Subgroups — C₂₉×#22466 #20317366

Order 7424.

1384 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#576	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#443	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#2951	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2897	C₂	1	2	yes	maximal, complemented
5	C₂₉×#1978	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1970	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1907	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1883	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1816	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1792	C₂	1	2	yes	maximal, complemented
11	C₂₉×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₉×H(5,𝔽₂)	C₂²	1	2	yes	—
13	C₂₉×#576	—	2	4	no	—
14	C₂₉×#576	C₄	1	8	yes	complemented
15	C₂×C₂₉×AGL(1,ℤ/8)	—	2	2	no	—
16	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
17	C₂×C₂₉×#135	—	2	1	no	—
18	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₂₉	—	2	1	no	—
20	C₂²×D₈×C₂₉	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×#131	C₂²	1	2	yes	complemented
23	C₂₉×#520	C₂²	1	2	yes	complemented
24	C₂₉×#443	—	2	4	no	—
25	C₂₉×#440	—	2	2	no	—
26	C₄×Q₁₆×C₂₉	—	2	1	no	—
27	C₄×D₈×C₂₉	—	2	1	no	—
28	C₂×C₂₉×#108	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₂₉×#104	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×#104	C₂²	1	2	yes	complemented
32	C₂₉×#418	—	2	2	no	—
33	C₂₉×#418	C₂²	1	2	yes	complemented
34	C₂₉×#417	—	2	2	no	—
35	C₂₉×#417	C₂²	1	2	yes	—
36	C₂₉×#417	C₂²	1	2	yes	complemented
37	C₂₉×#416	—	2	2	no	—
38	C₂₉×#416	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×#102	—	2	2	no	—
40	C₂×C₂₉×#102	C₂²	1	2	yes	complemented
41	C₂×C₂₉×#100	C₂²	1	2	yes	complemented
42	C₂₉×#405	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
44	C₂₉×#390	C₂²	1	2	yes	complemented
45	C₂₉×#343	C₂²	1	2	yes	complemented
46	C₂₉×#341	C₂²	1	1	yes	characteristic, complemented
47	C₂₉×#339	C₂²	1	1	yes	characteristic, complemented
48	C₂₉×H(5,𝔽₂)	—	2	4	no	—
49	C₂₉×H(5,𝔽₂)	—	2	4	no	—
50	C₂₉×H(5,𝔽₂)	—	4	2	no	—
51	C₂₉×H(5,𝔽₂)	C₂×C₄	1	8	yes	complemented
52	C₂×#41×C₂₉	—	2	2	no	—
53	C₂×#41×C₂₉	—	2	2	no	—
54	C₂×#41×C₂₉	C₂³	1	2	yes	—
55	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₂₉	—	2	2	no	—
57	C₂²×D₄×C₂₉	—	2	2	no	—
58	C₂²×D₄×C₂₉	—	4	2	no	—
59	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
60	C₂₉×AGL(1,ℤ/8)	—	2	4	no	—
