Subgroups — C₂₉×#19914 #20314814

Order 7424.

622 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3367	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3330	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3302	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3298	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1710	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1700	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1699	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1679	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1679	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1650	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1649	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1647	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1647	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1590	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×D₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#556	C₂²	1	1	yes	characteristic
17	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
18	C₂₉×#547	C₂²	1	1	yes	characteristic
19	C₂₉×#547	C₂²	1	1	yes	characteristic
20	C₂₉×#500	C₂²	1	1	yes	characteristic
21	C₂₉×#500	C₂²	1	1	yes	characteristic
22	C₂₉×#489	—	2	1	no	—
23	C₂₉×#487	C₂²	1	1	yes	characteristic
24	C₂₉×#487	C₂²	1	1	yes	characteristic
25	C₂₉×#487	C₂²	1	1	yes	characteristic
26	C₂₉×#487	C₂²	1	1	yes	characteristic
27	C₂₉×#485	—	2	1	no	—
28	C₂₉×#484	—	2	1	no	—
29	C₂₉×#483	—	2	1	no	—
30	C₂₉×#477	—	2	1	no	—
31	C₂₉×#475	C₂²	1	1	yes	characteristic
32	C₂₉×#474	C₂²	1	1	yes	characteristic
33	C₂₉×#474	C₂²	1	1	yes	characteristic
34	C₂₉×#474	C₂²	1	1	yes	characteristic
35	C₂₉×#468	—	2	1	no	—
36	C₂₉×#467	—	2	1	no	—
37	C₂₉×#465	—	2	1	no	—
38	C₂₉×#463	—	2	1	no	—
39	C₂₉×#462	C₂²	1	1	yes	characteristic
40	C₂₉×#461	C₂²	1	1	yes	characteristic
41	C₂₉×#461	C₂²	1	1	yes	characteristic
42	C₂₉×#461	C₂²	1	1	yes	characteristic
43	C₂₉×#452	—	2	1	no	—
44	C₂₉×#449	—	2	1	no	—
45	C₂₉×#448	—	2	1	no	—
46	C₂₉×#446	C₂²	1	1	yes	characteristic
47	C₂₉×#440	—	2	1	no	—
48	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
49	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
50	C₂₉×#436	C₂²	1	1	yes	characteristic
51	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
53	C₂₉×#417	—	2	1	no	—
54	C₂₉×#416	—	2	1	no	—
55	C₂×C₂₉×#103	—	2	1	no	—
56	C₂₉×#335	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×D₄⋊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×#41×C₂₉	—	2	1	no	—
69	C₂²×Q₈×C₂₉	—	2	1	no	—
70	C₂×Q₁₆×C₂₉	—	2	1	no	—
71	C₂×SD₁₆×C₂₉	—	2	1	no	—
72	C₂×SD₁₆×C₂₉	—	2	1	no	—
73	C₂×SD₁₆×C₂₉	—	2	1	no	—
74	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
75	C₂×D₈×C₂₉	D₄	1	1	yes	characteristic
76	C₂×M₁₆×C₂₉	—	2	1	no	—
77	C₂²×C₈×C₂₉	—	2	1	no	—
78	C₂²×C₈×C₂₉	—	2	1	no	—
79	C₂₉×C₄⋊Q₈	—	2	1	no	—
