Finite Group Databasebeta

← #14415691

Subgroups — #14415691

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6762C211yesmaximal, characteristic, complemented
2C2×D5⋊#208C211yesmaximal, characteristic, complemented
3C2×C3×#4027C211yesmaximal, characteristic
4#11752457C211yesmaximal, characteristic, complemented
5#11752417C211yesmaximal, characteristic, complemented
6#11752414C211yesmaximal, characteristic, complemented
7C4×#6762C211yesmaximal, characteristic, complemented
8#11752354C212yesmaximal, complemented
9#11752353C212yesmaximal, complemented
10#11752352C212yesmaximal, complemented
11#11752351C212yesmaximal, complemented
12#10617060—31nomaximal, Hall
13C22×C3×C22⋊D5C411yescharacteristic
14C23×C3×Dic5C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C2×#6762—24no—
17C2×#6762C2211yescharacteristic
18C2×#6762C2211yescharacteristic
19C2×#6762C2211yescharacteristic
20C2×#6762C2211yescharacteristic
21C2×#6762C2212yescomplemented
22C22×C3⋊#170C2212yescomplemented
23D5⋊#208—24no—
24C2×#6758C2212yescomplemented
25C2×D5⋊(C3⋊C8)C2212yescomplemented
26C2×C3×C5×C22⋊C4C411yescharacteristic
27C2×C3×#685C411yescharacteristic
28C2×C3×#683C411yescharacteristic
29C2×C3×C4×Dic5C2211yescharacteristic
30C3×#4027C411yescharacteristic
31C3×#4027C411yescharacteristic
32C3×#4027C411yescharacteristic
33C3×#4027C411yescharacteristic
34C3×#4027C2211yescharacteristic
35C3×#4027C2211yescharacteristic
36C3×#4027C2211yescharacteristic
37C3×#4027C2211yescharacteristic
38#91241C2212yescomplemented
39#91241C2212yescomplemented
40#91233C2212yescomplemented
41#91232C2212yescomplemented
42#91232C2212yescomplemented
43#91231C2212yescomplemented
44C4⋊(C3⋊#170)C2212yescomplemented
45C4×C3⋊#170C2212yescomplemented
46D4×#208—51nomaximal, Hall
47C22×#704—31no—
48C2×D5⋊M16—31no—
49C2×#4027D311yescharacteristic
50#65798—31no—
51#65758—31no—
52#65755—31no—
53C4×#704—31no—
54#65695—32no—
55#65694—32no—
56#65693—32no—
57#65692—32no—
58C24×C3×C5C2×C411yescharacteristic
59C23×C3×D5C2×C411yescharacteristic
60C22×C3×C4×C5C2×C411yescharacteristic
61C22×C3×C4×C5C2×C411yescharacteristic
62C2×C3×C22⋊D5—24no—
63C2×C3×C22⋊D5C2×C411yescharacteristic
64C2×C3×C22⋊D5C2×C411yescharacteristic
65C2×C3×C22⋊D5C2×C411yescharacteristic
66C2×C3×C22⋊D5C2×C411yescharacteristic
67C22×C3×Dic5—22no—
68C22×C3×Dic5—22no—
69C22×C3×Dic5C2×C411yescharacteristic
70C22×C3×Dic5C2×C411yescharacteristic
71C22×C3×Dic5C2×C411yescharacteristic
72C22×C3×Dic5C2×C411yescharacteristic
73C22×C3×Dic5C2311yescharacteristic
74C22×C3×Dic5C2311yescharacteristic
75C22×C3×Dic5C2311yescharacteristic
76C2×C3×C4×D5—22no—
77C2×C3×C4×D5—22no—
78C2×C3×C4×D5C2×C411yescharacteristic
