Subgroups — C₂₉×#33579 #20328479

Order 7424.

718 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#508	C₂	1	2	yes	maximal, complemented
2	C₂₉×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₂₉×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2211	C₂	1	2	yes	maximal, complemented
5	C₂₉×#2210	C₂	1	2	yes	maximal, complemented
6	C₂₉×#2209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2207	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#2206	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₉×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#2138	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₉×#135	—	2	1	no	—
13	C₂×C₂₉×#135	C₂²	1	2	yes	—
14	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
15	C₂₉×#532	—	2	1	no	—
16	C₄×#41×C₂₉	—	2	1	no	—
17	C₂₉×#508	—	2	8	no	—
18	C₂×C₂₉×Q₃₂	C₂²	1	2	yes	—
19	C₂×C₂₉×SD₃₂	C₂²	1	2	yes	—
20	C₂×C₂₉×SD₃₂	C₂²	1	2	yes	—
21	C₂×C₂₉×D₁₆	C₂²	1	2	yes	—
22	C₂²×C₁₆×C₂₉	C₂²	1	2	yes	—
23	C₂₉×#495	—	2	1	no	—
24	C₂₉×#495	C₂²	1	2	yes	—
25	C₂₉×#494	C₂²	1	1	yes	characteristic
26	C₂₉×#493	C₂²	1	1	yes	characteristic
27	C₂₉×#492	—	2	1	no	—
28	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
29	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
30	C₄×SD₁₆×C₂₉	—	2	1	no	—
31	C₄×SD₁₆×C₂₉	—	2	1	no	—
32	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
33	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
34	C₂₉×#427	C₂²	1	1	yes	characteristic
35	C₂₉×#416	—	2	1	no	—
36	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
37	C₂₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₂₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₂₉×C₄⋊C₁₆	C₂²	1	2	yes	—
40	C₂₉×#358	C₂²	1	2	yes	—
41	C₂₉×#358	C₂²	1	2	yes	—
42	C₂₉×#357	C₂²	1	2	yes	—
43	C₂₉×#357	C₂²	1	2	yes	—
44	C₂×#41×C₂₉	—	2	1	no	—
45	C₂×#41×C₂₉	—	2	2	no	—
46	C₂₉×#135	—	2	4	no	—
47	C₂₉×#135	—	2	2	no	—
48	C₂₉×#135	—	2	4	no	—
49	C₂₉×#135	—	4	4	no	—
50	C₂₉×#135	D₄	1	4	yes	complemented
51	C₂×Q₁₆×C₂₉	—	2	1	no	—
52	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
53	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
54	C₂×SD₁₆×C₂₉	—	2	1	no	—
55	C₂×SD₁₆×C₂₉	—	2	2	no	—
56	C₂×SD₁₆×C₂₉	—	2	2	no	—
57	C₂×D₈×C₂₉	—	2	1	no	—
58	C₂×D₈×C₂₉	C₂³	1	2	yes	—
59	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
62	C₂₉×C₄⋊Q₈	—	2	1	no	—
63	C₂₉×#127	—	2	1	no	—
64	C₂₉×#124	—	2	2	no	—
65	C₂₉×#121	—	4	1	no	—
66	C₂₉×#121	—	4	1	no	—
67	C₄×Q₈×C₂₉	—	2	1	no	—
68	C₄×Q₈×C₂₉	—	2	1	no	—
69	C₄×D₄×C₂₉	—	2	1	no	—
70	C₄×D₄×C₂₉	—	2	1	no	—
71	C₄×D₄×C₂₉	—	4	1	no	—
72	C₄×D₄×C₂₉	—	4	1	no	—
73	C₄×D₄×C₂₉	—	4	1	no	—
74	C₄×D₄×C₂₉	—	4	1	no	—
75	C₂₉×#117	—	2	1	no	—
76	C₂₉×#117	—	4	1	no	—
77	C₂×C₄²×C₂₉	—	4	1	no	—
78	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
79	C₂₉×Q₃₂	—	2	4	no	—
80	C₂₉×SD₃₂	—	2	4	no	—
81	C₂₉×SD₃₂	—	2	4	no	—
82	C₂₉×D₁₆	—	2	4	no	—
