Subgroups — C₂₉×#24346 #20319246

Order 7424.

1064 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#478	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#440	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2538	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2057	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2025	C₂	1	1	yes	maximal, characteristic
8	C₂₉×#2023	C₂	1	1	yes	maximal, characteristic
9	C₂₉×#1992	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1985	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1880	C₂	1	1	yes	maximal, characteristic
12	C₂₉×#1880	C₂	1	1	yes	maximal, characteristic
13	C₂₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
17	C₂₉×#557	—	2	4	no	—
18	C₂₉×#557	—	2	4	no	—
19	C₂×C₂₉×C₄⋊Q₈	—	2	1	no	—
20	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#125	—	2	1	no	—
22	C₂×C₂₉×#125	—	2	1	no	—
23	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₄×Q₈×C₂₉	—	2	1	no	—
27	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
32	C₂₉×#478	—	2	4	no	—
33	C₂₉×#440	—	2	4	no	—
34	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
35	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
36	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
37	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
41	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
42	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
43	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
44	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
45	C₂₉×#396	—	2	1	no	—
46	C₂₉×#396	—	2	1	no	—
47	C₂₉×#390	C₂²	1	1	yes	characteristic
48	C₂₉×#390	C₂²	1	1	yes	characteristic
49	C₂₉×#389	C₂²	1	1	yes	characteristic
50	C₂₉×#389	C₂²	1	1	yes	characteristic
51	C₂₉×#384	C₂²	1	1	yes	characteristic
52	C₂₉×#380	—	2	1	no	—
53	C₂₉×#340	C₂²	1	1	yes	characteristic
54	C₂₉×#340	C₂²	1	1	yes	characteristic
55	C₂₉×#340	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×#336	C₂²	1	1	yes	characteristic
60	C₂₉×#336	C₂²	1	1	yes	characteristic
61	C₂₉×#336	C₂²	1	1	yes	characteristic
62	C₂₉×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₂₉	—	2	1	no	—
64	C₂²×Q₈×C₂₉	D₄	1	1	yes	characteristic
65	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₂₉	—	2	1	no	—
68	C₂×SD₁₆×C₂₉	—	2	2	no	—
69	C₂×SD₁₆×C₂₉	—	2	2	no	—
70	C₂×SD₁₆×C₂₉	Q₈	1	4	yes	complemented
71	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
75	C₂₉×C₄⋊Q₈	—	2	8	no	—
76	C₂₉×C₄⋊Q₈	—	2	2	no	—
77	C₂₉×C₄⋊Q₈	—	2	2	no	—
78	C₂₉×#125	—	2	8	no	—
79	C₂₉×#125	—	2	8	no	—
80	C₂₉×#125	—	2	2	no	—
81	C₂₉×#125	—	2	2	no	—
82	C₂₉×#125	—	2	2	no	—
83	C₂₉×#125	D₄	1	4	yes	—
84	C₂₉×C₂²⋊Q₈	—	4	4	no	—
85	C₄×Q₈×C₂₉	—	2	8	no	—
86	C₄×Q₈×C₂₉	—	2	2	no	—
87	C₄×Q₈×C₂₉	—	2	2	no	—
88	C₄×Q₈×C₂₉	—	2	2	no	—
89	C₄×Q₈×C₂₉	—	2	2	no	—
90	C₄×Q₈×C₂₉	—	2	2	no	—
91	C₄×Q₈×C₂₉	—	2	2	no	—
92	C₄×Q₈×C₂₉	—	2	2	no	—
93	C₄×Q₈×C₂₉	D₄	1	4	yes	—
