Finite Group Databasebeta

← #14328151

Subgroups — #14328151

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
1C22×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
2C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×#91568C211yesmaximal, characteristic
4C2×D3×C22⋊Dic5C211yesmaximal, characteristic, complemented
5C2×#91440C211yesmaximal, characteristic, complemented
6#11751311C211yesmaximal, characteristic, complemented
7#11749495C211yesmaximal, characteristic, complemented
8Dic3×C22⋊Dic5C211yesmaximal, characteristic, complemented
9#11748916C211yesmaximal, characteristic, complemented
10#11748911C211yesmaximal, characteristic, complemented
11#11748905C211yesmaximal, characteristic, complemented
12#11748892C211yesmaximal, characteristic, complemented
13Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
14#11748718C211yesmaximal, characteristic, complemented
15#11748715C211yesmaximal, characteristic, complemented
16#10613830—31nomaximal, Hall
17C24×C5×D3C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic, complemented
22C22×#1201C2211yescharacteristic
23C22×#1201C2211yescharacteristic
24C22×D3×Dic5C2211yescharacteristic
25C22×D3×Dic5C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×#6719C2211yescharacteristic
28C2×#6712C2211yescharacteristic, complemented
29C2×#6712C2211yescharacteristic, complemented
30C2×C5×(C2×D3)⋊C4—24no—
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C5×(C2×D3)⋊C4C2211yescharacteristic
33C2×C5×(C2×D3)⋊C4C2211yescharacteristic
34C2×C5×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×C22⋊Dic5C2211yescharacteristic
36C3×C4×C22⋊D5—24no—
37C2×C3×#685C2211yescharacteristic, complemented
38C2×C3×#683C2211yescharacteristic, complemented
39C2×C3×C4×Dic5C2211yescharacteristic, complemented
40#91568C418yescomplemented
41D3×C22⋊Dic5—24no—
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45C2×(C2×D3)⋊Dic5C2211yescharacteristic
46C2×#6665C2211yescharacteristic, complemented
47C2×#6665C2211yescharacteristic, complemented
48C2×Dic3×Dic5C2211yescharacteristic, complemented
49C2×Dic3×Dic5C2211yescharacteristic, complemented
50#91440—24no—
51#91115C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57#82398—51nomaximal, Hall
58C22×C5×C22⋊C4—31no—
59C2×#4099—31no—
60C22×C22⋊Dic5—31no—
61C2×C4×C22⋊D5D311yescharacteristic, complemented
62C2×#4027—31no—
63#65502—31no—
64#65499—31no—
65C4×C22⋊Dic5—31no—
66#65247—31no—
67#65246—31no—
68#65245—31no—
69#65235—31no—
70#65234—31no—
71#65233—31no—
72C22⋊C4×Dic5—31no—
73C24×C3×C5C2311yescharacteristic
74C23×C5×D3—22no—
75C23×C5×D3—22no—
76C23×C5×D3—22no—
77C23×C5×D3—22no—
78C23×C5×D3—41no—
79C23×C5×D3—41no—
80C23×C5×D3C2×C414yescomplemented
81C23×C5×D3C2311yescharacteristic
