Subgroups — C₂₉×#21558 #20316458

Order 7424.

876 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3067	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2955	C₂	1	2	yes	maximal, complemented
3	C₂×C₂₉×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₂₉×#131	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1976	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1953	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1932	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1906	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1814	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1772	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1757	C₂	1	2	yes	maximal, complemented
12	C₂₉×#575	C₂²	1	2	yes	—
13	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
14	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
15	C₂×C₂₉×#131	C₂²	1	2	yes	—
16	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
17	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
18	C₂₉×#473	C₄	1	2	yes	complemented
19	C₂₉×#472	C₄	1	2	yes	complemented
20	C₂₉×#471	C₄	1	4	yes	complemented
21	C₂₉×#444	—	2	4	no	—
22	C₂₉×#443	—	2	1	no	—
23	C₂₉×#443	—	2	1	no	—
24	C₂₉×#443	—	2	1	no	—
25	C₂₉×#443	—	2	1	no	—
26	C₂₉×#443	—	2	4	no	—
27	C₂₉×#430	C₂²	1	2	yes	—
28	C₂×C₂₉×#108	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#108	C₂²	1	1	yes	characteristic
30	C₂₉×#427	C₂²	1	1	yes	characteristic
31	C₂₉×#421	C₂²	1	2	yes	—
32	C₂₉×#421	C₂²	1	2	yes	—
33	C₂×C₂₉×#104	C₂²	1	2	yes	—
34	C₂₉×#413	C₂²	1	2	yes	—
35	C₂₉×#410	C₂²	1	2	yes	—
36	C₂₉×#405	—	2	1	no	—
37	C₂₉×#405	—	2	1	no	—
38	C₂₉×#405	C₂²	1	1	yes	characteristic
39	C₂₉×#405	C₂²	1	2	yes	—
40	C₂₉×#405	C₂²	1	1	yes	characteristic
41	C₄×M₁₆×C₂₉	—	2	1	no	—
42	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₂₉	—	2	1	no	—
44	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
45	C₂₉×#344	C₂²	1	2	yes	—
46	C₂₉×#344	C₂²	1	2	yes	—
47	C₂₉×#339	C₂²	1	2	yes	—
48	C₂×#41×C₂₉	C₂³	1	2	yes	—
49	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
50	C₂₉×#137	—	2	2	no	—
51	C₂₉×#137	C₂×C₄	1	4	yes	—
52	C₂₉×AGL(1,ℤ/8)	—	2	2	no	—
53	C₂₉×AGL(1,ℤ/8)	C₂×C₄	1	4	yes	—
54	C₂₉×#135	—	2	4	no	—
55	C₂₉×#135	—	2	1	no	—
56	C₂₉×#135	—	2	1	no	—
57	C₂₉×#135	—	2	1	no	—
58	C₂₉×#135	—	2	1	no	—
59	C₂×Q₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×SD₁₆×C₂₉	C₂×C₄	1	2	yes	complemented
61	C₂×D₈×C₂₉	C₂×C₄	1	1	yes	characteristic, complemented
62	C₂₉×#131	—	2	1	no	—
63	C₂₉×#131	—	2	1	no	—
64	C₂₉×#131	—	2	1	no	—
65	C₂₉×#131	—	2	1	no	—
66	C₂₉×#131	—	2	2	no	—
67	C₂₉×#131	—	2	2	no	—
68	C₂₉×#131	—	2	2	no	—
69	C₂₉×#131	—	2	2	no	—
70	C₂₉×#131	C₂×C₄	1	2	yes	—
71	C₂₉×#131	C₂×C₄	1	2	yes	—
72	C₂₉×#131	D₄	1	2	yes	—
73	C₂₉×#131	D₄	1	2	yes	—
74	C₂×M₁₆×C₂₉	—	2	1	no	—
75	C₂×M₁₆×C₂₉	—	2	1	no	—
76	C₂×M₁₆×C₂₉	—	2	2	no	—
77	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
78	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
