Subgroups — C₂₉×#19456 #20314356

Order 7424.

722 conjugacy classes of subgroups.

The subgroup lattice has 514 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×#3110	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×#459	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2974	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1701	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1685	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×#1573	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1555	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1552	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₂₉	—	2	1	no	—
13	C₂₉×#533	C₂²	1	1	yes	characteristic
14	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
16	C₂₉×#492	C₂²	1	2	yes	complemented
17	C₂₉×#486	C₂²	1	2	yes	complemented
18	C₂₉×#484	—	2	1	no	—
19	C₂₉×#474	C₂²	1	1	yes	characteristic, complemented
20	C₂₉×#474	C₂²	1	1	yes	characteristic, complemented
21	C₂₉×#461	C₂²	1	1	yes	characteristic, complemented
22	C₂₉×#461	C₂²	1	1	yes	characteristic, complemented
23	C₂₉×#460	—	2	2	no	—
24	C₂₉×#459	—	2	1	no	—
25	C₂₉×#459	—	2	1	no	—
26	C₂₉×#459	C₂²	1	2	yes	—
27	C₂₉×#459	C₂²	1	2	yes	—
28	C₂₉×#450	—	2	1	no	—
29	C₂₉×#450	—	2	1	no	—
30	C₂₉×#450	—	2	1	no	—
31	C₂₉×#440	—	2	1	no	—
32	C₂₉×#440	—	2	1	no	—
33	C₂₉×#436	C₂²	1	2	yes	complemented
34	C₂₉×#435	—	2	2	no	—
35	C₈×D₄×C₂₉	C₂²	1	2	yes	complemented
36	C₂₉×#432	C₂²	1	1	yes	characteristic
37	C₂₉×#432	C₂²	1	1	yes	characteristic
38	C₂₉×#431	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×#102	—	2	1	no	—
41	C₂₉×#407	—	2	1	no	—
42	C₂×C₂₉×C₂²⋊C₈	—	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	complemented
48	C₂₉×#331	C₂²	1	2	yes	complemented
49	C₂²×D₄×C₂₉	—	2	1	no	—
50	C₂²×D₄×C₂₉	—	2	1	no	—
51	C₂²×D₄×C₂₉	—	2	1	no	—
52	C₂²×D₄×C₂₉	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₂₉	—	2	1	no	—
54	C₂×SD₁₆×C₂₉	—	2	1	no	—
55	C₂×SD₁₆×C₂₉	—	2	1	no	—
56	C₂×SD₁₆×C₂₉	—	2	2	no	—
57	C₂×SD₁₆×C₂₉	—	2	2	no	—
58	C₂×D₈×C₂₉	—	2	2	no	—
59	C₂×D₈×C₂₉	—	2	2	no	—
60	C₂×D₈×C₂₉	—	4	4	no	—
61	C₂×M₁₆×C₂₉	—	2	2	no	—
62	C₂²×C₈×C₂₉	—	2	1	no	—
63	C₂²×C₈×C₂₉	—	2	2	no	—
64	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₂₉×#127	—	2	1	no	—
67	C₂₉×#127	—	2	1	no	—
68	C₂₉×#127	—	2	1	no	—
69	C₂₉×#127	C₂³	1	2	yes	—
70	C₂₉×#125	—	2	1	no	—
71	C₂₉×C₂²⋊Q₈	—	2	1	no	—
72	C₂₉×C₂²⋊Q₈	—	2	1	no	—
73	C₄×Q₈×C₂₉	—	2	1	no	—
74	C₄×Q₈×C₂₉	—	2	1	no	—
75	C₄×D₄×C₂₉	—	2	1	no	—
76	C₄×D₄×C₂₉	—	2	1	no	—
77	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
78	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
79	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
80	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
81	C₂₉×#117	—	2	1	no	—
82	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
84	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
85	C₂₉×#107	—	2	1	no	—
86	C₂₉×#107	—	2	1	no	—
87	C₂₉×C₄⋊C₈	—	2	1	no	—
88	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
89	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
90	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
