Finite Group Databasebeta

← #14280233

Subgroups — #14280233

Order 1920.

952 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91235C211yesmaximal, characteristic
2C2×C3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
3C2×(C2×AGL(1,𝔽5))⋊Dic3C211yesmaximal, characteristic
4C2×(C2×AGL(1,𝔽5))⋊Dic3C211yesmaximal, characteristic
5C2×(C2×AGL(1,𝔽5))⋊Dic3C211yesmaximal, characteristic
6C2×(C2×AGL(1,𝔽5))⋊Dic3C211yesmaximal, characteristic
7D5×C3⋊#95C211yesmaximal, characteristic
8#10603803—31nomaximal, Hall
9C23×ΓL(1,𝔽16)C2211yescharacteristic
10C23×ΓL(1,𝔽16)C2211yescharacteristic
11C23×C3×AGL(1,𝔽5)C2211yescharacteristic
12C23×C3×AGL(1,𝔽5)C2211yescharacteristic
13C22×C3×C4×D5C2211yescharacteristic
14C22×D5×Dic3C2211yescharacteristic
15C22×D5×Dic3C2211yescharacteristic
16#91235—22no—
17C3×(C2×AGL(1,𝔽5))⋊C4—22no—
18(C2×AGL(1,𝔽5))⋊Dic3—22no—
19(C2×AGL(1,𝔽5))⋊Dic3—22no—
20(C2×AGL(1,𝔽5))⋊Dic3—22no—
21(C2×AGL(1,𝔽5))⋊Dic3—22no—
22#91115C411yescharacteristic, complemented
23C5×C3⋊#95C411yescharacteristic, complemented
24#90994C411yescharacteristic, complemented
25#90994C411yescharacteristic, complemented
26#69418—51nomaximal, Hall
27C2×(C2×AGL(1,𝔽5))⋊C4—31no—
28C2×(C2×AGL(1,𝔽5))⋊C4—31no—
29C2×(C2×AGL(1,𝔽5))⋊C4—31no—
30C2×(C2×AGL(1,𝔽5))⋊C4—31no—
31C2×(C2×AGL(1,𝔽5))⋊C4—31no—
32C2×(C2×AGL(1,𝔽5))⋊C4D311yescharacteristic
33D5×#95—31no—
34C23×C3×D5C2311yescharacteristic
35C22×ΓL(1,𝔽16)—21no—
36C22×ΓL(1,𝔽16)—21no—
37C22×ΓL(1,𝔽16)—21no—
38C22×ΓL(1,𝔽16)—21no—
39C22×ΓL(1,𝔽16)—21no—
40C22×ΓL(1,𝔽16)—21no—
41C22×ΓL(1,𝔽16)—21no—
42C22×ΓL(1,𝔽16)—21no—
43C22×ΓL(1,𝔽16)—21no—
44C22×ΓL(1,𝔽16)—21no—
45C22×ΓL(1,𝔽16)—21no—
46C22×ΓL(1,𝔽16)—21no—
47C22×ΓL(1,𝔽16)D412yes—
48C22×ΓL(1,𝔽16)Q812yes—
49C22×C3×AGL(1,𝔽5)—21no—
50C22×C3×AGL(1,𝔽5)—21no—
51C22×C3×AGL(1,𝔽5)—21no—
52C22×C3×AGL(1,𝔽5)—21no—
53C22×C3×AGL(1,𝔽5)—21no—
54C22×C3×AGL(1,𝔽5)—21no—
55C22×C3×AGL(1,𝔽5)—21no—
56C22×C3×AGL(1,𝔽5)—21no—
57C22×C3×AGL(1,𝔽5)—21no—
58C22×C3×AGL(1,𝔽5)—21no—
59C22×C3×AGL(1,𝔽5)—21no—
60C22×C3×AGL(1,𝔽5)—21no—
61C22×C3×AGL(1,𝔽5)D412yes—
62C22×C3×AGL(1,𝔽5)D412yes—
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—21no—
70C2×C3×C4×D5—21no—
71C2×C3×C4×D5—21no—
72C2×C3×C4×D5—21no—
73C2×C3×C4×D5—21no—
74C2×C3×C4×D5—21no—
75C2×D5×Dic3—21no—
76C2×D5×Dic3—21no—
77C2×D5×Dic3—21no—
78C2×D5×Dic3—21no—
79C2×D5×Dic3—21no—
80C2×D5×Dic3—21no—
81C2×D5×Dic3—21no—
82C2×D5×Dic3—21no—
83C2×D5×Dic3—21no—
84C2×D5×Dic3—21no—
85C2×D5×Dic3—21no—
