Subgroups — C₂₉×#60388 #20355288

Order 7424.

4874 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×H(7,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3585	C₂	1	2	yes	maximal, complemented
3	C₂₉×#3498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3021	C₂	1	6	yes	maximal, complemented
5	C₂₉×#3019	C₂	1	6	yes	maximal, complemented
6	C₂₉×#3018	C₂	1	6	yes	maximal, complemented
7	C₂×C₂₉×#453	C₂	1	6	yes	maximal, complemented
8	C₂₉×#2901	C₂	1	2	yes	maximal, complemented
9	C₂₉×#2888	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#585	—	2	8	no	—
11	C₂₉×#585	—	2	2	no	—
12	C₂₉×#585	C₂²	1	2	yes	—
13	C₂₉×#585	C₂²	1	6	yes	complemented
14	C₂×C₂₉×H(5,𝔽₂)	—	2	8	no	—
15	C₂×C₂₉×H(5,𝔽₂)	—	2	6	no	—
16	C₂×C₂₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×H(5,𝔽₂)	C₂²	1	6	yes	complemented
18	C₂×C₂₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
19	C₂₉×#577	—	2	8	no	—
20	C₂₉×#576	—	2	8	no	—
21	C₂₉×#575	C₂²	1	12	yes	complemented
22	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	12	yes	complemented
23	C₂₉×#568	C₂²	1	2	yes	complemented
24	C₂₉×#550	—	2	2	no	—
25	D₄²×C₂₉	—	2	6	no	—
26	C₂₉×#535	C₂²	1	3	yes	complemented
27	C₂₉×#535	C₂²	1	3	yes	complemented
28	C₂₉×#532	C₂²	1	3	yes	complemented
29	C₂×C₂₉×#127	C₂²	1	3	yes	complemented
30	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic, complemented
31	C₂₉×#456	C₂²	1	4	yes	complemented
32	C₂₉×#455	C₂²	1	12	yes	complemented
33	C₂₉×#454	C₂²	1	12	yes	complemented
34	C₂₉×#453	C₂²	1	12	yes	complemented
35	C₂₉×#453	C₂²	1	24	yes	complemented
36	C₂₉×#421	C₂²	1	12	yes	complemented
37	C₂×C₂₉×#104	C₂²	1	12	yes	complemented
38	C₂₉×#413	C₂²	1	6	yes	complemented
39	C₂×C₂₉×#100	C₂²	1	6	yes	complemented
40	C₂₉×2₋¹⁺⁴	—	2	8	no	—
41	C₂₉×2₋¹⁺⁴	—	2	2	no	—
42	C₂₉×2₋¹⁺⁴	—	2	12	no	—
43	C₂₉×2₋¹⁺⁴	D₄	1	8	yes	complemented
44	C₂₉×2₋¹⁺⁴	C₂³	1	4	yes	—
45	C₂₉×H(5,𝔽₂)	—	2	8	no	—
46	C₂₉×H(5,𝔽₂)	—	2	48	no	—
47	C₂₉×H(5,𝔽₂)	—	2	8	no	—
48	C₂₉×H(5,𝔽₂)	—	2	24	no	—
49	C₂₉×H(5,𝔽₂)	—	2	6	no	—
50	C₂₉×H(5,𝔽₂)	—	2	12	no	—
51	C₂₉×H(5,𝔽₂)	—	2	12	no	—
52	C₂₉×H(5,𝔽₂)	—	2	12	no	—
53	C₂₉×H(5,𝔽₂)	—	2	8	no	—
54	C₂₉×H(5,𝔽₂)	D₄	1	8	yes	complemented
55	C₂₉×H(5,𝔽₂)	C₂³	1	12	yes	—
56	C₂×#41×C₂₉	—	2	16	no	—
57	C₂×#41×C₂₉	—	2	24	no	—
58	C₂×#41×C₂₉	—	2	8	no	—
59	C₂×#41×C₂₉	—	2	24	no	—
60	C₂×#41×C₂₉	—	2	1	no	—
