Subgroups — C₁₃×#23680 #15710019

Order 3328.

956 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2073	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2054	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#2042	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2012	C₂	1	1	yes	maximal, characteristic
13	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#124	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×C₁₃×#117	—	2	1	no	—
23	C₄×C₁₃×SD₁₆	—	2	4	no	—
24	C₄×C₁₃×D₈	—	2	4	no	—
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	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×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#391	C₂²	1	1	yes	characteristic
40	C₁₃×#390	C₂²	1	1	yes	characteristic
41	C₁₃×#390	C₂²	1	1	yes	characteristic
42	C₁₃×#390	C₂²	1	1	yes	characteristic
43	C₁₃×#389	C₂²	1	1	yes	characteristic
44	C₁₃×#389	C₂²	1	1	yes	characteristic
45	C₁₃×#388	—	2	1	no	—
46	C₁₃×#388	—	2	1	no	—
47	C₁₃×#388	—	2	1	no	—
48	C₁₃×#388	—	2	1	no	—
49	C₁₃×#382	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
52	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
53	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
54	C₄³×C₁₃	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×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×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	C₂×C₁₃×SD₁₆	—	2	2	no	—
67	C₂×C₁₃×SD₁₆	—	2	2	no	—
68	C₂×C₁₃×SD₁₆	—	2	2	no	—
69	C₂×C₁₃×D₈	—	2	2	no	—
70	C₂×C₁₃×D₈	—	2	2	no	—
71	C₂×C₁₃×D₈	—	2	2	no	—
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
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	C₁₃×#124	—	2	2	no	—
77	C₁₃×#124	—	2	2	no	—
78	C₄×Q₈×C₁₃	—	2	2	no	—
79	C₄×Q₈×C₁₃	—	2	2	no	—
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	D₄	1	4	yes	—
84	C₁₃×#117	—	4	4	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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×C₄²×C₁₃	—	2	1	no	—
104	C₂×C₄²×C₁₃	—	2	1	no	—
105	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₁₃×#107	—	2	2	no	—
113	C₁₃×#106	—	2	2	no	—
114	C₁₃×C₄⋊C₈	—	2	2	no	—
115	C₁₃×C₄⋊C₈	—	2	2	no	—
116	C₁₃×#103	—	2	2	no	—
117	C₁₃×#103	—	2	2	no	—
118	C₁₃×#103	—	2	2	no	—
119	C₁₃×#102	—	2	2	no	—
120	C₁₃×#102	—	2	2	no	—
121	C₁₃×#102	—	2	2	no	—
122	C₁₃×#102	—	2	2	no	—
123	C₁₃×#102	—	2	2	no	—
124	C₄×C₈×C₁₃	—	2	2	no	—
125	C₄×C₈×C₁₃	—	2	2	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	#23680	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂⁴×C₁₃	—	2	1	no	—
135	C₂⁴×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×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	#41	1	2	yes	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
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	—	2	1	no	—
148	C₂×D₄×C₁₃	—	2	1	no	—
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
153	C₂×D₄×C₁₃	#41	1	2	yes	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	4	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	—	4	2	no	—
162	C₂²×C₄×C₁₃	—	4	2	no	—
163	C₂²×C₄×C₁₃	—	4	2	no	—
164	C₂²×C₄×C₁₃	—	4	2	no	—
165	C₂²×C₄×C₁₃	—	4	2	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	—	2	8	no	—
174	C₁₃×D₈	—	2	8	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	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	2	1	no	—
185	C₂×C₈×C₁₃	#41	1	2	yes	—
186	C₂×C₈×C₁₃	#41	1	2	yes	—
187	C₁₃×C₄⋊C₄	—	2	1	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	—	4	2	no	—
197	C₁₃×C₄⋊C₄	—	4	2	no	—
198	C₁₃×C₄⋊C₄	—	4	2	no	—
199	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
200	C₁₃×C₂²⋊C₄	—	2	4	no	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₁₃×C₂²⋊C₄	—	4	2	no	—
204	C₁₃×C₂²⋊C₄	—	4	2	no	—
205	C₁₃×C₂²⋊C₄	—	4	2	no	—
206	C₁₃×C₂²⋊C₄	—	4	2	no	—
207	C₁₃×C₂²⋊C₄	—	4	2	no	—
208	C₁₃×C₂²⋊C₄	—	4	2	no	—
209	C₁₃×C₂²⋊C₄	—	4	2	no	—
210	C₄²×C₁₃	—	2	2	no	—
