Finite Group Databasebeta

← #14323380

Subgroups — #14323380

Order 1920.

1616 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4039C211yesmaximal, characteristic, complemented
2C2×#91474C211yesmaximal, characteristic
3C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4#11751091C211yesmaximal, characteristic, complemented
5C5×#4990C211yesmaximal, characteristic, complemented
6#11748940C211yesmaximal, characteristic, complemented
7#11748915C211yesmaximal, characteristic, complemented
8#11748912C211yesmaximal, characteristic, complemented
9#11748907C211yesmaximal, characteristic, complemented
10#11748905C211yesmaximal, characteristic, complemented
11#11748896C211yesmaximal, characteristic, complemented
12#11748890C211yesmaximal, characteristic, complemented
13#11748829C211yesmaximal, characteristic, complemented
14#11748747C211yesmaximal, characteristic, complemented
15C4×#6665C211yesmaximal, characteristic, complemented
16#10607557—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C3×D20C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic, complemented
21C22×#1202C2211yescharacteristic
22C22×#1201C2211yescharacteristic
23C22×D5×Dic3C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
25C2×#6714C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×C4×Dic15C2211yescharacteristic, complemented
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C4×C5×Dic3C2211yescharacteristic, complemented
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic, complemented
35C2×C3×C4×Dic5C2211yescharacteristic, complemented
36C3×#4039—24no—
37C2×Dic3⋊Dic5C2211yescharacteristic, complemented
38C2×#6669C2211yescharacteristic, complemented
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×#6665C2211yescharacteristic
45C2×#6665C2211yescharacteristic, complemented
46C2×#6665C2211yescharacteristic, complemented
47#91474C418yescomplemented
48D5×(C2×D3)⋊C4—24no—
49#91115C2211yescharacteristic, complemented
50#91115C2211yescharacteristic, complemented
51C5×C3⋊#95C2211yescharacteristic, complemented
52C5×C3⋊#95C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#82395—51nomaximal, Hall
56C2×#4039D311yescharacteristic, complemented
57C2×#4028—31no—
58C2×D5×C22⋊C4—31no—
59C5×#388—31no—
60#65279—31no—
61#65246—31no—
62#65245—31no—
63#65244—31no—
64#65240—31no—
65#65228—31no—
66C4×#685—31no—
67#64958—31no—
68#64957—31no—
69#64954—31no—
70#64954—31no—
71C23×D15C2311yescharacteristic
72C23×C5×D3C2311yescharacteristic
73C23×C3×D5C2311yescharacteristic
74C23×C3×D5C2311yescharacteristic
75C22×D3×D5—22no—
76C22×D3×D5—22no—
77C22×D3×D5—41no—
78C22×D3×D5—41no—
79C22×D3×D5—41no—
80C22×D3×D5—41no—
81C22×D3×D5C2×C414yescomplemented
