Subgroups — C₁₃×#32278 #15718617

Order 3328.

772 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2501	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2083	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1934	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1925	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#126	—	2	1	no	—
17	C₂×C₁₃×#123	—	2	1	no	—
18	C₂×C₁₃×#123	—	2	1	no	—
19	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#400	—	2	1	no	—
36	C₁₃×#399	—	2	1	no	—
37	C₁₃×#399	—	2	1	no	—
38	C₁₃×#397	—	2	1	no	—
39	C₁₃×#390	C₂²	1	1	yes	characteristic
40	C₁₃×#390	C₂²	1	1	yes	characteristic
41	C₁₃×#389	C₂²	1	1	yes	characteristic
42	C₁₃×#389	C₂²	1	1	yes	characteristic
43	C₁₃×#387	—	2	1	no	—
44	C₁₃×#384	C₂²	1	1	yes	characteristic
45	C₁₃×#384	C₂²	1	1	yes	characteristic
46	C₁₃×#384	C₂²	1	1	yes	characteristic
47	C₁₃×#380	C₂²	1	1	yes	characteristic
48	C₁₃×#380	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
51	C₁₃×#340	C₂²	1	1	yes	characteristic
52	C₁₃×#340	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₁₃	—	2	1	no	—
60	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	—	2	1	no	—
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#126	—	4	4	no	—
68	C₁₃×#123	—	4	4	no	—
69	C₁₃×#123	—	4	4	no	—
70	C₁₃×#121	—	4	1	no	—
71	C₁₃×#121	—	4	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
98	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	—	2	1	no	—
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₁₃×#107	—	4	1	no	—
103	C₁₃×#107	—	4	1	no	—
104	C₁₃×#107	—	4	1	no	—
105	C₁₃×#107	—	4	1	no	—
106	C₁₃×#107	—	4	1	no	—
107	C₁₃×#107	—	4	1	no	—
108	C₁₃×C₄⋊C₈	—	2	2	no	—
109	C₁₃×#102	—	2	2	no	—
110	C₁₃×#102	—	2	2	no	—
111	C₁₃×#102	—	4	1	no	—
112	C₁₃×#102	—	4	1	no	—
113	C₁₃×C₂²⋊C₈	—	2	2	no	—
114	C₁₃×C₂²⋊C₈	—	2	2	no	—
115	C₄×C₈×C₁₃	—	2	2	no	—
116	C₁₃×#95	—	2	1	no	—
117	C₁₃×#95	—	2	1	no	—
118	C₁₃×#95	—	2	1	no	—
119	C₁₃×#95	—	2	1	no	—
120	C₁₃×#95	—	2	1	no	—
121	C₁₃×#95	D₄	1	1	yes	characteristic
122	C₁₃×#95	D₄	1	1	yes	characteristic
123	#32278	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂⁴×C₁₃	—	2	1	no	—
125	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂×D₄×C₁₃	—	2	1	no	—
127	C₂×D₄×C₁₃	—	2	1	no	—
128	C₂×D₄×C₁₃	—	2	1	no	—
129	C₂×D₄×C₁₃	—	2	1	no	—
130	C₂×D₄×C₁₃	—	2	1	no	—
131	C₂×D₄×C₁₃	—	2	1	no	—
132	C₂×D₄×C₁₃	—	4	2	no	—
133	C₂×D₄×C₁₃	—	4	2	no	—
134	C₂×D₄×C₁₃	—	4	2	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	4	2	no	—
149	C₂²×C₄×C₁₃	—	4	2	no	—
150	C₂²×C₄×C₁₃	—	4	2	no	—
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₂×C₈×C₁₃	—	2	1	no	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₂×C₈×C₁₃	—	2	1	no	—
161	C₂×C₈×C₁₃	—	2	1	no	—
162	C₂×C₈×C₁₃	—	2	1	no	—
163	C₂×C₈×C₁₃	—	2	1	no	—
164	C₂×C₈×C₁₃	—	2	1	no	—
165	C₂×C₈×C₁₃	—	2	1	no	—
166	C₂×C₈×C₁₃	—	2	1	no	—
167	C₂×C₈×C₁₃	#41	1	2	yes	—
168	C₂×C₈×C₁₃	#41	1	2	yes	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	4	2	no	—
184	C₁₃×C₄⋊C₄	—	4	2	no	—
185	C₁₃×C₄⋊C₄	—	4	2	no	—
186	C₁₃×C₄⋊C₄	—	4	2	no	—
187	C₁₃×C₄⋊C₄	—	4	2	no	—
188	C₁₃×C₄⋊C₄	—	4	2	no	—
189	C₁₃×C₄⋊C₄	—	4	2	no	—
190	C₁₃×C₄⋊C₄	—	4	2	no	—
191	C₁₃×C₄⋊C₄	—	4	2	no	—
192	C₁₃×C₂²⋊C₄	—	2	2	no	—
193	C₁₃×C₂²⋊C₄	—	4	2	no	—
194	C₁₃×C₂²⋊C₄	—	4	2	no	—
195	C₁₃×C₂²⋊C₄	—	4	2	no	—
196	C₁₃×C₂²⋊C₄	—	4	2	no	—
197	C₁₃×C₂²⋊C₄	—	4	2	no	—
198	C₁₃×C₂²⋊C₄	—	4	2	no	—
199	C₁₃×C₂²⋊C₄	—	4	2	no	—
200	C₁₃×C₂²⋊C₄	D₈	1	4	yes	—
201	C₄²×C₁₃	—	2	1	no	—
