Subgroups — C₁₃×#20562 #15706901

Order 3328.

1002 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1770	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1753	C₂	1	2	yes	maximal, complemented
8	C₈×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1750	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1744	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1729	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
13	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₂²	1	2	yes	—
16	C₁₃×#436	C₄	1	8	yes	complemented
17	C₈×D₄×C₁₃	C₄	1	8	yes	complemented
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₃×#97	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#390	C₄	1	2	yes	—
28	C₁₃×#389	C₄	1	2	yes	—
29	C₁₃×#388	C₄	1	4	yes	—
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₄³×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#336	C₂²	1	1	yes	characteristic
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₁₃×#336	C₂²	1	2	yes	—
36	C₁₃×#336	C₂²	1	2	yes	—
37	C₁₃×#336	C₂²	1	1	yes	characteristic
38	C₁₃×#336	C₂²	1	1	yes	characteristic
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
42	C₂×C₁₃×M₁₆	—	4	2	no	—
43	C₂×C₁₃×M₁₆	—	4	2	no	—
44	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	—
45	C₂²×C₈×C₁₃	—	4	2	no	—
46	C₂²×C₈×C₁₃	—	4	2	no	—
47	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
55	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
56	C₁₃×#117	—	4	2	no	—
57	C₁₃×#117	—	4	2	no	—
58	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
62	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
63	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
71	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
72	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
73	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
74	C₁₃×#97	—	4	2	no	—
75	C₄×C₈×C₁₃	—	4	2	no	—
76	C₄×C₈×C₁₃	—	4	2	no	—
77	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
78	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
79	C₁₃×#95	C₂×C₄	1	4	yes	—
80	C₁₃×#95	C₂×C₄	1	2	yes	—
81	#20562	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
83	C₂×D₄×C₁₃	—	2	4	no	—
84	C₂×D₄×C₁₃	C₄²	1	4	yes	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
98	C₁₃×M₁₆	—	4	8	no	—
99	C₂×C₈×C₁₃	—	2	1	no	—
100	C₂×C₈×C₁₃	—	2	2	no	—
101	C₂×C₈×C₁₃	—	2	2	no	—
102	C₂×C₈×C₁₃	—	2	2	no	—
103	C₂×C₈×C₁₃	—	2	1	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	1	no	—
106	C₂×C₈×C₁₃	—	2	1	no	—
107	C₂×C₈×C₁₃	—	2	1	no	—
108	C₂×C₈×C₁₃	—	2	1	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	4	8	no	—
112	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
117	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
118	C₁₃×C₄⋊C₄	—	2	4	no	—
119	C₁₃×C₄⋊C₄	—	4	4	no	—
120	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
121	C₁₃×C₂²⋊C₄	—	2	8	no	—
122	C₁₃×C₂²⋊C₄	—	4	4	no	—
123	C₁₃×C₂²⋊C₄	C₄²	1	8	yes	—
124	C₄²×C₁₃	—	2	4	no	—
125	C₄²×C₁₃	—	2	4	no	—
126	C₄²×C₁₃	—	2	1	no	—
127	C₄²×C₁₃	—	2	2	no	—
128	C₄²×C₁₃	—	2	2	no	—
129	C₄²×C₁₃	—	2	1	no	—
130	C₄²×C₁₃	—	2	1	no	—
131	C₄²×C₁₃	—	2	1	no	—
132	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
133	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
134	C₂×#436	C₂×C₁₃	1	1	yes	characteristic
135	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic
136	#2293	C₂×C₁₃	1	1	yes	characteristic
137	#1770	C₂×C₁₃	1	1	yes	characteristic, complemented
138	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
139	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#1753	C₂×C₁₃	1	2	yes	complemented
141	C₈×C₂²⋊C₄	C₂×C₁₃	1	2	yes	complemented
142	#1750	C₂×C₁₃	1	2	yes	complemented
143	#1744	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#1729	C₂×C₁₃	1	2	yes	complemented
145	C₂³×C₁₃	—	2	2	no	—
146	C₂³×C₁₃	—	2	2	no	—
147	C₂³×C₁₃	—	2	4	no	—
148	C₂³×C₁₃	—	2	4	no	—
149	C₂³×C₁₃	C₂×C₄²	1	4	yes	—
150	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
151	D₄×C₁₃	—	2	8	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	4	no	—
158	C₂×C₄×C₁₃	—	2	4	no	—
159	C₂×C₄×C₁₃	—	2	4	no	—
