Finite Group Databasebeta

← #14417150

Subgroups — #14417150

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756995C211yesmaximal, characteristic, complemented
2#11756837C211yesmaximal, characteristic, complemented
3D5×#949C211yesmaximal, characteristic
4C3×#65794C211yesmaximal, characteristic, complemented
5#11751966C212yesmaximal, complemented
6#11751965C212yesmaximal, complemented
7#11751942C212yesmaximal, complemented
8#11751941C212yesmaximal, complemented
9#11751728C211yesmaximal, characteristic, complemented
10C2×#91152C211yesmaximal, characteristic, complemented
11#11751694C211yesmaximal, characteristic, complemented
12#10617447—31nomaximal, Hall
13C3×D5×#41C2211yescharacteristic
14C2×D5×D12C2211yescharacteristic
15Q8×ΓL(1,𝔽16)C2212yescomplemented
16D4×ΓL(1,𝔽16)—22no—
17D4×ΓL(1,𝔽16)C2212yescomplemented
18#91989—21no—
19#91989C2211yescharacteristic
20C2×C4⋊ΓL(1,𝔽16)—21no—
21C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
22C3×#4130C2211yescharacteristic
23C2×C3×D5⋊C8C2211yescharacteristic
24D3×C22⋊AGL(1,𝔽5)—22no—
25#91921C2212yes—
26#91921C2212yes—
27AGL(1,𝔽5)×D12—21no—
28AGL(1,𝔽5)×D12—21no—
29#91838C411yescharacteristic, complemented
30C5×#949C411yescharacteristic, complemented
31#91502C412yescomplemented
32D5×#215C2212yes—
33#91478C412yescomplemented
34D5×#213C2212yes—
35#91301C411yescharacteristic, complemented
36#91299C411yescharacteristic, complemented
37D5×#208C2211yescharacteristic
38C3×#4009C2211yescharacteristic, complemented
39C3×#4009C2211yescharacteristic, complemented
40C3×#4007C2211yescharacteristic, complemented
41C3×#4007C2211yescharacteristic, complemented
42#91160C2212yescomplemented
43#91159C2212yescomplemented
44#91152C2212yes—
45#91152C2212yes—
46#91150C2212yescomplemented
47ΓL(1,𝔽16)⋊C8C2212yescomplemented
48#78820—51nomaximal, Hall
49#66266—31no—
50#66258—31no—
51D5×AGL(1,ℤ/8)—31no—
52#65794D311yescharacteristic, complemented
53C2×#4007—31no—
54#65735—32no—
55SD16×AGL(1,𝔽5)—32no—
56#65731—32no—
57D8×AGL(1,𝔽5)—32no—
58#65728—31no—
59#65727—31no—
60C22×D3×D5—21no—
61C22×ΓL(1,𝔽16)—21no—
62C22×ΓL(1,𝔽16)—22no—
63C2×D3×AGL(1,𝔽5)—22no—
64C2×D3×AGL(1,𝔽5)—22no—
65C3×C5×#41C2×C411yescharacteristic, complemented
66C2×D60C2×C411yescharacteristic, complemented
67C2×C5×D12C2×C411yescharacteristic, complemented
68C3×#713C2×C411yescharacteristic, complemented
69C3×Q8×D5C2311yescharacteristic
70C3×#711—21no—
71C3×#711C2×C411yescharacteristic, complemented
72C3×D4×D5—21no—
73C3×D4×D5C2311yescharacteristic
74C3×#709—21no—
75C3×#709C2×C411yescharacteristic, complemented
76C2×C3×C4×D5—21no—
77C2×C3×C4×D5C2311yescharacteristic
