Finite Group Databasebeta

← #14330664

Subgroups — #14330664

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4028C211yesmaximal, characteristic
2#11751052C211yesmaximal, characteristic, complemented
3C5×#4951C211yesmaximal, characteristic, complemented
4#11749518C211yesmaximal, characteristic, complemented
5#11749489C211yesmaximal, characteristic, complemented
6#11749488C211yesmaximal, characteristic, complemented
7#11749488C211yesmaximal, characteristic, complemented
8#11748896C211yesmaximal, characteristic, complemented
9#11748896C211yesmaximal, characteristic, complemented
10#11748796C211yesmaximal, characteristic, complemented
11#11748791C211yesmaximal, characteristic, complemented
12#11748785C211yesmaximal, characteristic, complemented
13#11748772C211yesmaximal, characteristic, complemented
14#11748771C211yesmaximal, characteristic, complemented
15#11748770C211yesmaximal, characteristic, complemented
16#10607571—31nomaximal, Hall
17C24×C3×D5C2211yescharacteristic
18C22×C3×C22⋊D5C2211yescharacteristic
19C22×C3×D20C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic, complemented
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25C2×C4⋊Dic15C2211yescharacteristic, complemented
26C2×C4×Dic15C2211yescharacteristic, complemented
27C2×C5×#217C2211yescharacteristic
28C2×C5×#217C2211yescharacteristic
29C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
30C2×C4×C5×Dic3C2211yescharacteristic, complemented
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C3×#4028C418yescomplemented
34C2×#6668C2211yescharacteristic, complemented
35C2×#6665C2211yescharacteristic
36C2×#6665C2211yescharacteristic
37C2×#6665C2211yescharacteristic
38C2×#6665C2211yescharacteristic
39C2×#6665C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic, complemented
44C2×#6665C2211yescharacteristic, complemented
45C2×#6665C2211yescharacteristic, complemented
46C2×Dic3×Dic5C2211yescharacteristic, complemented
47#91115C2211yescharacteristic, complemented
48#91115C2211yescharacteristic, complemented
49C5×C3⋊#95C2211yescharacteristic, complemented
50C5×C3⋊#95C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#82580—51nomaximal, Hall
54C2×#4028D311yescharacteristic
55C5×#388—31no—
56#65279—31no—
57#65277—31no—
58#65246—31no—
59#65245—31no—
60#65244—31no—
61#65244—31no—
62#65240—31no—
63#65229—31no—
64#65228—31no—
65#64959—31no—
66#64958—31no—
67#64954—31no—
68#64954—31no—
69C24×C3×C5C2311yescharacteristic
70C23×C3×D5—41no—
71C23×C3×D5—41no—
72C23×C3×D5—41no—
73C23×C3×D5—41no—
74C23×C3×D5—41no—
75C23×C3×D5—41no—
76C23×C3×D5C2×C414yescomplemented
77C23×C3×D5C2311yescharacteristic
78C23×C3×D5C2311yescharacteristic
79C23×C3×D5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C2×C3×C22⋊D5—41no—
91C2×C3×C22⋊D5—41no—
92C2×C3×C22⋊D5C2×C414yes—
93C22×C3×Dic5C2311yescharacteristic
94C2×C3×D20—41no—
95C2×C3×D20—41no—
96C2×C3×D20—41no—
97C2×C3×D20—41no—
98C2×C3×D20C2×C414yes—
