Subgroups — C₂×D₄×D₈×C₂₉ #20355939

Order 7424.

3710 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₂₉	C₂	1	2	yes	maximal, complemented
2	C₂×D₄²×C₂₉	C₂	1	2	yes	maximal, complemented
3	D₄×D₈×C₂₉	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₉×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₉×#466	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₉×#459	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₉×#447	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×D₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₈×D₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₂₉	—	2	2	no	—
11	C₂³×D₄×C₂₉	C₂²	1	4	yes	complemented
12	C₂²×D₈×C₂₉	—	2	16	no	—
13	C₂²×D₈×C₂₉	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₂₉	C₂²	1	4	yes	complemented
15	C₂²×D₈×C₂₉	C₂²	1	2	yes	complemented
16	C₂²×D₈×C₂₉	C₂²	1	2	yes	complemented
17	C₂²×D₈×C₂₉	C₂²	1	16	yes	complemented
18	C₂³×C₈×C₂₉	C₂²	1	2	yes	complemented
19	D₄²×C₂₉	—	2	8	no	—
20	D₄²×C₂₉	C₂²	1	16	yes	complemented
21	C₂×C₂₉×#127	C₂²	1	2	yes	complemented
22	C₂×C₂₉×#121	—	2	2	no	—
23	C₂×C₂₉×#121	C₂²	1	4	yes	complemented
24	C₂×C₂₉×#120	—	2	4	no	—
25	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	complemented
27	C₂₉×#493	C₂²	1	8	yes	complemented
28	C₂₉×#466	C₂²	1	16	yes	complemented
29	C₂₉×#459	C₂²	1	16	yes	complemented
30	C₂₉×#447	C₂²	1	32	yes	complemented
31	C₄×D₈×C₂₉	C₂²	1	8	yes	complemented
32	C₈×D₄×C₂₉	C₂²	1	8	yes	complemented
33	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂₉×#102	C₂²	1	2	yes	complemented
36	C₂×C₂₉×#102	C₂²	1	4	yes	complemented
37	C₂×C₂₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
38	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
39	C₂⁵×C₂₉	—	2	4	no	—
40	C₂²×D₄×C₂₉	—	2	16	no	—
41	C₂²×D₄×C₂₉	—	2	4	no	—
42	C₂²×D₄×C₂₉	—	2	16	no	—
43	C₂²×D₄×C₂₉	—	2	4	no	—
44	C₂²×D₄×C₂₉	—	2	2	no	—
45	C₂²×D₄×C₂₉	—	2	8	no	—
46	C₂²×D₄×C₂₉	—	2	2	no	—
47	C₂²×D₄×C₂₉	—	4	8	no	—
48	C₂²×D₄×C₂₉	—	4	16	no	—
49	C₂²×D₄×C₂₉	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₂₉	C₂³	1	4	yes	—
51	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
52	C₂²×D₄×C₂₉	C₂³	1	16	yes	complemented
53	C₂³×C₄×C₂₉	—	2	2	no	—
54	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
55	C₂×D₈×C₂₉	—	2	16	no	—
56	C₂×D₈×C₂₉	—	2	64	no	—
57	C₂×D₈×C₂₉	—	2	8	no	—
58	C₂×D₈×C₂₉	—	4	4	no	—
