Subgroups — C₂₉×#25320 #20320220

Order 7424.

894 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#461	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2542	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2072	C₂	1	2	yes	maximal, complemented
6	C₂₉×#2055	C₂	1	2	yes	maximal
7	C₂₉×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1939	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1880	C₂	1	2	yes	maximal
10	C₂₉×#1803	C₂	1	2	yes	maximal, complemented
11	C₄×C₂₉×#102	C₂	1	1	yes	maximal, characteristic
12	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	—
13	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₂₉×C₂²⋊Q₈	—	2	1	no	—
16	C₂×C₂₉×C₂²⋊Q₈	—	2	1	no	—
17	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
19	C₂₉×#487	—	2	4	no	—
20	C₂₉×#461	—	2	4	no	—
21	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₂₉×#103	C₂²	1	2	yes	—
24	C₂×C₂₉×#103	C₂²	1	2	yes	—
25	C₂×C₂₉×#103	C₂²	1	2	yes	—
26	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
29	C₂₉×#399	—	2	2	no	—
30	C₂₉×#391	C₂²	1	2	yes	—
31	C₂₉×#390	C₂²	1	2	yes	—
32	C₂₉×#389	—	2	1	no	—
33	C₂₉×#387	—	2	2	no	—
34	C₂₉×#384	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
36	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
38	C₂₉×#340	C₂²	1	2	yes	—
39	C₂₉×#340	C₂²	1	2	yes	—
40	C₂₉×#340	C₂²	1	1	yes	characteristic
41	C₂₉×#340	C₂²	1	1	yes	characteristic
42	C₂₉×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₂₉	—	2	1	no	—
44	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
45	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₂₉	—	2	1	no	—
47	C₂×SD₁₆×C₂₉	—	2	4	no	—
48	C₂×SD₁₆×C₂₉	—	2	4	no	—
49	C₂×SD₁₆×C₂₉	—	4	2	no	—
50	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
53	C₂₉×C₄⋊Q₈	—	2	2	no	—
54	C₂₉×C₄⋊Q₈	—	2	2	no	—
55	C₂₉×C₄⋊Q₈	—	2	2	no	—
56	C₂₉×C₄⋊Q₈	D₄	1	4	yes	—
57	C₂₉×C₂²⋊Q₈	—	4	4	no	—
58	C₂₉×C₂²⋊Q₈	—	4	4	no	—
59	C₄×Q₈×C₂₉	—	2	4	no	—
60	C₄×Q₈×C₂₉	—	4	2	no	—
61	C₄×D₄×C₂₉	—	2	2	no	—
62	C₄×D₄×C₂₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
78	C₂×C₄²×C₂₉	—	2	2	no	—
79	C₂×C₄²×C₂₉	—	2	1	no	—
80	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
81	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
82	C₂₉×C₄⋊C₈	—	2	2	no	—
83	C₂₉×C₄⋊C₈	—	4	2	no	—
84	C₂₉×#103	—	2	4	no	—
85	C₂₉×#103	—	2	4	no	—
86	C₂₉×#103	—	2	4	no	—
87	C₂₉×#102	—	2	2	no	—
88	C₂₉×#102	—	2	2	no	—
89	C₄×C₈×C₂₉	—	2	2	no	—
90	C₂₉×#95	—	2	2	no	—
91	C₂₉×#95	—	2	1	no	—
92	C₂₉×#95	—	2	2	no	—
93	C₂₉×#95	D₄	1	2	yes	—
94	C₂⁴×C₂₉	—	2	1	no	—
95	C₂×Q₈×C₂₉	—	2	2	no	—
96	C₂×Q₈×C₂₉	—	2	2	no	—
97	C₂×Q₈×C₂₉	—	2	2	no	—
98	C₂×Q₈×C₂₉	—	2	2	no	—
