Subgroups — C₁₃×#24109 #15710448

Order 3328.

1084 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2485	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2058	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2057	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1870	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1823	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₁₃×#554	—	2	4	no	—
18	C₁₃×#554	—	2	4	no	—
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#125	—	2	1	no	—
21	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
22	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃	—	2	1	no	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₁₃×#485	—	2	4	no	—
32	C₁₃×#428	—	2	4	no	—
33	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₃×#397	—	2	1	no	—
47	C₁₃×#394	—	2	1	no	—
48	C₁₃×#389	C₂²	1	1	yes	characteristic
49	C₁₃×#389	C₂²	1	1	yes	characteristic
50	C₁₃×#388	—	2	1	no	—
51	C₁₃×#387	—	2	1	no	—
52	C₁₃×#380	C₂²	1	1	yes	characteristic
53	C₁₃×#380	C₂²	1	1	yes	characteristic
54	C₁₃×#380	C₂²	1	1	yes	characteristic
55	C₁₃×#340	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×#340	C₂²	1	1	yes	characteristic
61	C₁₃×#336	C₂²	1	1	yes	characteristic
62	C₁₃×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	—	2	1	no	—
64	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	—	2	1	no	—
67	C₂³×C₄×C₁₃	—	2	1	no	—
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×M₁₆	—	2	2	no	—
71	C₂×C₁₃×M₁₆	—	2	2	no	—
72	C₂×C₁₃×M₁₆	—	2	2	no	—
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×C₄⋊Q₈	—	2	2	no	—
78	C₁₃×C₄⋊Q₈	—	2	2	no	—
79	C₁₃×#125	—	2	8	no	—
80	C₁₃×C₂²⋊Q₈	—	2	8	no	—
81	C₁₃×C₂²⋊Q₈	—	2	8	no	—
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	—	2	2	no	—
84	C₁₃×C₂²⋊Q₈	—	2	2	no	—
85	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
86	C₄×Q₈×C₁₃	—	2	2	no	—
87	C₄×Q₈×C₁₃	—	2	2	no	—
88	C₄×D₄×C₁₃	—	2	8	no	—
89	C₄×D₄×C₁₃	—	2	2	no	—
90	C₄×D₄×C₁₃	—	2	2	no	—
91	C₁₃×#117	—	2	2	no	—
92	C₁₃×#117	—	2	2	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
120	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
121	C₂×C₄²×C₁₃	—	2	1	no	—
122	C₂×C₄²×C₁₃	—	2	1	no	—
123	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
124	C₁₃×#107	—	2	2	no	—
125	C₁₃×#107	—	2	2	no	—
126	C₁₃×#107	—	2	2	no	—
127	C₁₃×#106	—	2	2	no	—
128	C₁₃×#106	—	2	2	no	—
129	C₁₃×#106	—	2	2	no	—
130	C₁₃×#103	—	2	2	no	—
131	C₁₃×#103	—	2	2	no	—
132	C₁₃×#103	—	2	2	no	—
133	C₁₃×#103	—	2	2	no	—
134	C₁₃×C₂²⋊C₈	—	2	2	no	—
135	C₁₃×C₂²⋊C₈	—	2	2	no	—
136	C₁₃×C₂²⋊C₈	—	2	2	no	—
137	C₁₃×#95	—	2	1	no	—
138	C₁₃×#95	—	2	1	no	—
139	C₁₃×#95	—	2	1	no	—
140	C₁₃×#95	—	2	1	no	—
141	C₁₃×#95	—	2	1	no	—
142	#24109	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂×Q₈×C₁₃	—	2	4	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	8	1	no	—
152	C₂×Q₈×C₁₃	—	8	1	no	—
153	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
154	C₂×D₄×C₁₃	—	2	2	no	—
155	C₂×D₄×C₁₃	—	2	2	no	—
156	C₂×D₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	4	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	2	1	no	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	—	2	1	no	—
177	C₂²×C₄×C₁₃	—	8	1	no	—
178	C₂²×C₄×C₁₃	—	8	1	no	—
179	C₂²×C₄×C₁₃	—	8	1	no	—
180	C₂²×C₄×C₁₃	—	8	1	no	—
181	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
