Subgroups — C₂×C₂₉×#1285 #20302847

Order 7424.

746 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#432	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1285	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₄⋊C₄×C₂₉	—	2	1	no	—
6	C₂²×C₄²×C₂₉	C₄	1	2	yes	—
7	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
8	C₂₉×#432	—	2	1	no	—
9	C₂₉×#432	—	2	1	no	—
10	C₂₉×#432	—	2	1	no	—
11	C₂₉×#432	—	2	1	no	—
12	C₂₉×#432	C₄	1	2	yes	complemented
13	C₂₉×#432	C₄	1	2	yes	complemented
14	C₂₉×#432	C₂²	1	2	yes	—
15	C₂₉×#432	C₂²	1	2	yes	—
16	C₂×C₂₉×C₄⋊C₈	—	2	1	no	—
17	C₂×C₂₉×C₄⋊C₈	C₄	1	2	yes	complemented
18	C₂×C₂₉×C₂²⋊C₈	—	2	1	no	—
19	C₂×C₂₉×C₂²⋊C₈	—	2	1	no	—
20	C₂×C₂₉×#97	—	2	1	no	—
21	C₂×C₂₉×#97	C₄	1	2	yes	complemented
22	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
23	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
24	C₄×C₄⋊C₄×C₂₉	C₄	1	2	yes	—
25	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
26	C₂×C₂₉×#95	—	2	1	no	—
27	C₂³×C₄×C₂₉	—	2	2	no	—
28	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₂₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₂₉	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₂₉	—	2	2	no	—
32	C₂²×C₈×C₂₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₂₉	—	2	8	no	—
34	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
35	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
36	C₂×C₄²×C₂₉	—	2	2	no	—
37	C₂×C₄²×C₂₉	—	4	4	no	—
38	C₂×C₄²×C₂₉	C₂×C₄	1	4	yes	—
39	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₂₉	Q₈	1	1	yes	characteristic
49	C₂×C₄²×C₂₉	Q₈	1	1	yes	characteristic
50	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
51	C₂₉×C₄⋊C₈	—	2	2	no	—
52	C₂₉×C₄⋊C₈	—	2	2	no	—
53	C₂₉×C₄⋊C₈	—	2	2	no	—
54	C₂₉×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
55	C₂₉×C₂²⋊C₈	—	2	2	no	—
56	C₂₉×C₂²⋊C₈	—	2	2	no	—
57	C₂₉×C₂²⋊C₈	—	2	2	no	—
58	C₂₉×C₂²⋊C₈	—	2	2	no	—
59	C₂₉×#97	—	2	2	no	—
60	C₂₉×#97	—	2	2	no	—
61	C₂₉×#97	—	2	2	no	—
62	C₂₉×#97	C₂×C₄	1	4	yes	complemented
63	C₂₉×#95	—	2	2	no	—
64	C₂₉×#95	—	2	2	no	—
65	C₂⁴×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₂₉	—	2	2	no	—
67	C₂²×C₄×C₂₉	—	2	2	no	—
68	C₂²×C₄×C₂₉	—	2	4	no	—
69	C₂²×C₄×C₂₉	—	2	8	no	—
70	C₂²×C₄×C₂₉	—	2	4	no	—
71	C₂²×C₄×C₂₉	—	4	2	no	—
72	C₂²×C₄×C₂₉	—	4	4	no	—
73	C₂²×C₄×C₂₉	—	4	4	no	—
74	C₂²×C₄×C₂₉	C₄²	1	1	yes	characteristic
75	C₂²×C₄×C₂₉	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
92	C₂×C₈×C₂₉	—	2	4	no	—
93	C₂×C₈×C₂₉	—	2	4	no	—
94	C₂×C₈×C₂₉	—	4	4	no	—
95	C₂×C₈×C₂₉	—	4	4	no	—
96	C₄⋊C₄×C₂₉	—	2	8	no	—
97	C₄⋊C₄×C₂₉	—	2	8	no	—
98	C₄²×C₂₉	—	4	4	no	—
99	C₄²×C₂₉	—	4	4	no	—
100	C₄²×C₂₉	C₄²	1	1	yes	characteristic
101	C₄²×C₂₉	C₄²	1	1	yes	characteristic
102	C₄²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
106	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₂₉	C₂×Q₈	1	1	yes	characteristic
116	C₂×#1285	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₂₉	—	2	2	no	—
118	C₂³×C₂₉	—	2	2	no	—
119	C₂³×C₂₉	#95	1	1	yes	characteristic
120	C₂³×C₂₉	#95	1	1	yes	characteristic
