Subgroups — C₁₃×#22628 #15708967

Order 3328.

724 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1940	C₂	1	2	yes	maximal, complemented
3	C₁₃×#1917	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1916	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1798	C₂	1	2	yes	maximal
6	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1771	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1750	C₂	1	2	yes	maximal
9	C₁₃×#1749	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×#117	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#97	C₂²	1	2	yes	—
19	C₂×C₁₃×#97	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
21	C₁₃×#384	C₄	1	1	yes	characteristic
22	C₁₃×#384	C₄	1	1	yes	characteristic
23	C₁₃×#382	C₄	1	2	yes	—
24	C₁₃×#380	C₄	1	2	yes	—
25	C₁₃×#380	C₄	1	1	yes	characteristic
26	C₁₃×#380	C₄	1	1	yes	characteristic
27	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
29	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₁₃×#336	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	C₁₃×#336	C₂²	1	1	yes	characteristic
36	C₁₃×#336	C₂²	1	1	yes	characteristic
37	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
44	C₁₃×#117	—	4	2	no	—
45	C₁₃×#117	—	4	2	no	—
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×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₁₃	—	2	4	no	—
57	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×C₄⋊C₈	—	2	4	no	—
64	C₁₃×C₄⋊C₈	—	4	2	no	—
65	C₁₃×C₄⋊C₈	—	4	2	no	—
66	C₁₃×C₂²⋊C₈	—	2	2	no	—
67	C₁₃×C₂²⋊C₈	—	2	4	no	—
68	C₁₃×C₂²⋊C₈	Q₈	1	4	yes	—
69	C₁₃×#97	—	2	4	no	—
70	C₁₃×#97	—	4	2	no	—
71	C₄×C₈×C₁₃	—	4	2	no	—
72	C₁₃×#95	C₂×C₄	1	2	yes	—
73	C₁₃×#95	C₂×C₄	1	2	yes	—
74	C₁₃×#95	C₂×C₄	1	2	yes	—
75	C₁₃×#95	C₂×C₄	1	2	yes	—
76	#22628	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	—	2	2	no	—
79	C₂²×C₄×C₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₃	—	2	2	no	—
82	C₂²×C₄×C₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₃	—	4	1	no	—
84	C₂²×C₄×C₁₃	—	4	1	no	—
85	C₂²×C₄×C₁₃	—	4	1	no	—
86	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₁₃	C₂²×C₄	1	2	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	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	C₂×Q₈	1	2	yes	—
96	C₂²×C₄×C₁₃	#41	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
98	C₂×C₈×C₁₃	—	2	2	no	—
99	C₂×C₈×C₁₃	—	2	2	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	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	—	2	2	no	—
109	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
110	C₁₃×C₄⋊C₄	—	2	4	no	—
111	C₁₃×C₄⋊C₄	—	4	1	no	—
112	C₁₃×C₄⋊C₄	—	4	1	no	—
113	C₁₃×C₄⋊C₄	—	4	1	no	—
114	C₁₃×C₄⋊C₄	—	4	1	no	—
115	C₁₃×C₄⋊C₄	—	4	2	no	—
116	C₁₃×C₄⋊C₄	—	4	2	no	—
117	C₁₃×C₄⋊C₄	—	4	2	no	—
118	C₁₃×C₂²⋊C₄	—	4	2	no	—
119	C₁₃×C₂²⋊C₄	—	4	2	no	—
120	C₄²×C₁₃	—	2	2	no	—
121	C₄²×C₁₃	—	2	2	no	—
122	C₄²×C₁₃	—	2	2	no	—
123	C₄²×C₁₃	—	2	2	no	—
124	C₄²×C₁₃	—	2	2	no	—
125	C₄²×C₁₃	—	2	2	no	—
126	C₄²×C₁₃	—	2	2	no	—
127	C₄²×C₁₃	#41	1	4	yes	—
128	#2285	C₂×C₁₃	1	1	yes	characteristic
129	#1940	C₂×C₁₃	1	2	yes	complemented
130	#1917	C₂×C₁₃	1	2	yes	complemented
131	#1916	C₂×C₁₃	1	2	yes	complemented
132	#1798	C₂×C₁₃	1	2	yes	—
133	#1797	C₂×C₁₃	1	1	yes	characteristic
134	#1771	C₂×C₁₃	1	2	yes	complemented
135	#1750	C₂×C₁₃	1	2	yes	—
136	#1749	C₂×C₁₃	1	1	yes	characteristic
137	C₂³×C₁₃	—	2	1	no	—
138	C₂³×C₁₃	—	2	1	no	—
139	C₂³×C₁₃	—	2	1	no	—
140	C₂³×C₁₃	—	2	1	no	—
141	C₂³×C₁₃	—	2	1	no	—
