Subgroups — C₂₉×#24931 #20319831

Order 7424.

870 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3098	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3013	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2951	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2898	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2095	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2078	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2052	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2039	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1930	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1929	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1882	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1876	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1859	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1816	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1793	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×#137	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
20	C₂₉×#537	C₂²	1	1	yes	characteristic
21	C₂₉×#520	C₂²	1	1	yes	characteristic
22	C₂₉×#520	C₂²	1	1	yes	characteristic
23	C₂₉×#485	—	2	1	no	—
24	C₂₉×#484	—	2	1	no	—
25	C₂₉×#482	—	2	1	no	—
26	C₂₉×#480	—	2	1	no	—
27	C₂₉×#452	—	2	1	no	—
28	C₂₉×#451	—	2	1	no	—
29	C₂₉×#449	—	2	1	no	—
30	C₂₉×#448	—	2	1	no	—
31	C₂₉×#440	—	2	1	no	—
32	C₂₉×#440	—	2	1	no	—
33	C₄×Q₁₆×C₂₉	—	2	1	no	—
34	C₄×D₈×C₂₉	—	2	1	no	—
35	C₂×C₂₉×#108	C₂²	1	1	yes	characteristic
36	C₂₉×#428	C₂²	1	1	yes	characteristic
37	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×#104	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×#104	C₂²	1	1	yes	characteristic
41	C₂×C₂₉×#104	C₂²	1	1	yes	characteristic
42	C₂₉×#419	—	2	1	no	—
43	C₂₉×#419	C₂²	1	1	yes	characteristic
44	C₂₉×#417	—	2	1	no	—
45	C₂₉×#417	C₂²	1	1	yes	characteristic
46	C₂₉×#417	C₂²	1	1	yes	characteristic
47	C₂₉×#417	C₂²	1	1	yes	characteristic
48	C₂₉×#417	C₂²	1	1	yes	characteristic
49	C₂₉×#417	C₂²	1	1	yes	characteristic
50	C₂₉×#416	—	2	1	no	—
51	C₂₉×#416	C₂²	1	1	yes	characteristic
52	C₂×C₂₉×#103	—	2	1	no	—
53	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
54	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
55	C₂×C₂₉×#101	C₂²	1	1	yes	characteristic
56	C₂₉×#408	C₂²	1	1	yes	characteristic
57	C₂₉×#408	C₂²	1	1	yes	characteristic
58	C₂₉×#405	C₂²	1	1	yes	characteristic
59	C₂₉×#391	C₂²	1	1	yes	characteristic
60	C₂₉×#384	C₂²	1	1	yes	characteristic
61	C₂₉×#343	C₂²	1	1	yes	characteristic
62	C₂₉×#343	C₂²	1	1	yes	characteristic
63	C₂₉×#343	C₂²	1	1	yes	characteristic
64	C₂₉×#341	C₂²	1	1	yes	characteristic
65	C₂₉×#339	C₂²	1	1	yes	characteristic
66	C₂₉×#336	C₂²	1	1	yes	characteristic
67	C₂₉×2₋¹⁺⁴	—	2	2	no	—
68	C₂₉×2₋¹⁺⁴	—	2	2	no	—
69	C₂₉×2₋¹⁺⁴	—	2	2	no	—
