Finite Group Databasebeta

← #14321069

Subgroups — #14321069

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×D5×Dic3C211yesmaximal, characteristic
2#11752449C211yesmaximal, characteristic
3C3×(C2×AGL(1,𝔽5))⋊Q8C211yesmaximal, characteristic
4#11751861C211yesmaximal, characteristic
5#11751859C211yesmaximal, characteristic
6Dic3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic
7#11751840C212yesmaximal
8#11751839C212yesmaximal
9#11751834C212yesmaximal
10#11751832C212yesmaximal
11C4×Dic3×AGL(1,𝔽5)C211yesmaximal, characteristic
12#10617209—31nomaximal, Hall
13C2×C3×Q8×D5C2211yescharacteristic
14C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
15C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
16C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
17C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
18C2×Dic3⋊AGL(1,𝔽5)C2212yes—
19C2×Dic3⋊AGL(1,𝔽5)C2212yes—
20C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
21C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
22C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
23C2×Dic3×AGL(1,𝔽5)C2212yes—
24C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
25Q8×Dic15C411yescharacteristic, complemented
26C5×Q8×Dic3C411yescharacteristic, complemented
27D5×C4⋊Dic3C2212yes—
28D5×C4⋊Dic3C2211yescharacteristic
29C4×D5×Dic3C2211yescharacteristic
30C4×D5×Dic3C2212yes—
31#91331C411yescharacteristic, complemented
32#91331C412yescomplemented
33Dic3×Dic10C411yescharacteristic, complemented
34Dic3×Dic10C412yescomplemented
35#91235C2212yes—
36#91235C2212yes—
37C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
38C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
39(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
40(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
41(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
42#76477—51nomaximal, Hall
43C4×Q8×D5—31no—
44(C2×AGL(1,𝔽5))⋊Q8—31no—
45(C2×AGL(1,𝔽5))⋊Q8D311yescharacteristic
46#65712—31no—
47#65712—31no—
48#65711—32no—
49#65711—32no—
50C4×C4⋊AGL(1,𝔽5)—32no—
51C4×C4⋊AGL(1,𝔽5)—31no—
52#65686—32no—
53C42×AGL(1,𝔽5)—31no—
54C22×ΓL(1,𝔽16)C2312yes—
55C22×ΓL(1,𝔽16)C2311yescharacteristic
56C22×ΓL(1,𝔽16)C2311yescharacteristic
57C22×C3×AGL(1,𝔽5)C2312yes—
58C22×C3×AGL(1,𝔽5)C2311yescharacteristic
59C22×C3×AGL(1,𝔽5)C2311yescharacteristic
60C2×C3×C5×Q8C2×C411yescharacteristic
61C3×Q8×D5—22no—
62C3×Q8×D5—22no—
63C2×C3×C4×D5C2312yes—
64C2×C3×C4×D5C2311yescharacteristic
65C2×C3×Dic10C2×C411yescharacteristic
66C2×C3×Dic10C2×C412yes—
