Finite Group Databasebeta

← D3×#11717377 #72231602

Subgroups — D3×#11717377 #72231602

Order 4800.

1968 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72231097C211yesmaximal, characteristic, complemented
2#72231045C211yesmaximal, characteristic, complemented
3#72231033C211yesmaximal, characteristic, complemented
4#72231031C211yesmaximal, characteristic, complemented
5#72231017C211yesmaximal, characteristic, complemented
6#72230748C211yesmaximal, characteristic, complemented
7#72229795C211yesmaximal, characteristic, complemented
8C3×#11717377C211yesmaximal, characteristic, complemented
9D3×C22⋊#1043C211yesmaximal, characteristic, complemented
10C22×D3×#1044C211yesmaximal, characteristic, complemented
11D3×#87831C211yesmaximal, characteristic, complemented
12D3×#87832C211yesmaximal, characteristic, complemented
13D3×#87886C211yesmaximal, characteristic
14D3×#87830C211yesmaximal, characteristic, complemented
15C2×D3×D5⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
16C2×#11717377—31nomaximal, Hall
17C22×D3×C5⋊D5C2211yescharacteristic
18C22×C3⋊#1044C2211yescharacteristic, complemented
19C22×C3×#1044C2211yescharacteristic, complemented
20C2×D3×D52C2211yescharacteristic
21C2×#10597183C2211yescharacteristic, complemented
22C2×#10597182C2211yescharacteristic, complemented
23C2×D5⋊ΓL(1,𝔽16)C2211yescharacteristic, complemented
24C2×D3×#1044—24no—
25C2×D3×#1044C2211yescharacteristic
26C2×D3×#1044C2211yescharacteristic
27C2×D3×#1044C2211yescharacteristic, complemented
28C2×D3×#1044C2211yescharacteristic, complemented
29C2×D3×#1043C2211yescharacteristic
30C2×D3×#1043C2211yescharacteristic
31C2×C3×D5⋊AGL(1,𝔽5)C2211yescharacteristic, complemented
32D3×D5⋊AGL(1,𝔽5)—24no—
33#11925664C2211yescharacteristic
34#11925646C412yescomplemented
35C5×D3×C22⋊D5C412yescomplemented
36C3×#87886C2211yescharacteristic
37#11925533C2211yescharacteristic, complemented
38C3×C22⋊#1043C2211yescharacteristic, complemented
39#11925429C2211yescharacteristic
40#11925428C412yescomplemented
41D3×#6038C412yescomplemented
42#11925419C2211yescharacteristic
43D3×#6036C2211yescharacteristic
44#11925361C2211yescharacteristic, complemented
45#11925360C2211yescharacteristic, complemented
46#11925359C2211yescharacteristic, complemented
47#11925356C2211yescharacteristic, complemented
48#11925355C2211yescharacteristic, complemented
49#11925354C2211yescharacteristic, complemented
50#11925351C2211yescharacteristic, complemented
51#11925350C2211yescharacteristic, complemented
52#11925349C2211yescharacteristic, complemented
53(C2×D3)⋊#1043C2211yescharacteristic, complemented
54(C2×D3)⋊#1043C2211yescharacteristic, complemented
55C3×#87832C2211yescharacteristic, complemented
56C3×#87831C2211yescharacteristic, complemented
57C3×#87830C2211yescharacteristic, complemented
58D3×D4×AGL(1,𝔽5)—52nomaximal
59C23×#1044—31no—
60C22×D5⋊AGL(1,𝔽5)—31no—
61C2×#87886—31no—
62C2×C22⋊#1043—31no—
63#11717377—31no—
64#11717377—31no—
65#11717377—31no—
66#11717377—31no—
67#11717377—31no—
68#11717377—31no—
69#11717377—31no—
70#11717377D311yescharacteristic, direct product factor
71C2×#87832—31no—
72C2×#87831—31no—
73C2×#87830—31no—
74C22×C3⋊(C5⋊D5)C2×C411yescharacteristic, complemented
75C22×C52×D3C2×C411yescharacteristic, complemented
76C22×C3×C5⋊D5C2311yescharacteristic
77C2×D15⋊D5C2311yescharacteristic
78C2×D5×D15C2×C412yescomplemented
79C2×D3×C5⋊D5—22no—
80C2×D3×C5⋊D5—22no—
