Subgroups — C₂×C₂₉×#2594 #20329752

Order 7424.

2074 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2594	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₂₉×#401	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×#398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₉×#397	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂₉×#396	C₂	1	1	yes	maximal, characteristic
6	C₂×C₂₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₉×#388	C₂	1	1	yes	maximal, characteristic
8	C₂×C₂₉×#388	C₂	1	1	yes	maximal, characteristic
9	C₂×C₂₉×#388	C₂	1	1	yes	maximal, characteristic
10	C₂×C₂₉×#388	C₂	1	1	yes	maximal, characteristic
11	C₂×C₂₉×#388	C₂	1	1	yes	maximal, characteristic
12	C₂×C₂₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
38	C₂₉×#401	C₂²	1	8	yes	complemented
39	C₂₉×#398	C₂²	1	8	yes	complemented
40	C₂₉×#397	C₂²	1	8	yes	—
41	C₂₉×#396	C₂²	1	8	yes	—
42	C₂₉×#389	C₂²	1	8	yes	complemented
43	C₂₉×#388	C₂²	1	8	yes	—
44	C₂₉×#388	C₂²	1	8	yes	—
45	C₂₉×#388	C₂²	1	8	yes	—
46	C₂₉×#388	C₂²	1	8	yes	—
47	C₂₉×#388	C₂²	1	8	yes	—
48	C₂₉×#387	C₂²	1	8	yes	complemented
49	C₂₉×#387	C₂²	1	8	yes	complemented
50	C₂₉×#387	C₂²	1	8	yes	complemented
51	C₄×C₄⋊C₄×C₂₉	C₂²	1	8	yes	complemented
52	C₄×C₄⋊C₄×C₂₉	C₂²	1	8	yes	complemented
53	C₂×C₂₉×#95	C₂²	1	1	yes	characteristic
54	C₂×C₂₉×#95	C₂²	1	1	yes	characteristic
55	C₂×C₂₉×#95	C₂²	1	1	yes	characteristic
56	C₂×C₂₉×#95	C₂²	1	1	yes	characteristic
57	C₂×C₂₉×#95	C₂²	1	1	yes	characteristic
58	C₂×C₂₉×#95	C₂²	1	1	yes	characteristic
59	C₂×C₂₉×#95	C₂²	1	1	yes	characteristic
60	C₂×C₂₉×#95	C₂²	1	1	yes	characteristic
61	C₂×C₂₉×#95	C₂²	1	1	yes	characteristic
62	C₂×C₂₉×#95	C₂²	1	1	yes	characteristic
63	C₂×C₂₉×#95	C₂²	1	1	yes	characteristic
64	C₂×C₂₉×#95	C₂²	1	1	yes	characteristic
65	C₂×C₂₉×#95	C₂²	1	1	yes	characteristic
66	C₂×C₂₉×#95	C₂²	1	1	yes	characteristic
67	C₂⁵×C₂₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
83	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
84	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
85	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
86	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
87	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
88	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
89	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
90	C₂×C₄⋊C₄×C₂₉	—	4	2	no	—
91	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₂₉	—	2	4	no	—
