Subgroups — C₁₃×#22677 #15709016

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2351	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1862	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1847	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
24	C₁₃×#440	—	2	4	no	—
25	C₁₃×#440	C₄	1	8	yes	complemented
26	C₄×C₁₃×SD₁₆	—	2	4	no	—
27	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#389	—	2	1	no	—
43	C₁₃×#389	—	2	1	no	—
44	C₁₃×#389	C₂²	1	1	yes	characteristic
45	C₁₃×#389	C₂²	1	1	yes	characteristic
46	C₁₃×#389	C₂²	1	1	yes	characteristic
47	C₁₃×#389	C₂²	1	1	yes	characteristic
48	C₁₃×#385	—	2	1	no	—
49	C₁₃×#385	—	2	1	no	—
50	C₁₃×#384	C₂²	1	1	yes	characteristic
51	C₁₃×#382	—	2	1	no	—
52	C₁₃×#382	C₂²	1	1	yes	characteristic
53	C₁₃×#380	—	2	1	no	—
54	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#340	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₁₃×#336	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	—	2	1	no	—
65	C₂³×C₄×C₁₃	—	2	1	no	—
66	C₂³×C₄×C₁₃	—	2	1	no	—
67	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
68	C₂×C₁₃×SD₁₆	D₄	1	4	yes	—
69	C₂×C₁₃×SD₁₆	Q₈	1	4	yes	—
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₄×Q₈×C₁₃	—	2	2	no	—
75	C₄×Q₈×C₁₃	—	2	2	no	—
76	C₄×Q₈×C₁₃	—	2	2	no	—
77	C₄×Q₈×C₁₃	—	4	1	no	—
78	C₄×Q₈×C₁₃	—	4	1	no	—
79	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	complemented
80	C₄×D₄×C₁₃	—	2	2	no	—
81	C₄×D₄×C₁₃	—	2	2	no	—
82	C₄×D₄×C₁₃	—	2	2	no	—
83	C₄×D₄×C₁₃	—	4	1	no	—
84	C₄×D₄×C₁₃	—	4	1	no	—
85	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
96	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₄²×C₁₃	—	2	1	no	—
108	C₂×C₄²×C₁₃	—	2	1	no	—
109	C₂×C₄²×C₁₃	—	2	1	no	—
110	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₁₃×#107	—	2	2	no	—
114	C₁₃×#107	—	4	1	no	—
115	C₁₃×#107	C₂×C₄	1	4	yes	complemented
116	C₁₃×#106	—	2	2	no	—
117	C₁₃×#106	—	4	1	no	—
118	C₁₃×C₄⋊C₈	—	2	2	no	—
119	C₁₃×#103	—	2	2	no	—
120	C₁₃×#103	—	2	2	no	—
121	C₁₃×#103	C₂×C₄	1	4	yes	complemented
122	C₁₃×#102	—	2	2	no	—
123	C₁₃×#102	—	2	2	no	—
124	C₁₃×#102	C₂×C₄	1	4	yes	—
125	C₁₃×#97	—	2	2	no	—
126	C₁₃×#97	C₂×C₄	1	4	yes	complemented
127	C₄×C₈×C₁₃	—	2	2	no	—
128	C₁₃×#95	—	2	1	no	—
129	C₁₃×#95	—	2	1	no	—
130	C₁₃×#95	—	2	1	no	—
131	C₁₃×#95	—	2	1	no	—
132	C₁₃×#95	—	2	1	no	—
133	C₁₃×#95	—	2	1	no	—
134	C₁₃×#95	D₄	1	1	yes	characteristic
135	C₁₃×#95	D₄	1	1	yes	characteristic
136	#22677	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂⁴×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	2	1	no	—
139	C₂×Q₈×C₁₃	—	2	1	no	—
140	C₂×Q₈×C₁₃	—	2	1	no	—
141	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
142	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
143	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
148	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
149	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	2	4	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	4	2	no	—
159	C₂²×C₄×C₁₃	—	4	2	no	—
160	C₂²×C₄×C₁₃	—	4	2	no	—
161	C₂²×C₄×C₁₃	—	4	2	no	—
162	C₂²×C₄×C₁₃	—	4	2	no	—
163	C₂²×C₄×C₁₃	—	4	2	no	—
164	C₂²×C₄×C₁₃	—	8	1	no	—
165	C₂²×C₄×C₁₃	—	8	1	no	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₁₃×SD₁₆	C₄⋊C₄	1	16	yes	complemented
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
183	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
184	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
185	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
186	C₁₃×C₄⋊C₄	—	2	4	no	—
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	4	1	no	—
199	C₁₃×C₄⋊C₄	—	4	2	no	—
200	C₁₃×C₄⋊C₄	—	4	2	no	—
201	C₁₃×C₄⋊C₄	—	4	2	no	—
202	C₁₃×C₄⋊C₄	—	4	2	no	—
203	C₁₃×C₄⋊C₄	—	4	2	no	—
204	C₁₃×C₄⋊C₄	—	4	2	no	—
205	C₁₃×C₄⋊C₄	—	4	2	no	—
206	C₁₃×C₄⋊C₄	—	8	1	no	—
207	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