67C2×D5×Dic3C2311yescharacteristic
68C2×D5×Dic3C2312yes—
69C2×D5×Dic3C2311yescharacteristic
70C4⋊ΓL(1,𝔽16)—22no—
71C4×ΓL(1,𝔽16)—22no—
72C3×C4⋊AGL(1,𝔽5)—22no—
73C3×C4×AGL(1,𝔽5)—22no—
74Dic3⋊AGL(1,𝔽5)—24no—
75Dic3⋊AGL(1,𝔽5)—24no—
76Dic3×AGL(1,𝔽5)—22no—
77Dic3×AGL(1,𝔽5)—22no—
78Dic3×AGL(1,𝔽5)—22no—
79Dic3×AGL(1,𝔽5)—24no—
80Dic3×AGL(1,𝔽5)Q814yescomplemented
81C4⋊Dic15C2×C412yes—
82C4⋊Dic15C2×C411yescharacteristic
83C4×Dic15C2×C412yes—
84C4×Dic15C2×C411yescharacteristic
85C5×C4⋊Dic3C2×C412yes—
86C5×C4⋊Dic3C2×C411yescharacteristic
87C4×C5×Dic3C2×C412yes—
88C4×C5×Dic3C2×C411yescharacteristic
89#6668C2×C412yes—
90#6668C2×C412yes—
91#6668C2×C412yes—
92Dic3×Dic5C2×C412yes—
93Dic3×Dic5C2×C411yescharacteristic
94Dic3×Dic5C2×C412yes—
95Dic3×Dic5C2×C411yescharacteristic
96C2×Q8×Dic3—51no—
97C3×#391—51no—
98#5229—51no—
99Dic3×C4⋊C4—51no—
100#4972—51no—
101C42×Dic3—51no—
102#4928—51no—
103#4654—52no—
104#4653—52no—
105#4649—52no—
106#4648—52no—
107C2×Q8×D5C2×D311yescharacteristic
108C2×C4⋊AGL(1,𝔽5)—32no—
109C2×C4⋊AGL(1,𝔽5)—32no—
110C2×C4⋊AGL(1,𝔽5)—31no—
111C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
112C2×C4×AGL(1,𝔽5)—31no—
113C2×C4×AGL(1,𝔽5)—31no—
114C2×C4×AGL(1,𝔽5)—31no—
115C2×C4×AGL(1,𝔽5)—31no—
116C2×C4×AGL(1,𝔽5)—32no—
117C2×C4×AGL(1,𝔽5)—31no—
118C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
119C4×C5×Q8—31no—
120Q8×Dic5—31no—
121D5×C4⋊C4—32no—
122D5×C4⋊C4—31no—
123#4033—32no—
124#4033—31no—
125C42×D5—31no—
126C42×D5—32no—
127C4×Dic10—31no—
128C4×Dic10—32no—
129(C2×AGL(1,𝔽5))⋊C4—32no—
130(C2×AGL(1,𝔽5))⋊C4—32no—
131(C2×AGL(1,𝔽5))⋊C4—32no—
132(C2×AGL(1,𝔽5))⋊C4—32no—
133(C2×AGL(1,𝔽5))⋊C4—32no—
134(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
135(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
136#2295—151noSylow
137C22×C3×D5C2411yescharacteristic
138C2×ΓL(1,𝔽16)—21no—
139C2×ΓL(1,𝔽16)—21no—
140C2×ΓL(1,𝔽16)—21no—
141C2×ΓL(1,𝔽16)—21no—
142C2×ΓL(1,𝔽16)—22no—
143C2×ΓL(1,𝔽16)—22no—
144C2×ΓL(1,𝔽16)—22no—
145C2×ΓL(1,𝔽16)C2×Q812yes—
146C2×ΓL(1,𝔽16)#4112yes—
147C2×C3×AGL(1,𝔽5)—21no—
148C2×C3×AGL(1,𝔽5)—21no—
149C2×C3×AGL(1,𝔽5)—21no—
150C2×C3×AGL(1,𝔽5)—21no—
151C2×C3×AGL(1,𝔽5)—22no—
152C2×C3×AGL(1,𝔽5)—22no—
153C2×C3×AGL(1,𝔽5)—22no—
154C2×C3×AGL(1,𝔽5)C2×Q812yes—
155C2×C3×AGL(1,𝔽5)#4112yes—
156C3×C5×Q8—22no—
157C2×C3×C4×C5C22×C412yes—
158C2×C3×C4×C5C22×C411yescharacteristic
159C2×Dic15C22×C411yescharacteristic
160C2×Dic15C22×C412yes—
161C2×Dic15C22×C411yescharacteristic
162C2×C5×Dic3C22×C411yescharacteristic
163C2×C5×Dic3C22×C412yes—
164C2×C5×Dic3C22×C411yescharacteristic
