Subgroups — C₂₉×#23040 #20317940

Order 7424.

1026 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#468	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×#428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2362	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2361	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1943	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1927	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1925	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1875	C₂	1	1	yes	maximal, characteristic
11	C₂₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×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	—	2	1	no	—
22	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
25	C₂₉×#468	C₄	1	8	yes	complemented
26	C₂₉×#440	—	2	4	no	—
27	C₂₉×#428	—	2	4	no	—
28	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#106	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×#103	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×#102	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
42	C₂₉×#391	C₂²	1	1	yes	characteristic
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	C₂₉×#385	—	2	1	no	—
52	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
53	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
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	—	2	1	no	—
67	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
68	C₂×SD₁₆×C₂₉	—	2	2	no	—
69	C₂×SD₁₆×C₂₉	—	2	2	no	—
70	C₂×SD₁₆×C₂₉	C₂×C₄	1	4	yes	complemented
71	C₂×M₁₆×C₂₉	—	2	2	no	—
72	C₂×M₁₆×C₂₉	—	2	2	no	—
73	C₂×M₁₆×C₂₉	C₂×C₄	1	4	yes	complemented
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	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
78	C₂₉×C₂²⋊Q₈	—	2	2	no	—
79	C₂₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	complemented
80	C₂₉×#121	—	2	2	no	—
81	C₂₉×#121	C₂×C₄	1	4	yes	—
82	C₄×Q₈×C₂₉	—	2	2	no	—
83	C₄×Q₈×C₂₉	—	4	1	no	—
84	C₄×D₄×C₂₉	—	2	2	no	—
85	C₄×D₄×C₂₉	—	4	1	no	—
86	C₄×D₄×C₂₉	—	4	4	no	—
87	C₂₉×#117	—	2	2	no	—
88	C₂₉×#117	—	4	1	no	—
89	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
91	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
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×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
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	—	2	1	no	—
114	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
116	C₂₉×#107	—	2	2	no	—
117	C₂₉×#107	C₂×C₄	1	4	yes	complemented
118	C₂₉×#107	D₄	1	4	yes	complemented
119	C₂₉×#106	—	2	2	no	—
120	C₂₉×#106	—	2	2	no	—
121	C₂₉×#103	—	2	2	no	—
122	C₂₉×#103	—	4	1	no	—
123	C₂₉×#103	C₂×C₄	1	4	yes	complemented
124	C₂₉×#102	—	2	2	no	—
125	C₂₉×#102	—	4	1	no	—
126	C₂₉×#102	C₂×C₄	1	4	yes	complemented
127	C₂₉×C₂²⋊C₈	—	2	2	no	—
128	C₂₉×#97	—	2	2	no	—
129	C₄×C₈×C₂₉	—	2	2	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	—	2	1	no	—
136	C₂₉×#95	D₄	1	1	yes	characteristic
137	C₂₉×#95	D₄	1	1	yes	characteristic
138	C₂⁴×C₂₉	—	2	1	no	—
139	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
145	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
146	C₂×D₄×C₂₉	—	2	4	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	—	2	1	no	—