99C2×C3×D20C2×C414yes—
100C2×D5×Dic3—41no—
101C2×D5×Dic3—41no—
102C2×D5×Dic3—41no—
103C3×C5×C22⋊C4C2×C414yescomplemented
104#6719—41no—
105#6719—41no—
106C4⋊Dic15—41no—
107C4×Dic15—41no—
108C5×#217—41no—
109C5×#217—41no—
110C5×C4⋊Dic3—41no—
111C4×C5×Dic3—41no—
112C3×#685C2×C414yescomplemented
113C3×#685C2×C414yescomplemented
114#6668—41no—
115#6665—41no—
116#6665—41no—
117#6665—41no—
118#6665—41no—
119#6665—41no—
120#6665—41no—
121#6665—41no—
122#6665—41no—
123#6665—41no—
124#6665—41no—
125#6665—41no—
126Dic3×Dic5—41no—
127C2×C3×#120—51no—
128#5247—51no—
129#5247—51no—
130#5221—51no—
131#5221—51no—
132#5221—51no—
133#5220—51no—
134#5220—51no—
135#5220—51no—
136#4951—51no—
137#4951—51no—
138#4951—51no—
139#4951—51no—
140#4951—51no—
141#4951D511yescharacteristic, complemented
142C24×D5C2×D311yescharacteristic
143C22×C22⋊D5C2×D311yescharacteristic
144C22×D20C2×D311yescharacteristic
145C22×D20C2×D311yescharacteristic
146C22×C4×D5—31no—
147C2×C5×C4⋊C4—31no—
148C2×C5×C22⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4C2×D311yescharacteristic
151C2×C42×C5—31no—
152C2×C22⋊Dic5—31no—
153C2×C22⋊Dic5—31no—
154C2×#685—31no—
155C2×#685—31no—
156C2×#685—31no—
157C2×#685—31no—
158C2×#685—31no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—31no—
162C2×#685—31no—
163C2×#685—31no—
164C2×#685—31no—
165C2×#685C2×D311yescharacteristic
166C2×#685C2×D311yescharacteristic
167C2×C4⋊Dic5—31no—
168C2×#683—31no—
169C2×C4×Dic5—31no—
170C2×C4×Dic5—31no—
171#4028Dic318yescomplemented
172C5×#95—31no—
173C5×#95—31no—
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#2375—151noSylow
179C23×C3×C5—21no—
180C23×C3×C5—21no—
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5C22×C412yes—
186C23×C3×C5C2411yescharacteristic
187C22×C3×D5—21no—
188C22×C3×D5—21no—
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5—21no—
192C22×C3×D5—21no—
193C22×C3×D5—21no—
194C22×C3×D5—21no—
195C22×C3×D5—21no—
196C22×C3×D5—21no—
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—21no—
201C22×C3×D5—21no—
202C22×C3×D5—21no—
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—44no—
206C22×C3×D5—44no—
207C22×C3×D5—44no—
208C22×C3×D5—44no—
209C22×C3×D5—44no—
210C22×C3×D5—44no—
211C22×C3×D5—44no—
212C22×C3×D5C22×C412yes—
213C22×C3×D5C22×C412yes—
214C22×C3×D5C22×C412yes—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5C22×C412yes—
220C2×C3×C4×C5C22×C412yes—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—21no—
231C2×Dic15—21no—
232C2×Dic15—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×Dic3—21no—
242C2×C5×Dic3—21no—
243C2×C5×Dic3—21no—
244C2×C5×Dic3—21no—
245C3×C22⋊D5—44no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5C22×C412yes—
249C3×D20—44no—
250C3×D20—44no—
251D5×Dic3—44no—
252C25×C3—51no—
253C22×C3×D4—51no—
254C22×C3×D4—51no—
255C22×C3×D4—51no—
256C23×Dic3—51no—
257C3×#120—58no—
258C2×C3×C22⋊C4—51no—
259C2×C3×C22⋊C4—51no—
260C2×C3×C22⋊C4C2×D511yescharacteristic
261C2×#217—51no—
