Subgroups — C₁₃×#24156 #15710495

Order 3328.

1394 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2033	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2000	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1877	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1862	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	—	2	1	no	—
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₁₃×#532	—	2	4	no	—
15	C₁₃×#532	—	2	4	no	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#124	—	2	1	no	—
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#121	—	2	1	no	—
21	C₂×C₁₃×#121	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃	—	2	1	no	—
24	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#477	—	2	4	no	—
27	C₁₃×#460	—	2	4	no	—
28	C₂×C₁₃×#107	C₂²	1	2	yes	—
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#103	C₂²	1	2	yes	—
32	C₂×C₁₃×#102	C₂²	1	2	yes	—
33	C₂×C₁₃×#102	C₂²	1	2	yes	—
34	C₂×C₁₃×#102	C₂²	1	2	yes	—
35	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₁₃×#391	C₂²	1	1	yes	characteristic
37	C₁₃×#389	C₂²	1	1	yes	characteristic
38	C₁₃×#387	—	2	1	no	—
39	C₁₃×#385	—	2	1	no	—
40	C₁₃×#380	C₂²	1	1	yes	characteristic
41	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
42	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₁₃×#340	C₂²	1	2	yes	—
46	C₁₃×#336	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	—	2	8	no	—
48	C₂×C₁₃×#41	—	4	4	no	—
49	C₂×C₁₃×#41	—	4	4	no	—
50	C₂²×Q₈×C₁₃	—	2	1	no	—
51	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₃	—	2	2	no	—
53	C₂²×D₄×C₁₃	—	2	1	no	—
54	C₂²×D₄×C₁₃	—	2	1	no	—
55	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₃	—	2	2	no	—
57	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×SD₁₆	—	2	4	no	—
61	C₂×C₁₃×SD₁₆	—	2	4	no	—
62	C₂×C₁₃×SD₁₆	—	4	2	no	—
63	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
64	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
65	C₁₃×C₄⋊Q₈	—	2	2	no	—
66	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
67	C₁₃×#127	—	2	2	no	—
68	C₁₃×#127	D₄	1	4	yes	—
69	C₁₃×#124	—	2	8	no	—
70	C₁₃×C₂²⋊Q₈	—	2	2	no	—
71	C₁₃×C₂²⋊Q₈	—	2	2	no	—
72	C₁₃×#121	—	2	8	no	—
73	C₁₃×#121	—	2	4	no	—
74	C₁₃×#121	—	2	4	no	—
75	C₄×Q₈×C₁₃	—	2	2	no	—
76	C₄×Q₈×C₁₃	—	2	2	no	—
77	C₄×D₄×C₁₃	—	2	8	no	—
78	C₄×D₄×C₁₃	—	2	4	no	—
79	C₄×D₄×C₁₃	—	2	4	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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	2	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₄²×C₁₃	—	2	2	no	—
93	C₂×C₄²×C₁₃	—	2	2	no	—
94	C₂×C₄²×C₁₃	—	2	1	no	—
95	C₂×C₄²×C₁₃	—	2	1	no	—
96	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#107	—	2	4	no	—
101	C₁₃×C₄⋊C₈	—	2	2	no	—
102	C₁₃×C₄⋊C₈	—	2	2	no	—
103	C₁₃×#103	—	2	4	no	—
104	C₁₃×#102	—	2	4	no	—
105	C₁₃×#102	—	2	4	no	—
106	C₁₃×#102	—	4	2	no	—
107	C₁₃×C₂²⋊C₈	—	4	2	no	—
108	C₁₃×#95	—	2	1	no	—
109	C₁₃×#95	—	2	1	no	—
110	C₁₃×#95	—	2	1	no	—
111	C₁₃×#95	—	2	1	no	—
112	C₁₃×#95	—	2	1	no	—
113	#24156	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂⁴×C₁₃	—	2	2	no	—
115	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₁₃×#41	—	4	32	no	—
117	C₂×Q₈×C₁₃	—	2	4	no	—
118	C₂×Q₈×C₁₃	—	2	1	no	—
119	C₂×Q₈×C₁₃	—	2	1	no	—
120	C₂×Q₈×C₁₃	—	2	1	no	—
121	C₂×Q₈×C₁₃	—	2	1	no	—
122	C₂×Q₈×C₁₃	—	2	1	no	—
