Finite Group Databasebeta

← #14415461

Subgroups — #14415461

Order 1920.

1004 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6762C211yesmaximal, characteristic, complemented
2C2×#91990C211yesmaximal, characteristic, complemented
3C3×#65920C211yesmaximal, characteristic
4C2×#91241C211yesmaximal, characteristic, complemented
5#11752434C211yesmaximal, characteristic, complemented
6#11752433C211yesmaximal, characteristic, complemented
7#11752432C211yesmaximal, characteristic, complemented
8#11752432C211yesmaximal, characteristic, complemented
9D4×C3⋊#170C211yesmaximal, characteristic, complemented
10#11752355C211yesmaximal, characteristic, complemented
11#11752354C211yesmaximal, characteristic, complemented
12#11752353C211yesmaximal, characteristic, complemented
13#11752352C211yesmaximal, characteristic, complemented
14#11752351C211yesmaximal, characteristic, complemented
15#11752350C211yesmaximal, characteristic, complemented
16#10617217—31nomaximal, Hall
17C23×C3×Dic5C2211yescharacteristic
18C2×C3×#711C2211yescharacteristic
19C2×#6762—24no—
20C2×#6762C2211yescharacteristic
21C2×#6762C2211yescharacteristic
22C2×#6762C2211yescharacteristic
23C2×#6762C2211yescharacteristic
24C2×#6762C2211yescharacteristic, complemented
25C22×C3⋊#170C2211yescharacteristic
26C22×C3⋊#170C2211yescharacteristic
27C22×C3⋊#170C2211yescharacteristic
28C22×C3⋊#170C2211yescharacteristic
29C22×C3⋊#170C2211yescharacteristic, complemented
30#91990—24no—
31C2×#6758C2211yescharacteristic, complemented
32C2×D5⋊(C3⋊C8)C2211yescharacteristic, complemented
33C3×C5×#120C411yescharacteristic
34C3×#4099C411yescharacteristic
35C3×#4085C411yescharacteristic
36C3×#4085C411yescharacteristic
37C3×#4081C411yescharacteristic
38C3×D4×Dic5C2211yescharacteristic
39C3×D4×Dic5C2211yescharacteristic
40C3×#4032C411yescharacteristic
41C3×#4027C2211yescharacteristic
42C3×#4027C2211yescharacteristic
43C3×#4024C411yescharacteristic
44C3×#4024C411yescharacteristic
45C3×#4023C2211yescharacteristic
46#91241C2211yescharacteristic
47#91241C2211yescharacteristic
48#91241C2211yescharacteristic
49#91241C2211yescharacteristic
50#91241C2211yescharacteristic, complemented
51#91241C2211yescharacteristic, complemented
52#91233C2211yescharacteristic, complemented
53#91233C2211yescharacteristic, complemented
54#91232C2211yescharacteristic, complemented
55#91232C2211yescharacteristic, complemented
56#91231C2211yescharacteristic, complemented
57#91231C2211yescharacteristic, complemented
58C4⋊(C3⋊#170)C2211yescharacteristic, complemented
59C4⋊(C3⋊#170)C2211yescharacteristic, complemented
60C4×C3⋊#170C2211yescharacteristic, complemented
61C4×C3⋊#170C2211yescharacteristic, complemented
62#82918—51nomaximal, Hall
63C22×#704—31no—
64C2×#4131—31no—
65#65920D311yescharacteristic
66C2×C22⋊#170—31no—
67#65775—31no—
68#65774—31no—
69#65773—31no—
70#65773—31no—
71D4×#170—31no—
72#65696—31no—
73#65695—31no—
74#65694—31no—
