Finite Group Databasebeta

← #14415805

Subgroups — #14415805

Order 1920.

1088 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×D5⋊ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
2C2×#91915C211yesmaximal, characteristic, complemented
3D3×#4039C211yesmaximal, characteristic
4#11752363C211yesmaximal, characteristic, complemented
5C3×#65704C211yesmaximal, characteristic, complemented
6#11751920C211yesmaximal, characteristic, complemented
7#11751919C211yesmaximal, characteristic, complemented
8#11751919C211yesmaximal, characteristic, complemented
9#11751907C211yesmaximal, characteristic, complemented
10#11751905C211yesmaximal, characteristic, complemented
11#11751894C211yesmaximal, characteristic, complemented
12#11751882C211yesmaximal, characteristic, complemented
13#11751881C211yesmaximal, characteristic, complemented
14#11751779C211yesmaximal, characteristic, complemented
15#11751763C211yesmaximal, characteristic, complemented
16#10617084—31nomaximal, Hall
17C2×D3×D20C411yescharacteristic
18C2×C4×D3×D5C2211yescharacteristic
19C2×C4×D3×D5C2211yescharacteristic
20C2×#6758C2211yescharacteristic, complemented
21C2×D5⋊(C3⋊C8)C2211yescharacteristic, complemented
22C2×C3×#700C2211yescharacteristic, complemented
23C2×C3×D5⋊C8C2211yescharacteristic, complemented
24C2×#6740C2211yescharacteristic, complemented
25C2×#6740C2211yescharacteristic, complemented
26C2×#6739C2211yescharacteristic
27C2×#6739C2211yescharacteristic
28C2×#6739C2211yescharacteristic
29C2×#6739C2211yescharacteristic
30C2×#6738C2211yescharacteristic, complemented
31C2×#6738C2211yescharacteristic, complemented
32D5⋊ΓL(1,𝔽25)—24no—
33#91915—24no—
34#91782C411yescharacteristic
35C5×D3×C4⋊C4C411yescharacteristic
36C3×#4039C2211yescharacteristic
37D3×#685C411yescharacteristic
38D3×#685C411yescharacteristic
39#91444C2211yescharacteristic
40#91444C2211yescharacteristic
41#91434C411yescharacteristic
42#91418C2211yescharacteristic
43C4×D3×Dic5C2211yescharacteristic
44#91396C411yescharacteristic
45#91396C411yescharacteristic
46#91233C2211yescharacteristic, complemented
47#91232C2211yescharacteristic, complemented
48#91232C2211yescharacteristic, complemented
49#91231C2211yescharacteristic, complemented
50C3×#4004C2211yescharacteristic, complemented
51C3×#4003C2211yescharacteristic, complemented
52C3×#4003C2211yescharacteristic, complemented
53C3×#4002C2211yescharacteristic, complemented
54Dic3⋊#170C2211yescharacteristic, complemented
55Dic3⋊#170C2211yescharacteristic, complemented
56#91171C2211yescharacteristic, complemented
57#91171C2211yescharacteristic, complemented
58#91171C2211yescharacteristic, complemented
59#91171C2211yescharacteristic, complemented
60Dic3×#170C2211yescharacteristic, complemented
61Dic3×#170C2211yescharacteristic, complemented
62#79483—51nomaximal, Hall
63C2×D5⋊M16—31no—
64C2×D5⋊M16—31no—
65C2×#4039—31no—
66#65758—31no—
67#65755—31no—
68#65755—31no—
69C4×#704—31no—
70#65705—31no—
71#65705—31no—