186	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
188	C₁₃×M₁₆	—	2	8	no	—
189	C₂×C₈×C₁₃	—	2	1	no	—
190	C₂×C₈×C₁₃	—	2	1	no	—
191	C₂×C₈×C₁₃	—	2	1	no	—
192	C₂×C₈×C₁₃	—	2	1	no	—
193	C₂×C₈×C₁₃	—	2	1	no	—
194	C₂×C₈×C₁₃	—	2	1	no	—
195	C₂×C₈×C₁₃	—	2	1	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
197	C₂×C₈×C₁₃	—	2	1	no	—
198	C₂×C₈×C₁₃	—	2	1	no	—
199	C₂×C₈×C₁₃	#41	1	2	yes	—
200	C₂×C₈×C₁₃	#41	1	2	yes	—
201	C₁₃×C₄⋊C₄	—	2	4	no	—
202	C₁₃×C₄⋊C₄	—	2	4	no	—
203	C₁₃×C₄⋊C₄	—	2	4	no	—
204	C₁₃×C₄⋊C₄	—	2	4	no	—
205	C₁₃×C₄⋊C₄	—	2	4	no	—
206	C₁₃×C₄⋊C₄	—	2	4	no	—
207	C₁₃×C₄⋊C₄	—	2	2	no	—
208	C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	2	1	no	—
211	C₁₃×C₄⋊C₄	—	2	1	no	—
212	C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	—	2	1	no	—
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	—	4	2	no	—
220	C₁₃×C₄⋊C₄	—	8	1	no	—
221	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
222	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
223	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
224	C₁₃×C₂²⋊C₄	—	2	4	no	—
225	C₁₃×C₂²⋊C₄	—	2	4	no	—
226	C₁₃×C₂²⋊C₄	—	2	2	no	—
227	C₁₃×C₂²⋊C₄	—	2	2	no	—
228	C₁₃×C₂²⋊C₄	—	4	2	no	—
229	C₁₃×C₂²⋊C₄	—	4	2	no	—
230	C₁₃×C₂²⋊C₄	—	8	1	no	—
231	C₁₃×C₂²⋊C₄	—	8	1	no	—
232	C₄²×C₁₃	—	2	4	no	—
233	C₄²×C₁₃	—	2	1	no	—
234	C₄²×C₁₃	—	2	1	no	—
235	C₄²×C₁₃	—	4	2	no	—
236	C₂×#554	C₂×C₁₃	1	1	yes	characteristic
237	C₂×#485	C₂×C₁₃	1	1	yes	characteristic, complemented
238	C₂×#428	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#2485	C₂×C₁₃	1	1	yes	characteristic
240	#2058	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#2057	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#2036	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#2035	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#1894	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#1870	C₂×C₁₃	1	1	yes	characteristic
246	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#1863	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#1853	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#1852	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#1823	C₂×C₁₃	1	1	yes	characteristic, complemented
251	C₂³×C₁₃	—	2	1	no	—
252	C₂³×C₁₃	—	2	1	no	—
253	C₂³×C₁₃	—	2	1	no	—
254	C₂³×C₁₃	—	2	1	no	—
255	C₂³×C₁₃	—	2	1	no	—
256	C₂³×C₁₃	—	2	1	no	—
257	C₂³×C₁₃	—	2	1	no	—
258	C₂³×C₁₃	—	2	1	no	—
259	C₂³×C₁₃	—	2	1	no	—
260	C₂³×C₁₃	—	2	1	no	—
261	C₂³×C₁₃	—	2	1	no	—
262	C₂³×C₁₃	—	2	1	no	—
263	C₂³×C₁₃	#120	1	2	yes	—
264	C₂³×C₁₃	#137	1	2	yes	—
265	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
266	Q₈×C₁₃	—	2	2	no	—
267	Q₈×C₁₃	—	2	2	no	—
268	Q₈×C₁₃	—	4	1	no	—
269	Q₈×C₁₃	—	4	1	no	—
270	Q₈×C₁₃	—	8	4	no	—
271	D₄×C₁₃	—	2	8	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	2	no	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	2	2	no	—
279	C₂×C₄×C₁₃	—	2	2	no	—
280	C₂×C₄×C₁₃	—	2	2	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	2	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	1	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	—	4	1	no	—
291	C₂×C₄×C₁₃	—	4	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	—	4	1	no	—
301	C₂×C₄×C₁₃	—	4	1	no	—
302	C₂×C₄×C₁₃	—	4	1	no	—
303	C₂×C₄×C₁₃	—	4	1	no	—
304	C₂×C₄×C₁₃	—	4	1	no	—
305	C₂×C₄×C₁₃	—	4	1	no	—
