Subgroups — C₂₉×#25684 #20320584

Order 7424.

1024 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#542	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×#488	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2629	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2034	C₂	1	1	yes	maximal, characteristic
8	C₂₉×#2033	C₂	1	1	yes	maximal, characteristic
9	C₂₉×#1990	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1959	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1865	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	C₂₉×#1862	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#542	—	2	4	no	—
17	C₂₉×#542	—	2	4	no	—
18	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#126	—	2	1	no	—
20	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#124	—	2	1	no	—
22	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#123	—	2	1	no	—
24	C₂×C₂₉×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
30	C₂₉×#501	—	2	4	no	—
31	C₂₉×#488	—	2	4	no	—
32	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
35	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
36	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
37	C₂×C₂₉×#103	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×#102	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
48	C₂₉×#398	—	2	1	no	—
49	C₂₉×#398	—	2	1	no	—
50	C₂₉×#396	—	2	1	no	—
51	C₂₉×#396	—	2	1	no	—
52	C₂₉×#389	C₂²	1	1	yes	characteristic
53	C₂₉×#389	C₂²	1	1	yes	characteristic
54	C₂₉×#384	C₂²	1	1	yes	characteristic
55	C₂₉×#380	C₂²	1	1	yes	characteristic
56	C₂₉×#380	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×#340	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	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₂₉	—	2	1	no	—
66	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₂₉	—	2	1	no	—
68	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
73	C₂₉×C₄⋊Q₈	—	2	2	no	—
74	C₂₉×C₄⋊Q₈	D₄	1	4	yes	—
75	C₂₉×#126	—	2	8	no	—
76	C₂₉×#125	—	2	2	no	—
77	C₂₉×#125	—	2	2	no	—
78	C₂₉×#124	—	2	8	no	—
79	C₂₉×#124	—	2	2	no	—
80	C₂₉×#124	D₄	1	4	yes	—
81	C₂₉×#123	—	2	8	no	—
82	C₂₉×C₂²⋊Q₈	—	2	8	no	—
83	C₂₉×C₂²⋊Q₈	—	2	2	no	—
84	C₂₉×C₂²⋊Q₈	—	2	2	no	—
85	C₂₉×#121	—	2	2	no	—
86	C₂₉×#121	—	2	2	no	—
87	C₄×Q₈×C₂₉	—	2	2	no	—
88	C₄×Q₈×C₂₉	—	2	2	no	—
89	C₄×D₄×C₂₉	—	2	2	no	—
90	C₄×D₄×C₂₉	—	2	2	no	—
91	C₂₉×#117	—	2	2	no	—
92	C₂₉×#117	—	2	2	no	—
93	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₂₉	—	2	1	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	D₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₂₉	—	2	1	no	—
120	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
122	C₂₉×#107	—	2	2	no	—
123	C₂₉×#107	—	2	2	no	—
124	C₂₉×#106	—	2	2	no	—
125	C₂₉×#106	—	2	2	no	—
126	C₂₉×#103	—	2	2	no	—
127	C₂₉×#103	—	2	2	no	—
128	C₂₉×#103	—	2	2	no	—
129	C₂₉×#103	—	2	2	no	—
130	C₂₉×#102	—	2	2	no	—
131	C₂₉×#102	—	2	2	no	—
132	C₂₉×#102	—	2	2	no	—