75#65693—31no—
76#65692—31no—
77#65691—31no—
78C24×C3×C5C2×C411yescharacteristic
79C2×C3×C5×D4C2×C411yescharacteristic
80C2×C3×C5×D4C2×C411yescharacteristic
81C2×C3×C5×D4C2×C411yescharacteristic
82C2×C3×C22⋊D5C2×C411yescharacteristic
83C2×C3×C22⋊D5C2×C411yescharacteristic
84C2×C3×C22⋊D5C2×C411yescharacteristic
85C2×C3×C22⋊D5C2×C411yescharacteristic
86C22×C3×Dic5—22no—
87C22×C3×Dic5—22no—
88C22×C3×Dic5C2×C411yescharacteristic
89C22×C3×Dic5C2×C411yescharacteristic
90C22×C3×Dic5C2×C411yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C3×#711—22no—
96C3×#711—22no—
97C2×C3×C4×D5C2311yescharacteristic
98C2×C3×Dic10C2×C411yescharacteristic
99#6762—22no—
100#6762—22no—
101#6762—22no—
102#6762—22no—
103#6762D414yescomplemented
104C2×C3⋊#170—22no—
105C2×C3⋊#170—22no—
106C2×C3⋊#170—22no—
107C2×C3⋊#170—22no—
108C2×C3⋊#170—22no—
109C2×C3⋊#170C2311yescharacteristic
110C2×C3⋊#170C2311yescharacteristic
111C2×C3⋊#170C2311yescharacteristic
112C2×C3⋊#170C2311yescharacteristic
113C2×C3⋊#170C2311yescharacteristic
114C2×C3⋊#170C2311yescharacteristic
115C2×C3⋊#170C2311yescharacteristic
116C2×C3⋊#170C2311yescharacteristic
117#6758—22no—
118D5⋊(C3⋊C8)—22no—
119C3×C5×C22⋊C4C2×C411yescharacteristic
120C3×C5×C22⋊C4C2×C411yescharacteristic
121C3×C5×C22⋊C4C2×C411yescharacteristic
122C3×C22⋊Dic5C2×C411yescharacteristic
123C3×C22⋊Dic5C2×C411yescharacteristic
124C3×C22⋊Dic5C2×C411yescharacteristic
125C3×C22⋊Dic5C2×C411yescharacteristic
126C3×C22⋊Dic5C2×C411yescharacteristic
127C3×#685C2×C411yescharacteristic
128C3×#685C2×C411yescharacteristic
129C3×C4⋊Dic5C2×C411yescharacteristic
130C3×C4⋊Dic5C2×C411yescharacteristic
131C3×#683C2×C411yescharacteristic
132C3×#683C2×C411yescharacteristic
133C3×#683C2×C411yescharacteristic
134C3×#683C2×C411yescharacteristic
135C3×C4×Dic5C2311yescharacteristic
136C3×C4×Dic5C2311yescharacteristic
137C3×#525—51no—
138C2×#948—51no—
139C22×#208—51no—
140#5234—51no—
141C2×#830—51no—
142#5012—51no—
143#5012—51no—
144#5011—51no—
145#5011—51no—
146#5011—51no—
147#5011—51no—
148D4×C3⋊C8—51no—
149D4×C3⋊C8—51no—
150#4999—51no—
151#4997—51no—
152C23×Dic5C2×D311yescharacteristic
153C2×#711C2×D311yescharacteristic
154C2×#704—31no—
155C2×#704—31no—
156C2×#704—31no—
157C2×#704—31no—
158C2×#704—31no—
159C2×#704—64no—
160C22×#170—31no—
161C22×#170—31no—
162C22×#170—31no—
163C22×#170—31no—
164C22×#170—31no—
165#4131—64no—
166C2×#700—31no—
167C2×D5⋊C8—31no—
168C5×#120Dic311yescharacteristic
169#4099Dic311yescharacteristic
170#4085Dic311yescharacteristic
171#4085Dic311yescharacteristic
172#4081Dic311yescharacteristic
173D4×Dic5C2×D311yescharacteristic
174D4×Dic5C2×D311yescharacteristic
175#4032Dic311yescharacteristic
176#4027C2×D311yescharacteristic
177#4027C2×D311yescharacteristic
178#4024Dic311yescharacteristic
179#4024Dic311yescharacteristic
180#4023C2×D311yescharacteristic
181C22⋊#170—31no—
182C22⋊#170—31no—
183C22⋊#170—31no—
184C22⋊#170—31no—
185C22⋊#170—31no—
