Subgroups — C₁₃×#20541 #15706880

Order 3328.

886 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#433	C₂	1	2	yes	maximal
2	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1771	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1771	C₂	1	2	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×#1750	C₂	1	2	yes	maximal
8	C₁₃×#1749	C₂	1	1	yes	maximal, characteristic
9	C₄×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#433	C₄	1	16	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	2	yes	—
17	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#97	C₂²	1	2	yes	—
21	C₂×C₁₃×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
26	C₁₃×#389	C₄	1	2	yes	—
27	C₁₃×#389	C₄	1	2	yes	—
28	C₁₃×#385	C₄	1	4	yes	—
29	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
31	C₁₃×#336	C₂²	1	2	yes	—
32	C₁₃×#336	C₂²	1	2	yes	—
33	C₁₃×#336	C₂²	1	2	yes	—
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
38	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
41	C₁₃×#117	—	4	1	no	—
42	C₁₃×#117	—	4	1	no	—
43	C₁₃×#117	C₂×C₄	1	8	yes	—
44	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
45	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
46	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
47	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₃	—	4	1	no	—
52	C₂×C₄²×C₁₃	—	4	1	no	—
53	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
56	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
58	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
59	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
60	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
61	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
62	C₁₃×#97	—	4	1	no	—
63	C₁₃×#97	—	4	1	no	—
64	C₁₃×#97	—	4	2	no	—
65	C₁₃×#97	C₂×C₄	1	8	yes	complemented
66	C₄×C₈×C₁₃	—	4	1	no	—
67	C₄×C₈×C₁₃	—	4	1	no	—
68	C₄×C₈×C₁₃	—	4	2	no	—
69	C₄×C₈×C₁₃	C₂×C₄	1	8	yes	complemented
70	C₁₃×#95	C₂×C₄	1	4	yes	—
71	C₁₃×#95	C₂×C₄	1	4	yes	—
72	#20541	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	—	2	1	no	—
75	C₂²×C₄×C₁₃	—	2	1	no	—
76	C₂²×C₄×C₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₃	—	2	4	no	—
78	C₂²×C₄×C₁₃	—	4	2	no	—
79	C₂²×C₄×C₁₃	—	4	2	no	—
80	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
82	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
88	C₂×C₈×C₁₃	—	2	2	no	—
89	C₂×C₈×C₁₃	—	2	2	no	—
90	C₂×C₈×C₁₃	—	2	2	no	—
91	C₂×C₈×C₁₃	—	2	2	no	—
92	C₂×C₈×C₁₃	—	2	2	no	—
93	C₂×C₈×C₁₃	—	2	2	no	—
94	C₂×C₈×C₁₃	—	2	2	no	—
95	C₂×C₈×C₁₃	—	2	2	no	—
96	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
97	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
98	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
99	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
100	C₁₃×C₄⋊C₄	—	2	8	no	—
101	C₁₃×C₄⋊C₄	—	4	4	no	—
102	C₁₃×C₄⋊C₄	—	4	2	no	—
103	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
104	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
105	C₁₃×C₂²⋊C₄	—	4	2	no	—
106	C₁₃×C₂²⋊C₄	C₄²	1	8	yes	—
107	C₄²×C₁₃	—	2	1	no	—
108	C₄²×C₁₃	—	2	1	no	—
109	C₄²×C₁₃	—	2	2	no	—
110	C₄²×C₁₃	—	2	1	no	—
111	C₄²×C₁₃	—	2	1	no	—
112	C₄²×C₁₃	—	2	2	no	—
113	C₄²×C₁₃	—	4	2	no	—
114	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
115	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
116	C₂×#433	C₂×C₁₃	1	2	yes	—
117	#2296	C₂×C₁₃	1	1	yes	characteristic
118	#1771	C₂×C₁₃	1	2	yes	complemented
119	#1771	C₂×C₁₃	1	2	yes	complemented
120	#1770	C₂×C₁₃	1	2	yes	complemented
121	C₈×C₄⋊C₄	C₂×C₁₃	1	2	yes	complemented
122	#1750	C₂×C₁₃	1	2	yes	—
123	#1749	C₂×C₁₃	1	1	yes	characteristic
124	C₄×C₂²⋊C₈	C₂×C₁₃	1	1	yes	characteristic
125	C₂³×C₁₃	—	2	1	no	—
126	C₂³×C₁₃	—	2	1	no	—
127	C₂³×C₁₃	—	2	2	no	—
128	C₂³×C₁₃	—	2	2	no	—
129	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
130	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₃	—	2	2	no	—
132	C₂×C₄×C₁₃	—	2	1	no	—
133	C₂×C₄×C₁₃	—	2	1	no	—
134	C₂×C₄×C₁₃	—	2	4	no	—
135	C₂×C₄×C₁₃	—	2	4	no	—
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	—	2	4	no	—
