Subgroups — C₂₉×#19827 #20314727

Order 7424.

668 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3362	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3362	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3332	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3284	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1717	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1697	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1682	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1677	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1666	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1645	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1635	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1621	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1621	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1583	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×#135	—	2	1	no	—
17	Q₈²×C₂₉	C₂²	1	1	yes	characteristic
18	C₂₉×#550	C₂²	1	1	yes	characteristic
19	C₂₉×#550	C₂²	1	1	yes	characteristic
20	C₂₉×#547	C₂²	1	1	yes	characteristic
21	C₂₉×#493	C₂²	1	1	yes	characteristic
22	C₂₉×#492	C₂²	1	1	yes	characteristic
23	C₂₉×#487	C₂²	1	1	yes	characteristic
24	C₂₉×#486	—	2	1	no	—
25	C₂₉×#486	—	2	1	no	—
26	C₂₉×#486	C₂²	1	1	yes	characteristic
27	C₂₉×#486	C₂²	1	1	yes	characteristic
28	C₂₉×#486	C₂²	1	1	yes	characteristic
29	C₂₉×#481	—	2	1	no	—
30	C₂₉×#476	—	2	1	no	—
31	C₂₉×#476	—	2	1	no	—
32	C₂₉×#476	C₂²	1	1	yes	characteristic
33	C₂₉×#476	C₂²	1	1	yes	characteristic
34	C₂₉×#475	C₂²	1	1	yes	characteristic
35	C₂₉×#469	—	2	1	no	—
36	C₂₉×#465	—	2	1	no	—
37	C₂₉×#462	C₂²	1	1	yes	characteristic
38	C₂₉×#460	—	2	1	no	—
39	C₂₉×#460	—	2	1	no	—
40	C₂₉×#460	C₂²	1	1	yes	characteristic
41	C₂₉×#460	C₂²	1	1	yes	characteristic
42	C₂₉×#459	C₂²	1	1	yes	characteristic
43	C₂₉×#459	C₂²	1	1	yes	characteristic
44	C₂₉×#452	—	2	1	no	—
45	C₂₉×#449	—	2	1	no	—
46	C₂₉×#449	—	2	1	no	—
47	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
49	C₄×SD₁₆×C₂₉	—	2	1	no	—
50	C₄×SD₁₆×C₂₉	—	2	1	no	—
51	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
52	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
53	C₂₉×#436	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
55	C₂₉×#417	—	2	1	no	—
56	C₂₉×#335	C₂²	1	1	yes	characteristic
57	C₂₉×#334	C₂²	1	1	yes	characteristic
58	C₂₉×#333	C₂²	1	1	yes	characteristic
59	C₂₉×#332	C₂²	1	1	yes	characteristic
60	C₂₉×#331	C₂²	1	1	yes	characteristic
61	C₂₉×#331	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	C₂₉×#322	C₂²	1	1	yes	characteristic
67	C₂×#41×C₂₉	—	2	1	no	—
68	C₂×#41×C₂₉	—	2	1	no	—
69	C₂×#41×C₂₉	—	2	1	no	—
70	C₂₉×#135	—	4	4	no	—
71	C₂×Q₁₆×C₂₉	—	2	1	no	—
