Finite Group Databasebeta

← #14325919

Subgroups — #14325919

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×D3×C22⋊D5C211yesmaximal, characteristic
2C2×#91770C211yesmaximal, characteristic, complemented
3C2×#91552C211yesmaximal, characteristic, complemented
4C22×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
5C2×#91473C211yesmaximal, characteristic, complemented
6C5×#4955C211yesmaximal, characteristic, complemented
7C3×#65247C211yesmaximal, characteristic, complemented
8#11749500C211yesmaximal, characteristic, complemented
9#11748940C211yesmaximal, characteristic, complemented
10#11748919C211yesmaximal, characteristic, complemented
11#11748918C211yesmaximal, characteristic, complemented
12#11748916C211yesmaximal, characteristic, complemented
13#11748915C211yesmaximal, characteristic, complemented
14#11748887C211yesmaximal, characteristic, complemented
15#11748886C211yesmaximal, characteristic, complemented
16#10605581—31nomaximal, Hall
17C24×C5×D3C2211yescharacteristic
18C23×D3×D5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C23×Dic15C2211yescharacteristic, complemented
21C22×C4×D15C2211yescharacteristic, complemented
22C22×C3×C22⋊D5C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic, complemented
24C2×D3×C22⋊D5—24no—
25C2×D3×C22⋊D5—24no—
26C2×D3×C22⋊D5C418yescomplemented
27C22×#1203C2211yescharacteristic
28C22×#1201C2211yescharacteristic
29C22×#1200C2211yescharacteristic, complemented
30C22×D3×Dic5C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
32C2×#6714C2211yescharacteristic, complemented
33C2×#6712C2211yescharacteristic, complemented
34C2×C4×Dic15C2211yescharacteristic, complemented
35#91770—24no—
36C2×C5×#217C2211yescharacteristic, complemented
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic
39C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×C3×#685C2211yescharacteristic, complemented
42C2×C3×#685C2211yescharacteristic, complemented
43#91552—24no—
44C2×#6669C2211yescharacteristic, complemented
45C2×#6667C2211yescharacteristic, complemented
46C2×(C2×D3)⋊Dic5—24no—
47C2×(C2×D3)⋊Dic5C2211yescharacteristic
48C2×(C2×D3)⋊Dic5C2211yescharacteristic
49C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
50C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
51C2×#6665C2211yescharacteristic, complemented
52C2×#6665C2211yescharacteristic, complemented
53C2×Dic3×Dic5C2211yescharacteristic, complemented
54#91473—24no—
55C3×#3963C2211yescharacteristic, complemented
56C3×#3963C2211yescharacteristic, complemented
57#90994C2211yescharacteristic, complemented
58#90994C2211yescharacteristic, complemented
59#74878—51nomaximal, Hall
60C23×C22⋊D5—31no—
61C22×C22⋊Dic5—31no—
62C2×#4027—31no—
63C2×#4027—31no—
64C2×D5×C22⋊C4—31no—
65C5×#379—31no—
66#65247—31no—
67#65247D311yescharacteristic, complemented
68#65246—31no—
69#65246—31no—
70#65245—31no—
71#65245—31no—
72#65244—31no—
73#65231—31no—
74C22⋊C4×Dic5—31no—
75C24×C3×C5C2311yescharacteristic
76C23×D15C2311yescharacteristic
77C23×C5×D3—22no—
78C23×C5×D3—22no—
79C23×C5×D3—22no—
80C23×C5×D3—22no—
81C23×C5×D3—41no—
82C23×C5×D3—41no—
83C23×C5×D3C2×C414yescomplemented
