Finite Group Databasebeta

← #14322821

Subgroups — #14322821

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#11750769C211yesmaximal, characteristic, complemented
5C5×#4667C211yesmaximal, characteristic, complemented
6C3×#64957C211yesmaximal, characteristic, complemented
7#11748900C211yesmaximal, characteristic, complemented
8#11748898C211yesmaximal, characteristic, complemented
9#11748894C211yesmaximal, characteristic, complemented
10#11748891C211yesmaximal, characteristic, complemented
11#11748887C211yesmaximal, characteristic, complemented
12#11748874C211yesmaximal, characteristic, complemented
13#11748786C211yesmaximal, characteristic, complemented
14#11748731C211yesmaximal, characteristic, complemented
15#11748703C211yesmaximal, characteristic, complemented
16#10605736—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×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×C4⋊Dic15C2211yescharacteristic, complemented
27C2×#6712C2211yescharacteristic, complemented
28C2×C5×(C2×D3)⋊C4C2211yescharacteristic
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic
30C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
31C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
35C2×C3×#683C2211yescharacteristic, complemented
36C2×#6669C2211yescharacteristic, complemented
37C2×#6668C2211yescharacteristic, complemented
38C2×#6667C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44#91473—24no—
45D3×#685C418yescomplemented
46D5×(C2×D3)⋊C4—24no—
47C3×C5×#95C2211yescharacteristic, complemented
48#91115C2211yescharacteristic, complemented
49C5×C3⋊#95C2211yescharacteristic, complemented
50C3×#3963C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#74591—51nomaximal, Hall
56C22×#685—31no—
57C2×D5×C22⋊C4—31no—
58C2×D5×C22⋊C4—31no—
59C5×#380—31no—
60#65501—31no—
61#65278—31no—
62#65278—31no—
63#65278—31no—
64#65278—31no—
65#65231—31no—
66#65231—31no—
67#64957—31no—
68#64957—31no—
69#64957—31no—
70#64957D311yescharacteristic, complemented
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—41no—
94C2×C4×C5×D3—41no—
95C2×C4×C5×D3C2×C414yescomplemented
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C2×C3×C4×D5—22no—
100C2×C3×C4×D5—41no—
101C2×C3×C4×D5—41no—
102C2×#1200—22no—
103C2×#1200—41no—
104C2×#1200—41no—
105C2×D3×Dic5—41no—
106C2×D3×Dic5—41no—
107C2×D3×Dic5C2×C414yescomplemented
108C2×D5×Dic3—22no—
109C2×D5×Dic3—41no—
110C2×D5×Dic3—41no—
111#6714—22no—
112#6714C2×C414yescomplemented
113C4⋊Dic15—41no—
114#6712—41no—
115C5×(C2×D3)⋊C4—22no—
116C5×(C2×D3)⋊C4—22no—
117C5×Dic3⋊C4—41no—
118C5×Dic3⋊C4—41no—
119C3×#685—22no—
120C3×#685C2×C414yescomplemented
121C3×C4⋊Dic5—41no—
122C3×#683—41no—
123#6669—41no—
124#6668—41no—
125#6667—22no—
126#6667C2×C414yescomplemented
127(C2×D3)⋊Dic5—22no—
128(C2×D3)⋊Dic5—22no—
129#6665—22no—
130#6665C2×C414yescomplemented
131C22×(C2×D3)⋊C4—51no—
132C2×D3×C22⋊C4—51no—
133C2×D3×C22⋊C4—51no—
134C3×#385—51no—
135#5210—51no—
136#4989—51no—
137#4989—51no—
138#4987—51no—
139#4987—51no—
140#4950—51no—
141#4946—51no—
142#4668—51no—
143#4668—51no—
144#4667—51no—
145#4667D511yescharacteristic, complemented
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⋊C4—31no—
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—38no—
