Subgroups — C₁₃×#32544 #15718883

Order 3328.

792 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2538	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2099	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2086	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2071	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2054	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1934	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1879	C₂	1	2	yes	maximal
9	C₁₃×#1862	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
14	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#102	C₂²	1	2	yes	—
17	C₂×C₁₃×#102	C₂²	1	2	yes	—
18	C₂×C₁₃×#102	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#396	—	2	2	no	—
21	C₁₃×#396	—	2	2	no	—
22	C₁₃×#390	C₂²	1	2	yes	—
23	C₁₃×#390	C₂²	1	2	yes	—
24	C₁₃×#389	C₂²	1	2	yes	—
25	C₁₃×#389	C₂²	1	2	yes	—
26	C₁₃×#384	C₂²	1	2	yes	—
27	C₁₃×#380	—	2	2	no	—
28	C₁₃×#340	C₂²	1	1	yes	characteristic
29	C₁₃×#340	C₂²	1	1	yes	characteristic
30	C₁₃×#340	C₂²	1	2	yes	—
31	C₁₃×#340	C₂²	1	2	yes	—
32	C₁₃×#340	C₂²	1	2	yes	—
33	C₁₃×#336	C₂²	1	2	yes	—
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₃	—	2	2	no	—
38	C₂×C₁₃×D₈	—	2	4	no	—
39	C₂×C₁₃×D₈	—	4	1	no	—
40	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
43	C₁₃×C₂²⋊Q₈	—	4	8	no	—
44	C₄×Q₈×C₁₃	—	4	1	no	—
45	C₄×Q₈×C₁₃	—	4	1	no	—
46	C₄×D₄×C₁₃	—	4	2	no	—
47	C₄×D₄×C₁₃	—	4	2	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
53	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×#107	—	4	1	no	—
65	C₁₃×C₄⋊C₈	—	4	1	no	—
66	C₁₃×#102	—	2	4	no	—
67	C₁₃×#102	—	2	4	no	—
68	C₁₃×#102	—	4	2	no	—
69	C₄×C₈×C₁₃	—	4	1	no	—
70	C₁₃×#95	—	2	2	no	—
71	C₁₃×#95	—	2	2	no	—
72	#32544	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₃	—	2	2	no	—
74	C₂×Q₈×C₁₃	—	4	1	no	—
75	C₂×Q₈×C₁₃	—	4	1	no	—
76	C₂×Q₈×C₁₃	D₈	1	4	yes	complemented
77	C₂×D₄×C₁₃	—	2	2	no	—
78	C₂×D₄×C₁₃	—	2	2	no	—
79	C₂×D₄×C₁₃	—	2	2	no	—
80	C₂×D₄×C₁₃	—	2	2	no	—
81	C₂×D₄×C₁₃	—	2	2	no	—
82	C₂×D₄×C₁₃	#41	1	4	yes	—
83	C₂²×C₄×C₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	4	4	no	—
87	C₂²×C₄×C₁₃	—	4	4	no	—
88	C₂²×C₄×C₁₃	—	4	4	no	—
89	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
94	C₁₃×D₈	—	4	4	no	—
95	C₂×C₈×C₁₃	—	2	2	no	—
96	C₂×C₈×C₁₃	—	2	2	no	—
97	C₂×C₈×C₁₃	—	2	2	no	—
98	C₂×C₈×C₁₃	—	2	2	no	—
99	C₂×C₈×C₁₃	—	2	1	no	—
100	C₂×C₈×C₁₃	—	2	1	no	—
101	C₂×C₈×C₁₃	—	2	2	no	—
102	C₁₃×C₄⋊C₄	—	2	2	no	—
103	C₁₃×C₄⋊C₄	—	2	2	no	—
104	C₁₃×C₄⋊C₄	—	2	2	no	—
105	C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₁₃×C₄⋊C₄	—	2	2	no	—
107	C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₁₃×C₄⋊C₄	—	4	2	no	—
109	C₁₃×C₄⋊C₄	—	4	1	no	—
110	C₁₃×C₄⋊C₄	—	4	4	no	—
111	C₁₃×C₄⋊C₄	—	4	4	no	—
112	C₁₃×C₄⋊C₄	—	4	4	no	—
113	C₁₃×C₄⋊C₄	—	8	2	no	—
114	C₁₃×C₂²⋊C₄	—	4	4	no	—
115	C₁₃×C₂²⋊C₄	—	4	4	no	—
116	C₁₃×C₂²⋊C₄	—	4	4	no	—
117	C₁₃×C₂²⋊C₄	—	8	2	no	—
118	C₁₃×C₂²⋊C₄	—	8	2	no	—
119	C₄²×C₁₃	—	2	1	no	—
120	C₄²×C₁₃	—	2	1	no	—
121	C₄²×C₁₃	—	2	2	no	—
122	C₄²×C₁₃	—	2	2	no	—
123	#2538	C₂×C₁₃	1	2	yes	complemented
124	#2099	C₂×C₁₃	1	2	yes	complemented
125	#2086	C₂×C₁₃	1	1	yes	characteristic, complemented
126	#2071	C₂×C₁₃	1	2	yes	complemented
127	#2054	C₂×C₁₃	1	1	yes	characteristic
128	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
129	#1934	C₂×C₁₃	1	2	yes	complemented
130	#1879	C₂×C₁₃	1	2	yes	—
131	#1862	C₂×C₁₃	1	2	yes	complemented
