Finite Group Databasebeta

← #14327484

Subgroups — #14327484

Order 1920.

1320 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
2C2×#91907C211yesmaximal, characteristic, complemented
3C4×D5×#67C211yesmaximal, characteristic
4#11752424C211yesmaximal, characteristic, complemented
5#11752022C212yesmaximal
6AGL(1,𝔽5)×#217C212yesmaximal, complemented
7#11751855C211yesmaximal, characteristic, complemented
8Dic3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
9#11751836C212yesmaximal, complemented
10#11751835C212yesmaximal, complemented
11#11751751C211yesmaximal, characteristic, complemented
12#10617179—31nomaximal, Hall
13C23×C3×AGL(1,𝔽5)C2212yes—
14C22×C3×C4×D5C2211yescharacteristic
15C2×D5×#67C2211yescharacteristic
16C2×C4×D3×D5C2211yescharacteristic
17C2×#6763C2212yes—
18C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
19C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
20C2×C3×C4⋊AGL(1,𝔽5)—24no—
21C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
22C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
23C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
24C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
25C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
26C2×Dic3×AGL(1,𝔽5)C2212yes—
27C2×Dic3×AGL(1,𝔽5)C2212yes—
28#91907—24no—
29C4×#1220C411yescharacteristic, complemented
30C4×C5×#67C411yescharacteristic, complemented
31#91552C411yescharacteristic, complemented
32Dic5×#67C411yescharacteristic, complemented
33D5×#217C2211yescharacteristic
34D5×(C2×D3)⋊C4C2211yescharacteristic
35#91444C411yescharacteristic, complemented
36C4×#1202C411yescharacteristic, complemented
37#91440C411yescharacteristic, complemented
38C4×#1201C411yescharacteristic, complemented
39D5×Dic3⋊C4C2211yescharacteristic
40C4×D5×Dic3C2211yescharacteristic
41#91235C2212yes—
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
44(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
45(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
46#82161—51nomaximal, Hall
47C2×#4130—31no—
48C22×C4⋊AGL(1,𝔽5)D311yescharacteristic, complemented
49C4×D4×D5—31no—
50#65779—32no—
51#65765—31no—
52#65765—31no—
53#65711—32no—
54#65700—32no—
55C22⋊C4×AGL(1,𝔽5)—32no—
56#65689—31no—
57C4×C4⋊AGL(1,𝔽5)—31no—
58C23×C3×D5C2311yescharacteristic
59C22×D3×D5C2311yescharacteristic
60C22×ΓL(1,𝔽16)C2312yes—
61C22×ΓL(1,𝔽16)C2312yes—
62C22×C3×AGL(1,𝔽5)—24no—
63C22×C3×AGL(1,𝔽5)—24no—
64C22×C3×AGL(1,𝔽5)—42no—
65C22×C3×AGL(1,𝔽5)C2312yes—
66C22×C3×AGL(1,𝔽5)C2312yes—
67C22×C3×C4×C5C2×C411yescharacteristic
68C2×#1220C2×C411yescharacteristic
69C2×C4×D15C2×C411yescharacteristic, complemented
70C2×C5×#67C2×C411yescharacteristic
