Finite Group Databasebeta

← #14322813

Subgroups — #14322813

Order 1920.

1632 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91473C211yesmaximal, characteristic
2C2×D3×#685C211yesmaximal, characteristic
3C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic
4#11751090C211yesmaximal, characteristic, complemented
5C5×#4989C211yesmaximal, characteristic, complemented
6C3×#65276C211yesmaximal, characteristic, complemented
7#11748898C211yesmaximal, characteristic, complemented
8#11748897C211yesmaximal, characteristic, complemented
9#11748895C211yesmaximal, characteristic, complemented
10#11748893C211yesmaximal, characteristic, complemented
11#11748885C211yesmaximal, characteristic, complemented
12#11748878C211yesmaximal, characteristic, complemented
13#11748738C211yesmaximal, characteristic, complemented
14#11748731C211yesmaximal, characteristic, complemented
15#11748722C211yesmaximal, characteristic, complemented
16#10606322—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×#1200C2211yescharacteristic
22C22×D3×Dic5C2211yescharacteristic
23C22×D5×Dic3C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
25C2×#6714C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6712C2211yescharacteristic, complemented
28C2×C5×(C2×D3)⋊C4C2211yescharacteristic
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic
30C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
34C2×Dic3⋊Dic5C2211yescharacteristic, complemented
35C2×#6669C2211yescharacteristic, complemented
36C2×#6668C2211yescharacteristic, complemented
37C2×#6668C2211yescharacteristic, complemented
38C2×#6667C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44#91473—24no—
45D3×#685—24no—
46D5×(C2×D3)⋊C4C418yescomplemented
47#91115C2211yescharacteristic, complemented
48#91115C2211yescharacteristic, complemented
49C5×C3⋊#95C2211yescharacteristic, complemented
50C5×C3⋊#95C2211yescharacteristic, complemented
51C3×#3963C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#74005—51nomaximal, Hall
56C22×#685—31no—
57C2×D5×C22⋊C4—31no—
58C2×D5×C22⋊C4—31no—
59C5×#385—31no—
60#65499—31no—
61#65278—31no—
62#65278—31no—
63#65276—31no—
64#65276D311yescharacteristic, complemented
65#65239—31no—
66#65235—31no—
67#64957—31no—
68#64957—31no—
69#64956—31no—
70#64956—31no—
71C23×D15C2311yescharacteristic
72C23×C5×D3C2311yescharacteristic
73C23×C3×D5C2311yescharacteristic
74C22×D3×D5—41no—
75C22×D3×D5—41no—
76C22×D3×D5—41no—
77C22×D3×D5—41no—
78C22×D3×D5C2×C414yes—
79C22×D3×D5D414yes—
80C22×D3×D5Q814yes—
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C2×C4×D15—22no—
88C2×C4×D15—41no—
89C2×C4×D15—41no—
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C22×C5×Dic3C2311yescharacteristic
93C2×C4×C5×D3—22no—
94C2×C4×C5×D3—41no—
95C2×C4×C5×D3—41no—
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C2×C3×C4×D5—41no—
100C2×C3×C4×D5—41no—
101C2×C3×C4×D5C2×C414yescomplemented
102C2×#1200—22no—
103C2×#1200—41no—