79	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
80	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₂₉	—	2	1	no	—
82	C₂²×C₈×C₂₉	—	2	1	no	—
83	C₂²×C₈×C₂₉	—	2	2	no	—
84	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
86	C₄×Q₈×C₂₉	—	2	1	no	—
87	C₄×D₄×C₂₉	—	2	1	no	—
88	C₄×D₄×C₂₉	—	2	2	no	—
89	C₂₉×#117	—	2	1	no	—
90	C₂₉×#117	C₂³	1	2	yes	—
91	C₂₉×#117	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₂₉	—	2	1	no	—
93	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
94	C₂₉×#108	—	2	4	no	—
95	C₂₉×#108	—	2	1	no	—
96	C₂₉×#108	—	2	1	no	—
97	C₂₉×#108	C₂×C₄	1	2	yes	complemented
98	C₂₉×#108	C₂×C₄	1	2	yes	complemented
99	C₂₉×#107	—	2	1	no	—
100	C₂₉×#106	—	2	1	no	—
101	C₂₉×#104	—	2	4	no	—
102	C₂₉×#104	—	2	4	no	—
103	C₂₉×#104	—	2	2	no	—
104	C₂₉×#104	—	2	2	no	—
105	C₂₉×#101	C₂×C₄	1	4	yes	complemented
106	C₂₉×#100	C₂×C₄	1	4	yes	complemented
107	C₂₉×#99	—	2	4	no	—
108	C₂₉×#97	—	2	2	no	—
109	C₂₉×#97	—	2	1	no	—
110	C₂₉×#97	—	2	1	no	—
111	C₂₉×#97	—	2	1	no	—
112	C₄×C₈×C₂₉	—	2	2	no	—
113	C₄×C₈×C₂₉	—	2	1	no	—
114	C₄×C₈×C₂₉	—	2	1	no	—
115	C₄×C₈×C₂₉	—	2	1	no	—
116	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
117	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
118	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
119	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
120	#41×C₂₉	—	2	1	no	—
121	#41×C₂₉	—	2	1	no	—
122	#41×C₂₉	—	2	2	no	—
123	#41×C₂₉	—	2	2	no	—
124	#41×C₂₉	—	2	2	no	—
125	#41×C₂₉	—	2	2	no	—
126	#41×C₂₉	C₂²×C₄	1	2	yes	—
127	#41×C₂₉	C₂×D₄	1	2	yes	—
128	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
129	C₂×Q₈×C₂₉	#41	1	1	yes	characteristic
130	C₂×D₄×C₂₉	—	2	1	no	—
131	C₂×D₄×C₂₉	—	2	2	no	—
132	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
133	C₂×D₄×C₂₉	#41	1	1	yes	characteristic
134	C₂²×C₄×C₂₉	—	2	1	no	—
135	C₂²×C₄×C₂₉	—	2	2	no	—
136	C₂²×C₄×C₂₉	—	2	1	no	—
137	C₂²×C₄×C₂₉	—	2	2	no	—
138	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
139	Q₁₆×C₂₉	—	2	4	no	—
140	Q₁₆×C₂₉	—	2	1	no	—
141	Q₁₆×C₂₉	—	2	1	no	—
142	SD₁₆×C₂₉	—	2	4	no	—
143	SD₁₆×C₂₉	—	2	4	no	—
144	SD₁₆×C₂₉	—	2	2	no	—
145	SD₁₆×C₂₉	—	2	2	no	—
146	D₈×C₂₉	—	2	4	no	—
147	D₈×C₂₉	—	2	1	no	—
148	D₈×C₂₉	—	2	1	no	—
149	M₁₆×C₂₉	—	2	1	no	—
150	M₁₆×C₂₉	—	2	1	no	—
151	M₁₆×C₂₉	—	2	2	no	—
152	M₁₆×C₂₉	—	2	2	no	—
153	M₁₆×C₂₉	—	2	2	no	—
154	M₁₆×C₂₉	—	2	2	no	—
155	M₁₆×C₂₉	—	2	2	no	—
156	M₁₆×C₂₉	—	2	2	no	—
157	M₁₆×C₂₉	—	2	2	no	—
158	M₁₆×C₂₉	—	4	2	no	—
159	M₁₆×C₂₉	—	4	2	no	—
160	M₁₆×C₂₉	C₂²×C₄	1	2	yes	—
161	M₁₆×C₂₉	C₂²×C₄	1	4	yes	—
162	M₁₆×C₂₉	C₂×D₄	1	2	yes	—
163	C₂×C₈×C₂₉	—	2	1	no	—
164	C₂×C₈×C₂₉	—	2	1	no	—
165	C₂×C₈×C₂₉	—	2	2	no	—
166	C₂×C₈×C₂₉	—	2	2	no	—
167	C₂×C₈×C₂₉	—	2	2	no	—
168	C₂×C₈×C₂₉	—	2	2	no	—
169	C₂×C₈×C₂₉	—	2	2	no	—
170	C₂×C₈×C₂₉	—	2	2	no	—
171	C₂×C₈×C₂₉	—	4	2	no	—
172	C₂×C₈×C₂₉	—	4	2	no	—
173	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
179	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₂₉	#41	1	1	yes	characteristic
182	C₂×C₈×C₂₉	#41	1	1	yes	characteristic
