Subgroups — C₂₉×#19352 #20314252

Order 7424.

712 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3239	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3217	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#492	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2966	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1686	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1685	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1666	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1665	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1555	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₂₉	—	2	1	no	—
13	C₂²×SD₁₆×C₂₉	—	2	1	no	—
14	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
16	C₂₉×#529	C₂²	1	1	yes	characteristic
17	C₂₉×#501	—	2	1	no	—
18	C₂₉×#496	—	2	1	no	—
19	C₂₉×#492	—	2	1	no	—
20	C₂₉×#492	—	2	1	no	—
21	C₂₉×#492	C₂²	1	2	yes	—
22	C₂₉×#492	C₂²	1	2	yes	—
23	C₂₉×#490	—	2	1	no	—
24	C₂₉×#489	—	2	1	no	—
25	C₂₉×#484	—	2	1	no	—
26	C₂₉×#481	—	2	1	no	—
27	C₂₉×#475	C₂²	1	2	yes	complemented
28	C₂₉×#474	C₂²	1	2	yes	complemented
29	C₂₉×#460	C₂²	1	2	yes	—
30	C₂₉×#459	C₂²	1	2	yes	—
31	C₂₉×#450	—	2	1	no	—
32	C₂₉×#447	—	2	1	no	—
33	C₂₉×#446	C₂²	1	1	yes	characteristic, complemented
34	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
35	C₂₉×#436	C₂²	1	1	yes	characteristic, complemented
36	C₂₉×#435	—	2	1	no	—
37	C₈×D₄×C₂₉	—	2	1	no	—
38	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
39	C₂₉×#433	—	2	1	no	—
40	C₂₉×#432	C₂²	1	1	yes	characteristic
41	C₂₉×#432	C₂²	1	1	yes	characteristic
42	C₂₉×#432	C₂²	1	1	yes	characteristic
43	C₂₉×#405	—	2	1	no	—
44	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
45	C₂₉×#335	C₂²	1	2	yes	complemented
46	C₂₉×#334	C₂²	1	2	yes	complemented
47	C₂₉×#332	C₂²	1	2	yes	complemented
48	C₂₉×#332	C₂²	1	2	yes	complemented
49	C₂₉×#331	C₂²	1	2	yes	—
50	C₂₉×#331	C₂²	1	2	yes	—
51	C₂²×Q₈×C₂₉	—	2	1	no	—
52	C₂²×D₄×C₂₉	—	2	1	no	—
53	C₂²×D₄×C₂₉	—	2	1	no	—
54	C₂²×D₄×C₂₉	—	2	1	no	—
55	C₂×SD₁₆×C₂₉	—	2	2	no	—
56	C₂×SD₁₆×C₂₉	—	2	2	no	—
57	C₂×SD₁₆×C₂₉	—	2	2	no	—
58	C₂×SD₁₆×C₂₉	—	2	2	no	—
59	C₂×SD₁₆×C₂₉	—	2	2	no	—
60	C₂×SD₁₆×C₂₉	—	4	4	no	—
61	C₂×SD₁₆×C₂₉	—	4	4	no	—
62	C₂×D₈×C₂₉	—	2	2	no	—
63	C₂×M₁₆×C₂₉	—	2	1	no	—
64	C₂²×C₈×C₂₉	—	2	1	no	—
65	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
66	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
67	C₂₉×C₄⋊Q₈	—	2	1	no	—
68	C₂₉×C₄⋊Q₈	—	2	1	no	—
69	C₂₉×C₄⋊Q₈	—	2	1	no	—
70	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
71	C₂₉×#127	—	2	1	no	—
72	C₂₉×#127	—	2	1	no	—
73	C₂₉×#127	—	2	1	no	—
74	C₂₉×#127	C₂³	1	2	yes	—
75	C₂₉×#126	—	2	1	no	—
76	C₂₉×#125	D₄	1	1	yes	characteristic
77	C₂₉×#124	D₄	1	1	yes	characteristic
78	C₂₉×#123	—	2	1	no	—
79	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
80	C₂₉×#121	D₄	1	1	yes	characteristic
81	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
82	C₄×D₄×C₂₉	—	2	1	no	—
83	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
84	C₂₉×#117	—	2	1	no	—
85	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
87	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
88	C₂₉×#107	—	2	2	no	—
89	C₂₉×#106	—	2	2	no	—
90	C₂₉×C₄⋊C₈	—	2	1	no	—