165C2×C3×Dic5C22×C412yes—
166C2×C3×Dic5C22×C411yescharacteristic
167C3×C4×D5—22no—
168C3×C4×D5—22no—
169C3×C4×D5#4112yes—
170C3×C4×D5#4112yes—
171C3×Dic10—22no—
172C3×Dic10—24no—
173D5×Dic3—21no—
174D5×Dic3—21no—
175D5×Dic3—22no—
176D5×Dic3—22no—
177D5×Dic3C2×Q812yes—
178D5×Dic3#4112yes—
179C22×C3×Q8—51no—
180C2×C3×C4⋊C4—51no—
181C2×C3×C42—51no—
182Q8×Dic3—51no—
183Q8×Dic3—52no—
184Q8×Dic3—51no—
185Q8×Dic3—52no—
186Q8×Dic3—51no—
187Q8×Dic3AGL(1,𝔽5)11yescharacteristic, complemented
188C2×C4⋊Dic3—52no—
189C2×C4⋊Dic3—51no—
190C2×C4⋊Dic3—51no—
191C2×Dic3⋊C4—52no—
192C2×Dic3⋊C4—52no—
193C2×C4×Dic3—51no—
194C2×C4×Dic3—52no—
195C2×C4×Dic3—51no—
196C2×C4×Dic3—52no—
197C2×C4×Dic3—51no—
198C2×C4×Dic3—51no—
199C2×C4×Dic3—51no—
200C2×C4×Dic3—51no—
201C3×#95—52no—
202C3×#95—52no—
203C3⋊#95—52no—
204C3⋊#95—52no—
205C3⋊#95—52no—
206C3⋊#95—52no—
207C3⋊#95—52no—
208C22×AGL(1,𝔽5)—31no—
209C22×AGL(1,𝔽5)—31no—
210C22×AGL(1,𝔽5)—32no—
211C22×AGL(1,𝔽5)C22×D312yes—
212C22×AGL(1,𝔽5)C22×D311yescharacteristic
213C22×AGL(1,𝔽5)C22×D311yescharacteristic
214C2×C5×Q8C4×D311yescharacteristic
215Q8×D5—22no—
216Q8×D5—22no—
217C2×C4×D5—31no—
218C2×C4×D5—31no—
219C2×C4×D5—32no—
220C2×C4×D5C22×D312yes—
221C2×C4×D5C22×D311yescharacteristic
222C2×Dic10C4×D311yescharacteristic
223C2×Dic10C4×D312yes—
224C4⋊AGL(1,𝔽5)—22no—
225C4⋊AGL(1,𝔽5)—64no—
226C4⋊AGL(1,𝔽5)—64no—
227C4⋊AGL(1,𝔽5)—62no—
228C4×AGL(1,𝔽5)—22no—
229C4×AGL(1,𝔽5)—34no—
230C4×AGL(1,𝔽5)—62no—
231C4×AGL(1,𝔽5)—64no—
232C4×AGL(1,𝔽5)—62no—
233C4×AGL(1,𝔽5)—62no—
234C4×AGL(1,𝔽5)—62no—
235C5×C4⋊C4—32no—
236C5×C4⋊C4—31no—
237C42×C5—32no—
238C42×C5—31no—
239C4⋊Dic5—32no—
240C4⋊Dic5—31no—
241#683—32no—
242#683—32no—
243#683—32no—
244C4×Dic5—32no—
245C4×Dic5—31no—
246C4×Dic5—32no—
247C4×Dic5—31no—
248C4×Dic5—32no—
249C4×Dic5—31no—
250C2×C4×Q8—151no—
251#391—51no—
252#391—151no—
253#389—151no—
254#389—151no—
255#387—152no—
256#387—152no—
257C4×C4⋊C4—152no—
258C4×C4⋊C4—151no—
259#376—152no—
260C43—151no—
261C22×C3×C5C23×C411yescharacteristic
262C2×C3×D5C22×Q811yescharacteristic
263C2×C3×D5C2×#4111yescharacteristic
264C2×C3×D5C2×#4111yescharacteristic
265C2×C3×D5C2×#4111yescharacteristic
266C2×C3×D5C2×#4111yescharacteristic
267C2×C3×D5C2×#4111yescharacteristic
268ΓL(1,𝔽16)—22no—
269ΓL(1,𝔽16)—22no—
270ΓL(1,𝔽16)—42no—
271C3×AGL(1,𝔽5)—22no—
272C3×AGL(1,𝔽5)—22no—
273C3×AGL(1,𝔽5)—42no—
274C3×C4×C5—22no—
275C3×C4×C5#11712yes—
276Dic15—21no—
277Dic15—22no—
278Dic15C4×Q812yes—
279C3×Dic5—22no—
280C3×Dic5#11712yes—
281C5×Dic3—21no—
282C5×Dic3—22no—
