Subgroups — C₂₉×#23033 #20317933

Order 7424.

982 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#465	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×#427	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2363	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#2362	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1973	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1944	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1927	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1926	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1875	C₂	1	1	yes	maximal, characteristic
11	C₂₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1776	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1752	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
24	C₂₉×#465	C₄	1	8	yes	complemented
25	C₂₉×#440	—	2	4	no	—
26	C₂₉×#427	—	2	4	no	—
27	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#107	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×#106	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×#102	C₂²	1	1	yes	characteristic
36	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
37	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
41	C₂₉×#391	C₂²	1	1	yes	characteristic
42	C₂₉×#390	—	2	1	no	—
43	C₂₉×#390	C₂²	1	1	yes	characteristic
44	C₂₉×#389	C₂²	1	1	yes	characteristic
45	C₂₉×#389	C₂²	1	1	yes	characteristic
46	C₂₉×#388	—	2	1	no	—
47	C₂₉×#388	—	2	1	no	—
48	C₂₉×#388	—	2	1	no	—
49	C₂₉×#387	—	2	1	no	—
50	C₂₉×#386	—	2	1	no	—
51	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
52	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
55	C₄×C₂²⋊C₄×C₂₉	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×#340	C₂²	1	1	yes	characteristic
60	C₂₉×#336	C₂²	1	1	yes	characteristic
61	C₂₉×#336	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₂₉	—	2	1	no	—
64	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₂₉	—	2	1	no	—
66	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
67	C₂×SD₁₆×C₂₉	—	2	2	no	—
68	C₂×SD₁₆×C₂₉	—	2	2	no	—
69	C₂×SD₁₆×C₂₉	C₂×C₄	1	4	yes	—
70	C₂²×C₈×C₂₉	—	2	2	no	—
71	C₂²×C₈×C₂₉	—	2	2	no	—
72	C₂²×C₈×C₂₉	C₂×C₄	1	4	yes	complemented
73	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
77	C₂₉×C₂²⋊Q₈	—	2	2	no	—
78	C₂₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	complemented
79	C₂₉×#121	—	2	2	no	—
80	C₂₉×#121	C₂×C₄	1	4	yes	—
81	C₄×Q₈×C₂₉	—	2	2	no	—
82	C₄×Q₈×C₂₉	—	4	1	no	—
83	C₄×D₄×C₂₉	—	2	2	no	—
84	C₄×D₄×C₂₉	—	4	1	no	—
85	C₂₉×#117	—	2	2	no	—
86	C₂₉×#117	—	2	2	no	—
87	C₂₉×#117	—	4	1	no	—
88	C₂₉×#117	—	4	1	no	—
89	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
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×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
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	—	2	1	no	—
112	C₂×C₄²×C₂₉	—	2	1	no	—
113	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
115	C₂₉×#107	—	2	2	no	—
116	C₂₉×#107	D₄	1	4	yes	complemented
117	C₂₉×#106	—	2	2	no	—
118	C₂₉×#106	—	2	2	no	—
119	C₂₉×#106	C₂×C₄	1	4	yes	complemented
120	C₂₉×#103	—	2	2	no	—
121	C₂₉×#103	—	4	1	no	—
122	C₂₉×#103	C₂×C₄	1	4	yes	complemented
123	C₂₉×#102	—	2	2	no	—