61	C₂₉×AGL(1,ℤ/8)	—	2	16	no	—
62	C₂₉×AGL(1,ℤ/8)	C₂×C₄	1	8	yes	complemented
63	C₂₉×#135	—	2	8	no	—
64	C₂₉×#135	C₂×C₄	1	4	yes	—
65	C₂₉×#135	D₄	1	4	yes	—
66	C₂×Q₁₆×C₂₉	D₄	1	1	yes	characteristic
67	C₂×SD₁₆×C₂₉	—	2	2	no	—
68	C₂×SD₁₆×C₂₉	D₄	1	2	yes	—
69	C₂×D₈×C₂₉	—	2	2	no	—
70	C₂×D₈×C₂₉	—	2	8	no	—
71	C₂×D₈×C₂₉	—	2	1	no	—
72	C₂×D₈×C₂₉	—	2	1	no	—
73	C₂×D₈×C₂₉	—	2	2	no	—
74	C₂×D₈×C₂₉	C₂×C₄	1	4	yes	complemented
75	C₂×D₈×C₂₉	D₄	1	1	yes	characteristic
76	C₂₉×#131	—	2	2	no	—
77	C₂₉×#131	—	2	4	no	—
78	C₂₉×#131	—	4	2	no	—
79	C₂₉×#131	C₂×C₄	1	4	yes	complemented
80	C₂×M₁₆×C₂₉	—	2	1	no	—
81	C₂×M₁₆×C₂₉	—	2	2	no	—
82	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
83	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₂₉	—	2	1	no	—
86	C₂²×C₈×C₂₉	—	2	2	no	—
87	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
89	C₄×Q₈×C₂₉	—	2	2	no	—
90	C₄×D₄×C₂₉	—	2	2	no	—
91	C₄×D₄×C₂₉	—	4	2	no	—
92	C₂₉×#117	—	2	2	no	—
93	C₂₉×#117	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
96	C₂×C₂²⋊C₄×C₂₉	—	4	2	no	—
97	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
98	C₂₉×#108	—	2	2	no	—
99	C₂₉×#107	—	2	1	no	—
100	C₂₉×#107	—	2	1	no	—
101	C₂₉×#104	—	2	4	no	—
102	C₂₉×#104	—	2	2	no	—
103	C₂₉×#103	—	2	2	no	—
104	C₂₉×#103	—	2	2	no	—
105	C₂₉×#103	D₄	1	1	yes	characteristic
106	C₂₉×#103	D₄	1	1	yes	characteristic
107	C₂₉×#102	—	2	2	no	—
108	C₂₉×#102	—	2	2	no	—
109	C₂₉×#102	—	2	2	no	—
110	C₂₉×#102	—	2	2	no	—
111	C₂₉×#102	—	2	2	no	—
112	C₂₉×#102	—	2	2	no	—
113	C₂₉×#102	D₄	1	1	yes	characteristic
114	C₂₉×#102	D₄	1	1	yes	characteristic
115	C₂₉×#100	—	4	2	no	—
116	C₂₉×#97	—	2	1	no	—
117	C₄×C₈×C₂₉	—	2	1	no	—
118	C₄×C₈×C₂₉	—	2	2	no	—
119	C₂⁴×C₂₉	—	2	2	no	—
120	C₂⁴×C₂₉	—	4	2	no	—
121	#41×C₂₉	—	2	1	no	—
122	#41×C₂₉	—	2	2	no	—
123	#41×C₂₉	—	2	2	no	—
124	#41×C₂₉	—	2	1	no	—
125	#41×C₂₉	—	2	8	no	—
126	#41×C₂₉	—	2	8	no	—
127	#41×C₂₉	—	4	4	no	—
128	#41×C₂₉	—	4	4	no	—
129	#41×C₂₉	C₂²×C₄	1	4	yes	—
130	#41×C₂₉	C₂²×C₄	1	2	yes	—
131	#41×C₂₉	C₂×D₄	1	4	yes	—
132	#41×C₂₉	#41	1	2	yes	—
133	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
135	C₂×D₄×C₂₉	—	2	2	no	—
136	C₂×D₄×C₂₉	—	2	1	no	—
137	C₂×D₄×C₂₉	—	2	8	no	—
138	C₂×D₄×C₂₉	—	2	8	no	—
139	C₂×D₄×C₂₉	—	2	2	no	—
140	C₂×D₄×C₂₉	—	2	2	no	—
141	C₂×D₄×C₂₉	—	2	2	no	—
142	C₂×D₄×C₂₉	—	2	2	no	—
143	C₂×D₄×C₂₉	—	2	2	no	—
144	C₂×D₄×C₂₉	—	4	4	no	—
145	C₂×D₄×C₂₉	—	4	4	no	—
146	C₂×D₄×C₂₉	—	4	2	no	—
147	C₂×D₄×C₂₉	—	4	2	no	—