79C2×C3×C4×D5C2×C411yescharacteristic
80C2×C3×C4×D5C2311yescharacteristic
81C2×C3×C4×D5C2311yescharacteristic
82#6762—22no—
83#6762—22no—
84#6762—22no—
85#6762—24no—
86#6762D414yescomplemented
87C2×C3⋊#170—24no—
88C2×C3⋊#170C2312yes—
89C2×C3⋊#170C2312yes—
90C2×C3⋊#170C2312yes—
91C2×C3⋊#170C2312yes—
92#6758—24no—
93D5⋊(C3⋊C8)—24no—
94C3×C5×C22⋊C4C2×C411yescharacteristic
95C3×C5×C22⋊C4C2×C411yescharacteristic
96C3×C5×C22⋊C4C2×C411yescharacteristic
97C3×C5×C22⋊C4C2×C411yescharacteristic
98C3×#685C2×C411yescharacteristic
99C3×#685C2×C411yescharacteristic
100C3×#685C2×C411yescharacteristic
101C3×#685C2×C411yescharacteristic
102C3×#683C2×C411yescharacteristic
103C3×#683C2×C411yescharacteristic
104C3×#683C2×C411yescharacteristic
105C3×#683C2×C411yescharacteristic
106C3×C4×Dic5C2×C411yescharacteristic
107C3×C4×Dic5C2×C411yescharacteristic
108C3×C4×Dic5C2311yescharacteristic
109C3×C4×Dic5C2311yescharacteristic
110C2×C3×C4×D4—51no—
111C22×#208—51no—
112C22×#208—51no—
113#5207—51no—
114#5207—51no—
115#5012—52no—
116#5011—52no—
117#5011—52no—
118D4×C3⋊C8—52no—
119#4924—51no—
120C4×#208—51no—
121C22×C22⋊D5Dic311yescharacteristic
122C23×Dic5C2×D311yescharacteristic
123C22×C4×D5C2×D311yescharacteristic
124C2×#704—31no—
125C2×#704—31no—
126C2×#704—31no—
127C2×#704—31no—
128C2×#704—32no—
129C2×#704—64no—
130C22×#170—32no—
131D5⋊M16—64no—
132C2×#700—32no—
133C2×D5⋊C8—32no—
134C2×C5×C22⋊C4Dic311yescharacteristic
135C2×#685Dic311yescharacteristic
136C2×#683Dic311yescharacteristic
137C2×C4×Dic5C2×D311yescharacteristic
138#4027Dic311yescharacteristic
139#4027Dic311yescharacteristic
140#4027Dic311yescharacteristic
141#4027Dic311yescharacteristic
142#4027C2×D311yescharacteristic
143#4027C2×D311yescharacteristic
144#4027C2×D311yescharacteristic
145#4027C2×D311yescharacteristic
146C22⋊#170—32no—
147C22⋊#170—32no—
148#4004—32no—
149#4003—32no—
150#4003—32no—
151#4002—32no—
152C4⋊#170—32no—
153C4×#170—32no—
154D4×M16—151noSylow
155C23×C3×C5—22no—
156C23×C3×C5—22no—
157C23×C3×C5—41no—
158C23×C3×C5C22×C411yescharacteristic
159C23×C3×C5C22×C411yescharacteristic
160C23×C3×C5C22×C411yescharacteristic
161C22×C3×D5—22no—
162C22×C3×D5—22no—
163C22×C3×D5—41no—
164C22×C3×D5C22×C411yescharacteristic
165C22×C3×D5C22×C411yescharacteristic
166C2×C3×C4×C5—22no—
167C2×C3×C4×C5—41no—
168C2×C3×C4×C5C22×C411yescharacteristic
169C2×C3×C4×C5C22×C411yescharacteristic
170C2×C3×C4×C5C22×C411yescharacteristic
171C2×C3×C4×C5C22×C411yescharacteristic
172C3×C22⋊D5—22no—
173C3×C22⋊D5—22no—
174C3×C22⋊D5—22no—
175C3×C22⋊D5M1614yescomplemented
176C2×C3×Dic5—22no—
177C2×C3×Dic5—22no—
178C2×C3×Dic5—22no—
179C2×C3×Dic5—22no—
180C2×C3×Dic5—21no—
181C2×C3×Dic5—21no—