101	C₂×C₂²⋊C₄×C₂₉	—	2	4	no	—
102	C₂×C₂²⋊C₄×C₂₉	—	2	4	no	—
103	C₂×C₂²⋊C₄×C₂₉	—	2	4	no	—
104	C₂×C₂²⋊C₄×C₂₉	—	2	4	no	—
105	C₂×C₂²⋊C₄×C₂₉	—	4	2	no	—
106	C₂×C₂²⋊C₄×C₂₉	—	4	2	no	—
107	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
114	C₂×C₄²×C₂₉	—	2	4	no	—
115	C₂×C₄²×C₂₉	—	2	4	no	—
116	C₂×C₄²×C₂₉	—	4	2	no	—
117	C₂×C₄²×C₂₉	—	4	2	no	—
118	C₂×C₄²×C₂₉	—	4	2	no	—
119	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
120	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
121	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
122	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
123	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
124	C₂₉×#95	C₂³	1	4	yes	—
125	C₂₉×#95	C₂³	1	4	yes	—
126	C₂₉×#95	C₂³	1	4	yes	—
127	C₂₉×#95	C₂³	1	4	yes	—
128	C₂₉×#95	C₂³	1	4	yes	—
129	C₂₉×#95	C₂³	1	4	yes	—
130	C₂₉×#95	C₂³	1	4	yes	—
131	C₂₉×#95	C₂³	1	4	yes	—
132	C₂₉×#95	C₂³	1	4	yes	—
133	C₂₉×#95	C₂³	1	4	yes	—
134	C₂₉×#95	C₂³	1	4	yes	—
135	C₂₉×#95	C₂³	1	4	yes	—
136	C₂₉×#95	C₂³	1	4	yes	—
137	C₂₉×#95	C₂³	1	4	yes	—
138	C₂⁴×C₂₉	—	2	2	no	—
139	C₂⁴×C₂₉	—	2	2	no	—
140	C₂⁴×C₂₉	—	2	2	no	—
141	C₂⁴×C₂₉	—	2	2	no	—
142	C₂⁴×C₂₉	—	2	2	no	—
143	C₂⁴×C₂₉	—	2	2	no	—
144	C₂⁴×C₂₉	—	2	2	no	—
145	C₂⁴×C₂₉	C₂⁴	1	2	yes	—
146	C₂⁴×C₂₉	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₂₉	—	2	2	no	—
148	C₂²×C₄×C₂₉	—	2	2	no	—
149	C₂²×C₄×C₂₉	—	2	2	no	—
150	C₂²×C₄×C₂₉	—	2	2	no	—
151	C₂²×C₄×C₂₉	—	2	2	no	—
152	C₂²×C₄×C₂₉	—	2	2	no	—
153	C₂²×C₄×C₂₉	—	2	2	no	—
154	C₂²×C₄×C₂₉	—	2	2	no	—
155	C₂²×C₄×C₂₉	—	2	2	no	—
156	C₂²×C₄×C₂₉	—	2	2	no	—
157	C₂²×C₄×C₂₉	—	2	2	no	—
158	C₂²×C₄×C₂₉	—	2	2	no	—
159	C₂²×C₄×C₂₉	—	2	2	no	—
160	C₂²×C₄×C₂₉	—	2	2	no	—
161	C₂²×C₄×C₂₉	—	2	2	no	—
162	C₂²×C₄×C₂₉	—	2	2	no	—
163	C₂²×C₄×C₂₉	—	2	2	no	—
164	C₂²×C₄×C₂₉	—	2	2	no	—
165	C₂²×C₄×C₂₉	—	2	2	no	—
166	C₂²×C₄×C₂₉	—	2	2	no	—
167	C₂²×C₄×C₂₉	—	2	2	no	—
168	C₂²×C₄×C₂₉	—	2	2	no	—
169	C₂²×C₄×C₂₉	—	2	2	no	—
170	C₂²×C₄×C₂₉	—	2	2	no	—
171	C₂²×C₄×C₂₉	—	2	2	no	—
172	C₂²×C₄×C₂₉	—	2	2	no	—
173	C₂²×C₄×C₂₉	—	2	2	no	—
174	C₂²×C₄×C₂₉	—	2	2	no	—
175	C₂²×C₄×C₂₉	—	2	2	no	—
176	C₂²×C₄×C₂₉	—	2	2	no	—
177	C₂²×C₄×C₂₉	—	2	2	no	—
178	C₂²×C₄×C₂₉	—	2	2	no	—
179	C₂²×C₄×C₂₉	—	2	2	no	—
180	C₂²×C₄×C₂₉	—	2	2	no	—
181	C₂²×C₄×C₂₉	—	2	2	no	—
182	C₂²×C₄×C₂₉	—	2	2	no	—
183	C₂²×C₄×C₂₉	—	2	2	no	—
184	C₂²×C₄×C₂₉	#41	1	4	yes	—
185	C₂²×C₄×C₂₉	#41	1	4	yes	—
186	C₂²×C₄×C₂₉	#41	1	4	yes	—
187	C₂²×C₄×C₂₉	#41	1	4	yes	—
