Subgroups — C₁₃×#26996 #15713335

Order 3328.

812 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3041	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2090	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2037	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2018	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2006	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1972	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1938	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1907	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1883	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1856	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1765	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
21	C₁₃×#537	C₂²	1	1	yes	characteristic
22	C₁₃×#535	C₂²	1	1	yes	characteristic
23	C₁₃×#520	C₂²	1	1	yes	characteristic
24	C₁₃×#518	C₂²	1	1	yes	characteristic
25	C₁₃×#485	—	2	1	no	—
26	C₁₃×#483	—	2	1	no	—
27	C₁₃×#482	—	2	1	no	—
28	C₁₃×#481	—	2	1	no	—
29	C₁₃×#469	—	2	1	no	—
30	C₁₃×#468	—	2	1	no	—
31	C₁₃×#466	—	2	1	no	—
32	C₁₃×#465	—	2	1	no	—
33	C₁₃×#463	—	2	1	no	—
34	C₁₃×#463	—	2	1	no	—
35	C₁₃×#459	—	2	1	no	—
36	C₁₃×#459	—	2	1	no	—
37	C₁₃×#442	—	2	1	no	—
38	C₁₃×#440	—	2	1	no	—
39	C₄×C₁₃×SD₁₆	—	2	1	no	—
40	C₄×C₁₃×D₈	—	2	1	no	—
41	C₁₃×#428	C₂²	1	1	yes	characteristic
42	C₁₃×#428	C₂²	1	1	yes	characteristic
43	C₁₃×#428	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
45	C₁₃×#424	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
48	C₁₃×#418	C₂²	1	1	yes	characteristic
49	C₁₃×#417	C₂²	1	1	yes	characteristic
50	C₁₃×#416	C₂²	1	1	yes	characteristic
51	C₁₃×#416	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
56	C₁₃×#408	C₂²	1	1	yes	characteristic
57	C₁₃×#405	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
59	C₁₃×#390	C₂²	1	1	yes	characteristic
60	C₁₃×#390	C₂²	1	1	yes	characteristic
61	C₁₃×#343	C₂²	1	1	yes	characteristic
62	C₁₃×#343	C₂²	1	1	yes	characteristic
63	C₁₃×#341	C₂²	1	1	yes	characteristic
64	C₁₃×#341	C₂²	1	1	yes	characteristic
65	C₁₃×#339	C₂²	1	1	yes	characteristic
66	C₁₃×#339	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
72	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
73	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
74	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
75	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
76	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
77	C₂×C₁₃×SD₁₆	—	2	1	no	—
78	C₂×C₁₃×SD₁₆	—	2	1	no	—
79	C₂×C₁₃×SD₁₆	—	2	1	no	—
80	C₂×C₁₃×D₈	—	2	1	no	—
81	C₂×C₁₃×D₈	—	2	1	no	—