86C2×D5×Dic3—21no—
87C2×C3×#95—51no—
88C2×C3⋊#95—51no—
89C2×C3⋊#95—51no—
90C2×C3⋊#95—51no—
91C2×C3⋊#95—51no—
92C2×C3⋊#95—51no—
93C2×C3⋊#95—51no—
94C23×AGL(1,𝔽5)—31no—
95C23×AGL(1,𝔽5)—31no—
96C23×AGL(1,𝔽5)C2×D311yescharacteristic
97C23×AGL(1,𝔽5)C2×D311yescharacteristic
98C22×C4×D5—31no—
99C22×C4×D5—31no—
100C22×C4×D5C2×D311yescharacteristic
101(C2×AGL(1,𝔽5))⋊C4—22no—
102(C2×AGL(1,𝔽5))⋊C4—62no—
103(C2×AGL(1,𝔽5))⋊C4—62no—
104(C2×AGL(1,𝔽5))⋊C4—62no—
105(C2×AGL(1,𝔽5))⋊C4—62no—
106(C2×AGL(1,𝔽5))⋊C4—62no—
107C5×#95—31no—
108#3963—31no—
109#3963—31no—
110#3963—31no—
111#1443—151noSylow
112C23×C3×C5C22×C411yescharacteristic
113C22×C3×D5C2×D411yescharacteristic
114C22×C3×D5C2×D411yescharacteristic
115C22×C3×D5C2×D411yescharacteristic
116C22×C3×D5C2×Q811yescharacteristic
117C22×C3×D5#4111yescharacteristic
118C22×C3×D5#4111yescharacteristic
119C22×C3×D5#4111yescharacteristic
120C22×C3×D5#4111yescharacteristic
121C22×C3×D5#4111yescharacteristic
122C22×C3×D5#4111yescharacteristic
123C22×C3×D5#4111yescharacteristic
124C22×C3×D5#4111yescharacteristic
125C22×C3×D5#4111yescharacteristic
126C22×C3×D5#4111yescharacteristic
127C2×ΓL(1,𝔽16)—22no—
128C2×ΓL(1,𝔽16)—22no—
129C2×ΓL(1,𝔽16)—22no—
130C2×ΓL(1,𝔽16)—22no—
131C2×ΓL(1,𝔽16)—22no—
132C2×ΓL(1,𝔽16)—22no—
133C2×ΓL(1,𝔽16)—41no—
134C2×ΓL(1,𝔽16)—41no—
135C2×ΓL(1,𝔽16)—41no—
136C2×ΓL(1,𝔽16)—41no—
137C2×ΓL(1,𝔽16)—41no—
138C2×ΓL(1,𝔽16)—41no—
139C2×ΓL(1,𝔽16)—41no—
140C2×ΓL(1,𝔽16)—41no—
141C2×C3×AGL(1,𝔽5)—22no—
142C2×C3×AGL(1,𝔽5)—22no—
143C2×C3×AGL(1,𝔽5)—22no—
144C2×C3×AGL(1,𝔽5)—22no—
145C2×C3×AGL(1,𝔽5)—22no—
146C2×C3×AGL(1,𝔽5)—22no—
147C2×C3×AGL(1,𝔽5)—41no—
148C2×C3×AGL(1,𝔽5)—41no—
149C2×C3×AGL(1,𝔽5)—41no—
150C2×C3×AGL(1,𝔽5)—41no—
151C2×C3×AGL(1,𝔽5)—41no—
152C2×C3×AGL(1,𝔽5)—41no—
153C2×C3×AGL(1,𝔽5)—41no—
154C2×C3×AGL(1,𝔽5)—41no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—21no—
157C2×C3×C4×C5—21no—
158C2×Dic15—21no—
159C2×Dic15—21no—
160C2×Dic15—21no—
161C2×Dic15—21no—
162C2×Dic15—21no—
163C2×Dic15—21no—
164C2×C5×Dic3—21no—
165C2×C5×Dic3—21no—
166C2×C5×Dic3—21no—
167C2×C5×Dic3—21no—
168C2×C5×Dic3—21no—
169C2×C5×Dic3—21no—
170C2×C3×Dic5—21no—
171C2×C3×Dic5—21no—
172C2×C3×Dic5—21no—
173C3×C4×D5—41no—
174C3×C4×D5—41no—
175C3×C4×D5—41no—
176C3×C4×D5—41no—
177D5×Dic3—41no—
178D5×Dic3—41no—
179D5×Dic3—41no—
180D5×Dic3—41no—
181D5×Dic3—41no—
182D5×Dic3—41no—
183D5×Dic3—41no—
184D5×Dic3—41no—
185C23×C3×C4—51no—
186C23×C3×C4—51no—
187C23×C3×C4—51no—
188C23×Dic3—51no—
