Finite Group Databasebeta

← #14328124

Subgroups — #14328124

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×C5×#893C211yesmaximal, characteristic, complemented
2C2×#91475C211yesmaximal, characteristic
3C2×#91473C211yesmaximal, characteristic, complemented
4C2×D3×#685C211yesmaximal, characteristic, complemented
5C2×C4×#1203C211yesmaximal, characteristic, complemented
6#11751090C211yesmaximal, characteristic, complemented
7C3×#65279C211yesmaximal, characteristic, complemented
8#11748919C211yesmaximal, characteristic, complemented
9#11748916C211yesmaximal, characteristic, complemented
10#11748910C211yesmaximal, characteristic, complemented
11#11748901C211yesmaximal, characteristic, complemented
12#11748881C211yesmaximal, characteristic, complemented
13Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
14#11748770C211yesmaximal, characteristic, complemented
15#11748722C211yesmaximal, characteristic, complemented
16#10614129—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C5×D12C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic, complemented
22C22×#1203C2211yescharacteristic
23C22×#1201C2211yescharacteristic
24C22×#1200C2211yescharacteristic
25C22×D3×Dic5C2211yescharacteristic
26C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
27C2×#6714C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×#6712C2211yescharacteristic, complemented
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
32C2×C4×C5×Dic3C2211yescharacteristic, complemented
33C5×#893—24no—
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×C4×Dic5C2211yescharacteristic, complemented
38C2×#6668C2211yescharacteristic, complemented
39C2×#6667C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
43C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
44C2×#6665C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46C2×Dic3×Dic5C2211yescharacteristic, complemented
47#91475C418yescomplemented
48#91473—24no—
49D3×#685—24no—
50C4×#1203—24no—
51#91115C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53C3×#3963C2211yescharacteristic, complemented
54C3×#3963C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57#75836—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#65502—31no—
65#65499—31no—
66#65279D311yescharacteristic, complemented
67#65278—31no—
68#65246—31no—
69#65245—31no—
70C22⋊C4×Dic5—31no—
71#65229—31no—
72C4×#685—31no—
73C23×D15C2311yescharacteristic
74C23×C5×D3C2311yescharacteristic
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×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C2×C4×D15—22no—
91C2×C4×D15—22no—
92C2×C4×D15—41no—
93C22×C5×Dic3C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C2×C5×D12—22no—
96C2×C5×D12—22no—
97C2×C5×D12C2×C414yescomplemented
98C2×C4×C5×D3—22no—
99C2×C4×C5×D3—22no—
100C2×C4×C5×D3—22no—
101C2×C4×C5×D3—22no—
102C2×C4×C5×D3—41no—
103C2×C4×C5×D3—41no—
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C2×#1203—22no—
108C2×#1203—22no—
109C2×#1203C2×C414yescomplemented
110C2×#1201—41no—
111C2×#1201—41no—
112C2×#1201C2×C414yescomplemented
113C2×#1200—22no—
114C2×#1200—22no—
115C2×#1200—41no—
116C2×D3×Dic5—22no—
117C2×D3×Dic5—22no—
118C2×D3×Dic5—41no—
119C3×C5×C4⋊C4—22no—
120#6714—22no—
121#6714C2×C414yescomplemented
