Finite Group Databasebeta

← #14327205

Subgroups — #14327205

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×D4×ΓL(1,𝔽16)C211yesmaximal, characteristic
2C2×C3×D4×AGL(1,𝔽5)C211yesmaximal, characteristic
3D4×D5×Dic3C211yesmaximal, characteristic
4#11752029C212yesmaximal, complemented
5#11752028C212yesmaximal, complemented
6#11752027C212yesmaximal, complemented
7C2×(C2×AGL(1,𝔽5))⋊Dic3C212yesmaximal, complemented
8#11751861C211yesmaximal, characteristic, complemented
9#11751859C211yesmaximal, characteristic, complemented
10C4×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
11#11751751C211yesmaximal, characteristic, complemented
12#10617178—31nomaximal, Hall
13C23×ΓL(1,𝔽16)C2212yes—
14C23×C3×AGL(1,𝔽5)C2212yes—
15C2×C3×D4×D5C2211yescharacteristic
16C22×D5×Dic3C2212yes—
17C2×#6763C2212yes—
18D4×ΓL(1,𝔽16)—24no—
19C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
20C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
21C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
22C3×D4×AGL(1,𝔽5)—24no—
23C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
24C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
25C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
26C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
27C2×Dic3⋊AGL(1,𝔽5)C2212yes—
28C2×Dic3⋊AGL(1,𝔽5)C2212yes—
29D4×Dic15C411yescharacteristic, complemented
30C5×D4×Dic3C411yescharacteristic, complemented
31#91559C412yescomplemented
32Dic3×C22⋊D5C412yescomplemented
33D5×#217C2212yes—
34#91434C411yescharacteristic, complemented
35Dic3×D20C411yescharacteristic, complemented
36D5×C4⋊Dic3C2211yescharacteristic
37C4×D5×Dic3C2211yescharacteristic
38(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
39(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
40(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
41(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
44#82334—51nomaximal, Hall
45C2×D4×AGL(1,𝔽5)—31no—
46C2×D4×AGL(1,𝔽5)D311yescharacteristic
47C4×D4×D5—31no—
48#65765—32no—
49C2×(C2×AGL(1,𝔽5))⋊C4—32no—
50#65712—31no—
51#65712—31no—
52#65699—32no—
53#65699—32no—
54#65689—31no—
55C4×C4⋊AGL(1,𝔽5)—31no—
56C23×C3×D5C2312yes—
57C22×ΓL(1,𝔽16)—24no—
58C22×ΓL(1,𝔽16)—24no—
59C22×ΓL(1,𝔽16)—42no—
60C22×ΓL(1,𝔽16)C2311yescharacteristic
61C22×ΓL(1,𝔽16)C2312yes—
62C22×ΓL(1,𝔽16)C2311yescharacteristic
63C22×C3×AGL(1,𝔽5)—24no—
64C22×C3×AGL(1,𝔽5)—24no—
65C22×C3×AGL(1,𝔽5)—42no—
66C22×C3×AGL(1,𝔽5)C2311yescharacteristic
67C22×C3×AGL(1,𝔽5)C2312yes—
68C22×C3×AGL(1,𝔽5)C2311yescharacteristic
69C2×C3×C5×D4C2×C411yescharacteristic
