Subgroups — C₂₉×#21704 #20316604

Order 7424.

1174 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#496	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×#440	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×D₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2328	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2326	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1973	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1972	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1970	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1958	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1957	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1847	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1726	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₂₉	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₂₉	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
26	C₂₉×#496	C₄	1	8	yes	complemented
27	C₂₉×#442	—	2	4	no	—
28	C₂₉×#440	—	2	4	no	—
29	C₄×SD₁₆×C₂₉	—	2	4	no	—
30	C₄×D₈×C₂₉	—	2	4	no	—
31	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
35	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
36	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
37	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
41	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
42	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
43	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
44	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
45	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
49	C₂₉×#391	C₂²	1	1	yes	characteristic
50	C₂₉×#390	C₂²	1	1	yes	characteristic
51	C₂₉×#390	C₂²	1	1	yes	characteristic
52	C₂₉×#390	C₂²	1	1	yes	characteristic
53	C₂₉×#388	—	2	2	no	—
54	C₂₉×#386	—	2	2	no	—
55	C₂₉×#386	—	2	2	no	—
56	C₂₉×#385	—	2	2	no	—
57	C₂₉×#384	C₂²	1	1	yes	characteristic
58	C₂₉×#382	C₂²	1	1	yes	characteristic
59	C₂₉×#376	C₂²	1	1	yes	characteristic
60	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₂₉	—	2	2	no	—
62	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₂₉	—	2	1	no	—
66	C₂³×C₄×C₂₉	—	2	1	no	—
67	C₂³×C₄×C₂₉	—	2	1	no	—
68	C₂×SD₁₆×C₂₉	—	2	2	no	—
69	C₂×SD₁₆×C₂₉	—	2	2	no	—
70	C₂×SD₁₆×C₂₉	—	2	2	no	—
71	C₂×SD₁₆×C₂₉	—	2	2	no	—
72	C₂×SD₁₆×C₂₉	C₂×C₄	1	4	yes	complemented
73	C₂×SD₁₆×C₂₉	C₂×C₄	1	4	yes	complemented
74	C₂×D₈×C₂₉	—	2	2	no	—
75	C₂×D₈×C₂₉	—	2	2	no	—
76	C₂×D₈×C₂₉	—	2	2	no	—
77	C₂×D₈×C₂₉	—	2	2	no	—
78	C₂×D₈×C₂₉	C₂×C₄	1	4	yes	complemented
79	C₂×D₈×C₂₉	C₂×C₄	1	4	yes	complemented
80	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
84	C₂₉×#127	—	2	2	no	—
85	C₂₉×#127	C₂×C₄	1	4	yes	complemented
86	C₂₉×#124	—	2	2	no	—
87	C₂₉×#124	C₂×C₄	1	4	yes	complemented
88	C₄×Q₈×C₂₉	—	2	2	no	—
89	C₄×Q₈×C₂₉	—	2	2	no	—
90	C₄×D₄×C₂₉	—	2	2	no	—
91	C₄×D₄×C₂₉	—	2	2	no	—
92	C₄×D₄×C₂₉	—	2	2	no	—
93	C₄×D₄×C₂₉	—	2	2	no	—
94	C₄×D₄×C₂₉	—	2	2	no	—
