Subgroups — C₂₉×#33848 #20328748

Order 7424.

696 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₉×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3285	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3280	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2249	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2217	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2217	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2211	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#2210	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#2189	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#2188	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#2186	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#2184	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂₉×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic, complemented
18	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₂₉	C₂²	1	1	yes	characteristic
20	C₂₉×#548	—	2	1	no	—
21	C₂₉×#546	—	2	1	no	—
22	C₂₉×#508	—	2	4	no	—
23	C₂×C₂₉×Q₃₂	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₂₉×Q₃₂	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₂₉×SD₃₂	—	2	4	no	—
26	C₂×C₂₉×SD₃₂	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×SD₃₂	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×SD₃₂	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×SD₃₂	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×SD₃₂	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₂₉×D₁₆	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×D₁₆	C₂²	1	1	yes	characteristic
33	C₂²×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
34	C₂²×C₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
35	C₂₉×#495	C₂²	1	1	yes	characteristic
36	C₂₉×#495	C₂²	1	1	yes	characteristic, complemented
37	C₂₉×#467	C₂²	1	1	yes	characteristic
38	C₂₉×#467	C₂²	1	1	yes	characteristic, complemented
39	C₂₉×#466	C₂²	1	1	yes	characteristic
40	C₂₉×#466	C₂²	1	1	yes	characteristic
41	C₂₉×#464	—	2	1	no	—
42	C₂₉×#463	—	2	1	no	—
43	C₂₉×#452	—	2	1	no	—
44	C₂₉×#450	—	2	1	no	—
45	C₂₉×#449	—	2	1	no	—
46	C₂₉×#448	—	2	1	no	—
47	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
48	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
49	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
50	C₂₉×#367	C₂²	1	1	yes	characteristic, complemented
51	C₂₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
52	C₂₉×#358	C₂²	1	1	yes	characteristic, complemented
53	C₂₉×#358	C₂²	1	1	yes	characteristic, complemented
54	C₂₉×#358	C₂²	1	1	yes	characteristic, complemented