189C23×Dic3—51no—
190C23×Dic3—51no—
191C23×Dic3—51no—
192C3×#95—102no—
193C3⋊#95—51no—
194C3⋊#95—51no—
195C3⋊#95—51no—
196C3⋊#95—102no—
197C3⋊#95—102no—
198C3⋊#95—102no—
199C3⋊#95—102no—
200C3⋊#95—102no—
201C3⋊#95AGL(1,𝔽5)11yescharacteristic, complemented
202C23×D5C22×D311yescharacteristic
203C22×AGL(1,𝔽5)—21no—
204C22×AGL(1,𝔽5)—21no—
205C22×AGL(1,𝔽5)—21no—
206C22×AGL(1,𝔽5)—21no—
207C22×AGL(1,𝔽5)—21no—
208C22×AGL(1,𝔽5)—21no—
209C22×AGL(1,𝔽5)—21no—
210C22×AGL(1,𝔽5)—21no—
211C22×AGL(1,𝔽5)—21no—
212C22×AGL(1,𝔽5)—21no—
213C22×AGL(1,𝔽5)—21no—
214C22×AGL(1,𝔽5)—21no—
215C22×AGL(1,𝔽5)—32no—
216C22×AGL(1,𝔽5)—32no—
217C22×AGL(1,𝔽5)—61no—
218C22×AGL(1,𝔽5)—61no—
219C22×AGL(1,𝔽5)—61no—
220C22×AGL(1,𝔽5)—61no—
221C22×AGL(1,𝔽5)—61no—
222C22×AGL(1,𝔽5)—61no—
223C22×AGL(1,𝔽5)—61no—
224C22×AGL(1,𝔽5)—61no—
225C22×AGL(1,𝔽5)—61no—
226C22×AGL(1,𝔽5)—61no—
227C22×AGL(1,𝔽5)—61no—
228C22×AGL(1,𝔽5)—61no—
229C22×AGL(1,𝔽5)D1212yes—
230C22×AGL(1,𝔽5)#6712yes—
231C22×C4×C5—31no—
232C22×C4×C5—31no—
233C22×C4×C5C4×D311yescharacteristic
234C22×Dic5—31no—
235C22×Dic5—31no—
236C22×Dic5C4×D311yescharacteristic
237C2×C4×D5—21no—
238C2×C4×D5—21no—
239C2×C4×D5—21no—
240C2×C4×D5—21no—
241C2×C4×D5—21no—
242C2×C4×D5—21no—
243C2×C4×D5—61no—
244C2×C4×D5—61no—
245C2×C4×D5—61no—
246C2×C4×D5—61no—
247C2×C4×D5—61no—
248C2×C4×D5—61no—
249C2×C4×D5—61no—
250C2×C4×D5—61no—
251C2×C4×D5—61no—
252C2×C4×D5—61no—
253C2×C4×D5—61no—
254C2×C4×D5—61no—
255C2×#95—51no—
256C2×#95—151no—
257C2×#95—151no—
258C2×#95—151no—
259C2×#95—151no—
260C2×#95—151no—
261C2×#95—151no—
262C22×C3×C5#11711yescharacteristic
263C22×C3×C5#11711yescharacteristic
264C22×C3×C5#11711yescharacteristic
265C22×C3×C5C4×D411yescharacteristic
266C22×C3×C5C4×D411yescharacteristic
267C22×C3×C5C4×D411yescharacteristic
268C22×C3×C5C4×Q811yescharacteristic
269C2×C3×D5#12111yescharacteristic
270C2×C3×D5#12111yescharacteristic
271C2×C3×D5#12111yescharacteristic
272C2×C3×D5C22⋊Q811yescharacteristic
273C2×C3×D5C22⋊Q811yescharacteristic
274C2×C3×D5C22⋊Q811yescharacteristic
275C2×C3×D5#12311yescharacteristic
276C2×C3×D5#12311yescharacteristic
277C2×C3×D5#12311yescharacteristic
278C2×C3×D5#12311yescharacteristic
279C2×C3×D5#12311yescharacteristic
280C2×C3×D5#12311yescharacteristic
281C2×C3×D5#12411yescharacteristic
282C2×C3×D5#12411yescharacteristic
283C2×C3×D5#12411yescharacteristic
284C2×C3×D5#12511yescharacteristic
285C2×C3×D5#12511yescharacteristic
286C2×C3×D5#12511yescharacteristic
