Finite Group Databasebeta

← #14323685

Subgroups — #14323685

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×AGL(1,𝔽5)×#67C211yesmaximal, characteristic
2C22×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
3D5×#886C211yesmaximal, characteristic
4#11752358C211yesmaximal, characteristic, complemented
5C3×C22⋊C4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
6#11752026C211yesmaximal, characteristic
7#11751984C211yesmaximal, characteristic, complemented
8#11751934C212yesmaximal, complemented
9#11751859C212yesmaximal, complemented
10#11751849C212yesmaximal, complemented
11#11751839C212yesmaximal, complemented
12#10617304—31nomaximal, Hall
13C23×ΓL(1,𝔽16)C2211yescharacteristic
14C23×C3×AGL(1,𝔽5)C2211yescharacteristic
15C22×D3×AGL(1,𝔽5)C2211yescharacteristic
16C2×D5×#67C2211yescharacteristic
17C22×D5×Dic3C2211yescharacteristic
18C2×#6763C2211yescharacteristic
19C2×C4⋊ΓL(1,𝔽16)C2212yes—
20C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
21C2×C3×C4×AGL(1,𝔽5)C2212yes—
22AGL(1,𝔽5)×#67—24no—
23C2×Dic3⋊AGL(1,𝔽5)—24no—
24C2×Dic3⋊AGL(1,𝔽5)C2212yes—
25C2×Dic3⋊AGL(1,𝔽5)C2212yes—
26C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
27C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
28C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
29C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
30#91775C411yescharacteristic, complemented
31C5×#886C411yescharacteristic, complemented
32C3×D5×C22⋊C4C2211yescharacteristic
33#91543C411yescharacteristic, complemented
34#91542C411yescharacteristic, complemented
35D5×(C2×D3)⋊C4C2212yes—
36#91414C412yescomplemented
37#91413C412yescomplemented
38D5×C4⋊Dic3C2212yes—
39#91235C2212yes—
40C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
41(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
44#73446—51nomaximal, Hall
45C2×D4×AGL(1,𝔽5)—31no—
46C22×C4⋊AGL(1,𝔽5)—31no—
47D5×#123—31no—
48#65779—31no—
49#65764—31no—
50#65712—32no—
51#65711—32no—
52#65700—32no—
53#65699—31no—
54#65699—32no—
55C22⋊C4×AGL(1,𝔽5)D311yescharacteristic, complemented
56C23×C3×D5C2311yescharacteristic
57C22×D3×D5C2311yescharacteristic
58C22×ΓL(1,𝔽16)—22no—
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)—42no—
64C22×C3×AGL(1,𝔽5)D414yes—
65C22×C3×AGL(1,𝔽5)C2312yes—
66C22×C3×AGL(1,𝔽5)C2311yescharacteristic
67C22×C3×AGL(1,𝔽5)C2311yescharacteristic
68C2×D3×AGL(1,𝔽5)—22no—
69C2×D3×AGL(1,𝔽5)—42no—
70C2×#1220C2×C411yescharacteristic
71C22×Dic15C2×C411yescharacteristic, complemented
