Subgroups — C₁₃×#17687 #15704026

Order 3328.

896 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3512	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2971	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1536	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1535	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1532	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1529	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1528	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1528	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1525	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1524	C₂	1	2	yes	maximal, complemented
12	C₁₃×#553	—	2	2	no	—
13	C₁₃×#553	—	2	2	no	—
14	C₁₃×#553	—	2	1	no	—
15	C₁₃×#553	—	2	1	no	—
16	C₁₃×#552	—	2	1	no	—
17	C₁₃×#552	—	2	1	no	—
18	C₁₃×#541	C₄	1	2	yes	—
19	C₁₃×#540	C₄	1	2	yes	—
20	C₁₃×#537	C₄	1	1	yes	characteristic
21	C₁₃×#537	C₄	1	1	yes	characteristic
22	C₁₃×#532	C₂²	1	1	yes	characteristic
23	C₁₃×#529	C₂²	1	2	yes	—
24	C₁₃×#529	C₂²	1	2	yes	—
25	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
26	C₁₃×#520	C₄	1	1	yes	characteristic
27	C₁₃×#520	C₄	1	1	yes	characteristic
28	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
29	C₁₃×#446	—	2	1	no	—
30	C₈×Q₈×C₁₃	—	2	1	no	—
31	C₁₃×#436	—	2	2	no	—
32	C₁₃×#436	—	2	1	no	—
33	C₁₃×#435	—	2	2	no	—
34	C₈×D₄×C₁₃	—	2	1	no	—
35	C₁₃×#432	C₂²	1	1	yes	characteristic
36	C₁₃×#432	C₂²	1	1	yes	characteristic
37	C₁₃×#432	C₂²	1	2	yes	—
38	C₁₃×#432	C₂²	1	2	yes	—
39	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
40	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
41	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#97	C₂²	1	2	yes	—
43	C₁₃×#330	C₂²	1	2	yes	—
44	C₁₃×#330	C₂²	1	2	yes	—
45	C₁₃×#330	C₂²	1	2	yes	—
46	C₁₃×#330	C₂²	1	2	yes	—
47	C₁₃×#329	C₂²	1	1	yes	characteristic
48	C₁₃×#329	C₂²	1	2	yes	—
49	C₁₃×#329	C₂²	1	1	yes	characteristic
50	C₁₃×#329	C₂²	1	1	yes	characteristic
51	C₁₃×#329	C₂²	1	1	yes	characteristic
52	C₁₃×#329	C₂²	1	2	yes	—
53	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
56	C₂×C₁₃×M₁₆	—	2	1	no	—
57	C₂×C₁₃×M₁₆	—	2	1	no	—
58	C₂×C₁₃×M₁₆	—	2	2	no	—
59	C₂²×C₈×C₁₃	—	2	2	no	—
60	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
61	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
62	C₁₃×#126	—	2	2	no	—
63	C₁₃×#126	—	2	2	no	—
64	C₁₃×#126	—	2	2	no	—
65	C₁₃×#126	—	2	2	no	—
66	C₁₃×#125	—	2	2	no	—
67	C₁₃×#125	—	2	2	no	—
68	C₁₃×#125	—	2	1	no	—
69	C₁₃×#125	—	2	1	no	—
70	C₁₃×#125	C₂×C₄	1	2	yes	—
71	C₁₃×#125	C₂³	1	2	yes	—
72	C₁₃×#124	C₂³	1	1	yes	characteristic
73	C₁₃×#124	C₂³	1	1	yes	characteristic
74	C₁₃×#123	—	2	2	no	—
75	C₁₃×#123	—	2	2	no	—
76	C₁₃×#123	—	2	2	no	—
77	C₁₃×#123	—	2	2	no	—
78	C₁₃×C₂²⋊Q₈	—	2	1	no	—
79	C₁₃×C₂²⋊Q₈	—	2	1	no	—
80	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
81	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
82	C₁₃×#121	—	2	1	no	—
83	C₁₃×#121	—	2	1	no	—
84	C₁₃×#121	—	2	2	no	—
85	C₁₃×#121	—	2	2	no	—
86	C₁₃×#121	—	2	1	no	—
87	C₁₃×#121	—	2	1	no	—
88	C₁₃×#121	—	2	2	no	—
89	C₁₃×#121	—	2	2	no	—
90	C₁₃×#121	C₂×C₄	1	2	yes	—
91	C₁₃×#121	C₂×C₄	1	2	yes	—
92	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
93	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
94	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
95	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
96	C₄×D₄×C₁₃	—	2	2	no	—
97	C₄×D₄×C₁₃	—	2	2	no	—