188	C₂²×C₄×C₂₉	#41	1	4	yes	—
189	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
203	C₄⋊C₄×C₂₉	—	2	8	no	—
204	C₄⋊C₄×C₂₉	—	2	8	no	—
205	C₄⋊C₄×C₂₉	—	2	8	no	—
206	C₄⋊C₄×C₂₉	—	2	8	no	—
207	C₄⋊C₄×C₂₉	—	2	8	no	—
208	C₄⋊C₄×C₂₉	—	2	8	no	—
209	C₄⋊C₄×C₂₉	—	2	8	no	—
210	C₄⋊C₄×C₂₉	—	2	8	no	—
211	C₄⋊C₄×C₂₉	—	4	4	no	—
212	C₂²⋊C₄×C₂₉	—	2	8	no	—
213	C₂²⋊C₄×C₂₉	—	2	8	no	—
214	C₂²⋊C₄×C₂₉	—	2	8	no	—
215	C₂²⋊C₄×C₂₉	—	2	8	no	—
216	C₂²⋊C₄×C₂₉	—	2	8	no	—
217	C₂²⋊C₄×C₂₉	—	4	4	no	—
218	C₂²⋊C₄×C₂₉	—	4	4	no	—
219	C₄²×C₂₉	—	2	8	no	—
220	C₄²×C₂₉	—	2	8	no	—
221	C₄²×C₂₉	—	4	4	no	—
222	C₄²×C₂₉	—	4	4	no	—
223	C₄²×C₂₉	—	4	4	no	—
224	C₂×#2594	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂³×C₂₉	—	2	2	no	—
226	C₂³×C₂₉	—	2	2	no	—
227	C₂³×C₂₉	—	2	2	no	—
228	C₂³×C₂₉	—	2	2	no	—
229	C₂³×C₂₉	—	2	2	no	—
230	C₂³×C₂₉	—	2	2	no	—
231	C₂³×C₂₉	—	2	2	no	—
232	C₂³×C₂₉	—	4	4	no	—
233	C₂³×C₂₉	—	4	4	no	—
234	C₂³×C₂₉	—	4	4	no	—
235	C₂³×C₂₉	—	4	4	no	—
236	C₂³×C₂₉	—	4	4	no	—
237	C₂³×C₂₉	—	4	4	no	—
238	C₂³×C₂₉	—	4	4	no	—
239	C₂³×C₂₉	C₂×#41	1	2	yes	—
240	C₂³×C₂₉	C₂×#41	1	2	yes	—
241	C₂³×C₂₉	C₂×#41	1	2	yes	—
242	C₂³×C₂₉	C₂×#41	1	2	yes	—
243	C₂³×C₂₉	C₂×#41	1	2	yes	—
244	C₂³×C₂₉	H(5,𝔽₂)	1	2	yes	—
245	C₂³×C₂₉	2₋¹⁺⁴	1	2	yes	—
246	C₂³×C₂₉	C₂⁵	1	1	yes	characteristic
247	C₂×C₄×C₂₉	—	2	8	no	—
248	C₂×C₄×C₂₉	—	2	8	no	—
249	C₂×C₄×C₂₉	—	2	8	no	—
250	C₂×C₄×C₂₉	—	2	8	no	—
251	C₂×C₄×C₂₉	—	2	8	no	—
252	C₂×C₄×C₂₉	—	2	2	no	—
253	C₂×C₄×C₂₉	—	2	2	no	—
254	C₂×C₄×C₂₉	—	2	2	no	—
255	C₂×C₄×C₂₉	—	2	2	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	2	no	—
264	C₂×C₄×C₂₉	—	2	2	no	—
265	C₂×C₄×C₂₉	—	2	2	no	—
266	C₂×C₄×C₂₉	—	2	2	no	—
267	C₂×C₄×C₂₉	—	2	2	no	—
268	C₂×C₄×C₂₉	—	2	2	no	—
269	C₂×C₄×C₂₉	—	2	2	no	—
270	C₂×C₄×C₂₉	—	2	2	no	—
271	C₂×C₄×C₂₉	—	2	2	no	—
272	C₂×C₄×C₂₉	—	2	2	no	—
273	C₂×C₄×C₂₉	—	2	2	no	—
274	C₂×C₄×C₂₉	—	2	2	no	—
275	C₂×C₄×C₂₉	—	2	2	no	—
276	C₂×C₄×C₂₉	—	2	2	no	—
277	C₂×C₄×C₂₉	—	2	2	no	—
278	C₂×C₄×C₂₉	—	2	2	no	—
279	C₂×C₄×C₂₉	—	2	2	no	—
280	C₂×C₄×C₂₉	—	2	2	no	—
281	C₂×C₄×C₂₉	—	2	2	no	—
282	C₂×C₄×C₂₉	—	2	2	no	—
283	C₂×C₄×C₂₉	—	2	2	no	—
284	C₂×C₄×C₂₉	—	2	2	no	—
285	C₂×C₄×C₂₉	—	2	2	no	—
286	C₂×C₄×C₂₉	—	2	2	no	—
287	C₂×C₄×C₂₉	—	2	2	no	—
288	C₂×C₄×C₂₉	—	2	2	no	—
289	C₂×C₄×C₂₉	—	4	4	no	—
290	C₂×C₄×C₂₉	—	4	4	no	—
291	C₂×C₄×C₂₉	—	4	4	no	—
292	C₂×C₄×C₂₉	—	4	4	no	—
293	C₂×C₄×C₂₉	—	4	4	no	—
294	C₂×C₄×C₂₉	—	4	4	no	—
295	C₂×C₄×C₂₉	—	4	4	no	—
296	C₂×C₄×C₂₉	—	4	4	no	—
297	C₂×C₄×C₂₉	—	4	4	no	—
