Finite Group Databasebeta

← #14330674

Subgroups — #14330674

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×#91474C211yesmaximal, characteristic
2#11751041C211yesmaximal, characteristic, complemented
3C5×#4940C211yesmaximal, characteristic, complemented
4C3×#65228C211yesmaximal, characteristic, complemented
5#11748940C211yesmaximal, characteristic, complemented
6#11748940C211yesmaximal, characteristic, complemented
7#11748916C211yesmaximal, characteristic, complemented
8#11748913C211yesmaximal, characteristic, complemented
9#11748906C211yesmaximal, characteristic, complemented
10#11748896C211yesmaximal, characteristic, complemented
11#11748872C211yesmaximal, characteristic, complemented
12#11748711C211yesmaximal, characteristic, complemented
13#11748707C211yesmaximal, characteristic, complemented
14#11748678C211yesmaximal, characteristic, complemented
15#11748675C211yesmaximal, characteristic, complemented
16#10607571—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C3×D20C2211yescharacteristic
19C22×#1202C2211yescharacteristic
20C22×#1201C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic, complemented
22C2×C3×C42×C5C2211yescharacteristic, complemented
23C2×#6714C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×#6712C2211yescharacteristic, complemented
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C5×(C2×D3)⋊C4C2211yescharacteristic
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic
30C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic, complemented
34C2×C3×#685C2211yescharacteristic, complemented
35C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
36C2×#6667C2211yescharacteristic
37C2×#6667C2211yescharacteristic
38C2×(C2×D3)⋊Dic5C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic, complemented
44C2×Dic3×Dic5C2211yescharacteristic, complemented
45C2×Dic3×Dic5C2211yescharacteristic, complemented
46#91474C418yescomplemented
47#91115C2211yescharacteristic, complemented
48#91115C2211yescharacteristic, complemented
49C5×C3⋊#95C2211yescharacteristic, complemented
50C5×C3⋊#95C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#76434—51nomaximal, Hall
54C2×#4028—31no—
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#65228D311yescharacteristic, complemented
65#64959—31no—
66#64958—31no—
67#64954—31no—
68#64954—31no—
69C23×D15C2311yescharacteristic
70C23×C5×D3C2311yescharacteristic
71C23×C3×D5C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C22×D3×D5—41no—
74C22×D3×D5—41no—
75C22×D3×D5—41no—
76C22×D3×D5—41no—
77C22×D3×D5—41no—
78C22×D3×D5—41no—
79C22×D3×D5C2×C414yescomplemented
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C2×C3×D20—41no—
92C2×C3×D20—41no—
93C2×C3×D20C2×C414yes—
94C2×#1202—41no—
95C2×#1202—41no—
96C2×#1202C2×C414yes—
97C2×#1201—41no—
98C2×#1201—41no—
99C2×#1201C2×C414yes—
100C2×D5×Dic3—41no—
101C2×D5×Dic3—41no—
102C2×D5×Dic3—41no—
103C3×C42×C5—41no—
104#6714—41no—
105#6714—41no—
106#6714C2×C414yescomplemented
107#6712—41no—
108C5×(C2×D3)⋊C4—41no—
109C5×(C2×D3)⋊C4—41no—
110C5×(C2×D3)⋊C4C2×C414yescomplemented
111C5×Dic3⋊C4—41no—
112C3×#685—41no—
113C3×#685—41no—
114C3×#685—41no—
115C3×#685—41no—
116C3×C4⋊Dic5—41no—