152	C₂×D₄×C₂₉	—	4	2	no	—
153	C₂×D₄×C₂₉	—	4	2	no	—
154	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
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	—	2	1	no	—
166	C₂²×C₄×C₂₉	—	4	2	no	—
167	C₂²×C₄×C₂₉	—	4	2	no	—
168	C₂²×C₄×C₂₉	—	4	2	no	—
169	C₂²×C₄×C₂₉	—	4	2	no	—
170	C₂²×C₄×C₂₉	—	8	1	no	—
171	C₂²×C₄×C₂₉	—	8	1	no	—
172	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
173	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₂₉	#41	1	2	yes	—
179	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
180	SD₁₆×C₂₉	—	2	8	no	—
181	M₁₆×C₂₉	—	2	8	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	—	2	1	no	—
187	C₂×C₈×C₂₉	—	2	1	no	—
188	C₂×C₈×C₂₉	—	2	1	no	—
189	C₂×C₈×C₂₉	—	2	1	no	—
190	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
191	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
192	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
193	C₂×C₈×C₂₉	#41	1	2	yes	—
194	C₄⋊C₄×C₂₉	—	2	4	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	—	2	1	no	—
200	C₄⋊C₄×C₂₉	—	2	1	no	—
201	C₄⋊C₄×C₂₉	—	2	1	no	—
202	C₄⋊C₄×C₂₉	—	2	1	no	—
203	C₄⋊C₄×C₂₉	—	4	2	no	—
204	C₄⋊C₄×C₂₉	—	4	2	no	—
205	C₄⋊C₄×C₂₉	—	4	2	no	—
206	C₄⋊C₄×C₂₉	—	4	2	no	—
207	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
208	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
209	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
210	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
211	C₂²⋊C₄×C₂₉	—	2	4	no	—
212	C₂²⋊C₄×C₂₉	—	2	4	no	—
213	C₂²⋊C₄×C₂₉	—	2	2	no	—
214	C₂²⋊C₄×C₂₉	—	4	1	no	—
215	C₂²⋊C₄×C₂₉	—	4	2	no	—
216	C₂²⋊C₄×C₂₉	—	4	2	no	—
217	C₂²⋊C₄×C₂₉	—	4	2	no	—
218	C₂²⋊C₄×C₂₉	—	8	1	no	—
219	C₄²×C₂₉	—	2	1	no	—
220	C₄²×C₂₉	—	2	1	no	—
221	C₄²×C₂₉	—	2	1	no	—
222	C₄²×C₂₉	—	2	1	no	—
223	C₄²×C₂₉	—	4	2	no	—
224	C₄²×C₂₉	—	4	2	no	—
225	C₄²×C₂₉	—	4	2	no	—
226	C₄²×C₂₉	—	4	2	no	—
227	#23040	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂³×C₂₉	—	2	1	no	—
229	C₂³×C₂₉	—	2	1	no	—
230	C₂³×C₂₉	—	2	1	no	—
231	C₂³×C₂₉	—	2	1	no	—
232	C₂³×C₂₉	—	2	1	no	—
233	C₂³×C₂₉	—	2	1	no	—
234	C₂³×C₂₉	—	2	2	no	—
235	C₂³×C₂₉	—	4	1	no	—
236	C₂³×C₂₉	—	4	1	no	—
237	C₂³×C₂₉	—	4	1	no	—
238	C₂³×C₂₉	—	4	1	no	—
239	C₂³×C₂₉	—	4	1	no	—
240	C₂³×C₂₉	—	4	1	no	—
241	C₂³×C₂₉	C₄×D₄	1	2	yes	—
242	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
243	Q₈×C₂₉	—	2	2	no	—
244	Q₈×C₂₉	—	2	2	no	—
245	Q₈×C₂₉	—	4	1	no	—
246	Q₈×C₂₉	—	4	1	no	—
247	D₄×C₂₉	—	2	2	no	—
248	D₄×C₂₉	—	2	2	no	—
249	D₄×C₂₉	—	4	8	no	—
250	D₄×C₂₉	—	4	1	no	—
251	D₄×C₂₉	—	4	1	no	—
252	C₂×C₄×C₂₉	—	2	1	no	—
253	C₂×C₄×C₂₉	—	2	1	no	—
254	C₂×C₄×C₂₉	—	2	1	no	—
255	C₂×C₄×C₂₉	—	2	1	no	—
256	C₂×C₄×C₂₉	—	2	2	no	—
257	C₂×C₄×C₂₉	—	2	2	no	—
258	C₂×C₄×C₂₉	—	2	2	no	—
259	C₂×C₄×C₂₉	—	2	2	no	—
260	C₂×C₄×C₂₉	—	2	2	no	—
261	C₂×C₄×C₂₉	—	2	2	no	—
262	C₂×C₄×C₂₉	—	2	2	no	—
263	C₂×C₄×C₂₉	—	2	1	no	—
264	C₂×C₄×C₂₉	—	2	1	no	—
265	C₂×C₄×C₂₉	—	2	2	no	—
266	C₂×C₄×C₂₉	—	2	2	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	—	2	1	no	—
273	C₂×C₄×C₂₉	—	2	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	—	4	1	no	—
289	C₂×C₄×C₂₉	—	4	1	no	—
290	C₂×C₄×C₂₉	—	8	4	no	—
291	C₂×C₄×C₂₉	—	8	4	no	—
