Subgroups — C₂₉×#35050 #20329950

Order 7424.

4146 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₂²⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#2849	C₂	1	2	yes	maximal, complemented
4	C₂₉×#2846	C₂	1	2	yes	maximal, complemented
5	C₂₉×#2626	C₂	1	2	yes	maximal, complemented
6	C₂₉×#2617	C₂	1	2	yes	maximal, complemented
7	C₂₉×#2561	C₂	1	2	yes	maximal, complemented
8	C₂₉×#2539	C₂	1	2	yes	maximal, complemented
9	C₂₉×#2534	C₂	1	4	yes	maximal, complemented
10	C₂₉×#2482	C₂	1	2	yes	maximal, complemented
11	C₂₉×#2411	C₂	1	4	yes	maximal, complemented
12	C₂₉×#2404	C₂	1	2	yes	maximal, complemented
13	C₂₉×#2321	C₂	1	4	yes	maximal, complemented
14	C₂₉×#2280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂⁶×C₂₉	C₂²	1	1	yes	characteristic
16	C₂²×#41×C₂₉	C₂²	1	1	yes	characteristic, complemented
17	C₂⁴×C₄×C₂₉	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₂₉	C₂²	1	1	yes	characteristic
19	C₂₉×#525	—	2	8	no	—
20	C₂×C₂₉×#123	C₂²	1	2	yes	complemented
21	C₂×C₂₉×#123	C₂²	1	4	yes	complemented
22	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₂₉×#120	C₂²	1	4	yes	—
27	C₂×C₂₉×#120	C₂²	1	2	yes	—
28	C₂×C₂₉×#120	C₂²	1	4	yes	—
29	C₂×C₂₉×#120	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	complemented
31	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	complemented
32	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₂₉×#117	C₂²	1	2	yes	complemented
34	C₂²×C₂²⋊C₄×C₂₉	—	2	8	no	—
35	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
36	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
37	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
38	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
39	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
40	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
41	C₂₉×#399	C₂²	1	4	yes	complemented
42	C₂₉×#397	C₂²	1	4	yes	complemented
43	C₂₉×#396	C₂²	1	8	yes	complemented
44	C₂₉×#394	C₂²	1	8	yes	complemented
45	C₂₉×#393	C₂²	1	4	yes	complemented
46	C₂₉×#392	C₂²	1	4	yes	complemented
47	C₂₉×#390	C₂²	1	8	yes	complemented
48	C₂₉×#388	C₂²	1	8	yes	complemented
49	C₂₉×#388	C₂²	1	8	yes	complemented
50	C₂₉×#386	C₂²	1	8	yes	complemented
51	C₂₉×#386	C₂²	1	4	yes	complemented
52	C₂₉×#386	C₂²	1	4	yes	complemented
53	C₂₉×#385	C₂²	1	4	yes	complemented
54	C₂₉×#385	C₂²	1	4	yes	complemented
55	C₂₉×#381	C₂²	1	2	yes	complemented
56	C₂₉×#381	C₂²	1	4	yes	complemented
57	C₂₉×#380	C₂²	1	2	yes	complemented
58	C₂₉×#380	C₂²	1	2	yes	complemented
59	C₂₉×#379	C₂²	1	4	yes	—
60	C₂₉×#379	C₂²	1	4	yes	—
61	C₂₉×#379	C₂²	1	2	yes	—
62	C₂₉×#379	C₂²	1	4	yes	—
63	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	complemented
65	C₂⁵×C₂₉	—	2	4	no	—
66	C₂⁵×C₂₉	—	2	8	no	—
67	C₂⁵×C₂₉	—	4	4	no	—
68	C₂⁵×C₂₉	—	4	4	no	—
69	C₂⁵×C₂₉	C₂³	1	1	yes	characteristic
70	C₂⁵×C₂₉	C₂³	1	2	yes	—
71	C₂⁵×C₂₉	C₂³	1	2	yes	—
72	C₂⁵×C₂₉	C₂³	1	2	yes	—
73	C₂×#41×C₂₉	—	2	4	no	—
74	C₂×#41×C₂₉	—	4	4	no	—
75	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic, complemented
76	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
77	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
78	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
