Subgroups — C₁₃×#33471 #15719810

Order 3328.

668 conjugacy classes of subgroups.

The subgroup lattice has 364 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	C₁₃×#2957	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×AGL(1,ℤ/16)	C₂	1	8	yes	maximal, complemented
5	C₁₃×#2155	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2145	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2110	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	C₁₃×#568	—	2	1	no	—
12	C₁₃×#518	—	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	C₂²	1	4	yes	complemented
20	C₁₃×#443	—	2	2	no	—
21	C₁₃×#442	C₂²	1	4	yes	complemented
22	C₄×C₁₃×D₈	—	2	2	no	—
23	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
24	C₁₃×#427	C₂²	1	1	yes	characteristic
25	C₁₃×#421	—	2	1	no	—
26	C₁₃×#418	—	2	1	no	—
27	C₁₃×#405	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	C₁₃×#135	—	2	1	no	—
35	C₁₃×#135	—	2	1	no	—
36	C₁₃×#135	C₂×C₄	1	2	yes	complemented
37	C₁₃×#135	C₂³	1	2	yes	—
38	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
39	C₂×C₁₃×SD₁₆	—	2	1	no	—
40	C₂×C₁₃×D₈	—	2	1	no	—
41	C₂×C₁₃×D₈	—	2	1	no	—
42	C₂×C₁₃×D₈	—	2	1	no	—
43	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
44	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
45	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic, complemented
46	C₂×C₁₃×D₈	C₂³	1	2	yes	—
47	C₁₃×#131	—	2	4	no	—
48	C₁₃×#131	—	4	2	no	—
49	C₂×C₁₃×M₁₆	—	2	1	no	—
50	C₂×C₁₃×M₁₆	—	4	2	no	—
51	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₄×D₄×C₁₃	—	2	4	no	—
54	C₄×D₄×C₁₃	—	4	2	no	—
55	C₁₃×#117	—	2	1	no	—
56	C₁₃×#117	D₄	1	1	yes	characteristic
57	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
58	C₁₃×SD₃₂	C₂×C₄	1	8	yes	complemented
59	C₁₃×D₁₆	C₂×C₄	1	8	yes	complemented
60	C₁₃×M₃₂	—	2	1	no	—
61	C₁₃×M₃₂	C₂×C₄	1	2	yes	complemented
62	C₁₃×M₃₂	C₂³	1	2	yes	—
63	C₁₃×M₃₂	C₂³	1	2	yes	—
64	C₂×C₁₃×C₁₆	—	2	1	no	—
65	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	complemented
66	C₁₃×#108	—	2	1	no	—
67	C₁₃×#108	C₂³	1	2	yes	—
68	C₁₃×#107	—	2	1	no	—
69	C₁₃×#106	C₂³	1	2	yes	—
70	C₁₃×#104	—	2	4	no	—
71	C₁₃×#102	—	2	4	no	—
72	C₁₃×#97	C₂³	1	2	yes	—
73	C₄×C₈×C₁₃	D₄	1	2	yes	—
74	#33471	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂⁴×C₁₃	—	4	1	no	—
76	C₁₃×#41	—	2	2	no	—
77	C₁₃×#41	—	2	2	no	—
78	C₁₃×#41	—	4	1	no	—
79	C₁₃×#41	—	4	1	no	—
80	C₂×Q₈×C₁₃	—	2	1	no	—
81	C₂×D₄×C₁₃	—	2	2	no	—
82	C₂×D₄×C₁₃	—	2	2	no	—
83	C₂×D₄×C₁₃	—	2	1	no	—
84	C₂×D₄×C₁₃	—	2	2	no	—
85	C₂×D₄×C₁₃	—	4	1	no	—
86	C₂×D₄×C₁₃	—	4	1	no	—
87	C₂×D₄×C₁₃	—	4	1	no	—
88	C₂×D₄×C₁₃	—	4	1	no	—
89	C₂²×C₄×C₁₃	—	4	4	no	—
90	C₂²×C₄×C₁₃	—	4	1	no	—
91	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
92	C₁₃×Q₁₆	—	2	1	no	—
93	C₁₃×Q₁₆	C₂²×C₄	1	2	yes	—
94	C₁₃×SD₁₆	—	2	2	no	—
95	C₁₃×SD₁₆	—	2	2	no	—
96	C₁₃×D₈	—	2	2	no	—
97	C₁₃×D₈	—	2	2	no	—
98	C₁₃×D₈	—	2	1	no	—
99	C₁₃×D₈	—	2	2	no	—
100	C₁₃×D₈	C₂²×C₄	1	2	yes	—
101	C₁₃×D₈	C₂²×C₄	1	4	yes	—
102	C₁₃×M₁₆	—	2	1	no	—
103	C₁₃×M₁₆	—	2	1	no	—
104	C₁₃×M₁₆	—	2	2	no	—
105	C₁₃×M₁₆	—	4	4	no	—
106	C₁₃×M₁₆	—	4	1	no	—
107	C₂×C₈×C₁₃	—	4	4	no	—
108	C₂×C₈×C₁₃	—	4	1	no	—
109	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
114	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
