Subgroups — C₁₃×#20468 #15706807

Order 3328.

950 conjugacy classes of subgroups.

The subgroup lattice has 396 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	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1768	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1750	C₂	1	2	yes	maximal
7	C₁₃×#1749	C₂	1	1	yes	maximal, characteristic
8	C₄×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1745	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1744	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1726	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#433	C₄	1	16	yes	complemented
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₃×#97	C₂²	1	2	yes	—
21	C₂×C₁₃×#97	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	2	yes	—
26	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
27	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
28	C₄×C₁₃×C₂²⋊C₄	C₄	1	2	yes	—
29	C₄×C₁₃×C₂²⋊C₄	C₄	1	2	yes	—
30	C₁₃×#376	C₂²	1	1	yes	characteristic
31	C₁₃×#376	C₂²	1	1	yes	characteristic
32	C₄³×C₁₃	C₂²	1	1	yes	characteristic
33	C₄³×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#336	C₂²	1	1	yes	characteristic
35	C₁₃×#336	C₂²	1	1	yes	characteristic
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	2	yes	—
40	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₁₃×#117	—	2	2	no	—
47	C₁₃×#117	—	2	2	no	—
48	C₁₃×#117	C₂×C₄	1	8	yes	—
49	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₃	—	2	4	no	—
56	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
60	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
68	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
69	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
70	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
71	C₁₃×#97	—	2	4	no	—
72	C₁₃×#97	—	2	4	no	—
73	C₁₃×#97	C₂×C₄	1	8	yes	complemented
74	C₄×C₈×C₁₃	—	2	4	no	—
75	C₄×C₈×C₁₃	—	2	4	no	—
76	C₄×C₈×C₁₃	C₂×C₄	1	8	yes	complemented
77	C₁₃×#95	C₂×C₄	1	2	yes	—
78	C₁₃×#95	C₂×C₄	1	2	yes	—
79	C₁₃×#95	C₂×C₄	1	2	yes	—
80	C₁₃×#95	C₂×C₄	1	2	yes	—
81	#20468	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₃	—	2	1	no	—
85	C₂²×C₄×C₁₃	—	2	1	no	—
86	C₂²×C₄×C₁₃	—	2	4	no	—
87	C₂²×C₄×C₁₃	—	2	4	no	—
88	C₂²×C₄×C₁₃	—	4	2	no	—
89	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	2	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
109	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
110	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
111	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
112	C₁₃×C₄⋊C₄	—	2	4	no	—
113	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
114	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
115	C₁₃×C₂²⋊C₄	—	2	4	no	—
116	C₁₃×C₂²⋊C₄	C₄²	1	4	yes	—
117	C₁₃×C₂²⋊C₄	C₄²	1	4	yes	—
118	C₄²×C₁₃	—	2	4	no	—
119	C₄²×C₁₃	—	2	4	no	—
120	C₄²×C₁₃	—	2	4	no	—
121	C₄²×C₁₃	—	2	2	no	—
122	C₄²×C₁₃	—	2	1	no	—
123	C₄²×C₁₃	—	2	1	no	—
124	C₄²×C₁₃	—	4	2	no	—
125	C₄²×C₁₃	—	4	2	no	—
126	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
127	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
128	C₄²×C₁₃	#41	1	2	yes	—
129	C₄²×C₁₃	#41	1	4	yes	—
130	C₄²×C₁₃	#41	1	2	yes	—
131	C₂×#433	C₂×C₁₃	1	2	yes	—
132	C₄×#117	C₂×C₁₃	1	1	yes	characteristic
133	#1768	C₂×C₁₃	1	2	yes	complemented
134	#1767	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
136	#1750	C₂×C₁₃	1	2	yes	—
137	#1749	C₂×C₁₃	1	1	yes	characteristic
138	C₄×C₂²⋊C₈	C₂×C₁₃	1	1	yes	characteristic
139	#1745	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#1744	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#1726	C₂×C₁₃	1	2	yes	complemented
142	C₂³×C₁₃	—	2	1	no	—
143	C₂³×C₁₃	—	2	1	no	—
144	C₂³×C₁₃	—	2	2	no	—
145	C₂³×C₁₃	—	2	2	no	—
146	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
147	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	2	2	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	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	4	no	—
161	C₂×C₄×C₁₃	—	2	4	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	4	8	no	—
166	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
167	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