83	C₂×C₁₆×C₂₉	—	2	4	no	—
84	C₂×C₁₆×C₂₉	C₂³	1	2	yes	—
85	C₂×C₁₆×C₂₉	C₂³	1	2	yes	—
86	C₂₉×#107	C₂³	1	1	yes	characteristic
87	C₂₉×#107	C₂³	1	1	yes	characteristic
88	C₂₉×#106	—	2	1	no	—
89	C₂₉×#103	—	2	1	no	—
90	C₂₉×#103	—	2	1	no	—
91	C₂₉×#102	—	2	1	no	—
92	C₂₉×#102	—	2	1	no	—
93	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
94	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
95	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
97	#41×C₂₉	—	2	4	no	—
98	#41×C₂₉	—	4	2	no	—
99	#41×C₂₉	—	4	4	no	—
100	#41×C₂₉	—	4	4	no	—
101	C₂×Q₈×C₂₉	—	2	1	no	—
102	C₂×Q₈×C₂₉	—	2	2	no	—
103	C₂×D₄×C₂₉	—	2	1	no	—
104	C₂×D₄×C₂₉	—	2	2	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	1	no	—
109	C₂²×C₄×C₂₉	—	4	1	no	—
110	C₂²×C₄×C₂₉	—	4	1	no	—
111	C₂²×C₄×C₂₉	—	4	1	no	—
112	C₂²×C₄×C₂₉	—	4	2	no	—
113	C₂²×C₄×C₂₉	D₈	1	1	yes	characteristic
114	C₂²×C₄×C₂₉	D₈	1	1	yes	characteristic
115	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
116	Q₁₆×C₂₉	—	2	2	no	—
117	Q₁₆×C₂₉	—	2	1	no	—
118	Q₁₆×C₂₉	—	2	2	no	—
119	Q₁₆×C₂₉	—	4	2	no	—
120	Q₁₆×C₂₉	C₂×D₄	1	2	yes	—
121	SD₁₆×C₂₉	—	2	4	no	—
122	SD₁₆×C₂₉	—	4	4	no	—
123	SD₁₆×C₂₉	—	4	4	no	—
124	D₈×C₂₉	—	2	2	no	—
125	D₈×C₂₉	—	2	1	no	—
126	D₈×C₂₉	—	2	2	no	—
127	D₈×C₂₉	—	4	2	no	—
128	D₈×C₂₉	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₂₉	—	2	2	no	—
130	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₂₉	#41	1	2	yes	—
135	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
136	C₄⋊C₄×C₂₉	—	2	1	no	—
137	C₄⋊C₄×C₂₉	—	2	1	no	—
138	C₄⋊C₄×C₂₉	—	4	1	no	—
139	C₄⋊C₄×C₂₉	—	4	1	no	—
140	C₄⋊C₄×C₂₉	—	4	1	no	—
141	C₄⋊C₄×C₂₉	—	4	1	no	—
142	C₂²⋊C₄×C₂₉	—	4	1	no	—
143	C₂²⋊C₄×C₂₉	—	4	1	no	—
144	C₂²⋊C₄×C₂₉	—	4	1	no	—
145	C₂²⋊C₄×C₂₉	—	4	2	no	—
146	C₂²⋊C₄×C₂₉	—	4	2	no	—
147	C₄²×C₂₉	—	4	1	no	—
148	C₄²×C₂₉	—	4	1	no	—
149	C₄²×C₂₉	—	4	1	no	—
150	C₄²×C₂₉	D₈	1	1	yes	characteristic
151	C₄²×C₂₉	D₈	1	1	yes	characteristic
152	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
154	C₁₆×C₂₉	—	2	2	no	—
155	C₁₆×C₂₉	—	2	2	no	—
156	#33579	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₂₉	—	4	1	no	—
158	C₂³×C₂₉	—	4	2	no	—
159	C₂³×C₂₉	C₂×D₈	1	1	yes	characteristic
160	Q₈×C₂₉	—	2	2	no	—
161	Q₈×C₂₉	—	4	1	no	—
162	Q₈×C₂₉	—	4	2	no	—
163	Q₈×C₂₉	—	4	2	no	—
164	D₄×C₂₉	—	2	2	no	—
165	D₄×C₂₉	—	4	4	no	—
166	D₄×C₂₉	—	4	2	no	—
167	D₄×C₂₉	—	4	1	no	—
168	D₄×C₂₉	—	4	2	no	—
169	D₄×C₂₉	—	8	2	no	—
170	D₄×C₂₉	—	8	4	no	—
171	D₄×C₂₉	—	8	2	no	—
172	C₂×C₄×C₂₉	—	2	2	no	—
173	C₂×C₄×C₂₉	—	4	1	no	—
174	C₂×C₄×C₂₉	—	4	1	no	—
175	C₂×C₄×C₂₉	—	4	4	no	—
176	C₂×C₄×C₂₉	—	4	1	no	—
177	C₂×C₄×C₂₉	—	4	1	no	—
178	C₂×C₄×C₂₉	—	4	2	no	—
179	C₂×C₄×C₂₉	—	8	2	no	—
180	C₂×C₄×C₂₉	—	8	4	no	—
181	C₂×C₄×C₂₉	—	8	2	no	—
182	C₂×C₄×C₂₉	#121	1	2	yes	—
183	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
184	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
185	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