104C2×#1200—41no—
105C2×D3×Dic5—22no—
106C2×D3×Dic5—41no—
107C2×D3×Dic5—41no—
108C2×D5×Dic3—41no—
109C2×D5×Dic3—41no—
110C2×D5×Dic3C2×C414yescomplemented
111C3×C5×C4⋊C4—41no—
112#6714—22no—
113#6714C2×C414yescomplemented
114#6712—41no—
115C5×(C2×D3)⋊C4—22no—
116C5×(C2×D3)⋊C4C2×C414yescomplemented
117C5×Dic3⋊C4—41no—
118C3×#685—22no—
119C3×#685—22no—
120C3×C4⋊Dic5—41no—
121Dic3⋊Dic5—41no—
122#6669—41no—
123#6668—41no—
124#6668—41no—
125#6667—22no—
126#6667C2×C414yescomplemented
127(C2×D3)⋊Dic5—22no—
128(C2×D3)⋊Dic5C2×C414yescomplemented
129#6665—22no—
130#6665—22no—
131C22×(C2×D3)⋊C4—51no—
132C2×D3×C22⋊C4—51no—
133C2×D3×C22⋊C4—51no—
134C3×#380—51no—
135#5212—51no—
136#4989—51no—
137#4989—51no—
138#4989—51no—
139#4989D511yescharacteristic, complemented
140#4942—51no—
141#4942—51no—
142#4668—51no—
143#4668—51no—
144#4668—51no—
145#4668—51no—
146C24×D5—31no—
147C23×C4×C5—31no—
148C23×Dic5—31no—
149C22×C4×D5—31no—
150C22×C4×D5—31no—
151C22×C4×D5—31no—
152C22×C4×D5C2×D311yescharacteristic
153C2×C5×C4⋊C4—31no—
154C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
155C2×C5×C22⋊C4—31no—
156C2×C5×C22⋊C4—31no—
157C2×C22⋊Dic5—31no—
158C2×C22⋊Dic5—31no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—31no—
162C2×#685—31no—
163C2×#685—31no—
164C2×#685—31no—
165C2×#685—64no—
166C2×#685C2×D311yescharacteristic
167C2×#685C2×D311yescharacteristic
168C2×C4⋊Dic5—31no—
169C2×C4⋊Dic5C2×D311yescharacteristic, complemented
170C2×#683—31no—
171C2×#683—31no—
172C2×#683—31no—
173C2×#683—31no—
174D5×C22⋊C4—38no—
175D5×C22⋊C4—64no—
176C5×#95—31no—
177C5×#95—31no—
178#3963—31no—
179#3963—31no—
180#3963—31no—
181#3963—31no—
182#3963C2×D311yescharacteristic, complemented
183#3963C2×D311yescharacteristic, complemented
184#2315—151noSylow
185C23×C3×C5C2411yescharacteristic
186C22×D15—21no—
187C22×D15—21no—
188C22×D15—21no—
189C22×D15—21no—
190C22×D15C22×C412yes—
191C22×D15C2×D412yes—
192C22×D15C2×Q812yes—
193C22×C5×D3—21no—
194C22×C5×D3—21no—
195C22×C5×D3—21no—
196C22×C5×D3—21no—
197C22×C5×D3C22×C412yes—
198C22×C5×D3C2×D412yes—
199C22×C5×D3C2×Q812yes—
200C22×C3×D5—21no—
201C22×C3×D5—21no—
202C22×C3×D5—21no—
203C22×C3×D5—21no—
204C22×C3×D5C22×C412yes—
205C22×C3×D5C2×D412yes—
206C22×C3×D5C2×Q812yes—
207C2×D3×D5—44no—
208C2×D3×D5—44no—
209C2×D3×D5—44no—
210C2×D3×D5—44no—
211C2×D3×D5—44no—
212C2×D3×D5—44no—
213C2×D3×D5C4⋊C4116yescomplemented
214C2×C3×C4×C5—21no—
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×C5C22×C412yes—
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—
232C4×D15—44no—
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—
242C4×C5×D3—44no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5—21no—
251C2×C3×Dic5C22×C412yes—
252C3×C4×D5—44no—
253#1200—44no—
254D3×Dic5—44no—
255D5×Dic3—44no—
256C24×D3—51no—
257C23×C3×C4—51no—
258C23×Dic3—51no—
259C22×C4×D3—51no—
260C22×C4×D3—51no—
261C22×C4×D3—51no—
262C22×C4×D3C2×D511yescharacteristic
263C2×C3×C4⋊C4—51no—
