Subgroups — C₁₃×#18710 #15705049

Order 3328.

852 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	C₁₃×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3251	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1653	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1652	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1645	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1644	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1628	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1626	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1623	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1622	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1559	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1494	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#563	—	2	2	no	—
17	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#557	—	2	1	no	—
19	C₁₃×#557	C₂²	1	1	yes	characteristic
20	C₁₃×#556	—	2	1	no	—
21	C₁₃×#556	—	2	1	no	—
22	C₁₃×#556	C₂²	1	1	yes	characteristic
23	C₁₃×#554	C₂²	1	1	yes	characteristic
24	C₁₃×#552	—	2	1	no	—
25	C₁₃×#544	—	2	1	no	—
26	C₁₃×#542	—	2	1	no	—
27	C₁₃×#541	—	2	1	no	—
28	C₁₃×#541	—	2	1	no	—
29	C₁₃×#541	—	2	2	no	—
30	C₁₃×#533	C₂²	1	1	yes	characteristic
31	C₁₃×#533	C₂²	1	1	yes	characteristic
32	C₁₃×#532	C₂²	1	1	yes	characteristic
33	C₁₃×#529	C₂²	1	1	yes	characteristic
34	C₁₃×#498	C₂²	1	1	yes	characteristic
35	C₁₃×#497	—	2	1	no	—
36	C₁₃×#492	C₂²	1	1	yes	characteristic
37	C₁₃×#489	—	2	1	no	—
38	C₁₃×#487	C₂²	1	1	yes	characteristic
39	C₁₃×#486	C₂²	1	1	yes	characteristic
40	C₁₃×#478	—	2	1	no	—
41	C₁₃×#475	C₂²	1	1	yes	characteristic
42	C₁₃×#474	C₂²	1	1	yes	characteristic
43	C₁₃×#469	—	2	1	no	—
44	C₁₃×#468	—	2	1	no	—
45	C₁₃×#465	—	2	2	no	—
46	C₁₃×#463	—	2	1	no	—
47	C₁₃×#462	C₂²	1	1	yes	characteristic
48	C₁₃×#462	C₂²	1	1	yes	characteristic
49	C₁₃×#460	C₂²	1	1	yes	characteristic
50	C₁₃×#460	C₂²	1	1	yes	characteristic
51	C₁₃×#460	C₂²	1	1	yes	characteristic
52	C₁₃×#459	C₂²	1	1	yes	characteristic
53	C₁₃×#452	—	2	1	no	—
54	C₁₃×#452	—	2	1	no	—
55	C₄×C₁₃×SD₁₆	—	2	2	no	—
56	C₁₃×#432	C₂²	1	1	yes	characteristic
57	C₁₃×#423	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
59	C₁₃×#333	C₂²	1	1	yes	characteristic
60	C₁₃×#333	C₂²	1	1	yes	characteristic
61	C₁₃×#332	C₂²	1	1	yes	characteristic
62	C₁₃×#332	C₂²	1	1	yes	characteristic
63	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
68	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
69	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#41	—	2	1	no	—
72	C₂×C₁₃×Q₁₆	—	2	1	no	—
73	C₂×C₁₃×Q₁₆	—	2	1	no	—
74	C₂×C₁₃×SD₁₆	—	2	2	no	—
75	C₂×C₁₃×SD₁₆	—	2	1	no	—
76	C₂×C₁₃×SD₁₆	—	2	1	no	—
77	C₂×C₁₃×SD₁₆	—	2	1	no	—
78	C₂×C₁₃×D₈	—	2	1	no	—
79	C₂×C₁₃×M₁₆	—	2	1	no	—
80	C₂²×C₈×C₁₃	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	—	2	2	no	—
82	C₁₃×C₄⋊Q₈	—	2	1	no	—
83	C₁₃×C₄⋊Q₈	—	2	2	no	—
84	C₁₃×C₄⋊Q₈	—	2	1	no	—
85	C₁₃×C₄⋊Q₈	—	2	1	no	—
86	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
