Subgroups — C₁₃×#20535 #15706874

Order 3328.

1038 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1771	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1770	C₂	1	2	yes	maximal, complemented
6	C₈×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1749	C₂	1	2	yes	maximal
8	C₄×C₁₃×C₂²⋊C₈	C₂	1	2	yes	maximal
9	C₂²×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
10	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#432	C₄	1	8	yes	complemented
13	C₁₃×#431	C₄	1	8	yes	complemented
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#97	C₂²	1	4	yes	—
20	C₂×C₁₃×#97	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	4	yes	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
23	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
24	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
25	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂×C₁₃×#95	C₄	1	2	yes	—
29	C₁₃×#336	C₂²	1	4	yes	—
30	C₁₃×#336	C₂²	1	4	yes	—
31	C₂³×C₄×C₁₃	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
35	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
36	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
37	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
38	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
39	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
40	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
41	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
42	C₂×C₄²×C₁₃	—	4	4	no	—
43	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
44	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
47	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
48	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
49	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
52	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
53	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
54	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
55	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
56	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
57	C₁₃×#97	—	4	4	no	—
58	C₁₃×#97	C₂×C₄	1	8	yes	complemented
59	C₄×C₈×C₁₃	—	4	4	no	—
60	C₄×C₈×C₁₃	C₂×C₄	1	8	yes	complemented
61	C₁₃×#95	C₂×C₄	1	2	yes	—
62	C₁₃×#95	C₂×C₄	1	4	yes	—
63	C₁₃×#95	C₂×C₄	1	2	yes	—
64	#20535	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
65	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₃	—	2	4	no	—
67	C₂²×C₄×C₁₃	—	2	4	no	—
68	C₂²×C₄×C₁₃	—	2	2	no	—
69	C₂²×C₄×C₁₃	—	2	2	no	—
70	C₂²×C₄×C₁₃	—	2	8	no	—
71	C₂²×C₄×C₁₃	—	2	8	no	—
72	C₂²×C₄×C₁₃	—	4	4	no	—
73	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
74	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
75	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
76	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
85	C₂×C₈×C₁₃	—	2	2	no	—
86	C₂×C₈×C₁₃	—	2	4	no	—
87	C₂×C₈×C₁₃	—	2	2	no	—
88	C₂×C₈×C₁₃	—	2	2	no	—
89	C₂×C₈×C₁₃	—	2	4	no	—
90	C₂×C₈×C₁₃	—	2	2	no	—
91	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
92	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
93	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
94	C₁₃×C₄⋊C₄	—	2	8	no	—
95	C₁₃×C₄⋊C₄	—	2	4	no	—
96	C₁₃×C₄⋊C₄	M₁₆	1	8	yes	—
97	C₄²×C₁₃	—	2	4	no	—
98	C₄²×C₁₃	—	2	4	no	—
99	C₄²×C₁₃	—	4	4	no	—
100	C₄²×C₁₃	C₄²	1	4	yes	—
101	C₄²×C₁₃	C₄²	1	4	yes	—
102	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
103	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
104	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
105	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
106	C₂×#432	C₂×C₁₃	1	1	yes	characteristic
107	C₂×#431	C₂×C₁₃	1	1	yes	characteristic
108	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
109	#1771	C₂×C₁₃	1	4	yes	complemented
110	#1770	C₂×C₁₃	1	2	yes	complemented
111	C₈×C₄⋊C₄	C₂×C₁₃	1	2	yes	complemented
112	#1749	C₂×C₁₃	1	2	yes	—
113	C₄×C₂²⋊C₈	C₂×C₁₃	1	2	yes	—
114	C₂³×C₁₃	—	2	1	no	—
115	C₂³×C₁₃	—	2	1	no	—
116	C₂³×C₁₃	—	2	2	no	—
117	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
118	C₂³×C₁₃	#131	1	4	yes	—
119	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
120	C₂×C₄×C₁₃	—	2	4	no	—
121	C₂×C₄×C₁₃	—	2	1	no	—
122	C₂×C₄×C₁₃	—	2	1	no	—
123	C₂×C₄×C₁₃	—	2	2	no	—
124	C₂×C₄×C₁₃	—	2	2	no	—
125	C₂×C₄×C₁₃	—	2	2	no	—
126	C₂×C₄×C₁₃	—	2	4	no	—
127	C₂×C₄×C₁₃	—	2	8	no	—
128	C₂×C₄×C₁₃	—	2	4	no	—
