Finite Group Databasebeta

← #14411985

Subgroups — #14411985

Order 1920.

1600 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92049C211yesmaximal, characteristic
2#11756245C211yesmaximal, characteristic, complemented
3#11755413C211yesmaximal, characteristic, complemented
4C2×C5×#806C211yesmaximal, characteristic, complemented
5C2×C3×#3938C211yesmaximal, characteristic, complemented
6C2×#90996C211yesmaximal, characteristic, complemented
7C2×#90995C211yesmaximal, characteristic, complemented
8#11747131C214yesmaximal, complemented
9#11747128C214yesmaximal, complemented
10#10610419—31nomaximal, Hall
11C22×#1220C2211yescharacteristic
12C22×C5×#67C2211yescharacteristic
13C22×C3×C22⋊D5C2211yescharacteristic
14#92049—22no—
15#92049—22no—
16#92049—22no—
17#92049—22no—
18C2×#6790C2212yes—
19C2×D3×C22⋊D5C412yescomplemented
20C2×D5×#67C412yescomplemented
21C2×#6782C412yescomplemented
22C2×#6780C2212yes—
23C2×#6779C412yescomplemented
24C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
25C2×#6719C2211yescharacteristic, complemented
26C4×#1220—22no—
27#91770—22no—
28C22⋊C4×D15C2212yescomplemented
29#91766C2212yescomplemented
30C2×C5×#217C2211yescharacteristic, complemented
31C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
32#91561C2212yescomplemented
33#91556—22no—
34#91552—22no—
35#91532C2212yescomplemented
36C5×#806C2214yescomplemented
37C3×#3938C2214yescomplemented
38#90996C2214yescomplemented
39#90995C2214yescomplemented
40#78688—51nomaximal, Hall
41C2×#4144—31no—
42#65820—31no—
43#65820—31no—
44C2×C5×#99—31no—
45C2×#3966—31no—
46C2×#3938—31no—
47C2×#3938D311yescharacteristic, complemented
48D5×#99—34no—
49#65029—34no—
50C24×C3×C5C2311yescharacteristic
51C23×D15C2311yescharacteristic
52C23×C5×D3C2×C411yescharacteristic, complemented
53C23×C3×D5C2×C411yescharacteristic, complemented
54C22×D3×D5C2×C412yescomplemented
55C22×C3×C4×C5—21no—
56C2×#1220C2×C412yes—
57C2×#1220C2×C412yes—
58C2×#1220D412yes—
59C2×#1220D412yes—
60C2×#1220D412yes—
61C2×#1220D412yes—
62C22×Dic15—21no—
63C22×Dic15C2311yescharacteristic
64C2×C4×D15—22no—
65C2×C5×#67—21no—
66C2×C5×#67—21no—
67C2×C5×#67—21no—
68C2×C5×#67—21no—
69C2×C5×#67C2×C412yescomplemented
70C2×C5×#67C2312yes—
71C22×C5×Dic3—21no—
72C22×C5×Dic3C2×C411yescharacteristic, complemented
73C2×C3×C22⋊D5—21no—
74C2×C3×C22⋊D5—21no—
75C2×C3×C22⋊D5—21no—
76C2×C3×C22⋊D5—21no—
77C2×C3×C22⋊D5C2×C412yescomplemented
78C2×C3×C22⋊D5C2312yes—
79C22×C3×Dic5—21no—
80C22×C3×Dic5C2×C411yescharacteristic, complemented
81#6790—24no—
82#6790—24no—
83D3×C22⋊D5—24no—
84D3×C22⋊D5—24no—
85D5×#67—24no—
86D5×#67—24no—
87C2×#1204C2×C412yescomplemented
88C2×#1203C2×C412yescomplemented
89C2×#1202C2×C412yescomplemented