78C2×#1203—21no—
79D5×D12—21no—
80D5×D12—21no—
81D5×D12C2×C412yescomplemented
82D5×D12C2312yes—
83#6763—22no—
84#6763D412yes—
85C4⋊ΓL(1,𝔽16)—22no—
86C4⋊ΓL(1,𝔽16)—21no—
87C4⋊ΓL(1,𝔽16)D411yescharacteristic
88C4⋊ΓL(1,𝔽16)D411yescharacteristic
89C4⋊ΓL(1,𝔽16)C2312yes—
90C4×ΓL(1,𝔽16)—22no—
91C4×ΓL(1,𝔽16)C2312yes—
92C3×C22⋊AGL(1,𝔽5)—21no—
93C2×C3×#170—21no—
94C3×C4⋊AGL(1,𝔽5)C2311yescharacteristic
95C3×C4⋊AGL(1,𝔽5)C2311yescharacteristic
96C3×C4×AGL(1,𝔽5)—21no—
97C3×D5⋊C8—21no—
98C3×D5⋊C8C2311yescharacteristic
99C3×D5⋊C8C2311yescharacteristic
100(C2×D3)⋊AGL(1,𝔽5)—22no—
101(C2×D3)⋊AGL(1,𝔽5)—22no—
102#6717C2×C412yescomplemented
103#6715C2×C412yescomplemented
104#6710C2×C411yescharacteristic, complemented
105C5×#215C2×C412yescomplemented
106C5×#213C2×C412yescomplemented
107C5×#208C2×C411yescharacteristic, complemented
108#6658C2×C412yescomplemented
109#6656C2×C412yescomplemented
110#6653C2×C412yescomplemented
111#6652C2×C412yescomplemented
112#6649C2×C412yescomplemented
113D5×C3⋊C8C2312yes—
114#5827—51no—
115C2×#949—51no—
116#5521—51no—
117C3×#416—51no—
118C2×#821—51no—
119#5101—51no—
120#4995—51no—
121#4817—52no—
122#4788—52no—
123#4785—52no—
124#4756—52no—
125D5×#41C2×D311yescharacteristic
126C2×D4×D5—31no—
127C2×C22⋊AGL(1,𝔽5)—62no—
128Q8×AGL(1,𝔽5)—32no—
129D4×AGL(1,𝔽5)—32no—
130D4×AGL(1,𝔽5)—32no—
131D4×AGL(1,𝔽5)—32no—
132D4×AGL(1,𝔽5)—61no—
133D4×AGL(1,𝔽5)—61no—
134D4×AGL(1,𝔽5)—62no—
135#4130—31no—
136#4130—61no—
137#4130C2×D311yescharacteristic
138C2×C4⋊AGL(1,𝔽5)—31no—
139C2×C4⋊AGL(1,𝔽5)—61no—
140C2×D5⋊C8C2×D311yescharacteristic
141C5×AGL(1,ℤ/8)—31no—
142#4095—31no—
143#4078—31no—
144#4060—32no—
145D5×SD16—32no—
146#4057—32no—
147D5×D8—32no—
148#4054—31no—
149D5×M16—31no—
150#4009C2×D311yescharacteristic, complemented
151#4009C2×D311yescharacteristic, complemented
152#4007—32no—
153#4007—32no—
154#4007C2×D311yescharacteristic, complemented
155#4007C2×D311yescharacteristic, complemented
156#3994—32no—
157#3993—32no—
158#3992—32no—
159C8×AGL(1,𝔽5)—32no—
160#2946—151noSylow
161C22×D15—21no—
162C22×C5×D3—21no—
163C22×C3×D5—21no—
164C22×C3×D5C2×D411yescharacteristic
165C2×D3×D5—22no—
166C2×D3×D5—22no—
167C2×D3×D5—81no—
168C2×D3×D5—81no—
169C2×ΓL(1,𝔽16)—22no—
170C2×ΓL(1,𝔽16)—82no—
171C2×ΓL(1,𝔽16)—81no—
172C2×ΓL(1,𝔽16)C2×D412yes—
173C2×ΓL(1,𝔽16)C2×D412yes—
174C2×C3×AGL(1,𝔽5)—21no—
175C2×C3×AGL(1,𝔽5)—21no—
176D3×AGL(1,𝔽5)—82no—
177D3×AGL(1,𝔽5)—82no—
178C3×C5×Q8C22×C411yescharacteristic
179C3×C5×D4—21no—
180C3×C5×D4C22×C411yescharacteristic
181C2×C3×C4×C5—21no—
182C2×C3×C4×C5C22×C411yescharacteristic
183D60—21no—
184D60C22×C412yes—
