Subgroups — C₂₉×#10849 #20305749

Order 7424.

1086 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#384	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₉×#340	C₂	1	4	yes	maximal
5	C₂³×C₈×C₂₉	C₂²	1	2	yes	—
6	C₂²×C₄⋊C₄×C₂₉	—	2	1	no	—
7	C₂²×C₄⋊C₄×C₂₉	—	2	1	no	—
8	C₂²×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
10	C₂²×C₄²×C₂₉	—	2	1	no	—
11	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
12	C₂×C₂₉×C₄⋊C₈	—	2	2	no	—
13	C₂×C₂₉×C₄⋊C₈	—	2	2	no	—
14	C₂×C₂₉×C₄⋊C₈	C₄	1	4	yes	complemented
15	C₂₉×#384	—	2	2	no	—
16	C₂₉×#384	C₄	1	4	yes	complemented
17	C₄×C₄⋊C₄×C₂₉	—	2	2	no	—
18	C₄×C₄⋊C₄×C₂₉	C₄	1	4	yes	complemented
19	C₂×C₂₉×#95	—	2	1	no	—
20	C₂₉×#340	—	2	8	no	—
21	C₂³×C₄×C₂₉	—	2	2	no	—
22	C₂³×C₄×C₂₉	—	2	2	no	—
23	C₂³×C₄×C₂₉	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₂₉	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
26	C₂²×C₈×C₂₉	—	2	4	no	—
27	C₂²×C₈×C₂₉	—	2	2	no	—
28	C₂²×C₈×C₂₉	—	2	2	no	—
29	C₂²×C₈×C₂₉	—	2	4	no	—
30	C₂²×C₈×C₂₉	C₂×C₄	1	4	yes	—
31	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
34	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
35	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
36	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
37	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
38	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
39	C₂×C₄⋊C₄×C₂₉	—	4	4	no	—
40	C₂×C₄⋊C₄×C₂₉	—	4	2	no	—
41	C₂×C₄⋊C₄×C₂₉	—	4	2	no	—
42	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	4	yes	—
43	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	4	yes	—
44	C₂×C₄⋊C₄×C₂₉	D₄	1	4	yes	—
45	C₂×C₄⋊C₄×C₂₉	Q₈	1	4	yes	—
46	C₂×C₄²×C₂₉	—	2	4	no	—
47	C₂×C₄²×C₂₉	—	4	2	no	—
48	C₂×C₄²×C₂₉	—	4	2	no	—
49	C₂×C₄²×C₂₉	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₂₉	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₂₉	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₂₉	D₄	1	2	yes	—
53	C₂×C₄²×C₂₉	D₄	1	2	yes	—
54	C₂×C₄²×C₂₉	Q₈	1	2	yes	—
55	C₂₉×C₄⋊C₈	—	2	8	no	—
56	C₂₉×#95	—	2	4	no	—
57	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₂₉	—	2	2	no	—
59	C₂²×C₄×C₂₉	—	2	2	no	—
60	C₂²×C₄×C₂₉	—	2	4	no	—
61	C₂²×C₄×C₂₉	—	2	4	no	—
62	C₂²×C₄×C₂₉	—	2	4	no	—
63	C₂²×C₄×C₂₉	—	2	4	no	—
64	C₂²×C₄×C₂₉	—	4	2	no	—
65	C₂²×C₄×C₂₉	—	4	2	no	—
66	C₂²×C₄×C₂₉	—	4	2	no	—
67	C₂²×C₄×C₂₉	—	4	2	no	—
68	C₂²×C₄×C₂₉	—	4	4	no	—
69	C₂²×C₄×C₂₉	—	4	2	no	—
70	C₂²×C₄×C₂₉	—	4	2	no	—
71	C₂²×C₄×C₂₉	—	4	4	no	—
72	C₂²×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
73	C₂²×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
74	C₂²×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
75	C₂²×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
76	C₂²×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
77	C₂²×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