160	C₂×C₄×C₁₃	—	2	4	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	4	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	4	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
168	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
169	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
170	C₂×C₄×C₁₃	#131	1	4	yes	—
171	C₂×C₄×C₁₃	#131	1	4	yes	—
172	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
178	C₈×C₁₃	—	2	2	no	—
179	C₈×C₁₃	—	2	4	no	—
180	C₈×C₁₃	—	2	4	no	—
181	C₈×C₁₃	—	2	2	no	—
182	C₈×C₁₃	—	2	2	no	—
183	C₈×C₁₃	—	2	2	no	—
184	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
185	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
186	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
187	C₂×#117	C₂²×C₁₃	1	2	yes	—
188	#436	C₄×C₁₃	1	8	yes	complemented
189	C₈×D₄	C₄×C₁₃	1	8	yes	complemented
190	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
193	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
194	C₂×#97	C₂²×C₁₃	1	2	yes	—
195	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
196	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
197	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
199	#390	C₄×C₁₃	1	2	yes	—
200	#389	C₄×C₁₃	1	2	yes	—
201	#388	C₄×C₁₃	1	4	yes	—
202	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
203	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
204	C₄³	C₂²×C₁₃	1	1	yes	characteristic
205	#336	C₂²×C₁₃	1	1	yes	characteristic
206	#336	C₂²×C₁₃	1	2	yes	—
207	#336	C₂²×C₁₃	1	2	yes	—
208	#336	C₂²×C₁₃	1	2	yes	—
209	#336	C₂²×C₁₃	1	1	yes	characteristic
210	#336	C₂²×C₁₃	1	1	yes	characteristic
211	#336	C₂²×C₁₃	1	1	yes	characteristic
212	C₂²×C₁₃	—	2	4	no	—
213	C₂²×C₁₃	—	2	4	no	—
214	C₂²×C₁₃	—	2	4	no	—
215	C₂²×C₁₃	—	4	4	no	—
216	C₂²×C₁₃	—	4	4	no	—
217	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
218	C₂²×C₁₃	#518	1	1	yes	characteristic
219	C₂²×C₁₃	#520	1	1	yes	characteristic
220	C₂²×C₁₃	C₂×#131	1	2	yes	—
221	C₂²×C₁₃	C₂×#131	1	2	yes	—
222	C₄×C₁₃	—	2	2	no	—
223	C₄×C₁₃	—	2	4	no	—
224	C₄×C₁₃	—	2	4	no	—
225	C₄×C₁₃	—	4	2	no	—
226	C₄×C₁₃	—	4	4	no	—
227	C₄×C₁₃	#405	1	4	yes	—
228	C₄×C₁₃	#518	1	1	yes	characteristic
229	C₄×C₁₃	#518	1	1	yes	characteristic
230	C₄×C₁₃	#520	1	1	yes	characteristic
231	C₄×C₁₃	#520	1	1	yes	characteristic
232	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
233	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
234	C₂×M₁₆	—	4	2	no	—
235	C₂×M₁₆	—	4	2	no	—
236	C₂×M₁₆	C₂×C₄×C₁₃	1	8	yes	—
237	C₂²×C₈	—	4	2	no	—
238	C₂²×C₈	—	4	2	no	—
239	C₂²×C₈	C₂×C₄×C₁₃	1	8	yes	—
240	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
242	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
244	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
245	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
246	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
247	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
248	#117	—	4	2	no	—
249	#117	—	4	2	no	—
250	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
251	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
252	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
254	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
255	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
256	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
257	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
258	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
260	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
262	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
263	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
264	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
265	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
266	#97	—	4	2	no	—
267	C₄×C₈	—	4	2	no	—
268	C₄×C₈	—	4	2	no	—
269	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
270	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
271	#95	C₂×C₄×C₁₃	1	4	yes	—
272	#95	C₂×C₄×C₁₃	1	2	yes	—
273	C₂×C₁₃	—	4	4	no	—
274	C₂×C₁₃	#2275	1	1	yes	characteristic
275	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
276	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
277	C₂×C₁₃	#2979	1	2	yes	—
278	C₂×C₁₃	#2994	1	2	yes	—