82C23×C5×D3C2311yescharacteristic
83C23×C3×D5C2311yescharacteristic
84C22×C3×C4×C5—22no—
85C22×C3×C4×C5—22no—
86C22×C3×C4×C5—41no—
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×C5×Dic3—22no—
94C22×C5×Dic3—22no—
95C22×C5×Dic3—41no—
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
98C2×C3×C22⋊D5—22no—
99C2×C3×C22⋊D5—22no—
100C2×C3×C22⋊D5C2×C414yescomplemented
101C22×C3×Dic5C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C2×C3×C4×D5—22no—
105C2×C3×C4×D5—22no—
106C2×C3×C4×D5—41no—
107C2×#1201—22no—
108C2×#1201—22no—
109C2×#1201—41no—
110C2×#1201—41no—
111C2×#1201C2×C414yescomplemented
112C2×#1201C2×C414yescomplemented
113C2×D3×Dic5—22no—
114C2×D3×Dic5—22no—
115C2×D3×Dic5—22no—
116C2×D3×Dic5—22no—
117C2×D3×Dic5—41no—
118C2×D3×Dic5—41no—
119#6719—22no—
120#6719C2×C414yescomplemented
121#6712—22no—
122#6712—41no—
123C5×(C2×D3)⋊C4—22no—
124C5×(C2×D3)⋊C4—22no—
125C5×(C2×D3)⋊C4—22no—
126C5×(C2×D3)⋊C4D414yescomplemented
127C3×C22⋊Dic5D414yescomplemented
128C3×#685—22no—
129C3×#683—22no—
130C3×C4×Dic5—22no—
131(C2×D3)⋊Dic5—22no—
132(C2×D3)⋊Dic5—22no—
133(C2×D3)⋊Dic5C2×C414yescomplemented
134(C2×D3)⋊Dic5C2×C414yescomplemented
135#6665—22no—
136#6665—41no—
137Dic3×Dic5—22no—
138Dic3×Dic5—41no—
139C2×C3×C4×D4—51no—
140C2×#937—51no—
141C2×C4×#67—51no—
142C22×(C2×D3)⋊C4D511yescharacteristic, complemented
143C2×D3×C22⋊C4—51no—
144#5220—51no—
145#5213—51no—
146#5210—51no—
147#4990—51no—
148#4989—51no—
149#4957—51no—
150#4956—51no—
151Dic3×C22⋊C4—51no—
152#4940—51no—
153C4×(C2×D3)⋊C4—51no—
154C25×C5—31no—
155C23×C4×C5—31no—
156C23×C4×C5C2×D311yescharacteristic
157C22×C22⋊D5—31no—
158C22×C22⋊D5—31no—
159C22×C22⋊D5C2×D311yescharacteristic
160C23×Dic5—31no—
161C23×Dic5—31no—
162C22×C4×D5C2×D311yescharacteristic, complemented
163C2×C5×C22⋊C4—31no—
164C2×C5×C22⋊C4—31no—
165C2×C5×C22⋊C4—31no—
166C2×C5×C22⋊C4—31no—
167C2×C5×C22⋊C4—64no—
168#4099—38no—
169C2×C22⋊Dic5—31no—
170C2×C22⋊Dic5—31no—
171C2×C22⋊Dic5—31no—
172C2×C22⋊Dic5—31no—
173C2×C22⋊Dic5—31no—
174C2×C22⋊Dic5—31no—
175C2×C22⋊Dic5—64no—
176C2×C22⋊Dic5C2×D311yescharacteristic
177C4×C22⋊D5—24no—
178C2×#685—31no—
179C2×#685—31no—
180C2×#685C2×D311yescharacteristic, complemented
181C2×#683—31no—
182C2×#683—31no—
183C2×#683C2×D311yescharacteristic, complemented
184C2×C4×Dic5—31no—
185C2×C4×Dic5—31no—
186C2×C4×Dic5C2×D311yescharacteristic, complemented
187#4027—64no—
188#3963—31no—
189#3963—31no—
190#3963—31no—
191#3963—31no—
192#3963—31no—
193#3963—31no—
194#2358—151noSylow
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5C22×C412yes—
200C23×C3×C5C2×D412yes—
201C23×C3×C5#4112yes—
202C23×C3×C5C2411yescharacteristic
203C22×C5×D3—21no—
204C22×C5×D3—21no—
205C22×C5×D3—21no—
206C22×C5×D3—21no—
207C22×C5×D3—28no—
208C22×C5×D3—21no—
209C22×C5×D3—21no—
