Subgroups — C₁₃×#22544 #15708883

Order 3328.

1098 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1983	C₂	1	2	yes	maximal
5	C₁₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1959	C₂	1	2	yes	maximal
7	C₁₃×#1956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1803	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1763	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#556	—	2	4	no	—
13	C₁₃×#556	C₄	1	8	yes	complemented
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#126	—	2	2	no	—
16	C₂×C₁₃×#124	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
18	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#117	—	2	1	no	—
23	C₁₃×#446	—	2	4	no	—
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₁₃×#103	C₂²	1	2	yes	—
28	C₂×C₁₃×#103	C₂²	1	2	yes	—
29	C₂×C₁₃×#103	C₂²	1	2	yes	—
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	2	yes	—
33	C₂×C₁₃×#97	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#389	—	2	1	no	—
36	C₁₃×#389	—	2	2	no	—
37	C₁₃×#384	C₂²	1	1	yes	characteristic
38	C₁₃×#384	C₂²	1	2	yes	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
40	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₁₃×#340	C₂²	1	1	yes	characteristic
42	C₁₃×#340	C₂²	1	1	yes	characteristic
43	C₁₃×#340	C₂²	1	2	yes	—
44	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
45	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	—	2	1	no	—
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×C₄⋊Q₈	—	2	2	no	—
52	C₁₃×C₄⋊Q₈	C₂×C₄	1	4	yes	—
53	C₁₃×#126	—	2	16	no	—
54	C₁₃×#124	—	2	4	no	—
55	C₁₃×#124	C₂×C₄	1	8	yes	—
56	C₁₃×C₂²⋊Q₈	—	2	8	no	—
57	C₄×Q₈×C₁₃	—	2	4	no	—
58	C₄×Q₈×C₁₃	—	4	4	no	—
59	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	—
60	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
61	C₄×Q₈×C₁₃	D₄	1	4	yes	—
62	C₄×D₄×C₁₃	—	2	2	no	—
63	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
64	C₁₃×#117	—	2	8	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
81	C₂×C₄²×C₁₃	—	2	2	no	—
82	C₂×C₄²×C₁₃	—	2	2	no	—
83	C₂×C₄²×C₁₃	—	2	1	no	—
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
86	C₁₃×C₄⋊C₈	—	2	2	no	—
87	C₁₃×C₄⋊C₈	—	2	4	no	—
88	C₁₃×#103	—	2	4	no	—
89	C₁₃×#103	—	2	4	no	—
90	C₁₃×#103	—	4	2	no	—
91	C₁₃×#103	—	4	2	no	—
92	C₁₃×#102	—	2	2	no	—
93	C₁₃×#102	—	2	2	no	—
94	C₁₃×#102	—	4	2	no	—
95	C₁₃×#97	—	2	4	no	—
96	C₄×C₈×C₁₃	—	2	2	no	—
97	C₁₃×#95	—	2	2	no	—
98	C₁₃×#95	—	2	1	no	—
99	#22544	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂⁴×C₁₃	—	2	1	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	C₂²⋊C₄	1	4	yes	—
109	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	—	2	1	no	—
112	C₂×D₄×C₁₃	—	2	1	no	—
113	C₂×D₄×C₁₃	—	2	1	no	—
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	4	2	no	—
123	C₂²×C₄×C₁₃	—	4	2	no	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	#41	1	2	yes	—
138	C₁₃×C₄⋊C₄	—	2	4	no	—
139	C₁₃×C₄⋊C₄	—	2	8	no	—
140	C₁₃×C₄⋊C₄	—	2	4	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	2	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₁₃×C₄⋊C₄	—	4	4	no	—
148	C₁₃×C₄⋊C₄	—	4	2	no	—
149	C₁₃×C₄⋊C₄	—	8	2	no	—
150	C₁₃×C₄⋊C₄	—	8	1	no	—
151	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