115	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
116	C₁₃×C₄⋊C₄	—	2	1	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₁₃×C₂²⋊C₄	—	4	4	no	—
120	C₁₃×C₂²⋊C₄	—	4	1	no	—
121	C₄²×C₁₃	—	4	1	no	—
122	C₄²×C₁₃	C₂×D₄	1	2	yes	—
123	C₁₃×C₁₆	—	2	2	no	—
124	C₁₃×C₁₆	C₂²×C₄	1	4	yes	—
125	C₂×#509	C₂×C₁₃	1	1	yes	characteristic
126	#2957	C₂×C₁₃	1	1	yes	characteristic, complemented
127	#2948	C₂×C₁₃	1	1	yes	characteristic, complemented
128	AGL(1,ℤ/16)	C₂×C₁₃	1	8	yes	complemented
129	#2155	C₂×C₁₃	1	1	yes	characteristic, complemented
130	C₂×#361	C₂×C₁₃	1	1	yes	characteristic, complemented
131	#2145	C₂×C₁₃	1	1	yes	characteristic, complemented
132	#2110	C₂×C₁₃	1	1	yes	characteristic, complemented
133	C₂³×C₁₃	—	4	2	no	—
134	C₂³×C₁₃	—	4	1	no	—
135	C₂³×C₁₃	—	4	2	no	—
136	C₂³×C₁₃	—	4	2	no	—
137	C₂³×C₁₃	—	16	2	no	—
138	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
139	Q₈×C₁₃	—	2	2	no	—
140	Q₈×C₁₃	—	4	1	no	—
141	D₄×C₁₃	—	2	4	no	—
142	D₄×C₁₃	—	2	2	no	—
143	D₄×C₁₃	—	4	2	no	—
144	D₄×C₁₃	—	4	2	no	—
145	D₄×C₁₃	—	4	2	no	—
146	D₄×C₁₃	—	4	2	no	—
147	D₄×C₁₃	—	4	2	no	—
148	D₄×C₁₃	—	4	1	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	4	1	no	—
151	C₂×C₄×C₁₃	—	4	2	no	—
152	C₂×C₄×C₁₃	—	4	2	no	—
153	C₂×C₄×C₁₃	—	4	2	no	—
154	C₂×C₄×C₁₃	—	16	4	no	—
155	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
159	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
161	C₈×C₁₃	—	2	2	no	—
162	C₈×C₁₃	—	4	2	no	—
163	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
164	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
165	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
166	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
167	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
168	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
169	#568	—	2	1	no	—
170	#518	—	2	1	no	—
171	#509	C₄×C₁₃	1	4	yes	complemented
172	#509	C₂²×C₁₃	1	4	yes	—
173	C₂×SD₃₂	C₄×C₁₃	1	2	yes	complemented
174	C₂×D₁₆	C₄×C₁₃	1	2	yes	complemented
175	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
176	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
177	#444	C₂²×C₁₃	1	4	yes	complemented
178	#443	—	2	2	no	—
179	#442	C₂²×C₁₃	1	4	yes	complemented
180	C₄×D₈	—	2	2	no	—
181	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
182	#427	C₂²×C₁₃	1	1	yes	characteristic
183	#421	—	2	1	no	—
184	#418	—	2	1	no	—
185	#405	C₂²×C₁₃	1	1	yes	characteristic
186	#365	C₂²×C₁₃	1	4	yes	complemented
187	#361	C₂²×C₁₃	1	4	yes	complemented
188	#360	C₂²×C₁₃	1	4	yes	complemented
189	#347	C₂²×C₁₃	1	4	yes	complemented
190	C₂²×C₁₃	—	4	1	no	—
191	C₂²×C₁₃	—	4	2	no	—
192	C₂²×C₁₃	—	4	4	no	—
193	C₂²×C₁₃	—	8	4	no	—
194	C₂²×C₁₃	—	16	1	no	—
195	C₂²×C₁₃	—	16	2	no	—
196	C₂²×C₁₃	—	16	2	no	—
197	C₂²×C₁₃	#442	1	1	yes	characteristic
198	C₂²×C₁₃	#442	1	1	yes	characteristic
199	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
200	C₄×C₁₃	—	4	2	no	—
201	C₄×C₁₃	—	4	2	no	—
202	C₄×C₁₃	—	8	2	no	—
203	C₄×C₁₃	#442	1	1	yes	characteristic
204	C₄×C₁₃	#442	1	1	yes	characteristic
205	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
206	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
207	C₂×#41	—	2	1	no	—