208	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
209	C₁₃×C₂²⋊C₄	—	2	4	no	—
210	C₁₃×C₂²⋊C₄	—	4	2	no	—
211	C₁₃×C₂²⋊C₄	—	4	2	no	—
212	C₄²×C₁₃	—	2	4	no	—
213	C₄²×C₁₃	—	2	1	no	—
214	C₄²×C₁₃	—	2	1	no	—
215	C₄²×C₁₃	—	2	1	no	—
216	C₄²×C₁₃	—	2	1	no	—
217	C₄²×C₁₃	—	4	2	no	—
218	C₄²×C₁₃	—	4	2	no	—
219	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
220	C₄²×C₁₃	#41	1	2	yes	—
221	C₂×#440	C₂×C₁₃	1	1	yes	characteristic
222	C₂×#440	C₂×C₁₃	1	1	yes	characteristic
223	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
224	#2351	C₂×C₁₃	1	1	yes	characteristic, complemented
225	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
226	#1943	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1864	C₂×C₁₃	1	1	yes	characteristic
230	#1863	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#1862	C₂×C₁₃	1	1	yes	characteristic
232	#1847	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#1804	C₂×C₁₃	1	1	yes	characteristic
234	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#1771	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₂³×C₁₃	—	2	2	no	—
237	C₂³×C₁₃	—	2	2	no	—
238	C₂³×C₁₃	—	2	2	no	—
239	C₂³×C₁₃	—	4	1	no	—
240	C₂³×C₁₃	—	4	1	no	—
241	C₂³×C₁₃	—	4	1	no	—
242	C₂³×C₁₃	—	4	1	no	—
243	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
244	Q₈×C₁₃	—	2	2	no	—
245	Q₈×C₁₃	—	2	2	no	—
246	Q₈×C₁₃	—	2	2	no	—
247	Q₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	complemented
248	D₄×C₁₃	—	2	2	no	—
249	D₄×C₁₃	—	2	2	no	—
250	D₄×C₁₃	—	2	2	no	—
251	D₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	4	8	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	—	4	1	no	—
282	C₂×C₄×C₁₃	—	4	1	no	—
283	C₂×C₄×C₁₃	—	4	1	no	—
284	C₂×C₄×C₁₃	—	4	1	no	—
285	C₂×C₄×C₁₃	—	4	1	no	—
286	C₂×C₄×C₁₃	—	4	1	no	—
287	C₂×C₄×C₁₃	—	4	1	no	—
288	C₂×C₄×C₁₃	—	4	1	no	—
289	C₂×C₄×C₁₃	—	8	4	no	—
290	C₂×C₄×C₁₃	—	8	4	no	—
291	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
292	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
293	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
294	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
295	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
297	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
299	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
300	C₈×C₁₃	—	2	2	no	—
301	C₈×C₁₃	—	4	1	no	—
302	C₈×C₁₃	—	4	1	no	—
303	C₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	complemented
304	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
311	C₂²×C₄⋊C₄	—	2	1	no	—
312	#440	—	2	4	no	—
313	#440	C₄×C₁₃	1	8	yes	complemented
314	C₄×SD₁₆	—	2	4	no	—
315	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
330	#389	—	2	1	no	—
331	#389	—	2	1	no	—
332	#389	C₂²×C₁₃	1	1	yes	characteristic
333	#389	C₂²×C₁₃	1	1	yes	characteristic
334	#389	C₂²×C₁₃	1	1	yes	characteristic
335	#389	C₂²×C₁₃	1	1	yes	characteristic
336	#385	—	2	1	no	—
337	#385	—	2	1	no	—
338	#384	C₂²×C₁₃	1	1	yes	characteristic
339	#382	—	2	1	no	—
340	#382	C₂²×C₁₃	1	1	yes	characteristic
341	#380	—	2	1	no	—
342	C₄×C₄⋊C₄	—	2	1	no	—
343	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
344	#340	C₂²×C₁₃	1	1	yes	characteristic
345	#340	C₂²×C₁₃	1	1	yes	characteristic
346	#340	C₂²×C₁₃	1	1	yes	characteristic
347	#340	C₂²×C₁₃	1	1	yes	characteristic
348	#336	C₂²×C₁₃	1	1	yes	characteristic
349	#336	C₂²×C₁₃	1	1	yes	characteristic
350	C₂²×C₁₃	—	2	4	no	—
351	C₂²×C₁₃	—	4	2	no	—
352	C₂²×C₁₃	—	4	2	no	—
353	C₂²×C₁₃	—	4	2	no	—
354	C₂²×C₁₃	—	4	2	no	—
355	C₂²×C₁₃	—	4	2	no	—
356	C₂²×C₁₃	—	4	2	no	—
357	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
358	C₂²×C₁₃	D₄²	1	1	yes	characteristic
359	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
360	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
361	C₂²×C₁₃	#575	1	1	yes	characteristic
362	C₂²×C₁₃	#577	1	1	yes	characteristic
363	C₂²×C₁₃	#578	1	1	yes	characteristic
