Subgroups — C₂₉×#28810 #20323710

Order 7424.

734 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#499	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#498	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2550	C₂	1	2	yes	maximal
4	C₂₉×#2059	C₂	1	2	yes	maximal
5	C₂₉×#2057	C₂	1	2	yes	maximal
6	C₂₉×#1949	C₂	1	2	yes	maximal
7	C₂₉×#1941	C₂	1	1	yes	maximal, characteristic
8	C₂₉×#1941	C₂	1	1	yes	maximal, characteristic
9	C₂₉×#1846	C₂	1	1	yes	maximal, characteristic
10	C₄×C₂₉×#106	C₂	1	1	yes	maximal, characteristic
11	C₈×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
12	C₂×C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
13	C₂×C₂₉×#125	C₂²	1	2	yes	—
14	C₂₉×#499	—	2	4	no	—
15	C₂₉×#498	—	2	4	no	—
16	C₂×C₂₉×#107	C₂²	1	2	yes	—
17	C₂×C₂₉×#107	C₂²	1	2	yes	—
18	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×#106	C₂²	1	2	yes	—
21	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
27	C₂₉×#398	—	2	2	no	—
28	C₂₉×#395	—	2	2	no	—
29	C₂₉×#391	—	2	2	no	—
30	C₂₉×#389	—	2	2	no	—
31	C₂₉×#389	C₂²	1	2	yes	—
32	C₂₉×#389	C₂²	1	2	yes	—
33	C₂₉×#382	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
36	C₂₉×#340	C₂²	1	2	yes	—
37	C₂₉×#340	C₂²	1	2	yes	—
38	C₂₉×#340	C₂²	1	2	yes	—
39	C₂₉×#336	C₂²	1	1	yes	characteristic
40	C₂₉×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₂₉	—	2	2	no	—
42	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
46	C₂₉×C₄⋊Q₈	—	2	4	no	—
47	C₂₉×C₄⋊Q₈	—	4	2	no	—
48	C₂₉×#125	—	2	4	no	—
49	C₂₉×#125	—	4	2	no	—
50	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₂₉	D₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
60	C₂×C₄²×C₂₉	—	2	2	no	—
61	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
64	C₂₉×#107	—	2	4	no	—
65	C₂₉×#107	—	4	2	no	—
66	C₂₉×#106	—	2	2	no	—
67	C₂₉×#106	—	2	2	no	—
68	C₂₉×#106	—	2	4	no	—
69	C₂₉×#106	D₄	1	4	yes	—
70	C₂₉×#106	Q₈	1	4	yes	complemented
71	C₂₉×C₄⋊C₈	Q₈	1	4	yes	complemented
72	C₄×C₈×C₂₉	—	2	2	no	—
73	C₄×C₈×C₂₉	—	2	2	no	—
74	C₄×C₈×C₂₉	Q₈	1	4	yes	complemented
75	C₂₉×#95	—	2	2	no	—
76	C₂₉×#95	—	2	2	no	—
77	C₂₉×#95	—	2	2	no	—
78	C₂₉×#95	—	2	2	no	—
79	C₂₉×#95	—	2	2	no	—
80	C₂₉×#95	D₄	1	2	yes	—
81	C₂×Q₈×C₂₉	—	4	4	no	—
82	C₂×Q₈×C₂₉	—	4	4	no	—
83	C₂×Q₈×C₂₉	—	8	2	no	—
84	C₂²×C₄×C₂₉	—	2	2	no	—
85	C₂²×C₄×C₂₉	—	2	2	no	—
86	C₂²×C₄×C₂₉	—	2	2	no	—
87	C₂²×C₄×C₂₉	—	2	2	no	—
88	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
93	C₂×C₈×C₂₉	—	2	1	no	—
94	C₂×C₈×C₂₉	—	2	1	no	—
95	C₂×C₈×C₂₉	—	2	1	no	—
96	C₂×C₈×C₂₉	—	2	1	no	—
97	C₂×C₈×C₂₉	—	2	1	no	—
98	C₂×C₈×C₂₉	—	2	1	no	—
99	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
100	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
101	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