117#6667—41no—
118#6667—41no—
119(C2×D3)⋊Dic5—41no—
120(C2×D3)⋊Dic5—41no—
121#6665—41no—
122#6665—41no—
123#6665—41no—
124#6665C2×C414yescomplemented
125Dic3×Dic5—41no—
126Dic3×Dic5—41no—
127C2×#937—51no—
128C3×#390—51no—
129#5220—51no—
130#4990—51no—
131#4990—51no—
132#4958—51no—
133#4958—51no—
134#4957—51no—
135#4957—51no—
136#4955—51no—
137#4955—51no—
138#4944—51no—
139#4944—51no—
140#4940—51no—
141#4940D511yescharacteristic, complemented
142C24×D5—31no—
143C22×C22⋊D5—31no—
144C22×D20—31no—
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⋊C4—31no—
151C2×C42×C5C2×D311yescharacteristic, complemented
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×#685C2×D311yescharacteristic
164C2×#685C2×D311yescharacteristic
165C2×#685C2×D311yescharacteristic, complemented
166C2×#685C2×D311yescharacteristic, complemented
167C2×C4⋊Dic5C2×D311yescharacteristic, complemented
168C2×#683—31no—
169C2×C4×Dic5—31no—
170C2×C4×Dic5—31no—
171#4028—38no—
172C5×#95—31no—
173C5×#95—31no—
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#2375—151noSylow
179C23×C3×C5C2411yescharacteristic
180C22×D15—21no—
181C22×D15—21no—
182C22×D15—21no—
183C22×D15—21no—
184C22×D15—21no—
185C22×D15—21no—
186C22×D15C22×C412yes—
187C22×C5×D3—21no—
188C22×C5×D3—21no—
189C22×C5×D3—21no—
190C22×C5×D3—21no—
191C22×C5×D3—21no—
192C22×C5×D3—21no—
193C22×C5×D3C22×C412yes—
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—21no—
206C22×C3×D5C22×C412yes—
207C22×C3×D5C22×C412yes—
208C2×D3×D5—44no—
209C2×D3×D5—44no—
210C2×D3×D5—44no—
211C2×D3×D5—44no—
212C2×D3×D5—44no—
213C2×D3×D5—44no—
214C2×D3×D5—44no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
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×C5C22×C412yes—
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×Dic15C22×C412yes—
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×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C3×D20—44no—
249#1202—44no—
250#1201—44no—
251D5×Dic3—44no—
252C24×D3—51no—
253C22×C3×D4—51no—
254C22×#67—51no—
255C22×#67—51no—
256C23×Dic3—51no—
257C2×C3×C4⋊C4—51no—
258C2×C3×C22⋊C4—51no—
259C2×C3×C22⋊C4—51no—
260C2×C3×C22⋊C4—51no—
261C2×C3×C22⋊C4—51no—
262C2×C3×C42C2×D511yescharacteristic, complemented
263C2×#217—51no—
264C2×#217—51no—
265C2×#217—51no—
266C2×#217—51no—
267#937—58no—
268C2×(C2×D3)⋊C4—51no—
269C2×(C2×D3)⋊C4—51no—
270C2×(C2×D3)⋊C4—51no—
271C2×(C2×D3)⋊C4—51no—
272C2×(C2×D3)⋊C4—51no—
273C2×(C2×D3)⋊C4—51no—
274C2×(C2×D3)⋊C4—51no—
275C2×(C2×D3)⋊C4C2×D511yescharacteristic
276C2×(C2×D3)⋊C4C2×D511yescharacteristic
277C2×(C2×D3)⋊C4C2×D511yescharacteristic
278C2×Dic3⋊C4—51no—
279C2×Dic3⋊C4C2×D511yescharacteristic, complemented
280C2×C4×Dic3—51no—
281C2×C4×Dic3—51no—
282C3⋊#95—51no—
283C3⋊#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95C2×D511yescharacteristic, complemented
287C3⋊#95C2×D511yescharacteristic, complemented
288C24×C5—31no—
289C23×D5—31no—
290C23×D5—34no—
291C23×D5—121no—
292C23×D5—121no—
293C23×D5—121no—
294C23×D5—121no—
295C23×D5—121no—
296C23×D5—121no—
297C23×D5C22×D311yescharacteristic
298C23×D5C22×D311yescharacteristic
299C22×C4×C5—31no—
300C22×C4×C5—31no—
301C22×C4×C5—31no—