208	C₂²×D₄	—	2	1	no	—
209	#135	—	2	1	no	—
210	#135	—	2	1	no	—
211	#135	C₂×C₄×C₁₃	1	2	yes	complemented
212	#135	C₂³×C₁₃	1	2	yes	—
213	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
214	C₂×SD₁₆	—	2	1	no	—
215	C₂×D₈	—	2	1	no	—
216	C₂×D₈	—	2	1	no	—
217	C₂×D₈	—	2	1	no	—
218	C₂×D₈	C₂×C₄×C₁₃	1	2	yes	—
219	C₂×D₈	C₂×C₄×C₁₃	1	2	yes	—
220	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
221	C₂×D₈	C₂³×C₁₃	1	2	yes	—
222	#131	—	2	4	no	—
223	#131	—	4	2	no	—
224	C₂×M₁₆	—	2	1	no	—
225	C₂×M₁₆	—	4	2	no	—
226	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
227	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
228	C₄×D₄	—	2	4	no	—
229	C₄×D₄	—	4	2	no	—
230	#117	—	2	1	no	—
231	#117	D₄×C₁₃	1	1	yes	characteristic
232	C₂×C₂²⋊C₄	—	4	2	no	—
233	SD₃₂	C₂×C₄×C₁₃	1	8	yes	complemented
234	D₁₆	C₂×C₄×C₁₃	1	8	yes	complemented
235	M₃₂	—	2	1	no	—
236	M₃₂	C₂×C₄×C₁₃	1	2	yes	complemented
237	M₃₂	C₂³×C₁₃	1	2	yes	—
238	M₃₂	C₂³×C₁₃	1	2	yes	—
239	C₂×C₁₆	—	2	1	no	—
240	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	complemented
241	#108	—	2	1	no	—
242	#108	C₂³×C₁₃	1	2	yes	—
243	#107	—	2	1	no	—
244	#106	C₂³×C₁₃	1	2	yes	—
245	#104	—	2	4	no	—
246	#102	—	2	4	no	—
247	#97	C₂³×C₁₃	1	2	yes	—
248	C₄×C₈	D₄×C₁₃	1	2	yes	—
249	C₂×C₁₃	—	2	1	no	—
250	C₂×C₁₃	—	2	1	no	—
251	C₂×C₁₃	—	2	1	no	—
252	C₂×C₁₃	—	8	4	no	—
253	C₂×C₁₃	—	8	2	no	—
254	C₂×C₁₃	C₂×#442	1	1	yes	characteristic
255	C₂⁴	—	4	1	no	—
256	#41	—	2	2	no	—
257	#41	—	2	2	no	—
258	#41	—	4	1	no	—
259	#41	—	4	1	no	—
260	C₂×Q₈	—	2	1	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	—	2	1	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	4	1	no	—
266	C₂×D₄	—	4	1	no	—
267	C₂×D₄	—	4	1	no	—
268	C₂×D₄	—	4	1	no	—
269	C₂²×C₄	—	4	4	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
272	Q₁₆	—	2	1	no	—
273	Q₁₆	C₂²×C₄×C₁₃	1	2	yes	—
274	SD₁₆	—	2	2	no	—
275	SD₁₆	—	2	2	no	—
276	D₈	—	2	2	no	—
277	D₈	—	2	2	no	—
278	D₈	—	2	1	no	—
279	D₈	—	2	2	no	—
280	D₈	C₂²×C₄×C₁₃	1	2	yes	—
281	D₈	C₂²×C₄×C₁₃	1	4	yes	—
282	M₁₆	—	2	1	no	—
283	M₁₆	—	2	1	no	—
284	M₁₆	—	2	2	no	—
285	M₁₆	—	4	4	no	—
286	M₁₆	—	4	1	no	—
287	C₂×C₈	—	4	4	no	—
288	C₂×C₈	—	4	1	no	—
289	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
290	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
291	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
292	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
293	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
294	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
295	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
296	C₄⋊C₄	—	2	1	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₂²⋊C₄	—	2	1	no	—
299	C₂²⋊C₄	—	4	4	no	—
300	C₂²⋊C₄	—	4	1	no	—
301	C₄²	—	4	1	no	—
302	C₄²	C₂×D₄×C₁₃	1	2	yes	—
303	C₁₆	—	2	2	no	—
304	C₁₆	C₂²×C₄×C₁₃	1	4	yes	—
305	C₁₃	#33471	1	1	yes	characteristic, direct product factor, Sylow
306	C₂³	—	4	2	no	—
307	C₂³	—	4	1	no	—
308	C₂³	—	4	2	no	—
309	C₂³	—	4	2	no	—
310	C₂³	—	16	2	no	—
311	C₂³	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
312	Q₈	—	2	2	no	—
313	Q₈	—	4	1	no	—
314	D₄	—	2	4	no	—
315	D₄	—	2	2	no	—
316	D₄	—	4	2	no	—
317	D₄	—	4	2	no	—
318	D₄	—	4	2	no	—
319	D₄	—	4	2	no	—
320	D₄	—	4	1	no	—