168	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
169	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
170	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
171	C₂×C₄×C₁₃	#117	1	4	yes	—
172	C₂×C₄×C₁₃	#117	1	4	yes	—
173	C₂×C₄×C₁₃	#131	1	4	yes	—
174	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
175	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
176	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
178	C₈×C₁₃	—	2	4	no	—
179	C₈×C₁₃	—	2	4	no	—
180	C₈×C₁₃	—	2	4	no	—
181	C₈×C₁₃	—	2	4	no	—
182	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
183	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
184	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
185	#433	C₄×C₁₃	1	16	yes	complemented
186	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
187	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
188	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
189	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
190	C₂×#97	C₂²×C₁₃	1	2	yes	—
191	C₂×#97	C₂²×C₁₃	1	2	yes	—
192	C₂×#97	C₂²×C₁₃	1	2	yes	—
193	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
194	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
195	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
196	C₄×C₄⋊C₄	C₄×C₁₃	1	2	yes	—
197	C₄×C₄⋊C₄	C₄×C₁₃	1	2	yes	—
198	C₄×C₂²⋊C₄	C₄×C₁₃	1	2	yes	—
199	C₄×C₂²⋊C₄	C₄×C₁₃	1	2	yes	—
200	#376	C₂²×C₁₃	1	1	yes	characteristic
201	#376	C₂²×C₁₃	1	1	yes	characteristic
202	C₄³	C₂²×C₁₃	1	1	yes	characteristic
203	C₄³	C₂²×C₁₃	1	1	yes	characteristic
204	#336	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	1	yes	characteristic
208	#336	C₂²×C₁₃	1	1	yes	characteristic
209	#336	C₂²×C₁₃	1	2	yes	—
210	C₂²×C₁₃	—	2	2	no	—
211	C₂²×C₁₃	—	2	2	no	—
212	C₂²×C₁₃	—	2	2	no	—
213	C₂²×C₁₃	—	4	2	no	—
214	C₂²×C₁₃	—	4	2	no	—
215	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
216	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
217	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
218	C₂²×C₁₃	C₂×#131	1	2	yes	—
219	C₂²×C₁₃	#568	1	2	yes	—
220	C₄×C₁₃	—	2	2	no	—
221	C₄×C₁₃	—	2	2	no	—
222	C₄×C₁₃	—	2	2	no	—
223	C₄×C₁₃	—	2	2	no	—
224	C₄×C₁₃	—	2	4	no	—
225	C₄×C₁₃	—	2	4	no	—
226	C₄×C₁₃	—	2	4	no	—
227	C₄×C₁₃	—	2	2	no	—
228	C₄×C₁₃	—	4	2	no	—
229	C₄×C₁₃	C₄×#41	1	2	yes	—
230	C₄×C₁₃	C₄×#41	1	2	yes	—
231	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
232	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
234	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
235	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
236	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
237	#117	—	2	2	no	—
238	#117	—	2	2	no	—
239	#117	C₂×C₄×C₁₃	1	8	yes	—
240	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
241	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
243	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
244	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
245	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
246	C₂×C₄²	—	2	4	no	—
247	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
248	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
249	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
250	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
251	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
252	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
254	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
257	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
258	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	complemented
259	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	complemented
260	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
261	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
262	#97	—	2	4	no	—
263	#97	—	2	4	no	—
264	#97	C₂×C₄×C₁₃	1	8	yes	complemented
265	C₄×C₈	—	2	4	no	—
266	C₄×C₈	—	2	4	no	—
267	C₄×C₈	C₂×C₄×C₁₃	1	8	yes	complemented
268	#95	C₂×C₄×C₁₃	1	2	yes	—
269	#95	C₂×C₄×C₁₃	1	2	yes	—
270	#95	C₂×C₄×C₁₃	1	2	yes	—
271	#95	C₂×C₄×C₁₃	1	2	yes	—
272	C₂×C₁₃	—	4	2	no	—
273	C₂×C₁₃	C₄×#117	1	1	yes	characteristic
