Subgroups — C₁₃×#10884 #15697223

Order 3328.

986 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#340	C₂	1	2	yes	maximal
4	C₂×C₁₃×#340	C₂	1	2	yes	maximal
5	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
7	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
8	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
9	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₃	—	2	1	no	—
12	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#389	—	2	2	no	—
14	C₁₃×#389	C₄	1	4	yes	complemented
15	C₄×C₁₃×C₄⋊C₄	—	2	4	no	—
16	C₂×C₁₃×#95	—	2	1	no	—
17	C₂×C₁₃×#95	—	2	1	no	—
18	C₁₃×#340	—	2	4	no	—
19	C₁₃×#340	C₄	1	8	yes	complemented
20	C₁₃×#336	—	2	2	no	—
21	C₂³×C₄×C₁₃	—	2	2	no	—
22	C₂³×C₄×C₁₃	—	2	1	no	—
23	C₂³×C₄×C₁₃	—	2	1	no	—
24	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	—	2	2	no	—
28	C₂²×C₈×C₁₃	—	2	2	no	—
29	C₂²×C₈×C₁₃	—	2	2	no	—
30	C₂²×C₈×C₁₃	—	2	2	no	—
31	C₂²×C₈×C₁₃	—	2	2	no	—
32	C₂²×C₈×C₁₃	—	2	2	no	—
33	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
34	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
35	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
36	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
37	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
38	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
39	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
40	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
41	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
42	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
43	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
44	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
45	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
46	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
47	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
48	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
49	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
50	C₂×C₁₃×C₄⋊C₄	Q₈	1	4	yes	—
51	C₂×C₄²×C₁₃	—	2	2	no	—
52	C₂×C₄²×C₁₃	—	2	2	no	—
53	C₂×C₄²×C₁₃	—	2	4	no	—
54	C₂×C₄²×C₁₃	—	4	2	no	—
55	C₂×C₄²×C₁₃	—	4	2	no	—
56	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₁₃	D₄	1	2	yes	—
58	C₁₃×#95	—	2	4	no	—
59	C₁₃×#95	—	2	4	no	—
60	#10884	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	—	2	1	no	—
63	C₂²×C₄×C₁₃	—	2	1	no	—
64	C₂²×C₄×C₁₃	—	2	1	no	—
65	C₂²×C₄×C₁₃	—	2	1	no	—
66	C₂²×C₄×C₁₃	—	2	2	no	—
67	C₂²×C₄×C₁₃	—	2	4	no	—
68	C₂²×C₄×C₁₃	—	2	4	no	—
69	C₂²×C₄×C₁₃	—	2	1	no	—
70	C₂²×C₄×C₁₃	—	2	4	no	—
71	C₂²×C₄×C₁₃	—	2	4	no	—
72	C₂²×C₄×C₁₃	—	2	1	no	—
73	C₂²×C₄×C₁₃	—	2	2	no	—
74	C₂²×C₄×C₁₃	—	2	2	no	—
75	C₂²×C₄×C₁₃	—	2	2	no	—
76	C₂²×C₄×C₁₃	—	4	2	no	—
77	C₂²×C₄×C₁₃	—	4	1	no	—
78	C₂²×C₄×C₁₃	—	4	1	no	—
79	C₂²×C₄×C₁₃	—	4	2	no	—
80	C₂²×C₄×C₁₃	—	4	2	no	—
81	C₂²×C₄×C₁₃	—	4	2	no	—
82	C₂²×C₄×C₁₃	—	4	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	—	4	1	no	—
87	C₂²×C₄×C₁₃	—	4	1	no	—
88	C₂²×C₄×C₁₃	—	4	1	no	—
89	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₁₃	D₈	1	2	yes	—
92	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
98	C₂²×C₄×C₁₃	#41	1	2	yes	—
99	C₂²×C₄×C₁₃	#41	1	2	yes	—
100	C₂²×C₄×C₁₃	#41	1	2	yes	—
101	C₂×C₈×C₁₃	—	2	4	no	—
102	C₂×C₈×C₁₃	—	2	4	no	—
103	C₂×C₈×C₁₃	—	2	4	no	—