186	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
187	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
188	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
189	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
190	C₈×C₂₉	—	2	1	no	—
191	C₈×C₂₉	—	2	1	no	—
192	C₈×C₂₉	#121	1	2	yes	—
193	C₈×C₂₉	C₂²×D₄	1	1	yes	characteristic
194	C₈×C₂₉	C₂×#41	1	1	yes	characteristic
195	C₂×#508	C₂×C₂₉	1	2	yes	complemented
196	#3147	C₂×C₂₉	1	1	yes	characteristic, complemented
197	C₄×#135	C₂×C₂₉	1	1	yes	characteristic, complemented
198	#2211	C₂×C₂₉	1	2	yes	complemented
199	#2210	C₂×C₂₉	1	2	yes	complemented
200	#2209	C₂×C₂₉	1	1	yes	characteristic, complemented
201	#2208	C₂×C₂₉	1	1	yes	characteristic, complemented
202	#2207	C₂×C₂₉	1	1	yes	characteristic, complemented
203	#2206	C₂×C₂₉	1	1	yes	characteristic, complemented
204	C₂×C₄⋊C₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
205	#2138	C₂×C₂₉	1	2	yes	complemented
206	C₂²×C₂₉	—	2	1	no	—
207	C₂²×C₂₉	—	2	1	no	—
208	C₂²×C₂₉	—	4	2	no	—
209	C₂²×C₂₉	—	8	1	no	—
210	C₂²×C₂₉	—	8	1	no	—
211	C₂²×C₂₉	—	8	2	no	—
212	C₂²×C₂₉	—	8	2	no	—
213	C₂²×C₂₉	—	8	2	no	—
214	C₂²×C₂₉	#459	1	2	yes	—
215	C₂²×C₂₉	C₂²×D₈	1	1	yes	characteristic
216	C₄×C₂₉	—	2	1	no	—
217	C₄×C₂₉	—	2	1	no	—
218	C₄×C₂₉	—	2	1	no	—
219	C₄×C₂₉	—	4	2	no	—
220	C₄×C₂₉	—	8	1	no	—
221	C₄×C₂₉	—	8	1	no	—
222	C₄×C₂₉	—	8	2	no	—
223	C₄×C₂₉	#459	1	2	yes	—
224	C₄×C₂₉	#508	1	2	yes	complemented
225	C₄×C₂₉	C₂×#121	1	1	yes	characteristic
226	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
227	C₂×#135	—	2	1	no	—
228	C₂×#135	C₂²×C₂₉	1	2	yes	—
229	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
230	#532	—	2	1	no	—
231	C₄×#41	—	2	1	no	—
232	#508	—	2	8	no	—
233	C₂×Q₃₂	C₂²×C₂₉	1	2	yes	—
234	C₂×SD₃₂	C₂²×C₂₉	1	2	yes	—
235	C₂×SD₃₂	C₂²×C₂₉	1	2	yes	—
236	C₂×D₁₆	C₂²×C₂₉	1	2	yes	—
237	C₂²×C₁₆	C₂²×C₂₉	1	2	yes	—
238	#495	—	2	1	no	—
239	#495	C₂²×C₂₉	1	2	yes	—
240	#494	C₂²×C₂₉	1	1	yes	characteristic
241	#493	C₂²×C₂₉	1	1	yes	characteristic
242	#492	—	2	1	no	—
243	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
244	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
245	C₄×SD₁₆	—	2	1	no	—
246	C₄×SD₁₆	—	2	1	no	—
247	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
248	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
249	#427	C₂²×C₂₉	1	1	yes	characteristic
250	#416	—	2	1	no	—
251	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
252	C₄⋊C₁₆	C₂²×C₂₉	1	1	yes	characteristic
253	C₄⋊C₁₆	C₂²×C₂₉	1	1	yes	characteristic
254	C₄⋊C₁₆	C₂²×C₂₉	1	2	yes	—
255	#358	C₂²×C₂₉	1	2	yes	—
256	#358	C₂²×C₂₉	1	2	yes	—
257	#357	C₂²×C₂₉	1	2	yes	—
258	#357	C₂²×C₂₉	1	2	yes	—
259	C₂×C₂₉	—	2	2	no	—
260	C₂×C₂₉	—	8	2	no	—
261	C₂×C₂₉	—	16	2	no	—
262	C₂×C₂₉	C₂×#459	1	1	yes	characteristic
263	C₂×C₂₉	C₂×#508	1	1	yes	characteristic