72C2×C5×#67C2×C411yescharacteristic
73C22×C5×Dic3C2×C411yescharacteristic, complemented
74C2×C3×C4×D5C2312yes—
75D5×#67—22no—
76D5×#67—22no—
77C2×#1202C2×C411yescharacteristic
78C2×#1201C2×C411yescharacteristic
79C2×D5×Dic3—22no—
80C2×D5×Dic3—22no—
81C2×D5×Dic3C2×C412yescomplemented
82C2×D5×Dic3C2311yescharacteristic
83C2×D5×Dic3C2312yes—
84#6763—22no—
85C4⋊ΓL(1,𝔽16)—42no—
86C3×C22⋊AGL(1,𝔽5)—22no—
87C3×C4×AGL(1,𝔽5)—42no—
88Dic3⋊AGL(1,𝔽5)—24no—
89Dic3⋊AGL(1,𝔽5)—24no—
90Dic3⋊AGL(1,𝔽5)—22no—
91(C2×D3)⋊AGL(1,𝔽5)—22no—
92(C2×D3)⋊AGL(1,𝔽5)—42no—
93Dic3×AGL(1,𝔽5)—22no—
94C3×C5×C22⋊C4C2×C411yescharacteristic, complemented
95#6714C2×C412yescomplemented
96C4⋊Dic15C2×C412yescomplemented
97C5×(C2×D3)⋊C4C2×C412yescomplemented
98C5×C4⋊Dic3C2×C412yescomplemented
99C3×C22⋊Dic5C2×C411yescharacteristic, complemented
100C3×#685C2×C412yescomplemented
101#6668C2×C412yescomplemented
102#6668C2×C412yescomplemented
103#6667C2×C412yescomplemented
104(C2×D3)⋊Dic5C2×C412yescomplemented
105C2×C4×#67—51no—
106C22×Dic3⋊C4—51no—
107C2×#886—51no—
108C3×C4×C22⋊C4—51no—
109#4958—51no—
110#4950—51no—
111#4943—51no—
112#4940—52no—
113#4928—52no—
114#4668—52no—
115#4653—52no—
116C23×AGL(1,𝔽5)—31no—
117C23×AGL(1,𝔽5)—31no—
118C23×AGL(1,𝔽5)C2×D311yescharacteristic
119C2×D4×D5—31no—
120C22×C4×D5—31no—
121C2×C22⋊AGL(1,𝔽5)—31no—
122C2×C22⋊AGL(1,𝔽5)—31no—
123C2×C22⋊AGL(1,𝔽5)—32no—
124C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
125D4×AGL(1,𝔽5)—64no—
126C2×C4⋊AGL(1,𝔽5)—32no—
127C2×C4⋊AGL(1,𝔽5)—32no—
128C2×C4⋊AGL(1,𝔽5)—31no—
129C2×C4⋊AGL(1,𝔽5)—32no—
130C2×C4⋊AGL(1,𝔽5)—64no—
131C2×C4×AGL(1,𝔽5)—31no—
132C2×C4×AGL(1,𝔽5)C2×D312yes—
133C5×#123—31no—
134#4081—31no—
135#4075—31no—
136#4040—32no—
137D5×C4⋊C4—32no—
138#4032—31no—
139#4029—32no—
140D5×C22⋊C4—32no—
141D5×C22⋊C4C2×D311yescharacteristic
142(C2×AGL(1,𝔽5))⋊C4—32no—
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#2322—151noSylow
148C23×C3×C5C22×C411yescharacteristic
149C22×D15C22×C411yescharacteristic
150C22×C5×D3C22×C411yescharacteristic
151C22×C3×D5—22no—
152C22×C3×D5—22no—
153C22×C3×D5C22×C411yescharacteristic
154C22×C3×D5C2×D412yes—
155C22×C3×D5#4112yes—
156C22×C3×D5C2411yescharacteristic
157C2×D3×D5—21no—
158C2×D3×D5—21no—
159C2×D3×D5—22no—
160C2×D3×D5—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)—22no—
166C2×ΓL(1,𝔽16)—22no—
167C2×ΓL(1,𝔽16)—22no—
168C2×ΓL(1,𝔽16)—44no—
169C2×C3×AGL(1,𝔽5)—22no—
170C2×C3×AGL(1,𝔽5)—22no—
171C2×C3×AGL(1,𝔽5)—22no—
172C2×C3×AGL(1,𝔽5)—22no—
173C2×C3×AGL(1,𝔽5)—22no—