94	C₄×D₄×C₂₉	—	2	2	no	—
95	C₄×D₄×C₂₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
122	C₂×C₄²×C₂₉	—	2	1	no	—
123	C₂×C₄²×C₂₉	—	2	1	no	—
124	C₂×C₄²×C₂₉	—	2	1	no	—
125	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
128	C₂₉×#107	—	2	2	no	—
129	C₂₉×#107	—	2	2	no	—
130	C₂₉×#106	—	2	2	no	—
131	C₂₉×C₄⋊C₈	—	2	2	no	—
132	C₂₉×#103	—	2	2	no	—
133	C₂₉×#103	—	2	2	no	—
134	C₂₉×#103	—	2	2	no	—
135	C₂₉×#102	—	2	2	no	—
136	C₂₉×#102	—	2	2	no	—
137	C₂₉×#102	—	2	2	no	—
138	C₂₉×#97	—	2	2	no	—
139	C₂₉×#95	—	2	1	no	—
140	C₂₉×#95	—	2	1	no	—
141	C₂⁴×C₂₉	—	2	1	no	—
142	C₂×Q₈×C₂₉	—	2	4	no	—
143	C₂×Q₈×C₂₉	—	2	2	no	—
144	C₂×Q₈×C₂₉	—	2	2	no	—
145	C₂×Q₈×C₂₉	—	2	1	no	—
146	C₂×Q₈×C₂₉	—	2	1	no	—
147	C₂×Q₈×C₂₉	—	2	1	no	—
148	C₂×Q₈×C₂₉	—	4	1	no	—
149	C₂×Q₈×C₂₉	—	4	2	no	—
150	C₂×Q₈×C₂₉	—	4	2	no	—
151	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
152	C₂×Q₈×C₂₉	C₂×Q₈	1	2	yes	—
153	C₂×Q₈×C₂₉	#41	1	2	yes	—
154	C₂×D₄×C₂₉	—	2	1	no	—
155	C₂×D₄×C₂₉	—	2	1	no	—
156	C₂×D₄×C₂₉	—	2	1	no	—
157	C₂×D₄×C₂₉	—	2	1	no	—
158	C₂×D₄×C₂₉	—	2	1	no	—
159	C₂×D₄×C₂₉	C₂×Q₈	1	2	yes	—
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	—	2	1	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	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
177	SD₁₆×C₂₉	—	2	8	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	—	2	1	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	C₂×Q₈	1	2	yes	—
190	C₄⋊C₄×C₂₉	—	2	4	no	—
191	C₄⋊C₄×C₂₉	—	2	4	no	—
192	C₄⋊C₄×C₂₉	—	2	4	no	—
193	C₄⋊C₄×C₂₉	—	2	4	no	—
194	C₄⋊C₄×C₂₉	—	2	4	no	—
195	C₄⋊C₄×C₂₉	—	2	4	no	—
196	C₄⋊C₄×C₂₉	—	2	4	no	—
197	C₄⋊C₄×C₂₉	—	2	4	no	—
198	C₄⋊C₄×C₂₉	—	2	2	no	—
199	C₄⋊C₄×C₂₉	—	2	2	no	—
200	C₄⋊C₄×C₂₉	—	2	2	no	—
201	C₄⋊C₄×C₂₉	—	2	1	no	—
202	C₄⋊C₄×C₂₉	—	2	1	no	—
203	C₄⋊C₄×C₂₉	—	2	1	no	—
204	C₄⋊C₄×C₂₉	—	2	1	no	—
205	C₄⋊C₄×C₂₉	—	2	1	no	—
206	C₄⋊C₄×C₂₉	—	2	1	no	—
207	C₄⋊C₄×C₂₉	—	2	1	no	—
208	C₄⋊C₄×C₂₉	—	2	1	no	—
209	C₄⋊C₄×C₂₉	—	2	1	no	—
210	C₄⋊C₄×C₂₉	—	4	2	no	—
211	C₄⋊C₄×C₂₉	—	4	2	no	—
212	C₄⋊C₄×C₂₉	—	4	2	no	—
213	C₄⋊C₄×C₂₉	—	8	1	no	—
214	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
215	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
216	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
217	C₂²⋊C₄×C₂₉	—	4	2	no	—
218	C₂²⋊C₄×C₂₉	—	4	2	no	—
219	C₂²⋊C₄×C₂₉	—	4	2	no	—
220	C₂²⋊C₄×C₂₉	—	8	1	no	—
221	C₂²⋊C₄×C₂₉	—	8	1	no	—
222	C₄²×C₂₉	—	2	4	no	—
223	C₄²×C₂₉	—	2	4	no	—
224	C₄²×C₂₉	—	2	4	no	—
225	C₄²×C₂₉	—	2	1	no	—
226	C₄²×C₂₉	—	2	1	no	—
227	C₄²×C₂₉	—	2	1	no	—
228	C₄²×C₂₉	—	2	1	no	—
229	C₄²×C₂₉	C₂×D₄	1	2	yes	—
230	C₄²×C₂₉	C₂×D₄	1	2	yes	—
231	#24346	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂³×C₂₉	—	2	2	no	—
233	C₂³×C₂₉	—	4	1	no	—
234	C₂³×C₂₉	—	4	1	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	C₂²×D₄	1	1	yes	characteristic
240	Q₈×C₂₉	—	2	2	no	—
241	Q₈×C₂₉	—	2	2	no	—
242	Q₈×C₂₉	—	2	2	no	—
243	Q₈×C₂₉	—	4	4	no	—
244	Q₈×C₂₉	—	4	8	no	—
245	Q₈×C₂₉	C₂²⋊Q₈	1	4	yes	complemented