183	C₂×C₈×C₂₉	#41	1	1	yes	characteristic
184	C₂×C₈×C₂₉	#41	1	1	yes	characteristic
185	C₄⋊C₄×C₂₉	—	2	2	no	—
186	C₄⋊C₄×C₂₉	—	2	1	no	—
187	C₄⋊C₄×C₂₉	—	2	2	no	—
188	C₂²⋊C₄×C₂₉	—	2	2	no	—
189	C₂²⋊C₄×C₂₉	—	2	2	no	—
190	C₂²⋊C₄×C₂₉	#41	1	2	yes	—
191	C₄²×C₂₉	—	2	2	no	—
192	C₄²×C₂₉	—	2	1	no	—
193	C₄²×C₂₉	—	2	1	no	—
194	C₄²×C₂₉	—	2	2	no	—
195	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
197	#21558	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂³×C₂₉	—	2	1	no	—
199	C₂³×C₂₉	—	2	2	no	—
200	C₂³×C₂₉	C₂×#41	1	1	yes	characteristic
201	Q₈×C₂₉	—	2	1	no	—
202	Q₈×C₂₉	—	2	2	no	—
203	Q₈×C₂₉	—	2	2	no	—
204	Q₈×C₂₉	C₄×D₄	1	2	yes	—
205	D₄×C₂₉	—	2	2	no	—
206	D₄×C₂₉	—	2	2	no	—
207	D₄×C₂₉	—	2	2	no	—
208	D₄×C₂₉	—	2	2	no	—
209	D₄×C₂₉	—	2	1	no	—
210	D₄×C₂₉	—	4	2	no	—
211	D₄×C₂₉	—	4	2	no	—
212	D₄×C₂₉	C₄×D₄	1	2	yes	—
213	C₂×C₄×C₂₉	—	2	1	no	—
214	C₂×C₄×C₂₉	—	2	1	no	—
215	C₂×C₄×C₂₉	—	2	2	no	—
216	C₂×C₄×C₂₉	—	2	2	no	—
217	C₂×C₄×C₂₉	—	2	2	no	—
218	C₂×C₄×C₂₉	—	2	2	no	—
219	C₂×C₄×C₂₉	—	2	1	no	—
220	C₂×C₄×C₂₉	—	4	2	no	—
221	C₂×C₄×C₂₉	—	4	4	no	—
222	C₂×C₄×C₂₉	—	4	2	no	—
223	C₂×C₄×C₂₉	—	4	2	no	—
224	C₂×C₄×C₂₉	—	4	2	no	—
225	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
226	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
231	C₈×C₂₉	—	2	2	no	—
232	C₈×C₂₉	—	2	4	no	—
233	C₈×C₂₉	—	2	2	no	—
234	C₈×C₂₉	—	4	2	no	—
235	C₈×C₂₉	C₄×D₄	1	1	yes	characteristic
236	C₈×C₂₉	C₄×D₄	1	1	yes	characteristic
237	C₈×C₂₉	C₄×D₄	1	1	yes	characteristic
238	C₈×C₂₉	C₄×D₄	1	1	yes	characteristic
239	C₈×C₂₉	#121	1	1	yes	characteristic
240	C₈×C₂₉	#121	1	1	yes	characteristic
241	C₈×C₂₉	#121	1	1	yes	characteristic
242	C₈×C₂₉	#121	1	1	yes	characteristic
243	#3067	C₂×C₂₉	1	1	yes	characteristic
244	#2955	C₂×C₂₉	1	2	yes	complemented
245	C₂×#443	C₂×C₂₉	1	1	yes	characteristic, complemented
246	C₄×#131	C₂×C₂₉	1	1	yes	characteristic, complemented
247	#1976	C₂×C₂₉	1	1	yes	characteristic, complemented
248	#1953	C₂×C₂₉	1	1	yes	characteristic, complemented
249	#1932	C₂×C₂₉	1	2	yes	complemented
250	#1906	C₂×C₂₉	1	2	yes	complemented
251	#1814	C₂×C₂₉	1	1	yes	characteristic, complemented
252	#1772	C₂×C₂₉	1	1	yes	characteristic, complemented
253	#1757	C₂×C₂₉	1	2	yes	complemented
254	C₂²×C₂₉	—	2	2	no	—
255	C₂²×C₂₉	—	4	1	no	—
256	C₂²×C₂₉	—	4	2	no	—
257	C₂²×C₂₉	—	4	2	no	—
258	C₂²×C₂₉	—	8	2	no	—
259	C₂²×C₂₉	C₄×#41	1	1	yes	characteristic
260	C₂²×C₂₉	#525	1	1	yes	characteristic
261	C₂²×C₂₉	#532	1	1	yes	characteristic
262	C₄×C₂₉	—	2	2	no	—
263	C₄×C₂₉	—	2	2	no	—
264	C₄×C₂₉	—	4	2	no	—
265	C₄×C₂₉	—	4	1	no	—
266	C₄×C₂₉	—	4	2	no	—
267	C₄×C₂₉	—	8	2	no	—
268	C₄×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
269	C₄×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
270	C₄×C₂₉	C₂×#121	1	1	yes	characteristic
271	C₄×C₂₉	#529	1	1	yes	characteristic
272	#575	C₂²×C₂₉	1	2	yes	—
273	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
274	C₂×#131	C₂²×C₂₉	1	2	yes	—
275	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
