Subgroups — C₂₉×#28816 #20323716

Order 7424.

758 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#501	C₂	1	2	yes	maximal
2	C₂₉×#2552	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2551	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2059	C₂	1	2	yes	maximal
5	C₂₉×#2057	C₂	1	2	yes	maximal
6	C₂₉×#1948	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#1947	C₂	1	1	yes	maximal, characteristic
8	C₂₉×#1944	C₂	1	2	yes	maximal
9	C₂₉×#1845	C₂	1	1	yes	maximal, characteristic
10	C₄×C₂₉×#106	C₂	1	1	yes	maximal, characteristic
11	C₂₉×#1770	C₂	1	1	yes	maximal, characteristic
12	C₂×C₂₉×C₄⋊Q₈	—	2	1	no	—
13	C₂×C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₂₉×#125	C₂²	1	2	yes	—
15	C₂₉×#501	—	2	8	no	—
16	C₂×C₂₉×#107	C₂²	1	2	yes	—
17	C₂×C₂₉×#107	C₂²	1	2	yes	—
18	C₂×C₂₉×#107	C₂²	1	2	yes	—
19	C₂×C₂₉×#106	C₂²	1	2	yes	—
20	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#97	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
25	C₂₉×#398	—	2	2	no	—
26	C₂₉×#395	—	2	2	no	—
27	C₂₉×#389	—	2	1	no	—
28	C₂₉×#389	—	2	1	no	—
29	C₂₉×#389	C₂²	1	2	yes	—
30	C₂₉×#389	C₂²	1	2	yes	—
31	C₂₉×#384	—	2	1	no	—
32	C₂₉×#384	C₂²	1	1	yes	characteristic
33	C₂₉×#384	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
37	C₂₉×#340	C₂²	1	2	yes	—
38	C₂₉×#340	C₂²	1	2	yes	—
39	C₂₉×#340	C₂²	1	1	yes	characteristic
40	C₂₉×#340	C₂²	1	1	yes	characteristic
41	C₂₉×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₂₉	—	2	2	no	—
43	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
44	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
46	C₂₉×C₄⋊Q₈	—	2	4	no	—
47	C₂₉×C₄⋊Q₈	—	4	2	no	—
48	C₂₉×C₄⋊Q₈	—	4	4	no	—
49	C₂₉×#125	—	2	4	no	—
50	C₂₉×#125	—	4	2	no	—
51	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₂₉	—	2	1	no	—
69	C₂×C₄²×C₂₉	—	2	1	no	—
70	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
71	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
72	C₂₉×#107	—	2	4	no	—
73	C₂₉×#107	—	2	4	no	—
74	C₂₉×#107	—	4	2	no	—
75	C₂₉×#106	—	2	4	no	—
76	C₂₉×#106	D₄	1	4	yes	—
77	C₂₉×#106	Q₈	1	4	yes	complemented
78	C₂₉×C₄⋊C₈	Q₈	1	4	yes	complemented
79	C₂₉×#97	—	2	4	no	—
80	C₄×C₈×C₂₉	Q₈	1	4	yes	complemented
81	C₂₉×#95	—	2	1	no	—
82	C₂₉×#95	—	2	1	no	—
83	C₂₉×#95	—	2	2	no	—
84	C₂₉×#95	—	2	2	no	—
85	C₂₉×#95	D₄	1	2	yes	—
86	C₂×Q₈×C₂₉	—	4	4	no	—
87	C₂×Q₈×C₂₉	—	4	4	no	—
88	C₂×Q₈×C₂₉	—	8	2	no	—
89	C₂²×C₄×C₂₉	—	2	1	no	—
90	C₂²×C₄×C₂₉	—	2	1	no	—
91	C₂²×C₄×C₂₉	—	2	1	no	—
92	C₂²×C₄×C₂₉	—	2	1	no	—
93	C₂²×C₄×C₂₉	—	2	2	no	—
94	C₂²×C₄×C₂₉	—	2	2	no	—
95	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
100	C₂×C₈×C₂₉	—	2	2	no	—
101	C₂×C₈×C₂₉	—	2	1	no	—
102	C₂×C₈×C₂₉	—	2	1	no	—
103	C₂×C₈×C₂₉	—	2	2	no	—
104	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
105	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
