Subgroups — C₂×C₂₉×#1274 #20302753

Order 7424.

758 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#431	C₂	1	2	yes	maximal
2	C₂×C₂₉×#376	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#1274	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄²×C₂₉	C₄	1	2	yes	—
5	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
6	C₂₉×#431	—	2	2	no	—
7	C₂₉×#431	—	2	2	no	—
8	C₂₉×#431	C₄	1	4	yes	complemented
9	C₂₉×#431	C₂²	1	4	yes	—
10	C₂×C₂₉×C₄⋊C₈	—	2	2	no	—
11	C₂×C₂₉×C₂²⋊C₈	—	2	2	no	—
12	C₂×C₄×C₈×C₂₉	C₄	1	4	yes	complemented
13	C₂₉×#376	—	2	2	no	—
14	C₂₉×#376	C₄	1	2	yes	—
15	C₂₉×#376	C₂²	1	2	yes	—
16	C₂×C₂₉×#95	—	2	2	no	—
17	C₂³×C₄×C₂₉	—	2	2	no	—
18	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂³×C₄×C₂₉	D₄	1	2	yes	—
20	C₂²×C₈×C₂₉	—	2	4	no	—
21	C₂×C₄²×C₂₉	—	2	2	no	—
22	C₂×C₄²×C₂₉	—	2	4	no	—
23	C₂×C₄²×C₂₉	C₈	1	8	yes	complemented
24	C₂×C₄²×C₂₉	C₂×C₄	1	4	yes	—
25	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₂₉	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₂₉	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₂₉	D₄	1	2	yes	—
29	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
30	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
31	C₂×C₄²×C₂₉	Q₈	1	1	yes	characteristic
32	C₂×C₄²×C₂₉	Q₈	1	1	yes	characteristic
33	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
34	C₂₉×C₄⋊C₈	—	2	4	no	—
35	C₂₉×C₄⋊C₈	—	2	4	no	—
36	C₂₉×C₂²⋊C₈	—	2	4	no	—
37	C₂₉×C₂²⋊C₈	—	2	4	no	—
38	C₄×C₈×C₂₉	—	2	4	no	—
39	C₄×C₈×C₂₉	C₂×C₄	1	8	yes	complemented
40	C₂₉×#95	—	2	4	no	—
41	C₂₉×#95	—	2	4	no	—
42	C₂⁴×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
43	C₂²×C₄×C₂₉	—	2	8	no	—
44	C₂²×C₄×C₂₉	—	2	4	no	—
45	C₂²×C₄×C₂₉	—	4	4	no	—
46	C₂²×C₄×C₂₉	—	4	8	no	—
47	C₂²×C₄×C₂₉	C₄²	1	1	yes	characteristic
48	C₂²×C₄×C₂₉	C₄²	1	1	yes	characteristic
49	C₂²×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
50	C₂²×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
51	C₂²×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
52	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
54	C₂²×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
55	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₂₉	C₂×C₈	1	4	yes	—
58	C₂²×C₄×C₂₉	M₁₆	1	4	yes	—
59	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
61	C₂×C₈×C₂₉	—	2	8	no	—
62	C₂×C₈×C₂₉	—	4	8	no	—
63	C₄²×C₂₉	—	2	8	no	—
64	C₄²×C₂₉	—	2	4	no	—
65	C₄²×C₂₉	C₄²	1	2	yes	—
66	C₄²×C₂₉	C₂²⋊C₄	1	2	yes	—
67	C₄²×C₂₉	C₂²⋊C₄	1	2	yes	—
68	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
