Subgroups — C₁₃×#22436 #15708775

Order 3328.

1818 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#442	C₂	1	2	yes	maximal, complemented
3	D₄×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1972	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1879	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1807	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1786	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1752	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
10	C₂²×C₁₃×D₈	—	2	8	no	—
11	C₂²×C₁₃×D₈	C₄	1	8	yes	complemented
12	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
17	C₂²×C₁₃×C₂²⋊C₄	—	2	2	no	—
18	C₁₃×#442	—	2	8	no	—
19	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
20	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
21	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
22	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
24	C₁₃×#390	C₂²	1	4	yes	complemented
25	C₁₃×#386	—	2	4	no	—
26	C₁₃×#380	C₂²	1	2	yes	—
27	C₁₃×#379	—	2	2	no	—
28	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₁₃×#340	C₂²	1	2	yes	complemented
30	C₁₃×#336	C₂²	1	2	yes	complemented
31	C₂⁵×C₁₃	—	2	2	no	—
32	C₂²×D₄×C₁₃	—	2	8	no	—
33	C₂²×D₄×C₁₃	—	2	2	no	—
34	C₂²×D₄×C₁₃	—	2	4	no	—
35	C₂²×D₄×C₁₃	—	4	4	no	—
36	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
37	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
38	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₃	—	2	4	no	—
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂×C₁₃×D₈	—	2	8	no	—
42	C₂×C₁₃×D₈	—	2	32	no	—
43	C₂×C₁₃×D₈	—	2	4	no	—
44	C₂×C₁₃×D₈	C₂×C₄	1	4	yes	—
45	C₂×C₁₃×D₈	C₂×C₄	1	8	yes	complemented
46	C₂×C₁₃×D₈	C₂×C₄	1	4	yes	complemented
47	C₂×C₁₃×D₈	D₄	1	8	yes	—
48	C₂²×C₈×C₁₃	—	2	4	no	—
49	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₄×D₄×C₁₃	—	2	8	no	—
54	C₄×D₄×C₁₃	—	4	4	no	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
61	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
62	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
63	C₁₃×#106	—	2	4	no	—
64	C₁₃×#102	—	2	8	no	—
65	C₁₃×#102	—	4	4	no	—
66	C₁₃×C₂²⋊C₈	—	2	2	no	—
67	C₁₃×#97	—	2	4	no	—
68	C₁₃×#95	—	2	2	no	—
69	C₁₃×#95	D₄	1	2	yes	—
70	#22436	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₂⁴×C₁₃	—	2	2	no	—
72	C₂⁴×C₁₃	—	2	2	no	—
73	C₂⁴×C₁₃	—	2	8	no	—
74	C₂⁴×C₁₃	—	4	8	no	—
75	C₂⁴×C₁₃	—	4	4	no	—
76	C₂⁴×C₁₃	—	4	4	no	—
77	C₂⁴×C₁₃	—	8	4	no	—
78	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
79	C₂×D₄×C₁₃	—	2	16	no	—
80	C₂×D₄×C₁₃	—	2	8	no	—
81	C₂×D₄×C₁₃	—	2	4	no	—
82	C₂×D₄×C₁₃	—	2	2	no	—
83	C₂×D₄×C₁₃	—	2	2	no	—
84	C₂×D₄×C₁₃	—	2	4	no	—
85	C₂×D₄×C₁₃	—	2	4	no	—
86	C₂×D₄×C₁₃	—	4	8	no	—
87	C₂×D₄×C₁₃	—	4	16	no	—
88	C₂×D₄×C₁₃	—	4	8	no	—
89	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
90	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
91	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	4	no	—
95	C₂²×C₄×C₁₃	—	4	8	no	—
96	C₂²×C₄×C₁₃	—	4	8	no	—
97	C₂²×C₄×C₁₃	—	8	4	no	—
98	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	#41	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
103	C₁₃×D₈	—	2	16	no	—
104	C₁₃×D₈	—	2	8	no	—
105	C₁₃×D₈	C₂²⋊C₄	1	16	yes	complemented
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	8	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
114	C₁₃×C₄⋊C₄	—	2	4	no	—
115	C₁₃×C₄⋊C₄	—	2	4	no	—