122#6712—41no—
123C5×(C2×D3)⋊C4—22no—
124C5×(C2×D3)⋊C4D414yescomplemented
125C4×C5×Dic3—22no—
126C3×#685—22no—
127C3×#685—22no—
128C3×#685C2×C414yescomplemented
129C3×C4×Dic5—22no—
130#6668—22no—
131#6667D414yescomplemented
132(C2×D3)⋊Dic5—22no—
133(C2×D3)⋊Dic5—22no—
134(C2×D3)⋊Dic5—41no—
135(C2×D3)⋊Dic5C2×C414yescomplemented
136#6665—22no—
137#6665—22no—
138Dic3×Dic5—41no—
139C2×#893D511yescharacteristic, complemented
140C2×#882—51no—
141C2×D3×C22⋊C4—51no—
142C2×D3×C22⋊C4—51no—
143C2×C4×D12—51no—
144C3×#388—51no—
145#4989—51no—
146#4957—51no—
147#4956—51no—
148#4951—51no—
149C4×(C2×D3)⋊C4—51no—
150#4668—51no—
151#4666—51no—
152#4665—51no—
153#4665—51no—
154C24×D5—31no—
155C22×C5×D4—31no—
156C23×C4×C5—31no—
157C23×C4×C5—31no—
158C22×C22⋊D5—31no—
159C22×C22⋊D5—31no—
160C23×Dic5—31no—
161C22×C4×D5—31no—
162C22×C4×D5—31no—
163C4×C5×D4—64no—
164C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
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⋊Dic5—31no—
172#4083—38no—
173C4×C22⋊D5—64no—
174C2×#685—31no—
175C2×#685—31no—
176C2×#685—31no—
177C2×#685—31no—
178C2×#685—31no—
179C2×#685—64no—
180C2×#685C2×D311yescharacteristic
181C2×#685C2×D311yescharacteristic
182C2×#685C2×D311yescharacteristic
183C2×#683—31no—
184C2×#683—31no—
185C2×C4×Dic5—31no—
186C2×C4×Dic5C2×D311yescharacteristic, complemented
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×C5C2411yescharacteristic
196C22×D15—21no—
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—21no—
200C22×D15C22×C412yes—
201C22×D15C2×D412yes—
202C22×D15#4112yes—
203C22×C5×D3—21no—
204C22×C5×D3—21no—
205C22×C5×D3—21no—
206C22×C5×D3—21no—
207C22×C5×D3—21no—
208C22×C5×D3—21no—
209C22×C5×D3—21no—
210C22×C5×D3—21no—
211C22×C5×D3—21no—
212C22×C5×D3—21no—
213C22×C5×D3C22×C412yes—
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—21no—
236C2×C3×C4×C5—21no—
237C2×C3×C4×C5—21no—
238C2×C3×C4×C5C22×C412yes—
239C2×C3×C4×C5C2×D412yes—
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—
249C4×D15—44no—
250C2×C5×Dic3—21no—
251C2×C5×Dic3—21no—
252C2×C5×Dic3—21no—
253C2×C5×Dic3—21no—
254C2×C5×Dic3C2×D412yes—
255C2×C5×Dic3C2×D412yes—
256C5×D12—28no—
257C4×C5×D3—44no—
258C4×C5×D3—44no—
259C2×C3×Dic5—21no—
260C2×C3×Dic5—21no—
261C2×C3×Dic5—21no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—21no—
264C2×C3×Dic5—21no—
265C2×C3×Dic5—21no—
266C2×C3×Dic5C22×C412yes—
267C2×C3×Dic5C2×D412yes—
268#1203—28no—
269#1201—44no—
270#1200—44no—
271D3×Dic5—44no—
272C24×D3—51no—
273C22×#67—51no—
274C22×D12—51no—
275C22×D12C2×D511yescharacteristic
276C22×C4×D3—51no—
277C22×C4×D3—51no—
278C22×C4×D3—51no—
279C22×C4×D3C2×D511yescharacteristic
280C22×C4×D3C2×D511yescharacteristic, complemented
281C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
282C2×C3×C22⋊C4—51no—
283C2×C3×C22⋊C4—51no—
284C2×C3×C22⋊C4—51no—
285C2×C3×C42—51no—
286C2×#217—51no—
287C2×#217—51no—
288C2×(C2×D3)⋊C4—51no—
289C2×(C2×D3)⋊C4—51no—
290C2×(C2×D3)⋊C4—51no—
291C2×(C2×D3)⋊C4—51no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4—51no—
294C2×(C2×D3)⋊C4—51no—
295C2×(C2×D3)⋊C4C2×D511yescharacteristic
296C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
297C2×C4⋊Dic3—51no—
298C2×Dic3⋊C4—51no—
299C2×C4×Dic3—51no—
300C2×C4×Dic3C2×D511yescharacteristic, complemented