95	C₄×D₄×C₂₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
98	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
103	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
107	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
108	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
109	C₂×C₄²×C₂₉	—	2	1	no	—
110	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
113	C₂₉×#107	—	2	2	no	—
114	C₂₉×#107	—	2	2	no	—
115	C₂₉×#106	—	2	2	no	—
116	C₂₉×#106	—	2	2	no	—
117	C₂₉×#103	—	2	2	no	—
118	C₂₉×#103	—	2	2	no	—
119	C₂₉×#102	—	2	2	no	—
120	C₂₉×#102	—	2	2	no	—
121	C₂₉×#102	—	2	2	no	—
122	C₂₉×#102	—	2	2	no	—
123	C₂₉×#102	—	2	2	no	—
124	C₂₉×#102	—	2	2	no	—
125	C₂₉×#97	—	2	2	no	—
126	C₂₉×#97	C₂×C₄	1	4	yes	complemented
127	C₂₉×#97	D₄	1	4	yes	complemented
128	C₄×C₈×C₂₉	—	2	2	no	—
129	C₄×C₈×C₂₉	—	2	2	no	—
130	C₄×C₈×C₂₉	D₄	1	4	yes	complemented
131	C₂₉×#95	—	2	2	no	—
132	C₂₉×#95	—	2	2	no	—
133	C₂₉×#95	D₄	1	2	yes	—
134	C₂₉×#95	D₄	1	2	yes	—
135	C₂⁴×C₂₉	—	2	1	no	—
136	C₂⁴×C₂₉	—	2	1	no	—
137	C₂⁴×C₂₉	—	2	1	no	—
138	C₂×Q₈×C₂₉	—	2	1	no	—
139	C₂×Q₈×C₂₉	—	2	1	no	—
140	C₂×Q₈×C₂₉	—	2	1	no	—
141	C₂×Q₈×C₂₉	—	2	1	no	—
142	C₂×Q₈×C₂₉	—	2	1	no	—
143	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
144	C₂×D₄×C₂₉	—	2	8	no	—
145	C₂×D₄×C₂₉	—	2	1	no	—
146	C₂×D₄×C₂₉	—	2	1	no	—
147	C₂×D₄×C₂₉	—	2	1	no	—
148	C₂×D₄×C₂₉	—	2	1	no	—
149	C₂×D₄×C₂₉	—	2	1	no	—
150	C₂×D₄×C₂₉	—	2	1	no	—
151	C₂×D₄×C₂₉	—	2	1	no	—
152	C₂×D₄×C₂₉	—	2	1	no	—
153	C₂×D₄×C₂₉	—	2	1	no	—
154	C₂×D₄×C₂₉	—	2	1	no	—
155	C₂×D₄×C₂₉	—	2	1	no	—
156	C₂×D₄×C₂₉	—	2	1	no	—
157	C₂×D₄×C₂₉	—	2	1	no	—
158	C₂×D₄×C₂₉	—	2	1	no	—
159	C₂×D₄×C₂₉	—	2	1	no	—
160	C₂×D₄×C₂₉	—	8	2	no	—
161	C₂×D₄×C₂₉	—	8	2	no	—
162	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
163	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
164	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
165	C₂²×C₄×C₂₉	—	2	1	no	—
166	C₂²×C₄×C₂₉	—	2	1	no	—
167	C₂²×C₄×C₂₉	—	2	1	no	—
168	C₂²×C₄×C₂₉	—	2	1	no	—
169	C₂²×C₄×C₂₉	—	2	1	no	—
170	C₂²×C₄×C₂₉	—	4	2	no	—
171	C₂²×C₄×C₂₉	—	4	2	no	—
172	C₂²×C₄×C₂₉	—	4	2	no	—
173	C₂²×C₄×C₂₉	—	8	2	no	—
174	C₂²×C₄×C₂₉	—	8	2	no	—
175	C₂²×C₄×C₂₉	—	8	2	no	—
176	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
181	SD₁₆×C₂₉	—	2	8	no	—
182	SD₁₆×C₂₉	—	2	8	no	—
183	D₈×C₂₉	—	2	8	no	—
184	D₈×C₂₉	—	2	8	no	—
185	C₂×C₈×C₂₉	—	2	1	no	—
186	C₂×C₈×C₂₉	—	2	1	no	—
187	C₂×C₈×C₂₉	—	2	1	no	—
188	C₂×C₈×C₂₉	—	2	1	no	—
189	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
190	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
191	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
192	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
193	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
194	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
195	C₂×C₈×C₂₉	#41	1	2	yes	—
196	C₂×C₈×C₂₉	#41	1	2	yes	—
197	C₄⋊C₄×C₂₉	—	2	1	no	—
198	C₄⋊C₄×C₂₉	—	2	1	no	—
199	C₄⋊C₄×C₂₉	—	2	1	no	—
