Subgroups — C₁₃×#26195 #15712534

Order 3328.

758 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3045	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2952	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2092	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2090	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2078	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2037	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1931	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1922	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1907	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1883	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1876	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1860	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1860	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
19	C₁₃×#535	C₂²	1	1	yes	characteristic
20	C₁₃×#520	C₂²	1	1	yes	characteristic
21	C₁₃×#520	C₂²	1	1	yes	characteristic
22	C₁₃×#520	C₂²	1	1	yes	characteristic
23	C₁₃×#482	—	2	1	no	—
24	C₁₃×#482	—	2	1	no	—
25	C₁₃×#481	—	2	1	no	—
26	C₁₃×#480	—	2	1	no	—
27	C₁₃×#464	—	2	1	no	—
28	C₁₃×#463	—	2	1	no	—
29	C₁₃×#460	—	2	1	no	—
30	C₁₃×#459	—	2	1	no	—
31	C₁₃×#442	—	2	1	no	—
32	C₁₃×#441	—	2	1	no	—
33	C₄×C₁₃×SD₁₆	—	2	1	no	—
34	C₄×C₁₃×SD₁₆	—	2	1	no	—
35	C₁₃×#428	—	2	1	no	—
36	C₁₃×#428	—	2	1	no	—
37	C₁₃×#428	C₂²	1	1	yes	characteristic
38	C₁₃×#428	C₂²	1	1	yes	characteristic
39	C₁₃×#428	C₂²	1	1	yes	characteristic
40	C₁₃×#427	—	2	1	no	—
41	C₁₃×#427	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#107	—	2	1	no	—
43	C₂×C₁₃×#107	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×#417	C₂²	1	1	yes	characteristic
51	C₁₃×#417	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	C₁₃×#408	C₂²	1	1	yes	characteristic
56	C₁₃×#405	C₂²	1	1	yes	characteristic
57	C₁₃×#390	C₂²	1	1	yes	characteristic
58	C₁₃×#382	C₂²	1	1	yes	characteristic
59	C₁₃×#343	C₂²	1	1	yes	characteristic
60	C₁₃×#343	C₂²	1	1	yes	characteristic
61	C₁₃×#343	C₂²	1	1	yes	characteristic
62	C₁₃×#341	C₂²	1	1	yes	characteristic
63	C₁₃×#341	C₂²	1	1	yes	characteristic
64	C₁₃×#339	C₂²	1	1	yes	characteristic
65	C₁₃×#339	C₂²	1	1	yes	characteristic
66	C₁₃×#336	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	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
71	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
72	C₁₃×#135	—	2	2	no	—
73	C₁₃×#135	—	2	2	no	—
74	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
75	C₂×C₁₃×SD₁₆	—	2	1	no	—
76	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
77	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
78	C₂×C₁₃×D₈	—	2	1	no	—
79	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
80	C₁₃×#131	—	2	2	no	—
