Finite Group Databasebeta

← #67×D5⋊AGL(1,𝔽5) #72259792

Subgroups — #67×D5⋊AGL(1,𝔽5) #72259792

Order 4800.

1892 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72231097C211yesmaximal, characteristic, complemented
2#72231092C211yesmaximal, characteristic, complemented
3#72231071C211yesmaximal, characteristic, complemented
4#67×#1044C211yesmaximal, characteristic, complemented
5#72231056C211yesmaximal, characteristic, complemented
6D52×#67C211yesmaximal, characteristic
7#72231022C211yesmaximal, characteristic, complemented
8#72231017C211yesmaximal, characteristic, complemented
9Dic3×D5⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
10#72230561C211yesmaximal, characteristic, complemented
11#67×#1043C211yesmaximal, characteristic, complemented
12C22×C3×D5⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
13#72224586C211yesmaximal, characteristic, complemented
14#72224585C211yesmaximal, characteristic, complemented
15C2×D3×D5⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
16D4×D5⋊AGL(1,𝔽5)—31nomaximal, Hall
17C22×C3×D52C2211yescharacteristic
18C22×C3×#1044C2211yescharacteristic, complemented
19C22×C3×#1043C2211yescharacteristic, complemented
20C2×D3×D52C2211yescharacteristic
21C2×#10597183C2211yescharacteristic, complemented
22C2×#10597182C2211yescharacteristic, complemented
23C2×D5⋊ΓL(1,𝔽16)C2211yescharacteristic
24C2×D5⋊ΓL(1,𝔽16)C2211yescharacteristic
25C2×D3×#1044C2211yescharacteristic, complemented
26C2×D3×#1043C2211yescharacteristic, complemented
27C2×C3×D5⋊AGL(1,𝔽5)—24no—
28C2×C3×D5⋊AGL(1,𝔽5)C2211yescharacteristic
29C2×C3×D5⋊AGL(1,𝔽5)C2211yescharacteristic
30C2×C3×D5⋊AGL(1,𝔽5)C2211yescharacteristic, complemented
31C2×C3×D5⋊AGL(1,𝔽5)C2211yescharacteristic, complemented
32D3×D5⋊AGL(1,𝔽5)—24no—
33#11925664C2211yescharacteristic
34D5×#1220C412yescomplemented
35#67×C5⋊D5C2211yescharacteristic
36C5×D5×#67C412yescomplemented
37#11925540C2211yescharacteristic, complemented
38#11925533C2211yescharacteristic, complemented
39#11925420C2211yescharacteristic
40#11925419C2211yescharacteristic
41D5×#1202C412yescomplemented
42D5×#1201C412yescomplemented
43D52×Dic3C2211yescharacteristic
44#11925361C2211yescharacteristic, complemented
45#11925360C2211yescharacteristic, complemented
46#11925359C2211yescharacteristic, complemented
47#11925356C2211yescharacteristic, complemented
48#11925355C2211yescharacteristic, complemented
49#11925354C2211yescharacteristic, complemented
50#11925350C2211yescharacteristic, complemented
51#11925350C2211yescharacteristic, complemented
52Dic3⋊#1044C2211yescharacteristic, complemented
53(C2×D3)⋊#1044C2211yescharacteristic, complemented
54Dic3×#1044C2211yescharacteristic, complemented
55Dic3⋊#1043C2211yescharacteristic, complemented
56(C2×D3)⋊#1043C2211yescharacteristic, complemented
57Dic3×#1043C2211yescharacteristic, complemented
58C2×AGL(1,𝔽5)×#67—52nomaximal
59C22×D5⋊AGL(1,𝔽5)—31no—
60C22×D5⋊AGL(1,𝔽5)D311yescharacteristic, complemented
61D4×D52—31no—
62D4×#1044—31no—
63D4×#1043—31no—
64#11717377—31no—
65#11717377—31no—
66D5⋊(C22⋊AGL(1,𝔽5))—31no—
67D5⋊(C22⋊AGL(1,𝔽5))—31no—
68#11717375—31no—
69#11717375—31no—
70#11717365—31no—
71D5⋊(C4⋊AGL(1,𝔽5))—31no—
72#11717363—31no—
73C4×D5⋊AGL(1,𝔽5)—31no—
74C22×C3×C5⋊D5C2311yescharacteristic
75C22×C3×C5×D5C2×C412yescomplemented
76C2×D15⋊D5C2311yescharacteristic
77C2×D5×D15C2×C412yescomplemented
78C2×D3×C5⋊D5C2311yescharacteristic
