Subgroups — C₁₃×#8894 #15695233

Order 3328.

602 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1296	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₄×C₁₃	—	2	1	no	—
9	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
11	C₂×C₁₃×#106	—	2	1	no	—
12	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#102	—	2	1	no	—
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#389	—	2	1	no	—
17	C₁₃×#385	—	2	2	no	—
18	C₁₃×#384	C₂²	1	1	yes	characteristic
19	C₁₃×#384	C₂²	1	1	yes	characteristic
20	C₁₃×#380	—	2	1	no	—
21	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₁₃×#340	—	2	1	no	—
23	C₁₃×#340	—	2	2	no	—
24	C₁₃×#340	—	2	1	no	—
25	C₁₃×D₄⋊C₈	C₄	1	4	yes	complemented
26	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₃	—	2	1	no	—
28	C₂³×C₄×C₁₃	—	2	2	no	—
29	C₂²×C₈×C₁₃	—	2	1	no	—
30	C₂²×C₈×C₁₃	—	2	1	no	—
31	C₂²×C₈×C₁₃	—	2	1	no	—
32	C₄×D₄×C₁₃	—	2	1	no	—
33	C₄×D₄×C₁₃	—	2	1	no	—
34	C₄×D₄×C₁₃	—	4	2	no	—
35	C₄×D₄×C₁₃	—	4	2	no	—
36	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
37	C₄×D₄×C₁₃	Q₈	1	2	yes	—
38	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
39	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
40	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
41	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
42	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
43	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
44	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
45	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
46	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
49	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
50	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
51	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
52	C₂×C₄²×C₁₃	—	2	1	no	—
53	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×#106	—	4	2	no	—
55	C₁₃×C₄⋊C₈	—	2	1	no	—
56	C₁₃×C₄⋊C₈	—	2	1	no	—
57	C₁₃×C₄⋊C₈	—	2	1	no	—
58	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
59	C₁₃×#102	—	4	2	no	—
60	C₄×C₈×C₁₃	—	2	1	no	—
61	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	complemented
62	C₁₃×#95	—	2	2	no	—
63	C₁₃×#95	—	2	1	no	—
64	#8894	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
65	C₂⁴×C₁₃	—	2	1	no	—
66	C₂×D₄×C₁₃	—	2	1	no	—
67	C₂×D₄×C₁₃	—	2	1	no	—
68	C₂×D₄×C₁₃	—	2	1	no	—
69	C₂×D₄×C₁₃	C₄⋊C₄	1	2	yes	—
70	C₂×D₄×C₁₃	SD₁₆	1	2	yes	—
71	C₂×D₄×C₁₃	SD₁₆	1	2	yes	—
72	C₂²×C₄×C₁₃	—	2	1	no	—
73	C₂²×C₄×C₁₃	—	2	1	no	—
74	C₂²×C₄×C₁₃	—	2	2	no	—
75	C₂²×C₄×C₁₃	—	2	2	no	—
76	C₂²×C₄×C₁₃	—	2	1	no	—
77	C₂²×C₄×C₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₃	—	4	4	no	—
79	C₂²×C₄×C₁₃	—	4	1	no	—
80	C₂²×C₄×C₁₃	—	4	1	no	—
81	C₂²×C₄×C₁₃	—	4	1	no	—
82	C₂²×C₄×C₁₃	—	4	1	no	—
83	C₂²×C₄×C₁₃	—	4	4	no	—
84	C₂²×C₄×C₁₃	—	4	1	no	—
85	C₂²×C₄×C₁₃	—	8	2	no	—
86	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂×C₈×C₁₃	—	2	2	no	—
90	C₂×C₈×C₁₃	—	2	2	no	—
91	C₂×C₈×C₁₃	—	4	1	no	—
92	C₂×C₈×C₁₃	—	4	1	no	—
93	C₂×C₈×C₁₃	—	4	1	no	—
94	C₂×C₈×C₁₃	—	4	1	no	—
95	C₂×C₈×C₁₃	—	4	1	no	—
96	C₂×C₈×C₁₃	—	4	1	no	—
97	C₂×C₈×C₁₃	—	4	1	no	—
