Finite Group Databasebeta

← #14321472

Subgroups — #14321472

Order 1920.

1648 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#67⋊C4C211yesmaximal, characteristic, complemented
2C2×#91571C211yesmaximal, characteristic
3C2×Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
4C22×Dic3×Dic5C211yesmaximal, characteristic, complemented
5C2×#91441C211yesmaximal, characteristic, complemented
6#11751043C211yesmaximal, characteristic, complemented
7C3×#65247C211yesmaximal, characteristic, complemented
8#11749492C211yesmaximal, characteristic, complemented
9#11748916C211yesmaximal, characteristic, complemented
10Dic3×#685C211yesmaximal, characteristic, complemented
11#11748723C211yesmaximal, characteristic, complemented
12#11748719C211yesmaximal, characteristic, complemented
13#11748711C211yesmaximal, characteristic, complemented
14#11748645C211yesmaximal, characteristic, complemented
15#11748633C211yesmaximal, characteristic, complemented
16C4×#4085—31nomaximal, Hall
17C23×Dic15C2211yescharacteristic
18C22×C5×#67C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C23×C3×Dic5C2211yescharacteristic
23C22×#1201C2211yescharacteristic
24C22×D5×Dic3C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×#6712C2211yescharacteristic
28C2×#6712C2211yescharacteristic
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic
30C2×C5×Dic3⋊C4C2211yescharacteristic
31C2×C4×C5×Dic3C2211yescharacteristic
32C5×#67⋊C4—24no—
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35#91571C418yescomplemented
36Dic3×C22⋊D5—24no—
37C2×#6669C2211yescharacteristic
38C2×#6668C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×Dic3×Dic5—24no—
45C2×Dic3×Dic5C2211yescharacteristic
46C2×Dic3×Dic5C2211yescharacteristic
47C2×Dic3×Dic5C2211yescharacteristic
48C2×Dic3×Dic5C2211yescharacteristic
49C2×Dic3×Dic5C2211yescharacteristic
50#91441—24no—
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#74660—51nomaximal, Hall
58C2×C4×C5×D4—31no—
59C2×#4085—31no—
60C2×C4×C22⋊D5—31no—
61C2×C4×C22⋊D5—31no—
62C22×C4×Dic5—31no—
63#65509—31no—
64C4×C22⋊Dic5—31no—
65#65279—31no—
66#65261—31no—
67#65247D311yescharacteristic, complemented
68#65246—31no—
69#65234—31no—
70#65231—31no—
71C4×#685—31no—
72C4×#683—31no—
73C24×C3×C5C2311yescharacteristic
74C23×C5×D3C2311yescharacteristic
75C23×C3×D5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×Dic15—22no—
79C22×Dic15—22no—
80C22×Dic15C2×C414yescomplemented
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C2×C5×#67—22no—
86C2×C5×#67—22no—
87C2×C5×#67C2×C414yescomplemented
88C22×C5×Dic3—22no—
89C22×C5×Dic3—22no—
90C22×C5×Dic3D414yescomplemented
91C22×C5×Dic3C2311yescharacteristic
92C22×C5×Dic3C2311yescharacteristic
93C22×C5×Dic3C2311yescharacteristic
94C2×C4×C5×D3—22no—
95C2×C4×C5×D3—22no—
96C2×C4×C5×D3—22no—
97C2×C3×C22⋊D5—22no—
98C2×C3×C22⋊D5—22no—
99C2×C3×C22⋊D5C2×C414yescomplemented
