Finite Group Databasebeta

← #14327207

Subgroups — #14327207

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91921C211yesmaximal, characteristic
2C2×AGL(1,𝔽5)×D12C211yesmaximal, characteristic
3D5×#893C211yesmaximal, characteristic
4#11752371C211yesmaximal, characteristic, complemented
5C3×#65712C211yesmaximal, characteristic, complemented
6#11751934C212yesmaximal, complemented
7#11751932C212yesmaximal, complemented
8D3×(C2×AGL(1,𝔽5))⋊C4C212yesmaximal, complemented
9C4×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
10#11751855C212yesmaximal, complemented
11#11751751C211yesmaximal, characteristic, complemented
12#10617178—31nomaximal, Hall
13C22×D3×AGL(1,𝔽5)C2212yes—
14C22×D3×AGL(1,𝔽5)C2212yes—
15C2×D5×D12C2211yescharacteristic
16C2×C4×D3×D5C2212yes—
17C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
18C2×C4⋊ΓL(1,𝔽16)C2212yes—
19C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
20C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
21C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
22C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
23C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
24C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
25C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
26C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
27#91921—24no—
28AGL(1,𝔽5)×D12—24no—
29#91782C411yescharacteristic, complemented
30C5×#893C411yescharacteristic, complemented
31C3×D5×C4⋊C4C2211yescharacteristic
32D5×(C2×D3)⋊C4C2212yes—
33#91446C412yescomplemented
34#91435C411yescharacteristic, complemented
35#91428C411yescharacteristic, complemented
36#91406C412yescomplemented
37C4×D5×Dic3C2211yescharacteristic
38#91235C2212yes—
39C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
40(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
41(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
42(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
43(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
44#76203—51nomaximal, Hall
45C2×D4×AGL(1,𝔽5)—31no—
46C2×D4×AGL(1,𝔽5)—31no—
47C4×D4×D5—31no—
48#65765—32no—
49C2×(C2×AGL(1,𝔽5))⋊C4—32no—
50#65712—31no—
51#65712D311yescharacteristic, complemented
52#65699—32no—
53#65699—32no—
54#65689—31no—
55C4×C4⋊AGL(1,𝔽5)—31no—
56C22×D3×D5C2312yes—
57C22×ΓL(1,𝔽16)C2311yescharacteristic
58C22×ΓL(1,𝔽16)C2312yes—
59C22×ΓL(1,𝔽16)C2311yescharacteristic
60C22×C3×AGL(1,𝔽5)C2311yescharacteristic
61C22×C3×AGL(1,𝔽5)C2312yes—
62C22×C3×AGL(1,𝔽5)C2311yescharacteristic
63C2×D3×AGL(1,𝔽5)—24no—
64C2×D3×AGL(1,𝔽5)—24no—
65C2×D3×AGL(1,𝔽5)—24no—
66C2×D3×AGL(1,𝔽5)—24no—
67C2×D3×AGL(1,𝔽5)—42no—
68C2×D3×AGL(1,𝔽5)—42no—