81C2×D3×C5⋊D5C2×C411yescharacteristic, complemented
82C2×D3×C5⋊D5C2×C411yescharacteristic, complemented
83C2×D3×C5⋊D5C2311yescharacteristic
84C2×D3×C5⋊D5C2311yescharacteristic
85C2×C5×D3×D5C2×C412yescomplemented
86C2×C3×D52C2311yescharacteristic
87C2×C3⋊#1044—22no—
88C2×C3⋊#1044C2311yescharacteristic
89C2×C3⋊#1044C2311yescharacteristic
90C2×C3⋊#1043C2311yescharacteristic
91C2×C3⋊#1043C2311yescharacteristic
92C2×C3×#1044—22no—
93C2×C3×#1044C2311yescharacteristic
94C2×C3×#1044C2311yescharacteristic
95C2×C3×#1043C2311yescharacteristic
96C2×C3×#1043C2311yescharacteristic
97D3×D52—22no—
98D3×D52—22no—
99#10597183—22no—
100#10597182—22no—
101D5⋊ΓL(1,𝔽16)—22no—
102D3×#1044—22no—
103D3×#1044—22no—
104D3×#1044—22no—
105D3×#1044D414yescomplemented
106D3×#1043—22no—
107D3×#1043—22no—
108C3×D5⋊AGL(1,𝔽5)—22no—
109C5×#1220C2×C412yescomplemented
110C3×C5×C22⋊D5C2×C412yescomplemented
111#10597127C2×C412yescomplemented
112#10597126C2311yescharacteristic
113#10597123C2×C412yescomplemented
114#10597122C2×C412yescomplemented
115#10597120C2×C412yescomplemented
116C5×#1203C2×C412yescomplemented
117C5×#1201C2×C412yescomplemented
118C5×D3×Dic5C2×C412yescomplemented
119C3×#6038C2×C412yescomplemented
120C3×#6036C2311yescharacteristic
121C22×D3×AGL(1,𝔽5)—52no—
122C22×D3×AGL(1,𝔽5)—52no—
123D3×D4×D5—52no—
124D4×ΓL(1,𝔽16)—52no—
125C3×D4×AGL(1,𝔽5)—52no—
126#67⋊AGL(1,𝔽5)—52no—
127#67⋊AGL(1,𝔽5)—52no—
128D3×C22⋊AGL(1,𝔽5)—52no—
129D3×C22⋊AGL(1,𝔽5)—52no—
130D3×C22⋊AGL(1,𝔽5)—102no—
131AGL(1,𝔽5)×#67—52no—
132AGL(1,𝔽5)×#67—52no—
133#91921—52no—
134D3×C4⋊AGL(1,𝔽5)—52no—
135AGL(1,𝔽5)×D12—52no—
136C4×D3×AGL(1,𝔽5)—52no—
137C23×C5⋊D5—31no—
138C22×D52—31no—
139C22×#1044—31no—
140C22×#1044—31no—
141C22×#1044—31no—
142C22×#1044—31no—
143C22×#1044—31no—
144C22×#1044—64no—
145C22×#1044C2×D311yescharacteristic, complemented
146C22×#1043—31no—
147C22×#1043—31no—
148C2×D5⋊AGL(1,𝔽5)—31no—
149C2×D5⋊AGL(1,𝔽5)—31no—
150C2×D5⋊AGL(1,𝔽5)—31no—
151C2×D5⋊AGL(1,𝔽5)—64no—
152C2×D5⋊AGL(1,𝔽5)C2×D311yescharacteristic, complemented
153C2×C5×C22⋊D5—32no—
154#87886—31no—
155#87886—31no—
156#87886—32no—
157#87886—32no—
158#87886—31no—
159#87886C2×D311yescharacteristic
160C2×#6038—32no—
161C2×#6036—31no—
162C22⋊#1043—31no—
163C22⋊#1043—31no—
164C22⋊#1043—31no—
165C22⋊#1043C2×D311yescharacteristic, complemented
166#87832—31no—
167#87832—31no—
168#87832—31no—
169#87832C2×D311yescharacteristic, complemented
170#87831—31no—
171#87831—31no—
172#87831—31no—
173#87831C2×D311yescharacteristic, complemented
174#87830—31no—
175#87830—31no—
176#87830—31no—
177#87830C2×D311yescharacteristic, complemented
178C2×D4×AGL(1,𝔽5)—152no—
179C22×C3×C52C22×C411yescharacteristic, complemented
180C2×C3⋊(C5⋊D5)—22no—
181C2×C3⋊(C5⋊D5)C22×C411yescharacteristic
182C2×C3⋊(C5⋊D5)C22×C411yescharacteristic, complemented
183C2×C5×D15C22×C412yescomplemented
184C2×C52×D3—22no—
185C2×C52×D3C22×C411yescharacteristic
186C2×C52×D3C22×C411yescharacteristic, complemented
187C2×C3×C5⋊D5—21no—
188C2×C3×C5⋊D5—21no—
189C2×C3×C5⋊D5C22×C411yescharacteristic, complemented
190C2×C3×C5⋊D5C2411yescharacteristic
191C2×C3×C5×D5C22×C412yescomplemented
192D15⋊D5—21no—
193D15⋊D5—21no—
194D5×D15—24no—
195D3×C5⋊D5—22no—
196D3×C5⋊D5—22no—
197D3×C5⋊D5—21no—
198D3×C5⋊D5—21no—
199D3×C5⋊D5C2×D412yes—
200D3×C5⋊D5#4112yes—
201C5×D3×D5—24no—
202C3×D52—21no—
203C3×D52—21no—
204C3⋊#1044—21no—
205C3⋊#1044C2×D412yescomplemented
206C3⋊#1043—21no—
207C3⋊#1043—21no—
208C3×#1044—21no—
