Subgroups — C₂×C₂₉×AGL(1,ℤ/16) #20328367

Order 7424.

710 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#509	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#444	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×#442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×AGL(1,ℤ/16)	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₂₉×#365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₉×#361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₉×#360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₉×#347	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
10	C₂²×D₈×C₂₉	C₂²	1	1	yes	characteristic
11	C₂×C₂₉×#131	—	2	1	no	—
12	C₂×C₄×D₄×C₂₉	—	2	1	no	—
13	C₂₉×#509	C₄	1	4	yes	complemented
14	C₂₉×#509	C₂²	1	4	yes	—
15	C₂×C₂₉×SD₃₂	C₄	1	2	yes	complemented
16	C₂×C₂₉×D₁₆	C₄	1	2	yes	complemented
17	C₂×C₂₉×M₃₂	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×M₃₂	C₂²	1	1	yes	characteristic
19	C₂₉×#444	—	2	2	no	—
20	C₂₉×#444	C₂²	1	4	yes	complemented
21	C₂₉×#442	—	2	2	no	—
22	C₂₉×#442	C₂²	1	4	yes	complemented
23	C₂×C₂₉×#108	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×#104	—	2	1	no	—
26	C₂×C₂₉×#102	—	2	1	no	—
27	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
28	C₂₉×#365	C₂²	1	4	yes	complemented
29	C₂₉×#361	C₂²	1	4	yes	complemented
30	C₂₉×#360	C₂²	1	4	yes	complemented
31	C₂₉×#347	C₂²	1	4	yes	complemented
32	C₂×#41×C₂₉	—	2	1	no	—
33	C₂²×D₄×C₂₉	—	2	1	no	—
34	C₂³×C₄×C₂₉	—	4	1	no	—
35	C₂₉×#135	—	2	1	no	—
36	C₂₉×#135	—	2	1	no	—
37	C₂₉×#135	C₂×C₄	1	2	yes	complemented
38	C₂₉×#135	C₂³	1	2	yes	—
39	C₂×Q₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic, complemented
40	C₂×SD₁₆×C₂₉	—	2	1	no	—
41	C₂×D₈×C₂₉	—	2	1	no	—
42	C₂×D₈×C₂₉	—	2	1	no	—
43	C₂×D₈×C₂₉	—	2	1	no	—
44	C₂×D₈×C₂₉	C₂×C₄	1	2	yes	—
45	C₂×D₈×C₂₉	C₂×C₄	1	2	yes	—
46	C₂×D₈×C₂₉	C₂×C₄	1	1	yes	characteristic, complemented
47	C₂×D₈×C₂₉	C₂³	1	2	yes	—
48	C₂₉×#131	—	2	4	no	—
49	C₂₉×#131	—	4	2	no	—
50	C₂×M₁₆×C₂₉	—	2	1	no	—
51	C₂×M₁₆×C₂₉	—	4	1	no	—
52	C₂²×C₈×C₂₉	—	4	1	no	—
53	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
55	C₄×D₄×C₂₉	—	2	4	no	—
56	C₄×D₄×C₂₉	—	4	2	no	—
57	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₂₉	—	4	1	no	—
59	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
60	C₂₉×SD₃₂	C₂×C₄	1	8	yes	complemented
61	C₂₉×D₁₆	C₂×C₄	1	8	yes	complemented
62	C₂₉×M₃₂	—	2	1	no	—
63	C₂₉×M₃₂	C₂×C₄	1	2	yes	complemented
64	C₂₉×M₃₂	C₂³	1	2	yes	—
65	C₂₉×M₃₂	C₂³	1	2	yes	—
66	C₂×C₁₆×C₂₉	—	2	1	no	—
67	C₂×C₁₆×C₂₉	C₂×C₄	1	2	yes	complemented
68	C₂₉×#108	—	2	1	no	—
69	C₂₉×#108	C₂³	1	2	yes	—
70	C₂₉×#106	—	2	1	no	—
71	C₂₉×#106	C₂³	1	2	yes	—
72	C₂₉×#104	—	2	4	no	—
73	C₂₉×#102	—	2	4	no	—
74	C₂₉×#97	D₄	1	2	yes	—
75	C₂₉×#97	C₂³	1	2	yes	—
76	C₂⁴×C₂₉	—	4	1	no	—
