Subgroups — C₁₃×#20550 #15706889

Order 3328.

994 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1770	C₂	1	2	yes	maximal, complemented
5	C₈×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1767	C₂	1	2	yes	maximal, complemented
7	C₄×C₁₃×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1753	C₂	1	4	yes	maximal
9	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
10	C₂×C₁₃×#117	C₄	1	2	yes	—
11	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#431	C₄	1	8	yes	complemented
13	C₁₃×#423	C₄	1	8	yes	complemented
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#97	C₂²	1	4	yes	—
20	C₂×C₄×C₈×C₁₃	C₂²	1	4	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
22	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
23	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₄×C₁₃×C₂²⋊C₄	C₄	1	2	yes	—
26	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₁₃×#376	C₄	1	2	yes	—
28	C₄³×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#336	C₂²	1	4	yes	—
30	C₁₃×#336	C₂²	1	4	yes	—
31	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
34	C₂×C₁₃×M₁₆	—	4	2	no	—
35	C₂×C₁₃×M₁₆	—	4	2	no	—
36	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	—
37	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
38	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
40	C₁₃×#117	—	2	8	no	—
41	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
42	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
43	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
44	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
45	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
46	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
49	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
50	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
51	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
52	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
55	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
56	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
57	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
58	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
59	C₁₃×#97	—	4	4	no	—
60	C₄×C₈×C₁₃	—	4	4	no	—
61	C₄×C₈×C₁₃	C₂×C₄	1	8	yes	—
62	C₁₃×#95	C₂×C₄	1	2	yes	—
63	C₁₃×#95	C₂×C₄	1	2	yes	—
64	C₁₃×#95	C₂×C₄	1	4	yes	—
65	#20550	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	—	2	4	no	—
68	C₂²×C₄×C₁₃	—	2	4	no	—
69	C₂²×C₄×C₁₃	—	2	1	no	—
70	C₂²×C₄×C₁₃	—	2	1	no	—
71	C₂²×C₄×C₁₃	—	2	1	no	—
72	C₂²×C₄×C₁₃	—	2	1	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	2	yes	—
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	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
85	C₁₃×M₁₆	—	4	8	no	—
86	C₂×C₈×C₁₃	—	2	2	no	—
87	C₂×C₈×C₁₃	—	2	4	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	—	2	2	no	—
92	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
93	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
94	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
95	C₁₃×C₄⋊C₄	—	2	4	no	—
96	C₁₃×C₄⋊C₄	M₁₆	1	8	yes	complemented
97	C₁₃×C₂²⋊C₄	—	2	8	no	—
98	C₄²×C₁₃	—	2	8	no	—
99	C₄²×C₁₃	—	2	8	no	—
100	C₄²×C₁₃	—	2	2	no	—
101	C₄²×C₁₃	—	2	2	no	—
102	C₄²×C₁₃	—	2	2	no	—
103	C₄²×C₁₃	—	2	2	no	—
104	C₄²×C₁₃	C₄²	1	4	yes	—
105	C₄²×C₁₃	C₄²	1	4	yes	—
106	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
107	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
108	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
109	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
110	C₂×#431	C₂×C₁₃	1	1	yes	characteristic
111	C₂×#423	C₂×C₁₃	1	1	yes	characteristic
112	C₄×#117	C₂×C₁₃	1	1	yes	characteristic
113	#1770	C₂×C₁₃	1	2	yes	complemented
114	C₈×C₄⋊C₄	C₂×C₁₃	1	2	yes	complemented
115	#1767	C₂×C₁₃	1	2	yes	complemented
116	C₄×C₄⋊C₈	C₂×C₁₃	1	2	yes	complemented
117	#1753	C₂×C₁₃	1	4	yes	—
118	C₂³×C₁₃	—	2	1	no	—
119	C₂³×C₁₃	—	2	1	no	—
120	C₂³×C₁₃	—	2	2	no	—
121	C₂³×C₁₃	—	2	2	no	—
122	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
123	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
124	C₂×C₄×C₁₃	—	2	4	no	—
125	C₂×C₄×C₁₃	—	2	1	no	—
126	C₂×C₄×C₁₃	—	2	1	no	—
127	C₂×C₄×C₁₃	—	2	2	no	—
128	C₂×C₄×C₁₃	—	2	4	no	—
129	C₂×C₄×C₁₃	—	2	2	no	—
130	C₂×C₄×C₁₃	—	2	2	no	—
131	C₂×C₄×C₁₃	—	2	2	no	—
132	C₂×C₄×C₁₃	—	2	2	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	8	no	—