79C2×C5×D3×D5C2×C412yescomplemented
80C2×C3×D52—22no—
81C2×C3×D52—22no—
82C2×C3×D52C2×C412yescomplemented
83C2×C3×D52C2311yescharacteristic
84C2×C3×D52C2311yescharacteristic
85C2×C3⋊#1044C2311yescharacteristic
86C2×C3⋊#1044C2311yescharacteristic
87C2×C3⋊#1043C2311yescharacteristic
88C2×C3⋊#1043C2311yescharacteristic
89C2×C3×#1044—22no—
90C2×C3×#1044C2311yescharacteristic
91C2×C3×#1044C2311yescharacteristic
92C2×C3×#1043—22no—
93C2×C3×#1043C2311yescharacteristic
94C2×C3×#1043C2311yescharacteristic
95D3×D52—22no—
96D3×D52—22no—
97#10597183—22no—
98#10597182—22no—
99D5⋊ΓL(1,𝔽16)—22no—
100D5⋊ΓL(1,𝔽16)—22no—
101D3×#1044—22no—
102D3×#1043—22no—
103C3×D5⋊AGL(1,𝔽5)—22no—
104C3×D5⋊AGL(1,𝔽5)—22no—
105C3×D5⋊AGL(1,𝔽5)—22no—
106C3×D5⋊AGL(1,𝔽5)D414yescomplemented
107#10597159C2×C411yescharacteristic, complemented
108C5×#1220C2×C412yescomplemented
109C52×#67C2×C411yescharacteristic, complemented
110#10597127C2×C412yescomplemented
111#10597126C2311yescharacteristic
112#10597123C2×C412yescomplemented
113#10597121C2×C412yescomplemented
114D5×Dic15C2×C412yescomplemented
115#10597115C2×C411yescharacteristic, complemented
116#10597114C2×C411yescharacteristic, complemented
117Dic3×C5⋊D5C2311yescharacteristic
118C5×#1202C2×C412yescomplemented
119C5×#1201C2×C412yescomplemented
120C5×D5×Dic3C2×C412yescomplemented
121C23×C3×AGL(1,𝔽5)—52no—
122C22×D3×AGL(1,𝔽5)—52no—
123C2×D5×#67—52no—
124C2×#6763—52no—
125AGL(1,𝔽5)×#67—52no—
126AGL(1,𝔽5)×#67—52no—
127AGL(1,𝔽5)×#67—52no—
128AGL(1,𝔽5)×#67—52no—
129AGL(1,𝔽5)×#67—52no—
130AGL(1,𝔽5)×#67—52no—
131AGL(1,𝔽5)×#67—52no—
132AGL(1,𝔽5)×#67—52no—
133AGL(1,𝔽5)×#67—102no—
134C2×Dic3⋊AGL(1,𝔽5)—52no—
135C2×(C2×D3)⋊AGL(1,𝔽5)—52no—
136C2×Dic3×AGL(1,𝔽5)—52no—
137C22×D52—31no—
138C22×D52C2×D311yescharacteristic
139C22×#1044—31no—
140C22×#1044C2×D311yescharacteristic, complemented
141C22×#1043—31no—
142C22×#1043C2×D311yescharacteristic, complemented
143C2×D5⋊AGL(1,𝔽5)—24no—
144C2×D5⋊AGL(1,𝔽5)—31no—
145C2×D5⋊AGL(1,𝔽5)—31no—
146C2×D5⋊AGL(1,𝔽5)—31no—
147C2×D5⋊AGL(1,𝔽5)—31no—
148C2×D5⋊AGL(1,𝔽5)—64no—
149C2×D5⋊AGL(1,𝔽5)C2×D311yescharacteristic
150C2×D5⋊AGL(1,𝔽5)C2×D311yescharacteristic
151C2×D5⋊AGL(1,𝔽5)C2×D311yescharacteristic, complemented
152C2×D5⋊AGL(1,𝔽5)C2×D311yescharacteristic, complemented
153D4×C5⋊D5—31no—
154C5×D4×D5—32no—
155#87886—31no—
156#87886—31no—
157D5×C22⋊D5—32no—
158D5×C22⋊D5—32no—
159#87877—31no—
160D5×D20—32no—
161C4×D52—31no—
162C22⋊#1044—31no—
163C22⋊#1044—31no—
164C4⋊#1044—31no—
165C4×#1044—31no—
166C22⋊#1043—31no—
167C22⋊#1043—31no—
168C4⋊#1043—31no—
169C4×#1043—31no—
170#87832—31no—
171#87832—31no—
172#87831—31no—
173#87831—31no—
174#87831—31no—
175#87831—31no—
176#87830—31no—
177#87830—31no—
178C2×D4×AGL(1,𝔽5)—152no—
179C22×C3×C52C22×C411yescharacteristic, complemented
180C2×C3⋊(C5⋊D5)C22×C411yescharacteristic, complemented
181C2×C5×D15C22×C412yescomplemented
182C2×C52×D3C22×C411yescharacteristic, complemented
183C2×C3×C5⋊D5—21no—
184C2×C3×C5⋊D5—21no—
185C2×C3×C5⋊D5C22×C411yescharacteristic, complemented
186C2×C3×C5⋊D5C2411yescharacteristic
187C2×C3×C5×D5—24no—
188C2×C3×C5×D5C22×C412yes—
189C2×C3×C5×D5C22×C412yescomplemented
190D15⋊D5—21no—
191D15⋊D5—21no—
192D5×D15—24no—
193D3×C5⋊D5—21no—
194D3×C5⋊D5—21no—
195C5×D3×D5—24no—
196C3×D52—21no—
197C3×D52—21no—
198C3×D52—24no—
199C3×D52C2×D412yes—
200C3×D52#4112yes—
201C3⋊#1044—21no—
202C3⋊#1044—21no—
203C3⋊#1043—21no—
204C3⋊#1043—21no—
205C3×#1044—21no—