302C22×C4×C5C22×D311yescharacteristic
303C22×C4×C5C22×D311yescharacteristic
304C22×C4×C5C22×D311yescharacteristic
305C2×C22⋊D5—34no—
306C2×C22⋊D5—121no—
307C2×C22⋊D5—121no—
308C22×Dic5—31no—
309C22×Dic5—31no—
310C22×Dic5—31no—
311C22×Dic5C22×D311yescharacteristic
312C22×Dic5C22×D311yescharacteristic
313C2×D20—34no—
314C2×D20—41no—
315C2×D20—41no—
316C2×D20—121no—
317C2×D20—121no—
318C2×D20C4×D314yes—
319C2×C4×D5—121no—
320C2×C4×D5—121no—
321C2×C4×D5—121no—
322C5×C4⋊C4—121no—
323C5×C22⋊C4—34no—
324C5×C22⋊C4—121no—
325C5×C22⋊C4—121no—
326C42×C5—41no—
327C22⋊Dic5—121no—
328C22⋊Dic5—121no—
329#685—34no—
330#685—34no—
331#685—41no—
332#685—41no—
333#685—41no—
334#685—41no—
335#685—121no—
336#685—121no—
337#685—121no—
338#685—121no—
339#685—121no—
340#685—121no—
341#685—121no—
342C4⋊Dic5—41no—
343#683—121no—
344C4×Dic5—121no—
345C4×Dic5—121no—
346C2×#120—151no—
347#390—51no—
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×C5C23×C411yescharacteristic
362C22×C3×C5H(5,𝔽2)11yescharacteristic
363C22×C3×C5H(5,𝔽2)11yescharacteristic
364C22×C3×C5H(5,𝔽2)11yescharacteristic
365C22×C3×C5H(5,𝔽2)11yescharacteristic
366C22×C3×C5H(5,𝔽2)11yescharacteristic
367C22×C3×C5H(5,𝔽2)11yescharacteristic
368C2×D15—22no—
369C2×D15—22no—
370C2×D15—22no—
371C2×D15—41no—
372C2×D15—41no—
373C2×D15—41no—
374C2×D15—41no—
375C2×C5×D3—22no—
376C2×C5×D3—22no—
377C2×C5×D3—22no—
378C2×C5×D3—41no—
379C2×C5×D3—41no—
380C2×C5×D3—41no—
381C2×C5×D3—41no—
382C2×C3×D5—22no—
383C2×C3×D5—22no—
384C2×C3×D5—22no—
385C2×C3×D5—22no—
386C2×C3×D5—22no—
387C2×C3×D5—22no—
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—
396D3×D5—416no—
397C3×C4×C5—22no—
398C3×C4×C5—41no—
399C3×C4×C5—41no—
400Dic15—22no—
401Dic15—41no—
402Dic15—41no—
403C3×Dic5—41no—
404C3×Dic5—41no—
405C5×Dic3—22no—
406C5×Dic3—41no—
407C5×Dic3—41no—
408C24×C3—51no—
409C24×C3—51no—
410C23×D3—51no—
411C23×D3—54no—
412C23×D3—201no—
413C23×D3—201no—
414C23×D3—201no—
415C23×D3—201no—
416C23×D3—201no—
417C23×D3—201no—
418C23×D3C22×D511yescharacteristic
419C2×C3×D4—54no—
420C2×C3×D4—201no—
421C2×C3×D4—201no—
422C22×C3×C4—51no—
423C22×C3×C4—51no—
424C22×C3×C4C22×D511yescharacteristic
425C22×C3×C4C22×D511yescharacteristic
426C22×C3×C4C22×D511yescharacteristic
427C2×#67—54no—
428C2×#67—54no—
429C2×#67—201no—
430C2×#67—201no—
431C2×#67—201no—
432C2×#67—201no—
433C22×Dic3—51no—
434C22×Dic3—51no—
435C22×Dic3—51no—
436C22×Dic3—201no—
437C22×Dic3—201no—
438C22×Dic3—201no—
439C22×Dic3C22×D511yescharacteristic
440C22×Dic3C22×D511yescharacteristic
441C22×Dic3C22×D511yescharacteristic
442C3×C4⋊C4—201no—
443C3×C22⋊C4—201no—
444C3×C22⋊C4—201no—
445C3×C22⋊C4—201no—
446C3×C22⋊C4—201no—
447C3×C42—41no—
448#217—54no—
449#217—201no—
450#217—201no—
451#217—201no—
452(C2×D3)⋊C4—41no—
453(C2×D3)⋊C4—41no—
454(C2×D3)⋊C4—54no—
455(C2×D3)⋊C4—201no—
456(C2×D3)⋊C4—201no—
457(C2×D3)⋊C4—201no—
458(C2×D3)⋊C4—201no—
459(C2×D3)⋊C4—201no—
460(C2×D3)⋊C4—201no—
461(C2×D3)⋊C4C4×D514yescomplemented
462Dic3⋊C4—41no—
463Dic3⋊C4—201no—
464C4×Dic3—201no—
465C4×Dic3—201no—
466C23×C5—32no—
467C23×C5—61no—
468C23×C5—61no—
469C23×C5—61no—
470C23×C5—61no—
471C23×C5—61no—
472C23×C5—61no—
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—32no—