298	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
299	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
300	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
301	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
302	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
303	#2594	C₂×C₂₉	1	16	yes	direct product factor
304	C₂×#401	C₂×C₂₉	1	1	yes	characteristic, complemented
305	C₂×#398	C₂×C₂₉	1	1	yes	characteristic, complemented
306	C₂×#397	C₂×C₂₉	1	1	yes	characteristic
307	C₂×#396	C₂×C₂₉	1	1	yes	characteristic
308	C₂×#389	C₂×C₂₉	1	1	yes	characteristic, complemented
309	C₂×#388	C₂×C₂₉	1	1	yes	characteristic
310	C₂×#388	C₂×C₂₉	1	1	yes	characteristic
311	C₂×#388	C₂×C₂₉	1	1	yes	characteristic
312	C₂×#388	C₂×C₂₉	1	1	yes	characteristic
313	C₂×#388	C₂×C₂₉	1	1	yes	characteristic
314	C₂×#387	C₂×C₂₉	1	1	yes	characteristic, complemented
315	C₂×#387	C₂×C₂₉	1	1	yes	characteristic, complemented
316	C₂×#387	C₂×C₂₉	1	1	yes	characteristic, complemented
317	C₂×C₄×C₄⋊C₄	C₂×C₂₉	1	1	yes	characteristic, complemented
318	C₂×C₄×C₄⋊C₄	C₂×C₂₉	1	1	yes	characteristic, complemented
319	C₂²×C₂₉	—	4	2	no	—
320	C₂²×C₂₉	—	4	2	no	—
321	C₂²×C₂₉	—	4	2	no	—
322	C₂²×C₂₉	—	4	2	no	—
323	C₂²×C₂₉	—	4	2	no	—
324	C₂²×C₂₉	—	4	2	no	—
325	C₂²×C₂₉	—	4	2	no	—
326	C₂²×C₂₉	—	8	8	no	—
327	C₂²×C₂₉	#529	1	4	yes	—
328	C₂²×C₂₉	#529	1	4	yes	—
329	C₂²×C₂₉	#539	1	4	yes	—
330	C₂²×C₂₉	#553	1	4	yes	—
331	C₂²×C₂₉	#553	1	4	yes	—
332	C₂²×C₂₉	#556	1	4	yes	—
333	C₂²×C₂₉	#556	1	4	yes	—
334	C₂²×C₂₉	C₂²×#41	1	1	yes	characteristic
335	C₂²×C₂₉	C₂²×#41	1	1	yes	characteristic
336	C₂²×C₂₉	C₂²×#41	1	1	yes	characteristic
337	C₂²×C₂₉	C₂²×#41	1	1	yes	characteristic
338	C₂²×C₂₉	C₂²×#41	1	1	yes	characteristic
339	C₂²×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
340	C₂²×C₂₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
341	C₄×C₂₉	—	2	4	no	—
342	C₄×C₂₉	—	2	4	no	—
343	C₄×C₂₉	—	2	4	no	—
344	C₄×C₂₉	—	2	4	no	—
345	C₄×C₂₉	—	2	4	no	—
346	C₄×C₂₉	—	4	2	no	—
347	C₄×C₂₉	—	4	2	no	—
348	C₄×C₂₉	—	4	2	no	—
349	C₄×C₂₉	—	4	2	no	—
350	C₄×C₂₉	—	4	2	no	—
351	C₄×C₂₉	—	4	2	no	—
352	C₄×C₂₉	—	4	2	no	—
353	C₄×C₂₉	—	4	2	no	—
354	C₄×C₂₉	—	4	2	no	—
355	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
356	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
357	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
358	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
