Finite Group Databasebeta

← #14327019

Subgroups — #14327019

Order 1920.

1552 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91770C211yesmaximal, characteristic
2C2×#91556C211yesmaximal, characteristic
3C2×#91552C211yesmaximal, characteristic
4C22×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
5C2×#91404C211yesmaximal, characteristic, complemented
6C5×#4942C211yesmaximal, characteristic, complemented
7C3×#65235C211yesmaximal, characteristic, complemented
8#11749515C211yesmaximal, characteristic, complemented
9#11748895C211yesmaximal, characteristic, complemented
10#11748882C211yesmaximal, characteristic, complemented
11#11748804C211yesmaximal, characteristic, complemented
12#11748729C211yesmaximal, characteristic, complemented
13#11748658C211yesmaximal, characteristic, complemented
14#11748651C211yesmaximal, characteristic, complemented
15#11748641C211yesmaximal, characteristic, complemented
16#10605741—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C23×C5×Dic3C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic
22C22×#1200C2211yescharacteristic
23C22×#1200C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×#6712C2211yescharacteristic
27C2×C4×Dic15C2211yescharacteristic
28#91770—24no—
29C2×C5×#217C2211yescharacteristic
30C2×C5×Dic3⋊C4C2211yescharacteristic
31C2×C5×Dic3⋊C4C2211yescharacteristic
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×C3×#683C2211yescharacteristic
34C2×C3×#683C2211yescharacteristic
35#91556C418yescomplemented
36#91552—24no—
37C2×Dic3⋊Dic5—24no—
38C2×Dic3⋊Dic5C2211yescharacteristic
39C2×Dic3⋊Dic5C2211yescharacteristic
40C2×Dic3⋊Dic5C2211yescharacteristic
41C2×Dic3⋊Dic5C2211yescharacteristic
42C2×#6669C2211yescharacteristic
43C2×#6669C2211yescharacteristic
44C2×#6668C2211yescharacteristic
45C2×#6668C2211yescharacteristic
46C2×#6667C2211yescharacteristic
47C2×#6667C2211yescharacteristic
48C2×Dic3×Dic5C2211yescharacteristic
49C2×Dic3×Dic5C2211yescharacteristic
50#91404—24no—
51C5×C3⋊#95C2211yescharacteristic
52C5×C3⋊#95C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#74393—51nomaximal, Hall
58C2×C4×C22⋊D5—31no—
59C22×C4⋊Dic5—31no—
60C2×D5×C4⋊C4—31no—
61C2×#4027—31no—
62C2×#4027—31no—
63C5×#380—31no—
64#65276—31no—
65#65265—31no—
66C4⋊C4×Dic5—31no—
67#65235—31no—
68#65235D311yescharacteristic, complemented
69#64957—31no—
70#64957—31no—
71#64936—31no—
72#64936—31no—
73C24×C3×C5C2311yescharacteristic
74C23×D15C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C2×#1220C2×C414yes—
78C2×#1220D414yes—
79C2×#1220Q814yes—
80C22×Dic15—22no—
81C22×Dic15—22no—
82C22×Dic15—41no—
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C2×C4×D15—22no—
87C2×C4×D15—22no—
88C2×C4×D15—41no—
89C22×C5×Dic3—22no—
90C22×C5×Dic3—22no—
91C22×C5×Dic3C2×C414yescomplemented