185C5×D12—21no—
186C5×D12C22×C412yes—
187C3×C22⋊D5—21no—
188C3×C22⋊D5—21no—
189C3×C22⋊D5—21no—
190C2×C3×Dic5—21no—
191C2×C3×Dic5#4111yescharacteristic
192C3×D20—21no—
193C3×D20C22×C411yescharacteristic
194C3×C4×D5—21no—
195C3×C4×D5—21no—
196C3×C4×D5—21no—
197C3×C4×D5C22×C411yescharacteristic
198C3×C4×D5C2×D411yescharacteristic
199C3×C4×D5#4111yescharacteristic
200C3×C4×D5C2411yescharacteristic
201C3×Dic10—21no—
202C3×Dic10C22×C411yescharacteristic
203#1203—22no—
204#1203—22no—
205C3×#170—21no—
206C3×#170—21no—
207C3⋊#168C22×C412yes—
208C5×C3⋊C8C22×C412yes—
209C2×C3×#41—51no—
210C22×D12—51no—
211C22×C3×C8—51no—
212C3×#117—51no—
213#949—51no—
214#949—51no—
215#949—52no—
216#949—52no—
217#949—51no—
218#949AGL(1,𝔽5)11yescharacteristic, complemented
219Q8×Dic3—52no—
220C2×#215—52no—
221D4×Dic3—52no—
222D4×Dic3—102no—
223C2×#213—52no—
224#926—51no—
225#926—101no—
226C2×C4⋊Dic3—51no—
227C2×C4⋊Dic3—101no—
228C2×#208—51no—
229#893—52no—
230#893—52no—
231D3×C22⋊C4—102no—
232C4×D12—101no—
233C4×D12—101no—
234C3×#103—51no—
235C3×#103—51no—
236C3×#102—51no—
237C3×#102—51no—
238#821—52no—
239#821—52no—
240#815—52no—
241C8×Dic3—52no—
242#808—52no—
243#807—52no—
244C23×D5—61no—
245C22×AGL(1,𝔽5)—62no—
246C22×AGL(1,𝔽5)—62no—
247C22×AGL(1,𝔽5)—62no—
248C22×AGL(1,𝔽5)—61no—
249C5×#41C4×D311yescharacteristic, complemented
250C2×C5×D4—31no—
251C2×C22⋊D5—61no—
252#713C4×D311yescharacteristic, complemented
253Q8×D5C22×D311yescharacteristic
254#711—21no—
255#711C4×D311yescharacteristic, complemented
256D4×D5—21no—
257D4×D5—32no—
258D4×D5—32no—
259D4×D5—61no—
260D4×D5—61no—
261D4×D5C22×D311yescharacteristic
262#709—21no—
263#709C4×D311yescharacteristic, complemented
264C2×D20—31no—
265C2×C4×D5—21no—
266C2×C4×D5C22×D311yescharacteristic
267C22⋊AGL(1,𝔽5)—21no—
268C22⋊AGL(1,𝔽5)—32no—
269C22⋊AGL(1,𝔽5)—62no—
270C22⋊AGL(1,𝔽5)—62no—
271C22⋊AGL(1,𝔽5)—62no—
272C2×#170—21no—
273C4⋊AGL(1,𝔽5)—31no—
274C4⋊AGL(1,𝔽5)—31no—
275C4⋊AGL(1,𝔽5)—32no—
276C4⋊AGL(1,𝔽5)—62no—
277C4⋊AGL(1,𝔽5)—61no—
278C4⋊AGL(1,𝔽5)C22×D311yescharacteristic
279C4⋊AGL(1,𝔽5)C22×D311yescharacteristic
280C4×AGL(1,𝔽5)—21no—
281C4×AGL(1,𝔽5)—32no—
282C4×AGL(1,𝔽5)—62no—
283D5⋊C8—21no—
284D5⋊C8C22×D311yescharacteristic
285D5⋊C8C22×D311yescharacteristic
286C5×SD16—32no—
287C5×D8—32no—
288C5×M16—31no—
289#688—32no—
290#687—32no—
291#686—32no—
292#686—32no—
293#681—31no—
294D40—32no—
295#677—32no—
296#676—32no—
297C8×D5—32no—
298C2×AGL(1,ℤ/8)—151no—
299#520—151no—
300#518—151no—
301#442—152no—
302#440—152no—
303C4×SD16—152no—
304C4×D8—152no—
305#428—151no—
306#416—51no—
307C2×#102—151no—
308#405—151no—
309C22×C3×C5—21no—