264	C₂×C₂₉	#3414	1	1	yes	characteristic
265	C₂×#41	—	2	1	no	—
266	C₂×#41	—	2	2	no	—
267	#135	—	2	4	no	—
268	#135	—	2	2	no	—
269	#135	—	2	4	no	—
270	#135	—	4	4	no	—
271	#135	D₄×C₂₉	1	4	yes	complemented
272	C₂×Q₁₆	—	2	1	no	—
273	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
274	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
275	C₂×SD₁₆	—	2	1	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×SD₁₆	—	2	2	no	—
278	C₂×D₈	—	2	1	no	—
279	C₂×D₈	C₂³×C₂₉	1	2	yes	—
280	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
281	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
283	C₄⋊Q₈	—	2	1	no	—
284	#127	—	2	1	no	—
285	#124	—	2	2	no	—
286	#121	—	4	1	no	—
287	#121	—	4	1	no	—
288	C₄×Q₈	—	2	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	4	1	no	—
293	C₄×D₄	—	4	1	no	—
294	C₄×D₄	—	4	1	no	—
295	C₄×D₄	—	4	1	no	—
296	#117	—	2	1	no	—
297	#117	—	4	1	no	—
298	C₂×C₄²	—	4	1	no	—
299	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
300	Q₃₂	—	2	4	no	—
301	SD₃₂	—	2	4	no	—
302	SD₃₂	—	2	4	no	—
303	D₁₆	—	2	4	no	—
304	C₂×C₁₆	—	2	4	no	—
305	C₂×C₁₆	C₂³×C₂₉	1	2	yes	—
306	C₂×C₁₆	C₂³×C₂₉	1	2	yes	—
307	#107	C₂³×C₂₉	1	1	yes	characteristic
308	#107	C₂³×C₂₉	1	1	yes	characteristic
309	#106	—	2	1	no	—
310	#103	—	2	1	no	—
311	#103	—	2	1	no	—
312	#102	—	2	1	no	—
313	#102	—	2	1	no	—
314	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
315	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
316	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
317	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
318	C₂₉	#33579	1	1	yes	characteristic, direct product factor, Sylow
319	#41	—	2	4	no	—
320	#41	—	4	2	no	—
321	#41	—	4	4	no	—
322	#41	—	4	4	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	4	1	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	D₈×C₂₉	1	1	yes	characteristic
336	C₂²×C₄	D₈×C₂₉	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
338	Q₁₆	—	2	2	no	—
339	Q₁₆	—	2	1	no	—
340	Q₁₆	—	2	2	no	—
341	Q₁₆	—	4	2	no	—
342	Q₁₆	C₂×D₄×C₂₉	1	2	yes	—
343	SD₁₆	—	2	4	no	—
344	SD₁₆	—	4	4	no	—
345	SD₁₆	—	4	4	no	—
346	D₈	—	2	2	no	—
347	D₈	—	2	1	no	—
348	D₈	—	2	2	no	—
349	D₈	—	4	2	no	—
350	D₈	C₂×D₄×C₂₉	1	2	yes	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
353	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
354	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
355	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
356	C₂×C₈	#41×C₂₉	1	2	yes	—
357	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	—	4	1	no	—
364	C₂²⋊C₄	—	4	1	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₂²⋊C₄	—	4	2	no	—
369	C₄²	—	4	1	no	—
370	C₄²	—	4	1	no	—
371	C₄²	—	4	1	no	—
372	C₄²	D₈×C₂₉	1	1	yes	characteristic
373	C₄²	D₈×C₂₉	1	1	yes	characteristic
374	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
375	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
