Subgroups — C₁₃×#18028 #15704367

Order 3328.

616 conjugacy classes of subgroups.

The subgroup lattice has 590 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×#2986	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2974	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1592	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1590	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1588	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1585	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1583	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1582	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1572	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1497	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1478	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1454	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#533	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#483	C₄	1	1	yes	characteristic
19	C₁₃×#483	C₄	1	1	yes	characteristic
20	C₁₃×#476	C₄	1	1	yes	characteristic
21	C₁₃×#476	C₄	1	1	yes	characteristic
22	C₁₃×#461	C₄	1	1	yes	characteristic
23	C₁₃×#461	C₄	1	1	yes	characteristic
24	C₁₃×#450	C₄	1	1	yes	characteristic
25	C₁₃×#450	C₄	1	1	yes	characteristic
26	C₁₃×#446	—	2	1	no	—
27	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
29	C₈×Q₈×C₁₃	—	2	1	no	—
30	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
31	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
32	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
33	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
36	C₁₃×#436	C₂²	1	1	yes	characteristic
37	C₁₃×#436	C₂²	1	1	yes	characteristic
38	C₁₃×#435	—	2	1	no	—
39	C₁₃×#435	—	2	1	no	—
40	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#433	—	2	1	no	—
43	C₁₃×#433	—	2	1	no	—
44	C₁₃×#432	C₂²	1	1	yes	characteristic
45	C₁₃×#431	C₂²	1	1	yes	characteristic
46	C₁₃×#431	C₂²	1	1	yes	characteristic
47	C₁₃×#431	C₂²	1	1	yes	characteristic
48	C₁₃×#431	C₂²	1	1	yes	characteristic
49	C₁₃×#407	—	2	1	no	—
50	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
51	C₁₃×#335	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#335	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#334	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#334	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
60	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
61	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
66	C₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
67	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	—	2	1	no	—
69	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
73	C₂×C₁₃×M₁₆	—	2	1	no	—
74	C₂×C₁₃×M₁₆	—	2	1	no	—
75	C₂²×C₈×C₁₃	—	2	1	no	—
76	C₂²×C₈×C₁₃	—	2	1	no	—
77	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
78	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
79	C₁₃×#125	—	2	1	no	—
80	C₁₃×C₂²⋊Q₈	—	2	1	no	—
81	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
82	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
83	C₄×Q₈×C₁₃	—	2	1	no	—
84	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₄×D₄×C₁₃	—	2	1	no	—
87	C₄×D₄×C₁₃	—	2	1	no	—
88	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
89	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
90	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×#117	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
97	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
98	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
99	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
100	C₁₃×C₄⋊C₈	—	2	1	no	—
101	C₁₃×C₄⋊C₈	—	2	1	no	—
102	C₁₃×C₄⋊C₈	—	2	1	no	—
103	C₁₃×C₄⋊C₈	—	2	1	no	—
104	C₁₃×C₄⋊C₈	—	2	1	no	—
105	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
106	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
107	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
108	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
109	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
110	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
111	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
114	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
115	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
116	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
117	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
118	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
119	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
120	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
121	C₁₃×C₂²⋊C₈	—	2	1	no	—
122	C₁₃×C₂²⋊C₈	—	2	1	no	—
123	C₁₃×C₂²⋊C₈	—	2	1	no	—
124	C₁₃×C₂²⋊C₈	—	2	1	no	—
125	C₁₃×C₂²⋊C₈	—	2	1	no	—
126	C₁₃×C₂²⋊C₈	—	2	1	no	—
127	C₁₃×C₂²⋊C₈	—	2	1	no	—
128	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
129	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