206C3×#1044C2×D412yescomplemented
207C3×#1043—21no—
208C3×#1043C2×D412yescomplemented
209C3⋊#1039C22×C411yescharacteristic, complemented
210C5×Dic15C22×C412yescomplemented
211C52×Dic3C22×C411yescharacteristic, complemented
212C23×C3×D5—52no—
213C22×D3×D5—52no—
214C22×ΓL(1,𝔽16)—52no—
215C22×ΓL(1,𝔽16)—52no—
216C22×C3×AGL(1,𝔽5)—52no—
217C22×C3×AGL(1,𝔽5)—52no—
218C22×C3×AGL(1,𝔽5)—52no—
219C22×C3×AGL(1,𝔽5)—52no—
220C22×C3×AGL(1,𝔽5)—52no—
221C22×C3×AGL(1,𝔽5)—52no—
222C22×C3×AGL(1,𝔽5)—108no—
223C22×C3×AGL(1,𝔽5)—102no—
224C2×D3×AGL(1,𝔽5)—52no—
225C2×D3×AGL(1,𝔽5)—52no—
226C2×D3×AGL(1,𝔽5)—52no—
227C2×D3×AGL(1,𝔽5)—52no—
228C2×D3×AGL(1,𝔽5)—108no—
229C2×D3×AGL(1,𝔽5)—102no—
230C2×#1220—52no—
231C2×C5×#67—52no—
232D5×#67—52no—
233D5×#67—52no—
234D5×#67—52no—
235D5×#67—52no—
236D5×#67—52no—
237D5×#67—52no—
238D5×#67—52no—
239D5×#67—102no—
240D5×#67AGL(1,𝔽5)12yescomplemented
241C2×#1202—52no—
242C2×#1201—52no—
243C2×D5×Dic3—52no—
244#6763—52no—
245#6763—52no—
246#6763—52no—
247#6763—52no—
248#6763—102no—
249Dic3⋊AGL(1,𝔽5)—52no—
250Dic3⋊AGL(1,𝔽5)—52no—
251Dic3⋊AGL(1,𝔽5)—52no—
252Dic3⋊AGL(1,𝔽5)—52no—
253Dic3⋊AGL(1,𝔽5)—102no—
254(C2×D3)⋊AGL(1,𝔽5)—52no—
255(C2×D3)⋊AGL(1,𝔽5)—52no—
256(C2×D3)⋊AGL(1,𝔽5)—52no—
257(C2×D3)⋊AGL(1,𝔽5)—52no—
258(C2×D3)⋊AGL(1,𝔽5)—102no—
259Dic3×AGL(1,𝔽5)—52no—
260Dic3×AGL(1,𝔽5)—52no—
261Dic3×AGL(1,𝔽5)—52no—
262Dic3×AGL(1,𝔽5)—52no—
263Dic3×AGL(1,𝔽5)—102no—
264C22×C5⋊D5—31no—
265C22×C5⋊D5C22×D311yescharacteristic
266C22×C5×D5—32no—
267C22×C5×D5C4×D312yescomplemented
268C2×D52—22no—
269C2×D52—22no—
270C2×D52—31no—
271C2×D52—32no—
272C2×D52—62no—
273C2×D52—62no—
274C2×D52C4×D312yescomplemented
275C2×D52C22×D311yescharacteristic
276C2×D52C22×D311yescharacteristic
277C2×#1044—22no—
278C2×#1044—31no—
279C2×#1044—31no—
280C2×#1044—62no—
281C2×#1044C22×D311yescharacteristic
282C2×#1044C22×D311yescharacteristic
283C2×#1043—22no—
284C2×#1043—31no—
285C2×#1043—31no—
286C2×#1043—62no—
287C2×#1043C22×D311yescharacteristic
288C2×#1043C22×D311yescharacteristic
289D5⋊AGL(1,𝔽5)—22no—
290D5⋊AGL(1,𝔽5)—22no—
291D5⋊AGL(1,𝔽5)—22no—
292D5⋊AGL(1,𝔽5)—62no—
293D5⋊AGL(1,𝔽5)—62no—
294D5⋊AGL(1,𝔽5)—62no—
295D5⋊AGL(1,𝔽5)—62no—
296D5⋊AGL(1,𝔽5)#6714yesdirect product factor
297C52×D4—31no—
298C22⋊(C5⋊D5)—31no—
299C22⋊(C5⋊D5)—31no—
300C4⋊(C5⋊D5)—31no—
301C4×C5⋊D5—31no—
302C5×C22⋊D5—32no—
303C5×C22⋊D5—32no—
304C5×D20—32no—
305C4×C5×D5—32no—
306#6038—32no—
307#6038—32no—
308#6037—32no—
309#6036—31no—
310D5×Dic5—32no—
311C2×C4×#67—251noHall
312C23×AGL(1,𝔽5)—52no—
313C23×AGL(1,𝔽5)—152no—
314C2×D4×D5—152no—
315C2×C22⋊AGL(1,𝔽5)—152no—
316C2×C22⋊AGL(1,𝔽5)—152no—
317D4×AGL(1,𝔽5)—152no—
318D4×AGL(1,𝔽5)—152no—
319D4×AGL(1,𝔽5)—152no—
320D4×AGL(1,𝔽5)—152no—
321D4×AGL(1,𝔽5)—152no—
322D4×AGL(1,𝔽5)—152no—
323D4×AGL(1,𝔽5)—152no—
324D4×AGL(1,𝔽5)—152no—
325D4×AGL(1,𝔽5)—302no—
326C2×C4⋊AGL(1,𝔽5)—152no—
327C2×C4×AGL(1,𝔽5)—152no—
328C2×C3×C52—21no—
329C2×C3×C52C23×C411yescharacteristic
330C3⋊(C5⋊D5)—21no—
331C5×D15—22no—
332C52×D3—21no—
333C3×C5⋊D5—21no—
334C3×C5⋊D5C22×D411yescharacteristic
335C3×C5⋊D5C2×#4111yescharacteristic
336C3×C5×D5—22no—
337C3×C5×D5C4×D414yescomplemented
338C23×C3×C5—52no—
339C22×D15—52no—
340C22×C5×D3—52no—
341C22×C3×D5—52no—
342C22×C3×D5—52no—
343C22×C3×D5—52no—
344C22×C3×D5—52no—
345C22×C3×D5—52no—
346C22×C3×D5—104no—
347C22×C3×D5—104no—
348C22×C3×D5—102no—
349C22×C3×D5C2×AGL(1,𝔽5)12yescomplemented
350C2×D3×D5—52no—
351C2×D3×D5—52no—
352C2×D3×D5—52no—