310C22×C3×C5C4×D411yescharacteristic
311C2×D15—22no—
312C2×D15—81no—
313C2×C5×D3—22no—
314C2×C5×D3—81no—
315C2×C3×D5—21no—
316C2×C3×D5—21no—
317C2×C3×D5—21no—
318C2×C3×D5—41no—
319C2×C3×D5—41no—
320C2×C3×D5C4×D411yescharacteristic
321C2×C3×D5C22×D411yescharacteristic
322D3×D5—42no—
323D3×D5—42no—
324D3×D5—82no—
325ΓL(1,𝔽16)—22no—
326ΓL(1,𝔽16)—22no—
327ΓL(1,𝔽16)—42no—
328C3×AGL(1,𝔽5)—41no—
329C3×AGL(1,𝔽5)—41no—
330C3×C4×C5—21no—
331C3×C4×C5C4×D411yescharacteristic
332C3×C4×C5C23×C411yescharacteristic
333C3×Dic5—21no—
334C3×Dic5C4×D411yescharacteristic
335C3×Dic5C2×#4111yescharacteristic
336C23×D3—101no—
337C3×#41—51no—
338C3×#41—51no—
339C3×#41—51no—
340C3×#41—101no—
341C3×#41—101no—
342C3×#41C2×AGL(1,𝔽5)11yescharacteristic, complemented
343C2×C3×Q8—51no—
344C2×C3×D4—51no—
345C2×C3×D4—101no—
346C22×C3×C4—51no—
347C22×C3×C4—101no—
348C22×Dic3—102no—
349C22×Dic3—101no—
350C2×D12—51no—
351C2×D12—52no—
352C2×D12—52no—
353C2×D12—101no—
354C2×D12—101no—
355C2×D12—101no—
356C2×D12C2×AGL(1,𝔽5)11yescharacteristic, complemented
357C2×C4×D3—102no—
358C2×C4×D3—102no—
359C2×C3×C8—51no—
360C2×C3×C8—51no—
361C2×C3×C8—101no—
362C2×C3×C8—101no—
363C3×C4⋊C4—51no—
364C3×C4⋊C4—51no—
365C3×C22⋊C4—101no—
366C3×C42—101no—
367#217—52no—
368#217—102no—
369#215—52no—
370#215—52no—
371#215—52no—
372#215C2×AGL(1,𝔽5)12yescomplemented
373#213—52no—
374#213—52no—
375#213—52no—
376#213C2×AGL(1,𝔽5)12yescomplemented
377(C2×D3)⋊C4—102no—
378(C2×D3)⋊C4—102no—
379C4⋊Dic3—51no—
380C4⋊Dic3—51no—
381C4⋊Dic3—52no—
382C4⋊Dic3—102no—
383C4⋊Dic3—101no—
384C4×Dic3—52no—
385C4×Dic3—102no—
386#208—51no—
387#208—52no—
388#208C2×AGL(1,𝔽5)11yescharacteristic, complemented
389C2×C3⋊C8—52no—
390C23×C5—61no—
391C22×D5—21no—
392C22×D5—61no—
393C22×D5—62no—
394C22×D5—62no—
395C22×D5—241no—
396C22×D5—241no—
397C22×D5D3×D411yescharacteristic
398C2×AGL(1,𝔽5)—21no—
399C2×AGL(1,𝔽5)—21no—
400C2×AGL(1,𝔽5)—32no—
401C2×AGL(1,𝔽5)—32no—
402C2×AGL(1,𝔽5)—62no—
403C2×AGL(1,𝔽5)—242no—
404C2×AGL(1,𝔽5)—242no—
405C2×AGL(1,𝔽5)—242no—
406C2×AGL(1,𝔽5)—241no—
407C5×Q8C2×C4×D311yescharacteristic
408C5×D4—21no—
409C5×D4—32no—
410C5×D4—61no—
411C5×D4C2×C4×D311yescharacteristic
412C2×C4×C5—21no—
413C2×C4×C5C2×C4×D311yescharacteristic
414C22⋊D5—21no—
415C22⋊D5—21no—
416C22⋊D5—21no—
417C22⋊D5—62no—
418C22⋊D5—62no—
419C2×Dic5—21no—
420C2×Dic5#23711yescharacteristic
421D20—21no—
422D20—32no—
423D20—61no—
424D20C2×C4×D311yescharacteristic
425C4×D5—21no—
426C4×D5—21no—
427C4×D5—21no—
428C4×D5C2×C4×D311yescharacteristic
429C4×D5D3×D411yescharacteristic
430C4×D5#23711yescharacteristic
431C4×D5C23×D311yescharacteristic
