Finite Group Databasebeta

← #67×#685 #14325926

Subgroups — #67×#685 #14325926

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×#67C211yesmaximal, characteristic
2C2×C4×C5×#67C211yesmaximal, characteristic, complemented
3C22×C3×#685C211yesmaximal, characteristic, complemented
4C2×Dic5×#67C211yesmaximal, characteristic, complemented
5C2×D3×#685C211yesmaximal, characteristic, complemented
6#11751314C211yesmaximal, characteristic, complemented
7#11749494C211yesmaximal, characteristic, complemented
8#11749488C211yesmaximal, characteristic, complemented
9#11748940C211yesmaximal, characteristic, complemented
10#11748913C211yesmaximal, characteristic, complemented
11#11748912C211yesmaximal, characteristic, complemented
12#11748911C211yesmaximal, characteristic, complemented
13#11748910C211yesmaximal, characteristic, complemented
14#11748878C211yesmaximal, characteristic, complemented
15Dic3×#685C211yesmaximal, characteristic, complemented
16D4×#685—31nomaximal, Hall
17C24×C3×D5C2211yescharacteristic
18C23×D3×D5C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic, complemented
20C22×#1220C2211yescharacteristic
21C22×C5×#67C2211yescharacteristic
22C22×C4×C5×D3C2211yescharacteristic, complemented
23C23×C3×Dic5C2211yescharacteristic, complemented
24C2×D5×#67—24no—
25C2×D5×#67—24no—
26C2×D5×#67C418yescomplemented
27C22×#1202C2211yescharacteristic
28C22×#1201C2211yescharacteristic
29C22×D3×Dic5C2211yescharacteristic, complemented
30C22×D5×Dic3C2211yescharacteristic
31C2×#6719C2211yescharacteristic, complemented
32C2×#6714C2211yescharacteristic, complemented
33C2×#6714C2211yescharacteristic, complemented
34C2×C5×#217C2211yescharacteristic, complemented
35C4×C5×#67—24no—
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
37C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
38C2×C4×C5×Dic3C2211yescharacteristic, complemented
39C2×C3×#685—24no—
40C2×C3×#685C2211yescharacteristic
41C2×C3×#685C2211yescharacteristic
42C2×C3×#685C2211yescharacteristic, complemented
43C2×C3×#685C2211yescharacteristic, complemented
44Dic5×#67—24no—
45C2×Dic3⋊Dic5C2211yescharacteristic, complemented
46C2×#6667C2211yescharacteristic, complemented
47C2×#6667C2211yescharacteristic, complemented
48C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
49C2×#6665C2211yescharacteristic
50C2×#6665C2211yescharacteristic
51C2×#6665C2211yescharacteristic, complemented
52C2×#6665C2211yescharacteristic, complemented
53C2×Dic3×Dic5C2211yescharacteristic, complemented
54D3×#685—24no—
55#91115C2211yescharacteristic, complemented
56#91115C2211yescharacteristic, complemented
57#90994C2211yescharacteristic, complemented
58#90994C2211yescharacteristic, complemented
59C22⋊C4×#67—51nomaximal, Hall
60C22×D4×D5—31no—
61C2×C4×C5×D4—31no—
62C2×D4×Dic5—31no—
63C22×#685—31no—
64C22×#685D311yescharacteristic, complemented
65#65502—31no—
66#65502—31no—
67#65277—31no—
68#65276—31no—
69#65247—31no—
70#65247—31no—
71#65244—31no—
72#65244—31no—
73#65228—31no—
74C4×#685—31no—
75C24×C3×C5C2311yescharacteristic
76C23×D15C2311yescharacteristic
77C23×C5×D3C2311yescharacteristic
78C23×C3×D5—22no—
79C23×C3×D5—22no—
80C23×C3×D5—22no—
81C23×C3×D5—22no—
82C23×C3×D5—41no—
83C23×C3×D5—41no—
84C23×C3×D5C2×C414yescomplemented
85C23×C3×D5C2311yescharacteristic
86C23×C3×D5C2311yescharacteristic
87C22×D3×D5—22no—
88C22×D3×D5—22no—
89C22×D3×D5—22no—
90C22×D3×D5—22no—
91C22×D3×D5—41no—
