Finite Group Databasebeta

← #14415402

Subgroups — #14415402

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91929C211yesmaximal, characteristic, complemented
2C2×#91927C211yesmaximal, characteristic, complemented
3#11754775C211yesmaximal, characteristic
4#11752432C211yesmaximal, characteristic, complemented
5C3×#65773C211yesmaximal, characteristic, complemented
6#11752053C211yesmaximal, characteristic, complemented
7#11752044C211yesmaximal, characteristic, complemented
8#11752040C211yesmaximal, characteristic, complemented
9#11752040C211yesmaximal, characteristic, complemented
10#11752039C211yesmaximal, characteristic, complemented
11#11752035C211yesmaximal, characteristic, complemented
12#11751923C211yesmaximal, characteristic, complemented
13#11751897C211yesmaximal, characteristic, complemented
14#11751891C211yesmaximal, characteristic, complemented
15#11751873C211yesmaximal, characteristic, complemented
16#10617362—31nomaximal, Hall
17C2×#6782C2211yescharacteristic
18C2×#6782C2211yescharacteristic
19C2×#6762C2211yescharacteristic
20C22×C3⋊#170C2211yescharacteristic
21C2×C3×#704C2211yescharacteristic
22C22×C3×#170C2211yescharacteristic
23C2×#6740C2211yescharacteristic
24C2×#6740C2211yescharacteristic
25C2×#6739C2211yescharacteristic
26C2×#6739C2211yescharacteristic
27C2×#6738C2211yescharacteristic
28C2×#6738C2211yescharacteristic
29#91929—24no—
30#91927—24no—
31C2×D3×#170C2211yescharacteristic
32C2×D3×#170C2211yescharacteristic
33#91827C411yescharacteristic
34C5×#940C411yescharacteristic
35C3×D4×Dic5C2211yescharacteristic
36#91557C411yescharacteristic
37#91557C411yescharacteristic
38Dic5×#67C2211yescharacteristic
39Dic5×#67C2211yescharacteristic
40#91525C411yescharacteristic
41#91525C411yescharacteristic
42#91469C411yescharacteristic
43#91466C411yescharacteristic
44Dic5×D12C2211yescharacteristic
45C4×#1200C2211yescharacteristic
46#91241C2211yescharacteristic
47#91241C2211yescharacteristic
48#91233C2211yescharacteristic
49#91231C2211yescharacteristic
50C3×C22⋊#170C2211yescharacteristic
51C3×C22⋊#170C2211yescharacteristic
52C3×#4004C2211yescharacteristic
53C3×#4002C2211yescharacteristic
54#91177C2211yescharacteristic
55#91177C2211yescharacteristic
56(C2×D3)⋊#170C2211yescharacteristic
57(C2×D3)⋊#170C2211yescharacteristic
58(C2×D3)⋊#170C2211yescharacteristic
59(C2×D3)⋊#170C2211yescharacteristic
60#91169C2211yescharacteristic
61#91169C2211yescharacteristic
62#79480—51nomaximal, Hall
63C2×#4131—31no—
64C2×#4131—31no—
65#66050—31no—
66#65776—31no—
67#65776—31no—
68#65773—31no—
69#65773—31no—
70#65773—31no—
71#65773—31no—
