Finite Group Databasebeta

← #14328160

Subgroups — #14328160

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×#67⋊C4C211yesmaximal, characteristic, complemented
2C2×C3×D5×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×#91563C211yesmaximal, characteristic
4C22×#6665C211yesmaximal, characteristic, complemented
5C2×C4×#1201C211yesmaximal, characteristic, complemented
6C22⋊C4×Dic15C211yesmaximal, characteristic, complemented
7#11749512C211yesmaximal, characteristic, complemented
8#11749501C211yesmaximal, characteristic, complemented
9#11748915C211yesmaximal, characteristic, complemented
10#11748910C211yesmaximal, characteristic, complemented
11#11748905C211yesmaximal, characteristic, complemented
12#11748709C211yesmaximal, characteristic, complemented
13#11748705C211yesmaximal, characteristic, complemented
14#11748703C211yesmaximal, characteristic, complemented
15C4×#6665C211yesmaximal, characteristic, complemented
16#10614129—31nomaximal, Hall
17C24×C3×D5C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C22×C5×#67C2211yescharacteristic
20C23×C5×Dic3C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic, complemented
22C22×C3×C4×D5C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C22×#1201C2211yescharacteristic
25C22×#1201C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×#6719C2211yescharacteristic
28C2×C4×Dic15C2211yescharacteristic, complemented
29C2×C4×Dic15C2211yescharacteristic, complemented
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
31C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
32C2×C4×C5×Dic3C2211yescharacteristic, complemented
33C5×#67⋊C4—24no—
34C2×C3×C22⋊Dic5C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C3×D5×C22⋊C4—24no—
38#91563C418yescomplemented
39C2×#6669C2211yescharacteristic, complemented
40C2×#6669C2211yescharacteristic, complemented
41C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
42C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
43C2×#6665—24no—
44C2×#6665C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46C2×#6665C2211yescharacteristic
47C2×#6665C2211yescharacteristic
48C2×#6665C2211yescharacteristic
49C2×#6665C2211yescharacteristic
50C4×#1201—24no—
51#91115C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57#82099—51nomaximal, Hall
58C2×C4×C5×D4—31no—
59C2×#4083—31no—
60C2×C4×C22⋊D5—31no—
61C22×#685—31no—
62C2×D5×C22⋊C4D311yescharacteristic, complemented
63#65509—31no—
64#65502—31no—
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×C5×D3C2311yescharacteristic
75C23×C3×D5—22no—
76C23×C3×D5—22no—
77C23×C3×D5—22no—
78C23×C3×D5—22no—
79C23×C3×D5—41no—
80C23×C3×D5—41no—
81C23×C3×D5C2×C414yescomplemented
82C23×C3×D5C2311yescharacteristic
83C23×C3×D5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×Dic15—22no—
87C22×Dic15—22no—
88C22×Dic15—41no—
89C22×Dic15C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C2×C5×#67—22no—
94C2×C5×#67—22no—
95C2×C5×#67C2×C414yescomplemented
96C22×C5×Dic3—22no—
97C22×C5×Dic3—22no—
98C22×C5×Dic3—41no—
99C22×C5×Dic3C2311yescharacteristic
100C22×C5×Dic3C2311yescharacteristic
101C22×C5×Dic3C2311yescharacteristic
102C2×C4×C5×D3—22no—
103C2×C4×C5×D3—22no—
104C2×C4×C5×D3—41no—
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C2×C3×C4×D5—22no—
108C2×C3×C4×D5—22no—
109C2×C3×C4×D5—22no—
