Subgroups — C₁₃×#18004 #15704343

Order 3328.

662 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3103	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2935	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1592	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1588	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1585	C₂	1	2	yes	maximal, complemented
7	C₁₃×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1571	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1492	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#131	—	2	1	no	—
13	C₁₃×#532	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#481	C₄	1	2	yes	—
16	C₁₃×#475	C₄	1	1	yes	characteristic
17	C₁₃×#475	C₄	1	1	yes	characteristic
18	C₁₃×#460	C₄	1	1	yes	characteristic
19	C₁₃×#460	C₄	1	1	yes	characteristic
20	C₁₃×#448	C₄	1	2	yes	—
21	C₁₃×#446	—	2	2	no	—
22	C₁₃×#446	C₂²	1	2	yes	—
23	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
24	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
25	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
26	C₁₃×#436	C₂²	1	2	yes	—
27	C₁₃×#435	—	2	2	no	—
28	C₈×D₄×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#431	C₂²	1	1	yes	characteristic
30	C₁₃×#423	—	2	1	no	—
31	C₁₃×#423	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₁₃×#408	—	2	1	no	—
34	C₄×C₁₃×M₁₆	—	2	1	no	—
35	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#335	C₂²	1	2	yes	—
38	C₁₃×#335	C₂²	1	2	yes	—
39	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
40	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
41	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
43	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
44	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
45	C₁₃×#322	C₂²	1	2	yes	—
46	C₁₃×#322	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	—	2	1	no	—
48	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
50	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
51	C₁₃×#131	—	4	4	no	—
52	C₂×C₁₃×M₁₆	—	2	1	no	—
53	C₂×C₁₃×M₁₆	—	2	2	no	—
54	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
55	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	—	2	1	no	—
57	C₂²×C₈×C₁₃	—	2	1	no	—
58	C₂²×C₈×C₁₃	—	2	2	no	—
59	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
60	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
61	C₁₃×#124	—	2	1	no	—
62	C₁₃×#121	—	2	1	no	—
63	C₁₃×#121	C₂×C₄	1	2	yes	—
64	C₄×Q₈×C₁₃	—	2	1	no	—
65	C₄×Q₈×C₁₃	—	2	1	no	—
66	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
67	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₄×D₄×C₁₃	—	2	1	no	—
71	C₄×D₄×C₁₃	C₂³	1	2	yes	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	—	2	1	no	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#106	C₂×C₄	1	2	yes	—
77	C₁₃×#106	C₂×C₄	1	2	yes	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×C₄⋊C₈	—	2	1	no	—
81	C₁₃×C₄⋊C₈	—	2	1	no	—
82	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
83	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
84	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
85	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₁₃×#103	C₂×C₄	1	2	yes	—
88	C₁₃×#103	C₂×C₄	1	2	yes	—
89	C₁₃×#102	C₂×C₄	1	2	yes	—
90	C₁₃×#102	C₂×C₄	1	2	yes	—
91	C₁₃×C₂²⋊C₈	—	2	2	no	—
92	C₁₃×C₂²⋊C₈	—	2	2	no	—
93	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
94	C₁₃×#97	—	2	2	no	—
95	C₁₃×#97	D₄	1	2	yes	—
96	C₄×C₈×C₁₃	—	2	2	no	—
97	C₄×C₈×C₁₃	—	2	1	no	—
98	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₃	C₂³	1	2	yes	—
101	C₄×C₈×C₁₃	C₂³	1	2	yes	—
102	#18004	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₁₃×#41	—	4	2	no	—
104	C₁₃×#41	—	4	2	no	—
105	C₂×Q₈×C₁₃	—	2	1	no	—
106	C₂×Q₈×C₁₃	—	2	1	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	4	1	no	—
109	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	—	2	1	no	—
113	C₂×D₄×C₁₃	—	2	1	no	—
114	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
121	C₁₃×SD₁₆	—	2	4	no	—
122	C₁₃×SD₁₆	—	4	2	no	—
123	C₁₃×M₁₆	—	2	2	no	—
124	C₁₃×M₁₆	—	2	2	no	—
125	C₁₃×M₁₆	—	4	4	no	—
126	C₁₃×M₁₆	—	4	2	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	1	no	—
130	C₂×C₈×C₁₃	—	2	1	no	—
131	C₂×C₈×C₁₃	—	2	1	no	—
132	C₂×C₈×C₁₃	—	4	2	no	—
133	C₂×C₈×C₁₃	—	4	4	no	—
134	C₂×C₈×C₁₃	—	4	2	no	—
135	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
146	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
147	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