61	C₂×#41×C₂₉	—	2	12	no	—
62	C₂×#41×C₂₉	—	2	12	no	—
63	C₂×#41×C₂₉	D₄	1	2	yes	—
64	C₂×#41×C₂₉	C₂³	1	12	yes	—
65	C₂×#41×C₂₉	C₂³	1	3	yes	—
66	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
67	C₂×#41×C₂₉	C₂³	1	3	yes	complemented
68	C₂²×D₄×C₂₉	—	2	24	no	—
69	C₂²×D₄×C₂₉	—	2	12	no	—
70	C₂²×D₄×C₂₉	—	2	12	no	—
71	C₂²×D₄×C₂₉	—	2	6	no	—
72	C₂²×D₄×C₂₉	—	2	3	no	—
73	C₂²×D₄×C₂₉	D₄	1	6	yes	—
74	C₂²×D₄×C₂₉	C₂³	1	3	yes	—
75	C₂²×D₄×C₂₉	C₂³	1	3	yes	complemented
76	C₂₉×#137	—	2	12	no	—
77	C₂₉×#137	C₂³	1	8	yes	complemented
78	C₂₉×AGL(1,ℤ/8)	—	2	24	no	—
79	C₂₉×AGL(1,ℤ/8)	—	2	12	no	—
80	C₂₉×AGL(1,ℤ/8)	C₂³	1	24	yes	complemented
81	C₂₉×#135	—	2	24	no	—
82	C₂×SD₁₆×C₂₉	—	2	12	no	—
83	C₂×D₈×C₂₉	—	2	12	no	—
84	C₂₉×#131	—	2	8	no	—
85	C₂×M₁₆×C₂₉	C₂³	1	12	yes	complemented
86	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
87	C₂₉×#127	—	2	6	no	—
88	C₂₉×#127	C₂³	1	3	yes	complemented
89	C₂₉×#127	C₂³	1	6	yes	complemented
90	C₂₉×#124	C₂³	1	3	yes	complemented
91	C₂₉×#124	C₂³	1	3	yes	complemented
92	C₂₉×#121	—	2	6	no	—
93	C₂₉×#121	—	2	6	no	—
94	C₂₉×#121	—	2	6	no	—
95	C₂₉×#120	—	2	6	no	—
96	C₂₉×#120	—	2	6	no	—
97	C₄×Q₈×C₂₉	—	2	1	no	—
98	C₄×D₄×C₂₉	—	2	3	no	—
99	C₄×D₄×C₂₉	—	2	6	no	—
100	C₂₉×#117	C₂³	1	3	yes	complemented
101	C₂×C₄²×C₂₉	C₂³	1	3	yes	complemented
102	C₂₉×#104	C₂³	1	8	yes	complemented
103	C₂₉×#104	C₂³	1	24	yes	complemented
104	C₂₉×#101	C₂³	1	4	yes	complemented
105	C₂₉×#100	C₂³	1	12	yes	complemented
106	C₂⁴×C₂₉	—	2	12	no	—
107	C₂⁴×C₂₉	—	2	3	no	—
108	C₂⁴×C₂₉	C₂×D₄	1	6	yes	—
109	#41×C₂₉	—	2	48	no	—
110	#41×C₂₉	—	2	48	no	—
111	#41×C₂₉	—	2	24	no	—
112	#41×C₂₉	—	2	24	no	—
113	#41×C₂₉	—	2	8	no	—
114	#41×C₂₉	—	2	8	no	—
115	#41×C₂₉	—	2	24	no	—
116	#41×C₂₉	—	2	24	no	—
117	#41×C₂₉	—	2	8	no	—
118	#41×C₂₉	—	2	8	no	—
119	#41×C₂₉	—	2	12	no	—
120	#41×C₂₉	—	2	12	no	—
121	#41×C₂₉	—	2	12	no	—
122	#41×C₂₉	—	2	12	no	—
123	#41×C₂₉	—	4	4	no	—
124	#41×C₂₉	C₂×D₄	1	8	yes	—
125	#41×C₂₉	C₂×D₄	1	24	yes	complemented
126	#41×C₂₉	C₂⁴	1	8	yes	—
127	C₂×Q₈×C₂₉	—	2	12	no	—
128	C₂×Q₈×C₂₉	—	2	8	no	—
129	C₂×Q₈×C₂₉	—	2	8	no	—
130	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
131	C₂×Q₈×C₂₉	C₂×D₄	1	12	yes	complemented
132	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
133	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
134	C₂×D₄×C₂₉	—	2	48	no	—
135	C₂×D₄×C₂₉	—	2	48	no	—
