Subgroups — C₁₃×#21894 #15708233

Order 3328.

1130 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1988	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1981	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1894	C₂	1	4	yes	maximal
7	C₁₃×#1803	C₂	1	4	yes	maximal, complemented
8	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
9	C₁₃×#533	—	2	4	no	—
10	C₁₃×#533	C₄	1	8	yes	complemented
11	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#125	—	2	1	no	—
14	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
17	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
18	C₂×C₁₃×#117	—	2	1	no	—
19	C₂×C₁₃×#117	—	2	1	no	—
20	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#423	—	2	4	no	—
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	8	yes	—
25	C₁₃×#384	C₂²	1	2	yes	—
26	C₁₃×#382	—	2	1	no	—
27	C₁₃×#380	—	2	1	no	—
28	C₁₃×#380	C₂²	1	2	yes	—
29	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
31	C₁₃×#340	C₂²	1	8	yes	—
32	C₂²×Q₈×C₁₃	—	2	1	no	—
33	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
37	C₂×C₁₃×M₁₆	—	2	4	no	—
38	C₂×C₁₃×M₁₆	—	4	4	no	—
39	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
40	C₁₃×C₄⋊Q₈	—	2	2	no	—
41	C₁₃×C₄⋊Q₈	—	2	2	no	—
42	C₁₃×C₄⋊Q₈	C₂×C₄	1	4	yes	—
43	C₁₃×C₄⋊Q₈	C₂×C₄	1	4	yes	—
44	C₁₃×#125	—	2	8	no	—
45	C₁₃×C₂²⋊Q₈	—	2	8	no	—
46	C₁₃×C₂²⋊Q₈	—	2	4	no	—
47	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
48	C₄×Q₈×C₁₃	—	2	8	no	—
49	C₄×Q₈×C₁₃	—	2	4	no	—
50	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	—
51	C₁₃×#117	—	2	8	no	—
52	C₁₃×#117	—	4	4	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₄²×C₁₃	—	2	2	no	—
65	C₂×C₄²×C₁₃	—	2	2	no	—
66	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	D₄	1	4	yes	—
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×C₄⋊C₈	—	2	4	no	—
73	C₁₃×C₄⋊C₈	—	2	4	no	—
74	C₁₃×#103	—	4	8	no	—
75	C₁₃×#95	—	2	2	no	—
76	C₁₃×#95	—	2	2	no	—
77	#21894	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
79	C₂×Q₈×C₁₃	—	2	4	no	—
80	C₂×Q₈×C₁₃	—	2	2	no	—
81	C₂×Q₈×C₁₃	—	2	4	no	—
82	C₂×Q₈×C₁₃	—	2	4	no	—
83	C₂×Q₈×C₁₃	—	4	2	no	—
84	C₂×Q₈×C₁₃	—	4	2	no	—
85	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	2	4	no	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	4	no	—
94	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
95	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
96	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
104	C₁₃×M₁₆	—	4	8	no	—
105	C₂×C₈×C₁₃	—	2	4	no	—
106	C₂×C₈×C₁₃	—	2	8	no	—
107	C₁₃×C₄⋊C₄	—	2	4	no	—
108	C₁₃×C₄⋊C₄	—	2	4	no	—
109	C₁₃×C₄⋊C₄	—	2	4	no	—
110	C₁₃×C₄⋊C₄	—	2	8	no	—
111	C₁₃×C₄⋊C₄	—	2	8	no	—
112	C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₁₃×C₄⋊C₄	—	2	4	no	—
114	C₁₃×C₄⋊C₄	—	2	4	no	—
115	C₁₃×C₄⋊C₄	—	4	4	no	—
116	C₁₃×C₄⋊C₄	—	4	4	no	—
117	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
118	C₁₃×C₂²⋊C₄	—	2	8	no	—
119	C₁₃×C₂²⋊C₄	—	4	4	no	—
120	C₄²×C₁₃	—	2	8	no	—
121	C₄²×C₁₃	—	4	4	no	—
122	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
123	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
124	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
125	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
126	C₄²×C₁₃	C₂×D₄	1	2	yes	—
127	C₄²×C₁₃	C₂×D₄	1	2	yes	—
128	C₂×#533	C₂×C₁₃	1	1	yes	characteristic
129	C₂×#423	C₂×C₁₃	1	1	yes	characteristic
130	#2285	C₂×C₁₃	1	1	yes	characteristic
131	#1988	C₂×C₁₃	1	2	yes	complemented
132	#1981	C₂×C₁₃	1	2	yes	complemented
133	#1894	C₂×C₁₃	1	4	yes	—
134	#1803	C₂×C₁₃	1	4	yes	complemented
135	C₂³×C₁₃	—	2	2	no	—
136	C₂³×C₁₃	—	2	1	no	—
