Subgroups — C₂₉×#19948 #20314848

Order 7424.

586 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3398	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3364	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3353	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#3302	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1707	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1694	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1689	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1680	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1679	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1654	C₂	1	1	yes	maximal, characteristic
11	C₂₉×#1653	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1652	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1652	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1590	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#557	C₂²	1	1	yes	characteristic
17	C₂₉×#556	C₂²	1	1	yes	characteristic
18	C₂₉×#556	C₂²	1	1	yes	characteristic
19	C₂₉×#547	C₂²	1	1	yes	characteristic
20	C₂₉×#500	C₂²	1	1	yes	characteristic
21	C₂₉×#498	C₂²	1	1	yes	characteristic
22	C₂₉×#498	C₂²	1	1	yes	characteristic
23	C₂₉×#497	—	2	1	no	—
24	C₂₉×#494	C₂²	1	1	yes	characteristic
25	C₂₉×#488	—	2	1	no	—
26	C₂₉×#487	C₂²	1	1	yes	characteristic
27	C₂₉×#487	C₂²	1	1	yes	characteristic
28	C₂₉×#485	—	2	1	no	—
29	C₂₉×#484	—	2	1	no	—
30	C₂₉×#482	—	2	1	no	—
31	C₂₉×#479	—	2	1	no	—
32	C₂₉×#475	C₂²	1	1	yes	characteristic
33	C₂₉×#474	C₂²	1	1	yes	characteristic
34	C₂₉×#474	C₂²	1	1	yes	characteristic
35	C₂₉×#474	C₂²	1	1	yes	characteristic
36	C₂₉×#468	—	2	1	no	—
37	C₂₉×#467	—	2	1	no	—
38	C₂₉×#464	—	2	1	no	—
39	C₂₉×#464	—	2	1	no	—
40	C₂₉×#462	—	2	1	no	—
41	C₂₉×#462	C₂²	1	1	yes	characteristic
42	C₂₉×#462	C₂²	1	1	yes	characteristic
43	C₂₉×#462	C₂²	1	1	yes	characteristic
44	C₂₉×#461	C₂²	1	1	yes	characteristic
45	C₂₉×#452	—	2	1	no	—
46	C₂₉×#446	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
48	C₂₉×#441	—	2	1	no	—
49	C₄×Q₁₆×C₂₉	—	2	1	no	—
50	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
51	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
52	C₂₉×#436	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
54	C₂₉×#428	—	2	1	no	—
55	C₂₉×#416	—	2	1	no	—
56	C₂₉×#334	C₂²	1	1	yes	characteristic
57	C₂₉×#334	C₂²	1	1	yes	characteristic
58	C₂₉×#332	C₂²	1	1	yes	characteristic
59	C₂₉×#332	C₂²	1	1	yes	characteristic
60	C₂₉×#332	C₂²	1	1	yes	characteristic
61	C₂₉×#332	C₂²	1	1	yes	characteristic
62	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₈²×C₂₉	C₂²	1	1	yes	characteristic
67	C₂×#41×C₂₉	—	2	1	no	—
68	C₂×Q₁₆×C₂₉	—	2	1	no	—
69	C₂×Q₁₆×C₂₉	—	2	1	no	—
70	C₂×Q₁₆×C₂₉	—	2	1	no	—
71	C₂×Q₁₆×C₂₉	—	2	1	no	—
72	C₂×Q₁₆×C₂₉	—	2	1	no	—
73	C₂×SD₁₆×C₂₉	—	2	1	no	—
74	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
75	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