182C2×C3×Dic5—21no—
183C2×C3×Dic5—21no—
184C2×C3×Dic5C22×C411yescharacteristic
185C2×C3×Dic5C22×C411yescharacteristic
186C2×C3×Dic5C22×C411yescharacteristic
187C2×C3×Dic5C22×C411yescharacteristic
188C2×C3×Dic5C22×C411yescharacteristic
189C2×C3×Dic5C2×D412yes—
190C2×C3×Dic5#4112yes—
191C2×C3×Dic5C2411yescharacteristic
192C3×C4×D5—22no—
193C3×C4×D5—22no—
194C3×C4×D5—21no—
195C3×C4×D5—21no—
196C3×C4×D5—21no—
197C3×C4×D5—21no—
198C3⋊#170—22no—
199C3⋊#170—22no—
200C3⋊#170—22no—
201C3⋊#170C2×D414yescomplemented
202C22×C3×D4—51no—
203C23×C3×C4—51no—
204C23×C3×C4—51no—
205C3×C4×D4—51no—
206C3×C4×D4—51no—
207C3×C4×D4—51no—
208C3×C4×D4—51no—
209C3×C4×D4—51no—
210C3×C4×D4—51no—
211C3×C4×D4—51no—
212C3×C4×D4—51no—
213C2×C3×C4⋊C4—51no—
214C2×C3×C22⋊C4—51no—
215C2×C3×C22⋊C4AGL(1,𝔽5)11yescharacteristic
216C2×C3×C42—51no—
217C2×#208—51no—
218C2×#208—51no—
219C2×#208—51no—
220C2×#208—51no—
221C2×#208—52no—
222C2×#208—52no—
223C2×#208—104no—
224C2×#208—104no—
225C22×C3⋊C8—52no—
226C22×C3⋊C8—52no—
227#830—52no—
228#830—52no—
229#830—52no—
230#830—52no—
231C4⋊(C3⋊C8)—52no—
232C4⋊(C3⋊C8)—52no—
233#803—52no—
234C4×C3⋊C8—52no—
235C24×C5C2×Dic311yescharacteristic
236C23×D5C2×Dic311yescharacteristic
237C22×C4×C5C2×Dic311yescharacteristic
238C22×C4×C5C2×Dic311yescharacteristic
239C2×C22⋊D5—24no—
240C2×C22⋊D5C2×Dic311yescharacteristic
241C2×C22⋊D5C2×Dic311yescharacteristic
242C2×C22⋊D5C2×Dic311yescharacteristic
243C2×C22⋊D5C2×Dic311yescharacteristic
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5C2×Dic311yescharacteristic
247C22×Dic5C2×Dic311yescharacteristic
248C22×Dic5C2×Dic311yescharacteristic
249C22×Dic5C2×Dic311yescharacteristic
250C22×Dic5C22×D311yescharacteristic
251C22×Dic5C22×D311yescharacteristic
252C22×Dic5C22×D311yescharacteristic
253C2×C4×D5—22no—
254C2×C4×D5—22no—
255C2×C4×D5C2×Dic311yescharacteristic
256C2×C4×D5C2×Dic311yescharacteristic
257C2×C4×D5C22×D311yescharacteristic
258C2×C4×D5C22×D311yescharacteristic
259#704—34no—
260#704—64no—
261#704—62no—
262#704—62no—
263#704—62no—
264C2×#170—32no—
265C2×#170—32no—
266C2×#170—32no—
267C2×#170—32no—
268C2×#170—64no—
269#700—64no—
270D5⋊C8—64no—
271C5×C22⋊C4C2×Dic311yescharacteristic
272C5×C22⋊C4C2×Dic311yescharacteristic
273C5×C22⋊C4C2×Dic311yescharacteristic
274C5×C22⋊C4C2×Dic311yescharacteristic
275#685C2×Dic311yescharacteristic
276#685C2×Dic311yescharacteristic
277#685C2×Dic311yescharacteristic
278#685C2×Dic311yescharacteristic
279#683C2×Dic311yescharacteristic
280#683C2×Dic311yescharacteristic
281#683C2×Dic311yescharacteristic
282#683C2×Dic311yescharacteristic
283C4×Dic5C2×Dic311yescharacteristic
284C4×Dic5C2×Dic311yescharacteristic
285C4×Dic5C22×D311yescharacteristic