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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₂₉×#126	—	4	1	no	—
85	C₂₉×#124	—	2	1	no	—
86	C₂₉×#123	—	4	1	no	—
87	C₂₉×#123	—	4	1	no	—
88	C₂₉×C₂²⋊Q₈	—	2	1	no	—
89	C₂₉×C₂²⋊Q₈	—	2	1	no	—
90	C₂₉×C₂²⋊Q₈	—	2	1	no	—
91	C₂₉×C₂²⋊Q₈	—	2	1	no	—
92	C₂₉×C₂²⋊Q₈	—	4	1	no	—
93	C₂₉×#121	—	2	1	no	—
94	C₂₉×#121	—	2	1	no	—
95	C₄×Q₈×C₂₉	—	2	1	no	—
96	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₂₉	—	2	1	no	—
98	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
101	C₂₉×#117	—	2	1	no	—
102	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
104	C₂₉×#107	—	2	1	no	—
105	C₂₉×#107	—	2	1	no	—
106	C₂₉×#107	—	2	1	no	—
107	C₂₉×#107	—	4	1	no	—
108	C₂₉×#107	—	4	1	no	—
109	C₂₉×#107	D₄	1	1	yes	characteristic
110	C₂₉×#106	—	2	1	no	—
111	C₂₉×#106	D₄	1	1	yes	characteristic
112	C₂₉×C₄⋊C₈	—	2	1	no	—
113	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₂₉×#103	—	2	1	no	—
118	C₂₉×#103	—	2	1	no	—
119	C₂₉×#103	—	2	1	no	—
120	C₂₉×#103	—	2	1	no	—
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×#102	—	2	1	no	—
132	C₂₉×#102	—	2	1	no	—
133	C₂₉×#102	—	2	1	no	—
134	C₂₉×#102	D₄	1	1	yes	characteristic
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×C₂²⋊C₈	—	2	1	no	—
140	C₂₉×#97	—	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	—	4	2	no	—
146	#41×C₂₉	—	8	1	no	—
147	#41×C₂₉	—	8	1	no	—
148	C₂×Q₈×C₂₉	—	2	1	no	—
149	C₂×Q₈×C₂₉	—	2	1	no	—
150	C₂×Q₈×C₂₉	—	2	1	no	—
151	C₂×Q₈×C₂₉	—	2	1	no	—
152	C₂×Q₈×C₂₉	—	4	1	no	—
153	C₂×Q₈×C₂₉	—	4	2	no	—
154	C₂×Q₈×C₂₉	—	8	1	no	—
155	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
156	C₂×D₄×C₂₉	—	4	1	no	—
157	C₂×D₄×C₂₉	—	4	1	no	—
158	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
159	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
160	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₂₉	—	2	1	no	—
162	C₂²×C₄×C₂₉	—	2	1	no	—
163	C₂²×C₄×C₂₉	—	2	1	no	—
164	C₂²×C₄×C₂₉	—	4	1	no	—
165	C₂²×C₄×C₂₉	—	4	1	no	—
166	C₂²×C₄×C₂₉	—	4	1	no	—
167	Q₁₆×C₂₉	—	8	1	no	—
168	SD₁₆×C₂₉	—	4	1	no	—
169	SD₁₆×C₂₉	—	4	2	no	—
170	SD₁₆×C₂₉	—	8	1	no	—
171	SD₁₆×C₂₉	—	8	1	no	—
172	D₈×C₂₉	—	2	2	no	—
173	M₁₆×C₂₉	—	8	1	no	—
174	C₂×C₈×C₂₉	—	2	1	no	—
175	C₂×C₈×C₂₉	—	2	1	no	—
176	C₂×C₈×C₂₉	—	2	1	no	—
177	C₂×C₈×C₂₉	—	2	1	no	—
178	C₂×C₈×C₂₉	—	2	1	no	—
179	C₂×C₈×C₂₉	—	8	1	no	—
180	C₂×C₈×C₂₉	—	8	1	no	—
181	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
185	C₄⋊C₄×C₂₉	—	2	1	no	—
186	C₄⋊C₄×C₂₉	—	2	1	no	—
187	C₄⋊C₄×C₂₉	—	2	1	no	—
188	C₄⋊C₄×C₂₉	—	2	1	no	—
189	C₄⋊C₄×C₂₉	—	2	1	no	—
190	C₄⋊C₄×C₂₉	—	2	1	no	—
191	C₄⋊C₄×C₂₉	—	2	1	no	—
192	C₄⋊C₄×C₂₉	—	2	1	no	—
193	C₄⋊C₄×C₂₉	—	2	1	no	—
194	C₄⋊C₄×C₂₉	—	4	1	no	—
195	C₄⋊C₄×C₂₉	—	4	1	no	—
196	C₄⋊C₄×C₂₉	—	4	1	no	—
197	C₄⋊C₄×C₂₉	—	4	1	no	—
198	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
199	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
200	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
