×C5#53811yescharacteristic
606C2×C3×C5#53811yescharacteristic
607D15—24no—
608D15—42no—
609D15—42no—
610C23×C3—21no—
611C23×C3—21no—
612C23×C3—21no—
613C23×C3—21no—
614C23×C3—21no—
615C23×C3—21no—
616C23×C3C2×C4×D512yes—
617C23×C3C23×D511yescharacteristic
618C22×D3—52no—
619C22×D3—52no—
620C22×D3—52no—
621C22×D3—52no—
622C22×D3—52no—
623C22×D3—108no—
624C22×D3—101no—
625C22×D3—101no—
626C22×D3—101no—
627C22×D3—101no—
628C22×D3—101no—
629C22×D3—101no—
630C22×D3—101no—
631C22×D3—101no—
632C22×D3—101no—
633C22×D3—101no—
634C22×D3—101no—
635C22×D3—101no—
636C22×D3—101no—
637C22×D3—101no—
638C22×D3—101no—
639C22×D3—101no—
640C22×D3—204no—
641C22×D3—204no—
642C22×D3—204no—
643C22×D3—204no—
644C22×D3—204no—
645C22×D3—204no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4C2×C4×D512yes—
662C2×C3×C4C2×C4×D512yes—
663C2×C3×C4D4×D512yes—
664#67—204no—
665C2×Dic3—52no—
666C2×Dic3—52no—
667C2×Dic3—101no—
668C2×Dic3—101no—
669C2×Dic3—101no—
670C2×Dic3—101no—
671C2×Dic3—101no—
672C2×Dic3—101no—
673C2×Dic3—101no—
674C2×Dic3—101no—
675C2×Dic3—101no—
676C2×Dic3—101no—
677C2×Dic3—101no—
678C2×Dic3—101no—
679C2×Dic3—101no—
680D12—108no—
681D12—204no—
682C4×D3—204no—
683C4×D3—204no—
684C4×D3—204no—
685C22×C5—22no—
686C22×C5—22no—
687C22×C5—22no—
688C22×C5—41no—
689C22×C5—41no—
690C22×C5—41no—
691C22×C5—41no—
692C22×C5C22×C4×D311yescharacteristic
693C22×C5C2×D3×D411yescharacteristic
694C22×C5#100411yescharacteristic
695C22×C5D3×#4111yescharacteristic
696C22×C5#100911yescharacteristic
697C22×C5#100911yescharacteristic
698C22×C5#100911yescharacteristic
699C2×D5—34no—
700C2×D5—62no—
701C2×D5—62no—
702C2×D5—62no—
703C2×D5—62no—
704C2×D5—62no—
705C2×D5—62no—
706C2×D5—62no—
707C2×D5—62no—
708C2×D5—62no—
709C2×D5—62no—
710C2×D5—62no—
711C2×D5—62no—
712C2×D5—1216no—
713C2×D5—121no—
714C2×D5—121no—
715C2×D5—121no—
716C2×D5—121no—
717C2×D5—121no—
718C2×D5—121no—
719C2×D5—121no—
720C2×D5—121no—
721C4×C5—22no—
722C4×C5—22no—
723C4×C5—22no—
724C4×C5—41no—
725C4×C5—41no—
726C4×C5—41no—
727Dic5—62no—
728Dic5—62no—
729Dic5—121no—
730Dic5—121no—
731Dic5—121no—
732C24—151no—
733C24—151no—
734C24—151no—
735C24—154no—
736C24—302no—
737C24—302no—
738C24—601no—
739C24—601no—
740C24—601no—
741C24—601no—
742C24C22×D1511yescharacteristic
743C2×D4—154no—
744C2×D4—154no—
745C2×D4—154no—
746C2×D4—302no—
747C2×D4—302no—
748C2×D4—601no—
749C2×D4—601no—
750C2×D4—601no—
751C2×D4—601no—
752C22×C4—151no—
753C22×C4—151no—
754C22×C4—154no—
755C22×C4—151no—
756C22×C4—151no—
757C22×C4—151no—
758C22×C4—302no—
759C22×C4—302no—
760C22×C4—601no—
761C22×C4—601no—
762C22×C4—601no—
763C22×C4—601no—
764C22×C4—601no—
765C22×C4—601no—
766C22×C4C22×D1511yescharacteristic
767C22×C4C22×D1511yescharacteristic
768C22×C4C22×D1511yescharacteristic
769C22×C4C22×D1511yescharacteristic
770C22×C4C22×D1511yescharacteristic
771C22×C4C22×D1511yescharacteristic
772C4⋊C4—22no—
773C4⋊C4—601no—
774C4⋊C4—601no—
775C22⋊C4—22no—
776C22⋊C4—41no—
777C22⋊C4—154no—
778C22⋊C4—154no—
779C22⋊C4—302no—