90C2×#1201C2×C412yescomplemented
91C2×#1200—22no—
92C2×#1200C2×C412yescomplemented
93#6782—24no—
94#6782—24no—
95C2×D3×Dic5C2×C412yescomplemented
96#6780—24no—
97#6780—24no—
98#6779—24no—
99#6779—24no—
100C2×D5×Dic3C2×C412yescomplemented
101C3×C5×C22⋊C4—21no—
102C3×C5×C22⋊C4C2312yes—
103#6719—21no—
104#6719C2312yes—
105#6714—22no—
106#6712—22no—
107C4×Dic15—22no—
108C5×#217—21no—
109C5×#217C2312yes—
110C3×C22⋊Dic5—21no—
111C3×C22⋊Dic5C2312yes—
112#6669—22no—
113#6667—22no—
114Dic3×Dic5—22no—
115C2×#1004—51no—
116#5486—51no—
117#5486—51no—
118C2×C3×#99—51no—
119C2×#834—51no—
120C2×#806—51no—
121C2×#806D511yescharacteristic, complemented
122D3×#99—54no—
123#4740—54no—
124C22×C5×D4—31no—
125C22×C22⋊D5—31no—
126C22×C22⋊D5—32no—
127C22×C22⋊D5C2×D311yescharacteristic
128#4144—62no—
129#4144—62no—
130#4144—62no—
131#4144—62no—
132C2×#711—32no—
133C2×#711—32no—
134C2×D4×D5—32no—
135C2×D4×D5—32no—
136C2×#709—32no—
137C2×C5×C22⋊C4—31no—
138C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
139C2×C22⋊Dic5—31no—
140C2×C22⋊Dic5C2×D311yescharacteristic, complemented
141C4×C22⋊D5—62no—
142C4×C22⋊D5—62no—
143#4027—62no—
144#4027—62no—
145D5×C22⋊C4—32no—
146D5×C22⋊C4—32no—
147#4023—32no—
148#4023—32no—
149C5×#99—34no—
150#3966—34no—
151#3938—34no—
152#3938C2×D314yescomplemented
153#2883—151noSylow
154C23×C3×C5—81no—
155C23×C3×C5C22×C411yescharacteristic
156C23×C3×C5C22×C411yescharacteristic
157C23×C3×C5C2×D411yescharacteristic
158C23×C3×C5C2×D411yescharacteristic
159C23×C3×C5C2×D411yescharacteristic
160C23×C3×C5C2×D411yescharacteristic
161C23×C3×C5C2411yescharacteristic
162C22×D15—81no—
163C22×D15C22×C412yes—
164C22×D15C2×D412yes—
165C22×D15C2×D412yes—
166C22×C5×D3—21no—
167C22×C5×D3—21no—
168C22×C5×D3—81no—
169C22×C5×D3C22×C412yes—
170C22×C3×D5—21no—
171C22×C3×D5—21no—
172C22×C3×D5—81no—
173C22×C3×D5C22×C412yes—
174C2×D3×D5—24no—
175C2×D3×D5—82no—
176C2×C3×C4×C5—22no—
177C2×C3×C4×C5—81no—
178#1220C22⋊C414yes—
179#1220C22⋊C414yes—
180#1220C22⋊C414yes—
181#1220C22⋊C414yes—
182C2×Dic15—22no—
183C2×Dic15—81no—
184C2×Dic15C22×C412yes—
185C2×Dic15C2×D412yes—
186C2×Dic15C2×D412yes—
187C4×D15—82no—
188C5×#67—22no—
189C5×#67—22no—
190C5×#67—22no—
191C5×#67—22no—
192C2×C5×Dic3—21no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—22no—
195C2×C5×Dic3—81no—
196C2×C5×Dic3C22×C412yes—
197C3×C22⋊D5—22no—
198C3×C22⋊D5—22no—
199C3×C22⋊D5—22no—
200C3×C22⋊D5—22no—
201C2×C3×Dic5—21no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—22no—
204C2×C3×Dic5—81no—
205C2×C3×Dic5C22×C412yes—
206#1204—24no—
207#1203—24no—
208#1202—24no—
209#1201—24no—
210#1200—24no—
211#1200—82no—
212D3×Dic5—24no—
213D5×Dic3—24no—
214C22×C3×D4—51no—
215C22×#67—51no—
216C22×#67—52no—