79	C₂²×D₄×C₂₉	C₂³	1	8	yes	—
80	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic, complemented
81	C₂³×C₄×C₂₉	—	2	4	no	—
82	C₂³×C₄×C₂₉	—	4	4	no	—
83	C₂³×C₄×C₂₉	—	4	4	no	—
84	C₂³×C₄×C₂₉	D₄	1	8	yes	complemented
85	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
86	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
90	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₂₉	C₂³	1	2	yes	complemented
95	C₂₉×#123	—	2	8	no	—
96	C₂₉×#123	—	4	8	no	—
97	C₂₉×C₂²⋊Q₈	—	2	4	no	—
98	C₂₉×C₂²⋊Q₈	—	2	4	no	—
99	C₂₉×#121	—	2	4	no	—
100	C₂₉×#121	—	2	4	no	—
101	C₂₉×#120	—	2	8	no	—
102	C₂₉×#120	—	2	16	no	—
103	C₂₉×#120	—	4	8	no	—
104	C₂₉×#120	—	4	8	no	—
105	C₄×D₄×C₂₉	—	2	8	no	—
106	C₄×D₄×C₂₉	—	2	8	no	—
107	C₂₉×#117	—	2	4	no	—
108	C₂₉×#117	—	4	4	no	—
109	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic, complemented
110	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic, complemented
111	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	complemented
112	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	complemented
113	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	complemented
114	C₂×C₄⋊C₄×C₂₉	C₂³	1	8	yes	complemented
115	C₂×C₂²⋊C₄×C₂₉	—	2	8	no	—
116	C₂×C₂²⋊C₄×C₂₉	—	2	8	no	—
117	C₂×C₂²⋊C₄×C₂₉	—	2	8	no	—
118	C₂×C₂²⋊C₄×C₂₉	—	2	8	no	—
119	C₂×C₂²⋊C₄×C₂₉	—	2	8	no	—
120	C₂×C₂²⋊C₄×C₂₉	—	2	8	no	—
121	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₂₉	C₂³	1	8	yes	—
132	C₂×C₂²⋊C₄×C₂₉	C₂³	1	8	yes	—
133	C₂×C₂²⋊C₄×C₂₉	C₂³	1	8	yes	—
134	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	complemented
135	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	complemented
136	C₂×C₂²⋊C₄×C₂₉	C₂³	1	8	yes	complemented
137	C₂×C₄²×C₂₉	C₂³	1	2	yes	complemented
138	C₂×C₄²×C₂₉	C₂³	1	4	yes	complemented
139	C₂₉×#95	C₂³	1	4	yes	complemented
140	C₂₉×#95	C₂³	1	4	yes	complemented
141	C₂₉×#95	C₂³	1	8	yes	complemented
142	C₂₉×#95	C₂³	1	8	yes	complemented
143	C₂⁴×C₂₉	—	2	4	no	—
144	C₂⁴×C₂₉	—	2	4	no	—
145	C₂⁴×C₂₉	—	2	4	no	—
146	C₂⁴×C₂₉	—	2	32	no	—
147	C₂⁴×C₂₉	—	2	4	no	—
148	C₂⁴×C₂₉	—	2	4	no	—
149	C₂⁴×C₂₉	—	2	4	no	—
150	C₂⁴×C₂₉	—	2	8	no	—
151	C₂⁴×C₂₉	—	2	8	no	—
152	C₂⁴×C₂₉	—	2	4	no	—
153	C₂⁴×C₂₉	—	2	8	no	—
154	C₂⁴×C₂₉	—	2	8	no	—
155	C₂⁴×C₂₉	—	4	4	no	—
156	C₂⁴×C₂₉	—	4	4	no	—
157	C₂⁴×C₂₉	—	4	4	no	—
158	C₂⁴×C₂₉	—	4	4	no	—
159	C₂⁴×C₂₉	—	4	64	no	—
160	C₂⁴×C₂₉	—	4	16	no	—
161	C₂⁴×C₂₉	—	4	16	no	—
162	C₂⁴×C₂₉	C₂×D₄	1	4	yes	—
163	C₂⁴×C₂₉	#41	1	8	yes	complemented
164	C₂⁴×C₂₉	C₂⁴	1	2	yes	—
165	C₂⁴×C₂₉	C₂⁴	1	4	yes	—
166	C₂⁴×C₂₉	C₂⁴	1	1	yes	characteristic
167	C₂⁴×C₂₉	C₂⁴	1	1	yes	characteristic
168	C₂⁴×C₂₉	C₂⁴	1	1	yes	characteristic
169	#41×C₂₉	—	4	16	no	—
170	C₂×Q₈×C₂₉	—	2	2	no	—
171	C₂×Q₈×C₂₉	—	4	2	no	—
172	C₂×D₄×C₂₉	—	2	4	no	—
173	C₂×D₄×C₂₉	—	2	4	no	—
174	C₂×D₄×C₂₉	—	2	4	no	—
175	C₂×D₄×C₂₉	—	2	8	no	—
176	C₂×D₄×C₂₉	—	2	8	no	—
177	C₂×D₄×C₂₉	—	2	8	no	—
178	C₂×D₄×C₂₉	—	2	16	no	—
179	C₂×D₄×C₂₉	—	2	2	no	—
180	C₂×D₄×C₂₉	—	4	2	no	—
181	C₂×D₄×C₂₉	—	4	8	no	—
182	C₂×D₄×C₂₉	—	4	8	no	—
183	C₂²×C₄×C₂₉	—	2	4	no	—
184	C₂²×C₄×C₂₉	—	2	4	no	—
185	C₂²×C₄×C₂₉	—	2	4	no	—
186	C₂²×C₄×C₂₉	—	2	4	no	—
187	C₂²×C₄×C₂₉	—	2	4	no	—
188	C₂²×C₄×C₂₉	—	2	8	no	—
189	C₂²×C₄×C₂₉	—	2	4	no	—
190	C₂²×C₄×C₂₉	—	4	16	no	—
