Finite Group Databasebeta

← #14327262

Subgroups — #14327262

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×ΓL(1,𝔽16)⋊Q8C211yesmaximal, characteristic
2C2×AGL(1,𝔽5)×Dic6C211yesmaximal, characteristic
3D5×#887C211yesmaximal, characteristic
4#11752371C211yesmaximal, characteristic
5C3×#65712C211yesmaximal, characteristic
6#11751860C212yesmaximal
7#11751860C211yesmaximal, characteristic
8C4×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic
9#11751844C212yesmaximal
10#11751837C212yesmaximal
11#11751834C212yesmaximal
12Q8×C4⋊AGL(1,𝔽5)—31nomaximal, Hall
13C2×D5×Dic6C2211yescharacteristic
14C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
15C2×C4⋊ΓL(1,𝔽16)C2212yes—
16C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
17C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
18C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
19C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
20C2×Dic3⋊AGL(1,𝔽5)C2212yes—
21C2×Dic3⋊AGL(1,𝔽5)C2212yes—
22C2×Dic3⋊AGL(1,𝔽5)C2212yes—
23C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
24C2×Dic3⋊AGL(1,𝔽5)C2212yes—
25C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
26C2×Dic3×AGL(1,𝔽5)C2212yes—
27C2×Dic3×AGL(1,𝔽5)C2212yes—
28ΓL(1,𝔽16)⋊Q8—24no—
29AGL(1,𝔽5)×Dic6—24no—
30#91776C411yescharacteristic, complemented
31C5×#887C411yescharacteristic, complemented
32C3×D5×C4⋊C4C2211yescharacteristic
33D5×Dic3⋊C4C2212yes—
34C4×D5×Dic3C2212yes—
35C4×D5×Dic3C2211yescharacteristic
36#91344C411yescharacteristic, complemented
37#91340C411yescharacteristic, complemented
38#91325C412yescomplemented
39#91324C412yescomplemented
40#91235C2212yes—
41C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
42(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
43(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
44#75981—51nomaximal, Hall
45C2×Q8×AGL(1,𝔽5)—31no—
46C2×Q8×AGL(1,𝔽5)—31no—
47C4×Q8×D5—31no—
48#65712—31no—
49#65712—32no—
50#65712—32no—
51#65712D311yescharacteristic
52#65688—32no—
53#65688—31no—
54C4×C4⋊AGL(1,𝔽5)—32no—
55C4×C4⋊AGL(1,𝔽5)—31no—
56C22×ΓL(1,𝔽16)C2312yes—
57C22×ΓL(1,𝔽16)C2311yescharacteristic
58C22×ΓL(1,𝔽16)C2311yescharacteristic
59C22×C3×AGL(1,𝔽5)C2312yes—
60C22×C3×AGL(1,𝔽5)C2311yescharacteristic
61C22×C3×AGL(1,𝔽5)C2311yescharacteristic
62C2×Dic30C2×C411yescharacteristic
63C2×C5×Dic6C2×C411yescharacteristic
64C2×C3×C4×D5C2312yes—
65C2×C3×C4×D5C2311yescharacteristic
66C2×#1204C2×C412yes—
67C2×D5×Dic3C2311yescharacteristic
68C2×D5×Dic3C2312yes—
69C2×D5×Dic3C2311yescharacteristic
70D5×Dic6D414yes—
71D5×Dic6Q814yes—
72C4⋊ΓL(1,𝔽16)—22no—
73C4⋊ΓL(1,𝔽16)—42no—
74C4×ΓL(1,𝔽16)—22no—