209C3×#1044C2×D412yescomplemented
210C3×#1043—21no—
211C3×#1043—21no—
212C5×Dic15C22×C412yescomplemented
213C3×C5×Dic5C22×C412yescomplemented
214C22×D3×D5—52no—
215C22×D3×D5—52no—
216C22×D3×D5—102no—
217C22×ΓL(1,𝔽16)—52no—
218C22×ΓL(1,𝔽16)—52no—
219C22×C3×AGL(1,𝔽5)—52no—
220C22×C3×AGL(1,𝔽5)—52no—
221C2×D3×AGL(1,𝔽5)—52no—
222C2×D3×AGL(1,𝔽5)—52no—
223C2×D3×AGL(1,𝔽5)—52no—
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)—52no—
229C2×D3×AGL(1,𝔽5)—108no—
230C2×D3×AGL(1,𝔽5)—108no—
231C2×D3×AGL(1,𝔽5)—102no—
232C2×D3×AGL(1,𝔽5)—102no—
233D4×D15—52no—
234C5×D3×D4—52no—
235C3×D4×D5—52no—
236#6790—52no—
237#6790—52no—
238D3×C22⋊D5—52no—
239D3×C22⋊D5AGL(1,𝔽5)12yescomplemented
240D5×#67—52no—
241D5×#67—52no—
242#6777—52no—
243D3×D20—52no—
244D5×D12—52no—
245C4×D3×D5—52no—
246#6763—52no—
247#6763—52no—
248#6763—102no—
249C4⋊ΓL(1,𝔽16)—52no—
250C4×ΓL(1,𝔽16)—52no—
251C3×C22⋊AGL(1,𝔽5)—52no—
252C3×C22⋊AGL(1,𝔽5)—52no—
253C3×C22⋊AGL(1,𝔽5)—102no—
254C3×C4⋊AGL(1,𝔽5)—52no—
255C3×C4×AGL(1,𝔽5)—52no—
256Dic3⋊AGL(1,𝔽5)—52no—
257Dic3⋊AGL(1,𝔽5)—52no—
258(C2×D3)⋊AGL(1,𝔽5)—52no—
259(C2×D3)⋊AGL(1,𝔽5)—52no—
260(C2×D3)⋊AGL(1,𝔽5)—52no—
261(C2×D3)⋊AGL(1,𝔽5)—52no—
262(C2×D3)⋊AGL(1,𝔽5)—102no—
263(C2×D3)⋊AGL(1,𝔽5)—102no—
264Dic3×AGL(1,𝔽5)—52no—
265Dic3×AGL(1,𝔽5)—52no—
266C23×C52—31no—
267C22×C5⋊D5—31no—
268C22×C5⋊D5—31no—
269C22×C5⋊D5—31no—
270C22×C5⋊D5—31no—
271C22×C5⋊D5—31no—
272C22×C5⋊D5—62no—
273C22×C5⋊D5—62no—
274C22×C5⋊D5C22×D311yescharacteristic
275C22×C5×D5—32no—
276C2×D52—31no—
277C2×D52—32no—
278C2×D52—62no—
279C2×D52—62no—
280C2×D52C22×D311yescharacteristic
281C2×#1044—22no—
282C2×#1044—31no—
283C2×#1044—34no—
284C2×#1044—31no—
285C2×#1044—62no—
286C2×#1044—62no—
287C2×#1044—62no—
288C2×#1044—62no—
289C2×#1044C22×D311yescharacteristic
290C2×#1044C22×D311yescharacteristic
291C2×#1043—31no—
292C2×#1043—31no—
293C2×#1043—62no—
294C2×#1043—62no—
295C2×#1043C22×D311yescharacteristic
296C2×#1043C22×D311yescharacteristic
297D5⋊AGL(1,𝔽5)—22no—
298D5⋊AGL(1,𝔽5)—62no—
299D5⋊AGL(1,𝔽5)—62no—
300D5⋊AGL(1,𝔽5)—62no—
301C5×C22⋊D5—32no—
302C5×C22⋊D5—32no—
303C5×C22⋊D5—32no—
304C5×C22⋊D5C4×D312yescomplemented
305C2×C5×Dic5—32no—
306#6038—32no—
307#6038—32no—
308#6038—32no—
309#6038C4×D312yescomplemented
310#6036—31no—
311#6036—32no—
312#6036C22×D311yescharacteristic
313C4×D3×D4—251noHall
314C23×AGL(1,𝔽5)—152no—
315C23×AGL(1,𝔽5)—152no—
316C2×D4×D5—152no—
317C2×C22⋊AGL(1,𝔽5)—152no—
318C2×C22⋊AGL(1,𝔽5)—152no—
319C2×C22⋊AGL(1,𝔽5)—302no—
320D4×AGL(1,𝔽5)—52no—
321D4×AGL(1,𝔽5)—152no—
322D4×AGL(1,𝔽5)—152no—
323D4×AGL(1,𝔽5)—152no—
324D4×AGL(1,𝔽5)—152no—
325D4×AGL(1,𝔽5)—152no—
326D4×AGL(1,𝔽5)—152no—
327D4×AGL(1,𝔽5)—152no—
328C2×C4⋊AGL(1,𝔽5)—152no—
329C2×C4×AGL(1,𝔽5)—152no—
330C2×C3×C52—21no—
331C2×C3×C52C23×C411yescharacteristic
332C3⋊(C5⋊D5)—21no—
333C3⋊(C5⋊D5)C4×D412yescomplemented
334C5×D15—22no—
335C52×D3—21no—
336C52×D3C4×D412yescomplemented
337C3×C5⋊D5—21no—
338C3×C5⋊D5C22×D411yescharacteristic
339C3×C5⋊D5C2×#4111yescharacteristic
340C3×C5×D5—22no—
341C22×D15—52no—
342C22×D15—52no—
343C22×D15—102no—
344C22×C5×D3—22no—
345C22×C5×D3—52no—
346C22×C5×D3C2×AGL(1,𝔽5)12yescomplemented
347C22×C3×D5—52no—
348C22×C3×D5—52no—
349C22×C3×D5—102no—
350C2×D3×D5—52no—
351C2×D3×D5—52no—
352C2×D3×D5—52no—
353C2×D3×D5—52no—
354C2×D3×D5—52no—
355C2×D3×D5—52no—
356C2×D3×D5—104no—
357C2×D3×D5—104no—
358C2×D3×D5—104no—
359C2×D3×D5—104no—
360C2×D3×D5—102no—
361C2×D3×D5—102no—
362C2×D3×D5—102no—
363C2×D3×D5—102no—