121	C₂³×C₂₉	#100	1	2	yes	—
122	C₂³×C₂₉	#101	1	2	yes	—
123	C₂³×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₂₉	—	2	2	no	—
125	C₂×C₄×C₂₉	—	2	2	no	—
126	C₂×C₄×C₂₉	—	2	2	no	—
127	C₂×C₄×C₂₉	—	2	2	no	—
128	C₂×C₄×C₂₉	—	2	2	no	—
129	C₂×C₄×C₂₉	—	2	2	no	—
130	C₂×C₄×C₂₉	—	2	2	no	—
131	C₂×C₄×C₂₉	—	2	1	no	—
132	C₂×C₄×C₂₉	—	2	1	no	—
133	C₂×C₄×C₂₉	—	2	1	no	—
134	C₂×C₄×C₂₉	—	2	1	no	—
135	C₂×C₄×C₂₉	—	2	2	no	—
136	C₂×C₄×C₂₉	—	2	2	no	—
137	C₂×C₄×C₂₉	—	2	2	no	—
138	C₂×C₄×C₂₉	—	2	2	no	—
139	C₂×C₄×C₂₉	—	2	8	no	—
140	C₂×C₄×C₂₉	—	4	1	no	—
141	C₂×C₄×C₂₉	—	4	1	no	—
142	C₂×C₄×C₂₉	—	4	1	no	—
143	C₂×C₄×C₂₉	—	4	1	no	—
144	C₂×C₄×C₂₉	—	4	16	no	—
145	C₂×C₄×C₂₉	—	4	4	no	—
146	C₂×C₄×C₂₉	—	4	4	no	—
147	C₂×C₄×C₂₉	#95	1	1	yes	characteristic
148	C₂×C₄×C₂₉	#95	1	1	yes	characteristic
149	C₂×C₄×C₂₉	#95	1	1	yes	characteristic
150	C₂×C₄×C₂₉	#95	1	1	yes	characteristic
151	C₂×C₄×C₂₉	#95	1	1	yes	characteristic
152	C₂×C₄×C₂₉	#95	1	1	yes	characteristic
153	C₂×C₄×C₂₉	#104	1	4	yes	—
154	C₂×C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₈×C₂₉	—	4	4	no	—
161	C₈×C₂₉	—	4	4	no	—
162	C₂×#432	C₂×C₂₉	1	1	yes	characteristic
163	C₂×#432	C₂×C₂₉	1	1	yes	characteristic
164	C₂×C₄×C₄⋊C₄	C₂×C₂₉	1	1	yes	characteristic
165	#1285	C₂×C₂₉	1	4	yes	direct product factor
166	C₂²×C₂₉	—	2	4	no	—
167	C₂²×C₂₉	—	2	4	no	—
168	C₂²×C₂₉	—	2	1	no	—
169	C₂²×C₂₉	—	2	1	no	—
170	C₂²×C₂₉	—	2	1	no	—
171	C₂²×C₂₉	—	2	1	no	—
172	C₂²×C₂₉	H(3,ℤ/4)	1	2	yes	—
173	C₂²×C₂₉	#339	1	2	yes	—
174	C₂²×C₂₉	#343	1	2	yes	—
175	C₂²×C₂₉	#343	1	2	yes	—
176	C₂²×C₂₉	C₂×#95	1	1	yes	characteristic
177	C₂²×C₂₉	C₂×#100	1	1	yes	characteristic
178	C₂²×C₂₉	C₂×#101	1	1	yes	characteristic
179	C₄×C₂₉	—	2	1	no	—
180	C₄×C₂₉	—	2	1	no	—
181	C₄×C₂₉	—	2	1	no	—
182	C₄×C₂₉	—	2	1	no	—
183	C₄×C₂₉	—	2	1	no	—
184	C₄×C₂₉	—	2	1	no	—
185	C₄×C₂₉	—	2	1	no	—
186	C₄×C₂₉	—	2	1	no	—
187	C₄×C₂₉	—	2	1	no	—
188	C₄×C₂₉	—	2	1	no	—
189	C₄×C₂₉	—	4	8	no	—
190	C₄×C₂₉	#339	1	2	yes	—
191	C₄×C₂₉	C₂×#104	1	2	yes	—
192	C₂²×C₄⋊C₄	—	2	1	no	—
193	C₂²×C₄²	C₄×C₂₉	1	2	yes	—
194	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
195	#432	—	2	1	no	—
196	#432	—	2	1	no	—
197	#432	—	2	1	no	—
198	#432	—	2	1	no	—
199	#432	C₄×C₂₉	1	2	yes	complemented
200	#432	C₄×C₂₉	1	2	yes	complemented
201	#432	C₂²×C₂₉	1	2	yes	—
202	#432	C₂²×C₂₉	1	2	yes	—
203	C₂×C₄⋊C₈	—	2	1	no	—
204	C₂×C₄⋊C₈	C₄×C₂₉	1	2	yes	complemented
205	C₂×C₂²⋊C₈	—	2	1	no	—
206	C₂×C₂²⋊C₈	—	2	1	no	—
207	C₂×#97	—	2	1	no	—
208	C₂×#97	C₄×C₂₉	1	2	yes	complemented
209	C₄×C₄⋊C₄	—	2	1	no	—
210	C₄×C₄⋊C₄	—	2	1	no	—
211	C₄×C₄⋊C₄	C₄×C₂₉	1	2	yes	—
212	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
213	C₂×#95	—	2	1	no	—
214	C₂×C₂₉	—	2	1	no	—
215	C₂×C₂₉	—	2	2	no	—
216	C₂×C₂₉	—	2	1	no	—
217	C₂×C₂₉	#1285	1	4	yes	direct product factor
218	C₂×C₂₉	C₂×H(3,ℤ/4)	1	1	yes	characteristic
219	C₂×C₂₉	C₂×#339	1	1	yes	characteristic
220	C₂×C₂₉	C₂×#343	1	1	yes	characteristic
221	C₂³×C₄	—	2	2	no	—
222	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
223	C₂³×C₄	D₄×C₂₉	1	1	yes	characteristic