81	C₁₃×#131	—	2	2	no	—
82	C₂×C₁₃×M₁₆	—	2	1	no	—
83	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₁₃	—	2	1	no	—
88	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₁₃×#127	—	2	1	no	—
91	C₁₃×#124	—	2	1	no	—
92	C₁₃×#121	—	2	1	no	—
93	C₁₃×#121	—	2	1	no	—
94	C₁₃×#120	—	4	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×Q₈×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	—	2	1	no	—
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	—	4	1	no	—
102	C₄×D₄×C₁₃	—	4	1	no	—
103	C₄×D₄×C₁₃	—	4	1	no	—
104	C₁₃×#117	—	2	1	no	—
105	C₁₃×#117	—	2	1	no	—
106	C₁₃×#117	—	2	1	no	—
107	C₁₃×#117	C₂³	1	1	yes	characteristic
108	C₁₃×#117	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
116	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
117	C₁₃×#107	—	2	1	no	—
118	C₁₃×#107	—	2	1	no	—
119	C₁₃×#107	—	2	1	no	—
120	C₁₃×#107	—	2	1	no	—
121	C₁₃×#107	—	2	1	no	—
122	C₁₃×#107	D₄	1	1	yes	characteristic
123	C₁₃×#107	D₄	1	1	yes	characteristic
124	C₁₃×#106	—	2	1	no	—
125	C₁₃×#106	—	2	1	no	—
126	C₁₃×#106	—	2	1	no	—
127	C₁₃×#106	—	2	1	no	—
128	C₁₃×#106	—	2	1	no	—
129	C₁₃×#106	D₄	1	1	yes	characteristic
130	C₁₃×#106	D₄	1	1	yes	characteristic
131	C₁₃×C₄⋊C₈	—	2	1	no	—
132	C₁₃×C₄⋊C₈	—	2	1	no	—
133	C₁₃×#104	—	2	2	no	—
134	C₁₃×#104	—	2	2	no	—
135	C₁₃×#103	—	2	1	no	—
136	C₁₃×#103	—	2	1	no	—
137	C₁₃×#103	—	2	1	no	—
138	C₁₃×#102	—	2	1	no	—
139	C₁₃×#102	—	2	1	no	—
140	C₁₃×#102	—	2	1	no	—
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×#100	—	2	2	no	—
148	C₁₃×C₂²⋊C₈	—	2	1	no	—
149	C₁₃×C₂²⋊C₈	—	2	1	no	—
150	C₁₃×#97	—	2	1	no	—
151	C₄×C₈×C₁₃	—	2	1	no	—
152	C₁₃×#95	—	4	1	no	—
153	#26195	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂⁴×C₁₃	—	2	1	no	—
155	C₁₃×#41	—	2	1	no	—
156	C₁₃×#41	—	2	1	no	—
157	C₁₃×#41	—	2	1	no	—
158	C₁₃×#41	—	2	1	no	—
159	C₁₃×#41	—	2	1	no	—
160	C₁₃×#41	—	2	1	no	—
161	C₁₃×#41	#41	1	2	yes	—
162	C₁₃×#41	#41	1	2	yes	—
163	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂×D₄×C₁₃	—	2	1	no	—
166	C₂×D₄×C₁₃	—	2	1	no	—
167	C₂×D₄×C₁₃	—	2	1	no	—
168	C₂×D₄×C₁₃	—	2	1	no	—
169	C₂×D₄×C₁₃	—	2	1	no	—
170	C₂×D₄×C₁₃	—	2	1	no	—
171	C₂×D₄×C₁₃	—	2	1	no	—
172	C₂×D₄×C₁₃	—	2	1	no	—
173	C₂×D₄×C₁₃	—	4	1	no	—
174	C₂×D₄×C₁₃	—	4	1	no	—
175	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	—	2	1	no	—
178	C₂²×C₄×C₁₃	—	2	1	no	—
179	C₂²×C₄×C₁₃	—	2	1	no	—
180	C₂²×C₄×C₁₃	—	2	1	no	—
181	C₂²×C₄×C₁₃	—	2	1	no	—
182	C₂²×C₄×C₁₃	—	2	1	no	—
183	C₂²×C₄×C₁₃	—	4	1	no	—
184	C₂²×C₄×C₁₃	—	4	1	no	—
185	C₂²×C₄×C₁₃	—	4	1	no	—
186	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₁₃×Q₁₆	—	2	2	no	—
188	C₁₃×SD₁₆	—	2	2	no	—
189	C₁₃×SD₁₆	—	2	2	no	—
190	C₁₃×SD₁₆	—	4	2	no	—
191	C₁₃×D₈	—	2	2	no	—
192	C₁₃×D₈	—	4	2	no	—
193	C₁₃×M₁₆	—	2	4	no	—
194	C₁₃×M₁₆	—	2	1	no	—