87	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
88	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
91	C₁₃×#127	C₂³	1	1	yes	characteristic
92	C₁₃×#126	—	2	2	no	—
93	C₁₃×#126	—	2	2	no	—
94	C₁₃×#126	—	2	2	no	—
95	C₁₃×#126	—	2	2	no	—
96	C₁₃×#126	—	2	2	no	—
97	C₁₃×#126	—	2	2	no	—
98	C₁₃×#126	—	2	1	no	—
99	C₁₃×#125	—	2	2	no	—
100	C₁₃×#125	—	2	2	no	—
101	C₁₃×#125	—	2	2	no	—
102	C₁₃×#125	—	2	2	no	—
103	C₁₃×#125	—	2	1	no	—
104	C₁₃×#125	—	2	2	no	—
105	C₁₃×#125	—	2	1	no	—
106	C₁₃×#125	—	2	1	no	—
107	C₁₃×#125	—	2	1	no	—
108	C₁₃×#125	D₄	1	1	yes	characteristic
109	C₁₃×#124	—	2	2	no	—
110	C₁₃×#124	—	2	1	no	—
111	C₁₃×#124	—	2	1	no	—
112	C₁₃×#124	D₄	1	1	yes	characteristic
113	C₁₃×#123	—	2	2	no	—
114	C₁₃×#123	—	2	1	no	—
115	C₁₃×C₂²⋊Q₈	—	2	2	no	—
116	C₁₃×C₂²⋊Q₈	—	2	2	no	—
117	C₁₃×C₂²⋊Q₈	—	2	1	no	—
118	C₁₃×C₂²⋊Q₈	—	2	1	no	—
119	C₁₃×C₂²⋊Q₈	—	2	2	no	—
120	C₁₃×C₂²⋊Q₈	—	2	1	no	—
121	C₁₃×C₂²⋊Q₈	—	2	1	no	—
122	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
123	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
124	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
125	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
126	C₁₃×#121	—	2	1	no	—
127	C₁₃×#121	—	2	1	no	—
128	C₁₃×#121	D₄	1	1	yes	characteristic
129	C₄×Q₈×C₁₃	—	2	2	no	—
130	C₄×Q₈×C₁₃	—	2	1	no	—
131	C₄×Q₈×C₁₃	—	2	1	no	—
132	C₄×Q₈×C₁₃	—	2	1	no	—
133	C₄×Q₈×C₁₃	—	2	1	no	—
134	C₄×Q₈×C₁₃	—	2	1	no	—
135	C₄×Q₈×C₁₃	—	2	1	no	—
136	C₄×Q₈×C₁₃	—	2	1	no	—
137	C₄×Q₈×C₁₃	D₄	1	2	yes	—
138	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
139	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
140	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
141	C₄×D₄×C₁₃	—	2	1	no	—
142	C₄×D₄×C₁₃	—	2	1	no	—
143	C₄×D₄×C₁₃	—	2	1	no	—
144	C₄×D₄×C₁₃	—	2	1	no	—
145	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
146	C₁₃×#117	—	2	2	no	—
147	C₁₃×#117	—	2	1	no	—
148	C₁₃×#117	—	2	1	no	—
149	C₁₃×#117	—	2	1	no	—
150	C₁₃×#117	—	2	1	no	—
151	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
153	C₁₃×#107	—	2	1	no	—
154	C₁₃×#106	—	2	2	no	—
155	C₁₃×#106	—	2	1	no	—
156	C₁₃×C₄⋊C₈	—	2	1	no	—
157	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₁₃×#103	—	2	2	no	—
162	C₁₃×#103	—	2	1	no	—
163	C₁₃×#103	—	2	1	no	—
164	C₁₃×#103	—	2	1	no	—
165	C₁₃×#102	—	2	1	no	—
166	C₁₃×#102	—	2	2	no	—
167	C₁₃×#102	—	2	1	no	—
168	C₁₃×#102	—	2	1	no	—
169	C₁₃×#102	—	2	1	no	—
170	C₁₃×#102	—	2	1	no	—
171	C₁₃×C₂²⋊C₈	—	2	1	no	—
172	C₁₃×#97	—	2	1	no	—
173	C₄×C₈×C₁₃	—	2	1	no	—
174	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
176	#18710	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₁₃×#41	—	8	1	no	—
178	C₁₃×#41	—	8	1	no	—
179	C₂×Q₈×C₁₃	—	2	2	no	—
180	C₂×Q₈×C₁₃	—	2	1	no	—
181	C₂×Q₈×C₁₃	—	2	1	no	—
182	C₂×Q₈×C₁₃	—	2	1	no	—
183	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	—	2	1	no	—
189	C₂×D₄×C₁₃	—	2	1	no	—
190	C₂×D₄×C₁₃	—	2	1	no	—
191	C₂×D₄×C₁₃	—	4	1	no	—
192	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₃	—	2	2	no	—
194	C₂²×C₄×C₁₃	—	2	1	no	—
195	C₂²×C₄×C₁₃	—	4	1	no	—