186C22⋊#170—31no—
187#4004—31no—
188#4004—31no—
189#4003—31no—
190#4003—31no—
191#4002—31no—
192#4002—31no—
193C4⋊#170—31no—
194C4⋊#170—31no—
195C4×#170—31no—
196C4×#170—31no—
197#2933—151noSylow
198C23×C3×C5—22no—
199C23×C3×C5—22no—
200C23×C3×C5—41no—
201C23×C3×C5C22×C411yescharacteristic
202C23×C3×C5C22×C411yescharacteristic
203C23×C3×C5C22×C411yescharacteristic
204C23×C3×C5C22×C411yescharacteristic
205C22×C3×D5C22×C411yescharacteristic
206C3×C5×D4—22no—
207C3×C5×D4—22no—
208C3×C5×D4—41no—
209C2×C3×C4×C5C22×C411yescharacteristic
210C2×C3×C4×C5C22×C411yescharacteristic
211C2×C3×C4×C5C22×C411yescharacteristic
212C3×C22⋊D5—22no—
213C3×C22⋊D5—22no—
214C3×C22⋊D5—22no—
215C3×C22⋊D5—41no—
216C2×C3×Dic5—22no—
217C2×C3×Dic5—22no—
218C2×C3×Dic5—22no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5C22×C411yescharacteristic
226C2×C3×Dic5C22×C411yescharacteristic
227C2×C3×Dic5C22×C411yescharacteristic
228C2×C3×Dic5C22×C411yescharacteristic
229C2×C3×Dic5C22×C411yescharacteristic
230C2×C3×Dic5C22×C411yescharacteristic
231C2×C3×Dic5C2×D412yes—
232C2×C3×Dic5#4112yes—
233C2×C3×Dic5C2411yescharacteristic
234C3×C4×D5—21no—
235C3×C4×D5—21no—
236C3×Dic10—22no—
237C3⋊#170—21no—
238C3⋊#170—21no—
239C3⋊#170—21no—
240C3⋊#170—21no—
241C3⋊#170—21no—
242C3⋊#170—21no—
243C3⋊#170C2×D412yes—
244C3⋊#170C2×D412yes—
245C2×C3×#41—51no—
246C23×C3×C4—51no—
247C3×#123—51no—
248C3×#123—51no—
249C3×C22⋊Q8—51no—
250C3×C22⋊Q8—51no—
251C3×#121—51no—
252C3×#121—51no—
253C3×#120—51no—
254C3×#120AGL(1,𝔽5)11yescharacteristic
255C3×C4×D4—51no—
256C3×C4×D4—51no—
257C3×C4×D4—51no—
258C3×C4×D4—51no—
259C3×#117—51no—
260#948—104no—
261C2×#208—51no—
262C2×#208—51no—
263C2×#208—51no—
264C2×#208—51no—
265C2×#208—51no—
266C2×#208—51no—
267C2×#208—104no—
268C22×C3⋊C8—51no—
269C22×C3⋊C8—51no—
270C22×C3⋊C8—51no—
271C22×C3⋊C8—51no—
272C22×C3⋊C8—51no—
273C22×C3⋊C8—51no—
274#830—51no—
275#830—51no—
276#830—51no—
277#830—51no—
278#830—51no—
279#830—51no—
280#830—51no—
281#830—51no—
282C4⋊(C3⋊C8)—51no—
283C4⋊(C3⋊C8)—51no—
284C4⋊(C3⋊C8)—51no—
285C4⋊(C3⋊C8)—51no—
286#803—51no—
287#803—51no—
288C4×C3⋊C8—51no—
289C4×C3⋊C8—51no—
290C24×C5C2×Dic311yescharacteristic
291C2×C5×D4C2×Dic311yescharacteristic
292C2×C5×D4C2×Dic311yescharacteristic
293C2×C5×D4C2×Dic311yescharacteristic
294C2×C22⋊D5C2×Dic311yescharacteristic
295C2×C22⋊D5C2×Dic311yescharacteristic
296C2×C22⋊D5C2×Dic311yescharacteristic
297C2×C22⋊D5C2×Dic311yescharacteristic
298C22×Dic5—22no—
299C22×Dic5—22no—
300C22×Dic5C2×Dic311yescharacteristic
301C22×Dic5C2×Dic311yescharacteristic
302C22×Dic5C2×Dic311yescharacteristic
303C22×Dic5C22×D311yescharacteristic
304C22×Dic5C22×D311yescharacteristic
305C22×Dic5C22×D311yescharacteristic
306C22×Dic5C22×D311yescharacteristic
307#711—22no—
308#711—22no—
309C2×C4×D5C22×D311yescharacteristic
310C2×Dic10C2×Dic311yescharacteristic
311#704—34no—
312#704—62no—
313#704—62no—
314#704—62no—
315#704—62no—
316C2×#170—31no—