59	C₂×D₈×C₂₉	D₄	1	8	yes	direct product factor
60	C₂×D₈×C₂₉	C₂³	1	4	yes	—
61	C₂×D₈×C₂₉	C₂³	1	16	yes	complemented
62	C₂×D₈×C₂₉	C₂³	1	8	yes	complemented
63	C₂×D₈×C₂₉	C₂³	1	8	yes	complemented
64	C₂²×C₈×C₂₉	—	2	8	no	—
65	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
66	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₂₉	C₂³	1	8	yes	complemented
69	C₂₉×#127	—	2	4	no	—
70	C₂₉×#127	C₂³	1	8	yes	complemented
71	C₂₉×#121	—	2	8	no	—
72	C₂₉×#121	—	2	16	no	—
73	C₂₉×#121	C₂³	1	16	yes	complemented
74	C₂₉×#120	—	2	32	no	—
75	C₄×D₄×C₂₉	—	2	4	no	—
76	C₄×D₄×C₂₉	D₄	1	4	yes	—
77	C₄×D₄×C₂₉	C₂³	1	4	yes	—
78	C₄×D₄×C₂₉	C₂³	1	8	yes	complemented
79	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
81	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₂₉	—	2	4	no	—
83	C₂×C₂²⋊C₄×C₂₉	D₄	1	2	yes	—
84	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
85	C₂₉×#107	C₂³	1	4	yes	complemented
86	C₂₉×C₄⋊C₈	C₂³	1	4	yes	complemented
87	C₂₉×#102	C₂³	1	8	yes	complemented
88	C₂₉×#102	C₂³	1	16	yes	complemented
89	C₂₉×C₂²⋊C₈	C₂³	1	8	yes	complemented
90	C₄×C₈×C₂₉	C₂³	1	4	yes	complemented
91	C₂⁴×C₂₉	—	2	2	no	—
92	C₂⁴×C₂₉	—	2	4	no	—
93	C₂⁴×C₂₉	—	2	16	no	—
94	C₂⁴×C₂₉	—	4	16	no	—
95	C₂⁴×C₂₉	—	4	16	no	—
96	C₂⁴×C₂₉	—	8	8	no	—
97	C₂⁴×C₂₉	C₂×D₄	1	2	yes	—
98	C₂×D₄×C₂₉	—	2	32	no	—
99	C₂×D₄×C₂₉	—	2	16	no	—
100	C₂×D₄×C₂₉	—	2	2	no	—
101	C₂×D₄×C₂₉	—	2	8	no	—
102	C₂×D₄×C₂₉	—	2	16	no	—
103	C₂×D₄×C₂₉	—	2	4	no	—
104	C₂×D₄×C₂₉	—	2	8	no	—
105	C₂×D₄×C₂₉	—	2	8	no	—
106	C₂×D₄×C₂₉	—	2	4	no	—
107	C₂×D₄×C₂₉	—	2	8	no	—
108	C₂×D₄×C₂₉	—	4	16	no	—
109	C₂×D₄×C₂₉	—	4	32	no	—
110	C₂×D₄×C₂₉	—	4	16	no	—
111	C₂×D₄×C₂₉	—	4	16	no	—
112	C₂×D₄×C₂₉	—	4	64	no	—
113	C₂×D₄×C₂₉	—	4	8	no	—
114	C₂×D₄×C₂₉	—	8	4	no	—
115	C₂×D₄×C₂₉	D₈	1	8	yes	direct product factor
116	C₂×D₄×C₂₉	C₂×D₄	1	4	yes	—
117	C₂×D₄×C₂₉	C₂×D₄	1	8	yes	complemented
118	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
119	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₂₉	—	2	4	no	—
121	C₂²×C₄×C₂₉	—	2	4	no	—
122	C₂²×C₄×C₂₉	—	2	2	no	—
123	C₂²×C₄×C₂₉	—	2	8	no	—
124	C₂²×C₄×C₂₉	—	4	8	no	—
125	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
131	D₈×C₂₉	—	2	32	no	—
132	D₈×C₂₉	—	2	16	no	—
133	D₈×C₂₉	—	4	8	no	—
134	D₈×C₂₉	C₂×D₄	1	16	yes	direct product factor
135	C₂×C₈×C₂₉	—	2	4	no	—
136	C₂×C₈×C₂₉	—	2	2	no	—
137	C₂×C₈×C₂₉	—	2	16	no	—
