Subgroups — C₁₃×#20521 #15706860

Order 3328.

866 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1771	C₂	1	2	yes	maximal
5	C₁₃×#1770	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1770	C₂	1	2	yes	maximal
7	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1768	C₂	1	2	yes	maximal
9	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1726	C₂	1	2	yes	maximal
11	C₄×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#446	C₄	1	8	yes	complemented
14	C₈×Q₈×C₁₃	C₄	1	8	yes	complemented
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#97	C₂²	1	2	yes	—
20	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#97	C₂²	1	2	yes	—
24	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#391	C₄	1	2	yes	—
31	C₁₃×#389	C₄	1	2	yes	—
32	C₁₃×#387	C₄	1	4	yes	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₁₃×#376	C₂²	1	2	yes	—
36	C₄³×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#336	C₂²	1	2	yes	—
38	C₁₃×#336	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	2	yes	—
40	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
48	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
49	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
51	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
56	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
59	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
61	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
62	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
63	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
64	C₁₃×#97	—	2	2	no	—
65	C₁₃×#97	—	2	4	no	—
66	C₁₃×#97	—	2	2	no	—
67	C₁₃×#97	—	2	2	no	—
68	C₁₃×#97	C₂×C₄	1	8	yes	—
69	C₁₃×#97	Q₈	1	4	yes	complemented
70	C₄×C₈×C₁₃	—	2	4	no	—
71	C₄×C₈×C₁₃	—	2	4	no	—
72	C₄×C₈×C₁₃	C₂×C₄	1	8	yes	—
73	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
74	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
75	C₁₃×#95	C₂×C₄	1	2	yes	—
76	C₁₃×#95	C₂×C₄	1	4	yes	—
77	C₁₃×#95	C₂×C₄	1	4	yes	—
78	C₁₃×#95	C₂×C₄	1	4	yes	—
79	#20521	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂×Q₈×C₁₃	—	2	4	no	—
81	C₂×Q₈×C₁₃	C₄²	1	4	yes	—
82	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	1	no	—
95	C₂×C₈×C₁₃	—	2	1	no	—
96	C₂×C₈×C₁₃	—	2	1	no	—
97	C₂×C₈×C₁₃	—	2	1	no	—
98	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
99	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
100	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
102	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
105	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
106	C₂×C₈×C₁₃	#41	1	2	yes	—
107	C₂×C₈×C₁₃	#41	1	2	yes	—
108	C₁₃×C₄⋊C₄	—	2	4	no	—
109	C₁₃×C₄⋊C₄	—	4	4	no	—
110	C₁₃×C₄⋊C₄	C₄²	1	8	yes	—
111	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
112	C₄²×C₁₃	—	2	4	no	—
113	C₄²×C₁₃	—	2	2	no	—
114	C₄²×C₁₃	—	2	2	no	—
115	C₄²×C₁₃	—	2	1	no	—
116	C₄²×C₁₃	—	2	1	no	—
117	C₄²×C₁₃	—	4	2	no	—
118	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
119	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
120	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
121	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
122	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
123	C₄²×C₁₃	#41	1	2	yes	—
124	C₂×#446	C₂×C₁₃	1	1	yes	characteristic
125	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic
126	#2295	C₂×C₁₃	1	1	yes	characteristic
127	#1771	C₂×C₁₃	1	2	yes	—
128	#1770	C₂×C₁₃	1	2	yes	—
129	#1770	C₂×C₁₃	1	1	yes	characteristic
130	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
131	#1768	C₂×C₁₃	1	2	yes	—
132	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
133	#1726	C₂×C₁₃	1	2	yes	—
134	C₄×#97	C₂×C₁₃	1	1	yes	characteristic
135	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
136	Q₈×C₁₃	—	2	8	no	—
137	C₂×C₄×C₁₃	—	2	2	no	—
138	C₂×C₄×C₁₃	—	2	4	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	4	no	—
142	C₂×C₄×C₁₃	—	2	4	no	—
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	4	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	4	no	—
148	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
149	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
150	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
151	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
152	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
153	C₂×C₄×C₁₃	#131	1	4	yes	—
154	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
160	C₈×C₁₃	—	2	4	no	—
161	C₈×C₁₃	—	2	4	no	—
162	C₈×C₁₃	—	2	2	no	—
163	C₈×C₁₃	—	2	2	no	—
164	C₈×C₁₃	C₄×Q₈	1	4	yes	—
165	C₈×C₁₃	C₄×Q₈	1	4	yes	—
166	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
167	#446	C₄×C₁₃	1	8	yes	complemented
168	C₈×Q₈	C₄×C₁₃	1	8	yes	complemented
169	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
170	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
171	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
172	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
173	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
174	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
175	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
176	C₂×#97	C₂²×C₁₃	1	2	yes	—
177	C₂×#97	C₂²×C₁₃	1	2	yes	—
178	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
179	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
180	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
181	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
182	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
183	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
184	#391	C₄×C₁₃	1	2	yes	—
185	#389	C₄×C₁₃	1	2	yes	—
186	#387	C₄×C₁₃	1	4	yes	—
187	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
188	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
189	#376	C₂²×C₁₃	1	2	yes	—
190	C₄³	C₂²×C₁₃	1	1	yes	characteristic
191	#336	C₂²×C₁₃	1	2	yes	—
192	#336	C₂²×C₁₃	1	2	yes	—
193	#336	C₂²×C₁₃	1	2	yes	—
194	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
195	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
196	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
197	C₂²×C₁₃	C₂×#131	1	2	yes	—
198	C₂²×C₁₃	#568	1	2	yes	—
199	C₄×C₁₃	—	2	4	no	—
200	C₄×C₁₃	—	2	2	no	—
201	C₄×C₁₃	—	2	4	no	—
202	C₄×C₁₃	—	2	4	no	—
203	C₄×C₁₃	—	4	2	no	—
204	C₄×C₁₃	—	4	4	no	—
205	C₄×C₁₃	#405	1	4	yes	—
206	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