276	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
277	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
278	#473	C₄×C₂₉	1	2	yes	complemented
279	#472	C₄×C₂₉	1	2	yes	complemented
280	#471	C₄×C₂₉	1	4	yes	complemented
281	#444	—	2	4	no	—
282	#443	—	2	4	no	—
283	#443	—	2	1	no	—
284	#443	—	2	1	no	—
285	#443	—	2	1	no	—
286	#443	—	2	1	no	—
287	#430	C₂²×C₂₉	1	2	yes	—
288	C₂×#108	C₂²×C₂₉	1	1	yes	characteristic
289	C₂×#108	C₂²×C₂₉	1	1	yes	characteristic
290	#427	C₂²×C₂₉	1	1	yes	characteristic
291	#421	C₂²×C₂₉	1	2	yes	—
292	#421	C₂²×C₂₉	1	2	yes	—
293	C₂×#104	C₂²×C₂₉	1	2	yes	—
294	#413	C₂²×C₂₉	1	2	yes	—
295	#410	C₂²×C₂₉	1	2	yes	—
296	#405	—	2	1	no	—
297	#405	—	2	1	no	—
298	#405	C₂²×C₂₉	1	1	yes	characteristic
299	#405	C₂²×C₂₉	1	1	yes	characteristic
300	#405	C₂²×C₂₉	1	2	yes	—
301	C₄×M₁₆	—	2	1	no	—
302	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
303	C₂×C₄×C₈	—	2	1	no	—
304	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
305	#344	C₂²×C₂₉	1	2	yes	—
306	#344	C₂²×C₂₉	1	2	yes	—
307	#339	C₂²×C₂₉	1	2	yes	—
308	C₂×C₂₉	—	2	1	no	—
309	C₂×C₂₉	—	2	1	no	—
310	C₂×C₂₉	—	2	1	no	—
311	C₂×C₂₉	—	4	2	no	—
312	C₂×C₂₉	—	8	2	no	—
313	C₂×C₂₉	C₄×#121	1	1	yes	characteristic
314	C₂×#41	C₂³×C₂₉	1	2	yes	—
315	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
316	#137	—	2	2	no	—
317	#137	C₂×C₄×C₂₉	1	4	yes	—
318	AGL(1,ℤ/8)	—	2	2	no	—
319	AGL(1,ℤ/8)	C₂×C₄×C₂₉	1	4	yes	—
320	#135	—	2	4	no	—
321	#135	—	2	1	no	—
322	#135	—	2	1	no	—
323	#135	—	2	1	no	—
324	#135	—	2	1	no	—
325	C₂×Q₁₆	C₂×C₄×C₂₉	1	1	yes	characteristic, complemented
326	C₂×SD₁₆	C₂×C₄×C₂₉	1	2	yes	complemented
327	C₂×D₈	C₂×C₄×C₂₉	1	1	yes	characteristic, complemented
328	#131	—	2	1	no	—
329	#131	—	2	1	no	—
330	#131	—	2	1	no	—
331	#131	—	2	1	no	—
332	#131	—	2	2	no	—
333	#131	—	2	2	no	—
334	#131	—	2	2	no	—
335	#131	—	2	2	no	—
336	#131	C₂×C₄×C₂₉	1	2	yes	—
337	#131	C₂×C₄×C₂₉	1	2	yes	—
338	#131	D₄×C₂₉	1	2	yes	—
339	#131	D₄×C₂₉	1	2	yes	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	—	2	2	no	—
343	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
344	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
345	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
346	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
347	C₂²×C₈	—	2	1	no	—
348	C₂²×C₈	—	2	1	no	—
349	C₂²×C₈	—	2	2	no	—
350	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
351	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
352	C₄×Q₈	—	2	1	no	—
353	C₄×D₄	—	2	1	no	—
354	C₄×D₄	—	2	2	no	—
355	#117	—	2	1	no	—
356	#117	C₂³×C₂₉	1	2	yes	—
357	#117	C₂³×C₂₉	1	1	yes	characteristic
358	C₂×C₄²	—	2	1	no	—
359	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
360	#108	—	2	4	no	—
361	#108	—	2	1	no	—
362	#108	—	2	1	no	—
363	#108	C₂×C₄×C₂₉	1	2	yes	complemented
364	#108	C₂×C₄×C₂₉	1	2	yes	complemented
365	#107	—	2	1	no	—
366	#106	—	2	1	no	—
367	#104	—	2	4	no	—
368	#104	—	2	4	no	—
369	#104	—	2	2	no	—