246	D₄×C₂₉	—	2	2	no	—
247	D₄×C₂₉	—	2	2	no	—
248	D₄×C₂₉	—	4	1	no	—
249	D₄×C₂₉	—	4	1	no	—
250	C₂×C₄×C₂₉	—	2	2	no	—
251	C₂×C₄×C₂₉	—	2	1	no	—
252	C₂×C₄×C₂₉	—	2	2	no	—
253	C₂×C₄×C₂₉	—	2	2	no	—
254	C₂×C₄×C₂₉	—	2	1	no	—
255	C₂×C₄×C₂₉	—	2	1	no	—
256	C₂×C₄×C₂₉	—	2	1	no	—
257	C₂×C₄×C₂₉	—	2	1	no	—
258	C₂×C₄×C₂₉	—	2	1	no	—
259	C₂×C₄×C₂₉	—	2	1	no	—
260	C₂×C₄×C₂₉	—	2	1	no	—
261	C₂×C₄×C₂₉	—	2	2	no	—
262	C₂×C₄×C₂₉	—	2	1	no	—
263	C₂×C₄×C₂₉	—	2	2	no	—
264	C₂×C₄×C₂₉	—	2	2	no	—
265	C₂×C₄×C₂₉	—	2	1	no	—
266	C₂×C₄×C₂₉	—	2	1	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	—	4	1	no	—
272	C₂×C₄×C₂₉	—	4	1	no	—
273	C₂×C₄×C₂₉	—	4	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	—	8	4	no	—
287	C₂×C₄×C₂₉	#120	1	2	yes	—
288	C₂×C₄×C₂₉	#120	1	2	yes	—
289	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
290	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
293	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
295	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
296	C₈×C₂₉	—	2	2	no	—
297	C₈×C₂₉	—	4	1	no	—
298	C₈×C₂₉	—	4	1	no	—
299	C₈×C₂₉	—	4	1	no	—
300	C₂×#557	C₂×C₂₉	1	1	yes	characteristic, complemented
301	C₂×#478	C₂×C₂₉	1	1	yes	characteristic
302	C₂×#440	C₂×C₂₉	1	1	yes	characteristic
303	#2538	C₂×C₂₉	1	1	yes	characteristic
304	#2059	C₂×C₂₉	1	1	yes	characteristic, complemented
305	#2057	C₂×C₂₉	1	1	yes	characteristic, complemented
306	#2025	C₂×C₂₉	1	1	yes	characteristic
307	#2023	C₂×C₂₉	1	1	yes	characteristic
308	#1992	C₂×C₂₉	1	1	yes	characteristic, complemented
309	#1985	C₂×C₂₉	1	1	yes	characteristic, complemented
310	#1880	C₂×C₂₉	1	1	yes	characteristic
311	#1880	C₂×C₂₉	1	1	yes	characteristic
312	#1865	C₂×C₂₉	1	1	yes	characteristic, complemented
313	#1863	C₂×C₂₉	1	1	yes	characteristic, complemented
314	#1803	C₂×C₂₉	1	1	yes	characteristic, complemented
315	C₂²×C₂₉	—	4	2	no	—
316	C₂²×C₂₉	—	4	2	no	—
317	C₂²×C₂₉	—	4	2	no	—
318	C₂²×C₂₉	—	8	1	no	—
319	C₂²×C₂₉	—	8	1	no	—
320	C₂²×C₂₉	—	8	1	no	—
321	C₂²×C₂₉	—	8	1	no	—
322	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
323	C₂²×C₂₉	#548	1	1	yes	characteristic
324	C₂²×C₂₉	D₄×Q₈	1	1	yes	characteristic
325	C₂²×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
326	C₂²×C₂₉	#575	1	1	yes	characteristic
327	C₂²×C₂₉	#577	1	1	yes	characteristic
328	C₂²×C₂₉	#578	1	1	yes	characteristic
329	C₄×C₂₉	—	2	4	no	—
330	C₄×C₂₉	—	2	2	no	—
331	C₄×C₂₉	—	2	2	no	—
332	C₄×C₂₉	—	2	2	no	—
333	C₄×C₂₉	—	4	1	no	—
334	C₄×C₂₉	—	4	2	no	—
335	C₄×C₂₉	—	4	2	no	—
336	C₄×C₂₉	—	4	1	no	—
337	C₄×C₂₉	—	4	1	no	—
338	C₄×C₂₉	—	4	2	no	—
339	C₄×C₂₉	—	8	1	no	—
340	C₄×C₂₉	—	8	1	no	—
341	C₄×C₂₉	—	8	1	no	—
342	C₄×C₂₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
343	C₄×C₂₉	#536	1	1	yes	characteristic
344	C₄×C₂₉	#548	1	1	yes	characteristic
345	C₄×C₂₉	D₄×Q₈	1	1	yes	characteristic
346	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
347	#557	—	2	4	no	—
