Subgroups — C₂₉×#17708 #20312608

Order 7424.

1018 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#431	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#423	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1550	C₂	1	4	yes	maximal, complemented
5	C₂₉×#1549	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1548	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1542	C₂	1	4	yes	maximal, complemented
8	C₂²×M₁₆×C₂₉	—	2	1	no	—
9	C₂₉×#533	—	2	1	no	—
10	C₂₉×#533	—	2	1	no	—
11	C₂₉×#533	—	2	1	no	—
12	C₂₉×#533	—	2	1	no	—
13	C₂₉×#533	C₄	1	2	yes	—
14	C₂₉×#533	C₄	1	2	yes	—
15	C₂₉×#533	C₂²	1	2	yes	—
16	C₂₉×#533	C₂²	1	2	yes	—
17	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#125	—	2	1	no	—
20	C₂×C₂₉×C₂²⋊Q₈	—	2	1	no	—
21	C₂×C₂₉×C₂²⋊Q₈	C₄	1	2	yes	—
22	C₂×C₄×Q₈×C₂₉	—	2	1	no	—
23	C₂×C₄×Q₈×C₂₉	C₄	1	2	yes	—
24	C₂×C₂₉×#117	—	2	1	no	—
25	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
26	C₂₉×#431	—	2	1	no	—
27	C₂₉×#431	—	2	1	no	—
28	C₂₉×#431	C₂²	1	2	yes	—
29	C₂₉×#431	C₂²	1	2	yes	—
30	C₂₉×#423	—	2	1	no	—
31	C₂₉×#423	—	2	1	no	—
32	C₂₉×#423	C₂²	1	2	yes	—
33	C₂₉×#423	C₂²	1	2	yes	—
34	C₂×C₂₉×C₄⋊C₈	—	2	1	no	—
35	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
36	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
37	C₂×C₂₉×C₂²⋊C₈	—	2	1	no	—
38	C₂×C₄×C₈×C₂₉	—	2	1	no	—
39	C₂₉×#333	C₂²	1	8	yes	complemented
40	C₂₉×#332	C₂²	1	8	yes	complemented
41	C₂²×Q₈×C₂₉	—	2	1	no	—
42	C₂²×Q₈×C₂₉	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₂₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₂₉	D₄	1	1	yes	characteristic
46	C₂×M₁₆×C₂₉	—	2	2	no	—
47	C₂×M₁₆×C₂₉	—	2	2	no	—
48	C₂×M₁₆×C₂₉	—	4	4	no	—
49	C₂²×C₈×C₂₉	—	2	2	no	—
50	C₂²×C₈×C₂₉	—	2	2	no	—
51	C₂₉×C₄⋊Q₈	—	2	1	no	—
52	C₂₉×C₄⋊Q₈	—	2	1	no	—
53	C₂₉×C₄⋊Q₈	—	2	1	no	—
54	C₂₉×C₄⋊Q₈	—	2	1	no	—
55	C₂₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
56	C₂₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
57	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₂₉×#125	—	2	2	no	—
60	C₂₉×#125	—	2	2	no	—
61	C₂₉×#125	—	2	2	no	—
62	C₂₉×#125	—	2	2	no	—
63	C₂₉×C₂²⋊Q₈	—	2	2	no	—
64	C₂₉×C₂²⋊Q₈	—	2	2	no	—
65	C₂₉×C₂²⋊Q₈	—	2	2	no	—
66	C₂₉×C₂²⋊Q₈	—	2	2	no	—
67	C₂₉×C₂²⋊Q₈	—	2	2	no	—
68	C₂₉×C₂²⋊Q₈	—	2	2	no	—
69	C₂₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
70	C₂₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
71	C₄×Q₈×C₂₉	—	2	2	no	—
72	C₄×Q₈×C₂₉	—	2	2	no	—
73	C₄×Q₈×C₂₉	—	2	2	no	—
74	C₄×Q₈×C₂₉	—	2	2	no	—
75	C₄×Q₈×C₂₉	—	2	2	no	—
76	C₄×Q₈×C₂₉	—	2	2	no	—
77	C₄×Q₈×C₂₉	C₂×C₄	1	4	yes	—
78	C₄×Q₈×C₂₉	C₂×C₄	1	4	yes	—
79	C₂₉×#117	—	2	2	no	—
80	C₂₉×#117	—	2	2	no	—
81	C₂₉×#117	—	2	2	no	—
82	C₂₉×#117	—	2	2	no	—
83	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
85	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
89	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
90	C₂×C₄²×C₂₉	—	2	2	no	—
91	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
103	C₂₉×C₄⋊C₈	—	2	2	no	—
104	C₂₉×C₄⋊C₈	—	2	2	no	—
105	C₂₉×C₄⋊C₈	—	2	2	no	—
106	C₂₉×C₄⋊C₈	—	2	2	no	—
107	C₂₉×C₄⋊C₈	C₂³	1	4	yes	—