317C2×#170—31no—
318C2×#170—31no—
319C2×#170—31no—
320C2×#170—31no—
321C2×#170—31no—
322C2×#170—31no—
323C2×#170—31no—
324C2×#170—62no—
325C2×#170—62no—
326C2×#170—62no—
327C2×#170—62no—
328C2×#170—62no—
329#700—62no—
330D5⋊C8—62no—
331C5×C22⋊C4C2×Dic311yescharacteristic
332C5×C22⋊C4C2×Dic311yescharacteristic
333C5×C22⋊C4C2×Dic311yescharacteristic
334C22⋊Dic5C2×Dic311yescharacteristic
335C22⋊Dic5C2×Dic311yescharacteristic
336C22⋊Dic5C2×Dic311yescharacteristic
337C22⋊Dic5C2×Dic311yescharacteristic
338C22⋊Dic5C2×Dic311yescharacteristic
339#685C2×Dic311yescharacteristic
340#685C2×Dic311yescharacteristic
341C4⋊Dic5C2×Dic311yescharacteristic
342C4⋊Dic5C2×Dic311yescharacteristic
343#683C2×Dic311yescharacteristic
344#683C2×Dic311yescharacteristic
345#683C2×Dic311yescharacteristic
346#683C2×Dic311yescharacteristic
347C4×Dic5C22×D311yescharacteristic
348C4×Dic5C22×D311yescharacteristic
349C2×#131—151no—
350C22×M16—151no—
351#525—51no—
352#436—151no—
353#436—151no—
354#435—151no—
355#435—151no—
356#435—151no—
357#435—151no—
358C8×D4—151no—
359C8×D4—151no—
360#424—151no—
361#408—151no—
362C2×C22⋊C8—151no—
363#405—151no—
364C22×C3×C5—21no—
365C22×C3×C5—21no—
366C22×C3×C5—21no—
367C22×C3×C5—21no—
368C22×C3×C5—21no—
369C22×C3×C5—21no—
370C22×C3×C5—21no—
371C22×C3×C5—21no—
372C22×C3×C5—21no—
373C22×C3×C5—21no—
374C22×C3×C5—44no—
375C22×C3×C5C4×D412yes—
376C22×C3×C5#13112yescomplemented
377C22×C3×C5C23×C411yescharacteristic
378C2×C3×D5—21no—
379C2×C3×D5—21no—
380C2×C3×D5—21no—
381C3×C4×C5—21no—
382C3×C4×C5—21no—
383C3×C4×C5—21no—
384C3×Dic5—21no—
385C3×Dic5—21no—
386C3×Dic5—21no—
387C3×Dic5—21no—
388C3×Dic5—21no—
389C3×Dic5C4×D412yes—
390C3×Dic5C22×D411yescharacteristic
391C3×Dic5C2×#4111yescharacteristic
392C24×C3C2×AGL(1,𝔽5)11yescharacteristic
393C3×#41—102no—
394C3×#41—102no—
395C2×C3×Q8—51no—
396C2×C3×D4—51no—
397C2×C3×D4—51no—
398C2×C3×D4—51no—
399C2×C3×D4—51no—
400C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
401C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
402C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
403C22×C3×C4—51no—
404C22×C3×C4—51no—
405C22×C3×C4—51no—
406C22×C3×C4—51no—
407C22×C3×C4—51no—
408C22×C3×C4—51no—
409C22×C3×C4—51no—
410C22×C3×C4—51no—
411C22×C3×C4—102no—
412C22×C3×C4—102no—
413C3×C4⋊C4—51no—
414C3×C4⋊C4—51no—
415C3×C4⋊C4—51no—
416C3×C4⋊C4—51no—
417C3×C4⋊C4—51no—
418C3×C4⋊C4—51no—
419C3×C22⋊C4—51no—
420C3×C22⋊C4—51no—
421C3×C22⋊C4—51no—
422C3×C22⋊C4—51no—
423C3×C22⋊C4—51no—
424C3×C22⋊C4—51no—
425C3×C22⋊C4—51no—
426C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
427C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
428C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
429C3×C42—51no—
430C3×C42—51no—
431#208—54no—
432#208—102no—
433#208—102no—
434#208—102no—
435#208—102no—
436#208—102no—
437C2×C3⋊C8—51no—
438C2×C3⋊C8—51no—
439C2×C3⋊C8—51no—
440C2×C3⋊C8—51no—
441C2×C3⋊C8—51no—
442C2×C3⋊C8—51no—
