Finite Group Databasebeta

← #14290597

Subgroups — #14290597

Order 1920.

400 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C3×#65876C211yesmaximal, characteristic
2C5×#5019C211yesmaximal, characteristic
3#11746962C211yesmaximal, characteristic, complemented
4#11746918C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic
6#11745856C211yesmaximal, characteristic, complemented
7#11745840C211yesmaximal, characteristic, complemented
8#10601842—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C2×C5×#214—21no—
11C5×#869C2211yescharacteristic
12C3×#4082—21no—
13C3×#4072—21no—
14C3×#4070—21no—
15C3×#4033—21no—
16C3×#4025—22no—
17C3×#4015C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C5×#810—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23#90989—22no—
24#90986—21no—
25#90970—21no—
26#71933—51nomaximal, Hall
27#65876D311yescharacteristic
28C5×#461—31no—
29#65383—31no—
30#65367—31no—
31D4⋊#168—31no—
32#64704—31no—
33#64702—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C5×Dic6—21no—
37C2×C3×Dic10—21no—
38C2×C3×Dic10D411yescharacteristic
39C3×C5×C4⋊C4D411yescharacteristic
40C3×C5×C22⋊C4—21no—
41C3×C42×C5C2311yescharacteristic
42C2×C3⋊#168—21no—
43C2×C3⋊#168—21no—
44C5×#214—42no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3—21no—
47C2×C5×C3⋊C8—21no—
48C3×C22⋊Dic5—22no—
49C3×C22⋊Dic5—22no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5D411yescharacteristic
52C3×C4⋊Dic5D412yes—
53C3×#683—22no—
54C3×#683—21no—
55C3×C4×Dic5—22no—
56C3×C4×Dic5—21no—
57C3×#556—51no—
58#5078—51no—
59#5020—51no—
60#5019D511yescharacteristic
61#4547—51no—
62#4535—51no—
63D4⋊(C3⋊C8)—51no—
64C2×C5×SD16—61no—
65C5×C4⋊Q8—31no—
66C4×C5×D4C2×D311yescharacteristic
67#4082—21no—
68#4072—21no—
69#4070—21no—
70#4033—21no—
71#4025—22no—
72#4015C2×D311yescharacteristic
73C4×Dic10C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C5×#103—61no—
76#3942—61no—
77#3940—61no—
78#3939—62no—
79C4⋊#168—31no—
80C4×#168—31no—
81#1650—151noSylow
82C23×C3×C5—21no—
83C3×C5×D4—21no—
84C3×C5×D4—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C5×Dic3—41no—
92C5×Dic6—41no—
93C5×Dic6—41no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—21no—
96C2×C3×Dic5—22no—
97C3×Dic10—21no—
98C3×Dic10—21no—
99C3×Dic10—41no—
100C3×Dic10—41no—
101C3⋊#168—22no—
102C3⋊#168—41no—
103C5×C3⋊C8—41no—
104C3×C4⋊Q8—51no—
105C3×#126—102no—
106C3×#124—101no—
107C3×C22⋊Q8—101no—
108C3×C4×Q8—51no—
109C3×C4×Q8—101no—
110C3×C4×D4C2×D511yescharacteristic
111C3×#117—101no—
112C2×#214—21no—
113#869C2×D511yescharacteristic
114#835—101no—
115#810—21no—
116#808—101no—
117#807—102no—
118C4⋊(C3⋊C8)—51no—
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C4×C3⋊C8—51no—
121C2×C5×Q8—61no—
122C2×C5×D4#6711yescharacteristic
123C22×C4×C5—21no—
124C2×Dic10—21no—
125C2×Dic10#6711yescharacteristic
126C5×SD16—122no—
127C2×C5×C8—61no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4—61no—
130C5×C4⋊C4#6711yescharacteristic
131C5×C22⋊C4—21no—
132C42×C5C22×D311yescharacteristic
133C22⋊Dic5—22no—
134C22⋊Dic5—22no—
135C4⋊Dic5—21no—
136C4⋊Dic5#6712yes—
137C4⋊Dic5#6711yescharacteristic
138#683—22no—
139#683—21no—
140C4×Dic5—22no—
141C4×Dic5—21no—
142C2×#168—61no—
143C2×#168—61no—
144#556—51no—
145#500—151no—
146#475—151no—
147#461—31no—
148#332—151no—
149Q8⋊C8—151no—
150D4⋊C8—151no—
151C22×C3×C5—41no—
152C22×C3×C5—41no—
153C22×C3×C5—41no—
154C22×C3×C5#12011yescharacteristic
155C3×C4×C5—21no—
156C3×C4×C5—41no—
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C3×C4×C5#13711yescharacteristic
161C3×Dic5—42no—
162C3×Dic5—41no—
163C3×Dic5—41no—
164C5×Dic3—81no—
165C2×C3×Q8—51no—
166C2×C3×Q8—101no—
167C2×C3×D4C22⋊D511yescharacteristic
168C22×C3×C4—21no—
169C2×Dic6—21no—
170C3×C4⋊C4—52no—
171C3×C4⋊C4—51no—
172C3×C4⋊C4—102no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—101no—
175C3×C4⋊C4C22⋊D511yescharacteristic
176C3×C22⋊C4—21no—
177C3×C22⋊C4—102no—
178C3×C22⋊C4—102no—
179C3×C42—102no—
180C3×C42—101no—
