Subgroups — C₁₃×#21810 #15708149

Order 3328.

1990 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1982	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1961	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1786	C₂	1	4	yes	maximal, complemented
7	C₂³×D₄×C₁₃	—	2	1	no	—
8	C₂³×D₄×C₁₃	—	2	1	no	—
9	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
10	C₂×C₁₃×#127	—	2	1	no	—
11	C₂×C₁₃×#127	—	2	1	no	—
12	C₂×C₁₃×#127	—	2	4	no	—
13	C₂×C₁₃×#127	C₄	1	8	yes	complemented
14	C₂×C₁₃×#127	C₂²	1	2	yes	—
15	C₂×C₁₃×#127	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#432	—	2	4	no	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
19	C₂×C₁₃×#102	C₂²	1	16	yes	complemented
20	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
22	C₁₃×#383	—	2	1	no	—
23	C₁₃×#382	C₂²	1	2	yes	complemented
24	C₁₃×#381	—	2	1	no	—
25	C₁₃×#380	C₂²	1	2	yes	—
26	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
27	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
28	C₁₃×#376	—	2	1	no	—
29	C₂⁵×C₁₃	—	2	2	no	—
30	C₂²×D₄×C₁₃	—	2	8	no	—
31	C₂²×D₄×C₁₃	—	2	8	no	—
32	C₂²×D₄×C₁₃	—	2	2	no	—
33	C₂²×D₄×C₁₃	—	2	4	no	—
34	C₂²×D₄×C₁₃	—	2	2	no	—
35	C₂²×D₄×C₁₃	—	2	2	no	—
36	C₂²×D₄×C₁₃	—	2	2	no	—
37	C₂²×D₄×C₁₃	—	2	2	no	—
38	C₂²×D₄×C₁₃	—	4	8	no	—
39	C₂²×D₄×C₁₃	—	4	8	no	—
40	C₂²×D₄×C₁₃	—	4	8	no	—
41	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	—
42	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
47	C₁₃×#127	—	2	8	no	—
48	C₁₃×#127	—	2	8	no	—
49	C₁₃×#127	—	2	4	no	—
50	C₁₃×#127	—	2	4	no	—
51	C₁₃×#127	C₂×C₄	1	8	yes	—
52	C₁₃×#127	C₂×C₄	1	8	yes	—
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
54	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
55	C₂×C₄²×C₁₃	—	2	2	no	—
56	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
57	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	D₄	1	4	yes	—
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×C₄⋊C₈	—	2	4	no	—
63	C₁₃×#102	—	4	16	no	—
64	C₁₃×C₂²⋊C₈	—	2	4	no	—
65	C₁₃×#97	—	2	4	no	—
66	C₁₃×#95	—	2	2	no	—
67	C₁₃×#95	—	2	2	no	—
68	C₁₃×#95	—	2	2	no	—
69	C₁₃×#95	—	2	2	no	—
70	#21810	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₂⁴×C₁₃	—	2	8	no	—
72	C₂⁴×C₁₃	—	2	4	no	—
73	C₂⁴×C₁₃	—	4	8	no	—
74	C₂⁴×C₁₃	—	4	8	no	—
75	C₂⁴×C₁₃	—	4	8	no	—
76	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
77	C₂×D₄×C₁₃	—	2	8	no	—
78	C₂×D₄×C₁₃	—	2	8	no	—
79	C₂×D₄×C₁₃	—	2	8	no	—
80	C₂×D₄×C₁₃	—	2	8	no	—
81	C₂×D₄×C₁₃	—	2	8	no	—
82	C₂×D₄×C₁₃	—	2	4	no	—
83	C₂×D₄×C₁₃	—	2	16	no	—
84	C₂×D₄×C₁₃	—	4	16	no	—
85	C₂×D₄×C₁₃	—	4	8	no	—
86	C₂×D₄×C₁₃	—	4	8	no	—
87	C₂×D₄×C₁₃	—	4	8	no	—
88	C₂×D₄×C₁₃	—	4	8	no	—
89	C₂×D₄×C₁₃	—	4	32	no	—
90	C₂×D₄×C₁₃	—	4	16	no	—
91	C₂×D₄×C₁₃	—	4	32	no	—
92	C₂×D₄×C₁₃	—	4	8	no	—
93	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
94	C₂²×C₄×C₁₃	—	2	4	no	—
95	C₂²×C₄×C₁₃	—	2	4	no	—
96	C₂²×C₄×C₁₃	—	2	4	no	—
97	C₂²×C₄×C₁₃	—	2	4	no	—