72#65773—31no—
73#65773—31no—
74#65773—31no—
75#65773D311yescharacteristic, complemented
76#65682—31no—
77#65676—31no—
78C2×C3×C5×D4C2×C411yescharacteristic
79C2×#1220C2×C411yescharacteristic
80C2×#1220C2×C411yescharacteristic
81C2×C4×D15C2×C411yescharacteristic
82C2×C5×#67C2×C411yescharacteristic
83C2×C5×#67C2×C411yescharacteristic
84C2×C5×#67C2×C411yescharacteristic
85C2×C5×#67C2×C411yescharacteristic
86C2×C5×D12C2×C411yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C2×#1204C2×C411yescharacteristic
90C2×#1204C2×C411yescharacteristic
91C2×#1203C2×C411yescharacteristic
92C2×#1203C2×C411yescharacteristic
93C2×#1200C2×C411yescharacteristic
94C2×#1200C2311yescharacteristic
95#6782—22no—
96#6782—22no—
97#6782—22no—
98#6782—22no—
99C2×D3×Dic5C2311yescharacteristic
100C2×D3×Dic5C2311yescharacteristic
101#6762—22no—
102C2×C3⋊#170—22no—
103C2×C3⋊#170C2311yescharacteristic
104C2×C3⋊#170C2311yescharacteristic
105C2×C3⋊#170C2311yescharacteristic
106C2×C3⋊#170C2311yescharacteristic
107C3×#704—22no—
108C2×C3×#170—22no—
109C2×C3×#170C2311yescharacteristic
110C2×C3×#170C2311yescharacteristic
111C2×C3×#170C2311yescharacteristic
112C2×C3×#170C2311yescharacteristic
113#6740—22no—
114#6740—22no—
115#6739—22no—
116#6739—22no—
117#6738—22no—
118#6738D414yescomplemented
119D3×#170—22no—
120D3×#170—22no—
121#6719C2×C411yescharacteristic
122#6719C2×C411yescharacteristic
123C4⋊Dic15C2×C411yescharacteristic
124C4×C5×Dic3C2×C411yescharacteristic
125C3×C22⋊Dic5C2×C411yescharacteristic
126C3×C22⋊Dic5C2×C411yescharacteristic
127C3×C4⋊Dic5C2×C411yescharacteristic
128C3×C4×Dic5C2311yescharacteristic
129Dic3⋊Dic5C2×C411yescharacteristic
130Dic3⋊Dic5C2×C411yescharacteristic
131(C2×D3)⋊Dic5C2×C411yescharacteristic
132(C2×D3)⋊Dic5C2×C411yescharacteristic
133(C2×D3)⋊Dic5C2×C411yescharacteristic
134(C2×D3)⋊Dic5C2×C411yescharacteristic
135Dic3×Dic5C2×C411yescharacteristic
136Dic3×Dic5C2311yescharacteristic
137C2×#907—51no—
138C2×#901—51no—
139#5548—51no—
140C3×#435—51no—
141#5127—51no—
142#5111—51no—
143#5011—51no—
144#4837—51no—
145#4836—51no—
146#4730—51no—
147#4728—51no—
148#4727—51no—
149#4727—51no—
150#4706—51no—
151D3×#97—51no—
152C2×#711—31no—
153C2×#711—31no—
154C2×#704—31no—
155C2×#704—31no—
156C2×#704—31no—
157C2×#704C2×D311yescharacteristic
158C22×#170—31no—
159C22×#170—31no—
160C22×#170—31no—
161C22×#170C2×D311yescharacteristic
162#4131—64no—
163#4131—64no—
164C2×#700—31no—
165C2×#700—31no—
166C2×D5⋊C8—31no—
167C2×D5⋊C8—31no—
168C5×#127—31no—
169#4084—31no—
170#4084—31no—
171#4084—31no—
172#4084—31no—
173#4082—31no—
174#4082—31no—
175D4×Dic5—31no—
