Subgroups — C₁₃×#33783 #15720122

Order 3328.

688 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2250	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2244	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2207	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2206	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2187	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2184	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2163	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×D₈	—	2	1	no	—
11	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
12	C₂×C₁₃×#127	—	2	1	no	—
13	C₁₃×#529	—	2	1	no	—
14	C₂×C₁₃×SD₃₂	C₂²	1	4	yes	complemented
15	C₂×C₁₃×D₁₆	C₂²	1	4	yes	complemented
16	C₁₃×#499	C₂²	1	1	yes	characteristic, complemented
17	C₁₃×#495	C₂²	1	1	yes	characteristic, complemented
18	C₁₃×#493	—	2	1	no	—
19	C₁₃×#493	—	2	1	no	—
20	C₁₃×#493	C₂²	1	2	yes	—
21	C₁₃×#493	C₂²	1	2	yes	—
22	C₁₃×#488	—	2	1	no	—
23	C₁₃×#467	C₂²	1	1	yes	characteristic
24	C₁₃×#466	C₂²	1	1	yes	characteristic
25	C₁₃×#465	—	2	1	no	—
26	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₄×C₁₃×SD₁₆	—	2	1	no	—
28	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
31	C₁₃×#357	C₂²	1	4	yes	complemented
32	C₁₃×#357	C₂²	1	4	yes	complemented
33	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
34	C₁₃×#346	C₂²	1	2	yes	complemented
35	C₂²×D₄×C₁₃	—	2	2	no	—
36	C₂²×D₄×C₁₃	—	4	1	no	—
37	C₂²×D₄×C₁₃	—	4	1	no	—
38	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
39	C₂×C₁₃×SD₁₆	—	2	1	no	—
40	C₂×C₁₃×D₈	—	2	2	no	—
41	C₂×C₁₃×D₈	—	2	2	no	—
42	C₂×C₁₃×D₈	—	2	2	no	—
43	C₂×C₁₃×D₈	—	4	4	no	—
44	C₂×C₁₃×D₈	—	4	4	no	—
45	C₂×C₁₃×D₈	C₂³	1	4	yes	—
46	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₁₃×#127	—	2	2	no	—
50	C₁₃×#127	—	2	2	no	—
51	C₁₃×#127	—	4	1	no	—
52	C₁₃×#127	—	4	1	no	—
53	C₁₃×#126	—	4	1	no	—
54	C₁₃×#125	—	2	1	no	—
55	C₁₃×#124	—	2	1	no	—
56	C₁₃×#123	—	4	1	no	—
57	C₁₃×C₂²⋊Q₈	—	2	1	no	—
58	C₁₃×#121	—	2	1	no	—
59	C₄×Q₈×C₁₃	—	2	1	no	—
60	C₄×D₄×C₁₃	—	2	1	no	—
61	C₄×D₄×C₁₃	—	4	1	no	—
62	C₁₃×#117	—	4	1	no	—
63	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
64	C₁₃×SD₃₂	—	4	4	no	—
65	C₁₃×D₁₆	—	4	4	no	—
66	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
67	C₁₃×#107	C₂³	1	1	yes	characteristic
68	C₁₃×#107	C₂³	1	1	yes	characteristic
69	C₁₃×#106	—	2	1	no	—
70	C₁₃×#103	—	2	1	no	—
71	C₁₃×#103	—	2	1	no	—
72	C₁₃×#102	—	2	1	no	—
73	C₁₃×#102	—	2	1	no	—
74	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
75	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
76	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	#33783	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂⁴×C₁₃	—	4	2	no	—
80	C₂×Q₈×C₁₃	—	2	1	no	—
81	C₂×D₄×C₁₃	—	2	1	no	—
82	C₂×D₄×C₁₃	—	2	4	no	—
83	C₂×D₄×C₁₃	—	4	4	no	—
84	C₂×D₄×C₁₃	—	4	4	no	—
85	C₂×D₄×C₁₃	—	4	1	no	—
86	C₂×D₄×C₁₃	—	4	2	no	—
87	C₂×D₄×C₁₃	—	4	2	no	—
88	C₂×D₄×C₁₃	—	4	2	no	—
89	C₂×D₄×C₁₃	—	4	2	no	—
90	C₂×D₄×C₁₃	—	4	2	no	—
91	C₂×D₄×C₁₃	—	8	4	no	—
92	C₂×D₄×C₁₃	—	8	4	no	—
93	C₂²×C₄×C₁₃	—	4	1	no	—
94	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₁₃×Q₁₆	—	2	2	no	—