124	C₂₉×#102	—	4	1	no	—
125	C₂₉×#102	C₂×C₄	1	4	yes	—
126	C₂₉×C₂²⋊C₈	—	2	2	no	—
127	C₂₉×#97	—	2	2	no	—
128	C₂₉×#97	—	2	2	no	—
129	C₂₉×#95	—	2	1	no	—
130	C₂₉×#95	—	2	1	no	—
131	C₂₉×#95	—	2	1	no	—
132	C₂₉×#95	—	2	1	no	—
133	C₂₉×#95	—	2	1	no	—
134	C₂₉×#95	—	2	1	no	—
135	C₂₉×#95	D₄	1	1	yes	characteristic
136	C₂₉×#95	D₄	1	1	yes	characteristic
137	C₂⁴×C₂₉	—	2	1	no	—
138	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
144	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
145	C₂×D₄×C₂₉	—	2	4	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	—	8	1	no	—
152	C₂×D₄×C₂₉	—	8	1	no	—
153	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
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	—	2	1	no	—
162	C₂²×C₄×C₂₉	—	2	1	no	—
163	C₂²×C₄×C₂₉	—	2	1	no	—
164	C₂²×C₄×C₂₉	—	2	1	no	—
165	C₂²×C₄×C₂₉	—	4	2	no	—
166	C₂²×C₄×C₂₉	—	4	2	no	—
167	C₂²×C₄×C₂₉	—	8	1	no	—
168	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
169	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₂₉	#41	1	2	yes	—
175	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
176	SD₁₆×C₂₉	—	2	8	no	—
177	C₂×C₈×C₂₉	—	2	1	no	—
178	C₂×C₈×C₂₉	—	2	1	no	—
179	C₂×C₈×C₂₉	—	2	8	no	—
180	C₂×C₈×C₂₉	—	2	1	no	—
181	C₂×C₈×C₂₉	—	2	1	no	—
182	C₂×C₈×C₂₉	—	2	1	no	—
183	C₂×C₈×C₂₉	—	2	1	no	—
184	C₂×C₈×C₂₉	—	2	1	no	—
185	C₂×C₈×C₂₉	—	2	1	no	—
186	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
187	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
188	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
189	C₂×C₈×C₂₉	#41	1	2	yes	—
190	C₄⋊C₄×C₂₉	—	2	4	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	—	2	1	no	—
195	C₄⋊C₄×C₂₉	—	2	1	no	—
196	C₄⋊C₄×C₂₉	—	2	1	no	—
197	C₄⋊C₄×C₂₉	—	2	1	no	—
198	C₄⋊C₄×C₂₉	—	2	1	no	—
199	C₄⋊C₄×C₂₉	—	4	2	no	—
200	C₄⋊C₄×C₂₉	—	4	2	no	—
201	C₄⋊C₄×C₂₉	—	8	1	no	—
202	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
203	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
204	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
205	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
206	C₂²⋊C₄×C₂₉	—	2	4	no	—
207	C₂²⋊C₄×C₂₉	—	2	4	no	—
208	C₂²⋊C₄×C₂₉	—	4	1	no	—
209	C₂²⋊C₄×C₂₉	—	4	1	no	—
210	C₂²⋊C₄×C₂₉	—	4	2	no	—
211	C₂²⋊C₄×C₂₉	—	4	2	no	—
212	C₂²⋊C₄×C₂₉	—	4	2	no	—
213	C₂²⋊C₄×C₂₉	—	4	2	no	—
214	C₂²⋊C₄×C₂₉	—	8	1	no	—
215	C₄²×C₂₉	—	2	1	no	—
216	C₄²×C₂₉	—	2	1	no	—
217	C₄²×C₂₉	—	2	1	no	—
218	C₄²×C₂₉	—	2	1	no	—
219	C₄²×C₂₉	—	4	2	no	—
220	C₄²×C₂₉	—	4	2	no	—
221	C₄²×C₂₉	—	4	2	no	—
222	C₄²×C₂₉	—	4	2	no	—
223	C₄²×C₂₉	—	8	1	no	—
224	#23033	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	2	no	—
232	C₂³×C₂₉	—	4	1	no	—
233	C₂³×C₂₉	—	4	1	no	—
234	C₂³×C₂₉	—	4	1	no	—
235	C₂³×C₂₉	—	4	1	no	—
236	C₂³×C₂₉	—	4	1	no	—
237	C₂³×C₂₉	—	4	1	no	—
238	C₂³×C₂₉	C₄×D₄	1	2	yes	—
239	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
240	Q₈×C₂₉	—	2	2	no	—
241	Q₈×C₂₉	—	2	2	no	—
242	Q₈×C₂₉	—	4	1	no	—
243	Q₈×C₂₉	—	4	1	no	—
244	D₄×C₂₉	—	2	2	no	—
245	D₄×C₂₉	—	2	2	no	—
246	D₄×C₂₉	—	4	1	no	—
247	D₄×C₂₉	—	4	1	no	—
248	D₄×C₂₉	—	8	4	no	—
249	C₂×C₄×C₂₉	—	2	1	no	—
250	C₂×C₄×C₂₉	—	2	1	no	—
251	C₂×C₄×C₂₉	—	2	2	no	—
252	C₂×C₄×C₂₉	—	2	2	no	—
253	C₂×C₄×C₂₉	—	2	2	no	—