135	C₂×C₄×C₁₃	—	2	8	no	—
136	C₂×C₄×C₁₃	—	2	4	no	—
137	C₂×C₄×C₁₃	—	2	4	no	—
138	C₂×C₄×C₁₃	—	2	4	no	—
139	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
140	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
141	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
142	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
143	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
144	C₂×C₄×C₁₃	C₂×M₁₆	1	8	yes	—
145	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
146	C₂×C₄×C₁₃	#131	1	4	yes	—
147	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
150	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
151	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
152	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
153	C₈×C₁₃	—	2	8	no	—
154	C₈×C₁₃	—	2	4	no	—
155	C₈×C₁₃	—	2	4	no	—
156	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
157	C₂×#117	C₄×C₁₃	1	2	yes	—
158	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
159	#431	C₄×C₁₃	1	8	yes	complemented
160	#423	C₄×C₁₃	1	8	yes	complemented
161	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
162	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
163	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
164	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
165	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
166	C₂×#97	C₂²×C₁₃	1	4	yes	—
167	C₂×C₄×C₈	C₂²×C₁₃	1	4	yes	—
168	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
169	C₄×C₄⋊C₄	C₄×C₁₃	1	2	yes	—
170	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
171	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
172	C₄×C₂²⋊C₄	C₄×C₁₃	1	2	yes	—
173	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
174	#376	C₄×C₁₃	1	2	yes	—
175	C₄³	C₂²×C₁₃	1	2	yes	—
176	#336	C₂²×C₁₃	1	4	yes	—
177	#336	C₂²×C₁₃	1	4	yes	—
178	C₂²×C₁₃	—	2	2	no	—
179	C₂²×C₁₃	—	2	2	no	—
180	C₂²×C₁₃	—	2	2	no	—
181	C₂²×C₁₃	—	4	2	no	—
182	C₂²×C₁₃	—	4	2	no	—
183	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
184	C₂²×C₁₃	#520	1	1	yes	characteristic
185	C₂²×C₁₃	#520	1	1	yes	characteristic
186	C₂²×C₁₃	C₂²×M₁₆	1	2	yes	—
187	C₂²×C₁₃	C₂×#131	1	2	yes	—
188	C₄×C₁₃	—	2	2	no	—
189	C₄×C₁₃	—	2	2	no	—
190	C₄×C₁₃	—	2	8	no	—
191	C₄×C₁₃	—	2	2	no	—
192	C₄×C₁₃	—	4	4	no	—
193	C₄×C₁₃	C₄×M₁₆	1	4	yes	—
194	C₄×C₁₃	#405	1	4	yes	—
195	C₄×C₁₃	#518	1	1	yes	characteristic
196	C₄×C₁₃	#519	1	1	yes	characteristic
197	C₄×C₁₃	#520	1	1	yes	characteristic
198	C₄×C₁₃	#520	1	1	yes	characteristic
199	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
200	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
201	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
202	C₂×M₁₆	—	4	2	no	—
203	C₂×M₁₆	—	4	2	no	—
204	C₂×M₁₆	C₂×C₄×C₁₃	1	8	yes	—
205	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
206	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
207	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
208	#117	—	2	8	no	—
209	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
210	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
211	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
212	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
213	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
214	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
215	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
216	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
217	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
218	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
219	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
220	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
221	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
222	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
223	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
224	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
225	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
226	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
227	#97	—	4	4	no	—
228	C₄×C₈	—	4	4	no	—
229	C₄×C₈	C₂×C₄×C₁₃	1	8	yes	—
230	#95	C₂×C₄×C₁₃	1	2	yes	—
231	#95	C₂×C₄×C₁₃	1	2	yes	—
232	#95	C₂×C₄×C₁₃	1	4	yes	—
233	C₂×C₁₃	—	4	2	no	—
234	C₂×C₁₃	#2274	1	1	yes	characteristic
235	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