123	C₂×Q₈×C₁₃	—	4	2	no	—
124	C₂×Q₈×C₁₃	—	4	2	no	—
125	C₂×Q₈×C₁₃	#41	1	2	yes	complemented
126	C₂×D₄×C₁₃	—	2	8	no	—
127	C₂×D₄×C₁₃	—	2	4	no	—
128	C₂×D₄×C₁₃	—	2	4	no	—
129	C₂×D₄×C₁₃	—	2	2	no	—
130	C₂×D₄×C₁₃	—	2	2	no	—
131	C₂×D₄×C₁₃	—	2	2	no	—
132	C₂×D₄×C₁₃	—	2	2	no	—
133	C₂×D₄×C₁₃	—	2	2	no	—
134	C₂×D₄×C₁₃	—	4	2	no	—
135	C₂×D₄×C₁₃	—	4	2	no	—
136	C₂×D₄×C₁₃	—	4	4	no	—
137	C₂×D₄×C₁₃	—	4	4	no	—
138	C₂×D₄×C₁₃	—	4	2	no	—
139	C₂×D₄×C₁₃	—	4	2	no	—
140	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₃	—	2	2	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	8	no	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₃	—	2	2	no	—
149	C₂²×C₄×C₁₃	—	2	2	no	—
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
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	—	4	4	no	—
160	C₂²×C₄×C₁₃	—	4	4	no	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₁₃×SD₁₆	—	4	8	no	—
168	C₂×C₈×C₁₃	—	2	2	no	—
169	C₂×C₈×C₁₃	—	2	2	no	—
170	C₂×C₈×C₁₃	—	2	2	no	—
171	C₂×C₈×C₁₃	—	2	2	no	—
172	C₂×C₈×C₁₃	—	2	2	no	—
173	C₂×C₈×C₁₃	—	2	2	no	—
174	C₁₃×C₄⋊C₄	—	2	4	no	—
175	C₁₃×C₄⋊C₄	—	2	4	no	—
176	C₁₃×C₄⋊C₄	—	2	2	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	—	4	2	no	—
183	C₁₃×C₄⋊C₄	—	4	2	no	—
184	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
185	C₁₃×C₄⋊C₄	#41	1	2	yes	complemented
186	C₁₃×C₂²⋊C₄	—	2	8	no	—
187	C₁₃×C₂²⋊C₄	—	2	8	no	—
188	C₁₃×C₂²⋊C₄	—	2	4	no	—
189	C₁₃×C₂²⋊C₄	—	4	2	no	—
190	C₄²×C₁₃	—	2	2	no	—
191	C₄²×C₁₃	—	2	2	no	—
192	C₄²×C₁₃	—	2	1	no	—
193	C₄²×C₁₃	—	2	1	no	—
194	C₄²×C₁₃	—	4	2	no	—
195	C₄²×C₁₃	—	4	2	no	—
196	C₄²×C₁₃	C₂×D₄	1	2	yes	—
197	C₄²×C₁₃	C₂×D₄	1	2	yes	—
198	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
199	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
201	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#2033	C₂×C₁₃	1	2	yes	complemented
203	#2000	C₂×C₁₃	1	2	yes	complemented
204	#1987	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#1982	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#1877	C₂×C₁₃	1	2	yes	complemented
207	#1862	C₂×C₁₃	1	2	yes	complemented
208	#1797	C₂×C₁₃	1	1	yes	characteristic, complemented
209	C₂³×C₁₃	—	2	1	no	—
210	C₂³×C₁₃	—	2	1	no	—
211	C₂³×C₁₃	—	2	1	no	—
212	C₂³×C₁₃	—	2	1	no	—
213	C₂³×C₁₃	—	2	1	no	—
214	C₂³×C₁₃	—	2	1	no	—
215	C₂³×C₁₃	—	2	4	no	—
216	C₂³×C₁₃	—	4	2	no	—
217	C₂³×C₁₃	—	4	2	no	—
218	C₂³×C₁₃	—	4	2	no	—
219	C₂³×C₁₃	—	4	2	no	—
220	C₂³×C₁₃	—	4	2	no	—
221	C₂³×C₁₃	—	4	2	no	—
222	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
223	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
224	Q₈×C₁₃	—	2	2	no	—
225	Q₈×C₁₃	—	2	2	no	—
226	Q₈×C₁₃	—	4	8	no	—
227	Q₈×C₁₃	—	4	1	no	—
228	Q₈×C₁₃	—	4	1	no	—
229	D₄×C₁₃	—	2	4	no	—
230	D₄×C₁₃	—	2	4	no	—
231	D₄×C₁₃	—	4	8	no	—
232	D₄×C₁₃	—	4	16	no	—
233	D₄×C₁₃	—	4	2	no	—
234	D₄×C₁₃	—	4	2	no	—
235	D₄×C₁₃	—	4	8	no	—
236	C₂×C₄×C₁₃	—	2	8	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	1	no	—
239	C₂×C₄×C₁₃	—	2	1	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	4	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	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	—	4	16	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	2	no	—
256	C₂×C₄×C₁₃	—	4	2	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	4	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	#120	1	2	yes	—