92C22×C5×Dic3C2311yescharacteristic
93C22×C5×Dic3C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C22×C5×Dic3C2311yescharacteristic
96C22×C3×Dic5—22no—
97C22×C3×Dic5—22no—
98C22×C3×Dic5—41no—
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C22×C3×Dic5C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C2×#1200—22no—
104C2×#1200—22no—
105C2×#1200—22no—
106C2×#1200—22no—
107C2×#1200—41no—
108C2×#1200C2×C414yescomplemented
109C3×C5×C22⋊C4—22no—
110#6714—22no—
111#6712—22no—
112C4×Dic15—22no—
113C5×#217—22no—
114C5×Dic3⋊C4—22no—
115C5×Dic3⋊C4—22no—
116C3×C22⋊Dic5C2×C414yescomplemented
117C3×#683—22no—
118C3×#683—41no—
119Dic3⋊Dic5—22no—
120Dic3⋊Dic5—22no—
121Dic3⋊Dic5—22no—
122Dic3⋊Dic5D414yescomplemented
123#6669—22no—
124#6669C2×C414yescomplemented
125#6668—22no—
126#6668—41no—
127#6667—22no—
128#6667C2×C414yescomplemented
129Dic3×Dic5—22no—
130Dic3×Dic5C2×C414yescomplemented
131C2×C4×#67—51no—
132C22×Dic3⋊C4—51no—
133C2×D3×C4⋊C4—51no—
134C2×#67⋊C4—51no—
135C2×#67⋊C4—51no—
136C3×#385—51no—
137#4989—51no—
138#4976—51no—
139#4975—51no—
140#4950—51no—
141#4942D511yescharacteristic, complemented
142#4668—51no—
143#4667—51no—
144#4649—51no—
145#4647—51no—
146C23×C4×C5—31no—
147C22×C22⋊D5—31no—
148C23×Dic5—31no—
149C23×Dic5C2×D311yescharacteristic
150C22×C4×D5—31no—
151C22×C4×D5—31no—
152C22×C4×D5—31no—
153C2×C5×C4⋊C4—31no—
154C2×C5×C4⋊C4—31no—
155C2×C5×C22⋊C4—31no—
156C2×C5×C22⋊C4C2×D311yescharacteristic
157C2×C22⋊Dic5C2×D311yescharacteristic
158C4×C22⋊D5—38no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—31no—
162C2×C4⋊Dic5—31no—
163C2×C4⋊Dic5—31no—
164C2×C4⋊Dic5—31no—
165C2×C4⋊Dic5—31no—
166C2×C4⋊Dic5—64no—
167C2×#683—31no—
168C2×#683—31no—
169C2×#683—31no—
170C2×#683—31no—
171C2×#683—31no—
172C2×#683C2×D311yescharacteristic
173C2×#683C2×D311yescharacteristic
174C2×C4×Dic5—31no—
175C2×C4×Dic5—31no—
176C2×C4×Dic5—31no—
177D5×C4⋊C4—64no—
178#4027—64no—
179#4027—64no—
180C5×#95—31no—
181C5×#95—31no—
182#3963—31no—
183#3963—31no—
184#3963C2×D311yescharacteristic
185#3963C2×D311yescharacteristic
186D4×C4⋊C4—151noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5C22×C412yes—
192C23×C3×C5C2×D412yes—
193C23×C3×C5C2×Q812yes—
194C23×C3×C5C2411yescharacteristic
195C22×D15—21no—
196C22×D15—21no—
197C22×D15—21no—
198C22×D15—21no—
199C22×D15C22×C412yes—
200C22×D15C2×D412yes—
201C22×D15C2×Q812yes—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208#1220C4⋊C4116yescomplemented
209C2×Dic15—21no—
210C2×Dic15—21no—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—21no—
214C2×Dic15—44no—
215C2×Dic15C22×C412yes—
216C2×Dic15C2×D412yes—
217C2×Dic15C2×D412yes—
218C2×Dic15C2×Q812yes—
219C4×D15—44no—
220C2×C5×Dic3—21no—
221C2×C5×Dic3—21no—
222C2×C5×Dic3—28no—
223C2×C5×Dic3—21no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—21no—
