Finite Group Databasebeta

← #14323230

Subgroups — #14323230

Order 1920.

1080 conjugacy classes of subgroups.

The subgroup lattice has 704 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
4#11752028C212yesmaximal, complemented
5#11752018C212yesmaximal, complemented
6#11752017C212yesmaximal, complemented
7#11751984C212yesmaximal, complemented
8#11751861C211yesmaximal, characteristic, complemented
9#11751859C211yesmaximal, characteristic, complemented
10Dic3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
11#11751748C211yesmaximal, characteristic, complemented
12#10617176—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)C2212yes—
24C2×Dic3⋊AGL(1,𝔽5)C2212yes—
25C2×Dic3×AGL(1,𝔽5)C2212yes—
26D4×Dic15C411yescharacteristic, complemented
27C5×D4×Dic3C411yescharacteristic, complemented
28#91559C412yescomplemented
29Dic3×C22⋊D5C412yescomplemented
30D5×#217C2212yes—
31#91434C411yescharacteristic, complemented
32Dic3×D20C411yescharacteristic, complemented
33D5×C4⋊Dic3C2211yescharacteristic
34C4×D5×Dic3C2211yescharacteristic
35(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
36(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
37(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
38(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
39(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
40(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
41(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
42#76295—51nomaximal, Hall
43C4×D4×D5—31no—
44#65780—31no—
45#65780D311yescharacteristic
46#65765—32no—
47#65764—32no—
48#65712—31no—
49#65712—31no—
50#65700—32no—
51#65700—32no—
52C4×C4⋊AGL(1,𝔽5)—31no—
53#65686—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×Dic3C2311yescharacteristic
74C2×D5×Dic3C2312yes—
75C2×D5×Dic3C2311yescharacteristic
76#6763—42no—
77#6763—42no—
78C4⋊ΓL(1,𝔽16)—22no—
79C4×ΓL(1,𝔽16)—22no—
80C3×C22⋊AGL(1,𝔽5)—42no—
81C3×C22⋊AGL(1,𝔽5)—42no—
82C3×C4⋊AGL(1,𝔽5)—22no—
83C3×C4×AGL(1,𝔽5)—22no—
84Dic3⋊AGL(1,𝔽5)—42no—
85Dic3⋊AGL(1,𝔽5)—42no—
86Dic3×AGL(1,𝔽5)—42no—
87#6719C2×C412yes—
88C4⋊Dic15C2×C411yescharacteristic
89C4×Dic15C2×C411yescharacteristic
90C5×#217C2×C412yes—
91C5×C4⋊Dic3C2×C411yescharacteristic
92C4×C5×Dic3C2×C411yescharacteristic
93#6668C2×C412yes—
94#6665C2×C412yes—
95#6665C2×C412yes—
96Dic3×Dic5C2×C411yescharacteristic
97Dic3×Dic5C2×C411yescharacteristic
98C2×D4×Dic3—51no—
99C3×#390—51no—
100#5221—51no—
101Dic3×C4⋊C4—51no—
102#4972—51no—
103#4945—52no—
104#4944—52no—
105#4943—52no—
106#4942—52no—
107#4932—51no—
108#4928—51no—
