Subgroups — C₂₉×#22109 #20317009

Order 7424.

728 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#433	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2396	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1984	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1924	C₂	1	1	yes	maximal, characteristic
9	C₂₉×#1924	C₂	1	1	yes	maximal, characteristic
10	C₂₉×#1923	C₂	1	1	yes	maximal, characteristic
11	C₂₉×#1923	C₂	1	1	yes	maximal, characteristic
12	C₂₉×#1917	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1916	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1798	C₂	1	1	yes	maximal, characteristic
15	C₂₉×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
18	C₂₉×#446	—	2	4	no	—
19	C₂₉×#433	—	2	4	no	—
20	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
38	C₂₉×#400	C₄	1	1	yes	characteristic
39	C₂₉×#399	C₄	1	1	yes	characteristic
40	C₂₉×#398	C₄	1	1	yes	characteristic
41	C₂₉×#398	C₄	1	1	yes	characteristic
42	C₂₉×#396	C₄	1	1	yes	characteristic
43	C₂₉×#396	C₄	1	1	yes	characteristic
44	C₂₉×#395	C₄	1	1	yes	characteristic
45	C₂₉×#393	C₄	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
49	C₄×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
50	C₄×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
51	C₂₉×#336	C₂²	1	1	yes	characteristic
52	C₂₉×#336	C₂²	1	1	yes	characteristic
53	C₂₉×#336	C₂²	1	1	yes	characteristic
54	C₂₉×#336	C₂²	1	1	yes	characteristic
55	C₂₉×#336	C₂²	1	1	yes	characteristic
56	C₂₉×#336	C₂²	1	1	yes	characteristic
57	C₂₉×#336	C₂²	1	1	yes	characteristic
58	C₂₉×#336	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	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
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	C₄×Q₈×C₂₉	—	2	2	no	—
72	C₄×Q₈×C₂₉	—	2	2	no	—
73	C₂₉×#117	—	2	2	no	—
74	C₂₉×#117	—	2	2	no	—
75	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
98	C₂₉×C₄⋊C₈	—	2	2	no	—
99	C₂₉×C₄⋊C₈	—	2	2	no	—
100	C₂₉×C₄⋊C₈	—	2	2	no	—
101	C₂₉×C₄⋊C₈	—	2	2	no	—
102	C₂₉×C₄⋊C₈	—	2	2	no	—
103	C₂₉×C₄⋊C₈	—	2	2	no	—
104	C₂₉×C₄⋊C₈	—	4	1	no	—
105	C₂₉×C₄⋊C₈	—	4	1	no	—
106	C₂₉×C₂²⋊C₈	—	2	2	no	—
107	C₂₉×C₂²⋊C₈	—	2	2	no	—
108	C₂₉×C₂²⋊C₈	—	4	1	no	—
109	C₂₉×C₂²⋊C₈	—	4	1	no	—
110	C₂₉×#97	—	2	2	no	—
111	C₂₉×#97	—	4	1	no	—
112	C₂₉×#97	D₄	1	4	yes	—
113	C₄×C₈×C₂₉	—	2	2	no	—
114	C₄×C₈×C₂₉	—	2	2	no	—
115	C₄×C₈×C₂₉	—	4	1	no	—
116	C₂₉×#95	C₂×C₄	1	1	yes	characteristic
117	C₂₉×#95	C₂×C₄	1	1	yes	characteristic
118	C₂₉×#95	C₂×C₄	1	1	yes	characteristic
119	C₂₉×#95	C₂×C₄	1	1	yes	characteristic
120	C₂₉×#95	C₂×C₄	1	1	yes	characteristic
121	C₂₉×#95	C₂×C₄	1	1	yes	characteristic
122	C₂₉×#95	C₂×C₄	1	1	yes	characteristic
123	C₂₉×#95	C₂×C₄	1	1	yes	characteristic
124	C₂₉×#95	C₂×C₄	1	1	yes	characteristic
125	C₂₉×#95	C₂×C₄	1	1	yes	characteristic
126	C₂⁴×C₂₉	C₂²×C₄	1	1	yes	characteristic
127	C₂×Q₈×C₂₉	—	2	2	no	—
128	C₂×Q₈×C₂₉	—	2	2	no	—
129	C₂×Q₈×C₂₉	—	4	1	no	—
130	C₂²×C₄×C₂₉	—	2	1	no	—
131	C₂²×C₄×C₂₉	—	2	1	no	—
132	C₂²×C₄×C₂₉	—	2	1	no	—
133	C₂²×C₄×C₂₉	—	2	1	no	—
134	C₂²×C₄×C₂₉	—	2	1	no	—
135	C₂²×C₄×C₂₉	—	2	1	no	—
136	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
150	C₂×C₈×C₂₉	—	2	1	no	—
151	C₂×C₈×C₂₉	—	2	1	no	—
152	C₂×C₈×C₂₉	—	2	1	no	—