55	C₂₉×#357	C₂²	1	1	yes	characteristic
56	C₂₉×#357	C₂²	1	1	yes	characteristic
57	C₂₉×#357	C₂²	1	1	yes	characteristic, complemented
58	C₂₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
59	C₂₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
61	C₂×#41×C₂₉	—	2	1	no	—
62	C₂×#41×C₂₉	—	2	1	no	—
63	C₂²×Q₈×C₂₉	—	2	1	no	—
64	C₂²×D₄×C₂₉	—	2	1	no	—
65	C₂₉×#135	—	2	2	no	—
66	C₂₉×#135	—	2	2	no	—
67	C₂₉×#135	—	4	1	no	—
68	C₂₉×#135	—	4	1	no	—
69	C₂×Q₁₆×C₂₉	—	2	2	no	—
70	C₂×Q₁₆×C₂₉	—	2	1	no	—
71	C₂×Q₁₆×C₂₉	—	4	1	no	—
72	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
73	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
74	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
75	C₂×SD₁₆×C₂₉	—	2	1	no	—
76	C₂×SD₁₆×C₂₉	—	2	1	no	—
77	C₂×SD₁₆×C₂₉	—	2	1	no	—
78	C₂×SD₁₆×C₂₉	—	2	1	no	—
79	C₂×D₈×C₂₉	—	2	2	no	—
80	C₂×D₈×C₂₉	—	2	1	no	—
81	C₂×D₈×C₂₉	—	4	1	no	—
82	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
83	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
84	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
87	C₂₉×#124	—	2	1	no	—
88	C₂₉×#124	—	2	1	no	—
89	C₂₉×#124	—	4	1	no	—
90	C₂₉×#123	—	4	1	no	—
91	C₂₉×C₂²⋊Q₈	—	2	1	no	—
92	C₂₉×C₂²⋊Q₈	—	2	1	no	—
93	C₂₉×C₂²⋊Q₈	—	4	1	no	—
94	C₂₉×#121	—	2	1	no	—
95	C₂₉×#121	—	2	1	no	—
96	C₂₉×#121	—	4	1	no	—
97	C₂₉×#121	—	4	1	no	—
98	C₂₉×#120	—	4	1	no	—
99	C₄×Q₈×C₂₉	—	2	1	no	—
100	C₄×D₄×C₂₉	—	2	1	no	—
101	C₄×D₄×C₂₉	—	4	1	no	—
102	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₂₉	—	4	1	no	—
104	C₂₉×Q₃₂	—	2	2	no	—
105	C₂₉×Q₃₂	—	4	1	no	—
106	C₂₉×SD₃₂	—	2	2	no	—
107	C₂₉×SD₃₂	—	2	2	no	—
108	C₂₉×SD₃₂	—	2	2	no	—
109	C₂₉×SD₃₂	—	2	2	no	—
110	C₂₉×SD₃₂	D₄	1	4	yes	complemented
111	C₂₉×D₁₆	—	2	2	no	—
112	C₂₉×D₁₆	—	4	1	no	—
113	C₂×C₁₆×C₂₉	—	2	2	no	—
114	C₂×C₁₆×C₂₉	—	2	2	no	—
115	C₂×C₁₆×C₂₉	C₂³	1	1	yes	characteristic
116	C₂×C₁₆×C₂₉	C₂³	1	1	yes	characteristic
117	C₂×C₁₆×C₂₉	C₂³	1	1	yes	characteristic
118	C₂×C₁₆×C₂₉	C₂³	1	1	yes	characteristic
119	C₂₉×#107	C₂³	1	1	yes	characteristic
120	C₂₉×#107	C₂³	1	1	yes	characteristic
121	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
122	C₂₉×#103	—	2	1	no	—
123	C₂₉×#103	—	2	1	no	—
124	C₂₉×#103	—	2	1	no	—
125	C₂₉×#102	—	2	1	no	—
126	C₂₉×#102	—	2	1	no	—
127	C₂₉×#102	—	2	1	no	—
128	C₂₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
129	C₂₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
130	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
131	C₂⁴×C₂₉	—	4	1	no	—
132	#41×C₂₉	—	4	2	no	—
133	#41×C₂₉	—	4	2	no	—
134	#41×C₂₉	—	8	1	no	—
135	#41×C₂₉	—	8	1	no	—
