Subgroups — C₂₉×#13363 #20308263

Order 7424.

450 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#357	C₂	1	2	yes	maximal
3	C₂₉×#1970	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1380	C₂	1	2	yes	maximal, complemented
5	C₂₉×#1374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×C₂₉×C₄⋊Q₈	—	2	1	no	—
8	C₂²×C₁₆×C₂₉	C₂²	1	2	yes	—
9	C₂₉×#500	—	2	4	no	—
10	C₂×C₂₉×#107	—	2	1	no	—
11	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
12	C₂×C₂₉×#107	C₂²	1	2	yes	—
13	C₂×C₂₉×#102	—	2	1	no	—
14	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
15	C₂₉×#390	—	2	1	no	—
16	C₂₉×#357	—	2	4	no	—
17	C₂²×Q₈×C₂₉	—	4	1	no	—
18	C₂²×D₄×C₂₉	—	2	1	no	—
19	C₂×D₈×C₂₉	—	2	2	no	—
20	C₂×D₈×C₂₉	—	2	2	no	—
21	C₂×D₈×C₂₉	—	2	1	no	—
22	C₂×D₈×C₂₉	Q₈	1	2	yes	complemented
23	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
24	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
25	C₂₉×C₄⋊Q₈	—	2	4	no	—
26	C₂₉×C₄⋊Q₈	—	4	2	no	—
27	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
30	C₂×C₂²⋊C₄×C₂₉	—	4	1	no	—
31	C₂×C₂²⋊C₄×C₂₉	—	4	1	no	—
32	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
33	C₂×C₁₆×C₂₉	—	2	2	no	—
34	C₂×C₁₆×C₂₉	—	2	2	no	—
35	C₂×C₁₆×C₂₉	—	2	2	no	—
36	C₂₉×#107	—	2	4	no	—
37	C₂₉×#107	—	2	2	no	—
38	C₂₉×#107	—	2	2	no	—
39	C₂₉×#107	D₄	1	4	yes	—
40	C₂₉×#102	—	4	2	no	—
41	C₄×C₈×C₂₉	—	2	2	no	—
42	C₂⁴×C₂₉	—	4	1	no	—
43	C₂×Q₈×C₂₉	—	4	4	no	—
44	C₂×Q₈×C₂₉	—	8	2	no	—
45	C₂×Q₈×C₂₉	—	8	2	no	—
46	C₂×D₄×C₂₉	—	2	2	no	—
47	C₂×D₄×C₂₉	—	4	1	no	—
48	C₂×D₄×C₂₉	—	4	1	no	—
49	C₂×D₄×C₂₉	—	4	1	no	—
50	C₂×D₄×C₂₉	—	4	1	no	—
51	C₂×D₄×C₂₉	—	4	1	no	—
52	C₂²×C₄×C₂₉	—	4	2	no	—
53	C₂²×C₄×C₂₉	—	4	1	no	—
54	C₂²×C₄×C₂₉	D₈	1	1	yes	characteristic
55	C₂²×C₄×C₂₉	D₈	1	1	yes	characteristic
56	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
57	D₈×C₂₉	—	2	4	no	—
58	D₈×C₂₉	—	4	2	no	—
59	C₂×C₈×C₂₉	—	2	1	no	—
60	C₂×C₈×C₂₉	—	2	1	no	—
61	C₂×C₈×C₂₉	SD₁₆	1	2	yes	—
62	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
63	C₂×C₈×C₂₉	C₂×Q₈	1	1	yes	characteristic
64	C₂×C₈×C₂₉	#41	1	2	yes	—
65	C₂×C₈×C₂₉	#41	1	1	yes	characteristic
66	C₄⋊C₄×C₂₉	—	2	4	no	—
67	C₄⋊C₄×C₂₉	—	4	4	no	—
68	C₄⋊C₄×C₂₉	—	4	2	no	—
69	C₄⋊C₄×C₂₉	—	4	1	no	—
70	C₄⋊C₄×C₂₉	—	4	1	no	—
71	C₂²⋊C₄×C₂₉	—	8	2	no	—
72	C₂²⋊C₄×C₂₉	—	8	2	no	—
73	C₄²×C₂₉	—	2	1	no	—
74	C₄²×C₂₉	—	2	1	no	—