274	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
275	C₂×C₁₃	#2875	1	1	yes	characteristic
276	C₂×C₁₃	#2924	1	2	yes	—
277	C₂×C₁₃	#2925	1	2	yes	—
278	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
286	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
287	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
288	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
289	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
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	2	yes	—
294	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
295	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
305	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
306	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
307	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	C₄²×C₁₃	1	4	yes	—
310	C₄⋊C₄	C₄²×C₁₃	1	4	yes	—
311	C₂²⋊C₄	—	2	4	no	—
312	C₂²⋊C₄	C₄²×C₁₃	1	4	yes	—
313	C₂²⋊C₄	C₄²×C₁₃	1	4	yes	—
314	C₄²	—	2	4	no	—
315	C₄²	—	2	4	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	1	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	4	2	no	—
321	C₄²	—	4	2	no	—
322	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
323	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
324	C₄²	C₁₃×#41	1	2	yes	—
325	C₄²	C₁₃×#41	1	4	yes	—
326	C₄²	C₁₃×#41	1	2	yes	—
327	C₁₃	#20468	1	1	yes	characteristic, direct product factor, Sylow
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	C₂×C₄²×C₁₃	1	2	yes	—
333	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	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	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	8	no	—
352	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
353	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
354	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
355	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
356	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
357	C₂×C₄	C₁₃×#117	1	4	yes	—
358	C₂×C₄	C₁₃×#117	1	4	yes	—
359	C₂×C₄	C₁₃×#131	1	4	yes	—
360	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
361	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
362	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
363	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
364	C₈	—	2	4	no	—
365	C₈	—	2	4	no	—
366	C₈	—	2	4	no	—
367	C₈	—	2	4	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	4	2	no	—
373	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
374	C₂²	C₂×C₁₃×#117	1	1	yes	characteristic
375	C₂²	C₂×C₁₃×#117	1	1	yes	characteristic
376	C₂²	C₂×C₁₃×#131	1	2	yes	—
377	C₂²	C₁₃×#568	1	2	yes	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	4	no	—
384	C₄	—	2	4	no	—
385	C₄	—	2	4	no	—
386	C₄	—	4	2	no	—
387	C₄	C₄×C₁₃×#41	1	2	yes	—
388	C₄	C₄×C₁₃×#41	1	2	yes	—
389	C₂	—	4	2	no	—
390	C₂	C₄×C₁₃×#117	1	1	yes	characteristic
391	C₂	C₄×C₁₃×#131	1	1	yes	characteristic
392	C₂	C₁₃×#2875	1	1	yes	characteristic
393	C₂	C₁₃×#2924	1	2	yes	—
394	C₂	C₁₃×#2925	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×#1768	C₂	semidirect
4. C₁₃×#1767	C₂	semidirect
5. C₄×C₁₃×C₄⋊C₈	C₂	semidirect
9. C₁₃×#1745	C₂	semidirect
10. C₁₃×#1744	C₂	semidirect
11. C₁₃×#1726	C₂	semidirect
15. C₁₃×#433	C₄	semidirect
67. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
68. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
73. C₁₃×#97	C₂×C₄	semidirect
76. C₄×C₈×C₁₃	C₂×C₄	semidirect
81. #20468	C₁₃	direct (N × H)
133. #1768	C₂×C₁₃	semidirect
134. #1767	C₂×C₁₃	semidirect
135. C₄×C₄⋊C₈	C₂×C₁₃	semidirect
139. #1745	C₂×C₁₃	semidirect
140. #1744	C₂×C₁₃	semidirect
141. #1726	C₂×C₁₃	semidirect
185. #433	C₄×C₁₃	semidirect
258. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
259. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
264. #97	C₂×C₄×C₁₃	semidirect
267. C₄×C₈	C₂×C₄×C₁₃	semidirect
327. C₁₃	#20468	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
C₄×C₁₃×#117	2
C₁₃×#1768	2
C₁₃×#1767	2
C₄×C₁₃×C₄⋊C₈	2
C₁₃×#1750	2
C₁₃×#1749	2
C₄×C₁₃×C₂²⋊C₈	2
C₁₃×#1745	2
C₁₃×#1744	2
C₁₃×#1726	2
#20468	13

Subgroups — C13×#20468 #15706807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20468 #15706807