364C2×D3×D5—204no—
365C2×D3×D5—204no—
366C2×D3×D5C2×AGL(1,𝔽5)12yescomplemented
367C2×ΓL(1,𝔽16)—52no—
368C2×ΓL(1,𝔽16)—52no—
369C2×ΓL(1,𝔽16)—52no—
370C2×ΓL(1,𝔽16)—52no—
371C2×ΓL(1,𝔽16)—104no—
372C2×ΓL(1,𝔽16)—104no—
373C2×ΓL(1,𝔽16)—102no—
374C2×ΓL(1,𝔽16)—102no—
375C2×C3×AGL(1,𝔽5)—52no—
376C2×C3×AGL(1,𝔽5)—52no—
377C2×C3×AGL(1,𝔽5)—52no—
378C2×C3×AGL(1,𝔽5)—52no—
379C2×C3×AGL(1,𝔽5)—104no—
380C2×C3×AGL(1,𝔽5)—104no—
381C2×C3×AGL(1,𝔽5)—102no—
382C2×C3×AGL(1,𝔽5)—102no—
383D3×AGL(1,𝔽5)—58no—
384D3×AGL(1,𝔽5)—104no—
385D3×AGL(1,𝔽5)—104no—
386D3×AGL(1,𝔽5)—104no—
387D3×AGL(1,𝔽5)—104no—
388D3×AGL(1,𝔽5)—104no—
389D3×AGL(1,𝔽5)—104no—
390D3×AGL(1,𝔽5)—104no—
391D3×AGL(1,𝔽5)—204no—
392D3×AGL(1,𝔽5)—204no—
393C3×C5×D4—52no—
394#1220—52no—
395#1220C2×AGL(1,𝔽5)12yescomplemented
396D60—52no—
397C4×D15—52no—
398C5×#67—52no—
399C5×#67—52no—
400C5×D12—52no—
401C4×C5×D3—52no—
402C3×C22⋊D5—52no—
403C3×C22⋊D5C2×AGL(1,𝔽5)12yescomplemented
404C3×D20—52no—
405C3×C4×D5—52no—
406#1203—52no—
407#1203C2×AGL(1,𝔽5)12yescomplemented
408#1202—52no—
409#1202—52no—
410#1201—52no—
411#1201C2×AGL(1,𝔽5)12yescomplemented
412#1200—52no—
413D3×Dic5C2×AGL(1,𝔽5)12yescomplemented
414D5×Dic3—52no—
415C22×C52—31no—
416C22×C52—31no—
417C22×C52—62no—
418C22×C52C2×C4×D311yescharacteristic, complemented
419C2×C5⋊D5—21no—
420C2×C5⋊D5—21no—
421C2×C5⋊D5—31no—
422C2×C5⋊D5—32no—
423C2×C5⋊D5—32no—
424C2×C5⋊D5—31no—
425C2×C5⋊D5—62no—
426C2×C5⋊D5—62no—
427C2×C5⋊D5—62no—
428C2×C5⋊D5—61no—
429C2×C5⋊D5—61no—
430C2×C5⋊D5C2×C4×D311yescharacteristic, complemented
431C2×C5⋊D5C23×D311yescharacteristic
432C2×C5×D5—32no—
433C2×C5×D5—64no—
434C2×C5×D5C2×C4×D312yescomplemented
435D52—21no—
436D52—21no—
437D52—64no—
438D52—61no—
439D52—61no—
440#1044—21no—
441#1044—32no—
442#1044—61no—
443#1044D3×D412yescomplemented
444#1043—21no—
445#1043—21no—
446#1043—61no—
447#1043—61no—
448C5×Dic5—32no—
449C5×Dic5C2×C4×D312yescomplemented
450C2×D3×D4—251no—
451C22×C4×D3—251no—
452C22×C4×D3—251no—
453C3×C4×D4—251no—
454D4×Dic3—251no—
455C4×#67—251no—
456C4×#67—251no—
457#893—251no—
458D3×C4⋊C4—251no—
459#67⋊C4—251no—
460#67⋊C4—251no—
461D3×C22⋊C4—251no—
462D3×C22⋊C4—251no—
463C4×D12—251no—
464C42×D3—251no—
465C23×D5—152no—
466C23×D5—152no—
467C23×D5—302no—
468C22×AGL(1,𝔽5)—52no—
469C22×AGL(1,𝔽5)—52no—
470C22×AGL(1,𝔽5)—152no—
471C22×AGL(1,𝔽5)—152no—
472C22×AGL(1,𝔽5)—152no—
473C22×AGL(1,𝔽5)—152no—
474C22×AGL(1,𝔽5)—152no—
475C22×AGL(1,𝔽5)—152no—
476C22×AGL(1,𝔽5)—152no—
477C22×AGL(1,𝔽5)—152no—
478C22×AGL(1,𝔽5)—152no—
479C22×AGL(1,𝔽5)—152no—
480C22×AGL(1,𝔽5)—302no—
481C22×AGL(1,𝔽5)—302no—
482C22×AGL(1,𝔽5)—308no—
483C22×AGL(1,𝔽5)—308no—
484C2×C5×D4—152no—
485C2×C22⋊D5—32no—
486C2×C22⋊D5—152no—
487D4×D5—52no—
488D4×D5—152no—
489D4×D5—152no—
490D4×D5—152no—
491D4×D5—152no—
492D4×D5—152no—
493D4×D5—152no—
494D4×D5—152no—
495C2×D20—152no—
496C2×C4×D5—152no—
497C22⋊AGL(1,𝔽5)—52no—
498C22⋊AGL(1,𝔽5)—52no—
499C22⋊AGL(1,𝔽5)—102no—
500C22⋊AGL(1,𝔽5)—152no—
501C22⋊AGL(1,𝔽5)—152no—
502C22⋊AGL(1,𝔽5)—152no—
503C22⋊AGL(1,𝔽5)—152no—
504C22⋊AGL(1,𝔽5)—152no—
505C22⋊AGL(1,𝔽5)—152no—
506C22⋊AGL(1,𝔽5)—302no—
507C22⋊AGL(1,𝔽5)—302no—
508C22⋊AGL(1,𝔽5)—302no—
509C4⋊AGL(1,𝔽5)—52no—
510C4⋊AGL(1,𝔽5)—152no—
511C4⋊AGL(1,𝔽5)—152no—
512C4⋊AGL(1,𝔽5)—152no—
513C4×AGL(1,𝔽5)—52no—
514C4×AGL(1,𝔽5)—152no—
515C4×AGL(1,𝔽5)—152no—
516C4×AGL(1,𝔽5)—152no—
517C3×C52C2×C4×D411yescharacteristic, complemented, Hall
518C2×C4×D4—751noSylow
519C22×C3×C5—22no—
520C22×C3×C5—52no—