226C2×C5×Dic3—21no—
227C2×C5×Dic3—21no—
228C2×C5×Dic3—21no—
229C2×C5×Dic3C22×C412yes—
230C2×C5×Dic3C22×C412yes—
231C2×C5×Dic3C2×D412yes—
232C2×C5×Dic3#4112yes—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—44no—
243C2×C3×Dic5C22×C412yes—
244C2×C3×Dic5C22×C412yes—
245C2×C3×Dic5C2×D412yes—
246#1200—28no—
247#1200—44no—
248C23×C3×C4—51no—
249C22×#67—51no—
250C23×Dic3—51no—
251C23×Dic3C2×D511yescharacteristic
252C22×C4×D3—51no—
253C22×C4×D3—51no—
254C22×C4×D3—51no—
255C2×C3×C4⋊C4—51no—
256C2×C3×C4⋊C4—51no—
257C2×C3×C22⋊C4—51no—
258C2×C3×C22⋊C4C2×D511yescharacteristic
259C2×#217C2×D511yescharacteristic
260C4×#67—104no—
261C2×(C2×D3)⋊C4—51no—
262C2×(C2×D3)⋊C4—51no—
263C2×(C2×D3)⋊C4—51no—
264C2×C4⋊Dic3—51no—
265C2×C4⋊Dic3—51no—
266C2×Dic3⋊C4—51no—
267C2×Dic3⋊C4—51no—
268C2×Dic3⋊C4—51no—
269C2×Dic3⋊C4—51no—
270C2×Dic3⋊C4—51no—
271C2×Dic3⋊C4—51no—
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4—104no—
274C2×Dic3⋊C4C2×D511yescharacteristic
275C2×Dic3⋊C4C2×D511yescharacteristic
276C2×C4×Dic3—51no—
277C2×C4×Dic3—51no—
278C2×C4×Dic3—51no—
279D3×C4⋊C4—104no—
280#67⋊C4—58no—
281#67⋊C4—104no—
282C3×#95—51no—
283C3×#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95C2×D511yescharacteristic
287C3⋊#95C2×D511yescharacteristic
288C24×C5C22×D311yescharacteristic
289C23×D5—31no—
290C22×C4×C5—31no—
291C22×C4×C5—34no—
292C22×C4×C5—31no—
293C22×C4×C5—31no—
294C22×C4×C5—31no—
295C22×C4×C5—62no—
296C22×C4×C5—62no—
297C22×C4×C5C22×D311yescharacteristic
298C22×C4×C5C22×D311yescharacteristic
299C2×C22⋊D5—34no—
300C2×C22⋊D5—34no—
301C2×C22⋊D5—34no—
302C22×Dic5—22no—
303C22×Dic5—22no—
304C22×Dic5—31no—
305C22×Dic5—31no—
306C22×Dic5—31no—
307C22×Dic5—41no—
308C22×Dic5—62no—
309C22×Dic5—62no—
310C22×Dic5—121no—
311C22×Dic5C22×D311yescharacteristic
312C22×Dic5C22×D311yescharacteristic
313C22×Dic5C22×D311yescharacteristic
314C22×Dic5C22×D311yescharacteristic
315C2×C4×D5—34no—
316C2×C4×D5—62no—
317C2×C4×D5—62no—
318C2×C4×D5—62no—
319C2×C4×D5—62no—
320C2×C4×D5—62no—
321C2×C4×D5—62no—
322C2×C4×D5—121no—
323C2×C4×D5—121no—
324C5×C4⋊C4—62no—
325C5×C4⋊C4—62no—
326C5×C22⋊C4—22no—
327C5×C22⋊C4—62no—
328C22⋊Dic5C4×D314yescomplemented
329#685—34no—
330#685—62no—
331#685—62no—
332C4⋊Dic5—34no—
333C4⋊Dic5—62no—
334C4⋊Dic5—62no—
335C4⋊Dic5—62no—
336#683—22no—
337#683—34no—
338#683—41no—
339#683—62no—
340#683—62no—
341#683—62no—
342#683—121no—
343C4×Dic5—34no—
344C4×Dic5—62no—
345C4×Dic5—62no—
346C2×C4×D4—151no—
347C2×C4×D4—151no—
348C2×C4×D4—151no—
349C22×C4⋊C4—151no—
350C22×C4⋊C4—151no—
351#389—151no—
352#389—151no—
353#385—51no—
354#385—151no—
355#385—151no—
356#385—151no—
357#384—151no—
358#380—31no—
359#380—151no—
360C4×C4⋊C4—151no—
361C22×C3×C5—22no—
362C22×C3×C5—22no—
363C22×C3×C5—22no—
364C22×C3×C5—22no—
