Subgroups — C₂₉×#26139 #20321039

Order 7424.

844 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#485	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#427	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#2415	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2354	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#2095	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2084	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2076	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1927	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1918	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1892	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1869	C₂	1	1	yes	maximal, characteristic
14	C₂₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
23	C₂₉×#485	—	2	4	no	—
24	C₂₉×#427	—	2	4	no	—
25	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
35	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂₉×#397	—	2	1	no	—
39	C₂₉×#394	—	2	1	no	—
40	C₂₉×#391	C₂²	1	1	yes	characteristic
41	C₂₉×#390	—	2	1	no	—
42	C₂₉×#389	—	2	1	no	—
43	C₂₉×#389	C₂²	1	1	yes	characteristic
44	C₂₉×#388	—	2	1	no	—
45	C₂₉×#388	—	2	1	no	—
46	C₂₉×#388	—	2	1	no	—
47	C₂₉×#384	C₂²	1	1	yes	characteristic
48	C₂₉×#380	C₂²	1	1	yes	characteristic
49	C₂₉×#380	C₂²	1	1	yes	characteristic
50	C₂₉×#380	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
52	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
53	C₂₉×#340	C₂²	1	1	yes	characteristic
54	C₂₉×#340	C₂²	1	1	yes	characteristic
55	C₂₉×#340	C₂²	1	1	yes	characteristic
56	C₂₉×#340	C₂²	1	1	yes	characteristic
57	C₂₉×#340	C₂²	1	1	yes	characteristic
58	C₂₉×#340	C₂²	1	1	yes	characteristic
59	C₂₉×#336	C₂²	1	1	yes	characteristic
60	C₂₉×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₂₉	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₂₉	—	2	2	no	—
66	C₂²×C₈×C₂₉	—	2	2	no	—
67	C₂²×C₈×C₂₉	—	2	2	no	—
68	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
72	C₂₉×C₂²⋊Q₈	—	2	2	no	—
73	C₂₉×C₂²⋊Q₈	—	2	2	no	—
74	C₂₉×C₂²⋊Q₈	—	2	2	no	—
75	C₂₉×C₂²⋊Q₈	—	4	1	no	—
76	C₄×D₄×C₂₉	—	2	2	no	—
77	C₄×D₄×C₂₉	—	2	2	no	—
78	C₂₉×#117	—	2	2	no	—
79	C₂₉×#117	—	2	2	no	—
80	C₂₉×#117	—	2	2	no	—
81	C₂₉×#117	—	4	1	no	—
82	C₂₉×#117	—	4	1	no	—
83	C₂₉×#117	—	4	1	no	—
84	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₂₉	—	2	1	no	—
108	C₂×C₄²×C₂₉	—	2	1	no	—
109	C₂×C₄²×C₂₉	—	2	1	no	—
110	C₂×C₄²×C₂₉	—	2	1	no	—
111	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
112	C₂₉×#107	—	2	2	no	—
113	C₂₉×#107	—	4	1	no	—
114	C₂₉×#107	D₄	1	4	yes	complemented
115	C₂₉×#106	—	2	2	no	—
116	C₂₉×#106	—	2	2	no	—
117	C₂₉×#106	—	2	2	no	—
118	C₂₉×#103	—	2	2	no	—
119	C₂₉×#103	—	2	2	no	—
120	C₂₉×#103	—	2	2	no	—
121	C₂₉×#103	—	4	1	no	—
122	C₂₉×C₂²⋊C₈	—	2	2	no	—
123	C₂₉×C₂²⋊C₈	—	2	2	no	—
124	C₂₉×C₂²⋊C₈	—	2	2	no	—
125	C₂₉×#95	—	2	1	no	—
126	C₂₉×#95	—	2	1	no	—
127	C₂₉×#95	—	2	1	no	—