202	C₂²⋊C₄×C₂₉	—	2	1	no	—
203	C₂²⋊C₄×C₂₉	—	2	1	no	—
204	C₂²⋊C₄×C₂₉	—	2	1	no	—
205	C₂²⋊C₄×C₂₉	—	4	1	no	—
206	C₂²⋊C₄×C₂₉	—	4	1	no	—
207	C₂²⋊C₄×C₂₉	—	4	1	no	—
208	C₂²⋊C₄×C₂₉	—	4	1	no	—
209	C₂²⋊C₄×C₂₉	—	4	1	no	—
210	C₄²×C₂₉	—	2	1	no	—
211	C₄²×C₂₉	—	4	1	no	—
212	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
213	#19914	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂³×C₂₉	—	2	1	no	—
215	C₂³×C₂₉	—	2	1	no	—
216	C₂³×C₂₉	—	2	1	no	—
217	Q₈×C₂₉	—	2	1	no	—
218	Q₈×C₂₉	—	2	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	Q₈×C₂₉	—	4	1	no	—
226	Q₈×C₂₉	—	4	1	no	—
227	Q₈×C₂₉	—	8	2	no	—
228	D₄×C₂₉	—	2	1	no	—
229	D₄×C₂₉	—	2	1	no	—
230	D₄×C₂₉	—	2	1	no	—
231	D₄×C₂₉	—	2	1	no	—
232	D₄×C₂₉	—	2	1	no	—
233	D₄×C₂₉	—	8	2	no	—
234	D₄×C₂₉	—	8	2	no	—
235	D₄×C₂₉	#135	1	2	yes	—
236	C₂×C₄×C₂₉	—	2	1	no	—
237	C₂×C₄×C₂₉	—	2	1	no	—
238	C₂×C₄×C₂₉	—	2	1	no	—
239	C₂×C₄×C₂₉	—	2	1	no	—
240	C₂×C₄×C₂₉	—	2	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	—	4	1	no	—
245	C₂×C₄×C₂₉	—	4	1	no	—
246	C₂×C₄×C₂₉	—	4	1	no	—
247	C₂×C₄×C₂₉	—	4	1	no	—
248	C₂×C₄×C₂₉	—	4	1	no	—
249	C₂×C₄×C₂₉	—	4	1	no	—
250	C₂×C₄×C₂₉	—	4	1	no	—
251	C₂×C₄×C₂₉	—	8	2	no	—
252	C₂×C₄×C₂₉	—	8	2	no	—
253	C₂×C₄×C₂₉	—	8	2	no	—
254	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
257	C₈×C₂₉	—	2	2	no	—
258	C₈×C₂₉	—	2	1	no	—
259	C₈×C₂₉	—	2	1	no	—
260	C₈×C₂₉	—	2	1	no	—
261	C₈×C₂₉	—	2	1	no	—
262	C₈×C₂₉	—	4	1	no	—
263	C₈×C₂₉	—	4	1	no	—
264	C₈×C₂₉	—	4	1	no	—
265	C₈×C₂₉	—	4	1	no	—
266	#3367	C₂×C₂₉	1	1	yes	characteristic, complemented
267	#3330	C₂×C₂₉	1	1	yes	characteristic
268	#3302	C₂×C₂₉	1	1	yes	characteristic, complemented
269	#3298	C₂×C₂₉	1	1	yes	characteristic, complemented
270	#1710	C₂×C₂₉	1	1	yes	characteristic, complemented
271	#1700	C₂×C₂₉	1	1	yes	characteristic, complemented
272	#1699	C₂×C₂₉	1	1	yes	characteristic, complemented
273	#1679	C₂×C₂₉	1	1	yes	characteristic, complemented
274	#1679	C₂×C₂₉	1	1	yes	characteristic, complemented
275	#1650	C₂×C₂₉	1	1	yes	characteristic, complemented
276	#1649	C₂×C₂₉	1	1	yes	characteristic, complemented
277	#1647	C₂×C₂₉	1	1	yes	characteristic, complemented
278	#1647	C₂×C₂₉	1	1	yes	characteristic, complemented
279	#1590	C₂×C₂₉	1	1	yes	characteristic, complemented
280	C₈×D₈	C₂×C₂₉	1	1	yes	characteristic, complemented
281	C₂²×C₂₉	—	2	2	no	—
282	C₂²×C₂₉	—	4	1	no	—
283	C₂²×C₂₉	—	4	1	no	—
284	C₂²×C₂₉	—	4	1	no	—
285	C₂²×C₂₉	—	4	1	no	—
286	C₂²×C₂₉	—	4	1	no	—
287	C₂²×C₂₉	—	4	1	no	—
288	C₂²×C₂₉	—	4	1	no	—
289	C₂²×C₂₉	—	4	1	no	—
290	C₂²×C₂₉	D₄²	1	1	yes	characteristic
291	C₄×C₂₉	—	2	1	no	—
292	C₄×C₂₉	—	4	1	no	—
293	C₄×C₂₉	—	4	1	no	—
294	C₄×C₂₉	—	4	1	no	—
295	C₄×C₂₉	—	4	1	no	—
296	C₄×C₂₉	—	4	1	no	—
297	C₄×C₂₉	—	8	1	no	—
298	C₄×C₂₉	—	8	1	no	—
299	C₄×C₂₉	—	8	1	no	—
300	C₄×C₂₉	—	8	1	no	—
301	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