104	C₂×C₈×C₁₃	—	4	2	no	—
105	C₂×C₈×C₁₃	—	4	2	no	—
106	C₂×C₈×C₁₃	—	4	2	no	—
107	C₂×C₈×C₁₃	—	4	2	no	—
108	C₁₃×C₄⋊C₄	—	2	2	no	—
109	C₁₃×C₄⋊C₄	—	2	4	no	—
110	C₁₃×C₄⋊C₄	—	2	4	no	—
111	C₁₃×C₄⋊C₄	—	2	4	no	—
112	C₁₃×C₄⋊C₄	—	2	4	no	—
113	C₁₃×C₄⋊C₄	—	2	4	no	—
114	C₁₃×C₄⋊C₄	—	4	8	no	—
115	C₁₃×C₄⋊C₄	—	4	2	no	—
116	C₁₃×C₄⋊C₄	C₄²	1	4	yes	complemented
117	C₁₃×C₄⋊C₄	C₄⋊C₄	1	8	yes	complemented
118	C₄²×C₁₃	—	2	4	no	—
119	C₄²×C₁₃	—	2	4	no	—
120	C₄²×C₁₃	—	4	8	no	—
121	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
122	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
123	C₂×#340	C₂×C₁₃	1	2	yes	—
124	C₂×#340	C₂×C₁₃	1	2	yes	—
125	C₂×#336	C₂×C₁₃	1	1	yes	characteristic
126	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂³×C₁₃	C₄×D₄	1	2	yes	—
128	C₂³×C₁₃	#120	1	1	yes	characteristic
129	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
130	C₂³×C₁₃	#123	1	1	yes	characteristic
131	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
132	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
133	C₂³×C₁₃	#135	1	2	yes	—
134	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
135	C₂³×C₁₃	#137	1	1	yes	characteristic
136	C₂³×C₁₃	#137	1	2	yes	—
137	C₂×C₄×C₁₃	—	2	2	no	—
138	C₂×C₄×C₁₃	—	2	2	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	4	no	—
144	C₂×C₄×C₁₃	—	2	8	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	4	2	no	—
149	C₂×C₄×C₁₃	—	4	2	no	—
150	C₂×C₄×C₁₃	—	4	4	no	—
151	C₂×C₄×C₁₃	—	4	4	no	—
152	C₂×C₄×C₁₃	—	4	4	no	—
153	C₂×C₄×C₁₃	—	4	4	no	—
154	C₂×C₄×C₁₃	—	4	4	no	—
155	C₂×C₄×C₁₃	—	4	2	no	—
156	C₂×C₄×C₁₃	—	4	4	no	—
157	C₂×C₄×C₁₃	—	4	4	no	—
158	C₂×C₄×C₁₃	—	4	4	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	8	1	no	—
164	C₂×C₄×C₁₃	—	8	1	no	—
165	C₂×C₄×C₁₃	—	8	1	no	—
166	C₂×C₄×C₁₃	—	8	1	no	—
167	C₂×C₄×C₁₃	#102	1	4	yes	—
168	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
170	C₂×C₄×C₁₃	#117	1	2	yes	—
171	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
176	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
177	C₂×C₄×C₁₃	#121	1	2	yes	—
178	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
179	C₂×C₄×C₁₃	#123	1	2	yes	—
180	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
181	C₂×C₄×C₁₃	#125	1	2	yes	—
182	C₂×C₄×C₁₃	#126	1	2	yes	—
183	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
184	C₈×C₁₃	—	4	4	no	—
185	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
186	C₂²×C₄⋊C₄	—	2	1	no	—
187	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
188	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
189	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
190	C₂²×C₄²	—	2	1	no	—
191	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
192	#389	—	2	2	no	—
193	#389	C₄×C₁₃	1	4	yes	complemented
194	C₄×C₄⋊C₄	—	2	4	no	—
195	C₂×#95	—	2	1	no	—
196	C₂×#95	—	2	1	no	—
197	#340	—	2	4	no	—
198	#340	C₄×C₁₃	1	8	yes	complemented
199	#336	—	2	2	no	—
200	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
201	C₂²×C₁₃	#385	1	2	yes	—
202	C₂²×C₁₃	#386	1	1	yes	characteristic
203	C₂²×C₁₃	#387	1	2	yes	—
204	C₂²×C₁₃	#391	1	1	yes	characteristic
205	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
206	C₂²×C₁₃	#416	1	1	yes	characteristic
207	C₂²×C₁₃	#417	1	1	yes	characteristic
208	C₂²×C₁₃	#419	1	1	yes	characteristic