195	C₁₃×M₁₆	—	2	1	no	—
196	C₁₃×M₁₆	—	2	1	no	—
197	C₁₃×M₁₆	—	2	1	no	—
198	C₁₃×M₁₆	—	2	1	no	—
199	C₁₃×M₁₆	—	2	1	no	—
200	C₁₃×M₁₆	—	2	1	no	—
201	C₁₃×M₁₆	#41	1	2	yes	—
202	C₂×C₈×C₁₃	—	2	4	no	—
203	C₂×C₈×C₁₃	—	2	1	no	—
204	C₂×C₈×C₁₃	—	2	1	no	—
205	C₂×C₈×C₁₃	—	2	1	no	—
206	C₂×C₈×C₁₃	—	2	1	no	—
207	C₂×C₈×C₁₃	—	2	1	no	—
208	C₂×C₈×C₁₃	—	2	1	no	—
209	C₂×C₈×C₁₃	—	2	1	no	—
210	C₂×C₈×C₁₃	—	2	1	no	—
211	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₁₃×C₄⋊C₄	—	2	1	no	—
216	C₁₃×C₄⋊C₄	—	2	1	no	—
217	C₁₃×C₄⋊C₄	—	2	1	no	—
218	C₁₃×C₄⋊C₄	—	2	1	no	—
219	C₁₃×C₄⋊C₄	—	2	1	no	—
220	C₁₃×C₄⋊C₄	—	2	1	no	—
221	C₁₃×C₄⋊C₄	—	4	1	no	—
222	C₁₃×C₄⋊C₄	—	4	1	no	—
223	C₁₃×C₄⋊C₄	—	4	1	no	—
224	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
225	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
226	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
227	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
228	C₁₃×C₂²⋊C₄	—	2	1	no	—
229	C₁₃×C₂²⋊C₄	—	2	1	no	—
230	C₁₃×C₂²⋊C₄	—	4	1	no	—
231	C₁₃×C₂²⋊C₄	—	4	1	no	—
232	C₁₃×C₂²⋊C₄	—	4	1	no	—
233	C₁₃×C₂²⋊C₄	—	4	1	no	—
234	C₁₃×C₂²⋊C₄	—	4	1	no	—
235	C₁₃×C₂²⋊C₄	—	8	2	no	—
236	C₄²×C₁₃	—	2	1	no	—
237	C₄²×C₁₃	—	2	1	no	—
238	C₄²×C₁₃	—	2	1	no	—
239	C₄²×C₁₃	—	2	1	no	—
240	C₄²×C₁₃	—	4	1	no	—
241	C₄²×C₁₃	—	4	1	no	—
242	C₄²×C₁₃	—	4	1	no	—
243	#3096	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#3045	C₂×C₁₃	1	1	yes	characteristic
245	#2952	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#2913	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#2092	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#2090	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#2078	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#2037	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#1931	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#1922	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#1907	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#1883	C₂×C₁₃	1	1	yes	characteristic, complemented
255	#1876	C₂×C₁₃	1	1	yes	characteristic, complemented
256	#1860	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#1860	C₂×C₁₃	1	1	yes	characteristic, complemented
258	C₂³×C₁₃	—	2	1	no	—
259	C₂³×C₁₃	—	2	1	no	—
260	C₂³×C₁₃	—	4	1	no	—
261	C₂³×C₁₃	—	4	1	no	—
262	C₂³×C₁₃	—	4	1	no	—
263	C₂³×C₁₃	—	8	1	no	—
264	C₂³×C₁₃	—	8	1	no	—
265	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
266	Q₈×C₁₃	—	2	1	no	—
267	Q₈×C₁₃	—	2	1	no	—
268	Q₈×C₁₃	—	2	1	no	—
269	Q₈×C₁₃	#123	1	2	yes	—
270	D₄×C₁₃	—	2	2	no	—
271	D₄×C₁₃	—	2	2	no	—
272	D₄×C₁₃	—	2	1	no	—
273	D₄×C₁₃	—	2	1	no	—
274	D₄×C₁₃	—	2	1	no	—
275	D₄×C₁₃	—	4	1	no	—
276	D₄×C₁₃	—	4	1	no	—
277	D₄×C₁₃	—	4	1	no	—
278	D₄×C₁₃	—	4	1	no	—
279	D₄×C₁₃	—	4	1	no	—
280	D₄×C₁₃	—	4	1	no	—
