Subgroups — C₁₃×#24659 #15710998

Order 3328.

960 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2036	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2000	C₂	1	2	yes	maximal
7	C₁₃×#1981	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×#1935	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₃	—	2	1	no	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#461	—	2	4	no	—
20	C₁₃×#432	—	2	4	no	—
21	C₂×C₁₃×#107	C₂²	1	2	yes	—
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₁₃×#97	C₂²	1	2	yes	—
30	C₁₃×#391	C₂²	1	2	yes	—
31	C₁₃×#390	C₂²	1	1	yes	characteristic
32	C₁₃×#389	—	2	1	no	—
33	C₁₃×#389	—	2	1	no	—
34	C₁₃×#389	C₂²	1	1	yes	characteristic
35	C₁₃×#388	—	2	1	no	—
36	C₁₃×#386	—	2	1	no	—
37	C₁₃×#384	C₂²	1	1	yes	characteristic
38	C₁₃×#380	—	2	1	no	—
39	C₁₃×#380	—	2	1	no	—
40	C₁₃×#380	C₂²	1	1	yes	characteristic
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	2	yes	—
46	C₂²×D₄×C₁₃	—	2	1	no	—
47	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	—	2	1	no	—
49	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×SD₁₆	—	2	4	no	—
53	C₂×C₁₃×SD₁₆	—	2	4	no	—
54	C₂×C₁₃×SD₁₆	—	4	2	no	—
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	—	2	2	no	—
59	C₁₃×C₂²⋊Q₈	—	4	2	no	—
60	C₁₃×C₂²⋊Q₈	—	4	2	no	—
61	C₁₃×#121	—	2	2	no	—
62	C₁₃×#121	—	2	2	no	—
63	C₄×D₄×C₁₃	—	2	2	no	—
64	C₄×D₄×C₁₃	—	2	2	no	—
65	C₄×D₄×C₁₃	—	4	4	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	1	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	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₁₃×#107	—	4	2	no	—
90	C₁₃×C₄⋊C₈	—	2	2	no	—
91	C₁₃×C₄⋊C₈	D₄	1	4	yes	complemented
92	C₁₃×#103	—	2	4	no	—
93	C₁₃×#103	—	2	4	no	—
94	C₁₃×#103	—	4	2	no	—
95	C₁₃×#102	—	4	2	no	—
96	C₁₃×C₂²⋊C₈	—	2	4	no	—
97	C₁₃×#97	—	2	4	no	—
98	C₁₃×#95	—	2	1	no	—
99	C₁₃×#95	—	2	1	no	—
100	C₁₃×#95	—	2	1	no	—
101	C₁₃×#95	—	2	2	no	—
102	C₁₃×#95	—	2	2	no	—
103	#24659	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂⁴×C₁₃	—	2	1	no	—
105	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	2	2	no	—
110	C₂×Q₈×C₁₃	—	2	2	no	—
111	C₂×Q₈×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	—	2	4	no	—
113	C₂×D₄×C₁₃	—	2	1	no	—
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	—	2	1	no	—
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	—	4	2	no	—
119	C₂×D₄×C₁₃	—	4	2	no	—
120	C₂×D₄×C₁₃	#41	1	2	yes	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	4	1	no	—
138	C₂²×C₄×C₁₃	—	4	2	no	—
139	C₂²×C₄×C₁₃	—	4	2	no	—
140	C₂²×C₄×C₁₃	—	4	2	no	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₁₃×SD₁₆	—	4	8	no	—
148	C₂×C₈×C₁₃	—	2	2	no	—
149	C₂×C₈×C₁₃	—	2	2	no	—
150	C₂×C₈×C₁₃	—	2	2	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	2	no	—
153	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	4	2	no	—
162	C₁₃×C₄⋊C₄	—	4	2	no	—
163	C₁₃×C₄⋊C₄	—	4	4	no	—
164	C₁₃×C₄⋊C₄	—	4	2	no	—
165	C₁₃×C₄⋊C₄	—	4	2	no	—
166	C₁₃×C₄⋊C₄	—	4	2	no	—
167	C₁₃×C₄⋊C₄	#41	1	2	yes	—
168	C₁₃×C₂²⋊C₄	—	2	4	no	—
169	C₁₃×C₂²⋊C₄	—	4	2	no	—
170	C₁₃×C₂²⋊C₄	—	4	2	no	—
171	C₁₃×C₂²⋊C₄	—	4	2	no	—
172	C₁₃×C₂²⋊C₄	—	4	4	no	—
173	C₁₃×C₂²⋊C₄	—	4	2	no	—
174	C₄²×C₁₃	—	2	2	no	—
175	C₄²×C₁₃	—	2	2	no	—
176	C₄²×C₁₃	—	2	1	no	—
177	C₄²×C₁₃	—	2	1	no	—
178	C₄²×C₁₃	—	4	2	no	—
179	C₄²×C₁₃	C₂×D₄	1	2	yes	—