196	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₁₃×Q₁₆	—	8	1	no	—
200	C₁₃×Q₁₆	—	8	1	no	—
201	C₁₃×SD₁₆	—	4	4	no	—
202	C₁₃×SD₁₆	—	8	1	no	—
203	C₁₃×SD₁₆	—	8	1	no	—
204	C₁₃×SD₁₆	—	8	1	no	—
205	C₁₃×D₈	—	8	1	no	—
206	C₁₃×M₁₆	—	8	1	no	—
207	C₂×C₈×C₁₃	—	2	1	no	—
208	C₂×C₈×C₁₃	—	2	1	no	—
209	C₂×C₈×C₁₃	—	2	1	no	—
210	C₂×C₈×C₁₃	—	2	1	no	—
211	C₂×C₈×C₁₃	—	2	1	no	—
212	C₂×C₈×C₁₃	—	2	1	no	—
213	C₂×C₈×C₁₃	—	4	2	no	—
214	C₁₃×C₄⋊C₄	—	2	2	no	—
215	C₁₃×C₄⋊C₄	—	2	2	no	—
216	C₁₃×C₄⋊C₄	—	2	2	no	—
217	C₁₃×C₄⋊C₄	—	2	2	no	—
218	C₁₃×C₄⋊C₄	—	2	2	no	—
219	C₁₃×C₄⋊C₄	—	2	2	no	—
220	C₁₃×C₄⋊C₄	—	2	2	no	—
221	C₁₃×C₄⋊C₄	—	2	2	no	—
222	C₁₃×C₄⋊C₄	—	2	1	no	—
223	C₁₃×C₄⋊C₄	—	2	1	no	—
224	C₁₃×C₄⋊C₄	—	2	1	no	—
225	C₁₃×C₄⋊C₄	—	2	1	no	—
226	C₁₃×C₄⋊C₄	—	2	1	no	—
227	C₁₃×C₄⋊C₄	—	2	1	no	—
228	C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₁₃×C₄⋊C₄	—	2	2	no	—
230	C₁₃×C₄⋊C₄	—	2	1	no	—
231	C₁₃×C₄⋊C₄	—	2	2	no	—
232	C₁₃×C₄⋊C₄	—	2	1	no	—
233	C₁₃×C₄⋊C₄	—	2	1	no	—
234	C₁₃×C₄⋊C₄	—	2	1	no	—
235	C₁₃×C₄⋊C₄	—	2	1	no	—
236	C₁₃×C₄⋊C₄	—	2	1	no	—
237	C₁₃×C₄⋊C₄	—	2	1	no	—
238	C₁₃×C₄⋊C₄	—	2	1	no	—
239	C₁₃×C₄⋊C₄	—	2	1	no	—
240	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
241	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
242	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
243	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
244	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
245	C₁₃×C₂²⋊C₄	—	2	2	no	—
246	C₁₃×C₂²⋊C₄	—	2	2	no	—
247	C₁₃×C₂²⋊C₄	—	2	2	no	—
248	C₁₃×C₂²⋊C₄	—	2	1	no	—
249	C₁₃×C₂²⋊C₄	—	2	2	no	—
250	C₁₃×C₂²⋊C₄	—	2	1	no	—
251	C₁₃×C₂²⋊C₄	—	2	1	no	—
252	C₁₃×C₂²⋊C₄	—	2	1	no	—
253	C₁₃×C₂²⋊C₄	—	2	1	no	—
254	C₁₃×C₂²⋊C₄	—	2	1	no	—
255	C₁₃×C₂²⋊C₄	—	2	1	no	—
256	C₁₃×C₂²⋊C₄	—	4	1	no	—
257	C₁₃×C₂²⋊C₄	—	4	1	no	—
258	C₄²×C₁₃	—	2	2	no	—
259	C₄²×C₁₃	—	2	2	no	—
260	C₄²×C₁₃	—	2	2	no	—
261	C₄²×C₁₃	—	2	2	no	—
262	C₄²×C₁₃	—	2	1	no	—
263	C₄²×C₁₃	—	2	1	no	—
264	C₄²×C₁₃	—	2	1	no	—
265	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
269	#3555	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#3251	C₂×C₁₃	1	1	yes	characteristic
271	#3216	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#3167	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#1653	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#1652	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#1645	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#1644	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#1628	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#1626	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#1623	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#1622	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#1559	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#1494	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#1493	C₂×C₁₃	1	1	yes	characteristic, complemented
284	C₂³×C₁₃	—	2	1	no	—
285	C₂³×C₁₃	—	4	1	no	—
286	C₂³×C₁₃	#120	1	1	yes	characteristic
287	Q₈×C₁₃	—	2	1	no	—
288	Q₈×C₁₃	—	2	1	no	—