133	C₂₉×#102	—	2	2	no	—
134	C₂₉×C₂²⋊C₈	—	2	2	no	—
135	C₂₉×C₂²⋊C₈	—	2	2	no	—
136	C₂₉×#97	—	2	2	no	—
137	C₄×C₈×C₂₉	—	2	2	no	—
138	C₂₉×#95	—	2	1	no	—
139	C₂₉×#95	—	2	1	no	—
140	C₂₉×#95	—	2	1	no	—
141	C₂₉×#95	—	2	1	no	—
142	C₂⁴×C₂₉	—	2	1	no	—
143	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
144	C₂×Q₈×C₂₉	—	2	4	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	—	2	1	no	—
149	C₂×Q₈×C₂₉	—	2	1	no	—
150	C₂×Q₈×C₂₉	—	8	1	no	—
151	C₂×Q₈×C₂₉	—	8	1	no	—
152	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
153	C₂×D₄×C₂₉	—	2	4	no	—
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	—	8	1	no	—
160	C₂×D₄×C₂₉	—	8	1	no	—
161	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
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	4	no	—
166	C₂²×C₄×C₂₉	—	2	1	no	—
167	C₂²×C₄×C₂₉	—	2	1	no	—
168	C₂²×C₄×C₂₉	—	2	1	no	—
169	C₂²×C₄×C₂₉	—	2	1	no	—
170	C₂²×C₄×C₂₉	—	2	1	no	—
171	C₂²×C₄×C₂₉	—	2	1	no	—
172	C₂²×C₄×C₂₉	—	2	1	no	—
173	C₂²×C₄×C₂₉	—	2	1	no	—
174	C₂²×C₄×C₂₉	—	2	1	no	—
175	C₂²×C₄×C₂₉	—	2	1	no	—
176	C₂²×C₄×C₂₉	—	8	1	no	—
177	C₂²×C₄×C₂₉	—	8	1	no	—
178	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
191	C₂×C₈×C₂₉	—	2	1	no	—
192	C₂×C₈×C₂₉	—	2	1	no	—
193	C₂×C₈×C₂₉	—	2	1	no	—
194	C₂×C₈×C₂₉	#41	1	2	yes	—
195	C₂×C₈×C₂₉	#41	1	2	yes	—
196	C₄⋊C₄×C₂₉	—	2	4	no	—
197	C₄⋊C₄×C₂₉	—	2	4	no	—
198	C₄⋊C₄×C₂₉	—	2	4	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	—	2	1	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	—	8	1	no	—
215	C₄⋊C₄×C₂₉	—	8	1	no	—
216	C₄⋊C₄×C₂₉	—	8	1	no	—
217	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
218	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
219	C₂²⋊C₄×C₂₉	—	2	4	no	—
220	C₂²⋊C₄×C₂₉	—	2	4	no	—
221	C₂²⋊C₄×C₂₉	—	2	4	no	—
222	C₂²⋊C₄×C₂₉	—	2	4	no	—
223	C₂²⋊C₄×C₂₉	—	2	4	no	—
224	C₂²⋊C₄×C₂₉	—	2	2	no	—
225	C₂²⋊C₄×C₂₉	—	2	2	no	—
226	C₂²⋊C₄×C₂₉	—	8	1	no	—
227	C₂²⋊C₄×C₂₉	—	8	1	no	—
228	C₄²×C₂₉	—	2	4	no	—
229	C₄²×C₂₉	—	2	1	no	—
230	C₄²×C₂₉	—	2	1	no	—
231	C₄²×C₂₉	C₂×D₄	1	2	yes	—
232	C₄²×C₂₉	C₂×D₄	1	2	yes	—
233	#25684	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂³×C₂₉	—	2	1	no	—
235	C₂³×C₂₉	—	2	2	no	—
236	C₂³×C₂₉	—	2	1	no	—
237	C₂³×C₂₉	—	2	1	no	—
238	C₂³×C₂₉	—	2	1	no	—
239	C₂³×C₂₉	—	2	1	no	—
240	C₂³×C₂₉	—	2	1	no	—
241	C₂³×C₂₉	—	2	1	no	—
242	C₂³×C₂₉	—	4	1	no	—
243	C₂³×C₂₉	—	4	1	no	—
244	C₂³×C₂₉	—	4	1	no	—
245	C₂³×C₂₉	—	4	1	no	—
246	C₂³×C₂₉	—	4	1	no	—
247	C₂³×C₂₉	—	4	1	no	—
248	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
249	Q₈×C₂₉	—	2	2	no	—
250	Q₈×C₂₉	—	2	2	no	—
251	Q₈×C₂₉	—	4	1	no	—
252	Q₈×C₂₉	—	4	1	no	—
253	Q₈×C₂₉	—	8	4	no	—
254	D₄×C₂₉	—	2	2	no	—
255	D₄×C₂₉	—	2	2	no	—
256	D₄×C₂₉	—	4	1	no	—
257	D₄×C₂₉	—	4	1	no	—
258	D₄×C₂₉	—	8	4	no	—
259	C₂×C₄×C₂₉	—	2	1	no	—
260	C₂×C₄×C₂₉	—	2	1	no	—
261	C₂×C₄×C₂₉	—	2	1	no	—
262	C₂×C₄×C₂₉	—	2	1	no	—
263	C₂×C₄×C₂₉	—	2	1	no	—
264	C₂×C₄×C₂₉	—	2	2	no	—
265	C₂×C₄×C₂₉	—	2	1	no	—
266	C₂×C₄×C₂₉	—	2	2	no	—
