Subgroups — C₂×C₁₃×AGL(1,ℤ/16) #15719806

Order 3328.

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×C₁₃×#509	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#444	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×AGL(1,ℤ/16)	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#347	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#131	—	2	1	no	—
12	C₂×C₄×D₄×C₁₃	—	2	1	no	—
13	C₁₃×#509	C₄	1	4	yes	complemented
14	C₁₃×#509	C₂²	1	4	yes	—
15	C₂×C₁₃×SD₃₂	C₄	1	2	yes	complemented
16	C₂×C₁₃×D₁₆	C₄	1	2	yes	complemented
17	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
19	C₁₃×#444	—	2	2	no	—
20	C₁₃×#444	C₂²	1	4	yes	complemented
21	C₁₃×#442	—	2	2	no	—
22	C₁₃×#442	C₂²	1	4	yes	complemented
23	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#104	—	2	1	no	—
26	C₂×C₁₃×#102	—	2	1	no	—
27	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
28	C₁₃×#365	C₂²	1	4	yes	complemented
29	C₁₃×#361	C₂²	1	4	yes	complemented
30	C₁₃×#360	C₂²	1	4	yes	complemented
31	C₁₃×#347	C₂²	1	4	yes	complemented
32	C₂×C₁₃×#41	—	2	1	no	—
33	C₂²×D₄×C₁₃	—	2	1	no	—
34	C₂³×C₄×C₁₃	—	4	1	no	—
35	C₁₃×#135	—	2	1	no	—
36	C₁₃×#135	—	2	1	no	—
37	C₁₃×#135	C₂×C₄	1	2	yes	complemented
38	C₁₃×#135	C₂³	1	2	yes	—
39	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
40	C₂×C₁₃×SD₁₆	—	2	1	no	—
41	C₂×C₁₃×D₈	—	2	1	no	—
42	C₂×C₁₃×D₈	—	2	1	no	—
43	C₂×C₁₃×D₈	—	2	1	no	—
44	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
45	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
46	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic, complemented
47	C₂×C₁₃×D₈	C₂³	1	2	yes	—
48	C₁₃×#131	—	2	4	no	—
49	C₁₃×#131	—	4	2	no	—
50	C₂×C₁₃×M₁₆	—	2	1	no	—
51	C₂×C₁₃×M₁₆	—	4	1	no	—
52	C₂²×C₈×C₁₃	—	4	1	no	—
53	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₄×D₄×C₁₃	—	2	4	no	—
56	C₄×D₄×C₁₃	—	4	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
59	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
60	C₁₃×SD₃₂	C₂×C₄	1	8	yes	complemented
61	C₁₃×D₁₆	C₂×C₄	1	8	yes	complemented
62	C₁₃×M₃₂	—	2	1	no	—
63	C₁₃×M₃₂	C₂×C₄	1	2	yes	complemented
64	C₁₃×M₃₂	C₂³	1	2	yes	—
65	C₁₃×M₃₂	C₂³	1	2	yes	—
66	C₂×C₁₃×C₁₆	—	2	1	no	—
67	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	complemented
68	C₁₃×#108	—	2	1	no	—
69	C₁₃×#108	C₂³	1	2	yes	—
70	C₁₃×#106	—	2	1	no	—
71	C₁₃×#106	C₂³	1	2	yes	—
72	C₁₃×#104	—	2	4	no	—
73	C₁₃×#102	—	2	4	no	—
74	C₁₃×#97	D₄	1	2	yes	—
75	C₁₃×#97	C₂³	1	2	yes	—
76	C₂×AGL(1,ℤ/16)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₃	—	4	1	no	—
78	C₁₃×#41	—	2	2	no	—
79	C₁₃×#41	—	2	2	no	—
80	C₁₃×#41	—	4	1	no	—
81	C₁₃×#41	—	4	1	no	—
82	C₂×Q₈×C₁₃	—	2	1	no	—
83	C₂×D₄×C₁₃	—	2	2	no	—
84	C₂×D₄×C₁₃	—	2	2	no	—
85	C₂×D₄×C₁₃	—	2	1	no	—
86	C₂×D₄×C₁₃	—	2	2	no	—
87	C₂×D₄×C₁₃	—	4	1	no	—
88	C₂×D₄×C₁₃	—	4	1	no	—
89	C₂×D₄×C₁₃	—	4	1	no	—
90	C₂×D₄×C₁₃	—	4	1	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	4	4	no	—
93	C₂²×C₄×C₁₃	—	4	1	no	—
94	C₂²×C₄×C₁₃	—	4	1	no	—
95	C₂²×C₄×C₁₃	—	8	4	no	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₁₃×Q₁₆	—	2	1	no	—
98	C₁₃×Q₁₆	C₂²×C₄	1	2	yes	complemented
99	C₁₃×SD₁₆	—	2	2	no	—
100	C₁₃×SD₁₆	—	2	2	no	—
101	C₁₃×D₈	—	2	2	no	—
102	C₁₃×D₈	—	2	2	no	—
103	C₁₃×D₈	—	2	1	no	—
104	C₁₃×D₈	—	2	2	no	—
105	C₁₃×D₈	C₂²×C₄	1	4	yes	—