91	C₂₉×C₄⋊C₈	—	2	1	no	—
92	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
93	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
94	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
95	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
96	C₂₉×#103	—	2	2	no	—
97	C₂₉×#102	—	2	2	no	—
98	C₂₉×#102	—	2	2	no	—
99	C₂₉×#102	—	2	2	no	—
100	C₂₉×C₂²⋊C₈	—	2	1	no	—
101	C₂₉×C₂²⋊C₈	—	2	1	no	—
102	C₂₉×C₂²⋊C₈	—	2	1	no	—
103	C₂₉×C₂²⋊C₈	—	2	1	no	—
104	C₂₉×C₂²⋊C₈	—	2	1	no	—
105	C₂₉×#97	—	2	1	no	—
106	C₂₉×#97	—	2	1	no	—
107	C₂₉×#97	—	2	1	no	—
108	C₂₉×#97	—	2	1	no	—
109	C₄×C₈×C₂₉	—	2	1	no	—
110	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
111	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
112	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
113	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
114	C₂⁴×C₂₉	—	4	1	no	—
115	C₂×Q₈×C₂₉	—	2	2	no	—
116	C₂×Q₈×C₂₉	—	4	2	no	—
117	C₂×Q₈×C₂₉	—	4	2	no	—
118	C₂×Q₈×C₂₉	—	4	1	no	—
119	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
120	C₂×D₄×C₂₉	—	2	1	no	—
121	C₂×D₄×C₂₉	—	2	2	no	—
122	C₂×D₄×C₂₉	—	2	2	no	—
123	C₂×D₄×C₂₉	—	2	2	no	—
124	C₂×D₄×C₂₉	—	4	2	no	—
125	C₂×D₄×C₂₉	—	4	2	no	—
126	C₂×D₄×C₂₉	—	4	1	no	—
127	C₂×D₄×C₂₉	—	4	1	no	—
128	C₂×D₄×C₂₉	—	4	1	no	—
129	C₂×D₄×C₂₉	—	8	2	no	—
130	C₂×D₄×C₂₉	—	8	2	no	—
131	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₂₉	—	2	1	no	—
133	C₂²×C₄×C₂₉	—	4	1	no	—
134	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
137	SD₁₆×C₂₉	—	4	4	no	—
138	SD₁₆×C₂₉	—	4	4	no	—
139	SD₁₆×C₂₉	—	4	4	no	—
140	SD₁₆×C₂₉	—	4	4	no	—
141	SD₁₆×C₂₉	—	8	2	no	—
142	D₈×C₂₉	—	8	2	no	—
143	M₁₆×C₂₉	—	4	2	no	—
144	C₂×C₈×C₂₉	—	2	2	no	—
145	C₂×C₈×C₂₉	—	2	2	no	—
146	C₂×C₈×C₂₉	—	2	1	no	—
147	C₂×C₈×C₂₉	—	2	1	no	—
148	C₂×C₈×C₂₉	—	2	2	no	—
149	C₂×C₈×C₂₉	—	2	2	no	—
150	C₂×C₈×C₂₉	—	4	2	no	—
151	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
155	C₄⋊C₄×C₂₉	—	2	1	no	—
156	C₄⋊C₄×C₂₉	—	2	1	no	—
157	C₄⋊C₄×C₂₉	—	2	1	no	—
158	C₄⋊C₄×C₂₉	—	2	1	no	—
159	C₄⋊C₄×C₂₉	—	2	2	no	—
160	C₄⋊C₄×C₂₉	—	2	2	no	—
161	C₄⋊C₄×C₂₉	—	4	1	no	—
162	C₄⋊C₄×C₂₉	—	4	1	no	—
163	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
164	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
165	C₂²⋊C₄×C₂₉	—	2	1	no	—
166	C₂²⋊C₄×C₂₉	—	2	1	no	—
167	C₂²⋊C₄×C₂₉	—	2	1	no	—
168	C₂²⋊C₄×C₂₉	—	2	1	no	—
169	C₂²⋊C₄×C₂₉	—	2	1	no	—
170	C₄²×C₂₉	—	2	1	no	—
171	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₂₉	#41	1	1	yes	characteristic
174	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
175	#19352	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂³×C₂₉	—	2	1	no	—
177	C₂³×C₂₉	—	4	2	no	—
178	C₂³×C₂₉	—	8	2	no	—
179	C₂³×C₂₉	—	8	2	no	—
180	C₂³×C₂₉	—	8	2	no	—
181	C₂³×C₂₉	#121	1	1	yes	characteristic
182	Q₈×C₂₉	—	2	2	no	—
183	Q₈×C₂₉	—	4	2	no	—
184	Q₈×C₂₉	—	4	2	no	—
185	Q₈×C₂₉	—	8	2	no	—
186	D₄×C₂₉	—	2	2	no	—
187	D₄×C₂₉	—	4	2	no	—
188	D₄×C₂₉	—	4	2	no	—
189	D₄×C₂₉	—	4	2	no	—
190	D₄×C₂₉	—	4	2	no	—
191	D₄×C₂₉	—	4	2	no	—
192	D₄×C₂₉	—	8	2	no	—
193	D₄×C₂₉	—	8	2	no	—
194	D₄×C₂₉	—	8	2	no	—
195	D₄×C₂₉	—	8	2	no	—
196	C₂×C₄×C₂₉	—	2	2	no	—
197	C₂×C₄×C₂₉	—	2	1	no	—
198	C₂×C₄×C₂₉	—	2	1	no	—
199	C₂×C₄×C₂₉	—	2	2	no	—
200	C₂×C₄×C₂₉	—	2	1	no	—
201	C₂×C₄×C₂₉	—	2	1	no	—
