Subgroups — C₂₉×#19483 #20314383

Order 7424.

688 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3208	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3107	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3038	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1702	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1686	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1681	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1665	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1574	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1561	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1545	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₉×AGL(1,ℤ/8)	—	2	1	no	—
13	C₂₉×#533	C₂²	1	1	yes	characteristic
14	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
15	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
16	C₂₉×#492	C₂²	1	2	yes	—
17	C₂₉×#486	C₂²	1	2	yes	—
18	C₂₉×#485	—	2	1	no	—
19	C₂₉×#475	C₂²	1	1	yes	characteristic, complemented
20	C₂₉×#474	C₂²	1	1	yes	characteristic, complemented
21	C₂₉×#462	C₂²	1	1	yes	characteristic, complemented
22	C₂₉×#461	C₂²	1	1	yes	characteristic, complemented
23	C₂₉×#460	—	2	1	no	—
24	C₂₉×#460	—	2	1	no	—
25	C₂₉×#460	—	2	1	no	—
26	C₂₉×#460	C₂²	1	2	yes	—
27	C₂₉×#459	—	2	1	no	—
28	C₂₉×#459	C₂²	1	2	yes	—
29	C₂₉×#452	—	2	1	no	—
30	C₂₉×#450	—	2	2	no	—
31	C₂₉×#446	C₂²	1	2	yes	complemented
32	C₄×Q₁₆×C₂₉	—	2	1	no	—
33	C₄×SD₁₆×C₂₉	—	2	1	no	—
34	C₂₉×#435	—	2	2	no	—
35	C₈×D₄×C₂₉	C₂²	1	2	yes	complemented
36	C₂₉×#432	—	2	1	no	—
37	C₂₉×#431	C₂²	1	1	yes	characteristic
38	C₂₉×#431	C₂²	1	1	yes	characteristic
39	C₂₉×#423	C₂²	1	1	yes	characteristic
40	C₂₉×#423	C₂²	1	1	yes	characteristic
41	C₂×C₂₉×C₄⋊C₈	—	2	1	no	—
42	C₂₉×#418	—	2	1	no	—
43	C₂₉×#335	C₂²	1	2	yes	complemented
44	C₂₉×#334	C₂²	1	2	yes	complemented
45	C₂₉×#332	C₂²	1	2	yes	complemented
46	C₂₉×#332	C₂²	1	2	yes	complemented
47	C₂₉×#331	C₂²	1	2	yes	—
48	C₂₉×#331	C₂²	1	2	yes	—
49	C₂×#41×C₂₉	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₂₉	—	2	1	no	—
51	C₂²×D₄×C₂₉	—	2	1	no	—
52	C₂²×D₄×C₂₉	—	2	1	no	—
53	C₂₉×AGL(1,ℤ/8)	—	4	4	no	—
54	C₂×Q₁₆×C₂₉	—	2	1	no	—
55	C₂×SD₁₆×C₂₉	—	2	2	no	—
56	C₂×SD₁₆×C₂₉	—	2	1	no	—
57	C₂×SD₁₆×C₂₉	—	2	2	no	—
58	C₂×SD₁₆×C₂₉	—	2	2	no	—
59	C₂×D₈×C₂₉	—	2	2	no	—
60	C₂×M₁₆×C₂₉	—	2	1	no	—
61	C₂×M₁₆×C₂₉	—	2	1	no	—
62	C₂²×C₈×C₂₉	—	2	2	no	—
63	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₂₉×#127	—	2	1	no	—
66	C₂₉×#127	—	2	1	no	—
67	C₂₉×#127	—	2	1	no	—
68	C₂₉×#127	C₂³	1	2	yes	—
69	C₂₉×#125	—	2	1	no	—
70	C₂₉×C₂²⋊Q₈	—	2	1	no	—
71	C₂₉×C₂²⋊Q₈	—	2	1	no	—
72	C₄×Q₈×C₂₉	—	2	1	no	—
73	C₄×Q₈×C₂₉	—	2	1	no	—
74	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
75	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
76	C₄×D₄×C₂₉	—	2	1	no	—
77	C₄×D₄×C₂₉	—	2	1	no	—
78	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
79	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
80	C₂₉×#117	—	2	1	no	—
81	C₂₉×#117	—	2	1	no	—
82	C₂₉×#117	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₂₉	—	2	1	no	—