138	C₂×C₄×C₁₃	—	2	4	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	4	no	—
141	C₂×C₄×C₁₃	—	2	4	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	2	4	no	—
145	C₂×C₄×C₁₃	—	4	8	no	—
146	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
147	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
148	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
149	C₂×C₄×C₁₃	#131	1	4	yes	—
150	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
151	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
152	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
153	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
154	C₈×C₁₃	—	2	4	no	—
155	C₈×C₁₃	—	2	4	no	—
156	C₈×C₁₃	—	2	4	no	—
157	C₈×C₁₃	—	2	4	no	—
158	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
159	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
160	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
161	#433	C₄×C₁₃	1	16	yes	complemented
162	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
163	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
164	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
165	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
166	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
167	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
168	C₂×#97	C₂²×C₁₃	1	2	yes	—
169	C₂×#97	C₂²×C₁₃	1	2	yes	—
170	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
171	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
172	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
173	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
174	#389	C₄×C₁₃	1	2	yes	—
175	#389	C₄×C₁₃	1	2	yes	—
176	#385	C₄×C₁₃	1	4	yes	—
177	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
178	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
179	#336	C₂²×C₁₃	1	2	yes	—
180	#336	C₂²×C₁₃	1	2	yes	—
181	#336	C₂²×C₁₃	1	2	yes	—
182	#336	C₂²×C₁₃	1	2	yes	—
183	C₂²×C₁₃	—	2	2	no	—
184	C₂²×C₁₃	—	2	2	no	—
185	C₂²×C₁₃	—	2	2	no	—
186	C₂²×C₁₃	—	4	2	no	—
187	C₂²×C₁₃	—	4	2	no	—
188	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
189	C₂²×C₁₃	#518	1	1	yes	characteristic
190	C₂²×C₁₃	#519	1	1	yes	characteristic
191	C₂²×C₁₃	C₂×#131	1	2	yes	—
192	C₂²×C₁₃	#568	1	2	yes	—
193	C₄×C₁₃	—	2	4	no	—
194	C₄×C₁₃	—	2	4	no	—
195	C₄×C₁₃	—	2	4	no	—
196	C₄×C₁₃	—	2	2	no	—
197	C₄×C₁₃	—	4	4	no	—
198	C₄×C₁₃	—	4	2	no	—
199	C₄×C₁₃	#520	1	2	yes	—
200	C₄×C₁₃	#520	1	2	yes	—
201	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
202	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
203	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
204	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
205	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
206	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
207	#117	—	4	1	no	—
208	#117	—	4	1	no	—
209	#117	C₂×C₄×C₁₃	1	8	yes	—
210	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
211	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
212	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
213	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
214	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
215	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
216	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
217	C₂×C₄²	—	4	1	no	—
218	C₂×C₄²	—	4	1	no	—
219	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
220	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
221	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
222	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
223	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
224	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	complemented
225	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	complemented
226	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
227	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
228	#97	—	4	1	no	—
229	#97	—	4	1	no	—
230	#97	—	4	2	no	—
231	#97	C₂×C₄×C₁₃	1	8	yes	complemented
232	C₄×C₈	—	4	1	no	—
