Finite Group Databasebeta

← #14415777

Subgroups — #14415777

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
1C22×#6739C211yesmaximal, characteristic, complemented
2C2×D5⋊ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
3D3×#4027C211yesmaximal, characteristic
4#11752351C211yesmaximal, characteristic, complemented
5C3×#65692C211yesmaximal, characteristic, complemented
6#11752054C211yesmaximal, characteristic, complemented
7#11752051C211yesmaximal, characteristic, complemented
8#11752046C211yesmaximal, characteristic, complemented
9#11751926C211yesmaximal, characteristic, complemented
10#11751924C211yesmaximal, characteristic, complemented
11#11751920C211yesmaximal, characteristic, complemented
12#11751919C211yesmaximal, characteristic, complemented
13#11751912C211yesmaximal, characteristic, complemented
14#11751909C211yesmaximal, characteristic, complemented
15C4×#6739C211yesmaximal, characteristic, complemented
16#10617060—31nomaximal, Hall
17C2×D3×C22⋊D5C411yescharacteristic
18C22×D3×Dic5C2211yescharacteristic
19C2×C4×D3×D5C2211yescharacteristic
20C22×C3⋊#170C2211yescharacteristic, complemented
21C2×D5⋊(C3⋊C8)C2211yescharacteristic, complemented
22C22×C3×#170C2211yescharacteristic, complemented
23C2×C3×D5⋊C8C2211yescharacteristic, complemented
24C2×#6740C2211yescharacteristic, complemented
25C2×#6740C2211yescharacteristic, complemented
26C2×#6739—24no—
27C2×#6739C2211yescharacteristic
28C2×#6739C2211yescharacteristic
29C2×#6739C2211yescharacteristic
30C2×#6739C2211yescharacteristic
31C2×#6739C2211yescharacteristic, complemented
32C2×#6739C2211yescharacteristic, complemented
33D5⋊ΓL(1,𝔽25)—24no—
34#91770C411yescharacteristic
35C5×D3×C22⋊C4C411yescharacteristic
36C3×#4027C2211yescharacteristic
37#91559C411yescharacteristic
38#91552C2211yescharacteristic
39D3×#685C411yescharacteristic
40#91442C411yescharacteristic
41#91440C2211yescharacteristic
42#91406C411yescharacteristic
43#91405C2211yescharacteristic
44D3×#683C411yescharacteristic
45C4×D3×Dic5C2211yescharacteristic
46#91241C2211yescharacteristic, complemented
47#91233C2211yescharacteristic, complemented
48#91232C2211yescharacteristic, complemented
49C4×C3⋊#170C2211yescharacteristic, complemented
50C3×C22⋊#170C2211yescharacteristic, complemented
51C3×#4004C2211yescharacteristic, complemented
52C3×#4003C2211yescharacteristic, complemented
53C3×C4×#170C2211yescharacteristic, complemented
54Dic3⋊#170C2211yescharacteristic, complemented
55Dic3⋊#170C2211yescharacteristic, complemented
56#91171C2211yescharacteristic, complemented
57#91171C2211yescharacteristic, complemented
58(C2×D3)⋊#170C2211yescharacteristic, complemented
59(C2×D3)⋊#170C2211yescharacteristic, complemented
60#91169C2211yescharacteristic, complemented
