Finite Group Databasebeta

← #14330956

Subgroups — #14330956

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4030C211yesmaximal, characteristic
2#11751051C211yesmaximal, characteristic, complemented
3C5×#4951C211yesmaximal, characteristic, complemented
4#11749518C211yesmaximal, characteristic, complemented
5#11749500C211yesmaximal, characteristic, complemented
6#11749500C211yesmaximal, characteristic, complemented
7#11749489C211yesmaximal, characteristic, complemented
8#11748899C211yesmaximal, characteristic, complemented
9#11748896C211yesmaximal, characteristic, complemented
10#11748785C211yesmaximal, characteristic, complemented
11#11748772C211yesmaximal, characteristic, complemented
12#11748759C211yesmaximal, characteristic, complemented
13#11748737C211yesmaximal, characteristic, complemented
14#11748691C211yesmaximal, characteristic, complemented
15#11748590C211yesmaximal, characteristic, complemented
16#10607221—31nomaximal, Hall
17C23×Dic15C2211yescharacteristic
18C22×C3×C22⋊D5C2211yescharacteristic
19C22×C3×C22⋊D5C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×D5×Dic3C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25C2×C4⋊Dic15C2211yescharacteristic
26C2×C4⋊Dic15C2211yescharacteristic
27C2×C5×#217C2211yescharacteristic
28C2×C5×#217C2211yescharacteristic
29C2×C5×C4⋊Dic3C2211yescharacteristic
30C2×C4×C5×Dic3C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#683C2211yescharacteristic
33C3×#4030C418yescomplemented
34C2×#6668C2211yescharacteristic
35C2×#6665C2211yescharacteristic
36C2×#6665C2211yescharacteristic
37C2×#6665C2211yescharacteristic
38C2×#6665C2211yescharacteristic
39C2×#6665C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43#91115C2211yescharacteristic
44#91115C2211yescharacteristic
45C5×C3⋊#95C2211yescharacteristic
46C5×C3⋊#95C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#82639—51nomaximal, Hall
54C2×#4030D311yescharacteristic
55C5×#388—31no—
56#65278—31no—
57#65276—31no—
58#65247—31no—
59#65247—31no—
60#65246—31no—
61#65245—31no—
62#65239—31no—
63#65228—31no—
64#65222—31no—
65#64959—31no—
66#64954—31no—
67#64953—31no—
68#64944—31no—
69C24×C3×C5C2311yescharacteristic
70C23×C3×D5C2311yescharacteristic
71C23×C3×D5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×Dic15—41no—
75C22×Dic15—41no—
76C22×Dic15—41no—
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C2×C3×C22⋊D5—41no—
86C2×C3×C22⋊D5—41no—
87C2×C3×C22⋊D5—41no—
88C2×C3×C22⋊D5—41no—
89C2×C3×C22⋊D5C2×C414yes—
90C2×C3×C22⋊D5C2×C414yescomplemented
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C2×C3×D20—41no—
94C2×C3×D20—41no—
95C2×C3×D20C2×C414yescomplemented
96C2×C3×C4×D5—41no—