432Dic10—21no—
433Dic10C2×C4×D311yescharacteristic
434#170—21no—
435#170—21no—
436C5×C8—32no—
437#168—32no—
438C2×#41—51no—
439C22×D4—151no—
440AGL(1,ℤ/8)—31no—
441AGL(1,ℤ/8)—151no—
442AGL(1,ℤ/8)—152no—
443AGL(1,ℤ/8)—152no—
444AGL(1,ℤ/8)—151no—
445AGL(1,ℤ/8)—151no—
446C2×SD16—152no—
447C2×D8—152no—
448C2×M16—151no—
449C22×C8—51no—
450C4×Q8—152no—
451C4×D4—152no—
452C4×D4—152no—
453C4×D4—152no—
454C4×D4—301no—
455C4×D4—301no—
456C4×D4—302no—
457#117—51no—
458#117—151no—
459#117—301no—
460C2×C4⋊C4—151no—
461C2×C4⋊C4—301no—
462C2×C22⋊C4—302no—
463#107—152no—
464#106—152no—
465#103—51no—
466#103—51no—
467#102—51no—
468#102—51no—
469#102—152no—
470#102—152no—
471#97—152no—
472C4×C8—152no—
473C2×C3×C5—21no—
474C2×C3×C5—41no—
475C2×C3×C5C2×C4×D411yescharacteristic
476D15—42no—
477C3×D5—21no—
478C3×D5—41no—
479C3×D5#57611yescharacteristic
480C3×D5#57711yescharacteristic
481C5×D3—42no—
482C23×C3—51no—
483C23×C3—101no—
484C22×D3—21no—
485C22×D3—102no—
486C22×D3—102no—
487C22×D3—101no—
488C22×D3—401no—
489C22×D3—401no—
490C3×Q8—51no—
491C3×Q8—101no—
492C3×Q8C22×AGL(1,𝔽5)11yescharacteristic
493C3×D4—21no—
494C3×D4—51no—
495C3×D4—101no—
496C3×D4—101no—
497C3×D4—101no—
498C3×D4—101no—
499C3×D4C22×AGL(1,𝔽5)11yescharacteristic
500C2×C3×C4—21no—
501C2×C3×C4—51no—
502C2×C3×C4—51no—
503C2×C3×C4—51no—
504C2×C3×C4—51no—
505C2×C3×C4—51no—
506C2×C3×C4—101no—
507C2×C3×C4—101no—
508C2×C3×C4—101no—
509C2×C3×C4—101no—
510C2×C3×C4—101no—
511C2×C3×C4—101no—
512C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
513C2×Dic3—52no—
514C2×Dic3—52no—
515C2×Dic3—102no—
516C2×Dic3—402no—
517C2×Dic3—401no—
518D12—21no—
519D12—52no—
520D12—102no—
521D12—102no—
522D12—101no—
523D12C22×AGL(1,𝔽5)12yes—
524C4×D3—402no—
525C4×D3—402no—
526C3×C8—101no—
527C3×C8—101no—
528C3⋊C8—52no—
529C3⋊C8C22×AGL(1,𝔽5)12yes—
530C22×C5—21no—
531C22×C5—62no—
532C22×C5—241no—
533C22×C5#67⋊C411yescharacteristic
534C2×D5—21no—
535C2×D5—21no—
536C2×D5—21no—
537C2×D5—41no—
538C2×D5—41no—
539C2×D5—62no—
540C2×D5—122no—
541C2×D5—122no—
542C2×D5—242no—
543C2×D5—241no—
544C2×D5#67⋊C411yescharacteristic
545C2×D5C2×D3×D411yescharacteristic
546AGL(1,𝔽5)—41no—
547AGL(1,𝔽5)—41no—
548AGL(1,𝔽5)—62no—
549AGL(1,𝔽5)—62no—
550AGL(1,𝔽5)—122no—
551C4×C5—21no—
552C4×C5#67⋊C411yescharacteristic
553C4×C5C22×C4×D311yescharacteristic
554Dic5—21no—
555Dic5#67⋊C411yescharacteristic
556Dic5C2×#23711yescharacteristic
557C24—301no—
558#41—51no—
559#41—51no—
560#41—51no—
561#41—101no—
562#41—101no—
563#41D3×AGL(1,𝔽5)11yescharacteristic, complemented
564C2×Q8—51no—
565C2×D4—31no—
566C2×D4—51no—
567C2×D4—101no—
568C2×D4—152no—
