Finite Group Databasebeta

← #14326661

Subgroups — #14326661

Order 1920.

1208 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91989C211yesmaximal, characteristic
2C2×#91923C211yesmaximal, characteristic
3C2×D5×Dic3⋊C4C211yesmaximal, characteristic
4C3×#65764C211yesmaximal, characteristic
5#11752028C211yesmaximal, characteristic
6Dic3×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic
7#11751984C211yesmaximal, characteristic
8#11751845C212yesmaximal, complemented
9#11751844C212yesmaximal, complemented
10#11751833C212yesmaximal, complemented
11#11751747C212yesmaximal, complemented
12#10617103—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C22×D5×Dic3C2211yescharacteristic
15C22×D5×Dic3C2211yescharacteristic
16C2×#6763C2211yescharacteristic
17C2×#6763C2211yescharacteristic
18#91989—24no—
19C2×C4⋊ΓL(1,𝔽16)C2212yes—
20C2×C4×ΓL(1,𝔽16)C2212yes—
21C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
22C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
23C2×Dic3⋊AGL(1,𝔽5)C2212yes—
24C2×Dic3⋊AGL(1,𝔽5)C2212yes—
25#91923—24no—
26C2×Dic3×AGL(1,𝔽5)C2212yes—
27C2×Dic3×AGL(1,𝔽5)C2212yes—
28C2×#6712C411yescharacteristic, complemented
29C2×C5×Dic3⋊C4C411yescharacteristic, complemented
30C2×Dic3⋊Dic5C411yescharacteristic, complemented
31C2×#6669C411yescharacteristic, complemented
32D5×Dic3⋊C4C411yescharacteristic, complemented
33D5×Dic3⋊C4C411yescharacteristic, complemented
34D5×Dic3⋊C4C411yescharacteristic, complemented
35D5×Dic3⋊C4C411yescharacteristic, complemented
36D5×Dic3⋊C4C2211yescharacteristic
37D5×Dic3⋊C4C2211yescharacteristic
38D5×Dic3⋊C4C2211yescharacteristic
39D5×Dic3⋊C4C2211yescharacteristic
40C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
41C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
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#74060—51nomaximal, Hall
47C2×#4130—31no—
48C2×#4130—31no—
49C2×D5×C4⋊C4—31no—
50#65765—31no—
51#65764—31no—
52#65764D311yescharacteristic
53C4×C22⋊AGL(1,𝔽5)—31no—
54#65712—32no—
55#65711—32no—
56#65711—32no—
57C4⋊C4×AGL(1,𝔽5)—32no—
58C23×C3×D5C2311yescharacteristic
59C22×ΓL(1,𝔽16)C2312yes—
60C22×ΓL(1,𝔽16)C2312yes—
61C22×C3×AGL(1,𝔽5)C2312yes—
62C22×C3×AGL(1,𝔽5)C2312yes—
63C22×C3×C4×C5C2×C411yescharacteristic
64C22×Dic15C2×C411yescharacteristic
65C22×Dic15C2×C411yescharacteristic
66C22×C5×Dic3C2×C411yescharacteristic
67C22×C5×Dic3C2×C411yescharacteristic
68C22×C3×Dic5C2×C411yescharacteristic
69C2×C3×C4×D5—22no—
70C2×C3×C4×D5—22no—
71C2×C3×C4×D5C2×C411yescharacteristic
72C2×C3×C4×D5C2×C411yescharacteristic
73C2×C3×C4×D5C2311yescharacteristic