264C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
265C2×C3×C22⋊C4—51no—
266C2×C3×C22⋊C4—51no—
267C2×#217—51no—
268C2×#217—51no—
269C2×(C2×D3)⋊C4—51no—
270C2×(C2×D3)⋊C4—51no—
271C2×(C2×D3)⋊C4—51no—
272C2×(C2×D3)⋊C4—58no—
273C2×(C2×D3)⋊C4—51no—
274C2×(C2×D3)⋊C4—51no—
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4C2×D511yescharacteristic
277C2×(C2×D3)⋊C4C2×D511yescharacteristic
278C2×C4⋊Dic3—51no—
279C2×C4⋊Dic3—51no—
280C2×Dic3⋊C4—51no—
281C2×Dic3⋊C4—51no—
282C2×Dic3⋊C4—51no—
283C2×Dic3⋊C4C2×D511yescharacteristic, complemented
284D3×C22⋊C4—104no—
285D3×C22⋊C4—104no—
286C3×#95—51no—
287C3×#95—51no—
288C3⋊#95—51no—
289C3⋊#95—51no—
290C3⋊#95—51no—
291C3⋊#95—51no—
292C3⋊#95C2×D511yescharacteristic, complemented
293C3⋊#95C2×D511yescharacteristic, complemented
294C24×C5—31no—
295C23×D5—31no—
296C23×D5—34no—
297C23×D5—34no—
298C23×D5—34no—
299C23×D5—121no—
300C23×D5—121no—
301C23×D5—121no—
302C23×D5—121no—
303C23×D5C22×D311yescharacteristic
304C22×C4×C5—31no—
305C22×C4×C5—31no—
306C22×C4×C5—31no—
307C22×C4×C5—62no—
308C22×C4×C5—121no—
309C22×C4×C5—121no—
310C22×C4×C5C22×D311yescharacteristic
311C22×C4×C5C22×D311yescharacteristic
312C22×C4×C5C22×D311yescharacteristic
313C22×Dic5—31no—
314C22×Dic5—31no—
315C22×Dic5—31no—
316C22×Dic5—62no—
317C22×Dic5—121no—
318C22×Dic5—121no—
319C22×Dic5C22×D311yescharacteristic
320C22×Dic5C22×D311yescharacteristic
321C22×Dic5C22×D311yescharacteristic
322C2×C4×D5—34no—
323C2×C4×D5—41no—
324C2×C4×D5—41no—
325C2×C4×D5—62no—
326C2×C4×D5—62no—
327C2×C4×D5—121no—
328C2×C4×D5—121no—
329C2×C4×D5—121no—
330C2×C4×D5—121no—
331C2×C4×D5—121no—
332C2×C4×D5—121no—
333C2×C4×D5C4×D314yescomplemented
334C5×C4⋊C4—41no—
335C5×C4⋊C4—121no—
336C5×C22⋊C4—34no—
337C5×C22⋊C4—62no—
338C22⋊Dic5—34no—
339C22⋊Dic5—62no—
340#685—22no—
341#685—22no—
342#685—34no—
343#685—34no—
344#685—62no—
345#685—62no—
346#685—62no—
347#685—62no—
348C4⋊Dic5—41no—
349C4⋊Dic5—121no—
350#683—121no—
351#683—121no—
352#683—121no—
353#683—121no—
354C22×C22⋊C4—151no—
355C22×C22⋊C4—151no—
356C22×C22⋊C4—151no—
357#385—31no—
358#385—151no—
359#385—151no—
360#385—151no—
361#385—151no—
362#385—151no—
363#385—151no—
364#385—151no—
365#380—51no—
366#380—151no—
367#380—151no—
368#380—151no—
369C22×C3×C5C23×C411yescharacteristic
370C22×C3×C5C22×D411yescharacteristic
371C22×C3×C5C22×Q811yescharacteristic
372C22×C3×C5H(5,𝔽2)11yescharacteristic
373C22×C3×C5H(5,𝔽2)11yescharacteristic
374C22×C3×C5H(5,𝔽2)11yescharacteristic
375C22×C3×C5H(5,𝔽2)11yescharacteristic
376C2×D15—22no—
377C2×D15—22no—
378C2×D15—22no—
379C2×D15—22no—
380C2×D15—22no—
381C2×D15—22no—
382C2×D15C2×C4⋊C414yes—
383C2×C5×D3—22no—
384C2×C5×D3—22no—
385C2×C5×D3—22no—
386C2×C5×D3—22no—
387C2×C5×D3—22no—
388C2×C5×D3—22no—
389C2×C5×D3C2×C4⋊C414yes—
390C2×C3×D5—22no—
391C2×C3×D5—22no—
392C2×C3×D5—22no—
393C2×C3×D5—22no—
394C2×C3×D5—22no—
395C2×C3×D5—22no—
396C2×C3×D5C2×C4⋊C414yes—
397D3×D5—416no—
398C3×C4×C5—22no—
399C3×C4×C5—41no—
