Subgroups — C₂₉×#33589 #20328489

Order 7424.

726 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3155	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2951	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2211	C₂	1	2	yes	maximal, complemented
6	C₂₉×#2210	C₂	1	2	yes	maximal, complemented
7	C₂₉×#2207	C₂	1	2	yes	maximal, complemented
8	C₂₉×#2206	C₂	1	2	yes	maximal, complemented
9	C₂₉×#2151	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#2139	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₉×#357	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₉×AGL(1,ℤ/8)	—	2	1	no	—
13	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
14	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
15	C₂²×D₈×C₂₉	C₂²	1	1	yes	characteristic
16	C₂₉×#535	—	2	1	no	—
17	C₂₉×#520	—	2	1	no	—
18	C₂₉×#509	—	2	4	no	—
19	C₂₉×#508	—	2	4	no	—
20	C₂×C₂₉×Q₃₂	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₂₉×SD₃₂	C₂²	1	2	yes	—
22	C₂×C₂₉×SD₃₂	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₂₉×SD₃₂	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₂₉×D₁₆	C₂²	1	2	yes	—
25	C₂×C₂₉×D₁₆	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₂₉×M₃₂	C₂²	1	1	yes	characteristic
27	C₂²×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
28	C₂₉×#496	—	2	2	no	—
29	C₂₉×#495	C₂²	1	2	yes	—
30	C₂₉×#493	C₂²	1	2	yes	—
31	C₂₉×#440	—	2	2	no	—
32	C₄×Q₁₆×C₂₉	C₂²	1	2	yes	complemented
33	C₄×D₈×C₂₉	C₂²	1	2	yes	complemented
34	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
35	C₂₉×#417	—	2	1	no	—
36	C₂₉×#405	C₂²	1	1	yes	characteristic
37	C₂₉×C₄⋊C₁₆	C₂²	1	2	yes	complemented
38	C₂₉×C₄⋊C₁₆	C₂²	1	2	yes	complemented
39	C₂₉×#358	C₂²	1	2	yes	complemented
40	C₂₉×#357	C₂²	1	2	yes	—
41	C₂₉×#357	C₂²	1	2	yes	—
42	C₂₉×#357	C₂²	1	2	yes	complemented
43	C₂×#41×C₂₉	—	2	1	no	—
44	C₂×#41×C₂₉	—	2	1	no	—
45	C₂²×D₄×C₂₉	—	2	1	no	—
46	C₂₉×AGL(1,ℤ/8)	—	4	4	no	—
47	C₂₉×#135	—	2	2	no	—
48	C₂₉×#135	—	2	2	no	—
49	C₂₉×#135	—	2	2	no	—
50	C₂₉×#135	D₄	1	4	yes	complemented
51	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
52	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
53	C₂×SD₁₆×C₂₉	—	2	1	no	—
54	C₂×SD₁₆×C₂₉	—	2	2	no	—
55	C₂×SD₁₆×C₂₉	—	2	1	no	—
56	C₂×D₈×C₂₉	—	2	2	no	—
57	C₂×D₈×C₂₉	—	2	2	no	—
58	C₂×D₈×C₂₉	—	2	1	no	—
59	C₂×D₈×C₂₉	—	2	2	no	—
60	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
61	C₂×D₈×C₂₉	C₂³	1	2	yes	—