70	C₂₉×2₋¹⁺⁴	—	4	1	no	—
71	C₂×#41×C₂₉	—	2	1	no	—
72	C₂×#41×C₂₉	—	2	1	no	—
73	C₂×#41×C₂₉	—	4	1	no	—
74	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
75	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
76	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
77	C₂²×Q₈×C₂₉	—	2	1	no	—
78	C₂²×Q₈×C₂₉	—	2	1	no	—
79	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
80	C₂₉×#137	—	2	2	no	—
81	C₂₉×#137	—	4	1	no	—
82	C₂₉×#135	—	2	2	no	—
83	C₂₉×#135	—	2	2	no	—
84	C₂×Q₁₆×C₂₉	—	2	1	no	—
85	C₂×Q₁₆×C₂₉	D₄	1	1	yes	characteristic
86	C₂×SD₁₆×C₂₉	—	2	1	no	—
87	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
88	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
89	C₂×D₈×C₂₉	D₄	1	1	yes	characteristic
90	C₂₉×#131	—	2	2	no	—
91	C₂₉×#131	—	4	1	no	—
92	C₂×M₁₆×C₂₉	—	2	1	no	—
93	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
94	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
95	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
96	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₂₉	—	2	1	no	—
98	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
100	C₂₉×C₂²⋊Q₈	—	2	1	no	—
101	C₂₉×C₂²⋊Q₈	—	2	1	no	—
102	C₂₉×#121	—	2	1	no	—
103	C₂₉×#121	—	2	1	no	—
104	C₂₉×#121	—	4	1	no	—
105	C₄×Q₈×C₂₉	—	2	1	no	—
106	C₄×Q₈×C₂₉	—	2	1	no	—
107	C₄×D₄×C₂₉	—	2	1	no	—
108	C₄×D₄×C₂₉	—	2	1	no	—
109	C₄×D₄×C₂₉	—	4	1	no	—
110	C₄×D₄×C₂₉	—	4	1	no	—
111	C₂₉×#117	—	2	1	no	—
112	C₂₉×#117	—	2	1	no	—
113	C₂₉×#117	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
115	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
116	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
117	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
121	C₂₉×#108	—	4	1	no	—
122	C₂₉×#107	—	2	1	no	—
123	C₂₉×#107	—	2	1	no	—
124	C₂₉×#107	—	2	1	no	—
125	C₂₉×#107	—	2	1	no	—
126	C₂₉×#107	—	2	1	no	—
127	C₂₉×#106	—	2	1	no	—
128	C₂₉×#104	—	2	2	no	—
129	C₂₉×#104	—	4	1	no	—
130	C₂₉×#104	—	4	1	no	—
131	C₂₉×#103	—	2	1	no	—
132	C₂₉×#103	—	2	1	no	—
133	C₂₉×#103	—	2	1	no	—
134	C₂₉×#103	—	2	1	no	—
135	C₂₉×#103	—	2	1	no	—
136	C₂₉×#103	—	2	1	no	—
137	C₂₉×#103	—	2	1	no	—
138	C₂₉×#103	—	2	1	no	—
139	C₂₉×#103	—	2	1	no	—
140	C₂₉×#103	—	2	1	no	—
141	C₂₉×#103	—	2	1	no	—
142	C₂₉×#103	D₄	1	1	yes	characteristic
143	C₂₉×#103	D₄	1	1	yes	characteristic
144	C₂₉×#102	—	2	1	no	—
145	C₂₉×#102	—	2	1	no	—
146	C₂₉×#102	—	2	1	no	—
147	C₂₉×#102	—	2	1	no	—
148	C₂₉×#102	—	2	1	no	—
149	C₂₉×#102	D₄	1	1	yes	characteristic
150	C₂₉×#102	D₄	1	1	yes	characteristic
151	C₂₉×#101	—	2	2	no	—
152	C₂₉×C₂²⋊C₈	—	2	1	no	—
153	C₂₉×C₂²⋊C₈	—	2	1	no	—
154	C₂₉×C₂²⋊C₈	—	2	1	no	—
155	C₂₉×C₂²⋊C₈	—	2	1	no	—
156	C₂₉×#97	—	2	1	no	—
157	C₄×C₈×C₂₉	—	2	1	no	—
158	C₂₉×#95	—	4	1	no	—
159	#41×C₂₉	—	2	1	no	—
160	#41×C₂₉	—	2	1	no	—
161	#41×C₂₉	—	2	4	no	—
162	#41×C₂₉	—	2	1	no	—
