Subgroups — C₂₉×#25359 #20320259

Order 7424.

764 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#476	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3036	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2935	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2079	C₂	1	2	yes	maximal, complemented
6	C₂₉×#2051	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1907	C₂	1	2	yes	maximal, complemented
10	C₂₉×#1815	C₂	1	2	yes	maximal, complemented
11	C₄×C₂₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂×C₂₉×#131	C₂²	1	2	yes	—
14	C₂₉×#532	C₂²	1	1	yes	characteristic
15	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
17	C₂₉×#489	—	2	2	no	—
18	C₂₉×#487	—	2	1	no	—
19	C₂₉×#486	—	2	1	no	—
20	C₂₉×#476	—	2	1	no	—
21	C₂₉×#476	—	2	2	no	—
22	C₂₉×#476	—	2	1	no	—
23	C₂₉×#463	—	2	2	no	—
24	C₂₉×#461	—	2	1	no	—
25	C₂₉×#459	—	2	1	no	—
26	C₂₉×#436	—	2	1	no	—
27	C₂₉×#435	—	2	2	no	—
28	C₈×D₄×C₂₉	—	2	1	no	—
29	C₂×C₂₉×#108	C₂²	1	2	yes	—
30	C₂×C₂₉×#106	C₂²	1	2	yes	—
31	C₂₉×#423	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂₉×#417	C₂²	1	2	yes	—
34	C₂₉×#417	C₂²	1	2	yes	—
35	C₂₉×#417	C₂²	1	2	yes	—
36	C₂×C₂₉×#102	C₂²	1	2	yes	—
37	C₂×C₂₉×#100	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×#100	C₂²	1	1	yes	characteristic
39	C₂₉×#408	C₂²	1	2	yes	—
40	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
41	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
42	C₂₉×#343	C₂²	1	2	yes	—
43	C₂₉×#343	C₂²	1	2	yes	—
44	C₂₉×#343	C₂²	1	1	yes	characteristic
45	C₂₉×#343	C₂²	1	1	yes	characteristic
46	C₂₉×#341	C₂²	1	2	yes	—
47	C₂×#41×C₂₉	C₂³	1	2	yes	—
48	C₂²×Q₈×C₂₉	—	2	1	no	—
49	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₂₉	—	2	1	no	—
51	C₂₉×AGL(1,ℤ/8)	—	2	4	no	—
52	C₂₉×AGL(1,ℤ/8)	—	4	2	no	—
53	C₂×SD₁₆×C₂₉	—	2	2	no	—
54	C₂×D₈×C₂₉	—	2	2	no	—
55	C₂₉×#131	—	2	4	no	—
56	C₂₉×#131	—	4	2	no	—
57	C₂×M₁₆×C₂₉	—	2	2	no	—
58	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
59	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
60	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
61	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₂₉	—	2	2	no	—
64	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
65	C₂₉×C₄⋊Q₈	—	2	1	no	—
66	C₂₉×C₄⋊Q₈	—	2	1	no	—
67	C₂₉×C₄⋊Q₈	—	2	1	no	—
68	C₂₉×C₄⋊Q₈	—	2	1	no	—
69	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
70	C₂₉×#127	D₄	1	1	yes	characteristic
71	C₂₉×#124	D₄	1	2	yes	—
72	C₂₉×#121	—	2	1	no	—
73	C₂₉×#121	—	2	1	no	—
74	C₄×D₄×C₂₉	—	2	1	no	—
75	C₄×D₄×C₂₉	—	2	1	no	—
76	C₄×D₄×C₂₉	—	2	1	no	—
77	C₄×D₄×C₂₉	—	2	1	no	—
78	C₄×D₄×C₂₉	—	2	1	no	—
79	C₄×D₄×C₂₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
84	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
85	C₂₉×#108	—	4	2	no	—
86	C₂₉×#106	—	2	2	no	—
87	C₂₉×#106	—	2	2	no	—
88	C₂₉×C₄⋊C₈	—	2	1	no	—
89	C₂₉×C₄⋊C₈	—	2	1	no	—
90	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
91	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
92	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
93	C₂₉×#103	—	2	2	no	—