137	C₂³×C₁₃	—	2	2	no	—
138	C₂³×C₁₃	—	2	1	no	—
139	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
140	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₁₃	—	2	8	no	—
142	Q₈×C₁₃	—	4	2	no	—
143	Q₈×C₁₃	—	4	2	no	—
144	Q₈×C₁₃	—	4	8	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	1	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	4	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	8	no	—
153	C₂×C₄×C₁₃	—	2	8	no	—
154	C₂×C₄×C₁₃	—	2	4	no	—
155	C₂×C₄×C₁₃	—	2	4	no	—
156	C₂×C₄×C₁₃	—	4	4	no	—
157	C₂×C₄×C₁₃	—	4	2	no	—
158	C₂×C₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	—	4	4	no	—
160	C₂×C₄×C₁₃	—	4	4	no	—
161	C₂×C₄×C₁₃	—	4	4	no	—
162	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
168	C₂×C₄×C₁₃	#137	1	2	yes	—
169	C₂×C₄×C₁₃	#137	1	4	yes	—
170	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
173	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
174	C₈×C₁₃	—	4	4	no	—
175	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
176	#533	—	2	4	no	—
177	#533	C₄×C₁₃	1	8	yes	complemented
178	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
179	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
180	C₂×#125	—	2	1	no	—
181	C₂×C₂²⋊Q₈	—	2	1	no	—
182	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
183	C₂×C₄×Q₈	—	2	1	no	—
184	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
185	C₂×#117	—	2	1	no	—
186	C₂×#117	—	2	1	no	—
187	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
188	#423	—	2	4	no	—
189	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
190	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
191	C₂×#103	C₂²×C₁₃	1	8	yes	—
192	#384	C₂²×C₁₃	1	2	yes	—
193	#382	—	2	1	no	—
194	#380	—	2	1	no	—
195	#380	C₂²×C₁₃	1	2	yes	—
196	C₄×C₄⋊C₄	—	2	1	no	—
197	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
198	#340	C₂²×C₁₃	1	8	yes	—
199	C₂²×C₁₃	—	2	2	no	—
200	C₂²×C₁₃	—	2	2	no	—
201	C₂²×C₁₃	—	2	2	no	—
202	C₂²×C₁₃	—	4	2	no	—
203	C₂²×C₁₃	—	4	2	no	—
204	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
205	C₂²×C₁₃	#537	1	2	yes	—
206	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
207	C₂²×C₁₃	C₂×#137	1	2	yes	—
208	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
209	C₄×C₁₃	—	2	2	no	—
210	C₄×C₁₃	—	2	2	no	—
211	C₄×C₁₃	—	2	2	no	—
212	C₄×C₁₃	—	4	4	no	—
213	C₄×C₁₃	—	4	4	no	—
214	C₄×C₁₃	—	8	4	no	—
215	C₄×C₁₃	#417	1	4	yes	—
216	C₄×C₁₃	#419	1	4	yes	—
217	C₄×C₁₃	#520	1	2	yes	—
218	C₄×C₁₃	#535	1	1	yes	characteristic
219	C₄×C₁₃	#536	1	1	yes	characteristic
220	C₂²×Q₈	—	2	1	no	—
221	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
222	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
223	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
224	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
225	C₂×M₁₆	—	2	4	no	—
226	C₂×M₁₆	—	4	4	no	—
227	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
228	C₄⋊Q₈	—	2	2	no	—
229	C₄⋊Q₈	—	2	2	no	—
230	C₄⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
231	C₄⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
232	#125	—	2	8	no	—
233	C₂²⋊Q₈	—	2	8	no	—
234	C₂²⋊Q₈	—	2	4	no	—
235	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	—
236	C₄×Q₈	—	2	8	no	—
237	C₄×Q₈	—	2	4	no	—
238	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	—
239	#117	—	2	8	no	—
240	#117	—	4	4	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
249	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
255	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
256	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