84C23×C5×D3C2311yescharacteristic
85C23×C5×D3C2311yescharacteristic
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×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C2×#1220C2×C414yes—
97C2×#1220D414yes—
98C2×#1220D414yes—
99C22×Dic15—22no—
100C22×Dic15—22no—
101C22×Dic15—41no—
102C22×Dic15C2311yescharacteristic
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C2×C4×D15—22no—
106C2×C4×D15—22no—
107C2×C4×D15—41no—
108C22×C5×Dic3C2311yescharacteristic
109C22×C5×Dic3C2311yescharacteristic
110C2×C3×C22⋊D5—22no—
111C2×C3×C22⋊D5—22no—
112C2×C3×C22⋊D5C2×C414yescomplemented
113C22×C3×Dic5—22no—
114C22×C3×Dic5—22no—
115C22×C3×Dic5—41no—
116C22×C3×Dic5C2311yescharacteristic
117C22×C3×Dic5C2311yescharacteristic
118C22×C3×Dic5C2311yescharacteristic
119D3×C22⋊D5—232no—
120C2×#1203—22no—
121C2×#1203—22no—
122C2×#1203C2×C414yescomplemented
123C2×#1201—22no—
124C2×#1201—22no—
125C2×#1201C2×C414yescomplemented
126C2×#1200—22no—
127C2×#1200—22no—
128C2×#1200—41no—
129C2×D3×Dic5—22no—
130C2×D3×Dic5—22no—
131C2×D3×Dic5C2×C414yescomplemented
132C3×C5×C22⋊C4—22no—
133#6714—22no—
134#6712—22no—
135C4×Dic15—22no—
136C5×#217—22no—
137C5×(C2×D3)⋊C4—22no—
138C5×(C2×D3)⋊C4—22no—
139C5×(C2×D3)⋊C4—41no—
140C5×(C2×D3)⋊C4—41no—
141C3×#685—22no—
142C3×#685—41no—
143#6669—22no—
144#6667—22no—
145(C2×D3)⋊Dic5—22no—
146(C2×D3)⋊Dic5—22no—
147(C2×D3)⋊Dic5—22no—
148(C2×D3)⋊Dic5D414yescomplemented
149#6665—22no—
150#6665—41no—
151Dic3×Dic5—22no—
152C22×D3×D4—51no—
153C2×C4×#67—51no—
154C22×(C2×D3)⋊C4—51no—
155C2×#67⋊C4—51no—
156C2×D3×C22⋊C4—51no—
157C3×#386—51no—
158#5220—51no—
159#4957—51no—
160#4957—51no—
161#4955—51no—
162#4955D511yescharacteristic, complemented
163#4667—51no—
164#4666—51no—
165#4665—51no—
166#4665—51no—
167C25×C5—31no—
168C24×D5—31no—
169C22×C22⋊D5—31no—
170C22×C22⋊D5—31no—
171C22×C22⋊D5—38no—
172C22×C22⋊D5—31no—
173C22×C22⋊D5—64no—
174C22×C22⋊D5—64no—
175C22×C22⋊D5C2×D311yescharacteristic
176C23×Dic5—31no—
177C23×Dic5—31no—
178C23×Dic5C2×D311yescharacteristic, complemented
179C22×C4×D5—31no—
180C22×C4×D5—31no—
181C2×C5×C22⋊C4—31no—
182C2×C5×C22⋊C4—31no—
183C2×C5×C22⋊C4—31no—
184C2×C5×C22⋊C4—31no—
185C2×C5×C22⋊C4—31no—
186C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
187C2×C22⋊Dic5—31no—
188C2×C22⋊Dic5—31no—
189C2×C22⋊Dic5—31no—
190C2×C22⋊Dic5—31no—
191C2×C22⋊Dic5—64no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685C2×D311yescharacteristic, complemented
197C2×#685C2×D311yescharacteristic, complemented
198C2×#683—31no—
199C2×#683—31no—
200C2×C4×Dic5—31no—
201C2×C4×Dic5—31no—
202#4027—64no—
203#4027—64no—
204D5×C22⋊C4—64no—
205#3963—31no—
206#3963—31no—
207#3963C2×D311yescharacteristic, complemented
208#3963C2×D311yescharacteristic, complemented
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×D15C22×C412yes—
223C22×D15C2×D412yes—
224C22×D15C2×D412yes—
225C22×C5×D3—21no—
226C22×C5×D3—21no—
227C22×C5×D3—21no—
228C22×C5×D3—21no—
229C22×C5×D3—28no—
230C22×C5×D3—21no—
231C22×C5×D3—21no—
232C22×C5×D3—21no—
233C22×C5×D3—21no—
234C22×C5×D3—21no—
235C22×C5×D3—21no—
236C22×C5×D3—28no—
237C22×C5×D3—44no—
238C22×C5×D3—44no—
239C22×C5×D3—44no—
240C22×C5×D3—44no—