109C2×D4×D5C2×D311yescharacteristic
110C22×C4×D5—32no—
111C2×C22⋊AGL(1,𝔽5)—32no—
112C2×C22⋊AGL(1,𝔽5)—32no—
113C2×C22⋊AGL(1,𝔽5)C2×D312yes—
114C2×C22⋊AGL(1,𝔽5)C2×D312yes—
115C2×C4⋊AGL(1,𝔽5)—31no—
116C2×C4⋊AGL(1,𝔽5)—32no—
117C2×C4⋊AGL(1,𝔽5)—32no—
118C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
119C2×C4×AGL(1,𝔽5)—31no—
120C2×C4×AGL(1,𝔽5)—32no—
121C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
122C4×C5×D4—31no—
123D4×Dic5—31no—
124C4×C22⋊D5—32no—
125#4039—31no—
126D5×C4⋊C4—31no—
127#4027—32no—
128D5×C22⋊C4—32no—
129C4×D20—31no—
130C42×D5—31no—
131(C2×AGL(1,𝔽5))⋊C4—31no—
132(C2×AGL(1,𝔽5))⋊C4—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#2319—151noSylow
139C23×C3×C5C22×C412yes—
140C22×C3×D5—22no—
141C22×C3×D5—22no—
142C22×C3×D5—22no—
143C22×C3×D5—22no—
144C22×C3×D5—22no—
145C22×C3×D5—22no—
146C22×C3×D5C22×C412yes—
147C22×C3×D5C2411yescharacteristic
148C2×ΓL(1,𝔽16)—21no—
149C2×ΓL(1,𝔽16)—21no—
150C2×ΓL(1,𝔽16)—22no—
151C2×ΓL(1,𝔽16)—22no—
152C2×ΓL(1,𝔽16)—21no—
153C2×ΓL(1,𝔽16)—22no—
154C2×ΓL(1,𝔽16)—21no—
155C2×ΓL(1,𝔽16)—21no—
156C2×ΓL(1,𝔽16)—21no—
157C2×C3×AGL(1,𝔽5)—21no—
158C2×C3×AGL(1,𝔽5)—21no—
159C2×C3×AGL(1,𝔽5)—22no—
160C2×C3×AGL(1,𝔽5)—22no—
161C2×C3×AGL(1,𝔽5)—21no—
162C2×C3×AGL(1,𝔽5)—22no—
163C2×C3×AGL(1,𝔽5)—21no—
164C2×C3×AGL(1,𝔽5)—21no—
165C2×C3×AGL(1,𝔽5)—21no—
166C3×C5×D4—22no—
167C2×C3×C4×C5C22×C411yescharacteristic
168C2×Dic15—42no—
169C2×Dic15C22×C411yescharacteristic
170C2×Dic15C22×C411yescharacteristic
171C2×Dic15C22×C412yes—
172C2×C5×Dic3—42no—
173C2×C5×Dic3C22×C411yescharacteristic
174C2×C5×Dic3C22×C411yescharacteristic
175C2×C5×Dic3C22×C412yes—
176C3×C22⋊D5—24no—
177C2×C3×Dic5C22×C411yescharacteristic
178C3×D20—22no—
179C3×C4×D5#4112yes—
180C3×C4×D5#4112yes—
181D5×Dic3—21no—
182D5×Dic3—22no—
183D5×Dic3—22no—
184D5×Dic3—21no—
185D5×Dic3—21no—
186D5×Dic3—21no—
187D5×Dic3—42no—
188D5×Dic3—42no—
189C22×C3×D4—51no—
190C23×Dic3—52no—
191C2×C3×C4⋊C4—51no—
192C2×C3×C22⋊C4—52no—
193C2×C3×C22⋊C4—52no—
194C2×C3×C42—51no—
195C2×#217—52no—
196C2×#217—52no—
197C2×#217—52no—
198D4×Dic3—51no—
199D4×Dic3—52no—
200D4×Dic3—52no—
201D4×Dic3—51no—
202D4×Dic3—51no—
203D4×Dic3AGL(1,𝔽5)11yescharacteristic, complemented
204C2×C4⋊Dic3—51no—
205C2×C4⋊Dic3—51no—
206C2×Dic3⋊C4—52no—
207C2×Dic3⋊C4—52no—
208C2×C4×Dic3—51no—
209C2×C4×Dic3—51no—
210C2×C4×Dic3—52no—
211C3⋊#95—52no—
212C3⋊#95—51no—
213C3⋊#95—51no—
214C3⋊#95—51no—
215C3⋊#95—51no—
216C3⋊#95—52no—
217C3⋊#95—52no—
218C23×D5C22×D312yes—
219C22×AGL(1,𝔽5)—31no—
220C22×AGL(1,𝔽5)—32no—
221C22×AGL(1,𝔽5)—31no—
222C22×AGL(1,𝔽5)C22×D312yes—