148	C₁₃×C₂²⋊C₄	—	2	2	no	—
149	C₁₃×C₂²⋊C₄	—	2	2	no	—
150	C₄²×C₁₃	—	2	1	no	—
151	C₄²×C₁₃	—	2	1	no	—
152	C₄²×C₁₃	—	2	1	no	—
153	C₄²×C₁₃	—	2	1	no	—
154	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₃	#41	1	1	yes	characteristic
157	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
158	#3103	C₂×C₁₃	1	1	yes	characteristic
159	Q₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#2935	C₂×C₁₃	1	1	yes	characteristic
161	#1592	C₂×C₁₃	1	2	yes	complemented
162	#1588	C₂×C₁₃	1	2	yes	complemented
163	#1585	C₂×C₁₃	1	2	yes	complemented
164	SD₁₆⋊C₈	C₂×C₁₃	1	2	yes	complemented
165	#1571	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#1492	C₂×C₁₃	1	1	yes	characteristic
167	C₂×Q₈⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#1451	C₂×C₁₃	1	1	yes	characteristic, complemented
169	C₂³×C₁₃	—	2	2	no	—
170	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
171	Q₈×C₁₃	—	2	1	no	—
172	Q₈×C₁₃	—	2	1	no	—
173	Q₈×C₁₃	—	2	1	no	—
174	Q₈×C₁₃	—	4	2	no	—
175	Q₈×C₁₃	—	4	2	no	—
176	Q₈×C₁₃	#131	1	2	yes	complemented
177	D₄×C₁₃	—	2	2	no	—
178	D₄×C₁₃	—	2	2	no	—
179	D₄×C₁₃	—	4	4	no	—
180	D₄×C₁₃	—	4	2	no	—
181	D₄×C₁₃	—	8	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	8	1	no	—
194	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
198	C₂×C₄×C₁₃	#137	1	2	yes	—
199	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
202	C₈×C₁₃	—	2	2	no	—
203	C₈×C₁₃	—	2	2	no	—
204	C₈×C₁₃	—	2	2	no	—
205	C₈×C₁₃	—	2	2	no	—
206	C₈×C₁₃	—	2	2	no	—
207	C₈×C₁₃	—	4	1	no	—
208	C₈×C₁₃	—	4	1	no	—
209	C₈×C₁₃	—	4	1	no	—
210	C₈×C₁₃	—	4	2	no	—
211	C₂×#131	—	2	1	no	—
212	#532	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
214	#481	C₄×C₁₃	1	2	yes	—
215	#475	C₄×C₁₃	1	1	yes	characteristic
216	#475	C₄×C₁₃	1	1	yes	characteristic
217	#460	C₄×C₁₃	1	1	yes	characteristic
218	#460	C₄×C₁₃	1	1	yes	characteristic
219	#448	C₄×C₁₃	1	2	yes	—
220	#446	—	2	2	no	—
221	#446	C₂²×C₁₃	1	2	yes	—
222	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
223	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
224	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
225	#436	C₂²×C₁₃	1	2	yes	—
226	#435	—	2	2	no	—
227	C₈×D₄	C₂²×C₁₃	1	2	yes	—
228	#431	C₂²×C₁₃	1	1	yes	characteristic
229	#423	—	2	1	no	—
230	#423	C₂²×C₁₃	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
232	#408	—	2	1	no	—
233	C₄×M₁₆	—	2	1	no	—
234	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
236	#335	C₂²×C₁₃	1	2	yes	—
237	#335	C₂²×C₁₃	1	2	yes	—
238	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
239	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
240	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
241	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
242	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
243	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
244	#322	C₂²×C₁₃	1	2	yes	—
245	#322	C₂²×C₁₃	1	2	yes	—
246	C₂²×C₁₃	—	2	1	no	—
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	—	4	2	no	—
249	C₂²×C₁₃	—	4	2	no	—
250	C₂²×C₁₃	—	4	2	no	—
251	C₂²×C₁₃	#440	1	2	yes	—
252	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
253	C₄×C₁₃	—	2	1	no	—
254	C₄×C₁₃	—	2	2	no	—
255	C₄×C₁₃	—	2	1	no	—
256	C₄×C₁₃	—	2	1	no	—
257	C₄×C₁₃	—	4	1	no	—
258	C₄×C₁₃	—	4	2	no	—
259	C₄×C₁₃	—	4	1	no	—
260	C₄×C₁₃	—	4	1	no	—
261	C₄×C₁₃	#440	1	2	yes	—
262	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
263	C₄×C₁₃	#568	1	1	yes	characteristic
264	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
265	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
266	C₂×#41	—	2	1	no	—
267	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
268	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
269	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
270	#131	—	4	4	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
274	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
275	C₂²×C₈	—	2	1	no	—
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	2	2	no	—
278	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
279	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
280	#124	—	2	1	no	—
281	#121	—	2	1	no	—
282	#121	C₂×C₄×C₁₃	1	2	yes	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×Q₈	—	2	1	no	—
285	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
286	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
287	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