138	C₂×C₈×C₂₉	C₂×D₄	1	4	yes	complemented
139	C₂×C₈×C₂₉	C₂⁴	1	4	yes	—
140	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
141	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
142	C₄⋊C₄×C₂₉	—	2	2	no	—
143	C₄⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
144	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
145	C₂²⋊C₄×C₂₉	—	2	8	no	—
146	C₂²⋊C₄×C₂₉	—	2	16	no	—
147	C₂²⋊C₄×C₂₉	C₂×D₄	1	8	yes	—
148	C₄²×C₂₉	C₂×D₄	1	2	yes	—
149	C₄²×C₂₉	C₂⁴	1	2	yes	—
150	C₂×D₄×D₈	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₂₉	—	2	4	no	—
152	C₂³×C₂₉	—	2	4	no	—
153	C₂³×C₂₉	—	2	8	no	—
154	C₂³×C₂₉	—	2	4	no	—
155	C₂³×C₂₉	—	2	8	no	—
156	C₂³×C₂₉	—	4	32	no	—
157	C₂³×C₂₉	—	4	4	no	—
158	C₂³×C₂₉	—	4	4	no	—
159	C₂³×C₂₉	—	4	8	no	—
160	C₂³×C₂₉	—	4	8	no	—
161	C₂³×C₂₉	—	4	32	no	—
162	C₂³×C₂₉	—	4	8	no	—
163	C₂³×C₂₉	—	8	16	no	—
164	C₂³×C₂₉	—	8	64	no	—
165	C₂³×C₂₉	C₂×D₈	1	8	yes	complemented
166	C₂³×C₂₉	C₂²×D₄	1	4	yes	—
167	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
168	D₄×C₂₉	—	2	8	no	—
169	D₄×C₂₉	—	2	8	no	—
170	D₄×C₂₉	—	2	4	no	—
171	D₄×C₂₉	—	2	8	no	—
172	D₄×C₂₉	—	4	32	no	—
173	D₄×C₂₉	—	4	32	no	—
174	D₄×C₂₉	—	4	8	no	—
175	D₄×C₂₉	—	4	16	no	—
176	D₄×C₂₉	—	8	8	no	—
177	D₄×C₂₉	C₂×D₈	1	16	yes	direct product factor
178	D₄×C₂₉	C₂²×D₄	1	8	yes	complemented
179	C₂×C₄×C₂₉	—	2	4	no	—
180	C₂×C₄×C₂₉	—	2	2	no	—
181	C₂×C₄×C₂₉	—	2	8	no	—
182	C₂×C₄×C₂₉	—	2	4	no	—
183	C₂×C₄×C₂₉	—	2	4	no	—
184	C₂×C₄×C₂₉	—	2	4	no	—
185	C₂×C₄×C₂₉	—	4	4	no	—
186	C₂×C₄×C₂₉	—	4	16	no	—
187	C₂×C₄×C₂₉	C₂×D₈	1	4	yes	complemented
188	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
189	C₂×C₄×C₂₉	C₂²×D₄	1	4	yes	—
190	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
192	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
194	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
195	C₈×C₂₉	—	2	4	no	—
196	C₈×C₂₉	—	2	2	no	—
197	C₈×C₂₉	C₂²×D₄	1	4	yes	complemented
198	C₂³×D₈	C₂×C₂₉	1	2	yes	complemented
199	C₂×D₄²	C₂×C₂₉	1	2	yes	complemented
200	D₄×D₈	C₂×C₂₉	1	16	yes	direct product factor
201	C₂×#493	C₂×C₂₉	1	1	yes	characteristic, complemented
202	C₂×#466	C₂×C₂₉	1	2	yes	complemented
203	C₂×#459	C₂×C₂₉	1	2	yes	complemented
204	C₂×#447	C₂×C₂₉	1	4	yes	complemented
205	C₂×C₄×D₈	C₂×C₂₉	1	1	yes	characteristic, complemented
206	C₂×C₈×D₄	C₂×C₂₉	1	1	yes	characteristic, complemented
