Subgroups — C₁₃×#22054 #15708393

Order 3328.

920 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#451	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2323	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2310	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1971	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1935	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1933	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1928	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1927	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1873	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1787	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1750	C₂	1	1	yes	maximal, characteristic
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
23	C₁₃×#451	C₄	1	8	yes	complemented
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#391	—	2	1	no	—
39	C₁₃×#391	—	2	1	no	—
40	C₁₃×#391	C₂²	1	1	yes	characteristic
41	C₁₃×#391	C₂²	1	1	yes	characteristic
42	C₁₃×#391	C₂²	1	1	yes	characteristic
43	C₁₃×#391	C₂²	1	1	yes	characteristic
44	C₁₃×#391	C₂²	1	1	yes	characteristic
45	C₁₃×#389	—	2	1	no	—
46	C₁₃×#389	C₂²	1	1	yes	characteristic
47	C₁₃×#388	—	2	1	no	—
48	C₁₃×#388	—	2	1	no	—
49	C₁₃×#387	—	2	1	no	—
50	C₁₃×#381	—	2	1	no	—
51	C₁₃×#381	—	2	1	no	—
52	C₁₃×#380	C₂²	1	1	yes	characteristic
53	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₁₃×#340	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×#336	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₂²×Q₈×C₁₃	—	2	1	no	—
61	C₂²×Q₈×C₁₃	—	2	2	no	—
62	C₂²×Q₈×C₁₃	—	4	1	no	—
63	C₂²×Q₈×C₁₃	—	4	1	no	—
64	C₂²×Q₈×C₁₃	—	4	1	no	—
65	C₂²×Q₈×C₁₃	—	4	1	no	—
66	C₂²×Q₈×C₁₃	C₂×C₄	1	4	yes	—
67	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	—	2	1	no	—
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×Q₁₆	—	4	1	no	—
73	C₂×C₁₃×Q₁₆	—	4	1	no	—
74	C₂×C₁₃×Q₁₆	—	4	1	no	—
75	C₂×C₁₃×Q₁₆	—	4	1	no	—
76	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	—
77	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	—
78	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
84	C₄×Q₈×C₁₃	—	4	1	no	—
85	C₄×Q₈×C₁₃	—	4	1	no	—
86	C₁₃×#117	—	4	1	no	—
87	C₁₃×#117	—	4	1	no	—
88	C₁₃×#117	—	4	1	no	—
89	C₁₃×#117	—	4	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	D₄	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
104	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₁₃	—	2	1	no	—
106	C₂×C₄²×C₁₃	—	2	1	no	—
107	C₂×C₄²×C₁₃	—	2	1	no	—
108	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×#107	—	4	1	no	—
111	C₁₃×#106	—	4	1	no	—
112	C₁₃×#103	—	4	1	no	—
113	C₁₃×#103	—	4	1	no	—
114	C₁₃×#103	—	4	1	no	—
115	C₁₃×#103	—	4	1	no	—
116	C₁₃×#103	—	4	1	no	—
117	C₁₃×#103	—	4	1	no	—
118	C₁₃×#103	C₂×C₄	1	4	yes	—
119	C₁₃×#103	C₂×C₄	1	4	yes	—
120	C₁₃×C₂²⋊C₈	—	2	2	no	—
121	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
122	C₁₃×#97	—	4	1	no	—
123	C₄×C₈×C₁₃	—	4	1	no	—
124	C₁₃×#95	—	2	1	no	—
125	C₁₃×#95	—	2	1	no	—
126	C₁₃×#95	—	2	1	no	—