267	C₂×C₄×C₂₉	—	2	1	no	—
268	C₂×C₄×C₂₉	—	2	2	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	—	2	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	—	4	1	no	—
291	C₂×C₄×C₂₉	—	4	1	no	—
292	C₂×C₄×C₂₉	—	4	1	no	—
293	C₂×C₄×C₂₉	—	4	1	no	—
294	C₂×C₄×C₂₉	—	4	1	no	—
295	C₂×C₄×C₂₉	—	4	1	no	—
296	C₂×C₄×C₂₉	—	4	1	no	—
297	C₂×C₄×C₂₉	—	8	4	no	—
298	C₂×C₄×C₂₉	#120	1	2	yes	—
299	C₂×C₄×C₂₉	#120	1	2	yes	—
300	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
303	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
304	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
305	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
306	C₈×C₂₉	—	2	2	no	—
307	C₈×C₂₉	—	2	2	no	—
308	C₈×C₂₉	—	4	1	no	—
309	C₈×C₂₉	—	4	1	no	—
310	C₂×#542	C₂×C₂₉	1	1	yes	characteristic
311	C₂×#501	C₂×C₂₉	1	1	yes	characteristic, complemented
312	C₂×#488	C₂×C₂₉	1	1	yes	characteristic, complemented
313	#2629	C₂×C₂₉	1	1	yes	characteristic, complemented
314	#2036	C₂×C₂₉	1	1	yes	characteristic, complemented
315	#2035	C₂×C₂₉	1	1	yes	characteristic, complemented
316	#2034	C₂×C₂₉	1	1	yes	characteristic
317	#2033	C₂×C₂₉	1	1	yes	characteristic
318	#1990	C₂×C₂₉	1	1	yes	characteristic, complemented
319	#1959	C₂×C₂₉	1	1	yes	characteristic, complemented
320	#1865	C₂×C₂₉	1	1	yes	characteristic, complemented
321	#1864	C₂×C₂₉	1	1	yes	characteristic, complemented
322	#1863	C₂×C₂₉	1	1	yes	characteristic, complemented
323	#1862	C₂×C₂₉	1	1	yes	characteristic, complemented
324	#1750	C₂×C₂₉	1	1	yes	characteristic, complemented
325	C₂²×C₂₉	—	4	1	no	—
326	C₂²×C₂₉	—	4	1	no	—
327	C₂²×C₂₉	—	4	1	no	—
328	C₂²×C₂₉	—	4	2	no	—
329	C₂²×C₂₉	—	4	1	no	—
330	C₂²×C₂₉	—	4	1	no	—
331	C₂²×C₂₉	—	4	2	no	—
332	C₂²×C₂₉	—	4	1	no	—
333	C₂²×C₂₉	—	4	1	no	—
334	C₂²×C₂₉	—	4	2	no	—
335	C₂²×C₂₉	—	8	1	no	—
336	C₂²×C₂₉	—	8	1	no	—
337	C₂²×C₂₉	—	8	1	no	—
338	C₂²×C₂₉	—	8	1	no	—
339	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
340	C₂²×C₂₉	#532	1	1	yes	characteristic
341	C₂²×C₂₉	#536	1	1	yes	characteristic
342	C₂²×C₂₉	#576	1	1	yes	characteristic
343	C₂²×C₂₉	#577	1	1	yes	characteristic
344	C₂²×C₂₉	#577	1	1	yes	characteristic
345	C₂²×C₂₉	#578	1	1	yes	characteristic
346	C₄×C₂₉	—	2	2	no	—
347	C₄×C₂₉	—	2	2	no	—
348	C₄×C₂₉	—	4	1	no	—
349	C₄×C₂₉	—	4	2	no	—
350	C₄×C₂₉	—	4	1	no	—
351	C₄×C₂₉	—	4	2	no	—
352	C₄×C₂₉	—	4	2	no	—
353	C₄×C₂₉	—	4	1	no	—
354	C₄×C₂₉	—	8	1	no	—
355	C₄×C₂₉	—	8	1	no	—
356	C₄×C₂₉	—	8	1	no	—
357	C₄×C₂₉	—	8	1	no	—
358	C₄×C₂₉	#547	1	1	yes	characteristic
359	C₄×C₂₉	#547	1	1	yes	characteristic
360	C₄×C₂₉	#548	1	1	yes	characteristic
361	C₄×C₂₉	#548	1	1	yes	characteristic
362	#542	—	2	4	no	—
363	#542	—	2	4	no	—
364	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
365	C₂×#126	—	2	1	no	—
366	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic
367	C₂×#124	—	2	1	no	—
368	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
369	C₂×#123	—	2	1	no	—
370	C₂×C₂²⋊Q₈	—	2	1	no	—