100C22×C3×Dic5—22no—
101C22×C3×Dic5—22no—
102C22×C3×Dic5—22no—
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C2×#1201—22no—
107C2×#1201—22no—
108C2×#1201C2×C414yescomplemented
109C2×D5×Dic3—22no—
110C2×D5×Dic3—22no—
111C2×D5×Dic3—22no—
112C3×C5×C22⋊C4—22no—
113#6719—22no—
114#6712—22no—
115#6712—22no—
116C5×(C2×D3)⋊C4—22no—
117C5×Dic3⋊C4—22no—
118C4×C5×Dic3—22no—
119C3×#685—22no—
120C3×#685—22no—
121#6669C2×C414yescomplemented
122#6668—22no—
123(C2×D3)⋊Dic5—22no—
124(C2×D3)⋊Dic5—22no—
125(C2×D3)⋊Dic5C2×C414yescomplemented
126#6665—22no—
127#6665C2×C414yescomplemented
128Dic3×Dic5—22no—
129Dic3×Dic5—22no—
130Dic3×Dic5—22no—
131Dic3×Dic5—22no—
132Dic3×Dic5D414yescomplemented
133C2×#939—51no—
134C2×D4×Dic3—51no—
135C22×C4×Dic3—51no—
136C2×#67⋊C4—51no—
137C2×#67⋊C4D511yescharacteristic, complemented
138C3×#386—51no—
139#5213—51no—
140#4957—51no—
141#4944—51no—
142#4942—51no—
143Dic3×C22⋊C4—51no—
144#4670—51no—
145#4666—51no—
146#4649—51no—
147#4647—51no—
148C22×C5×D4—31no—
149C23×C4×C5—31no—
150C23×C4×C5—31no—
151C22×C22⋊D5—31no—
152C22×C22⋊D5C2×D311yescharacteristic
153C23×Dic5—31no—
154C23×Dic5C2×D311yescharacteristic
155C22×C4×D5—31no—
156C4×C5×D4—64no—
157C2×C5×C4⋊C4—31no—
158C2×C5×C22⋊C4—31no—
159C2×C5×C22⋊C4C2×D311yescharacteristic
160C2×C42×C5—31no—
161C2×C22⋊Dic5—31no—
162C2×C22⋊Dic5—31no—
163C2×C22⋊Dic5—31no—
164C2×C22⋊Dic5—31no—
165#4085—38no—
166C4×C22⋊D5—64no—
167C4×C22⋊D5—64no—
168C2×#685—31no—
169C2×#685—31no—
170C2×#685C2×D311yescharacteristic
171C2×#685C2×D311yescharacteristic
172C2×#683—31no—
173C2×#683—31no—
174C2×#683—31no—
175C2×#683—31no—
176C2×C4×Dic5—31no—
177C2×C4×Dic5—31no—
178C2×C4×Dic5—31no—
179C2×C4×Dic5—31no—
180C2×C4×Dic5—31no—
181C2×C4×Dic5—64no—
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#3963C2×D311yescharacteristic
187#3963C2×D311yescharacteristic
188C4×#121—151noSylow
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5C22×C412yes—
194C23×C3×C5C2×D412yes—
195C23×C3×C5#4112yes—
196C23×C3×C5C2411yescharacteristic
197C22×C5×D3—21no—
198C22×C5×D3—21no—
199C22×C5×D3—21no—
200C22×C5×D3—21no—
201C22×C5×D3—21no—
202C22×C5×D3—21no—
203C22×C5×D3C22×C412yes—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—21no—
209C22×C3×D5—21no—
210C22×C3×D5C22×C412yes—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15—28no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15C22×C412yes—
227C2×Dic15C22×C412yes—
228C2×Dic15C2×D412yes—
229C2×Dic15#4112yes—
230C5×#67—28no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—28no—
236C2×C5×Dic3C22×C412yes—
237C2×C5×Dic3C2×D412yes—
238C2×C5×Dic3C2×D412yes—
239C2×C5×Dic3C2×D412yes—
240C2×C5×Dic3#4112yes—
241C4×C5×D3—44no—
242C3×C22⋊D5—28no—
243C2×C3×Dic5—28no—
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×Dic5C22×C412yes—
251C2×C3×Dic5C2×D412yes—
252C2×C3×Dic5#4112yes—
253#1201—28no—
254D5×Dic3—44no—