74C2×C3×C4×D5C2311yescharacteristic
75C2×D5×Dic3—22no—
76C2×D5×Dic3—22no—
77C2×D5×Dic3—24no—
78C2×D5×Dic3C2×C411yescharacteristic
79C2×D5×Dic3C2×C411yescharacteristic
80C2×D5×Dic3C2×C411yescharacteristic
81C2×D5×Dic3C2×C411yescharacteristic
82C2×D5×Dic3C2311yescharacteristic
83C2×D5×Dic3C2311yescharacteristic
84C2×D5×Dic3C2311yescharacteristic
85C2×D5×Dic3C2311yescharacteristic
86#6763—22no—
87#6763D414yes—
88C4⋊ΓL(1,𝔽16)—24no—
89C4×ΓL(1,𝔽16)—24no—
90C3×C22⋊AGL(1,𝔽5)—22no—
91C3×C22⋊AGL(1,𝔽5)—22no—
92Dic3⋊AGL(1,𝔽5)—24no—
93Dic3⋊AGL(1,𝔽5)—24no—
94Dic3×AGL(1,𝔽5)—24no—
95Dic3×AGL(1,𝔽5)—24no—
96#6712C2×C411yescharacteristic
97#6712C2×C411yescharacteristic
98#6712C2×C411yescharacteristic
99#6712C2×C411yescharacteristic
100C5×Dic3⋊C4C2×C411yescharacteristic
101C5×Dic3⋊C4C2×C411yescharacteristic
102C5×Dic3⋊C4C2×C411yescharacteristic
103C5×Dic3⋊C4C2×C411yescharacteristic
104Dic3⋊Dic5C2×C411yescharacteristic
105Dic3⋊Dic5C2×C411yescharacteristic
106Dic3⋊Dic5C2×C411yescharacteristic
107Dic3⋊Dic5C2×C411yescharacteristic
108#6669C2×C411yescharacteristic
109#6669C2×C411yescharacteristic
110#6669C2×C411yescharacteristic
111#6669C2×C411yescharacteristic
112C2×#926—51no—
113C22×Dic3⋊C4—51no—
114C2×#877—51no—
115C3×#381—51no—
116#4943—51no—
117#4942—51no—
118Dic3×C22⋊C4—51no—
119#4655—52no—
120#4652—52no—
121#4649—52no—
122#4647—52no—
123C22×C4×D5—31no—
124C22×C4×D5—31no—
125C22×C4×D5C2×D311yescharacteristic
126C2×C22⋊AGL(1,𝔽5)—31no—
127C2×C22⋊AGL(1,𝔽5)—31no—
128C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
129C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
130#4130—64no—
131#4130—64no—
132C2×C4⋊AGL(1,𝔽5)—32no—
133C2×C4⋊AGL(1,𝔽5)—32no—
134C2×C4⋊AGL(1,𝔽5)—32no—
135C2×C4×AGL(1,𝔽5)—32no—
136C2×C4×AGL(1,𝔽5)—32no—
137C2×C4×AGL(1,𝔽5)—32no—
138C2×C5×C4⋊C4—31no—
139C2×C4⋊Dic5—31no—
140C2×#683—31no—
141C2×#683—31no—
142D5×C4⋊C4—31no—
143D5×C4⋊C4—31no—
144D5×C4⋊C4—31no—
145D5×C4⋊C4—31no—
146D5×C4⋊C4—31no—
147D5×C4⋊C4—31no—
148D5×C4⋊C4—31no—
149D5×C4⋊C4—31no—
150(C2×AGL(1,𝔽5))⋊C4—32no—
151(C2×AGL(1,𝔽5))⋊C4—32no—
152(C2×AGL(1,𝔽5))⋊C4—32no—
153(C2×AGL(1,𝔽5))⋊C4—32no—
154(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
155(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
156#2344—151noSylow
157C23×C3×C5C22×C411yescharacteristic
158C22×C3×D5—22no—
159C22×C3×D5—22no—
160C22×C3×D5C22×C411yescharacteristic
161C22×C3×D5C2×D412yes—
162C22×C3×D5#4112yes—
163C22×C3×D5C2411yescharacteristic
164C2×ΓL(1,𝔽16)—22no—
165C2×ΓL(1,𝔽16)—22no—
166C2×ΓL(1,𝔽16)—22no—
167C2×ΓL(1,𝔽16)—22no—
168C2×ΓL(1,𝔽16)—22no—