94	C₂₉×#103	—	2	2	no	—
95	C₂₉×#103	—	2	2	no	—
96	C₂₉×#102	—	2	2	no	—
97	C₂₉×#102	—	2	2	no	—
98	C₂₉×#102	—	2	2	no	—
99	C₂₉×#102	—	2	2	no	—
100	C₂₉×#102	—	2	2	no	—
101	C₂₉×#100	—	2	2	no	—
102	C₂₉×#100	—	2	2	no	—
103	C₂₉×C₂²⋊C₈	—	2	2	no	—
104	C₂₉×C₂²⋊C₈	—	2	2	no	—
105	C₂₉×#97	—	2	1	no	—
106	C₂₉×#97	—	2	1	no	—
107	C₄×C₈×C₂₉	—	2	1	no	—
108	C₄×C₈×C₂₉	—	2	1	no	—
109	C₂⁴×C₂₉	—	2	1	no	—
110	#41×C₂₉	—	2	2	no	—
111	#41×C₂₉	—	2	2	no	—
112	#41×C₂₉	—	2	2	no	—
113	#41×C₂₉	—	2	2	no	—
114	C₂×Q₈×C₂₉	—	4	1	no	—
115	C₂×Q₈×C₂₉	—	4	1	no	—
116	C₂×Q₈×C₂₉	—	8	2	no	—
117	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
118	C₂×D₄×C₂₉	—	2	2	no	—
119	C₂×D₄×C₂₉	—	2	1	no	—
120	C₂×D₄×C₂₉	—	2	1	no	—
121	C₂×D₄×C₂₉	—	2	1	no	—
122	C₂×D₄×C₂₉	—	2	1	no	—
123	C₂×D₄×C₂₉	—	2	1	no	—
124	C₂×D₄×C₂₉	—	2	1	no	—
125	C₂×D₄×C₂₉	—	2	1	no	—
126	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
127	C₂×D₄×C₂₉	#41	1	2	yes	—
128	C₂²×C₄×C₂₉	—	2	2	no	—
129	C₂²×C₄×C₂₉	—	2	1	no	—
130	C₂²×C₄×C₂₉	—	2	2	no	—
131	C₂²×C₄×C₂₉	—	4	1	no	—
132	C₂²×C₄×C₂₉	—	4	1	no	—
133	C₂²×C₄×C₂₉	—	8	2	no	—
134	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
135	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
136	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
137	SD₁₆×C₂₉	—	4	4	no	—
138	D₈×C₂₉	—	4	4	no	—
139	M₁₆×C₂₉	—	2	1	no	—
140	M₁₆×C₂₉	—	2	2	no	—
141	M₁₆×C₂₉	—	2	1	no	—
142	M₁₆×C₂₉	—	2	1	no	—
143	M₁₆×C₂₉	—	2	1	no	—
144	M₁₆×C₂₉	—	2	2	no	—
145	M₁₆×C₂₉	—	2	1	no	—
146	M₁₆×C₂₉	—	2	1	no	—
147	M₁₆×C₂₉	—	2	1	no	—
148	M₁₆×C₂₉	—	4	4	no	—
149	M₁₆×C₂₉	#41	1	2	yes	—
150	C₂×C₈×C₂₉	—	2	1	no	—
151	C₂×C₈×C₂₉	—	2	2	no	—
152	C₂×C₈×C₂₉	—	2	2	no	—
153	C₂×C₈×C₂₉	—	2	2	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	—	4	4	no	—
158	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
159	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
160	C₄⋊C₄×C₂₉	—	2	1	no	—
161	C₄⋊C₄×C₂₉	—	2	1	no	—
162	C₄⋊C₄×C₂₉	—	2	1	no	—
163	C₄⋊C₄×C₂₉	—	2	1	no	—
164	C₄⋊C₄×C₂₉	—	2	2	no	—
165	C₄⋊C₄×C₂₉	—	2	2	no	—
166	C₄⋊C₄×C₂₉	—	4	1	no	—
167	C₄⋊C₄×C₂₉	—	4	1	no	—
168	C₂²⋊C₄×C₂₉	—	2	2	no	—
169	C₂²⋊C₄×C₂₉	—	2	2	no	—
170	C₂²⋊C₄×C₂₉	—	4	1	no	—
171	C₂²⋊C₄×C₂₉	—	4	1	no	—
172	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
176	#25359	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂³×C₂₉	—	2	2	no	—
178	C₂³×C₂₉	—	2	2	no	—
179	C₂³×C₂₉	—	4	1	no	—
180	C₂³×C₂₉	—	4	1	no	—
181	C₂³×C₂₉	—	8	1	no	—
182	C₂³×C₂₉	—	8	1	no	—
183	C₂³×C₂₉	C₂×#41	1	1	yes	characteristic
184	Q₈×C₂₉	—	2	2	no	—
185	Q₈×C₂₉	—	2	2	no	—
186	Q₈×C₂₉	—	8	2	no	—
187	Q₈×C₂₉	—	8	2	no	—
188	D₄×C₂₉	—	2	2	no	—
189	D₄×C₂₉	—	2	2	no	—
190	D₄×C₂₉	—	2	2	no	—
191	D₄×C₂₉	—	2	2	no	—
192	D₄×C₂₉	—	4	2	no	—
193	D₄×C₂₉	—	4	2	no	—
194	D₄×C₂₉	—	4	1	no	—
195	D₄×C₂₉	—	4	1	no	—
196	D₄×C₂₉	—	4	2	no	—
197	D₄×C₂₉	—	8	1	no	—
198	C₂×C₄×C₂₉	—	2	2	no	—
199	C₂×C₄×C₂₉	—	2	2	no	—
200	C₂×C₄×C₂₉	—	4	1	no	—
201	C₂×C₄×C₂₉	—	4	2	no	—
202	C₂×C₄×C₂₉	—	4	2	no	—
203	C₂×C₄×C₂₉	—	4	1	no	—
204	C₂×C₄×C₂₉	—	4	2	no	—
205	C₂×C₄×C₂₉	—	8	2	no	—
206	C₂×C₄×C₂₉	—	8	2	no	—