302	C₄×C₂₉	#575	1	1	yes	characteristic
303	C₄×C₂₉	#576	1	1	yes	characteristic
304	C₄×C₂₉	#577	1	1	yes	characteristic
305	#556	C₂²×C₂₉	1	1	yes	characteristic
306	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
307	#547	C₂²×C₂₉	1	1	yes	characteristic
308	#547	C₂²×C₂₉	1	1	yes	characteristic
309	#500	C₂²×C₂₉	1	1	yes	characteristic
310	#500	C₂²×C₂₉	1	1	yes	characteristic
311	#489	—	2	1	no	—
312	#487	C₂²×C₂₉	1	1	yes	characteristic
313	#487	C₂²×C₂₉	1	1	yes	characteristic
314	#487	C₂²×C₂₉	1	1	yes	characteristic
315	#487	C₂²×C₂₉	1	1	yes	characteristic
316	#485	—	2	1	no	—
317	#484	—	2	1	no	—
318	#483	—	2	1	no	—
319	#477	—	2	1	no	—
320	#475	C₂²×C₂₉	1	1	yes	characteristic
321	#474	C₂²×C₂₉	1	1	yes	characteristic
322	#474	C₂²×C₂₉	1	1	yes	characteristic
323	#474	C₂²×C₂₉	1	1	yes	characteristic
324	#468	—	2	1	no	—
325	#467	—	2	1	no	—
326	#465	—	2	1	no	—
327	#463	—	2	1	no	—
328	#462	C₂²×C₂₉	1	1	yes	characteristic
329	#461	C₂²×C₂₉	1	1	yes	characteristic
330	#461	C₂²×C₂₉	1	1	yes	characteristic
331	#461	C₂²×C₂₉	1	1	yes	characteristic
332	#452	—	2	1	no	—
333	#449	—	2	1	no	—
334	#448	—	2	1	no	—
335	#446	C₂²×C₂₉	1	1	yes	characteristic
336	#440	—	2	1	no	—
337	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
338	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
339	#436	C₂²×C₂₉	1	1	yes	characteristic
340	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
341	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
342	#417	—	2	1	no	—
343	#416	—	2	1	no	—
344	C₂×#103	—	2	1	no	—
345	#335	C₂²×C₂₉	1	1	yes	characteristic
346	#334	C₂²×C₂₉	1	1	yes	characteristic
347	#332	C₂²×C₂₉	1	1	yes	characteristic
348	#332	C₂²×C₂₉	1	1	yes	characteristic
349	#332	C₂²×C₂₉	1	1	yes	characteristic
350	#332	C₂²×C₂₉	1	1	yes	characteristic
351	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
352	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
353	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
354	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
355	C₈²	C₂²×C₂₉	1	1	yes	characteristic
356	C₂×C₂₉	—	4	2	no	—
357	C₂×C₂₉	—	8	1	no	—
358	C₂×C₂₉	—	8	1	no	—
359	C₂×C₂₉	#3273	1	1	yes	characteristic
360	C₂×C₂₉	#3282	1	1	yes	characteristic
361	C₂×C₂₉	#3293	1	1	yes	characteristic
362	C₂×#41	—	2	1	no	—
363	C₂×#41	—	2	1	no	—
364	C₂²×Q₈	—	2	1	no	—
365	C₂×Q₁₆	—	2	1	no	—
366	C₂×SD₁₆	—	2	1	no	—
367	C₂×SD₁₆	—	2	1	no	—
368	C₂×SD₁₆	—	2	1	no	—
369	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
370	C₂×D₈	D₄×C₂₉	1	1	yes	characteristic
371	C₂×M₁₆	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₄⋊Q₈	—	2	1	no	—
375	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
376	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
377	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
378	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
379	#126	—	4	1	no	—
380	#124	—	2	1	no	—