202	C₄²×C₁₃	—	2	1	no	—
203	C₄²×C₁₃	—	2	1	no	—
204	C₄²×C₁₃	—	2	1	no	—
205	C₄²×C₁₃	—	4	2	no	—
206	#2501	C₂×C₁₃	1	1	yes	characteristic
207	#2496	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#2099	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#2093	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#2083	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#2067	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#2033	C₂×C₁₃	1	1	yes	characteristic
213	#2033	C₂×C₁₃	1	1	yes	characteristic
214	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1934	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1925	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1923	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1852	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1852	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1845	C₂×C₁₃	1	1	yes	characteristic, complemented
221	C₂³×C₁₃	—	2	1	no	—
222	C₂³×C₁₃	—	2	1	no	—
223	C₂³×C₁₃	—	2	1	no	—
224	C₂³×C₁₃	—	2	1	no	—
225	C₂³×C₁₃	—	2	1	no	—
226	C₂³×C₁₃	—	2	1	no	—
227	C₂³×C₁₃	—	4	1	no	—
228	C₂³×C₁₃	—	4	1	no	—
229	C₂³×C₁₃	—	4	1	no	—
230	C₂³×C₁₃	—	4	1	no	—
231	C₂³×C₁₃	—	4	1	no	—
232	C₂³×C₁₃	—	4	1	no	—
233	C₂³×C₁₃	—	4	1	no	—
234	C₂³×C₁₃	C₂×D₈	1	2	yes	—
235	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	D₄×C₁₃	—	4	1	no	—
237	D₄×C₁₃	—	4	1	no	—
238	D₄×C₁₃	—	4	1	no	—
239	D₄×C₁₃	—	4	1	no	—
240	D₄×C₁₃	—	8	4	no	—
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	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	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	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	1	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	8	4	no	—
279	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
280	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
281	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
282	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
285	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
286	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
287	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
288	C₈×C₁₃	—	2	2	no	—
289	C₈×C₁₃	—	2	2	no	—
290	C₈×C₁₃	—	4	1	no	—
291	C₈×C₁₃	—	4	1	no	—
292	C₂×#126	—	2	1	no	—
293	C₂×#123	—	2	1	no	—
294	C₂×#123	—	2	1	no	—
295	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
296	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
311	#400	—	2	1	no	—
312	#399	—	2	1	no	—
313	#399	—	2	1	no	—
314	#397	—	2	1	no	—
315	#390	C₂²×C₁₃	1	1	yes	characteristic
316	#390	C₂²×C₁₃	1	1	yes	characteristic
317	#389	C₂²×C₁₃	1	1	yes	characteristic
318	#389	C₂²×C₁₃	1	1	yes	characteristic
319	#387	—	2	1	no	—
320	#384	C₂²×C₁₃	1	1	yes	characteristic
321	#384	C₂²×C₁₃	1	1	yes	characteristic
322	#384	C₂²×C₁₃	1	1	yes	characteristic
323	#380	C₂²×C₁₃	1	1	yes	characteristic
324	#380	C₂²×C₁₃	1	1	yes	characteristic
325	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
326	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
327	#340	C₂²×C₁₃	1	1	yes	characteristic
328	#340	C₂²×C₁₃	1	1	yes	characteristic
329	#340	C₂²×C₁₃	1	1	yes	characteristic
330	#340	C₂²×C₁₃	1	1	yes	characteristic
331	#340	C₂²×C₁₃	1	1	yes	characteristic
332	#340	C₂²×C₁₃	1	1	yes	characteristic
333	#336	C₂²×C₁₃	1	1	yes	characteristic
334	#336	C₂²×C₁₃	1	1	yes	characteristic
335	C₂²×C₁₃	—	2	2	no	—
336	C₂²×C₁₃	—	2	2	no	—
337	C₂²×C₁₃	—	2	2	no	—
338	C₂²×C₁₃	—	4	1	no	—
