Subgroups — C₂₉×#9234 #20304134

Order 7424.

604 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3103	C₂	1	1	yes	maximal, characteristic
2	C₄²×Q₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#1962	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1502	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1487	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1303	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1276	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#532	C₂²	1	1	yes	characteristic
9	C₂×C₄×Q₈×C₂₉	—	2	1	no	—
10	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
11	C₂₉×#481	—	2	1	no	—
12	C₂₉×#475	C₄	1	2	yes	complemented
13	C₂₉×#460	C₄	1	2	yes	complemented
14	C₂₉×#448	—	2	1	no	—
15	C₄×SD₁₆×C₂₉	—	2	2	no	—
16	C₂₉×#431	C₂²	1	1	yes	characteristic
17	C₂₉×#431	C₂²	1	1	yes	characteristic
18	C₂₉×#423	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#104	—	2	1	no	—
20	C₂×C₂₉×#104	—	2	1	no	—
21	C₄×C₄⋊C₄×C₂₉	—	2	2	no	—
22	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
23	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
24	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
25	C₄³×C₂₉	—	2	1	no	—
26	C₄³×C₂₉	C₂²	1	1	yes	characteristic
27	C₂₉×#327	—	2	2	no	—
28	C₂₉×Q₈⋊C₈	—	2	2	no	—
29	C₂×#41×C₂₉	—	2	1	no	—
30	C₂²×Q₈×C₂₉	D₄	1	1	yes	characteristic
31	C₂×SD₁₆×C₂₉	—	2	2	no	—
32	C₂×M₁₆×C₂₉	—	2	1	no	—
33	C₂₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
34	C₂₉×#127	C₂×C₄	1	1	yes	characteristic
35	C₂₉×#124	—	2	1	no	—
36	C₂₉×#121	—	2	1	no	—
37	C₂₉×#121	—	2	1	no	—
38	C₄×Q₈×C₂₉	—	2	8	no	—
39	C₄×Q₈×C₂₉	—	2	1	no	—
40	C₄×Q₈×C₂₉	—	2	1	no	—
41	C₄×Q₈×C₂₉	C₂×C₄	1	2	yes	—
42	C₄×Q₈×C₂₉	D₄	1	2	yes	—
43	C₄×D₄×C₂₉	—	2	1	no	—
44	C₄×D₄×C₂₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₂₉	—	2	2	no	—
50	C₂×C₄²×C₂₉	—	2	1	no	—
51	C₂×C₄²×C₂₉	—	2	1	no	—
52	C₂×C₄²×C₂₉	—	2	2	no	—
53	C₂×C₄²×C₂₉	—	2	1	no	—
54	C₂×C₄²×C₂₉	—	2	1	no	—
55	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
58	C₂₉×#106	—	2	2	no	—
59	C₂₉×C₄⋊C₈	—	2	1	no	—
60	C₂₉×C₄⋊C₈	—	2	1	no	—
61	C₂₉×C₄⋊C₈	—	2	1	no	—
62	C₂₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
63	C₂₉×#104	—	4	2	no	—
64	C₂₉×#104	—	4	2	no	—
65	C₂₉×#103	—	2	2	no	—
66	C₂₉×#102	—	2	2	no	—
67	C₂₉×C₂²⋊C₈	—	2	1	no	—
68	C₂₉×C₂²⋊C₈	—	2	1	no	—
69	C₄×C₈×C₂₉	—	2	1	no	—
70	C₄×C₈×C₂₉	—	2	1	no	—
71	C₂₉×#95	—	2	2	no	—
72	C₂₉×#95	D₄	1	2	yes	—
73	#41×C₂₉	—	4	1	no	—
74	#41×C₂₉	—	4	1	no	—
75	#41×C₂₉	—	4	1	no	—
76	#41×C₂₉	—	4	1	no	—
77	C₂×Q₈×C₂₉	—	2	4	no	—
78	C₂×Q₈×C₂₉	—	2	1	no	—
79	C₂×Q₈×C₂₉	—	2	1	no	—
80	C₂×Q₈×C₂₉	C₂²⋊C₄	1	2	yes	—
81	C₂×D₄×C₂₉	—	2	1	no	—
82	C₂×D₄×C₂₉	—	2	1	no	—
83	C₂×D₄×C₂₉	—	2	1	no	—
84	C₂×D₄×C₂₉	—	4	1	no	—
85	C₂²×C₄×C₂₉	—	2	1	no	—
86	C₂²×C₄×C₂₉	—	2	1	no	—
87	C₂²×C₄×C₂₉	—	2	2	no	—
88	C₂²×C₄×C₂₉	—	2	1	no	—
89	C₂²×C₄×C₂₉	—	2	1	no	—
90	C₂²×C₄×C₂₉	—	4	1	no	—
91	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