306	C₂×C₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	—	4	1	no	—
308	C₂×C₄×C₁₃	—	4	1	no	—
309	C₂×C₄×C₁₃	—	4	1	no	—
310	C₂×C₄×C₁₃	—	4	1	no	—
311	C₂×C₄×C₁₃	—	4	1	no	—
312	C₂×C₄×C₁₃	—	4	1	no	—
313	C₂×C₄×C₁₃	—	4	1	no	—
314	C₂×C₄×C₁₃	—	8	4	no	—
315	C₂×C₄×C₁₃	—	8	4	no	—
316	C₂×C₄×C₁₃	#120	1	2	yes	—
317	C₂×C₄×C₁₃	#137	1	2	yes	—
318	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
323	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
324	C₈×C₁₃	—	2	2	no	—
325	C₈×C₁₃	—	2	2	no	—
326	C₈×C₁₃	—	4	1	no	—
327	C₈×C₁₃	—	4	1	no	—
328	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
329	#554	—	2	4	no	—
330	#554	—	2	4	no	—
331	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×#125	—	2	1	no	—
333	C₂×C₂²⋊Q₈	—	2	1	no	—
334	C₂×C₂²⋊Q₈	—	2	1	no	—
335	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×C₄×D₄	—	2	1	no	—
339	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
341	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
342	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
343	#485	—	2	4	no	—
344	#428	—	2	4	no	—
345	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
353	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
354	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
355	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
356	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
358	#397	—	2	1	no	—
359	#394	—	2	1	no	—
360	#389	C₂²×C₁₃	1	1	yes	characteristic
361	#389	C₂²×C₁₃	1	1	yes	characteristic
362	#388	—	2	1	no	—
363	#387	—	2	1	no	—
364	#380	C₂²×C₁₃	1	1	yes	characteristic
365	#380	C₂²×C₁₃	1	1	yes	characteristic
366	#380	C₂²×C₁₃	1	1	yes	characteristic
367	#340	C₂²×C₁₃	1	1	yes	characteristic
368	#340	C₂²×C₁₃	1	1	yes	characteristic
369	#340	C₂²×C₁₃	1	1	yes	characteristic
370	#340	C₂²×C₁₃	1	1	yes	characteristic
371	#340	C₂²×C₁₃	1	1	yes	characteristic
372	#340	C₂²×C₁₃	1	1	yes	characteristic
373	#336	C₂²×C₁₃	1	1	yes	characteristic
374	#336	C₂²×C₁₃	1	1	yes	characteristic
375	C₂²×C₁₃	—	2	2	no	—
376	C₂²×C₁₃	—	2	2	no	—
377	C₂²×C₁₃	—	2	2	no	—
378	C₂²×C₁₃	—	2	2	no	—
379	C₂²×C₁₃	—	2	2	no	—
380	C₂²×C₁₃	—	2	2	no	—
381	C₂²×C₁₃	—	4	1	no	—
382	C₂²×C₁₃	—	4	1	no	—
383	C₂²×C₁₃	—	4	1	no	—
384	C₂²×C₁₃	—	4	1	no	—
385	C₂²×C₁₃	—	4	1	no	—
386	C₂²×C₁₃	—	4	1	no	—
387	C₂²×C₁₃	—	4	1	no	—
388	C₂²×C₁₃	—	4	1	no	—
389	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
390	C₂²×C₁₃	#547	1	1	yes	characteristic
391	C₂²×C₁₃	#547	1	1	yes	characteristic
392	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
393	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
394	C₂²×C₁₃	#576	1	1	yes	characteristic
395	C₂²×C₁₃	#577	1	1	yes	characteristic
396	C₄×C₁₃	—	2	2	no	—
397	C₄×C₁₃	—	2	2	no	—
398	C₄×C₁₃	—	4	1	no	—
399	C₄×C₁₃	—	4	2	no	—
400	C₄×C₁₃	—	4	1	no	—
401	C₄×C₁₃	—	4	2	no	—
402	C₄×C₁₃	—	4	2	no	—
403	C₄×C₁₃	—	4	2	no	—
404	C₄×C₁₃	—	8	1	no	—
405	C₄×C₁₃	—	8	1	no	—
406	C₄×C₁₃	—	8	1	no	—
407	C₄×C₁₃	—	8	1	no	—
408	C₄×C₁₃	#525	1	1	yes	characteristic
409	C₄×C₁₃	#536	1	1	yes	characteristic
410	C₄×C₁₃	#547	1	1	yes	characteristic
411	C₄×C₁₃	#547	1	1	yes	characteristic
412	C₂²×Q₈	—	2	1	no	—
413	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
414	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
415	C₂³×C₄	—	2	1	no	—
416	C₂³×C₄	—	2	1	no	—
417	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
