Subgroups — C₂₉×#8634 #20303534

Order 7424.

388 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2931	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#1536	C₂	1	2	yes	maximal
5	C₂₉×#1307	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₉×#131	C₄	1	2	yes	—
7	C₂₉×#532	C₂²	1	1	yes	characteristic
8	C₂₉×#436	—	2	1	no	—
9	C₂₉×#436	—	2	1	no	—
10	C₈×D₄×C₂₉	—	2	1	no	—
11	C₈×D₄×C₂₉	—	2	1	no	—
12	C₂₉×#432	C₂²	1	2	yes	—
13	C₂₉×#432	C₂²	1	2	yes	—
14	C₂₉×#423	C₂²	1	1	yes	characteristic
15	C₂₉×#408	C₄	1	2	yes	—
16	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
17	C₂₉×#335	—	2	1	no	—
18	C₂₉×#335	—	2	1	no	—
19	C₂₉×#334	—	2	1	no	—
20	C₂₉×#334	—	2	1	no	—
21	C₂₉×#329	—	2	4	no	—
22	C₂×#41×C₂₉	C₂×C₄	1	2	yes	—
23	C₂₉×#131	—	4	4	no	—
24	C₂×M₁₆×C₂₉	—	2	2	no	—
25	C₂×M₁₆×C₂₉	C₂×C₄	1	2	yes	—
26	C₂²×C₈×C₂₉	—	2	2	no	—
27	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
29	C₂₉×C₄⋊Q₈	Q₈	1	1	yes	characteristic
30	C₂₉×#127	Q₈	1	1	yes	characteristic
31	C₂₉×#124	D₄	1	2	yes	—
32	C₂₉×#121	—	2	1	no	—
33	C₂₉×#121	—	2	1	no	—
34	C₄×D₄×C₂₉	—	2	1	no	—
35	C₄×D₄×C₂₉	—	2	1	no	—
36	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
37	C₂₉×C₄⋊C₈	—	2	1	no	—
38	C₂₉×C₄⋊C₈	—	2	1	no	—
39	C₂₉×C₄⋊C₈	—	2	2	no	—
40	C₂₉×C₄⋊C₈	—	2	2	no	—
41	C₂₉×C₂²⋊C₈	—	2	2	no	—
42	C₂₉×C₂²⋊C₈	—	2	2	no	—
43	C₂₉×C₂²⋊C₈	—	2	2	no	—
44	C₂₉×C₂²⋊C₈	—	2	2	no	—
45	C₂₉×#97	—	2	2	no	—
46	C₂₉×#97	—	2	2	no	—
47	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
48	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
49	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
50	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
51	#41×C₂₉	—	4	2	no	—
52	#41×C₂₉	—	4	2	no	—
53	C₂×Q₈×C₂₉	C₄⋊C₄	1	2	yes	—
54	C₂×D₄×C₂₉	—	2	2	no	—
55	C₂×D₄×C₂₉	—	2	1	no	—
56	C₂×D₄×C₂₉	—	2	1	no	—
57	C₂×D₄×C₂₉	C₄⋊C₄	1	2	yes	—
58	C₂²×C₄×C₂₉	—	2	2	no	—
59	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
61	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
62	M₁₆×C₂₉	—	4	4	no	—
63	M₁₆×C₂₉	—	4	2	no	—
64	C₂×C₈×C₂₉	—	2	2	no	—
65	C₂×C₈×C₂₉	—	2	2	no	—
66	C₂×C₈×C₂₉	—	4	1	no	—
67	C₂×C₈×C₂₉	—	4	4	no	—
68	C₂×C₈×C₂₉	—	4	2	no	—
69	C₂×C₈×C₂₉	—	4	2	no	—
70	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₄⋊C₄×C₂₉	—	2	1	no	—
75	C₄⋊C₄×C₂₉	—	2	1	no	—
76	C₂²⋊C₄×C₂₉	—	2	2	no	—
77	C₂²⋊C₄×C₂₉	—	2	2	no	—
78	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
81	C₄²×C₂₉	C₂×Q₈	1	1	yes	characteristic
82	#8634	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂³×C₂₉	—	2	2	no	—
84	C₂³×C₂₉	#117	1	1	yes	characteristic
85	Q₈×C₂₉	—	4	2	no	—
86	D₄×C₂₉	—	4	2	no	—
87	D₄×C₂₉	—	4	2	no	—
88	D₄×C₂₉	—	4	2	no	—
89	D₄×C₂₉	—	4	4	no	—
90	C₂×C₄×C₂₉	—	2	1	no	—
91	C₂×C₄×C₂₉	—	2	1	no	—
92	C₂×C₄×C₂₉	—	2	2	no	—
93	C₂×C₄×C₂₉	—	4	1	no	—
94	C₂×C₄×C₂₉	—	4	1	no	—
95	C₂×C₄×C₂₉	—	4	2	no	—
96	C₂×C₄×C₂₉	—	4	2	no	—