255C22×C3×D4—51no—
256C23×C3×C4—51no—
257C22×#67—51no—
258C22×#67C2×D511yescharacteristic
259C23×Dic3—51no—
260C23×Dic3—51no—
261C23×Dic3C2×D511yescharacteristic
262C22×C4×D3C2×D511yescharacteristic
263C2×C3×C22⋊C4—51no—
264C2×C3×C22⋊C4—51no—
265C2×C3×C22⋊C4C2×D511yescharacteristic
266C2×#217—51no—
267C2×#217—51no—
268C2×#217—51no—
269#939—58no—
270D4×Dic3—104no—
271C2×(C2×D3)⋊C4—51no—
272C2×(C2×D3)⋊C4—51no—
273C2×(C2×D3)⋊C4—51no—
274C2×(C2×D3)⋊C4C2×D511yescharacteristic
275C2×C4⋊Dic3—51no—
276C2×Dic3⋊C4—51no—
277C2×Dic3⋊C4—51no—
278C2×Dic3⋊C4—51no—
279C2×Dic3⋊C4C2×D511yescharacteristic
280C2×C4×Dic3—51no—
281C2×C4×Dic3—51no—
282C2×C4×Dic3—51no—
283C2×C4×Dic3—51no—
284C2×C4×Dic3—51no—
285C2×C4×Dic3—104no—
286C2×C4×Dic3C2×D511yescharacteristic
287#67⋊C4—24no—
288#67⋊C4—104no—
289C3×#95—51no—
290C3×#95—51no—
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C24×C5—31no—
296C24×C5C22×D311yescharacteristic
297C23×D5C22×D311yescharacteristic
298C2×C5×D4—34no—
299C2×C5×D4—62no—
300C2×C5×D4—62no—
301C22×C4×C5—31no—
302C22×C4×C5—34no—
303C22×C4×C5—31no—
304C22×C4×C5—31no—
305C22×C4×C5—62no—
306C22×C4×C5—62no—
307C22×C4×C5—62no—
308C22×C4×C5—62no—
309C22×C4×C5—62no—
310C22×C4×C5C22×D311yescharacteristic
311C22×C4×C5C22×D311yescharacteristic
312C2×C22⋊D5—22no—
313C2×C22⋊D5—22no—
314C2×C22⋊D5—34no—
315C2×C22⋊D5—62no—
316C2×C22⋊D5—62no—
317C2×C22⋊D5C4×D314yescomplemented
318C22×Dic5—22no—
319C22×Dic5—22no—
320C22×Dic5—22no—
321C22×Dic5—31no—
322C22×Dic5—34no—
323C22×Dic5—31no—
324C22×Dic5—31no—
325C22×Dic5—31no—
326C22×Dic5—62no—
327C22×Dic5—62no—
328C22×Dic5C22×D311yescharacteristic
329C22×Dic5C22×D311yescharacteristic
330C22×Dic5C22×D311yescharacteristic
331C2×C4×D5—62no—
332C2×C4×D5—62no—
333C2×C4×D5—62no—
334C5×C4⋊C4—62no—
335C5×C22⋊C4—22no—
336C5×C22⋊C4—62no—
337C42×C5—62no—
338C22⋊Dic5—34no—
339C22⋊Dic5—62no—
340C22⋊Dic5—62no—
341C22⋊Dic5—62no—
342#685—22no—
343#685—22no—
344#685—34no—
345#685—62no—
346#683—34no—
347#683—62no—
348#683—62no—
349#683—62no—
350C4×Dic5—34no—
351C4×Dic5—62no—
352C4×Dic5—62no—
353C4×Dic5—62no—
354C4×Dic5—62no—
355C2×#121—151no—
356C2×C4×D4—31no—
357C2×C4×D4—151no—
358C2×C4×D4—151no—
359C22×C42—151no—
360#390—151no—
361#389—151no—
362#388—151no—
363#388—151no—
364#386—51no—
365#386—151no—
366#380—151no—
367C4×C4⋊C4—151no—
368C4×C22⋊C4—151no—
369C4×C22⋊C4—151no—
370C22×C3×C5—22no—
371C22×C3×C5—22no—
372C22×C3×C5—22no—
373C22×C3×C5—22no—
374C22×C3×C5—22no—
375C22×C3×C5—22no—
376C22×C3×C5C4×D414yescomplemented
377C22×C3×C5C23×C411yescharacteristic
378C22×C3×C5C22×D411yescharacteristic
379C22×C3×C5C22×D411yescharacteristic
380C22×C3×C5C2×#4111yescharacteristic
381C22×C3×C5C2×#4111yescharacteristic
382C22×C3×C5C2×#4111yescharacteristic
383C22×C3×C5C2×#4111yescharacteristic
384C2×C5×D3—22no—
385C2×C5×D3—22no—
386C2×C5×D3—22no—
387C2×C5×D3—41no—
388C2×C5×D3—41no—
