Finite Group Databasebeta

← #14328090

Subgroups — #14328090

Order 1920.

1120 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×D5×Dic3C211yesmaximal, characteristic
2#11752439C211yesmaximal, characteristic
3C3×#65780C211yesmaximal, characteristic
4Dic3×C22⋊AGL(1,𝔽5)C212yesmaximal, complemented
5#11752018C212yesmaximal, complemented
6#11752017C212yesmaximal, complemented
7#11751984C212yesmaximal, complemented
8C4×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
9#11751846C211yesmaximal, characteristic, complemented
10AGL(1,𝔽5)×C4⋊Dic3C211yesmaximal, characteristic, complemented
11#11751751C211yesmaximal, characteristic, complemented
12#10617182—31nomaximal, Hall
13C2×C3×D4×D5C2211yescharacteristic
14C22×D5×Dic3C2212yes—
15C2×#6763C2212yes—
16C2×#6763C2212yes—
17C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
18C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
19C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
20C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
21C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
22C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
23C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
24C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
25C2×Dic3×AGL(1,𝔽5)C2212yes—
26C2×Dic3×AGL(1,𝔽5)C2212yes—
27D4×Dic15C411yescharacteristic, complemented
28C5×D4×Dic3C411yescharacteristic, complemented
29#91559C412yescomplemented
30Dic3×C22⋊D5C412yescomplemented
31D5×#217C2212yes—
32#91434C411yescharacteristic, complemented
33Dic3×D20C411yescharacteristic, complemented
34D5×C4⋊Dic3C2211yescharacteristic
35C4×D5×Dic3C2211yescharacteristic
36(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
37(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
38(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
39(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
40(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
41(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
42#76303—51nomaximal, Hall
43C4×D4×D5—31no—
44#65780—31no—
45#65780D311yescharacteristic
46#65764—32no—
47C4×C22⋊AGL(1,𝔽5)—32no—
48C4⋊C4×AGL(1,𝔽5)—31no—
49C4⋊C4×AGL(1,𝔽5)—31no—
50#65700—32no—
51#65700—32no—
52#65689—31no—
53C4×C4⋊AGL(1,𝔽5)—31no—
54C23×C3×D5C2312yes—
55C22×ΓL(1,𝔽16)C2312yes—
56C22×ΓL(1,𝔽16)C2311yescharacteristic
57C22×ΓL(1,𝔽16)C2311yescharacteristic
58C22×C3×AGL(1,𝔽5)C2312yes—