102	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
103	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
104	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
105	C₄⋊C₄×C₂₉	—	2	4	no	—
106	C₄⋊C₄×C₂₉	—	2	2	no	—
107	C₄⋊C₄×C₂₉	—	2	2	no	—
108	C₄⋊C₄×C₂₉	—	2	2	no	—
109	C₄⋊C₄×C₂₉	—	2	2	no	—
110	C₄⋊C₄×C₂₉	—	2	2	no	—
111	C₄⋊C₄×C₂₉	—	2	2	no	—
112	C₄⋊C₄×C₂₉	—	4	4	no	—
113	C₄⋊C₄×C₂₉	—	4	4	no	—
114	C₄⋊C₄×C₂₉	—	4	4	no	—
115	C₄⋊C₄×C₂₉	—	4	4	no	—
116	C₄⋊C₄×C₂₉	—	8	2	no	—
117	C₄⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
118	C₄⋊C₄×C₂₉	C₂×Q₈	1	4	yes	—
119	C₄²×C₂₉	—	2	1	no	—
120	C₄²×C₂₉	—	2	1	no	—
121	C₄²×C₂₉	—	2	1	no	—
122	C₄²×C₂₉	—	2	1	no	—
123	C₄²×C₂₉	—	8	2	no	—
124	C₄²×C₂₉	C₂×Q₈	1	2	yes	—
125	C₄²×C₂₉	C₂×Q₈	1	2	yes	—
126	#28810	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
128	Q₈×C₂₉	—	8	8	no	—
129	C₂×C₄×C₂₉	—	2	2	no	—
130	C₂×C₄×C₂₉	—	2	2	no	—
131	C₂×C₄×C₂₉	—	2	2	no	—
132	C₂×C₄×C₂₉	—	2	2	no	—
133	C₂×C₄×C₂₉	—	2	2	no	—
134	C₂×C₄×C₂₉	—	2	4	no	—
135	C₂×C₄×C₂₉	—	2	4	no	—
136	C₂×C₄×C₂₉	—	2	2	no	—
137	C₂×C₄×C₂₉	—	2	2	no	—
138	C₂×C₄×C₂₉	—	4	2	no	—
139	C₂×C₄×C₂₉	—	4	2	no	—
140	C₂×C₄×C₂₉	—	4	2	no	—
141	C₂×C₄×C₂₉	—	4	2	no	—
142	C₂×C₄×C₂₉	—	4	2	no	—
143	C₂×C₄×C₂₉	—	4	2	no	—
144	C₂×C₄×C₂₉	—	4	2	no	—
145	C₂×C₄×C₂₉	—	4	2	no	—
146	C₂×C₄×C₂₉	—	4	2	no	—
147	C₂×C₄×C₂₉	—	4	2	no	—
148	C₂×C₄×C₂₉	C₄⋊Q₈	1	2	yes	—
149	C₂×C₄×C₂₉	C₄⋊Q₈	1	2	yes	—
150	C₂×C₄×C₂₉	#135	1	4	yes	—
151	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
156	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
157	C₈×C₂₉	—	2	2	no	—
158	C₈×C₂₉	—	2	2	no	—
159	C₈×C₂₉	—	2	2	no	—
160	C₈×C₂₉	C₄⋊Q₈	1	4	yes	—
161	C₂×#499	C₂×C₂₉	1	1	yes	characteristic
162	C₂×#498	C₂×C₂₉	1	1	yes	characteristic
163	#2550	C₂×C₂₉	1	2	yes	—
164	#2059	C₂×C₂₉	1	2	yes	—
165	#2057	C₂×C₂₉	1	2	yes	—
166	#1949	C₂×C₂₉	1	2	yes	—
167	#1941	C₂×C₂₉	1	1	yes	characteristic
168	#1941	C₂×C₂₉	1	1	yes	characteristic
169	#1846	C₂×C₂₉	1	1	yes	characteristic
170	C₄×#106	C₂×C₂₉	1	1	yes	characteristic
171	C₈×C₄⋊C₄	C₂×C₂₉	1	1	yes	characteristic
172	C₂²×C₂₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
173	C₂²×C₂₉	D₄²	1	1	yes	characteristic
174	C₂²×C₂₉	D₄×Q₈	1	1	yes	characteristic
175	C₂²×C₂₉	C₂×#135	1	2	yes	—
176	C₂²×C₂₉	#577	1	2	yes	—
177	C₄×C₂₉	—	2	2	no	—
178	C₄×C₂₉	—	2	2	no	—
179	C₄×C₂₉	—	2	4	no	—
180	C₄×C₂₉	—	4	4	no	—
181	C₄×C₂₉	—	4	2	no	—
182	C₄×C₂₉	—	4	4	no	—
183	C₄×C₂₉	—	8	2	no	—
184	C₄×C₂₉	—	8	2	no	—
185	C₄×C₂₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
186	C₄×C₂₉	#544	1	1	yes	characteristic
187	C₄×C₂₉	D₄×Q₈	1	1	yes	characteristic
188	C₄×C₂₉	Q₈²	1	1	yes	characteristic
189	C₂×C₄⋊Q₈	C₂²×C₂₉	1	2	yes	—
190	C₂×#125	C₂²×C₂₉	1	2	yes	—
191	#499	—	2	4	no	—