62	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
63	C₂×M₁₆×C₂₉	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
65	C₂₉×#127	—	2	2	no	—
66	C₂₉×#124	—	2	2	no	—
67	C₂₉×#121	—	4	1	no	—
68	C₂₉×#121	—	4	1	no	—
69	C₂₉×#120	—	4	2	no	—
70	C₄×Q₈×C₂₉	—	2	2	no	—
71	C₄×D₄×C₂₉	—	2	2	no	—
72	C₄×D₄×C₂₉	—	4	2	no	—
73	C₂₉×#117	—	4	1	no	—
74	C₂₉×#117	D₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
77	C₂₉×Q₃₂	—	2	2	no	—
78	C₂₉×SD₃₂	—	2	4	no	—
79	C₂₉×SD₃₂	—	2	2	no	—
80	C₂₉×SD₃₂	—	2	2	no	—
81	C₂₉×D₁₆	—	2	4	no	—
82	C₂₉×D₁₆	—	2	2	no	—
83	C₂₉×M₃₂	—	2	2	no	—
84	C₂×C₁₆×C₂₉	—	2	2	no	—
85	C₂×C₁₆×C₂₉	C₂³	1	1	yes	characteristic
86	C₂×C₁₆×C₂₉	C₂³	1	1	yes	characteristic
87	C₂×C₁₆×C₂₉	C₂³	1	2	yes	—
88	C₂₉×#107	—	2	1	no	—
89	C₂₉×#107	C₂³	1	2	yes	—
90	C₂₉×#103	—	2	2	no	—
91	C₂₉×#102	—	2	2	no	—
92	C₂₉×#97	D₄	1	2	yes	—
93	C₄×C₈×C₂₉	C₂³	1	2	yes	—
94	C₂⁴×C₂₉	—	4	1	no	—
95	#41×C₂₉	—	2	4	no	—
96	#41×C₂₉	—	4	2	no	—
97	#41×C₂₉	—	4	2	no	—
98	#41×C₂₉	—	4	2	no	—
99	C₂×Q₈×C₂₉	—	2	1	no	—
100	C₂×Q₈×C₂₉	—	2	1	no	—
101	C₂×D₄×C₂₉	—	2	1	no	—
102	C₂×D₄×C₂₉	—	2	2	no	—
103	C₂×D₄×C₂₉	—	2	1	no	—
104	C₂×D₄×C₂₉	—	4	1	no	—
105	C₂×D₄×C₂₉	—	4	1	no	—
106	C₂×D₄×C₂₉	—	4	2	no	—
107	C₂×D₄×C₂₉	—	4	1	no	—
108	C₂×D₄×C₂₉	—	4	2	no	—
109	C₂×D₄×C₂₉	—	4	2	no	—
110	C₂×D₄×C₂₉	—	4	2	no	—
111	C₂²×C₄×C₂₉	—	4	1	no	—
112	C₂²×C₄×C₂₉	—	4	1	no	—
113	C₂²×C₄×C₂₉	—	4	1	no	—
114	C₂²×C₄×C₂₉	—	4	2	no	—
115	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
116	Q₁₆×C₂₉	—	2	1	no	—
117	Q₁₆×C₂₉	—	2	1	no	—
118	Q₁₆×C₂₉	—	2	1	no	—
119	Q₁₆×C₂₉	C₂×D₄	1	2	yes	—
120	SD₁₆×C₂₉	—	2	4	no	—
121	SD₁₆×C₂₉	—	4	4	no	—
122	SD₁₆×C₂₉	—	4	2	no	—
123	D₈×C₂₉	—	2	2	no	—
124	D₈×C₂₉	—	2	1	no	—
125	D₈×C₂₉	—	2	1	no	—
126	D₈×C₂₉	—	2	2	no	—
127	D₈×C₂₉	—	2	1	no	—
128	D₈×C₂₉	—	4	4	no	—
129	D₈×C₂₉	—	4	2	no	—
130	D₈×C₂₉	C₂×D₄	1	2	yes	—
131	M₁₆×C₂₉	—	2	2	no	—
132	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₂₉	#41	1	2	yes	—
136	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
137	C₄⋊C₄×C₂₉	—	2	2	no	—
138	C₄⋊C₄×C₂₉	—	4	1	no	—
139	C₄⋊C₄×C₂₉	—	4	2	no	—
140	C₄⋊C₄×C₂₉	D₈	1	1	yes	characteristic
141	C₄⋊C₄×C₂₉	D₈	1	1	yes	characteristic
142	C₂²⋊C₄×C₂₉	—	4	2	no	—
143	C₂²⋊C₄×C₂₉	—	4	2	no	—
144	C₂²⋊C₄×C₂₉	—	4	2	no	—
145	C₂²⋊C₄×C₂₉	D₈	1	2	yes	—
146	C₄²×C₂₉	—	4	2	no	—
147	C₄²×C₂₉	C₂×D₄	1	2	yes	—
148	C₁₆×C₂₉	—	2	1	no	—
149	C₁₆×C₂₉	—	2	1	no	—
150	C₁₆×C₂₉	—	2	2	no	—