136	C₂×Q₈×C₂₉	—	2	1	no	—
137	C₂×Q₈×C₂₉	—	2	1	no	—
138	C₂×Q₈×C₂₉	—	2	1	no	—
139	C₂×Q₈×C₂₉	—	4	2	no	—
140	C₂×Q₈×C₂₉	—	4	1	no	—
141	C₂×Q₈×C₂₉	—	8	1	no	—
142	C₂×D₄×C₂₉	—	2	1	no	—
143	C₂×D₄×C₂₉	—	2	1	no	—
144	C₂×D₄×C₂₉	—	2	1	no	—
145	C₂×D₄×C₂₉	—	4	2	no	—
146	C₂×D₄×C₂₉	—	4	1	no	—
147	C₂×D₄×C₂₉	—	4	1	no	—
148	C₂×D₄×C₂₉	—	4	1	no	—
149	C₂×D₄×C₂₉	—	4	1	no	—
150	C₂×D₄×C₂₉	—	4	1	no	—
151	C₂×D₄×C₂₉	—	8	1	no	—
152	C₂×D₄×C₂₉	D₈	1	1	yes	characteristic
153	C₂²×C₄×C₂₉	—	4	1	no	—
154	C₂²×C₄×C₂₉	—	4	1	no	—
155	C₂²×C₄×C₂₉	—	4	1	no	—
156	C₂²×C₄×C₂₉	—	4	1	no	—
157	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
159	Q₁₆×C₂₉	—	2	1	no	—
160	Q₁₆×C₂₉	—	2	1	no	—
161	Q₁₆×C₂₉	—	2	1	no	—
162	Q₁₆×C₂₉	—	2	1	no	—
163	Q₁₆×C₂₉	—	2	1	no	—
164	Q₁₆×C₂₉	—	4	2	no	—
165	Q₁₆×C₂₉	C₂×D₄	1	2	yes	—
166	SD₁₆×C₂₉	—	4	2	no	—
167	SD₁₆×C₂₉	—	4	2	no	—
168	SD₁₆×C₂₉	—	8	1	no	—
169	SD₁₆×C₂₉	—	8	1	no	—
170	D₈×C₂₉	—	2	1	no	—
171	D₈×C₂₉	—	2	1	no	—
172	D₈×C₂₉	—	2	1	no	—
173	D₈×C₂₉	—	2	1	no	—
174	D₈×C₂₉	—	2	1	no	—
175	D₈×C₂₉	—	4	2	no	—
176	D₈×C₂₉	C₂×D₄	1	2	yes	—
177	C₂×C₈×C₂₉	—	2	1	no	—
178	C₂×C₈×C₂₉	—	2	1	no	—
179	C₂×C₈×C₂₉	—	2	1	no	—
180	C₂×C₈×C₂₉	—	2	1	no	—
181	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
185	C₄⋊C₄×C₂₉	—	2	1	no	—
186	C₄⋊C₄×C₂₉	—	2	1	no	—
187	C₄⋊C₄×C₂₉	—	4	1	no	—
188	C₄⋊C₄×C₂₉	—	4	1	no	—
189	C₄⋊C₄×C₂₉	—	4	1	no	—
190	C₄⋊C₄×C₂₉	D₈	1	1	yes	characteristic
191	C₂²⋊C₄×C₂₉	—	4	1	no	—
192	C₂²⋊C₄×C₂₉	—	4	1	no	—
193	C₂²⋊C₄×C₂₉	—	4	1	no	—
194	C₂²⋊C₄×C₂₉	—	4	1	no	—
195	C₂²⋊C₄×C₂₉	—	4	1	no	—
196	C₂²⋊C₄×C₂₉	—	4	1	no	—
197	C₂²⋊C₄×C₂₉	—	4	1	no	—
198	C₂²⋊C₄×C₂₉	—	4	1	no	—
199	C₂²⋊C₄×C₂₉	—	4	1	no	—
200	C₂²⋊C₄×C₂₉	D₈	1	1	yes	characteristic
201	C₂²⋊C₄×C₂₉	D₈	1	1	yes	characteristic
202	C₄²×C₂₉	—	4	1	no	—
203	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
204	C₁₆×C₂₉	—	2	1	no	—
205	C₁₆×C₂₉	—	2	1	no	—
206	C₁₆×C₂₉	—	2	1	no	—
207	C₁₆×C₂₉	C₂×D₄	1	2	yes	—
208	#33848	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂³×C₂₉	—	4	1	no	—
210	C₂³×C₂₉	—	4	1	no	—
211	C₂³×C₂₉	—	4	1	no	—
212	C₂³×C₂₉	—	8	2	no	—
213	C₂³×C₂₉	—	8	2	no	—
214	C₂³×C₂₉	—	16	1	no	—
215	C₂³×C₂₉	C₂×D₈	1	1	yes	characteristic
216	C₂³×C₂₉	C₂×D₈	1	1	yes	characteristic
217	Q₈×C₂₉	—	2	2	no	—
218	Q₈×C₂₉	—	4	1	no	—
219	Q₈×C₂₉	—	4	1	no	—
220	Q₈×C₂₉	—	4	1	no	—
221	Q₈×C₂₉	—	4	1	no	—
222	Q₈×C₂₉	—	4	1	no	—
223	Q₈×C₂₉	—	8	2	no	—
224	D₄×C₂₉	—	2	2	no	—
225	D₄×C₂₉	—	2	2	no	—
226	D₄×C₂₉	—	4	1	no	—
227	D₄×C₂₉	—	4	1	no	—
228	D₄×C₂₉	—	4	1	no	—
229	D₄×C₂₉	—	4	1	no	—
230	D₄×C₂₉	—	4	1	no	—
231	D₄×C₂₉	—	8	2	no	—
232	D₄×C₂₉	—	8	2	no	—
233	D₄×C₂₉	—	8	2	no	—
234	D₄×C₂₉	—	8	2	no	—