99	C₂×Q₈×C₂₉	—	2	2	no	—
100	C₂×Q₈×C₂₉	—	4	2	no	—
101	C₂×Q₈×C₂₉	—	4	2	no	—
102	C₂×Q₈×C₂₉	—	4	2	no	—
103	C₂×Q₈×C₂₉	C₂×D₄	1	4	yes	—
104	C₂×D₄×C₂₉	—	2	1	no	—
105	C₂×D₄×C₂₉	—	2	1	no	—
106	C₂×D₄×C₂₉	—	2	1	no	—
107	C₂×D₄×C₂₉	—	2	1	no	—
108	C₂×D₄×C₂₉	—	2	1	no	—
109	C₂×D₄×C₂₉	#41	1	2	yes	—
110	C₂²×C₄×C₂₉	—	2	1	no	—
111	C₂²×C₄×C₂₉	—	2	2	no	—
112	C₂²×C₄×C₂₉	—	2	1	no	—
113	C₂²×C₄×C₂₉	—	2	2	no	—
114	C₂²×C₄×C₂₉	—	2	1	no	—
115	C₂²×C₄×C₂₉	—	4	2	no	—
116	C₂²×C₄×C₂₉	—	4	2	no	—
117	C₂²×C₄×C₂₉	—	4	2	no	—
118	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
123	SD₁₆×C₂₉	—	4	8	no	—
124	C₂×C₈×C₂₉	—	2	2	no	—
125	C₂×C₈×C₂₉	—	2	1	no	—
126	C₂×C₈×C₂₉	—	2	1	no	—
127	C₂×C₈×C₂₉	—	2	2	no	—
128	C₂×C₈×C₂₉	—	2	1	no	—
129	C₂×C₈×C₂₉	—	2	1	no	—
130	C₂×C₈×C₂₉	—	2	2	no	—
131	C₂×C₈×C₂₉	—	2	1	no	—
132	C₂×C₈×C₂₉	—	2	1	no	—
133	C₄⋊C₄×C₂₉	—	2	4	no	—
134	C₄⋊C₄×C₂₉	—	2	4	no	—
135	C₄⋊C₄×C₂₉	—	2	2	no	—
136	C₄⋊C₄×C₂₉	—	2	1	no	—
137	C₄⋊C₄×C₂₉	—	2	1	no	—
138	C₄⋊C₄×C₂₉	—	2	2	no	—
139	C₄⋊C₄×C₂₉	—	2	1	no	—
140	C₄⋊C₄×C₂₉	—	2	2	no	—
141	C₄⋊C₄×C₂₉	—	2	1	no	—
142	C₄⋊C₄×C₂₉	—	2	1	no	—
143	C₄⋊C₄×C₂₉	—	4	4	no	—
144	C₄⋊C₄×C₂₉	—	4	4	no	—
145	C₄⋊C₄×C₂₉	—	4	2	no	—
146	C₄⋊C₄×C₂₉	—	4	4	no	—
147	C₄⋊C₄×C₂₉	SD₁₆	1	4	yes	complemented
148	C₄⋊C₄×C₂₉	#41	1	2	yes	—
149	C₂²⋊C₄×C₂₉	—	4	4	no	—
150	C₂²⋊C₄×C₂₉	—	4	2	no	—
151	C₂²⋊C₄×C₂₉	—	4	4	no	—
152	C₄²×C₂₉	—	2	2	no	—
153	C₄²×C₂₉	—	2	2	no	—
154	C₄²×C₂₉	—	4	4	no	—
155	C₄²×C₂₉	—	4	2	no	—
156	C₄²×C₂₉	C₂×D₄	1	2	yes	—
157	C₄²×C₂₉	#41	1	2	yes	—
158	#25320	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂³×C₂₉	—	2	2	no	—
160	C₂³×C₂₉	—	4	1	no	—
161	C₂³×C₂₉	—	4	1	no	—
162	C₂³×C₂₉	—	4	1	no	—
163	C₂³×C₂₉	—	4	1	no	—
164	C₂³×C₂₉	—	4	1	no	—
165	C₂³×C₂₉	—	4	1	no	—
166	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₂₉	—	2	4	no	—
168	Q₈×C₂₉	—	2	4	no	—
169	Q₈×C₂₉	—	4	2	no	—
170	Q₈×C₂₉	—	4	2	no	—
171	Q₈×C₂₉	—	8	4	no	—
172	D₄×C₂₉	—	2	2	no	—
173	D₄×C₂₉	—	2	2	no	—
174	D₄×C₂₉	—	4	1	no	—
175	D₄×C₂₉	—	4	1	no	—
176	C₂×C₄×C₂₉	—	2	2	no	—
177	C₂×C₄×C₂₉	—	2	2	no	—
178	C₂×C₄×C₂₉	—	2	1	no	—
179	C₂×C₄×C₂₉	—	2	1	no	—
180	C₂×C₄×C₂₉	—	2	4	no	—
181	C₂×C₄×C₂₉	—	2	2	no	—
182	C₂×C₄×C₂₉	—	2	2	no	—
183	C₂×C₄×C₂₉	—	2	2	no	—
184	C₂×C₄×C₂₉	—	2	2	no	—
185	C₂×C₄×C₂₉	—	4	2	no	—
186	C₂×C₄×C₂₉	—	4	2	no	—
187	C₂×C₄×C₂₉	—	4	1	no	—
188	C₂×C₄×C₂₉	—	4	1	no	—
189	C₂×C₄×C₂₉	—	4	1	no	—
190	C₂×C₄×C₂₉	—	4	2	no	—
191	C₂×C₄×C₂₉	—	4	1	no	—
192	C₂×C₄×C₂₉	—	4	2	no	—
193	C₂×C₄×C₂₉	—	4	1	no	—
194	C₂×C₄×C₂₉	—	4	1	no	—
195	C₂×C₄×C₂₉	—	4	2	no	—
196	C₂×C₄×C₂₉	—	4	1	no	—
197	C₂×C₄×C₂₉	—	4	1	no	—
198	C₂×C₄×C₂₉	—	8	4	no	—
199	C₂×C₄×C₂₉	#121	1	2	yes	—
200	C₂×C₄×C₂₉	#121	1	2	yes	—