279	C₂⁴	C₂²×C₄×C₁₃	1	2	yes	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	C₄²×C₁₃	1	4	yes	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
287	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
288	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
289	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
290	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
291	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
292	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
293	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
294	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
295	M₁₆	—	4	8	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	4	8	no	—
309	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
310	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
311	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
312	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
313	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
314	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	4	4	no	—
317	C₄⋊C₄	C₄²×C₁₃	1	4	yes	—
318	C₂²⋊C₄	—	2	8	no	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₂²⋊C₄	C₄²×C₁₃	1	8	yes	—
321	C₄²	—	2	4	no	—
322	C₄²	—	2	4	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	2	1	no	—
329	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
330	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
331	C₁₃	#20562	1	1	yes	characteristic, direct product factor, Sylow
332	C₂³	—	2	2	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	4	no	—
336	C₂³	C₂×C₄²×C₁₃	1	4	yes	—
337	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
338	D₄	—	2	8	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
355	C₂×C₄	C₂×C₄²×C₁₃	1	4	yes	—
356	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
357	C₂×C₄	C₁₃×#131	1	4	yes	—
358	C₂×C₄	C₁₃×#131	1	4	yes	—
359	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
360	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
361	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
364	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
365	C₈	—	2	2	no	—
366	C₈	—	2	4	no	—
367	C₈	—	2	4	no	—
368	C₈	—	2	2	no	—
369	C₈	—	2	2	no	—
370	C₈	—	2	2	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	4	4	no	—
376	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
377	C₂²	C₁₃×#518	1	1	yes	characteristic
378	C₂²	C₁₃×#520	1	1	yes	characteristic
379	C₂²	C₂×C₁₃×#131	1	2	yes	—
380	C₂²	C₂×C₁₃×#131	1	2	yes	—
381	C₄	—	2	4	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	4	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	4	no	—
386	C₄	C₁₃×#405	1	4	yes	—
387	C₄	C₁₃×#518	1	1	yes	characteristic
388	C₄	C₁₃×#518	1	1	yes	characteristic
389	C₄	C₁₃×#520	1	1	yes	characteristic
390	C₄	C₁₃×#520	1	1	yes	characteristic
391	C₂	—	4	4	no	—
392	C₂	C₁₃×#2275	1	1	yes	characteristic
393	C₂	C₂×C₁₃×#405	1	1	yes	characteristic
394	C₂	C₄×C₁₃×#131	1	1	yes	characteristic
395	C₂	C₁₃×#2979	1	2	yes	—
396	C₂	C₁₃×#2994	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	C₂²×D₄×C₁₃	C₂×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×#1770	C₂	semidirect
5. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
6. C₄×C₁₃×C₄⋊C₈	C₂	semidirect
7. C₁₃×#1753	C₂	semidirect
8. C₈×C₁₃×C₂²⋊C₄	C₂	semidirect
9. C₁₃×#1750	C₂	semidirect
10. C₁₃×#1744	C₂	semidirect
11. C₁₃×#1729	C₂	semidirect
16. C₁₃×#436	C₄	semidirect
17. C₈×D₄×C₁₃	C₄	semidirect
81. #20562	C₁₃	direct (N × H)
137. #1770	C₂×C₁₃	semidirect
138. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
139. C₄×C₄⋊C₈	C₂×C₁₃	semidirect
140. #1753	C₂×C₁₃	semidirect
141. C₈×C₂²⋊C₄	C₂×C₁₃	semidirect
142. #1750	C₂×C₁₃	semidirect
143. #1744	C₂×C₁₃	semidirect
144. #1729	C₂×C₁₃	semidirect
188. #436	C₄×C₁₃	semidirect
189. C₈×D₄	C₄×C₁₃	semidirect
331. C₁₃	#20562	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×#436	2
C₂×C₈×D₄×C₁₃	2
C₁₃×#2293	2
C₁₃×#1770	2
C₈×C₁₃×C₄⋊C₄	2
C₄×C₁₃×C₄⋊C₈	2
C₁₃×#1753	2
C₈×C₁₃×C₂²⋊C₄	2
C₁₃×#1750	2
C₁₃×#1744	2
C₁₃×#1729	2
#20562	13

Subgroups — C13×#20562 #15706901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20562 #15706901