223C22×AGL(1,𝔽5)C22×D311yescharacteristic
224C22×AGL(1,𝔽5)C22×D311yescharacteristic
225C2×C5×D4C4×D311yescharacteristic
226C22×C4×C5—32no—
227C2×C22⋊D5C4×D312yes—
228C22×Dic5—32no—
229D4×D5—22no—
230D4×D5—22no—
231C2×D20C4×D311yescharacteristic
232C2×C4×D5—31no—
233C2×C4×D5—32no—
234C2×C4×D5—31no—
235C2×C4×D5—32no—
236C2×C4×D5—32no—
237C2×C4×D5—122no—
238C2×C4×D5—122no—
239C2×C4×D5C22×D311yescharacteristic
240C22⋊AGL(1,𝔽5)—42no—
241C22⋊AGL(1,𝔽5)—42no—
242C22⋊AGL(1,𝔽5)—122no—
243C22⋊AGL(1,𝔽5)—122no—
244C4⋊AGL(1,𝔽5)—22no—
245C4⋊AGL(1,𝔽5)—62no—
246C4⋊AGL(1,𝔽5)—122no—
247C4⋊AGL(1,𝔽5)—122no—
248C4×AGL(1,𝔽5)—22no—
249C4×AGL(1,𝔽5)—62no—
250C4×AGL(1,𝔽5)—122no—
251C5×C4⋊C4—31no—
252C5×C22⋊C4—32no—
253C42×C5—31no—
254C22⋊Dic5—32no—
255#685—32no—
256#685—32no—
257C4⋊Dic5—31no—
258#683—32no—
259C4×Dic5—31no—
260C4×Dic5—31no—
261C4×Dic5—31no—
262C2×C4×D4—151no—
263#390—51no—
264#390—151no—
265#389—151no—
266#389—151no—
267#388—152no—
268#388—152no—
269#381—152no—
270#380—152no—
271C4×C4⋊C4—151no—
272#376—151no—
273C22×C3×C5—22no—
274C22×C3×C5—22no—
275C22×C3×C5—22no—
276C22×C3×C5C23×C411yescharacteristic
277C2×C3×D5—22no—
278C2×C3×D5—22no—
279C2×C3×D5—22no—
280C2×C3×D5—42no—
281C2×C3×D5—42no—
282C2×C3×D5—42no—
283C2×C3×D5—42no—
284C2×C3×D5C2×#4111yescharacteristic
285C2×C3×D5C2×#4111yescharacteristic
286C2×C3×D5H(5,𝔽2)11yescharacteristic
287C2×C3×D5H(5,𝔽2)11yescharacteristic
288C2×C3×D5H(5,𝔽2)11yescharacteristic
289C2×C3×D52−1+411yescharacteristic
290ΓL(1,𝔽16)—41no—
291ΓL(1,𝔽16)—42no—
292ΓL(1,𝔽16)—41no—
293C3×AGL(1,𝔽5)—42no—
294C3×AGL(1,𝔽5)—41no—
295C3×AGL(1,𝔽5)—41no—
296C3×C4×C5#11712yes—
297Dic15—21no—
298Dic15—22no—
299Dic15—21no—
300C3×Dic5#11712yes—
301C5×Dic3—21no—
302C5×Dic3—22no—
303C5×Dic3—21no—
304C24×C3—52no—
305C2×C3×D4—52no—
306C2×C3×D4—51no—
307C2×C3×D4—102no—
308C2×C3×D4—102no—
309C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
310C22×C3×C4—51no—
311C22×C3×C4—51no—
312C22×C3×C4—52no—
313C22×C3×C4—51no—
314C22×Dic3—52no—
315C22×Dic3—51no—
316C22×Dic3—51no—
317C22×Dic3—52no—
318C22×Dic3—52no—
319C22×Dic3—52no—
320C22×Dic3—51no—
321C22×Dic3—51no—
322C22×Dic3—52no—
323C22×Dic3—202no—
324C22×Dic3—202no—
325C22×Dic3C2×AGL(1,𝔽5)12yes—
326C3×C4⋊C4—102no—
327C3×C22⋊C4—202no—
328C3×C22⋊C4—202no—
329C3×C42—102no—
330#217—52no—
331#217—52no—
332#217—52no—
333#217—202no—
334#217—202no—
335#217C2×AGL(1,𝔽5)12yes—
336C4⋊Dic3—51no—
337C4⋊Dic3—52no—
338C4⋊Dic3—102no—
339C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
340Dic3⋊C4—202no—
341Dic3⋊C4—202no—
342C4×Dic3—51no—
