Finite Group Databasebeta

← C22⋊D5×ΓL(1,𝔽25) #14415716

Subgroups — C22⋊D5×ΓL(1,𝔽25) #14415716

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×C5×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
2C4×D3×C22⋊D5C211yesmaximal, characteristic
3C2×D5×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
4#11751212C211yesmaximal, characteristic, complemented
5C3×C8×C22⋊D5C211yesmaximal, characteristic, complemented
6#11748506C211yesmaximal, characteristic, complemented
7#11748505C211yesmaximal, characteristic, complemented
8C3⋊C8×C22⋊D5C211yesmaximal, characteristic, complemented
9#11748102C211yesmaximal, characteristic, complemented
10#11747709C211yesmaximal, characteristic, complemented
11#11747707C211yesmaximal, characteristic, complemented
12#11747703C211yesmaximal, characteristic, complemented
13#11747701C211yesmaximal, characteristic, complemented
14#11747590C211yesmaximal, characteristic, complemented
15Dic5×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
16M16×C22⋊D5—31nomaximal, Hall
17C22×C4×C5×D3C2211yescharacteristic
18C2×D3×C22⋊D5C411yescharacteristic
19C2×C4×D3×D5C2211yescharacteristic
20C22×C3×C5×C8C2211yescharacteristic, complemented
21C4×#1220C2211yescharacteristic
22C2×#6705C2211yescharacteristic, complemented
23C22×C5×C3⋊C8C2211yescharacteristic, complemented
24C2×C5×ΓL(1,𝔽25)—24no—
25C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
26C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
27C2×C5×ΓL(1,𝔽25)C2211yescharacteristic, complemented
28C2×C5×ΓL(1,𝔽25)C2211yescharacteristic, complemented
29C3×C4×C22⋊D5C2211yescharacteristic
30C2×C3×C8×D5C2211yescharacteristic, complemented
31#91556C411yescharacteristic
32D3×C22⋊Dic5C411yescharacteristic
33Dic3×C22⋊D5C411yescharacteristic
34D3×#685C411yescharacteristic
35#91446C411yescharacteristic
36C4×#1203C2211yescharacteristic
37#91441C411yescharacteristic
38C4×#1201C2211yescharacteristic
39D3×#683C411yescharacteristic
40C4×D3×Dic5C2211yescharacteristic
41C2×#6651C2211yescharacteristic, complemented
42C2×#6650C2211yescharacteristic
43C2×#6650C2211yescharacteristic
44C2×D5×C3⋊C8C2211yescharacteristic, complemented
45D5×ΓL(1,𝔽25)—24no—
46#91114C2211yescharacteristic, complemented
47#91104C2211yescharacteristic, complemented
48#91099C2211yescharacteristic, complemented
49#91098C2211yescharacteristic, complemented
50C3×C22⋊#168C2211yescharacteristic, complemented
51C3×#3952C2211yescharacteristic, complemented
52C3×#3946C2211yescharacteristic, complemented
53C3×C8×Dic5C2211yescharacteristic, complemented
54#90983C2211yescharacteristic, complemented