106	C₂×C₈×C₂₉	C₂×Q₈	1	4	yes	—
107	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
108	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
109	C₄⋊C₄×C₂₉	—	2	2	no	—
110	C₄⋊C₄×C₂₉	—	2	2	no	—
111	C₄⋊C₄×C₂₉	—	2	1	no	—
112	C₄⋊C₄×C₂₉	—	2	1	no	—
113	C₄⋊C₄×C₂₉	—	2	1	no	—
114	C₄⋊C₄×C₂₉	—	2	1	no	—
115	C₄⋊C₄×C₂₉	—	2	2	no	—
116	C₄⋊C₄×C₂₉	—	2	2	no	—
117	C₄⋊C₄×C₂₉	—	2	2	no	—
118	C₄⋊C₄×C₂₉	—	2	2	no	—
119	C₄⋊C₄×C₂₉	—	4	4	no	—
120	C₄⋊C₄×C₂₉	—	4	4	no	—
121	C₄⋊C₄×C₂₉	—	4	4	no	—
122	C₄⋊C₄×C₂₉	—	4	4	no	—
123	C₄⋊C₄×C₂₉	—	4	2	no	—
124	C₄⋊C₄×C₂₉	—	4	2	no	—
125	C₄⋊C₄×C₂₉	—	8	1	no	—
126	C₄⋊C₄×C₂₉	—	8	1	no	—
127	C₄⋊C₄×C₂₉	—	8	2	no	—
128	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
130	C₄⋊C₄×C₂₉	C₂×Q₈	1	2	yes	—
131	C₄⋊C₄×C₂₉	C₂×Q₈	1	2	yes	—
132	C₄²×C₂₉	—	2	2	no	—
133	C₄²×C₂₉	—	2	2	no	—
134	C₄²×C₂₉	—	4	2	no	—
135	C₄²×C₂₉	—	4	2	no	—
136	C₄²×C₂₉	C₂×Q₈	1	2	yes	—
137	C₄²×C₂₉	C₂×Q₈	1	2	yes	—
138	#28816	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₂₉	—	8	8	no	—
141	C₂×C₄×C₂₉	—	2	1	no	—
142	C₂×C₄×C₂₉	—	2	1	no	—
143	C₂×C₄×C₂₉	—	2	2	no	—
144	C₂×C₄×C₂₉	—	2	2	no	—
145	C₂×C₄×C₂₉	—	2	2	no	—
146	C₂×C₄×C₂₉	—	2	2	no	—
147	C₂×C₄×C₂₉	—	2	2	no	—
148	C₂×C₄×C₂₉	—	2	2	no	—
149	C₂×C₄×C₂₉	—	2	2	no	—
150	C₂×C₄×C₂₉	—	2	2	no	—
151	C₂×C₄×C₂₉	—	2	2	no	—
152	C₂×C₄×C₂₉	—	2	2	no	—
153	C₂×C₄×C₂₉	—	4	1	no	—
154	C₂×C₄×C₂₉	—	4	1	no	—
155	C₂×C₄×C₂₉	—	4	1	no	—
156	C₂×C₄×C₂₉	—	4	1	no	—
157	C₂×C₄×C₂₉	—	4	1	no	—
158	C₂×C₄×C₂₉	—	4	1	no	—
159	C₂×C₄×C₂₉	—	4	1	no	—
160	C₂×C₄×C₂₉	—	4	1	no	—
161	C₂×C₄×C₂₉	—	4	2	no	—
162	C₂×C₄×C₂₉	—	4	2	no	—
163	C₂×C₄×C₂₉	—	4	2	no	—
164	C₂×C₄×C₂₉	—	4	2	no	—
165	C₂×C₄×C₂₉	—	4	2	no	—
166	C₂×C₄×C₂₉	—	4	2	no	—
167	C₂×C₄×C₂₉	C₄⋊Q₈	1	2	yes	—
168	C₂×C₄×C₂₉	C₄⋊Q₈	1	2	yes	—
169	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
170	C₂×C₄×C₂₉	#137	1	2	yes	—
171	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
177	C₈×C₂₉	—	2	2	no	—
178	C₈×C₂₉	—	2	4	no	—
179	C₈×C₂₉	C₄⋊Q₈	1	4	yes	complemented
180	C₂×#501	C₂×C₂₉	1	2	yes	—
181	#2552	C₂×C₂₉	1	1	yes	characteristic
182	#2551	C₂×C₂₉	1	1	yes	characteristic
183	#2059	C₂×C₂₉	1	2	yes	—
184	#2057	C₂×C₂₉	1	2	yes	—
185	#1948	C₂×C₂₉	1	1	yes	characteristic
186	#1947	C₂×C₂₉	1	1	yes	characteristic
187	#1944	C₂×C₂₉	1	2	yes	—
188	#1845	C₂×C₂₉	1	1	yes	characteristic
189	C₄×#106	C₂×C₂₉	1	1	yes	characteristic
190	#1770	C₂×C₂₉	1	1	yes	characteristic
191	C₂²×C₂₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
192	C₂²×C₂₉	D₄²	1	1	yes	characteristic
193	C₂²×C₂₉	D₄×Q₈	1	1	yes	characteristic
194	C₂²×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₂²×C₂₉	C₂×#137	1	1	yes	characteristic
196	C₂²×C₂₉	#576	1	1	yes	characteristic
197	C₂²×C₂₉	#578	1	1	yes	characteristic
198	C₄×C₂₉	—	2	2	no	—
199	C₄×C₂₉	—	4	2	no	—
200	C₄×C₂₉	—	4	2	no	—
201	C₄×C₂₉	—	4	2	no	—
