Subgroups — C₂₉×#19796 #20314696

Order 7424.

598 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3369	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3302	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#3298	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1718	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1700	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1683	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1680	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1671	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×#1645	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1635	C₂	1	1	yes	maximal, characteristic
14	C₂₉×#1582	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	Q₈²×C₂₉	C₂²	1	1	yes	characteristic
17	C₂₉×#556	C₂²	1	1	yes	characteristic
18	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
19	C₂₉×#547	C₂²	1	1	yes	characteristic
20	C₂₉×#500	C₂²	1	1	yes	characteristic
21	C₂₉×#498	—	2	1	no	—
22	C₂₉×#498	C₂²	1	1	yes	characteristic
23	C₂₉×#489	—	2	1	no	—
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×#487	C₂²	1	1	yes	characteristic
28	C₂₉×#485	—	2	1	no	—
29	C₂₉×#483	—	2	1	no	—
30	C₂₉×#476	—	2	1	no	—
31	C₂₉×#476	C₂²	1	1	yes	characteristic
32	C₂₉×#476	C₂²	1	1	yes	characteristic
33	C₂₉×#475	—	2	1	no	—
34	C₂₉×#475	—	2	1	no	—
35	C₂₉×#475	C₂²	1	1	yes	characteristic
36	C₂₉×#475	C₂²	1	1	yes	characteristic
37	C₂₉×#474	C₂²	1	1	yes	characteristic
38	C₂₉×#467	—	2	1	no	—
39	C₂₉×#465	—	2	1	no	—
40	C₂₉×#464	—	2	1	no	—
41	C₂₉×#462	C₂²	1	1	yes	characteristic
42	C₂₉×#462	C₂²	1	1	yes	characteristic
43	C₂₉×#461	C₂²	1	1	yes	characteristic
44	C₂₉×#452	—	2	1	no	—
45	C₂₉×#448	—	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×SD₁₆×C₂₉	—	2	1	no	—
50	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
51	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
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×#333	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	C₂₉×#322	C₂²	1	1	yes	characteristic
67	C₂×#41×C₂₉	—	2	1	no	—
68	C₂²×Q₈×C₂₉	—	2	1	no	—
69	C₂×Q₁₆×C₂₉	—	2	1	no	—
70	C₂×Q₁₆×C₂₉	—	2	1	no	—
71	C₂×SD₁₆×C₂₉	—	2	1	no	—
72	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
73	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₂₉	—	2	1	no	—
75	C₂²×C₈×C₂₉	—	2	1	no	—
76	C₂₉×C₄⋊Q₈	—	2	1	no	—
77	C₂₉×C₄⋊Q₈	—	2	1	no	—
78	C₂₉×C₄⋊Q₈	—	2	1	no	—
79	C₂₉×C₄⋊Q₈	—	4	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×C₂²⋊Q₈	—	2	1	no	—
88	C₂₉×C₂²⋊Q₈	—	2	1	no	—
89	C₂₉×C₂²⋊Q₈	—	2	1	no	—
90	C₂₉×C₂²⋊Q₈	—	4	1	no	—
91	C₂₉×#121	—	2	1	no	—
92	C₄×Q₈×C₂₉	—	2	1	no	—
93	C₄×Q₈×C₂₉	—	2	1	no	—
94	C₄×Q₈×C₂₉	—	2	1	no	—
95	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
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	C₂₉×#117	—	2	1	no	—
101	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
102	C₂₉×#107	—	2	1	no	—
103	C₂₉×#107	—	4	1	no	—
104	C₂₉×#106	—	2	1	no	—
105	C₂₉×#106	—	2	1	no	—
106	C₂₉×#106	—	2	1	no	—
107	C₂₉×#106	—	2	1	no	—
108	C₂₉×#106	—	2	1	no	—
109	C₂₉×#106	—	2	1	no	—
110	C₂₉×#106	D₄	1	1	yes	characteristic
111	C₂₉×#106	D₄	1	1	yes	characteristic
112	C₂₉×C₄⋊C₈	—	2	1	no	—
113	C₂₉×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	—	4	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	—	4	1	no	—
151	C₂×Q₈×C₂₉	—	4	1	no	—
152	C₂×Q₈×C₂₉	—	4	2	no	—
153	C₂×Q₈×C₂₉	—	8	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	—	4	1	no	—
157	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
158	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₂₉	—	2	1	no	—