55#90982C2211yescharacteristic, complemented
56#90957C2211yescharacteristic, complemented
57(C2×D3)⋊#168C2211yescharacteristic, complemented
58(C2×D3)⋊#168C2211yescharacteristic, complemented
59#90955C2211yescharacteristic, complemented
60#90954C2211yescharacteristic, complemented
61Dic5×C3⋊C8C2211yescharacteristic, complemented
62D4×ΓL(1,𝔽25)—51nomaximal, Hall
63C22×C5×M16—31no—
64C2×C4×C22⋊D5—31no—
65C2×D5×M16—31no—
66#65496—31no—
67#65417—31no—
68#65417—31no—
69#65416—31no—
70#65416—31no—
71#65415—31no—
72#65407—31no—
73M16×Dic5—31no—
74#65400—31no—
75#65400—31no—
76C8×C22⋊D5—31no—
77C8×C22⋊D5D311yescharacteristic, complemented
78C23×C5×D3C2×C411yescharacteristic
79C22×D3×D5C2×C411yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C2×#1220C2×C411yescharacteristic
82C2×C4×D15C2311yescharacteristic
83C22×C5×Dic3C2×C411yescharacteristic
84C2×C4×C5×D3—22no—
85C2×C4×C5×D3—22no—
86C2×C4×C5×D3C2×C411yescharacteristic
87C2×C4×C5×D3C2×C411yescharacteristic
88C2×C4×C5×D3C2311yescharacteristic
89C2×C4×C5×D3C2311yescharacteristic
90C2×C3×C22⋊D5C2×C411yescharacteristic
91C2×C3×C4×D5C2311yescharacteristic
92D3×C22⋊D5—24no—
93C2×#1203C2×C411yescharacteristic
94C2×#1201C2×C411yescharacteristic
95C2×#1200C2×C411yescharacteristic
96C2×D3×Dic5C2×C411yescharacteristic
97C2×D3×Dic5C2×C411yescharacteristic
98C2×D3×Dic5C2×C411yescharacteristic
99C2×D5×Dic3C2×C411yescharacteristic
100C4×D3×D5—22no—
101C4×D3×D5—22no—
102C2×C3×C5×C8—22no—
103C2×C3×C5×C8C2311yescharacteristic
104C2×C3×C5×C8C2311yescharacteristic
105#6719C2×C411yescharacteristic
106#6714C2×C411yescharacteristic
107#6712C2×C411yescharacteristic
108C4×Dic15C2311yescharacteristic
109C2×C3⋊#168C2311yescharacteristic
110C2×C3⋊#168C2311yescharacteristic
111#6705—22no—
112C2×C5×C3⋊C8—22no—
113C2×C5×C3⋊C8C2311yescharacteristic
114C2×C5×C3⋊C8C2311yescharacteristic
115C5×ΓL(1,𝔽25)—22no—
116C5×ΓL(1,𝔽25)—22no—
117C5×ΓL(1,𝔽25)—22no—
118C5×ΓL(1,𝔽25)D414yescomplemented
119C3×C22⋊Dic5C2×C411yescharacteristic
120C3×#685C2×C411yescharacteristic
121C3×#683C2×C411yescharacteristic
122C3×C4×Dic5C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125C3×C8×D5—22no—
126#6669C2×C411yescharacteristic
127#6668C2×C411yescharacteristic
128#6667C2×C411yescharacteristic
129(C2×D3)⋊Dic5C2×C411yescharacteristic
130(C2×D3)⋊Dic5C2×C411yescharacteristic
131#6665C2×C411yescharacteristic
132Dic3×Dic5C2×C411yescharacteristic
133Dic3×Dic5C2×C411yescharacteristic
134#6651—22no—
135#6650—22no—
136#6650—22no—
137D5×C3⋊C8—22no—
138C22×ΓL(1,𝔽25)—51no—
139C22×ΓL(1,𝔽25)D511yescharacteristic, complemented
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—