281	D₄×C₁₃	—	16	1	no	—
282	D₄×C₁₃	—	16	1	no	—
283	D₄×C₁₃	#123	1	2	yes	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	2	no	—
287	C₂×C₄×C₁₃	—	2	1	no	—
288	C₂×C₄×C₁₃	—	2	1	no	—
289	C₂×C₄×C₁₃	—	2	1	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	1	no	—
292	C₂×C₄×C₁₃	—	4	1	no	—
293	C₂×C₄×C₁₃	—	4	1	no	—
294	C₂×C₄×C₁₃	—	4	1	no	—
295	C₂×C₄×C₁₃	—	4	1	no	—
296	C₂×C₄×C₁₃	—	4	1	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	—	4	1	no	—
299	C₂×C₄×C₁₃	—	4	1	no	—
300	C₂×C₄×C₁₃	—	8	1	no	—
301	C₂×C₄×C₁₃	—	8	1	no	—
302	C₂×C₄×C₁₃	—	8	1	no	—
303	C₂×C₄×C₁₃	—	16	1	no	—
304	C₂×C₄×C₁₃	—	16	1	no	—
305	C₂×C₄×C₁₃	—	16	1	no	—
306	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
310	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
311	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
312	C₈×C₁₃	—	2	1	no	—
313	C₈×C₁₃	—	2	1	no	—
314	C₈×C₁₃	—	2	1	no	—
315	C₈×C₁₃	—	2	2	no	—
316	C₈×C₁₃	—	2	1	no	—
317	C₈×C₁₃	—	4	1	no	—
318	C₈×C₁₃	—	4	1	no	—
319	C₈×C₁₃	—	4	1	no	—
320	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
323	#535	C₂²×C₁₃	1	1	yes	characteristic
324	#520	C₂²×C₁₃	1	1	yes	characteristic
325	#520	C₂²×C₁₃	1	1	yes	characteristic
326	#520	C₂²×C₁₃	1	1	yes	characteristic
327	#482	—	2	1	no	—
328	#482	—	2	1	no	—
329	#481	—	2	1	no	—
330	#480	—	2	1	no	—
331	#464	—	2	1	no	—
332	#463	—	2	1	no	—
333	#460	—	2	1	no	—
334	#459	—	2	1	no	—
335	#442	—	2	1	no	—
336	#441	—	2	1	no	—
337	C₄×SD₁₆	—	2	1	no	—
338	C₄×SD₁₆	—	2	1	no	—
339	#428	—	2	1	no	—
340	#428	—	2	1	no	—
341	#428	C₂²×C₁₃	1	1	yes	characteristic
342	#428	C₂²×C₁₃	1	1	yes	characteristic
343	#428	C₂²×C₁₃	1	1	yes	characteristic
344	#427	—	2	1	no	—
345	#427	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×#107	—	2	1	no	—
347	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
349	#424	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
352	#418	C₂²×C₁₃	1	1	yes	characteristic
353	#417	C₂²×C₁₃	1	1	yes	characteristic
354	#417	C₂²×C₁₃	1	1	yes	characteristic
355	#417	C₂²×C₁₃	1	1	yes	characteristic
356	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
359	#408	C₂²×C₁₃	1	1	yes	characteristic
360	#405	C₂²×C₁₃	1	1	yes	characteristic
361	#390	C₂²×C₁₃	1	1	yes	characteristic
362	#382	C₂²×C₁₃	1	1	yes	characteristic
363	#343	C₂²×C₁₃	1	1	yes	characteristic
364	#343	C₂²×C₁₃	1	1	yes	characteristic
365	#343	C₂²×C₁₃	1	1	yes	characteristic
366	#341	C₂²×C₁₃	1	1	yes	characteristic
367	#341	C₂²×C₁₃	1	1	yes	characteristic
368	#339	C₂²×C₁₃	1	1	yes	characteristic
369	#339	C₂²×C₁₃	1	1	yes	characteristic
370	#336	C₂²×C₁₃	1	1	yes	characteristic
371	C₂²×C₁₃	—	2	1	no	—
372	C₂²×C₁₃	—	2	1	no	—
373	C₂²×C₁₃	—	2	2	no	—
374	C₂²×C₁₃	—	4	1	no	—
375	C₂²×C₁₃	—	4	1	no	—
376	C₂²×C₁₃	—	4	1	no	—
377	C₂²×C₁₃	—	4	1	no	—