148	C₂×D₄×C₂₉	—	4	8	no	—
149	C₂×D₄×C₂₉	—	4	8	no	—
150	C₂×D₄×C₂₉	C₂²×C₄	1	4	yes	—
151	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
152	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₂₉	—	2	2	no	—
154	C₂²×C₄×C₂₉	—	2	1	no	—
155	C₂²×C₄×C₂₉	—	2	1	no	—
156	C₂²×C₄×C₂₉	—	2	2	no	—
157	C₂²×C₄×C₂₉	—	4	2	no	—
158	C₂²×C₄×C₂₉	—	4	2	no	—
159	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
160	Q₁₆×C₂₉	C₂²⋊C₄	1	4	yes	complemented
161	SD₁₆×C₂₉	—	2	8	no	—
162	SD₁₆×C₂₉	C₂²⋊C₄	1	8	yes	complemented
163	D₈×C₂₉	—	2	8	no	—
164	D₈×C₂₉	—	2	4	no	—
165	D₈×C₂₉	—	2	4	no	—
166	D₈×C₂₉	C₂²⋊C₄	1	4	yes	complemented
167	M₁₆×C₂₉	—	2	1	no	—
168	M₁₆×C₂₉	—	2	4	no	—
169	M₁₆×C₂₉	—	2	2	no	—
170	M₁₆×C₂₉	—	2	1	no	—
171	M₁₆×C₂₉	—	2	2	no	—
172	M₁₆×C₂₉	—	2	1	no	—
173	M₁₆×C₂₉	—	4	4	no	—
174	M₁₆×C₂₉	C₂²×C₄	1	2	yes	—
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	4	no	—
179	C₂×C₈×C₂₉	—	2	2	no	—
180	C₂×C₈×C₂₉	—	2	1	no	—
181	C₂×C₈×C₂₉	—	4	4	no	—
182	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
183	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
188	C₄⋊C₄×C₂₉	—	2	2	no	—
189	C₄⋊C₄×C₂₉	—	2	2	no	—
190	C₄⋊C₄×C₂₉	—	4	2	no	—
191	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
192	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
193	C₂²⋊C₄×C₂₉	—	2	1	no	—
194	C₂²⋊C₄×C₂₉	—	4	2	no	—
195	C₂²⋊C₄×C₂₉	—	8	4	no	—
196	C₄²×C₂₉	—	2	1	no	—
197	C₄²×C₂₉	—	2	1	no	—
198	C₄²×C₂₉	—	2	1	no	—
199	C₄²×C₂₉	—	4	2	no	—
200	#22466	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂³×C₂₉	—	2	2	no	—
202	C₂³×C₂₉	—	2	1	no	—
203	C₂³×C₂₉	—	2	4	no	—
204	C₂³×C₂₉	—	4	8	no	—
205	C₂³×C₂₉	—	4	2	no	—
206	C₂³×C₂₉	—	4	2	no	—
207	C₂³×C₂₉	—	8	2	no	—
208	C₂³×C₂₉	—	8	2	no	—
209	C₂³×C₂₉	—	16	2	no	—
210	C₂³×C₂₉	—	16	2	no	—
211	C₂³×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
212	Q₈×C₂₉	—	2	1	no	—
213	Q₈×C₂₉	—	2	2	no	—
214	Q₈×C₂₉	C₂×C₂²⋊C₄	1	4	yes	—
215	Q₈×C₂₉	C₄×D₄	1	2	yes	—
216	D₄×C₂₉	—	2	2	no	—
217	D₄×C₂₉	—	2	4	no	—
218	D₄×C₂₉	—	2	2	no	—
219	D₄×C₂₉	—	2	4	no	—
220	D₄×C₂₉	—	2	4	no	—
221	D₄×C₂₉	—	2	4	no	—
222	D₄×C₂₉	—	2	1	no	—
223	D₄×C₂₉	—	2	2	no	—
224	D₄×C₂₉	—	4	8	no	—
225	D₄×C₂₉	—	4	8	no	—
226	D₄×C₂₉	—	4	2	no	—
227	D₄×C₂₉	—	4	2	no	—
228	D₄×C₂₉	C₂×C₂²⋊C₄	1	4	yes	—
229	D₄×C₂₉	C₄×D₄	1	2	yes	—
230	C₂×C₄×C₂₉	—	2	2	no	—
231	C₂×C₄×C₂₉	—	2	1	no	—
232	C₂×C₄×C₂₉	—	2	2	no	—
233	C₂×C₄×C₂₉	—	2	4	no	—
234	C₂×C₄×C₂₉	—	2	4	no	—
235	C₂×C₄×C₂₉	—	2	2	no	—