153C23×C4×C5—31no—
154C22×C22⋊D5—31no—
155C22×C4×D5—31no—
156C2×C5×M16—31no—
157C2×C5×M16—31no—
158C2×C5×M16—31no—
159C2×C5×M16—31no—
160C2×C5×M16—64no—
161C22×C5×C8—31no—
162C22×C5×C8C2×D311yescharacteristic, complemented
163C2×C22⋊Dic5—31no—
164C4×C22⋊D5—31no—
165C4×C22⋊D5—31no—
166C4×C22⋊D5—31no—
167C4×C22⋊D5—31no—
168C4×C22⋊D5—31no—
169C4×C22⋊D5—31no—
170C4×C22⋊D5—31no—
171C4×C22⋊D5C2×D311yescharacteristic
172C2×#685—31no—
173C2×#683—31no—
174C2×C4×Dic5—31no—
175C2×#681—31no—
176C2×#681—31no—
177D5×M16—64no—
178C2×#676—31no—
179C2×#676—31no—
180C2×C8×D5—31no—
181C2×C8×D5C2×D311yescharacteristic, complemented
182C22⋊#168—31no—
183C22⋊#168—31no—
184C22⋊#168—31no—
185C22⋊#168C2×D311yescharacteristic, complemented
186#3952—31no—
187#3952—31no—
188#3952—31no—
189#3952C2×D311yescharacteristic, complemented
190#3947—31no—
191#3947—31no—
192#3946—31no—
193#3946—31no—
194#3946—31no—
195#3946C2×D311yescharacteristic, complemented
196C8×Dic5—31no—
197C8×Dic5C2×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×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5C22×C411yescharacteristic
213C2×C3×C4×C5C2411yescharacteristic
214#1220—22no—
215C2×Dic15C22×C411yescharacteristic
216C2×Dic15C22×C411yescharacteristic
217C2×Dic15C22×C411yescharacteristic
218C4×D15—21no—
219C4×D15—21no—
220C2×C5×Dic3—22no—
221C2×C5×Dic3C22×C411yescharacteristic
222C2×C5×Dic3C22×C411yescharacteristic
223C4×C5×D3—22no—
224C4×C5×D3—21no—
225C4×C5×D3—21no—
226C4×C5×D3—22no—
227C4×C5×D3C2×D412yes—
228C4×C5×D3#4112yes—
229C3×C22⋊D5M1614yescomplemented
230C2×C3×Dic5C22×C411yescharacteristic
231C2×C3×Dic5C22×C411yescharacteristic
232C2×C3×Dic5C22×C411yescharacteristic
233C3×C4×D5—21no—
234C3×C4×D5—21no—
235#1203—22no—
236#1201—22no—
237#1200—22no—
238D3×Dic5—22no—
239D3×Dic5—22no—
240D3×Dic5—41no—
241D5×Dic3—22no—
242C3×C5×C8—21no—
243C3×C5×C8C2×D412yescomplemented
244C3⋊#168—21no—
245C3⋊#168—21no—
246C3×#168—21no—
247C3×#168—21no—
248C5×C3⋊C8—21no—
249C5×C3⋊C8C2×D412yescomplemented
250C2×D3×D4—51no—
251C22×C4×D3—51no—
252C22×C4×D3C2×D511yescharacteristic
253C22×C3×C8—51no—
254C22×C3×C8C2×D511yescharacteristic, complemented
255C3×C4×D4—51no—
256D4×Dic3—51no—
257C4×#67—51no—
258C4×#67—51no—
259C22×C3⋊C8—51no—
260C22×C3⋊C8C2×D511yescharacteristic, complemented
261C2×ΓL(1,𝔽25)—24no—
262C2×ΓL(1,𝔽25)—51no—
263C2×ΓL(1,𝔽25)—51no—
264C2×ΓL(1,𝔽25)—51no—
265C2×ΓL(1,𝔽25)—51no—
266C2×ΓL(1,𝔽25)—104no—
267C2×ΓL(1,𝔽25)C2×D511yescharacteristic
268C2×ΓL(1,𝔽25)C2×D511yescharacteristic
269C2×ΓL(1,𝔽25)C2×D511yescharacteristic, complemented
270C2×ΓL(1,𝔽25)C2×D511yescharacteristic, complemented
271#893—51no—