180	C₄²×C₁₃	#41	1	2	yes	—
181	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
182	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#2857	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₄×#121	C₂×C₁₃	1	1	yes	characteristic
185	#2036	C₂×C₁₃	1	2	yes	complemented
186	#2000	C₂×C₁₃	1	2	yes	—
187	#1981	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#1973	C₂×C₁₃	1	2	yes	complemented
189	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#1935	C₂×C₁₃	1	2	yes	complemented
191	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂³×C₁₃	—	2	1	no	—
193	C₂³×C₁₃	—	2	1	no	—
194	C₂³×C₁₃	—	2	1	no	—
195	C₂³×C₁₃	—	2	1	no	—
196	C₂³×C₁₃	—	2	1	no	—
197	C₂³×C₁₃	—	2	1	no	—
198	C₂³×C₁₃	—	2	2	no	—
199	C₂³×C₁₃	—	4	1	no	—
200	C₂³×C₁₃	—	4	1	no	—
201	C₂³×C₁₃	—	4	1	no	—
202	C₂³×C₁₃	—	4	1	no	—
203	C₂³×C₁₃	—	4	1	no	—
204	C₂³×C₁₃	—	4	1	no	—
205	C₂³×C₁₃	#137	1	2	yes	—
206	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	Q₈×C₁₃	—	4	2	no	—
208	Q₈×C₁₃	—	4	2	no	—
209	Q₈×C₁₃	—	4	2	no	—
210	Q₈×C₁₃	—	4	2	no	—
211	D₄×C₁₃	—	2	2	no	—
212	D₄×C₁₃	—	2	2	no	—
213	D₄×C₁₃	—	4	8	no	—
214	D₄×C₁₃	—	4	1	no	—
215	D₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	2	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	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	4	4	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	1	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	4	4	no	—
236	C₂×C₄×C₁₃	—	4	1	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	4	2	no	—
240	C₂×C₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	—	8	4	no	—
249	C₂×C₄×C₁₃	#121	1	2	yes	—
250	C₂×C₄×C₁₃	#121	1	2	yes	—
251	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
252	C₂×C₄×C₁₃	#137	1	2	yes	—
253	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
257	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
258	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
259	C₈×C₁₃	—	2	4	no	—
260	C₈×C₁₃	—	4	2	no	—
261	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
262	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
264	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×C₄×D₄	—	2	1	no	—
266	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
267	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
268	#461	—	2	4	no	—
269	#432	—	2	4	no	—
270	C₂×#107	C₂²×C₁₃	1	2	yes	—
271	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×#103	C₂²×C₁₃	1	2	yes	—
274	C₂×#103	C₂²×C₁₃	1	2	yes	—
275	C₂×#103	C₂²×C₁₃	1	2	yes	—
276	C₂×#102	C₂²×C₁₃	1	2	yes	—
277	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
278	C₂×#97	C₂²×C₁₃	1	2	yes	—
279	#391	C₂²×C₁₃	1	2	yes	—
280	#390	C₂²×C₁₃	1	1	yes	characteristic
281	#389	—	2	1	no	—
282	#389	—	2	1	no	—
283	#389	C₂²×C₁₃	1	1	yes	characteristic
284	#388	—	2	1	no	—
285	#386	—	2	1	no	—
286	#384	C₂²×C₁₃	1	1	yes	characteristic
287	#380	—	2	1	no	—
288	#380	—	2	1	no	—
289	#380	C₂²×C₁₃	1	1	yes	characteristic
290	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
291	C₄×C₂²⋊C₄	—	2	1	no	—
292	#340	C₂²×C₁₃	1	2	yes	—
293	#340	C₂²×C₁₃	1	2	yes	—
294	C₂²×C₁₃	—	2	2	no	—
295	C₂²×C₁₃	—	2	2	no	—
296	C₂²×C₁₃	—	2	2	no	—
297	C₂²×C₁₃	—	4	1	no	—
298	C₂²×C₁₃	—	4	1	no	—
299	C₂²×C₁₃	—	4	1	no	—
300	C₂²×C₁₃	—	4	1	no	—
301	C₂²×C₁₃	—	4	2	no	—
