Subgroups — C₂₉×#22131 #20317031

Order 7424.

636 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3076	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#2922	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1986	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1946	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1938	C₂	1	2	yes	maximal
8	C₂₉×#1929	C₂	1	2	yes	maximal
9	C₂₉×#1922	C₂	1	2	yes	maximal, complemented
10	C₂₉×#1806	C₂	1	1	yes	maximal, characteristic
11	C₂₉×#1770	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#533	C₂²	1	1	yes	characteristic
13	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
14	C₂₉×#479	C₄	1	2	yes	complemented
15	C₂₉×#478	C₄	1	2	yes	complemented
16	C₂₉×#477	C₄	1	1	yes	characteristic, complemented
17	C₂₉×#476	C₄	1	1	yes	characteristic, complemented
18	C₂₉×#475	C₄	1	1	yes	characteristic, complemented
19	C₂₉×#474	C₄	1	1	yes	characteristic, complemented
20	C₂₉×#446	—	2	1	no	—
21	C₂₉×#446	—	2	1	no	—
22	C₈×Q₈×C₂₉	—	2	1	no	—
23	C₈×Q₈×C₂₉	—	2	1	no	—
24	C₂₉×#433	—	2	1	no	—
25	C₂₉×#433	—	2	1	no	—
26	C₂₉×#431	—	2	1	no	—
27	C₂₉×#431	—	2	1	no	—
28	C₂×C₂₉×#108	C₂²	1	2	yes	—
29	C₂₉×#427	C₂²	1	2	yes	—
30	C₂₉×#424	C₂²	1	1	yes	characteristic
31	C₂₉×#424	C₂²	1	2	yes	—
32	C₂₉×#424	C₂²	1	1	yes	characteristic
33	C₂₉×#423	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₂₉×#104	C₂²	1	2	yes	—
36	C₂₉×#416	C₂²	1	2	yes	—
37	C₂₉×#408	C₂²	1	1	yes	characteristic
38	C₂₉×#408	C₂²	1	1	yes	characteristic
39	C₂₉×#405	C₂²	1	2	yes	—
40	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
41	C₂×C₂₉×#97	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
44	C₂₉×#341	C₂²	1	2	yes	—
45	C₂₉×#339	C₂²	1	2	yes	—
46	C₂₉×#339	C₂²	1	2	yes	—
47	C₂₉×#339	C₂²	1	2	yes	—
48	C₂₉×#336	C₂²	1	2	yes	—
49	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
51	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
52	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
54	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
56	C₂₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
57	C₂₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
58	C₂₉×#125	C₂×C₄	1	2	yes	—
59	C₂₉×C₂²⋊Q₈	—	2	1	no	—
60	C₂₉×C₂²⋊Q₈	—	2	1	no	—
61	C₄×Q₈×C₂₉	—	2	1	no	—
62	C₄×Q₈×C₂₉	—	2	1	no	—
63	C₄×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
64	C₄×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
65	C₄×D₄×C₂₉	—	2	1	no	—
66	C₄×D₄×C₂₉	—	2	1	no	—
67	C₄×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
68	C₄×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
69	C₂₉×#117	—	2	1	no	—
70	C₂₉×#117	C₂³	1	1	yes	characteristic
71	C₂₉×#117	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
73	C₂×C₄²×C₂₉	—	2	1	no	—
74	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
75	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
76	C₂₉×#108	—	4	2	no	—
77	C₂₉×#107	C₂×C₄	1	2	yes	—
78	C₂₉×#107	C₂×C₄	1	2	yes	—
79	C₂₉×#106	C₂×C₄	1	2	yes	—
80	C₂₉×#106	C₂×C₄	1	2	yes	—
81	C₂₉×C₄⋊C₈	—	2	1	no	—
82	C₂₉×C₄⋊C₈	—	2	1	no	—
83	C₂₉×C₄⋊C₈	—	2	1	no	—
84	C₂₉×C₄⋊C₈	—	2	1	no	—
85	C₂₉×C₄⋊C₈	—	2	2	no	—