262C2×#217—51no—
263C2×#217—51no—
264C2×#217—51no—
265C2×#217—51no—
266C2×#217—51no—
267C2×#217—51no—
268C2×#217—51no—
269C2×#217—51no—
270C2×#217—51no—
271C2×#217—51no—
272C2×#217—51no—
273C2×#217—51no—
274C2×#217C2×D511yescharacteristic
275C2×#217C2×D511yescharacteristic
276C2×C4⋊Dic3—51no—
277C2×C4⋊Dic3—51no—
278C2×C4⋊Dic3C2×D511yescharacteristic, complemented
279C2×C4×Dic3—51no—
280C2×C4×Dic3—51no—
281C2×C4×Dic3C2×D511yescharacteristic, complemented
282C3⋊#95—51no—
283C3⋊#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95C2×D511yescharacteristic, complemented
287C3⋊#95C2×D511yescharacteristic, complemented
288C24×C5C22×D311yescharacteristic
289C23×D5—41no—
290C23×D5—41no—
291C23×D5—41no—
292C23×D5—41no—
293C23×D5—41no—
294C23×D5—41no—
295C23×D5C2×Dic314yescomplemented
296C23×D5C22×D311yescharacteristic
297C23×D5C22×D311yescharacteristic
298C23×D5C22×D311yescharacteristic
299C22×C4×C5—31no—
300C22×C4×C5—31no—
301C22×C4×C5—31no—
302C22×C4×C5—31no—
303C22×C4×C5C22×D311yescharacteristic
304C22×C4×C5C22×D311yescharacteristic
305C2×C22⋊D5—41no—
306C2×C22⋊D5—41no—
307C2×C22⋊D5C2×Dic314yes—
308C22×Dic5—31no—
309C22×Dic5—31no—
310C22×Dic5—31no—
311C22×Dic5—31no—
312C22×Dic5C22×D311yescharacteristic
313C2×D20—41no—
314C2×D20—41no—
315C2×D20—41no—
316C2×D20—41no—
317C2×D20C2×Dic314yes—
318C2×D20C2×Dic314yes—
319C2×C4×D5—121no—
320C2×C4×D5—121no—
321C2×C4×D5—121no—
322C5×C4⋊C4—121no—
323C5×C22⋊C4—121no—
324C5×C22⋊C4—121no—
325C5×C22⋊C4C2×Dic314yescomplemented
326C42×C5—121no—
327C22⋊Dic5—121no—
328C22⋊Dic5—121no—
329#685—121no—
330#685—121no—
331#685—121no—
332#685—121no—
333#685—121no—
334#685—121no—
335#685—121no—
336#685—121no—
337#685—121no—
338#685—121no—
339#685—121no—
340#685C2×Dic314yescomplemented
341#685C2×Dic314yescomplemented
342C4⋊Dic5—121no—
343#683—121no—
344C4×Dic5—121no—
345C4×Dic5—121no—
346C2×#120—51no—
347#390—151no—
348#390—151no—
349#390—151no—
350#388—31no—
351#388—151no—
352#388—151no—
353#388—151no—
354#388—151no—
355#388—151no—
356#386—151no—
357#386—151no—
358#386—151no—
359#379—151no—
360#379—151no—
361C22×C3×C5—22no—
362C22×C3×C5—22no—
363C22×C3×C5—22no—
364C22×C3×C5—41no—
365C22×C3×C5—41no—
366C22×C3×C5—41no—
367C22×C3×C5—41no—
368C22×C3×C5C23×C411yescharacteristic
369C22×C3×C5H(5,𝔽2)11yescharacteristic
370C22×C3×C5H(5,𝔽2)11yescharacteristic
371C22×C3×C5H(5,𝔽2)11yescharacteristic
372C22×C3×C5H(5,𝔽2)11yescharacteristic
373C22×C3×C5H(5,𝔽2)11yescharacteristic
374C22×C3×C5H(5,𝔽2)11yescharacteristic
375C2×C3×D5—22no—
376C2×C3×D5—22no—
377C2×C3×D5—22no—
378C2×C3×D5—22no—
379C2×C3×D5—22no—
380C2×C3×D5—22no—
381C2×C3×D5—22no—
382C2×C3×D5—22no—
383C2×C3×D5—22no—
384C2×C3×D5—416no—
385C2×C3×D5—41no—
386C2×C3×D5—41no—
387C2×C3×D5—41no—
388C2×C3×D5—41no—
389C2×C3×D5—41no—
390C2×C3×D5—41no—
391C2×C3×D5—41no—
392C2×C3×D5—41no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C3×C4×C5—22no—
398C3×C4×C5—22no—
399Dic15—41no—
400Dic15—41no—