400C3×C4×C5—41no—
401Dic15—22no—
402Dic15—41no—
403Dic15—41no—
404C3×Dic5—22no—
405C3×Dic5—41no—
406C3×Dic5—41no—
407C5×Dic3—22no—
408C5×Dic3—41no—
409C5×Dic3—41no—
410C24×C3—51no—
411C23×D3—51no—
412C23×D3—54no—
413C23×D3—54no—
414C23×D3—54no—
415C23×D3—201no—
416C23×D3—201no—
417C23×D3—201no—
418C23×D3—201no—
419C23×D3C22×D511yescharacteristic
420C22×C3×C4—51no—
421C22×C3×C4—54no—
422C22×C3×C4—51no—
423C22×C3×C4—51no—
424C22×C3×C4—201no—
425C22×C3×C4—201no—
426C22×C3×C4C22×D511yescharacteristic
427C22×C3×C4C22×D511yescharacteristic
428C22×C3×C4C22×D511yescharacteristic
429C22×Dic3—51no—
430C22×Dic3—54no—
431C22×Dic3—51no—
432C22×Dic3—51no—
433C22×Dic3—201no—
434C22×Dic3—201no—
435C22×Dic3C22×D511yescharacteristic
436C22×Dic3C22×D511yescharacteristic
437C22×Dic3C22×D511yescharacteristic
438C2×C4×D3—22no—
439C2×C4×D3—41no—
440C2×C4×D3—41no—
441C2×C4×D3—102no—
442C2×C4×D3—102no—
443C2×C4×D3—102no—
444C2×C4×D3—201no—
445C2×C4×D3—201no—
446C2×C4×D3—201no—
447C2×C4×D3—201no—
448C2×C4×D3—201no—
449C2×C4×D3—201no—
450C3×C4⋊C4—41no—
451C3×C4⋊C4—201no—
452C3×C22⋊C4—102no—
453C3×C22⋊C4—102no—
454#217—102no—
455#217—102no—
456(C2×D3)⋊C4—22no—
457(C2×D3)⋊C4—54no—
458(C2×D3)⋊C4—54no—
459(C2×D3)⋊C4—54no—
460(C2×D3)⋊C4—102no—
461(C2×D3)⋊C4—102no—
462(C2×D3)⋊C4—102no—
463(C2×D3)⋊C4C4×D514yescomplemented
464C4⋊Dic3—201no—
465C4⋊Dic3—201no—
466Dic3⋊C4—41no—
467Dic3⋊C4—201no—
468Dic3⋊C4—201no—
469Dic3⋊C4—201no—
470C23×C5—32no—
471C23×C5—32no—
472C23×C5—32no—
473C23×C5—61no—
474C23×C5—61no—
475C23×C5—61no—
476C23×C5—61no—
477C23×C5C23×D311yescharacteristic
478C22×D5—21no—
479C22×D5—21no—
480C22×D5—21no—
481C22×D5—21no—
482C22×D5—32no—
483C22×D5—32no—
484C22×D5—32no—
485C22×D5—316no—
486C22×D5—61no—
487C22×D5—61no—
488C22×D5—61no—
489C22×D5—61no—
490C22×D5—124no—
491C22×D5—124no—
492C22×D5—124no—
493C22×D5—124no—
494C22×D5—124no—
495C22×D5—124no—
496C22×D5C2×C4×D312yes—
497C22×D5D3×D412yes—
498C22×D5D3×Q812yes—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—21no—
502C2×C4×C5—21no—
503C2×C4×C5—21no—
504C2×C4×C5—21no—
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—32no—
508C2×C4×C5—61no—
509C2×C4×C5—61no—
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—124no—
517C2×C4×C5C2×C4×D312yes—
518C2×Dic5—21no—
519C2×Dic5—21no—
520C2×Dic5—21no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5—21no—
526C2×Dic5—32no—
527C2×Dic5—61no—
528C2×Dic5—61no—
529C2×Dic5—61no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5—124no—
536C2×Dic5C2×C4×D312yes—
537C4×D5—44no—
538C4×D5—124no—
539C4×D5—124no—
540C4×D5—124no—
541C25—151no—
542C23×C4—31no—
543C23×C4—51no—
544C23×C4—151no—
545C23×C4—151no—
546C23×C4—151no—
547C23×C4—151no—
548C2×C4⋊C4—31no—
549C2×C4⋊C4—51no—
550C2×C4⋊C4—151no—
551C2×C4⋊C4—151no—
552C2×C4⋊C4—151no—
553C2×C4⋊C4—151no—
554C2×C4⋊C4—151no—
555C2×C4⋊C4D3×D511yescharacteristic, complemented
556C2×C22⋊C4—31no—
557C2×C22⋊C4—31no—
558C2×C22⋊C4—51no—
559C2×C22⋊C4—51no—