521C22×C3×C5C22×AGL(1,𝔽5)12yescomplemented
522C2×D15—52no—
523C2×D15—52no—
524C2×D15—102no—
525C2×D15—102no—
526C2×D15—104no—
527C2×D15—104no—
528C2×D15—204no—
529C2×D15C22×AGL(1,𝔽5)12yescomplemented
530C2×C5×D3—24no—
531C2×C5×D3—22no—
532C2×C5×D3—22no—
533C2×C5×D3—44no—
534C2×C5×D3—52no—
535C2×C5×D3—104no—
536C2×C5×D3C22×AGL(1,𝔽5)12yes—
537C2×C5×D3C22×AGL(1,𝔽5)12yescomplemented
538C2×C3×D5—52no—
539C2×C3×D5—52no—
540C2×C3×D5—102no—
541C2×C3×D5—102no—
542C2×C3×D5—102no—
543C2×C3×D5—102no—
544C2×C3×D5—102no—
545C2×C3×D5—102no—
546C2×C3×D5—202no—
547C2×C3×D5—202no—
548C2×C3×D5C22×AGL(1,𝔽5)12yescomplemented
549D3×D5—24no—
550D3×D5—54no—
551D3×D5—54no—
552D3×D5—104no—
553D3×D5—104no—
554D3×D5—102no—
555D3×D5—102no—
556D3×D5—104no—
557D3×D5—104no—
558D3×D5—102no—
559D3×D5—102no—
560D3×D5—104no—
561D3×D5—204no—
562D3×D5—202no—
563D3×D5—202no—
564D3×D5—204no—
565ΓL(1,𝔽16)—54no—
566ΓL(1,𝔽16)—102no—
567ΓL(1,𝔽16)—102no—
568ΓL(1,𝔽16)—102no—
569ΓL(1,𝔽16)—202no—
570ΓL(1,𝔽16)—202no—
571C3×AGL(1,𝔽5)—54no—
572C3×AGL(1,𝔽5)—102no—
573C3×AGL(1,𝔽5)—102no—
574C3×AGL(1,𝔽5)—102no—
575C3×AGL(1,𝔽5)—202no—
576C3×AGL(1,𝔽5)—202no—
577C3×C4×C5—52no—
578Dic15C22×AGL(1,𝔽5)12yescomplemented
579C3×Dic5C22×AGL(1,𝔽5)12yescomplemented
580C5×Dic3—52no—
581C2×C52—21no—
582C2×C52—32no—
583C2×C52—61no—
584C2×C52C22×C4×D311yescharacteristic
585C5⋊D5—21no—
586C5⋊D5—32no—
587C5⋊D5—61no—
588C5⋊D5C2×D3×D411yescharacteristic
589C5⋊D5D3×#4111yescharacteristic
590C5×D5—22no—
591C5×D5—62no—
592C23×D3—251no—
593C23×D3—251no—
594C2×C3×D4—251no—
595C22×C3×C4—251no—
596C22×C3×C4—251no—
597C2×#67—251no—
598C2×#67—251no—
599C22×Dic3—251no—
600C22×Dic3—251no—
601D3×D4—52no—
602D3×D4—252no—
603D3×D4—252no—
604D3×D4—252no—
605C2×D12—251no—
606C2×C4×D3—251no—
607C2×C4×D3—251no—
608C2×C4×D3—251no—
609C2×C4×D3—251no—
610C2×C4×D3—251no—
611C2×C4×D3—251no—
612C2×C4×D3—251no—
613C2×C4×D3—251no—
614C2×C4×D3—251no—
615C2×C4×D3—504no—
616C2×C4×D3—504no—
617C3×C4⋊C4—251no—
618C3×C22⋊C4—251no—
619C3×C22⋊C4—251no—
620C3×C42—251no—
621#217—251no—
622#217—251no—
623(C2×D3)⋊C4—251no—
624(C2×D3)⋊C4—251no—
625(C2×D3)⋊C4—251no—
626(C2×D3)⋊C4—251no—
627C4⋊Dic3—251no—
628Dic3⋊C4—251no—
629Dic3⋊C4—251no—
630C4×Dic3—251no—
631C4×Dic3—251no—
632C4×Dic3—251no—
633C23×C5—32no—
634C23×C5—62no—
635C23×C5—152no—
636C22×D5—32no—
637C22×D5—52no—
638C22×D5—52no—
639C22×D5—102no—
640C22×D5—152no—
641C22×D5—152no—
642C22×D5—152no—
643C22×D5—152no—
644C22×D5—152no—
645C22×D5—152no—
646C22×D5—152no—
647C22×D5—152no—
648C22×D5—302no—
649C22×D5—302no—
650C22×D5—302no—
651C22×D5—302no—
652C22×D5—302no—
653C22×D5—304no—
654C22×D5—304no—
655C22×D5—304no—
656C22×D5—304no—
657C22×D5—604no—
658C22×D5—604no—
659C2×AGL(1,𝔽5)—52no—
660C2×AGL(1,𝔽5)—52no—
661C2×AGL(1,𝔽5)—52no—
662C2×AGL(1,𝔽5)—52no—
663C2×AGL(1,𝔽5)—102no—
664C2×AGL(1,𝔽5)—102no—
665C2×AGL(1,𝔽5)—104no—
666C2×AGL(1,𝔽5)—104no—
667C2×AGL(1,𝔽5)—158no—
668C2×AGL(1,𝔽5)—152no—
669C2×AGL(1,𝔽5)—152no—
670C2×AGL(1,𝔽5)—152no—
671C2×AGL(1,𝔽5)—152no—
672C2×AGL(1,𝔽5)—302no—
673C2×AGL(1,𝔽5)—302no—
674C2×AGL(1,𝔽5)—304no—
675C2×AGL(1,𝔽5)—304no—
676C2×AGL(1,𝔽5)—304no—
677C2×AGL(1,𝔽5)—304no—
678C2×AGL(1,𝔽5)—304no—
679C2×AGL(1,𝔽5)—304no—
680C2×AGL(1,𝔽5)—304no—
681C2×AGL(1,𝔽5)—304no—
682C2×AGL(1,𝔽5)—304no—
683C2×AGL(1,𝔽5)—604no—
684C2×AGL(1,𝔽5)—604no—
685C5×D4—52no—
686C5×D4—152no—
687C5×D4—152no—
688C5×D4—152no—
689C2×C4×C5—152no—
690C22⋊D5—32no—
691C22⋊D5—32no—
692C22⋊D5—32no—
693C22⋊D5—52no—