207	C₂×C₄×C₂₉	—	8	1	no	—
208	C₂×C₄×C₂₉	—	8	2	no	—
209	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
210	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
211	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
212	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
213	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
219	C₈×C₂₉	—	2	2	no	—
220	C₈×C₂₉	—	2	2	no	—
221	C₈×C₂₉	—	2	2	no	—
222	C₈×C₂₉	—	4	1	no	—
223	C₈×C₂₉	—	4	2	no	—
224	C₈×C₂₉	—	4	1	no	—
225	C₈×C₂₉	—	4	1	no	—
226	#3141	C₂×C₂₉	1	1	yes	characteristic, complemented
227	C₂×#476	C₂×C₂₉	1	1	yes	characteristic, complemented
228	#3036	C₂×C₂₉	1	1	yes	characteristic
229	#2935	C₂×C₂₉	1	1	yes	characteristic, complemented
230	#2079	C₂×C₂₉	1	2	yes	complemented
231	#2051	C₂×C₂₉	1	2	yes	complemented
232	#1997	C₂×C₂₉	1	1	yes	characteristic, complemented
233	#1950	C₂×C₂₉	1	1	yes	characteristic, complemented
234	#1907	C₂×C₂₉	1	2	yes	complemented
235	#1815	C₂×C₂₉	1	2	yes	complemented
236	C₄×#100	C₂×C₂₉	1	1	yes	characteristic, complemented
237	C₂²×C₂₉	—	2	1	no	—
238	C₂²×C₂₉	—	2	1	no	—
239	C₂²×C₂₉	—	4	2	no	—
240	C₂²×C₂₉	—	4	2	no	—
241	C₂²×C₂₉	—	4	2	no	—
242	C₂²×C₂₉	—	4	2	no	—
243	C₂²×C₂₉	—	8	2	no	—
244	C₂²×C₂₉	—	8	2	no	—
245	C₂²×C₂₉	—	8	1	no	—
246	C₂²×C₂₉	—	8	1	no	—
247	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
248	C₂²×C₂₉	#529	1	1	yes	characteristic
249	C₂²×C₂₉	#542	1	1	yes	characteristic
250	C₄×C₂₉	—	2	1	no	—
251	C₄×C₂₉	—	2	1	no	—
252	C₄×C₂₉	—	2	1	no	—
253	C₄×C₂₉	—	4	2	no	—
254	C₄×C₂₉	—	8	1	no	—
255	C₄×C₂₉	—	8	2	no	—
256	C₄×C₂₉	#471	1	2	yes	—
257	C₄×C₂₉	#546	1	1	yes	characteristic
258	C₄×C₂₉	#546	1	1	yes	characteristic
259	C₄×C₂₉	#547	1	1	yes	characteristic
260	C₄×C₂₉	#548	1	1	yes	characteristic
261	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	2	yes	—
262	C₂×#131	C₂²×C₂₉	1	2	yes	—
263	#532	C₂²×C₂₉	1	1	yes	characteristic
264	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
265	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
266	#489	—	2	2	no	—
267	#487	—	2	1	no	—
268	#486	—	2	1	no	—
269	#476	—	2	1	no	—
270	#476	—	2	2	no	—
271	#476	—	2	1	no	—
272	#463	—	2	2	no	—
273	#461	—	2	1	no	—
274	#459	—	2	1	no	—
275	#436	—	2	1	no	—
276	#435	—	2	2	no	—
277	C₈×D₄	—	2	1	no	—
278	C₂×#108	C₂²×C₂₉	1	2	yes	—
279	C₂×#106	C₂²×C₂₉	1	2	yes	—
280	#423	C₂²×C₂₉	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
282	#417	C₂²×C₂₉	1	2	yes	—
283	#417	C₂²×C₂₉	1	2	yes	—
284	#417	C₂²×C₂₉	1	2	yes	—
285	C₂×#102	C₂²×C₂₉	1	2	yes	—
286	C₂×#100	C₂²×C₂₉	1	1	yes	characteristic
287	C₂×#100	C₂²×C₂₉	1	1	yes	characteristic
288	#408	C₂²×C₂₉	1	2	yes	—
289	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
290	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
291	#343	C₂²×C₂₉	1	2	yes	—
292	#343	C₂²×C₂₉	1	1	yes	characteristic
293	#343	C₂²×C₂₉	1	2	yes	—
294	#343	C₂²×C₂₉	1	1	yes	characteristic
295	#341	C₂²×C₂₉	1	2	yes	—
296	C₂×C₂₉	—	2	1	no	—
297	C₂×C₂₉	—	2	1	no	—
298	C₂×C₂₉	—	8	2	no	—
299	C₂×C₂₉	—	8	2	no	—
300	C₂×C₂₉	#2427	1	1	yes	characteristic