75	C₁₆×C₂₉	—	4	2	no	—
76	#13363	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂³×C₂₉	—	4	2	no	—
78	C₂³×C₂₉	—	8	1	no	—
79	C₂³×C₂₉	—	8	1	no	—
80	C₂³×C₂₉	—	8	1	no	—
81	C₂³×C₂₉	—	8	1	no	—
82	C₂³×C₂₉	—	8	1	no	—
83	C₂³×C₂₉	—	8	1	no	—
84	C₂³×C₂₉	C₂×D₈	1	1	yes	characteristic
85	Q₈×C₂₉	—	8	8	no	—
86	D₄×C₂₉	—	4	2	no	—
87	D₄×C₂₉	—	4	2	no	—
88	D₄×C₂₉	—	8	1	no	—
89	D₄×C₂₉	—	8	1	no	—
90	C₂×C₄×C₂₉	—	2	1	no	—
91	C₂×C₄×C₂₉	—	2	1	no	—
92	C₂×C₄×C₂₉	—	2	1	no	—
93	C₂×C₄×C₂₉	—	2	1	no	—
94	C₂×C₄×C₂₉	—	4	4	no	—
95	C₂×C₄×C₂₉	—	8	2	no	—
96	C₂×C₄×C₂₉	—	8	2	no	—
97	C₂×C₄×C₂₉	—	8	1	no	—
98	C₂×C₄×C₂₉	—	8	1	no	—
99	C₂×C₄×C₂₉	—	8	1	no	—
100	C₂×C₄×C₂₉	D₁₆	1	2	yes	—
101	C₂×C₄×C₂₉	SD₃₂	1	2	yes	—
102	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
103	C₂×C₄×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
104	C₂×C₄×C₂₉	#124	1	1	yes	characteristic
105	C₂×C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
106	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
107	C₂×C₄×C₂₉	#137	1	1	yes	characteristic
108	C₈×C₂₉	—	2	2	no	—
109	C₈×C₂₉	C₂²⋊Q₈	1	2	yes	—
110	C₈×C₂₉	#124	1	2	yes	—
111	C₂×#500	C₂×C₂₉	1	1	yes	characteristic, complemented
112	C₂×#357	C₂×C₂₉	1	2	yes	—
113	#1970	C₂×C₂₉	1	1	yes	characteristic
114	#1380	C₂×C₂₉	1	2	yes	complemented
115	#1374	C₂×C₂₉	1	1	yes	characteristic, complemented
116	C₂²×C₂₉	—	8	2	no	—
117	C₂²×C₂₉	—	8	2	no	—
118	C₂²×C₂₉	—	8	2	no	—
119	C₂²×C₂₉	—	16	1	no	—
120	C₂²×C₂₉	—	16	1	no	—
121	C₂²×C₂₉	—	16	1	no	—
122	C₂²×C₂₉	—	16	1	no	—
123	C₂²×C₂₉	#447	1	1	yes	characteristic
124	C₂²×C₂₉	#474	1	1	yes	characteristic
125	C₂²×C₂₉	#486	1	1	yes	characteristic
126	C₂²×C₂₉	C₂×D₁₆	1	1	yes	characteristic
127	C₂²×C₂₉	C₂×SD₃₂	1	1	yes	characteristic
128	C₂²×C₂₉	#509	1	1	yes	characteristic
129	C₂²×C₂₉	#510	1	1	yes	characteristic
130	C₄×C₂₉	—	2	2	no	—
131	C₄×C₂₉	—	2	2	no	—
132	C₄×C₂₉	—	8	4	no	—
133	C₄×C₂₉	—	16	1	no	—
134	C₄×C₂₉	#393	1	1	yes	characteristic
135	C₄×C₂₉	#448	1	1	yes	characteristic
136	C₄×C₂₉	#476	1	1	yes	characteristic
137	C₄×C₂₉	#489	1	1	yes	characteristic
138	C₂²×D₈	C₂²×C₂₉	1	1	yes	characteristic
139	C₂×C₄⋊Q₈	—	2	1	no	—
140	C₂²×C₁₆	C₂²×C₂₉	1	2	yes	—
141	#500	—	2	4	no	—
142	C₂×#107	—	2	1	no	—
143	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
144	C₂×#107	C₂²×C₂₉	1	2	yes	—
145	C₂×#102	—	2	1	no	—
