Subgroups — C₁₃×#24144 #15710483

Order 3328.

1278 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2541	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2037	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2002	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1986	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1965	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1887	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1856	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1806	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
13	C₁₃×#559	—	2	1	no	—
14	C₁₃×#559	—	2	1	no	—
15	C₁₃×#550	—	2	1	no	—
16	C₁₃×#550	—	2	1	no	—
17	C₁₃×#546	—	2	2	no	—
18	C₁₃×#546	—	2	2	no	—
19	C₁₃×#540	—	2	2	no	—
20	C₁₃×#535	C₂²	1	2	yes	—
21	C₁₃×#533	C₂²	1	1	yes	characteristic
22	C₁₃×#532	—	2	1	no	—
23	C₁₃×#532	—	2	1	no	—
24	C₂×C₁₃×#127	C₂²	1	2	yes	—
25	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#121	—	2	2	no	—
27	C₁₃×#518	C₂²	1	2	yes	—
28	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#478	—	2	2	no	—
31	C₁₃×#476	—	2	1	no	—
32	C₁₃×#474	—	2	1	no	—
33	C₁₃×#442	—	2	1	no	—
34	C₁₃×#440	—	2	1	no	—
35	C₄×C₁₃×SD₁₆	—	2	1	no	—
36	C₄×C₁₃×D₈	—	2	1	no	—
37	C₁₃×#428	C₂²	1	2	yes	—
38	C₁₃×#428	C₂²	1	1	yes	characteristic
39	C₁₃×#423	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#104	C₂²	1	2	yes	—
41	C₁₃×#418	C₂²	1	2	yes	—
42	C₁₃×#418	C₂²	1	1	yes	characteristic
43	C₁₃×#417	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#100	C₂²	1	2	yes	—
45	C₂×C₁₃×#100	C₂²	1	2	yes	—
46	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
47	C₁₃×#392	—	2	2	no	—
48	C₁₃×#390	C₂²	1	2	yes	—
49	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₁₃×#339	C₂²	1	2	yes	—
51	C₁₃×#339	C₂²	1	2	yes	—
52	C₁₃×#339	C₂²	1	2	yes	—
53	C₂×C₁₃×#41	—	2	2	no	—
54	C₂×C₁₃×#41	—	2	2	no	—
55	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₁₃	—	2	4	no	—
57	C₂²×D₄×C₁₃	D₄	1	2	yes	—
58	C₂²×D₄×C₁₃	D₄	1	2	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	—	2	1	no	—
62	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
63	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
64	C₂×C₁₃×SD₁₆	—	2	1	no	—
65	C₂×C₁₃×D₈	—	2	1	no	—
66	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
68	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
69	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
70	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
71	C₁₃×#127	—	2	2	no	—
72	C₁₃×#127	—	2	4	no	—
73	C₁₃×#127	—	2	1	no	—
74	C₁₃×#127	—	2	1	no	—
75	C₁₃×#127	—	2	1	no	—
76	C₁₃×#127	—	2	1	no	—
77	C₁₃×#127	—	4	2	no	—
78	C₁₃×#125	D₄	1	2	yes	complemented
79	C₁₃×#124	—	2	2	no	—
80	C₁₃×#124	—	2	2	no	—
81	C₁₃×#124	—	2	2	no	—
82	C₁₃×#123	—	2	4	no	—
83	C₁₃×#123	—	2	4	no	—
84	C₁₃×C₂²⋊Q₈	—	2	1	no	—
85	C₁₃×C₂²⋊Q₈	—	2	1	no	—
86	C₁₃×#121	—	2	2	no	—
87	C₁₃×#121	—	2	2	no	—
88	C₁₃×#121	—	2	4	no	—
89	C₁₃×#121	—	2	4	no	—
90	C₁₃×#121	—	2	2	no	—
91	C₁₃×#121	—	2	2	no	—