136	C₂×D₄×C₂₉	—	2	24	no	—
137	C₂×D₄×C₂₉	—	2	48	no	—
138	C₂×D₄×C₂₉	—	2	12	no	—
139	C₂×D₄×C₂₉	—	2	24	no	—
140	C₂×D₄×C₂₉	—	2	12	no	—
141	C₂×D₄×C₂₉	—	2	24	no	—
142	C₂×D₄×C₂₉	—	2	24	no	—
143	C₂×D₄×C₂₉	—	2	24	no	—
144	C₂×D₄×C₂₉	—	2	6	no	—
145	C₂×D₄×C₂₉	—	2	3	no	—
146	C₂×D₄×C₂₉	—	2	12	no	—
147	C₂×D₄×C₂₉	—	2	12	no	—
148	C₂×D₄×C₂₉	—	2	12	no	—
149	C₂×D₄×C₂₉	—	2	3	no	—
150	C₂×D₄×C₂₉	—	4	12	no	—
151	C₂×D₄×C₂₉	—	8	12	no	—
152	C₂×D₄×C₂₉	C₂×D₄	1	6	yes	—
153	C₂×D₄×C₂₉	C₂×D₄	1	6	yes	—
154	C₂×D₄×C₂₉	C₂×D₄	1	3	yes	—
155	C₂×D₄×C₂₉	C₂×D₄	1	12	yes	complemented
156	C₂×D₄×C₂₉	C₂⁴	1	3	yes	—
157	C₂×D₄×C₂₉	C₂⁴	1	3	yes	—
158	C₂²×C₄×C₂₉	—	2	12	no	—
159	C₂²×C₄×C₂₉	—	2	24	no	—
160	C₂²×C₄×C₂₉	—	2	12	no	—
161	C₂²×C₄×C₂₉	—	2	3	no	—
162	C₂²×C₄×C₂₉	—	2	3	no	—
163	C₂²×C₄×C₂₉	C₂×D₄	1	6	yes	—
164	C₂²×C₄×C₂₉	C₂⁴	1	3	yes	—
165	Q₁₆×C₂₉	—	2	8	no	—
166	SD₁₆×C₂₉	—	2	24	no	—
167	SD₁₆×C₂₉	—	2	8	no	—
168	D₈×C₂₉	—	2	24	no	—
169	M₁₆×C₂₉	—	2	12	no	—
170	M₁₆×C₂₉	C₂⁴	1	8	yes	—
171	C₂×C₈×C₂₉	—	2	12	no	—
172	C₄⋊C₄×C₂₉	—	2	3	no	—
173	C₄⋊C₄×C₂₉	—	2	2	no	—
174	C₂²⋊C₄×C₂₉	—	2	3	no	—
175	C₂²⋊C₄×C₂₉	—	2	6	no	—
176	C₂²⋊C₄×C₂₉	—	2	6	no	—
177	C₄²×C₂₉	—	2	3	no	—
178	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
179	C₄²×C₂₉	C₂⁴	1	3	yes	—
180	#60388	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂³×C₂₉	—	2	24	no	—
182	C₂³×C₂₉	—	2	12	no	—
183	C₂³×C₂₉	—	2	12	no	—
184	C₂³×C₂₉	—	2	3	no	—
185	C₂³×C₂₉	—	4	6	no	—
186	C₂³×C₂₉	—	8	6	no	—
187	C₂³×C₂₉	—	8	6	no	—
188	C₂³×C₂₉	—	16	12	no	—
189	C₂³×C₂₉	C₂²×D₄	1	6	yes	—
190	C₂³×C₂₉	C₂²×D₄	1	3	yes	—
191	Q₈×C₂₉	—	2	8	no	—
192	Q₈×C₂₉	—	2	12	no	—
193	Q₈×C₂₉	—	2	2	no	—
194	Q₈×C₂₉	—	2	2	no	—
195	Q₈×C₂₉	#120	1	4	yes	—
196	Q₈×C₂₉	C₂²×D₄	1	8	yes	—
197	D₄×C₂₉	—	2	48	no	—
198	D₄×C₂₉	—	2	8	no	—
199	D₄×C₂₉	—	2	24	no	—
200	D₄×C₂₉	—	2	12	no	—
201	D₄×C₂₉	—	2	8	no	—
202	D₄×C₂₉	—	2	12	no	—
203	D₄×C₂₉	—	2	12	no	—
204	D₄×C₂₉	—	2	6	no	—
205	D₄×C₂₉	—	2	6	no	—
206	D₄×C₂₉	—	4	12	no	—
207	D₄×C₂₉	—	4	6	no	—
208	D₄×C₂₉	—	4	6	no	—
209	D₄×C₂₉	—	8	12	no	—
210	D₄×C₂₉	#120	1	12	yes	—
211	D₄×C₂₉	C₂²×D₄	1	8	yes	—
212	C₂×C₄×C₂₉	—	2	24	no	—
213	C₂×C₄×C₂₉	—	2	16	no	—
214	C₂×C₄×C₂₉	—	2	12	no	—
215	C₂×C₄×C₂₉	—	2	1	no	—
216	C₂×C₄×C₂₉	—	2	24	no	—
217	C₂×C₄×C₂₉	—	2	12	no	—
218	C₂×C₄×C₂₉	—	2	8	no	—
219	C₂×C₄×C₂₉	—	2	3	no	—
220	C₂×C₄×C₂₉	—	2	1	no	—
221	C₂×C₄×C₂₉	—	4	6	no	—