153	C₂×C₈×C₂₉	—	2	1	no	—
154	C₂×C₈×C₂₉	—	2	1	no	—
155	C₂×C₈×C₂₉	—	2	1	no	—
156	C₂×C₈×C₂₉	—	2	1	no	—
157	C₂×C₈×C₂₉	—	2	1	no	—
158	C₂×C₈×C₂₉	—	2	1	no	—
159	C₂×C₈×C₂₉	—	2	1	no	—
160	C₂×C₈×C₂₉	—	2	1	no	—
161	C₂×C₈×C₂₉	—	2	1	no	—
162	C₂×C₈×C₂₉	—	2	1	no	—
163	C₂×C₈×C₂₉	—	2	1	no	—
164	C₂×C₈×C₂₉	—	2	1	no	—
165	C₂×C₈×C₂₉	—	2	1	no	—
166	C₂×C₈×C₂₉	—	2	1	no	—
167	C₂×C₈×C₂₉	—	2	1	no	—
168	C₂×C₈×C₂₉	—	2	1	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	C₂×D₄	1	2	yes	—
173	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
174	C₄⋊C₄×C₂₉	—	2	2	no	—
175	C₄⋊C₄×C₂₉	—	2	2	no	—
176	C₄⋊C₄×C₂₉	—	2	2	no	—
177	C₄⋊C₄×C₂₉	—	2	2	no	—
178	C₄⋊C₄×C₂₉	—	2	2	no	—
179	C₄⋊C₄×C₂₉	—	2	2	no	—
180	C₄⋊C₄×C₂₉	—	2	2	no	—
181	C₄⋊C₄×C₂₉	—	2	2	no	—
182	C₄⋊C₄×C₂₉	—	4	1	no	—
183	C₄⋊C₄×C₂₉	—	4	1	no	—
184	C₄⋊C₄×C₂₉	—	4	1	no	—
185	C₂²⋊C₄×C₂₉	—	2	2	no	—
186	C₂²⋊C₄×C₂₉	—	2	2	no	—
187	C₂²⋊C₄×C₂₉	—	2	2	no	—
188	C₂²⋊C₄×C₂₉	—	2	2	no	—
189	C₂²⋊C₄×C₂₉	—	4	1	no	—
190	C₂²⋊C₄×C₂₉	—	4	1	no	—
191	C₄²×C₂₉	—	2	1	no	—
192	C₄²×C₂₉	—	2	1	no	—
193	C₄²×C₂₉	—	2	1	no	—
194	C₄²×C₂₉	—	2	1	no	—
195	C₄²×C₂₉	—	2	1	no	—
196	C₄²×C₂₉	—	2	1	no	—
197	C₄²×C₂₉	—	2	1	no	—
198	C₄²×C₂₉	—	2	1	no	—
199	C₄²×C₂₉	—	2	1	no	—
200	C₄²×C₂₉	—	2	1	no	—
201	C₄²×C₂₉	C₂×D₄	1	2	yes	—
202	C₄²×C₂₉	#41	1	2	yes	—
203	#22109	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂³×C₂₉	—	2	1	no	—
205	C₂³×C₂₉	—	2	1	no	—
206	C₂³×C₂₉	—	2	1	no	—
207	C₂³×C₂₉	—	2	1	no	—
208	C₂³×C₂₉	—	2	1	no	—
209	C₂³×C₂₉	—	2	1	no	—
210	C₂³×C₂₉	—	2	1	no	—
211	C₂³×C₂₉	C₂³×C₄	1	1	yes	characteristic
212	Q₈×C₂₉	—	4	4	no	—
213	C₂×C₄×C₂₉	—	2	1	no	—
214	C₂×C₄×C₂₉	—	2	1	no	—
215	C₂×C₄×C₂₉	—	2	1	no	—
216	C₂×C₄×C₂₉	—	2	1	no	—
217	C₂×C₄×C₂₉	—	2	1	no	—
218	C₂×C₄×C₂₉	—	2	1	no	—
219	C₂×C₄×C₂₉	—	2	1	no	—
220	C₂×C₄×C₂₉	—	2	1	no	—
221	C₂×C₄×C₂₉	—	2	1	no	—
222	C₂×C₄×C₂₉	—	2	1	no	—
223	C₂×C₄×C₂₉	—	2	1	no	—
224	C₂×C₄×C₂₉	—	2	1	no	—
225	C₂×C₄×C₂₉	—	2	1	no	—
226	C₂×C₄×C₂₉	—	2	1	no	—
227	C₂×C₄×C₂₉	—	2	1	no	—
228	C₂×C₄×C₂₉	—	2	1	no	—
229	C₂×C₄×C₂₉	—	2	1	no	—
230	C₂×C₄×C₂₉	—	2	1	no	—
231	C₂×C₄×C₂₉	—	2	1	no	—
232	C₂×C₄×C₂₉	—	2	1	no	—
233	C₂×C₄×C₂₉	—	2	1	no	—
234	C₂×C₄×C₂₉	—	2	1	no	—
235	C₂×C₄×C₂₉	—	2	1	no	—
236	C₂×C₄×C₂₉	—	2	1	no	—
237	C₂×C₄×C₂₉	—	2	1	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	1	no	—
243	C₂×C₄×C₂₉	—	2	1	no	—
244	C₂×C₄×C₂₉	—	2	1	no	—
245	C₂×C₄×C₂₉	—	2	1	no	—
246	C₂×C₄×C₂₉	—	2	1	no	—
247	C₂×C₄×C₂₉	—	2	1	no	—
248	C₂×C₄×C₂₉	—	4	1	no	—
249	C₂×C₄×C₂₉	—	4	1	no	—
250	C₂×C₄×C₂₉	—	4	1	no	—
251	C₂×C₄×C₂₉	—	4	1	no	—
252	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
253	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
254	C₂×C₄×C₂₉	#131	1	2	yes	—
255	C₂×C₄×C₂₉	#131	1	2	yes	—
256	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
259	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
260	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
261	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
262	C₈×C₂₉	—	2	2	no	—
263	C₈×C₂₉	—	2	2	no	—
264	C₈×C₂₉	—	4	1	no	—
265	C₈×C₂₉	—	4	1	no	—
266	C₈×C₂₉	—	4	1	no	—
267	C₈×C₂₉	—	4	1	no	—
268	C₈×C₂₉	—	4	1	no	—
269	C₈×C₂₉	—	4	1	no	—
270	C₂×#446	C₂×C₂₉	1	1	yes	characteristic, complemented
271	C₂×#433	C₂×C₂₉	1	1	yes	characteristic