92C22×D3×D5—41no—
93C22×D3×D5C2×C414yescomplemented
94C22×C3×C4×C5—22no—
95C22×C3×C4×C5—22no—
96C22×C3×C4×C5—41no—
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2311yescharacteristic
99C2×#1220—22no—
100C2×#1220—22no—
101C2×#1220C2×C414yescomplemented
102C22×Dic15C2311yescharacteristic
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C2×C5×#67C2×C414yes—
106C2×C5×#67D414yes—
107C2×C5×#67D414yes—
108C22×C5×Dic3C2311yescharacteristic
109C22×C5×Dic3C2311yescharacteristic
110C22×C5×Dic3C2311yescharacteristic
111C2×C4×C5×D3—22no—
112C2×C4×C5×D3—22no—
113C2×C4×C5×D3—41no—
114C22×C3×Dic5—22no—
115C22×C3×Dic5—22no—
116C22×C3×Dic5—41no—
117C22×C3×Dic5C2311yescharacteristic
118C22×C3×Dic5C2311yescharacteristic
119D5×#67—232no—
120C2×#1202—22no—
121C2×#1202—22no—
122C2×#1202C2×C414yescomplemented
123C2×#1201—22no—
124C2×#1201—22no—
125C2×#1201C2×C414yescomplemented
126C2×D3×Dic5—22no—
127C2×D3×Dic5—22no—
128C2×D3×Dic5—41no—
129C2×D5×Dic3—22no—
130C2×D5×Dic3—22no—
131C2×D5×Dic3C2×C414yescomplemented
132#6719—22no—
133#6714—22no—
134#6714—41no—
135C5×#217—22no—
136C5×(C2×D3)⋊C4—22no—
137C5×Dic3⋊C4—22no—
138C4×C5×Dic3—22no—
139C3×#685—22no—
140C3×#685—22no—
141C3×#685—22no—
142C3×#685D414yescomplemented
143Dic3⋊Dic5—22no—
144#6667—22no—
145#6667—41no—
146(C2×D3)⋊Dic5—22no—
147#6665—22no—
148#6665—22no—
149#6665—41no—
150#6665—41no—
151Dic3×Dic5—22no—
152C23×#67—51no—
153C22×C3×C22⋊C4—51no—
154C2×C4×#67—51no—
155C2×C4×#67D511yescharacteristic, complemented
156C2×D3×C22⋊C4—51no—
157#5247—51no—
158#5213—51no—
159#5213—51no—
160#4957—51no—
161#4957—51no—
162#4956—51no—
163#4956—51no—
164#4955—51no—
165#4942—51no—
166Dic3×C22⋊C4—51no—
167C24×D5—31no—
168C24×D5C2×D311yescharacteristic
169C22×C5×D4—31no—
170C23×C4×C5—31no—
171C23×C4×C5C2×D311yescharacteristic, complemented
172C22×C22⋊D5—31no—
173C22×C22⋊D5—31no—
174C23×Dic5—31no—
175C23×Dic5C2×D311yescharacteristic, complemented
176C2×D4×D5—38no—
177C2×D4×D5—64no—
178C2×D4×D5—64no—
179C22×D20—31no—
180C22×C4×D5—31no—
181C4×C5×D4—64no—
182C2×C5×C4⋊C4—31no—
183C2×C5×C22⋊C4—31no—
184C2×C5×C22⋊C4—31no—
185C2×C42×C5—31no—
186C2×C22⋊Dic5—31no—
187C2×C22⋊Dic5—31no—
188D4×Dic5—64no—
189C2×#685—24no—
190C2×#685—31no—
191C2×#685—31no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685—64no—
199C2×#685C2×D311yescharacteristic
200C2×#685C2×D311yescharacteristic
201C2×#685C2×D311yescharacteristic, complemented
202C2×#685C2×D311yescharacteristic, complemented
203C2×C4⋊Dic5—31no—
204C2×C4×Dic5—31no—
205#3963—31no—
206#3963—31no—
207#3963—31no—
208#3963—31no—
209D4×C22⋊C4—151noSylow
210C23×C3×C5—21no—
211C23×C3×C5—21no—
212C23×C3×C5—21no—
213C23×C3×C5—21no—
214C23×C3×C5C22×C412yes—
215C23×C3×C5C2×D412yes—
216C23×C3×C5C2×D412yes—
217C23×C3×C5C2411yescharacteristic
218C22×D15—21no—
219C22×D15—21no—
220C22×D15—21no—
221C22×D15—21no—
222C22×D15—21no—
223C22×D15—21no—
224C22×D15C22×C412yes—
225C22×C5×D3—21no—
226C22×C5×D3—21no—
227C22×C5×D3—21no—
228C22×C5×D3—21no—
229C22×C5×D3C22×C412yes—
230C22×C5×D3C2×D412yes—
231C22×C5×D3C2×D412yes—
232C22×C3×D5—21no—
233C22×C3×D5—21no—
234C22×C3×D5—21no—
235C22×C3×D5—21no—
236C22×C3×D5—28no—
237C22×C3×D5—21no—
238C22×C3×D5—21no—
239C22×C3×D5—21no—
240C22×C3×D5—21no—
241C22×C3×D5—21no—
242C22×C3×D5—21no—
243C22×C3×D5—28no—
244C22×C3×D5—44no—
245C22×C3×D5—44no—
246C22×C3×D5—44no—
247C22×C3×D5—44no—
248C22×C3×D5—44no—
249C22×C3×D5C22×C412yes—