69C2×D60C2×C411yescharacteristic
70C2×C4×D15C2×C412yescomplemented
71C2×C5×D12C2×C411yescharacteristic
72C2×C4×C5×D3C2×C412yescomplemented
73C2×C3×C4×D5C2312yes—
74C2×C3×C4×D5C2311yescharacteristic
75C2×#1203C2×C412yes—
76C2×#1200C2×C412yescomplemented
77C2×D3×Dic5C2×C412yescomplemented
78C2×D5×Dic3C2311yescharacteristic
79C2×D5×Dic3C2311yescharacteristic
80D5×D12D414yes—
81D5×D12Q814yes—
82C4×D3×D5—42no—
83C4×D3×D5—42no—
84C4⋊ΓL(1,𝔽16)—22no—
85C4⋊ΓL(1,𝔽16)—42no—
86C4×ΓL(1,𝔽16)—22no—
87C3×C4⋊AGL(1,𝔽5)—22no—
88C3×C4⋊AGL(1,𝔽5)—42no—
89C3×C4×AGL(1,𝔽5)—22no—
90Dic3⋊AGL(1,𝔽5)—22no—
91Dic3⋊AGL(1,𝔽5)—22no—
92(C2×D3)⋊AGL(1,𝔽5)—24no—
93(C2×D3)⋊AGL(1,𝔽5)—24no—
94C3×C5×C4⋊C4C2×C411yescharacteristic, complemented
95#6714C2×C412yescomplemented
96C4×Dic15C2×C411yescharacteristic, complemented
97C5×(C2×D3)⋊C4C2×C412yescomplemented
98C4×C5×Dic3C2×C411yescharacteristic, complemented
99C3×C4⋊Dic5C2×C411yescharacteristic, complemented
100C3×#683C2×C412yescomplemented
101#6667C2×C412yescomplemented
102(C2×D3)⋊Dic5C2×C412yescomplemented
103Dic3×Dic5C2×C411yescharacteristic, complemented
104Dic3×Dic5C2×C411yescharacteristic, complemented
105C2×#893—51no—
106C2×#893—51no—
107C2×C4×D12—51no—
108C3×#389—51no—
109#4989—52no—
110#4987—52no—
111#4984—51no—
112#4977—51no—
113C4×Dic3⋊C4—51no—
114#4668—52no—
115D3×#95—52no—
116C23×AGL(1,𝔽5)—32no—
117C23×AGL(1,𝔽5)—32no—
118C2×D4×D5—31no—
119C22×C4×D5—32no—
120C2×C22⋊AGL(1,𝔽5)—32no—
121C2×C22⋊AGL(1,𝔽5)—32no—
122D4×AGL(1,𝔽5)—64no—
123D4×AGL(1,𝔽5)—64no—
124C2×C4⋊AGL(1,𝔽5)—31no—
125C2×C4⋊AGL(1,𝔽5)—31no—
126C2×C4⋊AGL(1,𝔽5)—31no—
127C2×C4⋊AGL(1,𝔽5)—32no—
128C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
129C2×C4⋊AGL(1,𝔽5)C2×D312yes—
130C2×C4×AGL(1,𝔽5)—31no—
131C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
132C4×C5×D4—31no—
133D4×Dic5—31no—
134C4×C22⋊D5—32no—
135#4039—31no—
136D5×C4⋊C4C2×D311yescharacteristic
137#4027—32no—
138D5×C22⋊C4—32no—
139C4×D20—31no—
140C42×D5—31no—
141(C2×AGL(1,𝔽5))⋊C4—31no—
142(C2×AGL(1,𝔽5))⋊C4—31no—
143(C2×AGL(1,𝔽5))⋊C4—32no—
144(C2×AGL(1,𝔽5))⋊C4—32no—
145(C2×AGL(1,𝔽5))⋊C4—32no—
146(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
147#2349—151noSylow
148C22×D15C22×C412yes—
149C22×C5×D3C22×C412yes—
150C22×C3×D5C2411yescharacteristic
151C2×D3×D5—22no—
152C2×D3×D5—22no—
153C2×D3×D5—22no—
154C2×D3×D5—22no—
155C2×D3×D5C2×D414yes—
156C2×D3×D5C2×Q814yes—
157C2×ΓL(1,𝔽16)—21no—
158C2×ΓL(1,𝔽16)—21no—
159C2×ΓL(1,𝔽16)—21no—
160C2×ΓL(1,𝔽16)—22no—
161C2×ΓL(1,𝔽16)—21no—
162C2×ΓL(1,𝔽16)—22no—
163C2×ΓL(1,𝔽16)—21no—
164C2×ΓL(1,𝔽16)—22no—
165C2×ΓL(1,𝔽16)#4112yes—
166C2×C3×AGL(1,𝔽5)—21no—
167C2×C3×AGL(1,𝔽5)—21no—
168C2×C3×AGL(1,𝔽5)—21no—
169C2×C3×AGL(1,𝔽5)—22no—