254	C₂×C₄×C₂₉	—	2	2	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	1	no	—
259	C₂×C₄×C₂₉	—	2	1	no	—
260	C₂×C₄×C₂₉	—	2	2	no	—
261	C₂×C₄×C₂₉	—	2	2	no	—
262	C₂×C₄×C₂₉	—	2	1	no	—
263	C₂×C₄×C₂₉	—	2	1	no	—
264	C₂×C₄×C₂₉	—	2	1	no	—
265	C₂×C₄×C₂₉	—	2	1	no	—
266	C₂×C₄×C₂₉	—	2	1	no	—
267	C₂×C₄×C₂₉	—	2	1	no	—
268	C₂×C₄×C₂₉	—	2	1	no	—
269	C₂×C₄×C₂₉	—	2	1	no	—
270	C₂×C₄×C₂₉	—	2	1	no	—
271	C₂×C₄×C₂₉	—	2	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	—	4	1	no	—
281	C₂×C₄×C₂₉	—	4	1	no	—
282	C₂×C₄×C₂₉	—	4	1	no	—
283	C₂×C₄×C₂₉	—	4	1	no	—
284	C₂×C₄×C₂₉	—	4	1	no	—
285	C₂×C₄×C₂₉	—	4	1	no	—
286	C₂×C₄×C₂₉	—	4	1	no	—
287	C₂×C₄×C₂₉	—	4	1	no	—
288	C₂×C₄×C₂₉	—	8	4	no	—
289	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
290	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
291	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
295	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
296	C₈×C₂₉	—	2	2	no	—
297	C₈×C₂₉	—	4	1	no	—
298	C₈×C₂₉	—	4	1	no	—
299	C₈×C₂₉	C₄×D₄	1	4	yes	—
300	C₂×#465	C₂×C₂₉	1	1	yes	characteristic
301	C₂×#440	C₂×C₂₉	1	1	yes	characteristic, complemented
302	C₂×#427	C₂×C₂₉	1	1	yes	characteristic, complemented
303	#2363	C₂×C₂₉	1	1	yes	characteristic
304	#2362	C₂×C₂₉	1	1	yes	characteristic, complemented
305	#1973	C₂×C₂₉	1	1	yes	characteristic, complemented
306	#1944	C₂×C₂₉	1	1	yes	characteristic, complemented
307	#1927	C₂×C₂₉	1	1	yes	characteristic, complemented
308	#1926	C₂×C₂₉	1	1	yes	characteristic, complemented
309	#1875	C₂×C₂₉	1	1	yes	characteristic
310	#1873	C₂×C₂₉	1	1	yes	characteristic, complemented
311	#1865	C₂×C₂₉	1	1	yes	characteristic, complemented
312	#1864	C₂×C₂₉	1	1	yes	characteristic, complemented
313	#1776	C₂×C₂₉	1	1	yes	characteristic, complemented
314	#1752	C₂×C₂₉	1	1	yes	characteristic, complemented
315	C₂²×C₂₉	—	2	2	no	—
316	C₂²×C₂₉	—	2	2	no	—
317	C₂²×C₂₉	—	2	2	no	—
318	C₂²×C₂₉	—	4	1	no	—
319	C₂²×C₂₉	—	4	1	no	—
320	C₂²×C₂₉	—	4	1	no	—
321	C₂²×C₂₉	—	4	1	no	—
322	C₂²×C₂₉	—	4	2	no	—
323	C₂²×C₂₉	—	4	2	no	—
324	C₂²×C₂₉	—	4	2	no	—
325	C₂²×C₂₉	—	8	1	no	—
326	C₂²×C₂₉	—	8	1	no	—
327	C₂²×C₂₉	—	8	1	no	—
328	C₂²×C₂₉	—	8	1	no	—
329	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
330	C₂²×C₂₉	D₄²	1	1	yes	characteristic
331	C₂²×C₂₉	#547	1	1	yes	characteristic
332	C₂²×C₂₉	#575	1	1	yes	characteristic
333	C₂²×C₂₉	#575	1	1	yes	characteristic
334	C₂²×C₂₉	#577	1	1	yes	characteristic
335	C₂²×C₂₉	#577	1	1	yes	characteristic
336	C₄×C₂₉	—	2	2	no	—
337	C₄×C₂₉	—	4	1	no	—
338	C₄×C₂₉	—	4	1	no	—
339	C₄×C₂₉	—	4	2	no	—
340	C₄×C₂₉	—	4	2	no	—
341	C₄×C₂₉	—	4	2	no	—
342	C₄×C₂₉	—	4	1	no	—
343	C₄×C₂₉	—	4	2	no	—
344	C₄×C₂₉	—	4	2	no	—
345	C₄×C₂₉	—	4	1	no	—
346	C₄×C₂₉	—	8	1	no	—
347	C₄×C₂₉	—	8	1	no	—
348	C₄×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
349	C₄×C₂₉	#520	1	1	yes	characteristic
350	C₄×C₂₉	#548	1	1	yes	characteristic
351	C₄×C₂₉	#553	1	1	yes	characteristic
352	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
353	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
354	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
355	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
356	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