78	C₂²×C₄×C₂₉	D₈	1	2	yes	—
79	C₂²×C₄×C₂₉	SD₁₆	1	2	yes	—
80	C₂²×C₄×C₂₉	SD₁₆	1	2	yes	—
81	C₂²×C₄×C₂₉	Q₁₆	1	2	yes	—
82	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
89	C₂²×C₄×C₂₉	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₂₉	#41	1	2	yes	—
91	C₂²×C₄×C₂₉	#41	1	2	yes	—
92	C₂×C₈×C₂₉	—	2	4	no	—
93	C₂×C₈×C₂₉	—	2	8	no	—
94	C₂×C₈×C₂₉	—	4	4	no	—
95	C₂×C₈×C₂₉	—	4	2	no	—
96	C₂×C₈×C₂₉	—	4	2	no	—
97	C₄⋊C₄×C₂₉	—	2	4	no	—
98	C₄⋊C₄×C₂₉	—	2	4	no	—
99	C₄⋊C₄×C₂₉	—	2	4	no	—
100	C₄⋊C₄×C₂₉	—	2	8	no	—
101	C₄⋊C₄×C₂₉	—	4	8	no	—
102	C₄⋊C₄×C₂₉	—	4	8	no	—
103	C₄⋊C₄×C₂₉	—	4	2	no	—
104	C₄⋊C₄×C₂₉	—	4	2	no	—
105	C₄⋊C₄×C₂₉	C₄⋊C₄	1	8	yes	complemented
106	C₄²×C₂₉	—	4	8	no	—
107	C₄²×C₂₉	C₄²	1	4	yes	—
108	C₄²×C₂₉	C₂²⋊C₄	1	4	yes	—
109	C₄²×C₂₉	C₄⋊C₄	1	4	yes	—
110	C₄²×C₂₉	C₄⋊C₄	1	4	yes	—
111	#10849	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
113	C₂³×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
114	C₂³×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
115	C₂³×C₂₉	#121	1	2	yes	—
116	C₂³×C₂₉	C₂²⋊Q₈	1	2	yes	—
117	C₂³×C₂₉	C₂×D₈	1	1	yes	characteristic
118	C₂³×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
119	C₂³×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
120	C₂³×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
121	C₂³×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
122	C₂³×C₂₉	#137	1	2	yes	—
123	C₂×C₄×C₂₉	—	2	4	no	—
124	C₂×C₄×C₂₉	—	2	2	no	—
125	C₂×C₄×C₂₉	—	2	2	no	—
126	C₂×C₄×C₂₉	—	2	4	no	—
127	C₂×C₄×C₂₉	—	2	8	no	—
128	C₂×C₄×C₂₉	—	4	4	no	—
129	C₂×C₄×C₂₉	—	4	4	no	—
130	C₂×C₄×C₂₉	—	4	4	no	—
131	C₂×C₄×C₂₉	—	4	4	no	—
132	C₂×C₄×C₂₉	—	4	4	no	—
133	C₂×C₄×C₂₉	—	4	4	no	—
134	C₂×C₄×C₂₉	—	4	4	no	—
135	C₂×C₄×C₂₉	—	4	4	no	—
136	C₂×C₄×C₂₉	—	4	4	no	—
137	C₂×C₄×C₂₉	—	8	4	no	—
138	C₂×C₄×C₂₉	—	8	4	no	—
139	C₂×C₄×C₂₉	#95	1	4	yes	—
140	C₂×C₄×C₂₉	#95	1	4	yes	—
141	C₂×C₄×C₂₉	#102	1	4	yes	—
142	C₂×C₄×C₂₉	#102	1	4	yes	—
143	C₂×C₄×C₂₉	#103	1	4	yes	—
144	C₂×C₄×C₂₉	#103	1	4	yes	—
145	C₂×C₄×C₂₉	#106	1	4	yes	—
146	C₂×C₄×C₂₉	#107	1	4	yes	—
147	C₂×C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	2	yes	—
150	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₂₉	#117	1	2	yes	—
153	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
155	C₂×C₄×C₂₉	C₄×Q₈	1	2	yes	—
156	C₂×C₄×C₂₉	C₄×Q₈	1	2	yes	—
157	C₂×C₄×C₂₉	#121	1	2	yes	—
158	C₂×C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
159	C₂×C₄×C₂₉	#124	1	1	yes	characteristic
160	C₂×C₄×C₂₉	#124	1	1	yes	characteristic
161	C₂×C₄×C₂₉	#125	1	2	yes	—
162	C₂×C₄×C₂₉	#127	1	1	yes	characteristic
163	C₂×C₄×C₂₉	C₄⋊Q₈	1	2	yes	—
164	C₂×C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
165	C₈×C₂₉	—	4	4	no	—
166	C₂²×C₄⋊C₈	C₂×C₂₉	1	1	yes	characteristic
167	C₂×#384	C₂×C₂₉	1	1	yes	characteristic
168	C₂×C₄×C₄⋊C₄	C₂×C₂₉	1	1	yes	characteristic