97C2×C3×C4×D5—41no—
98C2×C3×C4×D5C2×C414yescomplemented
99C2×D5×Dic3—41no—
100C2×D5×Dic3—41no—
101C2×D5×Dic3—41no—
102C3×C5×C22⋊C4C2×C414yescomplemented
103#6719—41no—
104C4⋊Dic15—41no—
105C4⋊Dic15—41no—
106C5×#217—41no—
107C5×#217—41no—
108C5×C4⋊Dic3—41no—
109C4×C5×Dic3—41no—
110C3×#685C2×C414yescomplemented
111C3×#683C2×C414yescomplemented
112#6668—41no—
113#6665—41no—
114#6665—41no—
115#6665—41no—
116#6665—41no—
117#6665—41no—
118#6665—41no—
119#6665—41no—
120Dic3×Dic5—41no—
121C2×C3×#121—51no—
122#5221—51no—
123#5221—51no—
124#5220—51no—
125#5220—51no—
126#5220—51no—
127#5220—51no—
128#5212—51no—
129#5211—51no—
130#4980—51no—
131#4980—51no—
132#4951—51no—
133#4951D511yescharacteristic, complemented
134#4950—51no—
135#4950—51no—
136C22×C22⋊D5C2×D311yescharacteristic
137C22×C22⋊D5C2×D311yescharacteristic
138C23×Dic5—31no—
139C22×D20C2×D311yescharacteristic
140C22×C4×D5—31no—
141C22×C4×D5C2×D311yescharacteristic
142C2×C5×C4⋊C4—31no—
143C2×C5×C22⋊C4—31no—
144C2×C5×C22⋊C4—31no—
145C2×C5×C22⋊C4C2×D311yescharacteristic
146C2×C42×C5—31no—
147C2×C22⋊Dic5—31no—
148C2×#685—31no—
149C2×#685—31no—
150C2×#685—31no—
151C2×#685—31no—
152C2×#685—31no—
153C2×#685—31no—
154C2×#685—31no—
155C2×#685C2×D311yescharacteristic
156C2×C4⋊Dic5—31no—
157C2×C4⋊Dic5—31no—
158C2×#683—31no—
159C2×#683C2×D311yescharacteristic
160C2×C4×Dic5—31no—
161#4030Dic318yescomplemented
162C5×#95—31no—
163C5×#95—31no—
164#3963—31no—
165#3963—31no—
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172#2377—151noSylow
173C23×C3×C5—21no—
174C23×C3×C5—21no—
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5—21no—
178C23×C3×C5—21no—
179C23×C3×C5C22×C412yes—
180C23×C3×C5C2411yescharacteristic
181C22×C3×D5—21no—
182C22×C3×D5—21no—
183C22×C3×D5—21no—
184C22×C3×D5—21no—
185C22×C3×D5—21no—
186C22×C3×D5—21no—
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×D5C22×C412yes—
194C22×C3×D5C22×C412yes—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5C22×C412yes—
200C2×C3×C4×C5C22×C412yes—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15—21no—
207C2×Dic15—21no—
208C2×Dic15—21no—
209C2×Dic15—21no—
210C2×Dic15—21no—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—44no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3—21no—
216C2×C5×Dic3—21no—
217C2×C5×Dic3—21no—
218C2×C5×Dic3—21no—
219C2×C5×Dic3—21no—
220C2×C5×Dic3—21no—
221C2×C5×Dic3—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—21no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—21no—
226C3×C22⋊D5—44no—
227C3×C22⋊D5—44no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5C22×C412yes—
233C2×C3×Dic5C22×C412yes—
234C3×D20—44no—
235C3×C4×D5—44no—