321	D₄	—	4	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	16	4	no	—
328	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
329	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
330	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
331	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
332	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
333	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
334	C₈	—	2	2	no	—
335	C₈	—	4	2	no	—
336	C₈	C₄×D₄×C₁₃	1	1	yes	characteristic
337	C₈	C₄×D₄×C₁₃	1	1	yes	characteristic
338	C₈	C₂³×C₄×C₁₃	1	1	yes	characteristic
339	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
340	C₂²	—	4	1	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	4	4	no	—
343	C₂²	—	8	4	no	—
344	C₂²	—	16	1	no	—
345	C₂²	—	16	2	no	—
346	C₂²	—	16	2	no	—
347	C₂²	C₁₃×#442	1	1	yes	characteristic
348	C₂²	C₁₃×#442	1	1	yes	characteristic
349	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
350	C₄	—	4	2	no	—
351	C₄	—	4	2	no	—
352	C₄	—	8	2	no	—
353	C₄	C₁₃×#442	1	1	yes	characteristic
354	C₄	C₁₃×#442	1	1	yes	characteristic
355	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
356	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
357	C₂	—	2	1	no	—
358	C₂	—	2	1	no	—
359	C₂	—	2	1	no	—
360	C₂	—	8	4	no	—
361	C₂	—	8	2	no	—
362	C₂	C₂×C₁₃×#442	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	C₂×#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 ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2957	C₂	semidirect
3. C₁₃×#2948	C₂	semidirect
4. C₁₃×AGL(1,ℤ/16)	C₂	semidirect
5. C₁₃×#2155	C₂	semidirect
6. C₂×C₁₃×#361	C₂	semidirect
7. C₁₃×#2145	C₂	semidirect
8. C₁₃×#2110	C₂	semidirect
13. C₁₃×#509	C₄	semidirect
15. C₂×C₁₃×SD₃₂	C₄	semidirect
16. C₂×C₁₃×D₁₆	C₄	semidirect
19. C₁₃×#444	C₂²	semidirect
21. C₁₃×#442	C₂²	semidirect
28. C₁₃×#365	C₂²	semidirect
29. C₁₃×#361	C₂²	semidirect
30. C₁₃×#360	C₂²	semidirect
31. C₁₃×#347	C₂²	semidirect
36. C₁₃×#135	C₂×C₄	semidirect
38. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
45. C₂×C₁₃×D₈	C₂×C₄	semidirect
58. C₁₃×SD₃₂	C₂×C₄	semidirect
59. C₁₃×D₁₆	C₂×C₄	semidirect
61. C₁₃×M₃₂	C₂×C₄	semidirect
65. C₂×C₁₃×C₁₆	C₂×C₄	semidirect
74. #33471	C₁₃	direct (N × H)
126. #2957	C₂×C₁₃	semidirect
127. #2948	C₂×C₁₃	semidirect
128. AGL(1,ℤ/16)	C₂×C₁₃	semidirect
129. #2155	C₂×C₁₃	semidirect
130. C₂×#361	C₂×C₁₃	semidirect
131. #2145	C₂×C₁₃	semidirect
132. #2110	C₂×C₁₃	semidirect
171. #509	C₄×C₁₃	semidirect
173. C₂×SD₃₂	C₄×C₁₃	semidirect
174. C₂×D₁₆	C₄×C₁₃	semidirect
177. #444	C₂²×C₁₃	semidirect
179. #442	C₂²×C₁₃	semidirect
186. #365	C₂²×C₁₃	semidirect
187. #361	C₂²×C₁₃	semidirect
188. #360	C₂²×C₁₃	semidirect
189. #347	C₂²×C₁₃	semidirect
211. #135	C₂×C₄×C₁₃	semidirect
213. C₂×Q₁₆	C₂×C₄×C₁₃	semidirect
220. C₂×D₈	C₂×C₄×C₁₃	semidirect
233. SD₃₂	C₂×C₄×C₁₃	semidirect
234. D₁₆	C₂×C₄×C₁₃	semidirect
236. M₃₂	C₂×C₄×C₁₃	semidirect
240. C₂×C₁₆	C₂×C₄×C₁₃	semidirect
305. C₁₃	#33471	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
C₁₃×#2957	2
C₁₃×#2948	2
C₁₃×AGL(1,ℤ/16)	2
C₁₃×#2155	2
C₂×C₁₃×#361	2
C₁₃×#2145	2
C₁₃×#2110	2
#33471	13

Subgroups — C13×#33471 #15719810

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33471 #15719810