Subgroups — C₂₉×#34393 #20329293

Order 7424.

2510 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#532	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2377	C₂	1	4	yes	maximal, complemented
3	C₂₉×#2366	C₂	1	2	yes	maximal, complemented
4	C₂₉×#2365	C₂	1	2	yes	maximal, complemented
5	C₂₉×#2357	C₂	1	2	yes	maximal, complemented
6	C₂₉×#2349	C₂	1	2	yes	maximal, complemented
7	C₂₉×#2341	C₂	1	2	yes	maximal, complemented
8	C₂₉×#2339	C₂	1	2	yes	maximal, complemented
9	C₂₉×#2326	C₂	1	4	yes	maximal, complemented
10	C₂₉×#2324	C₂	1	4	yes	maximal, complemented
11	C₂₉×#2318	C₂	1	4	yes	maximal, complemented
12	C₂₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#2283	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₂₉	C₂²	1	2	yes	—
15	C₂₉×#532	C₄	1	16	yes	complemented
16	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×#124	C₂²	1	2	yes	—
19	C₂×C₂₉×#121	C₂²	1	2	yes	—
20	C₂×C₂₉×#121	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₂₉	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₂₉	C₂²	1	4	yes	—
23	C₂×C₄×D₄×C₂₉	C₂²	1	4	yes	—
24	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
26	C₂×C₂₉×#117	C₂²	1	2	yes	—
27	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
28	C₂₉×#391	C₂²	1	4	yes	—
29	C₂₉×#390	C₂²	1	8	yes	—
30	C₂₉×#390	C₂²	1	4	yes	—
31	C₂₉×#390	C₂²	1	4	yes	—
32	C₂₉×#389	C₂²	1	4	yes	—
33	C₂₉×#388	C₂²	1	8	yes	—
34	C₂₉×#388	C₂²	1	8	yes	—
35	C₂₉×#387	C₂²	1	8	yes	—
36	C₂₉×#386	C₂²	1	8	yes	—
37	C₂₉×#386	C₂²	1	8	yes	—
38	C₂₉×#385	C₂²	1	8	yes	—
39	C₂₉×#385	C₂²	1	8	yes	—
40	C₂₉×#384	C₂²	1	2	yes	—
41	C₂₉×#383	C₂²	1	2	yes	—
42	C₂₉×#382	C₂²	1	1	yes	characteristic
43	C₂₉×#382	C₂²	1	1	yes	characteristic
44	C₂₉×#382	C₂²	1	2	yes	—
45	C₂₉×#381	C₂²	1	2	yes	—
46	C₂₉×#381	C₂²	1	4	yes	—
47	C₂₉×#380	C₂²	1	2	yes	—
48	C₂₉×#380	C₂²	1	1	yes	characteristic
49	C₂₉×#380	C₂²	1	1	yes	characteristic
50	C₂₉×#380	C₂²	1	2	yes	—
51	C₂₉×#380	C₂²	1	4	yes	—
52	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
53	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
54	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
55	C₄×C₄⋊C₄×C₂₉	C₂²	1	4	yes	—
56	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
57	C₄×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
58	C₂₉×#376	C₂²	1	2	yes	—
59	C₂×C₂₉×#95	C₂²	1	4	yes	—
60	C₂×#41×C₂₉	—	4	8	no	—
61	C₂×#41×C₂₉	C₂×C₄	1	16	yes	complemented
62	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
63	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
64	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
65	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
66	C₂²×D₄×C₂₉	C₂³	1	4	yes	—