130	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
131	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
132	C₁₃×#97	—	2	1	no	—
133	C₁₃×#97	—	2	1	no	—
134	C₁₃×#97	—	2	1	no	—
135	C₄×C₈×C₁₃	—	2	1	no	—
136	C₄×C₈×C₁₃	—	2	1	no	—
137	C₄×C₈×C₁₃	—	2	1	no	—
138	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	#18028	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂⁴×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×D₄×C₁₃	—	2	2	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	4	1	no	—
152	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	8	1	no	—
160	C₂²×C₄×C₁₃	—	8	1	no	—
161	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
164	C₁₃×SD₁₆	—	2	2	no	—
165	C₁₃×SD₁₆	—	2	2	no	—
166	C₁₃×SD₁₆	—	4	1	no	—
167	C₁₃×SD₁₆	—	4	1	no	—
168	C₁₃×M₁₆	—	8	1	no	—
169	C₁₃×M₁₆	—	8	1	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	1	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	1	no	—
176	C₂×C₈×C₁₃	—	8	1	no	—
177	C₂×C₈×C₁₃	—	8	1	no	—
178	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₁₃×C₄⋊C₄	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
195	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
196	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
197	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
198	C₁₃×C₂²⋊C₄	—	2	1	no	—
199	C₁₃×C₂²⋊C₄	—	2	1	no	—
200	C₁₃×C₂²⋊C₄	—	2	1	no	—
201	C₁₃×C₂²⋊C₄	—	2	1	no	—
202	C₁₃×C₂²⋊C₄	—	2	1	no	—
203	C₁₃×C₂²⋊C₄	—	2	1	no	—
204	C₄²×C₁₃	—	2	1	no	—
205	C₄²×C₁₃	—	2	1	no	—
206	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
207	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₃	#41	1	1	yes	characteristic
209	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
210	#3101	C₂×C₁₃	1	1	yes	characteristic
211	#2986	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#2974	C₂×C₁₃	1	1	yes	characteristic
213	#1592	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1590	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1588	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1585	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1583	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1582	C₂×C₁₃	1	1	yes	characteristic, complemented
219	SD₁₆⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
220	C₈×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1572	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1497	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1478	C₂×C₁₃	1	1	yes	characteristic
224	#1454	C₂×C₁₃	1	1	yes	characteristic, complemented
225	C₂³×C₁₃	—	2	1	no	—
226	C₂³×C₁₃	—	2	1	no	—
227	C₂³×C₁₃	—	4	2	no	—
228	C₂³×C₁₃	—	4	2	no	—
229	C₂³×C₁₃	—	8	1	no	—
230	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
231	Q₈×C₁₃	—	2	1	no	—
232	Q₈×C₁₃	—	2	1	no	—
233	Q₈×C₁₃	—	2	1	no	—
234	Q₈×C₁₃	—	2	1	no	—
235	Q₈×C₁₃	—	4	2	no	—
236	D₄×C₁₃	—	2	1	no	—
237	D₄×C₁₃	—	2	1	no	—
238	D₄×C₁₃	—	2	1	no	—
239	D₄×C₁₃	—	4	2	no	—
240	D₄×C₁₃	#131	1	2	yes	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	8	1	no	—
257	C₂×C₄×C₁₃	—	8	1	no	—
258	C₂×C₄×C₁₃	—	8	1	no	—
259	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
265	C₈×C₁₃	—	2	1	no	—
266	C₈×C₁₃	—	2	1	no	—
267	C₈×C₁₃	—	2	1	no	—
268	C₈×C₁₃	—	2	1	no	—
269	C₈×C₁₃	—	2	1	no	—
270	C₈×C₁₃	—	2	1	no	—
271	C₈×C₁₃	—	2	1	no	—
272	C₈×C₁₃	—	2	1	no	—
273	C₈×C₁₃	—	4	1	no	—
274	C₈×C₁₃	—	4	1	no	—
275	C₈×C₁₃	—	4	1	no	—
276	C₈×C₁₃	—	4	1	no	—
277	C₈×C₁₃	—	4	1	no	—
278	C₈×C₁₃	—	4	1	no	—
279	#533	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
281	#483	C₄×C₁₃	1	1	yes	characteristic
282	#483	C₄×C₁₃	1	1	yes	characteristic
283	#476	C₄×C₁₃	1	1	yes	characteristic
284	#476	C₄×C₁₃	1	1	yes	characteristic
285	#461	C₄×C₁₃	1	1	yes	characteristic
286	#461	C₄×C₁₃	1	1	yes	characteristic
287	#450	C₄×C₁₃	1	1	yes	characteristic
288	#450	C₄×C₁₃	1	1	yes	characteristic
289	#446	—	2	1	no	—
290	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
291	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
292	C₈×Q₈	—	2	1	no	—
293	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
294	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
295	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
296	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
297	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
298	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
299	#436	C₂²×C₁₃	1	1	yes	characteristic
300	#436	C₂²×C₁₃	1	1	yes	characteristic
301	#435	—	2	1	no	—
302	#435	—	2	1	no	—
303	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
304	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
305	#433	—	2	1	no	—
306	#433	—	2	1	no	—
307	#432	C₂²×C₁₃	1	1	yes	characteristic
308	#431	C₂²×C₁₃	1	1	yes	characteristic
309	#431	C₂²×C₁₃	1	1	yes	characteristic
310	#431	C₂²×C₁₃	1	1	yes	characteristic
311	#431	C₂²×C₁₃	1	1	yes	characteristic
312	#407	—	2	1	no	—
313	C₂×C₂²⋊C₈	—	2	1	no	—