151	#33589	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂³×C₂₉	—	4	1	no	—
153	C₂³×C₂₉	—	4	2	no	—
154	C₂³×C₂₉	—	4	1	no	—
155	C₂³×C₂₉	—	8	2	no	—
156	C₂³×C₂₉	—	16	1	no	—
157	C₂³×C₂₉	—	16	1	no	—
158	C₂³×C₂₉	C₂×D₈	1	1	yes	characteristic
159	Q₈×C₂₉	—	2	2	no	—
160	Q₈×C₂₉	—	4	1	no	—
161	Q₈×C₂₉	—	4	1	no	—
162	Q₈×C₂₉	—	4	1	no	—
163	D₄×C₂₉	—	2	2	no	—
164	D₄×C₂₉	—	4	4	no	—
165	D₄×C₂₉	—	4	2	no	—
166	D₄×C₂₉	—	4	1	no	—
167	D₄×C₂₉	—	4	1	no	—
168	D₄×C₂₉	—	4	1	no	—
169	D₄×C₂₉	—	4	2	no	—
170	D₄×C₂₉	—	8	2	no	—
171	D₄×C₂₉	—	8	2	no	—
172	D₄×C₂₉	—	16	2	no	—
173	D₄×C₂₉	—	16	2	no	—
174	C₂×C₄×C₂₉	—	4	1	no	—
175	C₂×C₄×C₂₉	—	4	4	no	—
176	C₂×C₄×C₂₉	—	4	2	no	—
177	C₂×C₄×C₂₉	—	4	1	no	—
178	C₂×C₄×C₂₉	—	8	2	no	—
179	C₂×C₄×C₂₉	—	16	2	no	—
180	C₂×C₄×C₂₉	—	16	1	no	—
181	C₂×C₄×C₂₉	#121	1	2	yes	—
182	C₂×C₄×C₂₉	C₂×D₈	1	2	yes	—
183	C₂×C₄×C₂₉	C₂×D₈	1	2	yes	—
184	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
185	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
186	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
187	C₈×C₂₉	—	2	2	no	—
188	C₈×C₂₉	#121	1	2	yes	—
189	C₈×C₂₉	C₂²×D₄	1	1	yes	characteristic
190	C₈×C₂₉	C₂×#41	1	1	yes	characteristic
191	C₂×#509	C₂×C₂₉	1	1	yes	characteristic, complemented
192	C₂×#508	C₂×C₂₉	1	1	yes	characteristic, complemented
193	#3155	C₂×C₂₉	1	1	yes	characteristic, complemented
194	#2951	C₂×C₂₉	1	1	yes	characteristic, complemented
195	#2211	C₂×C₂₉	1	2	yes	complemented
196	#2210	C₂×C₂₉	1	2	yes	complemented
197	#2207	C₂×C₂₉	1	2	yes	complemented
198	#2206	C₂×C₂₉	1	2	yes	complemented
199	#2151	C₂×C₂₉	1	1	yes	characteristic, complemented
200	#2139	C₂×C₂₉	1	1	yes	characteristic, complemented
201	C₂×#357	C₂×C₂₉	1	1	yes	characteristic, complemented
202	C₂²×C₂₉	—	2	1	no	—
203	C₂²×C₂₉	—	2	1	no	—
204	C₂²×C₂₉	—	4	2	no	—
205	C₂²×C₂₉	—	8	1	no	—
206	C₂²×C₂₉	—	8	1	no	—
207	C₂²×C₂₉	—	8	1	no	—
208	C₂²×C₂₉	—	8	2	no	—
209	C₂²×C₂₉	—	8	1	no	—
210	C₂²×C₂₉	—	8	2	no	—
211	C₂²×C₂₉	—	8	1	no	—
212	C₂²×C₂₉	—	8	2	no	—
213	C₂²×C₂₉	—	16	4	no	—
214	C₂²×C₂₉	#459	1	2	yes	—
215	C₂²×C₂₉	C₂²×D₈	1	1	yes	characteristic
216	C₄×C₂₉	—	2	2	no	—
217	C₄×C₂₉	—	2	2	no	—
218	C₄×C₂₉	—	4	2	no	—
219	C₄×C₂₉	—	8	2	no	—
220	C₄×C₂₉	—	8	1	no	—
221	C₄×C₂₉	#459	1	2	yes	—
222	C₄×C₂₉	C₂×#121	1	1	yes	characteristic
223	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
224	C₂×AGL(1,ℤ/8)	—	2	1	no	—
225	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