287C2×C3×D5#12611yescharacteristic
288C2×C3×D5#12611yescharacteristic
289C2×C3×D5#12611yescharacteristic
290C2×C3×D5#12611yescharacteristic
291C2×C3×D5#12611yescharacteristic
292C2×C3×D5#12611yescharacteristic
293C2×C3×D5#12611yescharacteristic
294C2×C3×D5#12611yescharacteristic
295C2×C3×D5#12611yescharacteristic
296C2×C3×D5#12611yescharacteristic
297ΓL(1,𝔽16)—42no—
298ΓL(1,𝔽16)—42no—
299C3×AGL(1,𝔽5)—42no—
300C3×AGL(1,𝔽5)—42no—
301C3×C4×C5—41no—
302Dic15—41no—
303Dic15—41no—
304C3×Dic5—41no—
305C5×Dic3—41no—
306C5×Dic3—41no—
307C24×C3—51no—
308C22×C3×C4—52no—
309C22×C3×C4—52no—
310C22×C3×C4—51no—
311C22×C3×C4—101no—
312C22×C3×C4—101no—
313C22×C3×C4—101no—
314C22×C3×C4—101no—
315C22×C3×C4—101no—
316C22×C3×C4—101no—
317C22×C3×C4—101no—
318C22×C3×C4—101no—
319C22×C3×C4—101no—
320C22×C3×C4—101no—
321C22×C3×C4—101no—
322C22×C3×C4—101no—
323C22×C3×C4—101no—
324C22×C3×C4—101no—
325C22×C3×C4—101no—
326C22×C3×C4—101no—
327C22×C3×C4—101no—
328C22×C3×C4—101no—
329C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
330C22×Dic3—52no—
331C22×Dic3—52no—
332C22×Dic3—51no—
333C22×Dic3—51no—
334C22×Dic3—101no—
335C22×Dic3—101no—
336C22×Dic3—101no—
337C22×Dic3—101no—
338C22×Dic3—101no—
339C22×Dic3—101no—
340C22×Dic3—101no—
341C22×Dic3—101no—
342C22×Dic3—101no—
343C22×Dic3—101no—
344C22×Dic3—101no—
345C22×Dic3—101no—
346C22×Dic3—101no—
347C22×Dic3—101no—
348C22×Dic3—101no—
349C22×Dic3—101no—
350C22×Dic3—101no—
351C22×Dic3—101no—
352C22×Dic3—101no—
353C22×Dic3—101no—
354C22×Dic3—101no—
355C22×Dic3—101no—
356C22×Dic3—101no—
357C22×Dic3—101no—
358C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
359C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
360C23×C5C2×C4×D311yescharacteristic
361C22×D5C2×D1211yescharacteristic
362C22×D5#23511yescharacteristic
363C22×D5#23511yescharacteristic
364C22×D5#23511yescharacteristic
365C22×D5#23511yescharacteristic
366C22×D5D3×D411yescharacteristic
367C22×D5#23711yescharacteristic
368C22×D5#23711yescharacteristic
369C22×D5#23711yescharacteristic
370C22×D5#23711yescharacteristic
371C22×D5#23711yescharacteristic
372C22×D5D3×Q811yescharacteristic
373C22×D5#23911yescharacteristic
374C22×D5C2×#6711yescharacteristic
375C2×AGL(1,𝔽5)—22no—
376C2×AGL(1,𝔽5)—22no—
377C2×AGL(1,𝔽5)—22no—
378C2×AGL(1,𝔽5)—22no—
379C2×AGL(1,𝔽5)—22no—
380C2×AGL(1,𝔽5)—22no—
381C2×AGL(1,𝔽5)—41no—
382C2×AGL(1,𝔽5)—41no—
383C2×AGL(1,𝔽5)—41no—
384C2×AGL(1,𝔽5)—41no—
385C2×AGL(1,𝔽5)—41no—