211	C₄²×C₁₃	—	2	2	no	—
212	C₄²×C₁₃	—	2	2	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	1	no	—
218	C₄²×C₁₃	—	4	2	no	—
219	C₄²×C₁₃	—	4	2	no	—
220	C₄²×C₁₃	C₂×D₄	1	2	yes	—
221	C₄²×C₁₃	#41	1	2	yes	—
222	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
224	C₄×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#2293	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#2085	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#2073	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#2068	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#2065	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#2055	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#2054	C₂×C₁₃	1	1	yes	characteristic
232	#2042	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#2012	C₂×C₁₃	1	1	yes	characteristic
234	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
235	C₄×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₄×#102	C₂×C₁₃	1	1	yes	characteristic, complemented
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	—	4	1	no	—
244	C₂³×C₁₃	—	4	1	no	—
245	C₂³×C₁₃	—	4	1	no	—
246	C₂³×C₁₃	—	4	1	no	—
247	C₂³×C₁₃	—	4	1	no	—
248	C₂³×C₁₃	—	4	1	no	—
249	C₂³×C₁₃	—	4	1	no	—
250	C₂³×C₁₃	—	4	1	no	—
251	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
252	Q₈×C₁₃	—	2	2	no	—
253	Q₈×C₁₃	—	2	2	no	—
254	Q₈×C₁₃	—	4	1	no	—
255	Q₈×C₁₃	—	4	1	no	—
256	D₄×C₁₃	—	2	2	no	—
257	D₄×C₁₃	—	2	2	no	—
258	D₄×C₁₃	—	2	2	no	—
259	D₄×C₁₃	—	2	2	no	—
260	D₄×C₁₃	—	4	1	no	—
261	D₄×C₁₃	—	4	1	no	—
262	D₄×C₁₃	—	4	1	no	—
263	D₄×C₁₃	—	4	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	2	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	2	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	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	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	8	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	—	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	—	8	4	no	—
297	C₂×C₄×C₁₃	#121	1	2	yes	—
298	C₂×C₄×C₁₃	#121	1	2	yes	—
299	C₂×C₄×C₁₃	#135	1	2	yes	—
300	C₂×C₄×C₁₃	#135	1	2	yes	—
301	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
302	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
304	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
305	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
306	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
308	C₈×C₁₃	—	2	2	no	—
309	C₈×C₁₃	—	2	2	no	—
310	C₈×C₁₃	—	4	1	no	—
311	C₈×C₁₃	—	4	1	no	—
312	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
313	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×#117	—	2	1	no	—
319	C₄×SD₁₆	—	2	4	no	—
320	C₄×D₈	—	2	4	no	—
321	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
335	#391	C₂²×C₁₃	1	1	yes	characteristic
336	#390	C₂²×C₁₃	1	1	yes	characteristic
337	#390	C₂²×C₁₃	1	1	yes	characteristic
338	#390	C₂²×C₁₃	1	1	yes	characteristic
339	#389	C₂²×C₁₃	1	1	yes	characteristic
340	#389	C₂²×C₁₃	1	1	yes	characteristic
341	#388	—	2	1	no	—
342	#388	—	2	1	no	—
343	#388	—	2	1	no	—
344	#388	—	2	1	no	—
345	#382	C₂²×C₁₃	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
347	C₄×C₂²⋊C₄	—	2	1	no	—
348	C₄×C₂²⋊C₄	—	2	1	no	—
349	C₄×C₂²⋊C₄	—	2	1	no	—
350	C₄³	C₂²×C₁₃	1	1	yes	characteristic
351	#340	C₂²×C₁₃	1	1	yes	characteristic
352	#340	C₂²×C₁₃	1	1	yes	characteristic
353	#340	C₂²×C₁₃	1	1	yes	characteristic
354	#340	C₂²×C₁₃	1	1	yes	characteristic
355	#336	C₂²×C₁₃	1	1	yes	characteristic
356	#336	C₂²×C₁₃	1	1	yes	characteristic
357	C₂²×C₁₃	—	4	2	no	—
358	C₂²×C₁₃	—	4	2	no	—
359	C₂²×C₁₃	—	4	2	no	—
360	C₂²×C₁₃	—	4	2	no	—
361	C₂²×C₁₃	—	4	2	no	—
362	C₂²×C₁₃	—	4	2	no	—
363	C₂²×C₁₃	—	8	1	no	—
364	C₂²×C₁₃	—	8	1	no	—
365	C₂²×C₁₃	—	8	1	no	—
366	C₂²×C₁₃	—	8	1	no	—
367	C₂²×C₁₃	—	8	1	no	—
368	C₂²×C₁₃	—	8	1	no	—
369	C₂²×C₁₃	—	8	1	no	—
370	C₂²×C₁₃	—	8	1	no	—