365C22×C3×C5—22no—
366C22×C3×C5—22no—
367C22×C3×C5C2×C4⋊C414yescomplemented
368C22×C3×C5C23×C411yescharacteristic
369C22×C3×C5C22×D411yescharacteristic
370C22×C3×C5C22×D411yescharacteristic
371C22×C3×C5C22×Q811yescharacteristic
372C22×C3×C5C2×#4111yescharacteristic
373C22×C3×C5H(5,𝔽2)11yescharacteristic
374C22×C3×C52−1+411yescharacteristic
375C2×D15—22no—
376C2×D15—22no—
377C2×D15—22no—
378C2×D15—22no—
379C2×D15—22no—
380C2×D15—22no—
381C2×D15C2×C4⋊C414yescomplemented
382C3×C4×C5—41no—
383C3×C4×C5—41no—
384Dic15—22no—
385Dic15—41no—
386Dic15C2×C4⋊C414yescomplemented
387C3×Dic5—22no—
388C3×Dic5—22no—
389C3×Dic5—22no—
390C3×Dic5—41no—
391C5×Dic3—22no—
392C5×Dic3—41no—
393C5×Dic3—41no—
394C5×Dic3C4×D414yescomplemented
395C24×C3C22×D511yescharacteristic
396C23×D3—51no—
397C22×C3×C4—51no—
398C22×C3×C4—51no—
399C22×C3×C4—51no—
400C22×C3×C4—51no—
401C22×C3×C4—102no—
402C22×C3×C4—102no—
403C22×C3×C4—201no—
404C22×C3×C4C22×D511yescharacteristic
405C22×C3×C4C22×D511yescharacteristic
406C2×#67—54no—
407C2×#67—54no—
408C2×#67—54no—
409C22×Dic3—22no—
410C22×Dic3—22no—
411C22×Dic3—51no—
412C22×Dic3—51no—
413C22×Dic3—51no—
414C22×Dic3—102no—
415C22×Dic3—102no—
416C22×Dic3—201no—
417C22×Dic3C4×D514yescomplemented
418C22×Dic3C22×D511yescharacteristic
419C22×Dic3C22×D511yescharacteristic
420C22×Dic3C22×D511yescharacteristic
421C22×Dic3C22×D511yescharacteristic
422C2×C4×D3—54no—
423C2×C4×D3—102no—
424C2×C4×D3—102no—
425C2×C4×D3—102no—
426C2×C4×D3—102no—
427C2×C4×D3—102no—
428C2×C4×D3—102no—
429C2×C4×D3—201no—
430C2×C4×D3—201no—
431C3×C4⋊C4—102no—
432C3×C4⋊C4—201no—
433C3×C22⋊C4—22no—
434C3×C22⋊C4—54no—
435#217—22no—
436(C2×D3)⋊C4—54no—
437(C2×D3)⋊C4—102no—
438(C2×D3)⋊C4—102no—
439C4⋊Dic3—102no—
440C4⋊Dic3—201no—
441Dic3⋊C4—22no—
442Dic3⋊C4—22no—
443Dic3⋊C4—54no—
444Dic3⋊C4—54no—
445Dic3⋊C4—102no—
446Dic3⋊C4—102no—
447Dic3⋊C4—102no—
448Dic3⋊C4—102no—
449Dic3⋊C4—102no—
450C4×Dic3—54no—
451C4×Dic3—102no—
452C4×Dic3—102no—
453C23×C5—21no—
454C23×C5—21no—
455C23×C5—21no—
456C23×C5—21no—
457C23×C5C2×C4×D312yes—
458C23×C5D3×D412yes—
459C23×C5D3×Q812yes—
460C23×C5C23×D311yescharacteristic
461C22×D5—32no—
462C22×D5—32no—
463C22×D5—32no—
464C22×D5—61no—
465C22×D5—61no—
466C22×D5—61no—
467C22×D5—61no—
468C2×C4×C5—21no—
469C2×C4×C5—21no—
470C2×C4×C5—21no—
471C2×C4×C5—21no—
472C2×C4×C5—21no—
473C2×C4×C5—21no—
474C2×C4×C5—32no—
475C2×C4×C5—32no—
476C2×C4×C5—32no—
477C2×C4×C5—32no—
478C2×C4×C5—68no—
479C2×C4×C5—61no—
480C2×C4×C5—61no—
481C2×C4×C5—61no—
482C2×C4×C5—61no—
483C2×C4×C5—61no—
484C2×C4×C5—61no—
485C2×C4×C5—61no—
486C2×C4×C5—61no—
487C22⋊D5—316no—
488C2×Dic5—21no—
489C2×Dic5—21no—
490C2×Dic5—21no—
491C2×Dic5—21no—
492C2×Dic5—21no—
493C2×Dic5—21no—
494C2×Dic5—21no—
495C2×Dic5—21no—
496C2×Dic5—21no—
497C2×Dic5—32no—
498C2×Dic5—32no—