97	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
100	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
101	C₂×C₄×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
102	C₂×C₄×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
103	C₈×C₂₉	—	2	1	no	—
104	C₈×C₂₉	—	2	1	no	—
105	C₈×C₂₉	—	2	1	no	—
106	C₈×C₂₉	—	4	2	no	—
107	C₈×C₂₉	—	8	2	no	—
108	C₈×C₂₉	—	8	2	no	—
109	C₈×C₂₉	#100	1	2	yes	—
110	#2931	C₂×C₂₉	1	1	yes	characteristic
111	#1568	C₂×C₂₉	1	1	yes	characteristic, complemented
112	#1568	C₂×C₂₉	1	1	yes	characteristic, complemented
113	#1536	C₂×C₂₉	1	2	yes	—
114	#1307	C₂×C₂₉	1	2	yes	complemented
115	C₂²×C₂₉	—	2	1	no	—
116	C₂²×C₂₉	—	2	1	no	—
117	C₂²×C₂₉	—	2	1	no	—
118	C₂²×C₂₉	—	4	2	no	—
119	C₂²×C₂₉	—	4	2	no	—
120	C₂²×C₂₉	—	4	2	no	—
121	C₂²×C₂₉	#380	1	1	yes	characteristic
122	C₄×C₂₉	—	2	1	no	—
123	C₄×C₂₉	—	2	1	no	—
124	C₄×C₂₉	—	2	1	no	—
125	C₄×C₂₉	—	2	1	no	—
126	C₄×C₂₉	—	2	1	no	—
127	C₄×C₂₉	—	4	2	no	—
128	C₄×C₂₉	C₂×#100	1	1	yes	characteristic
129	C₄×C₂₉	#413	1	1	yes	characteristic
130	C₂×#131	C₄×C₂₉	1	2	yes	—
131	#532	C₂²×C₂₉	1	1	yes	characteristic
132	#436	—	2	1	no	—
133	#436	—	2	1	no	—
134	C₈×D₄	—	2	1	no	—
135	C₈×D₄	—	2	1	no	—
136	#432	C₂²×C₂₉	1	2	yes	—
137	#432	C₂²×C₂₉	1	2	yes	—
138	#423	C₂²×C₂₉	1	1	yes	characteristic
139	#408	C₄×C₂₉	1	2	yes	—
140	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
141	#335	—	2	1	no	—
142	#335	—	2	1	no	—
143	#334	—	2	1	no	—
144	#334	—	2	1	no	—
145	#329	—	2	4	no	—
146	C₂×C₂₉	—	4	1	no	—
147	C₂×C₂₉	—	8	2	no	—
148	C₂×C₂₉	#1800	1	1	yes	characteristic
149	C₂×C₂₉	#1814	1	1	yes	characteristic
150	C₂×C₂₉	#1814	1	1	yes	characteristic
151	C₂×#41	C₂×C₄×C₂₉	1	2	yes	—
152	#131	—	4	4	no	—
153	C₂×M₁₆	—	2	2	no	—
154	C₂×M₁₆	C₂×C₄×C₂₉	1	2	yes	—
155	C₂²×C₈	—	2	2	no	—
156	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
157	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
158	C₄⋊Q₈	Q₈×C₂₉	1	1	yes	characteristic
159	#127	Q₈×C₂₉	1	1	yes	characteristic
160	#124	D₄×C₂₉	1	2	yes	—
161	#121	—	2	1	no	—
162	#121	—	2	1	no	—
163	C₄×D₄	—	2	1	no	—
164	C₄×D₄	—	2	1	no	—
165	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
166	C₄⋊C₈	—	2	1	no	—
167	C₄⋊C₈	—	2	1	no	—
168	C₄⋊C₈	—	2	2	no	—
169	C₄⋊C₈	—	2	2	no	—
170	C₂²⋊C₈	—	2	2	no	—
171	C₂²⋊C₈	—	2	2	no	—
172	C₂²⋊C₈	—	2	2	no	—
173	C₂²⋊C₈	—	2	2	no	—
174	#97	—	2	2	no	—
175	#97	—	2	2	no	—
176	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
177	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
178	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
179	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
180	C₂₉	#8634	1	1	yes	characteristic, direct product factor, Sylow
181	#41	—	4	2	no	—
182	#41	—	4	2	no	—
183	C₂×Q₈	C₄⋊C₄×C₂₉	1	2	yes	—
184	C₂×D₄	—	2	2	no	—
185	C₂×D₄	—	2	1	no	—
186	C₂×D₄	—	2	1	no	—