207	C₂²×C₂₉	—	2	4	no	—
208	C₂²×C₂₉	—	2	16	no	—
209	C₂²×C₂₉	—	2	4	no	—
210	C₂²×C₂₉	—	2	8	no	—
211	C₂²×C₂₉	—	4	16	no	—
212	C₂²×C₂₉	—	4	4	no	—
213	C₂²×C₂₉	—	4	4	no	—
214	C₂²×C₂₉	—	4	8	no	—
215	C₂²×C₂₉	—	4	8	no	—
216	C₂²×C₂₉	—	4	8	no	—
217	C₂²×C₂₉	—	8	64	no	—
218	C₂²×C₂₉	—	8	16	no	—
219	C₂²×C₂₉	D₄²	1	2	yes	—
220	C₂²×C₂₉	C₂²×D₈	1	2	yes	—
221	C₂²×C₂₉	C₂²×D₈	1	8	yes	complemented
222	C₂²×C₂₉	#576	1	2	yes	—
223	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
224	C₄×C₂₉	—	2	4	no	—
225	C₄×C₂₉	—	2	2	no	—
226	C₄×C₂₉	—	4	4	no	—
227	C₄×C₂₉	D₄²	1	2	yes	—
228	C₄×C₂₉	C₂²×D₈	1	4	yes	complemented
229	C₄×C₂₉	C₂³×D₄	1	1	yes	characteristic
230	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
231	C₂³×D₄	—	2	2	no	—
232	C₂³×D₄	C₂²×C₂₉	1	4	yes	complemented
233	C₂²×D₈	—	2	16	no	—
234	C₂²×D₈	C₂²×C₂₉	1	1	yes	characteristic
235	C₂²×D₈	C₂²×C₂₉	1	2	yes	complemented
236	C₂²×D₈	C₂²×C₂₉	1	4	yes	complemented
237	C₂²×D₈	C₂²×C₂₉	1	2	yes	complemented
238	C₂²×D₈	C₂²×C₂₉	1	16	yes	complemented
239	C₂³×C₈	C₂²×C₂₉	1	2	yes	complemented
240	D₄²	—	2	8	no	—
241	D₄²	C₂²×C₂₉	1	16	yes	complemented
242	C₂×#127	C₂²×C₂₉	1	2	yes	complemented
243	C₂×#121	—	2	2	no	—
244	C₂×#121	C₂²×C₂₉	1	4	yes	complemented
245	C₂×#120	—	2	4	no	—
246	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
247	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	complemented
248	#493	C₂²×C₂₉	1	8	yes	complemented
249	#466	C₂²×C₂₉	1	16	yes	complemented
250	#459	C₂²×C₂₉	1	16	yes	complemented
251	#447	C₂²×C₂₉	1	32	yes	complemented
252	C₄×D₈	C₂²×C₂₉	1	8	yes	complemented
253	C₈×D₄	C₂²×C₂₉	1	8	yes	complemented
254	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic, complemented
255	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
256	C₂×#102	C₂²×C₂₉	1	2	yes	complemented
257	C₂×#102	C₂²×C₂₉	1	4	yes	complemented
258	C₂×C₂²⋊C₈	C₂²×C₂₉	1	2	yes	complemented
259	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
260	C₂×C₂₉	—	2	8	no	—
261	C₂×C₂₉	—	4	8	no	—
262	C₂×C₂₉	—	8	8	no	—
263	C₂×C₂₉	D₄×D₈	1	4	yes	direct product factor
264	C₂×C₂₉	C₂×D₄²	1	1	yes	characteristic
265	C₂×C₂₉	C₂³×D₈	1	1	yes	characteristic
266	C₂×C₂₉	C₂×#576	1	1	yes	characteristic
267	C₂⁵	—	2	4	no	—
268	C₂²×D₄	—	2	16	no	—
269	C₂²×D₄	—	2	4	no	—
270	C₂²×D₄	—	2	16	no	—
271	C₂²×D₄	—	2	4	no	—
272	C₂²×D₄	—	2	2	no	—
273	C₂²×D₄	—	2	8	no	—
274	C₂²×D₄	—	2	2	no	—