181C3×C42C22×D511yescharacteristic
182#214—42no—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—101no—
187C2×C3⋊C8—101no—
188C23×C5—21no—
189C5×Q8—121no—
190C5×Q8—121no—
191C5×D4—21no—
192C5×D4—21no—
193C2×C4×C5—21no—
194C2×C4×C5—41no—
195C2×C4×C5—41no—
196C2×C4×C5—121no—
197C2×C4×C5C2×#6711yescharacteristic
198C2×C4×C5C2×#6711yescharacteristic
199C2×C4×C5C2×#6711yescharacteristic
200C2×Dic5—21no—
201C2×Dic5—21no—
202C2×Dic5—22no—
203Dic10—21no—
204Dic10—21no—
205Dic10—41no—
206Dic10—41no—
207C5×C8—121no—
208#168—62no—
209#168—121no—
210C2×SD16—61no—
211C4⋊Q8—31no—
212C4⋊Q8—51no—
213#126—102no—
214#124—101no—
215C22⋊Q8—101no—
216C4×Q8—51no—
217C4×Q8—101no—
218C4×D4D3×D511yescharacteristic
219#117—101no—
220#107—302no—
221#106—301no—
222C4⋊C8—31no—
223C4⋊C8—151no—
224#103—61no—
225#103—301no—
226C4×C8—151no—
227C2×C3×C5—81no—
228C2×C3×C5#44911yescharacteristic
229C2×C3×C5#45211yescharacteristic
230C2×C3×C5#45611yescharacteristic
231C23×C3—21no—
232C3×Q8—101no—
233C3×Q8—101no—
234C3×Q8—201no—
235C3×Q8—201no—
236C3×D4—21no—
237C3×D4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—101no—
242C2×C3×C4—102no—
243C2×C3×C4—101no—
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4C2×C22⋊D511yescharacteristic
247C2×Dic3—41no—
248Dic6—41no—
249Dic6—41no—
250C3⋊C8—41no—
251C3⋊C8—102no—
252C3⋊C8—201no—
253C22×C5—41no—
254C22×C5—41no—
255C22×C5—41no—
256C22×C5#95311yescharacteristic
257C4×C5—21no—
258C4×C5—41no—
259C4×C5—241no—
260C4×C5#94911yescharacteristic
261C4×C5#95011yescharacteristic
262C4×C5#95011yescharacteristic
263C4×C5#95111yescharacteristic
264Dic5—42no—
265Dic5—41no—
266Dic5—41no—
267C2×Q8—51no—
268C2×Q8—61no—
269C2×Q8—101no—
270C2×D4#120111yescharacteristic
271C22×C4—21no—
272SD16—122no—
273C2×C8—61no—
274C2×C8—301no—
275C2×C8—301no—
276C4⋊C4—51no—
277C4⋊C4—52no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4—102no—
281C4⋊C4—101no—
282C4⋊C4—101no—
283C4⋊C4#120111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—102no—
286C22⋊C4—102no—
287C42—102no—
288C42—101no—
289C42C2×D3×D511yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3—41no—
292C22×C3—41no—
293C22×C3—41no—
294C22×C3#408311yescharacteristic
295C3×C4—21no—
296C3×C4—41no—
297C3×C4—202no—
298C3×C4—201no—
299C3×C4—201no—
300C3×C4#406111yescharacteristic
301C3×C4#406211yescharacteristic
302C3×C4#407811yescharacteristic
303C3×C4#409611yescharacteristic
304Dic3—81no—
305C2×C5—81no—
306C2×C5#523811yescharacteristic
307C2×C5#523911yescharacteristic
308C2×C5#524611yescharacteristic
309C23—21no—
310Q8—101no—
311Q8—101no—
312Q8—121no—
313Q8—121no—
314Q8—201no—
315Q8—201no—
316D4—21no—
317D4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—101no—
322C2×C4—102no—
323C2×C4—101no—
324C2×C4—121no—
325C2×C4C2×#120111yescharacteristic
326C2×C4D5×#6711yescharacteristic
327C2×C4D5×#6711yescharacteristic
328C8—121no—
329C8—302no—
330C8—601no—
331C2×C3—81no—
332C2×C3#6532611yescharacteristic
333C2×C3#6546211yescharacteristic
334C2×C3#6549411yescharacteristic
335C5#7193311yescharacteristic, complemented, Sylow
336C22—41no—
337C22—41no—
338C22—41no—
339C22#9156311yescharacteristic
340C4—21no—
341C4—41no—
342C4—201no—
343C4—202no—
344C4—201no—
345C4—241no—
346C4#9129711yescharacteristic
347C4#9129911yescharacteristic
348C4#9148411yescharacteristic
349C4#9149211yescharacteristic
350C3#1060184211yescharacteristic, complemented, Sylow
351C2—81no—
352C2#1174851111yescharacteristic
353C2#1174904711yescharacteristic
354C2#1174946211yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#1650
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #11746962C2semidirect
4. #11746918C2semidirect
6. #11745856C2semidirect
7. #11745840C2semidirect
290. C3×C5#1650semidirect
335. C5#71933semidirect
350. C3#10601842semidirect

Maximal subgroups

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

subgroupindex
C3×#658762
C5×#50192
#117469622
#117469182
D4⋊(C3⋊#168)2
#117458562
#117458402
#106018423
#719335