378	C₂²×C₁₃	—	4	1	no	—
379	C₂²×C₁₃	—	8	2	no	—
380	C₂²×C₁₃	—	8	1	no	—
381	C₂²×C₁₃	—	8	1	no	—
382	C₂²×C₁₃	—	8	1	no	—
383	C₂²×C₁₃	—	16	1	no	—
384	C₂²×C₁₃	#539	1	1	yes	characteristic
385	C₂²×C₁₃	D₄²	1	1	yes	characteristic
386	C₂²×C₁₃	#553	1	1	yes	characteristic
387	C₄×C₁₃	—	2	2	no	—
388	C₄×C₁₃	—	4	1	no	—
389	C₄×C₁₃	—	4	1	no	—
390	C₄×C₁₃	—	4	1	no	—
391	C₄×C₁₃	—	4	1	no	—
392	C₄×C₁₃	—	4	1	no	—
393	C₄×C₁₃	—	8	1	no	—
394	C₄×C₁₃	—	8	1	no	—
395	C₄×C₁₃	—	8	1	no	—
396	C₄×C₁₃	—	8	1	no	—
397	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
398	C₄×C₁₃	#525	1	1	yes	characteristic
399	C₄×C₁₃	#547	1	1	yes	characteristic
400	C₄×C₁₃	#548	1	1	yes	characteristic
401	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
402	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
403	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
404	AGL(1,ℤ/8)	—	2	2	no	—
405	AGL(1,ℤ/8)	—	2	2	no	—
406	#135	—	2	2	no	—
407	#135	—	2	2	no	—
408	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
409	C₂×SD₁₆	—	2	1	no	—
410	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
411	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
412	C₂×D₈	—	2	1	no	—
413	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
414	#131	—	2	2	no	—
415	#131	—	2	2	no	—
416	C₂×M₁₆	—	2	1	no	—
417	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
418	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
420	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
421	C₂²×C₈	—	2	1	no	—
422	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
424	#127	—	2	1	no	—
425	#124	—	2	1	no	—
426	#121	—	2	1	no	—
427	#121	—	2	1	no	—
428	#120	—	4	1	no	—
429	C₄×Q₈	—	2	1	no	—
430	C₄×Q₈	—	2	1	no	—
431	C₄×Q₈	—	2	1	no	—
432	C₄×D₄	—	2	1	no	—
433	C₄×D₄	—	2	1	no	—
434	C₄×D₄	—	2	1	no	—
435	C₄×D₄	—	4	1	no	—
436	C₄×D₄	—	4	1	no	—
437	C₄×D₄	—	4	1	no	—
438	#117	—	2	1	no	—
439	#117	—	2	1	no	—
440	#117	—	2	1	no	—
441	#117	C₂³×C₁₃	1	1	yes	characteristic
442	#117	C₂³×C₁₃	1	1	yes	characteristic
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
449	C₂×C₂²⋊C₄	—	4	1	no	—
450	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
451	#107	—	2	1	no	—
452	#107	—	2	1	no	—
453	#107	—	2	1	no	—
454	#107	—	2	1	no	—
455	#107	—	2	1	no	—
456	#107	D₄×C₁₃	1	1	yes	characteristic
457	#107	D₄×C₁₃	1	1	yes	characteristic
458	#106	—	2	1	no	—
459	#106	—	2	1	no	—
460	#106	—	2	1	no	—
461	#106	—	2	1	no	—
462	#106	—	2	1	no	—
463	#106	D₄×C₁₃	1	1	yes	characteristic
464	#106	D₄×C₁₃	1	1	yes	characteristic
465	C₄⋊C₈	—	2	1	no	—
466	C₄⋊C₈	—	2	1	no	—
467	#104	—	2	2	no	—
468	#104	—	2	2	no	—
469	#103	—	2	1	no	—
470	#103	—	2	1	no	—
471	#103	—	2	1	no	—
472	#102	—	2	1	no	—
473	#102	—	2	1	no	—
474	#102	—	2	1	no	—
475	#102	—	2	1	no	—
476	#102	—	2	1	no	—