191	C₂²×C₄×C₂₉	—	4	2	no	—
192	C₂²×C₄×C₂₉	—	4	2	no	—
193	C₂²×C₄×C₂₉	—	4	2	no	—
194	C₂²×C₄×C₂₉	—	4	2	no	—
195	C₂²×C₄×C₂₉	—	4	4	no	—
196	C₂²×C₄×C₂₉	—	4	4	no	—
197	C₂²×C₄×C₂₉	—	4	4	no	—
198	C₂²×C₄×C₂₉	—	4	16	no	—
199	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
200	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
201	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
205	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
208	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
214	C₄⋊C₄×C₂₉	—	2	2	no	—
215	C₄⋊C₄×C₂₉	—	2	2	no	—
216	C₄⋊C₄×C₂₉	—	2	4	no	—
217	C₄⋊C₄×C₂₉	—	2	4	no	—
218	C₄⋊C₄×C₂₉	—	4	4	no	—
219	C₄⋊C₄×C₂₉	—	4	8	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	16	no	—
224	C₂²⋊C₄×C₂₉	—	2	8	no	—
225	C₂²⋊C₄×C₂₉	—	2	8	no	—
226	C₂²⋊C₄×C₂₉	—	2	8	no	—
227	C₂²⋊C₄×C₂₉	—	2	8	no	—
228	C₂²⋊C₄×C₂₉	—	2	8	no	—
229	C₂²⋊C₄×C₂₉	—	2	8	no	—
230	C₂²⋊C₄×C₂₉	—	2	8	no	—
231	C₂²⋊C₄×C₂₉	—	2	4	no	—
232	C₂²⋊C₄×C₂₉	—	2	4	no	—
233	C₂²⋊C₄×C₂₉	—	4	8	no	—
234	C₂²⋊C₄×C₂₉	—	4	8	no	—
235	C₂²⋊C₄×C₂₉	—	4	8	no	—
236	C₄²×C₂₉	—	2	4	no	—
237	C₄²×C₂₉	—	4	4	no	—
238	#35050	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂³×C₂₉	—	2	32	no	—
240	C₂³×C₂₉	—	2	8	no	—
241	C₂³×C₂₉	—	2	8	no	—
242	C₂³×C₂₉	—	2	8	no	—
243	C₂³×C₂₉	—	2	2	no	—
244	C₂³×C₂₉	—	2	2	no	—
245	C₂³×C₂₉	—	2	2	no	—
246	C₂³×C₂₉	—	2	2	no	—
247	C₂³×C₂₉	—	2	2	no	—
248	C₂³×C₂₉	—	2	2	no	—
249	C₂³×C₂₉	—	2	16	no	—
250	C₂³×C₂₉	—	2	16	no	—
251	C₂³×C₂₉	—	2	16	no	—
252	C₂³×C₂₉	—	2	4	no	—
253	C₂³×C₂₉	—	2	4	no	—
254	C₂³×C₂₉	—	2	8	no	—
255	C₂³×C₂₉	—	2	8	no	—
256	C₂³×C₂₉	—	2	2	no	—
257	C₂³×C₂₉	—	2	4	no	—
258	C₂³×C₂₉	—	2	4	no	—
259	C₂³×C₂₉	—	2	4	no	—
260	C₂³×C₂₉	—	4	16	no	—
261	C₂³×C₂₉	—	4	32	no	—
262	C₂³×C₂₉	—	4	32	no	—
263	C₂³×C₂₉	—	4	128	no	—
264	C₂³×C₂₉	—	4	8	no	—
265	C₂³×C₂₉	—	4	8	no	—
266	C₂³×C₂₉	—	4	8	no	—
267	C₂³×C₂₉	—	4	8	no	—
268	C₂³×C₂₉	—	4	16	no	—
269	C₂³×C₂₉	—	4	8	no	—
270	C₂³×C₂₉	—	4	8	no	—
271	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
272	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
273	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
274	C₂³×C₂₉	C₂×#41	1	8	yes	—
275	C₂³×C₂₉	C₂×#41	1	4	yes	—
276	C₂³×C₂₉	H(5,𝔽₂)	1	4	yes	—
277	C₂³×C₂₉	H(5,𝔽₂)	1	4	yes	—
278	C₂³×C₂₉	C₂⁵	1	1	yes	characteristic
279	Q₈×C₂₉	—	4	4	no	—
280	D₄×C₂₉	—	4	4	no	—
281	D₄×C₂₉	—	4	8	no	—
282	D₄×C₂₉	—	4	8	no	—
283	D₄×C₂₉	—	4	8	no	—
284	D₄×C₂₉	—	8	16	no	—
285	C₂×C₄×C₂₉	—	2	8	no	—
286	C₂×C₄×C₂₉	—	2	8	no	—
287	C₂×C₄×C₂₉	—	2	2	no	—
288	C₂×C₄×C₂₉	—	2	2	no	—
289	C₂×C₄×C₂₉	—	2	2	no	—
290	C₂×C₄×C₂₉	—	2	2	no	—
291	C₂×C₄×C₂₉	—	2	2	no	—
292	C₂×C₄×C₂₉	—	2	2	no	—
293	C₂×C₄×C₂₉	—	2	4	no	—
294	C₂×C₄×C₂₉	—	2	2	no	—
295	C₂×C₄×C₂₉	—	2	4	no	—
296	C₂×C₄×C₂₉	—	2	8	no	—
297	C₂×C₄×C₂₉	—	2	8	no	—
298	C₂×C₄×C₂₉	—	2	8	no	—
299	C₂×C₄×C₂₉	—	2	4	no	—
300	C₂×C₄×C₂₉	—	2	4	no	—
301	C₂×C₄×C₂₉	—	2	8	no	—
302	C₂×C₄×C₂₉	—	4	4	no	—
303	C₂×C₄×C₂₉	—	4	4	no	—
304	C₂×C₄×C₂₉	—	4	4	no	—
305	C₂×C₄×C₂₉	—	4	4	no	—
306	C₂×C₄×C₂₉	—	4	8	no	—
307	C₂×C₄×C₂₉	—	4	8	no	—
308	C₂×C₄×C₂₉	—	4	8	no	—
309	C₂×C₄×C₂₉	—	4	8	no	—
310	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
314	C₂×#525	C₂×C₂₉	1	1	yes	characteristic, complemented