160	C₂²×C₄×C₂₉	—	2	1	no	—
161	C₂²×C₄×C₂₉	—	4	1	no	—
162	C₂²×C₄×C₂₉	—	4	1	no	—
163	Q₁₆×C₂₉	—	4	2	no	—
164	Q₁₆×C₂₉	—	8	1	no	—
165	SD₁₆×C₂₉	—	2	2	no	—
166	SD₁₆×C₂₉	—	2	2	no	—
167	SD₁₆×C₂₉	—	8	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	—	2	1	no	—
173	C₂×C₈×C₂₉	—	8	1	no	—
174	C₂×C₈×C₂₉	—	8	1	no	—
175	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
188	C₄⋊C₄×C₂₉	—	2	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	—	4	1	no	—
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	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
198	C₂²⋊C₄×C₂₉	—	2	1	no	—
199	C₂²⋊C₄×C₂₉	—	2	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	C₂⁴	1	1	yes	characteristic
209	#19796	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂³×C₂₉	—	2	1	no	—
211	C₂³×C₂₉	—	2	1	no	—
212	Q₈×C₂₉	—	2	1	no	—
213	Q₈×C₂₉	—	2	1	no	—
214	Q₈×C₂₉	—	2	1	no	—
215	Q₈×C₂₉	—	4	1	no	—
216	Q₈×C₂₉	—	4	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	—	8	2	no	—
222	Q₈×C₂₉	—	8	1	no	—
223	Q₈×C₂₉	—	16	1	no	—
224	Q₈×C₂₉	#135	1	2	yes	—
225	D₄×C₂₉	—	2	1	no	—
226	D₄×C₂₉	—	2	1	no	—
227	D₄×C₂₉	—	2	1	no	—
228	D₄×C₂₉	—	8	2	no	—
229	D₄×C₂₉	#137	1	2	yes	—
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	—	8	2	no	—
246	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
249	C₈×C₂₉	—	2	1	no	—
250	C₈×C₂₉	—	2	1	no	—
251	C₈×C₂₉	—	2	1	no	—
252	C₈×C₂₉	—	2	1	no	—
253	C₈×C₂₉	—	4	1	no	—
254	C₈×C₂₉	—	4	1	no	—
255	C₈×C₂₉	—	4	1	no	—
256	C₈×C₂₉	—	4	1	no	—
257	C₈×C₂₉	—	4	1	no	—
258	Q₈×SD₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
259	#3369	C₂×C₂₉	1	1	yes	characteristic, complemented
260	#3302	C₂×C₂₉	1	1	yes	characteristic
261	#3298	C₂×C₂₉	1	1	yes	characteristic
262	#1718	C₂×C₂₉	1	1	yes	characteristic, complemented
263	#1700	C₂×C₂₉	1	1	yes	characteristic, complemented
264	#1683	C₂×C₂₉	1	1	yes	characteristic, complemented
265	#1680	C₂×C₂₉	1	1	yes	characteristic, complemented
266	#1671	C₂×C₂₉	1	1	yes	characteristic, complemented
267	#1650	C₂×C₂₉	1	1	yes	characteristic, complemented
268	#1649	C₂×C₂₉	1	1	yes	characteristic, complemented
269	#1645	C₂×C₂₉	1	1	yes	characteristic, complemented
270	#1635	C₂×C₂₉	1	1	yes	characteristic
271	#1582	C₂×C₂₉	1	1	yes	characteristic, complemented
272	SD₁₆⋊C₈	C₂×C₂₉	1	1	yes	characteristic, complemented
273	C₂²×C₂₉	—	2	2	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	—	4	1	no	—
279	C₂²×C₂₉	D₄²	1	1	yes	characteristic
280	C₄×C₂₉	—	2	2	no	—
281	C₄×C₂₉	—	2	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	—	4	1	no	—
287	C₄×C₂₉	—	8	1	no	—
288	C₄×C₂₉	—	8	1	no	—
289	C₄×C₂₉	—	8	1	no	—
290	C₄×C₂₉	—	8	1	no	—
291	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
292	C₄×C₂₉	C₂×#137	1	1	yes	characteristic
293	C₄×C₂₉	#577	1	1	yes	characteristic
294	C₄×C₂₉	#577	1	1	yes	characteristic
295	Q₈²	C₂²×C₂₉	1	1	yes	characteristic
296	#556	C₂²×C₂₉	1	1	yes	characteristic
297	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
298	#547	C₂²×C₂₉	1	1	yes	characteristic
299	#500	C₂²×C₂₉	1	1	yes	characteristic
300	#498	—	2	1	no	—
301	#498	C₂²×C₂₉	1	1	yes	characteristic
302	#489	—	2	1	no	—
303	#487	C₂²×C₂₉	1	1	yes	characteristic
304	#487	C₂²×C₂₉	1	1	yes	characteristic
305	#487	C₂²×C₂₉	1	1	yes	characteristic
306	#487	C₂²×C₂₉	1	1	yes	characteristic
307	#485	—	2	1	no	—
308	#483	—	2	1	no	—
309	#476	—	2	1	no	—
310	#476	C₂²×C₂₉	1	1	yes	characteristic
311	#476	C₂²×C₂₉	1	1	yes	characteristic
312	#475	—	2	1	no	—
313	#475	—	2	1	no	—
314	#475	C₂²×C₂₉	1	1	yes	characteristic
315	#475	C₂²×C₂₉	1	1	yes	characteristic