386C2×AGL(1,𝔽5)—41no—
387C2×AGL(1,𝔽5)—41no—
388C2×AGL(1,𝔽5)—41no—
389C2×AGL(1,𝔽5)—62no—
390C2×AGL(1,𝔽5)—62no—
391C2×AGL(1,𝔽5)—62no—
392C2×AGL(1,𝔽5)—62no—
393C2×AGL(1,𝔽5)—62no—
394C2×AGL(1,𝔽5)—62no—
395C2×AGL(1,𝔽5)—121no—
396C2×AGL(1,𝔽5)—121no—
397C2×AGL(1,𝔽5)—121no—
398C2×AGL(1,𝔽5)—121no—
399C2×AGL(1,𝔽5)—121no—
400C2×AGL(1,𝔽5)—121no—
401C2×AGL(1,𝔽5)—121no—
402C2×AGL(1,𝔽5)—121no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—61no—
407C2×C4×C5—61no—
408C2×C4×C5—61no—
409C2×C4×C5—61no—
410C2×C4×C5—61no—
411C2×C4×C5—61no—
412C2×Dic5—21no—
413C2×Dic5—21no—
414C2×Dic5—21no—
415C2×Dic5—61no—
416C2×Dic5—61no—
417C2×Dic5—61no—
418C2×Dic5—61no—
419C2×Dic5—61no—
420C2×Dic5—61no—
421C4×D5—41no—
422C4×D5—41no—
423C4×D5—41no—
424C4×D5—41no—
425C4×D5—121no—
426C4×D5—121no—
427C4×D5—121no—
428C4×D5—121no—
429C4×D5—121no—
430C4×D5—121no—
431C4×D5—121no—
432C4×D5—121no—
433C23×C4—51no—
434C23×C4—51no—
435C23×C4—51no—
436C23×C4—151no—
437C23×C4—151no—
438C23×C4—151no—
439C23×C4—151no—
440#95—31no—
441#95—102no—
442#95—151no—
443#95—151no—
444#95—151no—
445#95—302no—
446#95—302no—
447#95—302no—
448#95—302no—
449#95—302no—
450C2×C3×C5#38311yescharacteristic
451C2×C3×C5#38711yescharacteristic
452C2×C3×C5#38711yescharacteristic
453C2×C3×C5#38711yescharacteristic
454C2×C3×C5#38811yescharacteristic
455C2×C3×C5#38811yescharacteristic
456C2×C3×C5#38811yescharacteristic
457C3×D5#39611yescharacteristic
458C3×D5#39711yescharacteristic
459C3×D5#39711yescharacteristic
460C3×D5#39711yescharacteristic
461C3×D5#40011yescharacteristic
462C3×D5#40011yescharacteristic
463C3×D5#40011yescharacteristic
464C3×D5#40111yescharacteristic
465C23×C3—51no—
466C23×C3—51no—
467C23×C3—51no—
468C23×C3—51no—
469C23×C3—51no—
470C23×C3—51no—
471C23×C3—51no—
472C23×C3—51no—
473C23×C3—51no—
474C23×C3—51no—
475C23×C3—51no—
476C23×C3—51no—
477C23×C3—51no—
478C23×C3—51no—
479C23×C3C22×AGL(1,𝔽5)11yescharacteristic
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—102no—
484C2×C3×C4—102no—
485C2×C3×C4—102no—
486C2×C3×C4—102no—
487C2×C3×C4—102no—
488C2×C3×C4—102no—
489C2×C3×C4—101no—
490C2×C3×C4—101no—
491C2×C3×C4—101no—
492C2×C3×C4—201no—
493C2×C3×C4—201no—
494C2×C3×C4—201no—
495C2×C3×C4—201no—
496C2×C3×C4—201no—
497C2×C3×C4—201no—
498C2×C3×C4—201no—
499C2×C3×C4—201no—
500C2×C3×C4—201no—
501C2×C3×C4—201no—
502C2×C3×C4—201no—
503C2×C3×C4—201no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—102no—
511C2×Dic3—102no—
512C2×Dic3—102no—