170C2×C3×AGL(1,𝔽5)—21no—
171C2×C3×AGL(1,𝔽5)—22no—
172C2×C3×AGL(1,𝔽5)—21no—
173C2×C3×AGL(1,𝔽5)—22no—
174C2×C3×AGL(1,𝔽5)#4112yes—
175D3×AGL(1,𝔽5)—48no—
176D3×AGL(1,𝔽5)—48no—
177C2×C3×C4×C5C22×C412yes—
178C2×C3×C4×C5C22×C411yescharacteristic
179C2×Dic15C22×C411yescharacteristic
180C2×Dic15C22×C411yescharacteristic
181D60C4⋊C414yescomplemented
182C4×D15—42no—
183C2×C5×Dic3C22×C411yescharacteristic
184C2×C5×Dic3C22×C411yescharacteristic
185C5×D12C4⋊C414yescomplemented
186C4×C5×D3—42no—
187C2×C3×Dic5C22×C412yes—
188C2×C3×Dic5C22×C411yescharacteristic
189C3×C4×D5—22no—
190C3×C4×D5—22no—
191C3×C4×D5C2×D412yes—
192C3×C4×D5C2×Q812yes—
193#1203C4⋊C418yescomplemented
194#1200—42no—
195D3×Dic5—42no—
196D5×Dic3—21no—
197D5×Dic3—21no—
198D5×Dic3—21no—
199D5×Dic3—21no—
200C22×D12—51no—
201C22×C4×D3—52no—
202C22×C4×D3—52no—
203C22×C4×D3—52no—
204C2×C3×C4⋊C4—51no—
205C2×C3×C4⋊C4—51no—
206C2×C3×C4⋊C4—52no—
207C2×C3×C42—51no—
208C2×(C2×D3)⋊C4—52no—
209C2×(C2×D3)⋊C4—52no—
210C2×(C2×D3)⋊C4—52no—
211C2×C4⋊Dic3—51no—
212C2×C4⋊Dic3—52no—
213C2×Dic3⋊C4—51no—
214C2×Dic3⋊C4—51no—
215C2×C4×Dic3—51no—
216C2×C4×Dic3—51no—
217#893—51no—
218#893—52no—
219#893—51no—
220#893—52no—
221#893—51no—
222#893—104no—
223#893AGL(1,𝔽5)11yescharacteristic, complemented
224C4×D12—104no—
225C3×#95—52no—
226C3⋊#95—51no—
227C3⋊#95—52no—
228C3⋊#95—52no—
229C3⋊#95—51no—
230C3⋊#95—52no—
231C23×D5—32no—
232C22×AGL(1,𝔽5)—31no—
233C22×AGL(1,𝔽5)—31no—
234C22×AGL(1,𝔽5)—32no—
235C22×AGL(1,𝔽5)—64no—
236C22×AGL(1,𝔽5)—64no—
237C22×AGL(1,𝔽5)—64no—
238C22×AGL(1,𝔽5)—64no—
239C22×AGL(1,𝔽5)—122no—
240C22×AGL(1,𝔽5)—122no—
241C22×AGL(1,𝔽5)C22×D311yescharacteristic
242C22×AGL(1,𝔽5)C22×D312yes—
243C22×AGL(1,𝔽5)C22×D311yescharacteristic
244C2×C5×D4—31no—
245C22×C4×C5—32no—
246C2×C22⋊D5—32no—
247C22×Dic5—32no—
248D4×D5—34no—
249D4×D5—34no—
250C2×D20—31no—
251C2×C4×D5—31no—
252C2×C4×D5—31no—
253C2×C4×D5—32no—
254C2×C4×D5—32no—
255C2×C4×D5—122no—
256C2×C4×D5—122no—
257C2×C4×D5C22×D312yes—
258C2×C4×D5C22×D311yescharacteristic
259C22⋊AGL(1,𝔽5)—64no—
260C22⋊AGL(1,𝔽5)—64no—
261C4⋊AGL(1,𝔽5)—22no—
262C4⋊AGL(1,𝔽5)—42no—
263C4⋊AGL(1,𝔽5)—62no—
264C4⋊AGL(1,𝔽5)—62no—
265C4⋊AGL(1,𝔽5)—62no—
266C4⋊AGL(1,𝔽5)—122no—
267C4×AGL(1,𝔽5)—22no—
268C4×AGL(1,𝔽5)—62no—
269C5×C4⋊C4C4×D311yescharacteristic, complemented
270C5×C22⋊C4—32no—
271C42×C5—31no—
272C22⋊Dic5—32no—
273#685—32no—
274#685—32no—
275C4⋊Dic5C4×D311yescharacteristic, complemented
276#683C4×D312yescomplemented
277C4×Dic5—31no—
278C4×Dic5—31no—
279C4×Dic5—31no—
280C2×C4×D4—151no—
281C2×C4×D4—151no—
282C2×C4×D4—151no—
283#389—51no—
284#389—151no—
285#385—152no—
286#385—152no—
287#382—151no—
288#380—152no—
289C4×C4⋊C4—151no—