210C22×C5×D3—21no—
211C22×C5×D3—21no—
212C22×C5×D3—21no—
213C22×C5×D3—21no—
214C22×C5×D3—28no—
215C22×C5×D3—44no—
216C22×C5×D3—44no—
217C22×C5×D3—44no—
218C22×C5×D3—44no—
219C22×C5×D3—44no—
220C22×C5×D3C22×C412yes—
221C22×C5×D3C22×C412yes—
222C22×C5×D3C2×D412yes—
223C22×C5×D3#4112yes—
224C22×C3×D5—21no—
225C22×C3×D5—21no—
226C22×C3×D5—21no—
227C22×C3×D5—21no—
228C22×C3×D5—21no—
229C22×C3×D5—21no—
230C22×C3×D5C22×C412yes—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5—21no—
236C2×C3×C4×C5—44no—
237C2×C3×C4×C5C2×D412yes—
238C2×Dic15—21no—
239C2×Dic15—21no—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15—21no—
243C2×Dic15—21no—
244C2×Dic15—21no—
245C2×Dic15—21no—
246C2×Dic15—21no—
247C2×Dic15—21no—
248C2×Dic15C22×C412yes—
249C2×Dic15C22×C412yes—
250C2×C5×Dic3—21no—
251C2×C5×Dic3—21no—
252C2×C5×Dic3—21no—
253C2×C5×Dic3—21no—
254C2×C5×Dic3—21no—
255C2×C5×Dic3—44no—
256C2×C5×Dic3C2×D412yes—
257C3×C22⋊D5—28no—
258C2×C3×Dic5—21no—
259C2×C3×Dic5—21no—
260C2×C3×Dic5—21no—
261C2×C3×Dic5—21no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—21no—
264C2×C3×Dic5C22×C412yes—
265C2×C3×Dic5C2×D412yes—
266C2×C3×Dic5C2×D412yes—
267C3×C4×D5—44no—
268#1201—28no—
269#1201—44no—
270D3×Dic5—44no—
271D3×Dic5—44no—
272C24×D3C2×D511yescharacteristic
273C22×C3×D4—51no—
274C23×C3×C4—51no—
275C23×C3×C4C2×D511yescharacteristic
276C22×#67—51no—
277C22×#67—51no—
278C23×Dic3C2×D511yescharacteristic
279C22×C4×D3—51no—
280C22×C4×D3—51no—
281C3×C4×D4—104no—
282C2×C3×C4⋊C4—51no—
283C2×C3×C22⋊C4—51no—
284C2×C3×C22⋊C4—51no—
285C2×C3×C42—51no—
286C2×#217—51no—
287C2×#217—51no—
288C2×#217—51no—
289C2×#217—51no—
290#937—58no—
291C4×#67—104no—
292C2×(C2×D3)⋊C4—24no—
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×(C2×D3)⋊C4C2×D511yescharacteristic
299C2×(C2×D3)⋊C4C2×D511yescharacteristic
300C2×(C2×D3)⋊C4C2×D511yescharacteristic
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×C4×Dic3—51no—
304C2×C4×Dic3—51no—
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×C5—31no—
314C24×C5—34no—
315C24×C5—62no—
316C24×C5—62no—
317C24×C5—62no—
318C24×C5—62no—
319C24×C5—121no—
320C24×C5—121no—
321C24×C5C22×D311yescharacteristic
322C23×D5C22×D311yescharacteristic
323C22×C4×C5—22no—
324C22×C4×C5—22no—
325C22×C4×C5—31no—
326C22×C4×C5—31no—
327C22×C4×C5—41no—
328C22×C4×C5—62no—
329C22×C4×C5—62no—
330C22×C4×C5—121no—
331C22×C4×C5C22×D311yescharacteristic
332C22×C4×C5C22×D311yescharacteristic
333C2×C22⋊D5—22no—
334C2×C22⋊D5—22no—
335C2×C22⋊D5—34no—
336C2×C22⋊D5—34no—
337C2×C22⋊D5—62no—
338C2×C22⋊D5—62no—
339C2×C22⋊D5—121no—
340C2×C22⋊D5—121no—
341C2×C22⋊D5C4×D314yescomplemented
342C22×Dic5—31no—
343C22×Dic5—31no—
344C22×Dic5—31no—
345C22×Dic5—31no—
346C22×Dic5—62no—
347C22×Dic5—62no—
348C22×Dic5—62no—