301#893—24no—
302#882—58no—
303D3×C22⋊C4—104no—
304D3×C22⋊C4—104no—
305C4×D12—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—
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—31no—
327C22×C4×C5—31no—
328C22×C4×C5—62no—
329C22×C4×C5—62no—
330C22×C4×C5—62no—
331C22×C4×C5—62no—
332C22×C4×C5—121no—
333C22×C4×C5—121no—
334C22×C4×C5C22×D311yescharacteristic
335C22×C4×C5C22×D311yescharacteristic
336C22×C4×C5C22×D311yescharacteristic
337C2×C22⋊D5—34no—
338C2×C22⋊D5—34no—
339C2×C22⋊D5—62no—
340C2×C22⋊D5—62no—
341C2×C22⋊D5—121no—
342C2×C22⋊D5—121no—
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—22no—
359C5×C22⋊C4—34no—
360C5×C22⋊C4—62no—
361C42×C5—62no—
362C22⋊Dic5—34no—
363C22⋊Dic5—62no—
364C22⋊Dic5—62no—
365C22⋊Dic5—121no—
366#685—22no—
367#685—22no—
368#685—34no—
369#685—34no—
370#685—62no—
371#685—62no—
372#685—62no—
373#685C4×D314yescomplemented
374#683—62no—
375#683—121no—
376C4×Dic5—22no—
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—51no—
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×C5C23×C411yescharacteristic
394C22×C3×C5C22×D411yescharacteristic
395C22×C3×C5C22×D411yescharacteristic
396C22×C3×C5C2×#4111yescharacteristic
397C22×C3×C5C2×#4111yescharacteristic
398C22×C3×C5H(5,𝔽2)11yescharacteristic
399C22×C3×C5H(5,𝔽2)11yescharacteristic
400C2×D15—22no—
401C2×D15—22no—
402C2×D15—22no—
403C2×D15—22no—
404C2×D15—22no—
405C2×D15—22no—
406C2×D15C4×D414yescomplemented
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—41no—
417C2×C5×D3—41no—
418C2×C5×D3—41no—
419C2×C5×D3—41no—
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—
431C3×C4×C5—41no—
432Dic15—22no—
433Dic15—41no—
434Dic15—41no—
435C3×Dic5—22no—
436C3×Dic5—22no—
437C3×Dic5—41no—
438C5×Dic3—22no—
439C5×Dic3—22no—
440C24×C3—51no—
441C23×D3—51no—
442C23×D3—54no—
443C23×D3—102no—
444C23×D3—102no—
445C23×D3—102no—
446C23×D3—102no—
447C23×D3—201no—
448C23×D3—201no—
449C23×D3C22×D511yescharacteristic
450C23×D3C22×D511yescharacteristic
451C22×C3×C4—51no—
452C22×C3×C4—51no—
453C22×C3×C4—51no—
454C22×C3×C4C22×D511yescharacteristic
455C22×C3×C4C22×D511yescharacteristic
456C22×C3×C4C22×D511yescharacteristic
457C2×#67—54no—
458C2×#67—201no—
459C2×#67—201no—
460C22×Dic3—51no—
461C22×Dic3—51no—
462C22×Dic3—51no—
463C22×Dic3C22×D511yescharacteristic
464C22×Dic3C22×D511yescharacteristic
465C2×D12—22no—
466C2×D12—22no—
467C2×D12—54no—
468C2×D12—102no—
469C2×D12—102no—
470C2×D12C4×D514yescomplemented
471C2×C4×D3—22no—
472C2×C4×D3—22no—
473C2×C4×D3—22no—
474C2×C4×D3—22no—
475C2×C4×D3—41no—
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×C4⋊C4—22no—
487C3×C22⋊C4—54no—
488C3×C22⋊C4—102no—
489C3×C22⋊C4—102no—
490C3×C42—102no—
491#217—102no—
492#217—102no—
493(C2×D3)⋊C4—22no—
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)⋊C4—102no—
500(C2×D3)⋊C4—201no—
501(C2×D3)⋊C4C22⋊D514yescomplemented
502C4⋊Dic3—102no—
503Dic3⋊C4—201no—
504C4×Dic3—22no—
505C4×Dic3—201no—
506C23×C5—32no—
507C23×C5—32no—
508C23×C5—32no—
509C23×C5—32no—
510C23×C5—61no—
511C23×C5—61no—
512C23×C5—61no—
513C23×C5—61no—
514C23×C5—61no—
515C23×C5—61no—
516C23×C5—61no—
517C23×C5—61no—
518C23×C5—61no—
519C23×C5—61no—
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—21no—
548C2×C4×C5—21no—
549C2×C4×C5—21no—
