Finite Group Databasebeta

← #14298395

Subgroups — #14298395

Order 1920.

632 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91404C211yesmaximal, characteristic
2#11752003C212yesmaximal
3#11746790C211yesmaximal, characteristic, complemented
4C3×#64919C211yesmaximal, characteristic, complemented
5#11746574C212yesmaximal, complemented
6#10604337—31nomaximal, Hall
7C22×C4×D15C411yescharacteristic
8C22×#1200C411yescharacteristic
9C22×#1200C2211yescharacteristic
10C2×#6762C2212yes—
11C2×C3×#704C2212yes—
12C2×C5×Dic3⋊C4C411yescharacteristic
13C2×C3×#683C2211yescharacteristic
14C2×Dic3⋊Dic5C411yescharacteristic
15C2×#6668C2211yescharacteristic
16#91404—22no—
17#91404—22no—
18#91171—22no—
19#91171—22no—
20#68990—51nomaximal, Hall
21C2×D5×C4⋊C4—31no—
22#65755—32no—
23#64919—31no—
24#64919—32no—
25#64919D311yescharacteristic, complemented
26C23×D15C2×C411yescharacteristic
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×Dic15C2×C411yescharacteristic
29C2×C4×D15—21no—
30C2×C4×D15—21no—
31C2×C4×D15—42no—
32C22×C5×Dic3C2×C411yescharacteristic
33C22×C5×Dic3C2×C411yescharacteristic
34C22×C3×Dic5C2×C411yescharacteristic
35C22×C3×Dic5C2311yescharacteristic
36C2×#1200—22no—
37C2×#1200—21no—
38C2×#1200—21no—
39C2×#1200—21no—
40C2×#1200—21no—
41C2×#1200—42no—
42C2×#1200D412yes—
43C2×#1200D412yes—
44#6762—22no—
45#6762—22no—
46C2×C3⋊#170—22no—
47C3×#704—22no—
48C3×#704—22no—
49C2×C3×#170—22no—
50C5×Dic3⋊C4—22no—
51C3×#683—22no—
52Dic3⋊Dic5—22no—
53#6668—22no—
54C2×D3×C4⋊C4—51no—
55#5126—52no—
56C3×#343—51no—
57#4554—52no—
58#4530—51no—
59C22×C4×D5—31no—
60C22×C4×D5—31no—
61C22×C4×D5—31no—
62C2×#704—32no—
63C2×#704C2×D312yes—
64C2×C5×C4⋊C4—31no—
65C2×C4⋊Dic5—31no—
66C2×#683—31no—
67C2×#683C2×D311yescharacteristic
68D5×C4⋊C4—62no—
69D5×C4⋊C4—62no—
70#4003—62no—
71#4003—62no—
72#1821—151noSylow
73C23×C3×C5C22×C411yescharacteristic
74C22×D15—21no—
75C22×D15—21no—
76C22×D15—22no—
77C22×D15—22no—
78C22×D15C22⋊C411yescharacteristic
79C22×D15C22⋊C411yescharacteristic
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—41no—
82C2×Dic15—21no—
83C2×Dic15—41no—
84C4×D15—42no—
85C4×D15—42no—
86C2×C5×Dic3—21no—
87C2×C5×Dic3—21no—
88C2×C5×Dic3—21no—
89C2×C5×Dic3—41no—
90C2×C5×Dic3C22⋊C412yes—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—41no—
93C2×C3×Dic5C2×D412yes—
94C2×C3×Dic5#4112yes—
95C2×C3×Dic5#4111yescharacteristic
96C2×C3×Dic5#4111yescharacteristic
97#1200—22no—
98#1200—22no—
99#1200—22no—
100#1200—22no—
101#1200—42no—
102#1200—42no—
103C3⋊#170—42no—
104C3×#170—42no—
105C22×C4×D3—51no—
106C22×C4×D3—51no—
107C22×C4×D3—51no—
108C2×C3×M16—52no—
109C2×C3×C4⋊C4—51no—
110C2×C4⋊Dic3—51no—
111C2×Dic3⋊C4—51no—
112C2×Dic3⋊C4AGL(1,𝔽5)11yescharacteristic
113C2×#208—52no—
114D3×C4⋊C4—102no—
115D3×C4⋊C4—102no—
116(C2×D3)⋊C8—102no—
117(C2×D3)⋊C8—102no—
118C23×D5—31no—
119C22×C4×C5—31no—
120C22×C4×C5—31no—
121C22×C4×C5C4×D311yescharacteristic
122C22×Dic5—31no—
123C22×Dic5C4×D311yescharacteristic
124C22×Dic5C22×D311yescharacteristic
125C2×C4×D5—32no—
126C2×C4×D5—32no—
127C2×C4×D5—62no—
128C2×C4×D5—61no—
129C2×C4×D5—61no—
130C2×C4×D5—61no—
