Subgroups — C₂₉×#21695 #20316595

Order 7424.

1126 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#492	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#440	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×SD₁₆×C₂₉	C₂	1	2	yes	maximal, complemented
4	C₂₉×#2328	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#2327	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1973	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1968	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1961	C₂	1	1	yes	maximal, characteristic
9	C₂₉×#1960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1846	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	—
14	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
18	C₂₉×#492	C₄	1	8	yes	complemented
19	C₂₉×#440	—	2	8	no	—
20	C₄×SD₁₆×C₂₉	—	2	8	no	—
21	C₂×C₂₉×#107	C₂²	1	2	yes	—
22	C₂×C₂₉×#106	C₂²	1	2	yes	—
23	C₂×C₂₉×#103	C₂²	1	2	yes	—
24	C₂×C₂₉×#103	C₂²	1	2	yes	—
25	C₂×C₂₉×#102	C₂²	1	2	yes	—
26	C₂×C₂₉×#102	C₂²	1	2	yes	—
27	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
33	C₂₉×#391	C₂²	1	2	yes	—
34	C₂₉×#390	C₂²	1	2	yes	—
35	C₂₉×#387	—	2	4	no	—
36	C₂₉×#386	—	2	4	no	—
37	C₂₉×#382	C₂²	1	1	yes	characteristic
38	C₂₉×#382	C₂²	1	1	yes	characteristic
39	C₂₉×#376	C₂²	1	1	yes	characteristic
40	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
41	C₂²×D₄×C₂₉	—	2	2	no	—
42	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₂₉	—	2	2	no	—
44	C₂×SD₁₆×C₂₉	—	2	4	no	—
45	C₂×SD₁₆×C₂₉	—	2	4	no	—
46	C₂×SD₁₆×C₂₉	—	2	4	no	—
47	C₂×SD₁₆×C₂₉	—	2	4	no	—
48	C₂×SD₁₆×C₂₉	C₂×C₄	1	8	yes	complemented
49	C₂×SD₁₆×C₂₉	C₂×C₄	1	8	yes	complemented
50	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
54	C₂₉×C₄⋊Q₈	—	2	2	no	—
55	C₂₉×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
56	C₂₉×#127	—	2	2	no	—
57	C₂₉×#127	C₂×C₄	1	4	yes	—
58	C₄×Q₈×C₂₉	—	2	4	no	—
59	C₄×Q₈×C₂₉	—	2	4	no	—
60	C₄×D₄×C₂₉	—	2	4	no	—
61	C₄×D₄×C₂₉	—	2	4	no	—
62	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₂₉	—	2	4	no	—
68	C₂×C₄²×C₂₉	—	2	2	no	—
69	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
72	C₂₉×#107	—	2	4	no	—
73	C₂₉×#106	—	2	4	no	—
74	C₂₉×#103	—	2	4	no	—
75	C₂₉×#103	—	2	4	no	—
76	C₂₉×#102	—	2	4	no	—
77	C₂₉×#102	—	2	4	no	—
78	C₂₉×#97	—	2	2	no	—
79	C₂₉×#97	—	2	2	no	—
80	C₂₉×#97	D₄	1	4	yes	complemented
81	C₄×C₈×C₂₉	—	2	2	no	—
82	C₄×C₈×C₂₉	C₂×C₄	1	4	yes	complemented
83	C₄×C₈×C₂₉	D₄	1	4	yes	complemented
84	C₂₉×#95	—	2	2	no	—
85	C₂₉×#95	—	2	2	no	—
86	C₂₉×#95	—	2	4	no	—
87	C₂₉×#95	D₄	1	4	yes	—
88	C₂⁴×C₂₉	—	2	2	no	—
89	C₂×Q₈×C₂₉	—	2	2	no	—
90	C₂×Q₈×C₂₉	—	2	2	no	—
91	C₂×Q₈×C₂₉	—	2	2	no	—
92	C₂×Q₈×C₂₉	—	2	2	no	—
93	C₂×Q₈×C₂₉	—	2	2	no	—
94	C₂×Q₈×C₂₉	C₂²×C₄	1	4	yes	—
95	C₂×D₄×C₂₉	—	2	8	no	—
96	C₂×D₄×C₂₉	—	2	2	no	—
97	C₂×D₄×C₂₉	—	2	2	no	—
98	C₂×D₄×C₂₉	—	2	2	no	—
99	C₂×D₄×C₂₉	—	2	2	no	—
100	C₂×D₄×C₂₉	—	2	2	no	—
101	C₂×D₄×C₂₉	—	8	4	no	—
102	C₂×D₄×C₂₉	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₂₉	—	2	2	no	—
104	C₂²×C₄×C₂₉	—	2	2	no	—
105	C₂²×C₄×C₂₉	—	2	2	no	—
106	C₂²×C₄×C₂₉	—	4	4	no	—
107	C₂²×C₄×C₂₉	—	8	4	no	—
108	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