353C2×D3×D5—104no—
354C2×D3×D5—104no—
355C2×D3×D5—102no—
356C2×D3×D5C2×AGL(1,𝔽5)12yescomplemented
357C2×ΓL(1,𝔽16)—52no—
358C2×ΓL(1,𝔽16)—52no—
359C2×ΓL(1,𝔽16)—52no—
360C2×ΓL(1,𝔽16)—52no—
361C2×ΓL(1,𝔽16)—104no—
362C2×ΓL(1,𝔽16)—104no—
363C2×ΓL(1,𝔽16)—102no—
364C2×ΓL(1,𝔽16)—102no—
365C2×C3×AGL(1,𝔽5)—58no—
366C2×C3×AGL(1,𝔽5)—52no—
367C2×C3×AGL(1,𝔽5)—52no—
368C2×C3×AGL(1,𝔽5)—52no—
369C2×C3×AGL(1,𝔽5)—52no—
370C2×C3×AGL(1,𝔽5)—104no—
371C2×C3×AGL(1,𝔽5)—104no—
372C2×C3×AGL(1,𝔽5)—104no—
373C2×C3×AGL(1,𝔽5)—104no—
374C2×C3×AGL(1,𝔽5)—104no—
375C2×C3×AGL(1,𝔽5)—102no—
376C2×C3×AGL(1,𝔽5)—102no—
377C2×C3×AGL(1,𝔽5)—204no—
378D3×AGL(1,𝔽5)—104no—
379D3×AGL(1,𝔽5)—104no—
380D3×AGL(1,𝔽5)—104no—
381D3×AGL(1,𝔽5)—104no—
382D3×AGL(1,𝔽5)—204no—
383#1220—52no—
384#1220—52no—
385#1220—52no—
386#1220—102no—
387#1220C2×AGL(1,𝔽5)12yescomplemented
388C2×Dic15—52no—
389C5×#67—22no—
390C5×#67—52no—
391C5×#67—52no—
392C5×#67—52no—
393C5×#67C2×AGL(1,𝔽5)12yescomplemented
394C2×C5×Dic3—52no—
395#1202—52no—
396#1202—52no—
397#1202—52no—
398#1202—102no—
399#1202C2×AGL(1,𝔽5)12yescomplemented
400#1201—52no—
401#1201—52no—
402#1201—52no—
403#1201—102no—
404#1201C2×AGL(1,𝔽5)12yescomplemented
405D5×Dic3—52no—
406D5×Dic3—52no—
407D5×Dic3—52no—
408D5×Dic3—102no—
409D5×Dic3C2×AGL(1,𝔽5)12yescomplemented
410C22×C52—31no—
411C22×C52C2×C4×D311yescharacteristic, complemented
412C2×C5⋊D5—21no—
413C2×C5⋊D5—21no—
414C2×C5⋊D5—31no—
415C2×C5⋊D5—61no—
416C2×C5⋊D5—61no—
417C2×C5⋊D5C2×C4×D311yescharacteristic, complemented
418C2×C5⋊D5C23×D311yescharacteristic
419C2×C5×D5—24no—
420C2×C5×D5—32no—
421C2×C5×D5—64no—
422C2×C5×D5C2×C4×D312yes—
423C2×C5×D5C2×C4×D312yescomplemented
424D52—24no—
425D52—21no—
426D52—21no—
427D52—64no—
428D52—61no—
429D52—61no—
430D52#23512yes—
431D52C2×#6712yes—
432#1044—21no—
433#1044—61no—
434#1044—61no—
435#1044C2×#6712yescomplemented
436#1043—21no—
437#1043—61no—
438#1043—61no—
439#1043C2×#6712yescomplemented
440C4×C52—31no—
441#1039—31no—
442C5×Dic5—32no—
443C23×C3×C4—251no—
444C22×#67—251no—
445C22×C4×D3—251no—
446C2×#217—251no—
447C4×#67—251no—
448C4×#67—251no—
449C4×#67—251no—
450C4×#67—251no—
451C4×#67—251no—
452C4×#67—251no—
453C4×#67—251no—
454C4×#67—251no—
455C2×(C2×D3)⋊C4—251no—
456C2×Dic3⋊C4—251no—
457C2×C4×Dic3—251no—
458C23×D5—52no—
459C23×D5—152no—
460C22×AGL(1,𝔽5)—52no—
461C22×AGL(1,𝔽5)—52no—
462C22×AGL(1,𝔽5)—52no—
463C22×AGL(1,𝔽5)—52no—
464C22×AGL(1,𝔽5)—52no—
465C22×AGL(1,𝔽5)—52no—
466C22×AGL(1,𝔽5)—102no—
467C22×AGL(1,𝔽5)—108no—
468C22×AGL(1,𝔽5)—152no—
469C22×AGL(1,𝔽5)—152no—
470C22×AGL(1,𝔽5)—152no—
471C22×AGL(1,𝔽5)—152no—
472C22×AGL(1,𝔽5)—152no—
473C22×AGL(1,𝔽5)—152no—
474C22×AGL(1,𝔽5)—302no—
475C22×AGL(1,𝔽5)—308no—
476C2×C5×D4—152no—
477C2×C22⋊D5—152no—
478C2×C22⋊D5—152no—
479D4×D5—32no—
480D4×D5—152no—
481D4×D5—152no—
482D4×D5—152no—
483D4×D5—152no—
484D4×D5—152no—
485D4×D5—152no—
486D4×D5—152no—
487D4×D5—302no—
488C2×D20—152no—
489C2×C4×D5—152no—
490C22⋊AGL(1,𝔽5)—152no—
491C22⋊AGL(1,𝔽5)—152no—
492C22⋊AGL(1,𝔽5)—152no—
493C22⋊AGL(1,𝔽5)—152no—
494C22⋊AGL(1,𝔽5)—152no—
495C22⋊AGL(1,𝔽5)—152no—
496C22⋊AGL(1,𝔽5)—152no—
497C22⋊AGL(1,𝔽5)—152no—
498C22⋊AGL(1,𝔽5)—302no—
499C22⋊AGL(1,𝔽5)—302no—
500C4⋊AGL(1,𝔽5)—152no—
501C4⋊AGL(1,𝔽5)—152no—
502C4⋊AGL(1,𝔽5)—152no—
503C4⋊AGL(1,𝔽5)—152no—
504C4⋊AGL(1,𝔽5)—302no—
505C4×AGL(1,𝔽5)—152no—
506C4×AGL(1,𝔽5)—152no—
507C4×AGL(1,𝔽5)—152no—
508C4×AGL(1,𝔽5)—152no—
509C4×AGL(1,𝔽5)—302no—