128	C₂₉×#95	—	2	1	no	—
129	C₂₉×#95	—	2	1	no	—
130	C₂₉×#95	—	2	1	no	—
131	C₂₉×#95	—	2	1	no	—
132	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
133	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
134	C₂×Q₈×C₂₉	—	2	1	no	—
135	C₂×Q₈×C₂₉	—	2	1	no	—
136	C₂×Q₈×C₂₉	—	2	1	no	—
137	C₂×Q₈×C₂₉	—	2	1	no	—
138	C₂×Q₈×C₂₉	—	2	1	no	—
139	C₂×Q₈×C₂₉	—	2	1	no	—
140	C₂×D₄×C₂₉	—	2	2	no	—
141	C₂×D₄×C₂₉	—	2	2	no	—
142	C₂×D₄×C₂₉	—	4	1	no	—
143	C₂²×C₄×C₂₉	—	2	1	no	—
144	C₂²×C₄×C₂₉	—	2	1	no	—
145	C₂²×C₄×C₂₉	—	2	1	no	—
146	C₂²×C₄×C₂₉	—	2	1	no	—
147	C₂²×C₄×C₂₉	—	2	1	no	—
148	C₂²×C₄×C₂₉	—	2	1	no	—
149	C₂²×C₄×C₂₉	—	2	1	no	—
150	C₂²×C₄×C₂₉	—	2	1	no	—
151	C₂²×C₄×C₂₉	—	2	1	no	—
152	C₂²×C₄×C₂₉	—	2	1	no	—
153	C₂²×C₄×C₂₉	—	2	1	no	—
154	C₂²×C₄×C₂₉	—	2	1	no	—
155	C₂²×C₄×C₂₉	—	2	1	no	—
156	C₂²×C₄×C₂₉	—	2	1	no	—
157	C₂²×C₄×C₂₉	—	2	1	no	—
158	C₂²×C₄×C₂₉	—	2	1	no	—
159	C₂²×C₄×C₂₉	—	2	1	no	—
160	C₂²×C₄×C₂₉	—	2	1	no	—
161	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₂₉	#41	1	2	yes	—
166	C₂²×C₄×C₂₉	#41	1	2	yes	—
167	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
168	C₂×C₈×C₂₉	—	2	8	no	—
169	C₂×C₈×C₂₉	—	2	1	no	—
170	C₂×C₈×C₂₉	—	2	1	no	—
171	C₂×C₈×C₂₉	—	2	1	no	—
172	C₂×C₈×C₂₉	—	2	1	no	—
173	C₂×C₈×C₂₉	—	2	1	no	—
174	C₂×C₈×C₂₉	—	2	1	no	—
175	C₂×C₈×C₂₉	—	2	1	no	—
176	C₂×C₈×C₂₉	—	2	1	no	—
177	C₂×C₈×C₂₉	—	2	1	no	—
178	C₂×C₈×C₂₉	—	2	1	no	—
179	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
180	C₂×C₈×C₂₉	#41	1	2	yes	—
181	C₄⋊C₄×C₂₉	—	2	2	no	—
182	C₄⋊C₄×C₂₉	—	2	1	no	—
183	C₄⋊C₄×C₂₉	—	2	1	no	—
184	C₄⋊C₄×C₂₉	—	2	1	no	—
185	C₄⋊C₄×C₂₉	—	2	1	no	—
186	C₄⋊C₄×C₂₉	—	2	1	no	—
187	C₄⋊C₄×C₂₉	—	2	1	no	—
188	C₄⋊C₄×C₂₉	—	2	1	no	—
189	C₄⋊C₄×C₂₉	—	2	1	no	—
190	C₄⋊C₄×C₂₉	—	2	1	no	—
191	C₄⋊C₄×C₂₉	—	2	1	no	—
192	C₄⋊C₄×C₂₉	—	2	1	no	—
193	C₄⋊C₄×C₂₉	—	2	1	no	—
194	C₄⋊C₄×C₂₉	—	4	2	no	—
195	C₄⋊C₄×C₂₉	—	4	2	no	—
196	C₄⋊C₄×C₂₉	—	4	2	no	—
197	C₄⋊C₄×C₂₉	—	4	2	no	—
198	C₄⋊C₄×C₂₉	—	8	1	no	—
199	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
200	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
201	C₂²⋊C₄×C₂₉	—	2	2	no	—
202	C₂²⋊C₄×C₂₉	—	2	2	no	—
203	C₂²⋊C₄×C₂₉	—	4	2	no	—
204	C₂²⋊C₄×C₂₉	—	4	2	no	—
205	C₂²⋊C₄×C₂₉	—	4	2	no	—
206	C₂²⋊C₄×C₂₉	—	4	2	no	—
207	C₂²⋊C₄×C₂₉	—	4	2	no	—
208	C₂²⋊C₄×C₂₉	—	4	2	no	—
209	C₂²⋊C₄×C₂₉	—	8	1	no	—
210	C₂²⋊C₄×C₂₉	—	8	1	no	—
211	C₄²×C₂₉	—	2	1	no	—
212	C₄²×C₂₉	—	2	1	no	—
213	C₄²×C₂₉	—	4	2	no	—
214	C₄²×C₂₉	—	4	2	no	—
215	C₄²×C₂₉	—	4	2	no	—
216	C₄²×C₂₉	—	4	2	no	—
217	#26139	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂³×C₂₉	—	2	1	no	—
219	C₂³×C₂₉	—	2	1	no	—
220	C₂³×C₂₉	—	2	1	no	—
221	C₂³×C₂₉	—	2	1	no	—
222	C₂³×C₂₉	—	2	1	no	—
223	C₂³×C₂₉	—	2	1	no	—
224	C₂³×C₂₉	—	2	1	no	—
225	C₂³×C₂₉	—	2	1	no	—
226	C₂³×C₂₉	—	2	1	no	—
227	C₂³×C₂₉	—	2	1	no	—
228	C₂³×C₂₉	—	2	1	no	—
229	C₂³×C₂₉	—	2	1	no	—
230	C₂³×C₂₉	—	2	1	no	—
231	C₂³×C₂₉	#123	1	2	yes	—
232	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
