Subgroups — C₂₉×#12871 #20307771

Order 7424.

442 conjugacy classes of subgroups.

The subgroup lattice has 254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₉×#107	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2112	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#1810	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1387	C₂	1	4	yes	maximal, complemented
5	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	C₂²×C₄⋊C₄×C₂₉	—	2	1	no	—
7	C₂×C₂₉×M₃₂	C₂²	1	2	yes	—
8	C₂×C₂₉×#108	C₂²	1	2	yes	—
9	C₂×C₂₉×#107	—	2	1	no	—
10	C₂×C₂₉×#107	—	2	1	no	—
11	C₂×C₂₉×#107	—	2	1	no	—
12	C₂×C₂₉×#107	C₄	1	2	yes	—
13	C₂×C₂₉×#107	C₄	1	2	yes	—
14	C₂×C₂₉×#107	C₂²	1	2	yes	—
15	C₂₉×#407	—	2	1	no	—
16	C₂₉×C₂²⋊C₁₆	—	2	1	no	—
17	C₂₉×C₂²⋊C₁₆	—	2	1	no	—
18	C₂₉×#341	—	2	1	no	—
19	C₂³×C₄×C₂₉	—	4	1	no	—
20	C₂³×C₄×C₂₉	D₄	1	1	yes	characteristic
21	C₂×M₁₆×C₂₉	—	2	2	no	—
22	C₂²×C₈×C₂₉	—	2	4	no	—
23	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
27	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
28	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
33	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
34	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
35	C₂₉×M₃₂	—	2	4	no	—
36	C₂×C₁₆×C₂₉	—	2	2	no	—
37	C₂₉×#108	—	2	4	no	—
38	C₂₉×#107	—	2	2	no	—
39	C₂₉×#107	—	2	2	no	—
40	C₂₉×#107	—	2	2	no	—
41	C₂₉×#107	C₂×C₄	1	4	yes	—
42	C₂₉×C₂²⋊C₈	—	4	1	no	—
43	C₂₉×C₂²⋊C₈	—	4	1	no	—
44	C₂⁴×C₂₉	SD₁₆	1	1	yes	characteristic
45	C₂²×C₄×C₂₉	—	2	2	no	—
46	C₂²×C₄×C₂₉	—	2	2	no	—
47	C₂²×C₄×C₂₉	—	4	2	no	—
48	C₂²×C₄×C₂₉	—	4	2	no	—
49	C₂²×C₄×C₂₉	—	4	2	no	—
50	C₂²×C₄×C₂₉	—	8	4	no	—
51	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₂₉	D₈	1	1	yes	characteristic
54	C₂²×C₄×C₂₉	D₈	1	1	yes	characteristic
55	C₂²×C₄×C₂₉	SD₁₆	1	1	yes	characteristic
56	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
57	M₁₆×C₂₉	—	4	2	no	—
58	M₁₆×C₂₉	—	4	2	no	—
59	C₂×C₈×C₂₉	—	2	2	no	—
60	C₂×C₈×C₂₉	—	2	2	no	—
61	C₂×C₈×C₂₉	—	2	2	no	—
62	C₂×C₈×C₂₉	—	2	2	no	—
63	C₂×C₈×C₂₉	—	2	2	no	—
64	C₂×C₈×C₂₉	—	4	2	no	—
65	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
69	C₂×C₈×C₂₉	#41	1	4	yes	—
70	C₄⋊C₄×C₂₉	—	2	4	no	—
71	C₄⋊C₄×C₂₉	—	4	2	no	—
72	C₄⋊C₄×C₂₉	—	4	2	no	—
73	C₄⋊C₄×C₂₉	—	4	2	no	—
74	C₁₆×C₂₉	—	4	2	no	—
75	#12871	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂³×C₂₉	—	2	2	no	—
77	C₂³×C₂₉	—	2	2	no	—
78	C₂³×C₂₉	—	2	2	no	—
79	C₂³×C₂₉	#102	1	1	yes	characteristic
80	C₂³×C₂₉	#102	1	1	yes	characteristic
81	C₂³×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
82	C₂×C₄×C₂₉	—	2	2	no	—
83	C₂×C₄×C₂₉	—	2	1	no	—
84	C₂×C₄×C₂₉	—	2	1	no	—
85	C₂×C₄×C₂₉	—	2	1	no	—
86	C₂×C₄×C₂₉	—	2	1	no	—
87	C₂×C₄×C₂₉	—	2	2	no	—
88	C₂×C₄×C₂₉	—	2	2	no	—