217C22×#67C2×D511yescharacteristic
218#1004—102no—
219#1004—102no—
220#1004—102no—
221#1004—102no—
222C2×#237—52no—
223C2×#237—52no—
224C2×D3×D4—52no—
225C2×D3×D4—52no—
226C2×#235—52no—
227C2×C3×C22⋊C4—51no—
228C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
229C2×#217—51no—
230C2×#217C2×D511yescharacteristic, complemented
231C4×#67—102no—
232C4×#67—102no—
233#67⋊C4—102no—
234#67⋊C4—102no—
235D3×C22⋊C4—52no—
236D3×C22⋊C4—52no—
237#877—52no—
238#877—52no—
239C3×#99—54no—
240#834—54no—
241#806—54no—
242#806C2×D514yescomplemented
243C24×C5—31no—
244C24×C5C22×D311yescharacteristic
245C23×D5—31no—
246C23×D5—32no—
247C23×D5C4×D311yescharacteristic, complemented
248C2×C5×D4—32no—
249C2×C5×D4—32no—
250C2×C5×D4—61no—
251C2×C5×D4—61no—
252C2×C5×D4—61no—
253C2×C5×D4—61no—
254C22×C4×C5—21no—
255C22×C4×C5—31no—
256C22×C4×C5—61no—
257C2×C22⋊D5—21no—
258C2×C22⋊D5—21no—
259C2×C22⋊D5—21no—
260C2×C22⋊D5—21no—
261C2×C22⋊D5—32no—
262C2×C22⋊D5—32no—
263C2×C22⋊D5—32no—
264C2×C22⋊D5—32no—
265C2×C22⋊D5—32no—
266C2×C22⋊D5—32no—
267C2×C22⋊D5—32no—
268C2×C22⋊D5—32no—
269C2×C22⋊D5—64no—
270C2×C22⋊D5—64no—
271C2×C22⋊D5C4×D312yescomplemented
272C2×C22⋊D5C22×D312yes—
273C22×Dic5—21no—
274C22×Dic5—31no—
275C22×Dic5—32no—
276C22×Dic5—61no—
277C22×Dic5C4×D311yescharacteristic, complemented
278#711—64no—
279#711—64no—
280#711—64no—
281#711—64no—
282D4×D5—64no—
283D4×D5—64no—
284D4×D5—64no—
285D4×D5—64no—
286#709—64no—
287#709—64no—
288C2×D20—32no—
289C2×C4×D5—32no—
290C2×C4×D5—32no—
291C2×C4×D5—62no—
292C2×C4×D5—62no—
293C2×Dic10—32no—
294C5×C22⋊C4—21no—
295C5×C22⋊C4—32no—
296C5×C22⋊C4—61no—
297C5×C22⋊C4C22×D312yes—
298C22⋊Dic5—21no—
299C22⋊Dic5—32no—
300C22⋊Dic5—61no—
301C22⋊Dic5C22×D312yes—
302#685—62no—
303#685—62no—
304#683—62no—
305#683—62no—
306C4×Dic5—62no—
307C4×Dic5—62no—
308C2×H(5,𝔽2)—151no—
309#518—151no—
310#518—151no—
311#410—154no—
312C2×#99—31no—
313C2×#99—51no—
314C2×#99—154no—
315C2×#99—151no—
316C2×#99—151no—
317C22×C3×C5—41no—
318C22×C3×C5—41no—
319C22×C3×C5—41no—
320C22×C3×C5—41no—
321C22×C3×C5—41no—
322C22×C3×C5—41no—
323C22×C3×C5—41no—
324C22×C3×C5C2×C22⋊C411yescharacteristic
325C22×C3×C5C2×C22⋊C411yescharacteristic
326C22×C3×C5C2×C22⋊C411yescharacteristic
327C22×C3×C5C2×C22⋊C411yescharacteristic
328C22×C3×C5C23×C411yescharacteristic
329C22×C3×C5C22×D411yescharacteristic
330C22×C3×C5C22×D411yescharacteristic
331C2×D15—42no—
332C2×D15—42no—
333C2×D15—42no—
334C2×D15C2×C22⋊C414yes—
335C2×C5×D3—22no—
336C2×C5×D3—42no—
337C2×C5×D3—81no—
338C2×C5×D3—81no—
339C2×C3×D5—22no—
340C2×C3×D5—42no—
341C2×C3×D5—81no—
342C2×C3×D5—81no—
343D3×D5—84no—
344C3×C4×C5—42no—
345Dic15—42no—
346Dic15C2×C22⋊C414yes—
347C3×Dic5—22no—
348C3×Dic5—42no—
349C5×Dic3—22no—
350C5×Dic3—42no—
