Finite Group Databasebeta

← #14328134

Subgroups — #14328134

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1220C211yesmaximal, characteristic, complemented
2C2×C4×C5×#67C211yesmaximal, characteristic, complemented
3C2×#91577C211yesmaximal, characteristic
4C2×#91473C211yesmaximal, characteristic, complemented
5C2×D3×#685C211yesmaximal, characteristic, complemented
6C3×#65502C211yesmaximal, characteristic, complemented
7#11749520C211yesmaximal, characteristic, complemented
8#11749519C211yesmaximal, characteristic, complemented
9#11749489C211yesmaximal, characteristic, complemented
10#11748886C211yesmaximal, characteristic, complemented
11#11748881C211yesmaximal, characteristic, complemented
12#11748731C211yesmaximal, characteristic, complemented
13#11748722C211yesmaximal, characteristic, complemented
14#11748709C211yesmaximal, characteristic, complemented
15#11748706C211yesmaximal, characteristic, complemented
16#10614129—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic, complemented
19C22×#1220C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C22×C5×#67C2211yescharacteristic
22C22×C4×C5×D3C2211yescharacteristic
23C22×C3×C22⋊D5C2211yescharacteristic
24C22×#1200C2211yescharacteristic
25C22×D3×Dic5C2211yescharacteristic
26C2×#6719C2211yescharacteristic, complemented
27C4×#1220—24no—
28C2×#6714C2211yescharacteristic
29C2×#6712C2211yescharacteristic, complemented
30C2×C4×Dic15C2211yescharacteristic, complemented
31C2×C5×#217C2211yescharacteristic, complemented
32C4×C5×#67—24no—
33C2×C5×(C2×D3)⋊C4C2211yescharacteristic
34C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
35C2×C4×C5×Dic3C2211yescharacteristic, complemented
36C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
37C2×C3×#685C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39#91577C418yescomplemented
40C2×#6668C2211yescharacteristic, complemented
41C2×#6667C2211yescharacteristic
42C2×#6667C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46C2×#6665C2211yescharacteristic
47C2×#6665C2211yescharacteristic
48C2×Dic3×Dic5C2211yescharacteristic, complemented
49#91473—24no—
50D3×#685—24no—
51C3×#3963C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57#74880—51nomaximal, Hall
58C2×C4×C5×D4—31no—
59C2×#4083—31no—
60C2×C4×C22⋊D5—31no—
61C22×#685—31no—
62C2×D5×C22⋊C4—31no—
63#65509—31no—
64#65502D311yescharacteristic, complemented
65#65499—31no—
66#65279—31no—
67#65278—31no—
68#65246—31no—
69#65245—31no—
70C22⋊C4×Dic5—31no—
71#65229—31no—
72C4×#685—31no—
73C24×C3×C5C2311yescharacteristic
74C23×D15C2311yescharacteristic
75C23×C5×D3C2311yescharacteristic
76C23×C3×D5C2311yescharacteristic
77C22×D3×D5—22no—
78C22×D3×D5—22no—
79C22×D3×D5—22no—
80C22×D3×D5—22no—
81C22×D3×D5—41no—
82C22×D3×D5—41no—
83C22×D3×D5C2×C414yescomplemented
84C22×C3×C4×C5—22no—
85C22×C3×C4×C5—22no—
86C22×C3×C4×C5—41no—
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C2×#1220—22no—