169C2×ΓL(1,𝔽16)C2×D414yes—
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)—22no—
175C2×C3×AGL(1,𝔽5)—22no—
176C2×C3×C4×C5—22no—
177C2×C3×C4×C5C22×C411yescharacteristic
178C2×C3×C4×C5C22×C411yescharacteristic
179C2×Dic15—22no—
180C2×Dic15—22no—
181C2×Dic15C22×C411yescharacteristic
182C2×Dic15C22×C411yescharacteristic
183C2×Dic15C22×C411yescharacteristic
184C2×Dic15C22×C411yescharacteristic
185C2×C5×Dic3—22no—
186C2×C5×Dic3—22no—
187C2×C5×Dic3C22×C411yescharacteristic
188C2×C5×Dic3C22×C411yescharacteristic
189C2×C5×Dic3C22×C411yescharacteristic
190C2×C5×Dic3C22×C411yescharacteristic
191C2×C3×Dic5—22no—
192C2×C3×Dic5C22×C411yescharacteristic
193C2×C3×Dic5C22×C411yescharacteristic
194C3×C4×D5—22no—
195C3×C4×D5—22no—
196C3×C4×D5—21no—
197C3×C4×D5—21no—
198C3×C4×D5—21no—
199C3×C4×D5—21no—
200D5×Dic3—22no—
201D5×Dic3—22no—
202D5×Dic3—21no—
203D5×Dic3—21no—
204D5×Dic3—22no—
205D5×Dic3—21no—
206D5×Dic3—21no—
207D5×Dic3—22no—
208D5×Dic3—22no—
209D5×Dic3#4114yes—
210C23×C3×C4—51no—
211C23×Dic3—51no—
212C23×Dic3—51no—
213C2×C3×C22⋊C4—51no—
214C2×C3×C22⋊C4—51no—
215C2×#217—51no—
216C2×#217—51no—
217#926—104no—
218C2×C4⋊Dic3—52no—
219C2×Dic3⋊C4—51no—
220C2×Dic3⋊C4—51no—
221C2×Dic3⋊C4—51no—
222C2×Dic3⋊C4—51no—
223C2×Dic3⋊C4—51no—
224C2×Dic3⋊C4—51no—
225C2×Dic3⋊C4—51no—
226C2×Dic3⋊C4—51no—
227C2×Dic3⋊C4—51no—
228C2×Dic3⋊C4—51no—
229C2×Dic3⋊C4—51no—
230C2×Dic3⋊C4—52no—
231C2×Dic3⋊C4—52no—
232C2×Dic3⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
233C2×C4×Dic3—52no—
234C2×C4×Dic3—52no—
235C2×C4×Dic3—52no—
236#877—104no—
237C3×#95—52no—
238C3×#95—52no—
239C3⋊#95—52no—
240C3⋊#95—52no—
241C3⋊#95—52no—
242C3⋊#95—52no—
243C23×D5C22×D311yescharacteristic
244C22×AGL(1,𝔽5)—32no—
245C22×AGL(1,𝔽5)—32no—
246C22×AGL(1,𝔽5)C22×D312yes—
247C22×AGL(1,𝔽5)C22×D312yes—
248C22×C4×C5—31no—
249C22×C4×C5—31no—
250C22×C4×C5C4×D311yescharacteristic
251C22×Dic5—31no—
252C22×Dic5—31no—
253C22×Dic5C4×D311yescharacteristic
254C2×C4×D5—22no—
255C2×C4×D5—22no—
256C2×C4×D5—31no—
257C2×C4×D5—31no—
258C2×C4×D5—31no—
259C2×C4×D5—31no—
260C2×C4×D5—31no—
261C2×C4×D5—31no—
262C2×C4×D5—31no—
263C2×C4×D5—31no—
264C2×C4×D5—64no—
265C2×C4×D5—62no—
266C2×C4×D5—62no—
267C2×C4×D5C4×D311yescharacteristic
268C2×C4×D5C4×D311yescharacteristic
269C2×C4×D5C22×D311yescharacteristic
270C2×C4×D5C22×D311yescharacteristic
271C22⋊AGL(1,𝔽5)—22no—
272C22⋊AGL(1,𝔽5)—22no—
273C22⋊AGL(1,𝔽5)—34no—
274C22⋊AGL(1,𝔽5)—62no—
275C4⋊AGL(1,𝔽5)—64no—
276C4⋊AGL(1,𝔽5)—64no—
277C4⋊AGL(1,𝔽5)—64no—
278C4×AGL(1,𝔽5)—64no—
279C4×AGL(1,𝔽5)—64no—
280C4×AGL(1,𝔽5)—64no—
281C5×C4⋊C4—31no—