418	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×M₁₆	—	2	2	no	—
420	C₂×M₁₆	—	2	2	no	—
421	C₂×M₁₆	—	2	2	no	—
422	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
424	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
425	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
426	C₄⋊Q₈	—	2	2	no	—
427	C₄⋊Q₈	—	2	2	no	—
428	#125	—	2	8	no	—
429	C₂²⋊Q₈	—	2	8	no	—
430	C₂²⋊Q₈	—	2	8	no	—
431	C₂²⋊Q₈	—	2	2	no	—
432	C₂²⋊Q₈	—	2	2	no	—
433	C₂²⋊Q₈	—	2	2	no	—
434	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
435	C₄×Q₈	—	2	2	no	—
436	C₄×Q₈	—	2	2	no	—
437	C₄×D₄	—	2	8	no	—
438	C₄×D₄	—	2	2	no	—
439	C₄×D₄	—	2	2	no	—
440	#117	—	2	2	no	—
441	#117	—	2	2	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	2	2	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	—	2	2	no	—
450	C₂×C₄⋊C₄	—	2	2	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
454	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
470	C₂×C₄²	—	2	1	no	—
471	C₂×C₄²	—	2	1	no	—
472	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
473	#107	—	2	2	no	—
474	#107	—	2	2	no	—
475	#107	—	2	2	no	—
476	#106	—	2	2	no	—
477	#106	—	2	2	no	—
478	#106	—	2	2	no	—
479	#103	—	2	2	no	—
480	#103	—	2	2	no	—
481	#103	—	2	2	no	—
482	#103	—	2	2	no	—
483	C₂²⋊C₈	—	2	2	no	—
484	C₂²⋊C₈	—	2	2	no	—
485	C₂²⋊C₈	—	2	2	no	—
486	#95	—	2	1	no	—
487	#95	—	2	1	no	—
488	#95	—	2	1	no	—
489	#95	—	2	1	no	—
490	#95	—	2	1	no	—
491	C₂×C₁₃	—	4	2	no	—
492	C₂×C₁₃	—	4	2	no	—
493	C₂×C₁₃	#2406	1	1	yes	characteristic
494	C₂×C₁₃	#3004	1	1	yes	characteristic
495	C₂×C₁₃	#3012	1	1	yes	characteristic
496	C₂×C₁₃	#3344	1	1	yes	characteristic
497	C₂×C₁₃	#3346	1	1	yes	characteristic
498	C₂×C₁₃	#3356	1	1	yes	characteristic
499	C₂×C₁₃	#3357	1	1	yes	characteristic
500	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
501	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
502	C₂×Q₈	—	2	4	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	8	1	no	—
509	C₂×Q₈	—	8	1	no	—
510	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
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	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	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	8	1	no	—
535	C₂²×C₄	—	8	1	no	—
536	C₂²×C₄	—	8	1	no	—
537	C₂²×C₄	—	8	1	no	—
538	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
539	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
540	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
541	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
542	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
543	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
544	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
545	M₁₆	—	2	8	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	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	C₁₃×#41	1	2	yes	—
557	C₂×C₈	C₁₃×#41	1	2	yes	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	4	2	no	—
577	C₄⋊C₄	—	8	1	no	—
578	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
579	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
580	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	2	no	—
584	C₂²⋊C₄	—	2	2	no	—
585	C₂²⋊C₄	—	4	2	no	—
586	C₂²⋊C₄	—	4	2	no	—
587	C₂²⋊C₄	—	8	1	no	—
588	C₂²⋊C₄	—	8	1	no	—
589	C₄²	—	2	4	no	—
590	C₄²	—	2	1	no	—