236	C₂×C₄×C₂₉	—	2	2	no	—
237	C₂×C₄×C₂₉	—	2	1	no	—
238	C₂×C₄×C₂₉	—	2	1	no	—
239	C₂×C₄×C₂₉	—	4	8	no	—
240	C₂×C₄×C₂₉	—	4	1	no	—
241	C₂×C₄×C₂₉	—	4	1	no	—
242	C₂×C₄×C₂₉	—	4	2	no	—
243	C₂×C₄×C₂₉	—	8	2	no	—
244	C₂×C₄×C₂₉	—	16	2	no	—
245	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
251	C₈×C₂₉	—	2	2	no	—
252	C₈×C₂₉	—	2	1	no	—
253	C₈×C₂₉	—	2	1	no	—
254	C₈×C₂₉	—	4	2	no	—
255	C₈×C₂₉	—	4	1	no	—
256	C₈×C₂₉	C₂×C₂²⋊C₄	1	2	yes	—
257	C₈×C₂₉	C₂×C₂²⋊C₄	1	2	yes	—
258	C₂×#576	C₂×C₂₉	1	1	yes	characteristic
259	C₂×#443	C₂×C₂₉	1	1	yes	characteristic, complemented
260	#2951	C₂×C₂₉	1	1	yes	characteristic, complemented
261	#2897	C₂×C₂₉	1	2	yes	complemented
262	#1978	C₂×C₂₉	1	1	yes	characteristic, complemented
263	#1970	C₂×C₂₉	1	1	yes	characteristic, complemented
264	#1907	C₂×C₂₉	1	2	yes	complemented
265	#1883	C₂×C₂₉	1	2	yes	complemented
266	#1816	C₂×C₂₉	1	1	yes	characteristic, complemented
267	#1792	C₂×C₂₉	1	2	yes	complemented
268	#1764	C₂×C₂₉	1	1	yes	characteristic, complemented
269	C₂²×C₂₉	—	2	1	no	—
270	C₂²×C₂₉	—	2	1	no	—
271	C₂²×C₂₉	—	2	2	no	—
272	C₂²×C₂₉	—	2	4	no	—
273	C₂²×C₂₉	—	4	2	no	—
274	C₂²×C₂₉	—	4	1	no	—
275	C₂²×C₂₉	—	4	2	no	—
276	C₂²×C₂₉	—	4	1	no	—
277	C₂²×C₂₉	—	4	4	no	—
278	C₂²×C₂₉	—	8	4	no	—
279	C₂²×C₂₉	—	8	2	no	—
280	C₂²×C₂₉	—	8	2	no	—
281	C₂²×C₂₉	—	16	2	no	—
282	C₂²×C₂₉	—	16	8	no	—
283	C₂²×C₂₉	#518	1	1	yes	characteristic
284	C₂²×C₂₉	D₄²	1	1	yes	characteristic
285	C₂²×C₂₉	#546	1	1	yes	characteristic
286	C₄×C₂₉	—	2	2	no	—
287	C₄×C₂₉	—	2	4	no	—
288	C₄×C₂₉	—	4	2	no	—
289	C₄×C₂₉	—	4	1	no	—
290	C₄×C₂₉	—	4	1	no	—
291	C₄×C₂₉	—	8	2	no	—
292	C₄×C₂₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
293	C₄×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
294	C₄×C₂₉	D₄²	1	1	yes	characteristic
295	C₄×C₂₉	#546	1	1	yes	characteristic
296	C₂×H(5,𝔽₂)	C₂²×C₂₉	1	2	yes	—
297	#576	—	2	4	no	—
298	#576	C₄×C₂₉	1	8	yes	complemented
299	C₂×AGL(1,ℤ/8)	—	2	2	no	—
300	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	2	yes	—
301	C₂×#135	—	2	1	no	—
302	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
303	C₂²×D₈	—	2	1	no	—
304	C₂²×D₈	C₂²×C₂₉	1	1	yes	characteristic
305	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
306	C₂×#131	C₂²×C₂₉	1	2	yes	complemented
307	#520	C₂²×C₂₉	1	2	yes	complemented
308	#443	—	2	4	no	—
309	#440	—	2	2	no	—
310	C₄×Q₁₆	—	2	1	no	—
311	C₄×D₈	—	2	1	no	—
312	C₂×#108	C₂²×C₂₉	1	1	yes	characteristic, complemented