86	C₂₉×C₄⋊C₈	—	2	2	no	—
87	C₂₉×C₄⋊C₈	—	2	1	no	—
88	C₂₉×C₄⋊C₈	—	2	1	no	—
89	C₂₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₂₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
91	C₂₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
92	C₂₉×#104	—	4	2	no	—
93	C₂₉×#103	C₂×C₄	1	2	yes	—
94	C₂₉×#103	C₂×C₄	1	2	yes	—
95	C₂₉×#102	C₂×C₄	1	2	yes	—
96	C₂₉×#102	C₂×C₄	1	2	yes	—
97	C₂₉×C₂²⋊C₈	—	2	1	no	—
98	C₂₉×C₂²⋊C₈	—	2	1	no	—
99	C₂₉×C₂²⋊C₈	—	2	1	no	—
100	C₂₉×C₂²⋊C₈	—	2	1	no	—
101	C₂₉×#97	—	2	2	no	—
102	C₂₉×#97	—	2	1	no	—
103	C₂₉×#97	—	4	2	no	—
104	C₄×C₈×C₂₉	—	2	2	no	—
105	C₄×C₈×C₂₉	—	2	1	no	—
106	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
107	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
108	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
109	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
110	C₂₉×#95	—	2	1	no	—
111	#41×C₂₉	—	2	1	no	—
112	#41×C₂₉	—	2	1	no	—
113	#41×C₂₉	—	2	1	no	—
114	#41×C₂₉	—	2	1	no	—
115	C₂×Q₈×C₂₉	—	2	1	no	—
116	C₂×Q₈×C₂₉	—	2	1	no	—
117	C₂×Q₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
118	C₂×D₄×C₂₉	—	2	1	no	—
119	C₂×D₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₂₉	—	2	1	no	—
121	C₂²×C₄×C₂₉	—	2	1	no	—
122	C₂²×C₄×C₂₉	—	2	1	no	—
123	C₂²×C₄×C₂₉	—	2	2	no	—
124	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
125	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
126	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
127	M₁₆×C₂₉	—	2	2	no	—
128	M₁₆×C₂₉	—	2	1	no	—
129	M₁₆×C₂₉	—	2	1	no	—
130	M₁₆×C₂₉	—	2	1	no	—
131	M₁₆×C₂₉	—	2	1	no	—
132	M₁₆×C₂₉	—	2	2	no	—
133	C₂×C₈×C₂₉	—	2	1	no	—
134	C₂×C₈×C₂₉	—	2	2	no	—
135	C₂×C₈×C₂₉	—	2	2	no	—
136	C₂×C₈×C₂₉	—	2	1	no	—
137	C₂×C₈×C₂₉	—	2	1	no	—
138	C₂×C₈×C₂₉	—	2	1	no	—
139	C₂×C₈×C₂₉	—	2	1	no	—
140	C₂×C₈×C₂₉	—	2	1	no	—
141	C₂×C₈×C₂₉	—	2	2	no	—
142	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
148	C₄⋊C₄×C₂₉	—	2	1	no	—
149	C₄⋊C₄×C₂₉	—	2	1	no	—
150	C₄⋊C₄×C₂₉	—	2	2	no	—
151	C₄⋊C₄×C₂₉	—	2	2	no	—
152	C₄⋊C₄×C₂₉	—	2	1	no	—
153	C₄⋊C₄×C₂₉	—	2	1	no	—
154	C₄⋊C₄×C₂₉	—	4	2	no	—
155	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
156	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
157	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
158	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
159	C₂²⋊C₄×C₂₉	—	2	1	no	—
160	C₂²⋊C₄×C₂₉	—	2	2	no	—
161	C₂²⋊C₄×C₂₉	—	2	1	no	—
162	C₂²⋊C₄×C₂₉	—	2	1	no	—
163	C₄²×C₂₉	—	2	1	no	—
164	C₄²×C₂₉	—	2	1	no	—
165	C₄²×C₂₉	—	2	1	no	—
166	C₄²×C₂₉	—	2	2	no	—
167	C₄²×C₂₉	—	2	2	no	—
168	C₄²×C₂₉	—	2	2	no	—
169	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
173	#22131	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂³×C₂₉	—	2	1	no	—
175	C₂³×C₂₉	C₂×#41	1	1	yes	characteristic
176	Q₈×C₂₉	—	2	1	no	—
177	Q₈×C₂₉	—	2	1	no	—
178	Q₈×C₂₉	—	4	2	no	—
179	Q₈×C₂₉	—	4	2	no	—
180	D₄×C₂₉	—	2	1	no	—
181	D₄×C₂₉	—	2	1	no	—
182	D₄×C₂₉	—	4	1	no	—
183	D₄×C₂₉	—	4	1	no	—
184	C₂×C₄×C₂₉	—	2	2	no	—
185	C₂×C₄×C₂₉	—	2	1	no	—
186	C₂×C₄×C₂₉	—	2	1	no	—
187	C₂×C₄×C₂₉	—	2	1	no	—
188	C₂×C₄×C₂₉	—	2	2	no	—
189	C₂×C₄×C₂₉	—	2	2	no	—
190	C₂×C₄×C₂₉	—	4	1	no	—