315	C₂³×C₂²⋊C₄	C₂×C₂₉	1	1	yes	characteristic, complemented
316	#2849	C₂×C₂₉	1	2	yes	complemented
317	#2846	C₂×C₂₉	1	2	yes	complemented
318	#2626	C₂×C₂₉	1	2	yes	complemented
319	#2617	C₂×C₂₉	1	2	yes	complemented
320	#2561	C₂×C₂₉	1	2	yes	complemented
321	#2539	C₂×C₂₉	1	2	yes	complemented
322	#2534	C₂×C₂₉	1	4	yes	complemented
323	#2482	C₂×C₂₉	1	2	yes	complemented
324	#2411	C₂×C₂₉	1	4	yes	complemented
325	#2404	C₂×C₂₉	1	2	yes	complemented
326	#2321	C₂×C₂₉	1	4	yes	complemented
327	#2280	C₂×C₂₉	1	1	yes	characteristic, complemented
328	C₂²×C₂₉	—	2	32	no	—
329	C₂²×C₂₉	—	2	2	no	—
330	C₂²×C₂₉	—	2	2	no	—
331	C₂²×C₂₉	—	2	2	no	—
332	C₂²×C₂₉	—	2	2	no	—
333	C₂²×C₂₉	—	2	2	no	—
334	C₂²×C₂₉	—	2	2	no	—
335	C₂²×C₂₉	—	2	8	no	—
336	C₂²×C₂₉	—	2	8	no	—
337	C₂²×C₂₉	—	2	8	no	—
338	C₂²×C₂₉	—	2	8	no	—
339	C₂²×C₂₉	—	2	16	no	—
340	C₂²×C₂₉	—	4	32	no	—
341	C₂²×C₂₉	—	4	32	no	—
342	C₂²×C₂₉	—	4	32	no	—
343	C₂²×C₂₉	—	4	4	no	—
344	C₂²×C₂₉	—	4	4	no	—
345	C₂²×C₂₉	—	4	8	no	—
346	C₂²×C₂₉	—	4	2	no	—
347	C₂²×C₂₉	—	4	2	no	—
348	C₂²×C₂₉	—	4	2	no	—
349	C₂²×C₂₉	—	4	8	no	—
350	C₂²×C₂₉	#525	1	4	yes	—
351	C₂²×C₂₉	#534	1	4	yes	—
352	C₂²×C₂₉	#535	1	4	yes	—
353	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
354	C₂²×C₂₉	C₂²×#41	1	2	yes	—
355	C₂²×C₂₉	C₂×H(5,𝔽₂)	1	2	yes	—
356	C₂²×C₂₉	C₂×H(5,𝔽₂)	1	2	yes	—
357	C₄×C₂₉	—	2	2	no	—
358	C₄×C₂₉	—	2	2	no	—
359	C₄×C₂₉	—	2	2	no	—
360	C₄×C₂₉	—	2	2	no	—
361	C₄×C₂₉	—	4	2	no	—
362	C₄×C₂₉	—	4	2	no	—
363	C₄×C₂₉	—	4	4	no	—
364	C₄×C₂₉	—	4	2	no	—
365	C₄×C₂₉	—	4	8	no	—
366	C₂⁶	C₂²×C₂₉	1	1	yes	characteristic
367	C₂²×#41	C₂²×C₂₉	1	1	yes	characteristic, complemented
368	C₂⁴×C₄	C₂²×C₂₉	1	1	yes	characteristic
369	C₂⁴×C₄	C₂²×C₂₉	1	1	yes	characteristic
370	#525	—	2	8	no	—
371	C₂×#123	C₂²×C₂₉	1	2	yes	complemented
372	C₂×#123	C₂²×C₂₉	1	4	yes	complemented
373	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
374	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
375	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic, complemented
376	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic, complemented
377	C₂×#120	C₂²×C₂₉	1	4	yes	—
378	C₂×#120	C₂²×C₂₉	1	2	yes	—
379	C₂×#120	C₂²×C₂₉	1	4	yes	—
380	C₂×#120	C₂²×C₂₉	1	4	yes	—
381	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	complemented
382	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	complemented
383	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic, complemented
384	C₂×#117	C₂²×C₂₉	1	2	yes	complemented
385	C₂²×C₂²⋊C₄	—	2	8	no	—
386	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
387	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
388	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
389	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
390	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
391	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
392	#399	C₂²×C₂₉	1	4	yes	complemented
393	#397	C₂²×C₂₉	1	4	yes	complemented
394	#396	C₂²×C₂₉	1	8	yes	complemented
395	#394	C₂²×C₂₉	1	8	yes	complemented
396	#393	C₂²×C₂₉	1	4	yes	complemented
397	#392	C₂²×C₂₉	1	4	yes	complemented
398	#390	C₂²×C₂₉	1	8	yes	complemented
399	#388	C₂²×C₂₉	1	8	yes	complemented
400	#388	C₂²×C₂₉	1	8	yes	complemented