70C22×Dic15C2×C412yescomplemented
71C22×C5×Dic3C2×C412yescomplemented
72C2×C3×C22⋊D5C2×C412yes—
73C3×D4×D5D414yes—
74C3×D4×D5Q814yes—
75C2×C3×D20C2×C411yescharacteristic
76C2×C3×C4×D5C2311yescharacteristic
77C2×D5×Dic3—42no—
78C2×D5×Dic3—42no—
79C2×D5×Dic3C2×C412yescomplemented
80C2×D5×Dic3C2×C412yescomplemented
81C2×D5×Dic3C2312yes—
82C2×D5×Dic3C2311yescharacteristic
83C2×D5×Dic3C2311yescharacteristic
84#6763—24no—
85C4⋊ΓL(1,𝔽16)—22no—
86C4×ΓL(1,𝔽16)—22no—
87C3×C22⋊AGL(1,𝔽5)—24no—
88C3×C4⋊AGL(1,𝔽5)—22no—
89C3×C4×AGL(1,𝔽5)—22no—
90Dic3⋊AGL(1,𝔽5)—22no—
91Dic3⋊AGL(1,𝔽5)—22no—
92Dic3⋊AGL(1,𝔽5)—42no—
93Dic3⋊AGL(1,𝔽5)—42no—
94#6719C2×C412yescomplemented
95C4⋊Dic15C2×C411yescharacteristic, complemented
96C4×Dic15C2×C411yescharacteristic, complemented
97C5×#217C2×C412yescomplemented
98C5×C4⋊Dic3C2×C411yescharacteristic, complemented
99C4×C5×Dic3C2×C411yescharacteristic, complemented
100#6668C2×C412yescomplemented
101#6665C2×C412yescomplemented
102#6665C2×C412yescomplemented
103Dic3×Dic5C2×C411yescharacteristic, complemented
104Dic3×Dic5C2×C411yescharacteristic, complemented
105C2×C3×C4×D4—51no—
106C2×D4×Dic3—51no—
107C2×D4×Dic3—51no—
108#5210—52no—
109C2×C3⋊#95—52no—
110#4977—51no—
111#4972—51no—
112#4946—52no—
113#4942—52no—
114C4×Dic3⋊C4—51no—
115#4928—51no—
116C23×AGL(1,𝔽5)—32no—
117C23×AGL(1,𝔽5)C2×D312yes—
118C2×D4×D5C2×D311yescharacteristic
119C22×C4×D5—32no—
120C2×C22⋊AGL(1,𝔽5)—32no—
121C2×C22⋊AGL(1,𝔽5)C2×D312yes—
122D4×AGL(1,𝔽5)—24no—
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)—32no—
129C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
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⋊C4—31no—
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))⋊C4—32no—
147#2349—151noSylow
148C23×C3×C5C22×C412yes—
149C22×C3×D5—22no—
150C22×C3×D5—22no—
151C22×C3×D5—22no—
152C22×C3×D5—22no—
153C22×C3×D5C22×C412yes—
154C22×C3×D5C2×D414yes—
155C22×C3×D5C2×Q814yes—
156C22×C3×D5C2411yescharacteristic
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)—48no—
166C2×ΓL(1,𝔽16)#4112yes—
167C2×C3×AGL(1,𝔽5)—21no—
168C2×C3×AGL(1,𝔽5)—21no—
169C2×C3×AGL(1,𝔽5)—21no—
170C2×C3×AGL(1,𝔽5)—22no—
171C2×C3×AGL(1,𝔽5)—21no—
172C2×C3×AGL(1,𝔽5)—22no—
173C2×C3×AGL(1,𝔽5)—21no—
174C2×C3×AGL(1,𝔽5)—22no—
175C2×C3×AGL(1,𝔽5)—48no—
176C2×C3×AGL(1,𝔽5)#4112yes—
177C3×C5×D4C4⋊C414yescomplemented
178C2×C3×C4×C5C22×C411yescharacteristic
179C2×Dic15—42no—
180C2×Dic15C22×C411yescharacteristic
181C2×Dic15C22×C411yescharacteristic
182C2×Dic15C22×C412yes—
183C2×C5×Dic3—42no—
184C2×C5×Dic3C22×C411yescharacteristic
185C2×C5×Dic3C22×C411yescharacteristic