233	Q₈×C₂₉	—	4	1	no	—
234	Q₈×C₂₉	—	4	1	no	—
235	Q₈×C₂₉	—	4	1	no	—
236	Q₈×C₂₉	—	4	1	no	—
237	D₄×C₂₉	—	4	4	no	—
238	C₂×C₄×C₂₉	—	2	1	no	—
239	C₂×C₄×C₂₉	—	2	1	no	—
240	C₂×C₄×C₂₉	—	2	1	no	—
241	C₂×C₄×C₂₉	—	2	1	no	—
242	C₂×C₄×C₂₉	—	2	2	no	—
243	C₂×C₄×C₂₉	—	2	2	no	—
244	C₂×C₄×C₂₉	—	2	2	no	—
245	C₂×C₄×C₂₉	—	2	2	no	—
246	C₂×C₄×C₂₉	—	2	1	no	—
247	C₂×C₄×C₂₉	—	2	1	no	—
248	C₂×C₄×C₂₉	—	2	2	no	—
249	C₂×C₄×C₂₉	—	2	1	no	—
250	C₂×C₄×C₂₉	—	2	2	no	—
251	C₂×C₄×C₂₉	—	2	1	no	—
252	C₂×C₄×C₂₉	—	2	1	no	—
253	C₂×C₄×C₂₉	—	2	1	no	—
254	C₂×C₄×C₂₉	—	4	1	no	—
255	C₂×C₄×C₂₉	—	4	1	no	—
256	C₂×C₄×C₂₉	—	4	1	no	—
257	C₂×C₄×C₂₉	—	4	1	no	—
258	C₂×C₄×C₂₉	—	4	1	no	—
259	C₂×C₄×C₂₉	—	4	1	no	—
260	C₂×C₄×C₂₉	—	4	1	no	—
261	C₂×C₄×C₂₉	—	4	1	no	—
262	C₂×C₄×C₂₉	—	4	1	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	1	no	—
270	C₂×C₄×C₂₉	—	4	1	no	—
271	C₂×C₄×C₂₉	—	4	1	no	—
272	C₂×C₄×C₂₉	—	4	1	no	—
273	C₂×C₄×C₂₉	—	4	1	no	—
274	C₂×C₄×C₂₉	—	4	1	no	—
275	C₂×C₄×C₂₉	—	4	1	no	—
276	C₂×C₄×C₂₉	—	4	1	no	—
277	C₂×C₄×C₂₉	—	4	1	no	—
278	C₂×C₄×C₂₉	—	4	1	no	—
279	C₂×C₄×C₂₉	—	4	1	no	—
280	C₂×C₄×C₂₉	#123	1	2	yes	—
281	C₂×C₄×C₂₉	#135	1	2	yes	—
282	C₂×C₄×C₂₉	C₂²×D₄	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	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
287	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
288	C₈×C₂₉	—	2	2	no	—
289	C₈×C₂₉	—	2	2	no	—
290	C₈×C₂₉	—	4	1	no	—
291	C₈×C₂₉	—	4	1	no	—
292	C₂×#485	C₂×C₂₉	1	1	yes	characteristic, complemented
293	C₂×#427	C₂×C₂₉	1	1	yes	characteristic, complemented
294	#2415	C₂×C₂₉	1	1	yes	characteristic
295	#2354	C₂×C₂₉	1	1	yes	characteristic
296	#2095	C₂×C₂₉	1	1	yes	characteristic, complemented
297	#2084	C₂×C₂₉	1	1	yes	characteristic, complemented
298	#2076	C₂×C₂₉	1	1	yes	characteristic, complemented
299	#2035	C₂×C₂₉	1	1	yes	characteristic, complemented
300	#1927	C₂×C₂₉	1	1	yes	characteristic, complemented
301	#1918	C₂×C₂₉	1	1	yes	characteristic, complemented
302	#1892	C₂×C₂₉	1	1	yes	characteristic, complemented
303	#1873	C₂×C₂₉	1	1	yes	characteristic, complemented
304	#1869	C₂×C₂₉	1	1	yes	characteristic
305	#1854	C₂×C₂₉	1	1	yes	characteristic, complemented
306	#1854	C₂×C₂₉	1	1	yes	characteristic, complemented
307	C₂²×C₂₉	—	2	2	no	—
308	C₂²×C₂₉	—	2	2	no	—
309	C₂²×C₂₉	—	2	2	no	—
310	C₂²×C₂₉	—	4	1	no	—
311	C₂²×C₂₉	—	4	1	no	—
312	C₂²×C₂₉	—	4	1	no	—
313	C₂²×C₂₉	—	4	1	no	—
314	C₂²×C₂₉	—	4	1	no	—
315	C₂²×C₂₉	—	4	1	no	—
316	C₂²×C₂₉	—	4	1	no	—
317	C₂²×C₂₉	—	4	1	no	—
318	C₂²×C₂₉	—	4	1	no	—
319	C₂²×C₂₉	—	4	1	no	—
320	C₂²×C₂₉	—	4	1	no	—
321	C₂²×C₂₉	C₂×#123	1	1	yes	characteristic
322	C₂²×C₂₉	D₄²	1	1	yes	characteristic
323	C₂²×C₂₉	#547	1	1	yes	characteristic
324	C₂²×C₂₉	C₂×#135	1	1	yes	characteristic
325	C₂²×C₂₉	#575	1	1	yes	characteristic
326	C₂²×C₂₉	#577	1	1	yes	characteristic
327	C₂²×C₂₉	#578	1	1	yes	characteristic
328	C₄×C₂₉	—	2	2	no	—
329	C₄×C₂₉	—	2	2	no	—
330	C₄×C₂₉	—	4	1	no	—
331	C₄×C₂₉	—	4	1	no	—