550C2×C4×C5—32no—
551C2×C4×C5—32no—
552C2×C4×C5—61no—
553C2×C4×C5—61no—
554C2×C4×C5—61no—
555C2×C4×C5—61no—
556C2×C4×C5—124no—
557C2×C4×C5—124no—
558C2×C4×C5C2×C4×D312yes—
559C2×C4×C5D3×D412yes—
560C22⋊D5—68no—
561C22⋊D5—124no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—21no—
566C2×Dic5—21no—
567C2×Dic5—21no—
568C2×Dic5—21no—
569C2×Dic5—32no—
570C2×Dic5—61no—
571C2×Dic5—61no—
572C2×Dic5—61no—
573C2×Dic5—61no—
574C2×Dic5—61no—
575C2×Dic5—61no—
576C2×Dic5—61no—
577C2×Dic5—61no—
578C2×Dic5—124no—
579C2×Dic5C2×C4×D312yes—
580C2×Dic5D3×D412yes—
581C4×D5—124no—
582C4×D5—124no—
583C25—151no—
584C22×D4—31no—
585C22×D4—151no—
586C22×D4—151no—
587C23×C4—31no—
588C23×C4—31no—
589C23×C4—151no—
590C23×C4—151no—
591C23×C4—151no—
592#120—158no—
593C4×D4—64no—
594C4×D4—304no—
595C2×C4⋊C4—151no—
596C2×C4⋊C4—151no—
597C2×C4⋊C4D3×D511yescharacteristic, complemented
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—51no—
616C2×C42—151no—
617#95—51no—
618#95—51no—
619#95—151no—
620#95—151no—
621#95—151no—
622#95—151no—
623C2×C3×C5C2×C4×D411yescharacteristic
624C2×C3×C5C2×C4×D411yescharacteristic
625C2×C3×C5#51811yescharacteristic
626C2×C3×C5D4211yescharacteristic
627C2×C3×C5#54611yescharacteristic
628C2×C3×C5#54611yescharacteristic
629C2×C3×C5#55111yescharacteristic
630D15—24no—
631C3×D5—42no—
632C5×D3—24no—
633C5×D3—42no—
634C23×C3—52no—
635C23×C3—101no—
636C23×C3—101no—
637C23×C3—101no—
638C23×C3—101no—
639C23×C3—101no—
640C23×C3—101no—
641C23×C3C23×D511yescharacteristic
642C22×D3—21no—
643C22×D3—21no—
644C22×D3—21no—
645C22×D3—21no—
646C22×D3—21no—
647C22×D3—21no—
648C22×D3—21no—
649C22×D3—21no—
650C22×D3—21no—
651C22×D3—21no—
652C22×D3—52no—
653C22×D3—52no—
654C22×D3—52no—
655C22×D3—108no—
656C22×D3—101no—
657C22×D3—101no—
658C22×D3—101no—
659C22×D3—101no—
660C22×D3—108no—
661C22×D3—204no—
662C22×D3—204no—
663C22×D3—204no—
664C22×D3—204no—
665C22×D3—204no—
666C22×D3C2×C4×D512yes—
667C22×D3C2×C4×D512yes—
668C22×D3#70912yes—
669C22×D3C2×C22⋊D512yes—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—52no—
678C2×C3×C4—52no—
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×C4—101no—
686C2×C3×C4C2×C4×D512yes—
687C2×C3×C4C2×C22⋊D512yes—
688#67—204no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—52no—
694C2×Dic3—101no—
695C2×Dic3—101no—
696C2×Dic3—101no—
697C2×Dic3—101no—
698C2×Dic3—101no—
699C2×Dic3—101no—
700C2×Dic3—101no—
701C2×Dic3—101no—
702C2×Dic3D4×D512yes—
703C2×Dic3C2×C22⋊D512yes—
704D12—28no—
705D12—108no—
706C4×D3—44no—
707C4×D3—44no—
708C4×D3—204no—
709C4×D3—204no—
710C4×D3—204no—
711C22×C5—34no—
712C22×C5—62no—
713C22×C5—62no—
714C22×C5—62no—
715C22×C5—62no—
716C22×C5—62no—
717C22×C5—62no—
718C22×C5—62no—
719C22×C5—62no—
720C22×C5—62no—
721C22×C5—121no—
722C22×C5—121no—
723C22×C5—121no—
724C22×C5—121no—
725C22×C5C22×C4×D311yescharacteristic
726C22×C5C2×D3×D411yescharacteristic
727C22×C5C2×D3×D411yescharacteristic
728C22×C5D3×#4111yescharacteristic
729C22×C5D3×#4111yescharacteristic
730C22×C5#100911yescharacteristic
731C22×C5#100911yescharacteristic
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—41no—
750C4×C5—62no—
751C4×C5—62no—
752Dic5—22no—
753Dic5—22no—
754Dic5—41no—
755Dic5—62no—
756Dic5—121no—
757Dic5—121no—
758C24—31no—
759C24—31no—