241C22×C5×D3—44no—
242C22×C5×D3C22×C412yes—
243C22×C5×D3C22×C412yes—
244C22×C5×D3C2×D412yes—
245C22×C5×D3#4112yes—
246C22×C3×D5—21no—
247C22×C3×D5—21no—
248C22×C3×D5—21no—
249C22×C3×D5—21no—
250C22×C3×D5—21no—
251C22×C3×D5—21no—
252C22×C3×D5C22×C412yes—
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—21no—
266#1220C22⋊C4116yescomplemented
267C2×Dic15—21no—
268C2×Dic15—21no—
269C2×Dic15—21no—
270C2×Dic15—21no—
271C2×Dic15—21no—
272C2×Dic15—44no—
273C2×Dic15C22×C412yes—
274C2×Dic15C2×D412yes—
275C2×Dic15C2×D412yes—
276C2×Dic15C2×D412yescomplemented
277C4×D15—44no—
278C2×C5×Dic3—21no—
279C2×C5×Dic3—21no—
280C2×C5×Dic3—21no—
281C2×C5×Dic3—21no—
282C2×C5×Dic3—21no—
283C2×C5×Dic3—21no—
284C3×C22⋊D5—28no—
285C2×C3×Dic5—21no—
286C2×C3×Dic5—21no—
287C2×C3×Dic5—21no—
288C2×C3×Dic5—21no—
289C2×C3×Dic5—21no—
290C2×C3×Dic5—21no—
291C2×C3×Dic5—21no—
292C2×C3×Dic5—44no—
293C2×C3×Dic5C22×C412yes—
294C2×C3×Dic5C2×D412yescomplemented
295#1203—28no—
296#1201—28no—
297#1200—44no—
298D3×Dic5—28no—
299C24×D3—51no—
300C24×D3C2×D511yescharacteristic
301C22×C3×D4—51no—
302C23×C3×C4—51no—
303C22×#67—51no—
304C22×#67—51no—
305C23×Dic3—51no—
306C2×D3×D4—58no—
307C2×D3×D4—104no—
308C2×D3×D4—104no—
309C22×D12—51no—
310C22×C4×D3—51no—
311C22×C4×D3—51no—
312C22×C4×D3—51no—
313C2×C3×C22⋊C4—51no—
314C2×C3×C22⋊C4—51no—
315C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
316C2×#217—51no—
317C2×#217—51no—
318C2×#217C2×D511yescharacteristic, complemented
319C4×#67—104no—
320C2×(C2×D3)⋊C4—51no—
321C2×(C2×D3)⋊C4—51no—
322C2×(C2×D3)⋊C4—51no—
323C2×(C2×D3)⋊C4—51no—
324C2×(C2×D3)⋊C4—51no—
325C2×(C2×D3)⋊C4—51no—
326C2×(C2×D3)⋊C4—104no—
327C2×(C2×D3)⋊C4C2×D511yescharacteristic
328C2×(C2×D3)⋊C4C2×D511yescharacteristic
329C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
330C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
331C2×Dic3⋊C4—51no—
332C2×Dic3⋊C4—51no—
333C2×C4×Dic3—51no—
334C2×C4×Dic3—51no—
335#67⋊C4—104no—
336D3×C22⋊C4—104no—
337C3×#95—51no—
338C3×#95—51no—
339C3⋊#95—51no—
340C3⋊#95—51no—
341C24×C5—31no—
342C24×C5—31no—
343C24×C5—34no—
344C24×C5—62no—
345C24×C5—62no—
346C24×C5—62no—
347C24×C5—62no—
348C24×C5—121no—
349C24×C5—121no—
350C24×C5C22×D311yescharacteristic
351C23×D5—31no—
352C23×D5—34no—
353C23×D5—62no—
354C23×D5—62no—
355C23×D5—62no—
356C23×D5—62no—
357C23×D5—121no—
358C23×D5—121no—
359C23×D5C22×D311yescharacteristic
360C22×C4×C5—31no—
361C22×C4×C5—31no—
362C22×C4×C5C22×D311yescharacteristic
363C22×C4×C5C22×D311yescharacteristic
364C2×C22⋊D5—22no—
365C2×C22⋊D5—22no—
366C2×C22⋊D5—34no—
367C2×C22⋊D5—34no—
368C2×C22⋊D5—34no—
369C2×C22⋊D5—34no—
370C2×C22⋊D5—34no—
371C2×C22⋊D5—62no—
372C2×C22⋊D5—62no—
373C2×C22⋊D5—62no—
374C2×C22⋊D5—62no—
375C2×C22⋊D5—632no—
376C2×C22⋊D5C4×D314yescomplemented
377C22×Dic5—22no—
378C22×Dic5—22no—
379C22×Dic5—31no—
380C22×Dic5—31no—
381C22×Dic5—34no—
382C22×Dic5—31no—
383C22×Dic5—41no—
384C22×Dic5—62no—
385C22×Dic5—62no—
386C22×Dic5—62no—
387C22×Dic5—62no—
388C22×Dic5—121no—
389C22×Dic5C22×D311yescharacteristic
390C22×Dic5C22×D311yescharacteristic
391C22×Dic5C22×D311yescharacteristic
392C2×C4×D5—62no—
393C2×C4×D5—62no—