187	C₂×D₄	C₄⋊C₄×C₂₉	1	2	yes	—
188	C₂²×C₄	—	2	2	no	—
189	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
190	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
191	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
192	M₁₆	—	4	4	no	—
193	M₁₆	—	4	2	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	—	4	1	no	—
197	C₂×C₈	—	4	4	no	—
198	C₂×C₈	—	4	2	no	—
199	C₂×C₈	—	4	2	no	—
200	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
201	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
202	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
203	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
204	C₄⋊C₄	—	2	1	no	—
205	C₄⋊C₄	—	2	1	no	—
206	C₂²⋊C₄	—	2	2	no	—
207	C₂²⋊C₄	—	2	2	no	—
208	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
209	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
210	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
211	C₄²	C₂×Q₈×C₂₉	1	1	yes	characteristic
212	C₂³	—	2	2	no	—
213	C₂³	C₂₉×#117	1	1	yes	characteristic
214	Q₈	—	4	2	no	—
215	D₄	—	4	2	no	—
216	D₄	—	4	2	no	—
217	D₄	—	4	2	no	—
218	D₄	—	4	4	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	4	1	no	—
223	C₂×C₄	—	4	1	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
227	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
228	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
229	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
230	C₂×C₄	C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
231	C₂×C₄	C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
232	C₈	—	2	1	no	—
233	C₈	—	2	1	no	—
234	C₈	—	2	1	no	—
235	C₈	—	4	2	no	—
236	C₈	—	8	2	no	—
237	C₈	—	8	2	no	—
238	C₈	C₂₉×#100	1	2	yes	—
239	C₂²	—	2	1	no	—
240	C₂²	—	2	1	no	—
241	C₂²	—	2	1	no	—
242	C₂²	—	4	2	no	—
243	C₂²	—	4	2	no	—
244	C₂²	—	4	2	no	—
245	C₂²	C₂₉×#380	1	1	yes	characteristic
246	C₄	—	2	1	no	—
247	C₄	—	2	1	no	—
248	C₄	—	2	1	no	—
249	C₄	—	2	1	no	—
250	C₄	—	2	1	no	—
251	C₄	—	4	2	no	—
252	C₄	C₂×C₂₉×#100	1	1	yes	characteristic
253	C₄	C₂₉×#413	1	1	yes	characteristic
254	C₂	—	4	1	no	—
255	C₂	—	8	2	no	—
256	C₂	C₂₉×#1800	1	1	yes	characteristic
257	C₂	C₂₉×#1814	1	1	yes	characteristic
258	C₂	C₂₉×#1814	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	#380
commutator	C₂²×C₄	C₂²×C₄×C₂₉
Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
prime radical	C₂₉×#532	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#1568	C₂	semidirect
3. C₂₉×#1568	C₂	semidirect
5. C₂₉×#1307	C₂	semidirect
82. #8634	C₂₉	direct (N × H)
111. #1568	C₂×C₂₉	semidirect
112. #1568	C₂×C₂₉	semidirect
114. #1307	C₂×C₂₉	semidirect
180. C₂₉	#8634	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#2931	2
C₂₉×#1568	2
C₂₉×#1536	2
C₂₉×#1307	2
#8634	29

Subgroups — C29×#8634 #20303534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#8634 #20303534