110C2×C3×C4×D5—22no—
111C2×C3×C4×D5—41no—
112C2×C3×C4×D5—41no—
113C2×#1201—22no—
114C2×#1201—22no—
115C2×#1201—41no—
116C2×#1201—41no—
117C2×#1201C2×C414yescomplemented
118C2×#1201C2×C414yescomplemented
119C3×C5×C22⋊C4D414yescomplemented
120#6719C2×C414yescomplemented
121C4×Dic15—22no—
122C4×Dic15—41no—
123C5×(C2×D3)⋊C4—22no—
124C5×Dic3⋊C4—22no—
125C4×C5×Dic3—22no—
126C3×C22⋊Dic5—22no—
127C3×#685—22no—
128C3×#685—22no—
129#6669—22no—
130#6669—41no—
131(C2×D3)⋊Dic5—22no—
132(C2×D3)⋊Dic5—41no—
133#6665—22no—
134#6665—22no—
135#6665—22no—
136#6665C2×C414yescomplemented
137#6665C2×C414yescomplemented
138#6665D414yescomplemented
139C22×C3×C22⋊C4—51no—
140C2×#953—51no—
141C22×#217—51no—
142C2×C4×#67—51no—
143C2×#67⋊C4D511yescharacteristic, complemented
144#5213—51no—
145#5210—51no—
146C4×#217—51no—
147#4958—51no—
148#4957—51no—
149#4956—51no—
150#4946—51no—
151#4945—51no—
152#4944—51no—
153Dic3×C22⋊C4—51no—
154C24×D5C2×D311yescharacteristic
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×D5C2×D311yescharacteristic
162C22×C4×D5C2×D311yescharacteristic
163C4×C5×D4—64no—
164C2×C5×C4⋊C4—31no—
165C2×C5×C22⋊C4—31no—
166C2×C5×C22⋊C4C2×D311yescharacteristic
167C2×C42×C5—31no—
168C2×C22⋊Dic5—31no—
169C2×C22⋊Dic5—31no—
170C2×C22⋊Dic5—31no—
171C2×C22⋊Dic5C2×D311yescharacteristic
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—24no—
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—21no—
208C22×C5×D3—21no—
209C22×C5×D3C22×C412yes—
210C22×C3×D5—21no—
211C22×C3×D5—21no—
212C22×C3×D5—21no—
213C22×C3×D5—21no—
214C22×C3×D5—28no—
215C22×C3×D5—21no—
216C22×C3×D5—21no—
217C22×C3×D5—21no—
218C22×C3×D5—21no—
219C22×C3×D5—21no—
220C22×C3×D5—21no—
221C22×C3×D5—28no—
222C22×C3×D5—44no—
223C22×C3×D5—44no—
224C22×C3×D5—44no—
225C22×C3×D5—44no—
226C22×C3×D5—44no—
227C22×C3×D5C22×C412yes—
228C22×C3×D5C22×C412yes—
229C22×C3×D5C2×D412yes—
230C22×C3×D5#4112yes—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5C2×D412yes—
236C2×C3×C4×C5C2×D412yes—
237C2×Dic15—21no—
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—44no—
247C2×Dic15C22×C412yes—
248C2×Dic15C22×C412yes—
249C2×Dic15C2×D412yes—
250C5×#67—28no—
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×Dic3—21no—
258C2×C5×Dic3—44no—
259C2×C5×Dic3C22×C412yes—
260C2×C5×Dic3C2×D412yes—
261C4×C5×D3—44no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—21no—
264C2×C3×Dic5—21no—
265C2×C3×Dic5—21no—
266C2×C3×Dic5—21no—
267C2×C3×Dic5—21no—
268C3×C4×D5—44no—
269C3×C4×D5—44no—
270#1201—28no—
271#1201—44no—
272C25×C3—51no—
273C23×C3×C4—51no—
274C23×C3×C4—51no—
275C22×#67—51no—
276C22×#67—51no—
277C22×#67C2×D511yescharacteristic
278C23×Dic3—51no—
279C23×Dic3C2×D511yescharacteristic
280C22×C4×D3C2×D511yescharacteristic, complemented
281C2×C3×C22⋊C4—51no—
282C2×C3×C22⋊C4—51no—
283C2×C3×C22⋊C4—51no—
284C2×C3×C22⋊C4—104no—
285C2×C3×C22⋊C4C2×D511yescharacteristic
286#953—58no—
287C2×#217—51no—
288C2×#217—51no—
289C2×#217—51no—
290C2×#217—51no—
291C2×#217—51no—
292C2×#217—51no—
293C2×#217—51no—
294C2×#217—104no—
295C4×#67—104no—
296C2×(C2×D3)⋊C4—51no—
297C2×(C2×D3)⋊C4—51no—
298C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
299C2×Dic3⋊C4—51no—
300C2×Dic3⋊C4—51no—
301C2×Dic3⋊C4C2×D511yescharacteristic, complemented
302C2×C4×Dic3—51no—
303C2×C4×Dic3—51no—
304C2×C4×Dic3C2×D511yescharacteristic, complemented