61#91169C2211yescharacteristic, complemented
62D4×ΓL(1,𝔽25)—51nomaximal, Hall
63C22×#704—31no—
64C2×D5⋊M16—31no—
65C2×#4027—31no—
66#65798—31no—
67#65758—31no—
68#65755—31no—
69C4×#704—31no—
70#65695—31no—
71#65695—31no—
72#65694—31no—
73#65694—31no—
74#65693—31no—
75#65693—31no—
76#65692—31no—
77#65692D311yescharacteristic, complemented
78C23×C5×D3C2×C411yescharacteristic
79C22×D3×D5C2×C411yescharacteristic
80C2×#1220C2×C411yescharacteristic
81C22×Dic15C2×C411yescharacteristic
82C2×C4×D15C2×C411yescharacteristic
83C2×C4×C5×D3C2×C411yescharacteristic
84C2×C4×C5×D3C2×C411yescharacteristic
85C2×C3×C22⋊D5C2×C411yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C2×C3×C4×D5C2311yescharacteristic
88D3×C22⋊D5—24no—
89C2×#1203C2×C411yescharacteristic
90C2×#1201C2×C411yescharacteristic
91C2×#1200C2311yescharacteristic
92C2×D3×Dic5—22no—
93C2×D3×Dic5—22no—
94C2×D3×Dic5C2×C411yescharacteristic
95C2×D3×Dic5C2×C411yescharacteristic
96C2×D3×Dic5C2×C411yescharacteristic
97C2×D3×Dic5C2311yescharacteristic
98C2×D3×Dic5C2311yescharacteristic
99C2×D5×Dic3C2×C411yescharacteristic
100C4×D3×D5—22no—
101C4×D3×D5—22no—
102C2×C3⋊#170—22no—
103C2×C3⋊#170C2311yescharacteristic
104C2×C3⋊#170C2311yescharacteristic
105C2×C3⋊#170C2311yescharacteristic
106C2×C3⋊#170C2311yescharacteristic
107D5⋊(C3⋊C8)—22no—
108C2×C3×#170—22no—
109C2×C3×#170C2311yescharacteristic
110C2×C3×#170C2311yescharacteristic
111C2×C3×#170C2311yescharacteristic
112C2×C3×#170C2311yescharacteristic
113C3×D5⋊C8—22no—
114#6740—22no—
115#6740—22no—
116#6739—22no—
117#6739—22no—
118#6739—22no—
119#6739—22no—
120#6739—22no—
121#6739D414yescomplemented
122C3×C5×C22⋊C4C2×C411yescharacteristic
123#6714C2×C411yescharacteristic
124#6712C2×C411yescharacteristic
125C4×Dic15C2×C411yescharacteristic
126C5×#217C2×C411yescharacteristic
127C5×(C2×D3)⋊C4C2×C411yescharacteristic
128C5×(C2×D3)⋊C4C2×C411yescharacteristic
129C3×#685C2×C411yescharacteristic
130C3×#683C2×C411yescharacteristic
131C3×C4×Dic5C2311yescharacteristic
132#6669C2×C411yescharacteristic
133#6668C2×C411yescharacteristic
134#6667C2×C411yescharacteristic
135#6665C2×C411yescharacteristic
136Dic3×Dic5C2×C411yescharacteristic
137Dic3×Dic5C2311yescharacteristic
138C22×ΓL(1,𝔽25)—51no—
139C22×ΓL(1,𝔽25)—51no—
140C4×D3×D4—51no—
141C3×C8×D4—51no—
142#5111—51no—
143#5111—51no—
144D4×C3⋊C8—51no—
145#4838—51no—
146#4837—51no—
147#4730—51no—
148#4730—51no—
149#4726—51no—
150#4726—51no—
151#4688—51no—
152C4×ΓL(1,𝔽25)—51no—
153C22×C22⋊D5—31no—
154C23×Dic5—31no—
155C22×C4×D5—31no—
156C2×#704—31no—
157C2×#704—31no—
158C2×#704—31no—
159C2×#704—31no—
160C2×#704—31no—
161C2×#704—31no—
162C2×#704—64no—
163C22×#170—31no—
164C22×#170C2×D311yescharacteristic, complemented