510C3×C52C2×C4×D411yescharacteristic, complemented, Hall
511C2×C4×D4—751noSylow
512C22×C3×C5—22no—
513C22×C3×C5—52no—
514C22×C3×C5—52no—
515C22×C3×C5—104no—
516C22×C3×C5C22×AGL(1,𝔽5)12yescomplemented
517C2×D15—52no—
518C2×D15—102no—
519C2×D15—104no—
520C2×D15C22×AGL(1,𝔽5)12yescomplemented
521C2×C5×D3—22no—
522C2×C5×D3—52no—
523C2×C5×D3—104no—
524C2×C5×D3C22×AGL(1,𝔽5)12yescomplemented
525C2×C3×D5—24no—
526C2×C3×D5—52no—
527C2×C3×D5—54no—
528C2×C3×D5—54no—
529C2×C3×D5—52no—
530C2×C3×D5—102no—
531C2×C3×D5—102no—
532C2×C3×D5—102no—
533C2×C3×D5—102no—
534C2×C3×D5—104no—
535C2×C3×D5—102no—
536C2×C3×D5—102no—
537C2×C3×D5—104no—
538C2×C3×D5—202no—
539C2×C3×D5—202no—
540C2×C3×D5C22×AGL(1,𝔽5)12yes—
541C2×C3×D5C22×AGL(1,𝔽5)12yescomplemented
542D3×D5—24no—
543D3×D5—102no—
544D3×D5—102no—
545D3×D5—102no—
546D3×D5—102no—
547D3×D5—104no—
548D3×D5—202no—
549D3×D5—202no—
550ΓL(1,𝔽16)—102no—
551ΓL(1,𝔽16)—102no—
552ΓL(1,𝔽16)—102no—
553ΓL(1,𝔽16)—102no—
554ΓL(1,𝔽16)—202no—
555ΓL(1,𝔽16)—202no—
556C3×AGL(1,𝔽5)—54no—
557C3×AGL(1,𝔽5)—54no—
558C3×AGL(1,𝔽5)—104no—
559C3×AGL(1,𝔽5)—102no—
560C3×AGL(1,𝔽5)—102no—
561C3×AGL(1,𝔽5)—202no—
562Dic15—52no—
563Dic15—102no—
564Dic15C22×AGL(1,𝔽5)12yescomplemented
565C5×Dic3—22no—
566C5×Dic3—52no—
567C5×Dic3C22×AGL(1,𝔽5)12yescomplemented
568C2×C52—21no—
569C2×C52—61no—
570C2×C52C22×C4×D311yescharacteristic
571C5⋊D5—21no—
572C5⋊D5—61no—
573C5⋊D5C2×#23511yescharacteristic
574C5⋊D5C22×#6711yescharacteristic
575C5×D5—22no—
576C5×D5—62no—
577C5×D5C4×#6714yescomplemented
578C24×C3—251no—
579C23×D3—251no—
580C22×C3×C4—251no—
581C22×C3×C4—251no—
582C22×C3×C4—251no—
583C22×C3×C4—251no—
584C22×C3×C4—251no—
585C22×C3×C4—251no—
586C22×C3×C4—504no—
587C2×#67—52no—
588C2×#67—252no—
589C2×#67—251no—
590C2×#67—251no—
591C2×#67—251no—
592C2×#67—252no—
593C2×#67—252no—
594C2×#67—251no—
595C22×Dic3—251no—
596C22×Dic3—251no—
597C22×Dic3—251no—
598C2×C4×D3—251no—
599C2×C4×D3—251no—
600C2×C4×D3—251no—
601C2×C4×D3—251no—
602C2×C4×D3—504no—
603#217—251no—
604#217—251no—
605#217—251no—
606#217—251no—
607(C2×D3)⋊C4—251no—
608(C2×D3)⋊C4—251no—
609(C2×D3)⋊C4—251no—
610(C2×D3)⋊C4—251no—
611Dic3⋊C4—251no—
612Dic3⋊C4—251no—
613Dic3⋊C4—251no—
614Dic3⋊C4—251no—
615C4×Dic3—251no—
616C4×Dic3—251no—
617C4×Dic3—251no—
618C4×Dic3—251no—
619C23×C5—52no—
620C23×C5—152no—
621C22×D5—32no—
622C22×D5—52no—
623C22×D5—52no—
624C22×D5—52no—
625C22×D5—52no—
626C22×D5—52no—
627C22×D5—102no—
628C22×D5—104no—
629C22×D5—104no—
630C22×D5—152no—
631C22×D5—152no—
632C22×D5—152no—
633C22×D5—152no—
634C22×D5—302no—
635C22×D5—304no—
636C22×D5—304no—
637C22×D5D3×AGL(1,𝔽5)12yescomplemented
638C2×AGL(1,𝔽5)—58no—
639C2×AGL(1,𝔽5)—52no—
640C2×AGL(1,𝔽5)—52no—
641C2×AGL(1,𝔽5)—52no—
642C2×AGL(1,𝔽5)—52no—
643C2×AGL(1,𝔽5)—102no—
644C2×AGL(1,𝔽5)—102no—
645C2×AGL(1,𝔽5)—104no—
646C2×AGL(1,𝔽5)—104no—
647C2×AGL(1,𝔽5)—104no—
648C2×AGL(1,𝔽5)—104no—
649C2×AGL(1,𝔽5)—104no—
650C2×AGL(1,𝔽5)—152no—
651C2×AGL(1,𝔽5)—152no—
652C2×AGL(1,𝔽5)—152no—
653C2×AGL(1,𝔽5)—152no—
654C2×AGL(1,𝔽5)—204no—
655C2×AGL(1,𝔽5)—302no—
656C2×AGL(1,𝔽5)—302no—
657C2×AGL(1,𝔽5)—304no—
658C2×AGL(1,𝔽5)—304no—
659C2×AGL(1,𝔽5)—304no—
660C2×AGL(1,𝔽5)—304no—
661C2×AGL(1,𝔽5)—304no—
662C2×AGL(1,𝔽5)—304no—
663C2×AGL(1,𝔽5)—604no—
664C5×D4—32no—
665C5×D4—62no—
666C5×D4—152no—
667C5×D4—152no—
668C5×D4—152no—
669C2×C4×C5—152no—
670C22⋊D5—32no—
671C22⋊D5—32no—
672C22⋊D5—152no—
673C22⋊D5—152no—
674C22⋊D5—152no—
675C22⋊D5—152no—
676C22⋊D5—152no—
677C22⋊D5—152no—
