Finite Group Databasebeta

← #14327132

Subgroups — #14327132

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
2C2×Dic3×C22⋊D5C211yesmaximal, characteristic
3C2×Dic3×C22⋊D5C211yesmaximal, characteristic
4#11751311C211yesmaximal, characteristic, complemented
5C2×C5×C3⋊#95C211yesmaximal, characteristic, complemented
6#11749513C211yesmaximal, characteristic, complemented
7#11749512C211yesmaximal, characteristic, complemented
8#11748890C211yesmaximal, characteristic, complemented
9#11748885C211yesmaximal, characteristic, complemented
10D5×C3⋊#95C211yesmaximal, characteristic, complemented
11#11748802C211yesmaximal, characteristic, complemented
12#11748704C211yesmaximal, characteristic, complemented
13#11748642C211yesmaximal, characteristic, complemented
14#11748640C211yesmaximal, characteristic, complemented
15#11748627C211yesmaximal, characteristic, complemented
16#10605100—31nomaximal, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C23×C5×Dic3C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×D5×Dic3C2211yescharacteristic
23C22×D5×Dic3C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×#6712C2211yescharacteristic
27C2×#6712C2211yescharacteristic
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C3×C4×C22⋊D5—24no—
30C2×C3×#685C2211yescharacteristic
31C2×C3×#683C2211yescharacteristic
32C2×C3×C4×Dic5C2211yescharacteristic
33Dic3×C22⋊D5—24no—
34Dic3×C22⋊D5C418yescomplemented
35C2×Dic3⋊Dic5C2211yescharacteristic
36C2×Dic3⋊Dic5C2211yescharacteristic
37C2×#6669C2211yescharacteristic
38C2×#6669C2211yescharacteristic
39C2×#6668C2211yescharacteristic
40C2×#6668C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47C5×C3⋊#95C2211yescharacteristic
48C5×C3⋊#95C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C5×C3⋊#95C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#82334—51nomaximal, Hall
56C2×C4×C22⋊D5—31no—
57C2×C4×C22⋊D5—31no—
58C2×C4×C22⋊D5D311yescharacteristic
59C2×C5×#95—31no—
60#65501—31no—
61#65499—31no—
62#65499—31no—
63#64957—31no—
64#64957—31no—
65#64956—31no—
66D5×#95—31no—
67#64939—31no—
68#64938—31no—
69#64936—31no—
70#64936—31no—
71C24×C3×C5C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C22×C3×C4×C5—22no—
74C22×C3×C4×C5—22no—
75C22×C3×C4×C5—41no—
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×C5×Dic3—22no—
83C22×C5×Dic3—22no—
84C22×C5×Dic3—41no—
85C22×C5×Dic3—41no—
86C22×C5×Dic3—41no—
87C22×C5×Dic3C2×C414yescomplemented
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C2×C3×C22⋊D5C2×C414yes—
93C2×C3×C22⋊D5D414yes—
94C2×C3×C22⋊D5Q814yes—
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C2×C3×C4×D5—22no—
99C2×C3×C4×D5—22no—
100C2×C3×C4×D5—41no—
101C2×D5×Dic3—22no—
102C2×D5×Dic3—22no—
103C2×D5×Dic3—41no—
104C2×D5×Dic3—41no—
105C2×D5×Dic3—41no—
106C2×D5×Dic3C2×C414yescomplemented
107#6719—22no—
108#6719C2×C414yescomplemented
109#6712—22no—
110#6712—41no—
111C3×C22⋊Dic5—22no—
112C3×#685—22no—
113C3×#683—22no—
114C3×C4×Dic5—22no—
