Subgroups — C₂₉×#7879 #20302779

Order 7424.

630 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#431	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1277	C₂	1	4	yes	maximal, complemented
5	C₂³×C₈×C₂₉	—	2	1	no	—
6	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
7	C₂₉×#432	—	2	2	no	—
8	C₂₉×#432	C₄	1	4	yes	—
9	C₂₉×#431	—	2	2	no	—
10	C₂₉×#431	—	2	2	no	—
11	C₂×C₂₉×C₄⋊C₈	—	2	1	no	—
12	C₂×C₂₉×C₄⋊C₈	—	2	2	no	—
13	C₂×C₂₉×C₄⋊C₈	C₄	1	4	yes	—
14	C₂×C₂₉×C₄⋊C₈	C₄	1	2	yes	—
15	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₂₉×C₂²⋊C₈	—	2	1	no	—
18	C₂×C₂₉×C₂²⋊C₈	C₄	1	2	yes	—
19	C₂×C₂₉×#97	—	2	1	no	—
20	C₂×C₄×C₈×C₂₉	C₂²	1	2	yes	—
21	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₂₉	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₂₉	Q₈	1	1	yes	characteristic
24	C₂²×C₈×C₂₉	—	2	4	no	—
25	C₂²×C₈×C₂₉	—	2	2	no	—
26	C₂²×C₈×C₂₉	—	2	2	no	—
27	C₂²×C₈×C₂₉	—	4	4	no	—
28	C₂²×C₈×C₂₉	C₂×C₄	1	4	yes	—
29	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄²×C₂₉	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₂₉	C₂×C₄	1	2	yes	—
32	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₂₉	D₄	1	2	yes	—
34	C₂×C₄²×C₂₉	D₄	1	2	yes	—
35	C₂×C₄²×C₂₉	Q₈	1	1	yes	characteristic
36	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
37	C₂₉×C₄⋊C₈	—	2	4	no	—
38	C₂₉×C₄⋊C₈	—	2	4	no	—
39	C₂₉×C₄⋊C₈	—	2	2	no	—
40	C₂₉×C₄⋊C₈	—	2	2	no	—
41	C₂₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
42	C₂₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
43	C₂₉×C₂²⋊C₈	—	2	4	no	—
44	C₂₉×C₂²⋊C₈	—	2	4	no	—
45	C₂₉×#97	—	2	4	no	—
46	C₄×C₈×C₂₉	—	2	2	no	—
47	C₄×C₈×C₂₉	—	2	2	no	—
48	C₂⁴×C₂₉	C₄⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₂₉	—	2	4	no	—
50	C₂²×C₄×C₂₉	—	2	4	no	—
51	C₂²×C₄×C₂₉	—	2	2	no	—
52	C₂²×C₄×C₂₉	—	2	2	no	—
53	C₂²×C₄×C₂₉	C₄²	1	2	yes	—
54	C₂²×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
61	C₂²×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
62	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
65	C₂×C₈×C₂₉	—	2	4	no	—
66	C₂×C₈×C₂₉	—	2	4	no	—
67	C₂×C₈×C₂₉	—	2	4	no	—
68	C₂×C₈×C₂₉	—	2	8	no	—
69	C₂×C₈×C₂₉	—	4	8	no	—
70	C₂×C₈×C₂₉	—	4	2	no	—
71	C₂×C₈×C₂₉	—	4	4	no	—
72	C₂×C₈×C₂₉	—	4	2	no	—
73	C₄²×C₂₉	C₄²	1	2	yes	—
74	C₄²×C₂₉	C₂²⋊C₄	1	2	yes	—
75	C₄²×C₂₉	C₂²⋊C₄	1	2	yes	—
76	C₄²×C₂₉	C₂²⋊C₄	1	2	yes	—
77	C₄²×C₂₉	C₄⋊C₄	1	2	yes	—
78	C₄²×C₂₉	C₄⋊C₄	1	2	yes	—
79	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
80	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
81	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
82	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
83	#7879	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂³×C₂₉	—	2	2	no	—
85	C₂³×C₂₉	—	2	2	no	—
86	C₂³×C₂₉	#95	1	2	yes	—
87	C₂³×C₂₉	#108	1	4	yes	—
88	C₂³×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₂₉	—	2	4	no	—
90	C₂×C₄×C₂₉	—	2	4	no	—
91	C₂×C₄×C₂₉	—	2	2	no	—
92	C₂×C₄×C₂₉	—	2	2	no	—
93	C₂×C₄×C₂₉	—	2	2	no	—
94	C₂×C₄×C₂₉	—	2	2	no	—
95	C₂×C₄×C₂₉	—	2	4	no	—
96	C₂×C₄×C₂₉	—	2	4	no	—
97	C₂×C₄×C₂₉	—	2	4	no	—
98	C₂×C₄×C₂₉	—	2	2	no	—
99	C₂×C₄×C₂₉	—	2	2	no	—