127	C₁₃×#95	—	2	1	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	—	2	1	no	—
135	C₁₃×#95	—	2	1	no	—
136	C₁₃×#95	—	2	1	no	—
137	#22054	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂×Q₈×C₁₃	—	2	4	no	—
140	C₂×Q₈×C₁₃	—	2	1	no	—
141	C₂×Q₈×C₁₃	—	2	1	no	—
142	C₂×Q₈×C₁₃	—	2	1	no	—
143	C₂×Q₈×C₁₃	—	2	1	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	2	1	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	—	2	1	no	—
152	C₂×Q₈×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	—	2	1	no	—
154	C₂×Q₈×C₁₃	—	2	1	no	—
155	C₂×Q₈×C₁₃	—	4	4	no	—
156	C₂×Q₈×C₁₃	—	4	4	no	—
157	C₂×Q₈×C₁₃	—	4	2	no	—
158	C₂×Q₈×C₁₃	—	4	2	no	—
159	C₂×Q₈×C₁₃	—	4	4	no	—
160	C₂×Q₈×C₁₃	—	4	4	no	—
161	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
162	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
163	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	4	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	—	4	2	no	—
178	C₂²×C₄×C₁₃	—	4	2	no	—
179	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
180	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
185	C₂²×C₄×C₁₃	#41	1	2	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₁₃×Q₁₆	—	4	4	no	—
188	C₁₃×Q₁₆	—	4	4	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	C₂²×C₄	1	2	yes	—
200	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
201	C₁₃×C₄⋊C₄	—	2	4	no	—
202	C₁₃×C₄⋊C₄	—	2	1	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	1	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	—	4	1	no	—
212	C₁₃×C₄⋊C₄	—	4	1	no	—
213	C₁₃×C₄⋊C₄	—	4	2	no	—
214	C₁₃×C₄⋊C₄	—	8	1	no	—
215	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
216	C₁₃×C₂²⋊C₄	—	2	4	no	—
217	C₁₃×C₂²⋊C₄	—	4	1	no	—
218	C₁₃×C₂²⋊C₄	—	4	1	no	—
219	C₁₃×C₂²⋊C₄	—	4	2	no	—
220	C₁₃×C₂²⋊C₄	—	8	1	no	—
221	C₄²×C₁₃	—	2	1	no	—
222	C₄²×C₁₃	—	2	1	no	—
223	C₄²×C₁₃	—	2	1	no	—
224	C₄²×C₁₃	—	2	1	no	—
225	C₄²×C₁₃	—	4	2	no	—
226	C₄²×C₁₃	—	4	2	no	—
227	C₄²×C₁₃	—	8	1	no	—
228	C₂×#451	C₂×C₁₃	1	1	yes	characteristic
229	#2323	C₂×C₁₃	1	1	yes	characteristic
230	#2310	C₂×C₁₃	1	1	yes	characteristic
231	#1971	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#1969	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#1935	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#1933	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#1928	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#1927	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#1873	C₂×C₁₃	1	1	yes	characteristic
240	#1854	C₂×C₁₃	1	1	yes	characteristic
241	#1787	C₂×C₁₃	1	1	yes	characteristic
242	#1750	C₂×C₁₃	1	1	yes	characteristic
243	C₂³×C₁₃	—	2	1	no	—
244	C₂³×C₁₃	—	2	1	no	—
245	C₂³×C₁₃	—	2	1	no	—
246	C₂³×C₁₃	—	2	1	no	—
247	C₂³×C₁₃	—	2	1	no	—
248	C₂³×C₁₃	—	2	1	no	—
249	C₂³×C₁₃	C₄×D₄	1	2	yes	—
250	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
251	Q₈×C₁₃	—	2	2	no	—
252	Q₈×C₁₃	—	2	2	no	—
253	Q₈×C₁₃	—	2	2	no	—
254	Q₈×C₁₃	—	2	2	no	—
255	Q₈×C₁₃	—	2	2	no	—
256	Q₈×C₁₃	—	2	2	no	—
257	Q₈×C₁₃	—	4	8	no	—
258	Q₈×C₁₃	—	4	1	no	—
259	Q₈×C₁₃	—	4	1	no	—
