Subgroups — C₂₉×#34953 #20329853

Order 7424.

2402 conjugacy classes of subgroups.

The subgroup lattice has 462 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	C₂²×C₄×Q₈×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2584	C₂	1	4	yes	maximal, complemented
4	C₂₉×#2583	C₂	1	4	yes	maximal
5	C₂₉×#2567	C₂	1	2	yes	maximal, complemented
6	C₂₉×#2546	C₂	1	2	yes	maximal, complemented
7	C₂₉×#2502	C₂	1	2	yes	maximal
8	C₂₉×#2434	C₂	1	2	yes	maximal
9	C₂₉×#2399	C₂	1	4	yes	maximal, complemented
10	C₄×C₂₉×C₄⋊Q₈	C₂	1	4	yes	maximal, complemented
11	C₂₉×#2296	C₂	1	4	yes	maximal
12	C₄×C₂₉×#117	C₂	1	1	yes	maximal, characteristic
13	C₂³×Q₈×C₂₉	C₂²	1	1	yes	characteristic
14	C₂₉×#533	—	2	8	no	—
15	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×C₄⋊Q₈	C₂²	1	4	yes	—
18	C₂×C₂₉×#125	C₂²	1	2	yes	—
19	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₂₉	—	2	8	no	—
22	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
28	C₂×C₂₉×#117	C₂²	1	2	yes	—
29	C₂×C₂₉×#117	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
32	C₂²×C₄²×C₂₉	C₂²	1	2	yes	—
33	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
34	C₂₉×#398	C₂²	1	8	yes	—
35	C₂₉×#398	C₂²	1	8	yes	—
36	C₂₉×#395	C₂²	1	8	yes	—
37	C₂₉×#395	C₂²	1	8	yes	—
38	C₂₉×#391	C₂²	1	4	yes	—
39	C₂₉×#391	C₂²	1	4	yes	—
40	C₂₉×#389	C₂²	1	8	yes	—
41	C₂₉×#389	C₂²	1	8	yes	—
42	C₂₉×#389	C₂²	1	16	yes	—
43	C₂₉×#385	C₂²	1	8	yes	—
44	C₂₉×#385	C₂²	1	8	yes	—
45	C₂₉×#384	C₂²	1	4	yes	—
46	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
47	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
48	C₄×C₄⋊C₄×C₂₉	C₂²	1	16	yes	—
49	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
50	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
51	C₂₉×#376	C₂²	1	2	yes	—
52	C₄³×C₂₉	C₂²	1	2	yes	—
53	C₂²×Q₈×C₂₉	—	2	8	no	—
54	C₂²×Q₈×C₂₉	—	2	4	no	—
55	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
56	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
57	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
58	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
59	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
60	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
64	C₂₉×C₄⋊Q₈	—	2	16	no	—
65	C₂₉×C₄⋊Q₈	—	2	4	no	—
66	C₂₉×C₄⋊Q₈	—	2	4	no	—
67	C₂₉×#125	—	2	8	no	—
68	C₂₉×C₂²⋊Q₈	—	2	8	no	—
69	C₂₉×C₂²⋊Q₈	—	2	8	no	—
70	C₄×Q₈×C₂₉	—	2	8	no	—
71	C₄×Q₈×C₂₉	—	2	8	no	—
72	C₄×Q₈×C₂₉	—	2	8	no	—
73	C₄×Q₈×C₂₉	—	2	8	no	—
74	C₄×Q₈×C₂₉	—	2	8	no	—
75	C₄×Q₈×C₂₉	—	2	8	no	—
76	C₂₉×#117	—	2	8	no	—
77	C₂₉×#117	Q₈	1	16	yes	complemented
78	C₂×C₄⋊C₄×C₂₉	—	2	8	no	—
79	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
80	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
82	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₂₉	C₂³	1	16	yes	—
91	C₂×C₄⋊C₄×C₂₉	C₂³	1	16	yes	—
92	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
95	C₂×C₄²×C₂₉	—	2	8	no	—
96	C₂×C₄²×C₂₉	D₄	1	8	yes	—
97	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
