Finite Group Databasebeta

← #14330658

Subgroups — #14330658

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×#91563C211yesmaximal, characteristic
2#11751046C211yesmaximal, characteristic, complemented
3C5×#4956C211yesmaximal, characteristic, complemented
4C3×#65244C211yesmaximal, characteristic, complemented
5#11749488C211yesmaximal, characteristic, complemented
6#11749482C211yesmaximal, characteristic, complemented
7#11749481C211yesmaximal, characteristic, complemented
8#11748916C211yesmaximal, characteristic, complemented
9#11748915C211yesmaximal, characteristic, complemented
10#11748910C211yesmaximal, characteristic, complemented
11#11748910C211yesmaximal, characteristic, complemented
12#11748712C211yesmaximal, characteristic, complemented
13#11748710C211yesmaximal, characteristic, complemented
14#11748708C211yesmaximal, characteristic, complemented
15#11748707C211yesmaximal, characteristic, complemented
16#10606613—31nomaximal, Hall
17C24×C3×D5C2211yescharacteristic
18C22×C5×#67C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic, complemented
20C22×#1201C2211yescharacteristic
21C22×#1201C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25C2×#6712C2211yescharacteristic, complemented
26C2×C4×Dic15C2211yescharacteristic, complemented
27C2×C5×#217C2211yescharacteristic
28C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34#91563C418yescomplemented
35C2×Dic3⋊Dic5C2211yescharacteristic, complemented
36C2×#6669C2211yescharacteristic, complemented
37C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
38C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
39C2×#6665C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×#6665C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic, 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#73851—51nomaximal, Hall
54C2×#4083—31no—
55C5×#386—31no—
56#65510—31no—
57#65502—31no—
58#65502—31no—
59#65246—31no—
60#65246—31no—
61#65244—31no—
62#65244D311yescharacteristic, complemented
63#65234—31no—
64#65234—31no—
65#64959—31no—
66#64959—31no—
67#64958—31no—
68#64958—31no—
69C24×C3×C5C2311yescharacteristic
70C23×C5×D3C2311yescharacteristic
71C23×C3×D5—41no—
72C23×C3×D5—41no—
73C23×C3×D5—41no—
74C23×C3×D5—41no—
75C23×C3×D5—41no—
76C23×C3×D5—41no—
77C23×C3×D5C2×C414yescomplemented
78C23×C3×D5C2311yescharacteristic
79C23×C3×D5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C2×C5×#67—41no—
87C2×C5×#67—41no—
88C2×C5×#67C2×C414yes—
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C2×C4×C5×D3—41no—
93C2×C4×C5×D3—41no—
94C2×C4×C5×D3—41no—
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C2×#1201—41no—
98C2×#1201—41no—
99C2×#1201—41no—
100C2×#1201—41no—
101C2×#1201C2×C414yes—
102C2×#1201C2×C414yes—
103C3×C5×C22⋊C4—41no—
104#6719—41no—
105#6719C2×C414yescomplemented
106#6712—41no—
107C4×Dic15—41no—
108C5×#217—41no—
109C5×(C2×D3)⋊C4—41no—
110C3×C22⋊Dic5—41no—
111C3×#685—41no—
112C3×#685—41no—
113C3×#685—41no—
114C3×#685—41no—
115Dic3⋊Dic5—41no—
116#6669—41no—
117(C2×D3)⋊Dic5—41no—
118(C2×D3)⋊Dic5—41no—
119#6665—41no—
120#6665—41no—
121#6665—41no—
122#6665—41no—
123#6665C2×C414yescomplemented
124#6665C2×C414yescomplemented
125Dic3×Dic5—41no—
126Dic3×Dic5—41no—
127C2×#953—51no—
128C3×#379—51no—
129#5247—51no—
130#4957—51no—