513C2×Dic3—102no—
514C2×Dic3—102no—
515C2×Dic3—102no—
516C2×Dic3—101no—
517C2×Dic3—101no—
518C2×Dic3—101no—
519C2×Dic3—101no—
520C2×Dic3—101no—
521C2×Dic3—101no—
522C2×Dic3—201no—
523C2×Dic3—201no—
524C2×Dic3—201no—
525C2×Dic3—201no—
526C2×Dic3—201no—
527C2×Dic3—201no—
528C2×Dic3—201no—
529C2×Dic3—201no—
530C2×Dic3—201no—
531C2×Dic3—201no—
532C2×Dic3—201no—
533C2×Dic3—201no—
534C2×Dic3—201no—
535C2×Dic3—201no—
536C2×Dic3—201no—
537C2×Dic3—201no—
538C22×C5#87211yescharacteristic
539C22×C5C4×D1211yescharacteristic
540C22×C5#87711yescharacteristic
541C22×C5#67⋊C411yescharacteristic
542C22×C5#88711yescharacteristic
543C22×C5#89211yescharacteristic
544C22×C5C4×#6711yescharacteristic
545C2×D5#87511yescharacteristic
546C2×D5#87611yescharacteristic
547C2×D5#87911yescharacteristic
548C2×D5#87911yescharacteristic
549C2×D5#87911yescharacteristic
550C2×D5#87911yescharacteristic
551C2×D5#87911yescharacteristic
552C2×D5#88311yescharacteristic
553C2×D5#88311yescharacteristic
554C2×D5#88511yescharacteristic
555C2×D5#88611yescharacteristic
556C2×D5#88611yescharacteristic
557C2×D5#88911yescharacteristic
558C2×D5#88911yescharacteristic
559C2×D5#88911yescharacteristic
560C2×D5#89511yescharacteristic
561C2×D5#89611yescharacteristic
562C2×D5#89711yescharacteristic
563C2×D5#89811yescharacteristic
564C2×D5#89811yescharacteristic
565C2×D5#89811yescharacteristic
566C2×D5#89811yescharacteristic
567C2×D5#92911yescharacteristic
568C2×D5#93011yescharacteristic
569C2×D5#93511yescharacteristic
570C2×D5#93611yescharacteristic
571C2×D5#93911yescharacteristic
572C2×D5#94611yescharacteristic
573AGL(1,𝔽5)—42no—
574AGL(1,𝔽5)—42no—
575AGL(1,𝔽5)—122no—
576AGL(1,𝔽5)—122no—
577C4×C5—41no—
578C4×C5—121no—
579C4×C5—121no—
580Dic5—41no—
581Dic5—121no—
582Dic5—121no—
583C24—51no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—52no—
587C22×C4—52no—
588C22×C4—51no—
589C22×C4—101no—
590C22×C4—101no—
591C22×C4—101no—
592C22×C4—101no—
593C22×C4—101no—
594C22×C4—101no—
595C22×C4—101no—
596C22×C4—101no—
597C22×C4—101no—
598C22×C4—101no—
599C22×C4—101no—
600C22×C4—101no—
601C22×C4—101no—
602C22×C4—101no—
603C22×C4—101no—
604C22×C4—101no—
605C22×C4—101no—
606C22×C4—101no—
607C22×C4—152no—
608C22×C4—152no—
609C22×C4—151no—
610C22×C4—151no—
611C22×C4—301no—
612C22×C4—301no—
613C22×C4—301no—
614C22×C4—301no—
615C22×C4—301no—
616C22×C4—301no—
617C22×C4—301no—
618C22×C4—301no—
619C22×C4—301no—
620C22×C4—301no—
621C22×C4—301no—