288	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
289	C₄×D₄	—	2	1	no	—
290	C₄×D₄	C₂³×C₁₃	1	2	yes	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
295	#106	C₂×C₄×C₁₃	1	2	yes	—
296	#106	C₂×C₄×C₁₃	1	2	yes	—
297	C₄⋊C₈	—	2	2	no	—
298	C₄⋊C₈	—	2	2	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
302	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
303	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
304	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
305	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
306	#103	C₂×C₄×C₁₃	1	2	yes	—
307	#103	C₂×C₄×C₁₃	1	2	yes	—
308	#102	C₂×C₄×C₁₃	1	2	yes	—
309	#102	C₂×C₄×C₁₃	1	2	yes	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
313	#97	—	2	2	no	—
314	#97	D₄×C₁₃	1	2	yes	—
315	C₄×C₈	—	2	2	no	—
316	C₄×C₈	—	2	1	no	—
317	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
318	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
319	C₄×C₈	C₂³×C₁₃	1	2	yes	—
320	C₄×C₈	C₂³×C₁₃	1	2	yes	—
321	C₂×C₁₃	—	2	2	no	—
322	C₂×C₁₃	—	8	2	no	—
323	C₂×C₁₃	#2933	1	1	yes	characteristic
324	C₂×C₁₃	C₂×#440	1	1	yes	characteristic
325	C₂×C₁₃	#2956	1	1	yes	characteristic
326	#41	—	4	2	no	—
327	#41	—	4	2	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	4	1	no	—
332	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
333	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
344	SD₁₆	—	2	4	no	—
345	SD₁₆	—	4	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	4	4	no	—
349	M₁₆	—	4	2	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	4	4	no	—
356	C₂×C₈	—	4	2	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
359	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
360	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
361	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
369	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
370	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
378	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
379	C₄²	C₁₃×#41	1	1	yes	characteristic
380	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
381	C₁₃	#18004	1	1	yes	characteristic, direct product factor, Sylow
382	C₂³	—	2	2	no	—
383	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	2	1	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	4	2	no	—
389	Q₈	C₁₃×#131	1	2	yes	complemented
390	D₄	—	2	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	2	no	—
394	D₄	—	8	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	8	1	no	—
407	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
408	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
409	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
410	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
411	C₂×C₄	C₁₃×#137	1	2	yes	—
412	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
414	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	4	1	no	—
421	C₈	—	4	1	no	—
422	C₈	—	4	1	no	—
423	C₈	—	4	2	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	C₁₃×#440	1	2	yes	—
430	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	4	1	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	C₁₃×#440	1	2	yes	—
440	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
441	C₄	C₁₃×#568	1	1	yes	characteristic
442	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
443	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
444	C₂	—	2	2	no	—
445	C₂	—	8	2	no	—
446	C₂	C₁₃×#2933	1	1	yes	characteristic
447	C₂	C₂×C₁₃×#440	1	1	yes	characteristic
448	C₂	C₁₃×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×C₁₃×M₁₆	C₂	semidirect
4. C₁₃×#1592	C₂	semidirect
5. C₁₃×#1588	C₂	semidirect
6. C₁₃×#1585	C₂	semidirect
7. C₁₃×SD₁₆⋊C₈	C₂	semidirect
8. C₁₃×#1571	C₂	semidirect
10. C₂×C₁₃×Q₈⋊C₈	C₂	semidirect
11. C₁₃×#1451	C₂	semidirect
102. #18004	C₁₃	direct (N × H)
159. Q₈×M₁₆	C₂×C₁₃	semidirect
161. #1592	C₂×C₁₃	semidirect
162. #1588	C₂×C₁₃	semidirect
163. #1585	C₂×C₁₃	semidirect
164. SD₁₆⋊C₈	C₂×C₁₃	semidirect
165. #1571	C₂×C₁₃	semidirect
167. C₂×Q₈⋊C₈	C₂×C₁₃	semidirect
168. #1451	C₂×C₁₃	semidirect
176. Q₈×C₁₃	#131	semidirect
381. C₁₃	#18004	direct (N × H)
389. Q₈	C₁₃×#131	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3103	2
Q₈×C₁₃×M₁₆	2
C₁₃×#2935	2
C₁₃×#1592	2
C₁₃×#1588	2
C₁₃×#1585	2
C₁₃×SD₁₆⋊C₈	2
C₁₃×#1571	2
C₁₃×#1492	2
C₂×C₁₃×Q₈⋊C₈	2
C₁₃×#1451	2
#18004	13

Subgroups — C13×#18004 #15704343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18004 #15704343