343C4×Dic3—51no—
344C4×Dic3—51no—
345C4×Dic3—102no—
346C4×Dic3—202no—
347C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
348C23×C5C2×C4×D312yes—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—22no—
352C22×D5—22no—
353C22×D5—22no—
354C22×D5—22no—
355C22×D5C2×C4×D312yes—
356C22×D5C23×D311yescharacteristic
357C2×AGL(1,𝔽5)—21no—
358C2×AGL(1,𝔽5)—21no—
359C2×AGL(1,𝔽5)—22no—
360C2×AGL(1,𝔽5)—22no—
361C2×AGL(1,𝔽5)—22no—
362C2×AGL(1,𝔽5)—21no—
363C2×AGL(1,𝔽5)—21no—
364C2×AGL(1,𝔽5)—21no—
365C2×AGL(1,𝔽5)—21no—
366C2×AGL(1,𝔽5)—61no—
367C2×AGL(1,𝔽5)—61no—
368C2×AGL(1,𝔽5)—62no—
369C2×AGL(1,𝔽5)—62no—
370C2×AGL(1,𝔽5)—61no—
371C2×AGL(1,𝔽5)—61no—
372C2×AGL(1,𝔽5)—62no—
373C2×AGL(1,𝔽5)—61no—
374C2×AGL(1,𝔽5)—61no—
375C5×D4—22no—
376C2×C4×C5—31no—
377C2×C4×C5—31no—
378C2×C4×C5—32no—
379C2×C4×C5—122no—
380C2×C4×C5C2×C4×D311yescharacteristic
381C22⋊D5—24no—
382C2×Dic5—31no—
383C2×Dic5—31no—
384C2×Dic5—32no—
385C2×Dic5—122no—
386C2×Dic5C2×C4×D311yescharacteristic
387D20—22no—
388C4×D5—61no—
389C4×D5—62no—
390C4×D5—61no—
391C4×D5—62no—
392C4×D5—61no—
393C4×D5—61no—
394C4×D5—122no—
395C4×D5—122no—
396C4×D5#23712yes—
397C4×D5#23712yes—
398C22×D4—51no—
399C23×C4—152no—
400C4×D4—31no—
401C4×D4—151no—
402C4×D4—152no—
403C4×D4—151no—
404C4×D4—152no—
405C4×D4—151no—
406C2×C4⋊C4—51no—
407C2×C4⋊C4—151no—
408C2×C4⋊C4—151no—
409C2×C4⋊C4—152no—
410C2×C4⋊C4—152no—
411C2×C22⋊C4—52no—
412C2×C22⋊C4—52no—
413C2×C22⋊C4—152no—
414C2×C22⋊C4—152no—
415C2×C22⋊C4—152no—
416C2×C42—51no—
417C2×C42—151no—
418C2×C42—151no—
419C2×C42—152no—
420#95—151no—
421#95—151no—
422#95—151no—
423#95—151no—
424#95—152no—
425#95—152no—
426#95—152no—
427C2×C3×C5—42no—
428C2×C3×C5C2×#11711yescharacteristic
429C2×C3×C5#51811yescharacteristic
430C2×C3×C5#52011yescharacteristic
431C3×D5—42no—
432C3×D5#54011yescharacteristic
433C3×D5#54011yescharacteristic
434C3×D5#54211yescharacteristic
435C3×D5#54211yescharacteristic
436C23×C3—51no—
437C23×C3—52no—
438C23×C3—102no—
439C23×C3—102no—
440C23×C3—102no—
441C23×C3—102no—
442C23×C3—102no—
443C23×C3—102no—
444C23×C3C22×AGL(1,𝔽5)12yes—
445C3×D4—22no—
446C3×D4—104no—
447C3×D4—102no—
448C2×C3×C4—51no—
449C2×C3×C4—52no—
450C2×C3×C4—52no—
451C2×C3×C4—102no—
452C2×C3×C4—101no—
453C2×C3×C4—102no—
454C2×C3×C4—101no—
455C2×C3×C4—101no—
456C2×C3×C4—101no—
457C2×C3×C4—101no—
458C2×C3×C4—102no—
459C2×C3×C4—101no—
460C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
461C2×Dic3—42no—
462C2×Dic3—51no—
463C2×Dic3—51no—
464C2×Dic3—52no—
465C2×Dic3—101no—
466C2×Dic3—102no—
467C2×Dic3—102no—
468C2×Dic3—101no—