477	#102	—	2	1	no	—
478	#102	—	2	1	no	—
479	#102	—	2	1	no	—
480	#102	—	2	1	no	—
481	#100	—	2	2	no	—
482	C₂²⋊C₈	—	2	1	no	—
483	C₂²⋊C₈	—	2	1	no	—
484	#97	—	2	1	no	—
485	C₄×C₈	—	2	1	no	—
486	#95	—	4	1	no	—
487	C₂×C₁₃	—	2	1	no	—
488	C₂×C₁₃	—	2	1	no	—
489	C₂×C₁₃	—	4	2	no	—
490	C₂×C₁₃	—	8	1	no	—
491	C₂×C₁₃	—	16	1	no	—
492	C₂×C₁₃	#2443	1	1	yes	characteristic
493	C₂×C₁₃	#3288	1	1	yes	characteristic
494	C₂×C₁₃	#3290	1	1	yes	characteristic
495	C₂⁴	—	2	1	no	—
496	#41	—	2	1	no	—
497	#41	—	2	1	no	—
498	#41	—	2	1	no	—
499	#41	—	2	1	no	—
500	#41	—	2	1	no	—
501	#41	—	2	1	no	—
502	#41	C₁₃×#41	1	2	yes	—
503	#41	C₁₃×#41	1	2	yes	—
504	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
505	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	4	1	no	—
515	C₂×D₄	—	4	1	no	—
516	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
517	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	4	1	no	—
525	C₂²×C₄	—	4	1	no	—
526	C₂²×C₄	—	4	1	no	—
527	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
528	Q₁₆	—	2	2	no	—
529	SD₁₆	—	2	2	no	—
530	SD₁₆	—	2	2	no	—
531	SD₁₆	—	4	2	no	—
532	D₈	—	2	2	no	—
533	D₈	—	4	2	no	—
534	M₁₆	—	2	4	no	—
535	M₁₆	—	2	1	no	—
536	M₁₆	—	2	1	no	—
537	M₁₆	—	2	1	no	—
538	M₁₆	—	2	1	no	—
539	M₁₆	—	2	1	no	—
540	M₁₆	—	2	1	no	—
541	M₁₆	—	2	1	no	—
542	M₁₆	C₁₃×#41	1	2	yes	—
543	C₂×C₈	—	2	4	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
553	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
554	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
555	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	4	1	no	—
563	C₄⋊C₄	—	4	1	no	—
564	C₄⋊C₄	—	4	1	no	—
565	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
566	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
567	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
568	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
569	C₂²⋊C₄	—	2	1	no	—
570	C₂²⋊C₄	—	2	1	no	—
571	C₂²⋊C₄	—	4	1	no	—
572	C₂²⋊C₄	—	4	1	no	—
573	C₂²⋊C₄	—	4	1	no	—
574	C₂²⋊C₄	—	4	1	no	—
575	C₂²⋊C₄	—	4	1	no	—
576	C₂²⋊C₄	—	8	2	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	4	1	no	—
582	C₄²	—	4	1	no	—
583	C₄²	—	4	1	no	—
584	C₁₃	#26195	1	1	yes	characteristic, direct product factor, Sylow
585	C₂³	—	2	1	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	8	1	no	—
591	C₂³	—	8	1	no	—
592	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
593	Q₈	—	2	1	no	—
594	Q₈	—	2	1	no	—
595	Q₈	—	2	1	no	—
596	Q₈	C₁₃×#123	1	2	yes	—
597	D₄	—	2	2	no	—
598	D₄	—	2	2	no	—
599	D₄	—	2	1	no	—
600	D₄	—	2	1	no	—
601	D₄	—	2	1	no	—
602	D₄	—	4	1	no	—
603	D₄	—	4	1	no	—
604	D₄	—	4	1	no	—
605	D₄	—	4	1	no	—
606	D₄	—	4	1	no	—
607	D₄	—	4	1	no	—
608	D₄	—	16	1	no	—
609	D₄	—	16	1	no	—
610	D₄	C₁₃×#123	1	2	yes	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	8	1	no	—
