Subgroups — C₂₉×#33835 #20328735

Order 7424.

670 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3285	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3283	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2251	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2220	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2216	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2210	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#2209	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#2189	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#2189	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#2188	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#2186	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#2175	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
20	C₂₉×#548	—	2	1	no	—
21	C₂₉×#547	—	2	1	no	—
22	C₂₉×#510	—	2	4	no	—
23	C₂₉×#508	—	2	4	no	—
24	C₂×C₂₉×Q₃₂	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×Q₃₂	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×Q₃₂	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×Q₃₂	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×SD₃₂	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×SD₃₂	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×SD₃₂	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×SD₃₂	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×D₁₆	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×M₃₂	C₂²	1	1	yes	characteristic
34	C₂²×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
35	C₂₉×#495	C₂²	1	1	yes	characteristic
36	C₂₉×#494	C₂²	1	1	yes	characteristic
37	C₂₉×#467	C₂²	1	1	yes	characteristic
38	C₂₉×#467	C₂²	1	1	yes	characteristic
39	C₂₉×#467	C₂²	1	1	yes	characteristic
40	C₂₉×#466	C₂²	1	1	yes	characteristic
41	C₂₉×#464	—	2	1	no	—
42	C₂₉×#461	—	2	1	no	—
43	C₂₉×#452	—	2	1	no	—
44	C₂₉×#452	—	2	1	no	—
45	C₂₉×#452	—	2	1	no	—
46	C₂₉×#448	—	2	1	no	—
47	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
48	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
49	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
50	C₂₉×#366	C₂²	1	1	yes	characteristic
51	C₂₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
52	C₂₉×#358	C₂²	1	1	yes	characteristic
53	C₂₉×#358	C₂²	1	1	yes	characteristic
54	C₂₉×#358	C₂²	1	1	yes	characteristic
55	C₂₉×#358	C₂²	1	1	yes	characteristic
56	C₂₉×#357	C₂²	1	1	yes	characteristic
57	C₂₉×#357	C₂²	1	1	yes	characteristic
58	C₂₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
59	C₂₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
60	C₂₉×#346	C₂²	1	1	yes	characteristic
61	C₂×#41×C₂₉	—	2	1	no	—
62	C₂×#41×C₂₉	—	2	1	no	—
63	C₂×#41×C₂₉	—	2	1	no	—
64	C₂²×Q₈×C₂₉	—	2	1	no	—
65	C₂₉×#135	—	2	2	no	—
66	C₂₉×#135	—	2	2	no	—
67	C₂₉×#135	—	2	2	no	—
68	C₂₉×#135	—	4	1	no	—
69	C₂₉×#135	—	4	1	no	—
70	C₂₉×#135	—	4	1	no	—
71	C₂×Q₁₆×C₂₉	—	2	2	no	—
72	C₂×Q₁₆×C₂₉	—	2	1	no	—
73	C₂×Q₁₆×C₂₉	—	2	1	no	—
74	C₂×Q₁₆×C₂₉	—	4	1	no	—