71C2×C4×C5×D3C2×C411yescharacteristic, complemented
72C22×C3×Dic5C2×C411yescharacteristic
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5—22no—
75C2×C3×C4×D5C2×C411yescharacteristic
76C2×C3×C4×D5C2×C411yescharacteristic
77C2×C3×C4×D5C2311yescharacteristic
78C2×C3×C4×D5C2311yescharacteristic
79D5×#67—22no—
80D5×#67—22no—
81C2×#1202C2×C411yescharacteristic
82C2×#1201C2×C411yescharacteristic
83C2×#1200C2×C411yescharacteristic, complemented
84C2×D3×Dic5C2×C411yescharacteristic, complemented
85C2×D5×Dic3C2311yescharacteristic
86C2×D5×Dic3C2311yescharacteristic
87C2×D5×Dic3C2311yescharacteristic
88C4×D3×D5—22no—
89C4×D3×D5—22no—
90#6763—24no—
91C4⋊ΓL(1,𝔽16)—22no—
92C4⋊ΓL(1,𝔽16)—22no—
93C3×C4⋊AGL(1,𝔽5)—24no—
94C3×C4⋊AGL(1,𝔽5)—22no—
95C3×C4⋊AGL(1,𝔽5)D414yescomplemented
96(C2×D3)⋊AGL(1,𝔽5)—24no—
97(C2×D3)⋊AGL(1,𝔽5)—42no—
98Dic3×AGL(1,𝔽5)—24no—
99Dic3×AGL(1,𝔽5)—42no—
100#6719C2×C411yescharacteristic
101#6714C2×C411yescharacteristic, complemented
102#6712C2×C411yescharacteristic, complemented
103C4×Dic15C2×C411yescharacteristic, complemented
104C5×#217C2×C411yescharacteristic
105C5×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
106C5×Dic3⋊C4C2×C411yescharacteristic, complemented
107C4×C5×Dic3C2×C411yescharacteristic, complemented
108Dic3⋊Dic5C2×C411yescharacteristic, complemented
109#6669C2×C411yescharacteristic, complemented
110#6667C2×C411yescharacteristic, complemented
111(C2×D3)⋊Dic5C2×C411yescharacteristic, complemented
112#6665C2×C411yescharacteristic
113#6665C2×C411yescharacteristic
114Dic3×Dic5C2×C411yescharacteristic, complemented
115Dic3×Dic5C2×C411yescharacteristic, complemented
116C22×C3×C4⋊C4—51no—
117C2×C4×#67—51no—
118C2×#892—51no—
119#5213—52no—
120#5212—51no—
121C4×#217—52no—
122#4990—52no—
123#4987—51no—
124#4978—52no—
125#4977—51no—
126Dic3×C4⋊C4—51no—
127C23×AGL(1,𝔽5)C2×D312yes—
128C2×D4×D5—31no—
129C22×C4×D5—31no—
130C22×C4×D5C2×D311yescharacteristic
131C2×C22⋊AGL(1,𝔽5)—32no—
132C2×C22⋊AGL(1,𝔽5)—32no—
133C2×C22⋊AGL(1,𝔽5)—32no—
134#4130—64no—
135C2×C4⋊AGL(1,𝔽5)—24no—
136C2×C4⋊AGL(1,𝔽5)—31no—
137C2×C4⋊AGL(1,𝔽5)—31no—
138C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
139C2×C4⋊AGL(1,𝔽5)C2×D312yes—
140C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
141C2×C4×AGL(1,𝔽5)—32no—
142C2×C4×AGL(1,𝔽5)—32no—
143C4×C5×D4—31no—
144D4×Dic5—31no—
145C4×C22⋊D5—31no—
146C4×C22⋊D5—31no—
147#4039—31no—
148D5×C4⋊C4—31no—
149#4027—31no—
150#4027—31no—
151D5×C22⋊C4—31no—
152D5×C22⋊C4—31no—
153C4×D20—31no—
154C42×D5—31no—
155(C2×AGL(1,𝔽5))⋊C4—32no—
156(C2×AGL(1,𝔽5))⋊C4—32no—
157(C2×AGL(1,𝔽5))⋊C4—32no—
158(C2×AGL(1,𝔽5))⋊C4—32no—
159(C2×AGL(1,𝔽5))⋊C4—32no—
160#2352—151noSylow
161C23×C3×C5C22×C411yescharacteristic