169	C₂×#340	C₂×C₂₉	1	4	yes	—
170	C₂²×C₂₉	C₂×#95	1	1	yes	characteristic
171	C₂²×C₂₉	#380	1	2	yes	—
172	C₂²×C₂₉	#389	1	2	yes	—
173	C₂²×C₂₉	#390	1	1	yes	characteristic
174	C₂²×C₂₉	#391	1	1	yes	characteristic
175	C₂²×C₂₉	C₂×#102	1	1	yes	characteristic
176	C₂²×C₂₉	C₂×#102	1	1	yes	characteristic
177	C₂²×C₂₉	C₂×#103	1	1	yes	characteristic
178	C₂²×C₂₉	C₂×#103	1	1	yes	characteristic
179	C₂²×C₂₉	#417	1	2	yes	—
180	C₂²×C₂₉	#418	1	1	yes	characteristic
181	C₂²×C₂₉	#419	1	1	yes	characteristic
182	C₂²×C₂₉	C₂×#106	1	1	yes	characteristic
183	C₂²×C₂₉	C₂×#107	1	1	yes	characteristic
184	C₂²×C₂₉	#428	1	2	yes	—
185	C₂²×C₂₉	#459	1	2	yes	—
186	C₂²×C₂₉	#460	1	2	yes	—
187	C₂²×C₂₉	#461	1	2	yes	—
188	C₂²×C₂₉	#462	1	2	yes	—
189	C₂²×C₂₉	#474	1	2	yes	—
190	C₂²×C₂₉	#475	1	2	yes	—
191	C₂²×C₂₉	#476	1	2	yes	—
192	C₂²×C₂₉	#477	1	2	yes	—
193	C₄×C₂₉	—	2	4	no	—
194	C₄×C₂₉	—	4	8	no	—
195	C₄×C₂₉	—	8	4	no	—
196	C₄×C₂₉	#340	1	8	yes	complemented
197	C₄×C₂₉	C₄×C₄⋊C₄	1	2	yes	—
198	C₄×C₂₉	#382	1	1	yes	characteristic
199	C₄×C₂₉	#384	1	1	yes	characteristic
200	C₄×C₂₉	#389	1	2	yes	—
201	C₄×C₂₉	#390	1	1	yes	characteristic
202	C₄×C₂₉	#391	1	1	yes	characteristic
203	C₂³×C₈	C₂²×C₂₉	1	2	yes	—
204	C₂²×C₄⋊C₄	—	2	1	no	—
205	C₂²×C₄⋊C₄	—	2	1	no	—
206	C₂²×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
207	C₂²×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
208	C₂²×C₄²	—	2	1	no	—
209	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
210	C₂×C₄⋊C₈	—	2	2	no	—
211	C₂×C₄⋊C₈	—	2	2	no	—
212	C₂×C₄⋊C₈	C₄×C₂₉	1	4	yes	complemented
213	#384	—	2	2	no	—
214	#384	C₄×C₂₉	1	4	yes	complemented
215	C₄×C₄⋊C₄	—	2	2	no	—
216	C₄×C₄⋊C₄	C₄×C₂₉	1	4	yes	complemented
217	C₂×#95	—	2	1	no	—
218	#340	—	2	8	no	—
219	C₂×C₂₉	C₄⋊#95	1	1	yes	characteristic
220	C₂×C₂₉	C₂×#340	1	1	yes	characteristic
221	C₂×C₂₉	#1736	1	1	yes	characteristic
222	C₂×C₂₉	#1802	1	2	yes	—
223	C₂×C₂₉	#1803	1	2	yes	—
224	C₂×C₂₉	#1947	1	2	yes	—
225	C₂×C₂₉	#1948	1	2	yes	—
226	C₂×C₂₉	#1981	1	1	yes	characteristic
227	C₂×C₂₉	#1982	1	1	yes	characteristic
228	C₂×C₂₉	#1987	1	1	yes	characteristic
229	C₂×C₂₉	#1988	1	1	yes	characteristic
230	C₂³×C₄	—	2	2	no	—
231	C₂³×C₄	—	2	2	no	—
232	C₂³×C₄	D₄×C₂₉	1	1	yes	characteristic
233	C₂³×C₄	D₄×C₂₉	1	1	yes	characteristic
234	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
235	C₂²×C₈	—	2	4	no	—
236	C₂²×C₈	—	2	2	no	—
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	—	2	4	no	—
239	C₂²×C₈	C₂×C₄×C₂₉	1	4	yes	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	4	no	—
244	C₂×C₄⋊C₄	—	2	4	no	—
245	C₂×C₄⋊C₄	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	4	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	4	4	no	—
249	C₂×C₄⋊C₄	—	4	2	no	—
250	C₂×C₄⋊C₄	—	4	2	no	—
251	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	4	yes	—