163C2×#685—31no—
164C2×#685—31no—
165C2×#685—31no—
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×#683C2×D311yescharacteristic, complemented
174D5×C22⋊C4—64no—
175D5×C22⋊C4—64no—
176C5×#95—31no—
177C5×#95C2×D311yescharacteristic, complemented
178#3963—31no—
179#3963—31no—
180#3963—31no—
181#3963—31no—
182#3963—31no—
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⋊C4—51no—
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—51no—
273C2×(C2×D3)⋊C4—51no—
274C2×(C2×D3)⋊C4—51no—
275C2×(C2×D3)⋊C4—104no—
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⋊C4C2×D511yescharacteristic, complemented
283C2×Dic3⋊C4C2×D511yescharacteristic, complemented
284D3×C22⋊C4—58no—
285D3×C22⋊C4—104no—
286C3×#95—51no—
287C3×#95C2×D511yescharacteristic, complemented
288C3⋊#95—51no—
289C3⋊#95—51no—
290C3⋊#95—51no—
291C3⋊#95—51no—
292C3⋊#95—51no—
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—34no—
306C22×C4×C5—31no—
307C22×C4×C5—31no—
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—34no—
315C22×Dic5—31no—
316C22×Dic5—31no—
317C22×Dic5—121no—
318C22×Dic5—121no—
319C22×Dic5C22×D311yescharacteristic
320C22×Dic5C22×D311yescharacteristic
321C22×Dic5C22×D311yescharacteristic
322C2×C4×D5—22no—
323C2×C4×D5—41no—
324C2×C4×D5—41no—
325C2×C4×D5—62no—
326C2×C4×D5—62no—
327C2×C4×D5—62no—
328C2×C4×D5—121no—
329C2×C4×D5—121no—
330C2×C4×D5—121no—
331C2×C4×D5—121no—
332C2×C4×D5—121no—
333C2×C4×D5—121no—
334C5×C4⋊C4—121no—
335C5×C4⋊C4—121no—
336C5×C22⋊C4—62no—
337C5×C22⋊C4—62no—
338C22⋊Dic5—62no—
339C22⋊Dic5—62no—
340#685—22no—
341#685—34no—
342#685—34no—
343#685—34no—
344#685—62no—
345#685—62no—
346#685—62no—
347#685C4×D314yescomplemented
348C4⋊Dic5—41no—
349C4⋊Dic5—121no—
350#683—41no—
351#683—121no—
352#683—121no—
353#683—121no—
354C22×C22⋊C4—151no—
355C22×C22⋊C4—151no—
356C22×C22⋊C4—151no—
357#385—51no—
358#385—151no—
359#385—151no—
360#385—151no—
361#385—151no—
362#385—151no—
363#385—151no—
364#385—151no—
365#380—31no—
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—51no—
422C22×C3×C4—51no—
423C22×C3×C4—102no—
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—51no—
431C22×Dic3—51no—
432C22×Dic3—102no—
433C22×Dic3—201no—
434C22×Dic3—201no—
435C22×Dic3C22×D511yescharacteristic
436C22×Dic3C22×D511yescharacteristic
437C22×Dic3C22×D511yescharacteristic
438C2×C4×D3—41no—
439C2×C4×D3—41no—
440C2×C4×D3—54no—
441C2×C4×D3—102no—
442C2×C4×D3—102no—
443C2×C4×D3—201no—
444C2×C4×D3—201no—
445C2×C4×D3—201no—
446C2×C4×D3—201no—
447C2×C4×D3—201no—
448C2×C4×D3—201no—
449C2×C4×D3C4×D514yescomplemented
450C3×C4⋊C4—201no—
451C3×C4⋊C4—201no—
452C3×C22⋊C4—54no—
453C3×C22⋊C4—102no—
454#217—54no—
455#217—102no—
456(C2×D3)⋊C4—22no—
457(C2×D3)⋊C4—22no—
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)⋊C4—102no—
464C4⋊Dic3—201no—
465C4⋊Dic3—201no—
466Dic3⋊C4—41no—
467Dic3⋊C4—41no—
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—31no—
550C2×C4⋊C4—51no—
551C2×C4⋊C4—51no—
552C2×C4⋊C4—151no—
553C2×C4⋊C4—151no—
554C2×C4⋊C4—151no—
555C2×C4⋊C4—151no—
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—51no—
573#95—151no—
574#95—151no—
575#95—151no—
576#95—151no—
577#95—151no—
578#95D3×D511yescharacteristic, complemented
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—34no—