269	C₂×C₄×C₁₃	#120	1	2	yes	—
270	C₂×C₄×C₁₃	#135	1	2	yes	—
271	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
272	C₂×C₄×C₁₃	#137	1	2	yes	—
273	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
278	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
279	C₈×C₁₃	—	4	2	no	—
280	C₈×C₁₃	—	4	2	no	—
281	C₂²×#41	—	2	1	no	—
282	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
283	#532	—	2	4	no	—
284	#532	—	2	4	no	—
285	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#124	—	2	1	no	—
288	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#121	—	2	1	no	—
290	C₂×#121	C₂²×C₁₃	1	2	yes	—
291	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×C₄×D₄	—	2	1	no	—
293	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
294	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
295	#477	—	2	4	no	—
296	#460	—	2	4	no	—
297	C₂×#107	C₂²×C₁₃	1	2	yes	—
298	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×#103	C₂²×C₁₃	1	2	yes	—
301	C₂×#102	C₂²×C₁₃	1	2	yes	—
302	C₂×#102	C₂²×C₁₃	1	2	yes	—
303	C₂×#102	C₂²×C₁₃	1	2	yes	—
304	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
305	#391	C₂²×C₁₃	1	1	yes	characteristic
306	#389	C₂²×C₁₃	1	1	yes	characteristic
307	#387	—	2	1	no	—
308	#385	—	2	1	no	—
309	#380	C₂²×C₁₃	1	1	yes	characteristic
310	C₄×C₄⋊C₄	—	2	1	no	—
311	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
312	C₄×C₂²⋊C₄	—	2	1	no	—
313	#340	C₂²×C₁₃	1	2	yes	—
314	#340	C₂²×C₁₃	1	2	yes	—
315	#336	C₂²×C₁₃	1	2	yes	—
316	C₂²×C₁₃	—	2	2	no	—
317	C₂²×C₁₃	—	2	2	no	—
318	C₂²×C₁₃	—	2	2	no	—
319	C₂²×C₁₃	—	4	1	no	—
320	C₂²×C₁₃	—	4	1	no	—
321	C₂²×C₁₃	—	4	1	no	—
322	C₂²×C₁₃	—	4	1	no	—
323	C₂²×C₁₃	—	4	4	no	—
324	C₂²×C₁₃	—	4	4	no	—
325	C₂²×C₁₃	—	4	4	no	—
326	C₂²×C₁₃	—	8	2	no	—
327	C₂²×C₁₃	—	8	2	no	—
328	C₂²×C₁₃	—	8	2	no	—
329	C₂²×C₁₃	—	8	2	no	—
330	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
331	C₂²×C₁₃	#525	1	1	yes	characteristic
332	C₂²×C₁₃	#537	1	1	yes	characteristic
333	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
334	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
335	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
336	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	4	2	no	—
340	C₄×C₁₃	—	4	1	no	—
341	C₄×C₁₃	—	4	2	no	—
342	C₄×C₁₃	—	4	1	no	—
343	C₄×C₁₃	—	4	4	no	—
344	C₄×C₁₃	—	8	1	no	—
345	C₄×C₁₃	—	8	1	no	—
346	C₄×C₁₃	#452	1	4	yes	—
347	C₄×C₁₃	#546	1	1	yes	characteristic
348	C₄×C₁₃	#547	1	1	yes	characteristic
349	C₄×C₁₃	#548	1	1	yes	characteristic
350	C₄×C₁₃	#550	1	1	yes	characteristic
351	C₂×#41	—	2	8	no	—
352	C₂×#41	—	4	4	no	—
353	C₂×#41	—	4	4	no	—
354	C₂²×Q₈	—	2	1	no	—
355	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
356	C₂²×D₄	—	2	2	no	—
357	C₂²×D₄	—	2	1	no	—
358	C₂²×D₄	—	2	1	no	—
359	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
360	C₂³×C₄	—	2	2	no	—
361	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
362	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
363	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
364	C₂×SD₁₆	—	2	4	no	—
365	C₂×SD₁₆	—	2	4	no	—
366	C₂×SD₁₆	—	4	2	no	—
367	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
368	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