351C24×C3—51no—
352C24×C3C22×D511yescharacteristic
353C23×D3—51no—
354C23×D3—52no—
355C23×D3C4×D511yescharacteristic, complemented
356C2×C3×D4—52no—
357C2×C3×D4—52no—
358C2×C3×D4—101no—
359C2×C3×D4—101no—
360C2×C3×D4—101no—
361C2×C3×D4—101no—
362C22×C3×C4—21no—
363C22×C3×C4—51no—
364C22×C3×C4—101no—
365C2×#67—21no—
366C2×#67—21no—
367C2×#67—21no—
368C2×#67—21no—
369C2×#67—52no—
370C2×#67—52no—
371C2×#67—52no—
372C2×#67—52no—
373C2×#67—52no—
374C2×#67—52no—
375C2×#67—52no—
376C2×#67—52no—
377C2×#67—104no—
378C2×#67—104no—
379C2×#67C4×D512yescomplemented
380C2×#67C22×D512yes—
381C22×Dic3—21no—
382C22×Dic3—51no—
383C22×Dic3—52no—
384C22×Dic3—101no—
385C22×Dic3C4×D511yescharacteristic, complemented
386#237—104no—
387#237—104no—
388#237—104no—
389#237—104no—
390D3×D4—104no—
391D3×D4—104no—
392D3×D4—104no—
393D3×D4—104no—
394#235—104no—
395#235—104no—
396C2×D12—52no—
397C2×C4×D3—52no—
398C2×C4×D3—52no—
399C2×C4×D3—102no—
400C2×C4×D3—102no—
401C2×Dic6—52no—
402C3×C22⋊C4—21no—
403C3×C22⋊C4—52no—
404C3×C22⋊C4—101no—
405C3×C22⋊C4C22×D512yes—
406#217—21no—
407#217—52no—
408#217—101no—
409#217C22×D512yes—
410(C2×D3)⋊C4—102no—
411(C2×D3)⋊C4—102no—
412Dic3⋊C4—102no—
413Dic3⋊C4—102no—
414C4×Dic3—102no—
415C4×Dic3—102no—
416C23×C5—32no—
417C23×C5—61no—
418C23×C5—61no—
419C23×C5—81no—
420C23×C5—241no—
421C23×C5C2×C4×D311yescharacteristic
422C23×C5C2×C4×D311yescharacteristic
423C23×C5D3×D411yescharacteristic
424C23×C5D3×D411yescharacteristic
425C23×C5D3×D411yescharacteristic
426C23×C5D3×D411yescharacteristic
427C23×C5C23×D311yescharacteristic
428C22×D5—21no—
429C22×D5—21no—
430C22×D5—32no—
431C22×D5—32no—
432C22×D5—32no—
433C22×D5—64no—
434C22×D5—81no—
435C22×D5—242no—
436C22×D5—241no—
437C22×D5C2×C4×D312yes—
438C5×D4—62no—
439C5×D4—62no—
440C5×D4—62no—
441C5×D4—62no—
442C2×C4×C5—22no—
443C2×C4×C5—32no—
444C2×C4×C5—61no—
445C2×C4×C5—61no—
446C2×C4×C5—62no—
447C2×C4×C5—81no—
448C2×C4×C5—241no—
449C22⋊D5—22no—
450C22⋊D5—22no—
451C22⋊D5—22no—
452C22⋊D5—22no—
453C22⋊D5—34no—
454C22⋊D5—34no—
455C22⋊D5—34no—
456C22⋊D5—34no—
457C22⋊D5—64no—
458C22⋊D5—64no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—22no—
462C2×Dic5—32no—
463C2×Dic5—32no—
464C2×Dic5—32no—
465C2×Dic5—64no—
466C2×Dic5—62no—
467C2×Dic5—81no—
468C2×Dic5—241no—
469C2×Dic5C2×C4×D312yes—
470D20—64no—
471C4×D5—64no—
472C4×D5—64no—
473C4×D5—242no—
474C4×D5—242no—
475Dic10—64no—
476H(5,𝔽2)—302no—
477H(5,𝔽2)—302no—
478H(5,𝔽2)—302no—
479H(5,𝔽2)—302no—
480C2×#41—152no—
481C2×#41—152no—
482C2×#41—152no—
483C22×D4—31no—
484C22×D4—51no—
485C22×D4—152no—
486C22×D4—152no—
487C22×D4—152no—
488C22×D4—151no—
489C4×D4—302no—
490C4×D4—302no—
491C4×D4—302no—
492C4×D4—302no—
493#117—152no—