302	C₂²×C₁₃	—	4	2	no	—
303	C₂²×C₁₃	—	4	2	no	—
304	C₂²×C₁₃	—	8	1	no	—
305	C₂²×C₁₃	—	8	1	no	—
306	C₂²×C₁₃	—	8	1	no	—
307	C₂²×C₁₃	—	8	1	no	—
308	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
309	C₂²×C₁₃	#525	1	1	yes	characteristic
310	C₂²×C₁₃	#535	1	1	yes	characteristic
311	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
312	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
313	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
314	C₂²×C₁₃	#575	1	1	yes	characteristic
315	C₄×C₁₃	—	2	2	no	—
316	C₄×C₁₃	—	4	2	no	—
317	C₄×C₁₃	—	4	1	no	—
318	C₄×C₁₃	—	4	1	no	—
319	C₄×C₁₃	—	4	1	no	—
320	C₄×C₁₃	—	8	2	no	—
321	C₄×C₁₃	—	8	2	no	—
322	C₄×C₁₃	—	8	1	no	—
323	C₄×C₁₃	—	8	1	no	—
324	C₄×C₁₃	#468	1	4	yes	—
325	C₄×C₁₃	#546	1	1	yes	characteristic
326	C₄×C₁₃	#550	1	1	yes	characteristic
327	C₄×C₁₃	#553	1	1	yes	characteristic
328	C₄×C₁₃	#555	1	1	yes	characteristic
329	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
334	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
336	C₂×SD₁₆	—	2	4	no	—
337	C₂×SD₁₆	—	2	4	no	—
338	C₂×SD₁₆	—	4	2	no	—
339	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
340	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
341	C₄⋊Q₈	—	2	2	no	—
342	C₄⋊Q₈	—	2	2	no	—
343	C₂²⋊Q₈	—	4	2	no	—
344	C₂²⋊Q₈	—	4	2	no	—
345	#121	—	2	2	no	—
346	#121	—	2	2	no	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	—	2	2	no	—
349	C₄×D₄	—	4	4	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₄²	—	2	2	no	—
367	C₂×C₄²	—	2	2	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
370	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
371	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
372	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
373	#107	—	4	2	no	—
374	C₄⋊C₈	—	2	2	no	—
375	C₄⋊C₈	D₄×C₁₃	1	4	yes	complemented
376	#103	—	2	4	no	—
377	#103	—	2	4	no	—
378	#103	—	4	2	no	—
379	#102	—	4	2	no	—
380	C₂²⋊C₈	—	2	4	no	—
381	#97	—	2	4	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	#95	—	2	2	no	—
386	#95	—	2	2	no	—
387	C₂×C₁₃	—	4	2	no	—
388	C₂×C₁₃	—	8	2	no	—
389	C₂×C₁₃	#2414	1	1	yes	characteristic
390	C₂×C₁₃	C₂×#468	1	1	yes	characteristic
391	C₂×C₁₃	#3056	1	1	yes	characteristic
392	C₂×C₁₃	#3110	1	1	yes	characteristic
393	C₂×C₁₃	#3116	1	1	yes	characteristic
394	C₂×C₁₃	#3214	1	1	yes	characteristic
395	C₂×C₁₃	#3218	1	1	yes	characteristic
396	C₂⁴	—	2	1	no	—
397	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	4	2	no	—
411	C₂×D₄	—	4	2	no	—
412	C₂×D₄	C₁₃×#41	1	2	yes	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	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	—	4	1	no	—
430	C₂²×C₄	—	4	2	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
438	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
439	SD₁₆	—	4	8	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	4	2	no	—
454	C₄⋊C₄	—	4	4	no	—
455	C₄⋊C₄	—	4	2	no	—
456	C₄⋊C₄	—	4	2	no	—
457	C₄⋊C₄	—	4	2	no	—
458	C₄⋊C₄	—	4	2	no	—
459	C₄⋊C₄	C₁₃×#41	1	2	yes	—
460	C₂²⋊C₄	—	2	4	no	—
461	C₂²⋊C₄	—	4	2	no	—
462	C₂²⋊C₄	—	4	2	no	—
463	C₂²⋊C₄	—	4	2	no	—
464	C₂²⋊C₄	—	4	4	no	—
465	C₂²⋊C₄	—	4	2	no	—
466	C₄²	—	2	2	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	4	2	no	—
471	C₄²	C₂×D₄×C₁₃	1	2	yes	—
472	C₄²	C₁₃×#41	1	2	yes	—