163	#41×C₂₉	—	2	1	no	—
164	#41×C₂₉	—	2	1	no	—
165	#41×C₂₉	—	2	1	no	—
166	#41×C₂₉	—	2	1	no	—
167	#41×C₂₉	—	2	1	no	—
168	#41×C₂₉	—	2	1	no	—
169	#41×C₂₉	—	2	1	no	—
170	#41×C₂₉	—	4	2	no	—
171	#41×C₂₉	—	4	4	no	—
172	#41×C₂₉	—	4	2	no	—
173	#41×C₂₉	—	4	4	no	—
174	#41×C₂₉	—	4	2	no	—
175	#41×C₂₉	#41	1	2	yes	—
176	#41×C₂₉	#41	1	2	yes	—
177	C₂×Q₈×C₂₉	—	2	1	no	—
178	C₂×Q₈×C₂₉	—	2	4	no	—
179	C₂×Q₈×C₂₉	—	2	1	no	—
180	C₂×Q₈×C₂₉	—	2	1	no	—
181	C₂×Q₈×C₂₉	—	2	1	no	—
182	C₂×Q₈×C₂₉	—	2	1	no	—
183	C₂×Q₈×C₂₉	—	4	1	no	—
184	C₂×Q₈×C₂₉	—	4	2	no	—
185	C₂×Q₈×C₂₉	—	4	2	no	—
186	C₂×Q₈×C₂₉	—	4	2	no	—
187	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
188	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
189	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
190	C₂×Q₈×C₂₉	#41	1	2	yes	—
191	C₂×D₄×C₂₉	—	2	1	no	—
192	C₂×D₄×C₂₉	—	2	1	no	—
193	C₂×D₄×C₂₉	—	2	1	no	—
194	C₂×D₄×C₂₉	—	4	1	no	—
195	C₂×D₄×C₂₉	—	4	1	no	—
196	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
197	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
198	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₂₉	—	2	1	no	—
200	C₂²×C₄×C₂₉	—	2	1	no	—
201	C₂²×C₄×C₂₉	—	2	1	no	—
202	C₂²×C₄×C₂₉	—	2	1	no	—
203	C₂²×C₄×C₂₉	—	2	1	no	—
204	C₂²×C₄×C₂₉	—	2	1	no	—
205	C₂²×C₄×C₂₉	—	2	1	no	—
206	C₂²×C₄×C₂₉	—	2	1	no	—
207	C₂²×C₄×C₂₉	—	4	1	no	—
208	C₂²×C₄×C₂₉	—	4	1	no	—
209	C₂²×C₄×C₂₉	—	4	1	no	—
210	C₂²×C₄×C₂₉	—	4	1	no	—
211	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
212	Q₁₆×C₂₉	—	2	2	no	—
213	Q₁₆×C₂₉	—	4	2	no	—
214	SD₁₆×C₂₉	—	2	2	no	—
215	SD₁₆×C₂₉	—	2	2	no	—
216	SD₁₆×C₂₉	—	4	2	no	—
217	D₈×C₂₉	—	2	2	no	—
218	M₁₆×C₂₉	—	2	1	no	—
219	M₁₆×C₂₉	—	2	1	no	—
220	M₁₆×C₂₉	—	2	1	no	—
221	M₁₆×C₂₉	—	2	1	no	—
222	M₁₆×C₂₉	—	2	1	no	—
223	M₁₆×C₂₉	—	2	1	no	—
224	M₁₆×C₂₉	—	2	1	no	—
225	M₁₆×C₂₉	—	2	1	no	—
226	M₁₆×C₂₉	—	4	2	no	—
227	C₂×C₈×C₂₉	—	2	1	no	—
228	C₂×C₈×C₂₉	—	2	1	no	—
229	C₂×C₈×C₂₉	—	2	1	no	—
230	C₂×C₈×C₂₉	—	2	1	no	—
231	C₂×C₈×C₂₉	—	2	1	no	—
232	C₂×C₈×C₂₉	—	2	1	no	—
233	C₂×C₈×C₂₉	—	2	1	no	—
234	C₂×C₈×C₂₉	—	2	1	no	—
235	C₂×C₈×C₂₉	—	4	2	no	—
236	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
237	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
238	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
239	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
240	C₄⋊C₄×C₂₉	—	2	1	no	—
241	C₄⋊C₄×C₂₉	—	2	1	no	—
242	C₄⋊C₄×C₂₉	—	2	1	no	—
243	C₄⋊C₄×C₂₉	—	2	1	no	—
244	C₄⋊C₄×C₂₉	—	2	1	no	—
245	C₄⋊C₄×C₂₉	—	2	1	no	—
246	C₄⋊C₄×C₂₉	—	4	1	no	—
247	C₄⋊C₄×C₂₉	—	4	1	no	—
248	C₄⋊C₄×C₂₉	—	4	1	no	—
249	C₄⋊C₄×C₂₉	—	8	2	no	—
250	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
251	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
252	C₂²⋊C₄×C₂₉	—	2	1	no	—
253	C₂²⋊C₄×C₂₉	—	4	1	no	—
254	C₂²⋊C₄×C₂₉	—	4	1	no	—
255	C₂²⋊C₄×C₂₉	—	4	1	no	—