222	C₂×C₄×C₂₉	—	4	6	no	—
223	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₂₉	C₂²×D₄	1	3	yes	—
225	C₂×C₄×C₂₉	C₂²×D₄	1	12	yes	—
226	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
227	C₈×C₂₉	—	2	8	no	—
228	H(7,𝔽₂)	C₂×C₂₉	1	1	yes	characteristic, complemented
229	#3585	C₂×C₂₉	1	2	yes	complemented
230	#3498	C₂×C₂₉	1	1	yes	characteristic, complemented
231	#3021	C₂×C₂₉	1	6	yes	complemented
232	#3019	C₂×C₂₉	1	6	yes	complemented
233	#3018	C₂×C₂₉	1	6	yes	complemented
234	C₂×#453	C₂×C₂₉	1	6	yes	complemented
235	#2901	C₂×C₂₉	1	2	yes	complemented
236	#2888	C₂×C₂₉	1	1	yes	characteristic, complemented
237	C₂²×C₂₉	—	2	6	no	—
238	C₂²×C₂₉	—	2	8	no	—
239	C₂²×C₂₉	—	4	3	no	—
240	C₂²×C₂₉	—	4	6	no	—
241	C₂²×C₂₉	—	4	6	no	—
242	C₂²×C₂₉	—	4	3	no	—
243	C₂²×C₂₉	—	8	12	no	—
244	C₂²×C₂₉	—	8	12	no	—
245	C₂²×C₂₉	—	8	24	no	—
246	C₂²×C₂₉	—	16	6	no	—
247	C₂²×C₂₉	C₂×#120	1	6	yes	—
248	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
249	C₄×C₂₉	—	2	2	no	—
250	C₄×C₂₉	—	2	8	no	—
251	C₄×C₂₉	—	2	2	no	—
252	C₄×C₂₉	—	4	3	no	—
253	C₄×C₂₉	—	4	1	no	—
254	C₄×C₂₉	C₂×#120	1	6	yes	—
255	C₄×C₂₉	C₂³×D₄	1	2	yes	—
256	#585	—	2	8	no	—
257	#585	—	2	2	no	—
258	#585	C₂²×C₂₉	1	2	yes	—
259	#585	C₂²×C₂₉	1	6	yes	complemented
260	C₂×H(5,𝔽₂)	—	2	8	no	—
261	C₂×H(5,𝔽₂)	—	2	6	no	—
262	C₂×H(5,𝔽₂)	C₂²×C₂₉	1	1	yes	characteristic
263	C₂×H(5,𝔽₂)	C₂²×C₂₉	1	6	yes	complemented
264	C₂×H(5,𝔽₂)	C₂²×C₂₉	1	1	yes	characteristic, complemented
265	#577	—	2	8	no	—
266	#576	—	2	8	no	—
267	#575	C₂²×C₂₉	1	12	yes	complemented
268	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	12	yes	complemented
269	#568	C₂²×C₂₉	1	2	yes	complemented
270	#550	—	2	2	no	—
271	D₄²	—	2	6	no	—
272	#535	C₂²×C₂₉	1	3	yes	complemented
273	#535	C₂²×C₂₉	1	3	yes	complemented
274	#532	C₂²×C₂₉	1	3	yes	complemented
275	C₂×#127	C₂²×C₂₉	1	3	yes	complemented
276	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic, complemented
277	#456	C₂²×C₂₉	1	4	yes	complemented
278	#455	C₂²×C₂₉	1	12	yes	complemented
279	#454	C₂²×C₂₉	1	12	yes	complemented
280	#453	C₂²×C₂₉	1	12	yes	complemented
281	#453	C₂²×C₂₉	1	24	yes	complemented
282	#421	C₂²×C₂₉	1	12	yes	complemented
283	C₂×#104	C₂²×C₂₉	1	12	yes	complemented
284	#413	C₂²×C₂₉	1	6	yes	complemented
285	C₂×#100	C₂²×C₂₉	1	6	yes	complemented
286	C₂×C₂₉	—	2	1	no	—
287	C₂×C₂₉	—	2	6	no	—