252	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	4	yes	—
253	C₂×C₄⋊C₄	D₄×C₂₉	1	4	yes	—
254	C₂×C₄⋊C₄	Q₈×C₂₉	1	4	yes	—
255	C₂×C₄²	—	2	4	no	—
256	C₂×C₄²	—	4	2	no	—
257	C₂×C₄²	—	4	2	no	—
258	C₂×C₄²	C₂×C₄×C₂₉	1	2	yes	—
259	C₂×C₄²	C₂×C₄×C₂₉	1	2	yes	—
260	C₂×C₄²	C₂×C₄×C₂₉	1	2	yes	—
261	C₂×C₄²	D₄×C₂₉	1	2	yes	—
262	C₂×C₄²	D₄×C₂₉	1	2	yes	—
263	C₂×C₄²	Q₈×C₂₉	1	2	yes	—
264	C₄⋊C₈	—	2	8	no	—
265	#95	—	2	4	no	—
266	C₂₉	#10849	1	1	yes	characteristic, direct product factor, Sylow
267	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	4	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	—	4	4	no	—
282	C₂²×C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
283	C₂²×C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
284	C₂²×C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
285	C₂²×C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
286	C₂²×C₄	C₄⋊C₄×C₂₉	1	2	yes	—
287	C₂²×C₄	C₄⋊C₄×C₂₉	1	2	yes	—
288	C₂²×C₄	D₈×C₂₉	1	2	yes	—
289	C₂²×C₄	SD₁₆×C₂₉	1	2	yes	—
290	C₂²×C₄	SD₁₆×C₂₉	1	2	yes	—
291	C₂²×C₄	Q₁₆×C₂₉	1	2	yes	—
292	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
298	C₂²×C₄	C₂×Q₈×C₂₉	1	1	yes	characteristic
299	C₂²×C₄	C₂×Q₈×C₂₉	1	2	yes	—
300	C₂²×C₄	#41×C₂₉	1	2	yes	—
301	C₂²×C₄	#41×C₂₉	1	2	yes	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	8	no	—
304	C₂×C₈	—	4	4	no	—
305	C₂×C₈	—	4	2	no	—
306	C₂×C₈	—	4	2	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	2	8	no	—
311	C₄⋊C₄	—	4	8	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	8	no	—
315	C₄⋊C₄	C₄⋊C₄×C₂₉	1	8	yes	complemented
316	C₄²	—	4	8	no	—
317	C₄²	C₄²×C₂₉	1	4	yes	—
318	C₄²	C₂²⋊C₄×C₂₉	1	4	yes	—
319	C₄²	C₄⋊C₄×C₂₉	1	4	yes	—
320	C₄²	C₄⋊C₄×C₂₉	1	4	yes	—
321	C₂³	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
322	C₂³	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
323	C₂³	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
324	C₂³	C₂₉×#121	1	2	yes	—
325	C₂³	C₂₉×C₂²⋊Q₈	1	2	yes	—
326	C₂³	C₂×D₈×C₂₉	1	1	yes	characteristic
327	C₂³	C₂×SD₁₆×C₂₉	1	1	yes	characteristic
328	C₂³	C₂×SD₁₆×C₂₉	1	1	yes	characteristic
329	C₂³	C₂×Q₁₆×C₂₉	1	1	yes	characteristic
330	C₂³	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
331	C₂³	C₂₉×#137	1	2	yes	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	8	4	no	—
347	C₂×C₄	—	8	4	no	—
348	C₂×C₄	C₂₉×#95	1	4	yes	—
349	C₂×C₄	C₂₉×#95	1	4	yes	—
350	C₂×C₄	C₂₉×#102	1	4	yes	—
351	C₂×C₄	C₂₉×#102	1	4	yes	—
352	C₂×C₄	C₂₉×#103	1	4	yes	—
353	C₂×C₄	C₂₉×#103	1	4	yes	—
354	C₂×C₄	C₂₉×#106	1	4	yes	—
355	C₂×C₄	C₂₉×#107	1	4	yes	—
356	C₂×C₄	C₂×C₄²×C₂₉	1	1	yes	characteristic
357	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	2	yes	—
359	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
361	C₂×C₄	C₂₉×#117	1	2	yes	—
362	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