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C2×C3×D20—22no—
94C2×C3×D20—22no—
95C2×C3×D20C2×C414yes—
96C2×C3×C4×D5—22no—
97C2×C3×C4×D5—41no—
98C2×C3×C4×D5—41no—
99C2×C3×C4×D5—41no—
100C2×C3×C4×D5—41no—
101C2×C3×C4×D5D414yescomplemented
102C2×#1202—41no—
103C2×#1202—41no—
104C2×#1202C2×C414yescomplemented
105C2×#1201—41no—
106C2×#1201—41no—
107C2×#1201C2×C414yescomplemented
108C2×D5×Dic3—22no—
109C2×D5×Dic3—41no—
110C2×D5×Dic3—41no—
111C3×C5×C4⋊C4—22no—
112#6714—22no—
113#6714—41no—
114#6714C2×C414yescomplemented
115C4×Dic15—41no—
116C5×(C2×D3)⋊C4—22no—
117C5×(C2×D3)⋊C4—41no—
118C5×(C2×D3)⋊C4C2×C414yescomplemented
119C4×C5×Dic3—41no—
120C3×#685—22no—
121C3×#685—22no—
122C3×C4×Dic5—22no—
123Dic3⋊Dic5—41no—
124#6669—41no—
125#6667—22no—
126#6667—41no—
127(C2×D3)⋊Dic5—22no—
128(C2×D3)⋊Dic5—41no—
129#6665—22no—
130#6665—41no—
131#6665—41no—
132#6665C2×C414yescomplemented
133C2×C3×C4×D4—51no—
134C2×#937—51no—
135C22×(C2×D3)⋊C4—51no—
136#5220—51no—
137#5213—51no—
138#5213—51no—
139C4×#217—51no—
140#4990—51no—
141#4990D511yescharacteristic, complemented
142#4957—51no—
143#4957—51no—
144#4955—51no—
145#4946—51no—
146#4940—51no—
147#4940—51no—
148C24×D5—31no—
149C22×C22⋊D5—31no—
150C22×D20—31no—
151C22×D20C2×D311yescharacteristic
152C22×C4×D5—31no—
153C22×C4×D5C2×D311yescharacteristic
154C22×C4×D5C2×D311yescharacteristic, complemented
155C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
156C2×C5×C22⋊C4—31no—
157C2×C5×C22⋊C4—31no—
158C2×C5×C22⋊C4—31no—
159C2×C42×C5—31no—
160C2×C22⋊Dic5—31no—
161C2×C22⋊Dic5—31no—
162C2×#685—31no—
163C2×#685—31no—
164C2×#685—31no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685—31no—
170C2×#685—31no—
171C2×#685C2×D311yescharacteristic
172C2×#685C2×D311yescharacteristic, complemented
173C2×C4⋊Dic5—31no—
174C2×#683—31no—
175C2×C4×Dic5—31no—
176C2×C4×Dic5C2×D311yescharacteristic, complemented
177#4039—24no—
178#4028—38no—
179D5×C22⋊C4—64no—
180C5×#95—31no—
181C5×#95—31no—
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#2321—151noSylow
187C23×C3×C5C2411yescharacteristic
188C22×D15—21no—
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—21no—
194C22×D15C22×C412yes—
195C22×C5×D3—21no—
196C22×C5×D3—21no—
197C22×C5×D3—21no—
198C22×C5×D3—21no—
199C22×C5×D3—21no—
200C22×C5×D3—21no—
201C22×C5×D3C22×C412yes—
202C22×C3×D5—21no—
203C22×C3×D5—21no—
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×D5—21no—
211C22×C3×D5—21no—
212C22×C3×D5C22×C412yes—
213C22×C3×D5C22×C412yes—
214C22×C3×D5C2×D412yes—
215C22×C3×D5#4112yes—
216C2×D3×D5—28no—
217C2×D3×D5—44no—
218C2×D3×D5—44no—
219C2×D3×D5—44no—
220C2×D3×D5—44no—
221C2×D3×D5—44no—
222C2×D3×D5—44no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5C22×C412yes—
231C2×C3×C4×C5C2×D412yes—