394C2×C4×D5—62no—
395C2×C4×D5—62no—
396C2×C4×D5—121no—
397C2×C4×D5—121no—
398C5×C22⋊C4—22no—
399C5×C22⋊C4—62no—
400C5×C22⋊C4—62no—
401C5×C22⋊C4—62no—
402C5×C22⋊C4—121no—
403C5×C22⋊C4—121no—
404C22⋊Dic5—34no—
405C22⋊Dic5—62no—
406C22⋊Dic5—62no—
407C22⋊Dic5—62no—
408#685—22no—
409#685—41no—
410#685—62no—
411#685—62no—
412#685—62no—
413#685—121no—
414#683—62no—
415#683—62no—
416C4×Dic5—62no—
417C4×Dic5—62no—
418C23×D4—151no—
419C2×C4×D4—151no—
420C2×C4×D4—151no—
421C22×C22⋊C4—151no—
422C22×C22⋊C4—151no—
423#390—151no—
424#390—151no—
425#386—51no—
426#386—151no—
427#386—151no—
428#386—151no—
429#380—151no—
430#379—31no—
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—22no—
451C2×D15—22no—
452C2×D15—22no—
453C2×D15C2×C22⋊C414yescomplemented
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×D3—22no—
461C2×C5×D3—22no—
462C2×C5×D3—22no—
463C2×C5×D3—416no—
464C2×C5×D3—41no—
465C2×C5×D3—41no—
466C2×C5×D3—41no—
467C2×C5×D3—41no—
468C2×C5×D3C4×D414yescomplemented
469C2×C3×D5—22no—
470C2×C3×D5—22no—
471C2×C3×D5—22no—
472C2×C3×D5—41no—
473C2×C3×D5—41no—
474C2×C3×D5—41no—
475C2×C3×D5—41no—
476D3×D5—416no—
477C3×C4×C5—41no—
478C3×C4×C5—41no—
479Dic15—22no—
480Dic15—41no—
481Dic15C2×C22⋊C414yescomplemented
482C3×Dic5—22no—
483C3×Dic5—22no—
484C3×Dic5—41no—
485C5×Dic3—41no—
486C5×Dic3—41no—
487C24×C3—51no—
488C24×C3C22×D511yescharacteristic
489C23×D3—22no—
490C23×D3—22no—
491C23×D3—22no—
492C23×D3—22no—
493C23×D3—41no—
494C23×D3—41no—
495C23×D3—51no—
496C23×D3—54no—
497C23×D3—102no—
498C23×D3—102no—
499C23×D3—102no—
500C23×D3—102no—
501C23×D3—201no—
502C23×D3—201no—
503C23×D3C4×D514yescomplemented
504C23×D3C22×D511yescharacteristic
505C23×D3C22×D511yescharacteristic
506C2×C3×D4—54no—
507C2×C3×D4—102no—
508C2×C3×D4—102no—
509C22×C3×C4—51no—
510C22×C3×C4—51no—
511C22×C3×C4—51no—
512C22×C3×C4—102no—
513C22×C3×C4—102no—
514C22×C3×C4—201no—
515C22×C3×C4C22×D511yescharacteristic
516C22×C3×C4C22×D511yescharacteristic
517C2×#67—54no—
518C2×#67—54no—
519C2×#67—54no—
520C2×#67—54no—
521C2×#67—102no—
522C2×#67—102no—
523C22×Dic3—51no—
524C22×Dic3—51no—
525C22×Dic3—51no—
526C22×Dic3—102no—
527C22×Dic3—102no—
528C22×Dic3—201no—
529C22×Dic3C22×D511yescharacteristic
530C22×Dic3C22×D511yescharacteristic
531D3×D4—1032no—
532C2×D12—54no—
533C2×D12—102no—
534C2×D12—102no—
535C2×C4×D3—54no—
536C2×C4×D3—102no—
537C2×C4×D3—102no—
538C2×C4×D3—102no—
539C2×C4×D3—102no—
540C2×C4×D3—102no—
541C2×C4×D3—102no—
542C2×C4×D3—201no—
543C2×C4×D3—201no—
544C3×C22⋊C4—22no—
545C3×C22⋊C4—102no—
546C3×C22⋊C4—201no—
547#217—22no—
548#217—102no—
549#217—201no—
550(C2×D3)⋊C4—22no—
551(C2×D3)⋊C4—22no—
552(C2×D3)⋊C4—41no—
553(C2×D3)⋊C4—41no—
554(C2×D3)⋊C4—54no—
555(C2×D3)⋊C4—102no—
556(C2×D3)⋊C4—102no—
557(C2×D3)⋊C4—102no—
558(C2×D3)⋊C4—102no—
559(C2×D3)⋊C4—102no—
560Dic3⋊C4—102no—
561Dic3⋊C4—102no—
562C4×Dic3—102no—
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—32no—
572C23×C5—68no—
573C23×C5—61no—
574C23×C5—61no—
575C23×C5—61no—
576C23×C5—61no—
577C23×C5—68no—
578C23×C5—61no—
579C23×C5—61no—
580C23×C5—61no—
581C23×C5—61no—
582C23×C5—61no—
583C23×C5—61no—
584C23×C5—124no—
585C23×C5—124no—
586C23×C5—124no—