90C2×#1220—22no—
91C2×#1220C2×C414yescomplemented
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C2×C4×D15—22no—
96C2×C4×D15—22no—
97C2×C4×D15—41no—
98C2×C5×#67—22no—
99C2×C5×#67—22no—
100C2×C5×#67C2×C414yescomplemented
101C22×C5×Dic3C2311yescharacteristic
102C22×C5×Dic3C2311yescharacteristic
103C22×C5×Dic3C2311yescharacteristic
104C2×C4×C5×D3—22no—
105C2×C4×C5×D3—22no—
106C2×C4×C5×D3—41no—
107C2×C3×C22⋊D5—41no—
108C2×C3×C22⋊D5—41no—
109C2×C3×C22⋊D5C2×C414yescomplemented
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2311yescharacteristic
113C2×#1200—22no—
114C2×#1200—22no—
115C2×#1200—41no—
116C2×D3×Dic5—22no—
117C2×D3×Dic5—22no—
118C2×D3×Dic5—41no—
119#6719—22no—
120#6714D414yescomplemented
121#6712—22no—
122C4×Dic15—22no—
123C5×#217—22no—
124C5×(C2×D3)⋊C4D414yescomplemented
125C5×Dic3⋊C4—22no—
126C4×C5×Dic3—22no—
127C3×C22⋊Dic5—41no—
128C3×#685—22no—
129C3×#685—22no—
130#6668—41no—
131#6667—22no—
132#6667C2×C414yescomplemented
133(C2×D3)⋊Dic5—22no—
134(C2×D3)⋊Dic5C2×C414yescomplemented
135#6665—22no—
136#6665—22no—
137#6665C2×C414yescomplemented
138Dic3×Dic5—41no—
139C2×#937—51no—
140C2×C4×#67—51no—
141C2×C4×#67D511yescharacteristic, complemented
142C2×D3×C22⋊C4—51no—
143C2×D3×C22⋊C4—51no—
144C3×#386—51no—
145#5221—51no—
146#4956—51no—
147#4956—51no—
148#4945—51no—
149#4945—51no—
150#4668—51no—
151#4668—51no—
152#4666—51no—
153#4666—51no—
154C24×D5—31no—
155C22×C5×D4—31no—
156C23×C4×C5—31no—
157C23×C4×C5C2×D311yescharacteristic, complemented
158C22×C22⋊D5—31no—
159C22×C22⋊D5C2×D311yescharacteristic
160C23×Dic5—31no—
161C22×C4×D5—31no—
162C22×C4×D5—31no—
163C4×C5×D4—64no—
164C2×C5×C4⋊C4—31no—
165C2×C5×C22⋊C4—31no—
166C2×C5×C22⋊C4—31no—
167C2×C42×C5—31no—
168C2×C22⋊Dic5—31no—
169C2×C22⋊Dic5—31no—
170C2×C22⋊Dic5—31no—
171C2×C22⋊Dic5C2×D311yescharacteristic, complemented
172#4083—38no—
173C4×C22⋊D5—64no—
174C2×#685—31no—
175C2×#685—31no—
176C2×#685—31no—
177C2×#685—31no—
178C2×#685—31no—
179C2×#685—31no—
180C2×#685—64no—
181C2×#685C2×D311yescharacteristic
182C2×#685C2×D311yescharacteristic
183C2×#683—31no—
184C2×#683—31no—
185C2×C4×Dic5—31no—
186C2×C4×Dic5—31no—
187D5×C22⋊C4—64no—
188#3963—31no—
189#3963—31no—
190#3963—31no—
191#3963—31no—
192#3963C2×D311yescharacteristic, complemented
193#3963C2×D311yescharacteristic, complemented
194#2358—151noSylow
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5—21no—
200C23×C3×C5—21no—
201C23×C3×C5C22×C412yes—
202C23×C3×C5C2411yescharacteristic
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—21no—
207C22×D15C22×C412yes—
208C22×D15C2×D412yes—
209C22×D15#4112yes—
210C22×C5×D3—21no—
211C22×C5×D3—21no—
212C22×C5×D3—21no—
213C22×C5×D3—21no—
214C22×C5×D3C22×C412yes—
215C22×C5×D3C2×D412yes—
216C22×C5×D3#4112yes—
217C22×C3×D5—21no—
218C22×C3×D5—21no—
219C22×C3×D5—21no—
220C22×C3×D5—21no—
221C22×C3×D5—21no—
222C22×C3×D5—21no—