236D5×Dic3—44no—
237C22×C3×D4—51no—
238C22×C3×D4—51no—
239C22×C3×D4—51no—
240C23×C3×C4—51no—
241C23×Dic3—51no—
242C23×Dic3—51no—
243C3×#121—58no—
244C2×C3×C4⋊C4—51no—
245C2×C3×C22⋊C4—51no—
246C2×C3×C22⋊C4C2×D511yescharacteristic
247C2×#217—51no—
248C2×#217—51no—
249C2×#217—51no—
250C2×#217—51no—
251C2×#217—51no—
252C2×#217—51no—
253C2×#217—51no—
254C2×#217—51no—
255C2×#217C2×D511yescharacteristic
256C2×#217C2×D511yescharacteristic
257C2×C4⋊Dic3—51no—
258C2×C4⋊Dic3—51no—
259C2×C4⋊Dic3—51no—
260C2×C4⋊Dic3C2×D511yescharacteristic
261C2×C4×Dic3—51no—
262C2×C4×Dic3C2×D511yescharacteristic
263C3⋊#95—51no—
264C3⋊#95—51no—
265C3⋊#95—51no—
266C3⋊#95—51no—
267C3⋊#95—51no—
268C3⋊#95—51no—
269C3⋊#95—51no—
270C3⋊#95—51no—
271C3⋊#95C2×D511yescharacteristic
272C3⋊#95C2×D511yescharacteristic
273C24×C5C22×D311yescharacteristic
274C23×D5C22×D311yescharacteristic
275C23×D5C22×D311yescharacteristic
276C22×C4×C5—31no—
277C22×C4×C5—31no—
278C22×C4×C5—31no—
279C22×C4×C5—31no—
280C22×C4×C5C22×D311yescharacteristic
281C22×C4×C5C22×D311yescharacteristic
282C2×C22⋊D5—41no—
283C2×C22⋊D5—41no—
284C2×C22⋊D5—41no—
285C2×C22⋊D5—41no—
286C2×C22⋊D5C2×Dic314yes—
287C2×C22⋊D5C2×Dic314yescomplemented
288C22×Dic5—31no—
289C22×Dic5—31no—
290C22×Dic5—31no—
291C22×Dic5—31no—
292C22×Dic5—121no—
293C22×Dic5—121no—
294C22×Dic5—121no—
295C22×Dic5C22×D311yescharacteristic
296C22×Dic5C22×D311yescharacteristic
297C2×D20—41no—
298C2×D20—41no—
299C2×D20C2×Dic314yescomplemented
300C2×C4×D5—41no—
301C2×C4×D5—41no—
302C2×C4×D5—121no—
303C2×C4×D5—121no—
304C2×C4×D5—121no—
305C2×C4×D5C2×Dic314yescomplemented
306C5×C4⋊C4—121no—
307C5×C22⋊C4—121no—
308C5×C22⋊C4—121no—
309C5×C22⋊C4C2×Dic314yescomplemented
310C42×C5—121no—
311C22⋊Dic5—121no—
312#685—121no—
313#685—121no—
314#685—121no—
315#685—121no—
316#685—121no—
317#685—121no—
318#685—121no—
319#685C2×Dic314yescomplemented
320C4⋊Dic5—121no—
321C4⋊Dic5—121no—
322#683—121no—
323#683C2×Dic314yescomplemented
324C4×Dic5—121no—
325C2×#121—51no—
326#390—151no—
327#390—151no—
328#388—31no—
329#388—151no—
330#387—151no—
331#387—151no—
332#386—151no—
333#386—151no—
334#386—151no—
335#386—151no—
336#385—151no—
337#385—151no—
338#381—151no—
339#380—151no—
340C22×C3×C5—22no—
341C22×C3×C5—22no—
342C22×C3×C5—22no—
343C22×C3×C5—41no—
344C22×C3×C5—41no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5C23×C411yescharacteristic
348C22×C3×C5H(5,𝔽2)11yescharacteristic
349C22×C3×C5H(5,𝔽2)11yescharacteristic
350C22×C3×C5H(5,𝔽2)11yescharacteristic
351C22×C3×C5H(5,𝔽2)11yescharacteristic
352C22×C3×C5H(5,𝔽2)11yescharacteristic
353C22×C3×C52−1+411yescharacteristic
354C2×C3×D5—22no—
355C2×C3×D5—22no—
356C2×C3×D5—22no—
