Subgroups — C₁₃×#24661 #15711000

Order 3328.

1016 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2856	C₂	1	1	yes	maximal, characteristic
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×#1982	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1973	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1936	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
13	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#121	—	2	1	no	—
16	C₂×C₁₃×#121	—	2	1	no	—
17	C₂×C₁₃×#121	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#460	—	2	4	no	—
21	C₁₃×#432	—	2	4	no	—
22	C₂×C₁₃×#107	C₂²	1	2	yes	—
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₂×C₁₃×#97	C₂²	1	2	yes	—
31	C₁₃×#391	C₂²	1	1	yes	characteristic
32	C₁₃×#390	—	2	1	no	—
33	C₁₃×#390	—	2	1	no	—
34	C₁₃×#390	C₂²	1	2	yes	—
35	C₁₃×#389	C₂²	1	1	yes	characteristic
36	C₁₃×#387	—	2	1	no	—
37	C₁₃×#385	—	2	1	no	—
38	C₁₃×#384	C₂²	1	1	yes	characteristic
39	C₁₃×#380	C₂²	1	1	yes	characteristic
40	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
41	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
43	C₁₃×#340	C₂²	1	2	yes	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₃	—	2	2	no	—
47	C₂²×D₄×C₁₃	—	2	1	no	—
48	C₂²×D₄×C₁₃	—	2	1	no	—
49	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×SD₁₆	—	2	4	no	—
54	C₂×C₁₃×SD₁₆	—	2	4	no	—
55	C₂×C₁₃×SD₁₆	—	4	2	no	—
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
58	C₁₃×#127	—	2	2	no	—
59	C₁₃×#127	—	2	2	no	—
60	C₁₃×C₂²⋊Q₈	—	2	2	no	—
61	C₁₃×C₂²⋊Q₈	—	2	2	no	—
62	C₁₃×#121	—	4	2	no	—
63	C₁₃×#121	—	4	2	no	—
64	C₁₃×#121	—	4	4	no	—
65	C₁₃×#121	—	4	4	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₄×Q₈×C₁₃	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
82	C₂×C₄²×C₁₃	—	2	2	no	—
83	C₂×C₄²×C₁₃	—	2	2	no	—
84	C₂×C₄²×C₁₃	—	2	1	no	—
85	C₂×C₄²×C₁₃	—	2	1	no	—
86	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
90	C₁₃×#107	—	4	2	no	—
91	C₁₃×C₄⋊C₈	—	2	2	no	—
92	C₁₃×C₄⋊C₈	D₄	1	4	yes	complemented
93	C₁₃×#103	—	4	2	no	—
94	C₁₃×#102	—	2	4	no	—
95	C₁₃×#102	—	2	4	no	—
96	C₁₃×#102	—	4	2	no	—
97	C₁₃×C₂²⋊C₈	—	2	4	no	—
98	C₁₃×#97	—	2	4	no	—
99	C₁₃×#95	—	2	1	no	—
100	C₁₃×#95	—	2	1	no	—
101	C₁₃×#95	—	2	1	no	—
102	C₁₃×#95	—	2	1	no	—
103	C₁₃×#95	—	2	1	no	—
104	#24661	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂⁴×C₁₃	—	2	2	no	—
106	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂×Q₈×C₁₃	—	2	1	no	—
108	C₂×Q₈×C₁₃	—	2	1	no	—
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	1	no	—
112	C₂×Q₈×C₁₃	#41	1	2	yes	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	2	2	no	—
115	C₂×D₄×C₁₃	—	2	2	no	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	4	2	no	—
120	C₂×D₄×C₁₃	—	4	2	no	—
121	C₂×D₄×C₁₃	—	4	4	no	—
122	C₂×D₄×C₁₃	—	4	4	no	—
123	C₂×D₄×C₁₃	—	4	4	no	—
124	C₂×D₄×C₁₃	—	4	2	no	—
125	C₂×D₄×C₁₃	—	4	2	no	—
126	C₂×D₄×C₁₃	—	4	2	no	—
127	C₂×D₄×C₁₃	—	4	2	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	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	2	no	—
144	C₂²×C₄×C₁₃	—	4	1	no	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₁₃×SD₁₆	—	4	8	no	—
152	C₂×C₈×C₁₃	—	2	2	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	—	2	2	no	—
157	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	4	2	no	—
167	C₁₃×C₄⋊C₄	—	4	2	no	—
168	C₁₃×C₄⋊C₄	—	4	2	no	—
169	C₁₃×C₄⋊C₄	—	4	2	no	—
170	C₁₃×C₄⋊C₄	#41	1	2	yes	—
171	C₁₃×C₂²⋊C₄	—	2	4	no	—
172	C₁₃×C₂²⋊C₄	—	4	4	no	—
173	C₁₃×C₂²⋊C₄	—	4	4	no	—
174	C₁₃×C₂²⋊C₄	—	4	4	no	—
175	C₁₃×C₂²⋊C₄	—	4	2	no	—