250C22×C3×D5C22×C412yes—
251C22×C3×D5C2×D412yes—
252C22×C3×D5#4112yes—
253C2×D3×D5—28no—
254C2×D3×D5—28no—
255C2×D3×D5—44no—
256C2×D3×D5—44no—
257C2×D3×D5—44no—
258C2×D3×D5—44no—
259C2×D3×D5—44no—
260C2×C3×C4×C5—21no—
261C2×C3×C4×C5—21no—
262C2×C3×C4×C5—21no—
263C2×C3×C4×C5—21no—
264C2×C3×C4×C5—21no—
265C2×C3×C4×C5—44no—
266C2×C3×C4×C5C2×D412yescomplemented
267#1220—28no—
268C2×Dic15—21no—
269C2×Dic15—21no—
270C2×Dic15—21no—
271C2×Dic15—21no—
272C2×Dic15—21no—
273C2×Dic15—21no—
274C2×Dic15—21no—
275C2×Dic15—21no—
276C2×Dic15C22×C412yes—
277C5×#67C22⋊C4116yescomplemented
278C2×C5×Dic3—21no—
279C2×C5×Dic3—21no—
280C2×C5×Dic3—21no—
281C2×C5×Dic3—21no—
282C2×C5×Dic3—21no—
283C2×C5×Dic3—21no—
284C2×C5×Dic3C22×C412yes—
285C2×C5×Dic3C2×D412yes—
286C2×C5×Dic3C2×D412yes—
287C4×C5×D3—44no—
288C2×C3×Dic5—21no—
289C2×C3×Dic5—21no—
290C2×C3×Dic5—21no—
291C2×C3×Dic5—21no—
292C2×C3×Dic5—21no—
293C2×C3×Dic5—44no—
294C2×C3×Dic5C2×D412yescomplemented
295#1202—28no—
296#1201—28no—
297D3×Dic5—44no—
298D5×Dic3—28no—
299C25×C3—51no—
300C24×D3—51no—
301C23×C3×C4—51no—
302C23×C3×C4C2×D511yescharacteristic, complemented
303C22×#67—51no—
304C22×#67—51no—
305C22×#67—58no—
306C22×#67—51no—
307C22×#67—104no—
308C22×#67—104no—
309C22×#67C2×D511yescharacteristic
310C23×Dic3—51no—
311C22×C4×D3—51no—
312C22×C4×D3C2×D511yescharacteristic, complemented
313C2×C3×C22⋊C4—51no—
314C2×C3×C22⋊C4—51no—
315C2×C3×C22⋊C4—51no—
316C2×C3×C22⋊C4—51no—
317C2×C3×C22⋊C4—104no—
318C2×#217—51no—
319C2×#217—51no—
320C2×#217—51no—
321C2×#217—51no—
322C2×#217—51no—
323C2×#217C2×D511yescharacteristic, complemented
324C4×#67—24no—
325C4×#67—104no—
326C2×(C2×D3)⋊C4—51no—
327C2×(C2×D3)⋊C4—51no—
328C2×(C2×D3)⋊C4—51no—
329C2×(C2×D3)⋊C4—51no—
330C2×(C2×D3)⋊C4—51no—
331C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
332C2×Dic3⋊C4—51no—
333C2×Dic3⋊C4C2×D511yescharacteristic, complemented
334C2×C4×Dic3—51no—
335C2×C4×Dic3C2×D511yescharacteristic, complemented
336D3×C22⋊C4—104no—
337C3⋊#95—51no—
338C3⋊#95—51no—
339C3⋊#95—51no—
340C3⋊#95—51no—
341C24×C5—31no—
342C24×C5C22×D311yescharacteristic
343C23×D5—22no—
344C23×D5—22no—
345C23×D5—22no—
346C23×D5—22no—
347C23×D5—31no—
348C23×D5—34no—
349C23×D5—41no—
350C23×D5—41no—
351C23×D5—62no—
352C23×D5—62no—
353C23×D5—62no—
354C23×D5—62no—
355C23×D5—121no—
356C23×D5—121no—
357C23×D5C4×D314yescomplemented
358C23×D5C22×D311yescharacteristic
359C23×D5C22×D311yescharacteristic
360C2×C5×D4—34no—
361C2×C5×D4—34no—
362C2×C5×D4—34no—
363C22×C4×C5—22no—
364C22×C4×C5—22no—
365C22×C4×C5—31no—
366C22×C4×C5—31no—
367C22×C4×C5—31no—
368C22×C4×C5—41no—
369C22×C4×C5—62no—
370C22×C4×C5—62no—
371C22×C4×C5—121no—
372C22×C4×C5C22×D311yescharacteristic
373C22×C4×C5C22×D311yescharacteristic
374C2×C22⋊D5—34no—
375C2×C22⋊D5—34no—
376C2×C22⋊D5—62no—
377C2×C22⋊D5—62no—
378C2×C22⋊D5—62no—
379C2×C22⋊D5—62no—
380C22×Dic5—22no—
381C22×Dic5—22no—
382C22×Dic5—31no—
383C22×Dic5—31no—
384C22×Dic5—31no—
385C22×Dic5—41no—
386C22×Dic5—62no—
387C22×Dic5—62no—
388C22×Dic5—121no—
389C22×Dic5C22×D311yescharacteristic
390C22×Dic5C22×D311yescharacteristic
391D4×D5—632no—
392C2×D20—34no—
393C2×D20—62no—
394C2×D20—62no—
395C2×C4×D5—34no—
396C2×C4×D5—62no—
397C2×C4×D5—62no—
398C5×C4⋊C4—62no—
399C5×C22⋊C4—62no—
400C5×C22⋊C4—62no—
401C42×C5—62no—
402C22⋊Dic5—62no—
403C22⋊Dic5—62no—
404#685—22no—
405#685—22no—
406#685—22no—
407#685—62no—
408#685—62no—
409#685—62no—
410#685—62no—