232C2×Dic15—21no—
233C2×Dic15—21no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236C2×Dic15—21no—
237C2×Dic15—21no—
238C2×Dic15—21no—
239C2×Dic15—21no—
240C2×Dic15C22×C412yes—
241C2×C5×Dic3—21no—
242C2×C5×Dic3—21no—
243C2×C5×Dic3—21no—
244C2×C5×Dic3—21no—
245C2×C5×Dic3—21no—
246C2×C5×Dic3—21no—
247C2×C5×Dic3—21no—
248C2×C5×Dic3—21no—
249C2×C5×Dic3C22×C412yes—
250C2×C3×Dic5—21no—
251C2×C3×Dic5—21no—
252C2×C3×Dic5—21no—
253C2×C3×Dic5—21no—
254C2×C3×Dic5—21no—
255C2×C3×Dic5C2×D412yes—
256C3×D20—28no—
257C3×C4×D5—44no—
258C3×C4×D5—44no—
259#1202—44no—
260#1201—44no—
261D5×Dic3—44no—
262C24×D3—51no—
263C22×C3×D4—51no—
264C23×C3×C4—51no—
265C23×C3×C4—51no—
266C22×#67—51no—
267C22×#67—51no—
268C23×Dic3—51no—
269C3×C4×D4—104no—
270C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
271C2×C3×C22⋊C4—51no—
272C2×C3×C22⋊C4—51no—
273C2×C3×C42—51no—
274C2×#217—51no—
275C2×#217—51no—
276C2×#217—51no—
277C2×#217—51no—
278#937—58no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4—51no—
282C2×(C2×D3)⋊C4—51no—
283C2×(C2×D3)⋊C4—51no—
284C2×(C2×D3)⋊C4—51no—
285C2×(C2×D3)⋊C4—51no—
286C2×(C2×D3)⋊C4—104no—
287C2×(C2×D3)⋊C4C2×D511yescharacteristic
288C2×(C2×D3)⋊C4C2×D511yescharacteristic
289C2×(C2×D3)⋊C4C2×D511yescharacteristic
290C2×Dic3⋊C4—51no—
291C2×Dic3⋊C4—51no—
292C2×C4×Dic3—51no—
293C2×C4×Dic3C2×D511yescharacteristic, complemented
294C3⋊#95—51no—
295C3⋊#95—51no—
296C3⋊#95—51no—
297C3⋊#95—51no—
298C3⋊#95C2×D511yescharacteristic, complemented
299C3⋊#95C2×D511yescharacteristic, complemented
300C24×C5—31no—
301C23×D5—31no—
302C23×D5—34no—
303C23×D5—62no—
304C23×D5—62no—
305C23×D5—121no—
306C23×D5—121no—
307C23×D5—121no—
308C23×D5—121no—
309C23×D5C22×D311yescharacteristic
310C23×D5C22×D311yescharacteristic
311C22×C4×C5—31no—
312C22×C4×C5—31no—
313C22×C4×C5—31no—
314C22×C4×C5C22×D311yescharacteristic
315C22×C4×C5C22×D311yescharacteristic
316C22×C4×C5C22×D311yescharacteristic
317C2×C22⋊D5—34no—
318C2×C22⋊D5—121no—
319C2×C22⋊D5—121no—
320C22×Dic5—31no—
321C22×Dic5—31no—
322C22×Dic5—31no—
323C22×Dic5C22×D311yescharacteristic
324C22×Dic5C22×D311yescharacteristic
325C2×D20—22no—
326C2×D20—22no—
327C2×D20—34no—
328C2×D20—121no—
329C2×D20—121no—
330C2×D20C4×D314yes—
331C2×C4×D5—22no—
332C2×C4×D5—41no—
333C2×C4×D5—41no—
334C2×C4×D5—41no—
335C2×C4×D5—41no—
336C2×C4×D5—62no—
337C2×C4×D5—121no—
338C2×C4×D5—121no—
339C2×C4×D5#6714yescomplemented
340C5×C4⋊C4—22no—
341C5×C22⋊C4—34no—
342C5×C22⋊C4—62no—
343C5×C22⋊C4—121no—
344C42×C5—121no—
345C22⋊Dic5—62no—
346C22⋊Dic5—121no—
347#685—22no—
348#685—22no—
349#685—34no—
350#685—34no—
351#685—62no—
352#685—62no—
353#685—62no—
354#685—121no—
355#685—121no—
356#685—121no—
357#685—121no—
358C4⋊Dic5—121no—
359#683—121no—
360C4×Dic5—22no—