84	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
85	C₂₉×#107	—	2	1	no	—
86	C₂₉×#106	—	2	1	no	—
87	C₂₉×C₄⋊C₈	—	2	2	no	—
88	C₂₉×C₄⋊C₈	—	2	1	no	—
89	C₂₉×C₄⋊C₈	—	2	1	no	—
90	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
91	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
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	1	no	—
97	C₂₉×#103	—	2	1	no	—
98	C₂₉×#103	—	2	1	no	—
99	C₂₉×#102	—	2	1	no	—
100	C₂₉×#102	—	2	2	no	—
101	C₂₉×#102	—	2	2	no	—
102	C₂₉×#102	—	2	2	no	—
103	C₂₉×#102	—	2	2	no	—
104	C₂₉×C₂²⋊C₈	—	2	1	no	—
105	C₂₉×C₂²⋊C₈	—	2	2	no	—
106	C₂₉×C₂²⋊C₈	D₄	1	2	yes	—
107	C₂₉×#97	—	2	2	no	—
108	C₄×C₈×C₂₉	—	2	1	no	—
109	C₄×C₈×C₂₉	C₂³	1	2	yes	—
110	C₂⁴×C₂₉	—	4	1	no	—
111	#41×C₂₉	—	2	2	no	—
112	#41×C₂₉	—	4	1	no	—
113	C₂×Q₈×C₂₉	—	2	1	no	—
114	C₂×Q₈×C₂₉	—	2	1	no	—
115	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
116	C₂×D₄×C₂₉	—	2	1	no	—
117	C₂×D₄×C₂₉	—	2	2	no	—
118	C₂×D₄×C₂₉	—	2	2	no	—
119	C₂×D₄×C₂₉	—	2	2	no	—
120	C₂×D₄×C₂₉	—	4	2	no	—
121	C₂×D₄×C₂₉	—	4	2	no	—
122	C₂×D₄×C₂₉	—	4	1	no	—
123	C₂×D₄×C₂₉	—	4	1	no	—
124	C₂×D₄×C₂₉	—	4	1	no	—
125	C₂×D₄×C₂₉	—	8	1	no	—
126	C₂×D₄×C₂₉	—	8	1	no	—
127	C₂×D₄×C₂₉	—	8	2	no	—
128	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₂₉	—	2	1	no	—
130	C₂²×C₄×C₂₉	—	2	1	no	—
131	C₂²×C₄×C₂₉	—	2	1	no	—
132	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
135	Q₁₆×C₂₉	—	4	2	no	—
136	SD₁₆×C₂₉	—	4	4	no	—
137	SD₁₆×C₂₉	—	4	2	no	—
138	SD₁₆×C₂₉	—	8	2	no	—
139	SD₁₆×C₂₉	—	8	2	no	—
140	D₈×C₂₉	—	4	4	no	—
141	M₁₆×C₂₉	—	4	2	no	—
142	M₁₆×C₂₉	—	8	1	no	—
143	C₂×C₈×C₂₉	—	2	2	no	—
144	C₂×C₈×C₂₉	—	2	2	no	—
145	C₂×C₈×C₂₉	—	2	1	no	—
146	C₂×C₈×C₂₉	—	2	1	no	—
147	C₂×C₈×C₂₉	—	8	2	no	—
148	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
150	C₄⋊C₄×C₂₉	—	2	1	no	—
151	C₄⋊C₄×C₂₉	—	2	1	no	—
152	C₄⋊C₄×C₂₉	—	2	1	no	—
153	C₄⋊C₄×C₂₉	—	2	1	no	—
154	C₄⋊C₄×C₂₉	—	2	1	no	—
155	C₄⋊C₄×C₂₉	—	2	1	no	—
156	C₄⋊C₄×C₂₉	—	4	1	no	—
157	C₄⋊C₄×C₂₉	—	4	1	no	—
158	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
159	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
160	C₂²⋊C₄×C₂₉	—	2	1	no	—
161	C₂²⋊C₄×C₂₉	—	2	1	no	—
162	C₂²⋊C₄×C₂₉	—	2	1	no	—
163	C₂²⋊C₄×C₂₉	—	4	1	no	—
164	C₄²×C₂₉	—	2	1	no	—
165	C₄²×C₂₉	—	2	1	no	—
166	C₄²×C₂₉	—	2	1	no	—
167	C₄²×C₂₉	—	4	1	no	—
168	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₂₉	#41	1	1	yes	characteristic
171	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
172	#19483	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂³×C₂₉	—	2	1	no	—
174	C₂³×C₂₉	—	4	2	no	—
175	C₂³×C₂₉	—	8	2	no	—
176	C₂³×C₂₉	—	8	2	no	—
177	C₂³×C₂₉	—	8	2	no	—
178	C₂³×C₂₉	#121	1	1	yes	characteristic
179	Q₈×C₂₉	—	2	1	no	—
180	Q₈×C₂₉	—	2	1	no	—
181	Q₈×C₂₉	—	4	1	no	—
182	Q₈×C₂₉	—	4	1	no	—
183	Q₈×C₂₉	—	4	1	no	—
184	Q₈×C₂₉	—	4	1	no	—
185	D₄×C₂₉	—	2	1	no	—
186	D₄×C₂₉	—	4	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	—	8	2	no	—
192	D₄×C₂₉	—	8	2	no	—
193	D₄×C₂₉	—	8	2	no	—
194	D₄×C₂₉	—	8	2	no	—
195	D₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
196	C₂×C₄×C₂₉	—	2	1	no	—