132	C₂³×C₁₃	—	2	4	no	—
133	C₂³×C₁₃	—	4	2	no	—
134	C₂³×C₁₃	—	4	2	no	—
135	C₂³×C₁₃	—	4	2	no	—
136	C₂³×C₁₃	—	4	2	no	—
137	C₂³×C₁₃	—	4	2	no	—
138	C₂³×C₁₃	—	4	2	no	—
139	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₁₃	—	4	4	no	—
141	D₄×C₁₃	—	2	4	no	—
142	D₄×C₁₃	—	2	4	no	—
143	D₄×C₁₃	—	4	2	no	—
144	D₄×C₁₃	—	4	2	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	1	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	4	2	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	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	8	8	no	—
164	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
165	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
166	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
167	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
168	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
170	C₈×C₁₃	—	4	2	no	—
171	C₈×C₁₃	—	4	1	no	—
172	C₈×C₁₃	—	4	1	no	—
173	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
174	C₂×C₂²⋊Q₈	—	2	2	no	—
175	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
176	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
177	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
178	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
179	C₂×#102	C₂²×C₁₃	1	2	yes	—
180	C₂×#102	C₂²×C₁₃	1	2	yes	—
181	C₂×#102	C₂²×C₁₃	1	2	yes	—
182	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
183	#396	—	2	2	no	—
184	#396	—	2	2	no	—
185	#390	C₂²×C₁₃	1	2	yes	—
186	#390	C₂²×C₁₃	1	2	yes	—
187	#389	C₂²×C₁₃	1	2	yes	—
188	#389	C₂²×C₁₃	1	2	yes	—
189	#384	C₂²×C₁₃	1	2	yes	—
190	#380	—	2	2	no	—
191	#340	C₂²×C₁₃	1	1	yes	characteristic
192	#340	C₂²×C₁₃	1	1	yes	characteristic
193	#340	C₂²×C₁₃	1	2	yes	—
194	#340	C₂²×C₁₃	1	2	yes	—
195	#340	C₂²×C₁₃	1	2	yes	—
196	#336	C₂²×C₁₃	1	2	yes	—
197	#336	C₂²×C₁₃	1	2	yes	—
198	C₂²×C₁₃	—	4	4	no	—
199	C₂²×C₁₃	—	4	4	no	—
200	C₂²×C₁₃	—	4	4	no	—
201	C₂²×C₁₃	—	8	2	no	—
202	C₂²×C₁₃	—	8	2	no	—
203	C₂²×C₁₃	—	8	2	no	—
204	C₂²×C₁₃	—	8	2	no	—
205	C₂²×C₁₃	#534	1	1	yes	characteristic
206	C₂²×C₁₃	#548	1	2	yes	—
207	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
208	C₂²×C₁₃	#575	1	1	yes	characteristic
209	C₂²×C₁₃	#577	1	2	yes	—
210	C₄×C₁₃	—	2	4	no	—
211	C₄×C₁₃	—	2	2	no	—
212	C₄×C₁₃	—	4	2	no	—
213	C₄×C₁₃	—	4	1	no	—
214	C₄×C₁₃	—	8	2	no	—
215	C₄×C₁₃	—	8	2	no	—
216	C₄×C₁₃	—	8	2	no	—
217	C₄×C₁₃	#539	1	2	yes	—
218	C₄×C₁₃	#551	1	1	yes	characteristic
219	C₄×C₁₃	#563	1	1	yes	characteristic
220	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
221	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
222	C₂³×C₄	—	2	2	no	—
223	C₂×D₈	—	2	4	no	—
224	C₂×D₈	—	4	1	no	—
225	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
227	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
228	C₂²⋊Q₈	—	4	8	no	—
229	C₄×Q₈	—	4	1	no	—
230	C₄×Q₈	—	4	1	no	—
231	C₄×D₄	—	4	2	no	—
232	C₄×D₄	—	4	2	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
238	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
240	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
241	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
242	C₂×C₂²⋊C₄	—	2	2	no	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₂²⋊C₄	—	2	2	no	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
248	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
249	#107	—	4	1	no	—
250	C₄⋊C₈	—	4	1	no	—
251	#102	—	2	4	no	—