381	#123	—	4	1	no	—
382	#123	—	4	1	no	—
383	C₂²⋊Q₈	—	2	1	no	—
384	C₂²⋊Q₈	—	2	1	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₂²⋊Q₈	—	2	1	no	—
387	C₂²⋊Q₈	—	4	1	no	—
388	#121	—	2	1	no	—
389	#121	—	2	1	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
394	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
395	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
396	#117	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	#107	—	2	1	no	—
400	#107	—	2	1	no	—
401	#107	—	2	1	no	—
402	#107	—	4	1	no	—
403	#107	—	4	1	no	—
404	#107	D₄×C₂₉	1	1	yes	characteristic
405	#106	—	2	1	no	—
406	#106	D₄×C₂₉	1	1	yes	characteristic
407	C₄⋊C₈	—	2	1	no	—
408	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
409	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
410	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
411	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
412	#103	—	2	1	no	—
413	#103	—	2	1	no	—
414	#103	—	2	1	no	—
415	#103	—	2	1	no	—
416	#103	—	2	1	no	—
417	#103	—	2	1	no	—
418	#103	—	2	1	no	—
419	#103	—	2	1	no	—
420	#103	—	2	1	no	—
421	#103	—	2	1	no	—
422	#103	—	2	1	no	—
423	#103	—	2	1	no	—
424	#103	—	2	1	no	—
425	#103	D₄×C₂₉	1	1	yes	characteristic
426	#102	—	2	1	no	—
427	#102	—	2	1	no	—
428	#102	—	2	1	no	—
429	#102	D₄×C₂₉	1	1	yes	characteristic
430	#102	D₄×C₂₉	1	1	yes	characteristic
431	#102	D₄×C₂₉	1	1	yes	characteristic
432	C₂²⋊C₈	—	2	1	no	—
433	C₂²⋊C₈	—	2	1	no	—
434	C₂²⋊C₈	—	2	1	no	—
435	#97	—	2	1	no	—
436	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
437	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
438	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
439	C₂₉	#19914	1	1	yes	characteristic, direct product factor, Sylow
440	#41	—	4	2	no	—
441	#41	—	4	2	no	—
442	#41	—	8	1	no	—
443	#41	—	8	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	4	1	no	—
449	C₂×Q₈	—	4	2	no	—
450	C₂×Q₈	—	8	1	no	—
451	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
452	C₂×D₄	—	4	1	no	—
453	C₂×D₄	—	4	1	no	—
454	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
455	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
456	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	—	4	1	no	—
462	C₂²×C₄	—	4	1	no	—
463	Q₁₆	—	8	1	no	—
464	SD₁₆	—	4	1	no	—
465	SD₁₆	—	4	2	no	—
466	SD₁₆	—	8	1	no	—
467	SD₁₆	—	8	1	no	—
468	D₈	—	2	2	no	—
469	M₁₆	—	8	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	8	1	no	—
476	C₂×C₈	—	8	1	no	—
477	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
478	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
479	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
480	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	4	1	no	—
491	C₄⋊C₄	—	4	1	no	—
492	C₄⋊C₄	—	4	1	no	—
493	C₄⋊C₄	—	4	1	no	—
494	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
495	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
