Finite Group Databasebeta

← #14322605

Subgroups — #14322605

Order 1920.

1344 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91473C211yesmaximal, characteristic
2C4×#6714C211yesmaximal, characteristic, complemented
3C5×#4940C211yesmaximal, characteristic, complemented
4C3×#65229C211yesmaximal, characteristic, complemented
5#11748940C211yesmaximal, characteristic
6#11748940C211yesmaximal, characteristic
7#11748882C211yesmaximal, characteristic, complemented
8#11748876C211yesmaximal, characteristic, complemented
9#11748794C211yesmaximal, characteristic, complemented
10#11748791C211yesmaximal, characteristic, complemented
11#11748723C211yesmaximal, characteristic, complemented
12#11748718C211yesmaximal, characteristic, complemented
13#11748712C211yesmaximal, characteristic, complemented
14#11748711C211yesmaximal, characteristic, complemented
15#11748670C211yesmaximal, characteristic, complemented
16#10607556—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×#1200C2211yescharacteristic
20C2×C3×C42×C5C2211yescharacteristic, complemented
21C2×#6714C2211yescharacteristic
22C2×#6714C2211yescharacteristic
23C2×C4×Dic15C2211yescharacteristic, complemented
24C2×C5×(C2×D3)⋊C4C2211yescharacteristic
25C2×C5×(C2×D3)⋊C4C2211yescharacteristic
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
28C2×C3×#685C2211yescharacteristic
29C2×C3×#685C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×#683C2211yescharacteristic, complemented
32C2×Dic3⋊Dic5C2211yescharacteristic, complemented
33C2×#6668C2211yescharacteristic, complemented
34C2×#6667C2211yescharacteristic
35C2×#6667C2211yescharacteristic
36C2×(C2×D3)⋊Dic5C2211yescharacteristic
37C2×(C2×D3)⋊Dic5C2211yescharacteristic
38C2×(C2×D3)⋊Dic5C2211yescharacteristic
39C2×#6665C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic, complemented
43C2×Dic3×Dic5C2211yescharacteristic, complemented
44#91473C418yescomplemented
45#91115C2211yescharacteristic, complemented
46#91115C2211yescharacteristic, complemented
47C5×C3⋊#95C2211yescharacteristic, complemented
48C5×C3⋊#95C2211yescharacteristic, complemented
49C3×#3963C2211yescharacteristic, complemented
50C3×#3963C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#75825—51nomaximal, Hall
54C2×D5×C22⋊C4—31no—
55C5×#388—31no—
56#65279—31no—
57#65276—31no—
58#65244—31no—
59#65244—31no—
60#65240—31no—
61#65234—31no—
62#65233—31no—
63#65229D311yescharacteristic, complemented
64C4×#685—31no—
65#64959—31no—
66#64958—31no—
67#64956—31no—
68#64955—31no—
69C23×D15C2311yescharacteristic
70C23×C5×D3C2311yescharacteristic
71C23×C3×D5C2311yescharacteristic
72C22×D3×D5—22no—
73C22×D3×D5—22no—
74C22×D3×D5—41no—
75C22×D3×D5—41no—
76C22×D3×D5—41no—
77C22×D3×D5—41no—
78C22×D3×D5C2×C414yes—
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C2×C4×D15—41no—