131C2×C4×D5—61no—
132C2×C4×D5—61no—
133C2×C4×D5—61no—
134C2×C4×D5—122no—
135C2×C4×D5—122no—
136#704—22no—
137#704—22no—
138#704—62no—
139#704—62no—
140C2×#170—22no—
141C2×#170—62no—
142C5×C4⋊C4—62no—
143C4⋊Dic5—62no—
144#683—22no—
145#683—62no—
146C22×C4⋊C4—151no—
147#407—152no—
148#343—51no—
149#343—151no—
150#343—152no—
151C22×C3×C5—21no—
152C22×C3×C5—21no—
153C22×C3×C5C2×C22⋊C411yescharacteristic
154C22×C3×C5#11711yescharacteristic
155C22×C3×C5#11711yescharacteristic
156C2×D15—24no—
157C2×D15—24no—
158C2×D15—21no—
159C2×D15—21no—
160C2×D15—21no—
161C2×D15—21no—
162C2×D15#10012yes—
163C2×D15#10112yes—
164C3×C4×C5—41no—
165Dic15—41no—
166C3×Dic5—41no—
167C3×Dic5#12312yes—
168C3×Dic5#12312yes—
169C5×Dic3—22no—
170C5×Dic3—41no—
171C23×D3—51no—
172C22×C3×C4—51no—
173C22×C3×C4—51no—
174C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
175C22×Dic3—51no—
176C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
177C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
178C2×C4×D3—52no—
179C2×C4×D3—52no—
180C2×C4×D3—101no—
181C2×C4×D3—102no—
182C2×C4×D3—101no—
183C2×C4×D3—101no—
184C2×C4×D3—101no—
185C2×C4×D3—101no—
186C2×C4×D3—101no—
187C2×C4×D3—202no—
188C2×C4×D3—202no—
189C3×M16—102no—
190C3×M16—102no—
191C2×C3×C8—102no—
192C3×C4⋊C4—102no—
193C4⋊Dic3—102no—
194Dic3⋊C4—22no—
195Dic3⋊C4—102no—
196#208—102no—
197#208—102no—
198C2×C3⋊C8—102no—
199C23×C5C2×C4×D311yescharacteristic
200C22×D5—31no—
201C22×D5—31no—
202C22×D5—62no—
203C22×D5—62no—
204C22×D5—61no—
205C22×D5—61no—
206C2×C4×C5—21no—
207C2×C4×C5—32no—
208C2×C4×C5—41no—
209C2×C4×C5—61no—
210C2×C4×C5—61no—
211C2×C4×C5—61no—
212C2×C4×C5—121no—
213C2×Dic5—21no—
214C2×Dic5—41no—
215C2×Dic5—61no—
216C2×Dic5—121no—
217C2×Dic5#23512yes—
218C2×Dic5D3×D412yes—
219C2×Dic5#23711yescharacteristic
220C2×Dic5#23911yescharacteristic
221C4×D5—62no—
222C4×D5—62no—
223C4×D5—62no—
224C4×D5—62no—
225C4×D5—122no—
226C4×D5—122no—
227C4×D5—122no—
228C4×D5—122no—
229#170—42no—
230#170—122no—
231C23×C4—151no—
232C23×C4—151no—
233C23×C4—151no—
234C2×M16—52no—
235C2×M16—152no—
236C2×C4⋊C4—31no—
237C2×C4⋊C4—51no—
238C2×C4⋊C4—151no—
239C2×C4⋊C4—151no—
240C2×C4⋊C4—302no—
241C2×C4⋊C4—302no—
242C22⋊C8—302no—
243C22⋊C8—302no—
244C2×C3×C5—21no—
245C2×C3×C5—21no—
246C2×C3×C5#38111yescharacteristic
247C2×C3×C5C2×#10011yescharacteristic
248C2×C3×C5C2×#10111yescharacteristic
249D15—22no—
250D15—22no—
251C23×C3C22×AGL(1,𝔽5)11yescharacteristic
252C22×D3—51no—
253C22×D3—51no—
254C22×D3—102no—
255C22×D3—102no—
256C22×D3—101no—
257C22×D3—101no—
258C2×C3×C4—21no—
259C2×C3×C4—41no—
260C2×C3×C4—51no—
261C2×C3×C4—52no—
262C2×C3×C4—51no—
263C2×C3×C4—52no—
264C2×C3×C4—101no—
265C2×C3×C4—201no—
266C2×Dic3—21no—
267C2×Dic3—21no—
268C2×Dic3—21no—
269C2×Dic3—41no—
270C2×Dic3—101no—
271C2×Dic3—201no—
272C2×Dic3C22⋊AGL(1,𝔽5)12yes—
273C4×D3—102no—
274C4×D3—102no—
275C4×D3—102no—
276C4×D3—102no—
277C4×D3—202no—
278C4×D3—202no—
279C4×D3—202no—
280C4×D3—202no—
281C3×C8—202no—
282C3⋊C8—202no—
283C22×C5—21no—
284C22×C5—21no—
285C22×C5#87211yescharacteristic
286C22×C5D3×C22⋊C411yescharacteristic
287C22×C5#89211yescharacteristic