283C5×Dic3C4×Q812yes—
284C2×C3×Q8—52no—
285C2×C3×Q8—51no—
286C2×C3×Q8—102no—
287C2×C3×Q8—102no—
288C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
289C22×C3×C4—51no—
290C22×C3×C4—51no—
291C22×C3×C4—51no—
292C22×C3×C4—52no—
293C22×C3×C4—52no—
294C22×Dic3—51no—
295C22×Dic3—51no—
296C22×Dic3—51no—
297C22×Dic3—51no—
298C22×Dic3—52no—
299C22×Dic3—52no—
300C3×C4⋊C4—102no—
301C3×C42—102no—
302C4⋊Dic3—52no—
303C4⋊Dic3—51no—
304C4⋊Dic3—52no—
305C4⋊Dic3—52no—
306C4⋊Dic3—52no—
307C4⋊Dic3—102no—
308C4⋊Dic3C2×AGL(1,𝔽5)12yes—
309C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
310Dic3⋊C4—104no—
311Dic3⋊C4—104no—
312C4×Dic3—54no—
313C4×Dic3—52no—
314C4×Dic3—51no—
315C4×Dic3—51no—
316C4×Dic3—52no—
317C4×Dic3—51no—
318C4×Dic3—52no—
319C4×Dic3—102no—
320C4×Dic3—104no—
321C4×Dic3—102no—
322C4×Dic3—102no—
323C4×Dic3—102no—
324C4×Dic3C2×AGL(1,𝔽5)12yes—
325C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
326C22×D5C23×D311yescharacteristic
327C2×AGL(1,𝔽5)—21no—
328C2×AGL(1,𝔽5)—21no—
329C2×AGL(1,𝔽5)—21no—
330C2×AGL(1,𝔽5)—21no—
331C2×AGL(1,𝔽5)—22no—
332C2×AGL(1,𝔽5)—22no—
333C2×AGL(1,𝔽5)—22no—
334C2×AGL(1,𝔽5)—32no—
335C2×AGL(1,𝔽5)—32no—
336C2×AGL(1,𝔽5)—61no—
337C2×AGL(1,𝔽5)—61no—
338C2×AGL(1,𝔽5)—61no—
339C2×AGL(1,𝔽5)—61no—
340C2×AGL(1,𝔽5)—62no—
341C2×AGL(1,𝔽5)—62no—
342C2×AGL(1,𝔽5)—62no—
343C2×AGL(1,𝔽5)D3×Q812yes—
344C2×AGL(1,𝔽5)#23912yes—
345C5×Q8—22no—
346C2×C4×C5—31no—
347C2×C4×C5—31no—
348C2×C4×C5—32no—
349C2×C4×C5C2×C4×D312yes—
350C2×C4×C5C2×C4×D311yescharacteristic
351C2×Dic5—31no—
352C2×Dic5—31no—
353C2×Dic5—32no—
354C2×Dic5C2×C4×D312yes—
355C2×Dic5C2×C4×D311yescharacteristic
356C4×D5—22no—
357C4×D5—22no—
358C4×D5—32no—
359C4×D5—32no—
360C4×D5—61no—
361C4×D5—62no—
362C4×D5—61no—
363C4×D5—62no—
364C4×D5#23712yes—
365C4×D5#23712yes—
366Dic10—22no—
367Dic10—24no—
368C22×Q8—51no—
369C4×Q8—31no—
370C4×Q8—152no—
371C4×Q8—151no—
372C4×Q8—152no—
373C4×Q8—151no—
374C4×Q8—151no—
375C2×C4⋊C4—51no—
376C2×C4⋊C4—152no—
377C2×C4⋊C4—151no—
378C2×C4⋊C4—152no—
379C2×C4⋊C4—152no—
380C2×C4⋊C4—151no—
381C2×C42—51no—
382C2×C42—151no—
383C2×C42—152no—
384C2×C42—151no—
385C2×C42—151no—
386C2×C42—151no—
387C2×C42—151no—
388C2×C42—151no—
389C2×C42—152no—
390#95—52no—
391#95—52no—
392#95—152no—
393#95—152no—
394#95—152no—
395#95—152no—
396#95—152no—
397C2×C3×C5C2×#11711yescharacteristic
398C2×C3×C5C2×C4×Q811yescharacteristic
399C2×C3×C5C4×#4111yescharacteristic
400C3×D5#52911yescharacteristic
401C3×D5#52911yescharacteristic
402C3×D5#53311yescharacteristic
403C3×D5#53311yescharacteristic