146	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
147	#390	—	2	1	no	—
148	#357	—	2	4	no	—
149	C₂×C₂₉	—	16	2	no	—
150	C₂×C₂₉	#2023	1	1	yes	characteristic
151	C₂×C₂₉	#2184	1	1	yes	characteristic
152	C₂×C₂₉	#2185	1	1	yes	characteristic
153	C₂×C₂₉	#2224	1	1	yes	characteristic
154	C₂×C₂₉	#2226	1	1	yes	characteristic
155	C₂×C₂₉	#2240	1	1	yes	characteristic
156	C₂×C₂₉	#2243	1	1	yes	characteristic
157	C₂²×Q₈	—	4	1	no	—
158	C₂²×D₄	—	2	1	no	—
159	C₂×D₈	—	2	2	no	—
160	C₂×D₈	—	2	2	no	—
161	C₂×D₈	—	2	1	no	—
162	C₂×D₈	Q₈×C₂₉	1	2	yes	complemented
163	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
164	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
165	C₄⋊Q₈	—	2	4	no	—
166	C₄⋊Q₈	—	4	2	no	—
167	C₂×C₄⋊C₄	—	2	2	no	—
168	C₂×C₄⋊C₄	—	2	1	no	—
169	C₂×C₄⋊C₄	—	4	1	no	—
170	C₂×C₂²⋊C₄	—	4	1	no	—
171	C₂×C₂²⋊C₄	—	4	1	no	—
172	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
173	C₂×C₁₆	—	2	2	no	—
174	C₂×C₁₆	—	2	2	no	—
175	C₂×C₁₆	—	2	2	no	—
176	#107	—	2	4	no	—
177	#107	—	2	2	no	—
178	#107	—	2	2	no	—
179	#107	D₄×C₂₉	1	4	yes	—
180	#102	—	4	2	no	—
181	C₄×C₈	—	2	2	no	—
182	C₂₉	#13363	1	1	yes	characteristic, direct product factor, Sylow
183	C₂⁴	—	4	1	no	—
184	C₂×Q₈	—	4	4	no	—
185	C₂×Q₈	—	8	2	no	—
186	C₂×Q₈	—	8	2	no	—
187	C₂×D₄	—	2	2	no	—
188	C₂×D₄	—	4	1	no	—
189	C₂×D₄	—	4	1	no	—
190	C₂×D₄	—	4	1	no	—
191	C₂×D₄	—	4	1	no	—
192	C₂×D₄	—	4	1	no	—
193	C₂²×C₄	—	4	2	no	—
194	C₂²×C₄	—	4	1	no	—
195	C₂²×C₄	D₈×C₂₉	1	1	yes	characteristic
196	C₂²×C₄	D₈×C₂₉	1	1	yes	characteristic
197	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
198	D₈	—	2	4	no	—
199	D₈	—	4	2	no	—
200	C₂×C₈	—	2	1	no	—
201	C₂×C₈	—	2	1	no	—
202	C₂×C₈	SD₁₆×C₂₉	1	2	yes	—
203	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
204	C₂×C₈	C₂×Q₈×C₂₉	1	1	yes	characteristic
205	C₂×C₈	#41×C₂₉	1	2	yes	—
206	C₂×C₈	#41×C₂₉	1	1	yes	characteristic
207	C₄⋊C₄	—	2	4	no	—
208	C₄⋊C₄	—	4	4	no	—
209	C₄⋊C₄	—	4	2	no	—
210	C₄⋊C₄	—	4	1	no	—
211	C₄⋊C₄	—	4	1	no	—
212	C₂²⋊C₄	—	8	2	no	—
213	C₂²⋊C₄	—	8	2	no	—
214	C₄²	—	2	1	no	—
215	C₄²	—	2	1	no	—
216	C₁₆	—	4	2	no	—
217	C₂³	—	4	2	no	—
218	C₂³	—	8	1	no	—
219	C₂³	—	8	1	no	—
220	C₂³	—	8	1	no	—
221	C₂³	—	8	1	no	—
222	C₂³	—	8	1	no	—
223	C₂³	—	8	1	no	—
224	C₂³	C₂×D₈×C₂₉	1	1	yes	characteristic
225	Q₈	—	8	8	no	—
226	D₄	—	4	2	no	—
227	D₄	—	4	2	no	—