162C22×D15C22×C411yescharacteristic
163C22×C5×D3C22×C411yescharacteristic
164C22×C3×D5—21no—
165C22×C3×D5—21no—
166C22×C3×D5—21no—
167C22×C3×D5—21no—
168C22×C3×D5C22×C411yescharacteristic
169C22×C3×D5#4112yes—
170C22×C3×D5#4112yes—
171C22×C3×D5C2411yescharacteristic
172C2×D3×D5—21no—
173C2×D3×D5—21no—
174C2×D3×D5—21no—
175C2×D3×D5—21no—
176C2×D3×D5—21no—
177C2×D3×D5—21no—
178C2×ΓL(1,𝔽16)—22no—
179C2×ΓL(1,𝔽16)—22no—
180C2×ΓL(1,𝔽16)—22no—
181C2×ΓL(1,𝔽16)—22no—
182C2×ΓL(1,𝔽16)—22no—
183C2×ΓL(1,𝔽16)—22no—
184C2×C3×AGL(1,𝔽5)—22no—
185C2×C3×AGL(1,𝔽5)—22no—
186C2×C3×AGL(1,𝔽5)—22no—
187C2×C3×AGL(1,𝔽5)—22no—
188C2×C3×AGL(1,𝔽5)—22no—
189C2×C3×AGL(1,𝔽5)—48no—
190C2×C3×AGL(1,𝔽5)C2×D414yes—
191C2×C3×C4×C5—22no—
192C2×C3×C4×C5C22×C411yescharacteristic
193C2×C3×C4×C5C22×C411yescharacteristic
194#1220—22no—
195C2×Dic15C22×C411yescharacteristic
196C2×Dic15C22×C411yescharacteristic
197C2×Dic15C22×C411yescharacteristic
198C4×D15—22no—
199C5×#67—22no—
200C2×C5×Dic3C22×C411yescharacteristic
201C2×C5×Dic3C22×C411yescharacteristic
202C2×C5×Dic3C22×C411yescharacteristic
203C4×C5×D3—22no—
204C2×C3×Dic5—22no—
205C2×C3×Dic5C22×C411yescharacteristic
206C2×C3×Dic5C22×C411yescharacteristic
207C3×C4×D5—21no—
208C3×C4×D5—21no—
209C3×C4×D5—22no—
210C3×C4×D5—22no—
211C3×C4×D5C2×D412yes—
212C3×C4×D5#4112yes—
213#1202—22no—
214#1201—22no—
215#1200—22no—
216D3×Dic5—22no—
217D5×Dic3—21no—
218D5×Dic3—21no—
219D5×Dic3—21no—
220D5×Dic3—21no—
221D5×Dic3—21no—
222D5×Dic3—21no—
223C23×C3×C4—51no—
224C23×C3×C4—52no—
225C22×#67—51no—
226C22×C4×D3—51no—
227C2×C3×C4⋊C4—51no—
228C2×C3×C4⋊C4—51no—
229C2×C3×C4⋊C4—52no—
230C2×C3×C4⋊C4—104no—
231C2×#217—51no—
232C2×#217—52no—
233C4×#67—51no—
234C4×#67—51no—
235C4×#67—51no—
236C4×#67—51no—
237C4×#67—51no—
238C4×#67—51no—
239C4×#67—51no—
240C4×#67AGL(1,𝔽5)11yescharacteristic, complemented
241C2×(C2×D3)⋊C4—51no—
242C2×(C2×D3)⋊C4—52no—
243C2×(C2×D3)⋊C4—52no—
244C2×C4⋊Dic3—51no—
245C2×C4⋊Dic3—51no—
246C2×Dic3⋊C4—51no—
247C2×C4×Dic3—51no—
248C2×C4×Dic3—52no—
249C2×C4×Dic3—52no—
250#892—104no—
251C3⋊#95—52no—
252C3⋊#95—52no—
253C3⋊#95—52no—
254C3⋊#95—52no—
255C3⋊#95—52no—
256C23×D5—31no—
257C23×D5C22×D311yescharacteristic
258C22×AGL(1,𝔽5)—24no—
259C22×AGL(1,𝔽5)—24no—
260C22×AGL(1,𝔽5)—32no—
261C22×AGL(1,𝔽5)—32no—
262C22×AGL(1,𝔽5)—42no—
263C22×AGL(1,𝔽5)C22×D312yes—
264C22×AGL(1,𝔽5)C22×D312yes—
265C2×C5×D4—31no—
266C22×C4×C5—31no—
267C22×C4×C5C4×D311yescharacteristic
268C2×C22⋊D5—31no—
269C2×C22⋊D5—31no—
270C22×Dic5—31no—
271C22×Dic5C4×D311yescharacteristic
272D4×D5—62no—
273D4×D5—62no—
274C2×D20—31no—
275C2×C4×D5—22no—
276C2×C4×D5—22no—
277C2×C4×D5—31no—
278C2×C4×D5—31no—
279C2×C4×D5—31no—
280C2×C4×D5—31no—
281C2×C4×D5—31no—