282C5×C4⋊C4—31no—
283C5×C4⋊C4—31no—
284C5×C4⋊C4—31no—
285C4⋊Dic5—31no—
286C4⋊Dic5—31no—
287C4⋊Dic5—31no—
288C4⋊Dic5—31no—
289#683—31no—
290#683—31no—
291#683—31no—
292#683—31no—
293#683—31no—
294#683—31no—
295#683—31no—
296#683—31no—
297C2×#117—151no—
298C2×#117—151no—
299C22×C4⋊C4—151no—
300#389—152no—
301#387—152no—
302#387—152no—
303#381—51no—
304#381—151no—
305#380—151no—
306C4×C4⋊C4—152no—
307C4×C22⋊C4—151no—
308C22×C3×C5—21no—
309C22×C3×C5—21no—
310C22×C3×C5C4×D412yes—
311C22×C3×C5C23×C411yescharacteristic
312C2×C3×D5—21no—
313C2×C3×D5—21no—
314C2×C3×D5—24no—
315C2×C3×D5—24no—
316C2×C3×D5C4×D412yes—
317C2×C3×D5C22×D411yescharacteristic
318C2×C3×D5C2×#4111yescharacteristic
319C2×C3×D5C2×#4112yes—
320C2×C3×D52−1+412yes—
321ΓL(1,𝔽16)—24no—
322ΓL(1,𝔽16)—42no—
323C3×AGL(1,𝔽5)—42no—
324C3×AGL(1,𝔽5)—42no—
325C3×C4×C5—21no—
326C3×C4×C5—21no—
327Dic15—21no—
328Dic15—21no—
329Dic15—21no—
330Dic15#11712yescomplemented
331C3×Dic5—21no—
332C3×Dic5—21no—
333C5×Dic3—21no—
334C5×Dic3—21no—
335C5×Dic3—21no—
336C5×Dic3#11712yescomplemented
337C24×C3—51no—
338C22×C3×C4—51no—
339C22×C3×C4—51no—
340C22×C3×C4—51no—
341C22×C3×C4—51no—
342C22×C3×C4—51no—
343C22×C3×C4—52no—
344C22×C3×C4—52no—
345C22×C3×C4—102no—
346C22×C3×C4—102no—
347C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
348C22×Dic3—51no—
349C22×Dic3—52no—
350C22×Dic3—51no—
351C22×Dic3—51no—
352C22×Dic3—51no—
353C22×Dic3—51no—
354C22×Dic3—51no—
355C22×Dic3—51no—
356C22×Dic3—51no—
357C22×Dic3—51no—
358C22×Dic3—51no—
359C22×Dic3—52no—
360C22×Dic3—104no—
361C22×Dic3—102no—
362C22×Dic3—102no—
363C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
364C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
365C3×C22⋊C4—102no—
366C3×C22⋊C4—102no—
367#217—54no—
368#217—102no—
369C4⋊Dic3—104no—
370Dic3⋊C4—51no—
371Dic3⋊C4—51no—
372Dic3⋊C4—51no—
373Dic3⋊C4—51no—
374Dic3⋊C4—51no—
375Dic3⋊C4—51no—
376Dic3⋊C4—51no—
377Dic3⋊C4—51no—
378Dic3⋊C4—51no—
379Dic3⋊C4—51no—
380Dic3⋊C4—51no—
381Dic3⋊C4—51no—
382Dic3⋊C4—104no—
383Dic3⋊C4—104no—
384Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
385Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
386Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
387Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
388C4×Dic3—104no—
389C4×Dic3—104no—
390C4×Dic3—104no—
391C23×C5C2×C4×D311yescharacteristic
392C22×D5—22no—
393C22×D5—22no—
394C22×D5C2×C4×D311yescharacteristic
395C22×D5D3×D412yes—
396C22×D5#23712yes—
397C22×D5C23×D311yescharacteristic
398C2×AGL(1,𝔽5)—22no—
399C2×AGL(1,𝔽5)—22no—
400C2×AGL(1,𝔽5)—22no—