191	C₂×C₄×C₂₉	—	4	2	no	—
192	C₂×C₄×C₂₉	—	4	1	no	—
193	C₂×C₄×C₂₉	—	4	1	no	—
194	C₂×C₄×C₂₉	—	4	2	no	—
195	C₂×C₄×C₂₉	—	4	2	no	—
196	C₂×C₄×C₂₉	—	4	2	no	—
197	C₂×C₄×C₂₉	—	4	2	no	—
198	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
206	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
207	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
208	C₈×C₂₉	—	2	2	no	—
209	C₈×C₂₉	—	2	2	no	—
210	C₈×C₂₉	—	2	1	no	—
211	C₈×C₂₉	—	2	1	no	—
212	C₈×C₂₉	—	2	1	no	—
213	C₈×C₂₉	—	2	1	no	—
214	C₈×C₂₉	—	4	1	no	—
215	C₈×C₂₉	—	4	1	no	—
216	C₈×C₂₉	—	4	2	no	—
217	#3076	C₂×C₂₉	1	1	yes	characteristic
218	#2960	C₂×C₂₉	1	1	yes	characteristic, complemented
219	#2922	C₂×C₂₉	1	1	yes	characteristic
220	#1986	C₂×C₂₉	1	1	yes	characteristic, complemented
221	#1950	C₂×C₂₉	1	1	yes	characteristic, complemented
222	#1946	C₂×C₂₉	1	2	yes	complemented
223	#1938	C₂×C₂₉	1	2	yes	—
224	#1929	C₂×C₂₉	1	2	yes	—
225	#1922	C₂×C₂₉	1	2	yes	complemented
226	#1806	C₂×C₂₉	1	1	yes	characteristic
227	#1770	C₂×C₂₉	1	1	yes	characteristic, complemented
228	C₂²×C₂₉	—	2	1	no	—
229	C₂²×C₂₉	—	2	1	no	—
230	C₂²×C₂₉	—	4	1	no	—
231	C₂²×C₂₉	—	4	1	no	—
232	C₂²×C₂₉	—	4	1	no	—
233	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
234	C₂²×C₂₉	#541	1	1	yes	characteristic
235	C₂²×C₂₉	#542	1	1	yes	characteristic
236	C₄×C₂₉	—	2	1	no	—
237	C₄×C₂₉	—	2	1	no	—
238	C₄×C₂₉	—	2	1	no	—
239	C₄×C₂₉	—	4	1	no	—
240	C₄×C₂₉	—	4	1	no	—
241	C₄×C₂₉	—	4	2	no	—
242	C₄×C₂₉	—	4	1	no	—
243	C₄×C₂₉	—	4	2	no	—
244	C₄×C₂₉	—	8	2	no	—
245	C₄×C₂₉	#444	1	2	yes	—
246	C₄×C₂₉	#519	1	1	yes	characteristic
247	C₄×C₂₉	#520	1	1	yes	characteristic
248	C₄×C₂₉	#536	1	1	yes	characteristic
249	C₄×C₂₉	#537	1	1	yes	characteristic
250	#533	C₂²×C₂₉	1	1	yes	characteristic
251	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
252	#479	C₄×C₂₉	1	2	yes	complemented
253	#478	C₄×C₂₉	1	2	yes	complemented
254	#477	C₄×C₂₉	1	1	yes	characteristic, complemented
255	#476	C₄×C₂₉	1	1	yes	characteristic, complemented
256	#475	C₄×C₂₉	1	1	yes	characteristic, complemented
257	#474	C₄×C₂₉	1	1	yes	characteristic, complemented
258	#446	—	2	1	no	—
259	#446	—	2	1	no	—
260	C₈×Q₈	—	2	1	no	—
261	C₈×Q₈	—	2	1	no	—
262	#433	—	2	1	no	—
263	#433	—	2	1	no	—
264	#431	—	2	1	no	—
265	#431	—	2	1	no	—
266	C₂×#108	C₂²×C₂₉	1	2	yes	—
267	#427	C₂²×C₂₉	1	2	yes	—
268	#424	C₂²×C₂₉	1	1	yes	characteristic
269	#424	C₂²×C₂₉	1	1	yes	characteristic
270	#424	C₂²×C₂₉	1	2	yes	—
271	#423	C₂²×C₂₉	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
273	C₂×#104	C₂²×C₂₉	1	2	yes	—
274	#416	C₂²×C₂₉	1	2	yes	—
275	#408	C₂²×C₂₉	1	1	yes	characteristic
276	#408	C₂²×C₂₉	1	1	yes	characteristic
277	#405	C₂²×C₂₉	1	2	yes	—
278	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
279	C₂×#97	C₂²×C₂₉	1	2	yes	—
280	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
281	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
282	#341	C₂²×C₂₉	1	2	yes	—
283	#339	C₂²×C₂₉	1	2	yes	—
284	#339	C₂²×C₂₉	1	2	yes	—
285	#339	C₂²×C₂₉	1	2	yes	—
286	#336	C₂²×C₂₉	1	2	yes	—
287	C₂×C₂₉	—	2	1	no	—
288	C₂×C₂₉	—	2	1	no	—
289	C₂×C₂₉	—	8	1	no	—