75C3×C4⋊AGL(1,𝔽5)—22no—
76C3×C4⋊AGL(1,𝔽5)—42no—
77C3×C4×AGL(1,𝔽5)—22no—
78Dic3⋊AGL(1,𝔽5)—24no—
79Dic3⋊AGL(1,𝔽5)—24no—
80Dic3⋊AGL(1,𝔽5)—24no—
81Dic3⋊AGL(1,𝔽5)—22no—
82Dic3⋊AGL(1,𝔽5)—42no—
83Dic3⋊AGL(1,𝔽5)Q814yescomplemented
84Dic3×AGL(1,𝔽5)—24no—
85Dic3×AGL(1,𝔽5)—24no—
86C3×C5×C4⋊C4C2×C411yescharacteristic
87#6712C2×C412yes—
88C4×Dic15C2×C412yes—
89C4×Dic15C2×C411yescharacteristic
90C5×Dic3⋊C4C2×C412yes—
91C4×C5×Dic3C2×C412yes—
92C4×C5×Dic3C2×C411yescharacteristic
93C3×C4⋊Dic5C2×C411yescharacteristic
94C3×#683C2×C412yes—
95Dic3⋊Dic5C2×C412yes—
96#6669C2×C412yes—
97Dic3×Dic5C2×C411yescharacteristic
98Dic3×Dic5C2×C412yes—
99Dic3×Dic5C2×C411yescharacteristic
100Dic3×Dic5C2×C412yes—
101C2×#887—51no—
102C2×#887—51no—
103C2×C4×Dic6—51no—
104C3×#389—51no—
105#4984—51no—
106#4976—52no—
107#4975—52no—
108#4975—51no—
109C4×Dic3⋊C4—51no—
110#4649—52no—
111#4647—52no—
112C2×Q8×D5—31no—
113Q8×AGL(1,𝔽5)—64no—
114Q8×AGL(1,𝔽5)—64no—
115C2×C4⋊AGL(1,𝔽5)—31no—
116C2×C4⋊AGL(1,𝔽5)—32no—
117C2×C4⋊AGL(1,𝔽5)—31no—
118C2×C4⋊AGL(1,𝔽5)—32no—
119C2×C4⋊AGL(1,𝔽5)—32no—
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
124C2×C4⋊AGL(1,𝔽5)C2×D312yes—
125C2×C4×AGL(1,𝔽5)—32no—
126C2×C4×AGL(1,𝔽5)—32no—
127C2×C4×AGL(1,𝔽5)—31no—
128C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
129C4×C5×Q8—31no—
130Q8×Dic5—31no—
131D5×C4⋊C4—32no—
132D5×C4⋊C4C2×D311yescharacteristic
133#4033—31no—
134#4033—32no—
135C42×D5—32no—
136C42×D5—31no—
137C4×Dic10—31no—
138C4×Dic10—32no—
139(C2×AGL(1,𝔽5))⋊C4—31no—
140(C2×AGL(1,𝔽5))⋊C4—31no—
141(C2×AGL(1,𝔽5))⋊C4—32no—
142(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
143Q8×C4⋊C4—151noSylow
144C22×C3×D5C2411yescharacteristic
145C2×ΓL(1,𝔽16)—21no—
146C2×ΓL(1,𝔽16)—21no—
147C2×ΓL(1,𝔽16)—22no—
148C2×ΓL(1,𝔽16)—21no—
149C2×ΓL(1,𝔽16)—22no—
150C2×ΓL(1,𝔽16)—21no—
151C2×ΓL(1,𝔽16)—22no—
152C2×ΓL(1,𝔽16)—21no—
153C2×ΓL(1,𝔽16)C2×Q812yes—
154C2×C3×AGL(1,𝔽5)—21no—
155C2×C3×AGL(1,𝔽5)—21no—
156C2×C3×AGL(1,𝔽5)—22no—
157C2×C3×AGL(1,𝔽5)—21no—
158C2×C3×AGL(1,𝔽5)—22no—
159C2×C3×AGL(1,𝔽5)—21no—
160C2×C3×AGL(1,𝔽5)—22no—
161C2×C3×AGL(1,𝔽5)—21no—
162C2×C3×AGL(1,𝔽5)C2×Q812yes—
163C2×C3×C4×C5C22×C412yes—
164C2×C3×C4×C5C22×C411yescharacteristic
165C2×Dic15C22×C411yescharacteristic
166C2×Dic15C22×C412yes—
167C2×Dic15C22×C411yescharacteristic
168Dic30C4⋊C414yescomplemented
169C2×C5×Dic3C22×C411yescharacteristic
170C2×C5×Dic3C22×C412yes—
171C2×C5×Dic3C22×C411yescharacteristic
172C5×Dic6C4⋊C414yescomplemented
173C2×C3×Dic5C22×C412yes—
174C2×C3×Dic5C22×C411yescharacteristic
175C3×C4×D5—22no—
176C3×C4×D5—22no—
177C3×C4×D5C2×D412yes—
178C3×C4×D5C2×Q812yes—
179#1204C4⋊C418yescomplemented