622C22×C4—301no—
623C22×C4—301no—
624C22×C4—301no—
625C22×C4—301no—
626C22×C4—301no—
627C22×C4—301no—
628C22×C4—301no—
629C22×C4—301no—
630C22×C4—301no—
631C22×C4—301no—
632C22×C4—301no—
633C22×C4—301no—
634C22×C4—301no—
635C22×C4D3×AGL(1,𝔽5)11yescharacteristic
636C3×C5#144311yescharacteristic, complemented, Hall
637C22×C3—51no—
638C22×C3—51no—
639C22×C3—51no—
640C22×C3—51no—
641C22×C3—51no—
642C22×C3—51no—
643C22×C3—51no—
644C22×C3—51no—
645C22×C3—51no—
646C22×C3—51no—
647C22×C3—51no—
648C22×C3—51no—
649C22×C3—51no—
650C22×C3—51no—
651C22×C3—51no—
652C22×C3—51no—
653C22×C3—51no—
654C22×C3—51no—
655C22×C3—51no—
656C22×C3—51no—
657C22×C3—51no—
658C22×C3—51no—
659C22×C3—51no—
660C22×C3—51no—
661C22×C3—51no—
662C22×C3—51no—
663C22×C3—51no—
664C22×C3—51no—
665C22×C3#413011yescharacteristic
666C22×C3#413011yescharacteristic
667C22×C3#413011yescharacteristic
668C22×C3D4×AGL(1,𝔽5)11yescharacteristic
669C22×C3D4×AGL(1,𝔽5)11yescharacteristic
670C22×C3D4×AGL(1,𝔽5)11yescharacteristic
671C22×C3Q8×AGL(1,𝔽5)11yescharacteristic
672C3×C4—41no—
673C3×C4—202no—
674C3×C4—202no—
675C3×C4—201no—
676Dic3—41no—
677Dic3—41no—
678Dic3—202no—
679Dic3—202no—
680Dic3—201no—
681Dic3—201no—
682C2×C5#465111yescharacteristic
683C2×C5#465211yescharacteristic
684C2×C5#465311yescharacteristic
685C2×C5#467011yescharacteristic
686C2×C5#494011yescharacteristic
687C2×C5#494511yescharacteristic
688C2×C5#497811yescharacteristic
689D5#465811yescharacteristic
690D5#465911yescharacteristic
691D5C3⋊#40111yescharacteristic
692D5#467411yescharacteristic
693D5#495211yescharacteristic
694D5#495311yescharacteristic
695D5#498511yescharacteristic
696D5#499411yescharacteristic
697C23—51no—
698C23—51no—
699C23—51no—
700C23—51no—
701C23—51no—
702C23—51no—
703C23—51no—
704C23—51no—
705C23—51no—
706C23—51no—
707C23—51no—
708C23—51no—
709C23—51no—
710C23—51no—
711C23C2×D3×AGL(1,𝔽5)11yescharacteristic
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—102no—
724C2×C4—102no—
725C2×C4—102no—
726C2×C4—102no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—201no—
731C2×C4—201no—
732C2×C4—201no—
733C2×C4—201no—
734C2×C4—201no—
735C2×C4—201no—
736C2×C4—201no—
737C2×C4—201no—
738C2×C4—201no—
739C2×C4—201no—
740C2×C4—201no—
741C2×C4—201no—
742C2×C4—302no—
743C2×C4—302no—
744C2×C4—302no—
745C2×C4—302no—
746C2×C4—302no—
747C2×C4—302no—
748C2×C4—301no—
749C2×C4—301no—
750C2×C4—301no—
751C2×C4—301no—
752C2×C4—301no—
753C2×C4—301no—