228	D₄	—	8	1	no	—
229	D₄	—	8	1	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	4	4	no	—
235	C₂×C₄	—	8	2	no	—
236	C₂×C₄	—	8	2	no	—
237	C₂×C₄	—	8	1	no	—
238	C₂×C₄	—	8	1	no	—
239	C₂×C₄	—	8	1	no	—
240	C₂×C₄	C₂₉×D₁₆	1	2	yes	—
241	C₂×C₄	C₂₉×SD₃₂	1	2	yes	—
242	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
243	C₂×C₄	C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
244	C₂×C₄	C₂₉×#124	1	1	yes	characteristic
245	C₂×C₄	C₂×SD₁₆×C₂₉	1	1	yes	characteristic
246	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
247	C₂×C₄	C₂₉×#137	1	1	yes	characteristic
248	C₈	—	2	2	no	—
249	C₈	C₂₉×C₂²⋊Q₈	1	2	yes	—
250	C₈	C₂₉×#124	1	2	yes	—
251	C₂²	—	8	2	no	—
252	C₂²	—	8	2	no	—
253	C₂²	—	8	2	no	—
254	C₂²	—	16	1	no	—
255	C₂²	—	16	1	no	—
256	C₂²	—	16	1	no	—
257	C₂²	—	16	1	no	—
258	C₂²	C₂₉×#447	1	1	yes	characteristic
259	C₂²	C₂₉×#474	1	1	yes	characteristic
260	C₂²	C₂₉×#486	1	1	yes	characteristic
261	C₂²	C₂×C₂₉×D₁₆	1	1	yes	characteristic
262	C₂²	C₂×C₂₉×SD₃₂	1	1	yes	characteristic
263	C₂²	C₂₉×#509	1	1	yes	characteristic
264	C₂²	C₂₉×#510	1	1	yes	characteristic
265	C₄	—	2	2	no	—
266	C₄	—	2	2	no	—
267	C₄	—	8	4	no	—
268	C₄	—	16	1	no	—
269	C₄	C₂₉×#393	1	1	yes	characteristic
270	C₄	C₂₉×#448	1	1	yes	characteristic
271	C₄	C₂₉×#476	1	1	yes	characteristic
272	C₄	C₂₉×#489	1	1	yes	characteristic
273	C₂	—	16	2	no	—
274	C₂	C₂₉×#2023	1	1	yes	characteristic
275	C₂	C₂₉×#2184	1	1	yes	characteristic
276	C₂	C₂₉×#2185	1	1	yes	characteristic
277	C₂	C₂₉×#2224	1	1	yes	characteristic
278	C₂	C₂₉×#2226	1	1	yes	characteristic
279	C₂	C₂₉×#2240	1	1	yes	characteristic
280	C₂	C₂₉×#2243	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₂₉
prime radical	C₂²×D₈×C₂₉	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ C₂×C₄×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#500	C₂	semidirect
4. C₂₉×#1380	C₂	semidirect
5. C₂₉×#1374	C₂	semidirect
22. C₂×D₈×C₂₉	Q₈	semidirect
76. #13363	C₂₉	direct (N × H)
111. C₂×#500	C₂×C₂₉	semidirect
114. #1380	C₂×C₂₉	semidirect
115. #1374	C₂×C₂₉	semidirect
162. C₂×D₈	Q₈×C₂₉	semidirect
182. C₂₉	#13363	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#500	2
C₂×C₂₉×#357	2
C₂₉×#1970	2
C₂₉×#1380	2
C₂₉×#1374	2
#13363	29

Subgroups — C29×#13363 #20308263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#13363 #20308263