197	C₂×C₄×C₂₉	—	2	1	no	—
198	C₂×C₄×C₂₉	—	2	1	no	—
199	C₂×C₄×C₂₉	—	2	1	no	—
200	C₂×C₄×C₂₉	—	2	2	no	—
201	C₂×C₄×C₂₉	—	2	1	no	—
202	C₂×C₄×C₂₉	—	2	1	no	—
203	C₂×C₄×C₂₉	—	2	1	no	—
204	C₂×C₄×C₂₉	—	4	2	no	—
205	C₂×C₄×C₂₉	—	4	1	no	—
206	C₂×C₄×C₂₉	—	4	1	no	—
207	C₂×C₄×C₂₉	—	4	2	no	—
208	C₂×C₄×C₂₉	—	4	1	no	—
209	C₂×C₄×C₂₉	—	4	1	no	—
210	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
211	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
212	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
213	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
216	C₈×C₂₉	—	2	2	no	—
217	C₈×C₂₉	—	2	2	no	—
218	C₈×C₂₉	—	4	2	no	—
219	C₈×C₂₉	—	4	1	no	—
220	C₈×C₂₉	—	4	1	no	—
221	C₈×C₂₉	—	4	2	no	—
222	#3208	C₂×C₂₉	1	1	yes	characteristic, complemented
223	#3107	C₂×C₂₉	1	1	yes	characteristic, complemented
224	#3038	C₂×C₂₉	1	1	yes	characteristic
225	#2990	C₂×C₂₉	1	1	yes	characteristic, complemented
226	#1702	C₂×C₂₉	1	2	yes	complemented
227	#1686	C₂×C₂₉	1	2	yes	complemented
228	#1681	C₂×C₂₉	1	2	yes	complemented
229	#1665	C₂×C₂₉	1	2	yes	complemented
230	#1574	C₂×C₂₉	1	1	yes	characteristic, complemented
231	#1561	C₂×C₂₉	1	1	yes	characteristic, complemented
232	#1545	C₂×C₂₉	1	1	yes	characteristic, complemented
233	C₂²×C₂₉	—	2	1	no	—
234	C₂²×C₂₉	—	2	1	no	—
235	C₂²×C₂₉	—	2	2	no	—
236	C₂²×C₂₉	—	2	1	no	—
237	C₂²×C₂₉	—	4	1	no	—
238	C₂²×C₂₉	—	4	1	no	—
239	C₂²×C₂₉	—	8	2	no	—
240	C₂²×C₂₉	—	8	2	no	—
241	C₂²×C₂₉	—	8	2	no	—
242	C₂²×C₂₉	—	16	4	no	—
243	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
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	1	no	—
251	C₄×C₂₉	—	8	1	no	—
252	C₄×C₂₉	#471	1	2	yes	—
253	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
254	C₄×C₂₉	#575	1	1	yes	characteristic
255	C₄×C₂₉	#576	1	1	yes	characteristic
256	C₄×C₂₉	#577	1	1	yes	characteristic
257	C₂×AGL(1,ℤ/8)	—	2	1	no	—
258	#533	C₂²×C₂₉	1	1	yes	characteristic
259	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
260	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
261	#492	C₂²×C₂₉	1	2	yes	—
262	#486	C₂²×C₂₉	1	2	yes	—
263	#485	—	2	1	no	—
264	#475	C₂²×C₂₉	1	1	yes	characteristic, complemented
265	#474	C₂²×C₂₉	1	1	yes	characteristic, complemented
266	#462	C₂²×C₂₉	1	1	yes	characteristic, complemented
267	#461	C₂²×C₂₉	1	1	yes	characteristic, complemented
268	#460	—	2	1	no	—
269	#460	—	2	1	no	—
270	#460	—	2	1	no	—
271	#460	C₂²×C₂₉	1	2	yes	—
272	#459	—	2	1	no	—
273	#459	C₂²×C₂₉	1	2	yes	—
274	#452	—	2	1	no	—
275	#450	—	2	2	no	—
276	#446	C₂²×C₂₉	1	2	yes	complemented
277	C₄×Q₁₆	—	2	1	no	—
278	C₄×SD₁₆	—	2	1	no	—
279	#435	—	2	2	no	—
280	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
281	#432	—	2	1	no	—
282	#431	C₂²×C₂₉	1	1	yes	characteristic
283	#431	C₂²×C₂₉	1	1	yes	characteristic
284	#423	C₂²×C₂₉	1	1	yes	characteristic
285	#423	C₂²×C₂₉	1	1	yes	characteristic
286	C₂×C₄⋊C₈	—	2	1	no	—
287	#418	—	2	1	no	—
288	#335	C₂²×C₂₉	1	2	yes	complemented
289	#334	C₂²×C₂₉	1	2	yes	complemented
290	#332	C₂²×C₂₉	1	2	yes	complemented
291	#332	C₂²×C₂₉	1	2	yes	complemented
