Subgroups — C₂₉×#25313 #20320213

Order 7424.

712 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3139	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3077	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#461	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2064	C₂	1	2	yes	maximal, complemented
6	C₂₉×#2046	C₂	1	2	yes	maximal
7	C₂₉×#1977	C₂	1	2	yes	maximal
8	C₂₉×#1966	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1930	C₂	1	2	yes	maximal, complemented
11	C₄×C₂₉×#100	C₂	1	1	yes	maximal, characteristic
12	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	—
13	C₂₉×#533	C₂²	1	1	yes	characteristic
14	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
16	C₂₉×#491	—	2	2	no	—
17	C₂₉×#487	—	2	1	no	—
18	C₂₉×#487	—	2	1	no	—
19	C₂₉×#478	—	2	2	no	—
20	C₂₉×#476	—	2	1	no	—
21	C₂₉×#474	—	2	1	no	—
22	C₂₉×#461	—	2	1	no	—
23	C₂₉×#461	—	2	1	no	—
24	C₂₉×#461	—	2	2	no	—
25	C₂₉×#446	—	2	1	no	—
26	C₂₉×#446	—	2	2	no	—
27	C₈×Q₈×C₂₉	—	2	1	no	—
28	C₂×C₂₉×#108	C₂²	1	2	yes	—
29	C₂₉×#428	C₂²	1	2	yes	—
30	C₂₉×#424	C₂²	1	2	yes	—
31	C₂₉×#423	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂₉×#419	C₂²	1	2	yes	—
34	C₂₉×#419	C₂²	1	2	yes	—
35	C₂₉×#418	C₂²	1	2	yes	—
36	C₂×C₂₉×#103	C₂²	1	2	yes	—
37	C₂×C₂₉×#101	C₂²	1	2	yes	—
38	C₂×C₂₉×#101	C₂²	1	2	yes	—
39	C₂×C₂₉×#100	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×#100	C₂²	1	1	yes	characteristic
41	C₂₉×#405	C₂²	1	2	yes	—
42	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
44	C₂₉×#343	C₂²	1	1	yes	characteristic
45	C₂₉×#343	C₂²	1	1	yes	characteristic
46	C₂₉×#341	C₂²	1	2	yes	—
47	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
48	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₂₉	—	2	1	no	—
50	C₂×SD₁₆×C₂₉	—	2	4	no	—
51	C₂×SD₁₆×C₂₉	—	2	2	no	—
52	C₂×SD₁₆×C₂₉	—	2	2	no	—
53	C₂×SD₁₆×C₂₉	—	4	2	no	—
54	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
55	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
56	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
60	C₂₉×C₄⋊Q₈	—	2	1	no	—
61	C₂₉×C₄⋊Q₈	—	2	1	no	—
62	C₂₉×C₄⋊Q₈	—	2	1	no	—
63	C₂₉×C₄⋊Q₈	—	2	1	no	—
64	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
65	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
66	C₂₉×#125	D₄	1	2	yes	—
67	C₂₉×C₂²⋊Q₈	—	2	1	no	—
68	C₂₉×C₂²⋊Q₈	—	2	1	no	—
69	C₄×Q₈×C₂₉	—	2	1	no	—
70	C₄×Q₈×C₂₉	—	2	1	no	—
71	C₄×D₄×C₂₉	—	2	1	no	—
72	C₄×D₄×C₂₉	—	2	1	no	—
73	C₄×D₄×C₂₉	—	2	1	no	—
74	C₄×D₄×C₂₉	—	2	1	no	—
75	C₂₉×#117	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
80	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
81	C₂₉×#108	—	4	2	no	—
82	C₂₉×#107	—	2	2	no	—
83	C₂₉×#106	—	2	2	no	—
84	C₂₉×C₄⋊C₈	—	2	2	no	—
85	C₂₉×C₄⋊C₈	—	2	2	no	—
86	C₂₉×C₄⋊C₈	—	2	1	no	—
87	C₂₉×C₄⋊C₈	—	2	1	no	—