780C22⋊C4—302no—
781C22⋊C4—302no—
782C22⋊C4—302no—
783C22⋊C4—302no—
784C22⋊C4—302no—
785C22⋊C4—601no—
786C22⋊C4—601no—
787C22⋊C4—601no—
788C22⋊C4—601no—
789C22⋊C4—601no—
790C22⋊C4C4×D1514yescomplemented
791C42—41no—
792C42—302no—
793C42—601no—
794C3×C5#232111yescharacteristic, complemented, Hall
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—41no—
799C22×C3—41no—
800C22×C3—41no—
801C22×C3—41no—
802C22×C3C22×C4×D511yescharacteristic
803C22×C3C2×D4×D511yescharacteristic
804C22×C3#414411yescharacteristic
805C22×C3D5×#4111yescharacteristic
806C22×C3#414911yescharacteristic
807C22×C3#414911yescharacteristic
808C22×C3#414911yescharacteristic
809C2×D3—54no—
810C2×D3—102no—
811C2×D3—102no—
812C2×D3—102no—
813C2×D3—102no—
814C2×D3—102no—
815C2×D3—102no—
816C2×D3—102no—
817C2×D3—102no—
818C2×D3—102no—
819C2×D3—102no—
820C2×D3—102no—
821C2×D3—102no—
822C2×D3—2016no—
823C2×D3—201no—
824C2×D3—201no—
825C2×D3—201no—
826C2×D3—201no—
827C2×D3—201no—
828C2×D3—201no—
829C2×D3—201no—
830C2×D3—201no—
831C3×C4—22no—
832C3×C4—22no—
833C3×C4—22no—
834C3×C4—41no—
835C3×C4—41no—
836C3×C4—41no—
837Dic3—102no—
838Dic3—102no—
839Dic3—201no—
840Dic3—201no—
841Dic3—201no—
842C2×C5—42no—
843C2×C5#552111yescharacteristic
844C2×C5C4×D3×D411yescharacteristic
845C2×C5#554511yescharacteristic
846C2×C5#560511yescharacteristic
847C2×C5#565711yescharacteristic
848C2×C5#567411yescharacteristic
849C2×C5#570411yescharacteristic
850D5—64no—
851D5—122no—
852D5—122no—
853C23—21no—
854C23—21no—
855C23—21no—
856C23—21no—
857C23—21no—
858C23—21no—
859C23—152no—
860C23—152no—
861C23—152no—
862C23—152no—
863C23—152no—
864C23—308no—
865C23—301no—
866C23—301no—
867C23—301no—
868C23—301no—
869C23—301no—
870C23—301no—
871C23—301no—
872C23—301no—
873C23—301no—
874C23—301no—
875C23—301no—
876C23—301no—
877C23—301no—
878C23—301no—
879C23—301no—
880C23—301no—
881C23—604no—
882C23—604no—
883C23—604no—
884C23—604no—
885C23—604no—
886C23—604no—
887C23C2×C4×D1512yes—
888C23C23×D1511yescharacteristic
889D4—308no—
890D4—604no—
891D4—604no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—152no—
908C2×C4—152no—
909C2×C4—301no—
910C2×C4—301no—
911C2×C4—301no—
912C2×C4—301no—
913C2×C4—301no—
914C2×C4—301no—
915C2×C4—301no—
916C2×C4—301no—
917C2×C4—301no—
918C2×C4—301no—
919C2×C4—301no—
920C2×C4—301no—
921C2×C4—301no—
922C2×C4—604no—
923C2×C4—604no—
924C2×C4—604no—
925C2×C4C2×C4×D1512yes—
926C2×C4C2×C4×D1512yes—
927C2×C4D4×D1512yes—
928C2×C3—42no—
929C2×C3#6585511yescharacteristic
930C2×C3C4×D4×D511yescharacteristic
931C2×C3#6587911yescharacteristic
932C2×C3#6593911yescharacteristic
933C2×C3#6599111yescharacteristic
934C2×C3#6600811yescharacteristic
935C2×C3#6603811yescharacteristic
936D3—104no—
937D3—202no—
938D3—202no—
939C5#7582611yescharacteristic, complemented, Sylow
940C22—22no—
941C22—22no—
942C22—22no—
943C22—41no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—154no—
948C22—302no—
949C22—302no—
950C22—302no—
951C22—302no—
952C22—302no—
953C22—302no—