591	C₄²	—	2	1	no	—
592	C₄²	—	4	2	no	—
593	C₁₃	#24109	1	1	yes	characteristic, direct product factor, Sylow
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	C₁₃×#120	1	2	yes	—
607	C₂³	C₁₃×#137	1	2	yes	—
608	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
609	Q₈	—	2	2	no	—
610	Q₈	—	2	2	no	—
611	Q₈	—	4	1	no	—
612	Q₈	—	4	1	no	—
613	Q₈	—	8	4	no	—
614	D₄	—	2	8	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	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	8	4	no	—
658	C₂×C₄	—	8	4	no	—
659	C₂×C₄	C₁₃×#120	1	2	yes	—
660	C₂×C₄	C₁₃×#137	1	2	yes	—
661	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
662	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
663	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
664	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
665	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
666	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
667	C₈	—	2	2	no	—
668	C₈	—	2	2	no	—
669	C₈	—	4	1	no	—
670	C₈	—	4	1	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	4	1	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	1	no	—
685	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
686	C₂²	C₁₃×#547	1	1	yes	characteristic
687	C₂²	C₁₃×#547	1	1	yes	characteristic
688	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
689	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
690	C₂²	C₁₃×#576	1	1	yes	characteristic
691	C₂²	C₁₃×#577	1	1	yes	characteristic
692	C₄	—	2	2	no	—
693	C₄	—	2	2	no	—
694	C₄	—	4	1	no	—
695	C₄	—	4	2	no	—
696	C₄	—	4	2	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	2	no	—
700	C₄	—	8	1	no	—
701	C₄	—	8	1	no	—
702	C₄	—	8	1	no	—
703	C₄	—	8	1	no	—
704	C₄	C₁₃×#525	1	1	yes	characteristic
705	C₄	C₁₃×#536	1	1	yes	characteristic
706	C₄	C₁₃×#547	1	1	yes	characteristic
707	C₄	C₁₃×#547	1	1	yes	characteristic
708	C₂	—	4	2	no	—
709	C₂	—	4	2	no	—
710	C₂	C₁₃×#2406	1	1	yes	characteristic
711	C₂	C₁₃×#3004	1	1	yes	characteristic
712	C₂	C₁₃×#3012	1	1	yes	characteristic
713	C₂	C₁₃×#3344	1	1	yes	characteristic
714	C₂	C₁₃×#3346	1	1	yes	characteristic
715	C₂	C₁₃×#3356	1	1	yes	characteristic
716	C₂	C₁₃×#3357	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#485	C₂	semidirect
3. C₂×C₁₃×#428	C₂	semidirect
5. C₁₃×#2058	C₂	semidirect
6. C₁₃×#2057	C₂	semidirect
7. C₁₃×#2036	C₂	semidirect
8. C₁₃×#2035	C₂	semidirect
9. C₁₃×#1894	C₂	semidirect
11. C₁₃×#1865	C₂	semidirect
12. C₁₃×#1863	C₂	semidirect
13. C₁₃×#1853	C₂	semidirect
14. C₁₃×#1852	C₂	semidirect
15. C₁₃×#1823	C₂	semidirect
142. #24109	C₁₃	direct (N × H)
237. C₂×#485	C₂×C₁₃	semidirect
238. C₂×#428	C₂×C₁₃	semidirect
240. #2058	C₂×C₁₃	semidirect
241. #2057	C₂×C₁₃	semidirect
242. #2036	C₂×C₁₃	semidirect
243. #2035	C₂×C₁₃	semidirect
244. #1894	C₂×C₁₃	semidirect
246. #1865	C₂×C₁₃	semidirect
247. #1863	C₂×C₁₃	semidirect
248. #1853	C₂×C₁₃	semidirect
249. #1852	C₂×C₁₃	semidirect
250. #1823	C₂×C₁₃	semidirect
593. C₁₃	#24109	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×#554	2
C₂×C₁₃×#485	2
C₂×C₁₃×#428	2
C₁₃×#2485	2
C₁₃×#2058	2
C₁₃×#2057	2
C₁₃×#2036	2
C₁₃×#2035	2
C₁₃×#1894	2
C₁₃×#1870	2
C₁₃×#1865	2
C₁₃×#1863	2
C₁₃×#1853	2
C₁₃×#1852	2
C₁₃×#1823	2
#24109	13

Subgroups — C13×#24109 #15710448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24109 #15710448