587C23×C5—124no—
588C23×C5—124no—
589C23×C5C2×C4×D312yes—
590C23×C5D3×D412yes—
591C23×C5D3×D412yes—
592C23×C5C23×D311yescharacteristic
593C22×D5—21no—
594C22×D5—21no—
595C22×D5—21no—
596C22×D5—21no—
597C22×D5—21no—
598C22×D5—21no—
599C22×D5—32no—
600C22×D5—32no—
601C22×D5—32no—
602C22×D5—68no—
603C22×D5—68no—
604C22×D5—61no—
605C22×D5—61no—
606C22×D5—61no—
607C22×D5—61no—
608C22×D5—124no—
609C22×D5—124no—
610C22×D5—124no—
611C22×D5—124no—
612C22×D5—124no—
613C22×D5C2×C4×D312yes—
614C2×C4×C5—21no—
615C2×C4×C5—21no—
616C2×C4×C5—21no—
617C2×C4×C5—21no—
618C2×C4×C5—21no—
619C2×C4×C5—21no—
620C2×C4×C5—61no—
621C2×C4×C5—61no—
622C2×C4×C5—61no—
623C2×C4×C5—61no—
624C2×C4×C5—61no—
625C2×C4×C5—61no—
626C22⋊D5—28no—
627C22⋊D5—316no—
628C22⋊D5—68no—
629C22⋊D5—68no—
630C2×Dic5—21no—
631C2×Dic5—21no—
632C2×Dic5—21no—
633C2×Dic5—21no—
634C2×Dic5—21no—
635C2×Dic5—21no—
636C2×Dic5—21no—
637C2×Dic5—32no—
638C2×Dic5—32no—
639C2×Dic5—32no—
640C2×Dic5—32no—
641C2×Dic5—44no—
642C2×Dic5—68no—
643C2×Dic5—61no—
644C2×Dic5—61no—
645C2×Dic5—61no—
646C2×Dic5—61no—
647C2×Dic5—61no—
648C2×Dic5—124no—
649C2×Dic5C2×C4×D312yes—
650C2×Dic5D3×D412yescomplemented
651C4×D5—124no—
652C4×D5—124no—
653C25—31no—
654C25—151no—
655C22×D4—51no—
656C22×D4—151no—
657C22×D4—158no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—304no—
661C22×D4—304no—
662C23×C4—51no—
663C23×C4—151no—
664C23×C4—151no—
665C23×C4—151no—
666C23×C4—151no—
667C4×D4—304no—
668C4×D4—304no—
669C2×C4⋊C4—151no—
670C2×C4⋊C4—151no—
671C2×C22⋊C4—31no—
672C2×C22⋊C4—31no—
673C2×C22⋊C4—31no—
674C2×C22⋊C4—31no—
675C2×C22⋊C4—31no—
676C2×C22⋊C4—51no—
677C2×C22⋊C4—51no—
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—304no—
687C2×C22⋊C4—304no—
688C2×C22⋊C4D3×D511yescharacteristic, complemented
689C2×C42—151no—
690C2×C42—151no—
691#95—51no—
692#95—51no—
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—24no—
704C3×D5—42no—
705C5×D3—24no—
706C5×D3—42no—
707C23×C3—21no—
708C23×C3—21no—
709C23×C3—21no—
710C23×C3—21no—
711C23×C3—52no—
712C23×C3—101no—
713C23×C3—101no—
714C23×C3—101no—
715C23×C3—101no—
716C23×C3—101no—
717C23×C3—101no—
718C23×C3C2×C4×D512yes—
719C23×C3D4×D512yes—
720C23×C3D4×D512yes—
721C23×C3C23×D511yescharacteristic
722C22×D3—21no—
723C22×D3—21no—
724C22×D3—21no—
725C22×D3—21no—
726C22×D3—21no—
727C22×D3—21no—
728C22×D3—21no—
729C22×D3—21no—
730C22×D3—21no—
731C22×D3—21no—
732C22×D3—28no—
733C22×D3—28no—
734C22×D3—44no—
735C22×D3—44no—
736C22×D3—44no—
737C22×D3—44no—
738C22×D3—44no—
739C22×D3—52no—
740C22×D3—52no—
741C22×D3—52no—
742C22×D3—108no—
743C22×D3—101no—
744C22×D3—101no—
745C22×D3—101no—
746C22×D3—101no—
747C22×D3—108no—
748C22×D3—204no—
749C22×D3—204no—
750C22×D3—204no—
751C22×D3—204no—
752C22×D3—204no—
753C22×D3C2×C4×D512yes—
754C22×D3C2×C4×D512yes—
755C22×D3D4×D512yes—
756C22×D3#71112yes—
757C3×D4—108no—
758C2×C3×C4—21no—
759C2×C3×C4—21no—
760C2×C3×C4—21no—
761C2×C3×C4—21no—
762C2×C3×C4—21no—
763C2×C3×C4—21no—
764C2×C3×C4—52no—
765C2×C3×C4—52no—
766C2×C3×C4—101no—
767C2×C3×C4—101no—
768C2×C3×C4—101no—
769C2×C3×C4—101no—
770C2×C3×C4—101no—
771C2×C3×C4—101no—
772C2×C3×C4—101no—
773C2×C3×C4—204no—