98	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
99	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
100	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
101	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
102	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
107	C₂₉×#95	C₂³	1	4	yes	—
108	C₂₉×#95	C₂³	1	4	yes	—
109	C₂₉×#95	C₂³	1	16	yes	—
110	C₂₉×#95	C₂³	1	16	yes	—
111	C₂⁴×C₂₉	C₂⁴	1	1	yes	characteristic
112	C₂×Q₈×C₂₉	—	2	32	no	—
113	C₂×Q₈×C₂₉	—	2	4	no	—
114	C₂×Q₈×C₂₉	—	2	4	no	—
115	C₂×Q₈×C₂₉	—	2	4	no	—
116	C₂×Q₈×C₂₉	—	2	4	no	—
117	C₂×Q₈×C₂₉	—	2	8	no	—
118	C₂×Q₈×C₂₉	—	2	4	no	—
119	C₂×Q₈×C₂₉	—	2	8	no	—
120	C₂×Q₈×C₂₉	—	4	4	no	—
121	C₂×Q₈×C₂₉	#41	1	8	yes	—
122	C₂²×C₄×C₂₉	—	2	4	no	—
123	C₂²×C₄×C₂₉	—	2	8	no	—
124	C₂²×C₄×C₂₉	—	2	4	no	—
125	C₂²×C₄×C₂₉	—	2	4	no	—
126	C₂²×C₄×C₂₉	—	4	2	no	—
127	C₂²×C₄×C₂₉	—	4	4	no	—
128	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₂₉	C₂×Q₈	1	8	yes	—
132	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
136	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
139	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
141	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
143	C₄⋊C₄×C₂₉	—	2	8	no	—
144	C₄⋊C₄×C₂₉	—	2	8	no	—
145	C₄⋊C₄×C₂₉	—	2	4	no	—
146	C₄⋊C₄×C₂₉	—	2	4	no	—
147	C₄⋊C₄×C₂₉	—	2	4	no	—
148	C₄⋊C₄×C₂₉	—	2	4	no	—
149	C₄⋊C₄×C₂₉	—	2	8	no	—
150	C₄⋊C₄×C₂₉	—	2	8	no	—
151	C₄⋊C₄×C₂₉	—	2	4	no	—
152	C₄⋊C₄×C₂₉	—	2	4	no	—
153	C₄⋊C₄×C₂₉	—	2	32	no	—
154	C₄⋊C₄×C₂₉	—	4	16	no	—
155	C₄⋊C₄×C₂₉	C₂×Q₈	1	16	yes	complemented
156	C₂²⋊C₄×C₂₉	—	2	8	no	—
157	C₂²⋊C₄×C₂₉	C₂×Q₈	1	16	yes	—
158	C₄²×C₂₉	—	2	8	no	—
159	C₄²×C₂₉	—	2	8	no	—
160	C₄²×C₂₉	—	2	8	no	—
161	C₄²×C₂₉	—	2	8	no	—
162	C₄²×C₂₉	—	4	4	no	—
163	C₄²×C₂₉	C₂×D₄	1	4	yes	—
164	C₄²×C₂₉	C₂×D₄	1	4	yes	—
165	C₄²×C₂₉	C₂×D₄	1	4	yes	—
166	C₄²×C₂₉	C₂×D₄	1	4	yes	—
167	C₄²×C₂₉	C₂×Q₈	1	16	yes	complemented
168	#34953	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂³×C₂₉	—	2	2	no	—
170	C₂³×C₂₉	—	2	2	no	—
171	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
172	C₂³×C₂₉	C₂²×Q₈	1	4	yes	—
173	C₂³×C₂₉	C₂⁵	1	1	yes	characteristic
174	Q₈×C₂₉	—	2	16	no	—
175	Q₈×C₂₉	—	2	16	no	—
176	Q₈×C₂₉	—	4	8	no	—
177	Q₈×C₂₉	—	4	8	no	—
178	C₂×C₄×C₂₉	—	2	16	no	—
179	C₂×C₄×C₂₉	—	2	4	no	—
180	C₂×C₄×C₂₉	—	2	8	no	—
181	C₂×C₄×C₂₉	—	2	2	no	—
182	C₂×C₄×C₂₉	—	2	4	no	—
183	C₂×C₄×C₂₉	—	2	2	no	—
184	C₂×C₄×C₂₉	—	2	8	no	—
185	C₂×C₄×C₂₉	—	2	2	no	—
186	C₂×C₄×C₂₉	—	2	8	no	—
187	C₂×C₄×C₂₉	—	2	4	no	—
188	C₂×C₄×C₂₉	—	2	4	no	—
189	C₂×C₄×C₂₉	—	2	4	no	—
190	C₂×C₄×C₂₉	—	2	8	no	—
191	C₂×C₄×C₂₉	—	2	8	no	—
192	C₂×C₄×C₂₉	—	2	8	no	—
193	C₂×C₄×C₂₉	—	4	4	no	—
194	C₂×C₄×C₂₉	—	4	8	no	—
195	C₂×C₄×C₂₉	C₄⋊Q₈	1	16	yes	complemented
196	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
202	C₂×C₄×C₂₉	C₂²×Q₈	1	16	yes	—
203	C₂×C₄×C₂₉	C₂²×Q₈	1	4	yes	—
204	C₂×C₄×C₂₉	C₂²×Q₈	1	4	yes	—
205	C₂×C₄×C₂₉	C₂×#41	1	8	yes	—
206	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