89	C₂×C₄×C₂₉	—	4	4	no	—
90	C₂×C₄×C₂₉	—	8	4	no	—
91	C₂×C₄×C₂₉	—	8	4	no	—
92	C₂×C₄×C₂₉	—	8	4	no	—
93	C₂×C₄×C₂₉	#102	1	1	yes	characteristic
94	C₂×C₄×C₂₉	#102	1	1	yes	characteristic
95	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×C₂₉	#123	1	2	yes	—
97	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
98	C₂×C₄×C₂₉	#137	1	2	yes	—
99	C₈×C₂₉	—	2	1	no	—
100	C₈×C₂₉	—	2	1	no	—
101	C₈×C₂₉	—	8	2	no	—
102	C₈×C₂₉	#117	1	2	yes	—
103	C₈×C₂₉	#123	1	2	yes	—
104	C₂²×#107	C₂×C₂₉	1	1	yes	characteristic
105	#2112	C₂×C₂₉	1	1	yes	characteristic
106	#1810	C₂×C₂₉	1	1	yes	characteristic
107	#1387	C₂×C₂₉	1	4	yes	complemented
108	C₂²×C₂₉	—	2	8	no	—
109	C₂²×C₂₉	—	2	1	no	—
110	C₂²×C₂₉	—	2	1	no	—
111	C₂²×C₂₉	—	2	1	no	—
112	C₂²×C₂₉	—	2	1	no	—
113	C₂²×C₂₉	—	2	1	no	—
114	C₂²×C₂₉	—	2	1	no	—
115	C₂²×C₂₉	#361	1	2	yes	—
116	C₂²×C₂₉	#362	1	2	yes	—
117	C₂²×C₂₉	C₂×#102	1	1	yes	characteristic
118	C₂²×C₂₉	#483	1	2	yes	—
119	C₄×C₂₉	—	2	1	no	—
120	C₄×C₂₉	—	2	1	no	—
121	C₄×C₂₉	—	8	4	no	—
122	C₄×C₂₉	#381	1	1	yes	characteristic
123	C₄×C₂₉	#419	1	1	yes	characteristic
124	C₄×C₂₉	#480	1	2	yes	—
125	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
126	C₂²×C₄⋊C₄	—	2	1	no	—
127	C₂×M₃₂	C₂²×C₂₉	1	2	yes	—
128	C₂×#108	C₂²×C₂₉	1	2	yes	—
129	C₂×#107	—	2	1	no	—
130	C₂×#107	—	2	1	no	—
131	C₂×#107	—	2	1	no	—
132	C₂×#107	C₄×C₂₉	1	2	yes	—
133	C₂×#107	C₄×C₂₉	1	2	yes	—
134	C₂×#107	C₂²×C₂₉	1	2	yes	—
135	#407	—	2	1	no	—
136	C₂²⋊C₁₆	—	2	1	no	—
137	C₂²⋊C₁₆	—	2	1	no	—
138	#341	—	2	1	no	—
139	C₂×C₂₉	—	2	2	no	—
140	C₂×C₂₉	—	2	2	no	—
141	C₂×C₂₉	—	2	2	no	—
142	C₂×C₂₉	#1823	1	1	yes	characteristic
143	C₂×C₂₉	C₂×#361	1	1	yes	characteristic
144	C₂×C₂₉	C₂×#362	1	1	yes	characteristic
145	C₂³×C₄	—	4	1	no	—
146	C₂³×C₄	D₄×C₂₉	1	1	yes	characteristic
147	C₂×M₁₆	—	2	2	no	—
148	C₂²×C₈	—	2	4	no	—
149	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
150	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
151	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
152	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
153	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
154	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
155	C₂×C₄⋊C₄	—	2	2	no	—
156	C₂×C₄⋊C₄	—	2	2	no	—
157	C₂×C₄⋊C₄	—	2	2	no	—
158	C₂×C₄⋊C₄	—	4	1	no	—
159	C₂×C₄⋊C₄	—	4	1	no	—
160	C₂×C₄⋊C₄	—	4	1	no	—
161	M₃₂	—	2	4	no	—
162	C₂×C₁₆	—	2	2	no	—
163	#108	—	2	4	no	—
164	#107	—	2	2	no	—
165	#107	—	2	2	no	—
166	#107	—	2	2	no	—
167	#107	C₂×C₄×C₂₉	1	4	yes	—
168	C₂²⋊C₈	—	4	1	no	—
169	C₂²⋊C₈	—	4	1	no	—
170	C₂₉	#12871	1	1	yes	characteristic, direct product factor, Sylow
171	C₂⁴	SD₁₆×C₂₉	1	1	yes	characteristic
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	4	2	no	—
175	C₂²×C₄	—	4	2	no	—