180D5×Dic3—21no—
181D5×Dic3—21no—
182D5×Dic3C2×D414yes—
183D5×Dic3C2×Q814yes—
184D5×Dic3C2×Q812yes—
185D5×Dic3#4112yes—
186C22×Dic6—51no—
187C2×C3×C4⋊C4—51no—
188C2×C3×C4⋊C4—51no—
189C2×C3×C4⋊C4—52no—
190C2×C3×C42—51no—
191C2×C4⋊Dic3—51no—
192C2×C4⋊Dic3—52no—
193C2×Dic3⋊C4—51no—
194C2×Dic3⋊C4—52no—
195C2×Dic3⋊C4—52no—
196C2×Dic3⋊C4—52no—
197C2×Dic3⋊C4—51no—
198C2×Dic3⋊C4—52no—
199C2×Dic3⋊C4—52no—
200C2×C4×Dic3—52no—
201C2×C4×Dic3—51no—
202C2×C4×Dic3—52no—
203C2×C4×Dic3—52no—
204C2×C4×Dic3—51no—
205#887—51no—
206#887—51no—
207#887—52no—
208#887—52no—
209#887—51no—
210#887—104no—
211#887AGL(1,𝔽5)11yescharacteristic, complemented
212C4×Dic6—104no—
213C3×#95—52no—
214C3⋊#95—51no—
215C3⋊#95—51no—
216C3⋊#95—52no—
217C22×AGL(1,𝔽5)—31no—
218C22×AGL(1,𝔽5)—32no—
219C22×AGL(1,𝔽5)—31no—
220C22×AGL(1,𝔽5)C22×D312yes—
221C22×AGL(1,𝔽5)C22×D311yescharacteristic
222C22×AGL(1,𝔽5)C22×D311yescharacteristic
223C2×C5×Q8—31no—
224Q8×D5—34no—
225Q8×D5—34no—
226C2×C4×D5—32no—
227C2×C4×D5—31no—
228C2×C4×D5—31no—
229C2×C4×D5C22×D312yes—
230C2×C4×D5C22×D311yescharacteristic
231C2×Dic10—31no—
232C2×Dic10—32no—
233C4⋊AGL(1,𝔽5)—22no—
234C4⋊AGL(1,𝔽5)—34no—
235C4⋊AGL(1,𝔽5)—42no—
236C4⋊AGL(1,𝔽5)—64no—
237C4⋊AGL(1,𝔽5)—64no—
238C4⋊AGL(1,𝔽5)—64no—
239C4⋊AGL(1,𝔽5)—62no—
240C4⋊AGL(1,𝔽5)—62no—
241C4⋊AGL(1,𝔽5)—122no—
242C4⋊AGL(1,𝔽5)—122no—
243C4×AGL(1,𝔽5)—22no—
244C4×AGL(1,𝔽5)—64no—
245C4×AGL(1,𝔽5)—64no—
246C4×AGL(1,𝔽5)—62no—
247C5×C4⋊C4—32no—
248C5×C4⋊C4C4×D311yescharacteristic
249C42×C5—32no—
250C42×C5—31no—
251C4⋊Dic5—32no—
252C4⋊Dic5C4×D311yescharacteristic
253#683—32no—
254#683—32no—
255#683C4×D312yes—
256C4×Dic5—32no—
257C4×Dic5—31no—
258C4×Dic5—32no—
259C4×Dic5—31no—
260C4×Dic5—31no—
261C4×Dic5—32no—
262C2×C4×Q8—151no—
263C2×C4×Q8—151no—
264C2×C4×Q8—151no—
265#389—51no—
266#389—152no—
267#389—152no—
268#389—151no—
269#384—151no—
270#384—152no—
271C4×C4⋊C4—152no—
272C4×C4⋊C4—151no—
273C22×C3×C5C23×C411yescharacteristic
274C2×C3×D5C22×D411yescharacteristic
275C2×C3×D5C22×Q811yescharacteristic
276C2×C3×D5C22×Q811yescharacteristic
277C2×C3×D5C2×#4111yescharacteristic
278C2×C3×D5H(5,𝔽2)11yescharacteristic
279C2×C3×D52−1+411yescharacteristic
280ΓL(1,𝔽16)—22no—
281ΓL(1,𝔽16)—42no—
282ΓL(1,𝔽16)—41no—
283C3×AGL(1,𝔽5)—22no—
284C3×AGL(1,𝔽5)—42no—
285C3×AGL(1,𝔽5)—41no—
286C3×C4×C5—22no—
287C3×C4×C5C2×C4⋊C412yes—
288Dic15—21no—
289Dic15C2×C4⋊C414yes—
290Dic15C4×Q812yescomplemented
291C3×Dic5—22no—
292C3×Dic5C2×C4⋊C412yes—
293C5×Dic3—21no—
294C5×Dic3C2×C4⋊C414yes—
295C5×Dic3C4×Q812yescomplemented
296C22×C3×C4—51no—
297C22×C3×C4—51no—
298C22×C3×C4—52no—
299C22×C3×C4—51no—
300C22×C3×C4—52no—