754C2×C4—601no—
755C2×C4—601no—
756C2×C4—601no—
757C2×C4—601no—
758C2×C4—601no—
759C2×C4—601no—
760C2×C4—601no—
761C2×C4—601no—
762C2×C4—601no—
763C2×C4—601no—
764C2×C4—601no—
765C2×C4—601no—
766C2×C4—601no—
767C2×C4—601no—
768C2×C4—601no—
769C2×C4—601no—
770C2×C3—51no—
771C2×C3—51no—
772C2×C3—51no—
773C2×C3—51no—
774C2×C3—51no—
775C2×C3—51no—
776C2×C3—51no—
777C2×C3—51no—
778C2×C3#6569011yescharacteristic
779C2×C3#6570011yescharacteristic
780C2×C3#6570011yescharacteristic
781C2×C3#6570011yescharacteristic
782C2×C3#6571111yescharacteristic
783C2×C3#6571111yescharacteristic
784C2×C3#6571111yescharacteristic
785C5#6941811yescharacteristic, complemented, Sylow
786C22—51no—
787C22—51no—
788C22—51no—
789C22—51no—
790C22—51no—
791C22—51no—
792C22—51no—
793C22—51no—
794C22—51no—
795C22—51no—
796C22—51no—
797C22—51no—
798C22—51no—
799C22—51no—
800C22—51no—
801C22—51no—
802C22—51no—
803C22—51no—
804C22—51no—
805C22—51no—
806C22—51no—
807C22—51no—
808C22—51no—
809C22—51no—
810C22—51no—
811C22—51no—
812C22—51no—
813C22—51no—
814C22#9190711yescharacteristic
815C22ΓL(1,𝔽16)⋊Q811yescharacteristic
816C22#9190911yescharacteristic
817C22AGL(1,𝔽5)×D1211yescharacteristic
818C22#9192311yescharacteristic
819C22AGL(1,𝔽5)×#6711yescharacteristic
820C22#67⋊AGL(1,𝔽5)11yescharacteristic
821C4—41no—
822C4—121no—
823C4—121no—
824C4—202no—
825C4—202no—
826C4—201no—
827C4—602no—
828C4—602no—
829C4—601no—
830C4—601no—
831C3#1060380311yescharacteristic, complemented, Sylow
832C2—51no—
833C2—51no—
834C2—51no—
835C2—51no—
836C2—51no—
837C2—51no—
838C2—51no—
839C2—51no—
840C2#1175174711yescharacteristic
841C2#1175175011yescharacteristic
842C2#1175183511yescharacteristic
843C2#1175183911yescharacteristic
844C2#1175184111yescharacteristic
845C2#1175184911yescharacteristic
846C2#1175201811yescharacteristic
subgroupG/H
center, FrattiniC23C2×D3×AGL(1,𝔽5)
commutator, socleC23×C3×C5C22×C4
FittingC22×C3×C4×C5C2×C4
prime radical, cosocleC23×C3×D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1443
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
22. #91115C4semidirect
23. C5×C3⋊#95C4semidirect
24. #90994C4semidirect
25. #90994C4semidirect
201. C3⋊#95AGL(1,𝔽5)semidirect
636. C3×C5#1443semidirect
785. C5#69418semidirect
831. C3#10603803semidirect

Maximal subgroups

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

subgroupindex
C2×#912352
C2×C3×(C2×AGL(1,𝔽5))⋊C42
C2×(C2×AGL(1,𝔽5))⋊Dic32
D5×C3⋊#952
#106038033
#694185