401Dic15—41no—
402Dic15—41no—
403C3×Dic5—22no—
404C5×Dic3—41no—
405C5×Dic3—41no—
406C5×Dic3—41no—
407C5×Dic3—41no—
408C24×C3—51no—
409C24×C3—51no—
410C24×C3—51no—
411C24×C3—54no—
412C24×C3—201no—
413C24×C3—201no—
414C24×C3—201no—
415C24×C3—201no—
416C24×C3—201no—
417C24×C3—201no—
418C24×C3C22×D511yescharacteristic
419C2×C3×D4—54no—
420C2×C3×D4—54no—
421C2×C3×D4—54no—
422C2×C3×D4—201no—
423C2×C3×D4—201no—
424C2×C3×D4—201no—
425C2×C3×D4—201no—
426C2×C3×D4—201no—
427C2×C3×D4—201no—
428C22×C3×C4—51no—
429C22×C3×C4C22×D511yescharacteristic
430C22×C3×C4C22×D511yescharacteristic
431C22×Dic3—51no—
432C22×Dic3—51no—
433C22×Dic3—51no—
434C22×Dic3—51no—
435C22×Dic3—201no—
436C22×Dic3—201no—
437C22×Dic3—201no—
438C22×Dic3C22×D511yescharacteristic
439C22×Dic3C22×D511yescharacteristic
440C22×Dic3C22×D511yescharacteristic
441C22×Dic3C22×D511yescharacteristic
442C3×C22⋊C4—54no—
443C3×C22⋊C4—54no—
444C3×C22⋊C4C4×D514yescomplemented
445#217—41no—
446#217—41no—
447#217—201no—
448#217—201no—
449#217—201no—
450#217—201no—
451#217—201no—
452#217—201no—
453#217—201no—
454#217—201no—
455#217—201no—
456#217—201no—
457#217—201no—
458#217—201no—
459#217—201no—
460C4⋊Dic3—41no—
461C4⋊Dic3—201no—
462C4⋊Dic3—201no—
463C4×Dic3—41no—
464C4×Dic3—201no—
465C4×Dic3—201no—
466C23×C5—21no—
467C23×C5—21no—
468C23×C5—21no—
469C23×C5—21no—
470C23×C5—21no—
471C23×C5—21no—
472C23×C5C22×Dic312yes—
473C23×C5C23×D311yescharacteristic
474C22×D5—21no—
475C22×D5—21no—
476C22×D5—21no—
477C22×D5—21no—
478C22×D5—21no—
479C22×D5—21no—
480C22×D5—21no—
481C22×D5—21no—
482C22×D5—21no—
483C22×D5—21no—
484C22×D5—21no—
485C22×D5—21no—
486C22×D5—21no—
487C22×D5—21no—
488C22×D5—21no—
489C22×D5—21no—
490C22×D5—21no—
491C22×D5—21no—
492C22×D5—44no—
493C22×D5—44no—
494C22×D5—44no—
495C22×D5—44no—
496C22×D5—44no—
497C22×D5—44no—
498C22×D5—44no—
499C22×D5C22×Dic312yes—
500C22×D5C22×Dic312yes—
501C22×D5C22×Dic312yes—
502C2×C4×C5—21no—
503C2×C4×C5—21no—
504C2×C4×C5—21no—
505C2×C4×C5—21no—
506C2×C4×C5—61no—
507C2×C4×C5—61no—
508C2×C4×C5—61no—
509C2×C4×C5—61no—
510C2×C4×C5—61no—
511C2×C4×C5—61no—
512C2×C4×C5—61no—
513C2×C4×C5—61no—
514C2×C4×C5—61no—
515C2×C4×C5—61no—
516C2×C4×C5—61no—
517C2×C4×C5—61no—
518C2×C4×C5C22×Dic312yes—
519C2×C4×C5C22×Dic312yes—
520C22⋊D5—44no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523C2×Dic5—61no—
524C2×Dic5—61no—
525C2×Dic5—61no—
526C2×Dic5—61no—
527C2×Dic5—61no—
528C2×Dic5—61no—
529C2×Dic5—61no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5C22×Dic312yes—
536D20—44no—
537D20—44no—
538C4×D5—124no—
539C25—51no—
540C22×D4—51no—
541C22×D4—51no—
542C22×D4—51no—
543C23×C4—151no—
544#120—58no—
545C2×C4⋊C4—31no—
546C2×C4⋊C4—151no—
547C2×C4⋊C4—151no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—51no—
551C2×C22⋊C4—51no—
552C2×C22⋊C4—151no—
553C2×C22⋊C4—151no—
554C2×C22⋊C4—151no—
555C2×C22⋊C4—151no—
556C2×C22⋊C4—151no—
557C2×C22⋊C4—151no—
558C2×C22⋊C4—151no—
559C2×C22⋊C4—151no—
560C2×C22⋊C4—151no—