165D5⋊M16—64no—
166C2×#700—31no—
167C2×#700—31no—
168C2×D5⋊C8—31no—
169C2×D5⋊C8C2×D311yescharacteristic, complemented
170C2×C5×C22⋊C4—31no—
171C2×#685—31no—
172C2×#683—31no—
173C2×C4×Dic5—31no—
174#4027—31no—
175#4027—31no—
176#4027—31no—
177#4027—31no—
178#4027—31no—
179#4027—31no—
180#4027—31no—
181#4027C2×D311yescharacteristic
182C22⋊#170—31no—
183C22⋊#170—31no—
184C22⋊#170—31no—
185C22⋊#170C2×D311yescharacteristic, complemented
186#4004—31no—
187#4004C2×D311yescharacteristic, complemented
188#4003—31no—
189#4003—31no—
190#4003—31no—
191#4003C2×D311yescharacteristic, complemented
192#4002—31no—
193#4002—31no—
194C4⋊#170—31no—
195C4⋊#170—31no—
196C4×#170—31no—
197C4×#170C2×D311yescharacteristic, complemented
198D4×M16—151noSylow
199C23×C3×C5C22×C411yescharacteristic
200C22×D15C22×C411yescharacteristic
201C22×C5×D3—22no—
202C22×C5×D3—22no—
203C22×C5×D3—41no—
204C22×C5×D3C22×C411yescharacteristic
205C22×C5×D3C22×C411yescharacteristic
206C22×C3×D5C22×C411yescharacteristic
207C2×D3×D5—22no—
208C2×D3×D5—22no—
209C2×D3×D5—41no—
210C2×C3×C4×C5C22×C411yescharacteristic
211C2×C3×C4×C5C22×C411yescharacteristic
212#1220—22no—
213C2×Dic15—22no—
214C2×Dic15C22×C411yescharacteristic
215C2×Dic15C22×C411yescharacteristic
216C2×Dic15C22×C411yescharacteristic
217C4×D15—22no—
218C2×C5×Dic3C22×C411yescharacteristic
219C2×C5×Dic3C22×C411yescharacteristic
220C4×C5×D3—22no—
221C4×C5×D3—41no—
222C3×C22⋊D5M1614yescomplemented
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5C22×C411yescharacteristic
226C2×C3×Dic5C22×C411yescharacteristic
227C2×C3×Dic5C2411yescharacteristic
228C3×C4×D5—21no—
229C3×C4×D5—21no—
230#1203—22no—
231#1201—22no—
232#1200—21no—
233#1200—21no—
234D3×Dic5—22no—
235D3×Dic5—22no—
236D3×Dic5—22no—
237D3×Dic5—21no—
238D3×Dic5—21no—
239D3×Dic5C2×D412yes—
240D3×Dic5#4112yes—
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—
253C22×C3×C8—51no—
254C22×C3×C8—51no—
255C3×C4×D4—51no—
256D4×Dic3—51no—
257C4×#67—51no—
258C4×#67—51no—
259C22×C3⋊C8—51no—
260C22×C3⋊C8—51no—
261C2×ΓL(1,𝔽25)—51no—
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)—51no—
269C2×ΓL(1,𝔽25)—104no—
270C2×ΓL(1,𝔽25)—104no—
271#893—51no—
272D3×C4⋊C4—51no—
273#67⋊C4—51no—
274#67⋊C4—51no—
275D3×C22⋊C4—51no—
276D3×C22⋊C4AGL(1,𝔽5)11yescharacteristic
277C4×D12—51no—
278C42×D3—51no—
279C3×C4⋊C8—51no—
280C3×C22⋊C8—51no—
281C3×C22⋊C8—51no—
282C3×C4×C8—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—
289#815—51no—
290#815—51no—
291Dic3⋊C8—51no—
292Dic3⋊C8—51no—
293C4⋊(C3⋊C8)—51no—
294C4×C3⋊C8—51no—
295C24×C5—31no—
296C23×D5—31no—
297C22×C4×C5—31no—
298C22×C4×C5—31no—
299C2×C22⋊D5—31no—
300C2×C22⋊D5—31no—
301C2×C22⋊D5—31no—
302C2×C22⋊D5—64no—
303C2×C22⋊D5C4×D311yescharacteristic
304C22×Dic5—31no—