174C2×C3×AGL(1,𝔽5)—44no—
175C2×C3×AGL(1,𝔽5)C2×D412yes—
176C2×C3×AGL(1,𝔽5)C2×D412yes—
177D3×AGL(1,𝔽5)—44no—
178C2×C3×C4×C5C22×C412yes—
179#1220—22no—
180C2×Dic15—22no—
181C2×Dic15C22×C412yes—
182C2×Dic15C22×C411yescharacteristic
183C5×#67—22no—
184C2×C5×Dic3—22no—
185C2×C5×Dic3C22×C412yes—
186C2×C5×Dic3C22×C411yescharacteristic
187C2×C3×Dic5C22×C412yes—
188C3×C4×D5—22no—
189C3×C4×D5—22no—
190#1202—22no—
191#1201—22no—
192D5×Dic3—24no—
193D5×Dic3—21no—
194D5×Dic3—22no—
195D5×Dic3—22no—
196D5×Dic3—21no—
197C23×C3×C4—51no—
198C22×#67—51no—
199C23×Dic3—51no—
200C23×Dic3—51no—
201C22×C4×D3—51no—
202C2×C3×C22⋊C4—51no—
203C2×C3×C22⋊C4—51no—
204C2×C3×C42—52no—
205C2×#217—51no—
206C4×#67—104no—
207C2×(C2×D3)⋊C4—52no—
208C2×(C2×D3)⋊C4—51no—
209C2×(C2×D3)⋊C4—52no—
210C2×C4⋊Dic3—52no—
211C2×C4⋊Dic3—52no—
212C2×Dic3⋊C4—52no—
213C2×Dic3⋊C4—51no—
214C2×Dic3⋊C4—52no—
215C2×Dic3⋊C4—104no—
216C2×C4×Dic3—51no—
217#886—51no—
218#886—51no—
219#886—51no—
220#886—52no—
221#886—52no—
222#886AGL(1,𝔽5)11yescharacteristic, complemented
223C3×#95—52no—
224C3⋊#95—52no—
225C3⋊#95—52no—
226C3⋊#95—52no—
227C3⋊#95—52no—
228C23×D5—31no—
229C23×D5C22×D311yescharacteristic
230C22×AGL(1,𝔽5)—31no—
231C22×AGL(1,𝔽5)—32no—
232C22×AGL(1,𝔽5)—31no—
233C22×AGL(1,𝔽5)—42no—
234C22×AGL(1,𝔽5)—62no—
235C22×AGL(1,𝔽5)—62no—
236C22×AGL(1,𝔽5)—122no—
237C22×AGL(1,𝔽5)—122no—
238C22×AGL(1,𝔽5)D1214yes—
239C22×AGL(1,𝔽5)C22×D312yes—
240C22×AGL(1,𝔽5)C22×D311yescharacteristic
241C22×AGL(1,𝔽5)C22×D311yescharacteristic
242C2×C5×D4—31no—
243C22×C4×C5—31no—
244C2×C22⋊D5—31no—
245C2×C22⋊D5—31no—
246C22×Dic5—31no—
247D4×D5—62no—
248D4×D5—62no—
249C2×D20—31no—
250C2×C4×D5—32no—
251C2×C4×D5—31no—
252C2×C4×D5—32no—
253C2×C4×D5—62no—
254C2×C4×D5—62no—
255C2×C4×D5C22×D312yes—
256C22⋊AGL(1,𝔽5)—22no—
257C22⋊AGL(1,𝔽5)—62no—
258C22⋊AGL(1,𝔽5)—62no—
259C22⋊AGL(1,𝔽5)—122no—
260C4⋊AGL(1,𝔽5)—64no—
261C4⋊AGL(1,𝔽5)—64no—
262C4⋊AGL(1,𝔽5)—62no—
263C4⋊AGL(1,𝔽5)—122no—
264C4×AGL(1,𝔽5)—42no—
265C4×AGL(1,𝔽5)—62no—
266C5×C4⋊C4—32no—
267C5×C22⋊C4—32no—
268C5×C22⋊C4C4×D311yescharacteristic, complemented
269C22⋊Dic5—32no—
270C22⋊Dic5C4×D311yescharacteristic, complemented
271#685—32no—
272#685—32no—
273#685C4×D312yescomplemented
274C4⋊Dic5—32no—
275#683—32no—
276#683—32no—
277C2×#123—151no—
278C2×C4×D4—151no—
279C22×C4⋊C4—151no—
280#389—152no—
281#388—152no—
282#387—152no—
283#386—151no—
284#385—152no—
285#385—151no—
286#381—151no—
287C4×C22⋊C4—51no—
288C22×C3×C5—22no—
289C22×C3×C5C4×D412yes—