202	C₂×C₄×C₂₉	—	2	1	no	—
203	C₂×C₄×C₂₉	—	4	1	no	—
204	C₂×C₄×C₂₉	—	4	1	no	—
205	C₂×C₄×C₂₉	—	4	2	no	—
206	C₂×C₄×C₂₉	—	8	2	no	—
207	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
208	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
209	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
210	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
213	C₈×C₂₉	—	2	1	no	—
214	C₈×C₂₉	—	2	1	no	—
215	C₈×C₂₉	—	4	1	no	—
216	C₈×C₂₉	—	4	1	no	—
217	C₈×C₂₉	—	4	2	no	—
218	C₈×C₂₉	—	4	2	no	—
219	C₈×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
220	C₈×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
221	#3239	C₂×C₂₉	1	1	yes	characteristic, complemented
222	#3217	C₂×C₂₉	1	1	yes	characteristic
223	C₂×#492	C₂×C₂₉	1	1	yes	characteristic, complemented
224	#2966	C₂×C₂₉	1	1	yes	characteristic, complemented
225	#1686	C₂×C₂₉	1	2	yes	complemented
226	#1685	C₂×C₂₉	1	2	yes	complemented
227	#1666	C₂×C₂₉	1	2	yes	complemented
228	#1665	C₂×C₂₉	1	2	yes	complemented
229	#1568	C₂×C₂₉	1	1	yes	characteristic, complemented
230	#1556	C₂×C₂₉	1	1	yes	characteristic, complemented
231	#1555	C₂×C₂₉	1	1	yes	characteristic, complemented
232	C₂²×C₂₉	—	2	1	no	—
233	C₂²×C₂₉	—	2	1	no	—
234	C₂²×C₂₉	—	4	1	no	—
235	C₂²×C₂₉	—	4	1	no	—
236	C₂²×C₂₉	—	4	1	no	—
237	C₂²×C₂₉	—	8	2	no	—
238	C₂²×C₂₉	—	8	2	no	—
239	C₂²×C₂₉	—	8	2	no	—
240	C₂²×C₂₉	—	16	4	no	—
241	C₂²×C₂₉	#471	1	2	yes	—
242	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
243	C₄×C₂₉	—	2	1	no	—
244	C₄×C₂₉	—	2	1	no	—
245	C₄×C₂₉	—	2	1	no	—
246	C₄×C₂₉	—	2	1	no	—
247	C₄×C₂₉	—	4	1	no	—
248	C₄×C₂₉	—	4	1	no	—
249	C₄×C₂₉	—	4	1	no	—
250	C₄×C₂₉	—	8	2	no	—
251	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
252	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
253	C₄×C₂₉	#577	1	2	yes	—
254	C₂²×SD₁₆	—	2	1	no	—
255	C₂²×SD₁₆	—	2	1	no	—
256	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
257	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
258	#529	C₂²×C₂₉	1	1	yes	characteristic
259	#501	—	2	1	no	—
260	#496	—	2	1	no	—
261	#492	—	2	1	no	—
262	#492	—	2	1	no	—
263	#492	C₂²×C₂₉	1	2	yes	—
264	#492	C₂²×C₂₉	1	2	yes	—
265	#490	—	2	1	no	—
266	#489	—	2	1	no	—
267	#484	—	2	1	no	—
268	#481	—	2	1	no	—
269	#475	C₂²×C₂₉	1	2	yes	complemented
270	#474	C₂²×C₂₉	1	2	yes	complemented
271	#460	C₂²×C₂₉	1	2	yes	—
272	#459	C₂²×C₂₉	1	2	yes	—
273	#450	—	2	1	no	—
274	#447	—	2	1	no	—
275	#446	C₂²×C₂₉	1	1	yes	characteristic, complemented
276	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
277	#436	C₂²×C₂₉	1	1	yes	characteristic, complemented
278	#435	—	2	1	no	—
279	C₈×D₄	—	2	1	no	—
280	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
281	#433	—	2	1	no	—
282	#432	C₂²×C₂₉	1	1	yes	characteristic
283	#432	C₂²×C₂₉	1	1	yes	characteristic
284	#432	C₂²×C₂₉	1	1	yes	characteristic
285	#405	—	2	1	no	—
286	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
287	#335	C₂²×C₂₉	1	2	yes	complemented
288	#334	C₂²×C₂₉	1	2	yes	complemented
289	#332	C₂²×C₂₉	1	2	yes	complemented
290	#332	C₂²×C₂₉	1	2	yes	complemented
291	#331	C₂²×C₂₉	1	2	yes	—
292	#331	C₂²×C₂₉	1	2	yes	—
293	C₂×C₂₉	—	2	2	no	—
294	C₂×C₂₉	—	8	1	no	—
295	C₂×C₂₉	—	16	2	no	—
296	C₂×C₂₉	#3038	1	1	yes	characteristic