86C2×C4×D15—41no—
87C2×C4×D15C2×C414yes—
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C2×#1200—41no—
95C2×#1200—41no—
96C2×#1200C2×C414yes—
97C3×C42×C5—41no—
98#6714—22no—
99#6714—22no—
100C4×Dic15—41no—
101C5×(C2×D3)⋊C4—41no—
102C5×(C2×D3)⋊C4—41no—
103C5×(C2×D3)⋊C4C2×C414yes—
104C5×Dic3⋊C4—41no—
105C3×#685—41no—
106C3×#685—41no—
107C3×#685C2×C414yes—
108C3×#683—41no—
109Dic3⋊Dic5—41no—
110#6668—41no—
111#6667—22no—
112#6667—22no—
113(C2×D3)⋊Dic5—41no—
114(C2×D3)⋊Dic5—41no—
115(C2×D3)⋊Dic5C2×C414yes—
116#6665—41no—
117#6665—41no—
118#6665C2×C414yes—
119Dic3×Dic5—41no—
120Dic3×Dic5—41no—
121C2×D3×C22⋊C4—51no—
122C3×#388—51no—
123#4990—51no—
124#4987—51no—
125#4955—51no—
126#4955—51no—
127#4951—51no—
128#4945—51no—
129#4944—51no—
130#4940D511yescharacteristic, complemented
131C4×(C2×D3)⋊C4—51no—
132#4670—51no—
133#4669—51no—
134#4667—51no—
135#4666—51no—
136C24×D5—31no—
137C22×C4×D5—31no—
138C22×C4×D5—31no—
139C2×C5×C4⋊C4—31no—
140C2×C5×C22⋊C4—31no—
141C2×C5×C22⋊C4—31no—
142C2×C5×C22⋊C4—31no—
143C2×C42×C5C2×D311yescharacteristic, complemented
144C2×C22⋊Dic5—31no—
145C2×C22⋊Dic5—31no—
146C2×C22⋊Dic5—31no—
147C2×#685—31no—
148C2×#685—31no—
149C2×#685—31no—
150C2×#685—31no—
151C2×#685—31no—
152C2×#685—31no—
153C2×#685—31no—
154C2×#685C2×D311yescharacteristic
155C2×#685C2×D311yescharacteristic
156C2×#685C2×D311yescharacteristic
157C2×C4⋊Dic5—31no—
158C2×#683—31no—
159C2×#683C2×D311yescharacteristic, complemented
160C2×C4×Dic5—31no—
161C2×C4×Dic5—31no—
162C2×C4×Dic5—31no—
163D5×C22⋊C4—38no—
164C5×#95—31no—
165C5×#95—31no—
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170#3963C2×D311yescharacteristic, complemented
171#3963C2×D311yescharacteristic, complemented
172#2312—151noSylow
173C23×C3×C5C2411yescharacteristic
174C22×D15—21no—
175C22×D15—21no—
176C22×D15—21no—
177C22×D15—21no—
178C22×D15C22×C412yes—
179C22×D15#4112yes—
180C22×D15#4112yes—
181C22×C5×D3—21no—
182C22×C5×D3—21no—
183C22×C5×D3—21no—
184C22×C5×D3—21no—
185C22×C5×D3—21no—
186C22×C5×D3—21no—
187C22×C5×D3C22×C412yes—
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×D5C22×C412yes—
195C2×D3×D5—28no—
196C2×D3×D5—44no—
197C2×D3×D5—44no—
198C2×D3×D5—44no—
199C2×D3×D5—44no—
200C2×D3×D5—44no—
201C2×D3×D5—44no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5C22×C412yes—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—21no—
214C2×Dic15—21no—
215C2×Dic15—21no—
216C2×Dic15—21no—
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15C22×C412yes—
220C4×D15—44no—
221C2×C5×Dic3—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—21no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—21no—
226C2×C5×Dic3—21no—
227C2×C5×Dic3—21no—
228C2×C5×Dic3—21no—
229C2×C5×Dic3C22×C412yes—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5C22×C412yes—