207	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
208	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
209	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
210	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
211	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
212	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
213	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
214	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
215	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
216	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
217	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
218	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
219	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
220	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
221	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
222	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
223	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
224	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
225	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
226	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
227	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
228	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
229	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
230	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
231	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
232	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
233	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
234	#97	—	2	2	no	—
235	#97	—	2	2	no	—
236	#97	—	2	4	no	—
237	#97	—	2	2	no	—
238	#97	C₂×C₄×C₁₃	1	8	yes	—
239	#97	Q₈×C₁₃	1	4	yes	complemented
240	C₄×C₈	—	2	4	no	—
241	C₄×C₈	—	2	4	no	—
242	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
243	C₄×C₈	C₂×C₄×C₁₃	1	8	yes	—
244	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
245	#95	C₂×C₄×C₁₃	1	4	yes	—
246	#95	C₂×C₄×C₁₃	1	4	yes	—
247	#95	C₂×C₄×C₁₃	1	2	yes	—
248	#95	C₂×C₄×C₁₃	1	4	yes	—
249	C₂×C₁₃	C₄²×Q₈	1	1	yes	characteristic
250	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
251	C₂×C₁₃	#2875	1	1	yes	characteristic
252	C₂×C₁₃	#2962	1	2	yes	—
253	C₂×C₁₃	#2969	1	2	yes	—
254	C₂×Q₈	—	2	4	no	—
255	C₂×Q₈	C₄²×C₁₃	1	4	yes	—
256	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
257	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
258	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
259	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
260	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
261	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
262	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
263	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	1	no	—
269	C₂×C₈	—	2	1	no	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	2	1	no	—
272	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
273	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
274	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
275	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
276	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
277	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
278	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
279	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
280	C₂×C₈	C₁₃×#41	1	2	yes	—
281	C₂×C₈	C₁₃×#41	1	2	yes	—
282	C₄⋊C₄	—	2	4	no	—
283	C₄⋊C₄	—	4	4	no	—
284	C₄⋊C₄	C₄²×C₁₃	1	8	yes	—
285	C₄⋊C₄	C₄²×C₁₃	1	4	yes	—
286	C₄²	—	2	4	no	—
287	C₄²	—	2	2	no	—
288	C₄²	—	2	1	no	—
289	C₄²	—	2	1	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	4	2	no	—
292	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
293	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
294	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
295	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
296	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
297	C₄²	C₁₃×#41	1	2	yes	—
298	C₁₃	#20521	1	1	yes	characteristic, direct product factor, Sylow
299	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
300	Q₈	—	2	8	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
313	C₂×C₄	C₂×C₄²×C₁₃	1	4	yes	—
314	C₂×C₄	C₂×C₄²×C₁₃	1	4	yes	—
315	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
316	C₂×C₄	C₄×Q₈×C₁₃	1	4	yes	—
317	C₂×C₄	C₁₃×#131	1	4	yes	—
318	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
319	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
320	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
321	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
322	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
323	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
324	C₈	—	2	4	no	—
325	C₈	—	2	4	no	—
326	C₈	—	2	2	no	—
327	C₈	—	2	2	no	—
328	C₈	C₄×Q₈×C₁₃	1	4	yes	—
329	C₈	C₄×Q₈×C₁₃	1	4	yes	—
330	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
331	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
332	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
333	C₂²	C₂×C₁₃×#131	1	2	yes	—
334	C₂²	C₁₃×#568	1	2	yes	—
335	C₄	—	2	4	no	—
336	C₄	—	2	2	no	—
337	C₄	—	2	4	no	—
338	C₄	—	2	4	no	—
339	C₄	—	4	2	no	—
340	C₄	—	4	4	no	—
341	C₄	C₁₃×#405	1	4	yes	—
342	C₄	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
343	C₄	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
344	C₄	C₄×C₁₃×#41	1	1	yes	characteristic
345	C₄	C₄×C₁₃×#41	1	1	yes	characteristic
346	C₂	C₄²×Q₈×C₁₃	1	1	yes	characteristic
347	C₂	C₂×C₁₃×#405	1	1	yes	characteristic
348	C₂	C₁₃×#2875	1	1	yes	characteristic
349	C₂	C₁₃×#2962	1	2	yes	—
350	C₂	C₁₃×#2969	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂²	C₂²×C₄²×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle, prime radical	C₂³×C₁₃	C₂³×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
13. C₁₃×#446	C₄	semidirect
14. C₈×Q₈×C₁₃	C₄	semidirect
69. C₁₃×#97	Q₈	semidirect
79. #20521	C₁₃	direct (N × H)
167. #446	C₄×C₁₃	semidirect
168. C₈×Q₈	C₄×C₁₃	semidirect
239. #97	Q₈×C₁₃	semidirect
298. C₁₃	#20521	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×#446	2
C₂×C₈×Q₈×C₁₃	2
C₁₃×#2295	2
C₁₃×#1771	2
C₁₃×#1770	2
C₈×C₁₃×C₄⋊C₄	2
C₁₃×#1768	2
C₄×C₁₃×C₄⋊C₈	2
C₁₃×#1726	2
C₄×C₁₃×#97	2
#20521	13

Subgroups — C13×#20521 #15706860

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20521 #15706860