401	#386	C₂²×C₂₉	1	8	yes	complemented
402	#386	C₂²×C₂₉	1	4	yes	complemented
403	#386	C₂²×C₂₉	1	4	yes	complemented
404	#385	C₂²×C₂₉	1	4	yes	complemented
405	#385	C₂²×C₂₉	1	4	yes	complemented
406	#381	C₂²×C₂₉	1	4	yes	complemented
407	#381	C₂²×C₂₉	1	2	yes	complemented
408	#380	C₂²×C₂₉	1	2	yes	complemented
409	#380	C₂²×C₂₉	1	2	yes	complemented
410	#379	C₂²×C₂₉	1	4	yes	—
411	#379	C₂²×C₂₉	1	4	yes	—
412	#379	C₂²×C₂₉	1	2	yes	—
413	#379	C₂²×C₂₉	1	4	yes	—
414	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	complemented
415	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	complemented
416	C₂×C₂₉	—	2	4	no	—
417	C₂×C₂₉	—	2	4	no	—
418	C₂×C₂₉	—	2	4	no	—
419	C₂×C₂₉	—	4	8	no	—
420	C₂×C₂₉	—	8	2	no	—
421	C₂×C₂₉	C₂×#525	1	1	yes	characteristic
422	C₂×C₂₉	C₂×#534	1	1	yes	characteristic
423	C₂×C₂₉	C₂×#535	1	1	yes	characteristic
424	C₂×C₂₉	#3490	1	4	yes	—
425	C₂⁵	—	2	4	no	—
426	C₂⁵	—	2	8	no	—
427	C₂⁵	—	4	4	no	—
428	C₂⁵	—	4	4	no	—
429	C₂⁵	C₂³×C₂₉	1	1	yes	characteristic
430	C₂⁵	C₂³×C₂₉	1	2	yes	—
431	C₂⁵	C₂³×C₂₉	1	2	yes	—
432	C₂⁵	C₂³×C₂₉	1	2	yes	—
433	C₂×#41	—	2	4	no	—
434	C₂×#41	—	4	4	no	—
435	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic, complemented
436	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
437	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
438	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
439	C₂²×D₄	C₂³×C₂₉	1	8	yes	—
440	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic, complemented
441	C₂³×C₄	—	2	4	no	—
442	C₂³×C₄	—	4	4	no	—
443	C₂³×C₄	—	4	4	no	—
444	C₂³×C₄	D₄×C₂₉	1	8	yes	complemented
445	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
446	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
449	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
450	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₂₉	1	2	yes	complemented
455	#123	—	2	8	no	—
456	#123	—	4	8	no	—
457	C₂²⋊Q₈	—	2	4	no	—
458	C₂²⋊Q₈	—	2	4	no	—
459	#121	—	2	4	no	—
460	#121	—	2	4	no	—
461	#120	—	2	8	no	—
462	#120	—	2	16	no	—
463	#120	—	4	8	no	—
464	#120	—	4	8	no	—
465	C₄×D₄	—	2	8	no	—
466	C₄×D₄	—	2	8	no	—
467	#117	—	2	4	no	—
468	#117	—	4	4	no	—
469	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic, complemented
470	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic, complemented
471	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	complemented
472	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	complemented
473	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	complemented
474	C₂×C₄⋊C₄	C₂³×C₂₉	1	8	yes	complemented
475	C₂×C₂²⋊C₄	—	2	8	no	—
476	C₂×C₂²⋊C₄	—	2	8	no	—
477	C₂×C₂²⋊C₄	—	2	8	no	—
478	C₂×C₂²⋊C₄	—	2	8	no	—
479	C₂×C₂²⋊C₄	—	2	8	no	—
480	C₂×C₂²⋊C₄	—	2	8	no	—
481	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₂₉	1	8	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₂₉	1	8	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₂₉	1	8	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	complemented
495	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	complemented
496	C₂×C₂²⋊C₄	C₂³×C₂₉	1	8	yes	complemented
497	C₂×C₄²	C₂³×C₂₉	1	2	yes	complemented
498	C₂×C₄²	C₂³×C₂₉	1	4	yes	complemented