349C22×Dic5—62no—
350C22×Dic5—121no—
351C22×Dic5—121no—
352C22×Dic5C22×D311yescharacteristic
353C22×Dic5C22×D311yescharacteristic
354C22×Dic5C22×D311yescharacteristic
355C2×C4×D5—22no—
356C2×C4×D5—22no—
357C2×C4×D5—41no—
358C5×C22⋊C4—34no—
359C5×C22⋊C4—62no—
360C5×C22⋊C4—62no—
361C5×C22⋊C4—62no—
362C22⋊Dic5—34no—
363C22⋊Dic5—34no—
364C22⋊Dic5—34no—
365C22⋊Dic5—62no—
366C22⋊Dic5—62no—
367C22⋊Dic5—62no—
368C22⋊Dic5#6714yescomplemented
369#685—22no—
370#685—62no—
371#685—121no—
372#683—22no—
373#683—62no—
374#683—121no—
375C4×Dic5—22no—
376C4×Dic5—62no—
377C4×Dic5—121no—
378C2×#120—151no—
379C2×C4×D4—51no—
380C2×C4×D4—151no—
381C22×C22⋊C4—31no—
382C22×C22⋊C4—151no—
383#390—151no—
384#388—151no—
385#388—151no—
386#386—151no—
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—22no—
397C22×C3×C5—22no—
398C22×C3×C5—22no—
399C22×C3×C5C4×D414yescomplemented
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×C5×D3—22no—
408C2×C5×D3—22no—
409C2×C5×D3—22no—
410C2×C5×D3—22no—
411C2×C5×D3—22no—
412C2×C5×D3—22no—
413C2×C5×D3—22no—
414C2×C5×D3—22no—
415C2×C5×D3—22no—
416C2×C5×D3—416no—
417C2×C5×D3—41no—
418C2×C5×D3—41no—
419C2×C5×D3—41no—
420C2×C5×D3—41no—
421C2×C5×D3C4×D414yescomplemented
422C2×C3×D5—22no—
423C2×C3×D5—22no—
424C2×C3×D5—22no—
425C2×C3×D5—41no—
426C2×C3×D5—41no—
427C2×C3×D5—41no—
428C2×C3×D5—41no—
429C3×C4×C5—22no—
430C3×C4×C5—41no—
431Dic15—22no—
432Dic15—22no—
433Dic15—41no—
434Dic15—41no—
435C3×Dic5—22no—
436C3×Dic5—22no—
437C3×Dic5—22no—
438C5×Dic3—22no—
439C5×Dic3—41no—
440C24×C3—51no—
441C24×C3C22×D511yescharacteristic
442C23×D3—22no—
443C23×D3—22no—
444C23×D3—22no—
445C23×D3—22no—
446C23×D3—41no—
447C23×D3—41no—
448C23×D3C4×D514yescomplemented
449C23×D3C22×D511yescharacteristic
450C23×D3C22×D511yescharacteristic
451C2×C3×D4—54no—
452C2×C3×D4—102no—
453C2×C3×D4—102no—
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×C4—102no—
461C22×C3×C4—102no—
462C22×C3×C4—201no—
463C22×C3×C4C22×D511yescharacteristic
464C22×C3×C4C22×D511yescharacteristic
465C2×#67—54no—
466C2×#67—54no—
467C2×#67—102no—
468C2×#67—102no—
469C2×#67—201no—
470C2×#67—201no—
471C22×Dic3—22no—
472C22×Dic3—22no—
473C22×Dic3—41no—
474C22×Dic3—51no—
475C22×Dic3—51no—
476C22×Dic3—51no—
477C22×Dic3—51no—
478C22×Dic3C22×D511yescharacteristic
479C22×Dic3C22×D511yescharacteristic
480C2×C4×D3—102no—
481C2×C4×D3—102no—
482C2×C4×D3—102no—
483C2×C4×D3—102no—
484C2×C4×D3—201no—
485C2×C4×D3—201no—
486C3×C4⋊C4—102no—
487C3×C22⋊C4—54no—
488C3×C22⋊C4—102no—
489C3×C42—102no—
490#217—54no—
491#217—102no—
492#217—102no—
493#217—201no—
494(C2×D3)⋊C4—22no—
495(C2×D3)⋊C4—22no—
496(C2×D3)⋊C4—22no—
497(C2×D3)⋊C4—54no—
498(C2×D3)⋊C4—54no—
499(C2×D3)⋊C4—102no—
500(C2×D3)⋊C4—102no—
501(C2×D3)⋊C4C22⋊D514yescomplemented