82	C₂×C₁₃×D₈	—	2	1	no	—
83	C₂×C₁₃×D₈	—	2	2	no	—
84	C₂×C₁₃×D₈	—	2	1	no	—
85	C₂×C₁₃×D₈	—	2	1	no	—
86	C₂×C₁₃×D₈	—	4	1	no	—
87	C₁₃×#131	—	2	2	no	—
88	C₁₃×#131	—	4	1	no	—
89	C₂×C₁₃×M₁₆	—	2	1	no	—
90	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₁₃	—	2	1	no	—
95	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×#127	—	2	1	no	—
98	C₁₃×#124	—	2	1	no	—
99	C₁₃×C₂²⋊Q₈	—	2	1	no	—
100	C₁₃×C₂²⋊Q₈	—	2	1	no	—
101	C₁₃×#121	—	2	1	no	—
102	C₁₃×#121	—	2	1	no	—
103	C₁₃×#121	—	2	1	no	—
104	C₁₃×#121	—	2	1	no	—
105	C₁₃×#121	—	4	1	no	—
106	C₁₃×#120	—	4	1	no	—
107	C₄×Q₈×C₁₃	—	2	1	no	—
108	C₄×D₄×C₁₃	—	2	1	no	—
109	C₄×D₄×C₁₃	—	2	1	no	—
110	C₄×D₄×C₁₃	—	2	1	no	—
111	C₄×D₄×C₁₃	—	2	1	no	—
112	C₄×D₄×C₁₃	—	2	1	no	—
113	C₄×D₄×C₁₃	—	4	1	no	—
114	C₁₃×#117	—	2	1	no	—
115	C₁₃×#117	C₂³	1	1	yes	characteristic
116	C₁₃×#117	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
123	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
124	C₁₃×#107	—	2	1	no	—
125	C₁₃×#107	—	2	1	no	—
126	C₁₃×#107	—	2	1	no	—
127	C₁₃×#106	—	2	1	no	—
128	C₁₃×#106	—	2	1	no	—
129	C₁₃×#106	—	2	1	no	—
130	C₁₃×#106	—	2	1	no	—
131	C₁₃×#106	—	2	1	no	—
132	C₁₃×C₄⋊C₈	—	2	1	no	—
133	C₁₃×C₄⋊C₈	—	2	1	no	—
134	C₁₃×#104	—	2	2	no	—
135	C₁₃×#104	—	4	1	no	—
136	C₁₃×#103	—	2	1	no	—
137	C₁₃×#103	D₄	1	1	yes	characteristic
138	C₁₃×#103	D₄	1	1	yes	characteristic
139	C₁₃×#103	D₄	1	1	yes	characteristic
140	C₁₃×#103	D₄	1	1	yes	characteristic
141	C₁₃×#102	—	2	1	no	—
142	C₁₃×#102	—	2	1	no	—
143	C₁₃×#102	—	2	1	no	—
144	C₁₃×#102	—	2	1	no	—
145	C₁₃×#102	—	2	1	no	—
146	C₁₃×#102	—	2	1	no	—
147	C₁₃×#102	—	2	1	no	—
148	C₁₃×#102	D₄	1	1	yes	characteristic
149	C₁₃×#102	D₄	1	1	yes	characteristic
150	C₁₃×#102	D₄	1	1	yes	characteristic
151	C₁₃×#102	D₄	1	1	yes	characteristic
152	C₁₃×#100	—	2	2	no	—
153	C₁₃×#100	—	2	2	no	—
154	C₁₃×C₂²⋊C₈	—	2	1	no	—
155	C₁₃×C₂²⋊C₈	—	2	1	no	—
156	C₁₃×#97	—	2	1	no	—
157	C₁₃×#97	—	4	1	no	—
158	C₄×C₈×C₁₃	—	2	1	no	—
159	#26996	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂⁴×C₁₃	—	2	1	no	—
161	C₂⁴×C₁₃	—	2	1	no	—
162	C₁₃×#41	—	2	1	no	—
163	C₁₃×#41	—	2	1	no	—
164	C₁₃×#41	—	2	1	no	—
165	C₁₃×#41	—	2	1	no	—
166	C₁₃×#41	—	2	1	no	—
167	C₁₃×#41	—	2	1	no	—
168	C₁₃×#41	—	2	1	no	—
169	C₁₃×#41	—	2	1	no	—
170	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂×D₄×C₁₃	—	2	1	no	—
173	C₂×D₄×C₁₃	—	2	1	no	—
174	C₂×D₄×C₁₃	—	2	1	no	—
175	C₂×D₄×C₁₃	—	2	1	no	—
176	C₂×D₄×C₁₃	—	2	1	no	—
177	C₂×D₄×C₁₃	—	2	1	no	—
178	C₂×D₄×C₁₃	—	2	1	no	—
179	C₂×D₄×C₁₃	—	2	1	no	—
180	C₂×D₄×C₁₃	—	2	1	no	—
181	C₂×D₄×C₁₃	—	2	1	no	—
182	C₂×D₄×C₁₃	—	2	1	no	—
183	C₂×D₄×C₁₃	—	2	1	no	—