91	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
92	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
93	C₂₉×#103	—	2	1	no	—
94	C₂₉×#103	—	2	1	no	—
95	C₂₉×#102	—	2	1	no	—
96	C₂₉×#102	—	2	1	no	—
97	C₂₉×#102	—	2	2	no	—
98	C₂₉×#102	—	2	2	no	—
99	C₂₉×#102	—	2	2	no	—
100	C₂₉×#102	—	2	2	no	—
101	C₂₉×C₂²⋊C₈	—	2	1	no	—
102	C₂₉×C₂²⋊C₈	—	2	1	no	—
103	C₂₉×C₂²⋊C₈	—	2	2	no	—
104	C₂₉×C₂²⋊C₈	—	2	2	no	—
105	C₂₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
106	C₂₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
107	C₂₉×#97	—	2	1	no	—
108	C₂₉×#97	—	2	1	no	—
109	C₄×C₈×C₂₉	C₂³	1	2	yes	—
110	C₂⁴×C₂₉	—	2	1	no	—
111	C₂⁴×C₂₉	—	4	1	no	—
112	C₂×Q₈×C₂₉	—	2	1	no	—
113	C₂×Q₈×C₂₉	—	2	1	no	—
114	C₂×D₄×C₂₉	—	2	2	no	—
115	C₂×D₄×C₂₉	—	2	1	no	—
116	C₂×D₄×C₂₉	—	2	2	no	—
117	C₂×D₄×C₂₉	—	2	2	no	—
118	C₂×D₄×C₂₉	—	2	2	no	—
119	C₂×D₄×C₂₉	—	4	1	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	2	no	—
126	C₂×D₄×C₂₉	—	8	2	no	—
127	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
133	C₂²×C₄×C₂₉	—	2	1	no	—
134	C₂²×C₄×C₂₉	—	8	2	no	—
135	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
138	SD₁₆×C₂₉	—	4	2	no	—
139	SD₁₆×C₂₉	—	4	2	no	—
140	SD₁₆×C₂₉	—	8	2	no	—
141	SD₁₆×C₂₉	—	8	2	no	—
142	D₈×C₂₉	—	4	4	no	—
143	D₈×C₂₉	—	4	4	no	—
144	M₁₆×C₂₉	—	8	2	no	—
145	C₂×C₈×C₂₉	—	2	2	no	—
146	C₂×C₈×C₂₉	—	2	2	no	—
147	C₂×C₈×C₂₉	—	2	1	no	—
148	C₂×C₈×C₂₉	—	2	1	no	—
149	C₂×C₈×C₂₉	—	4	2	no	—
150	C₂×C₈×C₂₉	—	8	2	no	—
151	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
157	C₄⋊C₄×C₂₉	—	2	1	no	—
158	C₄⋊C₄×C₂₉	—	4	1	no	—
159	C₄⋊C₄×C₂₉	—	4	1	no	—
160	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
161	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
162	C₂²⋊C₄×C₂₉	—	2	1	no	—
163	C₂²⋊C₄×C₂₉	—	2	1	no	—
164	C₂²⋊C₄×C₂₉	—	2	1	no	—
165	C₂²⋊C₄×C₂₉	—	2	1	no	—
166	C₂²⋊C₄×C₂₉	—	4	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	#19456	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂³×C₂₉	—	2	1	no	—
174	C₂³×C₂₉	—	2	1	no	—
175	C₂³×C₂₉	—	4	2	no	—
176	C₂³×C₂₉	—	4	2	no	—
177	C₂³×C₂₉	—	4	2	no	—
178	C₂³×C₂₉	—	8	1	no	—
179	C₂³×C₂₉	—	8	2	no	—
180	C₂³×C₂₉	—	8	2	no	—
181	C₂³×C₂₉	—	8	2	no	—
182	C₂³×C₂₉	#121	1	1	yes	characteristic
183	Q₈×C₂₉	—	4	1	no	—
184	Q₈×C₂₉	—	4	1	no	—
185	Q₈×C₂₉	—	4	2	no	—
186	D₄×C₂₉	—	2	1	no	—
187	D₄×C₂₉	—	2	1	no	—
188	D₄×C₂₉	—	2	1	no	—
189	D₄×C₂₉	—	4	2	no	—
190	D₄×C₂₉	—	4	2	no	—
191	D₄×C₂₉	—	4	2	no	—
192	D₄×C₂₉	—	4	2	no	—
193	D₄×C₂₉	—	4	2	no	—
194	D₄×C₂₉	—	8	2	no	—
195	D₄×C₂₉	—	8	2	no	—
196	D₄×C₂₉	—	8	2	no	—
197	D₄×C₂₉	—	8	2	no	—
198	D₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
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	2	no	—
203	C₂×C₄×C₂₉	—	2	1	no	—
204	C₂×C₄×C₂₉	—	2	1	no	—
205	C₂×C₄×C₂₉	—	4	2	no	—
206	C₂×C₄×C₂₉	—	4	2	no	—
207	C₂×C₄×C₂₉	—	4	1	no	—
208	C₂×C₄×C₂₉	—	4	1	no	—
209	C₂×C₄×C₂₉	—	8	1	no	—
210	C₂×C₄×C₂₉	—	8	1	no	—
211	C₂×C₄×C₂₉	—	8	1	no	—
212	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
213	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
214	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
215	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
218	C₈×C₂₉	—	2	2	no	—