678C22⋊D5—302no—
679C22⋊D5—302no—
680C2×Dic5—152no—
681D20—32no—
682D20—152no—
683D20—152no—
684D20—152no—
685D20—302no—
686C4×D5—32no—
687C4×D5—152no—
688C4×D5—152no—
689C4×D5—152no—
690C4×D5—302no—
691C22×D4—751no—
692C23×C4—251no—
693C23×C4—751no—
694C4×D4—751no—
695C4×D4—751no—
696C4×D4—751no—
697C4×D4—751no—
698C4×D4—751no—
699C4×D4—751no—
700C4×D4—751no—
701C4×D4—751no—
702C2×C4⋊C4—751no—
703C2×C22⋊C4—751no—
704C2×C22⋊C4—751no—
705C2×C42—751no—
706C2×C3×C5—22no—
707C2×C3×C5—22no—
708C2×C3×C5—42no—
709C2×C3×C5—54no—
710C2×C3×C5—102no—
711C2×C3×C5C23×AGL(1,𝔽5)12yes—
712D15—22no—
713D15—102no—
714D15—202no—
715C3×D5—22no—
716C3×D5—52no—
717C3×D5—52no—
718C3×D5—102no—
719C3×D5—102no—
720C3×D5—102no—
721C3×D5—202no—
722C3×D5D4×AGL(1,𝔽5)14yescomplemented
723C5×D3—22no—
724C5×D3—42no—
725C5×D3—102no—
726C52C2×C4×#6711yescharacteristic, complemented, Sylow
727C23×C3—52no—
728C23×C3—251no—
729C23×C3—251no—
730C23×C3—252no—
731C23×C3—251no—
732C23×C3—502no—
733C23×C3—502no—
734C22×D3—52no—
735C22×D3—251no—
736C22×D3—252no—
737C22×D3—251no—
738C22×D3—502no—
739C22×D3—502no—
740C2×C3×C4—251no—
741C2×C3×C4—251no—
742C2×C3×C4—254no—
743C2×C3×C4—251no—
744C2×C3×C4—251no—
745C2×C3×C4—502no—
746C2×C3×C4—502no—
747C2×C3×C4—502no—
748C2×C3×C4—502no—
749C2×C3×C4—502no—
750#67—52no—
751#67—52no—
752#67—52no—
753#67—252no—
754#67—252no—
755#67—252no—
756#67—251no—
757#67—251no—
758#67—251no—
759#67D5⋊AGL(1,𝔽5)11yescharacteristic, direct product factor
760C2×Dic3—52no—
761C2×Dic3—251no—
762C2×Dic3—252no—
763C2×Dic3—251no—
764C2×Dic3—251no—
765C2×Dic3—251no—
766C2×Dic3—251no—
767C2×Dic3—251no—
768C2×Dic3—502no—
769C2×Dic3—502no—
770C4×D3—502no—
771C4×D3—502no—
772C4×D3—502no—
773C4×D3—502no—
774C22×C5—22no—
775C22×C5—32no—
776C22×C5—52no—
777C22×C5—52no—
778C22×C5—62no—
779C22×C5—104no—
780C22×C5—152no—
781C22×C5—304no—
782C22×C5C2×D3×AGL(1,𝔽5)12yescomplemented
783C2×D5—24no—
784C2×D5—32no—
785C2×D5—52no—
786C2×D5—54no—
787C2×D5—54no—
788C2×D5—52no—
789C2×D5—64no—
790C2×D5—102no—
791C2×D5—102no—
792C2×D5—102no—
793C2×D5—102no—
794C2×D5—104no—
795C2×D5—102no—
796C2×D5—102no—
797C2×D5—104no—
798C2×D5—152no—
799C2×D5—202no—
800C2×D5—202no—
801C2×D5—302no—
802C2×D5—302no—
803C2×D5—302no—
804C2×D5—302no—
805C2×D5—302no—
806C2×D5—304no—
807C2×D5—304no—
808C2×D5—602no—
809C2×D5—602no—
810C2×D5C2×D3×AGL(1,𝔽5)12yes—
811C2×D5C2×D3×AGL(1,𝔽5)12yescomplemented
812AGL(1,𝔽5)—54no—
813AGL(1,𝔽5)—54no—
814AGL(1,𝔽5)—104no—
815AGL(1,𝔽5)—102no—
816AGL(1,𝔽5)—102no—
817AGL(1,𝔽5)—202no—
818AGL(1,𝔽5)—302no—
819AGL(1,𝔽5)—302no—
820AGL(1,𝔽5)—302no—
821AGL(1,𝔽5)—302no—
822AGL(1,𝔽5)—602no—
823AGL(1,𝔽5)—602no—
824C4×C5—32no—
825C4×C5—62no—
826C4×C5—152no—
827Dic5—32no—
828Dic5—152no—
829Dic5—302no—
830C24—251no—
831C24—751no—
832C2×D4—152no—
833C2×D4—752no—
834C2×D4—751no—
835C2×D4—751no—
836C2×D4—751no—
837C2×D4—751no—
838C2×D4—752no—
839C2×D4—752no—
840C22×C4—251no—
841C22×C4—251no—
842C22×C4—251no—
843C22×C4—251no—
844C22×C4—251no—
845C22×C4—251no—
846C22×C4—504no—
847C22×C4—751no—
848C22×C4—751no—
849C22×C4—751no—
850C22×C4—751no—
851C22×C4—751no—
852C22×C4—751no—
853C22×C4—751no—
854C22×C4—1504no—
855C4⋊C4—751no—
856C4⋊C4—751no—
857C4⋊C4—751no—
858C4⋊C4—751no—
859C22⋊C4—751no—
860C22⋊C4—751no—
861C22⋊C4—751no—
862C22⋊C4—751no—
863C22⋊C4—751no—
864C22⋊C4—751no—
865C22⋊C4—751no—
866C22⋊C4—751no—
867C42—751no—
868C42—751no—
869C42—751no—
870C42—751no—