282C2×C4×D5—62no—
283C2×C4×D5—62no—
284C2×C4×D5C4×D311yescharacteristic
285C2×C4×D5C4×D311yescharacteristic
286C2×C4×D5C22×D311yescharacteristic
287C2×C4×D5C22×D311yescharacteristic
288C22⋊AGL(1,𝔽5)—64no—
289C22⋊AGL(1,𝔽5)—64no—
290C22⋊AGL(1,𝔽5)—122no—
291C4⋊AGL(1,𝔽5)—24no—
292C4⋊AGL(1,𝔽5)—22no—
293C4⋊AGL(1,𝔽5)—62no—
294C4⋊AGL(1,𝔽5)—62no—
295C4⋊AGL(1,𝔽5)#6714yescomplemented
296C4×AGL(1,𝔽5)—64no—
297C4×AGL(1,𝔽5)—122no—
298C5×C4⋊C4—31no—
299C5×C22⋊C4—31no—
300C5×C22⋊C4—31no—
301C42×C5—31no—
302C22⋊Dic5—31no—
303C22⋊Dic5—31no—
304#685—31no—
305#685—31no—
306#685—31no—
307#685—31no—
308C4⋊Dic5—31no—
309#683—31no—
310#683—31no—
311C4×Dic5—31no—
312C4×Dic5—31no—
313C4×Dic5—31no—
314C2×C4×D4—151no—
315C2×#117—151no—
316C22×C4⋊C4—51no—
317#388—152no—
318#387—152no—
319#386—152no—
320#382—151no—
321#380—151no—
322#380—151no—
323C4×C4⋊C4—151no—
324C4×C22⋊C4—152no—
325C22×C3×C5—21no—
326C22×C3×C5—21no—
327C22×C3×C5#11712yescomplemented
328C22×C3×C5C23×C411yescharacteristic
329C2×D15—21no—
330C2×D15—21no—
331C2×D15—21no—
332C2×C5×D3—21no—
333C2×C5×D3—21no—
334C2×C5×D3—21no—
335C2×C3×D5—21no—
336C2×C3×D5—21no—
337C2×C3×D5—22no—
338C2×C3×D5—22no—
339C2×C3×D5—22no—
340C2×C3×D5—22no—
341C2×C3×D5#11712yescomplemented
342C2×C3×D5C22×D411yescharacteristic
343C2×C3×D5C2×#4111yescharacteristic
344C2×C3×D5C2×#4111yescharacteristic
345C2×C3×D5C2×#4111yescharacteristic
346C2×C3×D5H(5,𝔽2)11yescharacteristic
347C2×C3×D52−1+411yescharacteristic
348D3×D5—41no—
349D3×D5—41no—
350D3×D5—41no—
351D3×D5—41no—
352ΓL(1,𝔽16)—42no—
353ΓL(1,𝔽16)—42no—
354C3×AGL(1,𝔽5)—24no—
355C3×AGL(1,𝔽5)—42no—
356C3×C4×C5—21no—
357C3×C4×C5C4×D412yes—
358Dic15—21no—
359Dic15—21no—
360Dic15—21no—
361C3×Dic5—21no—
362C3×Dic5C4×D412yes—
363C5×Dic3—21no—
364C5×Dic3—21no—
365C5×Dic3—21no—
366C24×C3—51no—
367C23×D3—51no—
368C22×C3×C4—51no—
369C22×C3×C4—52no—
370C22×C3×C4—51no—
371C22×C3×C4—51no—
372C22×C3×C4—51no—
373C22×C3×C4—51no—
374C22×C3×C4—52no—
375C22×C3×C4—102no—
376C22×C3×C4—102no—
377C22×C3×C4—104no—
378C22×C3×C4—104no—
379C22×C3×C4—202no—
380C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
381C2×#67—51no—
382C2×#67—51no—
383C2×#67—51no—
384C2×#67—102no—
385C2×#67—102no—
386C2×#67C2×AGL(1,𝔽5)11yescharacteristic
387C22×Dic3—51no—
388C22×Dic3—51no—
389C22×Dic3—51no—
390C22×Dic3—52no—
391C22×Dic3—52no—
392C2×C4×D3—51no—
393C2×C4×D3—51no—
394C2×C4×D3—51no—
395C2×C4×D3—102no—
396C2×C4×D3—102no—
397C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
398C3×C4⋊C4—54no—
399C3×C4⋊C4—102no—
400C3×C4⋊C4—104no—
401#217—51no—
402#217—51no—
403#217—51no—
404#217—104no—
405#217C2×AGL(1,𝔽5)11yescharacteristic
406(C2×D3)⋊C4—51no—
407(C2×D3)⋊C4—51no—
408(C2×D3)⋊C4—51no—
409(C2×D3)⋊C4—104no—