290C22×C3×C5C23×C411yescharacteristic
291C2×D15—21no—
292C2×D15—22no—
293C2×C5×D3—21no—
294C2×C5×D3—22no—
295C2×C3×D5—22no—
296C2×C3×D5—22no—
297C2×C3×D5—22no—
298C2×C3×D5—24no—
299C2×C3×D5C4×D412yes—
300C2×C3×D5C22×D411yescharacteristic
301C2×C3×D5C2×#4111yescharacteristic
302C2×C3×D5H(5,𝔽2)12yes—
303C2×C3×D52−1+412yes—
304D3×D5—41no—
305D3×D5—41no—
306D3×D5—42no—
307ΓL(1,𝔽16)—41no—
308ΓL(1,𝔽16)—42no—
309ΓL(1,𝔽16)—41no—
310C3×AGL(1,𝔽5)—22no—
311C3×AGL(1,𝔽5)—22no—
312C3×AGL(1,𝔽5)—42no—
313C3×C4×C5—22no—
314Dic15—22no—
315Dic15—21no—
316C3×Dic5—22no—
317C5×Dic3—22no—
318C5×Dic3—21no—
319C24×C3—51no—
320C23×D3—51no—
321C22×C3×C4—51no—
322C22×C3×C4—51no—
323C22×C3×C4—54no—
324C22×C3×C4—52no—
325C22×C3×C4—52no—
326C22×C3×C4—202no—
327C2×#67—51no—
328C2×#67—51no—
329C2×#67—51no—
330C2×#67—102no—
331C2×#67—102no—
332C2×#67C2×AGL(1,𝔽5)11yescharacteristic
333C22×Dic3—51no—
334C22×Dic3—51no—
335C22×Dic3—52no—
336C22×Dic3—52no—
337C22×Dic3—51no—
338C22×Dic3—52no—
339C22×Dic3—51no—
340C22×Dic3—102no—
341C22×Dic3—102no—
342C22×Dic3—102no—
343C22×Dic3—202no—
344C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
345C2×C4×D3—102no—
346C2×C4×D3—202no—
347C3×C22⋊C4—51no—
348C3×C22⋊C4—52no—
349C3×C22⋊C4—102no—
350C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
351C3×C42—202no—
352#217—102no—
353(C2×D3)⋊C4—52no—
354(C2×D3)⋊C4—52no—
355(C2×D3)⋊C4—52no—
356(C2×D3)⋊C4—102no—
357(C2×D3)⋊C4—202no—
358(C2×D3)⋊C4C2×AGL(1,𝔽5)12yescomplemented
359C4⋊Dic3—52no—
360C4⋊Dic3—52no—
361C4⋊Dic3—52no—
362C4⋊Dic3—202no—
363C4⋊Dic3C2×AGL(1,𝔽5)12yescomplemented
364Dic3⋊C4—104no—
365Dic3⋊C4—104no—
366Dic3⋊C4—102no—
367C4×Dic3—102no—
368C23×C5—31no—
369C23×C5C2×C4×D311yescharacteristic
370C22×D5—22no—
371C22×D5—22no—
372C22×D5—31no—
373C22×D5—61no—
374C22×D5—61no—
375C22×D5—62no—
376C22×D5—62no—
377C22×D5C2×C4×D311yescharacteristic
378C22×D5C2×D1212yes—
379C22×D5#23512yes—
380C22×D5C23×D311yescharacteristic
381C2×AGL(1,𝔽5)—22no—
382C2×AGL(1,𝔽5)—22no—
383C2×AGL(1,𝔽5)—22no—
384C2×AGL(1,𝔽5)—22no—
385C2×AGL(1,𝔽5)—22no—
386C2×AGL(1,𝔽5)—44no—
387C2×AGL(1,𝔽5)—61no—
388C2×AGL(1,𝔽5)—62no—
389C2×AGL(1,𝔽5)—61no—
390C2×AGL(1,𝔽5)—62no—
391C2×AGL(1,𝔽5)—62no—
392C2×AGL(1,𝔽5)—62no—
393C2×AGL(1,𝔽5)—62no—
394C2×AGL(1,𝔽5)—124no—
395C2×AGL(1,𝔽5)—124no—
396C2×AGL(1,𝔽5)C2×D1212yes—
397C2×AGL(1,𝔽5)C2×D1212yes—
398C5×D4—62no—
399C2×C4×C5—31no—
400C2×C4×C5—32no—
401C2×C4×C5—62no—
402C2×C4×C5C2×C4×D312yes—
403C22⋊D5—62no—
404C22⋊D5—62no—
405C2×Dic5—31no—
406C2×Dic5—32no—
