Finite Group Databasebeta

← C2×C29×#1320 #20306335

Subgroups — C2×C29×#1320 #20306335

Order 7424.

626 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#407C211yesmaximal, characteristic
2C2×C29×#349C212yesmaximal, complemented
3C29×#1320C214yesmaximal, direct product factor
4C24×C4×C29C411yescharacteristic
5C22×M16×C29C411yescharacteristic
6C22×M16×C29C2211yescharacteristic
7C2×C29×M32—22no—
8C29×#407—22no—
9C29×#407C412yes—
10C29×#407C2212yes—
11C2×C29×C22⋊C8—22no—
12C29×#349—22no—
13C29×#349C2214yescomplemented
14C25×C29C811yescharacteristic
15C23×C4×C29—21no—
16C23×C4×C29—21no—
17C23×C4×C29—21no—
18C23×C4×C29—21no—
19C23×C4×C29—41no—
20C23×C4×C29—41no—
21C23×C4×C29—41no—
22C23×C4×C29—41no—
23C23×C4×C29C811yescharacteristic
24C23×C4×C29C812yes—
25C23×C4×C29C2×C411yescharacteristic
26C23×C4×C29C2×C412yes—
27C2×M16×C29—21no—
28C2×M16×C29—41no—
29C2×M16×C29—41no—
30C2×M16×C29—41no—
31C2×M16×C29—41no—
32C2×M16×C29C2×C412yes—
33C2×M16×C29C2×C411yescharacteristic
34C2×M16×C29D412yes—
35C2×M16×C29C2311yescharacteristic
36C22×C8×C29—21no—
37C22×C8×C29D412yes—
38C29×M32—24no—
39C29×M32—42no—
40C2×C16×C29—42no—
41C29×C22⋊C8—24no—
42C29×C22⋊C8—24no—
43C24×C29—21no—
44C24×C29—21no—
45C24×C29—41no—
46C24×C29—41no—
47C24×C29—44no—
48C24×C29C2×C811yescharacteristic
49C24×C29C2×C812yes—
50C22×C4×C29—21no—
51C22×C4×C29—21no—
52C22×C4×C29—21no—
53C22×C4×C29—21no—
54C22×C4×C29—21no—
55C22×C4×C29—21no—
56C22×C4×C29—22no—
57C22×C4×C29—22no—
58C22×C4×C29—22no—
59C22×C4×C29—22no—
60C22×C4×C29—42no—
61C22×C4×C29—42no—
62C22×C4×C29—42no—
63C22×C4×C29—42no—
64C22×C4×C29—42no—
65C22×C4×C29—42no—
66C22×C4×C29—42no—
67C22×C4×C29—42no—
68C22×C4×C29—42no—
69C22×C4×C29—42no—
70C22×C4×C29—41no—
71C22×C4×C29—41no—
72C22×C4×C29—41no—
73C22×C4×C29—41no—
74C22×C4×C29—41no—
75C22×C4×C29—41no—
76C22×C4×C29C22⋊C411yescharacteristic
77C22×C4×C29C22⋊C411yescharacteristic
78C22×C4×C29C2×C811yescharacteristic
79C22×C4×C29C2×C812yes—
80C22×C4×C29M1611yescharacteristic
81C22×C4×C29M1611yescharacteristic
82C22×C4×C29C22×C411yescharacteristic
83M16×C29—41no—
84M16×C29—42no—
85M16×C29—41no—
86M16×C29—42no—
87M16×C29—42no—
88C2×C8×C29—22no—
89C2×C8×C29—22no—
90C2×C8×C29—22no—
91C2×C8×C29—41no—
92C2×C8×C29—41no—
93C2×C8×C29C22⋊C412yes—
94C2×C8×C29C2×D412yes—
95C16×C29—44no—
96C2×#1320C2911yesmaximal, characteristic, direct product factor, Sylow
97C23×C29—24no—
98C23×C29—21no—
99C23×C29—21no—
100C23×C29—22no—
101C23×C29—42no—
102C23×C29—42no—
103C23×C29—44no—
104C23×C29—42no—
105C23×C29—42no—
106C23×C29—44no—
107C23×C29—44no—
108C23×C29—48no—
109C23×C29—44no—
110C23×C29—41no—
111C23×C29—41no—
112C23×C29C22⋊C811yescharacteristic
113C23×C29C22⋊C811yescharacteristic
114C23×C29C22×C811yescharacteristic
115C2×C4×C29—21no—
116C2×C4×C29—21no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29—22no—
126C2×C4×C29—44no—
127C2×C4×C29—44no—
128C2×C4×C29—42no—
129C2×C4×C29—41no—
130C2×C4×C29—41no—
131C2×C4×C29—42no—
132C2×C4×C29—42no—
133C2×C4×C29—42no—
134C2×C4×C29—42no—
135C2×C4×C29—42no—
136C2×C4×C29C22⋊C811yescharacteristic
137C2×C4×C29C22⋊C811yescharacteristic
138C2×C4×C29#9911yescharacteristic
139C2×C4×C29#9911yescharacteristic
140C2×C4×C29#10011yescharacteristic
141C2×C4×C29#10011yescharacteristic
142C2×C4×C29C2×C22⋊C411yescharacteristic
143C2×C4×C29C2×M1611yescharacteristic
144C8×C29—22no—
145C8×C29—22no—
146C8×C29—42no—
147C2×#407C2×C2911yescharacteristic
148C2×#349C2×C2912yescomplemented
149#1320C2×C2914yesdirect product factor
150C22×C29—22no—
151C22×C29—24no—
152C22×C29—21no—
153C22×C29—21no—
154C22×C29—41no—
155C22×C29—41no—
156C22×C29—42no—
157C22×C29—44no—
158C22×C29—42no—
159C22×C29—44no—
160C22×C29—44no—
161C22×C29—48no—
162C22×C29—44no—
163C22×C29—42no—
164C22×C29—42no—
165C22×C29#32311yescharacteristic
166C22×C29#32311yescharacteristic
167C22×C29C2×C22⋊C811yescharacteristic