116	C₁₃×C₂²⋊C₄	—	2	4	no	—
117	C₁₃×C₂²⋊C₄	—	4	8	no	—
118	C₁₃×C₂²⋊C₄	—	4	8	no	—
119	C₁₃×C₂²⋊C₄	—	4	4	no	—
120	C₁₃×C₂²⋊C₄	—	8	4	no	—
121	C₄²×C₁₃	—	2	2	no	—
122	C₄²×C₁₃	—	2	2	no	—
123	C₂³×D₈	C₂×C₁₃	1	1	yes	characteristic
124	C₂×#442	C₂×C₁₃	1	2	yes	complemented
125	D₄×C₂²⋊C₄	C₂×C₁₃	1	2	yes	complemented
126	#1972	C₂×C₁₃	1	2	yes	complemented
127	#1879	C₂×C₁₃	1	4	yes	complemented
128	#1807	C₂×C₁₃	1	1	yes	characteristic, complemented
129	#1786	C₂×C₁₃	1	2	yes	complemented
130	#1752	C₂×C₁₃	1	1	yes	characteristic, complemented
131	C₂³×C₁₃	—	2	2	no	—
132	C₂³×C₁₃	—	2	2	no	—
133	C₂³×C₁₃	—	2	4	no	—
134	C₂³×C₁₃	—	2	8	no	—
135	C₂³×C₁₃	—	2	4	no	—
136	C₂³×C₁₃	—	4	16	no	—
137	C₂³×C₁₃	—	4	2	no	—
138	C₂³×C₁₃	—	4	2	no	—
139	C₂³×C₁₃	—	4	4	no	—
140	C₂³×C₁₃	—	4	4	no	—
141	C₂³×C₁₃	—	4	2	no	—
142	C₂³×C₁₃	—	4	2	no	—
143	C₂³×C₁₃	—	4	4	no	—
144	C₂³×C₁₃	—	4	16	no	—
145	C₂³×C₁₃	—	8	8	no	—
146	C₂³×C₁₃	—	8	16	no	—
147	C₂³×C₁₃	—	8	16	no	—
148	C₂³×C₁₃	C₄×D₄	1	2	yes	—
149	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
150	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
151	D₄×C₁₃	—	2	4	no	—
152	D₄×C₁₃	—	2	4	no	—
153	D₄×C₁₃	—	2	4	no	—
154	D₄×C₁₃	—	2	8	no	—
155	D₄×C₁₃	—	4	16	no	—
156	D₄×C₁₃	—	4	4	no	—
157	D₄×C₁₃	C₂×C₂²⋊C₄	1	8	yes	complemented
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	4	no	—
162	C₂×C₄×C₁₃	—	2	4	no	—
163	C₂×C₄×C₁₃	—	2	4	no	—
164	C₂×C₄×C₁₃	—	2	4	no	—
165	C₂×C₄×C₁₃	—	4	4	no	—
166	C₂×C₄×C₁₃	—	4	4	no	—
167	C₂×C₄×C₁₃	—	4	4	no	—
168	C₂×C₄×C₁₃	—	8	16	no	—
169	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
172	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
174	C₈×C₁₃	—	2	2	no	—
175	C₈×C₁₃	—	4	2	no	—
176	C₈×C₁₃	C₂×C₂²⋊C₄	1	4	yes	complemented
177	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
178	C₂²×D₈	—	2	8	no	—
179	C₂²×D₈	C₄×C₁₃	1	8	yes	complemented
180	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
181	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
182	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
183	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
184	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
185	C₂²×C₂²⋊C₄	—	2	2	no	—
186	#442	—	2	8	no	—
187	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
188	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
189	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
190	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
192	#390	C₂²×C₁₃	1	4	yes	complemented
193	#386	—	2	4	no	—
194	#380	C₂²×C₁₃	1	2	yes	—
195	#379	—	2	2	no	—
196	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
197	#340	C₂²×C₁₃	1	2	yes	complemented
198	#336	C₂²×C₁₃	1	2	yes	complemented
199	C₂²×C₁₃	—	2	2	no	—
200	C₂²×C₁₃	—	2	2	no	—
201	C₂²×C₁₃	—	2	8	no	—
202	C₂²×C₁₃	—	2	8	no	—
203	C₂²×C₁₃	—	4	4	no	—
204	C₂²×C₁₃	—	4	4	no	—
205	C₂²×C₁₃	—	4	8	no	—
206	C₂²×C₁₃	—	4	8	no	—
207	C₂²×C₁₃	—	4	4	no	—
208	C₂²×C₁₃	—	4	4	no	—
209	C₂²×C₁₃	—	4	4	no	—
210	C₂²×C₁₃	—	8	32	no	—
211	C₂²×C₁₃	—	8	4	no	—
212	C₂²×C₁₃	—	8	4	no	—
213	C₂²×C₁₃	#442	1	4	yes	complemented
214	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
215	C₂²×C₁₃	D₄²	1	2	yes	—
216	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
217	C₂²×C₁₃	#576	1	2	yes	—
218	C₄×C₁₃	—	2	2	no	—
219	C₄×C₁₃	—	4	4	no	—
220	C₄×C₁₃	—	8	4	no	—
221	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
222	C₄×C₁₃	#518	1	1	yes	characteristic