239#1200—44no—
240C24×D3—51no—
241C22×C4×D3—51no—
242C22×C4×D3—51no—
243C2×C3×C4⋊C4—51no—
244C2×C3×C22⋊C4—51no—
245C2×C3×C22⋊C4—51no—
246C2×C3×C22⋊C4—51no—
247C2×C3×C42C2×D511yescharacteristic, complemented
248C2×#217—51no—
249C2×#217—51no—
250C2×#217—51no—
251C2×(C2×D3)⋊C4—51no—
252C2×(C2×D3)⋊C4—51no—
253C2×(C2×D3)⋊C4—51no—
254C2×(C2×D3)⋊C4—51no—
255C2×(C2×D3)⋊C4—51no—
256C2×(C2×D3)⋊C4—51no—
257C2×(C2×D3)⋊C4—51no—
258C2×(C2×D3)⋊C4C2×D511yescharacteristic
259C2×(C2×D3)⋊C4C2×D511yescharacteristic
260C2×(C2×D3)⋊C4C2×D511yescharacteristic
261C2×C4⋊Dic3—51no—
262C2×Dic3⋊C4—51no—
263C2×Dic3⋊C4C2×D511yescharacteristic, complemented
264C2×C4×Dic3—51no—
265C2×C4×Dic3—51no—
266C2×C4×Dic3—51no—
267D3×C22⋊C4—58no—
268C3×#95—51no—
269C3×#95—51no—
270C3⋊#95—51no—
271C3⋊#95—51no—
272C3⋊#95—51no—
273C3⋊#95—51no—
274C3⋊#95C2×D511yescharacteristic, complemented
275C3⋊#95C2×D511yescharacteristic, complemented
276C24×C5—31no—
277C23×D5—31no—
278C23×D5—34no—
279C23×D5—62no—
280C23×D5—62no—
281C23×D5—121no—
282C23×D5—121no—
283C23×D5—121no—
284C23×D5—121no—
285C23×D5C22×D311yescharacteristic
286C22×C4×C5—31no—
287C22×C4×C5—31no—
288C22×C4×C5—31no—
289C22×C4×C5C22×D311yescharacteristic
290C22×C4×C5C22×D311yescharacteristic
291C22×C4×C5C22×D311yescharacteristic
292C22×Dic5—31no—
293C22×Dic5—31no—
294C22×Dic5—31no—
295C22×Dic5C22×D311yescharacteristic
296C22×Dic5C22×D311yescharacteristic
297C22×Dic5C22×D311yescharacteristic
298C2×C4×D5—34no—
299C2×C4×D5—34no—
300C2×C4×D5—121no—
301C2×C4×D5—121no—
302C2×C4×D5—121no—
303C2×C4×D5—121no—
304C5×C4⋊C4—121no—
305C5×C22⋊C4—34no—
306C5×C22⋊C4—121no—
307C5×C22⋊C4—121no—
308C42×C5—41no—
309C22⋊Dic5—34no—
310C22⋊Dic5—121no—
311C22⋊Dic5—121no—
312#685—34no—
313#685—41no—
314#685—41no—
315#685—62no—
316#685—62no—
317#685—62no—
318#685—62no—
319#685—121no—
320#685—121no—
321#685C4×D314yes—
322C4⋊Dic5—121no—
323#683—41no—
324#683—121no—
325C4×Dic5—121no—
326C4×Dic5—121no—
327C4×Dic5—121no—
328C22×C22⋊C4—151no—
329#388—31no—
330#388—51no—
331#388—151no—
332#388—151no—
333#388—151no—
334#388—151no—
335#388—151no—
336#388—151no—
337#380—151no—
338#380—151no—
339#379—151no—
340#379—151no—
341C4×C22⋊C4—151no—
342C4×C22⋊C4—151no—
343C22×C3×C5C23×C411yescharacteristic
344C22×C3×C5C2×#4111yescharacteristic
345C22×C3×C5C2×#4111yescharacteristic
346C22×C3×C5H(5,𝔽2)11yescharacteristic
347C22×C3×C5H(5,𝔽2)11yescharacteristic
348C22×C3×C5H(5,𝔽2)11yescharacteristic
349C22×C3×C5H(5,𝔽2)11yescharacteristic
350C2×D15—22no—
351C2×D15—22no—
352C2×D15—22no—
353C2×D15—22no—
354C2×D15—22no—
355C2×D15—22no—
356C2×D15#11714yes—
357C2×C5×D3—22no—
358C2×C5×D3—22no—
359C2×C5×D3—22no—
360C2×C5×D3—41no—
361C2×C5×D3—41no—
362C2×C5×D3—41no—
363C2×C5×D3—41no—
364C2×C3×D5—22no—
365C2×C3×D5—22no—
366C2×C3×D5—22no—