301C22×Dic3—51no—
302C22×Dic3—52no—
303C22×Dic3—51no—
304C22×Dic3—51no—
305C22×Dic3—51no—
306C22×Dic3—52no—
307C2×Dic6—51no—
308C2×Dic6—52no—
309C2×Dic6—54no—
310C2×Dic6—54no—
311C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
312C3×C4⋊C4—52no—
313C3×C4⋊C4—51no—
314C3×C4⋊C4—102no—
315C3×C4⋊C4—202no—
316C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
317C3×C42—102no—
318C4⋊Dic3—102no—
319C4⋊Dic3—202no—
320Dic3⋊C4—54no—
321Dic3⋊C4—52no—
322Dic3⋊C4—52no—
323Dic3⋊C4—52no—
324Dic3⋊C4—104no—
325Dic3⋊C4—104no—
326Dic3⋊C4—104no—
327Dic3⋊C4—102no—
328Dic3⋊C4—202no—
329Dic3⋊C4C2×AGL(1,𝔽5)12yes—
330C4×Dic3—52no—
331C4×Dic3—51no—
332C4×Dic3—51no—
333C4×Dic3—52no—
334C4×Dic3—52no—
335C4×Dic3—51no—
336C4×Dic3—104no—
337C4×Dic3—104no—
338C4×Dic3—102no—
339C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
340C4×Dic3C2×AGL(1,𝔽5)12yes—
341C22×D5C23×D311yescharacteristic
342C2×AGL(1,𝔽5)—21no—
343C2×AGL(1,𝔽5)—21no—
344C2×AGL(1,𝔽5)—21no—
345C2×AGL(1,𝔽5)—22no—
346C2×AGL(1,𝔽5)—21no—
347C2×AGL(1,𝔽5)—22no—
348C2×AGL(1,𝔽5)—22no—
349C2×AGL(1,𝔽5)—21no—
350C2×AGL(1,𝔽5)—32no—
351C2×AGL(1,𝔽5)—61no—
352C2×AGL(1,𝔽5)—61no—
353C2×AGL(1,𝔽5)—62no—
354C2×AGL(1,𝔽5)—61no—
355C2×AGL(1,𝔽5)—61no—
356C2×AGL(1,𝔽5)—62no—
357C2×AGL(1,𝔽5)—62no—
358C2×AGL(1,𝔽5)—61no—
359C2×AGL(1,𝔽5)D3×Q812yes—
360C5×Q8—34no—
361C2×C4×C5—31no—
362C2×C4×C5—32no—
363C2×C4×C5—31no—
364C2×C4×C5C2×C4×D312yes—
365C2×C4×C5C2×C4×D311yescharacteristic
366C2×Dic5—31no—
367C2×Dic5—32no—
368C2×Dic5—31no—
369C2×Dic5C2×C4×D312yes—
370C2×Dic5C2×C4×D311yescharacteristic
371C4×D5—22no—
372C4×D5—22no—
373C4×D5—34no—
374C4×D5—32no—
375C4×D5—34no—
376C4×D5—32no—
377C4×D5—61no—
378C4×D5—61no—
379C4×D5D3×D412yes—
380C4×D5D3×Q812yes—
381Dic10—34no—
382Dic10—38no—
383C22×Q8—151no—
384C4×Q8—31no—
385C4×Q8—152no—
386C4×Q8—151no—
387C4×Q8—152no—
388C4×Q8—151no—
389C4×Q8—151no—
390C4×Q8—304no—
391C4×Q8—304no—
392C2×C4⋊C4—51no—
393C2×C4⋊C4—51no—
394C2×C4⋊C4—52no—
395C2×C4⋊C4—152no—
396C2×C4⋊C4—151no—
397C2×C4⋊C4—152no—
398C2×C4⋊C4—152no—
399C2×C4⋊C4—151no—
400C2×C4⋊C4—152no—
401C2×C4⋊C4—151no—
402C2×C4⋊C4—152no—
403C2×C4⋊C4—152no—
404C2×C42—51no—
405C2×C42—151no—
406C2×C42—152no—
407C2×C42—151no—
408C2×C42—152no—
409C2×C42—152no—
410#95—52no—
411#95—151no—
412#95—152no—
413#95—151no—
414C2×C3×C5C22×C4⋊C411yescharacteristic
415C2×C3×C5C2×C4×Q811yescharacteristic
416C2×C3×C5#52011yescharacteristic
417C3×D5D4×Q811yescharacteristic
418C3×D5#55011yescharacteristic
419C3×D5#55711yescharacteristic
420C3×D5Q8211yescharacteristic
421C23×C3—51no—
422C2×C3×C4—51no—
423C2×C3×C4—52no—
424C2×C3×C4—52no—
425C2×C3×C4—52no—
426C2×C3×C4—52no—