92	C₁₃×#121	—	4	8	no	—
93	C₁₃×#120	—	2	4	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic, complemented
97	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic, complemented
98	C₄×D₄×C₁₃	—	2	2	no	—
99	C₄×D₄×C₁₃	—	2	2	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	—	2	2	no	—
104	C₄×D₄×C₁₃	—	2	2	no	—
105	C₄×D₄×C₁₃	—	2	2	no	—
106	C₄×D₄×C₁₃	—	2	1	no	—
107	C₄×D₄×C₁₃	—	2	1	no	—
108	C₄×D₄×C₁₃	—	2	1	no	—
109	C₄×D₄×C₁₃	—	2	1	no	—
110	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic, complemented
111	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic, complemented
112	C₁₃×#117	—	2	1	no	—
113	C₁₃×#117	C₂³	1	1	yes	characteristic
114	C₁₃×#117	C₂³	1	2	yes	—
115	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₄²×C₁₃	—	2	1	no	—
121	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
123	C₁₃×#107	—	2	1	no	—
124	C₁₃×#107	—	2	2	no	—
125	C₁₃×#106	—	2	1	no	—
126	C₁₃×#106	—	2	2	no	—
127	C₁₃×C₄⋊C₈	—	2	1	no	—
128	C₁₃×C₄⋊C₈	—	2	1	no	—
129	C₁₃×#104	—	4	2	no	—
130	C₁₃×#103	—	2	1	no	—
131	C₁₃×#102	—	2	1	no	—
132	C₁₃×#102	—	2	1	no	—
133	C₁₃×#102	—	2	1	no	—
134	C₁₃×#102	—	2	2	no	—
135	C₁₃×#102	—	2	2	no	—
136	C₁₃×#100	—	2	4	no	—
137	C₁₃×#100	—	4	2	no	—
138	C₁₃×#97	—	2	1	no	—
139	C₄×C₈×C₁₃	—	2	1	no	—
140	C₁₃×#95	—	2	1	no	—
141	#24144	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂⁴×C₁₃	—	2	1	no	—
143	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
144	C₁₃×#41	—	2	1	no	—
145	C₁₃×#41	—	2	1	no	—
146	C₁₃×#41	—	2	1	no	—
147	C₁₃×#41	—	2	1	no	—
148	C₁₃×#41	—	8	4	no	—
149	C₁₃×#41	—	8	4	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	2	4	no	—
156	C₂×D₄×C₁₃	—	2	2	no	—
157	C₂×D₄×C₁₃	—	2	2	no	—
158	C₂×D₄×C₁₃	—	2	2	no	—
159	C₂×D₄×C₁₃	—	2	2	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	—	2	1	no	—
162	C₂×D₄×C₁₃	—	2	2	no	—
163	C₂×D₄×C₁₃	—	2	2	no	—
164	C₂×D₄×C₁₃	—	2	1	no	—
165	C₂×D₄×C₁₃	—	2	2	no	—
166	C₂×D₄×C₁₃	—	2	2	no	—
167	C₂×D₄×C₁₃	—	2	2	no	—
168	C₂×D₄×C₁₃	—	2	1	no	—
169	C₂×D₄×C₁₃	—	2	1	no	—
170	C₂×D₄×C₁₃	—	2	2	no	—
171	C₂×D₄×C₁₃	—	4	4	no	—
172	C₂×D₄×C₁₃	—	4	8	no	—
173	C₂×D₄×C₁₃	—	4	8	no	—
174	C₂×D₄×C₁₃	—	8	2	no	—
175	C₂×D₄×C₁₃	—	8	4	no	—
176	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂×D₄×C₁₃	#41	1	2	yes	complemented
178	C₂²×C₄×C₁₃	—	2	2	no	—
179	C₂²×C₄×C₁₃	—	2	4	no	—
180	C₂²×C₄×C₁₃	—	2	4	no	—
181	C₂²×C₄×C₁₃	—	2	1	no	—
182	C₂²×C₄×C₁₃	—	2	1	no	—
183	C₂²×C₄×C₁₃	—	2	1	no	—
184	C₂²×C₄×C₁₃	—	2	1	no	—
185	C₂²×C₄×C₁₃	—	4	4	no	—
186	C₂²×C₄×C₁₃	—	4	1	no	—
187	C₂²×C₄×C₁₃	—	4	1	no	—
188	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₁₃×SD₁₆	—	2	4	no	—
192	C₁₃×D₈	—	2	4	no	—
193	C₁₃×M₁₆	—	2	1	no	—
194	C₁₃×M₁₆	—	2	2	no	—
195	C₁₃×M₁₆	—	2	1	no	—
196	C₁₃×M₁₆	—	2	2	no	—
197	C₁₃×M₁₆	—	2	1	no	—
198	C₁₃×M₁₆	#41	1	2	yes	complemented
199	C₂×C₈×C₁₃	—	2	1	no	—
200	C₂×C₈×C₁₃	—	2	1	no	—
201	C₂×C₈×C₁₃	—	2	2	no	—
202	C₁₃×C₄⋊C₄	—	2	4	no	—
203	C₁₃×C₄⋊C₄	—	2	1	no	—
204	C₁₃×C₄⋊C₄	—	2	1	no	—
