Subgroups — C₁₃×#22683 #15709022

Order 3328.

986 conjugacy classes of subgroups.

The subgroup lattice has 462 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	2	yes	maximal
2	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2351	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2349	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1941	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1863	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1862	C₂	1	2	yes	maximal
8	C₁₃×#1846	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic
11	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₄×C₁₃×SD₁₆	—	2	8	no	—
18	C₄×C₁₃×SD₁₆	C₄	1	8	yes	complemented
19	C₂×C₁₃×#107	C₂²	1	2	yes	—
20	C₂×C₁₃×#106	C₂²	1	2	yes	—
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#389	—	2	2	no	—
30	C₁₃×#389	C₂²	1	2	yes	—
31	C₁₃×#389	C₂²	1	2	yes	—
32	C₁₃×#385	—	2	2	no	—
33	C₁₃×#382	—	2	1	no	—
34	C₁₃×#382	C₂²	1	1	yes	characteristic
35	C₁₃×#382	C₂²	1	1	yes	characteristic
36	C₁₃×#380	—	2	1	no	—
37	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#95	—	2	1	no	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	—	2	1	no	—
46	C₂³×C₄×C₁₃	—	2	2	no	—
47	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
48	C₂×C₁₃×SD₁₆	D₄	1	4	yes	—
49	C₂×C₁₃×SD₁₆	Q₈	1	4	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₄×Q₈×C₁₃	—	2	2	no	—
54	C₄×Q₈×C₁₃	—	2	4	no	—
55	C₄×Q₈×C₁₃	—	4	2	no	—
56	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	complemented
57	C₄×D₄×C₁₃	—	2	4	no	—
58	C₄×D₄×C₁₃	—	2	2	no	—
59	C₄×D₄×C₁₃	—	4	2	no	—
60	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	—	2	2	no	—
74	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#107	—	4	2	no	—
77	C₁₃×#106	—	2	4	no	—
78	C₁₃×#106	C₂×C₄	1	4	yes	complemented
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×#103	—	2	4	no	—
81	C₁₃×#103	C₂×C₄	1	4	yes	complemented
82	C₁₃×#102	—	2	4	no	—
83	C₁₃×#102	C₂×C₄	1	4	yes	—
84	C₄×C₈×C₁₃	—	2	4	no	—
85	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	2	no	—
89	C₁₃×#95	—	2	1	no	—
90	C₁₃×#95	—	2	1	no	—
91	C₁₃×#95	—	2	2	no	—
92	C₁₃×#95	D₄	1	1	yes	characteristic
93	C₁₃×#95	D₄	1	1	yes	characteristic
94	#22683	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	—	2	1	no	—
99	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
100	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
101	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
102	C₂×D₄×C₁₃	—	2	1	no	—
103	C₂×D₄×C₁₃	—	2	1	no	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
106	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	4	4	no	—
115	C₂²×C₄×C₁₃	—	4	4	no	—
116	C₂²×C₄×C₁₃	—	8	2	no	—
117	C₂²×C₄×C₁₃	—	8	2	no	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₁₃×SD₁₆	C₄⋊C₄	1	16	yes	complemented
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
133	C₁₃×C₄⋊C₄	—	2	4	no	—
134	C₁₃×C₄⋊C₄	—	2	4	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	4	4	no	—
142	C₁₃×C₄⋊C₄	—	4	4	no	—
143	C₁₃×C₄⋊C₄	—	8	2	no	—
144	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
145	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
146	C₁₃×C₂²⋊C₄	—	2	4	no	—
147	C₁₃×C₂²⋊C₄	—	4	4	no	—
148	C₄²×C₁₃	—	2	4	no	—
149	C₄²×C₁₃	—	2	2	no	—
150	C₄²×C₁₃	—	2	2	no	—
151	C₄²×C₁₃	—	4	4	no	—
152	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
153	C₄²×C₁₃	#41	1	2	yes	—
154	C₂×C₄×SD₁₆	C₂×C₁₃	1	2	yes	—
155	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
156	#2351	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#2349	C₂×C₁₃	1	1	yes	characteristic
158	#1941	C₂×C₁₃	1	2	yes	complemented
159	#1863	C₂×C₁₃	1	2	yes	complemented
160	#1862	C₂×C₁₃	1	2	yes	—
161	#1846	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#1804	C₂×C₁₃	1	1	yes	characteristic
164	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
165	C₂³×C₁₃	—	2	2	no	—
166	C₂³×C₁₃	—	2	2	no	—
167	C₂³×C₁₃	—	2	2	no	—
168	C₂³×C₁₃	—	4	2	no	—