499C2×Dic5—32no—
500C2×Dic5—32no—
501C2×Dic5—44no—
502C2×Dic5—61no—
503C2×Dic5—61no—
504C2×Dic5—61no—
505C2×Dic5—61no—
506C2×Dic5—61no—
507C2×Dic5—124no—
508C2×Dic5C2×C4×D312yes—
509C2×Dic5C2×C4×D312yes—
510C2×Dic5D3×D412yes—
511C4×D5—68no—
512C4×D5—124no—
513C4×D5—124no—
514C22×D4—151no—
515C23×C4—31no—
516C23×C4—51no—
517C23×C4—151no—
518C23×C4—151no—
519C23×C4—151no—
520C23×C4—151no—
521C4×D4—158no—
522C4×D4—304no—
523C4×D4—304no—
524C2×C4⋊C4—31no—
525C2×C4⋊C4—31no—
526C2×C4⋊C4—51no—
527C2×C4⋊C4—51no—
528C2×C4⋊C4—151no—
529C2×C4⋊C4—151no—
530C2×C4⋊C4—151no—
531C2×C4⋊C4—151no—
532C2×C4⋊C4—151no—
533C2×C4⋊C4—151no—
534C2×C4⋊C4—151no—
535C2×C4⋊C4—151no—
536C2×C4⋊C4—151no—
537C2×C4⋊C4—304no—
538C2×C4⋊C4—304no—
539C2×C22⋊C4—31no—
540C2×C22⋊C4—51no—
541C2×C22⋊C4—151no—
542C2×C22⋊C4—151no—
543C2×C22⋊C4—151no—
544C2×C22⋊C4D3×D511yescharacteristic
545C2×C42—151no—
546C2×C42—151no—
547C2×C42—151no—
548#95—31no—
549#95—31no—
550#95—51no—
551#95—51no—
552#95—151no—
553#95—151no—
554C2×C3×C5—24no—
555C2×C3×C5C22×C4⋊C411yescharacteristic
556C2×C3×C5C2×C4×D411yescharacteristic
557C2×C3×C5#52011yescharacteristic
558C2×C3×C5D4211yescharacteristic
559C2×C3×C5#54711yescharacteristic
560C2×C3×C5D4×Q811yescharacteristic
561C2×C3×C5#55411yescharacteristic
562D15—24no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3C2×C4×D512yes—
568C23×C3D4×D512yes—
569C23×C3Q8×D512yes—
570C23×C3C23×D511yescharacteristic
571C22×D3—52no—
572C22×D3—52no—
573C22×D3—52no—
574C22×D3—101no—
575C22×D3—101no—
576C22×D3—101no—
577C22×D3—101no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—52no—
585C2×C3×C4—52no—
586C2×C3×C4—52no—
587C2×C3×C4—101no—
588C2×C3×C4—101no—
589C2×C3×C4—101no—
590C2×C3×C4—101no—
591C2×C3×C4—101no—
592C2×C3×C4—101no—
593C2×C3×C4—101no—
594C2×C3×C4—101no—
595C2×C3×C4—101no—
596C2×C3×C4—204no—
597#67—516no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—28no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—52no—
608C2×Dic3—52no—
609C2×Dic3—52no—
610C2×Dic3—52no—
611C2×Dic3—101no—
612C2×Dic3—101no—
613C2×Dic3—101no—
614C2×Dic3—101no—
615C2×Dic3—101no—
616C2×Dic3—204no—
617C2×Dic3C2×C4×D512yes—
618C2×Dic3C2×C4×D512yes—
619C2×Dic3D4×D512yes—
620C2×Dic3#71112yes—
621C4×D3—108no—
622C4×D3—204no—
623C4×D3—204no—
624C22×C5—22no—
625C22×C5—22no—
626C22×C5—22no—
627C22×C5—22no—
628C22×C5—22no—
629C22×C5—22no—
630C22×C5D3×C4⋊C414yescomplemented
631C22×C5C22×C4×D311yescharacteristic
632C22×C5C2×D3×D411yescharacteristic
633C22×C5C2×D3×D411yescharacteristic
634C22×C5#100411yescharacteristic
635C22×C5C2×D3×Q811yescharacteristic
636C22×C5D3×#4111yescharacteristic
637C22×C5#101011yescharacteristic
638C2×D5—34no—
639C2×D5—62no—
640C2×D5—62no—
641C2×D5—62no—
642C2×D5—62no—
643C2×D5—62no—
644C2×D5—62no—
645C4×C5—34no—
646C4×C5—41no—