98	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
99	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
100	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₁₃	—	2	4	no	—
109	C₂×C₈×C₁₃	—	2	8	no	—
110	C₁₃×C₄⋊C₄	—	2	8	no	—
111	C₁₃×C₂²⋊C₄	—	4	4	no	—
112	C₄²×C₁₃	—	4	4	no	—
113	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
114	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
115	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
116	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
117	C₄²×C₁₃	C₂×D₄	1	2	yes	—
118	C₄²×C₁₃	C₂×D₄	1	2	yes	—
119	C₂²×#127	C₂×C₁₃	1	1	yes	characteristic
120	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
121	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
122	#1982	C₂×C₁₃	1	4	yes	complemented
123	#1961	C₂×C₁₃	1	4	yes	complemented
124	#1786	C₂×C₁₃	1	4	yes	complemented
125	C₂³×C₁₃	—	2	2	no	—
126	C₂³×C₁₃	—	2	2	no	—
127	C₂³×C₁₃	—	2	8	no	—
128	C₂³×C₁₃	—	4	16	no	—
129	C₂³×C₁₃	—	4	16	no	—
130	C₂³×C₁₃	—	4	8	no	—
131	C₂³×C₁₃	—	4	8	no	—
132	C₂³×C₁₃	—	4	8	no	—
133	C₂³×C₁₃	—	4	16	no	—
134	C₂³×C₁₃	—	8	32	no	—
135	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
136	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
137	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
138	D₄×C₁₃	—	2	16	no	—
139	D₄×C₁₃	—	4	16	no	—
140	D₄×C₁₃	—	4	16	no	—
141	D₄×C₁₃	—	4	16	no	—
142	D₄×C₁₃	—	4	16	no	—
143	D₄×C₁₃	—	4	8	no	—
144	D₄×C₁₃	—	4	16	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	8	no	—
150	C₂×C₄×C₁₃	—	2	4	no	—
151	C₂×C₄×C₁₃	—	2	4	no	—
152	C₂×C₄×C₁₃	—	2	8	no	—
153	C₂×C₄×C₁₃	—	4	4	no	—
154	C₂×C₄×C₁₃	—	4	4	no	—
155	C₂×C₄×C₁₃	—	4	4	no	—
156	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
162	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
165	C₈×C₁₃	—	4	4	no	—
166	C₂³×D₄	—	2	1	no	—
167	C₂³×D₄	—	2	1	no	—
168	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
169	C₂×#127	—	2	1	no	—
170	C₂×#127	—	2	1	no	—
171	C₂×#127	—	2	4	no	—
172	C₂×#127	C₄×C₁₃	1	8	yes	complemented
173	C₂×#127	C₂²×C₁₃	1	2	yes	—
174	C₂×#127	C₂²×C₁₃	1	2	yes	—
175	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
176	#432	—	2	4	no	—
177	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
178	C₂×#102	C₂²×C₁₃	1	16	yes	complemented
179	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
180	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
181	#383	—	2	1	no	—
182	#382	C₂²×C₁₃	1	2	yes	complemented
183	#381	—	2	1	no	—
184	#380	C₂²×C₁₃	1	2	yes	—
185	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
186	C₄×C₂²⋊C₄	—	2	1	no	—
187	#376	—	2	1	no	—
188	C₂²×C₁₃	—	2	2	no	—
189	C₂²×C₁₃	—	2	2	no	—
190	C₂²×C₁₃	—	2	8	no	—
191	C₂²×C₁₃	—	4	8	no	—
192	C₂²×C₁₃	—	4	8	no	—
193	C₂²×C₁₃	—	4	8	no	—
194	C₂²×C₁₃	—	8	32	no	—
195	C₂²×C₁₃	—	8	16	no	—
196	C₂²×C₁₃	#418	1	4	yes	—
197	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
198	C₂²×C₁₃	#535	1	2	yes	—