871C3×C5—22no—
872C3×C5C2×D4×AGL(1,𝔽5)12yescomplemented
873C22×C3—52no—
874C22×C3—52no—
875C22×C3—104no—
876C22×C3—252no—
877C22×C3—252no—
878C22×C3—251no—
879C22×C3—251no—
880C22×C3—501no—
881C22×C3—501no—
882C22×C3—504no—
883C22×C3—501no—
884C22×C3—501no—
885C22×C3C2×D5⋊AGL(1,𝔽5)11yescharacteristic, complemented
886C2×D3—52no—
887C2×D3—104no—
888C2×D3—251no—
889C2×D3—501no—
890C2×D3—501no—
891C2×D3—501no—
892C2×D3—501no—
893C2×D3—504no—
894C2×D3C2×D5⋊AGL(1,𝔽5)11yescharacteristic, complemented
895C3×C4—252no—
896C3×C4—252no—
897C3×C4—501no—
898C3×C4—501no—
899Dic3—52no—
900Dic3—251no—
901Dic3—501no—
902Dic3—501no—
903Dic3—501no—
904Dic3—501no—
905Dic3C2×D5⋊AGL(1,𝔽5)11yescharacteristic, complemented
906C2×C5—22no—
907C2×C5—22no—
908C2×C5—42no—
909C2×C5—54no—
910C2×C5—62no—
911C2×C5—102no—
912C2×C5—122no—
913C2×C5—302no—
914C2×C5C22×D3×AGL(1,𝔽5)12yes—
915D5—22no—
916D5—52no—
917D5—52no—
918D5—62no—
919D5—102no—
920D5—102no—
921D5—102no—
922D5—202no—
923D5—302no—
924D5—602no—
925D5AGL(1,𝔽5)×#6714yescomplemented
926C23—52no—
927C23—152no—
928C23—251no—
929C23—251no—
930C23—252no—
931C23—251no—
932C23—502no—
933C23—502no—
934C23—751no—
935C23—752no—
936C23—751no—
937C23—1502no—
938C23—1502no—
939D4—31no—
940D4—152no—
941D4—152no—
942D4—152no—
943D4—751no—
944D4—752no—
945D4—752no—
946D4—751no—
947D4—752no—
948D4—751no—
949C2×C4—152no—
950C2×C4—251no—
951C2×C4—251no—
952C2×C4—254no—
953C2×C4—251no—
954C2×C4—251no—
955C2×C4—502no—
956C2×C4—502no—
957C2×C4—502no—
958C2×C4—502no—
959C2×C4—502no—
960C2×C4—751no—
961C2×C4—751no—
962C2×C4—752no—
963C2×C4—751no—
964C2×C4—751no—
965C2×C4—751no—
966C2×C4—751no—
967C2×C4—1502no—
968C2×C4—1502no—
969C2×C4—1502no—
970C2×C4—1502no—
971C2×C4—1502no—
972C2×C4—1502no—
973C2×C3—21no—
974C2×C3—54no—
975C2×C3—102no—
976C2×C3—251no—
977C2×C3—251no—
978C2×C3—501no—
979C2×C3C22×D5⋊AGL(1,𝔽5)11yescharacteristic
980D3—21no—
981D3—102no—
982D3—501no—
983C5—22no—
984C5C2×AGL(1,𝔽5)×#6712yescomplemented
985C22—31no—
986C22—52no—
987C22—52no—
988C22—104no—
989C22—152no—
990C22—252no—
991C22—252no—
992C22—251no—
993C22—251no—
994C22—304no—
995C22—501no—
996C22—501no—
997C22—504no—
998C22—501no—
999C22—501no—
1000C22—751no—
1001C22—1504no—
1002C22—1501no—
1003C22—1501no—
1004C22—1501no—
1005C22—1501no—
1006C22D3×D5⋊AGL(1,𝔽5)11yescharacteristic, complemented
1007C4—31no—
1008C4—152no—
1009C4—252no—
1010C4—252no—
1011C4—501no—
1012C4—501no—
1013C4—751no—
1014C4—1501no—
1015C4—1501no—
1016C4—1501no—
1017C4—1501no—
1018C3D4×D5⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
1019C2—21no—
1020C2—54no—
1021C2—61no—
1022C2—102no—
1023C2—251no—
1024C2—251no—
1025C2—302no—
1026C2—501no—
1027C2—1501no—
1028C2C2×D3×D5⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC2C2×D3×D5⋊AGL(1,𝔽5)
commutator, socleC2×C3×C52C23×C4
FittingC22×C3×C52C22×C4
prime radicalD52×#67C2
cosocleC2×C3×C5⋊D5C24
hypercenterC22D3×D5⋊AGL(1,𝔽5)
hypocenterC3×C52C2×C4×D4
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. #72231097C2semidirect
2. #72231092C2semidirect
3. #72231071C2semidirect
4. #67×#1044C2semidirect
5. #72231056C2semidirect
7. #72231022C2semidirect
8. #72231017C2semidirect
9. Dic3×D5⋊AGL(1,𝔽5)C2semidirect
10. #72230561C2semidirect
11. #67×#1043C2semidirect
12. C22×C3×D5⋊AGL(1,𝔽5)C2semidirect
13. #72224586C2semidirect
14. #72224585C2semidirect
15. C2×D3×D5⋊AGL(1,𝔽5)C2semidirect
18. C22×C3×#1044C22semidirect