209	C₂²×C₁₃	C₄×D₈	1	2	yes	—
210	C₂²×C₁₃	C₄×SD₁₆	1	2	yes	—
211	C₂²×C₁₃	#440	1	2	yes	—
212	C₂²×C₁₃	#441	1	2	yes	—
213	C₂²×C₁₃	#447	1	1	yes	characteristic
214	C₂²×C₁₃	#448	1	1	yes	characteristic
215	C₂²×C₁₃	#452	1	2	yes	—
216	C₂²×C₁₃	#474	1	2	yes	—
217	C₂²×C₁₃	#475	1	2	yes	—
218	C₂²×C₁₃	#478	1	2	yes	—
219	C₂²×C₁₃	#479	1	2	yes	—
220	C₂²×C₁₃	#480	1	1	yes	characteristic
221	C₂²×C₁₃	#481	1	1	yes	characteristic
222	C₂²×C₁₃	#485	1	2	yes	—
223	C₄×C₁₃	—	2	4	no	—
224	C₄×C₁₃	—	4	8	no	—
225	C₄×C₁₃	—	4	2	no	—
226	C₄×C₁₃	—	4	4	no	—
227	C₄×C₁₃	—	8	2	no	—
228	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
229	C₄×C₁₃	#387	1	2	yes	—
230	C₄×C₁₃	#388	1	2	yes	—
231	C₄×C₁₃	#389	1	2	yes	—
232	C₂³×C₄	—	2	1	no	—
233	C₂³×C₄	—	2	2	no	—
234	C₂³×C₄	—	2	1	no	—
235	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
236	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
237	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	4	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	4	2	no	—
255	C₂×C₄⋊C₄	—	4	2	no	—
256	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
257	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
258	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
259	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
260	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
261	C₂×C₄⋊C₄	Q₈×C₁₃	1	4	yes	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	—	2	4	no	—
265	C₂×C₄²	—	4	2	no	—
266	C₂×C₄²	—	4	2	no	—
267	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
268	C₂×C₄²	D₄×C₁₃	1	2	yes	—
269	#95	—	2	4	no	—
270	#95	—	2	4	no	—
271	C₂×C₁₃	#1436	1	1	yes	characteristic
272	C₂×C₁₃	C₄×#102	1	1	yes	characteristic
273	C₂×C₁₃	#1763	1	1	yes	characteristic
274	C₂×C₁₃	#1862	1	2	yes	—
275	C₂×C₁₃	#1865	1	2	yes	—
276	C₂×C₁₃	#1873	1	1	yes	characteristic
277	C₂×C₁₃	#1874	1	1	yes	characteristic
278	C₂×C₁₃	#1918	1	2	yes	—
279	C₂×C₁₃	#1919	1	2	yes	—
280	C₂×C₁₃	#1988	1	1	yes	characteristic
281	C₂×C₁₃	#1989	1	1	yes	characteristic
282	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
311	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
312	C₂²×C₄	C₁₃×D₈	1	2	yes	—
313	C₂²×C₄	C₁₃×SD₁₆	1	2	yes	—
314	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
315	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
319	C₂²×C₄	C₁₃×#41	1	2	yes	—
320	C₂²×C₄	C₁₃×#41	1	2	yes	—
321	C₂²×C₄	C₁₃×#41	1	2	yes	—
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	2	4	no	—
324	C₂×C₈	—	2	4	no	—
325	C₂×C₈	—	4	2	no	—
326	C₂×C₈	—	4	2	no	—
327	C₂×C₈	—	4	2	no	—
328	C₂×C₈	—	4	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	4	8	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	C₄²×C₁₃	1	4	yes	complemented
338	C₄⋊C₄	C₁₃×C₄⋊C₄	1	8	yes	complemented
339	C₄²	—	2	4	no	—
340	C₄²	—	2	4	no	—
341	C₄²	—	4	8	no	—
342	C₁₃	#10884	1	1	yes	characteristic, direct product factor, Sylow
343	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
344	C₂³	C₄×D₄×C₁₃	1	2	yes	—
345	C₂³	C₁₃×#120	1	1	yes	characteristic
346	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
347	C₂³	C₁₃×#123	1	1	yes	characteristic
348	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
349	C₂³	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