184	C₂×D₄×C₁₃	—	2	1	no	—
185	C₂×D₄×C₁₃	—	4	1	no	—
186	C₂×D₄×C₁₃	—	4	1	no	—
187	C₂×D₄×C₁₃	—	4	1	no	—
188	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂×D₄×C₁₃	#41	1	2	yes	—
191	C₂²×C₄×C₁₃	—	2	1	no	—
192	C₂²×C₄×C₁₃	—	2	1	no	—
193	C₂²×C₄×C₁₃	—	2	1	no	—
194	C₂²×C₄×C₁₃	—	2	1	no	—
195	C₂²×C₄×C₁₃	—	2	1	no	—
196	C₂²×C₄×C₁₃	—	4	1	no	—
197	C₂²×C₄×C₁₃	—	4	1	no	—
198	C₂²×C₄×C₁₃	—	4	1	no	—
199	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
200	C₁₃×SD₁₆	—	2	4	no	—
201	C₁₃×SD₁₆	—	4	2	no	—
202	C₁₃×SD₁₆	—	4	2	no	—
203	C₁₃×D₈	—	2	4	no	—
204	C₁₃×D₈	—	4	2	no	—
205	C₁₃×D₈	—	4	2	no	—
206	C₁₃×D₈	—	4	2	no	—
207	C₁₃×D₈	—	4	2	no	—
208	C₁₃×M₁₆	—	2	1	no	—
209	C₁₃×M₁₆	—	2	1	no	—
210	C₁₃×M₁₆	—	2	1	no	—
211	C₁₃×M₁₆	—	2	1	no	—
212	C₁₃×M₁₆	—	2	1	no	—
213	C₁₃×M₁₆	—	2	1	no	—
214	C₁₃×M₁₆	—	4	2	no	—
215	C₁₃×M₁₆	#41	1	2	yes	—
216	C₁₃×M₁₆	#41	1	2	yes	—
217	C₂×C₈×C₁₃	—	2	1	no	—
218	C₂×C₈×C₁₃	—	2	1	no	—
219	C₂×C₈×C₁₃	—	2	1	no	—
220	C₂×C₈×C₁₃	—	2	1	no	—
221	C₂×C₈×C₁₃	—	2	1	no	—
222	C₂×C₈×C₁₃	—	2	1	no	—
223	C₂×C₈×C₁₃	—	2	1	no	—
224	C₂×C₈×C₁₃	—	2	1	no	—
225	C₂×C₈×C₁₃	—	4	2	no	—
226	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
228	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₁₃×C₄⋊C₄	—	2	1	no	—
231	C₁₃×C₄⋊C₄	—	2	1	no	—
232	C₁₃×C₄⋊C₄	—	2	1	no	—
233	C₁₃×C₄⋊C₄	—	2	1	no	—
234	C₁₃×C₄⋊C₄	—	4	1	no	—
235	C₁₃×C₄⋊C₄	—	4	1	no	—
236	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
237	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
238	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
239	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
240	C₁₃×C₂²⋊C₄	—	2	1	no	—
241	C₁₃×C₂²⋊C₄	—	2	1	no	—
242	C₁₃×C₂²⋊C₄	—	4	1	no	—
243	C₁₃×C₂²⋊C₄	—	4	1	no	—
244	C₁₃×C₂²⋊C₄	—	4	1	no	—
245	C₁₃×C₂²⋊C₄	—	4	1	no	—
246	C₁₃×C₂²⋊C₄	—	4	1	no	—
247	C₁₃×C₂²⋊C₄	—	4	1	no	—
248	C₁₃×C₂²⋊C₄	—	4	1	no	—
249	C₁₃×C₂²⋊C₄	—	8	2	no	—
250	C₁₃×C₂²⋊C₄	—	8	2	no	—
251	C₄²×C₁₃	—	2	1	no	—
252	C₄²×C₁₃	—	2	1	no	—
253	C₄²×C₁₃	—	2	1	no	—
254	C₄²×C₁₃	—	2	1	no	—
255	C₄²×C₁₃	—	4	1	no	—
256	#3099	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#3062	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#3041	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#2946	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#2090	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#2037	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#2018	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#2006	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#1972	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#1938	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#1931	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#1907	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#1883	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#1856	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#1765	C₂×C₁₃	1	1	yes	characteristic, complemented