88	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
89	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
90	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
91	C₂₉×#103	—	2	2	no	—
92	C₂₉×#103	—	2	2	no	—
93	C₂₉×#103	—	2	2	no	—
94	C₂₉×#103	—	2	2	no	—
95	C₂₉×#103	—	2	2	no	—
96	C₂₉×#103	—	2	2	no	—
97	C₂₉×#102	—	2	2	no	—
98	C₂₉×#102	—	2	2	no	—
99	C₂₉×#101	—	2	4	no	—
100	C₂₉×#101	—	4	2	no	—
101	C₂₉×#100	—	2	2	no	—
102	C₂₉×#100	—	2	2	no	—
103	C₂₉×#97	—	2	2	no	—
104	C₂₉×#97	—	2	1	no	—
105	C₂₉×#97	—	2	1	no	—
106	C₄×C₈×C₂₉	—	2	2	no	—
107	C₄×C₈×C₂₉	—	2	1	no	—
108	C₄×C₈×C₂₉	—	2	1	no	—
109	C₂⁴×C₂₉	—	2	1	no	—
110	C₂×Q₈×C₂₉	—	2	1	no	—
111	C₂×Q₈×C₂₉	—	2	1	no	—
112	C₂×Q₈×C₂₉	—	2	2	no	—
113	C₂×Q₈×C₂₉	—	2	2	no	—
114	C₂×Q₈×C₂₉	—	2	2	no	—
115	C₂×Q₈×C₂₉	—	2	2	no	—
116	C₂×Q₈×C₂₉	—	2	2	no	—
117	C₂×Q₈×C₂₉	—	2	2	no	—
118	C₂×D₄×C₂₉	—	2	1	no	—
119	C₂×D₄×C₂₉	—	2	1	no	—
120	C₂×D₄×C₂₉	—	2	1	no	—
121	C₂×D₄×C₂₉	—	2	1	no	—
122	C₂×D₄×C₂₉	—	2	1	no	—
123	C₂×D₄×C₂₉	#41	1	2	yes	—
124	C₂²×C₄×C₂₉	—	2	2	no	—
125	C₂²×C₄×C₂₉	—	2	1	no	—
126	C₂²×C₄×C₂₉	—	4	1	no	—
127	C₂²×C₄×C₂₉	—	4	1	no	—
128	C₂²×C₄×C₂₉	—	8	2	no	—
129	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
130	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
131	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
132	SD₁₆×C₂₉	—	4	4	no	—
133	SD₁₆×C₂₉	—	4	4	no	—
134	M₁₆×C₂₉	—	2	1	no	—
135	M₁₆×C₂₉	—	2	1	no	—
136	M₁₆×C₂₉	—	2	1	no	—
137	M₁₆×C₂₉	—	2	1	no	—
138	M₁₆×C₂₉	—	2	2	no	—
139	M₁₆×C₂₉	—	2	1	no	—
140	M₁₆×C₂₉	—	2	2	no	—
141	M₁₆×C₂₉	—	2	1	no	—
142	M₁₆×C₂₉	—	2	1	no	—
143	M₁₆×C₂₉	#41	1	2	yes	—
144	C₂×C₈×C₂₉	—	2	1	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	—	2	1	no	—
150	C₂×C₈×C₂₉	—	2	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	2	no	—
154	C₄⋊C₄×C₂₉	—	2	2	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	—	2	1	no	—
159	C₄⋊C₄×C₂₉	—	4	1	no	—
160	C₄⋊C₄×C₂₉	—	4	1	no	—
161	C₄⋊C₄×C₂₉	—	4	1	no	—
162	C₄⋊C₄×C₂₉	—	4	1	no	—
163	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
164	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
165	C₂²⋊C₄×C₂₉	—	2	2	no	—
166	C₂²⋊C₄×C₂₉	—	4	1	no	—
167	C₂²⋊C₄×C₂₉	—	4	1	no	—
168	C₄²×C₂₉	—	2	2	no	—
169	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
173	#25313	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂³×C₂₉	—	2	2	no	—
175	C₂³×C₂₉	—	4	1	no	—
176	C₂³×C₂₉	—	4	1	no	—
177	C₂³×C₂₉	—	8	1	no	—
178	C₂³×C₂₉	—	8	1	no	—
179	C₂³×C₂₉	C₂×#41	1	1	yes	characteristic
180	Q₈×C₂₉	—	4	2	no	—
181	Q₈×C₂₉	—	4	2	no	—
182	Q₈×C₂₉	—	4	2	no	—
183	Q₈×C₂₉	—	4	2	no	—
184	Q₈×C₂₉	—	4	2	no	—
185	Q₈×C₂₉	—	8	1	no	—
186	D₄×C₂₉	—	2	2	no	—
187	D₄×C₂₉	—	2	2	no	—
188	D₄×C₂₉	—	4	1	no	—
189	D₄×C₂₉	—	4	1	no	—
190	C₂×C₄×C₂₉	—	2	2	no	—
191	C₂×C₄×C₂₉	—	2	2	no	—
192	C₂×C₄×C₂₉	—	2	2	no	—
193	C₂×C₄×C₂₉	—	4	1	no	—