200	C₄⋊C₄×C₂₉	—	2	1	no	—
201	C₄⋊C₄×C₂₉	—	2	1	no	—
202	C₄⋊C₄×C₂₉	—	2	1	no	—
203	C₄⋊C₄×C₂₉	—	2	1	no	—
204	C₄⋊C₄×C₂₉	—	2	1	no	—
205	C₄⋊C₄×C₂₉	—	4	2	no	—
206	C₄⋊C₄×C₂₉	—	8	2	no	—
207	C₂²⋊C₄×C₂₉	—	2	8	no	—
208	C₂²⋊C₄×C₂₉	—	4	2	no	—
209	C₂²⋊C₄×C₂₉	—	4	2	no	—
210	C₂²⋊C₄×C₂₉	—	4	2	no	—
211	C₂²⋊C₄×C₂₉	—	8	2	no	—
212	C₂²⋊C₄×C₂₉	—	8	2	no	—
213	C₂²⋊C₄×C₂₉	—	8	2	no	—
214	C₄²×C₂₉	—	2	1	no	—
215	C₄²×C₂₉	—	2	1	no	—
216	C₄²×C₂₉	—	4	2	no	—
217	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
218	C₄²×C₂₉	C₂×D₄	1	2	yes	—
219	C₄²×C₂₉	C₂×D₄	1	2	yes	—
220	C₄²×C₂₉	#41	1	2	yes	—
221	#21704	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂³×C₂₉	—	2	2	no	—
223	C₂³×C₂₉	—	2	2	no	—
224	C₂³×C₂₉	—	2	2	no	—
225	C₂³×C₂₉	—	4	1	no	—
226	C₂³×C₂₉	—	4	1	no	—
227	C₂³×C₂₉	—	4	1	no	—
228	C₂³×C₂₉	—	4	1	no	—
229	C₂³×C₂₉	—	4	1	no	—
230	C₂³×C₂₉	—	4	1	no	—
231	C₂³×C₂₉	—	4	2	no	—
232	C₂³×C₂₉	—	4	2	no	—
233	C₂³×C₂₉	—	4	2	no	—
234	C₂³×C₂₉	—	4	2	no	—
235	C₂³×C₂₉	—	4	2	no	—
236	C₂³×C₂₉	—	4	2	no	—
237	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
238	Q₈×C₂₉	—	2	2	no	—
239	Q₈×C₂₉	—	2	2	no	—
240	Q₈×C₂₉	—	4	1	no	—
241	Q₈×C₂₉	—	4	1	no	—
242	D₄×C₂₉	—	2	2	no	—
243	D₄×C₂₉	—	2	2	no	—
244	D₄×C₂₉	—	2	2	no	—
245	D₄×C₂₉	—	2	2	no	—
246	D₄×C₂₉	—	2	2	no	—
247	D₄×C₂₉	—	2	2	no	—
248	D₄×C₂₉	—	4	1	no	—
249	D₄×C₂₉	—	4	1	no	—
250	D₄×C₂₉	—	4	1	no	—
251	D₄×C₂₉	—	4	1	no	—
252	D₄×C₂₉	—	4	1	no	—
253	D₄×C₂₉	—	4	1	no	—
254	D₄×C₂₉	—	8	8	no	—
255	C₂×C₄×C₂₉	—	2	2	no	—
256	C₂×C₄×C₂₉	—	2	2	no	—
257	C₂×C₄×C₂₉	—	2	2	no	—
258	C₂×C₄×C₂₉	—	2	2	no	—
259	C₂×C₄×C₂₉	—	2	2	no	—
260	C₂×C₄×C₂₉	—	2	2	no	—
261	C₂×C₄×C₂₉	—	2	2	no	—
262	C₂×C₄×C₂₉	—	2	2	no	—
263	C₂×C₄×C₂₉	—	4	1	no	—
264	C₂×C₄×C₂₉	—	4	1	no	—
265	C₂×C₄×C₂₉	—	4	1	no	—
266	C₂×C₄×C₂₉	—	4	1	no	—
267	C₂×C₄×C₂₉	—	4	1	no	—
268	C₂×C₄×C₂₉	—	4	1	no	—
269	C₂×C₄×C₂₉	—	4	2	no	—
270	C₂×C₄×C₂₉	—	4	2	no	—
271	C₂×C₄×C₂₉	—	4	2	no	—
272	C₂×C₄×C₂₉	—	4	2	no	—
273	C₂×C₄×C₂₉	—	8	4	no	—
274	C₂×C₄×C₂₉	—	8	4	no	—
275	C₂×C₄×C₂₉	—	8	4	no	—
276	C₂×C₄×C₂₉	C₄×D₄	1	4	yes	—
277	C₂×C₄×C₂₉	#127	1	2	yes	—
278	C₂×C₄×C₂₉	#127	1	2	yes	—
279	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
280	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
285	C₈×C₂₉	—	2	2	no	—
286	C₈×C₂₉	—	2	2	no	—
287	C₈×C₂₉	C₄×D₄	1	4	yes	—
288	C₈×C₂₉	C₄×D₄	1	4	yes	—
289	C₂×#496	C₂×C₂₉	1	1	yes	characteristic
290	C₂×#442	C₂×C₂₉	1	1	yes	characteristic, complemented
291	C₂×#440	C₂×C₂₉	1	1	yes	characteristic, complemented
292	C₂×C₄×SD₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
293	C₂×C₄×D₈	C₂×C₂₉	1	1	yes	characteristic, complemented
294	#2328	C₂×C₂₉	1	1	yes	characteristic, complemented
295	#2326	C₂×C₂₉	1	1	yes	characteristic, complemented
296	#1973	C₂×C₂₉	1	1	yes	characteristic, complemented
297	#1972	C₂×C₂₉	1	1	yes	characteristic, complemented
298	#1970	C₂×C₂₉	1	1	yes	characteristic, complemented
299	#1968	C₂×C₂₉	1	1	yes	characteristic, complemented