339	C₂²×C₁₃	—	4	1	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	4	1	no	—
342	C₂²×C₁₃	—	8	1	no	—
343	C₂²×C₁₃	—	8	1	no	—
344	C₂²×C₁₃	—	8	1	no	—
345	C₂²×C₁₃	—	8	1	no	—
346	C₂²×C₁₃	—	8	1	no	—
347	C₂²×C₁₃	—	8	1	no	—
348	C₂²×C₁₃	—	8	1	no	—
349	C₂²×C₁₃	#535	1	1	yes	characteristic
350	C₂²×C₁₃	#547	1	1	yes	characteristic
351	C₂²×C₁₃	#547	1	1	yes	characteristic
352	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
353	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
354	C₂²×C₁₃	#578	1	1	yes	characteristic
355	C₂²×C₁₃	#578	1	1	yes	characteristic
356	C₄×C₁₃	—	2	2	no	—
357	C₄×C₁₃	—	2	2	no	—
358	C₄×C₁₃	—	2	2	no	—
359	C₄×C₁₃	—	4	1	no	—
360	C₄×C₁₃	—	4	1	no	—
361	C₄×C₁₃	—	8	1	no	—
362	C₄×C₁₃	—	8	1	no	—
363	C₄×C₁₃	—	8	1	no	—
364	C₄×C₁₃	—	8	1	no	—
365	C₄×C₁₃	—	8	1	no	—
366	C₄×C₁₃	—	8	1	no	—
367	C₄×C₁₃	—	8	1	no	—
368	C₄×C₁₃	#539	1	1	yes	characteristic
369	C₄×C₁₃	#542	1	1	yes	characteristic
370	C₄×C₁₃	#553	1	1	yes	characteristic
371	C₄×C₁₃	#563	1	1	yes	characteristic
372	C₂²×D₄	—	2	1	no	—
373	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
374	C₂³×C₄	—	2	1	no	—
375	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
376	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
377	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
378	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
379	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
380	#126	—	4	4	no	—
381	#123	—	4	4	no	—
382	#123	—	4	4	no	—
383	#121	—	4	1	no	—
384	#121	—	4	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	4	1	no	—
395	C₂×C₄⋊C₄	—	4	1	no	—
396	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
411	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
412	C₂×C₄²	—	2	1	no	—
413	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
414	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
415	#107	—	4	1	no	—
416	#107	—	4	1	no	—
417	#107	—	4	1	no	—
418	#107	—	4	1	no	—
419	#107	—	4	1	no	—
420	#107	—	4	1	no	—
421	C₄⋊C₈	—	2	2	no	—
422	#102	—	2	2	no	—
423	#102	—	2	2	no	—
424	#102	—	4	1	no	—
425	#102	—	4	1	no	—
426	C₂²⋊C₈	—	2	2	no	—
427	C₂²⋊C₈	—	2	2	no	—
428	C₄×C₈	—	2	2	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	D₄×C₁₃	1	1	yes	characteristic
435	#95	D₄×C₁₃	1	1	yes	characteristic
436	C₂×C₁₃	—	4	2	no	—
437	C₂×C₁₃	—	16	1	no	—
438	C₂×C₁₃	#2718	1	1	yes	characteristic
439	C₂×C₁₃	#3205	1	1	yes	characteristic
440	C₂×C₁₃	#3223	1	1	yes	characteristic
441	C₂×C₁₃	#3334	1	1	yes	characteristic
442	C₂×C₁₃	#3334	1	1	yes	characteristic
443	C₂×C₁₃	#3343	1	1	yes	characteristic
444	C₂×C₁₃	#3353	1	1	yes	characteristic
445	C₂⁴	—	2	1	no	—
446	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	—	4	2	no	—
455	C₂×D₄	—	4	2	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	4	2	no	—
470	C₂²×C₄	—	4	2	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
473	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	C₁₃×#41	1	2	yes	—
489	C₂×C₈	C₁₃×#41	1	2	yes	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	4	2	no	—
505	C₄⋊C₄	—	4	2	no	—
506	C₄⋊C₄	—	4	2	no	—
507	C₄⋊C₄	—	4	2	no	—
508	C₄⋊C₄	—	4	2	no	—
509	C₄⋊C₄	—	4	2	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₄⋊C₄	—	4	2	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	4	2	no	—
515	C₂²⋊C₄	—	4	2	no	—
516	C₂²⋊C₄	—	4	2	no	—
517	C₂²⋊C₄	—	4	2	no	—
518	C₂²⋊C₄	—	4	2	no	—
519	C₂²⋊C₄	—	4	2	no	—
520	C₂²⋊C₄	—	4	2	no	—