371	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
372	C₂²×C₁₃	#525	1	1	yes	characteristic
373	C₂²×C₁₃	#532	1	1	yes	characteristic
374	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
375	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
376	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
377	C₂²×C₁₃	#575	1	1	yes	characteristic
378	C₄×C₁₃	—	2	2	no	—
379	C₄×C₁₃	—	2	2	no	—
380	C₄×C₁₃	—	4	1	no	—
381	C₄×C₁₃	—	4	1	no	—
382	C₄×C₁₃	—	4	2	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	#463	1	4	yes	—
390	C₄×C₁₃	#525	1	1	yes	characteristic
391	C₄×C₁₃	#525	1	1	yes	characteristic
392	C₄×C₁₃	#529	1	1	yes	characteristic
393	C₄×C₁₃	#529	1	1	yes	characteristic
394	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
395	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
396	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
397	C₂³×C₄	—	2	1	no	—
398	C₂³×C₄	—	2	1	no	—
399	C₂×SD₁₆	—	2	2	no	—
400	C₂×SD₁₆	—	2	2	no	—
401	C₂×SD₁₆	—	2	2	no	—
402	C₂×D₈	—	2	2	no	—
403	C₂×D₈	—	2	2	no	—
404	C₂×D₈	—	2	2	no	—
405	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
406	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
407	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
409	#124	—	2	2	no	—
410	#124	—	2	2	no	—
411	C₄×Q₈	—	2	2	no	—
412	C₄×Q₈	—	2	2	no	—
413	C₄×D₄	—	2	2	no	—
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	D₄×C₁₃	1	4	yes	—
417	#117	—	4	4	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₄²	—	2	1	no	—
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
439	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
440	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
441	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
445	#107	—	2	2	no	—
446	#106	—	2	2	no	—
447	C₄⋊C₈	—	2	2	no	—
448	C₄⋊C₈	—	2	2	no	—
449	#103	—	2	2	no	—
450	#103	—	2	2	no	—
451	#103	—	2	2	no	—
452	#102	—	2	2	no	—
453	#102	—	2	2	no	—
454	#102	—	2	2	no	—
455	#102	—	2	2	no	—
456	#102	—	2	2	no	—
457	C₄×C₈	—	2	2	no	—
458	C₄×C₈	—	2	2	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	C₂×C₁₃	—	8	2	no	—
467	C₂×C₁₃	—	8	2	no	—
468	C₂×C₁₃	#2392	1	1	yes	characteristic
469	C₂×C₁₃	C₂×#463	1	1	yes	characteristic
470	C₂×C₁₃	#3035	1	1	yes	characteristic
471	C₂×C₁₃	#3102	1	1	yes	characteristic
472	C₂×C₁₃	#3106	1	1	yes	characteristic
473	C₂×C₁₃	#3168	1	1	yes	characteristic
474	C₂×C₁₃	#3171	1	1	yes	characteristic
475	C₂⁴	—	2	1	no	—
476	C₂⁴	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	C₁₃×#41	1	2	yes	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
494	C₂×D₄	C₁₃×#41	1	2	yes	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	4	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	4	2	no	—
503	C₂²×C₄	—	4	2	no	—
504	C₂²×C₄	—	4	2	no	—
505	C₂²×C₄	—	4	2	no	—
506	C₂²×C₄	—	4	2	no	—
507	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
512	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
513	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
514	SD₁₆	—	2	8	no	—
515	D₈	—	2	8	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	C₁₃×#41	1	2	yes	—
527	C₂×C₈	C₁₃×#41	1	2	yes	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	4	2	no	—
538	C₄⋊C₄	—	4	2	no	—
539	C₄⋊C₄	—	4	2	no	—
540	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
541	C₂²⋊C₄	—	2	4	no	—
542	C₂²⋊C₄	—	2	4	no	—
543	C₂²⋊C₄	—	2	4	no	—
544	C₂²⋊C₄	—	4	2	no	—
545	C₂²⋊C₄	—	4	2	no	—
546	C₂²⋊C₄	—	4	2	no	—
547	C₂²⋊C₄	—	4	2	no	—
548	C₂²⋊C₄	—	4	2	no	—
549	C₂²⋊C₄	—	4	2	no	—
550	C₂²⋊C₄	—	4	2	no	—
551	C₄²	—	2	2	no	—
552	C₄²	—	2	2	no	—
553	C₄²	—	2	2	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	—	4	1	no	—
559	C₄²	—	4	2	no	—
560	C₄²	—	4	2	no	—
561	C₄²	C₂×D₄×C₁₃	1	2	yes	—
562	C₄²	C₁₃×#41	1	2	yes	—
563	C₁₃	#23680	1	1	yes	characteristic, direct product factor, Sylow
564	C₂³	—	2	2	no	—