202	C₄×C₂₉	—	4	2	no	—
203	C₄×C₂₉	—	4	2	no	—
204	C₄×C₂₉	—	4	2	no	—
205	C₄×C₂₉	—	8	2	no	—
206	C₄×C₂₉	—	8	2	no	—
207	C₄×C₂₉	#501	1	4	yes	complemented
208	C₄×C₂₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
209	C₄×C₂₉	#544	1	1	yes	characteristic
210	C₄×C₂₉	D₄×Q₈	1	1	yes	characteristic
211	C₄×C₂₉	Q₈²	1	1	yes	characteristic
212	C₂×C₄⋊Q₈	—	2	1	no	—
213	C₂×C₄⋊Q₈	C₂²×C₂₉	1	2	yes	—
214	C₂×#125	C₂²×C₂₉	1	2	yes	—
215	#501	—	2	8	no	—
216	C₂×#107	C₂²×C₂₉	1	2	yes	—
217	C₂×#107	C₂²×C₂₉	1	2	yes	—
218	C₂×#107	C₂²×C₂₉	1	2	yes	—
219	C₂×#106	C₂²×C₂₉	1	2	yes	—
220	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
221	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
222	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
223	C₂×#97	C₂²×C₂₉	1	2	yes	—
224	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
225	#398	—	2	2	no	—
226	#395	—	2	2	no	—
227	#389	—	2	1	no	—
228	#389	—	2	1	no	—
229	#389	C₂²×C₂₉	1	2	yes	—
230	#389	C₂²×C₂₉	1	2	yes	—
231	#384	—	2	1	no	—
232	#384	C₂²×C₂₉	1	1	yes	characteristic
233	#384	C₂²×C₂₉	1	1	yes	characteristic
234	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
235	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
236	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
237	#340	C₂²×C₂₉	1	1	yes	characteristic
238	#340	C₂²×C₂₉	1	2	yes	—
239	#340	C₂²×C₂₉	1	1	yes	characteristic
240	#340	C₂²×C₂₉	1	2	yes	—
241	#336	C₂²×C₂₉	1	2	yes	—
242	C₂×C₂₉	#2551	1	1	yes	characteristic
243	C₂×C₂₉	C₂×#501	1	1	yes	characteristic
244	C₂×C₂₉	#3164	1	1	yes	characteristic
245	C₂×C₂₉	#3274	1	1	yes	characteristic
246	C₂×C₂₉	#3276	1	1	yes	characteristic
247	C₂×C₂₉	#3385	1	1	yes	characteristic
248	C₂×C₂₉	#3386	1	1	yes	characteristic
249	C₂²×Q₈	—	2	2	no	—
250	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
252	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
253	C₄⋊Q₈	—	2	4	no	—
254	C₄⋊Q₈	—	4	2	no	—
255	C₄⋊Q₈	—	4	4	no	—
256	#125	—	2	4	no	—
257	#125	—	4	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
268	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
278	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
279	#107	—	2	4	no	—
280	#107	—	2	4	no	—
281	#107	—	4	2	no	—
282	#106	—	2	4	no	—
283	#106	D₄×C₂₉	1	4	yes	—
284	#106	Q₈×C₂₉	1	4	yes	complemented
285	C₄⋊C₈	Q₈×C₂₉	1	4	yes	complemented
286	#97	—	2	4	no	—
287	C₄×C₈	Q₈×C₂₉	1	4	yes	complemented
288	#95	—	2	1	no	—
289	#95	—	2	1	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	D₄×C₂₉	1	2	yes	—
293	C₂₉	#28816	1	1	yes	characteristic, direct product factor, Sylow
294	C₂×Q₈	—	4	4	no	—
295	C₂×Q₈	—	4	4	no	—
296	C₂×Q₈	—	8	2	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
313	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
314	C₂×C₈	C₂×Q₈×C₂₉	1	4	yes	—
315	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