176	C₄²×C₁₃	—	2	2	no	—
177	C₄²×C₁₃	—	2	2	no	—
178	C₄²×C₁₃	—	2	1	no	—
179	C₄²×C₁₃	—	2	1	no	—
180	C₄²×C₁₃	—	4	2	no	—
181	C₄²×C₁₃	—	4	2	no	—
182	C₄²×C₁₃	C₂×D₄	1	2	yes	—
183	C₄²×C₁₃	#41	1	2	yes	—
184	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
186	#2856	C₂×C₁₃	1	1	yes	characteristic
187	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#2033	C₂×C₁₃	1	2	yes	complemented
189	#2000	C₂×C₁₃	1	2	yes	complemented
190	#1982	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#1973	C₂×C₁₃	1	2	yes	complemented
192	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#1936	C₂×C₁₃	1	2	yes	complemented
194	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂³×C₁₃	—	2	1	no	—
196	C₂³×C₁₃	—	2	1	no	—
197	C₂³×C₁₃	—	2	1	no	—
198	C₂³×C₁₃	—	2	1	no	—
199	C₂³×C₁₃	—	2	1	no	—
200	C₂³×C₁₃	—	2	1	no	—
201	C₂³×C₁₃	—	4	2	no	—
202	C₂³×C₁₃	—	4	2	no	—
203	C₂³×C₁₃	—	4	2	no	—
204	C₂³×C₁₃	—	4	2	no	—
205	C₂³×C₁₃	—	4	2	no	—
206	C₂³×C₁₃	—	4	2	no	—
207	C₂³×C₁₃	—	4	2	no	—
208	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
209	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
210	Q₈×C₁₃	—	2	2	no	—
211	Q₈×C₁₃	—	2	2	no	—
212	Q₈×C₁₃	—	4	1	no	—
213	Q₈×C₁₃	—	4	1	no	—
214	D₄×C₁₃	—	4	2	no	—
215	D₄×C₁₃	—	4	2	no	—
216	D₄×C₁₃	—	4	2	no	—
217	D₄×C₁₃	—	4	2	no	—
218	D₄×C₁₃	—	8	4	no	—
219	D₄×C₁₃	—	8	8	no	—
220	D₄×C₁₃	—	8	4	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	4	4	no	—
235	C₂×C₄×C₁₃	—	4	1	no	—
236	C₂×C₄×C₁₃	—	4	1	no	—
237	C₂×C₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	4	1	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	4	1	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	4	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	—	4	2	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	#121	1	2	yes	—
254	C₂×C₄×C₁₃	#121	1	2	yes	—
255	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
256	C₂×C₄×C₁₃	#137	1	2	yes	—
257	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
262	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
263	C₈×C₁₃	—	2	4	no	—
264	C₈×C₁₃	—	4	2	no	—
265	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
266	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×#121	—	2	1	no	—
269	C₂×#121	—	2	1	no	—
270	C₂×#121	C₂²×C₁₃	1	2	yes	—
271	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
272	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
273	#460	—	2	4	no	—
274	#432	—	2	4	no	—
275	C₂×#107	C₂²×C₁₃	1	2	yes	—
276	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×#103	C₂²×C₁₃	1	2	yes	—
279	C₂×#102	C₂²×C₁₃	1	2	yes	—
280	C₂×#102	C₂²×C₁₃	1	2	yes	—
281	C₂×#102	C₂²×C₁₃	1	2	yes	—
282	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
283	C₂×#97	C₂²×C₁₃	1	2	yes	—
284	#391	C₂²×C₁₃	1	1	yes	characteristic
285	#390	—	2	1	no	—
286	#390	—	2	1	no	—
287	#390	C₂²×C₁₃	1	2	yes	—
288	#389	C₂²×C₁₃	1	1	yes	characteristic
289	#387	—	2	1	no	—
290	#385	—	2	1	no	—
291	#384	C₂²×C₁₃	1	1	yes	characteristic
292	#380	C₂²×C₁₃	1	1	yes	characteristic
293	C₄×C₄⋊C₄	—	2	1	no	—
294	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
295	C₄×C₂²⋊C₄	—	2	1	no	—
296	#340	C₂²×C₁₃	1	2	yes	—
297	#340	C₂²×C₁₃	1	2	yes	—
298	C₂²×C₁₃	—	2	2	no	—
299	C₂²×C₁₃	—	2	2	no	—
300	C₂²×C₁₃	—	2	2	no	—
301	C₂²×C₁₃	—	4	1	no	—
302	C₂²×C₁₃	—	4	1	no	—
303	C₂²×C₁₃	—	4	1	no	—
304	C₂²×C₁₃	—	4	1	no	—
305	C₂²×C₁₃	—	8	2	no	—
306	C₂²×C₁₃	—	8	2	no	—
307	C₂²×C₁₃	—	8	2	no	—
308	C₂²×C₁₃	—	8	2	no	—
309	C₂²×C₁₃	—	8	2	no	—
310	C₂²×C₁₃	—	8	2	no	—
311	C₂²×C₁₃	—	8	2	no	—