300	#1958	C₂×C₂₉	1	1	yes	characteristic, complemented
301	#1957	C₂×C₂₉	1	1	yes	characteristic, complemented
302	#1847	C₂×C₂₉	1	1	yes	characteristic, complemented
303	#1726	C₂×C₂₉	1	1	yes	characteristic, complemented
304	C₂²×C₂₉	—	4	2	no	—
305	C₂²×C₂₉	—	4	2	no	—
306	C₂²×C₂₉	—	4	2	no	—
307	C₂²×C₂₉	—	4	4	no	—
308	C₂²×C₂₉	—	4	4	no	—
309	C₂²×C₂₉	—	4	4	no	—
310	C₂²×C₂₉	—	8	1	no	—
311	C₂²×C₂₉	—	8	1	no	—
312	C₂²×C₂₉	—	8	1	no	—
313	C₂²×C₂₉	—	8	1	no	—
314	C₂²×C₂₉	—	8	1	no	—
315	C₂²×C₂₉	—	8	1	no	—
316	C₂²×C₂₉	—	8	2	no	—
317	C₂²×C₂₉	—	8	2	no	—
318	C₂²×C₂₉	—	8	2	no	—
319	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
320	C₂²×C₂₉	C₂×#127	1	1	yes	characteristic
321	C₂²×C₂₉	#532	1	1	yes	characteristic
322	C₂²×C₂₉	#576	1	2	yes	—
323	C₂²×C₂₉	#577	1	2	yes	—
324	C₄×C₂₉	—	2	2	no	—
325	C₄×C₂₉	—	2	2	no	—
326	C₄×C₂₉	—	2	4	no	—
327	C₄×C₂₉	—	4	2	no	—
328	C₄×C₂₉	—	4	2	no	—
329	C₄×C₂₉	—	8	1	no	—
330	C₄×C₂₉	—	8	1	no	—
331	C₄×C₂₉	—	8	1	no	—
332	C₄×C₂₉	—	8	1	no	—
333	C₄×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
334	C₄×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
335	C₄×C₂₉	#532	1	1	yes	characteristic
336	C₄×C₂₉	#532	1	1	yes	characteristic
337	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
338	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
339	C₂²×D₈	C₂²×C₂₉	1	1	yes	characteristic
340	C₂²×D₈	C₂²×C₂₉	1	1	yes	characteristic
341	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
342	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
343	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
344	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
345	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
346	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
347	#496	C₄×C₂₉	1	8	yes	complemented
348	#442	—	2	4	no	—
349	#440	—	2	4	no	—
350	C₄×SD₁₆	—	2	4	no	—
351	C₄×D₈	—	2	4	no	—
352	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
353	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
354	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
355	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
356	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
357	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
358	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
359	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
360	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
361	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
362	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
363	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
364	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
365	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
366	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
367	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
368	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
369	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