494#117—152no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—51no—
497C2×C22⋊C4—152no—
498C2×C22⋊C4—151no—
499C2×C22⋊C4—152no—
500C2×C22⋊C4D3×D511yescharacteristic, complemented
501#99—34no—
502#99—54no—
503#99—154no—
504#99—154no—
505C2×C3×C5—21no—
506C2×C3×C5—21no—
507C2×C3×C5—21no—
508C2×C3×C5—21no—
509C2×C3×C5—21no—
510C2×C3×C5—21no—
511C2×C3×C5—21no—
512C2×C3×C5C22×C22⋊C411yescharacteristic
513D15—24no—
514C3×D5—42no—
515C5×D3—42no—
516C23×C3—52no—
517C23×C3—81no—
518C23×C3—101no—
519C23×C3—101no—
520C23×C3—401no—
521C23×C3C2×C4×D511yescharacteristic
522C23×C3C2×C4×D511yescharacteristic
523C23×C3D4×D511yescharacteristic
524C23×C3D4×D511yescharacteristic
525C23×C3D4×D511yescharacteristic
526C23×C3D4×D511yescharacteristic
527C23×C3C23×D511yescharacteristic
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—52no—
531C22×D3—52no—
532C22×D3—52no—
533C22×D3—81no—
534C22×D3—104no—
535C22×D3—402no—
536C22×D3—401no—
537C22×D3C2×C4×D512yes—
538C3×D4—102no—
539C3×D4—102no—
540C3×D4—102no—
541C3×D4—102no—
542C2×C3×C4—22no—
543C2×C3×C4—52no—
544C2×C3×C4—81no—
545C2×C3×C4—101no—
546C2×C3×C4—101no—
547C2×C3×C4—102no—
548C2×C3×C4—401no—
549#67—22no—
550#67—22no—
551#67—22no—
552#67—22no—
553#67—54no—
554#67—54no—
555#67—54no—
556#67—54no—
557#67—104no—
558#67—104no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—22no—
562C2×Dic3—52no—
563C2×Dic3—52no—
564C2×Dic3—52no—
565C2×Dic3—81no—
566C2×Dic3—104no—
567C2×Dic3—102no—
568C2×Dic3—401no—
569C2×Dic3C2×C4×D512yes—
570D12—104no—
571C4×D3—104no—
572C4×D3—104no—
573C4×D3—402no—
574C4×D3—402no—
575Dic6—104no—
576C22×C5—41no—
577C22×C5—41no—
578C22×C5—41no—
579C22×C5—41no—
580C22×C5—41no—
581C22×C5—41no—
582C22×C5—41no—
583C22×C5—62no—
584C22×C5—122no—
585C22×C5—241no—
586C22×C5—241no—
587C22×C5D3×C22⋊C411yescharacteristic
588C22×C5D3×C22⋊C411yescharacteristic
589C22×C5D3×C22⋊C411yescharacteristic
590C22×C5D3×C22⋊C411yescharacteristic
591C22×C5C22×C4×D311yescharacteristic
592C22×C5C2×D3×D411yescharacteristic
593C22×C5C2×D3×D411yescharacteristic
594C2×D5—22no—
595C2×D5—34no—
596C2×D5—42no—
597C2×D5—81no—
598C2×D5—81no—
599C2×D5—122no—
600C2×D5—122no—
601C2×D5—122no—
602C2×D5—244no—
603C4×C5—42no—
604C4×C5—62no—
605C4×C5—122no—
606Dic5—22no—
607Dic5—34no—
608Dic5—42no—
609Dic5—122no—
610C24—31no—
611C24—51no—
612C24—152no—
613C24—151no—
614C24C2×D3×D511yescharacteristic
615#41—304no—
616#41—304no—
617#41—304no—
618#41—304no—
619#41—304no—
620#41—304no—
621C2×Q8—152no—
622C2×D4—32no—
623C2×D4—32no—
624C2×D4—52no—
625C2×D4—52no—
626C2×D4—61no—
627C2×D4—61no—
628C2×D4—61no—
629C2×D4—61no—
630C2×D4—101no—
631C2×D4—101no—
632C2×D4—101no—
633C2×D4—101no—
634C2×D4—152no—
635C2×D4—152no—
636C2×D4—152no—
637C2×D4—152no—
638C2×D4—152no—