219	C₈×C₂₉	—	2	2	no	—
220	C₈×C₂₉	—	4	2	no	—
221	C₈×C₂₉	—	4	1	no	—
222	C₈×C₂₉	—	4	1	no	—
223	C₈×C₂₉	—	4	2	no	—
224	#3208	C₂×C₂₉	1	1	yes	characteristic, complemented
225	#3110	C₂×C₂₉	1	1	yes	characteristic, complemented
226	C₂×#459	C₂×C₂₉	1	1	yes	characteristic
227	#2974	C₂×C₂₉	1	1	yes	characteristic, complemented
228	#1701	C₂×C₂₉	1	2	yes	complemented
229	#1685	C₂×C₂₉	1	2	yes	complemented
230	#1681	C₂×C₂₉	1	2	yes	complemented
231	#1665	C₂×C₂₉	1	2	yes	complemented
232	#1573	C₂×C₂₉	1	1	yes	characteristic, complemented
233	#1555	C₂×C₂₉	1	1	yes	characteristic, complemented
234	#1552	C₂×C₂₉	1	1	yes	characteristic, complemented
235	C₂²×C₂₉	—	2	1	no	—
236	C₂²×C₂₉	—	2	1	no	—
237	C₂²×C₂₉	—	2	2	no	—
238	C₂²×C₂₉	—	4	1	no	—
239	C₂²×C₂₉	—	4	1	no	—
240	C₂²×C₂₉	—	4	1	no	—
241	C₂²×C₂₉	—	4	1	no	—
242	C₂²×C₂₉	—	4	1	no	—
243	C₂²×C₂₉	—	8	4	no	—
244	C₂²×C₂₉	—	8	2	no	—
245	C₂²×C₂₉	—	8	2	no	—
246	C₂²×C₂₉	—	8	2	no	—
247	C₂²×C₂₉	—	16	4	no	—
248	C₂²×C₂₉	#471	1	2	yes	—
249	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
250	C₄×C₂₉	—	2	1	no	—
251	C₄×C₂₉	—	2	1	no	—
252	C₄×C₂₉	—	2	1	no	—
253	C₄×C₂₉	—	2	1	no	—
254	C₄×C₂₉	—	4	1	no	—
255	C₄×C₂₉	—	4	1	no	—
256	C₄×C₂₉	—	8	1	no	—
257	C₄×C₂₉	—	8	1	no	—
258	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
259	C₄×C₂₉	#575	1	1	yes	characteristic
260	C₄×C₂₉	#576	1	2	yes	—
261	C₂²×D₈	—	2	1	no	—
262	#533	C₂²×C₂₉	1	1	yes	characteristic
263	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
264	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
265	#492	C₂²×C₂₉	1	2	yes	complemented
266	#486	C₂²×C₂₉	1	2	yes	complemented
267	#484	—	2	1	no	—
268	#474	C₂²×C₂₉	1	1	yes	characteristic, complemented
269	#474	C₂²×C₂₉	1	1	yes	characteristic, complemented
270	#461	C₂²×C₂₉	1	1	yes	characteristic, complemented
271	#461	C₂²×C₂₉	1	1	yes	characteristic, complemented
272	#460	—	2	2	no	—
273	#459	—	2	1	no	—
274	#459	—	2	1	no	—
275	#459	C₂²×C₂₉	1	2	yes	—
276	#459	C₂²×C₂₉	1	2	yes	—
277	#450	—	2	1	no	—
278	#450	—	2	1	no	—
279	#450	—	2	1	no	—
280	#440	—	2	1	no	—
281	#440	—	2	1	no	—
282	#436	C₂²×C₂₉	1	2	yes	complemented
283	#435	—	2	2	no	—
284	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
285	#432	C₂²×C₂₉	1	1	yes	characteristic
286	#432	C₂²×C₂₉	1	1	yes	characteristic
287	#431	C₂²×C₂₉	1	1	yes	characteristic
288	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
289	C₂×#102	—	2	1	no	—
290	#407	—	2	1	no	—
291	C₂×C₂²⋊C₈	—	2	1	no	—
292	#335	C₂²×C₂₉	1	2	yes	complemented
293	#334	C₂²×C₂₉	1	2	yes	complemented
294	#332	C₂²×C₂₉	1	2	yes	complemented
295	#332	C₂²×C₂₉	1	2	yes	complemented
296	#331	C₂²×C₂₉	1	2	yes	complemented
297	#331	C₂²×C₂₉	1	2	yes	complemented
298	C₂×C₂₉	—	2	2	no	—
299	C₂×C₂₉	—	4	2	no	—
300	C₂×C₂₉	—	8	1	no	—
301	C₂×C₂₉	—	16	2	no	—
302	C₂×C₂₉	#3041	1	1	yes	characteristic
303	C₂×C₂₉	#3055	1	1	yes	characteristic
304	C₂×C₂₉	C₂×#471	1	1	yes	characteristic
305	C₂²×D₄	—	2	1	no	—
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	—	2	1	no	—
308	C₂²×D₄	D₄×C₂₉	1	1	yes	characteristic
309	C₂³×C₄	—	2	1	no	—
310	C₂×SD₁₆	—	2	1	no	—
311	C₂×SD₁₆	—	2	1	no	—
312	C₂×SD₁₆	—	2	2	no	—