348	#557	—	2	4	no	—
349	C₂×C₄⋊Q₈	—	2	1	no	—
350	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
351	C₂×#125	—	2	1	no	—
352	C₂×#125	—	2	1	no	—
353	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic
354	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic
355	C₂×C₂²⋊Q₈	—	2	1	no	—
356	C₂×C₄×Q₈	—	2	1	no	—
357	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
358	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
359	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
360	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
361	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
362	#478	—	2	4	no	—
363	#440	—	2	4	no	—
364	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
365	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
366	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
367	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
368	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
369	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
370	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
371	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
372	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
373	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
374	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
375	#396	—	2	1	no	—
376	#396	—	2	1	no	—
377	#390	C₂²×C₂₉	1	1	yes	characteristic
378	#390	C₂²×C₂₉	1	1	yes	characteristic
379	#389	C₂²×C₂₉	1	1	yes	characteristic
380	#389	C₂²×C₂₉	1	1	yes	characteristic
381	#384	C₂²×C₂₉	1	1	yes	characteristic
382	#380	—	2	1	no	—
383	#340	C₂²×C₂₉	1	1	yes	characteristic
384	#340	C₂²×C₂₉	1	1	yes	characteristic
385	#340	C₂²×C₂₉	1	1	yes	characteristic
386	#340	C₂²×C₂₉	1	1	yes	characteristic
387	#340	C₂²×C₂₉	1	1	yes	characteristic
388	#340	C₂²×C₂₉	1	1	yes	characteristic
389	#336	C₂²×C₂₉	1	1	yes	characteristic
390	#336	C₂²×C₂₉	1	1	yes	characteristic
391	#336	C₂²×C₂₉	1	1	yes	characteristic
392	#336	C₂²×C₂₉	1	1	yes	characteristic
393	C₂×C₂₉	—	8	2	no	—
394	C₂×C₂₉	#2409	1	1	yes	characteristic
395	C₂×C₂₉	#3006	1	1	yes	characteristic
396	C₂×C₂₉	#3013	1	1	yes	characteristic
397	C₂×C₂₉	#3368	1	1	yes	characteristic
398	C₂×C₂₉	#3377	1	1	yes	characteristic
399	C₂×C₂₉	#3386	1	1	yes	characteristic
400	C₂×C₂₉	#3388	1	1	yes	characteristic
401	C₂²×Q₈	—	2	1	no	—
402	C₂²×Q₈	D₄×C₂₉	1	1	yes	characteristic
403	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
404	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
405	C₂³×C₄	—	2	1	no	—
406	C₂×SD₁₆	—	2	2	no	—
407	C₂×SD₁₆	—	2	2	no	—
408	C₂×SD₁₆	Q₈×C₂₉	1	4	yes	complemented
409	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
412	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
413	C₄⋊Q₈	—	2	8	no	—
414	C₄⋊Q₈	—	2	2	no	—
415	C₄⋊Q₈	—	2	2	no	—
416	#125	—	2	8	no	—
417	#125	—	2	8	no	—
418	#125	—	2	2	no	—
419	#125	—	2	2	no	—
420	#125	—	2	2	no	—