647C4×C5—41no—
648C4×C5—62no—
649C4×C5—121no—
650C4×C5—121no—
651Dic5—22no—
652Dic5—22no—
653Dic5—22no—
654Dic5—34no—
655Dic5—41no—
656Dic5—62no—
657Dic5—121no—
658C24—151no—
659C24C2×D3×D511yescharacteristic
660C2×D4—154no—
661C2×D4—154no—
662C2×D4—154no—
663C22×C4—31no—
664C22×C4—34no—
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—51no—
669C22×C4—51no—
670C22×C4—51no—
671C22×C4—51no—
672C22×C4—62no—
673C22×C4—62no—
674C22×C4—102no—
675C22×C4—102no—
676C22×C4—154no—
677C22×C4—151no—
678C22×C4—151no—
679C22×C4—151no—
680C22×C4—201no—
681C22×C4—302no—
682C22×C4—302no—
683C22×C4—302no—
684C22×C4—302no—
685C22×C4—302no—
686C22×C4—302no—
687C22×C4—302no—
688C22×C4—302no—
689C22×C4—601no—
690C22×C4—601no—
691C22×C4—601no—
692C22×C4C2×D3×D511yescharacteristic
693C22×C4C2×D3×D511yescharacteristic
694C4⋊C4—62no—
695C4⋊C4—62no—
696C4⋊C4—102no—
697C4⋊C4—154no—
698C4⋊C4—154no—
699C4⋊C4—201no—
700C4⋊C4—302no—
701C4⋊C4—302no—
702C4⋊C4—302no—
703C4⋊C4—302no—
704C4⋊C4—302no—
705C4⋊C4—302no—
706C4⋊C4—601no—
707C22⋊C4—22no—
708C22⋊C4—54no—
709C22⋊C4—62no—
710C22⋊C4—154no—
711C22⋊C4—302no—
712C22⋊C4—302no—
713C42—154no—
714C42—302no—
715C42—302no—
716C3×C5D4×C4⋊C411yescharacteristic, complemented, Hall
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3D5×C4⋊C414yescomplemented
724C22×C3C22×C4×D511yescharacteristic
725C22×C3C2×D4×D511yescharacteristic
726C22×C3C2×D4×D511yescharacteristic
727C22×C3C2×#71111yescharacteristic
728C22×C3C2×Q8×D511yescharacteristic
729C22×C3#414911yescharacteristic
730C22×C3#415011yescharacteristic
731C2×D3—54no—
732C2×D3—102no—
733C2×D3—102no—
734C2×D3—102no—
735C2×D3—102no—
736C2×D3—102no—
737C2×D3—102no—
738C3×C4—41no—
739C3×C4—41no—
740C3×C4—102no—
741C3×C4—102no—
742C3×C4—102no—
743C3×C4—201no—
744Dic3—22no—
745Dic3—41no—
746Dic3—41no—
747Dic3—54no—
748Dic3—102no—
749Dic3—201no—
750Dic3#402714yescomplemented
751C2×C5—24no—
752C2×C5C2×D3×C4⋊C411yescharacteristic
753C2×C5C4×D3×D411yescharacteristic
754C2×C5#554611yescharacteristic
755C2×C5#559011yescharacteristic
756C2×C5#563211yescharacteristic
757C2×C5#563611yescharacteristic
758C2×C5#565511yescharacteristic
759D5—64no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—152no—
765C23—152no—
766C23—152no—
767C23—301no—
768C23—301no—
769C23—301no—
770C23—301no—
771C23D15⋊Q812yes—
772C23C4×D3×D512yes—
773C23#679012yes—
774C23C22×D3×D511yescharacteristic
775D4—1516no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—32no—
783C2×C4—32no—
784C2×C4—32no—
785C2×C4—32no—
786C2×C4—52no—
787C2×C4—52no—
788C2×C4—52no—
789C2×C4—68no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—101no—
799C2×C4—101no—
800C2×C4—101no—
801C2×C4—101no—
802C2×C4—101no—
803C2×C4—101no—
804C2×C4—101no—
805C2×C4—101no—
806C2×C4—101no—
807C2×C4—152no—
808C2×C4—152no—