357	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
358	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
359	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
360	#465	C₄×C₂₉	1	8	yes	complemented
361	#440	—	2	4	no	—
362	#427	—	2	4	no	—
363	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
364	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
365	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
366	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
367	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
368	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
369	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
370	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
371	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
372	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
373	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
374	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
375	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
376	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
377	#391	C₂²×C₂₉	1	1	yes	characteristic
378	#390	—	2	1	no	—
379	#390	C₂²×C₂₉	1	1	yes	characteristic
380	#389	C₂²×C₂₉	1	1	yes	characteristic
381	#389	C₂²×C₂₉	1	1	yes	characteristic
382	#388	—	2	1	no	—
383	#388	—	2	1	no	—
384	#388	—	2	1	no	—
385	#387	—	2	1	no	—
386	#386	—	2	1	no	—
387	C₄×C₄⋊C₄	—	2	1	no	—
388	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
389	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
390	C₄×C₂²⋊C₄	—	2	1	no	—
391	C₄×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
392	#340	C₂²×C₂₉	1	1	yes	characteristic
393	#340	C₂²×C₂₉	1	1	yes	characteristic
394	#340	C₂²×C₂₉	1	1	yes	characteristic
395	#340	C₂²×C₂₉	1	1	yes	characteristic
396	#336	C₂²×C₂₉	1	1	yes	characteristic
397	#336	C₂²×C₂₉	1	1	yes	characteristic
398	C₂×C₂₉	—	4	2	no	—
399	C₂×C₂₉	—	8	2	no	—
400	C₂×C₂₉	#2361	1	1	yes	characteristic
401	C₂×C₂₉	#2943	1	1	yes	characteristic
402	C₂×C₂₉	#2949	1	1	yes	characteristic
403	C₂×C₂₉	#3267	1	1	yes	characteristic
404	C₂×C₂₉	#3271	1	1	yes	characteristic
405	C₂×C₂₉	#3348	1	1	yes	characteristic
406	C₂×C₂₉	#3350	1	1	yes	characteristic
407	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
408	C₂²×D₄	—	2	1	no	—
409	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
410	C₂³×C₄	—	2	1	no	—
411	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
412	C₂×SD₁₆	—	2	2	no	—
413	C₂×SD₁₆	—	2	2	no	—
414	C₂×SD₁₆	C₂×C₄×C₂₉	1	4	yes	—
415	C₂²×C₈	—	2	2	no	—
416	C₂²×C₈	—	2	2	no	—
417	C₂²×C₈	C₂×C₄×C₂₉	1	4	yes	complemented
418	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
419	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
420	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
421	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
422	C₂²⋊Q₈	—	2	2	no	—
423	C₂²⋊Q₈	C₂×C₄×C₂₉	1	4	yes	complemented
424	#121	—	2	2	no	—
425	#121	C₂×C₄×C₂₉	1	4	yes	—
426	C₄×Q₈	—	2	2	no	—
427	C₄×Q₈	—	4	1	no	—
428	C₄×D₄	—	2	2	no	—
429	C₄×D₄	—	4	1	no	—
430	#117	—	2	2	no	—
431	#117	—	2	2	no	—
432	#117	—	4	1	no	—
433	#117	—	4	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
