Finite Group Databasebeta

← #14289597

Subgroups — #14289597

Order 1920.

436 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752718C211yesmaximal, characteristic
2#11751193C211yesmaximal, characteristic, complemented
3C5×#5084C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic, complemented
5#11745863C211yesmaximal, characteristic, complemented
6#11745836C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10601938—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C2×#6718—22no—
11#91758C2211yescharacteristic
12C4×C5×D12C2211yescharacteristic
13C3×C4×D20C2211yescharacteristic
14#91462—22no—
15#91456—21no—
16#91449—21no—
17#91358—21no—
18#91338—21no—
19C4×C3⋊#168C2211yescharacteristic
20C5×#809—21no—
21C5×#808—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×#3941—21no—
24C3×#3940—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71145—51nomaximal, Hall
27#65897—31no—
28C5×#476—31no—
29#65381—31no—
30#65373D311yescharacteristic, complemented
31D4⋊#168—31no—
32#64703—31no—
33#64701—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30D412yes—
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×#1201—22no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44#6718—44no—
45C4⋊Dic15—21no—
46C4⋊Dic15—21no—
47C2×C3⋊#168—21no—
48C5×(C2×D3)⋊C4—21no—
49C5×C4⋊Dic3D411yescharacteristic
50C2×C5×C3⋊C8—21no—
51C3×#685—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C2×C3×#168—21no—
54(C2×D3)⋊Dic5—22no—
55#6665—22no—
56Dic3×Dic5—22no—
57#5563—51no—
58C3×#476—51no—
59#5092—51no—
60#5084D511yescharacteristic, complemented
61D4⋊(C3⋊C8)—51no—
62#4483—51no—
63#4481—51no—
64C5×C4⋊Q8C2×D311yescharacteristic
65C4×C5×D4—31no—
66C2×#689—62no—
67#4084—61no—
68#4076—61no—
69#4072—61no—
70#4038—61no—
71#4031—62no—
72C4×D20C2×D311yescharacteristic
73#4015—31no—
74C5×#106—61no—
75C5×C4⋊C8—31no—
76C5×#102—61no—
77#3941—21no—
78#3940—21no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168—31no—
81#1634—151noSylow
82C22×C5×D3—21no—
83C22×C3×D5—21no—
84C3×C5×Q8—42no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—22no—
90Dic30—42no—
91C2×C5×Dic3—21no—
92C5×D12—21no—
93C5×D12—21no—
94C4×C5×D3—41no—
95C4×C5×D3—41no—
96C2×C3×Dic5—21no—
97C3×D20—21no—
98C3×D20—21no—
99C3×C4×D5—41no—
100C3×C4×D5—41no—
101#1201—82no—
102C3⋊#168—22no—
103C3×#168—41no—
104C5×C3⋊C8—41no—
105C3×C4⋊Q8C2×D511yescharacteristic
106C3×C4×D4—51no—
107C2×#216—102no—
108#938—101no—
109#930—101no—
110#926—101no—
111#892—101no—
112#885—102no—
113C4×D12C2×D511yescharacteristic
114#869—51no—
115C3×#106—101no—
116C3×C4⋊C8—51no—
117C3×#102—101no—
118#809—21no—
119#808—21no—
120C4⋊(C3⋊C8)C2×D511yescharacteristic
121C4×C3⋊C8—51no—
122C2×C5×Q8—21no—
123C2×C5×D4—31no—
124C22×C4×C5—61no—
125C2×C22⋊D5—62no—
126C2×D20#6711yescharacteristic
127C2×C4×D5—21no—
128C2×Dic10—32no—
129C2×C5×C8—61no—
130C5×C4⋊C4—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4—31no—
133C5×C22⋊C4—61no—
134C42×C5C22×D311yescharacteristic
135C22⋊Dic5—62no—
136#689—124no—
137#685—21no—
138#685—62no—
139C4⋊Dic5—61no—
140C4⋊Dic5—61no—
141C4⋊Dic5#6711yescharacteristic
142C4×Dic5—62no—
143C2×#168—21no—
144C2×#168—61no—
145#555—151no—
146#494—151no—
147#476—31no—
148#476—51no—
149#333—151no—
150D4⋊C8—151no—
151D4⋊C8—151no—
152C22×C3×C5#12011yescharacteristic
153C2×C5×D3—41no—
154C2×C5×D3—41no—
155C2×C5×D3—41no—
156C2×C3×D5—41no—
157C2×C3×D5—41no—
158C2×C3×D5—41no—
159C3×C4×C5—21no—
160C3×C4×C5—81no—
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×C4×C5#13711yescharacteristic
165Dic15—42no—
166C3×Dic5—41no—
167C5×Dic3—41no—
168C2×C3×Q8—21no—
169C2×C3×D4—51no—
170C22×C3×C4—101no—
171C2×#67—102no—
172C2×D12C22⋊D511yescharacteristic
173C2×C4×D3—21no—
174C2×Dic6—52no—
175C2×C3×C8—101no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—51no—
179C3×C22⋊C4—101no—
180C3×C42C22×D511yescharacteristic
181#217—102no—
182#216—204no—
183(C2×D3)⋊C4—21no—
184(C2×D3)⋊C4—102no—
185C4⋊Dic3—101no—
186C4⋊Dic3—101no—
187C4⋊Dic3C22⋊D511yescharacteristic
188C4×Dic3—102no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—101no—
191C23×C5—61no—
192C22×D5—21no—
193C5×Q8—42no—