233	C₄×C₈	—	4	1	no	—
234	C₄×C₈	—	4	2	no	—
235	C₄×C₈	C₂×C₄×C₁₃	1	8	yes	complemented
236	#95	C₂×C₄×C₁₃	1	4	yes	—
237	#95	C₂×C₄×C₁₃	1	4	yes	—
238	C₂×C₁₃	—	4	2	no	—
239	C₂×C₁₃	#2274	1	1	yes	characteristic
240	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
241	C₂×C₁₃	#2875	1	1	yes	characteristic
242	C₂×C₁₃	#2976	1	2	yes	—
243	C₂×C₁₃	#2985	1	2	yes	—
244	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
245	C₂²×C₄	—	2	1	no	—
246	C₂²×C₄	—	2	1	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	4	2	no	—
250	C₂²×C₄	—	4	2	no	—
251	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
252	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
253	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
254	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
255	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
256	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
257	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
258	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
268	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
269	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
270	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
271	C₄⋊C₄	—	2	8	no	—
272	C₄⋊C₄	—	4	2	no	—
273	C₄⋊C₄	—	4	4	no	—
274	C₄⋊C₄	C₄²×C₁₃	1	4	yes	—
275	C₄⋊C₄	C₄²×C₁₃	1	4	yes	—
276	C₂²⋊C₄	—	4	2	no	—
277	C₂²⋊C₄	C₄²×C₁₃	1	8	yes	—
278	C₄²	—	2	1	no	—
279	C₄²	—	2	1	no	—
280	C₄²	—	2	2	no	—
281	C₄²	—	2	1	no	—
282	C₄²	—	2	1	no	—
283	C₄²	—	2	2	no	—
284	C₄²	—	4	2	no	—
285	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
286	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
287	C₁₃	#20541	1	1	yes	characteristic, direct product factor, Sylow
288	C₂³	—	2	1	no	—
289	C₂³	—	2	1	no	—
290	C₂³	—	2	2	no	—
291	C₂³	—	2	2	no	—
292	C₂³	C₂×C₄²×C₁₃	1	2	yes	—
293	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	4	8	no	—
309	C₂×C₄	C₂×C₄²×C₁₃	1	4	yes	—
310	C₂×C₄	C₂×C₄²×C₁₃	1	4	yes	—
311	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
312	C₂×C₄	C₁₃×#131	1	4	yes	—
313	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
314	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
316	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
317	C₈	—	2	4	no	—
318	C₈	—	2	4	no	—
319	C₈	—	2	4	no	—
320	C₈	—	2	4	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	4	2	no	—
325	C₂²	—	4	2	no	—
326	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
327	C₂²	C₁₃×#518	1	1	yes	characteristic
328	C₂²	C₁₃×#519	1	1	yes	characteristic
329	C₂²	C₂×C₁₃×#131	1	2	yes	—
330	C₂²	C₁₃×#568	1	2	yes	—
331	C₄	—	2	2	no	—
332	C₄	—	2	4	no	—
333	C₄	—	2	4	no	—
334	C₄	—	2	4	no	—
335	C₄	—	4	4	no	—
336	C₄	—	4	2	no	—
337	C₄	C₁₃×#520	1	2	yes	—
338	C₄	C₁₃×#520	1	2	yes	—
339	C₂	—	4	2	no	—
340	C₂	C₁₃×#2274	1	1	yes	characteristic
341	C₂	C₄×C₁₃×#131	1	1	yes	characteristic
342	C₂	C₁₃×#2875	1	1	yes	characteristic
343	C₂	C₁₃×#2976	1	2	yes	—
344	C₂	C₁₃×#2985	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
3. C₁₃×#1771	C₂	semidirect
4. C₁₃×#1771	C₂	semidirect
5. C₁₃×#1770	C₂	semidirect
6. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
13. C₁₃×#433	C₄	semidirect
58. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
59. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
65. C₁₃×#97	C₂×C₄	semidirect
69. C₄×C₈×C₁₃	C₂×C₄	semidirect
72. #20541	C₁₃	direct (N × H)
118. #1771	C₂×C₁₃	semidirect
119. #1771	C₂×C₁₃	semidirect
120. #1770	C₂×C₁₃	semidirect
121. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
161. #433	C₄×C₁₃	semidirect
224. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
225. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
231. #97	C₂×C₄×C₁₃	semidirect
235. C₄×C₈	C₂×C₄×C₁₃	semidirect
287. C₁₃	#20541	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×#433	2
C₁₃×#2296	2
C₁₃×#1771	2
C₁₃×#1770	2
C₈×C₁₃×C₄⋊C₄	2
C₁₃×#1750	2
C₁₃×#1749	2
C₄×C₁₃×C₂²⋊C₈	2
#20541	13

Subgroups — C13×#20541 #15706880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20541 #15706880