305C22×Dic5—31no—
306C22×Dic5—31no—
307C22×Dic5—31no—
308C22×Dic5—31no—
309C22×Dic5—31no—
310C22×Dic5—62no—
311C22×Dic5—62no—
312C22×Dic5C22×D311yescharacteristic
313C2×C4×D5—31no—
314C2×C4×D5—31no—
315C2×C4×D5—31no—
316C2×C4×D5—62no—
317C2×C4×D5—62no—
318C2×C4×D5C22×D311yescharacteristic
319#704—34no—
320#704—62no—
321#704—62no—
322#704—62no—
323#704—62no—
324#704—62no—
325C2×#170—22no—
326C2×#170—31no—
327C2×#170—31no—
328C2×#170—31no—
329C2×#170—31no—
330C2×#170—62no—
331C2×#170C22×D311yescharacteristic
332C2×#170C22×D311yescharacteristic
333C2×#170C22×D311yescharacteristic
334C2×#170C22×D311yescharacteristic
335#700—62no—
336#700—62no—
337D5⋊C8—22no—
338D5⋊C8—62no—
339C5×C22⋊C4—31no—
340C5×C22⋊C4—31no—
341C5×C22⋊C4—31no—
342C5×C22⋊C4C4×D311yescharacteristic
343#685—31no—
344#685—31no—
345#685—31no—
346#685C4×D311yescharacteristic
347#683—31no—
348#683—31no—
349#683—31no—
350#683C4×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—151no—
361#435—151no—
362#435—151no—
363#435—151no—
364C8×D4—51no—
365C8×D4—151no—
366#423—151no—
367#407—151no—
368#407—151no—
369C4×M16—151no—
370C22×C3×C5—21no—
371C22×C3×C5—21no—
372C22×C3×C5C2×M1612yescomplemented
373C22×C3×C5C23×C411yescharacteristic
374C2×D15—21no—
375C2×D15—21no—
376C2×D15—21no—
377C2×C5×D3—21no—
378C2×C5×D3—21no—
379C2×C5×D3—21no—
380C2×C5×D3—21no—
381C2×C5×D3—21no—
382C2×C5×D3—44no—
383C2×C5×D3C4×D412yes—
384C2×C3×D5—21no—
385C2×C3×D5—21no—
386C2×C3×D5C2×M1612yescomplemented
387D3×D5—44no—
388C3×C4×C5—21no—
389C3×C4×C5—21no—
390Dic15—21no—
391Dic15—21no—
392Dic15C4×D412yes—
393C3×Dic5—21no—
394C3×Dic5C2×M1612yescomplemented
395C3×Dic5C22×D411yescharacteristic
396C3×Dic5C2×#4111yescharacteristic
397C5×Dic3—21no—
398C5×Dic3—21no—
399C23×D3—51no—
400C23×D3C2×AGL(1,𝔽5)11yescharacteristic
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—51no—
417C2×C4×D3—102no—
418C2×C4×D3—102no—
419C2×C4×D3—102no—
420C2×C4×D3—102no—
421C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
422C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
423C2×C3×C8—51no—
424C2×C3×C8—51no—
425C2×C3×C8—51no—
426C2×C3×C8—51no—
427C2×C3×C8—102no—
428C2×C3×C8—102no—
429C3×C4⋊C4—51no—
430C3×C22⋊C4—51no—
431C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
432C3×C42—51no—
433#217—51no—
434#217C2×AGL(1,𝔽5)11yescharacteristic
435(C2×D3)⋊C4—51no—
436(C2×D3)⋊C4—51no—
437(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
438(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
439C4⋊Dic3—51no—
440Dic3⋊C4—51no—
441Dic3⋊C4—51no—
442C4×Dic3—51no—
443C4×Dic3—51no—
444C4×Dic3—51no—
445C2×C3⋊C8—51no—
446C2×C3⋊C8—51no—
447C2×C3⋊C8—51no—
448C2×C3⋊C8—51no—
449C2×C3⋊C8—102no—
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—