314	#335	C₂²×C₁₃	1	1	yes	characteristic, complemented
315	#335	C₂²×C₁₃	1	1	yes	characteristic, complemented
316	#334	C₂²×C₁₃	1	1	yes	characteristic, complemented
317	#334	C₂²×C₁₃	1	1	yes	characteristic, complemented
318	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
319	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
320	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
321	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
322	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
323	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
324	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
325	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
326	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
327	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
328	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
329	C₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
330	C₂²×C₁₃	—	2	1	no	—
331	C₂²×C₁₃	—	2	2	no	—
332	C₂²×C₁₃	—	2	1	no	—
333	C₂²×C₁₃	—	2	1	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	—	4	1	no	—
336	C₂²×C₁₃	—	4	1	no	—
337	C₂²×C₁₃	—	4	1	no	—
338	C₂²×C₁₃	—	4	1	no	—
339	C₂²×C₁₃	—	8	4	no	—
340	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
341	C₄×C₁₃	—	2	1	no	—
342	C₄×C₁₃	—	2	1	no	—
343	C₄×C₁₃	—	2	1	no	—
344	C₄×C₁₃	—	2	1	no	—
345	C₄×C₁₃	—	4	1	no	—
346	C₄×C₁₃	—	4	1	no	—
347	C₄×C₁₃	—	4	1	no	—
348	C₄×C₁₃	—	4	1	no	—
349	C₄×C₁₃	—	4	1	no	—
350	C₄×C₁₃	—	4	1	no	—
351	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
352	C₄×C₁₃	#568	1	1	yes	characteristic
353	C₄×C₁₃	#577	1	1	yes	characteristic
354	C₄×C₁₃	#577	1	1	yes	characteristic
355	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
356	C₂³×C₄	—	2	1	no	—
357	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
358	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
359	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
360	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂²×C₈	—	2	1	no	—
364	C₂²×C₈	—	2	1	no	—
365	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
366	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
367	#125	—	2	1	no	—
368	C₂²⋊Q₈	—	2	1	no	—
369	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
370	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
371	C₄×Q₈	—	2	1	no	—
372	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
373	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	—	2	1	no	—
376	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
377	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
378	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
379	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
380	#117	—	2	1	no	—
381	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
384	#106	C₂×C₄×C₁₃	1	1	yes	characteristic
385	#106	C₂×C₄×C₁₃	1	1	yes	characteristic
386	#106	C₂×C₄×C₁₃	1	1	yes	characteristic
387	#106	C₂×C₄×C₁₃	1	1	yes	characteristic
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	2	1	no	—
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
394	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
395	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
396	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
397	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
398	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
399	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
400	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
401	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
402	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
403	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
404	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
405	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
406	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
407	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
408	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
409	C₂²⋊C₈	—	2	1	no	—
410	C₂²⋊C₈	—	2	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	2	1	no	—
414	C₂²⋊C₈	—	2	1	no	—
415	C₂²⋊C₈	—	2	1	no	—
416	C₂²⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
417	C₂²⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
418	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
419	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
420	#97	—	2	1	no	—
421	#97	—	2	1	no	—
422	#97	—	2	1	no	—
423	C₄×C₈	—	2	1	no	—
424	C₄×C₈	—	2	1	no	—
425	C₄×C₈	—	2	1	no	—
426	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
427	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
428	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
429	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
430	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
431	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×C₁₃	—	4	1	no	—
433	C₂×C₁₃	—	4	2	no	—