316	#474	C₂²×C₂₉	1	1	yes	characteristic
317	#467	—	2	1	no	—
318	#465	—	2	1	no	—
319	#464	—	2	1	no	—
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	#448	—	2	1	no	—
325	#446	C₂²×C₂₉	1	1	yes	characteristic
326	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
327	#441	—	2	1	no	—
328	C₄×SD₁₆	—	2	1	no	—
329	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
330	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
331	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
332	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
333	#416	—	2	1	no	—
334	C₂×#103	—	2	1	no	—
335	#335	C₂²×C₂₉	1	1	yes	characteristic
336	#334	C₂²×C₂₉	1	1	yes	characteristic
337	#333	C₂²×C₂₉	1	1	yes	characteristic
338	#332	C₂²×C₂₉	1	1	yes	characteristic
339	#332	C₂²×C₂₉	1	1	yes	characteristic
340	#332	C₂²×C₂₉	1	1	yes	characteristic
341	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
342	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
343	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
344	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
345	#322	C₂²×C₂₉	1	1	yes	characteristic
346	C₂×C₂₉	—	4	2	no	—
347	C₂×C₂₉	—	8	1	no	—
348	C₂×C₂₉	#3266	1	1	yes	characteristic
349	C₂×C₂₉	#3282	1	1	yes	characteristic
350	C₂×C₂₉	#3289	1	1	yes	characteristic
351	C₂×#41	—	2	1	no	—
352	C₂²×Q₈	—	2	1	no	—
353	C₂×Q₁₆	—	2	1	no	—
354	C₂×Q₁₆	—	2	1	no	—
355	C₂×SD₁₆	—	2	1	no	—
356	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
357	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
358	C₂²×C₈	—	2	1	no	—
359	C₂²×C₈	—	2	1	no	—
360	C₄⋊Q₈	—	2	1	no	—
361	C₄⋊Q₈	—	2	1	no	—
362	C₄⋊Q₈	—	2	1	no	—
363	C₄⋊Q₈	—	4	1	no	—
364	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
365	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
366	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
367	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
368	#126	—	4	1	no	—
369	#124	—	2	1	no	—
370	#123	—	4	1	no	—
371	C₂²⋊Q₈	—	2	1	no	—
372	C₂²⋊Q₈	—	2	1	no	—
373	C₂²⋊Q₈	—	2	1	no	—
374	C₂²⋊Q₈	—	4	1	no	—
375	#121	—	2	1	no	—
376	C₄×Q₈	—	2	1	no	—
377	C₄×Q₈	—	2	1	no	—
378	C₄×Q₈	—	2	1	no	—
379	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
380	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
383	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
384	#117	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	#107	—	2	1	no	—
387	#107	—	4	1	no	—
388	#106	—	2	1	no	—
389	#106	—	2	1	no	—
390	#106	—	2	1	no	—
391	#106	—	2	1	no	—
392	#106	—	2	1	no	—
393	#106	—	2	1	no	—
394	#106	D₄×C₂₉	1	1	yes	characteristic
395	#106	D₄×C₂₉	1	1	yes	characteristic
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	—	2	1	no	—
398	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
399	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
400	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
401	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
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	—	4	1	no	—
414	#103	D₄×C₂₉	1	1	yes	characteristic
415	#103	D₄×C₂₉	1	1	yes	characteristic
416	#102	—	2	1	no	—
417	#102	—	2	1	no	—
418	#102	—	2	1	no	—
419	#102	D₄×C₂₉	1	1	yes	characteristic
420	#102	D₄×C₂₉	1	1	yes	characteristic
421	C₂²⋊C₈	—	2	1	no	—
422	C₂²⋊C₈	—	2	1	no	—
423	#97	—	2	1	no	—
424	C₄×C₈	—	2	1	no	—
425	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
426	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
427	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
428	C₂₉	#19796	1	1	yes	characteristic, direct product factor, Sylow
429	#41	—	4	2	no	—
