Finite Group Databasebeta

← #14289530

Subgroups — #14289530

Order 1920.

428 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 90 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
1#11756338C211yesmaximal, characteristic
2C5×#5021C211yesmaximal, characteristic, complemented
3#11747096C211yesmaximal, characteristic, complemented
4#11746885C211yesmaximal, characteristic
5C3×Q8⋊#168C211yesmaximal, characteristic, complemented
6#11745863C211yesmaximal, characteristic, complemented
7#11745839C211yesmaximal, characteristic
8#10601949—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91835—21no—
11#91785—22no—
12C4⋊C4×D15—21no—
13C4×D60—21no—
14C4×D60C2211yescharacteristic
15#91759—21no—
16#91758C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C2×#6663—22no—
19C5×#835—21no—
20C5×#807—21no—
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24#90985—21no—
25#90969—21no—
26#68246—51nomaximal, Hall
27#65913—31no—
28C5×#477—31no—
29#65381—31no—
30#65373—31no—
31Q8⋊#168D311yescharacteristic, complemented
32#64703—31no—
33#64701—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×C4×D15—22no—
38C2×Dic30D412yes—
39C2×C5×Dic6—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C42×C5—21no—
43C3×C42×C5C2311yescharacteristic
44#6714—22no—
45#6714—21no—
46C4⋊Dic15—21no—
47C4⋊Dic15—21no—
48C4⋊Dic15D411yescharacteristic
49#6712—22no—
50#6712—22no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3—21no—
53C2×C5×C3⋊C8—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56#6663—44no—
57#5579—51no—
58#5021D511yescharacteristic, complemented
59#4842—51no—
60#4699—51no—
61C3×Q8⋊C8—51no—
62#4481—51no—
63#4459—51no—
64C5×C4⋊Q8—31no—
65C4×C5×Q8C2×D311yescharacteristic
66#4092—61no—
67C2×#689—62no—
68#4042—62no—
69D5×C4⋊C4—61no—
70C4×D20—31no—
71C4×D20—61no—
72#4016—61no—
73#4015—31no—
74C5×#107—61no—
75C5×C4⋊C8—31no—
76C5×#103—61no—
77#3941—61no—
78#3940—61no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168C2×D311yescharacteristic
81#1632—151noSylow
82C22×D15—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—21no—
91C2×Dic15—22no—
92D60—21no—
93D60Q1612yescomplemented
94C4×D15—41no—
95C4×D15—41no—
96C4×D15—82no—
97Dic30—42no—
98C2×C5×Dic3—41no—
99C5×Dic6—42no—
100C3×#168—22no—
101C3×#168—41no—
102C5×C3⋊C8—41no—
103C3×C4×Q8C2×D511yescharacteristic
104#946—101no—
105C2×Dic12—102no—
106#896—102no—
107D3×C4⋊C4—101no—
108C4×D12—51no—
109C4×D12—101no—
110#870—101no—
111#869—51no—
112#869C2×D511yescharacteristic
113C3×C4⋊C8—51no—
114C3×C4×C8—51no—
115#835—21no—
116#821—101no—
117#817—101no—
118#807—21no—
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C2×C5×Q8—61no—
121C2×C5×Q8D1211yescharacteristic
122C2×D20—31no—
123C2×C4×D5—61no—
124C2×C4×D5—62no—
125C2×Dic10—32no—
126C2×C5×C8—61no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4—61no—
130C5×C4⋊C4D1211yescharacteristic
131C42×C5—21no—
132C42×C5C22×D311yescharacteristic
133#689—124no—
134#685—62no—
135#685—61no—
136C4⋊Dic5—31no—
137C4⋊Dic5—61no—
138C4⋊Dic5—61no—
139#683—62no—
140#683—62no—
141C2×#168—21no—
142C2×#168—21no—
143#554—151no—
144#494—151no—
145#477—31no—
146#476—151no—
147#333—151no—
148Q8⋊C8—51no—
149D4⋊C8—151no—
150C22×C3×C5#12011yescharacteristic
151C2×D15—22no—
152C2×D15—41no—
153C2×D15—41no—
154C3×C4×C5—21no—
155C3×C4×C5—41no—
156C3×C4×C5—41no—
157C3×C4×C5C2×Q1611yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×C4×C5#13711yescharacteristic
161Dic15—41no—
162Dic15—42no—
163C5×Dic3—81no—
164C2×C3×Q8C22⋊D511yescharacteristic
165C2×D12—51no—
166C2×C4×D3—101no—
167C2×C4×D3—102no—
168C2×Dic6—21no—
169C2×Dic6—52no—
170C2×C3×C8—101no—
171C2×C3×C8—101no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4C22⋊D511yescharacteristic
174C3×C42—21no—
175C3×C42C22×D511yescharacteristic
176(C2×D3)⋊C4—102no—
177(C2×D3)⋊C4—101no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3—51no—
181C4⋊Dic3—101no—
182C4⋊Dic3—101no—
183Dic3⋊C4—102no—