371	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
372	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
373	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
374	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
375	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
376	#501	—	2	4	no	—
377	#488	—	2	4	no	—
378	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
379	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
380	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
381	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
382	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
383	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
384	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
385	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
386	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
387	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
388	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
389	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
390	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
391	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
392	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
393	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
394	#398	—	2	1	no	—
395	#398	—	2	1	no	—
396	#396	—	2	1	no	—
397	#396	—	2	1	no	—
398	#389	C₂²×C₂₉	1	1	yes	characteristic
399	#389	C₂²×C₂₉	1	1	yes	characteristic
400	#384	C₂²×C₂₉	1	1	yes	characteristic
401	#380	C₂²×C₂₉	1	1	yes	characteristic
402	#380	C₂²×C₂₉	1	1	yes	characteristic
403	#340	C₂²×C₂₉	1	1	yes	characteristic
404	#340	C₂²×C₂₉	1	1	yes	characteristic
405	#340	C₂²×C₂₉	1	1	yes	characteristic
406	#340	C₂²×C₂₉	1	1	yes	characteristic
407	#336	C₂²×C₂₉	1	1	yes	characteristic
408	#336	C₂²×C₂₉	1	1	yes	characteristic
409	C₂×C₂₉	—	8	1	no	—
410	C₂×C₂₉	—	8	2	no	—
411	C₂×C₂₉	#2432	1	1	yes	characteristic
412	C₂×C₂₉	#3012	1	1	yes	characteristic
413	C₂×C₂₉	#3013	1	1	yes	characteristic
414	C₂×C₂₉	#3178	1	1	yes	characteristic
415	C₂×C₂₉	#3179	1	1	yes	characteristic
416	C₂×C₂₉	#3243	1	1	yes	characteristic
417	C₂×C₂₉	#3244	1	1	yes	characteristic
418	C₂²×Q₈	—	2	1	no	—
419	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
420	C₂²×D₄	—	2	1	no	—
421	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
422	C₂³×C₄	—	2	1	no	—
423	C₂³×C₄	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×C₈	C₂³×C₂₉	1	1	yes	characteristic
428	C₄⋊Q₈	—	2	2	no	—
429	C₄⋊Q₈	D₄×C₂₉	1	4	yes	—
430	#126	—	2	8	no	—
431	#125	—	2	2	no	—
432	#125	—	2	2	no	—
433	#124	—	2	8	no	—
434	#124	—	2	2	no	—
435	#124	D₄×C₂₉	1	4	yes	—
436	#123	—	2	8	no	—
437	C₂²⋊Q₈	—	2	8	no	—
438	C₂²⋊Q₈	—	2	2	no	—
439	C₂²⋊Q₈	—	2	2	no	—
440	#121	—	2	2	no	—
441	#121	—	2	2	no	—
442	C₄×Q₈	—	2	2	no	—
443	C₄×Q₈	—	2	2	no	—
444	C₄×D₄	—	2	2	no	—
445	C₄×D₄	—	2	2	no	—
446	#117	—	2	2	no	—