168C4×C29—21no—
169C4×C29—21no—
170C4×C29—42no—
171C4×C29#32311yescharacteristic
172C4×C29#32311yescharacteristic
173C4×C29C2×#9911yescharacteristic
174C4×C29C2×#10011yescharacteristic
175C24×C4C4×C2911yescharacteristic
176C22×M16C4×C2911yescharacteristic
177C22×M16C22×C2911yescharacteristic
178C2×M32—22no—
179#407—22no—
180#407C4×C2912yes—
181#407C22×C2912yes—
182C2×C22⋊C8—22no—
183#349—22no—
184#349C22×C2914yescomplemented
185C2×C29—21no—
186C2×C29—21no—
187C2×C29—44no—
188C2×C29—41no—
189C2×C29—41no—
190C2×C29#132012yesdirect product factor
191C2×C29C2×#32311yescharacteristic
192C25C8×C2911yescharacteristic
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—41no—
198C23×C4—41no—
199C23×C4—41no—
200C23×C4—41no—
201C23×C4C8×C2911yescharacteristic
202C23×C4C8×C2912yes—
203C23×C4C2×C4×C2911yescharacteristic
204C23×C4C2×C4×C2912yes—
205C2×M16—21no—
206C2×M16—41no—
207C2×M16—41no—
208C2×M16—41no—
209C2×M16—41no—
210C2×M16C2×C4×C2912yes—
211C2×M16C2×C4×C2911yescharacteristic
212C2×M16D4×C2912yes—
213C2×M16C23×C2911yescharacteristic
214C22×C8—21no—
215C22×C8D4×C2912yes—
216M32—24no—
217M32—42no—
218C2×C16—42no—
219C22⋊C8—24no—
220C22⋊C8—24no—
221C29C2×#132011yescharacteristic, direct product factor, Sylow
222C24—21no—
223C24—21no—
224C24—41no—
225C24—41no—
226C24—44no—
227C24C2×C8×C2911yescharacteristic
228C24C2×C8×C2912yes—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4C22⋊C4×C2911yescharacteristic
256C22×C4C22⋊C4×C2911yescharacteristic
257C22×C4C2×C8×C2911yescharacteristic
258C22×C4C2×C8×C2912yes—
259C22×C4M16×C2911yescharacteristic
260C22×C4M16×C2911yescharacteristic
261C22×C4C22×C4×C2911yescharacteristic
262M16—41no—
263M16—42no—
264M16—41no—
265M16—42no—
266M16—42no—
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8C22⋊C4×C2912yes—
273C2×C8C2×D4×C2912yes—
274C16—44no—
275C23—24no—
276C23—21no—
277C23—21no—
278C23—22no—
279C23—42no—
280C23—42no—
281C23—44no—
282C23—42no—
283C23—42no—
284C23—44no—
285C23—44no—
286C23—48no—
287C23—44no—
288C23—41no—
289C23—41no—
290C23C29×C22⋊C811yescharacteristic
291C23C29×C22⋊C811yescharacteristic
292C23C22×C8×C2911yescharacteristic
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—44no—
305C2×C4—44no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4C29×C22⋊C811yescharacteristic
315C2×C4C29×C22⋊C811yescharacteristic
316C2×C4C29×#9911yescharacteristic
317C2×C4C29×#9911yescharacteristic
318C2×C4C29×#10011yescharacteristic
319C2×C4C29×#10011yescharacteristic
320C2×C4C2×C22⋊C4×C2911yescharacteristic
321C2×C4C2×M16×C2911yescharacteristic
322C8—22no—
323C8—22no—
324C8—42no—
325C22—22no—
326C22—24no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—42no—
332C22—44no—
333C22—42no—
334C22—44no—
335C22—44no—
336C22—48no—
337C22—42no—
338C22—44no—
339C22—42no—
340C22C29×#32311yescharacteristic
341C22C29×#32311yescharacteristic
342C22C2×C29×C22⋊C811yescharacteristic
343C4—21no—
344C4—21no—
345C4—42no—
346C4C29×#32311yescharacteristic
347C4C29×#32311yescharacteristic
348C4C2×C29×#9911yescharacteristic
349C4C2×C29×#10011yescharacteristic
350C2—21no—
351C2—21no—
352C2—44no—
353C2—41no—
354C2—41no—
355C2C29×#132012yesdirect product factor
356C2C2×C29×#32311yescharacteristic
subgroupG/H
centerC2×C4×C29#99
commutatorC23C22×C8×C29
Frattini, cosocleC2×M16C23×C29
socleC22×C29#323
prime radicalC25×C29C8
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C22×C4×C29 ◁ C22×M16×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#349C2semidirect
3. C29×#1320C2direct (N × H)
13. C29×#349C22semidirect
96. C2×#1320C29direct (N × H)
148. C2×#349C2×C29semidirect
149. #1320C2×C29direct (N × H)
184. #349C22×C29semidirect
190. C2×C29#1320direct (N × H)
221. C29C2×#1320direct (N × H)
355. C2C29×#1320direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4072
C2×C29×#3492
C29×#13202
C2×#132029