152	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	8	yes	—
153	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
154	C₁₃×C₄⋊C₄	#41	1	2	yes	—
155	C₁₃×C₂²⋊C₄	—	2	8	no	—
156	C₁₃×C₂²⋊C₄	—	2	4	no	—
157	C₁₃×C₂²⋊C₄	—	2	8	no	—
158	C₄²×C₁₃	—	2	8	no	—
159	C₄²×C₁₃	—	4	4	no	—
160	C₄²×C₁₃	—	4	2	no	—
161	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
162	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
163	C₄²×C₁₃	C₂×D₄	1	2	yes	—
164	C₄²×C₁₃	C₂×D₄	1	4	yes	—
165	C₂×#556	C₂×C₁₃	1	1	yes	characteristic
166	C₂×#446	C₂×C₁₃	1	1	yes	characteristic, complemented
167	Q₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#1983	C₂×C₁₃	1	2	yes	—
169	#1981	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#1959	C₂×C₁₃	1	2	yes	—
171	#1956	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#1803	C₂×C₁₃	1	2	yes	complemented
173	#1802	C₂×C₁₃	1	1	yes	characteristic
174	#1763	C₂×C₁₃	1	2	yes	complemented
175	C₄×#102	C₂×C₁₃	1	1	yes	characteristic
176	C₂³×C₁₃	—	2	2	no	—
177	C₂³×C₁₃	—	4	1	no	—
178	C₂³×C₁₃	—	4	1	no	—
179	C₂³×C₁₃	—	4	1	no	—
180	C₂³×C₁₃	—	4	1	no	—
181	C₂³×C₁₃	—	4	1	no	—
182	C₂³×C₁₃	—	4	1	no	—
183	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₁₃	—	2	8	no	—
185	Q₈×C₁₃	—	2	4	no	—
186	Q₈×C₁₃	—	2	4	no	—
187	Q₈×C₁₃	—	4	2	no	—
188	Q₈×C₁₃	—	4	2	no	—
189	D₄×C₁₃	—	2	2	no	—
190	D₄×C₁₃	—	2	2	no	—
191	D₄×C₁₃	—	4	1	no	—
192	D₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	4	8	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	4	2	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
216	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
217	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
218	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
219	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
220	C₂×C₄×C₁₃	#137	1	2	yes	—
221	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
226	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
227	C₈×C₁₃	—	2	2	no	—
228	C₈×C₁₃	—	4	1	no	—
229	C₈×C₁₃	—	4	2	no	—
230	#556	—	2	4	no	—
231	#556	C₄×C₁₃	1	8	yes	complemented
232	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×#126	—	2	2	no	—
234	C₂×#124	C₂²×C₁₃	1	2	yes	—
235	C₂×C₂²⋊Q₈	—	2	1	no	—
236	C₂×C₄×Q₈	—	2	1	no	—
237	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
238	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×#117	—	2	1	no	—
241	#446	—	2	4	no	—
242	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
244	C₂×#103	C₂²×C₁₃	1	2	yes	—
245	C₂×#103	C₂²×C₁₃	1	2	yes	—
246	C₂×#103	C₂²×C₁₃	1	2	yes	—
247	C₂×#103	C₂²×C₁₃	1	2	yes	—
248	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×#102	C₂²×C₁₃	1	2	yes	—
251	C₂×#97	C₂²×C₁₃	1	2	yes	—
252	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
253	#389	—	2	1	no	—
254	#389	—	2	2	no	—
255	#384	C₂²×C₁₃	1	1	yes	characteristic
256	#384	C₂²×C₁₃	1	2	yes	—
257	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
258	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
259	#340	C₂²×C₁₃	1	2	yes	—
260	#340	C₂²×C₁₃	1	1	yes	characteristic
261	#340	C₂²×C₁₃	1	1	yes	characteristic
262	C₂²×C₁₃	—	4	2	no	—
263	C₂²×C₁₃	—	4	2	no	—
264	C₂²×C₁₃	—	4	2	no	—
265	C₂²×C₁₃	—	8	1	no	—
266	C₂²×C₁₃	—	8	1	no	—
267	C₂²×C₁₃	—	8	1	no	—
268	C₂²×C₁₃	—	8	1	no	—