286C4×Dic5C22×D311yescharacteristic
287C22×M16—151no—
288C22×M16—151no—
289C2×C4×D4—51no—
290#436—152no—
291#435—152no—
292#435—152no—
293C8×D4—152no—
294#423—151no—
295#407—151no—
296#407—151no—
297C4×M16—151no—
298C22×C3×C5—21no—
299C22×C3×C5—21no—
300C22×C3×C5—21no—
301C22×C3×C5—21no—
302C22×C3×C5—21no—
303C22×C3×C5—21no—
304C22×C3×C5—21no—
305C22×C3×C5—44no—
306C22×C3×C5C4×D412yes—
307C22×C3×C5C2×M1612yescomplemented
308C22×C3×C5C23×C411yescharacteristic
309C2×C3×D5—21no—
310C2×C3×D5—21no—
311C2×C3×D5—21no—
312C2×C3×D5—21no—
313C2×C3×D5—21no—
314C2×C3×D5—44no—
315C2×C3×D5C2×M1612yescomplemented
316C3×C4×C5—21no—
317C3×C4×C5—21no—
318C3×C4×C5—21no—
319C3×C4×C5—21no—
320C3×Dic5—21no—
321C3×Dic5—21no—
322C3×Dic5—21no—
323C3×Dic5C4×D412yes—
324C3×Dic5C2×M1612yescomplemented
325C3×Dic5C22×D411yescharacteristic
326C3×Dic5C2×#4111yescharacteristic
327C24×C3—51no—
328C24×C3C2×AGL(1,𝔽5)11yescharacteristic
329C2×C3×D4—51no—
330C2×C3×D4—51no—
331C2×C3×D4—51no—
332C2×C3×D4—51no—
333C2×C3×D4—104no—
334C22×C3×C4—51no—
335C22×C3×C4—51no—
336C22×C3×C4—51no—
337C22×C3×C4—51no—
338C22×C3×C4—51no—
339C22×C3×C4—51no—
340C22×C3×C4—51no—
341C22×C3×C4—51no—
342C22×C3×C4—51no—
343C22×C3×C4—51no—
344C22×C3×C4—51no—
345C22×C3×C4—102no—
346C22×C3×C4—102no—
347C22×C3×C4—102no—
348C22×C3×C4—102no—
349C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
350C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
351C3×C4⋊C4—51no—
352C3×C4⋊C4—51no—
353C3×C4⋊C4—51no—
354C3×C4⋊C4—51no—
355C3×C22⋊C4—51no—
356C3×C22⋊C4—51no—
357C3×C22⋊C4—51no—
358C3×C22⋊C4—51no—
359C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
360C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
361C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
362C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
363C3×C42—51no—
364C3×C42—51no—
365C3×C42—51no—
366C3×C42—51no—
367#208—54no—
368#208—104no—
369#208—104no—
370#208—102no—
371#208—102no—
372#208—102no—
373C2×C3⋊C8—52no—
374C2×C3⋊C8—52no—
375C2×C3⋊C8—52no—
376C2×C3⋊C8—52no—
377C2×C3⋊C8—104no—
378C2×C3⋊C8—104no—
379C23×C5—22no—
380C23×C5—22no—
381C23×C5—41no—
382C23×C5C22×Dic311yescharacteristic
383C23×C5C22×Dic311yescharacteristic
384C23×C5C22×Dic311yescharacteristic
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—41no—
388C22×D5C22×Dic311yescharacteristic
389C22×D5C22×Dic311yescharacteristic
390C2×C4×C5—22no—
391C2×C4×C5—41no—
392C2×C4×C5C22×Dic311yescharacteristic
393C2×C4×C5C22×Dic311yescharacteristic
394C2×C4×C5C22×Dic311yescharacteristic
395C2×C4×C5C22×Dic311yescharacteristic
396C22⋊D5—22no—
397C22⋊D5—22no—
398C22⋊D5—22no—
399C22⋊D5#20814yescomplemented