76	C₂×M₁₆×C₂₉	—	2	1	no	—
77	C₂²×C₈×C₂₉	—	2	1	no	—
78	C₂₉×C₄⋊Q₈	—	2	1	no	—
79	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₂₉×#126	—	4	1	no	—
84	C₂₉×#126	—	4	1	no	—
85	C₂₉×#125	—	2	1	no	—
86	C₂₉×#125	—	4	1	no	—
87	C₂₉×#124	—	2	1	no	—
88	C₂₉×#124	—	2	1	no	—
89	C₂₉×#123	—	4	1	no	—
90	C₂₉×C₂²⋊Q₈	—	2	1	no	—
91	C₂₉×C₂²⋊Q₈	—	2	1	no	—
92	C₂₉×C₂²⋊Q₈	—	2	1	no	—
93	C₂₉×#121	—	2	1	no	—
94	C₄×Q₈×C₂₉	—	2	1	no	—
95	C₄×Q₈×C₂₉	—	2	1	no	—
96	C₄×Q₈×C₂₉	—	2	1	no	—
97	C₄×Q₈×C₂₉	—	2	1	no	—
98	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
99	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
102	C₂₉×#117	—	2	1	no	—
103	C₂₉×#117	—	2	1	no	—
104	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
105	C₂₉×#107	—	2	1	no	—
106	C₂₉×#107	—	2	1	no	—
107	C₂₉×#107	—	2	1	no	—
108	C₂₉×#107	—	2	1	no	—
109	C₂₉×#107	—	2	1	no	—
110	C₂₉×#106	—	2	1	no	—
111	C₂₉×#106	—	4	1	no	—
112	C₂₉×#106	—	4	1	no	—
113	C₂₉×#106	D₄	1	1	yes	characteristic
114	C₂₉×#106	D₄	1	1	yes	characteristic
115	C₂₉×C₄⋊C₈	—	2	1	no	—
116	C₂₉×C₄⋊C₈	—	2	1	no	—
117	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₂₉×#103	—	2	1	no	—
122	C₂₉×#103	—	2	1	no	—
123	C₂₉×#103	—	2	1	no	—
124	C₂₉×#103	—	2	1	no	—
125	C₂₉×#103	—	2	1	no	—
126	C₂₉×#103	—	2	1	no	—
127	C₂₉×#103	—	2	1	no	—
128	C₂₉×#103	—	2	1	no	—
129	C₂₉×#103	—	2	1	no	—
130	C₂₉×#103	D₄	1	1	yes	characteristic
131	C₂₉×#103	D₄	1	1	yes	characteristic
132	C₂₉×#102	—	2	1	no	—
133	C₂₉×#102	—	2	1	no	—
134	C₂₉×#102	—	2	1	no	—
135	C₂₉×#102	D₄	1	1	yes	characteristic
136	C₂₉×#102	D₄	1	1	yes	characteristic
137	C₂₉×C₂²⋊C₈	—	2	1	no	—
138	C₂₉×C₂²⋊C₈	—	2	1	no	—
139	C₂₉×#97	—	2	1	no	—
140	C₄×C₈×C₂₉	—	2	1	no	—
141	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
144	#41×C₂₉	—	4	2	no	—
145	#41×C₂₉	—	8	1	no	—
146	C₂×Q₈×C₂₉	—	2	1	no	—
147	C₂×Q₈×C₂₉	—	2	1	no	—
148	C₂×Q₈×C₂₉	—	2	1	no	—
149	C₂×Q₈×C₂₉	—	2	1	no	—
150	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
151	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₂₉	—	4	1	no	—
153	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₂₉	—	2	1	no	—
156	C₂²×C₄×C₂₉	—	2	1	no	—
157	C₂²×C₄×C₂₉	—	4	1	no	—
158	Q₁₆×C₂₉	—	4	2	no	—
159	Q₁₆×C₂₉	—	4	2	no	—
160	Q₁₆×C₂₉	—	8	1	no	—
161	Q₁₆×C₂₉	—	8	1	no	—
162	Q₁₆×C₂₉	—	8	1	no	—
163	SD₁₆×C₂₉	—	2	2	no	—
164	SD₁₆×C₂₉	—	4	1	no	—
165	SD₁₆×C₂₉	—	8	1	no	—
166	M₁₆×C₂₉	—	4	2	no	—
167	C₂×C₈×C₂₉	—	2	1	no	—
168	C₂×C₈×C₂₉	—	2	1	no	—
169	C₂×C₈×C₂₉	—	2	1	no	—
170	C₂×C₈×C₂₉	—	2	1	no	—
171	C₂×C₈×C₂₉	—	2	1	no	—
172	C₂×C₈×C₂₉	—	8	1	no	—
173	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₂₉	C₂×D₄	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	C₄⋊C₄×C₂₉	—	2	1	no	—
178	C₄⋊C₄×C₂₉	—	2	1	no	—
179	C₄⋊C₄×C₂₉	—	2	1	no	—
180	C₄⋊C₄×C₂₉	—	2	1	no	—
181	C₄⋊C₄×C₂₉	—	2	1	no	—
182	C₄⋊C₄×C₂₉	—	2	1	no	—
183	C₄⋊C₄×C₂₉	—	2	1	no	—
184	C₄⋊C₄×C₂₉	—	2	1	no	—
185	C₄⋊C₄×C₂₉	—	2	1	no	—
186	C₄⋊C₄×C₂₉	—	2	1	no	—