639C2×D4—152no—
640C2×D4—152no—
641C2×D4—152no—
642C2×D4—152no—
643C2×D4—304no—
644C2×D4—304no—
645C2×D4—304no—
646C2×D4—304no—
647C2×D4—304no—
648C2×D4—304no—
649C22×C4—21no—
650C22×C4—31no—
651C22×C4—51no—
652C22×C4—61no—
653C22×C4—101no—
654C22×C4—152no—
655C22×C4—152no—
656C22×C4—152no—
657C22×C4—151no—
658C22×C4—302no—
659C22×C4—302no—
660C22×C4—301no—
661C4⋊C4—302no—
662C4⋊C4—302no—
663C22⋊C4—21no—
664C22⋊C4—32no—
665C22⋊C4—52no—
666C22⋊C4—61no—
667C22⋊C4—101no—
668C22⋊C4—152no—
669C22⋊C4—302no—
670C22⋊C4—302no—
671C22⋊C4—301no—
672C22⋊C4C2×D3×D512yes—
673C42—302no—
674C42—302no—
675C3×C5#288311yescharacteristic, complemented, Hall
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—102no—
684C22×C3—202no—
685C22×C3—401no—
686C22×C3—401no—
687C22×C3D5×C22⋊C411yescharacteristic
688C22×C3D5×C22⋊C411yescharacteristic
689C22×C3D5×C22⋊C411yescharacteristic
690C22×C3D5×C22⋊C411yescharacteristic
691C22×C3C22×C4×D511yescharacteristic
692C22×C3C2×D4×D511yescharacteristic
693C22×C3C2×D4×D511yescharacteristic
694C2×D3—22no—
695C2×D3—42no—
696C2×D3—54no—
697C2×D3—81no—
698C2×D3—81no—
699C2×D3—202no—
700C2×D3—202no—
701C2×D3—202no—
702C2×D3—404no—
703C3×C4—42no—
704C3×C4—102no—
705C3×C4—202no—
706Dic3—22no—
707Dic3—42no—
708Dic3—54no—
709Dic3—202no—
710C2×C5—21no—
711C2×C5—21no—
712C2×C5—21no—
713C2×C5—21no—
714C2×C5—21no—
715C2×C5—21no—
716C2×C5—21no—
717C2×C5—122no—
718C2×C5C2×D3×C22⋊C411yescharacteristic
719D5—42no—
720D5—64no—
721C23—32no—
722C23—52no—
723C23—61no—
724C23—61no—
725C23—81no—
726C23—101no—
727C23—101no—
728C23—152no—
729C23—152no—
730C23—152no—
731C23—241no—
732C23—304no—
733C23—401no—
734C23—1201no—
735C23—1202no—
736C23C4×D3×D511yescharacteristic
737C23C4×D3×D511yescharacteristic
738C23#677711yescharacteristic
739C23#677711yescharacteristic
740C23#679011yescharacteristic
741C23#679011yescharacteristic
742C23C22×D3×D511yescharacteristic
743Q8—304no—
744D4—62no—
745D4—62no—
746D4—62no—
747D4—62no—
748D4—102no—
749D4—102no—
750D4—102no—
751D4—102no—
752D4—154no—
753D4—154no—
754D4—154no—
755D4—154no—
756D4—304no—
757D4—304no—
758D4—304no—
759C2×C4—22no—
760C2×C4—32no—
761C2×C4—52no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—62no—
765C2×C4—81no—
766C2×C4—101no—
767C2×C4—101no—
768C2×C4—102no—
769C2×C4—152no—
770C2×C4—152no—
771C2×C4—152no—
772C2×C4—241no—
773C2×C4—304no—
774C2×C4—304no—
775C2×C4—304no—
776C2×C4—302no—
777C2×C4—401no—
778C2×C4—1202no—
779C2×C4—1202no—
780C2×C4—1201no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—202no—
789C2×C3C2×D5×C22⋊C411yescharacteristic
790D3—42no—
791D3—104no—
792C5#7868811yescharacteristic, complemented, Sylow
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—62no—