112	SD₁₆×C₂₉	—	2	16	no	—
113	SD₁₆×C₂₉	—	2	16	no	—
114	C₂×C₈×C₂₉	—	2	1	no	—
115	C₂×C₈×C₂₉	—	2	1	no	—
116	C₂×C₈×C₂₉	—	2	1	no	—
117	C₂×C₈×C₂₉	—	2	1	no	—
118	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₂₉	#41	1	2	yes	—
125	C₂×C₈×C₂₉	#41	1	2	yes	—
126	C₄⋊C₄×C₂₉	—	2	8	no	—
127	C₄⋊C₄×C₂₉	—	2	2	no	—
128	C₄⋊C₄×C₂₉	—	2	2	no	—
129	C₄⋊C₄×C₂₉	—	2	2	no	—
130	C₄⋊C₄×C₂₉	—	2	2	no	—
131	C₄⋊C₄×C₂₉	—	4	4	no	—
132	C₂²⋊C₄×C₂₉	—	4	4	no	—
133	C₂²⋊C₄×C₂₉	—	8	4	no	—
134	C₄²×C₂₉	—	2	1	no	—
135	C₄²×C₂₉	—	2	1	no	—
136	C₄²×C₂₉	—	4	4	no	—
137	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
138	C₄²×C₂₉	C₂×D₄	1	2	yes	—
139	C₄²×C₂₉	C₂×D₄	1	2	yes	—
140	C₄²×C₂₉	#41	1	2	yes	—
141	#21695	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₂₉	—	2	4	no	—
143	C₂³×C₂₉	—	4	2	no	—
144	C₂³×C₂₉	—	4	2	no	—
145	C₂³×C₂₉	—	4	4	no	—
146	C₂³×C₂₉	—	4	4	no	—
147	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₂₉	—	2	4	no	—
149	Q₈×C₂₉	—	2	4	no	—
150	Q₈×C₂₉	—	4	2	no	—
151	Q₈×C₂₉	—	4	2	no	—
152	D₄×C₂₉	—	2	4	no	—
153	D₄×C₂₉	—	2	4	no	—
154	D₄×C₂₉	—	4	2	no	—
155	D₄×C₂₉	—	4	2	no	—
156	D₄×C₂₉	—	8	8	no	—
157	C₂×C₄×C₂₉	—	2	4	no	—
158	C₂×C₄×C₂₉	—	2	4	no	—
159	C₂×C₄×C₂₉	—	2	4	no	—
160	C₂×C₄×C₂₉	—	2	2	no	—
161	C₂×C₄×C₂₉	—	2	4	no	—
162	C₂×C₄×C₂₉	—	4	2	no	—
163	C₂×C₄×C₂₉	—	4	2	no	—
164	C₂×C₄×C₂₉	—	4	2	no	—
165	C₂×C₄×C₂₉	—	4	2	no	—
166	C₂×C₄×C₂₉	—	4	4	no	—
167	C₂×C₄×C₂₉	—	4	4	no	—
168	C₂×C₄×C₂₉	—	8	8	no	—
169	C₂×C₄×C₂₉	C₄×D₄	1	4	yes	—
170	C₂×C₄×C₂₉	#127	1	4	yes	—
171	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
177	C₈×C₂₉	—	2	2	no	—
178	C₈×C₂₉	—	2	2	no	—
179	C₈×C₂₉	C₄×D₄	1	4	yes	—
180	C₈×C₂₉	C₄×D₄	1	4	yes	—
181	C₂×#492	C₂×C₂₉	1	1	yes	characteristic
182	C₂×#440	C₂×C₂₉	1	2	yes	complemented
183	C₂×C₄×SD₁₆	C₂×C₂₉	1	2	yes	complemented
184	#2328	C₂×C₂₉	1	1	yes	characteristic
185	#2327	C₂×C₂₉	1	1	yes	characteristic, complemented
186	#1973	C₂×C₂₉	1	2	yes	complemented
187	#1968	C₂×C₂₉	1	2	yes	complemented
188	#1961	C₂×C₂₉	1	1	yes	characteristic
189	#1960	C₂×C₂₉	1	1	yes	characteristic, complemented
190	#1846	C₂×C₂₉	1	1	yes	characteristic, complemented
191	#1726	C₂×C₂₉	1	1	yes	characteristic, complemented
192	C₂²×C₂₉	—	4	4	no	—
193	C₂²×C₂₉	—	4	8	no	—
194	C₂²×C₂₉	—	8	2	no	—
195	C₂²×C₂₉	—	8	2	no	—
196	C₂²×C₂₉	—	8	4	no	—
197	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂²×C₂₉	C₂×#127	1	1	yes	characteristic
199	C₂²×C₂₉	#532	1	1	yes	characteristic
200	C₂²×C₂₉	#577	1	4	yes	—
201	C₄×C₂₉	—	2	4	no	—
202	C₄×C₂₉	—	2	4	no	—
203	C₄×C₂₉	—	4	4	no	—
204	C₄×C₂₉	—	4	2	no	—
205	C₄×C₂₉	—	8	2	no	—
206	C₄×C₂₉	—	8	2	no	—
207	C₄×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
208	C₄×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
209	C₄×C₂₉	#532	1	1	yes	characteristic
210	C₄×C₂₉	#532	1	1	yes	characteristic
211	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	—
212	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	—
213	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
214	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
215	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
216	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