713C22×C4—31no—
714C22×C4—31no—
715C22×C4—51no—
716C22×C4—51no—
717C22×C4—51no—
718C22×C4—102no—
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—121no—
742C4⋊C4—121no—
743C4⋊C4—201no—
744C4⋊C4—201no—
745C4⋊C4—601no—
746C4⋊C4—601no—
747C4⋊C4—601no—
748C4⋊C4—601no—
749C22⋊C4—54no—
750C22⋊C4—62no—
751C22⋊C4—62no—
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×C5C2×D3×C4⋊C411yescharacteristic
805C2×C5#554511yescharacteristic
806C2×C5#554511yescharacteristic
807C2×C5#558911yescharacteristic
808C2×C5#563411yescharacteristic
809C2×C5#563411yescharacteristic
810C2×C5#565311yescharacteristic
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×C3#6582011yescharacteristic
886C2×C3C2×D5×C4⋊C411yescharacteristic
887C2×C3#6585511yescharacteristic
888C2×C3#6593911yescharacteristic
889C2×C3#6593911yescharacteristic
890C2×C3#6596811yescharacteristic
891C2×C3#6596811yescharacteristic
892D3—24no—
893D3—104no—
894C5#7459111yescharacteristic, 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
919C22#9201911yescharacteristic
920C22D3×D4×D511yescharacteristic
921C22#9202511yescharacteristic
922C22#9202711yescharacteristic
923C22D3×Q8×D511yescharacteristic
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#1060573611yescharacteristic, complemented, Sylow
937C2—64no—
938C2—104no—
939C2—304no—
940C2#1175272711yescharacteristic
941C2#1175320211yescharacteristic
942C2#1175321311yescharacteristic
943C2#1175321511yescharacteristic
944C2D3×D5×C4⋊C411yescharacteristic
945C2#1175389011yescharacteristic
946C2#1175389211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D3×D5C22
hypercenter#95D3×D5
hypocenterC3×C5#2315
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. #11750769C2semidirect
5. C5×#4667C2semidirect
6. C3×#64957C2semidirect
7. #11748900C2semidirect
8. #11748898C2semidirect
9. #11748894C2semidirect
10. #11748891C2semidirect
11. #11748887C2semidirect
12. #11748874C2semidirect
13. #11748786C2semidirect
14. #11748731C2semidirect
15. #11748703C2semidirect
26. C2×C4⋊Dic15C22semidirect
27. C2×#6712C22semidirect
30. C2×C5×Dic3⋊C4C22semidirect
31. C2×C5×Dic3⋊C4C22semidirect
34. C2×C3×C4⋊Dic5C22semidirect
35. C2×C3×#683C22semidirect
36. C2×#6669C22semidirect
37. C2×#6668C22semidirect
45. D3×#685C4semidirect
47. C3×C5×#95C22semidirect
48. #91115C22semidirect
49. C5×C3⋊#95C22semidirect
50. C3×#3963C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
70. #64957D3semidirect
95. C2×C4×C5×D3C2×C4semidirect
107. C2×D3×Dic5C2×C4semidirect
112. #6714C2×C4semidirect
120. C3×#685C2×C4semidirect
126. #6667C2×C4semidirect
130. #6665C2×C4semidirect
145. #4667D5semidirect
169. C2×C4⋊Dic5C2×D3semidirect
173. C2×#683C2×D3semidirect
177. C5×#95C2×D3semidirect
183. #3963C2×D3semidirect
213. C2×D3×D5C4⋊C4semidirect
282. C2×Dic3⋊C4C2×D5semidirect
283. C2×Dic3⋊C4C2×D5semidirect
287. C3×#95C2×D5semidirect
293. C3⋊#95C2×D5semidirect
347. #685C4×D3semidirect
449. C2×C4×D3C4×D5semidirect
578. #95D3×D5semidirect
761. C3×C5#2315semidirect
894. C5#74591semidirect
936. C3#10605736semidirect

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
#117507692
C5×#46672
C3×#649572
#117489002
#117488982
#117488942
#117488912
#117488872
#117488742
#117487862
#117487312
#117487032
#106057363
#745915