288	C₂×C₂₉	—	4	6	no	—
289	C₂×C₂₉	—	4	8	no	—
290	C₂×C₂₉	—	8	3	no	—
291	C₂×C₂₉	C₂²×#120	1	1	yes	characteristic
292	2₋¹⁺⁴	—	2	8	no	—
293	2₋¹⁺⁴	—	2	2	no	—
294	2₋¹⁺⁴	—	2	12	no	—
295	2₋¹⁺⁴	D₄×C₂₉	1	8	yes	complemented
296	2₋¹⁺⁴	C₂³×C₂₉	1	4	yes	—
297	H(5,𝔽₂)	—	2	8	no	—
298	H(5,𝔽₂)	—	2	48	no	—
299	H(5,𝔽₂)	—	2	8	no	—
300	H(5,𝔽₂)	—	2	24	no	—
301	H(5,𝔽₂)	—	2	6	no	—
302	H(5,𝔽₂)	—	2	12	no	—
303	H(5,𝔽₂)	—	2	12	no	—
304	H(5,𝔽₂)	—	2	12	no	—
305	H(5,𝔽₂)	—	2	8	no	—
306	H(5,𝔽₂)	D₄×C₂₉	1	8	yes	complemented
307	H(5,𝔽₂)	C₂³×C₂₉	1	12	yes	—
308	C₂×#41	—	2	16	no	—
309	C₂×#41	—	2	24	no	—
310	C₂×#41	—	2	8	no	—
311	C₂×#41	—	2	24	no	—
312	C₂×#41	—	2	1	no	—
313	C₂×#41	—	2	12	no	—
314	C₂×#41	—	2	12	no	—
315	C₂×#41	D₄×C₂₉	1	2	yes	—
316	C₂×#41	C₂³×C₂₉	1	12	yes	—
317	C₂×#41	C₂³×C₂₉	1	3	yes	—
318	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
319	C₂×#41	C₂³×C₂₉	1	3	yes	complemented
320	C₂²×D₄	—	2	24	no	—
321	C₂²×D₄	—	2	12	no	—
322	C₂²×D₄	—	2	12	no	—
323	C₂²×D₄	—	2	6	no	—
324	C₂²×D₄	—	2	3	no	—
325	C₂²×D₄	D₄×C₂₉	1	6	yes	—
326	C₂²×D₄	C₂³×C₂₉	1	3	yes	—
327	C₂²×D₄	C₂³×C₂₉	1	3	yes	complemented
328	#137	—	2	12	no	—
329	#137	C₂³×C₂₉	1	8	yes	complemented
330	AGL(1,ℤ/8)	—	2	24	no	—
331	AGL(1,ℤ/8)	—	2	12	no	—
332	AGL(1,ℤ/8)	C₂³×C₂₉	1	24	yes	complemented
333	#135	—	2	24	no	—
334	C₂×SD₁₆	—	2	12	no	—
335	C₂×D₈	—	2	12	no	—
336	#131	—	2	8	no	—
337	C₂×M₁₆	C₂³×C₂₉	1	12	yes	complemented
338	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic, complemented
339	#127	—	2	6	no	—
340	#127	C₂³×C₂₉	1	3	yes	complemented
341	#127	C₂³×C₂₉	1	6	yes	complemented
342	#124	C₂³×C₂₉	1	3	yes	complemented
343	#124	C₂³×C₂₉	1	3	yes	complemented
344	#121	—	2	6	no	—
345	#121	—	2	6	no	—
346	#121	—	2	6	no	—
347	#120	—	2	6	no	—
348	#120	—	2	6	no	—
349	C₄×Q₈	—	2	1	no	—
350	C₄×D₄	—	2	3	no	—
351	C₄×D₄	—	2	6	no	—
352	#117	C₂³×C₂₉	1	3	yes	complemented
353	C₂×C₄²	C₂³×C₂₉	1	3	yes	complemented
354	#104	C₂³×C₂₉	1	8	yes	complemented
355	#104	C₂³×C₂₉	1	24	yes	complemented
356	#101	C₂³×C₂₉	1	4	yes	complemented
357	#100	C₂³×C₂₉	1	12	yes	complemented
358	C₂₉	#60388	1	1	yes	characteristic, direct product factor, Sylow
359	C₂⁴	—	2	12	no	—
360	C₂⁴	—	2	3	no	—
361	C₂⁴	C₂×D₄×C₂₉	1	6	yes	—
362	#41	—	2	48	no	—
363	#41	—	2	48	no	—
364	#41	—	2	24	no	—
365	#41	—	2	24	no	—
366	#41	—	2	8	no	—
367	#41	—	2	8	no	—
368	#41	—	2	24	no	—