499	#95	C₂³×C₂₉	1	4	yes	complemented
500	#95	C₂³×C₂₉	1	4	yes	complemented
501	#95	C₂³×C₂₉	1	8	yes	complemented
502	#95	C₂³×C₂₉	1	8	yes	complemented
503	C₂₉	#35050	1	1	yes	characteristic, direct product factor, Sylow
504	C₂⁴	—	2	4	no	—
505	C₂⁴	—	2	4	no	—
506	C₂⁴	—	2	4	no	—
507	C₂⁴	—	2	32	no	—
508	C₂⁴	—	2	4	no	—
509	C₂⁴	—	2	4	no	—
510	C₂⁴	—	2	4	no	—
511	C₂⁴	—	2	8	no	—
512	C₂⁴	—	2	8	no	—
513	C₂⁴	—	2	4	no	—
514	C₂⁴	—	2	8	no	—
515	C₂⁴	—	2	8	no	—
516	C₂⁴	—	4	4	no	—
517	C₂⁴	—	4	4	no	—
518	C₂⁴	—	4	4	no	—
519	C₂⁴	—	4	4	no	—
520	C₂⁴	—	4	64	no	—
521	C₂⁴	—	4	16	no	—
522	C₂⁴	—	4	16	no	—
523	C₂⁴	C₂×D₄×C₂₉	1	4	yes	—
524	C₂⁴	#41×C₂₉	1	8	yes	complemented
525	C₂⁴	C₂⁴×C₂₉	1	2	yes	—
526	C₂⁴	C₂⁴×C₂₉	1	4	yes	—
527	C₂⁴	C₂⁴×C₂₉	1	1	yes	characteristic
528	C₂⁴	C₂⁴×C₂₉	1	1	yes	characteristic
529	C₂⁴	C₂⁴×C₂₉	1	1	yes	characteristic
530	#41	—	4	16	no	—
531	C₂×Q₈	—	2	2	no	—
532	C₂×Q₈	—	4	2	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	8	no	—
537	C₂×D₄	—	2	8	no	—
538	C₂×D₄	—	2	8	no	—
539	C₂×D₄	—	2	16	no	—
540	C₂×D₄	—	2	2	no	—
541	C₂×D₄	—	4	2	no	—
542	C₂×D₄	—	4	8	no	—
543	C₂×D₄	—	4	8	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	—	2	8	no	—
550	C₂²×C₄	—	2	4	no	—
551	C₂²×C₄	—	4	16	no	—
552	C₂²×C₄	—	4	2	no	—
553	C₂²×C₄	—	4	2	no	—
554	C₂²×C₄	—	4	2	no	—
555	C₂²×C₄	—	4	2	no	—
556	C₂²×C₄	—	4	4	no	—
557	C₂²×C₄	—	4	4	no	—
558	C₂²×C₄	—	4	4	no	—
559	C₂²×C₄	—	4	16	no	—
560	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
561	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
562	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
563	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
564	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
565	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
566	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
568	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
570	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
573	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	4	4	no	—
580	C₄⋊C₄	—	4	8	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	16	no	—
585	C₂²⋊C₄	—	2	8	no	—
586	C₂²⋊C₄	—	2	8	no	—
587	C₂²⋊C₄	—	2	8	no	—
588	C₂²⋊C₄	—	2	8	no	—
589	C₂²⋊C₄	—	2	8	no	—
590	C₂²⋊C₄	—	2	8	no	—
591	C₂²⋊C₄	—	2	8	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	4	8	no	—
595	C₂²⋊C₄	—	4	8	no	—
596	C₂²⋊C₄	—	4	8	no	—
597	C₄²	—	2	4	no	—
598	C₄²	—	4	4	no	—
599	C₂³	—	2	32	no	—
600	C₂³	—	2	8	no	—
601	C₂³	—	2	8	no	—
602	C₂³	—	2	8	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	16	no	—
610	C₂³	—	2	16	no	—
611	C₂³	—	2	16	no	—
612	C₂³	—	2	4	no	—
613	C₂³	—	2	4	no	—
614	C₂³	—	2	8	no	—
615	C₂³	—	2	8	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	4	no	—
618	C₂³	—	2	4	no	—
619	C₂³	—	2	4	no	—
620	C₂³	—	4	16	no	—
621	C₂³	—	4	32	no	—
622	C₂³	—	4	32	no	—
623	C₂³	—	4	128	no	—
624	C₂³	—	4	8	no	—
625	C₂³	—	4	8	no	—
626	C₂³	—	4	8	no	—
627	C₂³	—	4	8	no	—
628	C₂³	—	4	16	no	—
629	C₂³	—	4	8	no	—
630	C₂³	—	4	8	no	—
631	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
632	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
633	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
634	C₂³	C₂×#41×C₂₉	1	8	yes	—