226	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
227	C₂²×D₈	C₂²×C₂₉	1	1	yes	characteristic
228	#535	—	2	1	no	—
229	#520	—	2	1	no	—
230	#509	—	2	4	no	—
231	#508	—	2	4	no	—
232	C₂×Q₃₂	C₂²×C₂₉	1	1	yes	characteristic, complemented
233	C₂×SD₃₂	C₂²×C₂₉	1	2	yes	—
234	C₂×SD₃₂	C₂²×C₂₉	1	1	yes	characteristic, complemented
235	C₂×SD₃₂	C₂²×C₂₉	1	1	yes	characteristic, complemented
236	C₂×D₁₆	C₂²×C₂₉	1	2	yes	—
237	C₂×D₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
238	C₂×M₃₂	C₂²×C₂₉	1	1	yes	characteristic
239	C₂²×C₁₆	C₂²×C₂₉	1	1	yes	characteristic
240	#496	—	2	2	no	—
241	#495	C₂²×C₂₉	1	2	yes	—
242	#493	C₂²×C₂₉	1	2	yes	—
243	#440	—	2	2	no	—
244	C₄×Q₁₆	C₂²×C₂₉	1	2	yes	complemented
245	C₄×D₈	C₂²×C₂₉	1	2	yes	complemented
246	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
247	#417	—	2	1	no	—
248	#405	C₂²×C₂₉	1	1	yes	characteristic
249	C₄⋊C₁₆	C₂²×C₂₉	1	2	yes	complemented
250	C₄⋊C₁₆	C₂²×C₂₉	1	2	yes	complemented
251	#358	C₂²×C₂₉	1	2	yes	complemented
252	#357	C₂²×C₂₉	1	2	yes	—
253	#357	C₂²×C₂₉	1	2	yes	—
254	#357	C₂²×C₂₉	1	2	yes	complemented
255	C₂×C₂₉	—	2	2	no	—
256	C₂×C₂₉	—	8	2	no	—
257	C₂×C₂₉	—	16	1	no	—
258	C₂×C₂₉	—	16	2	no	—
259	C₂×C₂₉	C₂×#459	1	1	yes	characteristic
260	C₂×C₂₉	#3415	1	1	yes	characteristic
261	C₂×C₂₉	#3416	1	1	yes	characteristic
262	C₂×#41	—	2	1	no	—
263	C₂×#41	—	2	1	no	—
264	C₂²×D₄	—	2	1	no	—
265	AGL(1,ℤ/8)	—	4	4	no	—
266	#135	—	2	2	no	—
267	#135	—	2	2	no	—
268	#135	—	2	2	no	—
269	#135	D₄×C₂₉	1	4	yes	complemented
270	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
271	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
272	C₂×SD₁₆	—	2	1	no	—
273	C₂×SD₁₆	—	2	1	no	—
274	C₂×SD₁₆	—	2	2	no	—
275	C₂×D₈	—	2	2	no	—
276	C₂×D₈	—	2	1	no	—
277	C₂×D₈	—	2	2	no	—
278	C₂×D₈	—	2	2	no	—
279	C₂×D₈	C₂³×C₂₉	1	2	yes	—
280	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
281	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
282	C₂×M₁₆	D₄×C₂₉	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
284	#127	—	2	2	no	—
285	#124	—	2	2	no	—
286	#121	—	4	1	no	—
287	#121	—	4	1	no	—
288	#120	—	4	2	no	—
289	C₄×Q₈	—	2	2	no	—
290	C₄×D₄	—	2	2	no	—
291	C₄×D₄	—	4	2	no	—
292	#117	—	4	1	no	—
293	#117	D₄×C₂₉	1	1	yes	characteristic
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	4	1	no	—
296	Q₃₂	—	2	2	no	—
297	SD₃₂	—	2	4	no	—
298	SD₃₂	—	2	2	no	—
299	SD₃₂	—	2	2	no	—
300	D₁₆	—	2	4	no	—