430	#41	—	8	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	4	1	no	—
436	C₂×Q₈	—	4	1	no	—
437	C₂×Q₈	—	4	2	no	—
438	C₂×Q₈	—	8	1	no	—
439	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
440	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
443	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	4	1	no	—
447	C₂²×C₄	—	4	1	no	—
448	Q₁₆	—	4	2	no	—
449	Q₁₆	—	8	1	no	—
450	SD₁₆	—	2	2	no	—
451	SD₁₆	—	2	2	no	—
452	SD₁₆	—	8	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	8	1	no	—
459	C₂×C₈	—	8	1	no	—
460	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
461	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
462	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
463	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
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	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	4	1	no	—
475	C₄⋊C₄	—	4	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	1	no	—
479	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
480	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
481	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
482	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	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	—	4	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	—	8	2	no	—
506	Q₈	—	8	1	no	—
507	Q₈	—	16	1	no	—
508	Q₈	C₂₉×#135	1	2	yes	—
509	D₄	—	2	1	no	—
510	D₄	—	2	1	no	—
511	D₄	—	2	1	no	—
512	D₄	—	8	2	no	—
513	D₄	C₂₉×#137	1	2	yes	—
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	—	2	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	—	4	1	no	—
528	C₂×C₄	—	8	2	no	—
529	C₂×C₄	—	8	2	no	—
530	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
531	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
532	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
533	C₈	—	2	1	no	—
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	1	no	—
548	C₂²	D₄²×C₂₉	1	1	yes	characteristic
549	C₄	—	2	2	no	—
550	C₄	—	2	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	—	8	1	no	—
559	C₄	—	8	1	no	—
560	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
561	C₄	C₂×C₂₉×#137	1	1	yes	characteristic
562	C₄	C₂₉×#577	1	1	yes	characteristic
563	C₄	C₂₉×#577	1	1	yes	characteristic
564	C₂	—	4	2	no	—
565	C₂	—	8	1	no	—
566	C₂	C₂₉×#3266	1	1	yes	characteristic
567	C₂	C₂₉×#3282	1	1	yes	characteristic
568	C₂	C₂₉×#3289	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. Q₈×SD₁₆×C₂₉	C₂	semidirect
2. C₂₉×#3369	C₂	semidirect
5. C₂₉×#1718	C₂	semidirect
6. C₂₉×#1700	C₂	semidirect
7. C₂₉×#1683	C₂	semidirect
8. C₂₉×#1680	C₂	semidirect
9. C₂₉×#1671	C₂	semidirect
10. C₂₉×#1650	C₂	semidirect
11. C₂₉×#1649	C₂	semidirect
12. C₂₉×#1645	C₂	semidirect
14. C₂₉×#1582	C₂	semidirect
15. C₂₉×SD₁₆⋊C₈	C₂	semidirect
209. #19796	C₂₉	direct (N × H)
258. Q₈×SD₁₆	C₂×C₂₉	semidirect
259. #3369	C₂×C₂₉	semidirect
262. #1718	C₂×C₂₉	semidirect
263. #1700	C₂×C₂₉	semidirect
264. #1683	C₂×C₂₉	semidirect
265. #1680	C₂×C₂₉	semidirect
266. #1671	C₂×C₂₉	semidirect
267. #1650	C₂×C₂₉	semidirect
268. #1649	C₂×C₂₉	semidirect
269. #1645	C₂×C₂₉	semidirect
271. #1582	C₂×C₂₉	semidirect
272. SD₁₆⋊C₈	C₂×C₂₉	semidirect
428. C₂₉	#19796	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×SD₁₆×C₂₉	2
C₂₉×#3369	2
C₂₉×#3302	2
C₂₉×#3298	2
C₂₉×#1718	2
C₂₉×#1700	2
C₂₉×#1683	2
C₂₉×#1680	2
C₂₉×#1671	2
C₂₉×#1650	2
C₂₉×#1649	2
C₂₉×#1645	2
C₂₉×#1635	2
C₂₉×#1582	2
C₂₉×SD₁₆⋊C₈	2
#19796	29

Subgroups — C29×#19796 #20314696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19796 #20314696