186C2×C5×Dic3C22×C412yes—
187C3×C22⋊D5C4⋊C418yescomplemented
188C2×C3×Dic5C22×C411yescharacteristic
189C3×D20C4⋊C414yescomplemented
190C3×C4×D5C2×D412yes—
191C3×C4×D5C2×Q812yes—
192D5×Dic3—21no—
193D5×Dic3—21no—
194D5×Dic3—22no—
195D5×Dic3—22no—
196D5×Dic3—21no—
197D5×Dic3—21no—
198D5×Dic3—42no—
199D5×Dic3—42no—
200C22×C3×D4—51no—
201C23×C3×C4—52no—
202C23×Dic3—52no—
203C23×Dic3—52no—
204C3×C4×D4—104no—
205C2×C3×C4⋊C4—51no—
206C2×C3×C22⋊C4—52no—
207C2×C3×C42—51no—
208C2×#217—52no—
209C2×#217—52no—
210D4×Dic3—51no—
211D4×Dic3—52no—
212D4×Dic3—52no—
213D4×Dic3—51no—
214D4×Dic3—51no—
215D4×Dic3—104no—
216D4×Dic3AGL(1,𝔽5)11yescharacteristic, complemented
217C2×C4⋊Dic3—51no—
218C2×C4⋊Dic3—51no—
219C2×Dic3⋊C4—51no—
220C2×Dic3⋊C4—51no—
221C2×Dic3⋊C4—52no—
222C2×Dic3⋊C4—52no—
223C2×C4×Dic3—51no—
224C2×C4×Dic3—51no—
225C3⋊#95—52no—
226C3⋊#95—51no—
227C3⋊#95—51no—
228C3⋊#95—52no—
229C3⋊#95—52no—
230C3⋊#95—52no—
231C23×D5C22×D312yes—
232C22×AGL(1,𝔽5)—24no—
233C22×AGL(1,𝔽5)—24no—
234C22×AGL(1,𝔽5)—31no—
235C22×AGL(1,𝔽5)—31no—
236C22×AGL(1,𝔽5)—32no—
237C22×AGL(1,𝔽5)—42no—
238C22×AGL(1,𝔽5)—64no—
239C22×AGL(1,𝔽5)—64no—
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×D4C4×D311yescharacteristic
245C22×C4×C5—32no—
246C2×C22⋊D5C4×D312yes—
247C22×Dic5—32no—
248D4×D5Dic614yes—
249D4×D5#6714yes—
250C2×D20C4×D311yescharacteristic
251C2×C4×D5—32no—
252C2×C4×D5—31no—
253C2×C4×D5—31no—
254C2×C4×D5—32no—
255C2×C4×D5—32no—
256C2×C4×D5—122no—
257C2×C4×D5—122no—
258C2×C4×D5C22×D311yescharacteristic
259C22⋊AGL(1,𝔽5)—24no—
260C22⋊AGL(1,𝔽5)—64no—
261C4⋊AGL(1,𝔽5)—22no—
262C4⋊AGL(1,𝔽5)—62no—
263C4⋊AGL(1,𝔽5)—62no—
264C4⋊AGL(1,𝔽5)—62no—
265C4⋊AGL(1,𝔽5)—122no—
266C4⋊AGL(1,𝔽5)—122no—
267C4×AGL(1,𝔽5)—22no—
268C4×AGL(1,𝔽5)—62no—
269C5×C4⋊C4—31no—
270C5×C22⋊C4—32no—
271C42×C5—31no—
272C22⋊Dic5—32no—
273#685—32no—
274#685—32no—
275C4⋊Dic5—31no—
276#683—32no—
277C4×Dic5—31no—
278C4×Dic5—31no—
279C4×Dic5—31no—
280C2×C4×D4—51no—
281C2×C4×D4—151no—
282C2×C4×D4—151no—
283#389—151no—
284#389—151no—
285#385—152no—
286#385—152no—
287#382—151no—
288#380—152no—
289C4×C4⋊C4—151no—
290C2×#95—152no—
291C22×C3×C5—22no—
292C22×C3×C5—22no—
293C22×C3×C5C2×C4⋊C414yes—
294C22×C3×C5C23×C411yescharacteristic
295C2×C3×D5—22no—
296C2×C3×D5—22no—
297C2×C3×D5—24no—
298C2×C3×D5—24no—
299C2×C3×D5—24no—
300C2×C3×D5—24no—
301C2×C3×D5C2×C4⋊C414yes—
302C2×C3×D5C22×D411yescharacteristic
303C2×C3×D5C22×Q811yescharacteristic
304C2×C3×D5C2×#4111yescharacteristic
305C2×C3×D5C2×#4111yescharacteristic
306C2×C3×D5H(5,𝔽2)11yescharacteristic