271	C₂³×C₁₃	—	2	1	no	—
272	C₂³×C₁₃	—	2	1	no	—
273	C₂³×C₁₃	—	2	2	no	—
274	C₂³×C₁₃	—	4	1	no	—
275	C₂³×C₁₃	—	4	1	no	—
276	C₂³×C₁₃	—	4	1	no	—
277	C₂³×C₁₃	—	4	1	no	—
278	C₂³×C₁₃	—	4	1	no	—
279	C₂³×C₁₃	—	8	1	no	—
280	C₂³×C₁₃	—	8	1	no	—
281	C₂³×C₁₃	—	8	1	no	—
282	C₂³×C₁₃	—	8	1	no	—
283	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
284	Q₈×C₁₃	—	2	1	no	—
285	Q₈×C₁₃	—	2	1	no	—
286	Q₈×C₁₃	—	2	1	no	—
287	Q₈×C₁₃	—	2	1	no	—
288	D₄×C₁₃	—	2	1	no	—
289	D₄×C₁₃	—	2	2	no	—
290	D₄×C₁₃	—	2	1	no	—
291	D₄×C₁₃	—	2	2	no	—
292	D₄×C₁₃	—	2	1	no	—
293	D₄×C₁₃	—	2	1	no	—
294	D₄×C₁₃	—	4	1	no	—
295	D₄×C₁₃	—	4	1	no	—
296	D₄×C₁₃	—	4	1	no	—
297	D₄×C₁₃	—	4	1	no	—
298	D₄×C₁₃	—	4	1	no	—
299	D₄×C₁₃	—	4	1	no	—
300	D₄×C₁₃	—	4	1	no	—
301	D₄×C₁₃	—	4	1	no	—
302	D₄×C₁₃	—	4	1	no	—
303	D₄×C₁₃	—	4	1	no	—
304	D₄×C₁₃	—	16	1	no	—
305	D₄×C₁₃	—	16	1	no	—
306	D₄×C₁₃	—	16	1	no	—
307	C₂×C₄×C₁₃	—	2	1	no	—
308	C₂×C₄×C₁₃	—	2	1	no	—
309	C₂×C₄×C₁₃	—	2	1	no	—
310	C₂×C₄×C₁₃	—	2	1	no	—
311	C₂×C₄×C₁₃	—	2	1	no	—
312	C₂×C₄×C₁₃	—	2	1	no	—
313	C₂×C₄×C₁₃	—	4	1	no	—
314	C₂×C₄×C₁₃	—	4	1	no	—
315	C₂×C₄×C₁₃	—	4	1	no	—
316	C₂×C₄×C₁₃	—	4	1	no	—
317	C₂×C₄×C₁₃	—	4	1	no	—
318	C₂×C₄×C₁₃	—	4	1	no	—
319	C₂×C₄×C₁₃	—	4	1	no	—
320	C₂×C₄×C₁₃	—	4	1	no	—
321	C₂×C₄×C₁₃	—	4	1	no	—
322	C₂×C₄×C₁₃	—	8	1	no	—
323	C₂×C₄×C₁₃	—	8	1	no	—
324	C₂×C₄×C₁₃	—	16	1	no	—
325	C₂×C₄×C₁₃	—	16	1	no	—
326	C₂×C₄×C₁₃	—	16	1	no	—
327	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
330	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
331	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
332	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
333	C₈×C₁₃	—	2	2	no	—
334	C₈×C₁₃	—	2	1	no	—
335	C₈×C₁₃	—	2	1	no	—
336	C₈×C₁₃	—	2	1	no	—
337	C₈×C₁₃	—	2	1	no	—
338	C₈×C₁₃	—	2	2	no	—
339	C₈×C₁₃	—	4	1	no	—
340	C₈×C₁₃	—	4	1	no	—
341	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
342	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
344	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
346	#537	C₂²×C₁₃	1	1	yes	characteristic
347	#535	C₂²×C₁₃	1	1	yes	characteristic
348	#520	C₂²×C₁₃	1	1	yes	characteristic
349	#518	C₂²×C₁₃	1	1	yes	characteristic
350	#485	—	2	1	no	—
351	#483	—	2	1	no	—
352	#482	—	2	1	no	—
353	#481	—	2	1	no	—
354	#469	—	2	1	no	—
355	#468	—	2	1	no	—