98	C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₁₃×C₄⋊C₄	—	4	2	no	—
103	C₁₃×C₄⋊C₄	—	4	4	no	—
104	C₁₃×C₄⋊C₄	—	4	2	no	—
105	C₁₃×C₄⋊C₄	—	4	1	no	—
106	C₁₃×C₄⋊C₄	—	4	1	no	—
107	C₁₃×C₄⋊C₄	—	4	1	no	—
108	C₁₃×C₄⋊C₄	—	4	1	no	—
109	C₁₃×C₄⋊C₄	—	4	1	no	—
110	C₁₃×C₄⋊C₄	—	4	1	no	—
111	C₁₃×C₄⋊C₄	—	4	1	no	—
112	C₁₃×C₄⋊C₄	—	4	1	no	—
113	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
114	C₁₃×C₄⋊C₄	D₈	1	2	yes	—
115	C₁₃×C₂²⋊C₄	—	2	2	no	—
116	C₁₃×C₂²⋊C₄	—	2	2	no	—
117	C₁₃×C₂²⋊C₄	—	4	4	no	—
118	C₄²×C₁₃	—	4	1	no	—
119	C₄²×C₁₃	—	4	1	no	—
120	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
122	C₄²×C₁₃	#41	1	1	yes	characteristic
123	C₄²×C₁₃	#41	1	1	yes	characteristic
124	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
125	#1948	C₂×C₁₃	1	1	yes	characteristic, complemented
126	#1834	C₂×C₁₃	1	1	yes	characteristic, complemented
127	#1802	C₂×C₁₃	1	1	yes	characteristic
128	C₂×D₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
129	#1296	C₂×C₁₃	1	1	yes	characteristic, complemented
130	#1279	C₂×C₁₃	1	1	yes	characteristic, complemented
131	C₂³×C₁₃	—	2	2	no	—
132	C₂³×C₁₃	—	2	2	no	—
133	C₂³×C₁₃	—	2	2	no	—
134	C₂³×C₁₃	—	4	1	no	—
135	C₂³×C₁₃	—	4	1	no	—
136	C₂³×C₁₃	—	4	1	no	—
137	C₂³×C₁₃	—	4	1	no	—
138	C₂³×C₁₃	#120	1	1	yes	characteristic
139	D₄×C₁₃	—	2	2	no	—
140	D₄×C₁₃	—	2	2	no	—
141	D₄×C₁₃	—	2	2	no	—
142	D₄×C₁₃	#106	1	4	yes	complemented
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	2	1	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	4	1	no	—
148	C₂×C₄×C₁₃	—	4	1	no	—
149	C₂×C₄×C₁₃	—	4	1	no	—
150	C₂×C₄×C₁₃	—	4	1	no	—
151	C₂×C₄×C₁₃	—	4	2	no	—
152	C₂×C₄×C₁₃	—	4	2	no	—
153	C₂×C₄×C₁₃	—	4	2	no	—
154	C₂×C₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	4	2	no	—
156	C₂×C₄×C₁₃	—	4	1	no	—
157	C₂×C₄×C₁₃	—	4	2	no	—
158	C₂×C₄×C₁₃	—	4	1	no	—
159	C₂×C₄×C₁₃	—	4	1	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	8	8	no	—
162	C₂×C₄×C₁₃	—	8	1	no	—
163	C₂×C₄×C₁₃	—	8	1	no	—
164	C₂×C₄×C₁₃	—	8	1	no	—
165	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
170	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
174	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
175	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
176	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
178	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
179	C₈×C₁₃	—	4	2	no	—
180	C₈×C₁₃	—	4	2	no	—
181	C₈×C₁₃	—	8	1	no	—
182	C₂×C₄×D₄	—	2	1	no	—
183	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
184	C₂²×C₄⋊C₄	—	2	1	no	—
185	C₂×#106	—	2	1	no	—
186	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
187	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
188	C₂×#102	—	2	1	no	—
189	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
190	#389	—	2	1	no	—
191	#385	—	2	2	no	—
192	#384	C₂²×C₁₃	1	1	yes	characteristic
193	#384	C₂²×C₁₃	1	1	yes	characteristic
194	#380	—	2	1	no	—
195	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
196	#340	—	2	1	no	—
197	#340	—	2	2	no	—
198	#340	—	2	1	no	—
199	D₄⋊C₈	C₄×C₁₃	1	4	yes	complemented
200	C₂²×C₁₃	—	2	4	no	—
201	C₂²×C₁₃	—	4	2	no	—
202	C₂²×C₁₃	—	4	2	no	—
203	C₂²×C₁₃	—	4	2	no	—