774#67—516no—
775#67—108no—
776C2×Dic3—21no—
777C2×Dic3—21no—
778C2×Dic3—21no—
779C2×Dic3—21no—
780C2×Dic3—21no—
781C2×Dic3—21no—
782C2×Dic3—52no—
783C2×Dic3—52no—
784C2×Dic3—52no—
785C2×Dic3—52no—
786C2×Dic3—101no—
787C2×Dic3—101no—
788C2×Dic3—101no—
789C2×Dic3—101no—
790C2×Dic3—101no—
791C2×Dic3—204no—
792D12—108no—
793C4×D3—108no—
794C4×D3—204no—
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×C5—62no—
810C22×C5—62no—
811C22×C5—62no—
812C22×C5—1216no—
813C22×C5—121no—
814C22×C5—121no—
815C22×C5—121no—
816C22×C5—121no—
817C22×C5D3×C22⋊C414yescomplemented
818C22×C5C22×C4×D311yescharacteristic
819C22×C5C2×D3×D411yescharacteristic
820C22×C5C2×D3×D411yescharacteristic
821C22×C5C2×D3×D411yescharacteristic
822C22×C5#100411yescharacteristic
823C22×C5D3×#4111yescharacteristic
824C22×C5#100911yescharacteristic
825C2×D5—22no—
826C2×D5—22no—
827C2×D5—22no—
828C2×D5—34no—
829C2×D5—41no—
830C2×D5—41no—
831C2×D5—41no—
832C2×D5—41no—
833C2×D5—62no—
834C2×D5—62no—
835C2×D5—62no—
836C2×D5—62no—
837C2×D5—62no—
838C2×D5—62no—
839C2×D5—1216no—
840C4×C5—41no—
841C4×C5—41no—
842C4×C5—121no—
843C4×C5—121no—
844Dic5—22no—
845Dic5—22no—
846Dic5—34no—
847Dic5—41no—
848Dic5—62no—
849Dic5—121no—
850C24—31no—
851C24—31no—
852C24—34no—
853C24—51no—
854C24—62no—
855C24—62no—
856C24—62no—
857C24—62no—
858C24—121no—
859C24—121no—
860C24—154no—
861C24—151no—
862C24—302no—
863C24—302no—
864C24—302no—
865C24—302no—
866C24—601no—
867C24—601no—
868C24C2×D3×D511yescharacteristic
869C2×D4—54no—
870C2×D4—102no—
871C2×D4—102no—
872C2×D4—154no—
873C2×D4—154no—
874C2×D4—154no—
875C2×D4—154no—
876C2×D4—154no—
877C2×D4—302no—
878C2×D4—302no—
879C2×D4—302no—
880C2×D4—302no—
881C2×D4—3032no—
882C22×C4—31no—
883C22×C4—31no—
884C22×C4—51no—
885C22×C4—51no—
886C22×C4—51no—
887C22×C4—102no—
888C22×C4—102no—
889C22×C4—154no—
890C22×C4—151no—
891C22×C4—151no—
892C22×C4—151no—
893C22×C4—201no—
894C22×C4—302no—
895C22×C4—302no—
896C22×C4—302no—
897C22×C4—302no—
898C22×C4—302no—
899C22×C4—302no—
900C22×C4—302no—
901C22×C4—302no—
902C22×C4—601no—
903C22×C4—601no—
904C22×C4—601no—
905C22×C4C2×D3×D511yescharacteristic
906C22×C4C2×D3×D511yescharacteristic
907C4⋊C4—302no—
908C4⋊C4—302no—
909C22⋊C4—22no—
910C22⋊C4—62no—
911C22⋊C4—62no—
912C22⋊C4—62no—
913C22⋊C4—102no—
914C22⋊C4—121no—
915C22⋊C4—121no—
916C22⋊C4—154no—
917C22⋊C4—201no—
918C22⋊C4—302no—
919C22⋊C4—302no—
920C22⋊C4—302no—
921C22⋊C4—302no—
922C22⋊C4—302no—
923C22⋊C4—302no—
924C22⋊C4—601no—
925C42—302no—
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—102no—
935C22×C3—102no—
936C22×C3—102no—
937C22×C3—201no—
938C22×C3—201no—
939C22×C3—201no—
940C22×C3—201no—
941C22×C3D5×C22⋊C414yescomplemented
942C22×C3C22×C4×D511yescharacteristic
943C22×C3C2×D4×D511yescharacteristic
944C22×C3C2×D4×D511yescharacteristic
945C22×C3C2×D4×D511yescharacteristic
946C22×C3C2×#71111yescharacteristic
947C22×C3#414411yescharacteristic
948C22×C3#414411yescharacteristic
949C2×D3—22no—
950C2×D3—22no—
951C2×D3—22no—
952C2×D3—22no—
953C2×D3—22no—
954C2×D3—22no—
955C2×D3—22no—
956C2×D3—22no—
957C2×D3—22no—
958C2×D3—416no—
959C2×D3—41no—
960C2×D3—41no—
961C2×D3—41no—