272D3×C4⋊C4—51no—
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×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—
299C22×C4×C5—31no—
300C22×C4×C5—31no—
301C22×C4×C5—31no—
302C22×C4×C5—62no—
303C22×C4×C5—62no—
304C22×C4×C5C22×D311yescharacteristic
305C2×C22⋊D5—31no—
306C2×C22⋊D5—31no—
307C2×C22⋊D5—31no—
308C2×C22⋊D5—64no—
309C2×C22⋊D5C4×D311yescharacteristic
310C22×Dic5—31no—
311C22×Dic5—31no—
312C22×Dic5—31no—
313C2×C4×D5—31no—
314C2×C4×D5—31no—
315C2×C4×D5—31no—
316C2×C4×D5—62no—
317C2×C4×D5—62no—
318C2×C4×D5C22×D311yescharacteristic
319C5×M16—34no—
320C5×M16—62no—
321C5×M16—62no—
322C5×M16—62no—
323C2×C5×C8—22no—
324C2×C5×C8—31no—
325C2×C5×C8—31no—
326C2×C5×C8—62no—
327C2×C5×C8C22×D311yescharacteristic
328C2×C5×C8C22×D311yescharacteristic
329C22⋊Dic5—31no—
330C22⋊Dic5—31no—
331C22⋊Dic5—31no—
332C22⋊Dic5C4×D311yescharacteristic
333#685—31no—
334#685—31no—
335#685—31no—
336#685C4×D311yescharacteristic
337#683—31no—
338#683—31no—
339#683—31no—
340#683C4×D311yescharacteristic
341C4×Dic5—31no—
342C4×Dic5—31no—
343C4×Dic5—31no—
344C4×Dic5C22×D311yescharacteristic
345#681—62no—
346#681—62no—
347C2×#168—31no—
348C2×#168—31no—
349C2×#168C22×D311yescharacteristic
350C2×#168C22×D311yescharacteristic
351#676—62no—
352#676—62no—
353C8×D5—22no—
354C8×D5—62no—
355C22×M16—31no—
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×C5C22×D411yescharacteristic
390C3×C4×C5C2×#4111yescharacteristic
391Dic15—21no—
392Dic15—21no—
393Dic15—21no—
394C3×Dic5—21no—
395C3×Dic5—21no—
396C3×Dic5C2×M1612yescomplemented
397C5×Dic3—21no—
398C5×Dic3C4×D412yes—
399C23×D3—51no—
400C23×D3C4×D511yescharacteristic
401C2×C3×D4—51no—
402C22×C3×C4—51no—
403C22×C3×C4C22×D511yescharacteristic
404C2×#67—51no—
405C2×#67—51no—
406C22×Dic3—51no—
407C22×Dic3C4×D511yescharacteristic
408D3×D4—104no—
409C2×D12—51no—
410C2×C4×D3—22no—
411C2×C4×D3—22no—
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×D3C4×D511yescharacteristic
420C2×C4×D3C4×D511yescharacteristic
421C2×C4×D3C22×D511yescharacteristic
422C2×C4×D3C22×D511yescharacteristic
423C2×C3×C8—22no—
424C2×C3×C8—51no—
425C2×C3×C8—51no—
426C2×C3×C8—102no—
427C2×C3×C8C22×D511yescharacteristic
428C2×C3×C8C22×D511yescharacteristic
429C3×C4⋊C4—51no—
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⋊Dic3—51no—
440Dic3⋊C4—51no—
441Dic3⋊C4—51no—
442C4×Dic3—51no—
443C4×Dic3—51no—
444C4×Dic3—51no—
445C2×C3⋊C8—22no—
446C2×C3⋊C8—51no—
447C2×C3⋊C8—51no—
448C2×C3⋊C8—102no—
449C2×C3⋊C8C22×D511yescharacteristic
450C2×C3⋊C8C22×D511yescharacteristic
451ΓL(1,𝔽25)—22no—
452ΓL(1,𝔽25)—22no—
453ΓL(1,𝔽25)—22no—
454ΓL(1,𝔽25)—102no—