205	C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₁₃×C₄⋊C₄	—	2	2	no	—
208	C₁₃×C₄⋊C₄	—	2	2	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	2	1	no	—
211	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
212	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
213	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
214	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
215	C₁₃×C₂²⋊C₄	—	2	4	no	—
216	C₁₃×C₂²⋊C₄	—	2	4	no	—
217	C₁₃×C₂²⋊C₄	—	2	4	no	—
218	C₁₃×C₂²⋊C₄	—	2	4	no	—
219	C₁₃×C₂²⋊C₄	—	2	1	no	—
220	C₁₃×C₂²⋊C₄	—	2	2	no	—
221	C₁₃×C₂²⋊C₄	—	2	1	no	—
222	C₁₃×C₂²⋊C₄	—	2	1	no	—
223	C₁₃×C₂²⋊C₄	—	4	8	no	—
224	C₁₃×C₂²⋊C₄	—	4	1	no	—
225	C₁₃×C₂²⋊C₄	—	4	1	no	—
226	C₄²×C₁₃	—	2	1	no	—
227	C₄²×C₁₃	—	2	1	no	—
228	C₄²×C₁₃	—	2	1	no	—
229	C₄²×C₁₃	—	2	2	no	—
230	C₄²×C₁₃	—	2	2	no	—
231	C₄²×C₁₃	—	2	2	no	—
232	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
233	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
236	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#3077	C₂×C₁₃	1	1	yes	characteristic, complemented
238	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#2541	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#2037	C₂×C₁₃	1	2	yes	complemented
241	#2002	C₂×C₁₃	1	2	yes	complemented
242	#1986	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#1965	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#1887	C₂×C₁₃	1	2	yes	complemented
245	#1856	C₂×C₁₃	1	2	yes	complemented
246	#1806	C₂×C₁₃	1	1	yes	characteristic, complemented
247	C₂³×C₁₃	—	2	4	no	—
248	C₂³×C₁₃	—	2	1	no	—
249	C₂³×C₁₃	—	2	2	no	—
250	C₂³×C₁₃	—	2	4	no	—
251	C₂³×C₁₃	—	2	4	no	—
252	C₂³×C₁₃	—	4	2	no	—
253	C₂³×C₁₃	—	4	2	no	—
254	C₂³×C₁₃	—	4	4	no	—
255	C₂³×C₁₃	—	4	4	no	—
256	C₂³×C₁₃	—	4	1	no	—
257	C₂³×C₁₃	—	4	1	no	—
258	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
259	Q₈×C₁₃	—	2	1	no	—
260	Q₈×C₁₃	—	2	1	no	—
261	Q₈×C₁₃	—	4	2	no	—
262	Q₈×C₁₃	—	4	2	no	—
263	D₄×C₁₃	—	2	1	no	—
264	D₄×C₁₃	—	2	2	no	—
265	D₄×C₁₃	—	2	1	no	—
266	D₄×C₁₃	—	2	2	no	—
267	D₄×C₁₃	—	4	4	no	—
268	D₄×C₁₃	—	4	1	no	—
269	D₄×C₁₃	—	4	1	no	—
270	D₄×C₁₃	—	4	2	no	—
271	D₄×C₁₃	—	4	1	no	—
272	D₄×C₁₃	—	4	2	no	—
273	D₄×C₁₃	—	4	2	no	—
274	D₄×C₁₃	—	4	1	no	—
275	D₄×C₁₃	—	4	2	no	—
276	D₄×C₁₃	—	4	4	no	—
277	D₄×C₁₃	—	8	2	no	—
278	D₄×C₁₃	—	8	2	no	—
279	D₄×C₁₃	—	8	4	no	—
280	D₄×C₁₃	—	8	4	no	—
281	D₄×C₁₃	—	8	16	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	4	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	1	no	—
286	C₂×C₄×C₁₃	—	2	1	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	2	no	—
289	C₂×C₄×C₁₃	—	4	1	no	—
290	C₂×C₄×C₁₃	—	4	2	no	—
291	C₂×C₄×C₁₃	—	4	2	no	—
292	C₂×C₄×C₁₃	—	4	2	no	—
293	C₂×C₄×C₁₃	—	4	1	no	—
294	C₂×C₄×C₁₃	—	4	1	no	—
295	C₂×C₄×C₁₃	—	4	2	no	—
296	C₂×C₄×C₁₃	—	4	2	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	—	8	2	no	—
299	C₂×C₄×C₁₃	—	8	4	no	—
300	C₂×C₄×C₁₃	—	8	4	no	—
301	C₂×C₄×C₁₃	—	8	2	no	—
302	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