356	#466	—	2	1	no	—
357	#465	—	2	1	no	—
358	#463	—	2	1	no	—
359	#463	—	2	1	no	—
360	#459	—	2	1	no	—
361	#459	—	2	1	no	—
362	#442	—	2	1	no	—
363	#440	—	2	1	no	—
364	C₄×SD₁₆	—	2	1	no	—
365	C₄×D₈	—	2	1	no	—
366	#428	C₂²×C₁₃	1	1	yes	characteristic
367	#428	C₂²×C₁₃	1	1	yes	characteristic
368	#428	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
370	#424	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
373	#418	C₂²×C₁₃	1	1	yes	characteristic
374	#417	C₂²×C₁₃	1	1	yes	characteristic
375	#416	C₂²×C₁₃	1	1	yes	characteristic
376	#416	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
381	#408	C₂²×C₁₃	1	1	yes	characteristic
382	#405	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
384	#390	C₂²×C₁₃	1	1	yes	characteristic
385	#390	C₂²×C₁₃	1	1	yes	characteristic
386	#343	C₂²×C₁₃	1	1	yes	characteristic
387	#343	C₂²×C₁₃	1	1	yes	characteristic
388	#341	C₂²×C₁₃	1	1	yes	characteristic
389	#341	C₂²×C₁₃	1	1	yes	characteristic
390	#339	C₂²×C₁₃	1	1	yes	characteristic
391	#339	C₂²×C₁₃	1	1	yes	characteristic
392	C₂²×C₁₃	—	2	1	no	—
393	C₂²×C₁₃	—	2	1	no	—
394	C₂²×C₁₃	—	4	1	no	—
395	C₂²×C₁₃	—	4	1	no	—
396	C₂²×C₁₃	—	4	2	no	—
397	C₂²×C₁₃	—	4	1	no	—
398	C₂²×C₁₃	—	4	1	no	—
399	C₂²×C₁₃	—	4	1	no	—
400	C₂²×C₁₃	—	4	1	no	—
401	C₂²×C₁₃	—	8	2	no	—
402	C₂²×C₁₃	—	8	2	no	—
403	C₂²×C₁₃	—	8	1	no	—
404	C₂²×C₁₃	—	8	1	no	—
405	C₂²×C₁₃	—	8	1	no	—
406	C₂²×C₁₃	—	8	1	no	—
407	C₂²×C₁₃	—	8	1	no	—
408	C₂²×C₁₃	—	16	1	no	—
409	C₂²×C₁₃	—	16	1	no	—
410	C₂²×C₁₃	#540	1	1	yes	characteristic
411	C₂²×C₁₃	D₄²	1	1	yes	characteristic
412	C₂²×C₁₃	#553	1	1	yes	characteristic
413	C₄×C₁₃	—	4	1	no	—
414	C₄×C₁₃	—	4	1	no	—
415	C₄×C₁₃	—	4	1	no	—
416	C₄×C₁₃	—	4	1	no	—
417	C₄×C₁₃	—	4	1	no	—
418	C₄×C₁₃	—	4	1	no	—
419	C₄×C₁₃	—	8	1	no	—
420	C₄×C₁₃	—	8	1	no	—
421	C₄×C₁₃	—	8	1	no	—
422	C₄×C₁₃	#525	1	1	yes	characteristic
423	C₄×C₁₃	#532	1	1	yes	characteristic
424	C₄×C₁₃	#546	1	1	yes	characteristic
425	C₄×C₁₃	#546	1	1	yes	characteristic
426	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
427	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
428	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
429	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
430	AGL(1,ℤ/8)	—	2	2	no	—
431	AGL(1,ℤ/8)	—	2	2	no	—
432	AGL(1,ℤ/8)	—	2	2	no	—
433	AGL(1,ℤ/8)	—	2	2	no	—
434	AGL(1,ℤ/8)	—	4	1	no	—
435	AGL(1,ℤ/8)	—	4	1	no	—
436	C₂×SD₁₆	—	2	1	no	—
437	C₂×SD₁₆	—	2	1	no	—
438	C₂×SD₁₆	—	2	1	no	—
439	C₂×D₈	—	2	1	no	—
440	C₂×D₈	—	2	1	no	—
441	C₂×D₈	—	2	1	no	—
442	C₂×D₈	—	2	2	no	—
443	C₂×D₈	—	2	1	no	—
444	C₂×D₈	—	2	1	no	—
445	C₂×D₈	—	4	1	no	—
446	#131	—	2	2	no	—