369	#41	—	2	24	no	—
370	#41	—	2	8	no	—
371	#41	—	2	8	no	—
372	#41	—	2	12	no	—
373	#41	—	2	12	no	—
374	#41	—	2	12	no	—
375	#41	—	2	12	no	—
376	#41	—	4	4	no	—
377	#41	C₂×D₄×C₂₉	1	8	yes	—
378	#41	C₂×D₄×C₂₉	1	24	yes	complemented
379	#41	C₂⁴×C₂₉	1	8	yes	—
380	C₂×Q₈	—	2	12	no	—
381	C₂×Q₈	—	2	8	no	—
382	C₂×Q₈	—	2	8	no	—
383	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
384	C₂×Q₈	C₂×D₄×C₂₉	1	12	yes	complemented
385	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
386	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
387	C₂×D₄	—	2	48	no	—
388	C₂×D₄	—	2	48	no	—
389	C₂×D₄	—	2	24	no	—
390	C₂×D₄	—	2	48	no	—
391	C₂×D₄	—	2	12	no	—
392	C₂×D₄	—	2	24	no	—
393	C₂×D₄	—	2	12	no	—
394	C₂×D₄	—	2	24	no	—
395	C₂×D₄	—	2	24	no	—
396	C₂×D₄	—	2	24	no	—
397	C₂×D₄	—	2	6	no	—
398	C₂×D₄	—	2	3	no	—
399	C₂×D₄	—	2	12	no	—
400	C₂×D₄	—	2	12	no	—
401	C₂×D₄	—	2	12	no	—
402	C₂×D₄	—	2	3	no	—
403	C₂×D₄	—	4	12	no	—
404	C₂×D₄	—	8	12	no	—
405	C₂×D₄	C₂×D₄×C₂₉	1	6	yes	—
406	C₂×D₄	C₂×D₄×C₂₉	1	6	yes	—
407	C₂×D₄	C₂×D₄×C₂₉	1	3	yes	—
408	C₂×D₄	C₂×D₄×C₂₉	1	12	yes	complemented
409	C₂×D₄	C₂⁴×C₂₉	1	3	yes	—
410	C₂×D₄	C₂⁴×C₂₉	1	3	yes	—
411	C₂²×C₄	—	2	12	no	—
412	C₂²×C₄	—	2	24	no	—
413	C₂²×C₄	—	2	12	no	—
414	C₂²×C₄	—	2	3	no	—
415	C₂²×C₄	—	2	3	no	—
416	C₂²×C₄	C₂×D₄×C₂₉	1	6	yes	—
417	C₂²×C₄	C₂⁴×C₂₉	1	3	yes	—
418	Q₁₆	—	2	8	no	—
419	SD₁₆	—	2	24	no	—
420	SD₁₆	—	2	8	no	—
421	D₈	—	2	24	no	—
422	M₁₆	—	2	12	no	—
423	M₁₆	C₂⁴×C₂₉	1	8	yes	—
424	C₂×C₈	—	2	12	no	—
425	C₄⋊C₄	—	2	3	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	3	no	—
428	C₂²⋊C₄	—	2	6	no	—
429	C₂²⋊C₄	—	2	6	no	—
430	C₄²	—	2	3	no	—
431	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
432	C₄²	C₂⁴×C₂₉	1	3	yes	—
433	C₂³	—	2	24	no	—
434	C₂³	—	2	12	no	—
435	C₂³	—	2	12	no	—
436	C₂³	—	2	3	no	—
437	C₂³	—	4	6	no	—
438	C₂³	—	8	6	no	—
439	C₂³	—	8	6	no	—
440	C₂³	—	16	12	no	—
441	C₂³	C₂²×D₄×C₂₉	1	6	yes	—
442	C₂³	C₂²×D₄×C₂₉	1	3	yes	—
443	Q₈	—	2	8	no	—
444	Q₈	—	2	12	no	—
445	Q₈	—	2	2	no	—
446	Q₈	—	2	2	no	—
447	Q₈	C₂₉×#120	1	4	yes	—
448	Q₈	C₂²×D₄×C₂₉	1	8	yes	—
449	D₄	—	2	48	no	—
450	D₄	—	2	8	no	—
451	D₄	—	2	24	no	—
452	D₄	—	2	12	no	—
453	D₄	—	2	8	no	—
454	D₄	—	2	12	no	—
455	D₄	—	2	12	no	—
456	D₄	—	2	6	no	—
457	D₄	—	2	6	no	—
458	D₄	—	4	12	no	—
459	D₄	—	4	6	no	—
460	D₄	—	4	6	no	—
461	D₄	—	8	12	no	—
462	D₄	C₂₉×#120	1	12	yes	—