292	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
293	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
294	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
295	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
299	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
300	C₈×C₂₉	—	2	2	no	—
301	C₈×C₂₉	—	4	1	no	—
302	C₈×C₂₉	—	4	1	no	—
303	C₈×C₂₉	C₄×D₄	1	4	yes	complemented
304	C₂×#468	C₂×C₂₉	1	1	yes	characteristic
305	C₂×#440	C₂×C₂₉	1	1	yes	characteristic, complemented
306	C₂×#428	C₂×C₂₉	1	1	yes	characteristic, complemented
307	#2362	C₂×C₂₉	1	1	yes	characteristic, complemented
308	#2361	C₂×C₂₉	1	1	yes	characteristic
309	#1968	C₂×C₂₉	1	1	yes	characteristic, complemented
310	#1943	C₂×C₂₉	1	1	yes	characteristic, complemented
311	#1927	C₂×C₂₉	1	1	yes	characteristic, complemented
312	#1925	C₂×C₂₉	1	1	yes	characteristic, complemented
313	#1875	C₂×C₂₉	1	1	yes	characteristic
314	#1872	C₂×C₂₉	1	1	yes	characteristic, complemented
315	#1864	C₂×C₂₉	1	1	yes	characteristic, complemented
316	#1863	C₂×C₂₉	1	1	yes	characteristic, complemented
317	C₄×#107	C₂×C₂₉	1	1	yes	characteristic, complemented
318	#1753	C₂×C₂₉	1	1	yes	characteristic, complemented
319	C₂²×C₂₉	—	2	2	no	—
320	C₂²×C₂₉	—	2	2	no	—
321	C₂²×C₂₉	—	2	2	no	—
322	C₂²×C₂₉	—	4	1	no	—
323	C₂²×C₂₉	—	4	1	no	—
324	C₂²×C₂₉	—	4	1	no	—
325	C₂²×C₂₉	—	4	1	no	—
326	C₂²×C₂₉	—	4	2	no	—
327	C₂²×C₂₉	—	4	2	no	—
328	C₂²×C₂₉	—	4	2	no	—
329	C₂²×C₂₉	—	8	1	no	—
330	C₂²×C₂₉	—	8	1	no	—
331	C₂²×C₂₉	—	8	1	no	—
332	C₂²×C₂₉	—	8	1	no	—
333	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
334	C₂²×C₂₉	D₄²	1	1	yes	characteristic
335	C₂²×C₂₉	#547	1	1	yes	characteristic
336	C₂²×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
337	C₂²×C₂₉	#575	1	1	yes	characteristic
338	C₂²×C₂₉	#577	1	1	yes	characteristic
339	C₂²×C₂₉	#578	1	1	yes	characteristic
340	C₄×C₂₉	—	2	2	no	—
341	C₄×C₂₉	—	2	2	no	—
342	C₄×C₂₉	—	4	1	no	—
343	C₄×C₂₉	—	4	2	no	—
344	C₄×C₂₉	—	4	2	no	—
345	C₄×C₂₉	—	4	2	no	—
346	C₄×C₂₉	—	4	1	no	—
347	C₄×C₂₉	—	4	2	no	—
348	C₄×C₂₉	—	4	2	no	—
349	C₄×C₂₉	—	4	1	no	—
350	C₄×C₂₉	—	8	1	no	—
351	C₄×C₂₉	—	8	1	no	—
352	C₄×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
353	C₄×C₂₉	#520	1	1	yes	characteristic
354	C₄×C₂₉	#548	1	1	yes	characteristic
355	C₄×C₂₉	#553	1	1	yes	characteristic
356	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
357	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
358	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
359	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
360	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
361	C₂×C₄×D₄	—	2	1	no	—
362	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
363	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
364	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
365	#468	C₄×C₂₉	1	8	yes	complemented
366	#440	—	2	4	no	—
367	#428	—	2	4	no	—
368	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
369	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
370	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
371	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
372	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