297	C₂×C₂₉	#3057	1	1	yes	characteristic
298	C₂×C₂₉	C₂×#471	1	1	yes	characteristic
299	C₂²×Q₈	—	2	1	no	—
300	C₂²×D₄	—	2	1	no	—
301	C₂²×D₄	—	2	1	no	—
302	C₂²×D₄	—	2	1	no	—
303	C₂×SD₁₆	—	2	2	no	—
304	C₂×SD₁₆	—	2	2	no	—
305	C₂×SD₁₆	—	2	2	no	—
306	C₂×SD₁₆	—	2	2	no	—
307	C₂×SD₁₆	—	2	2	no	—
308	C₂×SD₁₆	—	4	4	no	—
309	C₂×SD₁₆	—	4	4	no	—
310	C₂×D₈	—	2	2	no	—
311	C₂×M₁₆	—	2	1	no	—
312	C₂²×C₈	—	2	1	no	—
313	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
314	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
315	C₄⋊Q₈	—	2	1	no	—
316	C₄⋊Q₈	—	2	1	no	—
317	C₄⋊Q₈	—	2	1	no	—
318	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
319	#127	—	2	1	no	—
320	#127	—	2	1	no	—
321	#127	—	2	1	no	—
322	#127	C₂³×C₂₉	1	2	yes	—
323	#126	—	2	1	no	—
324	#125	D₄×C₂₉	1	1	yes	characteristic
325	#124	D₄×C₂₉	1	1	yes	characteristic
326	#123	—	2	1	no	—
327	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
328	#121	D₄×C₂₉	1	1	yes	characteristic
329	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
330	C₄×D₄	—	2	1	no	—
331	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
332	#117	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
336	#107	—	2	2	no	—
337	#106	—	2	2	no	—
338	C₄⋊C₈	—	2	1	no	—
339	C₄⋊C₈	—	2	1	no	—
340	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
341	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
342	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
343	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
344	#103	—	2	2	no	—
345	#102	—	2	2	no	—
346	#102	—	2	2	no	—
347	#102	—	2	2	no	—
348	C₂²⋊C₈	—	2	1	no	—
349	C₂²⋊C₈	—	2	1	no	—
350	C₂²⋊C₈	—	2	1	no	—
351	C₂²⋊C₈	—	2	1	no	—
352	C₂²⋊C₈	—	2	1	no	—
353	#97	—	2	1	no	—
354	#97	—	2	1	no	—
355	#97	—	2	1	no	—
356	#97	—	2	1	no	—
357	C₄×C₈	—	2	1	no	—
358	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
359	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
360	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
361	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
362	C₂₉	#19352	1	1	yes	characteristic, direct product factor, Sylow
363	C₂⁴	—	4	1	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	4	2	no	—
366	C₂×Q₈	—	4	2	no	—
367	C₂×Q₈	—	4	1	no	—
368	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	4	2	no	—
374	C₂×D₄	—	4	2	no	—
375	C₂×D₄	—	4	1	no	—
376	C₂×D₄	—	4	1	no	—
377	C₂×D₄	—	4	1	no	—
378	C₂×D₄	—	8	2	no	—
379	C₂×D₄	—	8	2	no	—
380	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
385	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
386	SD₁₆	—	4	4	no	—
387	SD₁₆	—	4	4	no	—
388	SD₁₆	—	4	4	no	—
389	SD₁₆	—	4	4	no	—
390	SD₁₆	—	8	2	no	—
391	D₈	—	8	2	no	—
392	M₁₆	—	4	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	4	2	no	—
400	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
401	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
402	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
403	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	4	1	no	—
411	C₄⋊C₄	—	4	1	no	—
412	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
413	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
421	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