561C2×C22⋊C4—151no—
562C2×C22⋊C4—151no—
563C2×C22⋊C4—151no—
564C2×C22⋊C4—151no—
565C2×C22⋊C4D3×D511yescharacteristic
566C2×C42—31no—
567C2×C42—151no—
568C2×C42—151no—
569#95—31no—
570#95—31no—
571#95—151no—
572#95—151no—
573#95—151no—
574#95—151no—
575C2×C3×C5—42no—
576C2×C3×C5#51811yescharacteristic
577C2×C3×C5#51811yescharacteristic
578C2×C3×C5#51811yescharacteristic
579C2×C3×C5#56011yescharacteristic
580C2×C3×C5#56011yescharacteristic
581C2×C3×C5#56011yescharacteristic
582C2×C3×C5H(3,𝔽4)11yescharacteristic
583C3×D5—42no—
584C3×D5—42no—
585C3×D5—42no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—21no—
591C23×C3—21no—
592C23×C3—52no—
593C23×C3—52no—
594C23×C3—52no—
595C23×C3—101no—
596C23×C3—101no—
597C23×C3—101no—
598C23×C3—101no—
599C23×C3—101no—
600C23×C3—101no—
601C23×C3—101no—
602C23×C3—101no—
603C23×C3—101no—
604C23×C3—101no—
605C23×C3—101no—
606C23×C3—101no—
607C23×C3—101no—
608C23×C3—101no—
609C23×C3—101no—
610C23×C3—101no—
611C23×C3—101no—
612C23×C3—101no—
613C23×C3—204no—
614C23×C3—204no—
615C23×C3—204no—
616C23×C3—204no—
617C23×C3—204no—
618C23×C3—204no—
619C23×C3—204no—
620C23×C3C2×C4×D512yes—
621C23×C3C23×D511yescharacteristic
622C3×D4—204no—
623C3×D4—204no—
624C3×D4—204no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—52no—
630C2×C3×C4—101no—
631C2×C3×C4—101no—
632C2×C3×C4C2×C4×D512yes—
633C2×C3×C4C2×C4×D512yes—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—101no—
647C2×Dic3—101no—
648C2×Dic3—101no—
649C2×Dic3—101no—
650C2×Dic3—101no—
651C2×Dic3—101no—
652C2×Dic3—101no—
653C2×Dic3—101no—
654C2×Dic3—101no—
655C2×Dic3—101no—
656C2×Dic3—101no—
657C2×Dic3—101no—
658C2×Dic3—204no—
659C22×C5—22no—
660C22×C5—22no—
661C22×C5—22no—
662C22×C5—41no—
663C22×C5—41no—
664C22×C5—41no—
665C22×C5—41no—
666C22×C5#100411yescharacteristic
667C22×C5#100411yescharacteristic
668C22×C5#100411yescharacteristic
669C22×C5#100411yescharacteristic
670C22×C5#100411yescharacteristic
671C22×C5#100411yescharacteristic
672C22×C5C23×Dic311yescharacteristic
673C2×D5—22no—
674C2×D5—22no—
675C2×D5—22no—
676C2×D5—22no—
677C2×D5—22no—
678C2×D5—22no—
679C2×D5—22no—
680C2×D5—22no—
681C2×D5—22no—
682C2×D5—416no—
683C2×D5—41no—
684C2×D5—41no—
685C2×D5—41no—
686C2×D5—41no—
687C2×D5—41no—
688C2×D5—41no—
689C2×D5—41no—
690C2×D5—41no—
691C2×D5—41no—
692C2×D5—41no—
693C2×D5—41no—
694C2×D5—41no—
695C4×C5—22no—
696C4×C5—22no—
697C4×C5—121no—
698C4×C5—121no—
699C4×C5—121no—
700C4×C5—121no—
701Dic5—22no—
702Dic5—121no—
703Dic5—121no—
704Dic5—121no—
705Dic5—121no—
706C24—51no—
707C24—51no—
708C24—51no—
709C24—54no—
710C24—201no—
711C24—201no—
712C24—201no—
713C24—201no—
714C24—201no—
715C24—201no—
716C24C2×D3×D511yescharacteristic
717C2×D4—54no—
718C2×D4—54no—
719C2×D4—54no—
720C2×D4—201no—
721C2×D4—201no—
722C2×D4—201no—
723C2×D4—201no—
724C2×D4—201no—
725C2×D4—201no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—31no—
729C22×C4—31no—
730C22×C4—51no—
731C22×C4—151no—
