Subgroups — C₂×C₂₉×#1699 #20314039

Order 7424.

726 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#474	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#461	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₉×#436	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1699	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₂₉×#335	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₉×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₉×#332	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×SD₁₆×C₂₉	—	2	1	no	—
10	C₂²×M₁₆×C₂₉	—	2	1	no	—
11	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
14	C₂₉×#487	—	2	2	no	—
15	C₂₉×#487	C₂²	1	4	yes	complemented
16	C₂₉×#474	—	2	2	no	—
17	C₂₉×#474	C₂²	1	4	yes	—
18	C₂₉×#461	—	2	2	no	—
19	C₂₉×#461	C₂²	1	4	yes	—
20	C₂₉×#436	—	2	2	no	—
21	C₂₉×#436	C₂²	1	4	yes	—
22	C₂×C₂₉×#107	—	2	1	no	—
23	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#103	—	2	1	no	—
27	C₂×C₂₉×#103	—	2	1	no	—
28	C₂×C₂₉×#103	—	2	1	no	—
29	C₂×C₂₉×#102	—	2	1	no	—
30	C₂×C₂₉×C₂²⋊C₈	—	2	1	no	—
31	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
32	C₂₉×#335	C₂²	1	4	yes	complemented
33	C₂₉×#332	C₂²	1	4	yes	complemented
34	C₂₉×#332	C₂²	1	4	yes	complemented
35	C₂²×Q₈×C₂₉	—	2	1	no	—
36	C₂²×Q₈×C₂₉	—	2	1	no	—
37	C₂²×D₄×C₂₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₂₉	—	2	1	no	—
39	C₂×SD₁₆×C₂₉	—	2	4	no	—
40	C₂×SD₁₆×C₂₉	—	4	4	no	—
41	C₂×M₁₆×C₂₉	—	2	4	no	—
42	C₂×M₁₆×C₂₉	—	4	4	no	—
43	C₂²×C₈×C₂₉	—	2	1	no	—
44	C₂²×C₈×C₂₉	—	2	1	no	—
45	C₂²×C₈×C₂₉	—	2	1	no	—
46	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
48	C₂₉×C₄⋊Q₈	—	2	1	no	—
49	C₂₉×C₄⋊Q₈	—	2	1	no	—
50	C₂₉×C₄⋊Q₈	—	2	1	no	—
51	C₂₉×C₄⋊Q₈	—	2	1	no	—
52	C₂₉×C₄⋊Q₈	—	2	1	no	—
53	C₂₉×C₄⋊Q₈	—	2	1	no	—
54	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
55	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₄×D₄×C₂₉	—	2	1	no	—
57	C₄×D₄×C₂₉	—	2	1	no	—
58	C₄×D₄×C₂₉	D₄	1	2	yes	—
59	C₄×D₄×C₂₉	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
66	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
67	C₂₉×#107	—	2	4	no	—
68	C₂₉×C₄⋊C₈	—	2	1	no	—
69	C₂₉×C₄⋊C₈	—	2	1	no	—
70	C₂₉×C₄⋊C₈	—	2	1	no	—
71	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
72	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
73	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
74	C₂₉×#103	—	2	4	no	—
75	C₂₉×#103	—	2	4	no	—
76	C₂₉×#103	—	2	4	no	—
77	C₂₉×#102	—	2	4	no	—
78	C₂₉×C₂²⋊C₈	—	2	4	no	—
79	C₄×C₈×C₂₉	D₄	1	2	yes	—
80	C₄×C₈×C₂₉	C₂³	1	2	yes	—
81	C₂⁴×C₂₉	—	2	1	no	—
82	C₂×Q₈×C₂₉	—	2	2	no	—
83	C₂×Q₈×C₂₉	—	2	2	no	—
84	C₂×Q₈×C₂₉	—	4	1	no	—
85	C₂×Q₈×C₂₉	—	4	1	no	—
86	C₂×Q₈×C₂₉	—	4	2	no	—
87	C₂×Q₈×C₂₉	—	4	2	no	—
88	C₂×Q₈×C₂₉	—	4	2	no	—
89	C₂×Q₈×C₂₉	—	4	2	no	—
90	C₂×D₄×C₂₉	—	2	1	no	—
91	C₂×D₄×C₂₉	—	2	2	no	—
92	C₂×D₄×C₂₉	—	2	2	no	—
93	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₂₉	—	2	1	no	—