370	#391	C₂²×C₂₉	1	1	yes	characteristic
371	#390	C₂²×C₂₉	1	1	yes	characteristic
372	#390	C₂²×C₂₉	1	1	yes	characteristic
373	#390	C₂²×C₂₉	1	1	yes	characteristic
374	#388	—	2	2	no	—
375	#386	—	2	2	no	—
376	#386	—	2	2	no	—
377	#385	—	2	2	no	—
378	#384	C₂²×C₂₉	1	1	yes	characteristic
379	#382	C₂²×C₂₉	1	1	yes	characteristic
380	#376	C₂²×C₂₉	1	1	yes	characteristic
381	C₂×C₂₉	—	8	2	no	—
382	C₂×C₂₉	—	8	2	no	—
383	C₂×C₂₉	—	8	2	no	—
384	C₂×C₂₉	C₄×#127	1	1	yes	characteristic
385	C₂×C₂₉	#2946	1	2	yes	—
386	C₂×C₂₉	#3154	1	1	yes	characteristic
387	C₂×C₂₉	#3155	1	1	yes	characteristic
388	C₂×C₂₉	#3179	1	2	yes	—
389	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
390	C₂²×D₄	—	2	2	no	—
391	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
392	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
393	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
394	C₂³×C₄	—	2	1	no	—
395	C₂³×C₄	—	2	1	no	—
396	C₂³×C₄	—	2	1	no	—
397	C₂×SD₁₆	—	2	2	no	—
398	C₂×SD₁₆	—	2	2	no	—
399	C₂×SD₁₆	—	2	2	no	—
400	C₂×SD₁₆	—	2	2	no	—
401	C₂×SD₁₆	C₂×C₄×C₂₉	1	4	yes	complemented
402	C₂×SD₁₆	C₂×C₄×C₂₉	1	4	yes	complemented
403	C₂×D₈	—	2	2	no	—
404	C₂×D₈	—	2	2	no	—
405	C₂×D₈	—	2	2	no	—
406	C₂×D₈	—	2	2	no	—
407	C₂×D₈	C₂×C₄×C₂₉	1	4	yes	complemented
408	C₂×D₈	C₂×C₄×C₂₉	1	4	yes	complemented
409	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
412	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
413	#127	—	2	2	no	—
414	#127	C₂×C₄×C₂₉	1	4	yes	complemented
415	#124	—	2	2	no	—
416	#124	C₂×C₄×C₂₉	1	4	yes	complemented
417	C₄×Q₈	—	2	2	no	—
418	C₄×Q₈	—	2	2	no	—
419	C₄×D₄	—	2	2	no	—
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	—	2	2	no	—
422	C₄×D₄	—	2	2	no	—
423	C₄×D₄	—	2	2	no	—
424	C₄×D₄	—	2	2	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	2	no	—
427	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
431	C₂×C₂²⋊C₄	—	2	2	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	2	no	—
436	C₂×C₂²⋊C₄	—	2	2	no	—
437	C₂×C₂²⋊C₄	—	2	2	no	—
438	C₂×C₄²	—	2	1	no	—
439	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
440	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
442	#107	—	2	2	no	—
443	#107	—	2	2	no	—
444	#106	—	2	2	no	—
445	#106	—	2	2	no	—
446	#103	—	2	2	no	—
447	#103	—	2	2	no	—
448	#102	—	2	2	no	—
449	#102	—	2	2	no	—
450	#102	—	2	2	no	—
451	#102	—	2	2	no	—
452	#102	—	2	2	no	—
453	#102	—	2	2	no	—
454	#97	—	2	2	no	—
455	#97	C₂×C₄×C₂₉	1	4	yes	complemented
456	#97	D₄×C₂₉	1	4	yes	complemented
457	C₄×C₈	—	2	2	no	—
458	C₄×C₈	—	2	2	no	—
459	C₄×C₈	D₄×C₂₉	1	4	yes	complemented
460	#95	—	2	2	no	—
461	#95	—	2	2	no	—
462	#95	D₄×C₂₉	1	2	yes	—
463	#95	D₄×C₂₉	1	2	yes	—
464	C₂₉	#21704	1	1	yes	characteristic, direct product factor, Sylow
465	C₂⁴	—	2	1	no	—
466	C₂⁴	—	2	1	no	—
467	C₂⁴	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
474	C₂×D₄	—	2	8	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	8	2	no	—