303	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
304	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
305	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
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	H(5,𝔽₂)	1	1	yes	characteristic
311	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
312	C₈×C₁₃	—	2	2	no	—
313	C₈×C₁₃	—	4	1	no	—
314	C₈×C₁₃	—	4	2	no	—
315	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
316	#559	—	2	1	no	—
317	#559	—	2	1	no	—
318	#550	—	2	1	no	—
319	#550	—	2	1	no	—
320	#546	—	2	2	no	—
321	#546	—	2	2	no	—
322	#540	—	2	2	no	—
323	#535	C₂²×C₁₃	1	2	yes	—
324	#533	C₂²×C₁₃	1	1	yes	characteristic
325	#532	—	2	1	no	—
326	#532	—	2	1	no	—
327	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#127	C₂²×C₁₃	1	2	yes	—
329	C₂×#121	—	2	2	no	—
330	#518	C₂²×C₁₃	1	2	yes	—
331	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
333	#478	—	2	2	no	—
334	#476	—	2	1	no	—
335	#474	—	2	1	no	—
336	#442	—	2	1	no	—
337	#440	—	2	1	no	—
338	C₄×SD₁₆	—	2	1	no	—
339	C₄×D₈	—	2	1	no	—
340	#428	C₂²×C₁₃	1	2	yes	—
341	#428	C₂²×C₁₃	1	1	yes	characteristic
342	#423	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×#104	C₂²×C₁₃	1	2	yes	—
344	#418	C₂²×C₁₃	1	2	yes	—
345	#418	C₂²×C₁₃	1	1	yes	characteristic
346	#417	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×#100	C₂²×C₁₃	1	2	yes	—
348	C₂×#100	C₂²×C₁₃	1	2	yes	—
349	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
350	#392	—	2	2	no	—
351	#390	C₂²×C₁₃	1	2	yes	—
352	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
353	#339	C₂²×C₁₃	1	2	yes	—
354	#339	C₂²×C₁₃	1	2	yes	—
355	#339	C₂²×C₁₃	1	2	yes	—
356	C₂²×C₁₃	—	2	1	no	—
357	C₂²×C₁₃	—	2	1	no	—
358	C₂²×C₁₃	—	4	4	no	—
359	C₂²×C₁₃	—	4	1	no	—
360	C₂²×C₁₃	—	4	2	no	—
361	C₂²×C₁₃	—	4	4	no	—
362	C₂²×C₁₃	—	4	1	no	—
363	C₂²×C₁₃	—	4	4	no	—
364	C₂²×C₁₃	—	4	1	no	—
365	C₂²×C₁₃	—	4	4	no	—
366	C₂²×C₁₃	—	8	4	no	—
367	C₂²×C₁₃	—	8	4	no	—
368	C₂²×C₁₃	—	8	2	no	—
369	C₂²×C₁₃	—	8	1	no	—
370	C₂²×C₁₃	—	8	1	no	—
371	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
372	C₂²×C₁₃	#546	1	1	yes	characteristic
373	C₂²×C₁₃	#547	1	1	yes	characteristic
374	C₄×C₁₃	—	2	1	no	—
375	C₄×C₁₃	—	2	1	no	—
376	C₄×C₁₃	—	2	1	no	—
377	C₄×C₁₃	—	4	4	no	—
378	C₄×C₁₃	—	4	1	no	—
379	C₄×C₁₃	—	4	1	no	—
380	C₄×C₁₃	—	4	2	no	—
381	C₄×C₁₃	—	4	1	no	—
382	C₄×C₁₃	—	4	2	no	—
383	C₄×C₁₃	—	8	1	no	—
384	C₄×C₁₃	#453	1	2	yes	—
385	C₄×C₁₃	#525	1	1	yes	characteristic
386	C₄×C₁₃	#537	1	1	yes	characteristic
387	C₄×C₁₃	#548	1	1	yes	characteristic
388	C₄×C₁₃	#550	1	1	yes	characteristic
389	C₂×#41	—	2	2	no	—
390	C₂×#41	—	2	2	no	—
391	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
392	C₂²×D₄	—	2	4	no	—
393	C₂²×D₄	D₄×C₁₃	1	2	yes	—
394	C₂²×D₄	D₄×C₁₃	1	2	yes	—
395	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
396	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
397	C₂³×C₄	—	2	1	no	—
398	AGL(1,ℤ/8)	—	2	2	no	—
399	AGL(1,ℤ/8)	—	2	2	no	—