224	C₂³×C₄	D₄×C₂₉	1	1	yes	characteristic
225	C₂²×C₈	—	2	2	no	—
226	C₂²×C₈	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	8	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄²	—	2	2	no	—
231	C₂×C₄²	—	4	4	no	—
232	C₂×C₄²	C₂×C₄×C₂₉	1	4	yes	—
233	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
234	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
235	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
236	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
237	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
238	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
239	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
240	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
241	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
242	C₂×C₄²	Q₈×C₂₉	1	1	yes	characteristic
243	C₂×C₄²	Q₈×C₂₉	1	1	yes	characteristic
244	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
245	C₄⋊C₈	—	2	2	no	—
246	C₄⋊C₈	—	2	2	no	—
247	C₄⋊C₈	—	2	2	no	—
248	C₄⋊C₈	C₂×C₄×C₂₉	1	4	yes	complemented
249	C₂²⋊C₈	—	2	2	no	—
250	C₂²⋊C₈	—	2	2	no	—
251	C₂²⋊C₈	—	2	2	no	—
252	C₂²⋊C₈	—	2	2	no	—
253	#97	—	2	2	no	—
254	#97	—	2	2	no	—
255	#97	—	2	2	no	—
256	#97	C₂×C₄×C₂₉	1	4	yes	complemented
257	#95	—	2	2	no	—
258	#95	—	2	2	no	—
259	C₂₉	C₂×#1285	1	1	yes	characteristic, direct product factor, Sylow
260	C₂⁴	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	8	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	—	4	4	no	—
268	C₂²×C₄	—	4	4	no	—
269	C₂²×C₄	C₄²×C₂₉	1	1	yes	characteristic
270	C₂²×C₄	C₄²×C₂₉	1	1	yes	characteristic
271	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
272	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
274	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
275	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
276	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
277	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
278	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
279	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
280	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
281	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
282	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
283	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
284	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	4	4	no	—
290	C₂×C₈	—	4	4	no	—
291	C₄⋊C₄	—	2	8	no	—
292	C₄⋊C₄	—	2	8	no	—
293	C₄²	—	4	4	no	—
294	C₄²	—	4	4	no	—
295	C₄²	C₄²×C₂₉	1	1	yes	characteristic
296	C₄²	C₄²×C₂₉	1	1	yes	characteristic
297	C₄²	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
298	C₄²	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
299	C₄²	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
300	C₄²	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
301	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
302	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
303	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