192	#498	—	2	4	no	—
193	C₂×#107	C₂²×C₂₉	1	2	yes	—
194	C₂×#107	C₂²×C₂₉	1	2	yes	—
195	C₂×#106	C₂²×C₂₉	1	2	yes	—
196	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
197	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
198	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
199	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
200	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
201	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
202	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
203	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
204	#398	—	2	2	no	—
205	#395	—	2	2	no	—
206	#391	—	2	2	no	—
207	#389	—	2	2	no	—
208	#389	C₂²×C₂₉	1	2	yes	—
209	#389	C₂²×C₂₉	1	2	yes	—
210	#382	C₂²×C₂₉	1	2	yes	—
211	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
212	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
213	#340	C₂²×C₂₉	1	2	yes	—
214	#340	C₂²×C₂₉	1	2	yes	—
215	#340	C₂²×C₂₉	1	2	yes	—
216	#336	C₂²×C₂₉	1	1	yes	characteristic
217	#336	C₂²×C₂₉	1	1	yes	characteristic
218	C₂×C₂₉	#2551	1	1	yes	characteristic
219	C₂×C₂₉	#3160	1	1	yes	characteristic
220	C₂×C₂₉	#3163	1	1	yes	characteristic
221	C₂×C₂₉	#3282	1	2	yes	—
222	C₂×C₂₉	#3381	1	2	yes	—
223	C₂²×Q₈	—	2	2	no	—
224	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
225	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
227	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
228	C₄⋊Q₈	—	2	4	no	—
229	C₄⋊Q₈	—	4	2	no	—
230	#125	—	2	4	no	—
231	#125	—	4	2	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	D₄×C₂₉	1	2	yes	—
238	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
239	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
240	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
241	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
242	C₂×C₄²	—	2	2	no	—
243	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
244	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
245	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
246	#107	—	2	4	no	—
247	#107	—	4	2	no	—
248	#106	—	2	2	no	—
249	#106	—	2	2	no	—
250	#106	—	2	4	no	—
251	#106	D₄×C₂₉	1	4	yes	—
252	#106	Q₈×C₂₉	1	4	yes	complemented
253	C₄⋊C₈	Q₈×C₂₉	1	4	yes	complemented
254	C₄×C₈	—	2	2	no	—
255	C₄×C₈	—	2	2	no	—
256	C₄×C₈	Q₈×C₂₉	1	4	yes	complemented
257	#95	—	2	2	no	—
258	#95	—	2	2	no	—
259	#95	—	2	2	no	—
260	#95	—	2	2	no	—
261	#95	—	2	2	no	—
262	#95	D₄×C₂₉	1	2	yes	—
263	C₂₉	#28810	1	1	yes	characteristic, direct product factor, Sylow
264	C₂×Q₈	—	4	4	no	—
265	C₂×Q₈	—	4	4	no	—
266	C₂×Q₈	—	8	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
272	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
275	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