72#65704—31no—
73#65704—31no—
74#65704—31no—
75#65704D311yescharacteristic, complemented
76#65702—31no—
77#65702—31no—
78C22×D3×D5C2×C411yescharacteristic
79C22×D3×D5C2×C411yescharacteristic
80C2×D60C2×C411yescharacteristic
81C2×C4×D15C2×C411yescharacteristic
82C2×C4×D15C2×C411yescharacteristic
83C2×C4×C5×D3C2×C411yescharacteristic
84C2×C4×C5×D3C2×C411yescharacteristic
85C2×C4×C5×D3C2×C411yescharacteristic
86C2×C3×D20C2×C411yescharacteristic
87C2×C3×C4×D5C2311yescharacteristic
88C2×C3×C4×D5C2311yescharacteristic
89C2×#1202C2×C411yescharacteristic
90C2×#1202C2×C411yescharacteristic
91C2×#1200C2311yescharacteristic
92C2×#1200C2311yescharacteristic
93C2×D3×Dic5C2×C411yescharacteristic
94C2×D3×Dic5C2311yescharacteristic
95C2×D5×Dic3C2×C411yescharacteristic
96C2×D5×Dic3C2×C411yescharacteristic
97D3×D20—24no—
98C4×D3×D5—22no—
99C4×D3×D5—22no—
100C4×D3×D5—22no—
101C4×D3×D5—22no—
102C2×C3⋊#170C2311yescharacteristic
103C2×C3⋊#170C2311yescharacteristic
104C2×C3⋊#170C2311yescharacteristic
105C2×C3⋊#170C2311yescharacteristic
106#6758—22no—
107D5⋊(C3⋊C8)—22no—
108C2×C3×#170C2311yescharacteristic
109C2×C3×#170C2311yescharacteristic
110C2×C3×#170C2311yescharacteristic
111C2×C3×#170C2311yescharacteristic
112C3×#700—22no—
113C3×D5⋊C8—22no—
114#6740—22no—
115#6740—22no—
116#6739—22no—
117#6739—22no—
118#6739—22no—
119#6739D414yescomplemented
120#6738—22no—
121#6738—22no—
122C3×C5×C4⋊C4C2×C411yescharacteristic
123#6714C2×C411yescharacteristic
124#6714C2×C411yescharacteristic
125C4×Dic15C2×C411yescharacteristic
126C5×C4⋊Dic3C2×C411yescharacteristic
127C5×Dic3⋊C4C2×C411yescharacteristic
128C5×Dic3⋊C4C2×C411yescharacteristic
129C3×#685C2×C411yescharacteristic
130C3×#685C2×C411yescharacteristic
131C3×C4×Dic5C2311yescharacteristic
132#6667C2×C411yescharacteristic
133#6667C2×C411yescharacteristic
134#6665C2×C411yescharacteristic
135#6665C2×C411yescharacteristic
136Dic3×Dic5C2×C411yescharacteristic
137Dic3×Dic5C2311yescharacteristic
138C2×D3×M16—51no—
139C22×ΓL(1,𝔽25)—51no—
140C4×D3×D4—51no—
141C3×#435—51no—
142#5128—51no—
143C8×#67—51no—
144#5011—51no—
145#4837—51no—
146#4836—51no—
147#4729—51no—
148#4726—51no—
149#4726—51no—
150#67⋊C8—51no—
151#4707—51no—
152#4706—51no—
153C22×D20—31no—
154C22×C4×D5—31no—
155C22×C4×D5—31no—
156C2×#704—31no—
157C2×#704—31no—
158C2×#704—31no—
159C2×#704—31no—
160D5⋊M16—64no—
161D5⋊M16—64no—
162C2×#700—31no—
163C2×#700—31no—
164C2×#700—31no—
165C2×#700C2×D311yescharacteristic, complemented
166C2×D5⋊C8—31no—
167C2×D5⋊C8—31no—
168C2×D5⋊C8—31no—
169C2×D5⋊C8C2×D311yescharacteristic, complemented
170C2×C5×C4⋊C4—31no—
171C2×#685—31no—
172C2×#685—31no—
173C2×C4×Dic5—31no—
174#4039—31no—
175#4039—31no—
176#4039—31no—
177#4039—31no—
178#4039—31no—
179#4039—31no—
180#4039—31no—
181#4039C2×D311yescharacteristic
182#4004—31no—
183#4004C2×D311yescharacteristic, complemented
184#4003—31no—
185#4003—31no—
186#4003—31no—
187#4003—31no—
188#4003—31no—
189#4003—31no—