447	#117	—	2	2	no	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	—	2	1	no	—
450	C₂×C₄⋊C₄	—	2	1	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	—	2	1	no	—
455	C₂×C₄⋊C₄	—	2	1	no	—
456	C₂×C₄⋊C₄	—	2	1	no	—
457	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
458	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	—	2	1	no	—
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	C₂×C₂²⋊C₄	—	2	1	no	—
472	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
473	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
474	C₂×C₄²	—	2	1	no	—
475	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
477	#107	—	2	2	no	—
478	#107	—	2	2	no	—
479	#106	—	2	2	no	—
480	#106	—	2	2	no	—
481	#103	—	2	2	no	—
482	#103	—	2	2	no	—
483	#103	—	2	2	no	—
484	#103	—	2	2	no	—
485	#102	—	2	2	no	—
486	#102	—	2	2	no	—
487	#102	—	2	2	no	—
488	#102	—	2	2	no	—
489	C₂²⋊C₈	—	2	2	no	—
490	C₂²⋊C₈	—	2	2	no	—
491	#97	—	2	2	no	—
492	C₄×C₈	—	2	2	no	—
493	#95	—	2	1	no	—
494	#95	—	2	1	no	—
495	#95	—	2	1	no	—
496	#95	—	2	1	no	—
497	C₂₉	#25684	1	1	yes	characteristic, direct product factor, Sylow
498	C₂⁴	—	2	1	no	—
499	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
500	C₂×Q₈	—	2	4	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	8	1	no	—
507	C₂×Q₈	—	8	1	no	—
508	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
509	C₂×D₄	—	2	4	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	8	1	no	—
516	C₂×D₄	—	8	1	no	—
517	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	8	1	no	—
533	C₂²×C₄	—	8	1	no	—
534	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
535	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
536	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
538	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
539	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	#41×C₂₉	1	2	yes	—
551	C₂×C₈	#41×C₂₉	1	2	yes	—
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	—	2	4	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	4	2	no	—
568	C₄⋊C₄	—	4	2	no	—
569	C₄⋊C₄	—	8	1	no	—
570	C₄⋊C₄	—	8	1	no	—
571	C₄⋊C₄	—	8	1	no	—
572	C₄⋊C₄	—	8	1	no	—
573	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
574	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	4	no	—
580	C₂²⋊C₄	—	2	2	no	—
581	C₂²⋊C₄	—	2	2	no	—
582	C₂²⋊C₄	—	8	1	no	—
583	C₂²⋊C₄	—	8	1	no	—
584	C₄²	—	2	4	no	—
585	C₄²	—	2	1	no	—
586	C₄²	—	2	1	no	—
587	C₄²	C₂×D₄×C₂₉	1	2	yes	—
588	C₄²	C₂×D₄×C₂₉	1	2	yes	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	—	4	1	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
604	Q₈	—	2	2	no	—
605	Q₈	—	2	2	no	—
606	Q₈	—	4	1	no	—
607	Q₈	—	4	1	no	—
608	Q₈	—	8	4	no	—
609	D₄	—	2	2	no	—
610	D₄	—	2	2	no	—
611	D₄	—	4	1	no	—
612	D₄	—	4	1	no	—
613	D₄	—	8	4	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	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	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	8	4	no	—
653	C₂×C₄	C₂₉×#120	1	2	yes	—