290C2×#95—152no—
291C22×C3×C5C23×C411yescharacteristic
292C2×D15—22no—
293C2×D15—22no—
294C2×D15C2×C4⋊C414yes—
295C2×C5×D3—22no—
296C2×C5×D3—22no—
297C2×C5×D3C2×C4⋊C414yes—
298C2×C3×D5C22×D411yescharacteristic
299C2×C3×D5C22×Q811yescharacteristic
300C2×C3×D5C2×#4111yescharacteristic
301C2×C3×D5C2×#4111yescharacteristic
302C2×C3×D5H(5,𝔽2)11yescharacteristic
303C2×C3×D5H(5,𝔽2)11yescharacteristic
304D3×D5—24no—
305D3×D5—24no—
306D3×D5—24no—
307D3×D5—24no—
308ΓL(1,𝔽16)—22no—
309ΓL(1,𝔽16)—42no—
310ΓL(1,𝔽16)—41no—
311C3×AGL(1,𝔽5)—22no—
312C3×AGL(1,𝔽5)—42no—
313C3×AGL(1,𝔽5)—41no—
314C3×C4×C5—22no—
315C3×C4×C5C2×C4⋊C412yes—
316Dic15—21no—
317Dic15—21no—
318C3×Dic5—22no—
319C3×Dic5C2×C4⋊C412yes—
320C5×Dic3—21no—
321C5×Dic3—21no—
322C23×D3—52no—
323C22×C3×C4—51no—
324C22×C3×C4—51no—
325C22×C3×C4—52no—
326C22×C3×C4—52no—
327C22×C3×C4—51no—
328C22×Dic3—51no—
329C22×Dic3—51no—
330C22×Dic3—51no—
331C22×Dic3—52no—
332C22×Dic3—51no—
333C2×D12—52no—
334C2×D12—51no—
335C2×D12—54no—
336C2×D12—54no—
337C2×D12C2×AGL(1,𝔽5)11yescharacteristic
338C2×C4×D3—52no—
339C2×C4×D3—52no—
340C2×C4×D3—52no—
341C2×C4×D3—104no—
342C2×C4×D3—104no—
343C2×C4×D3—104no—
344C2×C4×D3—104no—
345C2×C4×D3—202no—
346C2×C4×D3—202no—
347C2×C4×D3—202no—
348C2×C4×D3—202no—
349C2×C4×D3C2×AGL(1,𝔽5)12yescomplemented
350C3×C4⋊C4—52no—
351C3×C4⋊C4—51no—
352C3×C4⋊C4—102no—
353C3×C4⋊C4—202no—
354C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
355C3×C42—102no—
356(C2×D3)⋊C4—52no—
357(C2×D3)⋊C4—52no—
358(C2×D3)⋊C4—52no—
359(C2×D3)⋊C4—104no—
360(C2×D3)⋊C4—104no—
361(C2×D3)⋊C4C2×AGL(1,𝔽5)12yescomplemented
362C4⋊Dic3—102no—
363C4⋊Dic3—202no—
364Dic3⋊C4—102no—
365Dic3⋊C4—102no—
366C4×Dic3—51no—
367C4×Dic3—51no—
368C4×Dic3—51no—
369C4×Dic3—102no—
370C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
371C23×C5—32no—
372C22×D5—32no—
373C22×D5—34no—
374C22×D5—34no—
375C22×D5—62no—
376C22×D5—62no—
377C22×D5—62no—
378C22×D5—62no—
379C22×D5C23×D311yescharacteristic
380C2×AGL(1,𝔽5)—21no—
381C2×AGL(1,𝔽5)—21no—
382C2×AGL(1,𝔽5)—21no—
383C2×AGL(1,𝔽5)—22no—
384C2×AGL(1,𝔽5)—21no—
385C2×AGL(1,𝔽5)—22no—
386C2×AGL(1,𝔽5)—21no—
387C2×AGL(1,𝔽5)—22no—
388C2×AGL(1,𝔽5)—32no—
389C2×AGL(1,𝔽5)—61no—
390C2×AGL(1,𝔽5)—61no—
391C2×AGL(1,𝔽5)—61no—
392C2×AGL(1,𝔽5)—62no—
393C2×AGL(1,𝔽5)—61no—
394C2×AGL(1,𝔽5)—62no—
395C2×AGL(1,𝔽5)—61no—
396C2×AGL(1,𝔽5)—62no—
397C2×AGL(1,𝔽5)—128no—
398C2×AGL(1,𝔽5)—128no—
399C2×AGL(1,𝔽5)#23912yes—
400C5×D4—34no—
401C2×C4×C5—31no—
402C2×C4×C5—31no—
403C2×C4×C5—122no—
404C2×C4×C5C2×C4×D312yes—
405C2×C4×C5C2×C4×D311yescharacteristic
406C22⋊D5—38no—
407C2×Dic5—31no—
408C2×Dic5—31no—
409C2×Dic5—122no—
410C2×Dic5C2×C4×D312yes—
411C2×Dic5C2×C4×D311yescharacteristic