411#685—121no—
412#685—121no—
413#685—121no—
414#685—121no—
415#685#6714yesdirect product factor
416C4⋊Dic5—62no—
417C4×Dic5—62no—
418C23×D4—151no—
419C2×C4×D4—31no—
420C2×C4×D4—151no—
421C22×C22⋊C4—51no—
422C22×C22⋊C4—151no—
423#390—151no—
424#390—151no—
425#386—151no—
426#386—151no—
427#386—151no—
428#386—151no—
429#380—151no—
430#379—151no—
431#379—151no—
432C4×C22⋊C4—151no—
433C22×C3×C5—22no—
434C22×C3×C5—22no—
435C22×C3×C5—22no—
436C22×C3×C5—22no—
437C22×C3×C5—22no—
438C22×C3×C5—22no—
439C22×C3×C5C2×C22⋊C414yescomplemented
440C22×C3×C5C23×C411yescharacteristic
441C22×C3×C5C22×D411yescharacteristic
442C22×C3×C5C22×D411yescharacteristic
443C22×C3×C5C22×D411yescharacteristic
444C22×C3×C5C2×#4111yescharacteristic
445C22×C3×C5H(5,𝔽2)11yescharacteristic
446C22×C3×C5H(5,𝔽2)11yescharacteristic
447C2×D15—22no—
448C2×D15—22no—
449C2×D15—22no—
450C2×D15—41no—
451C2×D15—41no—
452C2×D15—41no—
453C2×D15—41no—
454C2×C5×D3—22no—
455C2×C5×D3—22no—
456C2×C5×D3—22no—
457C2×C5×D3—22no—
458C2×C5×D3—22no—
459C2×C5×D3—22no—
460C2×C5×D3C2×C22⋊C414yescomplemented
461C2×C3×D5—22no—
462C2×C3×D5—22no—
463C2×C3×D5—22no—
464C2×C3×D5—22no—
465C2×C3×D5—22no—
466C2×C3×D5—22no—
467C2×C3×D5—22no—
468C2×C3×D5—22no—
469C2×C3×D5—22no—
470C2×C3×D5—416no—
471C2×C3×D5—41no—
472C2×C3×D5—41no—
473C2×C3×D5—41no—
474C2×C3×D5—41no—
475C2×C3×D5C4×D414yescomplemented
476D3×D5—416no—
477C3×C4×C5—22no—
478C3×C4×C5—41no—
479Dic15—22no—
480Dic15—41no—
481Dic15—41no—
482C3×Dic5—22no—
483C3×Dic5—41no—
484C5×Dic3—41no—
485C5×Dic3—41no—
486C5×Dic3C2×C22⋊C414yescomplemented
487C24×C3—51no—
488C24×C3—51no—
489C24×C3—54no—
490C24×C3—102no—
491C24×C3—102no—
492C24×C3—102no—
493C24×C3—102no—
494C24×C3—201no—
495C24×C3—201no—
496C24×C3C22×D511yescharacteristic
497C23×D3—51no—
498C23×D3—54no—
499C23×D3—102no—
500C23×D3—102no—
501C23×D3—102no—
502C23×D3—102no—
503C23×D3—201no—
504C23×D3—201no—
505C23×D3C22×D511yescharacteristic
506C22×C3×C4—22no—
507C22×C3×C4—22no—
508C22×C3×C4—41no—
509C22×C3×C4—51no—
510C22×C3×C4—51no—
511C22×C3×C4—102no—
512C22×C3×C4—102no—
513C22×C3×C4—201no—
514C22×C3×C4C22×D511yescharacteristic
515C22×C3×C4C22×D511yescharacteristic
516C2×#67—54no—
517C2×#67—54no—
518C2×#67—54no—
519C2×#67—102no—
520C2×#67—102no—
521C2×#67—102no—
522C2×#67—102no—
523C2×#67—1032no—
524C2×#67—102no—
525C2×#67—102no—
526C2×#67C4×D514yes—
527C2×#67D2014yes—
528C2×#67C22⋊D514yes—
529C22×Dic3—51no—
530C22×Dic3—54no—
531C22×Dic3—51no—
532C22×Dic3—51no—
533C22×Dic3—102no—
534C22×Dic3—102no—
535C22×Dic3C22×D511yescharacteristic
536C22×Dic3C22×D511yescharacteristic
537C22×Dic3C22×D511yescharacteristic
538C2×C4×D3—22no—
539C2×C4×D3—22no—
540C2×C4×D3—41no—
541C2×C4×D3—102no—
542C2×C4×D3—102no—
543C2×C4×D3—201no—
544C3×C22⋊C4—54no—
545C3×C22⋊C4—102no—
546C3×C22⋊C4—102no—
547C3×C22⋊C4—102no—
548#217—22no—
549#217—102no—
550#217—102no—
551#217—102no—
552#217—201no—
553#217—201no—
554(C2×D3)⋊C4—22no—
555(C2×D3)⋊C4—102no—
556(C2×D3)⋊C4—102no—
557(C2×D3)⋊C4—102no—
558(C2×D3)⋊C4—201no—
559(C2×D3)⋊C4—201no—
560Dic3⋊C4—22no—
561Dic3⋊C4—102no—
562C4×Dic3—22no—
563C4×Dic3—102no—
564C23×C5—21no—
565C23×C5—21no—
566C23×C5—21no—
567C23×C5—21no—
568C23×C5—32no—
569C23×C5—32no—
570C23×C5—32no—
571C23×C5—61no—
572C23×C5—61no—
573C23×C5—61no—
574C23×C5—61no—
575C23×C5C2×C4×D312yes—
576C23×C5D3×D412yes—
577C23×C5D3×D412yes—
578C23×C5C23×D311yescharacteristic
579C22×D5—21no—
580C22×D5—21no—