289	Q₈×C₁₃	—	2	1	no	—
290	Q₈×C₁₃	—	2	1	no	—
291	Q₈×C₁₃	—	2	1	no	—
292	Q₈×C₁₃	—	2	1	no	—
293	Q₈×C₁₃	—	4	2	no	—
294	Q₈×C₁₃	—	4	1	no	—
295	Q₈×C₁₃	—	4	1	no	—
296	Q₈×C₁₃	—	4	1	no	—
297	Q₈×C₁₃	—	4	1	no	—
298	Q₈×C₁₃	—	8	1	no	—
299	Q₈×C₁₃	—	8	2	no	—
300	D₄×C₁₃	—	2	1	no	—
301	D₄×C₁₃	—	2	1	no	—
302	D₄×C₁₃	—	4	2	no	—
303	D₄×C₁₃	—	4	1	no	—
304	D₄×C₁₃	—	4	1	no	—
305	D₄×C₁₃	—	4	1	no	—
306	D₄×C₁₃	—	4	1	no	—
307	D₄×C₁₃	—	8	1	no	—
308	D₄×C₁₃	—	8	2	no	—
309	C₂×C₄×C₁₃	—	2	1	no	—
310	C₂×C₄×C₁₃	—	2	1	no	—
311	C₂×C₄×C₁₃	—	2	1	no	—
312	C₂×C₄×C₁₃	—	2	1	no	—
313	C₂×C₄×C₁₃	—	2	1	no	—
314	C₂×C₄×C₁₃	—	2	1	no	—
315	C₂×C₄×C₁₃	—	2	1	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	1	no	—
318	C₂×C₄×C₁₃	—	2	1	no	—
319	C₂×C₄×C₁₃	—	2	1	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	1	no	—
322	C₂×C₄×C₁₃	—	4	1	no	—
323	C₂×C₄×C₁₃	—	4	1	no	—
324	C₂×C₄×C₁₃	—	4	1	no	—
325	C₂×C₄×C₁₃	—	4	1	no	—
326	C₂×C₄×C₁₃	—	8	2	no	—
327	C₂×C₄×C₁₃	—	8	2	no	—
328	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
329	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
330	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
331	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
334	C₈×C₁₃	—	2	2	no	—
335	C₈×C₁₃	—	4	1	no	—
336	C₈×C₁₃	—	4	1	no	—
337	C₈×C₁₃	—	4	1	no	—
338	C₈×C₁₃	—	4	1	no	—
339	C₈×C₁₃	—	4	1	no	—
340	#563	—	2	2	no	—
341	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
342	#557	—	2	1	no	—
343	#557	C₂²×C₁₃	1	1	yes	characteristic
344	#556	—	2	1	no	—
345	#556	—	2	1	no	—
346	#556	C₂²×C₁₃	1	1	yes	characteristic
347	#554	C₂²×C₁₃	1	1	yes	characteristic
348	#552	—	2	1	no	—
349	#544	—	2	1	no	—
350	#542	—	2	1	no	—
351	#541	—	2	1	no	—
352	#541	—	2	1	no	—
353	#541	—	2	2	no	—
354	#533	C₂²×C₁₃	1	1	yes	characteristic
355	#533	C₂²×C₁₃	1	1	yes	characteristic
356	#532	C₂²×C₁₃	1	1	yes	characteristic
357	#529	C₂²×C₁₃	1	1	yes	characteristic
358	#498	C₂²×C₁₃	1	1	yes	characteristic
359	#497	—	2	1	no	—
360	#492	C₂²×C₁₃	1	1	yes	characteristic
361	#489	—	2	1	no	—
362	#487	C₂²×C₁₃	1	1	yes	characteristic
363	#486	C₂²×C₁₃	1	1	yes	characteristic
364	#478	—	2	1	no	—
365	#475	C₂²×C₁₃	1	1	yes	characteristic
366	#474	C₂²×C₁₃	1	1	yes	characteristic
367	#469	—	2	1	no	—
368	#468	—	2	1	no	—
369	#465	—	2	2	no	—
370	#463	—	2	1	no	—
371	#462	C₂²×C₁₃	1	1	yes	characteristic
372	#462	C₂²×C₁₃	1	1	yes	characteristic
373	#460	C₂²×C₁₃	1	1	yes	characteristic
374	#460	C₂²×C₁₃	1	1	yes	characteristic
375	#460	C₂²×C₁₃	1	1	yes	characteristic
376	#459	C₂²×C₁₃	1	1	yes	characteristic
377	#452	—	2	1	no	—
378	#452	—	2	1	no	—
379	C₄×SD₁₆	—	2	2	no	—
380	#432	C₂²×C₁₃	1	1	yes	characteristic
381	#423	C₂²×C₁₃	1	1	yes	characteristic
382	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
383	#333	C₂²×C₁₃	1	1	yes	characteristic
384	#333	C₂²×C₁₃	1	1	yes	characteristic
385	#332	C₂²×C₁₃	1	1	yes	characteristic
386	#332	C₂²×C₁₃	1	1	yes	characteristic
387	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
388	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