307C2×C3×D5H(5,𝔽2)11yescharacteristic
308ΓL(1,𝔽16)—22no—
309ΓL(1,𝔽16)—41no—
310ΓL(1,𝔽16)—42no—
311C3×AGL(1,𝔽5)—22no—
312C3×AGL(1,𝔽5)—41no—
313C3×AGL(1,𝔽5)—42no—
314C3×C4×C5C2×C4⋊C412yes—
315Dic15—21no—
316Dic15—21no—
317Dic15—22no—
318C3×Dic5C2×C4⋊C412yes—
319C5×Dic3—21no—
320C5×Dic3—21no—
321C5×Dic3—22no—
322C24×C3—52no—
323C2×C3×D4—52no—
324C2×C3×D4—54no—
325C2×C3×D4—54no—
326C2×C3×D4—51no—
327C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
328C22×C3×C4—51no—
329C22×C3×C4—51no—
330C22×C3×C4—52no—
331C22×C3×C4—51no—
332C22×C3×C4—104no—
333C22×C3×C4—104no—
334C22×C3×C4—202no—
335C22×Dic3—51no—
336C22×Dic3—52no—
337C22×Dic3—51no—
338C22×Dic3—51no—
339C22×Dic3—52no—
340C22×Dic3—52no—
341C22×Dic3—52no—
342C22×Dic3—52no—
343C22×Dic3—51no—
344C22×Dic3—104no—
345C22×Dic3—104no—
346C22×Dic3—202no—
347C22×Dic3—202no—
348C22×Dic3—202no—
349C22×Dic3C2×AGL(1,𝔽5)12yescomplemented
350C3×C4⋊C4—102no—
351C3×C22⋊C4—104no—
352C3×C42—102no—
353#217—52no—
354#217—52no—
355#217—52no—
356#217—104no—
357#217C2×AGL(1,𝔽5)12yescomplemented
358C4⋊Dic3—51no—
359C4⋊Dic3—52no—
360C4⋊Dic3—102no—
361C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
362Dic3⋊C4—102no—
363Dic3⋊C4—102no—
364Dic3⋊C4—202no—
365Dic3⋊C4—202no—
366C4×Dic3—51no—
367C4×Dic3—51no—
368C4×Dic3—51no—
369C4×Dic3—102no—
370C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
371C23×C5C2×C4×D312yes—
372C22×D5—22no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5C2×Dic614yes—
377C22×D5C2×C4×D312yes—
378C22×D5C2×#6714yes—
379C22×D5C23×D311yescharacteristic
380C2×AGL(1,𝔽5)—21no—
381C2×AGL(1,𝔽5)—21no—
382C2×AGL(1,𝔽5)—22no—
383C2×AGL(1,𝔽5)—22no—
384C2×AGL(1,𝔽5)—21no—
385C2×AGL(1,𝔽5)—21no—
386C2×AGL(1,𝔽5)—21no—
387C2×AGL(1,𝔽5)—22no—
388C2×AGL(1,𝔽5)—32no—
389C2×AGL(1,𝔽5)—48no—
390C2×AGL(1,𝔽5)—61no—
391C2×AGL(1,𝔽5)—61no—
392C2×AGL(1,𝔽5)—61no—
393C2×AGL(1,𝔽5)—61no—
394C2×AGL(1,𝔽5)—62no—
395C2×AGL(1,𝔽5)—62no—
396C2×AGL(1,𝔽5)—61no—
397C2×AGL(1,𝔽5)—62no—
398C2×AGL(1,𝔽5)—128no—
399C2×AGL(1,𝔽5)#23712yes—
400C5×D4Dic3⋊C414yescomplemented
401C2×C4×C5—31no—
402C2×C4×C5—31no—
403C2×C4×C5—32no—
404C2×C4×C5—122no—
405C2×C4×C5C2×C4×D311yescharacteristic
406C22⋊D5Dic3⋊C418yescomplemented
407C2×Dic5—31no—
408C2×Dic5—31no—
409C2×Dic5—32no—
410C2×Dic5—122no—
411C2×Dic5C2×C4×D311yescharacteristic
412D20Dic3⋊C414yescomplemented
413C4×D5—61no—
414C4×D5—62no—
415C4×D5—61no—
416C4×D5—61no—
417C4×D5—62no—
418C4×D5—61no—
419C4×D5—122no—
420C4×D5—122no—
421C4×D5C2×Dic612yes—
422C4×D5C2×#6712yes—
423C22×D4—51no—
424C23×C4—52no—
425C23×C4—152no—
426C23×C4—152no—
427C4×D4—31no—
428C4×D4—104no—