367C2×C3×D5—41no—
368C2×C3×D5—41no—
369C2×C3×D5—41no—
370C2×C3×D5—41no—
371D3×D5—416no—
372C3×C4×C5—22no—
373C3×C4×C5—41no—
374C3×C4×C5—41no—
375Dic15—22no—
376Dic15—41no—
377Dic15—41no—
378C3×Dic5—22no—
379C3×Dic5—41no—
380C3×Dic5—41no—
381C5×Dic3—22no—
382C5×Dic3—41no—
383C5×Dic3—41no—
384C24×C3—51no—
385C23×D3—51no—
386C23×D3—54no—
387C23×D3—102no—
388C23×D3—102no—
389C23×D3—201no—
390C23×D3—201no—
391C23×D3—201no—
392C23×D3—201no—
393C23×D3C22×D511yescharacteristic
394C22×C3×C4—51no—
395C22×C3×C4—51no—
396C22×C3×C4—51no—
397C22×C3×C4C22×D511yescharacteristic
398C22×C3×C4C22×D511yescharacteristic
399C22×C3×C4C22×D511yescharacteristic
400C22×Dic3—51no—
401C22×Dic3—51no—
402C22×Dic3—51no—
403C22×Dic3C22×D511yescharacteristic
404C22×Dic3C22×D511yescharacteristic
405C22×Dic3C22×D511yescharacteristic
406C2×C4×D3—54no—
407C2×C4×D3—54no—
408C2×C4×D3—201no—
409C2×C4×D3—201no—
410C2×C4×D3—201no—
411C2×C4×D3—201no—
412C3×C4⋊C4—201no—
413C3×C22⋊C4—54no—
414C3×C22⋊C4—201no—
415C3×C22⋊C4—201no—
416C3×C42—41no—
417#217—54no—
418#217—201no—
419#217—201no—
420(C2×D3)⋊C4—41no—
421(C2×D3)⋊C4—41no—
422(C2×D3)⋊C4—54no—
423(C2×D3)⋊C4—102no—
424(C2×D3)⋊C4—102no—
425(C2×D3)⋊C4—102no—
426(C2×D3)⋊C4—102no—
427(C2×D3)⋊C4—201no—
428(C2×D3)⋊C4—201no—
429(C2×D3)⋊C4C4×D514yes—
430C4⋊Dic3—201no—
431Dic3⋊C4—41no—
432Dic3⋊C4—201no—
433C4×Dic3—201no—
434C4×Dic3—201no—
435C4×Dic3—201no—
436C23×C5—32no—
437C23×C5—61no—
438C23×C5—61no—
439C23×C5—61no—
440C23×C5—61no—
441C23×C5—61no—
442C23×C5—61no—
443C23×C5C23×D311yescharacteristic
444C22×D5—21no—
445C22×D5—21no—
446C22×D5—21no—
447C22×D5—21no—
448C22×D5—21no—
449C22×D5—21no—
450C22×D5—32no—
451C22×D5—32no—
452C22×D5—32no—
453C22×D5—68no—
454C22×D5—61no—
455C22×D5—61no—
456C22×D5—61no—
457C22×D5—61no—
458C22×D5—124no—
459C22×D5—124no—
460C22×D5—124no—
461C22×D5—124no—
462C22×D5—124no—
463C22×D5—124no—
464C22×D5C2×C4×D312yes—
465C2×C4×C5—21no—
466C2×C4×C5—21no—
467C2×C4×C5—21no—
468C2×C4×C5—21no—
469C2×C4×C5—21no—
470C2×C4×C5—21no—
471C2×C4×C5—21no—
472C2×C4×C5—21no—
473C2×C4×C5—32no—
474C2×C4×C5—61no—
475C2×C4×C5—61no—
476C2×C4×C5—61no—
477C2×C4×C5—61no—
478C2×C4×C5—61no—
479C2×C4×C5—61no—
480C2×C4×C5—61no—
481C2×C4×C5—61no—
482C2×C4×C5C2×C4×D312yes—
483C2×Dic5—21no—
484C2×Dic5—21no—
485C2×Dic5—21no—
486C2×Dic5—21no—
487C2×Dic5—21no—
488C2×Dic5—21no—
489C2×Dic5—21no—
490C2×Dic5—21no—
491C2×Dic5—32no—
492C2×Dic5—61no—
493C2×Dic5—61no—
494C2×Dic5—61no—
495C2×Dic5—61no—
496C2×Dic5—61no—
497C2×Dic5—61no—
498C2×Dic5—61no—
499C2×Dic5—61no—
500C2×Dic5C2×C4×D312yes—
501C4×D5—124no—
502C4×D5—124no—
503C25—151no—
504C23×C4—151no—
505C23×C4—151no—
506C2×C4⋊C4—31no—
507C2×C4⋊C4—51no—
508C2×C4⋊C4—151no—
509C2×C4⋊C4—151no—
510C2×C22⋊C4—31no—
511C2×C22⋊C4—31no—
512C2×C22⋊C4—31no—
513C2×C22⋊C4—51no—