313	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic, complemented
314	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
315	C₂×#104	C₂²×C₂₉	1	2	yes	complemented
316	#418	—	2	2	no	—
317	#418	C₂²×C₂₉	1	2	yes	complemented
318	#417	—	2	2	no	—
319	#417	C₂²×C₂₉	1	2	yes	—
320	#417	C₂²×C₂₉	1	2	yes	complemented
321	#416	—	2	2	no	—
322	#416	C₂²×C₂₉	1	1	yes	characteristic
323	C₂×#102	—	2	2	no	—
324	C₂×#102	C₂²×C₂₉	1	2	yes	complemented
325	C₂×#100	C₂²×C₂₉	1	2	yes	complemented
326	#405	C₂²×C₂₉	1	1	yes	characteristic, complemented
327	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
328	#390	C₂²×C₂₉	1	2	yes	complemented
329	#343	C₂²×C₂₉	1	2	yes	complemented
330	#341	C₂²×C₂₉	1	1	yes	characteristic, complemented
331	#339	C₂²×C₂₉	1	1	yes	characteristic, complemented
332	C₂×C₂₉	—	2	1	no	—
333	C₂×C₂₉	—	2	1	no	—
334	C₂×C₂₉	—	4	4	no	—
335	C₂×C₂₉	—	4	2	no	—
336	C₂×C₂₉	—	8	4	no	—
337	C₂×C₂₉	D₄×C₂²⋊C₄	1	1	yes	characteristic
338	C₂×C₂₉	#3290	1	1	yes	characteristic
339	C₂×C₂₉	#3292	1	1	yes	characteristic
340	H(5,𝔽₂)	—	2	4	no	—
341	H(5,𝔽₂)	—	2	4	no	—
342	H(5,𝔽₂)	—	4	2	no	—
343	H(5,𝔽₂)	C₂×C₄×C₂₉	1	8	yes	complemented
344	C₂×#41	—	2	2	no	—
345	C₂×#41	—	2	2	no	—
346	C₂×#41	C₂³×C₂₉	1	2	yes	—
347	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
348	C₂²×D₄	—	2	2	no	—
349	C₂²×D₄	—	2	2	no	—
350	C₂²×D₄	—	4	2	no	—
351	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
352	AGL(1,ℤ/8)	—	2	4	no	—
353	AGL(1,ℤ/8)	—	2	16	no	—
354	AGL(1,ℤ/8)	C₂×C₄×C₂₉	1	8	yes	complemented
355	#135	—	2	8	no	—
356	#135	C₂×C₄×C₂₉	1	4	yes	—
357	#135	D₄×C₂₉	1	4	yes	—
358	C₂×Q₁₆	D₄×C₂₉	1	1	yes	characteristic
359	C₂×SD₁₆	—	2	2	no	—
360	C₂×SD₁₆	D₄×C₂₉	1	2	yes	—
361	C₂×D₈	—	2	2	no	—
362	C₂×D₈	—	2	8	no	—
363	C₂×D₈	—	2	1	no	—
364	C₂×D₈	—	2	1	no	—
365	C₂×D₈	—	2	2	no	—
366	C₂×D₈	C₂×C₄×C₂₉	1	4	yes	complemented
367	C₂×D₈	D₄×C₂₉	1	1	yes	characteristic
368	#131	—	2	2	no	—
369	#131	—	2	4	no	—
370	#131	—	4	2	no	—
371	#131	C₂×C₄×C₂₉	1	4	yes	complemented
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	2	no	—
374	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
375	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
376	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	2	2	no	—
379	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
381	C₄×Q₈	—	2	2	no	—
382	C₄×D₄	—	2	2	no	—
383	C₄×D₄	—	4	2	no	—
384	#117	—	2	2	no	—