98	C₁₃×SD₁₆	—	4	2	no	—
99	C₁₃×D₈	—	2	2	no	—
100	C₁₃×D₈	—	2	4	no	—
101	C₁₃×D₈	—	2	4	no	—
102	C₁₃×D₈	—	4	4	no	—
103	C₁₃×D₈	—	4	4	no	—
104	C₁₃×D₈	—	4	4	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
111	C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₁₃×C₄⋊C₄	—	2	1	no	—
113	C₁₃×C₄⋊C₄	—	4	1	no	—
114	C₁₃×C₄⋊C₄	—	4	1	no	—
115	C₁₃×C₄⋊C₄	—	4	1	no	—
116	C₁₃×C₄⋊C₄	—	4	1	no	—
117	C₁₃×C₂²⋊C₄	—	4	1	no	—
118	C₁₃×C₂²⋊C₄	—	4	1	no	—
119	C₁₃×C₂²⋊C₄	—	4	1	no	—
120	C₁₃×C₂²⋊C₄	—	4	1	no	—
121	C₁₃×C₂²⋊C₄	—	4	1	no	—
122	C₄²×C₁₃	—	4	1	no	—
123	C₄²×C₁₃	D₈	1	1	yes	characteristic
124	C₄²×C₁₃	D₈	1	1	yes	characteristic
125	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₁₃×C₁₆	—	2	4	no	—
128	#3168	C₂×C₁₃	1	1	yes	characteristic, complemented
129	C₂×#493	C₂×C₁₃	1	1	yes	characteristic, complemented
130	#2250	C₂×C₁₃	1	2	yes	complemented
131	#2244	C₂×C₁₃	1	2	yes	complemented
132	#2207	C₂×C₁₃	1	2	yes	complemented
133	#2206	C₂×C₁₃	1	2	yes	complemented
134	#2187	C₂×C₁₃	1	2	yes	complemented
135	#2184	C₂×C₁₃	1	2	yes	complemented
136	#2163	C₂×C₁₃	1	1	yes	characteristic, complemented
137	C₂³×C₁₃	—	4	1	no	—
138	C₂³×C₁₃	—	4	4	no	—
139	C₂³×C₁₃	—	8	4	no	—
140	C₂³×C₁₃	—	8	4	no	—
141	C₂³×C₁₃	—	8	4	no	—
142	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
143	Q₈×C₁₃	—	4	1	no	—
144	Q₈×C₁₃	—	4	1	no	—
145	D₄×C₁₃	—	4	4	no	—
146	D₄×C₁₃	—	4	1	no	—
147	D₄×C₁₃	—	4	4	no	—
148	D₄×C₁₃	—	4	1	no	—
149	D₄×C₁₃	—	8	4	no	—
150	D₄×C₁₃	—	8	4	no	—
151	D₄×C₁₃	—	8	4	no	—
152	D₄×C₁₃	—	8	4	no	—
153	D₄×C₁₃	—	8	2	no	—
154	D₄×C₁₃	—	8	4	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	1	no	—
157	C₂×C₄×C₁₃	—	2	1	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	4	1	no	—
160	C₂×C₄×C₁₃	—	4	1	no	—
161	C₂×C₄×C₁₃	—	4	1	no	—
162	C₂×C₄×C₁₃	—	8	2	no	—
163	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
169	C₈×C₁₃	—	2	1	no	—
170	C₈×C₁₃	—	2	1	no	—
171	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
172	C₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
173	C₂²×D₈	—	2	1	no	—
174	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
175	C₂×#127	—	2	1	no	—
176	#529	—	2	1	no	—
177	C₂×SD₃₂	C₂²×C₁₃	1	4	yes	complemented
178	C₂×D₁₆	C₂²×C₁₃	1	4	yes	complemented
179	#499	C₂²×C₁₃	1	1	yes	characteristic, complemented
180	#495	C₂²×C₁₃	1	1	yes	characteristic, complemented
181	#493	—	2	1	no	—
182	#493	—	2	1	no	—
183	#493	C₂²×C₁₃	1	2	yes	—
184	#493	C₂²×C₁₃	1	2	yes	—
185	#488	—	2	1	no	—
186	#467	C₂²×C₁₃	1	1	yes	characteristic
187	#466	C₂²×C₁₃	1	1	yes	characteristic
188	#465	—	2	1	no	—
189	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
190	C₄×SD₁₆	—	2	1	no	—
191	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
192	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
193	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
194	#357	C₂²×C₁₃	1	4	yes	complemented
195	#357	C₂²×C₁₃	1	4	yes	complemented
196	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
197	#346	C₂²×C₁₃	1	2	yes	complemented
198	C₂²×C₁₃	—	2	1	no	—
199	C₂²×C₁₃	—	2	1	no	—
200	C₂²×C₁₃	—	8	1	no	—