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—21no—
405C2×Dic5—21no—
406C2×Dic5—21no—
407C2×Dic5—21no—
408C2×Dic5D3×D412yes—
409C2×Dic5#23712yes—
410C2×Dic5C22×Dic311yescharacteristic
411C2×Dic5C22×Dic311yescharacteristic
412C2×Dic5C22×Dic311yescharacteristic
413C2×Dic5C22×Dic311yescharacteristic
414C2×Dic5C22×Dic311yescharacteristic
415C2×Dic5C23×D311yescharacteristic
416C4×D5—22no—
417C4×D5—22no—
418C4×D5—21no—
419C4×D5—21no—
420C4×D5—21no—
421C4×D5—21no—
422#170—34no—
423#170—62no—
424#170—62no—
425#170—62no—
426C22×D4—51no—
427C23×C4—51no—
428C23×C4—51no—
429C2×M16—151no—
430C2×M16—152no—
431C2×M16—151no—
432C2×M16—151no—
433C2×M16—152no—
434C2×M16—151no—
435C2×M16—304no—
436C2×M16—304no—
437C22×C8—152no—
438C22×C8—152no—
439C4×D4—51no—
440C4×D4—51no—
441C4×D4—51no—
442C4×D4—51no—
443C4×D4—51no—
444C4×D4—51no—
445C4×D4—51no—
446C4×D4—51no—
447C2×C4⋊C4—51no—
448C2×C22⋊C4—51no—
449C2×C22⋊C4ΓL(1,𝔽16)11yescharacteristic
450C2×C42—51no—
451C4⋊C8—152no—
452C4⋊C8—152no—
453C22⋊C8—152no—
454C22⋊C8—152no—
455C22⋊C8—152no—
456C22⋊C8—152no—
457#97—152no—
458C4×C8—152no—
459C2×C3×C5—22no—
460C2×C3×C5—22no—
461C2×C3×C5—41no—
462C2×C3×C5C2×C4×D411yescharacteristic
463C2×C3×C5C22×M1611yescharacteristic
464C2×C3×C5#56811yescharacteristic
465C3×D5—22no—
466C3×D5—41no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—41no—
470C23×C3—51no—
471C23×C3—51no—
472C23×C3—102no—
473C23×C3—102no—
474C23×C3—201no—
475C23×C3C22×AGL(1,𝔽5)11yescharacteristic
476C23×C3C22×AGL(1,𝔽5)11yescharacteristic
477C23×C3C22×AGL(1,𝔽5)11yescharacteristic
478C3×D4—54no—
479C3×D4—102no—
480C3×D4—102no—
481C3×D4—102no—
482C2×C3×C4—22no—
483C2×C3×C4—41no—
484C2×C3×C4—52no—
485C2×C3×C4—52no—
486C2×C3×C4—51no—
487C2×C3×C4—51no—
488C2×C3×C4—51no—
489C2×C3×C4—51no—
490C2×C3×C4—51no—
491C2×C3×C4—51no—
492C2×C3×C4—101no—
493C2×C3×C4—101no—
494C2×C3×C4—102no—
495C2×C3×C4—102no—
496C2×C3×C4—101no—
497C2×C3×C4—101no—
498C2×C3×C4—101no—
499C2×C3×C4—101no—
500C2×C3×C4—102no—
501C2×C3×C4—102no—
502C2×C3×C4—101no—
503C2×C3×C4—101no—
504C2×C3×C4—102no—
505C2×C3×C4—102no—
506C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
507C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
508C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
509C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
510C3⋊C8—54no—
511C3⋊C8—102no—
512C3⋊C8—102no—
513C3⋊C8—102no—
514C22×C5—21no—
515C22×C5—21no—
516C22×C5—21no—
517C22×C5—21no—
518C22×C5—21no—
519C22×C5—21no—
520C22×C5—21no—
521C22×C5—44no—
522C22×C5C2×#20812yescomplemented
523C22×C5D4×Dic312yes—
524C22×C5C23×Dic311yescharacteristic
525C2×D5—21no—
526C2×D5—21no—
527C2×D5—21no—
528C2×D5—21no—
529C2×D5—21no—