457ΓL(1,𝔽25)—102no—
458ΓL(1,𝔽25)—102no—
459C23×C5—31no—
460C23×C5—31no—
461C23×C5—62no—
462C23×C5—62no—
463C23×C5—121no—
464C23×C5C2×C4×D311yescharacteristic
465C22×D5—31no—
466C22×D5—62no—
467C22×D5—62no—
468C22×D5—121no—
469C22×D5C2×C4×D311yescharacteristic
470C2×C4×C5—31no—
471C2×C4×C5—31no—
472C2×C4×C5—62no—
473C2×C4×C5—121no—
474C2×C4×C5C2×C4×D311yescharacteristic
475C2×C4×C5C2×C4×D311yescharacteristic
476C22⋊D5—62no—
477C22⋊D5—62no—
478C22⋊D5—62no—
479C22⋊D5ΓL(1,𝔽25)14yescomplemented
480C2×Dic5—21no—
481C2×Dic5—21no—
482C2×Dic5—31no—
483C2×Dic5—32no—
484C2×Dic5—32no—
485C2×Dic5—31no—
486C2×Dic5—31no—
487C2×Dic5—62no—
488C2×Dic5—62no—
489C2×Dic5—62no—
490C2×Dic5—62no—
491C2×Dic5—61no—
492C2×Dic5—61no—
493C2×Dic5C2×C4×D311yescharacteristic
494C2×Dic5C2×C4×D311yescharacteristic
495C2×Dic5C23×D311yescharacteristic
496C4×D5—21no—
497C4×D5—21no—
498C4×D5—62no—
499C4×D5—62no—
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—151no—
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—51no—
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—151no—
536C2×C22⋊C4—31no—
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—151no—
552#97—151no—
553C4×C8—51no—
554C4×C8—151no—
555C2×C3×C5—22no—
556C2×C3×C5C2×C4×D411yescharacteristic
557C2×C3×C5C22×M1611yescharacteristic
558C2×C3×C5#56811yescharacteristic
559D15—41no—
560C3×D5—22no—
561C5×D3—22no—
562C5×D3—41no—
563C23×C3—51no—
564C23×C3C22×AGL(1,𝔽5)11yescharacteristic
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—41no—
568C22×D3—51no—
569C22×D3—102no—
570C22×D3—102no—
571C22×D3—201no—
572C22×D3C22×AGL(1,𝔽5)11yescharacteristic
573C22×D3C22×AGL(1,𝔽5)11yescharacteristic
574C3×D4—54no—
575C2×C3×C4—51no—
576C2×C3×C4—51no—
577C2×C3×C4—51no—
578C2×C3×C4—101no—
579C2×C3×C4—101no—
580C2×C3×C4—101no—
581C2×C3×C4—101no—
582C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
583C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
584#67—102no—
585#67—102no—
586C2×Dic3—51no—
587C2×Dic3—51no—
588C2×Dic3—51no—
589C2×Dic3—102no—
590C2×Dic3—102no—
591C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
592C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
593D12—102no—
594C4×D3—22no—
595C4×D3—41no—
596C4×D3—52no—
597C4×D3—52no—
598C4×D3—101no—
599C4×D3—101no—
600C4×D3—102no—
601C4×D3—102no—
602C4×D3—101no—
603C4×D3—101no—
604C4×D3—102no—
605C4×D3—102no—
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—21no—
615C22×C5—21no—
616C22×C5—32no—
617C22×C5—61no—
618C22×C5—61no—
619C22×C5—61no—
620C22×C5—61no—
621C22×C5—61no—
622C22×C5—124no—
623C22×C5C2×ΓL(1,𝔽25)12yescomplemented
624C22×C5C22×C4×D311yescharacteristic
625C2×D5—21no—
626C2×D5—21no—
627C2×D5—61no—
628C2×D5—61no—
629C2×D5—61no—
630C2×D5—124no—