373	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
374	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
375	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
376	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
377	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
378	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
379	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
380	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
381	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
382	#391	C₂²×C₂₉	1	1	yes	characteristic
383	#390	C₂²×C₂₉	1	1	yes	characteristic
384	#389	C₂²×C₂₉	1	1	yes	characteristic
385	#389	C₂²×C₂₉	1	1	yes	characteristic
386	#388	—	2	1	no	—
387	#388	—	2	1	no	—
388	#388	—	2	1	no	—
389	#387	—	2	1	no	—
390	#386	—	2	1	no	—
391	#385	—	2	1	no	—
392	C₄×C₄⋊C₄	—	2	1	no	—
393	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
394	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
395	C₄×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
396	#340	C₂²×C₂₉	1	1	yes	characteristic
397	#340	C₂²×C₂₉	1	1	yes	characteristic
398	#340	C₂²×C₂₉	1	1	yes	characteristic
399	#340	C₂²×C₂₉	1	1	yes	characteristic
400	#336	C₂²×C₂₉	1	1	yes	characteristic
401	#336	C₂²×C₂₉	1	1	yes	characteristic
402	C₂×C₂₉	—	4	2	no	—
403	C₂×C₂₉	—	8	2	no	—
404	C₂×C₂₉	#2361	1	1	yes	characteristic
405	C₂×C₂₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
406	C₂×C₂₉	#2947	1	1	yes	characteristic
407	C₂×C₂₉	#3272	1	1	yes	characteristic
408	C₂×C₂₉	#3277	1	1	yes	characteristic
409	C₂×C₂₉	#3343	1	1	yes	characteristic
410	C₂×C₂₉	#3350	1	1	yes	characteristic
411	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
412	C₂²×D₄	—	2	1	no	—
413	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
414	C₂³×C₄	—	2	1	no	—
415	C₂³×C₄	—	2	1	no	—
416	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
417	C₂×SD₁₆	—	2	2	no	—
418	C₂×SD₁₆	—	2	2	no	—
419	C₂×SD₁₆	C₂×C₄×C₂₉	1	4	yes	complemented
420	C₂×M₁₆	—	2	2	no	—
421	C₂×M₁₆	—	2	2	no	—
422	C₂×M₁₆	C₂×C₄×C₂₉	1	4	yes	complemented
423	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
424	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
425	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
426	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
427	C₂²⋊Q₈	—	2	2	no	—
428	C₂²⋊Q₈	C₂×C₄×C₂₉	1	4	yes	complemented
429	#121	—	2	2	no	—
430	#121	C₂×C₄×C₂₉	1	4	yes	—
431	C₄×Q₈	—	2	2	no	—
432	C₄×Q₈	—	4	1	no	—
433	C₄×D₄	—	2	2	no	—
434	C₄×D₄	—	4	1	no	—
435	C₄×D₄	—	4	4	no	—
436	#117	—	2	2	no	—
437	#117	—	4	1	no	—
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	—	2	2	no	—
440	C₂×C₄⋊C₄	—	2	1	no	—
441	C₂×C₄⋊C₄	—	2	1	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	4	1	no	—
445	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
458	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
459	C₂×C₄²	—	2	1	no	—
460	C₂×C₄²	—	2	1	no	—
461	C₂×C₄²	—	2	1	no	—
462	C₂×C₄²	—	2	1	no	—
463	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
465	#107	—	2	2	no	—
466	#107	C₂×C₄×C₂₉	1	4	yes	complemented
467	#107	D₄×C₂₉	1	4	yes	complemented
468	#106	—	2	2	no	—
469	#106	—	2	2	no	—
470	#103	—	2	2	no	—