223C22×C3×D5C22×C412yes—
224C2×D3×D5—28no—
225C2×D3×D5—28no—
226C2×D3×D5—44no—
227C2×D3×D5—44no—
228C2×D3×D5—44no—
229C2×D3×D5—44no—
230C2×D3×D5—44no—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5—44no—
236C2×C3×C4×C5C2×D412yes—
237C2×C3×C4×C5C2×D412yes—
238#1220—28no—
239C2×Dic15—21no—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15—21no—
243C2×Dic15—21no—
244C2×Dic15—21no—
245C2×Dic15—21no—
246C2×Dic15C22×C412yes—
247C2×Dic15C2×D412yes—
248C4×D15—44no—
249C5×#67—28no—
250C2×C5×Dic3—21no—
251C2×C5×Dic3—21no—
252C2×C5×Dic3—21no—
253C2×C5×Dic3—21no—
254C2×C5×Dic3—21no—
255C2×C5×Dic3—21no—
256C2×C5×Dic3—21no—
257C2×C5×Dic3C22×C412yes—
258C2×C5×Dic3C2×D412yes—
259C4×C5×D3—44no—
260C3×C22⋊D5—44no—
261C2×C3×Dic5—21no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—21no—
264C2×C3×Dic5—21no—
265C2×C3×Dic5—21no—
266C2×C3×Dic5—21no—
267C2×C3×Dic5—21no—
268C2×C3×Dic5—21no—
269C2×C3×Dic5C22×C412yes—
270#1200—44no—
271D3×Dic5—44no—
272C24×D3—51no—
273C22×C3×D4—51no—
274C23×C3×C4C2×D511yescharacteristic, complemented
275C22×#67—51no—
276C22×#67C2×D511yescharacteristic
277C22×C4×D3—51no—
278C22×C4×D3—51no—
279C22×C4×D3—51no—
280C22×C4×D3C2×D511yescharacteristic
281C2×C3×C22⋊C4—51no—
282C2×C3×C22⋊C4—51no—
283C2×C3×C22⋊C4—51no—
284C2×#217—51no—
285C2×#217—51no—
286C2×#217—51no—
287C2×#217—51no—
288C2×#217C2×D511yescharacteristic, complemented
289#937—58no—
290C4×#67—24no—
291C4×#67—104no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4—51no—
294C2×(C2×D3)⋊C4—51no—
295C2×(C2×D3)⋊C4—51no—
296C2×(C2×D3)⋊C4—51no—
297C2×(C2×D3)⋊C4C2×D511yescharacteristic
298C2×C4⋊Dic3—51no—
299C2×Dic3⋊C4—51no—
300C2×Dic3⋊C4C2×D511yescharacteristic, complemented
301C2×C4×Dic3—51no—
302C2×C4×Dic3—51no—
303C2×C4×Dic3C2×D511yescharacteristic, complemented
304D3×C22⋊C4—104no—
305D3×C22⋊C4—104no—
306C3×#95—51no—
307C3×#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95—51no—
311C3⋊#95—51no—
312C24×C5—31no—
313C24×C5C22×D311yescharacteristic
314C23×D5—31no—
315C23×D5—34no—
316C23×D5—62no—
317C23×D5—62no—
318C23×D5—62no—
319C23×D5—62no—
320C23×D5—121no—
321C23×D5—121no—
322C23×D5C22×D311yescharacteristic
323C2×C5×D4—34no—
324C2×C5×D4—62no—
325C2×C5×D4—62no—
326C22×C4×C5—22no—
327C22×C4×C5—22no—
328C22×C4×C5—31no—
329C22×C4×C5—31no—
330C22×C4×C5—31no—
331C22×C4×C5—41no—
332C22×C4×C5—62no—
333C22×C4×C5—62no—
334C22×C4×C5—121no—
335C22×C4×C5C22×D311yescharacteristic
336C22×C4×C5C22×D311yescharacteristic
337C2×C22⋊D5—34no—
338C2×C22⋊D5—41no—
339C2×C22⋊D5—41no—
340C2×C22⋊D5—62no—
341C2×C22⋊D5—62no—
342C2×C22⋊D5C4×D314yescomplemented
343C22×Dic5—31no—
344C22×Dic5—31no—
345C22×Dic5—31no—
346C22×Dic5—62no—
347C22×Dic5—62no—
348C22×Dic5—121no—
349C22×Dic5C22×D311yescharacteristic
350C22×Dic5C22×D311yescharacteristic
351C22×Dic5C22×D311yescharacteristic
352C2×C4×D5—62no—
353C2×C4×D5—62no—
354C2×C4×D5—62no—
355C2×C4×D5—62no—