169	C₂³×C₁₃	—	4	2	no	—
170	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₁₃	—	2	2	no	—
172	Q₈×C₁₃	—	2	2	no	—
173	Q₈×C₁₃	—	2	2	no	—
174	Q₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
175	D₄×C₁₃	—	2	2	no	—
176	D₄×C₁₃	—	2	2	no	—
177	D₄×C₁₃	—	2	2	no	—
178	D₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	8	4	no	—
200	C₂×C₄×C₁₃	—	8	8	no	—
201	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
202	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
203	C₂×C₄×C₁₃	#135	1	4	yes	—
204	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
210	C₈×C₁₃	—	2	2	no	—
211	C₈×C₁₃	—	4	2	no	—
212	C₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
213	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
215	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
217	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
218	C₄×SD₁₆	—	2	8	no	—
219	C₄×SD₁₆	C₄×C₁₃	1	8	yes	complemented
220	C₂×#107	C₂²×C₁₃	1	2	yes	—
221	C₂×#106	C₂²×C₁₃	1	2	yes	—
222	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#103	C₂²×C₁₃	1	2	yes	—
225	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×#102	C₂²×C₁₃	1	2	yes	—
227	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
229	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
230	#389	—	2	2	no	—
231	#389	C₂²×C₁₃	1	2	yes	—
232	#389	C₂²×C₁₃	1	2	yes	—
233	#385	—	2	2	no	—
234	#382	—	2	1	no	—
235	#382	C₂²×C₁₃	1	1	yes	characteristic
236	#382	C₂²×C₁₃	1	1	yes	characteristic
237	#380	—	2	1	no	—
238	C₄×C₄⋊C₄	—	2	1	no	—
239	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×#95	—	2	1	no	—
241	#340	C₂²×C₁₃	1	2	yes	—
242	#340	C₂²×C₁₃	1	2	yes	—
243	#336	C₂²×C₁₃	1	2	yes	—
244	C₂²×C₁₃	—	2	4	no	—
245	C₂²×C₁₃	—	4	4	no	—
246	C₂²×C₁₃	—	4	2	no	—
247	C₂²×C₁₃	—	4	2	no	—
248	C₂²×C₁₃	—	4	4	no	—
249	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
250	C₂²×C₁₃	D₄²	1	1	yes	characteristic
251	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
252	C₂²×C₁₃	C₂×#135	1	2	yes	—
253	C₂²×C₁₃	#577	1	2	yes	—
254	C₄×C₁₃	—	2	4	no	—
255	C₄×C₁₃	—	2	2	no	—
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	2	4	no	—
258	C₄×C₁₃	—	4	2	no	—
259	C₄×C₁₃	—	4	2	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	8	2	no	—
262	C₄×C₁₃	—	8	2	no	—
263	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
264	C₄×C₁₃	#520	1	1	yes	characteristic
265	C₄×C₁₃	#547	1	1	yes	characteristic
266	C₄×C₁₃	#554	1	1	yes	characteristic
267	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
268	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
269	C₂³×C₄	—	2	1	no	—
270	C₂³×C₄	—	2	2	no	—
271	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	—
272	C₂×SD₁₆	D₄×C₁₃	1	4	yes	—
273	C₂×SD₁₆	Q₈×C₁₃	1	4	yes	—
274	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
275	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
277	C₄×Q₈	—	2	2	no	—
278	C₄×Q₈	—	2	4	no	—
279	C₄×Q₈	—	4	2	no	—
280	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	complemented
281	C₄×D₄	—	2	4	no	—
282	C₄×D₄	—	2	2	no	—
283	C₄×D₄	—	4	2	no	—
284	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
299	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
300	#107	—	4	2	no	—
301	#106	—	2	4	no	—
302	#106	C₂×C₄×C₁₃	1	4	yes	complemented
303	C₄⋊C₈	—	2	2	no	—
304	#103	—	2	4	no	—
305	#103	C₂×C₄×C₁₃	1	4	yes	complemented
306	#102	—	2	4	no	—
307	#102	C₂×C₄×C₁₃	1	4	yes	—
308	C₄×C₈	—	2	4	no	—
309	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
310	#95	—	2	1	no	—
311	#95	—	2	2	no	—
312	#95	—	2	1	no	—
313	#95	—	2	2	no	—
314	#95	—	2	1	no	—
315	#95	—	2	1	no	—
316	#95	D₄×C₁₃	1	1	yes	characteristic
317	#95	D₄×C₁₃	1	1	yes	characteristic
318	C₂×C₁₃	—	4	4	no	—
319	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
320	C₂×C₁₃	C₄×#135	1	1	yes	characteristic
321	C₂×C₁₃	#2949	1	1	yes	characteristic
322	C₂×C₁₃	#3282	1	2	yes	—
323	C₂×C₁₃	#3381	1	2	yes	—
324	C₂⁴	—	2	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