256	C₂²⋊C₄×C₂₉	—	4	1	no	—
257	C₄²×C₂₉	—	2	1	no	—
258	C₄²×C₂₉	—	2	1	no	—
259	C₄²×C₂₉	—	2	1	no	—
260	C₄²×C₂₉	—	4	1	no	—
261	C₄²×C₂₉	—	4	1	no	—
262	#24931	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂³×C₂₉	—	2	1	no	—
264	C₂³×C₂₉	—	2	1	no	—
265	C₂³×C₂₉	—	2	1	no	—
266	C₂³×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
267	Q₈×C₂₉	—	2	1	no	—
268	Q₈×C₂₉	—	2	1	no	—
269	Q₈×C₂₉	—	2	1	no	—
270	Q₈×C₂₉	—	2	2	no	—
271	Q₈×C₂₉	—	2	2	no	—
272	Q₈×C₂₉	—	2	1	no	—
273	Q₈×C₂₉	—	2	1	no	—
274	Q₈×C₂₉	—	4	4	no	—
275	Q₈×C₂₉	—	4	1	no	—
276	Q₈×C₂₉	—	4	1	no	—
277	Q₈×C₂₉	#123	1	2	yes	—
278	D₄×C₂₉	—	2	2	no	—
279	D₄×C₂₉	—	2	2	no	—
280	D₄×C₂₉	—	2	1	no	—
281	D₄×C₂₉	—	2	1	no	—
282	D₄×C₂₉	—	2	1	no	—
283	D₄×C₂₉	—	2	1	no	—
284	D₄×C₂₉	—	2	1	no	—
285	D₄×C₂₉	—	4	4	no	—
286	D₄×C₂₉	—	4	1	no	—
287	D₄×C₂₉	—	4	1	no	—
288	D₄×C₂₉	—	4	1	no	—
289	D₄×C₂₉	—	4	1	no	—
290	D₄×C₂₉	—	16	1	no	—
291	D₄×C₂₉	#123	1	2	yes	—
292	C₂×C₄×C₂₉	—	2	1	no	—
293	C₂×C₄×C₂₉	—	2	2	no	—
294	C₂×C₄×C₂₉	—	2	2	no	—
295	C₂×C₄×C₂₉	—	2	2	no	—
296	C₂×C₄×C₂₉	—	2	1	no	—
297	C₂×C₄×C₂₉	—	2	1	no	—
298	C₂×C₄×C₂₉	—	2	1	no	—
299	C₂×C₄×C₂₉	—	2	1	no	—
300	C₂×C₄×C₂₉	—	2	2	no	—
301	C₂×C₄×C₂₉	—	4	4	no	—
302	C₂×C₄×C₂₉	—	4	1	no	—
303	C₂×C₄×C₂₉	—	4	4	no	—
304	C₂×C₄×C₂₉	—	4	1	no	—
305	C₂×C₄×C₂₉	—	4	1	no	—
306	C₂×C₄×C₂₉	—	4	1	no	—
307	C₂×C₄×C₂₉	—	4	1	no	—
308	C₂×C₄×C₂₉	—	4	1	no	—
309	C₂×C₄×C₂₉	—	4	1	no	—
310	C₂×C₄×C₂₉	—	4	1	no	—
311	C₂×C₄×C₂₉	—	4	1	no	—
312	C₂×C₄×C₂₉	—	4	1	no	—
313	C₂×C₄×C₂₉	—	4	1	no	—
314	C₂×C₄×C₂₉	—	8	1	no	—
315	C₂×C₄×C₂₉	—	8	1	no	—
316	C₂×C₄×C₂₉	—	8	1	no	—
317	C₂×C₄×C₂₉	—	16	1	no	—
318	C₂×C₄×C₂₉	—	16	1	no	—
319	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
323	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
324	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
325	C₈×C₂₉	—	2	1	no	—
326	C₈×C₂₉	—	2	1	no	—
327	C₈×C₂₉	—	2	1	no	—
328	C₈×C₂₉	—	2	1	no	—
329	C₈×C₂₉	—	4	1	no	—
330	C₈×C₂₉	—	4	1	no	—
331	C₈×C₂₉	—	4	1	no	—
332	C₈×C₂₉	—	4	1	no	—
333	#3098	C₂×C₂₉	1	1	yes	characteristic, complemented
334	#3013	C₂×C₂₉	1	1	yes	characteristic
335	#2951	C₂×C₂₉	1	1	yes	characteristic, complemented
336	#2898	C₂×C₂₉	1	1	yes	characteristic, complemented
337	#2095	C₂×C₂₉	1	1	yes	characteristic, complemented
338	#2078	C₂×C₂₉	1	1	yes	characteristic, complemented
339	#2052	C₂×C₂₉	1	1	yes	characteristic, complemented
340	#2039	C₂×C₂₉	1	1	yes	characteristic, complemented
341	#1930	C₂×C₂₉	1	1	yes	characteristic, complemented
342	#1929	C₂×C₂₉	1	1	yes	characteristic, complemented
343	#1882	C₂×C₂₉	1	1	yes	characteristic, complemented
344	#1876	C₂×C₂₉	1	1	yes	characteristic, complemented
345	#1859	C₂×C₂₉	1	1	yes	characteristic, complemented
346	#1816	C₂×C₂₉	1	1	yes	characteristic, complemented
347	#1793	C₂×C₂₉	1	1	yes	characteristic, complemented