487C22×D5—61no—
488C22×D5—61no—
489C22×D5—61no—
490C22×D5—61no—
491C22×D5—61no—
492C22×D5—61no—
493C22×D5—124no—
494C22×D5—124no—
495C22×D5—124no—
496C22×D5—124no—
497C22×D5—124no—
498C22×D5—124no—
499C22×D5—124no—
500C22×D5C2×C4×D312yes—
501C22×D5C2×C4×D312yes—
502C2×C4×C5—21no—
503C2×C4×C5—21no—
504C2×C4×C5—21no—
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—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×C5—61no—
519C2×C4×C5C2×C4×D312yes—
520C22⋊D5—124no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5—21no—
526C2×Dic5—21no—
527C2×Dic5—32no—
528C2×Dic5—61no—
529C2×Dic5—61no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5—61no—
536D20—44no—
537D20—124no—
538C4×D5—124no—
539C25—151no—
540C22×D4—51no—
541C22×D4—151no—
542C22×D4—151no—
543C23×C4—151no—
544#120—158no—
545C2×C4⋊C4—31no—
546C2×C4⋊C4—51no—
547C2×C4⋊C4—151no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—51no—
552C2×C22⋊C4—51no—
553C2×C22⋊C4—51no—
554C2×C22⋊C4—51no—
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⋊C4—151no—
566C2×C42—151no—
567C2×C42—151no—
568C2×C42D3×D511yescharacteristic, complemented
569#95—31no—
570#95—31no—
571#95—151no—
572#95—151no—
573#95—151no—
574#95—151no—
575C2×C3×C5#51811yescharacteristic
576C2×C3×C5#51811yescharacteristic
577C2×C3×C5#51811yescharacteristic
578C2×C3×C5#56011yescharacteristic
579C2×C3×C5#56011yescharacteristic
580C2×C3×C5#56011yescharacteristic
581C2×C3×C5H(3,𝔽4)11yescharacteristic
582D15—42no—
583C3×D5—42no—
584C3×D5—42no—
585C5×D3—42no—
586C23×C3—52no—
587C23×C3—52no—
588C23×C3—101no—
589C23×C3—101no—
590C23×C3—101no—
591C23×C3—101no—
592C23×C3—101no—
593C23×C3—101no—
594C23×C3—101no—
595C23×C3—101no—
596C23×C3—101no—
597C23×C3—101no—
598C23×C3—101no—
599C23×C3—101no—
600C23×C3C23×D511yescharacteristic
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—52no—
608C22×D3—101no—
609C22×D3—101no—
610C22×D3—101no—
611C22×D3—101no—
612C22×D3—101no—
613C22×D3—101no—
614C22×D3—204no—
615C22×D3—204no—
616C22×D3—204no—
617C22×D3—204no—
618C22×D3—204no—
619C22×D3—204no—
620C22×D3—204no—
621C22×D3C2×C4×D512yes—
622C3×D4—204no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—101no—
632C2×C3×C4—101no—
633C2×C3×C4—101no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4C2×C4×D512yes—
638#67—204no—
639#67—204no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—52no—
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—204no—
658C2×Dic3C2×C4×D512yes—
659C22×C5—62no—
660C22×C5—62no—
661C22×C5—62no—
662C22×C5—121no—
663C22×C5—121no—
664C22×C5—121no—
665C22×C5—121no—
666C22×C5C22×C4×D311yescharacteristic
667C22×C5#100411yescharacteristic
668C22×C5#100411yescharacteristic
669C22×C5#100411yescharacteristic
670C22×C5#100411yescharacteristic
671C22×C5#100911yescharacteristic
672C22×C5#100911yescharacteristic
673C2×D5—22no—
674C2×D5—22no—
675C2×D5—22no—
676C2×D5—22no—
677C2×D5—22no—
678C2×D5—22no—
679C2×D5—41no—
680C2×D5—41no—
681C2×D5—41no—
682C2×D5—41no—
683C2×D5—41no—
684C2×D5—41no—
685C2×D5—41no—
686C2×D5—41no—
687C2×D5—62no—
688C2×D5—62no—
689C2×D5—62no—
690C2×D5—1216no—
691C2×D5—121no—
692C2×D5—121no—
693C2×D5—121no—
694C2×D5—121no—