404C23×C3—51no—
405C3×Q8—22no—
406C3×Q8—104no—
407C3×Q8—102no—
408C2×C3×C4—51no—
409C2×C3×C4—52no—
410C2×C3×C4—52no—
411C2×C3×C4—52no—
412C2×C3×C4—52no—
413C2×C3×C4—52no—
414C2×C3×C4—102no—
415C2×C3×C4—102no—
416C2×C3×C4—101no—
417C2×C3×C4—101no—
418C2×C3×C4—101no—
419C2×C3×C4—101no—
420C2×C3×C4—102no—
421C2×C3×C4—102no—
422C2×C3×C4—102no—
423C2×C3×C4C22×AGL(1,𝔽5)12yes—
424C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
425C2×Dic3—51no—
426C2×Dic3—52no—
427C2×Dic3—52no—
428C2×Dic3—52no—
429C2×Dic3—52no—
430C2×Dic3—51no—
431C2×Dic3—52no—
432C2×Dic3—101no—
433C2×Dic3—101no—
434C2×Dic3—102no—
435C2×Dic3—102no—
436C2×Dic3—101no—
437C2×Dic3—101no—
438C2×Dic3—101no—
439C2×Dic3—101no—
440C2×Dic3—102no—
441C2×Dic3—102no—
442C2×Dic3—102no—
443C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
444C2×Dic3C22×AGL(1,𝔽5)12yes—
445C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
446C22×C5C22×C4×D311yescharacteristic
447C2×D5C2×#23711yescharacteristic
448C2×D5C2×#23711yescharacteristic
449C2×D5C2×D3×Q811yescharacteristic
450C2×D5C2×#23911yescharacteristic
451C2×D5D3×#4111yescharacteristic
452C2×D5D3×#4111yescharacteristic
453AGL(1,𝔽5)—22no—
454AGL(1,𝔽5)—22no—
455AGL(1,𝔽5)—42no—
456AGL(1,𝔽5)—62no—
457AGL(1,𝔽5)—62no—
458AGL(1,𝔽5)—122no—
459C4×C5—22no—
460C4×C5—32no—
461C4×C5—61no—
462C4×C5—62no—
463C4×C5#87712yes—
464Dic5—22no—
465Dic5—32no—
466Dic5—61no—
467Dic5—62no—
468Dic5#87712yes—
469C2×Q8—52no—
470C2×Q8—51no—
471C2×Q8—102no—
472C2×Q8—102no—
473C2×Q8D3×AGL(1,𝔽5)11yescharacteristic
474C22×C4—51no—
475C22×C4—51no—
476C22×C4—51no—
477C22×C4—52no—
478C22×C4—52no—
479C22×C4—151no—
480C22×C4—151no—
481C22×C4—152no—
482C22×C4—151no—
483C22×C4—151no—
484C22×C4—152no—
485C4⋊C4—32no—
486C4⋊C4—31no—
487C4⋊C4—102no—
488C4⋊C4—152no—
489C4⋊C4—152no—
490C4⋊C4—152no—
491C4⋊C4—152no—
492C4⋊C4—151no—
493C4⋊C4—304no—
494C4⋊C4—302no—
495C4⋊C4—304no—
496C42—32no—
497C42—31no—
498C42—102no—
499C42—151no—
500C42—152no—
501C42—151no—
502C42—152no—
503C42—154no—
504C42—152no—
505C42—151no—
506C42—302no—
507C42—302no—
508C42—302no—
509C42—302no—
510C42—304no—
511C3×C5#229511yescharacteristic, complemented, Hall
512C22×C3—51no—
513C22×C3—51no—
514C22×C3—51no—
515C22×C3—51no—
516C22×C3—51no—
517C22×C3—51no—
518C22×C3C23×AGL(1,𝔽5)11yescharacteristic
519C3×C4—22no—
520C3×C4—52no—
521C3×C4—102no—
522C3×C4—102no—
523C3×C4—102no—
524C3×C4—202no—
525C3×C4#413012yes—
526Dic3—21no—
527Dic3—22no—
528Dic3—52no—
529Dic3—102no—
530Dic3—102no—
531Dic3—101no—
532Dic3—102no—