67	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₂₉	C₂³	1	8	yes	—
70	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
72	C₂₉×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
73	C₂₉×#127	C₂×C₄	1	8	yes	—
74	C₂₉×#124	C₂×C₄	1	16	yes	complemented
75	C₂₉×#121	C₂×C₄	1	16	yes	complemented
76	C₂₉×#121	C₂×C₄	1	16	yes	complemented
77	C₄×Q₈×C₂₉	—	4	8	no	—
78	C₄×D₄×C₂₉	—	4	8	no	—
79	C₄×D₄×C₂₉	—	4	8	no	—
80	C₄×D₄×C₂₉	C₂×C₄	1	16	yes	complemented
81	C₄×D₄×C₂₉	C₂×C₄	1	16	yes	complemented
82	C₂₉×#117	—	4	4	no	—
83	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₂₉	C₂³	1	8	yes	—
89	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
92	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
93	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
94	C₂×C₂²⋊C₄×C₂₉	C₂³	1	8	yes	—
95	C₂×C₂²⋊C₄×C₂₉	C₂³	1	8	yes	—
96	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₂₉	C₂³	1	8	yes	—
98	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
100	C₂×C₄²×C₂₉	C₂×C₄	1	8	yes	complemented
101	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
102	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
103	C₂×C₄²×C₂₉	C₂³	1	8	yes	—
104	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
108	C₂₉×#95	C₂³	1	2	yes	—
109	C₂₉×#95	C₂³	1	2	yes	—
110	C₂₉×#95	C₂³	1	8	yes	—
111	C₂₉×#95	C₂³	1	4	yes	—
112	C₂₉×#95	C₂³	1	2	yes	—
113	C₂₉×#95	C₂³	1	2	yes	—
114	C₂₉×#95	C₂³	1	2	yes	—
115	C₂₉×#95	C₂³	1	2	yes	—
116	C₂₉×#95	C₂³	1	4	yes	—
117	C₂₉×#95	C₂³	1	4	yes	—
118	C₂₉×#95	C₂³	1	8	yes	—
119	C₂⁴×C₂₉	C₂⁴	1	1	yes	characteristic
120	C₂⁴×C₂₉	C₂⁴	1	4	yes	—
121	#41×C₂₉	—	4	32	no	—
122	C₂×Q₈×C₂₉	—	2	8	no	—
123	C₂×Q₈×C₂₉	C₂²×C₄	1	8	yes	—
124	C₂×D₄×C₂₉	—	2	4	no	—
125	C₂×D₄×C₂₉	—	2	8	no	—
126	C₂×D₄×C₂₉	—	2	4	no	—
127	C₂×D₄×C₂₉	—	4	4	no	—
128	C₂×D₄×C₂₉	—	4	8	no	—
129	C₂×D₄×C₂₉	C₂²×C₄	1	8	yes	—
130	C₂×D₄×C₂₉	C₂²×C₄	1	8	yes	—
131	C₂×D₄×C₂₉	C₂²×C₄	1	8	yes	—
132	C₂×D₄×C₂₉	C₂²×C₄	1	16	yes	—
133	C₂²×C₄×C₂₉	—	2	2	no	—
134	C₂²×C₄×C₂₉	—	2	4	no	—
135	C₂²×C₄×C₂₉	—	2	2	no	—
136	C₂²×C₄×C₂₉	—	4	2	no	—
137	C₂²×C₄×C₂₉	—	4	8	no	—
138	C₂²×C₄×C₂₉	—	4	8	no	—
139	C₂²×C₄×C₂₉	—	4	8	no	—
140	C₂²×C₄×C₂₉	—	4	8	no	—
141	C₂²×C₄×C₂₉	C₂²×C₄	1	4	yes	—
142	C₂²×C₄×C₂₉	C₂²×C₄	1	4	yes	—
143	C₂²×C₄×C₂₉	C₂²×C₄	1	4	yes	—
144	C₂²×C₄×C₂₉	C₂²×C₄	1	16	yes	—
145	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
150	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
151	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
153	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
154	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
156	C₄⋊C₄×C₂₉	—	2	4	no	—
157	C₄⋊C₄×C₂₉	—	2	4	no	—
158	C₄⋊C₄×C₂₉	—	2	4	no	—