269	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
270	C₂²×C₁₃	#548	1	1	yes	characteristic
271	C₂²×C₁₃	#550	1	1	yes	characteristic
272	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
273	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
274	C₂²×C₁₃	#577	1	1	yes	characteristic
275	C₂²×C₁₃	#578	1	1	yes	characteristic
276	C₄×C₁₃	—	2	4	no	—
277	C₄×C₁₃	—	2	4	no	—
278	C₄×C₁₃	—	2	2	no	—
279	C₄×C₁₃	—	4	4	no	—
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	—	4	2	no	—
282	C₄×C₁₃	—	8	1	no	—
283	C₄×C₁₃	—	8	2	no	—
284	C₄×C₁₃	#417	1	4	yes	—
285	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
286	C₄×C₁₃	#520	1	1	yes	characteristic
287	C₄×C₁₃	#548	1	1	yes	characteristic
288	C₄×C₁₃	#550	1	1	yes	characteristic
289	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
290	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
291	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
292	C₂³×C₄	—	2	1	no	—
293	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
294	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
295	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
296	C₄⋊Q₈	—	2	2	no	—
297	C₄⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
298	#126	—	2	16	no	—
299	#124	—	2	4	no	—
300	#124	C₂×C₄×C₁₃	1	8	yes	—
301	C₂²⋊Q₈	—	2	8	no	—
302	C₄×Q₈	—	2	4	no	—
303	C₄×Q₈	—	4	4	no	—
304	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	—
305	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
306	C₄×Q₈	D₄×C₁₃	1	4	yes	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
309	#117	—	2	8	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
318	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₄²	—	2	2	no	—
327	C₂×C₄²	—	2	2	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
331	C₄⋊C₈	—	2	2	no	—
332	C₄⋊C₈	—	2	4	no	—
333	#103	—	2	4	no	—
334	#103	—	2	4	no	—
335	#103	—	4	2	no	—
336	#103	—	4	2	no	—
337	#102	—	2	2	no	—
338	#102	—	2	2	no	—
339	#102	—	4	2	no	—
340	#97	—	2	4	no	—
341	C₄×C₈	—	2	2	no	—
342	#95	—	2	2	no	—
343	#95	—	2	1	no	—
344	C₂×C₁₃	—	8	2	no	—
345	C₂×C₁₃	#2341	1	1	yes	characteristic
346	C₂×C₁₃	C₂×#417	1	1	yes	characteristic
347	C₂×C₁₃	#2898	1	1	yes	characteristic
348	C₂×C₁₃	#3367	1	1	yes	characteristic
349	C₂×C₁₃	#3369	1	1	yes	characteristic
350	C₂×C₁₃	#3397	1	1	yes	characteristic
351	C₂×C₁₃	#3398	1	1	yes	characteristic
352	C₂⁴	—	2	1	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	C₁₃×C₂²⋊C₄	1	4	yes	—
361	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
377	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
379	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
380	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	C₁₃×#41	1	2	yes	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	8	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	4	4	no	—
400	C₄⋊C₄	—	4	2	no	—
401	C₄⋊C₄	—	8	2	no	—
402	C₄⋊C₄	—	8	1	no	—
403	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
404	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	8	yes	—
405	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
406	C₄⋊C₄	C₁₃×#41	1	2	yes	—
407	C₂²⋊C₄	—	2	8	no	—
408	C₂²⋊C₄	—	2	4	no	—
409	C₂²⋊C₄	—	2	8	no	—
410	C₄²	—	2	8	no	—
411	C₄²	—	4	4	no	—