514C2×C22⋊C4—51no—
515C2×C22⋊C4—51no—
516C2×C22⋊C4—158no—
517C2×C22⋊C4—151no—
518C2×C22⋊C4—151no—
519C2×C22⋊C4—151no—
520C2×C22⋊C4—151no—
521C2×C22⋊C4—151no—
522C2×C22⋊C4—151no—
523C2×C22⋊C4—151no—
524C2×C22⋊C4—151no—
525C2×C22⋊C4—151no—
526C2×C22⋊C4—151no—
527C2×C42—151no—
528C2×C42—151no—
529C2×C42—151no—
530C2×C42D3×D511yescharacteristic, complemented
531#95—31no—
532#95—31no—
533#95—51no—
534#95—51no—
535#95—151no—
536#95—151no—
537#95—151no—
538#95—151no—
539C2×C3×C5C2×#11711yescharacteristic
540C2×C3×C5#51811yescharacteristic
541C2×C3×C5#51811yescharacteristic
542C2×C3×C5#53811yescharacteristic
543C2×C3×C5#53811yescharacteristic
544C2×C3×C5#53811yescharacteristic
545C2×C3×C5#53811yescharacteristic
546D15—24no—
547C3×D5—42no—
548C5×D3—42no—
549C23×C3—52no—
550C23×C3—101no—
551C23×C3—101no—
552C23×C3—101no—
553C23×C3—101no—
554C23×C3—101no—
555C23×C3—101no—
556C23×C3C23×D511yescharacteristic
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—21no—
560C22×D3—21no—
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—52no—
564C22×D3—52no—
565C22×D3—52no—
566C22×D3—108no—
567C22×D3—101no—
568C22×D3—101no—
569C22×D3—101no—
570C22×D3—101no—
571C22×D3—204no—
572C22×D3—204no—
573C22×D3—204no—
574C22×D3—204no—
575C22×D3—204no—
576C22×D3—204no—
577C22×D3C2×C4×D512yes—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—52no—
587C2×C3×C4—101no—
588C2×C3×C4—101no—
589C2×C3×C4—101no—
590C2×C3×C4—101no—
591C2×C3×C4—101no—
592C2×C3×C4—101no—
593C2×C3×C4—101no—
594C2×C3×C4—101no—
595C2×C3×C4C2×C4×D512yes—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—52no—
605C2×Dic3—101no—
606C2×Dic3—101no—
607C2×Dic3—101no—
608C2×Dic3—101no—
609C2×Dic3—101no—
610C2×Dic3—101no—
611C2×Dic3—101no—
612C2×Dic3—101no—
613C2×Dic3C2×C4×D512yes—
614C4×D3—204no—
615C4×D3—204no—
616C22×C5—62no—
617C22×C5—62no—
618C22×C5—62no—
619C22×C5—121no—
620C22×C5—121no—
621C22×C5—121no—
622C22×C5—121no—
623C22×C5C22×C4×D311yescharacteristic
624C22×C5#100411yescharacteristic
625C22×C5#100411yescharacteristic
626C22×C5D3×#4111yescharacteristic
627C22×C5D3×#4111yescharacteristic
628C22×C5#100911yescharacteristic
629C22×C5#100911yescharacteristic
630C2×D5—22no—
631C2×D5—22no—
632C2×D5—22no—
633C2×D5—34no—
634C2×D5—41no—
635C2×D5—41no—
636C2×D5—41no—
637C2×D5—41no—
638C2×D5—62no—
639C2×D5—62no—
640C2×D5—62no—
641C2×D5—62no—
642C2×D5—62no—
643C2×D5—62no—
644C2×D5—1216no—
645C4×C5—22no—
646C4×C5—41no—
647C4×C5—41no—
648C4×C5—62no—
649C4×C5—121no—
650C4×C5—121no—
651Dic5—22no—
652Dic5—41no—
653Dic5—41no—
654Dic5—62no—
655Dic5—121no—
656Dic5—121no—
657C24—31no—
658C24—51no—
659C24—154no—
660C24—151no—
661C24—302no—
662C24—302no—
663C24—601no—
664C24—601no—
665C24—601no—
666C24—601no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—51no—
671C22×C4—51no—