447	#131	—	4	1	no	—
448	C₂×M₁₆	—	2	1	no	—
449	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
450	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
451	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
452	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
453	C₂²×C₈	—	2	1	no	—
454	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
455	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
456	#127	—	2	1	no	—
457	#124	—	2	1	no	—
458	C₂²⋊Q₈	—	2	1	no	—
459	C₂²⋊Q₈	—	2	1	no	—
460	#121	—	2	1	no	—
461	#121	—	2	1	no	—
462	#121	—	2	1	no	—
463	#121	—	2	1	no	—
464	#121	—	4	1	no	—
465	#120	—	4	1	no	—
466	C₄×Q₈	—	2	1	no	—
467	C₄×D₄	—	2	1	no	—
468	C₄×D₄	—	2	1	no	—
469	C₄×D₄	—	2	1	no	—
470	C₄×D₄	—	2	1	no	—
471	C₄×D₄	—	2	1	no	—
472	C₄×D₄	—	4	1	no	—
473	#117	—	2	1	no	—
474	#117	C₂³×C₁₃	1	1	yes	characteristic
475	#117	C₂³×C₁₃	1	1	yes	characteristic
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	—	4	1	no	—
480	C₂×C₂²⋊C₄	—	4	1	no	—
481	C₂×C₂²⋊C₄	—	4	1	no	—
482	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
483	#107	—	2	1	no	—
484	#107	—	2	1	no	—
485	#107	—	2	1	no	—
486	#106	—	2	1	no	—
487	#106	—	2	1	no	—
488	#106	—	2	1	no	—
489	#106	—	2	1	no	—
490	#106	—	2	1	no	—
491	C₄⋊C₈	—	2	1	no	—
492	C₄⋊C₈	—	2	1	no	—
493	#104	—	2	2	no	—
494	#104	—	4	1	no	—
495	#103	—	2	1	no	—
496	#103	D₄×C₁₃	1	1	yes	characteristic
497	#103	D₄×C₁₃	1	1	yes	characteristic
498	#103	D₄×C₁₃	1	1	yes	characteristic
499	#103	D₄×C₁₃	1	1	yes	characteristic
500	#102	—	2	1	no	—
501	#102	—	2	1	no	—
502	#102	—	2	1	no	—
503	#102	—	2	1	no	—
504	#102	—	2	1	no	—
505	#102	—	2	1	no	—
506	#102	—	2	1	no	—
507	#102	D₄×C₁₃	1	1	yes	characteristic
508	#102	D₄×C₁₃	1	1	yes	characteristic
509	#102	D₄×C₁₃	1	1	yes	characteristic
510	#102	D₄×C₁₃	1	1	yes	characteristic
511	#100	—	2	2	no	—
512	#100	—	2	2	no	—
513	C₂²⋊C₈	—	2	1	no	—
514	C₂²⋊C₈	—	2	1	no	—
515	#97	—	2	1	no	—
516	#97	—	4	1	no	—
517	C₄×C₈	—	2	1	no	—
518	C₂×C₁₃	—	2	1	no	—
519	C₂×C₁₃	—	2	1	no	—
520	C₂×C₁₃	—	8	1	no	—
521	C₂×C₁₃	—	8	1	no	—
522	C₂×C₁₃	—	8	2	no	—
523	C₂×C₁₃	—	16	1	no	—
524	C₂×C₁₃	#2464	1	1	yes	characteristic
525	C₂×C₁₃	#3288	1	1	yes	characteristic
526	C₂×C₁₃	#3288	1	1	yes	characteristic
527	C₂⁴	—	2	1	no	—
528	C₂⁴	—	2	1	no	—
529	#41	—	2	1	no	—
530	#41	—	2	1	no	—
531	#41	—	2	1	no	—
532	#41	—	2	1	no	—
533	#41	—	2	1	no	—
534	#41	—	2	1	no	—
535	#41	—	2	1	no	—
536	#41	—	2	1	no	—
537	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
538	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	4	1	no	—
553	C₂×D₄	—	4	1	no	—
554	C₂×D₄	—	4	1	no	—