159	C₄⋊C₄×C₂₉	—	2	4	no	—
160	C₄⋊C₄×C₂₉	—	4	4	no	—
161	C₄⋊C₄×C₂₉	—	4	4	no	—
162	C₄⋊C₄×C₂₉	—	4	8	no	—
163	C₄⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
164	C₄⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
165	C₂²⋊C₄×C₂₉	—	4	8	no	—
166	C₂²⋊C₄×C₂₉	—	4	4	no	—
167	C₂²⋊C₄×C₂₉	—	4	2	no	—
168	C₂²⋊C₄×C₂₉	—	4	2	no	—
169	C₂²⋊C₄×C₂₉	—	4	8	no	—
170	C₂²⋊C₄×C₂₉	—	4	8	no	—
171	C₂²⋊C₄×C₂₉	C₂²×C₄	1	16	yes	—
172	C₂²⋊C₄×C₂₉	C₂²×C₄	1	16	yes	—
173	C₄²×C₂₉	—	2	8	no	—
174	C₄²×C₂₉	—	2	8	no	—
175	C₄²×C₂₉	—	4	8	no	—
176	C₄²×C₂₉	C₂²×C₄	1	4	yes	—
177	C₄²×C₂₉	C₂²×C₄	1	4	yes	—
178	C₄²×C₂₉	C₂²×C₄	1	4	yes	—
179	C₄²×C₂₉	C₂²×C₄	1	4	yes	—
180	#34393	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂³×C₂₉	—	2	1	no	—
182	C₂³×C₂₉	—	2	4	no	—
183	C₂³×C₂₉	—	2	8	no	—
184	C₂³×C₂₉	—	2	2	no	—
185	C₂³×C₂₉	—	2	1	no	—
186	C₂³×C₂₉	—	2	4	no	—
187	C₂³×C₂₉	—	2	2	no	—
188	C₂³×C₂₉	—	2	8	no	—
189	C₂³×C₂₉	C₂³×C₄	1	8	yes	—
190	C₂³×C₂₉	C₂³×C₄	1	2	yes	—
191	C₂³×C₂₉	C₂⁵	1	1	yes	characteristic
192	Q₈×C₂₉	—	2	16	no	—
193	D₄×C₂₉	—	2	16	no	—
194	D₄×C₂₉	—	2	16	no	—
195	D₄×C₂₉	—	4	8	no	—
196	D₄×C₂₉	—	4	16	no	—
197	C₂×C₄×C₂₉	—	2	8	no	—
198	C₂×C₄×C₂₉	—	2	1	no	—
199	C₂×C₄×C₂₉	—	2	2	no	—
200	C₂×C₄×C₂₉	—	2	1	no	—
201	C₂×C₄×C₂₉	—	2	2	no	—
202	C₂×C₄×C₂₉	—	2	2	no	—
203	C₂×C₄×C₂₉	—	2	8	no	—
204	C₂×C₄×C₂₉	—	2	8	no	—
205	C₂×C₄×C₂₉	—	2	4	no	—
206	C₂×C₄×C₂₉	—	2	4	no	—
207	C₂×C₄×C₂₉	—	2	4	no	—
208	C₂×C₄×C₂₉	—	2	4	no	—
209	C₂×C₄×C₂₉	—	2	4	no	—
210	C₂×C₄×C₂₉	—	2	4	no	—
211	C₂×C₄×C₂₉	—	2	4	no	—
212	C₂×C₄×C₂₉	—	2	4	no	—
213	C₂×C₄×C₂₉	—	2	4	no	—
214	C₂×C₄×C₂₉	—	2	4	no	—
215	C₂×C₄×C₂₉	—	2	4	no	—
216	C₂×C₄×C₂₉	—	2	4	no	—
217	C₂×C₄×C₂₉	—	4	4	no	—
218	C₂×C₄×C₂₉	—	4	16	no	—
219	C₂×C₄×C₂₉	—	8	16	no	—
220	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
221	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
222	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
223	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
224	C₂×C₄×C₂₉	C₂³×C₄	1	8	yes	—
225	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
226	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
227	C₂×C₄×C₂₉	H(5,𝔽₂)	1	4	yes	—
228	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
229	C₂×C₄×C₂₉	2₋¹⁺⁴	1	2	yes	—
230	C₂×#532	C₂×C₂₉	1	1	yes	characteristic
231	#2377	C₂×C₂₉	1	4	yes	complemented
232	#2366	C₂×C₂₉	1	2	yes	complemented
233	#2365	C₂×C₂₉	1	2	yes	complemented
234	#2357	C₂×C₂₉	1	2	yes	complemented
235	#2349	C₂×C₂₉	1	2	yes	complemented
236	#2341	C₂×C₂₉	1	2	yes	complemented
237	#2339	C₂×C₂₉	1	2	yes	complemented
238	#2326	C₂×C₂₉	1	4	yes	complemented
239	#2324	C₂×C₂₉	1	4	yes	complemented
240	#2318	C₂×C₂₉	1	4	yes	complemented