100	C₂×C₄×C₂₉	#95	1	2	yes	—
101	C₂×C₄×C₂₉	#95	1	2	yes	—
102	C₂×C₄×C₂₉	#95	1	2	yes	—
103	C₂×C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
104	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₄×C₂₉	#131	1	4	yes	—
110	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
111	C₂×C₄×C₂₉	#137	1	2	yes	—
112	C₈×C₂₉	—	4	4	no	—
113	C₈×C₂₉	—	4	4	no	—
114	C₈×C₂₉	—	4	4	no	—
115	C₂×#432	C₂×C₂₉	1	1	yes	characteristic
116	C₂×#431	C₂×C₂₉	1	1	yes	characteristic
117	C₂²×C₄⋊C₈	C₂×C₂₉	1	1	yes	characteristic
118	#1277	C₂×C₂₉	1	4	yes	complemented
119	C₂²×C₂₉	—	2	8	no	—
120	C₂²×C₂₉	—	2	2	no	—
121	C₂²×C₂₉	—	2	2	no	—
122	C₂²×C₂₉	#341	1	4	yes	—
123	C₂²×C₂₉	C₂×#95	1	1	yes	characteristic
124	C₂²×C₂₉	#424	1	2	yes	—
125	C₂²×C₂₉	#428	1	2	yes	—
126	C₂²×C₂₉	C₂×#108	1	2	yes	—
127	C₄×C₂₉	—	2	2	no	—
128	C₄×C₂₉	—	2	2	no	—
129	C₄×C₂₉	—	2	2	no	—
130	C₄×C₂₉	—	2	1	no	—
131	C₄×C₂₉	—	2	1	no	—
132	C₄×C₂₉	#405	1	2	yes	—
133	C₄×C₂₉	#408	1	2	yes	—
134	C₄×C₂₉	#417	1	2	yes	—
135	C₄×C₂₉	#418	1	1	yes	characteristic
136	C₄×C₂₉	#419	1	1	yes	characteristic
137	C₂³×C₈	—	2	1	no	—
138	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
139	#432	—	2	2	no	—
140	#432	C₄×C₂₉	1	4	yes	—
141	#431	—	2	2	no	—
142	#431	—	2	2	no	—
143	C₂×C₄⋊C₈	—	2	1	no	—
144	C₂×C₄⋊C₈	—	2	2	no	—
145	C₂×C₄⋊C₈	C₄×C₂₉	1	2	yes	—
146	C₂×C₄⋊C₈	C₄×C₂₉	1	4	yes	—
147	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
148	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
149	C₂×C₂²⋊C₈	—	2	1	no	—
150	C₂×C₂²⋊C₈	C₄×C₂₉	1	2	yes	—
151	C₂×#97	—	2	1	no	—
152	C₂×C₄×C₈	C₂²×C₂₉	1	2	yes	—
153	C₂×C₂₉	—	2	4	no	—
154	C₂×C₂₉	#1573	1	4	yes	—
155	C₂×C₂₉	#1729	1	1	yes	characteristic
156	C₂×C₂₉	#1736	1	1	yes	characteristic
157	C₂×C₂₉	C₂×#341	1	1	yes	characteristic
158	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
159	C₂³×C₄	D₄×C₂₉	1	1	yes	characteristic
160	C₂³×C₄	Q₈×C₂₉	1	1	yes	characteristic
161	C₂²×C₈	—	2	4	no	—
162	C₂²×C₈	—	2	2	no	—
163	C₂²×C₈	—	2	2	no	—
164	C₂²×C₈	—	4	4	no	—
165	C₂²×C₈	C₂×C₄×C₂₉	1	4	yes	—
166	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
167	C₂×C₄²	C₂×C₄×C₂₉	1	2	yes	—
168	C₂×C₄²	C₂×C₄×C₂₉	1	2	yes	—
169	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
170	C₂×C₄²	D₄×C₂₉	1	2	yes	—
171	C₂×C₄²	D₄×C₂₉	1	2	yes	—
172	C₂×C₄²	Q₈×C₂₉	1	1	yes	characteristic
173	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
174	C₄⋊C₈	—	2	4	no	—
175	C₄⋊C₈	—	2	4	no	—
176	C₄⋊C₈	—	2	2	no	—
177	C₄⋊C₈	—	2	2	no	—
178	C₄⋊C₈	C₂×C₄×C₂₉	1	4	yes	—
179	C₄⋊C₈	C₂×C₄×C₂₉	1	4	yes	—
180	C₂²⋊C₈	—	2	4	no	—
181	C₂²⋊C₈	—	2	4	no	—
182	#97	—	2	4	no	—
183	C₄×C₈	—	2	2	no	—
184	C₄×C₈	—	2	2	no	—
185	C₂₉	#7879	1	1	yes	characteristic, direct product factor, Sylow
186	C₂⁴	C₄⋊C₄×C₂₉	1	1	yes	characteristic
187	C₂²×C₄	—	2	4	no	—
188	C₂²×C₄	—	2	4	no	—
189	C₂²×C₄	—	2	2	no	—
190	C₂²×C₄	—	2	2	no	—
191	C₂²×C₄	C₄²×C₂₉	1	2	yes	—
192	C₂²×C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
193	C₂²×C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
194	C₂²×C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
195	C₂²×C₄	C₄⋊C₄×C₂₉	1	2	yes	—
196	C₂²×C₄	C₄⋊C₄×C₂₉	1	2	yes	—