94	SD₁₆×C₂₉	—	4	4	no	—
95	M₁₆×C₂₉	—	4	1	no	—
96	M₁₆×C₂₉	—	4	1	no	—
97	C₂×C₈×C₂₉	—	2	2	no	—
98	C₂×C₈×C₂₉	—	4	1	no	—
99	C₂×C₈×C₂₉	—	4	1	no	—
100	C₄⋊C₄×C₂₉	—	2	8	no	—
101	C₄⋊C₄×C₂₉	—	2	4	no	—
102	C₄⋊C₄×C₂₉	—	2	2	no	—
103	C₄⋊C₄×C₂₉	—	2	2	no	—
104	C₄⋊C₄×C₂₉	—	2	1	no	—
105	C₄⋊C₄×C₂₉	—	2	1	no	—
106	C₄⋊C₄×C₂₉	—	2	1	no	—
107	C₄⋊C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
108	C₂²⋊C₄×C₂₉	—	4	1	no	—
109	C₂²⋊C₄×C₂₉	—	4	1	no	—
110	C₄²×C₂₉	—	2	8	no	—
111	C₄²×C₂₉	—	2	4	no	—
112	C₄²×C₂₉	—	2	2	no	—
113	C₄²×C₂₉	—	2	2	no	—
114	C₄²×C₂₉	—	2	1	no	—
115	C₄²×C₂₉	—	2	1	no	—
116	C₄²×C₂₉	—	2	1	no	—
117	C₄²×C₂₉	—	4	2	no	—
118	C₄²×C₂₉	—	4	4	no	—
119	C₄²×C₂₉	—	4	1	no	—
120	C₄²×C₂₉	—	4	1	no	—
121	C₄²×C₂₉	SD₁₆	1	2	yes	complemented
122	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₂₉	#41	1	1	yes	characteristic
125	C₄²×C₂₉	#41	1	1	yes	characteristic
126	#9234	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂³×C₂₉	—	4	1	no	—
128	C₂³×C₂₉	#120	1	1	yes	characteristic
129	Q₈×C₂₉	—	2	4	no	—
130	Q₈×C₂₉	—	2	2	no	—
131	Q₈×C₂₉	—	4	1	no	—
132	Q₈×C₂₉	—	4	1	no	—
133	Q₈×C₂₉	#104	1	4	yes	complemented
134	D₄×C₂₉	—	4	2	no	—
135	D₄×C₂₉	—	4	1	no	—
136	D₄×C₂₉	—	4	1	no	—
137	D₄×C₂₉	—	8	1	no	—
138	D₄×C₂₉	—	8	1	no	—
139	D₄×C₂₉	—	8	1	no	—
140	C₂×C₄×C₂₉	—	2	2	no	—
141	C₂×C₄×C₂₉	—	2	4	no	—
142	C₂×C₄×C₂₉	—	2	2	no	—
143	C₂×C₄×C₂₉	—	2	2	no	—
144	C₂×C₄×C₂₉	—	2	2	no	—
145	C₂×C₄×C₂₉	—	2	2	no	—
146	C₂×C₄×C₂₉	—	2	4	no	—
147	C₂×C₄×C₂₉	—	2	2	no	—
148	C₂×C₄×C₂₉	—	2	2	no	—
149	C₂×C₄×C₂₉	—	4	1	no	—
150	C₂×C₄×C₂₉	—	4	2	no	—
151	C₂×C₄×C₂₉	—	4	1	no	—
152	C₂×C₄×C₂₉	—	4	2	no	—
153	C₂×C₄×C₂₉	—	4	1	no	—
154	C₂×C₄×C₂₉	—	4	2	no	—
155	C₂×C₄×C₂₉	—	4	1	no	—
156	C₂×C₄×C₂₉	—	8	1	no	—
157	C₂×C₄×C₂₉	—	8	1	no	—
158	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
162	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
163	C₂×C₄×C₂₉	#123	1	1	yes	characteristic
164	C₂×C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
165	C₂×C₄×C₂₉	#135	1	1	yes	characteristic
166	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₂×C₄×C₂₉	#137	1	1	yes	characteristic
168	C₈×C₂₉	—	4	2	no	—
169	C₈×C₂₉	—	8	1	no	—
170	C₈×C₂₉	—	8	1	no	—
171	#3103	C₂×C₂₉	1	1	yes	characteristic
172	C₄²×Q₈	C₂×C₂₉	1	1	yes	characteristic, complemented
173	#1962	C₂×C₂₉	1	1	yes	characteristic
174	#1502	C₂×C₂₉	1	1	yes	characteristic
175	#1487	C₂×C₂₉	1	1	yes	characteristic, complemented
176	#1303	C₂×C₂₉	1	1	yes	characteristic, complemented
177	#1276	C₂×C₂₉	1	1	yes	characteristic, complemented
178	C₂²×C₂₉	—	2	1	no	—
179	C₂²×C₂₉	—	2	1	no	—
180	C₂²×C₂₉	—	8	1	no	—
181	C₂²×C₂₉	—	8	1	no	—
182	C₂²×C₂₉	—	8	1	no	—
183	C₂²×C₂₉	#386	1	1	yes	characteristic
184	C₂²×C₂₉	#448	1	1	yes	characteristic
185	C₂²×C₂₉	#449	1	1	yes	characteristic
186	C₄×C₂₉	—	2	4	no	—
187	C₄×C₂₉	—	2	4	no	—
188	C₄×C₂₉	—	2	1	no	—
189	C₄×C₂₉	—	2	1	no	—
190	C₄×C₂₉	—	2	1	no	—
191	C₄×C₂₉	—	4	2	no	—
192	C₄×C₂₉	—	4	4	no	—