201	C₂²×C₁₃	—	8	4	no	—
202	C₂²×C₁₃	—	8	4	no	—
203	C₂²×C₁₃	—	8	1	no	—
204	C₂²×C₁₃	—	8	4	no	—
205	C₂²×C₁₃	—	8	1	no	—
206	C₂²×C₁₃	—	16	8	no	—
207	C₂²×C₁₃	#509	1	2	yes	—
208	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
209	C₄×C₁₃	—	2	1	no	—
210	C₄×C₁₃	—	2	1	no	—
211	C₄×C₁₃	—	2	1	no	—
212	C₄×C₁₃	—	2	1	no	—
213	C₄×C₁₃	—	8	1	no	—
214	C₄×C₁₃	—	8	1	no	—
215	C₄×C₁₃	—	8	1	no	—
216	C₄×C₁₃	#509	1	2	yes	—
217	C₄×C₁₃	#535	1	1	yes	characteristic
218	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
219	C₂²×D₄	—	2	2	no	—
220	C₂²×D₄	—	4	1	no	—
221	C₂²×D₄	—	4	1	no	—
222	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
223	C₂×SD₁₆	—	2	1	no	—
224	C₂×D₈	—	2	2	no	—
225	C₂×D₈	—	2	2	no	—
226	C₂×D₈	—	2	2	no	—
227	C₂×D₈	—	4	4	no	—
228	C₂×D₈	—	4	4	no	—
229	C₂×D₈	C₂³×C₁₃	1	4	yes	—
230	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
231	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
233	#127	—	2	2	no	—
234	#127	—	2	2	no	—
235	#127	—	4	1	no	—
236	#127	—	4	1	no	—
237	#126	—	4	1	no	—
238	#125	—	2	1	no	—
239	#124	—	2	1	no	—
240	#123	—	4	1	no	—
241	C₂²⋊Q₈	—	2	1	no	—
242	#121	—	2	1	no	—
243	C₄×Q₈	—	2	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	4	1	no	—
246	#117	—	4	1	no	—
247	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
248	SD₃₂	—	4	4	no	—
249	D₁₆	—	4	4	no	—
250	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
251	#107	C₂³×C₁₃	1	1	yes	characteristic
252	#107	C₂³×C₁₃	1	1	yes	characteristic
253	#106	—	2	1	no	—
254	#103	—	2	1	no	—
255	#103	—	2	1	no	—
256	#102	—	2	1	no	—
257	#102	—	2	1	no	—
258	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
259	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
260	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
261	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
262	C₂×C₁₃	—	2	2	no	—
263	C₂×C₁₃	—	16	1	no	—
264	C₂×C₁₃	—	16	4	no	—
265	C₂×C₁₃	#3205	1	1	yes	characteristic
266	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
267	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
268	C₂⁴	—	4	2	no	—
269	C₂×Q₈	—	2	1	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	2	4	no	—
272	C₂×D₄	—	4	4	no	—
273	C₂×D₄	—	4	4	no	—
274	C₂×D₄	—	4	1	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	8	4	no	—
281	C₂×D₄	—	8	4	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
284	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
286	Q₁₆	—	2	2	no	—
287	SD₁₆	—	4	2	no	—
288	D₈	—	2	2	no	—
289	D₈	—	2	4	no	—
290	D₈	—	2	4	no	—
291	D₈	—	4	4	no	—
292	D₈	—	4	4	no	—
293	D₈	—	4	4	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
297	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
298	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
299	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₂²⋊C₄	—	4	1	no	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₂²⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	4	1	no	—
311	C₄²	—	4	1	no	—
312	C₄²	C₁₃×D₈	1	1	yes	characteristic
313	C₄²	C₁₃×D₈	1	1	yes	characteristic
314	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