59C22×C3×AGL(1,𝔽5)C2311yescharacteristic
60C22×C3×AGL(1,𝔽5)C2311yescharacteristic
61C2×C3×C5×D4C2×C411yescharacteristic
62C22×Dic15C2×C412yes—
63C22×C5×Dic3C2×C412yes—
64C2×C3×C22⋊D5C2×C412yes—
65C3×D4×D5—22no—
66C3×D4×D5—22no—
67C2×C3×D20C2×C411yescharacteristic
68C2×C3×C4×D5C2311yescharacteristic
69C2×D5×Dic3—42no—
70C2×D5×Dic3—42no—
71C2×D5×Dic3C2×C412yes—
72C2×D5×Dic3C2×C412yes—
73C2×D5×Dic3C2312yes—
74C2×D5×Dic3C2311yescharacteristic
75C2×D5×Dic3C2311yescharacteristic
76#6763—24no—
77#6763—42no—
78C4⋊ΓL(1,𝔽16)—22no—
79C4×ΓL(1,𝔽16)—22no—
80C3×C22⋊AGL(1,𝔽5)—24no—
81C3×C22⋊AGL(1,𝔽5)—42no—
82C3×C4⋊AGL(1,𝔽5)—22no—
83C3×C4×AGL(1,𝔽5)—22no—
84Dic3⋊AGL(1,𝔽5)—22no—
85Dic3⋊AGL(1,𝔽5)—22no—
86Dic3×AGL(1,𝔽5)—42no—
87Dic3×AGL(1,𝔽5)—42no—
88#6719C2×C412yes—
89C4⋊Dic15C2×C411yescharacteristic
90C4×Dic15C2×C411yescharacteristic
91C5×#217C2×C412yes—
92C5×C4⋊Dic3C2×C411yescharacteristic
93C4×C5×Dic3C2×C411yescharacteristic
94#6668C2×C412yes—
95#6665C2×C412yes—
96#6665C2×C412yes—
97Dic3×Dic5C2×C411yescharacteristic
98Dic3×Dic5C2×C411yescharacteristic
99C2×D4×Dic3—51no—
100C3×#390—51no—
101#5221—51no—
102#4977—51no—
103Dic3×C4⋊C4—51no—
104#4945—52no—
105#4944—52no—
106#4943—52no—
107Dic3×C22⋊C4—52no—
108C4×C4⋊Dic3—51no—
109C4×Dic3⋊C4—51no—
110C2×D4×D5C2×D311yescharacteristic
111C22×C4×D5—32no—
112C2×C22⋊AGL(1,𝔽5)—32no—
113C2×C22⋊AGL(1,𝔽5)—32no—
114C2×C22⋊AGL(1,𝔽5)C2×D312yes—
115C2×C22⋊AGL(1,𝔽5)C2×D312yes—
116C2×C4⋊AGL(1,𝔽5)—31no—
117C2×C4⋊AGL(1,𝔽5)—31no—
118C2×C4⋊AGL(1,𝔽5)—31no—
119C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
120C2×C4×AGL(1,𝔽5)—31no—
121C2×C4×AGL(1,𝔽5)—32no—
122C2×C4×AGL(1,𝔽5)—32no—
123C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
124C4×C5×D4—31no—
125D4×Dic5—31no—
126C4×C22⋊D5—32no—
127#4039—31no—
128D5×C4⋊C4—31no—
129#4027—32no—
130D5×C22⋊C4—32no—
131C4×D20—31no—
132C42×D5—31no—
133(C2×AGL(1,𝔽5))⋊C4—31no—
134(C2×AGL(1,𝔽5))⋊C4—31no—
135(C2×AGL(1,𝔽5))⋊C4—32no—
136(C2×AGL(1,𝔽5))⋊C4—32no—
137(C2×AGL(1,𝔽5))⋊C4—32no—
138(C2×AGL(1,𝔽5))⋊C4—32no—
139#2357—151noSylow
140C23×C3×C5C22×C412yes—
141C22×C3×D5—22no—
142C22×C3×D5—22no—
143C22×C3×D5—22no—
144C22×C3×D5—22no—
145C22×C3×D5—22no—
146C22×C3×D5—22no—
147C22×C3×D5C22×C412yes—
148C22×C3×D5C2411yescharacteristic
149C2×ΓL(1,𝔽16)—21no—
150C2×ΓL(1,𝔽16)—21no—
151C2×ΓL(1,𝔽16)—21no—
152C2×ΓL(1,𝔽16)—21no—
153C2×ΓL(1,𝔽16)—22no—
154C2×ΓL(1,𝔽16)—22no—
155C2×ΓL(1,𝔽16)—22no—