69	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
70	C₄²×C₂₉	C₄⋊C₄	1	2	yes	—
71	C₄²×C₂₉	C₄⋊C₄	1	2	yes	—
72	C₄²×C₂₉	C₂×C₈	1	8	yes	complemented
73	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
74	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₂₉	C₂×Q₈	1	1	yes	characteristic
76	C₂×#1274	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂³×C₂₉	—	2	4	no	—
78	C₂³×C₂₉	#95	1	1	yes	characteristic
79	C₂³×C₂₉	#95	1	1	yes	characteristic
80	C₂³×C₂₉	C₂²⋊C₈	1	4	yes	—
81	C₂³×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₂₉	—	2	4	no	—
83	C₂×C₄×C₂₉	—	2	4	no	—
84	C₂×C₄×C₂₉	—	2	8	no	—
85	C₂×C₄×C₂₉	—	4	2	no	—
86	C₂×C₄×C₂₉	—	4	2	no	—
87	C₂×C₄×C₂₉	—	4	2	no	—
88	C₂×C₄×C₂₉	—	4	2	no	—
89	C₂×C₄×C₂₉	—	4	8	no	—
90	C₂×C₄×C₂₉	—	4	16	no	—
91	C₂×C₄×C₂₉	#95	1	2	yes	—
92	C₂×C₄×C₂₉	#95	1	2	yes	—
93	C₂×C₄×C₂₉	#95	1	1	yes	characteristic
94	C₂×C₄×C₂₉	#95	1	1	yes	characteristic
95	C₂×C₄×C₂₉	C₄×C₈	1	2	yes	—
96	C₂×C₄×C₂₉	C₄×C₈	1	2	yes	—
97	C₂×C₄×C₂₉	#97	1	2	yes	—
98	C₂×C₄×C₂₉	#97	1	2	yes	—
99	C₂×C₄×C₂₉	C₂²⋊C₈	1	4	yes	—
100	C₂×C₄×C₂₉	C₄⋊C₈	1	4	yes	—
101	C₂×C₄×C₂₉	C₄⋊C₈	1	4	yes	—
102	C₂×C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
103	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	2	yes	—
104	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	2	yes	—
105	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×C₂₉	C₂²×C₈	1	2	yes	—
107	C₂×C₄×C₂₉	C₂×M₁₆	1	2	yes	—
108	C₈×C₂₉	—	4	8	no	—
109	C₂×#431	C₂×C₂₉	1	2	yes	—
110	C₂×#376	C₂×C₂₉	1	1	yes	characteristic
111	#1274	C₂×C₂₉	1	4	yes	direct product factor
112	C₂²×C₂₉	—	2	2	no	—
113	C₂²×C₂₉	—	2	2	no	—
114	C₂²×C₂₉	—	2	8	no	—
115	C₂²×C₂₉	#336	1	2	yes	—
116	C₂²×C₂₉	#336	1	2	yes	—
117	C₂²×C₂₉	H(3,ℤ/4)	1	4	yes	—
118	C₂²×C₂₉	C₂×#95	1	1	yes	characteristic
119	C₂²×C₂₉	C₂×C₂²⋊C₈	1	2	yes	—
120	C₄×C₂₉	—	2	2	no	—
121	C₄×C₂₉	—	2	2	no	—
122	C₄×C₂₉	—	2	2	no	—
123	C₄×C₂₉	—	2	2	no	—
124	C₄×C₂₉	—	4	8	no	—
125	C₄×C₂₉	#336	1	2	yes	—
126	C₄×C₂₉	#336	1	2	yes	—
127	C₄×C₂₉	C₂×C₄×C₈	1	1	yes	characteristic
128	C₄×C₂₉	C₂×#97	1	1	yes	characteristic
129	C₄×C₂₉	C₂×C₄⋊C₈	1	2	yes	—
130	C₂²×C₄²	C₄×C₂₉	1	2	yes	—
131	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
132	#431	—	2	2	no	—
133	#431	—	2	2	no	—
134	#431	C₄×C₂₉	1	4	yes	complemented
135	#431	C₂²×C₂₉	1	4	yes	—
136	C₂×C₄⋊C₈	—	2	2	no	—
137	C₂×C₂²⋊C₈	—	2	2	no	—
138	C₂×C₄×C₈	C₄×C₂₉	1	4	yes	complemented
139	#376	—	2	2	no	—
140	#376	C₄×C₂₉	1	2	yes	—
141	#376	C₂²×C₂₉	1	2	yes	—
142	C₂×#95	—	2	2	no	—
143	C₂×C₂₉	—	2	2	no	—
144	C₂×C₂₉	—	2	2	no	—