370	#104	—	2	2	no	—
371	#101	C₂×C₄×C₂₉	1	4	yes	complemented
372	#100	C₂×C₄×C₂₉	1	4	yes	complemented
373	#99	—	2	4	no	—
374	#97	—	2	1	no	—
375	#97	—	2	1	no	—
376	#97	—	2	2	no	—
377	#97	—	2	1	no	—
378	C₄×C₈	—	2	1	no	—
379	C₄×C₈	—	2	1	no	—
380	C₄×C₈	—	2	2	no	—
381	C₄×C₈	—	2	1	no	—
382	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
383	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
384	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
385	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
386	C₂₉	#21558	1	1	yes	characteristic, direct product factor, Sylow
387	#41	—	2	1	no	—
388	#41	—	2	1	no	—
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	2	2	no	—
392	#41	—	2	2	no	—
393	#41	C₂²×C₄×C₂₉	1	2	yes	—
394	#41	C₂×D₄×C₂₉	1	2	yes	—
395	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
396	C₂×Q₈	#41×C₂₉	1	1	yes	characteristic
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
400	C₂×D₄	#41×C₂₉	1	1	yes	characteristic
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
406	Q₁₆	—	2	4	no	—
407	Q₁₆	—	2	1	no	—
408	Q₁₆	—	2	1	no	—
409	SD₁₆	—	2	4	no	—
410	SD₁₆	—	2	4	no	—
411	SD₁₆	—	2	2	no	—
412	SD₁₆	—	2	2	no	—
413	D₈	—	2	4	no	—
414	D₈	—	2	1	no	—
415	D₈	—	2	1	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	2	1	no	—
418	M₁₆	—	2	2	no	—
419	M₁₆	—	2	2	no	—
420	M₁₆	—	2	2	no	—
421	M₁₆	—	2	2	no	—
422	M₁₆	—	2	2	no	—
423	M₁₆	—	2	2	no	—
424	M₁₆	—	2	2	no	—
425	M₁₆	—	4	2	no	—
426	M₁₆	—	4	2	no	—
427	M₁₆	C₂²×C₄×C₂₉	1	2	yes	—
428	M₁₆	C₂²×C₄×C₂₉	1	4	yes	—
429	M₁₆	C₂×D₄×C₂₉	1	2	yes	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	4	2	no	—
439	C₂×C₈	—	4	2	no	—
440	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
441	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
442	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
443	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
444	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
445	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
446	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
447	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
448	C₂×C₈	#41×C₂₉	1	1	yes	characteristic
449	C₂×C₈	#41×C₂₉	1	1	yes	characteristic
450	C₂×C₈	#41×C₂₉	1	1	yes	characteristic
451	C₂×C₈	#41×C₂₉	1	1	yes	characteristic
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	#41×C₂₉	1	2	yes	—
458	C₄²	—	2	2	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	2	no	—
462	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
463	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
464	C₂³	—	2	1	no	—
465	C₂³	—	2	2	no	—
466	C₂³	C₂×#41×C₂₉	1	1	yes	characteristic
467	Q₈	—	2	1	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	2	2	no	—
470	Q₈	C₄×D₄×C₂₉	1	2	yes	—
471	D₄	—	2	2	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	2	1	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	C₄×D₄×C₂₉	1	2	yes	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
494	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