400	C₂×SD₁₆	—	2	1	no	—
401	C₂×D₈	—	2	1	no	—
402	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
404	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
405	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic, complemented
406	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic, complemented
407	#127	—	2	2	no	—
408	#127	—	2	4	no	—
409	#127	—	2	1	no	—
410	#127	—	2	1	no	—
411	#127	—	2	1	no	—
412	#127	—	2	1	no	—
413	#127	—	4	2	no	—
414	#125	D₄×C₁₃	1	2	yes	complemented
415	#124	—	2	2	no	—
416	#124	—	2	2	no	—
417	#124	—	2	2	no	—
418	#123	—	2	4	no	—
419	#123	—	2	4	no	—
420	C₂²⋊Q₈	—	2	1	no	—
421	C₂²⋊Q₈	—	2	1	no	—
422	#121	—	2	2	no	—
423	#121	—	2	2	no	—
424	#121	—	2	4	no	—
425	#121	—	2	4	no	—
426	#121	—	2	2	no	—
427	#121	—	2	2	no	—
428	#121	—	4	8	no	—
429	#120	—	2	4	no	—
430	C₄×Q₈	—	2	1	no	—
431	C₄×Q₈	—	2	1	no	—
432	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic, complemented
433	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic, complemented
434	C₄×D₄	—	2	2	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	—	2	1	no	—
437	C₄×D₄	—	2	1	no	—
438	C₄×D₄	—	2	2	no	—
439	C₄×D₄	—	2	2	no	—
440	C₄×D₄	—	2	2	no	—
441	C₄×D₄	—	2	2	no	—
442	C₄×D₄	—	2	1	no	—
443	C₄×D₄	—	2	1	no	—
444	C₄×D₄	—	2	1	no	—
445	C₄×D₄	—	2	1	no	—
446	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic, complemented
447	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic, complemented
448	#117	—	2	1	no	—
449	#117	C₂³×C₁₃	1	1	yes	characteristic
450	#117	C₂³×C₁₃	1	2	yes	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	—	2	4	no	—
454	C₂×C₂²⋊C₄	—	2	4	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₄²	—	2	1	no	—
457	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
458	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
459	#107	—	2	1	no	—
460	#107	—	2	2	no	—
461	#106	—	2	1	no	—
462	#106	—	2	2	no	—
463	C₄⋊C₈	—	2	1	no	—
464	C₄⋊C₈	—	2	1	no	—
465	#104	—	4	2	no	—
466	#103	—	2	1	no	—
467	#102	—	2	1	no	—
468	#102	—	2	1	no	—
469	#102	—	2	1	no	—
470	#102	—	2	2	no	—
471	#102	—	2	2	no	—
472	#100	—	2	4	no	—
473	#100	—	4	2	no	—
474	#97	—	2	1	no	—
475	C₄×C₈	—	2	1	no	—
476	#95	—	2	1	no	—
477	C₂×C₁₃	—	2	1	no	—
478	C₂×C₁₃	—	2	1	no	—
479	C₂×C₁₃	—	8	1	no	—
480	C₂×C₁₃	—	8	4	no	—
481	C₂×C₁₃	—	8	2	no	—
482	C₂×C₁₃	#2407	1	1	yes	characteristic
483	C₂×C₁₃	C₂×#453	1	1	yes	characteristic
484	C₂×C₁₃	#3019	1	1	yes	characteristic
485	C₂⁴	—	2	1	no	—
486	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
487	#41	—	2	1	no	—
488	#41	—	2	1	no	—
489	#41	—	2	1	no	—
490	#41	—	2	1	no	—
491	#41	—	8	4	no	—
492	#41	—	8	4	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	4	no	—
498	C₂×D₄	—	2	4	no	—
499	C₂×D₄	—	2	2	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	2	no	—
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	4	4	no	—
515	C₂×D₄	—	4	8	no	—
516	C₂×D₄	—	4	8	no	—
517	C₂×D₄	—	8	2	no	—
518	C₂×D₄	—	8	4	no	—