275	C₂²×D₄	—	4	8	no	—
276	C₂²×D₄	—	4	16	no	—
277	C₂²×D₄	D₄×C₂₉	1	1	yes	characteristic
278	C₂²×D₄	C₂³×C₂₉	1	4	yes	—
279	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
280	C₂²×D₄	C₂³×C₂₉	1	16	yes	complemented
281	C₂³×C₄	—	2	2	no	—
282	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
283	C₂×D₈	—	2	16	no	—
284	C₂×D₈	—	2	64	no	—
285	C₂×D₈	—	2	8	no	—
286	C₂×D₈	—	4	4	no	—
287	C₂×D₈	D₄×C₂₉	1	8	yes	direct product factor
288	C₂×D₈	C₂³×C₂₉	1	4	yes	—
289	C₂×D₈	C₂³×C₂₉	1	16	yes	complemented
290	C₂×D₈	C₂³×C₂₉	1	8	yes	complemented
291	C₂×D₈	C₂³×C₂₉	1	8	yes	complemented
292	C₂²×C₈	—	2	8	no	—
293	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
294	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₂₉	1	8	yes	complemented
297	#127	—	2	4	no	—
298	#127	C₂³×C₂₉	1	8	yes	complemented
299	#121	—	2	8	no	—
300	#121	—	2	16	no	—
301	#121	C₂³×C₂₉	1	16	yes	complemented
302	#120	—	2	32	no	—
303	C₄×D₄	—	2	4	no	—
304	C₄×D₄	D₄×C₂₉	1	4	yes	—
305	C₄×D₄	C₂³×C₂₉	1	4	yes	—
306	C₄×D₄	C₂³×C₂₉	1	8	yes	complemented
307	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	4	no	—
311	C₂×C₂²⋊C₄	D₄×C₂₉	1	2	yes	—
312	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
313	#107	C₂³×C₂₉	1	4	yes	complemented
314	C₄⋊C₈	C₂³×C₂₉	1	4	yes	complemented
315	#102	C₂³×C₂₉	1	8	yes	complemented
316	#102	C₂³×C₂₉	1	16	yes	complemented
317	C₂²⋊C₈	C₂³×C₂₉	1	8	yes	complemented
318	C₄×C₈	C₂³×C₂₉	1	4	yes	complemented
319	C₂₉	C₂×D₄×D₈	1	1	yes	characteristic, direct product factor, Sylow
320	C₂⁴	—	2	2	no	—
321	C₂⁴	—	2	4	no	—
322	C₂⁴	—	2	16	no	—
323	C₂⁴	—	4	16	no	—
324	C₂⁴	—	4	16	no	—
325	C₂⁴	—	8	8	no	—
326	C₂⁴	C₂×D₄×C₂₉	1	2	yes	—
327	C₂×D₄	—	2	32	no	—
328	C₂×D₄	—	2	16	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	8	no	—
331	C₂×D₄	—	2	16	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	8	no	—
334	C₂×D₄	—	2	8	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	8	no	—
337	C₂×D₄	—	4	16	no	—
338	C₂×D₄	—	4	32	no	—
339	C₂×D₄	—	4	16	no	—
340	C₂×D₄	—	4	16	no	—
341	C₂×D₄	—	4	64	no	—
342	C₂×D₄	—	4	8	no	—
343	C₂×D₄	—	8	4	no	—
344	C₂×D₄	D₈×C₂₉	1	8	yes	direct product factor
345	C₂×D₄	C₂×D₄×C₂₉	1	4	yes	—
346	C₂×D₄	C₂×D₄×C₂₉	1	8	yes	complemented
347	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
348	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	8	no	—