760C24—51no—
761C24—154no—
762C24—151no—
763C24—302no—
764C24—302no—
765C24—302no—
766C24—302no—
767C24—601no—
768C24—601no—
769C2×D4—34no—
770C2×D4—62no—
771C2×D4—62no—
772C2×D4—154no—
773C2×D4—154no—
774C2×D4—302no—
775C2×D4—302no—
776C2×D4—601no—
777C2×D4—601no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—51no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—62no—
784C22×C4—62no—
785C22×C4—62no—
786C22×C4—62no—
787C22×C4—121no—
788C22×C4—121no—
789C22×C4—151no—
790C22×C4—151no—
791C22×C4—151no—
792C22×C4—302no—
793C22×C4—302no—
794C22×C4—302no—
795C22×C4—302no—
796C22×C4—302no—
797C22×C4—302no—
798C22×C4—601no—
799C22×C4—601no—
800C22×C4—601no—
801C22×C4C2×D3×D511yescharacteristic
802C22×C4C2×D3×D511yescharacteristic
803C22×C4C2×D3×D511yescharacteristic
804C4⋊C4—22no—
805C4⋊C4—302no—
806C4⋊C4—601no—
807C22⋊C4—34no—
808C22⋊C4—54no—
809C22⋊C4—62no—
810C22⋊C4—102no—
811C22⋊C4—102no—
812C22⋊C4—154no—
813C22⋊C4—154no—
814C22⋊C4—154no—
815C22⋊C4—302no—
816C22⋊C4—302no—
817C22⋊C4—302no—
818C22⋊C4—302no—
819C22⋊C4—302no—
820C22⋊C4—601no—
821C42—62no—
822C42—102no—
823C42—601no—
824C3×C5#235811yescharacteristic, complemented, Hall
825C22×C3—102no—
826C22×C3—102no—
827C22×C3—102no—
828C22×C3—201no—
829C22×C3—201no—
830C22×C3—201no—
831C22×C3—201no—
832C22×C3C22×C4×D511yescharacteristic
833C22×C3C2×#70911yescharacteristic
834C22×C3C2×D4×D511yescharacteristic
835C22×C3#414411yescharacteristic
836C22×C3D5×#4111yescharacteristic
837C22×C3#414911yescharacteristic
838C22×C3C22×C22⋊D511yescharacteristic
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—22no—
843C2×D3—22no—
844C2×D3—22no—
845C2×D3—22no—
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—41no—
849C2×D3—41no—
850C2×D3—41no—
851C2×D3—41no—
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—41no—
864C3×C4—102no—
865C3×C4—102no—
866C3×C4—201no—
867Dic3—22no—
868Dic3—22no—
869Dic3—102no—
870Dic3—201no—
871Dic3—201no—
872C2×C5—64no—
873C2×C5—122no—
874C2×C5#552111yescharacteristic
875C2×C5C4×D3×D411yescharacteristic
876C2×C5C4×D3×D411yescharacteristic
877C2×C5#560911yescharacteristic
878C2×C5#565411yescharacteristic
879C2×C5#567611yescharacteristic
880C2×C5#570511yescharacteristic
881D5—42no—
882D5—64no—
883C23—32no—
884C23—32no—
885C23—32no—
886C23—32no—
887C23—52no—
888C23—61no—
889C23—61no—
890C23—61no—
891C23—61no—
892C23—61no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—61no—
898C23—101no—
899C23—101no—
900C23—101no—
901C23—101no—
902C23—101no—
903C23—101no—
904C23—152no—
905C23—152no—
906C23—152no—
907C23—308no—
908C23—308no—
909C23—301no—
910C23—301no—
911C23—301no—
912C23—301no—
913C23—604no—
914C23—604no—
915C23—604no—
916C23—604no—
917C23—604no—
918C23C22×D3×D511yescharacteristic
919D4—68no—
920D4—308no—
921D4—604no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—32no—
930C2×C4—32no—
931C2×C4—52no—
932C2×C4—52no—
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—124no—
945C2×C4—124no—
946C2×C4—152no—
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—604no—
956C2×C4—604no—
957C2×C4—604no—
958C2×C4C4×D3×D512yes—
959C2×C4D3×C22⋊D512yes—
960C2×C3—202no—
961C2×C3C4×D4×D511yescharacteristic
962C2×C3#6587911yescharacteristic
963C2×C3#6588411yescharacteristic
964C2×C3#6589011yescharacteristic