207	C₂×#533	C₂×C₂₉	1	1	yes	characteristic
208	C₂²×C₄×Q₈	C₂×C₂₉	1	1	yes	characteristic
209	#2584	C₂×C₂₉	1	4	yes	complemented
210	#2583	C₂×C₂₉	1	4	yes	—
211	#2567	C₂×C₂₉	1	2	yes	complemented
212	#2546	C₂×C₂₉	1	2	yes	complemented
213	#2502	C₂×C₂₉	1	2	yes	—
214	#2434	C₂×C₂₉	1	2	yes	—
215	#2399	C₂×C₂₉	1	4	yes	complemented
216	C₄×C₄⋊Q₈	C₂×C₂₉	1	4	yes	complemented
217	#2296	C₂×C₂₉	1	4	yes	—
218	C₄×#117	C₂×C₂₉	1	1	yes	characteristic
219	C₂²×C₂₉	—	2	2	no	—
220	C₂²×C₂₉	—	2	2	no	—
221	C₂²×C₂₉	—	2	8	no	—
222	C₂²×C₂₉	C₂×C₄⋊Q₈	1	4	yes	—
223	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
224	C₂²×C₂₉	C₂³×Q₈	1	2	yes	—
225	C₂²×C₂₉	C₂²×#41	1	2	yes	—
226	C₂²×C₂₉	#585	1	2	yes	—
227	C₄×C₂₉	—	2	2	no	—
228	C₄×C₂₉	—	2	8	no	—
229	C₄×C₂₉	—	2	2	no	—
230	C₄×C₂₉	—	2	2	no	—
231	C₄×C₂₉	—	2	16	no	—
232	C₄×C₂₉	—	4	4	no	—
233	C₄×C₂₉	—	4	4	no	—
234	C₄×C₂₉	—	4	4	no	—
235	C₄×C₂₉	#525	1	4	yes	—
236	C₄×C₂₉	C₂×C₄⋊Q₈	1	4	yes	—
237	C₄×C₂₉	C₂×C₄⋊Q₈	1	4	yes	—
238	C₂³×Q₈	C₂²×C₂₉	1	1	yes	characteristic
239	#533	—	2	8	no	—
240	C₂×C₄⋊Q₈	C₂²×C₂₉	1	4	yes	—
241	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
242	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
243	C₂×#125	C₂²×C₂₉	1	2	yes	—
244	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	2	yes	—
245	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	2	yes	—
246	C₂×C₄×Q₈	—	2	8	no	—
247	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
248	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
249	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
250	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
251	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
252	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
253	C₂×#117	C₂²×C₂₉	1	2	yes	—
254	C₂×#117	C₂²×C₂₉	1	2	yes	—
255	C₂²×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
256	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
257	C₂²×C₄²	C₂²×C₂₉	1	2	yes	—
258	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
259	#398	C₂²×C₂₉	1	8	yes	—
260	#398	C₂²×C₂₉	1	8	yes	—
261	#395	C₂²×C₂₉	1	8	yes	—
262	#395	C₂²×C₂₉	1	8	yes	—
263	#391	C₂²×C₂₉	1	4	yes	—
264	#391	C₂²×C₂₉	1	4	yes	—
265	#389	C₂²×C₂₉	1	16	yes	—
266	#389	C₂²×C₂₉	1	8	yes	—
267	#389	C₂²×C₂₉	1	8	yes	—
268	#385	C₂²×C₂₉	1	8	yes	—
269	#385	C₂²×C₂₉	1	8	yes	—
270	#384	C₂²×C₂₉	1	4	yes	—
271	C₄×C₄⋊C₄	C₂²×C₂₉	1	16	yes	—
272	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
273	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
274	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
275	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
276	#376	C₂²×C₂₉	1	2	yes	—
277	C₄³	C₂²×C₂₉	1	2	yes	—
278	C₂×C₂₉	—	2	4	no	—
279	C₂×C₂₉	C₂×#525	1	1	yes	characteristic
280	C₂×C₂₉	C₂²×C₄⋊Q₈	1	1	yes	characteristic
281	C₂×C₂₉	#3449	1	1	yes	characteristic
282	C₂×C₂₉	Q₈×#41	1	4	yes	—
283	C₂²×Q₈	—	2	8	no	—
284	C₂²×Q₈	—	2	4	no	—
285	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