401C2×AGL(1,𝔽5)—22no—
402C2×AGL(1,𝔽5)—22no—
403C2×AGL(1,𝔽5)—22no—
404C2×AGL(1,𝔽5)—34no—
405C2×AGL(1,𝔽5)—62no—
406C2×AGL(1,𝔽5)—62no—
407C2×AGL(1,𝔽5)—62no—
408C2×AGL(1,𝔽5)—62no—
409C2×AGL(1,𝔽5)—62no—
410C2×C4×C5—22no—
411C2×C4×C5—31no—
412C2×C4×C5—31no—
413C2×C4×C5—31no—
414C2×C4×C5—31no—
415C2×C4×C5—62no—
416C2×C4×C5—62no—
417C2×C4×C5C2×C4×D311yescharacteristic
418C2×C4×C5C2×C4×D311yescharacteristic
419C2×Dic5—22no—
420C2×Dic5—31no—
421C2×Dic5—31no—
422C2×Dic5—31no—
423C2×Dic5—31no—
424C2×Dic5—62no—
425C2×Dic5—62no—
426C2×Dic5C2×C4×D311yescharacteristic
427C2×Dic5C2×C4×D311yescharacteristic
428C4×D5—22no—
429C4×D5—22no—
430C4×D5—21no—
431C4×D5—21no—
432C4×D5—21no—
433C4×D5—21no—
434C4×D5—34no—
435C4×D5—62no—
436C4×D5—62no—
437C4×D5—62no—
438C4×D5—62no—
439C4×D5—61no—
440C4×D5—61no—
441C4×D5—61no—
442C4×D5—61no—
443C4×D5—62no—
444C23×C4—51no—
445C23×C4—151no—
446C23×C4—151no—
447#117—304no—
448#117—304no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—151no—
451C2×C4⋊C4—151no—
452C2×C4⋊C4—151no—
453C2×C4⋊C4—151no—
454C2×C4⋊C4—151no—
455C2×C4⋊C4—151no—
456C2×C4⋊C4—151no—
457C2×C4⋊C4—151no—
458C2×C4⋊C4—151no—
459C2×C4⋊C4—151no—
460C2×C4⋊C4—151no—
461C2×C4⋊C4—152no—
462C2×C4⋊C4—152no—
463C2×C4⋊C4—152no—
464C2×C22⋊C4—51no—
465C2×C22⋊C4—51no—
466C2×C22⋊C4—151no—
467C2×C22⋊C4—151no—
468C2×C42—152no—
469C2×C42—152no—
470C2×C42—152no—
471#95—52no—
472#95—52no—
473#95—152no—
474#95—152no—
475#95—152no—
476#95—152no—
477C2×C3×C5—22no—
478C2×C3×C5C2×#11711yescharacteristic
479C2×C3×C5C2×C4×D411yescharacteristic
480C2×C3×C5#51911yescharacteristic
481C3×D5—22no—
482C3×D5#54712yes—
483C3×D5#55212yes—
484C23×C3—51no—
485C23×C3—52no—
486C23×C3—52no—
487C23×C3—51no—
488C23×C3—102no—
489C23×C3—102no—
490C23×C3C22×AGL(1,𝔽5)11yescharacteristic
491C2×C3×C4—22no—
492C2×C3×C4—51no—
493C2×C3×C4—51no—
494C2×C3×C4—101no—
495C2×C3×C4—101no—
496C2×C3×C4—101no—
497C2×C3×C4—101no—
498C2×C3×C4—102no—
499C2×C3×C4—102no—
500C2×C3×C4—102no—
501C2×C3×C4—102no—
502C2×C3×C4—102no—
503C2×C3×C4—102no—
504C2×C3×C4—102no—
505C2×C3×C4—102no—
506C2×C3×C4—102no—
507C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
508C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—51no—
512C2×Dic3—54no—
513C2×Dic3—54no—
514C2×Dic3—51no—
515C2×Dic3—51no—
516C2×Dic3—51no—
517C2×Dic3—102no—
518C2×Dic3—101no—
519C2×Dic3—101no—
520C2×Dic3—102no—
521C2×Dic3—101no—
522C2×Dic3—101no—
523C2×Dic3—102no—
524C2×Dic3—102no—
525C2×Dic3—102no—
526C2×Dic3—102no—
527C2×Dic3—102no—
528C2×Dic3—102no—
529C2×Dic3—102no—
530C2×Dic3—102no—
531C2×Dic3—102no—