631C2×D5C2×ΓL(1,𝔽25)12yescomplemented
632C4×C5—21no—
633C4×C5—21no—
634C4×C5—61no—
635C4×C5—61no—
636Dic5—21no—
637Dic5—32no—
638Dic5—61no—
639Dic5—61no—
640Dic5C2×ΓL(1,𝔽25)12yescomplemented
641Dic5C2×D3×D411yescharacteristic
642Dic5D3×#4111yescharacteristic
643C24—31no—
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—51no—
653C22×C4—51no—
654C22×C4—151no—
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—154no—
668M16—302no—
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—102no—
681C2×C8—151no—
682C2×C8—151no—
683C2×C8—151no—
684C2×C8—151no—
685C2×C8—302no—
686C2×C8—302no—
687C4⋊C4—51no—
688C4⋊C4—151no—
689C4⋊C4—151no—
690C4⋊C4—151no—
691C22⋊C4—31no—
692C22⋊C4—31no—
693C22⋊C4—31no—
694C22⋊C4—51no—
695C22⋊C4—151no—
696C22⋊C4—151no—
697C22⋊C4—151no—
698C22⋊C4D3×AGL(1,𝔽5)11yescharacteristic
699C42—51no—
700C42—151no—
701C42—151no—
702C42—151no—
703C3×C5D4×M1611yescharacteristic, complemented, Hall
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—52no—
707C22×C3—101no—
708C22×C3—101no—
709C22×C3D5⋊M1612yescomplemented
710C22×C3C23×AGL(1,𝔽5)11yescharacteristic
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—21no—
714C2×D3—21no—
715C2×D3—21no—
716C2×D3—44no—
717C2×D3—101no—
718C2×D3—101no—
719C2×D3—101no—
720C2×D3—204no—
721C2×D3D4×AGL(1,𝔽5)12yes—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—52no—
725C3×C4—51no—
726C3×C4—51no—
727C3×C4—101no—
728Dic3—21no—
729Dic3—21no—
730Dic3—52no—
731Dic3—101no—
732Dic3—101no—
733C2×C5—22no—
734C2×C5—62no—
735C2×C5—121no—
736C2×C5C4×D3×D411yescharacteristic
737C2×C5C22×ΓL(1,𝔽25)11yescharacteristic
738C2×C5#575011yescharacteristic
739D5—22no—
740D5—121no—
741C23—31no—
742C23—31no—
743C23—51no—
744C23—62no—
745C23—62no—
746C23—121no—
747C23—151no—
748C23—302no—
749C23—302no—
750C23—601no—
751C23C2×D3×AGL(1,𝔽5)11yescharacteristic
752D4—54no—
753D4—302no—
754D4—302no—
755D4—302no—
756C2×C4—31no—
757C2×C4—31no—
758C2×C4—51no—
759C2×C4—51no—
760C2×C4—51no—
761C2×C4—62no—
762C2×C4—101no—
763C2×C4—101no—
764C2×C4—101no—
765C2×C4—101no—
766C2×C4—121no—
767C2×C4—152no—
768C2×C4—152no—
769C2×C4—151no—
770C2×C4—151no—
771C2×C4—151no—
772C2×C4—302no—
773C2×C4—301no—
774C2×C4—301no—
775C2×C4—301no—
776C2×C4—301no—
777C2×C4—302no—
778C2×C4—302no—
779C2×C4—302no—
780C2×C4—302no—
781C2×C4—302no—
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—22no—
793C2×C3—102no—
794C2×C3C2×D5⋊M1611yescharacteristic
795C2×C3#6625611yescharacteristic
796C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
797D3—22no—
798D3—41no—
799D3—201no—
800C5D4×ΓL(1,𝔽25)11yescharacteristic, complemented, Sylow
801C22—21no—
802C22—21no—
803C22—32no—
804C22—52no—
805C22—61no—
806C22—61no—
807C22—61no—
808C22—61no—
809C22—61no—
810C22—101no—