115Dic3⋊Dic5—41no—
116Dic3⋊Dic5—41no—
117#6669—22no—
118#6669—41no—
119#6668—22no—
120#6668C2×C414yescomplemented
121#6665—22no—
122#6665C2×C414yescomplemented
123Dic3×Dic5—22no—
124Dic3×Dic5C2×C414yescomplemented
125C2×C3×C4×D4—51no—
126C2×D4×Dic3—51no—
127C2×D4×Dic3—51no—
128#5210—51no—
129#5210—51no—
130C2×C3⋊#95—51no—
131C2×C3⋊#95D511yescharacteristic, complemented
132#4977—51no—
133#4972—51no—
134#4946—51no—
135#4946—51no—
136#4942—51no—
137#4942—51no—
138C4×Dic3⋊C4—51no—
139#4928—51no—
140C23×C4×C5—31no—
141C23×C4×C5—31no—
142C23×C4×C5C2×D311yescharacteristic
143C22×C22⋊D5C2×D311yescharacteristic
144C22×C4×D5—31no—
145C22×C4×D5—31no—
146C22×C4×D5C2×D311yescharacteristic
147C2×C22⋊Dic5—31no—
148C2×C22⋊Dic5—31no—
149C2×C22⋊Dic5C2×D311yescharacteristic
150C4×C22⋊D5—24no—
151C4×C22⋊D5—38no—
152C4×C22⋊D5—64no—
153C2×#685—31no—
154C2×#685—31no—
155C2×#685C2×D311yescharacteristic
156C2×C4⋊Dic5—31no—
157C2×C4⋊Dic5—31no—
158C2×#683—31no—
159C2×#683—31no—
160C2×#683—31no—
161C2×#683—31no—
162C2×#683—31no—
163C2×#683—31no—
164C2×#683C2×D311yescharacteristic
165C2×C4×Dic5—31no—
166C2×C4×Dic5—31no—
167C2×C4×Dic5C2×D311yescharacteristic
168C5×#95—31no—
169C5×#95—31no—
170C5×#95—31no—
171C5×#95—31no—
172#3963—31no—
173#3963—31no—
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#2349—151noSylow
179C23×C3×C5—21no—
180C23×C3×C5—21no—
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5C22×C412yes—
184C23×C3×C5C2×D412yes—
185C23×C3×C5C2×Q812yes—
186C23×C3×C5C2411yescharacteristic
187C22×C3×D5—21no—
188C22×C3×D5—21no—
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5C22×C412yes—
192C22×C3×D5C2×D412yes—
193C22×C3×D5C2×Q812yes—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—44no—
200C2×C3×C4×C5#4112yes—
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×Dic15C22×C412yes—
212C2×Dic15C22×C412yes—
213C2×C5×Dic3—21no—
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—44no—
223C2×C5×Dic3—44no—
224C2×C5×Dic3C22×C412yes—
225C2×C5×Dic3C22×C412yes—
226C2×C5×Dic3#4112yes—
227C3×C22⋊D5C4⋊C4116yescomplemented
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5C22×C412yes—
235C2×C3×Dic5C2×D412yes—
236C2×C3×Dic5C2×Q812yes—
237C3×C4×D5—44no—
238D5×Dic3—44no—
239D5×Dic3—44no—
240C22×C3×D4—51no—
241C23×C3×C4—51no—
242C23×C3×C4C2×D511yescharacteristic
243C23×Dic3—51no—
244C23×Dic3—51no—
245C23×Dic3C2×D511yescharacteristic
246C23×Dic3C2×D511yescharacteristic
247C3×C4×D4—104no—
248C2×C3×C4⋊C4—51no—
249C2×C3×C22⋊C4—51no—
250C2×C3×C22⋊C4—51no—
251C2×C3×C42—51no—
252C2×#217—51no—
253C2×#217—51no—
254C2×#217—51no—
255C2×#217—51no—
256D4×Dic3—58no—
257D4×Dic3—104no—
258C2×C4⋊Dic3—51no—
259C2×C4⋊Dic3—51no—
260C2×Dic3⋊C4—51no—
261C2×Dic3⋊C4—51no—
262C2×Dic3⋊C4—51no—
263C2×Dic3⋊C4—51no—
264C2×Dic3⋊C4—51no—
265C2×Dic3⋊C4—51no—
266C2×C4×Dic3—51no—
267C2×C4×Dic3—51no—
268C3⋊#95—51no—
269C3⋊#95—51no—
270C3⋊#95—51no—
271C3⋊#95—51no—
272C3⋊#95—51no—
273C3⋊#95—51no—
274C3⋊#95C2×D511yescharacteristic