369	C₄⋊Q₈	—	2	2	no	—
370	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
371	#127	—	2	2	no	—
372	#127	D₄×C₁₃	1	4	yes	—
373	#124	—	2	8	no	—
374	C₂²⋊Q₈	—	2	2	no	—
375	C₂²⋊Q₈	—	2	2	no	—
376	#121	—	2	8	no	—
377	#121	—	2	4	no	—
378	#121	—	2	4	no	—
379	C₄×Q₈	—	2	2	no	—
380	C₄×Q₈	—	2	2	no	—
381	C₄×D₄	—	2	8	no	—
382	C₄×D₄	—	2	4	no	—
383	C₄×D₄	—	2	4	no	—
384	C₂×C₄⋊C₄	—	2	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	C₂³×C₁₃	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	—	2	2	no	—
394	C₂×C₂²⋊C₄	—	2	2	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₄²	—	2	2	no	—
397	C₂×C₄²	—	2	2	no	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
401	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
404	#107	—	2	4	no	—
405	C₄⋊C₈	—	2	2	no	—
406	C₄⋊C₈	—	2	2	no	—
407	#103	—	2	4	no	—
408	#102	—	2	4	no	—
409	#102	—	2	4	no	—
410	#102	—	4	2	no	—
411	C₂²⋊C₈	—	4	2	no	—
412	#95	—	2	1	no	—
413	#95	—	2	1	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	C₂×C₁₃	—	4	2	no	—
418	C₂×C₁₃	—	8	4	no	—
419	C₂×C₁₃	#2407	1	1	yes	characteristic
420	C₂×C₁₃	C₂×#452	1	1	yes	characteristic
421	C₂×C₁₃	#3003	1	1	yes	characteristic
422	C₂×C₁₃	#3106	1	1	yes	characteristic
423	C₂×C₁₃	#3112	1	1	yes	characteristic
424	C₂×C₁₃	#3247	1	1	yes	characteristic
425	C₂×C₁₃	#3254	1	1	yes	characteristic
426	C₂⁴	—	2	2	no	—
427	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
428	#41	—	4	32	no	—
429	C₂×Q₈	—	2	4	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	4	2	no	—
436	C₂×Q₈	—	4	2	no	—
437	C₂×Q₈	C₁₃×#41	1	2	yes	complemented
438	C₂×D₄	—	2	8	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	4	2	no	—
447	C₂×D₄	—	4	2	no	—
448	C₂×D₄	—	4	4	no	—
449	C₂×D₄	—	4	4	no	—
450	C₂×D₄	—	4	2	no	—
451	C₂×D₄	—	4	2	no	—
452	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	8	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	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	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	4	4	no	—
472	C₂²×C₄	—	4	4	no	—
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	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
479	SD₁₆	—	4	8	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	2	2	no	—
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	2	no	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	1	no	—
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	—	4	2	no	—
495	C₄⋊C₄	—	4	2	no	—
496	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
497	C₄⋊C₄	C₁₃×#41	1	2	yes	complemented
498	C₂²⋊C₄	—	2	8	no	—
499	C₂²⋊C₄	—	2	8	no	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	4	2	no	—
502	C₄²	—	2	2	no	—
503	C₄²	—	2	2	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	4	2	no	—
507	C₄²	—	4	2	no	—
508	C₄²	C₂×D₄×C₁₃	1	2	yes	—
509	C₄²	C₂×D₄×C₁₃	1	2	yes	—
510	C₁₃	#24156	1	1	yes	characteristic, direct product factor, Sylow
511	C₂³	—	2	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	4	2	no	—
520	C₂³	—	4	2	no	—
521	C₂³	—	4	2	no	—
522	C₂³	—	4	2	no	—
523	C₂³	—	4	2	no	—
524	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
525	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
526	Q₈	—	2	2	no	—
527	Q₈	—	2	2	no	—
528	Q₈	—	4	8	no	—
529	Q₈	—	4	1	no	—
530	Q₈	—	4	1	no	—
531	D₄	—	2	4	no	—