353	C₂²×C₄	—	4	8	no	—
354	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
357	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
358	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
359	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
360	D₈	—	2	32	no	—
361	D₈	—	2	16	no	—
362	D₈	—	4	8	no	—
363	D₈	C₂×D₄×C₂₉	1	16	yes	direct product factor
364	C₂×C₈	—	2	4	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	16	no	—
367	C₂×C₈	C₂×D₄×C₂₉	1	4	yes	complemented
368	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
369	C₂×C₈	C₂⁴×C₂₉	1	4	yes	—
370	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
373	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₂²⋊C₄	—	2	16	no	—
376	C₂²⋊C₄	C₂×D₄×C₂₉	1	8	yes	—
377	C₄²	C₂×D₄×C₂₉	1	2	yes	—
378	C₄²	C₂⁴×C₂₉	1	2	yes	—
379	C₂³	—	2	4	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	8	no	—
382	C₂³	—	2	4	no	—
383	C₂³	—	2	8	no	—
384	C₂³	—	4	32	no	—
385	C₂³	—	4	4	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	8	no	—
388	C₂³	—	4	8	no	—
389	C₂³	—	4	32	no	—
390	C₂³	—	4	8	no	—
391	C₂³	—	8	16	no	—
392	C₂³	—	8	64	no	—
393	C₂³	C₂×D₈×C₂₉	1	8	yes	complemented
394	C₂³	C₂²×D₄×C₂₉	1	4	yes	—
395	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
396	D₄	—	2	8	no	—
397	D₄	—	2	8	no	—
398	D₄	—	2	4	no	—
399	D₄	—	2	8	no	—
400	D₄	—	4	32	no	—
401	D₄	—	4	32	no	—
402	D₄	—	4	8	no	—
403	D₄	—	4	16	no	—
404	D₄	—	8	8	no	—
405	D₄	C₂×D₈×C₂₉	1	16	yes	direct product factor
406	D₄	C₂²×D₄×C₂₉	1	8	yes	complemented
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	16	no	—
415	C₂×C₄	C₂×D₈×C₂₉	1	4	yes	complemented
416	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
417	C₂×C₄	C₂²×D₄×C₂₉	1	4	yes	—
418	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
419	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
420	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
421	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
422	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
423	C₈	—	2	4	no	—
424	C₈	—	2	2	no	—
425	C₈	C₂²×D₄×C₂₉	1	4	yes	complemented
426	C₂²	—	2	4	no	—
427	C₂²	—	2	16	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	2	8	no	—
430	C₂²	—	4	16	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	8	no	—
434	C₂²	—	4	8	no	—
435	C₂²	—	4	8	no	—
436	C₂²	—	8	64	no	—
437	C₂²	—	8	16	no	—