275C3⋊#95C2×D511yescharacteristic
276C3⋊#95C2×D511yescharacteristic
277C3⋊#95C2×D511yescharacteristic
278C24×C5C22×D311yescharacteristic
279C23×D5C22×D311yescharacteristic
280C22×C4×C5—22no—
281C22×C4×C5—22no—
282C22×C4×C5—31no—
283C22×C4×C5—31no—
284C22×C4×C5—31no—
285C22×C4×C5—34no—
286C22×C4×C5—31no—
287C22×C4×C5—41no—
288C22×C4×C5—62no—
289C22×C4×C5—62no—
290C22×C4×C5—121no—
291C22×C4×C5—121no—
292C22×C4×C5—121no—
293C22×C4×C5C22×D311yescharacteristic
294C22×C4×C5C22×D311yescharacteristic
295C2×C22⋊D5Dic614yes—
296C2×C22⋊D5C4×D314yes—
297C2×C22⋊D5#6714yes—
298C22×Dic5—31no—
299C22×Dic5—31no—
300C22×Dic5—31no—
301C22×Dic5—31no—
302C22×Dic5C22×D311yescharacteristic
303C22×Dic5C22×D311yescharacteristic
304C22×Dic5C22×D311yescharacteristic
305C2×C4×D5—22no—
306C2×C4×D5—22no—
307C2×C4×D5—34no—
308C2×C4×D5—41no—
309C2×C4×D5—62no—
310C2×C4×D5—62no—
311C2×C4×D5—121no—
312C2×C4×D5—121no—
313C2×C4×D5—121no—
314C22⋊Dic5—22no—
315C22⋊Dic5—34no—
316C22⋊Dic5—62no—
317#685—22no—
318#685—34no—
319#685—62no—
320C4⋊Dic5—121no—
321C4⋊Dic5—121no—
322#683—22no—
323#683—34no—
324#683—62no—
325#683—62no—
326#683—62no—
327#683—121no—
328#683—121no—
329C4×Dic5—22no—
330C4×Dic5—34no—
331C4×Dic5—62no—
332C2×C4×D4—51no—
333C2×C4×D4—151no—
334C2×C4×D4—151no—
335#389—151no—
336#389—151no—
337#385—151no—
338#385—151no—
339#385—151no—
340#385—151no—
341#382—151no—
342#380—151no—
343#380—151no—
344C4×C4⋊C4—151no—
345C2×#95—31no—
346C2×#95—151no—
347C22×C3×C5—22no—
348C22×C3×C5—22no—
349C22×C3×C5—22no—
350C22×C3×C5—22no—
351C22×C3×C5—22no—
352C22×C3×C5—22no—
353C22×C3×C5C2×C4⋊C414yes—
354C22×C3×C5C23×C411yescharacteristic
355C22×C3×C5C22×D411yescharacteristic
356C22×C3×C5C22×Q811yescharacteristic
357C22×C3×C5C2×#4111yescharacteristic
358C22×C3×C5C2×#4111yescharacteristic
359C22×C3×C5H(5,𝔽2)11yescharacteristic
360C22×C3×C5H(5,𝔽2)11yescharacteristic
361C2×C3×D5—22no—
362C2×C3×D5—22no—
363C2×C3×D5—22no—
364C2×C3×D5—22no—
365C2×C3×D5—22no—
366C2×C3×D5—22no—
367C2×C3×D5C2×C4⋊C414yes—
368C3×C4×C5—22no—
369C3×C4×C5—41no—
370Dic15—22no—
371Dic15—22no—
372Dic15—41no—
373Dic15—41no—
374C3×Dic5—41no—
375C3×Dic5—41no—
376C3×Dic5C2×C4⋊C414yes—
377C5×Dic3—22no—
378C5×Dic3—22no—
379C5×Dic3—22no—
380C5×Dic3—41no—
381C24×C3—51no—
382C24×C3C22×D511yescharacteristic
383C2×C3×D4—54no—
384C2×C3×D4—54no—
385C2×C3×D4—54no—
386C22×C3×C4—22no—
387C22×C3×C4—22no—
388C22×C3×C4—41no—
389C22×C3×C4—51no—
390C22×C3×C4—51no—
391C22×C3×C4—51no—
392C22×C3×C4—102no—
393C22×C3×C4—102no—
394C22×C3×C4—201no—
395C22×C3×C4C22×D511yescharacteristic
396C22×C3×C4C22×D511yescharacteristic
397C22×Dic3—22no—
398C22×Dic3—22no—
399C22×Dic3—41no—
400C22×Dic3—41no—
401C22×Dic3—41no—
402C22×Dic3—51no—
403C22×Dic3—51no—
404C22×Dic3—54no—
405C22×Dic3—51no—
406C22×Dic3—51no—
407C22×Dic3—102no—
408C22×Dic3—102no—
409C22×Dic3—201no—
410C22×Dic3—201no—
411C22×Dic3—201no—
412C22×Dic3C4×D514yescomplemented
413C22×Dic3C22×D511yescharacteristic