389	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
390	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
391	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
392	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
393	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
394	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
395	C₂²×C₁₃	—	2	1	no	—
396	C₂²×C₁₃	—	2	1	no	—
397	C₂²×C₁₃	—	2	1	no	—
398	C₂²×C₁₃	—	4	1	no	—
399	C₂²×C₁₃	—	4	1	no	—
400	C₂²×C₁₃	—	4	1	no	—
401	C₂²×C₁₃	—	8	1	no	—
402	C₂²×C₁₃	—	8	1	no	—
403	C₂²×C₁₃	—	8	1	no	—
404	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
405	C₄×C₁₃	—	2	1	no	—
406	C₄×C₁₃	—	2	1	no	—
407	C₄×C₁₃	—	2	1	no	—
408	C₄×C₁₃	—	2	1	no	—
409	C₄×C₁₃	—	4	1	no	—
410	C₄×C₁₃	—	4	1	no	—
411	C₄×C₁₃	—	4	1	no	—
412	C₄×C₁₃	—	4	1	no	—
413	C₄×C₁₃	—	4	2	no	—
414	C₄×C₁₃	—	4	1	no	—
415	C₄×C₁₃	—	4	2	no	—
416	C₄×C₁₃	—	4	1	no	—
417	C₄×C₁₃	—	4	1	no	—
418	C₄×C₁₃	—	8	1	no	—
419	C₄×C₁₃	#577	1	1	yes	characteristic
420	C₄×C₁₃	#577	1	1	yes	characteristic
421	C₄×C₁₃	#577	1	1	yes	characteristic
422	C₄×C₁₃	#578	1	1	yes	characteristic
423	C₂×#41	—	2	1	no	—
424	C₂×Q₁₆	—	2	1	no	—
425	C₂×Q₁₆	—	2	1	no	—
426	C₂×SD₁₆	—	2	2	no	—
427	C₂×SD₁₆	—	2	1	no	—
428	C₂×SD₁₆	—	2	1	no	—
429	C₂×SD₁₆	—	2	1	no	—
430	C₂×D₈	—	2	1	no	—
431	C₂×M₁₆	—	2	1	no	—
432	C₂²×C₈	—	2	1	no	—
433	C₄⋊Q₈	—	2	2	no	—
434	C₄⋊Q₈	—	2	1	no	—
435	C₄⋊Q₈	—	2	2	no	—
436	C₄⋊Q₈	—	2	1	no	—
437	C₄⋊Q₈	—	2	1	no	—
438	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
439	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
440	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
441	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
442	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
443	#127	C₂³×C₁₃	1	1	yes	characteristic
444	#126	—	2	2	no	—
445	#126	—	2	2	no	—
446	#126	—	2	2	no	—
447	#126	—	2	2	no	—
448	#126	—	2	2	no	—
449	#126	—	2	2	no	—
450	#126	—	2	1	no	—
451	#125	—	2	2	no	—
452	#125	—	2	2	no	—
453	#125	—	2	2	no	—
454	#125	—	2	2	no	—
455	#125	—	2	1	no	—
456	#125	—	2	2	no	—
457	#125	—	2	1	no	—
458	#125	—	2	1	no	—
459	#125	—	2	1	no	—
460	#125	D₄×C₁₃	1	1	yes	characteristic
461	#124	—	2	2	no	—
462	#124	—	2	1	no	—
463	#124	—	2	1	no	—
464	#124	D₄×C₁₃	1	1	yes	characteristic
465	#123	—	2	2	no	—
466	#123	—	2	1	no	—
467	C₂²⋊Q₈	—	2	2	no	—
468	C₂²⋊Q₈	—	2	2	no	—
469	C₂²⋊Q₈	—	2	1	no	—
470	C₂²⋊Q₈	—	2	1	no	—
471	C₂²⋊Q₈	—	2	2	no	—
472	C₂²⋊Q₈	—	2	1	no	—
473	C₂²⋊Q₈	—	2	1	no	—
474	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
475	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
476	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
477	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
478	#121	—	2	1	no	—
479	#121	—	2	1	no	—
480	#121	D₄×C₁₃	1	1	yes	characteristic
481	C₄×Q₈	—	2	2	no	—
482	C₄×Q₈	—	2	1	no	—
483	C₄×Q₈	—	2	1	no	—
484	C₄×Q₈	—	2	1	no	—
485	C₄×Q₈	—	2	1	no	—
486	C₄×Q₈	—	2	1	no	—
487	C₄×Q₈	—	2	1	no	—
488	C₄×Q₈	—	2	1	no	—
489	C₄×Q₈	D₄×C₁₃	1	2	yes	—
490	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