72	C₂×SD₁₆×C₂₉	—	2	1	no	—
73	C₂×SD₁₆×C₂₉	—	2	1	no	—
74	C₂×SD₁₆×C₂₉	—	2	1	no	—
75	C₂×SD₁₆×C₂₉	—	2	1	no	—
76	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
77	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
78	C₂×D₈×C₂₉	—	2	1	no	—
79	C₂×D₈×C₂₉	—	2	1	no	—
80	C₂×D₈×C₂₉	—	4	1	no	—
81	C₂×M₁₆×C₂₉	—	2	1	no	—
82	C₂²×C₈×C₂₉	—	2	1	no	—
83	C₂₉×C₄⋊Q₈	—	2	1	no	—
84	C₂₉×C₄⋊Q₈	—	2	1	no	—
85	C₂₉×C₄⋊Q₈	—	4	1	no	—
86	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₂₉×#127	—	2	1	no	—
89	C₂₉×#127	—	2	1	no	—
90	C₂₉×#127	C₂³	1	1	yes	characteristic
91	C₂₉×#127	C₂³	1	1	yes	characteristic
92	C₂₉×#123	—	4	1	no	—
93	C₂₉×C₂²⋊Q₈	—	2	1	no	—
94	C₂₉×#121	—	2	1	no	—
95	C₂₉×#121	—	2	1	no	—
96	C₂₉×#121	—	2	1	no	—
97	C₂₉×#121	—	4	1	no	—
98	C₂₉×#121	—	4	1	no	—
99	C₄×Q₈×C₂₉	—	2	1	no	—
100	C₄×Q₈×C₂₉	—	2	1	no	—
101	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
102	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
103	C₄×D₄×C₂₉	—	2	1	no	—
104	C₄×D₄×C₂₉	—	2	1	no	—
105	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
106	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
108	C₂₉×#106	—	2	1	no	—
109	C₂₉×#106	—	2	1	no	—
110	C₂₉×#106	—	2	1	no	—
111	C₂₉×#106	D₄	1	1	yes	characteristic
112	C₂₉×#106	D₄	1	1	yes	characteristic
113	C₂₉×C₄⋊C₈	—	2	1	no	—
114	C₂₉×C₄⋊C₈	—	2	1	no	—
115	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₂₉×#103	—	2	1	no	—
120	C₂₉×#103	—	2	1	no	—
121	C₂₉×#103	—	4	1	no	—
122	C₂₉×#103	D₄	1	1	yes	characteristic
123	C₂₉×#103	D₄	1	1	yes	characteristic
124	C₂₉×#102	—	2	1	no	—
125	C₂₉×#102	—	2	1	no	—
126	C₂₉×#102	—	2	1	no	—
127	C₂₉×#102	—	2	1	no	—
128	C₂₉×#102	—	2	1	no	—
129	C₂₉×#102	—	2	1	no	—
130	C₂₉×#102	—	2	1	no	—
131	C₂₉×#102	—	2	1	no	—
132	C₂₉×#102	—	2	1	no	—
133	C₂₉×#102	—	2	1	no	—
134	C₂₉×#102	—	2	1	no	—
135	C₂₉×#102	—	2	1	no	—
136	C₂₉×#102	D₄	1	1	yes	characteristic
137	C₂₉×#102	D₄	1	1	yes	characteristic
138	C₂₉×C₂²⋊C₈	—	2	1	no	—
139	C₂₉×C₂²⋊C₈	—	2	1	no	—
140	C₄×C₈×C₂₉	—	2	1	no	—
141	C₄×C₈×C₂₉	—	2	1	no	—
142	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
145	#41×C₂₉	—	4	2	no	—
146	#41×C₂₉	—	4	2	no	—
147	#41×C₂₉	—	4	2	no	—
148	#41×C₂₉	—	8	1	no	—
149	#41×C₂₉	—	8	1	no	—
150	#41×C₂₉	—	8	1	no	—
151	C₂×Q₈×C₂₉	—	2	1	no	—
152	C₂×Q₈×C₂₉	—	2	1	no	—
153	C₂×Q₈×C₂₉	—	4	1	no	—
154	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
155	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
156	C₂×D₄×C₂₉	—	2	1	no	—
157	C₂×D₄×C₂₉	—	2	1	no	—
158	C₂×D₄×C₂₉	—	2	1	no	—
159	C₂×D₄×C₂₉	—	2	1	no	—
160	C₂×D₄×C₂₉	—	2	1	no	—
161	C₂×D₄×C₂₉	—	2	1	no	—
162	C₂×D₄×C₂₉	—	4	1	no	—
163	C₂×D₄×C₂₉	—	4	1	no	—
164	C₂×D₄×C₂₉	—	4	1	no	—
165	C₂×D₄×C₂₉	—	4	1	no	—
166	C₂×D₄×C₂₉	—	4	1	no	—
167	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