193	C₄×C₂₉	—	4	2	no	—
194	C₄×C₂₉	—	8	1	no	—
195	C₄×C₂₉	C₂×#104	1	2	yes	—
196	C₄×C₂₉	C₄×SD₁₆	1	1	yes	characteristic
197	C₄×C₂₉	#440	1	1	yes	characteristic
198	C₄×C₂₉	#460	1	1	yes	characteristic
199	C₄×C₂₉	#464	1	1	yes	characteristic
200	#532	C₂²×C₂₉	1	1	yes	characteristic
201	C₂×C₄×Q₈	—	2	1	no	—
202	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
203	#481	—	2	1	no	—
204	#475	C₄×C₂₉	1	2	yes	complemented
205	#460	C₄×C₂₉	1	2	yes	complemented
206	#448	—	2	1	no	—
207	C₄×SD₁₆	—	2	2	no	—
208	#431	C₂²×C₂₉	1	1	yes	characteristic
209	#431	C₂²×C₂₉	1	1	yes	characteristic
210	#423	C₂²×C₂₉	1	1	yes	characteristic
211	C₂×#104	—	2	1	no	—
212	C₂×#104	—	2	1	no	—
213	C₄×C₄⋊C₄	—	2	1	no	—
214	C₄×C₄⋊C₄	—	2	1	no	—
215	C₄×C₄⋊C₄	—	2	2	no	—
216	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
217	C₄³	—	2	1	no	—
218	C₄³	C₂²×C₂₉	1	1	yes	characteristic
219	#327	—	2	2	no	—
220	Q₈⋊C₈	—	2	2	no	—
221	C₂×C₂₉	—	2	1	no	—
222	C₂×C₂₉	—	2	1	no	—
223	C₂×C₂₉	—	16	1	no	—
224	C₂×C₂₉	#1880	1	1	yes	characteristic
225	C₂×C₂₉	#1896	1	1	yes	characteristic
226	C₂×C₂₉	#1906	1	1	yes	characteristic
227	C₂×#41	—	2	1	no	—
228	C₂²×Q₈	D₄×C₂₉	1	1	yes	characteristic
229	C₂×SD₁₆	—	2	2	no	—
230	C₂×M₁₆	—	2	1	no	—
231	C₄⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
232	#127	C₂×C₄×C₂₉	1	1	yes	characteristic
233	#124	—	2	1	no	—
234	#121	—	2	1	no	—
235	#121	—	2	1	no	—
236	C₄×Q₈	—	2	8	no	—
237	C₄×Q₈	—	2	1	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	C₂×C₄×C₂₉	1	2	yes	—
240	C₄×Q₈	D₄×C₂₉	1	2	yes	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	—	2	1	no	—
249	C₂×C₄²	—	2	1	no	—
250	C₂×C₄²	—	2	2	no	—
251	C₂×C₄²	—	2	1	no	—
252	C₂×C₄²	—	2	1	no	—
253	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
254	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
256	#106	—	2	2	no	—
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
261	#104	—	4	2	no	—
262	#104	—	4	2	no	—
263	#103	—	2	2	no	—
264	#102	—	2	2	no	—
265	C₂²⋊C₈	—	2	1	no	—
266	C₂²⋊C₈	—	2	1	no	—
267	C₄×C₈	—	2	1	no	—
268	C₄×C₈	—	2	1	no	—
269	#95	—	2	2	no	—
270	#95	D₄×C₂₉	1	2	yes	—
271	C₂₉	#9234	1	1	yes	characteristic, direct product factor, Sylow
272	#41	—	4	1	no	—
273	#41	—	4	1	no	—
274	#41	—	4	1	no	—
275	#41	—	4	1	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	C₂²⋊C₄×C₂₉	1	2	yes	—
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	4	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
293	SD₁₆	—	4	4	no	—
294	M₁₆	—	4	1	no	—
295	M₁₆	—	4	1	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	4	1	no	—
299	C₄⋊C₄	—	2	8	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₂²⋊C₄	—	4	1	no	—
309	C₄²	—	2	8	no	—
310	C₄²	—	2	4	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	2	1	no	—
314	C₄²	—	2	1	no	—
315	C₄²	—	2	1	no	—
316	C₄²	—	4	2	no	—
317	C₄²	—	4	4	no	—
318	C₄²	—	4	1	no	—
319	C₄²	—	4	1	no	—
320	C₄²	SD₁₆×C₂₉	1	2	yes	complemented