364	C₄×C₁₃	—	2	4	no	—
365	C₄×C₁₃	—	2	2	no	—
366	C₄×C₁₃	—	2	2	no	—
367	C₄×C₁₃	—	2	2	no	—
368	C₄×C₁₃	—	4	2	no	—
369	C₄×C₁₃	—	4	2	no	—
370	C₄×C₁₃	—	4	1	no	—
371	C₄×C₁₃	—	4	1	no	—
372	C₄×C₁₃	—	4	1	no	—
373	C₄×C₁₃	—	8	1	no	—
374	C₄×C₁₃	—	8	1	no	—
375	C₄×C₁₃	—	8	1	no	—
376	C₄×C₁₃	—	8	1	no	—
377	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
378	C₄×C₁₃	#520	1	1	yes	characteristic
379	C₄×C₁₃	#547	1	1	yes	characteristic
380	C₄×C₁₃	#554	1	1	yes	characteristic
381	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
382	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
383	C₂³×C₄	—	2	1	no	—
384	C₂³×C₄	—	2	1	no	—
385	C₂³×C₄	—	2	1	no	—
386	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	—
387	C₂×SD₁₆	D₄×C₁₃	1	4	yes	—
388	C₂×SD₁₆	Q₈×C₁₃	1	4	yes	—
389	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
390	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
391	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
392	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	—	2	2	no	—
396	C₄×Q₈	—	4	1	no	—
397	C₄×Q₈	—	4	1	no	—
398	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	complemented
399	C₄×D₄	—	2	2	no	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	—	2	2	no	—
402	C₄×D₄	—	4	1	no	—
403	C₄×D₄	—	4	1	no	—
404	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	4	4	no	—
415	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
416	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	2	1	no	—
429	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
430	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
432	#107	—	2	2	no	—
433	#107	—	4	1	no	—
434	#107	C₂×C₄×C₁₃	1	4	yes	complemented
435	#106	—	2	2	no	—
436	#106	—	4	1	no	—
437	C₄⋊C₈	—	2	2	no	—
438	#103	—	2	2	no	—
439	#103	—	2	2	no	—
440	#103	C₂×C₄×C₁₃	1	4	yes	complemented
441	#102	—	2	2	no	—
442	#102	—	2	2	no	—
443	#102	C₂×C₄×C₁₃	1	4	yes	—
444	#97	—	2	2	no	—
445	#97	C₂×C₄×C₁₃	1	4	yes	complemented
446	C₄×C₈	—	2	2	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	—	2	1	no	—
451	#95	—	2	1	no	—
452	#95	—	2	1	no	—
453	#95	D₄×C₁₃	1	1	yes	characteristic
454	#95	D₄×C₁₃	1	1	yes	characteristic
455	C₂×C₁₃	—	4	4	no	—
456	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
457	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
458	C₂×C₁₃	#2947	1	1	yes	characteristic
459	C₂×C₁₃	#3265	1	1	yes	characteristic
460	C₂×C₁₃	#3269	1	1	yes	characteristic
461	C₂×C₁₃	#3386	1	1	yes	characteristic
462	C₂×C₁₃	#3388	1	1	yes	characteristic
463	C₂⁴	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
468	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
469	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
474	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
475	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	—	4	2	no	—
486	C₂²×C₄	—	4	2	no	—
487	C₂²×C₄	—	4	2	no	—
488	C₂²×C₄	—	4	2	no	—
489	C₂²×C₄	—	4	2	no	—
490	C₂²×C₄	—	8	1	no	—
491	C₂²×C₄	—	8	1	no	—
492	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
498	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
499	SD₁₆	C₁₃×C₄⋊C₄	1	16	yes	complemented
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
509	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
510	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
511	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
512	C₄⋊C₄	—	2	4	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	4	1	no	—
525	C₄⋊C₄	—	4	2	no	—
526	C₄⋊C₄	—	4	2	no	—
527	C₄⋊C₄	—	4	2	no	—
528	C₄⋊C₄	—	4	2	no	—
529	C₄⋊C₄	—	4	2	no	—
530	C₄⋊C₄	—	4	2	no	—
531	C₄⋊C₄	—	4	2	no	—
532	C₄⋊C₄	—	8	1	no	—
533	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
534	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₂²⋊C₄	—	4	2	no	—
537	C₂²⋊C₄	—	4	2	no	—
538	C₄²	—	2	4	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	4	2	no	—