194	C₂×C₄×C₂₉	—	4	1	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	—	8	2	no	—
199	C₂×C₄×C₂₉	—	8	2	no	—
200	C₂×C₄×C₂₉	—	8	1	no	—
201	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
202	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
203	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
204	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
205	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
211	C₈×C₂₉	—	2	2	no	—
212	C₈×C₂₉	—	2	2	no	—
213	C₈×C₂₉	—	2	2	no	—
214	C₈×C₂₉	—	4	1	no	—
215	C₈×C₂₉	—	4	1	no	—
216	C₈×C₂₉	—	4	1	no	—
217	C₈×C₂₉	—	4	2	no	—
218	#3139	C₂×C₂₉	1	1	yes	characteristic, complemented
219	#3077	C₂×C₂₉	1	1	yes	characteristic
220	C₂×#461	C₂×C₂₉	1	1	yes	characteristic
221	#2962	C₂×C₂₉	1	1	yes	characteristic, complemented
222	#2064	C₂×C₂₉	1	2	yes	complemented
223	#2046	C₂×C₂₉	1	2	yes	—
224	#1977	C₂×C₂₉	1	2	yes	—
225	#1966	C₂×C₂₉	1	1	yes	characteristic, complemented
226	#1950	C₂×C₂₉	1	1	yes	characteristic, complemented
227	#1930	C₂×C₂₉	1	2	yes	complemented
228	C₄×#100	C₂×C₂₉	1	1	yes	characteristic
229	C₂²×C₂₉	—	2	1	no	—
230	C₂²×C₂₉	—	2	1	no	—
231	C₂²×C₂₉	—	4	2	no	—
232	C₂²×C₂₉	—	8	2	no	—
233	C₂²×C₂₉	—	8	2	no	—
234	C₂²×C₂₉	—	8	1	no	—
235	C₂²×C₂₉	—	8	1	no	—
236	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
237	C₂²×C₂₉	#529	1	1	yes	characteristic
238	C₂²×C₂₉	#542	1	1	yes	characteristic
239	C₄×C₂₉	—	2	1	no	—
240	C₄×C₂₉	—	2	1	no	—
241	C₄×C₂₉	—	2	1	no	—
242	C₄×C₂₉	—	4	2	no	—
243	C₄×C₂₉	—	4	2	no	—
244	C₄×C₂₉	—	8	2	no	—
245	C₄×C₂₉	—	8	1	no	—
246	C₄×C₂₉	#471	1	2	yes	—
247	C₄×C₂₉	#546	1	1	yes	characteristic
248	C₄×C₂₉	#548	1	1	yes	characteristic
249	C₄×C₂₉	#548	1	1	yes	characteristic
250	C₄×C₂₉	#550	1	1	yes	characteristic
251	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	—
252	#533	C₂²×C₂₉	1	1	yes	characteristic
253	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
255	#491	—	2	2	no	—
256	#487	—	2	1	no	—
257	#487	—	2	1	no	—
258	#478	—	2	2	no	—
259	#476	—	2	1	no	—
260	#474	—	2	1	no	—
261	#461	—	2	1	no	—
262	#461	—	2	2	no	—
263	#461	—	2	1	no	—
264	#446	—	2	2	no	—
265	#446	—	2	1	no	—
266	C₈×Q₈	—	2	1	no	—
267	C₂×#108	C₂²×C₂₉	1	2	yes	—
268	#428	C₂²×C₂₉	1	2	yes	—
269	#424	C₂²×C₂₉	1	2	yes	—
270	#423	C₂²×C₂₉	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
272	#419	C₂²×C₂₉	1	2	yes	—
273	#419	C₂²×C₂₉	1	2	yes	—
274	#418	C₂²×C₂₉	1	2	yes	—
275	C₂×#103	C₂²×C₂₉	1	2	yes	—
276	C₂×#101	C₂²×C₂₉	1	2	yes	—
277	C₂×#101	C₂²×C₂₉	1	2	yes	—
278	C₂×#100	C₂²×C₂₉	1	1	yes	characteristic
279	C₂×#100	C₂²×C₂₉	1	1	yes	characteristic
280	#405	C₂²×C₂₉	1	2	yes	—
281	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
282	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
283	#343	C₂²×C₂₉	1	1	yes	characteristic
284	#343	C₂²×C₂₉	1	1	yes	characteristic