204	C₂²×C₁₃	—	4	2	no	—
205	C₂²×C₁₃	—	4	2	no	—
206	C₂²×C₁₃	—	4	2	no	—
207	C₂²×C₁₃	#385	1	1	yes	characteristic
208	C₂²×C₁₃	#447	1	1	yes	characteristic
209	C₂²×C₁₃	#448	1	1	yes	characteristic
210	C₂²×C₁₃	#450	1	1	yes	characteristic
211	C₂²×C₁₃	#452	1	1	yes	characteristic
212	C₂²×C₁₃	#454	1	1	yes	characteristic
213	C₂²×C₁₃	#455	1	1	yes	characteristic
214	C₄×C₁₃	—	2	1	no	—
215	C₄×C₁₃	—	2	1	no	—
216	C₄×C₁₃	—	4	2	no	—
217	C₄×C₁₃	—	4	2	no	—
218	C₄×C₁₃	—	8	1	no	—
219	C₄×C₁₃	—	8	2	no	—
220	C₄×C₁₃	—	16	1	no	—
221	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
222	C₄×C₁₃	#428	1	1	yes	characteristic
223	C₄×C₁₃	C₄×D₈	1	1	yes	characteristic
224	C₄×C₁₃	#440	1	1	yes	characteristic
225	C₄×C₁₃	#474	1	1	yes	characteristic
226	C₄×C₁₃	#478	1	1	yes	characteristic
227	C₄×C₁₃	#481	1	1	yes	characteristic
228	C₄×C₁₃	#483	1	1	yes	characteristic
229	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
230	C₂³×C₄	—	2	1	no	—
231	C₂³×C₄	—	2	2	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	2	1	no	—
234	C₂²×C₈	—	2	1	no	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	4	2	no	—
238	C₄×D₄	—	4	2	no	—
239	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
240	C₄×D₄	Q₈×C₁₃	1	2	yes	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	4	2	no	—
248	C₂×C₄⋊C₄	—	4	2	no	—
249	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
250	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
251	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
252	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
257	#106	—	4	2	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	complemented
262	#102	—	4	2	no	—
263	C₄×C₈	—	2	1	no	—
264	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	complemented
265	#95	—	2	2	no	—
266	#95	—	2	1	no	—
267	C₂×C₁₃	—	4	4	no	—
268	C₂×C₁₃	#1627	1	1	yes	characteristic
269	C₂×C₁₃	#1635	1	1	yes	characteristic
270	C₂×C₁₃	#1639	1	1	yes	characteristic
271	C₂×C₁₃	#1643	1	1	yes	characteristic
272	C₂×C₁₃	#1853	1	1	yes	characteristic
273	C₂×C₁₃	#1860	1	1	yes	characteristic
274	C₂×C₁₃	#1862	1	1	yes	characteristic
275	C₂⁴	—	2	1	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	C₁₃×C₄⋊C₄	1	2	yes	—
280	C₂×D₄	C₁₃×SD₁₆	1	2	yes	—
281	C₂×D₄	C₁₃×SD₁₆	1	2	yes	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	4	4	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	4	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	8	2	no	—
296	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	4	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	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	C₁₃×C₄⋊C₄	1	2	yes	—
324	C₄⋊C₄	C₁₃×D₈	1	2	yes	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	4	4	no	—
328	C₄²	—	4	1	no	—
329	C₄²	—	4	1	no	—
330	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
331	C₄²	C₂×Q₈×C₁₃	1	1	yes	characteristic
332	C₄²	C₁₃×#41	1	1	yes	characteristic
333	C₄²	C₁₃×#41	1	1	yes	characteristic
334	C₁₃	#8894	1	1	yes	characteristic, direct product factor, Sylow
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	4	1	no	—
341	C₂³	—	4	1	no	—
342	C₂³	C₁₃×#120	1	1	yes	characteristic