235	D₄×C₂₉	—	16	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	—	4	1	no	—
241	C₂×C₄×C₂₉	—	4	1	no	—
242	C₂×C₄×C₂₉	—	4	1	no	—
243	C₂×C₄×C₂₉	—	4	1	no	—
244	C₂×C₄×C₂₉	—	4	1	no	—
245	C₂×C₄×C₂₉	—	8	2	no	—
246	C₂×C₄×C₂₉	—	8	2	no	—
247	C₂×C₄×C₂₉	—	8	2	no	—
248	C₂×C₄×C₂₉	—	16	1	no	—
249	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
250	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
251	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
252	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
253	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
254	C₈×C₂₉	—	2	1	no	—
255	C₈×C₂₉	—	2	1	no	—
256	C₈×C₂₉	—	2	1	no	—
257	C₈×C₂₉	C₂²×D₄	1	1	yes	characteristic
258	C₈×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
259	C₂×#508	C₂×C₂₉	1	1	yes	characteristic, complemented
260	C₂²×SD₃₂	C₂×C₂₉	1	1	yes	characteristic, complemented
261	#3285	C₂×C₂₉	1	1	yes	characteristic, complemented
262	#3280	C₂×C₂₉	1	1	yes	characteristic, complemented
263	#2249	C₂×C₂₉	1	1	yes	characteristic, complemented
264	#2217	C₂×C₂₉	1	1	yes	characteristic, complemented
265	#2217	C₂×C₂₉	1	1	yes	characteristic, complemented
266	#2211	C₂×C₂₉	1	1	yes	characteristic, complemented
267	#2210	C₂×C₂₉	1	1	yes	characteristic, complemented
268	#2189	C₂×C₂₉	1	1	yes	characteristic, complemented
269	#2188	C₂×C₂₉	1	1	yes	characteristic, complemented
270	#2186	C₂×C₂₉	1	1	yes	characteristic, complemented
271	#2184	C₂×C₂₉	1	1	yes	characteristic, complemented
272	C₄×SD₃₂	C₂×C₂₉	1	1	yes	characteristic, complemented
273	D₄×C₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
274	C₂²×C₂₉	—	2	1	no	—
275	C₂²×C₂₉	—	2	1	no	—
276	C₂²×C₂₉	—	2	1	no	—
277	C₂²×C₂₉	—	2	1	no	—
278	C₂²×C₂₉	—	2	1	no	—
279	C₂²×C₂₉	—	4	2	no	—
280	C₂²×C₂₉	—	8	1	no	—
281	C₂²×C₂₉	—	8	1	no	—
282	C₂²×C₂₉	—	8	1	no	—
283	C₂²×C₂₉	—	8	1	no	—
284	C₂²×C₂₉	—	8	1	no	—
285	C₂²×C₂₉	—	8	1	no	—
286	C₂²×C₂₉	—	8	1	no	—
287	C₂²×C₂₉	—	8	1	no	—
288	C₂²×C₂₉	—	16	4	no	—
289	C₂²×C₂₉	#508	1	2	yes	complemented
290	C₂²×C₂₉	C₂²×D₈	1	1	yes	characteristic
291	C₄×C₂₉	—	2	1	no	—
292	C₄×C₂₉	—	2	1	no	—
293	C₄×C₂₉	—	2	1	no	—
294	C₄×C₂₉	—	2	1	no	—
295	C₄×C₂₉	—	4	2	no	—
296	C₄×C₂₉	—	8	1	no	—
297	C₄×C₂₉	—	8	1	no	—
298	C₄×C₂₉	—	8	1	no	—
299	C₄×C₂₉	—	8	1	no	—
300	C₄×C₂₉	D₄²	1	1	yes	characteristic
301	C₄×C₂₉	#576	1	1	yes	characteristic
302	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
303	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic, complemented
304	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
305	C₂²×D₈	C₂²×C₂₉	1	1	yes	characteristic
306	#548	—	2	1	no	—