301	D₁₆	—	2	2	no	—
302	M₃₂	—	2	2	no	—
303	C₂×C₁₆	—	2	2	no	—
304	C₂×C₁₆	C₂³×C₂₉	1	1	yes	characteristic
305	C₂×C₁₆	C₂³×C₂₉	1	1	yes	characteristic
306	C₂×C₁₆	C₂³×C₂₉	1	2	yes	—
307	#107	—	2	1	no	—
308	#107	C₂³×C₂₉	1	2	yes	—
309	#103	—	2	2	no	—
310	#102	—	2	2	no	—
311	#97	D₄×C₂₉	1	2	yes	—
312	C₄×C₈	C₂³×C₂₉	1	2	yes	—
313	C₂₉	#33589	1	1	yes	characteristic, direct product factor, Sylow
314	C₂⁴	—	4	1	no	—
315	#41	—	2	4	no	—
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	2	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	4	2	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
336	Q₁₆	—	2	1	no	—
337	Q₁₆	—	2	1	no	—
338	Q₁₆	—	2	1	no	—
339	Q₁₆	C₂×D₄×C₂₉	1	2	yes	—
340	SD₁₆	—	2	4	no	—
341	SD₁₆	—	4	4	no	—
342	SD₁₆	—	4	2	no	—
343	D₈	—	2	2	no	—
344	D₈	—	2	1	no	—
345	D₈	—	2	1	no	—
346	D₈	—	2	2	no	—
347	D₈	—	2	1	no	—
348	D₈	—	4	4	no	—
349	D₈	—	4	2	no	—
350	D₈	C₂×D₄×C₂₉	1	2	yes	—
351	M₁₆	—	2	2	no	—
352	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
353	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
354	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
355	C₂×C₈	#41×C₂₉	1	2	yes	—
356	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	4	1	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	D₈×C₂₉	1	1	yes	characteristic
361	C₄⋊C₄	D₈×C₂₉	1	1	yes	characteristic
362	C₂²⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₂²⋊C₄	D₈×C₂₉	1	2	yes	—
366	C₄²	—	4	2	no	—
367	C₄²	C₂×D₄×C₂₉	1	2	yes	—
368	C₁₆	—	2	1	no	—
369	C₁₆	—	2	1	no	—
370	C₁₆	—	2	2	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	8	2	no	—
375	C₂³	—	16	1	no	—
376	C₂³	—	16	1	no	—
377	C₂³	C₂×D₈×C₂₉	1	1	yes	characteristic
378	Q₈	—	2	2	no	—
379	Q₈	—	4	1	no	—
380	Q₈	—	4	1	no	—
381	Q₈	—	4	1	no	—
382	D₄	—	2	2	no	—
383	D₄	—	4	4	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	1	no	—
386	D₄	—	4	1	no	—
387	D₄	—	4	1	no	—
388	D₄	—	4	2	no	—
389	D₄	—	8	2	no	—
390	D₄	—	8	2	no	—
391	D₄	—	16	2	no	—
392	D₄	—	16	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	8	2	no	—
398	C₂×C₄	—	16	2	no	—
399	C₂×C₄	—	16	1	no	—
400	C₂×C₄	C₂₉×#121	1	2	yes	—
401	C₂×C₄	C₂×D₈×C₂₉	1	2	yes	—
402	C₂×C₄	C₂×D₈×C₂₉	1	2	yes	—
403	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
404	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
405	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	C₂₉×#121	1	2	yes	—
408	C₈	C₂²×D₄×C₂₉	1	1	yes	characteristic