560C2×C22⋊C4—158no—
561C2×C22⋊C4—151no—
562C2×C22⋊C4—151no—
563C2×C22⋊C4—151no—
564C2×C22⋊C4—151no—
565C2×C22⋊C4—151no—
566C2×C22⋊C4—151no—
567C2×C22⋊C4—151no—
568C2×C22⋊C4—151no—
569C2×C22⋊C4—304no—
570C2×C22⋊C4—304no—
571#95—31no—
572#95—31no—
573#95—51no—
574#95—51no—
575#95—151no—
576#95—151no—
577#95—151no—
578#95—151no—
579C2×C3×C5C22×C4⋊C411yescharacteristic
580C2×C3×C5#51811yescharacteristic
581C2×C3×C5#51811yescharacteristic
582C2×C3×C5#53411yescharacteristic
583C2×C3×C5#53411yescharacteristic
584C2×C3×C5#54311yescharacteristic
585C2×C3×C5#54311yescharacteristic
586D15—24no—
587C3×D5—24no—
588C5×D3—24no—
589C23×C3—52no—
590C23×C3—52no—
591C23×C3—52no—
592C23×C3—101no—
593C23×C3—101no—
594C23×C3—101no—
595C23×C3—101no—
596C23×C3C23×D511yescharacteristic
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—52no—
602C22×D3—52no—
603C22×D3—52no—
604C22×D3—516no—
605C22×D3—101no—
606C22×D3—101no—
607C22×D3—101no—
608C22×D3—101no—
609C22×D3—204no—
610C22×D3—204no—
611C22×D3—204no—
612C22×D3—204no—
613C22×D3—204no—
614C22×D3—204no—
615C22×D3C2×C4×D512yes—
616C22×D3D4×D512yes—
617C22×D3Q8×D512yes—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—52no—
627C2×C3×C4—101no—
628C2×C3×C4—101no—
629C2×C3×C4—101no—
630C2×C3×C4—101no—
631C2×C3×C4—101no—
632C2×C3×C4—101no—
633C2×C3×C4—101no—
634C2×C3×C4—101no—
635C2×C3×C4—204no—
636C2×C3×C4C2×C4×D512yes—
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—101no—
647C2×Dic3—101no—
648C2×Dic3—101no—
649C2×Dic3—101no—
650C2×Dic3—101no—
651C2×Dic3—101no—
652C2×Dic3—101no—
653C2×Dic3—101no—
654C2×Dic3—204no—
655C2×Dic3C2×C4×D512yes—
656C4×D3—44no—
657C4×D3—204no—
658C4×D3—204no—
659C4×D3—204no—
660C22×C5—34no—
661C22×C5—62no—
662C22×C5—62no—
663C22×C5—62no—
664C22×C5—62no—
665C22×C5—62no—
666C22×C5—62no—
667C22×C5C22×C4×D311yescharacteristic
668C22×C5C2×D3×D411yescharacteristic
669C22×C5#100411yescharacteristic
670C22×C5#100411yescharacteristic
671C22×C5C2×D3×Q811yescharacteristic
672C22×C5#100911yescharacteristic
673C22×C5#100911yescharacteristic
674C2×D5—22no—
675C2×D5—22no—
676C2×D5—22no—
677C2×D5—22no—
678C2×D5—22no—
679C2×D5—22no—
680C2×D5—34no—
681C2×D5—62no—
682C2×D5—62no—
683C2×D5—62no—
684C2×D5—62no—
685C2×D5—62no—
686C2×D5—62no—
687C2×D5—1216no—
688C2×D5D3×C4⋊C414yes—
689C4×C5—22no—
690C4×C5—41no—
691C4×C5—41no—
692C4×C5—62no—
693C4×C5—121no—
694C4×C5—121no—
695Dic5—22no—
696Dic5—41no—
697Dic5—41no—
698Dic5—62no—
699Dic5—121no—
700Dic5—121no—
701C24—31no—
702C24—51no—
703C24—154no—
704C24—154no—
705C24—154no—
706C24—151no—
707C24—601no—
708C24—601no—
709C24—601no—
710C24—601no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—51no—
715C22×C4—54no—
716C22×C4—51no—
717C22×C4—51no—
718C22×C4—62no—
719C22×C4—121no—
720C22×C4—121no—
721C22×C4—154no—
722C22×C4—151no—
723C22×C4—151no—
724C22×C4—151no—
725C22×C4—201no—
726C22×C4—201no—
727C22×C4—302no—
728C22×C4—302no—
729C22×C4—302no—
730C22×C4—601no—