312	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
313	C₂²×C₁₃	#525	1	1	yes	characteristic
314	C₂²×C₁₃	#535	1	1	yes	characteristic
315	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
316	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
317	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
318	C₂²×C₁₃	#575	1	1	yes	characteristic
319	C₄×C₁₃	—	2	2	no	—
320	C₄×C₁₃	—	4	2	no	—
321	C₄×C₁₃	—	4	1	no	—
322	C₄×C₁₃	—	4	2	no	—
323	C₄×C₁₃	—	4	1	no	—
324	C₄×C₁₃	—	4	1	no	—
325	C₄×C₁₃	—	8	1	no	—
326	C₄×C₁₃	—	8	2	no	—
327	C₄×C₁₃	—	8	1	no	—
328	C₄×C₁₃	#468	1	4	yes	—
329	C₄×C₁₃	#546	1	1	yes	characteristic
330	C₄×C₁₃	#550	1	1	yes	characteristic
331	C₄×C₁₃	#553	1	1	yes	characteristic
332	C₄×C₁₃	#555	1	1	yes	characteristic
333	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
334	C₂²×D₄	—	2	2	no	—
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	—	2	1	no	—
337	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
338	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
339	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
340	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
341	C₂×SD₁₆	—	2	4	no	—
342	C₂×SD₁₆	—	2	4	no	—
343	C₂×SD₁₆	—	4	2	no	—
344	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
345	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
346	#127	—	2	2	no	—
347	#127	—	2	2	no	—
348	C₂²⋊Q₈	—	2	2	no	—
349	C₂²⋊Q₈	—	2	2	no	—
350	#121	—	4	2	no	—
351	#121	—	4	2	no	—
352	#121	—	4	4	no	—
353	#121	—	4	4	no	—
354	C₄×Q₈	—	2	2	no	—
355	C₄×Q₈	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₄²	—	2	2	no	—
371	C₂×C₄²	—	2	2	no	—
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
375	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
378	#107	—	4	2	no	—
379	C₄⋊C₈	—	2	2	no	—
380	C₄⋊C₈	D₄×C₁₃	1	4	yes	complemented
381	#103	—	4	2	no	—
382	#102	—	2	4	no	—
383	#102	—	2	4	no	—
384	#102	—	4	2	no	—
385	C₂²⋊C₈	—	2	4	no	—
386	#97	—	2	4	no	—
387	#95	—	2	1	no	—
388	#95	—	2	1	no	—
389	#95	—	2	1	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	C₂×C₁₃	—	4	2	no	—
393	C₂×C₁₃	—	16	2	no	—
394	C₂×C₁₃	#2414	1	1	yes	characteristic
395	C₂×C₁₃	C₂×#468	1	1	yes	characteristic
396	C₂×C₁₃	#3055	1	1	yes	characteristic
397	C₂×C₁₃	#3112	1	1	yes	characteristic
398	C₂×C₁₃	#3115	1	1	yes	characteristic
399	C₂×C₁₃	#3216	1	1	yes	characteristic
400	C₂×C₁₃	#3217	1	1	yes	characteristic
401	C₂⁴	—	2	2	no	—
402	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
403	C₂×Q₈	—	2	1	no	—
404	C₂×Q₈	—	2	1	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	C₁₃×#41	1	2	yes	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	4	2	no	—
416	C₂×D₄	—	4	2	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	—	4	4	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	—	4	2	no	—
422	C₂×D₄	—	4	2	no	—
423	C₂×D₄	—	4	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
446	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
447	SD₁₆	—	4	8	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	4	2	no	—
463	C₄⋊C₄	—	4	2	no	—
464	C₄⋊C₄	—	4	2	no	—
465	C₄⋊C₄	—	4	2	no	—
466	C₄⋊C₄	C₁₃×#41	1	2	yes	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	4	4	no	—
469	C₂²⋊C₄	—	4	4	no	—
470	C₂²⋊C₄	—	4	4	no	—
471	C₂²⋊C₄	—	4	2	no	—
472	C₄²	—	2	2	no	—
473	C₄²	—	2	2	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	4	2	no	—
477	C₄²	—	4	2	no	—
478	C₄²	C₂×D₄×C₁₃	1	2	yes	—
479	C₄²	C₁₃×#41	1	2	yes	—
480	C₁₃	#24661	1	1	yes	characteristic, direct product factor, Sylow