357C2×C3×D5—22no—
358C2×C3×D5—22no—
359C2×C3×D5—22no—
360C2×C3×D5—41no—
361C2×C3×D5—41no—
362C2×C3×D5—41no—
363C2×C3×D5—41no—
364C2×C3×D5—41no—
365C2×C3×D5—41no—
366C2×C3×D5—41no—
367C2×C3×D5—41no—
368C3×C4×C5—22no—
369C3×C4×C5—22no—
370Dic15—41no—
371Dic15—41no—
372Dic15—41no—
373Dic15—41no—
374C3×Dic5—22no—
375C3×Dic5—22no—
376C5×Dic3—41no—
377C5×Dic3—41no—
378C5×Dic3—41no—
379C5×Dic3—41no—
380C24×C3—51no—
381C24×C3—51no—
382C24×C3C22×D511yescharacteristic
383C2×C3×D4—54no—
384C2×C3×D4—54no—
385C2×C3×D4—54no—
386C2×C3×D4—201no—
387C2×C3×D4—201no—
388C2×C3×D4—201no—
389C2×C3×D4—201no—
390C2×C3×D4—201no—
391C2×C3×D4—201no—
392C22×C3×C4—51no—
393C22×C3×C4—51no—
394C22×C3×C4—54no—
395C22×C3×C4—201no—
396C22×C3×C4—201no—
397C22×C3×C4C22×D511yescharacteristic
398C22×C3×C4C22×D511yescharacteristic
399C22×Dic3—51no—
400C22×Dic3—51no—
401C22×Dic3—51no—
402C22×Dic3—51no—
403C22×Dic3—201no—
404C22×Dic3—201no—
405C22×Dic3—201no—
406C22×Dic3—201no—
407C22×Dic3—201no—
408C22×Dic3—201no—
409C22×Dic3C22×D511yescharacteristic
410C22×Dic3C22×D511yescharacteristic
411C22×Dic3C22×D511yescharacteristic
412C22×Dic3C22×D511yescharacteristic
413C3×C4⋊C4—54no—
414C3×C22⋊C4—54no—
415C3×C22⋊C4C4×D514yescomplemented
416#217—41no—
417#217—41no—
418#217—201no—
419#217—201no—
420#217—201no—
421#217—201no—
422#217—201no—
423#217—201no—
424#217—201no—
425#217—201no—
426C4⋊Dic3—41no—
427C4⋊Dic3—201no—
428C4⋊Dic3—201no—
429C4⋊Dic3—201no—
430C4×Dic3—41no—
431C4×Dic3—201no—
432C23×C5—21no—
433C23×C5—21no—
434C23×C5—21no—
435C23×C5—21no—
436C23×C5—21no—
437C23×C5—21no—
438C23×C5C22×Dic312yes—
439C23×C5C23×D311yescharacteristic
440C22×D5—21no—
441C22×D5—21no—
442C22×D5—21no—
443C22×D5—21no—
444C22×D5—21no—
445C22×D5—21no—
446C22×D5—21no—
447C22×D5—21no—
448C22×D5—21no—
449C22×D5—21no—
450C22×D5—21no—
451C22×D5—21no—
452C22×D5C22×Dic312yes—
453C22×D5C22×Dic312yes—
454C2×C4×C5—21no—
455C2×C4×C5—21no—
456C2×C4×C5—21no—
457C2×C4×C5—21no—
458C2×C4×C5—61no—
459C2×C4×C5—61no—
460C2×C4×C5—61no—
461C2×C4×C5—61no—
462C2×C4×C5—61no—
463C2×C4×C5—61no—
464C2×C4×C5—61no—
465C2×C4×C5—61no—
466C2×C4×C5—61no—
467C2×C4×C5—61no—
468C2×C4×C5—61no—
469C2×C4×C5—61no—
470C2×C4×C5C22×Dic312yes—
471C2×C4×C5C22×Dic312yes—
472C22⋊D5—44no—
473C22⋊D5—44no—
474C2×Dic5—21no—
475C2×Dic5—21no—
476C2×Dic5—21no—
477C2×Dic5—21no—
478C2×Dic5—61no—
479C2×Dic5—61no—
480C2×Dic5—61no—
481C2×Dic5—61no—
482C2×Dic5—61no—
483C2×Dic5—61no—
484C2×Dic5—61no—
485C2×Dic5—61no—
486C2×Dic5—61no—
487C2×Dic5—61no—
488C2×Dic5—61no—
489C2×Dic5—61no—
490C2×Dic5—124no—
491C2×Dic5C22×Dic312yes—
492C2×Dic5C22×Dic312yes—
493D20—44no—
494C4×D5—44no—
495C4×D5—124no—
496C22×D4—51no—