131#4957—51no—
132#4957—51no—
133#4956—51no—
134#4956—51no—
135#4956D511yescharacteristic, complemented
136#4945—51no—
137#4945—51no—
138#4945—51no—
139#4944—51no—
140#4944—51no—
141#4944—51no—
142C24×D5C2×D311yescharacteristic
143C22×C5×D4—31no—
144C23×C4×C5—31no—
145C22×C22⋊D5—31no—
146C22×C22⋊D5—31no—
147C2×C5×C22⋊C4—31no—
148C2×C5×C22⋊C4—31no—
149C2×C5×C22⋊C4C2×D311yescharacteristic
150C2×C22⋊Dic5—31no—
151C2×C22⋊Dic5—31no—
152C2×C22⋊Dic5—31no—
153C2×C22⋊Dic5—31no—
154C2×C22⋊Dic5C2×D311yescharacteristic
155#4083—38no—
156C2×#685—31no—
157C2×#685—31no—
158C2×#685—31no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—31no—
162C2×#685C2×D311yescharacteristic
163C2×#685C2×D311yescharacteristic
164C2×#685C2×D311yescharacteristic
165C2×#685C2×D311yescharacteristic
166C2×C4⋊Dic5—31no—
167C2×#683—31no—
168C2×#683—31no—
169C2×C4×Dic5—31no—
170C2×C4×Dic5—31no—
171C2×C4×Dic5—31no—
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×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×D5—44no—
207C22×C3×D5—44no—
208C22×C3×D5—44no—
209C22×C3×D5—44no—
210C22×C3×D5—44no—
211C22×C3×D5—44no—
212C22×C3×D5—44no—
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×C5—21no—
220C2×C3×C4×C5—21no—
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×Dic15C22×C412yes—
232C2×Dic15C22×C412yes—
233C5×#67—44no—
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×Dic3C22×C412yes—
243C4×C5×D3—44no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—21no—
250#1201—44no—
251#1201—44no—
252C25×C3—51no—
253C22×#67—51no—
254C22×#67—51no—
255C22×#67C2×D511yescharacteristic
256C22×C4×D3C2×D511yescharacteristic, complemented
257C2×C3×C22⋊C4—51no—
258C2×C3×C22⋊C4—51no—
259C2×C3×C22⋊C4—51no—
260C2×C3×C22⋊C4—51no—
261C2×C3×C22⋊C4—51no—
262C2×C3×C22⋊C4C2×D511yescharacteristic
263#953—58no—
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×#217C2×D511yescharacteristic
273C2×(C2×D3)⋊C4—51no—
274C2×(C2×D3)⋊C4—51no—
275C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
276C2×Dic3⋊C4—51no—
277C2×Dic3⋊C4—51no—
278C2×Dic3⋊C4—51no—
279C2×C4×Dic3—51no—
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—
289C24×C5C22×D311yescharacteristic
290C23×D5—41no—
291C23×D5—41no—
292C23×D5—41no—
293C23×D5—41no—
294C23×D5—41no—
295C23×D5—41no—
296C23×D5C4×D314yescomplemented
297C23×D5C22×D311yescharacteristic
298C23×D5C22×D311yescharacteristic
299C2×C5×D4—34no—
300C2×C5×D4—121no—
301C2×C5×D4—121no—
302C22×C4×C5—31no—
303C22×C4×C5—31no—
304C22×C4×C5—31no—
305C22×C4×C5—121no—
306C22×C4×C5—121no—
307C22×C4×C5—121no—
308C22×C4×C5C22×D311yescharacteristic
309C22×C4×C5C22×D311yescharacteristic
310C2×C22⋊D5—34no—
311C2×C22⋊D5—34no—
312C2×C22⋊D5—121no—
313C2×C22⋊D5—121no—
314C2×C22⋊D5—121no—
315C2×C22⋊D5—121no—
316C22×Dic5—31no—
317C22×Dic5—31no—
318C22×Dic5—31no—
319C22×Dic5—31no—
320C22×Dic5C22×D311yescharacteristic
321C22×Dic5C22×D311yescharacteristic
322C5×C22⋊C4—41no—
323C5×C22⋊C4—121no—
324C5×C22⋊C4—121no—
325C22⋊Dic5—34no—
326C22⋊Dic5—41no—
327C22⋊Dic5—121no—
328C22⋊Dic5—121no—
329C22⋊Dic5—121no—
330#685—34no—
331#685—34no—
332#685—41no—
333#685—41no—
334#685—41no—
335#685—41no—
336#685—121no—
337#685—121no—
338#685—121no—
339#685—121no—
340C4⋊Dic5—121no—
341#683—121no—
342#683—121no—
343C4×Dic5—121no—
344C4×Dic5—121no—