732C22×C4—151no—
733C22×C4—151no—
734C22×C4—151no—
735C22×C4—601no—
736C22×C4—601no—
737C22×C4—601no—
738C22×C4C2×D3×D511yescharacteristic
739C22×C4C2×D3×D511yescharacteristic
740C4⋊C4—121no—
741C4⋊C4—601no—
742C4⋊C4—601no—
743C22⋊C4—54no—
744C22⋊C4—54no—
745C22⋊C4—121no—
746C22⋊C4—121no—
747C22⋊C4—601no—
748C22⋊C4—601no—
749C22⋊C4—601no—
750C22⋊C4—601no—
751C22⋊C4—601no—
752C22⋊C4—601no—
753C22⋊C4—601no—
754C22⋊C4—601no—
755C22⋊C4—601no—
756C22⋊C4—601no—
757C22⋊C4—601no—
758C22⋊C4—601no—
759C22⋊C4—601no—
760C22⋊C4D5×Dic314yescomplemented
761C42—121no—
762C42—601no—
763C42—601no—
764C3×C5#237511yescharacteristic, complemented, Hall
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—102no—
773C22×C3—102no—
774C22×C3—102no—
775C22×C3—102no—
776C22×C3—102no—
777C22×C3—102no—
778C22×C3—102no—
779C22×C3—102no—
780C22×C3—102no—
781C22×C3—2016no—
782C22×C3—201no—
783C22×C3—201no—
784C22×C3—201no—
785C22×C3—201no—
786C22×C3—201no—
787C22×C3—201no—
788C22×C3—201no—
789C22×C3—201no—
790C22×C3—201no—
791C22×C3—201no—
792C22×C3—201no—
793C22×C3—201no—
794C22×C3C22×C4×D511yescharacteristic
795C22×C3#414411yescharacteristic
796C22×C3#414411yescharacteristic
797C22×C3#414911yescharacteristic
798C22×C3#414911yescharacteristic
799C22×C3#414911yescharacteristic
800C22×C3#414911yescharacteristic
801C3×C4—22no—
802C3×C4—22no—
803C3×C4—102no—
804Dic3—41no—
805Dic3—41no—
806Dic3—41no—
807Dic3—41no—
808Dic3—201no—
809Dic3—201no—
810Dic3—201no—
811Dic3—201no—
812C2×C5—42no—
813C2×C5#559411yescharacteristic
814C2×C5#559511yescharacteristic
815C2×C5#559511yescharacteristic
816C2×C5#559511yescharacteristic
817C2×C5#579811yescharacteristic
818C2×C5#579811yescharacteristic
819C2×C5#579811yescharacteristic
820D5—42no—
821D5—42no—
822D5—42no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—52no—
830C23—52no—
831C23—52no—
832C23—101no—
833C23—101no—
834C23—101no—
835C23—101no—
836C23—101no—
837C23—101no—
838C23—101no—
839C23—101no—
840C23—101no—
841C23—101no—
842C23—101no—
843C23—101no—
844C23—101no—
845C23—101no—
846C23—101no—
847C23—101no—
848C23—101no—
849C23—101no—
850C23—204no—
851C23—204no—
852C23—204no—
853C23—204no—
854C23—204no—
855C23—204no—
856C23—204no—
857C23C2×D5×Dic312yes—
858C23C22×D3×D511yescharacteristic
859D4—204no—
860D4—204no—
861D4—204no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—52no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—101no—
880C2×C4—101no—
881C2×C4—301no—
882C2×C4—301no—
883C2×C4—301no—
884C2×C4—301no—
885C2×C4—301no—
886C2×C4—301no—
887C2×C4—301no—
888C2×C4—301no—
889C2×C4—301no—
890C2×C4—301no—
891C2×C4—301no—
892C2×C4—301no—
893C2×C4—604no—
894C2×C4C2×D5×Dic312yes—
895C2×C4C2×D5×Dic312yes—
896C2×C3—42no—
897C2×C3—202no—
898C2×C3—202no—
899C2×C3—202no—
900C2×C3#6585511yescharacteristic
901C2×C3#6587911yescharacteristic
902C2×C3#6587911yescharacteristic
903C2×C3#6595411yescharacteristic
904C2×C3#6600011yescharacteristic