361C4×Dic5—121no—
362C2×#120—151no—
363C2×C4×D4—51no—
364C22×C22⋊C4—151no—
365#390—151no—
366#390—151no—
367#388—31no—
368#388—151no—
369#388—151no—
370#388—151no—
371#386—151no—
372#386—151no—
373#386—151no—
374#385—151no—
375#379—151no—
376C4×C22⋊C4—151no—
377C22×C3×C5C23×C411yescharacteristic
378C22×C3×C5C22×D411yescharacteristic
379C22×C3×C5C2×#4111yescharacteristic
380C22×C3×C5H(5,𝔽2)11yescharacteristic
381C22×C3×C5H(5,𝔽2)11yescharacteristic
382C22×C3×C5H(5,𝔽2)11yescharacteristic
383C22×C3×C5H(5,𝔽2)11yescharacteristic
384C2×D15—22no—
385C2×D15—22no—
386C2×D15—22no—
387C2×D15—41no—
388C2×D15—41no—
389C2×D15—41no—
390C2×D15—41no—
391C2×C5×D3—22no—
392C2×C5×D3—22no—
393C2×C5×D3—22no—
394C2×C5×D3—41no—
395C2×C5×D3—41no—
396C2×C5×D3—41no—
397C2×C5×D3—41no—
398C2×C3×D5—22no—
399C2×C3×D5—22no—
400C2×C3×D5—22no—
401C2×C3×D5—22no—
402C2×C3×D5—22no—
403C2×C3×D5—22no—
404C2×C3×D5—22no—
405C2×C3×D5—22no—
406C2×C3×D5—22no—
407C2×C3×D5—41no—
408C2×C3×D5—41no—
409C2×C3×D5—41no—
410C2×C3×D5—41no—
411C2×C3×D5C4×D414yes—
412D3×D5—416no—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415C3×C4×C5—41no—
416Dic15—22no—
417Dic15—41no—
418Dic15—41no—
419C3×Dic5—22no—
420C3×Dic5—41no—
421C5×Dic3—22no—
422C5×Dic3—41no—
423C5×Dic3—41no—
424C24×C3—51no—
425C24×C3—51no—
426C23×D3—51no—
427C23×D3—54no—
428C23×D3—102no—
429C23×D3—102no—
430C23×D3—201no—
431C23×D3—201no—
432C23×D3—201no—
433C23×D3—201no—
434C23×D3C22×D511yescharacteristic
435C2×C3×D4—54no—
436C2×C3×D4—102no—
437C2×C3×D4—102no—
438C22×C3×C4—51no—
439C22×C3×C4—54no—
440C22×C3×C4—51no—
441C22×C3×C4—102no—
442C22×C3×C4—201no—
443C22×C3×C4—201no—
444C22×C3×C4—201no—
445C22×C3×C4—201no—
446C22×C3×C4C22×D511yescharacteristic
447C22×C3×C4C22×D511yescharacteristic
448C22×C3×C4C22×D511yescharacteristic
449C2×#67—54no—
450C2×#67—54no—
451C2×#67—201no—
452C2×#67—201no—
453C2×#67—201no—
454C2×#67—201no—
455C22×Dic3—51no—
456C22×Dic3—51no—
457C22×Dic3—51no—
458C22×Dic3—102no—
459C22×Dic3—201no—
460C22×Dic3—201no—
461C22×Dic3C22×D511yescharacteristic
462C22×Dic3C22×D511yescharacteristic
463C22×Dic3C22×D511yescharacteristic
464C3×C4⋊C4—22no—
465C3×C22⋊C4—102no—
466C3×C22⋊C4—102no—
467C3×C42—102no—
468#217—54no—
469#217—102no—
470#217—201no—
471#217—201no—
472(C2×D3)⋊C4—22no—
473(C2×D3)⋊C4—41no—
474(C2×D3)⋊C4—54no—
475(C2×D3)⋊C4—102no—
476(C2×D3)⋊C4—102no—
477(C2×D3)⋊C4—102no—
478(C2×D3)⋊C4—201no—
479(C2×D3)⋊C4—201no—
480(C2×D3)⋊C4—201no—
481(C2×D3)⋊C4C4×D514yescomplemented
482Dic3⋊C4—201no—
483Dic3⋊C4—201no—
484C4×Dic3—41no—
485C4×Dic3—201no—
486C23×C5—32no—
487C23×C5—61no—
488C23×C5—61no—
489C23×C5—61no—
490C23×C5—61no—
491C23×C5—61no—
492C23×C5—61no—
493C23×C5C23×D311yescharacteristic
494C22×D5—21no—
495C22×D5—21no—