434	C₂×C₁₃	—	8	1	no	—
435	C₂×C₁₃	#2933	1	1	yes	characteristic
436	C₂×C₁₃	#2949	1	1	yes	characteristic
437	C₂×C₁₃	#2955	1	1	yes	characteristic
438	C₂⁴	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
441	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	4	1	no	—
445	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
446	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	8	1	no	—
453	C₂²×C₄	—	8	1	no	—
454	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
456	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
457	SD₁₆	—	2	2	no	—
458	SD₁₆	—	2	2	no	—
459	SD₁₆	—	4	1	no	—
460	SD₁₆	—	4	1	no	—
461	M₁₆	—	8	1	no	—
462	M₁₆	—	8	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	8	1	no	—
470	C₂×C₈	—	8	1	no	—
471	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
472	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
473	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
474	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
475	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
500	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
501	C₄²	C₁₃×#41	1	1	yes	characteristic
502	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
503	C₁₃	#18028	1	1	yes	characteristic, direct product factor, Sylow
504	C₂³	—	2	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	4	2	no	—
508	C₂³	—	8	1	no	—
509	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
510	Q₈	—	2	1	no	—
511	Q₈	—	2	1	no	—
512	Q₈	—	2	1	no	—
513	Q₈	—	2	1	no	—
514	Q₈	—	4	2	no	—
515	D₄	—	2	1	no	—
516	D₄	—	2	1	no	—
517	D₄	—	2	1	no	—
518	D₄	—	4	2	no	—
519	D₄	C₁₃×#131	1	2	yes	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	8	1	no	—
536	C₂×C₄	—	8	1	no	—
537	C₂×C₄	—	8	1	no	—
538	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
539	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
540	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
541	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
542	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
543	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
544	C₈	—	2	1	no	—
545	C₈	—	2	1	no	—
546	C₈	—	2	1	no	—
547	C₈	—	2	1	no	—
548	C₈	—	2	1	no	—
549	C₈	—	2	1	no	—
550	C₈	—	2	1	no	—
551	C₈	—	2	1	no	—
552	C₈	—	4	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₈	—	4	1	no	—
557	C₈	—	4	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	8	4	no	—
568	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
580	C₄	C₁₃×#568	1	1	yes	characteristic
581	C₄	C₁₃×#577	1	1	yes	characteristic
582	C₄	C₁₃×#577	1	1	yes	characteristic
583	C₂	—	4	1	no	—
584	C₂	—	4	2	no	—
585	C₂	—	8	1	no	—
586	C₂	C₁₃×#2933	1	1	yes	characteristic
587	C₂	C₁₃×#2949	1	1	yes	characteristic
588	C₂	C₁₃×#2955	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 ◁ C₁₃×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2986	C₂	semidirect
4. C₁₃×#1592	C₂	semidirect
5. C₁₃×#1590	C₂	semidirect
6. C₁₃×#1588	C₂	semidirect
7. C₁₃×#1585	C₂	semidirect
8. C₁₃×#1583	C₂	semidirect
9. C₁₃×#1582	C₂	semidirect
10. C₁₃×SD₁₆⋊C₈	C₂	semidirect
11. C₈×C₁₃×SD₁₆	C₂	semidirect
12. C₁₃×#1572	C₂	semidirect
13. C₁₃×#1497	C₂	semidirect
15. C₁₃×#1454	C₂	semidirect
27. C₁₃×#446	C₂²	semidirect
28. C₁₃×#446	C₂²	semidirect
30. C₈×Q₈×C₁₃	C₂²	semidirect
31. C₈×Q₈×C₁₃	C₂²	semidirect
51. C₁₃×#335	C₂²	semidirect
52. C₁₃×#335	C₂²	semidirect
53. C₁₃×#334	C₂²	semidirect
54. C₁₃×#334	C₂²	semidirect
55. C₁₃×Q₈⋊C₈	C₂²	semidirect
56. C₁₃×Q₈⋊C₈	C₂²	semidirect
57. C₁₃×Q₈⋊C₈	C₂²	semidirect
58. C₁₃×Q₈⋊C₈	C₂²	semidirect
63. C₁₃×#322	C₂²	semidirect
64. C₁₃×#322	C₂²	semidirect
65. C₁₃×#322	C₂²	semidirect
66. C₈²×C₁₃	C₂²	semidirect
144. #18028	C₁₃	direct (N × H)
211. #2986	C₂×C₁₃	semidirect
213. #1592	C₂×C₁₃	semidirect
214. #1590	C₂×C₁₃	semidirect
215. #1588	C₂×C₁₃	semidirect
216. #1585	C₂×C₁₃	semidirect
217. #1583	C₂×C₁₃	semidirect
218. #1582	C₂×C₁₃	semidirect
219. SD₁₆⋊C₈	C₂×C₁₃	semidirect
220. C₈×SD₁₆	C₂×C₁₃	semidirect
221. #1572	C₂×C₁₃	semidirect
222. #1497	C₂×C₁₃	semidirect
224. #1454	C₂×C₁₃	semidirect
290. #446	C₂²×C₁₃	semidirect
291. #446	C₂²×C₁₃	semidirect
293. C₈×Q₈	C₂²×C₁₃	semidirect
294. C₈×Q₈	C₂²×C₁₃	semidirect
314. #335	C₂²×C₁₃	semidirect
315. #335	C₂²×C₁₃	semidirect
316. #334	C₂²×C₁₃	semidirect
317. #334	C₂²×C₁₃	semidirect
318. Q₈⋊C₈	C₂²×C₁₃	semidirect
319. Q₈⋊C₈	C₂²×C₁₃	semidirect
320. Q₈⋊C₈	C₂²×C₁₃	semidirect
321. Q₈⋊C₈	C₂²×C₁₃	semidirect
326. #322	C₂²×C₁₃	semidirect
327. #322	C₂²×C₁₃	semidirect
328. #322	C₂²×C₁₃	semidirect
329. C₈²	C₂²×C₁₃	semidirect
503. C₁₃	#18028	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×#2986	2
C₁₃×#2974	2
C₁₃×#1592	2
C₁₃×#1590	2
C₁₃×#1588	2
C₁₃×#1585	2
C₁₃×#1583	2
C₁₃×#1582	2
C₁₃×SD₁₆⋊C₈	2
C₈×C₁₃×SD₁₆	2
C₁₃×#1572	2
C₁₃×#1497	2
C₁₃×#1478	2
C₁₃×#1454	2
#18028	13

Subgroups — C13×#18028 #15704367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18028 #15704367