77	#41×C₂₉	—	2	2	no	—
78	#41×C₂₉	—	2	2	no	—
79	#41×C₂₉	—	4	1	no	—
80	#41×C₂₉	—	4	1	no	—
81	C₂×Q₈×C₂₉	—	2	1	no	—
82	C₂×D₄×C₂₉	—	2	2	no	—
83	C₂×D₄×C₂₉	—	2	2	no	—
84	C₂×D₄×C₂₉	—	2	1	no	—
85	C₂×D₄×C₂₉	—	2	2	no	—
86	C₂×D₄×C₂₉	—	4	1	no	—
87	C₂×D₄×C₂₉	—	4	1	no	—
88	C₂×D₄×C₂₉	—	4	1	no	—
89	C₂×D₄×C₂₉	—	4	1	no	—
90	C₂²×C₄×C₂₉	—	2	1	no	—
91	C₂²×C₄×C₂₉	—	4	4	no	—
92	C₂²×C₄×C₂₉	—	4	1	no	—
93	C₂²×C₄×C₂₉	—	4	1	no	—
94	C₂²×C₄×C₂₉	—	8	4	no	—
95	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
96	Q₁₆×C₂₉	—	2	1	no	—
97	Q₁₆×C₂₉	C₂²×C₄	1	2	yes	complemented
98	SD₁₆×C₂₉	—	2	2	no	—
99	SD₁₆×C₂₉	—	2	2	no	—
100	D₈×C₂₉	—	2	2	no	—
101	D₈×C₂₉	—	2	2	no	—
102	D₈×C₂₉	—	2	1	no	—
103	D₈×C₂₉	—	2	2	no	—
104	D₈×C₂₉	C₂²×C₄	1	4	yes	—
105	D₈×C₂₉	C₂²×C₄	1	2	yes	complemented
106	M₁₆×C₂₉	—	2	2	no	—
107	M₁₆×C₂₉	—	4	4	no	—
108	M₁₆×C₂₉	—	4	1	no	—
109	C₂×C₈×C₂₉	—	2	1	no	—
110	C₂×C₈×C₂₉	—	2	1	no	—
111	C₂×C₈×C₂₉	—	4	4	no	—
112	C₂×C₈×C₂₉	—	4	1	no	—
113	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₂₉	#41	1	1	yes	characteristic
118	C₂×C₈×C₂₉	#41	1	1	yes	characteristic
119	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
120	C₄⋊C₄×C₂₉	—	2	2	no	—
121	C₄⋊C₄×C₂₉	—	4	1	no	—
122	C₂²⋊C₄×C₂₉	—	4	4	no	—
123	C₄²×C₂₉	—	2	1	no	—
124	C₄²×C₂₉	C₂×D₄	1	2	yes	—
125	C₁₆×C₂₉	—	2	2	no	—
126	C₁₆×C₂₉	C₂²×C₄	1	4	yes	complemented
127	C₂×AGL(1,ℤ/16)	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂³×C₂₉	—	4	2	no	—
129	C₂³×C₂₉	—	4	2	no	—
130	C₂³×C₂₉	—	4	1	no	—
131	C₂³×C₂₉	—	4	2	no	—
132	C₂³×C₂₉	—	8	2	no	—
133	C₂³×C₂₉	—	8	2	no	—
134	C₂³×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
135	Q₈×C₂₉	—	2	2	no	—
136	Q₈×C₂₉	—	4	1	no	—
137	D₄×C₂₉	—	2	4	no	—
138	D₄×C₂₉	—	2	2	no	—
139	D₄×C₂₉	—	4	2	no	—
140	D₄×C₂₉	—	4	2	no	—
141	D₄×C₂₉	—	4	2	no	—
142	D₄×C₂₉	—	4	2	no	—
143	D₄×C₂₉	—	4	2	no	—
144	D₄×C₂₉	—	4	1	no	—
145	C₂×C₄×C₂₉	—	2	2	no	—
146	C₂×C₄×C₂₉	—	4	2	no	—
147	C₂×C₄×C₂₉	—	4	1	no	—
148	C₂×C₄×C₂₉	—	4	2	no	—
149	C₂×C₄×C₂₉	—	4	2	no	—
150	C₂×C₄×C₂₉	—	4	2	no	—
151	C₂×C₄×C₂₉	—	8	8	no	—
152	C₂×C₄×C₂₉	—	8	2	no	—
153	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
156	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
159	C₈×C₂₉	—	2	2	no	—
160	C₈×C₂₉	—	4	2	no	—
161	C₈×C₂₉	C₄×D₄	1	1	yes	characteristic
162	C₈×C₂₉	C₄×D₄	1	1	yes	characteristic
163	C₈×C₂₉	C₂³×C₄	1	1	yes	characteristic
164	C₈×C₂₉	C₂×#41	1	1	yes	characteristic
165	C₂×#509	C₂×C₂₉	1	1	yes	characteristic
166	C₂×#444	C₂×C₂₉	1	1	yes	characteristic, complemented
167	C₂×#442	C₂×C₂₉	1	1	yes	characteristic, complemented
168	AGL(1,ℤ/16)	C₂×C₂₉	1	8	yes	direct product factor
169	C₂×#365	C₂×C₂₉	1	1	yes	characteristic, complemented
170	C₂×#361	C₂×C₂₉	1	1	yes	characteristic, complemented
171	C₂×#360	C₂×C₂₉	1	1	yes	characteristic, complemented