731C22×C4—601no—
732C22×C4—601no—
733C22×C4—601no—
734C22×C4—601no—
735C22×C4—601no—
736C22×C4—601no—
737C22×C4—601no—
738C22×C4C2×D3×D511yescharacteristic
739C22×C4C2×D3×D511yescharacteristic
740C22×C4C2×D3×D511yescharacteristic
741C4⋊C4—41no—
742C4⋊C4—121no—
743C4⋊C4—201no—
744C4⋊C4—601no—
745C4⋊C4—601no—
746C4⋊C4—601no—
747C4⋊C4—601no—
748C4⋊C4—601no—
749C22⋊C4—34no—
750C22⋊C4—62no—
751C22⋊C4—102no—
752C22⋊C4—102no—
753C22⋊C4—154no—
754C22⋊C4—154no—
755C22⋊C4—154no—
756C22⋊C4—302no—
757C22⋊C4—302no—
758C22⋊C4—302no—
759C22⋊C4—302no—
760C22⋊C4—302no—
761C3×C5#231511yescharacteristic, complemented, Hall
762C22×C3—54no—
763C22×C3—102no—
764C22×C3—102no—
765C22×C3—102no—
766C22×C3—102no—
767C22×C3—102no—
768C22×C3—102no—
769C22×C3C22×C4×D511yescharacteristic
770C22×C3C2×D4×D511yescharacteristic
771C22×C3#414411yescharacteristic
772C22×C3#414411yescharacteristic
773C22×C3C2×Q8×D511yescharacteristic
774C22×C3#414911yescharacteristic
775C22×C3#414911yescharacteristic
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—22no—
779C2×D3—22no—
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—54no—
783C2×D3—102no—
784C2×D3—102no—
785C2×D3—102no—
786C2×D3—102no—
787C2×D3—102no—
788C2×D3—102no—
789C2×D3—2016no—
790C2×D3D5×C4⋊C414yes—
791C3×C4—22no—
792C3×C4—41no—
793C3×C4—41no—
794C3×C4—102no—
795C3×C4—201no—
796C3×C4—201no—
797Dic3—22no—
798Dic3—41no—
799Dic3—41no—
800Dic3—102no—
801Dic3—201no—
802Dic3—201no—
803C2×C5—64no—
804C2×C5#548611yescharacteristic
805C2×C5C2×D3×C4⋊C411yescharacteristic
806C2×C5#552111yescharacteristic
807C2×C5#560511yescharacteristic
808C2×C5#560511yescharacteristic
809C2×C5#563411yescharacteristic
810C2×C5#563411yescharacteristic
811D5—24no—
812D5—64no—
813C23—32no—
814C23—32no—
815C23—32no—
816C23—52no—
817C23—52no—
818C23—52no—
819C23—61no—
820C23—61no—
821C23—61no—
822C23—61no—
823C23—101no—
824C23—101no—
825C23—101no—
826C23—101no—
827C23—1516no—
828C23—152no—
829C23—152no—
830C23—152no—
831C23—301no—
832C23—301no—
833C23—301no—
834C23—301no—
835C23—604no—
836C23—604no—
837C23—604no—
838C23—604no—
839C23—604no—
840C23—604no—
841C23C22×D3×D511yescharacteristic
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—32no—
851C2×C4—52no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—101no—
861C2×C4—101no—
862C2×C4—101no—
863C2×C4—101no—
864C2×C4—101no—
865C2×C4—101no—
866C2×C4—101no—
867C2×C4—101no—
868C2×C4—124no—
869C2×C4—152no—
870C2×C4—204no—
871C2×C4—301no—
872C2×C4—301no—
873C2×C4—301no—
874C2×C4—301no—
875C2×C4—301no—
876C2×C4—301no—
877C2×C4—301no—
878C2×C4—301no—
879C2×C4—604no—
880C2×C4—604no—
881C2×C4—604no—
882C2×C4—604no—
883C2×C4C4×D3×D512yes—
884C2×C3—104no—
885C2×C3C2×D5×C4⋊C411yescharacteristic
886C2×C3#6587911yescharacteristic
887C2×C3#6587911yescharacteristic
888C2×C3#6592311yescharacteristic
889C2×C3#6596811yescharacteristic
890C2×C3#6596811yescharacteristic
891C2×C3#6598711yescharacteristic
892D3—24no—
893D3—104no—