581C22×D5—21no—
582C22×D5—21no—
583C22×D5—28no—
584C22×D5—21no—
585C22×D5—21no—
586C22×D5—21no—
587C22×D5—21no—
588C22×D5—21no—
589C22×D5—21no—
590C22×D5—28no—
591C22×D5—32no—
592C22×D5—44no—
593C22×D5—44no—
594C22×D5—44no—
595C22×D5—44no—
596C22×D5—44no—
597C22×D5—68no—
598C22×D5—61no—
599C22×D5—61no—
600C22×D5—61no—
601C22×D5—61no—
602C22×D5—61no—
603C22×D5—61no—
604C22×D5—68no—
605C22×D5—124no—
606C22×D5—124no—
607C22×D5—124no—
608C22×D5—124no—
609C22×D5—124no—
610C22×D5C2×C4×D312yes—
611C22×D5C2×C4×D312yes—
612C22×D5#23512yes—
613C22×D5C2×#6712yes—
614C5×D4—316no—
615C2×C4×C5—21no—
616C2×C4×C5—21no—
617C2×C4×C5—21no—
618C2×C4×C5—21no—
619C2×C4×C5—21no—
620C2×C4×C5—32no—
621C2×C4×C5—32no—
622C2×C4×C5—32no—
623C2×C4×C5—44no—
624C2×C4×C5—61no—
625C2×C4×C5—61no—
626C2×C4×C5—61no—
627C2×C4×C5—61no—
628C2×C4×C5—61no—
629C2×C4×C5—61no—
630C2×C4×C5—124no—
631C2×C4×C5C2×#6712yescomplemented
632C22⋊D5—68no—
633C22⋊D5—68no—
634C2×Dic5—21no—
635C2×Dic5—21no—
636C2×Dic5—21no—
637C2×Dic5—21no—
638C2×Dic5—21no—
639C2×Dic5—32no—
640C2×Dic5—44no—
641C2×Dic5—61no—
642C2×Dic5—61no—
643C2×Dic5—61no—
644C2×Dic5—61no—
645C2×Dic5—61no—
646C2×Dic5—61no—
647C2×Dic5—61no—
648C2×Dic5—61no—
649C2×Dic5—124no—
650C2×Dic5C2×#6712yescomplemented
651D20—68no—
652C4×D5—68no—
653C25—51no—
654C25—151no—
655C22×D4—31no—
656C22×D4—151no—
657C22×D4—158no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—304no—
661C22×D4—304no—
662C23×C4—31no—
663C23×C4—51no—
664C23×C4—151no—
665C23×C4—151no—
666C23×C4D3×D511yescharacteristic, complemented
667C4×D4—64no—
668C4×D4—304no—
669C2×C4⋊C4—31no—
670C2×C4⋊C4—151no—
671C2×C22⋊C4—31no—
672C2×C22⋊C4—31no—
673C2×C22⋊C4—51no—
674C2×C22⋊C4—51no—
675C2×C22⋊C4—51no—
676C2×C22⋊C4—51no—
677C2×C22⋊C4—104no—
678C2×C22⋊C4—151no—
679C2×C22⋊C4—151no—
680C2×C22⋊C4—151no—
681C2×C22⋊C4—151no—
682C2×C22⋊C4—151no—
683C2×C22⋊C4—151no—
684C2×C22⋊C4—151no—
685C2×C22⋊C4—151no—
686C2×C22⋊C4—151no—
687C2×C22⋊C4—151no—
688C2×C22⋊C4—304no—
689C2×C42—31no—
690C2×C42—151no—
691#95—151no—
692#95—151no—
693#95—151no—
694#95—151no—
695C2×C3×C5—24no—
696C2×C3×C5C22×C22⋊C411yescharacteristic
697C2×C3×C5C2×C4×D411yescharacteristic
698C2×C3×C5#51811yescharacteristic
699C2×C3×C5D4211yescharacteristic
700C2×C3×C5D4211yescharacteristic
701C2×C3×C5#54611yescharacteristic
702C2×C3×C5#54611yescharacteristic
703D15—42no—
704C3×D5—24no—
705C3×D5—42no—
706C5×D3—24no—
707C23×C3—21no—
708C23×C3—21no—
709C23×C3—21no—
710C23×C3—21no—
711C23×C3—52no—
712C23×C3—52no—
713C23×C3—52no—
714C23×C3—52no—
715C23×C3—108no—
716C23×C3—101no—
717C23×C3—101no—
718C23×C3—101no—
719C23×C3—101no—
720C23×C3—101no—
721C23×C3—101no—
722C23×C3—101no—
723C23×C3—101no—
724C23×C3—101no—
725C23×C3—101no—
726C23×C3—108no—
727C23×C3—204no—
728C23×C3—204no—
729C23×C3—204no—
730C23×C3—204no—
731C23×C3—204no—
732C23×C3C2×C4×D512yes—
733C23×C3C2×D2012yes—
734C23×C3C2×C22⋊D512yes—
735C23×C3C23×D511yescharacteristic
736C22×D3—21no—
737C22×D3—21no—
738C22×D3—21no—
739C22×D3—21no—
740C22×D3—52no—
741C22×D3—108no—
742C22×D3—101no—
743C22×D3—101no—
744C22×D3—101no—
745C22×D3—101no—
746C22×D3—101no—
747C22×D3—101no—
748C22×D3—108no—
749C22×D3—204no—
750C22×D3—204no—
751C22×D3—204no—
752C22×D3—204no—
753C22×D3—204no—
754C22×D3C2×C4×D512yes—
755C22×D3C2×D2012yes—
756C22×D3C2×C22⋊D512yes—
757C2×C3×C4—21no—
758C2×C3×C4—21no—
759C2×C3×C4—21no—
760C2×C3×C4—21no—
761C2×C3×C4—21no—
762C2×C3×C4—44no—