359	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
360	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
361	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
362	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
363	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
364	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
365	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
366	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
367	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
368	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
369	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
370	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
371	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
372	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
373	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
374	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
375	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
376	#401	C₂²×C₂₉	1	8	yes	complemented
377	#398	C₂²×C₂₉	1	8	yes	complemented
378	#397	C₂²×C₂₉	1	8	yes	—
379	#396	C₂²×C₂₉	1	8	yes	—
380	#389	C₂²×C₂₉	1	8	yes	complemented
381	#388	C₂²×C₂₉	1	8	yes	—
382	#388	C₂²×C₂₉	1	8	yes	—
383	#388	C₂²×C₂₉	1	8	yes	—
384	#388	C₂²×C₂₉	1	8	yes	—
385	#388	C₂²×C₂₉	1	8	yes	—
386	#387	C₂²×C₂₉	1	8	yes	complemented
387	#387	C₂²×C₂₉	1	8	yes	complemented
388	#387	C₂²×C₂₉	1	8	yes	complemented
389	C₄×C₄⋊C₄	C₂²×C₂₉	1	8	yes	complemented
390	C₄×C₄⋊C₄	C₂²×C₂₉	1	8	yes	complemented
391	C₂×#95	C₂²×C₂₉	1	1	yes	characteristic
392	C₂×#95	C₂²×C₂₉	1	1	yes	characteristic
393	C₂×#95	C₂²×C₂₉	1	1	yes	characteristic
394	C₂×#95	C₂²×C₂₉	1	1	yes	characteristic
395	C₂×#95	C₂²×C₂₉	1	1	yes	characteristic
396	C₂×#95	C₂²×C₂₉	1	1	yes	characteristic
397	C₂×#95	C₂²×C₂₉	1	1	yes	characteristic
398	C₂×#95	C₂²×C₂₉	1	1	yes	characteristic
399	C₂×#95	C₂²×C₂₉	1	1	yes	characteristic
400	C₂×#95	C₂²×C₂₉	1	1	yes	characteristic
401	C₂×#95	C₂²×C₂₉	1	1	yes	characteristic
402	C₂×#95	C₂²×C₂₉	1	1	yes	characteristic
403	C₂×#95	C₂²×C₂₉	1	1	yes	characteristic
404	C₂×#95	C₂²×C₂₉	1	1	yes	characteristic
405	C₂×C₂₉	—	8	2	no	—
406	C₂×C₂₉	#2594	1	8	yes	direct product factor
407	C₂×C₂₉	C₂×#529	1	1	yes	characteristic
408	C₂×C₂₉	C₂×#529	1	1	yes	characteristic
409	C₂×C₂₉	C₂×#539	1	1	yes	characteristic
410	C₂×C₂₉	C₂×#553	1	1	yes	characteristic
411	C₂×C₂₉	C₂×#553	1	1	yes	characteristic