129	C₂×C₄×C₁₃	—	2	4	no	—
130	C₂×C₄×C₁₃	—	2	8	no	—
131	C₂×C₄×C₁₃	—	2	4	no	—
132	C₂×C₄×C₁₃	—	2	4	no	—
133	C₂×C₄×C₁₃	—	2	4	no	—
134	C₂×C₄×C₁₃	—	4	16	no	—
135	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
136	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
137	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
138	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
139	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
140	C₂×C₄×C₁₃	C₂×M₁₆	1	8	yes	—
141	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
142	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
145	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
146	C₈×C₁₃	—	2	4	no	—
147	C₈×C₁₃	—	2	8	no	—
148	C₈×C₁₃	—	2	4	no	—
149	C₂²×C₄⋊C₄	C₄×C₁₃	1	2	yes	—
150	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
151	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
152	#432	C₄×C₁₃	1	8	yes	complemented
153	#431	C₄×C₁₃	1	8	yes	complemented
154	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
155	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
156	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
157	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
158	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
159	C₂×#97	C₂²×C₁₃	1	4	yes	—
160	C₂×#97	C₂²×C₁₃	1	2	yes	—
161	C₂×C₄×C₈	C₂²×C₁₃	1	4	yes	—
162	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
163	C₄×C₄⋊C₄	C₄×C₁₃	1	2	yes	—
164	C₄×C₄⋊C₄	C₄×C₁₃	1	2	yes	—
165	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
166	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
167	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
168	C₂×#95	C₄×C₁₃	1	2	yes	—
169	#336	C₂²×C₁₃	1	4	yes	—
170	#336	C₂²×C₁₃	1	4	yes	—
171	C₂²×C₁₃	—	2	2	no	—
172	C₂²×C₁₃	—	2	4	no	—
173	C₂²×C₁₃	—	2	4	no	—
174	C₂²×C₁₃	—	2	2	no	—
175	C₂²×C₁₃	#405	1	4	yes	—
176	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
177	C₂²×C₁₃	#518	1	1	yes	characteristic
178	C₂²×C₁₃	#519	1	1	yes	characteristic
179	C₂²×C₁₃	C₂²×M₁₆	1	2	yes	—
180	C₂²×C₁₃	C₂×#131	1	2	yes	—
181	C₄×C₁₃	—	2	2	no	—
182	C₄×C₁₃	—	2	2	no	—
183	C₄×C₁₃	—	2	2	no	—
184	C₄×C₁₃	—	2	8	no	—
185	C₄×C₁₃	—	2	2	no	—
186	C₄×C₁₃	—	4	4	no	—
187	C₄×C₁₃	C₄×M₁₆	1	4	yes	—
188	C₄×C₁₃	#520	1	2	yes	—
189	C₄×C₁₃	#520	1	2	yes	—
190	C₂³×C₄	C₂×C₄×C₁₃	1	4	yes	—
191	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
192	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
193	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
194	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
195	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
196	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
197	C₂×C₄⋊C₄	—	2	8	no	—
198	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
199	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
200	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
201	C₂×C₄²	—	4	4	no	—
202	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
203	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
204	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
205	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
206	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
207	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
208	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
209	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
210	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
211	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	complemented
212	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	complemented
213	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
214	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
215	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
216	#97	—	4	4	no	—
217	#97	C₂×C₄×C₁₃	1	8	yes	complemented
218	C₄×C₈	—	4	4	no	—
219	C₄×C₈	C₂×C₄×C₁₃	1	8	yes	complemented
220	#95	C₂×C₄×C₁₃	1	2	yes	—
221	#95	C₂×C₄×C₁₃	1	4	yes	—
222	#95	C₂×C₄×C₁₃	1	2	yes	—
223	C₂×C₁₃	—	2	4	no	—
224	C₂×C₁₃	#2274	1	1	yes	characteristic
225	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
226	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
227	C₂×C₁₃	#2974	1	2	yes	—
228	C₂×C₁₃	#2984	1	2	yes	—
229	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	—	2	4	no	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	8	no	—