407C2×Dic5—62no—
408C2×Dic5C2×C4×D312yes—
409D20—62no—
410C4×D5—22no—
411C4×D5—22no—
412C4×D5—64no—
413C4×D5—61no—
414C4×D5—62no—
415C4×D5—62no—
416C4×D5—61no—
417C22×D4—151no—
418C23×C4—51no—
419C23×C4—151no—
420C23×C4—151no—
421C23×C4—151no—
422#123—31no—
423#123—152no—
424#123—152no—
425#123—151no—
426#123—151no—
427#123—151no—
428C4×D4—304no—
429C2×C4⋊C4—152no—
430C2×C4⋊C4—152no—
431C2×C4⋊C4—152no—
432C2×C4⋊C4—151no—
433C2×C4⋊C4—152no—
434C2×C4⋊C4—304no—
435C2×C22⋊C4—51no—
436C2×C22⋊C4—51no—
437C2×C22⋊C4—152no—
438C2×C22⋊C4—151no—
439C2×C22⋊C4—151no—
440C2×C22⋊C4—152no—
441C2×C42—52no—
442C2×C42—151no—
443#95—52no—
444#95—152no—
445#95—152no—
446#95—152no—
447#95—152no—
448C2×C3×C5—22no—
449C2×C3×C5C2×C4×D411yescharacteristic
450C2×C3×C5#52012yes—
451D15—41no—
452C3×D5—22no—
453C3×D5#53411yescharacteristic
454C3×D5#53611yescharacteristic
455C3×D5#53912yes—
456C5×D3—41no—
457C23×C3—51no—
458C23×C3—52no—
459C23×C3—52no—
460C23×C3—51no—
461C23×C3—102no—
462C23×C3—102no—
463C23×C3C22×AGL(1,𝔽5)11yescharacteristic
464C22×D3—51no—
465C22×D3—101no—
466C22×D3—102no—
467C22×D3—101no—
468C22×D3—102no—
469C22×D3C22×AGL(1,𝔽5)11yescharacteristic
470C2×C3×C4—52no—
471C2×C3×C4—52no—
472C2×C3×C4—52no—
473C2×C3×C4—102no—
474C2×C3×C4—102no—
475C2×C3×C4—102no—
476C2×C3×C4—102no—
477C2×C3×C4—102no—
478C2×C3×C4—102no—
479C2×C3×C4—102no—
480C2×C3×C4—204no—
481C2×C3×C4C22×AGL(1,𝔽5)12yes—
482#67—22no—
483#67—102no—
484#67—102no—
485#67—102no—
486C2×Dic3—22no—
487C2×Dic3—51no—
488C2×Dic3—52no—
489C2×Dic3—101no—
490C2×Dic3—102no—
491C2×Dic3—102no—
492C2×Dic3—104no—
493C2×Dic3—101no—
494C2×Dic3—102no—
495C2×Dic3—101no—
496C2×Dic3—102no—
497C2×Dic3—101no—
498C2×Dic3—102no—
499C2×Dic3—102no—
500C2×Dic3—102no—
501C2×Dic3—102no—
502C2×Dic3—204no—
503C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
504C2×Dic3C22×AGL(1,𝔽5)12yes—
505C4×D3—204no—
506C22×C5—22no—
507C22×C5—61no—
508C22×C5—62no—
509C22×C5C4×D1212yes—
510C22×C5C22×C4×D311yescharacteristic
511C2×D5—22no—
512C2×D5—22no—
513C2×D5—22no—
514C2×D5—24no—
515C2×D5—61no—
516C2×D5—62no—
517C2×D5—121no—
518C2×D5—121no—
519C2×D5—122no—
520C2×D5C4×D1212yes—
521C2×D5C22×D1211yescharacteristic
522C2×D5C2×#23511yescharacteristic
523C2×D5#100412yes—
524C2×D5#101012yes—
525AGL(1,𝔽5)—22no—
526AGL(1,𝔽5)—22no—
527AGL(1,𝔽5)—42no—
528AGL(1,𝔽5)—121no—
529AGL(1,𝔽5)—122no—
530AGL(1,𝔽5)—121no—
531C4×C5—22no—
532C4×C5—62no—
533C4×C5—61no—
534Dic5—22no—
535Dic5—62no—
536Dic5—61no—
537C24—51no—
538C24—151no—