176D4×Dic5—31no—
177D4×Dic5—31no—
178D4×Dic5C2×D311yescharacteristic
179C42×D5—31no—
180#4015—31no—
181C22⋊#170—31no—
182C22⋊#170—31no—
183C22⋊#170—31no—
184C22⋊#170—31no—
185C22⋊#170—31no—
186C22⋊#170—31no—
187C22⋊#170C2×D311yescharacteristic
188C22⋊#170C2×D311yescharacteristic
189#4004—31no—
190#4004—31no—
191#4004—31no—
192#4004C2×D311yescharacteristic
193#4002—31no—
194#4002—31no—
195#4002—31no—
196#4002C2×D311yescharacteristic
197#2932—151noSylow
198C23×C3×C5C22×C411yescharacteristic
199C23×C3×C5C22×C411yescharacteristic
200C22×D15C22×C411yescharacteristic
201C22×C5×D3C22×C411yescharacteristic
202C22×C5×D3C22×C411yescharacteristic
203C3×C5×D4—41no—
204C2×C3×C4×C5C22×C411yescharacteristic
205#1220—22no—
206#1220—22no—
207C2×Dic15C22×C411yescharacteristic
208C2×Dic15C22×C411yescharacteristic
209C2×Dic15C22×C411yescharacteristic
210C4×D15—41no—
211C5×#67—22no—
212C5×#67—22no—
213C5×#67—41no—
214C5×#67—41no—
215C2×C5×Dic3C22×C411yescharacteristic
216C2×C5×Dic3C22×C411yescharacteristic
217C5×D12—41no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5C22×C411yescharacteristic
223C2×C3×Dic5C22×C411yescharacteristic
224C2×C3×Dic5C22×C411yescharacteristic
225C2×C3×Dic5C2411yescharacteristic
226#1204—22no—
227#1204—22no—
228#1203—22no—
229#1203—22no—
230#1200—41no—
231#1200C2×D412yes—
232#1200#4112yes—
233D3×Dic5—21no—
234D3×Dic5—21no—
235D3×Dic5—21no—
236D3×Dic5—21no—
237C3⋊#170—21no—
238C3⋊#170—21no—
239C3⋊#170—21no—
240C3⋊#170C2×D412yes—
241C3×#170—21no—
242C3×#170—21no—
243C3×#170—21no—
244C3×#170C2×D412yes—
245C2×#235—51no—
246C2×#235—51no—
247C2×C3×M16—51no—
248C22×C3×C8—51no—
249C3×C4×D4—51no—
250#940AGL(1,𝔽5)11yescharacteristic
251#938—51no—
252C4×#67—51no—
253C4×#67—51no—
254C2×#208—51no—
255C22×C3⋊C8—51no—
256#907—104no—
257#901—104no—
258C2×ΓL(1,𝔽25)—51no—
259C2×ΓL(1,𝔽25)—51no—
260C2×ΓL(1,𝔽25)—51no—
261C2×ΓL(1,𝔽25)—51no—
262C2×D3×C8—51no—
263C2×D3×C8—51no—
264C2×D3×C8—51no—
265C2×D3×C8—51no—
266#895—51no—
267#888—51no—
268#885—51no—
269#885—51no—
270#884—51no—
271#884—51no—
272C4×D12—51no—
273C42×D3—51no—
274C3×C4⋊C8—51no—
275C3×C22⋊C8—51no—
276C3×C22⋊C8—51no—
277C3×#97—51no—
278#830—51no—
279#830—51no—
280(C2×D3)⋊C8—51no—
281(C2×D3)⋊C8—51no—
282(C2×D3)⋊C8—51no—
283(C2×D3)⋊C8—51no—
284#815—51no—
285#815—51no—
286Dic3⋊C8—51no—
287Dic3⋊C8—51no—
288C4⋊(C3⋊C8)—51no—
289#803—51no—
290C2×C5×D4—31no—
291C2×C5×D4—31no—
292C2×C5×D4—31no—
293C2×C5×D4—31no—
294C2×C5×D4—31no—
295C2×C5×D4C4×D311yescharacteristic
296C2×C22⋊D5—31no—
297C2×C22⋊D5—31no—
298C2×C22⋊D5—31no—
299C2×C22⋊D5—31no—
300C22×Dic5—31no—
301C22×Dic5—31no—