345C4×Dic5—121no—
346C2×#120—151no—
347#390—151no—
348#390—151no—
349#390—151no—
350#388—151no—
351#388—151no—
352#388—151no—
353#388—151no—
354#388—151no—
355#388—151no—
356#386—31no—
357#386—151no—
358#386—151no—
359#379—51no—
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×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—416no—
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—41no—
398C3×C4×C5—41no—
399Dic15—22no—
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—
410C24×C3—54no—
411C24×C3—201no—
412C24×C3—201no—
413C24×C3—201no—
414C24×C3—201no—
415C24×C3—201no—
416C24×C3—201no—
417C24×C3C22×D511yescharacteristic
418C23×D3C22×D511yescharacteristic
419C22×C3×C4—51no—
420C22×C3×C4—51no—
421C22×C3×C4C22×D511yescharacteristic
422C22×C3×C4C22×D511yescharacteristic
423C2×#67—41no—
424C2×#67—41no—
425C2×#67—54no—
426C2×#67—54no—
427C2×#67—201no—
428C2×#67—201no—
429C2×#67—201no—
430C2×#67—201no—
431C2×#67C4×D514yes—
432C22×Dic3—51no—
433C22×Dic3—51no—
434C22×Dic3—51no—
435C22×Dic3—51no—
436C22×Dic3C22×D511yescharacteristic
437C22×Dic3C22×D511yescharacteristic
438C22×Dic3C22×D511yescharacteristic
439C2×C4×D3—41no—
440C2×C4×D3—41no—
441C2×C4×D3—41no—
442C3×C22⋊C4—41no—
443C3×C22⋊C4—201no—
444C3×C22⋊C4—201no—
445C3×C22⋊C4—201no—
446C3×C22⋊C4—201no—
447C3×C22⋊C4—201no—
448#217—41no—
449#217—54no—
450#217—54no—
451#217—54no—
452#217—201no—
453#217—201no—
454#217—201no—
455#217—201no—
456#217—201no—
457(C2×D3)⋊C4—41no—
458(C2×D3)⋊C4—201no—
459(C2×D3)⋊C4—201no—
460Dic3⋊C4—201no—
461Dic3⋊C4—201no—
462Dic3⋊C4—201no—
463C4×Dic3—201no—
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×C5—32no—
473C23×C5—61no—
474C23×C5—61no—
475C23×C5—61no—
476C23×C5—61no—
477C23×C5—61no—
478C23×C5—61no—
479C23×C5C2×C4×D312yes—
480C23×C5C23×D311yescharacteristic
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—21no—
493C22×D5—44no—
494C22×D5—44no—
495C22×D5—44no—
496C22×D5—44no—
497C22×D5—44no—
498C22×D5—44no—
499C22×D5—44no—
500C22×D5C2×C4×D312yes—
501C22×D5C2×C4×D312yes—
502C5×D4—124no—
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—32no—
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×C5—124no—
519C22⋊D5—124no—
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—32no—
529C2×Dic5—61no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5—61no—
536C2×Dic5—61no—
537C2×Dic5—61no—
538C2×Dic5—61no—
539C25—51no—
540C22×D4—31no—
541C22×D4—151no—
542C22×D4—151no—
543C23×C4—31no—
544#120—158no—
545C2×C4⋊C4—151no—
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—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⋊C4D3×D511yescharacteristic
566C2×C42—151no—
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—
585C5×D3—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—101no—
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—204no—
607C23×C3—204no—
608C23×C3—204no—
609C23×C3—204no—
610C23×C3—204no—
611C23×C3—204no—
612C23×C3—204no—
613C23×C3C2×C4×D512yes—
614C23×C3C23×D511yescharacteristic
615C22×D3—21no—
616C22×D3—21no—
617C22×D3—21no—
618C22×D3—21no—
619C22×D3—21no—
620C22×D3—21no—
621C22×D3C2×C4×D512yes—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—101no—
629C2×C3×C4—101no—
630C2×C3×C4—101no—
631C2×C3×C4—101no—
632C2×C3×C4—101no—
633C2×C3×C4—101no—