106	C₁₃×D₈	C₂²×C₄	1	2	yes	complemented
107	C₁₃×M₁₆	—	2	2	no	—
108	C₁₃×M₁₆	—	4	4	no	—
109	C₁₃×M₁₆	—	4	1	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	4	4	no	—
113	C₂×C₈×C₁₃	—	4	1	no	—
114	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
119	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
120	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	4	1	no	—
123	C₁₃×C₂²⋊C₄	—	4	4	no	—
124	C₄²×C₁₃	—	2	1	no	—
125	C₄²×C₁₃	C₂×D₄	1	2	yes	—
126	C₁₃×C₁₆	—	2	2	no	—
127	C₁₃×C₁₆	C₂²×C₄	1	4	yes	complemented
128	C₂×#509	C₂×C₁₃	1	1	yes	characteristic
129	C₂×#444	C₂×C₁₃	1	1	yes	characteristic, complemented
130	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
131	AGL(1,ℤ/16)	C₂×C₁₃	1	8	yes	direct product factor
132	C₂×#365	C₂×C₁₃	1	1	yes	characteristic, complemented
133	C₂×#361	C₂×C₁₃	1	1	yes	characteristic, complemented
134	C₂×#360	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₂×#347	C₂×C₁₃	1	1	yes	characteristic, complemented
136	C₂³×C₁₃	—	4	2	no	—
137	C₂³×C₁₃	—	4	2	no	—
138	C₂³×C₁₃	—	4	1	no	—
139	C₂³×C₁₃	—	4	2	no	—
140	C₂³×C₁₃	—	8	2	no	—
141	C₂³×C₁₃	—	8	2	no	—
142	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
143	Q₈×C₁₃	—	2	2	no	—
144	Q₈×C₁₃	—	4	1	no	—
145	D₄×C₁₃	—	2	4	no	—
146	D₄×C₁₃	—	2	2	no	—
147	D₄×C₁₃	—	4	2	no	—
148	D₄×C₁₃	—	4	2	no	—
149	D₄×C₁₃	—	4	2	no	—
150	D₄×C₁₃	—	4	2	no	—
151	D₄×C₁₃	—	4	2	no	—
152	D₄×C₁₃	—	4	1	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	4	1	no	—
156	C₂×C₄×C₁₃	—	4	2	no	—
157	C₂×C₄×C₁₃	—	4	2	no	—
158	C₂×C₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	—	8	8	no	—
160	C₂×C₄×C₁₃	—	8	2	no	—
161	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
167	C₈×C₁₃	—	2	2	no	—
168	C₈×C₁₃	—	4	2	no	—
169	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
170	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
171	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
172	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
173	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
174	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
175	C₂×#131	—	2	1	no	—
176	C₂×C₄×D₄	—	2	1	no	—
177	#509	C₄×C₁₃	1	4	yes	complemented
178	#509	C₂²×C₁₃	1	4	yes	—
179	C₂×SD₃₂	C₄×C₁₃	1	2	yes	complemented
180	C₂×D₁₆	C₄×C₁₃	1	2	yes	complemented
181	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
182	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
183	#444	—	2	2	no	—
184	#444	C₂²×C₁₃	1	4	yes	complemented
185	#442	—	2	2	no	—
186	#442	C₂²×C₁₃	1	4	yes	complemented
187	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
188	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
189	C₂×#104	—	2	1	no	—
190	C₂×#102	—	2	1	no	—
191	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
192	#365	C₂²×C₁₃	1	4	yes	complemented
193	#361	C₂²×C₁₃	1	4	yes	complemented
194	#360	C₂²×C₁₃	1	4	yes	complemented
195	#347	C₂²×C₁₃	1	4	yes	complemented
196	C₂²×C₁₃	—	2	2	no	—
197	C₂²×C₁₃	—	4	2	no	—
198	C₂²×C₁₃	—	4	4	no	—
199	C₂²×C₁₃	—	8	2	no	—
200	C₂²×C₁₃	—	8	2	no	—
201	C₂²×C₁₃	—	8	4	no	—
202	C₂²×C₁₃	—	8	2	no	—
203	C₂²×C₁₃	—	8	4	no	—
204	C₂²×C₁₃	#442	1	1	yes	characteristic
205	C₂²×C₁₃	#442	1	1	yes	characteristic
206	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