307	#546	—	2	1	no	—
308	#508	—	2	4	no	—
309	C₂×Q₃₂	C₂²×C₂₉	1	1	yes	characteristic, complemented
310	C₂×Q₃₂	C₂²×C₂₉	1	1	yes	characteristic, complemented
311	C₂×SD₃₂	—	2	4	no	—
312	C₂×SD₃₂	C₂²×C₂₉	1	1	yes	characteristic
313	C₂×SD₃₂	C₂²×C₂₉	1	1	yes	characteristic
314	C₂×SD₃₂	C₂²×C₂₉	1	1	yes	characteristic
315	C₂×SD₃₂	C₂²×C₂₉	1	1	yes	characteristic
316	C₂×SD₃₂	C₂²×C₂₉	1	1	yes	characteristic, complemented
317	C₂×D₁₆	C₂²×C₂₉	1	1	yes	characteristic
318	C₂×D₁₆	C₂²×C₂₉	1	1	yes	characteristic
319	C₂²×C₁₆	C₂²×C₂₉	1	1	yes	characteristic
320	C₂²×C₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
321	#495	C₂²×C₂₉	1	1	yes	characteristic
322	#495	C₂²×C₂₉	1	1	yes	characteristic, complemented
323	#467	C₂²×C₂₉	1	1	yes	characteristic
324	#467	C₂²×C₂₉	1	1	yes	characteristic, complemented
325	#466	C₂²×C₂₉	1	1	yes	characteristic
326	#466	C₂²×C₂₉	1	1	yes	characteristic
327	#464	—	2	1	no	—
328	#463	—	2	1	no	—
329	#452	—	2	1	no	—
330	#450	—	2	1	no	—
331	#449	—	2	1	no	—
332	#448	—	2	1	no	—
333	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
334	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
335	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
336	#367	C₂²×C₂₉	1	1	yes	characteristic, complemented
337	C₄⋊C₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
338	#358	C₂²×C₂₉	1	1	yes	characteristic, complemented
339	#358	C₂²×C₂₉	1	1	yes	characteristic, complemented
340	#358	C₂²×C₂₉	1	1	yes	characteristic, complemented
341	#357	C₂²×C₂₉	1	1	yes	characteristic
342	#357	C₂²×C₂₉	1	1	yes	characteristic
343	#357	C₂²×C₂₉	1	1	yes	characteristic, complemented
344	C₂²⋊C₁₆	C₂²×C₂₉	1	1	yes	characteristic
345	C₂²⋊C₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
346	C₄×C₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
347	C₂×C₂₉	—	2	2	no	—
348	C₂×C₂₉	—	4	1	no	—
349	C₂×C₂₉	—	8	2	no	—
350	C₂×C₂₉	—	16	1	no	—
351	C₂×C₂₉	—	16	1	no	—
352	C₂×C₂₉	D₄×D₈	1	1	yes	characteristic
353	C₂×C₂₉	C₂×#508	1	1	yes	characteristic
354	C₂×C₂₉	#3416	1	1	yes	characteristic
355	C₂×#41	—	2	1	no	—
356	C₂×#41	—	2	1	no	—
357	C₂²×Q₈	—	2	1	no	—
358	C₂²×D₄	—	2	1	no	—
359	#135	—	2	2	no	—
360	#135	—	2	2	no	—
361	#135	—	4	1	no	—
362	#135	—	4	1	no	—
363	C₂×Q₁₆	—	2	2	no	—
364	C₂×Q₁₆	—	2	1	no	—
365	C₂×Q₁₆	—	4	1	no	—
366	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
367	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
368	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
369	C₂×SD₁₆	—	2	1	no	—
370	C₂×SD₁₆	—	2	1	no	—
371	C₂×SD₁₆	—	2	1	no	—
372	C₂×SD₁₆	—	2	1	no	—
373	C₂×D₈	—	2	2	no	—
374	C₂×D₈	—	2	1	no	—