491	C₂×D₄	—	8	2	no	—
492	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
493	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
494	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	4	2	no	—
501	C₂²×C₄	—	4	2	no	—
502	C₂²×C₄	—	4	2	no	—
503	C₂²×C₄	—	8	2	no	—
504	C₂²×C₄	—	8	2	no	—
505	C₂²×C₄	—	8	2	no	—
506	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
507	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
508	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
510	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
511	SD₁₆	—	2	8	no	—
512	SD₁₆	—	2	8	no	—
513	D₈	—	2	8	no	—
514	D₈	—	2	8	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
520	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
521	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
522	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
523	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
524	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
525	C₂×C₈	#41×C₂₉	1	2	yes	—
526	C₂×C₈	#41×C₂₉	1	2	yes	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	4	2	no	—
536	C₄⋊C₄	—	8	2	no	—
537	C₂²⋊C₄	—	2	8	no	—
538	C₂²⋊C₄	—	4	2	no	—
539	C₂²⋊C₄	—	4	2	no	—
540	C₂²⋊C₄	—	4	2	no	—
541	C₂²⋊C₄	—	8	2	no	—
542	C₂²⋊C₄	—	8	2	no	—
543	C₂²⋊C₄	—	8	2	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	4	2	no	—
547	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
548	C₄²	C₂×D₄×C₂₉	1	2	yes	—
549	C₄²	C₂×D₄×C₂₉	1	2	yes	—
550	C₄²	#41×C₂₉	1	2	yes	—
551	C₂³	—	2	2	no	—
552	C₂³	—	2	2	no	—
553	C₂³	—	2	2	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	—	4	1	no	—
560	C₂³	—	4	2	no	—
561	C₂³	—	4	2	no	—
562	C₂³	—	4	2	no	—
563	C₂³	—	4	2	no	—
564	C₂³	—	4	2	no	—
565	C₂³	—	4	2	no	—
566	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
567	Q₈	—	2	2	no	—
568	Q₈	—	2	2	no	—
569	Q₈	—	4	1	no	—
570	Q₈	—	4	1	no	—
571	D₄	—	2	2	no	—
572	D₄	—	2	2	no	—
573	D₄	—	2	2	no	—
574	D₄	—	2	2	no	—
575	D₄	—	2	2	no	—
576	D₄	—	2	2	no	—
577	D₄	—	4	1	no	—
578	D₄	—	4	1	no	—
579	D₄	—	4	1	no	—
580	D₄	—	4	1	no	—
581	D₄	—	4	1	no	—
582	D₄	—	4	1	no	—
583	D₄	—	8	8	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	8	4	no	—
603	C₂×C₄	—	8	4	no	—
604	C₂×C₄	—	8	4	no	—
605	C₂×C₄	C₄×D₄×C₂₉	1	4	yes	—
606	C₂×C₄	C₂₉×#127	1	2	yes	—
607	C₂×C₄	C₂₉×#127	1	2	yes	—
608	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
609	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
610	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
611	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
612	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
613	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
614	C₈	—	2	2	no	—
615	C₈	—	2	2	no	—
616	C₈	C₄×D₄×C₂₉	1	4	yes	—
617	C₈	C₄×D₄×C₂₉	1	4	yes	—
618	C₂²	—	4	4	no	—
619	C₂²	—	4	4	no	—
620	C₂²	—	4	4	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	8	1	no	—
625	C₂²	—	8	1	no	—
626	C₂²	—	8	1	no	—
627	C₂²	—	8	1	no	—