290	C₂×C₂₉	#2323	1	1	yes	characteristic
291	C₂×C₂₉	C₂×#444	1	1	yes	characteristic
292	C₂×C₂₉	#2955	1	1	yes	characteristic
293	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
294	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
295	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
296	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
297	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
298	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
300	C₄⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
301	C₄⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
302	#125	C₂×C₄×C₂₉	1	2	yes	—
303	C₂²⋊Q₈	—	2	1	no	—
304	C₂²⋊Q₈	—	2	1	no	—
305	C₄×Q₈	—	2	1	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
308	C₄×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
312	C₄×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
313	#117	—	2	1	no	—
314	#117	C₂³×C₂₉	1	1	yes	characteristic
315	#117	C₂³×C₂₉	1	2	yes	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
319	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
320	#108	—	4	2	no	—
321	#107	C₂×C₄×C₂₉	1	2	yes	—
322	#107	C₂×C₄×C₂₉	1	2	yes	—
323	#106	C₂×C₄×C₂₉	1	2	yes	—
324	#106	C₂×C₄×C₂₉	1	2	yes	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	—	2	1	no	—
328	C₄⋊C₈	—	2	1	no	—
329	C₄⋊C₈	—	2	2	no	—
330	C₄⋊C₈	—	2	2	no	—
331	C₄⋊C₈	—	2	1	no	—
332	C₄⋊C₈	—	2	1	no	—
333	C₄⋊C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
334	C₄⋊C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
335	C₄⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
336	#104	—	4	2	no	—
337	#103	C₂×C₄×C₂₉	1	2	yes	—
338	#103	C₂×C₄×C₂₉	1	2	yes	—
339	#102	C₂×C₄×C₂₉	1	2	yes	—
340	#102	C₂×C₄×C₂₉	1	2	yes	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	2	1	no	—
343	C₂²⋊C₈	—	2	1	no	—
344	C₂²⋊C₈	—	2	1	no	—
345	#97	—	2	2	no	—
346	#97	—	2	1	no	—
347	#97	—	4	2	no	—
348	C₄×C₈	—	2	2	no	—
349	C₄×C₈	—	2	1	no	—
350	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
351	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
352	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
353	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
354	#95	—	2	1	no	—
355	C₂₉	#22131	1	1	yes	characteristic, direct product factor, Sylow
356	#41	—	2	1	no	—
357	#41	—	2	1	no	—
358	#41	—	2	1	no	—
359	#41	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
370	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
372	M₁₆	—	2	2	no	—
373	M₁₆	—	2	1	no	—
374	M₁₆	—	2	1	no	—
375	M₁₆	—	2	1	no	—
376	M₁₆	—	2	1	no	—
377	M₁₆	—	2	2	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
388	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
389	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
390	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
391	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
392	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	4	2	no	—
400	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
401	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
402	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