385	#117	C₂³×C₂₉	1	1	yes	characteristic
386	C₂×C₄⋊C₄	—	2	2	no	—
387	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
388	C₂×C₂²⋊C₄	—	4	2	no	—
389	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
390	#108	—	2	2	no	—
391	#107	—	2	1	no	—
392	#107	—	2	1	no	—
393	#104	—	2	4	no	—
394	#104	—	2	2	no	—
395	#103	—	2	2	no	—
396	#103	—	2	2	no	—
397	#103	D₄×C₂₉	1	1	yes	characteristic
398	#103	D₄×C₂₉	1	1	yes	characteristic
399	#102	—	2	2	no	—
400	#102	—	2	2	no	—
401	#102	—	2	2	no	—
402	#102	—	2	2	no	—
403	#102	—	2	2	no	—
404	#102	—	2	2	no	—
405	#102	D₄×C₂₉	1	1	yes	characteristic
406	#102	D₄×C₂₉	1	1	yes	characteristic
407	#100	—	4	2	no	—
408	#97	—	2	1	no	—
409	C₄×C₈	—	2	2	no	—
410	C₄×C₈	—	2	1	no	—
411	C₂₉	#22466	1	1	yes	characteristic, direct product factor, Sylow
412	C₂⁴	—	2	2	no	—
413	C₂⁴	—	4	2	no	—
414	#41	—	2	1	no	—
415	#41	—	2	2	no	—
416	#41	—	2	2	no	—
417	#41	—	2	1	no	—
418	#41	—	2	8	no	—
419	#41	—	2	8	no	—
420	#41	—	4	4	no	—
421	#41	—	4	4	no	—
422	#41	C₂²×C₄×C₂₉	1	4	yes	—
423	#41	C₂²×C₄×C₂₉	1	2	yes	—
424	#41	C₂×D₄×C₂₉	1	4	yes	—
425	#41	#41×C₂₉	1	2	yes	—
426	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
427	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	8	no	—
431	C₂×D₄	—	2	8	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	4	4	no	—
438	C₂×D₄	—	4	4	no	—
439	C₂×D₄	—	4	2	no	—
440	C₂×D₄	—	4	2	no	—
441	C₂×D₄	—	4	8	no	—
442	C₂×D₄	—	4	8	no	—
443	C₂×D₄	C₂²×C₄×C₂₉	1	4	yes	—
444	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
445	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	4	2	no	—
451	C₂²×C₄	—	4	2	no	—
452	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
453	Q₁₆	C₂²⋊C₄×C₂₉	1	4	yes	complemented
454	SD₁₆	—	2	8	no	—
455	SD₁₆	C₂²⋊C₄×C₂₉	1	8	yes	complemented
456	D₈	—	2	8	no	—
457	D₈	—	2	4	no	—
458	D₈	—	2	4	no	—
459	D₈	C₂²⋊C₄×C₂₉	1	4	yes	complemented
460	M₁₆	—	2	1	no	—
461	M₁₆	—	2	4	no	—
462	M₁₆	—	2	2	no	—
463	M₁₆	—	2	1	no	—
464	M₁₆	—	2	1	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	—	4	4	no	—
467	M₁₆	C₂²×C₄×C₂₉	1	2	yes	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	4	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	4	4	no	—
475	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
476	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
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	2	yes	—
480	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	4	2	no	—