497C22×D4—51no—
498C22×D4—51no—
499C23×C4—51no—
500C23×C4—151no—
501C23×C4—151no—
502#121—58no—
503C2×C4⋊C4—31no—
504C2×C4⋊C4—51no—
505C2×C4⋊C4—151no—
506C2×C4⋊C4—151no—
507C2×C4⋊C4—151no—
508C2×C22⋊C4—31no—
509C2×C22⋊C4—31no—
510C2×C22⋊C4—51no—
511C2×C22⋊C4—151no—
512C2×C22⋊C4—151no—
513C2×C22⋊C4—151no—
514C2×C22⋊C4—151no—
515C2×C22⋊C4—151no—
516C2×C22⋊C4—151no—
517C2×C22⋊C4—151no—
518C2×C22⋊C4—151no—
519C2×C22⋊C4D3×D511yescharacteristic
520C2×C42—31no—
521C2×C42—151no—
522#95—31no—
523#95—31no—
524#95—151no—
525#95—151no—
526#95—151no—
527#95—151no—
528#95—151no—
529#95—151no—
530#95—151no—
531#95—151no—
532C2×C3×C5—42no—
533C2×C3×C5#51811yescharacteristic
534C2×C3×C5#51811yescharacteristic
535C2×C3×C5#52011yescharacteristic
536C2×C3×C5#56011yescharacteristic
537C2×C3×C5#56011yescharacteristic
538C2×C3×C5#56211yescharacteristic
539C2×C3×C5#56211yescharacteristic
540C3×D5—42no—
541C3×D5—42no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—52no—
549C23×C3—52no—
550C23×C3—101no—
551C23×C3—101no—
552C23×C3—101no—
553C23×C3—101no—
554C23×C3—101no—
555C23×C3—101no—
556C23×C3—101no—
557C23×C3—101no—
558C23×C3—101no—
559C23×C3—101no—
560C23×C3—101no—
561C23×C3—101no—
562C23×C3C2×C4×D512yes—
563C23×C3C23×D511yescharacteristic
564C3×D4—204no—
565C3×D4—204no—
566C3×D4—204no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—52no—
572C2×C3×C4—52no—
573C2×C3×C4—101no—
574C2×C3×C4—101no—
575C2×C3×C4—101no—
576C2×C3×C4—101no—
577C2×C3×C4—204no—
578C2×C3×C4C2×C4×D512yes—
579C2×C3×C4C2×C4×D512yes—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—101no—
593C2×Dic3—101no—
594C2×Dic3—101no—
595C2×Dic3—101no—
596C2×Dic3—101no—
597C2×Dic3—101no—
598C2×Dic3—101no—
599C2×Dic3—101no—
600C2×Dic3—101no—
601C2×Dic3—101no—
602C2×Dic3—101no—
603C2×Dic3—101no—
604C2×Dic3—204no—
605C2×Dic3—204no—
606C22×C5—22no—
607C22×C5—22no—
608C22×C5—22no—
609C22×C5—41no—
610C22×C5—41no—
611C22×C5—41no—
612C22×C5—41no—
613C22×C5#100411yescharacteristic
614C22×C5#100411yescharacteristic
615C22×C5#100411yescharacteristic
616C22×C5#100411yescharacteristic
617C22×C5#100911yescharacteristic
618C22×C5#101011yescharacteristic
619C22×C5C23×Dic311yescharacteristic
620C2×D5—22no—
621C2×D5—22no—
622C2×D5—22no—
623C2×D5—22no—
624C2×D5—22no—
625C2×D5—22no—
626C2×D5—41no—
627C2×D5—41no—
628C2×D5—41no—
629C2×D5—41no—
630C2×D5—41no—
631C2×D5—41no—
632C2×D5—41no—
633C2×D5—41no—
634C4×C5—22no—
635C4×C5—22no—
636C4×C5—121no—
637C4×C5—121no—
638C4×C5—121no—
639C4×C5—121no—
640Dic5—22no—
641Dic5—22no—
642Dic5—121no—
643Dic5—121no—
644Dic5—121no—
645Dic5—121no—
646C24—51no—
647C24—51no—
648C24C2×D3×D511yescharacteristic
649C2×D4—54no—