412D20—34no—
413C4×D5—22no—
414C4×D5—22no—
415C4×D5—61no—
416C4×D5—61no—
417C4×D5—61no—
418C4×D5—61no—
419C4×D5—122no—
420C4×D5—122no—
421C4×D5D3×D412yes—
422C4×D5D3×Q812yes—
423C22×D4—151no—
424C23×C4—152no—
425C23×C4—152no—
426C23×C4—152no—
427C4×D4—31no—
428C4×D4—151no—
429C4×D4—152no—
430C4×D4—152no—
431C4×D4—151no—
432C4×D4—151no—
433C4×D4—304no—
434C4×D4—304no—
435C2×C4⋊C4—51no—
436C2×C4⋊C4—51no—
437C2×C4⋊C4—52no—
438C2×C4⋊C4—151no—
439C2×C4⋊C4—151no—
440C2×C4⋊C4—151no—
441C2×C4⋊C4—152no—
442C2×C22⋊C4—152no—
443C2×C22⋊C4—152no—
444C2×C22⋊C4—152no—
445C2×C42—51no—
446C2×C42—151no—
447C2×C42—151no—
448#95—52no—
449#95—151no—
450#95—152no—
451#95—152no—
452#95—151no—
453#95—152no—
454C2×C3×C5C22×C4⋊C411yescharacteristic
455C2×C3×C5C4×#4111yescharacteristic
456C2×C3×C5#51811yescharacteristic
457D15—24no—
458C3×D5#54611yescharacteristic
459C3×D5#54611yescharacteristic
460C3×D5#55411yescharacteristic
461C3×D5#55411yescharacteristic
462C5×D3—24no—
463C23×C3—51no—
464C22×D3—52no—
465C22×D3—54no—
466C22×D3—54no—
467C22×D3—102no—
468C22×D3—102no—
469C22×D3—102no—
470C22×D3—102no—
471C22×D3C22×AGL(1,𝔽5)12yes—
472C2×C3×C4—51no—
473C2×C3×C4—52no—
474C2×C3×C4—52no—
475C2×C3×C4—52no—
476C2×C3×C4—52no—
477C2×C3×C4—102no—
478C2×C3×C4—102no—
479C2×C3×C4—101no—
480C2×C3×C4—101no—
481C2×C3×C4—101no—
482C2×C3×C4—101no—
483C2×C3×C4—102no—
484C2×C3×C4—101no—
485C2×C3×C4—102no—
486C2×C3×C4—102no—
487C2×C3×C4C22×AGL(1,𝔽5)12yes—
488C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
489C2×Dic3—52no—
490C2×Dic3—51no—
491C2×Dic3—51no—
492C2×Dic3—101no—
493C2×Dic3—101no—
494C2×Dic3—101no—
495C2×Dic3—101no—
496C2×Dic3—101no—
497C2×Dic3—101no—
498C2×Dic3—101no—
499C2×Dic3—101no—
500C2×Dic3—102no—
501C2×Dic3—101no—
502C2×Dic3—102no—
503C2×Dic3—102no—
504C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
505C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
506D12—58no—
507D12—54no—
508D12C4⋊AGL(1,𝔽5)14yescomplemented
509C4×D3—42no—
510C4×D3—202no—
511C4×D3—202no—
512C4×D3—202no—
513C4×D3—208no—
514C4×D3—208no—
515C22×C5—34no—
516C22×C5—62no—
517C22×C5—62no—
518C22×C5C22×C4×D311yescharacteristic
519C2×D5—34no—
520C2×D5—62no—
521C2×D5—62no—
522C2×D5—64no—
523C2×D5—64no—
524C2×D5—64no—
525C2×D5—64no—
526C2×D5C2×D3×D411yescharacteristic
527C2×D5#100411yescharacteristic
528C2×D5C2×D3×Q811yescharacteristic
529C2×D5C2×#23911yescharacteristic
530C2×D5D3×#4111yescharacteristic
531C2×D5#100911yescharacteristic
532AGL(1,𝔽5)—22no—
533AGL(1,𝔽5)—41no—
534AGL(1,𝔽5)—42no—
535AGL(1,𝔽5)—62no—
536AGL(1,𝔽5)—121no—
537AGL(1,𝔽5)—122no—
538C4×C5—22no—
539C4×C5—61no—
540C4×C5—61no—
541C4×C5D3×C4⋊C412yes—
542Dic5—22no—