429C4×D4—151no—
430C4×D4—152no—
431C4×D4—151no—
432C4×D4—152no—
433C4×D4—151no—
434C4×D4—304no—
435C2×C4⋊C4—51no—
436C2×C4⋊C4—151no—
437C2×C4⋊C4—151no—
438C2×C4⋊C4—151no—
439C2×C4⋊C4—151no—
440C2×C4⋊C4—152no—
441C2×C4⋊C4—152no—
442C2×C22⋊C4—52no—
443C2×C22⋊C4—152no—
444C2×C22⋊C4—152no—
445C2×C42—51no—
446C2×C42—151no—
447C2×C42—151no—
448#95—151no—
449#95—152no—
450#95—152no—
451#95—152no—
452#95—151no—
453#95—152no—
454C2×C3×C5—24no—
455C2×C3×C5C22×C4⋊C411yescharacteristic
456C2×C3×C5C4×#4111yescharacteristic
457C2×C3×C5#51811yescharacteristic
458C3×D5—24no—
459C3×D5#54611yescharacteristic
460C3×D5#54611yescharacteristic
461C3×D5#55411yescharacteristic
462C3×D5#55411yescharacteristic
463C23×C3—51no—
464C23×C3—54no—
465C23×C3—54no—
466C23×C3—52no—
467C23×C3—102no—
468C23×C3—102no—
469C23×C3—102no—
470C23×C3—102no—
471C23×C3C22×AGL(1,𝔽5)12yes—
472C3×D4—58no—
473C3×D4—54no—
474C3×D4C4⋊AGL(1,𝔽5)14yescomplemented
475C2×C3×C4—51no—
476C2×C3×C4—52no—
477C2×C3×C4—52no—
478C2×C3×C4—52no—
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×C4—208no—
488C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
489C2×Dic3—42no—
490C2×Dic3—52no—
491C2×Dic3—51no—
492C2×Dic3—51no—
493C2×Dic3—52no—
494C2×Dic3—101no—
495C2×Dic3—101no—
496C2×Dic3—102no—
497C2×Dic3—102no—
498C2×Dic3—101no—
499C2×Dic3—101no—
500C2×Dic3—101no—
501C2×Dic3—101no—
502C2×Dic3—101no—
503C2×Dic3—101no—
504C2×Dic3—101no—
505C2×Dic3—102no—
506C2×Dic3—102no—
507C2×Dic3—102no—
508C2×Dic3—202no—
509C2×Dic3—202no—
510C2×Dic3—202no—
511C2×Dic3—208no—
512C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
513C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
514C2×Dic3C22×AGL(1,𝔽5)12yes—
515C22×C5—22no—
516C22×C5—22no—
517C22×C5C2×Dic3⋊C414yes—
518C22×C5C22×C4×D311yescharacteristic
519C2×D5—22no—
520C2×D5—22no—
521C2×D5—24no—
522C2×D5—24no—
523C2×D5—24no—
524C2×D5—24no—
525C2×D5C2×Dic3⋊C414yes—
526C2×D5C22×Dic611yescharacteristic
527C2×D5C2×#23711yescharacteristic
528C2×D5#100411yescharacteristic
529C2×D5D3×#4111yescharacteristic
530C2×D5#100911yescharacteristic
531C2×D5C22×#6711yescharacteristic
532AGL(1,𝔽5)—22no—
533AGL(1,𝔽5)—42no—
534AGL(1,𝔽5)—41no—
535AGL(1,𝔽5)—62no—
536AGL(1,𝔽5)—121no—
537AGL(1,𝔽5)—122no—
538C4×C5—61no—
539C4×C5—61no—
540C4×C5—62no—
541C4×C5C2×Dic3⋊C412yes—
542Dic5—61no—
543Dic5—61no—
544Dic5—62no—
545Dic5C2×Dic3⋊C412yes—
546C24—52no—
547C2×D4—52no—
548C2×D4—54no—
549C2×D4—54no—
550C2×D4—51no—
551C2×D4D3×AGL(1,𝔽5)11yescharacteristic
552C22×C4—32no—
553C22×C4—51no—
554C22×C4—51no—
555C22×C4—52no—
556C22×C4—51no—