260	Q₈×C₁₃	—	4	1	no	—
261	Q₈×C₁₃	—	4	1	no	—
262	Q₈×C₁₃	—	4	1	no	—
263	Q₈×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	2	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	2	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	1	no	—
286	C₂×C₄×C₁₃	—	4	8	no	—
287	C₂×C₄×C₁₃	—	4	1	no	—
288	C₂×C₄×C₁₃	—	4	1	no	—
289	C₂×C₄×C₁₃	—	4	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	C₄×D₄	1	2	yes	—
308	C₂×C₄×C₁₃	C₂³×C₄	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	H(5,𝔽₂)	1	1	yes	characteristic
312	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
313	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
314	C₈×C₁₃	—	2	2	no	—
315	C₈×C₁₃	—	2	2	no	—
316	C₈×C₁₃	—	4	1	no	—
317	C₈×C₁₃	—	4	1	no	—
318	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
319	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
320	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
325	#451	C₄×C₁₃	1	8	yes	complemented
326	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
340	#391	—	2	1	no	—
341	#391	—	2	1	no	—
342	#391	C₂²×C₁₃	1	1	yes	characteristic
343	#391	C₂²×C₁₃	1	1	yes	characteristic
344	#391	C₂²×C₁₃	1	1	yes	characteristic
345	#391	C₂²×C₁₃	1	1	yes	characteristic
346	#391	C₂²×C₁₃	1	1	yes	characteristic
347	#389	—	2	1	no	—
348	#389	C₂²×C₁₃	1	1	yes	characteristic
349	#388	—	2	1	no	—
350	#388	—	2	1	no	—
351	#387	—	2	1	no	—
352	#381	—	2	1	no	—
353	#381	—	2	1	no	—
354	#380	C₂²×C₁₃	1	1	yes	characteristic
355	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
356	#340	C₂²×C₁₃	1	1	yes	characteristic
357	#340	C₂²×C₁₃	1	1	yes	characteristic
358	#340	C₂²×C₁₃	1	1	yes	characteristic
359	#340	C₂²×C₁₃	1	1	yes	characteristic
360	#336	C₂²×C₁₃	1	1	yes	characteristic
361	#336	C₂²×C₁₃	1	1	yes	characteristic
362	C₂²×C₁₃	—	2	2	no	—
363	C₂²×C₁₃	—	2	2	no	—
364	C₂²×C₁₃	—	2	2	no	—
365	C₂²×C₁₃	—	4	1	no	—
366	C₂²×C₁₃	—	4	1	no	—
367	C₂²×C₁₃	—	4	1	no	—
368	C₂²×C₁₃	—	4	1	no	—
369	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
370	C₂²×C₁₃	#534	1	1	yes	characteristic
371	C₂²×C₁₃	#535	1	1	yes	characteristic
372	C₂²×C₁₃	#577	1	1	yes	characteristic
373	C₂²×C₁₃	#578	1	1	yes	characteristic
374	C₂²×C₁₃	#578	1	1	yes	characteristic
375	C₂²×C₁₃	#578	1	1	yes	characteristic
376	C₄×C₁₃	—	2	2	no	—
377	C₄×C₁₃	—	4	2	no	—
378	C₄×C₁₃	—	4	2	no	—
379	C₄×C₁₃	—	4	2	no	—
380	C₄×C₁₃	—	4	1	no	—
381	C₄×C₁₃	—	4	1	no	—
382	C₄×C₁₃	—	4	1	no	—
383	C₄×C₁₃	—	4	1	no	—
384	C₄×C₁₃	—	4	2	no	—
385	C₄×C₁₃	—	8	1	no	—
386	C₄×C₁₃	—	8	1	no	—
387	C₄×C₁₃	—	8	1	no	—
388	C₄×C₁₃	—	8	1	no	—
389	C₄×C₁₃	#518	1	1	yes	characteristic
390	C₄×C₁₃	#518	1	1	yes	characteristic
391	C₄×C₁₃	#538	1	1	yes	characteristic
392	C₄×C₁₃	#538	1	1	yes	characteristic
393	C₂²×Q₈	—	2	1	no	—
394	C₂²×Q₈	—	2	2	no	—
395	C₂²×Q₈	—	4	1	no	—
396	C₂²×Q₈	—	4	1	no	—
397	C₂²×Q₈	—	4	1	no	—
398	C₂²×Q₈	—	4	1	no	—
399	C₂²×Q₈	C₂×C₄×C₁₃	1	4	yes	—
400	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
401	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
402	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