302C22×Dic5C22×D311yescharacteristic
303C22×Dic5C22×D311yescharacteristic
304#711—62no—
305#711—62no—
306#711—62no—
307#711—62no—
308C2×C4×D5—31no—
309C2×C4×D5—31no—
310C2×C4×D5—31no—
311C2×Dic10—31no—
312C2×Dic10—31no—
313#704—22no—
314#704—62no—
315#704—62no—
316#704—62no—
317C2×#170—22no—
318C2×#170—31no—
319C2×#170—31no—
320C2×#170—31no—
321C2×#170—31no—
322C2×#170—62no—
323C2×#170—62no—
324C2×#170—62no—
325C2×#170C22×D311yescharacteristic
326C2×#170C22×D311yescharacteristic
327C2×#170C22×D311yescharacteristic
328C2×#170C22×D311yescharacteristic
329#700—62no—
330#700—62no—
331D5⋊C8—34no—
332D5⋊C8—62no—
333C42×C5—31no—
334C22⋊Dic5—31no—
335C22⋊Dic5—31no—
336C22⋊Dic5—31no—
337C22⋊Dic5—31no—
338C22⋊Dic5—31no—
339C22⋊Dic5—31no—
340C22⋊Dic5C4×D311yescharacteristic
341C22⋊Dic5C4×D311yescharacteristic
342C4⋊Dic5—31no—
343C4⋊Dic5—31no—
344C4⋊Dic5—31no—
345C4⋊Dic5C4×D311yescharacteristic
346C4×Dic5—31no—
347C4×Dic5—31no—
348C4×Dic5C22×D311yescharacteristic
349C2×#131—151no—
350C2×#131—151no—
351#532—151no—
352#435—51no—
353#435—151no—
354#435—151no—
355#435—151no—
356#435—151no—
357#435—151no—
358#435—151no—
359#435—151no—
360#423—151no—
361#408—151no—
362#408—151no—
363C2×#97—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×C5C23×C411yescharacteristic
371C2×D15—21no—
372C2×D15—21no—
373C2×D15C4×D412yes—
374C2×C5×D3—21no—
375C2×C5×D3—21no—
376C2×C5×D3—21no—
377C2×C5×D3—21no—
378C2×C5×D3—21no—
379C2×C5×D3—21no—
380C3×C4×C5—21no—
381Dic15—21no—
382Dic15—21no—
383Dic15—21no—
384C3×Dic5—21no—
385C3×Dic5—21no—
386C3×Dic5—21no—
387C3×Dic5C22×D411yescharacteristic
388C3×Dic5C2×#4111yescharacteristic
389C5×Dic3—21no—
390C5×Dic3C4×D412yes—
391C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
392C22×C3×C4—51no—
393C22×C3×C4—51no—
394C2×#67—51no—
395C2×#67—51no—
396C2×#67C2×AGL(1,𝔽5)11yescharacteristic
397C2×#67C2×AGL(1,𝔽5)11yescharacteristic
398C2×#67C2×AGL(1,𝔽5)11yescharacteristic
399C2×#67C2×AGL(1,𝔽5)11yescharacteristic
400#235—102no—
401#235—102no—
402#235—102no—
403#235—102no—
404C2×D12—51no—
405C2×D12—51no—
406C2×D12C2×AGL(1,𝔽5)11yescharacteristic
407C2×C4×D3—51no—
408C2×C4×D3—51no—
409C2×C4×D3—51no—
410C2×C4×D3—51no—
411C2×C4×D3—51no—
412C2×Dic6—51no—
413C2×Dic6—51no—
414C3×M16—102no—
415C2×C3×C8—51no—
416C2×C3×C8—51no—
417C2×C3×C8—51no—
418C2×C3×C8—51no—
419C2×C3×C8—102no—
420C3×C4⋊C4—51no—
421C3×C22⋊C4—51no—
422C3×C22⋊C4—51no—
423C3×C42—51no—
424#217—51no—
425#217—51no—
426(C2×D3)⋊C4—51no—
427(C2×D3)⋊C4—51no—
428(C2×D3)⋊C4—51no—
429(C2×D3)⋊C4—51no—
430C4⋊Dic3—51no—
431Dic3⋊C4—51no—
432Dic3⋊C4—51no—
433C4×Dic3—51no—