108	C₂₉×C₄⋊C₈	C₂³	1	4	yes	—
109	C₂₉×C₂²⋊C₈	—	2	2	no	—
110	C₂₉×C₂²⋊C₈	—	2	2	no	—
111	C₄×C₈×C₂₉	—	2	2	no	—
112	C₄×C₈×C₂₉	—	2	2	no	—
113	C₂⁴×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×Q₈×C₂₉	—	2	2	no	—
115	C₂×Q₈×C₂₉	—	2	2	no	—
116	C₂×Q₈×C₂₉	—	2	2	no	—
117	C₂×Q₈×C₂₉	—	4	4	no	—
118	C₂×Q₈×C₂₉	—	4	4	no	—
119	C₂×Q₈×C₂₉	C₂²×C₄	1	4	yes	—
120	C₂²×C₄×C₂₉	—	2	2	no	—
121	C₂²×C₄×C₂₉	—	2	2	no	—
122	C₂²×C₄×C₂₉	—	4	2	no	—
123	C₂²×C₄×C₂₉	—	4	2	no	—
124	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×C₄×C₂₉	SD₁₆	1	4	yes	—
134	C₂²×C₄×C₂₉	Q₁₆	1	4	yes	—
135	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
144	M₁₆×C₂₉	—	4	4	no	—
145	M₁₆×C₂₉	—	4	4	no	—
146	C₂×C₈×C₂₉	—	2	4	no	—
147	C₂×C₈×C₂₉	—	2	4	no	—
148	C₂×C₈×C₂₉	—	4	4	no	—
149	C₂×C₈×C₂₉	—	4	4	no	—
150	C₄⋊C₄×C₂₉	—	2	2	no	—
151	C₄⋊C₄×C₂₉	—	2	2	no	—
152	C₄⋊C₄×C₂₉	—	2	2	no	—
153	C₄⋊C₄×C₂₉	—	2	4	no	—
154	C₄⋊C₄×C₂₉	—	2	4	no	—
155	C₄⋊C₄×C₂₉	—	2	4	no	—
156	C₄⋊C₄×C₂₉	—	2	4	no	—
157	C₄⋊C₄×C₂₉	—	2	2	no	—
158	C₄⋊C₄×C₂₉	—	2	2	no	—
159	C₄⋊C₄×C₂₉	—	2	2	no	—
160	C₄⋊C₄×C₂₉	—	2	2	no	—
161	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
162	C₂²⋊C₄×C₂₉	—	2	4	no	—
163	C₂²⋊C₄×C₂₉	—	2	4	no	—
164	C₄²×C₂₉	—	2	4	no	—
165	C₄²×C₂₉	—	2	4	no	—
166	C₄²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
167	C₄²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
168	C₄²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
169	C₄²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
170	C₄²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
182	#17708	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂³×C₂₉	—	4	1	no	—
184	C₂³×C₂₉	—	4	1	no	—
185	C₂³×C₂₉	#103	1	4	yes	—
186	C₂³×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂³×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂³×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	Q₈×C₂₉	—	4	4	no	—
190	Q₈×C₂₉	—	4	4	no	—
191	Q₈×C₂₉	—	4	4	no	—
192	Q₈×C₂₉	—	4	4	no	—
193	C₂×C₄×C₂₉	—	2	2	no	—
194	C₂×C₄×C₂₉	—	2	2	no	—
195	C₂×C₄×C₂₉	—	2	2	no	—
196	C₂×C₄×C₂₉	—	2	2	no	—
197	C₂×C₄×C₂₉	—	2	2	no	—
198	C₂×C₄×C₂₉	—	2	2	no	—
199	C₂×C₄×C₂₉	—	2	4	no	—
200	C₂×C₄×C₂₉	—	2	4	no	—
201	C₂×C₄×C₂₉	—	4	1	no	—
202	C₂×C₄×C₂₉	—	4	1	no	—
203	C₂×C₄×C₂₉	—	4	1	no	—
204	C₂×C₄×C₂₉	—	4	1	no	—
205	C₂×C₄×C₂₉	—	4	1	no	—
206	C₂×C₄×C₂₉	—	4	1	no	—
207	C₂×C₄×C₂₉	—	4	4	no	—
208	C₂×C₄×C₂₉	—	4	4	no	—
209	C₂×C₄×C₂₉	#103	1	4	yes	—
210	C₂×C₄×C₂₉	#103	1	4	yes	—
211	C₂×C₄×C₂₉	#103	1	4	yes	—
212	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
222	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
223	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
224	C₂×C₄×C₂₉	C₂×Q₁₆	1	2	yes	—
225	C₂×C₄×C₂₉	C₂×Q₁₆	1	2	yes	—
226	C₂×C₄×C₂₉	C₂×Q₁₆	1	2	yes	—
227	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
230	C₈×C₂₉	—	4	4	no	—
231	C₈×C₂₉	—	4	4	no	—
232	C₂×#533	C₂×C₂₉	1	1	yes	characteristic
233	C₂×#431	C₂×C₂₉	1	1	yes	characteristic
234	C₂×#423	C₂×C₂₉	1	1	yes	characteristic
235	#1550	C₂×C₂₉	1	4	yes	complemented
236	#1549	C₂×C₂₉	1	2	yes	complemented
237	#1548	C₂×C₂₉	1	2	yes	complemented