168	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₂₉	—	2	1	no	—
170	C₂²×C₄×C₂₉	—	2	1	no	—
171	C₂²×C₄×C₂₉	—	4	1	no	—
172	C₂²×C₄×C₂₉	—	4	1	no	—
173	C₂²×C₄×C₂₉	—	4	1	no	—
174	Q₁₆×C₂₉	—	4	2	no	—
175	SD₁₆×C₂₉	—	2	2	no	—
176	SD₁₆×C₂₉	—	2	2	no	—
177	SD₁₆×C₂₉	—	4	2	no	—
178	SD₁₆×C₂₉	—	4	2	no	—
179	SD₁₆×C₂₉	—	4	2	no	—
180	SD₁₆×C₂₉	—	8	1	no	—
181	D₈×C₂₉	—	4	2	no	—
182	D₈×C₂₉	—	8	1	no	—
183	D₈×C₂₉	—	8	2	no	—
184	M₁₆×C₂₉	—	8	1	no	—
185	C₂×C₈×C₂₉	—	2	1	no	—
186	C₂×C₈×C₂₉	—	2	1	no	—
187	C₂×C₈×C₂₉	—	2	1	no	—
188	C₂×C₈×C₂₉	—	2	1	no	—
189	C₂×C₈×C₂₉	—	2	1	no	—
190	C₂×C₈×C₂₉	—	4	2	no	—
191	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
192	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
193	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
194	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
195	C₄⋊C₄×C₂₉	—	2	1	no	—
196	C₄⋊C₄×C₂₉	—	2	1	no	—
197	C₄⋊C₄×C₂₉	—	2	1	no	—
198	C₄⋊C₄×C₂₉	—	2	1	no	—
199	C₄⋊C₄×C₂₉	—	2	1	no	—
200	C₄⋊C₄×C₂₉	—	2	1	no	—
201	C₄⋊C₄×C₂₉	—	4	1	no	—
202	C₄⋊C₄×C₂₉	—	4	1	no	—
203	C₄⋊C₄×C₂₉	—	4	1	no	—
204	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
205	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
206	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
207	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
208	C₂²⋊C₄×C₂₉	—	2	1	no	—
209	C₂²⋊C₄×C₂₉	—	2	1	no	—
210	C₂²⋊C₄×C₂₉	—	4	1	no	—
211	C₂²⋊C₄×C₂₉	—	4	1	no	—
212	C₂²⋊C₄×C₂₉	—	4	1	no	—
213	C₄²×C₂₉	—	2	1	no	—
214	C₄²×C₂₉	—	2	1	no	—
215	C₄²×C₂₉	—	4	1	no	—
216	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
217	#19827	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂³×C₂₉	—	2	1	no	—
219	C₂³×C₂₉	—	2	1	no	—
220	C₂³×C₂₉	—	4	1	no	—
221	C₂³×C₂₉	—	4	1	no	—
222	Q₈×C₂₉	—	2	1	no	—
223	Q₈×C₂₉	—	2	1	no	—
224	Q₈×C₂₉	—	4	1	no	—
225	Q₈×C₂₉	—	4	1	no	—
226	Q₈×C₂₉	—	8	1	no	—
227	Q₈×C₂₉	—	16	1	no	—
228	Q₈×C₂₉	#135	1	2	yes	complemented
229	Q₈×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
230	D₄×C₂₉	—	2	1	no	—
231	D₄×C₂₉	—	2	1	no	—
232	D₄×C₂₉	—	2	1	no	—
233	D₄×C₂₉	—	2	1	no	—
234	D₄×C₂₉	—	4	1	no	—
235	D₄×C₂₉	—	4	1	no	—
236	D₄×C₂₉	—	4	1	no	—
237	D₄×C₂₉	—	4	1	no	—
238	D₄×C₂₉	—	4	1	no	—
239	D₄×C₂₉	—	4	1	no	—
240	D₄×C₂₉	—	4	1	no	—
241	D₄×C₂₉	—	4	1	no	—
242	D₄×C₂₉	—	8	2	no	—
243	D₄×C₂₉	—	8	2	no	—
244	D₄×C₂₉	—	8	1	no	—
245	D₄×C₂₉	—	8	1	no	—
246	D₄×C₂₉	—	8	2	no	—
247	D₄×C₂₉	—	16	1	no	—
248	D₄×C₂₉	—	16	1	no	—
249	C₂×C₄×C₂₉	—	2	1	no	—
250	C₂×C₄×C₂₉	—	2	1	no	—
251	C₂×C₄×C₂₉	—	2	1	no	—
252	C₂×C₄×C₂₉	—	2	1	no	—
253	C₂×C₄×C₂₉	—	2	1	no	—
254	C₂×C₄×C₂₉	—	2	1	no	—
255	C₂×C₄×C₂₉	—	4	1	no	—
256	C₂×C₄×C₂₉	—	4	1	no	—
257	C₂×C₄×C₂₉	—	4	1	no	—
258	C₂×C₄×C₂₉	—	4	1	no	—
259	C₂×C₄×C₂₉	—	4	1	no	—
260	C₂×C₄×C₂₉	—	4	1	no	—