421	#125	D₄×C₂₉	1	4	yes	—
422	C₂²⋊Q₈	—	4	4	no	—
423	C₄×Q₈	—	2	8	no	—
424	C₄×Q₈	—	2	2	no	—
425	C₄×Q₈	—	2	2	no	—
426	C₄×Q₈	—	2	2	no	—
427	C₄×Q₈	—	2	2	no	—
428	C₄×Q₈	—	2	2	no	—
429	C₄×Q₈	—	2	2	no	—
430	C₄×Q₈	—	2	2	no	—
431	C₄×Q₈	D₄×C₂₉	1	4	yes	—
432	C₄×D₄	—	2	2	no	—
433	C₄×D₄	—	2	2	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	—	2	1	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	—	2	1	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
447	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
448	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	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	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
466	#107	—	2	2	no	—
467	#107	—	2	2	no	—
468	#106	—	2	2	no	—
469	C₄⋊C₈	—	2	2	no	—
470	#103	—	2	2	no	—
471	#103	—	2	2	no	—
472	#103	—	2	2	no	—
473	#102	—	2	2	no	—
474	#102	—	2	2	no	—
475	#102	—	2	2	no	—
476	#97	—	2	2	no	—
477	#95	—	2	1	no	—
478	#95	—	2	1	no	—
479	C₂₉	#24346	1	1	yes	characteristic, direct product factor, Sylow
480	C₂⁴	—	2	1	no	—
481	C₂×Q₈	—	2	4	no	—
482	C₂×Q₈	—	2	2	no	—
483	C₂×Q₈	—	2	2	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	4	1	no	—
488	C₂×Q₈	—	4	2	no	—
489	C₂×Q₈	—	4	2	no	—
490	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
491	C₂×Q₈	C₂×Q₈×C₂₉	1	2	yes	—
492	C₂×Q₈	#41×C₂₉	1	2	yes	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	C₂×Q₈×C₂₉	1	2	yes	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	4	2	no	—
507	C₂²×C₄	—	4	2	no	—
508	C₂²×C₄	—	4	2	no	—
509	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
512	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
513	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
514	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
515	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
516	SD₁₆	—	2	8	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	2	4	no	—
531	C₄⋊C₄	—	2	4	no	—
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	4	no	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	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	—	4	2	no	—
550	C₄⋊C₄	—	4	2	no	—
551	C₄⋊C₄	—	4	2	no	—
552	C₄⋊C₄	—	8	1	no	—
553	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
554	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
555	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	2	no	—
558	C₂²⋊C₄	—	4	2	no	—
559	C₂²⋊C₄	—	8	1	no	—
560	C₂²⋊C₄	—	8	1	no	—
561	C₄²	—	2	4	no	—
562	C₄²	—	2	4	no	—
563	C₄²	—	2	4	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	C₂×D₄×C₂₉	1	2	yes	—
569	C₄²	C₂×D₄×C₂₉	1	2	yes	—
570	C₂³	—	2	2	no	—
571	C₂³	—	4	1	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	4	1	no	—
577	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
578	Q₈	—	2	2	no	—
579	Q₈	—	2	2	no	—
580	Q₈	—	2	2	no	—
581	Q₈	—	4	4	no	—
582	Q₈	—	4	8	no	—
583	Q₈	C₂₉×C₂²⋊Q₈	1	4	yes	complemented
584	D₄	—	2	2	no	—