238	#1542	C₂×C₂₉	1	4	yes	complemented
239	C₂²×C₂₉	—	2	1	no	—
240	C₂²×C₂₉	—	2	1	no	—
241	C₂²×C₂₉	—	2	1	no	—
242	C₂²×C₂₉	—	2	1	no	—
243	C₂²×C₂₉	—	2	1	no	—
244	C₂²×C₂₉	—	2	1	no	—
245	C₂²×C₂₉	—	4	4	no	—
246	C₂²×C₂₉	C₂×#103	1	2	yes	—
247	C₂²×C₂₉	C₂×#103	1	2	yes	—
248	C₂²×C₂₉	C₂×#103	1	2	yes	—
249	C₂²×C₂₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
250	C₄×C₂₉	—	2	1	no	—
251	C₄×C₂₉	—	2	1	no	—
252	C₄×C₂₉	—	2	1	no	—
253	C₄×C₂₉	—	2	1	no	—
254	C₄×C₂₉	—	2	1	no	—
255	C₄×C₂₉	—	2	1	no	—
256	C₄×C₂₉	—	4	4	no	—
257	C₄×C₂₉	—	4	4	no	—
258	C₄×C₂₉	#413	1	2	yes	—
259	C₄×C₂₉	C₂×#103	1	2	yes	—
260	C₄×C₂₉	C₂×#103	1	2	yes	—
261	C₄×C₂₉	C₂×#103	1	2	yes	—
262	C₄×C₂₉	C₂²×SD₁₆	1	1	yes	characteristic
263	C₄×C₂₉	C₂²×Q₁₆	1	1	yes	characteristic
264	C₄×C₂₉	#575	1	2	yes	—
265	C₂²×M₁₆	—	2	1	no	—
266	#533	—	2	1	no	—
267	#533	—	2	1	no	—
268	#533	—	2	1	no	—
269	#533	—	2	1	no	—
270	#533	C₄×C₂₉	1	2	yes	—
271	#533	C₄×C₂₉	1	2	yes	—
272	#533	C₂²×C₂₉	1	2	yes	—
273	#533	C₂²×C₂₉	1	2	yes	—
274	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
275	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
276	C₂×#125	—	2	1	no	—
277	C₂×C₂²⋊Q₈	—	2	1	no	—
278	C₂×C₂²⋊Q₈	C₄×C₂₉	1	2	yes	—
279	C₂×C₄×Q₈	—	2	1	no	—
280	C₂×C₄×Q₈	C₄×C₂₉	1	2	yes	—
281	C₂×#117	—	2	1	no	—
282	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
283	#431	—	2	1	no	—
284	#431	—	2	1	no	—
285	#431	C₂²×C₂₉	1	2	yes	—
286	#431	C₂²×C₂₉	1	2	yes	—
287	#423	—	2	1	no	—
288	#423	—	2	1	no	—
289	#423	C₂²×C₂₉	1	2	yes	—
290	#423	C₂²×C₂₉	1	2	yes	—
291	C₂×C₄⋊C₈	—	2	1	no	—
292	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
293	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
294	C₂×C₂²⋊C₈	—	2	1	no	—
295	C₂×C₄×C₈	—	2	1	no	—
296	#333	C₂²×C₂₉	1	8	yes	complemented
297	#332	C₂²×C₂₉	1	8	yes	complemented
298	C₂×C₂₉	—	2	2	no	—
299	C₂×C₂₉	—	2	2	no	—
300	C₂×C₂₉	—	2	2	no	—
301	C₂×C₂₉	C₂×#413	1	1	yes	characteristic
302	C₂×C₂₉	C₂²×#103	1	1	yes	characteristic
303	C₂×C₂₉	#2896	1	1	yes	characteristic
304	C₂²×Q₈	—	2	1	no	—
305	C₂²×Q₈	C₂×C₄×C₂₉	1	2	yes	—
306	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
307	C₂³×C₄	D₄×C₂₉	1	1	yes	characteristic
308	C₂³×C₄	D₄×C₂₉	1	1	yes	characteristic
309	C₂×M₁₆	—	2	2	no	—
310	C₂×M₁₆	—	2	2	no	—
311	C₂×M₁₆	—	4	4	no	—
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	—	2	2	no	—
314	C₄⋊Q₈	—	2	1	no	—
315	C₄⋊Q₈	—	2	1	no	—
316	C₄⋊Q₈	—	2	1	no	—
317	C₄⋊Q₈	—	2	1	no	—
318	C₄⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
319	C₄⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
320	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
321	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
322	#125	—	2	2	no	—
323	#125	—	2	2	no	—
324	#125	—	2	2	no	—
325	#125	—	2	2	no	—
326	C₂²⋊Q₈	—	2	2	no	—
327	C₂²⋊Q₈	—	2	2	no	—
328	C₂²⋊Q₈	—	2	2	no	—
329	C₂²⋊Q₈	—	2	2	no	—
330	C₂²⋊Q₈	—	2	2	no	—
331	C₂²⋊Q₈	—	2	2	no	—
332	C₂²⋊Q₈	C₂×C₄×C₂₉	1	4	yes	—
333	C₂²⋊Q₈	C₂×C₄×C₂₉	1	4	yes	—
334	C₄×Q₈	—	2	2	no	—
335	C₄×Q₈	—	2	2	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	—	2	2	no	—
338	C₄×Q₈	—	2	2	no	—