272	#2396	C₂×C₂₉	1	1	yes	characteristic
273	#1984	C₂×C₂₉	1	1	yes	characteristic, complemented
274	#1940	C₂×C₂₉	1	1	yes	characteristic, complemented
275	#1939	C₂×C₂₉	1	1	yes	characteristic, complemented
276	#1939	C₂×C₂₉	1	1	yes	characteristic, complemented
277	#1924	C₂×C₂₉	1	1	yes	characteristic
278	#1924	C₂×C₂₉	1	1	yes	characteristic
279	#1923	C₂×C₂₉	1	1	yes	characteristic
280	#1923	C₂×C₂₉	1	1	yes	characteristic
281	#1917	C₂×C₂₉	1	1	yes	characteristic, complemented
282	#1916	C₂×C₂₉	1	1	yes	characteristic, complemented
283	#1798	C₂×C₂₉	1	1	yes	characteristic
284	#1771	C₂×C₂₉	1	1	yes	characteristic, complemented
285	C₂²×C₂₉	—	4	1	no	—
286	C₂²×C₂₉	—	4	1	no	—
287	C₂²×C₂₉	—	4	1	no	—
288	C₂²×C₂₉	—	4	1	no	—
289	C₂²×C₂₉	—	4	1	no	—
290	C₂²×C₂₉	—	4	1	no	—
291	C₂²×C₂₉	—	4	1	no	—
292	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
293	C₂²×C₂₉	#519	1	1	yes	characteristic
294	C₂²×C₂₉	#520	1	1	yes	characteristic
295	C₂²×C₂₉	C₂×#131	1	1	yes	characteristic
296	C₂²×C₂₉	C₂×#131	1	1	yes	characteristic
297	C₂²×C₂₉	#568	1	1	yes	characteristic
298	C₂²×C₂₉	#568	1	1	yes	characteristic
299	C₄×C₂₉	—	2	2	no	—
300	C₄×C₂₉	—	2	2	no	—
301	C₄×C₂₉	—	2	2	no	—
302	C₄×C₂₉	—	2	2	no	—
303	C₄×C₂₉	—	4	1	no	—
304	C₄×C₂₉	—	4	1	no	—
305	C₄×C₂₉	—	4	1	no	—
306	C₄×C₂₉	—	4	1	no	—
307	C₄×C₂₉	—	4	1	no	—
308	C₄×C₂₉	—	4	1	no	—
309	C₄×C₂₉	—	4	1	no	—
310	C₄×C₂₉	—	4	1	no	—
311	C₄×C₂₉	—	4	1	no	—
312	C₄×C₂₉	#536	1	1	yes	characteristic
313	C₄×C₂₉	#537	1	1	yes	characteristic
314	C₄×C₂₉	#541	1	1	yes	characteristic
315	C₄×C₂₉	#542	1	1	yes	characteristic
316	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
317	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
318	#446	—	2	4	no	—
319	#433	—	2	4	no	—
320	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
321	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
322	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
323	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
324	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
325	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
326	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
327	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
328	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
329	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
330	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
331	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
332	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
333	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
334	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
335	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
336	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
337	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
338	#400	C₄×C₂₉	1	1	yes	characteristic
339	#399	C₄×C₂₉	1	1	yes	characteristic
340	#398	C₄×C₂₉	1	1	yes	characteristic
341	#398	C₄×C₂₉	1	1	yes	characteristic
342	#396	C₄×C₂₉	1	1	yes	characteristic
343	#396	C₄×C₂₉	1	1	yes	characteristic
344	#395	C₄×C₂₉	1	1	yes	characteristic
345	#393	C₄×C₂₉	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
347	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