539C2×D4—31no—
540C2×D4—151no—
541C2×D4—151no—
542C2×D4—151no—
543C2×D4—302no—
544C2×D4—302no—
545C22×C4—31no—
546C22×C4—51no—
547C22×C4—51no—
548C22×C4—54no—
549C22×C4—52no—
550C22×C4—52no—
551C22×C4—151no—
552C22×C4—152no—
553C22×C4—152no—
554C22×C4—151no—
555C22×C4—151no—
556C22×C4—151no—
557C22×C4—152no—
558C22×C4—202no—
559C22×C4—302no—
560C22×C4—302no—
561C22×C4—302no—
562C22×C4—302no—
563C22×C4—602no—
564C22×C4—602no—
565C4⋊C4—32no—
566C4⋊C4—152no—
567C4⋊C4—152no—
568C4⋊C4—152no—
569C4⋊C4—304no—
570C4⋊C4—304no—
571C4⋊C4—302no—
572C4⋊C4—602no—
573C22⋊C4—32no—
574C22⋊C4—51no—
575C22⋊C4—52no—
576C22⋊C4—102no—
577C22⋊C4—152no—
578C22⋊C4—152no—
579C22⋊C4—152no—
580C22⋊C4—302no—
581C22⋊C4—302no—
582C22⋊C4—602no—
583C22⋊C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
584C42—202no—
585C42—302no—
586C3×C5#232211yescharacteristic, complemented, Hall
587C22×C3—22no—
588C22×C3—51no—
589C22×C3—51no—
590C22×C3—52no—
591C22×C3—52no—
592C22×C3—52no—
593C22×C3—102no—
594C22×C3—102no—
595C22×C3—104no—
596C22×C3—102no—
597C22×C3D4×AGL(1,𝔽5)12yes—
598C22×C3C23×AGL(1,𝔽5)11yescharacteristic
599C2×D3—21no—
600C2×D3—22no—
601C2×D3—101no—
602C2×D3—102no—
603C2×D3—201no—
604C2×D3—201no—
605C2×D3—202no—
606C3×C4—22no—
607C3×C4—102no—
608C3×C4—102no—
609C3×C4—102no—
610C3×C4—202no—
611Dic3—22no—
612Dic3—21no—
613Dic3—102no—
614Dic3—101no—
615Dic3—201no—
616Dic3—201no—
617Dic3—202no—
618C2×C5—22no—
619C2×C5—121no—
620C2×C5C2×C4×D1211yescharacteristic
621C2×C5#554612yes—
622D5—22no—
623D5—121no—
624D5#549311yescharacteristic
625D5#552611yescharacteristic
626D5#556412yes—
627C23—31no—
628C23—51no—
629C23—52no—
630C23—52no—
631C23—51no—
632C23—102no—
633C23—102no—
634C23—151no—
635C23—301no—
636C23—302no—
637C23—301no—
638C23—302no—
639C23C2×D3×AGL(1,𝔽5)11yescharacteristic
640D4—62no—
641D4—302no—
642D4—302no—
643D4—302no—
644C2×C4—32no—
645C2×C4—31no—
646C2×C4—52no—
647C2×C4—52no—
648C2×C4—52no—
649C2×C4—62no—
650C2×C4—102no—
651C2×C4—102no—
652C2×C4—102no—
653C2×C4—102no—
654C2×C4—102no—
655C2×C4—102no—
656C2×C4—102no—
657C2×C4—152no—
658C2×C4—151no—
659C2×C4—204no—
660C2×C4—301no—
661C2×C4—302no—
662C2×C4—302no—
663C2×C4—304no—
664C2×C4—301no—
665C2×C4—302no—
666C2×C4—301no—
667C2×C4—301no—
668C2×C4—302no—
669C2×C4—302no—
670C2×C4—302no—
671C2×C4—302no—
672C2×C4—302no—
673C2×C4—604no—
674C2×C4—604no—
675C2×C4C2×D3×AGL(1,𝔽5)12yes—
676C2×C3—22no—
677C2×C3—51no—
678C2×C3—51no—
679C2×C3—52no—
680C2×C3—102no—