491	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
492	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
493	C₄×D₄	—	2	1	no	—
494	C₄×D₄	—	2	1	no	—
495	C₄×D₄	—	2	1	no	—
496	C₄×D₄	—	2	1	no	—
497	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
498	#117	—	2	2	no	—
499	#117	—	2	1	no	—
500	#117	—	2	1	no	—
501	#117	—	2	1	no	—
502	#117	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
505	#107	—	2	1	no	—
506	#106	—	2	2	no	—
507	#106	—	2	1	no	—
508	C₄⋊C₈	—	2	1	no	—
509	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
510	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
511	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
512	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
513	#103	—	2	2	no	—
514	#103	—	2	1	no	—
515	#103	—	2	1	no	—
516	#103	—	2	1	no	—
517	#102	—	2	1	no	—
518	#102	—	2	2	no	—
519	#102	—	2	1	no	—
520	#102	—	2	1	no	—
521	#102	—	2	1	no	—
522	#102	—	2	1	no	—
523	C₂²⋊C₈	—	2	1	no	—
524	#97	—	2	1	no	—
525	C₄×C₈	—	2	1	no	—
526	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
527	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
528	C₂×C₁₃	—	4	1	no	—
529	C₂×C₁₃	—	8	1	no	—
530	C₂×C₁₃	—	16	1	no	—
531	C₂×C₁₃	#3010	1	1	yes	characteristic
532	C₂×C₁₃	#3013	1	1	yes	characteristic
533	C₂×C₁₃	#3018	1	1	yes	characteristic
534	#41	—	8	1	no	—
535	#41	—	8	1	no	—
536	C₂×Q₈	—	2	2	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
541	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
542	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
543	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	4	1	no	—
549	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	4	1	no	—
553	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
554	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
556	Q₁₆	—	8	1	no	—
557	Q₁₆	—	8	1	no	—
558	SD₁₆	—	4	4	no	—
559	SD₁₆	—	8	1	no	—
560	SD₁₆	—	8	1	no	—
561	SD₁₆	—	8	1	no	—
562	D₈	—	8	1	no	—
563	M₁₆	—	8	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	4	2	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	2	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
598	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
599	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
600	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
601	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	1	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	1	no	—
608	C₂²⋊C₄	—	2	1	no	—
609	C₂²⋊C₄	—	2	1	no	—
610	C₂²⋊C₄	—	2	1	no	—
611	C₂²⋊C₄	—	2	1	no	—
612	C₂²⋊C₄	—	2	1	no	—
613	C₂²⋊C₄	—	4	1	no	—
614	C₂²⋊C₄	—	4	1	no	—
615	C₄²	—	2	2	no	—
616	C₄²	—	2	2	no	—
617	C₄²	—	2	2	no	—
618	C₄²	—	2	2	no	—
619	C₄²	—	2	1	no	—
620	C₄²	—	2	1	no	—
621	C₄²	—	2	1	no	—
622	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
623	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
624	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
625	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
626	C₁₃	#18710	1	1	yes	characteristic, direct product factor, Sylow