502Dic3⋊C4—102no—
503Dic3⋊C4—201no—
504C4×Dic3—102no—
505C4×Dic3—201no—
506C23×C5—21no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5—32no—
511C23×C5—32no—
512C23×C5—32no—
513C23×C5—32no—
514C23×C5—68no—
515C23×C5—61no—
516C23×C5—61no—
517C23×C5—61no—
518C23×C5—61no—
519C23×C5—68no—
520C23×C5—61no—
521C23×C5—61no—
522C23×C5—61no—
523C23×C5—61no—
524C23×C5—61no—
525C23×C5—61no—
526C23×C5—124no—
527C23×C5—124no—
528C23×C5—124no—
529C23×C5—124no—
530C23×C5—124no—
531C23×C5C2×C4×D312yes—
532C23×C5#23512yes—
533C23×C5C2×#6712yes—
534C23×C5C23×D311yescharacteristic
535C22×D5—21no—
536C22×D5—21no—
537C22×D5—21no—
538C22×D5—21no—
539C22×D5—21no—
540C22×D5—21no—
541C22×D5C2×C4×D312yes—
542C2×C4×C5—21no—
543C2×C4×C5—21no—
544C2×C4×C5—21no—
545C2×C4×C5—21no—
546C2×C4×C5—21no—
547C2×C4×C5—32no—
548C2×C4×C5—44no—
549C2×C4×C5—61no—
550C2×C4×C5—61no—
551C2×C4×C5—61no—
552C2×C4×C5—61no—
553C2×C4×C5—61no—
554C2×C4×C5—124no—
555C2×C4×C5D3×D412yes—
556C22⋊D5—28no—
557C22⋊D5—68no—
558C22⋊D5—124no—
559C2×Dic5—21no—
560C2×Dic5—21no—
561C2×Dic5—21no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—32no—
566C2×Dic5—32no—
567C2×Dic5—61no—
568C2×Dic5—61no—
569C2×Dic5—61no—
570C2×Dic5—61no—
571C2×Dic5—61no—
572C2×Dic5—61no—
573C2×Dic5—61no—
574C2×Dic5—61no—
575C2×Dic5—61no—
576C2×Dic5—61no—
577C2×Dic5—124no—
578C2×Dic5—124no—
579C2×Dic5C2×C4×D312yes—
580C2×Dic5C2×#6712yes—
581C2×Dic5C2×#6712yes—
582C4×D5—44no—
583C25—31no—
584C22×D4—51no—
585C22×D4—151no—
586C22×D4—151no—
587C23×C4—31no—
588C23×C4—51no—
589C23×C4—151no—
590C23×C4—151no—
591C23×C4D3×D511yescharacteristic
592#120—158no—
593C4×D4—104no—
594C4×D4—304no—
595C2×C4⋊C4—51no—
596C2×C4⋊C4—151no—
597C2×C4⋊C4—151no—
598C2×C22⋊C4—31no—
599C2×C22⋊C4—31no—
600C2×C22⋊C4—31no—
601C2×C22⋊C4—31no—
602C2×C22⋊C4—51no—
603C2×C22⋊C4—51no—
604C2×C22⋊C4—64no—
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—151no—
613C2×C22⋊C4—304no—
614C2×C42—51no—
615C2×C42—151no—
616C2×C42—151no—
617#95—151no—
618#95—151no—
619#95—151no—
620#95—151no—
621#95—151no—
622#95—151no—
623C2×C3×C5—24no—
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
631C3×D5—42no—
632C5×D3—24no—
633C5×D3—42no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3—52no—
639C23×C3—101no—
640C23×C3—101no—
641C23×C3—101no—
642C23×C3—101no—
643C23×C3—101no—
644C23×C3—101no—
645C23×C3C2×C4×D512yes—
646C23×C3D4×D512yes—
647C23×C3#71112yes—
648C23×C3C23×D511yescharacteristic
649C22×D3—21no—
650C22×D3—21no—
651C22×D3—21no—
652C22×D3—21no—
653C22×D3—21no—
654C22×D3—21no—
655C22×D3—21no—
656C22×D3—21no—
657C22×D3—21no—
658C22×D3—21no—
659C22×D3—28no—
660C22×D3—28no—
661C22×D3—44no—
662C22×D3—44no—
663C22×D3—44no—
664C22×D3—44no—
665C22×D3—44no—
666C22×D3C2×C4×D512yes—
667C22×D3C2×C4×D512yes—