389C2×C5×D3—41no—
390C2×C5×D3—41no—
391C2×C3×D5—22no—
392C2×C3×D5—22no—
393C2×C3×D5—22no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C2×C3×D5—41no—
398C3×C4×C5—41no—
399C3×C4×C5—41no—
400Dic15—22no—
401Dic15—41no—
402Dic15—41no—
403Dic15C4×D414yescomplemented
404C3×Dic5—22no—
405C3×Dic5—22no—
406C3×Dic5—22no—
407C5×Dic3—22no—
408C5×Dic3—22no—
409C5×Dic3#12114yescomplemented
410C24×C3—51no—
411C24×C3C22×D511yescharacteristic
412C23×D3C22×D511yescharacteristic
413C2×C3×D4—54no—
414C2×C3×D4—102no—
415C2×C3×D4—102no—
416C22×C3×C4—51no—
417C22×C3×C4—51no—
418C22×C3×C4—51no—
419C22×C3×C4—102no—
420C22×C3×C4—102no—
421C22×C3×C4—102no—
422C22×C3×C4C22×D511yescharacteristic
423C22×C3×C4C22×D511yescharacteristic
424C2×#67—22no—
425C2×#67—22no—
426C2×#67—54no—
427C2×#67—102no—
428C2×#67—102no—
429C2×#67C4×D514yescomplemented
430C22×Dic3—22no—
431C22×Dic3—22no—
432C22×Dic3—51no—
433C22×Dic3—54no—
434C22×Dic3—51no—
435C22×Dic3—51no—
436C22×Dic3—51no—
437C22×Dic3—102no—
438C22×Dic3—102no—
439C22×Dic3—102no—
440C22×Dic3—102no—
441C22×Dic3—102no—
442C22×Dic3C22⋊D514yescomplemented
443C22×Dic3C22×D511yescharacteristic
444C22×Dic3C22×D511yescharacteristic
445C22×Dic3C22×D511yescharacteristic
446C2×C4×D3—22no—
447C2×C4×D3—22no—
448C2×C4×D3—22no—
449C3×C22⋊C4—22no—
450C3×C22⋊C4—102no—
451C3×C22⋊C4—102no—
452#217—54no—
453#217—102no—
454#217—102no—
455(C2×D3)⋊C4—22no—
456(C2×D3)⋊C4—54no—
457(C2×D3)⋊C4—102no—
458(C2×D3)⋊C4—102no—
459C4⋊Dic3—102no—
460Dic3⋊C4—22no—
461Dic3⋊C4—54no—
462Dic3⋊C4—102no—
463Dic3⋊C4—102no—
464C4×Dic3—22no—
465C4×Dic3—54no—
466C4×Dic3—102no—
467C4×Dic3—102no—
468C4×Dic3—102no—
469C4×Dic3—102no—
470C23×C5—21no—
471C23×C5—21no—
472C23×C5—21no—
473C23×C5—21no—
474C23×C5—32no—
475C23×C5—61no—
476C23×C5—61no—
477C23×C5—61no—
478C23×C5—61no—
479C23×C5—61no—
480C23×C5—61no—
481C23×C5C2×C4×D312yes—
482C23×C5D3×D412yes—
483C23×C5#23712yes—
484C23×C5C23×D311yescharacteristic
485C22×D5—21no—
486C22×D5—21no—
487C22×D5—21no—
488C22×D5—21no—
489C22×D5—21no—
490C22×D5—21no—
491C22×D5C2×C4×D312yes—
492C5×D4—68no—
493C2×C4×C5—21no—
494C2×C4×C5—21no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—21no—
499C2×C4×C5—32no—
500C2×C4×C5—32no—
501C2×C4×C5—32no—
502C2×C4×C5—32no—
503C2×C4×C5—32no—
504C2×C4×C5—68no—
505C2×C4×C5—61no—
506C2×C4×C5—61no—
507C2×C4×C5—61no—
508C2×C4×C5—61no—
509C2×C4×C5—124no—
510C22⋊D5—28no—
511C22⋊D5—68no—
512C2×Dic5—28no—
513C2×Dic5—21no—
514C2×Dic5—21no—
515C2×Dic5—21no—
516C2×Dic5—21no—
517C2×Dic5—21no—
518C2×Dic5—21no—
519C2×Dic5—32no—
520C2×Dic5—32no—
521C2×Dic5—32no—
522C2×Dic5—32no—
523C2×Dic5—68no—
524C2×Dic5—61no—
525C2×Dic5—61no—
526C2×Dic5—61no—
527C2×Dic5—61no—
528C2×Dic5—61no—
529C2×Dic5—61no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5C2×C4×D312yes—
533C2×Dic5D3×D412yes—
534C2×Dic5#23712yes—
535C4×D5—124no—
536C22×D4—31no—
537C22×D4—51no—
538C22×D4—151no—