261	C₂×C₄×C₂₉	—	8	2	no	—
262	C₂×C₄×C₂₉	—	8	2	no	—
263	C₂×C₄×C₂₉	—	8	2	no	—
264	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
267	C₈×C₂₉	—	2	1	no	—
268	C₈×C₂₉	—	2	1	no	—
269	C₈×C₂₉	—	2	1	no	—
270	C₈×C₂₉	—	2	1	no	—
271	C₈×C₂₉	—	4	1	no	—
272	C₈×C₂₉	—	4	1	no	—
273	C₈×C₂₉	—	4	1	no	—
274	C₈×C₂₉	—	4	1	no	—
275	C₈×C₂₉	—	4	1	no	—
276	#3362	C₂×C₂₉	1	1	yes	characteristic, complemented
277	#3362	C₂×C₂₉	1	1	yes	characteristic, complemented
278	#3332	C₂×C₂₉	1	1	yes	characteristic, complemented
279	#3284	C₂×C₂₉	1	1	yes	characteristic, complemented
280	#1717	C₂×C₂₉	1	1	yes	characteristic, complemented
281	#1697	C₂×C₂₉	1	1	yes	characteristic, complemented
282	#1682	C₂×C₂₉	1	1	yes	characteristic, complemented
283	#1677	C₂×C₂₉	1	1	yes	characteristic, complemented
284	#1666	C₂×C₂₉	1	1	yes	characteristic, complemented
285	#1645	C₂×C₂₉	1	1	yes	characteristic, complemented
286	#1635	C₂×C₂₉	1	1	yes	characteristic, complemented
287	#1621	C₂×C₂₉	1	1	yes	characteristic, complemented
288	#1621	C₂×C₂₉	1	1	yes	characteristic, complemented
289	#1583	C₂×C₂₉	1	1	yes	characteristic, complemented
290	SD₁₆⋊C₈	C₂×C₂₉	1	1	yes	characteristic, complemented
291	C₂²×C₂₉	—	4	1	no	—
292	C₂²×C₂₉	—	4	1	no	—
293	C₂²×C₂₉	—	4	1	no	—
294	C₂²×C₂₉	—	4	1	no	—
295	C₂²×C₂₉	—	4	1	no	—
296	C₂²×C₂₉	—	4	1	no	—
297	C₂²×C₂₉	—	8	1	no	—
298	C₂²×C₂₉	—	8	1	no	—
299	C₂²×C₂₉	—	8	1	no	—
300	C₂²×C₂₉	—	8	1	no	—
301	C₂²×C₂₉	—	8	1	no	—
302	C₂²×C₂₉	—	8	1	no	—
303	C₂²×C₂₉	D₄²	1	1	yes	characteristic
304	C₄×C₂₉	—	2	2	no	—
305	C₄×C₂₉	—	2	2	no	—
306	C₄×C₂₉	—	2	1	no	—
307	C₄×C₂₉	—	4	1	no	—
308	C₄×C₂₉	—	4	1	no	—
309	C₄×C₂₉	—	4	1	no	—
310	C₄×C₂₉	—	4	1	no	—
311	C₄×C₂₉	—	8	1	no	—
312	C₄×C₂₉	—	8	1	no	—
313	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
314	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
315	C₄×C₂₉	#577	1	1	yes	characteristic
316	C₄×C₂₉	#577	1	1	yes	characteristic
317	C₂×#135	—	2	1	no	—
318	Q₈²	C₂²×C₂₉	1	1	yes	characteristic
319	#550	C₂²×C₂₉	1	1	yes	characteristic
320	#550	C₂²×C₂₉	1	1	yes	characteristic
321	#547	C₂²×C₂₉	1	1	yes	characteristic
322	#493	C₂²×C₂₉	1	1	yes	characteristic
323	#492	C₂²×C₂₉	1	1	yes	characteristic
324	#487	C₂²×C₂₉	1	1	yes	characteristic
325	#486	—	2	1	no	—
326	#486	—	2	1	no	—
327	#486	C₂²×C₂₉	1	1	yes	characteristic
328	#486	C₂²×C₂₉	1	1	yes	characteristic
329	#486	C₂²×C₂₉	1	1	yes	characteristic
330	#481	—	2	1	no	—
331	#476	—	2	1	no	—
332	#476	—	2	1	no	—
333	#476	C₂²×C₂₉	1	1	yes	characteristic
334	#476	C₂²×C₂₉	1	1	yes	characteristic
335	#475	C₂²×C₂₉	1	1	yes	characteristic
336	#469	—	2	1	no	—
337	#465	—	2	1	no	—
338	#462	C₂²×C₂₉	1	1	yes	characteristic
339	#460	—	2	1	no	—
340	#460	—	2	1	no	—
341	#460	C₂²×C₂₉	1	1	yes	characteristic