668C22×D3#70912yes—
669C22×D3C2×C22⋊D512yes—
670C3×D4—108no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—44no—
677C2×C3×C4—52no—
678C2×C3×C4—52no—
679C2×C3×C4—52no—
680C2×C3×C4—101no—
681C2×C3×C4—101no—
682C2×C3×C4—101no—
683C2×C3×C4—101no—
684C2×C3×C4—101no—
685C2×C3×C4—101no—
686C2×C3×C4—204no—
687C2×C3×C4C2×C22⋊D512yes—
688#67—108no—
689#67—204no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—44no—
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×Dic3—101no—
706C2×Dic3—101no—
707C2×Dic3—101no—
708C2×Dic3C2×C22⋊D512yes—
709C4×D3—204no—
710C4×D3—204no—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—22no—
715C22×C5—22no—
716C22×C5—22no—
717C22×C5—34no—
718C22×C5—62no—
719C22×C5—62no—
720C22×C5—62no—
721C22×C5—62no—
722C22×C5—62no—
723C22×C5—62no—
724C22×C5—62no—
725C22×C5—62no—
726C22×C5—62no—
727C22×C5—1216no—
728C22×C5—121no—
729C22×C5—121no—
730C22×C5—121no—
731C22×C5—121no—
732C22×C5C4×#6714yescomplemented
733C22×C5C22×C4×D311yescharacteristic
734C22×C5C2×#23511yescharacteristic
735C22×C5C2×D3×D411yescharacteristic
736C22×C5#100411yescharacteristic
737C22×C5D3×#4111yescharacteristic
738C22×C5#100911yescharacteristic
739C22×C5C22×#6711yescharacteristic
740C2×D5—22no—
741C2×D5—22no—
742C2×D5—22no—
743C2×D5—41no—
744C2×D5—41no—
745C2×D5—41no—
746C2×D5—41no—
747C4×C5—22no—
748C4×C5—41no—
749C4×C5—62no—
750C4×C5—121no—
751Dic5—22no—
752Dic5—22no—
753Dic5—22no—
754Dic5—62no—
755Dic5—62no—
756Dic5—121no—
757Dic5—121no—
758C24—31no—
759C24—31no—
760C24—34no—
761C24—51no—
762C24—62no—
763C24—62no—
764C24—62no—
765C24—62no—
766C24—121no—
767C24—121no—
768C24C2×D3×D511yescharacteristic
769C2×D4—54no—
770C2×D4—102no—
771C2×D4—102no—
772C2×D4—154no—
773C2×D4—154no—
774C2×D4—302no—
775C2×D4—302no—
776C2×D4—601no—
777C2×D4—601no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—41no—
783C22×C4—51no—
784C22×C4—51no—
785C22×C4—51no—
786C22×C4—62no—
787C22×C4—62no—
788C22×C4—102no—
789C22×C4—102no—
790C22×C4—121no—
791C22×C4—151no—
792C22×C4—151no—
793C22×C4—151no—
794C22×C4—151no—
795C22×C4—201no—
796C22×C4—302no—
797C22×C4—302no—
798C22×C4—302no—
799C22×C4—302no—
800C22×C4—601no—
801C22×C4—601no—
802C22×C4C2×D3×D511yescharacteristic
803C22×C4C2×D3×D511yescharacteristic
804C4⋊C4—102no—
805C4⋊C4—302no—
806C4⋊C4—601no—
807C22⋊C4—34no—
808C22⋊C4—54no—
809C22⋊C4—62no—
810C22⋊C4—62no—
811C22⋊C4—62no—
812C22⋊C4—102no—
813C22⋊C4—154no—
814C22⋊C4—154no—
815C22⋊C4—154no—
816C22⋊C4—302no—
817C22⋊C4—302no—
818C22⋊C4—302no—
819C22⋊C4—302no—
820C22⋊C4—601no—
821C42—102no—
822C42—302no—
823C42—601no—
824C3×C5#235811yescharacteristic, complemented, Hall
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—102no—
832C22×C3—102no—
833C22×C3—102no—
834C22×C3—201no—
