Subgroups — C₁₃×#18000 #15704339

Order 3328.

672 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1592	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1588	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1585	C₂	1	2	yes	maximal, complemented
7	C₁₃×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1571	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×M₁₆	—	2	1	no	—
13	C₁₃×#533	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#483	C₄	1	2	yes	—
16	C₁₃×#476	C₄	1	1	yes	characteristic
17	C₁₃×#476	C₄	1	1	yes	characteristic
18	C₁₃×#461	C₄	1	1	yes	characteristic
19	C₁₃×#461	C₄	1	1	yes	characteristic
20	C₁₃×#450	C₄	1	2	yes	—
21	C₁₃×#446	—	2	2	no	—
22	C₁₃×#446	C₂²	1	2	yes	complemented
23	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
24	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
25	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
26	C₁₃×#436	C₂²	1	2	yes	—
27	C₁₃×#435	—	2	2	no	—
28	C₈×D₄×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#431	C₂²	1	1	yes	characteristic
30	C₁₃×#424	—	2	1	no	—
31	C₁₃×#423	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₁₃×#407	—	2	1	no	—
34	C₁₃×#405	—	2	1	no	—
35	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#335	C₂²	1	2	yes	complemented
38	C₁₃×#335	C₂²	1	2	yes	complemented
39	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
40	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
41	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
45	C₁₃×#322	C₂²	1	2	yes	complemented
46	C₁₃×#322	C₂²	1	2	yes	complemented
47	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	—	2	1	no	—
49	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
50	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
51	C₂×C₁₃×M₁₆	—	2	1	no	—
52	C₂×C₁₃×M₁₆	—	2	2	no	—
53	C₂×C₁₃×M₁₆	—	4	4	no	—
54	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
55	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	—	2	1	no	—
57	C₂²×C₈×C₁₃	—	2	1	no	—
58	C₂²×C₈×C₁₃	—	2	2	no	—
59	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
60	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
61	C₁₃×#125	—	2	1	no	—
62	C₁₃×C₂²⋊Q₈	—	2	1	no	—
63	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
64	C₄×Q₈×C₁₃	—	2	1	no	—
65	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
66	C₄×D₄×C₁₃	—	2	1	no	—
67	C₄×D₄×C₁₃	—	2	1	no	—
68	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
69	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
70	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×#117	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#106	C₂×C₄	1	2	yes	—
77	C₁₃×#106	C₂×C₄	1	2	yes	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×C₄⋊C₈	—	2	1	no	—
81	C₁₃×C₄⋊C₈	—	2	1	no	—
82	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
83	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
84	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
87	C₁₃×#103	C₂×C₄	1	2	yes	—
88	C₁₃×#103	C₂×C₄	1	2	yes	—
89	C₁₃×#102	C₂×C₄	1	2	yes	—
90	C₁₃×#102	C₂×C₄	1	2	yes	—
91	C₁₃×C₂²⋊C₈	—	2	2	no	—
92	C₁₃×C₂²⋊C₈	—	2	2	no	—
93	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
94	C₁₃×#97	—	2	2	no	—
95	C₁₃×#97	D₄	1	2	yes	—
96	C₄×C₈×C₁₃	—	2	2	no	—
97	C₄×C₈×C₁₃	—	2	1	no	—
98	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₃	C₂³	1	2	yes	—
101	C₄×C₈×C₁₃	C₂³	1	2	yes	—
102	#18000	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂⁴×C₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
106	C₂×D₄×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	—	4	1	no	—
109	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	4	2	no	—
117	C₂²×C₄×C₁₃	—	4	2	no	—
118	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
121	C₁₃×SD₁₆	—	2	4	no	—
122	C₁₃×SD₁₆	—	4	2	no	—
123	C₁₃×M₁₆	—	2	2	no	—
124	C₁₃×M₁₆	—	2	2	no	—
125	C₁₃×M₁₆	—	4	4	no	—
126	C₁₃×M₁₆	—	4	2	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	1	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	1	no	—
132	C₂×C₈×C₁₃	—	4	2	no	—
133	C₂×C₈×C₁₃	—	4	4	no	—
134	C₂×C₈×C₁₃	—	4	2	no	—
135	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
146	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
147	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
148	C₁₃×C₂²⋊C₄	—	2	2	no	—
149	C₁₃×C₂²⋊C₄	—	2	1	no	—
150	C₁₃×C₂²⋊C₄	—	2	1	no	—
151	C₁₃×C₂²⋊C₄	—	2	1	no	—
152	C₁₃×C₂²⋊C₄	—	2	1	no	—
153	C₄²×C₁₃	—	2	2	no	—
154	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₃	#41	1	1	yes	characteristic
157	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