533Dic3—202no—
534Dic3Q8×AGL(1,𝔽5)12yes—
535C2×C5C2×#87711yescharacteristic
536C2×C5C4×D3×Q811yescharacteristic
537C2×C5C4×#23911yescharacteristic
538D5#562211yescharacteristic
539D5#562411yescharacteristic
540D5#568011yescharacteristic
541D5#572811yescharacteristic
542C23—51no—
543Q8—22no—
544Q8—104no—
545Q8—102no—
546C2×C4—31no—
547C2×C4—31no—
548C2×C4—32no—
549C2×C4—51no—
550C2×C4—52no—
551C2×C4—52no—
552C2×C4—52no—
553C2×C4—52no—
554C2×C4—52no—
555C2×C4—102no—
556C2×C4—102no—
557C2×C4—101no—
558C2×C4—101no—
559C2×C4—101no—
560C2×C4—101no—
561C2×C4—102no—
562C2×C4—102no—
563C2×C4—102no—
564C2×C4—152no—
565C2×C4—152no—
566C2×C4—151no—
567C2×C4—152no—
568C2×C4—152no—
569C2×C4—151no—
570C2×C4—152no—
571C2×C4—301no—
572C2×C4—301no—
573C2×C4—302no—
574C2×C4—302no—
575C2×C4—301no—
576C2×C4—301no—
577C2×C4—301no—
578C2×C4—301no—
579C2×C4—302no—
580C2×C4—302no—
581C2×C4—302no—
582C2×C4C2×D3×AGL(1,𝔽5)12yes—
583C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
584C2×C3—51no—
585C2×C3—51no—
586C2×C3—51no—
587C2×C3—51no—
588C2×C3C2×#413011yescharacteristic
589C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
590C2×C3#41×AGL(1,𝔽5)11yescharacteristic
591C5#7647711yescharacteristic, complemented, Sylow
592C22—51no—
593C22—51no—
594C22—51no—
595C22—51no—
596C22—51no—
597C22—51no—
598C22C22×D3×AGL(1,𝔽5)11yescharacteristic
599C4—22no—
600C4—32no—
601C4—52no—
602C4—61no—
603C4—62no—
604C4—102no—
605C4—102no—
606C4—102no—
607C4—152no—
608C4—202no—
609C4—302no—
610C4—302no—
611C4—301no—
612C4—302no—
613C4—602no—
614C4#9192312yes—
615C3#1061720911yescharacteristic, complemented, Sylow
616C2—51no—
617C2—51no—
618C2—51no—
619C2—51no—
620C2D3×Q8×AGL(1,𝔽5)11yescharacteristic
621C2AGL(1,𝔽5)×#23911yescharacteristic
622C2C2×#9192311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×Q8C2×C4
prime radical, cosocleC22×C3×D5C24
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5#2295
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
25. Q8×Dic15C4semidirect
26. C5×Q8×Dic3C4semidirect
31. #91331C4semidirect
32. #91331C4semidirect
33. Dic3×Dic10C4semidirect
34. Dic3×Dic10C4semidirect
80. Dic3×AGL(1,𝔽5)Q8semidirect
187. Q8×Dic3AGL(1,𝔽5)semidirect
511. C3×C5#2295semidirect
591. C5#76477semidirect
615. C3#10617209semidirect

Maximal subgroups

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

subgroupindex
Q8×D5×Dic32
#117524492
C3×(C2×AGL(1,𝔽5))⋊Q82
#117518612
#117518592
Dic3×C4⋊AGL(1,𝔽5)2
#117518402
#117518392
#117518342
#117518322
C4×Dic3×AGL(1,𝔽5)2
#106172093
#764775