98	C₄×D₄×C₁₃	—	2	2	no	—
99	C₄×D₄×C₁₃	—	2	2	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
103	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
104	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
105	C₄×D₄×C₁₃	D₄	1	2	yes	—
106	C₄×D₄×C₁₃	D₄	1	2	yes	—
107	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
108	C₁₃×#117	—	2	1	no	—
109	C₁₃×#117	—	2	1	no	—
110	C₁₃×#117	—	2	2	no	—
111	C₁₃×#117	—	2	2	no	—
112	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
113	C₁₃×#117	C₂×C₄	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
119	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
122	C₁₃×C₄⋊C₈	—	2	1	no	—
123	C₁₃×C₄⋊C₈	—	2	2	no	—
124	C₁₃×C₄⋊C₈	—	2	2	no	—
125	C₁₃×C₄⋊C₈	—	2	1	no	—
126	C₁₃×C₂²⋊C₈	—	2	2	no	—
127	C₁₃×C₂²⋊C₈	—	2	1	no	—
128	C₁₃×C₂²⋊C₈	—	2	1	no	—
129	C₁₃×C₂²⋊C₈	—	2	2	no	—
130	C₁₃×#97	—	2	2	no	—
131	C₁₃×#97	C₂³	1	1	yes	characteristic
132	C₁₃×#97	C₂³	1	2	yes	—
133	C₁₃×#97	C₂³	1	1	yes	characteristic
134	C₁₃×#97	C₂³	1	2	yes	—
135	C₁₃×#97	C₂³	1	1	yes	characteristic
136	C₁₃×#97	C₂³	1	1	yes	characteristic
137	C₄×C₈×C₁₃	—	2	1	no	—
138	C₄×C₈×C₁₃	—	2	2	no	—
139	C₄×C₈×C₁₃	—	2	1	no	—
140	#17687	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₁₃×#41	—	4	2	no	—
142	C₁₃×#41	—	4	2	no	—
143	C₁₃×#41	—	4	2	no	—
144	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
145	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₄×C₁₃	—	2	1	no	—
148	C₂×D₄×C₁₃	—	2	1	no	—
149	C₂×D₄×C₁₃	—	2	2	no	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
154	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
155	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
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	2	no	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
169	C₁₃×M₁₆	—	4	2	no	—
170	C₁₃×M₁₆	—	4	4	no	—
171	C₁₃×M₁₆	—	4	2	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	2	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	2	no	—
178	C₂×C₈×C₁₃	—	4	4	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₁₃×C₄⋊C₄	—	2	2	no	—
183	C₁₃×C₄⋊C₄	—	2	2	no	—
184	C₁₃×C₄⋊C₄	—	2	2	no	—
185	C₁₃×C₄⋊C₄	—	2	2	no	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
192	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
193	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
194	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
195	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
196	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
197	C₁₃×C₂²⋊C₄	—	2	2	no	—
198	C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₁₃×C₂²⋊C₄	—	2	2	no	—
202	C₁₃×C₂²⋊C₄	—	2	2	no	—
203	C₁₃×C₂²⋊C₄	—	2	1	no	—
204	C₁₃×C₂²⋊C₄	—	2	1	no	—
205	C₁₃×C₂²⋊C₄	—	2	1	no	—
206	C₁₃×C₂²⋊C₄	—	2	1	no	—
207	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
208	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
209	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
210	C₄²×C₁₃	—	2	2	no	—
211	C₄²×C₁₃	—	2	2	no	—
212	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
213	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
214	C₄²×C₁₃	C₂×D₄	1	2	yes	—
215	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₁₃	C₂×D₄	1	2	yes	—
218	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
219	#3512	C₂×C₁₃	1	1	yes	characteristic
220	#2971	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#2970	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1536	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1535	C₂×C₁₃	1	2	yes	complemented