654	C₂×C₄	C₂₉×#120	1	2	yes	—
655	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
656	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
657	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
658	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
659	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
660	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
661	C₈	—	2	2	no	—
662	C₈	—	2	2	no	—
663	C₈	—	4	1	no	—
664	C₈	—	4	1	no	—
665	C₂²	—	4	1	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	2	no	—
670	C₂²	—	4	1	no	—
671	C₂²	—	4	1	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	4	1	no	—
674	C₂²	—	4	1	no	—
675	C₂²	—	8	1	no	—
676	C₂²	—	8	1	no	—
677	C₂²	—	8	1	no	—
678	C₂²	—	8	1	no	—
679	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
680	C₂²	C₂₉×#532	1	1	yes	characteristic
681	C₂²	C₂₉×#536	1	1	yes	characteristic
682	C₂²	C₂₉×#576	1	1	yes	characteristic
683	C₂²	C₂₉×#577	1	1	yes	characteristic
684	C₂²	C₂₉×#577	1	1	yes	characteristic
685	C₂²	C₂₉×#578	1	1	yes	characteristic
686	C₄	—	2	2	no	—
687	C₄	—	2	2	no	—
688	C₄	—	4	1	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	1	no	—
694	C₄	—	8	1	no	—
695	C₄	—	8	1	no	—
696	C₄	—	8	1	no	—
697	C₄	—	8	1	no	—
698	C₄	C₂₉×#547	1	1	yes	characteristic
699	C₄	C₂₉×#547	1	1	yes	characteristic
700	C₄	C₂₉×#548	1	1	yes	characteristic
701	C₄	C₂₉×#548	1	1	yes	characteristic
702	C₂	—	8	1	no	—
703	C₂	—	8	2	no	—
704	C₂	C₂₉×#2432	1	1	yes	characteristic
705	C₂	C₂₉×#3012	1	1	yes	characteristic
706	C₂	C₂₉×#3013	1	1	yes	characteristic
707	C₂	C₂₉×#3178	1	1	yes	characteristic
708	C₂	C₂₉×#3179	1	1	yes	characteristic
709	C₂	C₂₉×#3243	1	1	yes	characteristic
710	C₂	C₂₉×#3244	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₂₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₉×#501	C₂	semidirect
3. C₂×C₂₉×#488	C₂	semidirect
4. C₂₉×#2629	C₂	semidirect
5. C₂₉×#2036	C₂	semidirect
6. C₂₉×#2035	C₂	semidirect
9. C₂₉×#1990	C₂	semidirect
10. C₂₉×#1959	C₂	semidirect
11. C₂₉×#1865	C₂	semidirect
12. C₂₉×#1864	C₂	semidirect
13. C₂₉×#1863	C₂	semidirect
14. C₂₉×#1862	C₂	semidirect
15. C₂₉×#1750	C₂	semidirect
233. #25684	C₂₉	direct (N × H)
311. C₂×#501	C₂×C₂₉	semidirect
312. C₂×#488	C₂×C₂₉	semidirect
313. #2629	C₂×C₂₉	semidirect
314. #2036	C₂×C₂₉	semidirect
315. #2035	C₂×C₂₉	semidirect
318. #1990	C₂×C₂₉	semidirect
319. #1959	C₂×C₂₉	semidirect
320. #1865	C₂×C₂₉	semidirect
321. #1864	C₂×C₂₉	semidirect
322. #1863	C₂×C₂₉	semidirect
323. #1862	C₂×C₂₉	semidirect
324. #1750	C₂×C₂₉	semidirect
497. C₂₉	#25684	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#542	2
C₂×C₂₉×#501	2
C₂×C₂₉×#488	2
C₂₉×#2629	2
C₂₉×#2036	2
C₂₉×#2035	2
C₂₉×#2034	2
C₂₉×#2033	2
C₂₉×#1990	2
C₂₉×#1959	2
C₂₉×#1865	2
C₂₉×#1864	2
C₂₉×#1863	2
C₂₉×#1862	2
C₂₉×#1750	2
#25684	29

Subgroups — C29×#25684 #20320584

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#25684 #20320584