954C22—302no—
955C22—302no—
956C22—302no—
957C22—302no—
958C22—302no—
959C22—302no—
960C22—6016no—
961C22—601no—
962C22—601no—
963C22—601no—
964C22—601no—
965C22—601no—
966C22—601no—
967C22—601no—
968C22—601no—
969C22C22×C4×D1511yescharacteristic
970C22C2×D4×D1511yescharacteristic
971C22#9209511yescharacteristic
972C22#41×D1511yescharacteristic
973C22#9210011yescharacteristic
974C22#9210011yescharacteristic
975C22#9210011yescharacteristic
976C4—22no—
977C4—22no—
978C4—22no—
979C4—41no—
980C4—41no—
981C4—41no—
982C4—302no—
983C4—302no—
984C4—601no—
985C4—601no—
986C4—601no—
987C3#1060755711yescharacteristic, complemented, Sylow
988C2—42no—
989C2—304no—
990C2—602no—
991C2—602no—
992C2#1175628011yescharacteristic
993C2C4×D4×D1511yescharacteristic
994C2#1175630411yescharacteristic
995C2#1175636411yescharacteristic
996C2#1175641611yescharacteristic
997C2#1175643311yescharacteristic
998C2#1175646311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#388C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91771C2
hypercenter#388D15
hypocenterC3×C5#2321
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#91782C2semidirect
3. C2×C22⋊C4×D15C2semidirect
4. C3×C5×#388C2semidirect
5. #11751091C2semidirect
6. #11751058C2semidirect
7. #11751057C2semidirect
8. #11751056C2semidirect
9. #11751052C2semidirect
10. #11751040C2semidirect
11. C4×#6714C2semidirect
12. #11750770C2semidirect
13. #11750769C2semidirect
14. #11750766C2semidirect
15. #11750766C2semidirect
23. C22×C4×D15C22semidirect
24. C2×C3×C5×C4⋊C4C22semidirect
28. C2×C3×C42×C5C22semidirect
39. C2×#6714C22semidirect
40. C2×#6714C22semidirect
41. C2×#6714C22semidirect
42. C2×C4⋊Dic15C22semidirect
43. C2×#6712C22semidirect
44. C2×C4×Dic15C22semidirect
45. C2×C4×Dic15C22semidirect
47. #91771C4semidirect
49. C3×C5×#95C22semidirect
50. C3×C5×#95C22semidirect
51. #91115C22semidirect
52. #91115C22semidirect
53. #91115C22semidirect
54. #91115C22semidirect
59. C5×#388D3semidirect
78. C23×D15C2×C4semidirect
90. C2×#1220C2×C4semidirect
101. C2×D60C2×C4semidirect
110. C2×C4×D15D4semidirect
114. C3×C5×C22⋊C4C2×C4semidirect
127. #6714C2×C4semidirect
128. #6714C2×C4semidirect
136. C3×#388D5semidirect
155. C2×C5×C4⋊C4C2×D3semidirect
159. C2×C42×C5C2×D3semidirect
180. C5×#95C2×D3semidirect
181. C5×#95C2×D3semidirect
269. C2×C3×C4⋊C4C2×D5semidirect
273. C2×C3×C42C2×D5semidirect
294. C3×#95C2×D5semidirect
295. C3×#95C2×D5semidirect
343. C5×C22⋊C4C4×D3semidirect
370. #388D15semidirect
467. C3×C22⋊C4C4×D5semidirect
572. C2×C4⋊C4C2×D15semidirect
592. C2×C42C2×D15semidirect
597. #95C2×D15semidirect
598. #95C2×D15semidirect
790. C22⋊C4C4×D15semidirect
794. C3×C5#2321semidirect
939. C5#75826semidirect
987. C3#10607557semidirect

Maximal subgroups

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

subgroupindex
C2×#917822
C2×#917712
C2×C22⋊C4×D152
C3×C5×#3882
#117510912
#117510582
#117510572
#117510562
#117510522
#117510402
C4×#67142
#117507702
#117507692
#117507662
#106075573
#758265