190#4003C2×D311yescharacteristic, complemented
191#4003C2×D311yescharacteristic, complemented
192#4002—31no—
193#4002C2×D311yescharacteristic, complemented
194C4⋊#170—31no—
195C4⋊#170—31no—
196C4×#170—31no—
197C4×#170—31no—
198D4×M16—151noSylow
199C22×D15C22×C411yescharacteristic
200C22×D15C22×C411yescharacteristic
201C22×C5×D3C22×C411yescharacteristic
202C22×C3×D5C22×C411yescharacteristic
203C22×C3×D5C22×C411yescharacteristic
204C2×D3×D5—22no—
205C2×D3×D5—22no—
206C2×D3×D5—22no—
207C2×D3×D5—22no—
208C2×D3×D5—41no—
209C2×D3×D5—41no—
210C2×C3×C4×C5C22×C411yescharacteristic
211C2×C3×C4×C5C22×C411yescharacteristic
212C2×C3×C4×C5C22×C411yescharacteristic
213C2×Dic15C22×C411yescharacteristic
214C2×Dic15C22×C411yescharacteristic
215D60—22no—
216C4×D15—22no—
217C4×D15—22no—
218C2×C5×Dic3C22×C411yescharacteristic
219C2×C5×Dic3C22×C411yescharacteristic
220C2×C5×Dic3C22×C411yescharacteristic
221C4×C5×D3—22no—
222C4×C5×D3—22no—
223C4×C5×D3—22no—
224C2×C3×Dic5C22×C411yescharacteristic
225C2×C3×Dic5C2411yescharacteristic
226C3×D20—22no—
227C3×C4×D5—21no—
228C3×C4×D5—21no—
229C3×C4×D5—21no—
230C3×C4×D5—21no—
231#1202—22no—
232#1202M1614yescomplemented
233#1200—21no—
234#1200—21no—
235#1200—21no—
236#1200—21no—
237D3×Dic5—41no—
238D3×Dic5C2×D412yes—
239D3×Dic5#4112yes—
240D5×Dic3—22no—
241D5×Dic3—22no—
242C3⋊#170—21no—
243C3⋊#170—21no—
244C3⋊#170—21no—
245C3⋊#170C2×D412yescomplemented
246C3×#170—21no—
247C3×#170—21no—
248C3×#170—21no—
249C3×#170C2×D412yescomplemented
250C2×D3×D4—51no—
251C22×C4×D3—51no—
252C22×C4×D3—51no—
253C2×C3×M16—51no—
254C22×C3×C8—51no—
255C3×C4×D4—51no—
256D4×Dic3—51no—
257C4×#67—51no—
258C4×#67—51no—
259C2×#208—51no—
260C22×C3⋊C8—51no—
261D3×M16—104no—
262C2×ΓL(1,𝔽25)—51no—
263C2×ΓL(1,𝔽25)—51no—
264C2×ΓL(1,𝔽25)—51no—
265C2×ΓL(1,𝔽25)—51no—
266C2×ΓL(1,𝔽25)—51no—
267C2×ΓL(1,𝔽25)—51no—
268C2×ΓL(1,𝔽25)—104no—
269C2×D3×C8—51no—
270C2×D3×C8—51no—
271#893—51no—
272D3×C4⋊C4AGL(1,𝔽5)11yescharacteristic
273#67⋊C4—51no—
274#67⋊C4—51no—
275D3×C22⋊C4—51no—
276D3×C22⋊C4—51no—
277C4×D12—51no—
278C42×D3—51no—
279C3×C4⋊C8—51no—
280C3×C22⋊C8—51no—
281C3×C22⋊C8—51no—
282C3×#97—51no—
283#830—51no—
284#830—51no—
285(C2×D3)⋊C8—51no—
286(C2×D3)⋊C8—51no—
287(C2×D3)⋊C8—51no—
288(C2×D3)⋊C8—51no—
289Dic3⋊C8—51no—
290Dic3⋊C8—51no—
291C8×Dic3—51no—
292C8×Dic3—51no—
293C4⋊(C3⋊C8)—51no—
294#803—51no—
295C23×D5—31no—
296C23×D5—31no—
297C22×C4×C5—31no—
298C22×C4×C5—31no—
299C22×C4×C5—31no—
300C22×Dic5—31no—
301C22×Dic5—31no—
302C2×D20—31no—
303C2×D20—31no—
304C2×D20—31no—
305C2×D20—64no—
306C2×D20C4×D311yescharacteristic
307C2×C4×D5—31no—
308C2×C4×D5—31no—
309C2×C4×D5—31no—
310C2×C4×D5—31no—
311C2×C4×D5—31no—
312C2×C4×D5—31no—
313C2×C4×D5—62no—
314C2×C4×D5—62no—
315C2×C4×D5—62no—
316C2×C4×D5—62no—
317C2×C4×D5C22×D311yescharacteristic
318C2×C4×D5C22×D311yescharacteristic
319#704—34no—
320#704—62no—
321#704—62no—
322#704—62no—
323C2×#170—31no—
324C2×#170—31no—
325C2×#170—31no—
326C2×#170—31no—
327C2×#170C22×D311yescharacteristic