217	#492	C₄×C₂₉	1	8	yes	complemented
218	#440	—	2	8	no	—
219	C₄×SD₁₆	—	2	8	no	—
220	C₂×#107	C₂²×C₂₉	1	2	yes	—
221	C₂×#106	C₂²×C₂₉	1	2	yes	—
222	C₂×#103	C₂²×C₂₉	1	2	yes	—
223	C₂×#103	C₂²×C₂₉	1	2	yes	—
224	C₂×#102	C₂²×C₂₉	1	2	yes	—
225	C₂×#102	C₂²×C₂₉	1	2	yes	—
226	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
227	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
228	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
229	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
230	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
231	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
232	#391	C₂²×C₂₉	1	2	yes	—
233	#390	C₂²×C₂₉	1	2	yes	—
234	#387	—	2	4	no	—
235	#386	—	2	4	no	—
236	#382	C₂²×C₂₉	1	1	yes	characteristic
237	#382	C₂²×C₂₉	1	1	yes	characteristic
238	#376	C₂²×C₂₉	1	1	yes	characteristic
239	C₂×C₂₉	—	8	4	no	—
240	C₂×C₂₉	C₄×#127	1	1	yes	characteristic
241	C₂×C₂₉	#2949	1	2	yes	—
242	C₂×C₂₉	#3154	1	2	yes	—
243	C₂×C₂₉	#3174	1	2	yes	—
244	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
245	C₂²×D₄	—	2	2	no	—
246	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
247	C₂³×C₄	—	2	2	no	—
248	C₂×SD₁₆	—	2	4	no	—
249	C₂×SD₁₆	—	2	4	no	—
250	C₂×SD₁₆	—	2	4	no	—
251	C₂×SD₁₆	—	2	4	no	—
252	C₂×SD₁₆	C₂×C₄×C₂₉	1	8	yes	complemented
253	C₂×SD₁₆	C₂×C₄×C₂₉	1	8	yes	complemented
254	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
258	C₄⋊Q₈	—	2	2	no	—
259	C₄⋊Q₈	C₂×C₄×C₂₉	1	4	yes	complemented
260	#127	—	2	2	no	—
261	#127	C₂×C₄×C₂₉	1	4	yes	—
262	C₄×Q₈	—	2	4	no	—
263	C₄×Q₈	—	2	4	no	—
264	C₄×D₄	—	2	4	no	—
265	C₄×D₄	—	2	4	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	4	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
276	#107	—	2	4	no	—
277	#106	—	2	4	no	—
278	#103	—	2	4	no	—
279	#103	—	2	4	no	—
280	#102	—	2	4	no	—
281	#102	—	2	4	no	—
282	#97	—	2	2	no	—
283	#97	—	2	2	no	—
284	#97	D₄×C₂₉	1	4	yes	complemented
285	C₄×C₈	—	2	2	no	—
286	C₄×C₈	C₂×C₄×C₂₉	1	4	yes	complemented
287	C₄×C₈	D₄×C₂₉	1	4	yes	complemented
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	#95	—	2	4	no	—
291	#95	D₄×C₂₉	1	4	yes	—
292	C₂₉	#21695	1	1	yes	characteristic, direct product factor, Sylow
293	C₂⁴	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	C₂²×C₄×C₂₉	1	4	yes	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	8	4	no	—
307	C₂×D₄	C₂²×C₄×C₂₉	1	4	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	4	4	no	—
312	C₂²×C₄	—	8	4	no	—
313	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
316	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
317	SD₁₆	—	2	16	no	—
318	SD₁₆	—	2	16	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
324	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
325	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
326	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
327	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
328	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
329	C₂×C₈	#41×C₂₉	1	2	yes	—
330	C₂×C₈	#41×C₂₉	1	2	yes	—
331	C₄⋊C₄	—	2	8	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₂²⋊C₄	—	4	4	no	—