187	C₄⋊C₄×C₂₉	—	4	1	no	—
188	C₄⋊C₄×C₂₉	—	4	1	no	—
189	C₄⋊C₄×C₂₉	—	4	1	no	—
190	C₄⋊C₄×C₂₉	—	4	1	no	—
191	C₄⋊C₄×C₂₉	—	4	1	no	—
192	C₄⋊C₄×C₂₉	—	4	1	no	—
193	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
194	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
195	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
196	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
197	C₂²⋊C₄×C₂₉	—	2	1	no	—
198	C₂²⋊C₄×C₂₉	—	2	1	no	—
199	C₂²⋊C₄×C₂₉	—	4	1	no	—
200	C₂²⋊C₄×C₂₉	—	4	1	no	—
201	C₂²⋊C₄×C₂₉	—	4	1	no	—
202	C₂²⋊C₄×C₂₉	—	4	1	no	—
203	C₂²⋊C₄×C₂₉	—	4	1	no	—
204	C₄²×C₂₉	—	2	1	no	—
205	C₄²×C₂₉	—	2	1	no	—
206	C₄²×C₂₉	—	4	1	no	—
207	C₄²×C₂₉	—	4	1	no	—
208	C₄²×C₂₉	—	4	1	no	—
209	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
210	#19948	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂³×C₂₉	—	2	1	no	—
212	C₂³×C₂₉	—	2	1	no	—
213	Q₈×C₂₉	—	2	1	no	—
214	Q₈×C₂₉	—	2	1	no	—
215	Q₈×C₂₉	—	2	1	no	—
216	Q₈×C₂₉	—	2	1	no	—
217	Q₈×C₂₉	—	4	1	no	—
218	Q₈×C₂₉	—	4	1	no	—
219	Q₈×C₂₉	—	4	1	no	—
220	Q₈×C₂₉	—	4	1	no	—
221	Q₈×C₂₉	—	4	1	no	—
222	Q₈×C₂₉	—	4	1	no	—
223	Q₈×C₂₉	—	4	1	no	—
224	Q₈×C₂₉	—	4	1	no	—
225	D₄×C₂₉	—	2	1	no	—
226	D₄×C₂₉	—	2	1	no	—
227	D₄×C₂₉	—	2	1	no	—
228	D₄×C₂₉	—	2	1	no	—
229	D₄×C₂₉	—	8	2	no	—
230	C₂×C₄×C₂₉	—	2	1	no	—
231	C₂×C₄×C₂₉	—	2	1	no	—
232	C₂×C₄×C₂₉	—	2	1	no	—
233	C₂×C₄×C₂₉	—	2	1	no	—
234	C₂×C₄×C₂₉	—	2	1	no	—
235	C₂×C₄×C₂₉	—	2	1	no	—
236	C₂×C₄×C₂₉	—	4	1	no	—
237	C₂×C₄×C₂₉	—	4	1	no	—
238	C₂×C₄×C₂₉	—	4	1	no	—
239	C₂×C₄×C₂₉	—	4	1	no	—
240	C₂×C₄×C₂₉	—	4	1	no	—
241	C₂×C₄×C₂₉	—	4	1	no	—
242	C₂×C₄×C₂₉	—	4	1	no	—
243	C₂×C₄×C₂₉	—	4	1	no	—
244	C₂×C₄×C₂₉	—	8	2	no	—
245	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
248	C₈×C₂₉	—	2	2	no	—
249	C₈×C₂₉	—	2	1	no	—
250	C₈×C₂₉	—	2	1	no	—
251	C₈×C₂₉	—	2	1	no	—
252	C₈×C₂₉	—	4	1	no	—
253	C₈×C₂₉	—	4	1	no	—
254	C₈×C₂₉	—	4	1	no	—
255	C₈×C₂₉	—	4	1	no	—
256	C₈×C₂₉	#135	1	2	yes	—
257	#3398	C₂×C₂₉	1	1	yes	characteristic, complemented
258	#3364	C₂×C₂₉	1	1	yes	characteristic, complemented
259	#3353	C₂×C₂₉	1	1	yes	characteristic
260	#3302	C₂×C₂₉	1	1	yes	characteristic
261	#1707	C₂×C₂₉	1	1	yes	characteristic, complemented
262	#1694	C₂×C₂₉	1	1	yes	characteristic, complemented
263	#1689	C₂×C₂₉	1	1	yes	characteristic, complemented
264	#1680	C₂×C₂₉	1	1	yes	characteristic, complemented
265	#1679	C₂×C₂₉	1	1	yes	characteristic, complemented
266	#1654	C₂×C₂₉	1	1	yes	characteristic
267	#1653	C₂×C₂₉	1	1	yes	characteristic, complemented
268	#1652	C₂×C₂₉	1	1	yes	characteristic, complemented
269	#1652	C₂×C₂₉	1	1	yes	characteristic, complemented
270	#1590	C₂×C₂₉	1	1	yes	characteristic, complemented
271	C₈×SD₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
272	C₂²×C₂₉	—	4	1	no	—
273	C₂²×C₂₉	—	4	1	no	—
274	C₂²×C₂₉	—	4	1	no	—
275	C₂²×C₂₉	—	4	1	no	—
276	C₂²×C₂₉	—	4	1	no	—
277	C₂²×C₂₉	—	4	1	no	—
278	C₂²×C₂₉	D₄²	1	1	yes	characteristic