434C4×Dic3—51no—
435C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
436#208—102no—
437C2×C3⋊C8—51no—
438C2×C3⋊C8—51no—
439C2×C3⋊C8—51no—
440C2×C3⋊C8—51no—
441C2×C3⋊C8—102no—
442ΓL(1,𝔽25)—102no—
443ΓL(1,𝔽25)—102no—
444ΓL(1,𝔽25)—102no—
445ΓL(1,𝔽25)—102no—
446D3×C8—54no—
447D3×C8—102no—
448D3×C8—102no—
449D3×C8—102no—
450C23×C5—31no—
451C23×C5—31no—
452C23×C5C2×C4×D311yescharacteristic
453C23×C5C2×C4×D311yescharacteristic
454C22×D5—31no—
455C5×D4—41no—
456C5×D4—62no—
457C5×D4—62no—
458C5×D4—121no—
459C5×D4—121no—
460C5×D4—121no—
461C2×C4×C5—31no—
462C2×C4×C5—31no—
463C2×C4×C5C2×C4×D311yescharacteristic
464C22⋊D5—62no—
465C22⋊D5—62no—
466C22⋊D5—62no—
467C22⋊D5—62no—
468C2×Dic5—21no—
469C2×Dic5—21no—
470C2×Dic5—21no—
471C2×Dic5—21no—
472C2×Dic5—31no—
473C2×Dic5—31no—
474C2×Dic5—31no—
475C2×Dic5—61no—
476C2×Dic5—61no—
477C2×Dic5—61no—
478C2×Dic5—61no—
479C2×Dic5C2×C4×D311yescharacteristic
480C2×Dic5C2×C4×D311yescharacteristic
481C2×Dic5C2×C4×D311yescharacteristic
482C2×Dic5C23×D311yescharacteristic
483C4×D5—32no—
484C4×D5—32no—
485C4×D5—121no—
486C4×D5—121no—
487Dic10—62no—
488Dic10—62no—
489#170—21no—
490#170—21no—
491#170—21no—
492#170—32no—
493#170—61no—
494#170—61no—
495#170—61no—
496#170D3×D412yes—
497C2×#41—151no—
498C2×#41—151no—
499#131—304no—
500#131—304no—
501C2×M16—51no—
502C2×M16—151no—
503C2×M16—151no—
504C2×M16—151no—
505C2×M16—151no—
506C2×M16—151no—
507C22×C8—51no—
508C22×C8—151no—
509C22×C8—151no—
510C22×C8—151no—
511C22×C8—151no—
512C22×C8—151no—
513C4⋊Q8—151no—
514#127—31no—
515#124—151no—
516#124—151no—
517#121—151no—
518#121—151no—
519#121—151no—
520#121—151no—
521C4×D4—51no—
522C4×D4—151no—
523C4×D4—151no—
524C4×D4—151no—
525C2×C42—151no—
526C4⋊C8—51no—
527C4⋊C8—151no—
528C4⋊C8—151no—
529C4⋊C8—151no—
530C22⋊C8—51no—
531C22⋊C8—51no—
532C22⋊C8—151no—
533C22⋊C8—151no—
534C22⋊C8—151no—
535C22⋊C8—151no—
536C22⋊C8—151no—
537C22⋊C8—151no—
538#97—51no—
539#97—151no—
540#97—151no—
541#97—151no—
542C2×C3×C5—41no—
543C2×C3×C5—41no—
544C2×C3×C5C2×C4×D411yescharacteristic
545C2×C3×C5#56811yescharacteristic
546C2×C3×C5#56811yescharacteristic
547D15—22no—
548C5×D3—41no—
549C5×D3—41no—
550C23×C3C22×AGL(1,𝔽5)11yescharacteristic
551C23×C3C22×AGL(1,𝔽5)11yescharacteristic
552C22×D3—51no—
553C22×D3C22×AGL(1,𝔽5)11yescharacteristic
554C22×D3C22×AGL(1,𝔽5)11yescharacteristic
555C3×D4—41no—
556C2×C3×C4—51no—
557C2×C3×C4—51no—
558C2×C3×C4—51no—
559C2×C3×C4—51no—
560C2×C3×C4—101no—
561C2×C3×C4—101no—
562C2×C3×C4—101no—
563C2×C3×C4—101no—
564C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
565#67—22no—
566#67—22no—