375	C₂×D₈	—	4	1	no	—
376	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
377	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
378	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
379	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
381	#124	—	2	1	no	—
382	#124	—	2	1	no	—
383	#124	—	4	1	no	—
384	#123	—	4	1	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₂²⋊Q₈	—	2	1	no	—
387	C₂²⋊Q₈	—	4	1	no	—
388	#121	—	2	1	no	—
389	#121	—	2	1	no	—
390	#121	—	4	1	no	—
391	#121	—	4	1	no	—
392	#120	—	4	1	no	—
393	C₄×Q₈	—	2	1	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	—	4	1	no	—
396	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
397	C₂×C₂²⋊C₄	—	4	1	no	—
398	Q₃₂	—	2	2	no	—
399	Q₃₂	—	4	1	no	—
400	SD₃₂	—	2	2	no	—
401	SD₃₂	—	2	2	no	—
402	SD₃₂	—	2	2	no	—
403	SD₃₂	—	2	2	no	—
404	SD₃₂	D₄×C₂₉	1	4	yes	complemented
405	D₁₆	—	2	2	no	—
406	D₁₆	—	4	1	no	—
407	C₂×C₁₆	—	2	2	no	—
408	C₂×C₁₆	—	2	2	no	—
409	C₂×C₁₆	C₂³×C₂₉	1	1	yes	characteristic
410	C₂×C₁₆	C₂³×C₂₉	1	1	yes	characteristic
411	C₂×C₁₆	C₂³×C₂₉	1	1	yes	characteristic
412	C₂×C₁₆	C₂³×C₂₉	1	1	yes	characteristic
413	#107	C₂³×C₂₉	1	1	yes	characteristic
414	#107	C₂³×C₂₉	1	1	yes	characteristic
415	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
416	#103	—	2	1	no	—
417	#103	—	2	1	no	—
418	#103	—	2	1	no	—
419	#102	—	2	1	no	—
420	#102	—	2	1	no	—
421	#102	—	2	1	no	—
422	C₂²⋊C₈	D₄×C₂₉	1	1	yes	characteristic
423	C₂²⋊C₈	D₄×C₂₉	1	1	yes	characteristic
424	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
425	C₂₉	#33848	1	1	yes	characteristic, direct product factor, Sylow
426	C₂⁴	—	4	1	no	—
427	#41	—	4	2	no	—
428	#41	—	4	2	no	—
429	#41	—	8	1	no	—
430	#41	—	8	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	4	2	no	—
435	C₂×Q₈	—	4	1	no	—
436	C₂×Q₈	—	8	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	4	2	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	—	4	1	no	—
443	C₂×D₄	—	4	1	no	—
444	C₂×D₄	—	4	1	no	—
445	C₂×D₄	—	4	1	no	—
446	C₂×D₄	—	8	1	no	—
447	C₂×D₄	D₈×C₂₉	1	1	yes	characteristic
448	C₂²×C₄	—	4	1	no	—
449	C₂²×C₄	—	4	1	no	—
450	C₂²×C₄	—	4	1	no	—
451	C₂²×C₄	—	4	1	no	—
452	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
454	Q₁₆	—	2	1	no	—
455	Q₁₆	—	2	1	no	—
456	Q₁₆	—	2	1	no	—
457	Q₁₆	—	2	1	no	—
458	Q₁₆	—	2	1	no	—
459	Q₁₆	—	4	2	no	—
460	Q₁₆	C₂×D₄×C₂₉	1	2	yes	—
461	SD₁₆	—	4	2	no	—
462	SD₁₆	—	4	2	no	—
463	SD₁₆	—	8	1	no	—
464	SD₁₆	—	8	1	no	—
465	D₈	—	2	1	no	—
466	D₈	—	2	1	no	—
467	D₈	—	2	1	no	—
468	D₈	—	2	1	no	—
469	D₈	—	2	1	no	—
470	D₈	—	4	2	no	—
471	D₈	C₂×D₄×C₂₉	1	2	yes	—