224	#1532	C₂×C₁₃	1	2	yes	complemented
225	#1529	C₂×C₁₃	1	2	yes	complemented
226	#1528	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1528	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1525	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1524	C₂×C₁₃	1	2	yes	complemented
230	C₂³×C₁₃	—	2	1	no	—
231	C₂³×C₁₃	—	2	1	no	—
232	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
233	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	Q₈×C₁₃	—	2	2	no	—
235	Q₈×C₁₃	—	4	1	no	—
236	Q₈×C₁₃	—	4	1	no	—
237	D₄×C₁₃	—	2	2	no	—
238	D₄×C₁₃	—	4	2	no	—
239	D₄×C₁₃	—	4	1	no	—
240	D₄×C₁₃	—	4	1	no	—
241	D₄×C₁₃	—	4	2	no	—
242	D₄×C₁₃	—	4	2	no	—
243	D₄×C₁₃	—	8	1	no	—
244	D₄×C₁₃	—	8	1	no	—
245	D₄×C₁₃	—	8	2	no	—
246	D₄×C₁₃	—	8	2	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	4	2	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	2	no	—
257	C₂×C₄×C₁₃	—	4	2	no	—
258	C₂×C₄×C₁₃	—	4	2	no	—
259	C₂×C₄×C₁₃	—	8	2	no	—
260	C₂×C₄×C₁₃	—	8	2	no	—
261	C₂×C₄×C₁₃	—	8	1	no	—
262	C₂×C₄×C₁₃	—	8	1	no	—
263	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
264	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
265	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
268	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
272	C₈×C₁₃	—	2	2	no	—
273	C₈×C₁₃	—	2	2	no	—
274	C₈×C₁₃	—	4	2	no	—
275	C₈×C₁₃	—	4	1	no	—
276	C₈×C₁₃	—	4	2	no	—
277	C₈×C₁₃	—	4	1	no	—
278	#553	—	2	2	no	—
279	#553	—	2	2	no	—
280	#553	—	2	1	no	—
281	#553	—	2	1	no	—
282	#552	—	2	1	no	—
283	#552	—	2	1	no	—
284	#541	C₄×C₁₃	1	2	yes	—
285	#540	C₄×C₁₃	1	2	yes	—
286	#537	C₄×C₁₃	1	1	yes	characteristic
287	#537	C₄×C₁₃	1	1	yes	characteristic
288	#532	C₂²×C₁₃	1	1	yes	characteristic
289	#529	C₂²×C₁₃	1	2	yes	—
290	#529	C₂²×C₁₃	1	2	yes	—
291	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
292	#520	C₄×C₁₃	1	1	yes	characteristic
293	#520	C₄×C₁₃	1	1	yes	characteristic
294	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
295	#446	—	2	1	no	—
296	C₈×Q₈	—	2	1	no	—
297	#436	—	2	2	no	—
298	#436	—	2	1	no	—
299	#435	—	2	2	no	—
300	C₈×D₄	—	2	1	no	—
301	#432	C₂²×C₁₃	1	1	yes	characteristic
302	#432	C₂²×C₁₃	1	1	yes	characteristic
303	#432	C₂²×C₁₃	1	2	yes	—
304	#432	C₂²×C₁₃	1	2	yes	—
305	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
306	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
307	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×#97	C₂²×C₁₃	1	2	yes	—
309	#330	C₂²×C₁₃	1	2	yes	—
310	#330	C₂²×C₁₃	1	2	yes	—
311	#330	C₂²×C₁₃	1	2	yes	—
312	#330	C₂²×C₁₃	1	2	yes	—
313	#329	C₂²×C₁₃	1	2	yes	—
314	#329	C₂²×C₁₃	1	2	yes	—
315	#329	C₂²×C₁₃	1	1	yes	characteristic
316	#329	C₂²×C₁₃	1	1	yes	characteristic
317	#329	C₂²×C₁₃	1	1	yes	characteristic
318	#329	C₂²×C₁₃	1	1	yes	characteristic
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	2	2	no	—
321	C₂²×C₁₃	—	2	1	no	—
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	2	2	no	—
324	C₂²×C₁₃	—	2	2	no	—
325	C₂²×C₁₃	—	4	1	no	—
326	C₂²×C₁₃	—	4	1	no	—
327	C₂²×C₁₃	—	4	1	no	—
328	C₂²×C₁₃	—	4	1	no	—
329	C₂²×C₁₃	—	4	1	no	—
330	C₂²×C₁₃	—	4	1	no	—
331	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
332	C₄×C₁₃	—	2	1	no	—
333	C₄×C₁₃	—	2	2	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	1	no	—
339	C₄×C₁₃	—	2	1	no	—
340	C₄×C₁₃	—	4	1	no	—
341	C₄×C₁₃	—	4	1	no	—
342	C₄×C₁₃	—	4	2	no	—
343	C₄×C₁₃	—	4	2	no	—