348	C₂²×C₂₉	—	2	1	no	—
349	C₂²×C₂₉	—	2	1	no	—
350	C₂²×C₂₉	—	2	2	no	—
351	C₂²×C₂₉	—	4	1	no	—
352	C₂²×C₂₉	—	4	1	no	—
353	C₂²×C₂₉	—	4	1	no	—
354	C₂²×C₂₉	—	4	1	no	—
355	C₂²×C₂₉	—	4	1	no	—
356	C₂²×C₂₉	—	4	1	no	—
357	C₂²×C₂₉	—	4	1	no	—
358	C₂²×C₂₉	—	4	1	no	—
359	C₂²×C₂₉	#538	1	1	yes	characteristic
360	C₂²×C₂₉	D₄²	1	1	yes	characteristic
361	C₂²×C₂₉	#551	1	1	yes	characteristic
362	C₄×C₂₉	—	2	2	no	—
363	C₄×C₂₉	—	4	2	no	—
364	C₄×C₂₉	—	4	1	no	—
365	C₄×C₂₉	—	4	2	no	—
366	C₄×C₂₉	—	4	1	no	—
367	C₄×C₂₉	—	4	1	no	—
368	C₄×C₂₉	—	4	1	no	—
369	C₄×C₂₉	—	8	1	no	—
370	C₄×C₂₉	—	8	1	no	—
371	C₄×C₂₉	—	8	1	no	—
372	C₄×C₂₉	C₂×#123	1	1	yes	characteristic
373	C₄×C₂₉	#525	1	1	yes	characteristic
374	C₄×C₂₉	#546	1	1	yes	characteristic
375	C₄×C₂₉	#546	1	1	yes	characteristic
376	C₂×2₋¹⁺⁴	C₂²×C₂₉	1	1	yes	characteristic
377	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic
378	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
379	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
380	#537	C₂²×C₂₉	1	1	yes	characteristic
381	#520	C₂²×C₂₉	1	1	yes	characteristic
382	#520	C₂²×C₂₉	1	1	yes	characteristic
383	#485	—	2	1	no	—
384	#484	—	2	1	no	—
385	#482	—	2	1	no	—
386	#480	—	2	1	no	—
387	#452	—	2	1	no	—
388	#451	—	2	1	no	—
389	#449	—	2	1	no	—
390	#448	—	2	1	no	—
391	#440	—	2	1	no	—
392	#440	—	2	1	no	—
393	C₄×Q₁₆	—	2	1	no	—
394	C₄×D₈	—	2	1	no	—
395	C₂×#108	C₂²×C₂₉	1	1	yes	characteristic
396	#428	C₂²×C₂₉	1	1	yes	characteristic
397	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
398	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
399	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
400	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
401	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
402	#419	—	2	1	no	—
403	#419	C₂²×C₂₉	1	1	yes	characteristic
404	#417	—	2	1	no	—
405	#417	C₂²×C₂₉	1	1	yes	characteristic
406	#417	C₂²×C₂₉	1	1	yes	characteristic
407	#417	C₂²×C₂₉	1	1	yes	characteristic
408	#417	C₂²×C₂₉	1	1	yes	characteristic
409	#417	C₂²×C₂₉	1	1	yes	characteristic
410	#416	—	2	1	no	—
411	#416	C₂²×C₂₉	1	1	yes	characteristic
412	C₂×#103	—	2	1	no	—
413	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
414	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
415	C₂×#101	C₂²×C₂₉	1	1	yes	characteristic
416	#408	C₂²×C₂₉	1	1	yes	characteristic
417	#408	C₂²×C₂₉	1	1	yes	characteristic
418	#405	C₂²×C₂₉	1	1	yes	characteristic
419	#391	C₂²×C₂₉	1	1	yes	characteristic
420	#384	C₂²×C₂₉	1	1	yes	characteristic
421	#343	C₂²×C₂₉	1	1	yes	characteristic
422	#343	C₂²×C₂₉	1	1	yes	characteristic
423	#343	C₂²×C₂₉	1	1	yes	characteristic
424	#341	C₂²×C₂₉	1	1	yes	characteristic
425	#339	C₂²×C₂₉	1	1	yes	characteristic
426	#336	C₂²×C₂₉	1	1	yes	characteristic
427	C₂×C₂₉	—	2	1	no	—
428	C₂×C₂₉	—	2	1	no	—