414C22×Dic3C22×D511yescharacteristic
415C22×Dic3C22×D511yescharacteristic
416C22×Dic3C22×D511yescharacteristic
417C3×C4⋊C4—102no—
418C3×C22⋊C4—102no—
419C3×C22⋊C4—102no—
420C3×C42—102no—
421#217—54no—
422#217—54no—
423#217—102no—
424#217—102no—
425C4⋊Dic3—54no—
426C4⋊Dic3—102no—
427Dic3⋊C4—102no—
428Dic3⋊C4—102no—
429Dic3⋊C4—201no—
430Dic3⋊C4—201no—
431Dic3⋊C4—201no—
432Dic3⋊C4—201no—
433C4×Dic3—54no—
434C4×Dic3—102no—
435C23×C5—21no—
436C23×C5—21no—
437C23×C5—21no—
438C23×C5—21no—
439C23×C5C2×Dic612yes—
440C23×C5C2×C4×D312yes—
441C23×C5C2×#6712yes—
442C23×C5C23×D311yescharacteristic
443C22×D5—21no—
444C22×D5—21no—
445C22×D5—21no—
446C22×D5—21no—
447C22×D5C2×Dic612yes—
448C22×D5C2×C4×D312yes—
449C22×D5C2×#6712yes—
450C2×C4×C5—21no—
451C2×C4×C5—21no—
452C2×C4×C5—21no—
453C2×C4×C5—21no—
454C2×C4×C5—21no—
455C2×C4×C5—32no—
456C2×C4×C5—32no—
457C2×C4×C5—32no—
458C2×C4×C5—44no—
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—124no—
469C2×C4×C5—124no—
470C2×C4×C5#23712yes—
471C22⋊D5Dic3⋊C4116yescomplemented
472C2×Dic5—21no—
473C2×Dic5—21no—
474C2×Dic5—21no—
475C2×Dic5—21no—
476C2×Dic5—21no—
477C2×Dic5—21no—
478C2×Dic5—32no—
479C2×Dic5—32no—
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×Dic5C2×Dic612yes—
491C2×Dic5C2×C4×D312yes—
492C2×Dic5C2×#6712yes—
493C4×D5—44no—
494C4×D5—124no—
495C4×D5—124no—
496C22×D4—51no—
497C23×C4—31no—
498C23×C4—31no—
499C23×C4—51no—
500C23×C4—151no—
501C23×C4—151no—
502C23×C4D3×D511yescharacteristic
503C4×D4—104no—
504C4×D4—158no—
505C4×D4—304no—
506C2×C4⋊C4—51no—
507C2×C4⋊C4—151no—
508C2×C4⋊C4—151no—
509C2×C4⋊C4—151no—
510C2×C4⋊C4—151no—
511C2×C4⋊C4—151no—
512C2×C4⋊C4—151no—
513C2×C4⋊C4—151no—
514C2×C4⋊C4—151no—
515C2×C22⋊C4—51no—
516C2×C22⋊C4—51no—
517C2×C22⋊C4—151no—
518C2×C22⋊C4—151no—
519C2×C22⋊C4—151no—
520C2×C22⋊C4—151no—
521C2×C42—51no—
522C2×C42—151no—
523C2×C42—151no—
524#95—31no—
525#95—31no—
526#95—31no—
527#95—31no—
528#95—151no—
529#95—151no—
530#95—151no—
531#95—151no—
532#95—151no—
533#95—151no—
534C2×C3×C5—24no—
535C2×C3×C5C22×C4⋊C411yescharacteristic
536C2×C3×C5C4×#4111yescharacteristic
537C2×C3×C5#51811yescharacteristic
538C2×C3×C5#54611yescharacteristic
539C2×C3×C5#54611yescharacteristic
540C2×C3×C5#55411yescharacteristic
541C2×C3×C5#55411yescharacteristic
542C3×D5—24no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—52no—
548C23×C3—52no—
549C23×C3—52no—
550C23×C3—101no—
551C23×C3—101no—
552C23×C3—101no—
553C23×C3—101no—
554C23×C3C2×C4×D512yes—
555C23×C3D4×D512yes—
556C23×C3Q8×D512yes—
557C23×C3C23×D511yescharacteristic
558C3×D4—516no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—44no—
565C2×C3×C4—52no—
566C2×C3×C4—52no—
567C2×C3×C4—52no—
568C2×C3×C4—101no—
569C2×C3×C4—101no—
570C2×C3×C4—101no—
571C2×C3×C4—101no—
572C2×C3×C4—101no—
573C2×C3×C4—101no—
574C2×C3×C4—204no—
575C2×C3×C4#70912yes—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—44no—
586C2×Dic3—44no—
587C2×Dic3—52no—
588C2×Dic3—52no—
589C2×Dic3—101no—
590C2×Dic3—101no—