207	C₄×C₁₃	—	4	2	no	—
208	C₄×C₁₃	—	4	2	no	—
209	C₄×C₁₃	—	8	2	no	—
210	C₄×C₁₃	#442	1	1	yes	characteristic
211	C₄×C₁₃	#442	1	1	yes	characteristic
212	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
213	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₂×#41	—	2	1	no	—
215	C₂²×D₄	—	2	1	no	—
216	C₂³×C₄	—	4	1	no	—
217	#135	—	2	1	no	—
218	#135	—	2	1	no	—
219	#135	C₂×C₄×C₁₃	1	2	yes	complemented
220	#135	C₂³×C₁₃	1	2	yes	—
221	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
222	C₂×SD₁₆	—	2	1	no	—
223	C₂×D₈	—	2	1	no	—
224	C₂×D₈	—	2	1	no	—
225	C₂×D₈	—	2	1	no	—
226	C₂×D₈	C₂×C₄×C₁₃	1	2	yes	—
227	C₂×D₈	C₂×C₄×C₁₃	1	2	yes	—
228	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
229	C₂×D₈	C₂³×C₁₃	1	2	yes	—
230	#131	—	2	4	no	—
231	#131	—	4	2	no	—
232	C₂×M₁₆	—	2	1	no	—
233	C₂×M₁₆	—	4	1	no	—
234	C₂²×C₈	—	4	1	no	—
235	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
237	C₄×D₄	—	2	4	no	—
238	C₄×D₄	—	4	2	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₂²⋊C₄	—	4	1	no	—
241	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
242	SD₃₂	C₂×C₄×C₁₃	1	8	yes	complemented
243	D₁₆	C₂×C₄×C₁₃	1	8	yes	complemented
244	M₃₂	—	2	1	no	—
245	M₃₂	C₂×C₄×C₁₃	1	2	yes	complemented
246	M₃₂	C₂³×C₁₃	1	2	yes	—
247	M₃₂	C₂³×C₁₃	1	2	yes	—
248	C₂×C₁₆	—	2	1	no	—
249	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	complemented
250	#108	—	2	1	no	—
251	#108	C₂³×C₁₃	1	2	yes	—
252	#106	—	2	1	no	—
253	#106	C₂³×C₁₃	1	2	yes	—
254	#104	—	2	4	no	—
255	#102	—	2	4	no	—
256	#97	D₄×C₁₃	1	2	yes	—
257	#97	C₂³×C₁₃	1	2	yes	—
258	C₂×C₁₃	—	2	1	no	—
259	C₂×C₁₃	—	2	1	no	—
260	C₂×C₁₃	—	8	2	no	—
261	C₂×C₁₃	—	8	4	no	—
262	C₂×C₁₃	AGL(1,ℤ/16)	1	2	yes	direct product factor
263	C₂×C₁₃	C₂×#442	1	1	yes	characteristic
264	C₂⁴	—	4	1	no	—
265	#41	—	2	2	no	—
266	#41	—	2	2	no	—
267	#41	—	4	1	no	—
268	#41	—	4	1	no	—
269	C₂×Q₈	—	2	1	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	4	1	no	—
275	C₂×D₄	—	4	1	no	—
276	C₂×D₄	—	4	1	no	—
277	C₂×D₄	—	4	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	4	4	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	8	4	no	—
283	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
284	Q₁₆	—	2	1	no	—
285	Q₁₆	C₂²×C₄×C₁₃	1	2	yes	complemented
286	SD₁₆	—	2	2	no	—
287	SD₁₆	—	2	2	no	—
288	D₈	—	2	2	no	—
289	D₈	—	2	2	no	—
290	D₈	—	2	1	no	—
291	D₈	—	2	2	no	—
292	D₈	C₂²×C₄×C₁₃	1	4	yes	—
293	D₈	C₂²×C₄×C₁₃	1	2	yes	complemented
294	M₁₆	—	2	2	no	—
295	M₁₆	—	4	4	no	—
296	M₁₆	—	4	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	4	4	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
302	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
303	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
304	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
306	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
307	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	4	4	no	—
311	C₄²	—	2	1	no	—
312	C₄²	C₂×D₄×C₁₃	1	2	yes	—
313	C₁₆	—	2	2	no	—
314	C₁₆	C₂²×C₄×C₁₃	1	4	yes	complemented
315	C₁₃	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic, direct product factor, Sylow
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	C₁₃×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×C₁₃	1	1	yes	characteristic