356C2×C4×D5—121no—
357C2×C4×D5—121no—
358C5×C4⋊C4—62no—
359C5×C22⋊C4—34no—
360C5×C22⋊C4—62no—
361C42×C5—62no—
362C22⋊Dic5—34no—
363C22⋊Dic5—41no—
364C22⋊Dic5—62no—
365C22⋊Dic5—62no—
366#685—22no—
367#685—22no—
368#685—34no—
369#685—34no—
370#685—34no—
371#685—62no—
372#685—62no—
373#685—62no—
374#683—62no—
375#683—121no—
376C4×Dic5—62no—
377C4×Dic5—121no—
378C2×#120—151no—
379C2×C4×D4—31no—
380C2×C4×D4—151no—
381C22×C22⋊C4—151no—
382C22×C22⋊C4—151no—
383#390—151no—
384#388—151no—
385#388—151no—
386#386—51no—
387#386—151no—
388#386—151no—
389#385—151no—
390#385—151no—
391C4×C22⋊C4—151no—
392C4×C22⋊C4—151no—
393C22×C3×C5—22no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5—41no—
397C22×C3×C5—41no—
398C22×C3×C5—41no—
399C22×C3×C5—41no—
400C22×C3×C5C23×C411yescharacteristic
401C22×C3×C5C22×D411yescharacteristic
402C22×C3×C5C22×D411yescharacteristic
403C22×C3×C5C2×#4111yescharacteristic
404C22×C3×C5C2×#4111yescharacteristic
405C22×C3×C5H(5,𝔽2)11yescharacteristic
406C22×C3×C5H(5,𝔽2)11yescharacteristic
407C2×D15—22no—
408C2×D15—22no—
409C2×D15—22no—
410C2×D15—22no—
411C2×D15—22no—
412C2×D15—22no—
413C2×D15C4×D414yescomplemented
414C2×C5×D3—22no—
415C2×C5×D3—22no—
416C2×C5×D3—22no—
417C2×C5×D3—22no—
418C2×C5×D3—22no—
419C2×C5×D3—22no—
420C2×C5×D3C4×D414yescomplemented
421C2×C3×D5—22no—
422C2×C3×D5—22no—
423C2×C3×D5—22no—
424C2×C3×D5—41no—
425C2×C3×D5—41no—
426C2×C3×D5—41no—
427C2×C3×D5—41no—
428D3×D5—416no—
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431Dic15—22no—
432Dic15—22no—
433Dic15—41no—
434C3×Dic5—22no—
435C3×Dic5—41no—
436C3×Dic5—41no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3—41no—
440C24×C3—51no—
441C24×C3C22×D511yescharacteristic
442C23×D3—51no—
443C23×D3—54no—
444C23×D3—102no—
445C23×D3—102no—
446C23×D3—102no—
447C23×D3—102no—
448C23×D3—201no—
449C23×D3—201no—
450C23×D3C22×D511yescharacteristic
451C2×C3×D4—54no—
452C2×C3×D4—201no—
453C2×C3×D4—201no—
454C22×C3×C4—22no—
455C22×C3×C4—22no—
456C22×C3×C4—41no—
457C22×C3×C4—51no—
458C22×C3×C4—51no—
459C22×C3×C4—51no—
460C22×C3×C4C22×D511yescharacteristic
461C22×C3×C4C22×D511yescharacteristic
462C2×#67—22no—
463C2×#67—22no—
464C2×#67—54no—
465C2×#67—102no—
466C2×#67—102no—
467C2×#67C4×D514yescomplemented
468C22×Dic3—51no—
469C22×Dic3—51no—
470C22×Dic3—51no—
471C22×Dic3C22×D511yescharacteristic
472C22×Dic3C22×D511yescharacteristic
473C22×Dic3C22×D511yescharacteristic
474C2×C4×D3—22no—
475C2×C4×D3—22no—
476C2×C4×D3—41no—
477C2×C4×D3—102no—
478C2×C4×D3—102no—
479C2×C4×D3—102no—
480C2×C4×D3—102no—
481C2×C4×D3—102no—
482C2×C4×D3—102no—
483C2×C4×D3—201no—
484C2×C4×D3—201no—
485C2×C4×D3—201no—
486C3×C22⋊C4—102no—
487C3×C22⋊C4—102no—
488C3×C22⋊C4—201no—
489#217—22no—
490#217—54no—
491#217—102no—
492#217—102no—
493#217—102no—
494(C2×D3)⋊C4—54no—
495(C2×D3)⋊C4—54no—
496(C2×D3)⋊C4—54no—
497(C2×D3)⋊C4—102no—
498(C2×D3)⋊C4—102no—