496C22×D5—21no—
497C22×D5—21no—
498C22×D5—21no—
499C22×D5—21no—
500C22×D5—21no—
501C22×D5—21no—
502C22×D5—21no—
503C22×D5—21no—
504C22×D5—32no—
505C22×D5—61no—
506C22×D5—61no—
507C22×D5—61no—
508C22×D5—61no—
509C22×D5—61no—
510C22×D5—61no—
511C22×D5—68no—
512C22×D5—124no—
513C22×D5—124no—
514C22×D5—124no—
515C22×D5—124no—
516C22×D5—124no—
517C22×D5—124no—
518C22×D5C2×C4×D312yes—
519C22×D5C2×C4×D312yes—
520C22×D5#23512yes—
521C22×D5C2×#6712yes—
522C2×C4×C5—21no—
523C2×C4×C5—21no—
524C2×C4×C5—21no—
525C2×C4×C5—21no—
526C2×C4×C5—21no—
527C2×C4×C5—21no—
528C2×C4×C5—21no—
529C2×C4×C5—32no—
530C2×C4×C5—61no—
531C2×C4×C5—61no—
532C2×C4×C5—61no—
533C2×C4×C5—61no—
534C2×C4×C5—61no—
535C2×C4×C5—61no—
536C2×C4×C5—61no—
537C2×C4×C5—61no—
538C2×C4×C5C2×C4×D312yes—
539C2×C4×C5C2×#6712yes—
540C22⋊D5—124no—
541C2×Dic5—21no—
542C2×Dic5—21no—
543C2×Dic5—21no—
544C2×Dic5—21no—
545C2×Dic5—21no—
546C2×Dic5—32no—
547C2×Dic5—61no—
548C2×Dic5—61no—
549C2×Dic5—61no—
550C2×Dic5—61no—
551C2×Dic5—61no—
552C2×Dic5—61no—
553C2×Dic5—61no—
554C2×Dic5—61no—
555C2×Dic5C2×#6712yes—
556D20—28no—
557D20—124no—
558C4×D5—44no—
559C4×D5—44no—
560C4×D5—124no—
561C25—151no—
562C22×D4—51no—
563C22×D4—151no—
564C22×D4—151no—
565C23×C4—51no—
566C23×C4—51no—
567C23×C4—151no—
568#120—158no—
569C4×D4—104no—
570C2×C4⋊C4—151no—
571C2×C4⋊C4—151no—
572C2×C4⋊C4D3×D511yescharacteristic, complemented
573C2×C22⋊C4—31no—
574C2×C22⋊C4—31no—
575C2×C22⋊C4—31no—
576C2×C22⋊C4—51no—
577C2×C22⋊C4—51no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—151no—
584C2×C22⋊C4—151no—
585C2×C22⋊C4—151no—
586C2×C22⋊C4—151no—
587C2×C22⋊C4—151no—
588C2×C22⋊C4—151no—
589C2×C22⋊C4—304no—
590C2×C42—31no—
591C2×C42—51no—
592C2×C42—151no—
593#95—31no—
594#95—31no—
595#95—151no—
596#95—151no—
597#95—151no—
598#95—151no—
599C2×C3×C5C2×C4×D411yescharacteristic
600C2×C3×C5#51811yescharacteristic
601C2×C3×C5#51811yescharacteristic
602C2×C3×C5#53411yescharacteristic
603C2×C3×C5#53511yescharacteristic
604C2×C3×C5#53811yescharacteristic
605C2×C3×C5#53811yescharacteristic
606D15—42no—
607C3×D5—24no—
608C3×D5—42no—
609C5×D3—42no—
610C23×C3—52no—
611C23×C3—52no—
612C23×C3—52no—
613C23×C3—52no—
614C23×C3—101no—
615C23×C3—101no—
616C23×C3—101no—
617C23×C3—101no—
618C23×C3—101no—
619C23×C3—101no—
620C23×C3—101no—
621C23×C3—101no—
622C23×C3—101no—
623C23×C3—101no—
624C23×C3C23×D511yescharacteristic
625C22×D3—21no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—21no—
630C22×D3—21no—
631C22×D3—52no—
632C22×D3—108no—
633C22×D3—101no—
634C22×D3—101no—
635C22×D3—101no—
636C22×D3—101no—
637C22×D3—101no—
638C22×D3—101no—
639C22×D3—204no—
640C22×D3—204no—
641C22×D3—204no—
642C22×D3—204no—
643C22×D3—204no—
644C22×D3—204no—
645C22×D3C2×C4×D512yes—