835C22×C3—201no—
836C22×C3—201no—
837C22×C3—201no—
838C22×C3#402714yescomplemented
839C22×C3C22×C4×D511yescharacteristic
840C22×C3C2×#70911yescharacteristic
841C22×C3C2×D4×D511yescharacteristic
842C22×C3C2×#71111yescharacteristic
843C22×C3#414411yescharacteristic
844C22×C3#414411yescharacteristic
845C22×C3C22×C22⋊D511yescharacteristic
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—22no—
853C2×D3—22no—
854C2×D3—22no—
855C2×D3—416no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3C4×C22⋊D514yescomplemented
861C3×C4—22no—
862C3×C4—41no—
863C3×C4—102no—
864C3×C4—102no—
865C3×C4—102no—
866Dic3—22no—
867Dic3—41no—
868Dic3—102no—
869Dic3—102no—
870Dic3—201no—
871Dic3—201no—
872C2×C5—24no—
873C2×C5—64no—
874C2×C5—122no—
875C2×C5C4×D3×D411yescharacteristic
876C2×C5#554511yescharacteristic
877C2×C5#555011yescharacteristic
878C2×C5#555611yescharacteristic
879C2×C5C2×C4×#6711yescharacteristic
880C2×C5D4×#6711yescharacteristic
881C2×C5#582911yescharacteristic
882D5—42no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—32no—
888C23—32no—
889C23—32no—
890C23—32no—
891C23—52no—
892C23—68no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—68no—
898C23—61no—
899C23—61no—
900C23—61no—
901C23—61no—
902C23—61no—
903C23—61no—
904C23—101no—
905C23—101no—
906C23—101no—
907C23—101no—
908C23—101no—
909C23—101no—
910C23—124no—
911C23—124no—
912C23—124no—
913C23—124no—
914C23—124no—
915C23#677212yes—
916C23C4×D3×D512yes—
917C23D5×#6712yes—
918C23C22×D3×D511yescharacteristic
919D4—108no—
920D4—308no—
921D4—604no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—32no—
928C2×C4—44no—
929C2×C4—52no—
930C2×C4—52no—
931C2×C4—52no—
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—124no—
944C2×C4—152no—
945C2×C4—152no—
946C2×C4—204no—
947C2×C4—301no—
948C2×C4—301no—
949C2×C4—301no—
950C2×C4—301no—
951C2×C4—301no—
952C2×C4—301no—
953C2×C4—301no—
954C2×C4—301no—
955C2×C4—301no—
956C2×C4—301no—
957C2×C4—604no—
958C2×C4—604no—
959C2×C4D3×C22⋊D512yes—
960C2×C3—24no—
961C2×C3—202no—
962C2×C3C2×#402711yescharacteristic
963C2×C3#6582011yescharacteristic
964C2×C3#6582411yescharacteristic
965C2×C3#6582911yescharacteristic
966C2×C3C2×C4×C22⋊D511yescharacteristic
967C2×C3D4×C22⋊D511yescharacteristic
968C2×C3#6614011yescharacteristic
969D3—24no—
970D3—42no—
971C5#8239811yescharacteristic, complemented, Sylow
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—34no—
979C22—62no—
980C22—62no—
981C22—62no—
982C22—62no—
983C22—62no—
984C22—62no—
985C22—62no—
986C22—62no—
987C22—62no—
988C22—102no—
989C22—102no—
990C22—102no—
991C22—1216no—
992C22—121no—
993C22—121no—
994C22—121no—
995C22—121no—
996C22—201no—
997C22—201no—
998C22—201no—
999C22—201no—
1000C22#9144014yescomplemented