694C22⋊D5—152no—
695C22⋊D5—152no—
696C22⋊D5—152no—
697C22⋊D5D3×AGL(1,𝔽5)12yescomplemented
698C2×Dic5—32no—
699D20—52no—
700D20—152no—
701D20—152no—
702D20—152no—
703C4×D5—52no—
704C4×D5—152no—
705C4×D5—152no—
706C4×D5—152no—
707C22×D4—751no—
708C23×C4—751no—
709C23×C4—751no—
710C4×D4—251no—
711C4×D4—751no—
712C4×D4—751no—
713C4×D4—751no—
714C4×D4—751no—
715C4×D4—751no—
716C4×D4—751no—
717C4×D4—751no—
718C2×C4⋊C4—751no—
719C2×C22⋊C4—751no—
720C2×C22⋊C4—751no—
721C2×C42—751no—
722C2×C3×C5—22no—
723C2×C3×C5—22no—
724C2×C3×C5—42no—
725C2×C3×C5—102no—
726C2×C3×C5C23×AGL(1,𝔽5)12yes—
727D15—22no—
728D15—54no—
729D15—104no—
730D15—102no—
731D15—202no—
732C3×D5—22no—
733C3×D5—52no—
734C3×D5—52no—
735C3×D5—102no—
736C3×D5—102no—
737C3×D5—102no—
738C3×D5—202no—
739C5×D3—22no—
740C5×D3—24no—
741C5×D3—42no—
742C5×D3—102no—
743C5×D3D4×AGL(1,𝔽5)14yescomplemented
744C52C4×D3×D411yescharacteristic, complemented, Sylow
745C23×C3—251no—
746C23×C3—251no—
747C22×D3—52no—
748C22×D3—251no—
749C22×D3—252no—
750C22×D3—251no—
751C22×D3—251no—
752C22×D3—251no—
753C22×D3—251no—
754C22×D3—251no—
755C22×D3—502no—
756C22×D3—502no—
757C22×D3—502no—
758C22×D3—502no—
759C22×D3D5⋊AGL(1,𝔽5)11yescharacteristic, complemented
760C3×D4—52no—
761C3×D4—252no—
762C2×C3×C4—251no—
763C2×C3×C4—251no—
764C2×C3×C4—251no—
765C2×C3×C4—251no—
766C2×C3×C4—251no—
767C2×C3×C4—502no—
768C2×C3×C4—502no—
769#67—52no—
770#67—52no—
771#67—252no—
772#67—252no—
773C2×Dic3—251no—
774C2×Dic3—251no—
775C2×Dic3—251no—
776C2×Dic3—251no—
777C2×Dic3—251no—
778C2×Dic3—502no—
779C2×Dic3—502no—
780D12—52no—
781D12—252no—
782C4×D3—52no—
783C4×D3—252no—
784C4×D3—254no—
785C4×D3—502no—
786C4×D3—502no—
787C4×D3—502no—
788C4×D3—502no—
789C4×D3—502no—
790C4×D3—502no—
791C4×D3—502no—
792C22×C5—22no—
793C22×C5—32no—
794C22×C5—32no—
795C22×C5—52no—
796C22×C5—62no—
797C22×C5—62no—
798C22×C5—64no—
799C22×C5—124no—
800C22×C5—152no—
801C22×C5—304no—
802C22×C5C2×D3×AGL(1,𝔽5)12yescomplemented
803C2×D5—32no—
804C2×D5—52no—
805C2×D5—52no—
806C2×D5—64no—
807C2×D5—102no—
808C2×D5—102no—
809C2×D5—102no—
810C2×D5—102no—
811C2×D5—102no—
812C2×D5—102no—
813C2×D5—154no—
814C2×D5—154no—
815C2×D5—152no—
816C2×D5—152no—
817C2×D5—202no—
818C2×D5—202no—
819C2×D5—304no—
820C2×D5—304no—
821C2×D5—302no—
822C2×D5—302no—
823C2×D5—304no—
824C2×D5—302no—
825C2×D5—302no—
826C2×D5—302no—
827C2×D5—302no—
828C2×D5—304no—
829C2×D5—304no—
830C2×D5—304no—
831C2×D5—304no—
832C2×D5—602no—
833C2×D5—602no—
834C2×D5—604no—
835C2×D5—604no—
836C2×D5—604no—
837C2×D5C2×D3×AGL(1,𝔽5)12yescomplemented
838AGL(1,𝔽5)—54no—
839AGL(1,𝔽5)—102no—
840AGL(1,𝔽5)—102no—
841AGL(1,𝔽5)—102no—
842AGL(1,𝔽5)—154no—
843AGL(1,𝔽5)—202no—
844AGL(1,𝔽5)—202no—
845AGL(1,𝔽5)—302no—
846AGL(1,𝔽5)—302no—
847AGL(1,𝔽5)—302no—
848AGL(1,𝔽5)—602no—
849AGL(1,𝔽5)—602no—
850C4×C5—52no—
851C4×C5—152no—
852Dic5—32no—
853Dic5C2×D3×AGL(1,𝔽5)12yescomplemented
854C24—751no—
855C24—751no—
856C2×D4—152no—
857C2×D4—251no—
858C2×D4—752no—
859C2×D4—751no—
860C2×D4—752no—
861C2×D4—752no—
862C2×D4—751no—
863C2×D4—751no—
864C22×C4—251no—
865C22×C4—251no—
866C22×C4—751no—
867C22×C4—751no—
868C22×C4—751no—
869C22×C4—751no—
870C22×C4—751no—
871C22×C4—751no—
872C22×C4—751no—
873C22×C4—751no—
874C22×C4—751no—
875C22×C4—751no—
876C22×C4—751no—
877C22×C4—1504no—
878C22×C4—1504no—
879C4⋊C4—251no—
880C4⋊C4—751no—
881C4⋊C4—751no—
882C4⋊C4—751no—
883C22⋊C4—251no—
884C22⋊C4—251no—
885C22⋊C4—751no—
886C22⋊C4—751no—