286	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
287	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
288	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
289	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
290	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
291	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
292	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
293	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
294	C₄⋊Q₈	—	2	16	no	—
295	C₄⋊Q₈	—	2	4	no	—
296	C₄⋊Q₈	—	2	4	no	—
297	#125	—	2	8	no	—
298	C₂²⋊Q₈	—	2	8	no	—
299	C₂²⋊Q₈	—	2	8	no	—
300	C₄×Q₈	—	2	8	no	—
301	C₄×Q₈	—	2	8	no	—
302	C₄×Q₈	—	2	8	no	—
303	C₄×Q₈	—	2	8	no	—
304	C₄×Q₈	—	2	8	no	—
305	C₄×Q₈	—	2	8	no	—
306	#117	—	2	8	no	—
307	#117	Q₈×C₂₉	1	16	yes	complemented
308	C₂×C₄⋊C₄	—	2	8	no	—
309	C₂×C₄⋊C₄	—	2	4	no	—
310	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
312	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
313	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
317	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
318	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₂₉	1	16	yes	—
321	C₂×C₄⋊C₄	C₂³×C₂₉	1	16	yes	—
322	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
323	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
325	C₂×C₄²	—	2	8	no	—
326	C₂×C₄²	D₄×C₂₉	1	8	yes	—
327	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
328	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
329	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
330	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
331	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
332	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
337	#95	C₂³×C₂₉	1	4	yes	—
338	#95	C₂³×C₂₉	1	4	yes	—
339	#95	C₂³×C₂₉	1	16	yes	—
340	#95	C₂³×C₂₉	1	16	yes	—
341	C₂₉	#34953	1	1	yes	characteristic, direct product factor, Sylow
342	C₂⁴	C₂⁴×C₂₉	1	1	yes	characteristic
343	C₂×Q₈	—	2	32	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	—	2	4	no	—
346	C₂×Q₈	—	2	4	no	—
347	C₂×Q₈	—	2	4	no	—
348	C₂×Q₈	—	2	8	no	—
349	C₂×Q₈	—	2	4	no	—
350	C₂×Q₈	—	2	8	no	—
351	C₂×Q₈	—	4	4	no	—
352	C₂×Q₈	#41×C₂₉	1	8	yes	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	4	no	—
359	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
360	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
361	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
362	C₂²×C₄	C₂×Q₈×C₂₉	1	8	yes	—
363	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
364	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
365	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
366	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
368	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
369	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
370	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
371	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