223	C₄×C₁₃	#546	1	2	yes	—
224	C₂⁵	—	2	2	no	—
225	C₂²×D₄	—	2	8	no	—
226	C₂²×D₄	—	2	2	no	—
227	C₂²×D₄	—	2	4	no	—
228	C₂²×D₄	—	4	4	no	—
229	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
230	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
231	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
232	C₂³×C₄	—	2	4	no	—
233	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
234	C₂×D₈	—	2	8	no	—
235	C₂×D₈	—	2	32	no	—
236	C₂×D₈	—	2	4	no	—
237	C₂×D₈	C₂×C₄×C₁₃	1	4	yes	—
238	C₂×D₈	C₂×C₄×C₁₃	1	8	yes	complemented
239	C₂×D₈	C₂×C₄×C₁₃	1	4	yes	complemented
240	C₂×D₈	D₄×C₁₃	1	8	yes	—
241	C₂²×C₈	—	2	4	no	—
242	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
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	—	2	8	no	—
247	C₄×D₄	—	4	4	no	—
248	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	4	no	—
251	C₂×C₂²⋊C₄	—	2	4	no	—
252	C₂×C₂²⋊C₄	—	2	4	no	—
253	C₂×C₂²⋊C₄	—	4	8	no	—
254	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
255	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
256	#106	—	2	4	no	—
257	#102	—	2	8	no	—
258	#102	—	4	4	no	—
259	C₂²⋊C₈	—	2	2	no	—
260	#97	—	2	4	no	—
261	#95	—	2	2	no	—
262	#95	D₄×C₁₃	1	2	yes	—
263	C₂×C₁₃	—	2	4	no	—
264	C₂×C₁₃	—	4	8	no	—
265	C₂×C₁₃	—	8	4	no	—
266	C₂×C₁₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₁₃	C₂×#442	1	1	yes	characteristic
268	C₂×C₁₃	#2948	1	1	yes	characteristic
269	C₂×C₁₃	#3264	1	4	yes	—
270	C₂⁴	—	2	2	no	—
271	C₂⁴	—	2	2	no	—
272	C₂⁴	—	2	8	no	—
273	C₂⁴	—	4	8	no	—
274	C₂⁴	—	4	4	no	—
275	C₂⁴	—	4	4	no	—
276	C₂⁴	—	8	4	no	—
277	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
278	C₂×D₄	—	2	16	no	—
279	C₂×D₄	—	2	8	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	4	8	no	—
286	C₂×D₄	—	4	16	no	—
287	C₂×D₄	—	4	8	no	—
288	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
289	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
290	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	4	8	no	—
295	C₂²×C₄	—	4	8	no	—
296	C₂²×C₄	—	8	4	no	—
297	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
299	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₁₃×#41	1	2	yes	—
301	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
302	D₈	—	2	16	no	—
303	D₈	—	2	8	no	—
304	D₈	C₁₃×C₂²⋊C₄	1	16	yes	complemented
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	8	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
311	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
312	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₂²⋊C₄	—	2	4	no	—
316	C₂²⋊C₄	—	4	8	no	—
317	C₂²⋊C₄	—	4	8	no	—
318	C₂²⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	8	4	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₁₃	#22436	1	1	yes	characteristic, direct product factor, Sylow
323	C₂³	—	2	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	4	no	—
326	C₂³	—	2	8	no	—
327	C₂³	—	2	4	no	—
328	C₂³	—	4	16	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	4	no	—
332	C₂³	—	4	16	no	—
333	C₂³	—	4	4	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	8	8	no	—
338	C₂³	—	8	16	no	—
339	C₂³	—	8	16	no	—
340	C₂³	C₄×D₄×C₁₃	1	2	yes	—
341	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
342	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
343	D₄	—	2	4	no	—
344	D₄	—	2	4	no	—
345	D₄	—	2	4	no	—
346	D₄	—	2	8	no	—
347	D₄	—	4	16	no	—
348	D₄	—	4	4	no	—