410(C2×D3)⋊C4—202no—
411(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
412C4⋊Dic3—102no—
413C4⋊Dic3—102no—
414Dic3⋊C4—51no—
415Dic3⋊C4—51no—
416Dic3⋊C4—51no—
417Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
418C4×Dic3—51no—
419C4×Dic3—51no—
420C4×Dic3—51no—
421C4×Dic3—104no—
422C4×Dic3—202no—
423C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
424C23×C5—31no—
425C23×C5C2×C4×D311yescharacteristic
426C22×D5—21no—
427C22×D5—21no—
428C22×D5—21no—
429C22×D5—21no—
430C22×D5—31no—
431C22×D5—61no—
432C22×D5—61no—
433C22×D5—61no—
434C22×D5—61no—
435C22×D5—61no—
436C22×D5—61no—
437C22×D5C2×C4×D311yescharacteristic
438C22×D5#23712yes—
439C22×D5#23912yes—
440C22×D5C23×D311yescharacteristic
441C2×AGL(1,𝔽5)—22no—
442C2×AGL(1,𝔽5)—22no—
443C2×AGL(1,𝔽5)—22no—
444C2×AGL(1,𝔽5)—22no—
445C2×AGL(1,𝔽5)—22no—
446C2×AGL(1,𝔽5)—48no—
447C2×AGL(1,𝔽5)—62no—
448C2×AGL(1,𝔽5)—62no—
449C2×AGL(1,𝔽5)—62no—
450C2×AGL(1,𝔽5)—62no—
451C2×AGL(1,𝔽5)—62no—
452C2×AGL(1,𝔽5)—62no—
453C2×AGL(1,𝔽5)C2×#6714yes—
454C5×D4—62no—
455C2×C4×C5—22no—
456C2×C4×C5—31no—
457C2×C4×C5—31no—
458C2×C4×C5—31no—
459C2×C4×C5—62no—
460C2×C4×C5C2×C4×D311yescharacteristic
461C2×C4×C5C2×C4×D311yescharacteristic
462C22⋊D5—62no—
463C22⋊D5—62no—
464C2×Dic5—22no—
465C2×Dic5—31no—
466C2×Dic5—31no—
467C2×Dic5—31no—
468C2×Dic5—62no—
469C2×Dic5C2×C4×D311yescharacteristic
470C2×Dic5C2×C4×D311yescharacteristic
471D20—62no—
472C4×D5—21no—
473C4×D5—21no—
474C4×D5—22no—
475C4×D5—22no—
476C4×D5—61no—
477C4×D5—61no—
478C4×D5—61no—
479C4×D5—61no—
480C4×D5—61no—
481C4×D5—61no—
482C4×D5—62no—
483C4×D5—62no—
484C4×D5#23512yes—
485C4×D5C2×#6712yes—
486C22×D4—151no—
487C23×C4—51no—
488C23×C4—52no—
489C23×C4—151no—
490C4×D4—31no—
491C4×D4—151no—
492C4×D4—151no—
493C4×D4—151no—
494C4×D4—151no—
495C4×D4—151no—
496C4×D4—151no—
497C4×D4—151no—
498#117—304no—
499C2×C4⋊C4—51no—
500C2×C4⋊C4—51no—
501C2×C4⋊C4—52no—
502C2×C4⋊C4—104no—
503C2×C4⋊C4—151no—
504C2×C4⋊C4—151no—
505C2×C4⋊C4—151no—
506C2×C22⋊C4—151no—
507C2×C22⋊C4—151no—
508C2×C22⋊C4—152no—
509C2×C22⋊C4—152no—
510C2×C22⋊C4—152no—
511C2×C42—151no—
512C2×C42—152no—
513C2×C42—152no—
514#95—152no—
515#95—152no—
516#95—152no—
517#95—152no—
518#95—152no—
519C2×C3×C5—22no—
520C2×C3×C5C2×#11711yescharacteristic
521C2×C3×C5C2×C4×D411yescharacteristic
522C2×C3×C5#52011yescharacteristic
523D15—41no—
524C3×D5—22no—
525C3×D5#54611yescharacteristic
526C3×D5#54811yescharacteristic
527C3×D5#55211yescharacteristic
528C3×D5#55311yescharacteristic
529C5×D3—41no—
530C23×C3—51no—
531C23×C3—52no—
532C23×C3—52no—
533C23×C3—51no—
534C23×C3—101no—
535C23×C3—101no—
536C23×C3—101no—
537C23×C3—101no—
538C23×C3C22×AGL(1,𝔽5)11yescharacteristic