95	C₂²×C₄×C₂₉	—	2	2	no	—
96	C₂²×C₄×C₂₉	—	2	2	no	—
97	C₂²×C₄×C₂₉	—	4	2	no	—
98	C₂²×C₄×C₂₉	—	4	2	no	—
99	C₂²×C₄×C₂₉	—	4	1	no	—
100	C₂²×C₄×C₂₉	—	4	1	no	—
101	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
104	SD₁₆×C₂₉	—	4	8	no	—
105	M₁₆×C₂₉	—	4	8	no	—
106	C₂×C₈×C₂₉	—	2	2	no	—
107	C₂×C₈×C₂₉	—	2	2	no	—
108	C₂×C₈×C₂₉	—	2	2	no	—
109	C₂×C₈×C₂₉	—	2	2	no	—
110	C₂×C₈×C₂₉	—	2	2	no	—
111	C₂×C₈×C₂₉	—	4	2	no	—
112	C₂×C₈×C₂₉	—	4	2	no	—
113	C₂×C₈×C₂₉	—	4	2	no	—
114	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
116	C₄⋊C₄×C₂₉	—	2	1	no	—
117	C₄⋊C₄×C₂₉	—	2	2	no	—
118	C₄⋊C₄×C₂₉	—	2	2	no	—
119	C₄⋊C₄×C₂₉	—	2	2	no	—
120	C₄⋊C₄×C₂₉	—	2	2	no	—
121	C₄⋊C₄×C₂₉	—	4	1	no	—
122	C₄⋊C₄×C₂₉	—	4	1	no	—
123	C₄⋊C₄×C₂₉	—	4	1	no	—
124	C₄⋊C₄×C₂₉	—	4	1	no	—
125	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
126	C₂²⋊C₄×C₂₉	—	2	2	no	—
127	C₂²⋊C₄×C₂₉	—	2	2	no	—
128	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₂₉	#41	1	1	yes	characteristic
131	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
132	C₂×#1699	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₂₉	—	2	2	no	—
134	C₂³×C₂₉	—	4	2	no	—
135	C₂³×C₂₉	—	4	2	no	—
136	C₂³×C₂₉	—	4	2	no	—
137	C₂³×C₂₉	#121	1	1	yes	characteristic
138	Q₈×C₂₉	—	4	2	no	—
139	Q₈×C₂₉	—	4	2	no	—
140	Q₈×C₂₉	—	4	2	no	—
141	Q₈×C₂₉	—	4	2	no	—
142	Q₈×C₂₉	—	8	2	no	—
143	Q₈×C₂₉	—	8	2	no	—
144	D₄×C₂₉	—	2	2	no	—
145	D₄×C₂₉	—	2	2	no	—
146	D₄×C₂₉	—	4	2	no	—
147	C₂×C₄×C₂₉	—	2	2	no	—
148	C₂×C₄×C₂₉	—	2	2	no	—
149	C₂×C₄×C₂₉	—	4	2	no	—
150	C₂×C₄×C₂₉	—	4	2	no	—
151	C₂×C₄×C₂₉	—	4	2	no	—
152	C₂×C₄×C₂₉	—	4	4	no	—
153	C₂×C₄×C₂₉	—	4	2	no	—
154	C₂×C₄×C₂₉	—	4	2	no	—
155	C₂×C₄×C₂₉	—	8	2	no	—
156	C₂×C₄×C₂₉	—	8	2	no	—
157	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
158	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
159	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
160	C₂×C₄×C₂₉	#135	1	2	yes	—
161	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
162	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
163	C₂×C₄×C₂₉	#137	1	2	yes	—
164	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
167	C₈×C₂₉	—	2	2	no	—
168	C₈×C₂₉	—	2	2	no	—
169	C₈×C₂₉	—	4	2	no	—
170	C₈×C₂₉	—	4	2	no	—
171	C₈×C₂₉	—	4	2	no	—
172	C₂×#487	C₂×C₂₉	1	1	yes	characteristic, complemented
173	C₂×#474	C₂×C₂₉	1	1	yes	characteristic
174	C₂×#461	C₂×C₂₉	1	1	yes	characteristic
175	C₂×#436	C₂×C₂₉	1	1	yes	characteristic
176	#1699	C₂×C₂₉	1	8	yes	direct product factor
177	C₂×#335	C₂×C₂₉	1	1	yes	characteristic, complemented
178	C₂×#332	C₂×C₂₉	1	1	yes	characteristic, complemented
179	C₂×#332	C₂×C₂₉	1	1	yes	characteristic, complemented
180	C₂²×C₂₉	—	4	2	no	—
181	C₂²×C₂₉	—	4	2	no	—
182	C₂²×C₂₉	—	4	2	no	—
183	C₂²×C₂₉	—	8	4	no	—
184	C₂²×C₂₉	#463	1	2	yes	—
185	C₂²×C₂₉	#468	1	2	yes	—
186	C₂²×C₂₉	#473	1	2	yes	—
187	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
188	C₄×C₂₉	—	2	1	no	—
189	C₄×C₂₉	—	2	1	no	—