628	C₂×C₄	—	8	1	no	—
629	C₂×C₄	—	8	1	no	—
630	C₂×C₄	—	16	1	no	—
631	C₂×C₄	—	16	1	no	—
632	C₂×C₄	—	16	1	no	—
633	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
634	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
635	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
636	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
637	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
638	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
639	C₈	—	2	1	no	—
640	C₈	—	2	1	no	—
641	C₈	—	2	1	no	—
642	C₈	—	2	2	no	—
643	C₈	—	2	1	no	—
644	C₈	—	4	1	no	—
645	C₈	—	4	1	no	—
646	C₈	—	4	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	—	8	2	no	—
656	C₂²	—	8	1	no	—
657	C₂²	—	8	1	no	—
658	C₂²	—	8	1	no	—
659	C₂²	—	16	1	no	—
660	C₂²	C₁₃×#539	1	1	yes	characteristic
661	C₂²	D₄²×C₁₃	1	1	yes	characteristic
662	C₂²	C₁₃×#553	1	1	yes	characteristic
663	C₄	—	2	2	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	1	no	—
669	C₄	—	8	1	no	—
670	C₄	—	8	1	no	—
671	C₄	—	8	1	no	—
672	C₄	—	8	1	no	—
673	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
674	C₄	C₁₃×#525	1	1	yes	characteristic
675	C₄	C₁₃×#547	1	1	yes	characteristic
676	C₄	C₁₃×#548	1	1	yes	characteristic
677	C₂	—	2	1	no	—
678	C₂	—	2	1	no	—
679	C₂	—	4	2	no	—
680	C₂	—	8	1	no	—
681	C₂	—	16	1	no	—
682	C₂	C₁₃×#2443	1	1	yes	characteristic
683	C₂	C₁₃×#3288	1	1	yes	characteristic
684	C₂	C₁₃×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3045	C₂
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×#3096	C₂	semidirect
3. C₁₃×#2952	C₂	semidirect
4. C₁₃×#2913	C₂	semidirect
5. C₁₃×#2092	C₂	semidirect
6. C₁₃×#2090	C₂	semidirect
7. C₁₃×#2078	C₂	semidirect
8. C₁₃×#2037	C₂	semidirect
9. C₁₃×#1931	C₂	semidirect
10. C₁₃×#1922	C₂	semidirect
11. C₁₃×#1907	C₂	semidirect
12. C₁₃×#1883	C₂	semidirect
13. C₁₃×#1876	C₂	semidirect
14. C₁₃×#1860	C₂	semidirect
15. C₁₃×#1860	C₂	semidirect
153. #26195	C₁₃	direct (N × H)
243. #3096	C₂×C₁₃	semidirect
245. #2952	C₂×C₁₃	semidirect
246. #2913	C₂×C₁₃	semidirect
247. #2092	C₂×C₁₃	semidirect
248. #2090	C₂×C₁₃	semidirect
249. #2078	C₂×C₁₃	semidirect
250. #2037	C₂×C₁₃	semidirect
251. #1931	C₂×C₁₃	semidirect
252. #1922	C₂×C₁₃	semidirect
253. #1907	C₂×C₁₃	semidirect
254. #1883	C₂×C₁₃	semidirect
255. #1876	C₂×C₁₃	semidirect
256. #1860	C₂×C₁₃	semidirect
257. #1860	C₂×C₁₃	semidirect
584. C₁₃	#26195	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×#3096	2
C₁₃×#3045	2
C₁₃×#2952	2
C₁₃×#2913	2
C₁₃×#2092	2
C₁₃×#2090	2
C₁₃×#2078	2
C₁₃×#2037	2
C₁₃×#1931	2
C₁₃×#1922	2
C₁₃×#1907	2
C₁₃×#1883	2
C₁₃×#1876	2
C₁₃×#1860	2
#26195	13

Subgroups — C13×#26195 #15712534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26195 #15712534