172	C₂×#347	C₂×C₂₉	1	1	yes	characteristic, complemented
173	C₂²×C₂₉	—	2	2	no	—
174	C₂²×C₂₉	—	4	2	no	—
175	C₂²×C₂₉	—	4	4	no	—
176	C₂²×C₂₉	—	8	2	no	—
177	C₂²×C₂₉	—	8	2	no	—
178	C₂²×C₂₉	—	8	4	no	—
179	C₂²×C₂₉	—	8	2	no	—
180	C₂²×C₂₉	—	8	4	no	—
181	C₂²×C₂₉	#442	1	1	yes	characteristic
182	C₂²×C₂₉	#442	1	1	yes	characteristic
183	C₂²×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₄×C₂₉	—	4	2	no	—
185	C₄×C₂₉	—	4	2	no	—
186	C₄×C₂₉	—	8	2	no	—
187	C₄×C₂₉	#442	1	1	yes	characteristic
188	C₄×C₂₉	#442	1	1	yes	characteristic
189	C₄×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
190	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
192	C₂²×D₈	C₂²×C₂₉	1	1	yes	characteristic
193	C₂×#131	—	2	1	no	—
194	C₂×C₄×D₄	—	2	1	no	—
195	#509	C₄×C₂₉	1	4	yes	complemented
196	#509	C₂²×C₂₉	1	4	yes	—
197	C₂×SD₃₂	C₄×C₂₉	1	2	yes	complemented
198	C₂×D₁₆	C₄×C₂₉	1	2	yes	complemented
199	C₂×M₃₂	C₂²×C₂₉	1	1	yes	characteristic
200	C₂×M₃₂	C₂²×C₂₉	1	1	yes	characteristic
201	#444	—	2	2	no	—
202	#444	C₂²×C₂₉	1	4	yes	complemented
203	#442	—	2	2	no	—
204	#442	C₂²×C₂₉	1	4	yes	complemented
205	C₂×#108	C₂²×C₂₉	1	1	yes	characteristic
206	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
207	C₂×#104	—	2	1	no	—
208	C₂×#102	—	2	1	no	—
209	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
210	#365	C₂²×C₂₉	1	4	yes	complemented
211	#361	C₂²×C₂₉	1	4	yes	complemented
212	#360	C₂²×C₂₉	1	4	yes	complemented
213	#347	C₂²×C₂₉	1	4	yes	complemented
214	C₂×C₂₉	—	2	1	no	—
215	C₂×C₂₉	—	2	1	no	—
216	C₂×C₂₉	—	8	2	no	—
217	C₂×C₂₉	—	8	4	no	—
218	C₂×C₂₉	AGL(1,ℤ/16)	1	2	yes	direct product factor
219	C₂×C₂₉	C₂×#442	1	1	yes	characteristic
220	C₂×#41	—	2	1	no	—
221	C₂²×D₄	—	2	1	no	—
222	C₂³×C₄	—	4	1	no	—
223	#135	—	2	1	no	—
224	#135	—	2	1	no	—
225	#135	C₂×C₄×C₂₉	1	2	yes	complemented
226	#135	C₂³×C₂₉	1	2	yes	—
227	C₂×Q₁₆	C₂×C₄×C₂₉	1	1	yes	characteristic, complemented
228	C₂×SD₁₆	—	2	1	no	—
229	C₂×D₈	—	2	1	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂×D₈	—	2	1	no	—
232	C₂×D₈	C₂×C₄×C₂₉	1	2	yes	—
233	C₂×D₈	C₂×C₄×C₂₉	1	2	yes	—
234	C₂×D₈	C₂×C₄×C₂₉	1	1	yes	characteristic, complemented
235	C₂×D₈	C₂³×C₂₉	1	2	yes	—
236	#131	—	2	4	no	—
237	#131	—	4	2	no	—
238	C₂×M₁₆	—	2	1	no	—
239	C₂×M₁₆	—	4	1	no	—
240	C₂²×C₈	—	4	1	no	—
241	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
243	C₄×D₄	—	2	4	no	—
244	C₄×D₄	—	4	2	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₂²⋊C₄	—	4	1	no	—
247	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
248	SD₃₂	C₂×C₄×C₂₉	1	8	yes	complemented
249	D₁₆	C₂×C₄×C₂₉	1	8	yes	complemented
250	M₃₂	—	2	1	no	—
251	M₃₂	C₂×C₄×C₂₉	1	2	yes	complemented
252	M₃₂	C₂³×C₂₉	1	2	yes	—
253	M₃₂	C₂³×C₂₉	1	2	yes	—
254	C₂×C₁₆	—	2	1	no	—
255	C₂×C₁₆	C₂×C₄×C₂₉	1	2	yes	complemented
256	#108	—	2	1	no	—