532C2×Dic3—102no—
533C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
534C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
535C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
536C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
537C22×C5—21no—
538C22×C5—21no—
539C22×C5#67⋊C412yes—
540C22×C5C22×C4×D311yescharacteristic
541C2×D5—21no—
542C2×D5—21no—
543C2×D5—24no—
544C2×D5—24no—
545C2×D5#67⋊C412yes—
546C2×D5C2×D3×D411yescharacteristic
547C2×D5C2×#23711yescharacteristic
548C2×D5D3×#4112yes—
549C2×D5#101012yes—
550AGL(1,𝔽5)—42no—
551AGL(1,𝔽5)—42no—
552AGL(1,𝔽5)—64no—
553AGL(1,𝔽5)—122no—
554C4×C5—21no—
555C4×C5—21no—
556C4×C5—32no—
557C4×C5—61no—
558C4×C5—61no—
559C4×C5—61no—
560Dic5—21no—
561Dic5—21no—
562Dic5—32no—
563Dic5—61no—
564Dic5—61no—
565Dic5—61no—
566C24—51no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—51no—
570C22×C4—51no—
571C22×C4—51no—
572C22×C4—51no—
573C22×C4—51no—
574C22×C4—52no—
575C22×C4—52no—
576C22×C4—102no—
577C22×C4—102no—
578C22×C4—151no—
579C22×C4—151no—
580C22×C4—151no—
581C22×C4—151no—
582C22×C4—151no—
583C22×C4—151no—
584C22×C4—151no—
585C22×C4—151no—
586C22×C4—152no—
587C22×C4—151no—
588C22×C4—151no—
589C22×C4—152no—
590C22×C4—304no—
591C22×C4—302no—
592C22×C4—302no—
593C22×C4D3×AGL(1,𝔽5)11yescharacteristic
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—151no—
599C4⋊C4—151no—
600C4⋊C4—151no—
601C4⋊C4—151no—
602C4⋊C4—151no—
603C4⋊C4—151no—
604C4⋊C4—151no—
605C4⋊C4—151no—
606C4⋊C4—151no—
607C4⋊C4—151no—
608C4⋊C4—151no—
609C4⋊C4—151no—
610C4⋊C4—304no—
611C4⋊C4—304no—
612C4⋊C4—304no—
613C22⋊C4—102no—
614C22⋊C4—102no—
615C22⋊C4—154no—
616C22⋊C4—302no—
617C42—304no—
618C42—304no—
619C42—304no—
620C3×C5#234411yescharacteristic, complemented, Hall
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—52no—
624C22×C3—51no—
625C22×C3—51no—
626C22×C3—52no—
627C22×C3—52no—
628C22×C3—104no—
629C22×C3—104no—
630C22×C3—101no—
631C22×C3—101no—
632C22×C3D4×AGL(1,𝔽5)12yes—
633C22×C3C23×AGL(1,𝔽5)11yescharacteristic
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—101no—
637C3×C4—101no—
638C3×C4—202no—
639C3×C4—202no—
640Dic3—21no—
641Dic3—21no—
642Dic3—21no—
643Dic3—52no—
644Dic3—104no—
645Dic3—101no—
646Dic3—101no—
647Dic3—101no—
648Dic3—202no—
649Dic3#413012yescomplemented
650C2×C5—22no—
651C2×C5C2×#67⋊C411yescharacteristic
652C2×C5#551611yescharacteristic
653C2×C5D3×#11711yescharacteristic
654D5—22no—
655D5#565012yes—
656D5#565512yes—
657C23—51no—
658C23—52no—
659C23—52no—
660C23—51no—
661C23—102no—
662C23—102no—
663C23C2×D3×AGL(1,𝔽5)11yescharacteristic