763C2×C3×C4—52no—
764C2×C3×C4—101no—
765C2×C3×C4—101no—
766C2×C3×C4—101no—
767C2×C3×C4—101no—
768C2×C3×C4—101no—
769C2×C3×C4—204no—
770C2×C3×C4D4×D512yescomplemented
771#67—108no—
772#67—108no—
773#67—108no—
774#67#685116yesdirect product factor
775C2×Dic3—21no—
776C2×Dic3—21no—
777C2×Dic3—21no—
778C2×Dic3—21no—
779C2×Dic3—21no—
780C2×Dic3—21no—
781C2×Dic3—52no—
782C2×Dic3—101no—
783C2×Dic3—101no—
784C2×Dic3—108no—
785C2×Dic3—101no—
786C2×Dic3—101no—
787C2×Dic3—101no—
788C2×Dic3—101no—
789C2×Dic3—101no—
790C2×Dic3—101no—
791C2×Dic3C2×C4×D512yes—
792C2×Dic3C2×D2012yes—
793C2×Dic3C2×C22⋊D512yes—
794C4×D3—44no—
795C4×D3—204no—
796C22×C5—22no—
797C22×C5—22no—
798C22×C5—22no—
799C22×C5—22no—
800C22×C5—22no—
801C22×C5—22no—
802C22×C5—34no—
803C22×C5—62no—
804C22×C5—62no—
805C22×C5—62no—
806C22×C5—62no—
807C22×C5—62no—
808C22×C5—62no—
809C22×C5D3×C22⋊C414yescomplemented
810C22×C5C22×C4×D311yescharacteristic
811C22×C5C2×#23511yescharacteristic
812C22×C5C2×D3×D411yescharacteristic
813C22×C5C2×D3×D411yescharacteristic
814C22×C5#100411yescharacteristic
815C22×C5#100411yescharacteristic
816C22×C5C22×#6711yescharacteristic
817C2×D5—22no—
818C2×D5—22no—
819C2×D5—22no—
820C2×D5—22no—
821C2×D5—22no—
822C2×D5—22no—
823C2×D5—22no—
824C2×D5—22no—
825C2×D5—22no—
826C2×D5—416no—
827C2×D5—41no—
828C2×D5—41no—
829C2×D5—41no—
830C2×D5—41no—
831C2×D5—62no—
832C2×D5—62no—
833C2×D5—62no—
834C2×D5—1216no—
835C2×D5—121no—
836C2×D5—121no—
837C2×D5—121no—
838C2×D5—121no—
839C2×D5C4×#6714yescomplemented
840C4×C5—22no—
841C4×C5—34no—
842C4×C5—41no—
843C4×C5—121no—
844C4×C5—121no—
845Dic5—22no—
846Dic5—41no—
847Dic5—62no—
848Dic5—121no—
849Dic5—121no—
850C24—31no—
851C24—51no—
852C24—51no—
853C24—54no—
854C24—102no—
855C24—102no—
856C24—102no—
857C24—102no—
858C24—154no—
859C24—151no—
860C24—201no—
861C24—201no—
862C24—302no—
863C24—302no—
864C24—302no—
865C24—302no—
866C24—601no—
867C24—601no—
868C24C2×D3×D511yescharacteristic
869C2×D4—34no—
870C2×D4—34no—
871C2×D4—34no—
872C2×D4—154no—
873C2×D4—154no—
874C2×D4—154no—
875C2×D4—302no—
876C2×D4—302no—
877C2×D4—3032no—
878C2×D4—302no—
879C2×D4—302no—
880C2×D4—302no—
881C2×D4—302no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—31no—
885C22×C4—31no—
886C22×C4—31no—
887C22×C4—41no—
888C22×C4—51no—
889C22×C4—51no—
890C22×C4—62no—
891C22×C4—62no—
892C22×C4—102no—
893C22×C4—102no—
894C22×C4—121no—
895C22×C4—154no—
896C22×C4—151no—
897C22×C4—151no—
898C22×C4—151no—
899C22×C4—201no—
900C22×C4—302no—
901C22×C4—302no—
902C22×C4—302no—
903C22×C4—302no—
904C22×C4—601no—
905C22×C4C2×D3×D511yescharacteristic
906C22×C4C2×D3×D511yescharacteristic
907C4⋊C4—62no—
908C4⋊C4—302no—
909C22⋊C4—54no—
910C22⋊C4—62no—
911C22⋊C4—62no—
912C22⋊C4—102no—
913C22⋊C4—102no—
914C22⋊C4—102no—
915C22⋊C4—302no—
916C22⋊C4—302no—
917C22⋊C4—302no—
918C22⋊C4—302no—
919C22⋊C4—302no—
920C22⋊C4—302no—
921C22⋊C4—601no—
922C22⋊C4—601no—
923C22⋊C4—601no—
924C22⋊C4—601no—
925C42—62no—
926C42—302no—
927C3×C5D4×C22⋊C411yescharacteristic, complemented, Hall
928C22×C3—22no—
929C22×C3—22no—
930C22×C3—22no—
931C22×C3—22no—
932C22×C3—22no—
933C22×C3—22no—
934C22×C3—54no—
935C22×C3—102no—
936C22×C3—102no—
937C22×C3—102no—
938C22×C3—102no—
939C22×C3—102no—
940C22×C3—102no—
941C22×C3—102no—
942C22×C3—102no—
943C22×C3—102no—
944C22×C3—2016no—
945C22×C3—201no—
946C22×C3—201no—
947C22×C3—201no—
948C22×C3—201no—
949C22×C3C2×#68514yescomplemented