343	D₄	—	2	2	no	—
344	D₄	—	2	2	no	—
345	D₄	—	2	2	no	—
346	D₄	C₁₃×#106	1	4	yes	complemented
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	8	8	no	—
366	C₂×C₄	—	8	1	no	—
367	C₂×C₄	—	8	1	no	—
368	C₂×C₄	—	8	1	no	—
369	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
370	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
371	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
372	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
373	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
374	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
375	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
376	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
377	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
378	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
379	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
380	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
381	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
382	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
383	C₈	—	4	2	no	—
384	C₈	—	4	2	no	—
385	C₈	—	8	1	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	C₁₃×#385	1	1	yes	characteristic
394	C₂²	C₁₃×#447	1	1	yes	characteristic
395	C₂²	C₁₃×#448	1	1	yes	characteristic
396	C₂²	C₁₃×#450	1	1	yes	characteristic
397	C₂²	C₁₃×#452	1	1	yes	characteristic
398	C₂²	C₁₃×#454	1	1	yes	characteristic
399	C₂²	C₁₃×#455	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	8	1	no	—
405	C₄	—	8	2	no	—
406	C₄	—	16	1	no	—
407	C₄	C₂×C₁₃×#106	1	1	yes	characteristic
408	C₄	C₁₃×#428	1	1	yes	characteristic
409	C₄	C₄×C₁₃×D₈	1	1	yes	characteristic
410	C₄	C₁₃×#440	1	1	yes	characteristic
411	C₄	C₁₃×#474	1	1	yes	characteristic
412	C₄	C₁₃×#478	1	1	yes	characteristic
413	C₄	C₁₃×#481	1	1	yes	characteristic
414	C₄	C₁₃×#483	1	1	yes	characteristic
415	C₂	—	4	4	no	—
416	C₂	C₁₃×#1627	1	1	yes	characteristic
417	C₂	C₁₃×#1635	1	1	yes	characteristic
418	C₂	C₁₃×#1639	1	1	yes	characteristic
419	C₂	C₁₃×#1643	1	1	yes	characteristic
420	C₂	C₁₃×#1853	1	1	yes	characteristic
421	C₂	C₁₃×#1860	1	1	yes	characteristic
422	C₂	C₁₃×#1862	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#1948	C₂	semidirect
3. C₁₃×#1834	C₂	semidirect
6. C₁₃×#1296	C₂	semidirect
7. C₁₃×#1279	C₂	semidirect
25. C₁₃×D₄⋊C₈	C₄	semidirect
58. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
61. C₄×C₈×C₁₃	C₂×C₄	semidirect
64. #8894	C₁₃	direct (N × H)
125. #1948	C₂×C₁₃	semidirect
126. #1834	C₂×C₁₃	semidirect
129. #1296	C₂×C₁₃	semidirect
130. #1279	C₂×C₁₃	semidirect
142. D₄×C₁₃	#106	semidirect
199. D₄⋊C₈	C₄×C₁₃	semidirect
261. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
264. C₄×C₈	C₂×C₄×C₁₃	semidirect
334. C₁₃	#8894	direct (N × H)
346. D₄	C₁₃×#106	semidirect

Maximal subgroups

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

subgroup	index
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#1948	2
C₁₃×#1834	2
C₁₃×#1802	2
C₂×C₁₃×D₄⋊C₈	2
C₁₃×#1296	2
C₁₃×#1279	2
#8894	13

Subgroups — C13×#8894 #15695233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#8894 #15695233