539C23×C4—31no—
540C23×C4—31no—
541C23×C4—51no—
542C23×C4—151no—
543C23×C4—151no—
544#121—158no—
545C4×D4—64no—
546C4×D4—304no—
547C4×D4—304no—
548C2×C4⋊C4—31no—
549C2×C4⋊C4—151no—
550C2×C4⋊C4—151no—
551C2×C4⋊C4—151no—
552C2×C4⋊C4—151no—
553C2×C22⋊C4—31no—
554C2×C22⋊C4—51no—
555C2×C22⋊C4—51no—
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⋊C4D3×D511yescharacteristic
563C2×C42—31no—
564C2×C42—151no—
565C2×C42—151no—
566C2×C42—151no—
567C2×C42—151no—
568C2×C42—151no—
569C2×C42—304no—
570#95—51no—
571#95—51no—
572#95—151no—
573#95—151no—
574#95—151no—
575#95—151no—
576C2×C3×C5—24no—
577C2×C3×C5C2×C4×D411yescharacteristic
578C2×C3×C5C2×C4×D411yescharacteristic
579C2×C3×C5C4×#4111yescharacteristic
580C2×C3×C5C2×#12111yescharacteristic
581C2×C3×C5#52511yescharacteristic
582C2×C3×C5#52911yescharacteristic
583C2×C3×C5#53211yescharacteristic
584C3×D5—42no—
585C5×D3—42no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—52no—
591C23×C3—101no—
592C23×C3—101no—
593C23×C3—101no—
594C23×C3—101no—
595C23×C3—101no—
596C23×C3—101no—
597C23×C3C2×C4×D512yes—
598C23×C3#70912yes—
599C23×C3C2×C22⋊D512yes—
600C23×C3C23×D511yescharacteristic
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3C2×C4×D512yes—
608C3×D4—108no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—52no—
616C2×C3×C4—52no—
617C2×C3×C4—52no—
618C2×C3×C4—108no—
619C2×C3×C4—101no—
620C2×C3×C4—101no—
621C2×C3×C4—101no—
622C2×C3×C4—101no—
623C2×C3×C4—101no—
624C2×C3×C4—101no—
625#67—28no—
626#67—108no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—28no—
632C2×Dic3—52no—
633C2×Dic3—52no—
634C2×Dic3—52no—
635C2×Dic3—52no—
636C2×Dic3—108no—
637C2×Dic3—101no—
638C2×Dic3—101no—
639C2×Dic3—101no—
640C2×Dic3—101no—
641C2×Dic3—101no—
642C2×Dic3—101no—
643C2×Dic3—101no—
644C2×Dic3—101no—
645C2×Dic3—204no—
646C2×Dic3C2×C4×D512yes—
647C2×Dic3D4×D512yes—
648C2×Dic3#71112yes—
649C2×Dic3C2×C22⋊D512yes—
650C2×Dic3C2×C22⋊D512yes—
651C4×D3—44no—
652C22×C5—22no—
653C22×C5—22no—
654C22×C5—22no—
655C22×C5—22no—
656C22×C5—22no—
657C22×C5—22no—
658C22×C5—62no—
659C22×C5—62no—
660C22×C5—62no—
661C22×C5—121no—
662C22×C5—121no—
663C22×C5—121no—
664C22×C5—121no—
665C22×C5#67⋊C414yescomplemented
666C22×C5C22×C4×D311yescharacteristic
667C22×C5C2×D3×D411yescharacteristic
668C22×C5C2×D3×D411yescharacteristic
669C22×C5C2×#23711yescharacteristic
670C22×C5C2×#23711yescharacteristic
671C22×C5D3×#4111yescharacteristic
672C22×C5D3×#4111yescharacteristic
673C2×D5—22no—
674C2×D5—22no—
675C2×D5—22no—
676C2×D5—41no—
677C2×D5—41no—
678C2×D5—41no—
679C2×D5—41no—
680C4×C5—34no—
681C4×C5—41no—
682C4×C5—41no—
683C4×C5—62no—
684C4×C5—62no—
685Dic5—22no—
686Dic5—22no—
687Dic5—22no—
688Dic5—34no—
689Dic5—62no—
690Dic5—121no—
691Dic5—121no—
692C24—31no—
693C24—51no—
694C24C2×D3×D511yescharacteristic
695C2×D4—34no—
696C2×D4—54no—
697C2×D4—62no—
698C2×D4—62no—
699C2×D4—102no—