276	C₂×C₈	—	2	1	no	—
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	1	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
283	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
284	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
285	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
286	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
287	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	4	4	no	—
296	C₄⋊C₄	—	4	4	no	—
297	C₄⋊C₄	—	4	4	no	—
298	C₄⋊C₄	—	4	4	no	—
299	C₄⋊C₄	—	8	2	no	—
300	C₄⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
301	C₄⋊C₄	C₂×Q₈×C₂₉	1	4	yes	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	1	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	1	no	—
306	C₄²	—	8	2	no	—
307	C₄²	C₂×Q₈×C₂₉	1	2	yes	—
308	C₄²	C₂×Q₈×C₂₉	1	2	yes	—
309	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
310	Q₈	—	8	8	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	C₂₉×C₄⋊Q₈	1	2	yes	—
331	C₂×C₄	C₂₉×C₄⋊Q₈	1	2	yes	—
332	C₂×C₄	C₂₉×#135	1	4	yes	—
333	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
334	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
335	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
336	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
337	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
339	C₈	—	2	2	no	—
340	C₈	—	2	2	no	—
341	C₈	—	2	2	no	—
342	C₈	C₂₉×C₄⋊Q₈	1	4	yes	—
343	C₂²	C₂×C₂₉×C₄⋊Q₈	1	1	yes	characteristic
344	C₂²	D₄²×C₂₉	1	1	yes	characteristic
345	C₂²	D₄×Q₈×C₂₉	1	1	yes	characteristic
346	C₂²	C₂×C₂₉×#135	1	2	yes	—
347	C₂²	C₂₉×#577	1	2	yes	—
348	C₄	—	2	4	no	—
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	4	2	no	—
352	C₄	—	4	4	no	—
353	C₄	—	4	4	no	—
354	C₄	—	8	2	no	—
355	C₄	—	8	2	no	—
356	C₄	C₂×C₂₉×C₄⋊Q₈	1	1	yes	characteristic
357	C₄	C₂₉×#544	1	1	yes	characteristic
358	C₄	D₄×Q₈×C₂₉	1	1	yes	characteristic
359	C₄	Q₈²×C₂₉	1	1	yes	characteristic
360	C₂	C₂₉×#2551	1	1	yes	characteristic
361	C₂	C₂₉×#3160	1	1	yes	characteristic
362	C₂	C₂₉×#3163	1	1	yes	characteristic
363	C₂	C₂₉×#3282	1	2	yes	—
364	C₂	C₂₉×#3381	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
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
70. C₂₉×#106	Q₈	semidirect
71. C₂₉×C₄⋊C₈	Q₈	semidirect
74. C₄×C₈×C₂₉	Q₈	semidirect
126. #28810	C₂₉	direct (N × H)
252. #106	Q₈×C₂₉	semidirect
253. C₄⋊C₈	Q₈×C₂₉	semidirect
256. C₄×C₈	Q₈×C₂₉	semidirect
263. C₂₉	#28810	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×#499	2
C₂×C₂₉×#498	2
C₂₉×#2550	2
C₂₉×#2059	2
C₂₉×#2057	2
C₂₉×#1949	2
C₂₉×#1941	2
C₂₉×#1846	2
C₄×C₂₉×#106	2
C₈×C₄⋊C₄×C₂₉	2
#28810	29

Subgroups — C29×#28810 #20323710

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#28810 #20323710