543Dic5—61no—
544Dic5—61no—
545Dic5D3×C4⋊C412yes—
546C24—152no—
547C2×D4—31no—
548C2×D4—154no—
549C2×D4—154no—
550C2×D4—152no—
551C2×D4—151no—
552C22×C4—32no—
553C22×C4—51no—
554C22×C4—51no—
555C22×C4—52no—
556C22×C4—52no—
557C22×C4—51no—
558C22×C4—152no—
559C22×C4—151no—
560C22×C4—151no—
561C22×C4—152no—
562C22×C4—151no—
563C22×C4—152no—
564C22×C4—152no—
565C22×C4—151no—
566C22×C4—304no—
567C22×C4—304no—
568C22×C4—304no—
569C22×C4—304no—
570C22×C4—602no—
571C22×C4—602no—
572C22×C4—602no—
573C22×C4—602no—
574C4⋊C4—52no—
575C4⋊C4—51no—
576C4⋊C4—102no—
577C4⋊C4—202no—
578C4⋊C4—302no—
579C4⋊C4—302no—
580C4⋊C4—302no—
581C4⋊C4—602no—
582C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
583C22⋊C4—32no—
584C22⋊C4—152no—
585C22⋊C4—152no—
586C22⋊C4—152no—
587C22⋊C4—304no—
588C22⋊C4—304no—
589C42—31no—
590C42—102no—
591C42—151no—
592C42—151no—
593C42—151no—
594C42—302no—
595C3×C5#234911yescharacteristic, complemented, Hall
596C22×C3—51no—
597C22×C3—51no—
598C22×C3—51no—
599C22×C3—51no—
600C22×C3—51no—
601C22×C3—51no—
602C22×C3C23×AGL(1,𝔽5)11yescharacteristic
603C2×D3—22no—
604C2×D3—22no—
605C2×D3—54no—
606C2×D3—104no—
607C2×D3—104no—
608C2×D3—104no—
609C2×D3—104no—
610C2×D3—102no—
611C2×D3—102no—
612C2×D3C2×C4⋊AGL(1,𝔽5)14yes—
613C3×C4—22no—
614C3×C4—52no—
615C3×C4—102no—
616C3×C4—102no—
617C3×C4—202no—
618C3×C4—201no—
619C3×C4C2×C4⋊AGL(1,𝔽5)12yes—
620Dic3—21no—
621Dic3—21no—
622Dic3—102no—
623Dic3—101no—
624Dic3—101no—
625Dic3—202no—
626Dic3—201no—
627C2×C5—64no—
628C2×C5C2×D3×C4⋊C411yescharacteristic
629C2×C5#554511yescharacteristic
630C2×C5C4×#23911yescharacteristic
631D5—64no—
632D5#561211yescharacteristic
633D5#563011yescharacteristic
634D5#569011yescharacteristic
635D5#573011yescharacteristic
636C23—32no—
637C23—51no—
638C23—154no—
639C23—154no—
640C23—152no—
641C23—302no—
642C23—302no—
643C23—302no—
644C23—302no—
645D4—34no—
646D4—158no—
647D4—154no—
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—51no—
651C2×C4—52no—
652C2×C4—52no—
653C2×C4—52no—
654C2×C4—52no—
655C2×C4—102no—
656C2×C4—102no—
657C2×C4—101no—
658C2×C4—101no—
659C2×C4—101no—
660C2×C4—102no—
661C2×C4—101no—
662C2×C4—102no—
663C2×C4—101no—
664C2×C4—102no—
665C2×C4—122no—
666C2×C4—152no—
667C2×C4—151no—
668C2×C4—151no—
669C2×C4—301no—
670C2×C4—301no—
671C2×C4—301no—
672C2×C4—301no—
673C2×C4—301no—
674C2×C4—301no—
675C2×C4—301no—
676C2×C4—302no—
677C2×C4—301no—
678C2×C4—301no—
679C2×C4—302no—
680C2×C4—302no—
681C2×C4—602no—
682C2×C4—602no—
683C2×C4—602no—
684C2×C4—608no—
685C2×C4—608no—
686C2×C4C2×D3×AGL(1,𝔽5)12yes—
687C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
688C2×C3—51no—
689C2×C3—51no—
690C2×C3—51no—
691C2×C3—51no—