142	C₂³×C₁₃	—	2	1	no	—
143	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
144	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃	—	2	1	no	—
146	C₂×C₄×C₁₃	—	2	1	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	2	1	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	4	no	—
154	C₂×C₄×C₁₃	—	2	4	no	—
155	C₂×C₄×C₁₃	—	2	1	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	2	no	—
161	C₂×C₄×C₁₃	—	2	2	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	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	4	4	no	—
171	C₂×C₄×C₁₃	—	4	4	no	—
172	C₂×C₄×C₁₃	#117	1	2	yes	—
173	C₂×C₄×C₁₃	#117	1	2	yes	—
174	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
175	C₂×C₄×C₁₃	#131	1	2	yes	—
176	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
179	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
180	C₈×C₁₃	—	2	4	no	—
181	C₈×C₁₃	—	4	2	no	—
182	C₈×C₁₃	—	4	2	no	—
183	C₈×C₁₃	—	4	2	no	—
184	C₂×#117	C₂²×C₁₃	1	2	yes	—
185	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
186	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
187	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
188	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
189	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
190	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×#97	C₂²×C₁₃	1	2	yes	—
193	C₂×#97	C₂²×C₁₃	1	2	yes	—
194	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
195	#384	C₄×C₁₃	1	1	yes	characteristic
196	#384	C₄×C₁₃	1	1	yes	characteristic
197	#382	C₄×C₁₃	1	2	yes	—
198	#380	C₄×C₁₃	1	2	yes	—
199	#380	C₄×C₁₃	1	1	yes	characteristic
200	#380	C₄×C₁₃	1	1	yes	characteristic
201	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
202	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
203	C₄×C₄⋊C₄	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	2	yes	—
208	#336	C₂²×C₁₃	1	2	yes	—
209	#336	C₂²×C₁₃	1	2	yes	—
210	#336	C₂²×C₁₃	1	2	yes	—
211	C₂²×C₁₃	—	2	2	no	—
212	C₂²×C₁₃	—	2	2	no	—
213	C₂²×C₁₃	—	2	2	no	—
214	C₂²×C₁₃	—	4	1	no	—
215	C₂²×C₁₃	—	4	1	no	—
216	C₂²×C₁₃	—	4	1	no	—
217	C₂²×C₁₃	—	4	1	no	—
218	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
219	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
220	C₂²×C₁₃	#518	1	1	yes	characteristic
221	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
222	C₂²×C₁₃	#568	1	1	yes	characteristic
223	C₂²×C₁₃	#568	1	1	yes	characteristic
224	C₂²×C₁₃	#568	1	1	yes	characteristic
225	C₄×C₁₃	—	2	2	no	—
226	C₄×C₁₃	—	2	2	no	—
227	C₄×C₁₃	—	2	2	no	—
228	C₄×C₁₃	—	2	2	no	—
229	C₄×C₁₃	—	4	1	no	—
230	C₄×C₁₃	—	4	2	no	—
231	C₄×C₁₃	—	4	2	no	—
232	C₄×C₁₃	—	4	2	no	—
233	C₄×C₁₃	—	4	2	no	—
234	C₄×C₁₃	#553	1	2	yes	—
235	C₄×C₁₃	#554	1	2	yes	—
236	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
237	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
238	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
240	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
241	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
242	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
243	#117	—	4	2	no	—
244	#117	—	4	2	no	—
245	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
246	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
247	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
248	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
253	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
254	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