156C2×ΓL(1,𝔽16)—21no—
157C2×ΓL(1,𝔽16)#4112yes—
158C2×C3×AGL(1,𝔽5)—21no—
159C2×C3×AGL(1,𝔽5)—21no—
160C2×C3×AGL(1,𝔽5)—21no—
161C2×C3×AGL(1,𝔽5)—21no—
162C2×C3×AGL(1,𝔽5)—22no—
163C2×C3×AGL(1,𝔽5)—22no—
164C2×C3×AGL(1,𝔽5)—22no—
165C2×C3×AGL(1,𝔽5)—21no—
166C2×C3×AGL(1,𝔽5)#4112yes—
167C3×C5×D4—22no—
168C2×C3×C4×C5C22×C411yescharacteristic
169C2×Dic15—42no—
170C2×Dic15C22×C411yescharacteristic
171C2×Dic15C22×C411yescharacteristic
172C2×Dic15C22×C412yes—
173C2×C5×Dic3—42no—
174C2×C5×Dic3C22×C411yescharacteristic
175C2×C5×Dic3C22×C411yescharacteristic
176C2×C5×Dic3C22×C412yes—
177C3×C22⋊D5—24no—
178C2×C3×Dic5C22×C411yescharacteristic
179C3×D20—22no—
180C3×C4×D5#4112yes—
181C3×C4×D5#4112yes—
182D5×Dic3—21no—
183D5×Dic3—21no—
184D5×Dic3—22no—
185D5×Dic3—22no—
186D5×Dic3—21no—
187D5×Dic3—21no—
188D5×Dic3—42no—
189D5×Dic3—42no—
190C22×C3×D4—51no—
191C23×Dic3—52no—
192C2×C3×C4⋊C4—51no—
193C2×C3×C22⋊C4—52no—
194C2×C3×C22⋊C4—52no—
195C2×C3×C42—51no—
196C2×#217—52no—
197C2×#217—52no—
198C2×#217—52no—
199D4×Dic3—51no—
200D4×Dic3—52no—
201D4×Dic3—52no—
202D4×Dic3—51no—
203D4×Dic3—51no—
204D4×Dic3AGL(1,𝔽5)11yescharacteristic, complemented
205C2×C4⋊Dic3—51no—
206C2×C4⋊Dic3—51no—
207C2×Dic3⋊C4—51no—
208C2×Dic3⋊C4—51no—
209C2×C4×Dic3—51no—
210C2×C4×Dic3—51no—
211C2×C4×Dic3—52no—
212C2×C4×Dic3—52no—
213C3⋊#95—51no—
214C3⋊#95—51no—
215C3⋊#95—52no—
216C3⋊#95—52no—
217C3⋊#95—52no—
218C3⋊#95—52no—
219C23×D5C22×D312yes—
220C22×AGL(1,𝔽5)—31no—
221C22×AGL(1,𝔽5)—31no—
222C22×AGL(1,𝔽5)—32no—
223C22×AGL(1,𝔽5)C22×D312yes—
224C22×AGL(1,𝔽5)C22×D311yescharacteristic
225C22×AGL(1,𝔽5)C22×D311yescharacteristic
226C2×C5×D4C4×D311yescharacteristic
227C22×C4×C5—32no—
228C2×C22⋊D5C4×D312yes—
229C22×Dic5—32no—
230D4×D5—22no—
231D4×D5—22no—
232C2×D20C4×D311yescharacteristic
233C2×C4×D5—32no—
234C2×C4×D5—31no—
235C2×C4×D5—31no—
236C2×C4×D5—32no—
237C2×C4×D5—32no—
238C2×C4×D5—122no—
239C2×C4×D5—122no—
240C2×C4×D5C22×D311yescharacteristic
241C22⋊AGL(1,𝔽5)—24no—
242C22⋊AGL(1,𝔽5)—42no—
243C22⋊AGL(1,𝔽5)—64no—
244C22⋊AGL(1,𝔽5)—122no—
245C4⋊AGL(1,𝔽5)—22no—
246C4⋊AGL(1,𝔽5)—62no—
247C4⋊AGL(1,𝔽5)—62no—
248C4⋊AGL(1,𝔽5)—62no—
249C4×AGL(1,𝔽5)—22no—
250C4×AGL(1,𝔽5)—62no—
251C4×AGL(1,𝔽5)—122no—
252C4×AGL(1,𝔽5)—122no—
253C5×C4⋊C4—31no—
254C5×C22⋊C4—32no—
255C42×C5—31no—
256C22⋊Dic5—32no—
257#685—32no—
258#685—32no—
259C4⋊Dic5—31no—
260#683—32no—
261C4×Dic5—31no—
262C4×Dic5—31no—