422	C₄²	#41×C₂₉	1	1	yes	characteristic
423	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
424	C₂³	—	2	1	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	8	2	no	—
427	C₂³	—	8	2	no	—
428	C₂³	—	8	2	no	—
429	C₂³	C₂₉×#121	1	1	yes	characteristic
430	Q₈	—	2	2	no	—
431	Q₈	—	4	2	no	—
432	Q₈	—	4	2	no	—
433	Q₈	—	8	2	no	—
434	D₄	—	2	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	2	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	2	no	—
439	D₄	—	4	2	no	—
440	D₄	—	8	2	no	—
441	D₄	—	8	2	no	—
442	D₄	—	8	2	no	—
443	D₄	—	8	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	8	2	no	—
455	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
456	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
457	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
458	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
460	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
461	C₈	—	2	1	no	—
462	C₈	—	2	1	no	—
463	C₈	—	4	1	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	2	no	—
466	C₈	—	4	2	no	—
467	C₈	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
468	C₈	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	16	4	no	—
478	C₂²	C₂₉×#471	1	2	yes	—
479	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	8	2	no	—
488	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
489	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
490	C₄	C₂₉×#577	1	2	yes	—
491	C₂	—	2	2	no	—
492	C₂	—	8	1	no	—
493	C₂	—	16	2	no	—
494	C₂	C₂₉×#3038	1	1	yes	characteristic
495	C₂	C₂₉×#3057	1	1	yes	characteristic
496	C₂	C₂×C₂₉×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#3217	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3239	C₂	semidirect
3. C₂×C₂₉×#492	C₂	semidirect
4. C₂₉×#2966	C₂	semidirect
5. C₂₉×#1686	C₂	semidirect
6. C₂₉×#1685	C₂	semidirect
7. C₂₉×#1666	C₂	semidirect
8. C₂₉×#1665	C₂	semidirect
9. C₂₉×#1568	C₂	semidirect
10. C₂₉×#1556	C₂	semidirect
11. C₂₉×#1555	C₂	semidirect
27. C₂₉×#475	C₂²	semidirect
28. C₂₉×#474	C₂²	semidirect
33. C₂₉×#446	C₂²	semidirect
34. C₈×Q₈×C₂₉	C₂²	semidirect
35. C₂₉×#436	C₂²	semidirect
38. C₈×D₄×C₂₉	C₂²	semidirect
45. C₂₉×#335	C₂²	semidirect
46. C₂₉×#334	C₂²	semidirect
47. C₂₉×#332	C₂²	semidirect
48. C₂₉×#332	C₂²	semidirect
175. #19352	C₂₉	direct (N × H)
221. #3239	C₂×C₂₉	semidirect
223. C₂×#492	C₂×C₂₉	semidirect
224. #2966	C₂×C₂₉	semidirect
225. #1686	C₂×C₂₉	semidirect
226. #1685	C₂×C₂₉	semidirect
227. #1666	C₂×C₂₉	semidirect
228. #1665	C₂×C₂₉	semidirect
229. #1568	C₂×C₂₉	semidirect
230. #1556	C₂×C₂₉	semidirect
231. #1555	C₂×C₂₉	semidirect
269. #475	C₂²×C₂₉	semidirect
270. #474	C₂²×C₂₉	semidirect
275. #446	C₂²×C₂₉	semidirect
276. C₈×Q₈	C₂²×C₂₉	semidirect
277. #436	C₂²×C₂₉	semidirect
280. C₈×D₄	C₂²×C₂₉	semidirect
287. #335	C₂²×C₂₉	semidirect
288. #334	C₂²×C₂₉	semidirect
289. #332	C₂²×C₂₉	semidirect
290. #332	C₂²×C₂₉	semidirect
362. C₂₉	#19352	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#3239	2
C₂₉×#3217	2
C₂×C₂₉×#492	2
C₂₉×#2966	2
C₂₉×#1686	2
C₂₉×#1685	2
C₂₉×#1666	2
C₂₉×#1665	2
C₂₉×#1568	2
C₂₉×#1556	2
C₂₉×#1555	2
#19352	29

Subgroups — C29×#19352 #20314252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19352 #20314252