455ΓL(1,𝔽25)—102no—
456ΓL(1,𝔽25)—102no—
457ΓL(1,𝔽25)—102no—
458ΓL(1,𝔽25)C22⋊D514yesdirect product factor
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—21no—
471C2×C4×C5—21no—
472C2×C4×C5—31no—
473C2×C4×C5—32no—
474C2×C4×C5—32no—
475C2×C4×C5—31no—
476C2×C4×C5—62no—
477C2×C4×C5—62no—
478C2×C4×C5—62no—
479C2×C4×C5—61no—
480C2×C4×C5—61no—
481C2×C4×C5C2×C4×D311yescharacteristic
482C2×C4×C5C23×D311yescharacteristic
483C22⋊D5—62no—
484C22⋊D5—62no—
485C22⋊D5—62no—
486C22⋊D5ΓL(1,𝔽25)14yesdirect product factor
487C2×Dic5—31no—
488C2×Dic5—31no—
489C2×Dic5—31no—
490C2×Dic5—62no—
491C2×Dic5—62no—
492C2×Dic5—121no—
493C2×Dic5C2×C4×D311yescharacteristic
494C2×Dic5C2×C4×D311yescharacteristic
495C2×Dic5C2×C4×D311yescharacteristic
496C4×D5—21no—
497C4×D5—21no—
498C4×D5—62no—
499C4×D5—62no—
500C4×D5—61no—
501C4×D5—61no—
502C5×C8—21no—
503C5×C8—32no—
504C5×C8—61no—
505C5×C8D3×D412yescomplemented
506#168—21no—
507#168—21no—
508#168—61no—
509#168—61no—
510C22×D4—151no—
511C23×C4—31no—
512C23×C4—151no—
513C2×M16—31no—
514C2×M16—31no—
515C2×M16—31no—
516C2×M16—31no—
517C2×M16—64no—
518C2×M16—151no—
519C2×M16—151no—
520C2×M16—151no—
521C2×M16—151no—
522C2×M16—304no—
523C22×C8—31no—
524C22×C8—51no—
525C22×C8—151no—
526C22×C8D3×D511yescharacteristic, complemented
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—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—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×C3C2×C4×D511yescharacteristic
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—41no—
568C22×D3—51no—
569C22×D3—102no—
570C22×D3—102no—
571C22×D3—201no—
572C22×D3C2×C4×D511yescharacteristic
573C22×D3C2×C4×D511yescharacteristic
574C3×D4—54no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—51no—
578C2×C3×C4—51no—
579C2×C3×C4—51no—
580C2×C3×C4—101no—
581C2×C3×C4—101no—
582C2×C3×C4C2×C4×D511yescharacteristic
583C2×C3×C4C23×D511yescharacteristic
584#67—102no—
585#67—102no—
586C2×Dic3—22no—
587C2×Dic3—51no—
588C2×Dic3—51no—
589C2×Dic3—51no—
590C2×Dic3—102no—
591C2×Dic3C2×C4×D511yescharacteristic
592C2×Dic3C2×C4×D511yescharacteristic
593D12—102no—
594C4×D3—22no—
595C4×D3—21no—
596C4×D3—21no—
597C4×D3—22no—
598C4×D3—102no—
599C4×D3—102no—
600C4×D3—101no—
601C4×D3—101no—
602C4×D3—102no—
603C4×D3—201no—
604C4×D3#70912yes—
605C4×D3C2×C22⋊D512yes—
606C3×C8—21no—
607C3×C8—101no—
608C3×C8—101no—
609C3×C8C2×C22⋊D512yescomplemented
610C3⋊C8—21no—
611C3⋊C8—101no—
612C3⋊C8—101no—
613C3⋊C8C2×C22⋊D512yescomplemented
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—32no—
634C4×C5—61no—
635C4×C5C2×D3×D411yescharacteristic
636C4×C5D3×#4111yescharacteristic