634#67—44no—
635#67—204no—
636#67—204no—
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—52no—
646C2×Dic3—52no—
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×Dic3C2×C4×D512yes—
658C4×D3—44no—
659C22×C5—22no—
660C22×C5—22no—
661C22×C5—22no—
662C22×C5—41no—
663C22×C5—41no—
664C22×C5—41no—
665C22×C5—41no—
666C22×C5—62no—
667C22×C5—62no—
668C22×C5—62no—
669C22×C5—121no—
670C22×C5—121no—
671C22×C5—121no—
672C22×C5—121no—
673C22×C5C22×C4×D311yescharacteristic
674C22×C5#100411yescharacteristic
675C22×C5#100411yescharacteristic
676C22×C5#100411yescharacteristic
677C22×C5#100411yescharacteristic
678C22×C5#100411yescharacteristic
679C22×C5#100411yescharacteristic
680C2×D5—22no—
681C2×D5—22no—
682C2×D5—22no—
683C2×D5—22no—
684C2×D5—22no—
685C2×D5—22no—
686C2×D5—416no—
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—41no—
696C4×C5—41no—
697C4×C5—62no—
698C4×C5—121no—
699C4×C5—121no—
700Dic5—41no—
701Dic5—41no—
702Dic5—62no—
703Dic5—62no—
704Dic5—121no—
705Dic5—121no—
706C24—31no—
707C24—51no—
708C24—51no—
709C24—54no—
710C24—201no—
711C24—201no—
712C24—201no—
713C24—201no—
714C24—201no—
715C24—201no—
716C24C2×D3×D511yescharacteristic
717C2×D4—34no—
718C2×D4—121no—
719C2×D4—121no—
720C2×D4—154no—
721C2×D4—154no—
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—121no—
732C22×C4—121no—
733C22×C4—121no—
734C22×C4—151no—
735C22×C4—151no—
736C22×C4—151no—
737C22×C4—151no—
738C22×C4C2×D3×D511yescharacteristic
739C22×C4C2×D3×D511yescharacteristic
740C4⋊C4—601no—
741C4⋊C4—601no—
742C4⋊C4—601no—
743C22⋊C4—41no—
744C22⋊C4—121no—
745C22⋊C4—121no—
746C22⋊C4—154no—
747C22⋊C4—154no—
748C22⋊C4—154no—
749C22⋊C4—201no—
750C22⋊C4—201no—
751C22⋊C4—201no—
752C22⋊C4—201no—
753C22⋊C4—201no—
754C22⋊C4—601no—
755C22⋊C4—601no—
756C22⋊C4—601no—
757C22⋊C4—601no—
758C22⋊C4—601no—
759C22⋊C4—601no—
760C22⋊C4—601no—
761C42—601no—
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—2016no—
779C22×C3—201no—
780C22×C3—201no—
781C22×C3—201no—
782C22×C3—201no—
783C22×C3—201no—
784C22×C3—201no—
785C22×C3—201no—
786C22×C3—201no—
787C22×C3C22×C4×D511yescharacteristic
788C22×C3#414411yescharacteristic
789C22×C3#414411yescharacteristic
790C22×C3#414411yescharacteristic
791C22×C3#414411yescharacteristic
792C22×C3#414911yescharacteristic
793C22×C3#414911yescharacteristic
794C2×D3—22no—
795C2×D3—22no—
796C2×D3—22no—
797C2×D3—41no—
798C2×D3—41no—
799C2×D3—41no—
800C2×D3—41no—
801C3×C4—41no—
802C3×C4—41no—
803C3×C4—201no—
804C3×C4—201no—
805Dic3—22no—
806Dic3—41no—
807Dic3—41no—
808Dic3—102no—
809Dic3—102no—
810Dic3—201no—
811Dic3—201no—
812C2×C5—42no—
813C2×C5—122no—
814C2×C5#548611yescharacteristic
815C2×C5#548611yescharacteristic
816C2×C5#548611yescharacteristic
817C2×C5#559411yescharacteristic
818C2×C5#559511yescharacteristic
819C2×C5#559511yescharacteristic
820C2×C5#559511yescharacteristic
821D5—42no—
822D5—42no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—32no—
830C23—52no—
831C23—52no—
832C23—61no—
833C23—61no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23—61no—
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—
857C23C4×D3×D512yes—
858C23C22×D3×D511yescharacteristic
859D4—124no—
860D4—604no—
861D4—604no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—32no—