628	C₂²	—	8	1	no	—
629	C₂²	—	8	1	no	—
630	C₂²	—	8	2	no	—
631	C₂²	—	8	2	no	—
632	C₂²	—	8	2	no	—
633	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
634	C₂²	C₂×C₂₉×#127	1	1	yes	characteristic
635	C₂²	C₂₉×#532	1	1	yes	characteristic
636	C₂²	C₂₉×#576	1	2	yes	—
637	C₂²	C₂₉×#577	1	2	yes	—
638	C₄	—	2	4	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	2	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	2	no	—
643	C₄	—	8	1	no	—
644	C₄	—	8	1	no	—
645	C₄	—	8	1	no	—
646	C₄	—	8	1	no	—
647	C₄	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
648	C₄	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
649	C₄	C₂₉×#532	1	1	yes	characteristic
650	C₄	C₂₉×#532	1	1	yes	characteristic
651	C₂	—	8	2	no	—
652	C₂	—	8	2	no	—
653	C₂	—	8	2	no	—
654	C₂	C₄×C₂₉×#127	1	1	yes	characteristic
655	C₂	C₂₉×#2946	1	2	yes	—
656	C₂	C₂₉×#3154	1	1	yes	characteristic
657	C₂	C₂₉×#3155	1	1	yes	characteristic
658	C₂	C₂₉×#3179	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂₉×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₉×#442	C₂	semidirect
3. C₂×C₂₉×#440	C₂	semidirect
4. C₂×C₄×SD₁₆×C₂₉	C₂	semidirect
5. C₂×C₄×D₈×C₂₉	C₂	semidirect
6. C₂₉×#2328	C₂	semidirect
7. C₂₉×#2326	C₂	semidirect
8. C₂₉×#1973	C₂	semidirect
9. C₂₉×#1972	C₂	semidirect
10. C₂₉×#1970	C₂	semidirect
11. C₂₉×#1968	C₂	semidirect
12. C₂₉×#1958	C₂	semidirect
13. C₂₉×#1957	C₂	semidirect
14. C₂₉×#1847	C₂	semidirect
15. C₂₉×#1726	C₂	semidirect
26. C₂₉×#496	C₄	semidirect
72. C₂×SD₁₆×C₂₉	C₂×C₄	semidirect
73. C₂×SD₁₆×C₂₉	C₂×C₄	semidirect
78. C₂×D₈×C₂₉	C₂×C₄	semidirect
79. C₂×D₈×C₂₉	C₂×C₄	semidirect
85. C₂₉×#127	C₂×C₄	semidirect
87. C₂₉×#124	C₂×C₄	semidirect
126. C₂₉×#97	C₂×C₄	semidirect
127. C₂₉×#97	D₄	semidirect
130. C₄×C₈×C₂₉	D₄	semidirect
221. #21704	C₂₉	direct (N × H)
290. C₂×#442	C₂×C₂₉	semidirect
291. C₂×#440	C₂×C₂₉	semidirect
292. C₂×C₄×SD₁₆	C₂×C₂₉	semidirect
293. C₂×C₄×D₈	C₂×C₂₉	semidirect
294. #2328	C₂×C₂₉	semidirect
295. #2326	C₂×C₂₉	semidirect
296. #1973	C₂×C₂₉	semidirect
297. #1972	C₂×C₂₉	semidirect
298. #1970	C₂×C₂₉	semidirect
299. #1968	C₂×C₂₉	semidirect
300. #1958	C₂×C₂₉	semidirect
301. #1957	C₂×C₂₉	semidirect
302. #1847	C₂×C₂₉	semidirect
303. #1726	C₂×C₂₉	semidirect
347. #496	C₄×C₂₉	semidirect
401. C₂×SD₁₆	C₂×C₄×C₂₉	semidirect
402. C₂×SD₁₆	C₂×C₄×C₂₉	semidirect
407. C₂×D₈	C₂×C₄×C₂₉	semidirect
408. C₂×D₈	C₂×C₄×C₂₉	semidirect
414. #127	C₂×C₄×C₂₉	semidirect
416. #124	C₂×C₄×C₂₉	semidirect
455. #97	C₂×C₄×C₂₉	semidirect
456. #97	D₄×C₂₉	semidirect
459. C₄×C₈	D₄×C₂₉	semidirect
464. C₂₉	#21704	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×#496	2
C₂×C₂₉×#442	2
C₂×C₂₉×#440	2
C₂×C₄×SD₁₆×C₂₉	2
C₂×C₄×D₈×C₂₉	2
C₂₉×#2328	2
C₂₉×#2326	2
C₂₉×#1973	2
C₂₉×#1972	2
C₂₉×#1970	2
C₂₉×#1968	2
C₂₉×#1958	2
C₂₉×#1957	2
C₂₉×#1847	2
C₂₉×#1726	2
#21704	29

Subgroups — C29×#21704 #20316604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#21704 #20316604