376	C₁₆	—	2	2	no	—
377	C₁₆	—	2	2	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	2	no	—
380	C₂³	C₂×D₈×C₂₉	1	1	yes	characteristic
381	Q₈	—	2	2	no	—
382	Q₈	—	4	1	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	4	2	no	—
385	D₄	—	2	2	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	1	no	—
389	D₄	—	4	2	no	—
390	D₄	—	8	2	no	—
391	D₄	—	8	4	no	—
392	D₄	—	8	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	8	2	no	—
401	C₂×C₄	—	8	4	no	—
402	C₂×C₄	—	8	2	no	—
403	C₂×C₄	C₂₉×#121	1	2	yes	—
404	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
405	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
406	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
407	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
408	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
409	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
410	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	C₂₉×#121	1	2	yes	—
414	C₈	C₂²×D₄×C₂₉	1	1	yes	characteristic
415	C₈	C₂×#41×C₂₉	1	1	yes	characteristic
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	C₂₉×#459	1	2	yes	—
425	C₂²	C₂²×D₈×C₂₉	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	8	2	no	—
431	C₄	—	8	1	no	—
432	C₄	—	8	1	no	—
433	C₄	C₂₉×#459	1	2	yes	—
434	C₄	C₂₉×#508	1	2	yes	complemented
435	C₄	C₂×C₂₉×#121	1	1	yes	characteristic
436	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
437	C₂	—	2	2	no	—
438	C₂	—	8	2	no	—
439	C₂	—	16	2	no	—
440	C₂	C₂×C₂₉×#459	1	1	yes	characteristic
441	C₂	C₂×C₂₉×#508	1	1	yes	characteristic
442	C₂	C₂₉×#3414	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂²×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ C₂×C₄×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#508	C₂	semidirect
2. C₂₉×#3147	C₂	semidirect
3. C₄×C₂₉×#135	C₂	semidirect
4. C₂₉×#2211	C₂	semidirect
5. C₂₉×#2210	C₂	semidirect
6. C₂₉×#2209	C₂	semidirect
7. C₂₉×#2208	C₂	semidirect
8. C₂₉×#2207	C₂	semidirect
9. C₂₉×#2206	C₂	semidirect
10. C₂×C₂₉×C₄⋊C₁₆	C₂	semidirect
11. C₂₉×#2138	C₂	semidirect
50. C₂₉×#135	D₄	semidirect
156. #33579	C₂₉	direct (N × H)
195. C₂×#508	C₂×C₂₉	semidirect
196. #3147	C₂×C₂₉	semidirect
197. C₄×#135	C₂×C₂₉	semidirect
198. #2211	C₂×C₂₉	semidirect
199. #2210	C₂×C₂₉	semidirect
200. #2209	C₂×C₂₉	semidirect
201. #2208	C₂×C₂₉	semidirect
202. #2207	C₂×C₂₉	semidirect
203. #2206	C₂×C₂₉	semidirect
204. C₂×C₄⋊C₁₆	C₂×C₂₉	semidirect
205. #2138	C₂×C₂₉	semidirect
224. C₄×C₂₉	#508	semidirect
271. #135	D₄×C₂₉	semidirect
318. C₂₉	#33579	direct (N × H)
434. C₄	C₂₉×#508	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#508	2
C₂₉×#3147	2
C₄×C₂₉×#135	2
C₂₉×#2211	2
C₂₉×#2210	2
C₂₉×#2209	2
C₂₉×#2208	2
C₂₉×#2207	2
C₂₉×#2206	2
C₂×C₂₉×C₄⋊C₁₆	2
C₂₉×#2138	2
#33579	29

Subgroups — C29×#33579 #20328479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#33579 #20328479