257	#108	C₂³×C₂₉	1	2	yes	—
258	#106	—	2	1	no	—
259	#106	C₂³×C₂₉	1	2	yes	—
260	#104	—	2	4	no	—
261	#102	—	2	4	no	—
262	#97	D₄×C₂₉	1	2	yes	—
263	#97	C₂³×C₂₉	1	2	yes	—
264	C₂₉	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic, direct product factor, Sylow
265	C₂⁴	—	4	1	no	—
266	#41	—	2	2	no	—
267	#41	—	2	2	no	—
268	#41	—	4	1	no	—
269	#41	—	4	1	no	—
270	C₂×Q₈	—	2	1	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	4	1	no	—
276	C₂×D₄	—	4	1	no	—
277	C₂×D₄	—	4	1	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	4	4	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	8	4	no	—
284	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
285	Q₁₆	—	2	1	no	—
286	Q₁₆	C₂²×C₄×C₂₉	1	2	yes	complemented
287	SD₁₆	—	2	2	no	—
288	SD₁₆	—	2	2	no	—
289	D₈	—	2	2	no	—
290	D₈	—	2	2	no	—
291	D₈	—	2	1	no	—
292	D₈	—	2	2	no	—
293	D₈	C₂²×C₄×C₂₉	1	4	yes	—
294	D₈	C₂²×C₄×C₂₉	1	2	yes	complemented
295	M₁₆	—	2	2	no	—
296	M₁₆	—	4	4	no	—
297	M₁₆	—	4	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	4	4	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
303	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
305	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
306	C₂×C₈	#41×C₂₉	1	1	yes	characteristic
307	C₂×C₈	#41×C₂₉	1	1	yes	characteristic
308	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₂²⋊C₄	—	4	4	no	—
312	C₄²	—	2	1	no	—
313	C₄²	C₂×D₄×C₂₉	1	2	yes	—
314	C₁₆	—	2	2	no	—
315	C₁₆	C₂²×C₄×C₂₉	1	4	yes	complemented
316	C₂³	—	4	1	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	8	2	no	—
321	C₂³	—	8	2	no	—
322	C₂³	C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
323	Q₈	—	2	2	no	—
324	Q₈	—	4	1	no	—
325	D₄	—	2	4	no	—
326	D₄	—	2	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	2	no	—
329	D₄	—	4	2	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	1	no	—
332	D₄	—	4	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	8	8	no	—
340	C₂×C₄	—	8	2	no	—
341	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
342	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
343	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
344	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
345	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
346	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
347	C₈	—	2	2	no	—
348	C₈	—	4	2	no	—
349	C₈	C₄×D₄×C₂₉	1	1	yes	characteristic
350	C₈	C₄×D₄×C₂₉	1	1	yes	characteristic
351	C₈	C₂³×C₄×C₂₉	1	1	yes	characteristic
352	C₈	C₂×#41×C₂₉	1	1	yes	characteristic
353	C₂²	—	2	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	4	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	8	4	no	—
359	C₂²	—	8	4	no	—
360	C₂²	—	8	2	no	—
361	C₂²	C₂₉×#442	1	1	yes	characteristic
362	C₂²	C₂₉×#442	1	1	yes	characteristic