328C2×#170C22×D311yescharacteristic
329C2×#170C22×D311yescharacteristic
330C2×#170C22×D311yescharacteristic
331#700—22no—
332#700—62no—
333#700—62no—
334#700—62no—
335D5⋊C8—22no—
336D5⋊C8—62no—
337D5⋊C8—62no—
338D5⋊C8—62no—
339C5×C4⋊C4—31no—
340C5×C4⋊C4—31no—
341C5×C4⋊C4—31no—
342C5×C4⋊C4C4×D311yescharacteristic
343#685—31no—
344#685—31no—
345#685—31no—
346#685—31no—
347#685—31no—
348#685—31no—
349#685C4×D311yescharacteristic
350#685C4×D311yescharacteristic
351C4×Dic5—31no—
352C4×Dic5—31no—
353C4×Dic5—31no—
354C4×Dic5C22×D311yescharacteristic
355C22×M16—151no—
356C22×M16—151no—
357C2×C4×D4—151no—
358#436—151no—
359#436—151no—
360#435—51no—
361#435—151no—
362#435—151no—
363#435—151no—
364C8×D4—151no—
365C8×D4—151no—
366#423—151no—
367#407—151no—
368#407—151no—
369C4×M16—151no—
370C22×C3×C5C23×C411yescharacteristic
371C2×D15—21no—
372C2×D15—21no—
373C2×D15—21no—
374C2×D15—21no—
375C2×D15—21no—
376C2×D15C2×M1612yescomplemented
377C2×C5×D3—21no—
378C2×C5×D3—21no—
379C2×C5×D3C4×D412yes—
380C2×C3×D5—21no—
381C2×C3×D5—21no—
382C2×C3×D5—21no—
383C2×C3×D5—21no—
384C2×C3×D5—21no—
385C2×C3×D5C2×M1612yescomplemented
386D3×D5—44no—
387D3×D5—44no—
388C3×C4×C5—21no—
389C3×C4×C5—21no—
390C3×C4×C5—21no—
391Dic15—21no—
392Dic15C4×D412yes—
393C3×Dic5—21no—
394C3×Dic5C22×D411yescharacteristic
395C3×Dic5C2×#4111yescharacteristic
396C5×Dic3—21no—
397C5×Dic3—21no—
398C5×Dic3C2×M1612yescomplemented
399C23×D3—51no—
400C23×D3—51no—
401C2×C3×D4—51no—
402C22×C3×C4—51no—
403C22×C3×C4—51no—
404C2×#67—51no—
405C2×#67—51no—
406C22×Dic3—51no—
407C22×Dic3—51no—
408D3×D4—104no—
409C2×D12—51no—
410C2×C4×D3—51no—
411C2×C4×D3—51no—
412C2×C4×D3—51no—
413C2×C4×D3—51no—
414C2×C4×D3—51no—
415C2×C4×D3—51no—
416C2×C4×D3—102no—
417C2×C4×D3—102no—
418C2×C4×D3—102no—
419C2×C4×D3—102no—
420C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
421C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
422C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
423C3×M16—102no—
424C2×C3×C8—51no—
425C2×C3×C8—51no—
426C2×C3×C8—51no—
427C2×C3×C8—51no—
428C2×C3×C8—102no—
429C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
430C3×C22⋊C4—51no—
431C3×C22⋊C4—51no—
432C3×C42—51no—
433#217—51no—
434#217—51no—
435(C2×D3)⋊C4—51no—
436(C2×D3)⋊C4—51no—
437(C2×D3)⋊C4—51no—
438(C2×D3)⋊C4—51no—
439C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
440Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
441Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
442C4×Dic3—51no—
443C4×Dic3—51no—
444C4×Dic3—51no—
445#208—102no—
446C2×C3⋊C8—51no—
447C2×C3⋊C8—51no—
448C2×C3⋊C8—51no—
449C2×C3⋊C8—51no—
450C2×C3⋊C8—102no—
451ΓL(1,𝔽25)—54no—
452ΓL(1,𝔽25)—102no—
453ΓL(1,𝔽25)—102no—
454ΓL(1,𝔽25)—102no—
455ΓL(1,𝔽25)—102no—
456ΓL(1,𝔽25)—102no—
457D3×C8—102no—
458D3×C8—102no—
459C23×C5—31no—
460C22×D5—31no—
461C22×D5—31no—
462C22×D5—62no—
463C22×D5—62no—
464C22×D5—62no—
465C22×D5—62no—
466C22×D5—121no—
467C22×D5—121no—
468C22×D5C2×C4×D311yescharacteristic