305#67⋊C4—24no—
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—22no—
315C23×D5—22no—
316C23×D5—22no—
317C23×D5—22no—
318C23×D5—41no—
319C23×D5—41no—
320C23×D5C4×D314yescomplemented
321C23×D5C22×D311yescharacteristic
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—31no—
329C22×C4×C5—62no—
330C22×C4×C5—62no—
331C22×C4×C5—62no—
332C22×C4×C5—62no—
333C22×C4×C5—121no—
334C22×C4×C5—121no—
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—31no—
347C22×Dic5—62no—
348C22×Dic5—62no—
349C22×Dic5—121no—
350C22×Dic5C22×D311yescharacteristic
351C22×Dic5C22×D311yescharacteristic
352C2×C4×D5—22no—
353C2×C4×D5—22no—
354C2×C4×D5—22no—
355C2×C4×D5—22no—
356C2×C4×D5—41no—
357C2×C4×D5—41no—
358C5×C4⋊C4—62no—
359C5×C22⋊C4—62no—
360C5×C22⋊C4#6714yescomplemented
361C42×C5—62no—
362C22⋊Dic5—22no—
363C22⋊Dic5—34no—
364C22⋊Dic5—62no—
365C22⋊Dic5—121no—
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—51no—
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—41no—
411C2×C5×D3—41no—
412C2×C5×D3—41no—
413C2×C5×D3—41no—
414C2×C3×D5—22no—
415C2×C3×D5—22no—
416C2×C3×D5—22no—
417C2×C3×D5—22no—
418C2×C3×D5—22no—
419C2×C3×D5—22no—
420C2×C3×D5—22no—
421C2×C3×D5—22no—
422C2×C3×D5—22no—
423C2×C3×D5—416no—
424C2×C3×D5—41no—
425C2×C3×D5—41no—
426C2×C3×D5—41no—
427C2×C3×D5—41no—
428C2×C3×D5C4×D414yescomplemented
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431Dic15—22no—
432Dic15—22no—
433Dic15—22no—
434Dic15—41no—
435C3×Dic5—41no—
436C3×Dic5—41no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3—41no—
440C24×C3—51no—
441C24×C3—51no—
442C24×C3—54no—
443C24×C3—102no—
444C24×C3—102no—
445C24×C3—102no—
446C24×C3—102no—
447C24×C3—201no—
448C24×C3—201no—
449C24×C3C22×D511yescharacteristic
450C23×D3C22×D511yescharacteristic
451C22×C3×C4—51no—
452C22×C3×C4—51no—
453C22×C3×C4—102no—
454C22×C3×C4—102no—
455C22×C3×C4—102no—
456C22×C3×C4—102no—
457C22×C3×C4—201no—
458C22×C3×C4—201no—
459C22×C3×C4C22×D511yescharacteristic
460C22×C3×C4C22×D511yescharacteristic
461C2×#67—22no—
462C2×#67—22no—
463C2×#67—54no—
464C2×#67—54no—
465C2×#67—102no—
466C2×#67—102no—
467C2×#67—201no—
468C2×#67—201no—
469C2×#67C4×D514yescomplemented
470C22×Dic3—22no—
471C22×Dic3—22no—
472C22×Dic3—41no—
473C22×Dic3—51no—
474C22×Dic3—51no—
475C22×Dic3—51no—
476C22×Dic3—51no—
477C22×Dic3—102no—
478C22×Dic3—102no—
479C22×Dic3—201no—
480C22×Dic3C22×D511yescharacteristic
481C22×Dic3C22×D511yescharacteristic
482C22×Dic3C22×D511yescharacteristic
483C2×C4×D3—22no—
484C2×C4×D3—22no—
485C2×C4×D3—41no—
486C3×C22⋊C4—102no—
487C3×C22⋊C4—102no—
488C3×C22⋊C4—102no—
489C3×C22⋊C4C22⋊D514yescomplemented
490#217—54no—
491#217—54no—
492#217—54no—
493#217—54no—
494#217—102no—
495#217—102no—
496#217—102no—
497(C2×D3)⋊C4—22no—
498(C2×D3)⋊C4—102no—
499(C2×D3)⋊C4—201no—
500Dic3⋊C4—22no—
501Dic3⋊C4—102no—
502Dic3⋊C4—201no—
503C4×Dic3—22no—
504C4×Dic3—102no—
505C4×Dic3—201no—
506C23×C5—21no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5—32no—
511C23×C5—61no—
512C23×C5—61no—
513C23×C5—61no—
514C23×C5—61no—
515C23×C5—61no—
516C23×C5—61no—
517C23×C5C2×C4×D312yes—
518C23×C5#23512yes—
519C23×C5C2×#6712yes—
520C23×C5C23×D311yescharacteristic
521C22×D5—21no—
522C22×D5—21no—
523C22×D5—21no—
524C22×D5—21no—
525C22×D5—28no—
526C22×D5—21no—
527C22×D5—21no—
528C22×D5—21no—