499(C2×D3)⋊C4C22⋊D514yescomplemented
500C4⋊Dic3—201no—
501Dic3⋊C4—22no—
502Dic3⋊C4—102no—
503C4×Dic3—22no—
504C4×Dic3—102no—
505C4×Dic3—201no—
506C23×C5—21no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5—21no—
511C23×C5—21no—
512C23×C5—32no—
513C23×C5—32no—
514C23×C5—32no—
515C23×C5—61no—
516C23×C5—61no—
517C23×C5—61no—
518C23×C5—61no—
519C23×C5C2×C4×D312yes—
520C23×C5C23×D311yescharacteristic
521C22×D5—21no—
522C22×D5—21no—
523C22×D5—21no—
524C22×D5—21no—
525C22×D5—21no—
526C22×D5—21no—
527C22×D5—32no—
528C22×D5—32no—
529C22×D5—32no—
530C22×D5—68no—
531C22×D5—68no—
532C22×D5—61no—
533C22×D5—61no—
534C22×D5—61no—
535C22×D5—61no—
536C22×D5—124no—
537C22×D5—124no—
538C22×D5—124no—
539C22×D5—124no—
540C22×D5—124no—
541C22×D5C2×C4×D312yes—
542C5×D4—68no—
543C2×C4×C5—21no—
544C2×C4×C5—21no—
545C2×C4×C5—21no—
546C2×C4×C5—21no—
547C2×C4×C5—32no—
548C2×C4×C5—32no—
549C2×C4×C5—44no—
550C2×C4×C5—61no—
551C2×C4×C5—61no—
552C2×C4×C5—61no—
553C2×C4×C5—61no—
554C2×C4×C5—61no—
555C2×C4×C5—61no—
556C2×C4×C5—61no—
557C2×C4×C5—124no—
558C2×C4×C5D3×D412yes—
559C2×C4×C5D3×D412yes—
560C22⋊D5—44no—
561C22⋊D5—68no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—21no—
566C2×Dic5—21no—
567C2×Dic5—21no—
568C2×Dic5—21no—
569C2×Dic5—21no—
570C2×Dic5—32no—
571C2×Dic5—32no—
572C2×Dic5—61no—
573C2×Dic5—61no—
574C2×Dic5—61no—
575C2×Dic5—61no—
576C2×Dic5—61no—
577C2×Dic5—61no—
578C2×Dic5—61no—
579C2×Dic5—124no—
580C2×Dic5C2×C4×D312yes—
581C4×D5—124no—
582C4×D5—124no—
583C25—151no—
584C22×D4—31no—
585C22×D4—51no—
586C22×D4—151no—
587C23×C4—31no—
588C23×C4—151no—
589C23×C4—151no—
590C23×C4—151no—
591C23×C4D3×D511yescharacteristic, complemented
592#120—158no—
593C4×D4—64no—
594C4×D4—304no—
595C2×C4⋊C4—31no—
596C2×C4⋊C4—151no—
597C2×C4⋊C4—151no—
598C2×C22⋊C4—31no—
599C2×C22⋊C4—31no—
600C2×C22⋊C4—51no—
601C2×C22⋊C4—51no—
602C2×C22⋊C4—51no—
603C2×C22⋊C4—151no—
604C2×C22⋊C4—151no—
605C2×C22⋊C4—151no—
606C2×C22⋊C4—151no—
607C2×C22⋊C4—151no—
608C2×C22⋊C4—151no—
609C2×C22⋊C4—151no—
610C2×C22⋊C4—151no—
611C2×C22⋊C4—151no—
612C2×C22⋊C4—304no—
613C2×C22⋊C4—304no—
614C2×C42—31no—
615C2×C42—151no—
616C2×C42—151no—
617#95—51no—
618#95—51no—
619#95—151no—
620#95—151no—
621#95—151no—
622#95—151no—
623C2×C3×C5—42no—
624C2×C3×C5C2×C4×D411yescharacteristic
625C2×C3×C5C2×C4×D411yescharacteristic
626C2×C3×C5#51811yescharacteristic
627C2×C3×C5D4211yescharacteristic
628C2×C3×C5#54611yescharacteristic
629C2×C3×C5#54611yescharacteristic
630C2×C3×C5#55111yescharacteristic
631D15—24no—
632C3×D5—42no—
633C5×D3—24no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3—21no—
639C23×C3—21no—
640C23×C3—52no—
641C23×C3—101no—
642C23×C3—101no—
643C23×C3—101no—
644C23×C3—101no—
645C23×C3—101no—
646C23×C3—101no—
647C23×C3C2×C4×D512yes—
648C23×C3C23×D511yescharacteristic
649C22×D3—21no—
650C22×D3—21no—
651C22×D3—21no—
652C22×D3—21no—
653C22×D3—52no—
654C22×D3—52no—
655C22×D3—52no—