452	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
453	C₂×C₄²	—	2	1	no	—
454	C₂×C₄²	—	2	1	no	—
455	C₂×C₄²	—	2	1	no	—
456	C₂×C₄²	—	2	1	no	—
457	C₂×C₄²	—	2	1	no	—
458	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
459	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
460	#107	—	2	2	no	—
461	#107	D₄×C₂₉	1	4	yes	complemented
462	#106	—	2	2	no	—
463	#106	—	2	2	no	—
464	#106	C₂×C₄×C₂₉	1	4	yes	complemented
465	#103	—	2	2	no	—
466	#103	—	4	1	no	—
467	#103	C₂×C₄×C₂₉	1	4	yes	complemented
468	#102	—	2	2	no	—
469	#102	—	4	1	no	—
470	#102	C₂×C₄×C₂₉	1	4	yes	—
471	C₂²⋊C₈	—	2	2	no	—
472	#97	—	2	2	no	—
473	#97	—	2	2	no	—
474	#95	—	2	1	no	—
475	#95	—	2	1	no	—
476	#95	—	2	1	no	—
477	#95	—	2	1	no	—
478	#95	—	2	1	no	—
479	#95	—	2	1	no	—
480	#95	D₄×C₂₉	1	1	yes	characteristic
481	#95	D₄×C₂₉	1	1	yes	characteristic
482	C₂₉	#23033	1	1	yes	characteristic, direct product factor, Sylow
483	C₂⁴	—	2	1	no	—
484	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
491	C₂×D₄	—	2	4	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	8	1	no	—
498	C₂×D₄	—	8	1	no	—
499	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	4	2	no	—
512	C₂²×C₄	—	4	2	no	—
513	C₂²×C₄	—	8	1	no	—
514	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
515	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
516	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
517	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
518	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
519	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
520	C₂²×C₄	#41×C₂₉	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
522	SD₁₆	—	2	8	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	8	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
533	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
534	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
535	C₂×C₈	#41×C₂₉	1	2	yes	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	8	1	no	—
548	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
549	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
550	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
551	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
552	C₂²⋊C₄	—	2	4	no	—
553	C₂²⋊C₄	—	2	4	no	—
554	C₂²⋊C₄	—	4	1	no	—
555	C₂²⋊C₄	—	4	1	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	2	no	—
558	C₂²⋊C₄	—	4	2	no	—
559	C₂²⋊C₄	—	4	2	no	—
560	C₂²⋊C₄	—	8	1	no	—
561	C₄²	—	2	1	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	4	2	no	—
566	C₄²	—	4	2	no	—
567	C₄²	—	4	2	no	—
568	C₄²	—	4	2	no	—
569	C₄²	—	8	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	4	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	4	1	no	—
580	C₂³	—	4	1	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	C₄×D₄×C₂₉	1	2	yes	—
584	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	2	2	no	—
587	Q₈	—	4	1	no	—
588	Q₈	—	4	1	no	—
589	D₄	—	2	2	no	—
590	D₄	—	2	2	no	—
591	D₄	—	4	1	no	—
592	D₄	—	4	1	no	—
593	D₄	—	8	4	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	8	4	no	—
634	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