539C22×D3—51no—
540C22×D3—101no—
541C22×D3—101no—
542C22×D3—101no—
543C22×D3—101no—
544C22×D3—101no—
545C22×D3—101no—
546C22×D3C22×AGL(1,𝔽5)11yescharacteristic
547C2×C3×C4—22no—
548C2×C3×C4—51no—
549C2×C3×C4—52no—
550C2×C3×C4—52no—
551C2×C3×C4—54no—
552C2×C3×C4—51no—
553C2×C3×C4—102no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4—102no—
557C2×C3×C4—102no—
558C2×C3×C4—102no—
559C2×C3×C4—102no—
560C2×C3×C4—102no—
561C2×C3×C4—102no—
562C2×C3×C4—102no—
563C2×C3×C4—208no—
564C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
565C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
566#67—22no—
567#67—102no—
568#67—102no—
569#67—102no—
570C2×Dic3—51no—
571C2×Dic3—51no—
572C2×Dic3—51no—
573C2×Dic3—101no—
574C2×Dic3—101no—
575C2×Dic3—101no—
576C2×Dic3—101no—
577C2×Dic3—101no—
578C2×Dic3—101no—
579C2×Dic3—102no—
580C2×Dic3—102no—
581C2×Dic3—102no—
582C2×Dic3—102no—
583C2×Dic3—102no—
584C2×Dic3—102no—
585C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
586C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
587C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
588C4×D3—22no—
589C4×D3—102no—
590C4×D3—102no—
591C4×D3—102no—
592C22×C5—21no—
593C22×C5—21no—
594C22×C5—61no—
595C22×C5—61no—
596C22×C5—61no—
597C22×C5#89212yescomplemented
598C22×C5C22×C4×D311yescharacteristic
599C2×D5—21no—
600C2×D5—21no—
601C2×D5—22no—
602C2×D5—22no—
603C2×D5—22no—
604C2×D5—22no—
605C2×D5—61no—
606C2×D5—61no—
607C2×D5—61no—
608C2×D5—121no—
609C2×D5—121no—
610C2×D5—121no—
611C2×D5—121no—
612C2×D5#89212yescomplemented
613C2×D5C2×#23511yescharacteristic
614C2×D5C2×#23711yescharacteristic
615C2×D5#100411yescharacteristic
616C2×D5C2×#23911yescharacteristic
617C2×D5#100711yescharacteristic
618C2×D5C22×#6711yescharacteristic
619AGL(1,𝔽5)—24no—
620AGL(1,𝔽5)—42no—
621AGL(1,𝔽5)—122no—
622AGL(1,𝔽5)—122no—
623C4×C5—21no—
624C4×C5—61no—
625C4×C5—61no—
626C4×C5—61no—
627C4×C5C4×#6712yes—
628Dic5—21no—
629Dic5—61no—
630Dic5—61no—
631Dic5—61no—
632Dic5C4×#6712yes—
633C24—51no—
634C24—151no—
635C2×D4—31no—
636C2×D4—151no—
637C2×D4—151no—
638C2×D4—151no—
639C2×D4—302no—
640C2×D4—302no—
641C22×C4—31no—
642C22×C4—51no—
643C22×C4—52no—
644C22×C4—51no—
645C22×C4—51no—
646C22×C4—51no—
647C22×C4—51no—
648C22×C4—52no—
649C22×C4—102no—
650C22×C4—102no—
651C22×C4—104no—
652C22×C4—104no—
653C22×C4—151no—
654C22×C4—151no—
655C22×C4—151no—
656C22×C4—151no—
657C22×C4—151no—
658C22×C4—151no—
659C22×C4—152no—
660C22×C4—152no—
661C22×C4—202no—
662C22×C4—302no—
663C22×C4—302no—
664C22×C4D3×AGL(1,𝔽5)11yescharacteristic
665C4⋊C4—31no—
666C4⋊C4—54no—
667C4⋊C4—102no—
668C4⋊C4—104no—
669C4⋊C4—151no—
670C4⋊C4—151no—
671C4⋊C4—151no—
672C4⋊C4—302no—
673C4⋊C4—302no—