471	#103	—	4	1	no	—
472	#103	C₂×C₄×C₂₉	1	4	yes	complemented
473	#102	—	2	2	no	—
474	#102	—	4	1	no	—
475	#102	C₂×C₄×C₂₉	1	4	yes	complemented
476	C₂²⋊C₈	—	2	2	no	—
477	#97	—	2	2	no	—
478	C₄×C₈	—	2	2	no	—
479	#95	—	2	1	no	—
480	#95	—	2	1	no	—
481	#95	—	2	1	no	—
482	#95	—	2	1	no	—
483	#95	—	2	1	no	—
484	#95	—	2	1	no	—
485	#95	D₄×C₂₉	1	1	yes	characteristic
486	#95	D₄×C₂₉	1	1	yes	characteristic
487	C₂₉	#23040	1	1	yes	characteristic, direct product factor, Sylow
488	C₂⁴	—	2	1	no	—
489	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
496	C₂×D₄	—	2	4	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	4	2	no	—
503	C₂×D₄	—	4	2	no	—
504	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
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	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	—	4	2	no	—
520	C₂²×C₄	—	8	1	no	—
521	C₂²×C₄	—	8	1	no	—
522	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
523	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
526	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
527	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
528	C₂²×C₄	#41×C₂₉	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
530	SD₁₆	—	2	8	no	—
531	M₁₆	—	2	8	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
541	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
542	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
543	C₂×C₈	#41×C₂₉	1	2	yes	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	4	2	no	—
554	C₄⋊C₄	—	4	2	no	—
555	C₄⋊C₄	—	4	2	no	—
556	C₄⋊C₄	—	4	2	no	—
557	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
558	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
559	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
560	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
561	C₂²⋊C₄	—	2	4	no	—
562	C₂²⋊C₄	—	2	4	no	—
563	C₂²⋊C₄	—	2	2	no	—
564	C₂²⋊C₄	—	4	1	no	—
565	C₂²⋊C₄	—	4	2	no	—
566	C₂²⋊C₄	—	4	2	no	—
567	C₂²⋊C₄	—	4	2	no	—
568	C₂²⋊C₄	—	8	1	no	—
569	C₄²	—	2	1	no	—
570	C₄²	—	2	1	no	—
571	C₄²	—	2	1	no	—
572	C₄²	—	2	1	no	—
573	C₄²	—	4	2	no	—
574	C₄²	—	4	2	no	—
575	C₄²	—	4	2	no	—
576	C₄²	—	4	2	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	1	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	4	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	1	no	—
590	C₂³	C₄×D₄×C₂₉	1	2	yes	—
591	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
592	Q₈	—	2	2	no	—
593	Q₈	—	2	2	no	—
594	Q₈	—	4	1	no	—
595	Q₈	—	4	1	no	—
596	D₄	—	2	2	no	—
597	D₄	—	2	2	no	—
598	D₄	—	4	8	no	—
599	D₄	—	4	1	no	—
600	D₄	—	4	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	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	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	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	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	8	4	no	—
640	C₂×C₄	—	8	4	no	—
641	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
642	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
643	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
644	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
645	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