321	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
322	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
323	C₄²	#41×C₂₉	1	1	yes	characteristic
324	C₄²	#41×C₂₉	1	1	yes	characteristic
325	C₂³	—	4	1	no	—
326	C₂³	C₂₉×#120	1	1	yes	characteristic
327	Q₈	—	2	4	no	—
328	Q₈	—	2	2	no	—
329	Q₈	—	4	1	no	—
330	Q₈	—	4	1	no	—
331	Q₈	C₂₉×#104	1	4	yes	complemented
332	D₄	—	4	1	no	—
333	D₄	—	4	1	no	—
334	D₄	—	4	2	no	—
335	D₄	—	8	1	no	—
336	D₄	—	8	1	no	—
337	D₄	—	8	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	8	1	no	—
355	C₂×C₄	—	8	1	no	—
356	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
357	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
358	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
359	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
360	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
361	C₂×C₄	C₂₉×#123	1	1	yes	characteristic
362	C₂×C₄	C₂×SD₁₆×C₂₉	1	1	yes	characteristic
363	C₂×C₄	C₂₉×#135	1	1	yes	characteristic
364	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
365	C₂×C₄	C₂₉×#137	1	1	yes	characteristic
366	C₈	—	4	2	no	—
367	C₈	—	8	1	no	—
368	C₈	—	8	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	8	1	no	—
372	C₂²	—	8	1	no	—
373	C₂²	—	8	1	no	—
374	C₂²	C₂₉×#386	1	1	yes	characteristic
375	C₂²	C₂₉×#448	1	1	yes	characteristic
376	C₂²	C₂₉×#449	1	1	yes	characteristic
377	C₄	—	2	4	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	4	no	—
381	C₄	—	2	1	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	4	no	—
384	C₄	—	4	2	no	—
385	C₄	—	8	1	no	—
386	C₄	C₂×C₂₉×#104	1	2	yes	—
387	C₄	C₄×SD₁₆×C₂₉	1	1	yes	characteristic
388	C₄	C₂₉×#440	1	1	yes	characteristic
389	C₄	C₂₉×#460	1	1	yes	characteristic
390	C₄	C₂₉×#464	1	1	yes	characteristic
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	—	16	1	no	—
394	C₂	C₂₉×#1880	1	1	yes	characteristic
395	C₂	C₂₉×#1896	1	1	yes	characteristic
396	C₂	C₂₉×#1906	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	#121
commutator	C₄²	C₂²×C₄×C₂₉
Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
socle	C₂²×C₂₉	#386
prime radical	C₂₉×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄²×Q₈×C₂₉	C₂	semidirect
5. C₂₉×#1487	C₂	semidirect
6. C₂₉×#1303	C₂	semidirect
7. C₂₉×#1276	C₂	semidirect
12. C₂₉×#475	C₄	semidirect
13. C₂₉×#460	C₄	semidirect
121. C₄²×C₂₉	SD₁₆	semidirect
126. #9234	C₂₉	direct (N × H)
133. Q₈×C₂₉	#104	semidirect
172. C₄²×Q₈	C₂×C₂₉	semidirect
175. #1487	C₂×C₂₉	semidirect
176. #1303	C₂×C₂₉	semidirect
177. #1276	C₂×C₂₉	semidirect
204. #475	C₄×C₂₉	semidirect
205. #460	C₄×C₂₉	semidirect
271. C₂₉	#9234	direct (N × H)
320. C₄²	SD₁₆×C₂₉	semidirect
331. Q₈	C₂₉×#104	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₉×#3103	2
C₄²×Q₈×C₂₉	2
C₂₉×#1962	2
C₂₉×#1502	2
C₂₉×#1487	2
C₂₉×#1303	2
C₂₉×#1276	2
#9234	29

Subgroups — C29×#9234 #20304134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#9234 #20304134