194C5×D4—61no—
195C5×D4—61no—
196C2×C4×C5—41no—
197C2×C4×C5—61no—
198C2×C4×C5—121no—
199C2×C4×C5—121no—
200C2×C4×C5D3×D411yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C22⋊D5—242no—
204C2×Dic5—21no—
205C2×Dic5—62no—
206D20—21no—
207D20—21no—
208C4×D5—41no—
209C4×D5—41no—
210Dic10—122no—
211C5×C8—121no—
212#168—41no—
213#168—62no—
214C2×Q16—302no—
215C4⋊Q8—151no—
216C4⋊Q8D3×D511yescharacteristic
217#124—302no—
218#121—301no—
219#121—301no—
220C4×D4—31no—
221C4×D4—51no—
222#117—301no—
223#117—301no—
224#106—61no—
225#106—101no—
226C4⋊C8—31no—
227C4⋊C8—51no—
228#102—61no—
229#102—101no—
230C4×C8—151no—
231C2×C3×C5#45211yescharacteristic
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45311yescharacteristic
234C3×D5—81no—
235C5×D3—81no—
236C23×C3—101no—
237C22×D3—21no—
238C3×Q8—42no—
239C3×D4—101no—
240C3×D4—101no—
241C2×C3×C4—41no—
242C2×C3×C4—101no—
243C2×C3×C4—201no—
244C2×C3×C4—201no—
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C2×C3×C4C2×C22⋊D511yescharacteristic
248#67—402no—
249C2×Dic3—21no—
250C2×Dic3—102no—
251D12—21no—
252D12—21no—
253C4×D3—41no—
254C4×D3—41no—
255Dic6—202no—
256C3×C8—201no—
257C3⋊C8—41no—
258C3⋊C8—102no—
259C22×C5—121no—
260C22×C5—121no—
261C22×C5—121no—
262C22×C5#93711yescharacteristic
263C2×D5—41no—
264C2×D5—41no—
265C2×D5—41no—
266C4×C5—21no—
267C4×C5—81no—
268C4×C5—121no—
269C4×C5#91511yescharacteristic
270C4×C5#91611yescharacteristic
271C4×C5#94211yescharacteristic
272C4×C5#95011yescharacteristic
273Dic5—41no—
274Dic5—122no—
275C2×Q8—21no—
276C2×Q8—152no—
277C2×D4—31no—
278C2×D4—51no—
279C2×D4—302no—
280C22×C4—61no—
281C22×C4—101no—
282Q16—604no—
283C2×C8—61no—
284C2×C8—101no—
285C2×C8—301no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—31no—
289C4⋊C4—51no—
290C4⋊C4—301no—
291C4⋊C4—301no—
292C22⋊C4—61no—
293C22⋊C4—101no—
294C22⋊C4—302no—
295C22⋊C4—302no—
296C42—302no—
297C42C2×D3×D511yescharacteristic
298C3×C5#163411yescharacteristic, complemented, Hall
299C22×C3—201no—
300C22×C3—201no—
301C22×C3—201no—
302C22×C3#408311yescharacteristic
303C2×D3—41no—
304C2×D3—41no—
305C2×D3—41no—
306C3×C4—21no—
307C3×C4—81no—
308C3×C4—201no—
309C3×C4#406111yescharacteristic
310C3×C4#406211yescharacteristic
311C3×C4#408811yescharacteristic
312C3×C4#409611yescharacteristic
313Dic3—41no—
314Dic3—202no—
315C2×C5—241no—
316C2×C5#504711yescharacteristic
317C2×C5#517311yescharacteristic
318C2×C5#519811yescharacteristic
319D5—81no—
320C23—61no—
321C23—101no—
322Q8—42no—
323Q8—602no—
324D4—61no—
325D4—61no—
326D4—101no—
327D4—101no—
328D4—1202no—
329C2×C4—41no—
330C2×C4—61no—
331C2×C4—101no—
332C2×C4—121no—
333C2×C4—121no—
334C2×C4—201no—
335C2×C4—201no—
336C2×C4—302no—
337C2×C4D5×#6711yescharacteristic
338C2×C4D3×C22⋊D511yescharacteristic
339C2×C4#679011yescharacteristic
340C8—121no—
341C8—201no—
342C8—302no—
343C2×C3—401no—
344C2×C3#6533611yescharacteristic
345C2×C3#6546211yescharacteristic
346C2×C3#6548711yescharacteristic
347D3—81no—
348C5#7114511yescharacteristic, complemented, Sylow
349C22—121no—
350C22—121no—
351C22—121no—
352C22—201no—
353C22—201no—
354C22—201no—
355C22#9157711yescharacteristic
356C4—21no—
357C4—81no—
358C4—121no—
359C4—201no—
360C4—602no—
361C4#9151311yescharacteristic
362C4#9151411yescharacteristic
363C4#9151711yescharacteristic
364C4#9151811yescharacteristic
365C3#1060193811yescharacteristic, complemented, Sylow
366C2—241no—
367C2—401no—
368C2#1174916411yescharacteristic
369C2#1174940311yescharacteristic
370C2#1174940511yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radical#11752718C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1634
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. #11751193C2semidirect
3. C5×#5084C2semidirect
4. C3×#65373C2semidirect
5. #11745863C2semidirect
6. #11745836C2semidirect
7. #11745834C2semidirect
30. #65373D3semidirect
60. #5084D5semidirect
298. C3×C5#1634semidirect
348. C5#71145semidirect
365. C3#10601938semidirect

Maximal subgroups

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

subgroupindex
#117527182
#117511932
C5×#50842
C3×#653732
#117458632
#117458362
#117458342
#106019383
#711455