184Dic3⋊C4—102no—
185C2×C3⋊C8—21no—
186Dic12—204no—
187C22×D5—61no—
188C5×Q8—21no—
189C5×Q8—21no—
190C5×Q8—122no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—121no—
194C2×C4×C5C2×D1211yescharacteristic
195C2×C4×C5D3×D411yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×Dic5—61no—
198C2×Dic5—62no—
199D20—32no—
200D20—61no—
201C4×D5—121no—
202C4×D5—121no—
203C4×D5—242no—
204Dic10—122no—
205C5×C8—121no—
206#168—22no—
207#168—41no—
208C2×Q16—302no—
209C4⋊Q8—31no—
210C4⋊Q8—151no—
211#125—301no—
212C22⋊Q8—302no—
213C22⋊Q8—301no—
214C4×Q8D3×D511yescharacteristic
215C4×D4—151no—
216C4×D4—301no—
217C2×C4⋊C4—301no—
218#107—61no—
219#106—301no—
220C4⋊C8—31no—
221C4⋊C8—51no—
222#103—61no—
223#102—301no—
224C4×C8—51no—
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228D15—42no—
229C22×D3—101no—
230C3×Q8—21no—
231C3×Q8—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4D4×D511yescharacteristic
235C2×C3×C4D4×D511yescharacteristic
236C2×C3×C4C2×C22⋊D511yescharacteristic
237C2×Dic3—41no—
238C2×Dic3—101no—
239C2×Dic3—102no—
240D12—52no—
241D12—101no—
242C4×D3—201no—
243C4×D3—201no—
244C4×D3—402no—
245Dic6—42no—
246Dic6—202no—
247C3×C8—102no—
248C3×C8—201no—
249C3⋊C8—41no—
250C22×C5#88211yescharacteristic
251C2×D5—62no—
252C2×D5—121no—
253C2×D5—121no—
254C4×C5—21no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5—241no—
258C4×C5#90411yescharacteristic
259C4×C5#90911yescharacteristic
260C4×C5#91511yescharacteristic
261C4×C5D3×Q1611yescharacteristic
262Dic5—121no—
263Dic5—122no—
264C2×Q8—61no—
265C2×Q8—152no—
266C2×Q8#120311yescharacteristic
267C2×D4—151no—
268C22×C4—302no—
269C22×C4—301no—
270Q16—604no—
271C2×C8—61no—
272C2×C8—101no—
273C2×C8—101no—
274C4⋊C4—21no—
275C4⋊C4—61no—
276C4⋊C4—61no—
277C4⋊C4—151no—
278C4⋊C4—302no—
279C4⋊C4—302no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C4⋊C4#120311yescharacteristic
283C22⋊C4—302no—
284C22⋊C4—301no—
285C42—21no—
286C42C2×D3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3#408311yescharacteristic
289C2×D3—102no—
290C2×D3—201no—
291C2×D3—201no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4D5×Q1611yescharacteristic
296C3×C4#406411yescharacteristic
297C3×C4#408811yescharacteristic
298C3×C4#409611yescharacteristic
299Dic3—81no—
300Dic3—201no—
301Dic3—202no—
302C2×C5#473311yescharacteristic
303C2×C5#480911yescharacteristic
304C2×C5#482211yescharacteristic
305D5—122no—
306C23—301no—
307Q8—21no—
308Q8—21no—
309Q8—122no—
310Q8—602no—
311D4—152no—
312D4—301no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—121no—
316C2×C4—301no—
317C2×C4—302no—
318C2×C4—601no—
319C2×C4—601no—
320C2×C4—1202no—
321C2×C4C2×#120311yescharacteristic
322C2×C4#679011yescharacteristic
323C2×C4#679011yescharacteristic
324C8—102no—
325C8—121no—
326C8—201no—
327C2×C3#6533611yescharacteristic
328C2×C3#6547511yescharacteristic
329C2×C3#6548711yescharacteristic
330D3—202no—
331C5#6824611yescharacteristic, complemented, Sylow
332C22—302no—
333C22—601no—
334C22—601no—
335C22#9157311yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—241no—
340C4—602no—
341C4—601no—
342C4#9130311yescharacteristic
343C4#9132111yescharacteristic
344C4#9151111yescharacteristic
345C4#9152211yescharacteristic
346C3#1060194911yescharacteristic, complemented, Sylow
347C2—602no—
348C2#1174856611yescharacteristic
349C2#1174930811yescharacteristic
350C2#1174942211yescharacteristic
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1632
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C5×#5021C2semidirect
3. #11747096C2semidirect
5. C3×Q8⋊#168C2semidirect
6. #11745863C2semidirect
31. Q8⋊#168D3semidirect
58. #5021D5semidirect
93. D60Q16semidirect
287. C3×C5#1632semidirect
331. C5#68246semidirect
346. C3#10601949semidirect

Maximal subgroups

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

subgroupindex
#117563382
C5×#50212
#117470962
#117468852
C3×Q8⋊#1682
#117458632
#117458392
#106019493
#682465