681C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
682C2×C3#6626612yes—
683D3—41no—
684D3—201no—
685C5#7344611yescharacteristic, complemented, Sylow
686C22—22no—
687C22—51no—
688C22—51no—
689C22—52no—
690C22—52no—
691C22—52no—
692C22—61no—
693C22—62no—
694C22—102no—
695C22—104no—
696C22—102no—
697C22—102no—
698C22—301no—
699C22—302no—
700C22—601no—
701C22—602no—
702C22—601no—
703C22AGL(1,𝔽5)×D1212yes—
704C22C22×D3×AGL(1,𝔽5)11yescharacteristic
705C4—22no—
706C4—62no—
707C4—61no—
708C4—102no—
709C4—102no—
710C4—102no—
711C4—202no—
712C4—302no—
713C4—301no—
714C4—601no—
715C4—602no—
716C4—601no—
717C3#1061730411yescharacteristic, complemented, Sylow
718C2—22no—
719C2—51no—
720C2—52no—
721C2—51no—
722C2—102no—
723C2—121no—
724C2—601no—
725C2C2×AGL(1,𝔽5)×D1211yescharacteristic
726C2#1175684612yes—
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C22⋊C4C2×C4
prime radicalC2×D5×#67C22
cosocleC22×C3×D5C24
hypercenterC22⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2322
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×Dic3⋊AGL(1,𝔽5)C2semidirect
4. #11752358C2semidirect
5. C3×C22⋊C4×AGL(1,𝔽5)C2semidirect
7. #11751984C2semidirect
8. #11751934C2semidirect
9. #11751859C2semidirect
10. #11751849C2semidirect
11. #11751839C2semidirect
30. #91775C4semidirect
31. C5×#886C4semidirect
33. #91543C4semidirect
34. #91542C4semidirect
36. #91414C4semidirect
37. #91413C4semidirect
55. C22⋊C4×AGL(1,𝔽5)D3semidirect
71. C22×Dic15C2×C4semidirect
73. C22×C5×Dic3C2×C4semidirect
81. C2×D5×Dic3C2×C4semidirect
94. C3×C5×C22⋊C4C2×C4semidirect
95. #6714C2×C4semidirect
96. C4⋊Dic15C2×C4semidirect
97. C5×(C2×D3)⋊C4C2×C4semidirect
98. C5×C4⋊Dic3C2×C4semidirect
99. C3×C22⋊Dic5C2×C4semidirect
100. C3×#685C2×C4semidirect
101. #6668C2×C4semidirect
102. #6668C2×C4semidirect
103. #6667C2×C4semidirect
104. (C2×D3)⋊Dic5C2×C4semidirect
222. #886AGL(1,𝔽5)semidirect
268. C5×C22⋊C4C4×D3semidirect
270. C22⋊Dic5C4×D3semidirect
273. #685C4×D3semidirect
344. C22×Dic3C2×AGL(1,𝔽5)semidirect
350. C3×C22⋊C4C2×AGL(1,𝔽5)semidirect
358. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
363. C4⋊Dic3C2×AGL(1,𝔽5)semidirect
583. C22⋊C4D3×AGL(1,𝔽5)semidirect
586. C3×C5#2322semidirect
685. C5#73446semidirect
717. C3#10617304semidirect

Maximal subgroups

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

subgroupindex
C2×AGL(1,𝔽5)×#672
C22×Dic3⋊AGL(1,𝔽5)2
D5×#8862
#117523582
C3×C22⋊C4×AGL(1,𝔽5)2
#117520262
#117519842
#117519342
#117518592
#117518492
#117518392
#106173043
#734465