263C4×Dic5—31no—
264C2×C4×D4—151no—
265#390—51no—
266#390—151no—
267#388—152no—
268#388—152no—
269#382—151no—
270#381—152no—
271C4×C4⋊C4—151no—
272C4×C4⋊C4—151no—
273C4×C4⋊C4—151no—
274C4×C22⋊C4—152no—
275C22×C3×C5—22no—
276C22×C3×C5—22no—
277C22×C3×C5—22no—
278C22×C3×C5C23×C411yescharacteristic
279C2×C3×D5—22no—
280C2×C3×D5—22no—
281C2×C3×D5—22no—
282C2×C3×D5—42no—
283C2×C3×D5—42no—
284C2×C3×D5—42no—
285C2×C3×D5—42no—
286C2×C3×D5C2×#4111yescharacteristic
287C2×C3×D5C2×#4111yescharacteristic
288C2×C3×D5C2×#4111yescharacteristic
289C2×C3×D5C2×#4111yescharacteristic
290C2×C3×D5H(5,𝔽2)11yescharacteristic
291C2×C3×D5H(5,𝔽2)11yescharacteristic
292ΓL(1,𝔽16)—22no—
293ΓL(1,𝔽16)—41no—
294ΓL(1,𝔽16)—42no—
295C3×AGL(1,𝔽5)—22no—
296C3×AGL(1,𝔽5)—41no—
297C3×AGL(1,𝔽5)—42no—
298C3×C4×C5#11712yes—
299Dic15—21no—
300Dic15—21no—
301Dic15—22no—
302C3×Dic5#11712yes—
303C5×Dic3—21no—
304C5×Dic3—21no—
305C5×Dic3—22no—
306C24×C3—52no—
307C2×C3×D4—52no—
308C2×C3×D4—51no—
309C2×C3×D4—102no—
310C2×C3×D4—102no—
311C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
312C22×C3×C4—51no—
313C22×C3×C4—51no—
314C22×C3×C4—52no—
315C22×C3×C4—51no—
316C22×Dic3—51no—
317C22×Dic3—52no—
318C22×Dic3—51no—
319C22×Dic3—52no—
320C22×Dic3—51no—
321C22×Dic3—52no—
322C22×Dic3—52no—
323C22×Dic3—51no—
324C22×Dic3—52no—
325C22×Dic3—202no—
326C22×Dic3—202no—
327C22×Dic3C2×AGL(1,𝔽5)12yes—
328C3×C4⋊C4—102no—
329C3×C22⋊C4—104no—
330C3×C22⋊C4—202no—
331C3×C42—102no—
332#217—52no—
333#217—52no—
334#217—52no—
335#217—104no—
336#217—202no—
337#217C2×AGL(1,𝔽5)12yes—
338C4⋊Dic3—51no—
339C4⋊Dic3—52no—
340C4⋊Dic3—102no—
341C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
342Dic3⋊C4—102no—
343Dic3⋊C4—102no—
344C4×Dic3—51no—
345C4×Dic3—51no—
346C4×Dic3—51no—
347C4×Dic3—102no—
348C4×Dic3—202no—
349C4×Dic3—202no—
350C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
351C23×C5C2×C4×D312yes—
352C22×D5—22no—
353C22×D5—22no—
354C22×D5—22no—
355C22×D5—22no—
356C22×D5—22no—
357C22×D5—22no—
358C22×D5C2×C4×D312yes—
359C22×D5C23×D311yescharacteristic
360C2×AGL(1,𝔽5)—21no—
361C2×AGL(1,𝔽5)—21no—
362C2×AGL(1,𝔽5)—21no—
363C2×AGL(1,𝔽5)—22no—
364C2×AGL(1,𝔽5)—22no—
365C2×AGL(1,𝔽5)—22no—
366C2×AGL(1,𝔽5)—21no—
367C2×AGL(1,𝔽5)—21no—
368C2×AGL(1,𝔽5)—32no—
369C2×AGL(1,𝔽5)—61no—
370C2×AGL(1,𝔽5)—61no—
371C2×AGL(1,𝔽5)—61no—
372C2×AGL(1,𝔽5)—62no—
373C2×AGL(1,𝔽5)—61no—
374C2×AGL(1,𝔽5)—62no—