301	C₂×C₂₉	C₂×#471	1	1	yes	characteristic
302	C₂×C₂₉	#3068	1	1	yes	characteristic
303	C₂×#41	C₂³×C₂₉	1	2	yes	—
304	C₂²×Q₈	—	2	1	no	—
305	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
306	C₂³×C₄	—	2	1	no	—
307	AGL(1,ℤ/8)	—	2	4	no	—
308	AGL(1,ℤ/8)	—	4	2	no	—
309	C₂×SD₁₆	—	2	2	no	—
310	C₂×D₈	—	2	2	no	—
311	#131	—	2	4	no	—
312	#131	—	4	2	no	—
313	C₂×M₁₆	—	2	2	no	—
314	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
315	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
316	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
317	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
318	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
319	C₂²×C₈	—	2	2	no	—
320	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
321	C₄⋊Q₈	—	2	1	no	—
322	C₄⋊Q₈	—	2	1	no	—
323	C₄⋊Q₈	—	2	1	no	—
324	C₄⋊Q₈	—	2	1	no	—
325	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
326	#127	D₄×C₂₉	1	1	yes	characteristic
327	#124	D₄×C₂₉	1	2	yes	—
328	#121	—	2	1	no	—
329	#121	—	2	1	no	—
330	C₄×D₄	—	2	1	no	—
331	C₄×D₄	—	2	1	no	—
332	C₄×D₄	—	2	1	no	—
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	—	2	1	no	—
335	C₄×D₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
341	#108	—	4	2	no	—
342	#106	—	2	2	no	—
343	#106	—	2	2	no	—
344	C₄⋊C₈	—	2	1	no	—
345	C₄⋊C₈	—	2	1	no	—
346	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
347	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
348	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
349	#103	—	2	2	no	—
350	#103	—	2	2	no	—
351	#103	—	2	2	no	—
352	#102	—	2	2	no	—
353	#102	—	2	2	no	—
354	#102	—	2	2	no	—
355	#102	—	2	2	no	—
356	#102	—	2	2	no	—
357	#100	—	2	2	no	—
358	#100	—	2	2	no	—
359	C₂²⋊C₈	—	2	2	no	—
360	C₂²⋊C₈	—	2	2	no	—
361	#97	—	2	1	no	—
362	#97	—	2	1	no	—
363	C₄×C₈	—	2	1	no	—
364	C₄×C₈	—	2	1	no	—
365	C₂₉	#25359	1	1	yes	characteristic, direct product factor, Sylow
366	C₂⁴	—	2	1	no	—
367	#41	—	2	2	no	—
368	#41	—	2	2	no	—
369	#41	—	2	2	no	—
370	#41	—	2	2	no	—
371	C₂×Q₈	—	4	1	no	—
372	C₂×Q₈	—	4	1	no	—
373	C₂×Q₈	—	8	2	no	—
374	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
384	C₂×D₄	#41×C₂₉	1	2	yes	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	—	8	2	no	—
391	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
392	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
393	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
394	SD₁₆	—	4	4	no	—
395	D₈	—	4	4	no	—
396	M₁₆	—	2	1	no	—
397	M₁₆	—	2	1	no	—
398	M₁₆	—	2	1	no	—
399	M₁₆	—	2	1	no	—
400	M₁₆	—	2	2	no	—
401	M₁₆	—	2	1	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	1	no	—
404	M₁₆	—	2	1	no	—
405	M₁₆	—	4	4	no	—
406	M₁₆	#41×C₂₉	1	2	yes	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	4	4	no	—
415	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
416	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	4	1	no	—
424	C₄⋊C₄	—	4	1	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	4	1	no	—
428	C₂²⋊C₄	—	4	1	no	—
429	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