555	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
556	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
557	C₂×D₄	C₁₃×#41	1	2	yes	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	4	1	no	—
564	C₂²×C₄	—	4	1	no	—
565	C₂²×C₄	—	4	1	no	—
566	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
567	SD₁₆	—	2	4	no	—
568	SD₁₆	—	4	2	no	—
569	SD₁₆	—	4	2	no	—
570	D₈	—	2	4	no	—
571	D₈	—	4	2	no	—
572	D₈	—	4	2	no	—
573	D₈	—	4	2	no	—
574	D₈	—	4	2	no	—
575	M₁₆	—	2	1	no	—
576	M₁₆	—	2	1	no	—
577	M₁₆	—	2	1	no	—
578	M₁₆	—	2	1	no	—
579	M₁₆	—	2	1	no	—
580	M₁₆	—	2	1	no	—
581	M₁₆	—	4	2	no	—
582	M₁₆	C₁₃×#41	1	2	yes	—
583	M₁₆	C₁₃×#41	1	2	yes	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	4	2	no	—
593	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
594	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
595	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
596	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	4	1	no	—
602	C₄⋊C₄	—	4	1	no	—
603	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
604	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
605	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
606	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
607	C₂²⋊C₄	—	2	1	no	—
608	C₂²⋊C₄	—	2	1	no	—
609	C₂²⋊C₄	—	4	1	no	—
610	C₂²⋊C₄	—	4	1	no	—
611	C₂²⋊C₄	—	4	1	no	—
612	C₂²⋊C₄	—	4	1	no	—
613	C₂²⋊C₄	—	4	1	no	—
614	C₂²⋊C₄	—	4	1	no	—
615	C₂²⋊C₄	—	4	1	no	—
616	C₂²⋊C₄	—	8	2	no	—
617	C₂²⋊C₄	—	8	2	no	—
618	C₄²	—	2	1	no	—
619	C₄²	—	2	1	no	—
620	C₄²	—	2	1	no	—
621	C₄²	—	2	1	no	—
622	C₄²	—	4	1	no	—
623	C₁₃	#26996	1	1	yes	characteristic, direct product factor, Sylow
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	4	1	no	—
628	C₂³	—	4	1	no	—
629	C₂³	—	4	1	no	—
630	C₂³	—	4	1	no	—
631	C₂³	—	4	1	no	—
632	C₂³	—	8	1	no	—
633	C₂³	—	8	1	no	—
634	C₂³	—	8	1	no	—
635	C₂³	—	8	1	no	—
636	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
637	Q₈	—	2	1	no	—
638	Q₈	—	2	1	no	—
639	Q₈	—	2	1	no	—
640	Q₈	—	2	1	no	—
641	D₄	—	2	1	no	—
642	D₄	—	2	2	no	—
643	D₄	—	2	1	no	—
644	D₄	—	2	2	no	—
645	D₄	—	2	1	no	—
646	D₄	—	2	1	no	—
647	D₄	—	4	1	no	—
648	D₄	—	4	1	no	—
649	D₄	—	4	1	no	—
650	D₄	—	4	1	no	—
651	D₄	—	4	1	no	—
652	D₄	—	4	1	no	—
653	D₄	—	4	1	no	—
654	D₄	—	4	1	no	—
655	D₄	—	4	1	no	—
656	D₄	—	4	1	no	—
657	D₄	—	16	1	no	—
658	D₄	—	16	1	no	—
659	D₄	—	16	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	8	1	no	—
676	C₂×C₄	—	8	1	no	—
677	C₂×C₄	—	16	1	no	—
678	C₂×C₄	—	16	1	no	—
679	C₂×C₄	—	16	1	no	—
680	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
681	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