75	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
76	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
77	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
78	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
79	C₂×SD₁₆×C₂₉	—	2	1	no	—
80	C₂×SD₁₆×C₂₉	—	2	1	no	—
81	C₂×SD₁₆×C₂₉	—	2	1	no	—
82	C₂×SD₁₆×C₂₉	—	2	1	no	—
83	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
84	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
87	C₂₉×C₄⋊Q₈	—	2	1	no	—
88	C₂₉×#124	—	2	1	no	—
89	C₂₉×#124	—	4	1	no	—
90	C₂₉×#123	—	4	1	no	—
91	C₂₉×#123	—	4	1	no	—
92	C₂₉×C₂²⋊Q₈	—	2	1	no	—
93	C₂₉×C₂²⋊Q₈	—	2	1	no	—
94	C₂₉×C₂²⋊Q₈	—	2	1	no	—
95	C₂₉×C₂²⋊Q₈	—	4	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×D₄×C₂₉	—	2	1	no	—
101	C₄×D₄×C₂₉	—	4	1	no	—
102	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
104	C₂₉×Q₃₂	—	2	2	no	—
105	C₂₉×Q₃₂	—	2	2	no	—
106	C₂₉×Q₃₂	—	2	2	no	—
107	C₂₉×Q₃₂	—	4	1	no	—
108	C₂₉×SD₃₂	—	2	2	no	—
109	C₂₉×SD₃₂	—	2	2	no	—
110	C₂₉×SD₃₂	—	4	1	no	—
111	C₂₉×SD₃₂	D₄	1	4	yes	complemented
112	C₂₉×D₁₆	—	2	2	no	—
113	C₂₉×M₃₂	—	2	2	no	—
114	C₂×C₁₆×C₂₉	—	2	2	no	—
115	C₂×C₁₆×C₂₉	C₂³	1	1	yes	characteristic
116	C₂×C₁₆×C₂₉	C₂³	1	1	yes	characteristic
117	C₂×C₁₆×C₂₉	C₂³	1	1	yes	characteristic
118	C₂×C₁₆×C₂₉	C₂³	1	1	yes	characteristic
119	C₂₉×#107	C₂³	1	1	yes	characteristic
120	C₂₉×#107	C₂³	1	1	yes	characteristic
121	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
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×#102	—	2	1	no	—
127	C₂₉×#102	—	2	1	no	—
128	C₂₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
129	C₂₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
130	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
131	#41×C₂₉	—	4	2	no	—
132	#41×C₂₉	—	4	2	no	—
133	#41×C₂₉	—	4	2	no	—
134	#41×C₂₉	—	8	1	no	—
135	#41×C₂₉	—	8	1	no	—
136	#41×C₂₉	—	8	1	no	—
137	C₂×Q₈×C₂₉	—	2	1	no	—
138	C₂×Q₈×C₂₉	—	2	1	no	—
139	C₂×Q₈×C₂₉	—	2	1	no	—
140	C₂×Q₈×C₂₉	—	2	1	no	—
141	C₂×Q₈×C₂₉	—	4	2	no	—
142	C₂×Q₈×C₂₉	—	4	1	no	—
143	C₂×Q₈×C₂₉	—	8	1	no	—
144	C₂×D₄×C₂₉	—	2	1	no	—
145	C₂×D₄×C₂₉	—	2	1	no	—
146	C₂×D₄×C₂₉	—	4	1	no	—
147	C₂×D₄×C₂₉	—	4	1	no	—
148	C₂×D₄×C₂₉	—	4	1	no	—
149	C₂×D₄×C₂₉	—	4	1	no	—
150	C₂×D₄×C₂₉	D₈	1	1	yes	characteristic
151	C₂²×C₄×C₂₉	—	4	1	no	—
152	C₂²×C₄×C₂₉	—	4	1	no	—
153	C₂²×C₄×C₂₉	—	4	1	no	—
154	C₂²×C₄×C₂₉	—	4	1	no	—
155	C₂²×C₄×C₂₉	—	4	1	no	—
156	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
158	Q₁₆×C₂₉	—	2	1	no	—
159	Q₁₆×C₂₉	—	2	1	no	—
160	Q₁₆×C₂₉	—	2	1	no	—
161	Q₁₆×C₂₉	—	2	1	no	—
162	Q₁₆×C₂₉	—	2	1	no	—
163	Q₁₆×C₂₉	—	2	1	no	—
164	Q₁₆×C₂₉	—	2	1	no	—
165	Q₁₆×C₂₉	—	4	2	no	—
166	Q₁₆×C₂₉	—	8	1	no	—
167	Q₁₆×C₂₉	C₂×D₄	1	2	yes	—
168	SD₁₆×C₂₉	—	4	2	no	—
169	SD₁₆×C₂₉	—	4	2	no	—
170	SD₁₆×C₂₉	—	4	2	no	—
171	SD₁₆×C₂₉	—	8	1	no	—
172	D₈×C₂₉	—	2	1	no	—
173	D₈×C₂₉	—	2	1	no	—
174	D₈×C₂₉	—	2	1	no	—
175	D₈×C₂₉	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
180	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
184	C₄⋊C₄×C₂₉	—	2	1	no	—
185	C₄⋊C₄×C₂₉	—	2	1	no	—