438	C₂²	D₄²×C₂₉	1	2	yes	—
439	C₂²	C₂²×D₈×C₂₉	1	2	yes	—
440	C₂²	C₂²×D₈×C₂₉	1	8	yes	complemented
441	C₂²	C₂₉×#576	1	2	yes	—
442	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
443	C₄	—	2	4	no	—
444	C₄	—	2	2	no	—
445	C₄	—	4	4	no	—
446	C₄	D₄²×C₂₉	1	2	yes	—
447	C₄	C₂²×D₈×C₂₉	1	4	yes	complemented
448	C₄	C₂³×D₄×C₂₉	1	1	yes	characteristic
449	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂	—	2	8	no	—
451	C₂	—	4	8	no	—
452	C₂	—	8	8	no	—
453	C₂	D₄×D₈×C₂₉	1	4	yes	direct product factor
454	C₂	C₂×D₄²×C₂₉	1	1	yes	characteristic
455	C₂	C₂³×D₈×C₂₉	1	1	yes	characteristic
456	C₂	C₂×C₂₉×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₄×D₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×D₈×C₂₉	C₂	semidirect
2. C₂×D₄²×C₂₉	C₂	semidirect
3. D₄×D₈×C₂₉	C₂	direct (N × H)
4. C₂×C₂₉×#493	C₂	semidirect
5. C₂×C₂₉×#466	C₂	semidirect
6. C₂×C₂₉×#459	C₂	semidirect
7. C₂×C₂₉×#447	C₂	semidirect
8. C₂×C₄×D₈×C₂₉	C₂	semidirect
9. C₂×C₈×D₄×C₂₉	C₂	semidirect
11. C₂³×D₄×C₂₉	C₂²	semidirect
14. C₂²×D₈×C₂₉	C₂²	semidirect
15. C₂²×D₈×C₂₉	C₂²	semidirect
16. C₂²×D₈×C₂₉	C₂²	semidirect
17. C₂²×D₈×C₂₉	C₂²	semidirect
18. C₂³×C₈×C₂₉	C₂²	semidirect
20. D₄²×C₂₉	C₂²	semidirect
21. C₂×C₂₉×#127	C₂²	semidirect
23. C₂×C₂₉×#121	C₂²	semidirect
26. C₂×C₄×D₄×C₂₉	C₂²	semidirect
27. C₂₉×#493	C₂²	semidirect
28. C₂₉×#466	C₂²	semidirect
29. C₂₉×#459	C₂²	semidirect
30. C₂₉×#447	C₂²	semidirect
31. C₄×D₈×C₂₉	C₂²	semidirect
32. C₈×D₄×C₂₉	C₂²	semidirect
33. C₂×C₂₉×#107	C₂²	semidirect
34. C₂×C₂₉×C₄⋊C₈	C₂²	semidirect
35. C₂×C₂₉×#102	C₂²	semidirect
36. C₂×C₂₉×#102	C₂²	semidirect
37. C₂×C₂₉×C₂²⋊C₈	C₂²	semidirect
38. C₂×C₄×C₈×C₂₉	C₂²	semidirect
52. C₂²×D₄×C₂₉	C₂³	semidirect
59. C₂×D₈×C₂₉	D₄	direct (N × H)
61. C₂×D₈×C₂₉	C₂³	semidirect
62. C₂×D₈×C₂₉	C₂³	semidirect
63. C₂×D₈×C₂₉	C₂³	semidirect
68. C₂²×C₈×C₂₉	C₂³	semidirect
70. C₂₉×#127	C₂³	semidirect
73. C₂₉×#121	C₂³	semidirect
78. C₄×D₄×C₂₉	C₂³	semidirect
85. C₂₉×#107	C₂³	semidirect
86. C₂₉×C₄⋊C₈	C₂³	semidirect
87. C₂₉×#102	C₂³	semidirect
88. C₂₉×#102	C₂³	semidirect
89. C₂₉×C₂²⋊C₈	C₂³	semidirect
90. C₄×C₈×C₂₉	C₂³	semidirect
115. C₂×D₄×C₂₉	D₈	direct (N × H)
117. C₂×D₄×C₂₉	C₂×D₄	semidirect
134. D₈×C₂₉	C₂×D₄	direct (N × H)
138. C₂×C₈×C₂₉	C₂×D₄	semidirect
150. C₂×D₄×D₈	C₂₉	direct (N × H)
165. C₂³×C₂₉	C₂×D₈	semidirect
177. D₄×C₂₉	C₂×D₈	direct (N × H)