279	C₄×C₂₉	—	2	1	no	—
280	C₄×C₂₉	—	4	1	no	—
281	C₄×C₂₉	—	4	1	no	—
282	C₄×C₂₉	—	4	1	no	—
283	C₄×C₂₉	—	4	1	no	—
284	C₄×C₂₉	—	4	1	no	—
285	C₄×C₂₉	—	4	1	no	—
286	C₄×C₂₉	—	8	1	no	—
287	C₄×C₂₉	—	8	1	no	—
288	C₄×C₂₉	—	8	1	no	—
289	C₄×C₂₉	—	8	1	no	—
290	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
291	C₄×C₂₉	#575	1	1	yes	characteristic
292	C₄×C₂₉	#577	1	1	yes	characteristic
293	C₄×C₂₉	#577	1	1	yes	characteristic
294	#557	C₂²×C₂₉	1	1	yes	characteristic
295	#556	C₂²×C₂₉	1	1	yes	characteristic
296	#556	C₂²×C₂₉	1	1	yes	characteristic
297	#547	C₂²×C₂₉	1	1	yes	characteristic
298	#500	C₂²×C₂₉	1	1	yes	characteristic
299	#498	C₂²×C₂₉	1	1	yes	characteristic
300	#498	C₂²×C₂₉	1	1	yes	characteristic
301	#497	—	2	1	no	—
302	#494	C₂²×C₂₉	1	1	yes	characteristic
303	#488	—	2	1	no	—
304	#487	C₂²×C₂₉	1	1	yes	characteristic
305	#487	C₂²×C₂₉	1	1	yes	characteristic
306	#485	—	2	1	no	—
307	#484	—	2	1	no	—
308	#482	—	2	1	no	—
309	#479	—	2	1	no	—
310	#475	C₂²×C₂₉	1	1	yes	characteristic
311	#474	C₂²×C₂₉	1	1	yes	characteristic
312	#474	C₂²×C₂₉	1	1	yes	characteristic
313	#474	C₂²×C₂₉	1	1	yes	characteristic
314	#468	—	2	1	no	—
315	#467	—	2	1	no	—
316	#464	—	2	1	no	—
317	#464	—	2	1	no	—
318	#462	—	2	1	no	—
319	#462	C₂²×C₂₉	1	1	yes	characteristic
320	#462	C₂²×C₂₉	1	1	yes	characteristic
321	#462	C₂²×C₂₉	1	1	yes	characteristic
322	#461	C₂²×C₂₉	1	1	yes	characteristic
323	#452	—	2	1	no	—
324	#446	C₂²×C₂₉	1	1	yes	characteristic
325	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
326	#441	—	2	1	no	—
327	C₄×Q₁₆	—	2	1	no	—
328	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
329	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
330	#436	C₂²×C₂₉	1	1	yes	characteristic
331	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
332	#428	—	2	1	no	—
333	#416	—	2	1	no	—
334	#334	C₂²×C₂₉	1	1	yes	characteristic
335	#334	C₂²×C₂₉	1	1	yes	characteristic
336	#332	C₂²×C₂₉	1	1	yes	characteristic
337	#332	C₂²×C₂₉	1	1	yes	characteristic
338	#332	C₂²×C₂₉	1	1	yes	characteristic
339	#332	C₂²×C₂₉	1	1	yes	characteristic
340	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
341	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
342	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
343	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
344	C₈²	C₂²×C₂₉	1	1	yes	characteristic
345	C₂×C₂₉	—	8	1	no	—
346	C₂×C₂₉	—	8	1	no	—
347	C₂×C₂₉	#3275	1	1	yes	characteristic
348	C₂×C₂₉	#3284	1	1	yes	characteristic
349	C₂×C₂₉	#3293	1	1	yes	characteristic
350	C₂×#41	—	2	1	no	—
351	C₂×Q₁₆	—	2	1	no	—
352	C₂×Q₁₆	—	2	1	no	—
353	C₂×Q₁₆	—	2	1	no	—
354	C₂×Q₁₆	—	2	1	no	—
355	C₂×Q₁₆	—	2	1	no	—
356	C₂×SD₁₆	—	2	1	no	—
357	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
358	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
359	C₂×M₁₆	—	2	1	no	—
360	C₂²×C₈	—	2	1	no	—
361	C₄⋊Q₈	—	2	1	no	—