348	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
349	C₄×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
350	C₄×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
351	#336	C₂²×C₂₉	1	1	yes	characteristic
352	#336	C₂²×C₂₉	1	1	yes	characteristic
353	#336	C₂²×C₂₉	1	1	yes	characteristic
354	#336	C₂²×C₂₉	1	1	yes	characteristic
355	#336	C₂²×C₂₉	1	1	yes	characteristic
356	#336	C₂²×C₂₉	1	1	yes	characteristic
357	#336	C₂²×C₂₉	1	1	yes	characteristic
358	#336	C₂²×C₂₉	1	1	yes	characteristic
359	#336	C₂²×C₂₉	1	1	yes	characteristic
360	#336	C₂²×C₂₉	1	1	yes	characteristic
361	C₂×C₂₉	—	8	1	no	—
362	C₂×C₂₉	#2323	1	1	yes	characteristic
363	C₂×C₂₉	#2933	1	1	yes	characteristic
364	C₂×C₂₉	#2935	1	1	yes	characteristic
365	C₂×C₂₉	#2986	1	1	yes	characteristic
366	C₂×C₂₉	#2987	1	1	yes	characteristic
367	C₂×C₂₉	#2992	1	1	yes	characteristic
368	C₂×C₂₉	#2993	1	1	yes	characteristic
369	C₂²×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
370	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
373	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
374	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
375	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
376	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
377	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
378	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
379	C₄×Q₈	—	2	2	no	—
380	C₄×Q₈	—	2	2	no	—
381	#117	—	2	2	no	—
382	#117	—	2	2	no	—
383	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
395	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
396	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
397	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
398	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
399	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
404	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
405	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
406	C₄⋊C₈	—	2	2	no	—
407	C₄⋊C₈	—	2	2	no	—
408	C₄⋊C₈	—	2	2	no	—
409	C₄⋊C₈	—	2	2	no	—
410	C₄⋊C₈	—	2	2	no	—
411	C₄⋊C₈	—	2	2	no	—
412	C₄⋊C₈	—	4	1	no	—
413	C₄⋊C₈	—	4	1	no	—
414	C₂²⋊C₈	—	2	2	no	—
415	C₂²⋊C₈	—	2	2	no	—
416	C₂²⋊C₈	—	4	1	no	—
417	C₂²⋊C₈	—	4	1	no	—
418	#97	—	2	2	no	—
419	#97	—	4	1	no	—
420	#97	D₄×C₂₉	1	4	yes	—
421	C₄×C₈	—	2	2	no	—
422	C₄×C₈	—	2	2	no	—
423	C₄×C₈	—	4	1	no	—
424	#95	C₂×C₄×C₂₉	1	1	yes	characteristic
425	#95	C₂×C₄×C₂₉	1	1	yes	characteristic
426	#95	C₂×C₄×C₂₉	1	1	yes	characteristic
427	#95	C₂×C₄×C₂₉	1	1	yes	characteristic
428	#95	C₂×C₄×C₂₉	1	1	yes	characteristic
429	#95	C₂×C₄×C₂₉	1	1	yes	characteristic
430	#95	C₂×C₄×C₂₉	1	1	yes	characteristic
431	#95	C₂×C₄×C₂₉	1	1	yes	characteristic
432	#95	C₂×C₄×C₂₉	1	1	yes	characteristic
433	#95	C₂×C₄×C₂₉	1	1	yes	characteristic
434	C₂₉	#22109	1	1	yes	characteristic, direct product factor, Sylow
435	C₂⁴	C₂²×C₄×C₂₉	1	1	yes	characteristic
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	4	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
446	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
447	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
448	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