700C2×D4—102no—
701C2×D4—154no—
702C2×D4—302no—
703C2×D4—302no—
704C22×C4—31no—
705C22×C4—34no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—51no—
709C22×C4—51no—
710C22×C4—51no—
711C22×C4—62no—
712C22×C4—62no—
713C22×C4—62no—
714C22×C4—62no—
715C22×C4—62no—
716C22×C4—102no—
717C22×C4—102no—
718C22×C4—102no—
719C22×C4—151no—
720C22×C4—154no—
721C22×C4—151no—
722C22×C4—151no—
723C22×C4—151no—
724C22×C4—302no—
725C22×C4—302no—
726C22×C4—302no—
727C22×C4—302no—
728C22×C4—302no—
729C22×C4C2×D3×D511yescharacteristic
730C22×C4C2×D3×D511yescharacteristic
731C4⋊C4—62no—
732C4⋊C4—154no—
733C4⋊C4—302no—
734C4⋊C4—302no—
735C4⋊C4—302no—
736C22⋊C4—22no—
737C22⋊C4—62no—
738C22⋊C4—102no—
739C22⋊C4—102no—
740C22⋊C4—154no—
741C22⋊C4—154no—
742C22⋊C4—302no—
743C22⋊C4—302no—
744C22⋊C4—302no—
745C22⋊C4—302no—
746C42—62no—
747C42—154no—
748C42—302no—
749C42—302no—
750C42—302no—
751C42—302no—
752C3×C5C4×#12111yescharacteristic, complemented, Hall
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—102no—
760C22×C3—102no—
761C22×C3—102no—
762C22×C3—201no—
763C22×C3—201no—
764C22×C3—201no—
765C22×C3—201no—
766C22×C3C4×C22⋊D514yescomplemented
767C22×C3C22×C4×D511yescharacteristic
768C22×C3C2×#70911yescharacteristic
769C22×C3C2×D4×D511yescharacteristic
770C22×C3C2×#71111yescharacteristic
771C22×C3D5×#4111yescharacteristic
772C22×C3D5×#4111yescharacteristic
773C22×C3C22×C22⋊D511yescharacteristic
774C2×D3—22no—
775C2×D3—22no—
776C2×D3—22no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4—102no—
784C3×C4—102no—
785C3×C4—102no—
786Dic3—22no—
787Dic3—22no—
788Dic3—54no—
789Dic3—102no—
790Dic3—201no—
791Dic3—201no—
792Dic3#408514yescomplemented
793C2×C5—24no—
794C2×C5—122no—
795C2×C5C2×#67⋊C411yescharacteristic
796C2×C5C4×#23711yescharacteristic
797C2×C5C4×D3×D411yescharacteristic
798C2×C5#558611yescharacteristic
799C2×C5#559611yescharacteristic
800C2×C5D3×#12111yescharacteristic
801C2×C5#564911yescharacteristic
802D5—42no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—32no—
808C23—52no—
809C23—61no—
810C23—61no—
811C23—61no—
812C23—61no—
813C23—61no—
814C23—61no—
815C23—101no—
816C23—101no—
817C23—101no—
818C23—101no—
819C23—101no—
820C23—101no—
821C23#676512yes—
822C23C4×D3×D512yes—
823C23D3×C22⋊D512yes—
824C23C22×D3×D511yescharacteristic
825D4—68no—
826D4—108no—
827D4—308no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—32no—
835C2×C4—32no—
836C2×C4—32no—
837C2×C4—32no—
838C2×C4—32no—
839C2×C4—52no—
840C2×C4—52no—
841C2×C4—52no—
842C2×C4—68no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—108no—
848C2×C4—101no—
849C2×C4—101no—
850C2×C4—101no—
851C2×C4—101no—
852C2×C4—101no—
853C2×C4—101no—
854C2×C4—124no—
855C2×C4—152no—
856C2×C4—152no—
857C2×C4—152no—
858C2×C4—152no—
859C2×C4—308no—
860C2×C4—301no—
861C2×C4—301no—
862C2×C4—301no—
863C2×C4—301no—
864C2×C4—301no—
865C2×C4—301no—