473	C₁₃	#24659	1	1	yes	characteristic, direct product factor, Sylow
474	C₂³	—	2	1	no	—
475	C₂³	—	2	1	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	1	no	—
479	C₂³	—	2	1	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	4	1	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	C₁₃×#137	1	2	yes	—
488	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
489	Q₈	—	4	2	no	—
490	Q₈	—	4	2	no	—
491	Q₈	—	4	2	no	—
492	Q₈	—	4	2	no	—
493	D₄	—	2	2	no	—
494	D₄	—	2	2	no	—
495	D₄	—	4	8	no	—
496	D₄	—	4	1	no	—
497	D₄	—	4	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	4	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	8	4	no	—
531	C₂×C₄	C₁₃×#121	1	2	yes	—
532	C₂×C₄	C₁₃×#121	1	2	yes	—
533	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
534	C₂×C₄	C₁₃×#137	1	2	yes	—
535	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
536	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
537	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
538	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
539	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
540	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
541	C₈	—	2	4	no	—
542	C₈	—	4	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	8	1	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
558	C₂²	C₁₃×#525	1	1	yes	characteristic
559	C₂²	C₁₃×#535	1	1	yes	characteristic
560	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
561	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
562	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
563	C₂²	C₁₃×#575	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	1	no	—
569	C₄	—	8	1	no	—
570	C₄	—	8	2	no	—
571	C₄	—	8	2	no	—
572	C₄	—	8	1	no	—
573	C₄	C₁₃×#468	1	4	yes	—
574	C₄	C₁₃×#546	1	1	yes	characteristic
575	C₄	C₁₃×#550	1	1	yes	characteristic
576	C₄	C₁₃×#553	1	1	yes	characteristic
577	C₄	C₁₃×#555	1	1	yes	characteristic
578	C₂	—	4	2	no	—
579	C₂	—	8	2	no	—
580	C₂	C₁₃×#2414	1	1	yes	characteristic
581	C₂	C₂×C₁₃×#468	1	1	yes	characteristic
582	C₂	C₁₃×#3056	1	1	yes	characteristic
583	C₂	C₁₃×#3110	1	1	yes	characteristic
584	C₂	C₁₃×#3116	1	1	yes	characteristic
585	C₂	C₁₃×#3214	1	1	yes	characteristic
586	C₂	C₁₃×#3218	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 ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#461	C₂	semidirect
2. C₂×C₁₃×#432	C₂	semidirect
3. C₁₃×#2857	C₂	semidirect
5. C₁₃×#2036	C₂	semidirect
7. C₁₃×#1981	C₂	semidirect
8. C₁₃×#1973	C₂	semidirect
9. C₁₃×#1947	C₂	semidirect
10. C₁₃×#1935	C₂	semidirect
11. C₁₃×#1802	C₂	semidirect
91. C₁₃×C₄⋊C₈	D₄	semidirect
103. #24659	C₁₃	direct (N × H)
181. C₂×#461	C₂×C₁₃	semidirect
182. C₂×#432	C₂×C₁₃	semidirect
183. #2857	C₂×C₁₃	semidirect
185. #2036	C₂×C₁₃	semidirect
187. #1981	C₂×C₁₃	semidirect
188. #1973	C₂×C₁₃	semidirect
189. #1947	C₂×C₁₃	semidirect
190. #1935	C₂×C₁₃	semidirect
191. #1802	C₂×C₁₃	semidirect
375. C₄⋊C₈	D₄×C₁₃	semidirect
473. C₁₃	#24659	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×#461	2
C₂×C₁₃×#432	2
C₁₃×#2857	2
C₄×C₁₃×#121	2
C₁₃×#2036	2
C₁₃×#2000	2
C₁₃×#1981	2
C₁₃×#1973	2
C₁₃×#1947	2
C₁₃×#1935	2
C₁₃×#1802	2
#24659	13

Subgroups — C13×#24659 #15710998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24659 #15710998