557C22×C4—104no—
558C22×C4—104no—
559C22×C4—151no—
560C22×C4—151no—
561C22×C4—152no—
562C22×C4—152no—
563C22×C4—152no—
564C22×C4—151no—
565C22×C4—152no—
566C22×C4—152no—
567C22×C4—151no—
568C22×C4—202no—
569C22×C4—304no—
570C22×C4—304no—
571C22×C4—602no—
572C22×C4—602no—
573C22×C4—602no—
574C4⋊C4—31no—
575C4⋊C4—102no—
576C4⋊C4—152no—
577C4⋊C4—151no—
578C4⋊C4—302no—
579C4⋊C4—302no—
580C4⋊C4—302no—
581C4⋊C4—602no—
582C4⋊C4—602no—
583C22⋊C4—32no—
584C22⋊C4—104no—
585C22⋊C4—152no—
586C22⋊C4—152no—
587C22⋊C4—152no—
588C22⋊C4—304no—
589C42—31no—
590C42—102no—
591C42—151no—
592C42—151no—
593C42—151no—
594C42—302no—
595C3×C5#234911yescharacteristic, complemented, Hall
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—51no—
599C22×C3—51no—
600C22×C3—51no—
601C22×C3—51no—
602C22×C3—51no—
603C22×C3—51no—
604C22×C3—54no—
605C22×C3—104no—
606C22×C3—104no—
607C22×C3—104no—
608C22×C3—104no—
609C22×C3—102no—
610C22×C3—102no—
611C22×C3C2×C4⋊AGL(1,𝔽5)14yes—
612C22×C3C23×AGL(1,𝔽5)11yescharacteristic
613C3×C4—52no—
614C3×C4—102no—
615C3×C4—201no—
616C3×C4—202no—
617C3×C4C2×C4⋊AGL(1,𝔽5)12yes—
618Dic3—21no—
619Dic3—22no—
620Dic3—21no—
621Dic3—102no—
622Dic3—102no—
623Dic3—101no—
624Dic3—101no—
625Dic3—201no—
626Dic3—202no—
627C2×C5—24no—
628C2×C5C4×#23711yescharacteristic
629C2×C5#554511yescharacteristic
630C2×C5C22×Dic3⋊C411yescharacteristic
631D5—24no—
632D5#553911yescharacteristic
633D5#554311yescharacteristic
634D5#580611yescharacteristic
635D5#582911yescharacteristic
636C23—51no—
637C23—54no—
638C23—54no—
639C23—52no—
640C23—102no—
641C23—102no—
642C23—102no—
643C23—102no—
644C23C2×D3×AGL(1,𝔽5)12yes—
645D4—58no—
646D4—54no—
647D4Dic3⋊AGL(1,𝔽5)14yescomplemented
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—32no—
651C2×C4—51no—
652C2×C4—52no—
653C2×C4—52no—
654C2×C4—52no—
655C2×C4—101no—
656C2×C4—101no—
657C2×C4—101no—
658C2×C4—102no—
659C2×C4—101no—
660C2×C4—101no—
661C2×C4—102no—
662C2×C4—102no—
663C2×C4—122no—
664C2×C4—152no—
665C2×C4—151no—
666C2×C4—151no—
667C2×C4—152no—
668C2×C4—208no—
669C2×C4—301no—
670C2×C4—301no—
671C2×C4—302no—
672C2×C4—302no—
673C2×C4—301no—
674C2×C4—301no—
675C2×C4—301no—
676C2×C4—301no—
677C2×C4—301no—
678C2×C4—302no—
679C2×C4—301no—
680C2×C4—301no—
681C2×C4—302no—
682C2×C4—302no—
683C2×C4—602no—
684C2×C4—602no—
685C2×C4—602no—
686C2×C4—608no—
687C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
688C2×C3—24no—
689C2×C3—51no—
690C2×C3—51no—
691C2×C3—51no—
692C2×C3—51no—
693C2×C3—104no—
694C2×C3C22×C4⋊AGL(1,𝔽5)11yescharacteristic
695C2×C3#6625811yescharacteristic