569C2×D4—152no—
570C2×D4—151no—
571C2×D4—301no—
572C2×D4—301no—
573C2×D4—301no—
574C22×C4—51no—
575C22×C4—101no—
576C22×C4—302no—
577C22×C4—302no—
578C22×C4—302no—
579C22×C4—301no—
580SD16—32no—
581SD16—152no—
582SD16—152no—
583SD16—152no—
584D8—32no—
585D8—152no—
586D8—152no—
587D8—152no—
588M16—31no—
589M16—152no—
590M16—151no—
591C2×C8—51no—
592C2×C8—51no—
593C2×C8—101no—
594C2×C8—101no—
595C2×C8—152no—
596C4⋊C4—51no—
597C4⋊C4—51no—
598C4⋊C4—151no—
599C4⋊C4—151no—
600C4⋊C4—152no—
601C4⋊C4—301no—
602C4⋊C4—302no—
603C22⋊C4—101no—
604C22⋊C4—152no—
605C22⋊C4—302no—
606C22⋊C4—302no—
607C22⋊C4—302no—
608C42—101no—
609C42—152no—
610C42—302no—
611C3×C5#294611yescharacteristic, complemented, Hall
612C22×C3—21no—
613C22×C3—51no—
614C22×C3—51no—
615C22×C3—101no—
616C22×C3—101no—
617C22×C3—101no—
618C22×C3—201no—
619C22×C3—201no—
620C22×C3D4×AGL(1,𝔽5)11yescharacteristic
621C2×D3—22no—
622C2×D3—81no—
623C2×D3—102no—
624C2×D3—202no—
625C2×D3—202no—
626C2×D3—402no—
627C2×D3—401no—
628C3×C4—21no—
629C3×C4—51no—
630C3×C4—51no—
631C3×C4—101no—
632C3×C4—201no—
633C3×C4—201no—
634C3×C4D4×AGL(1,𝔽5)11yescharacteristic
635C3×C4C23×AGL(1,𝔽5)11yescharacteristic
636Dic3—102no—
637Dic3—102no—
638Dic3—202no—
639C2×C5—21no—
640C2×C5—41no—
641C2×C5—122no—
642C2×C5C2×#67⋊C411yescharacteristic
643D5—21no—
644D5—41no—
645D5—122no—
646D5#576911yescharacteristic
647D5#577011yescharacteristic
648C23—51no—
649C23—61no—
650C23—101no—
651C23—302no—
652C23—302no—
653C23—301no—
654C23—1201no—
655C23—1201no—
656Q8—51no—
657Q8—101no—
658Q8C2×D3×AGL(1,𝔽5)11yescharacteristic
659D4—21no—
660D4—32no—
661D4—51no—
662D4—61no—
663D4—101no—
664D4—101no—
665D4—101no—
666D4—101no—
667D4—152no—
668D4—302no—
669D4—302no—
670D4—301no—
671D4C2×D3×AGL(1,𝔽5)11yescharacteristic
672C2×C4—21no—
673C2×C4—51no—
674C2×C4—51no—
675C2×C4—51no—
676C2×C4—51no—
677C2×C4—51no—
678C2×C4—101no—
679C2×C4—101no—
680C2×C4—101no—
681C2×C4—101no—
682C2×C4—101no—
683C2×C4—101no—
684C2×C4—152no—
685C2×C4—152no—
686C2×C4—302no—
687C2×C4—1202no—
688C2×C4—1202no—
689C2×C4—1202no—
690C2×C4—1201no—
691C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
692C8—32no—
693C8—101no—
694C8—101no—
695C8—152no—
696C2×C3—21no—
697C2×C3—41no—
698C2×C3—51no—
699C2×C3—51no—
700C2×C3—101no—
701C2×C3—201no—
702C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
703D3—42no—
704D3—202no—
705C5#7882011yescharacteristic, complemented, Sylow
706C22—21no—
707C22—51no—
708C22—51no—
709C22—62no—
710C22—101no—
711C22—101no—
712C22—101no—
713C22—201no—
714C22—201no—
715C22—241no—
716C22—302no—
717C22—602no—
718C22—602no—
719C22—1201no—