429	C₂×C₂₉	—	4	2	no	—
430	C₂×C₂₉	—	8	1	no	—
431	C₂×C₂₉	—	8	1	no	—
432	C₂×C₂₉	#2418	1	1	yes	characteristic
433	C₂×C₂₉	#3288	1	1	yes	characteristic
434	C₂×C₂₉	#3293	1	1	yes	characteristic
435	2₋¹⁺⁴	—	2	2	no	—
436	2₋¹⁺⁴	—	2	2	no	—
437	2₋¹⁺⁴	—	2	2	no	—
438	2₋¹⁺⁴	—	4	1	no	—
439	C₂×#41	—	2	1	no	—
440	C₂×#41	—	2	1	no	—
441	C₂×#41	—	4	1	no	—
442	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
443	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
444	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
445	C₂²×Q₈	—	2	1	no	—
446	C₂²×Q₈	—	2	1	no	—
447	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
448	#137	—	2	2	no	—
449	#137	—	4	1	no	—
450	#135	—	2	2	no	—
451	#135	—	2	2	no	—
452	C₂×Q₁₆	—	2	1	no	—
453	C₂×Q₁₆	D₄×C₂₉	1	1	yes	characteristic
454	C₂×SD₁₆	—	2	1	no	—
455	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
456	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
457	C₂×D₈	D₄×C₂₉	1	1	yes	characteristic
458	#131	—	2	2	no	—
459	#131	—	4	1	no	—
460	C₂×M₁₆	—	2	1	no	—
461	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
462	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
463	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
464	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
465	C₂²×C₈	—	2	1	no	—
466	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
467	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
468	C₂²⋊Q₈	—	2	1	no	—
469	C₂²⋊Q₈	—	2	1	no	—
470	#121	—	2	1	no	—
471	#121	—	2	1	no	—
472	#121	—	4	1	no	—
473	C₄×Q₈	—	2	1	no	—
474	C₄×Q₈	—	2	1	no	—
475	C₄×D₄	—	2	1	no	—
476	C₄×D₄	—	2	1	no	—
477	C₄×D₄	—	4	1	no	—
478	C₄×D₄	—	4	1	no	—
479	#117	—	2	1	no	—
480	#117	—	2	1	no	—
481	#117	C₂³×C₂₉	1	1	yes	characteristic
482	C₂×C₄⋊C₄	—	2	1	no	—
483	C₂×C₄⋊C₄	—	2	1	no	—
484	C₂×C₄⋊C₄	—	4	1	no	—
485	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
488	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
489	#108	—	4	1	no	—
490	#107	—	2	1	no	—
491	#107	—	2	1	no	—
492	#107	—	2	1	no	—
493	#107	—	2	1	no	—
494	#107	—	2	1	no	—
495	#106	—	2	1	no	—
496	#104	—	2	2	no	—
497	#104	—	4	1	no	—
498	#104	—	4	1	no	—
499	#103	—	2	1	no	—
500	#103	—	2	1	no	—
501	#103	—	2	1	no	—
502	#103	—	2	1	no	—
503	#103	—	2	1	no	—
504	#103	—	2	1	no	—
505	#103	—	2	1	no	—
506	#103	—	2	1	no	—
507	#103	—	2	1	no	—
508	#103	—	2	1	no	—
509	#103	—	2	1	no	—
510	#103	D₄×C₂₉	1	1	yes	characteristic
511	#103	D₄×C₂₉	1	1	yes	characteristic
512	#102	—	2	1	no	—
513	#102	—	2	1	no	—
514	#102	—	2	1	no	—
515	#102	—	2	1	no	—
516	#102	—	2	1	no	—
517	#102	D₄×C₂₉	1	1	yes	characteristic
518	#102	D₄×C₂₉	1	1	yes	characteristic
519	#101	—	2	2	no	—
520	C₂²⋊C₈	—	2	1	no	—
521	C₂²⋊C₈	—	2	1	no	—
522	C₂²⋊C₈	—	2	1	no	—
523	C₂²⋊C₈	—	2	1	no	—
524	#97	—	2	1	no	—
525	C₄×C₈	—	2	1	no	—
526	#95	—	4	1	no	—