349	D₄	C₂×C₁₃×C₂²⋊C₄	1	8	yes	complemented
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	8	16	no	—
361	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
362	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
363	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
364	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
365	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
366	C₈	—	2	2	no	—
367	C₈	—	4	2	no	—
368	C₈	C₂×C₁₃×C₂²⋊C₄	1	4	yes	complemented
369	C₂²	—	2	8	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	8	no	—
373	C₂²	—	4	8	no	—
374	C₂²	—	4	8	no	—
375	C₂²	—	4	4	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	4	4	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	8	32	no	—
381	C₂²	—	8	4	no	—
382	C₂²	—	8	4	no	—
383	C₂²	C₁₃×#442	1	4	yes	complemented
384	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
385	C₂²	D₄²×C₁₃	1	2	yes	—
386	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
387	C₂²	C₁₃×#576	1	2	yes	—
388	C₄	—	2	2	no	—
389	C₄	—	4	4	no	—
390	C₄	—	8	4	no	—
391	C₄	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
392	C₄	C₁₃×#518	1	1	yes	characteristic
393	C₄	C₁₃×#546	1	2	yes	—
394	C₂	—	2	4	no	—
395	C₂	—	4	8	no	—
396	C₂	—	8	4	no	—
397	C₂	D₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
398	C₂	C₂×C₁₃×#442	1	1	yes	characteristic
399	C₂	C₁₃×#2948	1	1	yes	characteristic
400	C₂	C₁₃×#3264	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂³×C₁₃×D₈	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#442	C₂	semidirect
3. D₄×C₁₃×C₂²⋊C₄	C₂	semidirect
4. C₁₃×#1972	C₂	semidirect
5. C₁₃×#1879	C₂	semidirect
6. C₁₃×#1807	C₂	semidirect
7. C₁₃×#1786	C₂	semidirect
8. C₁₃×#1752	C₂	semidirect
11. C₂²×C₁₃×D₈	C₄	semidirect
16. C₂×C₄×D₄×C₁₃	C₂²	semidirect
19. C₂×C₁₃×#106	C₂²	semidirect
20. C₂×C₁₃×#102	C₂²	semidirect
21. C₂×C₁₃×#102	C₂²	semidirect
23. C₂×C₁₃×#97	C₂²	semidirect
24. C₁₃×#390	C₂²	semidirect
29. C₁₃×#340	C₂²	semidirect
30. C₁₃×#336	C₂²	semidirect
36. C₂²×D₄×C₁₃	C₂×C₄	semidirect
45. C₂×C₁₃×D₈	C₂×C₄	semidirect
46. C₂×C₁₃×D₈	C₂×C₄	semidirect
49. C₂²×C₈×C₁₃	C₂×C₄	semidirect
70. #22436	C₁₃	direct (N × H)
105. C₁₃×D₈	C₂²⋊C₄	semidirect
124. C₂×#442	C₂×C₁₃	semidirect
125. D₄×C₂²⋊C₄	C₂×C₁₃	semidirect
126. #1972	C₂×C₁₃	semidirect
127. #1879	C₂×C₁₃	semidirect
128. #1807	C₂×C₁₃	semidirect
129. #1786	C₂×C₁₃	semidirect
130. #1752	C₂×C₁₃	semidirect
157. D₄×C₁₃	C₂×C₂²⋊C₄	semidirect
176. C₈×C₁₃	C₂×C₂²⋊C₄	semidirect
179. C₂²×D₈	C₄×C₁₃	semidirect
184. C₂×C₄×D₄	C₂²×C₁₃	semidirect
187. C₂×#106	C₂²×C₁₃	semidirect
188. C₂×#102	C₂²×C₁₃	semidirect
189. C₂×#102	C₂²×C₁₃	semidirect
191. C₂×#97	C₂²×C₁₃	semidirect
192. #390	C₂²×C₁₃	semidirect
197. #340	C₂²×C₁₃	semidirect
198. #336	C₂²×C₁₃	semidirect
213. C₂²×C₁₃	#442	semidirect
229. C₂²×D₄	C₂×C₄×C₁₃	semidirect
238. C₂×D₈	C₂×C₄×C₁₃	semidirect
239. C₂×D₈	C₂×C₄×C₁₃	semidirect
242. C₂²×C₈	C₂×C₄×C₁₃	semidirect
304. D₈	C₁₃×C₂²⋊C₄	semidirect
322. C₁₃	#22436	direct (N × H)
349. D₄	C₂×C₁₃×C₂²⋊C₄	semidirect
368. C₈	C₂×C₁₃×C₂²⋊C₄	semidirect
383. C₂²	C₁₃×#442	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₁₃×D₈	2
C₂×C₁₃×#442	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#1972	2
C₁₃×#1879	2
C₁₃×#1807	2
C₁₃×#1786	2
C₁₃×#1752	2
#22436	13

Subgroups — C13×#22436 #15708775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22436 #15708775