241	#2285	C₂×C₂₉	1	1	yes	characteristic, complemented
242	#2283	C₂×C₂₉	1	1	yes	characteristic, complemented
243	C₂²×C₂₉	—	2	2	no	—
244	C₂²×C₂₉	—	2	8	no	—
245	C₂²×C₂₉	—	2	2	no	—
246	C₂²×C₂₉	—	2	8	no	—
247	C₂²×C₂₉	—	2	2	no	—
248	C₂²×C₂₉	—	2	8	no	—
249	C₂²×C₂₉	—	4	8	no	—
250	C₂²×C₂₉	—	4	2	no	—
251	C₂²×C₂₉	—	4	8	no	—
252	C₂²×C₂₉	—	4	2	no	—
253	C₂²×C₂₉	C₂⁴×C₄	1	1	yes	characteristic
254	C₂²×C₂₉	C₂×H(5,𝔽₂)	1	2	yes	—
255	C₂²×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
256	C₂²×C₂₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
257	C₂²×C₂₉	#585	1	2	yes	—
258	C₄×C₂₉	—	2	2	no	—
259	C₄×C₂₉	—	2	8	no	—
260	C₄×C₂₉	—	2	2	no	—
261	C₄×C₂₉	—	2	2	no	—
262	C₄×C₂₉	—	2	2	no	—
263	C₄×C₂₉	—	4	4	no	—
264	C₄×C₂₉	—	4	4	no	—
265	C₄×C₂₉	—	4	4	no	—
266	C₄×C₂₉	—	4	4	no	—
267	C₄×C₂₉	#518	1	4	yes	—
268	C₄×C₂₉	#520	1	4	yes	—
269	C₂²×#41	C₂²×C₂₉	1	2	yes	—
270	#532	C₄×C₂₉	1	16	yes	complemented
271	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
272	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
273	C₂×#124	C₂²×C₂₉	1	2	yes	—
274	C₂×#121	C₂²×C₂₉	1	2	yes	—
275	C₂×#121	C₂²×C₂₉	1	2	yes	—
276	C₂×C₄×Q₈	C₂²×C₂₉	1	4	yes	—
277	C₂×C₄×D₄	C₂²×C₂₉	1	4	yes	—
278	C₂×C₄×D₄	C₂²×C₂₉	1	4	yes	—
279	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
280	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
281	C₂×#117	C₂²×C₂₉	1	2	yes	—
282	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
283	#391	C₂²×C₂₉	1	4	yes	—
284	#390	C₂²×C₂₉	1	8	yes	—
285	#390	C₂²×C₂₉	1	4	yes	—
286	#390	C₂²×C₂₉	1	4	yes	—
287	#389	C₂²×C₂₉	1	4	yes	—
288	#388	C₂²×C₂₉	1	8	yes	—
289	#388	C₂²×C₂₉	1	8	yes	—
290	#387	C₂²×C₂₉	1	8	yes	—
291	#386	C₂²×C₂₉	1	8	yes	—
292	#386	C₂²×C₂₉	1	8	yes	—
293	#385	C₂²×C₂₉	1	8	yes	—
294	#385	C₂²×C₂₉	1	8	yes	—
295	#384	C₂²×C₂₉	1	2	yes	—
296	#383	C₂²×C₂₉	1	2	yes	—
297	#382	C₂²×C₂₉	1	2	yes	—
298	#382	C₂²×C₂₉	1	1	yes	characteristic
299	#382	C₂²×C₂₉	1	1	yes	characteristic
300	#381	C₂²×C₂₉	1	4	yes	—
301	#381	C₂²×C₂₉	1	2	yes	—
302	#380	C₂²×C₂₉	1	4	yes	—
303	#380	C₂²×C₂₉	1	2	yes	—
304	#380	C₂²×C₂₉	1	1	yes	characteristic
305	#380	C₂²×C₂₉	1	1	yes	characteristic
306	#380	C₂²×C₂₉	1	2	yes	—
307	C₄×C₄⋊C₄	C₂²×C₂₉	1	4	yes	—
308	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
309	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
310	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
311	C₄×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
312	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
313	#376	C₂²×C₂₉	1	2	yes	—
314	C₂×#95	C₂²×C₂₉	1	4	yes	—
315	C₂×C₂₉	—	4	2	no	—
316	C₂×C₂₉	—	4	8	no	—
317	C₂×C₂₉	C₂×#518	1	1	yes	characteristic