674C22⋊C4—31no—
675C22⋊C4—31no—
676C22⋊C4—151no—
677C22⋊C4—151no—
678C22⋊C4—151no—
679C22⋊C4—151no—
680C22⋊C4—151no—
681C22⋊C4—151no—
682C22⋊C4—304no—
683C22⋊C4—304no—
684C22⋊C4—602no—
685C42—31no—
686C42—151no—
687C42—151no—
688C42—151no—
689C42—304no—
690C42—602no—
691C3×C5#235211yescharacteristic, complemented, Hall
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—51no—
695C22×C3—51no—
696C22×C3—51no—
697C22×C3—51no—
698C22×C3—51no—
699C22×C3—51no—
700C22×C3—52no—
701C22×C3—102no—
702C22×C3—102no—
703C22×C3—102no—
704C22×C3—102no—
705C22×C3—101no—
706C22×C3—101no—
707C22×C3#413012yescomplemented
708C22×C3C23×AGL(1,𝔽5)11yescharacteristic
709C2×D3—21no—
710C2×D3—21no—
711C2×D3—21no—
712C2×D3—101no—
713C2×D3—101no—
714C2×D3—101no—
715C2×D3—201no—
716C2×D3—201no—
717C2×D3—201no—
718C2×D3—201no—
719C3×C4—21no—
720C3×C4—52no—
721C3×C4—104no—
722C3×C4—101no—
723C3×C4—202no—
724C3×C4D4×AGL(1,𝔽5)12yes—
725Dic3—21no—
726Dic3—21no—
727Dic3—21no—
728Dic3—101no—
729Dic3—101no—
730Dic3—101no—
731Dic3—202no—
732Dic3—202no—
733C2×C5—22no—
734C2×C5—121no—
735C2×C5C2×#89211yescharacteristic
736C2×C5#550411yescharacteristic
737C2×C5C2×C4×#6711yescharacteristic
738D5—22no—
739D5—121no—
740D5#551311yescharacteristic
741D5#551411yescharacteristic
742D5#580611yescharacteristic
743D5#581711yescharacteristic
744C23—31no—
745C23—51no—
746C23—52no—
747C23—52no—
748C23—51no—
749C23—101no—
750C23—101no—
751C23—101no—
752C23—101no—
753C23—151no—
754C23—301no—
755C23—301no—
756C23—301no—
757C23—301no—
758C23—301no—
759C23—301no—
760C23C2×D3×AGL(1,𝔽5)11yescharacteristic
761D4—62no—
762D4—302no—
763D4—302no—
764D4—302no—
765C2×C4—22no—
766C2×C4—31no—
767C2×C4—31no—
768C2×C4—31no—
769C2×C4—51no—
770C2×C4—52no—
771C2×C4—52no—
772C2×C4—54no—
773C2×C4—51no—
774C2×C4—62no—
775C2×C4—102no—
776C2×C4—101no—
777C2×C4—101no—
778C2×C4—102no—
779C2×C4—102no—
780C2×C4—102no—
781C2×C4—102no—
782C2×C4—102no—
783C2×C4—102no—
784C2×C4—102no—
785C2×C4—151no—
786C2×C4—151no—
787C2×C4—151no—
788C2×C4—208no—
789C2×C4—302no—
790C2×C4—302no—
791C2×C4—301no—
792C2×C4—301no—
793C2×C4—301no—
794C2×C4—301no—
795C2×C4—301no—
796C2×C4—301no—
797C2×C4—302no—
798C2×C4—302no—
799C2×C4—302no—
800C2×C4—302no—
801C2×C4—302no—
802C2×C4—302no—
803C2×C4—302no—
804C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
805C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
806C2×C3—22no—
807C2×C3—51no—
808C2×C3—51no—
809C2×C3—51no—
810C2×C3—51no—
811C2×C3—102no—
812C2×C3C2×#413011yescharacteristic
813C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
814C2×C3#6626611yescharacteristic
815D3—41no—
816D3—201no—
817C5#8216111yescharacteristic, complemented, Sylow
818C22—21no—