530C2×D5—44no—
531C2×D5C2×#20812yescomplemented
532C4×C5—21no—
533C4×C5—21no—
534C4×C5—21no—
535C4×C5—21no—
536Dic5—21no—
537Dic5—21no—
538Dic5—21no—
539Dic5C2×#20812yescomplemented
540Dic5D4×Dic312yes—
541Dic5C2×D3×D411yescharacteristic
542Dic5C2×#23711yescharacteristic
543C24—51no—
544C24C2×ΓL(1,𝔽16)11yescharacteristic
545C2×D4—51no—
546C2×D4—51no—
547C2×D4—51no—
548C2×D4—51no—
549C2×D4—104no—
550C22×C4—51no—
551C22×C4—51no—
552C22×C4—51no—
553C22×C4—51no—
554C22×C4—51no—
555C22×C4—51no—
556C22×C4—51no—
557C22×C4—51no—
558C22×C4—51no—
559C22×C4—51no—
560C22×C4—51no—
561C22×C4—102no—
562C22×C4—102no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
566C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
567M16—154no—
568M16—304no—
569M16—304no—
570M16—302no—
571M16—302no—
572M16—302no—
573C2×C8—152no—
574C2×C8—152no—
575C2×C8—152no—
576C2×C8—152no—
577C2×C8—304no—
578C2×C8—304no—
579C4⋊C4—51no—
580C4⋊C4—51no—
581C4⋊C4—51no—
582C4⋊C4—51no—
583C22⋊C4—51no—
584C22⋊C4—51no—
585C22⋊C4—51no—
586C22⋊C4—51no—
587C22⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
588C22⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
589C22⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
590C22⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
591C42—51no—
592C42—51no—
593C42—51no—
594C42—51no—
595C3×C5D4×M1611yescharacteristic, complemented, Hall
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—44no—
604C22×C3—52no—
605C22×C3—101no—
606C22×C3—101no—
607C22×C3—101no—
608C22×C3—101no—
609C22×C3—101no—
610C22×C3—204no—
611C22×C3D5⋊M1612yescomplemented
612C22×C3D4×AGL(1,𝔽5)12yes—
613C22×C3C23×AGL(1,𝔽5)11yescharacteristic
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—52no—
619C3×C4—52no—
620C3×C4—51no—
621C3×C4—51no—
622C3×C4—101no—
623C3×C4—101no—
624C3×C4—101no—
625C2×C5—22no—
626C2×C5—22no—
627C2×C5—41no—
628C2×C5C22×#20811yescharacteristic
629C2×C5C2×D4×Dic311yescharacteristic
630C2×C5#581911yescharacteristic
631D5—22no—
632D5—41no—
633C23—22no—
634C23—22no—
635C23—41no—
636C23—51no—
637C23—51no—
638C23—102no—
639C23—102no—
640C23—201no—
641C23C22×ΓL(1,𝔽16)11yescharacteristic
642C23C22×ΓL(1,𝔽16)11yescharacteristic
643C23C22×ΓL(1,𝔽16)11yescharacteristic
644D4—54no—
645D4—102no—
646D4—102no—
647D4—102no—
648C2×C4—22no—
649C2×C4—41no—
650C2×C4—52no—
651C2×C4—52no—
652C2×C4—51no—
653C2×C4—51no—
654C2×C4—51no—
655C2×C4—51no—
656C2×C4—51no—
657C2×C4—51no—
658C2×C4—101no—
659C2×C4—101no—
660C2×C4—101no—
661C2×C4—101no—
662C2×C4—102no—
663C2×C4—102no—
664C2×C4—101no—
665C2×C4—101no—
666C2×C4—101no—
667C2×C4—101no—
668C2×C4—102no—
669C2×C4—102no—
670C2×C4—102no—
671C2×C4—102no—