342	#460	C₂²×C₂₉	1	1	yes	characteristic
343	#459	C₂²×C₂₉	1	1	yes	characteristic
344	#459	C₂²×C₂₉	1	1	yes	characteristic
345	#452	—	2	1	no	—
346	#449	—	2	1	no	—
347	#449	—	2	1	no	—
348	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
349	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
350	C₄×SD₁₆	—	2	1	no	—
351	C₄×SD₁₆	—	2	1	no	—
352	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
353	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
354	#436	C₂²×C₂₉	1	1	yes	characteristic
355	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
356	#417	—	2	1	no	—
357	#335	C₂²×C₂₉	1	1	yes	characteristic
358	#334	C₂²×C₂₉	1	1	yes	characteristic
359	#333	C₂²×C₂₉	1	1	yes	characteristic
360	#332	C₂²×C₂₉	1	1	yes	characteristic
361	#331	C₂²×C₂₉	1	1	yes	characteristic
362	#331	C₂²×C₂₉	1	1	yes	characteristic
363	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
364	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
365	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
366	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
367	#322	C₂²×C₂₉	1	1	yes	characteristic
368	C₂×C₂₉	—	8	1	no	—
369	C₂×C₂₉	—	8	1	no	—
370	C₂×C₂₉	—	16	1	no	—
371	C₂×C₂₉	—	16	1	no	—
372	C₂×C₂₉	#3265	1	1	yes	characteristic
373	C₂×C₂₉	#3282	1	1	yes	characteristic
374	C₂×C₂₉	#3288	1	1	yes	characteristic
375	C₂×#41	—	2	1	no	—
376	C₂×#41	—	2	1	no	—
377	C₂×#41	—	2	1	no	—
378	#135	—	4	4	no	—
379	C₂×Q₁₆	—	2	1	no	—
380	C₂×SD₁₆	—	2	1	no	—
381	C₂×SD₁₆	—	2	1	no	—
382	C₂×SD₁₆	—	2	1	no	—
383	C₂×SD₁₆	—	2	1	no	—
384	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
385	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
386	C₂×D₈	—	2	1	no	—
387	C₂×D₈	—	2	1	no	—
388	C₂×D₈	—	4	1	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂²×C₈	—	2	1	no	—
391	C₄⋊Q₈	—	2	1	no	—
392	C₄⋊Q₈	—	2	1	no	—
393	C₄⋊Q₈	—	4	1	no	—
394	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
395	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
396	#127	—	2	1	no	—
397	#127	—	2	1	no	—
398	#127	C₂³×C₂₉	1	1	yes	characteristic
399	#127	C₂³×C₂₉	1	1	yes	characteristic
400	#123	—	4	1	no	—
401	C₂²⋊Q₈	—	2	1	no	—
402	#121	—	2	1	no	—
403	#121	—	2	1	no	—
404	#121	—	2	1	no	—
405	#121	—	4	1	no	—
406	#121	—	4	1	no	—
407	C₄×Q₈	—	2	1	no	—
408	C₄×Q₈	—	2	1	no	—
409	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
410	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
414	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
415	C₂×C₄⋊C₄	—	2	1	no	—
416	#106	—	2	1	no	—
417	#106	—	2	1	no	—
418	#106	—	2	1	no	—
419	#106	D₄×C₂₉	1	1	yes	characteristic
420	#106	D₄×C₂₉	1	1	yes	characteristic
421	C₄⋊C₈	—	2	1	no	—
422	C₄⋊C₈	—	2	1	no	—
423	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