332	C₄×C₂₉	—	4	2	no	—
333	C₄×C₂₉	—	4	2	no	—
334	C₄×C₂₉	—	8	1	no	—
335	C₄×C₂₉	—	8	1	no	—
336	C₄×C₂₉	—	8	1	no	—
337	C₄×C₂₉	—	8	1	no	—
338	C₄×C₂₉	—	8	1	no	—
339	C₄×C₂₉	—	8	1	no	—
340	C₄×C₂₉	#525	1	1	yes	characteristic
341	C₄×C₂₉	#539	1	1	yes	characteristic
342	C₄×C₂₉	#548	1	1	yes	characteristic
343	C₄×C₂₉	#553	1	1	yes	characteristic
344	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
345	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
346	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
347	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
348	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
349	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
350	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
351	#485	—	2	4	no	—
352	#427	—	2	4	no	—
353	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
354	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
355	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
356	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
357	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
358	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
359	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
360	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
361	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
362	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
363	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
364	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
365	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
366	#397	—	2	1	no	—
367	#394	—	2	1	no	—
368	#391	C₂²×C₂₉	1	1	yes	characteristic
369	#390	—	2	1	no	—
370	#389	—	2	1	no	—
371	#389	C₂²×C₂₉	1	1	yes	characteristic
372	#388	—	2	1	no	—
373	#388	—	2	1	no	—
374	#388	—	2	1	no	—
375	#384	C₂²×C₂₉	1	1	yes	characteristic
376	#380	C₂²×C₂₉	1	1	yes	characteristic
377	#380	C₂²×C₂₉	1	1	yes	characteristic
378	#380	C₂²×C₂₉	1	1	yes	characteristic
379	C₄×C₄⋊C₄	—	2	1	no	—
380	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
381	#340	C₂²×C₂₉	1	1	yes	characteristic
382	#340	C₂²×C₂₉	1	1	yes	characteristic
383	#340	C₂²×C₂₉	1	1	yes	characteristic
384	#340	C₂²×C₂₉	1	1	yes	characteristic
385	#340	C₂²×C₂₉	1	1	yes	characteristic
386	#340	C₂²×C₂₉	1	1	yes	characteristic
387	#336	C₂²×C₂₉	1	1	yes	characteristic
388	#336	C₂²×C₂₉	1	1	yes	characteristic
389	C₂×C₂₉	—	4	2	no	—
390	C₂×C₂₉	—	8	1	no	—
391	C₂×C₂₉	#2443	1	1	yes	characteristic
392	C₂×C₂₉	#3091	1	1	yes	characteristic
393	C₂×C₂₉	#3097	1	1	yes	characteristic
394	C₂×C₂₉	#3271	1	1	yes	characteristic
395	C₂×C₂₉	#3283	1	1	yes	characteristic
396	C₂×C₂₉	#3340	1	1	yes	characteristic
397	C₂×C₂₉	#3349	1	1	yes	characteristic
398	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
399	C₂²×D₄	D₄×C₂₉	1	1	yes	characteristic
400	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