363	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
364	C₂×C₄	C₄×Q₈×C₂₉	1	2	yes	—
365	C₂×C₄	C₄×Q₈×C₂₉	1	2	yes	—
366	C₂×C₄	C₂₉×#121	1	2	yes	—
367	C₂×C₄	C₂₉×C₂²⋊Q₈	1	2	yes	—
368	C₂×C₄	C₂₉×#124	1	1	yes	characteristic
369	C₂×C₄	C₂₉×#124	1	1	yes	characteristic
370	C₂×C₄	C₂₉×#125	1	2	yes	—
371	C₂×C₄	C₂₉×#127	1	1	yes	characteristic
372	C₂×C₄	C₂₉×C₄⋊Q₈	1	2	yes	—
373	C₂×C₄	C₂₉×C₄⋊Q₈	1	1	yes	characteristic
374	C₈	—	4	4	no	—
375	C₂²	C₂×C₂₉×#95	1	1	yes	characteristic
376	C₂²	C₂₉×#380	1	2	yes	—
377	C₂²	C₂₉×#389	1	2	yes	—
378	C₂²	C₂₉×#390	1	1	yes	characteristic
379	C₂²	C₂₉×#391	1	1	yes	characteristic
380	C₂²	C₂×C₂₉×#102	1	1	yes	characteristic
381	C₂²	C₂×C₂₉×#102	1	1	yes	characteristic
382	C₂²	C₂×C₂₉×#103	1	1	yes	characteristic
383	C₂²	C₂×C₂₉×#103	1	1	yes	characteristic
384	C₂²	C₂₉×#417	1	2	yes	—
385	C₂²	C₂₉×#418	1	1	yes	characteristic
386	C₂²	C₂₉×#419	1	1	yes	characteristic
387	C₂²	C₂×C₂₉×#106	1	1	yes	characteristic
388	C₂²	C₂×C₂₉×#107	1	1	yes	characteristic
389	C₂²	C₂₉×#428	1	2	yes	—
390	C₂²	C₂₉×#459	1	2	yes	—
391	C₂²	C₂₉×#460	1	2	yes	—
392	C₂²	C₂₉×#461	1	2	yes	—
393	C₂²	C₂₉×#462	1	2	yes	—
394	C₂²	C₂₉×#474	1	2	yes	—
395	C₂²	C₂₉×#475	1	2	yes	—
396	C₂²	C₂₉×#476	1	2	yes	—
397	C₂²	C₂₉×#477	1	2	yes	—
398	C₄	—	2	4	no	—
399	C₄	—	4	8	no	—
400	C₄	—	8	4	no	—
401	C₄	C₂₉×#340	1	8	yes	complemented
402	C₄	C₄×C₄⋊C₄×C₂₉	1	2	yes	—
403	C₄	C₂₉×#382	1	1	yes	characteristic
404	C₄	C₂₉×#384	1	1	yes	characteristic
405	C₄	C₂₉×#389	1	2	yes	—
406	C₄	C₂₉×#390	1	1	yes	characteristic
407	C₄	C₂₉×#391	1	1	yes	characteristic
408	C₂	C₂₉×C₄⋊#95	1	1	yes	characteristic
409	C₂	C₂×C₂₉×#340	1	1	yes	characteristic
410	C₂	C₂₉×#1736	1	1	yes	characteristic
411	C₂	C₂₉×#1802	1	2	yes	—
412	C₂	C₂₉×#1803	1	2	yes	—
413	C₂	C₂₉×#1947	1	2	yes	—
414	C₂	C₂₉×#1948	1	2	yes	—
415	C₂	C₂₉×#1981	1	1	yes	characteristic
416	C₂	C₂₉×#1982	1	1	yes	characteristic
417	C₂	C₂₉×#1987	1	1	yes	characteristic
418	C₂	C₂₉×#1988	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₂₉	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₂₉
Frattini, cosocle	C₂³×C₄	C₂³×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₉ ◁ C₂²×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
14. C₂×C₂₉×C₄⋊C₈	C₄	semidirect
16. C₂₉×#384	C₄	semidirect
18. C₄×C₄⋊C₄×C₂₉	C₄	semidirect
105. C₄⋊C₄×C₂₉	C₄⋊C₄	semidirect
111. #10849	C₂₉	direct (N × H)
196. C₄×C₂₉	#340	semidirect
212. C₂×C₄⋊C₈	C₄×C₂₉	semidirect
214. #384	C₄×C₂₉	semidirect
216. C₄×C₄⋊C₄	C₄×C₂₉	semidirect
266. C₂₉	#10849	direct (N × H)
315. C₄⋊C₄	C₄⋊C₄×C₂₉	semidirect
401. C₄	C₂₉×#340	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂₉×C₄⋊C₈	2
C₂×C₂₉×#384	2
C₂×C₄×C₄⋊C₄×C₂₉	2
C₂×C₂₉×#340	2
#10849	29

Subgroups — C29×#10849 #20305749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#10849 #20305749