449	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
450	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
451	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
452	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
453	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
454	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
455	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
456	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
457	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
458	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
482	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	4	1	no	—
492	C₄⋊C₄	—	4	1	no	—
493	C₄⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	C₂×D₄×C₂₉	1	2	yes	—
511	C₄²	#41×C₂₉	1	2	yes	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	C₂³×C₄×C₂₉	1	1	yes	characteristic
520	Q₈	—	4	4	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
561	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
562	C₂×C₄	C₂₉×#131	1	2	yes	—
563	C₂×C₄	C₂₉×#131	1	2	yes	—
564	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
565	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
566	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
567	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
568	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
569	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
570	C₈	—	2	2	no	—
571	C₈	—	2	2	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₈	—	4	1	no	—
577	C₈	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
586	C₂²	C₂₉×#519	1	1	yes	characteristic
587	C₂²	C₂₉×#520	1	1	yes	characteristic
588	C₂²	C₂×C₂₉×#131	1	1	yes	characteristic
589	C₂²	C₂×C₂₉×#131	1	1	yes	characteristic
590	C₂²	C₂₉×#568	1	1	yes	characteristic
591	C₂²	C₂₉×#568	1	1	yes	characteristic
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	C₂₉×#536	1	1	yes	characteristic
606	C₄	C₂₉×#537	1	1	yes	characteristic
607	C₄	C₂₉×#541	1	1	yes	characteristic
608	C₄	C₂₉×#542	1	1	yes	characteristic
609	C₂	—	8	1	no	—
610	C₂	C₂₉×#2323	1	1	yes	characteristic
611	C₂	C₂₉×#2933	1	1	yes	characteristic
612	C₂	C₂₉×#2935	1	1	yes	characteristic
613	C₂	C₂₉×#2986	1	1	yes	characteristic
614	C₂	C₂₉×#2987	1	1	yes	characteristic
615	C₂	C₂₉×#2992	1	1	yes	characteristic
616	C₂	C₂₉×#2993	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#446	C₂	semidirect
4. C₂₉×#1984	C₂	semidirect
5. C₂₉×#1940	C₂	semidirect
6. C₂₉×#1939	C₂	semidirect
7. C₂₉×#1939	C₂	semidirect
12. C₂₉×#1917	C₂	semidirect
13. C₂₉×#1916	C₂	semidirect
15. C₂₉×#1771	C₂	semidirect
203. #22109	C₂₉	direct (N × H)
270. C₂×#446	C₂×C₂₉	semidirect
273. #1984	C₂×C₂₉	semidirect
274. #1940	C₂×C₂₉	semidirect
275. #1939	C₂×C₂₉	semidirect
276. #1939	C₂×C₂₉	semidirect
281. #1917	C₂×C₂₉	semidirect
282. #1916	C₂×C₂₉	semidirect
284. #1771	C₂×C₂₉	semidirect
434. C₂₉	#22109	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×#446	2
C₂×C₂₉×#433	2
C₂₉×#2396	2
C₂₉×#1984	2
C₂₉×#1940	2
C₂₉×#1939	2
C₂₉×#1924	2
C₂₉×#1923	2
C₂₉×#1917	2
C₂₉×#1916	2
C₂₉×#1798	2
C₂₉×#1771	2
#22109	29

Subgroups — C29×#22109 #20317009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#22109 #20317009