201	C₂×C₄×C₂₉	C₂×SD₁₆	1	4	yes	—
202	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
203	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
204	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
210	C₈×C₂₉	—	4	1	no	—
211	C₈×C₂₉	—	4	2	no	—
212	C₈×C₂₉	—	4	1	no	—
213	C₂×#487	C₂×C₂₉	1	1	yes	characteristic, complemented
214	C₂×#461	C₂×C₂₉	1	1	yes	characteristic
215	#2542	C₂×C₂₉	1	1	yes	characteristic
216	#2365	C₂×C₂₉	1	1	yes	characteristic, complemented
217	#2072	C₂×C₂₉	1	2	yes	complemented
218	#2055	C₂×C₂₉	1	2	yes	—
219	#1988	C₂×C₂₉	1	1	yes	characteristic, complemented
220	#1939	C₂×C₂₉	1	1	yes	characteristic, complemented
221	#1880	C₂×C₂₉	1	2	yes	—
222	#1803	C₂×C₂₉	1	2	yes	complemented
223	C₄×#102	C₂×C₂₉	1	1	yes	characteristic
224	C₂²×C₂₉	—	4	2	no	—
225	C₂²×C₂₉	—	4	2	no	—
226	C₂²×C₂₉	—	4	2	no	—
227	C₂²×C₂₉	—	8	1	no	—
228	C₂²×C₂₉	—	8	1	no	—
229	C₂²×C₂₉	—	8	1	no	—
230	C₂²×C₂₉	—	8	1	no	—
231	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
232	C₂²×C₂₉	#546	1	1	yes	characteristic
233	C₂²×C₂₉	#548	1	1	yes	characteristic
234	C₂²×C₂₉	C₂²×SD₁₆	1	1	yes	characteristic
235	C₂²×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₂²×C₂₉	#578	1	1	yes	characteristic
237	C₂²×C₂₉	#578	1	1	yes	characteristic
238	C₄×C₂₉	—	2	4	no	—
239	C₄×C₂₉	—	2	2	no	—
240	C₄×C₂₉	—	4	2	no	—
241	C₄×C₂₉	—	4	2	no	—
242	C₄×C₂₉	—	4	4	no	—
243	C₄×C₂₉	—	8	1	no	—
244	C₄×C₂₉	—	8	1	no	—
245	C₄×C₂₉	—	8	2	no	—
246	C₄×C₂₉	#460	1	4	yes	—
247	C₄×C₂₉	#529	1	1	yes	characteristic
248	C₄×C₂₉	#542	1	1	yes	characteristic
249	C₄×C₂₉	#546	1	1	yes	characteristic
250	C₄×C₂₉	#547	1	1	yes	characteristic
251	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	—
252	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
253	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
254	C₂×C₂²⋊Q₈	—	2	1	no	—
255	C₂×C₂²⋊Q₈	—	2	1	no	—
256	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
257	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
258	#487	—	2	4	no	—
259	#461	—	2	4	no	—
260	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
262	C₂×#103	C₂²×C₂₉	1	2	yes	—
263	C₂×#103	C₂²×C₂₉	1	2	yes	—
264	C₂×#103	C₂²×C₂₉	1	2	yes	—
265	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
266	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
267	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
268	#399	—	2	2	no	—
269	#391	C₂²×C₂₉	1	2	yes	—
270	#390	C₂²×C₂₉	1	2	yes	—
271	#389	—	2	1	no	—
272	#387	—	2	2	no	—
273	#384	C₂²×C₂₉	1	2	yes	—
274	C₄×C₄⋊C₄	—	2	1	no	—
275	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