591C2×Dic3—101no—
592C2×Dic3—101no—
593C2×Dic3—101no—
594C2×Dic3—101no—
595C2×Dic3—101no—
596C2×Dic3—101no—
597C2×Dic3—101no—
598C2×Dic3—101no—
599C2×Dic3—204no—
600C2×Dic3—204no—
601C2×Dic3C2×C4×D512yes—
602C2×Dic3C2×C4×D512yes—
603C2×Dic3#70912yes—
604C22×C5—22no—
605C22×C5—22no—
606C22×C5—22no—
607C22×C5—22no—
608C22×C5—22no—
609C22×C5—22no—
610C22×C5C2×Dic3⋊C414yes—
611C22×C5C22×Dic611yescharacteristic
612C22×C5C22×C4×D311yescharacteristic
613C22×C5C2×#23711yescharacteristic
614C22×C5#100411yescharacteristic
615C22×C5D3×#4111yescharacteristic
616C22×C5#100911yescharacteristic
617C22×C5C22×#6711yescharacteristic
618C2×D5—22no—
619C2×D5—22no—
620C2×D5—22no—
621C2×D5—22no—
622C2×D5—22no—
623C2×D5—22no—
624C2×D5C2×Dic3⋊C414yes—
625C4×C5—22no—
626C4×C5—41no—
627C4×C5—62no—
628C4×C5—62no—
629C4×C5—62no—
630C4×C5—121no—
631Dic5—41no—
632Dic5—41no—
633Dic5—62no—
634Dic5—62no—
635Dic5—121no—
636Dic5—121no—
637Dic5C2×Dic3⋊C414yes—
638C24—51no—
639C24C2×D3×D511yescharacteristic
640C2×D4—54no—
641C2×D4—54no—
642C2×D4—54no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—34no—
649C22×C4—31no—
650C22×C4—41no—
651C22×C4—51no—
652C22×C4—51no—
653C22×C4—51no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4—102no—
657C22×C4—102no—
658C22×C4—121no—
659C22×C4—121no—
660C22×C4—121no—
661C22×C4—154no—
662C22×C4—151no—
663C22×C4—151no—
664C22×C4—151no—
665C22×C4—151no—
666C22×C4—201no—
667C22×C4—302no—
668C22×C4—302no—
669C22×C4—601no—
670C22×C4—601no—
671C22×C4—601no—
672C22×C4C2×D3×D511yescharacteristic
673C22×C4C2×D3×D511yescharacteristic
674C4⋊C4—102no—
675C4⋊C4—154no—
676C4⋊C4—302no—
677C4⋊C4—302no—
678C4⋊C4—302no—
679C4⋊C4—601no—
680C4⋊C4—601no—
681C4⋊C4—601no—
682C4⋊C4—601no—
683C22⋊C4—102no—
684C22⋊C4—102no—
685C22⋊C4—154no—
686C22⋊C4—154no—
687C22⋊C4—302no—
688C22⋊C4—302no—
689C42—102no—
690C42—154no—
691C42—302no—
692C3×C5#234911yescharacteristic, complemented, Hall
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—54no—
700C22×C3—102no—
701C22×C3—102no—
702C22×C3—102no—
703C22×C3—102no—
704C22×C3—102no—
705C22×C3—102no—
706C22×C3D5×C4⋊C414yes—
707C22×C3C22×C4×D511yescharacteristic
708C22×C3C2×#70911yescharacteristic
709C22×C3C2×#70911yescharacteristic
710C22×C3C2×D4×D511yescharacteristic
711C22×C3#414411yescharacteristic
712C22×C3#414411yescharacteristic
713C22×C3C2×Q8×D511yescharacteristic
714C3×C4—22no—
715C3×C4—41no—
716C3×C4—54no—
717C3×C4—201no—
718C3×C4—201no—
719Dic3—22no—
720Dic3—22no—
721Dic3—22no—
722Dic3—41no—
723Dic3—102no—
724Dic3—102no—
725Dic3—201no—
726Dic3—201no—
727C2×C5—24no—
728C2×C5C4×#23711yescharacteristic
729C2×C5#553911yescharacteristic
730C2×C5#554311yescharacteristic
731C2×C5#554511yescharacteristic
732C2×C5C22×Dic3⋊C411yescharacteristic
733C2×C5#580611yescharacteristic
734C2×C5#582911yescharacteristic
735D5—24no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—52no—
741C23—52no—
742C23—52no—
743C23—101no—
744C23—101no—
745C23—101no—