529C22×D5—21no—
530C22×D5—21no—
531C22×D5—21no—
532C22×D5—28no—
533C22×D5—44no—
534C22×D5—44no—
535C22×D5—44no—
536C22×D5—44no—
537C22×D5—44no—
538C22×D5C2×C4×D312yes—
539C22×D5C2×C4×D312yes—
540C22×D5D3×D412yes—
541C22×D5#23712yes—
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—61no—
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—124no—
557C2×C4×C5—124no—
558C2×C4×C5C2×#6712yes—
559C2×C4×C5C2×#6712yes—
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—32no—
569C2×Dic5—32no—
570C2×Dic5—32no—
571C2×Dic5—61no—
572C2×Dic5—61no—
573C2×Dic5—61no—
574C2×Dic5—61no—
575C2×Dic5—61no—
576C2×Dic5—61no—
577C2×Dic5—61no—
578C2×Dic5—61no—
579C2×Dic5—61no—
580C2×Dic5—124no—
581C4×D5—44no—
582C4×D5—44no—
583C25—51no—
584C22×D4—31no—
585C22×D4—151no—
586C22×D4—151no—
587C23×C4—31no—
588C23×C4—31no—
589C23×C4—51no—
590C23×C4—51no—
591C23×C4—151no—
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—51no—
600C2×C22⋊C4—51no—
601C2×C22⋊C4—51no—
602C2×C22⋊C4—104no—
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⋊C4D3×D511yescharacteristic
614C2×C42—31no—
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—24no—
632C3×D5—42no—
633C5×D3—42no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3—52no—
639C23×C3—52no—
640C23×C3—52no—
641C23×C3—52no—
642C23×C3—108no—
643C23×C3—101no—
644C23×C3—101no—
645C23×C3—101no—
646C23×C3—101no—
647C23×C3—101no—
648C23×C3—101no—
649C23×C3—101no—
650C23×C3—101no—
651C23×C3—101no—
652C23×C3—101no—
653C23×C3—108no—
654C23×C3—204no—
655C23×C3—204no—
656C23×C3—204no—
657C23×C3—204no—
658C23×C3—204no—
659C23×C3C2×C4×D512yes—
660C23×C3#70912yes—
661C23×C3C2×C22⋊D512yes—
662C23×C3C23×D511yescharacteristic
663C22×D3—21no—
664C22×D3—21no—
665C22×D3—21no—
666C22×D3—21no—
667C22×D3—21no—
668C22×D3—21no—
669C22×D3C2×C4×D512yes—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—101no—
675C2×C3×C4—101no—
676C2×C3×C4—101no—
677C2×C3×C4—101no—
678C2×C3×C4—101no—
679C2×C3×C4—101no—
680C2×C3×C4—204no—
681C2×C3×C4—204no—
682C2×C3×C4C2×C22⋊D512yes—
683C2×C3×C4C2×C22⋊D512yes—
684#67—28no—
685#67—108no—
686#67—204no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—44no—
695C2×Dic3—52no—
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—204no—
708C2×Dic3C2×C4×D512yes—
709C2×Dic3D4×D512yes—
710C4×D3—44no—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—22no—
715C22×C5—22no—
716C22×C5—22no—
717C22×C5—62no—
718C22×C5—62no—
719C22×C5—62no—
720C22×C5—121no—
721C22×C5—121no—
722C22×C5—121no—
723C22×C5—121no—
724C22×C5C4×#6714yescomplemented
725C22×C5C22×C4×D311yescharacteristic
726C22×C5C2×#23511yescharacteristic
727C22×C5C2×D3×D411yescharacteristic
728C22×C5C2×#23711yescharacteristic
729C22×C5#100411yescharacteristic
730C22×C5#100411yescharacteristic
731C22×C5C22×#6711yescharacteristic
732C2×D5—22no—
733C2×D5—22no—
734C2×D5—22no—
735C2×D5—22no—
736C2×D5—22no—
737C2×D5—22no—
738C2×D5—22no—
739C2×D5—22no—
740C2×D5—22no—
741C2×D5—416no—
742C2×D5—41no—
743C2×D5—41no—
744C2×D5—41no—
745C2×D5—41no—
746C2×D5#67⋊C414yescomplemented
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—62no—
750C4×C5—62no—
751C4×C5—121no—
752Dic5—41no—
753Dic5—41no—
754Dic5—62no—
755Dic5—62no—
756Dic5—62no—
757Dic5—121no—
758C24—31no—
759C24—51no—
760C24—51no—
761C24—54no—
762C24—102no—
763C24—102no—
764C24—102no—