567#67—41no—
568#67—41no—
569#67—102no—
570#67—102no—
571C2×Dic3—51no—
572C2×Dic3—51no—
573C2×Dic3—51no—
574C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
575C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
576D12—41no—
577D12—102no—
578D12—102no—
579C4×D3—52no—
580C4×D3—52no—
581C4×D3—101no—
582C4×D3—101no—
583C4×D3—101no—
584C4×D3—101no—
585C4×D3—201no—
586C4×D3—201no—
587Dic6—102no—
588Dic6—102no—
589C3×C8—52no—
590C3×C8—101no—
591C3×C8—101no—
592C3×C8—101no—
593C3⋊C8—52no—
594C3⋊C8—101no—
595C3⋊C8—101no—
596C3⋊C8—101no—
597C22×C5—21no—
598C22×C5—21no—
599C22×C5—21no—
600C22×C5—21no—
601C22×C5—21no—
602C22×C5—21no—
603C22×C5—61no—
604C22×C5—61no—
605C22×C5—61no—
606C22×C5—61no—
607C22×C5—61no—
608C22×C5—61no—
609C22×C5C22×C4×D311yescharacteristic
610C2×D5—32no—
611C2×D5—61no—
612C2×D5—61no—
613C4×C5—21no—
614C4×C5—32no—
615C4×C5—61no—
616Dic5—21no—
617Dic5—21no—
618Dic5—21no—
619Dic5—61no—
620Dic5—61no—
621Dic5—61no—
622Dic5C2×D3×D411yescharacteristic
623Dic5D3×#4111yescharacteristic
624#41—302no—
625#41—302no—
626#41—302no—
627#41—302no—
628C2×Q8—151no—
629C2×Q8—151no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—31no—
633C2×D4—31no—
634C2×D4—31no—
635C2×D4—151no—
636C2×D4—151no—
637C2×D4—151no—
638C2×D4—151no—
639C2×D4D3×AGL(1,𝔽5)11yescharacteristic
640C22×C4—51no—
641C22×C4—51no—
642C22×C4—151no—
643C22×C4—151no—
644C22×C4—151no—
645C22×C4—151no—
646C22×C4—151no—
647M16—102no—
648M16—302no—
649M16—302no—
650M16—302no—
651M16—302no—
652M16—302no—
653C2×C8—51no—
654C2×C8—51no—
655C2×C8—51no—
656C2×C8—51no—
657C2×C8—102no—
658C2×C8—154no—
659C2×C8—151no—
660C2×C8—151no—
661C2×C8—151no—
662C2×C8—151no—
663C2×C8—302no—
664C2×C8—302no—
665C2×C8—302no—
666C2×C8—302no—
667C4⋊C4—51no—
668C4⋊C4—151no—
669C4⋊C4—151no—
670C4⋊C4—151no—
671C22⋊C4—51no—
672C22⋊C4—51no—
673C22⋊C4—151no—
674C22⋊C4—151no—
675C22⋊C4—151no—
676C22⋊C4—151no—
677C22⋊C4—151no—
678C22⋊C4—151no—
679C42—31no—
680C42—51no—
681C42—151no—
682C42—151no—
683C3×C5#293211yescharacteristic, complemented, Hall
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3C23×AGL(1,𝔽5)11yescharacteristic
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—21no—
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—52no—
698C2×D3—101no—
699C2×D3—101no—
700C3×C4—21no—
701C3×C4—51no—
702C3×C4—51no—
703C3×C4—101no—
704C3×C4—101no—
705C3×C4—101no—
706Dic3—21no—
707Dic3—101no—
708Dic3—101no—
709Dic3—101no—
710Dic3D4×AGL(1,𝔽5)12yes—
711C2×C5—41no—
712C2×C5—41no—
713C2×C5—121no—
714C2×C5—121no—
715C2×C5C4×D3×D411yescharacteristic
716C2×C5#574511yescharacteristic