527	C₂₉	#24931	1	1	yes	characteristic, direct product factor, Sylow
528	#41	—	2	1	no	—
529	#41	—	2	1	no	—
530	#41	—	2	4	no	—
531	#41	—	2	1	no	—
532	#41	—	2	1	no	—
533	#41	—	2	1	no	—
534	#41	—	2	1	no	—
535	#41	—	2	1	no	—
536	#41	—	2	1	no	—
537	#41	—	2	1	no	—
538	#41	—	2	1	no	—
539	#41	—	4	2	no	—
540	#41	—	4	4	no	—
541	#41	—	4	2	no	—
542	#41	—	4	4	no	—
543	#41	—	4	2	no	—
544	#41	#41×C₂₉	1	2	yes	—
545	#41	#41×C₂₉	1	2	yes	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	—	2	4	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	4	1	no	—
553	C₂×Q₈	—	4	2	no	—
554	C₂×Q₈	—	4	2	no	—
555	C₂×Q₈	—	4	2	no	—
556	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
557	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
558	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
559	C₂×Q₈	#41×C₂₉	1	2	yes	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	4	1	no	—
564	C₂×D₄	—	4	1	no	—
565	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
566	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
567	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	4	1	no	—
577	C₂²×C₄	—	4	1	no	—
578	C₂²×C₄	—	4	1	no	—
579	C₂²×C₄	—	4	1	no	—
580	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
581	Q₁₆	—	2	2	no	—
582	Q₁₆	—	4	2	no	—
583	SD₁₆	—	2	2	no	—
584	SD₁₆	—	2	2	no	—
585	SD₁₆	—	4	2	no	—
586	D₈	—	2	2	no	—
587	M₁₆	—	2	1	no	—
588	M₁₆	—	2	1	no	—
589	M₁₆	—	2	1	no	—
590	M₁₆	—	2	1	no	—
591	M₁₆	—	2	1	no	—
592	M₁₆	—	2	1	no	—
593	M₁₆	—	2	1	no	—
594	M₁₆	—	2	1	no	—
595	M₁₆	—	4	2	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	2	1	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	4	2	no	—
605	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
606	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
607	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
608	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	4	1	no	—
616	C₄⋊C₄	—	4	1	no	—
617	C₄⋊C₄	—	4	1	no	—
618	C₄⋊C₄	—	8	2	no	—
619	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
620	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
621	C₂²⋊C₄	—	2	1	no	—
622	C₂²⋊C₄	—	4	1	no	—
623	C₂²⋊C₄	—	4	1	no	—
624	C₂²⋊C₄	—	4	1	no	—
625	C₂²⋊C₄	—	4	1	no	—
626	C₄²	—	2	1	no	—
627	C₄²	—	2	1	no	—
628	C₄²	—	2	1	no	—
629	C₄²	—	4	1	no	—
630	C₄²	—	4	1	no	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
635	Q₈	—	2	1	no	—
636	Q₈	—	2	1	no	—
637	Q₈	—	2	1	no	—
638	Q₈	—	2	2	no	—
639	Q₈	—	2	2	no	—
640	Q₈	—	2	1	no	—
641	Q₈	—	2	1	no	—
642	Q₈	—	4	4	no	—
643	Q₈	—	4	1	no	—
644	Q₈	—	4	1	no	—
645	Q₈	C₂₉×#123	1	2	yes	—
646	D₄	—	2	2	no	—
647	D₄	—	2	2	no	—
648	D₄	—	2	1	no	—
649	D₄	—	2	1	no	—
650	D₄	—	2	1	no	—
651	D₄	—	2	1	no	—
652	D₄	—	2	1	no	—
653	D₄	—	4	4	no	—
654	D₄	—	4	1	no	—
655	D₄	—	4	1	no	—
656	D₄	—	4	1	no	—
657	D₄	—	4	1	no	—
658	D₄	—	16	1	no	—