158	#3101	C₂×C₁₃	1	1	yes	characteristic
159	#2962	C₂×C₁₃	1	1	yes	characteristic, complemented
160	D₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic
161	#1592	C₂×C₁₃	1	2	yes	complemented
162	#1588	C₂×C₁₃	1	2	yes	complemented
163	#1585	C₂×C₁₃	1	2	yes	complemented
164	SD₁₆⋊C₈	C₂×C₁₃	1	2	yes	complemented
165	#1571	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#1493	C₂×C₁₃	1	1	yes	characteristic, complemented
167	C₂×D₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
168	#1451	C₂×C₁₃	1	1	yes	characteristic, complemented
169	C₂³×C₁₃	—	2	1	no	—
170	C₂³×C₁₃	—	2	1	no	—
171	C₂³×C₁₃	—	4	2	no	—
172	C₂³×C₁₃	—	4	2	no	—
173	C₂³×C₁₃	—	8	1	no	—
174	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
175	Q₈×C₁₃	—	2	2	no	—
176	Q₈×C₁₃	—	2	2	no	—
177	Q₈×C₁₃	—	8	1	no	—
178	D₄×C₁₃	—	2	1	no	—
179	D₄×C₁₃	—	2	1	no	—
180	D₄×C₁₃	—	2	1	no	—
181	D₄×C₁₃	—	4	2	no	—
182	D₄×C₁₃	#131	1	2	yes	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
201	C₂×C₄×C₁₃	#137	1	2	yes	—
202	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
205	C₈×C₁₃	—	2	2	no	—
206	C₈×C₁₃	—	2	2	no	—
207	C₈×C₁₃	—	2	2	no	—
208	C₈×C₁₃	—	2	2	no	—
209	C₈×C₁₃	—	2	2	no	—
210	C₈×C₁₃	—	4	1	no	—
211	C₈×C₁₃	—	4	1	no	—
212	C₈×C₁₃	—	4	1	no	—
213	C₈×C₁₃	—	4	2	no	—
214	C₂²×M₁₆	—	2	1	no	—
215	#533	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
217	#483	C₄×C₁₃	1	2	yes	—
218	#476	C₄×C₁₃	1	1	yes	characteristic
219	#476	C₄×C₁₃	1	1	yes	characteristic
220	#461	C₄×C₁₃	1	1	yes	characteristic
221	#461	C₄×C₁₃	1	1	yes	characteristic
222	#450	C₄×C₁₃	1	2	yes	—
223	#446	—	2	2	no	—
224	#446	C₂²×C₁₃	1	2	yes	complemented
225	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
226	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
227	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
228	#436	C₂²×C₁₃	1	2	yes	—
229	#435	—	2	2	no	—
230	C₈×D₄	C₂²×C₁₃	1	2	yes	—
231	#431	C₂²×C₁₃	1	1	yes	characteristic
232	#424	—	2	1	no	—
233	#423	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
235	#407	—	2	1	no	—
236	#405	—	2	1	no	—
237	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
239	#335	C₂²×C₁₃	1	2	yes	complemented
240	#335	C₂²×C₁₃	1	2	yes	complemented
241	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	complemented
242	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	complemented
243	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
244	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
245	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
246	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
247	#322	C₂²×C₁₃	1	2	yes	complemented
248	#322	C₂²×C₁₃	1	2	yes	complemented
249	C₂²×C₁₃	—	2	1	no	—
250	C₂²×C₁₃	—	2	1	no	—
251	C₂²×C₁₃	—	2	2	no	—
252	C₂²×C₁₃	—	4	1	no	—
253	C₂²×C₁₃	—	4	1	no	—
254	C₂²×C₁₃	—	4	1	no	—
255	C₂²×C₁₃	—	4	1	no	—
256	C₂²×C₁₃	—	4	1	no	—
257	C₂²×C₁₃	—	8	4	no	—
258	C₂²×C₁₃	#440	1	2	yes	—
259	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
260	C₄×C₁₃	—	2	1	no	—
261	C₄×C₁₃	—	2	1	no	—
262	C₄×C₁₃	—	2	1	no	—
263	C₄×C₁₃	—	4	2	no	—
264	C₄×C₁₃	—	4	1	no	—
265	C₄×C₁₃	—	4	1	no	—
266	C₄×C₁₃	—	4	2	no	—
267	C₄×C₁₃	#440	1	2	yes	—
268	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
269	C₄×C₁₃	#568	1	1	yes	characteristic
270	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
271	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
272	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
273	C₂³×C₄	—	2	1	no	—
274	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
275	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	—	4	4	no	—
279	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
280	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	—	2	2	no	—
284	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
285	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
286	#125	—	2	1	no	—
287	C₂²⋊Q₈	—	2	1	no	—
288	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
294	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
295	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
296	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
297	#117	—	2	1	no	—
298	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
301	#106	C₂×C₄×C₁₃	1	2	yes	—
302	#106	C₂×C₄×C₁₃	1	2	yes	—
303	C₄⋊C₈	—	2	2	no	—
304	C₄⋊C₈	—	2	2	no	—
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	—	2	1	no	—
307	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
308	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
309	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