695C4×C5—22no—
696C4×C5—41no—
697C4×C5—41no—
698C4×C5—62no—
699C4×C5—121no—
700C4×C5—121no—
701Dic5—41no—
702Dic5—41no—
703Dic5—62no—
704Dic5—121no—
705Dic5—121no—
706C24—31no—
707C24—51no—
708C24—51no—
709C24—154no—
710C24—151no—
711C24—601no—
712C24—601no—
713C24—601no—
714C24—601no—
715C24—601no—
716C24—601no—
717C2×D4—54no—
718C2×D4—154no—
719C2×D4—154no—
720C2×D4—201no—
721C2×D4—201no—
722C2×D4—601no—
723C2×D4—601no—
724C2×D4—601no—
725C2×D4—601no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—31no—
729C22×C4—51no—
730C22×C4—51no—
731C22×C4—151no—
732C22×C4—151no—
733C22×C4—151no—
734C22×C4—601no—
735C22×C4—601no—
736C22×C4—601no—
737C22×C4C2×D3×D511yescharacteristic
738C22×C4C2×D3×D511yescharacteristic
739C22×C4C2×D3×D511yescharacteristic
740C4⋊C4—121no—
741C4⋊C4—201no—
742C4⋊C4—601no—
743C22⋊C4—34no—
744C22⋊C4—121no—
745C22⋊C4—121no—
746C22⋊C4—154no—
747C22⋊C4—154no—
748C22⋊C4—201no—
749C22⋊C4—201no—
750C22⋊C4—201no—
751C22⋊C4—201no—
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⋊C4—601no—
761C42—41no—
762C42—601no—
763C42—601no—
764C3×C5#237511yescharacteristic, complemented, Hall
765C22×C3—102no—
766C22×C3—102no—
767C22×C3—102no—
768C22×C3—102no—
769C22×C3—102no—
770C22×C3—102no—
771C22×C3—201no—
772C22×C3—201no—
773C22×C3—201no—
774C22×C3—201no—
775C22×C3—201no—
776C22×C3—201no—
777C22×C3—201no—
778C22×C3—201no—
779C22×C3C22×C4×D511yescharacteristic
780C22×C3#414411yescharacteristic
781C22×C3#414411yescharacteristic
782C22×C3#414911yescharacteristic
783C22×C3#414911yescharacteristic
784C22×C3#414911yescharacteristic
785C22×C3#414911yescharacteristic
786C2×D3—22no—
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—41no—
790C2×D3—41no—
791C2×D3—41no—
792C2×D3—41no—
793C2×D3—102no—
794C2×D3—102no—
795C2×D3—102no—
796C2×D3—2016no—
797C2×D3—201no—
798C2×D3—201no—
799C2×D3—201no—
800C2×D3—201no—
801C3×C4—22no—
802C3×C4—41no—
803C3×C4—41no—
804C3×C4—201no—
805C3×C4—201no—
806Dic3—22no—
807Dic3—41no—
808Dic3—41no—
809Dic3—102no—
810Dic3—201no—
811Dic3—201no—
812C2×C5—122no—
813C2×C5#548611yescharacteristic
814C2×C5#554511yescharacteristic
815C2×C5#554511yescharacteristic
816C2×C5#562011yescharacteristic
817C2×C5#562011yescharacteristic
818C2×C5#568311yescharacteristic
819C2×C5#572011yescharacteristic
820D5—42no—
821D5—42no—
822D5—122no—
823C23—32no—
824C23—52no—
825C23—52no—
826C23—61no—
827C23—61no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23—61no—
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—152no—
845C23—301no—
846C23—301no—
847C23—301no—
848C23—301no—
849C23—301no—
850C23—301no—
851C23—604no—
852C23—604no—
853C23—604no—
854C23—604no—
855C23—604no—
856C23—604no—
857C23—604no—
858C23C22×D3×D511yescharacteristic
859D4—204no—
860D4—604no—
861D4—604no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—32no—
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—101no—
882C2×C4—101no—
883C2×C4—101no—
884C2×C4—101no—
885C2×C4—152no—
886C2×C4—301no—
887C2×C4—301no—
888C2×C4—301no—
889C2×C4—301no—
890C2×C4—301no—
891C2×C4—301no—
892C2×C4—301no—
893C2×C4—301no—
894C2×C4—604no—
895C2×C4C4×D3×D512yes—
896C2×C3—202no—
897C2×C3—202no—
898C2×C3#6585511yescharacteristic