427C2×C3×C4—102no—
428C2×C3×C4—102no—
429C2×C3×C4—101no—
430C2×C3×C4—101no—
431C2×C3×C4—102no—
432C2×C3×C4—101no—
433C2×C3×C4—101no—
434C2×C3×C4—102no—
435C2×C3×C4—102no—
436C2×C3×C4—101no—
437C2×C3×C4C22×AGL(1,𝔽5)12yes—
438C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
439C2×Dic3—51no—
440C2×Dic3—52no—
441C2×Dic3—54no—
442C2×Dic3—54no—
443C2×Dic3—52no—
444C2×Dic3—52no—
445C2×Dic3—52no—
446C2×Dic3—51no—
447C2×Dic3—101no—
448C2×Dic3—101no—
449C2×Dic3—101no—
450C2×Dic3—101no—
451C2×Dic3—101no—
452C2×Dic3—102no—
453C2×Dic3—101no—
454C2×Dic3—102no—
455C2×Dic3—102no—
456C2×Dic3—101no—
457C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
458C2×Dic3C22×AGL(1,𝔽5)12yes—
459C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
460Dic6—54no—
461Dic6—58no—
462Dic6C4⋊AGL(1,𝔽5)14yescomplemented
463C22×C5C22×C4×D311yescharacteristic
464C2×D5C2×D3×D411yescharacteristic
465C2×D5#100411yescharacteristic
466C2×D5C2×D3×Q811yescharacteristic
467C2×D5C2×D3×Q811yescharacteristic
468C2×D5D3×#4111yescharacteristic
469C2×D5#101011yescharacteristic
470AGL(1,𝔽5)—22no—
471AGL(1,𝔽5)—41no—
472AGL(1,𝔽5)—42no—
473AGL(1,𝔽5)—62no—
474AGL(1,𝔽5)—122no—
475AGL(1,𝔽5)—121no—
476C4×C5—22no—
477C4×C5—34no—
478C4×C5—32no—
479C4×C5—61no—
480C4×C5D3×C4⋊C412yes—
481Dic5—22no—
482Dic5—34no—
483Dic5—32no—
484Dic5—61no—
485Dic5D3×C4⋊C412yes—
486C2×Q8—31no—
487C2×Q8—152no—
488C2×Q8—154no—
489C2×Q8—154no—
490C2×Q8—151no—
491C22×C4—51no—
492C22×C4—51no—
493C22×C4—52no—
494C22×C4—52no—
495C22×C4—51no—
496C22×C4—151no—
497C22×C4—152no—
498C22×C4—151no—
499C22×C4—151no—
500C22×C4—151no—
501C22×C4—152no—
502C4⋊C4—32no—
503C4⋊C4—52no—
504C4⋊C4—51no—
505C4⋊C4—102no—
506C4⋊C4—152no—
507C4⋊C4—152no—
508C4⋊C4—154no—
509C4⋊C4—152no—
510C4⋊C4—202no—
511C4⋊C4—302no—
512C4⋊C4—304no—
513C4⋊C4—304no—
514C4⋊C4—304no—
515C4⋊C4—302no—
516C4⋊C4—602no—
517C4⋊C4—602no—
518C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
519C42—32no—
520C42—31no—
521C42—102no—
522C42—151no—
523C42—152no—
524C42—152no—
525C42—151no—
526C42—152no—
527C42—151no—
528C42—302no—
529C42—304no—
530C42—304no—
531C3×C5Q8×C4⋊C411yescharacteristic, complemented, Hall
532C22×C3—51no—
533C22×C3—51no—
534C22×C3—51no—
535C22×C3—51no—
536C22×C3—51no—
537C22×C3—51no—
538C22×C3C23×AGL(1,𝔽5)11yescharacteristic
539C3×C4—22no—
540C3×C4—52no—
541C3×C4—102no—
542C3×C4—102no—
543C3×C4—202no—
544C3×C4—201no—
545C3×C4C2×C4⋊AGL(1,𝔽5)12yes—
546Dic3—21no—
547Dic3—54no—
548Dic3—52no—
549Dic3—102no—
550Dic3—101no—
551Dic3—201no—
552Dic3—202no—
553Dic3C2×C4⋊AGL(1,𝔽5)14yes—
554Dic3Q8×AGL(1,𝔽5)12yescomplemented
555C2×C5C2×D3×C4⋊C411yescharacteristic