646C3×D4—108no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—52no—
655C2×C3×C4—101no—
656C2×C3×C4—101no—
657C2×C3×C4—101no—
658C2×C3×C4—101no—
659C2×C3×C4—101no—
660C2×C3×C4—204no—
661C2×C3×C4—204no—
662C2×C3×C4C2×C4×D512yes—
663C2×C3×C4D4×D512yes—
664#67—204no—
665#67—204no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—21no—
671C2×Dic3—21no—
672C2×Dic3—21no—
673C2×Dic3—21no—
674C2×Dic3—52no—
675C2×Dic3—101no—
676C2×Dic3—101no—
677C2×Dic3—101no—
678C2×Dic3—101no—
679C2×Dic3—101no—
680C2×Dic3—101no—
681C2×Dic3—101no—
682C2×Dic3—101no—
683C2×Dic3—204no—
684C2×Dic3C2×C4×D512yes—
685C22×C5—62no—
686C22×C5—62no—
687C22×C5—62no—
688C22×C5—121no—
689C22×C5—121no—
690C22×C5—121no—
691C22×C5—121no—
692C22×C5C22×C4×D311yescharacteristic
693C22×C5C2×#23511yescharacteristic
694C22×C5#100411yescharacteristic
695C22×C5#100411yescharacteristic
696C22×C5#100911yescharacteristic
697C22×C5#100911yescharacteristic
698C22×C5C22×#6711yescharacteristic
699C2×D5—22no—
700C2×D5—22no—
701C2×D5—22no—
702C2×D5—22no—
703C2×D5—22no—
704C2×D5—22no—
705C2×D5—22no—
706C2×D5—22no—
707C2×D5—22no—
708C2×D5—41no—
709C2×D5—41no—
710C2×D5—41no—
711C2×D5—41no—
712C2×D5—62no—
713C2×D5—62no—
714C2×D5—62no—
715C2×D5—1216no—
716C2×D5—121no—
717C2×D5—121no—
718C2×D5—121no—
719C2×D5—121no—
720C2×D5C4×#6714yes—
721C4×C5—22no—
722C4×C5—22no—
723C4×C5—41no—
724C4×C5—62no—
725C4×C5—121no—
726C4×C5—121no—
727Dic5—22no—
728Dic5—41no—
729Dic5—62no—
730Dic5—121no—
731Dic5—121no—
732C24—31no—
733C24—51no—
734C24—51no—
735C24—154no—
736C24—151no—
737C24—302no—
738C24—302no—
739C24—601no—
740C24—601no—
741C24—601no—
742C24—601no—
743C2×D4—54no—
744C2×D4—102no—
745C2×D4—102no—
746C2×D4—154no—
747C2×D4—154no—
748C2×D4—601no—
749C2×D4—601no—
750C2×D4—601no—
751C2×D4—601no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—51no—
756C22×C4—54no—
757C22×C4—51no—
758C22×C4—102no—
759C22×C4—151no—
760C22×C4—151no—
761C22×C4—151no—
762C22×C4—201no—
763C22×C4—201no—
764C22×C4—201no—
765C22×C4—201no—
766C22×C4—302no—
767C22×C4—601no—
768C22×C4—601no—
769C22×C4C2×D3×D511yescharacteristic
770C22×C4C2×D3×D511yescharacteristic
771C22×C4C2×D3×D511yescharacteristic
772C4⋊C4—22no—
773C4⋊C4—601no—
774C4⋊C4—601no—
775C22⋊C4—34no—
776C22⋊C4—62no—
777C22⋊C4—102no—
778C22⋊C4—102no—
779C22⋊C4—121no—
780C22⋊C4—154no—
781C22⋊C4—154no—
782C22⋊C4—302no—
783C22⋊C4—302no—
784C22⋊C4—302no—
785C22⋊C4—302no—
786C22⋊C4—601no—
787C22⋊C4—601no—
788C22⋊C4—601no—
789C22⋊C4—601no—
790C22⋊C4—601no—
791C42—102no—
792C42—121no—
793C42—601no—
794C3×C5#232111yescharacteristic, complemented, Hall
795C22×C3—54no—
796C22×C3—102no—
797C22×C3—102no—
798C22×C3—102no—
799C22×C3—102no—
800C22×C3—102no—
801C22×C3—102no—
802C22×C3—102no—