765C24—102no—
766C24—201no—
767C24—201no—
768C24C2×D3×D511yescharacteristic
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—31no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—62no—
784C22×C4—62no—
785C22×C4—62no—
786C22×C4—62no—
787C22×C4—102no—
788C22×C4—102no—
789C22×C4—102no—
790C22×C4—102no—
791C22×C4—121no—
792C22×C4—121no—
793C22×C4—151no—
794C22×C4—151no—
795C22×C4—151no—
796C22×C4—151no—
797C22×C4—201no—
798C22×C4—201no—
799C22×C4—302no—
800C22×C4—302no—
801C22×C4—601no—
802C22×C4C2×D3×D511yescharacteristic
803C22×C4C2×D3×D511yescharacteristic
804C4⋊C4—62no—
805C4⋊C4—302no—
806C4⋊C4—601no—
807C22⋊C4—62no—
808C22⋊C4—102no—
809C22⋊C4—102no—
810C22⋊C4—102no—
811C22⋊C4—154no—
812C22⋊C4—154no—
813C22⋊C4—154no—
814C22⋊C4—154no—
815C22⋊C4—302no—
816C22⋊C4—302no—
817C22⋊C4—302no—
818C22⋊C4—302no—
819C22⋊C4—601no—
820C22⋊C4#120114yescomplemented
821C42—62no—
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—54no—
832C22×C3—102no—
833C22×C3—102no—
834C22×C3—102no—
835C22×C3—102no—
836C22×C3—102no—
837C22×C3—102no—
838C22×C3—102no—
839C22×C3—102no—
840C22×C3—102no—
841C22×C3—2016no—
842C22×C3—201no—
843C22×C3—201no—
844C22×C3—201no—
845C22×C3—201no—
846C22×C3C4×C22⋊D514yescomplemented
847C22×C3C22×C4×D511yescharacteristic
848C22×C3C2×#70911yescharacteristic
849C22×C3C2×D4×D511yescharacteristic
850C22×C3#414411yescharacteristic
851C22×C3D5×#4111yescharacteristic
852C22×C3#414911yescharacteristic
853C22×C3C22×C22⋊D511yescharacteristic
854C2×D3—22no—
855C2×D3—22no—
856C2×D3—22no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—41no—
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—201no—
864C3×C4—201no—
865Dic3—22no—
866Dic3—22no—
867Dic3—41no—
868Dic3—102no—
869Dic3—102no—
870Dic3—102no—
871Dic3—201no—
872C2×C5—24no—
873C2×C5—122no—
874C2×C5C2×#67⋊C411yescharacteristic
875C2×C5#548611yescharacteristic
876C2×C5#549011yescharacteristic
877C2×C5#549511yescharacteristic
878C2×C5C2×C4×#6711yescharacteristic
879C2×C5D4×#6711yescharacteristic
880C2×C5#580611yescharacteristic
881D5—24no—
882D5—42no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—32no—
888C23—52no—
889C23—52no—
890C23—52no—
891C23—52no—
892C23—61no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—61no—
898C23—108no—
899C23—101no—
900C23—101no—
901C23—101no—
902C23—101no—
903C23—108no—
904C23—101no—
905C23—101no—
906C23—101no—
907C23—101no—
908C23—101no—
909C23—101no—
910C23—204no—
911C23—204no—
912C23—204no—
913C23—204no—
914C23—204no—
915C23#677112yes—
916C23C4×D3×D512yes—
917C23C2×#120112yes—
918C23C22×D3×D511yescharacteristic
919D4—68no—
920D4—308no—
921D4—604no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—32no—
927C2×C4—32no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—61no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—101no—
936C2×C4—101no—
937C2×C4—101no—
938C2×C4—101no—
939C2×C4—101no—
940C2×C4—101no—
941C2×C4—124no—
942C2×C4—124no—
943C2×C4—152no—
944C2×C4—152no—
945C2×C4—152no—
946C2×C4—204no—
947C2×C4—204no—
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×C4C2×#120112yes—
959C2×C4C2×#120112yes—
960C2×C3—24no—
961C2×C3—104no—
962C2×C3—202no—
963C2×C3C4×D4×D511yescharacteristic
964C2×C3#6587911yescharacteristic
965C2×C3#6588411yescharacteristic
966C2×C3#6589011yescharacteristic