363	C₂²	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	—	8	2	no	—
367	C₄	C₂₉×#442	1	1	yes	characteristic
368	C₄	C₂₉×#442	1	1	yes	characteristic
369	C₄	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
370	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
371	C₂	—	2	1	no	—
372	C₂	—	2	1	no	—
373	C₂	—	8	4	no	—
374	C₂	—	8	2	no	—
375	C₂	C₂₉×AGL(1,ℤ/16)	1	2	yes	direct product factor
376	C₂	C₂×C₂₉×#442	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	#442
commutator	C₈	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₈	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#509	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ C₂×C₂₉×#97 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₉×#444	C₂	semidirect
3. C₂×C₂₉×#442	C₂	semidirect
4. C₂₉×AGL(1,ℤ/16)	C₂	direct (N × H)
5. C₂×C₂₉×#365	C₂	semidirect
6. C₂×C₂₉×#361	C₂	semidirect
7. C₂×C₂₉×#360	C₂	semidirect
8. C₂×C₂₉×#347	C₂	semidirect
13. C₂₉×#509	C₄	semidirect
15. C₂×C₂₉×SD₃₂	C₄	semidirect
16. C₂×C₂₉×D₁₆	C₄	semidirect
20. C₂₉×#444	C₂²	semidirect
22. C₂₉×#442	C₂²	semidirect
28. C₂₉×#365	C₂²	semidirect
29. C₂₉×#361	C₂²	semidirect
30. C₂₉×#360	C₂²	semidirect
31. C₂₉×#347	C₂²	semidirect
37. C₂₉×#135	C₂×C₄	semidirect
39. C₂×Q₁₆×C₂₉	C₂×C₄	semidirect
46. C₂×D₈×C₂₉	C₂×C₄	semidirect
60. C₂₉×SD₃₂	C₂×C₄	semidirect
61. C₂₉×D₁₆	C₂×C₄	semidirect
63. C₂₉×M₃₂	C₂×C₄	semidirect
67. C₂×C₁₆×C₂₉	C₂×C₄	semidirect
97. Q₁₆×C₂₉	C₂²×C₄	semidirect
105. D₈×C₂₉	C₂²×C₄	semidirect
126. C₁₆×C₂₉	C₂²×C₄	semidirect
127. C₂×AGL(1,ℤ/16)	C₂₉	direct (N × H)
166. C₂×#444	C₂×C₂₉	semidirect
167. C₂×#442	C₂×C₂₉	semidirect
168. AGL(1,ℤ/16)	C₂×C₂₉	direct (N × H)
169. C₂×#365	C₂×C₂₉	semidirect
170. C₂×#361	C₂×C₂₉	semidirect
171. C₂×#360	C₂×C₂₉	semidirect
172. C₂×#347	C₂×C₂₉	semidirect
195. #509	C₄×C₂₉	semidirect
197. C₂×SD₃₂	C₄×C₂₉	semidirect
198. C₂×D₁₆	C₄×C₂₉	semidirect
202. #444	C₂²×C₂₉	semidirect
204. #442	C₂²×C₂₉	semidirect
210. #365	C₂²×C₂₉	semidirect
211. #361	C₂²×C₂₉	semidirect
212. #360	C₂²×C₂₉	semidirect
213. #347	C₂²×C₂₉	semidirect
218. C₂×C₂₉	AGL(1,ℤ/16)	direct (N × H)
225. #135	C₂×C₄×C₂₉	semidirect
227. C₂×Q₁₆	C₂×C₄×C₂₉	semidirect
234. C₂×D₈	C₂×C₄×C₂₉	semidirect
248. SD₃₂	C₂×C₄×C₂₉	semidirect
249. D₁₆	C₂×C₄×C₂₉	semidirect
251. M₃₂	C₂×C₄×C₂₉	semidirect
255. C₂×C₁₆	C₂×C₄×C₂₉	semidirect
264. C₂₉	C₂×AGL(1,ℤ/16)	direct (N × H)
286. Q₁₆	C₂²×C₄×C₂₉	semidirect
294. D₈	C₂²×C₄×C₂₉	semidirect
315. C₁₆	C₂²×C₄×C₂₉	semidirect
375. C₂	C₂₉×AGL(1,ℤ/16)	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×#509	2
C₂×C₂₉×#444	2
C₂×C₂₉×#442	2
C₂₉×AGL(1,ℤ/16)	2
C₂×C₂₉×#365	2
C₂×C₂₉×#361	2
C₂×C₂₉×#360	2
C₂×C₂₉×#347	2
C₂×AGL(1,ℤ/16)	29

Subgroups — C2×C29×AGL(1,ℤ/16) #20328367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×AGL(1,ℤ/16) #20328367