186	C₄⋊C₄×C₂₉	—	4	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	D₈	1	1	yes	characteristic
193	C₂²⋊C₄×C₂₉	—	4	1	no	—
194	C₂²⋊C₄×C₂₉	—	4	1	no	—
195	C₂²⋊C₄×C₂₉	—	4	1	no	—
196	C₂²⋊C₄×C₂₉	—	4	1	no	—
197	C₂²⋊C₄×C₂₉	—	4	1	no	—
198	C₂²⋊C₄×C₂₉	—	4	1	no	—
199	C₂²⋊C₄×C₂₉	—	4	1	no	—
200	C₂²⋊C₄×C₂₉	D₈	1	1	yes	characteristic
201	C₂²⋊C₄×C₂₉	D₈	1	1	yes	characteristic
202	C₄²×C₂₉	—	4	1	no	—
203	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
204	C₁₆×C₂₉	—	2	1	no	—
205	C₁₆×C₂₉	—	2	1	no	—
206	C₁₆×C₂₉	—	2	1	no	—
207	C₁₆×C₂₉	C₂×D₄	1	2	yes	—
208	#33835	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂³×C₂₉	—	4	1	no	—
210	C₂³×C₂₉	—	4	1	no	—
211	C₂³×C₂₉	C₂×D₈	1	1	yes	characteristic
212	C₂³×C₂₉	C₂×D₈	1	1	yes	characteristic
213	Q₈×C₂₉	—	2	2	no	—
214	Q₈×C₂₉	—	4	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	D₄×C₂₉	—	2	2	no	—
223	D₄×C₂₉	—	4	1	no	—
224	D₄×C₂₉	—	4	1	no	—
225	D₄×C₂₉	—	4	1	no	—
226	D₄×C₂₉	—	4	1	no	—
227	D₄×C₂₉	—	8	2	no	—
228	D₄×C₂₉	—	8	2	no	—
229	D₄×C₂₉	—	8	2	no	—
230	D₄×C₂₉	—	8	2	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	—	4	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	—	8	2	no	—
242	C₂×C₄×C₂₉	—	8	2	no	—
243	C₂×C₄×C₂₉	—	8	2	no	—
244	C₂×C₄×C₂₉	—	8	2	no	—
245	C₂×C₄×C₂₉	—	8	2	no	—
246	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
247	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
248	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
249	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
250	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
251	C₈×C₂₉	—	2	1	no	—
252	C₈×C₂₉	—	2	1	no	—
253	C₈×C₂₉	—	2	1	no	—
254	C₈×C₂₉	C₂²×D₄	1	1	yes	characteristic
255	C₈×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
256	C₂×#510	C₂×C₂₉	1	1	yes	characteristic, complemented
257	C₂×#508	C₂×C₂₉	1	1	yes	characteristic, complemented
258	#3285	C₂×C₂₉	1	1	yes	characteristic, complemented
259	#3283	C₂×C₂₉	1	1	yes	characteristic, complemented
260	#2251	C₂×C₂₉	1	1	yes	characteristic, complemented
261	#2220	C₂×C₂₉	1	1	yes	characteristic, complemented
262	#2216	C₂×C₂₉	1	1	yes	characteristic, complemented
263	#2210	C₂×C₂₉	1	1	yes	characteristic, complemented
264	#2209	C₂×C₂₉	1	1	yes	characteristic, complemented
265	#2189	C₂×C₂₉	1	1	yes	characteristic, complemented
266	#2189	C₂×C₂₉	1	1	yes	characteristic, complemented
267	#2188	C₂×C₂₉	1	1	yes	characteristic, complemented
268	#2186	C₂×C₂₉	1	1	yes	characteristic, complemented
269	#2175	C₂×C₂₉	1	1	yes	characteristic, complemented
270	#2168	C₂×C₂₉	1	1	yes	characteristic, complemented
271	C₂²×C₂₉	—	2	1	no	—
272	C₂²×C₂₉	—	2	1	no	—
273	C₂²×C₂₉	—	2	1	no	—
274	C₂²×C₂₉	—	2	1	no	—
275	C₂²×C₂₉	—	2	1	no	—
276	C₂²×C₂₉	—	2	1	no	—
277	C₂²×C₂₉	—	4	2	no	—
278	C₂²×C₂₉	—	8	1	no	—
279	C₂²×C₂₉	—	8	1	no	—
280	C₂²×C₂₉	—	8	1	no	—
281	C₂²×C₂₉	—	8	1	no	—
282	C₂²×C₂₉	—	8	1	no	—
283	C₂²×C₂₉	C₂²×D₈	1	1	yes	characteristic
284	C₄×C₂₉	—	2	1	no	—
285	C₄×C₂₉	—	2	1	no	—
286	C₄×C₂₉	—	2	1	no	—
287	C₄×C₂₉	—	2	1	no	—