803C22×C3—102no—
804C22×C3—102no—
805C22×C3—201no—
806C22×C3—201no—
807C22×C3—201no—
808C22×C3—201no—
809C22×C3C22×C4×D511yescharacteristic
810C22×C3C2×D4×D511yescharacteristic
811C22×C3#414411yescharacteristic
812C22×C3D5×#4111yescharacteristic
813C22×C3#414911yescharacteristic
814C22×C3#414911yescharacteristic
815C22×C3#414911yescharacteristic
816C2×D3—22no—
817C2×D3—22no—
818C2×D3—22no—
819C2×D3—41no—
820C2×D3—41no—
821C2×D3—41no—
822C2×D3—41no—
823C2×D3—102no—
824C2×D3—102no—
825C2×D3—102no—
826C2×D3—2016no—
827C2×D3—201no—
828C2×D3—201no—
829C2×D3—201no—
830C2×D3—201no—
831C3×C4—22no—
832C3×C4—22no—
833C3×C4—41no—
834C3×C4—102no—
835C3×C4—201no—
836Dic3—22no—
837Dic3—41no—
838Dic3—41no—
839Dic3—102no—
840Dic3—201no—
841Dic3—201no—
842C2×C5—122no—
843C2×C5#554511yescharacteristic
844C2×C5#554511yescharacteristic
845C2×C5#556011yescharacteristic
846C2×C5#556011yescharacteristic
847C2×C5C2×C4×#6711yescharacteristic
848C2×C5#580411yescharacteristic
849C2×C5#583011yescharacteristic
850D5—24no—
851D5—42no—
852D5—122no—
853C23—32no—
854C23—52no—
855C23—52no—
856C23—52no—
857C23—52no—
858C23—61no—
859C23—61no—
860C23—61no—
861C23—61no—
862C23—61no—
863C23—61no—
864C23—101no—
865C23—101no—
866C23—101no—
867C23—101no—
868C23—101no—
869C23—101no—
870C23—101no—
871C23—101no—
872C23—101no—
873C23—101no—
874C23—152no—
875C23—308no—
876C23—301no—
877C23—301no—
878C23—301no—
879C23—301no—
880C23—301no—
881C23—301no—
882C23—604no—
883C23—604no—
884C23—604no—
885C23—604no—
886C23—604no—
887C23—604no—
888C23C22×D3×D511yescharacteristic
889D4—108no—
890D4—604no—
891D4—604no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—32no—
900C2×C4—52no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—61no—
907C2×C4—61no—
908C2×C4—61no—
909C2×C4—101no—
910C2×C4—101no—
911C2×C4—101no—
912C2×C4—101no—
913C2×C4—101no—
914C2×C4—152no—
915C2×C4—204no—
916C2×C4—204no—
917C2×C4—301no—
918C2×C4—301no—
919C2×C4—301no—
920C2×C4—301no—
921C2×C4—301no—
922C2×C4—301no—
923C2×C4—301no—
924C2×C4—301no—
925C2×C4—604no—
926C2×C4C4×D3×D512yes—
927C2×C4D5×#6712yes—
928C2×C3—104no—
929C2×C3—202no—
930C2×C3#6585511yescharacteristic
931C2×C3C4×D4×D511yescharacteristic
932C2×C3#6587911yescharacteristic
933C2×C3#6593911yescharacteristic
934C2×C3#6599111yescharacteristic
935C2×C3#6600811yescharacteristic
936C2×C3#6603811yescharacteristic
937D3—42no—
938D3—202no—
939C5#8239511yescharacteristic, complemented, Sylow
940C22—54no—
941C22—62no—
942C22—62no—
943C22—62no—
944C22—102no—
945C22—102no—
946C22—102no—
947C22—102no—
948C22—102no—
949C22—102no—
950C22—102no—
951C22—102no—
952C22—102no—
953C22—121no—
954C22—121no—
955C22—121no—
956C22—121no—
957C22—201no—
958C22—201no—
959C22—201no—