899C2×C3#6587911yescharacteristic
900C2×C3#6587911yescharacteristic
901C2×C3#6595411yescharacteristic
902C2×C3#6600011yescharacteristic
903C2×C3#6601711yescharacteristic
904C2×C3#6604511yescharacteristic
905D3—42no—
906D3—202no—
907C5#7643411yescharacteristic, complemented, Sylow
908C22—62no—
909C22—62no—
910C22—62no—
911C22—102no—
912C22—102no—
913C22—102no—
914C22—102no—
915C22—102no—
916C22—102no—
917C22—121no—
918C22—121no—
919C22—121no—
920C22—121no—
921C22—201no—
922C22—201no—
923C22—201no—
924C22—201no—
925C22—201no—
926C22—201no—
927C22—201no—
928C22—201no—
929C22—302no—
930C22—302no—
931C22—302no—
932C22—6016no—
933C22—601no—
934C22—601no—
935C22—601no—
936C22—601no—
937C22C2×C4×D3×D511yescharacteristic
938C22#9201711yescharacteristic
939C22#9201711yescharacteristic
940C22#9201711yescharacteristic
941C22#9201811yescharacteristic
942C22#9201911yescharacteristic
943C22#9204911yescharacteristic
944C4—22no—
945C4—41no—
946C4—41no—
947C4—62no—
948C4—121no—
949C4—121no—
950C4—201no—
951C4—201no—
952C4—302no—
953C4—601no—
954C4—601no—
955C3#1060757111yescharacteristic, complemented, Sylow
956C2—122no—
957C2—202no—
958C2—202no—
959C2—602no—
960C2#1175272711yescharacteristic
961C2#1175272911yescharacteristic
962C2#1175277211yescharacteristic
963C2#1175277311yescharacteristic
964C2#1175462511yescharacteristic
965C2#1175468511yescharacteristic
966C2#1175468611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91474C2
hypercenterC2×C42D3×D5
hypocenterC3×C5#2375
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11751041C2semidirect
3. C5×#4940C2semidirect
4. C3×#65228C2semidirect
5. #11748940C2semidirect
6. #11748940C2semidirect
7. #11748916C2semidirect
8. #11748913C2semidirect
9. #11748906C2semidirect
10. #11748896C2semidirect
11. #11748872C2semidirect
12. #11748711C2semidirect
13. #11748707C2semidirect
14. #11748678C2semidirect
15. #11748675C2semidirect
21. C22×D5×Dic3C22semidirect
22. C2×C3×C42×C5C22semidirect
26. C2×#6712C22semidirect
30. C2×C5×Dic3⋊C4C22semidirect
33. C2×C3×#685C22semidirect
34. C2×C3×#685C22semidirect
35. C2×C3×C4⋊Dic5C22semidirect
43. C2×#6665C22semidirect
44. C2×Dic3×Dic5C22semidirect
45. C2×Dic3×Dic5C22semidirect
46. #91474C4semidirect
47. #91115C22semidirect
48. #91115C22semidirect
49. C5×C3⋊#95C22semidirect
50. C5×C3⋊#95C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
64. #65228D3semidirect
79. C22×D3×D5C2×C4semidirect
106. #6714C2×C4semidirect
110. C5×(C2×D3)⋊C4C2×C4semidirect
124. #6665C2×C4semidirect
141. #4940D5semidirect
151. C2×C42×C5C2×D3semidirect
165. C2×#685C2×D3semidirect
166. C2×#685C2×D3semidirect
167. C2×C4⋊Dic5C2×D3semidirect
262. C2×C3×C42C2×D5semidirect
279. C2×Dic3⋊C4C2×D5semidirect
286. C3⋊#95C2×D5semidirect
287. C3⋊#95C2×D5semidirect
461. (C2×D3)⋊C4C4×D5semidirect
568. C2×C42D3×D5semidirect
764. C3×C5#2375semidirect
907. C5#76434semidirect
955. C3#10607571semidirect

Maximal subgroups

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

subgroupindex
C2×#914742
#117510412
C5×#49402
C3×#652282
#117489402
#117489162
#117489132
#117489062
#117488962
#117488722
#117487112
#117487072
#117486782
#117486752
#106075713
#764345