962C2×D3—41no—
963C2×D3—54no—
964C2×D3—102no—
965C2×D3—102no—
966C2×D3—102no—
967C2×D3—102no—
968C2×D3—102no—
969C2×D3—102no—
970C2×D3—2016no—
971C2×D3#402714yescomplemented
972C3×C4—41no—
973C3×C4—41no—
974C3×C4—102no—
975C3×C4—102no—
976C3×C4—201no—
977Dic3—41no—
978Dic3—41no—
979Dic3—54no—
980Dic3—102no—
981Dic3—201no—
982C2×C5—24no—
983C2×C5—64no—
984C2×C5—122no—
985C2×C5C2×D3×C22⋊C411yescharacteristic
986C2×C5C4×D3×D411yescharacteristic
987C2×C5#554511yescharacteristic
988C2×C5#559011yescharacteristic
989C2×C5#560911yescharacteristic
990C2×C5#561011yescharacteristic
991C2×C5#565411yescharacteristic
992D5—42no—
993D5—64no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—32no—
999C23—32no—
1000C23—32no—
1001C23—32no—
1002C23—52no—
1003C23—68no—
1004C23—61no—
1005C23—61no—
1006C23—61no—
1007C23—61no—
1008C23—68no—
1009C23—61no—
1010C23—61no—
1011C23—61no—
1012C23—61no—
1013C23—61no—
1014C23—61no—
1015C23—101no—
1016C23—101no—
1017C23—101no—
1018C23—101no—
1019C23—101no—
1020C23—101no—
1021C23—124no—
1022C23—124no—
1023C23—124no—
1024C23—124no—
1025C23—124no—
1026C23—152no—
1027C23—152no—
1028C23—152no—
1029C23—308no—
1030C23—308no—
1031C23—301no—
1032C23—301no—
1033C23—301no—
1034C23—301no—
1035C23—604no—
1036C23—604no—
1037C23—604no—
1038C23—604no—
1039C23—604no—
1040C23C4×D3×D512yes—
1041C23#677712yes—
1042C23#679012yes—
1043C23C22×D3×D511yescharacteristic
1044D4—108no—
1045D4—1516no—
1046D4—308no—
1047D4—308no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—52no—
1055C2×C4—52no—
1056C2×C4—61no—
1057C2×C4—61no—
1058C2×C4—61no—
1059C2×C4—61no—
1060C2×C4—61no—
1061C2×C4—61no—
1062C2×C4—101no—
1063C2×C4—101no—
1064C2×C4—101no—
1065C2×C4—101no—
1066C2×C4—101no—
1067C2×C4—101no—
1068C2×C4—101no—
1069C2×C4—152no—
1070C2×C4—152no—
1071C2×C4—152no—
1072C2×C4—152no—
1073C2×C4—204no—
1074C2×C4—308no—
1075C2×C4—301no—
1076C2×C4—301no—
1077C2×C4—301no—
1078C2×C4—301no—
1079C2×C4—301no—
1080C2×C4—604no—
1081C2×C4—604no—
1082C2×C4—604no—
1083C2×C3—24no—
1084C2×C3—202no—
1085C2×C3C2×D5×C22⋊C411yescharacteristic
1086C2×C3C2×#402711yescharacteristic
1087C2×C3#6582011yescharacteristic
1088C2×C3#6592411yescharacteristic
1089C2×C3#6592411yescharacteristic
1090C2×C3#6592511yescharacteristic
1091C2×C3#6592511yescharacteristic
1092D3—24no—
1093D3—42no—
1094D3—104no—
1095C5#7487811yescharacteristic, complemented, Sylow
1096C22—22no—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—34no—
1103C22—62no—
1104C22—62no—
1105C22—62no—
1106C22—62no—
1107C22—62no—
1108C22—62no—
1109C22—62no—
1110C22—62no—
1111C22—62no—
1112C22—102no—
1113C22—102no—
1114C22—102no—
1115C22—1216no—
1116C22—121no—
1117C22—121no—
1118C22—121no—
1119C22—121no—
1120C22—154no—
1121C22—201no—
1122C22—201no—
1123C22—201no—
1124C22—201no—
1125C22—302no—
1126C22—302no—
1127C22—302no—
1128C22—302no—
1129C22—302no—
1130C22—302no—
1131C22—6016no—
1132C22#9147314yescomplemented
1133C22C2×C4×D3×D511yescharacteristic
1134C22C2×#677711yescharacteristic
1135C22D3×D4×D511yescharacteristic
1136C22D3×#71111yescharacteristic
1137C22#9202511yescharacteristic
1138C22#9202711yescharacteristic
1139C22C2×#679011yescharacteristic