252	#102	—	2	4	no	—
253	#102	—	4	2	no	—
254	C₄×C₈	—	4	1	no	—
255	#95	—	2	2	no	—
256	#95	—	2	2	no	—
257	C₂×C₁₃	—	8	4	no	—
258	C₂×C₁₃	#2728	1	1	yes	characteristic
259	C₂×C₁₃	#3186	1	1	yes	characteristic
260	C₂×C₁₃	#3204	1	1	yes	characteristic
261	C₂×C₁₃	#3358	1	2	yes	—
262	C₂×C₁₃	#3376	1	2	yes	—
263	C₂⁴	—	2	2	no	—
264	C₂×Q₈	—	4	1	no	—
265	C₂×Q₈	—	4	1	no	—
266	C₂×Q₈	C₁₃×D₈	1	4	yes	complemented
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	C₁₃×#41	1	4	yes	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	—	4	4	no	—
279	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
283	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
284	D₈	—	4	4	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	4	2	no	—
299	C₄⋊C₄	—	4	1	no	—
300	C₄⋊C₄	—	4	4	no	—
301	C₄⋊C₄	—	4	4	no	—
302	C₄⋊C₄	—	4	4	no	—
303	C₄⋊C₄	—	8	2	no	—
304	C₂²⋊C₄	—	4	4	no	—
305	C₂²⋊C₄	—	4	4	no	—
306	C₂²⋊C₄	—	4	4	no	—
307	C₂²⋊C₄	—	8	2	no	—
308	C₂²⋊C₄	—	8	2	no	—
309	C₄²	—	2	1	no	—
310	C₄²	—	2	1	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₁₃	#32544	1	1	yes	characteristic, direct product factor, Sylow
314	C₂³	—	2	4	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	4	2	no	—
321	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
322	Q₈	—	4	4	no	—
323	D₄	—	2	4	no	—
324	D₄	—	2	4	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	8	8	no	—
346	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
347	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
348	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
349	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
350	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
351	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
352	C₈	—	4	2	no	—
353	C₈	—	4	1	no	—
354	C₈	—	4	1	no	—
355	C₂²	—	4	4	no	—
356	C₂²	—	4	4	no	—
357	C₂²	—	4	4	no	—
358	C₂²	—	8	2	no	—
359	C₂²	—	8	2	no	—
360	C₂²	—	8	2	no	—
361	C₂²	—	8	2	no	—
362	C₂²	C₁₃×#534	1	1	yes	characteristic
363	C₂²	C₁₃×#548	1	2	yes	—
364	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
365	C₂²	C₁₃×#575	1	1	yes	characteristic
366	C₂²	C₁₃×#577	1	2	yes	—
367	C₄	—	2	4	no	—
368	C₄	—	2	2	no	—
369	C₄	—	4	2	no	—
370	C₄	—	4	1	no	—
371	C₄	—	8	2	no	—
372	C₄	—	8	2	no	—
373	C₄	—	8	2	no	—
374	C₄	C₁₃×#539	1	2	yes	—
375	C₄	C₁₃×#551	1	1	yes	characteristic
376	C₄	C₁₃×#563	1	1	yes	characteristic
377	C₂	—	8	4	no	—
378	C₂	C₁₃×#2728	1	1	yes	characteristic
379	C₂	C₁₃×#3186	1	1	yes	characteristic
380	C₂	C₁₃×#3204	1	1	yes	characteristic
381	C₂	C₁₃×#3358	1	2	yes	—
382	C₂	C₁₃×#3376	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2538	C₂	semidirect
2. C₁₃×#2099	C₂	semidirect
3. C₁₃×#2086	C₂	semidirect
4. C₁₃×#2071	C₂	semidirect
6. C₁₃×#1984	C₂	semidirect
7. C₁₃×#1934	C₂	semidirect
9. C₁₃×#1862	C₂	semidirect
72. #32544	C₁₃	direct (N × H)
76. C₂×Q₈×C₁₃	D₈	semidirect
123. #2538	C₂×C₁₃	semidirect
124. #2099	C₂×C₁₃	semidirect
125. #2086	C₂×C₁₃	semidirect
126. #2071	C₂×C₁₃	semidirect
128. #1984	C₂×C₁₃	semidirect
129. #1934	C₂×C₁₃	semidirect
131. #1862	C₂×C₁₃	semidirect
266. C₂×Q₈	C₁₃×D₈	semidirect
313. C₁₃	#32544	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×#2538	2
C₁₃×#2099	2
C₁₃×#2086	2
C₁₃×#2071	2
C₁₃×#2054	2
C₁₃×#1984	2
C₁₃×#1934	2
C₁₃×#1879	2
C₁₃×#1862	2
#32544	13

Subgroups — C13×#32544 #15718883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32544 #15718883