495	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
496	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	2	4	no	—
499	C₈	—	2	2	no	—
500	C₈	—	4	2	no	—
501	C₈	C₄×D₄×C₂₉	1	1	yes	characteristic
502	C₈	C₄×D₄×C₂₉	1	1	yes	characteristic
503	C₈	C₄×D₄×C₂₉	1	1	yes	characteristic
504	C₈	C₄×D₄×C₂₉	1	1	yes	characteristic
505	C₈	C₂₉×#121	1	1	yes	characteristic
506	C₈	C₂₉×#121	1	1	yes	characteristic
507	C₈	C₂₉×#121	1	1	yes	characteristic
508	C₈	C₂₉×#121	1	1	yes	characteristic
509	C₂²	—	2	2	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	8	2	no	—
514	C₂²	C₄×#41×C₂₉	1	1	yes	characteristic
515	C₂²	C₂₉×#525	1	1	yes	characteristic
516	C₂²	C₂₉×#532	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	2	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	2	no	—
522	C₄	—	8	2	no	—
523	C₄	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
524	C₄	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
525	C₄	C₂×C₂₉×#121	1	1	yes	characteristic
526	C₄	C₂₉×#529	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	4	2	no	—
531	C₂	—	8	2	no	—
532	C₂	C₄×C₂₉×#121	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₂₉	#121
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
socle	C₂×C₂₉	C₄×#121
prime radical	C₂₉×#3067	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₂₉ ◁ C₂²×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#2955	C₂	semidirect
3. C₂×C₂₉×#443	C₂	semidirect
4. C₄×C₂₉×#131	C₂	semidirect
5. C₂₉×#1976	C₂	semidirect
6. C₂₉×#1953	C₂	semidirect
7. C₂₉×#1932	C₂	semidirect
8. C₂₉×#1906	C₂	semidirect
9. C₂₉×#1814	C₂	semidirect
10. C₂₉×#1772	C₂	semidirect
11. C₂₉×#1757	C₂	semidirect
18. C₂₉×#473	C₄	semidirect
19. C₂₉×#472	C₄	semidirect
20. C₂₉×#471	C₄	semidirect
59. C₂×Q₁₆×C₂₉	C₂×C₄	semidirect
60. C₂×SD₁₆×C₂₉	C₂×C₄	semidirect
61. C₂×D₈×C₂₉	C₂×C₄	semidirect
97. C₂₉×#108	C₂×C₄	semidirect
98. C₂₉×#108	C₂×C₄	semidirect
105. C₂₉×#101	C₂×C₄	semidirect
106. C₂₉×#100	C₂×C₄	semidirect
197. #21558	C₂₉	direct (N × H)
244. #2955	C₂×C₂₉	semidirect
245. C₂×#443	C₂×C₂₉	semidirect
246. C₄×#131	C₂×C₂₉	semidirect
247. #1976	C₂×C₂₉	semidirect
248. #1953	C₂×C₂₉	semidirect
249. #1932	C₂×C₂₉	semidirect
250. #1906	C₂×C₂₉	semidirect
251. #1814	C₂×C₂₉	semidirect
252. #1772	C₂×C₂₉	semidirect
253. #1757	C₂×C₂₉	semidirect
278. #473	C₄×C₂₉	semidirect
279. #472	C₄×C₂₉	semidirect
280. #471	C₄×C₂₉	semidirect
325. C₂×Q₁₆	C₂×C₄×C₂₉	semidirect
326. C₂×SD₁₆	C₂×C₄×C₂₉	semidirect
327. C₂×D₈	C₂×C₄×C₂₉	semidirect
363. #108	C₂×C₄×C₂₉	semidirect
364. #108	C₂×C₄×C₂₉	semidirect
371. #101	C₂×C₄×C₂₉	semidirect
372. #100	C₂×C₄×C₂₉	semidirect
386. C₂₉	#21558	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×#3067	2
C₂₉×#2955	2
C₂×C₂₉×#443	2
C₄×C₂₉×#131	2
C₂₉×#1976	2
C₂₉×#1953	2
C₂₉×#1932	2
C₂₉×#1906	2
C₂₉×#1814	2
C₂₉×#1772	2
C₂₉×#1757	2
#21558	29

Subgroups — C29×#21558 #20316458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#21558 #20316458