255	C₂×C₄²	—	2	4	no	—
256	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
257	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
258	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
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	—	2	4	no	—
263	C₄⋊C₈	—	4	2	no	—
264	C₄⋊C₈	—	4	2	no	—
265	C₂²⋊C₈	—	2	4	no	—
266	C₂²⋊C₈	—	2	2	no	—
267	C₂²⋊C₈	Q₈×C₁₃	1	4	yes	—
268	#97	—	2	4	no	—
269	#97	—	4	2	no	—
270	C₄×C₈	—	4	2	no	—
271	#95	C₂×C₄×C₁₃	1	2	yes	—
272	#95	C₂×C₄×C₁₃	1	2	yes	—
273	#95	C₂×C₄×C₁₃	1	2	yes	—
274	#95	C₂×C₄×C₁₃	1	2	yes	—
275	C₂×C₁₃	—	4	2	no	—
276	C₂×C₁₃	#2345	1	1	yes	characteristic
277	C₂×C₁₃	#2921	1	1	yes	characteristic
278	C₂×C₁₃	#2924	1	1	yes	characteristic
279	C₂×C₁₃	#2961	1	1	yes	characteristic
280	C₂×C₁₃	#2962	1	1	yes	characteristic
281	C₂×C₁₃	#2980	1	1	yes	characteristic
282	C₂×C₁₃	#2981	1	1	yes	characteristic
283	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
294	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
295	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
296	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
297	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
301	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
302	C₂²×C₄	C₁₃×#41	1	2	yes	—
303	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	C₁₃×#41	1	4	yes	—
334	C₁₃	#22628	1	1	yes	characteristic, direct product factor, Sylow
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	C₄×Q₈×C₁₃	1	2	yes	—
342	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	C₁₃×#117	1	2	yes	—
371	C₂×C₄	C₁₃×#117	1	2	yes	—
372	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
373	C₂×C₄	C₁₃×#131	1	2	yes	—
374	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
375	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
376	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
377	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
378	C₈	—	2	4	no	—
379	C₈	—	4	2	no	—
380	C₈	—	4	2	no	—
381	C₈	—	4	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	C₂×C₁₃×#117	1	1	yes	characteristic
390	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
391	C₂²	C₁₃×#518	1	1	yes	characteristic
392	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
393	C₂²	C₁₃×#568	1	1	yes	characteristic
394	C₂²	C₁₃×#568	1	1	yes	characteristic
395	C₂²	C₁₃×#568	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	2	no	—
405	C₄	C₁₃×#553	1	2	yes	—
406	C₄	C₁₃×#554	1	2	yes	—
407	C₂	—	4	2	no	—
408	C₂	C₁₃×#2345	1	1	yes	characteristic
409	C₂	C₁₃×#2921	1	1	yes	characteristic
410	C₂	C₁₃×#2924	1	1	yes	characteristic
411	C₂	C₁₃×#2961	1	1	yes	characteristic
412	C₂	C₁₃×#2962	1	1	yes	characteristic
413	C₂	C₁₃×#2980	1	1	yes	characteristic
414	C₂	C₁₃×#2981	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂⁴×C₁₃	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₃×#1940	C₂	semidirect
3. C₁₃×#1917	C₂	semidirect
4. C₁₃×#1916	C₂	semidirect
7. C₁₃×#1771	C₂	semidirect
76. #22628	C₁₃	direct (N × H)
129. #1940	C₂×C₁₃	semidirect
130. #1917	C₂×C₁₃	semidirect
131. #1916	C₂×C₁₃	semidirect
134. #1771	C₂×C₁₃	semidirect
334. C₁₃	#22628	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#2285	2
C₁₃×#1940	2
C₁₃×#1917	2
C₁₃×#1916	2
C₁₃×#1798	2
C₁₃×#1797	2
C₁₃×#1771	2
C₁₃×#1750	2
C₁₃×#1749	2
#22628	13

Subgroups — C13×#22628 #15708967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22628 #15708967