519	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
520	C₂×D₄	C₁₃×#41	1	2	yes	complemented
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	4	no	—
523	C₂²×C₄	—	2	4	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	4	4	no	—
529	C₂²×C₄	—	4	1	no	—
530	C₂²×C₄	—	4	1	no	—
531	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
532	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
534	SD₁₆	—	2	4	no	—
535	D₈	—	2	4	no	—
536	M₁₆	—	2	1	no	—
537	M₁₆	—	2	2	no	—
538	M₁₆	—	2	1	no	—
539	M₁₆	—	2	2	no	—
540	M₁₆	—	2	1	no	—
541	M₁₆	C₁₃×#41	1	2	yes	complemented
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	2	no	—
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	2	no	—
551	C₄⋊C₄	—	2	2	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
555	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
556	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
557	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
558	C₂²⋊C₄	—	2	4	no	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	2	4	no	—
561	C₂²⋊C₄	—	2	4	no	—
562	C₂²⋊C₄	—	2	1	no	—
563	C₂²⋊C₄	—	2	2	no	—
564	C₂²⋊C₄	—	2	1	no	—
565	C₂²⋊C₄	—	2	1	no	—
566	C₂²⋊C₄	—	4	8	no	—
567	C₂²⋊C₄	—	4	1	no	—
568	C₂²⋊C₄	—	4	1	no	—
569	C₄²	—	2	1	no	—
570	C₄²	—	2	1	no	—
571	C₄²	—	2	1	no	—
572	C₄²	—	2	2	no	—
573	C₄²	—	2	2	no	—
574	C₄²	—	2	2	no	—
575	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
576	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
577	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
578	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
579	C₁₃	#24144	1	1	yes	characteristic, direct product factor, Sylow
580	C₂³	—	2	4	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	4	no	—
584	C₂³	—	2	4	no	—
585	C₂³	—	4	2	no	—
586	C₂³	—	4	2	no	—
587	C₂³	—	4	4	no	—
588	C₂³	—	4	4	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	4	1	no	—
591	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
592	Q₈	—	2	1	no	—
593	Q₈	—	2	1	no	—
594	Q₈	—	4	2	no	—
595	Q₈	—	4	2	no	—
596	D₄	—	2	1	no	—
597	D₄	—	2	2	no	—
598	D₄	—	2	1	no	—
599	D₄	—	2	2	no	—
600	D₄	—	4	4	no	—
601	D₄	—	4	1	no	—
602	D₄	—	4	1	no	—
603	D₄	—	4	4	no	—
604	D₄	—	4	2	no	—
605	D₄	—	4	1	no	—
606	D₄	—	4	2	no	—
607	D₄	—	4	2	no	—
608	D₄	—	4	1	no	—
609	D₄	—	4	2	no	—
610	D₄	—	8	2	no	—
611	D₄	—	8	2	no	—
612	D₄	—	8	4	no	—
613	D₄	—	8	4	no	—
614	D₄	—	8	16	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	—	4	2	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	8	2	no	—
632	C₂×C₄	—	8	4	no	—
633	C₂×C₄	—	8	4	no	—
634	C₂×C₄	—	8	2	no	—
635	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
636	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
637	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
638	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
639	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
640	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
641	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