285	#341	C₂²×C₂₉	1	2	yes	—
286	C₂×C₂₉	—	2	1	no	—
287	C₂×C₂₉	—	2	1	no	—
288	C₂×C₂₉	—	8	2	no	—
289	C₂×C₂₉	#2426	1	1	yes	characteristic
290	C₂×C₂₉	C₂×#471	1	1	yes	characteristic
291	C₂×C₂₉	#3069	1	1	yes	characteristic
292	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
293	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
294	C₂³×C₄	—	2	1	no	—
295	C₂×SD₁₆	—	2	4	no	—
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×SD₁₆	—	2	2	no	—
298	C₂×SD₁₆	—	4	2	no	—
299	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
300	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
301	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
302	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
303	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
305	C₄⋊Q₈	—	2	1	no	—
306	C₄⋊Q₈	—	2	1	no	—
307	C₄⋊Q₈	—	2	1	no	—
308	C₄⋊Q₈	—	2	1	no	—
309	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
310	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
311	#125	D₄×C₂₉	1	2	yes	—
312	C₂²⋊Q₈	—	2	1	no	—
313	C₂²⋊Q₈	—	2	1	no	—
314	C₄×Q₈	—	2	1	no	—
315	C₄×Q₈	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	—	2	1	no	—
319	C₄×D₄	—	2	1	no	—
320	#117	C₂³×C₂₉	1	2	yes	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
326	#108	—	4	2	no	—
327	#107	—	2	2	no	—
328	#106	—	2	2	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	D₄×C₂₉	1	1	yes	characteristic
334	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
335	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
336	#103	—	2	2	no	—
337	#103	—	2	2	no	—
338	#103	—	2	2	no	—
339	#103	—	2	2	no	—
340	#103	—	2	2	no	—
341	#103	—	2	2	no	—
342	#102	—	2	2	no	—
343	#102	—	2	2	no	—
344	#101	—	2	4	no	—
345	#101	—	4	2	no	—
346	#100	—	2	2	no	—
347	#100	—	2	2	no	—
348	#97	—	2	2	no	—
349	#97	—	2	1	no	—
350	#97	—	2	1	no	—
351	C₄×C₈	—	2	2	no	—
352	C₄×C₈	—	2	1	no	—
353	C₄×C₈	—	2	1	no	—
354	C₂₉	#25313	1	1	yes	characteristic, direct product factor, Sylow
355	C₂⁴	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	#41×C₂₉	1	2	yes	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	4	1	no	—
373	C₂²×C₄	—	4	1	no	—
374	C₂²×C₄	—	8	2	no	—
375	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
376	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
377	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
378	SD₁₆	—	4	4	no	—
379	SD₁₆	—	4	4	no	—
380	M₁₆	—	2	1	no	—
381	M₁₆	—	2	1	no	—
382	M₁₆	—	2	1	no	—
383	M₁₆	—	2	1	no	—
384	M₁₆	—	2	2	no	—
385	M₁₆	—	2	1	no	—
386	M₁₆	—	2	2	no	—
387	M₁₆	—	2	1	no	—
388	M₁₆	—	2	1	no	—
389	M₁₆	#41×C₂₉	1	2	yes	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
398	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	4	1	no	—
406	C₄⋊C₄	—	4	1	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