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	C₂×D₄×C₂₉	1	1	yes	characteristic
477	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
478	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
479	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	4	1	no	—
483	C₄⋊C₄	—	4	1	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₄⋊C₄	D₈×C₂₉	1	1	yes	characteristic
486	C₂²⋊C₄	—	4	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₂²⋊C₄	—	4	1	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₂²⋊C₄	—	4	1	no	—
493	C₂²⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	D₈×C₂₉	1	1	yes	characteristic
496	C₂²⋊C₄	D₈×C₂₉	1	1	yes	characteristic
497	C₄²	—	4	1	no	—
498	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
499	C₁₆	—	2	1	no	—
500	C₁₆	—	2	1	no	—
501	C₁₆	—	2	1	no	—
502	C₁₆	C₂×D₄×C₂₉	1	2	yes	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	1	no	—
505	C₂³	—	4	1	no	—
506	C₂³	—	8	2	no	—
507	C₂³	—	8	2	no	—
508	C₂³	—	16	1	no	—
509	C₂³	C₂×D₈×C₂₉	1	1	yes	characteristic
510	C₂³	C₂×D₈×C₂₉	1	1	yes	characteristic
511	Q₈	—	2	2	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	4	1	no	—
514	Q₈	—	4	1	no	—
515	Q₈	—	4	1	no	—
516	Q₈	—	4	1	no	—
517	Q₈	—	8	2	no	—
518	D₄	—	2	2	no	—
519	D₄	—	2	2	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	1	no	—
524	D₄	—	4	1	no	—
525	D₄	—	8	2	no	—
526	D₄	—	8	2	no	—
527	D₄	—	8	2	no	—
528	D₄	—	8	2	no	—
529	D₄	—	16	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	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	8	2	no	—
540	C₂×C₄	—	8	2	no	—
541	C₂×C₄	—	8	2	no	—
542	C₂×C₄	—	16	1	no	—
543	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
544	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
545	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
546	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
548	C₈	—	2	1	no	—
549	C₈	—	2	1	no	—
550	C₈	—	2	1	no	—
551	C₈	C₂²×D₄×C₂₉	1	1	yes	characteristic
552	C₈	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	8	1	no	—
560	C₂²	—	8	1	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	—	8	1	no	—
565	C₂²	—	8	1	no	—
566	C₂²	—	8	1	no	—
567	C₂²	—	16	4	no	—
568	C₂²	C₂₉×#508	1	2	yes	complemented
569	C₂²	C₂²×D₈×C₂₉	1	1	yes	characteristic
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	4	2	no	—
575	C₄	—	8	1	no	—
576	C₄	—	8	1	no	—
577	C₄	—	8	1	no	—
578	C₄	—	8	1	no	—
579	C₄	D₄²×C₂₉	1	1	yes	characteristic
580	C₄	C₂₉×#576	1	1	yes	characteristic
581	C₂	—	2	2	no	—
582	C₂	—	4	1	no	—
583	C₂	—	8	2	no	—
584	C₂	—	16	1	no	—
585	C₂	—	16	1	no	—
586	C₂	D₄×D₈×C₂₉	1	1	yes	characteristic
587	C₂	C₂×C₂₉×#508	1	1	yes	characteristic