412	C₂×C₂₉	C₂×#556	1	1	yes	characteristic
413	C₂×C₂₉	C₂×#556	1	1	yes	characteristic
414	C₂⁵	C₂³×C₂₉	1	1	yes	characteristic
415	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
416	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
418	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
419	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
420	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
422	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
427	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
429	C₂×C₄⋊C₄	—	2	4	no	—
430	C₂×C₄⋊C₄	—	2	4	no	—
431	C₂×C₄⋊C₄	—	2	4	no	—
432	C₂×C₄⋊C₄	—	2	4	no	—
433	C₂×C₄⋊C₄	—	2	4	no	—
434	C₂×C₄⋊C₄	—	2	4	no	—
435	C₂×C₄⋊C₄	—	2	4	no	—
436	C₂×C₄⋊C₄	—	2	4	no	—
437	C₂×C₄⋊C₄	—	4	2	no	—
438	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
439	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
440	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
441	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
442	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
443	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
445	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
446	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
447	C₂×C₂²⋊C₄	—	2	4	no	—
448	C₂×C₂²⋊C₄	—	2	4	no	—
449	C₂×C₂²⋊C₄	—	2	4	no	—
450	C₂×C₂²⋊C₄	—	2	4	no	—
451	C₂×C₂²⋊C₄	—	2	4	no	—
452	C₂×C₂²⋊C₄	—	4	2	no	—
453	C₂×C₂²⋊C₄	—	4	2	no	—
454	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
461	C₂×C₄²	—	2	4	no	—
462	C₂×C₄²	—	2	4	no	—
463	C₂×C₄²	—	4	2	no	—
464	C₂×C₄²	—	4	2	no	—
465	C₂×C₄²	—	4	2	no	—
466	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
467	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
468	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
469	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
470	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
471	#95	C₂³×C₂₉	1	4	yes	—
472	#95	C₂³×C₂₉	1	4	yes	—
473	#95	C₂³×C₂₉	1	4	yes	—
474	#95	C₂³×C₂₉	1	4	yes	—
475	#95	C₂³×C₂₉	1	4	yes	—
476	#95	C₂³×C₂₉	1	4	yes	—
477	#95	C₂³×C₂₉	1	4	yes	—
478	#95	C₂³×C₂₉	1	4	yes	—
479	#95	C₂³×C₂₉	1	4	yes	—
480	#95	C₂³×C₂₉	1	4	yes	—
481	#95	C₂³×C₂₉	1	4	yes	—
482	#95	C₂³×C₂₉	1	4	yes	—
483	#95	C₂³×C₂₉	1	4	yes	—
484	#95	C₂³×C₂₉	1	4	yes	—
485	C₂₉	C₂×#2594	1	1	yes	characteristic, direct product factor, Sylow
486	C₂⁴	—	2	2	no	—
487	C₂⁴	—	2	2	no	—
488	C₂⁴	—	2	2	no	—
489	C₂⁴	—	2	2	no	—