197	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
198	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
199	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
200	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
201	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
202	C₂²×C₄	C₂×Q₈×C₂₉	1	1	yes	characteristic
203	C₂×C₈	—	2	4	no	—
204	C₂×C₈	—	2	4	no	—
205	C₂×C₈	—	2	4	no	—
206	C₂×C₈	—	2	8	no	—
207	C₂×C₈	—	4	8	no	—
208	C₂×C₈	—	4	4	no	—
209	C₂×C₈	—	4	2	no	—
210	C₂×C₈	—	4	2	no	—
211	C₄²	C₄²×C₂₉	1	2	yes	—
212	C₄²	C₂²⋊C₄×C₂₉	1	2	yes	—
213	C₄²	C₂²⋊C₄×C₂₉	1	2	yes	—
214	C₄²	C₂²⋊C₄×C₂₉	1	2	yes	—
215	C₄²	C₄⋊C₄×C₂₉	1	2	yes	—
216	C₄²	C₄⋊C₄×C₂₉	1	2	yes	—
217	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
218	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
219	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
220	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
221	C₂³	—	2	2	no	—
222	C₂³	—	2	2	no	—
223	C₂³	C₂₉×#95	1	2	yes	—
224	C₂³	C₂₉×#108	1	4	yes	—
225	C₂³	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	2	4	no	—
230	C₂×C₄	—	2	4	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	4	no	—
233	C₂×C₄	—	2	4	no	—
234	C₂×C₄	—	2	4	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	C₂₉×#95	1	2	yes	—
238	C₂×C₄	C₂₉×#95	1	2	yes	—
239	C₂×C₄	C₂₉×#95	1	2	yes	—
240	C₂×C₄	C₂×C₄²×C₂₉	1	1	yes	characteristic
241	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
242	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
243	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
244	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
245	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
246	C₂×C₄	C₂₉×#131	1	4	yes	—
247	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
248	C₂×C₄	C₂₉×#137	1	2	yes	—
249	C₈	—	4	4	no	—
250	C₈	—	4	4	no	—
251	C₈	—	4	4	no	—
252	C₂²	—	2	2	no	—
253	C₂²	—	2	2	no	—
254	C₂²	—	2	8	no	—
255	C₂²	C₂₉×#341	1	4	yes	—
256	C₂²	C₂×C₂₉×#95	1	1	yes	characteristic
257	C₂²	C₂₉×#424	1	2	yes	—
258	C₂²	C₂₉×#428	1	2	yes	—
259	C₂²	C₂×C₂₉×#108	1	2	yes	—
260	C₄	—	2	2	no	—
261	C₄	—	2	2	no	—
262	C₄	—	2	1	no	—
263	C₄	—	2	1	no	—
264	C₄	—	2	2	no	—
265	C₄	C₂₉×#405	1	2	yes	—
266	C₄	C₂₉×#408	1	2	yes	—
267	C₄	C₂₉×#417	1	2	yes	—
268	C₄	C₂₉×#418	1	1	yes	characteristic
269	C₄	C₂₉×#419	1	1	yes	characteristic
270	C₂	—	2	4	no	—
271	C₂	C₂₉×#1573	1	4	yes	—
272	C₂	C₂₉×#1729	1	1	yes	characteristic
273	C₂	C₂₉×#1736	1	1	yes	characteristic
274	C₂	C₂×C₂₉×#341	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₂₉
Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
socle	C₂³×C₂₉	C₂×C₄⋊C₄
prime radical	C₂⁴×C₂₉	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₉ ◁ C₂²×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₉×#1277	C₂	semidirect
83. #7879	C₂₉	direct (N × H)
118. #1277	C₂×C₂₉	semidirect
185. C₂₉	#7879	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×#432	2
C₂×C₂₉×#431	2
C₂²×C₂₉×C₄⋊C₈	2
C₂₉×#1277	2
#7879	29

Subgroups — C29×#7879 #20302779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#7879 #20302779