720C22—1202no—
721C22#67⋊AGL(1,𝔽5)11yescharacteristic
722C4—21no—
723C4—51no—
724C4—51no—
725C4—101no—
726C4—201no—
727C4—201no—
728C4—302no—
729C4—302no—
730C4—602no—
731C4#67⋊AGL(1,𝔽5)11yescharacteristic
732C4C22×D3×AGL(1,𝔽5)11yescharacteristic
733C3#1061744711yescharacteristic, complemented, Sylow
734C2—21no—
735C2—41no—
736C2—51no—
737C2—51no—
738C2—101no—
739C2—122no—
740C2—201no—
741C2—602no—
742C2C2×#67⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2C2×#67⋊AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC3×C5×#41C2×C4
socleC2×C3×C5C2×C4×D4
prime radicalD5×#949C2
cosocleC3×C4×D5C24
hypercenter#41D3×AGL(1,𝔽5)
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. #11756995C2semidirect
2. #11756837C2semidirect
4. C3×#65794C2semidirect
5. #11751966C2semidirect
6. #11751965C2semidirect
7. #11751942C2semidirect
8. #11751941C2semidirect
9. #11751728C2semidirect
10. C2×#91152C2semidirect
11. #11751694C2semidirect
15. Q8×ΓL(1,𝔽16)C22semidirect
17. D4×ΓL(1,𝔽16)C22semidirect
29. #91838C4semidirect
30. C5×#949C4semidirect
31. #91502C4semidirect
33. #91478C4semidirect
35. #91301C4semidirect
36. #91299C4semidirect
38. C3×#4009C22semidirect
39. C3×#4009C22semidirect
40. C3×#4007C22semidirect
41. C3×#4007C22semidirect
42. #91160C22semidirect
43. #91159C22semidirect
46. #91150C22semidirect
47. ΓL(1,𝔽16)⋊C8C22semidirect
52. #65794D3semidirect
65. C3×C5×#41C2×C4semidirect
66. C2×D60C2×C4semidirect
67. C2×C5×D12C2×C4semidirect
68. C3×#713C2×C4semidirect
71. C3×#711C2×C4semidirect
75. C3×#709C2×C4semidirect
81. D5×D12C2×C4semidirect
102. #6717C2×C4semidirect
103. #6715C2×C4semidirect
104. #6710C2×C4semidirect
105. C5×#215C2×C4semidirect
106. C5×#213C2×C4semidirect
107. C5×#208C2×C4semidirect
108. #6658C2×C4semidirect
109. #6656C2×C4semidirect
110. #6653C2×C4semidirect
111. #6652C2×C4semidirect
112. #6649C2×C4semidirect
150. #4009C2×D3semidirect
151. #4009C2×D3semidirect
154. #4007C2×D3semidirect
155. #4007C2×D3semidirect
218. #949AGL(1,𝔽5)semidirect
249. C5×#41C4×D3semidirect
252. #713C4×D3semidirect
255. #711C4×D3semidirect
263. #709C4×D3semidirect
342. C3×#41C2×AGL(1,𝔽5)semidirect
356. C2×D12C2×AGL(1,𝔽5)semidirect
372. #215C2×AGL(1,𝔽5)semidirect
376. #213C2×AGL(1,𝔽5)semidirect
388. #208C2×AGL(1,𝔽5)semidirect
563. #41D3×AGL(1,𝔽5)semidirect
611. C3×C5#2946semidirect
705. C5#78820semidirect
733. C3#10617447semidirect

Maximal subgroups

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

subgroupindex
#117569952
#117568372
D5×#9492
C3×#657942
#117519662
#117519652
#117519422
#117519412
#117517282
C2×#911522
#117516942
#106174473
#788205