650C2×D4—54no—
651C2×D4—54no—
652C2×D4—201no—
653C2×D4—201no—
654C2×D4—201no—
655C2×D4—201no—
656C2×D4—201no—
657C2×D4—201no—
658C22×C4—31no—
659C22×C4—31no—
660C22×C4—31no—
661C22×C4—31no—
662C22×C4—51no—
663C22×C4—51no—
664C22×C4—54no—
665C22×C4—151no—
666C22×C4—151no—
667C22×C4—151no—
668C22×C4—151no—
669C22×C4—201no—
670C22×C4—201no—
671C22×C4—601no—
672C22×C4—601no—
673C22×C4—601no—
674C22×C4—601no—
675C22×C4—601no—
676C22×C4—601no—
677C22×C4C2×D3×D511yescharacteristic
678C22×C4C2×D3×D511yescharacteristic
679C4⋊C4—54no—
680C4⋊C4—121no—
681C4⋊C4—601no—
682C4⋊C4—601no—
683C4⋊C4—601no—
684C22⋊C4—54no—
685C22⋊C4—121no—
686C22⋊C4—121no—
687C22⋊C4—601no—
688C22⋊C4—601no—
689C22⋊C4—601no—
690C22⋊C4—601no—
691C22⋊C4—601no—
692C22⋊C4—601no—
693C22⋊C4—601no—
694C22⋊C4—601no—
695C22⋊C4D5×Dic314yescomplemented
696C42—121no—
697C42—601no—
698C3×C5#237711yescharacteristic, complemented, Hall
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—102no—
707C22×C3—102no—
708C22×C3—102no—
709C22×C3—102no—
710C22×C3—102no—
711C22×C3—102no—
712C22×C3—201no—
713C22×C3—201no—
714C22×C3—201no—
715C22×C3—201no—
716C22×C3—201no—
717C22×C3—201no—
718C22×C3—201no—
719C22×C3—201no—
720C22×C3C22×C4×D511yescharacteristic
721C22×C3#414411yescharacteristic
722C22×C3#414411yescharacteristic
723C22×C3#414911yescharacteristic
724C22×C3#414911yescharacteristic
725C22×C3#414911yescharacteristic
726C22×C3#415011yescharacteristic
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—102no—
730C3×C4—102no—
731Dic3—41no—
732Dic3—41no—
733Dic3—41no—
734Dic3—41no—
735Dic3—201no—
736Dic3—201no—
737Dic3—201no—
738Dic3—201no—
739C2×C5—42no—
740C2×C5#562011yescharacteristic
741C2×C5#562011yescharacteristic
742C2×C5#562111yescharacteristic
743C2×C5#562111yescharacteristic
744C2×C5#579811yescharacteristic
745C2×C5#579811yescharacteristic
746C2×C5#582711yescharacteristic
747D5—42no—
748D5—42no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—52no—
756C23—52no—
757C23—101no—
758C23—101no—
759C23—101no—
760C23—101no—
761C23—101no—
762C23—101no—
763C23—101no—
764C23—101no—
765C23—101no—
766C23—101no—
767C23—101no—
768C23—101no—
769C23C2×D5×Dic312yes—
770C23C22×D3×D511yescharacteristic
771D4—204no—
772D4—204no—
773D4—204no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—52no—
779C2×C4—52no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—101no—
793C2×C4—101no—
794C2×C4—101no—
795C2×C4—101no—
796C2×C4—204no—
797C2×C4—301no—
798C2×C4—301no—
799C2×C4—301no—
800C2×C4—301no—
801C2×C4—301no—
802C2×C4—301no—
803C2×C4—301no—
804C2×C4—301no—
805C2×C4—301no—
806C2×C4—301no—
807C2×C4—301no—
808C2×C4—301no—
809C2×C4—604no—
810C2×C4—604no—