236	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
237	C₂×C₁₃	#2990	1	2	yes	—
238	C₂×C₁₃	#2991	1	2	yes	—
239	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
240	C₂²×C₄	—	2	4	no	—
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	2	1	no	—
243	C₂²×C₄	—	2	1	no	—
244	C₂²×C₄	—	2	1	no	—
245	C₂²×C₄	—	2	1	no	—
246	C₂²×C₄	C₄²×C₁₃	1	4	yes	—
247	C₂²×C₄	C₄²×C₁₃	1	4	yes	—
248	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
249	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
250	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
251	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
252	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
253	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
254	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
255	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
256	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
257	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
258	M₁₆	—	4	8	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	4	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
266	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
267	C₂×C₈	C₂²×C₄×C₁₃	1	8	yes	—
268	C₄⋊C₄	—	2	4	no	—
269	C₄⋊C₄	C₁₃×M₁₆	1	8	yes	complemented
270	C₂²⋊C₄	—	2	8	no	—
271	C₄²	—	2	8	no	—
272	C₄²	—	2	8	no	—
273	C₄²	—	2	2	no	—
274	C₄²	—	2	2	no	—
275	C₄²	—	2	2	no	—
276	C₄²	—	2	2	no	—
277	C₄²	C₄²×C₁₃	1	4	yes	—
278	C₄²	C₄²×C₁₃	1	4	yes	—
279	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
280	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
281	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
282	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
283	C₁₃	#20550	1	1	yes	characteristic, direct product factor, Sylow
284	C₂³	—	2	1	no	—
285	C₂³	—	2	1	no	—
286	C₂³	—	2	2	no	—
287	C₂³	—	2	2	no	—
288	C₂³	C₂×C₄²×C₁₃	1	2	yes	—
289	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
306	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
307	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
308	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
309	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
310	C₂×C₄	C₂×C₁₃×M₁₆	1	8	yes	—
311	C₂×C₄	C₂×C₁₃×M₁₆	1	4	yes	—
312	C₂×C₄	C₁₃×#131	1	4	yes	—
313	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
314	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
315	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
316	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
317	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
318	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
319	C₈	—	2	8	no	—
320	C₈	—	2	4	no	—
321	C₈	—	2	4	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	4	2	no	—
326	C₂²	—	4	2	no	—
327	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
328	C₂²	C₁₃×#520	1	1	yes	characteristic
329	C₂²	C₁₃×#520	1	1	yes	characteristic
330	C₂²	C₂²×C₁₃×M₁₆	1	2	yes	—
331	C₂²	C₂×C₁₃×#131	1	2	yes	—
332	C₄	—	2	2	no	—
333	C₄	—	2	2	no	—
334	C₄	—	2	2	no	—
335	C₄	—	2	8	no	—
336	C₄	—	4	4	no	—
337	C₄	C₄×C₁₃×M₁₆	1	4	yes	—
338	C₄	C₁₃×#405	1	4	yes	—
339	C₄	C₁₃×#518	1	1	yes	characteristic
340	C₄	C₁₃×#519	1	1	yes	characteristic
341	C₄	C₁₃×#520	1	1	yes	characteristic
342	C₄	C₁₃×#520	1	1	yes	characteristic
343	C₂	—	4	2	no	—
344	C₂	C₁₃×#2274	1	1	yes	characteristic
345	C₂	C₂×C₄×C₁₃×M₁₆	1	1	yes	characteristic
346	C₂	C₂×C₁₃×#405	1	1	yes	characteristic
347	C₂	C₁₃×#2990	1	2	yes	—
348	C₂	C₁₃×#2991	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×#1770	C₂	semidirect
5. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
6. C₁₃×#1767	C₂	semidirect
7. C₄×C₁₃×C₄⋊C₈	C₂	semidirect
12. C₁₃×#431	C₄	semidirect
13. C₁₃×#423	C₄	semidirect
65. #20550	C₁₃	direct (N × H)
96. C₁₃×C₄⋊C₄	M₁₆	semidirect
113. #1770	C₂×C₁₃	semidirect
114. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
115. #1767	C₂×C₁₃	semidirect
116. C₄×C₄⋊C₈	C₂×C₁₃	semidirect
159. #431	C₄×C₁₃	semidirect
160. #423	C₄×C₁₃	semidirect
269. C₄⋊C₄	C₁₃×M₁₆	semidirect
283. C₁₃	#20550	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×#431	2
C₂×C₁₃×#423	2
C₄×C₁₃×#117	2
C₁₃×#1770	2
C₈×C₁₃×C₄⋊C₄	2
C₁₃×#1767	2
C₄×C₁₃×C₄⋊C₈	2
C₁₃×#1753	2
#20550	13

Subgroups — C13×#20550 #15706889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20550 #15706889