696C2×C3#41×AGL(1,𝔽5)11yescharacteristic
697C5#8233411yescharacteristic, complemented, Sylow
698C22—22no—
699C22—22no—
700C22—51no—
701C22—51no—
702C22—51no—
703C22—51no—
704C22—51no—
705C22—51no—
706C22—54no—
707C22—104no—
708C22—104no—
709C22—104no—
710C22—104no—
711C22—102no—
712C22—102no—
713C22C2×Dic3⋊AGL(1,𝔽5)14yes—
714C22C22×D3×AGL(1,𝔽5)11yescharacteristic
715C4—52no—
716C4—61no—
717C4—61no—
718C4—62no—
719C4—102no—
720C4—202no—
721C4—201no—
722C4—302no—
723C4—301no—
724C4—301no—
725C4—302no—
726C4—602no—
727C4—601no—
728C4C2×Dic3⋊AGL(1,𝔽5)12yes—
729C3#1061717811yescharacteristic, complemented, Sylow
730C2—24no—
731C2—51no—
732C2—51no—
733C2—51no—
734C2—51no—
735C2—104no—
736C2AGL(1,𝔽5)×#23711yescharacteristic
737C2#1175684511yescharacteristic
738C2C22×Dic3⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×D4C2×C4
prime radicalC2×C3×D4×D5C22
cosocleC22×C3×D5C24
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#2349
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
4. #11752029C2semidirect
5. #11752028C2semidirect
6. #11752027C2semidirect
7. C2×(C2×AGL(1,𝔽5))⋊Dic3C2semidirect
8. #11751861C2semidirect
9. #11751859C2semidirect
10. C4×Dic3⋊AGL(1,𝔽5)C2semidirect
11. #11751751C2semidirect
29. D4×Dic15C4semidirect
30. C5×D4×Dic3C4semidirect
31. #91559C4semidirect
32. Dic3×C22⋊D5C4semidirect
34. #91434C4semidirect
35. Dic3×D20C4semidirect
70. C22×Dic15C2×C4semidirect
71. C22×C5×Dic3C2×C4semidirect
79. C2×D5×Dic3C2×C4semidirect
80. C2×D5×Dic3C2×C4semidirect
94. #6719C2×C4semidirect
95. C4⋊Dic15C2×C4semidirect
96. C4×Dic15C2×C4semidirect
97. C5×#217C2×C4semidirect
98. C5×C4⋊Dic3C2×C4semidirect
99. C4×C5×Dic3C2×C4semidirect
100. #6668C2×C4semidirect
101. #6665C2×C4semidirect
102. #6665C2×C4semidirect
103. Dic3×Dic5C2×C4semidirect
104. Dic3×Dic5C2×C4semidirect
177. C3×C5×D4C4⋊C4semidirect
187. C3×C22⋊D5C4⋊C4semidirect
189. C3×D20C4⋊C4semidirect
216. D4×Dic3AGL(1,𝔽5)semidirect
349. C22×Dic3C2×AGL(1,𝔽5)semidirect
357. #217C2×AGL(1,𝔽5)semidirect
361. C4⋊Dic3C2×AGL(1,𝔽5)semidirect
370. C4×Dic3C2×AGL(1,𝔽5)semidirect
400. C5×D4Dic3⋊C4semidirect
406. C22⋊D5Dic3⋊C4semidirect
412. D20Dic3⋊C4semidirect
474. C3×D4C4⋊AGL(1,𝔽5)semidirect
595. C3×C5#2349semidirect
647. D4Dic3⋊AGL(1,𝔽5)semidirect
697. C5#82334semidirect
729. C3#10617178semidirect

Maximal subgroups

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

subgroupindex
C2×D4×ΓL(1,𝔽16)2
C2×C3×D4×AGL(1,𝔽5)2
D4×D5×Dic32
#117520292
#117520282
#117520272
C2×(C2×AGL(1,𝔽5))⋊Dic32
#117518612
#117518592
C4×Dic3⋊AGL(1,𝔽5)2
#117517512
#106171783
#823345