637Dic5—21no—
638Dic5—21no—
639Dic5—61no—
640Dic5—61no—
641Dic5—61no—
642Dic5C2×ΓL(1,𝔽25)12yescomplemented
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—31no—
653C22×C4—31no—
654C22×C4—31no—
655C22×C4—51no—
656C22×C4—62no—
657C22×C4—62no—
658C22×C4—151no—
659C22×C4—151no—
660C22×C4—151no—
661C22×C4—151no—
662C22×C4—151no—
663C22×C4—151no—
664C22×C4—302no—
665C22×C4—302no—
666C22×C4C2×D3×D511yescharacteristic
667M16—34no—
668M16—62no—
669M16—62no—
670M16—62no—
671M16—302no—
672M16—302no—
673M16—302no—
674M16—302no—
675C2×C8—22no—
676C2×C8—31no—
677C2×C8—31no—
678C2×C8—51no—
679C2×C8—51no—
680C2×C8—62no—
681C2×C8—102no—
682C2×C8—151no—
683C2×C8—151no—
684C2×C8—302no—
685C2×C8C2×D3×D511yescharacteristic
686C2×C8C2×D3×D511yescharacteristic
687C4⋊C4—51no—
688C4⋊C4—151no—
689C4⋊C4—151no—
690C4⋊C4—151no—
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—21no—
705C22×C3—21no—
706C22×C3—52no—
707C22×C3—101no—
708C22×C3—101no—
709C22×C3D5×M1612yescomplemented
710C22×C3C22×C4×D511yescharacteristic
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×D3C4×C22⋊D512yes—
722C3×C4—21no—
723C3×C4—52no—
724C3×C4—101no—
725C3×C4—101no—
726C3×C4C2×#70911yescharacteristic
727C3×C4C22×C22⋊D511yescharacteristic
728Dic3—21no—
729Dic3—101no—
730Dic3—101no—
731Dic3—101no—
732Dic3C4×C22⋊D512yes—
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—
751C23C4×D3×D511yescharacteristic
752D4—54no—
753D4—302no—
754D4—302no—
755D4—302no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—31no—
759C2×C4—32no—
760C2×C4—32no—
761C2×C4—31no—
762C2×C4—51no—
763C2×C4—51no—
764C2×C4—51no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—101no—
771C2×C4—101no—
772C2×C4—151no—
773C2×C4—151no—
774C2×C4—151no—
775C2×C4—302no—
776C2×C4—302no—
777C2×C4—302no—
778C2×C4—302no—
779C2×C4—301no—
780C2×C4—301no—
781C2×C4—601no—
782C2×C4C4×D3×D511yescharacteristic
783C2×C4C22×D3×D511yescharacteristic
784C8—21no—
785C8—32no—
786C8—61no—
787C8—101no—
788C8—101no—
789C8—301no—
790C8—301no—
791C8D3×C22⋊D512yescomplemented
792C2×C3—22no—
793C2×C3—102no—
794C2×C3C2×D5×M1611yescharacteristic
795C2×C3#6607911yescharacteristic
796C2×C3C2×C4×C22⋊D511yescharacteristic
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
818C22C2×C4×D3×D511yescharacteristic
819C4—21no—
820C4—32no—
821C4—52no—
822C4—61no—
823C4—101no—
824C4—101no—
825C4—301no—
826C4—301no—
827C4—301no—
828C4D3×#70911yescharacteristic
829C4C2×D3×C22⋊D511yescharacteristic
830C3M16×C22⋊D511yescharacteristic, complemented, Sylow
831C2—22no—
832C2—62no—
833C2—102no—
834C2—121no—
835C2—601no—
836C2C2×D5×ΓL(1,𝔽25)11yescharacteristic