887C22⋊C4—751no—
888C22⋊C4—751no—
889C22⋊C4—751no—
890C22⋊C4—751no—
891C42—251no—
892C42—751no—
893C42—751no—
894C42—751no—
895C3×C5—22no—
896C3×C5C2×D4×AGL(1,𝔽5)12yescomplemented
897C22×C3—52no—
898C22×C3—251no—
899C22×C3—251no—
900C22×C3—501no—
901C22×C3—501no—
902C22×C3—501no—
903C22×C3—501no—
904C22×C3C2×D5⋊AGL(1,𝔽5)11yescharacteristic, complemented
905C2×D3—22no—
906C2×D3—52no—
907C2×D3—104no—
908C2×D3—251no—
909C2×D3—252no—
910C2×D3—252no—
911C2×D3—251no—
912C2×D3—502no—
913C2×D3—501no—
914C2×D3—501no—
915C2×D3—501no—
916C2×D3—501no—
917C2×D3—504no—
918C2×D3—502no—
919C2×D3—502no—
920C2×D3C2×D5⋊AGL(1,𝔽5)11yescharacteristic
921C2×D3C2×D5⋊AGL(1,𝔽5)11yescharacteristic, complemented
922C3×C4—52no—
923C3×C4—252no—
924C3×C4—501no—
925C3×C4—501no—
926C3×C4—501no—
927Dic3—52no—
928Dic3—252no—
929Dic3—501no—
930Dic3—501no—
931Dic3—501no—
932C2×C5—22no—
933C2×C5—22no—
934C2×C5—34no—
935C2×C5—42no—
936C2×C5—64no—
937C2×C5—62no—
938C2×C5—102no—
939C2×C5—122no—
940C2×C5—302no—
941C2×C5C22×D3×AGL(1,𝔽5)12yes—
942D5—22no—
943D5—52no—
944D5—52no—
945D5—62no—
946D5—102no—
947D5—102no—
948D5—102no—
949D5—154no—
950D5—202no—
951D5—304no—
952D5—302no—
953D5—602no—
954C23—31no—
955C23—152no—
956C23—251no—
957C23—251no—
958C23—751no—
959C23—751no—
960C23—751no—
961C23—751no—
962C23—752no—
963C23—751no—
964C23—751no—
965C23—1502no—
966C23—1502no—
967C23—1502no—
968C23—1502no—
969D4—52no—
970D4—152no—
971D4—152no—
972D4—152no—
973D4—252no—
974D4—752no—
975D4—752no—
976D4—752no—
977C2×C4—152no—
978C2×C4—251no—
979C2×C4—251no—
980C2×C4—251no—
981C2×C4—251no—
982C2×C4—251no—
983C2×C4—502no—
984C2×C4—502no—
985C2×C4—752no—
986C2×C4—751no—
987C2×C4—754no—
988C2×C4—751no—
989C2×C4—751no—
990C2×C4—751no—
991C2×C4—751no—
992C2×C4—1502no—
993C2×C4—1502no—
994C2×C4—1502no—
995C2×C4—1502no—
996C2×C4—1502no—
997C2×C4—1502no—
998C2×C4—1502no—
999C2×C4—1502no—
1000C2×C4—1502no—
1001C2×C3—21no—
1002C2×C3—102no—
1003C2×C3—251no—
1004C2×C3—251no—
1005C2×C3—501no—
1006C2×C3C22×D5⋊AGL(1,𝔽5)11yescharacteristic
1007D3—21no—
1008D3—102no—
1009D3—252no—
1010D3—501no—
1011D3#1171737712yesdirect product factor
1012C5—22no—
1013C5D3×D4×AGL(1,𝔽5)12yescomplemented
1014C22—31no—
1015C22—31no—
1016C22—52no—
1017C22—62no—
1018C22—152no—
1019C22—251no—
1020C22—251no—
1021C22—304no—
1022C22—501no—
1023C22—501no—
1024C22—501no—
1025C22—501no—
1026C22—752no—
1027C22—752no—
1028C22—751no—
1029C22—751no—
1030C22—1502no—
1031C22—1502no—
1032C22—1501no—
1033C22—1501no—
1034C22—1502no—
1035C22—1504no—
1036C22—1501no—
1037C22—1501no—
1038C22D3×D5⋊AGL(1,𝔽5)11yescharacteristic, complemented
1039C4—52no—
1040C4—152no—
1041C4—252no—
1042C4—501no—
1043C4—501no—
1044C4—501no—
1045C4—752no—
1046C4—1501no—
1047C4—1501no—
1048C4—1501no—
1049C3C2×#1171737711yescharacteristic, complemented, Sylow
1050C2—21no—
1051C2—32no—
1052C2—61no—
1053C2—102no—
1054C2—251no—
1055C2—251no—
1056C2—302no—
1057C2—501no—
1058C2—752no—
1059C2—1501no—
1060C2C2×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 radicalD3×#87886C2
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. #72231045C2semidirect
3. #72231033C2semidirect
4. #72231031C2semidirect
5. #72231017C2semidirect
6. #72230748C2semidirect
7. #72229795C2semidirect
8. C3×#11717377C2semidirect
9. D3×C22⋊#1043C2semidirect
10. C22×D3×#1044C2semidirect
11. D3×#87831C2semidirect
12. D3×#87832C2semidirect
14. D3×#87830C2semidirect
15. C2×D3×D5⋊AGL(1,𝔽5)C2semidirect