490	C₂⁴	—	2	2	no	—
491	C₂⁴	—	2	2	no	—
492	C₂⁴	—	2	2	no	—
493	C₂⁴	C₂⁴×C₂₉	1	2	yes	—
494	C₂⁴	C₂⁴×C₂₉	1	1	yes	characteristic
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	#41×C₂₉	1	4	yes	—
533	C₂²×C₄	#41×C₂₉	1	4	yes	—
534	C₂²×C₄	#41×C₂₉	1	4	yes	—
535	C₂²×C₄	#41×C₂₉	1	4	yes	—
536	C₂²×C₄	#41×C₂₉	1	4	yes	—
537	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
538	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
539	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
551	C₄⋊C₄	—	2	8	no	—
552	C₄⋊C₄	—	2	8	no	—
553	C₄⋊C₄	—	2	8	no	—
554	C₄⋊C₄	—	2	8	no	—
555	C₄⋊C₄	—	2	8	no	—
556	C₄⋊C₄	—	2	8	no	—
557	C₄⋊C₄	—	2	8	no	—
558	C₄⋊C₄	—	2	8	no	—
559	C₄⋊C₄	—	4	4	no	—
560	C₂²⋊C₄	—	2	8	no	—
561	C₂²⋊C₄	—	2	8	no	—
562	C₂²⋊C₄	—	2	8	no	—
563	C₂²⋊C₄	—	2	8	no	—
564	C₂²⋊C₄	—	2	8	no	—
565	C₂²⋊C₄	—	4	4	no	—
566	C₂²⋊C₄	—	4	4	no	—
567	C₄²	—	2	8	no	—
568	C₄²	—	2	8	no	—
569	C₄²	—	4	4	no	—
570	C₄²	—	4	4	no	—
571	C₄²	—	4	4	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	4	4	no	—
580	C₂³	—	4	4	no	—
581	C₂³	—	4	4	no	—
582	C₂³	—	4	4	no	—
583	C₂³	—	4	4	no	—
584	C₂³	—	4	4	no	—
585	C₂³	—	4	4	no	—
586	C₂³	C₂×#41×C₂₉	1	2	yes	—
587	C₂³	C₂×#41×C₂₉	1	2	yes	—
588	C₂³	C₂×#41×C₂₉	1	2	yes	—
589	C₂³	C₂×#41×C₂₉	1	2	yes	—
590	C₂³	C₂×#41×C₂₉	1	2	yes	—
591	C₂³	C₂₉×H(5,𝔽₂)	1	2	yes	—
592	C₂³	C₂₉×2₋¹⁺⁴	1	2	yes	—
593	C₂³	C₂⁵×C₂₉	1	1	yes	characteristic
594	C₂×C₄	—	2	8	no	—
595	C₂×C₄	—	2	8	no	—
596	C₂×C₄	—	2	8	no	—
597	C₂×C₄	—	2	8	no	—
598	C₂×C₄	—	2	8	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	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	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	4	4	no	—
637	C₂×C₄	—	4	4	no	—
638	C₂×C₄	—	4	4	no	—
639	C₂×C₄	—	4	4	no	—
640	C₂×C₄	—	4	4	no	—
641	C₂×C₄	—	4	4	no	—
642	C₂×C₄	—	4	4	no	—
643	C₂×C₄	—	4	4	no	—
644	C₂×C₄	—	4	4	no	—
645	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
646	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
647	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
648	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
649	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	8	8	no	—
658	C₂²	C₂₉×#529	1	4	yes	—
659	C₂²	C₂₉×#529	1	4	yes	—
660	C₂²	C₂₉×#539	1	4	yes	—
661	C₂²	C₂₉×#553	1	4	yes	—
662	C₂²	C₂₉×#553	1	4	yes	—
663	C₂²	C₂₉×#556	1	4	yes	—
664	C₂²	C₂₉×#556	1	4	yes	—
665	C₂²	C₂²×#41×C₂₉	1	1	yes	characteristic
666	C₂²	C₂²×#41×C₂₉	1	1	yes	characteristic