819C22—21no—
820C22—51no—
821C22—51no—
822C22—51no—
823C22—51no—
824C22—51no—
825C22—51no—
826C22—52no—
827C22—61no—
828C22—61no—
829C22—61no—
830C22—102no—
831C22—102no—
832C22—102no—
833C22—102no—
834C22—101no—
835C22—101no—
836C22—301no—
837C22—301no—
838C22—301no—
839C22—601no—
840C22—601no—
841C22—601no—
842C22—601no—
843C22#9190712yescomplemented
844C22C22×D3×AGL(1,𝔽5)11yescharacteristic
845C4—21no—
846C4—52no—
847C4—61no—
848C4—61no—
849C4—61no—
850C4—104no—
851C4—101no—
852C4—202no—
853C4—301no—
854C4—301no—
855C4—301no—
856C4—602no—
857C4—602no—
858C4AGL(1,𝔽5)×#6712yes—
859C3#1061717911yescharacteristic, complemented, Sylow
860C2—22no—
861C2—51no—
862C2—51no—
863C2—51no—
864C2—51no—
865C2—102no—
866C2—121no—
867C2—601no—
868C2C2×#9190711yescharacteristic
869C2#1175683611yescharacteristic
870C2C2×AGL(1,𝔽5)×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalC2×D5×#67C22
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2352
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×C3×C4⋊AGL(1,𝔽5)C2semidirect
2. C2×#91907C2semidirect
4. #11752424C2semidirect
6. AGL(1,𝔽5)×#217C2semidirect
7. #11751855C2semidirect
8. Dic3×C4⋊AGL(1,𝔽5)C2semidirect
9. #11751836C2semidirect
10. #11751835C2semidirect
11. #11751751C2semidirect
29. C4×#1220C4semidirect
30. C4×C5×#67C4semidirect
31. #91552C4semidirect
32. Dic5×#67C4semidirect
35. #91444C4semidirect
36. C4×#1202C4semidirect
37. #91440C4semidirect
38. C4×#1201C4semidirect
48. C22×C4⋊AGL(1,𝔽5)D3semidirect
69. C2×C4×D15C2×C4semidirect
71. C2×C4×C5×D3C2×C4semidirect
83. C2×#1200C2×C4semidirect
84. C2×D3×Dic5C2×C4semidirect
95. C3×C4⋊AGL(1,𝔽5)D4semidirect
101. #6714C2×C4semidirect
102. #6712C2×C4semidirect
103. C4×Dic15C2×C4semidirect
105. C5×(C2×D3)⋊C4C2×C4semidirect
106. C5×Dic3⋊C4C2×C4semidirect
107. C4×C5×Dic3C2×C4semidirect
108. Dic3⋊Dic5C2×C4semidirect
109. #6669C2×C4semidirect
110. #6667C2×C4semidirect
111. (C2×D3)⋊Dic5C2×C4semidirect
114. Dic3×Dic5C2×C4semidirect
115. Dic3×Dic5C2×C4semidirect
240. C4×#67AGL(1,𝔽5)semidirect
295. C4⋊AGL(1,𝔽5)#67semidirect
327. C22×C3×C5#117semidirect
341. C2×C3×D5#117semidirect
397. C2×C4×D3C2×AGL(1,𝔽5)semidirect
411. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
417. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
423. C4×Dic3C2×AGL(1,𝔽5)semidirect
597. C22×C5#892semidirect
612. C2×D5#892semidirect
691. C3×C5#2352semidirect
707. C22×C3#4130semidirect
817. C5#82161semidirect
843. C22#91907semidirect
859. C3#10617179semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊AGL(1,𝔽5)2
C2×#919072
C4×D5×#672
#117524242
#117520222
AGL(1,𝔽5)×#2172
#117518552
Dic3×C4⋊AGL(1,𝔽5)2
#117518362
#117518352
#117517512
#106171793
#821615