692C2×C3C22×C4⋊AGL(1,𝔽5)11yescharacteristic
693C2×C3#6625811yescharacteristic
694C2×C3#41×AGL(1,𝔽5)11yescharacteristic
695D3—24no—
696D3—104no—
697C5#7620311yescharacteristic, complemented, Sylow
698C22—34no—
699C22—51no—
700C22—51no—
701C22—51no—
702C22—51no—
703C22—51no—
704C22—51no—
705C22—62no—
706C22—62no—
707C22—154no—
708C22—304no—
709C22—304no—
710C22—304no—
711C22—304no—
712C22—302no—
713C22—302no—
714C22C22×D3×AGL(1,𝔽5)11yescharacteristic
715C4—22no—
716C4—52no—
717C4—61no—
718C4—61no—
719C4—102no—
720C4—102no—
721C4—202no—
722C4—201no—
723C4—302no—
724C4—301no—
725C4—301no—
726C4—602no—
727C4—601no—
728C4D3×C4⋊AGL(1,𝔽5)12yes—
729C3#1061717811yescharacteristic, complemented, Sylow
730C2—51no—
731C2—51no—
732C2—51no—
733C2—51no—
734C2—64no—
735C2—304no—
736C2C2×D3×C4⋊AGL(1,𝔽5)11yescharacteristic
737C2#1175684511yescharacteristic
738C2AGL(1,𝔽5)×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radicalC2×D5×D12C22
cosocleC22×C3×D5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2349
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11752371C2semidirect
5. C3×#65712C2semidirect
6. #11751934C2semidirect
7. #11751932C2semidirect
8. D3×(C2×AGL(1,𝔽5))⋊C4C2semidirect
9. C4×Dic3⋊AGL(1,𝔽5)C2semidirect
10. #11751855C2semidirect
11. #11751751C2semidirect
29. #91782C4semidirect
30. C5×#893C4semidirect
33. #91446C4semidirect
34. #91435C4semidirect
35. #91428C4semidirect
36. #91406C4semidirect
51. #65712D3semidirect
70. C2×C4×D15C2×C4semidirect
72. C2×C4×C5×D3C2×C4semidirect
76. C2×#1200C2×C4semidirect
77. C2×D3×Dic5C2×C4semidirect
94. C3×C5×C4⋊C4C2×C4semidirect
95. #6714C2×C4semidirect
96. C4×Dic15C2×C4semidirect
97. C5×(C2×D3)⋊C4C2×C4semidirect
98. C4×C5×Dic3C2×C4semidirect
99. C3×C4⋊Dic5C2×C4semidirect
100. C3×#683C2×C4semidirect
101. #6667C2×C4semidirect
102. (C2×D3)⋊Dic5C2×C4semidirect
103. Dic3×Dic5C2×C4semidirect
104. Dic3×Dic5C2×C4semidirect
181. D60C4⋊C4semidirect
185. C5×D12C4⋊C4semidirect
193. #1203C4⋊C4semidirect
223. #893AGL(1,𝔽5)semidirect
269. C5×C4⋊C4C4×D3semidirect
275. C4⋊Dic5C4×D3semidirect
276. #683C4×D3semidirect
349. C2×C4×D3C2×AGL(1,𝔽5)semidirect
354. C3×C4⋊C4C2×AGL(1,𝔽5)semidirect
361. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
370. C4×Dic3C2×AGL(1,𝔽5)semidirect
508. D12C4⋊AGL(1,𝔽5)semidirect
582. C4⋊C4D3×AGL(1,𝔽5)semidirect
595. C3×C5#2349semidirect
697. C5#76203semidirect
729. C3#10617178semidirect

Maximal subgroups

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

subgroupindex
C2×#919212
C2×AGL(1,𝔽5)×D122
D5×#8932
#117523712
C3×#657122
#117519342
#117519322
D3×(C2×AGL(1,𝔽5))⋊C42
C4×Dic3⋊AGL(1,𝔽5)2
#117518552
#117517512
#106171783
#762035