469C22×D5C2×C4×D311yescharacteristic
470C2×C4×C5—31no—
471C2×C4×C5—31no—
472C2×C4×C5—31no—
473C2×C4×C5—62no—
474C2×C4×C5—62no—
475C2×C4×C5—62no—
476C2×C4×C5C2×C4×D311yescharacteristic
477C2×C4×C5C2×C4×D311yescharacteristic
478C2×C4×C5C2×C4×D311yescharacteristic
479C2×Dic5—31no—
480C2×Dic5—32no—
481C2×Dic5—32no—
482C2×Dic5—31no—
483C2×Dic5—121no—
484C2×Dic5C2×C4×D311yescharacteristic
485C2×Dic5C23×D311yescharacteristic
486D20—22no—
487D20—34no—
488D20—62no—
489D20—62no—
490C4×D5—21no—
491C4×D5—21no—
492C4×D5—21no—
493C4×D5—21no—
494C4×D5—62no—
495C4×D5—62no—
496C4×D5—62no—
497C4×D5—62no—
498C4×D5—61no—
499C4×D5—61no—
500C4×D5—61no—
501C4×D5—61no—
502#170—21no—
503#170—21no—
504#170—21no—
505#170—32no—
506#170—61no—
507#170—61no—
508#170—61no—
509#170D3×D412yescomplemented
510C22×D4—151no—
511C23×C4—151no—
512C23×C4—151no—
513C2×M16—51no—
514C2×M16—151no—
515C2×M16—151no—
516C2×M16—151no—
517C2×M16—151no—
518C2×M16—151no—
519C2×M16—151no—
520C2×M16—151no—
521C2×M16—304no—
522C2×M16—304no—
523C22×C8—51no—
524C22×C8—151no—
525C22×C8—151no—
526C22×C8—151no—
527C4×D4—51no—
528C4×D4—151no—
529C4×D4—151no—
530C4×D4—151no—
531C4×D4—151no—
532C4×D4—151no—
533C4×D4—151no—
534C4×D4—151no—
535C2×C4⋊C4—31no—
536C2×C22⋊C4—151no—
537C2×C22⋊C4—151no—
538C2×C42—151no—
539C4⋊C8—51no—
540C4⋊C8—151no—
541C4⋊C8—151no—
542C4⋊C8—151no—
543C22⋊C8—51no—
544C22⋊C8—51no—
545C22⋊C8—151no—
546C22⋊C8—151no—
547C22⋊C8—151no—
548C22⋊C8—151no—
549C22⋊C8—151no—
550C22⋊C8—151no—
551#97—51no—
552#97—151no—
553C4×C8—151no—
554C4×C8—151no—
555C2×C3×C5C2×C4×D411yescharacteristic
556C2×C3×C5C22×M1611yescharacteristic
557C2×C3×C5#56811yescharacteristic
558D15—22no—
559D15—41no—
560C3×D5—22no—
561C3×D5—41no—
562C5×D3—22no—
563C23×C3—51no—
564C23×C3—51no—
565C22×D3—51no—
566C22×D3—51no—
567C22×D3—102no—
568C22×D3—102no—
569C22×D3—102no—
570C22×D3—102no—
571C22×D3—201no—
572C22×D3—201no—
573C22×D3C22×AGL(1,𝔽5)11yescharacteristic
574C3×D4—102no—
575C2×C3×C4—51no—
576C2×C3×C4—51no—
577C2×C3×C4—101no—
578C2×C3×C4—101no—
579C2×C3×C4—101no—
580C2×C3×C4—101no—
581C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
582C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
583C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
584#67—54no—
585#67—102no—
586C2×Dic3—51no—
587C2×Dic3—51no—
588C2×Dic3—102no—
589C2×Dic3—102no—
590C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
591C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
592C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
593D12—102no—
594C4×D3—22no—
595C4×D3—22no—
596C4×D3—22no—
597C4×D3—52no—
598C4×D3—52no—
599C4×D3—101no—
600C4×D3—101no—
601C4×D3—101no—
602C4×D3—101no—
603C4×D3—102no—
604C4×D3—102no—
605C4×D3—201no—
606C3×C8—52no—
607C3×C8—101no—
608C3×C8—101no—
609C3×C8—101no—
610C3⋊C8—52no—
611C3⋊C8—101no—
612C3⋊C8—101no—
613C3⋊C8—101no—
614C22×C5—32no—
615C22×C5—61no—
616C22×C5—61no—
617C22×C5C22×C4×D311yescharacteristic
618C2×D5—21no—