667	C₂²	C₂²×#41×C₂₉	1	1	yes	characteristic
668	C₂²	C₂²×#41×C₂₉	1	1	yes	characteristic
669	C₂²	C₂²×#41×C₂₉	1	1	yes	characteristic
670	C₂²	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
671	C₂²	C₂×C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
672	C₄	—	2	4	no	—
673	C₄	—	2	4	no	—
674	C₄	—	2	4	no	—
675	C₄	—	2	4	no	—
676	C₄	—	2	4	no	—
677	C₄	—	4	2	no	—
678	C₄	—	4	2	no	—
679	C₄	—	4	2	no	—
680	C₄	—	4	2	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	2	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	2	no	—
686	C₂	—	8	2	no	—
687	C₂	C₂₉×#2594	1	8	yes	direct product factor
688	C₂	C₂×C₂₉×#529	1	1	yes	characteristic
689	C₂	C₂×C₂₉×#529	1	1	yes	characteristic
690	C₂	C₂×C₂₉×#539	1	1	yes	characteristic
691	C₂	C₂×C₂₉×#553	1	1	yes	characteristic
692	C₂	C₂×C₂₉×#553	1	1	yes	characteristic
693	C₂	C₂×C₂₉×#556	1	1	yes	characteristic
694	C₂	C₂×C₂₉×#556	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂₉×#2594	C₂	direct (N × H)
2. C₂×C₂₉×#401	C₂	semidirect
3. C₂×C₂₉×#398	C₂	semidirect
6. C₂×C₂₉×#389	C₂	semidirect
12. C₂×C₂₉×#387	C₂	semidirect
13. C₂×C₂₉×#387	C₂	semidirect
14. C₂×C₂₉×#387	C₂	semidirect
15. C₂×C₄×C₄⋊C₄×C₂₉	C₂	semidirect
16. C₂×C₄×C₄⋊C₄×C₂₉	C₂	semidirect
38. C₂₉×#401	C₂²	semidirect
39. C₂₉×#398	C₂²	semidirect
42. C₂₉×#389	C₂²	semidirect
48. C₂₉×#387	C₂²	semidirect
49. C₂₉×#387	C₂²	semidirect
50. C₂₉×#387	C₂²	semidirect
51. C₄×C₄⋊C₄×C₂₉	C₂²	semidirect
52. C₄×C₄⋊C₄×C₂₉	C₂²	semidirect
224. C₂×#2594	C₂₉	direct (N × H)
303. #2594	C₂×C₂₉	direct (N × H)
304. C₂×#401	C₂×C₂₉	semidirect
305. C₂×#398	C₂×C₂₉	semidirect
308. C₂×#389	C₂×C₂₉	semidirect
314. C₂×#387	C₂×C₂₉	semidirect
315. C₂×#387	C₂×C₂₉	semidirect
316. C₂×#387	C₂×C₂₉	semidirect
317. C₂×C₄×C₄⋊C₄	C₂×C₂₉	semidirect
318. C₂×C₄×C₄⋊C₄	C₂×C₂₉	semidirect
376. #401	C₂²×C₂₉	semidirect
377. #398	C₂²×C₂₉	semidirect
380. #389	C₂²×C₂₉	semidirect
386. #387	C₂²×C₂₉	semidirect
387. #387	C₂²×C₂₉	semidirect
388. #387	C₂²×C₂₉	semidirect
389. C₄×C₄⋊C₄	C₂²×C₂₉	semidirect
390. C₄×C₄⋊C₄	C₂²×C₂₉	semidirect
406. C₂×C₂₉	#2594	direct (N × H)
485. C₂₉	C₂×#2594	direct (N × H)
687. C₂	C₂₉×#2594	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#2594	2
C₂×C₂₉×#401	2
C₂×C₂₉×#398	2
C₂×C₂₉×#397	2
C₂×C₂₉×#396	2
C₂×C₂₉×#389	2
C₂×C₂₉×#388	2
C₂×C₂₉×#387	2
C₂×C₄×C₄⋊C₄×C₂₉	2
C₂×#2594	29

Subgroups — C2×C29×#2594 #20329752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#2594 #20329752