811C22—101no—
812C22—124no—
813C22—301no—
814C22—301no—
815C22—301no—
816C22—604no—
817C22D5⋊ΓL(1,𝔽25)12yescomplemented
818C22C22×D3×AGL(1,𝔽5)11yescharacteristic
819C4—21no—
820C4—21no—
821C4—52no—
822C4—51no—
823C4—51no—
824C4—61no—
825C4—61no—
826C4—101no—
827C4—152no—
828C4—301no—
829C4—301no—
830C3#1061706011yescharacteristic, complemented, Sylow
831C2—22no—
832C2—62no—
833C2—102no—
834C2—121no—
835C2—601no—
836C2C2×D5⋊ΓL(1,𝔽25)11yescharacteristic
837C2#1175684111yescharacteristic
838C2D3×D4×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C22⋊C4C2×C4
prime radicalC2×D3×C22⋊D5C4
cosocleC2×C3×Dic5C24
hypercenterC22⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5D4×M16
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6739C2semidirect
2. C2×D5⋊ΓL(1,𝔽25)C2semidirect
4. #11752351C2semidirect
5. C3×#65692C2semidirect
6. #11752054C2semidirect
7. #11752051C2semidirect
8. #11752046C2semidirect
9. #11751926C2semidirect
10. #11751924C2semidirect
11. #11751920C2semidirect
12. #11751919C2semidirect
13. #11751912C2semidirect
14. #11751909C2semidirect
15. C4×#6739C2semidirect
20. C22×C3⋊#170C22semidirect
21. C2×D5⋊(C3⋊C8)C22semidirect
22. C22×C3×#170C22semidirect
23. C2×C3×D5⋊C8C22semidirect
24. C2×#6740C22semidirect
25. C2×#6740C22semidirect
31. C2×#6739C22semidirect
32. C2×#6739C22semidirect
46. #91241C22semidirect
47. #91233C22semidirect
48. #91232C22semidirect
49. C4×C3⋊#170C22semidirect
50. C3×C22⋊#170C22semidirect
51. C3×#4004C22semidirect
52. C3×#4003C22semidirect
53. C3×C4×#170C22semidirect
54. Dic3⋊#170C22semidirect
55. Dic3⋊#170C22semidirect
56. #91171C22semidirect
57. #91171C22semidirect
58. (C2×D3)⋊#170C22semidirect
59. (C2×D3)⋊#170C22semidirect
60. #91169C22semidirect
61. #91169C22semidirect
77. #65692D3semidirect
121. #6739D4semidirect
164. C22×#170C2×D3semidirect
169. C2×D5⋊C8C2×D3semidirect
185. C22⋊#170C2×D3semidirect
187. #4004C2×D3semidirect
191. #4003C2×D3semidirect
197. C4×#170C2×D3semidirect
222. C3×C22⋊D5M16semidirect
245. C3⋊#170C2×D4semidirect
249. C3×#170C2×D4semidirect
372. C22×C3×C5C2×M16semidirect
386. C2×C3×D5C2×M16semidirect
394. C3×Dic5C2×M16semidirect
479. C22⋊D5ΓL(1,𝔽25)semidirect
509. #170D3×D4semidirect
623. C22×C5C2×ΓL(1,𝔽25)semidirect
631. C2×D5C2×ΓL(1,𝔽25)semidirect
640. Dic5C2×ΓL(1,𝔽25)semidirect
703. C3×C5D4×M16semidirect
709. C22×C3D5⋊M16semidirect
800. C5D4×ΓL(1,𝔽25)semidirect
817. C22D5⋊ΓL(1,𝔽25)semidirect
830. C3#10617060semidirect

Maximal subgroups

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

subgroupindex
C22×#67392
C2×D5⋊ΓL(1,𝔽25)2
D3×#40272
#117523512
C3×#656922
#117520542
#117520512
#117520462
#117519262
#117519242
#117519202
#117519192
#117519122
#117519092
C4×#67392
#106170603
D4×ΓL(1,𝔽25)5