646	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
647	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
648	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
649	C₈	—	2	2	no	—
650	C₈	—	4	1	no	—
651	C₈	—	4	1	no	—
652	C₈	C₄×D₄×C₂₉	1	4	yes	complemented
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	8	1	no	—
664	C₂²	—	8	1	no	—
665	C₂²	—	8	1	no	—
666	C₂²	—	8	1	no	—
667	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
668	C₂²	D₄²×C₂₉	1	1	yes	characteristic
669	C₂²	C₂₉×#547	1	1	yes	characteristic
670	C₂²	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
671	C₂²	C₂₉×#575	1	1	yes	characteristic
672	C₂²	C₂₉×#577	1	1	yes	characteristic
673	C₂²	C₂₉×#578	1	1	yes	characteristic
674	C₄	—	2	2	no	—
675	C₄	—	2	2	no	—
676	C₄	—	4	2	no	—
677	C₄	—	4	2	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	2	no	—
680	C₄	—	4	2	no	—
681	C₄	—	4	1	no	—
682	C₄	—	4	1	no	—
683	C₄	—	4	2	no	—
684	C₄	—	8	1	no	—
685	C₄	—	8	1	no	—
686	C₄	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
687	C₄	C₂₉×#520	1	1	yes	characteristic
688	C₄	C₂₉×#548	1	1	yes	characteristic
689	C₄	C₂₉×#553	1	1	yes	characteristic
690	C₂	—	4	2	no	—
691	C₂	—	8	2	no	—
692	C₂	C₂₉×#2361	1	1	yes	characteristic
693	C₂	C₄×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
694	C₂	C₂₉×#2947	1	1	yes	characteristic
695	C₂	C₂₉×#3272	1	1	yes	characteristic
696	C₂	C₂₉×#3277	1	1	yes	characteristic
697	C₂	C₂₉×#3343	1	1	yes	characteristic
698	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×#428	C₂	semidirect
4. C₂₉×#2362	C₂	semidirect
6. C₂₉×#1968	C₂	semidirect
7. C₂₉×#1943	C₂	semidirect
8. C₂₉×#1927	C₂	semidirect
9. C₂₉×#1925	C₂	semidirect
11. C₂₉×#1872	C₂	semidirect
12. C₂₉×#1864	C₂	semidirect
13. C₂₉×#1863	C₂	semidirect
14. C₄×C₂₉×#107	C₂	semidirect
15. C₂₉×#1753	C₂	semidirect
25. C₂₉×#468	C₄	semidirect
70. C₂×SD₁₆×C₂₉	C₂×C₄	semidirect
73. C₂×M₁₆×C₂₉	C₂×C₄	semidirect
79. C₂₉×C₂²⋊Q₈	C₂×C₄	semidirect
117. C₂₉×#107	C₂×C₄	semidirect
118. C₂₉×#107	D₄	semidirect
123. C₂₉×#103	C₂×C₄	semidirect
126. C₂₉×#102	C₂×C₄	semidirect
227. #23040	C₂₉	direct (N × H)
303. C₈×C₂₉	C₄×D₄	semidirect
305. C₂×#440	C₂×C₂₉	semidirect
306. C₂×#428	C₂×C₂₉	semidirect
307. #2362	C₂×C₂₉	semidirect
309. #1968	C₂×C₂₉	semidirect
310. #1943	C₂×C₂₉	semidirect
311. #1927	C₂×C₂₉	semidirect
312. #1925	C₂×C₂₉	semidirect
314. #1872	C₂×C₂₉	semidirect
315. #1864	C₂×C₂₉	semidirect
316. #1863	C₂×C₂₉	semidirect
317. C₄×#107	C₂×C₂₉	semidirect
318. #1753	C₂×C₂₉	semidirect
365. #468	C₄×C₂₉	semidirect
419. C₂×SD₁₆	C₂×C₄×C₂₉	semidirect
422. C₂×M₁₆	C₂×C₄×C₂₉	semidirect
428. C₂²⋊Q₈	C₂×C₄×C₂₉	semidirect
466. #107	C₂×C₄×C₂₉	semidirect
467. #107	D₄×C₂₉	semidirect
472. #103	C₂×C₄×C₂₉	semidirect
475. #102	C₂×C₄×C₂₉	semidirect
487. C₂₉	#23040	direct (N × H)
652. C₈	C₄×D₄×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#468	2
C₂×C₂₉×#440	2
C₂×C₂₉×#428	2
C₂₉×#2362	2
C₂₉×#2361	2
C₂₉×#1968	2
C₂₉×#1943	2
C₂₉×#1927	2
C₂₉×#1925	2
C₂₉×#1875	2
C₂₉×#1872	2
C₂₉×#1864	2
C₂₉×#1863	2
C₄×C₂₉×#107	2
C₂₉×#1753	2
#23040	29

Subgroups — C29×#23040 #20317940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#23040 #20317940