329	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
330	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
335	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
336	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	4	4	no	—
344	C₂²×C₄	—	4	4	no	—
345	C₂²×C₄	—	8	2	no	—
346	C₂²×C₄	—	8	2	no	—
347	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
351	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
352	SD₁₆	C₁₃×C₄⋊C₄	1	16	yes	complemented
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
359	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
360	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
361	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	—	4	4	no	—
372	C₄⋊C₄	—	8	2	no	—
373	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
374	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₄²	—	2	4	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	4	4	no	—
381	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
382	C₄²	C₁₃×#41	1	2	yes	—
383	C₁₃	#22683	1	1	yes	characteristic, direct product factor, Sylow
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
390	Q₈	—	2	2	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	Q₈	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
394	D₄	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	2	no	—
397	D₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	8	4	no	—
419	C₂×C₄	—	8	8	no	—
420	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
421	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
422	C₂×C₄	C₁₃×#135	1	4	yes	—
423	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
425	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
426	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
427	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
428	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
429	C₈	—	2	2	no	—
430	C₈	—	4	2	no	—
431	C₈	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
432	C₂²	—	2	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
438	C₂²	D₄²×C₁₃	1	1	yes	characteristic
439	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
440	C₂²	C₂×C₁₃×#135	1	2	yes	—
441	C₂²	C₁₃×#577	1	2	yes	—
442	C₄	—	2	4	no	—
443	C₄	—	2	4	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	8	2	no	—
450	C₄	—	8	2	no	—
451	C₄	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
452	C₄	C₁₃×#520	1	1	yes	characteristic
453	C₄	C₁₃×#547	1	1	yes	characteristic
454	C₄	C₁₃×#554	1	1	yes	characteristic
455	C₂	—	4	4	no	—
456	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
457	C₂	C₄×C₁₃×#135	1	1	yes	characteristic
458	C₂	C₁₃×#2949	1	1	yes	characteristic
459	C₂	C₁₃×#3282	1	2	yes	—
460	C₂	C₁₃×#3381	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2351	C₂	semidirect
5. C₁₃×#1941	C₂	semidirect
6. C₁₃×#1863	C₂	semidirect
8. C₁₃×#1846	C₂	semidirect
9. C₁₃×#1805	C₂	semidirect
11. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
18. C₄×C₁₃×SD₁₆	C₄	semidirect
56. C₄×Q₈×C₁₃	C₂×C₄	semidirect
78. C₁₃×#106	C₂×C₄	semidirect
81. C₁₃×#103	C₂×C₄	semidirect
85. C₄×C₈×C₁₃	C₂×C₄	semidirect
94. #22683	C₁₃	direct (N × H)
123. C₁₃×SD₁₆	C₄⋊C₄	semidirect
156. #2351	C₂×C₁₃	semidirect
158. #1941	C₂×C₁₃	semidirect
159. #1863	C₂×C₁₃	semidirect
161. #1846	C₂×C₁₃	semidirect
162. #1805	C₂×C₁₃	semidirect
164. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
219. C₄×SD₁₆	C₄×C₁₃	semidirect
280. C₄×Q₈	C₂×C₄×C₁₃	semidirect
302. #106	C₂×C₄×C₁₃	semidirect
305. #103	C₂×C₄×C₁₃	semidirect
309. C₄×C₈	C₂×C₄×C₁₃	semidirect
352. SD₁₆	C₁₃×C₄⋊C₄	semidirect
383. C₁₃	#22683	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
C₁₃×#2351	2
C₁₃×#2349	2
C₁₃×#1941	2
C₁₃×#1863	2
C₁₃×#1862	2
C₁₃×#1846	2
C₁₃×#1805	2
C₁₃×#1804	2
C₈×C₁₃×C₄⋊C₄	2
#22683	13

Subgroups — C13×#22683 #15709022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22683 #15709022