443C2×C3⋊C8—51no—
444C2×C3⋊C8—51no—
445C2×C3⋊C8—102no—
446C2×C3⋊C8—102no—
447C2×C3⋊C8—102no—
448C2×C3⋊C8—102no—
449C2×C3⋊C8—102no—
450C2×C3⋊C8—102no—
451C23×C5—22no—
452C23×C5—22no—
453C23×C5—41no—
454C23×C5C22×Dic311yescharacteristic
455C23×C5C22×Dic311yescharacteristic
456C23×C5C22×Dic311yescharacteristic
457C23×C5C22×Dic311yescharacteristic
458C22×D5C22×Dic311yescharacteristic
459C5×D4—22no—
460C5×D4—22no—
461C5×D4—41no—
462C2×C4×C5C22×Dic311yescharacteristic
463C2×C4×C5C22×Dic311yescharacteristic
464C2×C4×C5C22×Dic311yescharacteristic
465C22⋊D5—22no—
466C22⋊D5—22no—
467C22⋊D5—22no—
468C22⋊D5—41no—
469C2×Dic5—22no—
470C2×Dic5—22no—
471C2×Dic5—22no—
472C2×Dic5—21no—
473C2×Dic5—21no—
474C2×Dic5—21no—
475C2×Dic5—21no—
476C2×Dic5—21no—
477C2×Dic5—21no—
478C2×Dic5D3×D412yes—
479C2×Dic5#23712yes—
480C2×Dic5C22×Dic311yescharacteristic
481C2×Dic5C22×Dic311yescharacteristic
482C2×Dic5C22×Dic311yescharacteristic
483C2×Dic5C22×Dic311yescharacteristic
484C2×Dic5C22×Dic311yescharacteristic
485C2×Dic5C22×Dic311yescharacteristic
486C2×Dic5C23×D311yescharacteristic
487C4×D5—21no—
488C4×D5—21no—
489Dic10—22no—
490#170—32no—
491#170—32no—
492#170—61no—
493#170—61no—
494#170—61no—
495#170—61no—
496#170—61no—
497#170—61no—
498C2×#41—51no—
499C23×C4—51no—
500#131—304no—
501C2×M16—151no—
502C2×M16—151no—
503C2×M16—151no—
504C2×M16—151no—
505C2×M16—151no—
506C2×M16—151no—
507C2×M16—304no—
508C22×C8—151no—
509C22×C8—151no—
510C22×C8—151no—
511C22×C8—151no—
512C22×C8—151no—
513C22×C8—151no—
514#123—51no—
515#123—51no—
516C22⋊Q8—51no—
517C22⋊Q8—51no—
518#121—51no—
519#121—51no—
520#120—51no—
521#120ΓL(1,𝔽16)11yescharacteristic
522C4×D4—51no—
523C4×D4—51no—
524C4×D4—51no—
525C4×D4—51no—
526#117—51no—
527C4⋊C8—151no—
528C4⋊C8—151no—
529C4⋊C8—151no—
530C4⋊C8—151no—
531C22⋊C8—151no—
532C22⋊C8—151no—
533C22⋊C8—151no—
534C22⋊C8—151no—
535C22⋊C8—151no—
536C22⋊C8—151no—
537C22⋊C8—151no—
538C22⋊C8—151no—
539#97—151no—
540#97—151no—
541C4×C8—151no—
542C4×C8—151no—
543C2×C3×C5—22no—
544C2×C3×C5—22no—
545C2×C3×C5—41no—
546C2×C3×C5—41no—
547C2×C3×C5C2×C4×D411yescharacteristic
548C2×C3×C5C2×#13111yescharacteristic
549C2×C3×C5#56811yescharacteristic
550C3×D5—41no—
551C23×C3—22no—
552C23×C3—22no—
553C23×C3—41no—
554C23×C3—51no—
555C23×C3C22×AGL(1,𝔽5)11yescharacteristic
556C23×C3C22×AGL(1,𝔽5)11yescharacteristic
557C23×C3C22×AGL(1,𝔽5)11yescharacteristic
558C23×C3C22×AGL(1,𝔽5)11yescharacteristic
559C3×Q8—102no—
560C3×D4—22no—
561C3×D4—22no—
562C3×D4—41no—
563C3×D4—102no—
564C3×D4—102no—
565C3×D4—102no—
566C3×D4—201no—
567C2×C3×C4—52no—
568C2×C3×C4—52no—
569C2×C3×C4—51no—
570C2×C3×C4—51no—
571C2×C3×C4—51no—
572C2×C3×C4—51no—
573C2×C3×C4—51no—
574C2×C3×C4—51no—
575C2×C3×C4—51no—
576C2×C3×C4—101no—
577C2×C3×C4—101no—
578C2×C3×C4—101no—
579C2×C3×C4—101no—
580C2×C3×C4—101no—
581C2×C3×C4—102no—
582C2×C3×C4—102no—
583C2×C3×C4—101no—
584C2×C3×C4—101no—
585C2×C3×C4—101no—
586C2×C3×C4—102no—