664C2×C4—22no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—31no—
669C2×C4—51no—
670C2×C4—51no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—101no—
674C2×C4—101no—
675C2×C4—101no—
676C2×C4—101no—
677C2×C4—102no—
678C2×C4—102no—
679C2×C4—102no—
680C2×C4—102no—
681C2×C4—102no—
682C2×C4—102no—
683C2×C4—102no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—154no—
687C2×C4—151no—
688C2×C4—154no—
689C2×C4—151no—
690C2×C4—151no—
691C2×C4—151no—
692C2×C4—302no—
693C2×C4—302no—
694C2×C4—301no—
695C2×C4—301no—
696C2×C4—302no—
697C2×C4—301no—
698C2×C4—301no—
699C2×C4—302no—
700C2×C4—302no—
701C2×C4—302no—
702C2×C4—302no—
703C2×C4—302no—
704C2×C4—302no—
705C2×C4—302no—
706C2×C4—302no—
707C2×C4—302no—
708C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
709C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
710C2×C3—22no—
711C2×C3—52no—
712C2×C3—52no—
713C2×C3—102no—
714C2×C3C2×#413011yescharacteristic
715C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
716C2×C3#6626211yescharacteristic
717C5#7406011yescharacteristic, complemented, Sylow
718C22—21no—
719C22—21no—
720C22—52no—
721C22—52no—
722C22—51no—
723C22—51no—
724C22—52no—
725C22—104no—
726C22—104no—
727C22—101no—
728C22—101no—
729C22#67⋊AGL(1,𝔽5)12yes—
730C22C22×D3×AGL(1,𝔽5)11yescharacteristic
731C4—21no—
732C4—21no—
733C4—32no—
734C4—61no—
735C4—61no—
736C4—61no—
737C4—101no—
738C4—101no—
739C4—152no—
740C4—202no—
741C4—202no—
742C4—304no—
743C4—301no—
744C4—301no—
745C4—301no—
746C4—602no—
747C3#1061710311yescharacteristic, complemented, Sylow
748C2—22no—
749C2—52no—
750C2—52no—
751C2—102no—
752C2#1175681211yescharacteristic
753C2D3×#413011yescharacteristic
754C2C2×#67⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2344
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. #11751845C2semidirect
9. #11751844C2semidirect
10. #11751833C2semidirect
11. #11751747C2semidirect
28. C2×#6712C4semidirect
29. C2×C5×Dic3⋊C4C4semidirect
30. C2×Dic3⋊Dic5C4semidirect
31. C2×#6669C4semidirect
32. D5×Dic3⋊C4C4semidirect
33. D5×Dic3⋊C4C4semidirect
34. D5×Dic3⋊C4C4semidirect
35. D5×Dic3⋊C4C4semidirect
232. C2×Dic3⋊C4AGL(1,𝔽5)semidirect
330. Dic15#117semidirect
336. C5×Dic3#117semidirect
620. C3×C5#2344semidirect
649. Dic3#4130semidirect
717. C5#74060semidirect
747. C3#10617103semidirect

Maximal subgroups

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

subgroupindex
C2×#919892
C2×#919232
C2×D5×Dic3⋊C42
C3×#657642
#117520282
Dic3×C22⋊AGL(1,𝔽5)2
#117519842
#117518452
#117518442
#117518332
#117517472
#106171033
#740605