344	C₄×C₁₃	#413	1	2	yes	—
345	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
346	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
347	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	2	no	—
351	C₂²×C₈	—	2	2	no	—
352	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
353	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
354	#126	—	2	2	no	—
355	#126	—	2	2	no	—
356	#126	—	2	2	no	—
357	#126	—	2	2	no	—
358	#125	—	2	2	no	—
359	#125	—	2	2	no	—
360	#125	—	2	1	no	—
361	#125	—	2	1	no	—
362	#125	C₂×C₄×C₁₃	1	2	yes	—
363	#125	C₂³×C₁₃	1	2	yes	—
364	#124	C₂³×C₁₃	1	1	yes	characteristic
365	#124	C₂³×C₁₃	1	1	yes	characteristic
366	#123	—	2	2	no	—
367	#123	—	2	2	no	—
368	#123	—	2	2	no	—
369	#123	—	2	2	no	—
370	C₂²⋊Q₈	—	2	1	no	—
371	C₂²⋊Q₈	—	2	1	no	—
372	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
373	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
374	#121	—	2	1	no	—
375	#121	—	2	1	no	—
376	#121	—	2	2	no	—
377	#121	—	2	2	no	—
378	#121	—	2	1	no	—
379	#121	—	2	1	no	—
380	#121	—	2	2	no	—
381	#121	—	2	2	no	—
382	#121	C₂×C₄×C₁₃	1	2	yes	—
383	#121	C₂×C₄×C₁₃	1	2	yes	—
384	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
385	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
386	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
387	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
388	C₄×D₄	—	2	2	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
395	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
396	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
397	C₄×D₄	D₄×C₁₃	1	2	yes	—
398	C₄×D₄	D₄×C₁₃	1	2	yes	—
399	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
400	#117	—	2	1	no	—
401	#117	—	2	1	no	—
402	#117	—	2	2	no	—
403	#117	—	2	2	no	—
404	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
405	#117	C₂×C₄×C₁₃	1	2	yes	—
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	C₂×C₄×C₁₃	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
412	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
414	C₄⋊C₈	—	2	1	no	—
415	C₄⋊C₈	—	2	2	no	—
416	C₄⋊C₈	—	2	2	no	—
417	C₄⋊C₈	—	2	1	no	—
418	C₂²⋊C₈	—	2	2	no	—
419	C₂²⋊C₈	—	2	1	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	—	2	2	no	—
422	#97	—	2	2	no	—
423	#97	C₂³×C₁₃	1	1	yes	characteristic
424	#97	C₂³×C₁₃	1	2	yes	—
425	#97	C₂³×C₁₃	1	1	yes	characteristic
426	#97	C₂³×C₁₃	1	2	yes	—
427	#97	C₂³×C₁₃	1	1	yes	characteristic
428	#97	C₂³×C₁₃	1	1	yes	characteristic
429	C₄×C₈	—	2	1	no	—
430	C₄×C₈	—	2	2	no	—
431	C₄×C₈	—	2	1	no	—
432	C₂×C₁₃	—	4	1	no	—
433	C₂×C₁₃	—	4	2	no	—
434	C₂×C₁₃	—	8	1	no	—
435	C₂×C₁₃	—	8	1	no	—
436	C₂×C₁₃	C₂×#413	1	1	yes	characteristic
437	C₂×C₁₃	#2901	1	1	yes	characteristic
438	C₂×C₁₃	#2901	1	1	yes	characteristic
439	#41	—	4	2	no	—
440	#41	—	4	2	no	—
441	#41	—	4	2	no	—
442	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
443	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
444	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
452	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
453	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
454	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
463	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
466	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
467	M₁₆	—	4	2	no	—
468	M₁₆	—	4	4	no	—
469	M₁₆	—	4	2	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	4	4	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