235	C₂²×C₄	—	2	8	no	—
236	C₂²×C₄	—	4	4	no	—
237	C₂²×C₄	C₄²×C₁₃	1	4	yes	—
238	C₂²×C₄	C₄²×C₁₃	1	4	yes	—
239	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
240	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
241	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
242	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
243	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
244	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
245	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
246	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
247	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
248	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
249	C₂×C₈	—	2	2	no	—
250	C₂×C₈	—	2	4	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	4	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
256	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
257	C₂×C₈	C₂²×C₄×C₁₃	1	8	yes	—
258	C₄⋊C₄	—	2	8	no	—
259	C₄⋊C₄	—	2	4	no	—
260	C₄⋊C₄	C₁₃×M₁₆	1	8	yes	—
261	C₄²	—	2	4	no	—
262	C₄²	—	2	4	no	—
263	C₄²	—	4	4	no	—
264	C₄²	C₄²×C₁₃	1	4	yes	—
265	C₄²	C₄²×C₁₃	1	4	yes	—
266	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
267	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
268	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
269	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
270	C₁₃	#20535	1	1	yes	characteristic, direct product factor, Sylow
271	C₂³	—	2	1	no	—
272	C₂³	—	2	1	no	—
273	C₂³	—	2	2	no	—
274	C₂³	C₂×C₄²×C₁₃	1	2	yes	—
275	C₂³	C₁₃×#131	1	4	yes	—
276	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
277	C₂×C₄	—	2	8	no	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	2	1	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	4	no	—
285	C₂×C₄	—	2	8	no	—
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	4	16	no	—
292	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
293	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
294	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
295	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
296	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
297	C₂×C₄	C₂×C₁₃×M₁₆	1	8	yes	—
298	C₂×C₄	C₂×C₁₃×M₁₆	1	4	yes	—
299	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
300	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
301	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
302	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
303	C₈	—	2	4	no	—
304	C₈	—	2	8	no	—
305	C₈	—	2	4	no	—
306	C₂²	—	2	2	no	—
307	C₂²	—	2	2	no	—
308	C₂²	—	2	4	no	—
309	C₂²	—	2	4	no	—
310	C₂²	C₁₃×#405	1	4	yes	—
311	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
312	C₂²	C₁₃×#518	1	1	yes	characteristic
313	C₂²	C₁₃×#519	1	1	yes	characteristic
314	C₂²	C₂²×C₁₃×M₁₆	1	2	yes	—
315	C₂²	C₂×C₁₃×#131	1	2	yes	—
316	C₄	—	2	2	no	—
317	C₄	—	2	2	no	—
318	C₄	—	2	2	no	—
319	C₄	—	2	2	no	—
320	C₄	—	2	8	no	—
321	C₄	—	4	4	no	—
322	C₄	C₄×C₁₃×M₁₆	1	4	yes	—
323	C₄	C₁₃×#520	1	2	yes	—
324	C₄	C₁₃×#520	1	2	yes	—
325	C₂	—	2	4	no	—
326	C₂	C₁₃×#2274	1	1	yes	characteristic
327	C₂	C₂×C₄×C₁₃×M₁₆	1	1	yes	characteristic
328	C₂	C₂×C₁₃×#405	1	1	yes	characteristic
329	C₂	C₁₃×#2974	1	2	yes	—
330	C₂	C₁₃×#2984	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₁₃×#1771	C₂	semidirect
5. C₁₃×#1770	C₂	semidirect
6. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
12. C₁₃×#432	C₄	semidirect
13. C₁₃×#431	C₄	semidirect
52. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
53. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
58. C₁₃×#97	C₂×C₄	semidirect
60. C₄×C₈×C₁₃	C₂×C₄	semidirect
64. #20535	C₁₃	direct (N × H)
109. #1771	C₂×C₁₃	semidirect
110. #1770	C₂×C₁₃	semidirect
111. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
152. #432	C₄×C₁₃	semidirect
153. #431	C₄×C₁₃	semidirect
211. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
212. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
217. #97	C₂×C₄×C₁₃	semidirect
219. C₄×C₈	C₂×C₄×C₁₃	semidirect
270. C₁₃	#20535	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×#432	2
C₂×C₁₃×#431	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₁₃×#1771	2
C₁₃×#1770	2
C₈×C₁₃×C₄⋊C₄	2
C₁₃×#1749	2
C₄×C₁₃×C₂²⋊C₈	2
#20535	13

Subgroups — C13×#20535 #15706874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20535 #15706874