318	C₂×C₂₉	C₂×#520	1	1	yes	characteristic
319	C₂×C₂₉	#3428	1	1	yes	characteristic
320	C₂×C₂₉	#3546	1	2	yes	—
321	C₂×C₂₉	#3554	1	2	yes	—
322	C₂×#41	—	4	8	no	—
323	C₂×#41	C₂×C₄×C₂₉	1	16	yes	complemented
324	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
325	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
326	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
327	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
328	C₂²×D₄	C₂³×C₂₉	1	4	yes	—
329	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
330	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
331	C₂³×C₄	C₂³×C₂₉	1	8	yes	—
332	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
333	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
334	C₄⋊Q₈	C₂×C₄×C₂₉	1	8	yes	complemented
335	#127	C₂×C₄×C₂₉	1	8	yes	—
336	#124	C₂×C₄×C₂₉	1	16	yes	complemented
337	#121	C₂×C₄×C₂₉	1	16	yes	complemented
338	#121	C₂×C₄×C₂₉	1	16	yes	complemented
339	C₄×Q₈	—	4	8	no	—
340	C₄×D₄	—	4	8	no	—
341	C₄×D₄	—	4	8	no	—
342	C₄×D₄	C₂×C₄×C₂₉	1	16	yes	complemented
343	C₄×D₄	C₂×C₄×C₂₉	1	16	yes	complemented
344	#117	—	4	4	no	—
345	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
348	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
349	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
350	C₂×C₄⋊C₄	C₂³×C₂₉	1	8	yes	—
351	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
352	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₂₉	1	8	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₂₉	1	8	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₂₉	1	8	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
362	C₂×C₄²	C₂×C₄×C₂₉	1	8	yes	complemented
363	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
364	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
365	C₂×C₄²	C₂³×C₂₉	1	8	yes	—
366	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
369	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
370	#95	C₂³×C₂₉	1	2	yes	—
371	#95	C₂³×C₂₉	1	2	yes	—
372	#95	C₂³×C₂₉	1	8	yes	—
373	#95	C₂³×C₂₉	1	4	yes	—
374	#95	C₂³×C₂₉	1	2	yes	—
375	#95	C₂³×C₂₉	1	2	yes	—
376	#95	C₂³×C₂₉	1	2	yes	—
377	#95	C₂³×C₂₉	1	2	yes	—
378	#95	C₂³×C₂₉	1	4	yes	—
379	#95	C₂³×C₂₉	1	4	yes	—
380	#95	C₂³×C₂₉	1	8	yes	—
381	C₂₉	#34393	1	1	yes	characteristic, direct product factor, Sylow
382	C₂⁴	C₂⁴×C₂₉	1	1	yes	characteristic
383	C₂⁴	C₂⁴×C₂₉	1	4	yes	—
384	#41	—	4	32	no	—
385	C₂×Q₈	—	2	8	no	—
386	C₂×Q₈	C₂²×C₄×C₂₉	1	8	yes	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	8	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	4	8	no	—
391	C₂×D₄	—	4	4	no	—
392	C₂×D₄	C₂²×C₄×C₂₉	1	8	yes	—
393	C₂×D₄	C₂²×C₄×C₂₉	1	8	yes	—