619C2×D5—21no—
620C2×D5—21no—
621C2×D5—21no—
622C2×D5—21no—
623C2×D5—32no—
624C2×D5—61no—
625C2×D5—61no—
626C2×D5—61no—
627C2×D5—61no—
628C2×D5—61no—
629C2×D5—124no—
630C2×D5—124no—
631C2×D5D3×M1612yescomplemented
632C4×C5—21no—
633C4×C5—21no—
634C4×C5—21no—
635C4×C5—32no—
636C4×C5—61no—
637C4×C5—61no—
638Dic5—21no—
639Dic5—32no—
640Dic5—61no—
641Dic5C2×D3×D411yescharacteristic
642Dic5D3×#4111yescharacteristic
643C24—151no—
644C24—151no—
645C2×D4—51no—
646C2×D4—151no—
647C2×D4—151no—
648C2×D4—151no—
649C2×D4—304no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—31no—
653C22×C4—51no—
654C22×C4—51no—
655C22×C4—151no—
656C22×C4—151no—
657C22×C4—151no—
658C22×C4—151no—
659C22×C4—151no—
660C22×C4—151no—
661C22×C4—151no—
662C22×C4—151no—
663C22×C4—302no—
664C22×C4—302no—
665C22×C4—302no—
666C22×C4—302no—
667M16—102no—
668M16—154no—
669M16—302no—
670M16—302no—
671M16—302no—
672M16—302no—
673M16—302no—
674M16—302no—
675C2×C8—51no—
676C2×C8—51no—
677C2×C8—51no—
678C2×C8—51no—
679C2×C8—102no—
680C2×C8—151no—
681C2×C8—151no—
682C2×C8—151no—
683C2×C8—151no—
684C2×C8—302no—
685C2×C8—302no—
686C2×C8—302no—
687C4⋊C4—31no—
688C4⋊C4—31no—
689C4⋊C4—31no—
690C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
691C22⋊C4—51no—
692C22⋊C4—51no—
693C22⋊C4—151no—
694C22⋊C4—151no—
695C22⋊C4—151no—
696C22⋊C4—151no—
697C22⋊C4—151no—
698C22⋊C4—151no—
699C42—51no—
700C42—151no—
701C42—151no—
702C42—151no—
703C3×C5D4×M1611yescharacteristic, complemented, Hall
704C22×C3—52no—
705C22×C3—101no—
706C22×C3—101no—
707C22×C3—101no—
708C22×C3—101no—
709C22×C3—101no—
710C22×C3C23×AGL(1,𝔽5)11yescharacteristic
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—52no—
714C2×D3—101no—
715C2×D3—101no—
716C2×D3—101no—
717C2×D3—101no—
718C2×D3—101no—
719C2×D3—204no—
720C2×D3—204no—
721C2×D3D4×AGL(1,𝔽5)12yes—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—51no—
726C3×C4—51no—
727C3×C4—101no—
728Dic3—21no—
729Dic3—21no—
730Dic3—52no—
731Dic3—101no—
732Dic3D5⋊M1612yescomplemented
733C2×C5—62no—
734C2×C5C4×D3×D411yescharacteristic
735C2×C5C2×D3×M1611yescharacteristic
736C2×C5#575011yescharacteristic
737D5—22no—
738D5—41no—
739D5—62no—
740D5—121no—
741C23—31no—
742C23—51no—
743C23—51no—
744C23—151no—
745C23—151no—
746C23—302no—
747C23—302no—
748C23—302no—
749C23—302no—
750C23—601no—
751C23—601no—
752D4—102no—
753D4—154no—
754D4—302no—
755D4—302no—
756C2×C4—31no—
757C2×C4—31no—
758C2×C4—31no—
759C2×C4—51no—
760C2×C4—51no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—101no—
765C2×C4—101no—
766C2×C4—101no—
767C2×C4—101no—
768C2×C4—152no—
769C2×C4—152no—
770C2×C4—151no—
771C2×C4—151no—
772C2×C4—302no—
773C2×C4—302no—
774C2×C4—301no—
775C2×C4—301no—
776C2×C4—301no—
777C2×C4—301no—
778C2×C4—302no—
779C2×C4—302no—
780C2×C4—601no—
781C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
782C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
783C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
784C8—52no—
785C8—101no—