635	C₂³	C₂×#41×C₂₉	1	4	yes	—
636	C₂³	C₂₉×H(5,𝔽₂)	1	4	yes	—
637	C₂³	C₂₉×H(5,𝔽₂)	1	4	yes	—
638	C₂³	C₂⁵×C₂₉	1	1	yes	characteristic
639	Q₈	—	4	4	no	—
640	D₄	—	4	4	no	—
641	D₄	—	4	8	no	—
642	D₄	—	4	8	no	—
643	D₄	—	4	8	no	—
644	D₄	—	8	16	no	—
645	C₂×C₄	—	2	8	no	—
646	C₂×C₄	—	2	8	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	8	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	8	no	—
658	C₂×C₄	—	2	8	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	8	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	4	8	no	—
667	C₂×C₄	—	4	8	no	—
668	C₂×C₄	—	4	8	no	—
669	C₂×C₄	—	4	8	no	—
670	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
671	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
672	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
673	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
674	C₂²	—	2	32	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	8	no	—
680	C₂²	—	2	8	no	—
681	C₂²	—	2	8	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	16	no	—
685	C₂²	—	2	8	no	—
686	C₂²	—	4	32	no	—
687	C₂²	—	4	32	no	—
688	C₂²	—	4	32	no	—
689	C₂²	—	4	4	no	—
690	C₂²	—	4	4	no	—
691	C₂²	—	4	8	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	8	no	—
695	C₂²	—	4	2	no	—
696	C₂²	C₂₉×#525	1	4	yes	—
697	C₂²	C₂₉×#534	1	4	yes	—
698	C₂²	C₂₉×#535	1	4	yes	—
699	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
700	C₂²	C₂²×#41×C₂₉	1	2	yes	—
701	C₂²	C₂×C₂₉×H(5,𝔽₂)	1	2	yes	—
702	C₂²	C₂×C₂₉×H(5,𝔽₂)	1	2	yes	—
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	2	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	4	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	8	no	—
711	C₄	—	4	2	no	—
712	C₂	—	2	4	no	—
713	C₂	—	2	4	no	—
714	C₂	—	2	4	no	—
715	C₂	—	4	8	no	—
716	C₂	—	8	2	no	—
717	C₂	C₂×C₂₉×#525	1	1	yes	characteristic
718	C₂	C₂×C₂₉×#534	1	1	yes	characteristic
719	C₂	C₂×C₂₉×#535	1	1	yes	characteristic
720	C₂	C₂₉×#3490	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#525	C₂	semidirect
2. C₂³×C₂²⋊C₄×C₂₉	C₂	semidirect
3. C₂₉×#2849	C₂	semidirect
4. C₂₉×#2846	C₂	semidirect
5. C₂₉×#2626	C₂	semidirect
6. C₂₉×#2617	C₂	semidirect
7. C₂₉×#2561	C₂	semidirect
8. C₂₉×#2539	C₂	semidirect
9. C₂₉×#2534	C₂	semidirect
10. C₂₉×#2482	C₂	semidirect
11. C₂₉×#2411	C₂	semidirect
12. C₂₉×#2404	C₂	semidirect
13. C₂₉×#2321	C₂	semidirect
14. C₂₉×#2280	C₂	semidirect
16. C₂²×#41×C₂₉	C₂²	semidirect
20. C₂×C₂₉×#123	C₂²	semidirect
21. C₂×C₂₉×#123	C₂²	semidirect
22. C₂×C₂₉×C₂²⋊Q₈	C₂²	semidirect
23. C₂×C₂₉×C₂²⋊Q₈	C₂²	semidirect
24. C₂×C₂₉×#121	C₂²	semidirect
25. C₂×C₂₉×#121	C₂²	semidirect
30. C₂×C₄×D₄×C₂₉	C₂²	semidirect
31. C₂×C₄×D₄×C₂₉	C₂²	semidirect
32. C₂×C₂₉×#117	C₂²	semidirect
33. C₂×C₂₉×#117	C₂²	semidirect
41. C₂₉×#399	C₂²	semidirect
42. C₂₉×#397	C₂²	semidirect
43. C₂₉×#396	C₂²	semidirect
44. C₂₉×#394	C₂²	semidirect
45. C₂₉×#393	C₂²	semidirect
46. C₂₉×#392	C₂²	semidirect
47. C₂₉×#390	C₂²	semidirect
48. C₂₉×#388	C₂²	semidirect
49. C₂₉×#388	C₂²	semidirect
50. C₂₉×#386	C₂²	semidirect
51. C₂₉×#386	C₂²	semidirect
52. C₂₉×#386	C₂²	semidirect
53. C₂₉×#385	C₂²	semidirect
54. C₂₉×#385	C₂²	semidirect
55. C₂₉×#381	C₂²	semidirect
56. C₂₉×#381	C₂²	semidirect
57. C₂₉×#380	C₂²	semidirect