394	C₂×D₄	C₂²×C₄×C₂₉	1	8	yes	—
395	C₂×D₄	C₂²×C₄×C₂₉	1	16	yes	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	4	8	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	—	4	8	no	—
402	C₂²×C₄	—	4	8	no	—
403	C₂²×C₄	—	4	8	no	—
404	C₂²×C₄	C₂²×C₄×C₂₉	1	4	yes	—
405	C₂²×C₄	C₂²×C₄×C₂₉	1	4	yes	—
406	C₂²×C₄	C₂²×C₄×C₂₉	1	4	yes	—
407	C₂²×C₄	C₂²×C₄×C₂₉	1	16	yes	—
408	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
409	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
410	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
411	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
412	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
414	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
415	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
416	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
417	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
418	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	4	4	no	—
424	C₄⋊C₄	—	4	8	no	—
425	C₄⋊C₄	—	4	4	no	—
426	C₄⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
427	C₄⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
428	C₂²⋊C₄	—	4	2	no	—
429	C₂²⋊C₄	—	4	2	no	—
430	C₂²⋊C₄	—	4	8	no	—
431	C₂²⋊C₄	—	4	8	no	—
432	C₂²⋊C₄	—	4	8	no	—
433	C₂²⋊C₄	—	4	4	no	—
434	C₂²⋊C₄	C₂²×C₄×C₂₉	1	16	yes	—
435	C₂²⋊C₄	C₂²×C₄×C₂₉	1	16	yes	—
436	C₄²	—	2	8	no	—
437	C₄²	—	2	8	no	—
438	C₄²	—	4	8	no	—
439	C₄²	C₂²×C₄×C₂₉	1	4	yes	—
440	C₄²	C₂²×C₄×C₂₉	1	4	yes	—
441	C₄²	C₂²×C₄×C₂₉	1	4	yes	—
442	C₄²	C₂²×C₄×C₂₉	1	4	yes	—
443	C₂³	—	2	1	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	8	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	4	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	8	no	—
451	C₂³	C₂³×C₄×C₂₉	1	8	yes	—
452	C₂³	C₂³×C₄×C₂₉	1	2	yes	—
453	C₂³	C₂⁵×C₂₉	1	1	yes	characteristic
454	Q₈	—	2	16	no	—
455	D₄	—	2	16	no	—
456	D₄	—	2	16	no	—
457	D₄	—	4	16	no	—
458	D₄	—	4	8	no	—
459	C₂×C₄	—	2	8	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	4	16	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	8	16	no	—
482	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
483	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
484	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
485	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
486	C₂×C₄	C₂³×C₄×C₂₉	1	8	yes	—
487	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
488	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
489	C₂×C₄	C₂₉×H(5,𝔽₂)	1	4	yes	—
490	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
491	C₂×C₄	C₂₉×2₋¹⁺⁴	1	2	yes	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	8	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	8	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	8	no	—