403	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
404	C₂²⋊C₄	—	2	1	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	2	1	no	—
408	C₄²	—	2	1	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
415	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
416	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
417	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
418	C₂³	—	2	1	no	—
419	C₂³	C₂×#41×C₂₉	1	1	yes	characteristic
420	Q₈	—	2	1	no	—
421	Q₈	—	2	1	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	4	2	no	—
424	D₄	—	2	1	no	—
425	D₄	—	2	1	no	—
426	D₄	—	4	1	no	—
427	D₄	—	4	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
443	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
444	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
445	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
446	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
448	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
449	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
450	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
451	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
452	C₈	—	2	2	no	—
453	C₈	—	2	2	no	—
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	2	1	no	—
458	C₈	—	4	1	no	—
459	C₈	—	4	1	no	—
460	C₈	—	4	2	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
467	C₂²	C₂₉×#541	1	1	yes	characteristic
468	C₂²	C₂₉×#542	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	1	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	1	no	—
477	C₄	—	8	2	no	—
478	C₄	C₂₉×#444	1	2	yes	—
479	C₄	C₂₉×#519	1	1	yes	characteristic
480	C₄	C₂₉×#520	1	1	yes	characteristic
481	C₄	C₂₉×#536	1	1	yes	characteristic
482	C₄	C₂₉×#537	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	8	1	no	—
486	C₂	C₂₉×#2323	1	1	yes	characteristic
487	C₂	C₂×C₂₉×#444	1	1	yes	characteristic
488	C₂	C₂₉×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂×C₄×D₄
prime radical	C₂×#41×C₂₉	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂×C₄×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#2960	C₂	semidirect
4. C₂₉×#1986	C₂	semidirect
5. C₂₉×#1950	C₂	semidirect
6. C₂₉×#1946	C₂	semidirect
9. C₂₉×#1922	C₂	semidirect
11. C₂₉×#1770	C₂	semidirect
14. C₂₉×#479	C₄	semidirect
15. C₂₉×#478	C₄	semidirect
16. C₂₉×#477	C₄	semidirect
17. C₂₉×#476	C₄	semidirect
18. C₂₉×#475	C₄	semidirect
19. C₂₉×#474	C₄	semidirect
173. #22131	C₂₉	direct (N × H)
218. #2960	C₂×C₂₉	semidirect
220. #1986	C₂×C₂₉	semidirect
221. #1950	C₂×C₂₉	semidirect
222. #1946	C₂×C₂₉	semidirect
225. #1922	C₂×C₂₉	semidirect
227. #1770	C₂×C₂₉	semidirect
252. #479	C₄×C₂₉	semidirect
253. #478	C₄×C₂₉	semidirect
254. #477	C₄×C₂₉	semidirect
255. #476	C₄×C₂₉	semidirect
256. #475	C₄×C₂₉	semidirect
257. #474	C₄×C₂₉	semidirect
355. C₂₉	#22131	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×#3076	2
C₂₉×#2960	2
C₂₉×#2922	2
C₂₉×#1986	2
C₂₉×#1950	2
C₂₉×#1946	2
C₂₉×#1938	2
C₂₉×#1929	2
C₂₉×#1922	2
C₂₉×#1806	2
C₂₉×#1770	2
#22131	29

Subgroups — C29×#22131 #20317031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#22131 #20317031