276	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
277	#340	C₂²×C₂₉	1	2	yes	—
278	#340	C₂²×C₂₉	1	1	yes	characteristic
279	#340	C₂²×C₂₉	1	2	yes	—
280	#340	C₂²×C₂₉	1	1	yes	characteristic
281	#336	C₂²×C₂₉	1	2	yes	—
282	C₂×C₂₉	—	8	2	no	—
283	C₂×C₂₉	#2427	1	1	yes	characteristic
284	C₂×C₂₉	C₂×#460	1	1	yes	characteristic
285	C₂×C₂₉	#3044	1	1	yes	characteristic
286	C₂×C₂₉	#3298	1	1	yes	characteristic
287	C₂×C₂₉	#3330	1	1	yes	characteristic
288	C₂×C₂₉	#3359	1	1	yes	characteristic
289	C₂×C₂₉	#3367	1	1	yes	characteristic
290	C₂²×Q₈	—	2	1	no	—
291	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
292	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
293	C₂³×C₄	—	2	1	no	—
294	C₂×SD₁₆	—	2	4	no	—
295	C₂×SD₁₆	—	2	4	no	—
296	C₂×SD₁₆	—	4	2	no	—
297	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
298	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
300	C₄⋊Q₈	—	2	2	no	—
301	C₄⋊Q₈	—	2	2	no	—
302	C₄⋊Q₈	—	2	2	no	—
303	C₄⋊Q₈	D₄×C₂₉	1	4	yes	—
304	C₂²⋊Q₈	—	4	4	no	—
305	C₂²⋊Q₈	—	4	4	no	—
306	C₄×Q₈	—	2	4	no	—
307	C₄×Q₈	—	4	2	no	—
308	C₄×D₄	—	2	2	no	—
309	C₄×D₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
317	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₄²	—	2	2	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
328	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
329	C₄⋊C₈	—	2	2	no	—
330	C₄⋊C₈	—	4	2	no	—
331	#103	—	2	4	no	—
332	#103	—	2	4	no	—
333	#103	—	2	4	no	—
334	#102	—	2	2	no	—
335	#102	—	2	2	no	—
336	C₄×C₈	—	2	2	no	—
337	#95	—	2	2	no	—
338	#95	—	2	1	no	—
339	#95	—	2	2	no	—
340	#95	D₄×C₂₉	1	2	yes	—
341	C₂₉	#25320	1	1	yes	characteristic, direct product factor, Sylow
342	C₂⁴	—	2	1	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	4	2	no	—
349	C₂×Q₈	—	4	2	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	C₂×D₄×C₂₉	1	4	yes	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	#41×C₂₉	1	2	yes	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
370	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
371	SD₁₆	—	4	8	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	1	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	4	4	no	—
392	C₄⋊C₄	—	4	4	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₄⋊C₄	—	4	4	no	—
395	C₄⋊C₄	SD₁₆×C₂₉	1	4	yes	complemented
396	C₄⋊C₄	#41×C₂₉	1	2	yes	—
397	C₂²⋊C₄	—	4	4	no	—
398	C₂²⋊C₄	—	4	2	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	4	4	no	—
403	C₄²	—	4	2	no	—
404	C₄²	C₂×D₄×C₂₉	1	2	yes	—
405	C₄²	#41×C₂₉	1	2	yes	—
406	C₂³	—	2	2	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	1	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