965C2×C3C2×C4×C22⋊D511yescharacteristic
966C2×C3D4×C22⋊D511yescharacteristic
967C2×C3#6616311yescharacteristic
968D3—24no—
969D3—42no—
970D3—104no—
971C5#7583611yescharacteristic, complemented, Sylow
972C22—34no—
973C22—62no—
974C22—62no—
975C22—62no—
976C22—62no—
977C22—62no—
978C22—62no—
979C22—62no—
980C22—62no—
981C22—62no—
982C22—102no—
983C22—102no—
984C22—102no—
985C22—121no—
986C22—121no—
987C22—121no—
988C22—121no—
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
1003C22D3×D4×D511yescharacteristic
1004C22#9202711yescharacteristic
1005C22#9203411yescharacteristic
1006C22#9203511yescharacteristic
1007C22C2×D3×C22⋊D511yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—41no—
1011C4—62no—
1012C4—62no—
1013C4—102no—
1014C4—102no—
1015C4—201no—
1016C4—302no—
1017C4—601no—
1018C4—601no—
1019C3#1061412911yescharacteristic, complemented, Sylow
1020C2—64no—
1021C2—122no—
1022C2—202no—
1023C2—304no—
1024C2#1175383711yescharacteristic
1025C2#1175384011yescharacteristic
1026C2#1175385811yescharacteristic
1027C2#1175392011yescharacteristic
1028C2C4×D3×C22⋊D511yescharacteristic
1029C2#1175505311yescharacteristic
1030C2#1175528011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91475C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2358
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C5×#893C2semidirect
3. C2×#91473C2semidirect
4. C2×D3×#685C2semidirect
5. C2×C4×#1203C2semidirect
6. #11751090C2semidirect
7. C3×#65279C2semidirect
8. #11748919C2semidirect
9. #11748916C2semidirect
10. #11748910C2semidirect
11. #11748901C2semidirect
12. #11748881C2semidirect
13. Dic5×(C2×D3)⋊C4C2semidirect
14. #11748770C2semidirect
15. #11748722C2semidirect
21. C22×C4×C5×D3C22semidirect
26. C2×C3×C5×C4⋊C4C22semidirect
29. C2×#6712C22semidirect
31. C2×C5×(C2×D3)⋊C4C22semidirect
32. C2×C4×C5×Dic3C22semidirect
37. C2×C3×C4×Dic5C22semidirect
38. C2×#6668C22semidirect
42. C2×(C2×D3)⋊Dic5C22semidirect
43. C2×(C2×D3)⋊Dic5C22semidirect
46. C2×Dic3×Dic5C22semidirect
47. #91475C4semidirect
51. #91115C22semidirect
52. #91115C22semidirect
53. C3×#3963C22semidirect
54. C3×#3963C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
66. #65279D3semidirect
83. C22×D3×D5C2×C4semidirect
97. C2×C5×D12C2×C4semidirect
109. C2×#1203C2×C4semidirect
112. C2×#1201C2×C4semidirect
121. #6714C2×C4semidirect
124. C5×(C2×D3)⋊C4D4semidirect
128. C3×#685C2×C4semidirect
131. #6667D4semidirect
135. (C2×D3)⋊Dic5C2×C4semidirect
139. C2×#893D5semidirect
164. C2×C5×C4⋊C4C2×D3semidirect
186. C2×C4×Dic5C2×D3semidirect
192. #3963C2×D3semidirect
193. #3963C2×D3semidirect
280. C22×C4×D3C2×D5semidirect
281. C2×C3×C4⋊C4C2×D5semidirect
296. C2×(C2×D3)⋊C4C2×D5semidirect
300. C2×C4×Dic3C2×D5semidirect
373. #685C4×D3semidirect
406. C2×D15C4×D4semidirect
420. C2×C5×D3C4×D4semidirect
470. C2×D12C4×D5semidirect
501. (C2×D3)⋊C4C22⋊D5semidirect
597. C2×C4⋊C4D3×D5semidirect
824. C3×C5#2358semidirect
860. C2×D3C4×C22⋊D5semidirect
971. C5#75836semidirect
1019. C3#10614129semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8932
C2×#914752
C2×#914732
C2×D3×#6852
C2×C4×#12032
#117510902
C3×#652792
#117489192
#117489162
#117489102
#117489012
#117488812
Dic5×(C2×D3)⋊C42
#117487702
#117487222
#106141293
#758365