288	C₄×C₂₉	—	4	2	no	—
289	C₄×C₂₉	—	8	1	no	—
290	C₄×C₂₉	—	8	1	no	—
291	C₄×C₂₉	—	8	1	no	—
292	C₄×C₂₉	—	8	1	no	—
293	C₄×C₂₉	—	8	1	no	—
294	C₄×C₂₉	D₄²	1	1	yes	characteristic
295	C₄×C₂₉	#576	1	1	yes	characteristic
296	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
297	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
298	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
299	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
300	#548	—	2	1	no	—
301	#547	—	2	1	no	—
302	#510	—	2	4	no	—
303	#508	—	2	4	no	—
304	C₂×Q₃₂	C₂²×C₂₉	1	1	yes	characteristic
305	C₂×Q₃₂	C₂²×C₂₉	1	1	yes	characteristic
306	C₂×Q₃₂	C₂²×C₂₉	1	1	yes	characteristic
307	C₂×Q₃₂	C₂²×C₂₉	1	1	yes	characteristic
308	C₂×SD₃₂	C₂²×C₂₉	1	1	yes	characteristic
309	C₂×SD₃₂	C₂²×C₂₉	1	1	yes	characteristic
310	C₂×SD₃₂	C₂²×C₂₉	1	1	yes	characteristic
311	C₂×SD₃₂	C₂²×C₂₉	1	1	yes	characteristic
312	C₂×D₁₆	C₂²×C₂₉	1	1	yes	characteristic
313	C₂×M₃₂	C₂²×C₂₉	1	1	yes	characteristic
314	C₂²×C₁₆	C₂²×C₂₉	1	1	yes	characteristic
315	#495	C₂²×C₂₉	1	1	yes	characteristic
316	#494	C₂²×C₂₉	1	1	yes	characteristic
317	#467	C₂²×C₂₉	1	1	yes	characteristic
318	#467	C₂²×C₂₉	1	1	yes	characteristic
319	#467	C₂²×C₂₉	1	1	yes	characteristic
320	#466	C₂²×C₂₉	1	1	yes	characteristic
321	#464	—	2	1	no	—
322	#461	—	2	1	no	—
323	#452	—	2	1	no	—
324	#452	—	2	1	no	—
325	#452	—	2	1	no	—
326	#448	—	2	1	no	—
327	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
328	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
329	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
330	#366	C₂²×C₂₉	1	1	yes	characteristic
331	C₄⋊C₁₆	C₂²×C₂₉	1	1	yes	characteristic
332	#358	C₂²×C₂₉	1	1	yes	characteristic
333	#358	C₂²×C₂₉	1	1	yes	characteristic
334	#358	C₂²×C₂₉	1	1	yes	characteristic
335	#358	C₂²×C₂₉	1	1	yes	characteristic
336	#357	C₂²×C₂₉	1	1	yes	characteristic
337	#357	C₂²×C₂₉	1	1	yes	characteristic
338	C₂²⋊C₁₆	C₂²×C₂₉	1	1	yes	characteristic
339	C₂²⋊C₁₆	C₂²×C₂₉	1	1	yes	characteristic
340	#346	C₂²×C₂₉	1	1	yes	characteristic
341	C₂×C₂₉	—	4	1	no	—
342	C₂×C₂₉	—	4	1	no	—
343	C₂×C₂₉	—	8	2	no	—
344	C₂×C₂₉	—	16	1	no	—
345	C₂×C₂₉	D₄×D₈	1	1	yes	characteristic
346	C₂×C₂₉	#3414	1	1	yes	characteristic
347	C₂×C₂₉	#3417	1	1	yes	characteristic
348	C₂×#41	—	2	1	no	—
349	C₂×#41	—	2	1	no	—
350	C₂×#41	—	2	1	no	—
351	C₂²×Q₈	—	2	1	no	—
352	#135	—	2	2	no	—
353	#135	—	2	2	no	—
354	#135	—	2	2	no	—
355	#135	—	4	1	no	—
356	#135	—	4	1	no	—
357	#135	—	4	1	no	—
358	C₂×Q₁₆	—	2	2	no	—
359	C₂×Q₁₆	—	2	1	no	—
360	C₂×Q₁₆	—	2	1	no	—
361	C₂×Q₁₆	—	4	1	no	—
362	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
363	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
364	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
365	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
366	C₂×SD₁₆	—	2	1	no	—
367	C₂×SD₁₆	—	2	1	no	—
368	C₂×SD₁₆	—	2	1	no	—
369	C₂×SD₁₆	—	2	1	no	—
370	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
371	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