672C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
673C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
674C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
675C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
676C8—154no—
677C8—302no—
678C8—302no—
679C8—302no—
680C2×C3—22no—
681C2×C3—22no—
682C2×C3—41no—
683C2×C3—102no—
684C2×C3—201no—
685C2×C3C2×D5⋊M1611yescharacteristic
686C2×C3#6625611yescharacteristic
687C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
688C5D4×#20811yescharacteristic, complemented, Sylow
689C22—21no—
690C22—21no—
691C22—21no—
692C22—21no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—44no—
697C22—52no—
698C22—101no—
699C22—101no—
700C22—101no—
701C22—101no—
702C22—101no—
703C22—204no—
704C22D5⋊#20812yescomplemented
705C22D4×ΓL(1,𝔽16)12yes—
706C22C23×ΓL(1,𝔽16)11yescharacteristic
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—52no—
712C4—51no—
713C4—51no—
714C4—52no—
715C4—101no—
716C4—101no—
717C4—101no—
718C3#1061706011yescharacteristic, complemented, Sylow
719C2—22no—
720C2—22no—
721C2—41no—
722C2—102no—
723C2—201no—
724C2C2×D5⋊#20811yescharacteristic
725C2#1175698511yescharacteristic
726C2C2×D4×ΓL(1,𝔽16)11yescharacteristic
subgroupG/H
center, FrattiniC22C23×ΓL(1,𝔽16)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C4
prime radicalC22×C3×C22⋊D5C4
cosocleC2×C3×Dic5C24
hypercenterC2×C22⋊C4ΓL(1,𝔽16)
hypocenterC3×C5D4×M16
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6762C2semidirect
2. C2×D5⋊#208C2semidirect
4. #11752457C2semidirect
5. #11752417C2semidirect
6. #11752414C2semidirect
7. C4×#6762C2semidirect
8. #11752354C2semidirect
9. #11752353C2semidirect
10. #11752352C2semidirect
11. #11752351C2semidirect
21. C2×#6762C22semidirect
22. C22×C3⋊#170C22semidirect
24. C2×#6758C22semidirect
25. C2×D5⋊(C3⋊C8)C22semidirect
38. #91241C22semidirect
39. #91241C22semidirect
40. #91233C22semidirect
41. #91232C22semidirect
42. #91232C22semidirect
43. #91231C22semidirect
44. C4⋊(C3⋊#170)C22semidirect
45. C4×C3⋊#170C22semidirect
86. #6762D4semidirect
175. C3×C22⋊D5M16semidirect
201. C3⋊#170C2×D4semidirect
307. C22×C3×C5C2×M16semidirect
315. C2×C3×D5C2×M16semidirect
324. C3×Dic5C2×M16semidirect
399. C22⋊D5#208semidirect
522. C22×C5C2×#208semidirect
531. C2×D5C2×#208semidirect
539. Dic5C2×#208semidirect
595. C3×C5D4×M16semidirect
611. C22×C3D5⋊M16semidirect
688. C5D4×#208semidirect
704. C22D5⋊#208semidirect
718. C3#10617060semidirect

Maximal subgroups

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

subgroupindex
C22×#67622
C2×D5⋊#2082
C2×C3×#40272
#117524572
#117524172
#117524142
C4×#67622
#117523542
#117523532
#117523522
#117523512
#106170603
D4×#2085