837C2#1175395111yescharacteristic
838C2C4×D3×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C5×C8C22
prime radicalC2×D3×C22⋊D5C4
cosocleC2×C3×C4×C5C24
hypercenterC22×C8D3×D5
hypocenterC3×C5D4×M16
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C5×ΓL(1,𝔽25)C2semidirect
3. C2×D5×ΓL(1,𝔽25)C2semidirect
4. #11751212C2semidirect
5. C3×C8×C22⋊D5C2semidirect
6. #11748506C2semidirect
7. #11748505C2semidirect
8. C3⋊C8×C22⋊D5C2semidirect
9. #11748102C2semidirect
10. #11747709C2semidirect
11. #11747707C2semidirect
12. #11747703C2semidirect
13. #11747701C2semidirect
14. #11747590C2semidirect
15. Dic5×ΓL(1,𝔽25)C2semidirect
20. C22×C3×C5×C8C22semidirect
22. C2×#6705C22semidirect
23. C22×C5×C3⋊C8C22semidirect
27. C2×C5×ΓL(1,𝔽25)C22semidirect
28. C2×C5×ΓL(1,𝔽25)C22semidirect
30. C2×C3×C8×D5C22semidirect
41. C2×#6651C22semidirect
44. C2×D5×C3⋊C8C22semidirect
46. #91114C22semidirect
47. #91104C22semidirect
48. #91099C22semidirect
49. #91098C22semidirect
50. C3×C22⋊#168C22semidirect
51. C3×#3952C22semidirect
52. C3×#3946C22semidirect
53. C3×C8×Dic5C22semidirect
54. #90983C22semidirect
55. #90982C22semidirect
56. #90957C22semidirect
57. (C2×D3)⋊#168C22semidirect
58. (C2×D3)⋊#168C22semidirect
59. #90955C22semidirect
60. #90954C22semidirect
61. Dic5×C3⋊C8C22semidirect
77. C8×C22⋊D5D3semidirect
118. C5×ΓL(1,𝔽25)D4semidirect
139. C22×ΓL(1,𝔽25)D5semidirect
162. C22×C5×C8C2×D3semidirect
181. C2×C8×D5C2×D3semidirect
185. C22⋊#168C2×D3semidirect
189. #3952C2×D3semidirect
195. #3946C2×D3semidirect
197. C8×Dic5C2×D3semidirect
229. C3×C22⋊D5M16semidirect
243. C3×C5×C8C2×D4semidirect
249. C5×C3⋊C8C2×D4semidirect
254. C22×C3×C8C2×D5semidirect
260. C22×C3⋊C8C2×D5semidirect
269. C2×ΓL(1,𝔽25)C2×D5semidirect
270. C2×ΓL(1,𝔽25)C2×D5semidirect
372. C22×C3×C5C2×M16semidirect
386. C2×C3×D5C2×M16semidirect
396. C3×Dic5C2×M16semidirect
458. ΓL(1,𝔽25)C22⋊D5direct (N × H)
486. C22⋊D5ΓL(1,𝔽25)direct (N × H)
505. C5×C8D3×D4semidirect
526. C22×C8D3×D5semidirect
609. C3×C8C2×C22⋊D5semidirect
613. C3⋊C8C2×C22⋊D5semidirect
623. C22×C5C2×ΓL(1,𝔽25)semidirect
631. C2×D5C2×ΓL(1,𝔽25)semidirect
642. Dic5C2×ΓL(1,𝔽25)semidirect
703. C3×C5D4×M16semidirect
709. C22×C3D5×M16semidirect
791. C8D3×C22⋊D5semidirect
800. C5D4×ΓL(1,𝔽25)semidirect
817. C22D5×ΓL(1,𝔽25)semidirect
830. C3M16×C22⋊D5semidirect

Maximal subgroups

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

subgroupindex
C22×C5×ΓL(1,𝔽25)2
C4×D3×C22⋊D52
C2×D5×ΓL(1,𝔽25)2
#117512122
C3×C8×C22⋊D52
#117485062
#117485052
C3⋊C8×C22⋊D52
#117481022
#117477092
#117477072
#117477032
#117477012
#117475902
Dic5×ΓL(1,𝔽25)2
M16×C22⋊D53
D4×ΓL(1,𝔽25)5