746C23—101no—
747C23D5×Dic612yes—
748C23C4×D3×D512yes—
749C23D5×#6712yes—
750C23C22×D3×D511yescharacteristic
751D4—516no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—32no—
758C2×C4—32no—
759C2×C4—32no—
760C2×C4—44no—
761C2×C4—52no—
762C2×C4—52no—
763C2×C4—52no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—101no—
774C2×C4—101no—
775C2×C4—101no—
776C2×C4—101no—
777C2×C4—101no—
778C2×C4—101no—
779C2×C4—124no—
780C2×C4—124no—
781C2×C4—152no—
782C2×C4—152no—
783C2×C4—204no—
784C2×C4—301no—
785C2×C4—301no—
786C2×C4—301no—
787C2×C4—301no—
788C2×C4—301no—
789C2×C4—301no—
790C2×C4—301no—
791C2×C4—301no—
792C2×C4—301no—
793C2×C4—301no—
794C2×C4—604no—
795C2×C4—604no—
796C2×C4#677912yes—
797C2×C3—24no—
798C2×C3—104no—
799C2×C3C4×#70911yescharacteristic
800C2×C3#6582011yescharacteristic
801C2×C3#6582411yescharacteristic
802C2×C3#6582411yescharacteristic
803C2×C3C2×D5×C4⋊C411yescharacteristic
804C2×C3#6584511yescharacteristic
805C2×C3#6584511yescharacteristic
806C5#8233411yescharacteristic, complemented, Sylow
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—54no—
814C22—102no—
815C22—102no—
816C22—102no—
817C22—102no—
818C22—102no—
819C22—102no—
820C22D5×Dic3⋊C414yes—
821C22C2×D5×Dic611yescharacteristic
822C22C2×C4×D3×D511yescharacteristic
823C22D3×#70911yescharacteristic
824C22#9201811yescharacteristic
825C22C2×#677911yescharacteristic
826C22C2×D5×#6711yescharacteristic
827C22#9204911yescharacteristic
828C4—22no—
829C4—41no—
830C4—54no—
831C4—62no—
832C4—62no—
833C4—62no—
834C4—121no—
835C4—201no—
836C4—201no—
837C4—302no—
838C4—302no—
839C4—601no—
840C4—601no—
841C3#1060510011yescharacteristic, complemented, Sylow
842C2—24no—
843C2—104no—
844C2C2×D5×Dic3⋊C411yescharacteristic
845C2C4×#677911yescharacteristic
846C2#1175441911yescharacteristic
847C2#1175450011yescharacteristic
848C2#1175462711yescharacteristic
849C2#1175463611yescharacteristic
850C2#1175538011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2349
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. #11751311C2semidirect
5. C2×C5×C3⋊#95C2semidirect
6. #11749513C2semidirect
7. #11749512C2semidirect
8. #11748890C2semidirect
9. #11748885C2semidirect
10. D5×C3⋊#95C2semidirect
11. #11748802C2semidirect
12. #11748704C2semidirect
13. #11748642C2semidirect
14. #11748640C2semidirect
15. #11748627C2semidirect
34. Dic3×C22⋊D5C4semidirect
87. C22×C5×Dic3C2×C4semidirect
106. C2×D5×Dic3C2×C4semidirect
108. #6719C2×C4semidirect
120. #6668C2×C4semidirect
122. #6665C2×C4semidirect
124. Dic3×Dic5C2×C4semidirect
131. C2×C3⋊#95D5semidirect
227. C3×C22⋊D5C4⋊C4semidirect
412. C22×Dic3C4×D5semidirect
471. C22⋊D5Dic3⋊C4semidirect
692. C3×C5#2349semidirect
806. C5#82334semidirect
841. C3#10605100semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊D52
C2×Dic3×C22⋊D52
#117513112
C2×C5×C3⋊#952
#117495132
#117495122
#117488902
#117488852
D5×C3⋊#952
#117488022
#117487042
#117486422
#117486402
#117486272
#106051003
#823345