288C2×D5—32no—
289C2×D5—32no—
290C2×D5—64no—
291C2×D5—64no—
292C2×D5—61no—
293C2×D5—61no—
294C2×D5—61no—
295C2×D5—61no—
296C4×C5—41no—
297C4×C5—62no—
298C4×C5—121no—
299Dic5—41no—
300Dic5—121no—
301Dic5#88312yes—
302Dic5#89412yes—
303C24—151no—
304C22×C4—31no—
305C22×C4—31no—
306C22×C4—51no—
307C22×C4—51no—
308C22×C4—152no—
309C22×C4—152no—
310C22×C4—151no—
311C22×C4—301no—
312C22×C4—301no—
313C22×C4—301no—
314C22×C4—301no—
315C22×C4—302no—
316C22×C4—301no—
317C22×C4—301no—
318C22×C4—602no—
319C22×C4—602no—
320C22×C4D3×AGL(1,𝔽5)11yescharacteristic
321M16—102no—
322M16—102no—
323M16—302no—
324M16—302no—
325C2×C8—102no—
326C2×C8—302no—
327C4⋊C4—62no—
328C4⋊C4—102no—
329C4⋊C4—302no—
330C4⋊C4—302no—
331C3×C5#182111yescharacteristic, complemented, Hall
332C22×C3—21no—
333C22×C3—21no—
334C22×C3#413011yescharacteristic
335C22×C3#413011yescharacteristic
336C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
337C2×D3—52no—
338C2×D3—52no—
339C2×D3—104no—
340C2×D3—104no—
341C2×D3—101no—
342C2×D3—101no—
343C2×D3—101no—
344C2×D3—101no—
345C3×C4—41no—
346C3×C4—52no—
347C3×C4—52no—
348C3×C4—201no—
349Dic3—22no—
350Dic3—41no—
351Dic3—201no—
352C2×C5—21no—
353C2×C5—21no—
354C2×C5#466411yescharacteristic
355C2×C5D3×#10011yescharacteristic
356C2×C5D3×#10111yescharacteristic
357D5—62no—
358D5—62no—
359C23—151no—
360C23—151no—
361C23—302no—
362C23—302no—
363C23—301no—
364C23—301no—
365C23C2×D3×AGL(1,𝔽5)11yescharacteristic
366C2×C4—21no—
367C2×C4—32no—
368C2×C4—41no—
369C2×C4—51no—
370C2×C4—51no—
371C2×C4—52no—
372C2×C4—52no—
373C2×C4—61no—
374C2×C4—61no—
375C2×C4—61no—
376C2×C4—101no—
377C2×C4—121no—
378C2×C4—201no—
379C2×C4—302no—
380C2×C4—302no—
381C2×C4—302no—
382C2×C4—302no—
383C2×C4—301no—
384C2×C4—602no—
385C2×C4—602no—
386C2×C4—602no—
387C2×C4—602no—
388C2×C4—601no—
389C8—202no—
390C8—602no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3#6576411yescharacteristic
394C2×C3D5⋊#10011yescharacteristic
395C2×C3D5⋊#10111yescharacteristic
396D3—102no—
397D3—102no—
398C5#6899011yescharacteristic, complemented, Sylow
399C22—21no—
400C22—21no—
401C22—152no—
402C22—152no—
403C22—304no—
404C22—304no—
405C22—301no—
406C22—301no—
407C22—301no—
408C22—301no—
409C22#9190711yescharacteristic
410C22#9190911yescharacteristic
411C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
412C4—41no—
413C4—52no—
414C4—52no—
415C4—62no—
416C4—121no—
417C4—201no—
418C4—601no—
419C3#1060433711yescharacteristic, complemented, Sylow
420C2—21no—
421C2—21no—
422C2—302no—
423C2—302no—
424C2#1175185311yescharacteristic
425C2#1175191811yescharacteristic
426C2#1175205011yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×D15C2×C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1821
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #11746790C2semidirect
4. C3×#64919C2semidirect
5. #11746574C2semidirect
25. #64919D3semidirect
331. C3×C5#1821semidirect
398. C5#68990semidirect
419. C3#10604337semidirect

Maximal subgroups

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

subgroupindex
C2×#914042
#117520032
#117467902
C3×#649192
#117465742
#106043373
#689905