587C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
588C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
589C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
590C3⋊C8—52no—
591C3⋊C8—52no—
592C3⋊C8—101no—
593C3⋊C8—101no—
594C3⋊C8—101no—
595C3⋊C8—101no—
596C3⋊C8—101no—
597C3⋊C8—101no—
598C22×C5—21no—
599C22×C5—21no—
600C22×C5—21no—
601C22×C5—21no—
602C22×C5—21no—
603C22×C5—21no—
604C22×C5—21no—
605C22×C5—21no—
606C22×C5—21no—
607C22×C5—21no—
608C22×C5—44no—
609C22×C5D4×Dic312yes—
610C22×C5#94812yescomplemented
611C22×C5C23×Dic311yescharacteristic
612C2×D5—21no—
613C2×D5—21no—
614C2×D5—21no—
615C4×C5—21no—
616C4×C5—21no—
617C4×C5—21no—
618Dic5—21no—
619Dic5—21no—
620Dic5—21no—
621Dic5—21no—
622Dic5—21no—
623Dic5D4×Dic312yes—
624Dic5C2×D3×D411yescharacteristic
625Dic5C2×#23711yescharacteristic
626C24C2×ΓL(1,𝔽16)11yescharacteristic
627#41—102no—
628#41—102no—
629C2×Q8—51no—
630C2×D4—51no—
631C2×D4—51no—
632C2×D4—51no—
633C2×D4—51no—
634C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
635C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
636C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
637C22×C4—51no—
638C22×C4—51no—
639C22×C4—51no—
640C22×C4—51no—
641C22×C4—51no—
642C22×C4—51no—
643C22×C4—51no—
644C22×C4—51no—
645C22×C4—102no—
646C22×C4—102no—
647M16—154no—
648M16—302no—
649M16—302no—
650M16—302no—
651M16—302no—
652M16—302no—
653C2×C8—151no—
654C2×C8—151no—
655C2×C8—151no—
656C2×C8—151no—
657C2×C8—151no—
658C2×C8—151no—
659C2×C8—151no—
660C2×C8—151no—
661C2×C8—302no—
662C2×C8—302no—
663C2×C8—302no—
664C2×C8—302no—
665C2×C8—302no—
666C2×C8—302no—
667C4⋊C4—51no—
668C4⋊C4—51no—
669C4⋊C4—51no—
670C4⋊C4—51no—
671C4⋊C4—51no—
672C4⋊C4—51no—
673C22⋊C4—51no—
674C22⋊C4—51no—
675C22⋊C4—51no—
676C22⋊C4—51no—
677C22⋊C4—51no—
678C22⋊C4—51no—
679C22⋊C4—51no—
680C22⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
681C22⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
682C22⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
683C42—51no—
684C42—51no—
685C3×C5#293311yescharacteristic, complemented, Hall
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—44no—
697C22×C3—101no—
698C22×C3—101no—
699C22×C3—101no—
700C22×C3#413112yescomplemented
701C22×C3D4×AGL(1,𝔽5)12yes—
702C22×C3C23×AGL(1,𝔽5)11yescharacteristic
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—52no—
707C3×C4—51no—
708C3×C4—51no—
709C3×C4—101no—
710C3×C4—101no—
711C3×C4—101no—
712C3×C4—101no—
713C3×C4—101no—
714C2×C5—22no—
715C2×C5—22no—
716C2×C5—41no—
717C2×C5—41no—
718C2×C5C2×D4×Dic311yescharacteristic
719C2×C5C2×#94811yescharacteristic
720C2×C5#581911yescharacteristic
721D5—41no—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—51no—
726C23C22×ΓL(1,𝔽16)11yescharacteristic
727C23C22×ΓL(1,𝔽16)11yescharacteristic
728C23C22×ΓL(1,𝔽16)11yescharacteristic
729C23C22×ΓL(1,𝔽16)11yescharacteristic
730Q8—102no—
731D4—22no—
732D4—22no—
733D4—41no—
734D4—102no—