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	#103	—	2	1	no	—
428	#103	—	2	1	no	—
429	#103	—	4	1	no	—
430	#103	D₄×C₂₉	1	1	yes	characteristic
431	#103	D₄×C₂₉	1	1	yes	characteristic
432	#102	—	2	1	no	—
433	#102	—	2	1	no	—
434	#102	—	2	1	no	—
435	#102	—	2	1	no	—
436	#102	—	2	1	no	—
437	#102	—	2	1	no	—
438	#102	—	2	1	no	—
439	#102	—	2	1	no	—
440	#102	—	2	1	no	—
441	#102	—	2	1	no	—
442	#102	—	2	1	no	—
443	#102	—	2	1	no	—
444	#102	D₄×C₂₉	1	1	yes	characteristic
445	#102	D₄×C₂₉	1	1	yes	characteristic
446	C₂²⋊C₈	—	2	1	no	—
447	C₂²⋊C₈	—	2	1	no	—
448	C₄×C₈	—	2	1	no	—
449	C₄×C₈	—	2	1	no	—
450	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
451	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
452	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
453	C₂₉	#19827	1	1	yes	characteristic, direct product factor, Sylow
454	#41	—	4	2	no	—
455	#41	—	4	2	no	—
456	#41	—	4	2	no	—
457	#41	—	8	1	no	—
458	#41	—	8	1	no	—
459	#41	—	8	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	4	1	no	—
463	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
464	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	4	1	no	—
472	C₂×D₄	—	4	1	no	—
473	C₂×D₄	—	4	1	no	—
474	C₂×D₄	—	4	1	no	—
475	C₂×D₄	—	4	1	no	—
476	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
477	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	4	1	no	—
481	C₂²×C₄	—	4	1	no	—
482	C₂²×C₄	—	4	1	no	—
483	Q₁₆	—	4	2	no	—
484	SD₁₆	—	2	2	no	—
485	SD₁₆	—	2	2	no	—
486	SD₁₆	—	4	2	no	—
487	SD₁₆	—	4	2	no	—
488	SD₁₆	—	4	2	no	—
489	SD₁₆	—	8	1	no	—
490	D₈	—	4	2	no	—
491	D₈	—	8	1	no	—
492	D₈	—	8	2	no	—
493	M₁₆	—	8	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	4	2	no	—
500	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
501	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
502	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
503	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	4	1	no	—
511	C₄⋊C₄	—	4	1	no	—
512	C₄⋊C₄	—	4	1	no	—
513	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
514	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
515	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
516	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
517	C₂²⋊C₄	—	2	1	no	—
518	C₂²⋊C₄	—	2	1	no	—
519	C₂²⋊C₄	—	4	1	no	—
520	C₂²⋊C₄	—	4	1	no	—
521	C₂²⋊C₄	—	4	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	4	1	no	—
525	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	4	1	no	—
530	Q₈	—	2	1	no	—
531	Q₈	—	2	1	no	—
532	Q₈	—	4	1	no	—
533	Q₈	—	4	1	no	—
534	Q₈	—	8	1	no	—
535	Q₈	—	16	1	no	—
536	Q₈	C₂₉×#135	1	2	yes	complemented
537	Q₈	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
538	D₄	—	2	1	no	—
539	D₄	—	2	1	no	—
540	D₄	—	2	1	no	—