373	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	32	no	—
385	C₄⋊C₄	—	4	16	no	—
386	C₄⋊C₄	C₂×Q₈×C₂₉	1	16	yes	complemented
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	C₂×Q₈×C₂₉	1	16	yes	—
389	C₄²	—	2	8	no	—
390	C₄²	—	2	8	no	—
391	C₄²	—	2	8	no	—
392	C₄²	—	2	8	no	—
393	C₄²	—	4	4	no	—
394	C₄²	C₂×D₄×C₂₉	1	4	yes	—
395	C₄²	C₂×D₄×C₂₉	1	4	yes	—
396	C₄²	C₂×D₄×C₂₉	1	4	yes	—
397	C₄²	C₂×D₄×C₂₉	1	4	yes	—
398	C₄²	C₂×Q₈×C₂₉	1	16	yes	complemented
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
402	C₂³	C₂²×Q₈×C₂₉	1	4	yes	—
403	C₂³	C₂⁵×C₂₉	1	1	yes	characteristic
404	Q₈	—	2	16	no	—
405	Q₈	—	2	16	no	—
406	Q₈	—	4	8	no	—
407	Q₈	—	4	8	no	—
408	C₂×C₄	—	2	16	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	2	8	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	8	no	—
425	C₂×C₄	C₂₉×C₄⋊Q₈	1	16	yes	complemented
426	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
427	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
429	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
430	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
432	C₂×C₄	C₂²×Q₈×C₂₉	1	16	yes	—
433	C₂×C₄	C₂²×Q₈×C₂₉	1	4	yes	—
434	C₂×C₄	C₂²×Q₈×C₂₉	1	4	yes	—
435	C₂×C₄	C₂×#41×C₂₉	1	8	yes	—
436	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	8	no	—
439	C₂²	—	2	2	no	—
440	C₂²	C₂×C₂₉×C₄⋊Q₈	1	4	yes	—
441	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
442	C₂²	C₂³×Q₈×C₂₉	1	2	yes	—
443	C₂²	C₂²×#41×C₂₉	1	2	yes	—
444	C₂²	C₂₉×#585	1	2	yes	—
445	C₄	—	2	2	no	—
446	C₄	—	2	2	no	—
447	C₄	—	2	16	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	8	no	—
450	C₄	—	4	4	no	—
451	C₄	—	4	4	no	—
452	C₄	—	4	4	no	—
453	C₄	C₂₉×#525	1	4	yes	—
454	C₄	C₂×C₂₉×C₄⋊Q₈	1	4	yes	—
455	C₄	C₂×C₂₉×C₄⋊Q₈	1	4	yes	—
456	C₂	—	2	4	no	—
457	C₂	C₂×C₂₉×#525	1	1	yes	characteristic
458	C₂	C₂²×C₂₉×C₄⋊Q₈	1	1	yes	characteristic
459	C₂	C₂₉×#3449	1	1	yes	characteristic
460	C₂	Q₈×#41×C₂₉	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₉
socle	C₂³×C₂₉	C₂⁵
prime radical	C₂⁴×C₂₉	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₉×#2584	C₂	semidirect
5. C₂₉×#2567	C₂	semidirect
6. C₂₉×#2546	C₂	semidirect
9. C₂₉×#2399	C₂	semidirect
10. C₄×C₂₉×C₄⋊Q₈	C₂	semidirect
77. C₂₉×#117	Q₈	semidirect
155. C₄⋊C₄×C₂₉	C₂×Q₈	semidirect
167. C₄²×C₂₉	C₂×Q₈	semidirect
168. #34953	C₂₉	direct (N × H)
195. C₂×C₄×C₂₉	C₄⋊Q₈	semidirect
209. #2584	C₂×C₂₉	semidirect
211. #2567	C₂×C₂₉	semidirect
212. #2546	C₂×C₂₉	semidirect
215. #2399	C₂×C₂₉	semidirect
216. C₄×C₄⋊Q₈	C₂×C₂₉	semidirect
307. #117	Q₈×C₂₉	semidirect
341. C₂₉	#34953	direct (N × H)
386. C₄⋊C₄	C₂×Q₈×C₂₉	semidirect
398. C₄²	C₂×Q₈×C₂₉	semidirect
425. C₂×C₄	C₂₉×C₄⋊Q₈	semidirect

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
C₂²×C₄×Q₈×C₂₉	2
C₂₉×#2584	2
C₂₉×#2583	2
C₂₉×#2567	2
C₂₉×#2546	2
C₂₉×#2502	2
C₂₉×#2434	2
C₂₉×#2399	2
C₄×C₂₉×C₄⋊Q₈	2
C₂₉×#2296	2
C₄×C₂₉×#117	2
#34953	29

Subgroups — C29×#34953 #20329853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#34953 #20329853