176	C₂²×C₄	—	4	2	no	—
177	C₂²×C₄	—	8	4	no	—
178	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
179	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
180	C₂²×C₄	D₈×C₂₉	1	1	yes	characteristic
181	C₂²×C₄	D₈×C₂₉	1	1	yes	characteristic
182	C₂²×C₄	SD₁₆×C₂₉	1	1	yes	characteristic
183	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
184	M₁₆	—	4	2	no	—
185	M₁₆	—	4	2	no	—
186	C₂×C₈	—	2	2	no	—
187	C₂×C₈	—	2	2	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	—	2	2	no	—
191	C₂×C₈	—	4	2	no	—
192	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
193	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
194	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
195	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
196	C₂×C₈	#41×C₂₉	1	4	yes	—
197	C₄⋊C₄	—	2	4	no	—
198	C₄⋊C₄	—	4	2	no	—
199	C₄⋊C₄	—	4	2	no	—
200	C₄⋊C₄	—	4	2	no	—
201	C₁₆	—	4	2	no	—
202	C₂³	—	2	2	no	—
203	C₂³	—	2	2	no	—
204	C₂³	—	2	2	no	—
205	C₂³	C₂₉×#102	1	1	yes	characteristic
206	C₂³	C₂₉×#102	1	1	yes	characteristic
207	C₂³	C₂×SD₁₆×C₂₉	1	1	yes	characteristic
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	4	4	no	—
216	C₂×C₄	—	8	4	no	—
217	C₂×C₄	—	8	4	no	—
218	C₂×C₄	—	8	4	no	—
219	C₂×C₄	C₂₉×#102	1	1	yes	characteristic
220	C₂×C₄	C₂₉×#102	1	1	yes	characteristic
221	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
222	C₂×C₄	C₂₉×#123	1	2	yes	—
223	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
224	C₂×C₄	C₂₉×#137	1	2	yes	—
225	C₈	—	2	1	no	—
226	C₈	—	2	1	no	—
227	C₈	—	8	2	no	—
228	C₈	C₂₉×#117	1	2	yes	—
229	C₈	C₂₉×#123	1	2	yes	—
230	C₂²	—	2	8	no	—
231	C₂²	—	2	1	no	—
232	C₂²	—	2	1	no	—
233	C₂²	—	2	1	no	—
234	C₂²	—	2	1	no	—
235	C₂²	—	2	1	no	—
236	C₂²	—	2	1	no	—
237	C₂²	C₂₉×#361	1	2	yes	—
238	C₂²	C₂₉×#362	1	2	yes	—
239	C₂²	C₂×C₂₉×#102	1	1	yes	characteristic
240	C₂²	C₂₉×#483	1	2	yes	—
241	C₄	—	2	1	no	—
242	C₄	—	2	1	no	—
243	C₄	—	8	4	no	—
244	C₄	C₂₉×#381	1	1	yes	characteristic
245	C₄	C₂₉×#419	1	1	yes	characteristic
246	C₄	C₂₉×#480	1	2	yes	—
247	C₂	—	2	2	no	—
248	C₂	—	2	2	no	—
249	C₂	—	2	2	no	—
250	C₂	C₂₉×#1823	1	1	yes	characteristic
251	C₂	C₂×C₂₉×#361	1	1	yes	characteristic
252	C₂	C₂×C₂₉×#362	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₂₉
Frattini, cosocle	C₂²×C₈	C₂³×C₂₉
prime radical	C₂⁴×C₂₉	SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ C₂³×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₉×#1387	C₂	semidirect
75. #12871	C₂₉	direct (N × H)
107. #1387	C₂×C₂₉	semidirect
170. C₂₉	#12871	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂₉×#107	2
C₂₉×#2112	2
C₂₉×#1810	2
C₂₉×#1387	2
#12871	29

Subgroups — C29×#12871 #20307771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#12871 #20307771