145	C₂×C₂₉	#1274	1	4	yes	direct product factor
146	C₂×C₂₉	C₂×#336	1	1	yes	characteristic
147	C₂×C₂₉	C₂×H(3,ℤ/4)	1	2	yes	—
148	C₂³×C₄	—	2	2	no	—
149	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
150	C₂³×C₄	D₄×C₂₉	1	2	yes	—
151	C₂²×C₈	—	2	4	no	—
152	C₂×C₄²	—	2	2	no	—
153	C₂×C₄²	—	2	4	no	—
154	C₂×C₄²	C₈×C₂₉	1	8	yes	complemented
155	C₂×C₄²	C₂×C₄×C₂₉	1	4	yes	—
156	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
157	C₂×C₄²	C₂×C₄×C₂₉	1	2	yes	—
158	C₂×C₄²	C₂×C₄×C₂₉	1	2	yes	—
159	C₂×C₄²	D₄×C₂₉	1	2	yes	—
160	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
161	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
162	C₂×C₄²	Q₈×C₂₉	1	1	yes	characteristic
163	C₂×C₄²	Q₈×C₂₉	1	1	yes	characteristic
164	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
165	C₄⋊C₈	—	2	4	no	—
166	C₄⋊C₈	—	2	4	no	—
167	C₂²⋊C₈	—	2	4	no	—
168	C₂²⋊C₈	—	2	4	no	—
169	C₄×C₈	—	2	4	no	—
170	C₄×C₈	C₂×C₄×C₂₉	1	8	yes	complemented
171	#95	—	2	4	no	—
172	#95	—	2	4	no	—
173	C₂₉	C₂×#1274	1	1	yes	characteristic, direct product factor, Sylow
174	C₂⁴	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
175	C₂²×C₄	—	2	4	no	—
176	C₂²×C₄	—	2	8	no	—
177	C₂²×C₄	—	4	4	no	—
178	C₂²×C₄	—	4	8	no	—
179	C₂²×C₄	C₄²×C₂₉	1	1	yes	characteristic
180	C₂²×C₄	C₄²×C₂₉	1	1	yes	characteristic
181	C₂²×C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
182	C₂²×C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
183	C₂²×C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
184	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
185	C₂²×C₄	C₄⋊C₄×C₂₉	1	2	yes	—
186	C₂²×C₄	C₄⋊C₄×C₂₉	1	2	yes	—
187	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
188	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
189	C₂²×C₄	C₂×C₈×C₂₉	1	4	yes	—
190	C₂²×C₄	M₁₆×C₂₉	1	4	yes	—
191	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
192	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
193	C₂×C₈	—	2	8	no	—
194	C₂×C₈	—	4	8	no	—
195	C₄²	—	2	4	no	—
196	C₄²	—	2	8	no	—
197	C₄²	C₄²×C₂₉	1	2	yes	—
198	C₄²	C₂²⋊C₄×C₂₉	1	2	yes	—
199	C₄²	C₂²⋊C₄×C₂₉	1	2	yes	—
200	C₄²	C₄⋊C₄×C₂₉	1	2	yes	—
201	C₄²	C₄⋊C₄×C₂₉	1	2	yes	—
202	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
203	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
204	C₄²	C₂×C₈×C₂₉	1	8	yes	complemented
205	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
206	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
207	C₄²	C₂×Q₈×C₂₉	1	1	yes	characteristic
208	C₂³	—	2	4	no	—
209	C₂³	C₂₉×#95	1	1	yes	characteristic