463	D₄	C₂²×D₄×C₂₉	1	8	yes	—
464	C₂×C₄	—	2	24	no	—
465	C₂×C₄	—	2	16	no	—
466	C₂×C₄	—	2	12	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	24	no	—
469	C₂×C₄	—	2	12	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	3	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	4	6	no	—
474	C₂×C₄	—	4	6	no	—
475	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
476	C₂×C₄	C₂²×D₄×C₂₉	1	3	yes	—
477	C₂×C₄	C₂²×D₄×C₂₉	1	12	yes	—
478	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
479	C₈	—	2	8	no	—
480	C₂²	—	2	6	no	—
481	C₂²	—	2	8	no	—
482	C₂²	—	4	3	no	—
483	C₂²	—	4	6	no	—
484	C₂²	—	4	6	no	—
485	C₂²	—	4	3	no	—
486	C₂²	—	8	12	no	—
487	C₂²	—	8	12	no	—
488	C₂²	—	8	24	no	—
489	C₂²	—	16	6	no	—
490	C₂²	C₂×C₂₉×#120	1	6	yes	—
491	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
492	C₄	—	2	2	no	—
493	C₄	—	2	8	no	—
494	C₄	—	2	2	no	—
495	C₄	—	4	3	no	—
496	C₄	—	4	1	no	—
497	C₄	C₂×C₂₉×#120	1	6	yes	—
498	C₄	C₂³×D₄×C₂₉	1	2	yes	—
499	C₂	—	2	1	no	—
500	C₂	—	2	6	no	—
501	C₂	—	4	6	no	—
502	C₂	—	4	8	no	—
503	C₂	—	8	3	no	—
504	C₂	C₂²×C₂₉×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₉	C₂²×#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂×#41×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×H(7,𝔽₂)	C₂	semidirect
2. C₂₉×#3585	C₂	semidirect
3. C₂₉×#3498	C₂	semidirect
4. C₂₉×#3021	C₂	semidirect
5. C₂₉×#3019	C₂	semidirect
6. C₂₉×#3018	C₂	semidirect
7. C₂×C₂₉×#453	C₂	semidirect
8. C₂₉×#2901	C₂	semidirect
9. C₂₉×#2888	C₂	semidirect
13. C₂₉×#585	C₂²	semidirect
17. C₂×C₂₉×H(5,𝔽₂)	C₂²	semidirect
18. C₂×C₂₉×H(5,𝔽₂)	C₂²	semidirect
21. C₂₉×#575	C₂²	semidirect
22. C₂×C₂₉×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂₉×#568	C₂²	semidirect
26. C₂₉×#535	C₂²	semidirect
27. C₂₉×#535	C₂²	semidirect
28. C₂₉×#532	C₂²	semidirect
29. C₂×C₂₉×#127	C₂²	semidirect
30. C₄×#41×C₂₉	C₂²	semidirect
31. C₂₉×#456	C₂²	semidirect
32. C₂₉×#455	C₂²	semidirect
33. C₂₉×#454	C₂²	semidirect
34. C₂₉×#453	C₂²	semidirect
35. C₂₉×#453	C₂²	semidirect
36. C₂₉×#421	C₂²	semidirect
37. C₂×C₂₉×#104	C₂²	semidirect
38. C₂₉×#413	C₂²	semidirect
39. C₂×C₂₉×#100	C₂²	semidirect
43. C₂₉×2₋¹⁺⁴	D₄	semidirect
54. C₂₉×H(5,𝔽₂)	D₄	semidirect
67. C₂×#41×C₂₉	C₂³	semidirect
75. C₂²×D₄×C₂₉	C₂³	semidirect
77. C₂₉×#137	C₂³	semidirect
80. C₂₉×AGL(1,ℤ/8)	C₂³	semidirect