521	C₂²⋊C₄	C₁₃×D₈	1	4	yes	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	4	2	no	—
527	C₁₃	#32278	1	1	yes	characteristic, direct product factor, Sylow
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	4	1	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	4	1	no	—
538	C₂³	—	4	1	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	C₂×C₁₃×D₈	1	2	yes	—
542	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
543	D₄	—	4	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	D₄	—	8	4	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	8	4	no	—
586	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
587	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
588	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
589	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
590	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
591	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
592	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
593	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
594	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
595	C₈	—	2	2	no	—
596	C₈	—	2	2	no	—
597	C₈	—	4	1	no	—
598	C₈	—	4	1	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	8	1	no	—
607	C₂²	—	8	1	no	—
608	C₂²	—	8	1	no	—
609	C₂²	—	8	1	no	—
610	C₂²	—	8	1	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	C₁₃×#535	1	1	yes	characteristic
614	C₂²	C₁₃×#547	1	1	yes	characteristic
615	C₂²	C₁₃×#547	1	1	yes	characteristic
616	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
617	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
618	C₂²	C₁₃×#578	1	1	yes	characteristic
619	C₂²	C₁₃×#578	1	1	yes	characteristic
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	8	1	no	—
626	C₄	—	8	1	no	—
627	C₄	—	8	1	no	—
628	C₄	—	8	1	no	—
629	C₄	—	8	1	no	—
630	C₄	—	8	1	no	—
631	C₄	—	8	1	no	—
632	C₄	C₁₃×#539	1	1	yes	characteristic
633	C₄	C₁₃×#542	1	1	yes	characteristic
634	C₄	C₁₃×#553	1	1	yes	characteristic
635	C₄	C₁₃×#563	1	1	yes	characteristic
636	C₂	—	4	2	no	—
637	C₂	—	16	1	no	—
638	C₂	C₁₃×#2718	1	1	yes	characteristic
639	C₂	C₁₃×#3205	1	1	yes	characteristic
640	C₂	C₁₃×#3223	1	1	yes	characteristic
641	C₂	C₁₃×#3334	1	1	yes	characteristic
642	C₂	C₁₃×#3334	1	1	yes	characteristic
643	C₂	C₁₃×#3343	1	1	yes	characteristic
644	C₂	C₁₃×#3353	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2496	C₂	semidirect
3. C₁₃×#2099	C₂	semidirect
4. C₁₃×#2093	C₂	semidirect
5. C₁₃×#2083	C₂	semidirect
6. C₁₃×#2067	C₂	semidirect
9. C₁₃×#1947	C₂	semidirect
10. C₁₃×#1934	C₂	semidirect
11. C₁₃×#1925	C₂	semidirect
12. C₁₃×#1923	C₂	semidirect
13. C₁₃×#1852	C₂	semidirect
14. C₁₃×#1852	C₂	semidirect
15. C₁₃×#1845	C₂	semidirect
123. #32278	C₁₃	direct (N × H)
207. #2496	C₂×C₁₃	semidirect
208. #2099	C₂×C₁₃	semidirect
209. #2093	C₂×C₁₃	semidirect
210. #2083	C₂×C₁₃	semidirect
211. #2067	C₂×C₁₃	semidirect
214. #1947	C₂×C₁₃	semidirect
215. #1934	C₂×C₁₃	semidirect
216. #1925	C₂×C₁₃	semidirect
217. #1923	C₂×C₁₃	semidirect
218. #1852	C₂×C₁₃	semidirect
219. #1852	C₂×C₁₃	semidirect
220. #1845	C₂×C₁₃	semidirect
527. C₁₃	#32278	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×#2501	2
C₁₃×#2496	2
C₁₃×#2099	2
C₁₃×#2093	2
C₁₃×#2083	2
C₁₃×#2067	2
C₁₃×#2033	2
C₁₃×#1947	2
C₁₃×#1934	2
C₁₃×#1925	2
C₁₃×#1923	2
C₁₃×#1852	2
C₁₃×#1845	2
#32278	13

Subgroups — C13×#32278 #15718617

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32278 #15718617