339	C₄×Q₈	—	2	2	no	—
340	C₄×Q₈	C₂×C₄×C₂₉	1	4	yes	—
341	C₄×Q₈	C₂×C₄×C₂₉	1	4	yes	—
342	#117	—	2	2	no	—
343	#117	—	2	2	no	—
344	#117	—	2	2	no	—
345	#117	—	2	2	no	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₄²	—	2	2	no	—
354	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
355	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
356	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
357	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
358	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
359	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
360	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
361	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
362	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
363	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
366	C₄⋊C₈	—	2	2	no	—
367	C₄⋊C₈	—	2	2	no	—
368	C₄⋊C₈	—	2	2	no	—
369	C₄⋊C₈	—	2	2	no	—
370	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
371	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
372	C₂²⋊C₈	—	2	2	no	—
373	C₂²⋊C₈	—	2	2	no	—
374	C₄×C₈	—	2	2	no	—
375	C₄×C₈	—	2	2	no	—
376	C₂₉	#17708	1	1	yes	characteristic, direct product factor, Sylow
377	C₂⁴	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	4	4	no	—
382	C₂×Q₈	—	4	4	no	—
383	C₂×Q₈	C₂²×C₄×C₂₉	1	4	yes	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
389	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
390	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
391	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
392	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
393	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
394	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
395	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
396	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
397	C₂²×C₄	SD₁₆×C₂₉	1	4	yes	—
398	C₂²×C₄	Q₁₆×C₂₉	1	4	yes	—
399	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
400	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
401	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
408	M₁₆	—	4	4	no	—
409	M₁₆	—	4	4	no	—
410	C₂×C₈	—	2	4	no	—
411	C₂×C₈	—	2	4	no	—
412	C₂×C₈	—	4	4	no	—
413	C₂×C₈	—	4	4	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	2	4	no	—
428	C₄²	—	2	4	no	—
429	C₄²	—	2	4	no	—
430	C₄²	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
431	C₄²	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
432	C₄²	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
433	C₄²	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
434	C₄²	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
435	C₄²	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
436	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
437	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
438	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
439	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
440	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
441	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