809C2×C4—152no—
810C2×C4—152no—
811C2×C4—204no—
812C2×C4—308no—
813C2×C4—301no—
814C2×C4—301no—
815C2×C4—301no—
816C2×C4—301no—
817C2×C4—301no—
818C2×C4—604no—
819C2×C4—604no—
820C2×C4—604no—
821C2×C3—24no—
822C2×C3C2×#402711yescharacteristic
823C2×C3C2×D5×C4⋊C411yescharacteristic
824C2×C3#6585711yescharacteristic
825C2×C3#6594311yescharacteristic
826C2×C3#6594511yescharacteristic
827C2×C3#6596611yescharacteristic
828C2×C3#6596911yescharacteristic
829D3—104no—
830C5#7439311yescharacteristic, complemented, Sylow
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—154no—
838C22—302no—
839C22—302no—
840C22—302no—
841C22—302no—
842C22—302no—
843C22—302no—
844C22#9140414yescomplemented
845C22C2×D15⋊Q811yescharacteristic
846C22C2×C4×D3×D511yescharacteristic
847C22#9202011yescharacteristic
848C22D3×D4×D511yescharacteristic
849C22D3×#71111yescharacteristic
850C22#9202611yescharacteristic
851C22C2×#679011yescharacteristic
852C4—34no—
853C4—41no—
854C4—41no—
855C4—62no—
856C4—102no—
857C4—102no—
858C4—102no—
859C4—121no—
860C4—121no—
861C4—154no—
862C4—201no—
863C4—302no—
864C4—601no—
865C3#1060574111yescharacteristic, complemented, Sylow
866C2—24no—
867C2—304no—
868C2#1175281911yescharacteristic
869C2#1175286211yescharacteristic
870C2#1175300011yescharacteristic
871C2D3×#402711yescharacteristic
872C2C2×#9140411yescharacteristic
873C2#1175482511yescharacteristic
874C2#1175503911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5D4×C4⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C22×Dic3⋊Dic5C2semidirect
5. C2×#91404C2semidirect
6. C5×#4942C2semidirect
7. C3×#65235C2semidirect
8. #11749515C2semidirect
9. #11748895C2semidirect
10. #11748882C2semidirect
11. #11748804C2semidirect
12. #11748729C2semidirect
13. #11748658C2semidirect
14. #11748651C2semidirect
15. #11748641C2semidirect
35. #91556C4semidirect
68. #65235D3semidirect
91. C22×C5×Dic3C2×C4semidirect
108. C2×#1200C2×C4semidirect
116. C3×C22⋊Dic5C2×C4semidirect
122. Dic3⋊Dic5D4semidirect
124. #6669C2×C4semidirect
128. #6667C2×C4semidirect
130. Dic3×Dic5C2×C4semidirect
141. #4942D5semidirect
208. #1220C4⋊C4semidirect
328. C22⋊Dic5C4×D3semidirect
367. C22×C3×C5C2×C4⋊C4semidirect
381. C2×D15C2×C4⋊C4semidirect
386. Dic15C2×C4⋊C4semidirect
394. C5×Dic3C4×D4semidirect
417. C22×Dic3C4×D5semidirect
630. C22×C5D3×C4⋊C4semidirect
716. C3×C5D4×C4⋊C4semidirect
723. C22×C3D5×C4⋊C4semidirect
750. Dic3#4027semidirect
830. C5#74393semidirect
844. C22#91404semidirect
865. C3#10605741semidirect

Maximal subgroups

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

subgroupindex
C2×#917702
C2×#915562
C2×#915522
C22×Dic3⋊Dic52
C2×#914042
C5×#49422
C3×#652352
#117495152
#117488952
#117488822
#117488042
#117487292
#117486582
#117486512
#117486412
#106057413
#743935