410	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	4	1	no	—
413	C₂²⋊C₄	—	4	1	no	—
414	C₄²	—	2	2	no	—
415	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
416	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
417	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
418	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
419	C₂³	—	2	2	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	8	1	no	—
423	C₂³	—	8	1	no	—
424	C₂³	C₂×#41×C₂₉	1	1	yes	characteristic
425	Q₈	—	4	2	no	—
426	Q₈	—	4	2	no	—
427	Q₈	—	4	2	no	—
428	Q₈	—	4	2	no	—
429	Q₈	—	4	2	no	—
430	Q₈	—	8	1	no	—
431	D₄	—	2	2	no	—
432	D₄	—	2	2	no	—
433	D₄	—	4	1	no	—
434	D₄	—	4	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	8	2	no	—
444	C₂×C₄	—	8	2	no	—
445	C₂×C₄	—	8	1	no	—
446	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
447	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
448	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
449	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
450	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
454	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
455	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
456	C₈	—	2	2	no	—
457	C₈	—	2	2	no	—
458	C₈	—	2	2	no	—
459	C₈	—	4	1	no	—
460	C₈	—	4	1	no	—
461	C₈	—	4	1	no	—
462	C₈	—	4	2	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	8	2	no	—
468	C₂²	—	8	1	no	—
469	C₂²	—	8	1	no	—
470	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
471	C₂²	C₂₉×#529	1	1	yes	characteristic
472	C₂²	C₂₉×#542	1	1	yes	characteristic
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	8	2	no	—
479	C₄	—	8	1	no	—
480	C₄	C₂₉×#471	1	2	yes	—
481	C₄	C₂₉×#546	1	1	yes	characteristic
482	C₄	C₂₉×#548	1	1	yes	characteristic
483	C₄	C₂₉×#548	1	1	yes	characteristic
484	C₄	C₂₉×#550	1	1	yes	characteristic
485	C₂	—	2	1	no	—
486	C₂	—	2	1	no	—
487	C₂	—	8	2	no	—
488	C₂	C₂₉×#2426	1	1	yes	characteristic
489	C₂	C₂×C₂₉×#471	1	1	yes	characteristic
490	C₂	C₂₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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×#3139	C₂	semidirect
4. C₂₉×#2962	C₂	semidirect
5. C₂₉×#2064	C₂	semidirect
8. C₂₉×#1966	C₂	semidirect
9. C₂₉×#1950	C₂	semidirect
10. C₂₉×#1930	C₂	semidirect
173. #25313	C₂₉	direct (N × H)
218. #3139	C₂×C₂₉	semidirect
221. #2962	C₂×C₂₉	semidirect
222. #2064	C₂×C₂₉	semidirect
225. #1966	C₂×C₂₉	semidirect
226. #1950	C₂×C₂₉	semidirect
227. #1930	C₂×C₂₉	semidirect
354. C₂₉	#25313	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×#3139	2
C₂₉×#3077	2
C₂×C₂₉×#461	2
C₂₉×#2962	2
C₂₉×#2064	2
C₂₉×#2046	2
C₂₉×#1977	2
C₂₉×#1966	2
C₂₉×#1950	2
C₂₉×#1930	2
C₄×C₂₉×#100	2
#25313	29

Subgroups — C29×#25313 #20320213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#25313 #20320213