659	D₄	C₂₉×#123	1	2	yes	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	4	4	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	4	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	8	1	no	—
683	C₂×C₄	—	8	1	no	—
684	C₂×C₄	—	8	1	no	—
685	C₂×C₄	—	16	1	no	—
686	C₂×C₄	—	16	1	no	—
687	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
688	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
689	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
690	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
691	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
692	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
693	C₈	—	2	1	no	—
694	C₈	—	2	1	no	—
695	C₈	—	2	1	no	—
696	C₈	—	2	1	no	—
697	C₈	—	4	1	no	—
698	C₈	—	4	1	no	—
699	C₈	—	4	1	no	—
700	C₈	—	4	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	C₂₉×#538	1	1	yes	characteristic
713	C₂²	D₄²×C₂₉	1	1	yes	characteristic
714	C₂²	C₂₉×#551	1	1	yes	characteristic
715	C₄	—	2	2	no	—
716	C₄	—	4	2	no	—
717	C₄	—	4	1	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	1	no	—
722	C₄	—	8	1	no	—
723	C₄	—	8	1	no	—
724	C₄	—	8	1	no	—
725	C₄	C₂×C₂₉×#123	1	1	yes	characteristic
726	C₄	C₂₉×#525	1	1	yes	characteristic
727	C₄	C₂₉×#546	1	1	yes	characteristic
728	C₄	C₂₉×#546	1	1	yes	characteristic
729	C₂	—	2	1	no	—
730	C₂	—	2	1	no	—
731	C₂	—	4	2	no	—
732	C₂	—	8	1	no	—
733	C₂	—	8	1	no	—
734	C₂	C₂₉×#2418	1	1	yes	characteristic
735	C₂	C₂₉×#3288	1	1	yes	characteristic
736	C₂	C₂₉×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂₉×#3013	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3098	C₂	semidirect
3. C₂₉×#2951	C₂	semidirect
4. C₂₉×#2898	C₂	semidirect
5. C₂₉×#2095	C₂	semidirect
6. C₂₉×#2078	C₂	semidirect
7. C₂₉×#2052	C₂	semidirect
8. C₂₉×#2039	C₂	semidirect
9. C₂₉×#1930	C₂	semidirect
10. C₂₉×#1929	C₂	semidirect
11. C₂₉×#1882	C₂	semidirect
12. C₂₉×#1876	C₂	semidirect
13. C₂₉×#1859	C₂	semidirect
14. C₂₉×#1816	C₂	semidirect
15. C₂₉×#1793	C₂	semidirect
262. #24931	C₂₉	direct (N × H)
333. #3098	C₂×C₂₉	semidirect
335. #2951	C₂×C₂₉	semidirect
336. #2898	C₂×C₂₉	semidirect
337. #2095	C₂×C₂₉	semidirect
338. #2078	C₂×C₂₉	semidirect
339. #2052	C₂×C₂₉	semidirect
340. #2039	C₂×C₂₉	semidirect
341. #1930	C₂×C₂₉	semidirect
342. #1929	C₂×C₂₉	semidirect
343. #1882	C₂×C₂₉	semidirect
344. #1876	C₂×C₂₉	semidirect
345. #1859	C₂×C₂₉	semidirect
346. #1816	C₂×C₂₉	semidirect
347. #1793	C₂×C₂₉	semidirect
527. C₂₉	#24931	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₉×#3098	2
C₂₉×#3013	2
C₂₉×#2951	2
C₂₉×#2898	2
C₂₉×#2095	2
C₂₉×#2078	2
C₂₉×#2052	2
C₂₉×#2039	2
C₂₉×#1930	2
C₂₉×#1929	2
C₂₉×#1882	2
C₂₉×#1876	2
C₂₉×#1859	2
C₂₉×#1816	2
C₂₉×#1793	2
#24931	29

Subgroups — C29×#24931 #20319831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#24931 #20319831