19. C22×C3×#1043C22semidirect
21. C2×#10597183C22semidirect
22. C2×#10597182C22semidirect
25. C2×D3×#1044C22semidirect
26. C2×D3×#1043C22semidirect
30. C2×C3×D5⋊AGL(1,𝔽5)C22semidirect
31. C2×C3×D5⋊AGL(1,𝔽5)C22semidirect
34. D5×#1220C4semidirect
36. C5×D5×#67C4semidirect
37. #11925540C22semidirect
38. #11925533C22semidirect
41. D5×#1202C4semidirect
42. D5×#1201C4semidirect
44. #11925361C22semidirect
45. #11925360C22semidirect
46. #11925359C22semidirect
47. #11925356C22semidirect
48. #11925355C22semidirect
49. #11925354C22semidirect
50. #11925350C22semidirect
51. #11925350C22semidirect
52. Dic3⋊#1044C22semidirect
53. (C2×D3)⋊#1044C22semidirect
54. Dic3×#1044C22semidirect
55. Dic3⋊#1043C22semidirect
56. (C2×D3)⋊#1043C22semidirect
57. Dic3×#1043C22semidirect
60. C22×D5⋊AGL(1,𝔽5)D3semidirect
75. C22×C3×C5×D5C2×C4semidirect
77. C2×D5×D15C2×C4semidirect
79. C2×C5×D3×D5C2×C4semidirect
82. C2×C3×D52C2×C4semidirect
106. C3×D5⋊AGL(1,𝔽5)D4semidirect
107. #10597159C2×C4semidirect
108. C5×#1220C2×C4semidirect
109. C52×#67C2×C4semidirect
110. #10597127C2×C4semidirect
112. #10597123C2×C4semidirect
113. #10597121C2×C4semidirect
114. D5×Dic15C2×C4semidirect
115. #10597115C2×C4semidirect
116. #10597114C2×C4semidirect
118. C5×#1202C2×C4semidirect
119. C5×#1201C2×C4semidirect
120. C5×D5×Dic3C2×C4semidirect
140. C22×#1044C2×D3semidirect
142. C22×#1043C2×D3semidirect
151. C2×D5⋊AGL(1,𝔽5)C2×D3semidirect
152. C2×D5⋊AGL(1,𝔽5)C2×D3semidirect
179. C22×C3×C52C22×C4semidirect
180. C2×C3⋊(C5⋊D5)C22×C4semidirect
181. C2×C5×D15C22×C4semidirect
182. C2×C52×D3C22×C4semidirect
185. C2×C3×C5⋊D5C22×C4semidirect
189. C2×C3×C5×D5C22×C4semidirect
206. C3×#1044C2×D4semidirect
208. C3×#1043C2×D4semidirect
209. C3⋊#1039C22×C4semidirect
210. C5×Dic15C22×C4semidirect
211. C52×Dic3C22×C4semidirect
240. D5×#67AGL(1,𝔽5)semidirect
267. C22×C5×D5C4×D3semidirect
274. C2×D52C4×D3semidirect
296. D5⋊AGL(1,𝔽5)#67direct (N × H)
337. C3×C5×D5C4×D4semidirect
349. C22×C3×D5C2×AGL(1,𝔽5)semidirect
356. C2×D3×D5C2×AGL(1,𝔽5)semidirect
387. #1220C2×AGL(1,𝔽5)semidirect
393. C5×#67C2×AGL(1,𝔽5)semidirect
399. #1202C2×AGL(1,𝔽5)semidirect
404. #1201C2×AGL(1,𝔽5)semidirect
409. D5×Dic3C2×AGL(1,𝔽5)semidirect
411. C22×C52C2×C4×D3semidirect
417. C2×C5⋊D5C2×C4×D3semidirect
423. C2×C5×D5C2×C4×D3semidirect
435. #1044C2×#67semidirect
439. #1043C2×#67semidirect
510. C3×C52C2×C4×D4semidirect
516. C22×C3×C5C22×AGL(1,𝔽5)semidirect
520. C2×D15C22×AGL(1,𝔽5)semidirect
524. C2×C5×D3C22×AGL(1,𝔽5)semidirect
541. C2×C3×D5C22×AGL(1,𝔽5)semidirect
564. Dic15C22×AGL(1,𝔽5)semidirect
567. C5×Dic3C22×AGL(1,𝔽5)semidirect
577. C5×D5C4×#67semidirect
637. C22×D5D3×AGL(1,𝔽5)semidirect
722. C3×D5D4×AGL(1,𝔽5)semidirect
726. C52C2×C4×#67semidirect
759. #67D5⋊AGL(1,𝔽5)direct (N × H)
782. C22×C5C2×D3×AGL(1,𝔽5)semidirect
811. C2×D5C2×D3×AGL(1,𝔽5)semidirect
872. C3×C5C2×D4×AGL(1,𝔽5)semidirect
885. C22×C3C2×D5⋊AGL(1,𝔽5)semidirect
894. C2×D3C2×D5⋊AGL(1,𝔽5)semidirect
905. Dic3C2×D5⋊AGL(1,𝔽5)semidirect
925. D5AGL(1,𝔽5)×#67semidirect
984. C5C2×AGL(1,𝔽5)×#67semidirect
1006. C22D3×D5⋊AGL(1,𝔽5)semidirect
1018. C3D4×D5⋊AGL(1,𝔽5)semidirect

Maximal subgroups

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

subgroupindex
#722310972
#722310922
#722310712
#67×#10442
#722310562
D52×#672
#722310222
#722310172
Dic3×D5⋊AGL(1,𝔽5)2
#722305612
#67×#10432
C22×C3×D5⋊AGL(1,𝔽5)2
#722245862
#722245852
C2×D3×D5⋊AGL(1,𝔽5)2
D4×D5⋊AGL(1,𝔽5)3
C2×AGL(1,𝔽5)×#675