894C5#7400511yescharacteristic, complemented, Sylow
895C22—34no—
896C22—54no—
897C22—62no—
898C22—62no—
899C22—62no—
900C22—62no—
901C22—62no—
902C22—62no—
903C22—102no—
904C22—102no—
905C22—102no—
906C22—102no—
907C22—102no—
908C22—102no—
909C22—154no—
910C22—302no—
911C22—302no—
912C22—302no—
913C22—302no—
914C22—302no—
915C22—302no—
916C22—6016no—
917C22C2×C4×D3×D511yescharacteristic
918C22#9201711yescharacteristic
919C22D3×D4×D511yescharacteristic
920C22#9202711yescharacteristic
921C22D3×Q8×D511yescharacteristic
922C22#9203511yescharacteristic
923C22#9204911yescharacteristic
924C4—22no—
925C4—41no—
926C4—41no—
927C4—62no—
928C4—102no—
929C4—121no—
930C4—121no—
931C4—201no—
932C4—201no—
933C4—302no—
934C4—601no—
935C4—601no—
936C3#1060632211yescharacteristic, complemented, Sylow
937C2—64no—
938C2—104no—
939C2—304no—
940C2D3×D5×C4⋊C411yescharacteristic
941C2#1175383711yescharacteristic
942C2#1175384911yescharacteristic
943C2#1175389011yescharacteristic
944C2#1175462511yescharacteristic
945C2#1175502511yescharacteristic
946C2#1175528711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D3×D5C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2315
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11751090C2semidirect
5. C5×#4989C2semidirect
6. C3×#65276C2semidirect
7. #11748898C2semidirect
8. #11748897C2semidirect
9. #11748895C2semidirect
10. #11748893C2semidirect
11. #11748885C2semidirect
12. #11748878C2semidirect
13. #11748738C2semidirect
14. #11748731C2semidirect
15. #11748722C2semidirect
24. C2×C3×C5×C4⋊C4C22semidirect
27. C2×#6712C22semidirect
30. C2×C5×Dic3⋊C4C22semidirect
33. C2×C3×C4⋊Dic5C22semidirect
34. C2×Dic3⋊Dic5C22semidirect
35. C2×#6669C22semidirect
36. C2×#6668C22semidirect
37. C2×#6668C22semidirect
46. D5×(C2×D3)⋊C4C4semidirect
47. #91115C22semidirect
48. #91115C22semidirect
49. C5×C3⋊#95C22semidirect
50. C5×C3⋊#95C22semidirect
51. C3×#3963C22semidirect
52. C3×#3963C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
64. #65276D3semidirect
101. C2×C3×C4×D5C2×C4semidirect
110. C2×D5×Dic3C2×C4semidirect
113. #6714C2×C4semidirect
116. C5×(C2×D3)⋊C4C2×C4semidirect
126. #6667C2×C4semidirect
128. (C2×D3)⋊Dic5C2×C4semidirect
139. #4989D5semidirect
154. C2×C5×C4⋊C4C2×D3semidirect
169. C2×C4⋊Dic5C2×D3semidirect
182. #3963C2×D3semidirect
183. #3963C2×D3semidirect
213. C2×D3×D5C4⋊C4semidirect
264. C2×C3×C4⋊C4C2×D5semidirect
283. C2×Dic3⋊C4C2×D5semidirect
292. C3⋊#95C2×D5semidirect
293. C3⋊#95C2×D5semidirect
333. C2×C4×D5C4×D3semidirect
463. (C2×D3)⋊C4C4×D5semidirect
555. C2×C4⋊C4D3×D5semidirect
761. C3×C5#2315semidirect
894. C5#74005semidirect
936. C3#10606322semidirect

Maximal subgroups

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

subgroupindex
C2×#914732
C2×D3×#6852
C2×D5×(C2×D3)⋊C42
#117510902
C5×#49892
C3×#652762
#117488982
#117488972
#117488952
#117488932
#117488852
#117488782
#117487382
#117487312
#117487222
#106063223
#740055