442	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
443	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
444	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
445	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
446	C₂³	—	4	1	no	—
447	C₂³	—	4	1	no	—
448	C₂³	C₂₉×#103	1	4	yes	—
449	C₂³	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
450	C₂³	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
451	C₂³	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
452	Q₈	—	4	4	no	—
453	Q₈	—	4	4	no	—
454	Q₈	—	4	4	no	—
455	Q₈	—	4	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	C₂₉×#103	1	4	yes	—
473	C₂×C₄	C₂₉×#103	1	4	yes	—
474	C₂×C₄	C₂₉×#103	1	4	yes	—
475	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
476	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
477	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
478	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
479	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
480	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
481	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
482	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
483	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
484	C₂×C₄	C₂×SD₁₆×C₂₉	1	2	yes	—
485	C₂×C₄	C₂×SD₁₆×C₂₉	1	2	yes	—
486	C₂×C₄	C₂×SD₁₆×C₂₉	1	2	yes	—
487	C₂×C₄	C₂×Q₁₆×C₂₉	1	2	yes	—
488	C₂×C₄	C₂×Q₁₆×C₂₉	1	2	yes	—
489	C₂×C₄	C₂×Q₁₆×C₂₉	1	2	yes	—
490	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
493	C₈	—	4	4	no	—
494	C₈	—	4	4	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	4	4	no	—
502	C₂²	C₂×C₂₉×#103	1	2	yes	—
503	C₂²	C₂×C₂₉×#103	1	2	yes	—
504	C₂²	C₂×C₂₉×#103	1	2	yes	—
505	C₂²	C₂²×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	2	1	no	—
511	C₄	—	2	1	no	—
512	C₄	—	4	4	no	—
513	C₄	—	4	4	no	—
514	C₄	C₂₉×#413	1	2	yes	—
515	C₄	C₂×C₂₉×#103	1	2	yes	—
516	C₄	C₂×C₂₉×#103	1	2	yes	—
517	C₄	C₂×C₂₉×#103	1	2	yes	—
518	C₄	C₂²×SD₁₆×C₂₉	1	1	yes	characteristic
519	C₄	C₂²×Q₁₆×C₂₉	1	1	yes	characteristic
520	C₄	C₂₉×#575	1	2	yes	—
521	C₂	—	2	2	no	—
522	C₂	—	2	2	no	—
523	C₂	—	2	2	no	—
524	C₂	C₂×C₂₉×#413	1	1	yes	characteristic
525	C₂	C₂²×C₂₉×#103	1	1	yes	characteristic
526	C₂	C₂₉×#2896	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₄²	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₂₉	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂²×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₉×#1550	C₂	semidirect
5. C₂₉×#1549	C₂	semidirect
6. C₂₉×#1548	C₂	semidirect
7. C₂₉×#1542	C₂	semidirect
39. C₂₉×#333	C₂²	semidirect
40. C₂₉×#332	C₂²	semidirect
182. #17708	C₂₉	direct (N × H)
235. #1550	C₂×C₂₉	semidirect
236. #1549	C₂×C₂₉	semidirect
237. #1548	C₂×C₂₉	semidirect
238. #1542	C₂×C₂₉	semidirect
296. #333	C₂²×C₂₉	semidirect
297. #332	C₂²×C₂₉	semidirect
376. C₂₉	#17708	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×#533	2
C₂×C₂₉×#431	2
C₂×C₂₉×#423	2
C₂₉×#1550	2
C₂₉×#1549	2
C₂₉×#1548	2
C₂₉×#1542	2
#17708	29

Subgroups — C29×#17708 #20312608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#17708 #20312608