373	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
374	C₄⋊Q₈	—	2	1	no	—
375	#124	—	2	1	no	—
376	#124	—	4	1	no	—
377	#123	—	4	1	no	—
378	#123	—	4	1	no	—
379	C₂²⋊Q₈	—	2	1	no	—
380	C₂²⋊Q₈	—	2	1	no	—
381	C₂²⋊Q₈	—	2	1	no	—
382	C₂²⋊Q₈	—	4	1	no	—
383	#121	—	2	1	no	—
384	#121	—	4	1	no	—
385	#121	—	4	1	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	—	4	1	no	—
389	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
390	C₂×C₄⋊C₄	—	4	1	no	—
391	Q₃₂	—	2	2	no	—
392	Q₃₂	—	2	2	no	—
393	Q₃₂	—	2	2	no	—
394	Q₃₂	—	4	1	no	—
395	SD₃₂	—	2	2	no	—
396	SD₃₂	—	2	2	no	—
397	SD₃₂	—	4	1	no	—
398	SD₃₂	D₄×C₂₉	1	4	yes	complemented
399	D₁₆	—	2	2	no	—
400	M₃₂	—	2	2	no	—
401	C₂×C₁₆	—	2	2	no	—
402	C₂×C₁₆	C₂³×C₂₉	1	1	yes	characteristic
403	C₂×C₁₆	C₂³×C₂₉	1	1	yes	characteristic
404	C₂×C₁₆	C₂³×C₂₉	1	1	yes	characteristic
405	C₂×C₁₆	C₂³×C₂₉	1	1	yes	characteristic
406	#107	C₂³×C₂₉	1	1	yes	characteristic
407	#107	C₂³×C₂₉	1	1	yes	characteristic
408	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
409	#103	—	2	1	no	—
410	#103	—	2	1	no	—
411	#103	—	2	1	no	—
412	#103	—	2	1	no	—
413	#102	—	2	1	no	—
414	#102	—	2	1	no	—
415	C₂²⋊C₈	D₄×C₂₉	1	1	yes	characteristic
416	C₂²⋊C₈	D₄×C₂₉	1	1	yes	characteristic
417	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
418	C₂₉	#33835	1	1	yes	characteristic, direct product factor, Sylow
419	#41	—	4	2	no	—
420	#41	—	4	2	no	—
421	#41	—	4	2	no	—
422	#41	—	8	1	no	—
423	#41	—	8	1	no	—
424	#41	—	8	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	4	2	no	—
430	C₂×Q₈	—	4	1	no	—
431	C₂×Q₈	—	8	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	4	1	no	—
435	C₂×D₄	—	4	1	no	—
436	C₂×D₄	—	4	1	no	—
437	C₂×D₄	—	4	1	no	—
438	C₂×D₄	D₈×C₂₉	1	1	yes	characteristic
439	C₂²×C₄	—	4	1	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	—	4	1	no	—
442	C₂²×C₄	—	4	1	no	—
443	C₂²×C₄	—	4	1	no	—
444	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
446	Q₁₆	—	2	1	no	—
447	Q₁₆	—	2	1	no	—
448	Q₁₆	—	2	1	no	—
449	Q₁₆	—	2	1	no	—
450	Q₁₆	—	2	1	no	—
451	Q₁₆	—	2	1	no	—
452	Q₁₆	—	2	1	no	—
453	Q₁₆	—	4	2	no	—
454	Q₁₆	—	8	1	no	—
455	Q₁₆	C₂×D₄×C₂₉	1	2	yes	—
456	SD₁₆	—	4	2	no	—
457	SD₁₆	—	4	2	no	—
458	SD₁₆	—	4	2	no	—
459	SD₁₆	—	8	1	no	—
460	D₈	—	2	1	no	—
461	D₈	—	2	1	no	—
462	D₈	—	2	1	no	—
463	D₈	C₂×D₄×C₂₉	1	2	yes	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
469	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
470	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
471	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
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	—	4	1	no	—
480	C₄⋊C₄	D₈×C₂₉	1	1	yes	characteristic
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	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	C₂²⋊C₄	D₈×C₂₉	1	1	yes	characteristic
489	C₂²⋊C₄	D₈×C₂₉	1	1	yes	characteristic
490	C₄²	—	4	1	no	—
491	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
492	C₁₆	—	2	1	no	—
493	C₁₆	—	2	1	no	—
494	C₁₆	—	2	1	no	—
495	C₁₆	C₂×D₄×C₂₉	1	2	yes	—