541	D₄	—	2	1	no	—
542	D₄	—	4	1	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	8	2	no	—
551	D₄	—	8	2	no	—
552	D₄	—	8	1	no	—
553	D₄	—	8	1	no	—
554	D₄	—	8	2	no	—
555	D₄	—	16	1	no	—
556	D₄	—	16	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	8	2	no	—
570	C₂×C₄	—	8	2	no	—
571	C₂×C₄	—	8	2	no	—
572	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
573	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
574	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
575	C₈	—	2	1	no	—
576	C₈	—	2	1	no	—
577	C₈	—	2	1	no	—
578	C₈	—	2	1	no	—
579	C₈	—	4	1	no	—
580	C₈	—	4	1	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	1	no	—
583	C₈	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	8	1	no	—
591	C₂²	—	8	1	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	8	1	no	—
596	C₂²	D₄²×C₂₉	1	1	yes	characteristic
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	8	1	no	—
605	C₄	—	8	1	no	—
606	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
607	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
608	C₄	C₂₉×#577	1	1	yes	characteristic
609	C₄	C₂₉×#577	1	1	yes	characteristic
610	C₂	—	8	1	no	—
611	C₂	—	8	1	no	—
612	C₂	—	16	1	no	—
613	C₂	—	16	1	no	—
614	C₂	C₂₉×#3265	1	1	yes	characteristic
615	C₂	C₂₉×#3282	1	1	yes	characteristic
616	C₂	C₂₉×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
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×#3362	C₂	semidirect
2. C₂₉×#3362	C₂	semidirect
3. C₂₉×#3332	C₂	semidirect
4. C₂₉×#3284	C₂	semidirect
5. C₂₉×#1717	C₂	semidirect
6. C₂₉×#1697	C₂	semidirect
7. C₂₉×#1682	C₂	semidirect
8. C₂₉×#1677	C₂	semidirect
9. C₂₉×#1666	C₂	semidirect
10. C₂₉×#1645	C₂	semidirect
11. C₂₉×#1635	C₂	semidirect
12. C₂₉×#1621	C₂	semidirect
13. C₂₉×#1621	C₂	semidirect
14. C₂₉×#1583	C₂	semidirect
15. C₂₉×SD₁₆⋊C₈	C₂	semidirect
217. #19827	C₂₉	direct (N × H)
228. Q₈×C₂₉	#135	semidirect
276. #3362	C₂×C₂₉	semidirect
277. #3362	C₂×C₂₉	semidirect
278. #3332	C₂×C₂₉	semidirect
279. #3284	C₂×C₂₉	semidirect
280. #1717	C₂×C₂₉	semidirect
281. #1697	C₂×C₂₉	semidirect
282. #1682	C₂×C₂₉	semidirect
283. #1677	C₂×C₂₉	semidirect
284. #1666	C₂×C₂₉	semidirect
285. #1645	C₂×C₂₉	semidirect
286. #1635	C₂×C₂₉	semidirect
287. #1621	C₂×C₂₉	semidirect
288. #1621	C₂×C₂₉	semidirect
289. #1583	C₂×C₂₉	semidirect
290. SD₁₆⋊C₈	C₂×C₂₉	semidirect
453. C₂₉	#19827	direct (N × H)
536. Q₈	C₂₉×#135	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₉×#3362	2
C₂₉×#3332	2
C₂₉×#3284	2
C₂₉×#1717	2
C₂₉×#1697	2
C₂₉×#1682	2
C₂₉×#1677	2
C₂₉×#1666	2
C₂₉×#1645	2
C₂₉×#1635	2
C₂₉×#1621	2
C₂₉×#1583	2
C₂₉×SD₁₆⋊C₈	2
#19827	29

Subgroups — C29×#19827 #20314727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19827 #20314727