950C22×C3C22×C4×D511yescharacteristic
951C22×C3C22×D2011yescharacteristic
952C22×C3C2×D4×D511yescharacteristic
953C22×C3#414411yescharacteristic
954C22×C3D5×#4111yescharacteristic
955C22×C3#414911yescharacteristic
956C22×C3C22×C22⋊D511yescharacteristic
957C2×D3—22no—
958C2×D3—22no—
959C2×D3—22no—
960C2×D3—22no—
961C2×D3—22no—
962C2×D3—22no—
963C2×D3—102no—
964C2×D3—102no—
965C2×D3—102no—
966C2×D3—2016no—
967C2×D3—201no—
968C2×D3—201no—
969C2×D3—201no—
970C2×D3—201no—
971C2×D3C2×#68514yescomplemented
972C3×C4—22no—
973C3×C4—41no—
974C3×C4—102no—
975C3×C4—201no—
976Dic3—41no—
977Dic3—41no—
978Dic3—102no—
979Dic3—201no—
980Dic3—201no—
981Dic3C2×#68514yescomplemented
982C2×C5—24no—
983C2×C5—64no—
984C2×C5C2×D3×C22⋊C411yescharacteristic
985C2×C5#548611yescharacteristic
986C2×C5#549011yescharacteristic
987C2×C5#549011yescharacteristic
988C2×C5C2×C4×#6711yescharacteristic
989C2×C5D4×#6711yescharacteristic
990C2×C5D4×#6711yescharacteristic
991D5—24no—
992D5—42no—
993D5—122no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—32no—
999C23—32no—
1000C23—32no—
1001C23—52no—
1002C23—52no—
1003C23—52no—
1004C23—52no—
1005C23—61no—
1006C23—61no—
1007C23—61no—
1008C23—61no—
1009C23—108no—
1010C23—101no—
1011C23—101no—
1012C23—101no—
1013C23—101no—
1014C23—108no—
1015C23—101no—
1016C23—101no—
1017C23—101no—
1018C23—101no—
1019C23—101no—
1020C23—101no—
1021C23—152no—
1022C23—204no—
1023C23—204no—
1024C23—204no—
1025C23—204no—
1026C23—204no—
1027C23—308no—
1028C23—308no—
1029C23—301no—
1030C23—301no—
1031C23—301no—
1032C23—301no—
1033C23—301no—
1034C23—301no—
1035C23—604no—
1036C23—604no—
1037C23—604no—
1038C23—604no—
1039C23—604no—
1040C23C4×D3×D512yes—
1041C23D3×D2012yes—
1042C23D3×C22⋊D512yes—
1043C23C22×D3×D511yescharacteristic
1044D4—316no—
1045D4—308no—
1046D4—308no—
1047D4—308no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—32no—
1054C2×C4—32no—
1055C2×C4—32no—
1056C2×C4—44no—
1057C2×C4—52no—
1058C2×C4—61no—
1059C2×C4—61no—
1060C2×C4—61no—
1061C2×C4—61no—
1062C2×C4—61no—
1063C2×C4—61no—
1064C2×C4—101no—
1065C2×C4—101no—
1066C2×C4—101no—
1067C2×C4—101no—
1068C2×C4—101no—
1069C2×C4—124no—
1070C2×C4—152no—
1071C2×C4—204no—
1072C2×C4—308no—
1073C2×C4—301no—
1074C2×C4—301no—
1075C2×C4—301no—
1076C2×C4—301no—
1077C2×C4—301no—
1078C2×C4—301no—
1079C2×C4—301no—
1080C2×C4—301no—
1081C2×C4—604no—
1082C2×C4D5×#6712yescomplemented
1083C2×C3—24no—
1084C2×C3—104no—
1085C2×C3—202no—
1086C2×C3C4×D4×D511yescharacteristic
1087C2×C3#6587911yescharacteristic
1088C2×C3D4×D2011yescharacteristic
1089C2×C3#6588811yescharacteristic
1090C2×C3C22×#68511yescharacteristic
1091C2×C3D4×C22⋊D511yescharacteristic
1092C2×C3#6616311yescharacteristic
1093D3—24no—
1094D3—202no—
1095C5C22⋊C4×#6711yescharacteristic, complemented, Sylow
1096C22—22no—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—34no—
1103C22—54no—
1104C22—62no—
1105C22—62no—
1106C22—62no—
1107C22—62no—
1108C22—62no—
1109C22—62no—
1110C22—102no—
1111C22—102no—
1112C22—102no—
1113C22—102no—
1114C22—102no—
1115C22—102no—
1116C22—102no—
1117C22—102no—
1118C22—102no—
1119C22—2016no—
1120C22—201no—
1121C22—201no—
1122C22—201no—
1123C22—201no—
1124C22—302no—
1125C22—302no—
1126C22—302no—
1127C22—6016no—
1128C22—601no—
1129C22—601no—
1130C22—601no—
1131C22—601no—
1132C22D3×#68514yescomplemented
1133C22C2×C4×D3×D511yescharacteristic
1134C22C2×D3×D2011yescharacteristic
1135C22D5×#23511yescharacteristic