496	C₂³	—	4	1	no	—
497	C₂³	—	4	1	no	—
498	C₂³	C₂×D₈×C₂₉	1	1	yes	characteristic
499	C₂³	C₂×D₈×C₂₉	1	1	yes	characteristic
500	Q₈	—	2	2	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	Q₈	—	8	2	no	—
509	D₄	—	2	2	no	—
510	D₄	—	4	1	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	1	no	—
513	D₄	—	4	1	no	—
514	D₄	—	8	2	no	—
515	D₄	—	8	2	no	—
516	D₄	—	8	2	no	—
517	D₄	—	8	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	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	—	8	2	no	—
531	C₂×C₄	—	8	2	no	—
532	C₂×C₄	—	8	2	no	—
533	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
534	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
535	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
536	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
537	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	C₂²×D₄×C₂₉	1	1	yes	characteristic
542	C₈	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	8	1	no	—
551	C₂²	—	8	1	no	—
552	C₂²	—	8	1	no	—
553	C₂²	—	8	1	no	—
554	C₂²	—	8	1	no	—
555	C₂²	C₂²×D₈×C₂₉	1	1	yes	characteristic
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	4	2	no	—
561	C₄	—	8	1	no	—
562	C₄	—	8	1	no	—
563	C₄	—	8	1	no	—
564	C₄	—	8	1	no	—
565	C₄	—	8	1	no	—
566	C₄	D₄²×C₂₉	1	1	yes	characteristic
567	C₄	C₂₉×#576	1	1	yes	characteristic
568	C₂	—	4	1	no	—
569	C₂	—	4	1	no	—
570	C₂	—	8	2	no	—
571	C₂	—	16	1	no	—
572	C₂	D₄×D₈×C₂₉	1	1	yes	characteristic
573	C₂	C₂₉×#3414	1	1	yes	characteristic
574	C₂	C₂₉×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₂₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄×D₄×C₂₉ ◁ C₈×D₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#510	C₂	semidirect
2. C₂×C₂₉×#508	C₂	semidirect
3. C₂₉×#3285	C₂	semidirect
4. C₂₉×#3283	C₂	semidirect
5. C₂₉×#2251	C₂	semidirect
6. C₂₉×#2220	C₂	semidirect
7. C₂₉×#2216	C₂	semidirect
8. C₂₉×#2210	C₂	semidirect
9. C₂₉×#2209	C₂	semidirect
10. C₂₉×#2189	C₂	semidirect
11. C₂₉×#2189	C₂	semidirect
12. C₂₉×#2188	C₂	semidirect
13. C₂₉×#2186	C₂	semidirect
14. C₂₉×#2175	C₂	semidirect
15. C₂₉×#2168	C₂	semidirect
111. C₂₉×SD₃₂	D₄	semidirect
208. #33835	C₂₉	direct (N × H)
256. C₂×#510	C₂×C₂₉	semidirect
257. C₂×#508	C₂×C₂₉	semidirect
258. #3285	C₂×C₂₉	semidirect
259. #3283	C₂×C₂₉	semidirect
260. #2251	C₂×C₂₉	semidirect
261. #2220	C₂×C₂₉	semidirect
262. #2216	C₂×C₂₉	semidirect
263. #2210	C₂×C₂₉	semidirect
264. #2209	C₂×C₂₉	semidirect
265. #2189	C₂×C₂₉	semidirect
266. #2189	C₂×C₂₉	semidirect
267. #2188	C₂×C₂₉	semidirect
268. #2186	C₂×C₂₉	semidirect
269. #2175	C₂×C₂₉	semidirect
270. #2168	C₂×C₂₉	semidirect
398. SD₃₂	D₄×C₂₉	semidirect
418. C₂₉	#33835	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#510	2
C₂×C₂₉×#508	2
C₂₉×#3285	2
C₂₉×#3283	2
C₂₉×#2251	2
C₂₉×#2220	2
C₂₉×#2216	2
C₂₉×#2210	2
C₂₉×#2209	2
C₂₉×#2189	2
C₂₉×#2188	2
C₂₉×#2186	2
C₂₉×#2175	2
C₂₉×#2168	2
#33835	29

Subgroups — C29×#33835 #20328735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#33835 #20328735