544	C₄²	—	4	2	no	—
545	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
546	C₄²	C₁₃×#41	1	2	yes	—
547	C₁₃	#22677	1	1	yes	characteristic, direct product factor, Sylow
548	C₂³	—	2	2	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
556	Q₈	—	2	2	no	—
557	Q₈	—	2	2	no	—
558	Q₈	—	2	2	no	—
559	Q₈	C₂×C₁₃×C₄⋊C₄	1	4	yes	complemented
560	D₄	—	2	2	no	—
561	D₄	—	2	2	no	—
562	D₄	—	2	2	no	—
563	D₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	4	8	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	8	4	no	—
602	C₂×C₄	—	8	4	no	—
603	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
604	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
605	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
606	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
608	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
609	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
610	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
611	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
612	C₈	—	2	2	no	—
613	C₈	—	4	1	no	—
614	C₈	—	4	1	no	—
615	C₈	C₂×C₁₃×C₄⋊C₄	1	4	yes	complemented
616	C₂²	—	2	4	no	—
617	C₂²	—	4	2	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
624	C₂²	D₄²×C₁₃	1	1	yes	characteristic
625	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
626	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
627	C₂²	C₁₃×#575	1	1	yes	characteristic
628	C₂²	C₁₃×#577	1	1	yes	characteristic
629	C₂²	C₁₃×#578	1	1	yes	characteristic
630	C₄	—	2	2	no	—
631	C₄	—	2	4	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	2	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	1	no	—
636	C₄	—	4	1	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	2	no	—
639	C₄	—	8	1	no	—
640	C₄	—	8	1	no	—
641	C₄	—	8	1	no	—
642	C₄	—	8	1	no	—
643	C₄	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
644	C₄	C₁₃×#520	1	1	yes	characteristic
645	C₄	C₁₃×#547	1	1	yes	characteristic
646	C₄	C₁₃×#554	1	1	yes	characteristic
647	C₂	—	4	4	no	—
648	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
649	C₂	C₄×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
650	C₂	C₁₃×#2947	1	1	yes	characteristic
651	C₂	C₁₃×#3265	1	1	yes	characteristic
652	C₂	C₁₃×#3269	1	1	yes	characteristic
653	C₂	C₁₃×#3386	1	1	yes	characteristic
654	C₂	C₁₃×#3388	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 ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#2351	C₂	semidirect
6. C₁₃×#1943	C₂	semidirect
7. C₁₃×#1942	C₂	semidirect
8. C₁₃×#1865	C₂	semidirect
10. C₁₃×#1863	C₂	semidirect
12. C₁₃×#1847	C₂	semidirect
14. C₁₃×#1803	C₂	semidirect
15. C₁₃×#1771	C₂	semidirect
25. C₁₃×#440	C₄	semidirect
79. C₄×Q₈×C₁₃	C₂×C₄	semidirect
115. C₁₃×#107	C₂×C₄	semidirect
121. C₁₃×#103	C₂×C₄	semidirect
126. C₁₃×#97	C₂×C₄	semidirect
136. #22677	C₁₃	direct (N × H)
173. C₁₃×SD₁₆	C₄⋊C₄	semidirect
224. #2351	C₂×C₁₃	semidirect
226. #1943	C₂×C₁₃	semidirect
227. #1942	C₂×C₁₃	semidirect
228. #1865	C₂×C₁₃	semidirect
230. #1863	C₂×C₁₃	semidirect
232. #1847	C₂×C₁₃	semidirect
234. #1803	C₂×C₁₃	semidirect
235. #1771	C₂×C₁₃	semidirect
247. Q₈×C₁₃	C₂×C₄⋊C₄	semidirect
303. C₈×C₁₃	C₂×C₄⋊C₄	semidirect
313. #440	C₄×C₁₃	semidirect
398. C₄×Q₈	C₂×C₄×C₁₃	semidirect
434. #107	C₂×C₄×C₁₃	semidirect
440. #103	C₂×C₄×C₁₃	semidirect
445. #97	C₂×C₄×C₁₃	semidirect
499. SD₁₆	C₁₃×C₄⋊C₄	semidirect
547. C₁₃	#22677	direct (N × H)
559. Q₈	C₂×C₁₃×C₄⋊C₄	semidirect
615. C₈	C₂×C₁₃×C₄⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#440	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2351	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#1943	2
C₁₃×#1942	2
C₁₃×#1865	2
C₁₃×#1864	2
C₁₃×#1863	2
C₁₃×#1862	2
C₁₃×#1847	2
C₁₃×#1804	2
C₁₃×#1803	2
C₁₃×#1771	2
#22677	13

Subgroups — C13×#22677 #15709016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22677 #15709016