362	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
363	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
364	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
365	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
366	#126	—	4	1	no	—
367	#126	—	4	1	no	—
368	#125	—	2	1	no	—
369	#125	—	4	1	no	—
370	#124	—	2	1	no	—
371	#124	—	2	1	no	—
372	#123	—	4	1	no	—
373	C₂²⋊Q₈	—	2	1	no	—
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	#121	—	2	1	no	—
377	C₄×Q₈	—	2	1	no	—
378	C₄×Q₈	—	2	1	no	—
379	C₄×Q₈	—	2	1	no	—
380	C₄×Q₈	—	2	1	no	—
381	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
382	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
383	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
384	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
385	#117	—	2	1	no	—
386	#117	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	#107	—	2	1	no	—
389	#107	—	2	1	no	—
390	#107	—	2	1	no	—
391	#107	—	2	1	no	—
392	#107	—	2	1	no	—
393	#106	—	2	1	no	—
394	#106	—	4	1	no	—
395	#106	—	4	1	no	—
396	#106	D₄×C₂₉	1	1	yes	characteristic
397	#106	D₄×C₂₉	1	1	yes	characteristic
398	C₄⋊C₈	—	2	1	no	—
399	C₄⋊C₈	—	2	1	no	—
400	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
401	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
402	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
403	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
404	#103	—	2	1	no	—
405	#103	—	2	1	no	—
406	#103	—	2	1	no	—
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#103	—	2	1	no	—
410	#103	—	2	1	no	—
411	#103	—	2	1	no	—
412	#103	—	2	1	no	—
413	#103	D₄×C₂₉	1	1	yes	characteristic
414	#103	D₄×C₂₉	1	1	yes	characteristic
415	#102	—	2	1	no	—
416	#102	—	2	1	no	—
417	#102	—	2	1	no	—
418	#102	D₄×C₂₉	1	1	yes	characteristic
419	#102	D₄×C₂₉	1	1	yes	characteristic
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	—	2	1	no	—
422	#97	—	2	1	no	—
423	C₄×C₈	—	2	1	no	—
424	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
425	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
426	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
427	C₂₉	#19948	1	1	yes	characteristic, direct product factor, Sylow
428	#41	—	4	2	no	—
429	#41	—	8	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
435	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
436	C₂×D₄	—	4	1	no	—
437	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
438	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	4	1	no	—
442	Q₁₆	—	4	2	no	—
443	Q₁₆	—	4	2	no	—
444	Q₁₆	—	8	1	no	—
445	Q₁₆	—	8	1	no	—
446	Q₁₆	—	8	1	no	—
447	SD₁₆	—	2	2	no	—
448	SD₁₆	—	4	1	no	—
449	SD₁₆	—	8	1	no	—
450	M₁₆	—	4	2	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	8	1	no	—
457	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
458	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
459	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