967C2×C3C2×C4×C22⋊D511yescharacteristic
968C2×C3D4×C22⋊D511yescharacteristic
969C2×C3#6616311yescharacteristic
970D3—42no—
971C5#8209911yescharacteristic, complemented, Sylow
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—54no—
979C22—62no—
980C22—62no—
981C22—62no—
982C22—102no—
983C22—102no—
984C22—102no—
985C22—102no—
986C22—102no—
987C22—102no—
988C22—102no—
989C22—102no—
990C22—102no—
991C22—121no—
992C22—121no—
993C22—121no—
994C22—121no—
995C22—2016no—
996C22—201no—
997C22—201no—
998C22—201no—
999C22—201no—
1000C22C4×#120114yescomplemented
1001C22C2×#677111yescharacteristic
1002C22C2×C4×D3×D511yescharacteristic
1003C22D3×D4×D511yescharacteristic
1004C22D5×#23711yescharacteristic
1005C22#9202511yescharacteristic
1006C22#9202611yescharacteristic
1007C22C22×#120111yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—62no—
1011C4—62no—
1012C4—121no—
1013C4—201no—
1014C4—201no—
1015C4—302no—
1016C4—302no—
1017C4—302no—
1018C4—601no—
1019C3#1061412911yescharacteristic, complemented, Sylow
1020C2—24no—
1021C2—104no—
1022C2—122no—
1023C2—202no—
1024C2#1175307211yescharacteristic
1025C2#1175310111yescharacteristic
1026C2D5×#67⋊C411yescharacteristic
1027C2#1175320011yescharacteristic
1028C2C2×C4×#120111yescharacteristic
1029C2D4×#120111yescharacteristic
1030C2#1175496111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91563C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2358
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
1. C2×C5×#67⋊C4C2semidirect
2. C2×C3×D5×C22⋊C4C2semidirect
4. C22×#6665C2semidirect
5. C2×C4×#1201C2semidirect
6. C22⋊C4×Dic15C2semidirect
7. #11749512C2semidirect
8. #11749501C2semidirect
9. #11748915C2semidirect
10. #11748910C2semidirect
11. #11748905C2semidirect
12. #11748709C2semidirect
13. #11748705C2semidirect
14. #11748703C2semidirect
15. C4×#6665C2semidirect
21. C22×C4×C5×D3C22semidirect
28. C2×C4×Dic15C22semidirect
29. C2×C4×Dic15C22semidirect
30. C2×C5×(C2×D3)⋊C4C22semidirect
31. C2×C5×Dic3⋊C4C22semidirect
32. C2×C4×C5×Dic3C22semidirect
38. #91563C4semidirect
39. C2×#6669C22semidirect
40. C2×#6669C22semidirect
41. C2×(C2×D3)⋊Dic5C22semidirect
42. C2×(C2×D3)⋊Dic5C22semidirect
51. #91115C22semidirect
52. #91115C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
62. C2×D5×C22⋊C4D3semidirect
81. C23×C3×D5C2×C4semidirect
95. C2×C5×#67C2×C4semidirect
117. C2×#1201C2×C4semidirect
118. C2×#1201C2×C4semidirect
119. C3×C5×C22⋊C4D4semidirect
120. #6719C2×C4semidirect
136. #6665C2×C4semidirect
137. #6665C2×C4semidirect
138. #6665D4semidirect
143. C2×#67⋊C4D5semidirect
280. C22×C4×D3C2×D5semidirect
298. C2×(C2×D3)⋊C4C2×D5semidirect
301. C2×Dic3⋊C4C2×D5semidirect
304. C2×C4×Dic3C2×D5semidirect
320. C23×D5C4×D3semidirect
360. C5×C22⋊C4#67semidirect
399. C22×C3×C5C4×D4semidirect
428. C2×C3×D5C4×D4semidirect
469. C2×#67C4×D5semidirect
489. C3×C22⋊C4C22⋊D5semidirect
724. C22×C5C4×#67semidirect
746. C2×D5#67⋊C4semidirect
820. C22⋊C4#1201semidirect
824. C3×C5#2358semidirect
846. C22×C3C4×C22⋊D5semidirect
971. C5#82099semidirect
1000. C22C4×#1201semidirect
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×#67⋊C42
C2×C3×D5×C22⋊C42
C2×#915632
C22×#66652
C2×C4×#12012
C22⋊C4×Dic152
#117495122
#117495012
#117489152
#117489102
#117489052
#117487092
#117487052
#117487032
C4×#66652
#106141293
#820995