627	C₂³	—	2	1	no	—
628	C₂³	—	4	1	no	—
629	C₂³	C₁₃×#120	1	1	yes	characteristic
630	Q₈	—	2	1	no	—
631	Q₈	—	2	1	no	—
632	Q₈	—	2	1	no	—
633	Q₈	—	2	1	no	—
634	Q₈	—	2	1	no	—
635	Q₈	—	2	1	no	—
636	Q₈	—	4	2	no	—
637	Q₈	—	4	1	no	—
638	Q₈	—	4	1	no	—
639	Q₈	—	4	1	no	—
640	Q₈	—	4	1	no	—
641	Q₈	—	8	1	no	—
642	Q₈	—	8	2	no	—
643	D₄	—	2	1	no	—
644	D₄	—	2	1	no	—
645	D₄	—	4	2	no	—
646	D₄	—	4	1	no	—
647	D₄	—	4	1	no	—
648	D₄	—	4	1	no	—
649	D₄	—	4	1	no	—
650	D₄	—	8	1	no	—
651	D₄	—	8	2	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	8	2	no	—
670	C₂×C₄	—	8	2	no	—
671	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
672	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
673	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
674	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
675	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
676	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
677	C₈	—	2	2	no	—
678	C₈	—	4	1	no	—
679	C₈	—	4	1	no	—
680	C₈	—	4	1	no	—
681	C₈	—	4	1	no	—
682	C₈	—	4	1	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	—	8	1	no	—
692	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
693	C₄	—	2	1	no	—
694	C₄	—	2	1	no	—
695	C₄	—	2	1	no	—
696	C₄	—	2	1	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	2	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	1	no	—
705	C₄	—	4	1	no	—
706	C₄	—	8	1	no	—
707	C₄	C₁₃×#577	1	1	yes	characteristic
708	C₄	C₁₃×#577	1	1	yes	characteristic
709	C₄	C₁₃×#577	1	1	yes	characteristic
710	C₄	C₁₃×#578	1	1	yes	characteristic
711	C₂	—	4	1	no	—
712	C₂	—	8	1	no	—
713	C₂	—	16	1	no	—
714	C₂	C₁₃×#3010	1	1	yes	characteristic
715	C₂	C₁₃×#3013	1	1	yes	characteristic
716	C₂	C₁₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3251	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3555	C₂	semidirect
3. C₁₃×#3216	C₂	semidirect
4. C₁₃×#3167	C₂	semidirect
5. C₁₃×#1653	C₂	semidirect
6. C₁₃×#1652	C₂	semidirect
7. C₁₃×#1645	C₂	semidirect
8. C₁₃×#1644	C₂	semidirect
9. C₁₃×#1628	C₂	semidirect
10. C₁₃×#1626	C₂	semidirect
11. C₁₃×#1623	C₂	semidirect
12. C₁₃×#1622	C₂	semidirect
13. C₁₃×#1559	C₂	semidirect
14. C₁₃×#1494	C₂	semidirect
15. C₁₃×#1493	C₂	semidirect
176. #18710	C₁₃	direct (N × H)
269. #3555	C₂×C₁₃	semidirect
271. #3216	C₂×C₁₃	semidirect
272. #3167	C₂×C₁₃	semidirect
273. #1653	C₂×C₁₃	semidirect
274. #1652	C₂×C₁₃	semidirect
275. #1645	C₂×C₁₃	semidirect
276. #1644	C₂×C₁₃	semidirect
277. #1628	C₂×C₁₃	semidirect
278. #1626	C₂×C₁₃	semidirect
279. #1623	C₂×C₁₃	semidirect
280. #1622	C₂×C₁₃	semidirect
281. #1559	C₂×C₁₃	semidirect
282. #1494	C₂×C₁₃	semidirect
283. #1493	C₂×C₁₃	semidirect
626. C₁₃	#18710	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×#3555	2
C₁₃×#3251	2
C₁₃×#3216	2
C₁₃×#3167	2
C₁₃×#1653	2
C₁₃×#1652	2
C₁₃×#1645	2
C₁₃×#1644	2
C₁₃×#1628	2
C₁₃×#1626	2
C₁₃×#1623	2
C₁₃×#1622	2
C₁₃×#1559	2
C₁₃×#1494	2
C₁₃×#1493	2
#18710	13

Subgroups — C13×#18710 #15705049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18710 #15705049