292	#331	C₂²×C₂₉	1	2	yes	—
293	#331	C₂²×C₂₉	1	2	yes	—
294	C₂×C₂₉	—	4	1	no	—
295	C₂×C₂₉	—	4	2	no	—
296	C₂×C₂₉	—	16	2	no	—
297	C₂×C₂₉	#3045	1	1	yes	characteristic
298	C₂×C₂₉	#3055	1	1	yes	characteristic
299	C₂×C₂₉	C₂×#471	1	1	yes	characteristic
300	C₂×#41	D₄×C₂₉	1	1	yes	characteristic
301	C₂²×D₄	—	2	1	no	—
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	—	2	1	no	—
304	AGL(1,ℤ/8)	—	4	4	no	—
305	C₂×Q₁₆	—	2	1	no	—
306	C₂×SD₁₆	—	2	2	no	—
307	C₂×SD₁₆	—	2	1	no	—
308	C₂×SD₁₆	—	2	2	no	—
309	C₂×SD₁₆	—	2	2	no	—
310	C₂×D₈	—	2	2	no	—
311	C₂×M₁₆	—	2	1	no	—
312	C₂×M₁₆	—	2	1	no	—
313	C₂²×C₈	—	2	2	no	—
314	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
315	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
316	#127	—	2	1	no	—
317	#127	—	2	1	no	—
318	#127	—	2	1	no	—
319	#127	C₂³×C₂₉	1	2	yes	—
320	#125	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	C₂²⋊Q₈	—	2	1	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×Q₈	—	2	1	no	—
325	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
326	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
330	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
331	#117	—	2	1	no	—
332	#117	—	2	1	no	—
333	#117	D₄×C₂₉	1	1	yes	characteristic
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
336	#107	—	2	1	no	—
337	#106	—	2	1	no	—
338	C₄⋊C₈	—	2	2	no	—
339	C₄⋊C₈	—	2	1	no	—
340	C₄⋊C₈	—	2	1	no	—
341	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
342	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
343	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
344	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
345	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
346	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
347	#103	—	2	1	no	—
348	#103	—	2	1	no	—
349	#103	—	2	1	no	—
350	#102	—	2	1	no	—
351	#102	—	2	2	no	—
352	#102	—	2	2	no	—
353	#102	—	2	2	no	—
354	#102	—	2	2	no	—
355	C₂²⋊C₈	—	2	1	no	—
356	C₂²⋊C₈	—	2	2	no	—
357	C₂²⋊C₈	D₄×C₂₉	1	2	yes	—
358	#97	—	2	2	no	—
359	C₄×C₈	—	2	1	no	—
360	C₄×C₈	C₂³×C₂₉	1	2	yes	—
361	C₂₉	#19483	1	1	yes	characteristic, direct product factor, Sylow
362	C₂⁴	—	4	1	no	—
363	#41	—	2	2	no	—
364	#41	—	4	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	4	2	no	—
374	C₂×D₄	—	4	1	no	—
375	C₂×D₄	—	4	1	no	—
376	C₂×D₄	—	4	1	no	—
377	C₂×D₄	—	8	1	no	—
378	C₂×D₄	—	8	1	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	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
386	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
387	Q₁₆	—	4	2	no	—
388	SD₁₆	—	4	4	no	—
389	SD₁₆	—	4	2	no	—
390	SD₁₆	—	8	2	no	—
391	SD₁₆	—	8	2	no	—
392	D₈	—	4	4	no	—
393	M₁₆	—	4	2	no	—
394	M₁₆	—	8	1	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	—	8	2	no	—
400	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
401	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
409	C₄⋊C₄	—	4	1	no	—
410	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
411	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	4	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	4	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	1	no	—