316	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	4	4	no	—
328	C₄⋊C₄	—	4	4	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	8	1	no	—
334	C₄⋊C₄	—	8	1	no	—
335	C₄⋊C₄	—	8	2	no	—
336	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
337	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
338	C₄⋊C₄	C₂×Q₈×C₂₉	1	2	yes	—
339	C₄⋊C₄	C₂×Q₈×C₂₉	1	2	yes	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	4	2	no	—
343	C₄²	—	4	2	no	—
344	C₄²	C₂×Q₈×C₂₉	1	2	yes	—
345	C₄²	C₂×Q₈×C₂₉	1	2	yes	—
346	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
347	Q₈	—	8	8	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	C₂₉×C₄⋊Q₈	1	2	yes	—
375	C₂×C₄	C₂₉×C₄⋊Q₈	1	2	yes	—
376	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
377	C₂×C₄	C₂₉×#137	1	2	yes	—
378	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
379	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
380	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
381	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
382	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
383	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
384	C₈	—	2	2	no	—
385	C₈	—	2	4	no	—
386	C₈	C₂₉×C₄⋊Q₈	1	4	yes	complemented
387	C₂²	C₂×C₂₉×C₄⋊Q₈	1	1	yes	characteristic
388	C₂²	D₄²×C₂₉	1	1	yes	characteristic
389	C₂²	D₄×Q₈×C₂₉	1	1	yes	characteristic
390	C₂²	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
391	C₂²	C₂×C₂₉×#137	1	1	yes	characteristic
392	C₂²	C₂₉×#576	1	1	yes	characteristic
393	C₂²	C₂₉×#578	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	—	8	2	no	—
402	C₄	—	8	2	no	—
403	C₄	C₂₉×#501	1	4	yes	complemented
404	C₄	C₂×C₂₉×C₄⋊Q₈	1	1	yes	characteristic
405	C₄	C₂₉×#544	1	1	yes	characteristic
406	C₄	D₄×Q₈×C₂₉	1	1	yes	characteristic
407	C₄	Q₈²×C₂₉	1	1	yes	characteristic
408	C₂	C₂₉×#2551	1	1	yes	characteristic
409	C₂	C₂×C₂₉×#501	1	1	yes	characteristic
410	C₂	C₂₉×#3164	1	1	yes	characteristic
411	C₂	C₂₉×#3274	1	1	yes	characteristic
412	C₂	C₂₉×#3276	1	1	yes	characteristic
413	C₂	C₂₉×#3385	1	1	yes	characteristic
414	C₂	C₂₉×#3386	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
77. C₂₉×#106	Q₈	semidirect
78. C₂₉×C₄⋊C₈	Q₈	semidirect
80. C₄×C₈×C₂₉	Q₈	semidirect
138. #28816	C₂₉	direct (N × H)
179. C₈×C₂₉	C₄⋊Q₈	semidirect
207. C₄×C₂₉	#501	semidirect
284. #106	Q₈×C₂₉	semidirect
285. C₄⋊C₈	Q₈×C₂₉	semidirect
287. C₄×C₈	Q₈×C₂₉	semidirect
293. C₂₉	#28816	direct (N × H)
386. C₈	C₂₉×C₄⋊Q₈	semidirect
403. C₄	C₂₉×#501	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#501	2
C₂₉×#2552	2
C₂₉×#2551	2
C₂₉×#2059	2
C₂₉×#2057	2
C₂₉×#1948	2
C₂₉×#1947	2
C₂₉×#1944	2
C₂₉×#1845	2
C₄×C₂₉×#106	2
C₂₉×#1770	2
#28816	29

Subgroups — C29×#28816 #20323716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#28816 #20323716