375C2×AGL(1,𝔽5)—62no—
376C2×AGL(1,𝔽5)—61no—
377C2×AGL(1,𝔽5)#23712yes—
378C5×D4—22no—
379C2×C4×C5—31no—
380C2×C4×C5—31no—
381C2×C4×C5—32no—
382C2×C4×C5—122no—
383C2×C4×C5C2×C4×D311yescharacteristic
384C22⋊D5—24no—
385C2×Dic5—31no—
386C2×Dic5—31no—
387C2×Dic5—32no—
388C2×Dic5—122no—
389C2×Dic5C2×C4×D311yescharacteristic
390D20—22no—
391C4×D5—61no—
392C4×D5—62no—
393C4×D5—61no—
394C4×D5—61no—
395C4×D5—62no—
396C4×D5—61no—
397C4×D5—122no—
398C4×D5—122no—
399C4×D5#23712yes—
400C4×D5#23712yes—
401C22×D4—51no—
402C23×C4—152no—
403C4×D4—31no—
404C4×D4—151no—
405C4×D4—152no—
406C4×D4—151no—
407C4×D4—152no—
408C4×D4—151no—
409C2×C4⋊C4—51no—
410C2×C4⋊C4—151no—
411C2×C4⋊C4—151no—
412C2×C4⋊C4—151no—
413C2×C4⋊C4—151no—
414C2×C22⋊C4—52no—
415C2×C22⋊C4—52no—
416C2×C22⋊C4—152no—
417C2×C22⋊C4—152no—
418C2×C22⋊C4—152no—
419C2×C42—51no—
420C2×C42—151no—
421C2×C42—151no—
422C2×C42—152no—
423C2×C42—152no—
424#95—151no—
425#95—152no—
426#95—151no—
427#95—152no—
428#95—152no—
429#95—152no—
430C2×C3×C5—42no—
431C2×C3×C5C2×#11711yescharacteristic
432C2×C3×C5C4×#4111yescharacteristic
433C2×C3×C5#51811yescharacteristic
434C3×D5—42no—
435C3×D5#55311yescharacteristic
436C3×D5#55311yescharacteristic
437C3×D5#55911yescharacteristic
438C3×D5#55911yescharacteristic
439C23×C3—51no—
440C23×C3—52no—
441C23×C3—102no—
442C23×C3—102no—
443C23×C3—102no—
444C23×C3—102no—
445C23×C3—102no—
446C23×C3—102no—
447C23×C3C22×AGL(1,𝔽5)12yes—
448C3×D4—22no—
449C3×D4—104no—
450C3×D4—102no—
451C2×C3×C4—51no—
452C2×C3×C4—52no—
453C2×C3×C4—52no—
454C2×C3×C4—52no—
455C2×C3×C4—101no—
456C2×C3×C4—101no—
457C2×C3×C4—102no—
458C2×C3×C4—101no—
459C2×C3×C4—101no—
460C2×C3×C4—102no—
461C2×C3×C4—101no—
462C2×C3×C4—102no—
463C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
464C2×Dic3—42no—
465C2×Dic3—52no—
466C2×Dic3—51no—
467C2×Dic3—51no—
468C2×Dic3—52no—
469C2×Dic3—102no—
470C2×Dic3—102no—
471C2×Dic3—101no—
472C2×Dic3—101no—
473C2×Dic3—101no—
474C2×Dic3—101no—
475C2×Dic3—101no—
476C2×Dic3—101no—
477C2×Dic3—101no—
478C2×Dic3—102no—
479C2×Dic3—101no—
480C2×Dic3—102no—
481C2×Dic3—102no—
482C2×Dic3—101no—
483C2×Dic3—202no—
484C2×Dic3—202no—
485C2×Dic3—202no—
486C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
487C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
488C2×Dic3C22×AGL(1,𝔽5)12yes—
489C22×C5—22no—
490C22×C5—22no—
491C22×C5—22no—
492C22×C5C22×C4×D311yescharacteristic