656C22×D3—108no—
657C22×D3—101no—
658C22×D3—101no—
659C22×D3—101no—
660C22×D3—101no—
661C22×D3—108no—
662C22×D3—204no—
663C22×D3—204no—
664C22×D3—204no—
665C22×D3—204no—
666C22×D3—204no—
667C22×D3C2×C4×D512yes—
668C22×D3#70912yes—
669C22×D3C2×C22⋊D512yes—
670C3×D4—204no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—44no—
676C2×C3×C4—52no—
677C2×C3×C4—101no—
678C2×C3×C4—101no—
679C2×C3×C4—101no—
680C2×C3×C4—101no—
681C2×C3×C4—101no—
682C2×C3×C4—101no—
683C2×C3×C4—101no—
684C2×C3×C4—101no—
685C2×C3×C4D4×D512yes—
686C2×C3×C4C2×C22⋊D512yes—
687#67—28no—
688#67—108no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—52no—
697C2×Dic3—52no—
698C2×Dic3—101no—
699C2×Dic3—101no—
700C2×Dic3—101no—
701C2×Dic3—101no—
702C2×Dic3—101no—
703C2×Dic3—101no—
704C2×Dic3—101no—
705C2×Dic3C2×C4×D512yes—
706C2×Dic3C2×C22⋊D512yes—
707C4×D3—44no—
708C4×D3—204no—
709C4×D3—204no—
710C4×D3—204no—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—34no—
715C22×C5—41no—
716C22×C5—41no—
717C22×C5—41no—
718C22×C5—41no—
719C22×C5—62no—
720C22×C5—62no—
721C22×C5—62no—
722C22×C5—62no—
723C22×C5—62no—
724C22×C5—62no—
725C22×C5C22×C4×D311yescharacteristic
726C22×C5C2×D3×D411yescharacteristic
727C22×C5C2×D3×D411yescharacteristic
728C22×C5#100411yescharacteristic
729C22×C5#100411yescharacteristic
730C22×C5D3×#4111yescharacteristic
731C22×C5D3×#4111yescharacteristic
732C2×D5—22no—
733C2×D5—22no—
734C2×D5—22no—
735C2×D5—34no—
736C2×D5—41no—
737C2×D5—41no—
738C2×D5—41no—
739C2×D5—41no—
740C2×D5—62no—
741C2×D5—62no—
742C2×D5—62no—
743C2×D5—62no—
744C2×D5—62no—
745C2×D5—62no—
746C2×D5—1216no—
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—62no—
750C4×C5—62no—
751C4×C5—121no—
752Dic5—22no—
753Dic5—41no—
754Dic5—41no—
755Dic5—62no—
756Dic5—62no—
757Dic5—121no—
758C24—31no—
759C24—51no—
760C24—154no—
761C24—151no—
762C24—302no—
763C24—302no—
764C24—302no—
765C24—302no—
766C24—601no—
767C24—601no—
768C24C2×D3×D511yescharacteristic
769C2×D4—34no—
770C2×D4—54no—
771C2×D4—62no—
772C2×D4—62no—
773C2×D4—154no—
774C2×D4—201no—
775C2×D4—201no—
776C2×D4—302no—
777C2×D4—302no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—31no—
783C22×C4—41no—
784C22×C4—51no—
785C22×C4—51no—
786C22×C4—51no—
787C22×C4—62no—
788C22×C4—62no—
789C22×C4—121no—
790C22×C4—151no—
791C22×C4—151no—
792C22×C4—151no—
793C22×C4—302no—
794C22×C4—302no—
795C22×C4—302no—
796C22×C4—302no—
797C22×C4—302no—
798C22×C4—302no—
799C22×C4—601no—
800C22×C4—601no—
801C22×C4—601no—
802C22×C4C2×D3×D511yescharacteristic
803C22×C4C2×D3×D511yescharacteristic
804C4⋊C4—62no—
805C4⋊C4—302no—
806C4⋊C4—601no—
807C22⋊C4—34no—
808C22⋊C4—62no—
809C22⋊C4—102no—
810C22⋊C4—102no—
811C22⋊C4—154no—
812C22⋊C4—154no—
813C22⋊C4—154no—
814C22⋊C4—154no—
815C22⋊C4—201no—
816C22⋊C4—302no—
817C22⋊C4—302no—
818C22⋊C4—302no—
819C22⋊C4—302no—
820C22⋊C4—302no—
821C42—62no—
822C42—302no—
823C42—601no—