642	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
643	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
644	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
645	C₈	—	2	2	no	—
646	C₈	—	4	1	no	—
647	C₈	—	4	2	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	4	4	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	4	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	4	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	4	no	—
658	C₂²	—	8	4	no	—
659	C₂²	—	8	4	no	—
660	C₂²	—	8	2	no	—
661	C₂²	—	8	1	no	—
662	C₂²	—	8	1	no	—
663	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
664	C₂²	C₁₃×#546	1	1	yes	characteristic
665	C₂²	C₁₃×#547	1	1	yes	characteristic
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	1	no	—
669	C₄	—	4	4	no	—
670	C₄	—	4	1	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	1	no	—
675	C₄	—	8	1	no	—
676	C₄	C₁₃×#453	1	2	yes	—
677	C₄	C₁₃×#525	1	1	yes	characteristic
678	C₄	C₁₃×#537	1	1	yes	characteristic
679	C₄	C₁₃×#548	1	1	yes	characteristic
680	C₄	C₁₃×#550	1	1	yes	characteristic
681	C₂	—	2	1	no	—
682	C₂	—	2	1	no	—
683	C₂	—	8	2	no	—
684	C₂	—	8	4	no	—
685	C₂	—	8	1	no	—
686	C₂	C₁₃×#2407	1	1	yes	characteristic
687	C₂	C₂×C₁₃×#453	1	1	yes	characteristic
688	C₂	C₁₃×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3508	C₂	semidirect
2. C₁₃×#3077	C₂	semidirect
3. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
4. C₁₃×#2541	C₂	semidirect
5. C₁₃×#2037	C₂	semidirect
6. C₁₃×#2002	C₂	semidirect
7. C₁₃×#1986	C₂	semidirect
8. C₁₃×#1965	C₂	semidirect
9. C₁₃×#1887	C₂	semidirect
10. C₁₃×#1856	C₂	semidirect
11. C₁₃×#1806	C₂	semidirect
69. C₁₃×C₄⋊Q₈	D₄	semidirect
70. C₁₃×C₄⋊Q₈	D₄	semidirect
78. C₁₃×#125	D₄	semidirect
96. C₄×Q₈×C₁₃	D₄	semidirect
97. C₄×Q₈×C₁₃	D₄	semidirect
110. C₄×D₄×C₁₃	D₄	semidirect
111. C₄×D₄×C₁₃	D₄	semidirect
141. #24144	C₁₃	direct (N × H)
177. C₂×D₄×C₁₃	#41	semidirect
198. C₁₃×M₁₆	#41	semidirect
236. #3508	C₂×C₁₃	semidirect
237. #3077	C₂×C₁₃	semidirect
238. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
239. #2541	C₂×C₁₃	semidirect
240. #2037	C₂×C₁₃	semidirect
241. #2002	C₂×C₁₃	semidirect
242. #1986	C₂×C₁₃	semidirect
243. #1965	C₂×C₁₃	semidirect
244. #1887	C₂×C₁₃	semidirect
245. #1856	C₂×C₁₃	semidirect
246. #1806	C₂×C₁₃	semidirect
405. C₄⋊Q₈	D₄×C₁₃	semidirect
406. C₄⋊Q₈	D₄×C₁₃	semidirect
414. #125	D₄×C₁₃	semidirect
432. C₄×Q₈	D₄×C₁₃	semidirect
433. C₄×Q₈	D₄×C₁₃	semidirect
446. C₄×D₄	D₄×C₁₃	semidirect
447. C₄×D₄	D₄×C₁₃	semidirect
520. C₂×D₄	C₁₃×#41	semidirect
541. M₁₆	C₁₃×#41	semidirect
579. C₁₃	#24144	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×#3508	2
C₁₃×#3077	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₁₃×#2541	2
C₁₃×#2037	2
C₁₃×#2002	2
C₁₃×#1986	2
C₁₃×#1965	2
C₁₃×#1887	2
C₁₃×#1856	2
C₁₃×#1806	2
#24144	13

Subgroups — C13×#24144 #15710483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24144 #15710483