315	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
316	C₁₆	—	2	4	no	—
317	C₁₃	#33783	1	1	yes	characteristic, direct product factor, Sylow
318	C₂³	—	4	1	no	—
319	C₂³	—	4	4	no	—
320	C₂³	—	8	4	no	—
321	C₂³	—	8	4	no	—
322	C₂³	—	8	4	no	—
323	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
324	Q₈	—	4	1	no	—
325	Q₈	—	4	1	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	1	no	—
328	D₄	—	4	4	no	—
329	D₄	—	4	1	no	—
330	D₄	—	8	4	no	—
331	D₄	—	8	4	no	—
332	D₄	—	8	4	no	—
333	D₄	—	8	4	no	—
334	D₄	—	8	2	no	—
335	D₄	—	8	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	8	2	no	—
344	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
345	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
346	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
347	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
348	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
350	C₈	—	2	1	no	—
351	C₈	—	2	1	no	—
352	C₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
353	C₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	8	1	no	—
357	C₂²	—	8	4	no	—
358	C₂²	—	8	4	no	—
359	C₂²	—	8	1	no	—
360	C₂²	—	8	4	no	—
361	C₂²	—	8	1	no	—
362	C₂²	—	16	8	no	—
363	C₂²	C₁₃×#509	1	2	yes	—
364	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	8	1	no	—
370	C₄	—	8	1	no	—
371	C₄	—	8	1	no	—
372	C₄	C₁₃×#509	1	2	yes	—
373	C₄	C₁₃×#535	1	1	yes	characteristic
374	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
375	C₂	—	2	2	no	—
376	C₂	—	16	4	no	—
377	C₂	—	16	1	no	—
378	C₂	C₁₃×#3205	1	1	yes	characteristic
379	C₂	C₂×C₁₃×#509	1	1	yes	characteristic
380	C₂	C₂×C₁₃×#509	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3168	C₂	semidirect
2. C₂×C₁₃×#493	C₂	semidirect
3. C₁₃×#2250	C₂	semidirect
4. C₁₃×#2244	C₂	semidirect
5. C₁₃×#2207	C₂	semidirect
6. C₁₃×#2206	C₂	semidirect
7. C₁₃×#2187	C₂	semidirect
8. C₁₃×#2184	C₂	semidirect
9. C₁₃×#2163	C₂	semidirect
14. C₂×C₁₃×SD₃₂	C₂²	semidirect
15. C₂×C₁₃×D₁₆	C₂²	semidirect
16. C₁₃×#499	C₂²	semidirect
17. C₁₃×#495	C₂²	semidirect
26. C₄×C₁₃×Q₁₆	C₂²	semidirect
28. C₄×C₁₃×D₈	C₂²	semidirect
30. C₁₃×C₄⋊C₁₆	C₂²	semidirect
31. C₁₃×#357	C₂²	semidirect
32. C₁₃×#357	C₂²	semidirect
34. C₁₃×#346	C₂²	semidirect
78. #33783	C₁₃	direct (N × H)
128. #3168	C₂×C₁₃	semidirect
129. C₂×#493	C₂×C₁₃	semidirect
130. #2250	C₂×C₁₃	semidirect
131. #2244	C₂×C₁₃	semidirect
132. #2207	C₂×C₁₃	semidirect
133. #2206	C₂×C₁₃	semidirect
134. #2187	C₂×C₁₃	semidirect
135. #2184	C₂×C₁₃	semidirect
136. #2163	C₂×C₁₃	semidirect
177. C₂×SD₃₂	C₂²×C₁₃	semidirect
178. C₂×D₁₆	C₂²×C₁₃	semidirect
179. #499	C₂²×C₁₃	semidirect
180. #495	C₂²×C₁₃	semidirect
189. C₄×Q₁₆	C₂²×C₁₃	semidirect
191. C₄×D₈	C₂²×C₁₃	semidirect
193. C₄⋊C₁₆	C₂²×C₁₃	semidirect
194. #357	C₂²×C₁₃	semidirect
195. #357	C₂²×C₁₃	semidirect
197. #346	C₂²×C₁₃	semidirect
317. C₁₃	#33783	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3168	2
C₂×C₁₃×#493	2
C₁₃×#2250	2
C₁₃×#2244	2
C₁₃×#2207	2
C₁₃×#2206	2
C₁₃×#2187	2
C₁₃×#2184	2
C₁₃×#2163	2
#33783	13

Subgroups — C13×#33783 #15720122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33783 #15720122