735D4—102no—
736D4—102no—
737D4—201no—
738C2×C4—52no—
739C2×C4—52no—
740C2×C4—51no—
741C2×C4—51no—
742C2×C4—51no—
743C2×C4—51no—
744C2×C4—51no—
745C2×C4—51no—
746C2×C4—51no—
747C2×C4—101no—
748C2×C4—101no—
749C2×C4—101no—
750C2×C4—101no—
751C2×C4—101no—
752C2×C4—101no—
753C2×C4—101no—
754C2×C4—102no—
755C2×C4—102no—
756C2×C4—101no—
757C2×C4—102no—
758C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
759C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
760C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
761C8—152no—
762C8—152no—
763C8—301no—
764C8—301no—
765C8—301no—
766C8—301no—
767C8—301no—
768C8—301no—
769C2×C3—22no—
770C2×C3—22no—
771C2×C3—41no—
772C2×C3—41no—
773C2×C3—201no—
774C2×C3C2×#413111yescharacteristic
775C2×C3#6625611yescharacteristic
776C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
777C5#8291811yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—44no—
789C22—101no—
790C22—101no—
791C22—101no—
792C22#9199012yescomplemented
793C22D4×ΓL(1,𝔽16)12yes—
794C22C23×ΓL(1,𝔽16)11yescharacteristic
795C4—21no—
796C4—21no—
797C4—21no—
798C4—51no—
799C4—51no—
800C4—52no—
801C4—101no—
802C4—101no—
803C4—101no—
804C4—101no—
805C4—101no—
806C3#1061721711yescharacteristic, complemented, Sylow
807C2—22no—
808C2—22no—
809C2—41no—
810C2—41no—
811C2—201no—
812C2C2×#9199011yescharacteristic
813C2#1175698511yescharacteristic
814C2C2×D4×ΓL(1,𝔽16)11yescharacteristic
subgroupG/H
center, FrattiniC22C23×ΓL(1,𝔽16)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×#120C4
prime radicalC3×#65920C2
cosocleC2×C3×Dic5C24
hypercenter#120ΓL(1,𝔽16)
hypocenterC3×C5#2933
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C22×#6762C2semidirect
2. C2×#91990C2semidirect
4. C2×#91241C2semidirect
5. #11752434C2semidirect
6. #11752433C2semidirect
7. #11752432C2semidirect
8. #11752432C2semidirect
9. D4×C3⋊#170C2semidirect
10. #11752355C2semidirect
11. #11752354C2semidirect
12. #11752353C2semidirect
13. #11752352C2semidirect
14. #11752351C2semidirect
15. #11752350C2semidirect
24. C2×#6762C22semidirect
29. C22×C3⋊#170C22semidirect
31. C2×#6758C22semidirect
32. C2×D5⋊(C3⋊C8)C22semidirect
50. #91241C22semidirect
51. #91241C22semidirect
52. #91233C22semidirect
53. #91233C22semidirect
54. #91232C22semidirect
55. #91232C22semidirect
56. #91231C22semidirect
57. #91231C22semidirect
58. C4⋊(C3⋊#170)C22semidirect
59. C4⋊(C3⋊#170)C22semidirect
60. C4×C3⋊#170C22semidirect
61. C4×C3⋊#170C22semidirect
103. #6762D4semidirect
376. C22×C3×C5#131semidirect
610. C22×C5#948semidirect
685. C3×C5#2933semidirect
700. C22×C3#4131semidirect
777. C5#82918semidirect
792. C22#91990semidirect
806. C3#10617217semidirect

Maximal subgroups

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

subgroupindex
C22×#67622
C2×#919902
C3×#659202
C2×#912412
#117524342
#117524332
#117524322
D4×C3⋊#1702
#117523552
#117523542
#117523532
#117523522
#117523512
#117523502
#106172173
#829185