1136C22#9201711yescharacteristic
1137C22C2×D5×#6711yescharacteristic
1138C22C2×D3×C22⋊D511yescharacteristic
1139C22#9204911yescharacteristic
1140C4—22no—
1141C4—34no—
1142C4—41no—
1143C4—102no—
1144C4—121no—
1145C4—121no—
1146C4—201no—
1147C4—302no—
1148C4—601no—
1149C4—601no—
1150C3D4×#68511yescharacteristic, complemented, Sylow
1151C2—24no—
1152C2—64no—
1153C2—104no—
1154C2—202no—
1155C2—602no—
1156C2C2×D3×#68511yescharacteristic
1157C2C4×D5×#6711yescharacteristic
1158C2#1175462511yescharacteristic
1159C2#67×D2011yescharacteristic
1160C2#1175465011yescharacteristic
1161C2#1175465911yescharacteristic
1162C2#67×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×D5×#67C2
hypercenterC23×C4D3×D5
hypocenterC3×C5D4×C22⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C5×#67C2semidirect
3. C22×C3×#685C2semidirect
4. C2×Dic5×#67C2semidirect
5. C2×D3×#685C2semidirect
6. #11751314C2semidirect
7. #11749494C2semidirect
8. #11749488C2semidirect
9. #11748940C2semidirect
10. #11748913C2semidirect
11. #11748912C2semidirect
12. #11748911C2semidirect
13. #11748910C2semidirect
14. #11748878C2semidirect
15. Dic3×#685C2semidirect
19. C23×C3×C4×C5C22semidirect
22. C22×C4×C5×D3C22semidirect
23. C23×C3×Dic5C22semidirect
26. C2×D5×#67C4semidirect
29. C22×D3×Dic5C22semidirect
31. C2×#6719C22semidirect
32. C2×#6714C22semidirect
33. C2×#6714C22semidirect
34. C2×C5×#217C22semidirect
36. C2×C5×(C2×D3)⋊C4C22semidirect
37. C2×C5×Dic3⋊C4C22semidirect
38. C2×C4×C5×Dic3C22semidirect
42. C2×C3×#685C22semidirect
43. C2×C3×#685C22semidirect
45. C2×Dic3⋊Dic5C22semidirect
46. C2×#6667C22semidirect
47. C2×#6667C22semidirect
48. C2×(C2×D3)⋊Dic5C22semidirect
51. C2×#6665C22semidirect
52. C2×#6665C22semidirect
53. C2×Dic3×Dic5C22semidirect
55. #91115C22semidirect
56. #91115C22semidirect
57. #90994C22semidirect
58. #90994C22semidirect
64. C22×#685D3semidirect
84. C23×C3×D5C2×C4semidirect
93. C22×D3×D5C2×C4semidirect
101. C2×#1220C2×C4semidirect
122. C2×#1202C2×C4semidirect
125. C2×#1201C2×C4semidirect
131. C2×D5×Dic3C2×C4semidirect
142. C3×#685D4semidirect
155. C2×C4×#67D5semidirect
171. C23×C4×C5C2×D3semidirect
175. C23×Dic5C2×D3semidirect
201. C2×#685C2×D3semidirect
202. C2×#685C2×D3semidirect
266. C2×C3×C4×C5C2×D4semidirect
277. C5×#67C22⋊C4semidirect
294. C2×C3×Dic5C2×D4semidirect
302. C23×C3×C4C2×D5semidirect
312. C22×C4×D3C2×D5semidirect
323. C2×#217C2×D5semidirect
331. C2×(C2×D3)⋊C4C2×D5semidirect
333. C2×Dic3⋊C4C2×D5semidirect
335. C2×C4×Dic3C2×D5semidirect
357. C23×D5C4×D3semidirect
415. #685#67direct (N × H)
439. C22×C3×C5C2×C22⋊C4semidirect
460. C2×C5×D3C2×C22⋊C4semidirect
475. C2×C3×D5C4×D4semidirect
486. C5×Dic3C2×C22⋊C4semidirect
631. C2×C4×C5C2×#67semidirect
650. C2×Dic5C2×#67semidirect
666. C23×C4D3×D5semidirect
770. C2×C3×C4D4×D5semidirect
774. #67#685direct (N × H)
809. C22×C5D3×C22⋊C4semidirect
839. C2×D5C4×#67semidirect
927. C3×C5D4×C22⋊C4semidirect
949. C22×C3C2×#685semidirect
971. C2×D3C2×#685semidirect
981. Dic3C2×#685semidirect
1082. C2×C4D5×#67semidirect
1095. C5C22⋊C4×#67semidirect
1132. C22D3×#685semidirect
1150. C3D4×#685semidirect

Maximal subgroups

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

subgroupindex
C22×D5×#672
C2×C4×C5×#672
C22×C3×#6852
C2×Dic5×#672
C2×D3×#6852
#117513142
#117494942
#117494882
#117489402
#117489132
#117489122
#117489112
#117489102
#117488782
Dic3×#6852
D4×#6853
C22⋊C4×#675