493C2×D5—22no—
494C2×D5—22no—
495C2×D5—22no—
496C2×D5—42no—
497C2×D5—42no—
498C2×D5—42no—
499C2×D5—42no—
500C2×D5C2×#23711yescharacteristic
501C2×D5C2×#23711yescharacteristic
502C2×D5C2×#23711yescharacteristic
503C2×D5#100411yescharacteristic
504C2×D5D3×#4111yescharacteristic
505C2×D5#100911yescharacteristic
506AGL(1,𝔽5)—22no—
507AGL(1,𝔽5)—42no—
508AGL(1,𝔽5)—41no—
509AGL(1,𝔽5)—62no—
510AGL(1,𝔽5)—122no—
511AGL(1,𝔽5)—121no—
512C4×C5—61no—
513C4×C5—61no—
514C4×C5—62no—
515C4×C5#87712yes—
516Dic5—61no—
517Dic5—61no—
518Dic5—62no—
519Dic5#87712yes—
520C24—52no—
521C2×D4—52no—
522C2×D4—51no—
523C2×D4—102no—
524C2×D4—102no—
525C2×D4D3×AGL(1,𝔽5)11yescharacteristic
526C22×C4—32no—
527C22×C4—51no—
528C22×C4—51no—
529C22×C4—51no—
530C22×C4—52no—
531C22×C4—151no—
532C22×C4—152no—
533C22×C4—151no—
534C22×C4—152no—
535C22×C4—152no—
536C22×C4—151no—
537C22×C4—152no—
538C22×C4—151no—
539C22×C4—152no—
540C22×C4—602no—
541C22×C4—602no—
542C4⋊C4—31no—
543C4⋊C4—102no—
544C4⋊C4—152no—
545C4⋊C4—151no—
546C4⋊C4—302no—
547C4⋊C4—302no—
548C4⋊C4—302no—
549C22⋊C4—32no—
550C22⋊C4—104no—
551C22⋊C4—152no—
552C22⋊C4—152no—
553C22⋊C4—152no—
554C22⋊C4—202no—
555C22⋊C4—304no—
556C22⋊C4—602no—
557C42—31no—
558C42—102no—
559C42—151no—
560C42—151no—
561C42—151no—
562C42—302no—
563C42—602no—
564C42—602no—
565C3×C5#235711yescharacteristic, complemented, Hall
566C22×C3—22no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—51no—
570C22×C3—51no—
571C22×C3—51no—
572C22×C3—51no—
573C22×C3—51no—
574C22×C3—51no—
575C22×C3—102no—
576C22×C3—102no—
577C22×C3—102no—
578C22×C3—202no—
579C22×C3—202no—
580C22×C3—202no—
581C22×C3—202no—
582C22×C3C23×AGL(1,𝔽5)11yescharacteristic
583C3×C4—52no—
584C3×C4—102no—
585C3×C4—201no—
586C3×C4—202no—
587C3×C4#413012yes—
588Dic3—21no—
589Dic3—22no—
590Dic3—21no—
591Dic3—102no—
592Dic3—102no—
593Dic3—101no—
594Dic3—101no—
595Dic3—202no—
596Dic3—201no—
597C2×C5—42no—
598C2×C5C2×#87711yescharacteristic
599C2×C5C4×#23711yescharacteristic
600C2×C5#554511yescharacteristic
601D5—42no—
602D5#561411yescharacteristic
603D5#561811yescharacteristic
604D5#568111yescharacteristic
605D5#571311yescharacteristic
606C23—51no—
607C23—52no—
608C23—102no—
609C23—102no—
610C23—102no—
611C23—102no—
612C23—102no—
613C23—102no—
614C23C2×D3×AGL(1,𝔽5)12yes—
615D4—22no—
616D4—104no—
617D4—102no—
618C2×C4—31no—
619C2×C4—31no—
620C2×C4—32no—
621C2×C4—51no—