682	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
683	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
684	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
685	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
686	C₈	—	2	2	no	—
687	C₈	—	2	1	no	—
688	C₈	—	2	1	no	—
689	C₈	—	2	1	no	—
690	C₈	—	2	1	no	—
691	C₈	—	2	2	no	—
692	C₈	—	4	1	no	—
693	C₈	—	4	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	8	2	no	—
704	C₂²	—	8	2	no	—
705	C₂²	—	8	1	no	—
706	C₂²	—	8	1	no	—
707	C₂²	—	8	1	no	—
708	C₂²	—	8	1	no	—
709	C₂²	—	8	1	no	—
710	C₂²	—	16	1	no	—
711	C₂²	—	16	1	no	—
712	C₂²	C₁₃×#540	1	1	yes	characteristic
713	C₂²	D₄²×C₁₃	1	1	yes	characteristic
714	C₂²	C₁₃×#553	1	1	yes	characteristic
715	C₄	—	4	1	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	1	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	1	no	—
721	C₄	—	8	1	no	—
722	C₄	—	8	1	no	—
723	C₄	—	8	1	no	—
724	C₄	C₁₃×#525	1	1	yes	characteristic
725	C₄	C₁₃×#532	1	1	yes	characteristic
726	C₄	C₁₃×#546	1	1	yes	characteristic
727	C₄	C₁₃×#546	1	1	yes	characteristic
728	C₂	—	2	1	no	—
729	C₂	—	2	1	no	—
730	C₂	—	8	1	no	—
731	C₂	—	8	1	no	—
732	C₂	—	8	2	no	—
733	C₂	—	16	1	no	—
734	C₂	C₁₃×#2464	1	1	yes	characteristic
735	C₂	C₁₃×#3288	1	1	yes	characteristic
736	C₂	C₁₃×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3099	C₂	semidirect
2. C₁₃×#3062	C₂	semidirect
3. C₁₃×#3041	C₂	semidirect
4. C₁₃×#2946	C₂	semidirect
5. C₁₃×#2090	C₂	semidirect
6. C₁₃×#2037	C₂	semidirect
7. C₁₃×#2018	C₂	semidirect
8. C₁₃×#2006	C₂	semidirect
9. C₁₃×#1972	C₂	semidirect
10. C₁₃×#1938	C₂	semidirect
11. C₁₃×#1931	C₂	semidirect
12. C₁₃×#1907	C₂	semidirect
13. C₁₃×#1883	C₂	semidirect
14. C₁₃×#1856	C₂	semidirect
15. C₁₃×#1765	C₂	semidirect
159. #26996	C₁₃	direct (N × H)
256. #3099	C₂×C₁₃	semidirect
257. #3062	C₂×C₁₃	semidirect
258. #3041	C₂×C₁₃	semidirect
259. #2946	C₂×C₁₃	semidirect
260. #2090	C₂×C₁₃	semidirect
261. #2037	C₂×C₁₃	semidirect
262. #2018	C₂×C₁₃	semidirect
263. #2006	C₂×C₁₃	semidirect
264. #1972	C₂×C₁₃	semidirect
265. #1938	C₂×C₁₃	semidirect
266. #1931	C₂×C₁₃	semidirect
267. #1907	C₂×C₁₃	semidirect
268. #1883	C₂×C₁₃	semidirect
269. #1856	C₂×C₁₃	semidirect
270. #1765	C₂×C₁₃	semidirect
623. C₁₃	#26996	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3099	2
C₁₃×#3062	2
C₁₃×#3041	2
C₁₃×#2946	2
C₁₃×#2090	2
C₁₃×#2037	2
C₁₃×#2018	2
C₁₃×#2006	2
C₁₃×#1972	2
C₁₃×#1938	2
C₁₃×#1931	2
C₁₃×#1907	2
C₁₃×#1883	2
C₁₃×#1856	2
C₁₃×#1765	2
#26996	13

Subgroups — C13×#26996 #15713335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26996 #15713335