801C22—102no—
802C22—122no—
803C22—154no—
804C22—202no—
805C22—241no—
806C22—241no—
807C22—401no—
808C22—401no—
809C22—602no—
810C22—602no—
811C22—602no—
812C22—1204no—
813C22#9147311yescharacteristic
814C22#9147311yescharacteristic
815C22#9147311yescharacteristic
816C22#9147311yescharacteristic
817C22C2×C4×D3×D511yescharacteristic
818C22C2×#677711yescharacteristic
819C22C2×#679011yescharacteristic
820C4—42no—
821C4—62no—
822C4—102no—
823C4—122no—
824C4—154no—
825C4—202no—
826C4—602no—
827C3#1061041911yescharacteristic, complemented, Sylow
828C2—21no—
829C2—21no—
830C2—21no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—21no—
835C2—122no—
836C2—202no—
837C2—304no—
838C2C2×#9147311yescharacteristic
subgroupG/H
centerC2C2×#91473
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×#92049C2
cosocleC23×C3×C5C24
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2883
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #11756245C2semidirect
3. #11755413C2semidirect
4. C2×C5×#806C2semidirect
5. C2×C3×#3938C2semidirect
6. C2×#90996C2semidirect
7. C2×#90995C2semidirect
8. #11747131C2semidirect
9. #11747128C2semidirect
19. C2×D3×C22⋊D5C4semidirect
20. C2×D5×#67C4semidirect
21. C2×#6782C4semidirect
23. C2×#6779C4semidirect
24. C2×C3×C5×C22⋊C4C22semidirect
25. C2×#6719C22semidirect
28. C22⋊C4×D15C22semidirect
29. #91766C22semidirect
30. C2×C5×#217C22semidirect
31. C2×C3×C22⋊Dic5C22semidirect
32. #91561C22semidirect
35. #91532C22semidirect
36. C5×#806C22semidirect
37. C3×#3938C22semidirect
38. #90996C22semidirect
39. #90995C22semidirect
47. C2×#3938D3semidirect
52. C23×C5×D3C2×C4semidirect
53. C23×C3×D5C2×C4semidirect
54. C22×D3×D5C2×C4semidirect
69. C2×C5×#67C2×C4semidirect
72. C22×C5×Dic3C2×C4semidirect
77. C2×C3×C22⋊D5C2×C4semidirect
80. C22×C3×Dic5C2×C4semidirect
87. C2×#1204C2×C4semidirect
88. C2×#1203C2×C4semidirect
89. C2×#1202C2×C4semidirect
90. C2×#1201C2×C4semidirect
92. C2×#1200C2×C4semidirect
95. C2×D3×Dic5C2×C4semidirect
100. C2×D5×Dic3C2×C4semidirect
121. C2×#806D5semidirect
138. C2×C5×C22⋊C4C2×D3semidirect
140. C2×C22⋊Dic5C2×D3semidirect
152. #3938C2×D3semidirect
228. C2×C3×C22⋊C4C2×D5semidirect
230. C2×#217C2×D5semidirect
242. #806C2×D5semidirect
247. C23×D5C4×D3semidirect
271. C2×C22⋊D5C4×D3semidirect
277. C22×Dic5C4×D3semidirect
355. C23×D3C4×D5semidirect
379. C2×#67C4×D5semidirect
385. C22×Dic3C4×D5semidirect
500. C2×C22⋊C4D3×D5semidirect
675. C3×C5#2883semidirect
792. C5#78688semidirect
827. C3#10610419semidirect

Maximal subgroups

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

subgroupindex
C2×#920492
#117562452
#117554132
C2×C5×#8062
C2×C3×#39382
C2×#909962
C2×#909952
#117471312
#117471282
#106104193
#786885