672C22×C4—51no—
673C22×C4—154no—
674C22×C4—151no—
675C22×C4—154no—
676C22×C4—151no—
677C22×C4—151no—
678C22×C4—601no—
679C22×C4—601no—
680C22×C4—601no—
681C22×C4—601no—
682C22×C4C2×D3×D511yescharacteristic
683C22×C4C2×D3×D511yescharacteristic
684C22×C4C2×D3×D511yescharacteristic
685C4⋊C4—121no—
686C4⋊C4—201no—
687C4⋊C4—601no—
688C4⋊C4—601no—
689C22⋊C4—34no—
690C22⋊C4—54no—
691C22⋊C4—121no—
692C22⋊C4—121no—
693C22⋊C4—154no—
694C22⋊C4—154no—
695C22⋊C4—201no—
696C22⋊C4—201no—
697C22⋊C4—302no—
698C22⋊C4—302no—
699C22⋊C4—302no—
700C22⋊C4—302no—
701C22⋊C4—601no—
702C22⋊C4—601no—
703C22⋊C4—601no—
704C22⋊C4—601no—
705C42—41no—
706C42—601no—
707C42—601no—
708C42—601no—
709C3×C5#231211yescharacteristic, complemented, Hall
710C22×C3—102no—
711C22×C3—102no—
712C22×C3—102no—
713C22×C3—201no—
714C22×C3—201no—
715C22×C3—201no—
716C22×C3—201no—
717C22×C3C22×C4×D511yescharacteristic
718C22×C3#414411yescharacteristic
719C22×C3#414411yescharacteristic
720C22×C3D5×#4111yescharacteristic
721C22×C3D5×#4111yescharacteristic
722C22×C3#414911yescharacteristic
723C22×C3#414911yescharacteristic
724C2×D3—22no—
725C2×D3—22no—
726C2×D3—22no—
727C2×D3—41no—
728C2×D3—41no—
729C2×D3—41no—
730C2×D3—41no—
731C2×D3—54no—
732C2×D3—102no—
733C2×D3—102no—
734C2×D3—102no—
735C2×D3—102no—
736C2×D3—102no—
737C2×D3—102no—
738C2×D3—2016no—
739C3×C4—22no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—102no—
743C3×C4—201no—
744C3×C4—201no—
745Dic3—22no—
746Dic3—41no—
747Dic3—41no—
748Dic3—102no—
749Dic3—201no—
750Dic3—201no—
751C2×C5—122no—
752C2×C5D3×#11711yescharacteristic
753C2×C5#554511yescharacteristic
754C2×C5#554511yescharacteristic
755C2×C5#561311yescharacteristic
756C2×C5#565711yescharacteristic
757C2×C5#567811yescharacteristic
758C2×C5#570411yescharacteristic
759D5—42no—
760D5—64no—
761C23—32no—
762C23—52no—
763C23—61no—
764C23—61no—
765C23—61no—
766C23—61no—
767C23—61no—
768C23—61no—
769C23—101no—
770C23—101no—
771C23—101no—
772C23—101no—
773C23—101no—
774C23—101no—
775C23—152no—
776C23—152no—
777C23—152no—
778C23—308no—
779C23—301no—
780C23—301no—
781C23—301no—
782C23—301no—
783C23—604no—
784C23—604no—
785C23—604no—
786C23—604no—
787C23—604no—
788C23—604no—
789C23C22×D3×D511yescharacteristic
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—32no—
799C2×C4—52no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—101no—
809C2×C4—101no—
810C2×C4—101no—
811C2×C4—101no—
812C2×C4—101no—
813C2×C4—101no—
814C2×C4—101no—
815C2×C4—101no—
816C2×C4—152no—
817C2×C4—301no—
818C2×C4—301no—
819C2×C4—301no—
820C2×C4—301no—
821C2×C4—301no—
822C2×C4—301no—
823C2×C4—301no—
824C2×C4—301no—
825C2×C4—604no—
826C2×C4—604no—
827C2×C4C4×D3×D512yes—
828C2×C3—202no—
829C2×C3D5×#11711yescharacteristic
830C2×C3#6587911yescharacteristic
831C2×C3#6587911yescharacteristic