1001C22C2×#677211yescharacteristic
1002C22C2×C4×D3×D511yescharacteristic
1003C22D3×#70911yescharacteristic
1004C22#9201811yescharacteristic
1005C22C2×D5×#6711yescharacteristic
1006C22C2×D3×C22⋊D511yescharacteristic
1007C22#9204911yescharacteristic
1008C4—22no—
1009C4—41no—
1010C4—62no—
1011C4—102no—
1012C4—102no—
1013C4—102no—
1014C4—121no—
1015C4—302no—
1016C4—302no—
1017C4—601no—
1018C4—601no—
1019C3#1061383011yescharacteristic, complemented, Sylow
1020C2—24no—
1021C2—64no—
1022C2—122no—
1023C2—202no—
1024C2C2×#9144011yescharacteristic
1025C2#1175454011yescharacteristic
1026C2#1175457811yescharacteristic
1027C2C4×D3×C22⋊D511yescharacteristic
1028C2#1175462711yescharacteristic
1029C2#1175463611yescharacteristic
1030C2#67×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91568C2
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. C22×C5×(C2×D3)⋊C4C2semidirect
2. C2×C3×C4×C22⋊D5C2semidirect
4. C2×D3×C22⋊Dic5C2semidirect
5. C2×#91440C2semidirect
6. #11751311C2semidirect
7. #11749495C2semidirect
8. Dic3×C22⋊Dic5C2semidirect
9. #11748916C2semidirect
10. #11748911C2semidirect
11. #11748905C2semidirect
12. #11748892C2semidirect
13. Dic5×(C2×D3)⋊C4C2semidirect
14. #11748718C2semidirect
15. #11748715C2semidirect
21. C22×C3×C4×D5C22semidirect
28. C2×#6712C22semidirect
29. C2×#6712C22semidirect
37. C2×C3×#685C22semidirect
38. C2×C3×#683C22semidirect
39. C2×C3×C4×Dic5C22semidirect
40. #91568C4semidirect
46. C2×#6665C22semidirect
47. C2×#6665C22semidirect
48. C2×Dic3×Dic5C22semidirect
49. C2×Dic3×Dic5C22semidirect
51. #91115C22semidirect
52. #91115C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
61. C2×C4×C22⋊D5D3semidirect
80. C23×C5×D3C2×C4semidirect
100. C2×C3×C22⋊D5C2×C4semidirect
111. C2×#1201C2×C4semidirect
112. C2×#1201C2×C4semidirect
120. #6719C2×C4semidirect
126. C5×(C2×D3)⋊C4D4semidirect
127. C3×C22⋊Dic5D4semidirect
133. (C2×D3)⋊Dic5C2×C4semidirect
134. (C2×D3)⋊Dic5C2×C4semidirect
142. C22×(C2×D3)⋊C4D5semidirect
162. C22×C4×D5C2×D3semidirect
180. C2×#685C2×D3semidirect
183. C2×#683C2×D3semidirect
186. C2×C4×Dic5C2×D3semidirect
341. C2×C22⋊D5C4×D3semidirect
368. C22⋊Dic5#67semidirect
399. C22×C3×C5C4×D4semidirect
421. C2×C5×D3C4×D4semidirect
448. C23×D3C4×D5semidirect
501. (C2×D3)⋊C4C22⋊D5semidirect
732. C22×C5C4×#67semidirect
824. C3×C5#2358semidirect
838. C22×C3#4027semidirect
860. C2×D3C4×C22⋊D5semidirect
971. C5#82398semidirect
1000. C22#91440semidirect
1019. C3#10613830semidirect

Maximal subgroups

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

subgroupindex
C22×C5×(C2×D3)⋊C42
C2×C3×C4×C22⋊D52
C2×#915682
C2×D3×C22⋊Dic52
C2×#914402
#117513112
#117494952
Dic3×C22⋊Dic52
#117489162
#117489112
#117489052
#117488922
Dic5×(C2×D3)⋊C42
#117487182
#117487152
#106138303
#823985