401	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
402	C₂²×C₈	—	2	2	no	—
403	C₂²×C₈	—	2	2	no	—
404	C₂²×C₈	—	2	2	no	—
405	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
406	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
407	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
409	C₂²⋊Q₈	—	2	2	no	—
410	C₂²⋊Q₈	—	2	2	no	—
411	C₂²⋊Q₈	—	2	2	no	—
412	C₂²⋊Q₈	—	4	1	no	—
413	C₄×D₄	—	2	2	no	—
414	C₄×D₄	—	2	2	no	—
415	#117	—	2	2	no	—
416	#117	—	2	2	no	—
417	#117	—	2	2	no	—
418	#117	—	4	1	no	—
419	#117	—	4	1	no	—
420	#117	—	4	1	no	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
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×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	—	2	1	no	—
437	C₂×C₂²⋊C₄	—	2	1	no	—
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
443	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
444	C₂×C₄²	—	2	1	no	—
445	C₂×C₄²	—	2	1	no	—
446	C₂×C₄²	—	2	1	no	—
447	C₂×C₄²	—	2	1	no	—
448	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
449	#107	—	2	2	no	—
450	#107	—	4	1	no	—
451	#107	D₄×C₂₉	1	4	yes	complemented
452	#106	—	2	2	no	—
453	#106	—	2	2	no	—
454	#106	—	2	2	no	—
455	#103	—	2	2	no	—
456	#103	—	2	2	no	—
457	#103	—	2	2	no	—
458	#103	—	4	1	no	—
459	C₂²⋊C₈	—	2	2	no	—
460	C₂²⋊C₈	—	2	2	no	—
461	C₂²⋊C₈	—	2	2	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	—	2	1	no	—
468	#95	—	2	1	no	—
469	C₂₉	#26139	1	1	yes	characteristic, direct product factor, Sylow
470	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
471	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	4	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
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	C₂×D₄×C₂₉	1	1	yes	characteristic
500	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
501	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
502	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
503	C₂²×C₄	#41×C₂₉	1	2	yes	—
504	C₂²×C₄	#41×C₂₉	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
506	C₂×C₈	—	2	8	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
518	C₂×C₈	#41×C₂₉	1	2	yes	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
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	—	4	2	no	—
533	C₄⋊C₄	—	4	2	no	—
534	C₄⋊C₄	—	4	2	no	—
535	C₄⋊C₄	—	4	2	no	—
536	C₄⋊C₄	—	8	1	no	—
537	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
538	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	4	2	no	—
542	C₂²⋊C₄	—	4	2	no	—
543	C₂²⋊C₄	—	4	2	no	—
544	C₂²⋊C₄	—	4	2	no	—
545	C₂²⋊C₄	—	4	2	no	—
546	C₂²⋊C₄	—	4	2	no	—
547	C₂²⋊C₄	—	8	1	no	—
548	C₂²⋊C₄	—	8	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	4	2	no	—
552	C₄²	—	4	2	no	—
553	C₄²	—	4	2	no	—
554	C₄²	—	4	2	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	C₂₉×#123	1	2	yes	—
569	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
570	Q₈	—	4	1	no	—
571	Q₈	—	4	1	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	4	1	no	—