469C2×Dic3—101no—
470C2×Dic3—101no—
471C2×Dic3—101no—
472C2×Dic3—101no—
473C2×Dic3—102no—
474C2×Dic3—101no—
475C2×Dic3—102no—
476C2×Dic3—102no—
477C2×Dic3—101no—
478C2×Dic3—101no—
479C2×Dic3—101no—
480C2×Dic3—202no—
481C2×Dic3—202no—
482C2×Dic3—202no—
483C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
484C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
485C2×Dic3C22×AGL(1,𝔽5)12yes—
486C22×C5—22no—
487C22×C5—22no—
488C22×C5—22no—
489C22×C5C22×C4×D311yescharacteristic
490C2×D5—22no—
491C2×D5—22no—
492C2×D5—22no—
493C2×D5—42no—
494C2×D5—42no—
495C2×D5—42no—
496C2×D5—42no—
497C2×D5C2×#23711yescharacteristic
498C2×D5C2×#23711yescharacteristic
499C2×D5#100411yescharacteristic
500C2×D5#100411yescharacteristic
501C2×D5#100911yescharacteristic
502C2×D5#101011yescharacteristic
503AGL(1,𝔽5)—42no—
504AGL(1,𝔽5)—41no—
505AGL(1,𝔽5)—41no—
506AGL(1,𝔽5)—121no—
507AGL(1,𝔽5)—121no—
508AGL(1,𝔽5)—122no—
509C4×C5—61no—
510C4×C5—62no—
511C4×C5—61no—
512C4×C5#87712yes—
513Dic5—61no—
514Dic5—62no—
515Dic5—61no—
516Dic5#87712yes—
517C24—52no—
518C2×D4—52no—
519C2×D4—51no—
520C2×D4—102no—
521C2×D4—102no—
522C2×D4D3×AGL(1,𝔽5)11yescharacteristic
523C22×C4—32no—
524C22×C4—51no—
525C22×C4—51no—
526C22×C4—51no—
527C22×C4—52no—
528C22×C4—151no—
529C22×C4—151no—
530C22×C4—152no—
531C22×C4—152no—
532C22×C4—152no—
533C22×C4—152no—
534C22×C4—151no—
535C22×C4—151no—
536C22×C4—152no—
537C22×C4—602no—
538C22×C4—602no—
539C4⋊C4—31no—
540C4⋊C4—102no—
541C4⋊C4—152no—
542C4⋊C4—151no—
543C4⋊C4—302no—
544C4⋊C4—602no—
545C4⋊C4—602no—
546C22⋊C4—32no—
547C22⋊C4—152no—
548C22⋊C4—152no—
549C22⋊C4—152no—
550C22⋊C4—202no—
551C22⋊C4—202no—
552C22⋊C4—602no—
553C22⋊C4—602no—
554C42—31no—
555C42—102no—
556C42—151no—
557C42—151no—
558C42—151no—
559C42—302no—
560C42—602no—
561C3×C5#231911yescharacteristic, complemented, Hall
562C22×C3—22no—
563C22×C3—22no—
564C22×C3—22no—
565C22×C3—51no—
566C22×C3—51no—
567C22×C3—51no—
568C22×C3—51no—
569C22×C3—51no—
570C22×C3—51no—
571C22×C3—102no—
572C22×C3—102no—
573C22×C3—102no—
574C22×C3—202no—
575C22×C3—202no—
576C22×C3—202no—
577C22×C3—202no—
578C22×C3C23×AGL(1,𝔽5)11yescharacteristic
579C3×C4—52no—
580C3×C4—201no—
581C3×C4—202no—
582C3×C4—201no—
583C3×C4#413012yes—
584Dic3—21no—
585Dic3—22no—
586Dic3—21no—
587Dic3—102no—
588Dic3—101no—
589Dic3—101no—
590Dic3—202no—
591Dic3—201no—
592Dic3—201no—
593C2×C5—42no—
594C2×C5C2×#87711yescharacteristic
595C2×C5#554511yescharacteristic
596C2×C5#554611yescharacteristic
597D5—42no—
598D5#560311yescharacteristic
599D5#561911yescharacteristic