18. C22×C3⋊#1044C22semidirect
19. C22×C3×#1044C22semidirect
21. C2×#10597183C22semidirect
22. C2×#10597182C22semidirect
23. C2×D5⋊ΓL(1,𝔽16)C22semidirect
27. C2×D3×#1044C22semidirect
28. C2×D3×#1044C22semidirect
31. C2×C3×D5⋊AGL(1,𝔽5)C22semidirect
34. #11925646C4semidirect
35. C5×D3×C22⋊D5C4semidirect
37. #11925533C22semidirect
38. C3×C22⋊#1043C22semidirect
40. #11925428C4semidirect
41. D3×#6038C4semidirect
44. #11925361C22semidirect
45. #11925360C22semidirect
46. #11925359C22semidirect
47. #11925356C22semidirect
48. #11925355C22semidirect
49. #11925354C22semidirect
50. #11925351C22semidirect
51. #11925350C22semidirect
52. #11925349C22semidirect
53. (C2×D3)⋊#1043C22semidirect
54. (C2×D3)⋊#1043C22semidirect
55. C3×#87832C22semidirect
56. C3×#87831C22semidirect
57. C3×#87830C22semidirect
70. #11717377D3direct (N × H)
74. C22×C3⋊(C5⋊D5)C2×C4semidirect
75. C22×C52×D3C2×C4semidirect
78. C2×D5×D15C2×C4semidirect
81. C2×D3×C5⋊D5C2×C4semidirect
82. C2×D3×C5⋊D5C2×C4semidirect
85. C2×C5×D3×D5C2×C4semidirect
105. D3×#1044D4semidirect
109. C5×#1220C2×C4semidirect
110. C3×C5×C22⋊D5C2×C4semidirect
111. #10597127C2×C4semidirect
113. #10597123C2×C4semidirect
114. #10597122C2×C4semidirect
115. #10597120C2×C4semidirect
116. C5×#1203C2×C4semidirect
117. C5×#1201C2×C4semidirect
118. C5×D3×Dic5C2×C4semidirect
119. C3×#6038C2×C4semidirect
145. C22×#1044C2×D3semidirect
152. C2×D5⋊AGL(1,𝔽5)C2×D3semidirect
165. C22⋊#1043C2×D3semidirect
169. #87832C2×D3semidirect
173. #87831C2×D3semidirect
177. #87830C2×D3semidirect
179. C22×C3×C52C22×C4semidirect
182. C2×C3⋊(C5⋊D5)C22×C4semidirect
183. C2×C5×D15C22×C4semidirect
186. C2×C52×D3C22×C4semidirect
189. C2×C3×C5⋊D5C22×C4semidirect
191. C2×C3×C5×D5C22×C4semidirect
205. C3⋊#1044C2×D4semidirect
209. C3×#1044C2×D4semidirect
212. C5×Dic15C22×C4semidirect
213. C3×C5×Dic5C22×C4semidirect
239. D3×C22⋊D5AGL(1,𝔽5)semidirect
304. C5×C22⋊D5C4×D3semidirect
309. #6038C4×D3semidirect
333. C3⋊(C5⋊D5)C4×D4semidirect
336. C52×D3C4×D4semidirect
346. C22×C5×D3C2×AGL(1,𝔽5)semidirect
366. C2×D3×D5C2×AGL(1,𝔽5)semidirect
395. #1220C2×AGL(1,𝔽5)semidirect
403. C3×C22⋊D5C2×AGL(1,𝔽5)semidirect
407. #1203C2×AGL(1,𝔽5)semidirect
411. #1201C2×AGL(1,𝔽5)semidirect
413. D3×Dic5C2×AGL(1,𝔽5)semidirect
418. C22×C52C2×C4×D3semidirect
430. C2×C5⋊D5C2×C4×D3semidirect
434. C2×C5×D5C2×C4×D3semidirect
443. #1044D3×D4semidirect
449. C5×Dic5C2×C4×D3semidirect
517. C3×C52C2×C4×D4semidirect
521. C22×C3×C5C22×AGL(1,𝔽5)semidirect
529. C2×D15C22×AGL(1,𝔽5)semidirect
537. C2×C5×D3C22×AGL(1,𝔽5)semidirect
548. C2×C3×D5C22×AGL(1,𝔽5)semidirect
578. Dic15C22×AGL(1,𝔽5)semidirect
579. C3×Dic5C22×AGL(1,𝔽5)semidirect
697. C22⋊D5D3×AGL(1,𝔽5)semidirect
743. C5×D3D4×AGL(1,𝔽5)semidirect
744. C52C4×D3×D4semidirect
759. C22×D3D5⋊AGL(1,𝔽5)semidirect
802. C22×C5C2×D3×AGL(1,𝔽5)semidirect
837. C2×D5C2×D3×AGL(1,𝔽5)semidirect
853. Dic5C2×D3×AGL(1,𝔽5)semidirect
896. C3×C5C2×D4×AGL(1,𝔽5)semidirect
904. C22×C3C2×D5⋊AGL(1,𝔽5)semidirect
921. C2×D3C2×D5⋊AGL(1,𝔽5)semidirect
1011. D3#11717377direct (N × H)
1013. C5D3×D4×AGL(1,𝔽5)semidirect
1038. C22D3×D5⋊AGL(1,𝔽5)semidirect
1049. C3C2×#11717377semidirect

Maximal subgroups

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

subgroupindex
#722310972
#722310452
#722310332
#722310312
#722310172
#722307482
#722297952
C3×#117173772
D3×C22⋊#10432
C22×D3×#10442
D3×#878312
D3×#878322
D3×#878862
D3×#878302
C2×D3×D5⋊AGL(1,𝔽5)2
C2×#117173773
D3×D4×AGL(1,𝔽5)5