484	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
485	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	4	2	no	—
488	C₂²⋊C₄	—	8	4	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	4	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	4	8	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	2	no	—
499	C₂³	—	8	2	no	—
500	C₂³	—	8	2	no	—
501	C₂³	—	16	2	no	—
502	C₂³	—	16	2	no	—
503	C₂³	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
504	Q₈	—	2	1	no	—
505	Q₈	—	2	2	no	—
506	Q₈	C₂×C₂²⋊C₄×C₂₉	1	4	yes	—
507	Q₈	C₄×D₄×C₂₉	1	2	yes	—
508	D₄	—	2	2	no	—
509	D₄	—	2	4	no	—
510	D₄	—	2	2	no	—
511	D₄	—	2	4	no	—
512	D₄	—	2	4	no	—
513	D₄	—	2	4	no	—
514	D₄	—	2	1	no	—
515	D₄	—	2	2	no	—
516	D₄	—	4	8	no	—
517	D₄	—	4	8	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	2	no	—
520	D₄	C₂×C₂²⋊C₄×C₂₉	1	4	yes	—
521	D₄	C₄×D₄×C₂₉	1	2	yes	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	4	8	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	8	2	no	—
536	C₂×C₄	—	16	2	no	—
537	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
538	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
539	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
540	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
541	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
542	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
543	C₈	—	2	2	no	—
544	C₈	—	2	1	no	—
545	C₈	—	2	1	no	—
546	C₈	—	4	2	no	—
547	C₈	—	4	1	no	—
548	C₈	C₂×C₂²⋊C₄×C₂₉	1	2	yes	—
549	C₈	C₂×C₂²⋊C₄×C₂₉	1	2	yes	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	8	4	no	—
560	C₂²	—	8	2	no	—
561	C₂²	—	8	2	no	—
562	C₂²	—	16	2	no	—
563	C₂²	—	16	8	no	—
564	C₂²	C₂₉×#518	1	1	yes	characteristic
565	C₂²	D₄²×C₂₉	1	1	yes	characteristic
566	C₂²	C₂₉×#546	1	1	yes	characteristic
567	C₄	—	2	2	no	—
568	C₄	—	2	4	no	—
569	C₄	—	4	2	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	8	2	no	—
573	C₄	C₂²×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
574	C₄	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
575	C₄	D₄²×C₂₉	1	1	yes	characteristic
576	C₄	C₂₉×#546	1	1	yes	characteristic
577	C₂	—	2	1	no	—
578	C₂	—	2	1	no	—
579	C₂	—	4	2	no	—
580	C₂	—	4	4	no	—
581	C₂	—	8	4	no	—
582	C₂	D₄×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
583	C₂	C₂₉×#3290	1	1	yes	characteristic
584	C₂	C₂₉×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#576	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₉×#443	C₂	semidirect