338	C₂²⋊C₄	—	8	4	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	4	4	no	—
342	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
343	C₄²	C₂×D₄×C₂₉	1	2	yes	—
344	C₄²	C₂×D₄×C₂₉	1	2	yes	—
345	C₄²	#41×C₂₉	1	2	yes	—
346	C₂³	—	2	4	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	4	no	—
350	C₂³	—	4	4	no	—
351	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
352	Q₈	—	2	4	no	—
353	Q₈	—	2	4	no	—
354	Q₈	—	4	2	no	—
355	Q₈	—	4	2	no	—
356	D₄	—	2	4	no	—
357	D₄	—	2	4	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	8	8	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	8	8	no	—
373	C₂×C₄	C₄×D₄×C₂₉	1	4	yes	—
374	C₂×C₄	C₂₉×#127	1	4	yes	—
375	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
376	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
378	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
379	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
380	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
381	C₈	—	2	2	no	—
382	C₈	—	2	2	no	—
383	C₈	C₄×D₄×C₂₉	1	4	yes	—
384	C₈	C₄×D₄×C₂₉	1	4	yes	—
385	C₂²	—	4	8	no	—
386	C₂²	—	4	4	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	4	no	—
390	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
391	C₂²	C₂×C₂₉×#127	1	1	yes	characteristic
392	C₂²	C₂₉×#532	1	1	yes	characteristic
393	C₂²	C₂₉×#577	1	4	yes	—
394	C₄	—	2	4	no	—
395	C₄	—	2	4	no	—
396	C₄	—	4	4	no	—
397	C₄	—	4	2	no	—
398	C₄	—	8	2	no	—
399	C₄	—	8	2	no	—
400	C₄	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
401	C₄	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
402	C₄	C₂₉×#532	1	1	yes	characteristic
403	C₄	C₂₉×#532	1	1	yes	characteristic
404	C₂	—	8	4	no	—
405	C₂	C₄×C₂₉×#127	1	1	yes	characteristic
406	C₂	C₂₉×#2949	1	2	yes	—
407	C₂	C₂₉×#3154	1	2	yes	—
408	C₂	C₂₉×#3174	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂₉×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₉×#440	C₂	semidirect
3. C₂×C₄×SD₁₆×C₂₉	C₂	semidirect
5. C₂₉×#2327	C₂	semidirect
6. C₂₉×#1973	C₂	semidirect
7. C₂₉×#1968	C₂	semidirect
9. C₂₉×#1960	C₂	semidirect
10. C₂₉×#1846	C₂	semidirect
11. C₂₉×#1726	C₂	semidirect
18. C₂₉×#492	C₄	semidirect
48. C₂×SD₁₆×C₂₉	C₂×C₄	semidirect
49. C₂×SD₁₆×C₂₉	C₂×C₄	semidirect
55. C₂₉×C₄⋊Q₈	C₂×C₄	semidirect
80. C₂₉×#97	D₄	semidirect
82. C₄×C₈×C₂₉	C₂×C₄	semidirect
83. C₄×C₈×C₂₉	D₄	semidirect
141. #21695	C₂₉	direct (N × H)
182. C₂×#440	C₂×C₂₉	semidirect
183. C₂×C₄×SD₁₆	C₂×C₂₉	semidirect
185. #2327	C₂×C₂₉	semidirect
186. #1973	C₂×C₂₉	semidirect
187. #1968	C₂×C₂₉	semidirect
189. #1960	C₂×C₂₉	semidirect
190. #1846	C₂×C₂₉	semidirect
191. #1726	C₂×C₂₉	semidirect
217. #492	C₄×C₂₉	semidirect
252. C₂×SD₁₆	C₂×C₄×C₂₉	semidirect
253. C₂×SD₁₆	C₂×C₄×C₂₉	semidirect
259. C₄⋊Q₈	C₂×C₄×C₂₉	semidirect
284. #97	D₄×C₂₉	semidirect
286. C₄×C₈	C₂×C₄×C₂₉	semidirect
287. C₄×C₈	D₄×C₂₉	semidirect
292. C₂₉	#21695	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×#492	2
C₂×C₂₉×#440	2
C₂×C₄×SD₁₆×C₂₉	2
C₂₉×#2328	2
C₂₉×#2327	2
C₂₉×#1973	2
C₂₉×#1968	2
C₂₉×#1961	2
C₂₉×#1960	2
C₂₉×#1846	2
C₂₉×#1726	2
#21695	29

Subgroups — C29×#21695 #20316595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#21695 #20316595