532	D₄	—	2	4	no	—
533	D₄	—	4	8	no	—
534	D₄	—	4	16	no	—
535	D₄	—	4	8	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	C₂×C₄	—	2	8	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	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	—	4	16	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	4	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	C₁₃×#120	1	2	yes	—
571	C₂×C₄	C₁₃×#120	1	2	yes	—
572	C₂×C₄	C₁₃×#135	1	2	yes	—
573	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
574	C₂×C₄	C₁₃×#137	1	2	yes	—
575	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
577	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
578	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
579	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
580	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
581	C₈	—	4	2	no	—
582	C₈	—	4	2	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	4	4	no	—
592	C₂²	—	4	4	no	—
593	C₂²	—	8	2	no	—
594	C₂²	—	8	2	no	—
595	C₂²	—	8	2	no	—
596	C₂²	—	8	2	no	—
597	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
598	C₂²	C₁₃×#525	1	1	yes	characteristic
599	C₂²	C₁₃×#537	1	1	yes	characteristic
600	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
601	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
602	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
603	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	4	2	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	4	no	—
611	C₄	—	8	1	no	—
612	C₄	—	8	1	no	—
613	C₄	C₁₃×#452	1	4	yes	—
614	C₄	C₁₃×#546	1	1	yes	characteristic
615	C₄	C₁₃×#547	1	1	yes	characteristic
616	C₄	C₁₃×#548	1	1	yes	characteristic
617	C₄	C₁₃×#550	1	1	yes	characteristic
618	C₂	—	4	2	no	—
619	C₂	—	8	4	no	—
620	C₂	C₁₃×#2407	1	1	yes	characteristic
621	C₂	C₂×C₁₃×#452	1	1	yes	characteristic
622	C₂	C₁₃×#3003	1	1	yes	characteristic
623	C₂	C₁₃×#3106	1	1	yes	characteristic
624	C₂	C₁₃×#3112	1	1	yes	characteristic
625	C₂	C₁₃×#3247	1	1	yes	characteristic
626	C₂	C₁₃×#3254	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#532	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#477	C₂	semidirect
3. C₂×C₁₃×#460	C₂	semidirect
4. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
5. C₁₃×#2033	C₂	semidirect
6. C₁₃×#2000	C₂	semidirect
7. C₁₃×#1987	C₂	semidirect
8. C₁₃×#1982	C₂	semidirect
9. C₁₃×#1877	C₂	semidirect
10. C₁₃×#1862	C₂	semidirect
11. C₁₃×#1797	C₂	semidirect
113. #24156	C₁₃	direct (N × H)
125. C₂×Q₈×C₁₃	#41	semidirect
185. C₁₃×C₄⋊C₄	#41	semidirect
199. C₂×#477	C₂×C₁₃	semidirect
200. C₂×#460	C₂×C₁₃	semidirect
201. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
202. #2033	C₂×C₁₃	semidirect
203. #2000	C₂×C₁₃	semidirect
204. #1987	C₂×C₁₃	semidirect
205. #1982	C₂×C₁₃	semidirect
206. #1877	C₂×C₁₃	semidirect
207. #1862	C₂×C₁₃	semidirect
208. #1797	C₂×C₁₃	semidirect
437. C₂×Q₈	C₁₃×#41	semidirect
497. C₄⋊C₄	C₁₃×#41	semidirect
510. C₁₃	#24156	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×C₁₃×#532	2
C₂×C₁₃×#477	2
C₂×C₁₃×#460	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2033	2
C₁₃×#2000	2
C₁₃×#1987	2
C₁₃×#1982	2
C₁₃×#1877	2
C₁₃×#1862	2
C₁₃×#1797	2
#24156	13

Subgroups — C13×#24156 #15710495

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24156 #15710495