190	C₄×C₂₉	—	4	2	no	—
191	C₄×C₂₉	—	8	2	no	—
192	C₄×C₂₉	—	8	2	no	—
193	C₄×C₂₉	#463	1	2	yes	—
194	C₄×C₂₉	#468	1	2	yes	—
195	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
196	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
198	C₄×C₂₉	C₂×#137	1	1	yes	characteristic
199	C₂²×SD₁₆	—	2	1	no	—
200	C₂²×M₁₆	—	2	1	no	—
201	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
202	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
203	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
204	#487	—	2	2	no	—
205	#487	C₂²×C₂₉	1	4	yes	complemented
206	#474	—	2	2	no	—
207	#474	C₂²×C₂₉	1	4	yes	—
208	#461	—	2	2	no	—
209	#461	C₂²×C₂₉	1	4	yes	—
210	#436	—	2	2	no	—
211	#436	C₂²×C₂₉	1	4	yes	—
212	C₂×#107	—	2	1	no	—
213	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
214	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
215	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
216	C₂×#103	—	2	1	no	—
217	C₂×#103	—	2	1	no	—
218	C₂×#103	—	2	1	no	—
219	C₂×#102	—	2	1	no	—
220	C₂×C₂²⋊C₈	—	2	1	no	—
221	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
222	#335	C₂²×C₂₉	1	4	yes	complemented
223	#332	C₂²×C₂₉	1	4	yes	complemented
224	#332	C₂²×C₂₉	1	4	yes	complemented
225	C₂×C₂₉	—	8	2	no	—
226	C₂×C₂₉	#1699	1	4	yes	direct product factor
227	C₂×C₂₉	C₂×#463	1	1	yes	characteristic
228	C₂×C₂₉	C₂×#468	1	1	yes	characteristic
229	C₂×C₂₉	C₂×#473	1	1	yes	characteristic
230	C₂²×Q₈	—	2	1	no	—
231	C₂²×Q₈	—	2	1	no	—
232	C₂²×D₄	D₄×C₂₉	1	1	yes	characteristic
233	C₂³×C₄	—	2	1	no	—
234	C₂×SD₁₆	—	2	4	no	—
235	C₂×SD₁₆	—	4	4	no	—
236	C₂×M₁₆	—	2	4	no	—
237	C₂×M₁₆	—	4	4	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
242	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
250	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	D₄×C₂₉	1	2	yes	—
254	C₄×D₄	C₂³×C₂₉	1	2	yes	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	—	2	1	no	—
261	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
262	#107	—	2	4	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
267	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
268	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
269	#103	—	2	4	no	—
270	#103	—	2	4	no	—
271	#103	—	2	4	no	—
272	#102	—	2	4	no	—
273	C₂²⋊C₈	—	2	4	no	—
274	C₄×C₈	D₄×C₂₉	1	2	yes	—
275	C₄×C₈	C₂³×C₂₉	1	2	yes	—
276	C₂₉	C₂×#1699	1	1	yes	characteristic, direct product factor, Sylow
277	C₂⁴	—	2	1	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	4	1	no	—
281	C₂×Q₈	—	4	1	no	—
282	C₂×Q₈	—	4	2	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	—	4	2	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
299	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
300	SD₁₆	—	4	8	no	—
301	M₁₆	—	4	8	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	4	2	no	—
308	C₂×C₈	—	4	2	no	—
309	C₂×C₈	—	4	2	no	—
310	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