588	C₂	C₂₉×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₂₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄×D₄×C₂₉ ◁ C₈×D₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#508	C₂	semidirect
2. C₂²×C₂₉×SD₃₂	C₂	semidirect
3. C₂₉×#3285	C₂	semidirect
4. C₂₉×#3280	C₂	semidirect
5. C₂₉×#2249	C₂	semidirect
6. C₂₉×#2217	C₂	semidirect
7. C₂₉×#2217	C₂	semidirect
8. C₂₉×#2211	C₂	semidirect
9. C₂₉×#2210	C₂	semidirect
10. C₂₉×#2189	C₂	semidirect
11. C₂₉×#2188	C₂	semidirect
12. C₂₉×#2186	C₂	semidirect
13. C₂₉×#2184	C₂	semidirect
14. C₄×C₂₉×SD₃₂	C₂	semidirect
15. D₄×C₁₆×C₂₉	C₂	semidirect
17. C₂×C₂₉×#135	C₂²	semidirect
23. C₂×C₂₉×Q₃₂	C₂²	semidirect
24. C₂×C₂₉×Q₃₂	C₂²	semidirect
30. C₂×C₂₉×SD₃₂	C₂²	semidirect
34. C₂²×C₁₆×C₂₉	C₂²	semidirect
36. C₂₉×#495	C₂²	semidirect
38. C₂₉×#467	C₂²	semidirect
47. C₄×Q₁₆×C₂₉	C₂²	semidirect
50. C₂₉×#367	C₂²	semidirect
51. C₂₉×C₄⋊C₁₆	C₂²	semidirect
52. C₂₉×#358	C₂²	semidirect
53. C₂₉×#358	C₂²	semidirect
54. C₂₉×#358	C₂²	semidirect
57. C₂₉×#357	C₂²	semidirect
59. C₂₉×C₂²⋊C₁₆	C₂²	semidirect
60. C₄×C₁₆×C₂₉	C₂²	semidirect
110. C₂₉×SD₃₂	D₄	semidirect
208. #33848	C₂₉	direct (N × H)
259. C₂×#508	C₂×C₂₉	semidirect
260. C₂²×SD₃₂	C₂×C₂₉	semidirect
261. #3285	C₂×C₂₉	semidirect
262. #3280	C₂×C₂₉	semidirect
263. #2249	C₂×C₂₉	semidirect
264. #2217	C₂×C₂₉	semidirect
265. #2217	C₂×C₂₉	semidirect
266. #2211	C₂×C₂₉	semidirect
267. #2210	C₂×C₂₉	semidirect
268. #2189	C₂×C₂₉	semidirect
269. #2188	C₂×C₂₉	semidirect
270. #2186	C₂×C₂₉	semidirect
271. #2184	C₂×C₂₉	semidirect
272. C₄×SD₃₂	C₂×C₂₉	semidirect
273. D₄×C₁₆	C₂×C₂₉	semidirect
289. C₂²×C₂₉	#508	semidirect
303. C₂×#135	C₂²×C₂₉	semidirect
309. C₂×Q₃₂	C₂²×C₂₉	semidirect
310. C₂×Q₃₂	C₂²×C₂₉	semidirect
316. C₂×SD₃₂	C₂²×C₂₉	semidirect
320. C₂²×C₁₆	C₂²×C₂₉	semidirect
322. #495	C₂²×C₂₉	semidirect
324. #467	C₂²×C₂₉	semidirect
333. C₄×Q₁₆	C₂²×C₂₉	semidirect
336. #367	C₂²×C₂₉	semidirect
337. C₄⋊C₁₆	C₂²×C₂₉	semidirect
338. #358	C₂²×C₂₉	semidirect
339. #358	C₂²×C₂₉	semidirect
340. #358	C₂²×C₂₉	semidirect
343. #357	C₂²×C₂₉	semidirect
345. C₂²⋊C₁₆	C₂²×C₂₉	semidirect
346. C₄×C₁₆	C₂²×C₂₉	semidirect
404. SD₃₂	D₄×C₂₉	semidirect
425. C₂₉	#33848	direct (N × H)
568. C₂²	C₂₉×#508	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#508	2
C₂²×C₂₉×SD₃₂	2
C₂₉×#3285	2
C₂₉×#3280	2
C₂₉×#2249	2
C₂₉×#2217	2
C₂₉×#2211	2
C₂₉×#2210	2
C₂₉×#2189	2
C₂₉×#2188	2
C₂₉×#2186	2
C₂₉×#2184	2
C₄×C₂₉×SD₃₂	2
D₄×C₁₆×C₂₉	2
#33848	29

Subgroups — C29×#33848 #20328748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#33848 #20328748