3. C₂₉×#2951	C₂	semidirect
4. C₂₉×#2897	C₂	semidirect
5. C₂₉×#1978	C₂	semidirect
6. C₂₉×#1970	C₂	semidirect
7. C₂₉×#1907	C₂	semidirect
8. C₂₉×#1883	C₂	semidirect
9. C₂₉×#1816	C₂	semidirect
10. C₂₉×#1792	C₂	semidirect
11. C₂₉×#1764	C₂	semidirect
14. C₂₉×#576	C₄	semidirect
22. C₂×C₂₉×#131	C₂²	semidirect
23. C₂₉×#520	C₂²	semidirect
28. C₂×C₂₉×#108	C₂²	semidirect
29. C₂×C₂₉×#107	C₂²	semidirect
31. C₂×C₂₉×#104	C₂²	semidirect
33. C₂₉×#418	C₂²	semidirect
36. C₂₉×#417	C₂²	semidirect
40. C₂×C₂₉×#102	C₂²	semidirect
41. C₂×C₂₉×#100	C₂²	semidirect
42. C₂₉×#405	C₂²	semidirect
43. C₂×C₄×C₈×C₂₉	C₂²	semidirect
44. C₂₉×#390	C₂²	semidirect
45. C₂₉×#343	C₂²	semidirect
46. C₂₉×#341	C₂²	semidirect
47. C₂₉×#339	C₂²	semidirect
51. C₂₉×H(5,𝔽₂)	C₂×C₄	semidirect
62. C₂₉×AGL(1,ℤ/8)	C₂×C₄	semidirect
74. C₂×D₈×C₂₉	C₂×C₄	semidirect
79. C₂₉×#131	C₂×C₄	semidirect
160. Q₁₆×C₂₉	C₂²⋊C₄	semidirect
162. SD₁₆×C₂₉	C₂²⋊C₄	semidirect
166. D₈×C₂₉	C₂²⋊C₄	semidirect
200. #22466	C₂₉	direct (N × H)
259. C₂×#443	C₂×C₂₉	semidirect
260. #2951	C₂×C₂₉	semidirect
261. #2897	C₂×C₂₉	semidirect
262. #1978	C₂×C₂₉	semidirect
263. #1970	C₂×C₂₉	semidirect
264. #1907	C₂×C₂₉	semidirect
265. #1883	C₂×C₂₉	semidirect
266. #1816	C₂×C₂₉	semidirect
267. #1792	C₂×C₂₉	semidirect
268. #1764	C₂×C₂₉	semidirect
298. #576	C₄×C₂₉	semidirect
306. C₂×#131	C₂²×C₂₉	semidirect
307. #520	C₂²×C₂₉	semidirect
312. C₂×#108	C₂²×C₂₉	semidirect
313. C₂×#107	C₂²×C₂₉	semidirect
315. C₂×#104	C₂²×C₂₉	semidirect
317. #418	C₂²×C₂₉	semidirect
320. #417	C₂²×C₂₉	semidirect
324. C₂×#102	C₂²×C₂₉	semidirect
325. C₂×#100	C₂²×C₂₉	semidirect
326. #405	C₂²×C₂₉	semidirect
327. C₂×C₄×C₈	C₂²×C₂₉	semidirect
328. #390	C₂²×C₂₉	semidirect
329. #343	C₂²×C₂₉	semidirect
330. #341	C₂²×C₂₉	semidirect
331. #339	C₂²×C₂₉	semidirect
343. H(5,𝔽₂)	C₂×C₄×C₂₉	semidirect
354. AGL(1,ℤ/8)	C₂×C₄×C₂₉	semidirect
366. C₂×D₈	C₂×C₄×C₂₉	semidirect
371. #131	C₂×C₄×C₂₉	semidirect
411. C₂₉	#22466	direct (N × H)
453. Q₁₆	C₂²⋊C₄×C₂₉	semidirect
455. SD₁₆	C₂²⋊C₄×C₂₉	semidirect
459. D₈	C₂²⋊C₄×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#576	2
C₂×C₂₉×#443	2
C₂₉×#2951	2
C₂₉×#2897	2
C₂₉×#1978	2
C₂₉×#1970	2
C₂₉×#1907	2
C₂₉×#1883	2
C₂₉×#1816	2
C₂₉×#1792	2
C₂₉×#1764	2
#22466	29

Subgroups — C29×#22466 #20317366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#22466 #20317366