403	C₂³×C₄	—	2	1	no	—
404	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
405	C₂×Q₁₆	—	4	1	no	—
406	C₂×Q₁₆	—	4	1	no	—
407	C₂×Q₁₆	—	4	1	no	—
408	C₂×Q₁₆	—	4	1	no	—
409	C₂×Q₁₆	C₂×C₄×C₁₃	1	4	yes	—
410	C₂×Q₁₆	C₂×C₄×C₁₃	1	4	yes	—
411	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
412	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
413	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
414	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
415	C₂²⋊Q₈	—	2	2	no	—
416	C₂²⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
417	C₄×Q₈	—	4	1	no	—
418	C₄×Q₈	—	4	1	no	—
419	#117	—	4	1	no	—
420	#117	—	4	1	no	—
421	#117	—	4	1	no	—
422	#117	—	4	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
427	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
438	C₂×C₄²	—	2	1	no	—
439	C₂×C₄²	—	2	1	no	—
440	C₂×C₄²	—	2	1	no	—
441	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
443	#107	—	4	1	no	—
444	#106	—	4	1	no	—
445	#103	—	4	1	no	—
446	#103	—	4	1	no	—
447	#103	—	4	1	no	—
448	#103	—	4	1	no	—
449	#103	—	4	1	no	—
450	#103	—	4	1	no	—
451	#103	C₂×C₄×C₁₃	1	4	yes	—
452	#103	C₂×C₄×C₁₃	1	4	yes	—
453	C₂²⋊C₈	—	2	2	no	—
454	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
455	#97	—	4	1	no	—
456	C₄×C₈	—	4	1	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	#95	—	2	1	no	—
460	#95	—	2	1	no	—
461	#95	—	2	1	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	—	2	1	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	C₂×C₁₃	—	4	2	no	—
471	C₂×C₁₃	#2321	1	1	yes	characteristic
472	C₂×C₁₃	#2947	1	1	yes	characteristic
473	C₂×C₁₃	#2950	1	1	yes	characteristic
474	C₂×C₁₃	#3201	1	1	yes	characteristic
475	C₂×C₁₃	#3202	1	1	yes	characteristic
476	C₂×C₁₃	#3223	1	1	yes	characteristic
477	C₂×C₁₃	#3225	1	1	yes	characteristic
478	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
479	C₂×Q₈	—	2	4	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	4	4	no	—
496	C₂×Q₈	—	4	4	no	—
497	C₂×Q₈	—	4	2	no	—
498	C₂×Q₈	—	4	2	no	—
499	C₂×Q₈	—	4	4	no	—
500	C₂×Q₈	—	4	4	no	—
501	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
502	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
503	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
520	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
521	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
525	C₂²×C₄	C₁₃×#41	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
527	Q₁₆	—	4	4	no	—
528	Q₁₆	—	4	4	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
540	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	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	1	no	—
551	C₄⋊C₄	—	4	1	no	—
552	C₄⋊C₄	—	4	1	no	—
553	C₄⋊C₄	—	4	2	no	—
554	C₄⋊C₄	—	8	1	no	—
555	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
556	C₂²⋊C₄	—	2	4	no	—
557	C₂²⋊C₄	—	4	1	no	—
558	C₂²⋊C₄	—	4	1	no	—
559	C₂²⋊C₄	—	4	2	no	—
560	C₂²⋊C₄	—	8	1	no	—
561	C₄²	—	2	1	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	4	2	no	—
566	C₄²	—	4	2	no	—
567	C₄²	—	8	1	no	—