574	D₄	—	4	4	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	4	1	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	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	C₂₉×#123	1	2	yes	—
618	C₂×C₄	C₂₉×#135	1	2	yes	—
619	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
620	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
621	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
622	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
623	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
624	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
625	C₈	—	2	2	no	—
626	C₈	—	2	2	no	—
627	C₈	—	4	1	no	—
628	C₈	—	4	1	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	1	no	—
643	C₂²	C₂×C₂₉×#123	1	1	yes	characteristic
644	C₂²	D₄²×C₂₉	1	1	yes	characteristic
645	C₂²	C₂₉×#547	1	1	yes	characteristic
646	C₂²	C₂×C₂₉×#135	1	1	yes	characteristic
647	C₂²	C₂₉×#575	1	1	yes	characteristic
648	C₂²	C₂₉×#577	1	1	yes	characteristic
649	C₂²	C₂₉×#578	1	1	yes	characteristic
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	2	no	—
654	C₄	—	4	2	no	—
655	C₄	—	4	1	no	—
656	C₄	—	8	1	no	—
657	C₄	—	8	1	no	—
658	C₄	—	8	1	no	—
659	C₄	—	8	1	no	—
660	C₄	—	8	1	no	—
661	C₄	—	8	1	no	—
662	C₄	C₂₉×#525	1	1	yes	characteristic
663	C₄	C₂₉×#539	1	1	yes	characteristic
664	C₄	C₂₉×#548	1	1	yes	characteristic
665	C₄	C₂₉×#553	1	1	yes	characteristic
666	C₂	—	4	2	no	—
667	C₂	—	8	1	no	—
668	C₂	C₂₉×#2443	1	1	yes	characteristic
669	C₂	C₂₉×#3091	1	1	yes	characteristic
670	C₂	C₂₉×#3097	1	1	yes	characteristic
671	C₂	C₂₉×#3271	1	1	yes	characteristic
672	C₂	C₂₉×#3283	1	1	yes	characteristic
673	C₂	C₂₉×#3340	1	1	yes	characteristic
674	C₂	C₂₉×#3349	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#485	C₂	semidirect
2. C₂×C₂₉×#427	C₂	semidirect
5. C₂₉×#2095	C₂	semidirect
6. C₂₉×#2084	C₂	semidirect
7. C₂₉×#2076	C₂	semidirect
8. C₂₉×#2035	C₂	semidirect
9. C₂₉×#1927	C₂	semidirect
10. C₂₉×#1918	C₂	semidirect
11. C₂₉×#1892	C₂	semidirect
12. C₂₉×#1873	C₂	semidirect
14. C₂₉×#1854	C₂	semidirect
15. C₂₉×#1854	C₂	semidirect
114. C₂₉×#107	D₄	semidirect
217. #26139	C₂₉	direct (N × H)
292. C₂×#485	C₂×C₂₉	semidirect
293. C₂×#427	C₂×C₂₉	semidirect
296. #2095	C₂×C₂₉	semidirect
297. #2084	C₂×C₂₉	semidirect
298. #2076	C₂×C₂₉	semidirect
299. #2035	C₂×C₂₉	semidirect
300. #1927	C₂×C₂₉	semidirect
301. #1918	C₂×C₂₉	semidirect
302. #1892	C₂×C₂₉	semidirect
303. #1873	C₂×C₂₉	semidirect
305. #1854	C₂×C₂₉	semidirect
306. #1854	C₂×C₂₉	semidirect
451. #107	D₄×C₂₉	semidirect
469. C₂₉	#26139	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×#485	2
C₂×C₂₉×#427	2
C₂₉×#2415	2
C₂₉×#2354	2
C₂₉×#2095	2
C₂₉×#2084	2
C₂₉×#2076	2
C₂₉×#2035	2
C₂₉×#1927	2
C₂₉×#1918	2
C₂₉×#1892	2
C₂₉×#1873	2
C₂₉×#1869	2
C₂₉×#1854	2
#26139	29

Subgroups — C29×#26139 #20321039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#26139 #20321039