635	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
636	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
637	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
638	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
639	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
640	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
641	C₈	—	2	2	no	—
642	C₈	—	4	1	no	—
643	C₈	—	4	1	no	—
644	C₈	C₄×D₄×C₂₉	1	4	yes	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	8	1	no	—
656	C₂²	—	8	1	no	—
657	C₂²	—	8	1	no	—
658	C₂²	—	8	1	no	—
659	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
660	C₂²	D₄²×C₂₉	1	1	yes	characteristic
661	C₂²	C₂₉×#547	1	1	yes	characteristic
662	C₂²	C₂₉×#575	1	1	yes	characteristic
663	C₂²	C₂₉×#575	1	1	yes	characteristic
664	C₂²	C₂₉×#577	1	1	yes	characteristic
665	C₂²	C₂₉×#577	1	1	yes	characteristic
666	C₄	—	2	2	no	—
667	C₄	—	4	2	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	1	no	—
674	C₄	—	4	1	no	—
675	C₄	—	4	2	no	—
676	C₄	—	8	1	no	—
677	C₄	—	8	1	no	—
678	C₄	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
679	C₄	C₂₉×#520	1	1	yes	characteristic
680	C₄	C₂₉×#548	1	1	yes	characteristic
681	C₄	C₂₉×#553	1	1	yes	characteristic
682	C₂	—	4	2	no	—
683	C₂	—	8	2	no	—
684	C₂	C₂₉×#2361	1	1	yes	characteristic
685	C₂	C₂₉×#2943	1	1	yes	characteristic
686	C₂	C₂₉×#2949	1	1	yes	characteristic
687	C₂	C₂₉×#3267	1	1	yes	characteristic
688	C₂	C₂₉×#3271	1	1	yes	characteristic
689	C₂	C₂₉×#3348	1	1	yes	characteristic
690	C₂	C₂₉×#3350	1	1	yes	characteristic

	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×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₄×C₂²⋊C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₉×#440	C₂	semidirect
3. C₂×C₂₉×#427	C₂	semidirect
5. C₂₉×#2362	C₂	semidirect
6. C₂₉×#1973	C₂	semidirect
7. C₂₉×#1944	C₂	semidirect
8. C₂₉×#1927	C₂	semidirect
9. C₂₉×#1926	C₂	semidirect
11. C₂₉×#1873	C₂	semidirect
12. C₂₉×#1865	C₂	semidirect
13. C₂₉×#1864	C₂	semidirect
14. C₂₉×#1776	C₂	semidirect
15. C₂₉×#1752	C₂	semidirect
24. C₂₉×#465	C₄	semidirect
72. C₂²×C₈×C₂₉	C₂×C₄	semidirect
78. C₂₉×C₂²⋊Q₈	C₂×C₄	semidirect
116. C₂₉×#107	D₄	semidirect
119. C₂₉×#106	C₂×C₄	semidirect
122. C₂₉×#103	C₂×C₄	semidirect
224. #23033	C₂₉	direct (N × H)
301. C₂×#440	C₂×C₂₉	semidirect
302. C₂×#427	C₂×C₂₉	semidirect
304. #2362	C₂×C₂₉	semidirect
305. #1973	C₂×C₂₉	semidirect
306. #1944	C₂×C₂₉	semidirect
307. #1927	C₂×C₂₉	semidirect
308. #1926	C₂×C₂₉	semidirect
310. #1873	C₂×C₂₉	semidirect
311. #1865	C₂×C₂₉	semidirect
312. #1864	C₂×C₂₉	semidirect
313. #1776	C₂×C₂₉	semidirect
314. #1752	C₂×C₂₉	semidirect
360. #465	C₄×C₂₉	semidirect
417. C₂²×C₈	C₂×C₄×C₂₉	semidirect
423. C₂²⋊Q₈	C₂×C₄×C₂₉	semidirect
461. #107	D₄×C₂₉	semidirect
464. #106	C₂×C₄×C₂₉	semidirect
467. #103	C₂×C₄×C₂₉	semidirect
482. C₂₉	#23033	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×#465	2
C₂×C₂₉×#440	2
C₂×C₂₉×#427	2
C₂₉×#2363	2
C₂₉×#2362	2
C₂₉×#1973	2
C₂₉×#1944	2
C₂₉×#1927	2
C₂₉×#1926	2
C₂₉×#1875	2
C₂₉×#1873	2
C₂₉×#1865	2
C₂₉×#1864	2
C₂₉×#1776	2
C₂₉×#1752	2
#23033	29

Subgroups — C29×#23033 #20317933

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#23033 #20317933