313	C₂×SD₁₆	—	2	2	no	—
314	C₂×D₈	—	2	2	no	—
315	C₂×D₈	—	2	2	no	—
316	C₂×D₈	—	4	4	no	—
317	C₂×M₁₆	—	2	2	no	—
318	C₂²×C₈	—	2	1	no	—
319	C₂²×C₈	—	2	2	no	—
320	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
321	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
322	#127	—	2	1	no	—
323	#127	—	2	1	no	—
324	#127	—	2	1	no	—
325	#127	C₂³×C₂₉	1	2	yes	—
326	#125	—	2	1	no	—
327	C₂²⋊Q₈	—	2	1	no	—
328	C₂²⋊Q₈	—	2	1	no	—
329	C₄×Q₈	—	2	1	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×D₄	—	2	1	no	—
332	C₄×D₄	—	2	1	no	—
333	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
334	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
335	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
336	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
337	#117	—	2	1	no	—
338	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
341	#107	—	2	1	no	—
342	#107	—	2	1	no	—
343	C₄⋊C₈	—	2	1	no	—
344	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
345	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
346	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
347	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
348	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
349	#103	—	2	1	no	—
350	#103	—	2	1	no	—
351	#102	—	2	1	no	—
352	#102	—	2	1	no	—
353	#102	—	2	2	no	—
354	#102	—	2	2	no	—
355	#102	—	2	2	no	—
356	#102	—	2	2	no	—
357	C₂²⋊C₈	—	2	1	no	—
358	C₂²⋊C₈	—	2	1	no	—
359	C₂²⋊C₈	—	2	2	no	—
360	C₂²⋊C₈	—	2	2	no	—
361	C₂²⋊C₈	D₄×C₂₉	1	1	yes	characteristic
362	C₂²⋊C₈	D₄×C₂₉	1	1	yes	characteristic
363	#97	—	2	1	no	—
364	#97	—	2	1	no	—
365	C₄×C₈	C₂³×C₂₉	1	2	yes	—
366	C₂₉	#19456	1	1	yes	characteristic, direct product factor, Sylow
367	C₂⁴	—	2	1	no	—
368	C₂⁴	—	4	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	4	1	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	—	4	1	no	—
380	C₂×D₄	—	4	1	no	—
381	C₂×D₄	—	4	1	no	—
382	C₂×D₄	—	8	2	no	—
383	C₂×D₄	—	8	2	no	—
384	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
385	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	8	2	no	—
392	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
394	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
395	SD₁₆	—	4	2	no	—
396	SD₁₆	—	4	2	no	—
397	SD₁₆	—	8	2	no	—
398	SD₁₆	—	8	2	no	—
399	D₈	—	4	4	no	—
400	D₈	—	4	4	no	—
401	M₁₆	—	8	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	4	2	no	—
407	C₂×C₈	—	8	2	no	—
408	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
409	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	4	1	no	—
416	C₄⋊C₄	—	4	1	no	—
417	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
418	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	4	1	no	—
424	C₄²	—	4	1	no	—
425	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
426	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
427	C₄²	#41×C₂₉	1	1	yes	characteristic
428	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
429	C₂³	—	2	1	no	—
430	C₂³	—	2	1	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	8	1	no	—
435	C₂³	—	8	2	no	—
436	C₂³	—	8	2	no	—
437	C₂³	—	8	2	no	—
438	C₂³	C₂₉×#121	1	1	yes	characteristic