568	C₁₃	#22054	1	1	yes	characteristic, direct product factor, Sylow
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	C₄×D₄×C₁₃	1	2	yes	—
576	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
577	Q₈	—	2	2	no	—
578	Q₈	—	2	2	no	—
579	Q₈	—	2	2	no	—
580	Q₈	—	2	2	no	—
581	Q₈	—	2	2	no	—
582	Q₈	—	2	2	no	—
583	Q₈	—	4	8	no	—
584	Q₈	—	4	1	no	—
585	Q₈	—	4	1	no	—
586	Q₈	—	4	1	no	—
587	Q₈	—	4	1	no	—
588	Q₈	—	4	1	no	—
589	Q₈	—	4	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	4	8	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	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	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
634	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
635	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
636	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
637	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
638	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
639	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
640	C₈	—	2	2	no	—
641	C₈	—	2	2	no	—
642	C₈	—	4	1	no	—
643	C₈	—	4	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
652	C₂²	C₁₃×#534	1	1	yes	characteristic
653	C₂²	C₁₃×#535	1	1	yes	characteristic
654	C₂²	C₁₃×#577	1	1	yes	characteristic
655	C₂²	C₁₃×#578	1	1	yes	characteristic
656	C₂²	C₁₃×#578	1	1	yes	characteristic
657	C₂²	C₁₃×#578	1	1	yes	characteristic
658	C₄	—	2	2	no	—
659	C₄	—	4	2	no	—
660	C₄	—	4	2	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	2	no	—
667	C₄	—	8	1	no	—
668	C₄	—	8	1	no	—
669	C₄	—	8	1	no	—
670	C₄	—	8	1	no	—
671	C₄	C₁₃×#518	1	1	yes	characteristic
672	C₄	C₁₃×#518	1	1	yes	characteristic
673	C₄	C₁₃×#538	1	1	yes	characteristic
674	C₄	C₁₃×#538	1	1	yes	characteristic
675	C₂	—	4	2	no	—
676	C₂	C₁₃×#2321	1	1	yes	characteristic
677	C₂	C₁₃×#2947	1	1	yes	characteristic
678	C₂	C₁₃×#2950	1	1	yes	characteristic
679	C₂	C₁₃×#3201	1	1	yes	characteristic
680	C₂	C₁₃×#3202	1	1	yes	characteristic
681	C₂	C₁₃×#3223	1	1	yes	characteristic
682	C₂	C₁₃×#3225	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	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#1971	C₂	semidirect
5. C₁₃×#1969	C₂	semidirect
6. C₁₃×#1935	C₂	semidirect
7. C₁₃×#1933	C₂	semidirect
8. C₁₃×#1928	C₂	semidirect
9. C₁₃×#1927	C₂	semidirect
10. C₁₃×#1878	C₂	semidirect
11. C₁₃×#1878	C₂	semidirect
23. C₁₃×#451	C₄	semidirect
137. #22054	C₁₃	direct (N × H)
231. #1971	C₂×C₁₃	semidirect
232. #1969	C₂×C₁₃	semidirect
233. #1935	C₂×C₁₃	semidirect
234. #1933	C₂×C₁₃	semidirect
235. #1928	C₂×C₁₃	semidirect
236. #1927	C₂×C₁₃	semidirect
237. #1878	C₂×C₁₃	semidirect
238. #1878	C₂×C₁₃	semidirect
325. #451	C₄×C₁₃	semidirect
568. C₁₃	#22054	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×#451	2
C₁₃×#2323	2
C₁₃×#2310	2
C₁₃×#1971	2
C₁₃×#1969	2
C₁₃×#1935	2
C₁₃×#1933	2
C₁₃×#1928	2
C₁₃×#1927	2
C₁₃×#1878	2
C₁₃×#1873	2
C₁₃×#1854	2
C₁₃×#1787	2
C₁₃×#1750	2
#22054	13

Subgroups — C13×#22054 #15708393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22054 #15708393