342	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
343	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
344	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
345	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
346	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
347	C₈	—	2	2	no	—
348	C₈	—	4	2	no	—
349	C₈	C₄×D₄×C₁₃	1	1	yes	characteristic
350	C₈	C₄×D₄×C₁₃	1	1	yes	characteristic
351	C₈	C₂³×C₄×C₁₃	1	1	yes	characteristic
352	C₈	C₂×C₁₃×#41	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	2	no	—
360	C₂²	—	8	4	no	—
361	C₂²	C₁₃×#442	1	1	yes	characteristic
362	C₂²	C₁₃×#442	1	1	yes	characteristic
363	C₂²	C₂×C₁₃×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	C₁₃×#442	1	1	yes	characteristic
368	C₄	C₁₃×#442	1	1	yes	characteristic
369	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
370	C₄	C₂×C₁₃×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	C₁₃×AGL(1,ℤ/16)	1	2	yes	direct product factor
376	C₂	C₂×C₁₃×#442	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	#442
commutator	C₈	C₂³×C₄×C₁₃
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#509	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#444	C₂	semidirect
3. C₂×C₁₃×#442	C₂	semidirect
4. C₁₃×AGL(1,ℤ/16)	C₂	direct (N × H)
5. C₂×C₁₃×#365	C₂	semidirect
6. C₂×C₁₃×#361	C₂	semidirect
7. C₂×C₁₃×#360	C₂	semidirect
8. C₂×C₁₃×#347	C₂	semidirect
13. C₁₃×#509	C₄	semidirect
15. C₂×C₁₃×SD₃₂	C₄	semidirect
16. C₂×C₁₃×D₁₆	C₄	semidirect
20. C₁₃×#444	C₂²	semidirect
22. C₁₃×#442	C₂²	semidirect
28. C₁₃×#365	C₂²	semidirect
29. C₁₃×#361	C₂²	semidirect
30. C₁₃×#360	C₂²	semidirect
31. C₁₃×#347	C₂²	semidirect
37. C₁₃×#135	C₂×C₄	semidirect
39. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
46. C₂×C₁₃×D₈	C₂×C₄	semidirect
60. C₁₃×SD₃₂	C₂×C₄	semidirect
61. C₁₃×D₁₆	C₂×C₄	semidirect
63. C₁₃×M₃₂	C₂×C₄	semidirect
67. C₂×C₁₃×C₁₆	C₂×C₄	semidirect
76. C₂×AGL(1,ℤ/16)	C₁₃	direct (N × H)
98. C₁₃×Q₁₆	C₂²×C₄	semidirect
106. C₁₃×D₈	C₂²×C₄	semidirect
127. C₁₃×C₁₆	C₂²×C₄	semidirect
129. C₂×#444	C₂×C₁₃	semidirect
130. C₂×#442	C₂×C₁₃	semidirect
131. AGL(1,ℤ/16)	C₂×C₁₃	direct (N × H)
132. C₂×#365	C₂×C₁₃	semidirect
133. C₂×#361	C₂×C₁₃	semidirect
134. C₂×#360	C₂×C₁₃	semidirect
135. C₂×#347	C₂×C₁₃	semidirect
177. #509	C₄×C₁₃	semidirect
179. C₂×SD₃₂	C₄×C₁₃	semidirect
180. C₂×D₁₆	C₄×C₁₃	semidirect
184. #444	C₂²×C₁₃	semidirect
186. #442	C₂²×C₁₃	semidirect
192. #365	C₂²×C₁₃	semidirect
193. #361	C₂²×C₁₃	semidirect
194. #360	C₂²×C₁₃	semidirect
195. #347	C₂²×C₁₃	semidirect
219. #135	C₂×C₄×C₁₃	semidirect
221. C₂×Q₁₆	C₂×C₄×C₁₃	semidirect
228. C₂×D₈	C₂×C₄×C₁₃	semidirect
242. SD₃₂	C₂×C₄×C₁₃	semidirect
243. D₁₆	C₂×C₄×C₁₃	semidirect
245. M₃₂	C₂×C₄×C₁₃	semidirect
249. C₂×C₁₆	C₂×C₄×C₁₃	semidirect
262. C₂×C₁₃	AGL(1,ℤ/16)	direct (N × H)
285. Q₁₆	C₂²×C₄×C₁₃	semidirect
293. D₈	C₂²×C₄×C₁₃	semidirect
314. C₁₆	C₂²×C₄×C₁₃	semidirect
315. C₁₃	C₂×AGL(1,ℤ/16)	direct (N × H)
375. C₂	C₁₃×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×C₁₃×#509	2
C₂×C₁₃×#444	2
C₂×C₁₃×#442	2
C₁₃×AGL(1,ℤ/16)	2
C₂×C₁₃×#365	2
C₂×C₁₃×#361	2
C₂×C₁₃×#360	2
C₂×C₁₃×#347	2
C₂×AGL(1,ℤ/16)	13

Subgroups — C2×C13×AGL(1,ℤ/16) #15719806

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×AGL(1,ℤ/16) #15719806