199	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
200	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
201	C₄×C₁₃	—	2	2	no	—
202	C₄×C₁₃	—	2	2	no	—
203	C₄×C₁₃	—	2	2	no	—
204	C₄×C₁₃	—	2	2	no	—
205	C₄×C₁₃	—	8	4	no	—
206	C₄×C₁₃	#418	1	4	yes	—
207	C₄×C₁₃	#518	1	2	yes	—
208	C₄×C₁₃	#535	1	2	yes	—
209	C₂⁵	—	2	2	no	—
210	C₂²×D₄	—	2	8	no	—
211	C₂²×D₄	—	2	8	no	—
212	C₂²×D₄	—	2	2	no	—
213	C₂²×D₄	—	2	4	no	—
214	C₂²×D₄	—	2	2	no	—
215	C₂²×D₄	—	2	2	no	—
216	C₂²×D₄	—	2	2	no	—
217	C₂²×D₄	—	2	2	no	—
218	C₂²×D₄	—	4	8	no	—
219	C₂²×D₄	—	4	8	no	—
220	C₂²×D₄	—	4	8	no	—
221	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	—
222	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
223	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
224	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
225	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
227	#127	—	2	8	no	—
228	#127	—	2	8	no	—
229	#127	—	2	4	no	—
230	#127	—	2	4	no	—
231	#127	C₂×C₄×C₁₃	1	8	yes	—
232	#127	C₂×C₄×C₁₃	1	8	yes	—
233	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
234	C₂×C₂²⋊C₄	—	2	2	no	—
235	C₂×C₄²	—	2	2	no	—
236	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
237	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
238	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
239	C₂×C₄²	D₄×C₁₃	1	4	yes	—
240	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
242	C₄⋊C₈	—	2	4	no	—
243	#102	—	4	16	no	—
244	C₂²⋊C₈	—	2	4	no	—
245	#97	—	2	4	no	—
246	#95	—	2	2	no	—
247	#95	—	2	2	no	—
248	#95	—	2	2	no	—
249	#95	—	2	2	no	—
250	C₂×C₁₃	—	2	4	no	—
251	C₂×C₁₃	—	8	8	no	—
252	C₂×C₁₃	#2309	1	1	yes	characteristic
253	C₂×C₁₃	C₂×#418	1	1	yes	characteristic
254	C₂×C₁₃	C₂×#418	1	1	yes	characteristic
255	C₂×C₁₃	#3217	1	4	yes	—
256	C₂⁴	—	2	8	no	—
257	C₂⁴	—	2	4	no	—
258	C₂⁴	—	4	8	no	—
259	C₂⁴	—	4	8	no	—
260	C₂⁴	—	4	8	no	—
261	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
262	C₂×D₄	—	2	8	no	—
263	C₂×D₄	—	2	8	no	—
264	C₂×D₄	—	2	8	no	—
265	C₂×D₄	—	2	8	no	—
266	C₂×D₄	—	2	8	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	16	no	—
269	C₂×D₄	—	4	16	no	—
270	C₂×D₄	—	4	32	no	—
271	C₂×D₄	—	4	8	no	—
272	C₂×D₄	—	4	8	no	—
273	C₂×D₄	—	4	8	no	—
274	C₂×D₄	—	4	8	no	—
275	C₂×D₄	—	4	32	no	—
276	C₂×D₄	—	4	16	no	—
277	C₂×D₄	—	4	8	no	—
278	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
284	C₂²×C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
285	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
292	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	8	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₂²⋊C₄	—	4	4	no	—
297	C₄²	—	4	4	no	—
298	C₄²	C₁₃×C₂²⋊C₄	1	4	yes	—
299	C₄²	C₁₃×C₂²⋊C₄	1	4	yes	—
300	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
301	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
302	C₄²	C₂×D₄×C₁₃	1	2	yes	—
303	C₄²	C₂×D₄×C₁₃	1	2	yes	—
304	C₁₃	#21810	1	1	yes	characteristic, direct product factor, Sylow