257	C₂×C₄²	D₄×C₁₃	1	4	yes	—
258	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
260	C₄⋊C₈	—	2	4	no	—
261	C₄⋊C₈	—	2	4	no	—
262	#103	—	4	8	no	—
263	#95	—	2	2	no	—
264	#95	—	2	2	no	—
265	C₂×C₁₃	—	4	2	no	—
266	C₂×C₁₃	#2311	1	1	yes	characteristic
267	C₂×C₁₃	C₂×#419	1	1	yes	characteristic
268	C₂×C₁₃	C₂×#417	1	1	yes	characteristic
269	C₂×C₁₃	#3254	1	2	yes	—
270	C₂×C₁₃	#3255	1	2	yes	—
271	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	2	4	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	4	2	no	—
277	C₂×Q₈	—	4	2	no	—
278	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
288	C₂²×C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
289	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
290	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
297	M₁₆	—	4	8	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	2	8	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	2	8	no	—
304	C₄⋊C₄	—	2	8	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	4	4	no	—
309	C₄⋊C₄	—	4	4	no	—
310	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
311	C₂²⋊C₄	—	2	8	no	—
312	C₂²⋊C₄	—	4	4	no	—
313	C₄²	—	2	8	no	—
314	C₄²	—	4	4	no	—
315	C₄²	C₁₃×C₂²⋊C₄	1	4	yes	—
316	C₄²	C₁₃×C₂²⋊C₄	1	4	yes	—
317	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
318	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
319	C₄²	C₂×D₄×C₁₃	1	2	yes	—
320	C₄²	C₂×D₄×C₁₃	1	2	yes	—
321	C₁₃	#21894	1	1	yes	characteristic, direct product factor, Sylow
322	C₂³	—	2	2	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	1	no	—
326	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
327	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
328	Q₈	—	2	8	no	—
329	Q₈	—	4	8	no	—
330	Q₈	—	4	2	no	—
331	Q₈	—	4	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
350	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
351	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
352	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
353	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
354	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
355	C₂×C₄	C₁₃×#137	1	2	yes	—
356	C₂×C₄	C₁₃×#137	1	4	yes	—
357	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
359	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
360	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
361	C₈	—	4	4	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
368	C₂²	C₁₃×#537	1	2	yes	—
369	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
370	C₂²	C₂×C₁₃×#137	1	2	yes	—
371	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	4	4	no	—
376	C₄	—	4	4	no	—
377	C₄	—	8	4	no	—
378	C₄	C₁₃×#417	1	4	yes	—
379	C₄	C₁₃×#419	1	4	yes	—
380	C₄	C₁₃×#520	1	2	yes	—
381	C₄	C₁₃×#535	1	1	yes	characteristic
382	C₄	C₁₃×#536	1	1	yes	characteristic
383	C₂	—	4	2	no	—
384	C₂	C₁₃×#2311	1	1	yes	characteristic
385	C₂	C₂×C₁₃×#419	1	1	yes	characteristic
386	C₂	C₂×C₁₃×#417	1	1	yes	characteristic
387	C₂	C₁₃×#3254	1	2	yes	—
388	C₂	C₁₃×#3255	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#1988	C₂	semidirect
5. C₁₃×#1981	C₂	semidirect
7. C₁₃×#1803	C₂	semidirect
10. C₁₃×#533	C₄	semidirect
77. #21894	C₁₃	direct (N × H)
131. #1988	C₂×C₁₃	semidirect
132. #1981	C₂×C₁₃	semidirect
134. #1803	C₂×C₁₃	semidirect
177. #533	C₄×C₁₃	semidirect
321. C₁₃	#21894	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×#533	2
C₂×C₁₃×#423	2
C₁₃×#2285	2
C₁₃×#1988	2
C₁₃×#1981	2
C₁₃×#1894	2
C₁₃×#1803	2
#21894	13

Subgroups — C13×#21894 #15708233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21894 #15708233