58. C₂₉×#380	C₂²	semidirect
63. C₄×C₂²⋊C₄×C₂₉	C₂²	semidirect
64. C₄×C₂²⋊C₄×C₂₉	C₂²	semidirect
75. C₂²×Q₈×C₂₉	C₂³	semidirect
80. C₂²×D₄×C₂₉	C₂³	semidirect
84. C₂³×C₄×C₂₉	D₄	semidirect
94. C₂³×C₄×C₂₉	C₂³	semidirect
109. C₂×C₄⋊C₄×C₂₉	C₂³	semidirect
110. C₂×C₄⋊C₄×C₂₉	C₂³	semidirect
111. C₂×C₄⋊C₄×C₂₉	C₂³	semidirect
112. C₂×C₄⋊C₄×C₂₉	C₂³	semidirect
113. C₂×C₄⋊C₄×C₂₉	C₂³	semidirect
114. C₂×C₄⋊C₄×C₂₉	C₂³	semidirect
134. C₂×C₂²⋊C₄×C₂₉	C₂³	semidirect
135. C₂×C₂²⋊C₄×C₂₉	C₂³	semidirect
136. C₂×C₂²⋊C₄×C₂₉	C₂³	semidirect
137. C₂×C₄²×C₂₉	C₂³	semidirect
138. C₂×C₄²×C₂₉	C₂³	semidirect
139. C₂₉×#95	C₂³	semidirect
140. C₂₉×#95	C₂³	semidirect
141. C₂₉×#95	C₂³	semidirect
142. C₂₉×#95	C₂³	semidirect
163. C₂⁴×C₂₉	#41	semidirect
238. #35050	C₂₉	direct (N × H)
314. C₂×#525	C₂×C₂₉	semidirect
315. C₂³×C₂²⋊C₄	C₂×C₂₉	semidirect
316. #2849	C₂×C₂₉	semidirect
317. #2846	C₂×C₂₉	semidirect
318. #2626	C₂×C₂₉	semidirect
319. #2617	C₂×C₂₉	semidirect
320. #2561	C₂×C₂₉	semidirect
321. #2539	C₂×C₂₉	semidirect
322. #2534	C₂×C₂₉	semidirect
323. #2482	C₂×C₂₉	semidirect
324. #2411	C₂×C₂₉	semidirect
325. #2404	C₂×C₂₉	semidirect
326. #2321	C₂×C₂₉	semidirect
327. #2280	C₂×C₂₉	semidirect
367. C₂²×#41	C₂²×C₂₉	semidirect
371. C₂×#123	C₂²×C₂₉	semidirect
372. C₂×#123	C₂²×C₂₉	semidirect
373. C₂×C₂²⋊Q₈	C₂²×C₂₉	semidirect
374. C₂×C₂²⋊Q₈	C₂²×C₂₉	semidirect
375. C₂×#121	C₂²×C₂₉	semidirect
376. C₂×#121	C₂²×C₂₉	semidirect
381. C₂×C₄×D₄	C₂²×C₂₉	semidirect
382. C₂×C₄×D₄	C₂²×C₂₉	semidirect
383. C₂×#117	C₂²×C₂₉	semidirect
384. C₂×#117	C₂²×C₂₉	semidirect
392. #399	C₂²×C₂₉	semidirect
393. #397	C₂²×C₂₉	semidirect
394. #396	C₂²×C₂₉	semidirect
395. #394	C₂²×C₂₉	semidirect
396. #393	C₂²×C₂₉	semidirect
397. #392	C₂²×C₂₉	semidirect
398. #390	C₂²×C₂₉	semidirect
399. #388	C₂²×C₂₉	semidirect
400. #388	C₂²×C₂₉	semidirect
401. #386	C₂²×C₂₉	semidirect
402. #386	C₂²×C₂₉	semidirect
403. #386	C₂²×C₂₉	semidirect
404. #385	C₂²×C₂₉	semidirect
405. #385	C₂²×C₂₉	semidirect
406. #381	C₂²×C₂₉	semidirect
407. #381	C₂²×C₂₉	semidirect
408. #380	C₂²×C₂₉	semidirect
409. #380	C₂²×C₂₉	semidirect
414. C₄×C₂²⋊C₄	C₂²×C₂₉	semidirect
415. C₄×C₂²⋊C₄	C₂²×C₂₉	semidirect
435. C₂²×Q₈	C₂³×C₂₉	semidirect
440. C₂²×D₄	C₂³×C₂₉	semidirect
444. C₂³×C₄	D₄×C₂₉	semidirect
454. C₂³×C₄	C₂³×C₂₉	semidirect
469. C₂×C₄⋊C₄	C₂³×C₂₉	semidirect
470. C₂×C₄⋊C₄	C₂³×C₂₉	semidirect
471. C₂×C₄⋊C₄	C₂³×C₂₉	semidirect
472. C₂×C₄⋊C₄	C₂³×C₂₉	semidirect
473. C₂×C₄⋊C₄	C₂³×C₂₉	semidirect
474. C₂×C₄⋊C₄	C₂³×C₂₉	semidirect
494. C₂×C₂²⋊C₄	C₂³×C₂₉	semidirect
495. C₂×C₂²⋊C₄	C₂³×C₂₉	semidirect
496. C₂×C₂²⋊C₄	C₂³×C₂₉	semidirect
497. C₂×C₄²	C₂³×C₂₉	semidirect
498. C₂×C₄²	C₂³×C₂₉	semidirect
499. #95	C₂³×C₂₉	semidirect
500. #95	C₂³×C₂₉	semidirect
501. #95	C₂³×C₂₉	semidirect
502. #95	C₂³×C₂₉	semidirect
503. C₂₉	#35050	direct (N × H)
524. C₂⁴	#41×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×#525	2
C₂³×C₂²⋊C₄×C₂₉	2
C₂₉×#2849	2
C₂₉×#2846	2
C₂₉×#2626	2
C₂₉×#2617	2
C₂₉×#2561	2
C₂₉×#2539	2
C₂₉×#2534	2
C₂₉×#2482	2
C₂₉×#2411	2
C₂₉×#2404	2
C₂₉×#2321	2
C₂₉×#2280	2
#35050	29

Subgroups — C29×#35050 #20329950

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#35050 #20329950