305	C₂³	—	2	2	no	—
306	C₂³	—	2	2	no	—
307	C₂³	—	2	8	no	—
308	C₂³	—	4	16	no	—
309	C₂³	—	4	16	no	—
310	C₂³	—	4	16	no	—
311	C₂³	—	4	8	no	—
312	C₂³	—	4	8	no	—
313	C₂³	—	4	8	no	—
314	C₂³	—	8	32	no	—
315	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
316	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
317	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
318	D₄	—	2	16	no	—
319	D₄	—	4	16	no	—
320	D₄	—	4	16	no	—
321	D₄	—	4	16	no	—
322	D₄	—	4	16	no	—
323	D₄	—	4	16	no	—
324	D₄	—	4	8	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
337	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
338	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
339	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
340	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
341	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
342	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
344	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
345	C₈	—	4	4	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	8	no	—
349	C₂²	—	4	8	no	—
350	C₂²	—	4	8	no	—
351	C₂²	—	4	8	no	—
352	C₂²	—	8	32	no	—
353	C₂²	—	8	16	no	—
354	C₂²	C₁₃×#418	1	4	yes	—
355	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
356	C₂²	C₁₃×#535	1	2	yes	—
357	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
358	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
359	C₄	—	2	2	no	—
360	C₄	—	2	2	no	—
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	8	4	no	—
364	C₄	C₁₃×#418	1	4	yes	—
365	C₄	C₁₃×#518	1	2	yes	—
366	C₄	C₁₃×#535	1	2	yes	—
367	C₂	—	2	4	no	—
368	C₂	—	8	8	no	—
369	C₂	C₁₃×#2309	1	1	yes	characteristic
370	C₂	C₂×C₁₃×#418	1	1	yes	characteristic
371	C₂	C₂×C₁₃×#418	1	1	yes	characteristic
372	C₂	C₁₃×#3217	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#432	C₂	semidirect
3. C₁₃×#2283	C₂	semidirect
4. C₁₃×#1982	C₂	semidirect
5. C₁₃×#1961	C₂	semidirect
6. C₁₃×#1786	C₂	semidirect
13. C₂×C₁₃×#127	C₄	semidirect
18. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
19. C₂×C₁₃×#102	C₂²	semidirect
21. C₂×C₁₃×#97	C₂²	semidirect
23. C₁₃×#382	C₂²	semidirect
26. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
70. #21810	C₁₃	direct (N × H)
120. C₂×#432	C₂×C₁₃	semidirect
121. #2283	C₂×C₁₃	semidirect
122. #1982	C₂×C₁₃	semidirect
123. #1961	C₂×C₁₃	semidirect
124. #1786	C₂×C₁₃	semidirect
172. C₂×#127	C₄×C₁₃	semidirect
177. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
178. C₂×#102	C₂²×C₁₃	semidirect
180. C₂×#97	C₂²×C₁₃	semidirect
182. #382	C₂²×C₁₃	semidirect
185. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
304. C₁₃	#21810	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#127	2
C₂×C₁₃×#432	2
C₁₃×#2283	2
C₁₃×#1982	2
C₁₃×#1961	2
C₁₃×#1786	2
#21810	13

Subgroups — C13×#21810 #15708149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21810 #15708149