496	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
497	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	4	1	no	—
502	C₂²⋊C₄	—	4	1	no	—
503	C₂²⋊C₄	—	4	1	no	—
504	C₂²⋊C₄	—	4	1	no	—
505	C₂²⋊C₄	—	4	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	4	1	no	—
508	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
509	C₂³	—	2	1	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	2	1	no	—
512	Q₈	—	2	1	no	—
513	Q₈	—	2	1	no	—
514	Q₈	—	4	1	no	—
515	Q₈	—	4	1	no	—
516	Q₈	—	4	1	no	—
517	Q₈	—	4	1	no	—
518	Q₈	—	4	1	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	1	no	—
522	Q₈	—	8	2	no	—
523	D₄	—	2	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	8	2	no	—
529	D₄	—	8	2	no	—
530	D₄	C₂₉×#135	1	2	yes	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	8	2	no	—
547	C₂×C₄	—	8	2	no	—
548	C₂×C₄	—	8	2	no	—
549	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
551	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
552	C₈	—	2	2	no	—
553	C₈	—	2	1	no	—
554	C₈	—	2	1	no	—
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	D₄²×C₂₉	1	1	yes	characteristic
571	C₄	—	2	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	8	1	no	—
578	C₄	—	8	1	no	—
579	C₄	—	8	1	no	—
580	C₄	—	8	1	no	—
581	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
582	C₄	C₂₉×#575	1	1	yes	characteristic
583	C₄	C₂₉×#576	1	1	yes	characteristic
584	C₄	C₂₉×#577	1	1	yes	characteristic
585	C₂	—	4	2	no	—
586	C₂	—	8	1	no	—
587	C₂	—	8	1	no	—
588	C₂	C₂₉×#3273	1	1	yes	characteristic
589	C₂	C₂₉×#3282	1	1	yes	characteristic
590	C₂	C₂₉×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#3330	C₂
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×#3367	C₂	semidirect
3. C₂₉×#3302	C₂	semidirect
4. C₂₉×#3298	C₂	semidirect
5. C₂₉×#1710	C₂	semidirect
6. C₂₉×#1700	C₂	semidirect
7. C₂₉×#1699	C₂	semidirect
8. C₂₉×#1679	C₂	semidirect
9. C₂₉×#1679	C₂	semidirect
10. C₂₉×#1650	C₂	semidirect
11. C₂₉×#1649	C₂	semidirect
12. C₂₉×#1647	C₂	semidirect
13. C₂₉×#1647	C₂	semidirect
14. C₂₉×#1590	C₂	semidirect
15. C₈×D₈×C₂₉	C₂	semidirect
213. #19914	C₂₉	direct (N × H)
266. #3367	C₂×C₂₉	semidirect
268. #3302	C₂×C₂₉	semidirect
269. #3298	C₂×C₂₉	semidirect
270. #1710	C₂×C₂₉	semidirect
271. #1700	C₂×C₂₉	semidirect
272. #1699	C₂×C₂₉	semidirect
273. #1679	C₂×C₂₉	semidirect
274. #1679	C₂×C₂₉	semidirect
275. #1650	C₂×C₂₉	semidirect
276. #1649	C₂×C₂₉	semidirect
277. #1647	C₂×C₂₉	semidirect
278. #1647	C₂×C₂₉	semidirect
279. #1590	C₂×C₂₉	semidirect
280. C₈×D₈	C₂×C₂₉	semidirect
439. C₂₉	#19914	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×#3367	2
C₂₉×#3330	2
C₂₉×#3302	2
C₂₉×#3298	2
C₂₉×#1710	2
C₂₉×#1700	2
C₂₉×#1699	2
C₂₉×#1679	2
C₂₉×#1650	2
C₂₉×#1649	2
C₂₉×#1647	2
C₂₉×#1590	2
C₈×D₈×C₂₉	2
#19914	29

Subgroups — C29×#19914 #20314814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19914 #20314814