600D5#568211yescharacteristic
601D5#571911yescharacteristic
602C23—51no—
603C23—52no—
604C23—102no—
605C23—102no—
606C23—102no—
607C23—102no—
608C23—102no—
609C23—102no—
610C23C2×D3×AGL(1,𝔽5)12yes—
611D4—22no—
612D4—104no—
613D4—102no—
614C2×C4—31no—
615C2×C4—31no—
616C2×C4—32no—
617C2×C4—51no—
618C2×C4—52no—
619C2×C4—52no—
620C2×C4—101no—
621C2×C4—101no—
622C2×C4—102no—
623C2×C4—101no—
624C2×C4—101no—
625C2×C4—102no—
626C2×C4—102no—
627C2×C4—101no—
628C2×C4—101no—
629C2×C4—122no—
630C2×C4—151no—
631C2×C4—151no—
632C2×C4—152no—
633C2×C4—301no—
634C2×C4—302no—
635C2×C4—302no—
636C2×C4—301no—
637C2×C4—301no—
638C2×C4—301no—
639C2×C4—301no—
640C2×C4—301no—
641C2×C4—302no—
642C2×C4—301no—
643C2×C4—301no—
644C2×C4—302no—
645C2×C4—302no—
646C2×C4—301no—
647C2×C4—301no—
648C2×C4—602no—
649C2×C4—602no—
650C2×C4—602no—
651C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
652C2×C3—42no—
653C2×C3—51no—
654C2×C3—51no—
655C2×C3—51no—
656C2×C3—51no—
657C2×C3—202no—
658C2×C3C2×#413011yescharacteristic
659C2×C3#6625811yescharacteristic
660C2×C3#6626611yescharacteristic
661C5#7629511yescharacteristic, complemented, Sylow
662C22—22no—
663C22—22no—
664C22—22no—
665C22—51no—
666C22—51no—
667C22—51no—
668C22—51no—
669C22—51no—
670C22—51no—
671C22—102no—
672C22—102no—
673C22—102no—
674C22—202no—
675C22—202no—
676C22—202no—
677C22—202no—
678C22C22×D3×AGL(1,𝔽5)11yescharacteristic
679C4—52no—
680C4—61no—
681C4—62no—
682C4—61no—
683C4—202no—
684C4—201no—
685C4—201no—
686C4—301no—
687C4—302no—
688C4—301no—
689C4—601no—
690C4—602no—
691C4—601no—
692C4#9192312yes—
693C3#1061717611yescharacteristic, complemented, Sylow
694C2—42no—
695C2—51no—
696C2—51no—
697C2—51no—
698C2—51no—
699C2—202no—
700C2#1175684511yescharacteristic
701C2#1175684611yescharacteristic
702C2C2×#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#2319
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. #11752028C2semidirect
5. #11752018C2semidirect
6. #11752017C2semidirect
7. #11751984C2semidirect
8. #11751861C2semidirect
9. #11751859C2semidirect
10. Dic3×C4⋊AGL(1,𝔽5)C2semidirect
11. #11751748C2semidirect
26. D4×Dic15C4semidirect
27. C5×D4×Dic3C4semidirect
28. #91559C4semidirect
29. Dic3×C22⋊D5C4semidirect
31. #91434C4semidirect
32. Dic3×D20C4semidirect
203. D4×Dic3AGL(1,𝔽5)semidirect
561. C3×C5#2319semidirect
661. C5#76295semidirect
693. C3#10617176semidirect

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
#117520282
#117520182
#117520172
#117519842
#117518612
#117518592
Dic3×C4⋊AGL(1,𝔽5)2
#117517482
#106171763
#762955