412	C₄²	—	4	2	no	—
413	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
414	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
415	C₄²	C₂×D₄×C₁₃	1	2	yes	—
416	C₄²	C₂×D₄×C₁₃	1	4	yes	—
417	C₁₃	#22544	1	1	yes	characteristic, direct product factor, Sylow
418	C₂³	—	2	2	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	4	1	no	—
425	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
426	Q₈	—	2	8	no	—
427	Q₈	—	2	4	no	—
428	Q₈	—	2	4	no	—
429	Q₈	—	4	2	no	—
430	Q₈	—	4	2	no	—
431	D₄	—	2	2	no	—
432	D₄	—	2	2	no	—
433	D₄	—	4	1	no	—
434	D₄	—	4	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	8	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
458	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
459	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
460	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
461	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
462	C₂×C₄	C₁₃×#137	1	2	yes	—
463	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
465	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
466	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
467	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
468	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
469	C₈	—	2	2	no	—
470	C₈	—	4	1	no	—
471	C₈	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	8	1	no	—
476	C₂²	—	8	1	no	—
477	C₂²	—	8	1	no	—
478	C₂²	—	8	1	no	—
479	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
480	C₂²	C₁₃×#548	1	1	yes	characteristic
481	C₂²	C₁₃×#550	1	1	yes	characteristic
482	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
483	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
484	C₂²	C₁₃×#577	1	1	yes	characteristic
485	C₂²	C₁₃×#578	1	1	yes	characteristic
486	C₄	—	2	4	no	—
487	C₄	—	2	4	no	—
488	C₄	—	2	2	no	—
489	C₄	—	4	4	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	2	no	—
492	C₄	—	8	1	no	—
493	C₄	—	8	2	no	—
494	C₄	C₁₃×#417	1	4	yes	—
495	C₄	C₄×C₁₃×#41	1	1	yes	characteristic
496	C₄	C₁₃×#520	1	1	yes	characteristic
497	C₄	C₁₃×#548	1	1	yes	characteristic
498	C₄	C₁₃×#550	1	1	yes	characteristic
499	C₂	—	8	2	no	—
500	C₂	C₁₃×#2341	1	1	yes	characteristic
501	C₂	C₂×C₁₃×#417	1	1	yes	characteristic
502	C₂	C₁₃×#2898	1	1	yes	characteristic
503	C₂	C₁₃×#3367	1	1	yes	characteristic
504	C₂	C₁₃×#3369	1	1	yes	characteristic
505	C₂	C₁₃×#3397	1	1	yes	characteristic
506	C₂	C₁₃×#3398	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#446	C₂	semidirect
3. Q₈×C₁₃×C₄⋊C₄	C₂	semidirect
5. C₁₃×#1981	C₂	semidirect
7. C₁₃×#1956	C₂	semidirect
8. C₁₃×#1803	C₂	semidirect
10. C₁₃×#1763	C₂	semidirect
13. C₁₃×#556	C₄	semidirect
99. #22544	C₁₃	direct (N × H)
166. C₂×#446	C₂×C₁₃	semidirect
167. Q₈×C₄⋊C₄	C₂×C₁₃	semidirect
169. #1981	C₂×C₁₃	semidirect
171. #1956	C₂×C₁₃	semidirect
172. #1803	C₂×C₁₃	semidirect
174. #1763	C₂×C₁₃	semidirect
231. #556	C₄×C₁₃	semidirect
417. C₁₃	#22544	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×#556	2
C₂×C₁₃×#446	2
Q₈×C₁₃×C₄⋊C₄	2
C₁₃×#1983	2
C₁₃×#1981	2
C₁₃×#1959	2
C₁₃×#1956	2
C₁₃×#1803	2
C₁₃×#1802	2
C₁₃×#1763	2
C₄×C₁₃×#102	2
#22544	13

Subgroups — C13×#22544 #15708883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22544 #15708883