717C2×C5#575011yescharacteristic
718D5—62no—
719C23—31no—
720C23—31no—
721C23—151no—
722C23C2×D3×AGL(1,𝔽5)11yescharacteristic
723C23C2×D3×AGL(1,𝔽5)11yescharacteristic
724Q8—302no—
725Q8—302no—
726D4—41no—
727D4—62no—
728D4—62no—
729D4—121no—
730D4—121no—
731D4—121no—
732D4—302no—
733D4—302no—
734D4—302no—
735D4—302no—
736C2×C4—31no—
737C2×C4—31no—
738C2×C4—51no—
739C2×C4—51no—
740C2×C4—51no—
741C2×C4—51no—
742C2×C4—101no—
743C2×C4—101no—
744C2×C4—101no—
745C2×C4—101no—
746C2×C4—152no—
747C2×C4—152no—
748C2×C4—151no—
749C2×C4—151no—
750C2×C4—151no—
751C2×C4—301no—
752C2×C4—301no—
753C2×C4—301no—
754C2×C4—301no—
755C2×C4—601no—
756C2×C4—601no—
757C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
758C8—52no—
759C8—101no—
760C8—101no—
761C8—101no—
762C8—152no—
763C8—301no—
764C8—301no—
765C8—301no—
766C2×C3—41no—
767C2×C3—41no—
768C2×C3#6625611yescharacteristic
769C2×C3#6625611yescharacteristic
770C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
771D3—41no—
772D3—41no—
773D3—102no—
774C5#7948011yescharacteristic, complemented, Sylow
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—61no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—61no—
786C22—61no—
787C22—152no—
788C22—301no—
789C22—301no—
790C22C22×D3×AGL(1,𝔽5)11yescharacteristic
791C4—21no—
792C4—32no—
793C4—51no—
794C4—51no—
795C4—61no—
796C4—101no—
797C4—101no—
798C4—101no—
799C4—301no—
800C4—301no—
801C4—301no—
802C3#1061736211yescharacteristic, complemented, Sylow
803C2—41no—
804C2—41no—
805C2—121no—
806C2—121no—
807C2—302no—
808C2#1175684111yescharacteristic
809C2D3×D4×AGL(1,𝔽5)11yescharacteristic
810C2#1175686311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×D4C2×C4
prime radical#11754775C2
cosocleC2×C3×Dic5C24
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#2932
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#91929C2semidirect
2. C2×#91927C2semidirect
4. #11752432C2semidirect
5. C3×#65773C2semidirect
6. #11752053C2semidirect
7. #11752044C2semidirect
8. #11752040C2semidirect
9. #11752040C2semidirect
10. #11752039C2semidirect
11. #11752035C2semidirect
12. #11751923C2semidirect
13. #11751897C2semidirect
14. #11751891C2semidirect
15. #11751873C2semidirect
75. #65773D3semidirect
118. #6738D4semidirect
683. C3×C5#2932semidirect
774. C5#79480semidirect
802. C3#10617362semidirect

Maximal subgroups

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

subgroupindex
C2×#919292
C2×#919272
#117547752
#117524322
C3×#657732
#117520532
#117520442
#117520402
#117520392
#117520352
#117519232
#117518972
#117518912
#117518732
#106173623
#794805