622C2×C4—52no—
623C2×C4—52no—
624C2×C4—52no—
625C2×C4—101no—
626C2×C4—101no—
627C2×C4—101no—
628C2×C4—102no—
629C2×C4—102no—
630C2×C4—101no—
631C2×C4—102no—
632C2×C4—101no—
633C2×C4—122no—
634C2×C4—152no—
635C2×C4—151no—
636C2×C4—151no—
637C2×C4—152no—
638C2×C4—302no—
639C2×C4—302no—
640C2×C4—301no—
641C2×C4—301no—
642C2×C4—301no—
643C2×C4—301no—
644C2×C4—301no—
645C2×C4—301no—
646C2×C4—301no—
647C2×C4—302no—
648C2×C4—302no—
649C2×C4—301no—
650C2×C4—301no—
651C2×C4—302no—
652C2×C4—602no—
653C2×C4—602no—
654C2×C4—602no—
655C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
656C2×C3—42no—
657C2×C3—51no—
658C2×C3—51no—
659C2×C3—51no—
660C2×C3—51no—
661C2×C3—202no—
662C2×C3C2×#413011yescharacteristic
663C2×C3#6625811yescharacteristic
664C2×C3#41×AGL(1,𝔽5)11yescharacteristic
665C5#7630311yescharacteristic, complemented, Sylow
666C22—22no—
667C22—22no—
668C22—22no—
669C22—51no—
670C22—51no—
671C22—51no—
672C22—51no—
673C22—51no—
674C22—51no—
675C22—102no—
676C22—102no—
677C22—102no—
678C22—202no—
679C22—202no—
680C22—202no—
681C22—202no—
682C22C22×D3×AGL(1,𝔽5)11yescharacteristic
683C4—52no—
684C4—61no—
685C4—61no—
686C4—62no—
687C4—102no—
688C4—202no—
689C4—201no—
690C4—302no—
691C4—301no—
692C4—301no—
693C4—302no—
694C4—601no—
695C4—602no—
696C4#9192312yes—
697C3#1061718211yescharacteristic, complemented, Sylow
698C2—42no—
699C2—51no—
700C2—51no—
701C2—51no—
702C2—51no—
703C2—202no—
704C2AGL(1,𝔽5)×#23711yescharacteristic
705C2#1175684511yescharacteristic
706C2C2×#9192311yescharacteristic
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#2357
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. Dic3×C22⋊AGL(1,𝔽5)C2semidirect
5. #11752018C2semidirect
6. #11752017C2semidirect
7. #11751984C2semidirect
8. C4×Dic3⋊AGL(1,𝔽5)C2semidirect
9. #11751846C2semidirect
10. AGL(1,𝔽5)×C4⋊Dic3C2semidirect
11. #11751751C2semidirect
27. D4×Dic15C4semidirect
28. C5×D4×Dic3C4semidirect
29. #91559C4semidirect
30. Dic3×C22⋊D5C4semidirect
32. #91434C4semidirect
33. Dic3×D20C4semidirect
204. D4×Dic3AGL(1,𝔽5)semidirect
565. C3×C5#2357semidirect
665. C5#76303semidirect
697. C3#10617182semidirect

Maximal subgroups

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

subgroupindex
D4×D5×Dic32
#117524392
C3×#657802
Dic3×C22⋊AGL(1,𝔽5)2
#117520182
#117520172
#117519842
C4×Dic3⋊AGL(1,𝔽5)2
#117518462
AGL(1,𝔽5)×C4⋊Dic32
#117517512
#106171823
#763035