430	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
431	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
432	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	8	1	no	—
438	C₂³	—	8	1	no	—
439	C₂³	C₂×#41×C₂₉	1	1	yes	characteristic
440	Q₈	—	2	2	no	—
441	Q₈	—	2	2	no	—
442	Q₈	—	8	2	no	—
443	Q₈	—	8	2	no	—
444	D₄	—	2	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	2	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	4	2	no	—
450	D₄	—	4	2	no	—
451	D₄	—	4	1	no	—
452	D₄	—	4	1	no	—
453	D₄	—	8	1	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	8	2	no	—
462	C₂×C₄	—	8	2	no	—
463	C₂×C₄	—	8	1	no	—
464	C₂×C₄	—	8	2	no	—
465	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
466	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
467	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
468	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
469	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
471	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
472	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
473	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
474	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	2	no	—
478	C₈	—	4	2	no	—
479	C₈	—	4	1	no	—
480	C₈	—	4	1	no	—
481	C₈	—	4	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	8	2	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	1	no	—
491	C₂²	—	8	1	no	—
492	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
493	C₂²	C₂₉×#529	1	1	yes	characteristic
494	C₂²	C₂₉×#542	1	1	yes	characteristic
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	4	2	no	—
499	C₄	—	8	1	no	—
500	C₄	—	8	2	no	—
501	C₄	C₂₉×#471	1	2	yes	—
502	C₄	C₂₉×#546	1	1	yes	characteristic
503	C₄	C₂₉×#546	1	1	yes	characteristic
504	C₄	C₂₉×#547	1	1	yes	characteristic
505	C₄	C₂₉×#548	1	1	yes	characteristic
506	C₂	—	2	1	no	—
507	C₂	—	2	1	no	—
508	C₂	—	8	2	no	—
509	C₂	—	8	2	no	—
510	C₂	C₂₉×#2427	1	1	yes	characteristic
511	C₂	C₂×C₂₉×#471	1	1	yes	characteristic
512	C₂	C₂₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂₉×#3036	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3141	C₂	semidirect
2. C₂×C₂₉×#476	C₂	semidirect
4. C₂₉×#2935	C₂	semidirect
5. C₂₉×#2079	C₂	semidirect
6. C₂₉×#2051	C₂	semidirect
7. C₂₉×#1997	C₂	semidirect
8. C₂₉×#1950	C₂	semidirect
9. C₂₉×#1907	C₂	semidirect
10. C₂₉×#1815	C₂	semidirect
11. C₄×C₂₉×#100	C₂	semidirect
176. #25359	C₂₉	direct (N × H)
226. #3141	C₂×C₂₉	semidirect
227. C₂×#476	C₂×C₂₉	semidirect
229. #2935	C₂×C₂₉	semidirect
230. #2079	C₂×C₂₉	semidirect
231. #2051	C₂×C₂₉	semidirect
232. #1997	C₂×C₂₉	semidirect
233. #1950	C₂×C₂₉	semidirect
234. #1907	C₂×C₂₉	semidirect
235. #1815	C₂×C₂₉	semidirect
236. C₄×#100	C₂×C₂₉	semidirect
365. C₂₉	#25359	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×#3141	2
C₂×C₂₉×#476	2
C₂₉×#3036	2
C₂₉×#2935	2
C₂₉×#2079	2
C₂₉×#2051	2
C₂₉×#1997	2
C₂₉×#1950	2
C₂₉×#1907	2
C₂₉×#1815	2
C₄×C₂₉×#100	2
#25359	29

Subgroups — C29×#25359 #20320259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#25359 #20320259