85. C₂×M₁₆×C₂₉	C₂³	semidirect
86. C₂₉×C₄⋊Q₈	C₂³	semidirect
88. C₂₉×#127	C₂³	semidirect
89. C₂₉×#127	C₂³	semidirect
90. C₂₉×#124	C₂³	semidirect
91. C₂₉×#124	C₂³	semidirect
100. C₂₉×#117	C₂³	semidirect
101. C₂×C₄²×C₂₉	C₂³	semidirect
102. C₂₉×#104	C₂³	semidirect
103. C₂₉×#104	C₂³	semidirect
104. C₂₉×#101	C₂³	semidirect
105. C₂₉×#100	C₂³	semidirect
125. #41×C₂₉	C₂×D₄	semidirect
131. C₂×Q₈×C₂₉	C₂×D₄	semidirect
155. C₂×D₄×C₂₉	C₂×D₄	semidirect
180. #60388	C₂₉	direct (N × H)
228. H(7,𝔽₂)	C₂×C₂₉	semidirect
229. #3585	C₂×C₂₉	semidirect
230. #3498	C₂×C₂₉	semidirect
231. #3021	C₂×C₂₉	semidirect
232. #3019	C₂×C₂₉	semidirect
233. #3018	C₂×C₂₉	semidirect
234. C₂×#453	C₂×C₂₉	semidirect
235. #2901	C₂×C₂₉	semidirect
236. #2888	C₂×C₂₉	semidirect
259. #585	C₂²×C₂₉	semidirect
263. C₂×H(5,𝔽₂)	C₂²×C₂₉	semidirect
264. C₂×H(5,𝔽₂)	C₂²×C₂₉	semidirect
267. #575	C₂²×C₂₉	semidirect
268. C₂×AGL(1,ℤ/8)	C₂²×C₂₉	semidirect
269. #568	C₂²×C₂₉	semidirect
272. #535	C₂²×C₂₉	semidirect
273. #535	C₂²×C₂₉	semidirect
274. #532	C₂²×C₂₉	semidirect
275. C₂×#127	C₂²×C₂₉	semidirect
276. C₄×#41	C₂²×C₂₉	semidirect
277. #456	C₂²×C₂₉	semidirect
278. #455	C₂²×C₂₉	semidirect
279. #454	C₂²×C₂₉	semidirect
280. #453	C₂²×C₂₉	semidirect
281. #453	C₂²×C₂₉	semidirect
282. #421	C₂²×C₂₉	semidirect
283. C₂×#104	C₂²×C₂₉	semidirect
284. #413	C₂²×C₂₉	semidirect
285. C₂×#100	C₂²×C₂₉	semidirect
295. 2₋¹⁺⁴	D₄×C₂₉	semidirect
306. H(5,𝔽₂)	D₄×C₂₉	semidirect
319. C₂×#41	C₂³×C₂₉	semidirect
327. C₂²×D₄	C₂³×C₂₉	semidirect
329. #137	C₂³×C₂₉	semidirect
332. AGL(1,ℤ/8)	C₂³×C₂₉	semidirect
337. C₂×M₁₆	C₂³×C₂₉	semidirect
338. C₄⋊Q₈	C₂³×C₂₉	semidirect
340. #127	C₂³×C₂₉	semidirect
341. #127	C₂³×C₂₉	semidirect
342. #124	C₂³×C₂₉	semidirect
343. #124	C₂³×C₂₉	semidirect
352. #117	C₂³×C₂₉	semidirect
353. C₂×C₄²	C₂³×C₂₉	semidirect
354. #104	C₂³×C₂₉	semidirect
355. #104	C₂³×C₂₉	semidirect
356. #101	C₂³×C₂₉	semidirect
357. #100	C₂³×C₂₉	semidirect
358. C₂₉	#60388	direct (N × H)
378. #41	C₂×D₄×C₂₉	semidirect
384. C₂×Q₈	C₂×D₄×C₂₉	semidirect
408. C₂×D₄	C₂×D₄×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×H(7,𝔽₂)	2
C₂₉×#3585	2
C₂₉×#3498	2
C₂₉×#3021	2
C₂₉×#3019	2
C₂₉×#3018	2
C₂×C₂₉×#453	2
C₂₉×#2901	2
C₂₉×#2888	2
#60388	29

Subgroups — C29×#60388 #20355288

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#60388 #20355288