565	C₂³	—	2	2	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	1	no	—
570	C₂³	—	4	1	no	—
571	C₂³	—	4	1	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	4	1	no	—
577	C₂³	—	4	1	no	—
578	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
579	Q₈	—	2	2	no	—
580	Q₈	—	2	2	no	—
581	Q₈	—	4	1	no	—
582	Q₈	—	4	1	no	—
583	D₄	—	2	2	no	—
584	D₄	—	2	2	no	—
585	D₄	—	2	2	no	—
586	D₄	—	2	2	no	—
587	D₄	—	4	1	no	—
588	D₄	—	4	1	no	—
589	D₄	—	4	1	no	—
590	D₄	—	4	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	1	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	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	8	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	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	—	8	4	no	—
624	C₂×C₄	C₁₃×#121	1	2	yes	—
625	C₂×C₄	C₁₃×#121	1	2	yes	—
626	C₂×C₄	C₁₃×#135	1	2	yes	—
627	C₂×C₄	C₁₃×#135	1	2	yes	—
628	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
629	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
630	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
631	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
632	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
633	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
634	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
635	C₈	—	2	2	no	—
636	C₈	—	2	2	no	—
637	C₈	—	4	1	no	—
638	C₈	—	4	1	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	2	no	—
642	C₂²	—	4	2	no	—
643	C₂²	—	4	2	no	—
644	C₂²	—	4	2	no	—
645	C₂²	—	8	1	no	—
646	C₂²	—	8	1	no	—
647	C₂²	—	8	1	no	—
648	C₂²	—	8	1	no	—
649	C₂²	—	8	1	no	—
650	C₂²	—	8	1	no	—
651	C₂²	—	8	1	no	—
652	C₂²	—	8	1	no	—
653	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
654	C₂²	C₁₃×#525	1	1	yes	characteristic
655	C₂²	C₁₃×#532	1	1	yes	characteristic
656	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
657	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
658	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
659	C₂²	C₁₃×#575	1	1	yes	characteristic
660	C₄	—	2	2	no	—
661	C₄	—	2	2	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	2	no	—
666	C₄	—	4	1	no	—
667	C₄	—	8	1	no	—
668	C₄	—	8	1	no	—
669	C₄	—	8	1	no	—
670	C₄	—	8	1	no	—
671	C₄	C₁₃×#463	1	4	yes	—
672	C₄	C₁₃×#525	1	1	yes	characteristic
673	C₄	C₁₃×#525	1	1	yes	characteristic
674	C₄	C₁₃×#529	1	1	yes	characteristic
675	C₄	C₁₃×#529	1	1	yes	characteristic
676	C₂	—	8	2	no	—
677	C₂	—	8	2	no	—
678	C₂	C₁₃×#2392	1	1	yes	characteristic
679	C₂	C₂×C₁₃×#463	1	1	yes	characteristic
680	C₂	C₁₃×#3035	1	1	yes	characteristic
681	C₂	C₁₃×#3102	1	1	yes	characteristic
682	C₂	C₁₃×#3106	1	1	yes	characteristic
683	C₂	C₁₃×#3168	1	1	yes	characteristic
684	C₂	C₁₃×#3171	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
3. C₄×C₁₃×#124	C₂	semidirect
4. C₁₃×#2293	C₂	semidirect
5. C₁₃×#2085	C₂	semidirect
6. C₁₃×#2073	C₂	semidirect
7. C₁₃×#2068	C₂	semidirect
8. C₁₃×#2065	C₂	semidirect
9. C₁₃×#2055	C₂	semidirect
11. C₁₃×#2042	C₂	semidirect
13. C₄×C₁₃×C₄⋊C₈	C₂	semidirect
14. C₄×C₁₃×#103	C₂	semidirect
15. C₄×C₁₃×#102	C₂	semidirect
133. #23680	C₁₃	direct (N × H)
222. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
224. C₄×#124	C₂×C₁₃	semidirect
225. #2293	C₂×C₁₃	semidirect
226. #2085	C₂×C₁₃	semidirect
227. #2073	C₂×C₁₃	semidirect
228. #2068	C₂×C₁₃	semidirect
229. #2065	C₂×C₁₃	semidirect
230. #2055	C₂×C₁₃	semidirect
232. #2042	C₂×C₁₃	semidirect
234. C₄×C₄⋊C₈	C₂×C₁₃	semidirect
235. C₄×#103	C₂×C₁₃	semidirect
236. C₄×#102	C₂×C₁₃	semidirect
563. C₁₃	#23680	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×C₄×C₁₃×SD₁₆	2
C₂×C₄×C₁₃×D₈	2
C₄×C₁₃×#124	2
C₁₃×#2293	2
C₁₃×#2085	2
C₁₃×#2073	2
C₁₃×#2068	2
C₁₃×#2065	2
C₁₃×#2055	2
C₁₃×#2054	2
C₁₃×#2042	2
C₁₃×#2012	2
C₄×C₁₃×C₄⋊C₈	2
C₄×C₁₃×#103	2
C₄×C₁₃×#102	2
#23680	13

Subgroups — C13×#23680 #15710019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23680 #15710019