832C2×C3#6594711yescharacteristic
833C2×C3#6599111yescharacteristic
834C2×C3#6601211yescharacteristic
835C2×C3#6603811yescharacteristic
836D3—42no—
837D3—104no—
838C5#7582511yescharacteristic, complemented, Sylow
839C22—62no—
840C22—62no—
841C22—62no—
842C22—102no—
843C22—102no—
844C22—102no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—154no—
850C22—201no—
851C22—201no—
852C22—201no—
853C22—201no—
854C22—302no—
855C22—302no—
856C22—302no—
857C22—302no—
858C22—302no—
859C22—302no—
860C22—6016no—
861C22C2×C4×D3×D511yescharacteristic
862C22#9201611yescharacteristic
863C22#9201611yescharacteristic
864C22#9201711yescharacteristic
865C22#9201811yescharacteristic
866C22#9201911yescharacteristic
867C22#9204911yescharacteristic
868C4—22no—
869C4—41no—
870C4—41no—
871C4—62no—
872C4—102no—
873C4—121no—
874C4—121no—
875C4—201no—
876C4—201no—
877C4—302no—
878C4—601no—
879C4—601no—
880C3#1060755611yescharacteristic, complemented, Sylow
881C2—122no—
882C2—202no—
883C2—304no—
884C2#1175272311yescharacteristic
885C2#1175272911yescharacteristic
886C2#1175276911yescharacteristic
887C2#1175277011yescharacteristic
888C2#1175462911yescharacteristic
889C2#1175468211yescharacteristic
890C2#1175468311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D3×D5C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2312
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. C4×#6714C2semidirect
3. C5×#4940C2semidirect
4. C3×#65229C2semidirect
7. #11748882C2semidirect
8. #11748876C2semidirect
9. #11748794C2semidirect
10. #11748791C2semidirect
11. #11748723C2semidirect
12. #11748718C2semidirect
13. #11748712C2semidirect
14. #11748711C2semidirect
15. #11748670C2semidirect
20. C2×C3×C42×C5C22semidirect
23. C2×C4×Dic15C22semidirect
27. C2×C5×Dic3⋊C4C22semidirect
31. C2×C3×#683C22semidirect
32. C2×Dic3⋊Dic5C22semidirect
33. C2×#6668C22semidirect
42. C2×Dic3×Dic5C22semidirect
43. C2×Dic3×Dic5C22semidirect
44. #91473C4semidirect
45. #91115C22semidirect
46. #91115C22semidirect
47. C5×C3⋊#95C22semidirect
48. C5×C3⋊#95C22semidirect
49. C3×#3963C22semidirect
50. C3×#3963C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
63. #65229D3semidirect
130. #4940D5semidirect
143. C2×C42×C5C2×D3semidirect
159. C2×#683C2×D3semidirect
170. #3963C2×D3semidirect
171. #3963C2×D3semidirect
247. C2×C3×C42C2×D5semidirect
263. C2×Dic3⋊C4C2×D5semidirect
274. C3⋊#95C2×D5semidirect
275. C3⋊#95C2×D5semidirect
530. C2×C42D3×D5semidirect
709. C3×C5#2312semidirect
838. C5#75825semidirect
880. C3#10607556semidirect

Maximal subgroups

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

subgroupindex
C2×#914732
C4×#67142
C5×#49402
C3×#652292
#117489402
#117488822
#117488762
#117487942
#117487912
#117487232
#117487182
#117487122
#117487112
#117486702
#106075563
#758255