585	D₄	—	2	2	no	—
586	D₄	—	4	1	no	—
587	D₄	—	4	1	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	8	4	no	—
625	C₂×C₄	C₂₉×#120	1	2	yes	—
626	C₂×C₄	C₂₉×#120	1	2	yes	—
627	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
628	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
629	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
630	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
631	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
632	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
633	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
634	C₈	—	2	2	no	—
635	C₈	—	4	1	no	—
636	C₈	—	4	1	no	—
637	C₈	—	4	1	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	8	1	no	—
642	C₂²	—	8	1	no	—
643	C₂²	—	8	1	no	—
644	C₂²	—	8	1	no	—
645	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
646	C₂²	C₂₉×#548	1	1	yes	characteristic
647	C₂²	D₄×Q₈×C₂₉	1	1	yes	characteristic
648	C₂²	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
649	C₂²	C₂₉×#575	1	1	yes	characteristic
650	C₂²	C₂₉×#577	1	1	yes	characteristic
651	C₂²	C₂₉×#578	1	1	yes	characteristic
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	4	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	2	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	2	no	—
662	C₄	—	8	1	no	—
663	C₄	—	8	1	no	—
664	C₄	—	8	1	no	—
665	C₄	C₂×C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
666	C₄	C₂₉×#536	1	1	yes	characteristic
667	C₄	C₂₉×#548	1	1	yes	characteristic
668	C₄	D₄×Q₈×C₂₉	1	1	yes	characteristic
669	C₂	—	8	2	no	—
670	C₂	C₂₉×#2409	1	1	yes	characteristic
671	C₂	C₂₉×#3006	1	1	yes	characteristic
672	C₂	C₂₉×#3013	1	1	yes	characteristic
673	C₂	C₂₉×#3368	1	1	yes	characteristic
674	C₂	C₂₉×#3377	1	1	yes	characteristic
675	C₂	C₂₉×#3386	1	1	yes	characteristic
676	C₂	C₂₉×#3388	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₄×Q₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#557	C₂	semidirect
5. C₂₉×#2059	C₂	semidirect
6. C₂₉×#2057	C₂	semidirect
9. C₂₉×#1992	C₂	semidirect
10. C₂₉×#1985	C₂	semidirect
13. C₂₉×#1865	C₂	semidirect
14. C₂₉×#1863	C₂	semidirect
15. C₂₉×#1803	C₂	semidirect
70. C₂×SD₁₆×C₂₉	Q₈	semidirect
231. #24346	C₂₉	direct (N × H)
245. Q₈×C₂₉	C₂²⋊Q₈	semidirect
300. C₂×#557	C₂×C₂₉	semidirect
304. #2059	C₂×C₂₉	semidirect
305. #2057	C₂×C₂₉	semidirect
308. #1992	C₂×C₂₉	semidirect
309. #1985	C₂×C₂₉	semidirect
312. #1865	C₂×C₂₉	semidirect
313. #1863	C₂×C₂₉	semidirect
314. #1803	C₂×C₂₉	semidirect
408. C₂×SD₁₆	Q₈×C₂₉	semidirect
479. C₂₉	#24346	direct (N × H)
583. Q₈	C₂₉×C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#557	2
C₂×C₂₉×#478	2
C₂×C₂₉×#440	2
C₂₉×#2538	2
C₂₉×#2059	2
C₂₉×#2057	2
C₂₉×#2025	2
C₂₉×#2023	2
C₂₉×#1992	2
C₂₉×#1985	2
C₂₉×#1880	2
C₂₉×#1865	2
C₂₉×#1863	2
C₂₉×#1803	2
#24346	29

Subgroups — C29×#24346 #20319246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#24346 #20319246