178. D₄×C₂₉	C₂²×D₄	semidirect
187. C₂×C₄×C₂₉	C₂×D₈	semidirect
197. C₈×C₂₉	C₂²×D₄	semidirect
198. C₂³×D₈	C₂×C₂₉	semidirect
199. C₂×D₄²	C₂×C₂₉	semidirect
200. D₄×D₈	C₂×C₂₉	direct (N × H)
201. C₂×#493	C₂×C₂₉	semidirect
202. C₂×#466	C₂×C₂₉	semidirect
203. C₂×#459	C₂×C₂₉	semidirect
204. C₂×#447	C₂×C₂₉	semidirect
205. C₂×C₄×D₈	C₂×C₂₉	semidirect
206. C₂×C₈×D₄	C₂×C₂₉	semidirect
221. C₂²×C₂₉	C₂²×D₈	semidirect
228. C₄×C₂₉	C₂²×D₈	semidirect
232. C₂³×D₄	C₂²×C₂₉	semidirect
235. C₂²×D₈	C₂²×C₂₉	semidirect
236. C₂²×D₈	C₂²×C₂₉	semidirect
237. C₂²×D₈	C₂²×C₂₉	semidirect
238. C₂²×D₈	C₂²×C₂₉	semidirect
239. C₂³×C₈	C₂²×C₂₉	semidirect
241. D₄²	C₂²×C₂₉	semidirect
242. C₂×#127	C₂²×C₂₉	semidirect
244. C₂×#121	C₂²×C₂₉	semidirect
247. C₂×C₄×D₄	C₂²×C₂₉	semidirect
248. #493	C₂²×C₂₉	semidirect
249. #466	C₂²×C₂₉	semidirect
250. #459	C₂²×C₂₉	semidirect
251. #447	C₂²×C₂₉	semidirect
252. C₄×D₈	C₂²×C₂₉	semidirect
253. C₈×D₄	C₂²×C₂₉	semidirect
254. C₂×#107	C₂²×C₂₉	semidirect
255. C₂×C₄⋊C₈	C₂²×C₂₉	semidirect
256. C₂×#102	C₂²×C₂₉	semidirect
257. C₂×#102	C₂²×C₂₉	semidirect
258. C₂×C₂²⋊C₈	C₂²×C₂₉	semidirect
259. C₂×C₄×C₈	C₂²×C₂₉	semidirect
263. C₂×C₂₉	D₄×D₈	direct (N × H)
280. C₂²×D₄	C₂³×C₂₉	semidirect
287. C₂×D₈	D₄×C₂₉	direct (N × H)
289. C₂×D₈	C₂³×C₂₉	semidirect
290. C₂×D₈	C₂³×C₂₉	semidirect
291. C₂×D₈	C₂³×C₂₉	semidirect
296. C₂²×C₈	C₂³×C₂₉	semidirect
298. #127	C₂³×C₂₉	semidirect
301. #121	C₂³×C₂₉	semidirect
306. C₄×D₄	C₂³×C₂₉	semidirect
313. #107	C₂³×C₂₉	semidirect
314. C₄⋊C₈	C₂³×C₂₉	semidirect
315. #102	C₂³×C₂₉	semidirect
316. #102	C₂³×C₂₉	semidirect
317. C₂²⋊C₈	C₂³×C₂₉	semidirect
318. C₄×C₈	C₂³×C₂₉	semidirect
319. C₂₉	C₂×D₄×D₈	direct (N × H)
344. C₂×D₄	D₈×C₂₉	direct (N × H)
346. C₂×D₄	C₂×D₄×C₂₉	semidirect
363. D₈	C₂×D₄×C₂₉	direct (N × H)
367. C₂×C₈	C₂×D₄×C₂₉	semidirect
393. C₂³	C₂×D₈×C₂₉	semidirect
405. D₄	C₂×D₈×C₂₉	direct (N × H)
406. D₄	C₂²×D₄×C₂₉	semidirect
415. C₂×C₄	C₂×D₈×C₂₉	semidirect
425. C₈	C₂²×D₄×C₂₉	semidirect
440. C₂²	C₂²×D₈×C₂₉	semidirect
447. C₄	C₂²×D₈×C₂₉	semidirect
453. C₂	D₄×D₈×C₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₈×C₂₉	2
C₂×D₄²×C₂₉	2
D₄×D₈×C₂₉	2
C₂×C₂₉×#493	2
C₂×C₂₉×#466	2
C₂×C₂₉×#459	2
C₂×C₂₉×#447	2
C₂×C₄×D₈×C₂₉	2
C₂×C₈×D₄×C₂₉	2
C₂×D₄×D₈	29

Subgroups — C2×D4×D8×C29 #20355939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×D₈×C₂₉ #20355939