866C2×C4—301no—
867C2×C4—301no—
868C2×C4—604no—
869C2×C3—24no—
870C2×C3—202no—
871C2×C3C4×#71111yescharacteristic
872C2×C3#6587211yescharacteristic
873C2×C3C4×D4×D511yescharacteristic
874C2×C3#6588111yescharacteristic
875C2×C3C2×C4×C22⋊D511yescharacteristic
876C2×C3C2×#408511yescharacteristic
877C2×C3#6616611yescharacteristic
878D3—42no—
879C5#7466011yescharacteristic, complemented, Sylow
880C22—22no—
881C22—22no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—62no—
887C22—62no—
888C22—62no—
889C22—102no—
890C22—102no—
891C22—102no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—201no—
897C22—201no—
898C22—201no—
899C22—201no—
900C22#9144114yescomplemented
901C22C2×#676511yescharacteristic
902C22C2×C4×D3×D511yescharacteristic
903C22D3×D4×D511yescharacteristic
904C22D5×#23711yescharacteristic
905C22D3×#71111yescharacteristic
906C22#9202411yescharacteristic
907C22C2×D3×C22⋊D511yescharacteristic
908C4—34no—
909C4—41no—
910C4—41no—
911C4—62no—
912C4—62no—
913C4—102no—
914C4—102no—
915C4—102no—
916C4—154no—
917C4—302no—
918C4—601no—
919C4—601no—
920C3C4×#408511yescharacteristic, complemented, Sylow
921C2—24no—
922C2—122no—
923C2—202no—
924C2#1175282011yescharacteristic
925C2#1175282711yescharacteristic
926C2#1175298211yescharacteristic
927C2#1175320311yescharacteristic
928C2C2×#9144111yescharacteristic
929C2#1175480311yescharacteristic
930C2D3×#408511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91571C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C4×#121
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
1. C2×C5×#67⋊C4C2semidirect
3. C2×Dic3×C22⋊D5C2semidirect
4. C22×Dic3×Dic5C2semidirect
5. C2×#91441C2semidirect
6. #11751043C2semidirect
7. C3×#65247C2semidirect
8. #11749492C2semidirect
9. #11748916C2semidirect
10. Dic3×#685C2semidirect
11. #11748723C2semidirect
12. #11748719C2semidirect
13. #11748711C2semidirect
14. #11748645C2semidirect
15. #11748633C2semidirect
35. #91571C4semidirect
67. #65247D3semidirect
80. C22×Dic15C2×C4semidirect
87. C2×C5×#67C2×C4semidirect
90. C22×C5×Dic3D4semidirect
99. C2×C3×C22⋊D5C2×C4semidirect
108. C2×#1201C2×C4semidirect
121. #6669C2×C4semidirect
125. (C2×D3)⋊Dic5C2×C4semidirect
127. #6665C2×C4semidirect
132. Dic3×Dic5D4semidirect
137. C2×#67⋊C4D5semidirect
317. C2×C22⋊D5C4×D3semidirect
376. C22×C3×C5C4×D4semidirect
403. Dic15C4×D4semidirect
409. C5×Dic3#121semidirect
429. C2×#67C4×D5semidirect
442. C22×Dic3C22⋊D5semidirect
665. C22×C5#67⋊C4semidirect
752. C3×C5C4×#121semidirect
766. C22×C3C4×C22⋊D5semidirect
792. Dic3#4085semidirect
879. C5#74660semidirect
900. C22#91441semidirect
920. C3C4×#4085semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#67⋊C42
C2×#915712
C2×Dic3×C22⋊D52
C22×Dic3×Dic52
C2×#914412
#117510432
C3×#652472
#117494922
#117489162
Dic3×#6852
#117487232
#117487192
#117487112
#117486452
#117486332
C4×#40853
#746605