786C8—101no—
787C8—101no—
788C8—152no—
789C8—301no—
790C8—301no—
791C8—301no—
792C2×C3—102no—
793C2×C3—201no—
794C2×C3C2×D5⋊M1611yescharacteristic
795C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
796C2×C3#6626011yescharacteristic
797D3—22no—
798D3—102no—
799D3—201no—
800C5#7948311yescharacteristic, complemented, Sylow
801C22—32no—
802C22—52no—
803C22—61no—
804C22—61no—
805C22—101no—
806C22—101no—
807C22—101no—
808C22—101no—
809C22—101no—
810C22—152no—
811C22—301no—
812C22—301no—
813C22—301no—
814C22—301no—
815C22—301no—
816C22—604no—
817C22—604no—
818C22C22×D3×AGL(1,𝔽5)11yescharacteristic
819C4—21no—
820C4—21no—
821C4—21no—
822C4—32no—
823C4—51no—
824C4—51no—
825C4—61no—
826C4—61no—
827C4—101no—
828C4—152no—
829C4—301no—
830C3#1061708411yescharacteristic, complemented, Sylow
831C2—62no—
832C2—102no—
833C2—201no—
834C2—302no—
835C2—601no—
836C2D3×D5⋊M1611yescharacteristic
837C2D3×D4×AGL(1,𝔽5)11yescharacteristic
838C2#1175685111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radicalC2×D3×D20C4
cosocleC2×C3×Dic5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5D4×M16
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D5⋊ΓL(1,𝔽25)C2semidirect
2. C2×#91915C2semidirect
4. #11752363C2semidirect
5. C3×#65704C2semidirect
6. #11751920C2semidirect
7. #11751919C2semidirect
8. #11751919C2semidirect
9. #11751907C2semidirect
10. #11751905C2semidirect
11. #11751894C2semidirect
12. #11751882C2semidirect
13. #11751881C2semidirect
14. #11751779C2semidirect
15. #11751763C2semidirect
20. C2×#6758C22semidirect
21. C2×D5⋊(C3⋊C8)C22semidirect
22. C2×C3×#700C22semidirect
23. C2×C3×D5⋊C8C22semidirect
24. C2×#6740C22semidirect
25. C2×#6740C22semidirect
30. C2×#6738C22semidirect
31. C2×#6738C22semidirect
46. #91233C22semidirect
47. #91232C22semidirect
48. #91232C22semidirect
49. #91231C22semidirect
50. C3×#4004C22semidirect
51. C3×#4003C22semidirect
52. C3×#4003C22semidirect
53. C3×#4002C22semidirect
54. Dic3⋊#170C22semidirect
55. Dic3⋊#170C22semidirect
56. #91171C22semidirect
57. #91171C22semidirect
58. #91171C22semidirect
59. #91171C22semidirect
60. Dic3×#170C22semidirect
61. Dic3×#170C22semidirect
75. #65704D3semidirect
119. #6739D4semidirect
165. C2×#700C2×D3semidirect
169. C2×D5⋊C8C2×D3semidirect
183. #4004C2×D3semidirect
190. #4003C2×D3semidirect
191. #4003C2×D3semidirect
193. #4002C2×D3semidirect
232. #1202M16semidirect
245. C3⋊#170C2×D4semidirect
249. C3×#170C2×D4semidirect
376. C2×D15C2×M16semidirect
385. C2×C3×D5C2×M16semidirect
398. C5×Dic3C2×M16semidirect
509. #170D3×D4semidirect
631. C2×D5D3×M16semidirect
703. C3×C5D4×M16semidirect
732. Dic3D5⋊M16semidirect
800. C5#79483semidirect
830. C3#10617084semidirect

Maximal subgroups

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

subgroupindex
C2×D5⋊ΓL(1,𝔽25)2
C2×#919152
D3×#40392
#117523632
C3×#657042
#117519202
#117519192
#117519072
#117519052
#117518942
#117518822
#117518812
#117517792
#117517632
#106170843
#794835