439	Q₈	—	4	1	no	—
440	Q₈	—	4	1	no	—
441	Q₈	—	4	2	no	—
442	D₄	—	2	1	no	—
443	D₄	—	2	1	no	—
444	D₄	—	2	1	no	—
445	D₄	—	4	2	no	—
446	D₄	—	4	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	4	2	no	—
450	D₄	—	8	2	no	—
451	D₄	—	8	2	no	—
452	D₄	—	8	2	no	—
453	D₄	—	8	2	no	—
454	D₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	8	1	no	—
466	C₂×C₄	—	8	1	no	—
467	C₂×C₄	—	8	1	no	—
468	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
469	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
470	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
471	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
472	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
473	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	2	2	no	—
476	C₈	—	4	2	no	—
477	C₈	—	4	1	no	—
478	C₈	—	4	1	no	—
479	C₈	—	4	2	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	8	4	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	16	4	no	—
493	C₂²	C₂₉×#471	1	2	yes	—
494	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	4	1	no	—
500	C₄	—	4	1	no	—
501	C₄	—	8	1	no	—
502	C₄	—	8	1	no	—
503	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
504	C₄	C₂₉×#575	1	1	yes	characteristic
505	C₄	C₂₉×#576	1	2	yes	—
506	C₂	—	2	2	no	—
507	C₂	—	4	2	no	—
508	C₂	—	8	1	no	—
509	C₂	—	16	2	no	—
510	C₂	C₂₉×#3041	1	1	yes	characteristic
511	C₂	C₂₉×#3055	1	1	yes	characteristic
512	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	C₂×C₂₉×#459	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×#3110	C₂	semidirect
4. C₂₉×#2974	C₂	semidirect
5. C₂₉×#1701	C₂	semidirect
6. C₂₉×#1685	C₂	semidirect
7. C₂₉×#1681	C₂	semidirect
8. C₂₉×#1665	C₂	semidirect
9. C₂₉×#1573	C₂	semidirect
10. C₂₉×#1555	C₂	semidirect
11. C₂₉×#1552	C₂	semidirect
16. C₂₉×#492	C₂²	semidirect
17. C₂₉×#486	C₂²	semidirect
19. C₂₉×#474	C₂²	semidirect
20. C₂₉×#474	C₂²	semidirect
21. C₂₉×#461	C₂²	semidirect
22. C₂₉×#461	C₂²	semidirect
33. C₂₉×#436	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
47. C₂₉×#331	C₂²	semidirect
48. C₂₉×#331	C₂²	semidirect
172. #19456	C₂₉	direct (N × H)
224. #3208	C₂×C₂₉	semidirect
225. #3110	C₂×C₂₉	semidirect
227. #2974	C₂×C₂₉	semidirect
228. #1701	C₂×C₂₉	semidirect
229. #1685	C₂×C₂₉	semidirect
230. #1681	C₂×C₂₉	semidirect
231. #1665	C₂×C₂₉	semidirect
232. #1573	C₂×C₂₉	semidirect
233. #1555	C₂×C₂₉	semidirect
234. #1552	C₂×C₂₉	semidirect
265. #492	C₂²×C₂₉	semidirect
266. #486	C₂²×C₂₉	semidirect
268. #474	C₂²×C₂₉	semidirect
269. #474	C₂²×C₂₉	semidirect
270. #461	C₂²×C₂₉	semidirect
271. #461	C₂²×C₂₉	semidirect
282. #436	C₂²×C₂₉	semidirect
284. C₈×D₄	C₂²×C₂₉	semidirect
292. #335	C₂²×C₂₉	semidirect
293. #334	C₂²×C₂₉	semidirect
294. #332	C₂²×C₂₉	semidirect
295. #332	C₂²×C₂₉	semidirect
296. #331	C₂²×C₂₉	semidirect
297. #331	C₂²×C₂₉	semidirect
366. C₂₉	#19456	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×#3110	2
C₂×C₂₉×#459	2
C₂₉×#2974	2
C₂₉×#1701	2
C₂₉×#1685	2
C₂₉×#1681	2
C₂₉×#1665	2
C₂₉×#1573	2
C₂₉×#1555	2
C₂₉×#1552	2
#19456	29

Subgroups — C29×#19456 #20314356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19456 #20314356