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—101no—
878C2×C4—101no—
879C2×C4—101no—
880C2×C4—101no—
881C2×C4—101no—
882C2×C4—101no—
883C2×C4—124no—
884C2×C4—152no—
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—301no—
895C2×C4—301no—
896C2×C3—42no—
897C2×C3—202no—
898C2×C3—202no—
899C2×C3#6582011yescharacteristic
900C2×C3#6587911yescharacteristic
901C2×C3#6587911yescharacteristic
902C2×C3#6592811yescharacteristic
903C2×C3#6595411yescharacteristic
904C2×C3#6595411yescharacteristic
905C2×C3#6600011yescharacteristic
906D3—42no—
907C5#7385111yescharacteristic, complemented, Sylow
908C22—22no—
909C22—22no—
910C22—22no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—62no—
916C22—62no—
917C22—62no—
918C22—102no—
919C22—102no—
920C22—102no—
921C22—102no—
922C22—102no—
923C22—102no—
924C22—121no—
925C22—121no—
926C22—121no—
927C22—121no—
928C22—2016no—
929C22—201no—
930C22—201no—
931C22—201no—
932C22—201no—
933C22—201no—
934C22—201no—
935C22—201no—
936C22—201no—
937C22C2×C4×D3×D511yescharacteristic
938C22#9201711yescharacteristic
939C22#9202511yescharacteristic
940C22#9202511yescharacteristic
941C22#9202511yescharacteristic
942C22#9202611yescharacteristic
943C22#9204911yescharacteristic
944C4—41no—
945C4—41no—
946C4—62no—
947C4—121no—
948C4—121no—
949C4—201no—
950C4—201no—
951C4—302no—
952C4—302no—
953C4—601no—
954C4—601no—
955C3#1060661311yescharacteristic, complemented, Sylow
956C2—42no—
957C2—122no—
958C2—202no—
959C2—202no—
960C2#1175306511yescharacteristic
961C2#1175316211yescharacteristic
962C2#1175316311yescharacteristic
963C2#1175320011yescharacteristic
964C2#1175462511yescharacteristic
965C2#1175498311yescharacteristic
966C2#1175498411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91563C2
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. #11751046C2semidirect
3. C5×#4956C2semidirect
4. C3×#65244C2semidirect
5. #11749488C2semidirect
6. #11749482C2semidirect
7. #11749481C2semidirect
8. #11748916C2semidirect
9. #11748915C2semidirect
10. #11748910C2semidirect
11. #11748910C2semidirect
12. #11748712C2semidirect
13. #11748710C2semidirect
14. #11748708C2semidirect
15. #11748707C2semidirect
19. C22×C4×C5×D3C22semidirect
25. C2×#6712C22semidirect
26. C2×C4×Dic15C22semidirect
28. C2×C5×(C2×D3)⋊C4C22semidirect
34. #91563C4semidirect
35. C2×Dic3⋊Dic5C22semidirect
36. C2×#6669C22semidirect
37. C2×(C2×D3)⋊Dic5C22semidirect
38. C2×(C2×D3)⋊Dic5C22semidirect
45. C2×Dic3×Dic5C22semidirect
46. C2×Dic3×Dic5C22semidirect
47. #91115C22semidirect
48. #91115C22semidirect
49. C5×C3⋊#95C22semidirect
50. C5×C3⋊#95C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
62. #65244D3semidirect
77. C23×C3×D5C2×C4semidirect
105. #6719C2×C4semidirect
123. #6665C2×C4semidirect
124. #6665C2×C4semidirect
135. #4956D5semidirect
256. C22×C4×D3C2×D5semidirect
275. C2×(C2×D3)⋊C4C2×D5semidirect
286. C3⋊#95C2×D5semidirect
287. C3⋊#95C2×D5semidirect
296. C23×D5C4×D3semidirect
764. C3×C5#2375semidirect
907. C5#73851semidirect
955. C3#10606613semidirect

Maximal subgroups

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

subgroupindex
C2×#915632
#117510462
C5×#49562
C3×#652442
#117494882
#117494822
#117494812
#117489162
#117489152
#117489102
#117487122
#117487102
#117487082
#117487072
#106066133
#738515