556C2×C5#554611yescharacteristic
557C2×C5C4×D3×Q811yescharacteristic
558D5#559911yescharacteristic
559D5#563211yescharacteristic
560D5#568511yescharacteristic
561D5#572211yescharacteristic
562C23—51no—
563Q8—34no—
564Q8—158no—
565Q8—154no—
566C2×C4—31no—
567C2×C4—32no—
568C2×C4—31no—
569C2×C4—51no—
570C2×C4—52no—
571C2×C4—52no—
572C2×C4—52no—
573C2×C4—52no—
574C2×C4—102no—
575C2×C4—102no—
576C2×C4—101no—
577C2×C4—101no—
578C2×C4—101no—
579C2×C4—102no—
580C2×C4—101no—
581C2×C4—102no—
582C2×C4—102no—
583C2×C4—101no—
584C2×C4—154no—
585C2×C4—152no—
586C2×C4—152no—
587C2×C4—154no—
588C2×C4—151no—
589C2×C4—152no—
590C2×C4—152no—
591C2×C4—151no—
592C2×C4—301no—
593C2×C4—301no—
594C2×C4—301no—
595C2×C4—301no—
596C2×C4—301no—
597C2×C4—302no—
598C2×C4—301no—
599C2×C4—302no—
600C2×C4—302no—
601C2×C4—301no—
602C2×C4C2×D3×AGL(1,𝔽5)12yes—
603C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
604C2×C3—51no—
605C2×C3—51no—
606C2×C3—51no—
607C2×C3—51no—
608C2×C3C22×C4⋊AGL(1,𝔽5)11yescharacteristic
609C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
610C2×C3#6626611yescharacteristic
611C5#7598111yescharacteristic, complemented, Sylow
612C22—51no—
613C22—51no—
614C22—51no—
615C22—51no—
616C22—51no—
617C22—51no—
618C22C22×D3×AGL(1,𝔽5)11yescharacteristic
619C4—22no—
620C4—34no—
621C4—32no—
622C4—52no—
623C4—61no—
624C4—102no—
625C4—102no—
626C4—154no—
627C4—152no—
628C4—201no—
629C4—202no—
630C4—302no—
631C4—301no—
632C4—601no—
633C4—602no—
634C4D3×C4⋊AGL(1,𝔽5)12yes—
635C3Q8×C4⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
636C2—51no—
637C2—51no—
638C2—51no—
639C2—51no—
640C2C2×D3×C4⋊AGL(1,𝔽5)11yescharacteristic
641C2#1175684611yescharacteristic
642C2D3×Q8×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radical, cosocleC22×C3×D5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5Q8×C4⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
30. #91776C4semidirect
31. C5×#887C4semidirect
36. #91344C4semidirect
37. #91340C4semidirect
38. #91325C4semidirect
39. #91324C4semidirect
83. Dic3⋊AGL(1,𝔽5)Q8semidirect
168. Dic30C4⋊C4semidirect
172. C5×Dic6C4⋊C4semidirect
179. #1204C4⋊C4semidirect
211. #887AGL(1,𝔽5)semidirect
290. Dic15C4×Q8semidirect
295. C5×Dic3C4×Q8semidirect
462. Dic6C4⋊AGL(1,𝔽5)semidirect
531. C3×C5Q8×C4⋊C4semidirect
554. Dic3Q8×AGL(1,𝔽5)semidirect
611. C5#75981semidirect
635. C3Q8×C4⋊AGL(1,𝔽5)semidirect

Maximal subgroups

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

subgroupindex
C2×ΓL(1,𝔽16)⋊Q82
C2×AGL(1,𝔽5)×Dic62
D5×#8872
#117523712
C3×#657122
#117518602
C4×Dic3⋊AGL(1,𝔽5)2
#117518442
#117518372
#117518342
Q8×C4⋊AGL(1,𝔽5)3
#759815