304	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
305	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
306	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
307	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
308	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
309	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
310	C₄²	C₂×Q₈×C₂₉	1	1	yes	characteristic
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	C₂₉×#95	1	1	yes	characteristic
314	C₂³	C₂₉×#95	1	1	yes	characteristic
315	C₂³	C₂₉×#100	1	2	yes	—
316	C₂³	C₂₉×#101	1	2	yes	—
317	C₂³	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	16	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	C₂₉×#95	1	1	yes	characteristic
342	C₂×C₄	C₂₉×#95	1	1	yes	characteristic
343	C₂×C₄	C₂₉×#95	1	1	yes	characteristic
344	C₂×C₄	C₂₉×#95	1	1	yes	characteristic
345	C₂×C₄	C₂₉×#95	1	1	yes	characteristic
346	C₂×C₄	C₂₉×#95	1	1	yes	characteristic
347	C₂×C₄	C₂₉×#104	1	4	yes	—
348	C₂×C₄	C₂×C₄²×C₂₉	1	1	yes	characteristic
349	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
350	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
351	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
352	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
353	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
354	C₈	—	4	4	no	—
355	C₈	—	4	4	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	4	no	—
361	C₂²	—	2	4	no	—
362	C₂²	C₂₉×H(3,ℤ/4)	1	2	yes	—
363	C₂²	C₂₉×#339	1	2	yes	—
364	C₂²	C₂₉×#343	1	2	yes	—
365	C₂²	C₂₉×#343	1	2	yes	—
366	C₂²	C₂×C₂₉×#95	1	1	yes	characteristic
367	C₂²	C₂×C₂₉×#100	1	1	yes	characteristic
368	C₂²	C₂×C₂₉×#101	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	4	8	no	—
380	C₄	C₂₉×#339	1	2	yes	—
381	C₄	C₂×C₂₉×#104	1	2	yes	—
382	C₂	—	2	1	no	—
383	C₂	—	2	2	no	—
384	C₂	—	2	1	no	—
385	C₂	C₂₉×#1285	1	4	yes	direct product factor
386	C₂	C₂×C₂₉×H(3,ℤ/4)	1	1	yes	characteristic
387	C₂	C₂×C₂₉×#339	1	1	yes	characteristic
388	C₂	C₂×C₂₉×#343	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	#95
commutator	C₂×C₄	C₂×C₄²×C₂₉
Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
prime radical	C₂⁴×C₂₉	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂²×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₉×#1285	C₂	direct (N × H)
12. C₂₉×#432	C₄	semidirect
13. C₂₉×#432	C₄	semidirect
17. C₂×C₂₉×C₄⋊C₈	C₄	semidirect
21. C₂×C₂₉×#97	C₄	semidirect
54. C₂₉×C₄⋊C₈	C₂×C₄	semidirect
62. C₂₉×#97	C₂×C₄	semidirect
116. C₂×#1285	C₂₉	direct (N × H)
165. #1285	C₂×C₂₉	direct (N × H)
199. #432	C₄×C₂₉	semidirect
200. #432	C₄×C₂₉	semidirect
204. C₂×C₄⋊C₈	C₄×C₂₉	semidirect
208. C₂×#97	C₄×C₂₉	semidirect
217. C₂×C₂₉	#1285	direct (N × H)
248. C₄⋊C₈	C₂×C₄×C₂₉	semidirect
256. #97	C₂×C₄×C₂₉	semidirect
259. C₂₉	C₂×#1285	direct (N × H)
385. C₂	C₂₉×#1285	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×#432	2
C₂×C₄×C₄⋊C₄×C₂₉	2
C₂₉×#1285	2
C₂×#1285	29

Subgroups — C2×C29×#1285 #20302847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#1285 #20302847