310	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
311	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
312	#103	C₂×C₄×C₁₃	1	2	yes	—
313	#103	C₂×C₄×C₁₃	1	2	yes	—
314	#102	C₂×C₄×C₁₃	1	2	yes	—
315	#102	C₂×C₄×C₁₃	1	2	yes	—
316	C₂²⋊C₈	—	2	2	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
319	#97	—	2	2	no	—
320	#97	D₄×C₁₃	1	2	yes	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
324	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
325	C₄×C₈	C₂³×C₁₃	1	2	yes	—
326	C₄×C₈	C₂³×C₁₃	1	2	yes	—
327	C₂×C₁₃	—	2	2	no	—
328	C₂×C₁₃	—	4	2	no	—
329	C₂×C₁₃	—	8	1	no	—
330	C₂×C₁₃	#2933	1	1	yes	characteristic
331	C₂×C₁₃	C₂×#440	1	1	yes	characteristic
332	C₂×C₁₃	#2956	1	1	yes	characteristic
333	C₂⁴	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
340	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
351	SD₁₆	—	2	4	no	—
352	SD₁₆	—	4	2	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	4	4	no	—
356	M₁₆	—	4	2	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	4	4	no	—
363	C₂×C₈	—	4	2	no	—
364	C₂×C₈	—	4	2	no	—
365	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
366	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
367	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
368	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
376	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
377	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	1	no	—
380	C₂²⋊C₄	—	2	1	no	—
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₄²	—	2	2	no	—
384	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
385	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
386	C₄²	C₁₃×#41	1	1	yes	characteristic
387	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
388	C₁₃	#18000	1	1	yes	characteristic, direct product factor, Sylow
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	8	1	no	—
394	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	8	1	no	—
398	D₄	—	2	1	no	—
399	D₄	—	2	1	no	—
400	D₄	—	2	1	no	—
401	D₄	—	4	2	no	—
402	D₄	C₁₃×#131	1	2	yes	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
418	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
419	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
420	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
421	C₂×C₄	C₁₃×#137	1	2	yes	—
422	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
424	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	2	2	no	—
427	C₈	—	2	2	no	—
428	C₈	—	2	2	no	—
429	C₈	—	2	2	no	—
430	C₈	—	4	1	no	—
431	C₈	—	4	1	no	—
432	C₈	—	4	1	no	—
433	C₈	—	4	2	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	8	4	no	—
443	C₂²	C₁₃×#440	1	2	yes	—
444	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	2	no	—
452	C₄	C₁₃×#440	1	2	yes	—
453	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
454	C₄	C₁₃×#568	1	1	yes	characteristic
455	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
456	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	4	2	no	—
459	C₂	—	8	1	no	—
460	C₂	C₁₃×#2933	1	1	yes	characteristic
461	C₂	C₂×C₁₃×#440	1	1	yes	characteristic
462	C₂	C₁₃×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂²×D₄×C₁₃	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2962	C₂	semidirect
4. C₁₃×#1592	C₂	semidirect
5. C₁₃×#1588	C₂	semidirect
6. C₁₃×#1585	C₂	semidirect
7. C₁₃×SD₁₆⋊C₈	C₂	semidirect
8. C₁₃×#1571	C₂	semidirect
9. C₁₃×#1493	C₂	semidirect
11. C₁₃×#1451	C₂	semidirect
22. C₁₃×#446	C₂²	semidirect
23. C₈×Q₈×C₁₃	C₂²	semidirect
37. C₁₃×#335	C₂²	semidirect
38. C₁₃×#335	C₂²	semidirect
39. C₁₃×Q₈⋊C₈	C₂²	semidirect
40. C₁₃×Q₈⋊C₈	C₂²	semidirect
45. C₁₃×#322	C₂²	semidirect
46. C₁₃×#322	C₂²	semidirect
102. #18000	C₁₃	direct (N × H)
159. #2962	C₂×C₁₃	semidirect
161. #1592	C₂×C₁₃	semidirect
162. #1588	C₂×C₁₃	semidirect
163. #1585	C₂×C₁₃	semidirect
164. SD₁₆⋊C₈	C₂×C₁₃	semidirect
165. #1571	C₂×C₁₃	semidirect
166. #1493	C₂×C₁₃	semidirect
168. #1451	C₂×C₁₃	semidirect
224. #446	C₂²×C₁₃	semidirect
225. C₈×Q₈	C₂²×C₁₃	semidirect
239. #335	C₂²×C₁₃	semidirect
240. #335	C₂²×C₁₃	semidirect
241. Q₈⋊C₈	C₂²×C₁₃	semidirect
242. Q₈⋊C₈	C₂²×C₁₃	semidirect
247. #322	C₂²×C₁₃	semidirect
248. #322	C₂²×C₁₃	semidirect
388. C₁₃	#18000	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×#3101	2
C₁₃×#2962	2
D₄×C₁₃×M₁₆	2
C₁₃×#1592	2
C₁₃×#1588	2
C₁₃×#1585	2
C₁₃×SD₁₆⋊C₈	2
C₁₃×#1571	2
C₁₃×#1493	2
C₂×C₁₃×D₄⋊C₈	2
C₁₃×#1451	2
#18000	13

Subgroups — C13×#18000 #15704339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18000 #15704339