350	C₂³	C₁₃×#135	1	2	yes	—
351	C₂³	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
352	C₂³	C₁₃×#137	1	1	yes	characteristic
353	C₂³	C₁₃×#137	1	2	yes	—
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	4	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	8	1	no	—
381	C₂×C₄	—	8	1	no	—
382	C₂×C₄	—	8	1	no	—
383	C₂×C₄	—	8	1	no	—
384	C₂×C₄	C₁₃×#102	1	4	yes	—
385	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
386	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
387	C₂×C₄	C₁₃×#117	1	2	yes	—
388	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
389	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
390	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
391	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
392	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
393	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
394	C₂×C₄	C₁₃×#121	1	2	yes	—
395	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
396	C₂×C₄	C₁₃×#123	1	2	yes	—
397	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
398	C₂×C₄	C₁₃×#125	1	2	yes	—
399	C₂×C₄	C₁₃×#126	1	2	yes	—
400	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
401	C₈	—	4	4	no	—
402	C₂²	C₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
403	C₂²	C₁₃×#385	1	2	yes	—
404	C₂²	C₁₃×#386	1	1	yes	characteristic
405	C₂²	C₁₃×#387	1	2	yes	—
406	C₂²	C₁₃×#391	1	1	yes	characteristic
407	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
408	C₂²	C₁₃×#416	1	1	yes	characteristic
409	C₂²	C₁₃×#417	1	1	yes	characteristic
410	C₂²	C₁₃×#419	1	1	yes	characteristic
411	C₂²	C₄×C₁₃×D₈	1	2	yes	—
412	C₂²	C₄×C₁₃×SD₁₆	1	2	yes	—
413	C₂²	C₁₃×#440	1	2	yes	—
414	C₂²	C₁₃×#441	1	2	yes	—
415	C₂²	C₁₃×#447	1	1	yes	characteristic
416	C₂²	C₁₃×#448	1	1	yes	characteristic
417	C₂²	C₁₃×#452	1	2	yes	—
418	C₂²	C₁₃×#474	1	2	yes	—
419	C₂²	C₁₃×#475	1	2	yes	—
420	C₂²	C₁₃×#478	1	2	yes	—
421	C₂²	C₁₃×#479	1	2	yes	—
422	C₂²	C₁₃×#480	1	1	yes	characteristic
423	C₂²	C₁₃×#481	1	1	yes	characteristic
424	C₂²	C₁₃×#485	1	2	yes	—
425	C₄	—	2	4	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	8	no	—
428	C₄	—	4	2	no	—
429	C₄	—	8	2	no	—
430	C₄	C₄×C₁₃×C₄⋊C₄	1	2	yes	—
431	C₄	C₁₃×#387	1	2	yes	—
432	C₄	C₁₃×#388	1	2	yes	—
433	C₄	C₁₃×#389	1	2	yes	—
434	C₂	C₁₃×#1436	1	1	yes	characteristic
435	C₂	C₄×C₁₃×#102	1	1	yes	characteristic
436	C₂	C₁₃×#1763	1	1	yes	characteristic
437	C₂	C₁₃×#1862	1	2	yes	—
438	C₂	C₁₃×#1865	1	2	yes	—
439	C₂	C₁₃×#1873	1	1	yes	characteristic
440	C₂	C₁₃×#1874	1	1	yes	characteristic
441	C₂	C₁₃×#1918	1	2	yes	—
442	C₂	C₁₃×#1919	1	2	yes	—
443	C₂	C₁₃×#1988	1	1	yes	characteristic
444	C₂	C₁₃×#1989	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
14. C₁₃×#389	C₄	semidirect
19. C₁₃×#340	C₄	semidirect
60. #10884	C₁₃	direct (N × H)
116. C₁₃×C₄⋊C₄	C₄²	semidirect
117. C₁₃×C₄⋊C₄	C₄⋊C₄	semidirect
193. #389	C₄×C₁₃	semidirect
198. #340	C₄×C₁₃	semidirect
337. C₄⋊C₄	C₄²×C₁₃	semidirect
338. C₄⋊C₄	C₁₃×C₄⋊C₄	semidirect
342. C₁₃	#10884	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×#389	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×C₁₃×#340	2
C₂×C₁₃×#336	2
#10884	13

Subgroups — C13×#10884 #15697223

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10884 #15697223