811C2×C4C2×D5×Dic312yes—
812C2×C4C2×D5×Dic312yes—
813C2×C3—42no—
814C2×C3—202no—
815C2×C3—202no—
816C2×C3#6585711yescharacteristic
817C2×C3#6587911yescharacteristic
818C2×C3#6587911yescharacteristic
819C2×C3#6595411yescharacteristic
820C2×C3#6600111yescharacteristic
821C2×C3#6601811yescharacteristic
822C2×C3#6604511yescharacteristic
823C5#8263911yescharacteristic, complemented, Sylow
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—102no—
832C22—102no—
833C22—102no—
834C22—102no—
835C22—102no—
836C22—102no—
837C22—201no—
838C22—201no—
839C22—201no—
840C22—201no—
841C22—201no—
842C22—201no—
843C22—201no—
844C22—201no—
845C22#9200111yescharacteristic
846C22#9201911yescharacteristic
847C22#9202511yescharacteristic
848C22#9202511yescharacteristic
849C22#9202611yescharacteristic
850C22#9202611yescharacteristic
851C22C22×D5×Dic311yescharacteristic
852C4—22no—
853C4—22no—
854C4—102no—
855C4—102no—
856C4—121no—
857C4—121no—
858C4—121no—
859C4—121no—
860C4—601no—
861C4—601no—
862C4—601no—
863C4—601no—
864C3#1060722111yescharacteristic, complemented, Sylow
865C2—42no—
866C2—202no—
867C2—202no—
868C2#1175304611yescharacteristic
869C2#1175316811yescharacteristic
870C2#1175317911yescharacteristic
871C2#1175330111yescharacteristic
872C2#1175450911yescharacteristic
873C2#1175491011yescharacteristic
874C2#1175491011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C3×#4030C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2377
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. #11751051C2semidirect
3. C5×#4951C2semidirect
4. #11749518C2semidirect
5. #11749500C2semidirect
6. #11749500C2semidirect
7. #11749489C2semidirect
8. #11748899C2semidirect
9. #11748896C2semidirect
10. #11748785C2semidirect
11. #11748772C2semidirect
12. #11748759C2semidirect
13. #11748737C2semidirect
14. #11748691C2semidirect
15. #11748590C2semidirect
33. C3×#4030C4semidirect
90. C2×C3×C22⋊D5C2×C4semidirect
95. C2×C3×D20C2×C4semidirect
98. C2×C3×C4×D5C2×C4semidirect
102. C3×C5×C22⋊C4C2×C4semidirect
110. C3×#685C2×C4semidirect
111. C3×#683C2×C4semidirect
133. #4951D5semidirect
161. #4030Dic3semidirect
287. C2×C22⋊D5C2×Dic3semidirect
299. C2×D20C2×Dic3semidirect
305. C2×C4×D5C2×Dic3semidirect
309. C5×C22⋊C4C2×Dic3semidirect
319. #685C2×Dic3semidirect
323. #683C2×Dic3semidirect
415. C3×C22⋊C4C4×D5semidirect
695. C22⋊C4D5×Dic3semidirect
698. C3×C5#2377semidirect
823. C5#82639semidirect
864. C3#10607221semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40302
#117510512
C5×#49512
#117495182
#117495002
#117494892
#117488992
#117488962
#117487852
#117487722
#117487592
#117487372
#117486912
#117485902
#106072213
#826395