824C3×C5#235811yescharacteristic, complemented, Hall
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—102no—
833C22×C3—102no—
834C22×C3—102no—
835C22×C3—201no—
836C22×C3—201no—
837C22×C3—201no—
838C22×C3—201no—
839C22×C3C22×C4×D511yescharacteristic
840C22×C3C2×#70911yescharacteristic
841C22×C3C2×D4×D511yescharacteristic
842C22×C3#414411yescharacteristic
843C22×C3D5×#4111yescharacteristic
844C22×C3#414911yescharacteristic
845C22×C3C22×C22⋊D511yescharacteristic
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—54no—
853C2×D3—102no—
854C2×D3—102no—
855C2×D3—102no—
856C2×D3—102no—
857C2×D3—102no—
858C2×D3—102no—
859C2×D3—2016no—
860C2×D3C4×C22⋊D514yescomplemented
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—102no—
864C3×C4—201no—
865C3×C4—201no—
866Dic3—22no—
867Dic3—22no—
868Dic3—41no—
869Dic3—102no—
870Dic3—102no—
871Dic3—201no—
872C2×C5—42no—
873C2×C5—64no—
874C2×C5#548611yescharacteristic
875C2×C5C4×D3×D411yescharacteristic
876C2×C5C4×D3×D411yescharacteristic
877C2×C5#559011yescharacteristic
878C2×C5#561211yescharacteristic
879C2×C5#561211yescharacteristic
880C2×C5#565911yescharacteristic
881D5—42no—
882D5—64no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—21no—
889C23—32no—
890C23—32no—
891C23—32no—
892C23—52no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—101no—
898C23—101no—
899C23—101no—
900C23—101no—
901C23—101no—
902C23—101no—
903C23—152no—
904C23—152no—
905C23—152no—
906C23—308no—
907C23—308no—
908C23—301no—
909C23—301no—
910C23—301no—
911C23—301no—
912C23—604no—
913C23—604no—
914C23—604no—
915C23—604no—
916C23—604no—
917C23C4×D3×D512yes—
918C23C22×D3×D511yescharacteristic
919D4—68no—
920D4—204no—
921D4—308no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—32no—
927C2×C4—32no—
928C2×C4—44no—
929C2×C4—52no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—61no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—101no—
938C2×C4—101no—
939C2×C4—101no—
940C2×C4—101no—
941C2×C4—101no—
942C2×C4—101no—
943C2×C4—101no—
944C2×C4—101no—
945C2×C4—124no—
946C2×C4—152no—
947C2×C4—152no—
948C2×C4—301no—
949C2×C4—301no—
950C2×C4—301no—
951C2×C4—301no—
952C2×C4—301no—
953C2×C4—301no—
954C2×C4—301no—
955C2×C4—604no—
956C2×C4—604no—
957C2×C4—604no—
958C2×C4D3×C22⋊D512yes—
959C2×C4#679012yes—
960C2×C3—42no—
961C2×C3—202no—
962C2×C3C4×D4×D511yescharacteristic
963C2×C3#6587911yescharacteristic
964C2×C3#6588411yescharacteristic
965C2×C3#6589011yescharacteristic
966C2×C3C2×C4×C22⋊D511yescharacteristic
967C2×C3D4×C22⋊D511yescharacteristic
968C2×C3#6616311yescharacteristic
969D3—24no—
970D3—104no—
971C5#7488011yescharacteristic, complemented, Sylow
972C22—22no—
973C22—22no—
974C22—22no—
975C22—34no—
976C22—41no—
977C22—41no—
978C22—41no—
979C22—41no—
980C22—62no—
981C22—62no—
982C22—62no—
983C22—62no—
984C22—62no—
985C22—62no—
986C22—102no—
987C22—102no—
988C22—102no—
989C22—154no—