460	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	—	4	1	no	—
474	C₄⋊C₄	—	4	1	no	—
475	C₄⋊C₄	—	4	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
478	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
479	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
480	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	2	1	no	—
483	C₂²⋊C₄	—	4	1	no	—
484	C₂²⋊C₄	—	4	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	4	1	no	—
491	C₄²	—	4	1	no	—
492	C₄²	—	4	1	no	—
493	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	Q₈	—	2	1	no	—
497	Q₈	—	2	1	no	—
498	Q₈	—	2	1	no	—
499	Q₈	—	2	1	no	—
500	Q₈	—	4	1	no	—
501	Q₈	—	4	1	no	—
502	Q₈	—	4	1	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	4	1	no	—
507	Q₈	—	4	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	2	1	no	—
510	D₄	—	2	1	no	—
511	D₄	—	2	1	no	—
512	D₄	—	8	2	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	8	2	no	—
528	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
529	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
530	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
531	C₈	—	2	2	no	—
532	C₈	—	2	1	no	—
533	C₈	—	2	1	no	—
534	C₈	—	2	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	1	no	—
539	C₈	C₂₉×#135	1	2	yes	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	4	1	no	—
546	C₂²	D₄²×C₂₉	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	8	1	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
559	C₄	C₂₉×#575	1	1	yes	characteristic
560	C₄	C₂₉×#577	1	1	yes	characteristic
561	C₄	C₂₉×#577	1	1	yes	characteristic
562	C₂	—	8	1	no	—
563	C₂	—	8	1	no	—
564	C₂	C₂₉×#3275	1	1	yes	characteristic
565	C₂	C₂₉×#3284	1	1	yes	characteristic
566	C₂	C₂₉×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#547	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3398	C₂	semidirect
2. C₂₉×#3364	C₂	semidirect
5. C₂₉×#1707	C₂	semidirect
6. C₂₉×#1694	C₂	semidirect
7. C₂₉×#1689	C₂	semidirect
8. C₂₉×#1680	C₂	semidirect
9. C₂₉×#1679	C₂	semidirect
11. C₂₉×#1653	C₂	semidirect
12. C₂₉×#1652	C₂	semidirect
13. C₂₉×#1652	C₂	semidirect
14. C₂₉×#1590	C₂	semidirect
15. C₈×SD₁₆×C₂₉	C₂	semidirect
210. #19948	C₂₉	direct (N × H)
257. #3398	C₂×C₂₉	semidirect
258. #3364	C₂×C₂₉	semidirect
261. #1707	C₂×C₂₉	semidirect
262. #1694	C₂×C₂₉	semidirect
263. #1689	C₂×C₂₉	semidirect
264. #1680	C₂×C₂₉	semidirect
265. #1679	C₂×C₂₉	semidirect
267. #1653	C₂×C₂₉	semidirect
268. #1652	C₂×C₂₉	semidirect
269. #1652	C₂×C₂₉	semidirect
270. #1590	C₂×C₂₉	semidirect
271. C₈×SD₁₆	C₂×C₂₉	semidirect
427. C₂₉	#19948	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×#3398	2
C₂₉×#3364	2
C₂₉×#3353	2
C₂₉×#3302	2
C₂₉×#1707	2
C₂₉×#1694	2
C₂₉×#1689	2
C₂₉×#1680	2
C₂₉×#1679	2
C₂₉×#1654	2
C₂₉×#1653	2
C₂₉×#1652	2
C₂₉×#1590	2
C₈×SD₁₆×C₂₉	2
#19948	29

Subgroups — C29×#19948 #20314848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19948 #20314848