311	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
325	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
326	C₄²	#41×C₂₉	1	1	yes	characteristic
327	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
328	C₂³	—	2	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	C₂₉×#121	1	1	yes	characteristic
333	Q₈	—	4	2	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	2	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	8	2	no	—
338	Q₈	—	8	2	no	—
339	D₄	—	2	2	no	—
340	D₄	—	2	2	no	—
341	D₄	—	4	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	—	8	2	no	—
352	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
353	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
354	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
355	C₂×C₄	C₂₉×#135	1	2	yes	—
356	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
357	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
358	C₂×C₄	C₂₉×#137	1	2	yes	—
359	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
361	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
362	C₈	—	2	2	no	—
363	C₈	—	2	2	no	—
364	C₈	—	4	2	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	2	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	8	4	no	—
371	C₂²	C₂₉×#463	1	2	yes	—
372	C₂²	C₂₉×#468	1	2	yes	—
373	C₂²	C₂₉×#473	1	2	yes	—
374	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	2	no	—
379	C₄	—	8	2	no	—
380	C₄	C₂₉×#463	1	2	yes	—
381	C₄	C₂₉×#468	1	2	yes	—
382	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
383	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
384	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
385	C₄	C₂×C₂₉×#137	1	1	yes	characteristic
386	C₂	—	8	2	no	—
387	C₂	C₂₉×#1699	1	4	yes	direct product factor
388	C₂	C₂×C₂₉×#463	1	1	yes	characteristic
389	C₂	C₂×C₂₉×#468	1	1	yes	characteristic
390	C₂	C₂×C₂₉×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂²×D₄×C₂₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#487	C₂	semidirect
5. C₂₉×#1699	C₂	direct (N × H)
6. C₂×C₂₉×#335	C₂	semidirect
7. C₂×C₂₉×#332	C₂	semidirect
8. C₂×C₂₉×#332	C₂	semidirect
15. C₂₉×#487	C₂²	semidirect
32. C₂₉×#335	C₂²	semidirect
33. C₂₉×#332	C₂²	semidirect
34. C₂₉×#332	C₂²	semidirect
132. C₂×#1699	C₂₉	direct (N × H)
172. C₂×#487	C₂×C₂₉	semidirect
176. #1699	C₂×C₂₉	direct (N × H)
177. C₂×#335	C₂×C₂₉	semidirect
178. C₂×#332	C₂×C₂₉	semidirect
179. C₂×#332	C₂×C₂₉	semidirect
205. #487	C₂²×C₂₉	semidirect
222. #335	C₂²×C₂₉	semidirect
223. #332	C₂²×C₂₉	semidirect
224. #332	C₂²×C₂₉	semidirect
226. C₂×C₂₉	#1699	direct (N × H)
276. C₂₉	C₂×#1699	direct (N × H)
387. C₂	C₂₉×#1699	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×#487	2
C₂×C₂₉×#474	2
C₂×C₂₉×#461	2
C₂×C₂₉×#436	2
C₂₉×#1699	2
C₂×C₂₉×#335	2
C₂×C₂₉×#332	2
C₂×#1699	29

Subgroups — C2×C29×#1699 #20314039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#1699 #20314039