409	C₈	C₂×#41×C₂₉	1	1	yes	characteristic
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	16	4	no	—
422	C₂²	C₂₉×#459	1	2	yes	—
423	C₂²	C₂²×D₈×C₂₉	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	8	1	no	—
428	C₄	—	8	2	no	—
429	C₄	C₂₉×#459	1	2	yes	—
430	C₄	C₂×C₂₉×#121	1	1	yes	characteristic
431	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
432	C₂	—	2	2	no	—
433	C₂	—	8	2	no	—
434	C₂	—	16	2	no	—
435	C₂	—	16	1	no	—
436	C₂	C₂×C₂₉×#459	1	1	yes	characteristic
437	C₂	C₂₉×#3415	1	1	yes	characteristic
438	C₂	C₂₉×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₂₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂₉×#117 ◁ C₂₉×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#509	C₂	semidirect
2. C₂×C₂₉×#508	C₂	semidirect
3. C₂₉×#3155	C₂	semidirect
4. C₂₉×#2951	C₂	semidirect
5. C₂₉×#2211	C₂	semidirect
6. C₂₉×#2210	C₂	semidirect
7. C₂₉×#2207	C₂	semidirect
8. C₂₉×#2206	C₂	semidirect
9. C₂₉×#2151	C₂	semidirect
10. C₂₉×#2139	C₂	semidirect
11. C₂×C₂₉×#357	C₂	semidirect
20. C₂×C₂₉×Q₃₂	C₂²	semidirect
22. C₂×C₂₉×SD₃₂	C₂²	semidirect
23. C₂×C₂₉×SD₃₂	C₂²	semidirect
25. C₂×C₂₉×D₁₆	C₂²	semidirect
32. C₄×Q₁₆×C₂₉	C₂²	semidirect
33. C₄×D₈×C₂₉	C₂²	semidirect
37. C₂₉×C₄⋊C₁₆	C₂²	semidirect
38. C₂₉×C₄⋊C₁₆	C₂²	semidirect
39. C₂₉×#358	C₂²	semidirect
42. C₂₉×#357	C₂²	semidirect
50. C₂₉×#135	D₄	semidirect
151. #33589	C₂₉	direct (N × H)
191. C₂×#509	C₂×C₂₉	semidirect
192. C₂×#508	C₂×C₂₉	semidirect
193. #3155	C₂×C₂₉	semidirect
194. #2951	C₂×C₂₉	semidirect
195. #2211	C₂×C₂₉	semidirect
196. #2210	C₂×C₂₉	semidirect
197. #2207	C₂×C₂₉	semidirect
198. #2206	C₂×C₂₉	semidirect
199. #2151	C₂×C₂₉	semidirect
200. #2139	C₂×C₂₉	semidirect
201. C₂×#357	C₂×C₂₉	semidirect
232. C₂×Q₃₂	C₂²×C₂₉	semidirect
234. C₂×SD₃₂	C₂²×C₂₉	semidirect
235. C₂×SD₃₂	C₂²×C₂₉	semidirect
237. C₂×D₁₆	C₂²×C₂₉	semidirect
244. C₄×Q₁₆	C₂²×C₂₉	semidirect
245. C₄×D₈	C₂²×C₂₉	semidirect
249. C₄⋊C₁₆	C₂²×C₂₉	semidirect
250. C₄⋊C₁₆	C₂²×C₂₉	semidirect
251. #358	C₂²×C₂₉	semidirect
254. #357	C₂²×C₂₉	semidirect
269. #135	D₄×C₂₉	semidirect
313. C₂₉	#33589	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×#509	2
C₂×C₂₉×#508	2
C₂₉×#3155	2
C₂₉×#2951	2
C₂₉×#2211	2
C₂₉×#2210	2
C₂₉×#2207	2
C₂₉×#2206	2
C₂₉×#2151	2
C₂₉×#2139	2
C₂×C₂₉×#357	2
#33589	29

Subgroups — C29×#33589 #20328489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#33589 #20328489