1140C4—41no—
1141C4—41no—
1142C4—102no—
1143C4—102no—
1144C4—121no—
1145C4—121no—
1146C4—154no—
1147C4—201no—
1148C4—302no—
1149C4—601no—
1150C3#1060558111yescharacteristic, complemented, Sylow
1151C2—24no—
1152C2—64no—
1153C2—122no—
1154C2—202no—
1155C2—304no—
1156C2D3×#402711yescharacteristic
1157C2#1175320211yescharacteristic
1158C2#1175322511yescharacteristic
1159C2#1175327311yescharacteristic
1160C2C2×#9147311yescharacteristic
1161C2#1175505411yescharacteristic
1162C2#1175507211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×D3×C22⋊D5C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5D4×C22⋊C4
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
2. C2×#91770C2semidirect
3. C2×#91552C2semidirect
4. C22×(C2×D3)⋊Dic5C2semidirect
5. C2×#91473C2semidirect
6. C5×#4955C2semidirect
7. C3×#65247C2semidirect
8. #11749500C2semidirect
9. #11748940C2semidirect
10. #11748919C2semidirect
11. #11748918C2semidirect
12. #11748916C2semidirect
13. #11748915C2semidirect
14. #11748887C2semidirect
15. #11748886C2semidirect
20. C23×Dic15C22semidirect
21. C22×C4×D15C22semidirect
23. C23×C3×Dic5C22semidirect
26. C2×D3×C22⋊D5C4semidirect
29. C22×#1200C22semidirect
31. C2×C3×C5×C22⋊C4C22semidirect
32. C2×#6714C22semidirect
33. C2×#6712C22semidirect
34. C2×C4×Dic15C22semidirect
36. C2×C5×#217C22semidirect
39. C2×C5×(C2×D3)⋊C4C22semidirect
40. C2×C5×(C2×D3)⋊C4C22semidirect
41. C2×C3×#685C22semidirect
42. C2×C3×#685C22semidirect
44. C2×#6669C22semidirect
45. C2×#6667C22semidirect
49. C2×(C2×D3)⋊Dic5C22semidirect
50. C2×(C2×D3)⋊Dic5C22semidirect
51. C2×#6665C22semidirect
52. C2×#6665C22semidirect
53. C2×Dic3×Dic5C22semidirect
55. C3×#3963C22semidirect
56. C3×#3963C22semidirect
57. #90994C22semidirect
58. #90994C22semidirect
67. #65247D3semidirect
83. C23×C5×D3C2×C4semidirect
93. C22×D3×D5C2×C4semidirect
112. C2×C3×C22⋊D5C2×C4semidirect
122. C2×#1203C2×C4semidirect
125. C2×#1201C2×C4semidirect
131. C2×D3×Dic5C2×C4semidirect
148. (C2×D3)⋊Dic5D4semidirect
162. #4955D5semidirect
178. C23×Dic5C2×D3semidirect
186. C2×C5×C22⋊C4C2×D3semidirect
196. C2×#685C2×D3semidirect
197. C2×#685C2×D3semidirect
207. #3963C2×D3semidirect
208. #3963C2×D3semidirect
266. #1220C22⋊C4semidirect
276. C2×Dic15C2×D4semidirect
294. C2×C3×Dic5C2×D4semidirect
315. C2×C3×C22⋊C4C2×D5semidirect
318. C2×#217C2×D5semidirect
329. C2×(C2×D3)⋊C4C2×D5semidirect
330. C2×(C2×D3)⋊C4C2×D5semidirect
376. C2×C22⋊D5C4×D3semidirect
439. C22×C3×C5C2×C22⋊C4semidirect
453. C2×D15C2×C22⋊C4semidirect
468. C2×C5×D3C4×D4semidirect
481. Dic15C2×C22⋊C4semidirect
503. C23×D3C4×D5semidirect
650. C2×Dic5D3×D4semidirect
688. C2×C22⋊C4D3×D5semidirect
817. C22×C5D3×C22⋊C4semidirect
927. C3×C5D4×C22⋊C4semidirect
941. C22×C3D5×C22⋊C4semidirect
971. C2×D3#4027semidirect
1095. C5#74878semidirect
1132. C22#91473semidirect
1150. C3#10605581semidirect

Maximal subgroups

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

subgroupindex
C22×D3×C22⋊D52
C2×#917702
C2×#915522
C22×(C2×D3)⋊Dic52
C2×#914732
C5×#49552
C3×#652472
#117495002
#117489402
#117489192
#117489182
#117489162
#117489152
#117488872
#117488862
#106055813
#748785