481	C₂³	—	2	1	no	—
482	C₂³	—	2	1	no	—
483	C₂³	—	2	1	no	—
484	C₂³	—	2	1	no	—
485	C₂³	—	2	1	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	4	2	no	—
494	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
495	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
496	Q₈	—	2	2	no	—
497	Q₈	—	2	2	no	—
498	Q₈	—	4	1	no	—
499	Q₈	—	4	1	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	2	no	—
503	D₄	—	4	2	no	—
504	D₄	—	8	4	no	—
505	D₄	—	8	8	no	—
506	D₄	—	8	4	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	4	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	C₁₃×#121	1	2	yes	—
540	C₂×C₄	C₁₃×#121	1	2	yes	—
541	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
542	C₂×C₄	C₁₃×#137	1	2	yes	—
543	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
544	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
545	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
546	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
547	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
548	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
549	C₈	—	2	4	no	—
550	C₈	—	4	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	8	2	no	—
559	C₂²	—	8	2	no	—
560	C₂²	—	8	2	no	—
561	C₂²	—	8	2	no	—
562	C₂²	—	8	2	no	—
563	C₂²	—	8	2	no	—
564	C₂²	—	8	2	no	—
565	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
566	C₂²	C₁₃×#525	1	1	yes	characteristic
567	C₂²	C₁₃×#535	1	1	yes	characteristic
568	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
569	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
570	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
571	C₂²	C₁₃×#575	1	1	yes	characteristic
572	C₄	—	2	2	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	2	no	—
578	C₄	—	8	1	no	—
579	C₄	—	8	1	no	—
580	C₄	—	8	2	no	—
581	C₄	C₁₃×#468	1	4	yes	—
582	C₄	C₁₃×#546	1	1	yes	characteristic
583	C₄	C₁₃×#550	1	1	yes	characteristic
584	C₄	C₁₃×#553	1	1	yes	characteristic
585	C₄	C₁₃×#555	1	1	yes	characteristic
586	C₂	—	4	2	no	—
587	C₂	—	16	2	no	—
588	C₂	C₁₃×#2414	1	1	yes	characteristic
589	C₂	C₂×C₁₃×#468	1	1	yes	characteristic
590	C₂	C₁₃×#3055	1	1	yes	characteristic
591	C₂	C₁₃×#3112	1	1	yes	characteristic
592	C₂	C₁₃×#3115	1	1	yes	characteristic
593	C₂	C₁₃×#3216	1	1	yes	characteristic
594	C₂	C₁₃×#3217	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2856	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
1. C₂×C₁₃×#460	C₂	semidirect
2. C₂×C₁₃×#432	C₂	semidirect
4. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
5. C₁₃×#2033	C₂	semidirect
6. C₁₃×#2000	C₂	semidirect
7. C₁₃×#1982	C₂	semidirect
8. C₁₃×#1973	C₂	semidirect
9. C₁₃×#1947	C₂	semidirect
10. C₁₃×#1936	C₂	semidirect
11. C₁₃×#1803	C₂	semidirect
92. C₁₃×C₄⋊C₈	D₄	semidirect
104. #24661	C₁₃	direct (N × H)
184. C₂×#460	C₂×C₁₃	semidirect
185. C₂×#432	C₂×C₁₃	semidirect
187. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
188. #2033	C₂×C₁₃	semidirect
189. #2000	C₂×C₁₃	semidirect
190. #1982	C₂×C₁₃	semidirect
191. #1973	C₂×C₁₃	semidirect
192. #1947	C₂×C₁₃	semidirect
193. #1936	C₂×C₁₃	semidirect
194. #1803	C₂×C₁₃	semidirect
380. C₄⋊C₈	D₄×C₁₃	semidirect
480. C₁₃	#24661	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×#460	2
C₂×C₁₃×#432	2
C₁₃×#2856	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2033	2
C₁₃×#2000	2
C₁₃×#1982	2
C₁₃×#1973	2
C₁₃×#1947	2
C₁₃×#1936	2
C₁₃×#1803	2
#24661	13

Subgroups — C13×#24661 #15711000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24661 #15711000