990C22—201no—
991C22—201no—
992C22—201no—
993C22—201no—
994C22—302no—
995C22—302no—
996C22—302no—
997C22—302no—
998C22—302no—
999C22—302no—
1000C22—6016no—
1001C22C2×C4×D3×D511yescharacteristic
1002C22D3×#70911yescharacteristic
1003C22#9201611yescharacteristic
1004C22#9201711yescharacteristic
1005C22C2×D3×C22⋊D511yescharacteristic
1006C22C2×#679011yescharacteristic
1007C22#9204911yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—62no—
1011C4—62no—
1012C4—102no—
1013C4—121no—
1014C4—201no—
1015C4—201no—
1016C4—302no—
1017C4—302no—
1018C4—601no—
1019C3#1061412911yescharacteristic, complemented, Sylow
1020C2—42no—
1021C2—64no—
1022C2—202no—
1023C2—304no—
1024C2#1175462511yescharacteristic
1025C2C4×D3×C22⋊D511yescharacteristic
1026C2C4×#679011yescharacteristic
1027C2#1175465811yescharacteristic
1028C2#1175466711yescharacteristic
1029C2#1175468111yescharacteristic
1030C2#1175544011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91577C2
hypercenterC23×C4D3×D5
hypocenterC3×C5#2358
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×#1220C2semidirect
2. C2×C4×C5×#67C2semidirect
4. C2×#91473C2semidirect
5. C2×D3×#685C2semidirect
6. C3×#65502C2semidirect
7. #11749520C2semidirect
8. #11749519C2semidirect
9. #11749489C2semidirect
10. #11748886C2semidirect
11. #11748881C2semidirect
12. #11748731C2semidirect
13. #11748722C2semidirect
14. #11748709C2semidirect
15. #11748706C2semidirect
18. C23×C3×C4×C5C22semidirect
26. C2×#6719C22semidirect
29. C2×#6712C22semidirect
30. C2×C4×Dic15C22semidirect
31. C2×C5×#217C22semidirect
34. C2×C5×Dic3⋊C4C22semidirect
35. C2×C4×C5×Dic3C22semidirect
36. C2×C3×C22⋊Dic5C22semidirect
39. #91577C4semidirect
40. C2×#6668C22semidirect
48. C2×Dic3×Dic5C22semidirect
51. C3×#3963C22semidirect
52. C3×#3963C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
64. #65502D3semidirect
83. C22×D3×D5C2×C4semidirect
91. C2×#1220C2×C4semidirect
100. C2×C5×#67C2×C4semidirect
109. C2×C3×C22⋊D5C2×C4semidirect
120. #6714D4semidirect
124. C5×(C2×D3)⋊C4D4semidirect
132. #6667C2×C4semidirect
134. (C2×D3)⋊Dic5C2×C4semidirect
137. #6665C2×C4semidirect
141. C2×C4×#67D5semidirect
157. C23×C4×C5C2×D3semidirect
171. C2×C22⋊Dic5C2×D3semidirect
192. #3963C2×D3semidirect
193. #3963C2×D3semidirect
274. C23×C3×C4C2×D5semidirect
288. C2×#217C2×D5semidirect
300. C2×Dic3⋊C4C2×D5semidirect
303. C2×C4×Dic3C2×D5semidirect
342. C2×C22⋊D5C4×D3semidirect
413. C2×D15C4×D4semidirect
420. C2×C5×D3C4×D4semidirect
467. C2×#67C4×D5semidirect
499. (C2×D3)⋊C4C22⋊D5semidirect
591. C23×C4D3×D5semidirect
824. C3×C5#2358semidirect
860. C2×D3C4×C22⋊D5semidirect
971. C5#74880semidirect
1019. C3#10614129semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12202
C2×C4×C5×#672
C2×#915772
C2×#914732
C2×D3×#6852
C3×#655022
#117495202
#117495192
#117494892
#117488862
#117488812
#117487312
#117487222
#117487092
#117487062
#106141293
#748805