490	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
491	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
492	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
493	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
494	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
506	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
507	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
508	C₄²	—	2	2	no	—
509	C₄²	—	2	2	no	—
510	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
511	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
512	C₄²	C₂×D₄×C₁₃	1	2	yes	—
513	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
514	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
515	C₄²	C₂×D₄×C₁₃	1	2	yes	—
516	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
517	C₁₃	#17687	1	1	yes	characteristic, direct product factor, Sylow
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
521	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
522	Q₈	—	2	2	no	—
523	Q₈	—	4	1	no	—
524	Q₈	—	4	1	no	—
525	D₄	—	2	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	1	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	2	no	—
531	D₄	—	8	1	no	—
532	D₄	—	8	1	no	—
533	D₄	—	8	2	no	—
534	D₄	—	8	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	8	2	no	—
548	C₂×C₄	—	8	2	no	—
549	C₂×C₄	—	8	1	no	—
550	C₂×C₄	—	8	1	no	—
551	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
552	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
553	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
554	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
555	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
556	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
557	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
558	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
560	C₈	—	2	2	no	—
561	C₈	—	2	2	no	—
562	C₈	—	4	2	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	2	no	—
565	C₈	—	4	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
579	C₄	—	2	1	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	2	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	2	no	—
590	C₄	—	4	2	no	—
591	C₄	C₁₃×#413	1	2	yes	—
592	C₂	—	4	1	no	—
593	C₂	—	4	2	no	—
594	C₂	—	8	1	no	—
595	C₂	—	8	1	no	—
596	C₂	C₂×C₁₃×#413	1	1	yes	characteristic
597	C₂	C₁₃×#2901	1	1	yes	characteristic
598	C₂	C₁₃×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3512	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2971	C₂	semidirect
3. C₁₃×#2970	C₂	semidirect
4. C₁₃×#1536	C₂	semidirect
5. C₁₃×#1535	C₂	semidirect
6. C₁₃×#1532	C₂	semidirect
7. C₁₃×#1529	C₂	semidirect
8. C₁₃×#1528	C₂	semidirect
9. C₁₃×#1528	C₂	semidirect
10. C₁₃×#1525	C₂	semidirect
11. C₁₃×#1524	C₂	semidirect
140. #17687	C₁₃	direct (N × H)
220. #2971	C₂×C₁₃	semidirect
221. #2970	C₂×C₁₃	semidirect
222. #1536	C₂×C₁₃	semidirect
223. #1535	C₂×C₁₃	semidirect
224. #1532	C₂×C₁₃	semidirect
225. #1529	C₂×C₁₃	semidirect
226. #1528	C₂×C₁₃	semidirect
227. #1528	C₂×C₁₃	semidirect
228. #1525	C₂×C₁₃	semidirect
229. #1524	C₂×C₁₃	semidirect
517. C₁₃	#17687	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3512	2
C₁₃×#2971	2
C₁₃×#2970	2
C₁₃×#1536	2
C₁₃×#1535	2
C₁₃×#1532	2
C₁₃×#1529	2
C₁₃×#1528	2
C₁₃×#1525	2
C₁₃×#1524	2
#17687	13

Subgroups — C13×#17687 #15704026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17687 #15704026