431	Q₈	—	2	1	no	—
432	Q₈	—	4	1	no	—
433	Q₈	—	4	1	no	—
434	Q₈	—	4	1	no	—
435	Q₈	—	4	1	no	—
436	D₄	—	2	1	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	2	no	—
439	D₄	—	4	2	no	—
440	D₄	—	4	2	no	—
441	D₄	—	4	2	no	—
442	D₄	—	8	2	no	—
443	D₄	—	8	2	no	—
444	D₄	—	8	2	no	—
445	D₄	—	8	2	no	—
446	D₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
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	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
462	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
463	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
466	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	—	4	2	no	—
470	C₈	—	4	1	no	—
471	C₈	—	4	1	no	—
472	C₈	—	4	2	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	4	1	no	—
478	C₂²	—	4	1	no	—
479	C₂²	—	8	2	no	—
480	C₂²	—	8	2	no	—
481	C₂²	—	8	2	no	—
482	C₂²	—	16	4	no	—
483	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	4	1	no	—
488	C₄	—	4	1	no	—
489	C₄	—	4	1	no	—
490	C₄	—	8	1	no	—
491	C₄	—	8	1	no	—
492	C₄	C₂₉×#471	1	2	yes	—
493	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
494	C₄	C₂₉×#575	1	1	yes	characteristic
495	C₄	C₂₉×#576	1	1	yes	characteristic
496	C₄	C₂₉×#577	1	1	yes	characteristic
497	C₂	—	4	1	no	—
498	C₂	—	4	2	no	—
499	C₂	—	16	2	no	—
500	C₂	C₂₉×#3045	1	1	yes	characteristic
501	C₂	C₂₉×#3055	1	1	yes	characteristic
502	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×#3038	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×#3208	C₂	semidirect
2. C₂₉×#3107	C₂	semidirect
4. C₂₉×#2990	C₂	semidirect
5. C₂₉×#1702	C₂	semidirect
6. C₂₉×#1686	C₂	semidirect
7. C₂₉×#1681	C₂	semidirect
8. C₂₉×#1665	C₂	semidirect
9. C₂₉×#1574	C₂	semidirect
10. C₂₉×#1561	C₂	semidirect
11. C₂₉×#1545	C₂	semidirect
19. C₂₉×#475	C₂²	semidirect
20. C₂₉×#474	C₂²	semidirect
21. C₂₉×#462	C₂²	semidirect
22. C₂₉×#461	C₂²	semidirect
31. C₂₉×#446	C₂²	semidirect
35. C₈×D₄×C₂₉	C₂²	semidirect
43. C₂₉×#335	C₂²	semidirect
44. C₂₉×#334	C₂²	semidirect
45. C₂₉×#332	C₂²	semidirect
46. C₂₉×#332	C₂²	semidirect
172. #19483	C₂₉	direct (N × H)
222. #3208	C₂×C₂₉	semidirect
223. #3107	C₂×C₂₉	semidirect
225. #2990	C₂×C₂₉	semidirect
226. #1702	C₂×C₂₉	semidirect
227. #1686	C₂×C₂₉	semidirect
228. #1681	C₂×C₂₉	semidirect
229. #1665	C₂×C₂₉	semidirect
230. #1574	C₂×C₂₉	semidirect
231. #1561	C₂×C₂₉	semidirect
232. #1545	C₂×C₂₉	semidirect
264. #475	C₂²×C₂₉	semidirect
265. #474	C₂²×C₂₉	semidirect
266. #462	C₂²×C₂₉	semidirect
267. #461	C₂²×C₂₉	semidirect
276. #446	C₂²×C₂₉	semidirect
280. C₈×D₄	C₂²×C₂₉	semidirect
288. #335	C₂²×C₂₉	semidirect
289. #334	C₂²×C₂₉	semidirect
290. #332	C₂²×C₂₉	semidirect
291. #332	C₂²×C₂₉	semidirect
361. C₂₉	#19483	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×#3208	2
C₂₉×#3107	2
C₂₉×#3038	2
C₂₉×#2990	2
C₂₉×#1702	2
C₂₉×#1686	2
C₂₉×#1681	2
C₂₉×#1665	2
C₂₉×#1574	2
C₂₉×#1561	2
C₂₉×#1545	2
#19483	29

Subgroups — C29×#19483 #20314383

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19483 #20314383