905C2×C3#6601711yescharacteristic
906C2×C3#6604511yescharacteristic
907C5#8258011yescharacteristic, complemented, Sylow
908C22—22no—
909C22—22no—
910C22—22no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—102no—
916C22—102no—
917C22—102no—
918C22—102no—
919C22—102no—
920C22—102no—
921C22—102no—
922C22—102no—
923C22—102no—
924C22—2016no—
925C22—201no—
926C22—201no—
927C22—201no—
928C22—201no—
929C22—201no—
930C22—201no—
931C22—201no—
932C22—201no—
933C22—201no—
934C22—201no—
935C22—201no—
936C22—201no—
937C22#9201711yescharacteristic
938C22#9201711yescharacteristic
939C22#9202511yescharacteristic
940C22#9202511yescharacteristic
941C22#9202611yescharacteristic
942C22#9202611yescharacteristic
943C22C22×D5×Dic311yescharacteristic
944C4—22no—
945C4—22no—
946C4—102no—
947C4—121no—
948C4—121no—
949C4—121no—
950C4—121no—
951C4—601no—
952C4—601no—
953C4—601no—
954C4—601no—
955C3#1060757111yescharacteristic, complemented, Sylow
956C2—42no—
957C2—202no—
958C2—202no—
959C2—202no—
960C2#1175316211yescharacteristic
961C2#1175316311yescharacteristic
962C2#1175316511yescharacteristic
963C2#1175329911yescharacteristic
964C2#1175448811yescharacteristic
965C2#1175491011yescharacteristic
966C2#1175491011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C3×#4028C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2375
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
2. #11751052C2semidirect
3. C5×#4951C2semidirect
4. #11749518C2semidirect
5. #11749489C2semidirect
6. #11749488C2semidirect
7. #11749488C2semidirect
8. #11748896C2semidirect
9. #11748896C2semidirect
10. #11748796C2semidirect
11. #11748791C2semidirect
12. #11748785C2semidirect
13. #11748772C2semidirect
14. #11748771C2semidirect
15. #11748770C2semidirect
21. C22×D5×Dic3C22semidirect
25. C2×C4⋊Dic15C22semidirect
26. C2×C4×Dic15C22semidirect
29. C2×C5×C4⋊Dic3C22semidirect
30. C2×C4×C5×Dic3C22semidirect
33. C3×#4028C4semidirect
34. C2×#6668C22semidirect
43. C2×#6665C22semidirect
44. C2×#6665C22semidirect
45. C2×#6665C22semidirect
46. C2×Dic3×Dic5C22semidirect
47. #91115C22semidirect
48. #91115C22semidirect
49. C5×C3⋊#95C22semidirect
50. C5×C3⋊#95C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
76. C23×C3×D5C2×C4semidirect
103. C3×C5×C22⋊C4C2×C4semidirect
112. C3×#685C2×C4semidirect
113. C3×#685C2×C4semidirect
141. #4951D5semidirect
171. #4028Dic3semidirect
278. C2×C4⋊Dic3C2×D5semidirect
281. C2×C4×Dic3C2×D5semidirect
286. C3⋊#95C2×D5semidirect
287. C3⋊#95C2×D5semidirect
295. C23×D5C2×Dic3semidirect
325. C5×C22⋊C4C2×Dic3semidirect
340. #685C2×Dic3semidirect
341. #685C2×Dic3semidirect
444. C3×C22⋊C4C4×D5semidirect
760. C22⋊C4D5×Dic3semidirect
764. C3×C5#2375semidirect
907. C5#82580semidirect
955. C3#10607571semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40282
#117510522
C5×#49512
#117495182
#117494892
#117494882
#117488962
#117487962
#117487912
#117487852
#117487722
#117487712
#117487702
#106075713
#825805