414	Q₈	—	2	4	no	—
415	Q₈	—	2	4	no	—
416	Q₈	—	4	2	no	—
417	Q₈	—	4	2	no	—
418	Q₈	—	8	4	no	—
419	D₄	—	2	2	no	—
420	D₄	—	2	2	no	—
421	D₄	—	4	1	no	—
422	D₄	—	4	1	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	8	4	no	—
446	C₂×C₄	C₂₉×#121	1	2	yes	—
447	C₂×C₄	C₂₉×#121	1	2	yes	—
448	C₂×C₄	C₂×SD₁₆×C₂₉	1	4	yes	—
449	C₂×C₄	C₂×SD₁₆×C₂₉	1	2	yes	—
450	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
451	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
455	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
456	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
457	C₈	—	4	2	no	—
458	C₈	—	4	1	no	—
459	C₈	—	4	1	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	8	1	no	—
464	C₂²	—	8	1	no	—
465	C₂²	—	8	1	no	—
466	C₂²	—	8	1	no	—
467	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
468	C₂²	C₂₉×#546	1	1	yes	characteristic
469	C₂²	C₂₉×#548	1	1	yes	characteristic
470	C₂²	C₂²×SD₁₆×C₂₉	1	1	yes	characteristic
471	C₂²	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
472	C₂²	C₂₉×#578	1	1	yes	characteristic
473	C₂²	C₂₉×#578	1	1	yes	characteristic
474	C₄	—	2	4	no	—
475	C₄	—	2	2	no	—
476	C₄	—	4	4	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	8	1	no	—
480	C₄	—	8	2	no	—
481	C₄	—	8	1	no	—
482	C₄	C₂₉×#460	1	4	yes	—
483	C₄	C₂₉×#529	1	1	yes	characteristic
484	C₄	C₂₉×#542	1	1	yes	characteristic
485	C₄	C₂₉×#546	1	1	yes	characteristic
486	C₄	C₂₉×#547	1	1	yes	characteristic
487	C₂	—	8	2	no	—
488	C₂	C₂₉×#2427	1	1	yes	characteristic
489	C₂	C₂×C₂₉×#460	1	1	yes	characteristic
490	C₂	C₂₉×#3044	1	1	yes	characteristic
491	C₂	C₂₉×#3298	1	1	yes	characteristic
492	C₂	C₂₉×#3330	1	1	yes	characteristic
493	C₂	C₂₉×#3359	1	1	yes	characteristic
494	C₂	C₂₉×#3367	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 ◁ C₄×C₄⋊C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#487	C₂	semidirect
4. C₂₉×#2365	C₂	semidirect
5. C₂₉×#2072	C₂	semidirect
7. C₂₉×#1988	C₂	semidirect
8. C₂₉×#1939	C₂	semidirect
10. C₂₉×#1803	C₂	semidirect
147. C₄⋊C₄×C₂₉	SD₁₆	semidirect
158. #25320	C₂₉	direct (N × H)
213. C₂×#487	C₂×C₂₉	semidirect
216. #2365	C₂×C₂₉	semidirect
217. #2072	C₂×C₂₉	semidirect
219. #1988	C₂×C₂₉	semidirect
220. #1939	C₂×C₂₉	semidirect
222. #1803	C₂×C₂₉	semidirect
341. C₂₉	#25320	direct (N × H)
395. C₄⋊C₄	SD₁₆×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×#487	2
C₂×C₂₉×#461	2
C₂₉×#2542	2
C₂₉×#2365	2
C₂₉×#2072	2
C₂₉×#2055	2
C₂₉×#1988	2
C₂₉×#1939	2
C₂₉×#1880	2
C₂₉×#1803	2
C₄×C₂₉×#102	2
#25320	29

Subgroups — C29×#25320 #20320220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#25320 #20320220