960C22—201no—
961C22—302no—
962C22—302no—
963C22—302no—
964C22—6016no—
965C22—601no—
966C22—601no—
967C22—601no—
968C22—601no—
969C22C2×C4×D3×D511yescharacteristic
970C22D5×#23511yescharacteristic
971C22#9202511yescharacteristic
972C22#9202611yescharacteristic
973C22#9203511yescharacteristic
974C22#9203511yescharacteristic
975C22C2×D5×#6711yescharacteristic
976C4—22no—
977C4—22no—
978C4—41no—
979C4—62no—
980C4—102no—
981C4—121no—
982C4—121no—
983C4—201no—
984C4—302no—
985C4—601no—
986C4—601no—
987C3#1060755711yescharacteristic, complemented, Sylow
988C2—104no—
989C2—122no—
990C2—202no—
991C2—602no—
992C2#1175383911yescharacteristic
993C2#1175384111yescharacteristic
994C2#1175389411yescharacteristic
995C2#1175389511yescharacteristic
996C2C4×D5×#6711yescharacteristic
997C2#1175506111yescharacteristic
998C2#1175527211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91474C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2321
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
1. C2×C3×#4039C2semidirect
3. C2×D5×(C2×D3)⋊C4C2semidirect
4. #11751091C2semidirect
5. C5×#4990C2semidirect
6. #11748940C2semidirect
7. #11748915C2semidirect
8. #11748912C2semidirect
9. #11748907C2semidirect
10. #11748905C2semidirect
11. #11748896C2semidirect
12. #11748890C2semidirect
13. #11748829C2semidirect
14. #11748747C2semidirect
15. C4×#6665C2semidirect
20. C22×C3×C4×D5C22semidirect
24. C2×C3×C5×C4⋊C4C22semidirect
28. C2×C4×Dic15C22semidirect
32. C2×C4×C5×Dic3C22semidirect
34. C2×C3×#685C22semidirect
35. C2×C3×C4×Dic5C22semidirect
37. C2×Dic3⋊Dic5C22semidirect
38. C2×#6669C22semidirect
45. C2×#6665C22semidirect
46. C2×#6665C22semidirect
47. #91474C4semidirect
49. #91115C22semidirect
50. #91115C22semidirect
51. C5×C3⋊#95C22semidirect
52. C5×C3⋊#95C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
56. C2×#4039D3semidirect
81. C22×D3×D5C2×C4semidirect
101. C2×C3×C4×D5D4semidirect
104. C2×#1202C2×C4semidirect
107. C2×#1201C2×C4semidirect
114. #6714C2×C4semidirect
118. C5×(C2×D3)⋊C4C2×C4semidirect
132. #6665C2×C4semidirect
141. #4990D5semidirect
154. C22×C4×D5C2×D3semidirect
155. C2×C5×C4⋊C4C2×D3semidirect
172. C2×#685C2×D3semidirect
176. C2×C4×Dic5C2×D3semidirect
270. C2×C3×C4⋊C4C2×D5semidirect
293. C2×C4×Dic3C2×D5semidirect
298. C3⋊#95C2×D5semidirect
299. C3⋊#95C2×D5semidirect
339. C2×C4×D5#67semidirect
481. (C2×D3)⋊C4C4×D5semidirect
572. C2×C4⋊C4D3×D5semidirect
794. C3×C5#2321semidirect
939. C5#82395semidirect
987. C3#10607557semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40392
C2×#914742
C2×D5×(C2×D3)⋊C42
#117510912
C5×#49902
#117489402
#117489152
#117489122
#117489072
#117489052
#117488962
#117488902
#117488292
#117487472
C4×#66652
#106075573
#823955