210	C₂³	C₂₉×#95	1	1	yes	characteristic
211	C₂³	C₂₉×C₂²⋊C₈	1	4	yes	—
212	C₂³	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
213	C₂×C₄	—	2	4	no	—
214	C₂×C₄	—	2	4	no	—
215	C₂×C₄	—	2	8	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	4	8	no	—
221	C₂×C₄	—	4	16	no	—
222	C₂×C₄	C₂₉×#95	1	2	yes	—
223	C₂×C₄	C₂₉×#95	1	2	yes	—
224	C₂×C₄	C₂₉×#95	1	1	yes	characteristic
225	C₂×C₄	C₂₉×#95	1	1	yes	characteristic
226	C₂×C₄	C₄×C₈×C₂₉	1	2	yes	—
227	C₂×C₄	C₄×C₈×C₂₉	1	2	yes	—
228	C₂×C₄	C₂₉×#97	1	2	yes	—
229	C₂×C₄	C₂₉×#97	1	2	yes	—
230	C₂×C₄	C₂₉×C₂²⋊C₈	1	4	yes	—
231	C₂×C₄	C₂₉×C₄⋊C₈	1	4	yes	—
232	C₂×C₄	C₂₉×C₄⋊C₈	1	4	yes	—
233	C₂×C₄	C₂×C₄²×C₂₉	1	1	yes	characteristic
234	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	2	yes	—
235	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	2	yes	—
236	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
237	C₂×C₄	C₂²×C₈×C₂₉	1	2	yes	—
238	C₂×C₄	C₂×M₁₆×C₂₉	1	2	yes	—
239	C₈	—	4	8	no	—
240	C₂²	—	2	2	no	—
241	C₂²	—	2	2	no	—
242	C₂²	—	2	8	no	—
243	C₂²	C₂₉×#336	1	2	yes	—
244	C₂²	C₂₉×#336	1	2	yes	—
245	C₂²	C₂₉×H(3,ℤ/4)	1	4	yes	—
246	C₂²	C₂×C₂₉×#95	1	1	yes	characteristic
247	C₂²	C₂×C₂₉×C₂²⋊C₈	1	2	yes	—
248	C₄	—	2	2	no	—
249	C₄	—	2	2	no	—
250	C₄	—	2	2	no	—
251	C₄	—	2	2	no	—
252	C₄	—	4	8	no	—
253	C₄	C₂₉×#336	1	2	yes	—
254	C₄	C₂₉×#336	1	2	yes	—
255	C₄	C₂×C₄×C₈×C₂₉	1	1	yes	characteristic
256	C₄	C₂×C₂₉×#97	1	1	yes	characteristic
257	C₄	C₂×C₂₉×C₄⋊C₈	1	2	yes	—
258	C₂	—	2	2	no	—
259	C₂	—	2	2	no	—
260	C₂	C₂₉×#1274	1	4	yes	direct product factor
261	C₂	C₂×C₂₉×#336	1	1	yes	characteristic
262	C₂	C₂×C₂₉×H(3,ℤ/4)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₄²
commutator	C₄	C₂×C₄×C₈×C₂₉
Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
socle	C₂³×C₂₉	#95
prime radical	C₂⁴×C₂₉	C₂²⋊C₄
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₉×#1274	C₂	direct (N × H)
8. C₂₉×#431	C₄	semidirect
12. C₂×C₄×C₈×C₂₉	C₄	semidirect
23. C₂×C₄²×C₂₉	C₈	semidirect
39. C₄×C₈×C₂₉	C₂×C₄	semidirect
72. C₄²×C₂₉	C₂×C₈	semidirect
76. C₂×#1274	C₂₉	direct (N × H)
111. #1274	C₂×C₂₉	direct (N × H)
134. #431	C₄×C₂₉	semidirect
138. C₂×C₄×C₈	C₄×C₂₉	semidirect
145. C₂×C₂₉	#1274	direct (N × H)
154. C₂×C₄²	C₈×C₂₉	semidirect
170. C₄×C₈	C₂×C₄×C₂₉	semidirect
173. C₂₉	C₂×#1274	direct (N × H)
204. C₄²	C₂×C₈×C₂₉	semidirect
260. C₂	C₂₉×#1274	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×#431	2
C₂×C₂₉×#376	2
C₂₉×#1274	2
C₂×#1274	29

Subgroups — C2×C29×#1274 #20302753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#1274 #20302753