498	C₂²	—	4	8	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	8	no	—
501	C₂²	—	4	2	no	—
502	C₂²	C₂⁴×C₄×C₂₉	1	1	yes	characteristic
503	C₂²	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
504	C₂²	C₂×C₂₉×H(5,𝔽₂)	1	2	yes	—
505	C₂²	C₂×C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
506	C₂²	C₂₉×#585	1	2	yes	—
507	C₄	—	2	2	no	—
508	C₄	—	2	8	no	—
509	C₄	—	2	2	no	—
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	4	4	no	—
513	C₄	—	4	4	no	—
514	C₄	—	4	4	no	—
515	C₄	—	4	4	no	—
516	C₄	C₂₉×#518	1	4	yes	—
517	C₄	C₂₉×#520	1	4	yes	—
518	C₂	—	4	2	no	—
519	C₂	—	4	8	no	—
520	C₂	C₂×C₂₉×#518	1	1	yes	characteristic
521	C₂	C₂×C₂₉×#520	1	1	yes	characteristic
522	C₂	C₂₉×#3428	1	1	yes	characteristic
523	C₂	C₂₉×#3546	1	2	yes	—
524	C₂	C₂₉×#3554	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁵×C₂₉
prime radical	C₂×C₂₉×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#2377	C₂	semidirect
3. C₂₉×#2366	C₂	semidirect
4. C₂₉×#2365	C₂	semidirect
5. C₂₉×#2357	C₂	semidirect
6. C₂₉×#2349	C₂	semidirect
7. C₂₉×#2341	C₂	semidirect
8. C₂₉×#2339	C₂	semidirect
9. C₂₉×#2326	C₂	semidirect
10. C₂₉×#2324	C₂	semidirect
11. C₂₉×#2318	C₂	semidirect
12. C₂₉×#2285	C₂	semidirect
13. C₂₉×#2283	C₂	semidirect
15. C₂₉×#532	C₄	semidirect
61. C₂×#41×C₂₉	C₂×C₄	semidirect
72. C₂₉×C₄⋊Q₈	C₂×C₄	semidirect
74. C₂₉×#124	C₂×C₄	semidirect
75. C₂₉×#121	C₂×C₄	semidirect
76. C₂₉×#121	C₂×C₄	semidirect
80. C₄×D₄×C₂₉	C₂×C₄	semidirect
81. C₄×D₄×C₂₉	C₂×C₄	semidirect
100. C₂×C₄²×C₂₉	C₂×C₄	semidirect
180. #34393	C₂₉	direct (N × H)
231. #2377	C₂×C₂₉	semidirect
232. #2366	C₂×C₂₉	semidirect
233. #2365	C₂×C₂₉	semidirect
234. #2357	C₂×C₂₉	semidirect
235. #2349	C₂×C₂₉	semidirect
236. #2341	C₂×C₂₉	semidirect
237. #2339	C₂×C₂₉	semidirect
238. #2326	C₂×C₂₉	semidirect
239. #2324	C₂×C₂₉	semidirect
240. #2318	C₂×C₂₉	semidirect
241. #2285	C₂×C₂₉	semidirect
242. #2283	C₂×C₂₉	semidirect
270. #532	C₄×C₂₉	semidirect
323. C₂×#41	C₂×C₄×C₂₉	semidirect
334. C₄⋊Q₈	C₂×C₄×C₂₉	semidirect
336. #124	C₂×C₄×C₂₉	semidirect
337. #121	C₂×C₄×C₂₉	semidirect
338. #121	C₂×C₄×C₂₉	semidirect
342. C₄×D₄	C₂×C₄×C₂₉	semidirect
343. C₄×D₄	C₂×C₄×C₂₉	semidirect
362. C₂×C₄²	C₂×C₄×C₂₉	semidirect
381. C₂₉	#34393	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×#532	2
C₂₉×#2377	2
C₂₉×#2366	2
C₂₉×#2365	2
C₂₉×#2357	2
C₂₉×#2349	2
C₂₉×#2341	2
C₂₉×#2339	2
C₂₉×#2326	2
C₂₉×#2324	2
C₂₉×#2318	2
C₂₉×#2285	2
C₂₉×#2283	2
#34393	29

Subgroups — C29×#34393 #20329293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#34393 #20329293